leftri rightri

This is PART 28: Centers X(54001) - X(56000)

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) = {X(4),X(5)}-HARMONIC CONJUGATE OF X(186)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^6 - 3*a^2*b^4 + 2*b^6 + a^2*b^2*c^2 - 2*b^4*c^2 - 3*a^2*c^4 - 2*b^2*c^4 + 2*c^6) : :
X(54001) = 4 X[5] - X[38448], 5 X[3843] + X[35498]

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) = {X(2),X(5)}-HARMONIC CONJUGATE OF X(237)

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

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) = {X(3),X(4)}-HARMONIC CONJUGATE OF X(237)

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

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) = {X(3),X(5)}-HARMONIC CONJUGATE OF X(237)

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

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) = {X(4),X(5)}-HARMONIC CONJUGATE OF X(237)

Barycentrics    a^10*b^2 - a^8*b^4 - 3*a^6*b^6 + 5*a^4*b^8 - 2*a^2*b^10 + a^10*c^2 - 3*a^6*b^4*c^2 - 4*a^4*b^6*c^2 + 8*a^2*b^8*c^2 - 2*b^10*c^2 - a^8*c^4 - 3*a^6*b^2*c^4 - 2*a^4*b^4*c^4 - 6*a^2*b^6*c^4 + 8*b^8*c^4 - 3*a^6*c^6 - 4*a^4*b^2*c^6 - 6*a^2*b^4*c^6 - 12*b^6*c^6 + 5*a^4*c^8 + 8*a^2*b^2*c^8 + 8*b^4*c^8 - 2*a^2*c^10 - 2*b^2*c^10 : :

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) = {X(2),X(3)}-HARMONIC CONJUGATE OF X(2070)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - 3*a^4*b^2*c^2 + 7*a^2*b^4*c^2 - 2*b^6*c^2 + 7*a^2*b^2*c^4 + 6*b^4*c^4 + 2*a^2*c^6 - 2*b^2*c^6 - c^8) : :
X(54006) = X[3] + 2 X[7550], 3 X[3] - 2 X[44832], 3 X[381] - 4 X[50135], 5 X[1656] - 4 X[37990], 3 X[7550] + X[44832], 3 X[15246] - X[44832]

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) = {X(4),X(5)}-HARMONIC CONJUGATE OF X(2070)

Barycentrics    a^10 - 4*a^6*b^4 + 2*a^4*b^6 + 3*a^2*b^8 - 2*b^10 + a^6*b^2*c^2 - 3*a^4*b^4*c^2 - 4*a^2*b^6*c^2 + 6*b^8*c^2 - 4*a^6*c^4 - 3*a^4*b^2*c^4 + 2*a^2*b^4*c^4 - 4*b^6*c^4 + 2*a^4*c^6 - 4*a^2*b^2*c^6 - 4*b^4*c^6 + 3*a^2*c^8 + 6*b^2*c^8 - 2*c^10 : :
X(54007) = 2 X[4] + X[18364], 4 X[546] + X[35482]

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}

X(54008) = X(4)X(1903)∩X(9)X(355)

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

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}

X(54009) = X(9)X(119)∩X(208)X(429)

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

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}

X(54010) = X(4)X(7149)∩X(223)X(6259)

Barycentrics    (a-b-c)*(a^9-3*a^7*(b-c)^2-a^6*(b-c)^2*(b+c)+3*a^4*(b-c)^2*(b+c)^3+(b-c)^6*(b+c)^3-a^3*(b-c)^2*(b+c)^4-a^2*(b-c)^2*(b+c)^3*(3*b^2-2*b*c+3*c^2)+a^5*(b-c)^2*(3*b^2+2*b*c+3*c^2)) : :

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}

X(54011) = X(6)X(1885)∩X(393)X(1562)

Barycentrics    (a^2-b^2-c^2)*(a^12-9*a^8*(b^2-c^2)^2+(b^2-c^2)^6+16*a^6*(b^2-c^2)^2*(b^2+c^2)-a^4*(b^2-c^2)^2*(9*b^4+14*b^2*c^2+9*c^4)) : :

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}

X(54012) = X(2)X(98)∩X(4)X(373)

Barycentrics    a^6-a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)+a^2*(b^4-10*b^2*c^2+c^4) : :

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}

X(54013) = X(2)X(98)∩X(20)X(7998)

Barycentrics    3*a^6-3*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)+a^2*(b^4+10*b^2*c^2+c^4) : :

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) = ISOGONAL CONJUGATE OF X(36073)

Barycentrics    Cos[B + Pi/6] - Cos[C + Pi/6] : :

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) = ISOGONAL CONJUGATE OF X(36072)

Barycentrics    Cos[B - Pi/6] - Cos[C - Pi/6] : :

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) = X(102)X(2066)∩X(103)X(6502)

Barycentrics    Sin[A]^2/(Sin[B + Pi/4] - Sin[C + Pi/4]) : :

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) = ISOGONAL CONJUGATE OF X(54016)

Barycentrics    Sin[B + Pi/4] - Sin[C + Pi/4] : :

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) = X(102)X(5414)∩X(103)X(2067)

Barycentrics    Sin[A]^2/(-Sin[B - Pi/4] + Sin[C - Pi/4]) : :

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) = ISOCONAL CONJUGATE OF X(54018)

Barycentrics    Sin[B - Pi/4] - Sin[C - Pi/4] : :

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) = X(105)X(7052)∩X(106)X(7051)

Barycentrics    Sin[A]^2/(-Sin[B + Pi/6] + Sin[C + Pi/6]) : :

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) = ISOGONAL CONJUGATE OF X(54020)

Barycentrics    Sin[B + Pi/6] - Sin[C + Pi/6] : :

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) = X(104)X(19551)∩X(105)X(33655)

Barycentrics    Sin[A]^2/(Sin[B - Pi/6] - Sin[C - Pi/6]) : :

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) = ISOGONAL CONJUGATE OF X(54022)

Barycentrics    Sin[B - Pi/6] - Sin[C - Pi/6] : :

X(54023) lies on these lines: {30, 511}, {4453, 36669}, {36931, 49274}

X(54023) = isogonal conjugate of X(54022)

X(54024) = TRILINEAR POLE OF X(6)X(2154)

Barycentrics    (Sec[A + Pi/6]*Sin[A]^2)/(Cos[B + Pi/6] - Cos[C + Pi/6]) : :

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) = ISOGONAL CONJUGATE OF X(54024)

Barycentrics    Cos[A + Pi/6]*(Cos[B + Pi/6] - Cos[C + Pi/6]) : :

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) = TRILINEAR POLE OF X(6)X(2153)

Barycentrics    (Sec[A - Pi/6]*Sin[A]^2)/(-Cos[B - Pi/6] + Cos[C - Pi/6]) : :

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) = ISOGONAL CONJUGATE OF X(54026)

Barycentrics    Cos[A - Pi/6]*(-Cos[B - Pi/6] + Cos[C - Pi/6]) : :

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) = ISOGONAL CONJUGATE OF X(39384)

Barycentrics    Tan[B + Pi/4] - Tan[C + Pi/4] : :
Barycentrics    (b^2 - c^2)*(-a^2 + b^2 + c^2 - 2*S) : :

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) = ISOGONAL CONJUGATE OF X(39383)

Barycentrics    Tan[A + Pi/4]*(Tan[B + Pi/4] - Tan[C + Pi/4])::
Barycentrics    Cot[B + Pi/4] - Cot[C + Pi/4] : :
Barycentrics    (b^2 - c^2)*(-a^2 + b^2 + c^2 + 2*S) : :

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) = ISOTOMIC CONJUGATE OF X(54028)

Barycentrics    1/((b^2 - c^2)*(-a^2 + b^2 + c^2 - 2*S)) : :
Barycentrics    Sin[A - B]*Sin[A - C]*(Cos[B] - Sin[B])*(Cos[C] - Sin[C]) : :

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) = ISOTOMIC CONJUGATE OF X(54029)

Barycentrics    1/((b^2 - c^2)*(-a^2 + b^2 + c^2 + 2*S)) : :
Barycentrics    Sin[A - B]*Sin[A - C]*(Cos[B] + Sin[B])*(Cos[C] + Sin[C]) : :

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) = ISOGONAL CONJUGATE OF X(33971)

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

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) = X(4)X(276)∩X(20)X(76)

Barycentrics    b^2*c^2*(3*a^8 + 3*a^6*b^2 - 7*a^4*b^4 + a^2*b^6 + 3*a^6*c^2 - 4*a^4*b^2*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 - 7*a^4*c^4 - a^2*b^2*c^4 - 4*b^4*c^4 + a^2*c^6 + 2*b^2*c^6) : :

X(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) = ISOGONAL CONJUGATE OF X(311)

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

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) = X(2)X(29069)∩X(9)X(1746)

Barycentrics    a^5*b + a^4*b^2 - a^3*b^3 - a^2*b^4 + a^5*c + a^4*b*c - 2*a^3*b^2*c + a*b^4*c - b^5*c + a^4*c^2 - 2*a^3*b*c^2 + 2*a^2*b^2*c^2 - a*b^3*c^2 - a^3*c^3 - a*b^2*c^3 + 2*b^3*c^3 - a^2*c^4 + a*b*c^4 - b*c^5 : :
X(54035) = 2 X[72] + X[10454], X[3869] + 2 X[44039]

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) = X(2)X(6030)∩X(30)X(54)

Barycentrics    7*a^6 - a^4*b^2 - 4*a^2*b^4 - 2*b^6 - a^4*c^2 - a^2*b^2*c^2 + 2*b^4*c^2 - 4*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(54036) = 2 X[2] - 3 X[6030], 2 X[3521] - 5 X[8718], 2 X[69] - 5 X[41464], 4 X[550] - X[16835], 4 X[597] - 5 X[1176], 2 X[1657] + X[43599], 5 X[2916] - 3 X[21358], 3 X[3524] - 2 X[18488], X[3529] + 2 X[44866], X[5059] + 2 X[34563], 4 X[14641] - X[43846], 5 X[15321] - 8 X[34573], 3 X[15689] - X[33541], X[17800] + 2 X[43585], 2 X[22948] - 5 X[52093], X[49139] + 2 X[53779]

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) = X(2)X(5655)∩X(69)X(146)

Barycentrics    a^2*(a^12*b^2 - 4*a^10*b^4 + 5*a^8*b^6 - 5*a^4*b^10 + 4*a^2*b^12 - b^14 + a^12*c^2 - a^10*b^2*c^2 + 7*a^8*b^4*c^2 - 24*a^6*b^6*c^2 + 25*a^4*b^8*c^2 - 7*a^2*b^10*c^2 - b^12*c^2 - 4*a^10*c^4 + 7*a^8*b^2*c^4 + 19*a^6*b^4*c^4 - 14*a^4*b^6*c^4 - 17*a^2*b^8*c^4 + 9*b^10*c^4 + 5*a^8*c^6 - 24*a^6*b^2*c^6 - 14*a^4*b^4*c^6 + 40*a^2*b^6*c^6 - 7*b^8*c^6 + 25*a^4*b^2*c^8 - 17*a^2*b^4*c^8 - 7*b^6*c^8 - 5*a^4*c^10 - 7*a^2*b^2*c^10 + 9*b^4*c^10 + 4*a^2*c^12 - b^2*c^12 - c^14) : :
X(54037) = 2 X[12162] + X[14094], 2 X[146] + X[12219], X[146] + 2 X[12825], X[12219] - 4 X[12825], 5 X[3091] - 4 X[12099], 4 X[3819] - 3 X[15055], 3 X[3839] - 2 X[45237], 11 X[5056] - 8 X[16270], 2 X[5609] + X[18439], X[5889] - 4 X[38791], 4 X[5907] - X[15054], 4 X[5972] - 3 X[20791], 2 X[17853] - 3 X[20791], 4 X[6053] - X[12270], and many others

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) = X(2)X(34146)∩X(54)X(64)

Barycentrics    a^2*(a^14*b^2 - 3*a^12*b^4 + a^10*b^6 + 5*a^8*b^8 - 5*a^6*b^10 - a^4*b^12 + 3*a^2*b^14 - b^16 + a^14*c^2 - a^12*b^2*c^2 + 7*a^10*b^4*c^2 - 15*a^8*b^6*c^2 - a^6*b^8*c^2 + 17*a^4*b^10*c^2 - 7*a^2*b^12*c^2 - b^14*c^2 - 3*a^12*c^4 + 7*a^10*b^2*c^4 + 8*a^8*b^4*c^4 + 6*a^6*b^6*c^4 - 11*a^4*b^8*c^4 - 13*a^2*b^10*c^4 + 6*b^12*c^4 + a^10*c^6 - 15*a^8*b^2*c^6 + 6*a^6*b^4*c^6 - 10*a^4*b^6*c^6 + 17*a^2*b^8*c^6 + b^10*c^6 + 5*a^8*c^8 - a^6*b^2*c^8 - 11*a^4*b^4*c^8 + 17*a^2*b^6*c^8 - 10*b^8*c^8 - 5*a^6*c^10 + 17*a^4*b^2*c^10 - 13*a^2*b^4*c^10 + b^6*c^10 - a^4*c^12 - 7*a^2*b^2*c^12 + 6*b^4*c^12 + 3*a^2*c^14 - b^2*c^14 - c^16) : :
X(54038) = 2 X[9914] - 5 X[11444], X[12111] + 2 X[46373]

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) = X(2)X(5656)∩X(54)X(1593)

Barycentrics    a^2*(a^12*b^2 - 4*a^10*b^4 + 5*a^8*b^6 - 5*a^4*b^10 + 4*a^2*b^12 - b^14 + a^12*c^2 + a^10*b^2*c^2 + 8*a^8*b^4*c^2 - 38*a^6*b^6*c^2 + 41*a^4*b^8*c^2 - 11*a^2*b^10*c^2 - 2*b^12*c^2 - 4*a^10*c^4 + 8*a^8*b^2*c^4 + 52*a^6*b^4*c^4 - 36*a^4*b^6*c^4 - 32*a^2*b^8*c^4 + 12*b^10*c^4 + 5*a^8*c^6 - 38*a^6*b^2*c^6 - 36*a^4*b^4*c^6 + 78*a^2*b^6*c^6 - 9*b^8*c^6 + 41*a^4*b^2*c^8 - 32*a^2*b^4*c^8 - 9*b^6*c^8 - 5*a^4*c^10 - 11*a^2*b^2*c^10 + 12*b^4*c^10 + 4*a^2*c^12 - 2*b^2*c^12 - c^14) : :
X(54039) = X[12290] + 2 X[12315], 4 X[64] - 7 X[15056], 2 X[6225] + X[12111], X[6225] + 2 X[36982], X[12111] - 4 X[36982], 4 X[1498] - X[12279], 2 X[1498] + X[36983], X[12279] + 2 X[36983], 8 X[2883] - 5 X[10574], 4 X[7729] - 5 X[10574], 5 X[3522] - 2 X[30443], 4 X[5878] - X[5889], 8 X[6759] - 5 X[52093], X[11412] + 2 X[48672], 5 X[11439] - 2 X[12324], 5 X[11444] - 2 X[12250], 2 X[13093] - 5 X[15058], 8 X[23328] - 9 X[33879]

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) = X(2)X(16657)∩X(20)X(64)

Barycentrics    2*a^10 - 5*a^8*b^2 + 4*a^6*b^4 - 2*a^4*b^6 + 2*a^2*b^8 - b^10 - 5*a^8*c^2 + 18*a^6*b^2*c^2 - 10*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 + 4*a^6*c^4 - 10*a^4*b^2*c^4 + 8*a^2*b^4*c^4 - 2*b^6*c^4 - 2*a^4*c^6 - 6*a^2*b^2*c^6 - 2*b^4*c^6 + 2*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(54040) = 5 X[3] - 2 X[12370], 5 X[12022] - 4 X[12370], 2 X[20] + X[14516], 4 X[550] - X[34224], 4 X[548] - X[44076], 4 X[1216] - X[18560], 2 X[1657] + X[16659], 2 X[1885] - 5 X[11444], 2 X[5562] + X[52071], 5 X[3091] - 6 X[35283], 5 X[3522] - 2 X[6146], 7 X[3523] - 4 X[12241], X[3529] + 2 X[12134], X[5059] + 2 X[16655], and manyu others

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) = X(2)X(14845)∩X(3)X(54)

Barycentrics    a^2*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 - 11*a^4*b^2*c^2 + 9*a^2*b^4*c^2 + b^6*c^2 - 3*a^4*c^4 + 9*a^2*b^2*c^4 + 3*a^2*c^6 + b^2*c^6 - c^8) : :
X(54041) = 2 X[3] + X[2979], 10 X[3] - X[5889], 4 X[3] - X[5890], 7 X[3] + 2 X[6101], 11 X[3] - 2 X[6102], 14 X[3] - 5 X[10574], 5 X[3] + 4 X[10627], 8 X[3] + X[11412], 13 X[3] - 4 X[13630], 5 X[2979] + X[5889], 2 X[2979] + X[5890], 7 X[2979] - 4 X[6101], 11 X[2979] + 4 X[6102], 7 X[2979] + 5 X[10574], 5 X[2979] - 8 X[10627], and many others

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) = X(2)X(13340)∩X(3)X(54)

Barycentrics    a^2*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 - 8*a^4*b^2*c^2 + 6*a^2*b^4*c^2 + b^6*c^2 - 3*a^4*c^4 + 6*a^2*b^2*c^4 + 3*a^2*c^6 + b^2*c^6 - c^8) : :
X(54042) = 3 X[13340] + 2 X[13364], 7 X[3] - X[5889], 3 X[3] - X[5890], 2 X[3] + X[6101], 4 X[3] - X[6102], 11 X[3] - 5 X[10574], X[3] + 2 X[10627], 5 X[3] + X[11412], 5 X[3] - 2 X[13630], 5 X[3] - 3 X[20791], 7 X[2979] + X[5889], 3 X[2979] + X[5890], 4 X[2979] + X[6102], 11 X[2979] + 5 X[10574], 5 X[2979] - X[11412], and many others

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) = X(4)X(15066)∩X(2979)X(33971)

Barycentrics    a^12 - a^10*b^2 - 2*a^8*b^4 + 2*a^6*b^6 + a^4*b^8 - a^2*b^10 - a^10*c^2 + 2*a^8*b^2*c^2 + 22*a^6*b^4*c^2 - 24*a^4*b^6*c^2 + 3*a^2*b^8*c^2 - 2*b^10*c^2 - 2*a^8*c^4 + 22*a^6*b^2*c^4 - 26*a^4*b^4*c^4 - 2*a^2*b^6*c^4 + 8*b^8*c^4 + 2*a^6*c^6 - 24*a^4*b^2*c^6 - 2*a^2*b^4*c^6 - 12*b^6*c^6 + a^4*c^8 + 3*a^2*b^2*c^8 + 8*b^4*c^8 - a^2*c^10 - 2*b^2*c^10 : :

X(54043) lies on these lines: {4, 15066}, {2979, 33971}

X(54044) = X(3)X(54)∩X(5)X(11592)

Barycentrics    a^2*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 - 14*a^4*b^2*c^2 + 12*a^2*b^4*c^2 + b^6*c^2 - 3*a^4*c^4 + 12*a^2*b^2*c^4 + 3*a^2*c^6 + b^2*c^6 - c^8) : :
X(54044) = 3 X[3] + X[2979], 13 X[3] - X[5889], 5 X[3] - X[5890], 5 X[3] + X[6101], 7 X[3] - X[6102], 17 X[3] - 5 X[10574], 2 X[3] + X[10627], 11 X[3] + X[11412], 4 X[3] - X[13630], 7 X[3] - 3 X[20791], 13 X[2979] + 3 X[5889], 5 X[2979] + 3 X[5890], 5 X[2979] - 3 X[6101], 7 X[2979] + 3 X[6102], 17 X[2979] + 15 X[10574], and many others

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) = X(51)X(47065)∩X(184)X(47064)

Barycentrics    a^2*(a^18*b^2 - 7*a^16*b^4 + 22*a^14*b^6 - 42*a^12*b^8 + 56*a^10*b^10 - 56*a^8*b^12 + 42*a^6*b^14 - 22*a^4*b^16 + 7*a^2*b^18 - b^20 + a^18*c^2 - 13*a^16*b^2*c^2 + 44*a^14*b^4*c^2 - 64*a^12*b^6*c^2 + 40*a^10*b^8*c^2 + 4*a^8*b^10*c^2 - 32*a^6*b^12*c^2 + 36*a^4*b^14*c^2 - 21*a^2*b^16*c^2 + 5*b^18*c^2 - 7*a^16*c^4 + 44*a^14*b^2*c^4 - 78*a^12*b^4*c^4 + 45*a^10*b^6*c^4 + 7*a^8*b^8*c^4 - 19*a^6*b^10*c^4 + 7*a^4*b^12*c^4 + 6*a^2*b^14*c^4 - 5*b^16*c^4 + 22*a^14*c^6 - 64*a^12*b^2*c^6 + 45*a^10*b^4*c^6 - 9*a^8*b^6*c^6 + 9*a^6*b^8*c^6 - 21*a^4*b^10*c^6 + 38*a^2*b^12*c^6 - 20*b^14*c^6 - 42*a^12*c^8 + 40*a^10*b^2*c^8 + 7*a^8*b^4*c^8 + 9*a^6*b^6*c^8 - 30*a^2*b^10*c^8 + 70*b^12*c^8 + 56*a^10*c^10 + 4*a^8*b^2*c^10 - 19*a^6*b^4*c^10 - 21*a^4*b^6*c^10 - 30*a^2*b^8*c^10 - 98*b^10*c^10 - 56*a^8*c^12 - 32*a^6*b^2*c^12 + 7*a^4*b^4*c^12 + 38*a^2*b^6*c^12 + 70*b^8*c^12 + 42*a^6*c^14 + 36*a^4*b^2*c^14 + 6*a^2*b^4*c^14 - 20*b^6*c^14 - 22*a^4*c^16 - 21*a^2*b^2*c^16 - 5*b^4*c^16 + 7*a^2*c^18 + 5*b^2*c^18 - c^20) : :
X(54045) = 2 X[51] - 3 X[47065], 4 X[1141] - X[13505], X[13504] + 2 X[38587], X[11412] + 2 X[38683], 3 X[20791] - 4 X[38618]

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) = X(3)X(54)∩X(23)X(114)

Barycentrics    a^2*(a^10 - 3*a^8*b^2 + 4*a^6*b^4 - 4*a^4*b^6 + 3*a^2*b^8 - b^10 - 3*a^8*c^2 + 6*a^6*b^2*c^2 - 5*a^4*b^4*c^2 + a^2*b^6*c^2 + b^8*c^2 + 4*a^6*c^4 - 5*a^4*b^2*c^4 + a^2*b^4*c^4 - 4*a^4*c^6 + a^2*b^2*c^6 + 3*a^2*c^8 + b^2*c^8 - c^10) : :

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) = X(2)X13451)∩X(3)X(54)

Barycentrics    a^2*(2*a^6*b^2 - 6*a^4*b^4 + 6*a^2*b^6 - 2*b^8 + 2*a^6*c^2 - 13*a^4*b^2*c^2 + 9*a^2*b^4*c^2 + 2*b^6*c^2 - 6*a^4*c^4 + 9*a^2*b^2*c^4 + 6*a^2*c^6 + 2*b^2*c^6 - 2*c^8) : :
X(54047) = 7 X[2] - 4 X[13451], X[3] + 2 X[2979], 11 X[3] - 2 X[5889], 5 X[3] - 2 X[5890], 5 X[3] + 4 X[6101], 13 X[3] - 4 X[6102], 19 X[3] - 10 X[10574], X[3] + 8 X[10627], 7 X[3] + 2 X[11412], 17 X[3] - 8 X[13630], 3 X[3] - 2 X[20791], 11 X[2979] + X[5889], 5 X[2979] + X[5890], 5 X[2979] - 2 X[6101], 13 X[2979] + 2 X[6102], 19 X[2979] + 5 X[10574], and many others

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) = X(2)X13321)∩X(3)X(54)

Barycentrics    a^2*(2*a^6*b^2 - 6*a^4*b^4 + 6*a^2*b^6 - 2*b^8 + 2*a^6*c^2 - 7*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + 2*b^6*c^2 - 6*a^4*c^4 + 3*a^2*b^2*c^4 + 6*a^2*c^6 + 2*b^2*c^6 - 2*c^8) : :
X(54048) = 4 X[2] - 3 X[13321], 3 X[2] - 4 X[44324], 9 X[13321] - 16 X[44324], 5 X[3] - 2 X[5889], 3 X[3] - 2 X[5890], X[3] - 4 X[6101], 7 X[3] - 4 X[6102], 13 X[3] - 10 X[10574], 5 X[3] - 8 X[10627], X[3] + 2 X[11412], 11 X[3] - 8 X[13630], 7 X[3] - 6 X[20791], X[195] - 4 X[41590], 5 X[2979] - X[5889], 3 X[2979] - X[5890], 7 X[2979] - 2 X[6102], and many others

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) = ISOGONALCONJUGATE OF X(25149)

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

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) = X(2)X(10606)∩X(4)X(74)

Barycentrics    5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 22*a^4*b^6 - 7*a^2*b^8 - b^10 - 5*a^8*c^2 + 36*a^6*b^2*c^2 - 22*a^4*b^4*c^2 - 12*a^2*b^6*c^2 + 3*b^8*c^2 - 14*a^6*c^4 - 22*a^4*b^2*c^4 + 38*a^2*b^4*c^4 - 2*b^6*c^4 + 22*a^4*c^6 - 12*a^2*b^2*c^6 - 2*b^4*c^6 - 7*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(54050) = 3 X[2] - 4 X[23328], 3 X[10606] - 2 X[23328], 4 X[3] - X[6225], 2 X[3] + X[12250], 4 X[3] - 3 X[35260], 2 X[5656] - 3 X[35260], X[6225] + 2 X[12250], X[6225] - 3 X[35260], 2 X[12250] + 3 X[35260], X[4] - 4 X[3357], 5 X[4] - 8 X[20299], X[4] + 2 X[20427], 3 X[4] - 4 X[23325], 5 X[3357] - 2 X[20299], 2 X[3357] + X[20427], and many others

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) = X(2)X(515)∩X(20)X(78)

Barycentrics    5*a^7 - 7*a^6*b - 7*a^5*b^2 + 13*a^4*b^3 - a^3*b^4 - 5*a^2*b^5 + 3*a*b^6 - b^7 - 7*a^6*c + 2*a^5*b*c - a^4*b^2*c - 4*a^3*b^3*c + 7*a^2*b^4*c + 2*a*b^5*c + b^6*c - 7*a^5*c^2 - a^4*b*c^2 + 10*a^3*b^2*c^2 - 2*a^2*b^3*c^2 - 3*a*b^4*c^2 + 3*b^5*c^2 + 13*a^4*c^3 - 4*a^3*b*c^3 - 2*a^2*b^2*c^3 - 4*a*b^3*c^3 - 3*b^4*c^3 - a^3*c^4 + 7*a^2*b*c^4 - 3*a*b^2*c^4 - 3*b^3*c^4 - 5*a^2*c^5 + 2*a*b*c^5 + 3*b^2*c^5 + 3*a*c^6 + b*c^6 - c^7 : :
X(54051) = 4 X[3] - X[9799], X[8] - 4 X[11500], X[20] + 2 X[1490], 2 X[20] + X[6223], 4 X[1490] - X[6223], 2 X[72] + X[9960], 2 X[84] - 5 X[3522], 4 X[548] - X[12684], 4 X[550] - X[12246], 5 X[631] - 2 X[5787], 5 X[631] - 8 X[40262], X[5787] - 4 X[40262], X[962] - 4 X[6261], X[3146] - 4 X[6260], 7 X[3523] - 4 X[6245], 7 X[3528] - 4 X[34862], and many others

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) = X(7)X(104)∩X(8)X(20)

Barycentrics    5*a^7 - 3*a^6*b - 11*a^5*b^2 + 5*a^4*b^3 + 7*a^3*b^4 - a^2*b^5 - a*b^6 - b^7 - 3*a^6*c + 18*a^5*b*c - a^4*b^2*c - 12*a^3*b^3*c + 3*a^2*b^4*c - 6*a*b^5*c + b^6*c - 11*a^5*c^2 - a^4*b*c^2 + 10*a^3*b^2*c^2 - 2*a^2*b^3*c^2 + a*b^4*c^2 + 3*b^5*c^2 + 5*a^4*c^3 - 12*a^3*b*c^3 - 2*a^2*b^2*c^3 + 12*a*b^3*c^3 - 3*b^4*c^3 + 7*a^3*c^4 + 3*a^2*b*c^4 + a*b^2*c^4 - 3*b^3*c^4 - a^2*c^5 - 6*a*b*c^5 + 3*b^2*c^5 - a*c^6 + b*c^6 - c^7 : :
X(54052) = 4 X[3] - X[6223], 2 X[3] + X[12246], X[6223] + 2 X[12246], X[4] - 4 X[34862], X[8] - 4 X[1158], X[20] + 2 X[84], 2 X[20] + X[9799], 4 X[84] - X[9799], X[10864] + 2 X[31730], 4 X[140] - X[48664], 2 X[550] + X[12684], 5 X[631] - 2 X[6259], X[962] - 4 X[12114], X[1320] + 2 X[52116], 2 X[1490] - 5 X[3522], 7 X[3090] - 4 X[22792], and many others

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) = X(3)X(42452)∩X(20)X(394)

Barycentrics    11*a^16 - 12*a^14*b^2 - 96*a^12*b^4 + 276*a^10*b^6 - 290*a^8*b^8 + 124*a^6*b^10 - 8*a^4*b^12 - 4*a^2*b^14 - b^16 - 12*a^14*c^2 + 208*a^12*b^2*c^2 - 276*a^10*b^4*c^2 - 232*a^8*b^6*c^2 + 460*a^6*b^8*c^2 - 96*a^4*b^10*c^2 - 44*a^2*b^12*c^2 - 8*b^14*c^2 - 96*a^12*c^4 - 276*a^10*b^2*c^4 + 1044*a^8*b^4*c^4 - 584*a^6*b^6*c^4 - 312*a^4*b^8*c^4 + 156*a^2*b^10*c^4 + 68*b^12*c^4 + 276*a^10*c^6 - 232*a^8*b^2*c^6 - 584*a^6*b^4*c^6 + 832*a^4*b^6*c^6 - 108*a^2*b^8*c^6 - 184*b^10*c^6 - 290*a^8*c^8 + 460*a^6*b^2*c^8 - 312*a^4*b^4*c^8 - 108*a^2*b^6*c^8 + 250*b^8*c^8 + 124*a^6*c^10 - 96*a^4*b^2*c^10 + 156*a^2*b^4*c^10 - 184*b^6*c^10 - 8*a^4*c^12 - 44*a^2*b^2*c^12 + 68*b^4*c^12 - 4*a^2*c^14 - 8*b^2*c^14 - c^16 : :
X(54053) = X[4] - 4 X[20329], X[20] + 2 X[3346], 4 X[550] - X[36965], X[3146] - 4 X[33546], 2 X[3183] - 5 X[3522], 7 X[3523] - 4 X[6523], 11 X[5056] - 8 X[51342]

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) = X(20)X(78)∩X(189)X(972)

Barycentrics    5*a^12 - 2*a^11*b - 24*a^10*b^2 + 10*a^9*b^3 + 45*a^8*b^4 - 20*a^7*b^5 - 40*a^6*b^6 + 20*a^5*b^7 + 15*a^4*b^8 - 10*a^3*b^9 + 2*a*b^11 - b^12 - 2*a^11*c + 40*a^10*b*c - 6*a^9*b^2*c - 64*a^8*b^3*c - 20*a^7*b^4*c + 16*a^6*b^5*c + 52*a^5*b^6*c - 10*a^3*b^8*c + 8*a^2*b^9*c - 14*a*b^10*c - 24*a^10*c^2 - 6*a^9*b*c^2 + 38*a^8*b^2*c^2 + 40*a^7*b^3*c^2 - 8*a^6*b^4*c^2 - 52*a^5*b^5*c^2 + 4*a^4*b^6*c^2 + 8*a^3*b^7*c^2 - 16*a^2*b^8*c^2 + 10*a*b^9*c^2 + 6*b^10*c^2 + 10*a^9*c^3 - 64*a^8*b*c^3 + 40*a^7*b^2*c^3 + 64*a^6*b^3*c^3 - 20*a^5*b^4*c^3 - 56*a^3*b^6*c^3 + 26*a*b^8*c^3 + 45*a^8*c^4 - 20*a^7*b*c^4 - 8*a^6*b^2*c^4 - 20*a^5*b^3*c^4 - 38*a^4*b^4*c^4 + 68*a^3*b^5*c^4 + 16*a^2*b^6*c^4 - 28*a*b^7*c^4 - 15*b^8*c^4 - 20*a^7*c^5 + 16*a^6*b*c^5 - 52*a^5*b^2*c^5 + 68*a^3*b^4*c^5 - 16*a^2*b^5*c^5 + 4*a*b^6*c^5 - 40*a^6*c^6 + 52*a^5*b*c^6 + 4*a^4*b^2*c^6 - 56*a^3*b^3*c^6 + 16*a^2*b^4*c^6 + 4*a*b^5*c^6 + 20*b^6*c^6 + 20*a^5*c^7 + 8*a^3*b^2*c^7 - 28*a*b^4*c^7 + 15*a^4*c^8 - 10*a^3*b*c^8 - 16*a^2*b^2*c^8 + 26*a*b^3*c^8 - 15*b^4*c^8 - 10*a^3*c^9 + 8*a^2*b*c^9 + 10*a*b^2*c^9 - 14*a*b*c^10 + 6*b^2*c^10 + 2*a*c^11 - c^12 : :
X(54054) = X[20] + 2 X[3345], X[3146] - 4 X[47441], 2 X[3182] - 5 X[3522]

X(54054) lies on the cubic K1327 and these lines: {20, 78}, {189, 972}, {3146, 47441}, {3182, 3522}, {4313, 44696}, {9778, 11206}

X(54055) = X(2)X(52053)∩X(20)X(3413)

Barycentrics    3*(3*a^4 - 2*a^2*b^2 - b^4 - 2*a^2*c^2 + 2*b^2*c^2 - c^4)*Sqrt[-2*a^8 + 3*a^6*b^2 - 2*a^4*b^4 + 3*a^2*b^6 - 2*b^8 + 3*a^6*c^2 - 2*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + 3*b^6*c^2 - 2*a^4*c^4 - 2*a^2*b^2*c^4 - 2*b^4*c^4 + 3*a^2*c^6 + 3*b^2*c^6 - 2*c^8 + 2*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 3*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)] - 4*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*S + 4*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*S : :
X(54055) = 5 X[20] - 2 X[42411], X[20] + 2 X[42412], X[42411] + 5 X[42412], 5 X[3522] - 2 X[40851], X[5059] + 2 X[40852], 3 X[10304] - 2 X[39162]

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}

X(54056) = X(2)X(52054)∩X(20)X(3413)

Barycentrics    3*(3*a^4 - 2*a^2*b^2 - b^4 - 2*a^2*c^2 + 2*b^2*c^2 - c^4)*Sqrt[-2*a^8 + 3*a^6*b^2 - 2*a^4*b^4 + 3*a^2*b^6 - 2*b^8 + 3*a^6*c^2 - 2*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + 3*b^6*c^2 - 2*a^4*c^4 - 2*a^2*b^2*c^4 - 2*b^4*c^4 + 3*a^2*c^6 + 3*b^2*c^6 - 2*c^8 + 2*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 3*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6)] + 4*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*S - 4*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*S : :
X(54056) = X[20] + 2 X[42411], 5 X[20] - 2 X[42412], 5 X[42411] + X[42412], 5 X[3522] - 2 X[40852], X[5059] + 2 X[40851], 3 X[10304] - 2 X[39163]

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}

X(54057) = CIRCUMCIRCLE-INVERSE OF X(250)

Barycentrics    a^2*(a^2 - b^2)^2*(a^2 - c^2)^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8 - a^6*b^2 - 2*a^4*b^4 + 3*a^2*b^6 - b^8 - a^6*c^2 + 5*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - b^6*c^2 - 2*a^4*c^4 - 3*a^2*b^2*c^4 + 4*b^4*c^4 + 3*a^2*c^6 - b^2*c^6 - c^8) : :

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) = CIRCUMCIRCLE-INVERSE OF X(48)

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

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) = CIRCUMCIRCLE-INVERSE OF X(63)

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

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) = CIRCUMCIRCLE-INVERSE OF X(66)

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

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) = CIRCUMCIRCLE-INVERSE OF X(68)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*b^2*c^2 + c^4)*(a^4 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 7*a^6*b^2*c^2 - 7*a^4*b^4*c^2 + 5*a^2*b^6*c^2 - 2*b^8*c^2 + 2*a^6*c^4 - 7*a^4*b^2*c^4 + b^6*c^4 + 2*a^4*c^6 + 5*a^2*b^2*c^6 + b^4*c^6 - 3*a^2*c^8 - 2*b^2*c^8 + c^10) : :

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) = CIRCUMCIRCLE-INVERSE OF X(97)

Barycentrics    a^2*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)*(a^8 - 2*a^6*b^2 + 2*a^4*b^4 - 2*a^2*b^6 + b^8 - 2*a^6*c^2 + 5*a^4*b^2*c^2 - a^2*b^4*c^2 - 2*b^6*c^2 + 2*a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 - 2*a^2*c^6 - 2*b^2*c^6 + c^8) : :

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) = CIRCUMCIRCLE-INVERSE OF X(116)

Barycentrics    a^2*(a^8 - a^7*b - a^6*b^2 + a^5*b^3 - a^3*b^5 + a^2*b^6 + a*b^7 - b^8 - a^7*c + a^6*b*c + a^5*b^2*c - a^4*b^3*c + a^3*b^4*c - a^2*b^5*c - a*b^6*c + b^7*c - a^6*c^2 + a^5*b*c^2 - a*b^5*c^2 + b^6*c^2 + a^5*c^3 - a^4*b*c^3 + a*b^4*c^3 - b^5*c^3 + a^3*b*c^4 + a*b^3*c^4 - a^3*c^5 - a^2*b*c^5 - a*b^2*c^5 - b^3*c^5 + a^2*c^6 - a*b*c^6 + b^2*c^6 + a*c^7 + b*c^7 - c^8) : :

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) = CIRCUMCIRCLE-INVERSE OF X(119)

Barycentrics    a^2*(a^11 - a^10*b - 3*a^9*b^2 + 3*a^8*b^3 + 2*a^7*b^4 - 2*a^6*b^5 + 2*a^5*b^6 - 2*a^4*b^7 - 3*a^3*b^8 + 3*a^2*b^9 + a*b^10 - b^11 - a^10*c + 5*a^9*b*c - a^8*b^2*c - 10*a^7*b^3*c + 8*a^6*b^4*c - 8*a^4*b^6*c + 10*a^3*b^7*c + a^2*b^8*c - 5*a*b^9*c + b^10*c - 3*a^9*c^2 - a^8*b*c^2 + 10*a^7*b^2*c^2 - 2*a^6*b^3*c^2 - 10*a^5*b^4*c^2 + 10*a^4*b^5*c^2 + 2*a^3*b^6*c^2 - 10*a^2*b^7*c^2 + a*b^8*c^2 + 3*b^9*c^2 + 3*a^8*c^3 - 10*a^7*b*c^3 - 2*a^6*b^2*c^3 + 12*a^5*b^3*c^3 - 10*a^3*b^5*c^3 + 2*a^2*b^6*c^3 + 8*a*b^7*c^3 - 3*b^8*c^3 + 2*a^7*c^4 + 8*a^6*b*c^4 - 10*a^5*b^2*c^4 + 2*a^3*b^4*c^4 + 4*a^2*b^5*c^4 - 2*a*b^6*c^4 - 4*b^7*c^4 - 2*a^6*c^5 + 10*a^4*b^2*c^5 - 10*a^3*b^3*c^5 + 4*a^2*b^4*c^5 - 6*a*b^5*c^5 + 4*b^6*c^5 + 2*a^5*c^6 - 8*a^4*b*c^6 + 2*a^3*b^2*c^6 + 2*a^2*b^3*c^6 - 2*a*b^4*c^6 + 4*b^5*c^6 - 2*a^4*c^7 + 10*a^3*b*c^7 - 10*a^2*b^2*c^7 + 8*a*b^3*c^7 - 4*b^4*c^7 - 3*a^3*c^8 + a^2*b*c^8 + a*b^2*c^8 - 3*b^3*c^8 + 3*a^2*c^9 - 5*a*b*c^9 + 3*b^2*c^9 + a*c^10 + b*c^10 - c^11) : :

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) = CIRCUMCIRCLE-INVERSE OF X(123)

Barycentrics    a^2*(a^7 - a^6*b - a^5*b^2 + a^4*b^3 - a^3*b^4 + a^2*b^5 + a*b^6 - b^7 - a^6*c + 3*a^5*b*c - a^4*b^2*c + a^2*b^4*c - 3*a*b^5*c + b^6*c - a^5*c^2 - a^4*b*c^2 + 2*a^3*b^2*c^2 - 2*a^2*b^3*c^2 + a*b^4*c^2 + b^5*c^2 + a^4*c^3 - 2*a^2*b^2*c^3 + 2*a*b^3*c^3 - b^4*c^3 - a^3*c^4 + a^2*b*c^4 + a*b^2*c^4 - b^3*c^4 + a^2*c^5 - 3*a*b*c^5 + b^2*c^5 + a*c^6 + b*c^6 - c^7) : :
X(54065) = 3 X[9909] - X[13222]

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) = CIRCUMCIRCLE-INVERSE OF X(126)

Barycentrics    a^2*(a^10 - 2*a^8*b^2 - 3*a^6*b^4 + 3*a^4*b^6 + 2*a^2*b^8 - b^10 - 2*a^8*c^2 + 7*a^6*b^2*c^2 - 7*a^2*b^6*c^2 + 2*b^8*c^2 - 3*a^6*c^4 + 6*a^2*b^4*c^4 - b^6*c^4 + 3*a^4*c^6 - 7*a^2*b^2*c^6 - b^4*c^6 + 2*a^2*c^8 + 2*b^2*c^8 - c^10) : :

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) = CIRCUMCIRCLE-INVERSE OF X(128)

Barycentrics    a^2*(a^20 - 5*a^18*b^2 + 9*a^16*b^4 - 6*a^14*b^6 + 6*a^6*b^14 - 9*a^4*b^16 + 5*a^2*b^18 - b^20 - 5*a^18*c^2 + 16*a^16*b^2*c^2 - 12*a^14*b^4*c^2 - 12*a^12*b^6*c^2 + 25*a^10*b^8*c^2 - 15*a^8*b^10*c^2 - 6*a^6*b^12*c^2 + 22*a^4*b^14*c^2 - 18*a^2*b^16*c^2 + 5*b^18*c^2 + 9*a^16*c^4 - 12*a^14*b^2*c^4 - 7*a^12*b^4*c^4 + 14*a^10*b^6*c^4 - 6*a^8*b^8*c^4 + 6*a^6*b^10*c^4 - 17*a^4*b^12*c^4 + 24*a^2*b^14*c^4 - 11*b^16*c^4 - 6*a^14*c^6 - 12*a^12*b^2*c^6 + 14*a^10*b^4*c^6 + 6*a^8*b^6*c^6 - 6*a^6*b^8*c^6 + 2*a^4*b^10*c^6 - 14*a^2*b^12*c^6 + 16*b^14*c^6 + 25*a^10*b^2*c^8 - 6*a^8*b^4*c^8 - 6*a^6*b^6*c^8 + 4*a^4*b^8*c^8 + 3*a^2*b^10*c^8 - 20*b^12*c^8 - 15*a^8*b^2*c^10 + 6*a^6*b^4*c^10 + 2*a^4*b^6*c^10 + 3*a^2*b^8*c^10 + 22*b^10*c^10 - 6*a^6*b^2*c^12 - 17*a^4*b^4*c^12 - 14*a^2*b^6*c^12 - 20*b^8*c^12 + 6*a^6*c^14 + 22*a^4*b^2*c^14 + 24*a^2*b^4*c^14 + 16*b^6*c^14 - 9*a^4*c^16 - 18*a^2*b^2*c^16 - 11*b^4*c^16 + 5*a^2*c^18 + 5*b^2*c^18 - c^20) : :

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) = CIRCUMCIRCLE-INVERSE OF X(133)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^16 - 2*a^14*b^2 - 8*a^12*b^4 + 34*a^10*b^6 - 50*a^8*b^8 + 34*a^6*b^10 - 8*a^4*b^12 - 2*a^2*b^14 + b^16 - 2*a^14*c^2 + 17*a^12*b^2*c^2 - 31*a^10*b^4*c^2 - 6*a^8*b^6*c^2 + 64*a^6*b^8*c^2 - 59*a^4*b^10*c^2 + 17*a^2*b^12*c^2 - 8*a^12*c^4 - 31*a^10*b^2*c^4 + 108*a^8*b^4*c^4 - 98*a^6*b^6*c^4 + 28*a^4*b^8*c^4 + 9*a^2*b^10*c^4 - 8*b^12*c^4 + 34*a^10*c^6 - 6*a^8*b^2*c^6 - 98*a^6*b^4*c^6 + 78*a^4*b^6*c^6 - 24*a^2*b^8*c^6 + 16*b^10*c^6 - 50*a^8*c^8 + 64*a^6*b^2*c^8 + 28*a^4*b^4*c^8 - 24*a^2*b^6*c^8 - 18*b^8*c^8 + 34*a^6*c^10 - 59*a^4*b^2*c^10 + 9*a^2*b^4*c^10 + 16*b^6*c^10 - 8*a^4*c^12 + 17*a^2*b^2*c^12 - 8*b^4*c^12 - 2*a^2*c^14 + c^16) : :

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) = CIRCUMCIRCLE-INVERSE OF X(136)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^12 - 4*a^10*b^2 + 7*a^8*b^4 - 8*a^6*b^6 + 7*a^4*b^8 - 4*a^2*b^10 + b^12 - 4*a^10*c^2 + 11*a^8*b^2*c^2 - 11*a^6*b^4*c^2 + 3*a^4*b^6*c^2 + 3*a^2*b^8*c^2 - 2*b^10*c^2 + 7*a^8*c^4 - 11*a^6*b^2*c^4 + 8*a^4*b^4*c^4 - 3*a^2*b^6*c^4 + 3*b^8*c^4 - 8*a^6*c^6 + 3*a^4*b^2*c^6 - 3*a^2*b^4*c^6 - 4*b^6*c^6 + 7*a^4*c^8 + 3*a^2*b^2*c^8 + 3*b^4*c^8 - 4*a^2*c^10 - 2*b^2*c^10 + c^12) : :

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) = CIRCUMCIRCLE-INVERSE OF X(142)

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

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) = CIRCUMCIRCLE-INVERSE OF X(147)

Barycentrics    a^2*(a^12 - a^10*b^2 - a^8*b^4 + a^4*b^8 + a^2*b^10 - b^12 - a^10*c^2 - 2*a^8*b^2*c^2 + 3*a^6*b^4*c^2 - a^8*c^4 + 3*a^6*b^2*c^4 + a^4*b^4*c^4 - 3*a^2*b^6*c^4 - 3*a^2*b^4*c^6 + 2*b^6*c^6 + a^4*c^8 + a^2*c^10 - c^12) : :

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) = CIRCUMCIRCLE-INVERSE OF X(148)

Barycentrics    a^2*(a^8 - 3*a^6*b^2 + 3*a^2*b^6 - b^8 - 3*a^6*c^2 + 12*a^4*b^2*c^2 - 8*a^2*b^4*c^2 + 2*b^6*c^2 - 8*a^2*b^2*c^4 + b^4*c^4 + 3*a^2*c^6 + 2*b^2*c^6 - c^8) : :
X(54072) = 2 X[3] + X[14671]

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) = CIRCUMCIRCLE-INVERSE OF X(156)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^12 - 3*a^10*b^2 + 2*a^8*b^4 + 2*a^6*b^6 - 3*a^4*b^8 + a^2*b^10 - 3*a^10*c^2 + 6*a^8*b^2*c^2 - 5*a^6*b^4*c^2 + 3*a^4*b^6*c^2 - b^10*c^2 + 2*a^8*c^4 - 5*a^6*b^2*c^4 + a^4*b^4*c^4 - a^2*b^6*c^4 + 4*b^8*c^4 + 2*a^6*c^6 + 3*a^4*b^2*c^6 - a^2*b^4*c^6 - 6*b^6*c^6 - 3*a^4*c^8 + 4*b^4*c^8 + a^2*c^10 - b^2*c^10) : :
X(54073) = 5 X[110] + X[43578]

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) = CIRCUMCIRCLE-INVERSE OF X(157)

Barycentrics    a^8*b^2 - 2*a^6*b^4 + 2*a^4*b^6 - 2*a^2*b^8 + b^10 + a^8*c^2 + 2*a^6*b^2*c^2 - 2*a^4*b^4*c^2 - b^8*c^2 - 2*a^6*c^4 - 2*a^4*b^2*c^4 + 4*a^2*b^4*c^4 + 2*a^4*c^6 - 2*a^2*c^8 - b^2*c^8 + c^10 : :
X(54074) = 2 X[141] - 3 X[34138], 2 X[625] - 3 X[36471], X[193] - 3 X[41363], 5 X[3618] - 3 X[34137]

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) = CIRCUMCIRCLE-INVERSE OF X(159)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^8 - a^6*b^2 - a^4*b^4 + a^2*b^6 - b^8 - a^6*c^2 + 2*a^4*b^2*c^2 - a^2*b^4*c^2 - a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 + a^2*c^6 - c^8) : :
X(54075) = X[10317] + 3 X[34897], 5 X[631] - X[41377], 3 X[34366] - X[47286]

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) = CIRCUMCIRCLE-INVERSE OF X(160)

Barycentrics    a^10 - 2*a^8*b^2 + a^6*b^4 - 2*a^8*c^2 + a^6*b^2*c^2 + b^8*c^2 + a^6*c^4 - b^6*c^4 - b^4*c^6 + b^2*c^8 : :

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) = CIRCUMCIRCLE-INVERSE OF X(185)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^12 - 3*a^10*b^2 + 3*a^8*b^4 - 2*a^6*b^6 + 3*a^4*b^8 - 3*a^2*b^10 + b^12 - 3*a^10*c^2 + 7*a^8*b^2*c^2 - 2*a^6*b^4*c^2 - 8*a^4*b^6*c^2 + 9*a^2*b^8*c^2 - 3*b^10*c^2 + 3*a^8*c^4 - 2*a^6*b^2*c^4 + 10*a^4*b^4*c^4 - 6*a^2*b^6*c^4 + 3*b^8*c^4 - 2*a^6*c^6 - 8*a^4*b^2*c^6 - 6*a^2*b^4*c^6 - 2*b^6*c^6 + 3*a^4*c^8 + 9*a^2*b^2*c^8 + 3*b^4*c^8 - 3*a^2*c^10 - 3*b^2*c^10 + c^12) : :

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) = CIRCUMCIRCLE-INVERSE OF X(191)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 + a^6*b*c + 2*a^5*b^2*c - a^4*b^3*c - 2*a^3*b^4*c + a^2*b^5*c - b^7*c - 2*a^6*c^2 + 2*a^5*b*c^2 + 5*a^4*b^2*c^2 - 2*a^3*b^3*c^2 - 3*a^2*b^4*c^2 - a^4*b*c^3 - 2*a^3*b^2*c^3 - a^2*b^3*c^3 + 2*a*b^4*c^3 + b^5*c^3 - 2*a^3*b*c^4 - 3*a^2*b^2*c^4 + 2*a*b^3*c^4 + 2*b^4*c^4 + a^2*b*c^5 + b^3*c^5 + 2*a^2*c^6 - b*c^7 - c^8) : :

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) = CIRCUMCIRCLE-INVERSE OF X(198)

Barycentrics    a*(a - b - c)*(2*a^5 - a^4*b - 4*a^3*b^2 + 2*a^2*b^3 + 2*a*b^4 - b^5 - a^4*c + 8*a^3*b*c - 2*a^2*b^2*c - 4*a*b^3*c - b^4*c - 4*a^3*c^2 - 2*a^2*b*c^2 + 4*a*b^2*c^2 + 2*b^3*c^2 + 2*a^2*c^3 - 4*a*b*c^3 + 2*b^2*c^3 + 2*a*c^4 - b*c^4 - c^5) : :

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) = CIRCUMCIRCLE-INVERSE OF X(206)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^12 - 2*a^8*b^4 + a^4*b^8 + 3*a^8*b^2*c^2 - 2*a^4*b^6*c^2 - b^10*c^2 - 2*a^8*c^4 + 2*a^4*b^4*c^4 - 2*a^4*b^2*c^6 + 2*b^6*c^6 + a^4*c^8 - b^2*c^10) : :

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) = CIRCUMCIRCLE-INVERSE OF X(214)

Barycentrics    a^2*(a^5 - a^3*b^2 + a^2*b^3 - b^5 + a^3*b*c - 2*a^2*b^2*c - a*b^3*c + 2*b^4*c - a^3*c^2 - 2*a^2*b*c^2 + 4*a*b^2*c^2 - b^3*c^2 + a^2*c^3 - a*b*c^3 - b^2*c^3 + 2*b*c^4 - c^5) : :
X(54081) = 4 X[124] - 3 X[15050]

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) = CIRCUMCIRCLE-INVERSE OF X(216)

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

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) = CIRCUMCIRCLE-INVERSE OF X(221)

Barycentrics    a^2*(a + b - c)*(a - b + c)*(a^2 - b^2 - c^2)*(2*a^7 - 2*a^6*b - a^5*b^2 + 3*a^4*b^3 - 4*a^3*b^4 + 3*a*b^6 - b^7 - 2*a^6*c + 4*a^5*b*c - 3*a^4*b^2*c - 2*a^3*b^3*c + 6*a^2*b^4*c - 2*a*b^5*c - b^6*c - a^5*c^2 - 3*a^4*b*c^2 + 12*a^3*b^2*c^2 - 6*a^2*b^3*c^2 - 3*a*b^4*c^2 + b^5*c^2 + 3*a^4*c^3 - 2*a^3*b*c^3 - 6*a^2*b^2*c^3 + 4*a*b^3*c^3 + b^4*c^3 - 4*a^3*c^4 + 6*a^2*b*c^4 - 3*a*b^2*c^4 + b^3*c^4 - 2*a*b*c^5 + b^2*c^5 + 3*a*c^6 - b*c^6 - c^7) : :

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) = CIRCUMCIRCLE-INVERSE OF X(242)

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

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) = CIRCUMCIRCLE-INVERSE OF X(246)

Barycentrics    a^2*(a^12 - 2*a^10*b^2 + 3*a^6*b^6 - 4*a^4*b^8 + 3*a^2*b^10 - b^12 - 2*a^10*c^2 + 6*a^8*b^2*c^2 - 5*a^6*b^4*c^2 + 4*a^4*b^6*c^2 - 4*a^2*b^8*c^2 + b^10*c^2 - 5*a^6*b^2*c^4 + a^4*b^4*c^4 + a^2*b^6*c^4 + 2*b^8*c^4 + 3*a^6*c^6 + 4*a^4*b^2*c^6 + a^2*b^4*c^6 - 4*b^6*c^6 - 4*a^4*c^8 - 4*a^2*b^2*c^8 + 2*b^4*c^8 + 3*a^2*c^10 + b^2*c^10 - c^12) : :

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) = CIRCUMCIRCLE-INVERSE OF X(290)

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

X(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) = CIRCUMCIRCLE-INVERSE OF X(323)

Barycentrics    a^2*(4*a^10 - 12*a^8*b^2 + 14*a^6*b^4 - 10*a^4*b^6 + 6*a^2*b^8 - 2*b^10 - 12*a^8*c^2 + 23*a^6*b^2*c^2 - 13*a^4*b^4*c^2 - a^2*b^6*c^2 + 3*b^8*c^2 + 14*a^6*c^4 - 13*a^4*b^2*c^4 + 5*a^2*b^4*c^4 - b^6*c^4 - 10*a^4*c^6 - a^2*b^2*c^6 - b^4*c^6 + 6*a^2*c^8 + 3*b^2*c^8 - 2*c^10) : :

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) = CIRCUMCIRCLE-INVERSE OF X(325)

Barycentrics    a^2*(a^12 - 2*a^10*b^2 + a^8*b^4 - a^4*b^8 + 2*a^2*b^10 - b^12 - 2*a^10*c^2 - a^8*b^2*c^2 + 5*a^6*b^4*c^2 - 3*a^4*b^6*c^2 - a^2*b^8*c^2 + 2*b^10*c^2 + a^8*c^4 + 5*a^6*b^2*c^4 - 3*a^2*b^6*c^4 - b^8*c^4 - 3*a^4*b^2*c^6 - 3*a^2*b^4*c^6 + 4*b^6*c^6 - a^4*c^8 - a^2*b^2*c^8 - b^4*c^8 + 2*a^2*c^10 + 2*b^2*c^10 - c^12) : :

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) = CIRCUMCIRCLE-INVERSE OF X(339)

Barycentrics    a^14 - 2*a^12*b^2 + a^10*b^4 - a^6*b^8 + 2*a^4*b^10 - a^2*b^12 - 2*a^12*c^2 + 4*a^10*b^2*c^2 - 2*a^8*b^4*c^2 + 2*a^6*b^6*c^2 - 3*a^4*b^8*c^2 + a^2*b^10*c^2 + a^10*c^4 - 2*a^8*b^2*c^4 - a^6*b^4*c^4 + a^4*b^6*c^4 - a^2*b^8*c^4 + b^10*c^4 + 2*a^6*b^2*c^6 + a^4*b^4*c^6 + 2*a^2*b^6*c^6 - b^8*c^6 - a^6*c^8 - 3*a^4*b^2*c^8 - a^2*b^4*c^8 - b^6*c^8 + 2*a^4*c^10 + a^2*b^2*c^10 + b^4*c^10 - a^2*c^12 : :

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) = CIRCUMCIRCLE-INVERSE OF X(355)

Barycentrics    a^2*(a^8 - a^7*b - 2*a^6*b^2 + 3*a^5*b^3 - 3*a^3*b^5 + 2*a^2*b^6 + a*b^7 - b^8 - a^7*c + 3*a^6*b*c - a^5*b^2*c - 5*a^4*b^3*c + 5*a^3*b^4*c + a^2*b^5*c - 3*a*b^6*c + b^7*c - 2*a^6*c^2 - a^5*b*c^2 + 6*a^4*b^2*c^2 - a^3*b^3*c^2 - 5*a^2*b^4*c^2 + 2*a*b^5*c^2 + b^6*c^2 + 3*a^5*c^3 - 5*a^4*b*c^3 - a^3*b^2*c^3 + 4*a^2*b^3*c^3 - b^5*c^3 + 5*a^3*b*c^4 - 5*a^2*b^2*c^4 - 3*a^3*c^5 + a^2*b*c^5 + 2*a*b^2*c^5 - b^3*c^5 + 2*a^2*c^6 - 3*a*b*c^6 + b^2*c^6 + a*c^7 + b*c^7 - c^8) : :
X(54090) = 5 X[3] - X[35455], 5 X[1324] + X[35455]

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) = CIRCUMCIRCLE-INVERSE OF X(389)

Barycentrics    a^2*(a^10 - 4*a^8*b^2 + 7*a^6*b^4 - 7*a^4*b^6 + 4*a^2*b^8 - b^10 - 4*a^8*c^2 + 7*a^6*b^2*c^2 - 5*a^2*b^6*c^2 + 2*b^8*c^2 + 7*a^6*c^4 + 2*a^2*b^4*c^4 - b^6*c^4 - 7*a^4*c^6 - 5*a^2*b^2*c^6 - b^4*c^6 + 4*a^2*c^8 + 2*b^2*c^8 - c^10) : :

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) = CIRCUMCIRCLE-INVERSE OF X(394)

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

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) = CIRCUMCIRCLE-INVERSE OF X(411)

Barycentrics    a*(a^9 - 2*a^7*b^2 + 2*a^3*b^6 - a*b^8 - 2*a^7*b*c + 2*a^6*b^2*c + 3*a^5*b^3*c - 3*a^4*b^4*c - a*b^7*c + b^8*c - 2*a^7*c^2 + 2*a^6*b*c^2 + 3*a^5*b^2*c^2 + a^4*b^3*c^2 - 2*a^3*b^4*c^2 - 2*a^2*b^5*c^2 + a*b^6*c^2 - b^7*c^2 + 3*a^5*b*c^3 + a^4*b^2*c^3 - 4*a^3*b^3*c^3 + 2*a^2*b^4*c^3 + a*b^5*c^3 - 3*b^6*c^3 - 3*a^4*b*c^4 - 2*a^3*b^2*c^4 + 2*a^2*b^3*c^4 + 3*b^5*c^4 - 2*a^2*b^2*c^5 + a*b^3*c^5 + 3*b^4*c^5 + 2*a^3*c^6 + a*b^2*c^6 - 3*b^3*c^6 - a*b*c^7 - b^2*c^7 - a*c^8 + b*c^8) : :
X(54093) = 2 X[36001] + X[37919], 3 X[37940] - 2 X[51635]

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) = CIRCUMCIRCLE-INVERSE OF X(419)

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

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) = CIRCUMCIRCLE-INVERSE OF X(442)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*b*c - 2*a^5*b^2*c + 2*a^2*b^5*c + 2*a*b^6*c - 2*a^6*c^2 - 2*a^5*b*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 + 2*a*b^5*c^2 + 2*b^6*c^2 - 2*a^2*b^3*c^3 - 2*a*b^4*c^3 - a^2*b^2*c^4 - 2*a*b^3*c^4 - 2*b^4*c^4 + 2*a^2*b*c^5 + 2*a*b^2*c^5 + 2*a^2*c^6 + 2*a*b*c^6 + 2*b^2*c^6 - c^8) : :
X(54095) = 3 X[17532] - 4 X[37982]

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) = CIRCUMCIRCLE-INVERSE OF X(460)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 4*a^6*c^2 + 5*a^4*b^2*c^2 - 3*a^2*b^4*c^2 + 6*a^4*c^4 - 3*a^2*b^2*c^4 + 2*b^4*c^4 - 4*a^2*c^6 + c^8) : :

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}





leftri   Perspectors associated with Steiner-circumcevian triangles: X(54097)-X(54113) rightri

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)

underbar



X(54097) = X(2)X(3)∩X(193)X(44518)

Barycentrics    7*a^4 - 2*a^2*b^2 - 9*b^4 - 2*a^2*c^2 + 14*b^2*c^2 - 9*c^4 : :
X(54097) = 9 X[2] - 8 X[32970], 3 X[2] - 4 X[32972], 3 X[439] - 4 X[32970], 2 X[32970] - 3 X[32972]

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) = X(1)X(2)∩X(192)X(17448)

Barycentrics    a^2*b^2 - 6*a^2*b*c + 2*a*b^2*c + a^2*c^2 + 2*a*b*c^2 + b^2*c^2 : :
X(54098) = 9 X[2] - 8 X[27091], 4 X[27091] - 3 X[53675]

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) = X(2)X(32016)∩X(190)X(17494)

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

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) = X(3)X(95)∩X(4)X(290)

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

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) = X(2)X(1978)∩X(37)X(39028)

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

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) = X(2)X(1016)∩X(8)X(19950)

Barycentrics    a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3 - b^4 - 2*a^3*c + 8*a^2*b*c - 4*a*b^2*c + 2*b^3*c - a^2*c^2 - 4*a*b*c^2 - b^2*c^2 + 2*a*c^3 + 2*b*c^3 - c^4 : :
X(54102) = 3 X[2] - 4 X[6547], 2 X[4440] + X[39349], 5 X[4473] - 4 X[32094], 3 X[17487] - 4 X[32106], 5 X[27191] - 3 X[34024]

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) = X(2)X(39764)∩X(20)X(99)

Barycentrics    a^8 + a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - 2*b^8 + a^6*c^2 - 5*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + b^6*c^2 - 3*a^4*c^4 + 3*a^2*b^2*c^4 - 2*b^4*c^4 + 3*a^2*c^6 + b^2*c^6 - 2*c^8 : :
X(54103) = 4 X[3767] - 5 X[14061]

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) = X(2)X(4590)∩X(99)X(45212)

Barycentrics    a^8 - 2*a^6*b^2 - a^4*b^4 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 8*a^4*b^2*c^2 - 4*a^2*b^4*c^2 + 2*b^6*c^2 - a^4*c^4 - 4*a^2*b^2*c^4 - b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8 : :
X(54104) = 3 X[2] - 4 X[23991], 2 X[148] + X[39356], X[148] + 2 X[44373], X[39356] - 4 X[44373], 8 X[31644] - 9 X[41135], X[8596] + 2 X[18823], X[20094] - 4 X[23992], 5 X[40429] - 4 X[40553], 4 X[40511] - 3 X[44397]

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) = X(2)X(36422)∩X(5)X(95)

Barycentrics    a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*b^8 - a^6*c^2 - a^4*b^2*c^2 - 5*a^2*b^4*c^2 + 7*b^6*c^2 - 3*a^4*c^4 - 5*a^2*b^2*c^4 - 10*b^4*c^4 + 5*a^2*c^6 + 7*b^2*c^6 - 2*c^8 : :

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) = X(2)X(5034)∩X(147)X(193)

Barycentrics    a^8 - 2*a^6*b^2 - 4*a^4*b^4 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 - 10*a^4*b^2*c^2 + 2*a^2*b^4*c^2 + 2*b^6*c^2 - 4*a^4*c^4 + 2*a^2*b^2*c^4 + 2*b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8 : :

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) = X(2)X(6354)∩X(19)X(27)

Barycentrics    a^6 - a^5*b - 2*a^4*b^2 + 2*a^3*b^3 + a^2*b^4 - a*b^5 - a^5*c - a^4*b*c + a*b^4*c + b^5*c - 2*a^4*c^2 + 2*a^2*b^2*c^2 + 2*a^3*c^3 - 2*b^3*c^3 + a^2*c^4 + a*b*c^4 - a*c^5 + b*c^5 : :

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) = X(99)X(6563)∩X(110)X(685)

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

X(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) = X(2)X(31643)∩X(19)X(27)

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

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) = X(2)X(31611)∩X(99)X(901)

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

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) = X(2)X(6)∩X(20)X(40995)

Barycentrics    7*a^8 - 12*a^6*b^2 - 6*a^4*b^4 + 20*a^2*b^6 - 9*b^8 - 12*a^6*c^2 + 28*a^4*b^2*c^2 - 20*a^2*b^4*c^2 + 4*b^6*c^2 - 6*a^4*c^4 - 20*a^2*b^2*c^4 + 10*b^4*c^4 + 20*a^2*c^6 + 4*b^2*c^6 - 9*c^8 : :

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) = X(1)X(17208)∩X(2)X(1258)

Barycentrics    a^4*b^2 - a^2*b^4 + 2*a^4*b*c - 2*a*b^4*c + a^4*c^2 - b^4*c^2 - a^2*c^4 - 2*a*b*c^4 - b^2*c^4 : :

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) = X(2)X(1407)∩X(4)X(29958)

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

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) = ISOGONAL CONJUGATE OF X(32445)

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

X(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) = CEVAPOINT OF X(2) AND X(40900)

Barycentrics    (a^2 + b^2 - 3*c^2 - 2*Sqrt[3]*S)*(a^2 - 3*b^2 + c^2 - 2*Sqrt[3]*S) : :

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) = CEVAPOINT OF X(2) AND X(40901)

Barycentrics    (a^2 + b^2 - 3*c^2 + 2*Sqrt[3]*S)*(a^2 - 3*b^2 + c^2 + 2*Sqrt[3]*S) : :

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) = ISOGONAL CONJUGATE OF X(21779)

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

X(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) = ISOGONAL CONJUGATE OF X(21007)

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

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) = ISOGONAL CONJUGATE OF X(2305)

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

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) = ISOGONAL CONJUGATE OF X(21008)

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

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) = ISOGONAL CONJUGATE OF X(20986)

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

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) = ISOGONAL CONJUGATE OF X(5017)

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

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) = ISOGONAL CONJUGATE OF X(16781)

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

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) = ISOGONAL CONJUGATE OF X(3148)

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

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) = ISOGONAL CONJUGATE OF X(3145)

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

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) = ISOGONAL CONJUGATE OF X(12968)

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

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) = ISOGONAL CONJUGATE OF X(12963)

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

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) = ISOGONAL CONJUGATE OF X(34247)

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

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) = BARYCENTRIC QUOTIENT X(385)/X(384)

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

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) = BARYCENTRIC QUOTIENT X(384)/X(385)

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

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}

X(54131) = X(2)X(1350)∩X(6)X(30)

Barycentrics    a^6+8*a^4*(b^2+c^2)-2*(b^2-c^2)^2*(b^2+c^2)+a^2*(-7*b^4+6*b^2*c^2-7*c^4) : :
X(54131) = -2*X[2]+X[1350], -2*X[182]+X[3534], -2*X[1482]+X[50790]

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}

X(54132) = X(2)X(51)∩X(4)X(524)

Barycentrics    a^6-13*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+a^2*(11*b^4-6*b^2*c^2+11*c^4) : :
X(54132) = -2*X[599]+3*X[3545], -2*X[1352]+3*X[3839], -X[15681]+2*X[48906]

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}

X(54133) = X(7)X(3428)∩X(55)X(5762)

Barycentrics    3*a^9-5*a^8*(b+c)-2*(b-c)^6*(b+c)^3+a^7*(-7*b^2+6*b*c-7*c^2)+2*a*(b-c)^4*(b+c)^2*(b^2+c^2)+a^2*(b-c)^4*(7*b^3+17*b^2*c+17*b*c^2+7*c^3)+a^6*(13*b^3+3*b^2*c+3*b*c^2+13*c^3)-a^3*(b-c)^2*(5*b^4+4*b^3*c+6*b^2*c^2+4*b*c^3+5*c^4)+a^5*(7*b^4-8*b^3*c+26*b^2*c^2-8*b*c^3+7*c^4)-a^4*(13*b^5-7*b^4*c+10*b^3*c^2+10*b^2*c^3-7*b*c^4+13*c^5) : :

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)

X(54134) = X(4)X(5854)∩X(56)X(952)

Barycentrics    3*a^7+28*a^5*b*c-7*a^6*(b+c)-2*(b-c)^4*(b+c)^3+2*a*(b^2-c^2)^2*(3*b^2-8*b*c+3*c^2)+12*a^4*(b^3-2*b^2*c-2*b*c^2+c^3)-a^2*(b-c)^2*(3*b^3-23*b^2*c-23*b*c^2+3*c^3)-a^3*(9*b^4+12*b^3*c-50*b^2*c^2+12*b*c^3+9*c^4) : :

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}

X(54135) = X(4)X(527)∩X(9)X(1012)

Barycentrics    a*(a^8-8*a^6*(b^2+c^2)-(b-c)^4*(b+c)^2*(3*b^2+2*b*c+3*c^2)+8*a^2*b*(b-c)^2*c*(3*b^2+4*b*c+3*c^2)+4*a^5*(2*b^3+3*b^2*c+3*b*c^2+2*c^3)-8*a^3*(b-c)^2*(2*b^3+3*b^2*c+3*b*c^2+2*c^3)+2*a^4*(5*b^4-14*b^3*c+10*b^2*c^2-14*b*c^3+5*c^4)+4*a*(b-c)^2*(2*b^5-b^4*c-9*b^3*c^2-9*b^2*c^3-b*c^4+2*c^5)) : :

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}

X(54136) = X(4)X(758)∩X(1)X(7683)

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

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}

X(54137) = X(4)X(521)∩X(59)X(5840)

Barycentrics    a^12-2*a^11*(b+c)-2*a^9*b*c*(b+c)-(b-c)^6*(b+c)^4*(b^2+c^2)-19*a^6*b*(b-c)^2*c*(b^2+b*c+c^2)+a^10*(b^2+4*b*c+c^2)+a*(b-c)^6*(b+c)^3*(2*b^2+b*c+2*c^2)+5*a^7*(b-c)^2*(2*b^3+3*b^2*c+3*b*c^2+2*c^3)-a^5*(b-c)^4*(10*b^3+21*b^2*c+21*b*c^2+10*c^3)+a^8*(-5*b^4+7*b^3*c-3*b^2*c^2+7*b*c^3-5*c^4)-a^2*(b-c)^4*(b+c)^2*(b^4-b^3*c-b^2*c^2-b*c^3+c^4)-a^3*b*(b-c)^2*c*(5*b^5+5*b^4*c-2*b^3*c^2-2*b^2*c^3+5*b*c^4+5*c^5)+a^4*(b-c)^2*(5*b^6+13*b^5*c+2*b^4*c^2-4*b^3*c^3+2*b^2*c^4+13*b*c^5+5*c^6) : :

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)

X(54138) = X(2)X(49939)∩X(4)X(532)

Barycentrics    -sqrt(3)*a^2*(a^4+5*b^4-2*b^2*c^2+5*c^4-6*a^2*(b^2+c^2))+2*(5*a^4-4*(b^2-c^2)^2-a^2*(b^2+c^2))*S : :

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}

X(54139) = X(2)X(49940)∩X(4)X(533)

Barycentrics    -sqrt(3)*a^2*(a^4+5*b^4-2*b^2*c^2+5*c^4-6*a^2*(b^2+c^2))+2*(-5*a^4+4*(b^2-c^2)^2+a^2*(b^2+c^2))*S : :

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}

X(54140) = X(4)X(533)∩X(13)X(511)

Barycentrics    3*a^2*(a^4+5*b^4-2*b^2*c^2+5*c^4-6*a^2*(b^2+c^2))-2*sqrt(3)*(a^4-2*(b^2-c^2)^2+a^2*(b^2+c^2))*S : :

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}

X(54141) = X(4)X(532)∩X(14)X(511)

Barycentrics    3*a^2*(a^4+5*b^4-2*b^2*c^2+5*c^4-6*a^2*(b^2+c^2))+2*sqrt(3)*(a^4-2*(b^2-c^2)^2+a^2*(b^2+c^2))*S : :

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}

X(54142) = X(17)X(14540)∩X(627)X(5979)

Barycentrics    -3*a^8+2*(b^2-c^2)^4+10*a^6*(b^2+c^2)+a^4*(3*b^4+22*b^2*c^2+3*c^4)-12*a^2*(b^6+c^6)+2*sqrt(3)*(a^6+9*a^4*(b^2+c^2)-2*(b^2-c^2)^2*(b^2+c^2)+a^2*(-8*b^4+6*b^2*c^2-8*c^4))*S : :

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)

X(54143) = X(18)X(14541)∩X(628)X(5978)

Barycentrics    3*a^8-2*(b^2-c^2)^4-10*a^6*(b^2+c^2)-a^4*(3*b^4+22*b^2*c^2+3*c^4)+12*a^2*(b^6+c^6)+2*sqrt(3)*(a^6+9*a^4*(b^2+c^2)-2*(b^2-c^2)^2*(b^2+c^2)+a^2*(-8*b^4+6*b^2*c^2-8*c^4))*S : :

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)

X(54144) = X(19)X(18446)∩X(4329)X(51755)

Barycentrics    a*(a^11+a^10*(b+c)+a^8*(b-c)^2*(b+c)-a^9*(7*b^2+4*b*c+7*c^2)+2*a^5*(b+c)^2*(b^4-6*b^3*c+6*b^2*c^2-6*b*c^3+c^4)-(b-c)^4*(b+c)^3*(3*b^4-2*b^2*c^2+3*c^4)+a^2*(b-c)^2*(b+c)^3*(5*b^4-8*b^3*c+2*b^2*c^2-8*b*c^3+5*c^4)+2*a^7*(5*b^4+4*b^3*c+6*b^2*c^2+4*b*c^3+5*c^4)+a*(b-c)^4*(b+c)^2*(5*b^4+6*b^3*c+10*b^2*c^2+6*b*c^3+5*c^4)-a^3*(b^2-c^2)^2*(11*b^4-8*b^3*c+10*b^2*c^2-8*b*c^3+11*c^4)+a^6*(-6*b^5+2*b^4*c+8*b^3*c^2+8*b^2*c^3+2*b*c^4-6*c^5)+2*a^4*(b-c)^2*(b^5+b^4*c+b*c^4+c^5)) : :

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}

X(54145) = X(30)X(65)∩X(191)X(517)

Barycentrics    a*(a^8*(b+c)-6*a^4*b*(b-c)^2*c*(b+c)-2*a^7*(b+c)^2-(b-c)^6*(b+c)^3+a^6*(-2*b^3+3*b^2*c+3*b*c^2-2*c^3)+a^2*(b-c)^4*(2*b^3+7*b^2*c+7*b*c^2+2*c^3)+a*(b^2-c^2)^2*(2*b^4-5*b^3*c+2*b^2*c^2-5*b*c^3+2*c^4)+a^5*(6*b^4+3*b^3*c+2*b^2*c^2+3*b*c^3+6*c^4)+2*a^3*(-3*b^6+3*b^5*c+b^4*c^2-6*b^3*c^3+b^2*c^4+3*b*c^5-3*c^6)) : :

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)

X(54146) = X(22)X(36989)∩X(30)X(66)

Barycentrics    a^18-3*a^16*(b^2+c^2)+2*a^12*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^6*(b^2+c^2)^3-2*a^4*(b^2-c^2)^2*(b^2+c^2)^5+3*a^2*(b^2-c^2)^4*(b^2+c^2)^2*(b^4+c^4)+4*a^8*(b^2+c^2)^3*(b^4-b^2*c^2+c^4)+2*a^14*(b^4+5*b^2*c^2+c^4)-2*a^6*(b^2-c^2)^2*(b^8-5*b^6*c^2-4*b^4*c^4-5*b^2*c^6+c^8)-2*a^10*(2*b^8+9*b^6*c^2-6*b^4*c^4+9*b^2*c^6+2*c^8) : :

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)

X(54147) = X(4)X(9019)∩X(30)X(67)

Barycentrics    a^12-3*a^10*(b^2+c^2)+4*a^6*b^2*c^2*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)^2+3*a^8*(b^4+5*b^2*c^2+c^4)+a^2*(b^2-c^2)^2*(3*b^6-b^4*c^2-b^2*c^4+3*c^6)-a^4*(3*b^8+11*b^6*c^2-4*b^4*c^4+11*b^2*c^6+3*c^8) : :

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)

X(54148) = X(4)X(45780)∩X(30)X(64)

Barycentrics    (a^2-b^2-c^2)*(a^14-3*a^12*(b^2+c^2)+(b^2-c^2)^6*(b^2+c^2)-a^2*(b^2-c^2)^4*(3*b^4-4*b^2*c^2+3*c^4)+a^10*(3*b^4+16*b^2*c^2+3*c^4)-a^8*(b^6+11*b^4*c^2+11*b^2*c^4+c^6)+a^4*(b^2-c^2)^2*(3*b^6+b^4*c^2+b^2*c^4+3*c^6)-a^6*(b^8+8*b^6*c^2-26*b^4*c^4+8*b^2*c^6+c^8)) : :

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}

X(54149) = X(4)X(2393)∩X(30)X(69)

Barycentrics    a^12-4*a^10*(b^2+c^2)-12*a^6*b^2*c^2*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)^2-5*a^4*(b^4-c^4)^2+5*a^8*(b^4+6*b^2*c^2+c^4)+4*a^2*(b^2-c^2)^2*(b^6-2*b^4*c^2-2*b^2*c^4+c^6) : :

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}

X(54150) = X(28)X(1071)∩X(30)X(72)

Barycentrics    a*(a^11*(b+c)-a^10*(b+c)^2-(b^2-c^2)^4*(b^2+c^2)^2-a^9*(3*b^3+2*b^2*c+2*b*c^2+3*c^3)-2*a^4*(b^2-c^2)^2*(b^4-b^3*c-2*b^2*c^2-b*c^3+c^4)+a*(b-c)^4*(b+c)^3*(b^4+b^3*c+6*b^2*c^2+b*c^3+c^4)+a^8*(3*b^4+6*b^3*c-2*b^2*c^2+6*b*c^3+3*c^4)+2*a^7*(b^5+6*b^3*c^2+6*b^2*c^3+c^5)-2*a^6*(b^6+3*b^5*c-b^4*c^2-2*b^3*c^3-b^2*c^4+3*b*c^5+c^6)+a^2*(b^2-c^2)^2*(3*b^6-3*b^4*c^2-8*b^3*c^3-3*b^2*c^4+3*c^6)+2*a^5*(b^7+b^6*c-8*b^5*c^2+2*b^4*c^3+2*b^3*c^4-8*b^2*c^5+b*c^6+c^7)-a^3*(b-c)^2*(3*b^7+7*b^6*c+7*b^5*c^2+15*b^4*c^3+15*b^3*c^4+7*b^2*c^5+7*b*c^6+3*c^7)) : :

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)

X(54151) = X(31)X(30273)∩X(18805)X(30269)

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

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)

X(54152) = X(4)X(69)∩X(32)X(11257)

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

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}

X(54153) = X(30)X(37733)∩X(35)X(16113)

Barycentrics    a^10-a^9*(b+c)+2*a^7*(b-c)^2*(b+c)-(b-c)^6*(b+c)^4+a^8*(-3*b^2+2*b*c-3*c^2)+a*(b-c)^4*(b+c)^3*(b^2-b*c+c^2)+a^2*(b-c)^4*(b+c)^2*(3*b^2+5*b*c+3*c^2)+a^5*b*c*(5*b^3-2*b^2*c-2*b*c^2+5*c^3)+a^6*(4*b^4-b^3*c+13*b^2*c^2-b*c^3+4*c^4)-a^4*(4*b^6+2*b^5*c+3*b^4*c^2-6*b^3*c^3+3*b^2*c^4+2*b*c^5+4*c^6)-a^3*(2*b^7-5*b^5*c^2+3*b^4*c^3+3*b^3*c^4-5*b^2*c^5+2*c^7) : :

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)

X(54154) = X(1)X(6842)∩X(3)X(5441)

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

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}

X(54155) = X(3)X(12206)∩X(4)X(732)

Barycentrics    -(b^4*c^4*(b^2-c^2)^2)+a^8*(4*b^4+9*b^2*c^2+4*c^4)+a^6*(b^6+16*b^4*c^2+16*b^2*c^4+c^6)-a^4*(4*b^8+b^6*c^2-11*b^4*c^4+b^2*c^6+4*c^8)-a^2*(b^10+6*b^8*c^2+b^6*c^4+b^4*c^6+6*b^2*c^8+c^10) : :

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}

X(54156) = X(1)X(104)∩X(40)X(64)

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

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}

X(54157) = X(5)X(51)∩X(30)X(195)

Barycentrics    (-(b^2-c^2)^2+a^2*(b^2+c^2))*(5*a^6-9*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+3*a^2*(b^4+b^2*c^2+c^4)) : :

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}

X(54158) = X(4)X(15733)∩X(7)X(517)

Barycentrics    a^9-a^8*(b+c)+4*a^6*(b-c)^2*(b+c)+4*a^2*(b-c)^4*(b+c)^3-(b-c)^6*(b+c)^3+a^7*(-4*b^2+2*b*c-4*c^2)+a*(b-c)^4*(b+c)^2*(b^2+c^2)-2*a^3*(b^2-c^2)^2*(2*b^2+b*c+2*c^2)+2*a^5*(3*b^4+b^3*c+16*b^2*c^2+b*c^3+3*c^4)-2*a^4*(3*b^5-3*b^4*c+8*b^3*c^2+8*b^2*c^3-3*b*c^4+3*c^5) : :

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}

X(54159) = X(4)X(527)∩X(9)X(374)

Barycentrics    a*(a^8+8*a^2*b*c*(b^2-c^2)^2-8*a^6*(b^2+b*c+c^2)-(b-c)^4*(b+c)^2*(3*b^2-2*b*c+3*c^2)+8*a^5*(b^3+2*b^2*c+2*b*c^2+c^3)+2*a^4*(5*b^4-4*b^3*c+6*b^2*c^2-4*b*c^3+5*c^4)-16*a^3*(b^5+c^5)+8*a*(b-c)^2*(b^5-3*b^3*c^2-3*b^2*c^3+c^5)) : :

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}

X(54160) = X(4)X(17770)∩X(10)X(511)

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

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}

X(54161) = X(4)X(758)∩X(21)X(517)

Barycentrics    a*(a^8*(b+c)-(b-c)^6*(b+c)^3-a^7*(2*b^2+5*b*c+2*c^2)+2*a^4*b*c*(-4*b^3+3*b^2*c+3*b*c^2-4*c^3)-2*a^6*(b^3-2*b^2*c-2*b*c^2+c^3)+a*(b^2-c^2)^2*(2*b^4-5*b^3*c+5*b^2*c^2-5*b*c^3+2*c^4)-a^3*(b+c)^2*(6*b^4-17*b^3*c+24*b^2*c^2-17*b*c^3+6*c^4)+a^5*(6*b^4+5*b^3*c-3*b^2*c^2+5*b*c^3+6*c^4)+2*a^2*(b^7-5*b^5*c^2+4*b^4*c^3+4*b^3*c^4-5*b^2*c^5+c^7)) : :

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}

X(54162) = X(4)X(524)∩X(23)X(542)

Barycentrics    3*a^12-7*a^10*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)^2+a^8*(4*b^4+13*b^2*c^2+4*c^4)+a^6*(2*b^6+b^4*c^2+b^2*c^4+2*c^6)+a^2*(b^2-c^2)^2*(5*b^6+4*b^4*c^2+4*b^2*c^4+5*c^6)-a^4*(5*b^8+5*b^6*c^2-4*b^4*c^4+5*b^2*c^6+5*c^8) : :

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}

X(54163) = X(3)X(22533)∩X(30)X(11411)

Barycentrics    (a^2-b^2-c^2)*(3*a^14-8*a^12*(b^2+c^2)+2*(b^2-c^2)^6*(b^2+c^2)-a^2*(b^2-c^2)^4*(5*b^4-4*b^2*c^2+5*c^4)+a^10*(5*b^4+28*b^2*c^2+5*c^4)+4*a^4*(b^2-c^2)^2*(b^6+c^6)+2*a^8*(b^6-11*b^4*c^2-11*b^2*c^4+c^6)-a^6*(3*b^8+4*b^6*c^2-30*b^4*c^4+4*b^2*c^6+3*c^8)) : :

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}

X(54164) = X(25)X(3564)∩X(30)X(5921)

Barycentrics    3*a^12-9*a^10*(b^2+c^2)+7*a^2*(b^2-c^2)^4*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)^2+8*a^8*(b^4+5*b^2*c^2+c^4)+2*a^6*(b^6-17*b^4*c^2-17*b^2*c^4+c^6)+a^4*(-9*b^8+20*b^6*c^2+10*b^4*c^4+20*b^2*c^6-9*c^8) : :

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}

X(54165) = X(31)X(29010)∩X(75)X(30269)

Barycentrics    -(a^7*b*c)+a^8*(b+c)-a^4*(b-c)^2*(b+c)^3-2*b*(b-c)^2*c*(b+c)^3*(b^2-b*c+c^2)-a^3*(b+c)^4*(2*b^2-3*b*c+2*c^2)+2*a^5*(b^4+3*b^3*c+3*b*c^3+c^4)+2*a^2*b*c*(b^5+b^3*c^2+b^2*c^3+c^5) : :

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)

X(54166) = X(4)X(18768)∩X(32)X(2782)

Barycentrics    -(a^8*b^2*c^2)+a^10*(b^2+c^2)-2*b^2*c^2*(b^2-c^2)^2*(b^4+c^4)+2*a^2*b^2*c^2*(b^6+b^4*c^2+b^2*c^4+c^6)+a^6*(b^6+7*b^4*c^2+7*b^2*c^4+c^6)-a^4*(2*b^8+7*b^6*c^2-2*b^4*c^4+7*b^2*c^6+2*c^8) : :

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}

X(54167) = X(39)X(550)∩X(83)X(5188)

Barycentrics    4*b^4*c^4*(b^2-c^2)^2+a^10*(b^2+c^2)-31*a^6*b^2*c^2*(b^2+c^2)-11*a^8*(b^2+c^2)^2+a^4*(9*b^8+6*b^6*c^2-22*b^4*c^4+6*b^2*c^6+9*c^8)+a^2*(b^10+14*b^8*c^2-3*b^6*c^4-3*b^4*c^6+14*b^2*c^8+c^10) : :

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}

X(54168) = X(4)X(525)∩X(249)X(23698)

Barycentrics    a^14-2*a^12*(b^2+c^2)-(b^2-c^2)^6*(b^2+c^2)-a^10*(b^4-8*b^2*c^2+c^4)+2*a^4*(b^2-c^2)^2*(2*b^6+5*b^4*c^2+5*b^2*c^4+2*c^6)+a^8*(7*b^6-9*b^4*c^2-9*b^2*c^4+7*c^6)+a^6*(-9*b^8+5*b^6*c^2+9*b^4*c^4+5*b^2*c^6-9*c^8)+a^2*(b^2-c^2)^2*(b^8-7*b^6*c^2+3*b^4*c^4-7*b^2*c^6+c^8) : :

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)

X(54169) = X(2)X(1350)∩X(3)X(524)

Barycentrics    4*a^6+5*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-2*a^2*(5*b^4+6*b^2*c^2+5*c^4) : :
X(54169) = X[2]+X[1350], -X[4]+3*X[21358], -X[6]+3*X[3524], X[40]+X[47358], X[376]+X[599], -X[381]+2*X[20582], -2*X[575]+5*X[15712], -X[576]+4*X[3530], X[1352]+X[3534], -X[1386]+2*X[50828], X[3242]+X[50810], X[3830]+X[48873], X[6144]+X[51179], X[6776]+X[15533], X[11001]+X[36990], -3*X[14561]+5*X[15694], X[39899]+X[50961], -4*X[48892]+5*X[51134]

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}

X(54170) = X(30)X(69)∩X(2)X(1350)

Barycentrics    5*a^6+13*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2)-a^2*(17*b^4+6*b^2*c^2+17*c^4) : :
X(54170) = -2*X[6]+3*X[10304], -4*X[576]+7*X[3528], -X[1351]+2*X[8703], -X[3751]+2*X[50808], -8*X[3818]+11*X[Z51231], -X[3830]+2*X[48876], -3*X[5050]+4*X[34200], -X[6144]+2*X[51136], -X[11531]+2*X[51089], -6*X[14561]+7*X[15702]

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}

X(54171) = X(183)X(3524)∩X(458)X(1992)

Barycentrics    (a^6+b^6-13*b^4*c^2+11*b^2*c^4+c^6+a^4*(11*b^2-c^2)-a^2*(13*b^4+6*b^2*c^2+c^4))*(a^6+b^6+11*b^4*c^2-13*b^2*c^4+c^6-a^4*(b^2-11*c^2)-a^2*(b^4+6*b^2*c^2+13*c^4)) : :

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)}}

X(54172) = X(182)X(6090)∩X(183)X(3524)

Barycentrics    a^2*(a^6+b^6-13*b^4*c^2+11*b^2*c^4+c^6+a^4*(11*b^2-c^2)-a^2*(13*b^4+6*b^2*c^2+c^4))*(a^6+b^6+11*b^4*c^2-13*b^2*c^4+c^6-a^4*(b^2-11*c^2)-a^2*(b^4+6*b^2*c^2+13*c^4)) : :

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}

X(54173) = X(2)X(51)∩X(3)X(524)

Barycentrics    a^6+5*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-a^2*(7*b^4+6*b^2*c^2+7*c^4) : :
X(54173) = -X[6]+2*X[549], -2*X[576]+5*X[631], -3*X[5085]+4*X[12100], -3*X[38029]+4*X[50828], -2*X[48904]+5*X[51537]

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}

X(54174) = X(2)X(51)∩X(20)X(524)

Barycentrics    a^6+23*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-a^2*(25*b^4+6*b^2*c^2+25*c^4) : :
X(54174) = -8*X[182]+9*X[15705], -4*X[381]+5*X[3620], -8*X[576]+11*X[15717], -2*X[1351]+3*X[3524], -X[3830]+2*X[50978], -6*X[5050]+7*X[15698], -3*X[5093]+4*X[12100], -3*X[5102]+4*X[50983], -3*X[10516]+4*X[50982], -2*X[37517]+3*X[38064]

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}

X(54175) = X(9)X(7680)∩X(144)X(3428)

Barycentrics    4*a^9-8*a^8*(b+c)-(b-c)^6*(b+c)^3+a^7*(-7*b^2+8*b*c-7*c^2)+a^5*(b-c)^2*(b^2-8*b*c+c^2)-a*(b-c)^4*(b+c)^2*(b^2+4*b*c+c^2)+a^3*(b^2-c^2)^2*(3*b^2+4*b*c+3*c^2)+a^2*(b-c)^2*(b+c)^3*(7*b^2-10*b*c+7*c^2)+a^6*(21*b^3+11*b^2*c+11*b*c^2+21*c^3)-a^4*(19*b^5+3*b^4*c+10*b^3*c^2+10*b^2*c^3+3*b*c^4+19*c^5) : :

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}

X(54176) = X(1)X(1532)∩X(3)X(5854)

Barycentrics    4*a^7-8*a^6*(b+c)-(b-c)^4*(b+c)^3+a^5*(-3*b^2+32*b*c-3*c^2)-2*a^3*(b-c)^2*(3*b^2+16*b*c+3*c^2)+a*(b^2-c^2)^2*(5*b^2-12*b*c+5*c^2)-6*a^2*(b-c)^2*(b^3-3*b^2*c-3*b*c^2+c^3)+a^4*(15*b^3-23*b^2*c-23*b*c^2+15*c^3) : :

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}

X(54177) = X(20)X(5854)∩X(517)X(3529)

Barycentrics    7*a^7-15*a^6*(b+c)-3*(b-c)^4*(b+c)^3-3*a^5*(b^2-20*b*c+c^2)+a*(b^2-c^2)^2*(11*b^2-28*b*c+11*c^2)-a^2*(b-c)^2*(9*b^3-41*b^2*c-41*b*c^2+9*c^3)+a^4*(27*b^3-47*b^2*c-47*b*c^2+27*c^3)-a^3*(15*b^4+32*b^3*c-102*b^2*c^2+32*b*c^3+15*c^4) : :

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)

X(54178) = X(3)X(527)∩X(7)X(6282)

Barycentrics    3*a^8*(b+c)+16*a^6*b*c*(b+c)-4*a*b*(b-c)^4*c*(b+c)^2-(b-c)^6*(b+c)^3-8*a^7*(b^2+b*c+c^2)+8*a^2*(b-c)^4*(b^3+2*b^2*c+2*b*c^2+c^3)-8*a^3*(b-c)^2*(b^4-2*b^3*c-2*b*c^3+c^4)+4*a^5*(4*b^4-5*b^3*c+10*b^2*c^2-5*b*c^3+4*c^4)-2*a^4*(5*b^5+3*b^4*c+8*b^3*c^2+8*b^2*c^3+3*b*c^4+5*c^5) : :

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)

X(54179) = X(7)X(6925)∩X(20)X(527)

Barycentrics    a^9+3*a^8*(b+c)-(b-c)^6*(b+c)^3-3*a*(b^2-c^2)^4-8*a^7*(2*b^2+b*c+2*c^2)+4*a^6*(2*b^3+7*b^2*c+7*b*c^2+2*c^3)-8*a^3*(b-c)^2*(b^4-5*b^3*c-4*b^2*c^2-5*b*c^3+c^4)+a^5*(26*b^4-48*b^3*c+60*b^2*c^2-48*b*c^3+26*c^4)+4*a^2*(b-c)^2*(4*b^5-b^4*c-11*b^3*c^2-11*b^2*c^3-b*c^4+4*c^5)-2*a^4*(13*b^5-b^4*c+4*b^3*c^2+4*b^2*c^3-b*c^4+13*c^5) : :

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)

X(54180) = X(1)X(3430)∩X(3)X(758)

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

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)

X(54181) = X(20)X(758)∩X(8)X(3430)

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

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)

X(54182) = X(34)X(17520)∩X(65)X(1884)

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

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)

X(54183) = X(6)X(30)∩X(25)X(182)

Barycentrics    a^2*(a^10-3*a^8*(b^2+c^2)+2*a^6*(b^4+8*b^2*c^2+c^4)+(b^2-c^2)^2*(b^6-5*b^4*c^2-5*b^2*c^4+c^6)+2*a^4*(b^6-3*b^4*c^2-3*b^2*c^4+c^6)-a^2*(3*b^8+10*b^4*c^4+3*c^8)) : :

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}

X(54184) = X(20)X(2393)∩X(30)X(193)

Barycentrics    3*a^12-10*a^10*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)^2+a^8*(9*b^4+62*b^2*c^2+9*c^4)+4*a^6*(b^6-6*b^4*c^2-6*b^2*c^4+c^6)+6*a^2*(b^2-c^2)^2*(b^6-3*b^4*c^2-3*b^2*c^4+c^6)-a^4*(11*b^8+10*b^4*c^4+11*c^8) : :

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)

X(54185) = X(28)X(9940)∩X(30)X(553)

Barycentrics    a*(a^11*(b+c)-a^10*(b^2+c^2)-(b-c)^6*(b+c)^4*(b^2+c^2)-a^9*(3*b^3+2*b^2*c+2*b*c^2+3*c^3)-2*a^6*(b+c)^2*(b^4-b^3*c-3*b^2*c^2-b*c^3+c^4)+a*(b-c)^4*(b+c)^3*(b^4+b^3*c+4*b^2*c^2+b*c^3+c^4)+a^8*(3*b^4-4*b^2*c^2+3*c^4)+2*a^7*(b^5+7*b^3*c^2+7*b^2*c^3+c^5)-2*a^4*(b+c)^2*(b^6-5*b^5*c+8*b^4*c^2-4*b^3*c^3+8*b^2*c^4-5*b*c^5+c^6)+a^2*(b^2-c^2)^2*(3*b^6-6*b^5*c-b^4*c^2-8*b^3*c^3-b^2*c^4-6*b*c^5+3*c^6)+2*a^5*(b^7+b^6*c-11*b^5*c^2+b^4*c^3+b^3*c^4-11*b^2*c^5+b*c^6+c^7)-a^3*(b-c)^2*(3*b^7+7*b^6*c+b^5*c^2+5*b^4*c^3+5*b^3*c^4+b^2*c^5+7*b*c^6+3*c^7)) : :

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)

X(54186) = X(30)X(3868)∩X(1071)X(31293)

Barycentrics    a*(a^11*(b+c)-a^10*(b^2+b*c+c^2)-a^9*(3*b^3+2*b^2*c+2*b*c^2+3*c^3)-(b^2-c^2)^4*(b^4-b^3*c+2*b^2*c^2-b*c^3+c^4)+3*a^8*(b^4+b^3*c-b^2*c^2+b*c^3+c^4)+a*(b-c)^4*(b+c)^3*(b^4+b^3*c+5*b^2*c^2+b*c^3+c^4)+a^7*(2*b^5+13*b^3*c^2+13*b^2*c^3+2*c^5)+a^6*(-2*b^6-4*b^5*c+5*b^4*c^2+10*b^3*c^3+5*b^2*c^4-4*b*c^5-2*c^6)-a^4*(b+c)^2*(2*b^6-8*b^5*c+9*b^4*c^2-2*b^3*c^3+9*b^2*c^4-8*b*c^5+2*c^6)+a^2*(b^2-c^2)^2*(3*b^6-3*b^5*c-2*b^4*c^2-8*b^3*c^3-2*b^2*c^4-3*b*c^5+3*c^6)+a^5*(2*b^7+2*b^6*c-19*b^5*c^2+3*b^4*c^3+3*b^3*c^4-19*b^2*c^5+2*b*c^6+2*c^7)-a^3*(b-c)^2*(3*b^7+7*b^6*c+4*b^5*c^2+10*b^4*c^3+10*b^3*c^4+4*b^2*c^5+7*b*c^6+3*c^7)) : :

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)

X(54187) = X(3)X(6)∩X(315)X(11257)

Barycentrics    a^2*(b^10-3*b^8*c^2-2*b^6*c^4-2*b^4*c^6-3*b^2*c^8+c^10+a^8*(b^2+c^2)+2*a^4*(b^2+c^2)^3-4*a^2*(b^8+2*b^6*c^2+b^4*c^4+2*b^2*c^6+c^8)) : :

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}

X(54188) = X(20)X(185)∩X(32)X(32522)

Barycentrics    a^10*(b^2+c^2)-b^2*c^2*(b^2-c^2)^2*(b^4+c^4)+a^8*(2*b^4+3*b^2*c^2+2*c^4)+2*a^6*(b^6+7*b^4*c^2+7*b^2*c^4+c^6)-2*a^4*(3*b^8+7*b^6*c^2+b^4*c^4+7*b^2*c^6+3*c^8)+a^2*(b^10-3*b^8*c^2-2*b^6*c^4-2*b^4*c^6-3*b^2*c^8+c^10) : :

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}

X(54189) = X(4)X(69)∩X(183)X(3094)

Barycentrics    a^8*(b^2+c^2)-2*b^4*c^4*(b^2+c^2)+a^4*(b^2-c^2)^2*(b^2+c^2)-a^6*(b^4+c^4)-a^2*(b^8+2*b^6*c^2+8*b^4*c^4+2*b^2*c^6+c^8) : :

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)

X(54190) = X(21)X(31806)∩X(30)X(51113)

Barycentrics    a*(2*a^9-3*a^8*(b+c)+a^7*(-6*b^2+4*b*c-6*c^2)+3*a*b*c*(b^2-c^2)^2*(b^2-b*c+c^2)-(b-c)^4*(b+c)^3*(b^2+b*c+c^2)+2*a^6*(5*b^3+b^2*c+b*c^2+5*c^3)+a^5*(6*b^4-5*b^3*c+20*b^2*c^2-5*b*c^3+6*c^4)+a^2*(b-c)^2*(6*b^5+8*b^4*c+11*b^3*c^2+11*b^2*c^3+8*b*c^4+6*c^5)-a^4*(12*b^5-5*b^4*c+6*b^3*c^2+6*b^2*c^3-5*b*c^4+12*c^5)-a^3*(2*b^6+2*b^5*c+11*b^4*c^2-6*b^3*c^3+11*b^2*c^4+2*b*c^5+2*c^6)) : :

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)

X(54191) = X(517)X(3648)∩X(2475)X(5535)

Barycentrics    3*a^10-4*a^9*(b+c)-2*a*b*(b-c)^4*c*(b+c)^3-(b-c)^6*(b+c)^4+a^8*(-9*b^2+6*b*c-9*c^2)+12*a^7*(b^3+c^3)+a^2*(b^2-c^2)^2*(3*b^4+2*b^3*c-7*b^2*c^2+2*b*c^3+3*c^4)+a^6*(10*b^4-6*b^3*c+33*b^2*c^2-6*b*c^3+10*c^4)+2*a^3*(b-c)^2*(2*b^5+2*b^4*c+5*b^3*c^2+5*b^2*c^3+2*b*c^4+2*c^5)-2*a^5*(6*b^5-5*b^4*c+4*b^3*c^2+4*b^2*c^3-5*b*c^4+6*c^5)-2*a^4*(3*b^6+2*b^5*c+7*b^4*c^2-6*b^3*c^3+7*b^2*c^4+2*b*c^5+3*c^6) : :

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)

X(54192) = X(1)X(6940)∩X(3)X(758)

Barycentrics    a*(2*a^6-3*a^5*(b+c)+a^2*b*c*(-7*b^2+6*b*c-7*c^2)+a^4*(-3*b^2+8*b*c-3*c^2)+(b^2-c^2)^2*(b^2-b*c+c^2)-a*(b-c)^2*(3*b^3+2*b^2*c+2*b*c^2+3*c^3)+a^3*(6*b^3-b^2*c-b*c^2+6*c^3)) : :

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}

X(54193) = X(1)X(37163)∩X(20)X(758)

Barycentrics    3*a^7-5*a^6*(b+c)-(b-c)^4*(b+c)^3+a^5*(-3*b^2+13*b*c-3*c^2)+a*(b^2-c^2)^2*(3*b^2-5*b*c+3*c^2)-a^2*(b-c)^2*(3*b^3-b^2*c-b*c^2+3*c^3)+a^4*(9*b^3-3*b^2*c-3*b*c^2+9*c^3)-a^3*(3*b^4+8*b^3*c-10*b^2*c^2+8*b*c^3+3*c^4) : :

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}

X(54194) = X(34)X(40)∩X(65)X(1884)

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

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)

X(54195) = X(3)X(732)∩X(4)X(2896)

Barycentrics    a^10*(b^2+c^2)+b^2*c^2*(b^4-c^4)^2+a^8*(5*b^4+12*b^2*c^2+5*c^4)+a^6*(-3*b^6+2*b^4*c^2+2*b^2*c^4-3*c^6)-3*a^2*b^2*c^2*(b^6+5*b^4*c^2+5*b^2*c^4+c^6)-a^4*(3*b^8+15*b^6*c^2+22*b^4*c^4+15*b^2*c^6+3*c^8) : :

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}

X(54196) = X(20)X(732)∩X(83)X(6194)

Barycentrics    a^10*(b^2+c^2)+3*a^8*(3*b^4+7*b^2*c^2+3*c^4)-2*a^6*(b^6-9*b^4*c^2-9*b^2*c^4+c^6)+b^2*c^2*(b^8-b^6*c^2-b^2*c^6+c^8)-a^4*(7*b^8+16*b^6*c^2+11*b^4*c^4+16*b^2*c^6+7*c^8)-a^2*(b^10+9*b^8*c^2+16*b^6*c^4+16*b^4*c^6+9*b^2*c^8+c^10) : :

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)

X(54197) = X(20)X(6735)∩X(517)X(1394)

Barycentrics    a*(3*a^6-2*a^5*(b+c)-(b-c)^3*(b+c)^2*(b+3*c)+a^4*(-7*b^2+10*b*c-3*c^2)+4*a^3*(b^3-2*b*c^2+c^3)+a^2*(5*b^4-8*b^3*c+14*b^2*c^2-8*b*c^3-3*c^4)-2*a*(b^5-b^4*c+4*b^3*c^2-5*b*c^4+c^5))*(3*a^6-2*a^5*(b+c)+(b-c)^3*(b+c)^2*(3*b+c)+a^4*(-3*b^2+10*b*c-7*c^2)+4*a^3*(b^3-2*b^2*c+c^3)+a^2*(-3*b^4-8*b^3*c+14*b^2*c^2-8*b*c^3+5*c^4)-2*a*(b^5-5*b^4*c+4*b^2*c^3-b*c^4+c^5)) : :

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)}}

X(54198) = X(1)X(10309)∩X(10)X(119)

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

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}

X(54199) = X(4)X(7319)∩X(8)X(153)

Barycentrics    a^7+5*a^6*(b+c)+7*a^2*(b-c)^4*(b+c)-(b-c)^4*(b+c)^3-a*(b^2-c^2)^2*(5*b^2-2*b*c+5*c^2)-a^5*(7*b^2+6*b*c+7*c^2)+a^3*(b-c)^2*(11*b^2+26*b*c+11*c^2)+a^4*(-11*b^3+15*b^2*c+15*b*c^2-11*c^3) : :

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}

X(54200) = X(4)X(11)∩X(34)X(207)

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

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}

X(54201) = X(3)X(12325)∩X(5)X(7693)

Barycentrics    2*a^10-a^8*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)-2*a^6*(5*b^4+3*b^2*c^2+5*c^4)-a^2*(b^2-c^2)^2*(8*b^4+11*b^2*c^2+8*c^4)+a^4*(16*b^6+5*b^4*c^2+5*b^2*c^4+16*c^6) : :

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}

X(54202) = X(3)X(54)∩X(4)X(18551)

Barycentrics    a^2*(a^8+2*a^6*(b^2+c^2)-(b^2-c^2)^2*(5*b^4+6*b^2*c^2+5*c^4)-a^4*(12*b^4+7*b^2*c^2+12*c^4)+a^2*(14*b^6+b^4*c^2+b^2*c^4+14*c^6)) : :

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}

X(54203) = X(3)X(15348)∩X(9)X(374)

Barycentrics    a*(a^8+12*a^4*b^2*c^2-2*a^7*(b+c)-(b^2-c^2)^4-2*a^6*(b^2-b*c+c^2)+2*a^5*(3*b^3+b^2*c+b*c^2+3*c^3)+2*a^2*(b-c)^2*(b^4+b^3*c+2*b^2*c^2+b*c^3+c^4)+2*a*(b-c)^2*(b^5+3*b^4*c+3*b*c^4+c^5)-2*a^3*(3*b^5+b^4*c+4*b^3*c^2+4*b^2*c^3+b*c^4+3*c^5)) : :

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}

X(54204) = X(20)X(15733)∩X(144)X(517)

Barycentrics    3*a^9-5*a^8*(b+c)-(b-c)^6*(b+c)^3+a^7*(-8*b^2+6*b*c-8*c^2)-a*(b-c)^4*(b+c)^2*(b^2+4*b*c+c^2)-2*a^3*b*(b-c)^2*c*(3*b^2+2*b*c+3*c^2)+16*a^6*(b^3+c^3)+2*a^5*(3*b^4+b^3*c+28*b^2*c^2+b*c^3+3*c^4)-2*a^4*(9*b^5-b^4*c+16*b^3*c^2+16*b^2*c^3-b*c^4+9*c^5)+8*a^2*(b^7-4*b^5*c^2+3*b^4*c^3+3*b^3*c^4-4*b^2*c^5+c^7) : :

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)

X(54205) = X(3)X(527)∩X(9)X(6935)

Barycentrics    3*a^8*(b+c)+20*a^6*b*c*(b+c)-8*a^7*(b+c)^2-(b-c)^6*(b+c)^3+16*a^5*(b^2+c^2)^2-8*a^3*(b^3-b^2*c+b*c^2-c^3)^2-2*a^4*(5*b^5+7*b^4*c+12*b^3*c^2+12*b^2*c^3+7*b*c^4+5*c^5)+4*a^2*(2*b^7-3*b^6*c+b^5*c^2+b^2*c^5-3*b*c^6+2*c^7) : :

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}

X(54206) = X(7)X(517)∩X(20)X(527)

Barycentrics    a^9+3*a^8*(b+c)-(b-c)^6*(b+c)^3-8*a^3*(b-c)^4*(b^2+b*c+c^2)-8*a^7*(2*b^2+3*b*c+2*c^2)-a*(b-c)^4*(b+c)^2*(3*b^2-2*b*c+3*c^2)+4*a^6*(2*b^3+9*b^2*c+9*b*c^2+2*c^3)+4*a^2*(b-c)^4*(4*b^3+9*b^2*c+9*b*c^2+4*c^3)+a^5*(26*b^4-8*b^3*c+44*b^2*c^2-8*b*c^3+26*c^4)-2*a^4*(13*b^5+7*b^4*c+12*b^3*c^2+12*b^2*c^3+7*b*c^4+13*c^5) : :

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)

X(54207) = X(19)X(1877)∩X(33)X(42289)

Barycentrics    (a+b-c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(3*a^6-8*a^5*(b+c)+5*a^4*(b+c)^2-(b-c)^4*(b+c)^2+4*a^3*(b+c)^3-a^2*(b+c)^2*(7*b^2-2*b*c+7*c^2)+4*a*(b^5-b^4*c-b*c^4+c^5)) : :

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)

X(54208) = X(3)X(17770)∩X(511)X(1125)

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

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)

X(54209) = X(1)X(256)∩X(165)X(1046)

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

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}

X(54210) = X(29)X(1876)∩X(1829)X(1874)

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

See Ivan Pavlov, euclid 5829.

X(54210) lies on these lines: {29, 1876}, {1426, 4213}, {1829, 1874}

X(54210) = zosma transform of X(54160)

X(54211) = X(2)X(3357)∩X(20)X(394)

Barycentrics    5*a^10+a^8*(b^2+c^2)+34*a^4*(b^2-c^2)^2*(b^2+c^2)-3*(b^2-c^2)^4*(b^2+c^2)+a^6*(-30*b^4+52*b^2*c^2-30*c^4)-7*a^2*(b^2-c^2)^2*(b^4+6*b^2*c^2+c^4) : :

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}

X(54212) = X(3)X(758)∩X(30)X(5887)

Barycentrics    a*(a^8*(b+c)-(b-c)^4*(b+c)^3*(b^2-b*c+c^2)-2*a^7*(b^2+3*b*c+c^2)+a^4*b*c*(-11*b^3+5*b^2*c+5*b*c^2-11*c^3)+a^6*(-2*b^3+5*b^2*c+5*b*c^2-2*c^3)+2*a*(b^4-b^3*c+b*c^3-c^4)^2+a^5*(6*b^4+8*b^3*c-2*b^2*c^2+8*b*c^3+6*c^4)+a^2*(b-c)^2*(2*b^5+7*b^4*c+b^3*c^2+b^2*c^3+7*b*c^4+2*c^5)+2*a^3*(-3*b^6+b^5*c+b^4*c^2-8*b^3*c^3+b^2*c^4+b*c^5-3*c^6)) : :

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)

X(54213) = X(20)X(758)∩X(517)X(2475)

Barycentrics    a*(2*a^8*(b+c)-(b-c)^4*(b+c)^3*(2*b^2-3*b*c+2*c^2)-a^7*(4*b^2+11*b*c+4*c^2)+a^4*b*c*(-19*b^3+11*b^2*c+11*b*c^2-19*c^3)+a^6*(-4*b^3+9*b^2*c+9*b*c^2-4*c^3)+a*(b^2-c^2)^2*(4*b^4-9*b^3*c+11*b^2*c^2-9*b*c^3+4*c^4)+a^5*(12*b^4+13*b^3*c-5*b^2*c^2+13*b*c^3+12*c^4)+a^2*(b-c)^2*(4*b^5+11*b^4*c-3*b^3*c^2-3*b^2*c^3+11*b*c^4+4*c^5)+a^3*(-12*b^6+7*b^5*c+6*b^4*c^2-30*b^3*c^3+6*b^2*c^4+7*b*c^5-12*c^6)) : :

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)

X(54214) = X(65)X(1884)∩X(407)X(1877)

Barycentrics    (a+b-c)*(a-b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^7+6*a^5*b*c-5*a^6*(b+c)-(b-c)^4*(b+c)^3+2*a*(b^2-c^2)^2*(2*b^2-b*c+2*c^2)+a^4*(9*b^3+4*b^2*c+4*b*c^2+9*c^3)-2*a^3*(3*b^4+2*b^3*c-4*b^2*c^2+2*b*c^3+3*c^4)-a^2*(3*b^5+7*b^3*c^2+7*b^2*c^3+3*c^5)) : :

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)

X(54215) = X(3)X(524)∩X(4)X(22151)

Barycentrics    4*a^12-9*a^10*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)^2+3*a^8*(b^4+4*b^2*c^2+c^4)+a^2*(b^2-c^2)^2*(3*b^6-b^4*c^2-b^2*c^4+3*c^6)+a^6*(6*b^6+4*b^4*c^2+4*b^2*c^4+6*c^6)-2*a^4*(3*b^8+b^6*c^2+4*b^4*c^4+b^2*c^6+3*c^8) : :

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}

X(54216) = X(20)X(524)∩X(323)X(5921)

Barycentrics    7*a^12-16*a^10*(b^2+c^2)-3*(b^2-c^2)^4*(b^2+c^2)^2+a^8*(7*b^4+25*b^2*c^2+7*c^4)+a^2*(b^2-c^2)^2*(8*b^6+3*b^4*c^2+3*b^2*c^4+8*c^6)+a^6*(8*b^6+5*b^4*c^2+5*b^2*c^4+8*c^6)-a^4*(11*b^8+7*b^6*c^2+4*b^4*c^4+7*b^2*c^6+11*c^8) : :

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)

X(54217) = X(5)X(5504)∩X(30)X(155)

Barycentrics    (a^2-b^2-c^2)*(4*a^14-2*a^2*(b^2-c^2)^6-11*a^12*(b^2+c^2)+(b^2-c^2)^6*(b^2+c^2)+6*a^10*(b^4+6*b^2*c^2+c^4)+a^4*(b^2-c^2)^2*(3*b^6+5*b^4*c^2+5*b^2*c^4+3*c^6)+a^8*(7*b^6-31*b^4*c^2-31*b^2*c^4+7*c^6)-8*a^6*(b^8-4*b^4*c^4+c^8)) : :

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}

X(54218) = X(6)X(1596)∩X(30)X(1351)

Barycentrics    (a^2-b^2-c^2)*(4*a^10+28*a^6*b^2*c^2-7*a^8*(b^2+c^2)+6*a^4*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)-4*a^2*(b^2-c^2)^2*(b^4-3*b^2*c^2+c^4)) : :

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}

X(54219) = X(1370)X(3564)∩X(2393)X(5889)

Barycentrics    7*a^12-20*a^10*(b^2+c^2)-3*(b^2-c^2)^4*(b^2+c^2)^2+a^8*(15*b^4+82*b^2*c^2+15*c^4)+4*a^2*(b^2-c^2)^2*(3*b^6-4*b^4*c^2-4*b^2*c^4+3*c^6)+a^6*(8*b^6-68*b^4*c^2-68*b^2*c^4+8*c^6)+a^4*(-19*b^8+40*b^6*c^2-10*b^4*c^4+40*b^2*c^6-19*c^8) : :

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)

X(54220) = X(192)X(30269)∩X(2887)X(29010)

Barycentrics    2*a^8*(b+c)-b*(b-c)^2*c*(b+c)^3*(b^2-b*c+c^2)+a*(b-c)^2*(b+c)^4*(b^2-b*c+c^2)+a^4*b*c*(b^3+c^3)-2*a^6*(b^3+b^2*c+b*c^2+c^3)-2*a^3*(b+c)^2*(2*b^4-b^3*c+2*b^2*c^2-b*c^3+2*c^4)+a^5*(3*b^4+5*b^3*c+5*b*c^3+3*c^4) : :

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)

X(54221) = X(1278)X(30269)∩X(6327)X(29010)

Barycentrics    -(a^7*b*c)+3*a^8*(b+c)-3*b*(b-c)^2*c*(b+c)^3*(b^2-b*c+c^2)+a*(b-c)^2*(b+c)^4*(b^2-b*c+c^2)-2*a^6*(b^3+b^2*c+b*c^2+c^3)+a^5*(5*b^4+11*b^3*c+11*b*c^3+5*c^4)-a^3*(b+c)^2*(6*b^4-b^3*c+2*b^2*c^2-b*c^3+6*c^4)-a^4*(b^5-2*b^3*c^2-2*b^2*c^3+c^5)+2*a^2*b*c*(b^5+b^3*c^2+b^2*c^3+c^5) : :

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)

X(54222) = X(32)X(7709)∩X(39)X(1513)

Barycentrics    2*a^10*(b^2+c^2)-2*a^8*(b^2+c^2)^2-b^2*c^2*(b^2-c^2)^2*(b^4+c^4)+a^6*(3*b^6+5*b^4*c^2+5*b^2*c^4+3*c^6)-a^4*(4*b^8+9*b^6*c^2+4*b^4*c^4+9*b^2*c^6+4*c^8)+a^2*(b^10-b^8*c^2-b^2*c^8+c^10) : :

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}

X(54223) = X(194)X(8721)∩X(315)X(2782)

Barycentrics    3*a^10*(b^2+c^2)+4*a^6*(b^2+c^2)^3-3*b^2*c^2*(b^2-c^2)^2*(b^4+c^4)+a^2*(b^2+c^2)*(b^4+c^4)^2-a^8*(2*b^4+5*b^2*c^2+2*c^4)-2*a^4*(3*b^8+8*b^6*c^2+b^4*c^4+8*b^2*c^6+3*c^8) : :

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)

X(54224) = X(546)X(3934)∩X(2896)X(5188)

Barycentrics    a^10*(b^2+c^2)+a^8*(13*b^4+28*b^2*c^2+13*c^4)+a^6*(-8*b^6+3*b^4*c^2+3*b^2*c^4-8*c^6)+2*b^2*c^2*(b^8-b^6*c^2-b^2*c^6+c^8)-a^4*(7*b^8+34*b^6*c^2+44*b^4*c^4+34*b^2*c^6+7*c^8)+a^2*(b^10-8*b^8*c^2-25*b^6*c^4-25*b^4*c^6-8*b^2*c^8+c^10) : :

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)

X(54225) = X(76)X(382)∩X(511)X(7847)

Barycentrics    b^2*c^2*(b^2-c^2)^2*(b^4-b^2*c^2+c^4)+a^8*(12*b^4+25*b^2*c^2+12*c^4)+a^6*(-4*b^6+17*b^4*c^2+17*b^2*c^4-4*c^6)-11*a^2*b^2*c^2*(b^6+b^4*c^2+b^2*c^4+c^6)-a^4*(8*b^8+20*b^6*c^2+11*b^4*c^4+20*b^2*c^6+8*c^8) : :

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)

X(54226) = X(40)X(22117)∩X(165)X(7952)

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

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}

X(54227) = X(1)X(6223)∩X(4)X(3671)

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

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}

X(54228) = X(2)X(7992)∩X(4)X(5556)

Barycentrics    a^7+5*a^6*(b+c)-(b-c)^4*(b+c)^3+a^5*(-7*b^2+10*b*c-7*c^2)-a*(b^2-c^2)^2*(5*b^2+6*b*c+5*c^2)+a^3*(b-c)^2*(11*b^2+18*b*c+11*c^2)+a^4*(-11*b^3+7*b^2*c+7*b*c^2-11*c^3)+a^2*(b-c)^2*(7*b^3+b^2*c+b*c^2+7*c^3) : :

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) = ZOSMA TRANSFORM OF X(512)

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

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}

X(54230) = X(1)X(6163)∩X(100)X(6161)

Barycentrics    a*(a-b)*(a-c)*(a^4-b^4+2*b^3*c-b^2*c^2+2*b*c^3-c^4-2*a^3*(b+c)-a^2*(b^2-8*b*c+c^2)+2*a*(b^3-2*b^2*c-2*b*c^2+c^3)) : :

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}

X(54231) = X(1)X(9323)∩X(101)X(14825)

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

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)

X(54232) = X(3)X(101)∩X(4)X(514)

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

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}

X(54233) = X(4)X(101)∩X(3)X(514)

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

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}

X(54234) = X(4)X(9)∩X(25)X(1626)

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

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}

X(54235) = X(19)X(273)∩X(33)X(92)

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

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}

X(54236) = X(3)X(518)∩X(4)X(105)

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

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}

X(54237) = X(3)X(519)∩X(4)X(106)

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

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}

X(54238) = X(4)X(656)∩X(29)X(8062)

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

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}

X(54239) = X(4)X(522)∩X(19)X(657)

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

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}

X(54240) = X(1)X(8764)∩X(107)X(108)

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

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}

X(54241) = X(3)X(108)∩X(4)X(521)

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

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}

X(54242) = X(3)X(102)∩X(4)X(522)

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

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}

X(54243) = X(3)X(522)∩X(4)X(109)

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

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}

X(54244) = X(4)X(6003)∩X(162)X(250)

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

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}

X(54245) = X(4)X(28612)∩X(210)X(430)

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

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}

X(54246) = X(2)X(8877)∩X(6)X(41404)

Barycentrics    a^2*(a^2+b^2-2*c^2)*(a^2-2*b^2+c^2)*(a^10-6*a^8*(b^2+c^2)+a^6*(-7*b^4+52*b^2*c^2-7*c^4)-(b^2+c^2)^3*(b^4-b^2*c^2+c^4)+a^4*(7*b^6-33*b^4*c^2-33*b^2*c^4+7*c^6)+3*a^2*(2*b^8-4*b^6*c^2+15*b^4*c^4-4*b^2*c^6+2*c^8)) : :

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}

X(54247) = X(4)X(1577)∩X(19)X(4041)

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

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}

X(54248) = X(3)X(525)∩X(30)X(14850)

Barycentrics    (a^2-b^2-c^2)*(2*a^12-b^2*c^2*(b^2-c^2)^4-4*a^10*(b^2+c^2)+a^8*(b^4+10*b^2*c^2+c^4)+a^2*(b^2-c^2)^2*(3*b^6+b^4*c^2+b^2*c^4+3*c^6)+a^6*(5*b^6-9*b^4*c^2-9*b^2*c^4+5*c^6)+a^4*(-7*b^8+11*b^6*c^2-6*b^4*c^4+11*b^2*c^6-7*c^8)) : :

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}

X(54249) = X(37)X(513)∩X(241)X(514)

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

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}

X(54250) = X(6)X(513)∩X(665)X(2516)

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

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))

X(54251) = X(1)X(4785)∩X(42)X(649)

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

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}

X(54252) = X(38)X(661)∩X(240)X(522)

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

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}

X(54253) = X(239)X(514)∩X(513)X(1100)

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

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}

X(54254) = X(36)X(238)∩X(43)X(7234)

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

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}

X(54255) = X(36)X(30235)∩X(55)X(650)

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

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))

X(54256) = X(514)X(661)∩X(523)X(1213)

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

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}

X(54257) = X(216)X(520)∩X(441)X(525)

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

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}

X(54258) = X(44)X(513)∩X(1213)X(4806)

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

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}

X(54259) = X(6)X(523)∩X(525)X(3239)

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

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}

X(54260) = X(3)X(525)∩X(523)X(4885)

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

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}

X(54261) = X(1)X(514)∩X(522)X(676)

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

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}

X(54262) = X(2)X(3288)∩X(141)X(523)

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

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}

X(54263) = X(316)X(512)∩X(523)X(3589)

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

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}

X(54264) = X(142)X(522)∩X(514)X(661)

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

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}

X(54265) = X(2)X(4824)∩X(8)X(2533)

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

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}

X(54266) = X(522)X(650)∩X(1212)X(3900)

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

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}

X(54267) = X(230)X(231)∩X(694)X(804)

Barycentrics    (b-c)*(b+c)*(a^8-b^2*c^2*(b^2-c^2)^2+a^4*(b^4+b^2*c^2+c^4)-2*a^2*(b^6+c^6)) ::

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}

X(54268) = X(184)X(647)∩X(512)X(1570)

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

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}

X(54269) = X(30)X(511)∩X(51)X(647)

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

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}

X(54270) = X(11)X(1146)∩X(1647)X(4120)

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

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}

X(54271) = X(30)X(511)∩X(210)X(650)

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

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}

X(54272) = X(30)X(511)∩X(51)X(31174)

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

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}

X(54273) = X(460)X(512)∩X(882)X(1843)

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

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}

X(54274) = X(6)X(512)∩X(184)X(8644)

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

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}

X(54275) = X(6)X(4782)∩X(213)X(667)

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

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}

X(54276) = X(6)X(25423)∩X(669)X(881)

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

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}

X(54277) = X(44)X(513)∩X(1019)X(6626)

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

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}

X(54278) = X(9)X(24720)∩X(44)X(513)

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

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}

X(54279) = X(36)X(238)∩X(55)X(7234)

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

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) = X(2)X(44)∩X(9)X(69)

Barycentrics    3*a^2 - 2*a*b - b^2 - 2*a*c - c^2 : :
X(54280) = 4 X[3707] - X[42697

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(54281) = X(44)X(57)∩X(45)X(63)

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

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) = X(1)X(3)∩X(2)X(3230)

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

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) = X(4)X(9)∩X(37)X(91)

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

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) = X(2)X(37)∩X(57)X(92)

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

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) = X(3)X(37)∩X(6)X(31)

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

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) = X(1)X(88)∩X(4)X(9)

Barycentrics    a*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 2*a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2 - c^3) : :
X(54286) = 3 X[3359] - X[7171], 3 X[997] - 2 X[5289], 3 X[1376] - X[5289], 3 X[40726] - 2 X[51788]

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) = X(1)X(6)∩X(25)X(35)

Barycentrics    a*(a^3 - a^2*b - 3*a*b^2 - b^3 - a^2*c - 6*a*b*c - 5*b^2*c - 3*a*c^2 - 5*b*c^2 - c^3) : :

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) = X(8)X(35)∩X(10)X(12)

Barycentrics    (b + c)*(2*a^3 - a^2*b - 2*a*b^2 + b^3 - a^2*c + a*b*c - b^2*c - 2*a*c^2 - b*c^2 + c^3) : :
X(54288) = 3 X[10] - X[226], 2 X[226] - 3 X[3822], X[63] + 3 X[3679], X[1478] - 5 X[3617], 3 X[1478] + X[20078], 15 X[3617] + X[20078], X[5881] + 3 X[21165], X[5905] - 9 X[53620], 9 X[19875] - 5 X[31266], X[31164] - 5 X[51066]

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) = X(1)X(21)∩X(69)X(73)

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

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) = X(8)X(20)∩X(9)X(46)

Barycentrics    a*(3*a^3 + 3*a^2*b - 3*a*b^2 - 3*b^3 + 3*a^2*c - 2*a*b*c - b^2*c - 3*a*c^2 - b*c^2 - 3*c^3) : :
X(54290) = 5 X[1698] - 3 X[9612], 5 X[1698] - 6 X[26066], 4 X[1125] - 3 X[3485]

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) = X(1)X(76)∩X(2)X(11)

Barycentrics    a^4*b + a^2*b^3 + a^4*c + a*b^3*c + a*b^2*c^2 + b^3*c^2 + a^2*c^3 + a*b*c^3 + b^2*c^3 : :

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) = X(1)X(4)∩X(65)X(81)

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

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) = X(6)X(19)∩X(11)X(33)

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

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) = X(4)X(9)∩X(8)X(27)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^3 + 5*a^2*b + 3*a*b^2 - b^3 + 5*a^2*c + 6*a*b*c + b^2*c + 3*a*c^2 + b*c^2 - c^3) : :

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) = X(1)X(3)∩X(10)X(33)

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

X(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) = X(3)X(74)∩X(6)X(31)

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

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) = X(3)X(6)∩X(13)X(83)

Barycentrics    a^2*(Sqrt[3]*(a^2*(a^2 - b^2 - c^2) - 2*b^2*c^2) + 2*a^2*S) : :

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) = X(3)X(6)∩X(14)X(83)

Barycentrics    a^2*(Sqrt[3]*(a^2*(a^2 - b^2 - c^2) - 2*b^2*c^2) - 2*a^2*S) : :

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) = X(2)X(3)∩X(33)X(72)

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

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) = X(2)X(12)∩X(3)X(6)

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

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) = X(1)X(6)∩X(35)X(47)

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

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) = X(1)X(21)∩X(30)X(84)

Barycentrics    a*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - a^4*b*c - 3*a^3*b^2*c + a^2*b^3*c + 3*a*b^4*c - 3*a^4*c^2 - 3*a^3*b*c^2 + a*b^3*c^2 + b^4*c^2 + a^2*b*c^3 + a*b^2*c^3 + 3*a^2*c^4 + 3*a*b*c^4 + b^2*c^4 - c^6) : :
X(54302) = 4 X[8666] - X[16126], 4 X[5428] - X[11523], X[6762] + 2 X[16139]

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) = X(2)X(6)∩X(8)X(77)

Barycentrics    a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5 + a^4*c + 8*a^3*b*c - 2*a^2*b^2*c - 8*a*b^3*c + b^4*c - 2*a^3*c^2 - 2*a^2*b*c^2 - 2*a*b^2*c^2 - 2*b^3*c^2 - 2*a^2*c^3 - 8*a*b*c^3 - 2*b^2*c^3 + a*c^4 + b*c^4 + c^5 : :

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) = X(7)X(8)∩X(30)X(90)

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

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) = X(1)X(6)∩X(10)X(34)

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

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) = X(2)X(3)∩X(53)X(61)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*(a^2 - b^2 - c^2)^2 + 8*Sqrt[3]*S^3) : :

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) = X(2)X(3)∩X(53)X(62)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*(a^2 - b^2 - c^2)^2 - 8*Sqrt[3]*S^3) : :

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) = X(1)X(75)∩X(2)X(5105)

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

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) = X(1)X(2)∩X(44)X(100)

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

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) = X(1)X(89)∩X(6)X(41)

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

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) = X(2)X(7)∩X(10)X(38)

Barycentrics    a^2*b + 2*a*b^2 + b^3 + a^2*c + b^2*c + 2*a*c^2 + b*c^2 + c^3 : :

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) = X(1)X(25)∩X(3)X(42)

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

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) = X(1)X(60)∩X(8)X(21)

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

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) = X(2)X(92)∩X(4)X(75)

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

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) = X(1)X(88)∩X(65)X(82)

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

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) = X(6)X(43)∩X(8)X(48)

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

X(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) = X(1)X(39)∩X(6)X(78)

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

X(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) = X(1)X(2)∩X(21)X(46)

Barycentrics    a*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - 2*a*b*c - 3*b^2*c - a*c^2 - 3*b*c^2 + c^3) : :
X(54318) = 3 X[1] + X[4915], X[8] + 3 X[15933], X[4915] - 3 X[9623], X[1056] - 3 X[38053], X[1159] + 2 X[15254], X[1159] + 3 X[16857], 2 X[15254] - 3 X[16857], X[31393] - 3 X[38316], X[3577] + 2 X[52769], X[40587] + 2 X[42819], 2 X[6666] + X[14563]

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) = X(1)X(2)∩X(40)X(106)

Barycentrics    a*(a^3 - 3*a^2*b - 3*a*b^2 + b^3 - 3*a^2*c + 12*a*b*c - b^2*c - 3*a*c^2 - b*c^2 + c^3) : :

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) = X(1)X(3)∩X(21)X(34)

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

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) = X(6)X(31)∩X(28)X(34)

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

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) = X(3)X(9)∩X(6)X(31)

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

X(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) = X(3)X(6)∩X(21)X(90)

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

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) = X(4)X(9)∩X(37)X(41)

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

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) = X(6)X(31)∩X(100)X(109)

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

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) = X(1)X(3)∩X(25)X(38)

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

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) = X(19)X(25)∩X(39)X(42)

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

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) = X(21)X(37)∩X(99)X(101)

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

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) = X(1)X(6)∩X(41)X(43)

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

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) = X(1)X(6)∩X(63)X(101)

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

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) = X(8)X(31)∩X(10)X(21)

Barycentrics    a^4 + a*b^3 + a^2*b*c + a*b^2*c + b^3*c + a*b*c^2 + 2*b^2*c^2 + a*c^3 + b*c^3 : :

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) = X(3)X(6)∩X(76)X(110)

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

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) = X(2)X(11)∩X(6)X(101)

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

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) = X(3)X(6)∩X(67)X(69)

Barycentrics    a^2*(a^4*b^2 - b^6 + a^4*c^2 - a^2*b^2*c^2 - b^4*c^2 - b^2*c^4 - c^6) : :
X(54334) = 5 X[2] - 4 X[40670], 3 X[9971] - 4 X[16776], 5 X[9971] - 8 X[40670], 5 X[16776] - 6 X[40670], 4 X[3] - X[37473], X[6] + 2 X[3313], X[6] - 4 X[11574], 2 X[52] - 5 X[53093], 4 X[389] - 7 X[10541], 4 X[575] - X[6243], 2 X[576] + X[37484], X[1350] + 2 X[9967], 2 X[1350] + X[44439], 2 X[3098] + X[18438], X[3313] and many others

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) = X(1)X(2)∩X(75)X(99)

Barycentrics    a^4 - a^2*b^2 - a^2*b*c - 3*a*b^2*c - b^3*c - a^2*c^2 - 3*a*b*c^2 - 2*b^2*c^2 - b*c^3 : :

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) = X(10)X(31)∩X(32)X(37)

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

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) = X(3)X(63)∩X(35)X(42)

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

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) = X(7)X(8)∩X(9)X(39)

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

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) = X(1)X(3)∩X(73)X(81)

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

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) = X(2)X(3)∩X(34)X(81)

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

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) = X(1)X(2)∩X(6)X(22)

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

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) = X(1)X(7)∩X(55)X(80)

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

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) = X(2)X(3)∩X(34)X(63)

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

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) = X(7)X(8)∩X(37)X(63)

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

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) = X(2)X(3)∩X(8)X(88)

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

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) = X(2)X(34)∩X(10)X(73)

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

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) = X(2)X(6)∩X(54)X(67)

Barycentrics    a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 - 6*a^4*b^2*c^2 + a^2*b^4*c^2 - a^4*c^4 + a^2*b^2*c^4 - 2*b^4*c^4 - a^2*c^6 + c^8 : :
X(54347) = 5 X[3620] - X[45794], 3 X[13394] - 2 X[19127]

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) = X(2)X(11)∩X(21)X(84)

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

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) = X(3)X(54)∩X(6)X(41)

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

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) = X(1)X(3)∩X(8)X(47)

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

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) = X(6)X(31)∩X(44)X(58)

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

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) = X(1)X(21)∩X(43)X(88)

Barycentrics    a*(a^2 + 2*a*b - 2*b^2 + 2*a*c + 2*b*c - 2*c^2) : :
X(54352) = 3 X[750] - 4 X[37520]

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) = X(1)X(21)∩X(99)X(109)

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

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) = X(1)X(21)∩X(9)X(32)

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

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) = X(1)X(2)∩X(12)X(81)

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

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) = X(1)X(21)∩X(29)X(34)

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

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(54357) = X(2)X(7)∩X(10)X(21)

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

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) = X(1)X(6)∩X(7)X(27)

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

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) = X(8)X(9)∩X(19)X(25)

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

X(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) = X(1)X(24)∩X(42)X(65)

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

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) = X(4)X(46)∩X(8)X(11)

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

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) = X(2)X(14)∩X(6)X(25)

Barycentrics    a^2*(Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - 2*(a^2 + b^2 + c^2)*S) : :

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) = X(2)X(13)∩X(6)X(25)

Barycentrics    a^2*(Sqrt[3]*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) + 2*(a^2 + b^2 + c^2)*S) : :

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) = X(1)X(514)∩X(31)X(57)

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

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) = X(1)X(2)∩X(32)X(69)

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

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) = X(2)X(7)∩X(4)X(11)

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

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) = X(2)X(3)∩X(10)X(45)

Barycentrics    a^4 - 2*a^3*b - 3*a^2*b^2 - 2*a*b^3 - 2*b^4 - 2*a^3*c - 6*a^2*b*c - 6*a*b^2*c - 2*b^3*c - 3*a^2*c^2 - 6*a*b*c^2 - 2*a*c^3 - 2*b*c^3 - 2*c^4 : :
X(54367) = 3 X[19276] - 2 X[51668]

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) = X(1)X(19)∩X(4)X(35)

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

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) = X(1)X(2)∩X(48)X(57)

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

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) = X(4)X(9)∩X(7)X(90)

Barycentrics    a*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 - a^4*c + 4*a^3*b*c - 3*b^4*c - 2*a^3*c^2 - 2*a*b^2*c^2 + 4*b^3*c^2 + 2*a^2*c^3 + 4*b^2*c^3 + a*c^4 - 3*b*c^4 - c^5) : :
X(54370) = 3 X[7671] + X[12528], 4 X[15254] - X[43178], 3 X[9] - X[40], X[40] + 3 X[11372], X[2550] - 3 X[5817], 3 X[2550] - 5 X[5818], 9 X[5817] - 5 X[5818], X[35514] - 3 X[38057], 3 X[51090] + X[51118], X[7] - 3 X[38037], 3 X[3062] + 5 X[7987], X[3062] + 2 X[52769], 3 X[5732] - 5 X[7987], 5 X[7987] - 6 X[52769], and many others

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) = X(3)X(6)∩X(35)X(72)

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

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) = X(2)X(3)∩X(53)X(86)

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

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) = X(1)X(228)∩X(31)X(40)

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

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) = X(3)X(6)∩X(20)X(66)

Barycentrics    a^2*(a^10 - 4*a^6*b^4 + 2*a^4*b^6 + 3*a^2*b^8 - 2*b^10 - 4*a^6*b^2*c^2 + 4*a^2*b^6*c^2 - 4*a^6*c^4 + 2*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 4*a^2*b^2*c^6 + 2*b^4*c^6 + 3*a^2*c^8 - 2*c^10) : :
X(54374) = 2 X[3098] + X[37478], X[13352] - 4 X[14810]

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) = X(2)X(3)∩X(51)X(97)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^8 - 2*a^6*b^2 + 2*a^4*b^4 - 2*a^2*b^6 + b^8 - 2*a^6*c^2 + 5*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 5*b^6*c^2 + 2*a^4*c^4 + 2*a^2*b^2*c^4 + 8*b^4*c^4 - 2*a^2*c^6 - 5*b^2*c^6 + c^8) : :

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) = X(3)X(74)∩X(66)X(67)

Barycentrics    a^2*(a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 + a^4*b^4*c^2 - 2*b^8*c^2 - 2*a^6*c^4 + a^4*b^2*c^4 - 4*a^2*b^4*c^4 + 3*b^6*c^4 + 3*b^4*c^6 + 2*a^2*c^8 - 2*b^2*c^8 - c^10) : :
X(54376) = 5 X[74] - X[6241], 3 X[74] + X[12281], 3 X[74] - X[17854], 5 X[110] - 9 X[7998], 3 X[6241] + 5 X[12281], 3 X[6241] - 5 X[17854], 9 X[7998] - 10 X[13416], 4 X[11591] - 5 X[12358], X[12270] - 5 X[15021], 3 X[15055] + X[15100], 2 X[15101] + X[44573], 3 X[51] - 5 X[125], 6 X[51] - 5 X[1112], 9 X[51] - 10 X[11746], and many others

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) = X(6)X(19)∩X(44)X(56)

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

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) = X(1)X(6)∩X(2)X(13)

Barycentrics    a*(Sqrt[3]*(a^3 - a*b^2 - 2*a*b*c - 2*b^2*c - a*c^2 - 2*b*c^2) + 2*a*S) : :

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) = X(1)X(6)∩X(2)X(14)

Barycentrics    a*(Sqrt[3]*(a^3 - a*b^2 - 2*a*b*c - 2*b^2*c - a*c^2 - 2*b*c^2) - 2*a*S) : :

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) = X(2)X(3)∩X(114)X(132)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6) : :
X(54380) = 3 X[23234] - X[52094]

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) = X(2)X(3)∩X(53)X(136)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 - 6*a^4*b^2*c^2 + a^2*b^4*c^2 - a^4*c^4 + a^2*b^2*c^4 - 2*b^4*c^4 - a^2*c^6 + c^8) : :

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) = X(1)X(32)∩X(6)X(19)

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

X(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) = X(6)X(21)∩X(7)X(8)

Barycentrics    a*(2*a^3*b^2 - 2*a*b^4 + 3*a^3*b*c + 3*a^2*b^2*c - a*b^3*c - b^4*c + 2*a^3*c^2 + 3*a^2*b*c^2 - b^3*c^2 - a*b*c^3 - b^2*c^3 - 2*a*c^4 - b*c^4) : :
X(54383) = 3 X[2] - 4 X[4260], 3 X[1992] - 2 X[37516]

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) = X(4)X(70)∩X(30)X(52)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 + 2*a^4*b^2*c^2 + a^2*b^4*c^2 - 2*b^6*c^2 - a^4*c^4 + a^2*b^2*c^4 + 2*b^4*c^4 - a^2*c^6 - 2*b^2*c^6 + c^8) : :
X(54384) = 3 X[51] - 2 X[427], 3 X[3060] - X[7391], 3 X[3917] - 4 X[6676], 3 X[5890] - X[35481], 3 X[5891] - 4 X[46029], 6 X[5943] - 5 X[31236], 3 X[5946] - 2 X[44236], 3 X[9730] - 2 X[18570], 8 X[13413] - 9 X[14845], 2 X[15644] - 3 X[44837], 3 X[16226] - 2 X[44218]

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) = X(1)X(19)∩X(37)X(56)

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

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) = X(1)X(6)∩X(31)X(78)

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

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) = X(1)X(3)∩X(21)X(44)

Barycentrics    a*(4*a^3 - 3*a^2*b - 6*a*b^2 + b^3 - 3*a^2*c - 6*a*b*c - 3*b^2*c - 6*a*c^2 - 3*b*c^2 + c^3) : :
X(54387) = (3*r^2 + 6*r*R + s^2)*X[1] + 6*r^2*X[3]

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) = X(3)X(6)∩X(10)X(98)

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

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) = X(2)X(45)∩X(4)X(9)

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

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) = X(1)X(2)∩X(44)X(57)

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

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) = X(1)X(21)∩X(8)X(56)

Barycentrics    a*(a^3 - a*b^2 + 3*a*b*c - b^2*c - a*c^2 - b*c^2) : :
X(54391) = 3 X[21] - 2 X[48698], 3 X[2] - 4 X[15325], 4 X[11] - 3 X[37375], 2 X[5080] - 3 X[37375], 4 X[36] - 3 X[13587], 3 X[36] - X[48696], 2 X[100] - 3 X[13587], 3 X[100] - 2 X[48696], 9 X[13587] - 4 X[48696], X[1320] + 2 X[3218], X[36002] + 2 X[38669], 4 X[15326] - 3 X[36005], 2 X[3583] - 3 X[10707], and many others

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) = X(1)X(2)∩X(21)X(57)

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

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) = X(3)X(114)∩X(4)X(69)

Barycentrics    a^8 - a^6*b^2 + a^2*b^6 - b^8 - a^6*c^2 + a^2*b^4*c^2 + 2*b^6*c^2 + a^2*b^2*c^4 - 2*b^4*c^4 + a^2*c^6 + 2*b^2*c^6 - c^8 : :
X(54393) = 3 X[5] - 2 X[20576], 3 X[32] - 4 X[20576], 3 X[7818] - X[30270], 3 X[7818] + X[36997], 3 X[38317] - 2 X[39750], 4 X[140] - 5 X[7867], 3 X[7841] - X[39646], 5 X[1656] - 4 X[6680], 5 X[3091] - 3 X[9753], 5 X[3091] - X[20065], 3 X[9753] - X[20065], X[5017] - 3 X[10516], 3 X[7697] - 2 X[18806], 5 X[7851] - 3 X[9755], 3 X[14639] - X[36849]

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) = X(4)X(12)∩X(6)X(19)

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

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) = X(2)X(99)∩X(4)X(110)

Barycentrics    a^6*b^2 - a^4*b^4 - a^2*b^6 + b^8 + a^6*c^2 - 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 3*b^6*c^2 - a^4*c^4 + 2*a^2*b^2*c^4 + 4*b^4*c^4 - a^2*c^6 - 3*b^2*c^6 + c^8 : :

X(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) = X(4)X(9)∩X(29)X(33)

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

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) = X(4)X(9)∩X(25)X(36)

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

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) = X(2)X(72)∩X(7)X(10)

Barycentrics    a^4 + 4*a^3*b - 2*a^2*b^2 - 4*a*b^3 + b^4 + 4*a^3*c - 4*a*b^2*c - 2*a^2*c^2 - 4*a*b*c^2 - 2*b^2*c^2 - 4*a*c^3 + c^4 : :
X(54398) = 3 X[2] - 4 X[5791], 5 X[3091] - 4 X[5715], 2 X[4313] - 3 X[50742], 4 X[31424] - 3 X[50742]

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) = X(8)X(21)∩X(11)X(60)

Barycentrics    (a + b)*(a - b - c)*(a + c)*(2*a^4 + 2*a^3*b + a*b^3 + b^4 + 2*a^3*c + 2*a^2*b*c - a*b^2*c - a*b*c^2 - 2*b^2*c^2 + a*c^3 + c^4) : :
X(54399) = 3 X[21] - X[1043], X[79] - 3 X[33135]

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) = X(1)X(104)∩X(6)X(19)

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

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) = X(1)X(2)∩X(9)X(47)

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

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) = X(1)X(6)∩X(52)X(62)

Barycentrics    a^2*(b*c + Sqrt[3]*S) : :

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) = X(1)X(6)∩X(55)X(61)

Barycentrics    a^2*(b*c - Sqrt[3]*S) : :

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) = X(40)X(75)∩X(57)X(86)

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

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) = X(1)X(19)∩X(2)X(7)

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

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) = X(1)X(6)∩X(32)X(78)

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

X(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) = X(1)X(29)∩X(27)X(33)

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

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) = X(1)X(3)∩X(9)X(11)

Barycentrics    a*(a - b - c)*(a^4 - 2*a^2*b^2 + b^4 - 4*b^3*c - 2*a^2*c^2 + 6*b^2*c^2 - 4*b*c^3 + c^4) : :
X(54408) = (r^2 + 2*r*R - 2*R^2)*X[1] - 2*r*(r + R)*X[3]

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) = X(3)X(6)∩X(35)X(44)

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

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) = X(1)X(6)∩X(3)X(75)

Barycentrics    a*(a^4*b - a^2*b^3 + a^4*c + a^3*b*c - a^2*b^2*c - a*b^3*c - a^2*b*c^2 - 2*a*b^2*c^2 - 2*b^3*c^2 - a^2*c^3 - a*b*c^3 - 2*b^2*c^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) = X(3)X(6)∩X(21)X(73)

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

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) = X(4)X(69)∩X(24)X(99)

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

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) = X(2)X729)∩X(6)X(538)

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

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) = X(1)X1864)∩X(9)X(222)

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

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) = ISOGONAL CONJUGATE OF X(2931)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^12 - 2*a^10*b^2 - a^8*b^4 + 4*a^6*b^6 - a^4*b^8 - 2*a^2*b^10 + b^12 - 4*a^10*c^2 + 7*a^8*b^2*c^2 - 3*a^6*b^4*c^2 - a^4*b^6*c^2 + 3*a^2*b^8*c^2 - 2*b^10*c^2 + 7*a^8*c^4 - 5*a^6*b^2*c^4 + 4*a^4*b^4*c^4 - a^2*b^6*c^4 - b^8*c^4 - 8*a^6*c^6 - 5*a^4*b^2*c^6 - 3*a^2*b^4*c^6 + 4*b^6*c^6 + 7*a^4*c^8 + 7*a^2*b^2*c^8 - b^4*c^8 - 4*a^2*c^10 - 2*b^2*c^10 + c^12)*(a^12 - 4*a^10*b^2 + 7*a^8*b^4 - 8*a^6*b^6 + 7*a^4*b^8 - 4*a^2*b^10 + b^12 - 2*a^10*c^2 + 7*a^8*b^2*c^2 - 5*a^6*b^4*c^2 - 5*a^4*b^6*c^2 + 7*a^2*b^8*c^2 - 2*b^10*c^2 - a^8*c^4 - 3*a^6*b^2*c^4 + 4*a^4*b^4*c^4 - 3*a^2*b^6*c^4 - b^8*c^4 + 4*a^6*c^6 - a^4*b^2*c^6 - a^2*b^4*c^6 + 4*b^6*c^6 - a^4*c^8 + 3*a^2*b^2*c^8 - b^4*c^8 - 2*a^2*c^10 - 2*b^2*c^10 + c^12) : :

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) = X(1)X(6)∩X(25)X(41)

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

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) = X(3)X(6)∩X(21)X(60)

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

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) = X(1)X(2)∩X(6)X(19)

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

X(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) = X(1)X(21)∩X(2)X(41)

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

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(54420) = X(4)X(9)∩X(6)X(46)

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

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) = X(1)X(21)∩X(6)X(19)

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

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) = X(1)X(21)∩X(7)X(10)

Barycentrics    a*(a^3 + 3*a^2*b - a*b^2 - 3*b^3 + 3*a^2*c + 2*a*b*c - b^2*c - a*c^2 - b*c^2 - 3*c^3) : :
X(54422) = 3 X[1] - 4 X[8666], 2 X[21] - 3 X[54302], 2 X[3] - 3 X[3928], 3 X[3928] - X[11523], 4 X[5] - 3 X[28609], 3 X[20] - X[12536], X[20] - 3 X[28610], X[12536] - 9 X[28610], X[12632] - 3 X[34632], 3 X[40] - 2 X[3913], 4 X[3913] - 3 X[6765], X[3680] - 3 X[6762], 2 X[3680] - 3 X[12629], 3 X[165] - 2 X[3811], and many others

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) = X(3)X(6)∩X(37)X(78)

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

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) = X(1)X(19)∩X(9)X(65)

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

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) = X(6)X(7)∩X(8)X(34)

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

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) = X(1)X(2)∩X(6)X(25)

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

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) = X(1)X(2)∩X(3)X(47)

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

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) = X(1)X(25)∩X(4)X(36)

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

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) = X(2)X(58)∩X(8)X(20)

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

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) = X(4)X(35)∩X(9)X(21)

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

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) = X(3)X(6)∩X(25)X(34)

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

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) = X(1)X(21)∩X(5)X(57)

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

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}

X(54433) = X(1)X(2)∩X(3)X(345)

Barycentrics    (a^2 - b^2 - c^2)*(a^2 + b^2 + 2*b*c + c^2) : : X(54433) = 5 X[3616] - 4 X[30148]

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}

X(54434) = X(2)X(15032)∩X(5)X(323)

Barycentrics    a^2*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 4*a^6*c^2 + 7*a^4*b^2*c^2 - 8*a^2*b^4*c^2 + 5*b^6*c^2 + 6*a^4*c^4 - 8*a^2*b^2*c^4 - 12*b^4*c^4 - 4*a^2*c^6 + 5*b^2*c^6 + c^8) : :

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) = X(1)X(6)∩X(3)X(1250)

Barycentrics    a^2*(Sqrt[3]*b*c - S) : :

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) = X(1)X(6)∩X(15)X(56)

Barycentrics    a^2*(Sqrt[3]*b*c + S) : :

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) = X(1)X(6)∩X(3)X(202)

Barycentrics    a^2*(2*b*c + Sqrt[3]*S) : :

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) = X(1)X(6)∩X(3)X(203)

Barycentrics    a^2*(2*b*c - Sqrt[3]*S) : :

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) = X(2)X(99)∩X(3)X(74)

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

X(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) = X(99)X(109)∩X(100)X(101)

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

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) = X(4)X(11)∩X(72)X(74)

Barycentrics    a*(a^9 - 2*a^8*b - 2*a^7*b^2 + 6*a^6*b^3 - 6*a^4*b^5 + 2*a^3*b^6 + 2*a^2*b^7 - a*b^8 - 2*a^8*c + 3*a^7*b*c - a^6*b^2*c - 3*a^5*b^3*c + 9*a^4*b^4*c - 3*a^3*b^5*c - 7*a^2*b^6*c + 3*a*b^7*c + b^8*c - 2*a^7*c^2 - a^6*b*c^2 - 3*a^4*b^3*c^2 - 2*a^3*b^4*c^2 + 5*a^2*b^5*c^2 + 4*a*b^6*c^2 - b^7*c^2 + 6*a^6*c^3 - 3*a^5*b*c^3 - 3*a^4*b^2*c^3 + 6*a^3*b^3*c^3 - 3*a*b^5*c^3 - 3*b^6*c^3 + 9*a^4*b*c^4 - 2*a^3*b^2*c^4 - 6*a*b^4*c^4 + 3*b^5*c^4 - 6*a^4*c^5 - 3*a^3*b*c^5 + 5*a^2*b^2*c^5 - 3*a*b^3*c^5 + 3*b^4*c^5 + 2*a^3*c^6 - 7*a^2*b*c^6 + 4*a*b^2*c^6 - 3*b^3*c^6 + 2*a^2*c^7 + 3*a*b*c^7 - b^2*c^7 - a*c^8 + b*c^8) : :

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) = X(100)X(110)∩X(107)X(109)

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

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) = X(2)X(304)∩X(75)X(499)

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

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) = X(2)X(2003)∩X(6)X(63)

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

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}

X(54445) = X(2)X(515)∩X(7)X(36)

Barycentrics    7*a^4-2*a^3*(b+c)+2*a*(b-c)^2*(b+c)+a^2*(-8*b^2+4*b*c-8*c^2)+(b^2-c^2)^2 ::
X(54445) = 2*X[1]+7*X[3523], 8*X[3]+X[962], -2*X[4]+11*X[5550], 2*X[40]+7*X[3622], X[165]+2*X[551], -2*X[355]+11*X[3525], X[1482]+8*X[3530], X[3534]+2*X[38034], X[3655]+2*X[11231], -2*X[5881]+11*X[46933], 2*X[7982]+7*Z[15054], 8*X[8715]+X[12541], 2*X[11194]+X[25568], -X[11224]+4*X[51103], -X[12702]+10*X[15712], 2*X[41869]+7*X[50693]

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}

X(54446) = X(1482)X(4853)∩X(5902)X(7271)

Barycentrics    a^2*(a^4+2*a^3*b+7*b^4-2*a*b*(b-c)^2-2*b^3*c-8*b^2*c^2+2*b*c^3+c^4-2*a^2*(4*b^2+b*c+c^2))*(a^4+b^4+2*a^3*c+2*b^3*c-2*a*(b-c)^2*c-8*b^2*c^2-2*b*c^3+7*c^4-2*a^2*(b^2+b*c+4*c^2)) ::

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)

X(54447) = X(2)X(515)∩X(5)X(40)

Barycentrics    a^4+a^3*(b+c)-a*(b-c)^2*(b+c)+4*(b^2-c^2)^2-a^2*(5*b^2+2*b*c+5*c^2) ::
X(54447) = 2*X[3]+7*X[7989], X[4]+8*X[3634], 2*X[355]+7*X[3624], 2*X[382]+7*X[16192], -X[944]+10*X[19862], X[3655]+2*X[38138], X[3656]+2*X[38112], 2*X[11224]+X[50817], 2*X[18525]+7*X[30389]

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}

X(54448) = X(1)X(5068)∩X(2)X(515)

Barycentrics    5*a^4-4*a^3*(b+c)+4*a*(b-c)^2*(b+c)-7*(b^2-c^2)^2+2*a^2*(b^2+4*b*c+c^2) ::
X(54448) = -4*X[1]+13*X[5068], -8*X[3]+17*X[46932], 4*X[4]+5*X[3617], 4*X[40]+5*X[17578], -2*X[944]+11*X[5056], 2*X[962]+7*X[4678], -2*X[1482]+11*X[3855], X[3632]+8*X[12571], 2*X[3679]+X[9812], X[3830]+2*X[38112], 2*X[5886]+X[34627], 2*X[6361]+7*X[50688], 4*X[7982]+5*X[20052], 2*X[7991]+7*X[10248], -X[11224]+4*X[50802]

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}





leftri   Cyclocevian conjugates: X(54449)-X(54459) and X(55019)-X(55037)rightri

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}

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X(54449) = CYCLOCEVIAN CONJUGATE OF X(5)

Barycentrics    1/(c^2*(a^4 - 3*a^2*b^2 + 2*b^4 - 2*a^2*c^2 - 3*b^2*c^2 + c^4)*(2*a^4 - 3*a^2*b^2 + b^4 - 3*a^2*c^2 - 2*b^2*c^2 + c^4)*(-(a^2*b^2) + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4) + b^2*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(2*a^4 - 3*a^2*b^2 + b^4 - 3*a^2*c^2 - 2*b^2*c^2 + c^4)*(-(a^2*b^2) + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - 3*a^2*c^2 - 3*b^2*c^2 + 2*c^4) - a^2*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - 3*a^2*b^2 + 2*b^4 - 2*a^2*c^2 - 3*b^2*c^2 + c^4)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)*(a^4 - 2*a^2*b^2 + b^4 - 3*a^2*c^2 - 3*b^2*c^2 + 2*c^4)) : :

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) = CYCLOCEVIAN CONJUGATE OF X(63)

Barycentrics    (a^8 - 2*a^4*b^4 + b^8 - a^6*b*c - a^5*b^2*c + 2*a^4*b^3*c + 2*a^3*b^4*c - a^2*b^5*c - a*b^6*c - 2*a^6*c^2 - a^5*b*c^2 + 2*a^4*b^2*c^2 + 2*a^3*b^3*c^2 + 2*a^2*b^4*c^2 - a*b^5*c^2 - 2*b^6*c^2 - 2*a^4*b*c^3 - 2*a^3*b^2*c^3 - 2*a^2*b^3*c^3 - 2*a*b^4*c^3 - 2*a^3*b*c^4 - 4*a^2*b^2*c^4 - 2*a*b^3*c^4 + 3*a^2*b*c^5 + 3*a*b^2*c^5 + 2*a^2*c^6 + 3*a*b*c^6 + 2*b^2*c^6 - c^8)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - a^6*b*c - a^5*b^2*c - 2*a^4*b^3*c - 2*a^3*b^4*c + 3*a^2*b^5*c + 3*a*b^6*c - a^5*b*c^2 + 2*a^4*b^2*c^2 - 2*a^3*b^3*c^2 - 4*a^2*b^4*c^2 + 3*a*b^5*c^2 + 2*b^6*c^2 + 2*a^4*b*c^3 + 2*a^3*b^2*c^3 - 2*a^2*b^3*c^3 - 2*a*b^4*c^3 - 2*a^4*c^4 + 2*a^3*b*c^4 + 2*a^2*b^2*c^4 - 2*a*b^3*c^4 - a^2*b*c^5 - a*b^2*c^5 - a*b*c^6 - 2*b^2*c^6 + c^8) : :

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) = CYCLOCEVIAN CONJUGATE OF X(280)

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

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) = CYCLOCEVIAN CONJUGATE OF X(903)

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

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) = CYCLOCEVIAN CONJUGATE OF X(925)

Barycentrics    (a^8 - 2*a^6*b^2 + 2*a^4*b^4 - 2*a^2*b^6 + b^8 - 2*a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 2*b^6*c^2 - 5*a^2*b^2*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8)*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 3*a^4*b^2*c^2 - 5*a^2*b^4*c^2 + 2*b^6*c^2 + 2*a^4*c^4 + 3*a^2*b^2*c^4 - 2*a^2*c^6 - 2*b^2*c^6 + c^8) : :
X(54453) = X[323] - 4 X[9721]

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) = CYCLOCEVIAN CONJUGATE OF X(2995)

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

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) = CYCLOCEVIAN CONJUGATE OF X(3952)

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

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) = CYCLOCEVIAN CONJUGATE OF X(7261)

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

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) = CYCLOCEVIAN CONJUGATE OF X(7361)

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

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) = CYCLOCEVIAN CONJUGATE OF X(9295)

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

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) = CYCLOCEVIAN CONJUGATE OF X(9295)

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

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}





leftri  H-conics: X(54460) - X(54467)  rightri

This preamble and centers X(54460)-X(54467) were contributed by César Eliud Lozada, July 15, 2023.

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.

underbar

X(54460) = CENTER OF THE H-CONIC OF X(48)

Barycentrics    (-a^2+b^2+c^2)*(a^10-5*(b^2+c^2)*a^8+(b^2-c^2)^3*(b^4-c^4)-(b^4-c^4)^2*a^2+8*(b^4+b^2*c^2+c^4)*a^6-4*(b^6+c^6)*a^4-2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2)*S) : :

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) = CENTER OF THE H-CONIC OF X(49)

Barycentrics    a^2*((-a^2+b^2+c^2)^2-b^2*c^2)*((b^2+c^2)*a^10-(5*b^4+4*b^2*c^2+5*c^4)*a^8+5*(b^2+c^2)*(2*b^4-b^2*c^2+2*c^4)*a^6-2*(5*b^8+5*c^8-b^2*c^2*(b^4-b^2*c^2+c^4))*a^4+(b^4-c^4)*(b^2-c^2)*(5*b^4-3*b^2*c^2+5*c^4)*a^2-(b^2-c^2)^4*(b^4+c^4)) : :

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) = CENTER OF THE H-CONIC OF X(72)

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

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) = CENTER OF THE H-CONIC OF X(125)

Barycentrics    a^2*(-a^2+b^2+c^2)^2*((b^2+c^2)*a^10-(5*b^4+4*b^2*c^2+5*c^4)*a^8+2*(b^2+c^2)*(5*b^4-2*b^2*c^2+5*c^4)*a^6-2*(5*b^8-2*b^4*c^4+5*c^8)*a^4+(b^4-c^4)*(b^2-c^2)*(5*b^4-2*b^2*c^2+5*c^4)*a^2-(b^2-c^2)^4*(b^4+c^4)) : :

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) = CENTER OF THE H-CONIC OF X(222)

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

X(54464) lies on these lines: {3, 6213}, {3718, 13458}

X(54465) = CENTER OF THE H-CONIC OF X(563)

Barycentrics    (2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2)*S+a^10-5*(b^2+c^2)*a^8+8*(b^4+b^2*c^2+c^4)*a^6-4*(b^6+c^6)*a^4-(b^4-c^4)^2*a^2+(b^4-c^4)*(b^2-c^2)^3)*(-a^2+b^2+c^2) : :

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) = CENTER OF THE H-CONIC OF X(647)

Barycentrics    (-a^2+b^2+c^2)^2*(a^20-5*(b^2+c^2)*a^18+(9*b^4+16*b^2*c^2+9*c^4)*a^16-4*(b^2+c^2)^3*a^14-2*(5*b^8+5*c^8+6*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^12+2*(b^2+c^2)*(9*b^8+9*c^8+2*(b^4+5*b^2*c^2+c^4)*b^2*c^2)*a^10-2*(b^2+c^2)^2*(5*b^8+5*c^8-2*(b^4-b^2*c^2+c^4)*b^2*c^2)*a^8-4*(b^8-c^8)*(b^2-c^2)*(-4*b^2*c^2+(b^2-c^2)^2)*a^6+(b^2-c^2)^4*(9*b^8+9*c^8-2*(4*b^4+5*b^2*c^2+4*c^4)*b^2*c^2)*a^4-(b^2-c^2)^6*(b^2+c^2)*(5*b^4-6*b^2*c^2+5*c^4)*a^2+(b^2-c^2)^8*(b^4+c^4)) : :

X(54466) lies on these lines: {12359, 16196}

X(54467) = CENTER OF THE H-CONIC OF X(684)

Barycentrics    a^16-5*(b^2+c^2)*a^14+2*(5*b^4+7*b^2*c^2+5*c^4)*a^12-(b^2+c^2)*(11*b^4+2*b^2*c^2+11*c^4)*a^10+2*(5*b^8+5*c^8+b^2*c^2*(b^4+c^4))*a^8-(b^4-c^4)*(b^2-c^2)*(11*b^4-2*b^2*c^2+11*c^4)*a^6+2*(b^2-c^2)^2*(5*b^8+5*c^8-3*b^2*c^2*(b^4+c^4))*a^4-(b^4-c^4)*(b^2-c^2)^3*(5*b^4-6*b^2*c^2+5*c^4)*a^2+(b^2-c^2)^6*(b^4+c^4) : :

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}

X(54468) = X(105)X(1336)∩X(1282)X(6212)

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

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}

X(54469) = X(4)X(52164)∩X(100)X(13387)

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

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}

X(54470) = X(6)X(19)∩X(8048)X(13389)

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

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)

X(54471) = X(6)X(19)∩X(8048)X(13388)

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

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)

X(54472) = X(13)X(511)∩X(51)X(512)

Barycentrics    a^2*(sqrt(3)*(a^2+b^2-c^2)+2*S)*(sqrt(3)*(a^2-b^2+c^2)+2*S)*(-b^4+6*b^2*c^2-c^4+a^2*(b^2+c^2)+2*sqrt(3)*(b^2+c^2)*S) : :
X(54472) = X(13)-3*X(16461)

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)

X(54473) = X(14)X(511)∩X(51)X(512)

Barycentrics    a^2*(sqrt(3)*(a^2+b^2-c^2)-2*S)*(sqrt(3)*(a^2-b^2+c^2)-2*S)*(-b^4+6*b^2*c^2-c^4+a^2*(b^2+c^2)-2*sqrt(3)*(b^2+c^2)*S) : :
X(54473) = X(14)-3*X(16462)

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)
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)



leftri

Orthology centers related to bicevian conics: X(54474)-X(55009)

rightri

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) = X(1)X(3)∩X(2)X(10186)

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

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) = X(2)X(10723)∩X(4)X(41672)

Barycentrics    (5*a^6+5*b^6-12*b^4*c^2+13*b^2*c^4-6*c^6-a^4*(b^2+12*c^2)-a^2*(b^4+4*b^2*c^2-13*c^4))*(5*a^6-6*b^6+13*b^4*c^2-12*b^2*c^4+5*c^6-a^4*(12*b^2+c^2)+a^2*(13*b^4-4*b^2*c^2-c^4)) : :

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) = X(2)X(5585)∩X(30)X(10155)

Barycentrics    (13*a^2+13*b^2-11*c^2)*(13*a^2-11*b^2+13*c^2) : :

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) = X(2)X(48884)∩X(30)X(10159)

Barycentrics    (5*a^4-4*b^4-b^2*c^2+5*c^4-a^2*(b^2-8*c^2))*(5*a^4+5*b^4-b^2*c^2-4*c^4+a^2*(8*b^2-c^2)) : :

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) = X(30)X(10185)∩X(76)X(50989)

Barycentrics    (13*a^2+13*b^2-14*c^2)*(13*a^2-14*b^2+13*c^2) : :

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) = X(17)X(3845)∩X(18)X(3830)

Barycentrics    (a-b-c)*(a+b-c)*(a-b+c)*(a+b+c)*(121*a^4-122*(b^2-c^2)^2+a^2*(b^2+c^2-9*sqrt(-3*a^4-3*(b^2-c^2)^2+6*a^2*(b^2+c^2)))) : :
Barycentrics    1 / (9*Sqrt[3]*(-a^2 + b^2 + c^2) - 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] - 27*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(17)X(3830)∩X(18)X(3845)

Barycentrics    (a-b-c)*(a+b-c)*(a-b+c)*(a+b+c)*(121*a^4-122*(b^2-c^2)^2+a^2*(b^2+c^2+9*sqrt(-3*a^4-3*(b^2-c^2)^2+6*a^2*(b^2+c^2)))) : :
Barycentrics    1 / (9*Sqrt[3]*(-a^2 + b^2 + c^2) + 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] + 27*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(30)X(10290)∩X(1916)X(11645)

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

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) = X(2)X(38225)∩X(30)X(10484)

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

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) = X(4)X(34319)∩X(30)X(10511)

Barycentrics    (4*a^8-9*a^6*b^2+a^4*(b^4+4*b^2*c^2-8*c^4)-(b^2-c^2)^2*(5*b^4+b^2*c^2-4*c^4)+a^2*(9*b^6-5*b^4*c^2+4*b^2*c^4))*(4*a^8-9*a^6*c^2+(b^2-c^2)^2*(4*b^4-b^2*c^2-5*c^4)+a^4*(-8*b^4+4*b^2*c^2+c^4)+a^2*(4*b^4*c^2-5*b^2*c^4+9*c^6)) : :

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) = X(2)X(47610)∩X(76)X(616)

Barycentrics    sqrt(3)*(11*a^8-2*a^6*(b^2+c^2)-14*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(b^4+16*b^2*c^2+c^4)+2*a^4*(3*b^4-5*b^2*c^2+3*c^4))+6*(5*a^6-a^2*(b^2-c^2)^2-a^4*(b^2+c^2)-3*(b^2-c^2)^2*(b^2+c^2))*S : :

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) = X(2)X(47611)∩X(76)X(617)

Barycentrics    sqrt(3)*(11*a^8-2*a^6*(b^2+c^2)-14*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(b^4+16*b^2*c^2+c^4)+2*a^4*(3*b^4-5*b^2*c^2+3*c^4))+6*(-5*a^6+a^2*(b^2-c^2)^2+a^4*(b^2+c^2)+3*(b^2-c^2)^2*(b^2+c^2))*S : :

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) = X(2)X(34514)∩X(30)X(11140)

Barycentrics    (2*a^8-(b^2-c^2)^3*(b^2+2*c^2)-a^6*(5*b^2+2*c^2)+a^4*(3*b^4-4*b^2*c^2)+a^2*(b^6+5*b^4*c^2-4*b^2*c^4-2*c^6))*(2*a^8+(b^2-c^2)^3*(2*b^2+c^2)-a^6*(2*b^2+5*c^2)+a^4*(-4*b^2*c^2+3*c^4)+a^2*(-2*b^6-4*b^4*c^2+5*b^2*c^4+c^6)) : :

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) = X(2)X(5104)∩X(6)X(43535)

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

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) = X(2)X(52771)∩X(30)X(11172)

Barycentrics    (a^6-3*b^6+11*b^4*c^2-9*b^2*c^4+c^6-a^4*(9*b^2+5*c^2)+a^2*(11*b^4-2*b^2*c^2-5*c^4))*(a^6+b^6-9*b^4*c^2+11*b^2*c^4-3*c^6-a^4*(5*b^2+9*c^2)+a^2*(-5*b^4-2*b^2*c^2+11*c^4)) : :

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) = X(2)X(6777)∩X(17)X(542)

Barycentrics    3*sqrt(3)*(a^10-3*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+3*a^6*(b^4+b^2*c^2+c^4)+a^2*(b^2-c^2)^2*(2*b^4+5*b^2*c^2+2*c^4)-2*a^4*(b^6+c^6))-2*(13*a^8-12*a^6*(b^2+c^2)+(b^2-c^2)^2*(b^4-16*b^2*c^2+c^4)+a^4*(13*b^4-17*b^2*c^2+13*c^4)+a^2*(-15*b^6+16*b^4*c^2+16*b^2*c^4-15*c^6))*S : :

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) = X(2)X(6778)∩X(18)X(542)

Barycentrics    3*sqrt(3)*(a^10-3*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+3*a^6*(b^4+b^2*c^2+c^4)+a^2*(b^2-c^2)^2*(2*b^4+5*b^2*c^2+2*c^4)-2*a^4*(b^6+c^6))+2*(13*a^8-12*a^6*(b^2+c^2)+(b^2-c^2)^2*(b^4-16*b^2*c^2+c^4)+a^4*(13*b^4-17*b^2*c^2+13*c^4)+a^2*(-15*b^6+16*b^4*c^2+16*b^2*c^4-15*c^6))*S : :

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) = X(30)X(11608)∩X(226)X(542)

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

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) = X(10)X(2247)∩X(321)X(542)

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

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) = X(30)X(11668)∩X(98)X(38335)

Barycentrics    (10*a^2+10*b^2-11*c^2)*(10*a^2-11*b^2+10*c^2) : :

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) = X(6)X(33698)∩X(30)X(11669)

Barycentrics    (8*a^2+8*b^2-7*c^2)*(8*a^2-7*b^2+8*c^2) : :

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) = X(2)X(9717)∩X(74)X(671)

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

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) = X(4)X(34986)∩X(317)X(459)

Barycentrics    (2*a^6-(b^2-2*c^2)*(b^2-c^2)^2-a^4*(5*b^2+2*c^2)+2*a^2*(2*b^4+b^2*c^2-c^4))*(2*a^6+(b^2-c^2)^2*(2*b^2-c^2)-a^4*(2*b^2+5*c^2)+a^2*(-2*b^4+2*b^2*c^2+4*c^4)) : :

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) = X(10)X(35338)∩X(30)X(13576)

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

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) = X(2)X(15032)∩X(20)X(13582)

Barycentrics    (a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4-2*b^2*c^2+6*c^4)-2*a^2*(2*b^6+b^4*c^2-5*b^2*c^4+2*c^6))*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4-2*b^2*c^2+6*c^4)-2*a^2*(2*b^6-5*b^4*c^2+b^2*c^4+2*c^6)) : :

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) = X(10)X(16132)∩X(30)X(13583)

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

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) = X(2)X(15037)∩X(3)X(13582)

Barycentrics    (a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4+b^2*c^2+6*c^4)+a^2*(-4*b^6+7*b^4*c^2+b^2*c^4-4*c^6))*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4+b^2*c^2+6*c^4)+a^2*(-4*b^6+b^4*c^2+7*b^2*c^4-4*c^6)) : :

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) = X(30)X(14223)∩X(542)X(2394)

Barycentrics    (4*a^12-a^10*(11*b^2+5*c^2)+a^8*(11*b^4+11*b^2*c^2+2*c^4)+a^2*(b^2-c^2)^2*(4*b^6-2*b^4*c^2+b^2*c^4-5*c^6)-a^6*(5*b^6+9*b^4*c^2+2*c^6)-(b^2-c^2)^3*(2*b^6+2*b^4*c^2+b^2*c^4+4*c^6)-a^4*(b^8-9*b^6*c^2+6*b^4*c^4-2*c^8))*(4*a^12-a^10*(5*b^2+11*c^2)+a^8*(2*b^4+11*b^2*c^2+11*c^4)-a^2*(b^2-c^2)^2*(5*b^6-b^4*c^2+2*b^2*c^4-4*c^6)+(b^2-c^2)^3*(4*b^6+b^4*c^2+2*b^2*c^4+2*c^6)-a^6*(2*b^6+9*b^2*c^4+5*c^6)+a^4*(2*b^8-6*b^4*c^4+9*b^2*c^6-c^8)) : :

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) = X(30)X(14228)∩X(591)X(1132)

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

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) = X(2)X(9675)∩X(76)X(591)

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

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) = X(30)X(14236)∩X(671)X(13847)

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

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) = X(30)X(14240)∩X(671)X(13846)

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

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) = X(30)X(14243)∩X(1131)X(1991)

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

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) = X(30)X(14245)∩X(76)X(1991)

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

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) = X(30)X(1446)∩X(226)X(15938)

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

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) = X(6)X(11167)∩X(98)X(597)

Barycentrics    (a^4+b^4+5*b^2*c^2-2*c^4+a^2*(8*b^2+5*c^2))*(a^4-2*b^4+5*b^2*c^2+c^4+a^2*(5*b^2+8*c^2)) : :

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) = X(30)X(14534)∩X(429)X(16080)

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

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) = X(30)X(14554)∩X(226)X(1387)

Barycentrics    (2*a^5-a^4*(b+c)+(2*b-c)*(b^2-c^2)^2-a^3*(b^2-9*b*c+4*c^2)-a^2*(b^3+4*b^2*c+b*c^2-2*c^3)-a*(b^4-9*b^3*c+b^2*c^2+9*b*c^3-2*c^4))*(2*a^5-a^4*(b+c)-(b-2*c)*(b^2-c^2)^2-a^3*(4*b^2-9*b*c+c^2)+a^2*(2*b^3-b^2*c-4*b*c^2-c^3)+a*(2*b^4-9*b^3*c-b^2*c^2+9*b*c^3-c^4)) : :

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) = X(2)X(7687)∩X(4)X(3163)

Barycentrics    (5*a^8+a^2*(7*b^2-2*c^2)*(b^2-c^2)^2-a^6*(11*b^2+2*c^2)-(b^2-c^2)^3*(4*b^2+5*c^2)+a^4*(3*b^4+11*b^2*c^2-6*c^4))*(5*a^8-a^2*(2*b^2-7*c^2)*(b^2-c^2)^2+(b^2-c^2)^3*(5*b^2+4*c^2)-a^6*(2*b^2+11*c^2)+a^4*(-6*b^4+11*b^2*c^2+3*c^4)) : :

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) = X(30)X(16277)∩X(2394)X(23881)

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

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) = X(2)X(33708)∩X(30)X(1676)

Barycentrics    a^10+27*a^8*b^2+47*a^6*b^4-37*a^4*b^6+27*a^8*c^2+128*a^6*b^2*c^2+101*a^4*b^4*c^2+47*a^6*c^4+101*a^4*b^2*c^4-37*a^4*c^6-36*a^2*b^4*(b^2-c^2)^2-2*b^6*(b^2-c^2)^2-106*a^2*b^2*c^2*(b^2-c^2)^2-34*b^4*c^2*(b^2-c^2)^2-36*a^2*c^4*(b^2-c^2)^2-34*b^2*c^4*(b^2-c^2)^2-2*c^6*(b^2-c^2)^2+(8*a^8+49*a^6*b^2+9*a^4*b^4+49*a^6*c^2+110*a^4*b^2*c^2+9*a^4*c^4-53*a^2*b^2*(b^2-c^2)^2-13*b^4*(b^2-c^2)^2-53*a^2*c^2*(b^2-c^2)^2-46*b^2*c^2*(b^2-c^2)^2-13*c^4*(b^2-c^2)^2)*sqrt(b^2*c^2+a^2*(b^2+c^2)) : :

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) = X(2)X(33707)∩X(30)X(1677)

Barycentrics    a^10+27*a^8*b^2+47*a^6*b^4-37*a^4*b^6+27*a^8*c^2+128*a^6*b^2*c^2+101*a^4*b^4*c^2+47*a^6*c^4+101*a^4*b^2*c^4-37*a^4*c^6-36*a^2*b^4*(b^2-c^2)^2-2*b^6*(b^2-c^2)^2-106*a^2*b^2*c^2*(b^2-c^2)^2-34*b^4*c^2*(b^2-c^2)^2-36*a^2*c^4*(b^2-c^2)^2-34*b^2*c^4*(b^2-c^2)^2-2*c^6*(b^2-c^2)^2+(-8*a^8-49*a^6*b^2-9*a^4*b^4-49*a^6*c^2-110*a^4*b^2*c^2-9*a^4*c^4+53*a^2*b^2*(b^2-c^2)^2+13*b^4*(b^2-c^2)^2+53*a^2*c^2*(b^2-c^2)^2+46*b^2*c^2*(b^2-c^2)^2+13*c^4*(b^2-c^2)^2)*sqrt(b^2*c^2+a^2*(b^2+c^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) = X(30)X(1751)∩X(226)X(381)

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

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) = X(10)X(28854)∩X(30)X(17758)

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

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) = X(30)X(18366)∩X(13582)X(18403)

Barycentrics    (7*a^8-4*a^6*(4*b^2+c^2)-(b^2-c^2)^3*(5*b^2+7*c^2)+a^4*(6*b^4+13*b^2*c^2-6*c^4)+a^2*(8*b^6-17*b^4*c^2+13*b^2*c^4-4*c^6))*(7*a^8-4*a^6*(b^2+4*c^2)+(b^2-c^2)^3*(7*b^2+5*c^2)+a^4*(-6*b^4+13*b^2*c^2+6*c^4)+a^2*(-4*b^6+13*b^4*c^2-17*b^2*c^4+8*c^6)) : :

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) = X(2)X(41424)∩X(428)X(459)

Barycentrics    (7*a^4-5*b^4-2*b^2*c^2+7*c^4-2*a^2*(b^2-5*c^2))*(7*a^4+7*b^4-2*b^2*c^2-5*c^4+2*a^2*(5*b^2-c^2)) : :

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) = X(2)X(31860)∩X(20)X(43527)

Barycentrics    (5*a^4+5*b^4+2*b^2*c^2-7*c^4+2*a^2*(7*b^2+c^2))*(5*a^4-7*b^4+2*b^2*c^2+5*c^4+2*a^2*(b^2+7*c^2)) : :

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) = X(20)X(53102)∩X(30)X(18843)

Barycentrics    (a^4+b^4+10*b^2*c^2-11*c^4+2*a^2*(11*b^2+5*c^2))*(a^4-11*b^4+10*b^2*c^2+c^4+2*a^2*(5*b^2+11*c^2)) : :

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) = X(30)X(18844)∩X(83)X(15692)

Barycentrics    (a^4+b^4-14*b^2*c^2+13*c^4-2*a^2*(13*b^2+7*c^2))*(a^4+13*b^4-14*b^2*c^2+c^4-2*a^2*(7*b^2+13*c^2)) : :

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) = X(2)X(44456)∩X(4)X(9606)

Barycentrics    (a^4+b^4-8*b^2*c^2+7*c^4-2*a^2*(7*b^2+4*c^2))*(a^4+7*b^4-8*b^2*c^2+c^4-2*a^2*(4*b^2+7*c^2)) : :

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) = X(17)X(47865)∩X(30)X(21845)

Barycentrics    1 / (-4*a^2 + 5*b^2 + 5*c^2 + 4*Sqrt[3]*S) : :

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) = X(18)X(47866)∩X(30)X(21846)

Barycentrics    1 / (-4*a^2 + 5*b^2 + 5*c^2 - 4*Sqrt[3]*S) : :

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) = X(10)X(7359)∩X(30)X(226)

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

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) = X(2)X(3233)∩X(30)X(2394)

Barycentrics    (4*a^10-3*a^8*(3*b^2+c^2)+a^2*(b^2-c^2)^2*(3*b^4+2*b^2*c^2-3*c^4)+a^6*(5*b^4+8*b^2*c^2-c^4)-(b^2-c^2)^3*(2*b^4+3*b^2*c^2+4*c^4)-a^4*(b^6+4*b^4*c^2-2*b^2*c^4+c^6))*(4*a^10-3*a^8*(b^2+3*c^2)-a^2*(b^2-c^2)^2*(3*b^4-2*b^2*c^2-3*c^4)+(b^2-c^2)^3*(4*b^4+3*b^2*c^2+2*c^4)+a^6*(-b^4+8*b^2*c^2+5*c^4)-a^4*(b^6-2*b^4*c^2+4*b^2*c^4+c^6)) : :

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) = X(2)X(6739)∩X(80)X(226)

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

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) = X(30)X(30505)∩X(275)X(46511)

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

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) = X(30)X(30588)∩X(2394)X(4777)

Barycentrics    (2*a^5-4*a^4*(b+c)+a*(b+c)^2*(5*b^2-b*c-4*c^2)-a^3*(7*b^2+9*b*c+4*c^2)+a^2*(5*b^3-b^2*c-10*b*c^2-4*c^3)-(b+c)^2*(b^3-7*b^2*c+8*b*c^2-2*c^3))*(2*a^5-4*a^4*(b+c)-a*(b+c)^2*(4*b^2+b*c-5*c^2)-a^3*(4*b^2+9*b*c+7*c^2)-a^2*(4*b^3+10*b^2*c+b*c^2-5*c^3)+(b+c)^2*(2*b^3-8*b^2*c+7*b*c^2-c^3)) : :

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) = X(4)X(17809)∩X(25)X(53099)

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

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) = X(30)X(32022)∩X(3839)X(6625)

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

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) = X(10)X(2173)∩X(30)X(321)

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

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) = X(2)X(42197)∩X(30)X(3366)

Barycentrics    (a-b-c)*(a+b-c)*(a-b+c)*(a+b+c)*((8+5*sqrt(3))*a^4-2*(5+2*sqrt(3))*(b^2-c^2)^2+a^2*(-((-2+sqrt(3))*b^2)+2*c^2-sqrt(3)*c^2+3*sqrt(-a^4-(b^2-c^2)^2+2*a^2*(b^2+c^2)))) : :
Barycentrics    1 / (3*(2 + Sqrt[3])*(-a^2 + b^2 + c^2) + 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 + 3*(2 + Sqrt[3])*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(2)X(42195)∩X(30)X(3367)

Barycentrics    (a-b-c)*(a+b-c)*(a-b+c)*(a+b+c)*((-8+5*sqrt(3))*a^4-2*(-5+2*sqrt(3))*(b^2-c^2)^2+a^2*(-((2+sqrt(3))*b^2)-2*c^2-sqrt(3)*c^2+3*sqrt(-a^4-(b^2-c^2)^2+2*a^2*(b^2+c^2)))) : :
Barycentrics    1 / (3*(2 - Sqrt[3])*(-a^2 + b^2 + c^2) - 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 - 3*(2 - Sqrt[3])*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(30)X(3374)∩X(381)X(3387)

Barycentrics    (-8+5*sqrt(2))*a^4-2*(-5+2*sqrt(2))*(b^2-c^2)^2-a^2*((2+sqrt(2))*(b^2+c^2)-6*sqrt(2)*S) : :
Barycentrics    1 / (3*(-1 + Sqrt[2])*(-a^2 + b^2 + c^2) - 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 - 3*(-1 + Sqrt[2])*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(30)X(3387)∩X(381)X(3374)

Barycentrics    (-8+5*sqrt(2))*a^4-2*(-5+2*sqrt(2))*(b^2-c^2)^2-a^2*((2+sqrt(2))*(b^2+c^2)+6*sqrt(2)*S) : :
Barycentrics    1 / (3*(-1 + Sqrt[2])*(-a^2 + b^2 + c^2) + 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 + 3*(-1 + Sqrt[2])*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(2)X(42196)∩X(30)X(3392)

Barycentrics    (-8-5*sqrt(3))*a^4+2*(5+2*sqrt(3))*(b^2-c^2)^2+a^2*((-2+sqrt(3))*(b^2+c^2)+6*S) : :
Barycentrics    1 / (3*(2 + Sqrt[3])*(-a^2 + b^2 + c^2) - 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 - 3*(2 + Sqrt[3])*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(2)X(8627)∩X(76)X(754)

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

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) = X(30)X(3406)∩X(76)X(7818)

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

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) = X(30)X(34087)∩X(888)X(2394)

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

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) = X(2)X(42538)∩X(20)X(43564)

Barycentrics    12*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+(-143*a^4+145*(b^2-c^2)^2-2*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (6*(-a^2 + b^2 + c^2) + S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 + 12*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(2)X(42537)∩X(20)X(43565)

Barycentrics    12*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+(143*a^4-145*(b^2-c^2)^2+2*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (6*(-a^2 + b^2 + c^2) - S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 - 12*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(30)X(34258)∩X(381)X(14534)

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

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) = X(10)X(11645)∩X(30)X(34475)

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

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) = X(10)X(2794)∩X(115)X(3429)

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

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) = X(2)X(1625)∩X(4)X(7668)

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

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) = X(30)X(35353)∩X(536)X(2394)

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

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) = X(10)X(7262)∩X(30)X(3597)

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

X(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) = X(30)X(37874)∩X(381)X(801)

Barycentrics    (2*a^8-(b^2-c^2)^3*(b^2+2*c^2)-a^6*(5*b^2+2*c^2)+a^4*(3*b^4+17*b^2*c^2)+a^2*(b^6-16*b^4*c^2+17*b^2*c^4-2*c^6))*(2*a^8+(b^2-c^2)^3*(2*b^2+c^2)-a^6*(2*b^2+5*c^2)+a^4*(17*b^2*c^2+3*c^4)+a^2*(-2*b^6+17*b^4*c^2-16*b^2*c^4+c^6)) : :

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) = X(30)X(37892)∩X(275)X(14041)

Barycentrics    (2*a^8-a^6*(b^2+4*c^2)+(b^2-c^2)^2*(2*b^4-c^4)+a^4*(-2*b^4+2*b^2*c^2+c^4)-a^2*(b^6-2*b^4*c^2+7*b^2*c^4-2*c^6))*(2*a^8-a^6*(4*b^2+c^2)-(b^2-c^2)^2*(b^4-2*c^4)+a^4*(b^4+2*b^2*c^2-2*c^4)+a^2*(2*b^6-7*b^4*c^2+2*b^2*c^4-c^6)) : :

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) = X(30)X(38253)∩X(459)X(3543)

Barycentrics    (13*a^8+4*a^2*(b^2-c^2)^2*(5*b^2-c^2)-4*a^6*(7*b^2+c^2)-(b^2-c^2)^3*(11*b^2+13*c^2)+2*a^4*(3*b^4+14*b^2*c^2-9*c^4))*(13*a^8-4*a^2*(b^2-5*c^2)*(b^2-c^2)^2-4*a^6*(b^2+7*c^2)+(b^2-c^2)^3*(13*b^2+11*c^2)+a^4*(-18*b^4+28*b^2*c^2+6*c^4)) : :

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) = X(10)X(37589)∩X(30)X(38309)

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

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) = X(2)X(476)∩X(4)X(38395)

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

X(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) = X(4)X(52949)∩X(21)X(16080)

Barycentrics    (2*a^8-a^5*b*c*(b+c)+a^2*(b-2*c)*(b-c)^2*(b+c)^3-a*b*(b-c)^2*c*(b+c)^3-(b^2-c^2)^3*(b^2+2*c^2)-a^6*(5*b^2+b*c+2*c^2)+2*a^3*b*c*(b^3+b^2*c+b*c^2+c^3)+a^4*b*(3*b^3+2*b^2*c+5*b*c^2+2*c^3))*(2*a^8-a^5*b*c*(b+c)-a^2*(b-c)^2*(2*b-c)*(b+c)^3-a*b*(b-c)^2*c*(b+c)^3+(b^2-c^2)^3*(2*b^2+c^2)-a^6*(2*b^2+b*c+5*c^2)+2*a^3*b*c*(b^3+b^2*c+b*c^2+c^3)+a^4*c*(2*b^3+5*b^2*c+2*b*c^2+3*c^3)) : :

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) = X(4)X(51270)∩X(14)X(51254)

Barycentrics    sqrt(3)*(a^2-a*b+b^2-c^2)*(a^2+a*b+b^2-c^2)*(a^2-b^2-a*c+c^2)*(a^2-b^2+a*c+c^2)*(3*a^14-11*a^12*(b^2+c^2)-51*a^8*b^2*c^2*(b^2+c^2)+a^10*(12*b^4+41*b^2*c^2+12*c^4)-(b^2-c^2)^4*(2*b^6+5*b^4*c^2+5*b^2*c^4+2*c^6)+a^6*(-5*b^8+14*b^6*c^2+70*b^4*c^4+14*b^2*c^6-5*c^8)+a^2*(b^2-c^2)^2*(6*b^8-3*b^6*c^2-14*b^4*c^4-3*b^2*c^6+6*c^8)-a^4*(3*b^10-19*b^8*c^2+32*b^6*c^4+32*b^4*c^6-19*b^2*c^8+3*c^10))+(a^2-a*b+b^2-c^2)*(a^2+a*b+b^2-c^2)*(a^2-b^2-a*c+c^2)*(a^2-b^2+a*c+c^2)*(-6*a^12+2*b^2*c^2*(b^2-c^2)^4+24*a^10*(b^2+c^2)+4*a^2*b^2*c^2*(b^2-c^2)^2*(b^2+c^2)-2*a^8*(18*b^4+29*b^2*c^2+18*c^4)+4*a^6*(6*b^6+13*b^4*c^2+13*b^2*c^4+6*c^6)-2*a^4*(3*b^8+12*b^6*c^2+2*b^4*c^4+12*b^2*c^6+3*c^8))*S : :

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) = X(4)X(51277)∩X(13)X(51254)

Barycentrics    sqrt(3)*(a^2-a*b+b^2-c^2)*(a^2+a*b+b^2-c^2)*(a^2-b^2-a*c+c^2)*(a^2-b^2+a*c+c^2)*(3*a^14-11*a^12*(b^2+c^2)-51*a^8*b^2*c^2*(b^2+c^2)+a^10*(12*b^4+41*b^2*c^2+12*c^4)-(b^2-c^2)^4*(2*b^6+5*b^4*c^2+5*b^2*c^4+2*c^6)+a^6*(-5*b^8+14*b^6*c^2+70*b^4*c^4+14*b^2*c^6-5*c^8)+a^2*(b^2-c^2)^2*(6*b^8-3*b^6*c^2-14*b^4*c^4-3*b^2*c^6+6*c^8)-a^4*(3*b^10-19*b^8*c^2+32*b^6*c^4+32*b^4*c^6-19*b^2*c^8+3*c^10))+(a^2-a*b+b^2-c^2)*(a^2+a*b+b^2-c^2)*(a^2-b^2-a*c+c^2)*(a^2-b^2+a*c+c^2)*(6*a^12-2*b^2*c^2*(b^2-c^2)^4-24*a^10*(b^2+c^2)-4*a^2*b^2*c^2*(b^2-c^2)^2*(b^2+c^2)+a^8*(36*b^4+58*b^2*c^2+36*c^4)-4*a^6*(6*b^6+13*b^4*c^2+13*b^2*c^4+6*c^6)+a^4*(6*b^8+24*b^6*c^2+4*b^4*c^4+24*b^2*c^6+6*c^8))*S : :

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) = X(30)X(40178)∩X(3424)X(34621)

Barycentrics    (a^8+4*a^2*b^2*c^2*(b^2-5*c^2)-2*a^4*(b^2-c^2)^2+(b^4-c^4)^2)*(a^8-2*a^4*(b^2-c^2)^2+4*a^2*b^2*c^2*(-5*b^2+c^2)+(b^4-c^4)^2) : :

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) = X(30)X(40395)∩X(275)X(11113)

Barycentrics    (a^8+2*a^5*b*c*(b+c)+2*a*b*(b-c)^2*c*(b+c)^3+a^6*(2*b^2+2*b*c-c^2)+(b^2-c^2)^3*(b^2+2*c^2)+a^2*(b^2-c^2)^2*(2*b^2+2*b*c+5*c^2)-4*a^3*b*c*(b^3+b^2*c+b*c^2+c^3)-a^4*(6*b^4+4*b^3*c-b^2*c^2+4*b*c^3+3*c^4))*(a^8+2*a^5*b*c*(b+c)+2*a*b*(b-c)^2*c*(b+c)^3-(b^2-c^2)^3*(2*b^2+c^2)+a^6*(-b^2+2*b*c+2*c^2)+a^2*(b^2-c^2)^2*(5*b^2+2*b*c+2*c^2)-4*a^3*b*c*(b^3+b^2*c+b*c^2+c^3)-a^4*(3*b^4+4*b^3*c-b^2*c^2+4*b*c^3+6*c^4)) : :

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) = X(30)X(4049)∩X(519)X(2394)

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

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) = X(2)X(22797)∩X(13)X(10722)

Barycentrics    sqrt(3)*(a^8+a^4*b^2*c^2+8*a^6*(b^2+c^2)-10*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(b^4-11*b^2*c^2+c^4))+6*(-4*a^6+2*a^2*(b^2-c^2)^2-a^4*(b^2+c^2)+3*(b^2-c^2)^2*(b^2+c^2))*S : :

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) = X(2)X(22796)∩X(14)X(10722)

Barycentrics    sqrt(3)*(a^8+a^4*b^2*c^2+8*a^6*(b^2+c^2)-10*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(b^4-11*b^2*c^2+c^4))+6*(4*a^6-2*a^2*(b^2-c^2)^2+a^4*(b^2+c^2)-3*(b^2-c^2)^2*(b^2+c^2))*S : :

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) = X(10)X(24705)∩X(30)X(40718)

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

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) = X(30)X(4080)∩X(900)X(2394)

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

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) = X(20)X(43529)∩X(76)X(11180)

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

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) = X(30)X(42006)∩X(83)X(11645)

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

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) = X(2)X(22505)∩X(30)X(42010)

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

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) = X(30)X(42011)∩X(381)X(10153)

Barycentrics    (6*a^6+6*b^6-13*b^4*c^2+12*b^2*c^4-5*c^6-a^4*(2*b^2+13*c^2)-2*a^2*(b^4+5*b^2*c^2-6*c^4))*(6*a^6-5*b^6+12*b^4*c^2-13*b^2*c^4+6*c^6-a^4*(13*b^2+2*c^2)+2*a^2*(6*b^4-5*b^2*c^2-c^4)) : :

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) = X(2)X(9749)∩X(13)X(1503)

Barycentrics    sqrt(3)*(3*a^8+a^4*(b^2-c^2)^2-8*b^2*c^2*(b^2-c^2)^2+3*a^6*(b^2+c^2)-7*a^2*(b^2-c^2)^2*(b^2+c^2))+6*(3*a^6-a^2*(b^2-c^2)^2-2*(b^2-c^2)^2*(b^2+c^2))*S : :

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) = X(2)X(9750)∩X(14)X(1503)

Barycentrics    3*a^8+3*a^6*(b^2+c^2-2*sqrt(3)*S)-(b-c)^2*(b+c)^2*(-a^4-4*sqrt(3)*c^2*S+b^2*(8*c^2-4*sqrt(3)*S)+a^2*(7*b^2+7*c^2-2*sqrt(3)*S)) : :

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) = X(2)X(9736)∩X(4)X(5472)

Barycentrics    -3*a^8+6*a^6*(b^2+c^2)-8*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(2*b^4+5*b^2*c^2+2*c^4)+(b^2-c^2)^2*(3*b^4-7*b^2*c^2+3*c^4)+2*sqrt(3)*(-2*a^2*(b^2-c^2)^2+3*a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2))*S : :

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) = X(2)X(9735)∩X(4)X(5471)

Barycentrics    -3*a^8+6*a^6*(b^2+c^2)-8*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(2*b^4+5*b^2*c^2+2*c^4)+(b^2-c^2)^2*(3*b^4-7*b^2*c^2+3*c^4)+2*sqrt(3)*(2*a^2*(b^2-c^2)^2-3*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2))*S : :

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) = X(30)X(42410)∩X(6240)X(16080)

Barycentrics    (5*a^8-a^6*(11*b^2+2*c^2)-(b^2-c^2)^3*(4*b^2+5*c^2)+a^4*(3*b^4+5*b^2*c^2-6*c^4)+a^2*(7*b^6-10*b^4*c^2+5*b^2*c^4-2*c^6))*(5*a^8+(b^2-c^2)^3*(5*b^2+4*c^2)-a^6*(2*b^2+11*c^2)+a^4*(-6*b^4+5*b^2*c^2+3*c^4)+a^2*(-2*b^6+5*b^4*c^2-10*b^2*c^4+7*c^6)) : :

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) = X(13)X(43368)∩X(17)X(14893)

Barycentrics    -63*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+2*sqrt(3)*(-661*a^4+662*(b^2-c^2)^2-a^2*(b^2+c^2))*S : :
Barycentrics    1 / (21*Sqrt[3]*(-a^2 + b^2 + c^2) - 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] - 63*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(13)X(42682)∩X(18)X(14893)

Barycentrics    63*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+2*sqrt(3)*(-661*a^4+662*(b^2-c^2)^2-a^2*(b^2+c^2))*S : :
Barycentrics    1 / (21*Sqrt[3]*(-a^2 + b^2 + c^2) + 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] + 63*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(2)X(43367)∩X(4)X(42612)

Barycentrics    -45*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+2*sqrt(3)*(-337*a^4+338*(b^2-c^2)^2-a^2*(b^2+c^2))*S : :
Barycentrics    1 / (15*Sqrt[3]*(-a^2 + b^2 + c^2) - 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] - 45*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(2)X(43366)∩X(4)X(42613)

Barycentrics    -45*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+2*sqrt(3)*(337*a^4-338*(b^2-c^2)^2+a^2*(b^2+c^2))*S : :
Barycentrics    1 / (15*Sqrt[3]*(-a^2 + b^2 + c^2) + 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] + 45*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(4)X(43253)∩X(18)X(50687)

Barycentrics    -36*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+sqrt(3)*(-431*a^4+433*(b^2-c^2)^2-2*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (6*Sqrt[3]*(-a^2 + b^2 + c^2) - S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] - 36*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(4)X(43252)∩X(17)X(50687)

Barycentrics    36*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+sqrt(3)*(-431*a^4+433*(b^2-c^2)^2-2*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (6*Sqrt[3]*(-a^2 + b^2 + c^2) + S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] + 36*Cot[A]) : :    (Peter Moses, July 21, 2023)

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) = X(17)X(3839)∩X(18)X(3543)

Barycentrics    18*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+sqrt(3)*(107*a^4-109*(b^2-c^2)^2+2*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (3*Sqrt[3]*(-a^2 + b^2 + c^2) - S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] - 18*Cot[A]) : :    (Peter Moses, July 21, 2023)

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}

X(54581) = X(17)X(3543)∩X(18)X(3839)

Barycentrics    -18*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+sqrt(3)*(107*a^4-109*(b^2-c^2)^2+2*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (3*Sqrt[3]*(-a^2 + b^2 + c^2) + S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] + 18*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54581) lies on these lines: {2, 42097}, {13, 43398}, {14, 43365}, {17, 3543}, {18, 3839}, {20, 10188}, {30, 43447}, {376, 43445}, {381, 43446}, {383, 53098}, {2043, 43564}, {2044, 43565}, {3091, 10187}, {3146, 42794}, {3545, 43444}, {3830, 43542}, {3845, 43543}, {5318, 43553}, {5335, 12821}, {10304, 43443}, {12101, 33602}, {12817, 42134}, {12820, 41112}, {15640, 43544}, {15682, 42124}, {15692, 43441}, {17578, 42518}, {22235, 42147}, {22237, 49948}, {33605, 42125}, {33606, 42900}, {33607, 43243}, {33699, 42962}, {35749, 42035}, {36331, 42036}, {41099, 42137}, {41106, 42123}, {41107, 43547}, {41113, 43551}, {41119, 50688}, {42094, 43541}, {42108, 49905}, {42160, 43546}, {42508, 43465}, {42588, 43304}, {42590, 46333}, {42636, 49875}, {42898, 43556}, {42904, 49824}, {42918, 43545}, {42957, 43869}, {43228, 43540}, {43550, 49827}

X(54581) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(472), X(3839)}}, {{A, B, C, X(473), X(3543)}}, {{A, B, C, X(31361), X(41900)}}, {{A, B, C, X(40712), X(43699)}}
X(54581) = X(i)-cross conjugate of X(j) for these {i, j}: {43478, 43541}

X(54582) = X(2)X(43621)∩X(4)X(39593)

Barycentrics    (4*a^4+4*b^4+b^2*c^2-5*c^4+a^2*(10*b^2+c^2))*(4*a^4-5*b^4+b^2*c^2+4*c^4+a^2*(b^2+10*c^2)) : :

X(54582) lies on these lines: {2, 43621}, {4, 39593}, {30, 43527}, {76, 3845}, {83, 3830}, {381, 10159}, {383, 10188}, {428, 43530}, {598, 12101}, {1080, 10187}, {2394, 7950}, {5064, 16080}, {5066, 42787}, {10185, 13860}, {14269, 43676}, {15682, 18841}, {15687, 53102}, {18840, 41099}, {19708, 39784}, {33706, 42006}

X(54582) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(41940)}}, {{A, B, C, X(25), X(3845)}}, {{A, B, C, X(30), X(5064)}}, {{A, B, C, X(251), X(14487)}}, {{A, B, C, X(264), X(48895)}}, {{A, B, C, X(305), X(18550)}}, {{A, B, C, X(381), X(428)}}, {{A, B, C, X(427), X(3830)}}, {{A, B, C, X(1494), X(43726)}}, {{A, B, C, X(3108), X(13603)}}, {{A, B, C, X(3527), X(29011)}}, {{A, B, C, X(3534), X(52285)}}, {{A, B, C, X(3839), X(7714)}}, {{A, B, C, X(5094), X(12101)}}, {{A, B, C, X(5481), X(46848)}}, {{A, B, C, X(6995), X(41099)}}, {{A, B, C, X(7378), X(15682)}}, {{A, B, C, X(7408), X(41106)}}, {{A, B, C, X(7409), X(11001)}}, {{A, B, C, X(9307), X(48880)}}, {{A, B, C, X(13472), X(29322)}}, {{A, B, C, X(14388), X(39955)}}, {{A, B, C, X(14483), X(34572)}}, {{A, B, C, X(18361), X(22336)}}, {{A, B, C, X(22334), X(29316)}}, {{A, B, C, X(29180), X(46851)}}, {{A, B, C, X(32085), X(46204)}}, {{A, B, C, X(33696), X(52133)}}, {{A, B, C, X(34288), X(43621)}}

X(54583) = X(30)X(43528)∩X(1916)X(3845)

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

X(54583) lies on these lines: {30, 43528}, {381, 43529}, {1916, 3845}, {3407, 3830}, {10185, 37334}, {40824, 41099}

X(54583) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(419), X(3845)}}, {{A, B, C, X(1976), X(14487)}}, {{A, B, C, X(3830), X(5117)}}, {{A, B, C, X(6620), X(41099)}}, {{A, B, C, X(18550), X(40708)}}

X(54584) = X(30)X(43529)∩X(1916)X(3830)

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

X(54584) lies on these lines: {30, 43529}, {381, 43528}, {1916, 3830}, {3407, 3845}, {10185, 37446}, {15682, 40824}

X(54584) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(419), X(3830)}}, {{A, B, C, X(1976), X(13603)}}, {{A, B, C, X(3845), X(5117)}}, {{A, B, C, X(6620), X(15682)}}, {{A, B, C, X(9154), X(11058)}}

X(54585) = X(2)X(1531)∩X(4)X(15860)

Barycentrics    (4*a^8+a^6*(-7*b^2+2*c^2)+a^2*(b^2-c^2)^2*(11*b^2+2*c^2)-(b^2-c^2)^3*(5*b^2+4*c^2)+a^4*(-3*b^4+7*b^2*c^2-12*c^4))*(4*a^8+a^6*(2*b^2-7*c^2)+(b^2-c^2)^3*(4*b^2+5*c^2)+a^2*(b^2-c^2)^2*(2*b^2+11*c^2)+a^4*(-12*b^4+7*b^2*c^2-3*c^4)) : :

X(54585) lies on these lines: {2, 1531}, {4, 15860}, {30, 43530}, {275, 3830}, {381, 16080}, {459, 41099}, {1514, 14458}, {2052, 3845}, {3839, 18554}, {5893, 46727}, {34664, 43527}, {38253, 41106}, {43665, 46985}

X(54585) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(3845)}}, {{A, B, C, X(5), X(3830)}}, {{A, B, C, X(20), X(41099)}}, {{A, B, C, X(30), X(264)}}, {{A, B, C, X(253), X(376)}}, {{A, B, C, X(382), X(5066)}}, {{A, B, C, X(546), X(3534)}}, {{A, B, C, X(547), X(38335)}}, {{A, B, C, X(549), X(14269)}}, {{A, B, C, X(1294), X(36889)}}, {{A, B, C, X(1494), X(4846)}}, {{A, B, C, X(1513), X(11317)}}, {{A, B, C, X(1515), X(42854)}}, {{A, B, C, X(1656), X(12101)}}, {{A, B, C, X(1657), X(3860)}}, {{A, B, C, X(1989), X(16263)}}, {{A, B, C, X(2050), X(52246)}}, {{A, B, C, X(3091), X(15682)}}, {{A, B, C, X(3146), X(41106)}}, {{A, B, C, X(3521), X(15318)}}, {{A, B, C, X(3543), X(3545)}}, {{A, B, C, X(3627), X(19709)}}, {{A, B, C, X(3832), X(11001)}}, {{A, B, C, X(3843), X(8703)}}, {{A, B, C, X(3851), X(33699)}}, {{A, B, C, X(3855), X(15640)}}, {{A, B, C, X(3858), X(15685)}}, {{A, B, C, X(3861), X(15693)}}, {{A, B, C, X(5054), X(14893)}}, {{A, B, C, X(5055), X(15687)}}, {{A, B, C, X(5064), X(34664)}}, {{A, B, C, X(5071), X(50687)}}, {{A, B, C, X(5076), X(10109)}}, {{A, B, C, X(5627), X(9307)}}, {{A, B, C, X(8352), X(13860)}}, {{A, B, C, X(8884), X(46204)}}, {{A, B, C, X(13603), X(41891)}}, {{A, B, C, X(14093), X(41987)}}, {{A, B, C, X(14483), X(34570)}}, {{A, B, C, X(14487), X(41890)}}, {{A, B, C, X(14892), X(35434)}}, {{A, B, C, X(15319), X(31371)}}, {{A, B, C, X(15681), X(23046)}}, {{A, B, C, X(15684), X(38071)}}, {{A, B, C, X(15699), X(35403)}}, {{A, B, C, X(18323), X(39484)}}, {{A, B, C, X(18325), X(39487)}}, {{A, B, C, X(18386), X(44285)}}, {{A, B, C, X(18403), X(44287)}}, {{A, B, C, X(18854), X(31361)}}, {{A, B, C, X(19708), X(50689)}}, {{A, B, C, X(32533), X(46412)}}, {{A, B, C, X(35908), X(46985)}}, {{A, B, C, X(36448), X(42280)}}, {{A, B, C, X(36466), X(42281)}}, {{A, B, C, X(36490), X(36729)}}, {{A, B, C, X(36551), X(36730)}}, {{A, B, C, X(36720), X(36727)}}, {{A, B, C, X(36721), X(36728)}}, {{A, B, C, X(36722), X(36731)}}, {{A, B, C, X(40705), X(45821)}}, {{A, B, C, X(47310), X(47597)}}

X(54586) = X(2)X(37508)∩X(10)X(381)

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

X(54586) lies on these lines: {2, 37508}, {4, 48857}, {10, 381}, {27, 43530}, {30, 43531}, {226, 4021}, {321, 24048}, {469, 16080}, {2048, 10194}, {2394, 23879}, {3543, 19766}, {3839, 43533}, {4049, 28478}, {4052, 17133}, {6539, 31018}, {6996, 43527}, {7377, 10159}, {17758, 36731}

X(54586) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(4102)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(24048)}}, {{A, B, C, X(7), X(4021)}}, {{A, B, C, X(27), X(381)}}, {{A, B, C, X(30), X(469)}}, {{A, B, C, X(57), X(12702)}}, {{A, B, C, X(58), X(9566)}}, {{A, B, C, X(79), X(312)}}, {{A, B, C, X(80), X(42030)}}, {{A, B, C, X(81), X(16615)}}, {{A, B, C, X(92), X(12699)}}, {{A, B, C, X(278), X(18483)}}, {{A, B, C, X(306), X(4846)}}, {{A, B, C, X(333), X(5560)}}, {{A, B, C, X(428), X(7377)}}, {{A, B, C, X(514), X(28194)}}, {{A, B, C, X(519), X(28478)}}, {{A, B, C, X(553), X(31018)}}, {{A, B, C, X(903), X(10435)}}, {{A, B, C, X(967), X(3531)}}, {{A, B, C, X(1121), X(39980)}}, {{A, B, C, X(1171), X(14483)}}, {{A, B, C, X(1246), X(1494)}}, {{A, B, C, X(1255), X(10308)}}, {{A, B, C, X(1445), X(28609)}}, {{A, B, C, X(1479), X(1848)}}, {{A, B, C, X(1826), X(34288)}}, {{A, B, C, X(2339), X(17098)}}, {{A, B, C, X(3305), X(4654)}}, {{A, B, C, X(3545), X(6994)}}, {{A, B, C, X(3577), X(39948)}}, {{A, B, C, X(3667), X(17133)}}, {{A, B, C, X(3668), X(36889)}}, {{A, B, C, X(3839), X(7490)}}, {{A, B, C, X(4657), X(42034)}}, {{A, B, C, X(4921), X(31179)}}, {{A, B, C, X(5064), X(6996)}}, {{A, B, C, X(14004), X(36731)}}, {{A, B, C, X(15909), X(24703)}}, {{A, B, C, X(19722), X(41816)}}, {{A, B, C, X(19738), X(31143)}}, {{A, B, C, X(30608), X(33696)}}, {{A, B, C, X(34991), X(36603)}}, {{A, B, C, X(36908), X(52452)}}

X(54587) = X(10)X(376)∩X(30)X(43533)

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

X(54587) lies on these lines: {10, 376}, {30, 43533}, {321, 4488}, {2048, 3590}, {3545, 43531}, {7397, 10159}, {7402, 43527}, {7406, 43681}, {7490, 16080}

X(54587) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(27), X(376)}}, {{A, B, C, X(30), X(7490)}}, {{A, B, C, X(57), X(10308)}}, {{A, B, C, X(74), X(967)}}, {{A, B, C, X(84), X(39980)}}, {{A, B, C, X(104), X(39948)}}, {{A, B, C, X(189), X(52374)}}, {{A, B, C, X(333), X(3296)}}, {{A, B, C, X(428), X(7397)}}, {{A, B, C, X(461), X(36728)}}, {{A, B, C, X(469), X(3545)}}, {{A, B, C, X(1000), X(42030)}}, {{A, B, C, X(1171), X(3431)}}, {{A, B, C, X(3062), X(4488)}}, {{A, B, C, X(3524), X(6994)}}, {{A, B, C, X(4102), X(43734)}}, {{A, B, C, X(5064), X(7402)}}, {{A, B, C, X(5560), X(6557)}}, {{A, B, C, X(6996), X(7714)}}, {{A, B, C, X(8044), X(36889)}}, {{A, B, C, X(10429), X(34578)}}, {{A, B, C, X(16615), X(25430)}}, {{A, B, C, X(18850), X(40414)}}, {{A, B, C, X(30257), X(37216)}}, {{A, B, C, X(32040), X(32704)}}, {{A, B, C, X(33702), X(36908)}}, {{A, B, C, X(43733), X(43759)}}

X(54588) = X(30)X(43534)∩X(812)X(2394)

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

X(54588) lies on these lines: {30, 43534}, {226, 50181}, {528, 43677}, {544, 43683}, {812, 2394}, {5466, 28521}, {14223, 40459}, {16080, 31905}

X(54588) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(812)}}, {{A, B, C, X(79), X(50181)}}, {{A, B, C, X(524), X(28521)}}, {{A, B, C, X(528), X(6002)}}, {{A, B, C, X(542), X(40459)}}, {{A, B, C, X(544), X(6003)}}, {{A, B, C, X(1018), X(32678)}}

X(54589) = X(2)X(43451)∩X(76)X(530)

Barycentrics    sqrt(3)*(4*a^10-6*a^8*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)-a^6*(b^4+13*b^2*c^2+c^4)+a^2*(b^2-c^2)^2*(3*b^4+11*b^2*c^2+3*c^4)+2*a^4*(b^6-2*b^4*c^2-2*b^2*c^4+c^6))-2*(4*a^8+6*a^6*(b^2+c^2)-2*(b^2-c^2)^2*(b^4+5*b^2*c^2+c^4)+a^4*(b^4+7*b^2*c^2+c^4)+a^2*(-9*b^6+10*b^4*c^2+10*b^2*c^4-9*c^6))*S : :

X(54589) lies on these lines: {2, 43451}, {13, 11645}, {14, 22513}, {18, 37332}, {30, 43538}, {76, 530}, {262, 41022}, {531, 1916}, {542, 43539}, {671, 36969}, {3457, 36316}, {3849, 42035}, {6108, 10033}, {6115, 9774}, {6582, 40707}, {6778, 9830}, {11122, 51482}, {11603, 25154}, {12817, 14537}, {14492, 41108}, {41023, 43532}, {52649, 53430}

X(54589) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(512), X(530)}}, {{A, B, C, X(531), X(804)}}, {{A, B, C, X(3438), X(34533)}}, {{A, B, C, X(3440), X(46286)}}, {{A, B, C, X(3849), X(27551)}}, {{A, B, C, X(6582), X(8014)}}, {{A, B, C, X(9830), X(27550)}}, {{A, B, C, X(11645), X(23870)}}

X(54590) = X(2)X(43452)∩X(76)X(531)

Barycentrics    -3*(4*a^10-6*a^8*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)-a^6*(b^4+13*b^2*c^2+c^4)+a^2*(b^2-c^2)^2*(3*b^4+11*b^2*c^2+3*c^4)+2*a^4*(b^6-2*b^4*c^2-2*b^2*c^4+c^6))-2*sqrt(3)*(4*a^8+6*a^6*(b^2+c^2)-2*(b^2-c^2)^2*(b^4+5*b^2*c^2+c^4)+a^4*(b^4+7*b^2*c^2+c^4)+a^2*(-9*b^6+10*b^4*c^2+10*b^2*c^4-9*c^6))*S : :

X(54590) lies on these lines: {2, 43452}, {13, 22512}, {14, 11645}, {17, 37333}, {30, 43539}, {76, 531}, {262, 41023}, {530, 1916}, {542, 43538}, {671, 36970}, {3458, 36317}, {3849, 42036}, {6109, 10033}, {6114, 9774}, {6295, 40706}, {6777, 9830}, {11121, 51483}, {11602, 25164}, {12816, 14537}, {14492, 41107}, {41022, 43532}, {44289, 53442}

X(54590) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(512), X(531)}}, {{A, B, C, X(530), X(804)}}, {{A, B, C, X(3439), X(34534)}}, {{A, B, C, X(3441), X(46286)}}, {{A, B, C, X(3849), X(27550)}}, {{A, B, C, X(9830), X(27551)}}, {{A, B, C, X(11645), X(23871)}}

X(54591) = X(17)X(3627)∩X(18)X(3843)

Barycentrics    -21*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+2*sqrt(3)*(73*a^4-74*(b^2-c^2)^2+a^2*(b^2+c^2))*S : :
Barycentrics    1 / (7*Sqrt[3]*(-a^2 + b^2 + c^2) + 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] + 21*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54591) lies on these lines: {2, 42100}, {3, 43441}, {5, 43440}, {13, 38335}, {14, 14893}, {17, 3627}, {18, 3843}, {30, 43548}, {381, 43292}, {383, 53108}, {395, 43491}, {548, 43443}, {1080, 11668}, {1657, 10188}, {3091, 43330}, {3412, 22235}, {3545, 42931}, {3850, 10187}, {3853, 42802}, {5072, 42433}, {5318, 12821}, {10653, 33605}, {10654, 43556}, {11541, 43489}, {12101, 42799}, {12812, 42597}, {12817, 42094}, {14891, 42429}, {15684, 16808}, {15686, 43104}, {15689, 33417}, {15702, 43324}, {15712, 51916}, {16241, 33703}, {16268, 42971}, {16963, 43195}, {16965, 22237}, {17538, 43445}, {19107, 33607}, {21845, 41022}, {23046, 42121}, {33602, 44015}, {33604, 41101}, {33606, 42533}, {36969, 43543}, {36970, 43546}, {37640, 43492}, {37835, 43477}, {41943, 43204}, {41944, 43244}, {41983, 42919}, {42085, 43542}, {42086, 43373}, {42106, 46333}, {42134, 43553}, {42142, 43554}, {42145, 42928}, {42163, 42436}, {42431, 42996}, {42434, 43399}, {42516, 43311}, {42631, 43249}, {42632, 43199}, {42777, 43400}, {42813, 43021}, {42901, 43540}, {42973, 43552}, {42975, 43547}, {42983, 43006}, {43472, 44018}

X(54591) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(15), X(14490)}}, {{A, B, C, X(16), X(14487)}}, {{A, B, C, X(61), X(46848)}}, {{A, B, C, X(470), X(38335)}}, {{A, B, C, X(471), X(14893)}}, {{A, B, C, X(472), X(3843)}}, {{A, B, C, X(473), X(3627)}}, {{A, B, C, X(554), X(17501)}}, {{A, B, C, X(21400), X(40712)}}
X(54591) = X(i)-cross conjugate of X(j) for these {i, j}: {43472, 43551}, {44018, 43545}

X(54592) = X(17)X(3843)∩X(18)X(3627)

Barycentrics    -21*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+2*sqrt(3)*(-73*a^4+74*(b^2-c^2)^2-a^2*(b^2+c^2))*S : :
Barycentrics    1 / (7*Sqrt[3]*(-a^2 + b^2 + c^2) - 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (Sqrt[3] - 21*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54592) lies on these lines: {2, 42099}, {3, 43440}, {5, 43441}, {13, 14893}, {14, 38335}, {17, 3843}, {18, 3627}, {30, 43549}, {381, 43293}, {383, 11668}, {396, 43492}, {548, 43442}, {1080, 53108}, {1657, 10187}, {3091, 43331}, {3411, 22237}, {3545, 42930}, {3850, 10188}, {3853, 42801}, {5072, 42434}, {5321, 12820}, {10653, 43557}, {10654, 33604}, {11541, 43490}, {12101, 42800}, {12812, 42596}, {12816, 42093}, {14891, 42430}, {15684, 16809}, {15686, 43101}, {15689, 33416}, {15702, 43325}, {15712, 51915}, {16242, 33703}, {16267, 42970}, {16962, 43196}, {16964, 22235}, {17538, 43444}, {19106, 33606}, {21846, 41023}, {23046, 42124}, {33603, 44016}, {33605, 41100}, {33607, 42532}, {36969, 43547}, {36970, 43542}, {37641, 43491}, {37832, 43478}, {41943, 43245}, {41944, 43203}, {41983, 42918}, {42085, 43372}, {42086, 43543}, {42103, 46333}, {42133, 43552}, {42139, 43555}, {42144, 42929}, {42166, 42435}, {42432, 42997}, {42433, 43400}, {42517, 43310}, {42631, 43200}, {42632, 43248}, {42778, 43399}, {42814, 43020}, {42900, 43541}, {42972, 43553}, {42974, 43546}, {42982, 43007}, {43471, 44017}

X(54592) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(15), X(14487)}}, {{A, B, C, X(16), X(14490)}}, {{A, B, C, X(62), X(46848)}}, {{A, B, C, X(470), X(14893)}}, {{A, B, C, X(471), X(38335)}}, {{A, B, C, X(472), X(3627)}}, {{A, B, C, X(473), X(3843)}}, {{A, B, C, X(1081), X(17501)}}, {{A, B, C, X(21400), X(40711)}}
X(54592) = X(i)-cross conjugate of X(j) for these {i, j}: {43471, 43550}, {44017, 43544}

X(54593) = X(2)X(33613)∩X(18)X(547)

Barycentrics    63*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+2*sqrt(3)*(11*a^4+38*(b^2-c^2)^2-49*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (3*Sqrt[3]*(-a^2 + b^2 + c^2) + 14*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (7*Sqrt[3] + 9*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54593) lies on these lines: {2, 33613}, {4, 16962}, {13, 8703}, {14, 16960}, {15, 12820}, {16, 43554}, {17, 5054}, {18, 547}, {30, 43550}, {61, 43557}, {62, 43442}, {381, 42435}, {396, 3860}, {632, 10188}, {671, 47867}, {3391, 36453}, {3392, 36469}, {3530, 41974}, {5070, 10187}, {5079, 49908}, {5459, 11121}, {5488, 50860}, {11488, 33602}, {11540, 11542}, {12103, 42973}, {12816, 36967}, {12821, 41101}, {15681, 42156}, {15682, 43331}, {15692, 22235}, {15693, 43334}, {15701, 42931}, {15710, 42158}, {15719, 41107}, {16242, 43004}, {16644, 33607}, {16772, 43016}, {16808, 43369}, {16809, 33603}, {16963, 42610}, {16966, 42480}, {18582, 42532}, {19106, 41119}, {19710, 42929}, {21734, 42959}, {22489, 40707}, {33417, 43297}, {33458, 42035}, {33605, 37640}, {33606, 43228}, {35401, 42157}, {35752, 42062}, {36329, 49945}, {36968, 43294}, {36969, 42684}, {37832, 42507}, {38071, 41108}, {40693, 42521}, {41113, 42472}, {41122, 42496}, {41943, 42161}, {41978, 42162}, {41984, 42488}, {41985, 42801}, {42132, 43200}, {42136, 43476}, {42166, 42890}, {42420, 43484}, {42475, 43303}, {42512, 49875}, {42528, 49825}, {42591, 42779}, {42596, 43773}, {42777, 43207}, {42815, 43420}, {42917, 43549}, {42962, 43368}, {42976, 43553}, {43008, 43239}, {43015, 43333}, {43232, 49873}, {43237, 43329}, {43403, 43552}, {43555, 49811}

X(54593) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(16), X(44731)}}, {{A, B, C, X(61), X(36843)}}, {{A, B, C, X(470), X(8703)}}, {{A, B, C, X(471), X(19709)}}, {{A, B, C, X(472), X(547)}}, {{A, B, C, X(473), X(5054)}}, {{A, B, C, X(8742), X(30537)}}
X(54593) = midpoint of X(i) in X(j) for these {i,j}: {2, 49911}
X(54593) = complement of X(33613)
X(54593) = X(i)-cross conjugate of X(j) for these {i, j}: {43489, 43549}
X(54593) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16267, 42952, 43229}, {19709, 42520, 43335}, {43325, 43421, 36967}, {49903, 49907, 16960}

X(54594) = X(2)X(33612)∩X(17)X(547)

Barycentrics    63*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+2*sqrt(3)*(-11*a^4-38*(b^2-c^2)^2+49*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (3*Sqrt[3]*(-a^2 + b^2 + c^2) - 14*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (7*Sqrt[3] - 9*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54594) lies on these lines: {2, 33612}, {4, 16963}, {13, 16961}, {14, 8703}, {15, 43555}, {16, 12821}, {17, 547}, {18, 5054}, {30, 43551}, {61, 43443}, {62, 43556}, {381, 42436}, {395, 3860}, {632, 10187}, {671, 36769}, {3366, 36470}, {3367, 36452}, {3530, 41973}, {5070, 10188}, {5079, 49907}, {5460, 11122}, {5487, 50859}, {11489, 33603}, {11540, 11543}, {12103, 42972}, {12817, 36968}, {12820, 41100}, {15681, 42153}, {15682, 43330}, {15692, 22237}, {15693, 43335}, {15701, 42930}, {15710, 42157}, {15719, 41108}, {16241, 43005}, {16645, 33606}, {16773, 43017}, {16808, 33602}, {16809, 43368}, {16962, 42611}, {16967, 42481}, {18581, 42533}, {19107, 41120}, {19710, 42928}, {21734, 42958}, {22490, 40706}, {33416, 43296}, {33459, 42036}, {33604, 37641}, {33607, 43229}, {35401, 42158}, {35751, 49946}, {36330, 42063}, {36967, 43295}, {36970, 42685}, {37835, 42506}, {38071, 41107}, {40694, 42520}, {41112, 42473}, {41121, 42497}, {41944, 42160}, {41977, 42159}, {41984, 42489}, {41985, 42802}, {42129, 43199}, {42137, 43475}, {42163, 42891}, {42419, 43483}, {42474, 43302}, {42513, 49876}, {42529, 49824}, {42590, 42780}, {42597, 43774}, {42778, 43208}, {42816, 43421}, {42916, 43548}, {42963, 43369}, {42977, 43552}, {43009, 43238}, {43014, 43332}, {43233, 49874}, {43236, 43328}, {43404, 43553}, {43554, 49810}

X(54594) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(15), X(44731)}}, {{A, B, C, X(62), X(36836)}}, {{A, B, C, X(470), X(19709)}}, {{A, B, C, X(471), X(8703)}}, {{A, B, C, X(472), X(5054)}}, {{A, B, C, X(473), X(547)}}, {{A, B, C, X(8741), X(30537)}}
X(54594) = midpoint of X(i) in X(j) for these {i,j}: {2, 49914}
X(54594) = complement of X(33612)
X(54594) = X(i)-cross conjugate of X(j) for these {i, j}: {43490, 43548}
X(54594) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16268, 42953, 43228}, {19709, 42521, 43334}, {43324, 43420, 36968}, {49904, 49908, 16961}

X(54595) = X(30)X(43558)∩X(546)X(6489)

Barycentrics    15*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+(-224*a^4+226*(b^2-c^2)^2-2*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (15*(-a^2 + b^2 + c^2) + 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 + 15*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54595) lies on these lines: {30, 43558}, {381, 43559}, {382, 10195}, {485, 15687}, {486, 14269}, {546, 6489}, {2043, 43443}, {2044, 43442}, {3316, 42266}, {3317, 22644}, {3529, 43564}, {3590, 50688}, {3830, 43568}, {3845, 43569}, {3855, 43565}, {14241, 52666}, {32787, 43570}, {34089, 43254}, {36449, 43196}, {36467, 43195}, {38335, 43380}, {41969, 42269}, {42284, 43563}, {43504, 43566}

X(54595) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(1585), X(15687)}}, {{A, B, C, X(1586), X(14269)}}, {{A, B, C, X(6420), X(6489)}}

X(54596) = X(30)X(43559)∩X(546)X(6488)

Barycentrics    15*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+(224*a^4-226*(b^2-c^2)^2+2*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (15*(-a^2 + b^2 + c^2) - 2*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 - 15*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54596) lies on these lines: {30, 43559}, {381, 43558}, {382, 10194}, {485, 14269}, {486, 15687}, {546, 6488}, {2043, 43442}, {2044, 43443}, {3316, 22615}, {3317, 42267}, {3529, 43565}, {3591, 50688}, {3830, 43569}, {3845, 43568}, {3855, 43564}, {6561, 43536}, {14226, 52667}, {32788, 43571}, {34091, 43255}, {36450, 43195}, {36468, 43196}, {38335, 43381}, {41970, 42268}, {42283, 43562}, {43503, 43567}

X(54596) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(1585), X(14269)}}, {{A, B, C, X(1586), X(15687)}}, {{A, B, C, X(6419), X(6488)}}

X(54597) = X(2)X(6199)∩X(4)X(6426)

Barycentrics    12*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+(-7*a^4-25*(b^2-c^2)^2+32*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (3*(-a^2 + b^2 + c^2) - 8*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (4 - 3*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54597) lies on these lines: {2, 6199}, {4, 6426}, {6, 43536}, {13, 36447}, {14, 36465}, {30, 43561}, {376, 1132}, {381, 43560}, {485, 5071}, {486, 3524}, {547, 6500}, {615, 14226}, {631, 3591}, {1131, 3312}, {1151, 3317}, {1327, 3069}, {1328, 6396}, {1588, 34091}, {2043, 43557}, {2044, 43556}, {3071, 15715}, {3090, 3590}, {3316, 32787}, {3525, 9680}, {3528, 43571}, {3533, 6447}, {3543, 6408}, {3544, 31414}, {3839, 13993}, {5067, 6419}, {5491, 32808}, {6395, 42540}, {6440, 43209}, {6451, 15719}, {6470, 42579}, {6473, 35402}, {6475, 38335}, {6481, 42538}, {6565, 43406}, {6813, 47586}, {7388, 43681}, {7582, 34089}, {7586, 43386}, {8252, 41961}, {9540, 41947}, {9693, 43412}, {10577, 43558}, {11541, 35813}, {12819, 42561}, {13785, 15698}, {13935, 41951}, {13941, 15682}, {14241, 32788}, {15709, 52047}, {18762, 41099}, {19054, 43568}, {23273, 42417}, {23275, 43210}, {32786, 43569}, {38071, 42523}, {41949, 51850}, {41968, 43522}, {42215, 42527}, {42607, 43887}, {43510, 53519}

X(54597) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(6426)}}, {{A, B, C, X(6), X(6199)}}, {{A, B, C, X(54), X(1151)}}, {{A, B, C, X(376), X(3536)}}, {{A, B, C, X(492), X(19053)}}, {{A, B, C, X(493), X(14491)}}, {{A, B, C, X(494), X(3431)}}, {{A, B, C, X(1123), X(5551)}}, {{A, B, C, X(1152), X(6497)}}, {{A, B, C, X(1336), X(7317)}}, {{A, B, C, X(1585), X(5071)}}, {{A, B, C, X(1586), X(3524)}}, {{A, B, C, X(3300), X(43733)}}, {{A, B, C, X(3302), X(43734)}}, {{A, B, C, X(3535), X(3545)}}, {{A, B, C, X(5419), X(6419)}}, {{A, B, C, X(6396), X(20421)}}, {{A, B, C, X(6470), X(6500)}}, {{A, B, C, X(11738), X(41437)}}, {{A, B, C, X(13390), X(18490)}}, {{A, B, C, X(41515), X(52188)}}
X(54597) = isogonal conjugate of X(6395)
X(54597) = X(i)-cross conjugate of X(j) for these {i, j}: {23273, 4}, {42417, 1327}, {42567, 10195}, {42573, 1328}, {43518, 34089}
X(54597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {615, 14226, 19708}, {1132, 43212, 376}, {1328, 6396, 42537}, {42540, 42541, 6395}

X(54598) = X(30)X(43564)∩X(1131)X(6470)

Barycentrics    18*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+(-323*a^4+325*(b^2-c^2)^2-2*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (9*(-a^2 + b^2 + c^2) + S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 + 18*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54598) lies on these lines: {30, 43564}, {381, 43565}, {1131, 6470}, {1327, 43508}, {1328, 6436}, {3316, 3830}, {3317, 3845}, {3543, 10195}, {3590, 42577}, {3591, 6426}, {3839, 10194}, {6199, 12101}, {6221, 43536}, {6497, 41106}, {7374, 10185}, {9541, 43568}, {15640, 43558}, {15682, 34089}, {34091, 41099}, {42267, 43559}, {43256, 43569}

X(54598) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(588), X(6199)}}, {{A, B, C, X(1151), X(6470)}}, {{A, B, C, X(3312), X(6408)}}, {{A, B, C, X(3594), X(6426)}}, {{A, B, C, X(6396), X(6436)}}, {{A, B, C, X(6419), X(46848)}}, {{A, B, C, X(6497), X(6501)}}

X(54599) = X(30)X(43565)∩X(1132)X(6471)

Barycentrics    18*a^2*(a^4+(b^2-c^2)^2-2*a^2*(b^2+c^2))+(323*a^4-325*(b^2-c^2)^2+2*a^2*(b^2+c^2))*S : :
Barycentrics    1 / (9*(-a^2 + b^2 + c^2) - S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (1 - 18*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54599) lies on these lines: {30, 43565}, {381, 43564}, {1132, 6471}, {1327, 6435}, {1328, 43507}, {3316, 3845}, {3317, 3830}, {3543, 10194}, {3590, 6425}, {3591, 42576}, {3839, 10195}, {6395, 12101}, {6496, 41106}, {7000, 10185}, {15640, 43559}, {15682, 34091}, {34089, 41099}, {42266, 43558}, {43257, 43568}, {43536, 52047}

X(54599) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(589), X(6398)}}, {{A, B, C, X(1152), X(6471)}}, {{A, B, C, X(3311), X(6407)}}, {{A, B, C, X(3592), X(6425)}}, {{A, B, C, X(6200), X(6435)}}, {{A, B, C, X(6420), X(46848)}}, {{A, B, C, X(6496), X(6500)}}

X(54600) = X(98)X(2420)∩X(511)X(2394)

Barycentrics    (2*a^10*(b^2+c^2)+3*a^6*b^2*(b^2+c^2)^2-b^2*c^2*(b^2-c^2)^3*(b^2+2*c^2)-a^8*(5*b^4+5*b^2*c^2+2*c^4)-a^2*(b^2-c^2)^2*(b^6-2*b^4*c^2+b^2*c^4-2*c^6)+a^4*(b^8-6*b^6*c^2+3*b^2*c^6-2*c^8))*(2*a^10*(b^2+c^2)+3*a^6*c^2*(b^2+c^2)^2+b^2*c^2*(b^2-c^2)^3*(2*b^2+c^2)-a^8*(2*b^4+5*b^2*c^2+5*c^4)+a^2*(b^2-c^2)^2*(2*b^6-b^4*c^2+2*b^2*c^4-c^6)+a^4*(-2*b^8+3*b^6*c^2-6*b^2*c^6+c^8)) : :

X(54600) lies on these lines: {30, 43665}, {98, 2420}, {511, 2394}, {538, 43673}, {542, 46040}, {2782, 14223}, {4230, 16080}, {5969, 52459}

X(54600) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(511)}}, {{A, B, C, X(538), X(1503)}}, {{A, B, C, X(542), X(2782)}}, {{A, B, C, X(2710), X(53221)}}, {{A, B, C, X(2794), X(5969)}}, {{A, B, C, X(3228), X(41174)}}, {{A, B, C, X(11645), X(32515)}}, {{A, B, C, X(14356), X(52632)}}

X(54601) = X(30)X(43666)∩X(5189)X(10185)

Barycentrics    (3*a^6-3*(b^2-c^2)^3-3*a^4*(3*b^2+c^2)+a^2*(9*b^4-5*b^2*c^2-3*c^4))*(3*a^6+3*(b^2-c^2)^3-3*a^4*(b^2+3*c^2)+a^2*(-3*b^4-5*b^2*c^2+9*c^4)) : :

X(54601) lies on these lines: {30, 43666}, {5189, 10185}, {7394, 53098}, {7608, 37349}

X(54601) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(97), X(17505)}}, {{A, B, C, X(288), X(18363)}}, {{A, B, C, X(11588), X(13418)}}, {{A, B, C, X(37192), X(50687)}}, {{A, B, C, X(37349), X(52281)}}

X(54602) = X(30)X(43667)∩X(543)X(5466)

Barycentrics    (4*a^8-2*b^8+4*b^6*c^2+9*b^4*c^4-11*b^2*c^6+4*c^8-a^6*(11*b^2+5*c^2)+3*a^4*(3*b^4+5*b^2*c^2)+a^2*(4*b^6-30*b^4*c^2+15*b^2*c^4-5*c^6))*(4*a^8+4*b^8-11*b^6*c^2+9*b^4*c^4+4*b^2*c^6-2*c^8-a^6*(5*b^2+11*c^2)+3*a^4*(5*b^2*c^2+3*c^4)+a^2*(-5*b^6+15*b^4*c^2-30*b^2*c^4+4*c^6)) : :

X(54602) lies on these lines: {30, 43667}, {524, 9180}, {542, 43674}, {543, 5466}, {671, 9182}, {9166, 52940}, {14223, 52229}

X(54602) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(99), X(524)}}, {{A, B, C, X(115), X(9166)}}, {{A, B, C, X(148), X(41134)}}, {{A, B, C, X(538), X(9830)}}, {{A, B, C, X(542), X(52229)}}, {{A, B, C, X(690), X(9164)}}, {{A, B, C, X(3849), X(5969)}}, {{A, B, C, X(4590), X(51226)}}, {{A, B, C, X(6094), X(39450)}}, {{A, B, C, X(14061), X(41135)}}, {{A, B, C, X(50639), X(51224)}}
X(54602) = trilinear pole of line {1641, 523}
X(54602) = X(i)-cross conjugate of X(j) for these {i, j}: {44397, 2}

X(54603) = X(30)X(43668)∩X(538)X(5466)

Barycentrics    (2*a^6*(b^2+c^2)-b^2*c^2*(b^4+5*b^2*c^2-2*c^4)-a^4*(5*b^4+5*b^2*c^2+2*c^4)-a^2*(b^6-16*b^4*c^2+5*b^2*c^4-2*c^6))*(2*b^6*c^2-5*b^4*c^4-b^2*c^6+2*a^6*(b^2+c^2)-a^4*(2*b^4+5*b^2*c^2+5*c^4)+a^2*(2*b^6-5*b^4*c^2+16*b^2*c^4-c^6)) : :

X(54603) lies on these lines: {30, 43668}, {511, 43674}, {538, 5466}, {671, 23342}, {2782, 43667}, {5969, 9180}, {43665, 52229}

X(54603) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(511), X(52229)}}, {{A, B, C, X(524), X(538)}}, {{A, B, C, X(543), X(5969)}}, {{A, B, C, X(694), X(14609)}}, {{A, B, C, X(698), X(3849)}}, {{A, B, C, X(14608), X(39292)}}
X(54603) = trilinear pole of line {45672, 523}

X(54604) = X(30)X(43670)∩X(376)X(801)

Barycentrics    (a^8-(b^2-c^2)^3*(5*b^2+c^2)+2*a^6*(b^2+4*c^2)-2*a^4*(6*b^4-11*b^2*c^2+9*c^4)+2*a^2*(7*b^6-22*b^4*c^2+11*b^2*c^4+4*c^6))*(a^8+2*a^6*(4*b^2+c^2)+(b^2-c^2)^3*(b^2+5*c^2)-2*a^4*(9*b^4-11*b^2*c^2+6*c^4)+2*a^2*(4*b^6+11*b^4*c^2-22*b^2*c^4+7*c^6)) : :

X(54604) lies on these lines: {30, 43670}, {376, 801}, {3545, 37874}, {3590, 6812}, {3591, 6814}, {5656, 7612}, {6622, 16080}

X(54604) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(6622)}}, {{A, B, C, X(64), X(36889)}}, {{A, B, C, X(74), X(41489)}}, {{A, B, C, X(235), X(376)}}, {{A, B, C, X(1138), X(36612)}}, {{A, B, C, X(1141), X(18847)}}, {{A, B, C, X(1294), X(36611)}}, {{A, B, C, X(1494), X(6526)}}, {{A, B, C, X(1593), X(3545)}}, {{A, B, C, X(1989), X(43695)}}, {{A, B, C, X(6823), X(7714)}}, {{A, B, C, X(13381), X(45011)}}, {{A, B, C, X(15740), X(17703)}}, {{A, B, C, X(15749), X(46087)}}, {{A, B, C, X(16835), X(18854)}}, {{A, B, C, X(34208), X(35512)}}

X(54605) = X(30)X(43671)∩X(542)X(13576)

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

X(54605) lies on these lines: {30, 43671}, {542, 13576}, {918, 14223}, {2826, 9180}, {6054, 19635}

X(54605) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(542), X(918)}}, {{A, B, C, X(543), X(2826)}}, {{A, B, C, X(2862), X(9141)}}

X(54606) = X(30)X(43673)∩X(1503)X(2394)

Barycentrics    (4*a^12+3*a^4*b^2*c^2*(b^2-c^2)^2+6*a^8*c^2*(b^2+c^2)-3*a^10*(b^2+3*c^2)-3*a^2*(b^2-c^2)^3*(b^4+b^2*c^2+c^4)-a^6*(2*b^6-3*b^4*c^2+3*b^2*c^4+2*c^6)+(b^2-c^2)^3*(4*b^6+3*b^4*c^2+3*b^2*c^4+2*c^6))*(4*a^12+3*a^4*b^2*c^2*(b^2-c^2)^2+6*a^8*b^2*(b^2+c^2)-3*a^10*(3*b^2+c^2)+3*a^2*(b^2-c^2)^3*(b^4+b^2*c^2+c^4)-a^6*(2*b^6+3*b^4*c^2-3*b^2*c^4+2*c^6)-(b^2-c^2)^3*(2*b^6+3*b^4*c^2+3*b^2*c^4+4*c^6)) : :

X(54606) lies on these lines: {30, 43673}, {542, 52459}, {1503, 2394}, {2409, 16080}, {2794, 14223}

X(54606) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(935)}}, {{A, B, C, X(67), X(35906)}}, {{A, B, C, X(265), X(2419)}}, {{A, B, C, X(477), X(17986)}}, {{A, B, C, X(542), X(2794)}}, {{A, B, C, X(10735), X(34156)}}
X(54606) = trilinear pole of line {6793, 523}
X(54606) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 2394}

X(54607) = X(2)X(5914)∩X(111)X(5503)

Barycentrics    (a^2+b^2-2*c^2)*(a^2-2*b^2+c^2)*(4*a^4+4*b^4-b^2*c^2+c^4-a^2*(7*b^2+c^2))*(4*a^4+b^4-b^2*c^2+4*c^4-a^2*(b^2+7*c^2)) : :

X(54607) lies on these lines: {2, 5914}, {30, 43674}, {98, 42008}, {111, 5503}, {524, 5466}, {542, 43667}, {543, 9168}, {671, 5468}, {2394, 52229}, {5485, 14916}, {8781, 52141}, {11645, 43668}, {31125, 43535}

X(54607) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(52229)}}, {{A, B, C, X(352), X(52198)}}, {{A, B, C, X(511), X(32583)}}, {{A, B, C, X(524), X(892)}}, {{A, B, C, X(538), X(3849)}}, {{A, B, C, X(543), X(34760)}}, {{A, B, C, X(732), X(35359)}}, {{A, B, C, X(1641), X(18007)}}, {{A, B, C, X(1992), X(14916)}}, {{A, B, C, X(2770), X(9487)}}, {{A, B, C, X(5967), X(34898)}}, {{A, B, C, X(5969), X(9830)}}, {{A, B, C, X(9168), X(17948)}}, {{A, B, C, X(10557), X(53374)}}, {{A, B, C, X(45294), X(51226)}}, {{A, B, C, X(52141), X(52450)}}
X(54607) = trilinear pole of line {2482, 9164}
X(54607) = X(i)-isoconjugate-of-X(j) for these {i, j}: {922, 9166}, {36060, 52467}
X(54607) = X(i)-Dao conjugate of X(j) for these {i, j}: {1560, 52467}, {39061, 9166}
X(54607) = X(i)-cross conjugate of X(j) for these {i, j}: {1641, 2}, {18007, 892}
X(54607) = barycentric product X(i)*X(j) for these (i, j): {671, 9164}
X(54607) = barycentric quotient X(i)/X(j) for these (i, j): {468, 52467}, {671, 9166}, {9164, 524}

X(54608) = X(30)X(43676)∩X(76)X(3534)

Barycentrics    (7*a^4+7*b^4-5*b^2*c^2-2*c^4+a^2*(4*b^2-5*c^2))*(7*a^4-2*b^4-5*b^2*c^2+7*c^4+a^2*(-5*b^2+4*c^2)) : :

X(54608) lies on these lines: {30, 43676}, {76, 3534}, {83, 5066}, {381, 53102}, {542, 35005}, {549, 10159}, {671, 33699}, {1503, 53104}, {2394, 32478}, {2996, 15640}, {3830, 53105}, {3845, 53109}, {5055, 43527}, {5485, 47102}, {10155, 53015}, {10302, 15759}, {12101, 33698}, {15683, 43681}, {15698, 18840}, {18843, 41099}

X(54608) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(3534)}}, {{A, B, C, X(30), X(32478)}}, {{A, B, C, X(66), X(46204)}}, {{A, B, C, X(427), X(5066)}}, {{A, B, C, X(428), X(549)}}, {{A, B, C, X(468), X(33699)}}, {{A, B, C, X(1494), X(2980)}}, {{A, B, C, X(1799), X(13623)}}, {{A, B, C, X(3425), X(44763)}}, {{A, B, C, X(3830), X(37453)}}, {{A, B, C, X(5055), X(5064)}}, {{A, B, C, X(5966), X(16835)}}, {{A, B, C, X(6353), X(15640)}}, {{A, B, C, X(6995), X(15698)}}, {{A, B, C, X(7714), X(10304)}}, {{A, B, C, X(8884), X(18317)}}, {{A, B, C, X(10301), X(15759)}}, {{A, B, C, X(11058), X(17983)}}, {{A, B, C, X(13622), X(32085)}}, {{A, B, C, X(29322), X(43691)}}, {{A, B, C, X(36616), X(43656)}}, {{A, B, C, X(44957), X(47311)}}, {{A, B, C, X(45819), X(48911)}}
X(54608) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 53104}

X(54609) = X(30)X(43677)∩X(2394)X(6002)

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

X(54609) lies on these lines: {30, 43677}, {2394, 6002}, {28840, 43673}

X(54609) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(6002)}}, {{A, B, C, X(1503), X(28840)}}

X(54610) = X(4)X(52950)∩X(22)X(16080)

Barycentrics    (2*a^10-3*a^8*b^2-2*a^6*(b^4+c^4)-(b^2-c^2)^3*(b^4+3*b^2*c^2+2*c^4)+a^4*(4*b^6+6*b^2*c^4-2*c^6))*(2*a^10-3*a^8*c^2-2*a^6*(b^4+c^4)+(b^2-c^2)^3*(2*b^4+3*b^2*c^2+c^4)+a^4*(-2*b^6+6*b^4*c^2+4*c^6)) : :

X(54610) lies on these lines: {4, 52950}, {22, 16080}, {30, 43678}, {76, 52069}, {459, 34608}, {2052, 34603}, {2394, 8673}, {5133, 43530}, {7503, 10159}, {13160, 43527}, {16277, 34775}

X(54610) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(34603)}}, {{A, B, C, X(20), X(34608)}}, {{A, B, C, X(22), X(30)}}, {{A, B, C, X(25), X(52069)}}, {{A, B, C, X(68), X(34168)}}, {{A, B, C, X(251), X(16263)}}, {{A, B, C, X(265), X(18018)}}, {{A, B, C, X(305), X(2697)}}, {{A, B, C, X(376), X(7500)}}, {{A, B, C, X(381), X(5133)}}, {{A, B, C, X(427), X(18434)}}, {{A, B, C, X(428), X(7503)}}, {{A, B, C, X(1176), X(34570)}}, {{A, B, C, X(1297), X(18848)}}, {{A, B, C, X(1494), X(18124)}}, {{A, B, C, X(3534), X(37900)}}, {{A, B, C, X(3543), X(7494)}}, {{A, B, C, X(3830), X(7495)}}, {{A, B, C, X(5064), X(13160)}}, {{A, B, C, X(7387), X(52397)}}, {{A, B, C, X(9909), X(12225)}}, {{A, B, C, X(13575), X(18850)}}, {{A, B, C, X(15760), X(31133)}}, {{A, B, C, X(31152), X(47096)}}, {{A, B, C, X(34775), X(41375)}}, {{A, B, C, X(44210), X(52842)}}
X(54610) = trilinear pole of line {14396, 523}

X(54611) = X(30)X(43679)∩X(30506)X(43530)

Barycentrics    (-3*b^2*c^2*(b^2-c^2)^3+3*a^8*(b^2+c^2)-a^2*(b^2-c^2)^2*(3*b^4-2*b^2*c^2-3*c^4)-a^6*(9*b^4+4*b^2*c^2+3*c^4)+a^4*(9*b^6-4*b^4*c^2+2*b^2*c^4-3*c^6))*(3*b^2*c^2*(b^2-c^2)^3+3*a^8*(b^2+c^2)+a^2*(b^2-c^2)^2*(3*b^4+2*b^2*c^2-3*c^4)-a^6*(3*b^4+4*b^2*c^2+9*c^4)+a^4*(-3*b^6+2*b^4*c^2-4*b^2*c^4+9*c^6)) : :

X(54611) lies on these lines: {30, 43679}, {30506, 43530}

X(54611) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(381), X(30506)}}, {{A, B, C, X(8795), X(34570)}}, {{A, B, C, X(14941), X(17505)}}, {{A, B, C, X(21400), X(53174)}}

X(54612) = X(30)X(43681)∩X(76)X(11001)

Barycentrics    (13*a^4+13*b^4-8*b^2*c^2-5*c^4+2*a^2*(5*b^2-4*c^2))*(13*a^4-5*b^4-8*b^2*c^2+13*c^4+a^2*(-8*b^2+10*c^2)) : :

X(54612) lies on these lines: {30, 43681}, {76, 11001}, {83, 41106}, {1503, 10155}, {2996, 15682}, {3524, 10159}, {3830, 38259}, {3845, 18845}, {5071, 43527}, {5395, 41099}, {18840, 19708}, {53015, 53104}

X(54612) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(11001)}}, {{A, B, C, X(251), X(20421)}}, {{A, B, C, X(264), X(46212)}}, {{A, B, C, X(376), X(7714)}}, {{A, B, C, X(427), X(41106)}}, {{A, B, C, X(428), X(3524)}}, {{A, B, C, X(2980), X(36611)}}, {{A, B, C, X(3426), X(36616)}}, {{A, B, C, X(3830), X(38282)}}, {{A, B, C, X(3845), X(52299)}}, {{A, B, C, X(5064), X(5071)}}, {{A, B, C, X(6353), X(15682)}}, {{A, B, C, X(6995), X(19708)}}, {{A, B, C, X(8770), X(13603)}}, {{A, B, C, X(8889), X(41099)}}, {{A, B, C, X(11270), X(14486)}}, {{A, B, C, X(14489), X(46848)}}, {{A, B, C, X(16774), X(34288)}}, {{A, B, C, X(18847), X(40413)}}, {{A, B, C, X(22334), X(43662)}}
X(54612) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 10155}

X(54613) = X(30)X(43682)∩X(2394)X(35057)

Barycentrics    (a^2+a*b+b^2-c^2)*(a^2-b^2+a*c+c^2)*(2*a^6+b^6-2*a^5*c-3*b^2*c^4+2*c^6+a*c*(b+c)^2*(b^2+b*c-2*c^2)-a^4*(3*b^2+3*b*c+2*c^2)+a^3*c*(b^2+3*b*c+4*c^2)+a^2*c*(3*b^3+8*b^2*c+3*b*c^2-2*c^3))*(2*a^6-2*a^5*b+2*b^6-3*b^4*c^2+c^6-a*b*(b+c)^2*(2*b^2-b*c-c^2)+a^3*b*(4*b^2+3*b*c+c^2)-a^4*(2*b^2+3*b*c+3*c^2)+a^2*b*(-2*b^3+3*b^2*c+8*b*c^2+3*c^3)) : :

X(54613) lies on these lines: {30, 43682}, {2394, 35057}, {11107, 16080}

X(54613) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(30)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3058), X(48897)}}, {{A, B, C, X(5434), X(52524)}}, {{A, B, C, X(5627), X(6757)}}, {{A, B, C, X(12699), X(49744)}}, {{A, B, C, X(31162), X(49745)}}, {{A, B, C, X(35049), X(39273)}}, {{A, B, C, X(37631), X(41869)}}, {{A, B, C, X(49743), X(50865)}}

X(54614) = X(30)X(43688)∩X(76)X(11645)

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

X(54614) lies on these lines: {30, 43688}, {76, 11645}, {542, 10290}, {671, 48884}, {1916, 9878}, {2394, 25423}, {5466, 30217}, {5503, 8178}, {10159, 11178}

X(54614) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(25423)}}, {{A, B, C, X(74), X(18898)}}, {{A, B, C, X(512), X(11645)}}, {{A, B, C, X(524), X(30217)}}, {{A, B, C, X(2980), X(5641)}}, {{A, B, C, X(3426), X(46286)}}, {{A, B, C, X(3849), X(32472)}}, {{A, B, C, X(20421), X(44557)}}, {{A, B, C, X(28470), X(28562)}}, {{A, B, C, X(34288), X(43696)}}

X(54615) = X(30)X(43766)∩X(275)X(13482)

Barycentrics    (3*b^2*c^2*(b^2-c^2)^5+3*a^12*(b^2+c^2)-a^10*(9*b^4+8*b^2*c^2+15*c^4)-a^4*(b^2-c^2)^2*(9*b^6+b^4*c^2-17*b^2*c^4-15*c^6)+a^2*(b^2-c^2)^3*(3*b^6+b^4*c^2-b^2*c^4+3*c^6)+a^8*(6*b^6+17*b^4*c^2+5*b^2*c^4+30*c^6)+2*a^6*(3*b^8-12*b^6*c^2+5*b^4*c^4+3*b^2*c^6-15*c^8))*(-3*b^2*c^2*(b^2-c^2)^5+3*a^12*(b^2+c^2)-a^10*(15*b^4+8*b^2*c^2+9*c^4)+a^4*(b^2-c^2)^2*(15*b^6+17*b^4*c^2-b^2*c^4-9*c^6)-a^2*(b^2-c^2)^3*(3*b^6-b^4*c^2+b^2*c^4+3*c^6)+a^8*(30*b^6+5*b^4*c^2+17*b^2*c^4+6*c^6)+a^6*(-30*b^8+6*b^6*c^2+10*b^4*c^4-24*b^2*c^6+6*c^8)) : :

X(54615) lies on these lines: {30, 43766}, {275, 13482}, {10706, 39284}

X(54615) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(265), X(43767)}}, {{A, B, C, X(3521), X(13482)}}, {{A, B, C, X(33565), X(39985)}}

X(54616) = X(2)X(3793)∩X(4)X(10541)

Barycentrics    (7*a^2+7*b^2+c^2)*(7*a^2+b^2+7*c^2) : :

X(54616) lies on these lines: {2, 3793}, {4, 10541}, {5, 47586}, {30, 43951}, {83, 33230}, {98, 5071}, {262, 3524}, {376, 14484}, {524, 18840}, {597, 5485}, {620, 5503}, {631, 53099}, {671, 3618}, {1285, 15810}, {1916, 14039}, {1992, 10302}, {3090, 43537}, {3407, 33285}, {3424, 3545}, {3525, 7608}, {3544, 53100}, {3589, 18842}, {3590, 7375}, {3591, 7376}, {3800, 5466}, {5032, 16045}, {5067, 7607}, {5395, 33190}, {7770, 43681}, {7784, 18841}, {7790, 33698}, {7792, 11172}, {7803, 53106}, {7841, 18845}, {8370, 38259}, {8781, 33231}, {8859, 32957}, {10159, 21356}, {11001, 14492}, {11148, 14482}, {11167, 14762}, {11303, 43557}, {11304, 43556}, {11606, 32983}, {14069, 43529}, {14458, 41106}, {14494, 15702}, {14535, 16509}, {32951, 43528}, {32952, 41133}, {33224, 35005}, {33232, 53102}, {45964, 50739}

X(54616) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(10541)}}, {{A, B, C, X(6), X(21309)}}, {{A, B, C, X(69), X(47352)}}, {{A, B, C, X(297), X(5071)}}, {{A, B, C, X(376), X(52288)}}, {{A, B, C, X(419), X(14039)}}, {{A, B, C, X(420), X(32983)}}, {{A, B, C, X(427), X(33230)}}, {{A, B, C, X(458), X(3524)}}, {{A, B, C, X(460), X(33231)}}, {{A, B, C, X(524), X(3618)}}, {{A, B, C, X(597), X(1992)}}, {{A, B, C, X(989), X(36603)}}, {{A, B, C, X(1000), X(34914)}}, {{A, B, C, X(3296), X(34892)}}, {{A, B, C, X(3525), X(52281)}}, {{A, B, C, X(3545), X(52283)}}, {{A, B, C, X(3589), X(21356)}}, {{A, B, C, X(3619), X(48310)}}, {{A, B, C, X(5032), X(51171)}}, {{A, B, C, X(5067), X(52282)}}, {{A, B, C, X(5117), X(33285)}}, {{A, B, C, X(5551), X(30701)}}, {{A, B, C, X(5641), X(8797)}}, {{A, B, C, X(5650), X(22112)}}, {{A, B, C, X(6531), X(52188)}}, {{A, B, C, X(7714), X(16045)}}, {{A, B, C, X(7792), X(9770)}}, {{A, B, C, X(7841), X(52299)}}, {{A, B, C, X(8370), X(38282)}}, {{A, B, C, X(8753), X(39951)}}, {{A, B, C, X(8889), X(33190)}}, {{A, B, C, X(9154), X(9164)}}, {{A, B, C, X(9487), X(36953)}}, {{A, B, C, X(9515), X(11166)}}, {{A, B, C, X(11001), X(52289)}}, {{A, B, C, X(11148), X(37863)}}, {{A, B, C, X(11175), X(46123)}}, {{A, B, C, X(11331), X(41106)}}, {{A, B, C, X(14491), X(40802)}}, {{A, B, C, X(14621), X(18490)}}, {{A, B, C, X(14928), X(36890)}}, {{A, B, C, X(14929), X(36889)}}, {{A, B, C, X(15740), X(34897)}}, {{A, B, C, X(18852), X(42330)}}, {{A, B, C, X(23055), X(42849)}}, {{A, B, C, X(30712), X(36954)}}, {{A, B, C, X(36882), X(43696)}}, {{A, B, C, X(39389), X(41394)}}, {{A, B, C, X(42287), X(51737)}}, {{A, B, C, X(44556), X(44571)}}, {{A, B, C, X(46290), X(52695)}}
X(54616) = trilinear pole of line {47312, 523}

X(54617) = X(18)X(22491)∩X(30)X(43953)

Barycentrics    1 / (-a^2 + 2*b^2 + 2*c^2 - Sqrt[3]*S) : :

X(54617) lies on these lines: {18, 22491}, {30, 43953}, {671, 37641}, {1992, 9113}, {5485, 37785}, {10188, 47520}, {14848, 43954}, {32985, 33474}, {42035, 52021}, {43545, 50855}

X(54617) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(524), X(11080)}}

X(54618) = X(17)X(22492)∩X(30)X(43954)

Barycentrics    1 / (-a^2 + 2*b^2 + 2*c^2 + Sqrt[3]*S) : :

X(54618) lies on these lines: {17, 22492}, {30, 43954}, {671, 37640}, {1992, 9112}, {5485, 37786}, {10187, 47518}, {14848, 43953}, {32985, 33475}, {42036, 52022}, {43544, 50858}

X(54618) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(524), X(11085)}}

X(54619) = X(30)X(4444)∩X(740)X(2394)

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

X(54619) lies on these lines: {30, 4444}, {516, 4049}, {740, 2394}, {2398, 4080}, {28845, 35353}

X(54619) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(740)}}, {{A, B, C, X(80), X(39293)}}, {{A, B, C, X(515), X(28580)}}, {{A, B, C, X(516), X(519)}}, {{A, B, C, X(517), X(752)}}, {{A, B, C, X(518), X(28854)}}, {{A, B, C, X(527), X(28849)}}, {{A, B, C, X(528), X(28850)}}, {{A, B, C, X(536), X(28845)}}, {{A, B, C, X(545), X(28877)}}, {{A, B, C, X(2724), X(35168)}}, {{A, B, C, X(2784), X(2796)}}, {{A, B, C, X(4715), X(28889)}}, {{A, B, C, X(5847), X(28194)}}, {{A, B, C, X(9041), X(28893)}}, {{A, B, C, X(17764), X(28204)}}, {{A, B, C, X(17772), X(28198)}}, {{A, B, C, X(28503), X(28866)}}, {{A, B, C, X(28534), X(28870)}}, {{A, B, C, X(28538), X(28862)}}, {{A, B, C, X(28542), X(28901)}}
X(54619) = trilinear pole of line {51406, 523}

X(54620) = X(2)X(13202)∩X(30)X(44877)

Barycentrics    (7*a^8+a^6*(-13*b^2+2*c^2)-(b^2-c^2)^3*(8*b^2+7*c^2)+a^4*(-3*b^4+25*b^2*c^2-18*c^4)+a^2*(17*b^6-44*b^4*c^2+25*b^2*c^4+2*c^6))*(7*a^8+a^6*(2*b^2-13*c^2)+(b^2-c^2)^3*(7*b^2+8*c^2)+a^4*(-18*b^4+25*b^2*c^2-3*c^4)+a^2*(2*b^6+25*b^4*c^2-44*b^2*c^4+17*c^6)) : :

X(54620) lies on these lines: {2, 13202}, {30, 44877}, {2996, 39358}, {10151, 16080}, {43530, 44438}

X(54620) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(10151)}}, {{A, B, C, X(381), X(44438)}}, {{A, B, C, X(1294), X(5627)}}, {{A, B, C, X(1494), X(11744)}}, {{A, B, C, X(3426), X(22455)}}, {{A, B, C, X(9139), X(50531)}}, {{A, B, C, X(11410), X(14269)}}

X(54621) = X(30)X(45092)∩X(39)X(34087)

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

X(54621) lies on these lines: {30, 45092}, {39, 34087}, {76, 52961}, {83, 33875}, {538, 40016}, {7757, 40162}, {9466, 31630}, {9764, 40831}

X(54621) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(39), X(538)}}, {{A, B, C, X(194), X(7757)}}, {{A, B, C, X(3228), X(27375)}}, {{A, B, C, X(3934), X(9466)}}, {{A, B, C, X(5286), X(9764)}}, {{A, B, C, X(5309), X(8149)}}, {{A, B, C, X(6309), X(7739)}}, {{A, B, C, X(6683), X(14711)}}, {{A, B, C, X(7827), X(9865)}}, {{A, B, C, X(9495), X(42548)}}, {{A, B, C, X(39968), X(41440)}}
X(54621) = trilinear pole of line {14406, 523}

X(54622) = X(10)X(30332)∩X(30)X(45097)

Barycentrics    (7*a^2+7*b^2-2*b*c-5*c^2-2*a*(b+c))*(7*a^2-5*b^2-2*b*c+7*c^2-2*a*(b+c)) : :

X(54622) lies on these lines: {10, 30332}, {30, 45097}, {3543, 43672}, {21554, 53098}, {36728, 45098}, {43531, 50736}

X(54622) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(80), X(50836)}}, {{A, B, C, X(277), X(17501)}}, {{A, B, C, X(279), X(1121)}}, {{A, B, C, X(469), X(50736)}}, {{A, B, C, X(1016), X(36606)}}, {{A, B, C, X(1170), X(33576)}}, {{A, B, C, X(1509), X(46872)}}, {{A, B, C, X(2994), X(38009)}}, {{A, B, C, X(3543), X(26003)}}, {{A, B, C, X(3839), X(37448)}}, {{A, B, C, X(4866), X(39948)}}, {{A, B, C, X(5032), X(50074)}}, {{A, B, C, X(5560), X(10405)}}, {{A, B, C, X(8813), X(31371)}}, {{A, B, C, X(14377), X(36605)}}, {{A, B, C, X(17297), X(37681)}}

X(54623) = X(30)X(45098)∩X(2051)X(3543)

Barycentrics    (7*a^2+7*b^2+2*b*c-5*c^2+2*a*(b+c))*(7*a^2-5*b^2+2*b*c+7*c^2+2*a*(b+c)) : :

X(54623) lies on these lines: {30, 45098}, {226, 38314}, {321, 31145}, {2047, 43565}, {2051, 3543}, {3623, 4080}, {3839, 13478}, {4052, 51093}, {6998, 53098}, {7390, 7608}, {7407, 7607}, {17677, 18841}, {30588, 46934}, {36722, 45097}, {37144, 43446}, {37145, 43447}, {37654, 43533}, {45100, 50687}

X(54623) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(31145)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(1120)}}, {{A, B, C, X(8), X(38314)}}, {{A, B, C, X(80), X(30712)}}, {{A, B, C, X(145), X(5557)}}, {{A, B, C, X(519), X(3296)}}, {{A, B, C, X(903), X(1219)}}, {{A, B, C, X(996), X(36606)}}, {{A, B, C, X(1220), X(36588)}}, {{A, B, C, X(1509), X(36605)}}, {{A, B, C, X(3017), X(27571)}}, {{A, B, C, X(3241), X(20050)}}, {{A, B, C, X(3543), X(11109)}}, {{A, B, C, X(3616), X(51072)}}, {{A, B, C, X(3679), X(17501)}}, {{A, B, C, X(3839), X(17555)}}, {{A, B, C, X(3945), X(37654)}}, {{A, B, C, X(4373), X(5561)}}, {{A, B, C, X(4678), X(51108)}}, {{A, B, C, X(5032), X(50133)}}, {{A, B, C, X(5551), X(35577)}}, {{A, B, C, X(6553), X(43733)}}, {{A, B, C, X(6994), X(37150)}}, {{A, B, C, X(7378), X(17677)}}, {{A, B, C, X(7390), X(52281)}}, {{A, B, C, X(7407), X(52282)}}, {{A, B, C, X(7518), X(11113)}}, {{A, B, C, X(17313), X(37681)}}, {{A, B, C, X(19875), X(46930)}}, {{A, B, C, X(20052), X(51104)}}, {{A, B, C, X(24857), X(43731)}}, {{A, B, C, X(24858), X(43732)}}, {{A, B, C, X(43734), X(43972)}}

X(54624) = X(10)X(16670)∩X(376)X(2051)

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

X(54624) lies on these lines: {10, 16670}, {30, 45100}, {226, 13462}, {321, 3241}, {376, 2051}, {1751, 50741}, {2047, 3591}, {3524, 45098}, {3545, 13478}, {3621, 27797}, {3622, 4080}, {4049, 28225}, {4052, 51103}, {5395, 17677}, {5550, 30588}, {6998, 53099}, {7380, 43537}, {7407, 47586}, {7410, 7608}, {17313, 18840}, {22235, 37145}, {22237, 37144}, {37150, 43533}

X(54624) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(3241)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(8), X(25055)}}, {{A, B, C, X(29), X(36916)}}, {{A, B, C, X(65), X(39960)}}, {{A, B, C, X(79), X(36588)}}, {{A, B, C, X(80), X(28626)}}, {{A, B, C, X(86), X(1000)}}, {{A, B, C, X(145), X(51103)}}, {{A, B, C, X(376), X(11109)}}, {{A, B, C, X(519), X(3622)}}, {{A, B, C, X(551), X(3621)}}, {{A, B, C, X(903), X(26039)}}, {{A, B, C, X(937), X(39948)}}, {{A, B, C, X(996), X(18490)}}, {{A, B, C, X(1065), X(10307)}}, {{A, B, C, X(1219), X(5551)}}, {{A, B, C, X(1220), X(3296)}}, {{A, B, C, X(1224), X(5556)}}, {{A, B, C, X(3545), X(17555)}}, {{A, B, C, X(3616), X(4677)}}, {{A, B, C, X(3618), X(17313)}}, {{A, B, C, X(3624), X(51068)}}, {{A, B, C, X(3633), X(38314)}}, {{A, B, C, X(3679), X(5550)}}, {{A, B, C, X(3698), X(16408)}}, {{A, B, C, X(3828), X(46931)}}, {{A, B, C, X(4217), X(37168)}}, {{A, B, C, X(5125), X(50741)}}, {{A, B, C, X(5136), X(11111)}}, {{A, B, C, X(5558), X(24858)}}, {{A, B, C, X(5561), X(5936)}}, {{A, B, C, X(7320), X(24857)}}, {{A, B, C, X(7410), X(52281)}}, {{A, B, C, X(7490), X(37150)}}, {{A, B, C, X(7498), X(11113)}}, {{A, B, C, X(7714), X(13740)}}, {{A, B, C, X(8889), X(17677)}}, {{A, B, C, X(9780), X(19876)}}, {{A, B, C, X(16066), X(48817)}}, {{A, B, C, X(17132), X(28316)}}, {{A, B, C, X(29572), X(50287)}}, {{A, B, C, X(33696), X(34595)}}, {{A, B, C, X(39975), X(53114)}}, {{A, B, C, X(39982), X(51223)}}
X(54624) = trilinear pole of line {47768, 523}

X(54625) = X(30)X(45101)∩X(76)X(5861)

Barycentrics    -15*a^4+9*b^4-22*b^2*c^2+9*c^4-10*a^2*(b^2+c^2)-4*(4*a^2+b^2+c^2)*S : :

X(54625) lies on these lines: {30, 45101}, {76, 5861}, {381, 14229}, {591, 5490}, {671, 19054}, {1992, 42023}, {2996, 44647}, {3316, 26619}, {3590, 11294}, {3591, 32489}, {5485, 45420}, {5491, 14033}, {10195, 11292}, {13650, 42024}, {41895, 49262}, {45106, 45545}

X(54625) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5861)}}, {{A, B, C, X(524), X(19054)}}
X(54625) = isogonal conjugate of X(9600)
X(54625) = barycentric quotient X(i)/X(j) for these (i, j): {6, 9600}, {6417, 32565}

X(54626) = X(30)X(45102)∩X(76)X(5860)

Barycentrics    -7*a^6+11*b^6-15*b^4*c^2-15*b^2*c^4+11*c^6-39*a^4*(b^2+c^2)+3*a^2*(b^4-22*b^2*c^2+c^4)+2*(23*a^4-7*b^4+26*b^2*c^2-7*c^4+20*a^2*(b^2+c^2))*S : :

X(54626) lies on these lines: {30, 45102}, {76, 5860}, {381, 14244}, {671, 19053}, {1991, 5491}, {1992, 42024}, {2996, 44648}, {3317, 26620}, {3590, 32488}, {3591, 11293}, {5485, 45421}, {5490, 14033}, {10194, 11291}, {13771, 42023}, {41895, 49261}, {45107, 45544}

X(54626) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5860)}}, {{A, B, C, X(524), X(19053)}}
X(54626) = barycentric quotient X(i)/X(j) for these (i, j): {6418, 32572}

X(54627) = X(2)X(38423)∩X(486)X(597)

Barycentrics    8*a^4-7*b^4+22*b^2*c^2-7*c^4+19*a^2*(b^2+c^2)+6*(5*a^2+2*(b^2+c^2))*S : :

X(54627) lies on these lines: {2, 38423}, {30, 45106}, {76, 13637}, {485, 13663}, {486, 597}, {491, 10302}, {543, 38425}, {599, 31411}, {640, 34089}, {671, 13642}, {1992, 5490}, {3068, 5485}, {5503, 19058}, {8355, 31415}, {10194, 13783}, {10195, 11315}, {11167, 13638}, {13846, 42024}, {32787, 42023}

X(54627) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(491), X(597)}}, {{A, B, C, X(1659), X(34892)}}, {{A, B, C, X(1992), X(3068)}}, {{A, B, C, X(14121), X(34914)}}
X(54627) = midpoint of X(i) in X(j) for these {i,j}: {2, 38423}

X(54628) = X(2)X(38424)∩X(485)X(597)

Barycentrics    8*a^4-7*b^4+22*b^2*c^2-7*c^4+19*a^2*(b^2+c^2)-6*(5*a^2+2*(b^2+c^2))*S : :

X(54628) lies on these lines: {2, 38424}, {30, 45107}, {76, 13757}, {485, 597}, {486, 13783}, {492, 10302}, {543, 38426}, {639, 34091}, {671, 13761}, {1992, 5491}, {3069, 5485}, {5503, 19057}, {8355, 31415}, {10194, 11316}, {10195, 13663}, {11167, 13758}, {13847, 42023}, {32788, 42024}

X(54628) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(492), X(597)}}, {{A, B, C, X(1992), X(3069)}}, {{A, B, C, X(7090), X(34914)}}, {{A, B, C, X(13390), X(34892)}}
X(54628) = midpoint of X(i) in X(j) for these {i,j}: {2, 38424}

X(54629) = X(4)X(16622)∩X(30)X(45300)

Barycentrics    (a^6+(b^2-2*c^2)*(b^2-c^2)^2-a^4*(b^2+4*c^2)-a^2*(b^4+8*b^2*c^2-5*c^4))*(a^6-(b^2-c^2)^2*(2*b^2-c^2)-a^4*(4*b^2+c^2)+a^2*(5*b^4-8*b^2*c^2-c^4)) : :

X(54629) lies on these lines: {4, 16622}, {30, 45300}, {262, 34609}, {381, 13380}, {1368, 7608}, {5020, 7607}, {7396, 53099}, {7398, 43537}, {13599, 16072}, {41235, 43527}

X(54629) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(458), X(34609)}}, {{A, B, C, X(1368), X(52281)}}, {{A, B, C, X(5020), X(52282)}}, {{A, B, C, X(5064), X(41235)}}, {{A, B, C, X(6330), X(52395)}}, {{A, B, C, X(14615), X(36889)}}, {{A, B, C, X(15319), X(35061)}}, {{A, B, C, X(16620), X(16622)}}, {{A, B, C, X(31180), X(52253)}}, {{A, B, C, X(35140), X(46104)}}, {{A, B, C, X(39289), X(46111)}}
X(54629) = trilinear pole of line {46451, 523}

X(54630) = X(30)X(45964)∩X(6830)X(7607)

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

X(54630) lies on these lines: {30, 45964}, {6830, 7607}, {6844, 43537}, {6880, 53098}, {6905, 7608}, {13576, 18407}, {50701, 53099}

X(54630) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(4231), X(8370)}}, {{A, B, C, X(6830), X(52282)}}, {{A, B, C, X(6905), X(52281)}}, {{A, B, C, X(18407), X(46108)}}, {{A, B, C, X(28459), X(31926)}}, {{A, B, C, X(39979), X(44835)}}

X(54631) = X(2)X(42743)∩X(30)X(46040)

Barycentrics    (2*a^12*(b^2+c^2)+b^2*c^2*(b^2-c^2)^3*(2*b^4+c^4)-a^10*(3*b^4+7*b^2*c^2+6*c^4)+a^8*(b^6+8*b^4*c^2+8*b^2*c^4+7*c^6)+a^6*(b^8-6*b^6*c^2-3*b^4*c^4-3*b^2*c^6-5*c^8)+a^2*(b^2-c^2)^2*(2*b^8-3*b^6*c^2-c^8)-a^4*(3*b^10-8*b^8*c^2+3*b^6*c^4+b^2*c^8-3*c^10))*(2*a^12*(b^2+c^2)-b^2*c^2*(b^2-c^2)^3*(b^4+2*c^4)-a^10*(6*b^4+7*b^2*c^2+3*c^4)+a^8*(7*b^6+8*b^4*c^2+8*b^2*c^4+c^6)-a^2*(b^2-c^2)^2*(b^8+3*b^2*c^6-2*c^8)+a^6*(-5*b^8-3*b^6*c^2-3*b^4*c^4-6*b^2*c^6+c^8)+a^4*(3*b^10-b^8*c^2-3*b^4*c^6+8*b^2*c^8-3*c^10)) : :

X(54631) lies on these lines: {2, 42743}, {30, 46040}, {511, 14223}, {538, 52459}, {542, 43665}, {2394, 2782}, {5969, 43673}

X(54631) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(2782)}}, {{A, B, C, X(110), X(511)}}, {{A, B, C, X(538), X(2794)}}, {{A, B, C, X(1503), X(5969)}}, {{A, B, C, X(18020), X(47110)}}, {{A, B, C, X(27867), X(40083)}}

X(54632) = X(2)X(16165)∩X(4)X(52951)

Barycentrics    (2*a^10-3*a^8*c^2+a^2*b^2*c^2*(b^2-c^2)^2+a^6*(-2*b^4+b^2*c^2-2*c^4)+(b^2-c^2)^3*(2*b^4+3*b^2*c^2+c^4)-2*a^4*(b^6-2*b^4*c^2+b^2*c^4-2*c^6))*(2*a^10-3*a^8*b^2+a^2*b^2*c^2*(b^2-c^2)^2+a^6*(-2*b^4+b^2*c^2-2*c^4)-(b^2-c^2)^3*(b^4+3*b^2*c^2+2*c^4)+a^4*(4*b^6-2*b^4*c^2+4*b^2*c^4-2*c^6)) : :

X(54632) lies on these lines: {2, 16165}, {4, 52951}, {23, 16080}, {30, 46105}, {2394, 9517}, {3543, 14983}, {5169, 43530}, {10159, 14118}

X(54632) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(23), X(30)}}, {{A, B, C, X(265), X(2697)}}, {{A, B, C, X(376), X(7519)}}, {{A, B, C, X(381), X(5169)}}, {{A, B, C, X(428), X(14118)}}, {{A, B, C, X(1177), X(29180)}}, {{A, B, C, X(1302), X(53639)}}, {{A, B, C, X(1383), X(16263)}}, {{A, B, C, X(1494), X(13573)}}, {{A, B, C, X(1995), X(37077)}}, {{A, B, C, X(3543), X(7493)}}, {{A, B, C, X(3830), X(52300)}}, {{A, B, C, X(5133), X(7565)}}, {{A, B, C, X(6636), X(7540)}}, {{A, B, C, X(7426), X(10296)}}, {{A, B, C, X(7488), X(34603)}}, {{A, B, C, X(9076), X(11744)}}, {{A, B, C, X(10989), X(11799)}}, {{A, B, C, X(15364), X(41890)}}, {{A, B, C, X(18323), X(37907)}}, {{A, B, C, X(18434), X(45096)}}, {{A, B, C, X(18850), X(41896)}}, {{A, B, C, X(22455), X(39955)}}, {{A, B, C, X(29011), X(46429)}}, {{A, B, C, X(31304), X(34608)}}, {{A, B, C, X(40102), X(46255)}}

X(54633) = X(2)X(12295)∩X(30)X(46201)

Barycentrics    (7*a^8-a^6*(15*b^2+2*c^2)-(b^2-c^2)^3*(6*b^2+7*c^2)+a^4*(3*b^4+17*b^2*c^2-10*c^4)+a^2*(11*b^6-26*b^4*c^2+17*b^2*c^4-2*c^6))*(7*a^8+(b^2-c^2)^3*(7*b^2+6*c^2)-a^6*(2*b^2+15*c^2)+a^4*(-10*b^4+17*b^2*c^2+3*c^4)+a^2*(-2*b^6+17*b^4*c^2-26*b^2*c^4+11*c^6)) : :

X(54633) lies on these lines: {2, 12295}, {30, 46201}

X(54633) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(15036)}}, {{A, B, C, X(265), X(38726)}}, {{A, B, C, X(895), X(46429)}}, {{A, B, C, X(1173), X(22455)}}, {{A, B, C, X(1300), X(12295)}}, {{A, B, C, X(3830), X(18361)}}

X(54634) = X(2)X(41980)∩X(4)X(42725)

Barycentrics    sqrt(2)*(7*a^4-11*(b^2-c^2)^2+4*a^2*(b^2+c^2))+24*a^2*S : :
Barycentrics    1 / (3*Sqrt[2]*(-a^2 + b^2 + c^2) + 4*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (2 + 3*Sqrt[2]*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54634) lies on the Kiepert hyperbola and these lines: {2, 41980}, {4, 42725}, {6, 41099}, {30, 46473}, {376, 42645}, {381, 42726}, {3534, 42647}, {3543, 42783}, {12100, 42729}, {12822, 52666}, {12823, 19054}, {15698, 43622}, {15703, 43628}

X(54635) = X(2)X(41979)∩X(4)X(42726)

Barycentrics    sqrt(2)*(7*a^4-11*(b^2-c^2)^2+4*a^2*(b^2+c^2))-24*a^2*S : :
Barycentrics    1 / (3*Sqrt[2]*(-a^2 + b^2 + c^2) - 4*S) : :    (Peter Moses, July 21, 2023)
Barycentrics    1 / (2 - 3*Sqrt[2]*Cot[A]) : :    (Peter Moses, July 21, 2023)

X(54635) lies on these lines: {2, 41979}, {4, 42726}, {6, 41099}, {30, 46476}, {376, 42646}, {381, 42725}, {3534, 42648}, {3543, 42784}, {12100, 42730}, {12822, 19053}, {12823, 52667}, {15698, 43623}, {15703, 43629}

X(54635) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}

X(54636) = X(4)X(14531)∩X(30)X(46727)

Barycentrics    b^2*c^2*(3*a^4+3*(b^2-c^2)^2-2*a^2*(3*b^2+c^2))*(3*a^4+3*(b^2-c^2)^2-2*a^2*(b^2+3*c^2)) : :
X(54636) Barycentrics    1 / (-2 + 3*Cos[A]^2) : :    (Peter Moses, July 21, 2023)

X(54636) lies on these lines: {4, 14531}, {30, 46727}, {98, 53862}, {275, 37672}, {5395, 51481}, {7499, 7607}, {7539, 7608}, {18841, 40814}, {38253, 52147}, {45793, 53109}

X(54636) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(343), X(9289)}}, {{A, B, C, X(394), X(45187)}}, {{A, B, C, X(1502), X(42298)}}, {{A, B, C, X(6664), X(21969)}}, {{A, B, C, X(7499), X(52282)}}, {{A, B, C, X(7539), X(52281)}}
X(54636) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 3517}, {560, 32829}
X(54636) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 3517}, {6374, 32829}
X(54636) = X(i)-cross conjugate of X(j) for these {i, j}: {631, 264}
X(54636) = barycentric product X(i)*X(j) for these (i, j): {53862, 850}
X(54636) = barycentric quotient X(i)/X(j) for these (i, j): {4, 3517}, {76, 32829}, {53862, 110}

X(54637) = X(2)X(47287)∩X(4)X(15534)

Barycentrics    (5*a^2+5*b^2-13*c^2)*(5*a^2-13*b^2+5*c^2) : :

X(54637) lies on these lines: {2, 47287}, {4, 15534}, {30, 47586}, {76, 50994}, {98, 11001}, {148, 8587}, {262, 41106}, {376, 43537}, {524, 32532}, {543, 10153}, {631, 53859}, {671, 50992}, {1992, 45103}, {3424, 15682}, {3524, 7607}, {3525, 10185}, {3545, 53099}, {3845, 43951}, {5071, 7608}, {5485, 22165}, {5503, 36523}, {7612, 19708}, {7620, 18842}, {7841, 43681}, {7877, 53106}, {8352, 38259}, {8355, 32841}, {9741, 42011}, {10159, 33230}, {10302, 52713}, {11054, 53105}, {11167, 40344}, {11317, 18845}, {14039, 43528}, {14484, 41099}, {14976, 43535}, {18840, 34505}, {33285, 43529}, {41135, 42010}, {41254, 46210}, {41895, 47286}, {43448, 50993}

X(54637) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(50994)}}, {{A, B, C, X(69), X(15534)}}, {{A, B, C, X(297), X(11001)}}, {{A, B, C, X(428), X(33230)}}, {{A, B, C, X(458), X(41106)}}, {{A, B, C, X(524), X(50992)}}, {{A, B, C, X(1992), X(22165)}}, {{A, B, C, X(2987), X(20421)}}, {{A, B, C, X(3524), X(52282)}}, {{A, B, C, X(3618), X(51143)}}, {{A, B, C, X(3926), X(14843)}}, {{A, B, C, X(5071), X(52281)}}, {{A, B, C, X(6330), X(18847)}}, {{A, B, C, X(6464), X(11270)}}, {{A, B, C, X(6531), X(46212)}}, {{A, B, C, X(7714), X(33190)}}, {{A, B, C, X(8352), X(38282)}}, {{A, B, C, X(8584), X(50990)}}, {{A, B, C, X(11317), X(52299)}}, {{A, B, C, X(11738), X(40802)}}, {{A, B, C, X(15077), X(34897)}}, {{A, B, C, X(15682), X(52283)}}, {{A, B, C, X(18818), X(36611)}}, {{A, B, C, X(18851), X(52581)}}, {{A, B, C, X(19708), X(37174)}}, {{A, B, C, X(21356), X(42286)}}, {{A, B, C, X(22336), X(50993)}}, {{A, B, C, X(34892), X(43734)}}, {{A, B, C, X(34914), X(43733)}}, {{A, B, C, X(41099), X(52288)}}, {{A, B, C, X(44556), X(46645)}}
X(54637) = reflection of X(i) in X(j) for these {i,j}: {376, 43537}
X(54637) = X(i)-cross conjugate of X(j) for these {i, j}: {15533, 2}

X(54638) = X(30)X(52459)∩X(2394)X(2794)

Barycentrics    (4*a^14-a^12*(5*b^2+11*c^2)+3*a^10*(b^4+3*b^2*c^2+4*c^4)-a^2*(b^2-c^2)^3*(5*b^6+6*b^4*c^2+6*b^2*c^4+4*c^6)-a^8*(2*b^6+3*b^4*c^2+3*b^2*c^4+8*c^6)+(b^2-c^2)^3*(4*b^8+b^6*c^2+3*b^4*c^4+2*b^2*c^6+2*c^8)+a^6*(-2*b^8+10*b^6*c^2-9*b^4*c^4+b^2*c^6+4*c^8)+3*a^4*(b^10-b^8*c^2-3*b^6*c^4+4*b^4*c^6-c^10))*(4*a^14-a^12*(11*b^2+5*c^2)+3*a^10*(4*b^4+3*b^2*c^2+c^4)-a^8*(8*b^6+3*b^4*c^2+3*b^2*c^4+2*c^6)+a^2*(b^2-c^2)^3*(4*b^6+6*b^4*c^2+6*b^2*c^4+5*c^6)+a^6*(4*b^8+b^6*c^2-9*b^4*c^4+10*b^2*c^6-2*c^8)-(b^2-c^2)^3*(2*b^8+2*b^6*c^2+3*b^4*c^4+b^2*c^6+4*c^8)-3*a^4*(b^10-4*b^6*c^4+3*b^4*c^6+b^2*c^8-c^10)) : :

X(54638) lies on these lines: {30, 52459}, {542, 43673}, {1503, 14223}, {2394, 2794}

X(54638) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(2794)}}, {{A, B, C, X(107), X(9141)}}, {{A, B, C, X(542), X(1503)}}, {{A, B, C, X(30497), X(53639)}}
X(54638) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14223}

X(54639) = X(30)X(52519)∩X(76)X(5032)

Barycentrics    (11*a^2+11*b^2-c^2)*(11*a^2-b^2+11*c^2) : :

X(54639) lies on these lines: {30, 52519}, {76, 5032}, {83, 23334}, {262, 10304}, {549, 14494}, {597, 41895}, {671, 51171}, {3091, 53100}, {3526, 53098}, {3543, 14488}, {3618, 53101}, {5055, 7612}, {5395, 47352}, {7486, 7607}, {7608, 10303}, {7841, 18843}, {8781, 9167}, {9740, 42006}, {10155, 15709}, {10302, 11160}, {14032, 53141}, {14036, 40824}, {14484, 15683}, {14492, 15640}, {15022, 43537}, {15717, 53099}, {32971, 43676}, {32974, 53102}

X(54639) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5032)}}, {{A, B, C, X(458), X(10304)}}, {{A, B, C, X(524), X(51171)}}, {{A, B, C, X(597), X(5486)}}, {{A, B, C, X(2207), X(34572)}}, {{A, B, C, X(3329), X(9740)}}, {{A, B, C, X(3620), X(47352)}}, {{A, B, C, X(5055), X(37174)}}, {{A, B, C, X(6620), X(14036)}}, {{A, B, C, X(7486), X(52282)}}, {{A, B, C, X(9167), X(52450)}}, {{A, B, C, X(10303), X(52281)}}, {{A, B, C, X(15640), X(52289)}}, {{A, B, C, X(15683), X(52288)}}, {{A, B, C, X(23297), X(23334)}}

X(54640) = X(30)X(52583)∩X(459)X(44442)

Barycentrics    (3*a^10-3*a^8*(b^2-c^2)-3*(b^2-c^2)^3*(b^2+c^2)^2-2*a^6*(3*b^4+2*b^2*c^2+3*c^4)+a^2*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4)+2*a^4*(3*b^6+b^4*c^2+7*b^2*c^4-3*c^6))*(3*a^10+3*a^8*(b^2-c^2)+3*(b^2-c^2)^3*(b^2+c^2)^2-2*a^6*(3*b^4+2*b^2*c^2+3*c^4)+a^2*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4)+a^4*(-6*b^6+14*b^4*c^2+2*b^2*c^4+6*c^6)) : :

X(54640) lies on these lines: {30, 52583}, {459, 44442}, {1370, 16080}, {6815, 43527}, {6816, 10159}, {6997, 43530}, {18382, 40178}

X(54640) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(20), X(44442)}}, {{A, B, C, X(30), X(1370)}}, {{A, B, C, X(69), X(34570)}}, {{A, B, C, X(265), X(13575)}}, {{A, B, C, X(376), X(7391)}}, {{A, B, C, X(381), X(6997)}}, {{A, B, C, X(428), X(6816)}}, {{A, B, C, X(1297), X(15077)}}, {{A, B, C, X(1494), X(42484)}}, {{A, B, C, X(2697), X(6340)}}, {{A, B, C, X(3543), X(7386)}}, {{A, B, C, X(3545), X(7394)}}, {{A, B, C, X(3830), X(46336)}}, {{A, B, C, X(3839), X(7392)}}, {{A, B, C, X(5064), X(6815)}}, {{A, B, C, X(5071), X(37349)}}, {{A, B, C, X(5189), X(11001)}}, {{A, B, C, X(5481), X(31371)}}, {{A, B, C, X(6643), X(34603)}}, {{A, B, C, X(7533), X(41106)}}, {{A, B, C, X(10152), X(40186)}}, {{A, B, C, X(14489), X(17505)}}, {{A, B, C, X(15682), X(16063)}}, {{A, B, C, X(16774), X(41894)}}, {{A, B, C, X(18018), X(18850)}}, {{A, B, C, X(18019), X(18847)}}, {{A, B, C, X(18846), X(34168)}}, {{A, B, C, X(32533), X(40801)}}, {{A, B, C, X(34572), X(45011)}}, {{A, B, C, X(34608), X(37444)}}, {{A, B, C, X(34609), X(37201)}}, {{A, B, C, X(34938), X(52397)}}

X(54641) = X(2)X(2682)∩X(30)X(52940)

Barycentrics    (a^8-3*a^6*b^2-2*b^8+6*b^6*c^2-2*b^4*c^4-3*b^2*c^6+c^8+a^4*(-2*b^4+13*b^2*c^2-8*c^4)+a^2*(6*b^6-20*b^4*c^2+13*b^2*c^4))*(a^8+b^8-3*a^6*c^2-3*b^6*c^2-2*b^4*c^4+6*b^2*c^6-2*c^8+a^4*(-8*b^4+13*b^2*c^2-2*c^4)+a^2*(13*b^4*c^2-20*b^2*c^4+6*c^6)) : :

X(54641) lies on these lines: {2, 2682}, {30, 52940}, {2394, 33919}, {14639, 43667}

X(54641) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(2682)}}, {{A, B, C, X(2696), X(5627)}}, {{A, B, C, X(52752), X(53149)}}

X(54642) = X(30)X(53098)∩X(2996)X(15534)

Barycentrics    (19*a^2+19*b^2-17*c^2)*(19*a^2-17*b^2+19*c^2) : :

X(54642) lies on these lines: {30, 53098}, {2996, 15534}, {3091, 10185}, {3543, 7608}, {3830, 14494}, {3832, 53859}, {3839, 7607}, {3845, 7612}, {5032, 32532}, {8352, 18841}, {8781, 36521}, {10155, 15682}, {11167, 19569}, {11317, 18840}, {11669, 15640}, {41099, 53103}, {50687, 53099}

X(54642) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(54), X(11741)}}, {{A, B, C, X(193), X(15534)}}, {{A, B, C, X(251), X(47060)}}, {{A, B, C, X(3543), X(52281)}}, {{A, B, C, X(3839), X(52282)}}, {{A, B, C, X(3845), X(37174)}}, {{A, B, C, X(5032), X(50992)}}, {{A, B, C, X(6995), X(11317)}}, {{A, B, C, X(7378), X(8352)}}, {{A, B, C, X(36521), X(52450)}}, {{A, B, C, X(50994), X(51171)}}

X(54643) = X(2)X(42785)∩X(30)X(53102)

Barycentrics    (2*a^4+2*b^4+5*b^2*c^2-7*c^4+a^2*(14*b^2+5*c^2))*(2*a^4-7*b^4+5*b^2*c^2+2*c^4+a^2*(5*b^2+14*c^2)) : :

X(54643) lies on these lines: {2, 42785}, {30, 53102}, {76, 5066}, {83, 3534}, {381, 43676}, {549, 43527}, {598, 33699}, {3830, 53109}, {3845, 53105}, {5055, 10159}, {5395, 15640}, {5480, 11669}, {8587, 41151}, {15682, 18843}, {15698, 18841}, {43688, 44422}

X(54643) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(5066)}}, {{A, B, C, X(305), X(13623)}}, {{A, B, C, X(427), X(3534)}}, {{A, B, C, X(428), X(5055)}}, {{A, B, C, X(549), X(5064)}}, {{A, B, C, X(1989), X(42785)}}, {{A, B, C, X(3845), X(37453)}}, {{A, B, C, X(5094), X(33699)}}, {{A, B, C, X(5966), X(52518)}}, {{A, B, C, X(7378), X(15698)}}, {{A, B, C, X(8797), X(46212)}}, {{A, B, C, X(8889), X(15640)}}, {{A, B, C, X(35501), X(47311)}}, {{A, B, C, X(43726), X(46204)}}

X(54644) = X(4)X(18362)∩X(83)X(547)

Barycentrics    (5*a^4+2*b^4-7*b^2*c^2+5*c^4-a^2*(7*b^2+4*c^2))*(5*a^4+5*b^4-7*b^2*c^2+2*c^4-a^2*(4*b^2+7*c^2)) : :

X(54644) lies on these lines: {4, 18362}, {30, 53106}, {76, 5054}, {83, 547}, {230, 14492}, {381, 53107}, {383, 43551}, {598, 19709}, {632, 10159}, {671, 8703}, {1080, 43550}, {2996, 15692}, {3530, 43676}, {3545, 18844}, {3860, 45103}, {5070, 43527}, {5079, 53102}, {5395, 10356}, {5485, 15719}, {5487, 49106}, {5488, 49105}, {5503, 13468}, {6036, 35005}, {6055, 11606}, {7608, 9300}, {8781, 37671}, {9753, 52519}, {9766, 42011}, {10302, 11540}, {15681, 53105}, {16080, 52297}, {38071, 53109}, {40706, 52194}, {40707, 52193}, {43461, 53103}, {43530, 52298}

X(54644) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(5054)}}, {{A, B, C, X(30), X(52297)}}, {{A, B, C, X(95), X(1989)}}, {{A, B, C, X(230), X(37671)}}, {{A, B, C, X(381), X(52298)}}, {{A, B, C, X(427), X(547)}}, {{A, B, C, X(428), X(632)}}, {{A, B, C, X(468), X(8703)}}, {{A, B, C, X(1494), X(13481)}}, {{A, B, C, X(1799), X(15392)}}, {{A, B, C, X(2963), X(43458)}}, {{A, B, C, X(3860), X(52293)}}, {{A, B, C, X(4232), X(15719)}}, {{A, B, C, X(5064), X(5070)}}, {{A, B, C, X(5094), X(19709)}}, {{A, B, C, X(5481), X(5966)}}, {{A, B, C, X(6353), X(15692)}}, {{A, B, C, X(7610), X(14614)}}, {{A, B, C, X(7837), X(17004)}}, {{A, B, C, X(8770), X(11181)}}, {{A, B, C, X(8860), X(9766)}}, {{A, B, C, X(9300), X(37688)}}, {{A, B, C, X(10301), X(11540)}}, {{A, B, C, X(13468), X(22329)}}, {{A, B, C, X(14388), X(21448)}}, {{A, B, C, X(15681), X(37453)}}, {{A, B, C, X(17983), X(18361)}}, {{A, B, C, X(18362), X(30786)}}, {{A, B, C, X(29322), X(40801)}}, {{A, B, C, X(30537), X(32085)}}, {{A, B, C, X(34288), X(45857)}}, {{A, B, C, X(36948), X(52187)}}, {{A, B, C, X(37935), X(44210)}}, {{A, B, C, X(38730), X(52094)}}, {{A, B, C, X(40429), X(40829)}}, {{A, B, C, X(44556), X(46212)}}, {{A, B, C, X(44878), X(47596)}}
X(54644) = X(i)-vertex conjugate of X(j) for these {i, j}: {25, 14492}

X(54645) = X(2)X(44107)∩X(76)X(547)

Barycentrics    (2*a^4+2*b^4-7*b^2*c^2+5*c^4-a^2*(10*b^2+7*c^2))*(2*a^4+5*b^4-7*b^2*c^2+2*c^4-a^2*(7*b^2+10*c^2)) : :

X(54645) lies on these lines: {2, 44107}, {4, 31450}, {30, 53107}, {76, 547}, {83, 5054}, {376, 18844}, {381, 53106}, {383, 43550}, {598, 8703}, {632, 43527}, {671, 19709}, {1080, 43551}, {3530, 53102}, {3815, 14458}, {3860, 17503}, {5070, 10159}, {5079, 43676}, {5306, 7607}, {5395, 15692}, {9302, 33694}, {10155, 38227}, {14488, 43461}, {15681, 53109}, {15710, 18843}, {15719, 18842}, {16080, 52298}, {38071, 53105}, {43530, 52297}

X(54645) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(31652)}}, {{A, B, C, X(25), X(547)}}, {{A, B, C, X(30), X(52298)}}, {{A, B, C, X(264), X(18361)}}, {{A, B, C, X(381), X(52297)}}, {{A, B, C, X(427), X(5054)}}, {{A, B, C, X(428), X(5070)}}, {{A, B, C, X(468), X(19709)}}, {{A, B, C, X(632), X(5064)}}, {{A, B, C, X(842), X(39951)}}, {{A, B, C, X(3527), X(31846)}}, {{A, B, C, X(3613), X(11058)}}, {{A, B, C, X(3815), X(7788)}}, {{A, B, C, X(3860), X(52292)}}, {{A, B, C, X(5094), X(8703)}}, {{A, B, C, X(7714), X(46936)}}, {{A, B, C, X(8797), X(52188)}}, {{A, B, C, X(8801), X(52717)}}, {{A, B, C, X(8889), X(15692)}}, {{A, B, C, X(11184), X(41624)}}, {{A, B, C, X(15464), X(48911)}}, {{A, B, C, X(15719), X(52284)}}, {{A, B, C, X(34288), X(40410)}}, {{A, B, C, X(36889), X(45857)}}, {{A, B, C, X(37453), X(38071)}}, {{A, B, C, X(39955), X(43656)}}, {{A, B, C, X(45108), X(52154)}}

X(54646) = X(30)X(53108)∩X(98)X(14893)

Barycentrics    (11*a^2+11*b^2-10*c^2)*(11*a^2-10*b^2+11*c^2) : :

X(54646) lies on these lines: {30, 53108}, {98, 14893}, {262, 38335}, {381, 11668}, {671, 32455}, {3627, 7608}, {3843, 7607}, {3850, 10185}, {11303, 43440}, {11304, 43441}, {11669, 15684}, {14044, 43528}, {14066, 43529}, {23046, 53104}, {33698, 53418}, {33703, 53098}

X(54646) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(14487)}}, {{A, B, C, X(297), X(14893)}}, {{A, B, C, X(458), X(38335)}}, {{A, B, C, X(524), X(32455)}}, {{A, B, C, X(1509), X(33696)}}, {{A, B, C, X(3426), X(20251)}}, {{A, B, C, X(3527), X(11588)}}, {{A, B, C, X(3627), X(52281)}}, {{A, B, C, X(3843), X(52282)}}, {{A, B, C, X(11741), X(13472)}}, {{A, B, C, X(14483), X(32901)}}

X(54647) = X(30)X(53859)∩X(376)X(10185)

Barycentrics    (25*a^2+25*b^2-29*c^2)*(25*a^2-29*b^2+25*c^2) : :

X(54647) lies on these lines: {30, 53859}, {98, 41154}, {376, 10185}, {3424, 12101}, {3830, 43537}, {3845, 53099}, {5485, 51188}, {7607, 15682}, {7608, 41099}, {41106, 53098}

X(54647) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(1992), X(51188)}}, {{A, B, C, X(7714), X(8352)}}, {{A, B, C, X(11736), X(22334)}}, {{A, B, C, X(12101), X(52283)}}, {{A, B, C, X(15682), X(52282)}}, {{A, B, C, X(41099), X(52281)}}

X(54648) = X(10)X(3245)∩X(30)X(5397)

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

X(54648) lies on these lines: {10, 3245}, {30, 5397}, {6539, 26792}, {7608, 8229}, {11114, 43531}, {17297, 40013}

X(54648) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(21), X(4102)}}, {{A, B, C, X(27), X(17577)}}, {{A, B, C, X(57), X(3245)}}, {{A, B, C, X(79), X(18359)}}, {{A, B, C, X(81), X(1121)}}, {{A, B, C, X(92), X(5057)}}, {{A, B, C, X(469), X(11114)}}, {{A, B, C, X(553), X(26792)}}, {{A, B, C, X(903), X(3112)}}, {{A, B, C, X(1156), X(1255)}}, {{A, B, C, X(2990), X(16615)}}, {{A, B, C, X(4654), X(27065)}}, {{A, B, C, X(5561), X(31160)}}, {{A, B, C, X(8049), X(18821)}}, {{A, B, C, X(8229), X(52281)}}, {{A, B, C, X(14459), X(17389)}}, {{A, B, C, X(17098), X(39948)}}, {{A, B, C, X(17251), X(19684)}}, {{A, B, C, X(17297), X(32911)}}, {{A, B, C, X(30690), X(34578)}}, {{A, B, C, X(31143), X(46922)}}, {{A, B, C, X(31164), X(37787)}}, {{A, B, C, X(37279), X(52269)}}, {{A, B, C, X(39974), X(52208)}}, {{A, B, C, X(46104), X(53218)}}

X(54649) = X(381)X(1677)∩X(597)X(3845)

Barycentrics    -4*a^6+a^4*(b^2+c^2)+2*(b^2-c^2)^2*(b^2+c^2)+a^2*(b^4+c^4)+sqrt(b^2*c^2+a^2*(b^2+c^2))*(4*a^4-5*(b^2-c^2)^2+a^2*(b^2+c^2)) : :

X(54649) lies on the Kiepert hyperbola, K485 and these lines: {381, 1677}, {597, 3845}, {5404, 7753}, {10159, 10999}

X(54650) = X(381)X(1676)∩X(597)X(3845)

Barycentrics    -4*a^6+a^4*(b^2+c^2)+2*(b^2-c^2)^2*(b^2+c^2)+a^2*(b^4+c^4)+(-4*a^4+5*(b^2-c^2)^2-a^2*(b^2+c^2))*sqrt(b^2*c^2+a^2*(b^2+c^2)) : :

X(54650) lies on the Kiepert hyperbola, K485 and these lines: {381, 1676}, {597, 3845}, {5403, 7753}, {10159, 11000}, {16080, 16245}, {16246, 43530}

X(54651) = X(2)X(5915)∩X(4)X(14995)

Barycentrics    (4*a^8-3*a^6*(3*b^2+c^2)-(b^2-c^2)^2*(2*b^4+b^2*c^2-4*c^4)+2*a^4*(2*b^4+5*b^2*c^2-c^4)+a^2*(3*b^6-14*b^4*c^2+10*b^2*c^4-3*c^6))*(4*a^8-3*a^6*(b^2+3*c^2)-2*a^4*(b^4-5*b^2*c^2-2*c^4)+(b^2-c^2)^2*(4*b^4-b^2*c^2-2*c^4)+a^2*(-3*b^6+10*b^4*c^2-14*b^2*c^4+3*c^6)) : :

X(54651) lies on these lines: {2, 5915}, {4, 14995}, {30, 5466}, {524, 2394}, {542, 9180}, {543, 14223}, {671, 2407}, {1503, 43674}, {2794, 43667}, {3849, 43665}, {4235, 16080}, {5503, 48982}, {9830, 46040}, {43673, 52229}, {46069, 50941}

X(54651) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(524)}}, {{A, B, C, X(265), X(14977)}}, {{A, B, C, X(376), X(40890)}}, {{A, B, C, X(477), X(18823)}}, {{A, B, C, X(511), X(3849)}}, {{A, B, C, X(538), X(11645)}}, {{A, B, C, X(542), X(543)}}, {{A, B, C, X(754), X(19924)}}, {{A, B, C, X(1138), X(46275)}}, {{A, B, C, X(1503), X(52229)}}, {{A, B, C, X(2782), X(9830)}}, {{A, B, C, X(9080), X(9141)}}, {{A, B, C, X(13530), X(18818)}}, {{A, B, C, X(33007), X(35481)}}, {{A, B, C, X(36890), X(45774)}}, {{A, B, C, X(51227), X(53201)}}, {{A, B, C, X(51254), X(53173)}}
X(54651) = trilinear pole of line {5642, 523}
X(54651) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 43674}
X(54651) = X(i)-cross conjugate of X(j) for these {i, j}: {45331, 2}

X(54652) = X(2)X(22806)∩X(30)X(5490)

Barycentrics    -7*a^8-4*a^4*b^2*c^2-26*a^6*(b^2+c^2)+34*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(b^4-38*b^2*c^2+c^4)-12*(4*a^6-2*a^2*(b^2-c^2)^2+a^4*(b^2+c^2)-3*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54652) lies on these lines: {2, 22806}, {4, 49261}, {30, 5490}, {485, 13920}, {671, 33456}, {1131, 13674}, {3127, 43530}, {5200, 16080}, {5870, 14245}, {5871, 14240}, {6776, 22541}, {12818, 13687}, {13691, 42024}, {13748, 45101}, {14233, 45102}, {14492, 23259}, {39874, 49260}

X(54652) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(1989), X(24244)}}, {{A, B, C, X(3426), X(8577)}}, {{A, B, C, X(10262), X(24243)}}, {{A, B, C, X(36889), X(41515)}}

X(54653) = X(2)X(22807)∩X(30)X(5491)

Barycentrics    -7*a^8-4*a^4*b^2*c^2-26*a^6*(b^2+c^2)+34*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(b^4-38*b^2*c^2+c^4)+12*(4*a^6-2*a^2*(b^2-c^2)^2+a^4*(b^2+c^2)-3*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54653) lies on these lines: {2, 22807}, {4, 49262}, {30, 5491}, {486, 13849}, {671, 33457}, {1132, 13794}, {3128, 43530}, {5870, 14236}, {5871, 14231}, {6776, 19101}, {10159, 21737}, {10195, 21736}, {12819, 13807}, {13749, 45102}, {13810, 42023}, {14230, 45101}, {14492, 23249}, {16080, 52291}, {39874, 49263}

X(54653) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(1989), X(24243)}}, {{A, B, C, X(3426), X(8576)}}, {{A, B, C, X(10261), X(24244)}}, {{A, B, C, X(36889), X(41516)}}

X(54654) = X(30)X(6539)∩X(2394)X(4977)

Barycentrics    (4*a^5+7*a^4*(b+c)+a*(b+c)^2*(7*b^2-2*b*c-5*c^2)+a^3*(7*b^2+12*b*c+c^2)+a^2*(7*b^3+10*b^2*c-2*b*c^2-5*c^3)+(b+c)^2*(4*b^3-b^2*c-b*c^2-2*c^3))*(4*a^5+7*a^4*(b+c)-a*(b+c)^2*(5*b^2+2*b*c-7*c^2)+a^3*(b^2+12*b*c+7*c^2)-(b+c)^2*(2*b^3+b^2*c+b*c^2-4*c^3)+a^2*(-5*b^3-2*b^2*c+10*b*c^2+7*c^3)) : :

X(54654) lies on these lines: {30, 6539}, {321, 50215}, {2394, 4977}, {5466, 28306}, {16080, 31900}

X(54654) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(4977)}}, {{A, B, C, X(524), X(28306)}}, {{A, B, C, X(10308), X(50215)}}

X(54655) = X(2)X(50721)∩X(30)X(6568)

Barycentrics    -5*a^8-3*a^6*(b^2+c^2)+a^4*(-5*b^4+37*b^2*c^2-5*c^4)-(b^2-c^2)^2*(8*b^4-29*b^2*c^2+8*c^4)+a^2*(21*b^6-29*b^4*c^2-29*b^2*c^4+21*c^6)-24*(a^6+a^2*b^2*c^2-a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2))*S : :

X(54655) lies on the Kiepert hyperbola and these lines: {2, 50721}, {30, 6568}, {115, 14241}, {485, 19057}, {542, 1131}, {598, 13785}, {1327, 19058}, {6569, 11632}, {13968, 14229}, {14240, 49214}

X(54655) = reflection of X(i) in X(j) for these {i,j}: {14241, 115}
X(54655) = trilinear pole of line {13846, 523}

X(54656) = X(2)X(50722)∩X(30)X(6569)

Barycentrics    -5*a^8-3*a^6*(b^2+c^2)+a^4*(-5*b^4+37*b^2*c^2-5*c^4)-(b^2-c^2)^2*(8*b^4-29*b^2*c^2+8*c^4)+a^2*(21*b^6-29*b^4*c^2-29*b^2*c^4+21*c^6)+24*(a^6+a^2*b^2*c^2-a^4*(b^2+c^2)-(b^2-c^2)^2*(b^2+c^2))*S : :

X(54656) lies on the Kiepert hyperbola and these lines: {2, 50722}, {30, 6569}, {115, 14226}, {486, 19058}, {542, 1132}, {598, 13665}, {1328, 19057}, {6568, 11632}, {13908, 14244}, {14236, 49215}

X(54656) = reflection of X(i) in X(j) for these {i,j}: {14226, 115}
X(54656) = trilinear pole of line {13847, 523}

X(54657) = X(30)X(6625)∩X(3545)X(32022)

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

X(54657) lies on these lines: {30, 6625}, {3545, 32022}, {4212, 43530}, {4213, 16080}, {20292, 30588}

X(54657) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(4213)}}, {{A, B, C, X(42), X(74)}}, {{A, B, C, X(291), X(16615)}}, {{A, B, C, X(376), X(4207)}}, {{A, B, C, X(381), X(4212)}}, {{A, B, C, X(1138), X(2688)}}, {{A, B, C, X(1246), X(34288)}}, {{A, B, C, X(1494), X(1826)}}, {{A, B, C, X(1989), X(15320)}}, {{A, B, C, X(2350), X(14483)}}, {{A, B, C, X(3426), X(39967)}}, {{A, B, C, X(3431), X(39961)}}, {{A, B, C, X(3531), X(39966)}}, {{A, B, C, X(3545), X(4196)}}, {{A, B, C, X(10308), X(30571)}}, {{A, B, C, X(14491), X(39965)}}, {{A, B, C, X(17982), X(52374)}}, {{A, B, C, X(20292), X(32631)}}

X(54658) = X(2)X(13445)∩X(30)X(801)

Barycentrics    (a^8-a^6*(b^2-2*c^2)-(b^2-c^2)^3*(2*b^2+c^2)+a^4*(-3*b^4+13*b^2*c^2-6*c^4)+a^2*(5*b^6-20*b^4*c^2+13*b^2*c^4+2*c^6))*(a^8+a^6*(2*b^2-c^2)+(b^2-c^2)^3*(b^2+2*c^2)+a^4*(-6*b^4+13*b^2*c^2-3*c^4)+a^2*(2*b^6+13*b^4*c^2-20*b^2*c^4+5*c^6)) : :

X(54658) lies on these lines: {2, 13445}, {30, 801}, {235, 16080}, {275, 51892}, {381, 37874}, {1593, 43530}, {2883, 45300}, {3543, 43670}, {6812, 10195}, {6814, 10194}, {6823, 10159}, {11479, 43527}, {15811, 46729}

X(54658) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(235)}}, {{A, B, C, X(64), X(1494)}}, {{A, B, C, X(381), X(1593)}}, {{A, B, C, X(428), X(6823)}}, {{A, B, C, X(1105), X(1989)}}, {{A, B, C, X(1138), X(15424)}}, {{A, B, C, X(2693), X(5627)}}, {{A, B, C, X(3426), X(41489)}}, {{A, B, C, X(3532), X(18361)}}, {{A, B, C, X(3543), X(6622)}}, {{A, B, C, X(4846), X(40032)}}, {{A, B, C, X(5064), X(11479)}}, {{A, B, C, X(6526), X(36889)}}, {{A, B, C, X(9307), X(35512)}}, {{A, B, C, X(11744), X(32085)}}, {{A, B, C, X(13450), X(51892)}}, {{A, B, C, X(14860), X(22334)}}, {{A, B, C, X(15740), X(52187)}}, {{A, B, C, X(16934), X(17505)}}, {{A, B, C, X(18317), X(45195)}}, {{A, B, C, X(34288), X(43695)}}, {{A, B, C, X(45088), X(45857)}}

X(54659) = X(2)X(10722)∩X(30)X(8781)

Barycentrics    (5*a^6-4*b^6+7*b^4*c^2-8*b^2*c^4+5*c^6+a^4*(-8*b^2+c^2)+a^2*(7*b^4-6*b^2*c^2+c^4))*(5*a^6+5*b^6-8*b^4*c^2+7*b^2*c^4-4*c^6+a^4*(b^2-8*c^2)+a^2*(b^4-6*b^2*c^2+7*c^4)) : :

X(54659) lies on these lines: {2, 10722}, {30, 8781}, {76, 50955}, {83, 38079}, {262, 53017}, {460, 16080}, {542, 2996}, {2794, 7612}, {3424, 14639}, {3566, 14223}, {5503, 43460}, {6054, 40824}, {9880, 38259}, {14492, 53418}, {14494, 39838}

X(54659) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(460)}}, {{A, B, C, X(542), X(3566)}}, {{A, B, C, X(842), X(8753)}}, {{A, B, C, X(1494), X(38749)}}, {{A, B, C, X(1989), X(35142)}}, {{A, B, C, X(2374), X(9141)}}, {{A, B, C, X(2794), X(34579)}}, {{A, B, C, X(2796), X(28529)}}, {{A, B, C, X(3426), X(3455)}}, {{A, B, C, X(5641), X(6531)}}, {{A, B, C, X(6323), X(13603)}}, {{A, B, C, X(10630), X(14388)}}, {{A, B, C, X(14248), X(39644)}}, {{A, B, C, X(14639), X(45031)}}, {{A, B, C, X(33971), X(53017)}}, {{A, B, C, X(36889), X(47735)}}

X(54660) = X(30)X(8796)∩X(275)X(3545)

Barycentrics    (5*a^8-2*a^2*(b^2-c^2)^2*(b^2+4*c^2)-2*a^6*(7*b^2+4*c^2)-(b^2-c^2)^3*(b^2+5*c^2)+2*a^4*(6*b^4+7*b^2*c^2+3*c^4))*(5*a^8-2*a^2*(b^2-c^2)^2*(4*b^2+c^2)+(b^2-c^2)^3*(5*b^2+c^2)-2*a^6*(4*b^2+7*c^2)+2*a^4*(3*b^4+7*b^2*c^2+6*c^4)) : :

X(54660) lies on these lines: {30, 8796}, {275, 3545}, {376, 2052}, {459, 3524}, {631, 16080}, {2996, 34664}, {3090, 43530}, {3590, 6809}, {3591, 6810}, {7612, 12022}, {15682, 39284}, {15702, 38253}, {16072, 43670}

X(54660) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(376)}}, {{A, B, C, X(5), X(3545)}}, {{A, B, C, X(20), X(3524)}}, {{A, B, C, X(30), X(631)}}, {{A, B, C, X(68), X(18853)}}, {{A, B, C, X(69), X(18852)}}, {{A, B, C, X(95), X(18850)}}, {{A, B, C, X(140), X(15682)}}, {{A, B, C, X(265), X(8797)}}, {{A, B, C, X(381), X(3090)}}, {{A, B, C, X(382), X(15709)}}, {{A, B, C, X(548), X(15710)}}, {{A, B, C, X(549), X(3529)}}, {{A, B, C, X(550), X(15698)}}, {{A, B, C, X(1217), X(1494)}}, {{A, B, C, X(1300), X(17040)}}, {{A, B, C, X(1513), X(33190)}}, {{A, B, C, X(1656), X(41099)}}, {{A, B, C, X(1657), X(15719)}}, {{A, B, C, X(1989), X(14457)}}, {{A, B, C, X(3091), X(5071)}}, {{A, B, C, X(3146), X(15702)}}, {{A, B, C, X(3147), X(52069)}}, {{A, B, C, X(3431), X(41890)}}, {{A, B, C, X(3522), X(19708)}}, {{A, B, C, X(3523), X(11001)}}, {{A, B, C, X(3525), X(3543)}}, {{A, B, C, X(3528), X(10304)}}, {{A, B, C, X(3530), X(46333)}}, {{A, B, C, X(3533), X(3830)}}, {{A, B, C, X(3534), X(10299)}}, {{A, B, C, X(3839), X(5067)}}, {{A, B, C, X(3855), X(5055)}}, {{A, B, C, X(4550), X(43586)}}, {{A, B, C, X(4846), X(18847)}}, {{A, B, C, X(5054), X(33703)}}, {{A, B, C, X(5056), X(41106)}}, {{A, B, C, X(5651), X(15030)}}, {{A, B, C, X(6353), X(34664)}}, {{A, B, C, X(6622), X(16072)}}, {{A, B, C, X(6831), X(50741)}}, {{A, B, C, X(6877), X(52269)}}, {{A, B, C, X(6879), X(17577)}}, {{A, B, C, X(6880), X(11114)}}, {{A, B, C, X(6905), X(11111)}}, {{A, B, C, X(6927), X(11113)}}, {{A, B, C, X(6935), X(11112)}}, {{A, B, C, X(6956), X(17532)}}, {{A, B, C, X(6969), X(17556)}}, {{A, B, C, X(6977), X(17579)}}, {{A, B, C, X(7383), X(44442)}}, {{A, B, C, X(7395), X(7714)}}, {{A, B, C, X(7509), X(34608)}}, {{A, B, C, X(7552), X(18531)}}, {{A, B, C, X(8703), X(21735)}}, {{A, B, C, X(8884), X(52187)}}, {{A, B, C, X(10170), X(46261)}}, {{A, B, C, X(11541), X(15721)}}, {{A, B, C, X(11676), X(33215)}}, {{A, B, C, X(13452), X(45301)}}, {{A, B, C, X(13472), X(34570)}}, {{A, B, C, X(14033), X(37334)}}, {{A, B, C, X(14491), X(41891)}}, {{A, B, C, X(14542), X(30537)}}, {{A, B, C, X(14843), X(15319)}}, {{A, B, C, X(15077), X(18854)}}, {{A, B, C, X(15464), X(46255)}}, {{A, B, C, X(15692), X(17538)}}, {{A, B, C, X(15708), X(49138)}}, {{A, B, C, X(15715), X(50693)}}, {{A, B, C, X(16041), X(37446)}}, {{A, B, C, X(16263), X(46952)}}, {{A, B, C, X(18296), X(31846)}}, {{A, B, C, X(18317), X(42021)}}, {{A, B, C, X(22261), X(34288)}}, {{A, B, C, X(22270), X(31371)}}, {{A, B, C, X(22466), X(52154)}}, {{A, B, C, X(35483), X(44273)}}, {{A, B, C, X(35512), X(45838)}}, {{A, B, C, X(36612), X(43891)}}, {{A, B, C, X(50701), X(50739)}}

X(54661) = X(30)X(8808)∩X(2394)X(8058)

Barycentrics    (2*a^8+3*a^7*(b+c)+a^4*b*(b+c)^2*(3*b+c)+a^2*(b-c)^3*(b+c)^2*(b+2*c)-(b-c)^3*(b+c)^4*(b+2*c)-a^6*(5*b^2+5*b*c+2*c^2)+a^5*(-9*b^3-5*b^2*c+b*c^2-3*c^3)-a*(b^2-c^2)^2*(3*b^3-b^2*c+5*b*c^2-3*c^3)+a^3*(9*b^5+b^4*c-2*b^3*c^2+10*b^2*c^3+b*c^4-3*c^5))*(2*a^8+3*a^7*(b+c)-a^2*(b-c)^3*(b+c)^2*(2*b+c)+(b-c)^3*(b+c)^4*(2*b+c)+a^4*c*(b+c)^2*(b+3*c)-a^6*(2*b^2+5*b*c+5*c^2)+a^5*(-3*b^3+b^2*c-5*b*c^2-9*c^3)+a*(b^2-c^2)^2*(3*b^3-5*b^2*c+b*c^2-3*c^3)+a^3*(-3*b^5+b^4*c+10*b^3*c^2-2*b^2*c^3+b*c^4+9*c^5)) : :

X(54661) lies on these lines: {30, 8808}, {2394, 8058}

X(54661) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(6598)}}, {{A, B, C, X(412), X(11113)}}, {{A, B, C, X(1494), X(8806)}}, {{A, B, C, X(17532), X(52248)}}, {{A, B, C, X(33576), X(51498)}}

X(54662) = X(2)X(45772)∩X(4)X(5465)

Barycentrics    (4*a^10-a^8*(11*b^2+5*c^2)+a^6*(10*b^4+13*b^2*c^2+c^4)-(b^2-c^2)^2*(2*b^6+3*b^2*c^4-4*c^6)+a^4*(-5*b^6-6*b^4*c^2-6*b^2*c^4+c^6)+a^2*(4*b^8-2*b^6*c^2-6*b^4*c^4+13*b^2*c^6-5*c^8))*(4*a^10-a^8*(5*b^2+11*c^2)+a^6*(b^4+13*b^2*c^2+10*c^4)+a^4*(b^6-6*b^4*c^2-6*b^2*c^4-5*c^6)+(b^2-c^2)^2*(4*b^6-3*b^4*c^2-2*c^6)+a^2*(-5*b^8+13*b^6*c^2-6*b^4*c^4-2*b^2*c^6+4*c^8)) : :

X(54662) lies on these lines: {2, 45772}, {4, 5465}, {30, 9180}, {98, 1551}, {524, 14223}, {542, 5466}, {543, 2394}, {671, 14999}, {1503, 43667}, {2794, 43674}, {3849, 46040}, {9166, 39295}, {9830, 43665}, {12066, 41135}, {52229, 52459}

X(54662) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(543)}}, {{A, B, C, X(99), X(530)}}, {{A, B, C, X(265), X(5465)}}, {{A, B, C, X(297), X(1551)}}, {{A, B, C, X(511), X(6233)}}, {{A, B, C, X(524), X(542)}}, {{A, B, C, X(842), X(34539)}}, {{A, B, C, X(1494), X(45772)}}, {{A, B, C, X(2782), X(3849)}}, {{A, B, C, X(2794), X(52229)}}, {{A, B, C, X(5969), X(11645)}}, {{A, B, C, X(14932), X(51226)}}, {{A, B, C, X(18020), X(52094)}}
X(54662) = trilinear pole of line {45331, 45662}
X(54662) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 43667}

X(54663) = X(23)X(7608)∩X(30)X(9221)

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

X(54663) lies on these lines: {23, 7608}, {30, 9221}, {96, 7565}, {524, 11140}, {671, 1994}, {1510, 5466}, {3845, 18316}, {5169, 7607}, {7493, 53098}, {7519, 53099}, {46105, 52281}

X(54663) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(23), X(52281)}}, {{A, B, C, X(323), X(14483)}}, {{A, B, C, X(467), X(7565)}}, {{A, B, C, X(524), X(1510)}}, {{A, B, C, X(5169), X(52282)}}, {{A, B, C, X(6748), X(41890)}}, {{A, B, C, X(9141), X(46104)}}, {{A, B, C, X(11138), X(41907)}}, {{A, B, C, X(11139), X(41908)}}, {{A, B, C, X(31626), X(34802)}}

X(54664) = X(30)X(9290)∩X(436)X(16080)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^8-a^6*(4*b^2+5*c^2)+(b^2-c^2)^2*(b^4+2*c^4)+a^4*(3*b^4+4*b^2*c^2+6*c^4)+a^2*(-2*b^6+3*b^4*c^2+4*b^2*c^4-5*c^6))*(2*a^8-a^6*(5*b^2+4*c^2)+(b^2-c^2)^2*(2*b^4+c^4)+a^4*(6*b^4+4*b^2*c^2+3*c^4)+a^2*(-5*b^6+4*b^4*c^2+3*b^2*c^4-2*c^6)) : :

X(54664) lies on these lines: {30, 9290}, {436, 16080}, {10159, 37124}, {43530, 52249}

X(54664) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(436)}}, {{A, B, C, X(51), X(43952)}}, {{A, B, C, X(74), X(51477)}}, {{A, B, C, X(381), X(52249)}}, {{A, B, C, X(428), X(37124)}}, {{A, B, C, X(1173), X(17974)}}, {{A, B, C, X(1494), X(40402)}}, {{A, B, C, X(15321), X(39286)}}, {{A, B, C, X(39874), X(40065)}}

X(54665) = X(30)X(9381)∩X(2070)X(16080)

Barycentrics    (2*a^14-a^12*(4*b^2+7*c^2)+(b^2-c^2)^5*(2*b^4+3*b^2*c^2+c^4)+a^4*(-(b^2*c)+c^3)^2*(b^4+b^2*c^2+3*c^4)+a^10*(8*b^2*c^2+6*c^4)-a^2*(b^2-c^2)^3*(4*b^6+4*b^4*c^2+5*b^2*c^4+2*c^6)+a^8*(2*b^6+b^4*c^2-5*b^2*c^4+5*c^6)+a^6*(2*b^8-4*b^6*c^2-b^4*c^4+5*b^2*c^6-10*c^8))*(2*a^14-a^12*(7*b^2+4*c^2)+a^10*(6*b^4+8*b^2*c^2)+a^4*(b^3-b*c^2)^2*(3*b^4+b^2*c^2+c^4)-(b^2-c^2)^5*(b^4+3*b^2*c^2+2*c^4)+a^8*(5*b^6-5*b^4*c^2+b^2*c^4+2*c^6)+a^2*(b^2-c^2)^3*(2*b^6+5*b^4*c^2+4*b^2*c^4+4*c^6)-a^6*(10*b^8-5*b^6*c^2+b^4*c^4+4*b^2*c^6-2*c^8)) : :

X(54665) lies on these lines: {30, 9381}, {2070, 16080}, {39504, 43530}

X(54665) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(2070)}}, {{A, B, C, X(381), X(39504)}}, {{A, B, C, X(10201), X(31723)}}, {{A, B, C, X(46450), X(46451)}}

X(54666) = X(2)X(1879)∩X(30)X(96)

Barycentrics    (a^6+(b^2-2*c^2)*(b^2-c^2)^2-a^4*(b^2+4*c^2)-a^2*(b^4+2*b^2*c^2-5*c^4))*(a^6-(b^2-c^2)^2*(2*b^2-c^2)-a^4*(4*b^2+c^2)+a^2*(5*b^4-2*b^2*c^2-c^4)) : :

X(54666) lies on these lines: {2, 1879}, {4, 10116}, {22, 7607}, {30, 96}, {98, 34603}, {467, 16080}, {671, 41628}, {5133, 7608}, {5466, 20184}, {7495, 10185}, {7500, 43537}, {7612, 34608}, {10159, 41237}, {40448, 52069}, {41231, 43527}, {43530, 52253}, {43678, 52282}

X(54666) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(14806)}}, {{A, B, C, X(22), X(52282)}}, {{A, B, C, X(30), X(467)}}, {{A, B, C, X(64), X(1993)}}, {{A, B, C, X(297), X(34603)}}, {{A, B, C, X(324), X(1105)}}, {{A, B, C, X(343), X(3521)}}, {{A, B, C, X(381), X(52253)}}, {{A, B, C, X(428), X(41237)}}, {{A, B, C, X(524), X(20184)}}, {{A, B, C, X(1176), X(53863)}}, {{A, B, C, X(1263), X(45793)}}, {{A, B, C, X(1879), X(1989)}}, {{A, B, C, X(5064), X(41231)}}, {{A, B, C, X(5133), X(52281)}}, {{A, B, C, X(8794), X(40427)}}, {{A, B, C, X(32533), X(52350)}}, {{A, B, C, X(34608), X(37174)}}, {{A, B, C, X(35142), X(44176)}}, {{A, B, C, X(36616), X(39109)}}, {{A, B, C, X(52069), X(52280)}}
X(54666) = polar conjugate of X(10018)
X(54666) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 10018}
X(54666) = barycentric quotient X(i)/X(j) for these (i, j): {4, 10018}

X(54667) = X(275)X(41099)∩X(376)X(16080)

Barycentrics    (11*a^8+2*a^2*(5*b^2-4*c^2)*(b^2-c^2)^2-2*a^6*(13*b^2+4*c^2)-(b^2-c^2)^3*(7*b^2+11*c^2)+2*a^4*(6*b^4+13*b^2*c^2-3*c^4))*(11*a^8-2*a^2*(4*b^2-5*c^2)*(b^2-c^2)^2+(b^2-c^2)^3*(11*b^2+7*c^2)-2*a^6*(4*b^2+13*c^2)+a^4*(-6*b^4+26*b^2*c^2+12*c^4)) : :

X(54667) lies on these lines: {275, 41099}, {376, 16080}, {459, 11001}, {2052, 15682}, {2394, 9007}, {3545, 43530}, {3830, 8796}, {19708, 38253}

X(54667) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(15682)}}, {{A, B, C, X(5), X(41099)}}, {{A, B, C, X(20), X(11001)}}, {{A, B, C, X(30), X(69)}}, {{A, B, C, X(68), X(18317)}}, {{A, B, C, X(265), X(18852)}}, {{A, B, C, X(381), X(3545)}}, {{A, B, C, X(382), X(15698)}}, {{A, B, C, X(542), X(32817)}}, {{A, B, C, X(631), X(3521)}}, {{A, B, C, X(1494), X(18850)}}, {{A, B, C, X(3090), X(3845)}}, {{A, B, C, X(3091), X(41106)}}, {{A, B, C, X(3146), X(19708)}}, {{A, B, C, X(3346), X(14843)}}, {{A, B, C, X(3431), X(34570)}}, {{A, B, C, X(3524), X(3543)}}, {{A, B, C, X(3528), X(15640)}}, {{A, B, C, X(3529), X(3534)}}, {{A, B, C, X(3533), X(12101)}}, {{A, B, C, X(3627), X(15719)}}, {{A, B, C, X(3839), X(5071)}}, {{A, B, C, X(3855), X(5066)}}, {{A, B, C, X(5627), X(34208)}}, {{A, B, C, X(6526), X(46212)}}, {{A, B, C, X(7714), X(34664)}}, {{A, B, C, X(8703), X(33703)}}, {{A, B, C, X(10299), X(33699)}}, {{A, B, C, X(11180), X(32815)}}, {{A, B, C, X(11738), X(41890)}}, {{A, B, C, X(14093), X(35409)}}, {{A, B, C, X(15077), X(18851)}}, {{A, B, C, X(15681), X(46333)}}, {{A, B, C, X(15684), X(15710)}}, {{A, B, C, X(15687), X(15709)}}, {{A, B, C, X(15697), X(49138)}}, {{A, B, C, X(15702), X(50687)}}, {{A, B, C, X(15749), X(18853)}}, {{A, B, C, X(16263), X(52187)}}, {{A, B, C, X(18550), X(36948)}}, {{A, B, C, X(18854), X(32533)}}, {{A, B, C, X(20421), X(41894)}}, {{A, B, C, X(31371), X(46412)}}, {{A, B, C, X(32833), X(39874)}}, {{A, B, C, X(36436), X(36463)}}, {{A, B, C, X(36445), X(36454)}}

X(54668) = X(2)X(165)∩X(4)X(1886)

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

X(54668) lies on these lines: {2, 165}, {4, 1886}, {10, 17747}, {76, 4301}, {98, 26716}, {226, 4356}, {321, 4061}, {381, 28881}, {485, 49632}, {486, 49633}, {497, 4349}, {519, 5485}, {671, 2784}, {740, 4052}, {946, 17758}, {1446, 3671}, {1499, 4049}, {1738, 40840}, {2796, 5503}, {2996, 49495}, {3667, 4444}, {3950, 43534}, {4133, 34475}, {4229, 32014}, {4780, 11599}, {10157, 10440}, {11167, 28562}, {11372, 45097}, {18483, 48944}, {18840, 35680}, {19925, 43533}, {28905, 38140}, {43531, 48900}, {48649, 50290}

X(54668) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(210)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(2321)}}, {{A, B, C, X(37), X(3062)}}, {{A, B, C, X(42), X(103)}}, {{A, B, C, X(65), X(165)}}, {{A, B, C, X(79), X(4854)}}, {{A, B, C, X(225), X(1699)}}, {{A, B, C, X(430), X(4229)}}, {{A, B, C, X(469), X(49130)}}, {{A, B, C, X(497), X(39579)}}, {{A, B, C, X(516), X(523)}}, {{A, B, C, X(519), X(1499)}}, {{A, B, C, X(690), X(2784)}}, {{A, B, C, X(726), X(32472)}}, {{A, B, C, X(740), X(3667)}}, {{A, B, C, X(758), X(28292)}}, {{A, B, C, X(1014), X(4778)}}, {{A, B, C, X(1042), X(4301)}}, {{A, B, C, X(1427), X(34991)}}, {{A, B, C, X(1869), X(19925)}}, {{A, B, C, X(1903), X(21153)}}, {{A, B, C, X(2740), X(35148)}}, {{A, B, C, X(2793), X(2796)}}, {{A, B, C, X(3696), X(27475)}}, {{A, B, C, X(3701), X(5556)}}, {{A, B, C, X(3817), X(51870)}}, {{A, B, C, X(3925), X(3947)}}, {{A, B, C, X(3993), X(4133)}}, {{A, B, C, X(4028), X(49495)}}, {{A, B, C, X(4058), X(50290)}}, {{A, B, C, X(4082), X(14942)}}, {{A, B, C, X(4780), X(6541)}}, {{A, B, C, X(5257), X(28626)}}, {{A, B, C, X(5542), X(42289)}}, {{A, B, C, X(7988), X(52383)}}, {{A, B, C, X(8704), X(28562)}}, {{A, B, C, X(8818), X(38052)}}, {{A, B, C, X(9778), X(39130)}}, {{A, B, C, X(9812), X(41013)}}, {{A, B, C, X(10164), X(15232)}}, {{A, B, C, X(10435), X(42027)}}, {{A, B, C, X(15065), X(38306)}}, {{A, B, C, X(17766), X(32473)}}, {{A, B, C, X(50865), X(52382)}}
X(54668) = reflection of X(i) in X(j) for these {i,j}: {50808, 49631}
X(54668) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 5223}, {81, 42316}, {1333, 29616}
X(54668) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 5223}, {37, 29616}, {40586, 42316}
X(54668) = X(i)-cross conjugate of X(j) for these {i, j}: {3755, 10}
X(54668) = barycentric product X(i)*X(j) for these (i, j): {1441, 42317}, {26716, 850}, {32040, 523}
X(54668) = barycentric quotient X(i)/X(j) for these (i, j): {10, 29616}, {37, 5223}, {42, 42316}, {3668, 10004}, {26716, 110}, {32040, 99}, {42317, 21}
X(54668) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {516, 49631, 50808}

X(54669) = X(2)X(16652)∩X(13)X(41038)

Barycentrics    -9*(3*a^10+2*a^6*(b^2-c^2)^2-6*a^8*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(3*b^4+10*b^2*c^2+3*c^4))-2*sqrt(3)*(9*a^8-a^4*(b^2-c^2)^2-27*a^6*(b^2+c^2)+31*a^2*(b^2-c^2)^2*(b^2+c^2)-4*(b^2-c^2)^2*(3*b^4-8*b^2*c^2+3*c^4))*S : :

X(54669) lies on these lines: {2, 16652}, {13, 41038}, {18, 52838}, {532, 5485}, {1503, 12816}, {5868, 43550}, {9756, 36961}, {12820, 41039}, {14484, 42133}, {22235, 22832}, {22532, 43447}, {41022, 42062}

X(54669) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(523), X(8741)}}, {{A, B, C, X(532), X(1499)}}
X(54669) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 12816}

X(54670) = X(2)X(16653)∩X(14)X(41039)

Barycentrics    -9*(3*a^10+2*a^6*(b^2-c^2)^2-6*a^8*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(3*b^4+10*b^2*c^2+3*c^4))+2*sqrt(3)*(9*a^8-a^4*(b^2-c^2)^2-27*a^6*(b^2+c^2)+31*a^2*(b^2-c^2)^2*(b^2+c^2)-4*(b^2-c^2)^2*(3*b^4-8*b^2*c^2+3*c^4))*S : :

X(54670) lies on these lines: {2, 16653}, {14, 41039}, {17, 52839}, {533, 5485}, {1503, 12817}, {5869, 43551}, {9756, 36962}, {12821, 41038}, {14484, 42134}, {22237, 22831}, {22531, 43446}, {41023, 42063}

X(54670) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(523), X(8742)}}, {{A, B, C, X(533), X(1499)}}
X(54670) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 12817}

X(54671) = X(2)X(14982)∩X(2394)X(2780)

Barycentrics    (2*a^10-3*a^8*c^2+a^6*(-2*b^4+13*b^2*c^2-2*c^4)+a^2*b^2*c^2*(13*b^4-14*b^2*c^2+c^4)+(b^2-c^2)^3*(2*b^4+3*b^2*c^2+c^4)-2*a^4*(b^6-2*b^4*c^2+7*b^2*c^4-2*c^6))*(2*a^10-3*a^8*b^2+a^6*(-2*b^4+13*b^2*c^2-2*c^4)-(b^2-c^2)^3*(b^4+3*b^2*c^2+2*c^4)+a^2*b^2*c^2*(b^4-14*b^2*c^2+13*c^4)+2*a^4*(2*b^6-7*b^4*c^2+2*b^2*c^4-c^6)) : :

X(54671) lies on these lines: {2, 14982}, {2394, 2780}, {2986, 10989}, {16080, 37962}

X(54671) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(111)}}, {{A, B, C, X(381), X(45096)}}, {{A, B, C, X(403), X(10989)}}, {{A, B, C, X(1989), X(2697)}}, {{A, B, C, X(2373), X(50480)}}, {{A, B, C, X(2770), X(10293)}}, {{A, B, C, X(5505), X(8749)}}, {{A, B, C, X(5627), X(18019)}}, {{A, B, C, X(13574), X(43660)}}

X(54672) = X(2)X(49926)∩X(76)X(36365)

Barycentrics    3*(8*a^10-27*a^8*(b^2+c^2)-a^6*(5*b^4+23*b^2*c^2+5*c^4)+a^2*(b^2-c^2)^2*(21*b^4+79*b^2*c^2+21*c^4)-(b^2-c^2)^2*(10*b^6-19*b^4*c^2-19*b^2*c^4+10*c^6)+a^4*(13*b^6-14*b^4*c^2-14*b^2*c^4+13*c^6))-2*sqrt(3)*(22*a^8+29*a^6*(b^2+c^2)-37*a^2*(b^2-c^2)^2*(b^2+c^2)-a^4*(6*b^4+5*b^2*c^2+6*c^4)-(b^2-c^2)^2*(8*b^4+47*b^2*c^2+8*c^4))*S : :

X(54672) lies on these lines: {2, 49926}, {76, 36365}, {671, 36382}, {6773, 11602}, {22237, 44463}, {33602, 39874}, {43543, 53441}, {43551, 51754}

X(54672) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(21461)}}, {{A, B, C, X(1494), X(8741)}}, {{A, B, C, X(2993), X(11080)}}, {{A, B, C, X(3431), X(16459)}}, {{A, B, C, X(3479), X(8014)}}, {{A, B, C, X(34288), X(41897)}}

X(54673) = X(2)X(49925)∩X(76)X(36365)

Barycentrics    3*(8*a^10-27*a^8*(b^2+c^2)-a^6*(5*b^4+23*b^2*c^2+5*c^4)+a^2*(b^2-c^2)^2*(21*b^4+79*b^2*c^2+21*c^4)-(b^2-c^2)^2*(10*b^6-19*b^4*c^2-19*b^2*c^4+10*c^6)+a^4*(13*b^6-14*b^4*c^2-14*b^2*c^4+13*c^6))+2*sqrt(3)*(22*a^8+29*a^6*(b^2+c^2)-37*a^2*(b^2-c^2)^2*(b^2+c^2)-a^4*(6*b^4+5*b^2*c^2+6*c^4)-(b^2-c^2)^2*(8*b^4+47*b^2*c^2+8*c^4))*S : :

X(54673) lies on these lines: {2, 49925}, {76, 36364}, {671, 36383}, {6770, 11603}, {22235, 44459}, {33603, 39874}, {43542, 53429}, {43550, 51753}

X(54673) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(21462)}}, {{A, B, C, X(1494), X(8742)}}, {{A, B, C, X(2992), X(11085)}}, {{A, B, C, X(3431), X(16460)}}, {{A, B, C, X(3480), X(8015)}}, {{A, B, C, X(34288), X(41898)}}

X(54674) = X(2)X(19140)∩X(30)X(44262)

Barycentrics    (a^10+2*a^6*(b^2-c^2)^2-3*a^8*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)+a^4*(2*b^6+5*b^4*c^2-4*b^2*c^4+2*c^6)+a^2*(-3*b^8+5*b^6*c^2+5*b^4*c^4-4*b^2*c^6-3*c^8))*(a^10+2*a^6*(b^2-c^2)^2-3*a^8*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)+a^4*(2*b^6-4*b^4*c^2+5*b^2*c^4+2*c^6)+a^2*(-3*b^8-4*b^6*c^2+5*b^4*c^4+5*b^2*c^6-3*c^8)) : :

X(54674) lies on these lines: {2, 19140}, {76, 44262}, {13582, 37901}, {18316, 43460}

X(54674) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(44262)}}, {{A, B, C, X(74), X(52171)}}, {{A, B, C, X(842), X(1989)}}, {{A, B, C, X(1138), X(14388)}}, {{A, B, C, X(5627), X(9076)}}, {{A, B, C, X(6325), X(52192)}}, {{A, B, C, X(7799), X(18372)}}, {{A, B, C, X(13854), X(22455)}}, {{A, B, C, X(15364), X(30537)}}, {{A, B, C, X(18317), X(29011)}}, {{A, B, C, X(37901), X(37943)}}, {{A, B, C, X(43658), X(43917)}}

X(54675) = X(76)X(6054)∩X(83)X(37345)

Barycentrics    (a^8+b^8+3*b^6*c^2-5*b^4*c^4+3*b^2*c^6-2*c^8+3*a^6*(2*b^2+c^2)-a^4*(2*b^4+5*b^2*c^2+5*c^4)+a^2*(6*b^6-5*b^4*c^2-2*b^2*c^4+3*c^6))*(a^8-2*b^8+3*b^6*c^2-5*b^4*c^4+3*b^2*c^6+c^8+3*a^6*(b^2+2*c^2)-a^4*(5*b^4+5*b^2*c^2+2*c^4)+a^2*(3*b^6-2*b^4*c^2-5*b^2*c^4+6*c^6)) : :

X(54675) lies on these lines: {76, 6054}, {83, 37345}, {598, 10722}, {671, 43460}

X(54675) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(325), X(1989)}}, {{A, B, C, X(427), X(37345)}}, {{A, B, C, X(842), X(1976)}}, {{A, B, C, X(1494), X(36897)}}, {{A, B, C, X(43460), X(52094)}}

X(54676) = X(9)X(6539)∩X(10)X(3683)

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

X(54676) lies on these lines: {9, 6539}, {10, 3683}, {226, 1100}, {321, 3686}, {527, 43675}, {553, 1446}, {1839, 40149}, {2185, 32014}, {3187, 4080}, {4049, 29013}, {7413, 7608}, {10159, 37086}, {16080, 37279}, {17532, 43531}, {27412, 37375}, {37445, 43527}

X(54676) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(9), X(553)}}, {{A, B, C, X(27), X(80)}}, {{A, B, C, X(30), X(37279)}}, {{A, B, C, X(57), X(33576)}}, {{A, B, C, X(63), X(36599)}}, {{A, B, C, X(79), X(40435)}}, {{A, B, C, X(92), X(5560)}}, {{A, B, C, X(278), X(7319)}}, {{A, B, C, X(428), X(37086)}}, {{A, B, C, X(469), X(17532)}}, {{A, B, C, X(519), X(3187)}}, {{A, B, C, X(527), X(1708)}}, {{A, B, C, X(596), X(40394)}}, {{A, B, C, X(673), X(34612)}}, {{A, B, C, X(903), X(15314)}}, {{A, B, C, X(1121), X(6284)}}, {{A, B, C, X(1156), X(2982)}}, {{A, B, C, X(1903), X(39982)}}, {{A, B, C, X(2167), X(3065)}}, {{A, B, C, X(2184), X(36603)}}, {{A, B, C, X(2985), X(6650)}}, {{A, B, C, X(2994), X(14377)}}, {{A, B, C, X(3911), X(28609)}}, {{A, B, C, X(3929), X(52819)}}, {{A, B, C, X(4102), X(6598)}}, {{A, B, C, X(5064), X(37445)}}, {{A, B, C, X(5311), X(50095)}}, {{A, B, C, X(7413), X(52281)}}, {{A, B, C, X(8748), X(36910)}}, {{A, B, C, X(10308), X(40399)}}, {{A, B, C, X(17330), X(42028)}}, {{A, B, C, X(17378), X(19723)}}, {{A, B, C, X(17501), X(37887)}}, {{A, B, C, X(29423), X(42051)}}, {{A, B, C, X(30690), X(43758)}}, {{A, B, C, X(34303), X(34578)}}, {{A, B, C, X(38271), X(39980)}}, {{A, B, C, X(46922), X(49724)}}

X(54677) = X(2051)X(3017)∩X(3144)X(16080)

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

X(54677) lies on these lines: {2051, 3017}, {3144, 16080}

X(54677) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(3144)}}, {{A, B, C, X(74), X(1400)}}, {{A, B, C, X(104), X(13610)}}, {{A, B, C, X(225), X(1494)}}, {{A, B, C, X(376), X(37384)}}, {{A, B, C, X(1138), X(2695)}}, {{A, B, C, X(1989), X(15232)}}, {{A, B, C, X(3017), X(17751)}}, {{A, B, C, X(3426), X(45988)}}, {{A, B, C, X(8044), X(52383)}}

X(54678) = X(83)X(11179)∩X(262)X(7739)

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

X(54678) lies on these lines: {83, 11179}, {262, 7739}, {671, 31670}, {1916, 12243}, {3543, 11606}, {6776, 11170}, {7737, 14458}, {8182, 11167}, {9862, 43535}, {18842, 39874}, {43532, 46034}

X(54678) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(46296)}}, {{A, B, C, X(66), X(5641)}}, {{A, B, C, X(74), X(263)}}, {{A, B, C, X(290), X(34288)}}, {{A, B, C, X(420), X(3543)}}, {{A, B, C, X(694), X(3426)}}, {{A, B, C, X(843), X(11738)}}, {{A, B, C, X(7739), X(20023)}}, {{A, B, C, X(11175), X(14483)}}, {{A, B, C, X(11179), X(20021)}}, {{A, B, C, X(14490), X(52660)}}, {{A, B, C, X(19222), X(52187)}}, {{A, B, C, X(31670), X(44146)}}, {{A, B, C, X(41520), X(53221)}}

X(54679) = X(226)X(21578)∩X(381)X(24624)

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

X(54679) lies on these lines: {226, 21578}, {381, 24624}, {860, 43530}, {5136, 16080}, {8818, 18316}

X(54679) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(37525)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(1464)}}, {{A, B, C, X(7), X(21578)}}, {{A, B, C, X(30), X(5136)}}, {{A, B, C, X(104), X(39704)}}, {{A, B, C, X(381), X(860)}}, {{A, B, C, X(519), X(14497)}}, {{A, B, C, X(903), X(1065)}}, {{A, B, C, X(1243), X(39982)}}, {{A, B, C, X(1389), X(40436)}}, {{A, B, C, X(3296), X(51705)}}, {{A, B, C, X(3431), X(53114)}}, {{A, B, C, X(5561), X(18815)}}, {{A, B, C, X(17532), X(37381)}}, {{A, B, C, X(24858), X(34485)}}, {{A, B, C, X(36588), X(38306)}}, {{A, B, C, X(39798), X(44835)}}, {{A, B, C, X(52154), X(52383)}}

X(54680) = X(4)X(11255)∩X(94)X(44518)

Barycentrics    (a^8-3*a^6*b^2+a^4*(b^4+4*b^2*c^2-2*c^4)-(b^2-c^2)^2*(2*b^4+b^2*c^2-c^4)+a^2*(3*b^6-5*b^4*c^2+4*b^2*c^4))*(a^8-3*a^6*c^2+(b^2-c^2)^2*(b^4-b^2*c^2-2*c^4)+a^4*(-2*b^4+4*b^2*c^2+c^4)+a^2*(4*b^4*c^2-5*b^2*c^4+3*c^6)) : :

X(54680) lies on these lines: {4, 11255}, {94, 44518}, {7607, 14118}, {7841, 46105}

X(54680) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(18449)}}, {{A, B, C, X(23), X(7841)}}, {{A, B, C, X(5169), X(8370)}}, {{A, B, C, X(7519), X(33190)}}, {{A, B, C, X(7565), X(41231)}}, {{A, B, C, X(8352), X(52300)}}, {{A, B, C, X(11255), X(40441)}}, {{A, B, C, X(14118), X(52282)}}, {{A, B, C, X(18880), X(33565)}}, {{A, B, C, X(44518), X(52418)}}

X(54681) = (name pending)

Barycentrics    (2*a^8-2*a^6*(b^2-2*c^2)-2*(b^2-c^2)^3*(2*b^2+c^2)+a^4*(-6*b^4+5*b^2*c^2-12*c^4)+a^2*(10*b^6-19*b^4*c^2+5*b^2*c^4+4*c^6))*(2*a^8+a^6*(4*b^2-2*c^2)+2*(b^2-c^2)^3*(b^2+2*c^2)+a^4*(-12*b^4+5*b^2*c^2-6*c^4)+a^2*(4*b^6+5*b^4*c^2-19*b^2*c^4+10*c^6)) : :

X(54681) lies on these lines: {35473, 43530}

X(54681) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(381)}}, {{A, B, C, X(376), X(6188)}}, {{A, B, C, X(1138), X(4846)}}, {{A, B, C, X(1494), X(20421)}}, {{A, B, C, X(3431), X(5627)}}, {{A, B, C, X(3545), X(35481)}}, {{A, B, C, X(11564), X(48911)}}, {{A, B, C, X(18550), X(52154)}}, {{A, B, C, X(19307), X(20480)}}, {{A, B, C, X(35485), X(41106)}}, {{A, B, C, X(38006), X(52187)}}, {{A, B, C, X(45736), X(46412)}}

X(54682) = X(262)X(34664)∩X(275)X(7841)

Barycentrics    (2*a^8-3*a^6*c^2-a^2*c^2*(b^4+10*b^2*c^2-3*c^4)+(b^2-c^2)^2*(2*b^4+b^2*c^2-c^4)-a^4*(4*b^4+b^2*c^2+c^4))*(2*a^8-3*a^6*b^2-(b^2-c^2)^2*(b^4-b^2*c^2-2*c^4)-a^4*(b^4+b^2*c^2+4*c^4)+a^2*(3*b^6-10*b^4*c^2-b^2*c^4)) : :

X(54682) lies on these lines: {262, 34664}, {275, 7841}, {2052, 8370}, {6656, 43530}, {7395, 7608}, {7399, 7607}, {7770, 16080}, {11317, 39284}

X(54682) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(8370)}}, {{A, B, C, X(5), X(7841)}}, {{A, B, C, X(30), X(7770)}}, {{A, B, C, X(140), X(11317)}}, {{A, B, C, X(141), X(18434)}}, {{A, B, C, X(265), X(31360)}}, {{A, B, C, X(308), X(16263)}}, {{A, B, C, X(376), X(32971)}}, {{A, B, C, X(381), X(6656)}}, {{A, B, C, X(458), X(34664)}}, {{A, B, C, X(524), X(14528)}}, {{A, B, C, X(1656), X(8352)}}, {{A, B, C, X(3091), X(33190)}}, {{A, B, C, X(3524), X(32979)}}, {{A, B, C, X(3543), X(16045)}}, {{A, B, C, X(3545), X(32974)}}, {{A, B, C, X(3832), X(33230)}}, {{A, B, C, X(3839), X(32956)}}, {{A, B, C, X(5055), X(33229)}}, {{A, B, C, X(5071), X(32982)}}, {{A, B, C, X(7377), X(17677)}}, {{A, B, C, X(7395), X(52281)}}, {{A, B, C, X(7399), X(52282)}}, {{A, B, C, X(17928), X(37855)}}

X(54683) = X(7608)X(14118)∩X(8370)X(46105)

Barycentrics    (2*a^8-3*a^6*b^2-(b^2-c^2)^2*(b^4-b^2*c^2-2*c^4)-a^4*(b^4-2*b^2*c^2+4*c^4)+a^2*(3*b^6-7*b^4*c^2+2*b^2*c^4))*(2*a^8-3*a^6*c^2+(b^2-c^2)^2*(2*b^4+b^2*c^2-c^4)-a^4*(4*b^4-2*b^2*c^2+c^4)+a^2*(2*b^4*c^2-7*b^2*c^4+3*c^6)) : :

X(54683) lies on these lines: {7608, 14118}, {8370, 46105}, {9221, 34664}

X(54683) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(23), X(8370)}}, {{A, B, C, X(683), X(9141)}}, {{A, B, C, X(5169), X(7841)}}, {{A, B, C, X(7565), X(41237)}}, {{A, B, C, X(11317), X(52300)}}, {{A, B, C, X(14118), X(52281)}}, {{A, B, C, X(30535), X(44549)}}, {{A, B, C, X(37077), X(41238)}}

X(54684) = X(262)X(52069)∩X(7503)X(7608)

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

X(54684) lies on these lines: {262, 52069}, {7503, 7608}, {7607, 13160}, {8370, 43678}, {16080, 41231}, {41237, 43530}

X(54684) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(22), X(8370)}}, {{A, B, C, X(30), X(41231)}}, {{A, B, C, X(381), X(41237)}}, {{A, B, C, X(458), X(52069)}}, {{A, B, C, X(5133), X(7841)}}, {{A, B, C, X(7495), X(11317)}}, {{A, B, C, X(7503), X(52281)}}, {{A, B, C, X(7770), X(34603)}}, {{A, B, C, X(13160), X(52282)}}, {{A, B, C, X(16263), X(42354)}}, {{A, B, C, X(32971), X(34608)}}, {{A, B, C, X(34664), X(52253)}}

X(54685) = X(4)X(9968)∩X(24)X(7607)

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

X(54685) lies on these lines: {4, 9968}, {24, 7607}, {83, 37765}, {98, 7576}, {275, 5523}, {428, 16277}, {671, 32002}, {1594, 7608}, {5392, 52282}, {7487, 43537}, {10018, 10185}, {11140, 44146}, {40393, 52281}

X(54685) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(24), X(52282)}}, {{A, B, C, X(53), X(5523)}}, {{A, B, C, X(297), X(7576)}}, {{A, B, C, X(525), X(15321)}}, {{A, B, C, X(1179), X(18027)}}, {{A, B, C, X(1594), X(52281)}}, {{A, B, C, X(5641), X(8795)}}, {{A, B, C, X(9968), X(22334)}}, {{A, B, C, X(14618), X(32085)}}, {{A, B, C, X(16835), X(28724)}}, {{A, B, C, X(32002), X(44146)}}
X(54685) = polar conjugate of X(7495)
X(54685) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 7495}
X(54685) = barycentric quotient X(i)/X(j) for these (i, j): {4, 7495}

X(54686) = X(10)X(33095)∩X(226)X(4360)

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

X(54686) lies on these lines: {10, 33095}, {226, 4360}, {314, 40013}, {381, 3597}, {7607, 19544}, {7608, 37360}, {41236, 43527}

X(54686) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(80), X(2985)}}, {{A, B, C, X(314), X(903)}}, {{A, B, C, X(596), X(34527)}}, {{A, B, C, X(1016), X(39700)}}, {{A, B, C, X(2481), X(46104)}}, {{A, B, C, X(4654), X(17260)}}, {{A, B, C, X(5064), X(41236)}}, {{A, B, C, X(17251), X(19722)}}, {{A, B, C, X(17289), X(42029)}}, {{A, B, C, X(17330), X(37631)}}, {{A, B, C, X(17577), X(44734)}}, {{A, B, C, X(19544), X(52282)}}, {{A, B, C, X(19786), X(42034)}}, {{A, B, C, X(19796), X(46747)}}, {{A, B, C, X(21353), X(39974)}}, {{A, B, C, X(26736), X(35170)}}, {{A, B, C, X(33095), X(52374)}}, {{A, B, C, X(37360), X(52281)}}, {{A, B, C, X(39696), X(43734)}}, {{A, B, C, X(41816), X(46922)}}
X(54686) = trilinear pole of line {47793, 47872}

X(54687) = X(10)X(36721)∩X(226)X(11238)

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

X(54687) lies on these lines: {10, 36721}, {226, 11238}, {381, 17758}, {4080, 36845}, {10159, 36652}, {10582, 30588}, {13727, 43527}, {14004, 43530}, {36722, 43531}

X(54687) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(27), X(36721)}}, {{A, B, C, X(80), X(1088)}}, {{A, B, C, X(273), X(36910)}}, {{A, B, C, X(381), X(14004)}}, {{A, B, C, X(428), X(36652)}}, {{A, B, C, X(461), X(3839)}}, {{A, B, C, X(469), X(36722)}}, {{A, B, C, X(519), X(3427)}}, {{A, B, C, X(903), X(3062)}}, {{A, B, C, X(1280), X(10308)}}, {{A, B, C, X(3668), X(52187)}}, {{A, B, C, X(3679), X(10582)}}, {{A, B, C, X(4674), X(14490)}}, {{A, B, C, X(5064), X(13727)}}, {{A, B, C, X(5560), X(11238)}}, {{A, B, C, X(5561), X(21453)}}, {{A, B, C, X(15909), X(39704)}}, {{A, B, C, X(36590), X(36620)}}

X(54688) = X(226)X(30305)∩X(1029)X(50687)

Barycentrics    (a^5+a^4*(b+c)+(b-c)^2*(b+c)^3-2*a^3*(b^2+6*b*c+c^2)-2*a^2*(b^3+b^2*c+b*c^2+c^3)+a*(b^4+12*b^3*c-2*b^2*c^2-12*b*c^3+c^4))*(a^5+a^4*(b+c)+(b-c)^2*(b+c)^3-2*a^3*(b^2+6*b*c+c^2)-2*a^2*(b^3+b^2*c+b*c^2+c^3)+a*(b^4-12*b^3*c-2*b^2*c^2+12*b*c^3+c^4)) : :

X(54688) lies on these lines: {226, 30305}, {1029, 50687}, {1446, 15956}, {4194, 16080}, {4200, 43530}, {17758, 37427}

X(54688) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(31393)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(30305)}}, {{A, B, C, X(30), X(4194)}}, {{A, B, C, X(37), X(14490)}}, {{A, B, C, X(40), X(39980)}}, {{A, B, C, X(64), X(39974)}}, {{A, B, C, X(65), X(52187)}}, {{A, B, C, X(79), X(31162)}}, {{A, B, C, X(280), X(17098)}}, {{A, B, C, X(346), X(15956)}}, {{A, B, C, X(381), X(4200)}}, {{A, B, C, X(406), X(3543)}}, {{A, B, C, X(451), X(50687)}}, {{A, B, C, X(475), X(3839)}}, {{A, B, C, X(941), X(3426)}}, {{A, B, C, X(1219), X(16615)}}, {{A, B, C, X(1440), X(5561)}}, {{A, B, C, X(3296), X(44040)}}, {{A, B, C, X(3531), X(39956)}}, {{A, B, C, X(5665), X(36910)}}, {{A, B, C, X(10309), X(39704)}}, {{A, B, C, X(14004), X(37427)}}, {{A, B, C, X(14483), X(39975)}}, {{A, B, C, X(34288), X(51502)}}, {{A, B, C, X(34619), X(36845)}}, {{A, B, C, X(36722), X(37102)}}, {{A, B, C, X(39982), X(52518)}}

X(54689) = X(4)X(48842)∩X(10)X(3545)

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

X(54689) lies on these lines: {4, 48842}, {10, 3545}, {376, 43531}, {381, 43533}, {2048, 3591}, {7397, 43527}, {7402, 10159}, {7490, 43530}

X(54689) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(27), X(3545)}}, {{A, B, C, X(57), X(16615)}}, {{A, B, C, X(79), X(6557)}}, {{A, B, C, X(312), X(3296)}}, {{A, B, C, X(376), X(469)}}, {{A, B, C, X(381), X(7490)}}, {{A, B, C, X(428), X(7402)}}, {{A, B, C, X(461), X(36731)}}, {{A, B, C, X(967), X(14483)}}, {{A, B, C, X(1000), X(4102)}}, {{A, B, C, X(1058), X(1848)}}, {{A, B, C, X(1171), X(14491)}}, {{A, B, C, X(1246), X(36889)}}, {{A, B, C, X(1389), X(39948)}}, {{A, B, C, X(1494), X(8814)}}, {{A, B, C, X(1826), X(52187)}}, {{A, B, C, X(3577), X(34991)}}, {{A, B, C, X(4846), X(48842)}}, {{A, B, C, X(5064), X(7397)}}, {{A, B, C, X(5071), X(6994)}}, {{A, B, C, X(7377), X(7714)}}, {{A, B, C, X(10308), X(25430)}}, {{A, B, C, X(10435), X(36588)}}, {{A, B, C, X(14497), X(42467)}}, {{A, B, C, X(14555), X(37631)}}, {{A, B, C, X(31162), X(52374)}}, {{A, B, C, X(42030), X(43734)}}

X(54690) = X(226)X(10385)∩X(376)X(17758)

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

X(54690) lies on these lines: {226, 10385}, {376, 17758}, {461, 16080}, {1446, 5543}, {2394, 4843}, {3332, 45097}, {36682, 43527}, {36722, 43533}

X(54690) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(5543)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(36625)}}, {{A, B, C, X(30), X(461)}}, {{A, B, C, X(79), X(50865)}}, {{A, B, C, X(200), X(15933)}}, {{A, B, C, X(376), X(14004)}}, {{A, B, C, X(972), X(39980)}}, {{A, B, C, X(1000), X(21453)}}, {{A, B, C, X(3296), X(10385)}}, {{A, B, C, X(5064), X(36682)}}, {{A, B, C, X(5561), X(36620)}}, {{A, B, C, X(5665), X(36627)}}, {{A, B, C, X(7490), X(36722)}}, {{A, B, C, X(7714), X(13727)}}, {{A, B, C, X(8814), X(52187)}}, {{A, B, C, X(10307), X(39704)}}, {{A, B, C, X(15909), X(36588)}}

X(54691) = X(381)X(45964)∩X(6830)X(7608)

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

X(54691) lies on these lines: {381, 45964}, {6830, 7608}, {6844, 53099}, {6879, 53098}, {6905, 7607}, {43537, 50701}

X(54691) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(4231), X(7841)}}, {{A, B, C, X(6830), X(52281)}}, {{A, B, C, X(6905), X(52282)}}, {{A, B, C, X(39957), X(44835)}}

X(54692) = X(3149)X(7607)∩X(6831)X(7608)

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

X(54692) lies on these lines: {3149, 7607}, {6831, 7608}, {6956, 53098}, {11341, 43530}, {43537, 50700}, {45964, 52269}

X(54692) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(381), X(11341)}}, {{A, B, C, X(3149), X(52282)}}, {{A, B, C, X(6831), X(52281)}}, {{A, B, C, X(8370), X(37362)}}, {{A, B, C, X(15909), X(34914)}}

X(54693) = X(28)X(43530)∩X(321)X(381)

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

X(54693) lies on these lines: {28, 43530}, {321, 381}, {5142, 16080}, {37431, 43527}

X(54693) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(28), X(381)}}, {{A, B, C, X(30), X(5142)}}, {{A, B, C, X(1169), X(14483)}}, {{A, B, C, X(1494), X(51223)}}, {{A, B, C, X(3531), X(46010)}}, {{A, B, C, X(3545), X(4198)}}, {{A, B, C, X(3839), X(7521)}}, {{A, B, C, X(4492), X(10308)}}, {{A, B, C, X(4846), X(20336)}}, {{A, B, C, X(5064), X(37431)}}, {{A, B, C, X(34288), X(41013)}}

X(54694) = X(321)X(28194)∩X(10159)X(37088)

Barycentrics    (2*a^5+5*a^4*(b+c)-(b+c)^3*(b^2+b*c-2*c^2)+a^3*(2*b^2+3*b*c+5*c^2)+a^2*(-4*b^3-b^2*c+8*b*c^2+5*c^3)-a*(4*b^4+3*b^3*c+b^2*c^2-3*b*c^3-5*c^4))*(2*a^5+5*a^4*(b+c)+(b+c)^3*(2*b^2-b*c-c^2)+a^3*(5*b^2+3*b*c+2*c^2)+a^2*(5*b^3+8*b^2*c-b*c^2-4*c^3)+a*(5*b^4+3*b^3*c-b^2*c^2-3*b*c^3-4*c^4)) : :

X(54694) lies on these lines: {321, 28194}, {10159, 37088}, {16080, 37390}

X(54694) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(37390)}}, {{A, B, C, X(428), X(37088)}}, {{A, B, C, X(513), X(28194)}}, {{A, B, C, X(752), X(28478)}}, {{A, B, C, X(14490), X(14553)}}, {{A, B, C, X(17133), X(28475)}}, {{A, B, C, X(34288), X(39130)}}

X(54695) = X(6833)X(43537)∩X(6834)X(53099)

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

X(54695) lies on these lines: {6833, 43537}, {6834, 53099}, {6847, 47586}, {6949, 7608}, {6952, 7607}

X(54695) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(39957)}}, {{A, B, C, X(104), X(34914)}}, {{A, B, C, X(1389), X(34892)}}, {{A, B, C, X(3296), X(41791)}}, {{A, B, C, X(6949), X(52281)}}, {{A, B, C, X(6952), X(52282)}}, {{A, B, C, X(14483), X(39979)}}, {{A, B, C, X(34621), X(37276)}}, {{A, B, C, X(34897), X(43724)}}

X(54696) = X(226)X(3656)∩X(381)X(14554)

Barycentrics    (a^5-2*a^4*(b+c)-(2*b-c)*(b^2-c^2)^2+a^3*(-2*b^2+9*b*c+c^2)+a^2*(4*b^3+b^2*c-2*b*c^2+c^3)+a*(b^4-9*b^3*c+b^2*c^2+9*b*c^3-2*c^4))*(a^5-2*a^4*(b+c)+a^3*(b^2+9*b*c-2*c^2)+(b-2*c)*(b^2-c^2)^2+a^2*(b^3-2*b^2*c+b*c^2+4*c^3)+a*(-2*b^4+9*b^3*c+b^2*c^2-9*b*c^3+c^4)) : :

X(54696) lies on these lines: {226, 3656}, {381, 14554}, {4080, 12648}

X(54696) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(36596)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(36590)}}, {{A, B, C, X(79), X(3656)}}, {{A, B, C, X(519), X(12648)}}, {{A, B, C, X(903), X(3577)}}, {{A, B, C, X(3062), X(3679)}}, {{A, B, C, X(3531), X(4674)}}, {{A, B, C, X(6735), X(10072)}}, {{A, B, C, X(39704), X(46435)}}

X(54697) = X(10)X(52524)∩X(2394)X(3910)

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

X(54697) lies on these lines: {10, 52524}, {2394, 3910}

X(54697) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(3910)}}, {{A, B, C, X(79), X(46880)}}, {{A, B, C, X(345), X(34800)}}, {{A, B, C, X(10308), X(37870)}}, {{A, B, C, X(16615), X(30710)}}, {{A, B, C, X(52374), X(52524)}}

X(54698) = (name pending)

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

X(54698) lies on these lines: {11105, 16080}

X(54698) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(36590)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(11105)}}, {{A, B, C, X(84), X(3679)}}, {{A, B, C, X(903), X(1389)}}, {{A, B, C, X(1065), X(23959)}}, {{A, B, C, X(3582), X(3615)}}, {{A, B, C, X(4674), X(14483)}}

X(54699) = X(10)X(48903)∩X(536)X(43683)

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

X(54699) lies on these lines: {10, 48903}, {536, 43683}, {2394, 23876}, {3666, 43682}, {6003, 35353}

X(54699) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(23876)}}, {{A, B, C, X(35), X(3666)}}, {{A, B, C, X(81), X(2687)}}, {{A, B, C, X(522), X(46880)}}, {{A, B, C, X(536), X(6003)}}, {{A, B, C, X(29348), X(32849)}}, {{A, B, C, X(34800), X(52351)}}, {{A, B, C, X(48903), X(52374)}}

X(54700) = X(10)X(500)∩X(583)X(2051)

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

X(54700) lies on these lines: {10, 500}, {321, 16585}, {583, 2051}, {2394, 23875}, {13576, 41853}

X(54700) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(23875)}}, {{A, B, C, X(58), X(500)}}, {{A, B, C, X(572), X(583)}}, {{A, B, C, X(28840), X(29016)}}, {{A, B, C, X(34800), X(52381)}}

X(54701) = X(517)X(34475)∩X(28470)X(35353)

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

X(54701) lies on these lines: {517, 34475}, {28470, 35353}

X(54701) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(517), X(4785)}}, {{A, B, C, X(536), X(28470)}}, {{A, B, C, X(3666), X(42030)}}, {{A, B, C, X(3845), X(31916)}}, {{A, B, C, X(5560), X(27424)}}, {{A, B, C, X(28468), X(28562)}}

X(54702) = X(2052)X(48814)∩X(11110)X(16080)

Barycentrics    (2*a^8-a^7*(b+c)-a*(b-c)^2*(b+c)^3*(b^2+4*b*c+c^2)-a^6*(7*b^2+5*b*c+4*c^2)-(b-c)^2*(b+c)^3*(b^3+3*b*c^2-2*c^3)+a^5*(b^3-3*b^2*c-3*b*c^2+c^3)-a^2*(b+c)^2*(b^4+b^3*c-5*b^2*c^2-5*b*c^3+4*c^4)+a^4*(7*b^4+9*b^3*c+11*b^2*c^2+9*b*c^3+4*c^4)+a^3*(b^5+9*b^4*c+14*b^3*c^2+14*b^2*c^3+9*b*c^4+c^5))*(2*a^8-a^7*(b+c)-a*(b-c)^2*(b+c)^3*(b^2+4*b*c+c^2)-a^6*(4*b^2+5*b*c+7*c^2)+(b-c)^2*(b+c)^3*(2*b^3-3*b^2*c-c^3)+a^5*(b^3-3*b^2*c-3*b*c^2+c^3)-a^2*(b+c)^2*(4*b^4-5*b^3*c-5*b^2*c^2+b*c^3+c^4)+a^4*(4*b^4+9*b^3*c+11*b^2*c^2+9*b*c^3+7*c^4)+a^3*(b^5+9*b^4*c+14*b^3*c^2+14*b^2*c^3+9*b*c^4+c^5)) : :

X(54702) lies on these lines: {2052, 48814}, {11110, 16080}

X(54702) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(48814)}}, {{A, B, C, X(30), X(11110)}}, {{A, B, C, X(376), X(13736)}}, {{A, B, C, X(7415), X(13745)}}

X(54703) = X(4)X(34779)∩X(83)X(10549)

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

X(54703) lies on these lines: {4, 34779}, {83, 10549}, {98, 3575}, {262, 7507}, {275, 5254}, {317, 2996}, {393, 5395}, {598, 2207}, {3515, 7607}, {12362, 40448}

X(54703) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(53), X(5254)}}, {{A, B, C, X(66), X(9289)}}, {{A, B, C, X(70), X(34386)}}, {{A, B, C, X(287), X(6145)}}, {{A, B, C, X(458), X(7507)}}, {{A, B, C, X(683), X(8795)}}, {{A, B, C, X(1179), X(14618)}}, {{A, B, C, X(3426), X(34779)}}, {{A, B, C, X(3515), X(52282)}}, {{A, B, C, X(3926), X(38442)}}, {{A, B, C, X(6531), X(10549)}}, {{A, B, C, X(8884), X(18027)}}, {{A, B, C, X(12362), X(52280)}}, {{A, B, C, X(14376), X(44836)}}, {{A, B, C, X(14542), X(42313)}}, {{A, B, C, X(14860), X(16081)}}, {{A, B, C, X(18855), X(42298)}}, {{A, B, C, X(38447), X(44549)}}
X(54703) = polar conjugate of X(6676)
X(54703) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 6676}, {63, 21637}, {255, 7745}, {18063, 39201}
X(54703) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 6676}, {3162, 21637}, {6523, 7745}
X(54703) = barycentric quotient X(i)/X(j) for these (i, j): {4, 6676}, {25, 21637}, {393, 7745}, {823, 18063}

X(54704) = X(3543)X(52583)∩X(7391)X(16080)

Barycentrics    (3*a^10+3*a^8*(b^2-c^2)+3*(b^2-c^2)^3*(b^2+c^2)^2-2*a^6*(3*b^4+b^2*c^2+3*c^4)+a^2*(b^2-c^2)^2*(3*b^4+4*b^2*c^2+3*c^4)-2*a^4*(3*b^6-5*b^4*c^2+b^2*c^4-3*c^6))*(3*a^10-3*a^8*(b^2-c^2)-3*(b^2-c^2)^3*(b^2+c^2)^2-2*a^6*(3*b^4+b^2*c^2+3*c^4)+a^2*(b^2-c^2)^2*(3*b^4+4*b^2*c^2+3*c^4)+2*a^4*(3*b^6-b^4*c^2+5*b^2*c^4-3*c^6)) : :

X(54704) lies on these lines: {3543, 52583}, {7391, 16080}, {7394, 43530}, {38253, 44442}

X(54704) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(7391)}}, {{A, B, C, X(66), X(34570)}}, {{A, B, C, X(381), X(7394)}}, {{A, B, C, X(1297), X(32533)}}, {{A, B, C, X(1370), X(3543)}}, {{A, B, C, X(3146), X(44442)}}, {{A, B, C, X(3545), X(37349)}}, {{A, B, C, X(3830), X(16063)}}, {{A, B, C, X(3839), X(6997)}}, {{A, B, C, X(5189), X(15682)}}, {{A, B, C, X(7386), X(50687)}}, {{A, B, C, X(7533), X(41099)}}, {{A, B, C, X(13575), X(43699)}}, {{A, B, C, X(14457), X(34572)}}, {{A, B, C, X(17505), X(40801)}}, {{A, B, C, X(31133), X(44440)}}, {{A, B, C, X(34603), X(37444)}}

X(54705) = X(83)X(34007)∩X(275)X(37349)

Barycentrics    (a^10+a^8*(-b^2+c^2)-(b^2-c^2)^3*(b^2+c^2)^2-a^6*(2*b^4+b^2*c^2+2*c^4)+2*a^4*(b^6+2*b^2*c^4-c^6)+a^2*(b^8-b^6*c^2-b^2*c^6+c^8))*(a^10+a^8*(b^2-c^2)+(b^2-c^2)^3*(b^2+c^2)^2-a^6*(2*b^4+b^2*c^2+2*c^4)+a^4*(-2*b^6+4*b^4*c^2+2*c^6)+a^2*(b^8-b^6*c^2-b^2*c^6+c^8)) : :

X(54705) lies on these lines: {83, 34007}, {275, 37349}, {459, 7391}, {1370, 38253}, {2394, 36853}, {3146, 52583}, {3153, 46105}, {3424, 18382}, {5189, 16080}, {7533, 43530}

X(54705) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(37349)}}, {{A, B, C, X(20), X(7391)}}, {{A, B, C, X(23), X(3153)}}, {{A, B, C, X(30), X(5189)}}, {{A, B, C, X(66), X(41894)}}, {{A, B, C, X(67), X(34570)}}, {{A, B, C, X(250), X(18125)}}, {{A, B, C, X(251), X(22466)}}, {{A, B, C, X(265), X(1297)}}, {{A, B, C, X(381), X(7533)}}, {{A, B, C, X(427), X(34007)}}, {{A, B, C, X(858), X(52403)}}, {{A, B, C, X(895), X(13573)}}, {{A, B, C, X(1370), X(3146)}}, {{A, B, C, X(2475), X(37456)}}, {{A, B, C, X(3091), X(7394)}}, {{A, B, C, X(3521), X(5481)}}, {{A, B, C, X(3543), X(16063)}}, {{A, B, C, X(3832), X(6997)}}, {{A, B, C, X(5059), X(44442)}}, {{A, B, C, X(5900), X(29322)}}, {{A, B, C, X(6145), X(41513)}}, {{A, B, C, X(6815), X(7409)}}, {{A, B, C, X(6816), X(7408)}}, {{A, B, C, X(7386), X(17578)}}, {{A, B, C, X(7392), X(50689)}}, {{A, B, C, X(7492), X(31723)}}, {{A, B, C, X(7500), X(37444)}}, {{A, B, C, X(7519), X(18531)}}, {{A, B, C, X(7574), X(37901)}}, {{A, B, C, X(10002), X(18382)}}, {{A, B, C, X(11744), X(29180)}}, {{A, B, C, X(13575), X(15749)}}, {{A, B, C, X(14457), X(39955)}}, {{A, B, C, X(14790), X(20062)}}, {{A, B, C, X(14957), X(40236)}}, {{A, B, C, X(15321), X(41890)}}, {{A, B, C, X(18018), X(18848)}}, {{A, B, C, X(18019), X(34168)}}, {{A, B, C, X(18403), X(37760)}}, {{A, B, C, X(18569), X(37913)}}, {{A, B, C, X(18572), X(37909)}}, {{A, B, C, X(20063), X(46450)}}, {{A, B, C, X(21400), X(40801)}}, {{A, B, C, X(29011), X(33565)}}, {{A, B, C, X(31074), X(50009)}}, {{A, B, C, X(31099), X(44440)}}, {{A, B, C, X(41896), X(43699)}}, {{A, B, C, X(42484), X(52443)}}, {{A, B, C, X(46336), X(50687)}}
X(54705) = X(i)-cross conjugate of X(j) for these {i, j}: {52058, 2}

X(54706) = X(2)X(48872)∩X(76)X(50689)

Barycentrics    (7*a^4+7*b^4+2*b^2*c^2-9*c^4+2*a^2*(9*b^2+c^2))*(7*a^4-9*b^4+2*b^2*c^2+7*c^4+2*a^2*(b^2+9*c^2)) : :

X(54706) lies on these lines: {2, 48872}, {76, 50689}, {83, 17578}, {459, 7409}, {3146, 18841}, {3832, 18840}, {3854, 10159}, {5059, 43527}, {7000, 34089}, {7374, 34091}, {7378, 38253}, {18842, 50687}

X(54706) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(20), X(7409)}}, {{A, B, C, X(25), X(50689)}}, {{A, B, C, X(427), X(17578)}}, {{A, B, C, X(428), X(3854)}}, {{A, B, C, X(1297), X(3531)}}, {{A, B, C, X(1799), X(18296)}}, {{A, B, C, X(3089), X(37349)}}, {{A, B, C, X(3091), X(7408)}}, {{A, B, C, X(3108), X(22334)}}, {{A, B, C, X(3146), X(7378)}}, {{A, B, C, X(3832), X(6995)}}, {{A, B, C, X(3839), X(52301)}}, {{A, B, C, X(5059), X(5064)}}, {{A, B, C, X(8801), X(45819)}}, {{A, B, C, X(14457), X(41513)}}, {{A, B, C, X(14487), X(14495)}}, {{A, B, C, X(14490), X(29180)}}, {{A, B, C, X(14491), X(29011)}}, {{A, B, C, X(15321), X(52224)}}, {{A, B, C, X(18018), X(31361)}}, {{A, B, C, X(39955), X(52518)}}, {{A, B, C, X(43726), X(52443)}}, {{A, B, C, X(48872), X(52223)}}, {{A, B, C, X(50687), X(52284)}}, {{A, B, C, X(50693), X(52285)}}
X(54706) = X(i)-cross conjugate of X(j) for these {i, j}: {14930, 2}

X(54707) = X(76)X(41106)∩X(83)X(11001)

Barycentrics    (5*a^4+5*b^4+8*b^2*c^2-13*c^4+a^2*(26*b^2+8*c^2))*(5*a^4-13*b^4+8*b^2*c^2+5*c^4+a^2*(8*b^2+26*c^2)) : :

X(54707) lies on these lines: {76, 41106}, {83, 11001}, {381, 43681}, {2996, 41099}, {3524, 43527}, {3830, 18845}, {3845, 38259}, {5071, 10159}, {5395, 15682}, {5480, 53103}, {18841, 19708}

X(54707) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(41106)}}, {{A, B, C, X(427), X(11001)}}, {{A, B, C, X(428), X(5071)}}, {{A, B, C, X(3108), X(20421)}}, {{A, B, C, X(3524), X(5064)}}, {{A, B, C, X(3531), X(36616)}}, {{A, B, C, X(3545), X(7714)}}, {{A, B, C, X(3613), X(46204)}}, {{A, B, C, X(3830), X(52299)}}, {{A, B, C, X(3845), X(38282)}}, {{A, B, C, X(6353), X(41099)}}, {{A, B, C, X(7378), X(19708)}}, {{A, B, C, X(8770), X(14487)}}, {{A, B, C, X(8889), X(15682)}}, {{A, B, C, X(11181), X(14491)}}, {{A, B, C, X(11738), X(39951)}}, {{A, B, C, X(32085), X(46212)}}, {{A, B, C, X(34288), X(43458)}}, {{A, B, C, X(36611), X(43726)}}, {{A, B, C, X(38006), X(39978)}}

X(54708) = X(76)X(36583)∩X(83)X(36512)

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

X(54708) lies on these lines: {76, 36583}, {83, 36512}, {10159, 36561}, {19548, 43527}, {36571, 43530}

X(54708) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(36583)}}, {{A, B, C, X(381), X(36571)}}, {{A, B, C, X(427), X(36512)}}, {{A, B, C, X(428), X(36561)}}, {{A, B, C, X(5064), X(19548)}}

X(54709) = X(76)X(16072)∩X(1368)X(16080)

Barycentrics    (a^10+3*a^8*c^2+3*a^2*(b^2-c^2)^2*(b^4+c^4)-(b^2-c^2)^3*(2*b^4+3*b^2*c^2+c^4)-2*a^6*(2*b^4+3*b^2*c^2+2*c^4)+2*a^4*(b^6+3*b^4*c^2+6*b^2*c^4-2*c^6))*(a^10+3*a^8*b^2+3*a^2*(b^2-c^2)^2*(b^4+c^4)+(b^2-c^2)^3*(b^4+3*b^2*c^2+2*c^4)-2*a^6*(2*b^4+3*b^2*c^2+2*c^4)+2*a^4*(-2*b^6+6*b^4*c^2+3*b^2*c^4+c^6)) : :

X(54709) lies on these lines: {76, 16072}, {1368, 16080}, {2052, 34609}, {5020, 43530}, {31180, 43678}

X(54709) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(34609)}}, {{A, B, C, X(22), X(31180)}}, {{A, B, C, X(25), X(16072)}}, {{A, B, C, X(30), X(1368)}}, {{A, B, C, X(265), X(40413)}}, {{A, B, C, X(305), X(1294)}}, {{A, B, C, X(376), X(7396)}}, {{A, B, C, X(381), X(5020)}}, {{A, B, C, X(858), X(44458)}}, {{A, B, C, X(1494), X(6391)}}, {{A, B, C, X(3545), X(7398)}}, {{A, B, C, X(6340), X(18850)}}, {{A, B, C, X(8703), X(47315)}}, {{A, B, C, X(14489), X(14860)}}, {{A, B, C, X(15319), X(40801)}}, {{A, B, C, X(21312), X(31152)}}, {{A, B, C, X(44212), X(44920)}}

X(54710) = X(2)X(33630)∩X(4)X(15153)

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

X(54710) lies on these lines: {2, 33630}, {4, 15153}, {25, 47586}, {275, 14361}, {297, 43681}, {393, 38253}, {472, 43557}, {473, 43556}, {3424, 7714}, {3524, 40448}, {3535, 3590}, {3536, 3591}, {3545, 31363}, {5064, 43951}, {5071, 13599}, {6353, 43537}, {7607, 38282}, {7608, 52299}, {8796, 51358}, {8889, 53099}, {13582, 37192}, {18845, 52281}, {38259, 52282}, {52290, 53859}

X(54710) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(64), X(36609)}}, {{A, B, C, X(196), X(52374)}}, {{A, B, C, X(393), X(33630)}}, {{A, B, C, X(394), X(13452)}}, {{A, B, C, X(1073), X(16835)}}, {{A, B, C, X(3524), X(52280)}}, {{A, B, C, X(7003), X(36910)}}, {{A, B, C, X(7714), X(52283)}}, {{A, B, C, X(13157), X(13450)}}, {{A, B, C, X(36121), X(39980)}}, {{A, B, C, X(37192), X(37943)}}, {{A, B, C, X(38264), X(42374)}}, {{A, B, C, X(38282), X(52282)}}, {{A, B, C, X(42468), X(52581)}}, {{A, B, C, X(52281), X(52299)}}
X(54710) = polar conjugate of X(3522)
X(54710) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 3522}
X(54710) = X(i)-cross conjugate of X(j) for these {i, j}: {1906, 264}
X(54710) = barycentric product X(i)*X(j) for these (i, j): {22334, 264}
X(54710) = barycentric quotient X(i)/X(j) for these (i, j): {4, 3522}, {8801, 51830}, {22334, 3}

X(54711) = X(2052)X(34664)∩X(7395)X(16080)

Barycentrics    (2*a^14-a^12*(7*b^2+4*c^2)+6*a^10*(b^4+2*b^2*c^2)+2*a^2*(b^2-c^2)^4*(b^4-2*b^2*c^2-2*c^4)-(b^2-c^2)^5*(b^4+3*b^2*c^2+2*c^4)+a^8*(5*b^6-6*b^4*c^2+15*b^2*c^4+2*c^6)-2*a^6*(5*b^8+8*b^6*c^2+20*b^2*c^6-c^8)+3*a^4*(b^10+8*b^8*c^2-14*b^6*c^4+5*b^2*c^8))*(2*a^14-a^12*(4*b^2+7*c^2)-2*a^2*(b^2-c^2)^4*(2*b^4+2*b^2*c^2-c^4)+6*a^10*(2*b^2*c^2+c^4)+(b^2-c^2)^5*(2*b^4+3*b^2*c^2+c^4)+a^8*(2*b^6+15*b^4*c^2-6*b^2*c^4+5*c^6)+2*a^6*(b^8-20*b^6*c^2-8*b^2*c^6-5*c^8)+3*a^4*(5*b^8*c^2-14*b^4*c^6+8*b^2*c^8+c^10)) : :

X(54711) lies on these lines: {2052, 34664}, {7395, 16080}, {7399, 43530}

X(54711) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(34664)}}, {{A, B, C, X(30), X(7395)}}, {{A, B, C, X(381), X(7399)}}, {{A, B, C, X(6804), X(34621)}}, {{A, B, C, X(6823), X(16072)}}, {{A, B, C, X(7509), X(52069)}}

X(54712) = X(226)X(30308)∩X(461)X(43530)

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

X(54712) lies on these lines: {226, 30308}, {461, 43530}, {3545, 17758}, {10159, 36682}, {36721, 43533}

X(54712) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(30350)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(80), X(36620)}}, {{A, B, C, X(273), X(36916)}}, {{A, B, C, X(381), X(461)}}, {{A, B, C, X(428), X(36682)}}, {{A, B, C, X(903), X(10307)}}, {{A, B, C, X(972), X(36603)}}, {{A, B, C, X(1000), X(1088)}}, {{A, B, C, X(3062), X(36588)}}, {{A, B, C, X(3545), X(14004)}}, {{A, B, C, X(5560), X(30308)}}, {{A, B, C, X(7490), X(36721)}}, {{A, B, C, X(7714), X(36652)}}, {{A, B, C, X(8814), X(52188)}}, {{A, B, C, X(10308), X(39959)}}, {{A, B, C, X(33576), X(36627)}}

X(54713) = X(2)X(11156)∩X(381)X(8781)

Barycentrics    (4*a^6-5*b^6+8*b^4*c^2-7*b^2*c^4+4*c^6+a^4*(-7*b^2+2*c^2)+2*a^2*(4*b^4+c^4))*(4*a^6+4*b^6-7*b^4*c^2+8*b^2*c^4-5*c^6+a^4*(2*b^2-7*c^2)+2*a^2*(b^4+4*c^4)) : :

X(54713) lies on these lines: {2, 11156}, {381, 8781}, {460, 43530}, {671, 18440}, {1916, 9880}, {2996, 11180}, {5395, 5476}, {14458, 53419}

X(54713) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(381), X(460)}}, {{A, B, C, X(3426), X(9515)}}, {{A, B, C, X(3531), X(14906)}}, {{A, B, C, X(5203), X(18440)}}, {{A, B, C, X(5641), X(9307)}}, {{A, B, C, X(16263), X(39645)}}, {{A, B, C, X(34288), X(35142)}}

X(54714) = X(598)X(48906)∩X(2996)X(20423)

Barycentrics    (2*a^6+2*b^6-11*b^4*c^2+10*b^2*c^4-c^6-a^4*(8*b^2+11*c^2)-2*a^2*(4*b^4+6*b^2*c^2-5*c^4))*(2*a^6-b^6+10*b^4*c^2-11*b^2*c^4+2*c^6-a^4*(11*b^2+8*c^2)+2*a^2*(5*b^4-6*b^2*c^2-4*c^4)) : :

X(54714) lies on these lines: {598, 48906}, {2996, 20423}, {9993, 11167}, {10033, 11172}, {11645, 53101}, {14458, 53418}, {40925, 53099}

X(54714) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(512), X(3531)}}, {{A, B, C, X(3426), X(43950)}}, {{A, B, C, X(14483), X(44557)}}, {{A, B, C, X(14487), X(52230)}}, {{A, B, C, X(18550), X(48906)}}

X(54715) = X(83)X(46267)∩X(98)X(14537)

Barycentrics    (2*a^6-b^6+7*b^4*c^2-8*b^2*c^4+2*c^6-a^4*(8*b^2+5*c^2)+a^2*(7*b^4-9*b^2*c^2-5*c^4))*(2*a^6+2*b^6-8*b^4*c^2+7*b^2*c^4-c^6-a^4*(5*b^2+8*c^2)+a^2*(-5*b^4-9*b^2*c^2+7*c^4)) : :

X(54715) lies on these lines: {83, 46267}, {98, 14537}, {3845, 43535}, {7608, 11676}, {11172, 41099}, {11645, 45103}, {15980, 43528}, {35930, 43529}

X(54715) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(43950)}}, {{A, B, C, X(512), X(14483)}}, {{A, B, C, X(11676), X(52281)}}, {{A, B, C, X(14491), X(44557)}}

X(54716) = X(83)X(43273)∩X(5485)X(31670)

Barycentrics    (2*a^6+2*b^6+7*b^4*c^2-8*b^2*c^4-c^6+a^4*(10*b^2+7*c^2)+2*a^2*(5*b^4+3*b^2*c^2-4*c^4))*(2*a^6-b^6-8*b^4*c^2+7*b^2*c^4+2*c^6+a^4*(7*b^2+10*c^2)+a^2*(-8*b^4+6*b^2*c^2+10*c^4)) : :

X(54716) lies on these lines: {83, 43273}, {5485, 31670}, {5503, 48657}, {7739, 14484}, {11645, 18842}, {14458, 18907}, {14485, 36990}, {18840, 50977}, {18841, 38064}, {43951, 46034}

X(54716) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(512), X(14490)}}, {{A, B, C, X(3426), X(44557)}}, {{A, B, C, X(14486), X(53774)}}, {{A, B, C, X(18434), X(43273)}}

X(54717) = X(2)X(48879)∩X(76)X(14269)

Barycentrics    (7*a^4+7*b^4+b^2*c^2-8*c^4+a^2*(16*b^2+c^2))*(7*a^4-8*b^4+b^2*c^2+7*c^4+a^2*(b^2+16*c^2)) : :

X(54717) lies on these lines: {2, 48879}, {76, 14269}, {83, 15687}, {382, 43527}, {383, 43443}, {546, 10159}, {1080, 43442}, {3845, 10302}, {7872, 18841}, {16080, 52285}

X(54717) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(14269)}}, {{A, B, C, X(30), X(52285)}}, {{A, B, C, X(382), X(5064)}}, {{A, B, C, X(427), X(15687)}}, {{A, B, C, X(428), X(546)}}, {{A, B, C, X(1173), X(29322)}}, {{A, B, C, X(3845), X(10301)}}, {{A, B, C, X(14388), X(14487)}}, {{A, B, C, X(29011), X(34572)}}, {{A, B, C, X(29316), X(46848)}}, {{A, B, C, X(45857), X(48911)}}

X(54718) = X(2)X(11155)∩X(671)X(21850)

Barycentrics    (a^6-2*b^6+11*b^4*c^2-10*b^2*c^4+c^6-a^4*(10*b^2+7*c^2)+a^2*(11*b^4-6*b^2*c^2-7*c^4))*(a^6+b^6-10*b^4*c^2+11*b^2*c^4-2*c^6-a^4*(7*b^2+10*c^2)+a^2*(-7*b^4-6*b^2*c^2+11*c^4)) : :

X(54718) lies on these lines: {2, 11155}, {671, 21850}, {5395, 11179}, {8724, 8781}, {9880, 11606}, {10722, 43535}, {14492, 53419}

X(54718) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(843), X(13603)}}, {{A, B, C, X(3531), X(30495)}}, {{A, B, C, X(5203), X(21850)}}, {{A, B, C, X(8724), X(34174)}}

X(54719) = X(6833)X(53099)∩X(6834)X(43537)

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

X(54719) lies on these lines: {6833, 53099}, {6834, 43537}, {6848, 47586}, {6949, 7607}, {6952, 7608}

X(54719) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(39979)}}, {{A, B, C, X(104), X(34892)}}, {{A, B, C, X(1389), X(34914)}}, {{A, B, C, X(6949), X(52282)}}, {{A, B, C, X(6952), X(52281)}}, {{A, B, C, X(14483), X(39957)}}, {{A, B, C, X(34578), X(47645)}}

X(54720) = X(4)X(20583)∩X(376)X(53104)

Barycentrics    (13*a^2+13*b^2-17*c^2)*(13*a^2-17*b^2+13*c^2) : :

X(54720) lies on these lines: {4, 20583}, {376, 53104}, {382, 43537}, {546, 53099}, {550, 53859}, {1992, 53105}, {3424, 15687}, {3529, 7607}, {3544, 53098}, {3545, 11669}, {3855, 7608}, {5485, 40341}, {8596, 35005}, {10185, 10299}, {11668, 15710}, {14269, 14484}, {18842, 53419}, {18844, 44518}, {47586, 50688}

X(54720) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(66), X(1992)}}, {{A, B, C, X(69), X(20583)}}, {{A, B, C, X(249), X(11741)}}, {{A, B, C, X(599), X(43726)}}, {{A, B, C, X(3426), X(11736)}}, {{A, B, C, X(3529), X(52282)}}, {{A, B, C, X(3613), X(23054)}}, {{A, B, C, X(3855), X(52281)}}, {{A, B, C, X(6464), X(46851)}}, {{A, B, C, X(7714), X(33229)}}, {{A, B, C, X(11738), X(21399)}}, {{A, B, C, X(14269), X(52288)}}, {{A, B, C, X(15687), X(52283)}}, {{A, B, C, X(34164), X(36877)}}, {{A, B, C, X(43699), X(51136)}}

X(54721) = X(226)X(48819)∩X(321)X(31162)

Barycentrics    (a^5+4*a^4*(b+c)+(b+c)^3*(b^2+b*c-2*c^2)+a^3*(7*b^2+3*b*c+4*c^2)+a^2*(7*b^3+10*b^2*c+b*c^2-2*c^3)+a*(4*b^4+3*b^3*c+b^2*c^2-3*b*c^3-5*c^4))*(a^5+4*a^4*(b+c)-(b+c)^3*(2*b^2-b*c-c^2)+a^3*(4*b^2+3*b*c+7*c^2)+a^2*(-2*b^3+b^2*c+10*b*c^2+7*c^3)+a*(-5*b^4-3*b^3*c+b^2*c^2+3*b*c^3+4*c^4)) : :

X(54721) lies on these lines: {226, 48819}, {321, 31162}, {37088, 43527}, {37390, 43530}

X(54721) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(79), X(48819)}}, {{A, B, C, X(381), X(37390)}}, {{A, B, C, X(4968), X(36588)}}, {{A, B, C, X(5064), X(37088)}}, {{A, B, C, X(31162), X(52372)}}, {{A, B, C, X(39130), X(52187)}}

X(54722) = (name pending)

Barycentrics    (a^5-2*a^4*(b+c)-a^3*(5*b^2+3*b*c+5*c^2)+a^2*(b^3-2*b^2*c-8*b*c^2-5*c^3)+(b+c)^2*(b^3+2*b^2*c-4*b*c^2+c^3)+a*(4*b^4+3*b^3*c-2*b^2*c^2-3*b*c^3-2*c^4))*(a^5-2*a^4*(b+c)-a^3*(5*b^2+3*b*c+5*c^2)+a^2*(-5*b^3-8*b^2*c-2*b*c^2+c^3)+(b+c)^2*(b^3-4*b^2*c+2*b*c^2+c^3)+a*(-2*b^4-3*b^3*c-2*b^2*c^2+3*b*c^3+4*c^4)) : :

X(54722) lies on these lines: {3144, 43530}

X(54722) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(381), X(3144)}}, {{A, B, C, X(959), X(1168)}}, {{A, B, C, X(1400), X(14483)}}, {{A, B, C, X(3531), X(45988)}}, {{A, B, C, X(3545), X(37384)}}, {{A, B, C, X(15232), X(30537)}}

X(54723) = X(2)X(15092)∩X(76)X(9880)

Barycentrics    (4*a^6+4*b^6-10*b^4*c^2+11*b^2*c^4-5*c^6-a^4*(b^2+10*c^2)-a^2*(b^4+3*b^2*c^2-11*c^4))*(4*a^6-5*b^6+11*b^4*c^2-10*b^2*c^4+4*c^6-a^4*(10*b^2+c^2)+a^2*(11*b^4-3*b^2*c^2-c^4)) : :

X(54723) lies on these lines: {2, 15092}, {76, 9880}, {98, 39563}, {542, 53105}, {6321, 35005}, {12243, 38259}, {14492, 33694}, {14639, 53104}

X(54723) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(265), X(47389)}}, {{A, B, C, X(2696), X(14728)}}, {{A, B, C, X(2796), X(28553)}}, {{A, B, C, X(3455), X(14483)}}, {{A, B, C, X(5641), X(38730)}}, {{A, B, C, X(8753), X(9880)}}, {{A, B, C, X(9141), X(43663)}}, {{A, B, C, X(13603), X(52239)}}

X(54724) = X(2)X(9301)∩X(6)X(9302)

Barycentrics    (a^6+b^6+2*b^4*c^2-4*b^2*c^4+c^6-4*a^4*(b^2+c^2)+a^2*(2*b^4-9*b^2*c^2-4*c^4))*(a^6+b^6-4*b^4*c^2+2*b^2*c^4+c^6-4*a^4*(b^2+c^2)+a^2*(-4*b^4-9*b^2*c^2+2*c^4)) : :

X(54724) lies on these lines: {2, 9301}, {6, 9302}, {76, 5476}, {83, 10168}, {98, 7753}, {381, 11606}, {420, 43530}, {671, 19130}, {1916, 8724}, {5475, 14458}, {6033, 43535}, {6034, 43532}, {8176, 11167}, {10159, 40107}

X(54724) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(9301)}}, {{A, B, C, X(263), X(5476)}}, {{A, B, C, X(290), X(30537)}}, {{A, B, C, X(381), X(420)}}, {{A, B, C, X(694), X(14483)}}, {{A, B, C, X(1989), X(42299)}}, {{A, B, C, X(2698), X(30499)}}, {{A, B, C, X(3431), X(9515)}}, {{A, B, C, X(3531), X(52660)}}, {{A, B, C, X(3613), X(5641)}}, {{A, B, C, X(5627), X(46296)}}, {{A, B, C, X(7753), X(14356)}}, {{A, B, C, X(8724), X(36820)}}, {{A, B, C, X(10168), X(20021)}}, {{A, B, C, X(14387), X(18361)}}

X(54725) = X(98)X(5467)∩X(538)X(2394)

Barycentrics    (-(b^2*c^2*(b^2-2*c^2)*(b^2-c^2)^2)+2*a^8*(b^2+c^2)-a^6*(5*b^4+5*b^2*c^2+2*c^4)+2*a^4*(2*b^6+b^4*c^2+4*b^2*c^4-c^6)-a^2*(b^8+2*b^6*c^2-2*b^4*c^4+5*b^2*c^6-2*c^8))*(b^2*c^2*(b^2-c^2)^2*(2*b^2-c^2)+2*a^8*(b^2+c^2)-a^6*(2*b^4+5*b^2*c^2+5*c^4)+a^4*(-2*b^6+8*b^4*c^2+2*b^2*c^4+4*c^6)+a^2*(2*b^8-5*b^6*c^2+2*b^4*c^4-2*b^2*c^6-c^8)) : :

X(54725) lies on these lines: {98, 5467}, {511, 5466}, {524, 43665}, {538, 2394}, {543, 46040}, {671, 2421}, {1503, 43668}, {2782, 9180}, {2986, 35279}, {5969, 14223}, {22486, 34289}

X(54725) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(538)}}, {{A, B, C, X(74), X(14608)}}, {{A, B, C, X(511), X(524)}}, {{A, B, C, X(542), X(5969)}}, {{A, B, C, X(543), X(2782)}}, {{A, B, C, X(698), X(11645)}}, {{A, B, C, X(732), X(19924)}}, {{A, B, C, X(842), X(35146)}}, {{A, B, C, X(3849), X(32515)}}, {{A, B, C, X(9141), X(9150)}}, {{A, B, C, X(35279), X(52451)}}
X(54725) = trilinear pole of line {9155, 523}
X(54725) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 43668}

X(54726) = X(226)X(37704)∩X(4194)X(43530)

Barycentrics    (a^5+a^4*(b+c)+(b-c)^2*(b+c)^3-2*a^3*(b^2-6*b*c+c^2)-2*a^2*(b^3+b^2*c+b*c^2+c^3)+a*(b^4+12*b^3*c-2*b^2*c^2-12*b*c^3+c^4))*(a^5+a^4*(b+c)+(b-c)^2*(b+c)^3-2*a^3*(b^2-6*b*c+c^2)-2*a^2*(b^3+b^2*c+b*c^2+c^3)+a*(b^4-12*b^3*c-2*b^2*c^2+12*b*c^3+c^4)) : :

X(54726) lies on these lines: {226, 37704}, {4194, 43530}, {4200, 16080}

X(54726) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(4200)}}, {{A, B, C, X(40), X(36603)}}, {{A, B, C, X(64), X(39982)}}, {{A, B, C, X(65), X(52188)}}, {{A, B, C, X(74), X(39975)}}, {{A, B, C, X(80), X(1440)}}, {{A, B, C, X(280), X(36599)}}, {{A, B, C, X(381), X(4194)}}, {{A, B, C, X(406), X(3839)}}, {{A, B, C, X(475), X(3543)}}, {{A, B, C, X(903), X(10309)}}, {{A, B, C, X(941), X(3531)}}, {{A, B, C, X(1219), X(10308)}}, {{A, B, C, X(3426), X(39956)}}, {{A, B, C, X(5560), X(38021)}}, {{A, B, C, X(11546), X(36916)}}, {{A, B, C, X(14490), X(39798)}}, {{A, B, C, X(22334), X(39960)}}, {{A, B, C, X(33576), X(36910)}}, {{A, B, C, X(36721), X(37102)}}, {{A, B, C, X(39974), X(52518)}}, {{A, B, C, X(39984), X(43713)}}, {{A, B, C, X(50687), X(52252)}}, {{A, B, C, X(51502), X(52187)}}

X(54727) = X(2)X(51340)∩X(381)X(1029)

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

X(54727) lies on these lines: {2, 51340}, {226, 3582}, {381, 1029}, {451, 43530}, {5046, 13582}, {16080, 52252}

X(54727) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(39960)}}, {{A, B, C, X(6), X(51340)}}, {{A, B, C, X(8), X(3582)}}, {{A, B, C, X(30), X(52252)}}, {{A, B, C, X(37), X(14483)}}, {{A, B, C, X(54), X(39982)}}, {{A, B, C, X(65), X(30537)}}, {{A, B, C, X(74), X(39798)}}, {{A, B, C, X(376), X(475)}}, {{A, B, C, X(381), X(451)}}, {{A, B, C, X(406), X(3545)}}, {{A, B, C, X(941), X(14491)}}, {{A, B, C, X(1000), X(7318)}}, {{A, B, C, X(1138), X(39748)}}, {{A, B, C, X(1173), X(39974)}}, {{A, B, C, X(1224), X(10308)}}, {{A, B, C, X(1440), X(18490)}}, {{A, B, C, X(1989), X(51500)}}, {{A, B, C, X(3431), X(39956)}}, {{A, B, C, X(3524), X(4200)}}, {{A, B, C, X(3531), X(39983)}}, {{A, B, C, X(4194), X(5071)}}, {{A, B, C, X(5046), X(37943)}}, {{A, B, C, X(5553), X(36588)}}, {{A, B, C, X(7040), X(36916)}}, {{A, B, C, X(7537), X(11113)}}, {{A, B, C, X(24858), X(37518)}}, {{A, B, C, X(38460), X(45700)}}

X(54728) = X(381)X(13576)∩X(3309)X(35353)

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

X(54728) lies on these lines: {381, 13576}, {3309, 35353}, {15149, 43530}, {28854, 40718}

X(54728) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(39971)}}, {{A, B, C, X(274), X(16615)}}, {{A, B, C, X(344), X(536)}}, {{A, B, C, X(381), X(15149)}}, {{A, B, C, X(517), X(4762)}}, {{A, B, C, X(824), X(28854)}}, {{A, B, C, X(1389), X(3227)}}, {{A, B, C, X(2788), X(35103)}}, {{A, B, C, X(3295), X(3666)}}, {{A, B, C, X(3531), X(39981)}}, {{A, B, C, X(3577), X(36871)}}, {{A, B, C, X(10308), X(32009)}}, {{A, B, C, X(14483), X(37128)}}, {{A, B, C, X(14491), X(39952)}}, {{A, B, C, X(39768), X(52652)}}

X(54729) = X(6831)X(7607)∩X(6927)X(53098)

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

X(54729) lies on these lines: {3149, 7608}, {6831, 7607}, {6927, 53098}, {11341, 16080}, {50700, 53099}

X(54729) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(11341)}}, {{A, B, C, X(3149), X(52281)}}, {{A, B, C, X(6831), X(52282)}}, {{A, B, C, X(7841), X(37362)}}, {{A, B, C, X(15909), X(34892)}}

X(54730) = X(381)X(16277)∩X(5392)X(8370)

Barycentrics    (2*a^8-3*a^6*b^2-(b^2-c^2)^2*(b^4-b^2*c^2-2*c^4)-a^4*(b^4+7*b^2*c^2+4*c^4)+a^2*(3*b^6-4*b^4*c^2-7*b^2*c^4))*(2*a^8-3*a^6*c^2+(b^2-c^2)^2*(2*b^4+b^2*c^2-c^4)-a^4*(4*b^4+7*b^2*c^2+c^4)+a^2*(-7*b^4*c^2-4*b^2*c^4+3*c^6)) : :

X(54730) lies on these lines: {381, 16277}, {5392, 8370}, {7509, 7608}, {7607, 14788}, {7841, 40393}

X(54730) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(24), X(8370)}}, {{A, B, C, X(524), X(43908)}}, {{A, B, C, X(599), X(38433)}}, {{A, B, C, X(1594), X(7841)}}, {{A, B, C, X(4846), X(40404)}}, {{A, B, C, X(6642), X(37855)}}, {{A, B, C, X(6662), X(13377)}}, {{A, B, C, X(7509), X(52281)}}, {{A, B, C, X(7576), X(7770)}}, {{A, B, C, X(8352), X(52296)}}, {{A, B, C, X(10018), X(11317)}}, {{A, B, C, X(14788), X(52282)}}

X(54731) = X(2)X(43456)∩X(83)X(6054)

Barycentrics    (a^8+b^8+b^4*c^4-3*b^2*c^6+c^8+a^2*c^2*(b^4-5*b^2*c^2-3*c^4)+a^4*(4*b^4+b^2*c^2+c^4))*(a^8+b^8-3*b^6*c^2+b^4*c^4+c^8+a^4*(b^4+b^2*c^2+4*c^4)+a^2*(-3*b^6-5*b^4*c^2+b^2*c^4)) : :

X(54731) lies on these lines: {2, 43456}, {76, 11632}, {83, 6054}, {262, 6034}, {542, 3407}, {598, 6033}, {7753, 11170}, {11646, 14458}

X(54731) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(694), X(842)}}, {{A, B, C, X(1989), X(36897)}}, {{A, B, C, X(6034), X(8842)}}, {{A, B, C, X(6054), X(20021)}}, {{A, B, C, X(11060), X(11632)}}, {{A, B, C, X(32085), X(43456)}}, {{A, B, C, X(34288), X(43664)}}
X(54731) = X(i)-vertex conjugate of X(j) for these {i, j}: {3455, 14458}

X(54732) = X(401)X(43530)∩X(16080)X(52247)

Barycentrics    (a^8+a^6*(b^2-2*c^2)+a^2*(b^2-c^2)^2*(b^2+4*c^2)+(b^2-c^2)^2*(b^4-2*c^4)-a^4*(4*b^4-2*b^2*c^2+c^4))*(a^8+a^6*(-2*b^2+c^2)+a^2*(b^2-c^2)^2*(4*b^2+c^2)-(b^2-c^2)^2*(2*b^4-c^4)-a^4*(b^4-2*b^2*c^2+4*c^4)) : :

X(54732) lies on these lines: {401, 43530}, {16080, 52247}

X(54732) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(52247)}}, {{A, B, C, X(264), X(15351)}}, {{A, B, C, X(381), X(401)}}, {{A, B, C, X(1494), X(43711)}}, {{A, B, C, X(1972), X(4846)}}, {{A, B, C, X(2450), X(11361)}}, {{A, B, C, X(3148), X(14041)}}, {{A, B, C, X(3521), X(18027)}}, {{A, B, C, X(3839), X(37188)}}, {{A, B, C, X(15319), X(38256)}}, {{A, B, C, X(18550), X(23582)}}

X(54733) = X(262)X(16261)∩X(3845)X(30505)

Barycentrics    (b^2*c^2*(b^2-c^2)^2+a^6*(b^2+c^2)-2*a^4*(b^4-3*b^2*c^2+c^4)+a^2*(b^6+6*b^4*c^2-12*b^2*c^4+c^6))*(b^2*c^2*(b^2-c^2)^2+a^6*(b^2+c^2)-2*a^4*(b^4-3*b^2*c^2+c^4)+a^2*(b^6-12*b^4*c^2+6*b^2*c^4+c^6)) : :

X(54733) lies on these lines: {262, 16261}, {3845, 30505}, {10706, 14492}, {16080, 46511}

X(54733) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(46511)}}, {{A, B, C, X(74), X(3228)}}, {{A, B, C, X(308), X(13603)}}, {{A, B, C, X(1296), X(6094)}}, {{A, B, C, X(2998), X(11738)}}, {{A, B, C, X(3426), X(9462)}}, {{A, B, C, X(3845), X(37125)}}, {{A, B, C, X(4580), X(34802)}}, {{A, B, C, X(5627), X(43098)}}, {{A, B, C, X(14388), X(38278)}}, {{A, B, C, X(14487), X(39968)}}, {{A, B, C, X(16261), X(44144)}}, {{A, B, C, X(20421), X(38262)}}, {{A, B, C, X(34898), X(43702)}}, {{A, B, C, X(37337), X(41099)}}
X(54733) = trilinear pole of line {373, 523}

X(54734) = X(76)X(19709)∩X(83)X(8703)

Barycentrics    (a^4+b^4+7*b^2*c^2-8*c^4+a^2*(16*b^2+7*c^2))*(a^4-8*b^4+7*b^2*c^2+c^4+a^2*(7*b^2+16*c^2)) : :

X(54734) lies on these lines: {76, 19709}, {83, 8703}, {547, 10159}, {671, 3860}, {3830, 53107}, {3845, 53106}, {5054, 43527}, {15681, 53102}, {15682, 18844}, {15719, 18841}, {23234, 35005}, {38071, 43676}, {42006, 44422}

X(54734) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(19709)}}, {{A, B, C, X(427), X(8703)}}, {{A, B, C, X(428), X(547)}}, {{A, B, C, X(468), X(3860)}}, {{A, B, C, X(842), X(34572)}}, {{A, B, C, X(1494), X(45108)}}, {{A, B, C, X(3108), X(14388)}}, {{A, B, C, X(3830), X(52298)}}, {{A, B, C, X(3845), X(52297)}}, {{A, B, C, X(5054), X(5064)}}, {{A, B, C, X(7249), X(13602)}}, {{A, B, C, X(7378), X(15719)}}, {{A, B, C, X(11058), X(11169)}}, {{A, B, C, X(11540), X(52285)}}

X(54735) = X(10)X(11114)∩X(321)X(17346)

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

X(54735) lies on these lines: {10, 11114}, {321, 17346}, {381, 5397}, {1962, 48841}, {3060, 33519}, {4049, 29178}, {7607, 8229}, {17577, 43531}

X(54735) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(21), X(42030)}}, {{A, B, C, X(27), X(1121)}}, {{A, B, C, X(81), X(751)}}, {{A, B, C, X(85), X(43758)}}, {{A, B, C, X(90), X(39948)}}, {{A, B, C, X(469), X(17577)}}, {{A, B, C, X(519), X(29178)}}, {{A, B, C, X(2006), X(17501)}}, {{A, B, C, X(2094), X(50573)}}, {{A, B, C, X(2990), X(10308)}}, {{A, B, C, X(2994), X(52393)}}, {{A, B, C, X(5278), X(17392)}}, {{A, B, C, X(5560), X(18359)}}, {{A, B, C, X(6994), X(11111)}}, {{A, B, C, X(7357), X(18821)}}, {{A, B, C, X(8229), X(52282)}}, {{A, B, C, X(14377), X(21739)}}, {{A, B, C, X(19806), X(42044)}}, {{A, B, C, X(30711), X(34919)}}, {{A, B, C, X(36599), X(39980)}}, {{A, B, C, X(37652), X(50133)}}

X(54736) = X(83)X(34613)∩X(3861)X(46220)

Barycentrics    (a^8-a^6*(b^2-2*c^2)-(b^2-c^2)^3*(2*b^2+c^2)-a^4*(3*b^4+17*b^2*c^2+6*c^4)+a^2*(5*b^6+10*b^4*c^2-17*b^2*c^4+2*c^6))*(a^8+a^6*(2*b^2-c^2)+(b^2-c^2)^3*(b^2+2*c^2)-a^4*(6*b^4+17*b^2*c^2+3*c^4)+a^2*(2*b^6-17*b^4*c^2+10*b^2*c^4+5*c^6)) : :

X(54736) lies on these lines: {83, 34613}, {3861, 46220}, {10323, 43527}, {10594, 43530}, {15559, 16080}

X(54736) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(15559)}}, {{A, B, C, X(381), X(10594)}}, {{A, B, C, X(427), X(34613)}}, {{A, B, C, X(1173), X(1494)}}, {{A, B, C, X(5064), X(10323)}}, {{A, B, C, X(7403), X(7576)}}, {{A, B, C, X(14487), X(33631)}}, {{A, B, C, X(38005), X(46259)}}, {{A, B, C, X(45108), X(45138)}}, {{A, B, C, X(46199), X(52187)}}

X(54737) = X(76)X(31173)∩X(671)X(7798)

Barycentrics    (2*a^4+2*b^4+b^2*c^2-4*c^4+a^2*(7*b^2+c^2))*(2*a^4-4*b^4+b^2*c^2+2*c^4+a^2*(b^2+7*c^2)) : :

X(54737) lies on these lines: {76, 31173}, {671, 7798}, {1992, 11606}, {3552, 43527}, {5466, 31176}, {5485, 7779}, {7766, 43535}, {7840, 43688}, {10159, 32966}, {11648, 45103}, {18840, 33006}, {18841, 33007}, {18842, 52942}

X(54737) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(428), X(32966)}}, {{A, B, C, X(1383), X(31173)}}, {{A, B, C, X(1992), X(7779)}}, {{A, B, C, X(3228), X(13377)}}, {{A, B, C, X(3552), X(5064)}}, {{A, B, C, X(6995), X(33006)}}, {{A, B, C, X(7378), X(33007)}}, {{A, B, C, X(7408), X(32984)}}, {{A, B, C, X(7409), X(32985)}}, {{A, B, C, X(7714), X(32993)}}, {{A, B, C, X(7766), X(7840)}}, {{A, B, C, X(7774), X(44367)}}, {{A, B, C, X(7798), X(31176)}}, {{A, B, C, X(9831), X(30498)}}, {{A, B, C, X(18575), X(18818)}}, {{A, B, C, X(22336), X(36882)}}, {{A, B, C, X(31105), X(40890)}}, {{A, B, C, X(33601), X(52898)}}, {{A, B, C, X(52284), X(52942)}}

X(54738) = X(94)X(542)∩X(115)X(18316)

Barycentrics    (2*a^10-3*a^8*(2*b^2+c^2)+a^6*(7*b^4+4*b^2*c^2+c^4)-(b^2-c^2)^3*(b^4+2*c^4)+a^4*(-5*b^6+b^4*c^2-2*b^2*c^4+c^6)+a^2*(3*b^8-5*b^6*c^2+b^4*c^4+4*b^2*c^6-3*c^8))*(2*a^10-3*a^8*(b^2+2*c^2)+(b^2-c^2)^3*(2*b^4+c^4)+a^6*(b^4+4*b^2*c^2+7*c^4)+a^4*(b^6-2*b^4*c^2+b^2*c^4-5*c^6)+a^2*(-3*b^8+4*b^6*c^2+b^4*c^4-5*b^2*c^6+3*c^8)) : :

X(54738) lies on these lines: {94, 542}, {115, 18316}, {381, 39295}, {526, 14223}, {671, 18332}, {2394, 15111}, {7578, 18867}, {13582, 39120}, {16080, 20774}, {35235, 43530}

X(54738) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(526)}}, {{A, B, C, X(30), X(14052)}}, {{A, B, C, X(115), X(381)}}, {{A, B, C, X(842), X(9141)}}, {{A, B, C, X(1138), X(13485)}}, {{A, B, C, X(2715), X(36885)}}, {{A, B, C, X(3818), X(6034)}}, {{A, B, C, X(5309), X(6033)}}, {{A, B, C, X(5475), X(11632)}}, {{A, B, C, X(5476), X(11646)}}, {{A, B, C, X(5627), X(5962)}}, {{A, B, C, X(6128), X(15928)}}, {{A, B, C, X(7577), X(18867)}}, {{A, B, C, X(7753), X(12188)}}, {{A, B, C, X(9154), X(52192)}}, {{A, B, C, X(9214), X(9307)}}, {{A, B, C, X(10412), X(52154)}}
X(54738) = reflection of X(i) in X(j) for these {i,j}: {18316, 115}

X(54739) = X(4)X(4259)∩X(10)X(1072)

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

X(54739) lies on these lines: {2, 34460}, {4, 4259}, {5, 45964}, {10, 1072}, {98, 6905}, {226, 1111}, {262, 6830}, {321, 34387}, {517, 13576}, {1064, 28850}, {1751, 1764}, {2783, 43671}, {2826, 35353}, {2973, 40149}, {3424, 50701}, {6844, 14484}, {6879, 14494}, {6880, 7612}, {6996, 24624}

X(54739) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(1231)}}, {{A, B, C, X(80), X(4391)}}, {{A, B, C, X(104), X(335)}}, {{A, B, C, X(241), X(517)}}, {{A, B, C, X(257), X(1389)}}, {{A, B, C, X(277), X(331)}}, {{A, B, C, X(278), X(1072)}}, {{A, B, C, X(297), X(6905)}}, {{A, B, C, X(458), X(6830)}}, {{A, B, C, X(536), X(2826)}}, {{A, B, C, X(537), X(28468)}}, {{A, B, C, X(673), X(17924)}}, {{A, B, C, X(693), X(43093)}}, {{A, B, C, X(824), X(28850)}}, {{A, B, C, X(860), X(6996)}}, {{A, B, C, X(942), X(3666)}}, {{A, B, C, X(953), X(17946)}}, {{A, B, C, X(997), X(26575)}}, {{A, B, C, X(1111), X(2481)}}, {{A, B, C, X(1243), X(39957)}}, {{A, B, C, X(1292), X(53213)}}, {{A, B, C, X(2801), X(23876)}}, {{A, B, C, X(3427), X(39749)}}, {{A, B, C, X(3673), X(53237)}}, {{A, B, C, X(4231), X(6656)}}, {{A, B, C, X(5136), X(7377)}}, {{A, B, C, X(6829), X(11341)}}, {{A, B, C, X(6844), X(52288)}}, {{A, B, C, X(6880), X(37174)}}, {{A, B, C, X(6881), X(31926)}}, {{A, B, C, X(17947), X(40437)}}, {{A, B, C, X(23887), X(29069)}}, {{A, B, C, X(24002), X(34578)}}, {{A, B, C, X(24297), X(52517)}}, {{A, B, C, X(34485), X(34914)}}, {{A, B, C, X(36952), X(43724)}}, {{A, B, C, X(37086), X(37381)}}, {{A, B, C, X(38306), X(39716)}}, {{A, B, C, X(39700), X(42467)}}, {{A, B, C, X(40704), X(46802)}}, {{A, B, C, X(50701), X(52283)}}
X(54739) = trilinear pole of line {17874, 40166}

X(54740) = X(376)X(32022)∩X(381)X(6625)

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

X(54740) lies on these lines: {376, 32022}, {381, 6625}, {4212, 16080}, {4213, 43530}

X(54740) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(4212)}}, {{A, B, C, X(42), X(14483)}}, {{A, B, C, X(74), X(2350)}}, {{A, B, C, X(291), X(10308)}}, {{A, B, C, X(376), X(4196)}}, {{A, B, C, X(381), X(4213)}}, {{A, B, C, X(3426), X(39966)}}, {{A, B, C, X(3431), X(39965)}}, {{A, B, C, X(3531), X(39967)}}, {{A, B, C, X(3545), X(4207)}}, {{A, B, C, X(7714), X(36670)}}, {{A, B, C, X(14491), X(39961)}}, {{A, B, C, X(15320), X(30537)}}, {{A, B, C, X(16615), X(30571)}}

X(54741) = X(1596)X(43530)∩X(1597)X(16080)

Barycentrics    (2*a^8-(b^2-c^2)^3*(b^2+2*c^2)-a^6*(5*b^2+2*c^2)+a^4*(3*b^4+29*b^2*c^2)+a^2*(b^6-28*b^4*c^2+29*b^2*c^4-2*c^6))*(2*a^8+(b^2-c^2)^3*(2*b^2+c^2)-a^6*(2*b^2+5*c^2)+a^4*(29*b^2*c^2+3*c^4)+a^2*(-2*b^6+29*b^4*c^2-28*b^2*c^4+c^6)) : :

X(54741) lies on these lines: {1596, 43530}, {1597, 16080}

X(54741) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(1597)}}, {{A, B, C, X(1294), X(52187)}}, {{A, B, C, X(1494), X(45088)}}, {{A, B, C, X(14269), X(37942)}}, {{A, B, C, X(22334), X(48911)}}, {{A, B, C, X(35512), X(52188)}}

X(54742) = X(10159)X(12082)∩X(14488)X(32111)

Barycentrics    (2*a^8-(b^2-c^2)^3*(b^2+2*c^2)-a^6*(5*b^2+2*c^2)+a^4*(3*b^4-25*b^2*c^2)+a^2*(b^6+26*b^4*c^2-25*b^2*c^4-2*c^6))*(2*a^8+(b^2-c^2)^3*(2*b^2+c^2)-a^6*(2*b^2+5*c^2)+a^4*(-25*b^2*c^2+3*c^4)+a^2*(-2*b^6-25*b^4*c^2+26*b^2*c^4+c^6)) : :

X(54742) lies on these lines: {10159, 12082}, {14488, 32111}

X(54742) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(14490)}}, {{A, B, C, X(428), X(12082)}}, {{A, B, C, X(7576), X(18534)}}, {{A, B, C, X(18317), X(45819)}}, {{A, B, C, X(21765), X(43660)}}, {{A, B, C, X(43970), X(48911)}}

X(54743) = X(381)X(43665)∩X(4230)X(43530)

Barycentrics    (a^10*(b^2+c^2)-b^2*c^2*(b^2-c^2)^3*(2*b^2+c^2)-a^8*(b^4+b^2*c^2-2*c^4)-a^2*(b^2-c^2)^2*(2*b^6-4*b^4*c^2-b^2*c^4-c^6)-3*a^6*(b^6-b^4*c^2+2*c^6)+a^4*(5*b^8-9*b^6*c^2+6*b^4*c^4+2*c^8))*(a^10*(b^2+c^2)+b^2*c^2*(b^2-c^2)^3*(b^2+2*c^2)+a^8*(2*b^4-b^2*c^2-c^4)+a^2*(b^2-c^2)^2*(b^6+b^4*c^2+4*b^2*c^4-2*c^6)-3*a^6*(2*b^6-b^2*c^4+c^6)+a^4*(2*b^8+6*b^4*c^4-9*b^2*c^6+5*c^8)) : :

X(54743) lies on these lines: {381, 43665}, {4230, 43530}

X(54743) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(381), X(4230)}}, {{A, B, C, X(1494), X(9513)}}, {{A, B, C, X(2698), X(5627)}}, {{A, B, C, X(39427), X(43917)}}

X(54744) = X(10)X(33094)∩X(4049)X(29216)

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

X(54744) lies on these lines: {10, 33094}, {4049, 29216}, {4080, 20017}, {4220, 7607}, {10159, 33736}, {43537, 50698}

X(54744) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(80), X(39700)}}, {{A, B, C, X(428), X(33736)}}, {{A, B, C, X(519), X(20017)}}, {{A, B, C, X(903), X(2997)}}, {{A, B, C, X(2345), X(4980)}}, {{A, B, C, X(2481), X(44176)}}, {{A, B, C, X(4220), X(52282)}}, {{A, B, C, X(4358), X(42047)}}, {{A, B, C, X(5560), X(40394)}}, {{A, B, C, X(7017), X(11604)}}, {{A, B, C, X(17271), X(19738)}}, {{A, B, C, X(17346), X(42045)}}, {{A, B, C, X(30582), X(39983)}}
X(54744) = trilinear pole of line {47794, 47875}

X(54745) = X(226)X(17577)∩X(1751)X(11114)

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

X(54745) lies on these lines: {226, 17577}, {1751, 11114}, {2051, 52269}

X(54745) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(21), X(903)}}, {{A, B, C, X(29), X(17577)}}, {{A, B, C, X(341), X(36590)}}, {{A, B, C, X(1121), X(40445)}}, {{A, B, C, X(1156), X(1257)}}, {{A, B, C, X(3467), X(34772)}}, {{A, B, C, X(3679), X(17098)}}, {{A, B, C, X(5125), X(11114)}}, {{A, B, C, X(7466), X(17677)}}, {{A, B, C, X(11109), X(52269)}}, {{A, B, C, X(15936), X(17330)}}

X(54746) = X(2)X(44909)∩X(3424)X(15311)

Barycentrics    (a^8+4*a^2*(b^2-c^2)^2*(4*b^2+c^2)+a^6*(-8*b^2+4*c^2)+2*a^4*(b^4+4*b^2*c^2-5*c^4)-(b^2-c^2)^2*(11*b^4+6*b^2*c^2-c^4))*(a^8+4*a^6*(b^2-2*c^2)+4*a^2*(b^2-c^2)^2*(b^2+4*c^2)+(b^2-c^2)^2*(b^4-6*b^2*c^2-11*c^4)+2*a^4*(-5*b^4+4*b^2*c^2+c^4)) : :

X(54746) lies on these lines: {2, 44909}, {3424, 15311}, {11348, 43530}

X(54746) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(20), X(34579)}}, {{A, B, C, X(253), X(525)}}, {{A, B, C, X(381), X(11348)}}, {{A, B, C, X(393), X(44909)}}, {{A, B, C, X(3346), X(52581)}}, {{A, B, C, X(3543), X(44334)}}, {{A, B, C, X(6330), X(16251)}}

X(54747) = X(1513)X(43528)∩X(10159)X(37334)

Barycentrics    (2*a^8+2*b^8-2*b^6*c^2+3*b^4*c^4-2*b^2*c^6-c^8+a^6*(b^2-2*c^2)+a^4*(6*b^4+2*b^2*c^2+3*c^4)+a^2*(b^6+2*b^4*c^2+5*b^2*c^4-2*c^6))*(2*a^8-b^8-2*b^6*c^2+3*b^4*c^4-2*b^2*c^6+2*c^8+a^6*(-2*b^2+c^2)+a^4*(3*b^4+2*b^2*c^2+6*c^4)+a^2*(-2*b^6+5*b^4*c^2+2*b^2*c^4+c^6)) : :

X(54747) lies on these lines: {1513, 43528}, {10159, 37334}, {13860, 43529}, {37446, 43527}

X(54747) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(428), X(37334)}}, {{A, B, C, X(523), X(5306)}}, {{A, B, C, X(5064), X(37446)}}
X(54747) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 43528}, {3456, 7612}

X(54748) = X(83)X(7837)∩X(3098)X(14458)

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

X(54748) lies on these lines: {83, 7837}, {3098, 14458}, {3314, 14492}, {3407, 37671}, {5309, 10159}, {7772, 16896}, {8556, 8587}, {18840, 19570}, {18841, 46226}

X(54748) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(141), X(7837)}}, {{A, B, C, X(264), X(40042)}}, {{A, B, C, X(1239), X(44168)}}, {{A, B, C, X(3108), X(41443)}}, {{A, B, C, X(3314), X(37671)}}, {{A, B, C, X(5064), X(16896)}}, {{A, B, C, X(5309), X(39998)}}, {{A, B, C, X(9300), X(16986)}}, {{A, B, C, X(9516), X(40829)}}, {{A, B, C, X(12054), X(48673)}}, {{A, B, C, X(19570), X(40022)}}
X(54748) = X(i)-isoconjugate-of-X(j) for these {i, j}: {5332, 17716}

X(54749) = X(98)X(14693)∩X(262)X(38224)

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

X(54749) lies on these lines: {98, 14693}, {262, 38224}, {542, 3406}, {1916, 14568}, {3399, 7827}, {5152, 9890}, {7607, 52090}, {7749, 10131}, {7794, 43529}, {9166, 14492}, {11606, 33265}, {14458, 14830}, {26613, 43535}

X(54749) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(694)}}, {{A, B, C, X(420), X(33265)}}, {{A, B, C, X(512), X(46314)}}, {{A, B, C, X(729), X(46306)}}, {{A, B, C, X(1989), X(35146)}}, {{A, B, C, X(3978), X(14568)}}, {{A, B, C, X(14659), X(46316)}}, {{A, B, C, X(18896), X(43098)}}, {{A, B, C, X(20026), X(47646)}}
X(54749) = trilinear pole of line {41624, 523}

X(54750) = X(98)X(13586)∩X(262)X(23514)

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

X(54750) lies on these lines: {98, 13586}, {262, 23514}, {538, 8781}, {2782, 7612}, {2996, 5969}, {3424, 33193}, {7607, 7907}, {7608, 32967}, {8591, 11172}, {32963, 53099}, {32964, 43537}, {32976, 53098}, {33244, 47586}, {33257, 53100}, {34087, 51481}

X(54750) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(13586)}}, {{A, B, C, X(511), X(47113)}}, {{A, B, C, X(538), X(51481)}}, {{A, B, C, X(2987), X(3455)}}, {{A, B, C, X(3566), X(5969)}}, {{A, B, C, X(7907), X(52282)}}, {{A, B, C, X(30535), X(41440)}}, {{A, B, C, X(32967), X(52281)}}, {{A, B, C, X(33193), X(52283)}}, {{A, B, C, X(33216), X(37174)}}

X(54751) = X(4)X(22486)∩X(98)X(1003)

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

X(54751) lies on these lines: {4, 22486}, {98, 1003}, {262, 33228}, {538, 40824}, {7607, 7807}, {7608, 7887}, {7612, 33191}, {7757, 8781}, {19687, 53100}, {32955, 53098}, {32972, 53099}, {32973, 43537}, {32981, 47586}, {33231, 53103}, {34087, 40814}

X(54751) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(1003)}}, {{A, B, C, X(458), X(33228)}}, {{A, B, C, X(538), X(40814)}}, {{A, B, C, X(7757), X(51481)}}, {{A, B, C, X(7807), X(52282)}}, {{A, B, C, X(7887), X(52281)}}, {{A, B, C, X(9307), X(35146)}}, {{A, B, C, X(9515), X(14906)}}, {{A, B, C, X(14608), X(44146)}}, {{A, B, C, X(22486), X(42313)}}, {{A, B, C, X(33191), X(37174)}}, {{A, B, C, X(34154), X(41440)}}

X(54752) = X(262)X(7827)∩X(7607)X(37466)

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

X(54752) lies on these lines: {262, 7827}, {7607, 37466}, {11167, 26613}, {13086, 42006}

X(54752) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(263)}}, {{A, B, C, X(694), X(14906)}}, {{A, B, C, X(7827), X(20023)}}, {{A, B, C, X(21399), X(46310)}}, {{A, B, C, X(34288), X(35146)}}, {{A, B, C, X(37466), X(52282)}}

X(54753) = X(98)X(33016)∩X(262)X(33017)

Barycentrics    (3*a^6-3*b^6+7*b^4*c^2-11*b^2*c^4+3*c^6-a^4*(11*b^2+5*c^2)+a^2*(7*b^4-12*b^2*c^2-5*c^4))*(3*a^6+3*b^6-11*b^4*c^2+7*b^2*c^4-3*c^6-a^4*(5*b^2+11*c^2)+a^2*(-5*b^4-12*b^2*c^2+7*c^4)) : :

X(54753) lies on these lines: {98, 33016}, {262, 33017}, {6655, 53099}, {7607, 16924}, {7608, 7791}, {7612, 32983}, {14494, 32986}, {16043, 53098}, {16044, 43537}, {33018, 47586}, {33020, 53859}

X(54753) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(33016)}}, {{A, B, C, X(458), X(33017)}}, {{A, B, C, X(2021), X(5034)}}, {{A, B, C, X(5013), X(30496)}}, {{A, B, C, X(7791), X(52281)}}, {{A, B, C, X(16924), X(52282)}}, {{A, B, C, X(32983), X(37174)}}

X(54754) = X(6833)X(7607)∩X(6834)X(7608)

Barycentrics    (a^5+b^5-4*a^3*b*c-b^4*c-b*c^4+c^5-a^4*(b+c)-2*a^2*b*c*(b+c)-a*(b^4+4*b^3*c+2*b^2*c^2-8*b*c^3+c^4))*(a^5+b^5-4*a^3*b*c-b^4*c-b*c^4+c^5-a^4*(b+c)-2*a^2*b*c*(b+c)-a*(b^4-8*b^3*c+2*b^2*c^2+4*b*c^3+c^4)) : :

X(54754) lies on these lines: {6833, 7607}, {6834, 7608}, {6847, 43537}, {6848, 53099}, {6949, 53098}, {37434, 47586}

X(54754) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(79), X(41791)}}, {{A, B, C, X(84), X(34914)}}, {{A, B, C, X(3426), X(39957)}}, {{A, B, C, X(3531), X(39979)}}, {{A, B, C, X(3577), X(34892)}}, {{A, B, C, X(6833), X(52282)}}, {{A, B, C, X(6834), X(52281)}}, {{A, B, C, X(16615), X(30701)}}

X(54755) = X(6833)X(7608)∩X(6834)X(7607)

Barycentrics    (a^5+b^5+8*a^3*b*c-b^4*c-b*c^4+c^5-a^4*(b+c)-2*a^2*b*c*(b+c)-a*(b^4+4*b^3*c+2*b^2*c^2-8*b*c^3+c^4))*(a^5+b^5+8*a^3*b*c-b^4*c-b*c^4+c^5-a^4*(b+c)-2*a^2*b*c*(b+c)-a*(b^4-8*b^3*c+2*b^2*c^2+4*b*c^3+c^4)) : :

X(54755) lies on these lines: {6833, 7608}, {6834, 7607}, {6847, 53099}, {6848, 43537}, {6952, 53098}

X(54755) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(84), X(34892)}}, {{A, B, C, X(3426), X(39979)}}, {{A, B, C, X(3531), X(39957)}}, {{A, B, C, X(3577), X(34914)}}, {{A, B, C, X(5560), X(41791)}}, {{A, B, C, X(6833), X(52281)}}, {{A, B, C, X(6834), X(52282)}}, {{A, B, C, X(10308), X(30701)}}

X(54756) = X(10)X(44447)∩X(7607)X(26118)

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

X(54756) lies on these lines: {10, 44447}, {7607, 26118}, {37456, 43537}

X(54756) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(79), X(2994)}}, {{A, B, C, X(81), X(5556)}}, {{A, B, C, X(1214), X(32533)}}, {{A, B, C, X(1255), X(7319)}}, {{A, B, C, X(1824), X(36616)}}, {{A, B, C, X(4102), X(30513)}}, {{A, B, C, X(5561), X(39980)}}, {{A, B, C, X(10405), X(52393)}}, {{A, B, C, X(11114), X(37181)}}, {{A, B, C, X(17501), X(25430)}}, {{A, B, C, X(25417), X(43733)}}, {{A, B, C, X(26118), X(52282)}}, {{A, B, C, X(27789), X(43734)}}, {{A, B, C, X(34914), X(45132)}}, {{A, B, C, X(37276), X(50687)}}, {{A, B, C, X(42030), X(43740)}}
X(54756) = trilinear pole of line {48564, 523}

X(54757) = X(226)X(10072)∩X(321)X(48806)

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

X(54757) lies on these lines: {226, 10072}, {321, 48806}, {406, 43530}, {475, 16080}, {1029, 3839}, {4080, 10529}

X(54757) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(51816)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(39982)}}, {{A, B, C, X(8), X(10072)}}, {{A, B, C, X(30), X(475)}}, {{A, B, C, X(37), X(3531)}}, {{A, B, C, X(64), X(39960)}}, {{A, B, C, X(74), X(39956)}}, {{A, B, C, X(80), X(7318)}}, {{A, B, C, X(376), X(4200)}}, {{A, B, C, X(381), X(406)}}, {{A, B, C, X(451), X(3839)}}, {{A, B, C, X(519), X(10529)}}, {{A, B, C, X(903), X(5553)}}, {{A, B, C, X(937), X(52374)}}, {{A, B, C, X(941), X(14483)}}, {{A, B, C, X(943), X(11546)}}, {{A, B, C, X(1000), X(1440)}}, {{A, B, C, X(3426), X(39798)}}, {{A, B, C, X(3431), X(39975)}}, {{A, B, C, X(3527), X(39974)}}, {{A, B, C, X(3543), X(52252)}}, {{A, B, C, X(3545), X(4194)}}, {{A, B, C, X(7040), X(36910)}}, {{A, B, C, X(10308), X(48806)}}, {{A, B, C, X(10309), X(36588)}}, {{A, B, C, X(12648), X(45700)}}, {{A, B, C, X(16005), X(39711)}}, {{A, B, C, X(34625), X(36846)}}, {{A, B, C, X(36610), X(44040)}}, {{A, B, C, X(36721), X(37382)}}, {{A, B, C, X(36916), X(40836)}}, {{A, B, C, X(51223), X(52188)}}

X(54758) = X(4)X(37503)∩X(226)X(5119)

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

X(54758) lies on these lines: {4, 37503}, {226, 5119}, {406, 16080}, {475, 43530}, {1029, 3543}, {3332, 5397}, {4080, 10528}

X(54758) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(5119)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(37503)}}, {{A, B, C, X(8), X(10056)}}, {{A, B, C, X(30), X(406)}}, {{A, B, C, X(37), X(3426)}}, {{A, B, C, X(40), X(39948)}}, {{A, B, C, X(65), X(34288)}}, {{A, B, C, X(74), X(941)}}, {{A, B, C, X(376), X(4194)}}, {{A, B, C, X(381), X(475)}}, {{A, B, C, X(451), X(3543)}}, {{A, B, C, X(461), X(37427)}}, {{A, B, C, X(519), X(10528)}}, {{A, B, C, X(522), X(3296)}}, {{A, B, C, X(943), X(36916)}}, {{A, B, C, X(3527), X(39982)}}, {{A, B, C, X(3531), X(39798)}}, {{A, B, C, X(3545), X(4200)}}, {{A, B, C, X(3839), X(52252)}}, {{A, B, C, X(3870), X(34619)}}, {{A, B, C, X(5553), X(39704)}}, {{A, B, C, X(5561), X(7318)}}, {{A, B, C, X(5665), X(7040)}}, {{A, B, C, X(6095), X(14497)}}, {{A, B, C, X(12649), X(45701)}}, {{A, B, C, X(14483), X(39956)}}, {{A, B, C, X(14490), X(39983)}}, {{A, B, C, X(14491), X(39975)}}, {{A, B, C, X(17133), X(28292)}}, {{A, B, C, X(18317), X(31503)}}, {{A, B, C, X(28478), X(28580)}}, {{A, B, C, X(30257), X(30730)}}, {{A, B, C, X(36722), X(37382)}}, {{A, B, C, X(36889), X(41013)}}, {{A, B, C, X(39960), X(52518)}}, {{A, B, C, X(45095), X(52487)}}, {{A, B, C, X(51223), X(52187)}}

X(54759) = X(10)X(5225)∩X(4080)X(20043)

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

X(54759) lies on these lines: {10, 5225}, {4080, 20043}, {26118, 53099}

X(54759) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(8), X(39948)}}, {{A, B, C, X(57), X(7319)}}, {{A, B, C, X(80), X(39980)}}, {{A, B, C, X(81), X(43734)}}, {{A, B, C, X(189), X(5560)}}, {{A, B, C, X(278), X(5225)}}, {{A, B, C, X(519), X(20043)}}, {{A, B, C, X(553), X(15998)}}, {{A, B, C, X(1214), X(31371)}}, {{A, B, C, X(1255), X(43733)}}, {{A, B, C, X(1412), X(41446)}}, {{A, B, C, X(3839), X(37276)}}, {{A, B, C, X(4102), X(6601)}}, {{A, B, C, X(4654), X(18230)}}, {{A, B, C, X(5551), X(27789)}}, {{A, B, C, X(5556), X(25430)}}, {{A, B, C, X(7317), X(25417)}}, {{A, B, C, X(8056), X(17501)}}, {{A, B, C, X(9580), X(52374)}}

X(54760) = X(10)X(3474)∩X(144)X(6539)

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

X(54760) lies on these lines: {10, 3474}, {144, 6539}, {321, 32099}, {5225, 39948}, {26118, 43537}, {37456, 47586}

X(54760) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(3929)}}, {{A, B, C, X(57), X(5128)}}, {{A, B, C, X(79), X(189)}}, {{A, B, C, X(81), X(43733)}}, {{A, B, C, X(144), X(553)}}, {{A, B, C, X(278), X(5229)}}, {{A, B, C, X(1214), X(15077)}}, {{A, B, C, X(1255), X(43734)}}, {{A, B, C, X(1412), X(41439)}}, {{A, B, C, X(2994), X(3296)}}, {{A, B, C, X(3474), X(10509)}}, {{A, B, C, X(3543), X(37276)}}, {{A, B, C, X(4654), X(5273)}}, {{A, B, C, X(5551), X(25417)}}, {{A, B, C, X(5561), X(36603)}}, {{A, B, C, X(6601), X(42030)}}, {{A, B, C, X(7317), X(27789)}}, {{A, B, C, X(7319), X(25430)}}, {{A, B, C, X(9579), X(52374)}}, {{A, B, C, X(11111), X(37181)}}, {{A, B, C, X(36609), X(52037)}}

X(54761) = X(1370)X(7607)∩X(3524)X(43666)

Barycentrics    (3*a^6-3*(b^2-c^2)^3-3*a^4*(3*b^2+c^2)+a^2*(9*b^4-2*b^2*c^2-3*c^4))*(3*a^6+3*(b^2-c^2)^3-3*a^4*(b^2+3*c^2)+a^2*(-3*b^4-2*b^2*c^2+9*c^4)) : :

X(54761) lies on these lines: {1370, 7607}, {3524, 43666}, {6504, 37672}, {6805, 43564}, {6806, 43565}, {6997, 7608}, {7391, 43537}, {7392, 53098}, {7394, 53099}, {7612, 44442}, {10185, 46336}, {16063, 53859}, {16080, 37192}, {52282, 52583}

X(54761) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(37192)}}, {{A, B, C, X(97), X(15077)}}, {{A, B, C, X(394), X(32533)}}, {{A, B, C, X(1073), X(17505)}}, {{A, B, C, X(1370), X(52282)}}, {{A, B, C, X(1993), X(38442)}}, {{A, B, C, X(3543), X(6820)}}, {{A, B, C, X(3839), X(6819)}}, {{A, B, C, X(6145), X(6515)}}, {{A, B, C, X(6997), X(52281)}}, {{A, B, C, X(14593), X(36616)}}, {{A, B, C, X(14919), X(18296)}}, {{A, B, C, X(21400), X(36609)}}, {{A, B, C, X(31371), X(31626)}}, {{A, B, C, X(37174), X(44442)}}, {{A, B, C, X(38443), X(43756)}}

X(54762) = X(376)X(43666)∩X(5189)X(53859)

Barycentrics    (3*a^6-3*(b^2-c^2)^3-3*a^4*(3*b^2+c^2)+a^2*(9*b^4-4*b^2*c^2-3*c^4))*(3*a^6+3*(b^2-c^2)^3-3*a^4*(b^2+3*c^2)+a^2*(-3*b^4-4*b^2*c^2+9*c^4)) : :

X(54762) lies on these lines: {376, 43666}, {5189, 53859}, {6997, 53098}, {7391, 7607}, {7394, 7608}, {10185, 16063}, {37349, 53099}, {44442, 53103}

X(54762) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(97), X(32533)}}, {{A, B, C, X(394), X(17505)}}, {{A, B, C, X(3543), X(37192)}}, {{A, B, C, X(6820), X(50687)}}, {{A, B, C, X(7391), X(52282)}}, {{A, B, C, X(7394), X(52281)}}

X(54763) = X(2)X(44683)∩X(275)X(376)

Barycentrics    (a^8+2*a^6*(4*b^2+c^2)+(b^2-c^2)^3*(b^2+5*c^2)+2*a^2*(b^2-c^2)^2*(4*b^2+7*c^2)-2*a^4*(9*b^4+b^2*c^2+6*c^4))*(a^8-(b^2-c^2)^3*(5*b^2+c^2)+2*a^6*(b^2+4*c^2)+2*a^2*(b^2-c^2)^2*(7*b^2+4*c^2)-2*a^4*(6*b^4+b^2*c^2+9*c^4)) : :

X(54763) lies on these lines: {2, 44683}, {4, 52703}, {275, 376}, {381, 8796}, {459, 5071}, {631, 43530}, {2052, 3545}, {3090, 16080}, {3590, 6810}, {3591, 6809}, {5395, 34664}, {39284, 41099}

X(54763) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(3545)}}, {{A, B, C, X(5), X(376)}}, {{A, B, C, X(20), X(5071)}}, {{A, B, C, X(30), X(3090)}}, {{A, B, C, X(68), X(381)}}, {{A, B, C, X(69), X(44683)}}, {{A, B, C, X(140), X(41099)}}, {{A, B, C, X(253), X(46455)}}, {{A, B, C, X(265), X(36948)}}, {{A, B, C, X(546), X(15709)}}, {{A, B, C, X(547), X(33703)}}, {{A, B, C, X(549), X(3855)}}, {{A, B, C, X(1093), X(52187)}}, {{A, B, C, X(1494), X(18855)}}, {{A, B, C, X(1656), X(15682)}}, {{A, B, C, X(1989), X(14542)}}, {{A, B, C, X(3091), X(3524)}}, {{A, B, C, X(3149), X(50741)}}, {{A, B, C, X(3431), X(41891)}}, {{A, B, C, X(3521), X(18849)}}, {{A, B, C, X(3523), X(41106)}}, {{A, B, C, X(3525), X(3839)}}, {{A, B, C, X(3529), X(5055)}}, {{A, B, C, X(3533), X(3845)}}, {{A, B, C, X(3543), X(5067)}}, {{A, B, C, X(3544), X(10304)}}, {{A, B, C, X(3613), X(35512)}}, {{A, B, C, X(3832), X(15702)}}, {{A, B, C, X(3851), X(15698)}}, {{A, B, C, X(4846), X(8797)}}, {{A, B, C, X(5056), X(11001)}}, {{A, B, C, X(5066), X(10299)}}, {{A, B, C, X(5068), X(19708)}}, {{A, B, C, X(5072), X(15710)}}, {{A, B, C, X(5079), X(46333)}}, {{A, B, C, X(6526), X(52188)}}, {{A, B, C, X(6830), X(11111)}}, {{A, B, C, X(6844), X(50739)}}, {{A, B, C, X(6878), X(52269)}}, {{A, B, C, X(6879), X(11114)}}, {{A, B, C, X(6880), X(17577)}}, {{A, B, C, X(6927), X(17532)}}, {{A, B, C, X(6935), X(17556)}}, {{A, B, C, X(6956), X(11113)}}, {{A, B, C, X(6969), X(11112)}}, {{A, B, C, X(6977), X(37375)}}, {{A, B, C, X(7399), X(7714)}}, {{A, B, C, X(7552), X(18420)}}, {{A, B, C, X(8889), X(34664)}}, {{A, B, C, X(13472), X(45301)}}, {{A, B, C, X(13634), X(36683)}}, {{A, B, C, X(13860), X(33190)}}, {{A, B, C, X(14033), X(37446)}}, {{A, B, C, X(14457), X(30537)}}, {{A, B, C, X(14491), X(41890)}}, {{A, B, C, X(14787), X(46450)}}, {{A, B, C, X(14788), X(34608)}}, {{A, B, C, X(15077), X(22270)}}, {{A, B, C, X(15749), X(46452)}}, {{A, B, C, X(16041), X(37334)}}, {{A, B, C, X(17040), X(52487)}}, {{A, B, C, X(18847), X(31846)}}, {{A, B, C, X(18850), X(40410)}}, {{A, B, C, X(19709), X(21735)}}, {{A, B, C, X(22268), X(32533)}}

X(54764) = X(1370)X(7608)∩X(5071)X(43666)

Barycentrics    (3*a^6-3*(b^2-c^2)^3-3*a^4*(3*b^2+c^2)+a^2*(9*b^4-10*b^2*c^2-3*c^4))*(3*a^6+3*(b^2-c^2)^3-3*a^4*(b^2+3*c^2)+a^2*(-3*b^4-10*b^2*c^2+9*c^4)) : :

X(54764) lies on these lines: {1370, 7608}, {5071, 43666}, {5485, 41628}, {6805, 43565}, {6806, 43564}, {6997, 7607}, {7386, 53098}, {7391, 53099}, {7394, 43537}, {14494, 44442}, {37192, 43530}, {37349, 47586}, {52281, 52583}

X(54764) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(97), X(31371)}}, {{A, B, C, X(381), X(37192)}}, {{A, B, C, X(1370), X(52281)}}, {{A, B, C, X(1992), X(41628)}}, {{A, B, C, X(3543), X(6819)}}, {{A, B, C, X(3839), X(6820)}}, {{A, B, C, X(6997), X(52282)}}, {{A, B, C, X(15077), X(31626)}}, {{A, B, C, X(18550), X(36609)}}

X(54765) = X(1370)X(53098)∩X(3545)X(43666)

Barycentrics    (3*a^6-3*(b^2-c^2)^3-3*a^4*(3*b^2+c^2)+a^2*(9*b^4-8*b^2*c^2-3*c^4))*(3*a^6+3*(b^2-c^2)^3-3*a^4*(b^2+3*c^2)+a^2*(-3*b^4-8*b^2*c^2+9*c^4)) : :

X(54765) lies on these lines: {1370, 53098}, {3545, 43666}, {7391, 7608}, {7394, 7607}, {7533, 53859}, {10155, 44442}, {37349, 43537}

X(54765) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3839), X(37192)}}, {{A, B, C, X(6819), X(50687)}}, {{A, B, C, X(7391), X(52281)}}, {{A, B, C, X(7394), X(52282)}}, {{A, B, C, X(11741), X(15740)}}, {{A, B, C, X(31626), X(32533)}}, {{A, B, C, X(37644), X(37672)}}

X(54766) = X(7608)X(26118)∩X(37456)X(53099)

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

X(54766) lies on these lines: {7608, 26118}, {37456, 53099}

X(54766) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(57), X(17501)}}, {{A, B, C, X(80), X(39948)}}, {{A, B, C, X(81), X(7319)}}, {{A, B, C, X(1255), X(5556)}}, {{A, B, C, X(2994), X(5560)}}, {{A, B, C, X(4102), X(43740)}}, {{A, B, C, X(17577), X(37181)}}, {{A, B, C, X(25417), X(43734)}}, {{A, B, C, X(26118), X(52281)}}, {{A, B, C, X(27789), X(43733)}}, {{A, B, C, X(30513), X(42030)}}, {{A, B, C, X(34892), X(45132)}}, {{A, B, C, X(37654), X(42045)}}
X(54766) = trilinear pole of line {48561, 523}

X(54767) = X(2)X(38736)∩X(542)X(38259)

Barycentrics    (7*a^6+7*b^6-16*b^4*c^2+17*b^2*c^4-8*c^6-a^4*(b^2+16*c^2)-a^2*(b^4+6*b^2*c^2-17*c^4))*(7*a^6-8*b^6+17*b^4*c^2-16*b^2*c^4+7*c^6-a^4*(16*b^2+c^2)+a^2*(17*b^4-6*b^2*c^2-c^4)) : :

X(54767) lies on these lines: {2, 38736}, {542, 38259}, {2996, 9880}, {7612, 14639}

X(54767) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(1494), X(38736)}}, {{A, B, C, X(3455), X(3531)}}, {{A, B, C, X(5203), X(52094)}}, {{A, B, C, X(6323), X(14487)}}, {{A, B, C, X(8753), X(43656)}}, {{A, B, C, X(35142), X(39809)}}, {{A, B, C, X(40819), X(51215)}}

X(54768) = X(10)X(535)∩X(321)X(527)

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

X(54768) lies on these lines: {10, 535}, {63, 6539}, {226, 6610}, {321, 527}, {553, 40149}, {4049, 29148}, {4080, 31164}, {17346, 34258}, {17556, 43531}

X(54768) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(27), X(11112)}}, {{A, B, C, X(57), X(513)}}, {{A, B, C, X(63), X(553)}}, {{A, B, C, X(79), X(34234)}}, {{A, B, C, X(333), X(3254)}}, {{A, B, C, X(469), X(17556)}}, {{A, B, C, X(519), X(29148)}}, {{A, B, C, X(752), X(28846)}}, {{A, B, C, X(940), X(17346)}}, {{A, B, C, X(1121), X(34606)}}, {{A, B, C, X(1255), X(24297)}}, {{A, B, C, X(3680), X(42030)}}, {{A, B, C, X(3911), X(5561)}}, {{A, B, C, X(4102), X(34918)}}, {{A, B, C, X(4654), X(5745)}}, {{A, B, C, X(5307), X(10106)}}, {{A, B, C, X(7091), X(39948)}}, {{A, B, C, X(7224), X(18821)}}, {{A, B, C, X(7354), X(52374)}}, {{A, B, C, X(16834), X(49990)}}, {{A, B, C, X(29573), X(50758)}}, {{A, B, C, X(29594), X(29829)}}, {{A, B, C, X(32010), X(39704)}}, {{A, B, C, X(37683), X(50133)}}
X(54768) = trilinear pole of line {14413, 523}

X(54769) = X(4)X(32136)∩X(7607)X(31074)

Barycentrics    (2*a^6+(b^2-c^2)^2*(2*b^2-c^2)-a^4*(2*b^2+5*c^2)-a^2*(2*b^4+b^2*c^2-4*c^4))*(2*a^6-(b^2-2*c^2)*(b^2-c^2)^2-a^4*(5*b^2+2*c^2)+a^2*(4*b^4-b^2*c^2-2*c^4)) : :

X(54769) lies on these lines: {4, 32136}, {7607, 31074}, {7608, 13595}, {9221, 38321}, {10159, 46571}, {10185, 30745}

X(54769) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(97), X(32136)}}, {{A, B, C, X(428), X(46571)}}, {{A, B, C, X(6748), X(41891)}}, {{A, B, C, X(13595), X(52281)}}, {{A, B, C, X(31074), X(52282)}}
X(54769) = trilinear pole of line {16532, 523}

X(54770) = X(4)X(46922)∩X(10)X(24695)

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

X(54770) lies on these lines: {4, 46922}, {10, 24695}, {226, 29597}, {321, 50079}, {4080, 29585}, {5485, 17378}, {6625, 33032}, {7379, 43537}, {7385, 53099}

X(54770) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(50079)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(3227)}}, {{A, B, C, X(8), X(29597)}}, {{A, B, C, X(69), X(46922)}}, {{A, B, C, X(79), X(36871)}}, {{A, B, C, X(274), X(5556)}}, {{A, B, C, X(330), X(43733)}}, {{A, B, C, X(519), X(29585)}}, {{A, B, C, X(1509), X(10405)}}, {{A, B, C, X(1992), X(17378)}}, {{A, B, C, X(2333), X(36616)}}, {{A, B, C, X(3241), X(29605)}}, {{A, B, C, X(4212), X(33031)}}, {{A, B, C, X(4213), X(33032)}}, {{A, B, C, X(4654), X(26065)}}, {{A, B, C, X(5551), X(38247)}}, {{A, B, C, X(5561), X(39721)}}, {{A, B, C, X(5665), X(40403)}}, {{A, B, C, X(6630), X(18490)}}, {{A, B, C, X(7261), X(35170)}}, {{A, B, C, X(7319), X(32009)}}, {{A, B, C, X(17392), X(37654)}}, {{A, B, C, X(17947), X(34919)}}, {{A, B, C, X(20568), X(39716)}}, {{A, B, C, X(39738), X(43734)}}
X(54770) = trilinear pole of line {47761, 47785}

X(54771) = X(671)X(11433)∩X(858)X(53099)

Barycentrics    (a^6+(b^2-5*c^2)*(b^2-c^2)^2-a^4*(b^2+7*c^2)-a^2*(b^4+18*b^2*c^2-11*c^4))*(a^6-(b^2-c^2)^2*(5*b^2-c^2)-a^4*(7*b^2+c^2)+a^2*(11*b^4-18*b^2*c^2-c^4)) : :

X(54771) lies on these lines: {671, 11433}, {858, 53099}, {1995, 43537}, {5032, 43670}, {7607, 40132}, {7608, 16051}, {10601, 18842}, {14484, 31133}

X(54771) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(524), X(11433)}}, {{A, B, C, X(6524), X(34288)}}, {{A, B, C, X(8797), X(46111)}}, {{A, B, C, X(10601), X(21356)}}, {{A, B, C, X(16051), X(52281)}}, {{A, B, C, X(31133), X(52288)}}, {{A, B, C, X(36889), X(46104)}}, {{A, B, C, X(40132), X(52282)}}, {{A, B, C, X(42287), X(45835)}}

X(54772) = X(22)X(53099)∩X(96)X(3545)

Barycentrics    (5*a^6-(b^2-5*c^2)*(b^2-c^2)^2-a^4*(11*b^2+5*c^2)+a^2*(7*b^4-10*b^2*c^2-5*c^4))*(5*a^6+(b^2-c^2)^2*(5*b^2-c^2)-a^4*(5*b^2+11*c^2)+a^2*(-5*b^4-10*b^2*c^2+7*c^4)) : :

X(54772) lies on these lines: {22, 53099}, {96, 3545}, {262, 34608}, {5133, 43537}, {7494, 7608}, {14484, 34603}, {31363, 52069}

X(54772) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(343), X(15749)}}, {{A, B, C, X(376), X(52253)}}, {{A, B, C, X(458), X(34608)}}, {{A, B, C, X(467), X(3545)}}, {{A, B, C, X(7494), X(52281)}}, {{A, B, C, X(7714), X(41231)}}, {{A, B, C, X(11427), X(14457)}}, {{A, B, C, X(31371), X(52350)}}, {{A, B, C, X(34603), X(52288)}}, {{A, B, C, X(40065), X(41894)}}

X(54773) = X(2)X(41413)∩X(76)X(41624)

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

X(54773) lies on these lines: {2, 41413}, {76, 41624}, {83, 7910}, {262, 29181}, {597, 14458}, {2548, 18840}, {3424, 14561}, {5306, 11167}, {5395, 33210}, {7788, 10302}, {7922, 10159}, {8357, 53102}, {8362, 43527}, {9774, 14492}, {14484, 48901}, {14537, 18842}, {14976, 33202}

X(54773) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(41413)}}, {{A, B, C, X(25), X(43950)}}, {{A, B, C, X(427), X(11287)}}, {{A, B, C, X(512), X(39951)}}, {{A, B, C, X(597), X(7788)}}, {{A, B, C, X(2548), X(42037)}}, {{A, B, C, X(3108), X(44557)}}, {{A, B, C, X(3618), X(8801)}}, {{A, B, C, X(5064), X(8362)}}, {{A, B, C, X(5306), X(11163)}}, {{A, B, C, X(7736), X(47735)}}, {{A, B, C, X(8889), X(33210)}}, {{A, B, C, X(9300), X(14614)}}, {{A, B, C, X(10014), X(17980)}}, {{A, B, C, X(18575), X(44571)}}, {{A, B, C, X(23878), X(29181)}}, {{A, B, C, X(31360), X(43098)}}

X(54774) = X(4)X(3292)∩X(394)X(671)

Barycentrics    (2*a^6-(b^2-2*c^2)*(b^2-c^2)^2-a^4*(5*b^2+2*c^2)+a^2*(4*b^4+6*b^2*c^2-2*c^4))*(2*a^6+(b^2-c^2)^2*(2*b^2-c^2)-a^4*(2*b^2+5*c^2)+a^2*(-2*b^4+6*b^2*c^2+4*c^4)) : :

X(54774) lies on these lines: {4, 3292}, {94, 44133}, {98, 31152}, {394, 671}, {520, 5466}, {524, 2052}, {2797, 9180}, {7607, 30739}, {7608, 11284}, {11427, 18842}, {37672, 39284}, {46517, 53100}

X(54774) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(31152)}}, {{A, B, C, X(305), X(5641)}}, {{A, B, C, X(340), X(44133)}}, {{A, B, C, X(394), X(520)}}, {{A, B, C, X(543), X(2797)}}, {{A, B, C, X(1275), X(2994)}}, {{A, B, C, X(1494), X(34405)}}, {{A, B, C, X(5905), X(7058)}}, {{A, B, C, X(9141), X(34412)}}, {{A, B, C, X(11284), X(52281)}}, {{A, B, C, X(11427), X(21356)}}, {{A, B, C, X(21358), X(37649)}}, {{A, B, C, X(30739), X(52282)}}

X(54775) = X(10)X(32933)∩X(321)X(4445)

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

X(54775) lies on these lines: {10, 32933}, {321, 4445}, {7607, 19649}, {43537, 50699}

X(54775) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(903), X(2995)}}, {{A, B, C, X(3578), X(17378)}}, {{A, B, C, X(4980), X(19822)}}, {{A, B, C, X(17251), X(42025)}}, {{A, B, C, X(19649), X(52282)}}, {{A, B, C, X(19799), X(50102)}}, {{A, B, C, X(24993), X(50043)}}
X(54775) = trilinear pole of line {47795, 47888}

X(54776) = X(4)X(41628)∩X(6515)X(39284)

Barycentrics    (a^6-(b^2-c^2)^2*(5*b^2-c^2)-a^4*(7*b^2+c^2)+a^2*(11*b^4+2*b^2*c^2-c^4))*(a^6+(b^2-5*c^2)*(b^2-c^2)^2-a^4*(b^2+7*c^2)+a^2*(-b^4+2*b^2*c^2+11*c^4)) : :

X(54776) lies on these lines: {4, 41628}, {6515, 39284}, {6636, 43537}, {20062, 47586}, {37353, 53099}

X(54776) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(69), X(41628)}}, {{A, B, C, X(13157), X(27353)}}, {{A, B, C, X(36889), X(42355)}}
X(54776) = X(i)-cross conjugate of X(j) for these {i, j}: {42021, 8797}

X(54777) = X(3547)X(7607)∩X(7404)X(7608)

Barycentrics    (a^8+8*a^2*b^2*c^2*(b^2-2*c^2)+(b^4-c^4)^2-2*a^4*(b^4-4*b^2*c^2+c^4))*(a^8+8*a^2*b^2*c^2*(-2*b^2+c^2)+(b^4-c^4)^2-2*a^4*(b^4-4*b^2*c^2+c^4)) : :

X(54777) lies on these lines: {3547, 7607}, {7404, 7608}, {34603, 40178}

X(54777) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(6339)}}, {{A, B, C, X(3547), X(52282)}}, {{A, B, C, X(7404), X(52281)}}, {{A, B, C, X(10630), X(51316)}}, {{A, B, C, X(40832), X(42373)}}

X(54778) = X(23)X(43537)∩X(524)X(6504)

Barycentrics    (a^6+(b^2-5*c^2)*(b^2-c^2)^2-a^4*(b^2+7*c^2)-a^2*(b^4+6*b^2*c^2-11*c^4))*(a^6-(b^2-c^2)^2*(5*b^2-c^2)-a^4*(7*b^2+c^2)+a^2*(11*b^4-6*b^2*c^2-c^4)) : :

X(54778) lies on these lines: {23, 43537}, {524, 6504}, {671, 6515}, {3545, 9221}, {5169, 53099}, {5422, 18842}, {7493, 7607}, {7519, 47586}, {15682, 18316}, {52300, 53859}

X(54778) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(64), X(43756)}}, {{A, B, C, X(394), X(34802)}}, {{A, B, C, X(524), X(6515)}}, {{A, B, C, X(1989), X(14593)}}, {{A, B, C, X(3580), X(35512)}}, {{A, B, C, X(5422), X(21356)}}, {{A, B, C, X(5641), X(13575)}}, {{A, B, C, X(5900), X(37644)}}, {{A, B, C, X(7493), X(52282)}}, {{A, B, C, X(11744), X(37645)}}, {{A, B, C, X(13157), X(27361)}}, {{A, B, C, X(31626), X(43697)}}, {{A, B, C, X(34287), X(46275)}}, {{A, B, C, X(36889), X(44176)}}
X(54778) = polar conjugate of X(35486)
X(54778) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 35486}

X(54779) = X(98)X(34621)∩X(3543)X(40178)

Barycentrics    (a^8+16*a^2*b^2*c^2*(b^2-2*c^2)+(b^4-c^4)^2-2*a^4*(b^4-8*b^2*c^2+c^4))*(a^8+16*a^2*b^2*c^2*(-2*b^2+c^2)+(b^4-c^4)^2-2*a^4*(b^4-8*b^2*c^2+c^4)) : :

X(54779) lies on these lines: {98, 34621}, {3543, 40178}, {7400, 7607}, {43537, 52404}

X(54779) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(6339)}}, {{A, B, C, X(297), X(34621)}}, {{A, B, C, X(3088), X(8370)}}, {{A, B, C, X(3089), X(7841)}}, {{A, B, C, X(3532), X(34898)}}, {{A, B, C, X(7400), X(52282)}}

X(54780) = X(6834)X(53098)∩X(6847)X(7607)

Barycentrics    (a^5+b^5-10*a^3*b*c-b^4*c-b*c^4+c^5-a^4*(b+c)-2*a^2*b*c*(b+c)-a*(b^4+10*b^3*c+2*b^2*c^2-14*b*c^3+c^4))*(a^5+b^5-10*a^3*b*c-b^4*c-b*c^4+c^5-a^4*(b+c)-2*a^2*b*c*(b+c)-a*(b^4-14*b^3*c+2*b^2*c^2+10*b*c^3+c^4)) : :

X(54780) lies on these lines: {6834, 53098}, {6847, 7607}, {6848, 7608}, {37434, 43537}

X(54780) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3062), X(34914)}}, {{A, B, C, X(6847), X(52282)}}, {{A, B, C, X(6848), X(52281)}}, {{A, B, C, X(14490), X(39957)}}

X(54781) = X(96)X(3543)∩X(5133)X(53098)

Barycentrics    (5*a^6-(7*b^2-5*c^2)*(b^2-c^2)^2-a^4*(17*b^2+5*c^2)+a^2*(19*b^4-10*b^2*c^2-5*c^4))*(5*a^6+(5*b^2-7*c^2)*(b^2-c^2)^2-a^4*(5*b^2+17*c^2)+a^2*(-5*b^4-10*b^2*c^2+19*c^4)) : :

X(54781) lies on these lines: {96, 3543}, {5133, 53098}, {7500, 7607}, {7612, 34603}, {34608, 53103}

X(54781) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(324), X(18846)}}, {{A, B, C, X(467), X(3543)}}, {{A, B, C, X(3839), X(52253)}}, {{A, B, C, X(7500), X(52282)}}, {{A, B, C, X(17505), X(52350)}}, {{A, B, C, X(34603), X(37174)}}

X(54782) = X(524)X(13579)∩X(671)X(45794)

Barycentrics    (a^6+(b^2-5*c^2)*(b^2-c^2)^2-a^4*(b^2+7*c^2)-a^2*(b^4-11*c^4))*(a^6-(b^2-c^2)^2*(5*b^2-c^2)-a^4*(7*b^2+c^2)+a^2*(11*b^4-c^4)) : :

X(54782) lies on these lines: {524, 13579}, {671, 45794}, {7492, 43537}, {18842, 34545}, {20063, 47586}

X(54782) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(524), X(45794)}}, {{A, B, C, X(21356), X(34545)}}, {{A, B, C, X(36889), X(46138)}}

X(54783) = X(4)X(1493)∩X(94)X(41628)

Barycentrics    (2*a^6-(b^2-2*c^2)*(b^2-c^2)^2-a^4*(5*b^2+2*c^2)+a^2*(4*b^4+b^2*c^2-2*c^4))*(2*a^6+(b^2-c^2)^2*(2*b^2-c^2)-a^4*(2*b^2+5*c^2)+a^2*(-2*b^4+b^2*c^2+4*c^4)) : :

X(54783) lies on these lines: {4, 1493}, {94, 41628}, {1994, 39284}, {7607, 31101}

X(54783) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(97), X(1493)}}, {{A, B, C, X(323), X(41628)}}, {{A, B, C, X(13157), X(14918)}}, {{A, B, C, X(16770), X(40711)}}, {{A, B, C, X(16771), X(40712)}}, {{A, B, C, X(31101), X(52282)}}
X(54783) = barycentric product X(i)*X(j) for these (i, j): {32535, 95}
X(54783) = barycentric quotient X(i)/X(j) for these (i, j): {32535, 5}

X(54784) = X(394)X(5485)∩X(598)X(11427)

Barycentrics    (5*a^6-(b^2-5*c^2)*(b^2-c^2)^2-a^4*(11*b^2+5*c^2)+a^2*(7*b^4+6*b^2*c^2-5*c^4))*(5*a^6+(b^2-c^2)^2*(5*b^2-c^2)-a^4*(5*b^2+11*c^2)+a^2*(-5*b^4+6*b^2*c^2+7*c^4)) : :

X(54784) lies on these lines: {394, 5485}, {598, 11427}, {858, 43537}, {1992, 2052}, {1995, 53099}, {3424, 31133}, {6504, 40112}, {7607, 16051}, {7608, 40132}, {31099, 47586}, {31363, 38323}, {38253, 44569}

X(54784) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(394), X(895)}}, {{A, B, C, X(599), X(11427)}}, {{A, B, C, X(6515), X(40112)}}, {{A, B, C, X(7714), X(41238)}}, {{A, B, C, X(9141), X(13575)}}, {{A, B, C, X(11064), X(43699)}}, {{A, B, C, X(14491), X(15066)}}, {{A, B, C, X(16051), X(52282)}}, {{A, B, C, X(31133), X(52283)}}, {{A, B, C, X(33565), X(37645)}}, {{A, B, C, X(34405), X(36889)}}, {{A, B, C, X(36609), X(38260)}}, {{A, B, C, X(40132), X(52281)}}

X(54785) = X(98)X(44442)∩X(1370)X(43537)

Barycentrics    (3*a^6-3*(b^2-c^2)^3-3*a^4*(3*b^2+c^2)+a^2*(9*b^4+2*b^2*c^2-3*c^4))*(3*a^6+3*(b^2-c^2)^3-3*a^4*(b^2+3*c^2)+a^2*(-3*b^4+2*b^2*c^2+9*c^4)) : :

X(54785) lies on these lines: {98, 44442}, {1370, 43537}, {1992, 39284}, {3539, 43564}, {3540, 43565}, {6805, 10195}, {6806, 10194}, {6819, 43530}, {6820, 16080}, {6997, 53099}, {7386, 7607}, {7391, 47586}, {7392, 7608}, {15702, 43666}, {46336, 53859}

X(54785) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(6820)}}, {{A, B, C, X(265), X(36609)}}, {{A, B, C, X(297), X(44442)}}, {{A, B, C, X(376), X(37192)}}, {{A, B, C, X(381), X(6819)}}, {{A, B, C, X(394), X(15077)}}, {{A, B, C, X(1032), X(15749)}}, {{A, B, C, X(1073), X(32533)}}, {{A, B, C, X(2987), X(16774)}}, {{A, B, C, X(6464), X(38442)}}, {{A, B, C, X(6524), X(36616)}}, {{A, B, C, X(7386), X(52282)}}, {{A, B, C, X(7392), X(52281)}}, {{A, B, C, X(11433), X(22466)}}
X(54785) = X(i)-cross conjugate of X(j) for these {i, j}: {37672, 2}

X(54786) = X(2)X(4720)∩X(10)X(4873)

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

X(54786) lies on these lines: {2, 4720}, {4, 17330}, {8, 30588}, {10, 4873}, {226, 3679}, {321, 53620}, {376, 13478}, {381, 45100}, {2047, 3590}, {2051, 3545}, {2996, 17677}, {3617, 4080}, {4049, 28161}, {4052, 4745}, {5071, 45098}, {5485, 17251}, {5721, 45097}, {6625, 50074}, {6998, 43537}, {7380, 53099}, {7390, 47586}, {7410, 7607}, {11111, 24624}, {22235, 37144}, {22237, 37145}

X(54786) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(9333)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(8), X(3679)}}, {{A, B, C, X(29), X(50741)}}, {{A, B, C, X(69), X(17330)}}, {{A, B, C, X(75), X(1000)}}, {{A, B, C, X(80), X(5726)}}, {{A, B, C, X(145), X(4745)}}, {{A, B, C, X(318), X(36916)}}, {{A, B, C, X(376), X(17555)}}, {{A, B, C, X(461), X(17528)}}, {{A, B, C, X(519), X(1219)}}, {{A, B, C, X(860), X(11111)}}, {{A, B, C, X(903), X(3296)}}, {{A, B, C, X(941), X(4674)}}, {{A, B, C, X(957), X(4492)}}, {{A, B, C, X(966), X(17378)}}, {{A, B, C, X(1224), X(7319)}}, {{A, B, C, X(1654), X(50074)}}, {{A, B, C, X(1992), X(17251)}}, {{A, B, C, X(3241), X(13606)}}, {{A, B, C, X(3545), X(11109)}}, {{A, B, C, X(3616), X(43732)}}, {{A, B, C, X(3621), X(38098)}}, {{A, B, C, X(3632), X(51068)}}, {{A, B, C, X(3828), X(46933)}}, {{A, B, C, X(4373), X(18490)}}, {{A, B, C, X(4668), X(51072)}}, {{A, B, C, X(4669), X(4678)}}, {{A, B, C, X(4733), X(37715)}}, {{A, B, C, X(5558), X(24857)}}, {{A, B, C, X(5561), X(28626)}}, {{A, B, C, X(6353), X(17677)}}, {{A, B, C, X(7320), X(24858)}}, {{A, B, C, X(7410), X(52282)}}, {{A, B, C, X(7498), X(17532)}}, {{A, B, C, X(7714), X(16062)}}, {{A, B, C, X(9780), X(17501)}}, {{A, B, C, X(12867), X(44692)}}, {{A, B, C, X(17271), X(37654)}}, {{A, B, C, X(17751), X(48852)}}, {{A, B, C, X(20052), X(51067)}}, {{A, B, C, X(25006), X(34619)}}, {{A, B, C, X(29593), X(50287)}}, {{A, B, C, X(34288), X(48847)}}, {{A, B, C, X(38955), X(46772)}}, {{A, B, C, X(39704), X(43733)}}, {{A, B, C, X(39974), X(51223)}}, {{A, B, C, X(46932), X(51069)}}
X(54786) = trilinear pole of line {4944, 47765}

X(54787) = X(226)X(3545)∩X(376)X(1751)

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

X(54787) lies on these lines: {226, 3545}, {376, 1751}, {7498, 43530}

X(54787) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(29), X(3545)}}, {{A, B, C, X(84), X(36588)}}, {{A, B, C, X(158), X(36916)}}, {{A, B, C, X(225), X(52187)}}, {{A, B, C, X(273), X(1000)}}, {{A, B, C, X(376), X(5125)}}, {{A, B, C, X(381), X(7498)}}, {{A, B, C, X(903), X(10305)}}, {{A, B, C, X(5071), X(7518)}}, {{A, B, C, X(7513), X(50741)}}, {{A, B, C, X(11111), X(37381)}}, {{A, B, C, X(40836), X(43734)}}

X(54788) = X(10)X(3928)∩X(321)X(21296)

Barycentrics    (3*a^3+3*a^2*(b+c)+3*(b-c)*(b+c)^2+a*(3*b^2+8*b*c-3*c^2))*(3*a^3+3*a^2*(b+c)-3*(b-c)*(b+c)^2+a*(-3*b^2+8*b*c+3*c^2)) : :

X(54788) lies on these lines: {10, 3928}, {321, 21296}, {5229, 39980}, {6539, 9965}, {16080, 37276}, {26118, 47586}

X(54788) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(3928)}}, {{A, B, C, X(30), X(37276)}}, {{A, B, C, X(57), X(43733)}}, {{A, B, C, X(79), X(36603)}}, {{A, B, C, X(81), X(5551)}}, {{A, B, C, X(189), X(3296)}}, {{A, B, C, X(553), X(9965)}}, {{A, B, C, X(1255), X(7317)}}, {{A, B, C, X(4654), X(5744)}}, {{A, B, C, X(5556), X(8056)}}, {{A, B, C, X(11578), X(36627)}}, {{A, B, C, X(15998), X(42030)}}, {{A, B, C, X(16774), X(39957)}}, {{A, B, C, X(25430), X(43734)}}, {{A, B, C, X(36609), X(43724)}}, {{A, B, C, X(37181), X(50739)}}

X(54789) = (name pending)

Barycentrics    (a^5+a^4*(b+c)+(b-c)^2*(b+c)^3-2*a^3*(b^2+9*b*c+c^2)-2*a^2*(b^3+b^2*c+b*c^2+c^3)+a*(b^4+18*b^3*c-2*b^2*c^2-18*b*c^3+c^4))*(a^5+a^4*(b+c)+(b-c)^2*(b+c)^3-2*a^3*(b^2+9*b*c+c^2)-2*a^2*(b^3+b^2*c+b*c^2+c^3)+a*(b^4-18*b^3*c-2*b^2*c^2+18*b*c^3+c^4)) : :

X(54789) lies on these lines:

X(54789) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(84), X(24857)}}, {{A, B, C, X(406), X(3830)}}, {{A, B, C, X(475), X(3845)}}, {{A, B, C, X(941), X(13603)}}, {{A, B, C, X(3426), X(39974)}}, {{A, B, C, X(3531), X(39982)}}, {{A, B, C, X(3577), X(24858)}}, {{A, B, C, X(4194), X(15682)}}, {{A, B, C, X(4200), X(41099)}}, {{A, B, C, X(14487), X(39956)}}

X(54790) = X(226)X(376)∩X(1751)X(3545)

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

X(54790) lies on these lines: {226, 376}, {1751, 3545}, {7498, 16080}

X(54790) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(30282)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(29), X(376)}}, {{A, B, C, X(30), X(7498)}}, {{A, B, C, X(461), X(37428)}}, {{A, B, C, X(3345), X(39948)}}, {{A, B, C, X(3524), X(7518)}}, {{A, B, C, X(3545), X(5125)}}, {{A, B, C, X(10305), X(39704)}}, {{A, B, C, X(40836), X(43733)}}

X(54791) = X(427)X(10185)∩X(428)X(7608)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(5*a^4+5*b^4-9*b^2*c^2+4*c^4-a^2*(10*b^2+9*c^2))*(5*a^4+4*b^4-9*b^2*c^2+5*c^4-a^2*(9*b^2+10*c^2)) : :

X(54791) lies on these lines: {427, 10185}, {428, 7608}, {472, 10188}, {473, 10187}, {3830, 13599}, {3845, 40448}, {5064, 7607}, {7378, 53859}, {7714, 53098}, {10159, 52281}, {43527, 52282}

X(54791) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(288), X(16835)}}, {{A, B, C, X(428), X(52281)}}, {{A, B, C, X(3845), X(52280)}}, {{A, B, C, X(5064), X(52282)}}, {{A, B, C, X(6748), X(30537)}}, {{A, B, C, X(8352), X(15809)}}, {{A, B, C, X(31626), X(46848)}}

X(54792) = X(23)X(53099)∩X(376)X(9221)

Barycentrics    (5*a^6-(b^2-5*c^2)*(b^2-c^2)^2-a^4*(11*b^2+5*c^2)+a^2*(7*b^4-6*b^2*c^2-5*c^4))*(5*a^6+(b^2-c^2)^2*(5*b^2-c^2)-a^4*(5*b^2+11*c^2)+a^2*(-5*b^4-6*b^2*c^2+7*c^4)) : :

X(54792) lies on these lines: {23, 53099}, {376, 9221}, {1992, 5392}, {1993, 5485}, {5169, 43537}, {7493, 7608}, {18316, 41099}

X(54792) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(97), X(43697)}}, {{A, B, C, X(1992), X(1993)}}, {{A, B, C, X(3527), X(43756)}}, {{A, B, C, X(7493), X(52281)}}, {{A, B, C, X(11433), X(40112)}}, {{A, B, C, X(36889), X(44175)}}, {{A, B, C, X(37645), X(45088)}}

X(54793) = X(10)X(24708)∩X(3543)X(13576)

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

X(54793) lies on these lines: {10, 24708}, {3543, 13576}

X(54793) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(39952)}}, {{A, B, C, X(84), X(3227)}}, {{A, B, C, X(330), X(10308)}}, {{A, B, C, X(3062), X(36871)}}, {{A, B, C, X(3426), X(37128)}}, {{A, B, C, X(3531), X(39971)}}, {{A, B, C, X(3543), X(15149)}}, {{A, B, C, X(9442), X(24708)}}, {{A, B, C, X(14490), X(39981)}}, {{A, B, C, X(16615), X(39738)}}

X(54794) = X(7608)X(37456)∩X(26118)X(53098)

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

X(54794) lies on these lines: {7608, 37456}, {26118, 53098}

X(54794) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(81), X(17501)}}, {{A, B, C, X(4102), X(11604)}}, {{A, B, C, X(5556), X(27789)}}, {{A, B, C, X(5560), X(39948)}}, {{A, B, C, X(7319), X(25417)}}, {{A, B, C, X(21739), X(33696)}}, {{A, B, C, X(34529), X(52374)}}, {{A, B, C, X(37456), X(52281)}}

X(54795) = X(10)X(4473)∩X(226)X(29584)

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

X(54795) lies on these lines: {10, 4473}, {226, 29584}, {4080, 20016}, {5485, 50074}, {6539, 21711}, {6625, 46922}, {7379, 7608}, {7385, 7607}, {29586, 30588}, {32022, 33032}

X(54795) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(8), X(29584)}}, {{A, B, C, X(80), X(3227)}}, {{A, B, C, X(274), X(17501)}}, {{A, B, C, X(330), X(7319)}}, {{A, B, C, X(519), X(20016)}}, {{A, B, C, X(903), X(4473)}}, {{A, B, C, X(1000), X(39720)}}, {{A, B, C, X(1654), X(46922)}}, {{A, B, C, X(1992), X(50074)}}, {{A, B, C, X(3679), X(29586)}}, {{A, B, C, X(4196), X(33032)}}, {{A, B, C, X(4207), X(33031)}}, {{A, B, C, X(5556), X(39738)}}, {{A, B, C, X(5560), X(36871)}}, {{A, B, C, X(7379), X(52281)}}, {{A, B, C, X(7385), X(52282)}}, {{A, B, C, X(34578), X(35170)}}, {{A, B, C, X(37654), X(50133)}}, {{A, B, C, X(38247), X(43734)}}
X(54795) = trilinear pole of line {10180, 10196}

X(54796) = X(98)X(38323)∩X(2986)X(5254)

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

X(54796) lies on these lines: {98, 38323}, {2986, 5254}, {5392, 34505}, {7607, 17928}, {18840, 26162}, {41238, 43530}

X(54796) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(38323)}}, {{A, B, C, X(381), X(41238)}}, {{A, B, C, X(683), X(5641)}}, {{A, B, C, X(858), X(8370)}}, {{A, B, C, X(1995), X(7841)}}, {{A, B, C, X(7770), X(31133)}}, {{A, B, C, X(10604), X(44175)}}, {{A, B, C, X(17928), X(52282)}}, {{A, B, C, X(26162), X(42037)}}

X(54797) = X(262)X(44442)∩X(459)X(41244)

Barycentrics    (3*a^6-3*(b^2-c^2)^3-3*a^4*(3*b^2+c^2)+a^2*(9*b^4-14*b^2*c^2-3*c^4))*(3*a^6+3*(b^2-c^2)^3-3*a^4*(b^2+3*c^2)+a^2*(-3*b^4-14*b^2*c^2+9*c^4)) : :

X(54797) lies on these lines: {262, 44442}, {459, 41244}, {1370, 53099}, {3539, 43565}, {3540, 43564}, {6805, 10194}, {6806, 10195}, {6819, 16080}, {6820, 43530}, {6997, 43537}, {7386, 7608}, {7392, 7607}, {7394, 47586}

X(54797) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(6819)}}, {{A, B, C, X(381), X(6820)}}, {{A, B, C, X(394), X(31371)}}, {{A, B, C, X(458), X(44442)}}, {{A, B, C, X(3521), X(36609)}}, {{A, B, C, X(3545), X(37192)}}, {{A, B, C, X(7386), X(52281)}}, {{A, B, C, X(7392), X(52282)}}, {{A, B, C, X(8797), X(39289)}}, {{A, B, C, X(11433), X(14542)}}, {{A, B, C, X(13157), X(40449)}}, {{A, B, C, X(16774), X(30535)}}

X(54798) = X(262)X(7667)∩X(7484)X(7608)

Barycentrics    (2*a^6+(b^2-c^2)^2*(2*b^2-c^2)-a^4*(2*b^2+5*c^2)-2*a^2*(b^4+5*b^2*c^2-2*c^4))*(2*a^6-(b^2-2*c^2)*(b^2-c^2)^2-a^4*(5*b^2+2*c^2)+2*a^2*(2*b^4-5*b^2*c^2-c^4)) : :

X(54798) lies on these lines: {262, 7667}, {7484, 7608}, {7607, 37439}

X(54798) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(64), X(10601)}}, {{A, B, C, X(264), X(39289)}}, {{A, B, C, X(458), X(7667)}}, {{A, B, C, X(7484), X(52281)}}, {{A, B, C, X(37439), X(52282)}}

X(54799) = X(6906)X(7607)∩X(6941)X(7608)

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

X(54799) lies on these lines: {6906, 7607}, {6941, 7608}, {13576, 18516}

X(54799) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6906), X(52282)}}, {{A, B, C, X(6941), X(52281)}}, {{A, B, C, X(18516), X(46108)}}, {{A, B, C, X(34914), X(46435)}}

X(54800) = X(2)X(10991)∩X(76)X(45018)

Barycentrics    (5*a^6+5*b^6-4*b^4*c^2+b^2*c^4-2*c^6+a^4*(3*b^2-4*c^2)+a^2*(3*b^4-8*b^2*c^2+c^4))*(5*a^6-2*b^6+b^4*c^2-4*b^2*c^4+5*c^6+a^4*(-4*b^2+3*c^2)+a^2*(b^4-8*b^2*c^2+3*c^4)) : :

X(54800) lies on these lines: {2, 10991}, {76, 45018}, {2794, 14484}, {3424, 11623}, {5485, 38664}, {7904, 43529}, {9862, 14494}, {10722, 14488}, {14907, 40824}

X(54800) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(64), X(6323)}}, {{A, B, C, X(67), X(6531)}}, {{A, B, C, X(74), X(45018)}}, {{A, B, C, X(729), X(43702)}}, {{A, B, C, X(2207), X(3455)}}, {{A, B, C, X(8753), X(29180)}}, {{A, B, C, X(11623), X(45031)}}, {{A, B, C, X(17983), X(35140)}}
X(54800) = trilinear pole of line {5304, 523}

X(54801) = X(2)X(18353)∩X(4)X(11264)

Barycentrics    (a^6+(b^2-2*c^2)*(b^2-c^2)^2-a^4*(b^2+4*c^2)-a^2*(b^4+b^2*c^2-5*c^4))*(a^6-(b^2-c^2)^2*(2*b^2-c^2)-a^4*(4*b^2+c^2)+a^2*(5*b^4-b^2*c^2-c^4)) : :

X(54801) lies on these lines: {2, 18353}, {4, 11264}, {6636, 7607}, {7608, 37353}, {20062, 43537}

X(54801) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(1994)}}, {{A, B, C, X(1989), X(18353)}}, {{A, B, C, X(6636), X(52282)}}, {{A, B, C, X(14129), X(32535)}}, {{A, B, C, X(16770), X(40712)}}, {{A, B, C, X(16771), X(40711)}}, {{A, B, C, X(17711), X(41628)}}, {{A, B, C, X(37353), X(52281)}}, {{A, B, C, X(37672), X(44555)}}
X(54801) = X(i)-cross conjugate of X(j) for these {i, j}: {41628, 2}

X(54802) = X(1503)X(43688)∩X(2794)X(10290)

Barycentrics    (4*a^8+4*b^8-b^6*c^2-b^2*c^6-2*c^8+a^6*(5*b^2-c^2)+a^4*(6*b^4-5*b^2*c^2)+a^2*(5*b^6-5*b^4*c^2+b^2*c^4-c^6))*(4*a^8-2*b^8-b^6*c^2-b^2*c^6+4*c^8-a^6*(b^2-5*c^2)+a^4*(-5*b^2*c^2+6*c^4)+a^2*(-b^6+b^4*c^2-5*b^2*c^4+5*c^6)) : :

X(54802) lies on these lines: {1503, 43688}, {2394, 30217}, {2794, 10290}, {25423, 43673}

X(54802) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(30217)}}, {{A, B, C, X(1503), X(25423)}}, {{A, B, C, X(11645), X(32472)}}
X(54802) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 43688}

X(54803) = X(76)X(40112)∩X(94)X(50187)

Barycentrics    (4*a^6+(b^2-c^2)^2*(b^2+4*c^2)-a^4*(7*b^2+4*c^2)+2*a^2*(b^4-2*c^4))*(4*a^6+(b^2-c^2)^2*(4*b^2+c^2)-a^4*(4*b^2+7*c^2)+a^2*(-4*b^4+2*c^4)) : :

X(54803) lies on these lines: {76, 40112}, {94, 50187}, {262, 7426}, {597, 34289}, {598, 14389}, {2394, 36900}, {5485, 37645}, {10302, 15066}, {11656, 43532}

X(54803) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(40112)}}, {{A, B, C, X(264), X(9141)}}, {{A, B, C, X(458), X(7426)}}, {{A, B, C, X(597), X(15066)}}, {{A, B, C, X(599), X(14389)}}, {{A, B, C, X(1992), X(37645)}}, {{A, B, C, X(34351), X(52253)}}, {{A, B, C, X(36900), X(46809)}}
X(54803) = trilinear pole of line {44265, 523}
X(54803) = X(i)-cross conjugate of X(j) for these {i, j}: {7579, 264}

X(54804) = X(671)X(53504)∩X(5475)X(43535)

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

X(54804) lies on these lines: {671, 53504}, {5475, 43535}, {5476, 43532}

X(54804) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3114), X(34898)}}, {{A, B, C, X(11175), X(32901)}}, {{A, B, C, X(18818), X(42299)}}
X(54804) = trilinear pole of line {22734, 523}

X(54805) = X(98)X(18362)∩X(262)X(14537)

Barycentrics    (4*a^6+4*b^6-7*b^4*c^2+5*b^2*c^4-2*c^6-a^4*(b^2+7*c^2)-a^2*(b^4+9*b^2*c^2-5*c^4))*(4*a^6-2*b^6+5*b^4*c^2-7*b^2*c^4+4*c^6-a^4*(7*b^2+c^2)+a^2*(5*b^4-9*b^2*c^2-c^4)) : :

X(54805) lies on these lines: {98, 18362}, {262, 14537}, {3849, 42011}, {11645, 17503}, {35925, 43529}

X(54805) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(290), X(48911)}}, {{A, B, C, X(512), X(3431)}}, {{A, B, C, X(9154), X(18361)}}, {{A, B, C, X(11166), X(11738)}}, {{A, B, C, X(14491), X(43950)}}

X(54806) = X(736)X(43688)∩X(1916)X(7812)

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

X(54806) lies on these lines: {736, 43688}, {1916, 7812}, {3407, 7817}, {7775, 22498}, {7821, 43529}, {7883, 10000}

X(54806) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(512), X(18898)}}, {{A, B, C, X(736), X(25423)}}, {{A, B, C, X(14906), X(46286)}}, {{A, B, C, X(32901), X(44557)}}

X(54807) = X(76)X(44555)∩X(262)X(9159)

Barycentrics    (a^6+(b^2-2*c^2)*(b^2-c^2)^2-a^4*(b^2+4*c^2)-a^2*(b^4+9*b^2*c^2-5*c^4))*(a^6-(b^2-c^2)^2*(2*b^2-c^2)-a^4*(4*b^2+c^2)+a^2*(5*b^4-9*b^2*c^2-c^4)) : :

X(54807) lies on these lines: {76, 44555}, {262, 9159}, {597, 7578}, {598, 15018}, {5485, 37644}, {7607, 16042}

X(54807) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(44555)}}, {{A, B, C, X(458), X(10989)}}, {{A, B, C, X(599), X(15018)}}, {{A, B, C, X(1992), X(37644)}}, {{A, B, C, X(5505), X(30535)}}, {{A, B, C, X(5640), X(9513)}}, {{A, B, C, X(16042), X(52282)}}
X(54807) = trilinear pole of line {11622, 44266}

X(54808) = X(868)X(16080)∩X(1316)X(43530)

Barycentrics    (a^12-3*a^10*b^2+3*a^8*(b^4+b^2*c^2-c^4)+3*a^2*(b^3-b*c^2)^2*(2*b^4+c^4)-(b^2-c^2)^3*(2*b^6+c^6)+a^6*(b^6-6*b^4*c^2+4*c^6)-3*a^4*(2*b^8-3*b^6*c^2+c^8))*(a^12-3*a^10*c^2+3*a^8*(-b^4+b^2*c^2+c^4)+3*a^2*(-(b^2*c)+c^3)^2*(b^4+2*c^4)+a^6*(4*b^6-6*b^2*c^4+c^6)+(b^2-c^2)^3*(b^6+2*c^6)-3*a^4*(b^8-3*b^2*c^6+2*c^8)) : :

X(54808) lies on these lines: {868, 16080}, {1316, 43530}, {14223, 14639}

X(54808) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(868)}}, {{A, B, C, X(381), X(1316)}}, {{A, B, C, X(879), X(1494)}}, {{A, B, C, X(935), X(5627)}}, {{A, B, C, X(1640), X(16076)}}, {{A, B, C, X(3845), X(15000)}}, {{A, B, C, X(7422), X(53161)}}, {{A, B, C, X(10097), X(35908)}}, {{A, B, C, X(14582), X(42308)}}, {{A, B, C, X(17983), X(35906)}}, {{A, B, C, X(31621), X(47388)}}, {{A, B, C, X(36163), X(47076)}}, {{A, B, C, X(48259), X(53201)}}

X(54809) = X(94)X(3845)∩X(3830)X(7578)

Barycentrics    (4*a^8+a^6*(-7*b^2+2*c^2)-(b^2-c^2)^3*(5*b^2+4*c^2)-a^4*(3*b^4+2*b^2*c^2+12*c^4)+a^2*(11*b^6-11*b^4*c^2-2*b^2*c^4+2*c^6))*(4*a^8+a^6*(2*b^2-7*c^2)+(b^2-c^2)^3*(4*b^2+5*c^2)-a^4*(12*b^4+2*b^2*c^2+3*c^4)+a^2*(2*b^6-2*b^4*c^2-11*b^2*c^4+11*c^6)) : :

X(54809) lies on these lines: {94, 3845}, {3830, 7578}, {18559, 43530}

X(54809) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(38305)}}, {{A, B, C, X(186), X(3845)}}, {{A, B, C, X(328), X(18550)}}, {{A, B, C, X(381), X(6344)}}, {{A, B, C, X(3830), X(7577)}}, {{A, B, C, X(5066), X(19307)}}, {{A, B, C, X(14487), X(14910)}}, {{A, B, C, X(15424), X(51032)}}, {{A, B, C, X(18533), X(41099)}}

X(54810) = X(2)X(20772)∩X(16080)X(37777)

Barycentrics    (2*a^10-3*a^8*b^2+a^6*(-2*b^4+7*b^2*c^2-2*c^4)-(b^2-c^2)^3*(b^4+3*b^2*c^2+2*c^4)+a^2*b^2*c^2*(b^4-8*b^2*c^2+7*c^4)+a^4*(4*b^6-8*b^4*c^2+4*b^2*c^4-2*c^6))*(2*a^10-3*a^8*c^2+a^6*(-2*b^4+7*b^2*c^2-2*c^4)+a^2*b^2*c^2*(7*b^4-8*b^2*c^2+c^4)+(b^2-c^2)^3*(2*b^4+3*b^2*c^2+c^4)-2*a^4*(b^6-2*b^4*c^2+4*b^2*c^4-2*c^6)) : :

X(54810) lies on these lines: {2, 20772}, {16080, 37777}

X(54810) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(3563)}}, {{A, B, C, X(1138), X(34168)}}, {{A, B, C, X(1989), X(48379)}}, {{A, B, C, X(2697), X(6344)}}, {{A, B, C, X(2980), X(45835)}}, {{A, B, C, X(10422), X(29011)}}, {{A, B, C, X(11744), X(40118)}}, {{A, B, C, X(16868), X(31133)}}, {{A, B, C, X(29180), X(48362)}}

X(54811) = X(98)X(5118)∩X(698)X(2394)

Barycentrics    (b^4*c^4*(b^2-c^2)^2+a^8*(b^2+c^2)^2-a^6*(2*b^6+b^4*c^2+7*b^2*c^4+2*c^6)+a^4*(b^8-b^6*c^2+6*b^4*c^4+5*b^2*c^6+c^8)+a^2*(2*b^8*c^2-7*b^6*c^4+5*b^4*c^6-4*b^2*c^8))*(b^4*c^4*(b^2-c^2)^2+a^8*(b^2+c^2)^2-a^6*(2*b^6+7*b^4*c^2+b^2*c^4+2*c^6)+a^4*(b^8+5*b^6*c^2+6*b^4*c^4-b^2*c^6+c^8)+a^2*(-4*b^8*c^2+5*b^6*c^4-7*b^4*c^6+2*b^2*c^8)) : :

X(54811) lies on these lines: {98, 5118}, {538, 43665}, {698, 2394}, {2396, 34087}, {5466, 32515}, {5969, 46040}

X(54811) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(698)}}, {{A, B, C, X(74), X(39292)}}, {{A, B, C, X(511), X(538)}}, {{A, B, C, X(524), X(32515)}}, {{A, B, C, X(2782), X(5969)}}
X(54811) = trilinear pole of line {6786, 523}

X(54812) = X(4)X(45248)∩X(459)X(37672)

Barycentrics    (9*a^6+3*(b^2-c^2)^2*(b^2+3*c^2)-3*a^4*(5*b^2+3*c^2)+a^2*(3*b^4+22*b^2*c^2-9*c^4))*(9*a^6+3*(b^2-c^2)^2*(3*b^2+c^2)-3*a^4*(3*b^2+5*c^2)+a^2*(-9*b^4+22*b^2*c^2+3*c^4)) : :

X(54812) lies on these lines: {4, 45248}, {459, 37672}, {6677, 53099}, {30771, 43537}

X(54812) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(68), X(37878)}}, {{A, B, C, X(1249), X(34570)}}, {{A, B, C, X(36609), X(37669)}}, {{A, B, C, X(38263), X(42287)}}

X(54813) = X(83)X(12101)∩X(3830)X(43527)

Barycentrics    (13*a^4+13*b^4+b^2*c^2-14*c^4+a^2*(28*b^2+c^2))*(13*a^4-14*b^4+b^2*c^2+13*c^4+a^2*(b^2+28*c^2)) : :

X(54813) lies on these lines: {83, 12101}, {3830, 43527}, {3845, 10159}

X(54813) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(427), X(12101)}}, {{A, B, C, X(428), X(3845)}}, {{A, B, C, X(3830), X(5064)}}, {{A, B, C, X(14487), X(34572)}}, {{A, B, C, X(29322), X(52518)}}, {{A, B, C, X(33699), X(52285)}}

X(54814) = X(2)X(22676)∩X(83)X(10541)

Barycentrics    (7*b^4*c^2-6*b^2*c^4-c^6+a^4*(8*b^2+7*c^2)+2*a^2*(4*b^4+5*b^2*c^2-3*c^4))*(a^4*(7*b^2+8*c^2)-b^2*(b^4+6*b^2*c^2-7*c^4)+a^2*(-6*b^4+10*b^2*c^2+8*c^4)) : :

X(54814) lies on these lines: {2, 22676}, {83, 10541}, {98, 21309}, {671, 53023}, {7607, 40927}, {14532, 14535}, {18842, 25406}

X(54814) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(39), X(10541)}}, {{A, B, C, X(511), X(3531)}}, {{A, B, C, X(3426), X(30499)}}, {{A, B, C, X(3785), X(15077)}}, {{A, B, C, X(6531), X(21765)}}, {{A, B, C, X(14495), X(53774)}}, {{A, B, C, X(18575), X(22682)}}, {{A, B, C, X(22676), X(42299)}}, {{A, B, C, X(40927), X(52282)}}

X(54815) = X(76)X(50687)∩X(383)X(43444)

Barycentrics    (13*a^4-11*b^4-2*b^2*c^2+13*c^4-2*a^2*(b^2-11*c^2))*(13*a^4+13*b^4-2*b^2*c^2-11*c^4+a^2*(22*b^2-2*c^2)) : :

X(54815) lies on these lines: {76, 50687}, {383, 43444}, {428, 38253}, {1080, 43445}, {3146, 10159}, {3543, 18840}, {3832, 43527}, {3839, 18841}, {7000, 43565}, {7374, 43564}, {7408, 16080}, {7409, 43530}, {14492, 14930}

X(54815) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(50687)}}, {{A, B, C, X(30), X(7408)}}, {{A, B, C, X(64), X(34572)}}, {{A, B, C, X(251), X(14490)}}, {{A, B, C, X(381), X(7409)}}, {{A, B, C, X(428), X(3146)}}, {{A, B, C, X(3425), X(46851)}}, {{A, B, C, X(3426), X(39955)}}, {{A, B, C, X(3543), X(6995)}}, {{A, B, C, X(3830), X(52301)}}, {{A, B, C, X(3832), X(5064)}}, {{A, B, C, X(3839), X(7378)}}, {{A, B, C, X(7714), X(17578)}}, {{A, B, C, X(11058), X(21765)}}, {{A, B, C, X(14495), X(46848)}}, {{A, B, C, X(14930), X(37671)}}, {{A, B, C, X(15321), X(35510)}}, {{A, B, C, X(18575), X(46212)}}, {{A, B, C, X(48911), X(52188)}}

X(54816) = X(4)X(52994)∩X(5569)X(43535)

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

X(54816) lies on these lines: {4, 52994}, {5569, 43535}, {7608, 7760}, {7801, 42006}, {7812, 11170}, {11606, 13086}

X(54816) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(52994)}}, {{A, B, C, X(263), X(20251)}}, {{A, B, C, X(9217), X(30541)}}, {{A, B, C, X(13086), X(40850)}}, {{A, B, C, X(30495), X(46314)}}, {{A, B, C, X(44557), X(46306)}}

X(54817) = X(3153)X(43537)∩X(7391)X(10511)

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

X(54817) lies on these lines: {3153, 43537}, {7391, 10511}, {7607, 18531}, {7608, 18420}

X(54817) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(316), X(13575)}}, {{A, B, C, X(1992), X(52189)}}, {{A, B, C, X(2987), X(43949)}}, {{A, B, C, X(6464), X(38447)}}, {{A, B, C, X(16774), X(32901)}}, {{A, B, C, X(18420), X(52281)}}, {{A, B, C, X(18531), X(52282)}}, {{A, B, C, X(18876), X(32533)}}

X(54818) = X(3153)X(53099)∩X(7394)X(10511)

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

X(54818) lies on these lines: {3153, 53099}, {7394, 10511}, {7607, 18420}, {7608, 18531}

X(54818) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(18420), X(52282)}}, {{A, B, C, X(18531), X(52281)}}, {{A, B, C, X(30535), X(43949)}}, {{A, B, C, X(30541), X(44836)}}

X(54819) = X(4)X(50149)∩X(98)X(5465)

Barycentrics    (2*a^8-3*a^6*(b^2-c^2)-(b^2-c^2)^2*(4*b^4-b^2*c^2-2*c^4)-2*a^4*(2*b^4-4*b^2*c^2+5*c^4)+a^2*(9*b^6-16*b^4*c^2+8*b^2*c^4+3*c^6))*(2*a^8+3*a^6*(b^2-c^2)+(b^2-c^2)^2*(2*b^4+b^2*c^2-4*c^4)-2*a^4*(5*b^4-4*b^2*c^2+2*c^4)+a^2*(3*b^6+8*b^4*c^2-16*b^2*c^4+9*c^6)) : :

X(54819) lies on these lines: {4, 50149}, {98, 5465}, {381, 5466}, {4235, 43530}, {14559, 18316}

X(54819) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(46245)}}, {{A, B, C, X(381), X(4235)}}, {{A, B, C, X(3545), X(40890)}}, {{A, B, C, X(4846), X(14977)}}, {{A, B, C, X(5465), X(14356)}}, {{A, B, C, X(5627), X(18823)}}, {{A, B, C, X(10293), X(36882)}}, {{A, B, C, X(33006), X(35481)}}
X(54819) = trilinear pole of line {32225, 523}

X(54820) = X(2)X(18418)∩X(1885)X(43530)

Barycentrics    (4*a^8+a^6*(-7*b^2+2*c^2)-(b^2-c^2)^3*(5*b^2+4*c^2)+a^4*(-3*b^4+19*b^2*c^2-12*c^4)+a^2*(11*b^6-32*b^4*c^2+19*b^2*c^4+2*c^6))*(4*a^8+a^6*(2*b^2-7*c^2)+(b^2-c^2)^3*(4*b^2+5*c^2)+a^4*(-12*b^4+19*b^2*c^2-3*c^4)+a^2*(2*b^6+19*b^4*c^2-32*b^2*c^4+11*c^6)) : :

X(54820) lies on these lines: {2, 18418}, {1885, 43530}, {3543, 41899}, {16080, 37197}, {34622, 44877}

X(54820) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(1093)}}, {{A, B, C, X(64), X(46426)}}, {{A, B, C, X(381), X(1885)}}, {{A, B, C, X(1494), X(43695)}}, {{A, B, C, X(1989), X(18418)}}, {{A, B, C, X(3516), X(3845)}}, {{A, B, C, X(5627), X(15318)}}, {{A, B, C, X(9307), X(11744)}}, {{A, B, C, X(10151), X(34622)}}, {{A, B, C, X(31371), X(52187)}}

X(54821) = X(10)X(24341)∩X(98)X(1012)

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

X(54821) lies on these lines: {10, 24341}, {98, 1012}, {262, 1532}, {6932, 45964}, {6935, 7612}, {6969, 14494}, {7377, 14554}

X(54821) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(52517)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(4391)}}, {{A, B, C, X(84), X(257)}}, {{A, B, C, X(297), X(1012)}}, {{A, B, C, X(335), X(3577)}}, {{A, B, C, X(458), X(1532)}}, {{A, B, C, X(1231), X(15077)}}, {{A, B, C, X(1509), X(5553)}}, {{A, B, C, X(2481), X(18810)}}, {{A, B, C, X(5555), X(41791)}}, {{A, B, C, X(6907), X(11341)}}, {{A, B, C, X(6935), X(37174)}}, {{A, B, C, X(9289), X(43724)}}, {{A, B, C, X(9311), X(34863)}}, {{A, B, C, X(14621), X(46435)}}

X(54822) = X(4)X(35701)∩X(98)X(754)

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

X(54822) lies on these lines: {4, 35701}, {98, 754}, {262, 9890}, {524, 9302}, {543, 14492}, {732, 43532}, {3399, 5969}, {7607, 13086}, {8290, 14033}, {8587, 9889}, {9478, 33285}, {11606, 14041}, {12073, 43667}, {13188, 14484}

X(54822) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(46310)}}, {{A, B, C, X(420), X(14041)}}, {{A, B, C, X(694), X(8753)}}, {{A, B, C, X(754), X(2799)}}, {{A, B, C, X(3455), X(11175)}}, {{A, B, C, X(3978), X(46290)}}, {{A, B, C, X(5969), X(20027)}}, {{A, B, C, X(9154), X(25322)}}, {{A, B, C, X(15412), X(39939)}}, {{A, B, C, X(43098), X(43696)}}

X(54823) = X(76)X(39563)∩X(83)X(11648)

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

X(54823) lies on these lines: {76, 39563}, {83, 11648}, {98, 48904}, {598, 39593}, {7766, 14458}, {7788, 43688}, {7933, 10159}, {10302, 18546}, {18840, 33251}

X(54823) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(40829)}}, {{A, B, C, X(290), X(7766)}}, {{A, B, C, X(428), X(7933)}}, {{A, B, C, X(1494), X(38262)}}, {{A, B, C, X(3228), X(11058)}}, {{A, B, C, X(5306), X(7897)}}, {{A, B, C, X(6995), X(33251)}}, {{A, B, C, X(7408), X(33223)}}, {{A, B, C, X(9464), X(39593)}}, {{A, B, C, X(11648), X(31125)}}, {{A, B, C, X(18361), X(43098)}}
X(54823) = X(i)-cross conjugate of X(j) for these {i, j}: {7837, 2}

X(54824) = X(5392)X(14041)∩X(11361)X(40393)

Barycentrics    (a^8+a^6*(-2*b^2+c^2)-(b^2-c^2)^2*(2*b^4-c^4)-a^4*(b^4+2*b^2*c^2+4*c^4)+a^2*(4*b^6+b^4*c^2-2*b^2*c^4+c^6))*(a^8+a^6*(b^2-2*c^2)+(b^2-c^2)^2*(b^4-2*c^4)-a^4*(4*b^4+2*b^2*c^2+c^4)+a^2*(b^6-2*b^4*c^2+b^2*c^4+4*c^6)) : :

X(54824) lies on these lines: {5392, 14041}, {11361, 40393}

X(54824) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(43098)}}, {{A, B, C, X(24), X(14041)}}, {{A, B, C, X(1594), X(11361)}}, {{A, B, C, X(5025), X(7576)}}, {{A, B, C, X(6664), X(38305)}}, {{A, B, C, X(7487), X(16041)}}, {{A, B, C, X(8882), X(14498)}}, {{A, B, C, X(42407), X(44836)}}

X(54825) = X(83)X(37855)∩X(378)X(7607)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^6+2*b^6-b^4*c^2-2*b^2*c^4+c^6-a^4*(2*b^2+c^2)-a^2*(b^4-10*b^2*c^2+c^4))*(a^6+b^6-2*b^4*c^2-b^2*c^4+2*c^6-a^4*(b^2+2*c^2)-a^2*(b^4-10*b^2*c^2+c^4)) : :

X(54825) lies on these lines: {83, 37855}, {378, 7607}, {403, 7608}, {2986, 52281}, {6623, 53099}, {10185, 37118}, {15014, 43528}, {34289, 52282}

X(54825) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(378), X(52282)}}, {{A, B, C, X(403), X(52281)}}, {{A, B, C, X(427), X(5203)}}, {{A, B, C, X(34386), X(43891)}}, {{A, B, C, X(40413), X(44146)}}

X(54826) = X(76)X(20423)∩X(83)X(38064)

Barycentrics    (a^6+b^6+5*b^4*c^2-7*b^2*c^4+c^6-7*a^4*(b^2+c^2)+a^2*(5*b^4-12*b^2*c^2-7*c^4))*(a^6+b^6-7*b^4*c^2+5*b^2*c^4+c^6-7*a^4*(b^2+c^2)+a^2*(-7*b^4-12*b^2*c^2+5*c^4)) : :

X(54826) lies on these lines: {76, 20423}, {83, 38064}, {598, 46264}, {2549, 14492}, {3839, 11606}, {5503, 9890}, {14853, 43532}

X(54826) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(11175)}}, {{A, B, C, X(263), X(8753)}}, {{A, B, C, X(420), X(3839)}}, {{A, B, C, X(694), X(3531)}}, {{A, B, C, X(5627), X(20022)}}, {{A, B, C, X(9154), X(38005)}}, {{A, B, C, X(19222), X(52188)}}, {{A, B, C, X(20021), X(38064)}}, {{A, B, C, X(32581), X(46264)}}, {{A, B, C, X(34288), X(42299)}}, {{A, B, C, X(46142), X(52187)}}

X(54827) = X(2)X(37496)∩X(381)X(13582)

Barycentrics    (a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4+13*b^2*c^2+6*c^4)-a^2*(4*b^6+5*b^4*c^2-13*b^2*c^4+4*c^6))*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4+13*b^2*c^2+6*c^4)-a^2*(4*b^6-13*b^4*c^2+5*b^2*c^4+4*c^6)) : :

X(54827) lies on these lines: {2, 37496}, {381, 13582}, {3830, 11538}, {3845, 13585}, {6504, 41106}, {10982, 43666}, {13579, 41099}, {18366, 44287}, {37943, 43530}

X(54827) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(1138)}}, {{A, B, C, X(30), X(45108)}}, {{A, B, C, X(54), X(18317)}}, {{A, B, C, X(74), X(30537)}}, {{A, B, C, X(381), X(37943)}}, {{A, B, C, X(1494), X(45972)}}, {{A, B, C, X(1989), X(14483)}}, {{A, B, C, X(2963), X(14487)}}, {{A, B, C, X(3088), X(19708)}}, {{A, B, C, X(3459), X(52518)}}, {{A, B, C, X(3531), X(52154)}}, {{A, B, C, X(3534), X(35482)}}, {{A, B, C, X(3541), X(11001)}}, {{A, B, C, X(3542), X(41106)}}, {{A, B, C, X(3613), X(5627)}}, {{A, B, C, X(3830), X(6143)}}, {{A, B, C, X(3845), X(14940)}}, {{A, B, C, X(6188), X(52188)}}, {{A, B, C, X(7505), X(41099)}}, {{A, B, C, X(8487), X(38542)}}, {{A, B, C, X(13452), X(46412)}}, {{A, B, C, X(13530), X(22336)}}, {{A, B, C, X(13619), X(44287)}}, {{A, B, C, X(14491), X(34288)}}, {{A, B, C, X(15682), X(37119)}}, {{A, B, C, X(17703), X(31846)}}, {{A, B, C, X(20421), X(46952)}}, {{A, B, C, X(22268), X(46848)}}

X(54828) = X(275)X(11361)∩X(381)X(37892)

Barycentrics    (a^8-a^4*(b^2-2*c^2)^2+a^6*(-2*b^2+c^2)-(b^2-c^2)^2*(2*b^4-c^4)+a^2*(4*b^6-5*b^4*c^2+4*b^2*c^4+c^6))*(a^8+a^6*(b^2-2*c^2)-a^4*(-2*b^2+c^2)^2+(b^2-c^2)^2*(b^4-2*c^4)+a^2*(b^6+4*b^4*c^2-5*b^2*c^4+4*c^6)) : :

X(54828) lies on these lines: {275, 11361}, {381, 37892}, {384, 43530}, {459, 16041}, {2052, 14041}, {3406, 34664}, {5025, 16080}, {33285, 38253}

X(54828) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(14041)}}, {{A, B, C, X(5), X(11361)}}, {{A, B, C, X(20), X(16041)}}, {{A, B, C, X(30), X(5025)}}, {{A, B, C, X(64), X(43098)}}, {{A, B, C, X(376), X(14063)}}, {{A, B, C, X(381), X(384)}}, {{A, B, C, X(382), X(14046)}}, {{A, B, C, X(546), X(14036)}}, {{A, B, C, X(547), X(14066)}}, {{A, B, C, X(549), X(14062)}}, {{A, B, C, X(1494), X(43714)}}, {{A, B, C, X(1502), X(11744)}}, {{A, B, C, X(1657), X(33291)}}, {{A, B, C, X(3091), X(14033)}}, {{A, B, C, X(3146), X(33285)}}, {{A, B, C, X(3524), X(32996)}}, {{A, B, C, X(3534), X(14045)}}, {{A, B, C, X(3543), X(14064)}}, {{A, B, C, X(3545), X(14035)}}, {{A, B, C, X(3830), X(7901)}}, {{A, B, C, X(3832), X(14039)}}, {{A, B, C, X(3839), X(14001)}}, {{A, B, C, X(3845), X(7892)}}, {{A, B, C, X(3860), X(14040)}}, {{A, B, C, X(4846), X(9229)}}, {{A, B, C, X(5054), X(14044)}}, {{A, B, C, X(5055), X(14042)}}, {{A, B, C, X(5066), X(14034)}}, {{A, B, C, X(5071), X(14068)}}, {{A, B, C, X(5073), X(33288)}}, {{A, B, C, X(5999), X(7841)}}, {{A, B, C, X(7833), X(15980)}}, {{A, B, C, X(8370), X(13862)}}, {{A, B, C, X(11001), X(33290)}}, {{A, B, C, X(14031), X(41106)}}, {{A, B, C, X(14032), X(38071)}}, {{A, B, C, X(14037), X(41099)}}, {{A, B, C, X(14038), X(23046)}}, {{A, B, C, X(14043), X(14269)}}, {{A, B, C, X(14047), X(38335)}}, {{A, B, C, X(14065), X(15687)}}, {{A, B, C, X(14067), X(14893)}}, {{A, B, C, X(14498), X(41890)}}, {{A, B, C, X(15681), X(33289)}}, {{A, B, C, X(15682), X(33283)}}, {{A, B, C, X(15683), X(33292)}}, {{A, B, C, X(15684), X(33284)}}, {{A, B, C, X(15685), X(33293)}}, {{A, B, C, X(18434), X(40416)}}, {{A, B, C, X(32951), X(50687)}}, {{A, B, C, X(33013), X(35930)}}

X(54829) = X(2)X(39524)∩X(5025)X(13582)

Barycentrics    (a^8-2*a^6*(b^2+c^2)+(b^2-c^2)^2*(b^4+c^4)+a^4*(2*b^4+b^2*c^2+2*c^4)+a^2*(-2*b^6+b^4*c^2-5*b^2*c^4-2*c^6))*(a^8-2*a^6*(b^2+c^2)+(b^2-c^2)^2*(b^4+c^4)+a^4*(2*b^4+b^2*c^2+2*c^4)+a^2*(-2*b^6-5*b^4*c^2+b^2*c^4-2*c^6)) : :

X(54829) lies on these lines: {2, 39524}, {5025, 13582}, {6504, 33285}, {11361, 11538}, {13579, 16041}, {13585, 14041}

X(54829) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(1141), X(6664)}}, {{A, B, C, X(1502), X(33565)}}, {{A, B, C, X(2963), X(14498)}}, {{A, B, C, X(3431), X(42407)}}, {{A, B, C, X(3541), X(14039)}}, {{A, B, C, X(3542), X(33285)}}, {{A, B, C, X(5025), X(37943)}}, {{A, B, C, X(6143), X(11361)}}, {{A, B, C, X(7505), X(16041)}}, {{A, B, C, X(7799), X(51256)}}, {{A, B, C, X(9229), X(45972)}}, {{A, B, C, X(14033), X(37119)}}, {{A, B, C, X(14036), X(35482)}}, {{A, B, C, X(14041), X(14940)}}, {{A, B, C, X(34288), X(39524)}}

X(54830) = X(2)X(13207)∩X(98)X(9463)

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

X(54830) lies on these lines: {2, 13207}, {83, 37465}, {98, 9463}, {3407, 11003}, {5996, 43665}

X(54830) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(263), X(523)}}, {{A, B, C, X(325), X(5996)}}, {{A, B, C, X(427), X(37465)}}, {{A, B, C, X(694), X(18575)}}, {{A, B, C, X(1383), X(13207)}}, {{A, B, C, X(9513), X(11593)}}, {{A, B, C, X(13240), X(46316)}}
X(54830) = trilinear pole of line {47580, 523}

X(54831) = X(4)X(17392)∩X(10)X(6173)

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

X(54831) lies on these lines: {4, 17392}, {10, 6173}, {226, 21314}, {1056, 13576}, {3545, 43672}, {4080, 29621}, {5071, 45097}, {5485, 17313}, {17346, 32022}, {17528, 43533}, {21554, 43537}, {36731, 45100}

X(54831) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(7), X(6173)}}, {{A, B, C, X(69), X(17392)}}, {{A, B, C, X(80), X(38097)}}, {{A, B, C, X(85), X(3296)}}, {{A, B, C, X(277), X(43733)}}, {{A, B, C, X(279), X(5551)}}, {{A, B, C, X(376), X(37448)}}, {{A, B, C, X(514), X(18490)}}, {{A, B, C, X(519), X(29621)}}, {{A, B, C, X(527), X(30275)}}, {{A, B, C, X(1000), X(1121)}}, {{A, B, C, X(1056), X(5236)}}, {{A, B, C, X(1992), X(17313)}}, {{A, B, C, X(3545), X(26003)}}, {{A, B, C, X(4648), X(17346)}}, {{A, B, C, X(4654), X(9776)}}, {{A, B, C, X(5556), X(42326)}}, {{A, B, C, X(5557), X(27818)}}, {{A, B, C, X(5561), X(42318)}}, {{A, B, C, X(7490), X(17528)}}, {{A, B, C, X(7714), X(33838)}}, {{A, B, C, X(17300), X(50133)}}, {{A, B, C, X(37276), X(37427)}}, {{A, B, C, X(37389), X(50741)}}, {{A, B, C, X(39948), X(41790)}}, {{A, B, C, X(40029), X(42335)}}

X(54832) = X(4)X(41334)∩X(5)X(43679)

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

X(54832) lies on these lines: {4, 41334}, {5, 43679}, {6, 35098}, {76, 5889}, {262, 22240}, {275, 5012}, {2052, 5640}

X(54832) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5012)}}, {{A, B, C, X(264), X(17500)}}, {{A, B, C, X(290), X(5481)}}, {{A, B, C, X(1297), X(46104)}}, {{A, B, C, X(3521), X(14941)}}, {{A, B, C, X(4846), X(5640)}}, {{A, B, C, X(5889), X(9292)}}, {{A, B, C, X(8795), X(41891)}}, {{A, B, C, X(33971), X(42354)}}

X(54833) = X(98)X(33006)∩X(262)X(33007)

Barycentrics    (5*a^6+5*b^6-9*b^4*c^2+9*b^2*c^4-c^6-3*a^4*(b^2+3*c^2)-3*a^2*(b^4+4*b^2*c^2-3*c^4))*(5*a^6-b^6+9*b^4*c^2-9*b^2*c^4+5*c^6-3*a^4*(3*b^2+c^2)+3*a^2*(3*b^4-4*b^2*c^2-c^4)) : :

X(54833) lies on these lines: {98, 33006}, {262, 33007}, {671, 52674}, {3552, 53099}, {7607, 32961}, {7608, 16925}, {7612, 32984}, {10484, 11147}, {14492, 52942}, {14494, 32985}, {32966, 43537}, {32970, 53098}, {32993, 47586}

X(54833) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(33006)}}, {{A, B, C, X(458), X(33007)}}, {{A, B, C, X(16925), X(52281)}}, {{A, B, C, X(32961), X(52282)}}, {{A, B, C, X(32984), X(37174)}}, {{A, B, C, X(52289), X(52942)}}

X(54834) = X(262)X(3017)∩X(542)X(43531)

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

X(54834) lies on these lines: {262, 3017}, {542, 43531}, {598, 32431}, {11599, 11632}, {14223, 23879}, {17133, 34899}

X(54834) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(542), X(23879)}}, {{A, B, C, X(2786), X(28194)}}, {{A, B, C, X(2789), X(17133)}}, {{A, B, C, X(2796), X(28478)}}

X(54835) = X(2394)X(20188)∩X(9221)X(16658)

Barycentrics    (2*a^8-(b^2-c^2)^3*(b^2+2*c^2)-a^6*(5*b^2+2*c^2)+a^4*(3*b^4-10*b^2*c^2)+a^2*(b^6+11*b^4*c^2-10*b^2*c^4-2*c^6))*(2*a^8+(b^2-c^2)^3*(2*b^2+c^2)-a^6*(2*b^2+5*c^2)+a^4*(-10*b^2*c^2+3*c^4)+a^2*(-2*b^6-10*b^4*c^2+11*b^2*c^4+c^6)) : :

X(54835) lies on these lines: {2394, 20188}, {9221, 16658}, {14492, 15032}, {16080, 34484}

X(54835) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(20188)}}, {{A, B, C, X(1138), X(1179)}}, {{A, B, C, X(1173), X(43970)}}, {{A, B, C, X(6344), X(15321)}}, {{A, B, C, X(7517), X(18559)}}, {{A, B, C, X(7576), X(12088)}}, {{A, B, C, X(11815), X(16620)}}, {{A, B, C, X(15032), X(16264)}}, {{A, B, C, X(15619), X(46848)}}, {{A, B, C, X(17711), X(18361)}}, {{A, B, C, X(18349), X(34288)}}

X(54836) = X(4)X(9813)∩X(262)X(16072)

Barycentrics    (a^8-3*a^6*c^2-a^2*c^2*(b^4+10*b^2*c^2-3*c^4)+(b^2-c^2)^2*(b^4-b^2*c^2-2*c^4)+a^4*(-2*b^4-b^2*c^2+c^4))*(a^8-3*a^6*b^2+a^4*(b^4-b^2*c^2-2*c^4)-(b^2-c^2)^2*(2*b^4+b^2*c^2-c^4)+a^2*(3*b^6-10*b^4*c^2-b^2*c^4)) : :

X(54836) lies on these lines: {4, 9813}, {262, 16072}, {34664, 45300}, {41235, 43530}

X(54836) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(381), X(41235)}}, {{A, B, C, X(458), X(16072)}}, {{A, B, C, X(1368), X(8370)}}, {{A, B, C, X(5020), X(7841)}}, {{A, B, C, X(6391), X(9813)}}, {{A, B, C, X(7398), X(33190)}}, {{A, B, C, X(7770), X(34609)}}, {{A, B, C, X(15319), X(46735)}}, {{A, B, C, X(31180), X(41231)}}

X(54837) = X(4)X(1138)∩X(74)X(14451)

Barycentrics    (a^4-2*b^4+b^2*c^2+c^4+a^2*(b^2-2*c^2))*(a^4+b^4+b^2*c^2-2*c^4+a^2*(-2*b^2+c^2))*(a^8+2*a^6*(b^2-2*c^2)+(b^2-c^2)^4+a^4*(-6*b^4+b^2*c^2+6*c^4)+a^2*(2*b^6+b^4*c^2+b^2*c^4-4*c^6))*(a^8+(b^2-c^2)^4+a^6*(-4*b^2+2*c^2)+a^4*(6*b^4+b^2*c^2-6*c^4)+a^2*(-4*b^6+b^4*c^2+b^2*c^4+2*c^6)) : :

X(54837) lies on these lines: {4, 1138}, {74, 14451}, {94, 1494}, {5627, 40662}, {11070, 16080}, {13582, 14919}, {18366, 46808}, {34289, 40705}

X(54837) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(323), X(40662)}}, {{A, B, C, X(3470), X(14919)}}, {{A, B, C, X(5627), X(40384)}}, {{A, B, C, X(10421), X(31621)}}, {{A, B, C, X(14165), X(46809)}}
X(54837) = trilinear pole of line {1138, 40630}
X(54837) = X(i)-isoconjugate-of-X(j) for these {i, j}: {30, 19303}, {399, 2173}, {662, 42656}, {1272, 9406}
X(54837) = X(i)-Dao conjugate of X(j) for these {i, j}: {1084, 42656}, {9410, 1272}, {36896, 399}
X(54837) = X(i)-cross conjugate of X(j) for these {i, j}: {5627, 1494}, {11070, 1138}, {18781, 40705}, {40384, 16080}
X(54837) = barycentric product X(i)*X(j) for these (i, j): {1138, 1494}, {11070, 31621}, {18781, 40423}, {40705, 74}
X(54837) = barycentric quotient X(i)/X(j) for these (i, j): {74, 399}, {512, 42656}, {1138, 30}, {1494, 1272}, {2132, 15773}, {2159, 19303}, {2394, 14566}, {3470, 15766}, {5627, 14993}, {8749, 52166}, {11070, 3163}, {14451, 10272}, {18781, 113}, {20123, 16163}, {40356, 9408}, {40662, 45694}, {40705, 3260}, {46035, 15774}

X(54838) = X(275)X(15682)∩X(376)X(43530)

Barycentrics    (7*a^8+2*a^6*(4*b^2-5*c^2)+(b^2-c^2)^3*(7*b^2+11*c^2)+2*a^2*(b^2-c^2)^2*(4*b^2+13*c^2)-2*a^4*(15*b^4-5*b^2*c^2+6*c^4))*(7*a^8+2*a^2*(b^2-c^2)^2*(13*b^2+4*c^2)-(b^2-c^2)^3*(11*b^2+7*c^2)+a^6*(-10*b^2+8*c^2)-2*a^4*(6*b^4-5*b^2*c^2+15*c^4)) : :

X(54838) lies on these lines: {275, 15682}, {376, 43530}, {459, 41106}, {2052, 41099}, {3545, 16080}, {3845, 8796}

X(54838) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(41099)}}, {{A, B, C, X(5), X(15682)}}, {{A, B, C, X(20), X(41106)}}, {{A, B, C, X(30), X(3545)}}, {{A, B, C, X(376), X(381)}}, {{A, B, C, X(546), X(15698)}}, {{A, B, C, X(631), X(3845)}}, {{A, B, C, X(1494), X(36445)}}, {{A, B, C, X(3090), X(3830)}}, {{A, B, C, X(3091), X(11001)}}, {{A, B, C, X(3521), X(18853)}}, {{A, B, C, X(3524), X(3839)}}, {{A, B, C, X(3529), X(5066)}}, {{A, B, C, X(3534), X(3855)}}, {{A, B, C, X(3543), X(5071)}}, {{A, B, C, X(3544), X(15640)}}, {{A, B, C, X(3832), X(19708)}}, {{A, B, C, X(3843), X(15719)}}, {{A, B, C, X(3860), X(21735)}}, {{A, B, C, X(8797), X(18550)}}, {{A, B, C, X(11738), X(41891)}}, {{A, B, C, X(14269), X(15709)}}, {{A, B, C, X(14491), X(34570)}}, {{A, B, C, X(14892), X(35409)}}, {{A, B, C, X(15077), X(43970)}}, {{A, B, C, X(15710), X(23046)}}, {{A, B, C, X(18296), X(22270)}}, {{A, B, C, X(18850), X(36436)}}, {{A, B, C, X(18854), X(31371)}}, {{A, B, C, X(19709), X(33703)}}, {{A, B, C, X(38071), X(46333)}}

X(54839) = X(76)X(5182)∩X(262)X(12150)

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

X(54839) lies on these lines: {76, 5182}, {262, 12150}, {1916, 2021}, {2996, 53765}, {5503, 26613}, {7907, 43529}, {9166, 14458}, {12191, 33244}, {32967, 43528}, {33216, 40824}

X(54839) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(249), X(729)}}, {{A, B, C, X(419), X(13586)}}, {{A, B, C, X(512), X(46322)}}, {{A, B, C, X(1691), X(2021)}}, {{A, B, C, X(5970), X(8753)}}, {{A, B, C, X(6531), X(35146)}}, {{A, B, C, X(6620), X(33216)}}
X(54839) = trilinear pole of line {14614, 523}

X(54840) = X(2)X(22561)∩X(83)X(8593)

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

X(54840) lies on these lines: {2, 22561}, {83, 8593}, {262, 11632}, {542, 11170}, {598, 11646}, {1916, 11054}, {7608, 38664}, {7771, 11167}, {9889, 11606}, {11669, 14692}, {43535, 51224}

X(54840) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(263), X(6323)}}, {{A, B, C, X(290), X(18818)}}, {{A, B, C, X(420), X(40246)}}, {{A, B, C, X(694), X(843)}}, {{A, B, C, X(3978), X(11054)}}, {{A, B, C, X(6094), X(35146)}}, {{A, B, C, X(8593), X(20021)}}, {{A, B, C, X(9889), X(40850)}}, {{A, B, C, X(10630), X(46316)}}, {{A, B, C, X(14970), X(34898)}}
X(54840) = X(i)-vertex conjugate of X(j) for these {i, j}: {598, 3455}

X(54841) = X(76)X(6034)∩X(94)X(3978)

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

X(54841) lies on these lines: {76, 6034}, {94, 3978}, {98, 7809}, {99, 14492}, {262, 15561}, {1916, 7799}, {3407, 7753}, {5149, 19686}, {6033, 14458}, {32833, 43688}, {34289, 41259}

X(54841) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(99), X(9211)}}, {{A, B, C, X(249), X(46310)}}, {{A, B, C, X(512), X(46284)}}, {{A, B, C, X(694), X(6034)}}, {{A, B, C, X(755), X(46322)}}, {{A, B, C, X(1989), X(14970)}}, {{A, B, C, X(3978), X(7799)}}, {{A, B, C, X(5641), X(18896)}}, {{A, B, C, X(7809), X(20022)}}, {{A, B, C, X(32833), X(41259)}}, {{A, B, C, X(42359), X(52154)}}
X(54841) = trilinear pole of line {37671, 523}

X(54842) = X(515)X(4049)∩X(758)X(2394)

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

X(54842) lies on these lines: {515, 4049}, {758, 2394}, {4242, 16080}, {29046, 35353}

X(54842) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(758)}}, {{A, B, C, X(265), X(15065)}}, {{A, B, C, X(515), X(519)}}, {{A, B, C, X(516), X(527)}}, {{A, B, C, X(528), X(2801)}}, {{A, B, C, X(536), X(29046)}}, {{A, B, C, X(544), X(28850)}}, {{A, B, C, X(752), X(29069)}}, {{A, B, C, X(2723), X(18821)}}, {{A, B, C, X(2792), X(2796)}}, {{A, B, C, X(36910), X(52392)}}

X(54843) = X(4)X(5201)∩X(262)X(11459)

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

X(54843) lies on these lines: {4, 5201}, {262, 11459}, {381, 30505}, {2052, 46511}, {6504, 32986}, {6655, 13582}, {13579, 33017}, {37125, 43530}

X(54843) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(4580)}}, {{A, B, C, X(54), X(3228)}}, {{A, B, C, X(74), X(308)}}, {{A, B, C, X(141), X(43917)}}, {{A, B, C, X(381), X(37125)}}, {{A, B, C, X(695), X(1989)}}, {{A, B, C, X(1138), X(39953)}}, {{A, B, C, X(2998), X(3431)}}, {{A, B, C, X(3426), X(34816)}}, {{A, B, C, X(3541), X(32983)}}, {{A, B, C, X(3542), X(32986)}}, {{A, B, C, X(3545), X(37337)}}, {{A, B, C, X(6344), X(9229)}}, {{A, B, C, X(6655), X(37943)}}, {{A, B, C, X(7505), X(33017)}}, {{A, B, C, X(7552), X(40889)}}, {{A, B, C, X(11459), X(44144)}}, {{A, B, C, X(13597), X(40416)}}, {{A, B, C, X(14483), X(39968)}}, {{A, B, C, X(14490), X(24861)}}, {{A, B, C, X(15412), X(30541)}}, {{A, B, C, X(30496), X(52154)}}, {{A, B, C, X(33016), X(37119)}}

X(54844) = X(262)X(5656)∩X(3088)X(43530)

Barycentrics    (a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4-20*b^2*c^2+6*c^4)-4*a^2*(b^6+5*b^4*c^2-7*b^2*c^4+c^6))*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4-20*b^2*c^2+6*c^4)-4*a^2*(b^6-7*b^4*c^2+5*b^2*c^4+c^6)) : :

X(54844) lies on these lines: {76, 34621}, {262, 5656}, {3088, 43530}, {3089, 16080}, {3424, 16654}, {3543, 6504}, {6807, 10195}, {6808, 10194}, {7400, 10159}, {13579, 50687}, {13582, 17578}, {34781, 45300}

X(54844) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(52187)}}, {{A, B, C, X(20), X(1179)}}, {{A, B, C, X(25), X(34621)}}, {{A, B, C, X(30), X(3089)}}, {{A, B, C, X(40), X(52374)}}, {{A, B, C, X(64), X(34288)}}, {{A, B, C, X(74), X(52223)}}, {{A, B, C, X(84), X(36910)}}, {{A, B, C, X(381), X(3088)}}, {{A, B, C, X(393), X(3426)}}, {{A, B, C, X(428), X(7400)}}, {{A, B, C, X(1093), X(36889)}}, {{A, B, C, X(1138), X(46429)}}, {{A, B, C, X(1217), X(1989)}}, {{A, B, C, X(2165), X(14490)}}, {{A, B, C, X(2980), X(18850)}}, {{A, B, C, X(3346), X(16835)}}, {{A, B, C, X(3527), X(46412)}}, {{A, B, C, X(3531), X(46952)}}, {{A, B, C, X(3541), X(3839)}}, {{A, B, C, X(3542), X(3543)}}, {{A, B, C, X(5627), X(13573)}}, {{A, B, C, X(5656), X(33971)}}, {{A, B, C, X(7505), X(50687)}}, {{A, B, C, X(7714), X(52404)}}, {{A, B, C, X(8801), X(43917)}}, {{A, B, C, X(10002), X(16654)}}, {{A, B, C, X(11058), X(16620)}}, {{A, B, C, X(13603), X(51316)}}, {{A, B, C, X(14483), X(52224)}}, {{A, B, C, X(17578), X(37943)}}, {{A, B, C, X(17703), X(18855)}}, {{A, B, C, X(18317), X(20726)}}, {{A, B, C, X(32085), X(35512)}}, {{A, B, C, X(34223), X(52154)}}, {{A, B, C, X(34285), X(45088)}}, {{A, B, C, X(44275), X(49670)}}

X(54845) = X(2)X(39884)∩X(6)X(52519)

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

X(54845) lies on these lines: {2, 39884}, {6, 52519}, {76, 3529}, {83, 3855}, {147, 42010}, {262, 39874}, {376, 10302}, {382, 2996}, {546, 5395}, {1503, 14494}, {3528, 18840}, {3544, 18841}, {7607, 53015}, {7710, 53108}, {7735, 53100}, {10159, 10299}, {11668, 43460}, {14269, 53101}, {14484, 14912}, {15687, 41895}, {17129, 43681}, {38259, 50688}

X(54845) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(3529)}}, {{A, B, C, X(66), X(44556)}}, {{A, B, C, X(69), X(45819)}}, {{A, B, C, X(74), X(14486)}}, {{A, B, C, X(251), X(11270)}}, {{A, B, C, X(376), X(10301)}}, {{A, B, C, X(382), X(6353)}}, {{A, B, C, X(427), X(3855)}}, {{A, B, C, X(428), X(10299)}}, {{A, B, C, X(546), X(8889)}}, {{A, B, C, X(550), X(7714)}}, {{A, B, C, X(1297), X(11738)}}, {{A, B, C, X(1383), X(29011)}}, {{A, B, C, X(2980), X(34208)}}, {{A, B, C, X(3090), X(52285)}}, {{A, B, C, X(3425), X(13452)}}, {{A, B, C, X(3426), X(3563)}}, {{A, B, C, X(3431), X(14495)}}, {{A, B, C, X(3528), X(6995)}}, {{A, B, C, X(3544), X(7378)}}, {{A, B, C, X(6340), X(32533)}}, {{A, B, C, X(7394), X(35482)}}, {{A, B, C, X(8801), X(14842)}}, {{A, B, C, X(11169), X(34285)}}, {{A, B, C, X(11816), X(18853)}}, {{A, B, C, X(13530), X(18852)}}, {{A, B, C, X(13603), X(43662)}}, {{A, B, C, X(14489), X(14490)}}, {{A, B, C, X(15424), X(18018)}}, {{A, B, C, X(15687), X(52290)}}, {{A, B, C, X(16774), X(32085)}}, {{A, B, C, X(18846), X(40413)}}, {{A, B, C, X(18849), X(40801)}}, {{A, B, C, X(20421), X(29316)}}, {{A, B, C, X(30542), X(43726)}}, {{A, B, C, X(33971), X(39874)}}, {{A, B, C, X(38282), X(50688)}}, {{A, B, C, X(43733), X(52133)}}
X(54845) = trilinear pole of line {47456, 523}
X(54845) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14494}

X(54846) = X(2)X(9873)∩X(76)X(18440)

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

X(54846) lies on these lines: {2, 9873}, {76, 18440}, {1916, 10722}, {5395, 19130}, {6033, 8781}, {7745, 14492}, {7789, 43460}, {32006, 40824}

X(54846) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(38826)}}, {{A, B, C, X(755), X(13603)}}, {{A, B, C, X(761), X(10308)}}, {{A, B, C, X(2353), X(3426)}}, {{A, B, C, X(2710), X(16835)}}, {{A, B, C, X(2980), X(35142)}}, {{A, B, C, X(6033), X(34174)}}, {{A, B, C, X(6531), X(9873)}}, {{A, B, C, X(7745), X(16264)}}, {{A, B, C, X(32006), X(43976)}}

X(54847) = X(2)X(37825)∩X(262)X(397)

Barycentrics    sqrt(3)*(-2*a^8+a^6*(b^2+c^2)+5*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(b^4-5*b^2*c^2+c^4)-3*a^4*(b^4-b^2*c^2+c^4))+(12*a^6-6*a^4*(b^2+c^2)-6*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54847) lies on these lines: {2, 37825}, {3, 40706}, {14, 16630}, {76, 52193}, {98, 5869}, {262, 397}, {462, 2052}, {5344, 43954}, {5980, 8781}, {6770, 11121}, {6776, 22237}, {11122, 22532}, {11257, 43539}, {11602, 41020}, {11603, 42157}, {12817, 41114}, {41025, 43551}, {42999, 43953}

X(54847) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(3441)}}, {{A, B, C, X(264), X(11082)}}, {{A, B, C, X(2980), X(11139)}}, {{A, B, C, X(2992), X(8738)}}, {{A, B, C, X(2993), X(8742)}}, {{A, B, C, X(3442), X(16257)}}, {{A, B, C, X(3443), X(41443)}}, {{A, B, C, X(8737), X(41898)}}, {{A, B, C, X(11138), X(45838)}}
X(54847) = isogonal conjugate of X(47068)

X(54848) = X(2)X(37824)∩X(262)X(398)

Barycentrics    sqrt(3)*(-2*a^8+a^6*(b^2+c^2)+5*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(b^4-5*b^2*c^2+c^4)-3*a^4*(b^4-b^2*c^2+c^4))+6*(-2*a^6+a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2))*S : :

X(54848) lies on these lines: {2, 37824}, {3, 40707}, {13, 16631}, {76, 52194}, {98, 5868}, {262, 398}, {463, 2052}, {5343, 43953}, {5981, 8781}, {6773, 11122}, {6776, 22235}, {11121, 22531}, {11257, 43538}, {11602, 42158}, {11603, 41021}, {12816, 41115}, {41024, 43550}, {42998, 43954}

X(54848) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(3440)}}, {{A, B, C, X(264), X(11087)}}, {{A, B, C, X(2980), X(11138)}}, {{A, B, C, X(2992), X(8741)}}, {{A, B, C, X(2993), X(8737)}}, {{A, B, C, X(3442), X(41443)}}, {{A, B, C, X(3443), X(16258)}}, {{A, B, C, X(8738), X(41897)}}, {{A, B, C, X(11139), X(45838)}}
X(54848) = isogonal conjugate of X(47066)

X(54849) = X(18)X(6776)∩X(20)X(11122)

Barycentrics    3*(-2*a^10+5*a^8*(b^2+c^2)+2*a^4*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)-2*a^2*(b^4-c^4)^2-4*a^6*(b^4+c^4))-sqrt(3)*(11*a^8-10*a^6*(b^2+c^2)-14*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(b^4-14*b^2*c^2+c^4)+12*a^4*(b^4-b^2*c^2+c^4))*S : :

X(54849) lies on these lines: {18, 6776}, {20, 11122}, {262, 42998}, {398, 43953}, {3522, 5488}, {5340, 43954}, {6770, 40707}, {12816, 41117}, {22531, 40706}, {22532, 43676}, {33606, 41128}, {41037, 43547}, {43542, 52688}

X(54849) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(3458)}}, {{A, B, C, X(66), X(11082)}}, {{A, B, C, X(69), X(8738)}}, {{A, B, C, X(393), X(2992)}}, {{A, B, C, X(2993), X(34285)}}, {{A, B, C, X(14528), X(34534)}}
X(54849) = isogonal conjugate of X(5865)
X(54849) = X(i)-cross conjugate of X(j) for these {i, j}: {5869, 4}

X(54850) = X(17)X(6776)∩X(20)X(11121)

Barycentrics    3*(2*a^10-5*a^8*(b^2+c^2)-2*a^4*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+2*a^2*(b^4-c^4)^2+4*a^6*(b^4+c^4))-sqrt(3)*(11*a^8-10*a^6*(b^2+c^2)-14*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(b^4-14*b^2*c^2+c^4)+12*a^4*(b^4-b^2*c^2+c^4))*S : :

X(54850) lies on these lines: {17, 6776}, {20, 11121}, {262, 42999}, {397, 43954}, {3522, 5487}, {5339, 43953}, {6773, 40706}, {10210, 13579}, {12817, 41118}, {22531, 43676}, {22532, 40707}, {33607, 41129}, {41036, 43546}, {43543, 52689}

X(54850) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(3457)}}, {{A, B, C, X(66), X(11087)}}, {{A, B, C, X(69), X(8737)}}, {{A, B, C, X(393), X(2993)}}, {{A, B, C, X(2992), X(34285)}}, {{A, B, C, X(14528), X(34533)}}
X(54850) = isogonal conjugate of X(5864)
X(54850) = X(i)-cross conjugate of X(j) for these {i, j}: {5868, 4}

X(54851) = X(76)X(8703)∩X(83)X(19709)

Barycentrics    (8*a^4+8*b^4-7*b^2*c^2-c^4+a^2*(2*b^2-7*c^2))*(8*a^4-b^4-7*b^2*c^2+8*c^4+a^2*(-7*b^2+2*c^2)) : :

X(54851) lies on these lines: {76, 8703}, {83, 19709}, {547, 43527}, {598, 3860}, {3830, 53106}, {3845, 53107}, {5054, 10159}, {5485, 47101}, {11177, 35005}, {15681, 43676}, {15719, 18840}, {18844, 41099}, {33706, 43688}, {34682, 53109}, {38071, 53102}, {52519, 53015}

X(54851) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(8703)}}, {{A, B, C, X(427), X(19709)}}, {{A, B, C, X(428), X(5054)}}, {{A, B, C, X(547), X(5064)}}, {{A, B, C, X(842), X(36616)}}, {{A, B, C, X(1494), X(46204)}}, {{A, B, C, X(3830), X(52297)}}, {{A, B, C, X(3845), X(52298)}}, {{A, B, C, X(3860), X(5094)}}, {{A, B, C, X(6995), X(15719)}}, {{A, B, C, X(7714), X(15692)}}, {{A, B, C, X(18317), X(34449)}}, {{A, B, C, X(36889), X(46212)}}, {{A, B, C, X(44878), X(47313)}}

X(54852) = X(76)X(15684)∩X(83)X(23046)

Barycentrics    (13*a^4+13*b^4-5*b^2*c^2-8*c^4+a^2*(16*b^2-5*c^2))*(13*a^4-8*b^4-5*b^2*c^2+13*c^4+a^2*(-5*b^2+16*c^2)) : :

X(54852) lies on these lines: {76, 15684}, {83, 23046}, {548, 10159}, {3627, 43676}, {3843, 53102}, {5072, 43527}, {11669, 36990}, {14893, 53109}, {18840, 46333}, {38335, 53105}

X(54852) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(15684)}}, {{A, B, C, X(427), X(23046)}}, {{A, B, C, X(428), X(548)}}, {{A, B, C, X(5064), X(5072)}}, {{A, B, C, X(5966), X(46848)}}, {{A, B, C, X(6995), X(46333)}}, {{A, B, C, X(7714), X(49140)}}, {{A, B, C, X(11058), X(32085)}}, {{A, B, C, X(14495), X(43691)}}, {{A, B, C, X(29316), X(34572)}}, {{A, B, C, X(37453), X(38335)}}

X(54853) = X(98)X(45331)∩X(671)X(46067)

Barycentrics    (a^10+a^8*(4*b^2+c^2)-a^6*(5*b^4+11*b^2*c^2+5*c^4)+(b^2-c^2)^2*(b^6+3*b^4*c^2-2*c^6)+a^4*(-5*b^6+18*b^4*c^2+9*b^2*c^4+c^6)+a^2*(4*b^8-11*b^6*c^2+9*b^4*c^4-14*b^2*c^6+4*c^8))*(a^10+a^8*(b^2+4*c^2)-a^6*(5*b^4+11*b^2*c^2+5*c^4)+a^4*(b^6+9*b^4*c^2+18*b^2*c^4-5*c^6)-(b^2-c^2)^2*(2*b^6-3*b^2*c^4-c^6)+a^2*(4*b^8-14*b^6*c^2+9*b^4*c^4-11*b^2*c^6+4*c^8)) : :

X(54853) lies on these lines: {98, 45331}, {671, 46067}, {5466, 34320}, {6054, 9180}, {11167, 40879}

X(54853) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(37858)}}, {{A, B, C, X(325), X(45331)}}, {{A, B, C, X(468), X(46067)}}, {{A, B, C, X(842), X(18823)}}, {{A, B, C, X(1296), X(10717)}}, {{A, B, C, X(2696), X(17708)}}, {{A, B, C, X(6094), X(43084)}}, {{A, B, C, X(9080), X(35139)}}, {{A, B, C, X(11163), X(40879)}}, {{A, B, C, X(22329), X(34175)}}, {{A, B, C, X(30528), X(53199)}}
X(54853) = trilinear pole of line {5648, 5653}

X(54854) = X(2)X(18511)∩X(3590)X(36656)

Barycentrics    55*a^8+16*a^4*b^2*c^2+50*a^6*(b^2+c^2)-82*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(23*b^4+98*b^2*c^2+23*c^4)+(96*a^6+24*a^4*b^2-48*a^2*b^4-72*b^6+24*a^4*c^2+96*a^2*b^2*c^2+72*b^4*c^2-48*a^2*c^4+72*b^2*c^4-72*c^6)*S : :

X(54854) lies on these lines: {2, 18511}, {3590, 36656}, {3591, 36714}, {10159, 36701}, {14227, 45101}, {14242, 14245}, {14492, 23273}, {15682, 42023}, {36665, 43527}

X(54854) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(1989), X(10262)}}, {{A, B, C, X(13603), X(41444)}}
X(54854) = isogonal conjugate of X(35247)

X(54855) = X(2)X(18509)∩X(3590)X(36709)

Barycentrics    55*a^8+16*a^4*b^2*c^2+50*a^6*(b^2+c^2)-82*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(23*b^4+98*b^2*c^2+23*c^4)-(96*a^6+24*a^4*b^2-48*a^2*b^4-72*b^6+24*a^4*c^2+96*a^2*b^2*c^2+72*b^4*c^2-48*a^2*c^4+72*b^2*c^4-72*c^6)*S : :

X(54855) lies on these lines: {2, 18509}, {3590, 36709}, {3591, 36655}, {10159, 36703}, {14227, 14231}, {14242, 45102}, {14492, 23267}, {15682, 42024}, {16080, 19219}, {36664, 43527}

X(54855) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(1989), X(10261)}}, {{A, B, C, X(13603), X(41445)}}
X(54855) = isogonal conjugate of X(35246)

X(54856) = X(76)X(50967)∩X(262)X(46034)

Barycentrics    (a^6+b^6+11*b^4*c^2-13*b^2*c^4+c^6+11*a^4*(b^2+c^2)+a^2*(11*b^4+6*b^2*c^2-13*c^4))*(a^6+b^6-13*b^4*c^2+11*b^2*c^4+c^6+11*a^4*(b^2+c^2)+a^2*(-13*b^4+6*b^2*c^2+11*c^4)) : :

X(54856) lies on these lines: {76, 50967}, {262, 46034}, {6776, 14485}, {11606, 50687}, {14492, 43448}

X(54856) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(263), X(3426)}}, {{A, B, C, X(290), X(52187)}}, {{A, B, C, X(420), X(50687)}}, {{A, B, C, X(694), X(14490)}}, {{A, B, C, X(3531), X(11175)}}, {{A, B, C, X(11736), X(23700)}}, {{A, B, C, X(13603), X(52230)}}, {{A, B, C, X(16264), X(43448)}}, {{A, B, C, X(20021), X(45088)}}, {{A, B, C, X(33971), X(46034)}}, {{A, B, C, X(42299), X(52188)}}

X(54857) = X(4)X(5368)∩X(76)X(1657)

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

X(54857) lies on these lines: {4, 5368}, {76, 1657}, {83, 3850}, {548, 10302}, {598, 3843}, {671, 3627}, {801, 47315}, {1503, 7608}, {2996, 50691}, {5485, 7751}, {7810, 17538}, {7844, 18841}, {9302, 10991}, {10159, 15712}, {14893, 45103}, {17503, 38335}, {18840, 21735}, {34604, 41895}, {36990, 53100}, {37463, 43548}, {37464, 43549}, {43460, 53104}, {43461, 53098}, {43532, 52854}, {53015, 53103}

X(54857) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(1657)}}, {{A, B, C, X(64), X(11181)}}, {{A, B, C, X(67), X(32085)}}, {{A, B, C, X(95), X(22336)}}, {{A, B, C, X(235), X(47315)}}, {{A, B, C, X(251), X(29316)}}, {{A, B, C, X(428), X(15712)}}, {{A, B, C, X(468), X(3627)}}, {{A, B, C, X(548), X(10301)}}, {{A, B, C, X(842), X(16835)}}, {{A, B, C, X(1383), X(13452)}}, {{A, B, C, X(1799), X(14861)}}, {{A, B, C, X(2697), X(15319)}}, {{A, B, C, X(2980), X(13481)}}, {{A, B, C, X(3425), X(29322)}}, {{A, B, C, X(3426), X(43656)}}, {{A, B, C, X(3519), X(5368)}}, {{A, B, C, X(3532), X(14486)}}, {{A, B, C, X(3843), X(5094)}}, {{A, B, C, X(4232), X(33703)}}, {{A, B, C, X(6353), X(50691)}}, {{A, B, C, X(6995), X(21735)}}, {{A, B, C, X(7751), X(22100)}}, {{A, B, C, X(8884), X(41522)}}, {{A, B, C, X(14495), X(14528)}}, {{A, B, C, X(14893), X(52293)}}, {{A, B, C, X(15321), X(43458)}}, {{A, B, C, X(17538), X(52301)}}, {{A, B, C, X(21400), X(30786)}}, {{A, B, C, X(37458), X(37899)}}, {{A, B, C, X(38005), X(45857)}}, {{A, B, C, X(38335), X(52292)}}, {{A, B, C, X(43732), X(52133)}}
X(54857) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 7608}

X(54858) = X(76)X(33878)∩X(83)X(48906)

Barycentrics    (a^6+b^6+4*b^4*c^2-5*b^2*c^4+a^4*(5*b^2+4*c^2)+a^2*(5*b^4+2*b^2*c^2-5*c^4))*(a^6-5*b^4*c^2+4*b^2*c^4+c^6+a^4*(4*b^2+5*c^2)+a^2*(-5*b^4+2*b^2*c^2+5*c^4)) : :

X(54858) lies on these lines: {76, 33878}, {83, 48906}, {2996, 31670}, {3424, 12110}, {5254, 14492}, {6248, 12122}, {8781, 51872}, {9698, 14494}, {10155, 15428}, {10357, 18840}, {10722, 11606}, {12203, 43527}

X(54858) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(32), X(3426)}}, {{A, B, C, X(74), X(42346)}}, {{A, B, C, X(182), X(52518)}}, {{A, B, C, X(265), X(3933)}}, {{A, B, C, X(729), X(13603)}}, {{A, B, C, X(1078), X(45138)}}, {{A, B, C, X(3224), X(14490)}}, {{A, B, C, X(3531), X(10014)}}, {{A, B, C, X(5254), X(16264)}}, {{A, B, C, X(10308), X(14665)}}, {{A, B, C, X(10519), X(15740)}}, {{A, B, C, X(12110), X(45031)}}, {{A, B, C, X(14383), X(33971)}}, {{A, B, C, X(15321), X(35142)}}, {{A, B, C, X(22334), X(36615)}}, {{A, B, C, X(27375), X(46320)}}, {{A, B, C, X(34174), X(51872)}}, {{A, B, C, X(42299), X(45857)}}

X(54859) = X(376)X(5503)∩X(5485)X(6776)

Barycentrics    (7*a^6-3*b^6+5*b^4*c^2-9*b^2*c^4+7*c^6+a^4*(-9*b^2+c^2)+a^2*(5*b^4-14*b^2*c^2+c^4))*(7*a^6+7*b^6-9*b^4*c^2+5*b^2*c^4-3*c^6+a^4*(b^2-9*c^2)+a^2*(b^4-14*b^2*c^2+5*c^4)) : :

X(54859) lies on these lines: {376, 5503}, {5485, 6776}, {7608, 36998}, {8781, 14907}, {39874, 43532}

X(54859) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(8753)}}, {{A, B, C, X(69), X(9154)}}, {{A, B, C, X(376), X(48260)}}, {{A, B, C, X(6524), X(40102)}}, {{A, B, C, X(14907), X(36875)}}, {{A, B, C, X(20421), X(23700)}}, {{A, B, C, X(32581), X(44836)}}

X(54860) = X(2)X(13349)∩X(18)X(41098)

Barycentrics    sqrt(3)*(-2*a^10+5*a^8*(b^2+c^2)+2*a^4*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)-2*a^2*(b^4-c^4)^2-4*a^6*(b^4+c^4))+2*(2*a^8-5*a^6*(b^2+c^2)+7*a^2*(b^2-c^2)^2*(b^2+c^2)-a^4*(b^4-b^2*c^2+c^4)-(b^2-c^2)^2*(3*b^4-7*b^2*c^2+3*c^4))*S : :

X(54860) lies on these lines: {2, 13349}, {18, 41098}, {98, 41039}, {262, 5318}, {381, 42063}, {671, 13102}, {5335, 43953}, {6776, 43541}, {11603, 23013}, {14639, 16943}, {33517, 43538}, {42134, 43954}

X(54860) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(264), X(20429)}}, {{A, B, C, X(3438), X(34154)}}, {{A, B, C, X(3441), X(16257)}}, {{A, B, C, X(8742), X(9307)}}, {{A, B, C, X(11139), X(45819)}}, {{A, B, C, X(21462), X(23717)}}
X(54860) = isogonal conjugate of X(9735)

X(54861) = X(2)X(13350)∩X(17)X(41094)

Barycentrics    sqrt(3)*(-2*a^10+5*a^8*(b^2+c^2)+2*a^4*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^4*(b^2+c^2)-2*a^2*(b^4-c^4)^2-4*a^6*(b^4+c^4))+2*(-2*a^8+5*a^6*(b^2+c^2)-7*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(b^4-b^2*c^2+c^4)+(b^2-c^2)^2*(3*b^4-7*b^2*c^2+3*c^4))*S : :

X(54861) lies on these lines: {2, 13350}, {17, 41094}, {98, 41038}, {262, 5321}, {381, 42062}, {671, 13103}, {5334, 43954}, {6776, 43540}, {11602, 23006}, {14639, 16942}, {33518, 43539}, {42133, 43953}

X(54861) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(264), X(20428)}}, {{A, B, C, X(3439), X(34154)}}, {{A, B, C, X(3440), X(16258)}}, {{A, B, C, X(8741), X(9307)}}, {{A, B, C, X(11138), X(45819)}}, {{A, B, C, X(21461), X(23716)}}
X(54861) = isogonal conjugate of X(9736)

X(54862) = X(4)X(48848)∩X(381)X(32022)

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

X(54862) lies on these lines: {4, 48848}, {381, 32022}, {3543, 6625}, {4196, 43530}, {4207, 16080}, {36670, 43527}

X(54862) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(4207)}}, {{A, B, C, X(42), X(3426)}}, {{A, B, C, X(74), X(39961)}}, {{A, B, C, X(381), X(4196)}}, {{A, B, C, X(1002), X(16615)}}, {{A, B, C, X(1246), X(52187)}}, {{A, B, C, X(1826), X(36889)}}, {{A, B, C, X(2350), X(3531)}}, {{A, B, C, X(3543), X(4213)}}, {{A, B, C, X(3839), X(4212)}}, {{A, B, C, X(4846), X(48848)}}, {{A, B, C, X(5064), X(36670)}}, {{A, B, C, X(14483), X(39965)}}, {{A, B, C, X(14490), X(39967)}}, {{A, B, C, X(15320), X(34288)}}, {{A, B, C, X(39948), X(45137)}}

X(54863) = X(262)X(16654)∩X(1595)X(43530)

Barycentrics    (2*a^8-(b^2-c^2)^3*(b^2+2*c^2)-a^6*(5*b^2+2*c^2)+a^4*(3*b^4-19*b^2*c^2)+a^2*(b^6+20*b^4*c^2-19*b^2*c^4-2*c^6))*(2*a^8+(b^2-c^2)^3*(2*b^2+c^2)-a^6*(2*b^2+5*c^2)+a^4*(-19*b^2*c^2+3*c^4)+a^2*(-2*b^6-19*b^4*c^2+20*b^2*c^4+c^6)) : :

X(54863) lies on these lines: {262, 16654}, {1595, 43530}, {1598, 16080}, {5656, 43951}, {10159, 11414}, {13599, 16656}

X(54863) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(428), X(11414)}}, {{A, B, C, X(3830), X(21841)}}, {{A, B, C, X(14490), X(16263)}}, {{A, B, C, X(15318), X(34288)}}, {{A, B, C, X(16654), X(33971)}}, {{A, B, C, X(16656), X(41365)}}

X(54864) = X(2)X(30532)∩X(4)X(15019)

Barycentrics    (a^6+(b^2-2*c^2)*(b^2-c^2)^2-a^4*(b^2+4*c^2)-a^2*(b^4+6*b^2*c^2-5*c^4))*(a^6-(b^2-c^2)^2*(2*b^2-c^2)-a^4*(4*b^2+c^2)+a^2*(5*b^4-6*b^2*c^2-c^4)) : :

X(54864) lies on these lines: {2, 30532}, {4, 15019}, {262, 31133}, {275, 37765}, {324, 46105}, {597, 40393}, {598, 5422}, {801, 40112}, {858, 7608}, {1992, 6504}, {1995, 7607}, {5485, 6515}, {10302, 37636}, {11140, 44555}, {16051, 53098}, {31099, 53099}, {38323, 40448}, {41238, 43527}, {42410, 44569}

X(54864) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(287), X(45835)}}, {{A, B, C, X(324), X(37765)}}, {{A, B, C, X(458), X(31133)}}, {{A, B, C, X(597), X(37636)}}, {{A, B, C, X(599), X(5422)}}, {{A, B, C, X(858), X(52281)}}, {{A, B, C, X(895), X(15019)}}, {{A, B, C, X(1494), X(44176)}}, {{A, B, C, X(1992), X(6515)}}, {{A, B, C, X(1994), X(44555)}}, {{A, B, C, X(1995), X(52282)}}, {{A, B, C, X(5064), X(41238)}}, {{A, B, C, X(5641), X(46104)}}, {{A, B, C, X(9141), X(40413)}}, {{A, B, C, X(13567), X(40112)}}, {{A, B, C, X(14490), X(15066)}}, {{A, B, C, X(14593), X(34288)}}, {{A, B, C, X(38323), X(52280)}}
X(54864) = trilinear pole of line {32084, 523}
X(54864) = polar conjugate of X(37118)
X(54864) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 37118}

X(54865) = X(13582)X(31723)∩X(16080)X(47485)

Barycentrics    (4*a^8-2*(b^2-c^2)^3*(b^2+2*c^2)-2*a^6*(5*b^2+2*c^2)+a^4*(6*b^4-5*b^2*c^2)+a^2*(2*b^6+7*b^4*c^2-5*b^2*c^4-4*c^6))*(4*a^8+2*(b^2-c^2)^3*(2*b^2+c^2)-2*a^6*(2*b^2+5*c^2)+a^4*(-5*b^2*c^2+6*c^4)+a^2*(-4*b^6-5*b^4*c^2+7*b^2*c^4+2*c^6)) : :

X(54865) lies on these lines: {13582, 31723}, {16080, 47485}

X(54865) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(11738)}}, {{A, B, C, X(54), X(48911)}}, {{A, B, C, X(66), X(1138)}}, {{A, B, C, X(2980), X(5627)}}, {{A, B, C, X(3426), X(14579)}}, {{A, B, C, X(7556), X(18559)}}, {{A, B, C, X(13139), X(30537)}}, {{A, B, C, X(13452), X(15619)}}, {{A, B, C, X(13472), X(43970)}}, {{A, B, C, X(31723), X(37943)}}, {{A, B, C, X(33565), X(34288)}}, {{A, B, C, X(34285), X(38006)}}, {{A, B, C, X(45972), X(52187)}}

X(54866) = X(20)X(43676)∩X(76)X(10304)

Barycentrics    (11*a^4+11*b^4-10*b^2*c^2-c^4+2*a^2*(b^2-5*c^2))*(11*a^4-b^4-10*b^2*c^2+11*c^4+2*a^2*(-5*b^2+c^2)) : :

X(54866) lies on these lines: {20, 43676}, {76, 10304}, {381, 18843}, {549, 18840}, {671, 15640}, {2996, 15683}, {3091, 53102}, {3534, 5485}, {3543, 53105}, {3839, 53109}, {5055, 18841}, {5066, 18842}, {5304, 14492}, {6776, 11669}, {7000, 43571}, {7374, 43570}, {7486, 43527}, {8781, 11177}, {9300, 53099}, {10159, 10303}, {18844, 23046}, {32532, 33699}, {43681, 50693}, {43951, 53015}

X(54866) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(10304)}}, {{A, B, C, X(67), X(46204)}}, {{A, B, C, X(253), X(1989)}}, {{A, B, C, X(428), X(10303)}}, {{A, B, C, X(468), X(15640)}}, {{A, B, C, X(549), X(6995)}}, {{A, B, C, X(1297), X(36616)}}, {{A, B, C, X(2980), X(52187)}}, {{A, B, C, X(3534), X(4232)}}, {{A, B, C, X(3543), X(11744)}}, {{A, B, C, X(5055), X(7378)}}, {{A, B, C, X(5064), X(7486)}}, {{A, B, C, X(5066), X(52284)}}, {{A, B, C, X(5304), X(37671)}}, {{A, B, C, X(5966), X(13452)}}, {{A, B, C, X(6353), X(15683)}}, {{A, B, C, X(7408), X(15709)}}, {{A, B, C, X(7714), X(15717)}}, {{A, B, C, X(7837), X(37667)}}, {{A, B, C, X(8801), X(52154)}}, {{A, B, C, X(9740), X(14614)}}, {{A, B, C, X(11177), X(51820)}}, {{A, B, C, X(13622), X(34285)}}, {{A, B, C, X(14486), X(34572)}}, {{A, B, C, X(15698), X(52301)}}, {{A, B, C, X(16774), X(46208)}}, {{A, B, C, X(29180), X(44763)}}, {{A, B, C, X(36611), X(52443)}}, {{A, B, C, X(36889), X(51316)}}, {{A, B, C, X(45838), X(52188)}}

X(54867) = X(4)X(11431)∩X(53)X(459)

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

X(54867) lies on these lines: {2, 42459}, {4, 11431}, {25, 43537}, {53, 459}, {98, 7714}, {275, 1249}, {376, 40448}, {381, 31363}, {427, 53099}, {428, 3424}, {468, 53859}, {472, 22237}, {473, 22235}, {1585, 3590}, {1586, 3591}, {2996, 52282}, {3535, 10195}, {3536, 10194}, {3545, 13599}, {5064, 14484}, {5395, 52281}, {6353, 7607}, {6504, 41628}, {6995, 47586}, {7608, 8889}, {8796, 14361}, {10159, 52283}, {10185, 52290}, {11433, 39284}, {37174, 43681}, {43527, 52288}, {52299, 53098}

X(54867) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(53), X(1249)}}, {{A, B, C, X(97), X(13452)}}, {{A, B, C, X(297), X(7714)}}, {{A, B, C, X(324), X(36612)}}, {{A, B, C, X(376), X(52280)}}, {{A, B, C, X(394), X(16835)}}, {{A, B, C, X(428), X(52283)}}, {{A, B, C, X(1073), X(22334)}}, {{A, B, C, X(3426), X(36609)}}, {{A, B, C, X(5064), X(52288)}}, {{A, B, C, X(6353), X(52282)}}, {{A, B, C, X(6515), X(41628)}}, {{A, B, C, X(7003), X(36916)}}, {{A, B, C, X(8795), X(36889)}}, {{A, B, C, X(8889), X(52281)}}, {{A, B, C, X(11433), X(44732)}}, {{A, B, C, X(13472), X(31626)}}, {{A, B, C, X(15321), X(42287)}}, {{A, B, C, X(36121), X(39948)}}, {{A, B, C, X(36603), X(40397)}}, {{A, B, C, X(40065), X(46952)}}
X(54867) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 3523}, {63, 17809}, {255, 40065}
X(54867) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 3523}, {3162, 17809}, {6523, 40065}
X(54867) = X(i)-cross conjugate of X(j) for these {i, j}: {1907, 264}, {7738, 34208}
X(54867) = barycentric product X(i)*X(j) for these (i, j): {264, 52518}
X(54867) = barycentric quotient X(i)/X(j) for these (i, j): {4, 3523}, {25, 17809}, {393, 40065}, {52518, 3}

X(54868) = X(98)X(53418)∩X(576)X(2996)

Barycentrics    (3*a^6-2*b^6+9*b^4*c^2-10*b^2*c^4+3*c^6-5*a^4*(2*b^2+c^2)+a^2*(9*b^4-10*b^2*c^2-5*c^4))*(3*a^6+3*b^6-10*b^4*c^2+9*b^2*c^4-2*c^6-5*a^4*(b^2+2*c^2)+a^2*(-5*b^4-10*b^2*c^2+9*c^4)) : :

X(54868) lies on these lines: {98, 53418}, {262, 44526}, {574, 14494}, {576, 2996}, {598, 5050}, {1916, 32469}, {3053, 7607}, {5052, 43532}, {7612, 7737}, {9753, 11172}, {11179, 53101}, {14458, 53017}, {14639, 43535}, {14853, 41895}, {19661, 38224}

X(54868) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(512), X(2080)}}, {{A, B, C, X(574), X(3426)}}, {{A, B, C, X(576), X(3053)}}, {{A, B, C, X(843), X(14483)}}, {{A, B, C, X(3531), X(30498)}}, {{A, B, C, X(5033), X(32447)}}, {{A, B, C, X(5038), X(13334)}}, {{A, B, C, X(18575), X(35142)}}

X(54869) = X(2)X(11151)∩X(187)X(7612)

Barycentrics    (2*a^6+2*b^6-9*b^4*c^2+10*b^2*c^4-3*c^6-a^4*(4*b^2+9*c^2)-2*a^2*(2*b^4+2*b^2*c^2-5*c^4))*(2*a^6-3*b^6+10*b^4*c^2-9*b^2*c^4+2*c^6-a^4*(9*b^2+4*c^2)+2*a^2*(5*b^4-2*b^2*c^2-2*c^4)) : :

X(54869) lies on these lines: {2, 11151}, {187, 7612}, {262, 53419}, {575, 5395}, {598, 50979}, {671, 1351}, {2549, 14494}, {5013, 7608}, {5034, 11170}, {5485, 51179}, {6776, 53101}, {8781, 13188}, {9880, 43535}, {20423, 41895}, {31455, 53098}, {36998, 47586}, {39646, 53109}

X(54869) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(187), X(1351)}}, {{A, B, C, X(575), X(5013)}}, {{A, B, C, X(2065), X(14906)}}, {{A, B, C, X(5034), X(11171)}}, {{A, B, C, X(5171), X(13330)}}, {{A, B, C, X(6776), X(43699)}}, {{A, B, C, X(13188), X(14265)}}

X(54870) = X(459)X(7576)∩X(3543)X(5392)

Barycentrics    (7*a^8-4*a^6*(b^2+4*c^2)+(b^2-c^2)^3*(7*b^2+5*c^2)+a^4*(-6*b^4-8*b^2*c^2+6*c^4)-4*a^2*(b^6+2*b^4*c^2-b^2*c^4-2*c^6))*(7*a^8-4*a^6*(4*b^2+c^2)-(b^2-c^2)^3*(5*b^2+7*c^2)+a^4*(6*b^4-8*b^2*c^2-6*c^4)+4*a^2*(2*b^6+b^4*c^2-2*b^2*c^4-c^6)) : :

X(54870) lies on these lines: {459, 7576}, {3543, 5392}, {3839, 40393}, {7487, 16080}, {14484, 18396}, {16657, 43951}

X(54870) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(20), X(7576)}}, {{A, B, C, X(24), X(3543)}}, {{A, B, C, X(30), X(7487)}}, {{A, B, C, X(68), X(52187)}}, {{A, B, C, X(393), X(44836)}}, {{A, B, C, X(1166), X(13452)}}, {{A, B, C, X(1217), X(15619)}}, {{A, B, C, X(1494), X(38442)}}, {{A, B, C, X(1594), X(3839)}}, {{A, B, C, X(1989), X(18855)}}, {{A, B, C, X(3147), X(50687)}}, {{A, B, C, X(3426), X(8882)}}, {{A, B, C, X(4846), X(44684)}}, {{A, B, C, X(6145), X(34288)}}, {{A, B, C, X(8884), X(36889)}}, {{A, B, C, X(15321), X(18850)}}, {{A, B, C, X(16251), X(44177)}}, {{A, B, C, X(16835), X(31361)}}, {{A, B, C, X(17505), X(32132)}}, {{A, B, C, X(18559), X(31304)}}, {{A, B, C, X(20563), X(43699)}}, {{A, B, C, X(31846), X(46217)}}, {{A, B, C, X(33565), X(45833)}}, {{A, B, C, X(34285), X(46412)}}

X(54871) = X(4)X(8538)∩X(96)X(34664)

Barycentrics    (a^8-3*a^6*b^2+a^4*(b^4+5*b^2*c^2-2*c^4)-(b^2-c^2)^2*(2*b^4+b^2*c^2-c^4)+a^2*(3*b^6-4*b^4*c^2+5*b^2*c^4))*(a^8-3*a^6*c^2+(b^2-c^2)^2*(b^4-b^2*c^2-2*c^4)+a^4*(-2*b^4+5*b^2*c^2+c^4)+a^2*(5*b^4*c^2-4*b^2*c^4+3*c^6)) : :

X(54871) lies on these lines: {4, 8538}, {96, 34664}, {98, 52069}, {7503, 7607}, {7608, 13160}, {7841, 43678}, {16080, 41237}, {41231, 43530}

X(54871) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(8538)}}, {{A, B, C, X(22), X(7841)}}, {{A, B, C, X(30), X(41237)}}, {{A, B, C, X(297), X(52069)}}, {{A, B, C, X(381), X(41231)}}, {{A, B, C, X(467), X(34664)}}, {{A, B, C, X(1176), X(11416)}}, {{A, B, C, X(5133), X(8370)}}, {{A, B, C, X(6656), X(34603)}}, {{A, B, C, X(7495), X(8352)}}, {{A, B, C, X(7500), X(33190)}}, {{A, B, C, X(7503), X(52282)}}, {{A, B, C, X(9229), X(15351)}}, {{A, B, C, X(13160), X(52281)}}, {{A, B, C, X(32974), X(34608)}}

X(54872) = X(76)X(14645)∩X(98)X(13449)

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

X(54872) lies on these lines: {76, 14645}, {98, 13449}, {262, 11361}, {384, 7608}, {3399, 8370}, {3406, 7841}, {3564, 43532}, {5025, 7607}, {7612, 16041}, {7901, 10185}, {9830, 41895}, {10155, 14039}, {10484, 11164}, {11669, 14036}, {14001, 53098}, {14033, 14494}, {14035, 53099}, {14046, 53104}, {14062, 53100}, {14063, 43537}, {17503, 52088}, {32996, 47586}, {33283, 53859}, {33285, 53103}, {37892, 52281}

X(54872) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(14041)}}, {{A, B, C, X(384), X(52281)}}, {{A, B, C, X(458), X(11361)}}, {{A, B, C, X(512), X(2987)}}, {{A, B, C, X(3455), X(30535)}}, {{A, B, C, X(5025), X(52282)}}, {{A, B, C, X(9154), X(9227)}}, {{A, B, C, X(13449), X(44132)}}, {{A, B, C, X(16041), X(37174)}}, {{A, B, C, X(23698), X(23878)}}
X(54872) = trilinear pole of line {11633, 13468}

X(54873) = X(2)X(32152)∩X(4)X(39764)

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

X(54873) lies on these lines: {2, 32152}, {4, 39764}, {76, 11898}, {1506, 10155}, {6776, 38259}, {7612, 36998}, {8781, 21166}, {39646, 53105}

X(54873) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(11898)}}, {{A, B, C, X(54), X(23700)}}, {{A, B, C, X(182), X(30496)}}, {{A, B, C, X(511), X(8601)}}, {{A, B, C, X(3425), X(14248)}}, {{A, B, C, X(6776), X(31371)}}, {{A, B, C, X(9307), X(47735)}}, {{A, B, C, X(14265), X(21166)}}

X(54874) = X(2)X(9757)∩X(4)X(19102)

Barycentrics    a^4*(b^2-c^2)^2+9*a^6*(b^2+c^2)-13*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(3*b^4-14*b^2*c^2+3*c^4)+6*(3*a^6-a^2*(b^2-c^2)^2-2*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54874) lies on these lines: {2, 9757}, {4, 19102}, {6, 45106}, {76, 6278}, {98, 13834}, {485, 7694}, {486, 13763}, {1131, 5870}, {1327, 1503}, {3316, 12257}, {3564, 42024}, {3590, 48735}, {5485, 32421}, {5490, 12124}, {5871, 43560}, {6561, 10839}, {8781, 9758}, {12818, 13749}, {12819, 14239}, {14232, 49221}, {14240, 45407}, {14245, 19103}, {14484, 23259}, {42283, 45107}

X(54874) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(488), X(15740)}}, {{A, B, C, X(523), X(41515)}}, {{A, B, C, X(1499), X(32421)}}, {{A, B, C, X(3426), X(41483)}}
X(54874) = isogonal conjugate of X(45498)
X(54874) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 1327}

X(54875) = X(485)X(14227)∩X(1131)X(14242)

Barycentrics    6*(3*a^10+2*a^6*(b^2-c^2)^2-6*a^8*(b^2+c^2)-2*(b^2-c^2)^4*(b^2+c^2)+a^2*(b^2-c^2)^2*(3*b^4+10*b^2*c^2+3*c^4))+(-27*a^8-8*a^4*(b^2-c^2)^2-18*a^6*(b^2+c^2)+50*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(3*b^4+58*b^2*c^2+3*c^4))*S : :

X(54875) lies on these lines: {485, 14227}, {1131, 14242}, {1503, 14241}, {3316, 5870}, {3317, 13748}, {10783, 14245}, {10784, 45101}, {10843, 43509}, {14484, 23273}, {23267, 45106}

X(54875) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(10262), X(18575)}}
X(54875) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14241}

X(54876) = X(2)X(9758)∩X(4)X(19105)

Barycentrics    a^4*(b^2-c^2)^2+9*a^6*(b^2+c^2)-13*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(3*b^4-14*b^2*c^2+3*c^4)+6*(-3*a^6+a^2*(b^2-c^2)^2+2*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54876) lies on these lines: {2, 9758}, {4, 19105}, {6, 45107}, {76, 6281}, {98, 13711}, {485, 13644}, {486, 7694}, {1132, 5871}, {1328, 1503}, {3317, 12256}, {3564, 42023}, {3591, 48734}, {5485, 32419}, {5491, 12123}, {5870, 43561}, {6560, 10840}, {8781, 9757}, {12818, 14235}, {12819, 13748}, {14231, 19104}, {14236, 45406}, {14237, 49220}, {14484, 23249}, {42284, 45106}

X(54876) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(487), X(15740)}}, {{A, B, C, X(523), X(41516)}}, {{A, B, C, X(1499), X(32419)}}, {{A, B, C, X(3426), X(41484)}}
X(54876) = isogonal conjugate of X(45499)
X(54876) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 1328}

X(54877) = X(262)X(14233)∩X(1503)X(14240)

Barycentrics    -4*a^10+8*a^6*b^2*c^2+7*a^8*(b^2+c^2)-2*a^4*(b^2-c^2)^2*(b^2+c^2)+3*(b^2-c^2)^4*(b^2+c^2)-4*a^2*(b^2-c^2)^2*(b^4+4*b^2*c^2+c^4)+(a^4*b^2*c^2+10*a^6*(b^2+c^2)-12*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(2*b^4-13*b^2*c^2+2*c^4))*S : :

X(54877) lies on these lines: {262, 14233}, {1503, 14240}, {6568, 10722}, {13748, 14245}, {14236, 14239}, {14488, 45863}, {14492, 23261}, {45106, 45406}

X(54877) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(842), X(8948)}}, {{A, B, C, X(3521), X(6401)}}, {{A, B, C, X(13603), X(41483)}}
X(54877) = isogonal conjugate of X(7690)
X(54877) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14240}

X(54878) = X(262)X(14230)∩X(1503)X(14236)

Barycentrics    -4*a^10+8*a^6*b^2*c^2+7*a^8*(b^2+c^2)-2*a^4*(b^2-c^2)^2*(b^2+c^2)+3*(b^2-c^2)^4*(b^2+c^2)-4*a^2*(b^2-c^2)^2*(b^4+4*b^2*c^2+c^4)+(-(a^4*b^2*c^2)-10*a^6*(b^2+c^2)+12*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(2*b^4-13*b^2*c^2+2*c^4))*S : :

X(54878) lies on these lines: {262, 14230}, {1503, 14236}, {6569, 10722}, {13749, 14231}, {14235, 14240}, {14488, 45862}, {14492, 23251}, {45107, 45407}

X(54878) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(842), X(8946)}}, {{A, B, C, X(3521), X(6402)}}, {{A, B, C, X(13603), X(41484)}}
X(54878) = isogonal conjugate of X(7692)
X(54878) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14236}

X(54879) = X(3830)X(5392)∩X(3845)X(40393)

Barycentrics    (5*a^8-a^6*(11*b^2+2*c^2)-(b^2-c^2)^3*(4*b^2+5*c^2)+a^4*(3*b^4-7*b^2*c^2-6*c^4)+a^2*(7*b^6+2*b^4*c^2-7*b^2*c^4-2*c^6))*(5*a^8+(b^2-c^2)^3*(5*b^2+4*c^2)-a^6*(2*b^2+11*c^2)+a^4*(-6*b^4-7*b^2*c^2+3*c^4)+a^2*(-2*b^6-7*b^4*c^2+2*b^2*c^4+7*c^6)) : :

X(54879) lies on these lines: {3830, 5392}, {3845, 40393}, {7576, 16080}

X(54879) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(24), X(3830)}}, {{A, B, C, X(30), X(7576)}}, {{A, B, C, X(381), X(2980)}}, {{A, B, C, X(847), X(46204)}}, {{A, B, C, X(1166), X(16835)}}, {{A, B, C, X(1594), X(3845)}}, {{A, B, C, X(5627), X(32085)}}, {{A, B, C, X(7487), X(15682)}}, {{A, B, C, X(8882), X(13603)}}, {{A, B, C, X(10018), X(12101)}}, {{A, B, C, X(34288), X(44836)}}

X(54880) = X(10)X(37427)∩X(16080)X(37102)

Barycentrics    (a^5-3*a^4*(b+c)+2*a^2*(b-c)^2*(b+c)+(b-c)^4*(b+c)+2*a^3*(b^2-4*b*c+c^2)-a*(3*b^4+8*b^3*c+2*b^2*c^2-16*b*c^3+3*c^4))*(a^5-3*a^4*(b+c)+2*a^2*(b-c)^2*(b+c)+(b-c)^4*(b+c)+2*a^3*(b^2-4*b*c+c^2)-a*(3*b^4-16*b^3*c+2*b^2*c^2+8*b*c^3+3*c^4)) : :

X(54880) lies on these lines: {10, 37427}, {16080, 37102}

X(54880) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(27), X(37427)}}, {{A, B, C, X(30), X(37102)}}, {{A, B, C, X(279), X(10308)}}, {{A, B, C, X(1121), X(3427)}}, {{A, B, C, X(3062), X(34578)}}, {{A, B, C, X(3426), X(42290)}}, {{A, B, C, X(3543), X(37382)}}, {{A, B, C, X(4194), X(36728)}}, {{A, B, C, X(4200), X(36731)}}, {{A, B, C, X(34234), X(38009)}}, {{A, B, C, X(41514), X(52374)}}

X(54881) = X(98)X(9181)∩X(511)X(9180)

Barycentrics    (2*a^10*(b^2+c^2)-a^8*(6*b^4+7*b^2*c^2+3*c^4)+a^6*(5*b^6+13*b^4*c^2+4*b^2*c^4+2*c^6)-b^2*c^2*(b^8-5*b^4*c^4+6*b^2*c^6-2*c^8)-a^4*(11*b^6*c^2+6*b^4*c^4-4*b^2*c^6+3*c^8)-a^2*(b^10-8*b^8*c^2+11*b^6*c^4-13*b^4*c^6+7*b^2*c^8-2*c^10))*(2*a^10*(b^2+c^2)-a^8*(3*b^4+7*b^2*c^2+6*c^4)+a^6*(2*b^6+4*b^4*c^2+13*b^2*c^4+5*c^6)-a^4*(3*b^8-4*b^6*c^2+6*b^4*c^4+11*b^2*c^6)+b^2*c^2*(2*b^8-6*b^6*c^2+5*b^4*c^4-c^8)+a^2*(2*b^10-7*b^8*c^2+13*b^6*c^4-11*b^4*c^6+8*b^2*c^8-c^10)) : :

X(54881) lies on these lines: {98, 9181}, {511, 9180}, {524, 46040}, {538, 14223}, {543, 43665}, {2394, 5969}, {2782, 5466}, {2794, 43668}

X(54881) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(5969)}}, {{A, B, C, X(511), X(543)}}, {{A, B, C, X(524), X(2782)}}, {{A, B, C, X(538), X(542)}}, {{A, B, C, X(3228), X(43654)}}, {{A, B, C, X(4590), X(53605)}}, {{A, B, C, X(9066), X(9141)}}, {{A, B, C, X(9830), X(32515)}}

X(54882) = X(10)X(34746)∩X(226)X(36728)

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

X(54882) lies on these lines: {10, 34746}, {226, 36728}, {1751, 36731}, {16080, 37389}

X(54882) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(27), X(37428)}}, {{A, B, C, X(29), X(36728)}}, {{A, B, C, X(30), X(37389)}}, {{A, B, C, X(515), X(4762)}}, {{A, B, C, X(527), X(1445)}}, {{A, B, C, X(1170), X(10308)}}, {{A, B, C, X(5125), X(36731)}}, {{A, B, C, X(7160), X(42030)}}, {{A, B, C, X(28846), X(28854)}}

X(54883) = X(2)X(22080)∩X(4)X(20970)

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

X(54883) lies on these lines: {2, 22080}, {3, 32014}, {4, 20970}, {10, 24045}, {76, 41014}, {226, 17592}, {275, 1889}, {430, 2052}, {2996, 20018}, {3690, 6539}

X(54883) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(17592)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(430)}}, {{A, B, C, X(5), X(1889)}}, {{A, B, C, X(6), X(48886)}}, {{A, B, C, X(27), X(36687)}}, {{A, B, C, X(79), X(32023)}}, {{A, B, C, X(264), X(15320)}}, {{A, B, C, X(847), X(917)}}, {{A, B, C, X(972), X(16615)}}, {{A, B, C, X(1246), X(1826)}}, {{A, B, C, X(1389), X(45137)}}, {{A, B, C, X(4028), X(20018)}}, {{A, B, C, X(6994), X(36684)}}, {{A, B, C, X(14377), X(17982)}}

X(54884) = X(2)X(48929)∩X(76)X(36654)

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

X(54884) lies on these lines: {2, 48929}, {76, 36654}, {226, 24217}, {4049, 48075}, {4080, 4430}

X(54884) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(48929)}}, {{A, B, C, X(25), X(36654)}}, {{A, B, C, X(80), X(24217)}}, {{A, B, C, X(264), X(48938)}}, {{A, B, C, X(1002), X(29308)}}, {{A, B, C, X(4430), X(48075)}}, {{A, B, C, X(29342), X(30651)}}

X(54885) = X(376)X(6625)∩X(4049)X(28511)

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

X(54885) lies on these lines: {376, 6625}, {4049, 28511}, {5071, 32022}, {9352, 30588}

X(54885) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(42), X(3431)}}, {{A, B, C, X(74), X(39967)}}, {{A, B, C, X(376), X(4213)}}, {{A, B, C, X(519), X(28511)}}, {{A, B, C, X(1246), X(1989)}}, {{A, B, C, X(2350), X(14491)}}, {{A, B, C, X(3524), X(4207)}}, {{A, B, C, X(3545), X(4212)}}, {{A, B, C, X(4196), X(5071)}}, {{A, B, C, X(9352), X(32631)}}, {{A, B, C, X(14483), X(39966)}}, {{A, B, C, X(15320), X(52154)}}, {{A, B, C, X(16615), X(52654)}}

X(54886) = X(6504)X(50687)∩X(6807)X(43564)

Barycentrics    (a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4-44*b^2*c^2+6*c^4)-4*a^2*(b^6+11*b^4*c^2-13*b^2*c^4+c^6))*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+a^4*(6*b^4-44*b^2*c^2+6*c^4)-4*a^2*(b^6-13*b^4*c^2+11*b^2*c^4+c^6)) : :

X(54886) lies on these lines: {6504, 50687}, {6807, 43564}, {6808, 43565}, {10159, 52404}, {18840, 34621}

X(54886) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(64), X(52187)}}, {{A, B, C, X(84), X(36916)}}, {{A, B, C, X(254), X(46851)}}, {{A, B, C, X(393), X(14490)}}, {{A, B, C, X(428), X(52404)}}, {{A, B, C, X(3088), X(3839)}}, {{A, B, C, X(3089), X(3543)}}, {{A, B, C, X(3346), X(22334)}}, {{A, B, C, X(3426), X(52223)}}, {{A, B, C, X(3531), X(46412)}}, {{A, B, C, X(3542), X(50687)}}, {{A, B, C, X(6995), X(34621)}}, {{A, B, C, X(52188), X(52518)}}

X(54887) = X(262)X(5871)∩X(1503)X(45102)

Barycentrics    15*a^8+4*a^4*b^2*c^2+10*a^6*(b^2+c^2)-18*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(7*b^4+22*b^2*c^2+7*c^4)-4*(4*a^6-2*a^2*(b^2-c^2)^2+a^4*(b^2+c^2)-3*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54887) lies on these lines: {262, 5871}, {1503, 45102}, {1587, 14492}, {5491, 48659}, {5870, 14231}, {6201, 14488}, {10195, 48467}, {13749, 45101}, {14229, 36990}, {14484, 45407}

X(54887) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(2980), X(10261)}}, {{A, B, C, X(3426), X(8946)}}, {{A, B, C, X(15321), X(24244)}}
X(54887) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 45102}

X(54888) = X(262)X(5870)∩X(1503)X(45101)

Barycentrics    15*a^8+4*a^4*b^2*c^2+10*a^6*(b^2+c^2)-18*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(7*b^4+22*b^2*c^2+7*c^4)+4*(4*a^6-2*a^2*(b^2-c^2)^2+a^4*(b^2+c^2)-3*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54888) lies on these lines: {262, 5870}, {1503, 45101}, {1588, 14492}, {5490, 48660}, {5871, 14245}, {6202, 14488}, {10194, 48466}, {13748, 45102}, {14244, 36990}, {14484, 45406}

X(54888) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(2980), X(10262)}}, {{A, B, C, X(3426), X(8948)}}, {{A, B, C, X(15321), X(24243)}}
X(54888) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 45101}

X(54889) = X(1003)X(18841)∩X(5032)X(14458)

Barycentrics    (3*a^4+3*b^4+2*b^2*c^2-9*c^4+2*a^2*(7*b^2+c^2))*(3*a^4-9*b^4+2*b^2*c^2+3*c^4+2*a^2*(b^2+7*c^2)) : :

X(54889) lies on these lines: {1003, 18841}, {5032, 14458}, {10159, 32972}, {18840, 33228}, {32973, 43527}, {37071, 53098}, {41624, 41895}

X(54889) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(428), X(32972)}}, {{A, B, C, X(1003), X(7378)}}, {{A, B, C, X(3228), X(8801)}}, {{A, B, C, X(5032), X(7788)}}, {{A, B, C, X(5064), X(32973)}}, {{A, B, C, X(6995), X(33228)}}, {{A, B, C, X(7409), X(33191)}}, {{A, B, C, X(7714), X(32980)}}, {{A, B, C, X(11160), X(41624)}}, {{A, B, C, X(31133), X(35940)}}, {{A, B, C, X(43098), X(52188)}}

X(54890) = X(2)X(29317)∩X(76)X(3843)

Barycentrics    (3*a^4+3*b^4+b^2*c^2-4*c^4+a^2*(8*b^2+c^2))*(3*a^4-4*b^4+b^2*c^2+3*c^4+a^2*(b^2+8*c^2)) : :

X(54890) lies on these lines: {2, 29317}, {76, 3843}, {83, 3627}, {383, 43548}, {598, 38335}, {671, 14893}, {1080, 43549}, {1513, 53108}, {1657, 43527}, {3399, 22682}, {3850, 10159}, {4045, 18841}, {5395, 51860}, {7612, 9993}, {7900, 43681}, {9302, 14639}, {9748, 47586}, {9751, 48895}, {9755, 53100}, {10302, 23046}, {10841, 36712}, {10842, 36711}, {11606, 41623}, {11668, 13860}, {14458, 53023}, {37463, 43440}, {37464, 43441}

X(54890) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(3843)}}, {{A, B, C, X(54), X(29322)}}, {{A, B, C, X(264), X(21765)}}, {{A, B, C, X(427), X(3627)}}, {{A, B, C, X(468), X(14893)}}, {{A, B, C, X(523), X(29317)}}, {{A, B, C, X(548), X(52285)}}, {{A, B, C, X(842), X(14487)}}, {{A, B, C, X(1173), X(29011)}}, {{A, B, C, X(1494), X(22336)}}, {{A, B, C, X(1657), X(5064)}}, {{A, B, C, X(1799), X(21400)}}, {{A, B, C, X(2980), X(14840)}}, {{A, B, C, X(3108), X(29316)}}, {{A, B, C, X(3425), X(3531)}}, {{A, B, C, X(5094), X(38335)}}, {{A, B, C, X(5481), X(13603)}}, {{A, B, C, X(7249), X(17501)}}, {{A, B, C, X(7378), X(33703)}}, {{A, B, C, X(7409), X(17538)}}, {{A, B, C, X(10301), X(23046)}}, {{A, B, C, X(14388), X(14483)}}, {{A, B, C, X(15321), X(45857)}}, {{A, B, C, X(18575), X(32085)}}, {{A, B, C, X(22728), X(42288)}}, {{A, B, C, X(29180), X(46848)}}, {{A, B, C, X(32473), X(41623)}}, {{A, B, C, X(41513), X(43891)}}
X(54890) = X(i)-vertex conjugate of X(j) for these {i, j}: {3425, 53108}

X(54891) = X(76)X(17800)∩X(83)X(3857)

Barycentrics    (9*a^4+9*b^4-5*b^2*c^2-4*c^4+a^2*(8*b^2-5*c^2))*(9*a^4-4*b^4-5*b^2*c^2+9*c^4+a^2*(-5*b^2+8*c^2)) : :

X(54891) lies on these lines: {76, 17800}, {83, 3857}, {3861, 53109}, {5076, 53105}, {7710, 53098}, {9756, 11668}, {10185, 43460}, {11541, 17131}

X(54891) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(17800)}}, {{A, B, C, X(427), X(3857)}}, {{A, B, C, X(5076), X(37453)}}, {{A, B, C, X(14486), X(43691)}}

X(54892) = X(25)X(53098)∩X(428)X(14494)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(7*a^4+7*b^4-12*b^2*c^2+5*c^4-2*a^2*(7*b^2+6*c^2))*(7*a^4+5*b^4-12*b^2*c^2+7*c^4-2*a^2*(6*b^2+7*c^2)) : :

X(54892) lies on these lines: {25, 53098}, {428, 14494}, {472, 43447}, {473, 43446}, {1585, 43565}, {1586, 43564}, {3543, 13599}, {3839, 40448}, {5064, 7612}, {6995, 7608}, {7378, 7607}, {7408, 53099}, {7409, 43537}, {7714, 10155}, {10185, 52284}, {18840, 52281}, {18841, 52282}, {31363, 50687}, {35884, 53104}, {37174, 43527}

X(54892) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(97), X(52518)}}, {{A, B, C, X(288), X(13452)}}, {{A, B, C, X(3839), X(52280)}}, {{A, B, C, X(5064), X(37174)}}, {{A, B, C, X(6748), X(46952)}}, {{A, B, C, X(6995), X(52281)}}, {{A, B, C, X(7378), X(52282)}}, {{A, B, C, X(11741), X(45302)}}, {{A, B, C, X(22334), X(31626)}}, {{A, B, C, X(31361), X(34287)}}, {{A, B, C, X(31610), X(36809)}}

X(54893) = X(427)X(53098)∩X(428)X(7612)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(5*a^4+7*b^4-12*b^2*c^2+5*c^4-2*a^2*(6*b^2+5*c^2))*(5*a^4+5*b^4-12*b^2*c^2+7*c^4-2*a^2*(5*b^2+6*c^2)) : :

X(54893) lies on these lines: {427, 53098}, {428, 7612}, {472, 43446}, {473, 43447}, {1585, 43564}, {1586, 43565}, {2996, 41628}, {3543, 40448}, {3839, 13599}, {4232, 10185}, {5064, 14494}, {6995, 7607}, {7378, 7608}, {7408, 43537}, {7409, 53099}, {7714, 53103}, {10159, 37174}, {18840, 52282}, {18841, 52281}, {52301, 53859}

X(54893) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(97), X(22334)}}, {{A, B, C, X(193), X(41628)}}, {{A, B, C, X(428), X(37174)}}, {{A, B, C, X(3087), X(30537)}}, {{A, B, C, X(3543), X(52280)}}, {{A, B, C, X(6995), X(52282)}}, {{A, B, C, X(7378), X(52281)}}, {{A, B, C, X(31626), X(52518)}}
X(54893) = polar conjugate of X(3533)
X(54893) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 3533}

X(54894) = X(2)X(53017)∩X(98)X(53016)

Barycentrics    (9*a^6+9*b^6-17*b^4*c^2+15*b^2*c^4-7*c^6-a^4*(b^2+17*c^2)-a^2*(b^4+14*b^2*c^2-15*c^4))*(9*a^6-7*b^6+15*b^4*c^2-17*b^2*c^4+9*c^6-a^4*(17*b^2+c^2)+a^2*(15*b^4-14*b^2*c^2-c^4)) : :

X(54894) lies on these lines: {2, 53017}, {98, 53016}, {1503, 41895}, {3564, 5485}, {5503, 23698}, {7607, 39647}, {7694, 8781}, {9742, 40824}, {13881, 43537}, {14484, 53418}, {17503, 46034}

X(54894) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(393), X(53017)}}, {{A, B, C, X(523), X(47735)}}, {{A, B, C, X(1499), X(3564)}}, {{A, B, C, X(2793), X(23698)}}, {{A, B, C, X(6337), X(31371)}}, {{A, B, C, X(11166), X(14490)}}, {{A, B, C, X(14384), X(38738)}}, {{A, B, C, X(28296), X(28526)}}
X(54894) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 41895}

X(54895) = X(76)X(34725)∩X(262)X(18405)

Barycentrics    (5*a^8+(b^2-c^2)^3*(5*b^2+4*c^2)-a^6*(2*b^2+11*c^2)-a^4*(6*b^4+b^2*c^2-3*c^4)-a^2*(2*b^6+b^4*c^2+4*b^2*c^4-7*c^6))*(5*a^8-a^6*(11*b^2+2*c^2)-(b^2-c^2)^3*(4*b^2+5*c^2)+a^4*(3*b^4-b^2*c^2-6*c^4)+a^2*(7*b^6-4*b^4*c^2-b^2*c^4-2*c^6)) : :

X(54895) lies on these lines: {76, 34725}, {262, 18405}, {3575, 16080}, {7507, 43530}, {10159, 12362}

X(54895) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(34725)}}, {{A, B, C, X(381), X(7507)}}, {{A, B, C, X(428), X(12362)}}, {{A, B, C, X(1179), X(5627)}}, {{A, B, C, X(1494), X(6145)}}, {{A, B, C, X(1989), X(14860)}}, {{A, B, C, X(3515), X(3830)}}, {{A, B, C, X(7576), X(12225)}}, {{A, B, C, X(15077), X(52187)}}, {{A, B, C, X(16263), X(44836)}}, {{A, B, C, X(18405), X(33971)}}, {{A, B, C, X(18434), X(32085)}}, {{A, B, C, X(18560), X(38320)}}, {{A, B, C, X(34288), X(38443)}}, {{A, B, C, X(38305), X(40410)}}

X(54896) = X(20)X(10185)∩X(381)X(53098)

Barycentrics    (17*a^2+17*b^2-19*c^2)*(17*a^2-19*b^2+17*c^2) : :

X(54896) lies on these lines: {20, 10185}, {381, 53098}, {3146, 53859}, {3543, 7607}, {3830, 7612}, {3839, 7608}, {3845, 14494}, {5032, 17503}, {5395, 51185}, {8352, 18840}, {8584, 41895}, {8781, 15300}, {10155, 41099}, {11167, 14976}, {11317, 18841}, {15640, 53104}, {15682, 53103}, {20094, 42010}, {43537, 50687}

X(54896) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3108), X(47060)}}, {{A, B, C, X(3543), X(52282)}}, {{A, B, C, X(3620), X(51185)}}, {{A, B, C, X(3830), X(37174)}}, {{A, B, C, X(3839), X(52281)}}, {{A, B, C, X(5032), X(15533)}}, {{A, B, C, X(6995), X(8352)}}, {{A, B, C, X(7378), X(11317)}}, {{A, B, C, X(8584), X(11160)}}, {{A, B, C, X(8801), X(18818)}}, {{A, B, C, X(15300), X(52450)}}, {{A, B, C, X(46204), X(47735)}}, {{A, B, C, X(50991), X(51171)}}

X(54897) = X(275)X(11317)∩X(2052)X(2052)

Barycentrics    (4*a^8-9*a^6*b^2+a^4*(b^4+13*b^2*c^2-8*c^4)-(b^2-c^2)^2*(5*b^4+b^2*c^2-4*c^4)+a^2*(9*b^6-14*b^4*c^2+13*b^2*c^4))*(4*a^8-9*a^6*c^2+(b^2-c^2)^2*(4*b^4-b^2*c^2-5*c^4)+a^4*(-8*b^4+13*b^2*c^2+c^4)+a^2*(13*b^4*c^2-14*b^2*c^4+9*c^6)) : :

X(54897) lies on these lines: {275, 11317}, {2052, 2052}, {7395, 10185}, {7607, 34664}, {7841, 16080}, {8370, 43530}

X(54897) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(8352)}}, {{A, B, C, X(5), X(11317)}}, {{A, B, C, X(30), X(7841)}}, {{A, B, C, X(381), X(8370)}}, {{A, B, C, X(1093), X(18818)}}, {{A, B, C, X(3534), X(33229)}}, {{A, B, C, X(3543), X(33190)}}, {{A, B, C, X(3830), X(6656)}}, {{A, B, C, X(3845), X(7770)}}, {{A, B, C, X(11001), X(32982)}}, {{A, B, C, X(15682), X(32974)}}, {{A, B, C, X(18550), X(31360)}}, {{A, B, C, X(18848), X(37765)}}, {{A, B, C, X(22466), X(34898)}}, {{A, B, C, X(32971), X(41099)}}, {{A, B, C, X(32979), X(41106)}}, {{A, B, C, X(33230), X(50687)}}, {{A, B, C, X(34664), X(52282)}}

X(54898) = X(4)X(11511)∩X(98)X(34664)

Barycentrics    (a^8-3*a^6*b^2+a^4*(b^4+7*b^2*c^2-2*c^4)-(b^2-c^2)^2*(2*b^4+b^2*c^2-c^4)+a^2*(3*b^6-2*b^4*c^2+7*b^2*c^4))*(a^8-3*a^6*c^2+(b^2-c^2)^2*(b^4-b^2*c^2-2*c^4)+a^4*(-2*b^4+7*b^2*c^2+c^4)+a^2*(7*b^4*c^2-2*b^2*c^4+3*c^6)) : :

X(54898) lies on these lines: {4, 11511}, {98, 34664}, {275, 8370}, {459, 33190}, {2052, 7841}, {6656, 16080}, {7395, 7607}, {7399, 7608}, {7770, 43530}, {8352, 39284}, {10511, 14118}, {16277, 52069}, {33230, 38253}

X(54898) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(7841)}}, {{A, B, C, X(5), X(8370)}}, {{A, B, C, X(20), X(33190)}}, {{A, B, C, X(30), X(6656)}}, {{A, B, C, X(140), X(8352)}}, {{A, B, C, X(141), X(11744)}}, {{A, B, C, X(297), X(34664)}}, {{A, B, C, X(376), X(32974)}}, {{A, B, C, X(381), X(7770)}}, {{A, B, C, X(549), X(33229)}}, {{A, B, C, X(599), X(3532)}}, {{A, B, C, X(1294), X(9229)}}, {{A, B, C, X(1656), X(11317)}}, {{A, B, C, X(3146), X(33230)}}, {{A, B, C, X(3524), X(32982)}}, {{A, B, C, X(3543), X(32956)}}, {{A, B, C, X(3545), X(32971)}}, {{A, B, C, X(3839), X(16045)}}, {{A, B, C, X(4846), X(31360)}}, {{A, B, C, X(5071), X(32979)}}, {{A, B, C, X(6996), X(17677)}}, {{A, B, C, X(7395), X(52282)}}, {{A, B, C, X(7399), X(52281)}}, {{A, B, C, X(7470), X(7924)}}, {{A, B, C, X(15683), X(33232)}}

X(54899) = X(94)X(14041)∩X(5999)X(10511)

Barycentrics    (a^8+a^6*(-2*b^2+c^2)-(b^2-c^2)^2*(2*b^4-c^4)-a^4*(b^4-b^2*c^2+4*c^4)+a^2*(4*b^6-2*b^4*c^2+b^2*c^4+c^6))*(a^8+a^6*(b^2-2*c^2)+(b^2-c^2)^2*(b^4-2*c^4)-a^4*(4*b^4-b^2*c^2+c^4)+a^2*(b^6+b^4*c^2-2*b^2*c^4+4*c^6)) : :

X(54899) lies on these lines: {94, 14041}, {5999, 10511}, {7578, 11361}, {10706, 14458}

X(54899) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(74), X(43098)}}, {{A, B, C, X(186), X(14041)}}, {{A, B, C, X(381), X(9462)}}, {{A, B, C, X(477), X(18023)}}, {{A, B, C, X(3228), X(5627)}}, {{A, B, C, X(4590), X(11564)}}, {{A, B, C, X(5025), X(18559)}}, {{A, B, C, X(7577), X(11361)}}, {{A, B, C, X(13530), X(40429)}}, {{A, B, C, X(14498), X(14910)}}, {{A, B, C, X(16041), X(18533)}}, {{A, B, C, X(18317), X(36882)}}, {{A, B, C, X(42407), X(43949)}}

X(54900) = X(226)X(10710)∩X(1013)X(43530)

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

X(54900) lies on these lines: {226, 10710}, {1013, 43530}, {1446, 52269}, {16080, 37371}

X(54900) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(37371)}}, {{A, B, C, X(103), X(18821)}}, {{A, B, C, X(381), X(1013)}}, {{A, B, C, X(1156), X(2341)}}, {{A, B, C, X(1494), X(37142)}}, {{A, B, C, X(4183), X(52269)}}, {{A, B, C, X(4219), X(17577)}}, {{A, B, C, X(11114), X(37372)}}

X(54901) = X(76)X(3849)∩X(262)X(11645)

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

X(54901) lies on these lines: {76, 3849}, {262, 11645}, {524, 43688}, {543, 10290}, {671, 7766}, {1916, 9830}, {3552, 10159}, {3734, 10302}, {5466, 25423}, {5485, 44367}, {5503, 14931}, {7607, 10033}, {8592, 10811}, {9770, 35005}, {9774, 11669}, {14537, 17503}, {18840, 33007}, {18841, 33006}, {28562, 34475}, {30217, 43674}, {32966, 43527}, {40824, 41136}

X(54901) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(251), X(9939)}}, {{A, B, C, X(263), X(22564)}}, {{A, B, C, X(428), X(3552)}}, {{A, B, C, X(512), X(1383)}}, {{A, B, C, X(524), X(7766)}}, {{A, B, C, X(804), X(9830)}}, {{A, B, C, X(1992), X(44367)}}, {{A, B, C, X(4232), X(52942)}}, {{A, B, C, X(4785), X(28562)}}, {{A, B, C, X(5064), X(32966)}}, {{A, B, C, X(6658), X(7714)}}, {{A, B, C, X(6995), X(33007)}}, {{A, B, C, X(7378), X(33006)}}, {{A, B, C, X(7408), X(32985)}}, {{A, B, C, X(7409), X(32984)}}, {{A, B, C, X(7735), X(41136)}}, {{A, B, C, X(11645), X(23878)}}, {{A, B, C, X(13377), X(18818)}}, {{A, B, C, X(15321), X(36882)}}, {{A, B, C, X(18823), X(45819)}}, {{A, B, C, X(21765), X(35511)}}, {{A, B, C, X(30217), X(52229)}}, {{A, B, C, X(34288), X(46275)}}
X(54901) = trilinear pole of line {45680, 523}

X(54902) = X(262)X(46127)∩X(2986)X(5182)

Barycentrics    (b^2*c^2*(b^2-2*c^2)*(b^2-c^2)^2+a^8*(b^2+c^2)-a^6*(b^4-5*b^2*c^2+4*c^4)-a^4*(b^6+2*b^4*c^2+8*b^2*c^4-5*c^6)+a^2*(b^8+5*b^6*c^2-8*b^4*c^4+8*b^2*c^6-2*c^8))*(-(b^2*c^2*(b^2-c^2)^2*(2*b^2-c^2))+a^8*(b^2+c^2)-a^6*(4*b^4-5*b^2*c^2+c^4)+a^4*(5*b^6-8*b^4*c^2-2*b^2*c^4-c^6)+a^2*(-2*b^8+8*b^6*c^2-8*b^4*c^4+5*b^2*c^6+c^8)) : :

X(54902) lies on these lines: {262, 46127}, {2986, 5182}, {3399, 45284}, {11167, 46777}, {12150, 39295}

X(54902) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(182), X(46127)}}, {{A, B, C, X(3398), X(45284)}}, {{A, B, C, X(5182), X(52451)}}, {{A, B, C, X(11163), X(46777)}}

X(54903) = X(262)X(11648)∩X(3830)X(43535)

Barycentrics    (a^6-2*b^6+8*b^4*c^2-7*b^2*c^4+c^6-a^4*(7*b^2+4*c^2)+a^2*(8*b^4-3*b^2*c^2-4*c^4))*(a^6+b^6-7*b^4*c^2+8*b^2*c^4-2*c^6-a^4*(4*b^2+7*c^2)+a^2*(-4*b^4-3*b^2*c^2+8*c^4)) : :

X(54903) lies on these lines: {262, 11648}, {3830, 43535}, {7607, 11676}, {11167, 18546}, {11172, 15682}, {15980, 43529}, {35930, 43528}

X(54903) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(290), X(18361)}}, {{A, B, C, X(3426), X(9217)}}, {{A, B, C, X(5641), X(11058)}}, {{A, B, C, X(11676), X(52282)}}, {{A, B, C, X(14483), X(30495)}}

X(54904) = X(381)X(42006)∩X(598)X(48884)

Barycentrics    (a^6+b^6+5*b^4*c^2-4*b^2*c^4-2*c^6+a^4*(8*b^2+5*c^2)+a^2*(8*b^4+9*b^2*c^2-4*c^4))*(a^6-2*b^6-4*b^4*c^2+5*b^2*c^4+c^6+a^4*(5*b^2+8*c^2)+a^2*(-4*b^4+9*b^2*c^2+8*c^4)) : :

X(54904) lies on these lines: {381, 42006}, {598, 48884}, {1916, 48657}, {7470, 43527}, {10159, 50977}, {43529, 44230}, {43532, 53023}

X(54904) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5064), X(7470)}}, {{A, B, C, X(8753), X(14487)}}, {{A, B, C, X(13603), X(30495)}}, {{A, B, C, X(32581), X(48884)}}, {{A, B, C, X(36820), X(48657)}}

X(54905) = X(4)X(34624)∩X(76)X(9766)

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

X(54905) lies on these lines: {4, 34624}, {76, 9766}, {83, 8356}, {98, 18583}, {671, 9300}, {2548, 2996}, {3399, 44422}, {3406, 12150}, {3407, 52669}, {3424, 33748}, {5395, 7747}, {7608, 37451}, {7612, 14561}, {7752, 18840}, {7794, 32987}, {8781, 53484}, {9166, 9302}, {9765, 42006}, {10159, 32992}, {11167, 14614}, {11285, 43527}, {11648, 41895}, {13571, 32991}, {14494, 51212}, {18841, 43459}, {33234, 53102}

X(54905) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(9766)}}, {{A, B, C, X(25), X(44543)}}, {{A, B, C, X(249), X(3108)}}, {{A, B, C, X(427), X(8356)}}, {{A, B, C, X(428), X(32992)}}, {{A, B, C, X(524), X(9300)}}, {{A, B, C, X(1016), X(7249)}}, {{A, B, C, X(1031), X(45857)}}, {{A, B, C, X(1509), X(4518)}}, {{A, B, C, X(3815), X(13468)}}, {{A, B, C, X(5064), X(11285)}}, {{A, B, C, X(7714), X(32987)}}, {{A, B, C, X(7752), X(42037)}}, {{A, B, C, X(8556), X(42849)}}, {{A, B, C, X(8889), X(33272)}}, {{A, B, C, X(11163), X(14614)}}, {{A, B, C, X(12150), X(45093)}}, {{A, B, C, X(13377), X(18361)}}, {{A, B, C, X(17980), X(42346)}}, {{A, B, C, X(37451), X(52281)}}, {{A, B, C, X(39968), X(43098)}}, {{A, B, C, X(40410), X(52395)}}
X(54905) = X(i)-cross conjugate of X(j) for these {i, j}: {32473, 99}

X(54906) = X(2)X(5033)∩X(4)X(7856)

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

X(54906) lies on these lines: {2, 5033}, {4, 7856}, {6, 33692}, {32, 2996}, {76, 1003}, {83, 33228}, {98, 39884}, {182, 14494}, {262, 5050}, {671, 5306}, {1078, 18840}, {1916, 5052}, {3399, 13334}, {4027, 35005}, {5182, 8781}, {5503, 41624}, {7607, 37071}, {7787, 18845}, {7807, 10159}, {7887, 43527}, {10302, 26613}, {11602, 12204}, {11603, 12205}, {19687, 43676}, {30505, 42037}, {32477, 51122}, {32981, 43681}

X(54906) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(5033)}}, {{A, B, C, X(25), X(729)}}, {{A, B, C, X(32), X(3053)}}, {{A, B, C, X(95), X(52395)}}, {{A, B, C, X(182), X(5050)}}, {{A, B, C, X(249), X(251)}}, {{A, B, C, X(427), X(33228)}}, {{A, B, C, X(428), X(7807)}}, {{A, B, C, X(524), X(5306)}}, {{A, B, C, X(699), X(42288)}}, {{A, B, C, X(1078), X(42037)}}, {{A, B, C, X(1509), X(52133)}}, {{A, B, C, X(1691), X(5052)}}, {{A, B, C, X(1799), X(12150)}}, {{A, B, C, X(2980), X(9462)}}, {{A, B, C, X(3224), X(36616)}}, {{A, B, C, X(3228), X(32085)}}, {{A, B, C, X(3398), X(13334)}}, {{A, B, C, X(5064), X(7887)}}, {{A, B, C, X(5182), X(51820)}}, {{A, B, C, X(6995), X(33191)}}, {{A, B, C, X(7408), X(33231)}}, {{A, B, C, X(7714), X(32973)}}, {{A, B, C, X(8770), X(14906)}}, {{A, B, C, X(9300), X(13468)}}, {{A, B, C, X(11636), X(47443)}}, {{A, B, C, X(22329), X(41624)}}, {{A, B, C, X(22336), X(36953)}}, {{A, B, C, X(23582), X(40413)}}, {{A, B, C, X(35146), X(41932)}}, {{A, B, C, X(37071), X(52282)}}, {{A, B, C, X(40820), X(47646)}}, {{A, B, C, X(41909), X(45819)}}, {{A, B, C, X(42346), X(47643)}}
X(54906) = trilinear pole of line {52238, 523}
X(54906) = X(i)-vertex conjugate of X(j) for these {i, j}: {83, 47643}
X(54906) = X(i)-cross conjugate of X(j) for these {i, j}: {32472, 99}

X(54907) = X(76)X(41628)∩X(262)X(52397)

Barycentrics    (2*a^6-(b^2-2*c^2)*(b^2-c^2)^2-a^4*(5*b^2+2*c^2)+a^2*(4*b^4-8*b^2*c^2-2*c^4))*(2*a^6+(b^2-c^2)^2*(2*b^2-c^2)-a^4*(2*b^2+5*c^2)-2*a^2*(b^4+4*b^2*c^2-2*c^4)) : :

X(54907) lies on these lines: {76, 41628}, {262, 52397}, {5422, 39284}, {7485, 7608}, {7607, 37990}

X(54907) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(5422)}}, {{A, B, C, X(6), X(41628)}}, {{A, B, C, X(458), X(52397)}}, {{A, B, C, X(7485), X(52281)}}, {{A, B, C, X(30535), X(41435)}}, {{A, B, C, X(37990), X(52282)}}

X(54908) = X(9221)X(16654)∩X(12112)X(14492)

Barycentrics    (2*a^8-(b^2-c^2)^3*(b^2+2*c^2)-a^6*(5*b^2+2*c^2)+a^4*(3*b^4-16*b^2*c^2)+a^2*(b^6+17*b^4*c^2-16*b^2*c^4-2*c^6))*(2*a^8+(b^2-c^2)^3*(2*b^2+c^2)-a^6*(2*b^2+5*c^2)+a^4*(-16*b^2*c^2+3*c^4)+a^2*(-2*b^6-16*b^4*c^2+17*b^2*c^4+c^6)) : :

X(54908) lies on these lines: {9221, 16654}, {12112, 14492}, {16080, 52294}

X(54908) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(13603)}}, {{A, B, C, X(1138), X(32085)}}, {{A, B, C, X(3527), X(48911)}}, {{A, B, C, X(5627), X(15321)}}, {{A, B, C, X(7530), X(18559)}}, {{A, B, C, X(7576), X(37925)}}, {{A, B, C, X(12112), X(16264)}}, {{A, B, C, X(13597), X(30537)}}, {{A, B, C, X(19307), X(43458)}}

X(54909) = X(76)X(34613)∩X(262)X(16658)

Barycentrics    (2*a^8-(b^2-c^2)^3*(b^2+2*c^2)-a^6*(5*b^2+2*c^2)+a^4*(3*b^4-13*b^2*c^2)+a^2*(b^6+14*b^4*c^2-13*b^2*c^4-2*c^6))*(2*a^8+(b^2-c^2)^3*(2*b^2+c^2)-a^6*(2*b^2+5*c^2)+a^4*(-13*b^2*c^2+3*c^4)+a^2*(-2*b^6-13*b^4*c^2+14*b^2*c^4+c^6)) : :

X(54909) lies on these lines: {76, 34613}, {262, 16658}, {5076, 46220}, {10159, 10323}, {10594, 16080}, {11456, 14492}, {15559, 43530}

X(54909) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(34613)}}, {{A, B, C, X(30), X(10594)}}, {{A, B, C, X(381), X(15559)}}, {{A, B, C, X(428), X(10323)}}, {{A, B, C, X(7387), X(7576)}}, {{A, B, C, X(11058), X(45195)}}, {{A, B, C, X(11456), X(16264)}}, {{A, B, C, X(13603), X(16263)}}, {{A, B, C, X(16658), X(33971)}}, {{A, B, C, X(18848), X(46848)}}, {{A, B, C, X(31846), X(45090)}}, {{A, B, C, X(34288), X(46199)}}, {{A, B, C, X(43726), X(45138)}}, {{A, B, C, X(45819), X(46259)}}

X(54910) = X(262)X(10691)∩X(7608)X(16419)

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

X(54910) lies on these lines: {262, 10691}, {7608, 16419}, {10601, 39284}

X(54910) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(288), X(5422)}}, {{A, B, C, X(305), X(39289)}}, {{A, B, C, X(458), X(10691)}}, {{A, B, C, X(3504), X(5943)}}, {{A, B, C, X(16419), X(52281)}}, {{A, B, C, X(17825), X(22334)}}

X(54911) = X(98)X(10691)∩X(598)X(37672)

Barycentrics    (a^6-(b^2-c^2)^2*(2*b^2-c^2)-a^4*(4*b^2+c^2)+a^2*(5*b^4+8*b^2*c^2-c^4))*(a^6+(b^2-2*c^2)*(b^2-c^2)^2-a^4*(b^2+4*c^2)+a^2*(-b^4+8*b^2*c^2+5*c^4)) : :

X(54911) lies on these lines: {98, 10691}, {598, 37672}, {7607, 16419}

X(54911) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(10691)}}, {{A, B, C, X(599), X(37672)}}, {{A, B, C, X(1494), X(42333)}}, {{A, B, C, X(3091), X(32834)}}, {{A, B, C, X(16419), X(52282)}}, {{A, B, C, X(34384), X(35140)}}
X(54911) = trilinear pole of line {44450, 523}
X(54911) = X(i)-Dao conjugate of X(j) for these {i, j}: {233, 34564}
X(54911) = barycentric quotient X(i)/X(j) for these (i, j): {140, 34564}

X(54912) = X(381)X(11140)∩X(3518)X(43530)

Barycentrics    (a^8-a^6*(b^2-2*c^2)-(b^2-c^2)^3*(2*b^2+c^2)-a^4*(3*b^4+8*b^2*c^2+6*c^4)+a^2*(5*b^6+b^4*c^2-8*b^2*c^4+2*c^6))*(a^8+a^6*(2*b^2-c^2)+(b^2-c^2)^3*(b^2+2*c^2)-a^4*(6*b^4+8*b^2*c^2+3*c^4)+a^2*(2*b^6-8*b^4*c^2+b^2*c^4+5*c^6)) : :

X(54912) lies on these lines: {381, 11140}, {3518, 43530}, {7540, 7578}, {14458, 15032}, {16080, 52295}, {18840, 34827}

X(54912) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(52295)}}, {{A, B, C, X(93), X(34288)}}, {{A, B, C, X(381), X(3518)}}, {{A, B, C, X(1141), X(45090)}}, {{A, B, C, X(1173), X(34225)}}, {{A, B, C, X(1494), X(13472)}}, {{A, B, C, X(1989), X(16837)}}, {{A, B, C, X(3447), X(3527)}}, {{A, B, C, X(3545), X(37122)}}, {{A, B, C, X(5576), X(18559)}}, {{A, B, C, X(6344), X(43726)}}, {{A, B, C, X(7540), X(7577)}}, {{A, B, C, X(7547), X(37939)}}, {{A, B, C, X(11058), X(43908)}}, {{A, B, C, X(11816), X(52154)}}, {{A, B, C, X(13490), X(16868)}}, {{A, B, C, X(14865), X(31181)}}, {{A, B, C, X(18349), X(36889)}}, {{A, B, C, X(18361), X(34567)}}

X(54913) = X(2)X(53507)∩X(4)X(11422)

Barycentrics    (2*a^6+(b^2-c^2)^2*(2*b^2-c^2)-a^4*(2*b^2+5*c^2)-2*a^2*(b^4-2*c^4))*(2*a^6-(b^2-2*c^2)*(b^2-c^2)^2-a^4*(5*b^2+2*c^2)+a^2*(4*b^4-2*c^4)) : :

X(54913) lies on these lines: {2, 53507}, {4, 11422}, {98, 31133}, {524, 5392}, {671, 1993}, {858, 7607}, {924, 5466}, {1995, 7608}, {5032, 8796}, {10159, 41238}, {13599, 38323}, {26958, 46201}, {31099, 43537}, {40132, 53098}

X(54913) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(97), X(895)}}, {{A, B, C, X(297), X(31133)}}, {{A, B, C, X(428), X(41238)}}, {{A, B, C, X(524), X(924)}}, {{A, B, C, X(858), X(52282)}}, {{A, B, C, X(1494), X(44175)}}, {{A, B, C, X(1995), X(52281)}}, {{A, B, C, X(3531), X(15066)}}, {{A, B, C, X(3580), X(18434)}}, {{A, B, C, X(5641), X(18018)}}, {{A, B, C, X(9141), X(44176)}}, {{A, B, C, X(16263), X(40427)}}, {{A, B, C, X(20564), X(32002)}}, {{A, B, C, X(37672), X(41628)}}, {{A, B, C, X(42313), X(45835)}}
X(54913) = trilinear pole of line {44214, 523}

X(54914) = X(4)X(11565)∩X(6636)X(7608)

Barycentrics    (2*a^6-(b^2-2*c^2)*(b^2-c^2)^2-a^4*(5*b^2+2*c^2)+a^2*(4*b^4-5*b^2*c^2-2*c^4))*(2*a^6+(b^2-c^2)^2*(2*b^2-c^2)-a^4*(2*b^2+5*c^2)+a^2*(-2*b^4-5*b^2*c^2+4*c^4)) : :

X(54914) lies on these lines: {4, 11565}, {6636, 7608}, {7570, 10185}, {7607, 37353}, {11140, 41628}, {20062, 53099}, {34545, 39284}

X(54914) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(14129)}}, {{A, B, C, X(323), X(44549)}}, {{A, B, C, X(1173), X(1994)}}, {{A, B, C, X(6636), X(52281)}}, {{A, B, C, X(34545), X(36153)}}, {{A, B, C, X(37353), X(52282)}}, {{A, B, C, X(45011), X(45794)}}

X(54915) = X(98)X(8370)∩X(262)X(7841)

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

X(54915) lies on these lines: {98, 8370}, {262, 7841}, {6656, 7608}, {7607, 7770}, {8352, 14492}, {10155, 33230}, {11317, 14458}, {14494, 33190}, {32956, 53098}, {32971, 43537}, {32974, 53099}, {32979, 47586}, {34511, 40824}

X(54915) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(8370)}}, {{A, B, C, X(458), X(7841)}}, {{A, B, C, X(6656), X(52281)}}, {{A, B, C, X(7770), X(52282)}}, {{A, B, C, X(8352), X(52289)}}, {{A, B, C, X(11317), X(11331)}}, {{A, B, C, X(34511), X(40814)}}, {{A, B, C, X(43950), X(46310)}}

X(54916) = X(98)X(7841)∩X(262)X(8370)

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

X(54916) lies on these lines: {98, 7841}, {262, 8370}, {6656, 7607}, {7608, 7770}, {7612, 33190}, {7801, 40824}, {7870, 8781}, {8352, 14458}, {11317, 14492}, {16045, 53098}, {32971, 53099}, {32974, 43537}, {32982, 47586}, {33229, 53100}, {33230, 53103}

X(54916) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(7841)}}, {{A, B, C, X(458), X(8370)}}, {{A, B, C, X(512), X(40802)}}, {{A, B, C, X(2987), X(44557)}}, {{A, B, C, X(6656), X(52282)}}, {{A, B, C, X(7770), X(52281)}}, {{A, B, C, X(7801), X(40814)}}, {{A, B, C, X(7870), X(51481)}}, {{A, B, C, X(8352), X(11331)}}, {{A, B, C, X(11317), X(52289)}}, {{A, B, C, X(14906), X(43950)}}, {{A, B, C, X(30495), X(46310)}}, {{A, B, C, X(33190), X(37174)}}, {{A, B, C, X(37855), X(41238)}}

X(54917) = X(2)X(29323)∩X(4)X(34571)

Barycentrics    (6*a^4-5*b^4-b^2*c^2+6*c^4-a^2*(b^2-10*c^2))*(6*a^4+6*b^4-b^2*c^2-5*c^4+a^2*(10*b^2-c^2)) : :

X(54917) lies on these lines: {2, 29323}, {4, 34571}, {76, 3853}, {671, 35403}, {3858, 43527}, {5073, 7910}, {7861, 18841}, {9754, 53859}, {43460, 53099}

X(54917) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(34571)}}, {{A, B, C, X(25), X(3853)}}, {{A, B, C, X(251), X(46848)}}, {{A, B, C, X(305), X(17505)}}, {{A, B, C, X(428), X(5073)}}, {{A, B, C, X(468), X(35403)}}, {{A, B, C, X(523), X(29323)}}, {{A, B, C, X(1297), X(46851)}}, {{A, B, C, X(3425), X(14490)}}, {{A, B, C, X(3527), X(29316)}}, {{A, B, C, X(3858), X(5064)}}, {{A, B, C, X(5481), X(14487)}}, {{A, B, C, X(7408), X(49138)}}, {{A, B, C, X(9307), X(21765)}}, {{A, B, C, X(18535), X(47095)}}, {{A, B, C, X(22334), X(29011)}}, {{A, B, C, X(29322), X(39955)}}

X(54918) = X(4)X(16279)∩X(98)X(541)

Barycentrics    (a^8-3*a^6*(b^2-c^2)+a^4*(-2*b^4+7*b^2*c^2-8*c^4)-(b^2-c^2)^2*(5*b^4+b^2*c^2-c^4)+a^2*(9*b^6-17*b^4*c^2+7*b^2*c^4+3*c^6))*(a^8+3*a^6*(b^2-c^2)+(b^2-c^2)^2*(b^4-b^2*c^2-5*c^4)+a^4*(-8*b^4+7*b^2*c^2-2*c^4)+a^2*(3*b^6+7*b^4*c^2-17*b^2*c^4+9*c^6)) : :

X(54918) lies on these lines: {4, 16279}, {94, 41135}, {98, 541}, {543, 2986}, {5461, 46201}, {9166, 16080}, {41134, 44877}

X(54918) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(99), X(36889)}}, {{A, B, C, X(115), X(34288)}}, {{A, B, C, X(524), X(52475)}}, {{A, B, C, X(541), X(2799)}}, {{A, B, C, X(4846), X(16279)}}, {{A, B, C, X(11656), X(14356)}}, {{A, B, C, X(36882), X(51480)}}, {{A, B, C, X(46245), X(53201)}}
X(54918) = trilinear pole of line {44569, 523}

X(54919) = X(83)X(38323)∩X(858)X(16080)

Barycentrics    (a^10+3*a^8*c^2-4*a^6*(b^4+b^2*c^2+c^4)-(b^2-c^2)^3*(2*b^4+3*b^2*c^2+c^4)+a^2*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4)+2*a^4*(b^6+b^4*c^2+4*b^2*c^4-2*c^6))*(a^10+3*a^8*b^2-4*a^6*(b^4+b^2*c^2+c^4)+(b^2-c^2)^3*(b^4+3*b^2*c^2+2*c^4)+a^2*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4)+2*a^4*(-2*b^6+4*b^4*c^2+b^2*c^4+c^6)) : :

X(54919) lies on these lines: {83, 38323}, {858, 16080}, {1995, 43530}, {2052, 31133}, {17928, 43527}

X(54919) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(31133)}}, {{A, B, C, X(30), X(858)}}, {{A, B, C, X(95), X(45835)}}, {{A, B, C, X(250), X(895)}}, {{A, B, C, X(265), X(2373)}}, {{A, B, C, X(325), X(47110)}}, {{A, B, C, X(376), X(31099)}}, {{A, B, C, X(381), X(1995)}}, {{A, B, C, X(427), X(38323)}}, {{A, B, C, X(1294), X(18019)}}, {{A, B, C, X(1302), X(6528)}}, {{A, B, C, X(2697), X(30786)}}, {{A, B, C, X(3108), X(22455)}}, {{A, B, C, X(3260), X(16075)}}, {{A, B, C, X(3543), X(16051)}}, {{A, B, C, X(3563), X(5627)}}, {{A, B, C, X(3839), X(40132)}}, {{A, B, C, X(5064), X(17928)}}, {{A, B, C, X(7426), X(10297)}}, {{A, B, C, X(7464), X(10989)}}, {{A, B, C, X(10603), X(43699)}}, {{A, B, C, X(11413), X(34609)}}, {{A, B, C, X(11585), X(34603)}}, {{A, B, C, X(23335), X(52397)}}, {{A, B, C, X(29011), X(48362)}}, {{A, B, C, X(30247), X(44766)}}

X(54920) = X(76)X(5079)∩X(83)X(3530)

Barycentrics    (a^4+b^4-7*b^2*c^2+6*c^4-a^2*(12*b^2+7*c^2))*(a^4+6*b^4-7*b^2*c^2+c^4-a^2*(7*b^2+12*c^2)) : :

X(54920) lies on these lines: {76, 5079}, {83, 3530}, {382, 53107}, {546, 53106}, {547, 10302}, {598, 15681}, {671, 38071}, {3529, 18844}, {9753, 53098}, {15710, 18842}

X(54920) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(5079)}}, {{A, B, C, X(382), X(52298)}}, {{A, B, C, X(427), X(3530)}}, {{A, B, C, X(468), X(38071)}}, {{A, B, C, X(546), X(52297)}}, {{A, B, C, X(547), X(10301)}}, {{A, B, C, X(632), X(52285)}}, {{A, B, C, X(3613), X(11169)}}, {{A, B, C, X(4518), X(13602)}}, {{A, B, C, X(5094), X(15681)}}, {{A, B, C, X(14489), X(43656)}}, {{A, B, C, X(15710), X(52284)}}, {{A, B, C, X(29011), X(39389)}}, {{A, B, C, X(40410), X(45819)}}

X(54921) = X(147)X(10153)∩X(671)X(38747)

Barycentrics    (11*a^4+3*b^4-14*b^2*c^2+11*c^4-2*a^2*(7*b^2+3*c^2))*(11*a^4+11*b^4-14*b^2*c^2+3*c^4-2*a^2*(3*b^2+7*c^2)) : :

X(54921) lies on these lines: {147, 10153}, {671, 38747}, {2996, 21734}, {3091, 18844}, {3146, 53106}, {3832, 53107}, {5485, 15692}, {6055, 46944}, {8781, 10513}, {14494, 14930}, {18841, 46936}, {37689, 43951}, {38253, 52297}

X(54921) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(230), X(10513)}}, {{A, B, C, X(393), X(30542)}}, {{A, B, C, X(632), X(7408)}}, {{A, B, C, X(1297), X(40103)}}, {{A, B, C, X(1383), X(44731)}}, {{A, B, C, X(2165), X(35510)}}, {{A, B, C, X(3146), X(52297)}}, {{A, B, C, X(3832), X(52298)}}, {{A, B, C, X(4232), X(15692)}}, {{A, B, C, X(5054), X(52301)}}, {{A, B, C, X(5070), X(7409)}}, {{A, B, C, X(6353), X(21734)}}, {{A, B, C, X(7378), X(46936)}}, {{A, B, C, X(14930), X(34229)}}, {{A, B, C, X(21448), X(29180)}}, {{A, B, C, X(44556), X(46208)}}, {{A, B, C, X(45819), X(52224)}}, {{A, B, C, X(45838), X(51316)}}

X(54922) = X(98)X(7667)∩X(275)X(37873)

Barycentrics    (a^6-(b^2-c^2)^2*(2*b^2-c^2)-a^4*(4*b^2+c^2)+a^2*(5*b^4+4*b^2*c^2-c^4))*(a^6+(b^2-2*c^2)*(b^2-c^2)^2-a^4*(b^2+4*c^2)+a^2*(-b^4+4*b^2*c^2+5*c^4)) : :

X(54922) lies on these lines: {98, 7667}, {275, 37873}, {317, 8796}, {524, 39284}, {5392, 44149}, {7484, 7607}, {7608, 37439}

X(54922) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(287), X(6664)}}, {{A, B, C, X(297), X(7667)}}, {{A, B, C, X(317), X(44149)}}, {{A, B, C, X(1494), X(34385)}}, {{A, B, C, X(7484), X(52282)}}, {{A, B, C, X(10318), X(30496)}}, {{A, B, C, X(34384), X(35142)}}, {{A, B, C, X(37439), X(52281)}}
X(54922) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 43844}, {48, 21841}
X(54922) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 43844}, {1249, 21841}
X(54922) = barycentric quotient X(i)/X(j) for these (i, j): {3, 43844}, {4, 21841}

X(54923) = X(275)X(50687)∩X(459)X(3839)

Barycentrics    (11*a^8+4*a^6*(-5*b^2+c^2)+4*a^2*(b^2-c^2)^2*(7*b^2+c^2)-(b^2-c^2)^3*(13*b^2+11*c^2)+a^4*(-6*b^4+20*b^2*c^2-30*c^4))*(11*a^8+4*a^6*(b^2-5*c^2)+4*a^2*(b^2-c^2)^2*(b^2+7*c^2)+(b^2-c^2)^3*(11*b^2+13*c^2)+a^4*(-30*b^4+20*b^2*c^2-6*c^4)) : :

X(54923) lies on these lines: {275, 50687}, {381, 38253}, {459, 3839}, {3146, 43530}, {3832, 16080}

X(54923) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(50687)}}, {{A, B, C, X(20), X(3839)}}, {{A, B, C, X(30), X(3832)}}, {{A, B, C, X(376), X(15319)}}, {{A, B, C, X(381), X(1217)}}, {{A, B, C, X(546), X(15683)}}, {{A, B, C, X(1494), X(31371)}}, {{A, B, C, X(3091), X(3543)}}, {{A, B, C, X(3522), X(3845)}}, {{A, B, C, X(3531), X(41894)}}, {{A, B, C, X(3545), X(17578)}}, {{A, B, C, X(3830), X(5068)}}, {{A, B, C, X(3854), X(15682)}}, {{A, B, C, X(3861), X(15705)}}, {{A, B, C, X(4846), X(35510)}}, {{A, B, C, X(5059), X(41099)}}, {{A, B, C, X(7394), X(34621)}}, {{A, B, C, X(7409), X(34664)}}, {{A, B, C, X(14269), X(15717)}}, {{A, B, C, X(14490), X(41891)}}, {{A, B, C, X(14860), X(31361)}}, {{A, B, C, X(15022), X(15687)}}, {{A, B, C, X(16251), X(18550)}}, {{A, B, C, X(16263), X(46208)}}, {{A, B, C, X(21400), X(46412)}}, {{A, B, C, X(22466), X(52188)}}, {{A, B, C, X(32533), X(43970)}}, {{A, B, C, X(34285), X(38445)}}, {{A, B, C, X(34570), X(52518)}}, {{A, B, C, X(36413), X(52452)}}, {{A, B, C, X(38439), X(45838)}}, {{A, B, C, X(41106), X(50690)}}

X(54924) = X(275)X(12101)∩X(3830)X(43530)

Barycentrics    (13*a^8+a^6*(-25*b^2+2*c^2)+a^2*(b^2-c^2)^2*(29*b^2+2*c^2)-(b^2-c^2)^3*(14*b^2+13*c^2)+a^4*(-3*b^4+25*b^2*c^2-30*c^4))*(13*a^8+a^6*(2*b^2-25*c^2)+(b^2-c^2)^3*(13*b^2+14*c^2)+a^2*(b^2-c^2)^2*(2*b^2+29*c^2)+a^4*(-30*b^4+25*b^2*c^2-3*c^4)) : :

X(54924) lies on these lines: {275, 12101}, {3830, 43530}, {3845, 16080}

X(54924) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(12101)}}, {{A, B, C, X(30), X(3845)}}, {{A, B, C, X(381), X(3830)}}, {{A, B, C, X(546), X(33699)}}, {{A, B, C, X(1494), X(18550)}}, {{A, B, C, X(3534), X(14269)}}, {{A, B, C, X(3543), X(18852)}}, {{A, B, C, X(3627), X(3860)}}, {{A, B, C, X(3839), X(15682)}}, {{A, B, C, X(3861), X(19710)}}, {{A, B, C, X(5066), X(15687)}}, {{A, B, C, X(8703), X(14893)}}, {{A, B, C, X(14487), X(34570)}}, {{A, B, C, X(15319), X(18317)}}, {{A, B, C, X(16263), X(46204)}}, {{A, B, C, X(17505), X(43970)}}, {{A, B, C, X(18566), X(44287)}}, {{A, B, C, X(19709), X(38335)}}, {{A, B, C, X(41106), X(50687)}}

X(54925) = X(4)X(2407)∩X(94)X(148)

Barycentrics    (a^8-a^6*(3*b^2+c^2)+a^4*(2*b^4+3*b^2*c^2)-(b^2-c^2)^2*(b^4+b^2*c^2-c^4)+a^2*(b^6-5*b^4*c^2+3*b^2*c^4-c^6))*(a^8-a^6*(b^2+3*c^2)+(b^2-c^2)^2*(b^4-b^2*c^2-c^4)+a^4*(3*b^2*c^2+2*c^4)+a^2*(-b^6+3*b^4*c^2-5*b^2*c^4+c^6)) : :

X(54925) lies on these lines: {4, 2407}, {69, 2394}, {94, 148}, {98, 17702}, {99, 16080}, {115, 2986}, {2482, 46201}, {5466, 36163}, {9003, 9180}, {14061, 44877}, {14223, 46229}, {18366, 20094}, {35923, 43665}, {52552, 52624}

X(54925) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(18879)}}, {{A, B, C, X(30), X(46230)}}, {{A, B, C, X(68), X(15421)}}, {{A, B, C, X(69), X(99)}}, {{A, B, C, X(115), X(2165)}}, {{A, B, C, X(249), X(2693)}}, {{A, B, C, X(265), X(15928)}}, {{A, B, C, X(525), X(16934)}}, {{A, B, C, X(542), X(32833)}}, {{A, B, C, X(543), X(9003)}}, {{A, B, C, X(2799), X(17702)}}, {{A, B, C, X(2857), X(44146)}}, {{A, B, C, X(4230), X(35923)}}, {{A, B, C, X(4235), X(36163)}}, {{A, B, C, X(4590), X(53201)}}, {{A, B, C, X(7799), X(46270)}}, {{A, B, C, X(9293), X(45838)}}, {{A, B, C, X(9513), X(30541)}}, {{A, B, C, X(14907), X(50567)}}, {{A, B, C, X(34208), X(42345)}}, {{A, B, C, X(35922), X(40890)}}, {{A, B, C, X(39450), X(44556)}}, {{A, B, C, X(41174), X(53229)}}, {{A, B, C, X(46250), X(53200)}}, {{A, B, C, X(51254), X(52624)}}
X(54925) = reflection of X(i) in X(j) for these {i,j}: {2986, 115}
X(54925) = trilinear pole of line {11064, 523}
X(54925) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2159, 16319}
X(54925) = X(i)-Dao conjugate of X(j) for these {i, j}: {3163, 16319}
X(54925) = X(i)-cross conjugate of X(j) for these {i, j}: {40879, 2}
X(54925) = barycentric quotient X(i)/X(j) for these (i, j): {30, 16319}, {265, 34310}, {10420, 53776}

X(54926) = X(262)X(31152)∩X(275)X(597)

Barycentrics    (a^6+(b^2-2*c^2)*(b^2-c^2)^2-a^4*(b^2+4*c^2)-a^2*(b^4+12*b^2*c^2-5*c^4))*(a^6-(b^2-c^2)^2*(2*b^2-c^2)-a^4*(4*b^2+c^2)+a^2*(5*b^4-12*b^2*c^2-c^4)) : :

X(54926) lies on these lines: {262, 31152}, {275, 597}, {343, 10302}, {598, 10601}, {5485, 11433}, {7607, 11284}, {7608, 30739}

X(54926) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(343), X(597)}}, {{A, B, C, X(458), X(31152)}}, {{A, B, C, X(599), X(10601)}}, {{A, B, C, X(1494), X(46104)}}, {{A, B, C, X(1992), X(11433)}}, {{A, B, C, X(6524), X(52187)}}, {{A, B, C, X(11284), X(52282)}}, {{A, B, C, X(11744), X(37648)}}, {{A, B, C, X(23292), X(44569)}}, {{A, B, C, X(30739), X(52281)}}, {{A, B, C, X(34545), X(44555)}}, {{A, B, C, X(40410), X(46111)}}

X(54927) = X(2)X(9220)∩X(23)X(7607)

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

X(54927) lies on these lines: {2, 9220}, {4, 45732}, {23, 7607}, {381, 9221}, {598, 34545}, {1992, 13579}, {3830, 18316}, {5169, 7608}, {5392, 44555}, {5485, 45794}, {7519, 43537}, {7552, 43666}, {7578, 53416}, {10185, 52300}, {46105, 52282}

X(54927) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(23), X(52282)}}, {{A, B, C, X(97), X(34802)}}, {{A, B, C, X(323), X(3426)}}, {{A, B, C, X(599), X(34545)}}, {{A, B, C, X(1989), X(9220)}}, {{A, B, C, X(1992), X(45794)}}, {{A, B, C, X(1993), X(44555)}}, {{A, B, C, X(5169), X(52281)}}, {{A, B, C, X(5641), X(44176)}}, {{A, B, C, X(7565), X(52253)}}
X(54927) = trilinear pole of line {44282, 523}

X(54928) = X(2)X(4877)∩X(10)X(1836)

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

X(54928) lies on these lines: {2, 4877}, {10, 1836}, {226, 16777}, {321, 4007}, {329, 6539}, {553, 8808}, {1446, 4654}, {1751, 1901}, {7413, 7607}, {10159, 37445}, {10716, 52167}, {11113, 43531}, {18147, 40012}, {31164, 43675}, {37086, 43527}, {37279, 43530}

X(54928) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(9), X(3715)}}, {{A, B, C, X(27), X(5561)}}, {{A, B, C, X(57), X(28609)}}, {{A, B, C, X(63), X(17098)}}, {{A, B, C, X(79), X(92)}}, {{A, B, C, X(278), X(5556)}}, {{A, B, C, X(329), X(553)}}, {{A, B, C, X(342), X(10400)}}, {{A, B, C, X(381), X(37279)}}, {{A, B, C, X(428), X(37445)}}, {{A, B, C, X(469), X(11113)}}, {{A, B, C, X(967), X(47947)}}, {{A, B, C, X(996), X(39700)}}, {{A, B, C, X(1121), X(5665)}}, {{A, B, C, X(1708), X(31164)}}, {{A, B, C, X(1836), X(23062)}}, {{A, B, C, X(1903), X(39974)}}, {{A, B, C, X(2184), X(3466)}}, {{A, B, C, X(3175), X(18147)}}, {{A, B, C, X(5064), X(37086)}}, {{A, B, C, X(5560), X(40435)}}, {{A, B, C, X(6358), X(8818)}}, {{A, B, C, X(6598), X(42030)}}, {{A, B, C, X(6994), X(50741)}}, {{A, B, C, X(7108), X(10570)}}, {{A, B, C, X(7413), X(52282)}}, {{A, B, C, X(10895), X(40573)}}, {{A, B, C, X(14377), X(30690)}}, {{A, B, C, X(15314), X(39704)}}, {{A, B, C, X(16615), X(40399)}}, {{A, B, C, X(17271), X(19722)}}, {{A, B, C, X(17303), X(42029)}}, {{A, B, C, X(17346), X(37631)}}, {{A, B, C, X(25430), X(33576)}}
X(54928) = trilinear pole of line {47835, 523}

X(54929) = X(2)X(17454)∩X(76)X(3578)

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

X(54929) lies on these lines: {2, 17454}, {10, 41872}, {76, 3578}, {445, 43530}, {3681, 34475}, {4049, 29270}, {6175, 43531}, {18316, 45926}, {32014, 40214}

X(54929) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(41872)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(3578)}}, {{A, B, C, X(8), X(52393)}}, {{A, B, C, X(27), X(4102)}}, {{A, B, C, X(80), X(52374)}}, {{A, B, C, X(81), X(32635)}}, {{A, B, C, X(92), X(43758)}}, {{A, B, C, X(381), X(445)}}, {{A, B, C, X(469), X(6175)}}, {{A, B, C, X(519), X(29270)}}, {{A, B, C, X(553), X(25417)}}, {{A, B, C, X(673), X(49719)}}, {{A, B, C, X(3969), X(52382)}}, {{A, B, C, X(4654), X(5561)}}, {{A, B, C, X(5278), X(37631)}}, {{A, B, C, X(5560), X(30690)}}, {{A, B, C, X(7162), X(39948)}}, {{A, B, C, X(7319), X(15474)}}, {{A, B, C, X(19684), X(49730)}}, {{A, B, C, X(19723), X(42045)}}, {{A, B, C, X(19738), X(49724)}}, {{A, B, C, X(19742), X(50256)}}

X(54930) = X(22)X(43537)∩X(96)X(376)

Barycentrics    (a^6+(b^2-5*c^2)*(b^2-c^2)^2-a^4*(b^2+7*c^2)-a^2*(b^4+2*b^2*c^2-11*c^4))*(a^6-(b^2-c^2)^2*(5*b^2-c^2)-a^4*(7*b^2+c^2)+a^2*(11*b^4-2*b^2*c^2-c^4)) : :

X(54930) lies on these lines: {22, 43537}, {96, 376}, {98, 34608}, {3424, 34603}, {5133, 53099}, {7494, 7607}, {7495, 53859}, {7500, 47586}

X(54930) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(297), X(34608)}}, {{A, B, C, X(324), X(18853)}}, {{A, B, C, X(343), X(15740)}}, {{A, B, C, X(376), X(467)}}, {{A, B, C, X(1993), X(11270)}}, {{A, B, C, X(3545), X(52253)}}, {{A, B, C, X(6340), X(46111)}}, {{A, B, C, X(7494), X(52282)}}, {{A, B, C, X(7714), X(41237)}}, {{A, B, C, X(8800), X(13157)}}, {{A, B, C, X(15077), X(52350)}}, {{A, B, C, X(34603), X(52283)}}

X(54931) = X(459)X(34603)∩X(3543)X(43678)

Barycentrics    (7*a^10+3*a^8*(b^2-3*c^2)+3*a^2*(b^4-c^4)^2-10*a^6*(b^4+c^4)+(b^2-c^2)^3*(7*b^4+12*b^2*c^2+5*c^4)-2*a^4*(5*b^6-9*b^4*c^2+3*b^2*c^4-7*c^6))*(7*a^10+a^8*(-9*b^2+3*c^2)+3*a^2*(b^4-c^4)^2-10*a^6*(b^4+c^4)-(b^2-c^2)^3*(5*b^4+12*b^2*c^2+7*c^4)+2*a^4*(7*b^6-3*b^4*c^2+9*b^2*c^4-5*c^6)) : :

X(54931) lies on these lines: {459, 34603}, {3543, 43678}, {7500, 16080}, {18840, 52069}, {34608, 38253}

X(54931) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(20), X(34603)}}, {{A, B, C, X(22), X(3543)}}, {{A, B, C, X(30), X(7500)}}, {{A, B, C, X(427), X(38445)}}, {{A, B, C, X(3146), X(34608)}}, {{A, B, C, X(3839), X(5133)}}, {{A, B, C, X(6995), X(52069)}}, {{A, B, C, X(7494), X(50687)}}, {{A, B, C, X(15640), X(37900)}}, {{A, B, C, X(15749), X(34168)}}, {{A, B, C, X(18018), X(43699)}}, {{A, B, C, X(34207), X(34570)}}

X(54932) = X(2475)X(16080)∩X(5046)X(43530)

Barycentrics    (3*a^8+a^6*(b-6*c)*c+a^5*b*c*(b+c)+a*b*(b-c)^2*c*(b+c)^3+a^2*c*(b+6*c)*(b^2-c^2)^2+3*(b^2-c^2)^3*(b^2+c^2)-2*a^4*b*(3*b^3+b^2*c-3*b*c^2+c^3)-2*a^3*b*c*(b^3+b^2*c+b*c^2+c^3))*(3*a^8+a^6*b*(-6*b+c)+a^5*b*c*(b+c)+a*b*(b-c)^2*c*(b+c)^3+a^2*b*(6*b+c)*(b^2-c^2)^2-3*(b^2-c^2)^3*(b^2+c^2)-2*a^3*b*c*(b^3+b^2*c+b*c^2+c^3)-2*a^4*c*(b^3-3*b^2*c+b*c^2+3*c^3)) : :

X(54932) lies on these lines: {2475, 16080}, {5046, 43530}

X(54932) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(2475)}}, {{A, B, C, X(65), X(34570)}}, {{A, B, C, X(377), X(3543)}}, {{A, B, C, X(381), X(5046)}}, {{A, B, C, X(443), X(50687)}}, {{A, B, C, X(2478), X(3839)}}, {{A, B, C, X(3845), X(37162)}}, {{A, B, C, X(6175), X(37433)}}, {{A, B, C, X(6839), X(11114)}}, {{A, B, C, X(6840), X(17577)}}, {{A, B, C, X(6894), X(11113)}}, {{A, B, C, X(6895), X(17532)}}, {{A, B, C, X(10431), X(50736)}}, {{A, B, C, X(13729), X(37375)}}, {{A, B, C, X(15677), X(37230)}}, {{A, B, C, X(17579), X(37437)}}, {{A, B, C, X(17677), X(37456)}}, {{A, B, C, X(22466), X(39974)}}

X(54933) = X(2)X(392)∩X(4)X(4277)

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

X(54933) lies on these lines: {2, 392}, {4, 4277}, {10, 21801}, {40, 43531}, {76, 3262}, {98, 32722}, {226, 4424}, {321, 17757}, {536, 5485}, {671, 2783}, {946, 3987}, {1056, 3666}, {1499, 35353}, {1519, 2051}, {4052, 53036}, {4221, 14534}, {4444, 28468}, {5397, 48363}, {5503, 35103}, {5767, 13478}, {5818, 43533}, {17869, 51870}

X(54933) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(3701)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(4277)}}, {{A, B, C, X(12), X(3753)}}, {{A, B, C, X(28), X(30444)}}, {{A, B, C, X(37), X(104)}}, {{A, B, C, X(65), X(517)}}, {{A, B, C, X(72), X(44861)}}, {{A, B, C, X(225), X(5603)}}, {{A, B, C, X(429), X(4221)}}, {{A, B, C, X(536), X(1499)}}, {{A, B, C, X(690), X(2783)}}, {{A, B, C, X(712), X(32472)}}, {{A, B, C, X(740), X(28468)}}, {{A, B, C, X(1000), X(2321)}}, {{A, B, C, X(1056), X(39579)}}, {{A, B, C, X(1065), X(18082)}}, {{A, B, C, X(1243), X(40504)}}, {{A, B, C, X(1245), X(3417)}}, {{A, B, C, X(1441), X(3577)}}, {{A, B, C, X(1519), X(17869)}}, {{A, B, C, X(1826), X(5657)}}, {{A, B, C, X(1869), X(5818)}}, {{A, B, C, X(2746), X(35147)}}, {{A, B, C, X(2793), X(35103)}}, {{A, B, C, X(3656), X(52382)}}, {{A, B, C, X(3666), X(3704)}}, {{A, B, C, X(3667), X(52353)}}, {{A, B, C, X(3671), X(4346)}}, {{A, B, C, X(3695), X(4646)}}, {{A, B, C, X(4082), X(11578)}}, {{A, B, C, X(5886), X(15320)}}, {{A, B, C, X(11231), X(23959)}}, {{A, B, C, X(14493), X(20336)}}, {{A, B, C, X(14497), X(15065)}}, {{A, B, C, X(15232), X(26446)}}, {{A, B, C, X(30713), X(44733)}}, {{A, B, C, X(37619), X(52567)}}, {{A, B, C, X(43733), X(45104)}}, {{A, B, C, X(43917), X(44835)}}
X(54933) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 956}, {81, 2267}
X(54933) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 956}, {40586, 2267}
X(54933) = barycentric product X(i)*X(j) for these (i, j): {321, 957}, {32722, 850}
X(54933) = barycentric quotient X(i)/X(j) for these (i, j): {37, 956}, {42, 2267}, {957, 81}, {32722, 110}

X(54934) = X(76)X(15681)∩X(83)X(38071)

Barycentrics    (11*a^4+11*b^4-7*b^2*c^2-4*c^4+a^2*(8*b^2-7*c^2))*(11*a^4-4*b^4-7*b^2*c^2+11*c^4+a^2*(-7*b^2+8*c^2)) : :

X(54934) lies on these lines: {76, 15681}, {83, 38071}, {1503, 53108}, {3530, 10159}, {5079, 43527}, {8703, 10302}, {14269, 53107}, {15687, 53106}, {15710, 18840}

X(54934) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(25), X(15681)}}, {{A, B, C, X(427), X(38071)}}, {{A, B, C, X(428), X(3530)}}, {{A, B, C, X(547), X(52285)}}, {{A, B, C, X(2980), X(11058)}}, {{A, B, C, X(5064), X(5079)}}, {{A, B, C, X(6995), X(15710)}}, {{A, B, C, X(8703), X(10301)}}, {{A, B, C, X(14269), X(52298)}}, {{A, B, C, X(15687), X(52297)}}, {{A, B, C, X(18361), X(32085)}}
X(54934) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 53108}

X(54935) = X(2)X(45542)∩X(262)X(13748)

Barycentrics    3*a^8+a^4*b^2*c^2+4*a^6*(b^2+c^2)-6*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(b^4+7*b^2*c^2+c^4)+(8*a^6-4*a^2*(b^2-c^2)^2+2*a^4*(b^2+c^2)-6*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54935) lies on these lines: {2, 45542}, {262, 13748}, {486, 9873}, {1503, 14245}, {3071, 14492}, {3590, 45511}, {5870, 45101}, {13749, 14240}, {14231, 14233}, {14238, 36990}, {14488, 45441}, {45106, 45407}

X(54935) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(264), X(10262)}}, {{A, B, C, X(13603), X(32420)}}
X(54935) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14245}

X(54936) = X(2)X(45543)∩X(262)X(13749)

Barycentrics    3*a^8+a^4*b^2*c^2+4*a^6*(b^2+c^2)-6*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(b^4+7*b^2*c^2+c^4)+(-8*a^6+4*a^2*(b^2-c^2)^2-2*a^4*(b^2+c^2)+6*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54936) lies on these lines: {2, 45543}, {262, 13749}, {485, 9873}, {1503, 14231}, {3070, 14492}, {3591, 45510}, {5871, 45102}, {13748, 14236}, {14230, 14245}, {14234, 36990}, {14488, 45440}, {45107, 45406}

X(54936) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(264), X(10261)}}, {{A, B, C, X(13603), X(32422)}}
X(54936) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 14231}

X(54937) = X(2)X(16626)∩X(13)X(22832)

Barycentrics    3*(2*a^10-5*a^8*(b^2+c^2)-2*a^4*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+2*a^2*(b^4-c^4)^2+4*a^6*(b^4+c^4))+sqrt(3)*(a^8-5*a^6*(b^2+c^2)+11*a^2*(b^2-c^2)^2*(b^2+c^2)-3*a^4*(b^4-b^2*c^2+c^4)-(b^2-c^2)^2*(4*b^4-11*b^2*c^2+4*c^4))*S : :

X(54937) lies on these lines: {2, 16626}, {13, 22832}, {14, 52838}, {18, 44666}, {262, 5339}, {5365, 43953}, {5488, 5965}, {6776, 43556}, {8550, 21845}, {12817, 51754}, {42999, 43954}

X(54937) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(54), X(16459)}}, {{A, B, C, X(95), X(11139)}}, {{A, B, C, X(2993), X(8741)}}, {{A, B, C, X(3443), X(11060)}}, {{A, B, C, X(5965), X(30216)}}, {{A, B, C, X(8737), X(41897)}}, {{A, B, C, X(8884), X(14373)}}, {{A, B, C, X(11138), X(32085)}}

X(54938) = X(2)X(16627)∩X(13)X(52839)

Barycentrics    sqrt(3)*(2*a^10-5*a^8*(b^2+c^2)-2*a^4*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)+2*a^2*(b^4-c^4)^2+4*a^6*(b^4+c^4))+(-a^8+5*a^6*(b^2+c^2)-11*a^2*(b^2-c^2)^2*(b^2+c^2)+3*a^4*(b^4-b^2*c^2+c^4)+(b^2-c^2)^2*(4*b^4-11*b^2*c^2+4*c^4))*S : :

X(54938) lies on these lines: {2, 16627}, {13, 52839}, {14, 22831}, {17, 44667}, {262, 5340}, {5366, 43954}, {5487, 5965}, {6776, 43557}, {8550, 21846}, {12816, 51753}, {42998, 43953}

X(54938) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(54), X(16460)}}, {{A, B, C, X(95), X(11138)}}, {{A, B, C, X(2992), X(8742)}}, {{A, B, C, X(3442), X(11060)}}, {{A, B, C, X(5965), X(30215)}}, {{A, B, C, X(8738), X(41898)}}, {{A, B, C, X(8884), X(14372)}}, {{A, B, C, X(11139), X(32085)}}

X(54939) = X(1503)X(43954)∩X(3146)X(5487)

Barycentrics    13*a^8+4*a^4*b^2*c^2+14*a^6*(b^2+c^2)-22*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(5*b^4+26*b^2*c^2+5*c^4)+4*sqrt(3)*(4*a^6-2*a^2*(b^2-c^2)^2+a^4*(b^2+c^2)-3*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54939) lies on these lines: {1503, 43954}, {3146, 5487}, {3543, 11121}, {5334, 14492}, {41038, 43953}, {43446, 52689}, {43538, 44459}

X(54939) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(64), X(34533)}}, {{A, B, C, X(66), X(11080)}}, {{A, B, C, X(2993), X(52187)}}, {{A, B, C, X(3426), X(3457)}}, {{A, B, C, X(8737), X(36889)}}
X(54939) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 43954}

X(54940) = X(1503)X(43953)∩X(3146)X(5488)

Barycentrics    13*a^8+4*a^4*b^2*c^2+14*a^6*(b^2+c^2)-22*a^2*(b^2-c^2)^2*(b^2+c^2)-(b^2-c^2)^2*(5*b^4+26*b^2*c^2+5*c^4)-4*sqrt(3)*(4*a^6-2*a^2*(b^2-c^2)^2+a^4*(b^2+c^2)-3*(b^2-c^2)^2*(b^2+c^2))*S : :

X(54940) lies on these lines: {1503, 43953}, {3146, 5488}, {3543, 11122}, {5335, 14492}, {41039, 43954}, {43447, 52688}, {43539, 44463}

X(54940) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(64), X(34534)}}, {{A, B, C, X(66), X(11085)}}, {{A, B, C, X(2992), X(52187)}}, {{A, B, C, X(3426), X(3458)}}, {{A, B, C, X(8738), X(36889)}}
X(54940) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 43953}

X(54941) = X(2)X(1514)∩X(2986)X(3543)

Barycentrics    (5*a^8+a^6*(-8*b^2+4*c^2)-(b^2-c^2)^3*(7*b^2+5*c^2)-2*a^4*(3*b^4-16*b^2*c^2+9*c^4)+4*a^2*(4*b^6-13*b^4*c^2+8*b^2*c^4+c^6))*(5*a^8+4*a^6*(b^2-2*c^2)+(b^2-c^2)^3*(5*b^2+7*c^2)-2*a^4*(9*b^4-16*b^2*c^2+3*c^4)+4*a^2*(b^6+8*b^4*c^2-13*b^2*c^4+4*c^6)) : :

X(54941) lies on these lines: {2, 1514}, {2986, 3543}, {3839, 34289}, {6623, 16080}

X(54941) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(393)}}, {{A, B, C, X(253), X(5627)}}, {{A, B, C, X(376), X(9307)}}, {{A, B, C, X(378), X(3839)}}, {{A, B, C, X(381), X(8801)}}, {{A, B, C, X(403), X(3543)}}, {{A, B, C, X(1494), X(35512)}}, {{A, B, C, X(1989), X(18850)}}, {{A, B, C, X(3426), X(8749)}}, {{A, B, C, X(4846), X(52187)}}, {{A, B, C, X(10419), X(11738)}}, {{A, B, C, X(11744), X(34288)}}, {{A, B, C, X(16251), X(51967)}}, {{A, B, C, X(17703), X(18846)}}, {{A, B, C, X(22466), X(48911)}}, {{A, B, C, X(45088), X(52188)}}

X(54942) = X(2)X(12112)∩X(3543)X(13582)

Barycentrics    (a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+2*a^4*(3*b^4-7*b^2*c^2+3*c^4)-2*a^2*(2*b^6+7*b^4*c^2-11*b^2*c^4+2*c^6))*(a^8+(b^2-c^2)^4-4*a^6*(b^2+c^2)+2*a^4*(3*b^4-7*b^2*c^2+3*c^4)-2*a^2*(2*b^6-11*b^4*c^2+7*b^2*c^4+2*c^6)) : :

X(54942) lies on these lines: {2, 12112}, {3543, 13582}, {3830, 13579}, {5656, 9221}, {6504, 15682}, {34621, 43681}

X(54942) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(2980)}}, {{A, B, C, X(64), X(18317)}}, {{A, B, C, X(66), X(5627)}}, {{A, B, C, X(74), X(34288)}}, {{A, B, C, X(381), X(15321)}}, {{A, B, C, X(393), X(841)}}, {{A, B, C, X(1173), X(46412)}}, {{A, B, C, X(1217), X(46212)}}, {{A, B, C, X(1989), X(3426)}}, {{A, B, C, X(2165), X(13603)}}, {{A, B, C, X(3088), X(41106)}}, {{A, B, C, X(3089), X(11001)}}, {{A, B, C, X(3431), X(52187)}}, {{A, B, C, X(3531), X(30537)}}, {{A, B, C, X(3541), X(41099)}}, {{A, B, C, X(3542), X(15682)}}, {{A, B, C, X(3543), X(37943)}}, {{A, B, C, X(3830), X(7505)}}, {{A, B, C, X(3845), X(37119)}}, {{A, B, C, X(6344), X(36889)}}, {{A, B, C, X(13597), X(45088)}}, {{A, B, C, X(14490), X(52154)}}, {{A, B, C, X(14491), X(52188)}}, {{A, B, C, X(16835), X(46204)}}, {{A, B, C, X(20421), X(52223)}}, {{A, B, C, X(35481), X(44275)}}

X(54943) = X(94)X(3543)∩X(459)X(18559)

Barycentrics    (7*a^8-4*a^6*(b^2+4*c^2)+(b^2-c^2)^3*(7*b^2+5*c^2)+a^4*(-6*b^4+4*b^2*c^2+6*c^4)-4*a^2*(b^6-b^4*c^2+2*b^2*c^4-2*c^6))*(7*a^8-4*a^6*(4*b^2+c^2)-(b^2-c^2)^3*(5*b^2+7*c^2)+a^4*(6*b^4+4*b^2*c^2-6*c^4)+4*a^2*(2*b^6-2*b^4*c^2+b^2*c^4-c^6)) : :

X(54943) lies on these lines: {94, 3543}, {459, 18559}, {3839, 7578}, {16080, 18533}

X(54943) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(20), X(18559)}}, {{A, B, C, X(30), X(66)}}, {{A, B, C, X(68), X(18361)}}, {{A, B, C, X(186), X(3543)}}, {{A, B, C, X(253), X(1138)}}, {{A, B, C, X(254), X(38443)}}, {{A, B, C, X(265), X(34288)}}, {{A, B, C, X(328), X(43699)}}, {{A, B, C, X(376), X(16774)}}, {{A, B, C, X(381), X(2165)}}, {{A, B, C, X(393), X(5627)}}, {{A, B, C, X(1179), X(15749)}}, {{A, B, C, X(1300), X(36889)}}, {{A, B, C, X(1494), X(16263)}}, {{A, B, C, X(1989), X(18434)}}, {{A, B, C, X(2980), X(12028)}}, {{A, B, C, X(3091), X(3459)}}, {{A, B, C, X(3426), X(14910)}}, {{A, B, C, X(3830), X(35486)}}, {{A, B, C, X(3839), X(7577)}}, {{A, B, C, X(5962), X(52149)}}, {{A, B, C, X(6145), X(11058)}}, {{A, B, C, X(7576), X(18124)}}, {{A, B, C, X(13452), X(31361)}}, {{A, B, C, X(15619), X(32533)}}, {{A, B, C, X(15682), X(37460)}}, {{A, B, C, X(18532), X(34570)}}, {{A, B, C, X(34449), X(38436)}}, {{A, B, C, X(38445), X(43917)}}

X(54944) = X(2)X(1533)∩X(275)X(1515)

Barycentrics    (a^8-a^6*(b^2-2*c^2)-(b^2-c^2)^3*(2*b^2+c^2)+a^4*(-3*b^4+25*b^2*c^2-6*c^4)+a^2*(5*b^6-32*b^4*c^2+25*b^2*c^4+2*c^6))*(a^8+a^6*(2*b^2-c^2)+(b^2-c^2)^3*(b^2+2*c^2)+a^4*(-6*b^4+25*b^2*c^2-3*c^4)+a^2*(2*b^6+25*b^4*c^2-32*b^2*c^4+5*c^6)) : :

X(54944) lies on these lines: {2, 1533}, {275, 1515}, {1514, 14492}, {1596, 16080}, {1597, 43530}

X(54944) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(1533)}}, {{A, B, C, X(53), X(1515)}}, {{A, B, C, X(64), X(18361)}}, {{A, B, C, X(376), X(52223)}}, {{A, B, C, X(381), X(1597)}}, {{A, B, C, X(841), X(5627)}}, {{A, B, C, X(1294), X(34288)}}, {{A, B, C, X(1494), X(3426)}}, {{A, B, C, X(1514), X(16264)}}, {{A, B, C, X(7576), X(47096)}}, {{A, B, C, X(11058), X(15319)}}, {{A, B, C, X(15687), X(37942)}}, {{A, B, C, X(35512), X(52187)}}

X(54945) = X(6756)X(16080)∩X(14488)X(18396)

Barycentrics    (5*a^8-a^6*(11*b^2+2*c^2)-(b^2-c^2)^3*(4*b^2+5*c^2)+a^4*(3*b^4-13*b^2*c^2-6*c^4)+a^2*(7*b^6+8*b^4*c^2-13*b^2*c^4-2*c^6))*(5*a^8+(b^2-c^2)^3*(5*b^2+4*c^2)-a^6*(2*b^2+11*c^2)+a^4*(-6*b^4-13*b^2*c^2+3*c^4)+a^2*(-2*b^6-13*b^4*c^2+8*b^2*c^4+7*c^6)) : :

X(54945) lies on these lines: {6756, 16080}, {14488, 18396}

X(54945) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(6756)}}, {{A, B, C, X(1294), X(15321)}}, {{A, B, C, X(3517), X(3830)}}, {{A, B, C, X(11058), X(14863)}}, {{A, B, C, X(14979), X(46848)}}, {{A, B, C, X(15319), X(34288)}}, {{A, B, C, X(18361), X(38433)}}, {{A, B, C, X(18494), X(34726)}}, {{A, B, C, X(38442), X(52187)}}

X(54946) = X(226)X(3749)∩X(262)X(3332)

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

X(54946) lies on these lines: {226, 3749}, {262, 3332}, {4080, 20075}, {6776, 43672}, {18840, 36489}, {18841, 36473}, {32022, 36526}

X(54946) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(3749)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(55), X(29242)}}, {{A, B, C, X(1002), X(15323)}}, {{A, B, C, X(2726), X(40154)}}, {{A, B, C, X(3332), X(33971)}}, {{A, B, C, X(4196), X(36526)}}, {{A, B, C, X(4207), X(36474)}}, {{A, B, C, X(6995), X(36489)}}, {{A, B, C, X(7378), X(36473)}}, {{A, B, C, X(7408), X(36484)}}, {{A, B, C, X(18490), X(48257)}}, {{A, B, C, X(28076), X(49127)}}, {{A, B, C, X(29330), X(30651)}}

X(54947) = (name pending)

Barycentrics    (a^5+a^4*(b+c)+(b-c)^2*(b+c)^3-a^3*(2*b^2+9*b*c+2*c^2)-2*a^2*(b^3+b^2*c+b*c^2+c^3)+a*(b^4+9*b^3*c-2*b^2*c^2-9*b*c^3+c^4))*(a^5+a^4*(b+c)+(b-c)^2*(b+c)^3-a^3*(2*b^2+9*b*c+2*c^2)-2*a^2*(b^3+b^2*c+b*c^2+c^3)+a*(b^4-9*b^3*c-2*b^2*c^2+9*b*c^3+c^4)) : :

X(54947) lies on these lines: {1029, 3830}

X(54947) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(13603)}}, {{A, B, C, X(74), X(39974)}}, {{A, B, C, X(104), X(24857)}}, {{A, B, C, X(406), X(15682)}}, {{A, B, C, X(451), X(3830)}}, {{A, B, C, X(475), X(41099)}}, {{A, B, C, X(941), X(11738)}}, {{A, B, C, X(1389), X(24858)}}, {{A, B, C, X(3531), X(39960)}}, {{A, B, C, X(3845), X(52252)}}, {{A, B, C, X(4194), X(11001)}}, {{A, B, C, X(4200), X(41106)}}, {{A, B, C, X(14483), X(39982)}}, {{A, B, C, X(14487), X(39798)}}

X(54948) = X(99)X(52775)∩X(648)X(42381)

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

X(54948) lies on these lines: {99, 52775}, {648, 42381}, {34406, 46137}, {35169, 36118}, {35174, 52938}

X(54948) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}
X(54948) = X(i)-isoconjugate-of-X(j) for these {i, j}: {663, 53850}, {2638, 53279}, {36054, 40968}
X(54948) = X(i)-cross conjugate of X(j) for these {i, j}: {52775, 42381}
X(54948) = barycentric product X(i)*X(j) for these (i, j): {13149, 34406}, {42381, 69}, {52775, 76}
X(54948) = barycentric quotient X(i)/X(j) for these (i, j): {651, 53850}, {13149, 41004}, {23984, 53279}, {36118, 26934}, {36127, 40968}, {42381, 4}, {52775, 6}

X(54949) = X(99)X(52777)∩X(671)X(27377)

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

X(54949) lies on these lines: {99, 52777}, {648, 42393}, {671, 27377}, {18831, 53351}

X(54949) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(27364), X(35360)}}
X(54949) = X(i)-isoconjugate-of-X(j) for these {i, j}: {822, 53418}
X(54949) = X(i)-cross conjugate of X(j) for these {i, j}: {5094, 23582}, {52777, 42393}
X(54949) = barycentric product X(i)*X(j) for these (i, j): {42393, 69}, {52777, 76}
X(54949) = barycentric quotient X(i)/X(j) for these (i, j): {107, 53418}, {42393, 4}, {52777, 6}

X(54950) = TRILINEAR POLE OF LINE {2, 276}

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

X(54950) lies on these lines: {99, 52779}, {290, 8795}, {648, 42401}, {2966, 16813}, {3228, 8794}, {6528, 42369}, {46151, 53196}

X(54950) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(6368), X(42331)}}, {{A, B, C, X(8795), X(16813)}}, {{A, B, C, X(16039), X(42355)}}, {{A, B, C, X(18315), X(41208)}}
X(54950) = trilinear pole of line {2, 276}
X(54950) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 42293}, {217, 822}, {418, 810}, {656, 44088}, {2179, 32320}, {9247, 17434}, {15451, 52430}, {32676, 41219}, {42080, 52604}
X(54950) = X(i)-Dao conjugate of X(j) for these {i, j}: {338, 41212}, {1249, 42293}, {15526, 41219}, {39062, 418}, {40596, 44088}
X(54950) = X(i)-Ceva conjugate of X(j) for these {i, j}: {42369, 42401}
X(54950) = X(i)-cross conjugate of X(j) for these {i, j}: {6528, 42405}, {42331, 264}, {52779, 42401}
X(54950) = barycentric product X(i)*X(j) for these (i, j): {3, 42369}, {264, 42405}, {276, 6528}, {670, 8794}, {6331, 8795}, {15352, 34384}, {16813, 18022}, {18027, 18831}, {42401, 69}, {52779, 76}
X(54950) = barycentric quotient X(i)/X(j) for these (i, j): {4, 42293}, {95, 32320}, {107, 217}, {112, 44088}, {264, 17434}, {275, 39201}, {276, 520}, {324, 34983}, {525, 41219}, {648, 418}, {933, 14585}, {2052, 15451}, {6331, 5562}, {6528, 216}, {6529, 40981}, {8794, 512}, {8795, 647}, {8884, 3049}, {15352, 51}, {15412, 34980}, {15958, 36433}, {16813, 184}, {18027, 6368}, {18314, 41212}, {18315, 23606}, {18831, 577}, {34384, 52613}, {34538, 52604}, {35360, 46394}, {36126, 2179}, {40440, 822}, {41210, 52177}, {42369, 264}, {42401, 4}, {42405, 3}, {43752, 1636}, {52779, 6}, {52939, 19210}

X(54951) = X(190)X(4558)∩X(648)X(4556)

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

X(54951) lies on these lines: {86, 34393}, {190, 4558}, {648, 4556}, {662, 32038}, {668, 4592}, {671, 13478}, {1121, 19607}, {1414, 18026}, {1494, 17378}, {2217, 18827}, {2995, 14616}, {10570, 35141}, {15232, 35162}, {17731, 35149}, {33295, 35164}, {37792, 53193}

X(54951) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(110), X(36037)}}, {{A, B, C, X(112), X(2363)}}, {{A, B, C, X(658), X(4563)}}, {{A, B, C, X(925), X(1897)}}, {{A, B, C, X(1414), X(4556)}}, {{A, B, C, X(2407), X(17378)}}, {{A, B, C, X(3565), X(36086)}}, {{A, B, C, X(5545), X(36048)}}, {{A, B, C, X(6578), X(18315)}}, {{A, B, C, X(7257), X(47318)}}, {{A, B, C, X(32653), X(36050)}}
X(54951) = trilinear pole of line {2, 572}
X(54951) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 52310}, {37, 6589}, {42, 21189}, {512, 3869}, {513, 22276}, {523, 3185}, {573, 661}, {649, 21078}, {650, 40590}, {656, 3192}, {798, 4417}, {810, 17555}, {1500, 16754}, {2501, 22134}, {3709, 17080}, {4041, 10571}, {4225, 4705}, {4559, 38345}, {34242, 53562}, {40452, 42661}, {42664, 53081}
X(54951) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 52310}, {5375, 21078}, {31998, 4417}, {36830, 573}, {39026, 22276}, {39054, 3869}, {39062, 17555}, {40589, 6589}, {40592, 21189}, {40596, 3192}, {40625, 124}
X(54951) = X(i)-cross conjugate of X(j) for these {i, j}: {109, 662}, {10446, 18020}, {37683, 4590}
X(54951) = barycentric product X(i)*X(j) for these (i, j): {274, 36050}, {310, 32653}, {2217, 799}, {2995, 662}, {10570, 4573}, {13478, 99}, {15232, 4610}, {17206, 26704}, {19607, 664}, {44765, 86}
X(54951) = barycentric quotient X(i)/X(j) for these (i, j): {3, 52310}, {58, 6589}, {81, 21189}, {99, 4417}, {100, 21078}, {101, 22276}, {109, 40590}, {110, 573}, {112, 3192}, {163, 3185}, {648, 17555}, {662, 3869}, {757, 16754}, {1414, 17080}, {2217, 661}, {2995, 1577}, {3737, 38345}, {4556, 4225}, {4560, 124}, {4563, 51612}, {4565, 10571}, {4575, 22134}, {10570, 3700}, {13478, 523}, {15232, 4024}, {15386, 4559}, {19607, 522}, {23189, 47411}, {26704, 1826}, {32653, 42}, {36050, 37}, {44765, 10}, {52310, 52308}, {53082, 47842}

X(54952) = TRILINEAR POLE OF LINE {2, 219}

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

X(54952) lies on these lines: {99, 15439}, {100, 18026}, {190, 4587}, {331, 11517}, {648, 4552}, {664, 1331}, {668, 4571}, {943, 2481}, {1121, 40435}, {1414, 53649}, {1793, 14616}, {1808, 18827}, {1809, 18816}, {1810, 35160}, {2982, 3227}, {4569, 6516}, {4998, 35156}, {6528, 36797}, {6648, 32651}, {35139, 46405}, {45393, 46133}

X(54952) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(21), X(43344)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(100), X(1331)}}, {{A, B, C, X(645), X(51566)}}, {{A, B, C, X(651), X(1305)}}, {{A, B, C, X(655), X(4566)}}, {{A, B, C, X(811), X(13136)}}, {{A, B, C, X(927), X(1414)}}, {{A, B, C, X(1783), X(44876)}}, {{A, B, C, X(4561), X(6335)}}, {{A, B, C, X(7259), X(36802)}}
X(54952) = trilinear pole of line {2, 219}
X(54952) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 52306}, {55, 50354}, {57, 33525}, {513, 14547}, {522, 40956}, {647, 46884}, {649, 40937}, {650, 2260}, {652, 1841}, {661, 46882}, {663, 942}, {667, 6734}, {1459, 1859}, {1838, 1946}, {2194, 23752}, {2294, 7252}, {3063, 5249}, {3064, 14597}, {3733, 40967}, {3737, 40952}, {4017, 8021}, {4303, 18344}, {4560, 40978}, {7004, 53323}, {7649, 23207}, {8611, 46890}, {8648, 45926}, {23595, 52425}, {51641, 51978}
X(54952) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 52306}, {223, 50354}, {1214, 23752}, {5375, 40937}, {5452, 33525}, {6631, 6734}, {10001, 5249}, {34961, 8021}, {36830, 46882}, {39007, 41214}, {39026, 14547}, {39052, 46884}, {39053, 1838}
X(54952) = X(i)-Zayin conjugate of X(j) for these {i, j}: {2954, 649}
X(54952) = X(i)-cross conjugate of X(j) for these {i, j}: {21, 4564}, {72, 46102}, {1441, 4998}, {3219, 1275}, {34772, 1016}
X(54952) = barycentric product X(i)*X(j) for these (i, j): {312, 36048}, {1794, 46404}, {2259, 4572}, {2982, 668}, {4554, 943}, {15439, 76}, {32651, 3596}, {40412, 4552}, {40422, 651}, {40435, 664}, {40447, 6516}, {40573, 4561}, {52560, 645}
X(54952) = barycentric quotient X(i)/X(j) for these (i, j): {3, 52306}, {55, 33525}, {57, 50354}, {100, 40937}, {101, 14547}, {108, 1841}, {109, 2260}, {110, 46882}, {162, 46884}, {190, 6734}, {226, 23752}, {273, 23595}, {645, 51978}, {651, 942}, {653, 1838}, {655, 45926}, {664, 5249}, {906, 23207}, {943, 650}, {1018, 40967}, {1175, 7252}, {1415, 40956}, {1783, 1859}, {1794, 652}, {1813, 4303}, {2259, 663}, {2982, 513}, {4551, 2294}, {4552, 442}, {4559, 40952}, {5546, 8021}, {6516, 18607}, {7115, 53323}, {14775, 8735}, {15439, 6}, {23067, 18591}, {32651, 56}, {35320, 1953}, {36048, 57}, {36059, 14597}, {40412, 4560}, {40422, 4391}, {40435, 522}, {40447, 44426}, {40572, 8676}, {40573, 7649}, {52306, 41214}, {52560, 7178}, {52610, 39791}

X(54953) = TRILINEAR POLE OF LINE {2, 222}

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

X(54953) lies on these lines: {1, 53209}, {7, 46136}, {56, 53218}, {65, 35151}, {85, 35164}, {99, 2720}, {104, 927}, {109, 48325}, {190, 1813}, {241, 46804}, {320, 34393}, {331, 53786}, {648, 4560}, {651, 44550}, {664, 4025}, {666, 2401}, {668, 4998}, {693, 934}, {903, 17078}, {905, 46102}, {1121, 34234}, {1262, 17496}, {1441, 46141}, {1809, 30806}, {2250, 35144}, {2405, 32647}, {3227, 34051}, {4586, 32669}, {6604, 18821}, {6648, 15420}, {10538, 14198}, {14733, 53343}, {18025, 51565}, {18206, 35145}, {35141, 38955}, {35157, 43728}, {35168, 40218}, {35175, 39126}, {36819, 53210}, {37628, 41353}, {52640, 53207}

X(54953) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(929)}}, {{A, B, C, X(21), X(677)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(100), X(5548)}}, {{A, B, C, X(104), X(32641)}}, {{A, B, C, X(108), X(32647)}}, {{A, B, C, X(655), X(22464)}}, {{A, B, C, X(693), X(4025)}}, {{A, B, C, X(883), X(38468)}}, {{A, B, C, X(927), X(4564)}}, {{A, B, C, X(934), X(1813)}}, {{A, B, C, X(961), X(32735)}}, {{A, B, C, X(1309), X(36037)}}, {{A, B, C, X(1320), X(43353)}}, {{A, B, C, X(1476), X(14733)}}, {{A, B, C, X(2720), X(32702)}}, {{A, B, C, X(2737), X(36086)}}, {{A, B, C, X(5088), X(18206)}}, {{A, B, C, X(8269), X(46962)}}, {{A, B, C, X(13138), X(36797)}}
X(54953) = trilinear pole of line {2, 222}
X(54953) = isogonal conjugate of X(53549)
X(54953) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 53549}, {6, 46393}, {9, 3310}, {19, 52307}, {31, 2804}, {33, 8677}, {41, 10015}, {55, 1769}, {212, 39534}, {318, 23220}, {517, 663}, {643, 42752}, {650, 2183}, {652, 14571}, {657, 1465}, {667, 6735}, {692, 35015}, {859, 4041}, {908, 3063}, {1457, 3900}, {1785, 1946}, {2149, 52316}, {2161, 53046}, {2170, 2427}, {2175, 36038}, {2195, 42758}, {2310, 23981}, {2342, 42757}, {3270, 23706}, {3737, 51377}, {3939, 42753}, {4895, 14260}, {7252, 21801}, {8641, 22464}, {8750, 35014}, {14936, 24029}, {18344, 22350}, {18889, 42762}, {36086, 42771}, {36110, 41215}, {37628, 42072}, {42078, 43728}, {43924, 51380}
X(54953) = X(i)-vertex conjugate of X(j) for these {i, j}: {21, 32735}
X(54953) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 2804}, {3, 53549}, {6, 52307}, {9, 46393}, {223, 1769}, {478, 3310}, {650, 52316}, {651, 34345}, {1086, 35015}, {3160, 10015}, {6631, 6735}, {10001, 908}, {16591, 42767}, {26932, 35014}, {38989, 42771}, {39004, 41215}, {39053, 1785}, {39063, 42758}, {40584, 53046}, {40593, 36038}, {40615, 42754}, {40617, 42753}, {40622, 42759}, {40625, 14010}, {40837, 39534}, {46398, 3326}, {52659, 23757}, {52870, 42762}
X(54953) = X(i)-Zayin conjugate of X(j) for these {i, j}: {1, 53549}, {43, 46393}, {9355, 2183}
X(54953) = X(i)-cross conjugate of X(j) for these {i, j}: {517, 46102}, {2406, 658}, {2804, 2}, {3218, 1275}, {3904, 85}, {7451, 662}, {23087, 81}, {23981, 651}, {36037, 13136}, {38460, 1016}, {43728, 34234}, {51565, 39294}
X(54953) = barycentric product X(i)*X(j) for these (i, j): {104, 4554}, {304, 36110}, {305, 32702}, {319, 47317}, {320, 53811}, {1275, 43728}, {1309, 348}, {1795, 46404}, {2250, 4625}, {2342, 46406}, {2401, 4998}, {2720, 76}, {4569, 52663}, {4572, 909}, {13136, 7}, {13149, 1809}, {16082, 6516}, {18816, 651}, {32641, 6063}, {32669, 561}, {34051, 668}, {34085, 36819}, {34234, 664}, {36037, 85}, {36795, 934}, {37136, 75}, {38955, 4573}, {39294, 4025}, {40218, 4555}, {51565, 658}
X(54953) = barycentric quotient X(i)/X(j) for these (i, j): {1, 46393}, {2, 2804}, {3, 52307}, {6, 53549}, {7, 10015}, {11, 52316}, {36, 53046}, {56, 3310}, {57, 1769}, {59, 2427}, {85, 36038}, {104, 650}, {108, 14571}, {109, 2183}, {190, 6735}, {222, 8677}, {241, 42758}, {278, 39534}, {320, 53045}, {514, 35015}, {644, 51380}, {651, 517}, {653, 1785}, {658, 22464}, {664, 908}, {665, 42771}, {883, 51390}, {905, 35014}, {909, 663}, {934, 1465}, {1262, 23981}, {1309, 281}, {1323, 42762}, {1332, 51379}, {1434, 23788}, {1461, 1457}, {1465, 42757}, {1795, 652}, {1813, 22350}, {2250, 4041}, {2342, 657}, {2401, 11}, {2405, 25640}, {2423, 3271}, {2720, 6}, {3669, 42753}, {3676, 42754}, {3911, 23757}, {4453, 46398}, {4551, 21801}, {4552, 17757}, {4554, 3262}, {4559, 51377}, {4560, 14010}, {4565, 859}, {4573, 17139}, {4582, 51984}, {4998, 2397}, {5723, 42763}, {6357, 42750}, {7045, 24029}, {7128, 23706}, {7178, 42759}, {7180, 42752}, {7181, 42760}, {10015, 3326}, {13136, 8}, {14578, 1946}, {14776, 607}, {15405, 2431}, {15501, 14298}, {16082, 44426}, {16609, 42767}, {17094, 42761}, {17923, 53047}, {18593, 42768}, {18816, 4391}, {23981, 23980}, {24029, 24028}, {30725, 3259}, {32641, 55}, {32669, 31}, {32702, 25}, {32714, 1875}, {32735, 51987}, {34050, 42755}, {34051, 513}, {34234, 522}, {34858, 3063}, {35321, 7069}, {35328, 20958}, {36037, 9}, {36110, 19}, {36123, 3064}, {36795, 4397}, {36921, 4944}, {36944, 1639}, {37136, 1}, {37628, 34591}, {38955, 3700}, {39294, 1897}, {40218, 900}, {43034, 42751}, {43035, 42756}, {43037, 42764}, {43040, 42766}, {43042, 42770}, {43043, 35013}, {43044, 42772}, {43047, 45884}, {43728, 1146}, {43933, 8735}, {45145, 4526}, {46102, 53151}, {47317, 79}, {51565, 3239}, {52307, 41215}, {52316, 52315}, {52411, 23220}, {52640, 14400}, {52663, 3900}, {53332, 51407}, {53811, 80}

X(54954) = X(394)X(6528)∩X(648)X(1075)

Barycentrics    (a^12*(b^2-c^2)+a^2*b^4*(b^2-c^2)^3*(b^2+3*c^2)-c^2*(b^3-b*c^2)^4+a^10*(-3*b^4+4*c^4)+a^8*(2*b^6+9*b^4*c^2-6*b^2*c^4-6*c^6)+2*a^6*(b^8-8*b^6*c^2+b^4*c^4+4*b^2*c^6+2*c^8)-a^4*(3*b^10-9*b^8*c^2-2*b^6*c^4+4*b^4*c^6+3*b^2*c^8+c^10))*(a^12*(b^2-c^2)+b^2*c^4*(b^2-c^2)^4+a^2*c^4*(b^2-c^2)^3*(3*b^2+c^2)+a^10*(-4*b^4+3*c^4)+a^8*(6*b^6+6*b^4*c^2-9*b^2*c^4-2*c^6)-2*a^6*(2*b^8+4*b^6*c^2+b^4*c^4-8*b^2*c^6+c^8)+a^4*(b^10+3*b^8*c^2+4*b^6*c^4-2*b^4*c^6-9*b^2*c^8+3*c^10)) : :

X(54954) lies on these lines: {99, 46717}, {394, 6528}, {648, 1075}

X(54954) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(63), X(1943)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(394), X(801)}}, {{A, B, C, X(1075), X(2052)}}, {{A, B, C, X(5897), X(34538)}}
X(54954) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 52463}
X(54954) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 52463}
X(54954) = barycentric quotient X(i)/X(j) for these (i, j): {3, 52463}

X(54955) = X(99)X(2858)∩X(15439)X(7799)

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

X(54955) lies on the Steiner circumellipse and on these lines: {99, 2858}, {3228, 7799}, {4577, 47389}, {14728, 53080}

X(54955) = isotomic conjugate of X(2872)
X(54955) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 2872}, {1924, 14568}, {1973, 2510}
X(54955) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 2872}, {6337, 2510}, {9428, 14568}
X(54955) = X(i)-cross conjugate of X(j) for these {i, j}: {2872, 2}, {35549, 34537}
X(54955) = barycentric product X(i)*X(j) for these (i, j): {2858, 76}
X(54955) = barycentric quotient X(i)/X(j) for these (i, j): {2, 2872}, {69, 2510}, {670, 14568}, {2858, 6}

X(54956) = X(3225)X(40322)∩X(3228)X(6339)

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

X(54956) lies on these lines: {3225, 40322}, {3228, 6339}, {6342, 6392}, {35136, 52608}

X(54956) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}
X(54956) = trilinear pole of line {2, 6338}
X(54956) = X(i)-isoconjugate-of-X(j) for these {i, j}: {669, 33781}, {798, 1611}, {1924, 6392}, {1973, 2519}, {9426, 33787}
X(54956) = X(i)-Dao conjugate of X(j) for these {i, j}: {6337, 2519}, {6342, 512}, {9428, 6392}, {31998, 1611}
X(54956) = X(i)-cross conjugate of X(j) for these {i, j}: {6562, 308}
X(54956) = barycentric product X(i)*X(j) for these (i, j): {6339, 670}, {40322, 4609}
X(54956) = barycentric quotient X(i)/X(j) for these (i, j): {69, 2519}, {99, 1611}, {670, 6392}, {799, 33781}, {2396, 51426}, {4563, 19588}, {4602, 33787}, {6339, 512}, {30558, 8651}, {40322, 669}, {52608, 19583}

X(54957) = TRILINEAR POLE OF LINE {2, 33935}

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

X(54957) lies on these lines: {4505, 6540}

X(54957) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(789), X(4033)}}, {{A, B, C, X(799), X(6386)}}, {{A, B, C, X(1492), X(3952)}}, {{A, B, C, X(1978), X(4623)}}, {{A, B, C, X(8050), X(42363)}}, {{A, B, C, X(33948), X(52935)}}
X(54957) = trilinear pole of line {2, 33935}
X(54957) = X(i)-isoconjugate-of-X(j) for these {i, j}: {32, 48275}, {560, 50334}, {667, 5311}, {669, 25526}, {1919, 17303}, {1924, 30599}, {1973, 2523}
X(54957) = X(i)-Dao conjugate of X(j) for these {i, j}: {6337, 2523}, {6374, 50334}, {6376, 48275}, {6631, 5311}, {9296, 17303}, {9428, 30599}
X(54957) = X(i)-cross conjugate of X(j) for these {i, j}: {17321, 31625}
X(54957) = barycentric quotient X(i)/X(j) for these (i, j): {69, 2523}, {75, 48275}, {76, 50334}, {190, 5311}, {319, 30600}, {668, 17303}, {670, 30599}, {799, 25526}, {4554, 10404}

X(54958) = X(99)X(4176)∩X(305)X(6528)

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

X(54958) lies on these lines: {99, 4176}, {305, 6528}, {648, 3926}, {32815, 53639}

X(54958) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(305), X(3926)}}, {{A, B, C, X(2366), X(6330)}}, {{A, B, C, X(3346), X(3424)}}
X(54958) = trilinear pole of line {2, 4143}
X(54958) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1973, 15341}
X(54958) = X(i)-Dao conjugate of X(j) for these {i, j}: {6337, 15341}
X(54958) = barycentric quotient X(i)/X(j) for these (i, j): {69, 15341}

X(54959) = TRILINEAR POLE OF LINE {2, 265}

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

X(54959) lies on these lines: {323, 1494}, {476, 648}, {671, 18316}, {2407, 35139}, {5641, 40879}, {6528, 41392}, {14590, 16077}, {14999, 53192}, {22455, 39986}, {43768, 46138}

X(54959) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(323), X(2407)}}, {{A, B, C, X(476), X(39290)}}, {{A, B, C, X(5468), X(41626)}}, {{A, B, C, X(14999), X(40879)}}, {{A, B, C, X(17708), X(30528)}}, {{A, B, C, X(32662), X(41392)}}
X(54959) = trilinear pole of line {2, 265}
X(54959) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 14314}, {381, 2624}, {661, 3581}, {798, 52149}, {18477, 47230}, {32679, 34417}
X(54959) = X(i)-vertex conjugate of X(j) for these {i, j}: {14560, 14590}
X(54959) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 14314}, {31998, 52149}, {36830, 3581}
X(54959) = barycentric product X(i)*X(j) for these (i, j): {3431, 35139}, {18316, 99}, {39290, 46809}
X(54959) = barycentric quotient X(i)/X(j) for these (i, j): {3, 14314}, {99, 52149}, {110, 3581}, {476, 381}, {3431, 526}, {14559, 32225}, {14560, 34417}, {18316, 523}, {32662, 5158}, {35139, 44135}, {36061, 18477}, {39290, 46808}, {41392, 18487}, {43530, 44427}, {46809, 5664}, {51545, 52743}

X(54960) = X(290)X(40996)∩X(648)X(30476)

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

X(54960) lies on these lines: {290, 40996}, {648, 30476}

X(54960) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(253), X(22456)}}
X(54960) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1973, 45325}
X(54960) = X(i)-Dao conjugate of X(j) for these {i, j}: {6337, 45325}
X(54960) = X(i)-cross conjugate of X(j) for these {i, j}: {52744, 76}
X(54960) = barycentric quotient X(i)/X(j) for these (i, j): {69, 45325}

X(54961) = X(20)X(64)∩X(8719)X(11206)

Barycentrics    a^14-13*a^12*(b^2+c^2)-a^2*(b^2-c^2)^4*(5*b^4+22*b^2*c^2+5*c^4)+a^10*(9*b^4+46*b^2*c^2+9*c^4)-a^6*(b^2-c^2)^2*(69*b^4+86*b^2*c^2+69*c^4)+(b^2-c^2)^4*(b^6+7*b^4*c^2+7*b^2*c^4+c^6)+a^4*(b^2-c^2)^2*(33*b^6+47*b^4*c^2+47*b^2*c^4+33*c^6)+a^8*(43*b^6-67*b^4*c^2-67*b^2*c^4+43*c^6) : :

X(54961) lies on these lines: {20, 64}, {6776, 14900}, {7710, 15311}, {8719, 11206}, {8721, 12250}, {10606, 53015}

X(54961) = reflection of X(i) in X(j) for these {i,j}: {11206, 8719}, {53015, 10606}

X(54962) = X(2782)X(6391)∩X(15311)X(43702)

Barycentrics    (a^10*c^2+b^2*c^2*(b^2-c^2)^3*(b^2+c^2)+a^8*(4*b^4-b^2*c^2-2*c^4)-a^2*(-(b^2*c)+c^3)^2*(b^4-4*b^2*c^2+c^4)+a^6*(-8*b^6+6*b^2*c^4)+2*a^4*(2*b^8+2*b^4*c^4-5*b^2*c^6+c^8))*(a^10*b^2-b^2*c^2*(b^2-c^2)^3*(b^2+c^2)-a^8*(2*b^4+b^2*c^2-4*c^4)-a^2*(b^3-b*c^2)^2*(b^4-4*b^2*c^2+c^4)+a^6*(6*b^4*c^2-8*c^6)+2*a^4*(b^8-5*b^6*c^2+2*b^4*c^4+2*c^8)) : :

X(54962) lies on these lines: {2782, 6391}, {15311, 43702}

X(54962) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(3), X(4)}}, {{A, B, C, X(98), X(23582)}}, {{A, B, C, X(1513), X(15014)}}, {{A, B, C, X(2782), X(3566)}}, {{A, B, C, X(15459), X(30247)}}, {{A, B, C, X(16081), X(48259)}}, {{A, B, C, X(20186), X(34383)}}, {{A, B, C, X(32319), X(46104)}}
X(54962) = X(i)-vertex conjugate of X(j) for these {i, j}: {14908, 47388}

X(54963) = X(4)X(147)∩X(30)X(14970)

Barycentrics    a^2*(-b^2+a*c)*(b^2+a*c)*(a*b-c^2)*(a*b+c^2)*(a^6-b^6+5*a^2*b^2*c^2+4*b^4*c^2+4*b^2*c^4-c^6) : :

X(54963) lies on these lines: {4, 147}, {30, 14970}, {694, 3098}, {733, 12054}

X(54963) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(3), X(13571)}}, {{A, B, C, X(4), X(21513)}}
X(54963) = barycentric product X(i)*X(j) for these (i, j): {1916, 21513}
X(54963) = barycentric quotient X(i)/X(j) for these (i, j): {21513, 385}

X(54964) = X(2)X(7711)∩X(30)X(83)

Barycentrics    4*a^8+b^8-b^6*c^2-b^2*c^6+c^8+5*a^6*(b^2+c^2)-4*a^4*(3*b^4+8*b^2*c^2+3*c^4)+a^2*(2*b^6-17*b^4*c^2-17*b^2*c^4+2*c^6) : :

X(54964) lies on these lines: {2, 7711}, {3, 51860}, {30, 83}, {39, 549}, {140, 7799}, {547, 7859}, {597, 5092}, {1153, 12040}, {5054, 7754}, {5066, 43460}, {5116, 38064}, {6661, 32516}, {7832, 10124}, {7836, 15694}, {7880, 11539}, {9605, 42787}, {10168, 24256}, {10302, 11540}, {11812, 22329}, {12100, 26613}, {40344, 50664}, {50983, 52995}

X(54965) = X(4)X(543)∩X(99)X(1499)

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

X(54965) lies on these lines: {4, 543}, {98, 47047}, {99, 1499}, {114, 52450}, {2782, 51927}, {21732, 34246}

X(54965) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(4), X(99)}}, {{A, B, C, X(98), X(36898)}}, {{A, B, C, X(543), X(3564)}}, {{A, B, C, X(30247), X(44145)}}
X(54965) = reflection of X(i) in X(j) for these {i,j}: {52450, 114}, {98, 47047}
X(54965) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2793, 36051}, {8773, 9135}
X(54965) = X(i)-Dao conjugate of X(j) for these {i, j}: {114, 2793}, {39072, 9135}
X(54965) = barycentric product X(i)*X(j) for these (i, j): {230, 46144}, {2709, 51481}, {4226, 5503}
X(54965) = barycentric quotient X(i)/X(j) for these (i, j): {230, 2793}, {1692, 9135}, {2709, 2987}, {4226, 22329}, {46144, 8781}

X(54966) = X(190)X(1259)∩X(283)X(648)

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

X(54966) lies on these lines: {63, 18026}, {99, 6514}, {190, 1259}, {283, 648}, {333, 6528}, {394, 664}, {668, 3719}, {1944, 44360}, {4569, 7183}, {35154, 40888}

X(54966) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(63), X(271)}}, {{A, B, C, X(92), X(6360)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(1944), X(8777)}}, {{A, B, C, X(1948), X(40843)}}, {{A, B, C, X(40882), X(40888)}}
X(54966) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 8763}, {25, 44360}
X(54966) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 8763}, {6505, 44360}
X(54966) = X(i)-cross conjugate of X(j) for these {i, j}: {1948, 333}, {40843, 8777}, {52774, 8764}
X(54966) = barycentric product X(i)*X(j) for these (i, j): {69, 8764}, {52774, 76}
X(54966) = barycentric quotient X(i)/X(j) for these (i, j): {3, 8763}, {63, 44360}, {8764, 4}, {52774, 6}

X(54967) = X(646)X(666)∩X(648)X(7258)

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

X(54967) lies on these lines: {99, 52778}, {646, 666}, {648, 7258}, {2481, 3596}, {3227, 30701}, {4562, 48070}, {6386, 46135}, {6613, 8269}, {7084, 18824}, {7123, 18825}, {14727, 31625}

X(54967) = trilinear pole of line {2, 30701}
X(54967) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(646), X(3596)}}, {{A, B, C, X(660), X(8750)}}, {{A, B, C, X(4583), X(6335)}}, {{A, B, C, X(8048), X(27834)}}, {{A, B, C, X(47815), X(47819)}}
X(54967) = X(i)-isoconjugate-of-X(j) for these {i, j}: {32, 48398}, {58, 50490}, {614, 667}, {649, 16502}, {810, 4211}, {1019, 21750}, {1106, 17115}, {1633, 3248}, {1919, 4000}, {1924, 16750}, {1977, 3732}, {1980, 3673}, {2206, 48403}, {3063, 28017}, {3733, 40934}, {5324, 51641}, {7083, 43924}, {7254, 8020}, {23620, 43925}
X(54967) = X(i)-Dao conjugate of X(j) for these {i, j}: {10, 50490}, {5375, 16502}, {6376, 48398}, {6552, 17115}, {6631, 614}, {9296, 4000}, {9428, 16750}, {10001, 28017}, {39062, 4211}, {40603, 48403}
X(54967) = X(i)-cross conjugate of X(j) for these {i, j}: {304, 7035}, {346, 31625}, {10327, 1016}, {47663, 274}, {52778, 42384}
X(54967) = barycentric product X(i)*X(j) for these (i, j): {646, 8817}, {6386, 7123}, {27808, 40403}, {30701, 668}, {42384, 69}, {48070, 7035}, {52778, 76}
X(54967) = barycentric quotient X(i)/X(j) for these (i, j): {37, 50490}, {75, 48398}, {100, 16502}, {190, 614}, {321, 48403}, {346, 17115}, {644, 7083}, {645, 5324}, {646, 497}, {648, 4211}, {664, 28017}, {668, 4000}, {670, 16750}, {1016, 1633}, {1018, 40934}, {1332, 1473}, {1978, 3673}, {3699, 2082}, {3952, 16583}, {4033, 3914}, {4552, 40961}, {4554, 7195}, {4557, 21750}, {4561, 7289}, {4571, 7124}, {4574, 22363}, {4578, 30706}, {6335, 1851}, {6558, 4319}, {7035, 3732}, {7084, 1919}, {7123, 667}, {7131, 43924}, {8269, 1407}, {8817, 3669}, {20336, 21107}, {27808, 53510}, {30701, 513}, {30705, 43932}, {30730, 40965}, {40403, 3733}, {40521, 21813}, {42384, 4}, {48070, 244}, {52609, 17441}, {52778, 6}

X(54968) = X(99)X(52776)∩X(648)X(42389)

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

X(54968) lies on the Steiner circumellipse and on these lines: {99, 52776}, {648, 42389}, {653, 53206}, {18816, 34398}

X(54968) = X(i)-isoconjugate-of-X(j) for these {i, j}: {255, 2520}, {663, 53847}, {1946, 20277}, {4336, 23224}, {17188, 39201}, {23727, 52425}
X(54968) = X(i)-Dao conjugate of X(j) for these {i, j}: {6523, 2520}, {39053, 20277}, {39060, 17073}
X(54968) = X(i)-cross conjugate of X(j) for these {i, j}: {52776, 42389}
X(54968) = barycentric product X(i)*X(j) for these (i, j): {34398, 6335}, {34409, 54240}, {42389, 69}, {52776, 76}
X(54968) = barycentric quotient X(i)/X(j) for these (i, j): {273, 23727}, {393, 2520}, {651, 53847}, {653, 20277}, {823, 17188}, {18026, 17073}, {34398, 905}, {37741, 36054}, {42389, 4}, {52776, 6}, {54240, 1836}

X(54969) = X(3)X(94)∩X(4)X(50)

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

X(54969) lies on these lines: {2, 567}, {3, 94}, {4, 50}, {5, 7578}, {6, 9221}, {13, 46113}, {14, 46112}, {76, 7550}, {83, 14789}, {186, 2052}, {275, 7577}, {1199, 13599}, {3153, 13585}, {5392, 35921}, {7514, 11140}, {8796, 18533}, {9381, 51256}, {13579, 18531}, {14385, 16080}, {16868, 53170}, {18316, 18396}, {18559, 39284}, {39295, 47390}

X(54969) = Cundy-Parry Phi of X(94)
X(54969) = isogonal conjugate of X(568)
X(54969) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(3), X(50)}}, {{A, B, C, X(5), X(7577)}}, {{A, B, C, X(6), X(567)}}, {{A, B, C, X(24), X(15620)}}, {{A, B, C, X(25), X(7550)}}, {{A, B, C, X(54), X(13530)}}, {{A, B, C, X(68), X(93)}}, {{A, B, C, X(69), X(46262)}}, {{A, B, C, X(74), X(45838)}}, {{A, B, C, X(95), X(1300)}}, {{A, B, C, X(140), X(18559)}}, {{A, B, C, X(254), X(18349)}}, {{A, B, C, X(264), X(33565)}}, {{A, B, C, X(265), X(2963)}}, {{A, B, C, X(376), X(35486)}}, {{A, B, C, X(427), X(14789)}}, {{A, B, C, X(631), X(18533)}}, {{A, B, C, X(847), X(3459)}}, {{A, B, C, X(1093), X(43891)}}, {{A, B, C, X(1105), X(11270)}}, {{A, B, C, X(1138), X(46259)}}, {{A, B, C, X(1173), X(34449)}}, {{A, B, C, X(1199), X(41365)}}, {{A, B, C, X(1294), X(20421)}}, {{A, B, C, X(2072), X(16868)}}, {{A, B, C, X(2165), X(6344)}}, {{A, B, C, X(2980), X(14483)}}, {{A, B, C, X(3153), X(14940)}}, {{A, B, C, X(3426), X(13597)}}, {{A, B, C, X(3518), X(7514)}}, {{A, B, C, X(3520), X(6644)}}, {{A, B, C, X(3524), X(37460)}}, {{A, B, C, X(3527), X(11816)}}, {{A, B, C, X(3532), X(13489)}}, {{A, B, C, X(3563), X(40102)}}, {{A, B, C, X(5449), X(9927)}}, {{A, B, C, X(5627), X(52154)}}, {{A, B, C, X(6145), X(14938)}}, {{A, B, C, X(7505), X(18531)}}, {{A, B, C, X(8884), X(11169)}}, {{A, B, C, X(9307), X(45972)}}, {{A, B, C, X(10298), X(21844)}}, {{A, B, C, X(11738), X(45138)}}, {{A, B, C, X(11815), X(43908)}}, {{A, B, C, X(12112), X(41372)}}, {{A, B, C, X(13418), X(46199)}}, {{A, B, C, X(14457), X(15424)}}, {{A, B, C, X(14491), X(32085)}}, {{A, B, C, X(15454), X(52763)}}, {{A, B, C, X(17506), X(18324)}}, {{A, B, C, X(18396), X(37638)}}, {{A, B, C, X(18420), X(37119)}}, {{A, B, C, X(21448), X(40118)}}, {{A, B, C, X(34208), X(39437)}}, {{A, B, C, X(35912), X(52494)}}, {{A, B, C, X(37347), X(52295)}}, {{A, B, C, X(38534), X(41890)}}, {{A, B, C, X(40800), X(46090)}}, {{A, B, C, X(45781), X(52487)}}
X(54969) = X(2980)-vertex conjugate of X(3431)
X(54969) = X(12022)-cross conjugate of X(4)

X(54970) = TRILINEAR POLE OF LINE {2, 72}

Barycentrics    1/((b-c)*(-a^3+2*b*c*(b+c)+a*(b+c)^2)) : :

X(54970) lies on these lines: {99, 1332}, {100, 648}, {286, 51574}, {668, 52609}, {2215, 3226}, {2335, 2481}, {3227, 51223}, {4552, 18026}, {6335, 6528}, {13397, 14545}, {14616, 19808}, {18591, 40422}, {18666, 52386}

X(54970) = isotomic conjugate of X(23882)
X(54970) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(100), X(1332)}}, {{A, B, C, X(643), X(646)}}, {{A, B, C, X(651), X(13149)}}, {{A, B, C, X(662), X(833)}}, {{A, B, C, X(1025), X(25521)}}, {{A, B, C, X(1292), X(36099)}}, {{A, B, C, X(4572), X(51563)}}, {{A, B, C, X(4606), X(13138)}}, {{A, B, C, X(4624), X(44327)}}, {{A, B, C, X(15455), X(30610)}}, {{A, B, C, X(17321), X(42720)}}, {{A, B, C, X(27834), X(46480)}}
X(54970) = trilinear pole of line {2, 72}
X(54970) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 46385}, {28, 46382}, {31, 23882}, {405, 649}, {514, 5320}, {650, 1451}, {663, 37543}, {667, 5271}, {1918, 15417}, {1919, 44140}, {14549, 21007}, {22383, 39585}
X(54970) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 23882}, {9, 46385}, {5375, 405}, {6631, 5271}, {9296, 44140}, {34021, 15417}, {40591, 46382}
X(54970) = X(i)-cross conjugate of X(j) for these {i, j}: {377, 4998}, {23882, 2}, {26872, 46102}, {50557, 32009}
X(54970) = barycentric product X(i)*X(j) for these (i, j): {1978, 2215}, {2335, 4554}, {20336, 36077}, {36080, 76}, {51223, 668}
X(54970) = barycentric quotient X(i)/X(j) for these (i, j): {1, 46385}, {2, 23882}, {71, 46382}, {100, 405}, {109, 1451}, {190, 5271}, {274, 15417}, {651, 37543}, {668, 44140}, {692, 5320}, {1897, 39585}, {2215, 649}, {2335, 650}, {3952, 5295}, {36077, 28}, {36080, 6}, {45128, 48297}, {51223, 513}, {51875, 15313}, {52609, 42706}

X(54971) = X(76)X(14259)∩X(99)X(907)

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

X(54971) lies on these lines: {69, 51830}, {76, 14259}, {99, 907}, {290, 34817}, {305, 40189}, {315, 46739}, {648, 4576}, {671, 3096}, {1975, 40187}, {2966, 14588}, {3228, 39951}, {4563, 4577}, {8801, 35142}, {14970, 40708}, {18827, 23051}, {35179, 53350}, {40022, 40182}

X(54971) = isogonal conjugate of X(3804)
X(54971) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(110), X(37223)}}, {{A, B, C, X(877), X(44149)}}, {{A, B, C, X(927), X(37218)}}, {{A, B, C, X(1296), X(32713)}}, {{A, B, C, X(1576), X(39639)}}, {{A, B, C, X(1634), X(26714)}}, {{A, B, C, X(4235), X(33190)}}, {{A, B, C, X(4563), X(4576)}}, {{A, B, C, X(4616), X(37205)}}, {{A, B, C, X(6233), X(32737)}}, {{A, B, C, X(9133), X(43187)}}, {{A, B, C, X(18315), X(35575)}}, {{A, B, C, X(32734), X(53885)}}
X(54971) = trilinear pole of line {2, 3933}
X(54971) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3804}, {31, 3800}, {42, 3803}, {213, 48060}, {661, 30435}, {669, 39731}, {798, 3618}, {810, 6995}, {1918, 48109}, {1924, 40022}, {2084, 42037}, {3806, 46289}
X(54971) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3800}, {3, 3804}, {39, 3806}, {6626, 48060}, {9428, 40022}, {31998, 3618}, {34021, 48109}, {36830, 30435}, {39062, 6995}, {40182, 512}, {40592, 3803}
X(54971) = X(i)-cross conjugate of X(j) for these {i, j}: {3620, 4590}, {3800, 2}, {7770, 34537}, {49298, 32014}
X(54971) = barycentric product X(i)*X(j) for these (i, j): {76, 907}, {4563, 8801}, {18840, 99}, {23051, 799}, {34817, 6331}, {39951, 670}
X(54971) = barycentric quotient X(i)/X(j) for these (i, j): {2, 3800}, {6, 3804}, {81, 3803}, {86, 48060}, {99, 3618}, {110, 30435}, {141, 3806}, {274, 48109}, {648, 6995}, {670, 40022}, {799, 39731}, {907, 6}, {4558, 3796}, {4563, 3785}, {4576, 8362}, {4577, 42037}, {5468, 3793}, {8801, 2501}, {18840, 523}, {23051, 661}, {34817, 647}, {39951, 512}, {41676, 3867}

X(54972) = X(2)X(283)∩X(3)X(226)

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

X(54972) lies on these lines: {1, 40149}, {2, 283}, {3, 226}, {4, 284}, {5, 1751}, {10, 219}, {12, 6056}, {29, 2052}, {76, 332}, {77, 1446}, {78, 321}, {102, 3485}, {273, 8555}, {275, 5125}, {388, 947}, {459, 7498}, {498, 1754}, {581, 7513}, {940, 1433}, {942, 5760}, {946, 1036}, {951, 3487}, {1029, 6895}, {1037, 21620}, {1057, 12053}, {1069, 1210}, {1478, 52185}, {1795, 37522}, {2051, 3149}, {3422, 12047}, {3478, 13464}, {5703, 40442}, {5757, 37151}, {6828, 24624}, {6831, 13478}, {6918, 14554}, {6927, 45098}, {7015, 10441}, {7100, 43682}, {7163, 13407}, {7518, 8796}, {11608, 17973}, {22836, 43683}, {24220, 36907}, {27398, 34258}, {40395, 45924}, {43675, 52676}, {45100, 50700}

X(54972) = isogonal conjugate of X(581)
X(54972) = trilinear pole of line {523, 652}
X(54972) = Cundy-Parry Phi of X(226)
X(54972) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 581}, {57, 15830}
X(54972) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 581}, {5452, 15830}
X(54972) = X(i)-cross conjugate of X(j) for these {i, j}: {26956, 522}
X(54972) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(5), X(5125)}}, {{A, B, C, X(6), X(580)}}, {{A, B, C, X(7), X(3615)}}, {{A, B, C, X(8), X(13411)}}, {{A, B, C, X(20), X(7498)}}, {{A, B, C, X(34), X(46010)}}, {{A, B, C, X(35), X(50317)}}, {{A, B, C, X(40), X(940)}}, {{A, B, C, X(46), X(5707)}}, {{A, B, C, X(57), X(5706)}}, {{A, B, C, X(65), X(37530)}}, {{A, B, C, X(68), X(307)}}, {{A, B, C, X(69), X(39130)}}, {{A, B, C, X(79), X(91)}}, {{A, B, C, X(80), X(11374)}}, {{A, B, C, X(84), X(86)}}, {{A, B, C, X(158), X(7110)}}, {{A, B, C, X(171), X(10441)}}, {{A, B, C, X(225), X(2165)}}, {{A, B, C, X(281), X(1034)}}, {{A, B, C, X(318), X(5812)}}, {{A, B, C, X(388), X(946)}}, {{A, B, C, X(405), X(7513)}}, {{A, B, C, X(406), X(6836)}}, {{A, B, C, X(411), X(5136)}}, {{A, B, C, X(412), X(7532)}}, {{A, B, C, X(451), X(6895)}}, {{A, B, C, X(461), X(37423)}}, {{A, B, C, X(475), X(6835)}}, {{A, B, C, X(484), X(45931)}}, {{A, B, C, X(497), X(21620)}}, {{A, B, C, X(498), X(6734)}}, {{A, B, C, X(517), X(37522)}}, {{A, B, C, X(572), X(19763)}}, {{A, B, C, X(596), X(39695)}}, {{A, B, C, X(631), X(7518)}}, {{A, B, C, X(847), X(6757)}}, {{A, B, C, X(860), X(6828)}}, {{A, B, C, X(936), X(19860)}}, {{A, B, C, X(937), X(967)}}, {{A, B, C, X(938), X(6745)}}, {{A, B, C, X(942), X(1754)}}, {{A, B, C, X(943), X(2287)}}, {{A, B, C, X(950), X(3487)}}, {{A, B, C, X(963), X(10013)}}, {{A, B, C, X(986), X(37527)}}, {{A, B, C, X(996), X(1257)}}, {{A, B, C, X(1056), X(12053)}}, {{A, B, C, X(1210), X(5552)}}, {{A, B, C, X(1220), X(3577)}}, {{A, B, C, X(1224), X(15909)}}, {{A, B, C, X(1242), X(52384)}}, {{A, B, C, X(1478), X(12047)}}, {{A, B, C, X(1479), X(13407)}}, {{A, B, C, X(1699), X(5290)}}, {{A, B, C, X(1715), X(41344)}}, {{A, B, C, X(1764), X(5711)}}, {{A, B, C, X(1826), X(20029)}}, {{A, B, C, X(1895), X(17188)}}, {{A, B, C, X(2475), X(7537)}}, {{A, B, C, X(2476), X(37381)}}, {{A, B, C, X(3149), X(11109)}}, {{A, B, C, X(3333), X(37537)}}, {{A, B, C, X(3336), X(45923)}}, {{A, B, C, X(3476), X(13464)}}, {{A, B, C, X(3527), X(39748)}}, {{A, B, C, X(3576), X(19765)}}, {{A, B, C, X(4194), X(6865)}}, {{A, B, C, X(4200), X(6864)}}, {{A, B, C, X(5255), X(37521)}}, {{A, B, C, X(5264), X(37536)}}, {{A, B, C, X(5270), X(18393)}}, {{A, B, C, X(5482), X(37610)}}, {{A, B, C, X(5553), X(43972)}}, {{A, B, C, X(5554), X(6700)}}, {{A, B, C, X(5558), X(40450)}}, {{A, B, C, X(5603), X(10106)}}, {{A, B, C, X(5665), X(36123)}}, {{A, B, C, X(5703), X(6737)}}, {{A, B, C, X(5716), X(34937)}}, {{A, B, C, X(5738), X(27395)}}, {{A, B, C, X(6355), X(18641)}}, {{A, B, C, X(6824), X(37189)}}, {{A, B, C, X(6831), X(17555)}}, {{A, B, C, X(6894), X(52252)}}, {{A, B, C, X(6943), X(11105)}}, {{A, B, C, X(6998), X(11341)}}, {{A, B, C, X(7049), X(36421)}}, {{A, B, C, X(7160), X(14942)}}, {{A, B, C, X(7412), X(27378)}}, {{A, B, C, X(7524), X(7572)}}, {{A, B, C, X(7531), X(7538)}}, {{A, B, C, X(8814), X(51502)}}, {{A, B, C, X(10305), X(30712)}}, {{A, B, C, X(10361), X(47372)}}, {{A, B, C, X(10429), X(28626)}}, {{A, B, C, X(10573), X(27385)}}, {{A, B, C, X(11517), X(52676)}}, {{A, B, C, X(13161), X(26098)}}, {{A, B, C, X(15232), X(45838)}}, {{A, B, C, X(16062), X(37362)}}, {{A, B, C, X(18541), X(43732)}}, {{A, B, C, X(19782), X(37552)}}, {{A, B, C, X(22836), X(34772)}}, {{A, B, C, X(23617), X(44861)}}, {{A, B, C, X(24537), X(37380)}}, {{A, B, C, X(25015), X(37372)}}, {{A, B, C, X(26023), X(36687)}}, {{A, B, C, X(27402), X(37028)}}, {{A, B, C, X(34485), X(34860)}}, {{A, B, C, X(35612), X(37570)}}, {{A, B, C, X(43724), X(52389)}}
X(54972) = barycentric product X(i)*X(j) for these (i, j): {2219, 75}
X(54972) = barycentric quotient X(i)/X(j) for these (i, j): {6, 581}, {55, 15830}, {2219, 1}

X(54973) = X(2)X(6528)∩X(3)X(648)

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

X(54973) lies on these lines: {2, 6528}, {3, 648}, {30, 14941}, {97, 18831}, {99, 394}, {190, 3682}, {290, 53173}, {376, 54032}, {401, 14919}, {664, 40152}, {668, 3998}, {670, 3926}, {671, 2797}, {892, 40888}, {1073, 53639}, {1214, 18026}, {2966, 17974}, {4577, 28724}, {5641, 10718}, {15164, 46811}, {15165, 46814}, {26922, 54030}, {31626, 33513}, {34579, 37765}, {36900, 53201}, {37200, 38686}, {46134, 52350}, {54100, 54114}

X(54973) = reflection of X(i) in X(j) for these {i,j}: {2, 35071}, {6528, 2}
X(54973) = isogonal conjugate of X(3331)
X(54973) = trilinear pole of line {2, 23613}
X(54973) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3331}, {19, 852}, {9406, 52766}, {24021, 33571}, {32676, 52744}
X(54973) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 3331}, {6, 852}, {520, 33571}, {9410, 52766}, {15526, 52744}
X(54973) = X(i)-cross conjugate of X(j) for these {i, j}: {33571, 520}
X(54973) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(3)}}, {{A, B, C, X(4), X(35941)}}, {{A, B, C, X(30), X(401)}}, {{A, B, C, X(74), X(15412)}}, {{A, B, C, X(76), X(34861)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(249), X(40832)}}, {{A, B, C, X(264), X(47383)}}, {{A, B, C, X(265), X(15351)}}, {{A, B, C, X(287), X(1294)}}, {{A, B, C, X(308), X(30541)}}, {{A, B, C, X(376), X(458)}}, {{A, B, C, X(381), X(51350)}}, {{A, B, C, X(524), X(2797)}}, {{A, B, C, X(525), X(1972)}}, {{A, B, C, X(1003), X(37190)}}, {{A, B, C, X(1105), X(34386)}}, {{A, B, C, X(1989), X(39849)}}, {{A, B, C, X(3426), X(40815)}}, {{A, B, C, X(3431), X(42300)}}, {{A, B, C, X(3524), X(37067)}}, {{A, B, C, X(6662), X(9290)}}, {{A, B, C, X(7841), X(35926)}}, {{A, B, C, X(8613), X(47301)}}, {{A, B, C, X(9289), X(15318)}}, {{A, B, C, X(13586), X(21531)}}, {{A, B, C, X(20573), X(30477)}}, {{A, B, C, X(23878), X(39683)}}, {{A, B, C, X(35474), X(40884)}}, {{A, B, C, X(35937), X(37124)}}, {{A, B, C, X(36889), X(43711)}}, {{A, B, C, X(46789), X(46809)}}
X(54973) = barycentric product X(i)*X(j) for these (i, j): {26717, 76}, {32725, 52617}
X(54973) = barycentric quotient X(i)/X(j) for these (i, j): {3, 852}, {6, 3331}, {525, 52744}, {852, 52066}, {1494, 52766}, {26717, 6}, {32725, 32713}, {35071, 33571}, {36139, 24019}

X(54974) = X(2)X(52574)∩X(320)X(519)

Barycentrics    (a+b-2*c)^2*(a-2*b+c)^2 : :
X(54974) = X[4440]+2*X[35121]

X(54974) lies on these lines: {2, 52574}, {85, 14628}, {88, 40833}, {320, 519}, {545, 1016}, {1086, 35168}, {1168, 39704}, {1318, 4618}, {2226, 4615}, {2726, 39414}, {3911, 17078}, {4358, 4945}, {4440, 35121}, {4997, 36915}, {6548, 6550}, {16088, 37168}, {17079, 40218}, {18821, 36590}, {19875, 40095}, {19883, 52759}, {24183, 36592}, {25055, 27922}, {32028, 36954}

X(54974) = midpoint of X(i) and X(j) for these {i,j}: {903, 9460}
X(54974) = reflection of X(i) in X(j) for these {i,j}: {32028, 41138}, {4555, 9460}
X(54974) = isogonal conjugate of X(1017)
X(54974) = trilinear pole of line {903, 4453}
X(54974) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1017}, {6, 678}, {19, 22371}, {31, 4370}, {32, 4738}, {41, 1317}, {44, 902}, {48, 42070}, {58, 21821}, {519, 2251}, {560, 36791}, {604, 4152}, {667, 53582}, {692, 6544}, {1023, 1960}, {1110, 35092}, {1252, 42084}, {1404, 3689}, {1415, 4543}, {1635, 23344}, {1918, 16729}, {2149, 4542}, {3285, 21805}, {4358, 9459}, {8028, 9456}, {8756, 23202}, {17455, 40172}, {32665, 33922}, {52680, 52963}
X(54974) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 4370}, {3, 1017}, {6, 22371}, {9, 678}, {10, 21821}, {514, 35092}, {650, 4542}, {661, 42084}, {1015, 3251}, {1086, 6544}, {1146, 4543}, {1249, 42070}, {3160, 1317}, {3161, 4152}, {4370, 8028}, {6374, 36791}, {6376, 4738}, {6631, 53582}, {9460, 519}, {34021, 16729}, {35092, 33922}, {40594, 44}, {40595, 902}, {40615, 39771}
X(54974) = X(i)-cross conjugate of X(j) for these {i, j}: {2, 903}, {514, 4555}, {1086, 6548}, {24183, 75}, {30575, 679}, {37691, 7}, {44009, 190}, {52574, 20568}
X(54974) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(514)}}, {{A, B, C, X(76), X(1266)}}, {{A, B, C, X(85), X(320)}}, {{A, B, C, X(88), X(1168)}}, {{A, B, C, X(239), X(19875)}}, {{A, B, C, X(274), X(17160)}}, {{A, B, C, X(279), X(4887)}}, {{A, B, C, X(545), X(1086)}}, {{A, B, C, X(598), X(35158)}}, {{A, B, C, X(671), X(6185)}}, {{A, B, C, X(673), X(35170)}}, {{A, B, C, X(903), X(20568)}}, {{A, B, C, X(1022), X(46795)}}, {{A, B, C, X(2226), X(30575)}}, {{A, B, C, X(3227), X(24841)}}, {{A, B, C, X(3912), X(38314)}}, {{A, B, C, X(4049), X(17953)}}, {{A, B, C, X(4080), X(42026)}}, {{A, B, C, X(4370), X(40514)}}, {{A, B, C, X(4555), X(4615)}}, {{A, B, C, X(4590), X(32014)}}, {{A, B, C, X(5385), X(37131)}}, {{A, B, C, X(6542), X(19883)}}, {{A, B, C, X(10302), X(35172)}}, {{A, B, C, X(17310), X(25055)}}, {{A, B, C, X(23582), X(35161)}}, {{A, B, C, X(24183), X(36791)}}, {{A, B, C, X(24441), X(31139)}}, {{A, B, C, X(27191), X(41138)}}, {{A, B, C, X(29590), X(38098)}}, {{A, B, C, X(31621), X(35169)}}, {{A, B, C, X(36590), X(46790)}}, {{A, B, C, X(44168), X(53223)}}, {{A, B, C, X(49727), X(49741)}}
X(54974) = barycentric product X(i)*X(j) for these (i, j): {274, 30575}, {679, 75}, {903, 903}, {1318, 6063}, {1502, 41935}, {2226, 76}, {3261, 4638}, {4049, 4615}, {4555, 6548}, {4618, 693}, {20568, 88}, {36594, 39704}, {40833, 4945}
X(54974) = barycentric quotient X(i)/X(j) for these (i, j): {1, 678}, {2, 4370}, {3, 22371}, {4, 42070}, {6, 1017}, {7, 1317}, {8, 4152}, {11, 4542}, {37, 21821}, {75, 4738}, {76, 36791}, {88, 44}, {106, 902}, {190, 53582}, {244, 42084}, {274, 16729}, {513, 3251}, {514, 6544}, {519, 8028}, {522, 4543}, {679, 1}, {900, 33922}, {901, 23344}, {903, 519}, {1022, 1635}, {1086, 35092}, {1168, 40172}, {1318, 55}, {1320, 3689}, {1358, 14027}, {1797, 22356}, {2226, 6}, {2403, 14425}, {3257, 1023}, {3261, 52627}, {3676, 39771}, {4049, 4120}, {4080, 3943}, {4555, 17780}, {4582, 30731}, {4618, 100}, {4638, 101}, {4674, 21805}, {4945, 4908}, {4997, 2325}, {6336, 8756}, {6545, 14442}, {6548, 900}, {6549, 1647}, {6550, 46050}, {7336, 52337}, {8661, 14637}, {9456, 2251}, {20568, 4358}, {23345, 1960}, {23838, 4895}, {27922, 4432}, {30575, 37}, {36058, 23202}, {36588, 36924}, {36594, 3679}, {36887, 6174}, {39264, 23644}, {39414, 901}, {40215, 17455}, {41935, 32}, {42084, 14835}, {52206, 20972}, {52553, 214}, {52574, 16594}, {53240, 51463}
X(54974) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {519, 9460, 4555}, {679, 36594, 903}, {903, 9460, 519}

X(54975) = X(2)X(39020)∩X(20)X(648)

Barycentrics    (a^8+a^6*(4*b^2-5*c^2)+(b^2-c^2)^2*(b^4-3*b^2*c^2-2*c^4)+5*a^4*(-2*b^4+b^2*c^2+c^4)+a^2*(4*b^6+5*b^4*c^2-10*b^2*c^4+c^6))*(a^8-2*b^8+b^6*c^2+5*b^4*c^4-5*b^2*c^6+c^8+a^6*(-5*b^2+4*c^2)+5*a^4*(b^4+b^2*c^2-2*c^4)+a^2*(b^6-10*b^4*c^2+5*b^2*c^4+4*c^6)) : :

X(54975) lies on these lines: {2, 39020}, {20, 648}, {30, 14944}, {99, 37669}, {441, 16077}, {668, 42699}, {1494, 39473}, {6528, 15466}, {10718, 35140}

X(54975) = reflection of X(i) in X(j) for these {i,j}: {2, 39020}, {53639, 2}
X(54975) = trilinear pole of line {2, 8057}
X(54975) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 34147}
X(54975) = X(i)-vertex conjugate of X(j) for these {i, j}: {6330, 34190}
X(54975) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 34147}
X(54975) = X(i)-cross conjugate of X(j) for these {i, j}: {10714, 1494}, {51939, 95}
X(54975) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(20)}}, {{A, B, C, X(4), X(15258)}}, {{A, B, C, X(30), X(441)}}, {{A, B, C, X(98), X(14900)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(287), X(15351)}}, {{A, B, C, X(376), X(52283)}}, {{A, B, C, X(525), X(1294)}}, {{A, B, C, X(935), X(10718)}}, {{A, B, C, X(1297), X(38676)}}, {{A, B, C, X(2693), X(18876)}}, {{A, B, C, X(2996), X(52441)}}, {{A, B, C, X(3346), X(52581)}}, {{A, B, C, X(3926), X(18848)}}, {{A, B, C, X(4846), X(42330)}}, {{A, B, C, X(14860), X(54114)}}, {{A, B, C, X(16251), X(42287)}}, {{A, B, C, X(43660), X(46105)}}
X(54975) = barycentric quotient X(i)/X(j) for these (i, j): {3, 34147}

X(54976) = X(3)X(6528)∩X(99)X(1092)

Barycentrics    (a^10*(b^2-c^2)-b^4*c^2*(b^2-c^2)^3+a^8*(-4*b^4+3*c^4)+a^6*(6*b^6+b^4*c^2-3*b^2*c^4-3*c^6)+a^2*(b^10-3*b^6*c^4+2*b^4*c^6)+a^4*(-4*b^8+b^6*c^2+2*b^2*c^6+c^8))*(a^10*(b^2-c^2)-b^2*c^4*(b^2-c^2)^3+a^8*(-3*b^4+4*c^4)+a^6*(3*b^6+3*b^4*c^2-b^2*c^4-6*c^6)-a^4*(b^8+2*b^6*c^2+b^2*c^6-4*c^8)-a^2*(2*b^6*c^4-3*b^4*c^6+c^10)) : :

X(54976) lies on these lines: {3, 6528}, {99, 1092}, {264, 40800}, {401, 46841}, {577, 648}, {670, 3964}, {14379, 53639}, {16391, 46134}, {18026, 22341}, {18831, 19210}, {20477, 36608}

X(54976) = trilinear pole of line {2, 32320}
X(54976) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 46841}
X(54976) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 46841}
X(54976) = X(i)-cross conjugate of X(j) for these {i, j}: {14941, 287}, {16089, 95}
X(54976) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(51350)}}, {{A, B, C, X(3), X(95)}}, {{A, B, C, X(69), X(38256)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(248), X(48259)}}, {{A, B, C, X(264), X(3164)}}, {{A, B, C, X(276), X(40410)}}, {{A, B, C, X(287), X(401)}}, {{A, B, C, X(458), X(35941)}}, {{A, B, C, X(14941), X(16089)}}, {{A, B, C, X(35926), X(37190)}}
X(54976) = barycentric quotient X(i)/X(j) for these (i, j): {3, 46841}

X(54977) = X(1)X(24484)∩X(2)X(3675)

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

Lies on these lines: {1, 24484}, {2, 3675}, {81, 3110}, {105, 1015}, {120, 668}, {291, 2809}, {528, 3227}, {537, 34892}, {764, 14267}, {1280, 10699}, {1358, 34018}, {1643, 43928}, {1929, 5540}, {2401, 51832}, {2787, 10773}, {2795, 39925}, {2810, 10760}, {2836, 17946}, {2838, 16100}, {5376, 34230}, {6714, 27195}, {9263, 20344}, {10712, 33908}, {14947, 43671}X(54977) = midpoint of X(i) in X(j) for these {i,j}: {9263, 20344}
X(54977) = reflection of X(i) in X(j) for these {i,j}: {105, 1015}, {668, 120}
X(54977) = isogonal conjugate of X(1083)
X(54977) = trilinear pole of line {3290,5098}
X(54977) = antipode of X(105) in the circumconic {A,B,C,X(2),X(105)}
X(54977) = intersection, other than A, B, C, of circumconics: {{A, B, C, X(1), X(2)}}, {{A, B, C, X(4), X(668)}}, {{A, B, C, X(6), X(876)}}, {{A, B, C, X(7), X(1027)}}, {{A, B, C, X(8), X(1024)}}, {{A, B, C, X(19), X(5377)}}, {{A, B, C, X(56), X(764)}}, {{A, B, C, X(58), X(24484)}}, {{A, B, C, X(65), X(5091)}}, {{A, B, C, X(267), X(5540)}}, {{A, B, C, X(513), X(18821)}}, {{A, B, C, X(514), X(52030)}}, {{A, B, C, X(518), X(3669)}}, {{A, B, C, X(528), X(891)}}, {{A, B, C, X(537), X(2832)}}, {{A, B, C, X(749), X(5378)}}, {{A, B, C, X(812), X(2809)}}, {{A, B, C, X(1019), X(2113)}}, {{A, B, C, X(1438), X(7233)}}, {{A, B, C, X(2214), X(19977)}}, {{A, B, C, X(2711), X(9322)}}, {{A, B, C, X(2787), X(2836)}}, {{A, B, C, X(2810), X(2826)}}, {{A, B, C, X(2837), X(35103)}}, {{A, B, C, X(3263), X(41934)}}, {{A, B, C, X(4998), X(6591)}}, {{A, B, C, X(6084), X(14839)}}, {{A, B, C, X(8047), X(18108)}}, {{A, B, C, X(9267), X(34434)}}, {{A, B, C, X(9309), X(35355)}}, {{A, B, C, X(15382), X(28838)}}, {{A, B, C, X(19895), X(39798)}}, {{A, B, C, X(35160), X(51845)}}, {{A, B, C, X(35353), X(43692)}}
X(54977) = barycentric product X(i)*X(j) for these (i, j): {513, 53213}
X(54977) = barycentric quotient X(i)/X(j) for these (i, j): {6, 1083}, {53213, 668}

X(54978) = X(4)X(2023)∩X(76)X(114)

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

X(54978) lies on these lines: {2, 38383}, {4, 2023}, {76, 114}, {83, 13335}, {98, 1692}, {511, 8781}, {1513, 1916}, {2782, 2996}, {3399, 3815}, {3407, 13860}, {3566, 46040}, {5395, 38741}, {5976, 40824}, {9772, 43688}, {39663, 43532}

X(54978) = isogonal conjugate of X(2456)
X(54978) = X(i)-vertex conjugate of X(j) for these {i, j}: {1916, 3425}, {41533, 43532}
X(54978) = intersection, other than A, B, C, of circumconics: {{A,B,C,X(2),X(4)}}, {{A,B,C,X(25),X(37446)}}, {{A,B,C,X(39),X(13335)}}, {{A,B,C,X(114),X(511)}}, {{A,B,C,X(325),X(38383)}}, {{A,B,C,X(419),X(1513)}}, {{A,B,C,X(427),X(37334)}}, {{A,B,C,X(2023),X(40708)}}, {{A,B,C,X(2698),X(17980)}}, {{A,B,C,X(2782),X(3566)}}, {{A,B,C,X(2967),X(52009)}}, {{A,B,C,X(3815),X(45108)}}, {{A,B,C,X(5117),X(13860)}}, {{A,B,C,X(6530),X(46235)}}, {{A,B,C,X(14941),X(15391)}}, {{A,B,C,X(40801),X(41533)}}, {{A,B,C,X(41517),X(43702)}}, {{A,B,C,X(47388),X(51454)}}

X(54980) = X(2)X(3121)∩X(6)X(1045)

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

X(54980) lies on cubic K323 and on these lines: {2, 3121}, {6, 1045}, {37, 1084}, {42, 2107}, {75, 25054}, {111, 53624}, {239, 2669}, {518, 694}, {536, 3228}, {670, 3739}, {742, 25326}, {1015, 36225}, {2248, 8301}, {2667, 9403}, {2805, 14948}, {3212, 42290}, {3572, 21832}, {3696, 16606}, {3952, 21820}, {4698, 31639}, {6651, 39971}, {16098, 44670}, {25318, 49496}, {31238, 36950}, {33888, 40776}

X(54980) = midpoint of X(i) in X(j) for these {i,j}: {75, 25054}
X(54980) = reflection of X(i) in X(j) for these {i,j}: {37, 1084}, {670, 3739}
X(54980) = trilinear pole of line {16589,22222}
X(54980) = perspector of circumconic {{A, B, C, X(53216), X(53624)}}
X(54980) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2106}, {6, 2669}, {27, 20796}, {31, 40874}, {32, 41535}, {58, 17759}, {63, 15148}, {81, 2664}, {86, 21788}, {741, 39916}, {757, 21897}, {1333, 52049}, {18268, 39028}, {18827, 51331}
X(54980) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 40874}, {3, 2106}, {9, 2669}, {10, 17759}, {37, 52049}, {3162, 15148}, {6376, 41535}, {8299, 39916}, {35068, 39028}, {40586, 2664}, {40600, 21788}, {40607, 21897}
X(54980) = X(2665)-Ceva conjugate of X(2107)
X(54980) = X(i)-cross conjugate of X(j) for these {i, j}: {291, 9278}, {740, 37}
X(54980) = antipode of X(37) in the circumconic {A,B,C,X(2),X(37)}
X(54980) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(40749)}}, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(31), X(42358)}}, {{A, B, C, X(75), X(1045)}}, {{A, B, C, X(210), X(52652)}}, {{A, B, C, X(239), X(4094)}}, {{A, B, C, X(257), X(7148)}}, {{A, B, C, X(274), X(1500)}}, {{A, B, C, X(291), X(740)}}, {{A, B, C, X(335), X(661)}}, {{A, B, C, X(512), X(3227)}}, {{A, B, C, X(518), X(804)}}, {{A, B, C, X(536), X(888)}}, {{A, B, C, X(670), X(3952)}}, {{A, B, C, X(673), X(2238)}}, {{A, B, C, X(756), X(27483)}}, {{A, B, C, X(872), X(893)}}, {{A, B, C, X(1084), X(3121)}}, {{A, B, C, X(1215), X(52175)}}, {{A, B, C, X(1222), X(2295)}}, {{A, B, C, X(1575), X(20681)}}, {{A, B, C, X(2107), X(39925)}}, {{A, B, C, X(3112), X(9421)}}, {{A, B, C, X(3212), X(3696)}}, {{A, B, C, X(3226), X(19580)}}, {{A, B, C, X(3739), X(21820)}}, {{A, B, C, X(4041), X(52517)}}, {{A, B, C, X(4705), X(11611)}}, {{A, B, C, X(6651), X(20693)}}, {{A, B, C, X(9035), X(44670)}}, {{A, B, C, X(9359), X(18149)}}, {{A, B, C, X(17989), X(19623)}}, {{A, B, C, X(18793), X(18794)}}, {{A, B, C, X(20683), X(46802)}}, {{A, B, C, X(20694), X(24578)}}, {{A, B, C, X(21805), X(46797)}}, {{A, B, C, X(21902), X(42027)}}, {{A, B, C, X(40844), X(50491)}}, {{A, B, C, X(44330), X(46536)}}, {{A, B, C, X(46801), X(52959)}}, {{A, B, C, X(46805), X(51377)}}
X(54980) = barycentric product X(i)*X(j) for these (i, j): {10, 2665}, {37, 39925}, {321, 51333}, {512, 53216}, {523, 53624}, {2107, 75}, {40769, 43534}, {43685, 6}
X(54980) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2669}, {2, 40874}, {6, 2106}, {10, 52049}, {25, 15148}, {37, 17759}, {42, 2664}, {75, 41535}, {213, 21788}, {228, 20796}, {740, 39028}, {1500, 21897}, {2107, 1}, {2238, 39916}, {2665, 86}, {8937, 6626}, {21832, 27854}, {39925, 274}, {40769, 33295}, {41333, 51331}, {43685, 76}, {51333, 81}, {53216, 670}, {53624, 99}

X(54979) = X(99)X(29241)∩X(648)X(4600)

Barycentrics    1/((b-c)*(2*a^3-a^2*(b+c)+(b-c)^2*(b+c))) : :

X(54979) lies on these lines: {99, 29241}, {190, 42402}, {648, 4600}, {889, 35365}

X(54979) = isotomic conjugate of X(29240)
X(54979) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(75), X(35574)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(645), X(6386)}}, {{A, B, C, X(4583), X(13136)}}, {{A, B, C, X(4608), X(48269)}}, {{A, B, C, X(4628), X(29273)}}, {{A, B, C, X(8750), X(29083)}}
X(54979) = trilinear pole of line {2, 4561}
X(54979) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 29240}, {667, 3011}, {1973, 2504}, {3121, 4237}
X(54979) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 29240}, {6337, 2504}, {6631, 3011}
X(54979) = X(i)-cross conjugate of X(j) for these {i, j}: {3006, 1016}, {29240, 2}
X(54979) = barycentric product X(i)*X(j) for these (i, j): {29241, 76}, {31625, 35365}
X(54979) = barycentric quotient X(i)/X(j) for these (i, j): {2, 29240}, {69, 2504}, {190, 3011}, {4561, 9028}, {4563, 51607}, {4600, 4237}, {29241, 6}, {35365, 1015}

X(54980) = X(2)X(3121)∩X(6)X(1045)

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

X(54980) lies on cubic K323 and on these lines: {2, 3121}, {6, 1045}, {37, 1084}, {42, 2107}, {75, 25054}, {111, 53624}, {239, 2669}, {518, 694}, {536, 3228}, {670, 3739}, {742, 25326}, {1015, 36225}, {2248, 8301}, {2667, 9403}, {2805, 14948}, {3212, 42290}, {3572, 21832}, {3696, 16606}, {3952, 21820}, {4698, 31639}, {6651, 39971}, {16098, 44670}, {25318, 49496}, {31238, 36950}, {33888, 40776}

X(54980) = midpoint of X(i) in X(j) for these {i,j}: {75, 25054}
X(54980) = reflection of X(i) in X(j) for these {i,j}: {37, 1084}, {670, 3739}
X(54980) = trilinear pole of line {16589,22222}
X(54980) = perspector of circumconic {{A, B, C, X(53216), X(53624)}}
X(54980) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2106}, {6, 2669}, {27, 20796}, {31, 40874}, {32, 41535}, {58, 17759}, {63, 15148}, {81, 2664}, {86, 21788}, {741, 39916}, {757, 21897}, {1333, 52049}, {18268, 39028}, {18827, 51331}
X(54980) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 40874}, {3, 2106}, {9, 2669}, {10, 17759}, {37, 52049}, {3162, 15148}, {6376, 41535}, {8299, 39916}, {35068, 39028}, {40586, 2664}, {40600, 21788}, {40607, 21897}
X(54980) = X(2665)-Ceva conjugate of X(2107)
X(54980) = X(i)-cross conjugate of X(j) for these {i, j}: {291, 9278}, {740, 37}
X(54980) = antipode of X(37) in the circumconic {A,B,C,X(2),X(37)}
X(54980) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(40749)}}, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(31), X(42358)}}, {{A, B, C, X(75), X(1045)}}, {{A, B, C, X(210), X(52652)}}, {{A, B, C, X(239), X(4094)}}, {{A, B, C, X(257), X(7148)}}, {{A, B, C, X(274), X(1500)}}, {{A, B, C, X(291), X(740)}}, {{A, B, C, X(335), X(661)}}, {{A, B, C, X(512), X(3227)}}, {{A, B, C, X(518), X(804)}}, {{A, B, C, X(536), X(888)}}, {{A, B, C, X(670), X(3952)}}, {{A, B, C, X(673), X(2238)}}, {{A, B, C, X(756), X(27483)}}, {{A, B, C, X(872), X(893)}}, {{A, B, C, X(1084), X(3121)}}, {{A, B, C, X(1215), X(52175)}}, {{A, B, C, X(1222), X(2295)}}, {{A, B, C, X(1575), X(20681)}}, {{A, B, C, X(2107), X(39925)}}, {{A, B, C, X(3112), X(9421)}}, {{A, B, C, X(3212), X(3696)}}, {{A, B, C, X(3226), X(19580)}}, {{A, B, C, X(3739), X(21820)}}, {{A, B, C, X(4041), X(52517)}}, {{A, B, C, X(4705), X(11611)}}, {{A, B, C, X(6651), X(20693)}}, {{A, B, C, X(9035), X(44670)}}, {{A, B, C, X(9359), X(18149)}}, {{A, B, C, X(17989), X(19623)}}, {{A, B, C, X(18793), X(18794)}}, {{A, B, C, X(20683), X(46802)}}, {{A, B, C, X(20694), X(24578)}}, {{A, B, C, X(21805), X(46797)}}, {{A, B, C, X(21902), X(42027)}}, {{A, B, C, X(40844), X(50491)}}, {{A, B, C, X(44330), X(46536)}}, {{A, B, C, X(46801), X(52959)}}, {{A, B, C, X(46805), X(51377)}}
X(54980) = barycentric product X(i)*X(j) for these (i, j): {10, 2665}, {37, 39925}, {321, 51333}, {512, 53216}, {523, 53624}, {2107, 75}, {40769, 43534}, {43685, 6}
X(54980) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2669}, {2, 40874}, {6, 2106}, {10, 52049}, {25, 15148}, {37, 17759}, {42, 2664}, {75, 41535}, {213, 21788}, {228, 20796}, {740, 39028}, {1500, 21897}, {2107, 1}, {2238, 39916}, {2665, 86}, {8937, 6626}, {21832, 27854}, {39925, 274}, {40769, 33295}, {41333, 51331}, {43685, 76}, {51333, 81}, {53216, 670}, {53624, 99}

X(54981) = X(1)X(6)∩X(31)X(101)

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

X(54981) lies on these lines: {1, 6}, {2, 3997}, {31, 101}, {35, 14974}, {41, 595}, {42, 9331}, {43, 1018}, {57, 4559}, {58, 9310}, {75, 46899}, {81, 29597}, {106, 2279}, {111, 5202}, {239, 4671}, {292, 2163}, {386, 1334}, {519, 37657}, {574, 8624}, {644, 16834}, {672, 995}, {729, 28841}, {758, 26242}, {869, 902}, {894, 52716}, {978, 16549}, {994, 18785}, {1017, 5008}, {1046, 17736}, {1054, 6205}, {1055, 4257}, {1185, 8616}, {1193, 3730}, {1201, 4253}, {1213, 19871}, {1384, 2223}, {1475, 9336}, {1500, 5312}, {1572, 5540}, {1698, 2295}, {2177, 3747}, {2238, 3679}, {2251, 21793}, {2270, 21770}, {2271, 3746}, {2276, 5313}, {2280, 40091}, {2291, 32722}, {2301, 21059}, {2664, 8621}, {3009, 9463}, {3051, 23573}, {3208, 3293}, {3216, 3501}, {3231, 40749}, {3290, 5902}, {3509, 49500}, {3550, 9431}, {3620, 27248}, {3624, 17750}, {3633, 3780}, {3684, 37610}, {3725, 10434}, {3726, 3894}, {3729, 27644}, {3735, 3899}, {3760, 17033}, {3761, 24514}, {3869, 16600}, {3876, 28594}, {3915, 4251}, {3929, 40153}, {3931, 4520}, {4115, 32925}, {4144, 34542}, {4256, 41423}, {4383, 14535}, {4384, 37680}, {4888, 28350}, {4919, 49494}, {5010, 17735}, {5021, 5563}, {5024, 37575}, {5165, 8610}, {5276, 48854}, {5697, 41015}, {5903, 16583}, {7280, 21008}, {9259, 37587}, {13462, 52635}, {14210, 35274}, {14996, 16826}, {15989, 49723}, {16827, 17116}, {16829, 17349}, {16831, 37633}, {17117, 32104}, {17137, 30110}, {17152, 30107}, {17753, 24790}, {17754, 49997}, {19875, 37673}, {20109, 27097}, {20985, 41415}, {21309, 37590}, {21753, 42042}, {21904, 52964}, {21935, 24045}, {24512, 25055}, {25264, 25269}, {25590, 27623}, {26689, 33942}, {26715, 32726}, {29573, 37676}, {29580, 37685}, {36274, 48352}, {36531, 40747}, {36871, 50127}, {37675, 39586}, {39797, 39970}

X(54981) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36871}, {513, 37209}, {514, 29351}
X(54981) = perspector of circumconic {{A, B, C, X(100), X(34075)}}
X(54981) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 36871}, {39026, 37209}
X(54981) = X(i)-Zayin conjugate of X(j) for these {i, j}: {1, 36871}, {47761, 650}
X(54981) = intersection, other than A, B, C, of circumconics {{A,B,C,X(1),X(739)}}, {{A,B,C,X(31),X(3230)}}, {{A,B,C,X(37),X(4664)}}, {{A,B,C,X(44),X(2279)}}, {{A,B,C,X(45),X(292)}}, {{A,B,C,X(57),X(45751)}}, {{A,B,C,X(101),X(23343)}}, {{A,B,C,X(106),X(1001)}}, {{A,B,C,X(111),X(5251)}}, {{A,B,C,X(238),X(2163)}}, {{A,B,C,X(518),X(994)}}, {{A,B,C,X(609),X(765)}}, {{A,B,C,X(729),X(4649)}}, {{A,B,C,X(840),X(45765)}}, {{A,B,C,X(956),X(2291)}}, {{A,B,C,X(1023),X(8693)}}, {{A,B,C,X(5258),X(28334)}}, {{A,B,C,X(5259),X(28338)}}, {{A,B,C,X(9319),X(16506)}}, {{A,B,C,X(16552),X(39970)}}, {{A,B,C,X(16975),X(36871)}}, {{A,B,C,X(21061),X(41441)}}, {{A,B,C,X(21384),X(39797)}}
X(54981) = barycentric product X(i)*X(j) for these (i, j): {1, 3240}, {100, 29350}, {101, 4776}, {4664, 6}
X(54981) = barycentric quotient X(i)/X(j) for these (i, j): {6, 36871}, {101, 37209}, {692, 29351}, {3240, 75}, {4664, 76}, {4776, 3261}, {29350, 693}
X(54981) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1743, 45751}, {6, 16483, 16784}, {6, 2176, 3230}, {31, 101, 609}, {41, 595, 7031}, {213, 3230, 6}, {218, 1191, 5299}, {220, 16466, 5280}, {3230, 16782, 16489}, {16969, 20963, 1}, {24514, 40859, 3761}

X(54982) = X(99)X(1310)∩X(648)X(799)

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

X(54982) lies on these lines: {76, 14258}, {99, 1310}, {190, 37215}, {304, 31158}, {648, 799}, {1245, 18826}, {1472, 18824}, {2221, 18825}, {2281, 3225}, {2481, 30479}, {4554, 6648}, {4572, 18026}, {40073, 54109}

X(54982) = trilinear pole of line {2, 304}
X(54982) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 8646}, {6, 2484}, {31, 8678}, {32, 6590}, {58, 50494}, {512, 44119}, {560, 2517}, {612, 667}, {649, 54416}, {663, 1460}, {669, 1010}, {798, 2303}, {810, 4206}, {1918, 47844}, {1919, 2345}, {1973, 2522}, {1974, 23874}, {1980, 4385}, {2206, 48395}, {2212, 51644}, {2285, 3063}, {4320, 8641}, {9426, 44154}
X(54982) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 8678}, {3, 8646}, {9, 2484}, {10, 50494}, {5375, 54416}, {6337, 2522}, {6374, 2517}, {6376, 6590}, {6631, 612}, {9296, 2345}, {10001, 2285}, {31998, 2303}, {34021, 47844}, {39054, 44119}, {39062, 4206}, {40603, 48395}
X(54982) = X(i)-cross conjugate of X(j) for these {i, j}: {3672, 31625}, {8678, 2}, {39731, 7035}, {45746, 274}
X(54982) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(75), X(37218)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(100), X(42363)}}, {{A, B, C, X(789), X(6335)}}, {{A, B, C, X(799), X(4572)}}, {{A, B, C, X(833), X(36086)}}, {{A, B, C, X(934), X(53332)}}, {{A, B, C, X(1310), X(36099)}}, {{A, B, C, X(1633), X(3952)}}, {{A, B, C, X(1978), X(4625)}}, {{A, B, C, X(3903), X(8750)}}, {{A, B, C, X(4554), X(4623)}}, {{A, B, C, X(47814), X(47820)}}
X(54982) = barycentric product X(i)*X(j) for these (i, j): {305, 36099}, {1245, 4602}, {1310, 76}, {1633, 40831}, {2221, 6386}, {2281, 4609}, {2339, 4572}, {30479, 4554}, {32691, 40364}, {37215, 75}
X(54982) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2484}, {2, 8678}, {6, 8646}, {37, 50494}, {69, 2522}, {75, 6590}, {76, 2517}, {99, 2303}, {100, 54416}, {190, 612}, {274, 47844}, {304, 23874}, {321, 48395}, {348, 51644}, {646, 3974}, {648, 4206}, {651, 1460}, {658, 4320}, {662, 44119}, {664, 2285}, {668, 2345}, {799, 1010}, {1036, 3063}, {1245, 798}, {1310, 6}, {1332, 7085}, {1472, 1919}, {1633, 1184}, {1978, 4385}, {2221, 667}, {2281, 669}, {2339, 663}, {4554, 388}, {4561, 5227}, {4566, 8898}, {4569, 7365}, {4573, 5323}, {4602, 44154}, {6335, 7102}, {6516, 2286}, {13149, 7103}, {15413, 26933}, {30479, 650}, {32691, 1973}, {36099, 25}, {36838, 7197}, {37215, 1}, {53643, 40184}

X(54983) = X(99)X(1306)∩X(493)X(3228)

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

X(54983) lies on the Steiner circumellipse and on these lines: {99, 1306}, {493, 3228}, {671, 5490}, {3225, 26454}, {4563, 54031}, {14970, 26347}, {24244, 35142}

X(54983) = trilinear pole of line {2, 493}
X(54983) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 6423}, {798, 3068}, {810, 5200}, {1973, 17431}, {2489, 19215}
X(54983) = X(i)-Dao conjugate of X(j) for these {i, j}: {6337, 17431}, {31998, 3068}, {33365, 6562}, {36830, 6423}, {39062, 5200}
X(54983) = X(i)-cross conjugate of X(j) for these {i, j}: {1270, 4590}
X(54983) = barycentric product X(i)*X(j) for these (i, j): {493, 670}, {1306, 76}, {5490, 99}, {24244, 4563}, {26347, 689}, {26454, 4609}, {52608, 8948}
X(54983) = barycentric quotient X(i)/X(j) for these (i, j): {69, 17431}, {99, 3068}, {110, 6423}, {492, 14325}, {493, 512}, {648, 5200}, {1306, 6}, {1307, 45595}, {3069, 6562}, {4558, 10132}, {4563, 488}, {4592, 19215}, {5490, 523}, {8948, 2489}, {24244, 2501}, {26347, 3005}, {26454, 669}, {52608, 46742}

X(54984) = X(99)X(1307)∩X(494)X(3228)

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

X(54984) lies on the Steiner circumellipse and on these lines: {99, 1307}, {494, 3228}, {671, 5491}, {3225, 26461}, {4563, 54030}, {14970, 45594}, {24243, 35142}

X(54984) = trilinear pole of line {2, 494}
X(54984) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 6424}, {798, 3069}, {810, 52291}, {1973, 17432}, {2489, 19216}
X(54984) = X(i)-Dao conjugate of X(j) for these {i, j}: {6337, 17432}, {31998, 3069}, {33364, 6562}, {36830, 6424}, {39062, 52291}
X(54984) = X(i)-cross conjugate of X(j) for these {i, j}: {1271, 4590}
X(54984) = barycentric product X(i)*X(j) for these (i, j): {494, 670}, {1307, 76}, {5491, 99}, {24243, 4563}, {26461, 4609}, {45594, 689}, {52608, 8946}
X(54984) = barycentric quotient X(i)/X(j) for these (i, j): {69, 17432}, {99, 3069}, {110, 6424}, {491, 14326}, {494, 512}, {648, 52291}, {1306, 45596}, {1307, 6}, {3068, 6562}, {4558, 10133}, {4563, 487}, {4592, 19216}, {5491, 523}, {8946, 2489}, {24243, 2501}, {26461, 669}, {45594, 3005}, {52608, 46743}

X(54985) = X(99)X(8709)∩X(350)X(3226)

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

X(54985) lies on these lines: {76, 35119}, {99, 8709}, {190, 20979}, {313, 35165}, {350, 3226}, {513, 6386}, {536, 40844}, {668, 4083}, {670, 17217}, {700, 43096}, {727, 18824}, {1921, 33679}, {1978, 31147}, {3227, 18145}, {3228, 27809}, {4479, 18822}, {4562, 27853}, {4586, 5388}, {17790, 35143}, {18793, 18826}, {18825, 20332}, {18827, 19567}, {20530, 40881}, {33680, 52049}, {33769, 53219}

X(54985) = isotomic conjugate of X(6373)
X(54985) = reflection of X(i) in X(j) for these {i,j}: {40881, 20530}
X(54985) = trilinear pole of line {2, 1978}
X(54985) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 6373}, {292, 38367}, {560, 3837}, {649, 21760}, {667, 3009}, {669, 18792}, {692, 52633}, {726, 1980}, {875, 20663}, {1501, 20908}, {1575, 1919}, {1973, 22092}, {20979, 51864}
X(54985) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 6373}, {1086, 52633}, {5375, 21760}, {6337, 22092}, {6374, 3837}, {6631, 3009}, {9296, 1575}, {19557, 38367}, {33678, 649}
X(54985) = X(i)-cross conjugate of X(j) for these {i, j}: {350, 31625}, {659, 308}, {4583, 36803}, {6373, 2}, {20352, 1016}, {20561, 4998}
X(54985) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(350), X(4583)}}, {{A, B, C, X(513), X(4083)}}, {{A, B, C, X(700), X(730)}}, {{A, B, C, X(3766), X(35119)}}, {{A, B, C, X(5388), X(31625)}}, {{A, B, C, X(14295), X(18004)}}, {{A, B, C, X(23354), X(40881)}}, {{A, B, C, X(27853), X(36803)}}, {{A, B, C, X(41144), X(41314)}}
X(54985) = barycentric product X(i)*X(j) for these (i, j): {76, 8709}, {1978, 3226}, {18793, 4602}, {18830, 40844}, {20332, 6386}, {27809, 670}, {32020, 668}, {36799, 4572}
X(54985) = barycentric quotient X(i)/X(j) for these (i, j): {2, 6373}, {69, 22092}, {76, 3837}, {100, 21760}, {190, 3009}, {238, 38367}, {313, 21053}, {514, 52633}, {561, 20908}, {668, 1575}, {727, 1919}, {799, 18792}, {874, 17475}, {932, 51864}, {1332, 20777}, {1978, 726}, {3226, 649}, {3253, 8632}, {3261, 21140}, {3570, 20663}, {3952, 21830}, {4554, 1463}, {4561, 20785}, {4562, 40155}, {4572, 43040}, {4583, 52656}, {6386, 52043}, {8709, 6}, {8851, 3063}, {18793, 798}, {18830, 40881}, {20332, 667}, {23354, 20671}, {23355, 1977}, {27809, 512}, {27853, 17793}, {31625, 23354}, {32020, 513}, {34077, 1980}, {36799, 663}, {40844, 4083}

X(54986) = X(8)X(35176)∩X(290)X(322)

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

X(54986) lies on these lines: {8, 35176}, {69, 18827}, {75, 35159}, {99, 3882}, {290, 322}, {648, 3570}, {661, 7258}, {671, 43677}, {903, 42051}, {3226, 28366}, {4417, 14616}, {4551, 6648}, {4562, 52609}, {18816, 30078}, {33677, 53222}

X(54986) = isotomic conjugate of X(6002)
X(54986) = trilinear pole of line {2, 986}
X(54986) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 6002}, {110, 16613}, {649, 5247}, {667, 1999}, {1973, 24560}
X(54986) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 6002}, {244, 16613}, {5375, 5247}, {6337, 24560}, {6631, 1999}
X(54986) = X(i)-cross conjugate of X(j) for these {i, j}: {4017, 75}, {6002, 2}, {7257, 27805}, {26545, 76}
X(54986) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(8), X(7258)}}, {{A, B, C, X(69), X(3570)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(651), X(1978)}}, {{A, B, C, X(662), X(3882)}}, {{A, B, C, X(799), X(4552)}}, {{A, B, C, X(1020), X(4602)}}, {{A, B, C, X(3257), X(26700)}}, {{A, B, C, X(4103), X(15322)}}, {{A, B, C, X(4417), X(4585)}}, {{A, B, C, X(4573), X(8052)}}, {{A, B, C, X(4598), X(6335)}}, {{A, B, C, X(4615), X(38340)}}, {{A, B, C, X(15455), X(37205)}}, {{A, B, C, X(24004), X(42051)}}, {{A, B, C, X(24029), X(30078)}}, {{A, B, C, X(24621), X(27853)}}, {{A, B, C, X(42363), X(51563)}}, {{A, B, C, X(51560), X(54458)}}
X(54986) = barycentric product X(i)*X(j) for these (i, j): {6010, 76}, {43677, 99}
X(54986) = barycentric quotient X(i)/X(j) for these (i, j): {2, 6002}, {69, 24560}, {100, 5247}, {190, 1999}, {322, 25022}, {661, 16613}, {6010, 6}, {26545, 44950}, {43677, 523}, {53332, 39774}

X(54987) = X(69)X(2481)∩X(99)X(1292)

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

X(54987) lies on these lines: {69, 2481}, {75, 35160}, {76, 14268}, {99, 1292}, {190, 25736}, {277, 3227}, {322, 18025}, {325, 35152}, {666, 1332}, {693, 4578}, {883, 18026}, {903, 18043}, {1121, 16284}, {1909, 35176}, {2191, 3226}, {2414, 32041}, {3262, 18821}, {3699, 53653}, {4554, 6606}, {18816, 44133}, {23819, 27834}, {33677, 35167}, {40154, 42697}, {44134, 46133}

X(54987) = isogonal conjugate of X(8642)
X(54987) = isotomic conjugate of X(3309)
X(54987) = trilinear pole of line {2, 277}
X(54987) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 8642}, {31, 3309}, {32, 4468}, {41, 43049}, {55, 51652}, {218, 649}, {344, 1919}, {513, 21059}, {663, 1617}, {667, 3870}, {672, 2440}, {798, 41610}, {810, 4233}, {1397, 44448}, {1415, 38375}, {1445, 3063}, {1576, 21945}, {1973, 24562}, {2175, 31605}, {2402, 9454}, {3733, 4878}, {4350, 8641}, {4904, 32739}, {6600, 43924}, {7719, 22383}, {23760, 23990}
X(54987) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3309}, {3, 8642}, {223, 51652}, {1146, 38375}, {3160, 43049}, {4858, 21945}, {5375, 218}, {6337, 24562}, {6376, 4468}, {6631, 3870}, {9296, 344}, {10001, 1445}, {31998, 41610}, {33675, 2402}, {39026, 21059}, {39062, 4233}, {40593, 31605}, {40619, 4904}
X(54987) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {37206, 34547}
X(54987) = X(i)-cross conjugate of X(j) for these {i, j}: {644, 4554}, {3309, 2}, {24002, 75}, {25266, 31624}, {26546, 76}, {34784, 765}, {47676, 274}
X(54987) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(7), X(27834)}}, {{A, B, C, X(8), X(4578)}}, {{A, B, C, X(69), X(883)}}, {{A, B, C, X(75), X(646)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(264), X(6386)}}, {{A, B, C, X(523), X(2788)}}, {{A, B, C, X(1978), X(13149)}}, {{A, B, C, X(4572), X(6335)}}, {{A, B, C, X(8050), X(13138)}}, {{A, B, C, X(9086), X(38340)}}, {{A, B, C, X(28474), X(51223)}}
X(54987) = barycentric product X(i)*X(j) for these (i, j): {277, 668}, {1292, 76}, {1978, 2191}, {2414, 2481}, {4554, 6601}, {37206, 75}, {40154, 646}
X(54987) = barycentric quotient X(i)/X(j) for these (i, j): {2, 3309}, {6, 8642}, {7, 43049}, {57, 51652}, {69, 24562}, {75, 4468}, {85, 31605}, {99, 41610}, {100, 218}, {101, 21059}, {105, 2440}, {190, 3870}, {277, 513}, {312, 44448}, {522, 38375}, {644, 6600}, {648, 4233}, {651, 1617}, {658, 4350}, {664, 1445}, {668, 344}, {693, 4904}, {1018, 4878}, {1111, 23760}, {1292, 6}, {1577, 21945}, {1897, 7719}, {2191, 649}, {2397, 51378}, {2402, 15636}, {2414, 518}, {2428, 2223}, {2481, 2402}, {3952, 3991}, {4552, 41539}, {4554, 6604}, {4569, 17093}, {4572, 21609}, {6516, 23144}, {6601, 650}, {17107, 43924}, {24002, 40615}, {25009, 38386}, {26546, 5511}, {36041, 1438}, {37206, 1}, {40154, 3669}, {51560, 31638}, {53647, 27819}

X(54988) = X(99)X(1294)∩X(394)X(648)

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

X(54988) lies on these lines: {69, 6528}, {99, 1294}, {264, 15394}, {290, 43701}, {394, 648}, {670, 4176}, {2966, 40888}, {3260, 16077}, {18026, 52385}

X(54988) = isotomic conjugate of X(6000)
X(54988) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(4), X(21312)}}, {{A, B, C, X(69), X(394)}}, {{A, B, C, X(76), X(44133)}}, {{A, B, C, X(99), X(190)}}, {{A, B, C, X(253), X(8795)}}, {{A, B, C, X(264), X(14615)}}, {{A, B, C, X(315), X(44134)}}, {{A, B, C, X(325), X(40888)}}, {{A, B, C, X(328), X(3260)}}, {{A, B, C, X(523), X(2790)}}, {{A, B, C, X(850), X(51967)}}, {{A, B, C, X(2706), X(18877)}}, {{A, B, C, X(14387), X(40009)}}, {{A, B, C, X(15072), X(15305)}}, {{A, B, C, X(18817), X(40705)}}, {{A, B, C, X(32230), X(34168)}}, {{A, B, C, X(34385), X(34410)}}, {{A, B, C, X(35510), X(42355)}}, {{A, B, C, X(36889), X(46104)}}
X(54988) = trilinear pole of line {2, 2416}
X(54988) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 6000}, {810, 46587}, {822, 2442}, {1973, 44436}, {2159, 47433}, {2173, 51964}, {9247, 51358}, {51385, 52430}
X(54988) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 6000}, {3163, 47433}, {6337, 44436}, {36896, 51964}, {39062, 46587}
X(54988) = X(i)-cross conjugate of X(j) for these {i, j}: {6000, 2}, {14919, 40832}, {41077, 6331}, {46106, 76}
X(54988) = barycentric product X(i)*X(j) for these (i, j): {1294, 76}, {2416, 6528}, {32646, 52617}, {43701, 6331}
X(54988) = barycentric quotient X(i)/X(j) for these (i, j): {2, 6000}, {30, 47433}, {69, 44436}, {74, 51964}, {107, 2442}, {264, 51358}, {648, 46587}, {1294, 6}, {2052, 51385}, {2416, 520}, {2430, 39201}, {2986, 51895}, {6528, 2404}, {11064, 40948}, {14919, 39174}, {15404, 18877}, {15466, 1559}, {16080, 52646}, {32646, 32713}, {36043, 24019}, {43701, 647}, {46106, 133}, {52147, 1515}, {53789, 3284}

X(54989) = X(99)X(2365)∩X(332)X(648)

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

X(54989) lies on these lines: {99, 2365}, {190, 1264}, {304, 18026}, {332, 648}, {664, 3926}, {6528, 28660}

X(54989) = isotomic conjugate of X(2385)
X(54989) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(304), X(332)}}, {{A, B, C, X(3346), X(3427)}}
X(54989) = trilinear pole of line {2, 52587}
X(54989) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 2385}, {1973, 45271}
X(54989) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 2385}, {6337, 45271}
X(54989) = barycentric product X(i)*X(j) for these (i, j): {2365, 76}
X(54989) = barycentric quotient X(i)/X(j) for these (i, j): {2, 2385}, {69, 45271}, {2365, 6}

X(54990) = X(290)X(8024)∩X(2396)X(4577)

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

X(54990) lies on these lines: {290, 8024}, {671, 33184}, {2396, 4577}, {2966, 4576}

X(54990) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(99), X(190)}}, {{A, B, C, X(689), X(39291)}}, {{A, B, C, X(930), X(41513)}}, {{A, B, C, X(1296), X(14560)}}, {{A, B, C, X(1576), X(30254)}}, {{A, B, C, X(2396), X(4576)}}, {{A, B, C, X(4235), X(33184)}}, {{A, B, C, X(30255), X(32737)}}, {{A, B, C, X(32716), X(39629)}}
X(54990) = trilinear pole of line {2, 4121}
X(54990) = X(i)-isoconjugate-of-X(j) for these {i, j}: {798, 7792}, {1973, 50547}
X(54990) = X(i)-Dao conjugate of X(j) for these {i, j}: {6337, 50547}, {31998, 7792}
X(54990) = X(i)-cross conjugate of X(j) for these {i, j}: {3314, 4590}
X(54990) = barycentric quotient X(i)/X(j) for these (i, j): {69, 50547}, {99, 7792}

X(54991) = X(2)X(15265)∩X(4)X(39)

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

X(54991) lies on these lines: {2, 15265}, {4, 39}, {6, 32444}, {32, 11424}, {115, 3117}, {187, 6785}, {216, 31670}, {217, 7772}, {237, 574}, {248, 15033}, {381, 11672}, {3229, 43620}, {3815, 44227}, {5476, 5661}, {7746, 37121}, {7757, 39355}, {9291, 37337}, {9605, 12315}, {11185, 36212}, {11550, 14773}, {32452, 42442}, {37114, 37512}, {52967, 53023}

X(54991) = complement of X(54033)
X(54991) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 7709, 39682}

X(54992) = X(2)X(3)∩X(112)X(5896)

Barycentrics    a^2*(3*a^8+28*a^4*b^2*c^2-6*a^6*(b^2+c^2)-(b^2-c^2)^2*(3*b^4+14*b^2*c^2+3*c^4)+2*a^2*(3*b^6-7*b^4*c^2-7*b^2*c^4+3*c^6)) : :

X(54992) lies on these lines: {2, 3}, {64, 12164}, {74, 38263}, {112, 5896}, {155, 13093}, {511, 10606}, {519, 34703}, {541, 12302}, {542, 2935}, {543, 3984 {999, 7221}, {1147, 12315}, {1192, 13598}, {1204, 21969}, {1327, 8276}, {1328, 8277}, {1351, 10605}, {1609, 6128}, {1993, 13445}, {2138, 22120}, {2794, 9876}, {3167, 6000}, {3, 4348}, {3357, 37498}, {3426, 10564}, {5093, 5890}, {5434, 16541}, {5644, 15045}, {5889, 34469}, {6090, 15305}, {6247, 12429}, {6407, 11265}, {6408, 11266}, {7592, 13482}, {78 22468}, {8567, 46730}, {8716, 34808}, {8780, 51394}, {8996, 13800}, {9605, 18373}, {9786, 21849}, {9861, 39831}, {9919, 12901}, {10575, 19347}, {10982, 16226}, 381, 35602}, {11402, 15072}, {11425, 46850}, {11426, 40647}, {11598, 34777}, {11645, 39879}, {12038, 14530}, {12099, 15055}, {12117, 39803}, {12118, 34780}, {12, 34148}, {12290, 43572}, {12303, 32419}, {12304, 32421}, {12310, 13293}, {12410, 28194}, {13142, 18913}, {13175, 39860}, {13754, 35450}, {14855, 37506}, {14915, 32063}, {15033, 53091}, {15138, 44469}, {15811, 41427}, {18475, 35237}, {18931, 41588}, {19924, 37488}, {21663, 33586}, {226648672}, {23327, 29181}, {28204, 34713}, {29959, 31884}, {32062, 35259}, {33582, 53273}, {3489727766}, {37491, 44883}, {37853, 48910}

X(54992) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(5896)}}, {{A, B, C, X(20), X(34570)}}, {{A, B, X(30), X(38263)}}, {{A, B, C, X(64), X(6622)}}, {{A, B, C, X(74), X(38282)}}, {{A, B, C, X(1294), X(9909)}}, {{A, B, C, X(2693), X(5159)}}{A, B, C, X(3426), X(6623)}}, {{A, B, C, X(3516), X(45300)}}, {{A, B, C, X(4235),33405)}}, {{A, B, C, X(5897), X(7396)}}, {{A, B, C, X(10151), X(41489)}}, {{A, B, C, X(32534), X(43660)}}, {{A, B, C, X(34426), X(39568)}}, {{A, B, C, X(36609), X(45200)}}
X(54992) = midpoint of X(i) and X(j) for these {i,j}: {34703, 34723}, {64, 37672}
X(54992) = reflection of X(i) in X(j) for these {i,j}: {12164, 37672}, {18324, 11250}, {3167, 37497}, {32063, 47391}, {37672, 13346}, {7387, 18324}, {9909, 3}
X(54992) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10245, 18324}, {3, 1593, 11479}, {3, 18535, 6644}, {3, 30, 9909}, {3, 382, 3517}, {3, 5073, 9714}, {3, 9818, 16}, {30, 18324, 7387}, {64, 13346, 12164}, {2071, 3543, 15078}, {2072, 3517, 5020}, {3543, 15078, 25}, {6000, 37497, 3167}, {7387, 18324, 10245}, {11413, 12086, 1593}, {12084, 15, 3}, {14915, 47391, 32063}

X(54993) = X(2)X(3)∩X(99)X(1350)

Barycentrics    a^8+2*b^2*c^2*(b^2-c^2)^2-9*a^6*(b^2+c^2)+a^2*(b^2+c^2)^3+a^4*(7*b^4+4*b^2*c^2+7*c^4) : :

X(54993) lies on these lines: {2, 3}, {99, 1350}, {182, 39656}, {183, 8722}, {262, 52771}, {511, 31859}, {543, 33997}, {1351, 7709}, {1503, 14907}, {1975, 5188}, {2080, 9755}, {2794, 35705}, {3053, 12203}, {3184, 38660}, {3499, 16936}, {3972, 5085}, {5017, 44882}, {5050, 10788}, {5116, 44541}, {5171, 39646}, {5210, 34473}, {5921, 15428}, {5989, 38738}, {7750, 8721}, {7754, 11257}, {7757, 11477}, {7771, 9756}, {7788, 14981}, {7811, 15069}, {7815, 52854}, {7831, 10516}, {8667, 38664}, {8716, 53097}, {9605, 32522}, {9741, 54174}, {10723, 44531}, {10991, 47101}, {11174, 21163}, {12150, 53093}, {14689, 38663}, {15482, 22682}, {16111, 38653}, {16163, 38661}, {18860, 51580}, {22521, 53091}, {23235, 33706}, {24466, 38655}, {29181, 50659}, {32448, 54188}, {34229, 46034}, {35424, 48892}, {38654, 38749}, {38657, 38761}, {38736, 48885}, {43152, 48891}, {43273, 51224}, {48906, 50685}, {52691, 54131}, {53142, 54170}

X(54993) = reflection of X(i) in X(j) for these {i,j}: {183, 8722}, {13860, 3}, {3543, 3363}
X(54993) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1105), X(11285)}}, {{A, B, C, X(1294), X(13860)}}, {{A, B, C, X(1297), X(34098)}}, {{A, B, C, X(15740), X(32968)}}
X(54993) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11676, 1003}, {3, 14532, 5999}, {3, 30, 13860}, {3, 4, 11285}, {20, 5999, 14532}, {30, 3363, 3543}, {99, 22676, 1350}, {376, 11676, 3}, {1350, 8719, 99}

X(54994) = X(2)X(3)∩X(6)X(14831)

Barycentrics    a^2*(3*a^8+8*a^4*b^2*c^2-6*a^6*(b^2+c^2)-(b^2-c^2)^2*(3*b^4+10*b^2*c^2+3*c^4)+2*a^2*(3*b^6+b^4*c^2+b^2*c^4+3*c^6)) : :

X(54994) lies on these lines: {2, 3}, {6, 14831}, {54, 12164}, {64, 10984}, {74, 12017}, {154, 15030}, {159, 47353}, {182, 10605}, {185, 37476}, {394, 11430}, {539, 12166}, {541, 13171}, {542, 12168}, {543, 39803}, {569, 12163}, {578, 12160}, {1204, 37514}, {1209, 12293}, {1350, 12039}, {1351, 15033}, {1989, 34866}, {2935, 31521}, {3058, 10831}, {3167, 11459}, {3426, 15080}, {3531, 48912}, {3763, 16163}, {3796, 6000}, {3917, 37497}, {3964, 32833}, {4550, 18451}, {5050, 5890}, {5085, 10606}, {5157, 34778}, {5434, 10832}, {5476, 32600}, {5562, 11425}, {5621, 34319}, {5642, 32607}, {5655, 12412}, {5889, 11426}, {5891, 6090}, {5907, 19357}, {6054, 9876}, {6515, 44683}, {6800, 15305}, {7689, 36752}, {8192, 28204}, {8193, 28194}, {8780, 11464}, {9220, 44541}, {9659, 11238}, {9672, 11237}, {9682, 42602}, {9707, 15058}, {9723, 19454}, {9777, 37489}, {9786, 16226}, {9880, 39828}, {9911, 50865}, {9912, 50908}, {9915, 41043}, {9916, 41042}, {9971, 31884}, {10601, 11438}, {10610, 32139}, {10829, 34697}, {10830, 34746}, {10982, 21849}, {11202, 35259}, {11204, 16836}, {11365, 38021}, {11402, 13754}, {11412, 13482}, {11424, 17834}, {11432, 13434}, {11793, 35602}, {12111, 19347}, {12165, 12228}, {12315, 52525}, {12824, 15055}, {13093, 15062}, {13367, 17814}, {14482, 36413}, {14805, 18445}, {14907, 45198}, {15035, 45082}, {15056, 51033}, {15072, 35450}, {15177, 31162}, {15577, 47354}, {15578, 50983}, {17811, 51394}, {17821, 33537}, {17825, 37487}, {18362, 44527}, {18374, 53094}, {18390, 37638}, {18396, 21243}, {19005, 35823}, {19006, 35822}, {20410, 38717}, {20423, 37488}, {21663, 37475}, {26216, 30435}, {32062, 35268}, {32321, 32401}, {33540, 43898}, {34469, 40647}, {34774, 44883}, {37478, 44413}, {37491, 54132}, {38699, 51240}, {39879, 51023}, {51224, 54091}, {52703, 52952}

X(54994) = reflection of X(i) in X(j) for these {i,j}: {11402, 37506}
X(54994) = X(i)-vertex conjugate of X(j) for these {i, j}: {523, 47340}
X(54994) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(74), X(8889)}}, {{A, B, C, X(250), X(47340)}}, {{A, B, C, X(1105), X(9715)}}, {{A, B, C, X(1989), X(3089)}}, {{A, B, C, X(2693), X(46517)}}, {{A, B, C, X(3515), X(40448)}}, {{A, B, C, X(3546), X(46412)}}, {{A, B, C, X(5879), X(37198)}}, {{A, B, C, X(10303), X(45301)}}, {{A, B, C, X(10323), X(34426)}}, {{A, B, C, X(30100), X(34439)}}, {{A, B, C, X(35372), X(37942)}}, {{A, B, C, X(35477), X(43660)}}
X(54994) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11479, 24}, {3, 14130, 12085}, {3, 1593, 11414}, {3, 1597, 22}, {3, 1598, 7488}, {3, 18534, 7502}, {3, 18570, 11410}, {3, 381, 14070}, {3, 4, 9715}, {3, 5, 3515}, {3, 5020, 186}, {3, 6642, 15750}, {3, 7503, 7395}, {3, 7514, 7484}, {3, 7526, 1593}, {3, 7529, 1658}, {3, 9818, 25}, {5, 18568, 381}, {20, 5133, 18494}, {22, 7527, 1597}, {381, 18568, 18386}, {1593, 3515, 12173}, {2043, 2044, 3575}, {2071, 7485, 3}, {4550, 18475, 18451}, {6800, 15305, 32063}, {15765, 18585, 3549}, {18451, 18475, 26864}, {21663, 43650, 37475}, {32620, 39242, 6090}, {32620, 47391, 5891}

X(54995) = X(2)X(3)∩X(74)X(524)

Barycentrics    8*a^10-15*a^8*(b^2+c^2)-(b^2-c^2)^4*(b^2+c^2)-2*a^6*(b^4-29*b^2*c^2+c^4)-2*a^2*(b^2-c^2)^2*(3*b^4+13*b^2*c^2+3*c^4)+16*a^4*(b^6-2*b^4*c^2-2*b^2*c^4+c^6) : :

X(54995) lies on these lines: {2, 3}, {74, 524}, {99, 841}, {477, 1296}, {541, 10564}, {691, 43660}, {842, 30256}, {935, 53909}, {1294, 10098}, {1300, 53961}, {1503, 5648}, {2687, 53901}, {2691, 53907}, {2693, 30247}, {2777, 13857}, {2966, 38894}, {3576, 47495}, {5085, 47544}, {5622, 43576}, {5642, 32111}, {5657, 47488}, {5890, 8584}, {7967, 47493}, {8705, 50965}, {9158, 38701}, {10101, 53917}, {10519, 47473}, {10605, 15534}, {10606, 15533}, {10706, 11064}, {11179, 32220}, {11645, 16163}, {11649, 36987}, {14912, 47541}, {15035, 35266}, {15036, 15448}, {15055, 15360}, {15362, 38728}, {19924, 37853}, {20187, 32710}, {22329, 46981}, {26613, 47584}, {32113, 54169}, {36900, 46984}, {38064, 47581}, {38314, 47471}, {39382, 53934}, {44541, 47275}, {47169, 53095}, {47455, 50983}, {47465, 51132}, {51110, 51713}, {53189, 53908}

X(54995) = midpoint of X(i) and X(j) for these {i,j}: {10296, 15683}, {20, 10989}, {376, 7464}, {40112, 50434}, {7574, 15681}
X(54995) = reflection of X(i) in X(j) for these {i,j}: {10295, 376}, {10706, 11064}, {11799, 549}, {22329, 46981}, {381, 15122}, {3543, 10297}, {32111, 5642}, {32113, 54169}, {32220, 11179}, {36900, 46984}, {40112, 10564}, {7426, 3}
X(54995) = anticomplement of X(47332)
X(54995) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(25), X(841)}}, {{A, B, C, X(74), X(37962)}}, {{A, B, C, X(468), X(43660)}}, {{A, B, C, X(477), X(4232)}}, {{A, B, C, X(1294), X(7426)}}, {{A, B, C, X(1296), X(7480)}}, {{A, B, C, X(1597), X(10419)}}, {{A, B, C, X(1995), X(2693)}}, {{A, B, C, X(2696), X(4240)}}, {{A, B, C, X(2697), X(26255)}}, {{A, B, C, X(3839), X(50480)}}, {{A, B, C, X(5897), X(37980)}}, {{A, B, C, X(7471), X(20187)}}, {{A, B, C, X(7473), X(30256)}}, {{A, B, C, X(10098), X(46587)}}, {{A, B, C, X(11799), X(18317)}}, {{A, B, C, X(16387), X(39434)}}, {{A, B, C, X(30247), X(31510)}}
X(54995) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 30, 7426}, {20, 2071, 16387}, {30, 10297, 3543}, {30, 15122, 381}, {30, 376, 10295}, {30, 549, 11799}, {378, 10295, 403}, {2071, 7464, 378}, {10296, 15683, 30}, {40112, 50434, 541}

X(54996) = X(2)X(3)∩X(99)X(1503)

Barycentrics    4*a^8-5*a^6*(b^2+c^2)-(b^2-c^2)^2*(b^4+c^4)+a^4*(5*b^4+4*b^2*c^2+5*c^4)-a^2*(3*b^6+b^4*c^2+b^2*c^4+3*c^6) : :

X(54996) lies on these lines: {2, 3}, {98, 47286}, {99, 1503}, {112, 44704}, {147, 6390}, {157, 53481}, {187, 38747}, {230, 34473}, {262, 53489}, {316, 8781}, {325, 2794}, {511, 38642}, {516, 15903}, {538, 10991}, {625, 39838}, {691, 53931}, {1296, 2857}, {1350, 14907}, {1499, 3268}, {1691, 29181}, {2021, 6781}, {2080, 38742}, {2782, 47287}, {2966, 41175}, {3094, 44882}, {3184, 38649}, {3564, 9862}, {3788, 36997}, {3933, 9863}, {3972, 5480}, {5921, 32817}, {5976, 38738}, {6036, 39663}, {6776, 31859}, {7709, 48906}, {7750, 30270}, {7757, 8550}, {7762, 36998}, {8719, 48905}, {9756, 11185}, {10723, 44534}, {10735, 51454}, {10788, 21850}, {11064, 35278}, {11177, 52229}, {12203, 34870}, {14482, 33748}, {14689, 14961}, {15069, 32833}, {16111, 38641}, {16163, 38650}, {16320, 38704}, {21166, 43460}, {21445, 43453}, {22676, 48881}, {24466, 38643}, {29012, 38736}, {29317, 52992}, {31670, 39656}, {32448, 40252}, {32815, 53015}, {35002, 38741}, {38645, 38773}, {38646, 38761}, {40825, 51212}, {51737, 52691}

X(54996) = midpoint of X(i) and X(j) for these {i,j}: {20, 5999}, {35002, 38741}, {8597, 15683}
X(54996) = reflection of X(i) in X(j) for these {i,j}: {147, 6390}, {187, 38747}, {1513, 3}, {10723, 53419}, {325, 18860}, {39838, 625}, {47286, 98}, {51438, 1350}, {53499, 44882}, {8598, 376}
X(54996) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(4), X(46145)}}, {{A, B, C, X(25), X(2710)}}, {{A, B, C, X(1105), X(7807)}}, {{A, B, C, X(1294), X(1513)}}, {{A, B, C, X(2693), X(37930)}}, {{A, B, C, X(2794), X(50641)}}, {{A, B, C, X(2857), X(4232)}}, {{A, B, C, X(14064), X(15740)}}, {{A, B, C, X(43702), X(46522)}}
X(54996) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 30, 1513}, {3, 4, 7807}, {3, 7866, 3523}, {20, 5999, 30}, {30, 376, 8598}, {2794, 18860, 325}, {3522, 7791, 3}, {3534, 14532, 20}

X(54997) = X(4)X(9)∩X(952)X(1222)

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

X(54997) lies on these lines: {4, 9}, {140, 31227}, {517, 33126}, {952, 1222}, {5731, 36510}, {17526, 25965}, {17677, 29243}, {28212, 30449}, {33940, 50425}

X(54998) = X(6)X(40254)∩X(69)X(2782)

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

X(54998) lies on these lines: {6, 40254}, {69, 2782}, {248, 2080}, {879, 11632}, {4846, 37348}, {6000, 43702}, {11171, 43718}, {11672, 52771}, {16068, 36214}, {43705, 51455}, {46316, 51229}

X(54998) = trilinear pole of line {373, 647}
X(54998) = isogonal conjugate of X(11676)
X(54998) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 43702}, {511, 3455}
X(54998) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3), X(4)}}, {{A, B, C, X(30), X(52692)}}, {{A, B, C, X(98), X(512)}}, {{A, B, C, X(182), X(598)}}, {{A, B, C, X(262), X(30495)}}, {{A, B, C, X(378), X(37348)}}, {{A, B, C, X(511), X(671)}}, {{A, B, C, X(525), X(14941)}}, {{A, B, C, X(690), X(9161)}}, {{A, B, C, X(691), X(11632)}}, {{A, B, C, X(694), X(2698)}}, {{A, B, C, X(755), X(53774)}}, {{A, B, C, X(1296), X(6094)}}, {{A, B, C, X(1297), X(11606)}}, {{A, B, C, X(1499), X(34383)}}, {{A, B, C, X(2021), X(2456)}}, {{A, B, C, X(2052), X(40254)}}, {{A, B, C, X(2065), X(3455)}}, {{A, B, C, X(2211), X(14908)}}, {{A, B, C, X(3406), X(8601)}}, {{A, B, C, X(3425), X(14906)}}, {{A, B, C, X(3504), X(32319)}}, {{A, B, C, X(5050), X(52771)}}, {{A, B, C, X(5485), X(40803)}}, {{A, B, C, X(7607), X(54413)}}, {{A, B, C, X(7608), X(41440)}}, {{A, B, C, X(12054), X(50652)}}, {{A, B, C, X(14485), X(30499)}}, {{A, B, C, X(16098), X(52631)}}, {{A, B, C, X(23700), X(37841)}}, {{A, B, C, X(26717), X(38279)}}, {{A, B, C, X(39683), X(53200)}}, {{A, B, C, X(40801), X(54122)}}

X(54999) = X(511)X(13172)∩X(512)X(14651)

Barycentrics    a^2*(-(b^6*c^2)+4*b^4*c^4-4*b^2*c^6+c^8+a^6*(2*b^2-c^2)-2*a^4*(2*b^4+b^2*c^2-2*c^4)+a^2*(2*b^6-2*b^4*c^2+5*b^2*c^4-4*c^6))*(-b^8+4*b^6*c^2-4*b^4*c^4+b^2*c^6+a^6*(b^2-2*c^2)+a^4*(-4*b^4+2*b^2*c^2+4*c^4)+a^2*(4*b^6-5*b^4*c^2+2*b^2*c^4-2*c^6)) : :

X(54999) lies on these lines: {237, 35265}, {511, 13172}, {512, 14651}, {2211, 35006}, {11171, 14251}, {39561, 51980}

X(54999) = isogonal conjugate of X(13188)
X(54999) = X(i)-vertex conjugate of X(j) for these {i, j}: {4, 9217}
X(54999) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3), X(35006)}}, {{A, B, C, X(4), X(32)}}, {{A, B, C, X(54), X(8601)}}, {{A, B, C, X(74), X(34130)}}, {{A, B, C, X(112), X(14651)}}, {{A, B, C, X(187), X(39561)}}, {{A, B, C, X(249), X(5395)}}, {{A, B, C, X(691), X(1138)}}, {{A, B, C, X(729), X(43532)}}, {{A, B, C, X(842), X(3424)}}, {{A, B, C, X(843), X(2065)}}, {{A, B, C, X(1691), X(11171)}}, {{A, B, C, X(2710), X(13452)}}, {{A, B, C, X(3563), X(13172)}}, {{A, B, C, X(5970), X(7612)}}, {{A, B, C, X(8599), X(32730)}}, {{A, B, C, X(10630), X(14491)}}, {{A, B, C, X(11170), X(44557)}}, {{A, B, C, X(11270), X(23700)}}, {{A, B, C, X(30491), X(47388)}}, {{A, B, C, X(41932), X(52692)}}

X(55000) = X(7)X(2808)∩X(9)X(28850)

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

X(55000) lies on these lines: {7, 2808}, {9, 28850}, {294, 14197}, {515, 43751}, {6601, 14839}, {9442, 53617}, {11200, 40779}

X(55000) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(4)}}, {{A, B, C, X(55), X(52506)}}, {{A, B, C, X(103), X(52508)}}, {{A, B, C, X(514), X(14197)}}, {{A, B, C, X(655), X(32041)}}, {{A, B, C, X(668), X(39634)}}, {{A, B, C, X(673), X(2724)}}, {{A, B, C, X(1861), X(1952)}}, {{A, B, C, X(2795), X(28473)}}, {{A, B, C, X(2808), X(3900)}}, {{A, B, C, X(3309), X(14839)}}, {{A, B, C, X(11200), X(42309)}}, {{A, B, C, X(28848), X(52030)}}, {{A, B, C, X(40704), X(46802)}}
X(55000) = trilinear pole of line {650, 17718}

X(55001) = X(8)X(2808)∩X(101)X(43163)

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

X(55001) lies on these lines: {8, 2808}, {101, 43163}, {3680, 28850}

X(55001) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(4)}}, {{A, B, C, X(513), X(911)}}, {{A, B, C, X(3667), X(28850)}}, {{A, B, C, X(7192), X(15731)}}, {{A, B, C, X(10025), X(34018)}}, {{A, B, C, X(14839), X(30198)}}
X(55001) = trilinear pole of line {650, 17728}

X(55002) = X(9)X(2808)∩X(294)X(23694)

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

X(55002) lies on these lines: {9, 2808}, {294, 23694}, {946, 42311}, {6001, 43751}, {6601, 28850}, {14839, 42470}

X(55002) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(1), X(4)}}, {{A, B, C, X(103), X(514)}}, {{A, B, C, X(3309), X(28850)}}, {{A, B, C, X(28842), X(35145)}}
X(55002) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 43751}

X(55003) = X(10)X(542)∩X(30)X(11599)

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

X(55003) lies on these lines: {10, 542}, {30, 11599}, {423, 16080}, {514, 14223}, {524, 34899}, {543, 4052}, {671, 37792}, {2394, 2786}, {2782, 34475}, {2789, 5466}, {2796, 43677}, {3667, 9180}, {4785, 46040}, {28296, 43667}

X(55003) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(423)}}, {{A, B, C, X(514), X(542)}}, {{A, B, C, X(524), X(2789)}}, {{A, B, C, X(543), X(3667)}}, {{A, B, C, X(675), X(9141)}}, {{A, B, C, X(2782), X(4785)}}, {{A, B, C, X(2784), X(28840)}}, {{A, B, C, X(2796), X(6002)}}, {{A, B, C, X(5969), X(28470)}}, {{A, B, C, X(9830), X(28565)}}, {{A, B, C, X(14645), X(28529)}}

X(55004) = X(1)X(1424)∩X(3)X(2176)

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

X(55004) lies on these lines: {1, 1424}, {3, 2176}, {4, 1969}, {5, 20255}, {30, 511}, {40, 32462}, {970, 21874}, {3262, 44151}, {3869, 32117}, {4531, 12782}, {30269, 30487}

X(55004) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(4), X(788)}}, {{A, B, C, X(824), X(1969)}}, {{A, B, C, X(30665), X(40717)}}
X(55004) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 788}
X(55004) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4, 44951}
X(55004) = X(i)-complementary conjugate of X(j) for these {i, j}: {1, 44951}
X(55004) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {517, 15310, 28850}

X(55005) = X(3)X(695)∩X(30)X(511)

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

X(55005) lies on these lines: {3, 695}, {4, 18022}, {5, 6310}, {20, 10340}, {30, 511}, {51, 8370}, {74, 53918}, {76, 40951}, {110, 37896}, {115, 14962}, {182, 30495}, {184, 35924}, {194, 4173}, {211, 7816}, {230, 35060}, {263, 14033}, {325, 5167}, {376, 35687}, {384, 27374}, {550, 14135}, {694, 35399}, {1350, 32463}, {1568, 36183}, {2080, 51325}, {2979, 7833}, {3060, 11361}, {3098, 6195}, {3292, 37927}, {3491, 3933}, {3492, 10547}, {3819, 8359}, {3917, 8356}, {5055, 12525}, {5891, 37345}, {6390, 51427}, {6688, 8367}, {6784, 14568}, {6786, 7799}, {6787, 7809}, {7748, 41262}, {7893, 32547}, {9737, 35934}, {9879, 14041}, {9917, 32445}, {11287, 52658}, {11673, 13586}, {11675, 33813}, {19570, 46303}, {20326, 38071}, {21177, 36213}, {23061, 36182}, {24729, 52967}, {30270, 36960}, {33008, 34095}, {35297, 47638}, {36165, 41586}, {37898, 38661}, {37991, 43574}, {39099, 49122}, {51396, 52471}

X(55005) = isogonal conjugate of X(53889)
X(55005) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(688)}}, {{A, B, C, X(512), X(45092)}}, {{A, B, C, X(523), X(695)}}, {{A, B, C, X(525), X(40016)}}, {{A, B, C, X(782), X(8623)}}, {{A, B, C, X(826), X(18022)}}, {{A, B, C, X(20022), X(39469)}}
X(55005) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 688}
X(55005) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4, 44947}
X(55005) = X(i)-complementary conjugate of X(j) for these {i, j}: {1, 44947}, {53889, 10}
X(55005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {538, 2387, 34383}, {14133, 14134, 3}, {14133, 31989, 48262}, {14134, 31989, 14133}

X(55006) = X(4)X(32)∩X(30)X(290)

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

X(55006) lies on these lines: {4, 32}, {20, 53174}, {30, 290}, {74, 52190}, {237, 43460}, {262, 9475}, {287, 46264}, {542, 39355}, {1503, 1987}, {3269, 11257}, {5191, 37988}, {6033, 54086}, {6394, 14907}, {9409, 43665}, {9934, 11653}, {10733, 14712}, {16081, 16264}, {17974, 52525}, {32444, 51869}, {40853, 46806}

X(55006) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(32), X(16263)}}, {{A, B, C, X(74), X(10312)}}, {{A, B, C, X(1987), X(10311)}}

X(55007) = X(2)X(5191)∩X(30)X(76)

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

X(55007) lies on these lines: {2, 5191}, {3, 7849}, {4, 19569}, {15, 48656}, {16, 48655}, {30, 76}, {32, 381}, {376, 2896}, {512, 18435}, {538, 40252}, {542, 1569}, {547, 7846}, {549, 3096}, {598, 5066}, {599, 3098}, {1352, 38741}, {1503, 22677}, {2076, 47353}, {2782, 9878}, {2794, 7697}, {3095, 7837}, {3524, 7945}, {3654, 9857}, {3830, 3849}, {3845, 9993}, {5054, 7874}, {5055, 7886}, {5071, 10583}, {5309, 37243}, {5613, 42673}, {5617, 42672}, {5921, 14692}, {6287, 36998}, {7576, 11386}, {7788, 35002}, {7914, 15694}, {7924, 14880}, {8354, 39882}, {9300, 37345}, {9774, 11149}, {9941, 28204}, {9983, 34623}, {9986, 13685}, {9987, 13805}, {10008, 11180}, {10038, 11237}, {10047, 11238}, {10056, 10873}, {10072, 10874}, {10304, 10357}, {10828, 14070}, {11178, 24273}, {11368, 51709}, {11632, 43449}, {11648, 12188}, {12497, 28198}, {13846, 45376}, {13847, 45375}, {14976, 15682}, {15693, 15810}, {28194, 49561}, {31730, 49560}, {34200, 42787}, {35456, 50955}, {35822, 44604}, {35823, 44605}, {44224, 47005}, {51872, 52088}

X(55007) = midpoint of X(i) and X(j) for these {i,j}: {11057, 14458}, {14976, 15682}, {7811, 9873}
X(55007) = reflection of X(i) in X(j) for these {i,j}: {376, 34510}, {52088, 51872}, {7811, 32151}, {9821, 7811}
X(55007) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30, 32151, 7811}, {30, 7811, 9821}, {32, 18503, 18500}, {9862, 9996, 26316}, {9981, 9982, 3094}, {11057, 14458, 30}
X(55007) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(3098), X(11057)}}, {{A, B, C, X(11058), X(14387)}}, {{A, B, C, X(14458), X(14479)}}

X(55008) = X(2)X(3)∩X(6)X(9862)

Barycentrics    2*a^8-b^8+b^6*c^2+b^2*c^6-c^8-2*a^6*(b^2+c^2)-2*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(3*b^4+5*b^2*c^2+3*c^4) : :

X(55008) lies on these lines: {2, 3}, {6, 9862}, {39, 9873}, {98, 5309}, {99, 3818}, {147, 9878}, {183, 43453}, {187, 9993}, {262, 2794}, {511, 7811}, {524, 34623}, {542, 7757}, {543, 10033}, {574, 43460}, {754, 13085}, {1352, 32833}, {1503, 7709}, {1976, 15033}, {2001, 13352}, {2782, 10335}, {3095, 7837}, {3098, 7831}, {3106, 41022}, {3107, 41023}, {3314, 9996}, {3399, 11257}, {3406, 12110}, {3849, 34733}, {3972, 19130}, {5188, 40344}, {5475, 10722}, {5476, 12150}, {5480, 10788}, {6033, 7777}, {6034, 12176}, {6054, 9888}, {6148, 11188}, {7737, 39095}, {7799, 9737}, {7806, 12042}, {7809, 54393}, {7810, 33706}, {7812, 44422}, {7823, 14881}, {7832, 10356}, {7864, 14880}, {7865, 30270}, {7875, 26316}, {7880, 18860}, {7891, 18500}, {7893, 32151}, {7904, 9821}, {7906, 18503}, {8716, 47353}, {9300, 40923}, {9753, 21445}, {9756, 14651}, {10000, 52995}, {10345, 12054}, {10796, 38741}, {11057, 32152}, {11645, 34624}, {12251, 37671}, {14853, 22521}, {14907, 31670}, {15032, 34945}, {18440, 31859}, {20423, 35431}, {22676, 29317}, {22693, 44666}, {22694, 44667}, {24206, 47005}, {31168, 50977}, {34615, 54131}, {39656, 53023}

X(55008) = midpoint of X(i) and X(j) for these {i,j}: {147, 9878}, {11257, 14458}, {7837, 9863}
X(55008) = reflection of X(i) in X(j) for these {i,j}: {11057, 32152}, {11361, 381}, {12251, 37671}, {376, 8356}, {33706, 7810}, {5188, 40344}, {7812, 44422}, {7837, 3095}
X(55008) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5, 7892}, {20, 3091, 14031}, {30, 381, 11361}, {30, 8356, 376}, {376, 3545, 14039}, {383, 1080, 13862}, {2043, 2044, 384}, {19130, 38749, 3972}
X(55008) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3399), X(11331)}}, {{A, B, C, X(3406), X(52289)}}, {{A, B, C, X(7892), X(40448)}}, {{A, B, C, X(7901), X(13599)}}, {{A, B, C, X(31363), X(33283)}}

X(55009) = X(2)X(5191)∩X(4)X(6034)

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

X(55009) lies on these lines: {2, 5191}, {3, 43529}, {4, 6034}, {5, 43528}, {30, 1916}, {76, 542}, {115, 14458}, {262, 2794}, {376, 40824}, {381, 3407}, {419, 16080}, {511, 10290}, {512, 14223}, {598, 19130}, {671, 11645}, {804, 2394}, {1503, 43532}, {2482, 9774}, {2782, 43688}, {2784, 34475}, {2996, 12243}, {3424, 14651}, {3849, 5503}, {5117, 43530}, {5149, 6054}, {5461, 10033}, {5466, 13307}, {5485, 9830}, {7607, 10991}, {7608, 37334}, {7809, 8781}, {7874, 23234}, {8592, 48657}, {9180, 32472}, {9302, 11646}, {9880, 53105}, {10302, 43150}, {10722, 14492}, {11057, 38749}, {11177, 32528}, {11606, 11632}, {11623, 53100}, {14488, 39838}, {19120, 43273}, {23878, 52459}, {25423, 46040}, {28562, 34899}, {33432, 42024}, {33433, 42023}, {35005, 38741}, {38664, 43676}, {41022, 43539}, {41023, 43538}

X(55009) = reflection of X(i) in X(j) for these {i,j}: {10722, 14537}, {11057, 38749}, {14458, 115}
X(55009) = isogonal conjugate of X(35002)
X(55009) = trilinear pole of line {5306, 6041}
X(55009) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 43532}, {3455, 9302}
X(55009) = intersection, other than A, B, C, of these circumonics: {{A, B, C, X(2), X(4)}}, {{A, B, C, X(6), X(26316)}}, {{A, B, C, X(30), X(419)}}, {{A, B, C, X(67), X(9154)}}, {{A, B, C, X(74), X(512)}}, {{A, B, C, X(111), X(9141)}}, {{A, B, C, X(265), X(6034)}}, {{A, B, C, X(290), X(12042)}}, {{A, B, C, X(327), X(52154)}}, {{A, B, C, X(376), X(6620)}}, {{A, B, C, X(381), X(5117)}}, {{A, B, C, X(543), X(32472)}}, {{A, B, C, X(690), X(11645)}}, {{A, B, C, X(1494), X(6531)}}, {{A, B, C, X(1499), X(9830)}}, {{A, B, C, X(1989), X(5641)}}, {{A, B, C, X(2207), X(41533)}}, {{A, B, C, X(2367), X(30492)}}, {{A, B, C, X(2698), X(43702)}}, {{A, B, C, X(2782), X(25423)}}, {{A, B, C, X(2784), X(4785)}}, {{A, B, C, X(2789), X(28562)}}, {{A, B, C, X(2793), X(3849)}}, {{A, B, C, X(2794), X(23878)}}, {{A, B, C, X(2796), X(28470)}}, {{A, B, C, X(3431), X(44557)}}, {{A, B, C, X(5969), X(30217)}}, {{A, B, C, X(6323), X(11738)}}, {{A, B, C, X(6325), X(8599)}}, {{A, B, C, X(6344), X(52618)}}, {{A, B, C, X(7809), X(34174)}}, {{A, B, C, X(9999), X(14388)}}, {{A, B, C, X(10293), X(53605)}}, {{A, B, C, X(10630), X(53890)}}, {{A, B, C, X(11058), X(14387)}}, {{A, B, C, X(14483), X(43950)}}, {{A, B, C, X(14487), X(52239)}}, {{A, B, C, X(14651), X(45031)}}, {{A, B, C, X(19130), X(32581)}}, {{A, B, C, X(29011), X(53774)}}, {{A, B, C, X(34288), X(54124)}}, {{A, B, C, X(34897), X(47388)}}, {{A, B, C, X(35474), X(50707)}}, {{A, B, C, X(37334), X(52281)}}, {{A, B, C, X(37446), X(52282)}}, {{A, B, C, X(38520), X(40352)}}

X(55010) = X(1)X(30)∩X(7)X(27)

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

See Elias Hagos and César Lozada, euclid 5958.

X(55010) lies on these lines: {1, 30}, {2, 7359}, {7, 27}, {37, 226}, {56, 36011}, {57, 1723}, {65, 23604}, {92, 16608}, {196, 17905}, {218, 948}, {219, 5905}, {323, 17483}, {347, 3151}, {388, 37098}, {442, 40967}, {553, 1086}, {651, 2982}, {896, 41549}, {942, 1838}, {1211, 18698}, {1284, 1617}, {1362, 1365}, {1441, 26942}, {1446, 20618}, {1455, 4298}, {1714, 5221}, {1754, 11246}, {1786, 2160}, {2257, 23681}, {2328, 17768}, {2822, 15902}, {3173, 6180}, {3485, 51721}, {3487, 30266}, {3580, 30690}, {3671, 5930}, {3712, 25664}, {3982, 6610}, {4077, 21104}, {4292, 44243}, {4312, 7070}, {4383, 24779}, {4442, 15590}, {4466, 53036}, {4847, 49483}, {5226, 31256}, {5249, 16585}, {5307, 15946}, {5333, 41808}, {5435, 31204}, {5721, 5902}, {5723, 52423}, {7522, 24316}, {7536, 24315}, {13407, 37528}, {16133, 33100}, {16591, 40615}, {17075, 19684}, {17092, 27186}, {18134, 25252}, {19796, 32007}, {24470, 52407}, {31153, 33151}, {31292, 41819}, {37800, 52424}, {40622, 52659}

X(55010) = midpoint of X(554) and X(1081)
X(55010) = reflection of X(i) in X(j) for these (i, j): (440, 25361), (1762, 6678)
X(55010) = polar conjugate of the isogonal conjugate of X(39791)
X(55010) = cross-difference of every pair of points on the line X(9404)X(21789)
X(55010) = crosspoint of X(i) and X(j) for these {i,j}: {7, 1446}, {226, 43682}, {331, 1441}
X(55010) = crosssum of X(i) and X(j) for these {i,j}: {284, 35192}, {2194, 52425}
X(55010) = X(2)-beth conjugate of-X(17056)
X(55010) = X(i)-Ceva conjugate of-X(j) for these (i, j): (7, 942), (651, 7178), (1441, 41393), (13149, 17094), (21907, 18593)
X(55010) = X(2294)-cross conjugate of-X(442)
X(55010) = X(i)-Dao Conjugate of-X(j) for these (i, j): (442, 2287), (478, 1175), (942, 219), (1214, 40435), (3160, 40412), (16585, 333), (16732, 4391), (18591, 21), (36908, 2982), (39007, 23090), (40590, 943), (40611, 2259), (40837, 40395), (40937, 8), (52119, 3700)
X(55010) = X(i)-isoconjugate of-X(j) for these {i, j}: {9, 1175}, {21, 2259}, {41, 40412}, {78, 40570}, {212, 40395}, {284, 943}, {1021, 15439}, {1172, 1794}, {2194, 40435}, {2328, 2982}
X(55010) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (7, 40412), (56, 1175), (65, 943), (73, 1794), (226, 40435), (278, 40395), (442, 8), (500, 35193), (608, 40570), (942, 21), (1234, 3596), (1400, 2259), (1427, 2982), (1441, 40422), (1838, 29), (1841, 1172), (1844, 11107), (1859, 4183), (1865, 281), (2260, 284), (2294, 9), (4303, 283), (5249, 333), (6046, 52560), (6734, 1043), (8021, 6061), (14547, 2328), (14597, 2193), (18591, 219), (18607, 1812), (21675, 2321), (23752, 522), (37992, 442), (37993, 8021), (39791, 3), (40149, 40447), (40937, 2287), (40952, 55), (40956, 2194), (40967, 200), (40978, 41), (41393, 72), (44095, 41502), (45926, 6740), (46882, 7054), (46883, 270), (46884, 2326), (46890, 2189), (50354, 3737), (52306, 23090)
X(55010) = inverse in circumhyperbola dual of Yff parabola of X(553)
X(55010) = pole of the tripolar of X(1446) wrt incircle
X(55010) = barycentric product of X(i) and X(j) for these {i, j}: {7, 442}, {56, 1234}, {85, 2294}, {226, 5249}, {264, 39791}
X(55010) = trilinear product of X(i) and X(j) for these {i, j}: {7, 2294}, {27, 41393}, {57, 442}, {65, 5249}, {77, 1865}
X(55010) = trilinear quotient of X(i) and X(j) for these (i, j): (34, 40570), (57, 1175), (65, 2259), (85, 40412), (226, 943)
X(55010) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (7, 278, 37543), (7, 18625, 81), (81, 18625, 6357), (226, 3668, 1214), (226, 18593, 17056), (4654, 52374, 37631), (6354, 52023, 226), (18593, 25080, 1214), (41003, 50197, 226), (47057, 52374, 43066)

X(55011) = X(10)X(42304) ∩ X(21627)X(34860)

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

See César Lozada, euclid 5967.

X(55011) lies on these lines: {10, 42304}, {21627, 34860}

X(55011) = X(i)-isoconjugate of-X(j) for these {i, j}: {3217, 4383}, {3913, 3915}, {16946, 30568}
X(55011) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (34860, 30568), (39956, 3913), (42304, 3875)
X(55011) = barycentric product of X(34860) and X(42304)
X(55011) = trilinear product of X(39956) and X(42304)
X(55011) = trilinear quotient of X(i) and X(j) for these (i, j): (34860, 3913), (39956, 3217), (40012, 30568), (42304, 4383)

X(55012) = X(36)X(21907) ∩ X(484)X(5620)

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

See César Lozada, euclid 5967.

X(55012) lies on these lines: {36, 21907}, {484, 5620}, {1290, 41345}, {5902, 38938}

X(55012) = X(4564)-isoconjugate of-X(35090)
X(55012) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3271, 35090), (11604, 32849)
X(55012) = barycentric product of X(11604) and X(21907)
X(55012) = trilinear quotient of X(2170) and X(35090)

X(55013) = X(55)X(277) ∩ X(2191)X(2293)

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

See César Lozada, euclid 5967.

X(55013) lies on these lines: {55, 277}, {354, 14268}, {1292, 37578}, {2191, 2293}, {3059, 4863}, {8012, 54408}, {24477, 37206}

X(55013) = X(i)-isoconjugate of-X(j) for these {i, j}: {218, 1445}, {1617, 3870}, {4350, 6600}, {6604, 21059}, {7719, 23144}
X(55013) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (277, 6604), (2191, 1445), (6601, 344), (17107, 4350), (40154, 17093)
X(55013) = barycentric product of X(277) and X(6601)
X(55013) = trilinear product of X(2191) and X(6601)
X(55013) = trilinear quotient of X(i) and X(j) for these (i, j): (277, 1445), (2191, 1617), (6601, 3870), (40154, 4350)

X(55014) = X(171)X(39724) ∩ X(7184)X(7191)

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

See César Lozada, euclid 5967.

X(55014) lies on these lines: {171, 39724}, {4514, 43749}, {7184, 7191}

X(55014) = X(3961)-isoconjugate of-X(41346)
X(55014) = X(43749)-reciprocal conjugate of-X(17280)
X(55014) = barycentric product of X(39724) and X(43749)
X(55014) = trilinear product of X(7194) and X(43749)
X(55014) = trilinear quotient of X(i) and X(j) for these (i, j): (7194, 41346), (43749, 3961)

X(55015) = X(7)X(8) ∩ X(40)X(347)

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

See César Lozada, euclid 5967.

X(55015) lies on these lines: {7, 8}, {19, 54425}, {40, 347}, {77, 30503}, {151, 4329}, {196, 329}, {273, 962}, {517, 1119}, {651, 3197}, {653, 27382}, {1118, 34408}, {1439, 31788}, {1804, 3160}, {2093, 3668}, {3101, 18623}, {5657, 6356}, {6046, 37567}, {6060, 9778}, {6254, 54228}, {7279, 37601}, {8232, 54424}, {9780, 53821}, {22132, 32714}

X(55015) = isotomic conjugate of X(46355)
X(55015) = cevapoint of X(1103) and X(40212)
X(55015) = X(i)-beth conjugate of-X(j) for these (i, j): (322, 342), (664, 5932)
X(55015) = X(322)-Ceva conjugate of-X(347)
X(55015) = X(i)-Dao Conjugate of-X(j) for these (i, j): (2, 46355), (57, 84), (223, 1256), (281, 7003), (8058, 4081)
X(55015) = X(i)-isoconjugate of-X(j) for these {i, j}: {31, 46355}, {55, 1256}, {84, 2192}, {189, 7118}, {268, 7129}, {271, 7151}, {280, 2208}, {282, 1436}, {285, 2357}, {1422, 7367}, {1433, 7008}, {2188, 40836}, {7154, 41081}
X(55015) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2, 46355), (40, 282), (57, 1256), (196, 40836), (198, 2192), (208, 7129), (221, 1436), (223, 84), (227, 1903), (322, 34404), (329, 280), (347, 189), (1103, 9), (1817, 285), (2187, 7118), (2199, 2208), (2331, 7008), (3195, 7154), (3209, 7151), (3318, 1146), (6354, 7157), (6611, 1413), (7011, 1433), (7013, 41081), (7074, 7367), (7078, 268), (7952, 7003), (14256, 1440), (21871, 53013), (40212, 1), (40702, 309)
X(55015) = barycentric product of X(i) and X(j) for these {i, j}: {40, 40702}, {75, 40212}, {85, 1103}, {223, 322}
X(55015) = trilinear product of X(i) and X(j) for these {i, j}: {2, 40212}, {7, 1103}, {40, 347}, {198, 40702}, {221, 322}
X(55015) = trilinear quotient of X(i) and X(j) for these (i, j): (7, 1256), (40, 2192), (75, 46355), (196, 7129), (198, 7118)
X(55015) = (X(4329), X(4566))-harmonic conjugate of X(5932)

X(55016) = X(8)X(11) ∩ X(20)X(100)

Barycentrics    (-a+b+c)*((b+c)*a^2-2*b*c*a-(b^2-c^2)*(b-c))^2 : :
X(55016) = 2*X(1145)-X(18802) = 4*X(6667)-5*X(31246) = 4*X(6691)-5*X(31235) = X(10680)-3*X(38752) = X(12764)-3*X(31141) = 2*X(24928)-3*X(34123) = 2*X(32612)-3*X(38760) = 3*X(34474)-X(37002)

See César Lozada, euclid 5967.

X(55016) lies on these lines: {8, 11}, {10, 12736}, {12, 8256}, {20, 100}, {40, 46435}, {55, 30513}, {56, 3035}, {72, 17654}, {78, 952}, {80, 200}, {104, 3421}, {119, 517}, {120, 52304}, {214, 6745}, {313, 20895}, {322, 18749}, {480, 528}, {495, 3306}, {518, 12832}, {529, 4996}, {644, 5514}, {956, 6713}, {1260, 12331}, {1317, 4511}, {1387, 3820}, {2057, 12751}, {2478, 13278}, {2800, 21075}, {2802, 6736}, {2975, 21154}, {3452, 15558}, {3632, 5533}, {3679, 8068}, {3689, 12743}, {3940, 19914}, {4081, 52409}, {4187, 25416}, {4847, 6702}, {4853, 16173}, {4882, 37718}, {5080, 52836}, {5086, 38156}, {5687, 5840}, {6049, 27383}, {6068, 17768}, {6244, 33898}, {6667, 9711}, {6691, 15888}, {6734, 34122}, {6737, 15863}, {7681, 11681}, {7962, 12641}, {8069, 45701}, {8582, 18240}, {8679, 51007}, {10522, 13273}, {10680, 38752}, {10724, 17784}, {10742, 35448}, {12527, 46684}, {12619, 34790}, {12665, 17615}, {20076, 27525}, {21290, 51565}, {21664, 23101}, {22273, 22280}, {23513, 24390}, {24028, 26611}, {24928, 27385}, {24982, 50196}, {25640, 53151}, {26482, 37828}, {30323, 39692}, {32612, 38760}, {34474, 37002}, {38211, 40659}

X(55016) = midpoint of X(i) and X(j) for these (i, j): {100, 3436}, {10742, 35448}
X(55016) = reflection of X(i) in X(j) for these (i, j): (11, 1329), (56, 3035), (18802, 1145)
X(55016) = crosspoint of X(2397) and X(4998)
X(55016) = crosssum of X(2423) and X(3271)
X(55016) = X(6735)-beth conjugate of-X(119)
X(55016) = X(i)-Ceva conjugate of-X(j) for these (i, j): (4998, 2397), (51984, 6735)
X(55016) = X(i)-Dao Conjugate of-X(j) for these (i, j): (517, 56), (1145, 104), (2804, 11), (5452, 41933), (23980, 34051), (24028, 32486), (35014, 513), (44675, 52178), (45247, 10428)
X(55016) = X(i)-isoconjugate of-X(j) for these {i, j}: {57, 41933}, {909, 34051}, {2401, 32669}, {2423, 37136}
X(55016) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (55, 41933), (517, 34051), (1145, 40218), (1361, 1407), (2397, 54953), (2427, 2720), (2804, 2401), (3326, 1086), (6073, 43043), (6735, 34234), (15632, 651), (21664, 278), (23101, 1465), (23980, 56), (24028, 57), (26611, 7), (41215, 7117), (42072, 608), (42078, 604), (42757, 3669), (51380, 52663), (53549, 2423)
X(55016) = barycentric product of X(i) and X(j) for these {i, j}: {8, 26611}, {312, 24028}, {345, 21664}, {646, 42757}, {908, 6735}
X(55016) = trilinear product of X(i) and X(j) for these {i, j}: {8, 24028}, {9, 26611}, {78, 21664}, {312, 23980}, {341, 1361}
X(55016) = trilinear quotient of X(i) and X(j) for these (i, j): (9, 41933), (908, 34051), (1361, 1106), (2397, 37136), (2427, 32669)
X(55016) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (908, 39776, 1537), (1145, 1537, 39776), (1145, 17757, 119), (3035, 12607, 10956), (14503, 14504, 6735), (51362, 51380, 6735)

X(55017) = X(1)X(14508) ∩ X(476)X(26700)

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

See César Lozada, euclid 5967.

X(55017) lies on these lines: {1, 14508}, {476, 26700}, {523, 38340}, {35049, 39751}, {46819, 50148}

X(55017) = isogonal conjugate of X(3024)
X(55017) = cevapoint of X(26700) and X(52382)
X(55017) = crosssum of X(3024) and X(3024)
X(55017) = X(i)-cross conjugate of-X(j) for these (i, j): (1030, 651), (8818, 38340), (16117, 100)
X(55017) = X(i)-Dao Conjugate of-X(j) for these (i, j): (3, 3024), (223, 7266)
X(55017) = X(i)-isoconjugate of-X(j) for these {i, j}: {35, 53524}, {55, 7266}, {2310, 7279}, {2477, 24026}, {2605, 35057}, {2611, 35193}, {4420, 53542}, {6741, 17104}, {7202, 52405}, {8287, 35192}, {9404, 14838}, {11107, 22094}
X(55017) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (57, 7266), (1262, 7279), (2160, 53524), (8818, 6741), (23979, 2477), (26700, 14838), (34922, 52412), (38340, 4467), (43682, 17886), (52372, 7202), (52382, 8287)
X(55017) = barycentric product of X(i) and X(j) for these {i, j}: {6742, 38340}, {6757, 35049}, {15455, 26700}, {34922, 52381}
X(55017) = trilinear product of X(i) and X(j) for these {i, j}: {6742, 26700}, {7100, 34922}, {8818, 35049}
X(55017) = trilinear quotient of X(i) and X(j) for these (i, j): (7, 7266), (79, 53524), (6742, 35057), (6757, 6741), (7045, 7279)

X(55018) = X(1)X(14510) ∩ X(805)X(29055)

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

See César Lozada, euclid 5967.

X(55018) lies on these lines: {1, 14510}, {512, 37137}, {805, 29055}

X(55018) = isogonal conjugate of X(3023)
X(55018) = crosssum of X(3023) and X(3023)
X(55018) = X(i)-cross conjugate of-X(j) for these (i, j): (21779, 651), (40729, 37137)
X(55018) = X(3)-Dao Conjugate of-X(3023)
X(55018) = X(i)-isoconjugate of-X(j) for these {i, j}: {8, 7207}, {171, 4459}, {1111, 10799}, {2170, 6645}, {2329, 7200}, {3287, 4369}, {3907, 4367}, {4140, 18200}, {7081, 53541}, {16592, 27958}, {17103, 40608}
X(55018) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (59, 6645), (604, 7207), (893, 4459), (1431, 7200), (23990, 10799), (29055, 4369), (30658, 4124), (37137, 4374), (40099, 34387), (40729, 40608)
X(55018) = barycentric product of X(i) and X(j) for these {i, j}: {59, 40099}, {3903, 37137}, {27805, 29055}, {29055, 27805}
X(55018) = trilinear product of X(i) and X(j) for these {i, j}: {2149, 40099}, {3903, 29055}
X(55018) = trilinear quotient of X(i) and X(j) for these (i, j): (56, 7207), (256, 4459), (1110, 10799), (1431, 53541), (1432, 7200)

X(55019) = X(8)X(76) ∩ X(35517)X(50441)

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

See César Lozada, euclid 5967.

X(55019) lies on these lines: {8, 76}, {35517, 50441}

X(55019) = X(i)-Dao Conjugate of-X(j) for these (i, j): (516, 56), (40869, 52213), (50441, 103)
X(55019) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1360, 1407), (3234, 109), (21665, 278), (23972, 56), (24014, 57), (30807, 43736), (35517, 52156), (40869, 103), (41339, 911), (42073, 608), (42077, 604), (50441, 52213), (51376, 36056)
X(55019) = barycentric product of X(i) and X(j) for these {i, j}: {312, 24014}, {345, 21665}, {3234, 35519}, {3596, 23972}
X(55019) = trilinear product of X(i) and X(j) for these {i, j}: {8, 24014}, {78, 21665}, {312, 23972}, {341, 1360}
X(55019) = trilinear quotient of X(i) and X(j) for these (i, j): (1360, 1106), (3234, 1415), (21665, 34), (23972, 604), (24014, 56)

X(55020) = CYCLOCEVIAN CONJUGATE OF X(24243)

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

X(55020) = isogonal conjugate of X(3156)
X(55020) = isotomic conjugate of X(638)
X(55020) = anticomplement of X(10960)
X(55020) = cyclocevian conjugate of X(24243)
X(55020) = isotomic conjugate of the anticomplement of X(372)
X(55020) = isotomic conjugate of the complement of X(43133)
X(55020) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3156}, {31, 638}
X(55020) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 638}, {3, 3156}
X(55020) = cevapoint of X(i) and X(j) for these (i,j): {2, 43133}, {6, 45428}, {125, 54028}
X(55020) = trilinear pole of line {647, 14333}
X(55020) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 638}, {6, 3156}, {372, 10960}, {493, 26292}

X(55021) = CYCLOCEVIAN CONJUGATE OF X(24244)

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

X(55021) lies on the Jerabek circumhyperbola and these lines: {2, 6414}, {3, 490}, {6, 1586}, {64, 13749}, {68, 637}, {69, 45806}, {248, 3068}, {264, 1899}, {401, 26945}, {1588, 24243}, {6290, 6810}, {6413, 11417}, {6415, 45420}, {12322, 15077}, {12323, 15740}, {45441, 52518}

X(55021) = isogonal conjugate of X(3155)
X(55021) = isotomic conjugate of X(637)
X(55021) = anticomplement of X(10962)
X(55021) = cyclocevian conjugate of X(24244)
X(55021) = isotomic conjugate of the anticomplement of X(371)
X(55021) = isotomic conjugate of the complement of X(43134)
X(55021) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3155}, {31, 637}
X(55021) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 637}, {3, 3155}, {10960, 26875}
X(55021) = cevapoint of X(i) and X(j) for these (i,j): {2, 43134}, {6, 45429}, {125, 54029}
X(55021) = trilinear pole of line {647, 14334}
X(55021) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 637}, {6, 3155}, {371, 10962}, {372, 26875}, {494, 26293}

X(55022) = CYCLOCEVIAN CONJUGATE OF X(36917)

Barycentrics    (a^4 - 2*a^2*b^2 + b^4 + a^2*b*c + a*b^2*c - a*b*c^2 - c^4)*(a^4 - b^4 + a^2*b*c - a*b^2*c - 2*a^2*c^2 + a*b*c^2 + c^4) : :
X(55022) = 5 X[31247] - 4 X[36949]

X(55022) lies on these lines: {2, 40584}, {63, 2895}, {69, 2836}, {77, 997}, {81, 26932}, {286, 34387}, {340, 18816}, {524, 1814}, {651, 1211}, {758, 52392}, {1444, 4996}, {2766, 43363}, {2995, 39990}, {5080, 20566}, {11604, 14616}, {13532, 18815}, {16554, 37656}, {30690, 41910}, {31247, 36949}

X(55022) = midpoint of X(2895) and X(37781)
X(55022) = reflection of X(i) in X(j) for these {i,j}: {81, 26932}, {651, 1211}
X(55022) = isogonal conjugate of X(20989)
X(55022) = isotomic conjugate of X(5080)
X(55022) = anticomplement of X(40584)
X(55022) = cyclocevian conjugate of X(36917)
X(55022) = isotomic conjugate of the anticomplement of X(36)
X(55022) = isotomic conjugate of the complement of X(20067)
X(55022) = isotomic conjugate of the isogonal conjugate of X(34442)
X(55022) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20989}, {6, 16548}, {19, 22123}, {31, 5080}, {32, 20920}, {41, 37798}, {42, 1325}, {101, 47227}, {692, 21180}, {1333, 21066}, {2161, 40584}, {2850, 8750}, {6187, 52368}
X(55022) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 5080}, {3, 20989}, {6, 22123}, {9, 16548}, {37, 21066}, {1015, 47227}, {1086, 21180}, {3160, 37798}, {6376, 20920}, {26932, 2850}, {40592, 1325}, {40612, 52368}
X(55022) = cevapoint of X(i) and X(j) for these (i,j): {2, 20067}, {758, 1211}, {3738, 26932}, {15614, 23884}
X(55022) = trilinear pole of line {905, 3666}
X(55022) = barycentric product X(i)*X(j) for these {i,j}: {7, 52500}, {76, 34442}, {274, 10693}, {2766, 15413}
X(55022) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16548}, {2, 5080}, {3, 22123}, {6, 20989}, {7, 37798}, {10, 21066}, {36, 40584}, {75, 20920}, {81, 1325}, {513, 47227}, {514, 21180}, {905, 2850}, {2766, 1783}, {3218, 52368}, {10693, 37}, {18609, 12826}, {34442, 6}, {51470, 17796}, {52500, 8}

X(55023) = CYCLOCEVIAN CONJUGATE OF X(38259)

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

X(55023) lies on the cubics K170, the curve Q066, and these lines: {2, 14248}, {4, 19583}, {25, 193}, {487, 8948}, {488, 8946}, {1370, 41521}, {1611, 2207}, {2129, 2333}, {4176, 42068}, {5139, 6340}, {6524, 21447}, {7386, 15591}, {7392, 14593}, {7494, 15517}, {8753, 38282}, {8854, 8940}, {8855, 8944}, {17980, 37187}, {40819, 53067}

X(55023) = isogonal conjugate of X(19588)
X(55023) = isotomic conjugate of X(19583)
X(55023) = polar conjugate of X(6392)
X(55023) = cyclocevian conjugate of X(38259)
X(55023) = isotomic conjugate of the anticomplement of X(8770)
X(55023) = isotomic conjugate of the isogonal conjugate of X(15369)
X(55023) = polar conjugate of the isotomic conjugate of X(6339)
X(55023) = polar conjugate of the isogonal conjugate of X(40322)
X(55023) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2129, 20080}, {30558, 4329}, {53067, 6360}
X(55023) = X(i)-isoconjugate of X(j) for these (i,j): {1, 19588}, {3, 33781}, {6, 2128}, {19, 6461}, {31, 19583}, {48, 6392}, {63, 1611}, {184, 33787}, {293, 51426}, {662, 2519}, {1973, 6338}, {18156, 53068}
X(55023) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 19583}, {3, 19588}, {6, 6461}, {9, 2128}, {132, 51426}, {1084, 2519}, {1249, 6392}, {3162, 1611}, {6337, 6338}, {6342, 69}, {15261, 53068}, {30558, 39127}, {36103, 33781}
X(55023) = cevapoint of X(i) and X(j) for these (i,j): {6, 39653}, {512, 15525}, {523, 5139}, {647, 42068}, {6339, 30558}, {15369, 40322}
X(55023) = trilinear pole of line {2489, 2506}
X(55023) = barycentric product X(i)*X(j) for these {i,j}: {4, 6339}, {75, 2129}, {76, 15369}, {264, 40322}, {30558, 34208}
X(55023) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2128}, {2, 19583}, {3, 6461}, {4, 6392}, {6, 19588}, {19, 33781}, {25, 1611}, {69, 6338}, {92, 33787}, {232, 51426}, {512, 2519}, {2129, 1}, {6339, 69}, {15369, 6}, {30558, 6337}, {40322, 3}, {53059, 53068}, {53067, 3167}

X(55024) = CYCLOCEVIAN CONJUGATE OF X(39695)

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

X(55024) lies on these lines: {322, 3436}, {329, 1763}, {342, 14257}, {347, 21147}, {3718, 52366}, {7219, 8048}, {8822, 16049}, {41083, 41364}

X(55024) = isotomic conjugate of X(52366)
X(55024) = cyclocevian conjugate of X(39695)
X(55024) = isotomic conjugate of the anticomplement of X(34)
X(55024) = X(31)-isoconjugate of X(52366)
X(55024) = X(2)-Dao conjugate of X(52366)
X(55024) = cevapoint of X(i) and X(j) for these (i,j): {123, 514}, {513, 16596}
X(55024) = trilinear pole of line {6588, 14837}
X(55024) = barycentric quotient X(2)/X(52366)

X(55025) = CYCLOCEVIAN CONJUGATE OF X(39719)

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

X(55025) lies on these lines: {42, 17198}, {319, 4553}, {670, 17153}, {1442, 46153}, {1634, 8053}, {3219, 6651}, {4576, 17135}, {7282, 46152}, {14616, 46155}

X(55025) = isogonal conjugate of X(23398)
X(55025) = cyclocevian conjugate of X(39719)
X(55025) = isotomic conjugate of the anticomplement of X(3747)
X(55025) = X(1)-isoconjugate of X(23398)
X(55025) = X(3)-Dao conjugate of X(23398)
X(55025) = cevapoint of X(i) and X(j) for these (i,j): {141, 740}, {812, 53564}, {4155, 8287}, {17731, 33954}
X(55025) = trilinear pole of line {39, 14838}
X(55025) = barycentric quotient X(6)/X(23398)

X(55026) = CYCLOCEVIAN CONJUGATE OF X(39726)

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

X(55026) lies on these lines: {2, 7239}, {239, 3219}, {319, 350}, {870, 17140}, {982, 7192}, {984, 27807}, {1442, 1447}, {1479, 7357}, {3112, 17165}, {3952, 7033}, {4392, 54128}, {7226, 41527}, {8041, 35119}, {21208, 40148}, {21217, 39362}, {24166, 39747}, {33295, 34443}

X(55026) = isogonal conjugate of X(20990)
X(55026) = isotomic conjugate of X(17165)
X(55026) = anticomplement of X(40585)
X(55026) = polar conjugate of X(17915)
X(55026) = cyclocevian conjugate of X(39726)
X(55026) = isotomic conjugate of the anticomplement of X(38)
X(55026) = isotomic conjugate of the complement of X(20068)
X(55026) = isotomic conjugate of the isogonal conjugate of X(34443)
X(55026) = X(34443)-anticomplementary conjugate of X(2896)
X(55026) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20990}, {6, 16549}, {19, 22164}, {31, 17165}, {32, 18040}, {48, 17915}, {58, 21865}, {251, 40585}, {692, 50337}, {1333, 21067}
X(55026) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 17165}, {3, 20990}, {6, 22164}, {9, 16549}, {10, 21865}, {37, 21067}, {1086, 50337}, {1249, 17915}, {6376, 18040}, {40620, 26822}
X(55026) = cevapoint of X(i) and X(j) for these (i,j): {2, 20068}, {513, 21208}, {732, 19563}, {826, 8287}, {23885, 53835}
X(55026) = trilinear pole of line {812, 14838}
X(55026) = barycentric product X(76)*X(34443)
X(55026) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16549}, {2, 17165}, {3, 22164}, {4, 17915}, {6, 20990}, {10, 21067}, {37, 21865}, {38, 40585}, {75, 18040}, {514, 50337}, {7192, 26822}, {34443, 6}
X(55026) = {X(3112),X(33798)}-harmonic conjugate of X(17165)

X(55027) = CYCLOCEVIAN CONJUGATE OF X(39748)

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

X(55027) lies on the Kiepert circumhyperbola and these lines: {2, 1030}, {4, 37509}, {6, 1029}, {10, 3583}, {76, 2895}, {149, 4865}, {226, 7269}, {262, 37456}, {321, 4886}, {2475, 43531}, {4052, 50306}, {5397, 6839}, {6625, 19717}, {6949, 43666}, {7382, 14996}, {10431, 45097}, {14494, 26118}, {16044, 27041}, {17167, 17758}, {19742, 54119}, {19786, 30588}, {32863, 40013}

X(55027) = isogonal conjugate of X(5124)
X(55027) = isotomic conjugate of X(32863)
X(55027) = polar conjugate of X(52252)
X(55027) = cyclocevian conjugate of X(39748)
X(55027) = isotomic conjugate of the anticomplement of X(32911)
X(55027) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5124}, {6, 6763}, {31, 32863}, {48, 52252}
X(55027) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 32863}, {3, 5124}, {9, 6763}, {1249, 52252}
X(55027) = cevapoint of X(115) and X(4132)
X(55027) = trilinear pole of line {523, 21179}
X(55027) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 6763}, {2, 32863}, {4, 52252}, {6, 5124}

X(55028) = CYCLOCEVIAN CONJUGATE OF X(39953)

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

X(55028) lies on Kiepert circumhyperbola and these lines: {2, 160}, {6, 30505}, {76, 2979}, {83, 5012}, {98, 1627}, {237, 43679}, {262, 1180}, {1676, 41379}, {1677, 41378}, {1916, 8267}, {7391, 54122}, {11550, 21646}, {16030, 37988}, {18840, 37190}, {33769, 40016}

X(55028) = isogonal conjugate of X(8266)
X(55028) = anticomplement of X(34452)
X(55028) = cyclocevian conjugate of X(39953)
X(55028) = isogonal conjugate of the anticomplement of X(3613)
X(55028) = isotomic conjugate of the anticomplement of X(3051)
X(55028) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8266}, {32, 18051}, {75, 40643}, {3112, 34452}
X(55028) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 8266}, {206, 40643}, {6376, 18051}
X(55028) = cevapoint of X(i) and X(j) for these (i,j): {115, 688}, {512, 7668}, {826, 53575}
X(55028) = trilinear pole of line {523, 52590}
X(55028) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 8266}, {32, 40643}, {75, 18051}, {3051, 34452}

X(55029) = CYCLOCEVIAN CONJUGATE OF X(41895)

Barycentrics    (a^6 - 9*a^4*b^2 - 9*a^2*b^4 + b^6 + a^4*c^2 + 26*a^2*b^2*c^2 + b^4*c^2 - a^2*c^4 - b^2*c^4 - c^6)*(a^6 + a^4*b^2 - a^2*b^4 - b^6 - 9*a^4*c^2 + 26*a^2*b^2*c^2 - b^4*c^2 - 9*a^2*c^4 + b^2*c^4 + c^6) : :

X(55029) lies on the curve Q066 and these lines: {2, 14262}, {4, 39157}, {69, 34166}, {1992, 1995}, {4232, 11580}, {5512, 32133}, {7493, 52141}, {9084, 37748}, {11059, 11185}, {13608, 52174}

X(55029) = cyclocevian conjugate of X(41895)
X(55029) = isotomic conjugate of the anticomplement of X(21448)
X(55029) = cevapoint of X(i) and X(j) for these (i,j): {512, 35133}, {523, 5512}
X(55029) = trilinear pole of line {1499, 7652}

X(55030) = CYCLOCEVIAN CONJUGATE OF X(42361)

Barycentrics    (a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5 - a^4*c + 4*a^3*b*c - 6*a^2*b^2*c + 4*a*b^3*c - b^4*c - 2*a^3*c^2 + 6*a^2*b*c^2 + 6*a*b^2*c^2 - 2*b^3*c^2 + 2*a^2*c^3 - 12*a*b*c^3 + 2*b^2*c^3 + a*c^4 + b*c^4 - c^5)*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 + a^4*c + 4*a^3*b*c + 6*a^2*b^2*c - 12*a*b^3*c + b^4*c - 2*a^3*c^2 - 6*a^2*b*c^2 + 6*a*b^2*c^2 + 2*b^3*c^2 - 2*a^2*c^3 + 4*a*b*c^3 - 2*b^2*c^3 + a*c^4 - b*c^4 + c^5) : :

X(55030) lies on these lines: {7, 42872}, {40, 144}, {223, 3160}, {329, 16284}, {341, 44797}, {962, 48357}, {972, 12246}, {14256, 50561}

X(55030) = cyclocevian conjugate of X(42361)
X(55030) = isotomic conjugate of the anticomplement of X(269)
X(55030) = X(53086)-anticomplementary conjugate of X(36845)
X(55030) = X(i)-isoconjugate of X(j) for these (i,j): {6, 10860}, {41, 34060}, {55, 34488}
X(55030) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 10860}, {223, 34488}, {3160, 34060}
X(55030) = cevapoint of X(i) and X(j) for these (i,j): {513, 13609}, {514, 5514}
X(55030) = trilinear pole of line {6129, 7658}
X(55030) = barycentric product X(75)*X(53086)
X(55030) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 10860}, {7, 34060}, {57, 34488}, {53086, 1}

X(55031) = CYCLOCEVIAN CONJUGATE OF X(44177)

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

X(55031) lies on these lines: {4, 8905}, {69, 254}, {311, 847}, {317, 6193}, {393, 467}, {1179, 39110}, {1300, 44128}, {41231, 47735}

X(55031) = isotomic conjugate of X(6193)
X(55031) = cyclocevian conjugate of X(44177)
X(55031) = isotomic conjugate of the anticomplement of X(68)
X(55031) = isotomic conjugate of the isogonal conjugate of X(34428)
X(55031) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {34428, 18664}, {39110, 6360}
X(55031) = X(i)-isoconjugate of X(j) for these (i,j): {31, 6193}, {47, 39111}, {2148, 41523}
X(55031) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 6193}, {216, 41523}, {34853, 39111}, {52032, 8905}
X(55031) = cevapoint of X(i) and X(j) for these (i,j): {136, 525}, {2971, 17434}
X(55031) = barycentric product X(i)*X(j) for these {i,j}: {76, 34428}, {305, 41525}, {6504, 39115}, {14518, 28706}
X(55031) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 6193}, {5, 41523}, {343, 8905}, {2165, 39111}, {5392, 40698}, {14518, 8882}, {34428, 6}, {39110, 571}, {39115, 6515}, {41525, 25}

X(55032) = CYCLOCEVIAN CONJUGATE OF X(46270)

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

X(55032) lies on these lines: {22, 1634}, {69, 25045}, {110, 7768}, {315, 4576}, {340, 15107}, {3260, 46155}, {3268, 46147}, {4456, 46148}, {4463, 4553}, {7879, 8743}, {33314, 36827}, {44134, 46151}

X(55032) = cyclocevian conjugate of X(46270)
X(55032) = isotomic conjugate of the anticomplement of X(1495)
X(55032) = cevapoint of X(i) and X(j) for these (i,j): {30, 141}, {127, 9033}, {323, 6636}, {3936, 4450}
X(55032) = trilinear pole of line {39, 2485}

X(55033) = CYCLOCEVIAN CONJUGATE OF X(46271)

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

X(55033) lies on these lines: {2, 25053}, {69, 160}, {110, 1799}, {264, 46151}, {305, 2979}, {306, 46148}, {307, 46153}, {328, 46155}, {1441, 46152}, {2419, 46164}, {4553, 20336}, {6403, 18018}, {14252, 42313}, {14957, 18024}, {14977, 46154}, {15526, 36425}, {20021, 53331}, {22339, 46167}, {22340, 46166}, {30786, 36827}, {34767, 46147}, {40708, 46161}, {46165, 53369}

X(55033) = isotomic conjugate of X(14957)
X(55033) = anticomplement of X(40601)
X(55033) = cyclocevian conjugate of X(46271)
X(55033) = isotomic conjugate of the anticomplement of X(237)
X(55033) = isotomic conjugate of the complement of X(46518)
X(55033) = X(i)-isoconjugate of X(j) for these (i,j): {6, 16564}, {19, 14965}, {31, 14957}, {1821, 40601}
X(55033) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 14957}, {6, 14965}, {9, 16564}
X(55033) = cevapoint of X(i) and X(j) for these (i,j): {2, 46518}, {141, 511}, {2799, 53575}, {15526, 39469}
X(55033) = trilinear pole of line {39, 525}
X(55033) = X(2)-lineconjugate of X(40601)
X(55033) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16564}, {2, 14957}, {3, 14965}, {237, 40601}

X(55034) = CYCLOCEVIAN CONJUGATE OF X(46274)

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

X(55034) lies on these lines: {2, 38996}, {69, 6664}, {110, 6573}, {1634, 10330}, {4563, 36827}, {4609, 44445}, {5468, 35325}, {7854, 46156}

X(55034) = isogonal conjugate of X(21006)
X(55034) = isotomic conjugate of X(44445)
X(55034) = anticomplement of X(38996)
X(55034) = cyclocevian conjugate of X(46274)
X(55034) = isotomic conjugate of the anticomplement of X(669)
X(55034) = isotomic conjugate of the complement of X(31299)
X(55034) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21006}, {19, 22159}, {31, 44445}, {32, 20953}, {58, 22322}, {82, 8711}, {512, 33760}, {661, 1627}, {669, 18064}, {798, 7760}, {799, 38996}
X(55034) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 44445}, {3, 21006}, {6, 22159}, {10, 22322}, {141, 8711}, {6376, 20953}, {31998, 7760}, {36830, 1627}, {39054, 33760}
X(55034) = cevapoint of X(i) and X(j) for these (i,j): {2, 31299}, {141, 512}, {513, 21240}, {523, 626}, {688, 6292}
X(55034) = trilinear pole of line {39, 698}
X(55034) = X(2)-line conjugate of X(38996)
X(55034) = barycentric product X(i)*X(j) for these {i,j}: {99, 6664}, {141, 6573}
X(55034) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 44445}, {3, 22159}, {6, 21006}, {37, 22322}, {39, 8711}, {75, 20953}, {99, 7760}, {110, 1627}, {662, 33760}, {669, 38996}, {689, 41297}, {799, 18064}, {6573, 83}, {6664, 523}

X(55035) = CYCLOCEVIAN CONJUGATE OF X(54117)

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

X(55035) lies on the Feuerbach circumhyperbola and these lines: {1, 9551}, {2, 40600}, {8, 22271}, {9, 3588}, {21, 5263}, {149, 11609}, {256, 33095}, {314, 17135}, {497, 941}, {1041, 5307}, {1400, 43739}, {2481, 17220}, {3434, 30479}, {6385, 17137}, {6601, 36855}, {15315, 24248}, {16678, 17077}, {17138, 20556}, {30970, 33847}, {34444, 53564}, {37717, 43073}, {43740, 54383}

X(55035) = isogonal conjugate of X(16678)
X(55035) = isotomic conjugate of X(17137)
X(55035) = anticomplement of X(40600)
X(55035) = polar conjugate of X(17913)
X(55035) = cyclocevian conjugate of X(54117)
X(55035) = isogonal conjugate of the anticomplement of X(44411)
X(55035) = isotomic conjugate of the anticomplement of X(213)
X(55035) = isotomic conjugate of the complement of X(20109)
X(55035) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16678}, {6, 16574}, {19, 23124}, {31, 17137}, {32, 18138}, {48, 17913}, {58, 22275}, {86, 40600}, {692, 23785}, {1333, 22008}
X(55035) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 17137}, {3, 16678}, {6, 23124}, {9, 16574}, {10, 22275}, {37, 22008}, {1086, 23785}, {1249, 17913}, {6376, 18138}
X(55035) = cevapoint of X(i) and X(j) for these (i,j): {2, 20109}, {11, 512}, {513, 53564}, {523, 21252}, {740, 20542}
X(55035) = trilinear pole of line {650, 784}
X(55035) = barycentric product X(274)*X(40516)
X(55035) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16574}, {2, 17137}, {3, 23124}, {4, 17913}, {6, 16678}, {10, 22008}, {37, 22275}, {75, 18138}, {213, 40600}, {514, 23785}, {40516, 37}

X(55036) = CYCLOCEVIAN CONJUGATE OF X(54119)

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

X(55036) lies on the curve Q066 and these lines: {1, 46880}, {2, 10571}, {8, 573}, {58, 19607}, {145, 14753}, {312, 3869}, {333, 1610}, {2995, 20028}, {17137, 20245}, {18359, 34242}, {33650, 39992}, {36007, 52133}, {38955, 51558}

X(55036) = reflection of X(145) in X(14753)
X(55036) = isogonal conjugate of X(23361)
X(55036) = isotomic conjugate of X(20245)
X(55036) = anticomplement of X(40611)
X(55036) = cyclocevian conjugate of X(54119)
X(55036) = isotomic conjugate of the anticomplement of X(1400)
X(55036) = X(43739)-anticomplementary conjugate of X(17778)
X(55036) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23361}, {2, 52159}, {6, 1764}, {19, 23131}, {21, 40611}, {31, 20245}, {32, 21596}, {58, 22299}, {81, 3588}, {692, 23799}, {1193, 40455}, {1333, 22020}
X(55036) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 20245}, {3, 23361}, {6, 23131}, {9, 1764}, {10, 22299}, {37, 22020}, {1086, 23799}, {6376, 21596}, {32664, 52159}, {40586, 3588}
X(55036) = cevapoint of X(i) and X(j) for these (i,j): {124, 523}, {512, 1146}, {513, 34589}
X(55036) = trilinear pole of line {522, 6589}
X(55036) = barycentric product X(75)*X(43739)
X(55036) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1764}, {2, 20245}, {3, 23131}, {6, 23361}, {10, 22020}, {31, 52159}, {37, 22299}, {42, 3588}, {75, 21596}, {514, 23799}, {1400, 40611}, {2298, 40455}, {43739, 1}

X(55037) = CYCLOCEVIAN CONJUGATE OF X(54120)

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

X(55037) lies on the cubics K131 and K1002 and these lines: {2, 41532}, {8, 18760}, {31, 41534}, {42, 41350}, {55, 38814}, {171, 19554}, {210, 1654}, {256, 40777}, {846, 1334}, {1920, 4645}, {6542, 52211}, {30661, 30669}

X(55037) = isogonal conjugate of X(8424)
X(55037) = isotomic conjugate of X(30660)
X(55037) = cyclocevian conjugate of X(54120)
X(55037) = isotomic conjugate of the anticomplement of X(893)
X(55037) = isogonal conjugate of the isotomic conjugate of X(18760)
X(55037) = X(18784)-anticomplementary conjugate of X(6646)
X(55037) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8424}, {2, 53128}, {6, 17739}, {9, 40765}, {31, 30660}, {55, 40723}, {75, 18759}, {893, 27963}, {2344, 40797}, {17798, 39920}
X(55037) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 30660}, {3, 8424}, {9, 17739}, {206, 18759}, {223, 40723}, {478, 40765}, {32664, 53128}, {40597, 27963}
X(55037) = cevapoint of X(513) and X(40608)
X(55037) = trilinear pole of line {3709, 3805}
X(55037) = barycentric product X(i)*X(j) for these {i,j}: {6, 18760}, {7, 40792}, {75, 18784}, {335, 16366}, {7179, 40771}
X(55037) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17739}, {2, 30660}, {6, 8424}, {31, 53128}, {32, 18759}, {56, 40765}, {57, 40723}, {171, 27963}, {1469, 40797}, {3512, 39920}, {16366, 239}, {18760, 76}, {18784, 1}, {40771, 52133}, {40792, 8}

X(55038) = X(3)X(54)∩X(51)X(110)

Barycentrics    a^2*(3*a^4 - 5*a^2*b^2 + 2*b^4 - 5*a^2*c^2 - b^2*c^2 + 2*c^4) : :
X(55038) = 2 X[3] - 5 X[54], X[3] + 5 X[195], X[3] - 10 X[1493], 8 X[3] - 5 X[7691], 7 X[3] - 10 X[10610], 11 X[3] - 5 X[12307], 7 X[3] + 5 X[12316], 4 X[3] + 5 X[15801], 17 X[3] - 5 X[54202], X[54] + 2 X[195], X[54] - 4 X[1493], 4 X[54] - X[7691], 7 X[54] - 4 X[10610], 11 X[54] - 2 X[12307], 7 X[54] + 2 X[12316], and many others

X(55038) lise on the Thomson-Gibert-Moses hyperbola, the cubic K1329, and these lines: {2, 5965}, {3, 54}, {6, 11451}, {23, 44108}, {51, 110}, {52, 9706}, {143, 9705}, {154, 3060}, {184, 7712}, {193, 41594}, {251, 20976}, {275, 35311}, {323, 3819}, {392, 16858}, {394, 5646}, {511, 6030}, {539, 3545}, {547, 50708}, {550, 20585}, {576, 9544}, {826, 5652}, {930, 40634}, {973, 12280}, {1173, 18350}, {1199, 5892}, {1201, 1203}, {1209, 5067}, {1351, 26881}, {1353, 15059}, {2056, 39024}, {2888, 5056}, {2914, 13596}, {2981, 3170}, {3167, 5640}, {3171, 6151}, {3292, 5643}, {3519, 8254}, {3533, 6689}, {3543, 5656}, {3574, 3832}, {3629, 13622}, {3845, 5655}, {3850, 6288}, {3853, 20424}, {4993, 10184}, {5041, 34945}, {5059, 10619}, {5093, 35264}, {5422, 5544}, {5644, 6090}, {5645, 5651}, {5648, 8584}, {5663, 13482}, {5891, 13434}, {5946, 43572}, {6242, 10115}, {6353, 41599}, {6431, 49256}, {6432, 49257}, {6636, 44109}, {7979, 33179}, {7998, 37672}, {9140, 15131}, {9306, 9716}, {9545, 11202}, {9777, 10546}, {9905, 11531}, {10066, 51803}, {10545, 15004}, {10601, 14924}, {11216, 15531}, {11426, 15056}, {11443, 53019}, {11455, 18445}, {11702, 14483}, {11803, 15800}, {12111, 15739}, {12226, 40632}, {12254, 33703}, {12965, 19095}, {12971, 19096}, {13352, 13445}, {13353, 44324}, {13364, 14627}, {14049, 36853}, {14845, 41597}, {14855, 15032}, {15018, 44111}, {15033, 18435}, {15062, 37472}, {15080, 17809}, {15089, 43580}, {15532, 44056}, {16239, 21230}, {18859, 43596}, {18950, 26913}, {20115, 34484}, {21849, 35265}, {22115, 43584}, {23292, 41724}, {24981, 37349}, {29317, 54036}, {30531, 41991}, {31802, 41482}, {32062, 43605}, {32368, 34751}, {32379, 34750}, {37495, 43602}, {40112, 45298}, {40317, 51170}, {41588, 41596}, {43836, 45969}, {44077, 47485}

X(55038) = reflection of X(i) in X(j) for these {i,j}: {3519, 21357}, {21357, 8254}, {41713, 51}
X(55038) = Thomson-isogonal conjugate of X(550)
X(55038) = X(897)-isoconjugate of X(13412)
X(55038) = X(6593)-Dao conjugate of X(13412)
X(55038) = crossdifference of every pair of points on line {12077, 13412}
X(55038) = barycentric quotient X(187)/X(13412)
X(55038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {54, 195, 15801}, {54, 15801, 7691}, {110, 1994, 53863}, {184, 37517, 37913}, {195, 1493, 54}, {1993, 5012, 23061}, {1993, 11402, 2979}, {1993, 11422, 5012}, {1994, 13595, 5097}, {1994, 34986, 110}, {2979, 11402, 5012}, {2979, 11422, 11402}, {3292, 34566, 6688}, {6688, 34566, 34545}, {6689, 13431, 12325}, {11803, 36966, 15800}, {20976, 45843, 251}

X(55039) = X(3)X(54)∩X(49)X(51)

Barycentrics    a^2*(3*a^8 - 10*a^6*b^2 + 12*a^4*b^4 - 6*a^2*b^6 + b^8 - 10*a^6*c^2 + 11*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 4*b^6*c^2 + 12*a^4*c^4 + 3*a^2*b^2*c^4 + 6*b^4*c^4 - 6*a^2*c^6 - 4*b^2*c^6 + c^8) : :
X(55039) = X[3] - 4 X[54], X[3] + 2 X[195], X[3] + 8 X[1493], 7 X[3] - 4 X[7691], 5 X[3] - 8 X[10610], 5 X[3] - 2 X[12307], 2 X[3] + X[12316], 5 X[3] + 4 X[15801], 4 X[3] - X[54202], 2 X[54] + X[195], X[54] + 2 X[1493], 7 X[54] - X[7691], 5 X[54] - 2 X[10610], 10 X[54] - X[12307], 8 X[54] + X[12316], 5 X[54] + X[15801], and many others

X(55039)_ lies on the cubic K1329 and these lines: {2, 21357}, {3, 54}, {4, 22051}, {6, 3200}, {20, 54157}, {24, 12175}, {25, 52417}, {49, 51}, {52, 40632}, {55, 51803}, {56, 35197}, {110, 13364}, {140, 12325}, {143, 9706}, {154, 9704}, {184, 5899}, {265, 14049}, {323, 44324}, {378, 2914}, {381, 9143}, {382, 12254}, {399, 11702}, {511, 34006}, {539, 3167}, {567, 5891}, {568, 11202}, {576, 37923}, {578, 18435}, {599, 5050}, {1199, 43809}, {1209, 5070}, {1263, 31675}, {1351, 19150}, {1482, 9905}, {1656, 2888}, {1657, 11803}, {1994, 2070}, {1995, 53124}, {2917, 37493}, {3060, 37956}, {3295, 47378}, {3311, 12971}, {3312, 12965}, {3515, 6242}, {3517, 6152}, {3519, 6689}, {3523, 54201}, {3526, 11271}, {3564, 48411}, {3567, 13368}, {3574, 3843}, {3819, 13353}, {3830, 18400}, {3851, 6288}, {5073, 10619}, {5093, 19153}, {5446, 44108}, {5448, 43835}, {5462, 34566}, {5692, 10246}, {5892, 13366}, {5946, 32609}, {6000, 17824}, {6090, 15703}, {6143, 32165}, {6343, 11671}, {6417, 49256}, {6418, 49257}, {6500, 19096}, {6501, 19095}, {6640, 18950}, {6644, 11935}, {6767, 10066}, {7373, 10082}, {7502, 11004}, {7506, 41713}, {7545, 9544}, {7577, 11804}, {7730, 13321}, {9545, 45735}, {9705, 10095}, {9707, 12291}, {9715, 12226}, {9977, 53092}, {10115, 19357}, {10125, 13418}, {10282, 17846}, {10606, 10628}, {10620, 43580}, {10677, 11486}, {10678, 11485}, {11432, 12234}, {11451, 22462}, {11472, 12308}, {12000, 49192}, {12001, 49191}, {12099, 54073}, {12266, 37624}, {12902, 18388}, {13352, 35452}, {13363, 43572}, {13431, 32348}, {13451, 35265}, {13512, 14071}, {14635, 19176}, {14845, 18350}, {14855, 37495}, {15002, 42059}, {15019, 15039}, {15032, 18859}, {15040, 15053}, {18946, 31804}, {19468, 44515}, {22550, 42016}, {27357, 38539}, {32345, 35450}, {34545, 40111}, {34783, 43581}, {36853, 44263}, {36987, 37496}, {38638, 47391}, {43586, 44111}, {44076, 54007}, {45800, 53038}, {46372, 48669}, {53019, 53091}

X(55039) = reflection of X(i) in X(j) for these {i,j}: {154, 10274}, {9920, 154}, {35450, 32345}
X(55039) = anticomplement of X(21357)
X(55039) = orthocentroidal-circle-inverse of X(25147)
X(55039) = crossdifference of every pair of points on line {12077, 45147}
X(55039) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 195, 12316}, {3, 12316, 54202}, {49, 14627, 13621}, {54, 195, 3}, {54, 1493, 195}, {54, 15801, 10610}, {110, 15038, 21308}, {143, 15532, 13423}, {195, 12307, 15801}, {567, 34986, 50461}, {2888, 8254, 1656}, {3574, 48675, 3843}, {6343, 31674, 11671}, {9704, 36749, 18378}, {10610, 12307, 3}, {10610, 15801, 12307}, {11597, 43704, 5898}, {12254, 20424, 382}, {13366, 22115, 15037}, {22051, 36966, 4}, {32136, 34148, 43845}, {34148, 43845, 3}

X(55040) = X(2)X(371)∩X(3)X(6281)

Barycentrics    4*a^4 - 5*a^2*b^2 + b^4 - 5*a^2*c^2 - 2*b^2*c^2 + c^4 - 2*(a^2 - 2*b^2 - 2*c^2)*S : :
X(55040) = 5 X[2] - 4 X[6119], 5 X[2] - X[12221], 4 X[2] - X[22484], X[486] + 2 X[487], X[486] - 4 X[642], 5 X[486] - 8 X[6119], 5 X[486] - 2 X[12221], X[487] + 2 X[642], 5 X[487] + 4 X[6119], 5 X[487] + X[12221], 4 X[487] + X[22484], 5 X[642] - 2 X[6119], 10 X[642] - X[12221], 8 X[642] - X[22484], 4 X[6119] - X[12221], and many others

X(55040) lies on the cubic K1330 and these lines: {2, 371}, {3, 6281}, {6, 13650}, {30, 6290}, {69, 41490}, {99, 491}, {140, 49317}, {372, 5861}, {485, 42024}, {489, 42268}, {519, 7980}, {524, 19146}, {549, 599}, {590, 13711}, {591, 5420}, {615, 13770}, {631, 48734}, {640, 42260}, {1078, 32808}, {1271, 6396}, {1327, 5491}, {1328, 32492}, {1991, 34511}, {2044, 35743}, {2996, 43568}, {3058, 12958}, {3068, 14482}, {3096, 43526}, {3524, 12256}, {3534, 48659}, {3545, 6251}, {3582, 10083}, {3584, 10067}, {3595, 6564}, {3763, 35255}, {3830, 22596}, {3839, 12296}, {5054, 6280}, {5055, 12601}, {5064, 12147}, {5434, 12948}, {5463, 36437}, {5464, 36455}, {5591, 6200}, {6054, 9758}, {6179, 35684}, {6279, 43121}, {6337, 13821}, {6453, 7376}, {6561, 45473}, {6565, 26362}, {7375, 35812}, {7388, 9681}, {7615, 42602}, {7692, 13810}, {7739, 13846}, {7757, 13637}, {7799, 32809}, {7865, 9986}, {8592, 33340}, {8997, 13834}, {9605, 19105}, {9738, 10514}, {9741, 26620}, {9906, 19875}, {11237, 18989}, {11238, 13081}, {12268, 25055}, {12928, 34612}, {12938, 34606}, {13132, 45701}, {13133, 45700}, {13847, 44648}, {13934, 19104}, {13989, 41672}, {15709, 49048}, {19709, 22809}, {21356, 49786}, {22563, 23698}, {22601, 38412}, {22615, 23312}, {23263, 51952}, {32806, 42277}, {32807, 42601}, {35256, 40341}, {36775, 36778}

X(55040) = midpoint of X(i) and X(j) for these {i,j}: {2, 487}, {3534, 48659}, {9867, 9891}, {22598, 36371}, {22600, 36374}
X(55040) = reflection of X(i) in X(j) for these {i,j}: {2, 642}, {486, 2}, {3830, 22596}, {12158, 22594}, {22484, 486}, {36391, 33451}, {36394, 33449}
X(55040) = Thomson-isogonal conjugate of X(6396)
X(55040) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 26289, 35823}, {487, 642, 486}, {6119, 12221, 486}, {6300, 6301, 487}, {13821, 32811, 53131}

X(55041) = X(2)X(372)∩X(3)X(6278)

Barycentrics    4*a^4 - 5*a^2*b^2 + b^4 - 5*a^2*c^2 - 2*b^2*c^2 + c^4 + 2*(a^2 - 2*b^2 - 2*c^2)*S : :
X(55041) = 5 X[2] - 4 X[6118], 5 X[2] - X[12222], 4 X[2] - X[22485], X[485] + 2 X[488], X[485] - 4 X[641], 5 X[485] - 8 X[6118], 5 X[485] - 2 X[12222], X[488] + 2 X[641], 5 X[488] + 4 X[6118], 5 X[488] + X[12222], 4 X[488] + X[22485], 5 X[641] - 2 X[6118], 10 X[641] - X[12222], 8 X[641] - X[22485], 4 X[6118] - X[12222], and many others

X(55041) lies on the cubic K1330 and these lines: {2, 372}, {3, 6278}, {6, 13771}, {30, 6289}, {69, 41491}, {99, 492}, {140, 49318}, {371, 5860}, {486, 42023}, {490, 42269}, {519, 7981}, {524, 19145}, {549, 599}, {590, 13651}, {591, 34511}, {615, 13834}, {631, 48735}, {639, 42261}, {1078, 32809}, {1270, 6200}, {1327, 32495}, {1328, 5490}, {1991, 5418}, {2996, 43569}, {3058, 12959}, {3069, 14482}, {3096, 43525}, {3524, 12257}, {3534, 48660}, {3545, 6250}, {3582, 10084}, {3584, 10068}, {3593, 6565}, {3763, 35256}, {3830, 22625}, {3839, 12297}, {5054, 6279}, {5055, 12602}, {5064, 12148}, {5434, 12949}, {5463, 36455}, {5464, 36437}, {5590, 6396}, {6054, 9757}, {6179, 35685}, {6280, 43120}, {6337, 13701}, {6454, 7375}, {6560, 45472}, {6564, 26361}, {7376, 35813}, {7615, 42603}, {7690, 13691}, {7739, 13847}, {7757, 13757}, {7799, 32808}, {7865, 9987}, {8592, 33341}, {8997, 41672}, {9605, 19102}, {9739, 10515}, {9741, 26619}, {9907, 19875}, {11237, 18988}, {11238, 13082}, {12269, 25055}, {12929, 34612}, {12939, 34606}, {13134, 45701}, {13135, 45700}, {13711, 13989}, {13846, 44647}, {13882, 19103}, {15709, 49049}, {19709, 22810}, {21356, 49787}, {22562, 23698}, {22630, 38412}, {22644, 23311}, {23253, 51953}, {32805, 42274}, {35255, 40341}, {36775, 36779}

X(55041) = midpoint of X(i) and X(j) for these {i,j}: {2, 488}, {3534, 48660}, {9868, 9893}, {22627, 36370}, {22629, 36372}
X(55041) = reflection of X(i) in X(j) for these {i,j}: {2, 641}, {485, 2}, {3830, 22625}, {12159, 22623}, {22485, 485}, {36390, 33450}, {36392, 33448}
X(55041) = Thomson-isogonal conjugate of X(6200)
X(55041) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 26288, 35822}, {488, 641, 485}, {6118, 12222, 485}, {6304, 6305, 488}, {13701, 32810, 53130}






leftri   Centers of circumconics: X(55042)-X(55073  rightri

Contributed by Clark Kimberling and Peter Moses July 25, 2023.

In the plane of a triangle ABC, let P = p : q : r and U = u : v : w be distinct points. The center of the circumconic {{A,B,C,P,U}} is given by

p u (r v - q w)(p v w (r - q) - q w u (p + r) + r u v (p + q ) : :

See X(34585).

underbar



X(55042) = CENTER OF CIRCUMCONIC {{A,B,C,X(1),X(35)}}

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

X(55042) lies on the circumellipse of the medial and incentral triangles and on these lines: {1, 9405}, {11, 3134}, {36, 39987}, {55, 45235}, {56, 39174}, {500, 2646}, {1015, 2088}, {1464, 11709}, {2605, 3024}, {7004, 38982}

X(55042) = complement of the isogonal conjugate of X(48382)
X(55042) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 9404}, {1459, 37361}, {7414, 20316}, {48382, 10}
X(55042) = X(2)-Ceva conjugate of X(9404)
X(55042) = X(34800)-isoconjugate of X(34922)
X(55042) = X(9404)-Dao conjugate of X(2)
X(55042) = barycentric quotient X(48382)/X(38340)

X(55043) = CENTER OF CIRCUMCONIC {{A,B,C,X(1),X(38)}}

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

X(55043) lies on the circumellipse of the medial and incentral triangles and on these lines: {11, 4475}, {214, 17457}, {2084, 20982}, {2170, 40623}, {2292, 8299}, {2643, 17761}, {4118, 18061}, {17456, 40614}, {17463, 38986}, {17793, 21336}, {39046, 40936}

X(55043) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 8061}, {667, 53423}, {1333, 21212}, {3733, 29655}, {3961, 31946}, {18077, 626}, {33954, 21260}, {40145, 18076}
X(55043) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 8061}, {3512, 46387}, {39725, 513}
X(55043) = X(i)-Dao conjugate of X(j) for these (i,j): {8061, 2}, {21194, 20934}
X(55043) = barycentric product X(3005)*X(18077)
X(55043) = barycentric quotient X(18077)/X(689)

X(55044) = CENTER OF CIRCUMCONIC {{A,B,C,X(1),X(40)}}

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

X(55044) lies on the circumellipse of the medial and incentral triangles and on these lines: {1, 53844}, {3, 102}, {11, 122}, {33, 46831}, {34, 52543}, {36, 12096}, {55, 53852}, {56, 14379}, {116, 35970}, {123, 10017}, {212, 53847}, {216, 2331}, {244, 35014}, {828, 33883}, {1015, 35071}, {1040, 6509}, {1073, 2192}, {1214, 10164}, {1364, 2638}, {2968, 34589}, {2972, 3270}, {3100, 44436}, {3318, 6129}, {6285, 8798}, {7004, 7117}, {7011, 7074}, {7049, 15318}, {7288, 31377}, {8054, 47413}, {10165, 17102}, {10535, 34147}, {15526, 17421}, {16573, 53561}, {16596, 38357}, {20749, 22057}, {22072, 22341}, {22082, 53850}, {23207, 39046}, {40613, 40946}, {46974, 54192}, {47409, 47411}, {47432, 53557}

X(55044) = complement of the isogonal conjugate of X(23224)
X(55044) = complement of the isotomic conjugate of X(4131)
X(55044) = isogonal conjugate of the polar conjugate of X(16596)
X(55044) = X(i)-complementary conjugate of X(j) for these (i,j): {3, 20316}, {31, 14298}, {58, 520}, {109, 3042}, {184, 3239}, {222, 46396}, {255, 513}, {326, 21260}, {394, 3835}, {520, 3454}, {577, 514}, {603, 521}, {605, 6365}, {606, 6364}, {649, 13567}, {652, 41883}, {663, 15849}, {667, 24005}, {810, 50036}, {822, 1211}, {905, 20305}, {1092, 20315}, {1364, 124}, {1397, 52587}, {1437, 8062}, {1444, 21259}, {1459, 5}, {1474, 52585}, {1790, 30476}, {1795, 8677}, {1804, 17072}, {1919, 3767}, {1946, 20262}, {2206, 6587}, {2289, 20317}, {2638, 5514}, {3682, 31946}, {3926, 21262}, {3990, 4129}, {4025, 21243}, {4055, 661}, {4091, 141}, {4131, 2887}, {6056, 4521}, {7125, 4885}, {7254, 34830}, {7335, 522}, {9247, 2509}, {14585, 6586}, {17216, 53575}, {18604, 4369}, {21122, 53851}, {22383, 226}, {23189, 34831}, {23224, 10}, {24018, 21245}, {30805, 626}, {32320, 440}, {32657, 39470}, {32660, 36949}, {36054, 3452}, {38985, 47601}, {39201, 1213}, {39687, 13609}, {51640, 442}, {52411, 14837}, {52430, 650}
X(55044) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 520}, {2, 14298}, {222, 36054}, {280, 521}, {1073, 652}, {1295, 8677}, {3346, 513}, {7011, 10397}, {24031, 1364}
X(55044) = X(i)-isoconjugate of X(j) for these (i,j): {280, 24033}, {282, 23984}, {653, 40117}, {2192, 24032}, {7003, 7128}, {7012, 40836}, {7129, 46102}, {13138, 36127}, {23985, 34404}, {32652, 52938}, {36049, 54240}
X(55044) = X(i)-Dao conjugate of X(j) for these (i,j): {57, 24032}, {521, 280}, {656, 7020}, {5514, 54240}, {14298, 2}, {14331, 15466}, {14837, 264}, {16596, 52938}, {24018, 75}
X(55044) = crossdifference of every pair of points on line {108, 40117}
X(55044) = barycentric product X(i)*X(j) for these {i,j}: {3, 16596}, {63, 53557}, {221, 23983}, {222, 7358}, {223, 24031}, {227, 16731}, {329, 1364}, {347, 35072}, {348, 47432}, {394, 38357}, {1804, 5514}, {1819, 4466}, {2638, 40702}, {2968, 7011}, {4025, 10397}, {4091, 8058}, {4131, 14298}, {7013, 34591}, {7078, 26932}, {17896, 36054}
X(55044) = barycentric quotient X(i)/X(j) for these {i,j}: {221, 23984}, {223, 24032}, {1364, 189}, {1946, 40117}, {2199, 24033}, {2638, 282}, {3270, 7003}, {4091, 53642}, {6129, 54240}, {7078, 46102}, {7114, 7128}, {7117, 40836}, {7215, 34400}, {7358, 7017}, {10397, 1897}, {14837, 52938}, {16596, 264}, {23224, 37141}, {24031, 34404}, {34591, 7020}, {35072, 280}, {36054, 13138}, {38357, 2052}, {39687, 2192}, {47432, 281}, {53557, 92}
X(55044) = {X(3),X(36055)}-harmonic conjugate of X(54083)

X(55045) = CENTER OF CIRCUMCONIC {{A,B,C,X(1),X(45)}}

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

X(55045) lies on the circumellipse of the medial and incentral triangles and on these lines: {2, 4674}, {42, 34586}, {214, 3720}, {244, 48244}, {1086, 4379}, {1647, 17761}, {2643, 38982}, {3120, 34589}, {4689, 8299}, {4793, 27749}, {17793, 30970}

X(55045) = complement of the isotomic conjugate of X(47780)
X(55045) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 4893}, {604, 48321}, {649, 5241}, {4828, 626}, {5035, 514}, {37633, 3835}, {47780, 2887}, {48320, 141}
X(55045) = X(2)-Ceva conjugate of X(4893)
X(55045) = X(i)-isoconjugate of X(j) for these (i,j): {5385, 39974}, {5549, 46480}
X(55045) = X(4893)-Dao conjugate of X(2)
X(55045) = barycentric product X(i)*X(j) for these {i,j}: {4775, 4828}, {4777, 48320}, {4893, 47780}
X(55045) = barycentric quotient X(48320)/X(4597)

X(55046) = CENTER OF CIRCUMCONIC {{A,B,C,X(2),X(19)}}

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

X(55046) lies on the Steiner inellipse and these lines: {2, 54982}, {115, 5517}, {1015, 17463}, {1084, 14936}, {3124, 42067}, {6184, 34261}, {15526, 16592}, {35094, 53543}

X(55046) = complement of X(54982)
X(55046) = complement of the isogonal conjugate of X(8646)
X(55046) = complement of the isotomic conjugate of X(8678)
X(55046) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 48044}, {31, 8678}, {612, 21260}, {669, 4205}, {1010, 23301}, {1460, 17072}, {1918, 47842}, {1919, 4657}, {1974, 23874}, {1980, 37592}, {2303, 42327}, {2345, 21262}, {2484, 141}, {2517, 21235}, {4206, 21259}, {6590, 626}, {8646, 10}, {8678, 2887}, {44119, 512}, {50494, 3454}, {54416, 3835}
X(55046) = X(2)-Ceva conjugate of X(8678)
X(55046) = X(1310)-isoconjugate of X(37215)
X(55046) = X(8678)-Dao conjugate of X(2)
X(55046) = barycentric product X(i)*X(j) for these {i,j}: {2484, 6590}, {2517, 8646}, {8678, 8678}, {47844, 50494}
X(55046) = barycentric quotient X(i)/X(j) for these {i,j}: {2484, 37215}, {8646, 1310}, {8678, 54982}

X(55047) = CENTER OF CIRCUMCONIC {{A,B,C,X(2),X(22)}}

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

X(55047) lies on the Steiner inellipse and these lines: {32, 39172}, {115, 53822}, {160, 206}, {216, 23976}, {2482, 22401}, {3163, 40938}, {5158, 53851}, {14396, 38356}, {16582, 35075}, {19615, 36417}, {39013, 41172}

X(55047) = complement of the isotomic conjugate of X(8673)
X(55047) = X(i)-complementary conjugate of X(j) for these (i,j): {22, 21259}, {31, 8673}, {206, 8062}, {560, 47125}, {647, 16607}, {656, 6697}, {810, 427}, {2172, 30476}, {2485, 20305}, {3049, 16580}, {8673, 2887}, {9247, 3265}, {10316, 4369}, {17453, 525}, {20806, 42327}, {20968, 16612}, {21122, 942}, {22075, 14838}, {34254, 21263}, {38356, 21253}
X(55047) = X(2)-Ceva conjugate of X(8673)
X(55047) = X(i)-Dao conjugate of X(j) for these (i,j): {3265, 40421}, {8673, 2}
X(55047) = barycentric product X(i)*X(j) for these {i,j}: {22, 47413}, {127, 10316}, {8673, 8673}, {15526, 36414}, {20806, 38356}, {39172, 53822}
X(55047) = barycentric quotient X(i)/X(j) for these {i,j}: {10316, 44183}, {22075, 15388}, {36414, 23582}, {38356, 43678}, {47413, 18018}

X(55048) = CENTER OF CIRCUMCONIC {{A,B,C,X(2),X(23)}}

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

X(55048) lies on the Steiner inellipse and these lines: {115, 2485}, {216, 23967}, {232, 3163}, {647, 15526}, {2482, 14961}, {3003, 23976}, {3284, 6593}, {10317, 18374}, {14396, 39000}, {18334, 41172}

X(55048) = complement of the isogonal conjugate of X(42659)
X(55048) = complement of the isotomic conjugate of X(9517)
X(55048) = X(i)-complementary conjugate of X(j) for these (i,j): {23, 21259}, {31, 9517}, {560, 47138}, {647, 21234}, {810, 858}, {2492, 20305}, {3049, 16581}, {9247, 14417}, {9517, 2887}, {10317, 4369}, {18374, 8062}, {22151, 42327}, {37804, 21263}, {42659, 10}
X(55048) = X(2)-Ceva conjugate of X(9517)
X(55048) = X(9517)-Dao conjugate of X(2)
X(55048) = crossdifference of every pair of points on line {935, 46592}
X(55048) = barycentric product X(i)*X(j) for these {i,j}: {9517, 9517}, {15526, 36415}
X(55048) = barycentric quotient X(i)/X(j) for these {i,j}: {36415, 23582}, {42659, 935}

X(55049) = CENTER OF CIRCUMCONIC {{A,B,C,X(2),X(31)}}

Barycentrics    a^6*(b - c)^2*(b^2 + b*c + c^2)^2 : :
X(55049) = 3 X[2] + X[39347], X[39347] - 3 X[43095], 3 X[43095] + X[46132]

X(55049) lies on the Steiner inellipse and these lines: {2, 39347}, {31, 14945}, {115, 53823}, {1084, 3271}, {6377, 35119}, {9468, 51328}, {14402, 14436}, {21838, 35068}

X(55049) = midpoint of X(i) and X(j) for these {i,j}: {2, 43095}, {31, 14945}, {39347, 46132}
X(55049) = complement of X(46132)
X(55049) = complement of the isogonal conjugate of X(8630)
X(55049) = complement of the isotomic conjugate of X(788)
X(55049) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 788}, {560, 4874}, {788, 2887}, {824, 40379}, {869, 21260}, {1491, 21235}, {1501, 824}, {1919, 21264}, {1980, 24325}, {2276, 21262}, {3250, 626}, {3736, 23301}, {8630, 10}, {14598, 30665}, {18900, 513}, {40415, 9006}, {40728, 3835}, {40736, 21191}, {40773, 21263}, {46386, 141}, {46503, 21259}
X(55049) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 788}, {31, 9006}
X(55049) = X(i)-isoconjugate of X(j) for these (i,j): {789, 37133}, {870, 5388}, {1492, 52611}, {4586, 46132}
X(55049) = X(i)-Dao conjugate of X(j) for these (i,j): {788, 2}, {824, 40362}, {38995, 52611}
X(55049) = crossdifference of every pair of points on line {789, 17996}
X(55049) = barycentric product X(i)*X(j) for these {i,j}: {788, 788}, {1491, 8630}, {3250, 46386}, {4475, 18900}
X(55049) = barycentric quotient X(i)/X(j) for these {i,j}: {788, 46132}, {3250, 52611}, {8630, 789}, {40728, 5388}, {46386, 37133}
X(55049) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 39347, 46132}, {43095, 46132, 39347}

X(55050) = CENTER OF CIRCUMCONIC {{A,B,C,X(2),X(32)}}

Barycentrics    a^8*(b - c)^2*(b + c)^2*(b^2 + c^2)^2 : :
X(55050) = X[42371] + 3 X[43094]

X(55050) lies on the Steiner inellipse and these lines: {2, 42371}, {32, 14946}, {115, 35971}, {538, 9496}, {782, 15449}, {1084, 14990}, {3005, 39010}, {3051, 17965}, {6680, 39082}, {6683, 39076}, {9427, 9494}, {11672, 13357}, {14403, 14406}, {35073, 44562}, {35078, 52591}, {39009, 47421}, {40359, 42486}

X(55050) = midpoint of X(i) and X(j) for these {i,j}: {2, 43094}, {32, 14946}
X(55050) = reflection of X(i) in X(j) for these {i,j}: {39076, 6683}, {39082, 6680}
X(55050) = complement of X(42371)
X(55050) = complement of the isogonal conjugate of X(9494)
X(55050) = complement of the isotomic conjugate of X(688)
X(55050) = medial-isogonal conjugate of X(42291)
X(55050) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 42291}, {31, 688}, {39, 21263}, {669, 21238}, {688, 2887}, {1501, 8060}, {1917, 826}, {1923, 512}, {1924, 3934}, {1964, 23301}, {2084, 626}, {3005, 21235}, {3051, 42327}, {4117, 7668}, {8061, 40379}, {9426, 1215}, {9494, 10}, {21814, 21262}, {27369, 21259}, {41267, 21260}, {41331, 4369}
X(55050) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 688}, {39953, 512}, {42486, 826}
X(55050) = X(i)-isoconjugate of X(j) for these (i,j): {689, 37204}, {4593, 42371}
X(55050) = X(i)-Dao conjugate of X(j) for these (i,j): {688, 2}, {826, 40359}, {52042, 44168}
X(55050) = crossdifference of every pair of points on line {689, 17995}
X(55050) = barycentric product X(i)*X(j) for these {i,j}: {669, 2531}, {688, 688}, {3005, 9494}, {8041, 9427}, {9233, 15449}
X(55050) = barycentric quotient X(i)/X(j) for these {i,j}: {688, 42371}, {2531, 4609}, {9494, 689}, {15449, 40359}

X(55051) = CENTER OF CIRCUMCONIC {{A,B,C,X(4),X(39)}}

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

X(55051) lies on the incircle and these lines: {2, 43357}, {114, 9478}, {115, 14990}, {132, 46026}, {2679, 7668}, {5099, 6071}, {6784, 46656}, {7790, 44947}, {8288, 9151}, {19130, 44953}, {35971, 39691}

X(55051) = complement of X(43357)
X(55051) = X(i)-complementary conjugate of X(j) for these (i,j): {82, 54263}, {3329, 4369}, {12212, 14838}, {14318, 37}, {51312, 826}

X(55052) = CENTER OF CIRCUMCONIC {{A,B,C,X(4),X(60)}}

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

X(55052) lies on the nine-point circle and these lines: {2, 43345}, {115, 38345}, {5521, 38390}, {5532, 15612}, {10017, 53524}, {15608, 53566}, {15611, 53525}, {37613, 42423}, {38357, 38964}

X(55052) = complement of X(43345)
X(55052) = X(i)-complementary conjugate of X(j) for these (i,j): {10039, 513}, {31837, 20315}

X(55053) = CENTER OF CIRCUMCONIC {{A,B,C,X(6),X(31)}}

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

X(55053) lies on these lines: {2, 54458}, {6, 4553}, {1977, 3124}, {2300, 36213}, {3063, 21762}, {3125, 4164}, {6386, 18825}, {16470, 19557}, {17197, 44312}

X(55053) = complement of X(54458)
X(55053) = complement of the isogonal conjugate of X(21005)
X(55053) = complement of the isotomic conjugate of X(21301)
X(55053) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 667}, {20952, 626}, {21005, 10}, {21099, 21245}, {21210, 21252}, {21301, 2887}, {21389, 141}, {22157, 18589}, {32926, 21260}
X(55053) = X(2)-Ceva conjugate of X(667)
X(55053) = X(190)-isoconjugate of X(54458)
X(55053) = X(667)-Dao conjugate of X(2)
X(55053) = crossdifference of every pair of points on line {4553, 53332}
X(55053) = X(i)-lineconjugate of X(j) for these (i,j): {2, 54458}, {6, 4553}
X(55053) = barycentric product X(i)*X(j) for these {i,j}: {31, 21210}, {513, 21005}, {649, 21389}, {667, 21301}, {1919, 20952}, {3248, 32926}, {6591, 22157}
X(55053) = barycentric quotient X(i)/X(j) for these {i,j}: {667, 54458}, {21005, 668}, {21210, 561}, {21301, 6386}, {21389, 1978}

X(55054) = CENTER OF CIRCUMCONIC {{A,B,C,X(6),X(38)}}

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

X(55054) lies on these lines: {125, 244}, {1084, 20982}, {1203, 6593}, {3122, 38363}, {3271, 8054}, {7117, 38991}, {21755, 38996}, {28479, 32736}

X(55054) = X(i)-complementary conjugate of X(j) for these (i,j): {82, 6371}, {6371, 21249}, {18108, 3831}, {48131, 21248}
X(55054) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 6371}, {56, 8635}
X(55054) = X(831)-isoconjugate of X(8707)
X(55054) = X(3004)-Dao conjugate of X(76)
X(55054) = crossdifference of every pair of points on line {36147, 54328}
X(55054) = barycentric product X(i)*X(j) for these {i,j}: {7, 38364}, {830, 48131}, {2483, 3004}, {4509, 8635}, {6371, 47660}
X(55054) = barycentric quotient X(i)/X(j) for these {i,j}: {2483, 8707}, {8635, 36147}, {38364, 8}

X(55055) = CENTER OF CIRCUMCONIC {{A,B,C,X(6),X(44)}}

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

X(55055) lies on these lines: {6, 46162}, {44, 4434}, {798, 3124}, {1017, 21830}, {8659, 39011}, {9025, 20972}, {17455, 36213}, {21191, 44312}

X(55055) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 1960}, {32927, 21260}
X(55055) = X(2)-Ceva conjugate of X(1960)
X(55055) = X(1960)-Dao conjugate of X(2)
X(55055) = X(6)-line conjugate of X(46162)

X(55056) = CENTER OF CIRCUMCONIC {{A,B,C,X(7),X(10)}}

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

X(55056) lies on these lines: {11, 24185}, {1365, 40617}, {3120, 8287}, {4657, 16597}, {16591, 21471}, {16594, 31253}, {21093, 31993}, {21709, 21944}

X(55056) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 15309}, {31, 4841}, {15309, 141}, {17019, 3835}, {28653, 21260}, {47678, 21245}, {50498, 1211}
X(55056) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 4841}, {7, 15309}
X(55056) = X(4627)-isoconjugate of X(15322)
X(55056) = X(4841)-Dao conjugate of X(2)
X(55056) = barycentric product X(i)*X(j) for these {i,j}: {4778, 47678}, {4815, 15309}
X(55056) = barycentric quotient X(i)/X(j) for these {i,j}: {4822, 15322}, {15309, 4614}, {47678, 53658}, {50498, 8694}

X(55057) = CENTER OF CIRCUMCONIC {{A,B,C,X(7),X(19)}}

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

X(55057)) lies on these lines: {11, 31892}, {65, 20455}, {442, 46842}, {1086, 3675}, {3140, 8287}, {4014, 26932}, {4904, 38989}, {5880, 16593}, {14936, 16592}, {37541, 47522}

X(55057) = complement of the isogonal conjugate of X(50336)
X(55057) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 28846}, {513, 49511}, {649, 4384}, {3751, 513}, {4078, 31946}, {14013, 30476}, {17316, 3835}, {28846, 141}, {30758, 21260}, {48047, 3454}, {50336, 10}
X(55057) = X(7)-Ceva conjugate of X(28846)
X(55057) = barycentric product X(28846)*X(47123)

X(55058) = CENTER OF CIRCUMCONIC {{A,B,C,X(7),X(20)}}

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

X(55058) lies on these lines: {3, 108}, {11, 31893}, {84, 3342}, {123, 13612}, {223, 1040}, {1863, 37072}, {2816, 3184}, {2968, 7004}, {3346, 7149}, {6260, 52659}, {7515, 16594}, {8287, 13611}, {9371, 51368}, {10017, 46663}, {13609, 35072}, {16596, 38357}, {17102, 20264}, {20209, 52389}, {35014, 40617}, {35580, 38977}

X(55058) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 14331}, {40, 20316}, {219, 20318}, {221, 521}, {223, 46396}, {521, 20306}, {603, 8058}, {652, 20205}, {663, 20263}, {810, 1901}, {905, 21239}, {1409, 24018}, {1410, 17898}, {1415, 40535}, {1459, 946}, {1817, 30476}, {1946, 281}, {2187, 3239}, {2199, 14837}, {2360, 8062}, {3194, 520}, {3195, 14298}, {6129, 5}, {7011, 4885}, {7013, 17072}, {7078, 513}, {7114, 522}, {8822, 21259}, {10397, 3452}, {14298, 41883}, {14837, 20305}, {15501, 8677}, {17896, 21243}, {22383, 57}, {36055, 6087}, {39201, 46837}, {47432, 5514}, {53557, 124}
X(55058) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 14331}, {280, 8058}, {1034, 521}, {1895, 8057}, {41904, 6087}, {46352, 14837}
X(55058) = X(i)-Dao conjugate of X(j) for these (i,j): {14298, 1073}, {14302, 46350}, {14331, 2}, {14837, 253}, {17898, 318}, {21172, 280}, {24018, 19611}
X(55058) = barycentric product X(i)*X(j) for these {i,j}: {20, 16596}, {347, 40616}, {7358, 18623}, {18750, 53557}, {37669, 38357}
X(55058) = barycentric quotient X(i)/X(j) for these {i,j}: {16596, 253}, {38357, 459}, {40616, 280}, {47432, 30457}, {53557, 2184}

X(55059) = CENTER OF CIRCUMCONIC {{A,B,C,X(7),X(37)}}

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

X(55059) lies on these lines: {10, 20694}, {1086, 4934}, {1365, 40615}, {2486, 8287}, {3120, 3121}, {3649, 39063}, {16591, 33149}, {16593, 31336}, {16597, 34824}, {17761, 38989}

X(55059) = Fuhrmann-circle-inverse of X(15425)
X(55059) = complement of the isogonal conjugate of X(4784)
X(55059) = medial-isogonal conjugate of X(4806)
X(55059) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 4806}, {6, 28840}, {58, 54265}, {106, 45342}, {513, 3775}, {649, 24603}, {3842, 31946}, {4649, 513}, {4784, 10}, {4824, 3454}, {4913, 1329}, {4948, 21251}, {16826, 3835}, {20142, 27854}, {28840, 141}, {31904, 30476}, {51311, 4369}, {51314, 42327}, {51356, 512}
X(55059) = X(7)-Ceva conjugate of X(28840)
X(55059) = X(4913)-Dao conjugate of X(8)
X(55059) = barycentric product X(i)*X(j) for these {i,j}: {4762, 4824}, {4804, 28840}
X(55059) = barycentric quotient X(i)/X(j) for these {i,j}: {4824, 32041}, {28840, 51563}

X(55060) = CENTER OF CIRCUMCONIC {{A,B,C,X(7),X(56)}}

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

X(55060) lies on these lines: {7, 799}, {11, 1356}, {57, 16575}, {65, 3178}, {226, 46842}, {1086, 1357}, {1284, 9364}, {3125, 16592}, {3649, 16594}, {8287, 53566}, {10427, 39780}, {16593, 39793}, {17477, 51641}

X(55060) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 6002}, {31, 7180}, {512, 34528}, {649, 3687}, {661, 46828}, {667, 28244}, {1999, 3835}, {5247, 513}, {6002, 141}, {16613, 8287}, {24560, 1368}, {43924, 24178}
X(55060) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 7180}, {7, 6002}
X(55060) = X(i)-isoconjugate of X(j) for these (i,j): {645, 6010}, {5546, 54986}
X(55060) = X(i)-Dao conjugate of X(j) for these (i,j): {7180, 2}, {16613, 7258}
X(55060) = barycentric product X(i)*X(j) for these {i,j}: {7, 16613}, {1999, 53540}, {4017, 6002}, {5247, 53545}
X(55060) = barycentric quotient X(i)/X(j) for these {i,j}: {4017, 54986}, {6002, 7257}, {16613, 8}, {51641, 6010}

X(55061) = CENTER OF CIRCUMCONIC {{A,B,C,X(7),X(66)}}

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

X(55061) lies on these lines: {2, 1492}, {12, 39063}, {116, 38989}, {125, 16592}, {1086, 21210}, {3271, 8287}, {3454, 46842}, {15254, 16593}, {20550, 26582}

X(55061) = complement of X(1492)
X(55061) = complement of the isogonal conjugate of X(1491)
X(55061) = medial-isogonal conjugate of X(4874)
X(55061) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 4874}, {6, 824}, {75, 788}, {256, 3805}, {291, 30665}, {513, 24325}, {514, 21264}, {649, 17023}, {753, 33904}, {788, 37}, {824, 141}, {869, 650}, {984, 513}, {1469, 522}, {1491, 10}, {2276, 514}, {3250, 2}, {3661, 3835}, {3736, 523}, {3773, 31946}, {3781, 20315}, {3797, 27854}, {3799, 24003}, {3805, 51575}, {3807, 27076}, {3862, 812}, {3864, 3837}, {4122, 3454}, {4475, 11}, {4481, 3739}, {4486, 20333}, {4517, 4521}, {4522, 1329}, {4951, 21251}, {7146, 4885}, {7179, 17072}, {7204, 3900}, {8626, 33568}, {8630, 16584}, {16514, 27929}, {18900, 52589}, {23596, 20541}, {29956, 3008}, {30654, 5976}, {30665, 17793}, {30671, 3912}, {30870, 21235}, {30966, 512}, {31909, 30476}, {33931, 21260}, {40728, 6586}, {40773, 4369}, {45782, 4083}, {46386, 39}, {46503, 16612}, {51837, 21191}, {52029, 3716}, {52655, 31286}
X(55061) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 824}, {66, 788}
X(55061) = X(3415)-isoconjugate of X(5384)
X(55061) = X(4522)-Dao conjugate of X(8)
X(55061) = barycentric quotient X(i)/X(j) for these {i,j}: {5282, 5384}, {50459, 825}

X(55062) = CENTER OF CIRCUMCONIC {{A,B,C,X(8),X(43)}}

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

X(55062) lies on these lines: {8, 2053}, {3123, 21138}, {3756, 25574}, {4083, 5518}, {4110, 52871}, {8256, 9311}, {25135, 51381}, {36639, 40609}, {40663, 43062}

X(55062) = midpoint of X(8) and X(8851)
X(55062) = complement of the isogonal conjugate of X(48330)
X(55062) = X(i)-complementary conjugate of X(j) for these (i,j): {649, 3662}, {667, 17448}, {3550, 513}, {4090, 31946}, {17105, 4083}, {17350, 3835}, {23472, 2}, {24524, 21260}, {24840, 124}, {31286, 141}, {48330, 10}
X(55062) = X(31286)-Dao conjugate of X(7)
X(55062) = crossdifference of every pair of points on line {25577, 34071}
X(55062) = barycentric product X(i)*X(j) for these {i,j}: {192, 24840}, {4147, 31286}
X(55062) = barycentric quotient X(24840)/X(330)

X(55063) = CENTER OF CIRCUMCONIC {{A,B,C,X(8),X(63)}}

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

X(55063) lies on these lines: {9, 20265}, {40, 2883}, {123, 13613}, {219, 1249}, {220, 46829}, {2968, 34591}, {5514, 7358}, {6506, 8286}, {8805, 40838}, {20207, 26942}, {31653, 35968}, {35072, 39020}

X(55063) = X(i)-complementary conjugate of X(j) for these (i,j): {20, 17072}, {25, 14302}, {154, 522}, {204, 521}, {219, 20319}, {521, 20309}, {522, 23332}, {610, 4885}, {649, 18634}, {652, 20208}, {663, 4}, {1249, 46396}, {1394, 3900}, {1946, 52389}, {2299, 8057}, {3063, 1427}, {3172, 14837}, {6587, 17052}, {7070, 513}, {14308, 3454}, {14331, 141}, {18623, 46399}, {21172, 2886}, {27382, 3835}, {42658, 18641}, {44695, 20316}, {51508, 4142}, {52346, 21260}
X(55063) = X(i)-Ceva conjugate of X(j) for these (i,j): {63, 8057}, {1032, 521}
X(55063) = X(36079)-isoconjugate of X(40117)
X(55063) = X(i)-Dao conjugate of X(j) for these (i,j): {6129, 459}, {6587, 6355}, {14331, 7}, {17898, 92}, {21172, 189}
X(55063) = barycentric product X(i)*X(j) for these {i,j}: {20, 7358}, {329, 40616}, {5514, 37669}, {14615, 47432}, {16596, 27382}, {52346, 53557}
X(55063) = barycentric quotient X(i)/X(j) for these {i,j}: {122, 6355}, {1562, 13853}, {5514, 459}, {7358, 253}, {40616, 189}, {47432, 64}, {53557, 8809}

X(55064) = CENTER OF CIRCUMCONIC {{A,B,C,X(9),X(33)}}

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

X(55064) lies on these lines: {661, 4934}, {2170, 4965}, {2310, 3709}, {2486, 21044}, {3121, 36197}, {4092, 4171}, {4422, 24384}, {4625, 35144}, {10868, 15587}, {24224, 45661}

X(55064) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 4041}, {22042, 21245}, {23821, 21252}
X(55064) = X(2)-Ceva conjugate of X(4041)
X(55064) = X(4041)-Dao conjugate of X(2)
X(55064) = barycentric product X(i)*X(j) for these {i,j}: {210, 23821}, {650, 22042}
X(55064) = barycentric quotient X(22042)/X(4554)

X(55065) = CENTER OF CIRCUMCONIC {{A,B,C,X(10),X(12)}}

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

X(55065) lies on these lines: {10, 4427}, {1109, 4036}, {2611, 4705}, {3120, 18004}, {3932, 21729}, {4024, 6627}, {4610, 35162}, {8013, 20679}, {21674, 27716}, {21709, 21710}, {24185, 24186}

X(55065) = complement of the isotomic conjugate of X(17161)
X(55065) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 4024}, {17161, 2887}, {18158, 626}, {32025, 21260}, {33761, 3835}, {33771, 513}, {33775, 21262}
X(55065) = X(2)-Ceva conjugate of X(4024)
X(55065) = X(1101)-isoconjugate of X(43972)
X(55065) = X(i)-Dao conjugate of X(j) for these (i,j): {523, 43972}, {4024, 2}
X(55065) = barycentric product X(i)*X(j) for these {i,j}: {115, 32025}, {338, 33771}, {1109, 33761}, {2643, 33775}, {4024, 17161}, {4705, 18158}
X(55065) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 43972}, {17161, 4610}, {18158, 4623}, {32025, 4590}, {33761, 24041}, {33771, 249}, {33775, 24037}
X(55065) = {X(21043),X(21054)}-harmonic conjugate of X(3120)

X(55066) = CENTER OF CIRCUMCONIC {{A,B,C,X(19),X(31)}}

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

X(55066) lies on these lines: {9, 25120}, {219, 2196}, {692, 9247}, {822, 43963}, {2083, 16560}, {3271, 6139}, {3708, 17463}, {4020, 52880}

X(55066) = complement of the isogonal conjugate of X(23864)
X(55066) = complement of the isotomic conjugate of X(21300)
X(55066) = X(i)-complementary conjugate of X(j) for these (i,j): {21, 25128}, {31, 810}, {3063, 53476}, {13588, 17072}, {21300, 2887}, {21348, 17052}, {21388, 141}, {21610, 626}, {22443, 18642}, {23145, 18589}, {23655, 442}, {23864, 10}, {51949, 1577}
X(55066) = X(2)-Ceva conjugate of X(810)
X(55066) = X(46102)-isoconjugate of X(54128)
X(55066) = X(i)-Dao conjugate of X(j) for these (i,j): {810, 2}, {5518, 46404}, {17072, 92}
X(55066) = barycentric product X(i)*X(j) for these {i,j}: {212, 23772}, {521, 23655}, {647, 21388}, {650, 22443}, {652, 21348}, {656, 23864}, {661, 23145}, {810, 21300}, {1946, 17072}, {3049, 21610}, {3501, 7117}, {7004, 34247}, {26932, 51949}
X(55066) = barycentric quotient X(i)/X(j) for these {i,j}: {21348, 46404}, {21388, 6331}, {22443, 4554}, {23145, 799}, {23655, 18026}, {23864, 811}, {51949, 46102}

X(55067) = CENTER OF CIRCUMCONIC {{A,B,C,X(21),X(27)}}

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

X(55067) lies on these lines: {58, 40129}, {284, 35342}, {1019, 1111}, {1021, 2170}, {1625, 32486}, {1781, 40979}, {4267, 41239}, {4466, 17197}, {26244, 46196}

X(55067) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 3737}, {604, 26146}, {24235, 21252}
X(55067) = X(2)-Ceva conjugate of X(3737)
X(55067) = X(3737)-Dao conjugate of X(2)
X(55067) = barycentric product X(21)*X(24235)
X(55067) = barycentric quotient X(24235)/X(1441)

X(55068) = CENTER OF CIRCUMCONIC {{A,B,C,X(21),X(29)}}

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

X(55068) lies on these lines: {21, 48897}, {29, 52524}, {2328, 53388}, {3109, 33810}, {3120, 45740}, {3737, 7004}, {11107, 37732}, {14010, 45741}, {17194, 47057}

X(55068) = X(31)-complementary conjugate of X(1021)
X(55068) = X(2)-Ceva conjugate of X(1021)
X(55068) = X(1021)-Dao conjugate of X(2)

X(55069) = CENTER OF CIRCUMCONIC {{A,B,C,X(25),X(66)}}

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

X(55069) lies on these lines: {2, 32713}, {3, 15116}, {122, 125}, {127, 2881}, {6389, 51337}, {6697, 20208}, {15449, 35071}, {20625, 46662}, {34841, 40484}, {35968, 46063}

X(55069) = complement of X(32713)
X(55069) = complement of the isogonal conjugate of X(3265)
X(55069) = complement of the isotomic conjugate of X(52617)
X(55069) = medial-isogonal conjugate of X(6587)
X(55069) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 6587}, {3, 16612}, {10, 14298}, {31, 52588}, {48, 2485}, {63, 525}, {65, 52587}, {69, 8062}, {71, 2509}, {72, 3239}, {73, 6588}, {75, 520}, {92, 52585}, {99, 23998}, {107, 24017}, {255, 647}, {304, 30476}, {305, 21259}, {307, 521}, {326, 523}, {336, 6130}, {394, 14838}, {520, 37}, {521, 40942}, {522, 9119}, {523, 24005}, {525, 226}, {647, 16583}, {650, 52530}, {656, 6}, {661, 3767}, {662, 23583}, {810, 1196}, {822, 39}, {905, 40940}, {1020, 23982}, {1214, 14837}, {1231, 46396}, {1367, 8286}, {1439, 21172}, {1444, 21187}, {1459, 40941}, {1577, 13567}, {2169, 16040}, {2584, 8106}, {2585, 8105}, {2632, 115}, {2962, 14346}, {2972, 16573}, {3265, 10}, {3267, 20305}, {3269, 16592}, {3682, 650}, {3708, 6388}, {3926, 4369}, {3990, 6586}, {3998, 514}, {4025, 942}, {4055, 52589}, {4064, 50036}, {4086, 15849}, {4091, 3666}, {4131, 1125}, {4143, 18589}, {4558, 16599}, {4566, 24030}, {4592, 5972}, {5489, 24040}, {6332, 6708}, {6507, 52584}, {6517, 34977}, {7183, 17069}, {8611, 46835}, {14208, 5}, {15413, 34830}, {15414, 21231}, {15526, 8287}, {17094, 1210}, {17216, 11}, {17879, 125}, {17898, 20265}, {18604, 52597}, {19611, 8057}, {20336, 20316}, {20580, 36908}, {22341, 6589}, {24018, 2}, {24019, 23591}, {24020, 122}, {24031, 34591}, {30805, 3739}, {35200, 46425}, {35518, 34831}, {36793, 21253}, {39201, 16584}, {40152, 905}, {44706, 17434}, {51640, 17053}, {51664, 3772}, {52355, 20262}, {52385, 522}, {52387, 661}, {52389, 14331}, {52396, 513}, {52430, 52590}, {52565, 4885}, {52613, 1214}, {52616, 960}, {52617, 2887}, {53173, 16609}
X(55069) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 52588}, {66, 520}, {13575, 525}, {34427, 826}, {42484, 523}
X(55069) = X(i)-isoconjugate of X(j) for these (i,j): {162, 39417}, {24000, 34207}, {39733, 41937}
X(55069) = X(i)-Dao conjugate of X(j) for these (i,j): {125, 39417}, {525, 13575}, {647, 52583}, {17434, 52041}, {47125, 17907}, {52588, 2}, {53822, 107}
X(55069) = crossdifference of every pair of points on line {112, 39417}
X(55069) = barycentric product X(i)*X(j) for these {i,j}: {125, 28419}, {159, 36793}, {339, 23115}, {1370, 15526}, {2632, 21582}, {3265, 47125}, {7068, 18629}, {14376, 53822}, {17879, 18596}, {23974, 41766}, {52588, 52617}
X(55069) = barycentric quotient X(i)/X(j) for these {i,j}: {125, 52583}, {159, 23964}, {647, 39417}, {1370, 23582}, {2972, 52041}, {3269, 34207}, {15526, 13575}, {17879, 39733}, {18596, 24000}, {20975, 40144}, {21582, 23999}, {23115, 250}, {28419, 18020}, {36793, 40009}, {41361, 32230}, {41766, 23590}, {47125, 107}, {47413, 40358}, {52588, 32713}, {53822, 17907}
X(55069) = {X(122),X(15526)}-harmonic conjugate of X(47413)

X(55070) = CENTER OF CIRCUMCONIC {{A,B,C,X(32),X(66)}}

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

X(55070) lies on these lines: {2, 4630}, {125, 46654}, {2972, 3005}, {3819, 21248}, {6292, 35282}, {14416, 14424}, {15116, 26156}, {23285, 36793}

X(55070) = complement of X(4630)
X(55070) = complement of the isogonal conjugate of X(23285)
X(55070) = X(i)-complementary conjugate of X(j) for these (i,j): {38, 647}, {75, 826}, {76, 8060}, {141, 14838}, {427, 16612}, {523, 16600}, {661, 1194}, {693, 29654}, {798, 52536}, {826, 37}, {850, 1215}, {1109, 3124}, {1235, 8062}, {1441, 4142}, {1577, 3589}, {1634, 23993}, {1821, 14316}, {1928, 688}, {1930, 523}, {1934, 5113}, {1964, 52590}, {2084, 8265}, {2525, 1214}, {2528, 16587}, {3005, 16584}, {3954, 6586}, {4077, 17061}, {4576, 16598}, {8024, 4369}, {8061, 39}, {14208, 6676}, {15523, 650}, {16696, 52597}, {16703, 21196}, {16732, 21208}, {16747, 21187}, {16887, 31947}, {16892, 3666}, {17442, 2485}, {17879, 47413}, {18070, 7829}, {20883, 525}, {20902, 339}, {20948, 3934}, {21016, 2509}, {21035, 52589}, {21108, 40941}, {21123, 52535}, {23285, 10}, {23881, 16582}, {23994, 7668}, {24006, 5305}, {28654, 29512}, {31067, 28594}, {35309, 23988}, {39691, 16592}, {41676, 16599}, {44173, 21238}, {46277, 32193}, {48084, 1125}, {48278, 40937}, {52568, 42327}
X(55070) = X(i)-Ceva conjugate of X(j) for these (i,j): {66, 826}, {315, 23881}
X(55070) = X(34072)-isoconjugate of X(53657)
X(55070) = X(i)-Dao conjugate of X(j) for these (i,j): {826, 66}, {15449, 53657}, {23881, 315}, {47413, 827}
X(55070) = barycentric product X(i)*X(j) for these {i,j}: {315, 15449}, {826, 23881}, {2528, 33294}, {7794, 53569}
X(55070) = barycentric quotient X(i)/X(j) for these {i,j}: {826, 53657}, {2528, 44766}, {15449, 66}, {23881, 4577}, {33294, 52936}, {39691, 16277}, {53569, 52395}

X(55071) = CENTER OF CIRCUMCONIC {{A,B,C,X(50),X(67)}}

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

X(55071) lies on these lines: {141, 36189}, {511, 868}, {526, 53132}, {3134, 3580}, {3154, 7998}, {3569, 41172}, {14918, 35235}, {18438, 37987}, {38987, 41167}

X(55071) = complement of the isogonal conjugate of X(53266)
X(55071) = X(i)-complementary conjugate of X(j) for these (i,j): {661, 51389}, {53266, 10}
X(55071) = barycentric quotient X(47049)/X(39295)

X(55072) = CENTER OF CIRCUMCONIC {{A,B,C,X(52),X(54)}}

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

X(55072) lies on these lines: {51, 23181}, {125, 136}, {134, 41213}, {137, 46655}, {184, 54069}, {195, 568}, {3574, 34835}, {5562, 40678}, {6754, 34338}, {11424, 15827}, {14397, 39013}, {38984, 41218}

X(55072) = isotomic conjugate of the isogonal conjugate of X(41213)
X(55072) = X(i)-complementary conjugate of X(j) for these (i,j): {2216, 924}, {50946, 34825}
X(55072) = X(i)-Ceva conjugate of X(j) for these (i,j): {54, 924}, {43756, 2081}, {52032, 52317}
X(55072) = X(162)-isoconjugate of X(52932)
X(55072) = X(i)-Dao conjugate of X(j) for these (i,j): {125, 52932}, {134, 110}, {139, 30450}, {924, 54}, {52584, 34385}
X(55072) = crossdifference of every pair of points on line {925, 32661}
X(55072) = barycentric product X(i)*X(j) for these {i,j}: {76, 41213}, {95, 41222}, {136, 52032}, {311, 39013}, {338, 3133}, {343, 34338}, {2180, 17881}, {6368, 15423}, {6563, 52317}, {6754, 28706}, {39113, 47421}
X(55072) = barycentric quotient X(i)/X(j) for these {i,j}: {647, 52932}, {3133, 249}, {6754, 8882}, {15423, 18831}, {34338, 275}, {34952, 32692}, {39013, 54}, {41213, 6}, {41222, 5}, {47421, 96}, {52317, 925}

X(55073) = CENTER OF CIRCUMCONIC {{A,B,C,X(52),X(68)}}

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

X(55073) lies on these lines: {2, 15958}, {68, 52932}, {125, 20625}, {128, 17702}, {135, 46655}, {137, 6368}, {403, 52122}, {450, 14918}, {539, 27196}, {1209, 10170}, {2970, 18314}, {3124, 17434}, {5943, 34836}, {10213, 38615}, {11275, 14769}, {13754, 16336}, {14391, 35442}, {30210, 46439}, {31376, 43839}

X(55073) = reflection of X(38615) in X(10213)
X(55073) = complement of X(15958)
X(55073) = complement of the isogonal conjugate of X(23290)
X(55073) = X(i)-complementary conjugate of X(j) for these (i,j): {53, 14838}, {158, 6368}, {324, 4369}, {661, 46832}, {1096, 16040}, {1109, 2972}, {1577, 34828}, {1953, 52584}, {2181, 647}, {2501, 16577}, {2618, 3}, {12077, 1214}, {13450, 8062}, {14569, 16612}, {14618, 21231}, {15451, 828}, {18314, 18589}, {21102, 37565}, {23290, 10}, {24006, 140}, {35360, 16598}, {41221, 16573}, {51513, 37}, {51801, 8562}, {52604, 23993}
X(55073) = X(68)-Ceva conjugate of X(6368)
X(55073) = X(i)-Dao conjugate of X(j) for these (i,j): {139, 16813}, {6368, 68}, {15450, 32692}, {47421, 18315}
X(55073) = crossdifference of every pair of points on line {933, 32692}
X(55073) = barycentric product X(i)*X(j) for these {i,j}: {317, 39019}, {467, 35442}, {7763, 24862}, {20563, 41222}
X(55073) = barycentric quotient X(i)/X(j) for these {i,j}: {6563, 52939}, {15451, 32692}, {24862, 2165}, {39019, 68}, {41222, 24}, {52317, 933}

X(55074) = X(158)-isoconjugate-of-X(39243)

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

See Ivan Pavlov, euclid 5891.

X(55074) lies on these lines: {140, 6709}

X(55074) = X(158)-isoconjugate-of-X(39243)
X(55074) = X(1147)-Dao conjugate of X(39243)
X(55074) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(14767)}}, {{A, B, C, X(3), X(140)}}, {{A, B, C, X(95), X(216)}}, {{A, B, C, X(97), X(6709)}}, {{A, B, C, X(577), X(36948)}}, {{A, B, C, X(631), X(14379)}}, {{A, B, C, X(647), X(53864)}}, {{A, B, C, X(5158), X(50664)}}, {{A, B, C, X(5562), X(22268)}}, {{A, B, C, X(14642), X(44658)}}
X(55074) = barycentric product X(i)*X(j) for these (i, j): {3, 40207}, {30102, 394}
X(55074) = barycentric quotient X(i)/X(j) for these (i, j): {577, 39243}, {30102, 2052}, {40207, 264}

X(55075) = X(39)X(14990)∩X(732)X(3589)

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

See Ivan Pavlov, euclid 5891.

X(55075) lies on cubic K554 and on these lines: {39, 14990}, {512, 14822}, {732, 3589}, {733, 39397}, {1015, 14992}, {3978, 52570}, {5007, 8623}, {21802, 27846}

X(55075) = X(14990)-isoconjugate-of-X(24037)
X(55075) = X(512)-Dao conjugate of X(14990)
X(55075) = X(19609)-Ceva conjugate of X(512)
X(55075) = X(51906)-cross conjugate of X(512)
X(55075) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1015)}}, {{A, B, C, X(2), X(3934)}}, {{A, B, C, X(4), X(41440)}}, {{A, B, C, X(6), X(3589)}}, {{A, B, C, X(32), X(11175)}}, {{A, B, C, X(39), X(83)}}, {{A, B, C, X(76), X(43950)}}, {{A, B, C, X(251), X(6704)}}, {{A, B, C, X(511), X(592)}}, {{A, B, C, X(574), X(11270)}}, {{A, B, C, X(598), X(17042)}}, {{A, B, C, X(733), X(51827)}}, {{A, B, C, X(1500), X(14991)}}, {{A, B, C, X(2028), X(14630)}}, {{A, B, C, X(2029), X(14631)}}, {{A, B, C, X(2489), X(44571)}}, {{A, B, C, X(3108), X(7829)}}, {{A, B, C, X(3406), X(30499)}}, {{A, B, C, X(3527), X(7607)}}, {{A, B, C, X(3618), X(53059)}}, {{A, B, C, X(5305), X(39951)}}, {{A, B, C, X(5395), X(30495)}}, {{A, B, C, X(14658), X(39389)}}, {{A, B, C, X(14990), X(51906)}}, {{A, B, C, X(27366), X(30505)}}, {{A, B, C, X(30496), X(53102)}}, {{A, B, C, X(31622), X(39939)}}
X(55075) = barycentric quotient X(i)/X(j) for these (i, j): {1084, 14990}, {19609, 4576}

X(55076) = X(1)X(14549)∩X(10)X(141)

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

See Ivan Pavlov, euclid 5891.

X(55076) lies on these lines: {1, 14549}, {8, 16713}, {10, 141}, {11, 7064}, {210, 41797}, {281, 46884}, {594, 6184}, {765, 17277}, {1229, 3701}, {1441, 4967}, {1838, 1861}, {2321, 3693}, {2350, 14624}, {2809, 21231}, {3006, 22008}, {3679, 36819}, {3688, 17197}, {4078, 10916}, {4858, 21039}, {5220, 48888}, {5936, 39734}, {6067, 17059}, {13156, 39130}, {15065, 45926}, {17334, 23821}, {21803, 29690}, {24326, 25353}, {35141, 53649}, {48628, 54118}

X(55076) = trilinear pole of line {3700, 6362}
X(55076) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 33765}, {55, 38859}, {56, 1621}, {57, 4251}, {108, 22160}, {109, 4040}, {593, 20616}, {603, 14004}, {604, 17277}, {651, 21007}, {1106, 3996}, {1262, 38347}, {1397, 17143}, {1408, 4651}, {1412, 3294}, {1415, 17494}, {2149, 17761}, {4043, 16947}, {4564, 38346}, {7045, 38365}, {7341, 40607}, {40088, 41280}
X(55076) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1621}, {11, 4040}, {223, 38859}, {650, 17761}, {1146, 17494}, {1577, 40619}, {3160, 33765}, {3161, 17277}, {5452, 4251}, {6552, 3996}, {6741, 4151}, {7952, 14004}, {17115, 38365}, {38983, 22160}, {38991, 21007}, {40599, 3294}, {40624, 20954}
X(55076) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40216, 17758}
X(55076) = X(i)-cross conjugate of X(j) for these {i, j}: {4111, 2321}, {4858, 522}, {21039, 9}
X(55076) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(270)}}, {{A, B, C, X(2), X(142)}}, {{A, B, C, X(4), X(21620)}}, {{A, B, C, X(7), X(5542)}}, {{A, B, C, X(8), X(10)}}, {{A, B, C, X(9), X(75)}}, {{A, B, C, X(21), X(596)}}, {{A, B, C, X(29), X(1224)}}, {{A, B, C, X(55), X(7241)}}, {{A, B, C, X(80), X(495)}}, {{A, B, C, X(85), X(6706)}}, {{A, B, C, X(86), X(3254)}}, {{A, B, C, X(91), X(7162)}}, {{A, B, C, X(95), X(44184)}}, {{A, B, C, X(141), X(333)}}, {{A, B, C, X(158), X(7160)}}, {{A, B, C, X(200), X(25006)}}, {{A, B, C, X(210), X(22271)}}, {{A, B, C, X(219), X(307)}}, {{A, B, C, X(220), X(33298)}}, {{A, B, C, X(225), X(2334)}}, {{A, B, C, X(256), X(2316)}}, {{A, B, C, X(261), X(43749)}}, {{A, B, C, X(274), X(27390)}}, {{A, B, C, X(282), X(42015)}}, {{A, B, C, X(284), X(291)}}, {{A, B, C, X(312), X(3706)}}, {{A, B, C, X(314), X(4518)}}, {{A, B, C, X(318), X(4866)}}, {{A, B, C, X(321), X(27514)}}, {{A, B, C, X(341), X(4662)}}, {{A, B, C, X(346), X(24393)}}, {{A, B, C, X(594), X(4086)}}, {{A, B, C, X(673), X(51150)}}, {{A, B, C, X(749), X(2364)}}, {{A, B, C, X(894), X(25353)}}, {{A, B, C, X(903), X(3255)}}, {{A, B, C, X(946), X(13599)}}, {{A, B, C, X(958), X(22021)}}, {{A, B, C, X(1002), X(2335)}}, {{A, B, C, X(1088), X(10390)}}, {{A, B, C, X(1172), X(1390)}}, {{A, B, C, X(1219), X(24391)}}, {{A, B, C, X(1220), X(6598)}}, {{A, B, C, X(1223), X(52156)}}, {{A, B, C, X(1268), X(3826)}}, {{A, B, C, X(1320), X(5883)}}, {{A, B, C, X(1440), X(45097)}}, {{A, B, C, X(1737), X(3872)}}, {{A, B, C, X(2191), X(3676)}}, {{A, B, C, X(2320), X(39697)}}, {{A, B, C, X(2325), X(49701)}}, {{A, B, C, X(2344), X(39714)}}, {{A, B, C, X(2346), X(18815)}}, {{A, B, C, X(2648), X(39977)}}, {{A, B, C, X(2962), X(7161)}}, {{A, B, C, X(3615), X(43741)}}, {{A, B, C, X(3617), X(6736)}}, {{A, B, C, X(3679), X(6735)}}, {{A, B, C, X(3680), X(3812)}}, {{A, B, C, X(3686), X(3775)}}, {{A, B, C, X(3687), X(31330)}}, {{A, B, C, X(3705), X(3741)}}, {{A, B, C, X(3737), X(39798)}}, {{A, B, C, X(3834), X(30608)}}, {{A, B, C, X(3836), X(4119)}}, {{A, B, C, X(3907), X(3963)}}, {{A, B, C, X(3912), X(20567)}}, {{A, B, C, X(3939), X(4572)}}, {{A, B, C, X(4041), X(7064)}}, {{A, B, C, X(4076), X(49697)}}, {{A, B, C, X(4110), X(4147)}}, {{A, B, C, X(4357), X(17754)}}, {{A, B, C, X(4373), X(34919)}}, {{A, B, C, X(4451), X(49457)}}, {{A, B, C, X(4853), X(24982)}}, {{A, B, C, X(4858), X(17277)}}, {{A, B, C, X(4876), X(39712)}}, {{A, B, C, X(4997), X(34824)}}, {{A, B, C, X(5231), X(26015)}}, {{A, B, C, X(5397), X(24298)}}, {{A, B, C, X(7081), X(29673)}}, {{A, B, C, X(7155), X(49479)}}, {{A, B, C, X(10481), X(15658)}}, {{A, B, C, X(10527), X(10916)}}, {{A, B, C, X(11019), X(38254)}}, {{A, B, C, X(12607), X(34918)}}, {{A, B, C, X(15841), X(36620)}}, {{A, B, C, X(15910), X(44687)}}, {{A, B, C, X(16608), X(40435)}}, {{A, B, C, X(17062), X(17743)}}, {{A, B, C, X(17073), X(26006)}}, {{A, B, C, X(17239), X(42030)}}, {{A, B, C, X(17787), X(24326)}}, {{A, B, C, X(21258), X(32008)}}, {{A, B, C, X(21677), X(52357)}}, {{A, B, C, X(27483), X(36796)}}, {{A, B, C, X(28626), X(38054)}}, {{A, B, C, X(30479), X(49511)}}, {{A, B, C, X(31618), X(43971)}}, {{A, B, C, X(32635), X(44040)}}, {{A, B, C, X(35057), X(40999)}}, {{A, B, C, X(36798), X(49491)}}, {{A, B, C, X(40593), X(52980)}}, {{A, B, C, X(43531), X(43740)}}, {{A, B, C, X(49481), X(52652)}}
X(55076) = barycentric product X(i)*X(j) for these (i, j): {210, 40004}, {522, 54118}, {2321, 39734}, {2350, 3596}, {3700, 53649}, {3701, 39950}, {13476, 312}, {17758, 8}, {40216, 9}
X(55076) = barycentric quotient X(i)/X(j) for these (i, j): {7, 33765}, {8, 17277}, {9, 1621}, {11, 17761}, {55, 4251}, {57, 38859}, {210, 3294}, {281, 14004}, {312, 17143}, {346, 3996}, {522, 17494}, {650, 4040}, {652, 22160}, {663, 21007}, {756, 20616}, {2310, 38347}, {2321, 4651}, {2350, 56}, {3271, 38346}, {3596, 18152}, {3700, 4151}, {3701, 4043}, {3706, 29773}, {4391, 20954}, {4858, 40619}, {13476, 57}, {14549, 37543}, {14936, 38365}, {17758, 7}, {21044, 2486}, {21808, 43915}, {25128, 27168}, {28659, 40088}, {34589, 26847}, {39734, 1434}, {39950, 1014}, {40216, 85}, {42462, 42454}, {43076, 4565}, {53649, 4573}, {54118, 664}

X(55077) = (name pending)

Barycentrics    a*(a-b-c)*(-(b*(b-3*c)*(b-c)^2)+a^3*(3*b+c)-a^2*(7*b^2+3*b*c+2*c^2)+a*(5*b^3-3*b^2*c-3*b*c^2+c^3))*((b-c)^2*(3*b-c)*c+a^3*(b+3*c)-a^2*(2*b^2+3*b*c+7*c^2)+a*(b^3-3*b^2*c-3*b*c^2+5*c^3)) : :

See Ivan Pavlov, euclid 5891.

X(55077) lies on these lines: {6666, 6706}

X(55077) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6706)}}, {{A, B, C, X(9), X(6666)}}, {{A, B, C, X(1212), X(3900)}}, {{A, B, C, X(1392), X(34522)}}

X(55078) = X(163)-isoconjugate-of-X(14779)

Barycentrics    (b+c)*(4*a^2+9*a*b+4*b^2+7*a*c+7*b*c+c^2)*(4*a^2+7*a*b+b^2+9*a*c+7*b*c+4*c^2) : :

See Ivan Pavlov, euclid 5891.

X(55078) lies on these lines: {3634, 6707}

X(55078) = X(163)-isoconjugate-of-X(14779)
X(55078) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 14779}
X(55078) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6707)}}, {{A, B, C, X(10), X(3634)}}, {{A, B, C, X(12), X(1698)}}, {{A, B, C, X(523), X(1213)}}, {{A, B, C, X(594), X(28650)}}, {{A, B, C, X(2165), X(51501)}}, {{A, B, C, X(9780), X(27577)}}
X(55078) = barycentric quotient X(i)/X(j) for these (i, j): {523, 14779}

X(55079) = X(2)X(46394)∩X(5)X(276)

Barycentrics    b^2*c^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^8-b^2*c^2*(b^2-c^2)^2-5*a^6*(b^2+c^2)-3*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(7*b^4+3*b^2*c^2+7*c^4)) : :

See Ivan Pavlov, euclid 5891.

X(55079) lies on circumconic {{A, B, C, X(14941), X(39243)}} and on these lines: {2, 46394}, {5, 276}, {264, 1656}, {547, 42368}, {1506, 16081}, {3090, 18027}, {3628, 16089}, {13434, 18831}

X(55079) = isotomic conjugate of X(55074)
X(55079) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55074}, {9247, 40207}, {30102, 52430}
X(55079) = barycentric product X(i)*X(j) for these (i, j): {18027, 39243}
X(55079) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55074}, {264, 40207}, {2052, 30102}, {39243, 577}
X(55079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 276, 6528}

X(55080) = X(95)X(632)∩X(140)X(18831)

Barycentrics    (a^4+b^4-b^2*c^2-a^2*(2*b^2+c^2))*(a^4-b^2*c^2+c^4-a^2*(b^2+2*c^2))*(a^8-9*a^6*(b^2+c^2)-15*a^2*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^2*(4*b^4-9*b^2*c^2+4*c^4)+a^4*(19*b^4+11*b^2*c^2+19*c^4)) : :

See Ivan Pavlov, euclid 5891.

X(55080) lies on these lines: {95, 632}, {140, 18831}

X(55080) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2179, 40208}
X(55080) = barycentric quotient X(i)/X(j) for these (i, j): {95, 40208}
X(55080) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 31617, 18831}

X(55081) = X(2)X(31613)∩X(141)X(308)

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

See Ivan Pavlov, euclid 5891.

X(55081) lies on these lines: {2, 31613}, {75, 31625}, {76, 3763}, {110, 41296}, {141, 308}, {1502, 3619}, {3978, 34573}, {6374, 21358}, {7794, 26192}, {7868, 40022}, {7931, 26235}, {8024, 16988}, {18092, 38303}, {32027, 52570}, {40826, 44136}

X(55081) = isotomic conjugate of X(55075)
X(55081) = intersection, other than A, B, C, of circumconics {{A, B, C, X(694), X(31613)}}, {{A, B, C, X(10159), X(14970)}}
X(55081) = barycentric product X(i)*X(j) for these (i, j): {14990, 44168}
X(55081) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55075}, {4576, 19609}, {14990, 1084}
X(55081) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 308, 670}

X(55082) = X(1)X(85)∩X(7)X(21)

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

See Ivan Pavlov, euclid 5891.

X(55082) lies on these lines: {1, 85}, {2, 220}, {3, 17753}, {5, 150}, {6, 26125}, {7, 21}, {8, 5543}, {9, 10012}, {12, 37678}, {29, 331}, {37, 41246}, {41, 673}, {57, 16831}, {65, 1447}, {75, 78}, {77, 17394}, {83, 226}, {100, 20244}, {101, 2140}, {175, 13453}, {176, 13436}, {183, 21281}, {190, 18055}, {219, 25521}, {222, 42028}, {241, 16826}, {278, 31926}, {279, 3622}, {307, 17322}, {333, 23151}, {349, 350}, {388, 37632}, {551, 10481}, {644, 28742}, {651, 46922}, {663, 52621}, {910, 27000}, {946, 4872}, {948, 26626}, {958, 30946}, {1043, 4441}, {1086, 21008}, {1088, 4350}, {1125, 9436}, {1212, 10025}, {1231, 26234}, {1319, 4059}, {1323, 3636}, {1385, 5088}, {1388, 7223}, {1414, 1509}, {1418, 28639}, {1441, 4360}, {1445, 4687}, {1446, 38459}, {1500, 43063}, {1565, 5901}, {1621, 33765}, {2099, 3212}, {2329, 20335}, {2975, 20347}, {3061, 24333}, {3160, 17079}, {3177, 34522}, {3207, 4209}, {3241, 31994}, {3244, 25719}, {3294, 17687}, {3333, 7183}, {3475, 28053}, {3618, 8232}, {3664, 24202}, {3672, 5736}, {3684, 20257}, {3720, 7196}, {3742, 9446}, {3758, 8545}, {3870, 17158}, {3872, 16284}, {3890, 23839}, {3911, 32013}, {3996, 17143}, {4056, 18393}, {4123, 21609}, {4210, 8049}, {4251, 17761}, {4328, 8583}, {4364, 17950}, {4440, 7783}, {4511, 20880}, {4561, 33933}, {4564, 17758}, {4573, 33770}, {4648, 27093}, {4670, 40862}, {4861, 30806}, {4911, 12047}, {4955, 32636}, {5018, 50293}, {5195, 22791}, {5219, 25529}, {5249, 26006}, {5253, 6516}, {5256, 19790}, {5263, 10030}, {5550, 32098}, {5603, 17170}, {5886, 17181}, {6147, 16091}, {6180, 17379}, {6603, 6706}, {6649, 37633}, {7131, 27475}, {7146, 36538}, {7179, 11375}, {7185, 24796}, {7210, 34036}, {7225, 41526}, {9310, 30949}, {9318, 9322}, {9780, 32003}, {10283, 38941}, {10520, 12563}, {10582, 31627}, {11011, 24805}, {11109, 18026}, {11240, 17378}, {11553, 33954}, {11680, 21285}, {12513, 36854}, {14189, 42819}, {14548, 14986}, {14829, 17137}, {16549, 25532}, {16706, 21617}, {16788, 17681}, {17045, 17086}, {17077, 28777}, {17152, 37670}, {17234, 28420}, {17258, 41572}, {17302, 17966}, {17320, 22464}, {17380, 37800}, {17381, 28739}, {18162, 34830}, {19684, 37076}, {20057, 25718}, {20247, 34195}, {20271, 26273}, {24179, 44735}, {24190, 33828}, {24214, 37617}, {24549, 30545}, {25083, 32939}, {25507, 27339}, {25935, 37774}, {25964, 27547}, {26140, 33839}, {26279, 26562}, {26526, 27068}, {26531, 31640}, {27304, 37658}, {27950, 37233}, {28969, 28985}, {30625, 31169}, {30985, 52134}, {33865, 39542}, {37674, 40420}, {38316, 42309}, {44675, 53597}, {46934, 51351}

X(55082) = perspector of circumconic {{A, B, C, X(4573), X(6606)}}
X(55082) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 2350}, {31, 55076}, {41, 17758}, {55, 13476}, {1334, 39950}, {2175, 40216}, {3063, 54118}, {4041, 43076}
X(55082) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55076}, {223, 13476}, {478, 2350}, {693, 4858}, {3160, 17758}, {3720, 4111}, {3925, 21039}, {10001, 54118}, {17761, 4041}, {40593, 40216}
X(55082) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4564, 664}
X(55082) = X(i)-cross conjugate of X(j) for these {i, j}: {1621, 17277}
X(55082) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2141)}}, {{A, B, C, X(2), X(17169)}}, {{A, B, C, X(7), X(18097)}}, {{A, B, C, X(10), X(25557)}}, {{A, B, C, X(21), X(1621)}}, {{A, B, C, X(83), X(86)}}, {{A, B, C, X(142), X(21258)}}, {{A, B, C, X(226), X(3665)}}, {{A, B, C, X(1001), X(3294)}}, {{A, B, C, X(1014), X(1170)}}, {{A, B, C, X(1111), X(17758)}}, {{A, B, C, X(1434), X(21453)}}, {{A, B, C, X(1444), X(31637)}}, {{A, B, C, X(3616), X(4651)}}, {{A, B, C, X(3673), X(27475)}}, {{A, B, C, X(4043), X(17321)}}, {{A, B, C, X(4151), X(17768)}}, {{A, B, C, X(5249), X(23581)}}, {{A, B, C, X(7131), X(40719)}}, {{A, B, C, X(10013), X(20992)}}, {{A, B, C, X(16705), X(18152)}}, {{A, B, C, X(16831), X(29773)}}, {{A, B, C, X(17139), X(20954)}}, {{A, B, C, X(17183), X(18086)}}, {{A, B, C, X(17687), X(31926)}}, {{A, B, C, X(20615), X(20616)}}, {{A, B, C, X(33947), X(40094)}}, {{A, B, C, X(35576), X(52783)}}
X(55082) = barycentric product X(i)*X(j) for these (i, j): {279, 3996}, {312, 38859}, {1014, 4043}, {1429, 40094}, {1434, 4651}, {1621, 85}, {2486, 4620}, {4040, 4554}, {4151, 4573}, {4251, 6063}, {14004, 348}, {17143, 57}, {17277, 7}, {17494, 664}, {17761, 4998}, {18152, 56}, {20616, 873}, {20954, 651}, {21007, 4572}, {22160, 46404}, {33765, 8}, {40088, 604}, {40619, 4564}
X(55082) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55076}, {7, 17758}, {56, 2350}, {57, 13476}, {85, 40216}, {664, 54118}, {1014, 39950}, {1434, 39734}, {1621, 9}, {2486, 21044}, {3294, 210}, {3996, 346}, {4040, 650}, {4043, 3701}, {4151, 3700}, {4251, 55}, {4565, 43076}, {4573, 53649}, {4651, 2321}, {14004, 281}, {17143, 312}, {17277, 8}, {17494, 522}, {17761, 11}, {18152, 3596}, {20616, 756}, {20954, 4391}, {21007, 663}, {22160, 652}, {26847, 34589}, {27168, 25128}, {29773, 3706}, {33765, 7}, {37543, 14549}, {38346, 3271}, {38347, 2310}, {38365, 14936}, {38859, 57}, {40088, 28659}, {40619, 4858}, {42454, 42462}, {43915, 21808}
X(55082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 40719, 85}, {1, 48900, 14942}, {1, 85, 664}, {2, 220, 32008}, {2, 6604, 33298}, {7, 17084, 3665}, {7, 3485, 33949}, {7, 3616, 348}, {7, 56, 1434}, {57, 16831, 31225}, {101, 2140, 17682}, {226, 1429, 41245}, {1319, 4059, 7176}, {1441, 7269, 4360}, {3160, 32086, 17079}, {3649, 7198, 7}, {3665, 15950, 17084}, {4328, 10436, 39126}, {11011, 24805, 43037}, {11375, 30617, 7179}, {17045, 52023, 17086}, {17095, 32007, 9436}, {26531, 46835, 31640}, {32086, 38314, 3160}

X(55083) = X(2)X(33770)∩X(99)X(1125)

Barycentrics    (a+b)*(a+c)*(a^2+4*b^2+9*b*c+4*c^2+7*a*(b+c)) : :

See Ivan Pavlov, euclid 5891.

X(55083) lies on these lines: {2, 33770}, {86, 16477}, {99, 1125}, {261, 30598}, {1078, 15668}, {1509, 3624}, {5333, 29609}, {6626, 19883}, {17023, 25507}, {17731, 19878}, {20536, 51586}, {28618, 29637}, {32004, 51073}, {34595, 51356}

X(55083) = isotomic conjugate of X(55078)
X(55083) = barycentric product X(i)*X(j) for these (i, j): {14779, 99}
X(55083) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55078}, {14779, 523}
X(55083) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1125, 32014, 99}

X(55084) = X(4)X(1173)∩X(51)X(107)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^8-b^2*c^2*(b^2-c^2)^2-5*a^6*(b^2+c^2)-3*a^2*(b^2-c^2)^2*(b^2+c^2)+a^4*(7*b^4+3*b^2*c^2+7*c^4)) : :

See Ivan Pavlov, euclid 5891.

X(55084) lies circumconic {{A, B, C, X(1173), X(1298)}} and on these lines: {4, 1173}, {6, 1629}, {51, 107}, {340, 37990}, {648, 30506}, {1899, 53027}, {2052, 9777}, {3060, 36794}, {3087, 52448}, {3527, 14249}, {6755, 42873}, {10110, 51031}, {21969, 37124}, {34565, 41204}, {37453, 43530}, {37505, 38808}, {42400, 44107}X(55084) = isogonal conjugate of X(55074)
X(55084) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 55074}, {48, 40207}, {255, 30102}
X(55084) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 55074}, {1249, 40207}, {6523, 30102}
X(55084) = barycentric product X(i)*X(j) for these (i, j): {6, 55079}, {2052, 39243}
X(55084) = barycentric quotient X(i)/X(j) for these (i, j): {4, 40207}, {6, 55074}, {393, 30102}, {39243, 394}, {55079, 76}
X(55084) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {51, 275, 107}, {30506, 53863, 648}

X(55085) = X(1)X(1016)∩X(39)X(83)

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

See Ivan Pavlov, euclid 5891.

X(55085) lies on these lines: {1, 1016}, {2, 3108}, {3, 7878}, {4, 34624}, {5, 6054}, {6, 1078}, {20, 52691}, {32, 33004}, {39, 83}, {61, 6295}, {62, 6582}, {76, 9605}, {98, 11272}, {110, 42444}, {115, 33024}, {141, 7905}, {183, 7894}, {194, 7808}, {262, 12203}, {315, 33202}, {316, 8357}, {325, 7859}, {382, 598}, {385, 5041}, {574, 7787}, {575, 10753}, {576, 631}, {597, 7807}, {620, 10583}, {625, 7923}, {648, 37125}, {671, 7765}, {732, 39397}, {754, 33021}, {1003, 22332}, {1007, 32953}, {1207, 32748}, {1241, 39951}, {1506, 7797}, {1992, 32960}, {2023, 52034}, {2142, 14822}, {2548, 7790}, {2549, 14068}, {2896, 7838}, {3096, 7774}, {3398, 34473}, {3411, 11307}, {3412, 11308}, {3530, 26613}, {3552, 53096}, {3589, 7832}, {3618, 7763}, {3767, 32999}, {3785, 14930}, {3788, 7875}, {3815, 7828}, {3934, 7839}, {3972, 5013}, {4045, 7785}, {5007, 7824}, {5024, 7782}, {5028, 31400}, {5111, 6329}, {5254, 15031}, {5286, 32987}, {5309, 16921}, {5346, 17004}, {5475, 7864}, {6292, 7779}, {6636, 42037}, {6655, 7753}, {6656, 7809}, {6680, 36849}, {6704, 7813}, {7470, 44422}, {7709, 10358}, {7736, 7752}, {7737, 33253}, {7739, 16924}, {7745, 7847}, {7746, 7920}, {7747, 19691}, {7748, 14066}, {7757, 7770}, {7759, 7876}, {7761, 7921}, {7762, 7831}, {7766, 7815}, {7768, 8362}, {7769, 7792}, {7771, 30435}, {7773, 7918}, {7775, 7933}, {7776, 7937}, {7777, 7834}, {7778, 7943}, {7780, 41940}, {7784, 7926}, {7789, 19702}, {7791, 7812}, {7793, 15482}, {7798, 31276}, {7799, 7819}, {7800, 7877}, {7801, 16895}, {7802, 33023}, {7806, 31455}, {7811, 16043}, {7814, 7866}, {7817, 32967}, {7821, 7948}, {7822, 7906}, {7830, 20088}, {7836, 7889}, {7837, 7854}, {7840, 7849}, {7843, 7924}, {7845, 7928}, {7852, 7925}, {7853, 7941}, {7855, 16986}, {7857, 16989}, {7860, 11287}, {7861, 33289}, {7862, 7932}, {7863, 19689}, {7865, 7946}, {7868, 7871}, {7870, 33217}, {7879, 7949}, {7880, 19694}, {7881, 47355}, {7884, 7887}, {7886, 17005}, {7895, 39784}, {7897, 7914}, {7900, 7935}, {7902, 32966}, {7903, 7938}, {7912, 7913}, {7915, 7947}, {7922, 9766}, {8178, 10353}, {8356, 12156}, {8367, 11054}, {8370, 9607}, {8724, 44237}, {9737, 10359}, {9770, 33221}, {11171, 12110}, {11184, 33218}, {11648, 33018}, {12055, 42421}, {13586, 31652}, {14537, 33256}, {14568, 32992}, {14630, 14632}, {14631, 14633}, {15559, 37765}, {16045, 32833}, {16712, 17681}, {16898, 34511}, {16951, 37875}, {17128, 32450}, {17129, 31239}, {17398, 55083}, {18362, 33010}, {18502, 32516}, {18600, 29479}, {19661, 44682}, {22385, 36511}, {24512, 33770}, {31404, 52250}, {31407, 32972}, {31417, 33006}, {31448, 53680}, {31450, 32964}, {31457, 33274}, {31492, 51185}, {32821, 43527}, {33225, 41134}, {33273, 35007}, {36157, 47290}, {36794, 39575}, {38739, 42788}, {38854, 42548}, {39674, 41331}, {39675, 40425}, {45108, 52395}, {47618, 49112}

X(55085) = isogonal conjugate of X(55075)
X(55085) = perspector of circumconic {{A, B, C, X(35137), X(41209)}}
X(55085) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(732), X(51827)}}, {{A, B, C, X(733), X(3108)}}, {{A, B, C, X(3589), X(7829)}}, {{A, B, C, X(7794), X(45108)}}, {{A, B, C, X(10159), X(14970)}}, {{A, B, C, X(14990), X(51906)}}
X(55085) = barycentric product X(i)*X(j) for these (i, j): {6, 55081}, {14990, 34537}
X(55085) = barycentric quotient X(i)/X(j) for these (i, j): {6, 55075}, {1634, 19609}, {14990, 3124}, {55081, 76}
X(55085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13571, 7794}, {2, 51860, 7829}, {2, 7764, 7909}, {2, 7772, 7760}, {2, 7794, 10159}, {3, 7878, 12150}, {5, 32467, 38664}, {6, 11285, 6179}, {39, 3329, 83}, {39, 7804, 7783}, {325, 7859, 7944}, {597, 9606, 7807}, {3618, 7763, 7846}, {5041, 6683, 385}, {6179, 7786, 11285}, {6292, 7779, 32027}, {6656, 7858, 7809}, {6656, 9300, 7858}, {6704, 7813, 46226}, {7736, 7803, 7752}, {7752, 7803, 7919}, {7759, 7876, 7883}, {7765, 16044, 671}, {7768, 8362, 31168}, {7777, 7834, 7899}, {7829, 9698, 2}, {7840, 16897, 7849}, {7947, 16987, 7915}, {16989, 31401, 7857}, {42548, 51983, 38854}

X(55086) = X(1)X(201)∩X(31)X(57)

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

See Ivan Pavlov, euclid 5891.

X(55086) lies on these lines: {1, 201}, {6, 1174}, {7, 17127}, {31, 57}, {33, 15299}, {36, 1064}, {40, 1497}, {42, 2078}, {47, 3338}, {51, 20999}, {55, 13329}, {56, 58}, {65, 595}, {73, 1203}, {81, 7677}, {165, 52428}, {171, 3911}, {181, 4279}, {182, 23853}, {223, 16469}, {226, 238}, {251, 1400}, {255, 3333}, {278, 2299}, {283, 3616}, {354, 2361}, {386, 37579}, {388, 1724}, {497, 1754}, {552, 1414}, {572, 16678}, {578, 947}, {581, 7742}, {582, 3295}, {601, 15803}, {603, 3361}, {604, 16878}, {605, 51841}, {606, 51842}, {692, 18613}, {748, 5219}, {750, 31231}, {774, 33178}, {902, 3256}, {950, 37570}, {990, 30223}, {991, 37578}, {999, 5398}, {1001, 2328}, {1014, 39673}, {1054, 26741}, {1188, 38835}, {1193, 37583}, {1210, 3072}, {1214, 1386}, {1253, 10389}, {1279, 5173}, {1331, 3873}, {1393, 15932}, {1399, 32636}, {1402, 1428}, {1420, 1468}, {1438, 9447}, {1445, 8270}, {1453, 21147}, {1454, 24046}, {1457, 5315}, {1458, 2003}, {1460, 5156}, {1470, 4257}, {1622, 11425}, {1758, 29821}, {1780, 3485}, {1788, 5264}, {1876, 14975}, {1935, 4298}, {1936, 11019}, {2056, 9259}, {2099, 40091}, {2149, 2350}, {2277, 38864}, {2323, 25941}, {2964, 3337}, {3052, 37541}, {3073, 4292}, {3074, 21620}, {3086, 37530}, {3190, 45728}, {3340, 3915}, {3451, 5042}, {3670, 7098}, {3744, 14523}, {3870, 3939}, {3920, 37787}, {4253, 22131}, {4256, 5172}, {4260, 20761}, {4551, 32911}, {4552, 17150}, {4565, 33774}, {4641, 17625}, {4722, 53531}, {4848, 5255}, {5045, 52408}, {5083, 32913}, {5127, 15950}, {5247, 10106}, {5348, 17728}, {5396, 41345}, {5399, 37509}, {5435, 17126}, {6354, 15253}, {6358, 32914}, {7288, 37522}, {7299, 10404}, {9352, 35281}, {10473, 38832}, {13740, 52357}, {14547, 15931}, {16475, 45126}, {16687, 23067}, {17596, 26740}, {20229, 38849}, {20470, 20986}, {20760, 43149}, {21454, 30653}, {24880, 26481}, {25525, 25885}, {25938, 31190}, {26892, 53298}, {29015, 36082}, {32726, 53622}, {33107, 37797}, {34986, 36942}, {35338, 35977}, {37540, 51476}, {41230, 41342}

X(55086) = isogonal conjugate of X(55076)
X(55086) = perspector of circumconic {{A, B, C, X(4565), X(36146)}}
X(55086) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 55076}, {8, 13476}, {9, 17758}, {55, 40216}, {210, 39734}, {312, 2350}, {650, 54118}, {1334, 40004}, {2321, 39950}, {4041, 53649}, {4086, 43076}
X(55086) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 55076}, {223, 40216}, {478, 17758}, {17761, 4086}
X(55086) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2149, 109}
X(55086) = X(i)-cross conjugate of X(j) for these {i, j}: {38365, 21007}
X(55086) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(57), X(33765)}}, {{A, B, C, X(58), X(105)}}, {{A, B, C, X(59), X(552)}}, {{A, B, C, X(201), X(39791)}}, {{A, B, C, X(244), X(2350)}}, {{A, B, C, X(593), X(6185)}}, {{A, B, C, X(614), X(2279)}}, {{A, B, C, X(859), X(2163)}}, {{A, B, C, X(959), X(4306)}}, {{A, B, C, X(995), X(4651)}}, {{A, B, C, X(1400), X(1401)}}, {{A, B, C, X(1408), X(1416)}}, {{A, B, C, X(1412), X(1462)}}, {{A, B, C, X(1437), X(1794)}}, {{A, B, C, X(1475), X(23653)}}, {{A, B, C, X(2194), X(2195)}}, {{A, B, C, X(3294), X(16466)}}, {{A, B, C, X(17277), X(40153)}}, {{A, B, C, X(32726), X(33634)}}
X(55086) = barycentric product X(i)*X(j) for these (i, j): {6, 55082}, {109, 17494}, {1014, 3294}, {1275, 38365}, {1397, 18152}, {1407, 3996}, {1408, 4043}, {1412, 4651}, {1415, 20954}, {1621, 57}, {2149, 40619}, {2486, 52378}, {4040, 651}, {4151, 4565}, {4251, 7}, {14004, 222}, {17143, 604}, {17277, 56}, {17761, 59}, {20616, 757}, {21007, 664}, {22160, 653}, {33765, 55}, {38346, 4998}, {38347, 7045}, {38859, 9}, {42454, 4619}
X(55086) = barycentric quotient X(i)/X(j) for these (i, j): {6, 55076}, {56, 17758}, {57, 40216}, {109, 54118}, {604, 13476}, {1014, 40004}, {1397, 2350}, {1408, 39950}, {1412, 39734}, {1621, 312}, {3294, 3701}, {4040, 4391}, {4251, 8}, {4565, 53649}, {4651, 30713}, {14004, 7017}, {17143, 28659}, {17277, 3596}, {17494, 35519}, {17761, 34387}, {18152, 40363}, {20616, 1089}, {21007, 522}, {22160, 6332}, {33765, 6063}, {38346, 11}, {38347, 24026}, {38365, 1146}, {38859, 85}, {55082, 76}
X(55086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14827, 1174}, {31, 1471, 57}, {31, 57, 109}, {56, 1397, 1412}, {56, 16466, 10571}, {57, 7290, 34036}, {2078, 52423, 42}

X(55087) = X(6)X(38859)∩X(934)X(1170)

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

See Ivan Pavlov, euclid 5891.

X(55087) lies on these lines: {6, 38859}, {934, 1170}, {5045, 37787}, {11349, 52423}

X(55087) = isogonal conjugate of X(55077)
X(55087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1170, 1475, 934}

X(55088) = X(6)X(33774)∩X(81)X(15254)

Barycentrics    a^2*(a+b)*(a+c)*(a^2+4*b^2+9*b*c+4*c^2+7*a*(b+c)) : :

See Ivan Pavlov, euclid 5891.

X(55088) lies on these lines: {6, 33774}, {81, 15254}, {110, 1171}, {1993, 37248}

X(55088) = isogonal conjugate of X(55078)
X(55088) = barycentric product X(i)*X(j) for these (i, j): {6, 55083}, {110, 14779}
X(55088) = barycentric quotient X(i)/X(j) for these (i, j): {6, 55078}, {14779, 850}, {55083, 76}
X(55088) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1171, 2308, 110}

X(55089) = (name pending)

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

See Ivan Pavlov, euclid 5891.

X(55089) lies on these lines: {3670, 8229}

X(55089) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3670)}}, {{A, B, C, X(2), X(388)}}, {{A, B, C, X(4), X(3615)}}, {{A, B, C, X(7), X(3597)}}, {{A, B, C, X(8), X(262)}}, {{A, B, C, X(12), X(5253)}}, {{A, B, C, X(28), X(37983)}}, {{A, B, C, X(29), X(8229)}}, {{A, B, C, X(56), X(11681)}}, {{A, B, C, X(58), X(41013)}}, {{A, B, C, X(65), X(693)}}, {{A, B, C, X(225), X(20028)}}, {{A, B, C, X(256), X(3701)}}, {{A, B, C, X(264), X(959)}}, {{A, B, C, X(513), X(51870)}}, {{A, B, C, X(1838), X(5603)}}, {{A, B, C, X(3427), X(13599)}}, {{A, B, C, X(3613), X(34434)}}, {{A, B, C, X(10429), X(13380)}}, {{A, B, C, X(18891), X(47819)}}, {{A, B, C, X(31359), X(45964)}}, {{A, B, C, X(32023), X(50040)}}, {{A, B, C, X(39949), X(45095)}}, {{A, B, C, X(45108), X(46187)}}

X(55090) = X(2)X(24048)∩X(758)X(942)

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

See Ivan Pavlov, euclid 5891.

X(55090) lies on these lines: {2, 24048}, {226, 24224}, {553, 3664}, {758, 942}, {1870, 31900}, {3218, 8025}, {3487, 24931}, {3687, 3936}, {3752, 24185}, {11036, 25650}, {12433, 46975}, {17011, 18653}, {20924, 52572}, {21081, 21620}, {24195, 37662}

X(55090) = trilinear pole of line {4977, 17420}
X(55090) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 5260}, {101, 50346}, {1110, 24224}
X(55090) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 5260}, {514, 24224}, {1015, 50346}
X(55090) = X(i)-cross conjugate of X(j) for these {i, j}: {17197, 514}
X(55090) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(312)}}, {{A, B, C, X(2), X(553)}}, {{A, B, C, X(4), X(18249)}}, {{A, B, C, X(7), X(261)}}, {{A, B, C, X(10), X(37870)}}, {{A, B, C, X(27), X(6675)}}, {{A, B, C, X(57), X(942)}}, {{A, B, C, X(65), X(53083)}}, {{A, B, C, X(79), X(333)}}, {{A, B, C, X(81), X(226)}}, {{A, B, C, X(85), X(39980)}}, {{A, B, C, X(86), X(6703)}}, {{A, B, C, X(92), X(39948)}}, {{A, B, C, X(106), X(43071)}}, {{A, B, C, X(257), X(4052)}}, {{A, B, C, X(279), X(12563)}}, {{A, B, C, X(306), X(7100)}}, {{A, B, C, X(335), X(6682)}}, {{A, B, C, X(354), X(20367)}}, {{A, B, C, X(519), X(34527)}}, {{A, B, C, X(522), X(46880)}}, {{A, B, C, X(940), X(3670)}}, {{A, B, C, X(996), X(39696)}}, {{A, B, C, X(1000), X(45100)}}, {{A, B, C, X(1100), X(8818)}}, {{A, B, C, X(1255), X(14554)}}, {{A, B, C, X(1427), X(39950)}}, {{A, B, C, X(1434), X(11281)}}, {{A, B, C, X(2006), X(37737)}}, {{A, B, C, X(2214), X(7094)}}, {{A, B, C, X(3239), X(7073)}}, {{A, B, C, X(3676), X(39734)}}, {{A, B, C, X(3742), X(8056)}}, {{A, B, C, X(3911), X(26842)}}, {{A, B, C, X(3912), X(29821)}}, {{A, B, C, X(3969), X(17190)}}, {{A, B, C, X(4102), X(13606)}}, {{A, B, C, X(4556), X(4605)}}, {{A, B, C, X(4975), X(34064)}}, {{A, B, C, X(4999), X(5557)}}, {{A, B, C, X(5558), X(38255)}}, {{A, B, C, X(5560), X(42030)}}, {{A, B, C, X(6679), X(14621)}}, {{A, B, C, X(8258), X(14534)}}, {{A, B, C, X(9328), X(25417)}}, {{A, B, C, X(11019), X(27399)}}, {{A, B, C, X(14844), X(21196)}}, {{A, B, C, X(16137), X(52374)}}, {{A, B, C, X(17011), X(21081)}}, {{A, B, C, X(17023), X(32783)}}, {{A, B, C, X(17197), X(24224)}}, {{A, B, C, X(18490), X(45098)}}, {{A, B, C, X(18653), X(21192)}}, {{A, B, C, X(25650), X(40940)}}, {{A, B, C, X(30588), X(39747)}}, {{A, B, C, X(30710), X(39697)}}, {{A, B, C, X(34258), X(42285)}}, {{A, B, C, X(39714), X(40418)}}, {{A, B, C, X(39723), X(43948)}}, {{A, B, C, X(40438), X(40716)}}
X(55090) = barycentric quotient X(i)/X(j) for these (i, j): {1, 5260}, {513, 50346}, {1086, 24224}, {17197, 40625}

X(55091) = X(10)X(45926)∩X(758)X(942)

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

See Ivan Pavlov, euclid 5891.

X(55091) lies on these lines: {10, 45926}, {758, 942}, {860, 1838}, {1243, 31806}, {3686, 3965}, {3702, 6734}, {4357, 24564}, {4511, 46877}, {4736, 6533}

X(55091) = X(i)-isoconjugate-of-X(j) for these {i, j}: {56, 5260}, {109, 50346}, {2149, 24224}
X(55091) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 5260}, {11, 50346}, {650, 24224}
X(55091) = X(i)-cross conjugate of X(j) for these {i, j}: {8040, 7110}
X(55091) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(270)}}, {{A, B, C, X(2), X(5745)}}, {{A, B, C, X(7), X(12563)}}, {{A, B, C, X(8), X(261)}}, {{A, B, C, X(9), X(341)}}, {{A, B, C, X(10), X(21)}}, {{A, B, C, X(29), X(6675)}}, {{A, B, C, X(79), X(16137)}}, {{A, B, C, X(80), X(37737)}}, {{A, B, C, X(86), X(6598)}}, {{A, B, C, X(200), X(24564)}}, {{A, B, C, X(281), X(18249)}}, {{A, B, C, X(285), X(12867)}}, {{A, B, C, X(333), X(6703)}}, {{A, B, C, X(515), X(40448)}}, {{A, B, C, X(596), X(2320)}}, {{A, B, C, X(959), X(2335)}}, {{A, B, C, X(1006), X(31806)}}, {{A, B, C, X(1036), X(39945)}}, {{A, B, C, X(1043), X(7110)}}, {{A, B, C, X(1067), X(5559)}}, {{A, B, C, X(1220), X(4999)}}, {{A, B, C, X(1224), X(51565)}}, {{A, B, C, X(2316), X(43073)}}, {{A, B, C, X(2646), X(41501)}}, {{A, B, C, X(3452), X(38000)}}, {{A, B, C, X(3680), X(3742)}}, {{A, B, C, X(3717), X(33944)}}, {{A, B, C, X(4168), X(6679)}}, {{A, B, C, X(4518), X(6682)}}, {{A, B, C, X(6596), X(8261)}}, {{A, B, C, X(7320), X(38254)}}, {{A, B, C, X(9119), X(31435)}}, {{A, B, C, X(11604), X(43972)}}, {{A, B, C, X(17097), X(43672)}}, {{A, B, C, X(17947), X(32014)}}, {{A, B, C, X(34919), X(43533)}}, {{A, B, C, X(39954), X(40656)}}
X(55091) = barycentric product X(i)*X(j) for these (i, j): {55090, 8}
X(55091) = barycentric quotient X(i)/X(j) for these (i, j): {9, 5260}, {11, 24224}, {650, 50346}, {55090, 7}

X(55092) = (name pending)

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

See Ivan Pavlov, euclid 5891.

X(55092) lies on these lines: {5284, 40619}

X(55092) = intersection, other than A, B, C, of circumconics {{A, B, C, X(11), X(1621)}}, {{A, B, C, X(21), X(846)}}, {{A, B, C, X(55), X(5284)}}, {{A, B, C, X(885), X(17194)}}, {{A, B, C, X(2346), X(9445)}}

X(55093) = X(1203)X(4038)∩X(3634)X(3743)

Barycentrics    a*(3*b*(b+c)^2+a^2*(3*b+c)+a*(6*b^2+9*b*c+c^2))*(3*c*(b+c)^2+a^2*(b+3*c)+a*(b^2+9*b*c+6*c^2)) : :

See Ivan Pavlov, euclid 5891.

X(55093) lies on these lines: {1203, 4038}, {3634, 3743}, {3723, 4272}

X(55093) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3634)}}, {{A, B, C, X(2), X(2334)}}, {{A, B, C, X(10), X(34585)}}, {{A, B, C, X(37), X(58)}}, {{A, B, C, X(65), X(4038)}}, {{A, B, C, X(513), X(1125)}}, {{A, B, C, X(2292), X(40106)}}, {{A, B, C, X(3445), X(39983)}}, {{A, B, C, X(9277), X(32636)}}, {{A, B, C, X(17038), X(20615)}}, {{A, B, C, X(31359), X(40027)}}, {{A, B, C, X(32014), X(47915)}}

X(55094) = X(2)X(2221)∩X(7)X(183)

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

See Ivan Pavlov, euclid 5891.

X(55094) lies on these lines: {2, 2221}, {7, 183}, {69, 5552}, {75, 404}, {86, 26115}, {100, 314}, {261, 5260}, {313, 1444}, {332, 17751}, {750, 10436}, {894, 26243}, {1014, 1909}, {1240, 40455}, {1817, 19810}, {2975, 3596}, {3263, 37261}, {3785, 21279}, {4191, 4441}, {4357, 32918}, {4553, 22281}, {5291, 44418}, {7270, 14005}, {10447, 25440}, {14829, 17077}, {16451, 44140}, {17189, 24170}, {17763, 39774}, {17790, 38871}, {20891, 21495}

X(55094) = isotomic conjugate of X(55089)

X(55095) = X(2)X(594)∩X(8)X(12)

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

See Ivan Pavlov, euclid 5891.

X(55095) lies on these lines: {1, 19280}, {2, 594}, {8, 12}, {9, 42034}, {10, 33135}, {37, 25059}, {57, 75}, {63, 42029}, {81, 31025}, {86, 1999}, {100, 17163}, {190, 321}, {192, 5737}, {226, 319}, {239, 44417}, {306, 41878}, {312, 3305}, {320, 3982}, {329, 17346}, {484, 4647}, {536, 38000}, {658, 52421}, {664, 52358}, {668, 27792}, {673, 40033}, {894, 41629}, {903, 26840}, {908, 4886}, {1043, 5295}, {1150, 28605}, {1211, 32025}, {1220, 27368}, {1654, 4415}, {1961, 27798}, {2321, 31205}, {2901, 11110}, {3210, 37660}, {3218, 4980}, {3452, 50095}, {3578, 17484}, {3617, 37614}, {3661, 3772}, {3666, 17160}, {3687, 5564}, {3695, 25446}, {3696, 7081}, {3699, 4651}, {3706, 3748}, {3714, 16824}, {3741, 17598}, {3752, 17117}, {3769, 50314}, {3773, 33138}, {3775, 33152}, {3782, 17273}, {3875, 18229}, {3883, 51783}, {3940, 48850}, {3944, 50308}, {3995, 5235}, {3996, 26227}, {4042, 32937}, {4054, 33066}, {4080, 43990}, {4095, 4384}, {4114, 7321}, {4362, 5263}, {4363, 37683}, {4365, 32917}, {4389, 30699}, {4399, 37662}, {4418, 9340}, {4431, 5745}, {4442, 33083}, {4457, 5524}, {4654, 17361}, {4656, 17256}, {4665, 37646}, {4671, 5278}, {4673, 31393}, {4683, 48642}, {4699, 37674}, {4714, 51285}, {4716, 6685}, {4751, 17022}, {4883, 38473}, {4967, 39595}, {4997, 7332}, {5249, 17297}, {5273, 50107}, {5361, 32933}, {5712, 17377}, {6535, 33115}, {6542, 17056}, {6703, 28604}, {6996, 33941}, {7308, 20942}, {9965, 49722}, {10449, 15934}, {11263, 41822}, {14552, 17347}, {16816, 36647}, {16832, 32009}, {17019, 25507}, {17119, 17490}, {17227, 23681}, {17228, 25527}, {17234, 34255}, {17241, 41867}, {17257, 42047}, {17259, 20170}, {17260, 35652}, {17261, 22034}, {17271, 27184}, {17283, 24789}, {17289, 40940}, {17294, 25525}, {17295, 18134}, {17303, 29841}, {17304, 19830}, {17305, 19785}, {17307, 19786}, {17308, 19812}, {17326, 50063}, {17335, 30568}, {17390, 26109}, {17719, 21085}, {17763, 21020}, {17777, 41002}, {18044, 19803}, {19684, 25417}, {19732, 41839}, {19742, 41242}, {19744, 27268}, {19810, 30713}, {20879, 34234}, {20926, 33935}, {21024, 27321}, {21242, 32866}, {24627, 42051}, {25385, 32861}, {25529, 30831}, {26580, 41816}, {29670, 49459}, {29766, 30599}, {29873, 48648}, {30350, 35613}, {30832, 33133}, {30970, 32928}, {31035, 31311}, {31126, 33090}, {31136, 32923}, {31241, 32924}, {31330, 32926}, {32018, 34016}, {32772, 50756}, {32779, 41806}, {32780, 50755}, {32914, 32942}, {32916, 49474}, {33082, 48643}, {33099, 48641}, {33130, 49560}, {33164, 48644}, {35176, 53647}, {37655, 42697}, {39698, 39962}

X(55095) = isotomic conjugate of X(55090)
X(55095) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55090}, {604, 55091}
X(55095) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55090}, {3161, 55091}, {4560, 17197}, {24224, 23755}
X(55095) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1255), X(5260)}}, {{A, B, C, X(1268), X(14616)}}, {{A, B, C, X(2161), X(52555)}}, {{A, B, C, X(3687), X(20882)}}, {{A, B, C, X(4102), X(30710)}}, {{A, B, C, X(6539), X(18359)}}, {{A, B, C, X(7332), X(24224)}}
X(55095) = barycentric product X(i)*X(j) for these (i, j): {1016, 24224}, {5260, 75}, {50346, 668}
X(55095) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55090}, {8, 55091}, {5260, 1}, {24224, 1086}, {40625, 17197}, {50346, 513}
X(55095) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 11679, 14829}, {312, 5271, 17277}, {321, 333, 190}, {1150, 28605, 32939}, {1999, 31993, 86}, {3782, 37653, 17273}, {46175, 46176, 1268}

X(55096) = X(7)X(12)∩X(75)X(78)

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

See Ivan Pavlov, euclid 5891.

X(55096) lies on these lines: {2, 6354}, {7, 12}, {65, 3786}, {75, 78}, {77, 41847}, {85, 269}, {86, 664}, {226, 19808}, {307, 28653}, {894, 26671}, {1213, 17950}, {1214, 25507}, {1215, 7274}, {1445, 4751}, {1943, 42028}, {3619, 30275}, {3663, 17593}, {3668, 17095}, {3739, 41246}, {3945, 5724}, {4363, 26125}, {4472, 52023}, {4699, 5228}, {5550, 36640}, {6358, 34064}, {7269, 17160}, {9436, 32780}, {11683, 29967}, {14828, 44735}, {17086, 17398}, {17256, 41572}, {17289, 21617}, {17322, 22464}, {17381, 37800}, {24603, 52819}, {24993, 38459}, {25964, 31640}, {26059, 32024}, {27420, 32008}, {34393, 45198}

X(55096) = isotomic conjugate of X(55091)
X(55096) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55091}, {41, 55090}
X(55096) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55091}, {3160, 55090}
X(55096) = X(i)-cross conjugate of X(j) for these {i, j}: {5260, 55095}
X(55096) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1220), X(5260)}}, {{A, B, C, X(1268), X(14616)}}, {{A, B, C, X(5249), X(18690)}}, {{A, B, C, X(39977), X(50346)}}
X(55096) = barycentric product X(i)*X(j) for these (i, j): {4554, 50346}, {5260, 85}, {24224, 4998}, {55095, 7}
X(55096) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55091}, {7, 55090}, {5260, 9}, {24224, 11}, {50346, 650}, {55095, 8}
X(55096) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {86, 1441, 664}, {25590, 40719, 39126}

X(55097) = X(75)X(3624)∩X(274)X(313)

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

See Ivan Pavlov, euclid 5891.

X(55097) lies on these lines: {75, 3624}, {86, 3293}, {274, 313}, {314, 43223}, {646, 28604}, {668, 1268}, {1698, 44139}, {4472, 25457}, {10436, 16569}, {24944, 32026}

X(55097) = isotomic conjugate of X(55093)

X(55098) = X(3)X(2594)∩X(6)X(1036)

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

See Ivan Pavlov, euclid 5891.

X(55098) lies on these lines: {1, 44085}, {3, 2594}, {6, 1036}, {8, 20986}, {10, 1437}, {12, 37527}, {21, 692}, {55, 13323}, {56, 182}, {60, 6043}, {65, 3955}, {72, 31811}, {110, 5260}, {171, 1408}, {184, 958}, {283, 52139}, {518, 26924}, {569, 11249}, {578, 3428}, {580, 16678}, {960, 26890}, {1126, 9275}, {1385, 10074}, {1397, 5710}, {1399, 37619}, {1468, 5135}, {1682, 20958}, {1891, 2203}, {2194, 5247}, {2330, 37539}, {2975, 5012}, {3193, 22299}, {3704, 17977}, {3796, 22654}, {3812, 26884}, {5085, 34046}, {5137, 13161}, {5157, 22769}, {5197, 24440}, {5302, 26885}, {5584, 13346}, {5752, 16473}, {7299, 31394}, {8193, 36742}, {8555, 45916}, {10269, 13336}, {10459, 52434}, {10984, 12114}, {13352, 35239}, {13353, 22765}, {14118, 53291}, {14529, 19860}, {16049, 22300}, {20989, 23841}, {21368, 42440}, {25524, 43650}, {36059, 37558}, {36558, 45885}, {36746, 37577}, {37431, 50362}, {37471, 37535}, {37474, 37601}, {37482, 37557}, {41229, 42463}

X(55098) = isogonal conjugate of X(55089)
X(55098) = barycentric product X(i)*X(j) for these (i, j): {6, 55094}
X(55098) = barycentric quotient X(i)/X(j) for these (i, j): {6, 55089}, {55094, 76}

X(55099) = X(1)X(26963)∩X(256)X(291)

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

See Ivan Pavlov, euclid 5891.

X(55099) lies on these lines: {1, 26963}, {86, 4553}, {256, 291}, {16696, 18082}, {34585, 40092}

X(55100) = X(1)X(572)∩X(6)X(595)

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

See Ivan Pavlov, euclid 5891.

X(55100) lies on these lines: {1, 572}, {6, 595}, {9, 943}, {12, 32431}, {21, 21061}, {35, 1400}, {37, 101}, {41, 3731}, {45, 584}, {48, 3247}, {55, 181}, {103, 50658}, {169, 380}, {171, 41430}, {172, 33628}, {190, 22012}, {198, 4262}, {346, 16788}, {390, 5764}, {405, 3713}, {496, 17398}, {579, 24047}, {594, 37730}, {692, 4068}, {909, 17438}, {954, 5776}, {1001, 5783}, {1100, 5053}, {1255, 40214}, {1388, 38855}, {1412, 37595}, {1429, 4021}, {1438, 39977}, {1442, 1461}, {1449, 2267}, {1474, 6198}, {1726, 28606}, {1743, 2280}, {1781, 21808}, {1790, 17019}, {1901, 5134}, {1958, 16831}, {2092, 33771}, {2185, 34064}, {2260, 5030}, {2264, 16601}, {2269, 3746}, {2276, 38831}, {2277, 4256}, {2278, 9327}, {2287, 3294}, {2294, 16548}, {2300, 40091}, {2329, 3950}, {2345, 3488}, {3085, 5816}, {3169, 25439}, {3204, 4289}, {3303, 38296}, {3723, 7113}, {3943, 15174}, {3970, 5279}, {4264, 5301}, {4268, 16884}, {4275, 34819}, {4314, 10445}, {4335, 24309}, {4343, 40910}, {4890, 17798}, {5110, 17053}, {5114, 21769}, {5172, 38864}, {5722, 17303}, {5746, 17732}, {5747, 24045}, {5749, 16783}, {9310, 16673}, {10469, 13740}, {13404, 29957}, {16503, 30331}, {17261, 40744}, {17299, 37739}, {17355, 41239}, {17388, 37728}, {17454, 19297}, {18755, 21796}, {21078, 34772}, {21353, 40589}, {24224, 55096}, {29456, 55094}

X(55100) = isogonal conjugate of X(55090)
X(55100) = perspector of circumconic {{A, B, C, X(8701), X(36098)}}
X(55100) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 55090}, {57, 55091}
X(55100) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 55090}, {5452, 55091}
X(55100) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(759), X(943)}}, {{A, B, C, X(2161), X(52555)}}, {{A, B, C, X(2259), X(28615)}}, {{A, B, C, X(2269), X(17440)}}, {{A, B, C, X(2298), X(2341)}}, {{A, B, C, X(39977), X(50346)}}
X(55100) = barycentric product X(i)*X(j) for these (i, j): {1, 5260}, {6, 55095}, {55, 55096}, {100, 50346}, {1252, 24224}
X(55100) = barycentric quotient X(i)/X(j) for these (i, j): {6, 55090}, {55, 55091}, {5260, 75}, {24224, 23989}, {50346, 693}, {55095, 76}, {55096, 6063}
X(55100) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2268, 572}, {35, 1400, 37508}, {37, 284, 101}, {4289, 16675, 3204}, {7005, 7006, 1126}

X(55101) = X(1)X(201)∩X(58)X(65)

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

See Ivan Pavlov, euclid 5891.

X(55101) lies on these lines: {1, 201}, {6, 1630}, {12, 24880}, {31, 3340}, {42, 37583}, {46, 37469}, {56, 181}, {57, 961}, {58, 65}, {81, 37558}, {102, 389}, {171, 4848}, {184, 41401}, {226, 5247}, {255, 11529}, {388, 1714}, {595, 2099}, {601, 2093}, {603, 3339}, {958, 37543}, {995, 26437}, {999, 36754}, {1042, 2003}, {1066, 1450}, {1104, 5173}, {1193, 18772}, {1203, 1457}, {1220, 52357}, {1331, 34195}, {1416, 52029}, {1420, 1471}, {1428, 10475}, {1453, 34036}, {1455, 37544}, {1469, 38831}, {1496, 11518}, {1497, 7982}, {1610, 1730}, {1724, 3485}, {1754, 3486}, {1758, 41547}, {1788, 37522}, {1834, 38945}, {1935, 3671}, {1936, 6738}, {2092, 38864}, {2646, 13329}, {2975, 16574}, {3304, 38293}, {3911, 5530}, {3939, 34772}, {4252, 37541}, {4257, 11509}, {4323, 17127}, {4424, 7098}, {4641, 12709}, {5172, 33771}, {6358, 27368}, {7991, 52428}, {10474, 38832}, {10680, 36752}, {11011, 40091}, {17966, 20970}, {18391, 37530}, {30115, 41538}, {31794, 52407}, {34030, 37642}, {34586, 37509}, {37539, 41539}, {44547, 45272}

X(55101) = isogonal conjugate of X(55091)
X(55101) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(759), X(943)}}, {{A, B, C, X(1243), X(31806)}}
X(55101) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 55091}, {9, 55090}
X(55101) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 55091}, {478, 55090}
X(55101) = barycentric product X(i)*X(j) for these (i, j): {6, 55096}, {56, 55095}, {5260, 57}, {24224, 59}, {50346, 651}, {55100, 7}
X(55101) = barycentric quotient X(i)/X(j) for these (i, j): {6, 55091}, {56, 55090}, {5260, 312}, {24224, 34387}, {50346, 4391}, {55095, 3596}, {55096, 76}, {55100, 8}
X(55101) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1451, 55086}, {58, 65, 109}

X(55102) = X(59)X(13476)∩X(65)X(4649)

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

See Ivan Pavlov, euclid 5891.

X(55102) lies on these lines: {59, 13476}, {65, 4649}, {354, 9440}, {651, 43915}, {2283, 18164}, {2346, 40636}, {3322, 15615}

X(55102) = isogonal conjugate of X(55092)

X(55103) = X(1)X(4127)∩X(10)X(81)

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

See Ivan Pavlov, euclid 5891.

X(55103) lies on these lines: {1, 4127}, {6, 3616}, {10, 81}, {21, 4649}, {100, 1126}, {145, 4195}, {651, 3649}, {940, 19877}, {1203, 3636}, {1468, 4279}, {1961, 32635}, {3578, 19865}, {3624, 32911}, {3702, 17120}, {3889, 16475}, {4005, 4663}, {4018, 17016}, {4038, 17536}, {4533, 37594}, {4658, 5260}, {4678, 5711}, {5710, 20053}, {6361, 36742}, {7277, 14450}, {9345, 17534}, {14996, 46932}, {15792, 30581}, {16828, 42025}, {19874, 42028}, {19878, 37680}, {22791, 36750}, {26115, 41629}, {33115, 49564}, {33139, 49743}

X(55103) = isogonal conjugate of X(55093)
X(55103) = barycentric product X(i)*X(j) for these (i, j): {6, 55097}
X(55103) = barycentric quotient X(i)/X(j) for these (i, j): {6, 55093}, {55097, 76}

X(55104) = X(3)X(63)∩X(4)X(9)

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

See Ivan Pavlov, euclid 5973.

X(55104) lies on these lines: {1, 201}, {2, 5709}, {3, 63}, {4, 9}, {5, 3305}, {6, 37528}, {7, 37407}, {8, 6987}, {20, 3219}, {21, 37531}, {24, 5285}, {34, 3074}, {35, 920}, {37, 5706}, {44, 15852}, {46, 226}, {55, 12710}, {57, 631}, {77, 3157}, {84, 376}, {90, 4302}, {100, 12691}, {140, 3306}, {144, 37108}, {165, 191}, {173, 8128}, {182, 26924}, {185, 3690}, {198, 40660}, {200, 10268}, {210, 11500}, {219, 1181}, {220, 1498}, {227, 34032}, {255, 1038}, {258, 8127}, {329, 3359}, {387, 8557}, {389, 26893}, {392, 22770}, {405, 517}, {411, 3876}, {440, 8251}, {442, 5812}, {452, 5554}, {474, 37623}, {484, 4338}, {515, 41229}, {549, 37612}, {578, 26890}, {581, 51875}, {601, 1707}, {610, 38856}, {612, 3072}, {774, 1253}, {908, 6825}, {936, 6905}, {938, 5766}, {942, 954}, {944, 6737}, {946, 6832}, {950, 1728}, {956, 31786}, {958, 14110}, {960, 3428}, {962, 6846}, {968, 37529}, {970, 2339}, {971, 37426}, {975, 37530}, {984, 37570}, {997, 11012}, {1012, 31445}, {1040, 44706}, {1060, 52408}, {1064, 54386}, {1075, 1712}, {1092, 3955}, {1125, 6878}, {1210, 6947}, {1214, 7078}, {1331, 54289}, {1454, 5432}, {1479, 10395}, {1593, 26867}, {1697, 3488}, {1698, 5715}, {1699, 6990}, {1709, 31730}, {1762, 30266}, {1763, 1782}, {1767, 8762}, {1768, 16192}, {1858, 37601}, {1864, 37568}, {1872, 54299}, {2095, 5439}, {2287, 37418}, {2323, 7592}, {2328, 30733}, {2900, 8715}, {2975, 37611}, {3085, 37550}, {3086, 54408}, {3090, 7308}, {3091, 27065}, {3146, 18540}, {3149, 5044}, {3218, 3523}, {3220, 10323}, {3295, 5728}, {3336, 5586}, {3338, 10165}, {3358, 9799}, {3419, 5690}, {3452, 6834}, {3522, 7171}, {3524, 3928}, {3525, 5437}, {3528, 9841}, {3538, 26929}, {3560, 37585}, {3576, 11523}, {3579, 5777}, {3586, 11010}, {3601, 6875}, {3624, 5536}, {3634, 6877}, {3654, 11113}, {3666, 36745}, {3678, 17857}, {3681, 5534}, {3683, 7957}, {3692, 3695}, {3719, 54433}, {3746, 10399}, {3753, 37224}, {3781, 5562}, {3811, 10902}, {3868, 6986}, {3870, 10267}, {3874, 52769}, {3911, 6967}, {4055, 54421}, {4292, 6897}, {4294, 30223}, {4423, 13374}, {4512, 6769}, {4640, 10310}, {4641, 36746}, {4679, 7681}, {4847, 12116}, {4882, 38665}, {5056, 35595}, {5067, 51780}, {5128, 5714}, {5129, 5804}, {5218, 7098}, {5219, 6853}, {5220, 14872}, {5227, 6776}, {5248, 37569}, {5249, 6989}, {5256, 36754}, {5273, 6847}, {5287, 5707}, {5316, 6983}, {5436, 7982}, {5438, 6942}, {5506, 7988}, {5535, 25525}, {5584, 6001}, {5603, 16845}, {5692, 6261}, {5693, 7688}, {5705, 6830}, {5744, 6926}, {5745, 6833}, {5757, 37151}, {5762, 8728}, {5763, 6675}, {5767, 21061}, {5768, 37423}, {5771, 6922}, {5787, 37428}, {5791, 6831}, {5794, 11827}, {5798, 17303}, {5811, 37421}, {5887, 35239}, {5904, 15931}, {5905, 37112}, {5927, 37411}, {6172, 6223}, {6198, 7070}, {6241, 26915}, {6245, 6899}, {6260, 40256}, {6282, 6906}, {6284, 7082}, {6356, 7013}, {6457, 26940}, {6700, 6880}, {6734, 6827}, {6745, 37560}, {6759, 26885}, {6762, 7967}, {6763, 7987}, {6824, 54357}, {6836, 51755}, {6838, 31018}, {6843, 9780}, {6845, 31446}, {6848, 18228}, {6863, 30852}, {6876, 52026}, {6883, 24474}, {6898, 7682}, {6902, 9581}, {6913, 12702}, {6920, 7991}, {6940, 15803}, {6949, 30827}, {6951, 9579}, {6954, 27385}, {6960, 27131}, {6992, 12649}, {6998, 40131}, {7162, 10056}, {7193, 10984}, {7289, 10519}, {7400, 27509}, {7411, 12528}, {7413, 29828}, {7964, 12688}, {8226, 12699}, {8227, 24468}, {8273, 12675}, {8726, 21153}, {8884, 26941}, {9119, 54322}, {10303, 27003}, {10306, 13615}, {10398, 53053}, {10531, 40998}, {10680, 31838}, {10786, 21075}, {11248, 35258}, {11249, 19861}, {11414, 24320}, {11456, 52405}, {11520, 37615}, {12111, 26911}, {12115, 12527}, {12511, 31803}, {12515, 13257}, {12526, 30503}, {13442, 48882}, {13731, 21371}, {15171, 54203}, {15296, 25466}, {15298, 21620}, {15644, 26892}, {15908, 24703}, {15972, 48917}, {17185, 47512}, {17532, 50821}, {17699, 31452}, {18506, 33761}, {18909, 26872}, {21161, 54302}, {22076, 30675}, {22350, 54320}, {22753, 25917}, {22937, 26285}, {24299, 28466}, {26286, 35262}, {26889, 37515}, {30282, 54432}, {34629, 50836}, {34772, 37106}, {34790, 51489}, {36483, 36543}, {36484, 36540}, {36504, 36575}, {36747, 54444}, {37000, 42012}, {37403, 52027}, {37438, 37826}, {37625, 54318}, {45126, 54301}, {46684, 54441}

X(55104) = midpoint of X(3951) and X(10884)
X(55104) = reflection of X(i) in X(j) for these {i,j}: {10884, 3}, {11520, 37615}
X(55104) = perspector of circumconic {{A, B, C, X(1332), X(1897)}}
X(55104) = X(i)-Dao conjugate of X(j) for these {i, j}: {31653, 514}, {49183, 4}
X(55104) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(19)}}, {{A, B, C, X(4), X(63)}}, {{A, B, C, X(9), X(1259)}}, {{A, B, C, X(10), X(3998)}}, {{A, B, C, X(72), X(1826)}}, {{A, B, C, X(78), X(281)}}, {{A, B, C, X(104), X(10884)}}, {{A, B, C, X(201), X(21675)}}, {{A, B, C, X(228), X(2333)}}, {{A, B, C, X(242), X(20769)}}, {{A, B, C, X(580), X(39943)}}, {{A, B, C, X(1260), X(7079)}}, {{A, B, C, X(1444), X(18909)}}, {{A, B, C, X(1791), X(18446)}}, {{A, B, C, X(1839), X(3916)}}, {{A, B, C, X(1861), X(25083)}}, {{A, B, C, X(2184), X(39574)}}, {{A, B, C, X(2354), X(22345)}}, {{A, B, C, X(5440), X(8756)}}, {{A, B, C, X(22060), X(40975)}}, {{A, B, C, X(39585), X(54972)}}
X(55104) = barycentric product X(i)*X(j) for these (i, j): {1, 26872}, {345, 37550}, {3085, 63}, {3553, 69}, {19349, 312}, {26956, 4564}, {37383, 3998}
X(55104) = barycentric quotient X(i)/X(j) for these (i, j): {3085, 92}, {3553, 4}, {18909, 54284}, {19349, 57}, {26872, 75}, {26956, 4858}, {37550, 278}
X(55104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 26921, 63}, {3, 26938, 7085}, {3, 31837, 78}, {3, 3927, 1071}, {3, 3940, 33597}, {3, 72, 18446}, {3, 912, 10884}, {4, 26878, 9}, {9, 40, 4}, {20, 3219, 7330}, {35, 18397, 10393}, {40, 12705, 6361}, {40, 1706, 48363}, {84, 37551, 376}, {140, 37532, 3306}, {165, 1490, 3651}, {165, 191, 1158}, {200, 10268, 11491}, {226, 6684, 6889}, {411, 3876, 5720}, {1697, 10396, 3488}, {1698, 5715, 6829}, {1728, 5119, 950}, {3524, 26877, 37526}, {3579, 5777, 7580}, {3587, 7330, 20}, {3683, 7957, 11496}, {3928, 37526, 26877}, {3929, 37551, 84}, {3951, 10884, 912}, {5693, 7688, 12520}, {5812, 26446, 442}, {6212, 6213, 71}, {6282, 31424, 6906}, {6883, 24474, 54392}, {7085, 26935, 3}, {7411, 12528, 41854}, {12511, 31803, 50528}, {15556, 54430, 1}, {21153, 54422, 8726}, {31445, 31793, 1012}, {37423, 54398, 5768}

X(55105) = X(3)X(19)∩X(4)X(63)

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

See Ivan Pavlov, euclid 5973.

X(55105) lies on these lines: {3, 19}, {4, 63}, {28, 1790}, {34, 222}, {57, 1118}, {58, 5317}, {286, 17206}, {580, 39943}, {581, 54405}, {967, 1430}, {1071, 37377}, {1119, 7177}, {1767, 37544}, {1796, 4219}, {1797, 36125}, {1841, 36746}, {1848, 6824}, {3211, 36747}, {3306, 7543}, {3359, 54294}, {3587, 6197}, {4198, 5768}, {5787, 7511}, {5805, 15763}, {6245, 42467}, {7171, 37379}, {7490, 37534}, {7513, 55104}, {7534, 24467}, {8751, 36057}, {11471, 37584}, {15762, 37532}, {18451, 24474}

X(55105) = isogonal conjugate of X(55104)
X(55105) = trilinear pole of line {1459, 6591}
X(55105) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 55104}, {3, 3085}, {6, 26872}, {8, 19349}, {59, 26956}, {63, 3553}, {78, 37550}, {3682, 37383}, {18909, 42019}
X(55105) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 55104}, {9, 26872}, {3162, 3553}, {6615, 26956}, {36103, 3085}, {49171, 18909}
X(55105) = X(i)-cross conjugate of X(j) for these {i, j}: {1451, 1}, {22479, 34}
X(55105) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(270)}}, {{A, B, C, X(3), X(27)}}, {{A, B, C, X(4), X(19)}}, {{A, B, C, X(9), X(3527)}}, {{A, B, C, X(21), X(51496)}}, {{A, B, C, X(29), X(7497)}}, {{A, B, C, X(33), X(7040)}}, {{A, B, C, X(40), X(3426)}}, {{A, B, C, X(56), X(5709)}}, {{A, B, C, X(64), X(2160)}}, {{A, B, C, X(65), X(18443)}}, {{A, B, C, X(68), X(15314)}}, {{A, B, C, X(79), X(921)}}, {{A, B, C, X(90), X(284)}}, {{A, B, C, X(92), X(1871)}}, {{A, B, C, X(104), X(51223)}}, {{A, B, C, X(158), X(1039)}}, {{A, B, C, X(267), X(3062)}}, {{A, B, C, X(278), X(1217)}}, {{A, B, C, X(279), X(3346)}}, {{A, B, C, X(580), X(1708)}}, {{A, B, C, X(775), X(1088)}}, {{A, B, C, X(943), X(955)}}, {{A, B, C, X(951), X(7284)}}, {{A, B, C, X(961), X(3427)}}, {{A, B, C, X(1041), X(2190)}}, {{A, B, C, X(1172), X(40836)}}, {{A, B, C, X(1295), X(10429)}}, {{A, B, C, X(1420), X(2095)}}, {{A, B, C, X(1436), X(7330)}}, {{A, B, C, X(1476), X(51497)}}, {{A, B, C, X(2051), X(9895)}}, {{A, B, C, X(2161), X(52518)}}, {{A, B, C, X(2217), X(51755)}}, {{A, B, C, X(3531), X(41441)}}, {{A, B, C, X(3601), X(5708)}}, {{A, B, C, X(3668), X(28787)}}, {{A, B, C, X(4219), X(31900)}}, {{A, B, C, X(4227), X(14018)}}, {{A, B, C, X(7091), X(51498)}}, {{A, B, C, X(7100), X(8809)}}, {{A, B, C, X(7501), X(31902)}}, {{A, B, C, X(8726), X(37544)}}, {{A, B, C, X(8814), X(10305)}}, {{A, B, C, X(11518), X(15934)}}, {{A, B, C, X(11546), X(40396)}}, {{A, B, C, X(13739), X(15762)}}, {{A, B, C, X(13855), X(47849)}}, {{A, B, C, X(15803), X(37582)}}, {{A, B, C, X(24474), X(34489)}}, {{A, B, C, X(37531), X(37566)}}, {{A, B, C, X(37532), X(37583)}}
X(55105) = barycentric quotient X(i)/X(j) for these (i, j): {1, 26872}, {6, 55104}, {19, 3085}, {25, 3553}, {604, 19349}, {608, 37550}, {2170, 26956}, {3554, 18909}, {5317, 37383}

X(55106) = X(69)X(92)∩X(264)X(304)

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

See Ivan Pavlov, euclid 5973.

X(55106) lies on these lines: {69, 92}, {264, 304}, {273, 348}, {286, 17206}, {31637, 54235}

X(55106) = intersection, other than A, B, C, of circumconics {{A, B, C, X(27), X(37181)}}, {{A, B, C, X(69), X(85)}}, {{A, B, C, X(92), X(264)}}, {{A, B, C, X(189), X(7318)}}, {{A, B, C, X(253), X(30690)}}, {{A, B, C, X(312), X(8797)}}, {{A, B, C, X(322), X(36889)}}, {{A, B, C, X(333), X(20570)}}, {{A, B, C, X(44186), X(44188)}}
X(55106) = isotomic conjugate of X(55104)
X(55106) = polar conjugate of X(3553)
X(55106) = trilinear pole of line {4025, 17924}
X(55106) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55104}, {32, 26872}, {48, 3553}, {55, 19349}, {184, 3085}, {212, 37550}, {4055, 37383}
X(55106) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55104}, {223, 19349}, {1249, 3553}, {1577, 26956}, {6376, 26872}, {40837, 37550}
X(55106) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55104}, {4, 3553}, {57, 19349}, {75, 26872}, {92, 3085}, {278, 37550}, {4858, 26956}, {54284, 18909}, {55105, 6}

X(55107) = X(2)X(158)∩X(75)X(2052)

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

See Ivan Pavlov, euclid 5973.

X(55107) lies on these lines: {2, 158}, {27, 55105}, {75, 2052}, {86, 55106}, {12649, 37192}

X(55107) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(158), X(2052)}}, {{A, B, C, X(318), X(8796)}}, {{A, B, C, X(3998), X(8808)}}
X(55107) = polar conjugate of X(55104)
X(55107) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 55104}, {184, 26872}, {219, 19349}, {255, 3553}, {577, 3085}, {2289, 37550}
X(55107) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 55104}, {6523, 3553}
X(55107) = X(i)-cross conjugate of X(j) for these {i, j}: {55105, 55106}
X(55107) = barycentric product X(i)*X(j) for these (i, j): {4, 55106}, {264, 55105}
X(55107) = barycentric quotient X(i)/X(j) for these (i, j): {4, 55104}, {34, 19349}, {92, 26872}, {158, 3085}, {393, 3553}, {1118, 37550}, {55105, 3}, {55106, 69}

X(55108) = X(3)X(142)∩X(5)X(226)

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

See Ivan Pavlov, euclid 5973.

X(55108) lies on these lines: {1, 6826}, {2, 5709}, {3, 142}, {4, 5249}, {5, 226}, {7, 6846}, {9, 6887}, {10, 6881}, {11, 9946}, {20, 27186}, {28, 17167}, {40, 6989}, {57, 499}, {63, 6832}, {78, 6854}, {84, 6173}, {119, 3947}, {355, 6738}, {381, 5787}, {443, 5603}, {496, 11018}, {515, 30143}, {517, 8728}, {551, 24299}, {553, 24467}, {581, 53599}, {908, 3090}, {936, 5761}, {938, 6843}, {950, 6917}, {962, 3587}, {1062, 40960}, {1071, 8226}, {1074, 2654}, {1385, 20420}, {1467, 6893}, {1478, 34489}, {1490, 6849}, {1519, 6847}, {1595, 25365}, {1656, 2095}, {1699, 6851}, {1738, 37529}, {1838, 37523}, {2886, 13374}, {3008, 36754}, {3073, 50307}, {3091, 5768}, {3218, 6884}, {3306, 6833}, {3358, 38037}, {3475, 5534}, {3487, 5720}, {3560, 4292}, {3576, 6869}, {3601, 4309}, {3616, 50701}, {3628, 5316}, {3649, 7958}, {3664, 36742}, {3671, 5887}, {3742, 9942}, {3812, 7680}, {3817, 6245}, {3824, 5806}, {3838, 7681}, {3851, 9842}, {3868, 6991}, {3872, 10597}, {3911, 6862}, {4297, 13151}, {4298, 22758}, {4301, 37585}, {4338, 6892}, {4666, 12116}, {4667, 36750}, {4675, 36746}, {5056, 31053}, {5177, 5804}, {5219, 6944}, {5226, 6964}, {5257, 5755}, {5333, 37418}, {5436, 6868}, {5437, 6891}, {5439, 6831}, {5443, 39599}, {5587, 11518}, {5693, 11551}, {5705, 6858}, {5706, 24789}, {5707, 40940}, {5714, 6939}, {5715, 6827}, {5745, 6861}, {5762, 50205}, {5763, 38171}, {5770, 7988}, {5812, 11108}, {5817, 41857}, {5842, 51715}, {5883, 12616}, {5884, 12617}, {5901, 12053}, {5905, 6886}, {6247, 21258}, {6282, 11522}, {6675, 11230}, {6684, 37584}, {6692, 6958}, {6705, 10199}, {6734, 6829}, {6769, 38052}, {6825, 25525}, {6834, 31266}, {6835, 18446}, {6842, 7682}, {6857, 41012}, {6867, 9581}, {6882, 9843}, {6888, 27003}, {6894, 18444}, {6911, 13411}, {6918, 11374}, {6930, 9579}, {6946, 27385}, {6983, 30852}, {6993, 12649}, {7171, 37434}, {7486, 27131}, {7497, 24701}, {7686, 25466}, {7741, 30274}, {8727, 9940}, {9614, 10383}, {9815, 51759}, {9956, 21075}, {10167, 37447}, {10175, 21077}, {10246, 51723}, {10247, 21627}, {10306, 37271}, {10532, 19860}, {11019, 26470}, {11227, 38034}, {11281, 37837}, {11499, 13405}, {12261, 52831}, {12437, 49600}, {12572, 37826}, {12611, 13226}, {12645, 36867}, {12675, 25557}, {12704, 19854}, {13464, 30144}, {14986, 30275}, {15762, 25361}, {16290, 21062}, {16617, 41547}, {17278, 36745}, {17605, 37566}, {17814, 37543}, {17866, 52565}, {18542, 19925}, {19843, 52457}, {19883, 28465}, {20330, 31419}, {21625, 37726}, {21635, 23513}, {22791, 31793}, {24301, 51698}, {24541, 37306}, {26332, 54318}, {26446, 50726}, {30985, 36672}, {31162, 37551}, {37526, 38021}, {37544, 39542}, {37695, 41344}

X(55108) = midpoint of X(i) and X(j) for these {i,j}: {10532, 19860}, {37615, 44229}, {4, 10884}
X(55108) = complement of X(55104)
X(55108) = X(13395)-Ceva conjugate of X(514)
X(55108) = X(i)-complementary conjugate of X(j) for these {i, j}: {55105, 10}, {55106, 2887}, {55107, 20305}
X(55108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 6147, 5777}, {5, 942, 51755}, {7, 6846, 7330}, {57, 8227, 6824}, {142, 946, 3}, {443, 5603, 37531}, {962, 37407, 3587}, {1490, 38150, 6849}, {1656, 2095, 5791}, {1699, 8726, 6851}, {3487, 6864, 5720}, {3817, 11263, 12608}, {3817, 6245, 6841}, {3824, 5806, 6907}, {5901, 37281, 24929}, {6841, 10202, 6245}, {6847, 9776, 37534}, {6861, 37532, 5745}, {9940, 9955, 8727}, {11230, 37623, 6675}, {31590, 31591, 34830}, {37615, 44229, 515}

X(55109) = X(1)X(7)∩X(4)X(912)

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

See Ivan Pavlov, euclid 5973.

X(55109) lies on these lines: {1, 7}, {2, 5709}, {4, 912}, {5, 31018}, {8, 2894}, {9, 6886}, {10, 6993}, {21, 5603}, {27, 3193}, {40, 5249}, {57, 6890}, {63, 946}, {72, 5805}, {84, 11240}, {149, 9964}, {220, 5829}, {224, 37569}, {226, 6838}, {278, 3562}, {283, 37113}, {329, 3091}, {376, 24299}, {377, 517}, {405, 5762}, {411, 3487}, {412, 1068}, {474, 5763}, {515, 11520}, {908, 6953}, {938, 6840}, {942, 6836}, {960, 5832}, {1004, 10306}, {1012, 10680}, {1058, 11020}, {1071, 10431}, {1086, 37537}, {1259, 22753}, {1389, 34617}, {1479, 18389}, {1482, 37468}, {1519, 10530}, {1537, 13279}, {1699, 10916}, {1728, 41563}, {1754, 24159}, {2095, 6831}, {2478, 5812}, {3072, 26228}, {3146, 17483}, {3218, 6847}, {3219, 6846}, {3241, 32905}, {3254, 10429}, {3333, 16134}, {3436, 7686}, {3474, 37579}, {3485, 26357}, {3522, 26842}, {3523, 9776}, {3543, 6223}, {3616, 11012}, {3832, 5811}, {3873, 9960}, {3876, 6864}, {3916, 6974}, {3927, 8226}, {4190, 37531}, {4197, 5657}, {4208, 24987}, {5046, 5804}, {5056, 5705}, {5068, 26792}, {5082, 41228}, {5226, 6960}, {5273, 5536}, {5435, 6972}, {5493, 16208}, {5584, 38454}, {5706, 19785}, {5707, 19645}, {5708, 37374}, {5714, 6932}, {5744, 6888}, {5748, 6979}, {5759, 6986}, {5761, 6905}, {5768, 6895}, {5770, 6845}, {5787, 24473}, {5806, 6957}, {5816, 17746}, {5880, 7957}, {5901, 35252}, {6147, 7580}, {6173, 37551}, {6260, 31164}, {6361, 7411}, {6604, 12324}, {6832, 26921}, {6833, 37532}, {6848, 31053}, {6854, 31837}, {6870, 51755}, {6887, 26878}, {6889, 37584}, {6897, 37585}, {6899, 10202}, {6908, 31019}, {6910, 37623}, {6916, 10597}, {6926, 27003}, {6934, 37533}, {6962, 11374}, {6964, 27131}, {6966, 37582}, {6992, 54392}, {7078, 37800}, {7330, 20078}, {7988, 31446}, {8227, 54357}, {8273, 25557}, {9778, 10902}, {9799, 9812}, {9809, 10248}, {9965, 10529}, {10122, 16155}, {10246, 44238}, {10391, 12701}, {10396, 41572}, {10525, 16159}, {10587, 20070}, {10806, 11220}, {10883, 26470}, {10940, 11248}, {10943, 37447}, {11496, 44447}, {11522, 31424}, {12609, 41338}, {12700, 17616}, {13243, 37726}, {13408, 48890}, {13907, 49226}, {13965, 49227}, {15741, 40950}, {16202, 28174}, {17529, 38107}, {17552, 21168}, {17558, 24541}, {18446, 50695}, {18544, 40273}, {19782, 29243}, {22770, 37228}, {24470, 37022}, {27186, 37407}, {28610, 45700}, {30946, 36693}, {31435, 38036}, {31900, 41608}, {34772, 50701}, {37104, 37782}, {37387, 42461}, {39898, 54383}, {52682, 54158}

X(55109) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(4341)}}, {{A, B, C, X(77), X(43740)}}, {{A, B, C, X(269), X(39267)}}, {{A, B, C, X(10429), X(38459)}}
X(55109) = reflection of X(i) in X(j) for these {i,j}: {20, 10884}, {55104, 55108}
X(55109) = anticomplement of X(55104)
X(55109) = X(i)-Ceva conjugate of X(j) for these {i, j}: {55106, 2}
X(55109) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {55105, 8}, {55106, 6327}, {55107, 21270}
X(55109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 11036, 18444}, {40, 5249, 37112}, {63, 946, 6837}, {72, 5805, 6835}, {516, 10884, 20}, {946, 12704, 10527}, {962, 5734, 30305}, {1071, 12699, 10431}, {3832, 17484, 5811}, {3868, 43740, 12649}, {5715, 6734, 3091}, {31551, 31552, 17220}, {39772, 49177, 37433}, {48482, 49177, 9812}, {55104, 55108, 2}

X(55110) = X(2)X(268)∩X(4)X(57)

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

See Ivan Pavlov, euclid 5973.

X(55110) lies on these lines: {2, 268}, {4, 57}, {7, 92}, {20, 7011}, {27, 1014}, {56, 37379}, {222, 1249}, {226, 282}, {269, 278}, {280, 377}, {281, 1767}, {342, 9776}, {388, 39130}, {393, 1407}, {443, 52389}, {459, 26932}, {479, 1847}, {653, 9965}, {917, 8059}, {1071, 3176}, {1214, 6916}, {1396, 1413}, {1433, 37543}, {1436, 7490}, {1462, 7151}, {1473, 6618}, {1903, 8814}, {1947, 32000}, {2192, 3332}, {3079, 3220}, {3086, 8886}, {3218, 6820}, {3937, 6524}, {5249, 41081}, {5732, 44695}, {5784, 7046}, {6619, 26933}, {6819, 27003}, {7154, 37102}, {8732, 37279}, {8817, 34404}, {15728, 40117}, {16596, 41514}, {18026, 18141}, {18678, 34050}, {23958, 37192}, {34399, 44189}, {34400, 44129}, {37141, 37203}, {37790, 52803}, {40065, 52424}

X(55110) = polar conjugate of X(7080)
X(55110) = trilinear pole of line {3669, 7649}
X(55110) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 2324}, {9, 7078}, {37, 1819}, {40, 219}, {48, 7080}, {63, 7074}, {77, 7368}, {78, 198}, {100, 10397}, {200, 7011}, {212, 329}, {220, 7013}, {221, 3692}, {223, 1260}, {227, 2327}, {228, 27398}, {268, 1103}, {283, 21871}, {322, 52425}, {345, 2187}, {346, 7114}, {347, 1802}, {394, 40971}, {906, 8058}, {1110, 16596}, {1252, 53557}, {1259, 2331}, {1265, 2199}, {1331, 14298}, {1817, 2318}, {2149, 7358}, {2193, 21075}, {2289, 7952}, {2360, 3694}, {3195, 3719}, {4564, 47432}, {4587, 6129}, {8822, 52370}
X(55110) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 7078}, {514, 16596}, {650, 7358}, {661, 53557}, {1249, 7080}, {3162, 7074}, {3341, 3692}, {5190, 8058}, {5521, 14298}, {6609, 7011}, {8054, 10397}, {36103, 2324}, {40589, 1819}, {40837, 329}, {47345, 21075}
X(55110) = X(i)-cross conjugate of X(j) for these {i, j}: {1118, 1119}, {1413, 1440}, {1435, 278}, {3942, 17925}, {7129, 40836}
X(55110) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10396)}}, {{A, B, C, X(2), X(1210)}}, {{A, B, C, X(4), X(27)}}, {{A, B, C, X(7), X(57)}}, {{A, B, C, X(63), X(10305)}}, {{A, B, C, X(84), X(189)}}, {{A, B, C, X(196), X(208)}}, {{A, B, C, X(223), X(45818)}}, {{A, B, C, X(279), X(4292)}}, {{A, B, C, X(329), X(15239)}}, {{A, B, C, X(393), X(1856)}}, {{A, B, C, X(459), X(17924)}}, {{A, B, C, X(514), X(34546)}}, {{A, B, C, X(905), X(1032)}}, {{A, B, C, X(1256), X(3341)}}, {{A, B, C, X(1413), X(34400)}}, {{A, B, C, X(1440), X(8808)}}, {{A, B, C, X(1712), X(7149)}}, {{A, B, C, X(1751), X(6601)}}, {{A, B, C, X(2006), X(6557)}}, {{A, B, C, X(2051), X(7682)}}, {{A, B, C, X(2184), X(10309)}}, {{A, B, C, X(2982), X(3296)}}, {{A, B, C, X(2994), X(34056)}}, {{A, B, C, X(3182), X(8810)}}, {{A, B, C, X(6245), X(13478)}}, {{A, B, C, X(6504), X(21907)}}, {{A, B, C, X(6524), X(6591)}}, {{A, B, C, X(7003), X(7008)}}, {{A, B, C, X(9309), X(40407)}}, {{A, B, C, X(9579), X(52374)}}, {{A, B, C, X(31900), X(37181)}}, {{A, B, C, X(37392), X(44734)}}
X(55110) = barycentric product X(i)*X(j) for these (i, j): {27, 8808}, {189, 278}, {269, 7020}, {273, 84}, {279, 7003}, {286, 52384}, {309, 34}, {1088, 7008}, {1119, 280}, {1256, 342}, {1413, 264}, {1422, 92}, {1435, 34404}, {1436, 331}, {1440, 4}, {1847, 282}, {2358, 274}, {6063, 7151}, {6612, 7017}, {7129, 85}, {13853, 46103}, {17924, 37141}, {24002, 40117}, {34400, 393}, {40836, 7}, {44190, 608}, {46107, 8059}, {53642, 7649}
X(55110) = barycentric quotient X(i)/X(j) for these (i, j): {4, 7080}, {11, 7358}, {19, 2324}, {25, 7074}, {27, 27398}, {34, 40}, {56, 7078}, {58, 1819}, {84, 78}, {189, 345}, {208, 1103}, {225, 21075}, {244, 53557}, {269, 7013}, {273, 322}, {278, 329}, {280, 1265}, {282, 3692}, {285, 1792}, {309, 3718}, {607, 7368}, {608, 198}, {649, 10397}, {1086, 16596}, {1096, 40971}, {1106, 7114}, {1118, 7952}, {1119, 347}, {1256, 271}, {1395, 2187}, {1396, 1817}, {1398, 221}, {1407, 7011}, {1413, 3}, {1422, 63}, {1426, 227}, {1433, 1259}, {1435, 223}, {1436, 219}, {1440, 69}, {1847, 40702}, {1880, 21871}, {1903, 3694}, {2192, 1260}, {2208, 212}, {2357, 2318}, {2358, 37}, {2969, 38357}, {3271, 47432}, {6591, 14298}, {6612, 222}, {7003, 346}, {7008, 200}, {7020, 341}, {7118, 1802}, {7129, 9}, {7151, 55}, {7154, 220}, {7337, 3195}, {7649, 8058}, {8059, 1331}, {8735, 5514}, {8808, 306}, {13138, 4571}, {13853, 26942}, {34400, 3926}, {34404, 52406}, {36049, 4587}, {37141, 1332}, {38362, 3318}, {39130, 3710}, {40117, 644}, {40836, 8}, {41081, 3719}, {43923, 6129}, {52037, 3998}, {52384, 72}, {53642, 4561}
X(55110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 189, 52037}, {7, 44697, 196}

X(55111) = X(3)X(48)∩X(9)X(55)

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

See Ivan Pavlov, euclid 5973.

X(55111) lies on these lines: {1, 51498}, {3, 48}, {6, 1167}, {9, 55}, {19, 1598}, {40, 198}, {100, 27382}, {101, 1604}, {220, 2301}, {268, 271}, {281, 5687}, {284, 2343}, {518, 1741}, {579, 1617}, {610, 10310}, {906, 15905}, {1033, 1783}, {1103, 3342}, {1332, 3964}, {1376, 40942}, {1436, 2077}, {1609, 17796}, {1696, 54424}, {1723, 11508}, {1903, 17857}, {2092, 16283}, {2178, 6603}, {2262, 37569}, {2266, 54358}, {2270, 6769}, {2323, 5120}, {2550, 51366}, {2911, 8573}, {3189, 53994}, {3295, 40937}, {3553, 50195}, {3695, 5774}, {3811, 9119}, {4571, 30681}, {5537, 18594}, {6510, 7053}, {6745, 20263}, {6913, 26063}, {7011, 7013}, {7124, 22071}, {7957, 54420}, {8804, 11500}, {10902, 54322}, {14004, 17784}, {15817, 37601}, {15851, 22122}, {17455, 36743}, {18598, 53280}, {19588, 20796}, {21482, 26872}, {22123, 38292}, {22124, 22350}, {23089, 26934}, {24310, 37269}, {28783, 47849}, {37541, 54405}, {52978, 53850}

X(55111) = perspector of circumconic {{A, B, C, X(644), X(1331)}}
X(55111) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 55110}, {4, 1422}, {7, 7129}, {19, 1440}, {27, 52384}, {28, 8808}, {34, 189}, {57, 40836}, {84, 278}, {85, 7151}, {86, 2358}, {92, 1413}, {196, 1256}, {269, 7003}, {270, 13853}, {273, 1436}, {279, 7008}, {280, 1435}, {282, 1119}, {309, 608}, {318, 6612}, {331, 2208}, {1088, 7154}, {1096, 34400}, {1118, 41081}, {1395, 44190}, {1396, 39130}, {1398, 34404}, {1407, 7020}, {1847, 2192}, {3676, 40117}, {6591, 53642}, {7649, 37141}, {8059, 17924}, {8747, 52037}, {40397, 52571}, {40446, 42549}, {43923, 44327}
X(55111) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 55110}, {6, 1440}, {57, 1847}, {5452, 40836}, {6503, 34400}, {6600, 7003}, {11517, 189}, {14298, 1565}, {14837, 23989}, {22391, 1413}, {24771, 7020}, {36033, 1422}, {40591, 8808}, {40600, 2358}
X(55111) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1259, 1260}, {3692, 219}, {7080, 7074}
X(55111) = X(i)-cross conjugate of X(j) for these {i, j}: {7368, 1260}
X(55111) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(9)}}, {{A, B, C, X(6), X(196)}}, {{A, B, C, X(19), X(30223)}}, {{A, B, C, X(48), X(55)}}, {{A, B, C, X(64), X(7003)}}, {{A, B, C, X(71), X(210)}}, {{A, B, C, X(200), X(219)}}, {{A, B, C, X(221), X(2264)}}, {{A, B, C, X(223), X(284)}}, {{A, B, C, X(281), X(1073)}}, {{A, B, C, X(282), X(52063)}}, {{A, B, C, X(346), X(394)}}, {{A, B, C, X(380), X(1036)}}, {{A, B, C, X(480), X(1802)}}, {{A, B, C, X(916), X(8058)}}, {{A, B, C, X(1172), X(15501)}}, {{A, B, C, X(1260), X(2289)}}, {{A, B, C, X(1795), X(51341)}}, {{A, B, C, X(1817), X(13615)}}, {{A, B, C, X(1818), X(3693)}}, {{A, B, C, X(2199), X(7083)}}, {{A, B, C, X(2252), X(14298)}}, {{A, B, C, X(2259), X(2331)}}, {{A, B, C, X(2335), X(7952)}}, {{A, B, C, X(2348), X(20780)}}, {{A, B, C, X(2900), X(3211)}}, {{A, B, C, X(3158), X(20818)}}, {{A, B, C, X(3174), X(22153)}}, {{A, B, C, X(3682), X(3694)}}, {{A, B, C, X(3683), X(22054)}}, {{A, B, C, X(3684), X(7193)}}, {{A, B, C, X(3689), X(10397)}}, {{A, B, C, X(3964), X(15742)}}, {{A, B, C, X(4254), X(39167)}}, {{A, B, C, X(7115), X(15905)}}, {{A, B, C, X(14100), X(22088)}}, {{A, B, C, X(16596), X(47432)}}, {{A, B, C, X(30681), X(44717)}}, {{A, B, C, X(36609), X(36910)}}
X(55111) = barycentric product X(i)*X(j) for these (i, j): {3, 7080}, {10, 1819}, {40, 78}, {59, 7358}, {69, 7074}, {198, 345}, {200, 7013}, {212, 322}, {219, 329}, {223, 3692}, {326, 40971}, {341, 7114}, {346, 7011}, {348, 7368}, {1103, 271}, {1252, 16596}, {1259, 7952}, {1260, 347}, {1264, 3195}, {1265, 221}, {1331, 8058}, {1332, 14298}, {1792, 227}, {1802, 40702}, {1812, 21871}, {1817, 3694}, {2187, 3718}, {2199, 52406}, {2318, 8822}, {2324, 63}, {2331, 3719}, {2360, 3710}, {4571, 6129}, {7078, 8}, {10397, 190}, {14837, 4587}, {15501, 51379}, {21075, 283}, {27398, 71}, {30681, 6611}, {44717, 5514}, {47432, 4998}, {53009, 6514}, {53557, 765}
X(55111) = barycentric quotient X(i)/X(j) for these (i, j): {3, 1440}, {6, 55110}, {40, 273}, {41, 7129}, {48, 1422}, {55, 40836}, {71, 8808}, {78, 309}, {184, 1413}, {198, 278}, {200, 7020}, {212, 84}, {213, 2358}, {219, 189}, {220, 7003}, {221, 1119}, {223, 1847}, {228, 52384}, {329, 331}, {345, 44190}, {394, 34400}, {906, 37141}, {1103, 342}, {1253, 7008}, {1260, 280}, {1331, 53642}, {1802, 282}, {1819, 86}, {2175, 7151}, {2187, 34}, {2188, 1256}, {2197, 13853}, {2199, 1435}, {2289, 41081}, {2318, 39130}, {2324, 92}, {3195, 1118}, {3692, 34404}, {3990, 52037}, {4587, 44327}, {6056, 1433}, {7011, 279}, {7013, 1088}, {7066, 6355}, {7074, 4}, {7078, 7}, {7080, 264}, {7114, 269}, {7358, 34387}, {7368, 281}, {8058, 46107}, {10397, 514}, {14298, 17924}, {14827, 7154}, {16596, 23989}, {21871, 40149}, {27398, 44129}, {32656, 8059}, {38357, 2973}, {40971, 158}, {47432, 11}, {52370, 1903}, {52411, 6612}, {52425, 1436}, {53557, 1111}
X(55111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {71, 1802, 219}, {198, 7368, 2324}, {906, 22132, 15905}, {3694, 51376, 9}

X(55112) = X(8)X(210)∩X(63)X(69)

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

See Ivan Pavlov, euclid 5973.

X(55112) lies on these lines: {2, 2256}, {4, 4158}, {8, 210}, {63, 69}, {100, 11206}, {190, 54113}, {219, 23600}, {278, 40863}, {322, 329}, {333, 2343}, {344, 18928}, {346, 3969}, {644, 27540}, {1032, 42699}, {1102, 34400}, {1211, 4513}, {1264, 44189}, {1332, 37669}, {2295, 5712}, {5271, 28808}, {5435, 18141}, {6172, 42033}, {6335, 14361}, {6515, 32849}, {6604, 18134}, {6735, 27413}, {7074, 7080}, {11433, 17776}, {17778, 27544}, {18639, 26942}, {21232, 28108}, {27539, 51407}

X(55112) = perspector of circumconic {{A, B, C, X(646), X(4561)}}
X(55112) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 1413}, {25, 1422}, {31, 55110}, {33, 6612}, {34, 1436}, {56, 7129}, {57, 7151}, {58, 2358}, {84, 608}, {189, 1395}, {269, 7154}, {278, 2208}, {282, 1398}, {604, 40836}, {1106, 7003}, {1119, 7118}, {1256, 3209}, {1396, 2357}, {1407, 7008}, {1435, 2192}, {1440, 1973}, {1474, 52384}, {2203, 8808}, {6591, 8059}, {7020, 52410}, {7337, 41081}, {36049, 43923}, {40117, 43924}
X(55112) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 7129}, {2, 55110}, {6, 1413}, {10, 2358}, {57, 1435}, {281, 1118}, {3161, 40836}, {5452, 7151}, {5514, 43923}, {6129, 8735}, {6337, 1440}, {6338, 34400}, {6505, 1422}, {6552, 7003}, {6600, 7154}, {11517, 1436}, {14298, 3937}, {14837, 1086}, {24018, 3942}, {24771, 7008}, {51574, 52384}
X(55112) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1264, 1265}, {4998, 4571}, {52406, 345}
X(55112) = X(i)-cross conjugate of X(j) for these {i, j}: {55111, 7080}
X(55112) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(40701)}}, {{A, B, C, X(8), X(63)}}, {{A, B, C, X(40), X(2551)}}, {{A, B, C, X(69), X(312)}}, {{A, B, C, X(71), X(210)}}, {{A, B, C, X(92), X(26871)}}, {{A, B, C, X(196), X(1837)}}, {{A, B, C, X(223), X(497)}}, {{A, B, C, X(268), X(2256)}}, {{A, B, C, X(306), X(3701)}}, {{A, B, C, X(333), X(40702)}}, {{A, B, C, X(341), X(345)}}, {{A, B, C, X(347), X(18650)}}, {{A, B, C, X(960), X(7078)}}, {{A, B, C, X(1265), X(3719)}}, {{A, B, C, X(1817), X(2478)}}, {{A, B, C, X(1819), X(3876)}}, {{A, B, C, X(2324), X(3974)}}, {{A, B, C, X(2899), X(8897)}}, {{A, B, C, X(3057), X(7011)}}, {{A, B, C, X(3692), X(5423)}}, {{A, B, C, X(3702), X(4001)}}, {{A, B, C, X(3977), X(4723)}}, {{A, B, C, X(6350), X(40435)}}, {{A, B, C, X(7013), X(18228)}}, {{A, B, C, X(7017), X(34403)}}, {{A, B, C, X(8058), X(9028)}}, {{A, B, C, X(8822), X(30479)}}, {{A, B, C, X(8896), X(21075)}}, {{A, B, C, X(10397), X(20785)}}, {{A, B, C, X(18921), X(47372)}}, {{A, B, C, X(22370), X(27538)}}, {{A, B, C, X(37669), X(46102)}}
X(55112) = barycentric product X(i)*X(j) for these (i, j): {69, 7080}, {223, 52406}, {305, 7074}, {322, 78}, {329, 345}, {341, 7013}, {1016, 16596}, {1264, 7952}, {1265, 347}, {1819, 313}, {2324, 304}, {3596, 7078}, {3692, 40702}, {3710, 8822}, {3718, 40}, {4561, 8058}, {4998, 7358}, {10397, 1978}, {14256, 30681}, {17896, 4571}, {21075, 332}, {27398, 306}, {53557, 7035}, {55111, 76}
X(55112) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55110}, {3, 1413}, {8, 40836}, {9, 7129}, {37, 2358}, {40, 34}, {55, 7151}, {63, 1422}, {69, 1440}, {72, 52384}, {78, 84}, {198, 608}, {200, 7008}, {212, 2208}, {219, 1436}, {220, 7154}, {221, 1398}, {222, 6612}, {223, 1435}, {227, 1426}, {271, 1256}, {306, 8808}, {322, 273}, {329, 278}, {341, 7020}, {345, 189}, {346, 7003}, {347, 1119}, {644, 40117}, {1103, 208}, {1259, 1433}, {1260, 2192}, {1265, 280}, {1331, 8059}, {1332, 37141}, {1792, 285}, {1802, 7118}, {1817, 1396}, {1819, 58}, {2187, 1395}, {2318, 2357}, {2324, 19}, {3195, 7337}, {3318, 38362}, {3692, 282}, {3694, 1903}, {3710, 39130}, {3718, 309}, {3719, 41081}, {3926, 34400}, {3998, 52037}, {4561, 53642}, {4571, 13138}, {4587, 36049}, {5514, 8735}, {6129, 43923}, {7011, 1407}, {7013, 269}, {7074, 25}, {7078, 56}, {7080, 4}, {7114, 1106}, {7358, 11}, {7368, 607}, {7952, 1118}, {8058, 7649}, {10397, 649}, {14298, 6591}, {16596, 1086}, {21075, 225}, {21871, 1880}, {26942, 13853}, {27398, 27}, {38357, 2969}, {40702, 1847}, {40971, 1096}, {47432, 3271}, {52406, 34404}, {53557, 244}, {55111, 6}
X(55112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {306, 26872, 69}, {306, 3692, 345}, {13425, 13458, 1265}

X(55113) = X(2)X(268)∩X(9)X(223)

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

See Ivan Pavlov, euclid 5973.

X(55113) lies on these lines: {2, 268}, {3, 3452}, {9, 223}, {329, 7011}, {405, 7952}, {440, 38015}, {441, 27539}, {908, 6617}, {960, 15836}, {1260, 7358}, {1809, 6557}, {5745, 20206}, {6708, 6913}, {18228, 21482}, {20208, 41883}, {35072, 37679}, {40535, 40837}

X(55113) = complement of X(55110)
X(55113) = center of circumconic {{A, B, C, X(1305), X(27834)}}
X(55113) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1305, 8058}
X(55113) = X(i)-complementary conjugate of X(j) for these {i, j}: {40, 16608}, {48, 3086}, {78, 21239}, {198, 1210}, {212, 57}, {219, 946}, {220, 20263}, {906, 8058}, {1110, 40535}, {1260, 20205}, {1802, 281}, {1819, 3739}, {2187, 3772}, {2199, 17054}, {2324, 5}, {3692, 20306}, {7011, 11019}, {7013, 21258}, {7074, 226}, {7078, 142}, {7080, 20305}, {7114, 4000}, {7368, 20262}, {10397, 11}, {14827, 20311}, {40971, 13567}, {52370, 1901}, {52425, 1108}, {55111, 10}, {55112, 2887}

X(55114) = X(2)X(268)∩X(20)X(78)

Barycentrics    3*a^12+8*a^9*b*c*(b+c)-16*a^5*b^2*(b-c)^2*c^2*(b+c)-(b^2-c^2)^6-8*a*b*(b-c)^4*c*(b+c)^3*(b^2+c^2)+16*a^3*b*(b-c)^2*c*(b+c)^3*(b^2-b*c+c^2)+a^4*(b-c)^2*(b+c)^4*(5*b^2+6*b*c+5*c^2)-2*a^10*(7*b^2-4*b*c+7*c^2)-16*a^7*b*c*(b^3+c^3)+2*a^2*(b-c)^2*(b+c)^4*(b^4-6*b^3*c+2*b^2*c^2-6*b*c^3+c^4)+a^8*(25*b^4-16*b^3*c+14*b^2*c^2-16*b*c^3+25*c^4)-4*a^6*(5*b^6-b^4*c^2-8*b^3*c^3-b^2*c^4+5*c^6) : :

See Ivan Pavlov, euclid 5973.

X(55114) lies on these lines: {2, 268}, {20, 78}, {63, 5932}, {144, 6360}, {452, 1895}, {6527, 54113}

X(55114) = reflection of X(i) in X(j) for these {i,j}: {55110, 55113}
X(55114) = anticomplement of X(55110)
X(55114) = X(i)-Ceva conjugate of X(j) for these {i, j}: {55112, 2}
X(55114) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {78, 21279}, {198, 12649}, {212, 9965}, {219, 962}, {906, 8058}, {1110, 653}, {1260, 189}, {1331, 4131}, {1792, 20246}, {1819, 75}, {2149, 13138}, {2187, 30699}, {2199, 11851}, {2289, 280}, {2324, 4}, {2327, 20220}, {4587, 4397}, {7011, 36845}, {7013, 6604}, {7074, 5905}, {7078, 7}, {7080, 21270}, {7114, 4452}, {7368, 5942}, {10397, 149}, {27398, 20242}, {40971, 6515}, {55111, 8}, {55112, 6327}
X(55114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55110, 55113, 2}

X(55115) = X(33)X(64)∩X(51)X(1827)

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

See Ivan Pavlov, euclid 5973.

X(55115) lies on these lines: {33, 64}, {51, 1827}, {210, 5514}, {354, 6611}, {1856, 1903}, {1863, 1864}, {2192, 2262}, {10382, 15239}, {17441, 17642}

X(55115) = zosma transform of X(55110)

X(55116) = X(4)X(9)∩X(20)X(268)

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

See Ivan Pavlov, euclid 5973.

X(55116) lies on these lines: {1, 20263}, {2, 7011}, {4, 9}, {8, 7003}, {12, 1696}, {20, 268}, {63, 55110}, {69, 6335}, {72, 3176}, {92, 18228}, {144, 653}, {196, 329}, {198, 5514}, {200, 7007}, {210, 1857}, {219, 1249}, {220, 393}, {223, 52063}, {278, 3452}, {282, 515}, {347, 16596}, {388, 40942}, {459, 26942}, {610, 12667}, {958, 7498}, {965, 46011}, {1103, 2324}, {1119, 37805}, {1741, 1788}, {1837, 53994}, {1846, 31141}, {1865, 38930}, {1895, 5815}, {1948, 32000}, {2343, 8748}, {3079, 5285}, {3219, 6820}, {3436, 27382}, {3690, 6524}, {5084, 17916}, {5125, 8165}, {5273, 52412}, {5328, 17923}, {5745, 37276}, {6618, 7085}, {6619, 21015}, {6819, 27065}, {6827, 42018}, {6939, 44916}, {7017, 14555}, {7071, 28120}, {7080, 55111}, {9119, 18391}, {9121, 47441}, {12527, 44696}, {14361, 26872}, {15817, 37441}, {17555, 27508}, {17857, 18283}, {17917, 30827}, {21871, 47372}, {27509, 52283}, {28130, 28137}, {33630, 52405}, {34909, 34910}, {37417, 38860}

X(55116) = isotomic conjugate of X(34400)
X(55116) = polar conjugate of X(1440)
X(55116) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 1422}, {31, 34400}, {48, 1440}, {56, 41081}, {57, 1433}, {58, 52037}, {63, 1413}, {77, 1436}, {78, 6612}, {84, 222}, {189, 603}, {255, 55110}, {268, 269}, {271, 1407}, {279, 2188}, {280, 7099}, {282, 7053}, {285, 52373}, {309, 52411}, {348, 2208}, {905, 8059}, {1014, 41087}, {1106, 44189}, {1256, 7011}, {1412, 52389}, {1437, 8808}, {1459, 37141}, {1790, 52384}, {1804, 7129}, {2150, 6355}, {2192, 7177}, {7056, 7118}, {7125, 40836}, {7151, 7183}, {7341, 53010}, {22383, 53642}
X(55116) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 41081}, {2, 34400}, {10, 52037}, {57, 7177}, {281, 7}, {1249, 1440}, {3086, 26871}, {3162, 1413}, {5452, 1433}, {6129, 26932}, {6523, 55110}, {6552, 44189}, {6600, 268}, {7952, 189}, {8058, 16596}, {14298, 7215}, {23050, 282}, {24771, 271}, {36103, 1422}, {40599, 52389}
X(55116) = X(i)-Ceva conjugate of X(j) for these {i, j}: {8, 7046}, {7101, 281}
X(55116) = X(i)-cross conjugate of X(j) for these {i, j}: {2331, 281}, {7074, 7080}, {21871, 2324}, {40971, 7952}
X(55116) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(12705)}}, {{A, B, C, X(2), X(20262)}}, {{A, B, C, X(4), X(342)}}, {{A, B, C, X(7), X(11372)}}, {{A, B, C, X(8), X(40)}}, {{A, B, C, X(9), X(329)}}, {{A, B, C, X(10), X(7080)}}, {{A, B, C, X(12), X(21686)}}, {{A, B, C, X(19), X(196)}}, {{A, B, C, X(71), X(210)}}, {{A, B, C, X(198), X(2183)}}, {{A, B, C, X(223), X(2270)}}, {{A, B, C, X(227), X(41506)}}, {{A, B, C, X(314), X(12717)}}, {{A, B, C, X(322), X(2550)}}, {{A, B, C, X(347), X(516)}}, {{A, B, C, X(497), X(43916)}}, {{A, B, C, X(573), X(46014)}}, {{A, B, C, X(966), X(27398)}}, {{A, B, C, X(1000), X(15501)}}, {{A, B, C, X(1542), X(51375)}}, {{A, B, C, X(1706), X(34918)}}, {{A, B, C, X(1826), X(53009)}}, {{A, B, C, X(1855), X(40701)}}, {{A, B, C, X(2321), X(8804)}}, {{A, B, C, X(2354), X(3195)}}, {{A, B, C, X(3194), X(7713)}}, {{A, B, C, X(3596), X(49653)}}, {{A, B, C, X(5587), X(30513)}}, {{A, B, C, X(5698), X(8822)}}, {{A, B, C, X(6210), X(30479)}}, {{A, B, C, X(6361), X(15998)}}, {{A, B, C, X(6520), X(55110)}}, {{A, B, C, X(6554), X(40702)}}, {{A, B, C, X(7110), X(23058)}}, {{A, B, C, X(8074), X(14837)}}, {{A, B, C, X(17896), X(45281)}}, {{A, B, C, X(41869), X(43740)}}
X(55116) = barycentric product X(i)*X(j) for these (i, j): {4, 7080}, {196, 346}, {198, 7017}, {200, 342}, {208, 341}, {220, 40701}, {223, 7101}, {264, 7074}, {281, 329}, {318, 40}, {322, 33}, {331, 7368}, {333, 53009}, {347, 7046}, {393, 55112}, {1103, 7020}, {1826, 27398}, {1897, 8058}, {2052, 55111}, {2321, 41083}, {2324, 92}, {2331, 312}, {3194, 3701}, {3195, 3596}, {3699, 54239}, {7952, 8}, {14298, 6335}, {15742, 38357}, {21075, 29}, {21871, 31623}, {38362, 4076}, {40702, 7079}, {40971, 75}, {46102, 5514}, {47372, 78}, {53008, 8822}
X(55116) = barycentric quotient X(i)/X(j) for these (i, j): {2, 34400}, {4, 1440}, {9, 41081}, {12, 6355}, {19, 1422}, {25, 1413}, {33, 84}, {37, 52037}, {40, 77}, {55, 1433}, {196, 279}, {198, 222}, {200, 271}, {208, 269}, {210, 52389}, {220, 268}, {221, 7053}, {223, 7177}, {227, 1439}, {281, 189}, {318, 309}, {322, 7182}, {329, 348}, {342, 1088}, {346, 44189}, {347, 7056}, {393, 55110}, {607, 1436}, {608, 6612}, {1103, 7013}, {1253, 2188}, {1334, 41087}, {1783, 37141}, {1824, 52384}, {1826, 8808}, {1855, 13156}, {1857, 40836}, {1897, 53642}, {2187, 603}, {2199, 7099}, {2212, 2208}, {2324, 63}, {2331, 57}, {3194, 1014}, {3195, 56}, {3209, 1407}, {4183, 285}, {5514, 26932}, {6059, 7151}, {7008, 1256}, {7017, 44190}, {7046, 280}, {7071, 2192}, {7074, 3}, {7078, 1804}, {7079, 282}, {7080, 69}, {7101, 34404}, {7368, 219}, {7952, 7}, {8058, 4025}, {8736, 13853}, {8750, 8059}, {10397, 4091}, {14256, 30682}, {14298, 905}, {21075, 307}, {21871, 1214}, {27398, 17206}, {38015, 26871}, {38357, 1565}, {38362, 1358}, {40971, 1}, {41083, 1434}, {44695, 41084}, {47372, 273}, {47432, 1364}, {53008, 39130}, {53009, 226}, {53011, 52078}, {54239, 3676}, {55111, 394}, {55112, 3926}
X(55116) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {198, 5514, 38015}, {1826, 7079, 281}, {2331, 53009, 7952}, {13426, 13454, 7046}

X(55117) = X(3)X(1433)∩X(56)X(84)

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

See Ivan Pavlov, euclid 5973.

X(55117) lies on these lines: {3, 1433}, {27, 1014}, {55, 39558}, {56, 84}, {57, 1422}, {58, 1413}, {63, 268}, {103, 1617}, {189, 5435}, {222, 22063}, {280, 54391}, {282, 5120}, {1460, 7350}, {1767, 43044}, {2208, 3423}, {6507, 55111}, {7338, 54052}, {8808, 13478}, {9376, 39130}, {17206, 34400}

X(55117) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 55116}, {2, 40971}, {4, 2324}, {8, 2331}, {9, 7952}, {19, 7080}, {21, 53009}, {29, 21871}, {33, 329}, {40, 281}, {92, 7074}, {158, 55111}, {196, 200}, {198, 318}, {208, 346}, {210, 41083}, {219, 47372}, {220, 342}, {221, 7101}, {223, 7046}, {227, 2322}, {273, 7368}, {312, 3195}, {322, 607}, {341, 3209}, {347, 7079}, {644, 54239}, {1096, 55112}, {1103, 7003}, {1172, 21075}, {1253, 40701}, {1783, 8058}, {1817, 53008}, {1824, 27398}, {1897, 14298}, {2187, 7017}, {2321, 3194}, {5514, 7012}, {7071, 40702}
X(55117) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 55116}, {6, 7080}, {478, 7952}, {1147, 55111}, {3341, 7101}, {6503, 55112}, {6609, 196}, {17113, 40701}, {22391, 7074}, {32664, 40971}, {34467, 14298}, {36033, 2324}, {39006, 8058}, {40611, 53009}
X(55117) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1440, 1413}, {41081, 222}
X(55117) = X(i)-cross conjugate of X(j) for these {i, j}: {56, 7053}, {7099, 222}
X(55117) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3), X(27)}}, {{A, B, C, X(6), X(2262)}}, {{A, B, C, X(19), X(30223)}}, {{A, B, C, X(25), X(22383)}}, {{A, B, C, X(28), X(6617)}}, {{A, B, C, X(56), X(6611)}}, {{A, B, C, X(60), X(46355)}}, {{A, B, C, X(64), X(196)}}, {{A, B, C, X(102), X(223)}}, {{A, B, C, X(219), X(3451)}}, {{A, B, C, X(268), X(1436)}}, {{A, B, C, X(278), X(905)}}, {{A, B, C, X(279), X(394)}}, {{A, B, C, X(652), X(11051)}}, {{A, B, C, X(1014), X(1804)}}, {{A, B, C, X(1036), X(40407)}}, {{A, B, C, X(1256), X(1422)}}, {{A, B, C, X(1413), X(34400)}}, {{A, B, C, X(1817), X(37252)}}, {{A, B, C, X(2189), X(15905)}}, {{A, B, C, X(4131), X(39732)}}, {{A, B, C, X(15314), X(52559)}}, {{A, B, C, X(36609), X(52374)}}, {{A, B, C, X(42549), X(44189)}}
X(55117) = barycentric product X(i)*X(j) for these (i, j): {60, 6355}, {77, 84}, {189, 222}, {268, 279}, {269, 271}, {280, 7053}, {282, 7177}, {309, 603}, {345, 6612}, {394, 55110}, {1014, 52389}, {1088, 2188}, {1256, 7013}, {1407, 44189}, {1413, 69}, {1422, 63}, {1433, 7}, {1434, 41087}, {1436, 348}, {1439, 285}, {1440, 3}, {1444, 52384}, {1459, 53642}, {1790, 8808}, {1804, 40836}, {2192, 7056}, {2208, 7182}, {4025, 8059}, {7055, 7151}, {7129, 7183}, {13156, 1803}, {30682, 7367}, {34400, 6}, {34404, 7099}, {37141, 905}, {41081, 57}, {44190, 52411}, {52037, 81}
X(55117) = barycentric quotient X(i)/X(j) for these (i, j): {3, 7080}, {6, 55116}, {31, 40971}, {34, 47372}, {48, 2324}, {56, 7952}, {73, 21075}, {77, 322}, {84, 318}, {184, 7074}, {189, 7017}, {222, 329}, {268, 346}, {269, 342}, {271, 341}, {279, 40701}, {282, 7101}, {394, 55112}, {577, 55111}, {603, 40}, {604, 2331}, {1106, 208}, {1256, 7020}, {1357, 38362}, {1364, 7358}, {1397, 3195}, {1400, 53009}, {1407, 196}, {1408, 3194}, {1409, 21871}, {1410, 227}, {1412, 41083}, {1413, 4}, {1422, 92}, {1433, 8}, {1436, 281}, {1440, 264}, {1459, 8058}, {1790, 27398}, {2188, 200}, {2192, 7046}, {2208, 33}, {2357, 53008}, {3937, 38357}, {6355, 34388}, {6612, 278}, {7053, 347}, {7099, 223}, {7114, 1103}, {7117, 5514}, {7118, 7079}, {7151, 1857}, {7177, 40702}, {7335, 7078}, {8059, 1897}, {22383, 14298}, {34400, 76}, {37141, 6335}, {41081, 312}, {41087, 2321}, {43924, 54239}, {51660, 1528}, {52037, 321}, {52384, 41013}, {52389, 3701}, {52410, 3209}, {52411, 198}, {52425, 7368}, {55110, 2052}
X(55117) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1436, 6612, 1422}

X(55118) = X(3)X(142)∩X(7)X(268)

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

See Ivan Pavlov, euclid 5973.

X(55118) lies on these lines: {2, 7011}, {3, 142}, {7, 268}, {10, 38290}, {56, 18634}, {226, 55113}, {281, 40535}, {515, 20206}, {856, 18643}, {999, 16608}, {1073, 37543}, {1214, 5437}, {1376, 38288}, {1436, 41010}, {3295, 17043}, {3333, 52389}, {4423, 53847}, {5249, 6617}, {6389, 21258}, {6911, 14743}, {7053, 26932}, {8071, 24780}, {8257, 42018}, {9709, 38284}, {11347, 17917}, {16408, 20764}, {18642, 22754}, {21239, 40555}, {25931, 37800}, {26006, 55111}, {26333, 53833}

X(55118) = complement of X(55116)
X(55118) = X(i)-complementary conjugate of X(j) for these {i, j}: {48, 38015}, {84, 41883}, {222, 6260}, {255, 55113}, {603, 223}, {604, 46836}, {905, 46663}, {1407, 20264}, {1413, 226}, {1422, 5}, {1433, 3452}, {1436, 20262}, {2188, 6554}, {2208, 46835}, {6612, 1210}, {7053, 20206}, {7099, 7952}, {7129, 15849}, {7177, 20307}, {37141, 20316}, {41081, 1329}, {52037, 3454}, {52410, 20312}, {52411, 40943}, {55117, 10}

X(55119) = X(1)X(7)∩X(2)X(7011)

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

See Ivan Pavlov, euclid 5973.

X(55119) lies on these lines: {1, 7}, {2, 7011}, {4, 38290}, {8, 7013}, {56, 27402}, {253, 51565}, {273, 50700}, {342, 44695}, {515, 5932}, {651, 22124}, {653, 7003}, {934, 1440}, {944, 1439}, {1119, 38554}, {1441, 6904}, {1804, 2975}, {5129, 53821}, {5603, 10400}, {5905, 55114}, {6356, 6987}, {6360, 21454}, {6527, 6604}, {9119, 12848}, {9965, 52037}, {11348, 28739}, {24604, 38860}, {46421, 52419}, {46422, 52420}

X(55119) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(20), X(51565)}}, {{A, B, C, X(253), X(22464)}}, {{A, B, C, X(280), X(962)}}
X(55119) = reflection of X(i) in X(j) for these {i,j}: {55116, 55118}
X(55119) = anticomplement of X(55116)
X(55119) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {222, 6223}, {255, 55114}, {271, 54113}, {603, 20211}, {1412, 1895}, {1413, 5905}, {1422, 4}, {1433, 329}, {1436, 5942}, {2188, 30695}, {2208, 30694}, {6612, 12649}, {7053, 5932}, {8059, 4391}, {37141, 20293}, {41081, 3436}, {52037, 1330}, {55110, 5906}, {55117, 8}
X(55119) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55116, 55118, 2}

X(55120) = X(1)X(1604)∩X(6)X(19)

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

See Ivan Pavlov, euclid 5973.

X(55120) lies on these lines: {1, 1604}, {6, 19}, {25, 55115}, {198, 3057}, {517, 2270}, {910, 17642}, {1146, 1903}, {1407, 42549}, {1436, 3554}, {1457, 40943}, {1519, 15849}, {1851, 10374}, {2183, 21871}, {2355, 44121}, {2646, 11434}, {4875, 15656}, {6001, 53994}, {7129, 51399}, {7957, 34526}, {12672, 20262}, {12688, 54008}, {14110, 54420}

X(55120) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1604), X(34546)}}, {{A, B, C, X(2331), X(8602)}}
X(55120) = zosma transform of X(55116)

X(55121) = X(30)X(511)∩X(113)X(131)

Barycentrics    (b-c)*(b+c)*(a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-2*a^2*(b^4-b^2*c^2+c^4)) : :
X(55121) = -X[2492]+X[45801], -X[6333]+X[35522], -X[45792]+X[53369]

See Ivan Pavlov, euclid 5973.

X(55121) lies on these lines: {3, 40047}, {4, 15453}, {6, 14273}, {30, 511}, {64, 14220}, {66, 35909}, {67, 35364}, {74, 1300}, {110, 925}, {113, 131}, {125, 136}, {159, 53272}, {206, 5027}, {265, 13556}, {351, 13290}, {476, 35189}, {684, 14424}, {686, 12828}, {879, 1177}, {1116, 45309}, {1272, 3268}, {1514, 52475}, {1637, 1989}, {1640, 14398}, {1853, 15356}, {2071, 15470}, {2492, 45801}, {2935, 41077}, {3569, 32312}, {3657, 10693}, {5095, 38359}, {5181, 36790}, {5494, 44428}, {5642, 45687}, {5653, 47139}, {5961, 13289}, {5972, 6132}, {6130, 32193}, {6333, 35522}, {6699, 34840}, {7669, 10117}, {8029, 36255}, {9123, 14932}, {9135, 32313}, {9138, 9979}, {9142, 48988}, {9145, 48957}, {9147, 53383}, {9180, 54918}, {9512, 54085}, {10118, 53563}, {10278, 42736}, {10412, 46008}, {10721, 44990}, {10733, 44974}, {11123, 42737}, {11616, 15577}, {11744, 14380}, {12064, 45259}, {13293, 13496}, {14264, 39985}, {14397, 52742}, {14417, 15131}, {14428, 45321}, {14559, 53274}, {14809, 39477}, {14854, 15475}, {14977, 39905}, {15055, 38718}, {15113, 45689}, {15116, 41167}, {15329, 41512}, {16003, 21667}, {16220, 19902}, {16221, 46414}, {16235, 45681}, {18039, 20299}, {19506, 22823}, {20127, 30511}, {23315, 53567}, {32112, 32125}, {37853, 38401}, {39904, 41719}, {39987, 52010}, {40879, 53710}, {41189, 48286}, {44921, 46686}, {45311, 45688}, {45756, 50342}, {45792, 53369}, {48953, 48958}, {48984, 48989}

X(55121) = isogonal conjugate of X(10420)
X(55121) = isotomic conjugate of X(18878)
X(55121) = polar conjugate of X(687)
X(55121) = perspector of circumconic {{A, B, C, X(2), X(403)}}
X(55121) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 10420}, {3, 36114}, {19, 43755}, {31, 18878}, {48, 687}, {63, 32708}, {110, 36053}, {162, 5504}, {163, 2986}, {661, 18879}, {662, 14910}, {1101, 15328}, {1300, 4575}, {15454, 36034}, {32680, 52557}, {36061, 38936}, {36145, 52505}
X(55121) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 17702}, {125, 13558}, {131, 2931}, {265, 5961}, {12121, 13496}, {12310, 34844}, {34310, 52153}
X(55121) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 18878}, {3, 10420}, {6, 43755}, {113, 110}, {115, 2986}, {125, 5504}, {136, 1300}, {244, 36053}, {523, 15328}, {647, 15421}, {1084, 14910}, {1249, 687}, {2088, 323}, {3003, 2407}, {3134, 43574}, {3162, 32708}, {3258, 15454}, {3580, 10411}, {6334, 3268}, {16178, 4}, {16221, 38936}, {34834, 99}, {35588, 1147}, {36103, 36114}, {36830, 18879}, {36901, 40832}, {39005, 3}, {39013, 52505}, {39021, 2}, {46414, 17702}, {47230, 44427}
X(55121) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2, 39021}, {4, 16221}, {74, 125}, {94, 115}, {110, 46085}, {323, 10413}, {476, 39170}, {925, 131}, {16237, 3003}, {18808, 523}, {18878, 2}, {41512, 113}, {44427, 1637}, {51967, 15526}, {53953, 3}
X(55121) = X(i)-complementary conjugate of X(j) for these {i, j}: {1, 16221}, {31, 39021}, {162, 46085}, {687, 20305}, {2986, 21253}, {4575, 131}, {5504, 34846}, {10420, 10}, {14910, 8287}, {18878, 2887}, {18879, 4369}, {32708, 226}, {36034, 39170}, {36053, 125}, {36114, 5}, {43755, 18589}
X(55121) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {687, 21270}, {2986, 21294}, {10420, 8}, {14910, 21221}, {18878, 6327}, {18879, 7192}, {32708, 5905}, {36053, 3448}, {36114, 4}, {43755, 4329}
X(55121) = X(i)-cross conjugate of X(j) for these {i, j}: {686, 6334}, {21731, 47236}, {39021, 2}, {46414, 17702}
X(55121) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(17702)}}, {{A, B, C, X(6), X(14984)}}, {{A, B, C, X(30), X(113)}}, {{A, B, C, X(64), X(5663)}}, {{A, B, C, X(66), X(542)}}, {{A, B, C, X(67), X(3564)}}, {{A, B, C, X(74), X(13754)}}, {{A, B, C, X(110), X(136)}}, {{A, B, C, X(125), X(520)}}, {{A, B, C, X(131), X(265)}}, {{A, B, C, X(338), X(525)}}, {{A, B, C, X(476), X(16221)}}, {{A, B, C, X(511), X(1177)}}, {{A, B, C, X(512), X(8754)}}, {{A, B, C, X(523), X(925)}}, {{A, B, C, X(524), X(3580)}}, {{A, B, C, X(526), X(2433)}}, {{A, B, C, X(539), X(33565)}}, {{A, B, C, X(541), X(35512)}}, {{A, B, C, X(758), X(1725)}}, {{A, B, C, X(850), X(8675)}}, {{A, B, C, X(895), X(34382)}}, {{A, B, C, X(912), X(10693)}}, {{A, B, C, X(1154), X(1986)}}, {{A, B, C, X(1976), X(2393)}}, {{A, B, C, X(2394), X(46229)}}, {{A, B, C, X(2771), X(43703)}}, {{A, B, C, X(2777), X(43695)}}, {{A, B, C, X(2781), X(34207)}}, {{A, B, C, X(2799), X(16237)}}, {{A, B, C, X(2850), X(3657)}}, {{A, B, C, X(5466), X(9003)}}, {{A, B, C, X(5505), X(8681)}}, {{A, B, C, X(5961), X(38534)}}, {{A, B, C, X(6145), X(32423)}}, {{A, B, C, X(8057), X(14220)}}, {{A, B, C, X(8612), X(32438)}}, {{A, B, C, X(8673), X(35909)}}, {{A, B, C, X(8677), X(42759)}}, {{A, B, C, X(9019), X(12824)}}, {{A, B, C, X(9033), X(14582)}}, {{A, B, C, X(9517), X(35364)}}, {{A, B, C, X(10100), X(34381)}}, {{A, B, C, X(12140), X(39118)}}, {{A, B, C, X(12295), X(44990)}}, {{A, B, C, X(16080), X(34310)}}, {{A, B, C, X(18878), X(39021)}}, {{A, B, C, X(30512), X(43088)}}, {{A, B, C, X(39469), X(44114)}}
X(55121) = barycentric product X(i)*X(j) for these (i, j): {4, 6334}, {113, 2394}, {125, 16237}, {264, 686}, {403, 525}, {1577, 1725}, {2799, 52451}, {3003, 850}, {3267, 44084}, {3580, 523}, {10412, 34834}, {12828, 14977}, {13754, 14618}, {14264, 41079}, {14566, 18781}, {14592, 1986}, {15329, 338}, {18609, 4036}, {18878, 39021}, {21731, 76}, {39170, 44427}, {43673, 53568}, {44138, 647}, {47236, 69}, {52504, 924}
X(55121) = barycentric quotient X(i)/X(j) for these (i, j): {2, 18878}, {3, 43755}, {4, 687}, {6, 10420}, {19, 36114}, {25, 32708}, {110, 18879}, {113, 2407}, {115, 15328}, {125, 15421}, {403, 648}, {512, 14910}, {523, 2986}, {647, 5504}, {661, 36053}, {686, 3}, {850, 40832}, {924, 52505}, {1637, 15454}, {1640, 51456}, {1725, 662}, {1986, 14590}, {2088, 15470}, {2315, 4575}, {2394, 40423}, {2433, 10419}, {2501, 1300}, {3003, 110}, {3580, 99}, {6334, 69}, {10412, 40427}, {12824, 52630}, {12828, 4235}, {13754, 4558}, {14264, 44769}, {14270, 52557}, {14582, 12028}, {15329, 249}, {16221, 44427}, {16237, 18020}, {18609, 52935}, {21731, 6}, {34834, 10411}, {39985, 30528}, {41079, 52552}, {41221, 35361}, {41512, 39295}, {44084, 112}, {44138, 6331}, {47230, 38936}, {47236, 4}, {51821, 32640}, {52000, 41679}, {52451, 2966}, {52504, 46134}, {52743, 39371}, {53568, 34211}
X(55121) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {351, 13291, 14697}, {523, 45147, 526}, {523, 525, 8675}, {523, 526, 9033}, {523, 690, 9003}, {525, 2780, 690}, {2574, 2575, 924}, {5663, 53802, 17702}, {9131, 14698, 110}, {13290, 13291, 351}, {23283, 23284, 1637}, {23870, 23871, 46229}

X(55122) = X(2)X(9131)∩X(30)X(511)

Barycentrics    (b-c)*(b+c)*(2*a^4+(b^2-c^2)^2-a^2*(b^2+c^2)) : :
X(55122) = -X[351]+X[1637], -X[647]+X[12075], -X[669]+X[12077], -X[3268]+X[53365], -X[9147]+X[9979], -X[10190]+X[45689], -X[31296]+X[47126], -X[41298]+X[44445]

See Ivan Pavlov, euclid 5973.

X(55122) lies on these lines: {2, 9131}, {25, 47236}, {30, 511}, {39, 7656}, {98, 3563}, {99, 3565}, {114, 2974}, {115, 2971}, {351, 1637}, {476, 32729}, {620, 6131}, {647, 12075}, {669, 12077}, {850, 50553}, {878, 39644}, {1116, 9175}, {1281, 48408}, {1632, 40866}, {1640, 9135}, {1976, 2395}, {1989, 9178}, {2079, 7669}, {2394, 54659}, {2408, 18007}, {2489, 51513}, {2492, 6140}, {2501, 6562}, {2508, 8574}, {2518, 18117}, {2858, 9133}, {3268, 53365}, {4226, 52035}, {5113, 54267}, {5466, 9123}, {5477, 42663}, {5988, 23770}, {6033, 6334}, {6036, 6132}, {6091, 14977}, {7631, 52584}, {8371, 9125}, {9143, 14698}, {9147, 9979}, {9148, 11123}, {9180, 41895}, {9185, 9485}, {9191, 44010}, {9200, 13304}, {9201, 13305}, {9409, 42553}, {9861, 53263}, {9862, 44427}, {10190, 45689}, {10278, 11176}, {11616, 25644}, {13290, 36255}, {13316, 13320}, {13317, 13319}, {14265, 46039}, {16220, 44202}, {18308, 18309}, {19598, 39842}, {19912, 44203}, {22505, 44921}, {31296, 47126}, {34174, 36875}, {34810, 47082}, {35453, 53247}, {35522, 36955}, {39841, 44826}, {39860, 46609}, {39904, 53374}, {41190, 48286}, {41298, 44445}, {43665, 54978}, {44568, 45317}, {45329, 45680}, {48539, 48947}, {48540, 48980}, {52006, 53166}

X(55122) = isogonal conjugate of X(10425)
X(55122) = perspector of circumconic {{A, B, C, X(2), X(230)}}
X(55122) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 10425}, {3, 36105}, {63, 32697}, {99, 36051}, {110, 8773}, {162, 43705}, {163, 8781}, {662, 2987}, {799, 32654}, {811, 42065}, {3563, 4592}, {4575, 35142}, {23997, 40428}, {24041, 35364}, {34157, 36036}, {36034, 36891}, {36084, 52091}
X(55122) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 23698}, {115, 2079}, {6321, 51460}, {31842, 39828}, {35453, 38736}
X(55122) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 10425}, {114, 99}, {115, 8781}, {125, 43705}, {136, 35142}, {230, 2396}, {244, 8773}, {868, 325}, {1084, 2987}, {2679, 34157}, {3005, 35364}, {3162, 32697}, {3258, 36891}, {5139, 3563}, {17423, 42065}, {34156, 17932}, {35067, 4563}, {36103, 36105}, {36472, 14253}, {38986, 36051}, {38987, 52091}, {38996, 32654}, {39001, 3}, {39069, 662}, {39072, 110}, {41181, 3926}, {51610, 3564}
X(55122) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4, 36472}, {98, 115}, {925, 35067}, {3565, 31842}, {4226, 230}, {17932, 3767}, {35142, 6388}, {44768, 6}, {52035, 5477}, {53149, 512}
X(55122) = X(i)-complementary conjugate of X(j) for these {i, j}: {1, 36472}, {2987, 8287}, {4575, 35067}, {4592, 31842}, {8773, 125}, {8781, 21253}, {10425, 10}, {32654, 16592}, {32697, 226}, {35364, 24040}, {36051, 115}, {36105, 5}, {42065, 16573}, {43705, 34846}
X(55122) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {2987, 21221}, {8773, 3448}, {8781, 21294}, {10425, 8}, {32654, 21220}, {32697, 5905}, {36051, 148}, {36105, 4}
X(55122) = X(i)-cross conjugate of X(j) for these {i, j}: {51610, 3564}
X(55122) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(14645)}}, {{A, B, C, X(4), X(14384)}}, {{A, B, C, X(25), X(14984)}}, {{A, B, C, X(30), X(460)}}, {{A, B, C, X(32), X(34347)}}, {{A, B, C, X(98), X(2974)}}, {{A, B, C, X(99), X(3566)}}, {{A, B, C, X(114), X(511)}}, {{A, B, C, X(115), X(525)}}, {{A, B, C, X(230), X(524)}}, {{A, B, C, X(325), X(36898)}}, {{A, B, C, X(512), X(2971)}}, {{A, B, C, X(520), X(20975)}}, {{A, B, C, X(521), X(4516)}}, {{A, B, C, X(523), X(8754)}}, {{A, B, C, X(526), X(9178)}}, {{A, B, C, X(538), X(51481)}}, {{A, B, C, X(542), X(36875)}}, {{A, B, C, X(543), X(41895)}}, {{A, B, C, X(661), X(8774)}}, {{A, B, C, X(690), X(4226)}}, {{A, B, C, X(732), X(12829)}}, {{A, B, C, X(740), X(1733)}}, {{A, B, C, X(758), X(8772)}}, {{A, B, C, X(924), X(2489)}}, {{A, B, C, X(1510), X(18105)}}, {{A, B, C, X(2393), X(44099)}}, {{A, B, C, X(2395), X(2799)}}, {{A, B, C, X(2782), X(14265)}}, {{A, B, C, X(2858), X(9131)}}, {{A, B, C, X(3455), X(13754)}}, {{A, B, C, X(5969), X(47734)}}, {{A, B, C, X(6368), X(41221)}}, {{A, B, C, X(8677), X(42752)}}, {{A, B, C, X(11599), X(28526)}}, {{A, B, C, X(31842), X(34382)}}
X(55122) = barycentric product X(i)*X(j) for these (i, j): {114, 2395}, {115, 4226}, {230, 523}, {460, 525}, {512, 51481}, {1577, 8772}, {1637, 36875}, {1640, 34174}, {1648, 52035}, {1692, 850}, {1733, 661}, {2394, 51431}, {2501, 3564}, {2799, 51820}, {3267, 44099}, {5466, 5477}, {14265, 3569}, {14618, 52144}, {20578, 6782}, {20579, 6783}, {35136, 51613}, {36472, 44768}, {41181, 685}, {42663, 76}, {43665, 51335}, {44145, 647}, {47734, 804}, {52450, 690}
X(55122) = barycentric quotient X(i)/X(j) for these (i, j): {6, 10425}, {19, 36105}, {25, 32697}, {114, 2396}, {230, 99}, {460, 648}, {512, 2987}, {523, 8781}, {647, 43705}, {661, 8773}, {669, 32654}, {798, 36051}, {1637, 36891}, {1692, 110}, {1733, 799}, {2395, 40428}, {2422, 2065}, {2489, 3563}, {2491, 34157}, {2501, 35142}, {3049, 42065}, {3124, 35364}, {3564, 4563}, {3569, 52091}, {4226, 4590}, {5477, 5468}, {6132, 14253}, {8772, 662}, {12829, 17941}, {14265, 43187}, {14384, 44768}, {34174, 6035}, {41181, 6333}, {42663, 6}, {44099, 112}, {44145, 6331}, {47734, 18829}, {51335, 2421}, {51431, 2407}, {51481, 670}, {51613, 3566}, {51820, 2966}, {52035, 52940}, {52144, 4558}, {52450, 892}
X(55122) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9131, 45687}, {2, 9134, 45688}, {523, 23878, 826}, {523, 2793, 690}, {523, 804, 2799}, {2501, 6562, 8651}, {2782, 53796, 23698}, {2869, 2872, 512}, {3413, 3414, 3566}, {5466, 9123, 9189}, {6132, 7663, 44817}, {7663, 44817, 37742}, {9148, 11123, 14417}, {10278, 11176, 44564}, {10278, 14610, 11176}, {11616, 44823, 39477}

X(55123) = X(30)X(511)∩X(116)X(17463)

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

See Ivan Pavlov, euclid 5973.

X(55123) lies on these lines: {30, 511}, {101, 26705}, {103, 41905}, {116, 17463}, {118, 20622}, {676, 28346}, {1282, 47695}, {3730, 46042}, {15064, 30692}

X(55123) = isogonal conjugate of X(35184)
X(55123) = perspector of circumconic {{A, B, C, X(2), X(25259)}}
X(55123) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 35184}, {3, 36109}, {63, 32701}, {911, 43190}, {14377, 36039}, {26705, 36056}
X(55123) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 35184}, {116, 103}, {1566, 14377}, {3162, 32701}, {6586, 2400}, {20622, 26705}, {23972, 43190}, {36103, 36109}
X(55123) = X(i)-Ceva conjugate of X(j) for these {i, j}: {101, 118}, {18025, 40618}, {41321, 516}
X(55123) = X(i)-complementary conjugate of X(j) for these {i, j}: {911, 40618}, {32642, 40606}, {32701, 226}, {35184, 10}, {36109, 5}
X(55123) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {32701, 5905}, {35184, 8}, {36039, 17732}, {36109, 4}
X(55123) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(39993)}}, {{A, B, C, X(103), X(20622)}}, {{A, B, C, X(116), X(514)}}, {{A, B, C, X(118), X(916)}}, {{A, B, C, X(513), X(17463)}}, {{A, B, C, X(516), X(21665)}}, {{A, B, C, X(523), X(21045)}}, {{A, B, C, X(674), X(35517)}}, {{A, B, C, X(676), X(4977)}}, {{A, B, C, X(1734), X(3900)}}, {{A, B, C, X(1897), X(40618)}}, {{A, B, C, X(2398), X(23887)}}, {{A, B, C, X(2772), X(4184)}}, {{A, B, C, X(2784), X(33297)}}, {{A, B, C, X(2801), X(3681)}}, {{A, B, C, X(2808), X(3730)}}, {{A, B, C, X(5845), X(17233)}}, {{A, B, C, X(6586), X(9000)}}, {{A, B, C, X(8677), X(42756)}}
X(55123) = barycentric product X(i)*X(j) for these (i, j): {116, 2398}, {1734, 30807}, {17233, 676}, {17463, 42719}, {25259, 516}, {35517, 6586}, {40618, 41321}
X(55123) = barycentric quotient X(i)/X(j) for these (i, j): {6, 35184}, {19, 36109}, {25, 32701}, {116, 2400}, {516, 43190}, {676, 14377}, {1734, 36101}, {1886, 26705}, {2426, 15378}, {3730, 677}, {6586, 103}, {15624, 36039}, {20974, 2424}, {21133, 15634}, {22388, 32657}, {25259, 18025}, {35517, 31624}

X(55124) = X(1)X(44428)∩X(30)X(511)

Barycentrics    (a-b-c)*(b-c)*(-(a^3*b*c*(b+c))+a*b*(b-c)^2*c*(b+c)+a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2-b*c+c^2)-a^2*(b-c)^2*(2*b^2+3*b*c+2*c^2)) : :
X(55124) = -X[19925]+X[44929], -X[21112]+X[42455]

See Ivan Pavlov, euclid 5973.

X(55124) lies on these lines: {1, 44428}, {30, 511}, {102, 32706}, {109, 14544}, {124, 20620}, {946, 39534}, {1125, 44815}, {6718, 24025}, {10015, 14312}, {19925, 44929}, {21112, 42455}

X(55124) = isogonal conjugate of X(35187)
X(55124) = perspector of circumconic {{A, B, C, X(2), X(46110)}}
X(55124) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 35187}, {3, 36113}, {63, 32707}, {1415, 2988}, {32706, 36059}, {36040, 54243}
X(55124) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 35187}, {117, 109}, {1146, 2988}, {3162, 32707}, {8607, 2406}, {10017, 54243}, {20620, 32706}, {36103, 36113}
X(55124) = X(i)-Ceva conjugate of X(j) for these {i, j}: {102, 124}, {53152, 522}
X(55124) = X(i)-complementary conjugate of X(j) for these {i, j}: {32707, 226}, {35187, 10}, {36113, 5}
X(55124) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {32707, 5905}, {35187, 8}, {36113, 4}
X(55124) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(109), X(20620)}}, {{A, B, C, X(117), X(515)}}, {{A, B, C, X(517), X(1735)}}, {{A, B, C, X(521), X(24026)}}, {{A, B, C, X(522), X(21666)}}, {{A, B, C, X(952), X(10570)}}, {{A, B, C, X(2773), X(7450)}}, {{A, B, C, X(2818), X(54242)}}, {{A, B, C, X(8607), X(8679)}}, {{A, B, C, X(8677), X(35015)}}, {{A, B, C, X(8999), X(35519)}}, {{A, B, C, X(13754), X(40081)}}
X(55124) = barycentric product X(i)*X(j) for these (i, j): {117, 2399}, {1735, 4391}, {35519, 8607}
X(55124) = barycentric quotient X(i)/X(j) for these (i, j): {6, 35187}, {19, 36113}, {25, 32707}, {117, 2406}, {522, 2988}, {1735, 651}, {2432, 15379}, {3064, 32706}, {7450, 52378}, {8607, 109}
X(55124) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2804, 6369, 23887}

X(55125) = X(30)X(511)∩X(103)X(917)

Barycentrics    (b-c)*(b^5-b^3*c^2-b^2*c^3+c^5-a*(b^2-c^2)^2+a^3*(b^2+c^2)-a^2*(b^3+c^3)) : :
X(55125) = -X[4077]+X[23726], -X[6591]+X[21184]

See Ivan Pavlov, euclid 5973.

X(55125) lies on these lines: {30, 511}, {101, 1305}, {103, 917}, {116, 2973}, {118, 34335}, {150, 47680}, {1282, 48408}, {2501, 23723}, {2504, 40940}, {2977, 28346}, {4077, 23726}, {6591, 21184}, {6710, 16578}, {10708, 53380}, {11712, 11797}, {14838, 33525}, {17094, 23806}, {23737, 40166}

X(55125) = isogonal conjugate of X(35182)
X(55125) = perspector of circumconic {{A, B, C, X(2), X(46107)}}
X(55125) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 35182}, {3, 36107}, {63, 32699}, {692, 2989}, {906, 917}, {36039, 54233}
X(55125) = X(i)-vertex conjugate of X(j) for these {i, j}: {116, 54063}
X(55125) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 35182}, {118, 101}, {1086, 2989}, {1566, 54233}, {3162, 32699}, {5190, 917}, {8608, 2398}, {36103, 36107}, {39003, 3}
X(55125) = X(i)-Ceva conjugate of X(j) for these {i, j}: {103, 116}, {53150, 514}
X(55125) = X(i)-complementary conjugate of X(j) for these {i, j}: {2989, 21252}, {32699, 226}, {35182, 10}, {36107, 5}
X(55125) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {2989, 21293}, {32699, 5905}, {35182, 8}, {36107, 4}
X(55125) = intersection, other than A, B, C, of circumconics {{A, B, C, X(101), X(5190)}}, {{A, B, C, X(103), X(916)}}, {{A, B, C, X(118), X(516)}}, {{A, B, C, X(514), X(1305)}}, {{A, B, C, X(518), X(1736)}}, {{A, B, C, X(519), X(48381)}}, {{A, B, C, X(520), X(4466)}}, {{A, B, C, X(521), X(4858)}}, {{A, B, C, X(525), X(21207)}}, {{A, B, C, X(674), X(8608)}}, {{A, B, C, X(2774), X(4243)}}, {{A, B, C, X(2808), X(54232)}}, {{A, B, C, X(3261), X(9000)}}, {{A, B, C, X(8677), X(42754)}}, {{A, B, C, X(13754), X(40076)}}
X(55125) = barycentric product X(i)*X(j) for these (i, j): {118, 2400}, {1736, 693}, {3261, 8608}, {21207, 4243}, {46107, 916}, {48381, 514}
X(55125) = barycentric quotient X(i)/X(j) for these (i, j): {6, 35182}, {19, 36107}, {25, 32699}, {118, 2398}, {514, 2989}, {676, 54233}, {916, 1331}, {1736, 100}, {2253, 906}, {2424, 15380}, {4243, 4570}, {7649, 917}, {8608, 101}, {48381, 190}, {54232, 677}
X(55125) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {824, 28161, 23879}

X(55126) = X(11)X(2969)∩X(30)X(511)

Barycentrics    (b-c)*(a^3*(b+c)-a*(b-c)^2*(b+c)+(b^2-c^2)^2-a^2*(b^2+c^2)) : :
X(55126) = -X[656]+X[21119], -X[665]+X[47137], -X[1769]+X[21132], -X[3960]+X[21180], -X[4017]+X[21102], -X[10015]+X[21112], -X[14429]+X[14430], -X[21105]+X[53532], -X[25569]+X[28114], -X[48350]+X[48400]

See Ivan Pavlov, euclid 5973.

X(55126) lies on these lines: {11, 2969}, {30, 511}, {80, 47680}, {100, 13397}, {104, 915}, {119, 34332}, {656, 21119}, {659, 14667}, {665, 47137}, {676, 15253}, {1411, 30725}, {1635, 14400}, {1769, 21132}, {2501, 43060}, {2977, 3035}, {3669, 47394}, {3960, 21180}, {4017, 21102}, {6713, 44815}, {7649, 51648}, {9131, 9978}, {9810, 13264}, {9811, 13263}, {9979, 9980}, {10015, 21112}, {11125, 14413}, {13266, 47695}, {13277, 48326}, {14312, 42455}, {14429, 14430}, {21104, 23758}, {21105, 53532}, {21202, 43041}, {23678, 26078}, {23732, 48346}, {23745, 23757}, {23779, 23781}, {25569, 28114}, {26275, 42454}, {38325, 47705}, {39478, 44805}, {41191, 48286}, {43974, 50333}, {44409, 48283}, {48350, 48400}, {48539, 48690}, {48540, 48691}, {48959, 48965}, {48990, 48997}, {53342, 53364}

X(55126) = isogonal conjugate of X(6099)
X(55126) = perspector of circumconic {{A, B, C, X(2), X(1737)}}
X(55126) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6099}, {3, 36106}, {63, 32698}, {100, 36052}, {101, 2990}, {109, 45393}, {906, 37203}, {913, 1332}, {915, 1331}, {3657, 4570}, {32656, 46133}, {36037, 39173}
X(55126) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 5840}, {11, 14667}, {18862, 24466}
X(55126) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 6099}, {11, 45393}, {119, 100}, {1015, 2990}, {3162, 32698}, {3259, 39173}, {5190, 37203}, {5521, 915}, {8054, 36052}, {8609, 2397}, {36103, 36106}, {39002, 3}, {42769, 513}, {50330, 3657}, {53525, 4511}
X(55126) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4, 15608}, {104, 11}, {13397, 42423}, {18815, 1086}, {43933, 513}, {44428, 53522}
X(55126) = X(i)-complementary conjugate of X(j) for these {i, j}: {1, 15608}, {1331, 42423}, {2990, 116}, {6099, 10}, {32655, 1086}, {32698, 226}, {36052, 11}, {36106, 5}, {45393, 124}
X(55126) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {2990, 150}, {6099, 8}, {32655, 4440}, {32698, 5905}, {36052, 149}, {36106, 4}, {45393, 33650}
X(55126) = X(i)-cross conjugate of X(j) for these {i, j}: {42769, 513}
X(55126) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(5840)}}, {{A, B, C, X(6), X(34372)}}, {{A, B, C, X(11), X(521)}}, {{A, B, C, X(30), X(39991)}}, {{A, B, C, X(100), X(5521)}}, {{A, B, C, X(104), X(912)}}, {{A, B, C, X(119), X(517)}}, {{A, B, C, X(513), X(2969)}}, {{A, B, C, X(518), X(8609)}}, {{A, B, C, X(519), X(1737)}}, {{A, B, C, X(520), X(18210)}}, {{A, B, C, X(525), X(16732)}}, {{A, B, C, X(527), X(12831)}}, {{A, B, C, X(528), X(52456)}}, {{A, B, C, X(536), X(48380)}}, {{A, B, C, X(693), X(9001)}}, {{A, B, C, X(758), X(11570)}}, {{A, B, C, X(876), X(928)}}, {{A, B, C, X(914), X(9028)}}, {{A, B, C, X(916), X(2252)}}, {{A, B, C, X(952), X(14266)}}, {{A, B, C, X(2875), X(51824)}}, {{A, B, C, X(3658), X(8674)}}, {{A, B, C, X(3900), X(42069)}}, {{A, B, C, X(8677), X(42753)}}, {{A, B, C, X(13754), X(34442)}}, {{A, B, C, X(23770), X(34381)}}
X(55126) = barycentric product X(i)*X(j) for these (i, j): {119, 2401}, {693, 8609}, {1737, 514}, {2252, 46107}, {7649, 914}, {10015, 14266}, {16082, 42769}, {16732, 3658}, {17924, 912}, {18838, 4391}, {46110, 51649}, {48380, 513}, {52456, 918}
X(55126) = barycentric quotient X(i)/X(j) for these (i, j): {6, 6099}, {19, 36106}, {25, 32698}, {119, 2397}, {513, 2990}, {649, 36052}, {650, 45393}, {667, 32655}, {912, 1332}, {914, 4561}, {1737, 190}, {2252, 1331}, {2423, 15381}, {3125, 3657}, {3310, 39173}, {3658, 4567}, {6591, 915}, {7649, 37203}, {8609, 100}, {11570, 4585}, {14266, 13136}, {17924, 46133}, {18838, 651}, {48380, 668}, {51649, 1813}, {51824, 32641}, {52456, 666}
X(55126) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {514, 522, 9001}, {523, 6362, 4777}, {523, 900, 2804}, {659, 53304, 39200}, {900, 6366, 8674}, {2804, 2826, 900}, {3307, 3308, 15313}, {6550, 35013, 513}, {21112, 53527, 10015}, {30725, 53522, 53314}, {39478, 46610, 44807}, {44805, 44807, 39478}

X(55127) = X(30)X(511)∩X(107)X(1301)

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

See Ivan Pavlov, euclid 5973.

X(55127) lies on these lines: {30, 511}, {107, 1301}, {122, 35968}, {133, 50937}, {1294, 5897}, {14703, 53255}

X(55127) = isogonal conjugate of X(46968)
X(55127) = perspector of circumconic {{A, B, C, X(2), X(1559)}}
X(55127) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46968}, {255, 39464}, {14379, 36043}
X(55127) = X(i)-vertex conjugate of X(j) for these {i, j}: {133, 54068}
X(55127) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46968}, {122, 1294}, {6523, 39464}, {6587, 2416}, {14345, 41077}, {35579, 14379}, {50937, 1301}
X(55127) = X(i)-Ceva conjugate of X(j) for these {i, j}: {107, 133}, {5897, 35968}, {15459, 1249}
X(55127) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {39464, 5906}, {46968, 8}
X(55127) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(2777)}}, {{A, B, C, X(30), X(133)}}, {{A, B, C, X(107), X(8057)}}, {{A, B, C, X(122), X(520)}}, {{A, B, C, X(1249), X(9530)}}, {{A, B, C, X(1294), X(15311)}}, {{A, B, C, X(2404), X(39473)}}, {{A, B, C, X(2790), X(14615)}}, {{A, B, C, X(2816), X(5930)}}, {{A, B, C, X(2822), X(8804)}}, {{A, B, C, X(2828), X(52345)}}, {{A, B, C, X(5663), X(51895)}}, {{A, B, C, X(5897), X(6000)}}, {{A, B, C, X(6587), X(9007)}}, {{A, B, C, X(14249), X(53803)}}, {{A, B, C, X(30211), X(35968)}}
X(55127) = barycentric product X(i)*X(j) for these (i, j): {122, 2404}, {1559, 525}, {20580, 51385}, {51358, 8057}
X(55127) = barycentric quotient X(i)/X(j) for these (i, j): {6, 46968}, {122, 2416}, {393, 39464}, {1559, 648}, {1562, 43701}, {2404, 44181}, {2442, 15384}, {6000, 46639}, {6525, 32646}, {6587, 1294}, {14345, 53789}, {51358, 53639}
X(55127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 6086, 9033}, {6086, 9033, 2848}

X(55128) = X(30)X(511)∩X(117)X(14304)

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

See Ivan Pavlov, euclid 5973.

X(55128) lies on these lines: {30, 511}, {102, 41904}, {109, 23987}, {117, 14304}, {124, 34588}, {946, 14312}, {11700, 53522}, {48286, 54081}

X(55128) = isogonal conjugate of X(35183)
X(55128) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 35183}, {3, 36108}, {63, 32700}, {102, 36050}, {10570, 36040}, {26704, 36055}, {32653, 36100}, {32677, 44765}
X(55128) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 35183}, {124, 102}, {3162, 32700}, {6589, 2399}, {10017, 10570}, {23986, 44765}, {36103, 36108}, {51221, 26704}
X(55128) = X(i)-Ceva conjugate of X(j) for these {i, j}: {109, 117}, {23987, 515}, {34393, 40626}, {41904, 38977}
X(55128) = X(i)-complementary conjugate of X(j) for these {i, j}: {32677, 40626}, {32700, 226}, {35183, 10}, {36050, 117}, {36055, 38977}, {36108, 5}
X(55128) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {32700, 5905}, {35183, 8}, {36050, 151}, {36108, 4}
X(55128) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(39992)}}, {{A, B, C, X(102), X(51221)}}, {{A, B, C, X(124), X(522)}}, {{A, B, C, X(515), X(41904)}}, {{A, B, C, X(517), X(34242)}}, {{A, B, C, X(521), X(14304)}}, {{A, B, C, X(573), X(2807)}}, {{A, B, C, X(653), X(40626)}}, {{A, B, C, X(758), X(11700)}}, {{A, B, C, X(952), X(54243)}}, {{A, B, C, X(2779), X(4225)}}, {{A, B, C, X(2800), X(3869)}}, {{A, B, C, X(2818), X(10571)}}, {{A, B, C, X(6589), X(8999)}}, {{A, B, C, X(8677), X(42755)}}, {{A, B, C, X(8679), X(35516)}}
X(55128) = barycentric product X(i)*X(j) for these (i, j): {124, 2406}, {4417, 53522}, {14304, 17080}, {23987, 40626}, {24035, 34588}, {35516, 6589}
X(55128) = barycentric quotient X(i)/X(j) for these (i, j): {6, 35183}, {19, 36108}, {25, 32700}, {124, 2399}, {515, 44765}, {2182, 36050}, {2425, 15386}, {6589, 102}, {8755, 26704}, {21189, 36100}, {53522, 13478}
X(55128) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {522, 2846, 2849}, {6087, 39471, 515}

X(55129) = X(30)X(511)∩X(112)X(1289)

Barycentrics    (b-c)*(b+c)*(-a^4+b^4+c^4)*(-2*a^6+a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)) : :
X(55129) = -X[2485]+Y[12772], -X[10192]+X[14345]

See Ivan Pavlov, euclid 5973.

X(55129) lies on these lines: {30, 511}, {112, 1289}, {127, 47413}, {132, 50938}, {1297, 34168}, {2507, 38652}, {6333, 46164}, {9131, 13114}, {9157, 9979}, {10192, 14345}, {13526, 46099}, {14273, 40234}, {16230, 19165}, {19164, 53345}, {25644, 34217}, {41188, 48286}, {46614, 52737}, {48539, 48954}, {48540, 48985}

X(55129) = isogonal conjugate of X(46967)
X(55129) = perspector of circumconic {{A, B, C, X(2), X(21458)}}
X(55129) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46967}, {14376, 36046}
X(55129) = X(i)-vertex conjugate of X(j) for these {i, j}: {132, 34131}
X(55129) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46967}, {127, 1297}, {2485, 2419}, {23976, 44766}, {33504, 14376}, {47413, 46164}, {50938, 1289}
X(55129) = X(i)-Ceva conjugate of X(j) for these {i, j}: {112, 132}, {685, 206}, {23977, 1503}, {34168, 53822}
X(55129) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {36046, 41361}, {46967, 8}
X(55129) = intersection, other than A, B, C, of circumconics {{A, B, C, X(22), X(2781)}}, {{A, B, C, X(30), X(11605)}}, {{A, B, C, X(112), X(8673)}}, {{A, B, C, X(127), X(525)}}, {{A, B, C, X(132), X(511)}}, {{A, B, C, X(315), X(2794)}}, {{A, B, C, X(520), X(2485)}}, {{A, B, C, X(1297), X(34146)}}, {{A, B, C, X(1503), X(34168)}}, {{A, B, C, X(2393), X(30737)}}, {{A, B, C, X(2825), X(4456)}}, {{A, B, C, X(2831), X(4463)}}, {{A, B, C, X(8743), X(53795)}}, {{A, B, C, X(9019), X(28343)}}, {{A, B, C, X(9530), X(52448)}}, {{A, B, C, X(13754), X(40080)}}, {{A, B, C, X(14917), X(42671)}}, {{A, B, C, X(23881), X(46151)}}
X(55129) = barycentric product X(i)*X(j) for these (i, j): {127, 2409}, {1503, 33294}, {2485, 30737}, {21458, 23881}, {34211, 53569}, {39473, 52448}
X(55129) = barycentric quotient X(i)/X(j) for these (i, j): {6, 46967}, {127, 2419}, {1503, 44766}, {2409, 44183}, {2445, 15388}, {2485, 1297}, {8743, 44770}, {16318, 1289}, {17409, 32649}, {21458, 53657}, {33294, 35140}, {38356, 2435}, {53569, 43673}
X(55129) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 2881, 2799}, {2799, 2848, 2881}, {2848, 55127, 9530}

X(55130) = X(30)X(511)∩X(476)X(2407)

Barycentrics    (b-c)*(b+c)*(-a^2+b^2-b*c+c^2)*(-a^2+b^2+b*c+c^2)*(2*a^8+(b^2-c^2)^4-2*a^6*(b^2+c^2)-a^4*(b^4-4*b^2*c^2+c^4)) : :
X(55130) = -X[3268]+X[52149], -X[14273]+X[47322]

See Ivan Pavlov, euclid 5973.

X(55130) lies on these lines: {30, 511}, {186, 14222}, {476, 2407}, {477, 32710}, {3258, 16186}, {3268, 52149}, {9131, 9158}, {9979, 41626}, {14273, 47322}, {14989, 18808}, {15453, 17511}, {16230, 47327}, {20957, 50472}, {22104, 24975}, {25641, 42424}, {34291, 47219}, {53255, 54077}

X(55130) = isogonal conjugate of X(35189)
X(55130) = perspector of circumconic {{A, B, C, X(2), X(44427)}}
X(55130) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 35189}, {3, 36116}, {63, 32711}, {32710, 36061}, {36034, 51349}
X(55130) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 35189}, {526, 53234}, {3018, 2410}, {3162, 32711}, {3258, 51349}, {16221, 32710}, {25641, 476}, {36103, 36116}, {46414, 39170}
X(55130) = X(i)-Ceva conjugate of X(j) for these {i, j}: {477, 3258}, {10420, 42424}, {53158, 526}
X(55130) = X(i)-complementary conjugate of X(j) for these {i, j}: {32711, 226}, {35189, 10}, {36061, 42424}, {36116, 5}
X(55130) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {32711, 5905}, {35189, 8}, {36116, 4}
X(55130) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(5962)}}, {{A, B, C, X(186), X(13754)}}, {{A, B, C, X(476), X(16221)}}, {{A, B, C, X(477), X(17702)}}, {{A, B, C, X(520), X(15470)}}, {{A, B, C, X(523), X(7471)}}, {{A, B, C, X(526), X(10420)}}, {{A, B, C, X(542), X(3018)}}, {{A, B, C, X(3258), X(9033)}}, {{A, B, C, X(3268), X(9003)}}, {{A, B, C, X(5663), X(15468)}}, {{A, B, C, X(8675), X(9213)}}
X(55130) = barycentric product X(i)*X(j) for these (i, j): {2411, 25641}, {3018, 3268}, {15468, 41079}, {17702, 44427}, {34150, 5664}
X(55130) = barycentric quotient X(i)/X(j) for these (i, j): {6, 35189}, {19, 36116}, {25, 32711}, {1637, 51349}, {2088, 15453}, {2436, 15396}, {3018, 476}, {7471, 39295}, {15468, 44769}, {18334, 53234}, {25641, 2410}, {34150, 39290}, {47230, 32710}, {52743, 15469}
X(55130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {186, 15470, 44808}, {30511, 43088, 15328}

X(55131) = X(23)X(9131)∩X(30)X(511)

Barycentrics    (b-c)*(b+c)*(-2*a^2+b^2+c^2)*(a^6*(b^2+c^2)-a^4*(b^2+c^2)^2+(b^2-c^2)^2*(b^4-b^2*c^2+c^4)-a^2*(b^6-2*b^4*c^2-2*b^2*c^4+c^6)) : :
X(55131) = -X[23]+X[9131], -X[187]+X[14273], -X[7426]+X[45687], -X[45688]+X[47097]

See Ivan Pavlov, euclid 5973.

X(55131) lies on these lines: {23, 9131}, {30, 511}, {187, 14273}, {323, 14698}, {468, 52476}, {476, 5468}, {477, 23700}, {691, 53351}, {842, 40118}, {858, 9134}, {1648, 3258}, {2501, 24855}, {5099, 48317}, {5203, 52475}, {7426, 45687}, {7468, 14221}, {8430, 47138}, {9213, 9979}, {11053, 22104}, {11123, 47219}, {14731, 45291}, {18311, 44814}, {35522, 51479}, {37742, 40544}, {41185, 48286}, {45688, 47097}

X(55131) = isogonal conjugate of X(35191)
X(55131) = perspector of circumconic {{A, B, C, X(2), X(54395)}}
X(55131) = X(i)-vertex conjugate of X(j) for these {i, j}: {5099, 14729}
X(55131) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 35191}, {1649, 51480}, {2493, 50941}, {16188, 691}, {35582, 51474}, {48317, 40118}
X(55131) = X(i)-Ceva conjugate of X(j) for these {i, j}: {842, 5099}, {53156, 690}
X(55131) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(5203)}}, {{A, B, C, X(187), X(13754)}}, {{A, B, C, X(468), X(3564)}}, {{A, B, C, X(476), X(55122)}}, {{A, B, C, X(477), X(23698)}}, {{A, B, C, X(512), X(7468)}}, {{A, B, C, X(523), X(14221)}}, {{A, B, C, X(525), X(52628)}}, {{A, B, C, X(526), X(10425)}}, {{A, B, C, X(542), X(16188)}}, {{A, B, C, X(691), X(48317)}}, {{A, B, C, X(842), X(14984)}}, {{A, B, C, X(2493), X(2854)}}, {{A, B, C, X(3566), X(52475)}}, {{A, B, C, X(5099), X(9517)}}, {{A, B, C, X(5663), X(23700)}}, {{A, B, C, X(14273), X(55121)}}, {{A, B, C, X(22105), X(45147)}}, {{A, B, C, X(38939), X(53793)}}
X(55131) = barycentric product X(i)*X(j) for these (i, j): {2493, 35522}, {14221, 1648}, {16188, 50942}, {52628, 7468}, {54395, 690}
X(55131) = barycentric quotient X(i)/X(j) for these (i, j): {6, 35191}, {1648, 51480}, {2493, 691}, {14221, 52940}, {14273, 40118}, {16188, 50941}, {54395, 892}

X(55132) = X(5)X(14225)∩X(30)X(511)

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

See Ivan Pavlov, euclid 5973.

X(55132) lies on these lines: {5, 14225}, {30, 511}, {128, 18402}, {137, 20625}, {930, 933}, {1141, 18401}, {3569, 42445}, {6334, 15367}, {8562, 11701}, {10412, 38899}, {11587, 44427}, {11671, 44004}, {13512, 38585}, {14398, 53038}, {14769, 16230}, {24978, 34837}, {38615, 38616}, {44976, 44977}

X(55132) = isogonal conjugate of X(46966)
X(55132) = perspector of circumconic {{A, B, C, X(2), X(14918)}}
X(55132) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46966}, {1141, 36134}, {36129, 46089}
X(55132) = X(i)-vertex conjugate of X(j) for these {i, j}: {128, 54067}, {15959, 20625}
X(55132) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46966}, {137, 1141}, {338, 46138}, {1154, 52603}, {2972, 50463}, {6368, 43083}, {6663, 476}, {12077, 2413}, {14920, 18831}, {15345, 43965}, {15450, 11077}, {17433, 54}, {18402, 933}, {35591, 25044}
X(55132) = X(i)-Ceva conjugate of X(j) for these {i, j}: {930, 128}, {6662, 3258}, {18401, 20625}, {25043, 43958}, {38899, 137}
X(55132) = X(i)-complementary conjugate of X(j) for these {i, j}: {36134, 128}, {46966, 10}
X(55132) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5), X(32423)}}, {{A, B, C, X(30), X(1263)}}, {{A, B, C, X(128), X(539)}}, {{A, B, C, X(137), X(933)}}, {{A, B, C, X(512), X(41221)}}, {{A, B, C, X(520), X(35442)}}, {{A, B, C, X(523), X(14225)}}, {{A, B, C, X(525), X(41078)}}, {{A, B, C, X(542), X(36412)}}, {{A, B, C, X(924), X(2081)}}, {{A, B, C, X(930), X(6368)}}, {{A, B, C, X(1141), X(18400)}}, {{A, B, C, X(1154), X(18401)}}, {{A, B, C, X(1273), X(5965)}}, {{A, B, C, X(10412), X(25149)}}, {{A, B, C, X(11062), X(44668)}}, {{A, B, C, X(25043), X(25150)}}, {{A, B, C, X(46062), X(53176)}}
X(55132) = barycentric product X(i)*X(j) for these (i, j): {1087, 32679}, {1154, 18314}, {2081, 311}, {3268, 36412}, {12077, 1273}, {14918, 6368}, {41078, 5}, {45793, 526}
X(55132) = barycentric quotient X(i)/X(j) for these (i, j): {6, 46966}, {137, 2413}, {340, 52939}, {1087, 32680}, {1154, 18315}, {2081, 54}, {2290, 36134}, {11062, 933}, {12077, 1141}, {14918, 18831}, {15451, 11077}, {17434, 50463}, {18314, 46138}, {24862, 14582}, {34520, 43965}, {34983, 50433}, {36412, 476}, {39019, 43083}, {41078, 95}, {45793, 35139}
X(55132) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 45147, 25149}

X(55133) = X(30)X(511)∩X(120)X(20621)

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

See Ivan Pavlov, euclid 5973.

X(55133) lies on these lines: {30, 511}, {105, 26703}, {120, 20621}, {676, 6714}, {1292, 26706}, {1358, 4081}, {2402, 28071}, {3904, 10699}, {4453, 24477}, {11523, 49276}, {11716, 48286}, {25568, 30565}

X(55133) = isogonal conjugate of X(35185)
X(55133) = perspector of circumconic {{A, B, C, X(2), X(3434)}}
X(55133) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 35185}, {3, 36111}, {63, 32703}, {919, 44178}, {3433, 36086}, {13577, 32666}, {26706, 36057}, {36041, 54236}, {36146, 40141}
X(55133) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 35185}, {55, 52927}, {3162, 32703}, {5511, 105}, {5519, 54236}, {20621, 26706}, {35094, 13577}, {36103, 36111}, {38980, 44178}, {38989, 3433}, {39014, 40141}
X(55133) = X(i)-Ceva conjugate of X(j) for these {i, j}: {666, 5452}, {1292, 120}, {52927, 2886}
X(55133) = X(i)-complementary conjugate of X(j) for these {i, j}: {32666, 5452}, {32703, 226}, {35185, 10}, {36111, 5}
X(55133) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {32703, 5905}, {35185, 8}, {36111, 4}
X(55133) = intersection, other than A, B, C, of circumconics {{A, B, C, X(105), X(3827)}}, {{A, B, C, X(120), X(34381)}}, {{A, B, C, X(169), X(2809)}}, {{A, B, C, X(513), X(40576)}}, {{A, B, C, X(514), X(21185)}}, {{A, B, C, X(518), X(26703)}}, {{A, B, C, X(521), X(50333)}}, {{A, B, C, X(528), X(3434)}}, {{A, B, C, X(1486), X(2876)}}, {{A, B, C, X(2254), X(15313)}}, {{A, B, C, X(2835), X(34036)}}, {{A, B, C, X(2836), X(4228)}}, {{A, B, C, X(3263), X(9004)}}, {{A, B, C, X(3309), X(5511)}}, {{A, B, C, X(4762), X(26546)}}, {{A, B, C, X(5452), X(6063)}}, {{A, B, C, X(5845), X(37800)}}, {{A, B, C, X(6182), X(11934)}}, {{A, B, C, X(8677), X(42758)}}, {{A, B, C, X(13754), X(40084)}}, {{A, B, C, X(14268), X(28915)}}
X(55133) = barycentric product X(i)*X(j) for these (i, j): {2414, 5511}, {3434, 918}, {11934, 40704}, {20927, 2254}, {21073, 23829}, {21185, 3912}, {26546, 518}, {27826, 4925}, {37800, 50333}
X(55133) = barycentric quotient X(i)/X(j) for these (i, j): {6, 35185}, {19, 36111}, {25, 32703}, {169, 36086}, {665, 3433}, {918, 13577}, {926, 40141}, {1486, 919}, {2254, 44178}, {2428, 15402}, {3434, 666}, {5089, 26706}, {5452, 52927}, {5511, 2402}, {11934, 294}, {20927, 51560}, {21185, 673}, {26546, 2481}, {34036, 36146}, {37800, 927}
X(55133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 6362, 4762}, {2804, 2826, 528}, {42341, 52305, 918}

X(55134) = X(30)X(511)∩X(106)X(2370)

Barycentrics    (2*a-b-c)*(b-c)*(-b^3-3*a*b*c+2*b^2*c+2*b*c^2-c^3+a^2*(b+c)) : :
X(55134) = -X[551]+X[25996]

See Ivan Pavlov, euclid 5973.

X(55134) lies on these lines: {10, 25923}, {30, 511}, {106, 2370}, {121, 4768}, {551, 25996}, {1054, 47695}, {1293, 32704}, {1647, 24026}, {3679, 25020}, {3904, 13541}, {3912, 26568}, {10713, 53342}, {11717, 53522}, {11814, 50333}, {22837, 53314}, {26078, 45700}, {26144, 45701}, {27545, 34619}, {43042, 53594}, {48182, 49554}

X(55134) = isogonal conjugate of X(35186)
X(55134) = perspector of circumconic {{A, B, C, X(2), X(46109)}}
X(55134) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 35186}, {3, 36112}, {63, 32705}, {32704, 36058}, {36042, 54237}
X(55134) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 35186}, {3162, 32705}, {5510, 106}, {5516, 54237}, {20619, 32704}, {36103, 36112}
X(55134) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1293, 121}
X(55134) = X(i)-complementary conjugate of X(j) for these {i, j}: {32705, 226}, {35186, 10}, {36112, 5}
X(55134) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {32705, 5905}, {35186, 8}, {36112, 4}
X(55134) = intersection, other than A, B, C, of circumconics {{A, B, C, X(106), X(2390)}}, {{A, B, C, X(517), X(6095)}}, {{A, B, C, X(519), X(2370)}}, {{A, B, C, X(520), X(14429)}}, {{A, B, C, X(521), X(4768)}}, {{A, B, C, X(1293), X(32475)}}, {{A, B, C, X(2802), X(14923)}}, {{A, B, C, X(2842), X(7419)}}, {{A, B, C, X(3264), X(9026)}}, {{A, B, C, X(3667), X(5510)}}, {{A, B, C, X(4139), X(30572)}}, {{A, B, C, X(8677), X(23757)}}, {{A, B, C, X(14261), X(53790)}}
X(55134) = barycentric product X(i)*X(j) for these (i, j): {2415, 5510}, {14923, 3762}, {32475, 46109}
X(55134) = barycentric quotient X(i)/X(j) for these (i, j): {6, 35186}, {19, 36112}, {25, 32705}, {2429, 15403}, {5510, 2403}, {7419, 4591}, {8756, 32704}, {14425, 54237}, {14923, 3257}, {32475, 1797}

X(55135) = X(2)X(10103)∩X(30)X(511)

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

See Ivan Pavlov, euclid 5973.

X(55135) lies on these lines: {2, 10103}, {30, 511}, {69, 39905}, {111, 2373}, {126, 1560}, {351, 14272}, {1296, 30247}, {1637, 9172}, {2395, 6096}, {2408, 42008}, {2433, 6094}, {2492, 6719}, {3268, 10717}, {5512, 14672}, {6131, 14610}, {6333, 36883}, {7610, 9189}, {8177, 13232}, {9125, 23287}, {9129, 14697}, {9131, 9156}, {9134, 9178}, {9191, 9770}, {10765, 53331}, {11616, 14655}, {11621, 34506}, {14278, 53365}, {14657, 44806}, {34010, 34105}, {40556, 44813}, {40879, 53736}, {41184, 48286}, {53272, 54066}

X(55135) = isogonal conjugate of X(35188)
X(55135) = perspector of circumconic {{A, B, C, X(2), X(11185)}}
X(55135) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 35188}, {3, 36115}, {63, 32709}, {5486, 36142}, {13608, 36045}, {14908, 37217}, {30247, 36060}
X(55135) = X(i)-vertex conjugate of X(j) for these {i, j}: {3, 23699}, {126, 54066}, {10748, 14655}, {14657, 14672}
X(55135) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 35188}, {574, 32583}, {1560, 30247}, {3162, 32709}, {5512, 111}, {10354, 1296}, {23992, 5486}, {31654, 13608}, {36103, 36115}
X(55135) = X(i)-Ceva conjugate of X(j) for these {i, j}: {892, 8542}, {1296, 126}, {2373, 14672}, {34166, 5512}, {41896, 5099}
X(55135) = X(i)-complementary conjugate of X(j) for these {i, j}: {32709, 226}, {35188, 10}, {36060, 14672}, {36115, 5}, {36142, 8542}, {37217, 34517}
X(55135) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {32709, 5905}, {35188, 8}, {36045, 34165}, {36115, 4}, {37217, 34518}
X(55135) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(23699)}}, {{A, B, C, X(30), X(6094)}}, {{A, B, C, X(111), X(1560)}}, {{A, B, C, X(126), X(8681)}}, {{A, B, C, X(511), X(6096)}}, {{A, B, C, X(512), X(10103)}}, {{A, B, C, X(520), X(14417)}}, {{A, B, C, X(524), X(2373)}}, {{A, B, C, X(525), X(35522)}}, {{A, B, C, X(543), X(11185)}}, {{A, B, C, X(1296), X(30209)}}, {{A, B, C, X(1499), X(5512)}}, {{A, B, C, X(1503), X(53773)}}, {{A, B, C, X(1995), X(2854)}}, {{A, B, C, X(2433), X(9023)}}, {{A, B, C, X(2882), X(14948)}}, {{A, B, C, X(3266), X(9027)}}, {{A, B, C, X(3566), X(22105)}}, {{A, B, C, X(8542), X(17430)}}, {{A, B, C, X(8677), X(42760)}}, {{A, B, C, X(9003), X(50942)}}, {{A, B, C, X(9004), X(42713)}}, {{A, B, C, X(9227), X(13493)}}, {{A, B, C, X(9517), X(18311)}}, {{A, B, C, X(13377), X(32424)}}, {{A, B, C, X(13754), X(40078)}}, {{A, B, C, X(14262), X(33962)}}, {{A, B, C, X(14984), X(41614)}}, {{A, B, C, X(36882), X(52229)}}
X(55135) = barycentric product X(i)*X(j) for these (i, j): {1995, 35522}, {2418, 5512}, {11185, 690}, {30209, 44146}, {36890, 44203}, {37855, 525}, {53777, 850}
X(55135) = barycentric quotient X(i)/X(j) for these (i, j): {6, 35188}, {19, 36115}, {25, 32709}, {468, 30247}, {690, 5486}, {1995, 691}, {2434, 15406}, {5512, 2408}, {8542, 32583}, {9125, 13608}, {11185, 892}, {19136, 32729}, {29959, 36827}, {30209, 895}, {34166, 39296}, {37855, 648}, {44203, 9214}, {52174, 32648}, {53777, 110}
X(55135) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2492, 18310, 44564}, {2793, 2799, 543}, {2799, 23878, 46229}, {9178, 14277, 9134}, {9979, 14977, 47138}, {14273, 14417, 18311}, {18311, 35522, 14417}

X(55136) = X(30)X(511)∩X(135)X(136)

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

See Ivan Pavlov, euclid 5973.

X(55136) lies on these lines: {30, 511}, {135, 136}, {925, 4558}, {1299, 1300}, {5961, 43088}, {6334, 39118}, {9131, 52125}, {13558, 16230}, {14910, 47236}, {15328, 15478}, {22823, 44921}, {34840, 44816}, {34843, 34844}

X(55135) = isogonal conjugate of X(46969)
X(55136) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 46969}, {36145, 43756}
X(55136) = X(i)-vertex conjugate of X(j) for these {i, j}: {136, 54069}
X(55136) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 46969}, {131, 925}, {135, 1299}, {35235, 5962}, {39013, 43756}
X(55136) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1300, 136}, {30512, 12095}
X(55136) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(131), X(1299)}}, {{A, B, C, X(135), X(925)}}, {{A, B, C, X(136), X(523)}}, {{A, B, C, X(924), X(13398)}}, {{A, B, C, X(1300), X(44665)}}, {{A, B, C, X(3564), X(16310)}}, {{A, B, C, X(4558), X(15423)}}, {{A, B, C, X(17702), X(43973)}}, {{A, B, C, X(30512), X(43088)}}
X(55136) = barycentric product X(i)*X(j) for these (i, j): {12095, 14618}, {16310, 6563}, {44427, 53169}
X(55136) = barycentric quotient X(i)/X(j) for these (i, j): {6, 46969}, {924, 43756}, {6753, 1299}, {12095, 4558}, {16310, 925}, {47421, 43709}

X(55137) = X(30)X(511)∩X(105)X(15344)

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

See Ivan Pavlov, euclid 5973.

X(55137) lies on these lines: {30, 511}, {105, 15344}, {120, 23770}, {2977, 6714}, {5511, 53990}, {47680, 50911}

X(55137) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(47104)}}, {{A, B, C, X(105), X(34381)}}, {{A, B, C, X(120), X(518)}}, {{A, B, C, X(513), X(23770)}}, {{A, B, C, X(528), X(51832)}}, {{A, B, C, X(918), X(2402)}}, {{A, B, C, X(1738), X(5853)}}, {{A, B, C, X(2775), X(4236)}}, {{A, B, C, X(2826), X(53358)}}, {{A, B, C, X(3290), X(9004)}}, {{A, B, C, X(4468), X(28846)}}, {{A, B, C, X(14267), X(28915)}}
X(55137) = X(i)-isoconjugate-of-X(j) for these {i, j}: {34159, 36041}
X(55137) = X(i)-Dao conjugate of X(j) for these {i, j}: {120, 1292}, {3290, 2414}, {5519, 34159}, {53990, 15344}
X(55137) = X(i)-Ceva conjugate of X(j) for these {i, j}: {105, 5511}, {7233, 40615}
X(55137) = barycentric product X(i)*X(j) for these (i, j): {120, 2402}, {1738, 4468}, {4904, 53358}, {20504, 31638}, {23770, 344}
X(55137) = barycentric quotient X(i)/X(j) for these (i, j): {120, 2414}, {344, 35574}, {1738, 37206}, {2440, 15382}, {3290, 1292}, {3309, 2991}, {20455, 2428}, {23770, 277}

X(55138) = X(30)X(511)∩X(106)X(40101)

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

See Ivan Pavlov, euclid 5973.

X(55138) lies on these lines: {30, 511}, {106, 40101}, {1022, 23678}, {1054, 48408}, {4939, 5510}, {11814, 23770}, {21290, 47680}

X(55138) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(121), X(519)}}, {{A, B, C, X(521), X(4939)}}, {{A, B, C, X(1739), X(3880)}}, {{A, B, C, X(2403), X(23888)}}, {{A, B, C, X(4132), X(4404)}}, {{A, B, C, X(4462), X(29148)}}, {{A, B, C, X(5510), X(32475)}}, {{A, B, C, X(8610), X(9026)}}, {{A, B, C, X(39264), X(53790)}}
X(55138) = X(i)-isoconjugate-of-X(j) for these {i, j}: {34080, 46638}
X(55138) = X(i)-Dao conjugate of X(j) for these {i, j}: {121, 1293}, {8610, 2415}, {40621, 46638}
X(55138) = X(i)-Ceva conjugate of X(j) for these {i, j}: {106, 5510}
X(55138) = barycentric product X(i)*X(j) for these (i, j): {121, 2403}, {1739, 4462}, {16753, 4404}
X(55138) = barycentric quotient X(i)/X(j) for these (i, j): {121, 2415}, {1739, 27834}, {2441, 15383}, {3667, 46638}, {8610, 1293}, {23644, 2429}

X(55139) = X(30)X(511)∩X(108)X(40097)

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

See Ivan Pavlov, euclid 5973.

X(55139) lies on these lines: {30, 511}, {108, 40097}, {14312, 25640}, {53304, 54064}

X(55139) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(39990)}}, {{A, B, C, X(123), X(521)}}, {{A, B, C, X(517), X(25640)}}, {{A, B, C, X(1766), X(2823)}}, {{A, B, C, X(2778), X(16049)}}, {{A, B, C, X(2817), X(21147)}}, {{A, B, C, X(2829), X(3436)}}, {{A, B, C, X(6588), X(9051)}}, {{A, B, C, X(8058), X(21186)}}
X(55139) = X(i)-isoconjugate-of-X(j) for these {i, j}: {36044, 39167}
X(55139) = X(i)-Dao conjugate of X(j) for these {i, j}: {123, 1295}, {6588, 2417}, {35580, 39167}, {53991, 40097}
X(55139) = X(i)-Ceva conjugate of X(j) for these {i, j}: {108, 25640}
X(55139) = barycentric product X(i)*X(j) for these (i, j): {123, 2405}
X(55139) = barycentric quotient X(i)/X(j) for these (i, j): {123, 2417}, {2443, 15385}, {6001, 46640}, {6588, 1295}, {14312, 34277}, {17408, 32647}
X(55139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 6087, 2804}

X(55140) = X(30)X(511)∩X(111)X(2374)

Barycentrics    (b-c)*(b+c)*(-5*a^2+b^2+c^2)*(b^4-4*b^2*c^2+c^4+a^2*(b^2+c^2)) : :
X(55140) = -X[9178]+X[44564]

See Ivan Pavlov, euclid 5973.

X(55140) lies on these lines: {30, 511}, {111, 2374}, {126, 9134}, {1296, 20187}, {2408, 9125}, {5512, 53992}, {6131, 6719}, {9156, 9979}, {9172, 45687}, {9178, 44564}, {11616, 14657}, {16220, 19901}, {41186, 48286}

X(55140) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(34171)}}, {{A, B, C, X(111), X(8681)}}, {{A, B, C, X(126), X(524)}}, {{A, B, C, X(523), X(9134)}}, {{A, B, C, X(543), X(36874)}}, {{A, B, C, X(690), X(2408)}}, {{A, B, C, X(1296), X(20186)}}, {{A, B, C, X(1499), X(20187)}}, {{A, B, C, X(1992), X(14645)}}, {{A, B, C, X(2780), X(11634)}}, {{A, B, C, X(2793), X(53367)}}, {{A, B, C, X(3291), X(9027)}}, {{A, B, C, X(5512), X(30209)}}, {{A, B, C, X(9125), X(33915)}}, {{A, B, C, X(14263), X(33962)}}, {{A, B, C, X(17983), X(52881)}}, {{A, B, C, X(47286), X(52229)}}
X(55140) = perspector of circumconic {{A, B, C, X(2), X(47286)}}
X(55140) = X(i)-isoconjugate-of-X(j) for these {i, j}: {34161, 36045}
X(55140) = X(i)-Dao conjugate of X(j) for these {i, j}: {126, 1296}, {3291, 2418}, {31654, 34161}, {35133, 41909}, {53992, 2374}
X(55140) = X(i)-Ceva conjugate of X(j) for these {i, j}: {111, 5512}, {8599, 21905}, {9133, 11165}, {9227, 35133}, {35179, 52881}
X(55140) = barycentric product X(i)*X(j) for these (i, j): {126, 2408}, {1499, 47286}, {1992, 9134}, {53367, 6791}
X(55140) = barycentric quotient X(i)/X(j) for these (i, j): {126, 2418}, {1499, 41909}, {2408, 44182}, {2444, 15387}, {3291, 1296}, {9125, 34161}, {9134, 5485}, {47286, 35179}, {51819, 32648}
X(55140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9178, 47139, 44564}

X(55141) = X(30)X(511)∩X(476)X(1304)

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

See Ivan Pavlov, euclid 5973.

X(55141) lies on these lines: {30, 511}, {402, 22104}, {476, 1304}, {477, 2693}, {1553, 12369}, {1637, 18487}, {1650, 3258}, {1651, 47219}, {2070, 53255}, {6070, 13212}, {9158, 9979}, {11050, 34312}, {11251, 18809}, {11845, 38700}, {14731, 45289}, {15144, 47627}, {16230, 47324}, {20957, 53320}, {23105, 34104}, {31379, 45681}, {32162, 38609}, {38580, 38595}, {44892, 47004}, {44967, 44992}, {47138, 47322}

X(55141) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(1553)}}, {{A, B, C, X(476), X(9033)}}, {{A, B, C, X(477), X(2777)}}, {{A, B, C, X(520), X(1650)}}, {{A, B, C, X(523), X(6070)}}, {{A, B, C, X(525), X(39290)}}, {{A, B, C, X(526), X(1304)}}, {{A, B, C, X(542), X(35520)}}, {{A, B, C, X(1138), X(32417)}}, {{A, B, C, X(1637), X(9003)}}, {{A, B, C, X(2693), X(5663)}}, {{A, B, C, X(2781), X(47228)}}, {{A, B, C, X(6000), X(52493)}}, {{A, B, C, X(11589), X(13754)}}, {{A, B, C, X(12790), X(20957)}}, {{A, B, C, X(14254), X(16168)}}, {{A, B, C, X(16171), X(53178)}}, {{A, B, C, X(17702), X(25641)}}
X(55141) = perspector of circumconic {{A, B, C, X(2), X(11251)}}
X(55141) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 36117}, {63, 32712}, {477, 36034}, {1304, 36062}, {2159, 30528}, {14385, 36047}, {32640, 36102}, {36151, 44769}
X(55141) = X(i)-Dao conjugate of X(j) for these {i, j}: {1637, 2411}, {3162, 32712}, {3163, 30528}, {3258, 477}, {5663, 53233}, {9033, 53235}, {18809, 1304}, {35581, 14385}, {36103, 36117}
X(55141) = X(i)-Ceva conjugate of X(j) for these {i, j}: {476, 25641}, {2693, 16177}, {11251, 13212}, {34209, 6070}, {53159, 9033}
X(55141) = X(i)-complementary conjugate of X(j) for these {i, j}: {32712, 226}, {36034, 25641}, {36062, 16177}, {36117, 5}
X(55141) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {32712, 5905}, {36034, 34193}, {36117, 4}
X(55141) = X(i)-cross conjugate of X(j) for these {i, j}: {13212, 11251}
X(55141) = barycentric product X(i)*X(j) for these (i, j): {338, 42742}, {1553, 2394}, {1637, 35520}, {2407, 6070}, {2410, 3258}, {11251, 525}, {13212, 648}, {34209, 5664}, {41079, 5663}, {52493, 52624}
X(55141) = barycentric quotient X(i)/X(j) for these (i, j): {19, 36117}, {25, 32712}, {30, 30528}, {1553, 2407}, {1637, 477}, {2437, 15395}, {2631, 36062}, {3258, 2411}, {5663, 44769}, {6070, 2394}, {9409, 32663}, {11251, 648}, {13212, 525}, {14583, 32650}, {34209, 39290}, {36035, 36102}, {39008, 53235}, {42742, 249}, {47228, 1304}, {52493, 34568}, {52743, 34210}
X(55141) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30, 523, 9033}

X(55142) = X(2)X(47219)∩X(30)X(511)

Barycentrics    (b-c)*(b+c)*(-a^4+b^4-b^2*c^2+c^4)*(-2*a^6+2*a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-a^2*(b^4+c^4)) : :
X(55142) = -X[23]+X[9979], -X[187]+X[47138], -X[468]+X[44564], -X[1495]+X[14697], -X[3268]+X[10989], -X[9131]+X[9213]

See Ivan Pavlov, euclid 5973.

X(55142) lies on these lines: {2, 47219}, {23, 9979}, {30, 511}, {186, 25644}, {187, 47138}, {468, 44564}, {476, 2395}, {477, 2710}, {691, 935}, {842, 2697}, {858, 14417}, {1495, 14697}, {1637, 7426}, {2070, 53265}, {3258, 36471}, {3268, 10989}, {5099, 18311}, {5523, 8430}, {5938, 53272}, {7473, 35907}, {9131, 9213}, {11799, 44203}, {16092, 34366}, {16188, 18312}, {16760, 47214}, {17986, 47105}, {18310, 40544}, {22104, 47218}, {25641, 45158}, {30476, 47216}, {41175, 53728}, {41183, 48286}, {44202, 44265}, {44204, 44266}, {44568, 46995}, {44967, 45148}, {50942, 53161}

X(55142) = intersection, other than A, B, C, of circumconics {{A, B, C, X(23), X(511)}}, {{A, B, C, X(30), X(316)}}, {{A, B, C, X(468), X(34366)}}, {{A, B, C, X(476), X(2799)}}, {{A, B, C, X(477), X(2794)}}, {{A, B, C, X(523), X(35907)}}, {{A, B, C, X(524), X(16092)}}, {{A, B, C, X(525), X(7473)}}, {{A, B, C, X(526), X(2492)}}, {{A, B, C, X(542), X(2697)}}, {{A, B, C, X(690), X(935)}}, {{A, B, C, X(691), X(9517)}}, {{A, B, C, X(842), X(2781)}}, {{A, B, C, X(1503), X(17986)}}, {{A, B, C, X(1640), X(3906)}}, {{A, B, C, X(2710), X(5663)}}, {{A, B, C, X(3564), X(51456)}}, {{A, B, C, X(13754), X(54060)}}, {{A, B, C, X(14246), X(53793)}}, {{A, B, C, X(14984), X(16188)}}, {{A, B, C, X(20403), X(53177)}}, {{A, B, C, X(39469), X(42659)}}, {{A, B, C, X(39474), X(53232)}}
X(55142) = perspector of circumconic {{A, B, C, X(2), X(9979)}}
X(55142) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2157, 5649}
X(55142) = X(i)-Dao conjugate of X(j) for these {i, j}: {542, 53232}, {2492, 50942}, {5099, 842}, {23967, 17708}, {35582, 14357}, {35594, 51472}, {40583, 5649}, {42426, 935}
X(55142) = X(i)-Ceva conjugate of X(j) for these {i, j}: {691, 16188}, {2697, 38971}, {20404, 52533}, {53155, 542}
X(55142) = barycentric product X(i)*X(j) for these (i, j): {542, 9979}, {1640, 316}, {16092, 18311}, {18312, 23}, {32313, 671}, {33752, 46786}, {40074, 6041}, {50941, 5099}
X(55142) = barycentric quotient X(i)/X(j) for these (i, j): {23, 5649}, {316, 6035}, {542, 17708}, {1640, 67}, {2492, 842}, {5099, 50942}, {6041, 3455}, {6103, 935}, {9979, 5641}, {18311, 52094}, {18312, 18019}, {23967, 53232}, {32313, 524}, {33752, 46787}, {52951, 51263}
X(55142) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30, 523, 2799}

X(55143) = X(30)X(511)∩X(805)X(877)

Barycentrics    a^2*(b-c)*(b+c)*(-b^4-c^4+a^2*(b^2+c^2))*(-(b^2*c^2*(b^2-c^2)^2)+a^6*(b^2+c^2)+a^2*b^2*c^2*(b^2+c^2)-a^4*(b^2+c^2)^2) : :
X(55143) = -X[3268]+X[33873], -X[25644]+X[35375]

See Ivan Pavlov, euclid 5973.

X(55143) lies on these lines: {30, 511}, {805, 877}, {1637, 47638}, {2076, 53265}, {2679, 38974}, {2698, 48259}, {3268, 33873}, {5996, 46807}, {8029, 23611}, {8430, 51543}, {9979, 11673}, {13170, 53378}, {25644, 35375}

X(55143) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(52446)}}, {{A, B, C, X(511), X(6072)}}, {{A, B, C, X(512), X(6071)}}, {{A, B, C, X(523), X(44114)}}, {{A, B, C, X(524), X(51543)}}, {{A, B, C, X(525), X(41172)}}, {{A, B, C, X(526), X(43112)}}, {{A, B, C, X(804), X(2679)}}, {{A, B, C, X(805), X(39469)}}, {{A, B, C, X(2782), X(48259)}}, {{A, B, C, X(2794), X(37841)}}, {{A, B, C, X(3564), X(51455)}}, {{A, B, C, X(8430), X(23878)}}
X(55143) = perspector of circumconic {{A, B, C, X(2), X(3569)}}
X(55143) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2698, 36036}, {36084, 46142}
X(55143) = X(i)-Dao conjugate of X(j) for these {i, j}: {2679, 2698}, {38987, 46142}
X(55143) = X(i)-Ceva conjugate of X(j) for these {i, j}: {805, 33330}, {16068, 6071}, {48259, 38974}
X(55143) = X(i)-complementary conjugate of X(j) for these {i, j}: {36036, 33330}
X(55143) = barycentric product X(i)*X(j) for these (i, j): {2395, 6072}, {2396, 6071}, {2782, 3569}, {41167, 48452}
X(55143) = barycentric quotient X(i)/X(j) for these (i, j): {2491, 2698}, {2782, 43187}, {3569, 46142}, {6071, 2395}, {6072, 2396}, {16068, 39291}, {44114, 46040}
X(55143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {511, 512, 39469}

X(55144) = X(30)X(511)∩X(653)X(934)

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

See Ivan Pavlov, euclid 5973.

X(55144) lies on these lines: {30, 511}, {653, 934}, {5514, 16596}, {40535, 40555}, {42772, 44993}

X(55144) = intersection, other than A, B, C, of circumconics {{A, B, C, X(516), X(48357)}}, {{A, B, C, X(521), X(16596)}}, {{A, B, C, X(527), X(28344)}}, {{A, B, C, X(653), X(8058)}}, {{A, B, C, X(972), X(50930)}}, {{A, B, C, X(3900), X(5514)}}, {{A, B, C, X(6001), X(43044)}}, {{A, B, C, X(7358), X(13149)}}, {{A, B, C, X(8677), X(42772)}}
X(55144) = perspector of circumconic {{A, B, C, X(2), X(17896)}}
X(55144) = X(i)-isoconjugate-of-X(j) for these {i, j}: {972, 36049}
X(55144) = X(i)-Dao conjugate of X(j) for these {i, j}: {5514, 972}, {35593, 7367}, {50930, 40117}
X(55144) = X(i)-Ceva conjugate of X(j) for these {i, j}: {934, 44993}, {46137, 7358}
X(55144) = X(i)-complementary conjugate of X(j) for these {i, j}: {36049, 44993}
X(55144) = barycentric product X(i)*X(j) for these (i, j): {17896, 971}, {51364, 8058}
X(55144) = barycentric quotient X(i)/X(j) for these (i, j): {971, 13138}, {2272, 36049}, {6129, 972}, {17896, 46137}, {43044, 37141}, {51364, 53642}

X(55145) = X(30)X(511)∩X(4081)X(5514)

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

See Ivan Pavlov, euclid 5973.

X(55145) lies on these lines: {30, 511}, {934, 46964}, {972, 51762}, {4081, 5514}, {13529, 53285}

X(55145) = intersection, other than A, B, C, of circumconics {{A, B, C, X(513), X(42069)}}, {{A, B, C, X(521), X(4081)}}, {{A, B, C, X(934), X(38966)}}, {{A, B, C, X(971), X(44993)}}, {{A, B, C, X(3900), X(46964)}}
X(55145) = X(i)-Dao conjugate of X(j) for these {i, j}: {38966, 51762}, {44993, 934}
X(55145) = X(i)-Ceva conjugate of X(j) for these {i, j}: {972, 5514}

X(55146) = X(30)X(511)∩X(476)X(2720)

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

See Ivan Pavlov, euclid 5973.

X(55146) lies on these lines: {30, 511}, {186, 44807}, {476, 2720}, {477, 2745}, {1290, 2766}, {2070, 53304}, {2687, 2694}

X(55146) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(5080)}}, {{A, B, C, X(476), X(2804)}}, {{A, B, C, X(477), X(2829)}}, {{A, B, C, X(517), X(1325)}}, {{A, B, C, X(521), X(37966)}}, {{A, B, C, X(526), X(2720)}}, {{A, B, C, X(1290), X(2850)}}, {{A, B, C, X(2687), X(2778)}}, {{A, B, C, X(2694), X(2771)}}, {{A, B, C, X(2745), X(5663)}}, {{A, B, C, X(2766), X(5520)}}
X(55146) = X(i)-Dao conjugate of X(j) for these {i, j}: {5520, 2687}
X(55146) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1290, 42422}
X(55146) = barycentric quotient X(i)/X(j) for these (i, j): {47227, 2687}
X(55146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30, 523, 2804}

X(55147) = X(30)X(511)∩X(476)X(6099)

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

See Ivan Pavlov, euclid 5973.

X(55147) lies on these lines: {30, 511}, {476, 6099}, {477, 43078}, {1290, 53952}, {2687, 53921}, {3258, 15608}, {5520, 53988}

X(55147) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(38952)}}, {{A, B, C, X(477), X(5840)}}, {{A, B, C, X(513), X(7477)}}, {{A, B, C, X(526), X(6099)}}, {{A, B, C, X(2771), X(42422)}}, {{A, B, C, X(2850), X(5520)}}, {{A, B, C, X(5172), X(13754)}}, {{A, B, C, X(5663), X(43078)}}
X(55147) = X(i)-Dao conjugate of X(j) for these {i, j}: {42422, 1290}, {53988, 53921}
X(55147) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2687, 5520}
X(55147) = barycentric quotient X(i)/X(j) for these (i, j): {47235, 53921}

X(55148) = X(30)X(511)∩X(477)X(23701)

Barycentrics    (b-c)*(b+c)*(-b^6-4*a^2*b^2*c^2+2*b^4*c^2+2*b^2*c^4-c^6+a^4*(b^2+c^2))*(4*a^6-a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)+a^2*(-4*b^4+6*b^2*c^2-4*c^4)) : :
X(55148) = -X[5913]+X[47138], -X[18311]+X[47219]

See Ivan Pavlov, euclid 5973.

X(55148) lies on these lines: {30, 511}, {476, 35188}, {477, 23701}, {2696, 10098}, {2770, 53929}, {5913, 47138}, {14977, 34320}, {18311, 47219}

X(55148) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(38951)}}, {{A, B, C, X(477), X(23699)}}, {{A, B, C, X(524), X(7426)}}, {{A, B, C, X(526), X(35188)}}, {{A, B, C, X(2780), X(10098)}}, {{A, B, C, X(5663), X(23701)}}, {{A, B, C, X(7482), X(30209)}}, {{A, B, C, X(9027), X(46783)}}
X(55148) = perspector of circumconic {{A, B, C, X(2), X(52483)}}
X(55148) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2696, 31655}
X(55148) = barycentric quotient X(i)/X(j) for these (i, j): {44467, 10098}

X(55149) = X(30)X(511)∩X(759)X(39435)

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

See Ivan Pavlov, euclid 5973.

X(55149) lies on these lines: {30, 511}, {759, 39435}, {1283, 47695}, {4768, 23555}, {6011, 30250}, {31845, 42768}

X(55149) = intersection, other than A, B, C, of circumconics {{A, B, C, X(515), X(5620)}}, {{A, B, C, X(758), X(39435)}}, {{A, B, C, X(6003), X(30250)}}, {{A, B, C, X(6011), X(30212)}}, {{A, B, C, X(6757), X(11101)}}, {{A, B, C, X(8677), X(42768)}}
X(55149) = X(i)-Dao conjugate of X(j) for these {i, j}: {42425, 759}, {53982, 30250}
X(55149) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6011, 31845}
X(55149) = barycentric product X(i)*X(j) for these (i, j): {4707, 5086}
X(55149) = barycentric quotient X(i)/X(j) for these (i, j): {5086, 47318}, {11101, 37140}

X(55150) = X(30)X(511)∩X(1141)X(2383)

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

See Ivan Pavlov, euclid 5973.

X(55150) lies on these lines: {30, 511}, {137, 53986}, {930, 20185}, {1141, 2383}, {3327, 47017}, {14652, 44808}, {14656, 15959}, {39183, 50946}

X(55150) = intersection, other than A, B, C, of circumconics {{A, B, C, X(128), X(1154)}}, {{A, B, C, X(137), X(6368)}}, {{A, B, C, X(231), X(5965)}}, {{A, B, C, X(539), X(1141)}}, {{A, B, C, X(930), X(20184)}}, {{A, B, C, X(1510), X(20185)}}, {{A, B, C, X(13754), X(34418)}}, {{A, B, C, X(25150), X(32535)}}, {{A, B, C, X(40631), X(50708)}}, {{A, B, C, X(43969), X(46002)}}
X(55150) = X(i)-vertex conjugate of X(j) for these {i, j}: {137, 14656}
X(55150) = X(i)-Dao conjugate of X(j) for these {i, j}: {128, 930}, {53986, 2383}
X(55150) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1141, 137}
X(55150) = barycentric product X(i)*X(j) for these (i, j): {128, 2413}, {231, 41298}, {14618, 45083}, {20577, 40631}, {32002, 52742}
X(55150) = barycentric quotient X(i)/X(j) for these (i, j): {231, 930}, {45083, 4558}, {52742, 3519}

X(55151) = X(30)X(511)∩X(1560)X(42665)

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

See Ivan Pavlov, euclid 5973.

X(55151) lies on these lines: {30, 511}, {1560, 42665}, {8428, 14273}, {14655, 44806}, {30247, 39382}

X(55151) = intersection, other than A, B, C, of circumconics {{A, B, C, X(520), X(42665)}}, {{A, B, C, X(524), X(1560)}}, {{A, B, C, X(525), X(47138)}}, {{A, B, C, X(2781), X(19153)}}, {{A, B, C, X(14672), X(30209)}}, {{A, B, C, X(23699), X(34165)}}
X(55151) = perspector of circumconic {{A, B, C, X(2), X(5523)}}
X(55151) = X(i)-vertex conjugate of X(j) for these {i, j}: {1560, 8428}
X(55151) = X(i)-Dao conjugate of X(j) for these {i, j}: {14672, 2373}
X(55151) = X(i)-Ceva conjugate of X(j) for these {i, j}: {30247, 1560}
X(55151) = barycentric product X(i)*X(j) for these (i, j): {47138, 7493}
X(55151) = barycentric quotient X(i)/X(j) for these (i, j): {14580, 39382}

X(55152) = X(32)X(14384)∩X(115)X(3566)

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

See Ivan Pavlov, euclid 5973.

X(55152) lies on circumconics {{A, B, C, X(230), X(51613)}} and on these lines: {32, 14384}, {115, 3566}, {230, 35067}, {523, 15525}, {1084, 2489}, {1992, 35087}, {2482, 44401}, {3163, 21973}, {15526, 23991}, {39009, 41178}

X(55152) = center of circumconic {{A, B, C, X(2), X(230)}}
X(55152) = X(i)-Dao conjugate of X(j) for these {i, j}: {51610, 4563}
X(55152) = X(i)-Ceva conjugate of X(j) for these {i, j}: {14384, 42663}
X(55152) = X(i)-complementary conjugate of X(j) for these {i, j}: {230, 42327}, {460, 21259}, {560, 6132}, {798, 44377}, {1692, 4369}, {1733, 23301}, {1924, 36212}, {8772, 512}, {42663, 10}, {44099, 8062}, {51481, 21263}
X(55152) = barycentric product X(i)*X(j) for these (i, j): {2971, 2974}, {14384, 36472}
X(55152) = barycentric quotient X(i)/X(j) for these (i, j): {42663, 10425}

X(55153) = X(2)X(54953)∩X(119)X(1566)

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

See Ivan Pavlov, euclid 5973.

X(55153) lies on these lines: {2, 54953}, {44, 23986}, {119, 1566}, {220, 35113}, {650, 5514}, {960, 35083}, {1015, 6506}, {1086, 14837}, {1146, 3239}, {1212, 35116}, {1577, 15526}, {1785, 14571}, {2254, 46415}, {2323, 3163}, {6603, 23972}, {26932, 45664}, {33573, 45950}, {34586, 35066}, {35110, 43035}, {35508, 52946}, {38353, 46393}

X(55153) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1785), X(3326)}}, {{A, B, C, X(2804), X(54953)}}, {{A, B, C, X(14571), X(52316)}}
X(55153) = perspector of circumconic {{A, B, C, X(2804), X(43737)}}
X(55153) = center of circumconic {{A, B, C, X(2), X(908)}}
X(55153) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2720, 37136}, {7045, 41933}, {32669, 54953}
X(55153) = X(i)-Dao conjugate of X(j) for these {i, j}: {517, 1262}, {2804, 2}, {17115, 41933}, {23757, 34234}, {34345, 37781}, {35014, 651}, {38981, 37136}
X(55153) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2, 2804}, {54451, 8677}
X(55153) = X(i)-complementary conjugate of X(j) for these {i, j}: {31, 2804}, {33, 8677}, {517, 17072}, {663, 517}, {667, 44675}, {810, 856}, {1457, 3900}, {1465, 46399}, {1769, 2886}, {2183, 4885}, {2427, 21232}, {2804, 2887}, {3063, 3911}, {3310, 142}, {6735, 21260}, {8677, 34822}, {10015, 17046}, {14571, 46396}, {23220, 17102}, {35015, 21252}, {36038, 17047}, {42752, 8286}, {42753, 17059}, {46393, 141}, {52307, 18589}, {53549, 10}, {54364, 926}
X(55153) = barycentric product X(i)*X(j) for these (i, j): {264, 41215}, {1146, 26611}, {2397, 52316}, {2804, 2804}, {3259, 51984}, {3326, 8}, {4998, 52315}, {14010, 17757}, {14503, 14504}, {15632, 42455}, {21664, 2968}, {23978, 23980}, {24026, 24028}, {35015, 6735}, {42757, 4397}, {52114, 54241}
X(55153) = barycentric quotient X(i)/X(j) for these (i, j): {1361, 7339}, {2804, 54953}, {3326, 7}, {14936, 41933}, {23980, 1262}, {24028, 7045}, {26611, 1275}, {35012, 7053}, {41215, 3}, {41220, 7335}, {42078, 24027}, {42757, 934}, {46393, 37136}, {52315, 11}, {52316, 2401}, {53549, 2720}

X(55154) = X(1)X(15995)∩X(3680)X(31560)

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

See Stanley Rabinowitz and Peter Moses, euclid 5975.

X(55154) lies on the Feuerbach circumhyperbola and these lines: {1, 15995}, {3680, 31560}

X(55154) = isotomic conjugate of the anticomplement of X(44635)

X(55155) = X(1)X(15996)∩X(3680)X(31559)

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

See Stanley Rabinowitz and Peter Moses, euclid 5975.

X(55155) lies on the Feuerbach circumhyperbola and these lines: {1, 15996}, {3680, 31559}

X(55155) = isotomic conjugate of the anticomplement of X(44636)

X(55156) = X(2)X(54608)∩X(1495)X(55038)

Barycentrics    a^2*(49*a^4 - 35*a^2*b^2 - 14*b^4 - 35*a^2*c^2 + 37*b^2*c^2 - 14*c^4) : :

X(55156) lies on the Thomson-Gibert-Moses hyperbola, the cubic K1332, and these lines: {2, 54608}, {1495, 55038}, {3167, 15107}, {3630, 5648}, {5544, 10546}, {5643, 35265}, {5644, 26864}, {5645, 10545}, {5654, 33703}, {5655, 15686}, {9716, 37517}

X(55156) = Thomson-isogonal conjugate of X(15687)

X(55157) = X(2)X(8780)∩X(6)X(40350)

Barycentrics    a^2*(25*a^4 - 20*a^2*b^2 - 5*b^4 - 20*a^2*c^2 + 22*b^2*c^2 - 5*c^4) : :
X(55157) = 6 X[2] - 5 X[40920]

X(55157) lies on the Thomson-Gibert-Moses hyperbola, the cubic K1331, and these lines: {2, 8780}, {6, 40350}, {25, 55038}, {110, 33878}, {154, 3098}, {182, 14924}, {184, 5644}, {354, 16491}, {382, 1514}, {392, 13369}, {546, 43841}, {550, 5656}, {1351, 9716}, {1495, 3167}, {1503, 31856}, {1511, 32063}, {1995, 5645}, {3426, 10540}, {3529, 32605}, {3581, 12164}, {3631, 34774}, {3851, 10619}, {5020, 50664}, {5050, 5643}, {5092, 5646}, {5544, 35259}, {5648, 40341}, {5653, 42663}, {5655, 15681}, {5888, 6800}, {6030, 15066}, {6090, 7712}, {6144, 32267}, {6221, 41419}, {6391, 45082}, {8651, 34291}, {10545, 35264}, {11008, 32220}, {11456, 48670}, {11820, 32609}, {15068, 48669}, {15688, 35254}, {35266, 39899}, {37909, 51174}

X(55157) = Thomson-isogonal conjugate of X(3543)

X(55158) = X(6)X(12041)∩X(20)X(14852)

Barycentrics    a^2*(25*a^8 - 40*a^6*b^2 - 30*a^4*b^4 + 80*a^2*b^6 - 35*b^8 - 40*a^6*c^2 + 148*a^4*b^2*c^2 - 92*a^2*b^4*c^2 - 16*b^6*c^2 - 30*a^4*c^4 - 92*a^2*b^2*c^4 + 102*b^4*c^4 + 80*a^2*c^6 - 16*b^2*c^6 - 35*c^8) : :
X(55158) = 3 X[381] - 5 X[40920]

X(55158) lies on the cubic K1331 and these lines: {6, 12041}, {20, 14852}, {30, 43713}, {74, 47391}, {140, 8567}, {381, 6699}, {599, 8703}, {3524, 51425}, {3627, 37487}, {5092, 11204}, {5692, 35242}, {8718, 38438}, {9934, 10606}, {10546, 11472}, {10564, 12163}, {10605, 55039}, {11468, 37483}, {11935, 15041}, {12101, 31860}, {35259, 52055}

X(55159) = X(2)X(15517)∩X(3)X(49)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(5*a^8 - 10*a^6*b^2 + 8*a^4*b^4 - 6*a^2*b^6 + 3*b^8 - 10*a^6*c^2 + 8*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 8*b^6*c^2 + 8*a^4*c^4 + 2*a^2*b^2*c^4 + 10*b^4*c^4 - 6*a^2*c^6 - 8*b^2*c^6 + 3*c^8) : :

X(55159) lies on the cubic K1331 and these lines: {2, 15517}, {3, 49}, {22, 3563}, {3534, 13556}, {6289, 8964}, {9715, 34428}, {9909, 40809}, {14852, 27087}, {15818, 36748}

X(55159) = {X(3),X(12095)}-harmonic conjugate of X(47391)

X(55160) = X(2)X(36)∩X(3)X(5660)

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

X(55160) lies on these lines: {2, 36}, {3, 5660}, {35, 5698}, {80, 956}, {100, 5692}, {165, 5720}, {908, 15175}, {1001, 37701}, {2975, 15079}, {3158, 3899}, {3428, 5659}, {4867, 25439}, {5010, 31142}, {5526, 17756}, {5657, 44425}, {11344, 37731}, {16154, 37286}, {31018, 35204}

X(55161) = X(2)X(101)∩X(3)X(142)

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

X(55161) lies on the cubic K1265 and these lines: {2, 101}, {3, 142}, {7, 5030}, {36, 30949}, {55, 17761}, {56, 17758}, {86, 14964}, {140, 21258}, {141, 43149}, {183, 30109}, {214, 24331}, {379, 29603}, {499, 26101}, {514, 34522}, {572, 25521}, {574, 1086}, {673, 4262}, {927, 38884}, {993, 20335}, {1385, 6706}, {2646, 24774}, {3306, 6205}, {3911, 5228}, {3924, 24786}, {4000, 4256}, {4904, 5432}, {5719, 51150}, {7815, 20255}, {7824, 24190}, {8715, 20257}, {9317, 37525}, {9327, 27253}, {11285, 24170}, {11375, 40690}, {15482, 25350}, {16439, 22000}, {17044, 20328}, {17048, 30143}, {17050, 25440}, {17201, 27146}, {17753, 24047}, {21264, 48863}, {24036, 24333}, {24596, 35342}

X(55161) = X(44876)-Ceva conjugate of X(514)
X(55161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 2140, 14377}, {142, 10165, 51775}, {1125, 48932, 52015}, {20328, 38028, 17044}

X(55162) = X(2)X(4262)∩X(99)X(17297)

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

X(55162) lies on these lines: {2, 4262}, {99, 17297}, {116, 6174}, {142, 214}, {544, 29594}, {545, 22035}, {599, 47039}, {1018, 3218}, {6054, 13635}, {7757, 17378}, {10707, 25532}, {11112, 17758}, {17205, 17392}, {17313, 47040}, {17390, 39697}

X(55162) = Thomson-isogonal conjugate of X(13329)

X(55163) = X(3)X(32578)∩X(9)X(165)

Barycentrics    a^2*(a^4 - 6*a^2*b^2 + 8*a*b^3 - 3*b^4 + 6*a^2*b*c - 4*a*b^2*c - 2*b^3*c - 6*a^2*c^2 - 4*a*b*c^2 + 10*b^2*c^2 + 8*a*c^3 - 2*b*c^3 - 3*c^4) : :

X(55163) lies on these lines: {3, 32578}, {9, 165}, {55, 101}, {57, 43065}, {169, 1155}, {218, 37541}, {220, 5537}, {672, 47041}, {1200, 2280}, {1615, 15931}, {2267, 2272}, {3119, 5779}, {5657, 36028}, {5744, 24596}, {6244, 8012}, {8074, 17729}, {10857, 45721}, {17601, 52084}

X(55163) = {X(910),X(15855)}-harmonic conjugate of X(165)

X(55164) = X(2)X(187)∩X(3)X(6054)

Barycentrics    4*a^4 - 4*a^2*b^2 - 2*b^4 - 4*a^2*c^2 - b^2*c^2 - 2*c^4 : :
X(55164) = 2 X[2] + X[11057], 5 X[2] - 2 X[14537], 5 X[2] - 4 X[14762], 5 X[2] + X[14976], 7 X[2] - X[19569], X[2] - 4 X[40344], 5 X[598] - 4 X[14537], 5 X[598] - 8 X[14762], 5 X[598] + 2 X[14976], X[598] - 4 X[15810], 7 X[598] - 2 X[19569], X[598] - 8 X[40344], 5 X[11057] + 4 X[14537], 5 X[11057] + 8 X[14762], and many others

X(55164) lies on Kiepert circumhyperbola of the Brocard triangle, the cubic K1333, and these lines: {2, 187}, {3, 6054}, {30, 7697}, {39, 9939}, {69, 9741}, {76, 543}, {99, 599}, {141, 8598}, {182, 41137}, {183, 671}, {299, 36775}, {315, 9770}, {325, 12040}, {376, 1352}, {512, 7998}, {524, 3094}, {538, 32480}, {542, 22677}, {549, 41133}, {551, 3821}, {574, 7840}, {620, 11149}, {626, 9167}, {691, 36194}, {1003, 21358}, {1078, 7610}, {1992, 14482}, {2482, 3314}, {2549, 11054}, {2794, 9743}, {2896, 7782}, {3053, 7943}, {3096, 8369}, {3534, 10302}, {3545, 14160}, {3642, 5463}, {3643, 5464}, {3734, 9855}, {3785, 7847}, {5013, 7949}, {5023, 7944}, {5025, 14971}, {5055, 39656}, {5206, 7928}, {5319, 6179}, {5461, 17004}, {5980, 11296}, {5981, 11295}, {6322, 35138}, {6655, 41135}, {6781, 16986}, {7615, 33017}, {7617, 14041}, {7618, 7799}, {7620, 33272}, {7622, 7818}, {7750, 7786}, {7752, 9771}, {7768, 32965}, {7775, 7824}, {7778, 50571}, {7784, 7940}, {7788, 11165}, {7790, 22329}, {7793, 7817}, {7794, 33275}, {7795, 33208}, {7800, 33007}, {7802, 8370}, {7809, 11184}, {7814, 7873}, {7815, 33013}, {7821, 33022}, {7828, 33190}, {7832, 32985}, {7835, 27088}, {7848, 39785}, {7849, 33014}, {7854, 33260}, {7857, 8360}, {7858, 32990}, {7865, 10000}, {7869, 33276}, {7871, 7929}, {7878, 33021}, {7884, 11287}, {7897, 8589}, {7911, 11318}, {7917, 15815}, {7924, 8859}, {7926, 11163}, {7931, 8588}, {7935, 7942}, {7938, 15513}, {7939, 15515}, {7946, 31652}, {8352, 11168}, {8354, 37671}, {8358, 41624}, {8703, 55007}, {8860, 14061}, {9466, 32479}, {9731, 51185}, {10008, 32833}, {10242, 40277}, {10807, 32456}, {11147, 19708}, {11178, 11676}, {11185, 42850}, {11299, 13083}, {11300, 13084}, {11303, 33411}, {11304, 33410}, {11317, 15271}, {12150, 47352}, {13637, 38425}, {13757, 38426}, {14568, 32986}, {14977, 23878}, {15533, 31859}, {15597, 33228}, {15709, 41400}, {17130, 33267}, {17271, 47039}, {17297, 47040}, {19924, 55008}, {20582, 35954}, {22165, 45796}, {25562, 38749}, {32547, 52042}, {32817, 50990}, {32836, 53141}, {33019, 47617}, {33233, 51237}, {33234, 34505}, {33474, 47067}, {33475, 47069}, {35278, 47596}, {35948, 55041}, {35949, 55040}, {36207, 39061}, {37350, 37688}, {47353, 54993}, {48310, 53484}, {54169, 54996}

X(55164) = midpoint of X(i) and X(j) for these {i,j}: {598, 11057}, {7811, 52691}, {15533, 33683}
X(55164) = reflection of X(i) in X(j) for these {i,j}: {2, 15810}, {598, 2}, {7757, 52691}, {8592, 2482}, {9774, 3}, {14537, 14762}, {15810, 40344}, {52088, 8592}, {52691, 8356}
X(55164) = isotomic conjugate of X(13377)
X(55164) = isotomic conjugate of the isogonal conjugate of X(353)
X(55164) = Thomson-isogonal conjugate of X(182)
X(55164) = X(31)-isoconjugate of X(13377)
X(55164) = X(2)-Dao conjugate of X(13377)
X(55164) = barycentric product X(76)*X(353)
X(55164) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 13377}, {353, 6}
X(55164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6031, 51541}, {2, 7898, 31173}, {2, 8182, 26613}, {2, 14907, 51224}, {2, 14976, 14537}, {2, 51224, 3972}, {3, 7883, 7870}, {3, 7936, 7922}, {183, 5077, 671}, {599, 35955, 99}, {1003, 31168, 47005}, {1078, 9166, 7610}, {5206, 7928, 7930}, {7610, 7841, 9166}, {7750, 8359, 7812}, {7761, 7771, 7934}, {7784, 43459, 7940}, {7810, 7830, 7833}, {7810, 7833, 76}, {7811, 8356, 7757}, {7812, 8359, 7786}, {7830, 7904, 76}, {7831, 14907, 3972}, {7831, 51224, 2}, {7833, 7904, 7810}, {7870, 7883, 7922}, {7870, 7936, 7883}, {7873, 33004, 7814}, {7929, 37512, 7871}

X(55165) = X(2)X(353)∩X(3)X(40251)

Barycentrics    a^2*(4*a^8 - 14*a^6*b^2 + 12*a^4*b^4 + a^2*b^6 - 2*b^8 - 14*a^6*c^2 + 9*a^4*b^2*c^2 + 4*b^6*c^2 + 12*a^4*c^4 - 15*b^4*c^4 + a^2*c^6 + 4*b^2*c^6 - 2*c^8) : :

X(55165) lies on Thomson-Gibert-Moses hyperbola, the cubic K1333, and these lines: {2, 353}, {3, 40251}, {6, 17430}, {110, 5104}, {111, 5038}, {1383, 9716}, {1495, 33876}, {1915, 55038}, {3124, 5645}, {3167, 11173}, {3288, 5653}, {5191, 34099}, {5544, 20998}, {8566, 9155}, {10485, 44420}, {34291, 39232}

X(55165) = crossdifference of every pair of points on line {9208, 49102}

X(55166) = X(3)X(6)∩X(373)X(376)

Barycentrics    a^8*(b^2+c^2)+a^6*(-3*b^4+32*b^2*c^2-3*c^4)-a^2*(b^2-c^2)^2*(b^4+c^4)+a^4*(3*b^6-35*b^4*c^2-35*b^2*c^4+3*c^6) : :
X(55166) = X[51]+5*X[19708], X[373]+X[376], -X[381]+2*X[12045], 5*X[548]+4*X[32205], 5*X[550]+4*X[44863], X[3534]+2*X[6688], -X[3830]+4*X[10219], -X[3917]+7*X[15698], X[5890]+11*X[15715], -X[5891]+7*X[15700], X[5946]+5*X[15714], -X[7998]+5*X[15692], X[11002]+X[36987], X[14845]+X[15689], X[14855]+5*X[15693], X[15045]+3*X[15710], -X[15060]+7*X[19711], -X[15067]+7*X[44682]

See Tran Quang Hung and Ivan Pavlov, euclid 5983.

X(55166) lies on these lines: {3, 6}, {51, 19708}, {140, 46847}, {373, 376}, {381, 12045}, {548, 32205}, {549, 14915}, {550, 44863}, {631, 13474}, {2777, 43957}, {3426, 5646}, {3522, 11695}, {3523, 12279}, {3524, 5650}, {3528, 10110}, {3530, 10170}, {3534, 6688}, {3537, 18390}, {3819, 5663}, {3830, 10219}, {3917, 15698}, {5447, 45956}, {5640, 10304}, {5890, 15715}, {5891, 15700}, {5892, 13451}, {5907, 15712}, {5943, 8703}, {5946, 15714}, {7998, 15692}, {9027, 51737}, {9781, 40284}, {10299, 11459}, {11002, 36987}, {11793, 15072}, {12108, 14641}, {13363, 13598}, {13570, 15681}, {13754, 17504}, {14845, 15689}, {14855, 15693}, {15035, 22352}, {15045, 15710}, {15055, 15246}, {15060, 19711}, {15067, 44682}, {15701, 16194}, {15702, 32062}, {15705, 20791}, {15720, 44870}, {15759, 21849}, {16187, 35237}, {16226, 16981}, {34417, 41463}lies on these lines: {3, 6}, {51, 19708}, {140, 46847}, {373, 376}, {381, 12045}, {548, 32205}, {549, 14915}, {550, 44863}, {631, 13474}, {2777, 43957}, {3426, 5646}, {3522, 11695}, {3523, 12279}, {3524, 5650}, {3528, 10110}, {3530, 10170}, {3534, 6688}, {3537, 18390}, {3819, 5663}, {3830, 10219}, {3917, 15698}, {5447, 45956}, {5640, 10304}, {5890, 15715}, {5891, 15700}, {5892, 13451}, {5907, 15712}, {5943, 8703}, {5946, 15714}, {7998, 15692}, {9027, 51737}, {9781, 40284}, {10299, 11459}, {11002, 36987}, {11793, 15072}, {12108, 14641}, {13363, 13598}, {13570, 15681}, {13754, 17504}, {14845, 15689}, {14855, 15693}, {15035, 22352}, {15045, 15710}, {15055, 15246}, {15060, 19711}, {15067, 44682}, {15701, 16194}, {15702, 32062}, {15705, 20791}, {15720, 44870}, {15759, 21849}, {16187, 35237}, {16226, 16981}, {34417, 41463}

X(56166) = midpoint of X(i) and X(j) for these {i,j}: {11002, 36987}, {14845, 15689}, {373, 376}
X(56166) = reflection of X(i) in X(j) for these {i,j}: {13474, 16261}, {15082, 549}, {381, 12045}
X(56166) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 17704, 15644}, {3, 37470, 14810}, {9730, 17704, 16836}, {15644, 16836, 9730}

X(55167) = X(2)X(3)∩X(182)X(20194)

Barycentrics    2*a^8+(b^2-c^2)^4+9*a^6*(b^2+c^2)-a^4*(7*b^4+10*b^2*c^2+7*c^4)-a^2*(5*b^6+11*b^4*c^2+11*b^2*c^4+5*c^6) : :
X(55167) = X[1350]+X[15048], X[2549]+3*X[31884], -X[3734]+3*X[21167], X[6776]+X[14929], -X[7737]+5*X[53094], X[7761]+X[44882]

See Tran Quang Hung and Ivan Pavlov, euclid 5983.

X(55167) lies on these lines: {2, 3}, {182, 20194}, {511, 40281}, {1350, 15048}, {2549, 31884}, {3734, 21167}, {4045, 29181}, {5085, 18907}, {5188, 5305}, {6776, 14929}, {7737, 53094}, {7739, 53097}, {7761, 44882}, {7767, 12203}, {7792, 22676}, {11574, 53795}, {52229, 54169}

X(56167) = midpoint of X(i) and X(j) for these {i,j}: {1350, 15048}, {6776, 14929}, {7761, 44882}

X(55168) = X(1)X(164)∩X(3)X(167)

Barycentrics    Sin[A]*(Sin[A/2]*(3*Sin[A] + Sin[B] + Sin[C]) - Sin[B/2]*(3*Sin[A] + Sin[B] + 3*Sin[C]) - Sin[C/2]*(3*Sin[A] + 3*Sin[B] + Sin[C])) : :
Barycentrics    a*((3*a + b + c)*sin(A/2) - (3*a + b + 3*c)*sin(B/2) - (3*a + 3*b + c)*sin(C/2)) : : (César Eliud Lozada, August 3, 2023)
X(55168) = X[1] + 2 X[164], X[1] - 4 X[12523], 5 X[1] - 2 X[12656], X[164] + 2 X[12523], 5 X[164] + X[12656], 10 X[12523] - X[12656], 4 X[3] - X[167], 4 X[1125] - X[9807], 7 X[3624] - 4 X[21633], 5 X[7987] - 2 X[12844], 4 X[12518] - 7 X[16192]

X(55168) lies on these lines: {1, 164}, {3, 167}, {177, 3361}, {1125, 9807}, {3576, 53810}, {3601, 17641}, {3624, 21633}, {3659, 10234}, {5234, 18258}, {7987, 12844}, {8109, 12518}, {8422, 53053}, {12443, 15803}, {12539, 31424}

X(55168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {164, 12523, 1}, {258, 8077, 1}, {7588, 8078, 1}

X(55169) = X(1)X(164)∩X(40)X(167)

Barycentrics    Sin[A]*(Sin[A/2]*(Sin[A] + 3*Sin[B] + 3*Sin[C]) - Sin[B/2]*(Sin[A] + 3*Sin[B] + Sin[C]) - Sin[C/2]*(Sin[A] + Sin[B] + 3*Sin[C])) : :
Barycentrics    a*((a + 3*b + 3*c)*sin(A/2) - (a + 3*b + c)*sin(B/2) - (a + b + 3*c)*sin(C/2)) : : (César Eliud Lozada, August 3, 2023)
X(55169) = 3 X[1] - 4 X[12523], 3 X[1] - 2 X[12656], 3 X[164] - 2 X[12523], 3 X[164] - X[12656], 3 X[165] - 2 X[12844], 5 X[1698] - 4 X[21633], 8 X[12622] - 9 X[19875]

X(55169) lies on these lines: {1, 164}, {10, 9807}, {40, 167}, {165, 12844}, {177, 3339}, {1697, 17641}, {1698, 21633}, {8422, 9819}, {10980, 12908}, {11691, 12526}, {12539, 54422}, {12622, 19875}, {30337, 32183}

X(55169) = reflection of X(i) in X(j) for these {i,j}: {1, 164}, {167, 40}, {9807, 10}, {12656, 12523}
X(55169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {164, 12656, 12523}, {258, 8093, 1}, {7588, 11534, 1}, {8077, 11899, 1}, {8078, 8094, 1}, {12523, 12656, 1}

X(55170) = X(1)X(164)∩X(177)X(5221)

Barycentrics    Sin[A]*(Sin[A/2]*(Sin[A] + 2*Sin[B] + 2*Sin[C]) - Sin[B/2]*(Sin[A] + 2*Sin[B] + Sin[C]) - Sin[C/2]*(Sin[A] + Sin[B] + 2*Sin[C])) : :
Barycentrics    a*((a + 2*b + 2*c)*sin(A/2) - (a + 2*b + c)*sin(B/2) - (a + b + 2*c)*sin(C/2)) : : (César Eliud Lozada, August 3, 2023)
X(55170) = X[1] - 3 X[164], 2 X[1] - 3 X[12523], 5 X[1] - 3 X[12656], 5 X[164] - X[12656], 5 X[12523] - 2 X[12656], 4 X[3579] - 3 X[12518], 4 X[3634] - 3 X[21633], 7 X[9780] - 3 X[9807], 7 X[9780] - 6 X[12622], 3 X[12844] - 5 X[35242]

X(55170) lies on these lines: {1, 164}, {177, 5221}, {3579, 12518}, {3634, 21633}, {5708, 12443}, {7991, 11222}, {9780, 9807}, {11684, 11691}, {12844, 35242}

X(55170) = reflection of X(i) in X(j) for these {i,j}: {9807, 12622}, {12523, 164}

X(55171) = X(1)X(164)∩X(177)X(32636)

Barycentrics    Sin[A]*(Sin[A/2]*(2*Sin[A] + Sin[B] + Sin[C]) - Sin[B/2]*(2*Sin[A] + Sin[B] + 2*Sin[C]) - Sin[C/2]*(2*Sin[A] + 2*Sin[B] + Sin[C])) : :
Barycentrics    a*((2*a + b + c)*sin(A/2) - (2*a + b + 2*c)*sin(B/2) - (2*a + 2*b + c)*sin(C/2)) : : (César Eliud Lozada, August 3, 2023)
X(55171) = X[1] + 3 X[164], X[1] - 3 X[12523], 7 X[1] - 3 X[12656], 7 X[164] + X[12656], 7 X[12523] - X[12656], 4 X[3634] - 3 X[12622], 11 X[5550] - 3 X[9807], 3 X[12518] - 5 X[35242], 3 X[12614] - 2 X[18483], 5 X[19862] - 3 X[21633]

X(55171) lies on these lines: {1, 164}, {177, 32636}, {3634, 12622}, {5221, 31768}, {5302, 18258}, {5550, 9807}, {12443, 37582}, {12518, 35242}, {12614, 18483}, {13624, 53810}, {19862, 21633}

X(55171) = midpoint of X(164) and X(12523)

X(55172) = X(1)X(164)∩X(55)X(31767)

Barycentrics    Sin[A]*(Sin[A/2]*(2*Sin[A] - Sin[B] - Sin[C]) - Sin[B/2]*(2*Sin[A] - Sin[B] + 2*Sin[C]) - Sin[C/2]*(2*Sin[A] + 2*Sin[B] - Sin[C])) : :
Barycentrics    a*((2*a - b - c)*sin(A/2) - (2*a - b + 2*c)*sin(B/2) - (2*a + 2*b - c)*sin(C/2)) : : (César Eliud Lozada, August 3, 2023)
X(55172) = 3 X[1] + X[164], 5 X[1] - X[12656], X[164] - 3 X[12523], 5 X[164] + 3 X[12656], 5 X[12523] + X[12656], 3 X[165] + X[11528], X[167] - 9 X[30392], 3 X[551] - X[21633], 3 X[3576] - X[12518], X[9807] - 9 X[38314]

X(55172) lies on these lines: {1, 164}, {55, 31767}, {56, 31768}, {106, 10496}, {165, 11528}, {167, 30392}, {177, 1319}, {226, 31734}, {515, 12614}, {551, 21633}, {1125, 12622}, {2646, 8422}, {3576, 12518}, {4304, 31770}, {4311, 31735}, {9807, 38314}, {11191, 20323}, {11234, 37080}, {12053, 31769}, {12443, 24929}, {12908, 24928}, {15178, 53810}

X(55172) = midpoint of X(i) and X(j) for these {i,j}: {1, 12523}, {12443, 32183}
X(55172) = reflection of X(12622) in X(1125)

X(55173) = X(1)X(164)∩X(8)X(12622)

Barycentrics    Sin[A]*(Sin[A/2]*(Sin[A] - 2*Sin[B] - 2*Sin[C]) - Sin[B/2]*(Sin[A] - 2*Sin[B] + Sin[C]) - Sin[C/2]*(Sin[A] + Sin[B] - 2*Sin[C])) : :
Barycentrics    a*((a - 2*b - 2*c)*sin(A/2) - (a - 2*b + c)*sin(B/2) - (a + b - 2*c)*sin(C/2)) : : (César Eliud Lozada, August 3, 2023)
X(55173) = 3 X[1] - X[164], 2 X[164] - 3 X[12523], X[164] + 3 X[12656], X[12523] + 2 X[12656], X[167] + 3 X[11224], 3 X[11224] - X[11528], 3 X[3241] + X[9807], 3 X[5603] - 2 X[12614]

X(55173) lies on these lines: {1, 164}, {8, 12622}, {167, 11223}, {177, 2099}, {517, 12518}, {519, 21633}, {2098, 8422}, {3241, 9807}, {3340, 31768}, {3476, 31734}, {3486, 31769}, {4295, 31735}, {5048, 17641}, {5289, 18258}, {5603, 12614}, {7962, 31767}, {7982, 12844}, {10222, 53810}, {12443, 15934}, {30305, 31770}

X(55173) = midpoint of X(i) and X(j) for these {i,j}: {1, 12656}, {167, 11528}, {7982, 12844}
X(55173) = reflection of X(i) in X(j) for these {i,j}: {8, 12622}, {12523, 1}
X(55173) = {X(167),X(11224)}-harmonic conjugate of X(11528)

X(55174) = X(1)X(164)∩X(30)X(511)

Barycentrics    Sin[A]*(Sin[A/2]*(Sin[B] + Sin[C]) - Sin[B/2]*Sin[B] - Sin[C/2]*Sin[C]) : :
Barycentrics    a*((b + c)*sin(A/2) - b*sin(B/2) - c*sin(C/2)) : : (César Eliud Lozada, August 3, 2023)

X(55174) lies on these lines: {1, 164}, {8, 9807}, {10, 12622}, {30, 511}, {40, 12518}, {65, 177}, {72, 12694}, {167, 845}, {259, 504}, {354, 11191}, {363, 10234}, {942, 12443}, {946, 12614}, {950, 31769}, {960, 18258}, {2292, 13091}, {3057, 8422}, {3868, 12539}, {3869, 11691}, {4292, 31735}, {5919, 11234}, {7670, 7672}, {8140, 11527}, {9805, 12879}, {9806, 12884}, {9808, 13090}, {9957, 32183}, {10106, 31734}, {10506, 13385}, {10624, 31770}, {10914, 17657}, {12435, 12554}, {12445, 13092}, {12813, 31794}, {31779, 31784}, {31781, 31783}, {31786, 31791}, {31788, 31790}, {31792, 31796}, {31793, 31801}, {31798, 31800}

X(55174) = Thomson-isogonal conjugate of X(10496)
X(55174) = crossdifference of every pair of points on line {6, 45877}
X(55174) = barycentric quotient X(i)/X(j) for these {i,j}: {12386, 8836}, {45260, 48843}
X(55174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 164, 12523}, {10, 21633, 12622}, {40, 12844, 12518}, {65, 177, 31768}, {164, 12656, 1}, {258, 11534, 1}, {3057, 8422, 31767}, {3057, 17641, 8422}, {5571, 31766, 1}, {8078, 11899, 1}, {8093, 8094, 1}

X(55175) = X(1)X(164)∩X(40)X(11528)

Barycentrics    Sin[A]*(Sin[A/2]*(3*Sin[A] - Sin[B] - Sin[C]) - Sin[B/2]*(3*Sin[A] - Sin[B] + 3*Sin[C]) - Sin[C/2]*(3*Sin[A] + 3*Sin[B] - Sin[C])) : :
Barycentrics    a*((3*a - b - c)*sin(A/2) - (3*a - b + 3*c)*sin(B/2) - (3*a + 3*b - c)*sin(C/2)) : : (César Eliud Lozada, August 3, 2023)
X(55175) = 2 X[1] + X[164], X[1] + 2 X[12523], 4 X[1] - X[12656], X[164] - 4 X[12523], 2 X[164] + X[12656], 8 X[12523] + X[12656], 2 X[40] + X[11528], X[167] - 7 X[30389], 4 X[1385] - X[12844], X[8422] + 2 X[12443], 5 X[3616] - 2 X[21633], 7 X[3622] - X[9807], 7 X[3624] - 4 X[12622], X[5691] - 4 X[12614], 5 X[7987] - 2 X[12518], X[12646] + 2 X[52797]

X(55175) lies on these lines: {1, 164}, {40, 11528}, {167, 30389}, {177, 1420}, {363, 3659}, {1385, 12844}, {3361, 31768}, {3601, 8422}, {3616, 21633}, {3622, 9807}, {3624, 12622}, {5290, 31734}, {5436, 12694}, {5691, 12614}, {7370, 52999}, {7987, 12518}, {10246, 53810}, {10389, 11234}, {10496, 45086}, {12646, 52797}, {17641, 34471}, {31767, 53053}, {31769, 51785}

X(55175) = Thomson-isogonal conjugate of X(164)
X(55175) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 164, 12656}, {1, 12523, 164}

X(55176) = X(1)X(164)∩X(177)X(1388)

Barycentrics    Sin[A]*(Sin[A/2]*(3*Sin[A] - 2*Sin[B] - 2*Sin[C]) - Sin[B/2]*(3*Sin[A] - 2*Sin[B] + 3*Sin[C]) - Sin[C/2]*(3*Sin[A] + 3*Sin[B] - 2*Sin[C])) : :
Barycentrics    a*((3*a - 2*b - 2*c)*sin(A/2) - (3*a - 2*b + 3*c)*sin(B/2) - (3*a + 3*b - 2*c)*sin(C/2)) : : (César Eliud Lozada, August 3, 2023)
X(55176) = 5 X[1] + X[164], 2 X[1] + X[12523], 7 X[1] - X[12656], 2 X[164] - 5 X[12523], 7 X[164] + 5 X[12656], 7 X[12523] + 2 X[12656], X[944] + 2 X[12614], 4 X[1385] - X[12518], 5 X[3616] - 2 X[12622], 4 X[3636] - X[21633], 5 X[7987] + X[11528]

X(55176) lies on these lines: {1, 164}, {177, 1388}, {944, 12614}, {1385, 12518}, {1420, 31768}, {3485, 31734}, {3601, 31767}, {3616, 12622}, {3636, 21633}, {4305, 31770}, {7987, 11528}, {8422, 34471}

X(55177) = THOMPSON-ISOGONAL CONJUGATE OF X(32)

Barycentrics    4*a^8 + 4*a^6*b^2 - 4*a^4*b^4 - 2*a^2*b^6 - 2*b^8 + 4*a^6*c^2 - 5*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + b^6*c^2 - 4*a^4*c^4 - 2*a^2*b^2*c^4 + 2*b^4*c^4 - 2*a^2*c^6 + b^2*c^6 - 2*c^8 : :
X(55177) = 2 X[2] - 3 X[9774], 4 X[2] - 3 X[10033], 3 X[9774] - X[14458], 3 X[10033] - 2 X[14458], 3 X[20] - X[14976], 3 X[598] - 2 X[3830], 4 X[8703] - 3 X[55164], 2 X[55007] - 3 X[55164], 3 X[15688] - 2 X[34510], 7 X[15698] - 6 X[15810], 5 X[19708] - 4 X[40344]

X(55177) lies on the cubic K1334 and these lines: {2, 1495}, {3, 31168}, {4, 54773}, {20, 7946}, {30, 3095}, {99, 3534}, {147, 48898}, {262, 29012}, {376, 7801}, {381, 12203}, {524, 39882}, {542, 33706}, {543, 55009}, {598, 3830}, {754, 6309}, {1503, 22712}, {2549, 14482}, {3314, 48892}, {3329, 48884}, {3845, 7790}, {3849, 9741}, {5188, 34623}, {5306, 20194}, {6272, 32419}, {6273, 32421}, {7470, 7818}, {7779, 48880}, {7835, 12100}, {7837, 19924}, {7919, 19709}, {8356, 9873}, {8667, 9830}, {8703, 55007}, {9168, 32472}, {9744, 14927}, {9751, 10516}, {9766, 48905}, {9862, 9890}, {9993, 48906}, {10131, 14041}, {11287, 34681}, {15688, 34510}, {15698, 15810}, {19708, 40344}, {54645, 54901}

X(55177) = reflection of X(i) in X(j) for these {i,j}: {9873, 8356}, {10033, 9774}, {11057, 3534}, {11257, 34624}, {14458, 2}, {15682, 14537}, {34623, 5188}, {55007, 8703}
X(55177) = Thomson-isogonal conjugate of X(32)
X(55177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14458, 10033}, {8703, 55007, 55164}, {9774, 14458, 2}

X(55178) = THOMPSON-ISOGONAL CONJUGATE OF X(39)

Barycentrics    3*a^8 + 7*a^6*b^2 - 5*a^4*b^4 - 5*a^2*b^6 + 7*a^6*c^2 - 3*a^4*b^2*c^2 - 15*a^2*b^4*c^2 + b^6*c^2 - 5*a^4*c^4 - 15*a^2*b^2*c^4 - 2*b^4*c^4 - 5*a^2*c^6 + b^2*c^6 : :
X(55178) = 4 X[3] - X[32467], X[3399] + 2 X[5188], 2 X[3534] + 3 X[10302]

X(55178) lies on the cubgic K1334 and these lines: {2, 3098}, {3, 6179}, {30, 6287}, {98, 14810}, {99, 8703}, {376, 7810}, {511, 9751}, {538, 6308}, {543, 9302}, {551, 13634}, {574, 14482}, {1078, 35248}, {3399, 5188}, {3524, 30270}, {3534, 10302}, {3734, 11001}, {5104, 9300}, {5984, 33751}, {6054, 54169}, {7470, 9466}, {7788, 9774}, {7865, 34681}, {7944, 42787}, {8182, 9741}, {8556, 9756}, {8592, 45109}, {9168, 32473}, {9737, 15692}, {9821, 12150}, {9888, 46893}, {10304, 39647}, {12100, 26613}, {16986, 48880}, {16988, 48895}, {22564, 52995}, {37455, 44422}

X(55178) = reflection of X(i) in X(j) for these {i,j}: {14492, 2}, {54964, 12100}
X(55178) = Thomson-isogonal conjugate of X(39)



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Tripoles of mixed polar lines: X(55179)-X(55285)

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This preamble and centers X(55179)-X(55285) were contributed by Ivan Pavlov, August 3, 2023.

Let P and Q be two points and CP and CQ their polar conics in the cubic K . The polar lines of P in CQ and Q in CP coincide. This common polar line is here introduced as the mixed polar line of P and Q in K.

In general, for the cubic k1 x^2 y + k2 x y^2 + k3 x^2 z + k4 x z^2 + k5 y^2 z + k6 y z^2 + k7 x^3 + k8 y^3 + k9 z^3 + k10 x y z, the mixed polar line of {u,v,w} and {p,q,r} is given by these coefficients:
{2*(3*k7*p+k1*q+k3*r)*u+(2*k1*p+2*k2*q+k10*r)*v+(2*k3*p+k10*q+2*k4*r)*w,
(2*k1*p+2*k2*q+k10*r)*u+2*(k2*p+3*k8*q+k5*r)*v+(k10*p+2*k5*q+2*k6*r)*w
(2*k3*p+k10*q+2*k4*r)*u+(k10*p+2*k5*q+2*k6*r)*v+2*(k4*p+k6*q+3*k9*r)*w}

In this section, we consider some mixed polar lines wrt K001 Neuberg cubic and K002 Thomson cubic.

Examples of {m, n, l} for which the mixed polar line of X(m) and X(n) in K001 is the tripolar of the isotomic conjugate of X(l) follow:
{1,30,32679}; {2,3,31072}; {2,20,12077}; {2,30,3268}; {3,6,23285}; {3,30,8552}; {4,30,44427}; {5,30,46603}; {6,30,526}
Following are some examples of {m, n, l} for which the mixed polar line of X(m) and X(n) in K002 is the tripolar of the isotomic conjugate of X(l):
{1,2,661}; {1,6,4374; {1,8,48334}; {1,9,20906}; {1,10,48131}; {1,42,47672}; {1,43,693}; {1,44,21433}; {1,46,23685}; {1,57,21438}; {1,63,20909}; {1,200,48398}

X(55179) = TRILINEAR POLE OF LINE {484, 1046}

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

X(55179) lies on these lines:

X(55179) = trilinear pole of line {484, 1046}
X(55179) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4556)}}, {{A, B, C, X(110), X(15455)}}, {{A, B, C, X(651), X(1255)}}, {{A, B, C, X(662), X(38470)}}, {{A, B, C, X(1020), X(47318)}}, {{A, B, C, X(4033), X(4584)}}, {{A, B, C, X(4552), X(4629)}}, {{A, B, C, X(6335), X(29313)}}, {{A, B, C, X(27789), X(42362)}}
X(55179) = tripole of the mixed polar line of X(1) and X(3) in K001

X(55180) = X(2)X(52597)∩X(75)X(7265)

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

X(55180) lies on these lines: {2, 52597}, {75, 7265}, {850, 14838}, {905, 3739}, {1019, 52602}, {1577, 17899}, {4086, 21187}, {4359, 4391}, {4374, 50449}, {10479, 21050}, {18154, 47678}, {20891, 23685}, {35519, 47795}

X(55180) = isotomic conjugate of X(55179)
X(55180) = intersection, other than A, B, C, of circumconics {{A, B, C, X(15455), X(21192)}}
X(55180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4359, 4391, 21192}, {17899, 24622, 1577}

X(55181) = (name pending)

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

X(55181) lies on these lines:

X(55181) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(190), X(932)}}, {{A, B, C, X(943), X(1414)}}
X(55181) = tripole of the mixed polar line of X(1) and X(9) in K001

X(55182) = X(8)X(4705)∩X(514)X(3687)

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

X(55182) lies on these lines: {8, 4705}, {514, 3687}, {4147, 6734}, {24018, 24622}, {29168, 47699}, {32679, 55180}, {44448, 48010}

X(55182) = isotomic conjugate of the tripole of the mixed polar line of X(1) and X(20) in K001

X(55183) = (name pending)

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

X(55183) lies on these lines:

X(55183) = trilinear pole of line {978, 4225}
X(55183) = X(i)-isoconjugate-of-X(j) for these {i, j}: {37, 48283}, {42, 47795}, {512, 32933}, {661, 25440}, {8818, 48389}
X(55183) = X(i)-Dao conjugate of X(j) for these {i, j}: {36830, 25440}, {39054, 32933}, {40589, 48283}, {40592, 47795}
X(55183) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(15455)}}, {{A, B, C, X(81), X(662)}}, {{A, B, C, X(190), X(43350)}}, {{A, B, C, X(645), X(4591)}}, {{A, B, C, X(648), X(4556)}}, {{A, B, C, X(651), X(28166)}}, {{A, B, C, X(4552), X(25417)}}, {{A, B, C, X(4565), X(47318)}}, {{A, B, C, X(4573), X(4629)}}, {{A, B, C, X(4625), X(40438)}}
X(55183) = tripole of the mixed polar line of X(1) and X(40) in K001
X(55183) = barycentric quotient X(i)/X(j) for these (i, j): {58, 48283}, {81, 47795}, {110, 25440}, {662, 32933}, {17104, 48389}

X(55184) = X(75)X(14838)∩X(321)X(1577)

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

X(55184) lies on these lines: {75, 14838}, {321, 1577}, {514, 21438}, {525, 52623}, {661, 20634}, {850, 7265}, {1089, 21052}, {2901, 17478}, {4041, 4647}, {4086, 36035}, {4151, 42031}, {4363, 7254}, {4560, 28605}, {4838, 4978}, {4980, 45671}, {6358, 51664}, {8045, 21437}, {14349, 20909}, {18155, 23883}, {20906, 48054}, {20908, 21834}, {20949, 48051}, {21611, 48003}, {23875, 35519}, {42034, 45324}

X(55184) = midpoint of X(i) and X(j) for these {i,j}: {21438, 23685}
X(55184) = isotomic conjugate of X(55183)
X(55184) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4049), X(47795)}}
X(55184) = barycentric product X(i)*X(j) for these (i, j): {313, 48283}, {321, 47795}, {1577, 32933}, {25440, 850}
X(55184) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55183}, {25440, 110}, {32933, 662}, {47795, 81}, {48283, 58}, {48389, 17104}
X(55184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21438, 23685, 514}

X(55185) = TRILINEAR POLE OF LINE {9, 2173}

X(55185) = X(1)X(44693)nX(145)X(6740)
Barycentrics    a*(a-b)*(a-c)*(a^3+b^3-a^2*(b-2*c)-a*(b-c)^2+2*b^2*c-b*c^2-2*c^3)*(a^3-2*b^3-a*(b-c)^2+a^2*(2*b-c)-b^2*c+2*b*c^2+c^3) : :

X(55185) lies on these lines: {1, 44693}, {145, 6740}, {1320, 2771}, {3244, 51565}, {26700, 35057}

X(55185) = reflection of X(i) in X(j) for these {i,j}: {44693, 1}
X(55185) = trilinear pole of line {9, 2173}
X(55185) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 41800}, {513, 3579}, {649, 17781}, {3650, 50344}
X(55185) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 41800}, {5375, 17781}, {39026, 3579}
X(55185) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(162)}}, {{A, B, C, X(100), X(643)}}, {{A, B, C, X(519), X(2771)}}, {{A, B, C, X(596), X(14147)}}, {{A, B, C, X(662), X(42362)}}, {{A, B, C, X(677), X(28176)}}, {{A, B, C, X(1023), X(3555)}}, {{A, B, C, X(1331), X(28148)}}, {{A, B, C, X(1392), X(4242)}}, {{A, B, C, X(2398), X(3957)}}, {{A, B, C, X(3257), X(44765)}}, {{A, B, C, X(4604), X(46640)}}, {{A, B, C, X(4637), X(25417)}}, {{A, B, C, X(5380), X(8690)}}, {{A, B, C, X(11278), X(23703)}}, {{A, B, C, X(14497), X(30250)}}
X(55185) = tripole of the mixed polar line of X(1) and X(43) in K001
X(55185) = barycentric product X(i)*X(j) for these (i, j): {10308, 190}
X(55185) = barycentric quotient X(i)/X(j) for these (i, j): {1, 41800}, {100, 17781}, {101, 3579}, {10308, 514}, {35342, 3650}

X(55186) = X(75)X(14208)∩X(522)X(693)

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

X(55186) lies on these lines: {75, 14208}, {522, 693}, {903, 46141}, {1577, 23883}, {2481, 53207}, {3762, 23875}, {5249, 8611}, {15413, 17894}, {16612, 19785}, {17498, 19789}, {42325, 53357}, {46107, 50450}

X(55186) = isotomic conjugate of X(55185)
X(55186) = perspector of circumconic {{A, B, C, X(85), X(33805)}}
X(55186) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55185}, {692, 10308}
X(55186) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55185}, {1086, 10308}, {41800, 35057}
X(55186) = X(i)-Ceva conjugate of X(j) for these {i, j}: {18160, 1577}
X(55186) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1461, 3648}, {6614, 41808}, {6742, 54113}, {13486, 18750}, {26700, 329}, {38340, 3436}, {52372, 37781}, {52374, 33650}
X(55186) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3676), X(41800)}}, {{A, B, C, X(4373), X(41804)}}, {{A, B, C, X(9436), X(17781)}}, {{A, B, C, X(21453), X(51364)}}, {{A, B, C, X(22464), X(39710)}}
X(55186) = barycentric product X(i)*X(j) for these (i, j): {3261, 3579}, {17781, 693}, {41800, 75}
X(55186) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55185}, {514, 10308}, {3579, 101}, {3650, 35342}, {17781, 100}, {41800, 1}
X(55186) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4025, 17896, 36038}

X(55187) = X(2)X(1577)∩X(8)X(21259)

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

X(55187) lies on these lines: {2, 1577}, {8, 21259}, {514, 27114}, {649, 27167}, {1019, 26983}, {1769, 8062}, {3907, 26115}, {4151, 19863}, {4369, 26114}, {4581, 48209}, {4728, 27193}, {7254, 19684}, {14288, 48246}, {16342, 21789}, {17418, 48186}, {19767, 21300}, {21052, 26030}, {26775, 50449}, {26822, 48568}, {27014, 47793}, {27293, 27647}, {31296, 52597}

X(55187) = perspector of circumconic {{A, B, C, X(14616), X(39693)}}
X(55187) = isotomic conjugate of the tripole of the mixed polar line of X(3) and X(8) in K001

X(55188) = X(647)X(7656)∩X(1637)X(2525)

Barycentrics    (b-c)*(b+c)*(2*a^4+b^4+6*b^2*c^2+c^4-3*a^2*(b^2+c^2)) : :
X(55188) = -6*X[23301]+X[50543]

X(55188) lies on these lines: {525, 31277}, {647, 7656}, {826, 31279}, {850, 14417}, {1637, 2525}, {2799, 31072}, {3265, 12077}, {23301, 50543}, {45689, 47126}

X(55188) = isotomic conjugate of the tripole of the mixed polar line of X(3) and X(51) in K001
X(55188) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2525, 30476, 1637}, {3265, 31174, 12077}, {30474, 30476, 2525}

X(55189) = X(3788)X(52145)∩X(4235)X(53273)

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

X(55189) lies on these lines: {3788, 52145}, {4235, 53273}

X(55189) = trilinear pole of line {3313, 6467}
X(55189) = X(i)-isoconjugate-of-X(j) for these {i, j}: {798, 16276}
X(55189) = X(i)-vertex conjugate of X(j) for these {i, j}: {32729, 53657}
X(55189) = X(i)-Dao conjugate of X(j) for these {i, j}: {31998, 16276}
X(55189) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(99)}}, {{A, B, C, X(110), X(4611)}}, {{A, B, C, X(112), X(40347)}}, {{A, B, C, X(907), X(6331)}}, {{A, B, C, X(1289), X(4563)}}, {{A, B, C, X(2396), X(3788)}}, {{A, B, C, X(2409), X(28405)}}, {{A, B, C, X(4576), X(6572)}}, {{A, B, C, X(7953), X(11794)}}, {{A, B, C, X(14376), X(32661)}}, {{A, B, C, X(41769), X(46607)}}
X(55189) = tripole of the mixed polar line of X(3) and X(69) in K001
X(55189) = barycentric quotient X(i)/X(j) for these (i, j): {99, 16276}

X(55190) = X(2)X(523)∩X(69)X(2451)

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

X(55190) lies on these lines: {2, 523}, {69, 2451}, {193, 39520}, {850, 2485}, {2489, 3267}, {2492, 23285}, {3049, 3618}, {3050, 3589}, {5025, 44823}, {6655, 44821}, {7907, 46609}, {9979, 23881}, {16043, 42660}, {18105, 44445}, {18314, 44817}, {26170, 46615}, {31277, 52598}, {33259, 44822}, {33752, 37125}, {39141, 39513}

X(55190) = perspector of circumconic {{A, B, C, X(671), X(683)}}
X(55190) = isotomic conjugate of X(55189)
X(55190) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(16276)}}
X(55190) = barycentric product X(i)*X(j) for these (i, j): {16276, 523}
X(55190) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55189}, {16276, 99}
X(55190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {850, 2485, 4580}, {2489, 30476, 3267}

X(55191) = TRILINEAR POLE OF LINE {193, 17710}

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

X(55191) lies on these lines:

X(55191) = trilinear pole of line {193, 17710}
X(55191) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7953)}}, {{A, B, C, X(99), X(30610)}}, {{A, B, C, X(11636), X(52608)}}
X(55191) = tripole of the mixed polar line of X(3) and X(141) in K001

X(55192) = X(523)X(4885)∩X(2492)X(23285)

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

X(55192) lies on these lines: {523, 4885}, {1510, 54262}, {2485, 31174}, {2492, 23285}, {8891, 31067}, {9148, 18105}, {20188, 24284}

X(55192) = midpoint of X(i) and X(j) for these {i,j}: {2492, 23285}
X(55192) = isotomic conjugate of X(55191)
X(55192) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23285, 55190, 2492}, {31072, 55190, 23285}

X(55193) = X(2)X(17899)∩X(525)X(17495)

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

X(55193) lies on these lines: {2, 17899}, {525, 17495}, {4560, 50453}, {14838, 31296}, {16754, 19804}, {17069, 17496}, {31072, 55187}

X(55193) = isotomic conjugate of the tripole of the mixed polar line of X(3) and X(145) in K001

X(55194) = X(12)X(4998)∩X(274)X(4567)

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

X(55194) lies on these lines: {12, 4998}, {274, 4567}, {1043, 4600}, {1252, 6645}, {1434, 4620}, {4564, 7340}, {4573, 45273}, {4590, 52379}

X(55194) = trilinear pole of line {59, 4600}
X(55194) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 8034}, {11, 798}, {210, 21143}, {213, 21132}, {244, 3709}, {512, 2170}, {522, 3121}, {649, 4516}, {650, 3122}, {657, 53540}, {661, 3271}, {663, 3125}, {667, 21044}, {669, 4858}, {764, 1334}, {810, 8735}, {1015, 4041}, {1084, 18155}, {1146, 51641}, {1357, 4171}, {1402, 42462}, {1918, 40166}, {1924, 34387}, {1977, 4086}, {2084, 18101}, {2150, 8029}, {2185, 22260}, {2194, 21131}, {2204, 21134}, {2310, 7180}, {2321, 8027}, {2489, 7004}, {2643, 7252}, {3022, 7216}, {3063, 3120}, {3119, 7250}, {3124, 3737}, {3248, 3700}, {3249, 3701}, {4017, 14936}, {4079, 18191}, {4524, 53538}, {7063, 7199}, {7064, 8042}, {8611, 42067}, {8641, 53545}, {17197, 50487}, {23099, 52379}, {36197, 43924}
X(55194) = X(i)-Dao conjugate of X(j) for these {i, j}: {478, 8034}, {1214, 21131}, {5375, 4516}, {6626, 21132}, {6631, 21044}, {9428, 34387}, {10001, 3120}, {31998, 11}, {34021, 40166}, {34961, 14936}, {36830, 3271}, {39054, 2170}, {39062, 8735}, {40605, 42462}, {40620, 7336}
X(55194) = X(i)-cross conjugate of X(j) for these {i, j}: {645, 4600}, {799, 4590}, {1414, 7340}, {4552, 4998}, {4563, 4601}, {4573, 4620}
X(55194) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(12), X(4552)}}, {{A, B, C, X(99), X(274)}}, {{A, B, C, X(645), X(1043)}}, {{A, B, C, X(651), X(961)}}, {{A, B, C, X(799), X(52379)}}, {{A, B, C, X(1408), X(4565)}}, {{A, B, C, X(1434), X(4573)}}, {{A, B, C, X(2966), X(4584)}}, {{A, B, C, X(4579), X(6645)}}, {{A, B, C, X(4619), X(31615)}}, {{A, B, C, X(14584), X(45273)}}
X(55194) = tripole of the mixed polar line of X(2) and X(11) in K002
X(55194) = barycentric product X(i)*X(j) for these (i, j): {12, 31614}, {59, 670}, {190, 4620}, {274, 31615}, {1016, 4573}, {1275, 645}, {1414, 7035}, {1434, 6632}, {1978, 52378}, {2149, 4602}, {3952, 7340}, {4076, 4616}, {4552, 4590}, {4554, 4567}, {4563, 46102}, {4564, 799}, {4566, 6064}, {4570, 4572}, {4600, 664}, {4601, 651}, {4625, 765}, {4998, 99}, {7045, 7257}, {24037, 4551}, {28660, 4619}, {31625, 4565}, {34537, 4559}, {44717, 6331}, {52608, 7115}
X(55194) = barycentric quotient X(i)/X(j) for these (i, j): {12, 8029}, {56, 8034}, {59, 512}, {86, 21132}, {99, 11}, {100, 4516}, {109, 3122}, {110, 3271}, {181, 22260}, {190, 21044}, {226, 21131}, {249, 7252}, {274, 40166}, {307, 21134}, {314, 42455}, {333, 42462}, {643, 2310}, {644, 36197}, {645, 1146}, {648, 8735}, {651, 3125}, {658, 53545}, {662, 2170}, {664, 3120}, {670, 34387}, {765, 4041}, {799, 4858}, {934, 53540}, {1014, 764}, {1016, 3700}, {1043, 23615}, {1252, 3709}, {1262, 7180}, {1275, 7178}, {1332, 53560}, {1408, 8027}, {1412, 21143}, {1414, 244}, {1415, 3121}, {1434, 6545}, {2149, 798}, {3699, 52335}, {3952, 4092}, {4551, 2643}, {4552, 115}, {4554, 16732}, {4558, 7117}, {4559, 3124}, {4563, 26932}, {4564, 661}, {4565, 1015}, {4566, 1365}, {4567, 650}, {4570, 663}, {4572, 21207}, {4573, 1086}, {4577, 18101}, {4579, 40608}, {4590, 4560}, {4592, 7004}, {4600, 522}, {4601, 4391}, {4610, 17197}, {4616, 1358}, {4619, 1400}, {4620, 514}, {4625, 1111}, {4637, 53538}, {4998, 523}, {5379, 18344}, {5546, 14936}, {6064, 7253}, {6065, 4524}, {6516, 18210}, {6632, 2321}, {6649, 53559}, {7035, 4086}, {7045, 4017}, {7115, 2489}, {7192, 7336}, {7253, 5532}, {7256, 4081}, {7257, 24026}, {7259, 3119}, {7339, 7250}, {7340, 7192}, {16704, 52338}, {16947, 3249}, {17095, 21141}, {18155, 1090}, {21859, 21833}, {23067, 20975}, {23981, 42752}, {24027, 51641}, {24037, 18155}, {24041, 3737}, {30941, 52305}, {31614, 261}, {31615, 37}, {34388, 23105}, {36797, 42069}, {44699, 44705}, {44710, 15451}, {44717, 647}, {44724, 44729}, {46102, 2501}, {47443, 2189}, {52378, 649}, {52379, 40213}, {52935, 18191}

X(55195) = X(37)X(523)∩X(261)X(4560)

Barycentrics    (a-b-c)*(b-c)^3*(b+c) : :
X(55195) = -X[192]+3*X[53359]

X(55195) lies on these lines: {37, 523}, {192, 53359}, {261, 4560}, {514, 3664}, {522, 3686}, {650, 40937}, {661, 2171}, {665, 47137}, {850, 20234}, {1577, 46826}, {1637, 21828}, {1880, 2501}, {2321, 3700}, {2804, 4526}, {3668, 7178}, {4024, 21810}, {4036, 20654}, {4041, 21039}, {4455, 55122}, {4467, 17117}, {4530, 14393}, {4705, 21698}, {6089, 21832}, {6550, 21143}, {8029, 8034}, {21131, 21134}, {23810, 24098}, {27045, 41298}

X(55195) = isotomic conjugate of X(55194)
X(55195) = reflection of X(i) in X(j) for these {i,j}: {24098, 23810}, {665, 47137}
X(55195) = perspector of circumconic {{A, B, C, X(11), X(3120)}}
X(55195) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 4619}, {31, 55194}, {58, 31615}, {59, 662}, {99, 2149}, {100, 52378}, {109, 4567}, {110, 4564}, {162, 44717}, {163, 4998}, {201, 47443}, {249, 4551}, {643, 1262}, {645, 24027}, {651, 4570}, {692, 4620}, {765, 4565}, {1101, 4552}, {1110, 4573}, {1252, 1414}, {1408, 6632}, {1415, 4600}, {1813, 5379}, {4558, 7012}, {4559, 24041}, {4575, 46102}, {4592, 7115}, {4625, 23990}, {4635, 6066}, {4637, 6065}, {5546, 7045}, {7257, 23979}, {7259, 7339}
X(55195) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55194}, {10, 31615}, {11, 4567}, {115, 4998}, {125, 44717}, {136, 46102}, {244, 4564}, {513, 4565}, {514, 4573}, {522, 645}, {523, 4552}, {650, 99}, {661, 1414}, {905, 4563}, {1084, 59}, {1086, 4620}, {1146, 4600}, {1577, 799}, {3005, 4559}, {3709, 4579}, {4988, 664}, {5139, 7115}, {6608, 7259}, {6615, 662}, {6741, 1016}, {8054, 52378}, {15450, 44710}, {17115, 5546}, {35509, 30941}, {38986, 2149}, {38991, 4570}, {40608, 1252}, {40611, 4619}, {40620, 7340}, {40622, 1275}, {40624, 4601}, {40625, 4590}, {40627, 109}, {40628, 4592}, {50330, 651}, {50497, 1415}, {55060, 1262}, {55064, 765}, {55067, 24041}
X(55195) = X(i)-Ceva conjugate of X(j) for these {i, j}: {523, 4516}, {661, 115}, {2395, 39786}, {2501, 3125}, {3700, 21044}, {4086, 4092}, {4560, 11}, {4858, 7336}, {7178, 3120}
X(55195) = intersection, other than A, B, C, of circumconics {{A, B, C, X(11), X(261)}}, {{A, B, C, X(37), X(4516)}}, {{A, B, C, X(115), X(2170)}}, {{A, B, C, X(512), X(52331)}}, {{A, B, C, X(523), X(52305)}}, {{A, B, C, X(647), X(52313)}}, {{A, B, C, X(661), X(46384)}}, {{A, B, C, X(1880), X(3125)}}, {{A, B, C, X(2189), X(3271)}}, {{A, B, C, X(2321), X(4530)}}, {{A, B, C, X(2501), X(52316)}}, {{A, B, C, X(3120), X(3668)}}, {{A, B, C, X(3664), X(41182)}}, {{A, B, C, X(3700), X(52338)}}, {{A, B, C, X(4024), X(52341)}}, {{A, B, C, X(4086), X(7336)}}, {{A, B, C, X(4092), X(4858)}}, {{A, B, C, X(7178), X(52334)}}, {{A, B, C, X(12077), X(52325)}}, {{A, B, C, X(23989), X(40099)}}
X(55195) = barycentric product X(i)*X(j) for these (i, j): {10, 21132}, {11, 523}, {37, 40166}, {115, 4560}, {226, 42462}, {244, 4086}, {261, 8029}, {338, 7252}, {525, 8735}, {1042, 23104}, {1086, 3700}, {1090, 4551}, {1109, 3737}, {1111, 4041}, {1146, 7178}, {1334, 23100}, {1365, 7253}, {1577, 2170}, {2171, 40213}, {2310, 4077}, {2321, 6545}, {2501, 26932}, {2969, 52355}, {3064, 4466}, {3120, 522}, {3122, 35519}, {3125, 4391}, {3239, 53545}, {3271, 850}, {3596, 8034}, {3676, 52335}, {3701, 764}, {3952, 7336}, {4049, 4530}, {4080, 52338}, {4092, 7192}, {4397, 53540}, {4516, 693}, {4566, 5532}, {4858, 661}, {13576, 52305}, {14554, 52341}, {14618, 7117}, {16732, 650}, {17094, 42069}, {17197, 4024}, {17924, 53560}, {18021, 22260}, {18101, 826}, {18155, 2643}, {18191, 4036}, {18210, 44426}, {21044, 514}, {21131, 333}, {21134, 29}, {21141, 7110}, {21143, 30713}, {21207, 663}, {23105, 60}, {23189, 2970}, {23615, 3668}, {23775, 6598}, {23978, 7180}, {23989, 3709}, {24002, 36197}, {24006, 7004}, {24026, 4017}, {34387, 512}, {35352, 4124}, {42455, 65}, {42759, 43728}
X(55195) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55194}, {11, 99}, {37, 31615}, {115, 4552}, {244, 1414}, {261, 31614}, {512, 59}, {514, 4620}, {522, 4600}, {523, 4998}, {647, 44717}, {649, 52378}, {650, 4567}, {661, 4564}, {663, 4570}, {764, 1014}, {798, 2149}, {1015, 4565}, {1086, 4573}, {1090, 18155}, {1111, 4625}, {1146, 645}, {1358, 4616}, {1365, 4566}, {1400, 4619}, {2170, 662}, {2189, 47443}, {2310, 643}, {2321, 6632}, {2489, 7115}, {2501, 46102}, {2643, 4551}, {3119, 7259}, {3120, 664}, {3121, 1415}, {3122, 109}, {3124, 4559}, {3125, 651}, {3249, 16947}, {3271, 110}, {3700, 1016}, {3709, 1252}, {3737, 24041}, {4017, 7045}, {4041, 765}, {4081, 7256}, {4086, 7035}, {4092, 3952}, {4391, 4601}, {4516, 100}, {4524, 6065}, {4560, 4590}, {4858, 799}, {5532, 7253}, {6545, 1434}, {7004, 4592}, {7117, 4558}, {7178, 1275}, {7180, 1262}, {7192, 7340}, {7250, 7339}, {7252, 249}, {7253, 6064}, {7336, 7192}, {8027, 1408}, {8029, 12}, {8034, 56}, {8735, 648}, {14936, 5546}, {15451, 44710}, {16732, 4554}, {17197, 4610}, {18101, 4577}, {18155, 24037}, {18191, 52935}, {18210, 6516}, {18344, 5379}, {20975, 23067}, {21044, 190}, {21131, 226}, {21132, 86}, {21134, 307}, {21141, 17095}, {21143, 1412}, {21207, 4572}, {21833, 21859}, {22260, 181}, {23105, 34388}, {23615, 1043}, {24026, 7257}, {26932, 4563}, {34387, 670}, {36197, 644}, {40166, 274}, {40213, 52379}, {40608, 4579}, {42069, 36797}, {42455, 314}, {42462, 333}, {42752, 23981}, {44705, 44699}, {44729, 44724}, {51641, 24027}, {52305, 30941}, {52335, 3699}, {52338, 16704}, {53538, 4637}, {53540, 934}, {53545, 658}, {53559, 6649}, {53560, 1332}
X(55195) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47137, 55126, 665}

X(55196) = TRILINEAR POLE OF LINE {60, 261}

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

X(55196) lies on these lines: {11, 261}, {593, 4366}, {643, 6064}, {799, 4590}, {4556, 4610}, {4612, 4631}, {4636, 14432}

X(55196) = trilinear pole of line {60, 261}
X(55196) = X(i)-isoconjugate-of-X(j) for these {i, j}: {12, 798}, {65, 4079}, {109, 21833}, {181, 661}, {201, 2489}, {226, 50487}, {512, 2171}, {594, 51641}, {669, 6358}, {756, 7180}, {762, 43924}, {810, 8736}, {872, 7178}, {1254, 3709}, {1356, 4033}, {1400, 4705}, {1402, 4024}, {1415, 21043}, {1441, 53581}, {1500, 4017}, {1924, 34388}, {2149, 8029}, {2643, 4559}, {3122, 21859}, {3124, 4551}, {4077, 7109}, {4171, 7143}, {4524, 7147}, {4564, 22260}, {4572, 52065}, {7064, 7216}
X(55196) = X(i)-Dao conjugate of X(j) for these {i, j}: {11, 21833}, {650, 8029}, {1146, 21043}, {9428, 34388}, {31998, 12}, {34961, 1500}, {36830, 181}, {39054, 2171}, {39062, 8736}, {40582, 4705}, {40602, 4079}, {40605, 4024}, {40620, 1365}, {40625, 115}, {40626, 21046}, {55067, 2643}
X(55196) = X(i)-cross conjugate of X(j) for these {i, j}: {2185, 6064}, {4560, 261}, {52379, 4590}
X(55196) = intersection, other than A, B, C, of circumconics {{A, B, C, X(11), X(4560)}}, {{A, B, C, X(643), X(2185)}}, {{A, B, C, X(799), X(52379)}}, {{A, B, C, X(2966), X(4603)}}, {{A, B, C, X(4556), X(4612)}}, {{A, B, C, X(4610), X(4631)}}, {{A, B, C, X(7252), X(8632)}}
X(55196) = tripole of the mixed polar line of X(2) and X(12) in K002
X(55196) = barycentric product X(i)*X(j) for these (i, j): {11, 31614}, {21, 4623}, {60, 670}, {110, 18021}, {261, 99}, {274, 4612}, {284, 52612}, {310, 4636}, {314, 52935}, {333, 4610}, {552, 7256}, {643, 873}, {646, 763}, {1098, 4625}, {1509, 645}, {2150, 4602}, {2185, 799}, {2189, 52608}, {3699, 6628}, {4560, 4590}, {4563, 46103}, {4573, 7058}, {4631, 81}, {6064, 7192}, {7253, 7340}, {7257, 757}, {18155, 24041}, {24037, 3737}, {26856, 55194}, {28660, 4556}, {30606, 4615}, {34537, 7252}, {52379, 662}
X(55196) = barycentric quotient X(i)/X(j) for these (i, j): {11, 8029}, {21, 4705}, {60, 512}, {99, 12}, {110, 181}, {249, 4559}, {261, 523}, {284, 4079}, {314, 4036}, {332, 4064}, {333, 4024}, {522, 21043}, {593, 7180}, {643, 756}, {644, 762}, {645, 594}, {648, 8736}, {650, 21833}, {662, 2171}, {670, 34388}, {757, 4017}, {763, 3669}, {799, 6358}, {849, 51641}, {873, 4077}, {1098, 4041}, {1414, 1254}, {1509, 7178}, {2150, 798}, {2185, 661}, {2189, 2489}, {2194, 50487}, {3271, 22260}, {3699, 6535}, {3737, 2643}, {3952, 6058}, {4267, 42661}, {4556, 1400}, {4558, 2197}, {4560, 115}, {4563, 26942}, {4566, 7314}, {4567, 21859}, {4573, 6354}, {4590, 4552}, {4592, 201}, {4610, 226}, {4612, 37}, {4616, 6046}, {4620, 4605}, {4623, 1441}, {4631, 321}, {4636, 42}, {4637, 7147}, {5546, 1500}, {6061, 4524}, {6064, 3952}, {6332, 21046}, {6628, 3676}, {7054, 3709}, {7058, 3700}, {7192, 1365}, {7252, 3124}, {7253, 4092}, {7256, 6057}, {7257, 1089}, {7340, 4566}, {7341, 7250}, {9273, 32675}, {17197, 21131}, {17219, 21134}, {18021, 850}, {18155, 1109}, {23189, 20975}, {23609, 8641}, {24041, 4551}, {26856, 55195}, {28660, 52623}, {30606, 4120}, {31614, 4998}, {34387, 23105}, {36797, 7140}, {46103, 2501}, {47443, 7115}, {52379, 1577}, {52612, 349}, {52914, 1824}, {52935, 65}

X(55197) = X(12)X(40475)∩X(661)X(2171)

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

X(55197) lies on these lines: {12, 40475}, {181, 12072}, {514, 23733}, {523, 7180}, {661, 2171}, {2501, 3709}, {2610, 4024}, {4017, 4838}, {4077, 6358}, {4552, 4998}, {4820, 23876}, {7178, 23879}, {7234, 55122}, {26983, 41298}, {39771, 53587}

X(55197) = isotomic conjugate of X(55196)
X(55197) = perspector of circumconic {{A, B, C, X(12), X(8736)}}
X(55197) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 4556}, {31, 55196}, {58, 4612}, {60, 662}, {81, 4636}, {99, 2150}, {110, 2185}, {163, 261}, {249, 3737}, {270, 4558}, {284, 52935}, {593, 643}, {645, 849}, {658, 23609}, {757, 5546}, {763, 3939}, {1098, 4565}, {1101, 4560}, {1414, 7054}, {1576, 52379}, {1790, 52914}, {2189, 4592}, {2194, 4610}, {2206, 4631}, {3738, 9273}, {3904, 9274}, {4575, 46103}, {4637, 6061}, {6514, 52920}, {7004, 47443}, {7252, 24041}, {7258, 7342}, {7259, 7341}, {18155, 23357}, {18604, 52921}
X(55197) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55196}, {10, 4612}, {115, 261}, {136, 46103}, {244, 2185}, {523, 4560}, {1084, 60}, {1214, 4610}, {3005, 7252}, {4075, 645}, {4858, 52379}, {5139, 2189}, {6741, 7058}, {15267, 4565}, {21709, 3686}, {36901, 18021}, {38986, 2150}, {40586, 4636}, {40590, 52935}, {40603, 4631}, {40607, 5546}, {40608, 7054}, {40611, 4556}, {40615, 6628}, {40617, 763}, {40622, 1509}, {55060, 593}, {55064, 1098}, {55065, 333}
X(55197) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2171, 115}, {4552, 12}, {6358, 1365}
X(55197) = intersection, other than A, B, C, of circumconics {{A, B, C, X(12), X(4998)}}, {{A, B, C, X(115), X(661)}}, {{A, B, C, X(181), X(7115)}}, {{A, B, C, X(2623), X(42666)}}, {{A, B, C, X(4024), X(31010)}}, {{A, B, C, X(6058), X(6358)}}, {{A, B, C, X(6367), X(23879)}}, {{A, B, C, X(12071), X(17422)}}, {{A, B, C, X(28654), X(40098)}}
X(55197) = barycentric product X(i)*X(j) for these (i, j): {12, 523}, {115, 4552}, {181, 850}, {201, 24006}, {225, 4064}, {226, 4024}, {338, 4559}, {349, 4079}, {525, 8736}, {594, 7178}, {1089, 4017}, {1091, 3737}, {1109, 4551}, {1254, 4086}, {1365, 3952}, {1400, 52623}, {1441, 4705}, {1577, 2171}, {2501, 26942}, {3676, 6535}, {3700, 6354}, {4036, 65}, {4077, 756}, {4092, 4566}, {4103, 53545}, {4998, 8029}, {6058, 7192}, {6358, 661}, {7253, 7314}, {14618, 2197}, {15065, 51663}, {16732, 21859}, {17094, 7140}, {21043, 664}, {21044, 4605}, {21046, 653}, {21833, 4554}, {23067, 2970}, {23105, 59}, {24002, 762}, {28654, 7180}, {30572, 4013}, {34388, 512}, {35352, 7235}, {52383, 6370}
X(55197) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55196}, {12, 99}, {37, 4612}, {42, 4636}, {65, 52935}, {115, 4560}, {181, 110}, {201, 4592}, {226, 4610}, {321, 4631}, {349, 52612}, {512, 60}, {523, 261}, {594, 645}, {661, 2185}, {756, 643}, {762, 644}, {798, 2150}, {850, 18021}, {1089, 7257}, {1109, 18155}, {1254, 1414}, {1365, 7192}, {1400, 4556}, {1441, 4623}, {1500, 5546}, {1577, 52379}, {1824, 52914}, {2171, 662}, {2197, 4558}, {2489, 2189}, {2501, 46103}, {2643, 3737}, {3124, 7252}, {3669, 763}, {3676, 6628}, {3700, 7058}, {3709, 7054}, {3952, 6064}, {4017, 757}, {4024, 333}, {4036, 314}, {4041, 1098}, {4064, 332}, {4077, 873}, {4079, 284}, {4092, 7253}, {4120, 30606}, {4524, 6061}, {4551, 24041}, {4552, 4590}, {4559, 249}, {4566, 7340}, {4605, 4620}, {4705, 21}, {4998, 31614}, {6046, 4616}, {6057, 7256}, {6058, 3952}, {6354, 4573}, {6358, 799}, {6535, 3699}, {7115, 47443}, {7140, 36797}, {7147, 4637}, {7178, 1509}, {7180, 593}, {7250, 7341}, {7314, 4566}, {8029, 11}, {8641, 23609}, {8736, 648}, {20975, 23189}, {21043, 522}, {21046, 6332}, {21131, 17197}, {21134, 17219}, {21833, 650}, {21859, 4567}, {22260, 3271}, {23105, 34387}, {26942, 4563}, {32675, 9273}, {34388, 670}, {42661, 4267}, {50487, 2194}, {51641, 849}, {52623, 28660}, {55195, 26856}
X(55197) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 12077, 55195}

X(55198) = TRILINEAR POLE OF LINE {61, 302}

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

X(55198) lies on these lines: {76, 11131}, {99, 110}, {670, 32037}, {4590, 23896}, {6331, 36306}, {7769, 8838}, {7782, 14170}, {11059, 37776}, {14904, 39691}, {32302, 36792}

X(55198) = trilinear pole of line {61, 302}
X(55198) = X(i)-isoconjugate-of-X(j) for these {i, j}: {17, 798}, {661, 21461}, {810, 8741}, {1924, 34389}, {2643, 16806}
X(55198) = X(i)-Dao conjugate of X(j) for these {i, j}: {9428, 34389}, {10640, 512}, {11130, 6138}, {31998, 17}, {36830, 21461}, {39062, 8741}
X(55198) = X(i)-cross conjugate of X(j) for these {i, j}: {23872, 302}
X(55198) = intersection, other than A, B, C, of circumconics {{A, B, C, X(61), X(5118)}}, {{A, B, C, X(302), X(5468)}}, {{A, B, C, X(473), X(4226)}}, {{A, B, C, X(690), X(23872)}}, {{A, B, C, X(16771), X(23896)}}
X(55198) = tripole of the mixed polar line of X(2) and X(17) in K002
X(55198) = barycentric product X(i)*X(j) for these (i, j): {61, 670}, {302, 99}, {4563, 473}, {10642, 52608}, {11132, 23896}, {23872, 4590}, {32037, 7769}, {52348, 6331}, {52605, 76}
X(55198) = barycentric quotient X(i)/X(j) for these (i, j): {61, 512}, {99, 17}, {110, 21461}, {249, 16806}, {302, 523}, {473, 2501}, {648, 8741}, {670, 34389}, {4558, 32585}, {4563, 40712}, {4590, 32036}, {7769, 23873}, {8838, 20578}, {10409, 34321}, {10642, 2489}, {11126, 6138}, {11132, 23871}, {11146, 6137}, {14570, 36300}, {16771, 20579}, {17402, 8603}, {17403, 51890}, {23872, 115}, {23895, 11139}, {23896, 11087}, {32037, 2963}, {35314, 36304}, {52220, 23283}, {52348, 647}, {52605, 6}, {52606, 51547}, {52671, 51513}, {52929, 21462}

X(55199) = X(17)X(5466)∩X(523)X(14446)

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

X(55199) lies on these lines: {17, 5466}, {476, 16806}, {523, 14446}, {647, 20578}, {850, 23873}, {892, 32036}, {2395, 21461}, {2501, 6137}, {5472, 12077}, {8018, 8029}, {8741, 18808}, {10412, 36300}, {14610, 22934}, {15328, 32585}, {19779, 23871}

X(55199) = isogonal conjugate of X(52605)
X(55199) = isotomic conjugate of X(55198)
X(55199) = perspector of circumconic {{A, B, C, X(17), X(2963)}}
X(55199) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 52605}, {61, 662}, {162, 52348}, {163, 302}, {473, 4575}, {1101, 23872}, {2964, 32037}, {3376, 17403}, {4592, 10642}, {23896, 35199}
X(55199) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 52605}, {115, 302}, {125, 52348}, {136, 473}, {523, 23872}, {1084, 61}, {5139, 10642}, {21975, 32037}, {38993, 11146}, {38994, 11126}, {43962, 11132}, {46604, 16807}
X(55199) = X(i)-Ceva conjugate of X(j) for these {i, j}: {16806, 36300}, {32036, 17}
X(55199) = X(i)-cross conjugate of X(j) for these {i, j}: {6138, 20579}
X(55199) = intersection, other than A, B, C, of circumconics {{A, B, C, X(115), X(23871)}}, {{A, B, C, X(476), X(523)}}, {{A, B, C, X(512), X(23873)}}, {{A, B, C, X(647), X(6137)}}, {{A, B, C, X(2623), X(6138)}}
X(55199) = barycentric product X(i)*X(j) for these (i, j): {17, 523}, {115, 32036}, {525, 8741}, {2501, 40712}, {11087, 23871}, {11139, 23870}, {11600, 23283}, {14618, 32585}, {15412, 36300}, {16806, 338}, {19779, 20579}, {21461, 850}, {23873, 2963}, {34389, 512}
X(55199) = barycentric quotient X(i)/X(j) for these (i, j): {6, 52605}, {17, 99}, {115, 23872}, {512, 61}, {523, 302}, {647, 52348}, {2489, 10642}, {2501, 473}, {2963, 32037}, {6137, 11146}, {6138, 11126}, {8603, 17402}, {8741, 648}, {11087, 23896}, {11139, 23895}, {16806, 249}, {20578, 8838}, {20579, 16771}, {21461, 110}, {21462, 52929}, {23283, 52220}, {23871, 11132}, {23873, 7769}, {32036, 4590}, {32585, 4558}, {34321, 10409}, {34389, 670}, {36300, 14570}, {36304, 35314}, {40712, 4563}, {51513, 52671}, {51547, 52606}, {51890, 17403}

X(55200) = TRILINEAR POLE OF LINE {62, 303}

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

X(55200) lies on these lines: {76, 11130}, {99, 110}, {670, 32036}, {4590, 23895}, {6331, 36309}, {7769, 8836}, {7782, 14169}, {11059, 37775}, {14905, 39691}, {32301, 36792}

X(55200) = trilinear pole of line {62, 303}
X(55200) = X(i)-isoconjugate-of-X(j) for these {i, j}: {18, 798}, {661, 21462}, {810, 8742}, {1924, 34390}, {2643, 16807}
X(55200) = X(i)-Dao conjugate of X(j) for these {i, j}: {9428, 34390}, {10639, 512}, {11131, 6137}, {31998, 18}, {36830, 21462}, {39062, 8742}
X(55200) = X(i)-cross conjugate of X(j) for these {i, j}: {23873, 303}
X(55200) = intersection, other than A, B, C, of circumconics {{A, B, C, X(62), X(5118)}}, {{A, B, C, X(303), X(5468)}}, {{A, B, C, X(472), X(4226)}}, {{A, B, C, X(690), X(23873)}}, {{A, B, C, X(16770), X(23895)}}
X(55200) = tripole of the mixed polar line of X(2) and X(18) in K002
X(55200) = barycentric product X(i)*X(j) for these (i, j): {62, 670}, {303, 99}, {4563, 472}, {10641, 52608}, {11133, 23895}, {23873, 4590}, {32036, 7769}, {52349, 6331}, {52606, 76}
X(55200) = barycentric quotient X(i)/X(j) for these (i, j): {62, 512}, {99, 18}, {110, 21462}, {249, 16807}, {303, 523}, {472, 2501}, {648, 8742}, {670, 34390}, {4558, 32586}, {4563, 40711}, {4590, 32037}, {7769, 23872}, {8836, 20579}, {10410, 34322}, {10641, 2489}, {11127, 6137}, {11133, 23870}, {11145, 6138}, {14570, 36301}, {16770, 20578}, {17402, 51891}, {17403, 8604}, {23873, 115}, {23895, 11082}, {23896, 11138}, {32036, 2963}, {35315, 36305}, {52221, 23284}, {52349, 647}, {52605, 51546}, {52606, 6}, {52670, 51513}, {52930, 21461}

X(55201) = X(18)X(5466)∩X(523)X(14447)

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

X(55201) lies on these lines: {18, 5466}, {476, 16807}, {523, 14447}, {647, 20579}, {850, 23872}, {892, 32037}, {2395, 21462}, {2501, 6138}, {5471, 12077}, {8019, 8029}, {8742, 18808}, {10412, 36301}, {14610, 22889}, {15328, 32586}, {19778, 23870}

X(55199) = isogonal conjugate of X(52606)
X(55199) = isotomic conjugate of X(55199)
X(55201) = perspector of circumconic {{A, B, C, X(18), X(2963)}}
X(55201) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 52606}, {62, 662}, {162, 52349}, {163, 303}, {472, 4575}, {1101, 23873}, {2964, 32036}, {3383, 17402}, {4592, 10641}, {23895, 35198}
X(55201) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 52606}, {115, 303}, {125, 52349}, {136, 472}, {523, 23873}, {1084, 62}, {5139, 10641}, {21975, 32036}, {38993, 11127}, {38994, 11145}, {43961, 11133}, {46604, 16806}
X(55201) = X(i)-Ceva conjugate of X(j) for these {i, j}: {16807, 36301}, {32037, 18}
X(55201) = X(i)-cross conjugate of X(j) for these {i, j}: {6137, 20578}
X(55201) = intersection, other than A, B, C, of circumconics {{A, B, C, X(115), X(23870)}}, {{A, B, C, X(476), X(523)}}, {{A, B, C, X(512), X(23872)}}, {{A, B, C, X(647), X(6138)}}, {{A, B, C, X(2623), X(6137)}}
X(55201) = barycentric product X(i)*X(j) for these (i, j): {18, 523}, {115, 32037}, {525, 8742}, {2501, 40711}, {11082, 23870}, {11138, 23871}, {11601, 23284}, {14618, 32586}, {15412, 36301}, {16807, 338}, {19778, 20578}, {21462, 850}, {23872, 2963}, {34390, 512}
X(55201) = barycentric quotient X(i)/X(j) for these (i, j): {6, 52606}, {18, 99}, {115, 23873}, {512, 62}, {523, 303}, {647, 52349}, {2489, 10641}, {2501, 472}, {2963, 32036}, {6137, 11127}, {6138, 11145}, {8604, 17403}, {8742, 648}, {11082, 23895}, {11138, 23896}, {16807, 249}, {20578, 16770}, {20579, 8836}, {21461, 52930}, {21462, 110}, {23284, 52221}, {23870, 11133}, {23872, 7769}, {32037, 4590}, {32586, 4558}, {34322, 10410}, {34390, 670}, {36301, 14570}, {36305, 35315}, {40711, 4563}, {51513, 52670}, {51546, 52605}, {51891, 17402}

X(55202) = TRILINEAR POLE OF LINE {63, 304}

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

X(55202) lies on these lines: {75, 8773}, {99, 1310}, {304, 20902}, {326, 336}, {332, 31637}, {662, 799}, {664, 670}, {811, 4602}, {897, 18060}, {1332, 4563}, {1444, 22378}, {4561, 52608}, {4601, 7258}, {4616, 7256}, {8777, 28660}, {15419, 52609}, {17206, 22066}, {18064, 36289}, {20888, 24227}

X(55202) = trilinear pole of line {63, 304}
X(55202) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 669}, {6, 2489}, {19, 798}, {25, 512}, {27, 53581}, {28, 50487}, {32, 2501}, {33, 51641}, {92, 1924}, {99, 42068}, {110, 2971}, {112, 3124}, {213, 6591}, {217, 15422}, {232, 2422}, {237, 53149}, {250, 22260}, {264, 9426}, {351, 8753}, {393, 3049}, {419, 881}, {520, 52439}, {523, 1974}, {525, 36417}, {560, 24006}, {607, 7180}, {608, 3709}, {647, 2207}, {648, 1084}, {649, 2333}, {661, 1973}, {667, 1824}, {688, 32085}, {810, 1096}, {811, 4117}, {850, 44162}, {862, 875}, {878, 34854}, {882, 44089}, {1356, 36797}, {1395, 4041}, {1398, 4524}, {1402, 18344}, {1426, 8641}, {1474, 4079}, {1500, 43925}, {1501, 14618}, {1576, 8754}, {1637, 40354}, {1783, 3121}, {1826, 1919}, {1843, 18105}, {1880, 3063}, {1918, 7649}, {1976, 17994}, {1980, 41013}, {2203, 4705}, {2205, 17924}, {2211, 2395}, {2212, 4017}, {2433, 14581}, {2491, 6531}, {2623, 3199}, {2643, 32676}, {2970, 14574}, {3122, 8750}, {3563, 42663}, {4230, 15630}, {4557, 42067}, {5027, 17980}, {6331, 9427}, {6524, 39201}, {6528, 23216}, {7071, 7250}, {7109, 17925}, {8541, 46001}, {8651, 14248}, {8749, 14398}, {8752, 14407}, {9178, 44102}, {9407, 18808}, {9494, 46104}, {10311, 52631}, {11060, 47230}, {13400, 46680}, {14270, 18384}, {14273, 32740}, {14573, 23290}, {14593, 34952}, {14601, 16230}, {14776, 42752}, {15475, 34397}, {18020, 23099}, {20975, 32713}, {32320, 36434}, {32696, 44114}, {33581, 44705}, {34212, 51437}, {34859, 51404}, {35325, 51906}, {35364, 44099}, {40144, 52588}, {40351, 41079}, {47643, 54273}, {50494, 51686}, {51513, 54034}
X(55202) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 798}, {9, 2489}, {244, 2971}, {4858, 8754}, {5375, 2333}, {6337, 661}, {6338, 656}, {6374, 24006}, {6376, 2501}, {6503, 810}, {6505, 512}, {6626, 6591}, {6631, 1824}, {9296, 1826}, {9428, 92}, {10001, 1880}, {15526, 2643}, {17423, 4117}, {22391, 1924}, {26932, 3122}, {31998, 19}, {34021, 7649}, {34591, 3124}, {34961, 2212}, {36033, 669}, {36830, 1973}, {38986, 42068}, {39006, 3121}, {39040, 17994}, {39052, 2207}, {39054, 25}, {39062, 1096}, {40591, 50487}, {40605, 18344}, {40618, 3125}, {40626, 4516}, {51574, 4079}, {52881, 2642}, {55066, 1084}
X(55202) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4602, 799}
X(55202) = X(i)-cross conjugate of X(j) for these {i, j}: {810, 63}, {4561, 4563}, {4592, 799}, {14208, 304}, {22387, 3}, {24560, 348}
X(55202) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(69), X(3570)}}, {{A, B, C, X(162), X(1633)}}, {{A, B, C, X(304), X(24039)}}, {{A, B, C, X(336), X(662)}}, {{A, B, C, X(656), X(9396)}}, {{A, B, C, X(670), X(4631)}}, {{A, B, C, X(799), X(4572)}}, {{A, B, C, X(823), X(36036)}}, {{A, B, C, X(4563), X(4610)}}, {{A, B, C, X(4575), X(46153)}}, {{A, B, C, X(4623), X(52608)}}, {{A, B, C, X(14208), X(20902)}}, {{A, B, C, X(17876), X(24006)}}, {{A, B, C, X(36084), X(36126)}}
X(55202) = tripole of the mixed polar line of X(2) and X(19) in K002
X(55202) = barycentric product X(i)*X(j) for these (i, j): {1, 52608}, {3, 4602}, {63, 670}, {69, 799}, {110, 40364}, {163, 40050}, {274, 4561}, {304, 99}, {305, 662}, {306, 4623}, {307, 4631}, {326, 6331}, {332, 4554}, {345, 4625}, {348, 7257}, {645, 7182}, {1102, 6528}, {1265, 4635}, {1331, 6385}, {1332, 310}, {1444, 1978}, {1502, 4575}, {1577, 47389}, {1790, 6386}, {1792, 46406}, {1812, 4572}, {1813, 40072}, {1928, 32661}, {2128, 54956}, {2396, 336}, {3265, 46254}, {3718, 4573}, {3926, 811}, {3933, 4593}, {3977, 4634}, {4020, 42371}, {4025, 4601}, {4176, 823}, {4558, 561}, {4563, 75}, {4592, 76}, {4609, 48}, {4616, 52406}, {7056, 7258}, {14208, 4590}, {15413, 4600}, {15419, 7035}, {17206, 668}, {17880, 55194}, {17932, 46238}, {20336, 4610}, {20902, 31614}, {23999, 4143}, {24037, 525}, {24039, 30786}, {24041, 3267}, {28660, 6516}, {34537, 656}, {35518, 4620}, {35567, 45220}, {36036, 6393}, {37204, 3917}, {40071, 52935}, {44168, 810}, {52609, 873}, {52612, 72}
X(55202) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2489}, {3, 798}, {48, 669}, {63, 512}, {69, 661}, {71, 50487}, {72, 4079}, {75, 2501}, {76, 24006}, {77, 7180}, {78, 3709}, {86, 6591}, {99, 19}, {100, 2333}, {110, 1973}, {162, 2207}, {163, 1974}, {184, 1924}, {190, 1824}, {222, 51641}, {228, 53581}, {249, 32676}, {255, 3049}, {274, 7649}, {283, 3063}, {293, 2422}, {304, 523}, {305, 1577}, {306, 4705}, {310, 17924}, {314, 3064}, {326, 647}, {332, 650}, {333, 18344}, {336, 2395}, {345, 4041}, {348, 4017}, {394, 810}, {525, 2643}, {561, 14618}, {643, 607}, {645, 33}, {646, 53008}, {648, 1096}, {656, 3124}, {658, 1426}, {661, 2971}, {662, 25}, {664, 1880}, {668, 1826}, {670, 92}, {757, 43925}, {798, 42068}, {799, 4}, {810, 1084}, {811, 393}, {823, 6524}, {873, 17925}, {892, 36128}, {905, 3122}, {906, 1918}, {1019, 42067}, {1102, 520}, {1264, 8611}, {1265, 4171}, {1331, 213}, {1332, 42}, {1414, 608}, {1434, 43923}, {1437, 1919}, {1444, 649}, {1459, 3121}, {1577, 8754}, {1633, 8020}, {1790, 667}, {1792, 657}, {1812, 663}, {1813, 1402}, {1821, 53149}, {1959, 17994}, {1978, 41013}, {2327, 8641}, {2396, 240}, {2617, 3199}, {3049, 4117}, {3265, 3708}, {3267, 1109}, {3570, 862}, {3692, 4524}, {3708, 22260}, {3718, 3700}, {3882, 44092}, {3917, 2084}, {3926, 656}, {3927, 4826}, {3933, 8061}, {3942, 8034}, {3958, 8663}, {3964, 822}, {3977, 4730}, {4001, 4983}, {4020, 688}, {4025, 3125}, {4033, 7140}, {4064, 21833}, {4143, 2632}, {4176, 24018}, {4554, 225}, {4556, 2203}, {4558, 31}, {4561, 37}, {4563, 1}, {4565, 1395}, {4567, 8750}, {4571, 1334}, {4572, 40149}, {4573, 34}, {4574, 872}, {4575, 32}, {4576, 17442}, {4585, 44113}, {4590, 162}, {4592, 6}, {4593, 32085}, {4600, 1783}, {4601, 1897}, {4602, 264}, {4609, 1969}, {4610, 28}, {4612, 2299}, {4615, 36125}, {4616, 1435}, {4620, 108}, {4622, 8752}, {4623, 27}, {4625, 278}, {4631, 29}, {4634, 6336}, {4635, 1119}, {4636, 2204}, {4637, 1398}, {4652, 4832}, {5227, 50494}, {5440, 14407}, {5546, 2212}, {6331, 158}, {6332, 4516}, {6385, 46107}, {6390, 2642}, {6507, 39201}, {6514, 1946}, {6516, 1400}, {6517, 1409}, {6528, 6520}, {7055, 51664}, {7056, 7216}, {7177, 7250}, {7182, 7178}, {7199, 2969}, {7254, 3248}, {7256, 7079}, {7257, 281}, {7258, 7046}, {7259, 7071}, {7289, 50490}, {8033, 54229}, {9247, 9426}, {14208, 115}, {14210, 14273}, {14213, 51513}, {14570, 2181}, {15411, 2310}, {15413, 3120}, {15416, 52335}, {15419, 244}, {16703, 21108}, {17206, 513}, {17880, 55195}, {17932, 1910}, {18020, 24019}, {18062, 428}, {18155, 8735}, {18695, 12077}, {18750, 44705}, {19591, 54273}, {19799, 48395}, {20336, 4024}, {20769, 4455}, {20794, 23503}, {20902, 8029}, {20948, 2970}, {21406, 12075}, {22090, 21835}, {22093, 21755}, {22370, 50491}, {23092, 38986}, {23181, 2179}, {23889, 44102}, {23997, 2211}, {23999, 6529}, {24018, 20975}, {24019, 52439}, {24037, 648}, {24039, 468}, {24041, 112}, {24560, 16613}, {28660, 44426}, {28706, 2618}, {30786, 23894}, {30805, 18210}, {32656, 2205}, {32661, 560}, {32676, 36417}, {32680, 18384}, {33805, 18808}, {34016, 54244}, {34055, 18105}, {34386, 2616}, {34537, 811}, {35518, 21044}, {36034, 40354}, {36036, 6531}, {36061, 11060}, {36085, 8753}, {36126, 36434}, {36841, 204}, {37134, 17980}, {37204, 46104}, {40050, 20948}, {40071, 4036}, {40072, 46110}, {40364, 850}, {40440, 15422}, {43187, 36120}, {44179, 6753}, {45220, 2514}, {46238, 16230}, {46254, 107}, {46810, 2588}, {46813, 2589}, {47389, 662}, {52437, 2624}, {52608, 75}, {52609, 756}, {52612, 286}, {52616, 53560}, {52617, 20902}, {52935, 1474}, {53642, 2358}, {54404, 50492}, {54983, 19218}, {54984, 19217}, {55194, 7012}, {55196, 270}
X(55202) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4625, 7257, 670}

X(55203) = TRILINEAR POLE OF LINE {69, 70}

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

X(55203) lies on these lines: {99, 1288}, {20564, 30786}

X(55203) = trilinear pole of line {69, 70}
X(55203) = X(i)-isoconjugate-of-X(j) for these {i, j}: {26, 798}, {661, 44078}, {810, 8746}, {1924, 44128}
X(55203) = X(i)-Dao conjugate of X(j) for these {i, j}: {9428, 44128}, {31998, 26}, {36830, 44078}, {39062, 8746}
X(55203) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(46963)}}, {{A, B, C, X(99), X(4554)}}, {{A, B, C, X(4235), X(30803)}}, {{A, B, C, X(30441), X(43755)}}
X(55203) = tripole of the mixed polar line of X(2) and X(26) in K002
X(55203) = barycentric product X(i)*X(j) for these (i, j): {670, 70}, {1288, 305}, {2158, 4602}, {20564, 99}
X(55203) = barycentric quotient X(i)/X(j) for these (i, j): {70, 512}, {99, 26}, {110, 44078}, {648, 8746}, {670, 44128}, {1288, 25}, {2158, 798}, {2407, 52953}, {18020, 52918}, {20564, 523}

X(55204) = X(112)X(53923)∩X(230)X(231)

Barycentrics    a^2*(b-c)*(b+c)*(a^8-2*a^6*(b^2+c^2)-(b^2-c^2)^2*(b^4+c^4)+2*a^2*(b^6+c^6)) : :

X(55204) lies on these lines: {112, 53923}, {230, 231}, {686, 30442}, {3049, 52317}, {3265, 44817}, {3569, 30451}, {7648, 53331}, {14397, 32320}, {14398, 17434}, {24978, 52584}

X(55204) = isotomic conjugate of X(55203)
X(55204) = complement of isotomic conjugate of XI46963)
X(55204) = perspector of circumconic {{A, B, C, X(4), X(26)}}
X(55204) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55203}, {63, 1288}, {70, 662}, {99, 2158}, {163, 20564}
X(55204) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55203}, {115, 20564}, {1084, 70}, {3162, 1288}, {38986, 2158}, {52120, 2}
X(55204) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2, 52120}, {52917, 184}, {52918, 44078}
X(55204) = X(i)-complementary conjugate of X(j) for these {i, j}: {31, 52120}, {46963, 2887}
X(55204) = intersection, other than A, B, C, of circumconics {{A, B, C, X(26), X(468)}}, {{A, B, C, X(232), X(44078)}}, {{A, B, C, X(1990), X(8746)}}, {{A, B, C, X(16230), X(52918)}}, {{A, B, C, X(46963), X(52120)}}
X(55204) = barycentric product X(i)*X(j) for these (i, j): {26, 523}, {125, 52918}, {525, 8746}, {2394, 52953}, {44078, 850}, {44128, 512}, {46963, 52120}
X(55204) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55203}, {25, 1288}, {26, 99}, {512, 70}, {523, 20564}, {798, 2158}, {8746, 648}, {44078, 110}, {44128, 670}, {52918, 18020}, {52953, 2407}
X(55204) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {647, 2489, 12077}, {2485, 6753, 647}, {2492, 16040, 2501}

X(55205) = TRILINEAR POLE OF LINE {77, 332}

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

X(55205) lies on these lines: {99, 6183}, {658, 799}, {670, 53642}, {1414, 4623}, {6516, 55202}

X(55205) = trilinear pole of line {77, 332}
X(55205) = X(i)-isoconjugate-of-X(j) for these {i, j}: {25, 3709}, {29, 53581}, {33, 798}, {55, 2489}, {213, 18344}, {281, 669}, {318, 1924}, {512, 607}, {608, 4524}, {645, 42068}, {647, 6059}, {648, 7063}, {661, 2212}, {663, 2333}, {1084, 36797}, {1172, 50487}, {1395, 4171}, {1824, 3063}, {1857, 3049}, {1880, 8641}, {1918, 3064}, {1919, 53008}, {1973, 4041}, {1974, 3700}, {2175, 2501}, {2204, 4705}, {2205, 44426}, {2299, 4079}, {2971, 5546}, {7017, 9426}, {7064, 43925}, {7071, 7180}, {7079, 51641}, {9447, 24006}, {9448, 14618}, {36417, 52355}
X(55205) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 2489}, {226, 4079}, {6337, 4041}, {6338, 8611}, {6505, 3709}, {6626, 18344}, {9296, 53008}, {9428, 318}, {10001, 1824}, {31998, 33}, {34021, 3064}, {36830, 2212}, {39052, 6059}, {39054, 607}, {40593, 2501}, {40618, 4516}, {40626, 36197}, {55066, 7063}
X(55205) = X(i)-cross conjugate of X(j) for these {i, j}: {4563, 55202}
X(55205) = intersection, other than A, B, C, of circumconics {{A, B, C, X(658), X(1414)}}, {{A, B, C, X(799), X(4563)}}, {{A, B, C, X(4558), X(4584)}}, {{A, B, C, X(4592), X(17206)}}, {{A, B, C, X(4623), X(52608)}}, {{A, B, C, X(4625), X(46406)}}
X(55205) = tripole of the mixed polar line of X(2) and X(33) in K002
X(55205) = barycentric product X(i)*X(j) for these (i, j): {222, 4602}, {304, 4573}, {307, 4623}, {310, 6516}, {332, 4569}, {345, 4635}, {348, 799}, {670, 77}, {1214, 52612}, {1231, 4610}, {1414, 305}, {1444, 4572}, {1792, 52937}, {1812, 46406}, {1813, 6385}, {3718, 4616}, {4077, 47389}, {4563, 85}, {4592, 6063}, {4609, 603}, {4625, 69}, {6331, 7183}, {7055, 811}, {7056, 7257}, {7182, 99}, {14208, 7340}, {15413, 4620}, {17094, 24037}, {17206, 4554}, {20567, 4558}, {30682, 7258}, {34537, 51664}, {40364, 4565}, {41283, 4575}, {52608, 57}, {55202, 7}
X(55205) = barycentric quotient X(i)/X(j) for these (i, j): {57, 2489}, {63, 3709}, {69, 4041}, {73, 50487}, {77, 512}, {78, 4524}, {85, 2501}, {86, 18344}, {99, 33}, {110, 2212}, {162, 6059}, {222, 798}, {274, 3064}, {283, 8641}, {304, 3700}, {305, 4086}, {307, 4705}, {310, 44426}, {332, 3900}, {345, 4171}, {348, 661}, {603, 669}, {643, 7071}, {645, 7079}, {651, 2333}, {658, 1880}, {662, 607}, {664, 1824}, {668, 53008}, {670, 318}, {799, 281}, {810, 7063}, {811, 1857}, {1038, 50494}, {1214, 4079}, {1231, 4024}, {1332, 1334}, {1409, 53581}, {1414, 25}, {1434, 6591}, {1444, 663}, {1790, 3063}, {1792, 4105}, {1804, 810}, {1812, 657}, {1813, 213}, {3926, 8611}, {4017, 2971}, {4025, 4516}, {4077, 8754}, {4554, 1826}, {4556, 2204}, {4558, 41}, {4561, 210}, {4563, 9}, {4565, 1973}, {4569, 225}, {4572, 41013}, {4573, 19}, {4575, 2175}, {4592, 55}, {4602, 7017}, {4610, 1172}, {4612, 2332}, {4616, 34}, {4620, 1783}, {4623, 29}, {4625, 4}, {4626, 1426}, {4631, 2322}, {4635, 278}, {4637, 608}, {4652, 8653}, {6063, 24006}, {6332, 36197}, {6385, 46110}, {6516, 42}, {6517, 228}, {7053, 51641}, {7055, 656}, {7056, 4017}, {7125, 3049}, {7177, 7180}, {7182, 523}, {7183, 647}, {7199, 8735}, {7203, 42067}, {7257, 7046}, {7340, 162}, {14208, 4092}, {15411, 3119}, {15413, 21044}, {15419, 2170}, {17094, 2643}, {17206, 650}, {18155, 42069}, {20567, 14618}, {23067, 872}, {24037, 36797}, {30682, 7216}, {30805, 53560}, {32660, 2205}, {32661, 9447}, {33673, 44705}, {35518, 52335}, {36059, 1918}, {36841, 7156}, {46406, 40149}, {47389, 643}, {51641, 42068}, {51664, 3124}, {52379, 17926}, {52411, 1924}, {52608, 312}, {52612, 31623}, {52935, 2299}, {55196, 2326}, {55202, 8}

X(55206) = X(19)X(35347)∩X(661)X(2501)

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

X(55206) lies on these lines: {19, 35347}, {657, 4041}, {661, 2501}, {798, 2333}, {1826, 21099}, {1880, 4017}, {2489, 3709}, {3064, 3239}, {4893, 6591}, {21016, 21055}, {21957, 24018}

X(55206) = polar conjugate of X(4625)
X(55206) = isotomic conjugate of X(55205)
X(55206) = perspector of circumconic {{A, B, C, X(33), X(225)}}
X(55206) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 4573}, {7, 4558}, {27, 6517}, {31, 55205}, {48, 4625}, {56, 4563}, {57, 4592}, {59, 15419}, {63, 1414}, {69, 4565}, {73, 4610}, {77, 662}, {78, 4637}, {81, 6516}, {85, 4575}, {86, 1813}, {99, 222}, {109, 17206}, {110, 348}, {112, 7055}, {162, 7183}, {163, 7182}, {212, 4635}, {219, 4616}, {249, 17094}, {261, 52610}, {274, 36059}, {283, 658}, {307, 4556}, {310, 32660}, {332, 1461}, {552, 4574}, {603, 799}, {604, 55202}, {643, 7177}, {645, 7053}, {647, 7340}, {648, 1804}, {651, 1444}, {664, 1790}, {670, 52411}, {811, 7125}, {934, 1812}, {1014, 1332}, {1214, 52935}, {1275, 23189}, {1331, 1434}, {1367, 47443}, {1397, 52608}, {1409, 4623}, {1410, 4631}, {1412, 4561}, {1425, 55196}, {1437, 4554}, {1439, 4612}, {1459, 4620}, {1509, 23067}, {1792, 4617}, {2193, 4569}, {2327, 4626}, {3937, 55194}, {4025, 52378}, {4619, 17219}, {4998, 7254}, {5546, 7056}, {6063, 32661}, {6331, 7335}, {6514, 36118}, {7099, 7257}, {7180, 47389}, {7192, 44717}, {7339, 15411}, {7341, 52609}, {17932, 43034}, {18026, 18604}, {24041, 51664}, {46254, 51640}
X(55206) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4563}, {2, 55205}, {11, 17206}, {115, 7182}, {125, 7183}, {136, 85}, {244, 348}, {1084, 77}, {1249, 4625}, {3005, 51664}, {3161, 55202}, {3162, 1414}, {5139, 57}, {5452, 4592}, {5521, 1434}, {6608, 15411}, {6615, 15419}, {6741, 304}, {7952, 799}, {14714, 1812}, {17423, 7125}, {20620, 274}, {23050, 645}, {34591, 7055}, {35508, 332}, {36103, 4573}, {38966, 333}, {38986, 222}, {38991, 1444}, {38996, 603}, {39025, 1790}, {39052, 7340}, {40586, 6516}, {40599, 4561}, {40600, 1813}, {40608, 63}, {40837, 4635}, {47345, 4569}, {55060, 7177}, {55064, 69}, {55065, 1231}, {55066, 1804}
X(55206) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1880, 4516}
X(55206) = X(i)-cross conjugate of X(j) for these {i, j}: {4079, 3709}
X(55206) = intersection, other than A, B, C, of circumconics {{A, B, C, X(512), X(8058)}}, {{A, B, C, X(523), X(6182)}}, {{A, B, C, X(657), X(661)}}, {{A, B, C, X(798), X(46393)}}, {{A, B, C, X(2489), X(3064)}}, {{A, B, C, X(4017), X(4516)}}, {{A, B, C, X(4041), X(4086)}}, {{A, B, C, X(4079), X(8611)}}, {{A, B, C, X(18344), X(44426)}}, {{A, B, C, X(50332), X(50459)}}
X(55206) = barycentric product X(i)*X(j) for these (i, j): {4, 4041}, {10, 18344}, {19, 3700}, {25, 4086}, {29, 4705}, {33, 523}, {42, 44426}, {108, 52335}, {162, 4092}, {210, 7649}, {213, 46110}, {225, 3900}, {273, 4524}, {278, 4171}, {281, 661}, {318, 512}, {393, 8611}, {513, 53008}, {643, 8754}, {1018, 8735}, {1021, 8736}, {1039, 48395}, {1096, 52355}, {1172, 4024}, {1334, 17924}, {1426, 4163}, {1577, 607}, {1783, 21044}, {1824, 522}, {1826, 650}, {1857, 656}, {1880, 3239}, {1897, 4516}, {2204, 52623}, {2212, 850}, {2299, 4036}, {2321, 6591}, {2326, 55197}, {2333, 4391}, {2489, 312}, {2501, 9}, {2643, 36797}, {2969, 4069}, {2971, 7257}, {3064, 37}, {3119, 52607}, {3709, 92}, {3737, 7140}, {4017, 7046}, {4077, 7071}, {4082, 43923}, {7017, 798}, {7079, 7178}, {7101, 7180}, {14208, 6059}, {14618, 41}, {14775, 40967}, {17926, 2171}, {21043, 52914}, {24006, 55}, {31623, 4079}, {34857, 44428}, {36197, 653}, {40149, 657}, {41013, 663}, {42069, 4551}, {44113, 52356}, {44130, 50487}, {44687, 51513}, {44692, 44705}, {44694, 53149}, {53013, 54239}
X(55206) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55205}, {4, 4625}, {8, 55202}, {9, 4563}, {19, 4573}, {25, 1414}, {29, 4623}, {33, 99}, {34, 4616}, {41, 4558}, {42, 6516}, {55, 4592}, {162, 7340}, {210, 4561}, {213, 1813}, {225, 4569}, {228, 6517}, {278, 4635}, {281, 799}, {312, 52608}, {318, 670}, {512, 77}, {523, 7182}, {607, 662}, {608, 4637}, {643, 47389}, {647, 7183}, {650, 17206}, {656, 7055}, {657, 1812}, {661, 348}, {663, 1444}, {669, 603}, {798, 222}, {810, 1804}, {872, 23067}, {1172, 4610}, {1334, 1332}, {1426, 4626}, {1783, 4620}, {1824, 664}, {1826, 4554}, {1857, 811}, {1880, 658}, {1918, 36059}, {1924, 52411}, {1973, 4565}, {2170, 15419}, {2175, 4575}, {2204, 4556}, {2205, 32660}, {2212, 110}, {2299, 52935}, {2322, 4631}, {2326, 55196}, {2332, 4612}, {2333, 651}, {2489, 57}, {2501, 85}, {2643, 17094}, {2971, 4017}, {3049, 7125}, {3063, 1790}, {3064, 274}, {3119, 15411}, {3124, 51664}, {3700, 304}, {3709, 63}, {3900, 332}, {4017, 7056}, {4024, 1231}, {4041, 69}, {4079, 1214}, {4086, 305}, {4092, 14208}, {4105, 1792}, {4171, 345}, {4516, 4025}, {4524, 78}, {4705, 307}, {6059, 162}, {6591, 1434}, {7017, 4602}, {7046, 7257}, {7063, 810}, {7071, 643}, {7079, 645}, {7156, 36841}, {7180, 7177}, {7216, 30682}, {8611, 3926}, {8641, 283}, {8653, 4652}, {8735, 7199}, {8754, 4077}, {9447, 32661}, {14618, 20567}, {17926, 52379}, {18344, 86}, {21044, 15413}, {24006, 6063}, {31623, 52612}, {36197, 6332}, {36797, 24037}, {40149, 46406}, {41013, 4572}, {42067, 7203}, {42068, 51641}, {42069, 18155}, {44426, 310}, {44705, 33673}, {46110, 6385}, {50487, 73}, {50494, 1038}, {51641, 7053}, {52335, 35518}, {53008, 668}, {53560, 30805}, {53581, 1409}

X(55207) = TRILINEAR POLE OF LINE {78, 332}

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

X(55207) lies on these lines: {190, 670}, {643, 4631}, {1332, 4563}, {52608, 55205}

X(55207) = trilinear pole of line {78, 332}
X(55207) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 51641}, {25, 7180}, {34, 798}, {56, 2489}, {108, 3121}, {181, 43925}, {213, 43923}, {225, 1919}, {273, 1924}, {278, 669}, {331, 9426}, {512, 608}, {607, 7250}, {647, 7337}, {648, 1356}, {661, 1395}, {667, 1880}, {1106, 55206}, {1118, 3049}, {1396, 50487}, {1397, 2501}, {1398, 3709}, {1402, 6591}, {1426, 3063}, {1973, 4017}, {1974, 7178}, {1980, 40149}, {2212, 7216}, {2333, 43924}, {2971, 4565}, {3122, 32674}, {4559, 42067}, {4573, 42068}, {7115, 8034}, {14618, 41280}, {17094, 36417}, {32702, 42752}
X(55207) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 2489}, {6, 51641}, {6337, 4017}, {6338, 51664}, {6505, 7180}, {6552, 55206}, {6626, 43923}, {6631, 1880}, {9296, 225}, {9428, 273}, {10001, 1426}, {11517, 798}, {31998, 34}, {34961, 1973}, {35072, 3122}, {36830, 1395}, {38983, 3121}, {39052, 7337}, {39054, 608}, {40605, 6591}, {40618, 53540}, {40626, 3125}, {40628, 8034}, {55064, 2971}, {55066, 1356}, {55067, 42067}
X(55207) = X(i)-Ceva conjugate of X(j) for these {i, j}: {52608, 55202}
X(55207) = intersection, other than A, B, C, of circumconics {{A, B, C, X(190), X(643)}}, {{A, B, C, X(670), X(4631)}}, {{A, B, C, X(799), X(4563)}}, {{A, B, C, X(1978), X(7257)}}, {{A, B, C, X(4558), X(4603)}}
X(55207) = tripole of the mixed polar line of X(2) and X(34) in K002
X(55207) = barycentric product X(i)*X(j) for these (i, j): {69, 7257}, {212, 4609}, {219, 4602}, {283, 6386}, {304, 645}, {305, 643}, {306, 4631}, {310, 4571}, {312, 4563}, {314, 4561}, {332, 668}, {345, 799}, {346, 55205}, {348, 7258}, {670, 78}, {1264, 811}, {1265, 4625}, {1331, 40072}, {1332, 28660}, {1792, 4572}, {1812, 1978}, {3596, 4592}, {3694, 52612}, {3710, 4623}, {3718, 99}, {3719, 6331}, {4086, 47389}, {4573, 52406}, {4587, 6385}, {4601, 6332}, {7182, 7256}, {14208, 6064}, {15416, 4620}, {17206, 646}, {24037, 52355}, {28659, 4558}, {30681, 4635}, {34537, 8611}, {35518, 4600}, {40071, 4612}, {40363, 4575}, {40364, 5546}, {52369, 55196}, {52379, 52609}, {52608, 9}, {55202, 8}
X(55207) = barycentric quotient X(i)/X(j) for these (i, j): {3, 51641}, {9, 2489}, {63, 7180}, {69, 4017}, {77, 7250}, {78, 512}, {86, 43923}, {99, 34}, {110, 1395}, {162, 7337}, {190, 1880}, {212, 669}, {219, 798}, {283, 667}, {304, 7178}, {305, 4077}, {312, 2501}, {314, 7649}, {332, 513}, {333, 6591}, {345, 661}, {346, 55206}, {348, 7216}, {521, 3122}, {643, 25}, {644, 2333}, {645, 19}, {646, 1826}, {652, 3121}, {662, 608}, {664, 1426}, {668, 225}, {670, 273}, {799, 278}, {810, 1356}, {811, 1118}, {874, 1874}, {1040, 50490}, {1043, 18344}, {1259, 810}, {1264, 656}, {1265, 4041}, {1331, 1402}, {1332, 1400}, {1414, 1398}, {1444, 43924}, {1792, 663}, {1808, 875}, {1812, 649}, {1978, 40149}, {2185, 43925}, {2193, 1919}, {2289, 3049}, {2318, 50487}, {2327, 3063}, {3596, 24006}, {3692, 3709}, {3694, 4079}, {3699, 1824}, {3710, 4705}, {3718, 523}, {3719, 647}, {3737, 42067}, {3926, 51664}, {3964, 51640}, {4025, 53540}, {4033, 8736}, {4041, 2971}, {4086, 8754}, {4558, 604}, {4561, 65}, {4563, 57}, {4567, 32674}, {4571, 42}, {4573, 1435}, {4575, 1397}, {4587, 213}, {4592, 56}, {4600, 108}, {4601, 653}, {4602, 331}, {4610, 1396}, {4612, 1474}, {4620, 32714}, {4625, 1119}, {4631, 27}, {4636, 2203}, {5546, 1973}, {6064, 162}, {6332, 3125}, {6514, 22383}, {6516, 1042}, {6517, 1410}, {7004, 8034}, {7256, 33}, {7257, 4}, {7258, 281}, {7259, 607}, {8611, 3124}, {14208, 1365}, {15411, 2170}, {15413, 53545}, {15416, 21044}, {15419, 53538}, {17206, 3669}, {17219, 764}, {18155, 2969}, {23189, 3248}, {24560, 55060}, {28659, 14618}, {28660, 17924}, {30681, 4171}, {35518, 3120}, {36797, 1096}, {36841, 3213}, {40072, 46107}, {44327, 2358}, {44694, 17994}, {44722, 4729}, {47389, 1414}, {52346, 44705}, {52355, 2643}, {52369, 55197}, {52370, 53581}, {52379, 17925}, {52406, 3700}, {52425, 1924}, {52608, 85}, {52609, 2171}, {52616, 18210}, {52978, 14407}, {55194, 7128}, {55202, 7}, {55205, 279}

X(55208) = X(108)X(2702)∩X(514)X(3064)

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

X(55208) lies on these lines: {108, 2702}, {278, 17921}, {514, 3064}, {608, 43925}, {649, 4017}, {661, 2501}, {2489, 7180}, {4822, 18344}, {6753, 21828}, {7649, 50332}, {13401, 51662}, {18026, 53195}

X(55208) = polar conjugate of X(7257)
X(55208) = isotomic conjugate of X(55207)
X(55208) = perspector of circumconic {{A, B, C, X(34), X(225)}}
X(55208) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 645}, {8, 4558}, {9, 4592}, {21, 1332}, {31, 55207}, {41, 55202}, {48, 7257}, {55, 4563}, {59, 15411}, {60, 52609}, {63, 643}, {69, 5546}, {72, 4612}, {77, 7259}, {78, 662}, {81, 4571}, {86, 4587}, {99, 219}, {100, 1812}, {101, 332}, {110, 345}, {112, 1264}, {162, 3719}, {163, 3718}, {212, 799}, {222, 7256}, {228, 4631}, {249, 52355}, {261, 4574}, {284, 4561}, {306, 4636}, {312, 4575}, {314, 906}, {333, 1331}, {394, 36797}, {521, 4567}, {603, 7258}, {644, 1444}, {646, 1437}, {647, 6064}, {648, 1259}, {651, 1792}, {652, 4600}, {664, 2327}, {668, 2193}, {670, 52425}, {811, 2289}, {1016, 23189}, {1043, 1813}, {1253, 55205}, {1260, 4573}, {1265, 4565}, {1414, 3692}, {1790, 3699}, {1793, 4585}, {1802, 4625}, {1808, 3570}, {1819, 44327}, {1897, 6514}, {1946, 4601}, {2175, 52608}, {2287, 6516}, {2318, 4610}, {2322, 6517}, {3270, 55194}, {3596, 32661}, {3690, 55196}, {3694, 52935}, {3709, 47389}, {3710, 4556}, {3939, 17206}, {3998, 52914}, {4076, 7254}, {4570, 6332}, {4622, 52978}, {4623, 52370}, {4998, 23090}, {6056, 6331}, {6065, 15419}, {7058, 23067}, {7068, 47443}, {7253, 44717}, {8611, 24041}, {28660, 32656}
X(55208) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55207}, {115, 3718}, {125, 3719}, {136, 312}, {223, 4563}, {244, 345}, {478, 4592}, {1015, 332}, {1084, 78}, {1249, 7257}, {3005, 8611}, {3160, 55202}, {3162, 643}, {4988, 35518}, {5139, 9}, {5190, 314}, {5521, 333}, {6615, 15411}, {6741, 52406}, {7180, 24560}, {7952, 7258}, {8054, 1812}, {17113, 55205}, {17423, 2289}, {34467, 6514}, {34591, 1264}, {36103, 645}, {38986, 219}, {38991, 1792}, {38996, 212}, {39025, 2327}, {39052, 6064}, {39053, 4601}, {40586, 4571}, {40590, 4561}, {40593, 52608}, {40600, 4587}, {40608, 3692}, {40611, 1332}, {40617, 17206}, {40622, 304}, {40627, 521}, {40837, 799}, {47345, 668}, {50330, 6332}, {50497, 652}, {55053, 283}, {55060, 63}, {55064, 1265}, {55066, 1259}
X(55208) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2358, 3125}, {6591, 7180}
X(55208) = X(i)-cross conjugate of X(j) for these {i, j}: {51641, 4017}
X(55208) = intersection, other than A, B, C, of circumconics {{A, B, C, X(512), X(514)}}, {{A, B, C, X(1426), X(38461)}}, {{A, B, C, X(1880), X(37790)}}, {{A, B, C, X(2489), X(3064)}}, {{A, B, C, X(2501), X(6591)}}, {{A, B, C, X(4017), X(4077)}}, {{A, B, C, X(51641), X(51664)}}
X(55208) = barycentric product X(i)*X(j) for these (i, j): {4, 4017}, {10, 43923}, {19, 7178}, {25, 4077}, {34, 523}, {65, 7649}, {108, 3120}, {225, 513}, {226, 6591}, {264, 51641}, {273, 512}, {278, 661}, {279, 55206}, {281, 7216}, {318, 7250}, {331, 798}, {393, 51664}, {1019, 8736}, {1020, 8735}, {1041, 48403}, {1042, 44426}, {1093, 51640}, {1096, 17094}, {1118, 656}, {1119, 4041}, {1365, 162}, {1395, 850}, {1396, 4024}, {1398, 4086}, {1400, 17924}, {1402, 46107}, {1414, 8754}, {1426, 522}, {1427, 3064}, {1435, 3700}, {1577, 608}, {1783, 53545}, {1824, 3676}, {1826, 3669}, {1847, 3709}, {1874, 876}, {1880, 514}, {1897, 53540}, {1919, 52575}, {2170, 52607}, {2333, 24002}, {2489, 85}, {2501, 57}, {2969, 4551}, {2971, 4625}, {3121, 46404}, {3125, 653}, {7140, 7203}, {7180, 92}, {14208, 7337}, {14618, 604}, {14837, 2358}, {15422, 44708}, {16732, 32674}, {17925, 2171}, {17926, 7147}, {18026, 3122}, {18210, 36127}, {18344, 3668}, {18808, 51654}, {21044, 32714}, {24006, 56}, {30572, 36125}, {36110, 42759}, {36118, 4516}, {36124, 53551}, {40149, 649}, {41013, 43924}, {43925, 6358}, {43932, 53008}, {44705, 8809}, {52382, 54244}, {52384, 54239}, {55195, 7128}
X(55208) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55207}, {4, 7257}, {7, 55202}, {19, 645}, {25, 643}, {27, 4631}, {33, 7256}, {34, 99}, {42, 4571}, {56, 4592}, {57, 4563}, {65, 4561}, {85, 52608}, {108, 4600}, {162, 6064}, {213, 4587}, {225, 668}, {273, 670}, {278, 799}, {279, 55205}, {281, 7258}, {331, 4602}, {512, 78}, {513, 332}, {523, 3718}, {604, 4558}, {607, 7259}, {608, 662}, {647, 3719}, {649, 1812}, {653, 4601}, {656, 1264}, {661, 345}, {663, 1792}, {667, 283}, {669, 212}, {764, 17219}, {798, 219}, {810, 1259}, {875, 1808}, {1042, 6516}, {1096, 36797}, {1118, 811}, {1119, 4625}, {1356, 810}, {1365, 14208}, {1395, 110}, {1396, 4610}, {1397, 4575}, {1398, 1414}, {1400, 1332}, {1402, 1331}, {1410, 6517}, {1414, 47389}, {1426, 664}, {1435, 4573}, {1474, 4612}, {1824, 3699}, {1826, 646}, {1874, 874}, {1880, 190}, {1919, 2193}, {1924, 52425}, {1973, 5546}, {2170, 15411}, {2171, 52609}, {2203, 4636}, {2333, 644}, {2358, 44327}, {2489, 9}, {2501, 312}, {2643, 52355}, {2969, 18155}, {2971, 4041}, {3049, 2289}, {3063, 2327}, {3120, 35518}, {3121, 652}, {3122, 521}, {3124, 8611}, {3125, 6332}, {3213, 36841}, {3248, 23189}, {3669, 17206}, {3700, 52406}, {3709, 3692}, {4017, 69}, {4041, 1265}, {4077, 305}, {4079, 3694}, {4171, 30681}, {4705, 3710}, {4729, 44722}, {6591, 333}, {7128, 55194}, {7178, 304}, {7180, 63}, {7216, 348}, {7250, 77}, {7337, 162}, {7649, 314}, {8034, 7004}, {8736, 4033}, {8754, 4086}, {14407, 52978}, {14618, 28659}, {17924, 28660}, {17925, 52379}, {17994, 44694}, {18210, 52616}, {18344, 1043}, {21044, 15416}, {22383, 6514}, {24006, 3596}, {32674, 4567}, {32714, 4620}, {40149, 1978}, {42067, 3737}, {43923, 86}, {43924, 1444}, {43925, 2185}, {44705, 52346}, {46107, 40072}, {50487, 2318}, {50490, 1040}, {51640, 3964}, {51641, 3}, {51664, 3926}, {53538, 15419}, {53540, 4025}, {53545, 15413}, {53581, 52370}, {55060, 24560}, {55197, 52369}, {55206, 346}
X(55208) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 2501, 55206}

X(55209) = TRILINEAR POLE OF LINE {79, 314}

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

X(55209) lies on these lines: {274, 16734}, {799, 38340}, {3261, 4610}, {4597, 35139}, {6742, 7257}, {14195, 52002}

X(55209) = trilinear pole of line {79, 314}
X(55209) = X(i)-isoconjugate-of-X(j) for these {i, j}: {35, 798}, {213, 2605}, {319, 1924}, {512, 2174}, {560, 7265}, {647, 14975}, {663, 21741}, {669, 3219}, {692, 20982}, {1399, 3709}, {1402, 9404}, {1576, 21824}, {1918, 14838}, {1919, 3678}, {1922, 53563}, {1980, 3969}, {2161, 14270}, {2200, 54244}, {2205, 4467}, {2333, 23226}, {2489, 52408}, {2594, 3063}, {2611, 32739}, {2624, 6187}, {3049, 6198}, {4079, 17104}, {9426, 33939}, {40214, 50487}, {51641, 52405}
X(55209) = X(i)-Dao conjugate of X(j) for these {i, j}: {1086, 20982}, {4858, 21824}, {6374, 7265}, {6626, 2605}, {7110, 42653}, {9296, 3678}, {9428, 319}, {10001, 2594}, {31998, 35}, {34021, 14838}, {36901, 21054}, {39028, 53563}, {39052, 14975}, {39054, 2174}, {39060, 1825}, {40584, 14270}, {40605, 9404}, {40612, 2624}, {40618, 22094}, {40619, 2611}, {40620, 53542}
X(55209) = X(i)-cross conjugate of X(j) for these {i, j}: {35519, 310}, {47795, 86}
X(55209) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4603)}}, {{A, B, C, X(274), X(4554)}}, {{A, B, C, X(799), X(4631)}}, {{A, B, C, X(1978), X(31624)}}, {{A, B, C, X(4584), X(11794)}}, {{A, B, C, X(6742), X(15455)}}, {{A, B, C, X(37870), X(42343)}}
X(55209) = tripole of the mixed polar line of X(2) and X(35) in K002
X(55209) = barycentric product X(i)*X(j) for these (i, j): {310, 6742}, {320, 35139}, {670, 79}, {1978, 52393}, {2160, 4602}, {3615, 4572}, {4609, 6186}, {4623, 6757}, {4625, 52344}, {13486, 561}, {15455, 274}, {20565, 99}, {20924, 32680}, {26700, 40072}, {28660, 38340}, {30690, 799}, {40075, 476}, {43682, 4631}, {52375, 6386}, {52381, 6331}, {52612, 8818}
X(55209) = barycentric quotient X(i)/X(j) for these (i, j): {36, 14270}, {76, 7265}, {79, 512}, {86, 2605}, {99, 35}, {162, 14975}, {274, 14838}, {286, 54244}, {310, 4467}, {314, 35057}, {320, 526}, {333, 9404}, {350, 53563}, {476, 6187}, {514, 20982}, {645, 52405}, {651, 21741}, {662, 2174}, {664, 2594}, {668, 3678}, {670, 319}, {693, 2611}, {799, 3219}, {811, 6198}, {850, 21054}, {1414, 1399}, {1444, 23226}, {1577, 21824}, {1789, 1946}, {1978, 3969}, {2160, 798}, {3218, 2624}, {3261, 8287}, {3615, 663}, {4025, 22094}, {4552, 21794}, {4554, 16577}, {4572, 40999}, {4573, 2003}, {4592, 52408}, {4602, 33939}, {4610, 40214}, {4612, 35192}, {4625, 1442}, {4707, 2088}, {6186, 669}, {6331, 52412}, {6385, 18160}, {6516, 22342}, {6742, 42}, {6757, 4705}, {7100, 810}, {7110, 3709}, {7192, 53542}, {7199, 7202}, {7257, 4420}, {8818, 4079}, {13486, 31}, {15455, 37}, {17923, 47230}, {18026, 1825}, {18155, 53524}, {20565, 523}, {20924, 32679}, {23989, 21141}, {26700, 1402}, {27808, 7206}, {30599, 30600}, {30690, 661}, {30941, 53554}, {32680, 2161}, {35049, 1415}, {35139, 80}, {35519, 6741}, {38340, 1400}, {40075, 3268}, {40495, 17886}, {52344, 4041}, {52372, 51641}, {52374, 7180}, {52375, 667}, {52381, 647}, {52393, 649}, {52569, 4983}, {52612, 34016}, {52935, 17104}

X(55210) = X(37)X(650)∩X(647)X(661)

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

X(55210) lies on these lines: {37, 650}, {101, 32671}, {213, 22383}, {228, 8641}, {321, 31209}, {351, 7234}, {514, 23787}, {647, 661}, {649, 4057}, {657, 10397}, {665, 4979}, {669, 50496}, {798, 42664}, {824, 27648}, {905, 47971}, {1213, 21721}, {1400, 2433}, {1635, 52326}, {1637, 55197}, {1962, 21727}, {2081, 2624}, {2605, 9404}, {2786, 16751}, {3005, 4455}, {3175, 44567}, {3250, 53581}, {3995, 27115}, {4041, 21831}, {4064, 46380}, {4374, 25594}, {4467, 7265}, {4687, 18154}, {4705, 42653}, {4765, 22042}, {4785, 24083}, {4813, 43060}, {4893, 6589}, {6753, 55206}, {8651, 50494}, {16577, 21141}, {17990, 50487}, {21053, 21901}, {21196, 24948}, {21225, 27293}, {21348, 48275}, {21800, 21832}, {22000, 23806}, {22043, 48008}, {22044, 45745}, {22046, 30023}, {24084, 48268}, {24924, 25084}, {25098, 27674}, {25258, 27527}, {27045, 31296}, {28374, 48094}, {31287, 31993}, {31947, 50342}, {47661, 47678}, {47794, 52623}, {51652, 51871}

X(55210) = isotomic conjugate of X(55209)
X(55210) = perspector of circumconic {{A, B, C, X(35), X(65)}}
X(55210) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 13486}, {21, 38340}, {31, 55209}, {36, 32680}, {58, 15455}, {79, 662}, {81, 6742}, {99, 2160}, {100, 52393}, {110, 30690}, {162, 52381}, {163, 20565}, {190, 52375}, {320, 32678}, {333, 26700}, {476, 3218}, {522, 35049}, {643, 52374}, {645, 52372}, {648, 7100}, {651, 3615}, {653, 1789}, {799, 6186}, {1414, 7110}, {4556, 6757}, {4565, 52344}, {4573, 7073}, {4612, 52382}, {4629, 52569}, {4636, 43682}, {7113, 35139}, {8818, 52935}, {14560, 20924}, {17923, 36061}, {22128, 36129}, {23895, 39152}, {23896, 39153}, {39295, 53527}, {46456, 52407}
X(55210) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55209}, {10, 15455}, {115, 20565}, {125, 52381}, {244, 30690}, {1084, 79}, {3700, 35519}, {8054, 52393}, {8287, 274}, {14838, 3261}, {15898, 32680}, {16221, 17923}, {18334, 320}, {32664, 13486}, {38986, 2160}, {38991, 3615}, {38996, 6186}, {40586, 6742}, {40608, 7110}, {40611, 38340}, {55042, 333}, {55053, 52375}, {55060, 52374}, {55064, 52344}, {55066, 7100}
X(55210) = X(i)-Ceva conjugate of X(j) for these {i, j}: {37, 21824}, {101, 2174}, {109, 42}, {3219, 53542}, {16577, 2611}, {52412, 21054}
X(55210) = X(i)-cross conjugate of X(j) for these {i, j}: {21824, 21794}
X(55210) = intersection, other than A, B, C, of circumconics {{A, B, C, X(37), X(2174)}}, {{A, B, C, X(42), X(2003)}}, {{A, B, C, X(101), X(4024)}}, {{A, B, C, X(186), X(46555)}}, {{A, B, C, X(512), X(23883)}}, {{A, B, C, X(526), X(4777)}}, {{A, B, C, X(650), X(2624)}}, {{A, B, C, X(661), X(2433)}}, {{A, B, C, X(798), X(30600)}}, {{A, B, C, X(2081), X(21044)}}, {{A, B, C, X(2605), X(4017)}}, {{A, B, C, X(7180), X(14838)}}, {{A, B, C, X(8672), X(35057)}}, {{A, B, C, X(19297), X(52555)}}, {{A, B, C, X(32679), X(47874)}}
X(55210) = barycentric product X(i)*X(j) for these (i, j): {6, 7265}, {10, 2605}, {35, 523}, {42, 4467}, {100, 2611}, {101, 8287}, {109, 6741}, {110, 21054}, {190, 20982}, {226, 9404}, {291, 53563}, {319, 512}, {526, 80}, {1018, 7202}, {1252, 21141}, {1399, 4086}, {1442, 4041}, {1500, 16755}, {1577, 2174}, {1825, 521}, {1897, 22094}, {2003, 3700}, {2088, 47318}, {2161, 32679}, {2594, 522}, {2616, 35194}, {3219, 661}, {3268, 6187}, {3678, 513}, {3733, 7206}, {3952, 53542}, {3969, 649}, {4017, 4420}, {4551, 53524}, {6198, 656}, {13576, 53554}, {14208, 14975}, {14270, 20566}, {14838, 37}, {16577, 650}, {17095, 3709}, {17104, 4036}, {17454, 31010}, {17886, 692}, {18160, 213}, {18359, 2624}, {21741, 4391}, {21794, 4560}, {21824, 662}, {21828, 41226}, {22342, 44426}, {23226, 41013}, {23883, 28625}, {24006, 52408}, {33939, 798}, {34016, 4079}, {35057, 65}, {40214, 4024}, {40999, 663}, {42033, 7180}, {44427, 52431}, {47230, 52351}, {52405, 7178}, {52412, 647}, {54244, 72}
X(55210) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55209}, {31, 13486}, {35, 99}, {37, 15455}, {42, 6742}, {80, 35139}, {319, 670}, {512, 79}, {523, 20565}, {526, 320}, {647, 52381}, {649, 52393}, {661, 30690}, {663, 3615}, {667, 52375}, {669, 6186}, {798, 2160}, {810, 7100}, {1399, 1414}, {1400, 38340}, {1402, 26700}, {1415, 35049}, {1442, 4625}, {1825, 18026}, {1946, 1789}, {2003, 4573}, {2088, 4707}, {2161, 32680}, {2174, 662}, {2594, 664}, {2605, 86}, {2611, 693}, {2624, 3218}, {3219, 799}, {3268, 40075}, {3678, 668}, {3709, 7110}, {3969, 1978}, {4041, 52344}, {4079, 8818}, {4420, 7257}, {4467, 310}, {4705, 6757}, {4983, 52569}, {6187, 476}, {6198, 811}, {6741, 35519}, {7180, 52374}, {7202, 7199}, {7206, 27808}, {7265, 76}, {8287, 3261}, {9404, 333}, {14270, 36}, {14838, 274}, {14975, 162}, {16577, 4554}, {17104, 52935}, {17886, 40495}, {18160, 6385}, {20982, 514}, {21054, 850}, {21141, 23989}, {21741, 651}, {21794, 4552}, {21824, 1577}, {22094, 4025}, {22342, 6516}, {23226, 1444}, {30600, 30599}, {32679, 20924}, {33939, 4602}, {34016, 52612}, {35057, 314}, {35192, 4612}, {40214, 4610}, {40999, 4572}, {47230, 17923}, {51641, 52372}, {52405, 645}, {52408, 4592}, {52412, 6331}, {53524, 18155}, {53542, 7192}, {53554, 30941}, {53563, 350}, {54244, 286}
X(55210) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 650, 4024}, {647, 3709, 661}, {647, 661, 21828}, {649, 4079, 50498}, {3005, 4455, 50486}, {4765, 22042, 24089}, {24948, 28606, 21196}, {25098, 27674, 47886}

X(55211) = TRILINEAR POLE OF LINE {84, 309}

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

X(55211) lies on these lines: {799, 37141}, {4563, 7257}, {4625, 6331}, {14195, 52007}, {44327, 55202}

X(55211) = trilinear pole of line {84, 309}
X(55211) = X(i)-isoconjugate-of-X(j) for these {i, j}: {40, 798}, {198, 512}, {213, 6129}, {221, 3709}, {227, 3063}, {322, 1924}, {329, 669}, {647, 3195}, {661, 2187}, {667, 21871}, {810, 2331}, {1402, 14298}, {1817, 50487}, {1918, 14837}, {1919, 21075}, {2199, 4041}, {2200, 54239}, {2205, 17896}, {2324, 51641}, {2360, 4079}, {2489, 7078}, {3049, 7952}, {4524, 6611}, {7074, 7180}, {7114, 55206}, {7250, 7368}, {8822, 53581}
X(55211) = X(i)-Dao conjugate of X(j) for these {i, j}: {3341, 3709}, {6626, 6129}, {6631, 21871}, {9296, 21075}, {9428, 322}, {10001, 227}, {31998, 40}, {34021, 14837}, {36830, 2187}, {39052, 3195}, {39054, 198}, {39062, 2331}, {40605, 14298}
X(55211) = X(i)-cross conjugate of X(j) for these {i, j}: {811, 4625}, {4573, 799}
X(55211) = intersection, other than A, B, C, of circumconics {{A, B, C, X(86), X(4637)}}, {{A, B, C, X(799), X(4631)}}, {{A, B, C, X(811), X(4573)}}, {{A, B, C, X(4563), X(4610)}}, {{A, B, C, X(7035), X(31619)}}, {{A, B, C, X(13138), X(37141)}}
X(55211) = tripole of the mixed polar line of X(2) and X(40) in K002
X(55211) = barycentric product X(i)*X(j) for these (i, j): {189, 799}, {274, 44327}, {280, 4625}, {285, 4572}, {309, 99}, {314, 53642}, {670, 84}, {1436, 4602}, {1440, 7257}, {1903, 52612}, {2208, 4609}, {4631, 8808}, {13138, 310}, {28660, 37141}, {34404, 4573}, {36049, 6385}, {39130, 4623}, {40072, 8059}, {40836, 55202}, {41081, 6331}, {44190, 662}, {52608, 7129}, {55110, 55207}, {55205, 7003}
X(55211) = barycentric quotient X(i)/X(j) for these (i, j): {84, 512}, {86, 6129}, {99, 40}, {110, 2187}, {162, 3195}, {189, 661}, {190, 21871}, {274, 14837}, {280, 4041}, {282, 3709}, {285, 663}, {286, 54239}, {309, 523}, {310, 17896}, {314, 8058}, {333, 14298}, {643, 7074}, {645, 2324}, {648, 2331}, {662, 198}, {664, 227}, {668, 21075}, {670, 322}, {799, 329}, {811, 7952}, {1413, 51641}, {1414, 221}, {1422, 7180}, {1433, 810}, {1436, 798}, {1440, 4017}, {1812, 10397}, {1903, 4079}, {2208, 669}, {2357, 50487}, {4565, 2199}, {4573, 223}, {4592, 7078}, {4610, 1817}, {4623, 8822}, {4625, 347}, {4631, 27398}, {4635, 14256}, {4637, 6611}, {6335, 53009}, {6528, 47372}, {7003, 55206}, {7129, 2489}, {7257, 7080}, {7259, 7368}, {8059, 1402}, {13138, 42}, {18155, 38357}, {32652, 1918}, {34400, 51664}, {34404, 3700}, {36049, 213}, {36797, 40971}, {37141, 1400}, {39130, 4705}, {40117, 2333}, {41081, 647}, {44189, 8611}, {44190, 1577}, {44327, 37}, {52935, 2360}, {53642, 65}, {55110, 55208}, {55207, 55112}

X(55212) = X(9)X(16612)∩X(37)X(8611)

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

X(55212) lies on these lines: {9, 16612}, {37, 8611}, {244, 46101}, {514, 23792}, {647, 661}, {649, 6615}, {650, 1769}, {652, 6588}, {656, 3700}, {657, 6591}, {822, 1400}, {905, 25924}, {1459, 46389}, {1635, 17424}, {1637, 4931}, {2254, 48269}, {2268, 22382}, {2501, 4024}, {3239, 21189}, {4120, 9209}, {4529, 26080}, {4813, 48092}, {4820, 50338}, {4838, 12077}, {4988, 47122}, {6129, 10397}, {6589, 46393}, {6590, 17420}, {9404, 47227}, {14321, 53527}, {14837, 17896}, {17434, 21808}, {20521, 26695}, {24417, 25666}, {25084, 25900}, {25258, 26545}, {26017, 26146}, {28398, 48131}, {48026, 50354}

X(55212) = isotomic conjugate of X(55211)
X(55212) = perspector of circumconic {{A, B, C, X(40), X(65)}}
X(55212) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 37141}, {31, 55211}, {58, 44327}, {81, 13138}, {84, 662}, {86, 36049}, {110, 189}, {162, 41081}, {163, 309}, {274, 32652}, {280, 4565}, {282, 1414}, {284, 53642}, {285, 651}, {333, 8059}, {643, 1422}, {645, 1413}, {648, 1433}, {799, 2208}, {1440, 5546}, {1444, 40117}, {1576, 44190}, {1903, 52935}, {2192, 4573}, {2357, 4610}, {4556, 39130}, {4558, 40836}, {4563, 7151}, {4592, 7129}, {4612, 52384}, {4616, 7367}, {4625, 7118}, {4636, 8808}, {6612, 7256}, {36797, 55117}, {41084, 46639}, {52037, 52914}
X(55212) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55211}, {10, 44327}, {57, 4573}, {115, 309}, {125, 41081}, {244, 189}, {281, 811}, {1084, 84}, {4858, 44190}, {5139, 7129}, {5514, 86}, {6741, 34404}, {16596, 274}, {38986, 1436}, {38991, 285}, {38996, 2208}, {40586, 13138}, {40590, 53642}, {40600, 36049}, {40608, 282}, {40611, 37141}, {55044, 333}, {55060, 1422}, {55063, 332}, {55064, 280}, {55066, 1433}
X(55212) = X(i)-Ceva conjugate of X(j) for these {i, j}: {656, 4041}, {3700, 661}
X(55212) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(647), X(4041)}}, {{A, B, C, X(661), X(14298)}}, {{A, B, C, X(756), X(3195)}}, {{A, B, C, X(1254), X(41088)}}, {{A, B, C, X(2395), X(25022)}}, {{A, B, C, X(2501), X(4017)}}, {{A, B, C, X(7180), X(14837)}}, {{A, B, C, X(8058), X(8672)}}
X(55212) = barycentric product X(i)*X(j) for these (i, j): {10, 6129}, {40, 523}, {65, 8058}, {196, 8611}, {208, 52355}, {221, 4086}, {223, 3700}, {227, 522}, {322, 512}, {329, 661}, {347, 4041}, {656, 7952}, {1020, 5514}, {1577, 198}, {1817, 4024}, {2187, 850}, {2324, 7178}, {2331, 525}, {2360, 4036}, {3194, 4064}, {3709, 40702}, {4017, 7080}, {4077, 7074}, {4705, 8822}, {10397, 40149}, {14208, 3195}, {14256, 4171}, {14298, 226}, {14837, 37}, {17094, 40971}, {17896, 42}, {17898, 41088}, {21075, 513}, {21871, 514}, {24006, 7078}, {38357, 4551}, {38374, 4069}, {47372, 520}, {51664, 55116}, {53009, 905}, {54239, 72}, {55112, 55208}
X(55212) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55211}, {37, 44327}, {40, 99}, {42, 13138}, {65, 53642}, {198, 662}, {213, 36049}, {221, 1414}, {223, 4573}, {227, 664}, {322, 670}, {329, 799}, {347, 4625}, {512, 84}, {523, 309}, {647, 41081}, {661, 189}, {663, 285}, {669, 2208}, {798, 1436}, {810, 1433}, {1400, 37141}, {1402, 8059}, {1577, 44190}, {1817, 4610}, {1918, 32652}, {2187, 110}, {2199, 4565}, {2324, 645}, {2331, 648}, {2333, 40117}, {2360, 52935}, {2489, 7129}, {3195, 162}, {3700, 34404}, {3709, 282}, {4017, 1440}, {4041, 280}, {4079, 1903}, {4705, 39130}, {6129, 86}, {6611, 4637}, {7074, 643}, {7078, 4592}, {7080, 7257}, {7180, 1422}, {7368, 7259}, {7952, 811}, {8058, 314}, {8611, 44189}, {8822, 4623}, {10397, 1812}, {14256, 4635}, {14298, 333}, {14837, 274}, {17896, 310}, {21075, 668}, {21871, 190}, {27398, 4631}, {38357, 18155}, {40971, 36797}, {47372, 6528}, {50487, 2357}, {51641, 1413}, {51664, 34400}, {53009, 6335}, {54239, 286}, {55112, 55207}, {55206, 7003}, {55208, 55110}

X(55213) = TRILINEAR POLE OF LINE {85, 6385}

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

X(55213) lies on these lines: {99, 34083}, {274, 34084}, {670, 4569}, {799, 34085}, {4554, 4602}, {4572, 4609}, {52612, 55205}

X(55213) = trilinear pole of line {85, 6385}
X(55213) = X(i)-isoconjugate-of-X(j) for these {i, j}: {8, 9426}, {9, 1924}, {32, 3709}, {41, 798}, {55, 669}, {110, 7063}, {210, 1980}, {213, 3063}, {284, 53581}, {512, 2175}, {523, 9448}, {560, 4041}, {607, 3049}, {643, 4117}, {645, 9427}, {650, 2205}, {661, 9447}, {663, 1918}, {810, 2212}, {1084, 5546}, {1253, 51641}, {1334, 1919}, {1397, 4524}, {1402, 8641}, {1501, 3700}, {1917, 4086}, {2194, 50487}, {2489, 52425}, {4092, 14574}, {4455, 18265}, {4612, 52065}, {6059, 39201}, {6064, 23610}, {6066, 8034}, {7109, 7252}, {7180, 14827}, {9247, 55206}, {23216, 36797}, {44162, 52355}
X(55213) = X(i)-Dao conjugate of X(j) for these {i, j}: {223, 669}, {244, 7063}, {478, 1924}, {1214, 50487}, {3160, 798}, {6374, 4041}, {6376, 3709}, {6626, 3063}, {9296, 1334}, {9428, 9}, {10001, 213}, {17113, 51641}, {31998, 41}, {34021, 663}, {36830, 9447}, {39054, 2175}, {39060, 2333}, {39062, 2212}, {40590, 53581}, {40593, 512}, {40605, 8641}, {40615, 3121}, {55060, 4117}
X(55213) = X(i)-cross conjugate of X(j) for these {i, j}: {670, 4602}, {4017, 85}
X(55213) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(75), X(27805)}}, {{A, B, C, X(310), X(799)}}, {{A, B, C, X(4554), X(4569)}}, {{A, B, C, X(4602), X(4609)}}, {{A, B, C, X(52608), X(52612)}}
X(55213) = tripole of the mixed polar line of X(2) and X(41) in K002
X(55213) = barycentric product X(i)*X(j) for these (i, j): {163, 41287}, {264, 55205}, {273, 52608}, {274, 4572}, {310, 4554}, {314, 46406}, {331, 55202}, {349, 4623}, {670, 85}, {1414, 1502}, {1434, 6386}, {1441, 52612}, {1928, 4565}, {3596, 4635}, {3665, 37204}, {4017, 44168}, {4573, 561}, {4601, 52621}, {4602, 7}, {4609, 57}, {4625, 76}, {6063, 799}, {6331, 7182}, {6385, 664}, {7205, 7260}, {18033, 4639}, {18157, 46135}, {20567, 99}, {20948, 7340}, {28659, 4616}, {28660, 4569}, {34537, 4077}, {40072, 658}, {40363, 4637}, {40495, 4620}, {41283, 662}, {52421, 55209}
X(55213) = barycentric quotient X(i)/X(j) for these (i, j): {7, 798}, {56, 1924}, {57, 669}, {65, 53581}, {75, 3709}, {76, 4041}, {77, 3049}, {85, 512}, {86, 3063}, {99, 41}, {109, 2205}, {110, 9447}, {163, 9448}, {226, 50487}, {264, 55206}, {273, 2489}, {274, 663}, {279, 51641}, {305, 8611}, {310, 650}, {312, 4524}, {314, 657}, {333, 8641}, {348, 810}, {349, 4705}, {561, 3700}, {604, 9426}, {643, 14827}, {645, 1253}, {648, 2212}, {651, 1918}, {658, 1402}, {661, 7063}, {662, 2175}, {664, 213}, {668, 1334}, {670, 9}, {799, 55}, {811, 607}, {823, 6059}, {873, 7252}, {883, 39258}, {1014, 1919}, {1088, 7180}, {1412, 1980}, {1414, 32}, {1424, 9491}, {1434, 667}, {1441, 4079}, {1502, 4086}, {1978, 210}, {3261, 4516}, {3596, 4171}, {3665, 2084}, {3676, 3121}, {4017, 1084}, {4033, 7064}, {4077, 3124}, {4551, 7109}, {4552, 872}, {4554, 42}, {4561, 52370}, {4563, 212}, {4565, 560}, {4569, 1400}, {4572, 37}, {4573, 31}, {4576, 40972}, {4584, 18265}, {4589, 51858}, {4592, 52425}, {4601, 3939}, {4602, 8}, {4609, 312}, {4610, 2194}, {4616, 604}, {4620, 692}, {4623, 284}, {4625, 6}, {4631, 2328}, {4634, 2316}, {4635, 56}, {4637, 1397}, {4639, 7077}, {6063, 661}, {6331, 33}, {6385, 522}, {6386, 2321}, {6516, 2200}, {7055, 822}, {7180, 4117}, {7182, 647}, {7183, 39201}, {7196, 7234}, {7199, 3271}, {7203, 1977}, {7216, 1356}, {7256, 6602}, {7257, 220}, {7258, 480}, {7340, 163}, {10030, 4455}, {16708, 2488}, {16739, 52326}, {17082, 23503}, {17096, 3248}, {17206, 1946}, {18021, 1021}, {18026, 2333}, {18033, 21832}, {18155, 14936}, {18157, 926}, {18206, 8638}, {19804, 8653}, {20567, 523}, {20924, 53562}, {20948, 4092}, {23062, 7250}, {24002, 3122}, {24037, 5546}, {27853, 4433}, {28660, 3900}, {30545, 50491}, {30941, 46388}, {31625, 4069}, {33298, 21837}, {33946, 4531}, {33949, 50488}, {34537, 643}, {35519, 36197}, {36838, 1042}, {40072, 3239}, {40364, 52355}, {40495, 21044}, {41283, 1577}, {41287, 20948}, {44129, 18344}, {44168, 7257}, {45196, 42661}, {46135, 18785}, {46404, 1824}, {46405, 34857}, {46406, 65}, {51641, 9427}, {52379, 21789}, {52421, 55210}, {52608, 78}, {52612, 21}, {52619, 2170}, {52621, 3125}, {52937, 1427}, {53236, 21127}, {55194, 1110}, {55202, 219}, {55205, 3}, {55207, 1260}, {55208, 42068}, {55209, 7073}, {55211, 2192}

X(55214) = X(647)X(661)∩X(649)X(1769)

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

X(55214) lies on these lines: {647, 661}, {649, 1769}, {656, 4024}, {1400, 55208}, {2254, 48266}, {2610, 8611}, {3700, 53527}, {4041, 4838}, {4369, 24417}, {4813, 50354}, {4820, 50350}, {4905, 49284}, {4979, 6615}, {6590, 21189}, {17420, 48275}, {23792, 48398}, {23800, 48269}, {46389, 51648}, {48019, 48151}

X(55214) = perspector of circumconic {{A, B, C, X(46), X(65)}}
X(55214) = X(i)-isoconjugate-of-X(j) for these {i, j}: {90, 662}, {99, 2164}, {107, 6512}, {110, 2994}, {162, 6513}, {163, 20570}, {333, 36082}, {648, 1069}, {4558, 7040}, {4565, 36626}, {4573, 7072}, {5546, 7318}
X(55214) = X(i)-Dao conjugate of X(j) for these {i, j}: {63, 4563}, {115, 20570}, {125, 6513}, {244, 2994}, {1084, 90}, {6506, 332}, {38985, 6512}, {38986, 2164}, {55064, 36626}, {55066, 1069}
X(55214) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2501, 661}, {52610, 1254}
X(55214) = intersection, other than A, B, C, of circumconics {{A, B, C, X(661), X(46389)}}, {{A, B, C, X(1254), X(3157)}}, {{A, B, C, X(4017), X(51648)}}, {{A, B, C, X(4041), X(55210)}}, {{A, B, C, X(7180), X(21188)}}
X(55214) = isotomic conjugate of the tripole of the mixed polar line of X(2) and X(46) in K002
X(55214) = barycentric product X(i)*X(j) for these (i, j): {10, 51648}, {46, 523}, {226, 46389}, {1020, 6506}, {1068, 656}, {1406, 4086}, {1577, 2178}, {2501, 6505}, {4017, 5552}, {5905, 661}, {20930, 512}, {21077, 513}, {21188, 37}, {21853, 514}, {24006, 3157}, {52033, 525}
X(55214) = barycentric quotient X(i)/X(j) for these (i, j): {46, 99}, {512, 90}, {523, 20570}, {647, 6513}, {661, 2994}, {798, 2164}, {810, 1069}, {822, 6512}, {1068, 811}, {1402, 36082}, {1406, 1414}, {2178, 662}, {3157, 4592}, {4017, 7318}, {4041, 36626}, {5552, 7257}, {5905, 799}, {6505, 4563}, {20930, 670}, {21077, 668}, {21188, 274}, {21853, 190}, {31631, 4631}, {46389, 333}, {51648, 86}, {52033, 648}
X(55214) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4017, 55212, 661}

X(55215) = TRILINEAR POLE OF LINE {75, 91}

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

X(55215) lies on these lines: {668, 46134}, {789, 925}, {4593, 36145}, {5392, 40017}, {20571, 46277}, {20641, 46273}

X(55215) = trilinear pole of line {75, 91}
X(55215) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 34952}, {24, 3049}, {25, 30451}, {32, 924}, {47, 798}, {184, 6753}, {213, 34948}, {512, 571}, {523, 52436}, {647, 44077}, {669, 1993}, {1147, 2489}, {1501, 6563}, {1576, 47421}, {1924, 44179}, {1974, 52584}, {1980, 42700}, {2501, 52435}, {7763, 9426}, {8745, 39201}, {11060, 44808}, {14397, 40352}, {18605, 50487}, {19627, 43088}, {32692, 41213}, {32734, 39013}, {52317, 54034}
X(55215) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 34952}, {4858, 47421}, {6376, 924}, {6505, 30451}, {6626, 34948}, {9428, 44179}, {31998, 47}, {34853, 798}, {37864, 1924}, {39052, 44077}, {39054, 571}
X(55215) = intersection, other than A, B, C, of circumconics {{A, B, C, X(668), X(789)}}
X(55215) = tripole of the mixed polar line of X(2) and X(47) in K002
X(55215) = barycentric product X(i)*X(j) for these (i, j): {304, 30450}, {561, 925}, {670, 91}, {1502, 36145}, {1928, 32734}, {2165, 4602}, {5392, 799}, {20563, 811}, {20571, 99}, {46134, 75}, {55202, 847}
X(55215) = barycentric quotient X(i)/X(j) for these (i, j): {1, 34952}, {63, 30451}, {68, 810}, {75, 924}, {86, 34948}, {91, 512}, {92, 6753}, {99, 47}, {162, 44077}, {163, 52436}, {304, 52584}, {561, 6563}, {662, 571}, {670, 44179}, {799, 1993}, {811, 24}, {823, 8745}, {925, 31}, {1577, 47421}, {1820, 3049}, {1978, 42700}, {2165, 798}, {4558, 563}, {4575, 52435}, {4592, 1147}, {4602, 7763}, {4610, 18605}, {5392, 661}, {6331, 1748}, {14206, 14397}, {14213, 52317}, {14570, 2180}, {20563, 656}, {20571, 523}, {23999, 52917}, {24001, 52952}, {30450, 19}, {32734, 560}, {34385, 2616}, {36145, 32}, {37802, 2624}, {44173, 17881}, {46134, 1}, {46254, 41679}, {52350, 822}, {55202, 9723}

X(55216) = PERSPECTOR OF CIRCUMCONIC {{A, B, C, X(1), X(47)}}

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

X(55216) lies on these lines: {44, 513}, {810, 8648}, {1400, 55208}

X(55216) = isotomic conjugate of X(55215)
X(55216) = perspector of circumconic {{A, B, C, X(1), X(47)}}
X(55216) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 925}, {3, 30450}, {6, 46134}, {31, 55215}, {68, 648}, {75, 36145}, {76, 32734}, {91, 662}, {96, 14570}, {99, 2165}, {107, 52350}, {110, 5392}, {112, 20563}, {163, 20571}, {311, 32692}, {467, 52932}, {476, 37802}, {485, 54030}, {486, 54031}, {811, 1820}, {847, 4558}, {1625, 34385}, {2351, 6331}, {4563, 14593}, {10420, 52504}, {13398, 39116}, {14618, 44174}, {15352, 16391}, {34391, 39384}, {34392, 39383}, {39416, 40697}
X(55216) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55215}, {9, 46134}, {115, 20571}, {135, 92}, {206, 36145}, {244, 5392}, {577, 4592}, {1084, 91}, {17423, 1820}, {32664, 925}, {34116, 662}, {34591, 20563}, {36103, 30450}, {38985, 52350}, {38986, 2165}, {39013, 75}, {47421, 18695}, {52584, 20948}, {55066, 68}
X(55216) = X(i)-Ceva conjugate of X(j) for these {i, j}: {163, 563}, {2158, 3708}, {4575, 31}, {24006, 810}, {34948, 34952}
X(55216) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(45886)}}, {{A, B, C, X(19), X(563)}}, {{A, B, C, X(24), X(851)}}, {{A, B, C, X(47), X(896)}}, {{A, B, C, X(48), X(2314)}}, {{A, B, C, X(317), X(44151)}}, {{A, B, C, X(513), X(924)}}, {{A, B, C, X(571), X(2245)}}, {{A, B, C, X(649), X(34952)}}, {{A, B, C, X(650), X(6753)}}, {{A, B, C, X(652), X(30451)}}, {{A, B, C, X(1400), X(2252)}}, {{A, B, C, X(1491), X(6563)}}, {{A, B, C, X(1575), X(42700)}}, {{A, B, C, X(1748), X(1755)}}, {{A, B, C, X(1993), X(2238)}}, {{A, B, C, X(2155), X(2173)}}, {{A, B, C, X(2180), X(2290)}}, {{A, B, C, X(2229), X(7763)}}, {{A, B, C, X(2234), X(44179)}}, {{A, B, C, X(2522), X(52584)}}, {{A, B, C, X(2600), X(8648)}}, {{A, B, C, X(2610), X(47421)}}, {{A, B, C, X(3330), X(8745)}}, {{A, B, C, X(18116), X(43088)}}, {{A, B, C, X(39690), X(44077)}}
X(55216) = barycentric product X(i)*X(j) for these (i, j): {1, 924}, {10, 34948}, {19, 52584}, {24, 656}, {31, 6563}, {47, 523}, {63, 6753}, {136, 4575}, {317, 810}, {1147, 24006}, {1576, 17881}, {1577, 571}, {1748, 647}, {1993, 661}, {2166, 44808}, {2167, 52317}, {2616, 52}, {2632, 52917}, {3708, 41679}, {7763, 798}, {11547, 822}, {14208, 44077}, {14397, 2349}, {14618, 563}, {15412, 2180}, {15423, 1820}, {18605, 4024}, {18883, 2624}, {20948, 52436}, {24018, 8745}, {30451, 92}, {34952, 75}, {42700, 649}, {43088, 6149}, {44179, 512}, {47421, 662}
X(55216) = barycentric quotient X(i)/X(j) for these (i, j): {1, 46134}, {2, 55215}, {19, 30450}, {24, 811}, {31, 925}, {32, 36145}, {47, 99}, {512, 91}, {523, 20571}, {560, 32734}, {563, 4558}, {571, 662}, {656, 20563}, {661, 5392}, {798, 2165}, {810, 68}, {822, 52350}, {924, 75}, {1147, 4592}, {1748, 6331}, {1993, 799}, {2180, 14570}, {2616, 34385}, {2624, 37802}, {3049, 1820}, {6563, 561}, {6753, 92}, {7763, 4602}, {8745, 823}, {9723, 55202}, {14397, 14206}, {17881, 44173}, {18605, 4610}, {30451, 63}, {34948, 86}, {34952, 1}, {41679, 46254}, {42700, 1978}, {44077, 162}, {44179, 670}, {47421, 1577}, {52317, 14213}, {52435, 4575}, {52436, 163}, {52584, 304}, {52917, 23999}, {52952, 24001}

X(55217) = TRILINEAR POLE OF LINE {93, 264}

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

X(55217) lies on these lines: {930, 22456}, {6331, 38342}, {6528, 46139}, {20572, 46111}

X(55217) = trilinear pole of line {93, 264}
X(55217) = X(i)-isoconjugate-of-X(j) for these {i, j}: {49, 798}, {810, 2965}, {1510, 9247}, {1924, 44180}, {1973, 37084}, {2964, 3049}
X(55217) = X(i)-Dao conjugate of X(j) for these {i, j}: {338, 47424}, {6337, 37084}, {9428, 44180}, {21975, 3049}, {31998, 49}, {39062, 2965}, {39171, 42293}
X(55217) = intersection, other than A, B, C, of circumconics {{A, B, C, X(930), X(11140)}}, {{A, B, C, X(6331), X(6528)}}
X(55217) = tripole of the mixed polar line of X(2) and X(49) in K002
X(55217) = barycentric product X(i)*X(j) for these (i, j): {264, 46139}, {670, 93}, {11140, 6331}, {18022, 930}, {20572, 99}, {32737, 44161}, {38342, 76}
X(55217) = barycentric quotient X(i)/X(j) for these (i, j): {69, 37084}, {93, 512}, {99, 49}, {264, 1510}, {340, 44809}, {562, 14270}, {648, 2965}, {670, 44180}, {811, 2964}, {930, 184}, {2962, 810}, {2963, 3049}, {3519, 39201}, {6331, 1994}, {6528, 3518}, {11140, 647}, {14111, 34952}, {18022, 41298}, {18314, 47424}, {18831, 25044}, {20572, 523}, {25043, 15451}, {32737, 14575}, {36148, 9247}, {38342, 6}, {46139, 3}

X(55218) = TRILINEAR POLE OF LINE {95, 183}

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

X(55218) lies on these lines: {670, 18831}, {933, 35567}, {4563, 42405}, {34386, 52568}, {35575, 52779}

X(55218) = trilinear pole of line {95, 183}
X(55218) = X(i)-isoconjugate-of-X(j) for these {i, j}: {5, 1924}, {51, 798}, {512, 2179}, {560, 12077}, {661, 40981}, {669, 1953}, {810, 3199}, {1084, 2617}, {1096, 42293}, {1501, 2618}, {1917, 18314}, {1919, 21807}, {1973, 15451}, {1980, 21011}, {2181, 3049}, {2205, 21102}, {4117, 14570}, {9247, 51513}, {9426, 14213}, {18180, 53581}
X(55218) = X(i)-Dao conjugate of X(j) for these {i, j}: {6337, 15451}, {6338, 17434}, {6374, 12077}, {6503, 42293}, {9296, 21807}, {9428, 5}, {31998, 51}, {36830, 40981}, {36901, 41221}, {39054, 2179}, {39062, 3199}
X(55218) = X(i)-cross conjugate of X(j) for these {i, j}: {1502, 34537}, {2623, 95}, {15412, 41488}
X(55218) = intersection, other than A, B, C, of circumconics {{A, B, C, X(76), X(46139)}}, {{A, B, C, X(99), X(43187)}}, {{A, B, C, X(648), X(907)}}, {{A, B, C, X(670), X(35567)}}, {{A, B, C, X(4563), X(35575)}}, {{A, B, C, X(18831), X(41208)}}
X(55218) = tripole of the mixed polar line of X(2) and X(51) in K002
X(55218) = barycentric product X(i)*X(j) for these (i, j): {275, 52608}, {276, 4563}, {670, 95}, {1502, 18315}, {1928, 36134}, {2167, 4602}, {2623, 44168}, {3926, 42405}, {3964, 54950}, {4176, 52779}, {4609, 54}, {14586, 40362}, {15412, 34537}, {15958, 44161}, {16030, 42371}, {18831, 305}, {28706, 52939}, {34384, 99}, {34386, 6331}, {40050, 933}, {40440, 55202}, {41488, 4576}, {44687, 55213}
X(55218) = barycentric quotient X(i)/X(j) for these (i, j): {54, 669}, {69, 15451}, {76, 12077}, {95, 512}, {97, 3049}, {99, 51}, {110, 40981}, {264, 51513}, {275, 2489}, {276, 2501}, {305, 6368}, {310, 21102}, {394, 42293}, {561, 2618}, {648, 3199}, {662, 2179}, {668, 21807}, {670, 5}, {689, 17500}, {799, 1953}, {811, 2181}, {850, 41221}, {933, 1974}, {1502, 18314}, {1634, 27374}, {1978, 21011}, {2148, 1924}, {2167, 798}, {2421, 52967}, {2623, 1084}, {3926, 17434}, {4558, 217}, {4563, 216}, {4590, 1625}, {4602, 14213}, {4609, 311}, {4623, 18180}, {4625, 1393}, {6331, 53}, {6528, 14569}, {7257, 7069}, {7763, 52317}, {7799, 2081}, {8901, 22260}, {14586, 1501}, {14587, 14574}, {15412, 3124}, {15414, 3269}, {15958, 14575}, {16030, 688}, {16813, 2207}, {18020, 52604}, {18022, 23290}, {18315, 32}, {18831, 25}, {24037, 2617}, {34384, 523}, {34386, 647}, {34537, 14570}, {36134, 560}, {39182, 51906}, {39287, 18105}, {40362, 15415}, {40832, 35361}, {42300, 52631}, {42405, 393}, {43768, 14398}, {45799, 42650}, {46138, 15475}, {47389, 23181}, {52347, 34983}, {52608, 343}, {52612, 17167}, {52617, 35442}, {52779, 6524}, {52939, 8882}, {54034, 9426}, {54950, 1093}, {55202, 44706}, {55205, 44708}

X(55219) = X(6)X(1510)∩X(512)X(1692)

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

X(55219) lies on these lines: {6, 1510}, {53, 23290}, {112, 46248}, {512, 1692}, {523, 3569}, {684, 45907}, {688, 22260}, {770, 2501}, {924, 2451}, {2081, 2600}, {2422, 18105}, {2485, 3288}, {2491, 3005}, {2492, 3050}, {2872, 21006}, {3124, 30452}, {3267, 54262}, {9426, 42663}, {14560, 23963}, {15450, 24862}, {15451, 42293}

X(55219) = reflection of X(i) in X(j) for these {i,j}: {3049, 2489}, {3050, 2492}, {3267, 54262}, {3288, 2485}, {42663, 9426}
X(55219) = isotomic conjugate of X(55218)
X(55219) = perspector of circumconic {{A, B, C, X(5), X(25)}}
X(55219) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55218}, {54, 799}, {63, 18831}, {75, 18315}, {76, 36134}, {95, 662}, {97, 811}, {99, 2167}, {162, 34386}, {163, 34384}, {255, 42405}, {275, 4592}, {276, 4575}, {304, 933}, {326, 16813}, {561, 14586}, {670, 2148}, {1969, 15958}, {2169, 6331}, {2190, 4563}, {2616, 4590}, {2623, 24037}, {4100, 54950}, {4554, 35196}, {4558, 40440}, {4573, 44687}, {4585, 39277}, {4593, 16030}, {4602, 54034}, {4998, 39177}, {6507, 52779}, {8882, 55202}, {14587, 20948}, {15412, 24041}, {15414, 24000}, {23286, 46254}, {44706, 52939}
X(55219) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55218}, {5, 4563}, {115, 34384}, {125, 34386}, {130, 394}, {136, 276}, {137, 76}, {206, 18315}, {216, 670}, {338, 1502}, {512, 2623}, {1084, 95}, {2972, 3926}, {3005, 15412}, {3162, 18831}, {5139, 275}, {6523, 42405}, {14363, 6331}, {15259, 16813}, {15450, 69}, {17423, 97}, {17433, 7799}, {35441, 52617}, {38986, 2167}, {38996, 54}, {39019, 305}, {40368, 14586}, {40588, 99}, {52032, 52608}, {52878, 2421}, {55050, 16030}
X(55219) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32, 3124}, {53, 41221}, {393, 20975}, {1625, 51}, {2501, 51513}, {12077, 15451}, {14593, 2971}, {41536, 41213}, {52604, 40981}
X(55219) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5), X(46522)}}, {{A, B, C, X(25), X(52887)}}, {{A, B, C, X(51), X(41586)}}, {{A, B, C, X(53), X(2211)}}, {{A, B, C, X(216), X(1692)}}, {{A, B, C, X(311), X(52460)}}, {{A, B, C, X(512), X(6368)}}, {{A, B, C, X(669), X(52317)}}, {{A, B, C, X(798), X(2600)}}, {{A, B, C, X(1510), X(32737)}}, {{A, B, C, X(2081), X(3124)}}, {{A, B, C, X(2422), X(18314)}}, {{A, B, C, X(2489), X(12077)}}, {{A, B, C, X(2501), X(3049)}}, {{A, B, C, X(2623), X(35441)}}, {{A, B, C, X(3199), X(14581)}}, {{A, B, C, X(3709), X(52319)}}, {{A, B, C, X(4079), X(52322)}}, {{A, B, C, X(7180), X(52318)}}, {{A, B, C, X(14391), X(14398)}}, {{A, B, C, X(17994), X(18105)}}, {{A, B, C, X(51363), X(51437)}}
X(55219) = barycentric product X(i)*X(j) for these (i, j): {3, 51513}, {5, 512}, {25, 6368}, {51, 523}, {53, 647}, {110, 41221}, {115, 1625}, {125, 52604}, {137, 32737}, {184, 23290}, {216, 2501}, {311, 669}, {1154, 15475}, {1263, 6140}, {1393, 4041}, {1501, 15415}, {1577, 2179}, {1953, 661}, {1989, 2081}, {2052, 42293}, {2165, 52317}, {2170, 35307}, {2181, 656}, {2433, 52945}, {2489, 343}, {2491, 53245}, {2617, 2643}, {2618, 31}, {2623, 36412}, {3003, 35361}, {3049, 324}, {3199, 525}, {3459, 42650}, {4017, 7069}, {11060, 41078}, {11062, 14582}, {12077, 6}, {13450, 39201}, {14213, 798}, {14391, 8749}, {14569, 520}, {14570, 3124}, {14618, 217}, {15451, 4}, {17167, 4079}, {17434, 393}, {17500, 3005}, {17994, 53174}, {18180, 4705}, {18314, 32}, {20975, 35360}, {21011, 649}, {21102, 42}, {21807, 513}, {23181, 8754}, {24862, 933}, {27364, 8651}, {27374, 52618}, {32713, 35442}, {33631, 35441}, {34212, 51363}, {34294, 35319}, {34983, 8884}, {39180, 53386}, {39569, 878}, {40981, 850}, {41586, 9178}, {43665, 52967}, {44705, 8798}, {44708, 55206}, {44716, 53149}
X(55219) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55218}, {5, 670}, {25, 18831}, {32, 18315}, {51, 99}, {53, 6331}, {216, 4563}, {217, 4558}, {311, 4609}, {343, 52608}, {393, 42405}, {512, 95}, {523, 34384}, {560, 36134}, {647, 34386}, {669, 54}, {688, 16030}, {798, 2167}, {1084, 2623}, {1093, 54950}, {1393, 4625}, {1501, 14586}, {1625, 4590}, {1924, 2148}, {1953, 799}, {1974, 933}, {2081, 7799}, {2179, 662}, {2181, 811}, {2207, 16813}, {2489, 275}, {2501, 276}, {2617, 24037}, {2618, 561}, {3049, 97}, {3124, 15412}, {3199, 648}, {3269, 15414}, {6368, 305}, {6524, 52779}, {7069, 7257}, {8882, 52939}, {9426, 54034}, {12077, 76}, {14213, 4602}, {14398, 43768}, {14569, 6528}, {14570, 34537}, {14574, 14587}, {14575, 15958}, {15415, 40362}, {15451, 69}, {15475, 46138}, {17167, 52612}, {17434, 3926}, {17500, 689}, {18105, 39287}, {18180, 4623}, {18314, 1502}, {21011, 1978}, {21102, 310}, {21807, 668}, {22260, 8901}, {23181, 47389}, {23290, 18022}, {27374, 1634}, {34983, 52347}, {35361, 40832}, {35442, 52617}, {40981, 110}, {41221, 850}, {42293, 394}, {42650, 45799}, {44706, 55202}, {44708, 55205}, {51513, 264}, {51906, 39182}, {52317, 7763}, {52604, 18020}, {52631, 42300}, {52967, 2421}
X(55219) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {512, 2489, 3049}, {2489, 3049, 14398}, {2492, 20188, 3050}, {12077, 52317, 17434}

X(55220) = TRILINEAR POLE OF LINE {17, 76}

Barycentrics    (a-b)*b^2*(a+b)*(a-c)*c^2*(a+c)*(a^4-b^4+2*b^2*c^2-c^4+4*sqrt(3)*a^2*S+12*S^2) : :

X(55220) lies on these lines: {17, 34087}, {99, 930}, {670, 32036}, {689, 16806}, {11128, 23962}, {18023, 34389}, {18024, 40712}, {30736, 40667}

X(55220) = trilinear pole of line {17, 76}
X(55220) = X(i)-isoconjugate-of-X(j) for these {i, j}: {61, 798}, {302, 1924}, {560, 23872}, {810, 10642}
X(55220) = X(i)-Dao conjugate of X(j) for these {i, j}: {6374, 23872}, {9428, 302}, {31998, 61}, {39062, 10642}
X(55220) = intersection, other than A, B, C, of circumconics {{A, B, C, X(670), X(689)}}
X(55220) = tripole of the mixed polar line of X(2) and X(61) in K002
X(55220) = barycentric product X(i)*X(j) for these (i, j): {17, 670}, {303, 46139}, {1502, 16806}, {21461, 4609}, {32036, 76}, {34389, 99}, {36300, 55218}, {40712, 6331}, {52349, 55217}, {52608, 8741}
X(55220) = barycentric quotient X(i)/X(j) for these (i, j): {17, 512}, {76, 23872}, {99, 61}, {303, 1510}, {648, 10642}, {670, 302}, {930, 21462}, {4563, 52348}, {4590, 52605}, {6331, 473}, {8741, 2489}, {16806, 32}, {17402, 11137}, {17403, 11135}, {19779, 6138}, {21461, 669}, {23895, 11083}, {23896, 11141}, {32036, 6}, {32037, 51546}, {32585, 3049}, {34389, 523}, {36300, 55219}, {36839, 16463}, {38342, 8742}, {40712, 647}, {46139, 18}, {52606, 2965}

X(55221) = X(187)X(237)∩X(462)X(2501)

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

X(55221) lies on these lines: {115, 38994}, {187, 237}, {462, 2501}, {523, 14447}, {1291, 16807}, {1499, 41034}, {1510, 52971}, {2623, 34394}, {5472, 12077}, {5994, 23357}, {5995, 36830}, {14446, 48441}, {23872, 41298}, {35322, 35329}

X(55221) = reflection of X(i) in X(j) for these {i,j}: {6138, 6137}
X(55221) = isogonal conjugate of X(32036)
X(55221) = isotomic conjugate of X(55220)
X(55221) = perspector of circumconic {{A, B, C, X(6), X(18)}}
X(55221) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 32036}, {17, 662}, {75, 16806}, {162, 40712}, {163, 34389}, {303, 36148}, {799, 21461}, {811, 32585}, {2962, 52606}, {3375, 23896}, {4592, 8741}
X(55221) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 32036}, {115, 34389}, {125, 40712}, {206, 16806}, {1084, 17}, {5139, 8741}, {10640, 99}, {15609, 298}, {17423, 32585}, {38994, 19779}, {38996, 21461}, {39018, 303}, {53986, 472}
X(55221) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3442, 20975}, {5994, 11135}, {11085, 43968}, {16806, 6}, {20579, 6138}, {52605, 61}
X(55221) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(11126)}}, {{A, B, C, X(18), X(45935)}}, {{A, B, C, X(61), X(187)}}, {{A, B, C, X(237), X(473)}}, {{A, B, C, X(302), X(3231)}}, {{A, B, C, X(512), X(23872)}}, {{A, B, C, X(523), X(1291)}}, {{A, B, C, X(647), X(20578)}}, {{A, B, C, X(1495), X(10642)}}, {{A, B, C, X(2378), X(8446)}}, {{A, B, C, X(2379), X(6104)}}, {{A, B, C, X(2501), X(6137)}}, {{A, B, C, X(2623), X(6138)}}, {{A, B, C, X(3441), X(10632)}}, {{A, B, C, X(6140), X(16807)}}, {{A, B, C, X(8742), X(34394)}}, {{A, B, C, X(11083), X(39410)}}, {{A, B, C, X(11085), X(11135)}}, {{A, B, C, X(11146), X(51546)}}, {{A, B, C, X(52144), X(52348)}}
X(55221) = barycentric product X(i)*X(j) for these (i, j): {115, 52605}, {302, 512}, {473, 647}, {523, 61}, {1510, 18}, {2501, 52348}, {6137, 8838}, {10642, 525}, {11083, 23870}, {11126, 20579}, {11141, 23871}, {11146, 20578}, {16771, 6138}, {17403, 43968}, {21462, 41298}, {23284, 6104}, {23286, 52671}, {23872, 6}, {23873, 51546}
X(55221) = barycentric quotient X(i)/X(j) for these (i, j): {6, 32036}, {18, 46139}, {32, 16806}, {61, 99}, {302, 670}, {473, 6331}, {512, 17}, {523, 34389}, {647, 40712}, {669, 21461}, {1510, 303}, {2489, 8741}, {2965, 52606}, {3049, 32585}, {6138, 19779}, {8742, 38342}, {10642, 648}, {11083, 23895}, {11135, 17403}, {11137, 17402}, {11141, 23896}, {16463, 36839}, {21462, 930}, {23872, 76}, {51546, 32037}, {52348, 4563}, {52605, 4590}, {55219, 36300}
X(55221) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {512, 6137, 6138}

X(55222) = TRILINEAR POLE OF LINE {18, 76}

Barycentrics    (a-b)*b^2*(a+b)*(a-c)*c^2*(a+c)*(a^4-b^4+2*b^2*c^2-c^4-4*sqrt(3)*a^2*S+12*S^2) : :

X(55222) lies on these lines: {18, 34087}, {99, 930}, {670, 32037}, {689, 16807}, {11129, 23962}, {18023, 34390}, {18024, 40711}, {30736, 40668}

X(55222) = trilinear pole of line {18, 76}
X(55222) = X(i)-isoconjugate-of-X(j) for these {i, j}: {62, 798}, {303, 1924}, {560, 23873}, {810, 10641}
X(55222) = X(i)-Dao conjugate of X(j) for these {i, j}: {6374, 23873}, {9428, 303}, {31998, 62}, {39062, 10641}
X(55222) = intersection, other than A, B, C, of circumconics {{A, B, C, X(670), X(689)}}
X(55222) = tripole of the mixed polar line of X(2) and X(62) in K002
X(55222) = barycentric product X(i)*X(j) for these (i, j): {18, 670}, {302, 46139}, {1502, 16807}, {21462, 4609}, {32037, 76}, {34390, 99}, {36301, 55218}, {40711, 6331}, {52348, 55217}, {52608, 8742}
X(55222) = barycentric quotient X(i)/X(j) for these (i, j): {18, 512}, {76, 23873}, {99, 62}, {302, 1510}, {648, 10641}, {670, 303}, {930, 21461}, {4563, 52349}, {4590, 52606}, {6331, 472}, {8742, 2489}, {16807, 32}, {17402, 11136}, {17403, 11134}, {19778, 6137}, {21462, 669}, {23895, 11142}, {23896, 11088}, {32036, 51547}, {32037, 6}, {32586, 3049}, {34390, 523}, {36301, 55219}, {36840, 16464}, {38342, 8741}, {40711, 647}, {46139, 17}, {52605, 2965}

X(55223) = PERSPECTOR OF CIRCUMCONIC {{A, B, C, X(6), X(17)}}

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

X(55223) lies on these lines: {115, 38993}, {187, 237}, {463, 2501}, {523, 14446}, {1291, 16806}, {1499, 41035}, {1510, 52972}, {2623, 34395}, {5471, 12077}, {5994, 36830}, {5995, 23357}, {14447, 48442}, {23873, 41298}, {35323, 35330}

X(55223) = reflection of X(i) in X(j) for these {i,j}: {6137, 6138}
X(55223) = isogonal conjugate of X(32037)
X(55223) = isotomic conjugate of X(55222)
X(55223) = perspector of circumconic {{A, B, C, X(6), X(17)}}
X(55223) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 32037}, {18, 662}, {75, 16807}, {162, 40711}, {163, 34390}, {302, 36148}, {799, 21462}, {811, 32586}, {2962, 52605}, {3384, 23895}, {4592, 8742}
X(55223) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 32037}, {115, 34390}, {125, 40711}, {206, 16807}, {1084, 18}, {5139, 8742}, {10639, 99}, {15610, 299}, {17423, 32586}, {38993, 19778}, {38996, 21462}, {39018, 302}, {53986, 473}
X(55223) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3443, 20975}, {5995, 11136}, {11080, 43967}, {16807, 6}, {20578, 6137}, {52606, 62}
X(55223) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(11127)}}, {{A, B, C, X(17), X(45935)}}, {{A, B, C, X(62), X(187)}}, {{A, B, C, X(237), X(472)}}, {{A, B, C, X(303), X(3231)}}, {{A, B, C, X(512), X(23873)}}, {{A, B, C, X(523), X(1291)}}, {{A, B, C, X(647), X(20579)}}, {{A, B, C, X(1495), X(10641)}}, {{A, B, C, X(2378), X(6105)}}, {{A, B, C, X(2379), X(8456)}}, {{A, B, C, X(2501), X(6138)}}, {{A, B, C, X(2623), X(6137)}}, {{A, B, C, X(3440), X(10633)}}, {{A, B, C, X(6140), X(16806)}}, {{A, B, C, X(8741), X(34395)}}, {{A, B, C, X(11080), X(11136)}}, {{A, B, C, X(11088), X(39411)}}, {{A, B, C, X(11145), X(51547)}}, {{A, B, C, X(52144), X(52349)}}
X(55223) = barycentric product X(i)*X(j) for these (i, j): {115, 52606}, {303, 512}, {472, 647}, {523, 62}, {1510, 17}, {2501, 52349}, {6138, 8836}, {10641, 525}, {11088, 23871}, {11127, 20578}, {11142, 23870}, {11145, 20579}, {16770, 6137}, {17402, 43967}, {21461, 41298}, {23283, 6105}, {23286, 52670}, {23872, 51547}, {23873, 6}
X(55223) = barycentric quotient X(i)/X(j) for these (i, j): {6, 32037}, {17, 46139}, {32, 16807}, {62, 99}, {303, 670}, {472, 6331}, {512, 18}, {523, 34390}, {647, 40711}, {669, 21462}, {1510, 302}, {2489, 8742}, {2965, 52605}, {3049, 32586}, {6137, 19778}, {8741, 38342}, {10641, 648}, {11088, 23896}, {11134, 17403}, {11136, 17402}, {11142, 23895}, {16464, 36840}, {21461, 930}, {23873, 76}, {51547, 32036}, {52349, 4563}, {52606, 4590}, {55219, 36301}
X(55223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {512, 6138, 6137}

X(55224) = X(99)X(1624)∩X(648)X(670)

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

X(55224) lies on these lines: {76, 44877}, {99, 1624}, {274, 25939}, {648, 670}, {658, 799}, {2396, 43188}, {11056, 55081}, {44326, 52608}, {44327, 55202}

X(55224) = trilinear pole of line {20, 14615}
X(55224) = X(i)-isoconjugate-of-X(j) for these {i, j}: {64, 798}, {253, 1924}, {512, 2155}, {661, 33581}, {669, 2184}, {810, 41489}, {2489, 19614}, {4117, 44326}, {30457, 51641}
X(55224) = X(i)-Dao conjugate of X(j) for these {i, j}: {4, 2489}, {122, 3124}, {9428, 253}, {31998, 64}, {36830, 33581}, {39020, 20975}, {39054, 2155}, {39062, 41489}, {40616, 3122}, {45245, 512}, {45248, 3049}, {45249, 55219}, {52874, 14398}
X(55224) = X(i)-Ceva conjugate of X(j) for these {i, j}: {52608, 670}
X(55224) = intersection, other than A, B, C, of circumconics {{A, B, C, X(648), X(658)}}, {{A, B, C, X(1624), X(46639)}}, {{A, B, C, X(2421), X(37669)}}, {{A, B, C, X(6331), X(46406)}}, {{A, B, C, X(8057), X(9035)}}
X(55224) = tripole of the mixed polar line of X(2) and X(64) in K002
X(55224) = barycentric product X(i)*X(j) for these (i, j): {20, 670}, {154, 4609}, {305, 52913}, {1249, 52608}, {1895, 55202}, {4602, 610}, {4623, 52345}, {4625, 52346}, {14615, 99}, {15466, 4563}, {17898, 24037}, {18750, 799}, {33673, 7257}, {34537, 6587}, {36841, 76}, {37669, 6331}, {42459, 55218}, {44697, 55207}, {52612, 8804}, {55213, 7070}
X(55224) = barycentric quotient X(i)/X(j) for these (i, j): {20, 512}, {99, 64}, {110, 33581}, {154, 669}, {610, 798}, {645, 30457}, {648, 41489}, {662, 2155}, {670, 253}, {799, 2184}, {1249, 2489}, {1394, 51641}, {3198, 50487}, {4558, 14642}, {4561, 53012}, {4563, 1073}, {4590, 46639}, {4592, 19614}, {4609, 41530}, {4625, 8809}, {6331, 459}, {6528, 6526}, {6587, 3124}, {7257, 44692}, {8057, 20975}, {8804, 4079}, {14615, 523}, {15466, 2501}, {15905, 3049}, {17898, 2643}, {18020, 1301}, {18623, 7180}, {18750, 661}, {20580, 3269}, {21172, 3122}, {27382, 3709}, {33673, 4017}, {34537, 44326}, {35602, 39201}, {36841, 6}, {37669, 647}, {42459, 55219}, {44697, 55208}, {44704, 17994}, {44705, 2971}, {52345, 4705}, {52346, 4041}, {52578, 44705}, {52608, 34403}, {52913, 25}, {53050, 42658}, {53639, 31942}, {55202, 19611}
X(55224) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4563, 6331, 670}

X(55225) = TRILINEAR POLE OF LINE {22, 315}

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

X(55225) lies on these lines: {99, 827}, {315, 53569}, {648, 670}, {809, 3222}, {877, 32713}, {892, 35136}, {1084, 36849}, {1632, 17941}, {2396, 4558}, {3978, 18371}, {4590, 36841}, {4609, 44766}, {5468, 53350}, {7763, 46184}, {20806, 31636}, {23583, 32458}, {35138, 54971}

X(55225) = trilinear pole of line {22, 315}
X(55225) = X(i)-isoconjugate-of-X(j) for these {i, j}: {66, 798}, {661, 2353}, {810, 13854}, {1577, 40146}, {1924, 18018}, {2084, 16277}, {9426, 46244}
X(55225) = X(i)-Dao conjugate of X(j) for these {i, j}: {32, 669}, {127, 3124}, {3265, 5489}, {9428, 18018}, {31998, 66}, {36830, 2353}, {39054, 2156}, {39062, 13854}, {55047, 20975}
X(55225) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4609, 99}
X(55225) = X(i)-cross conjugate of X(j) for these {i, j}: {33294, 315}
X(55225) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(315), X(35136)}}, {{A, B, C, X(648), X(827)}}, {{A, B, C, X(1576), X(35325)}}, {{A, B, C, X(2421), X(20806)}}, {{A, B, C, X(4577), X(6331)}}, {{A, B, C, X(8673), X(9035)}}, {{A, B, C, X(9479), X(23881)}}, {{A, B, C, X(22105), X(33294)}}, {{A, B, C, X(32713), X(44767)}}
X(55225) = tripole of the mixed polar line of X(2) and X(66) in K002
X(55225) = barycentric product X(i)*X(j) for these (i, j): {22, 670}, {110, 40073}, {206, 4609}, {305, 52915}, {315, 99}, {1760, 799}, {2172, 4602}, {2396, 31636}, {2485, 34537}, {3313, 689}, {4123, 4625}, {4150, 4610}, {4456, 52612}, {4463, 4623}, {4611, 76}, {7210, 7257}, {16757, 4601}, {17076, 645}, {17907, 4563}, {20641, 662}, {20806, 6331}, {21178, 4600}, {23208, 42371}, {31614, 53569}, {33294, 4590}, {34254, 648}, {41761, 42297}, {52608, 8743}
X(55225) = barycentric quotient X(i)/X(j) for these (i, j): {22, 512}, {99, 66}, {110, 2353}, {206, 669}, {315, 523}, {648, 13854}, {662, 2156}, {670, 18018}, {1576, 40146}, {1760, 661}, {2172, 798}, {2396, 34138}, {2485, 3124}, {3313, 3005}, {4123, 4041}, {4150, 4024}, {4456, 4079}, {4463, 4705}, {4563, 14376}, {4577, 16277}, {4590, 44766}, {4602, 46244}, {4609, 40421}, {4611, 6}, {6331, 43678}, {7210, 4017}, {8673, 20975}, {8743, 2489}, {10316, 3049}, {11610, 2422}, {16757, 3125}, {17076, 7178}, {17186, 1919}, {17453, 1924}, {17907, 2501}, {18020, 1289}, {20641, 1577}, {20806, 647}, {20968, 9426}, {21034, 53581}, {21178, 3120}, {23181, 27372}, {23208, 688}, {23881, 39691}, {31636, 2395}, {33294, 115}, {34254, 525}, {40073, 850}, {47443, 15388}, {52915, 25}, {52950, 14398}, {53569, 8029}
X(55225) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {648, 4563, 670}

X(55226) = TRILINEAR POLE OF LINE {23, 316}

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

X(55226) lies on these lines: {6, 76}, {99, 5467}, {316, 10510}, {385, 21906}, {523, 17941}, {524, 22254}, {648, 670}, {691, 35569}, {882, 41209}, {892, 5466}, {1078, 46127}, {2396, 2407}, {3163, 32458}, {3228, 36849}, {4226, 33799}, {4577, 4630}, {7769, 41335}, {7799, 45331}, {7809, 14995}, {7811, 50149}, {9479, 46291}, {10008, 40138}, {10411, 14221}, {17708, 53080}, {18023, 48540}, {18311, 52630}, {22151, 40074}, {23342, 31998}, {32740, 53375}

X(55226) = trilinear pole of line {23, 316}
X(55226) = X(i)-isoconjugate-of-X(j) for these {i, j}: {67, 798}, {512, 2157}, {661, 3455}, {688, 37221}, {810, 8791}, {1924, 18019}, {2084, 9076}
X(55226) = X(i)-Dao conjugate of X(j) for these {i, j}: {187, 351}, {316, 32193}, {2492, 33919}, {5099, 3124}, {7664, 826}, {9428, 18019}, {31998, 67}, {36830, 3455}, {39054, 2157}, {39062, 8791}, {40583, 512}, {55048, 20975}
X(55226) = X(i)-Ceva conjugate of X(j) for these {i, j}: {53080, 99}
X(55226) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {34072, 39356}, {36142, 39346}
X(55226) = X(i)-cross conjugate of X(j) for these {i, j}: {9979, 316}, {18311, 52551}
X(55226) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(4630)}}, {{A, B, C, X(23), X(44767)}}, {{A, B, C, X(76), X(4577)}}, {{A, B, C, X(83), X(648)}}, {{A, B, C, X(308), X(6035)}}, {{A, B, C, X(316), X(892)}}, {{A, B, C, X(524), X(53379)}}, {{A, B, C, X(685), X(37801)}}, {{A, B, C, X(687), X(37765)}}, {{A, B, C, X(732), X(9019)}}, {{A, B, C, X(2421), X(22151)}}, {{A, B, C, X(5466), X(9979)}}, {{A, B, C, X(5467), X(10510)}}, {{A, B, C, X(7664), X(34760)}}, {{A, B, C, X(9035), X(9517)}}, {{A, B, C, X(10330), X(42554)}}
X(55226) = tripole of the mixed polar line of X(2) and X(67) in K002
X(55226) = barycentric product X(i)*X(j) for these (i, j): {23, 670}, {110, 40074}, {305, 52916}, {316, 99}, {689, 9019}, {2492, 34537}, {4590, 9979}, {7664, 892}, {16568, 799}, {17088, 645}, {18311, 52940}, {18374, 4609}, {18715, 4593}, {20944, 662}, {21094, 4610}, {21205, 4600}, {22151, 6331}, {37765, 4563}, {37801, 55225}, {37804, 648}, {52551, 5468}, {52608, 8744}, {52630, 76}, {53080, 6593}
X(55226) = barycentric quotient X(i)/X(j) for these (i, j): {23, 512}, {99, 67}, {110, 3455}, {316, 523}, {648, 8791}, {662, 2157}, {670, 18019}, {892, 10415}, {2492, 3124}, {4563, 34897}, {4577, 9076}, {4590, 17708}, {4593, 37221}, {5099, 33919}, {5468, 14357}, {6331, 46105}, {6593, 351}, {7664, 690}, {8744, 2489}, {9019, 3005}, {9517, 20975}, {9979, 115}, {10317, 3049}, {10510, 17414}, {12824, 21731}, {14246, 9178}, {16165, 9409}, {16568, 661}, {17088, 7178}, {17941, 36820}, {18020, 935}, {18311, 1648}, {18374, 669}, {18715, 8061}, {20944, 1577}, {21094, 4024}, {21205, 3120}, {22151, 647}, {33752, 44114}, {34539, 39413}, {35138, 10511}, {37765, 2501}, {37804, 525}, {40074, 850}, {52076, 51441}, {52449, 15475}, {52551, 5466}, {52630, 6}, {52916, 25}, {52951, 14398}, {55142, 51428}
X(55226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {648, 55225, 670}, {2396, 2407, 4590}, {5468, 53351, 53367}, {53351, 53367, 892}

X(55227) = TRILINEAR POLE OF LINE {24, 317}

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

X(55227) lies on these lines: {76, 41253}, {99, 933}, {107, 10425}, {110, 877}, {112, 2396}, {136, 317}, {323, 44132}, {648, 670}, {4576, 35311}, {5468, 35360}, {14638, 44326}, {20976, 50437}, {43187, 44766}

X(55227) = trilinear pole of line {24, 317}
X(55227) = X(i)-isoconjugate-of-X(j) for these {i, j}: {68, 798}, {91, 3049}, {512, 1820}, {661, 2351}, {810, 2165}, {822, 14593}, {1924, 20563}, {2168, 15451}, {3708, 32734}, {20975, 36145}, {23216, 55215}
X(55227) = X(i)-Dao conjugate of X(j) for these {i, j}: {135, 3124}, {139, 41221}, {343, 17434}, {577, 39201}, {2501, 8029}, {9428, 20563}, {31998, 68}, {34116, 3049}, {36830, 2351}, {39013, 20975}, {39054, 1820}, {39062, 2165}
X(55227) = X(i)-Ceva conjugate of X(j) for these {i, j}: {31614, 18020}, {42405, 6331}
X(55227) = X(i)-cross conjugate of X(j) for these {i, j}: {11547, 18020}
X(55227) = intersection, other than A, B, C, of circumconics {{A, B, C, X(107), X(11547)}}, {{A, B, C, X(136), X(52476)}}, {{A, B, C, X(648), X(933)}}, {{A, B, C, X(670), X(42297)}}, {{A, B, C, X(924), X(9035)}}, {{A, B, C, X(1993), X(2421)}}, {{A, B, C, X(4563), X(10425)}}, {{A, B, C, X(5392), X(44062)}}, {{A, B, C, X(6331), X(18831)}}, {{A, B, C, X(7763), X(44326)}}, {{A, B, C, X(15418), X(44179)}}
X(55227) = tripole of the mixed polar line of X(2) and X(68) in K002
X(55227) = barycentric product X(i)*X(j) for these (i, j): {24, 670}, {136, 31614}, {305, 52917}, {317, 99}, {648, 7763}, {1748, 799}, {1993, 6331}, {6528, 9723}, {11547, 4563}, {14576, 55218}, {18020, 6563}, {18831, 39113}, {22456, 51439}, {31635, 877}, {34537, 6753}, {41679, 76}, {42405, 52032}, {44077, 4609}, {44179, 811}, {52608, 8745}
X(55227) = barycentric quotient X(i)/X(j) for these (i, j): {24, 512}, {47, 810}, {52, 15451}, {99, 68}, {107, 14593}, {110, 2351}, {136, 8029}, {250, 32734}, {317, 523}, {467, 12077}, {571, 3049}, {648, 2165}, {662, 1820}, {670, 20563}, {811, 91}, {924, 20975}, {933, 41271}, {1147, 39201}, {1748, 661}, {1993, 647}, {4563, 52350}, {6331, 5392}, {6528, 847}, {6563, 125}, {6753, 3124}, {7763, 525}, {8745, 2489}, {9723, 520}, {11547, 2501}, {14576, 55219}, {15423, 47421}, {18020, 925}, {18605, 22383}, {18831, 96}, {18883, 14582}, {31635, 879}, {39113, 6368}, {41679, 6}, {44077, 669}, {44179, 656}, {51393, 9409}, {51439, 684}, {52000, 21731}, {52032, 17434}, {52415, 15475}, {52416, 14270}, {52432, 34952}, {52584, 3269}, {52917, 25}, {52952, 14398}
X(55227) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {648, 4563, 6331}

X(55228) = X(70)X(10097)∩X(1288)X(2715)

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

X(55228) lies on these lines: {70, 10097}, {1288, 2715}

X(55228) = perspector of circumconic {{A, B, C, X(70), X(20564)}}
X(55228) = X(i)-isoconjugate-of-X(j) for these {i, j}: {26, 662}, {63, 52918}, {163, 44128}, {799, 44078}, {4592, 8746}, {24041, 55204}
X(55228) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 44128}, {1084, 26}, {3005, 55204}, {3162, 52918}, {5139, 8746}, {38996, 44078}
X(55228) = X(i)-cross conjugate of X(j) for these {i, j}: {34952, 523}
X(55228) = intersection, other than A, B, C, of circumconics {{A, B, C, X(512), X(525)}}, {{A, B, C, X(2394), X(15422)}}, {{A, B, C, X(11140), X(41271)}}
X(55228) = isotomic conjugate of the tripole of the mixed polar line of X(2) and X(70) in K002
X(55228) = barycentric product X(i)*X(j) for these (i, j): {125, 1288}, {523, 70}, {1577, 2158}, {3124, 55203}, {20564, 512}
X(55228) = barycentric quotient X(i)/X(j) for these (i, j): {25, 52918}, {70, 99}, {512, 26}, {523, 44128}, {669, 44078}, {1288, 18020}, {2158, 662}, {2489, 8746}, {3124, 55204}, {14398, 52953}, {20564, 670}, {34952, 34116}, {55203, 34537}

X(55229) = TRILINEAR POLE OF LINE {27, 310}

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

X(55229) lies on these lines: {648, 670}, {811, 4602}, {3261, 4556}, {4610, 52919}, {6335, 36806}

X(55229) = trilinear pole of line {27, 310}
X(55229) = polar conjugate of X(4079)
X(55229) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 50487}, {37, 3049}, {42, 810}, {48, 4079}, {63, 53581}, {71, 798}, {72, 669}, {181, 1946}, {184, 4705}, {213, 647}, {228, 512}, {306, 1924}, {525, 2205}, {560, 4064}, {656, 1918}, {661, 2200}, {667, 3690}, {668, 23216}, {692, 20975}, {822, 2333}, {872, 1459}, {878, 5360}, {905, 7109}, {906, 3124}, {1084, 1332}, {1356, 4571}, {1409, 3709}, {1410, 4524}, {1425, 8641}, {1500, 22383}, {1824, 39201}, {1919, 3949}, {1980, 3695}, {2196, 46390}, {2197, 3063}, {2318, 51641}, {2422, 42702}, {2489, 3990}, {2643, 32656}, {3121, 4574}, {3708, 32739}, {4024, 9247}, {4036, 14575}, {4117, 4561}, {4563, 52065}, {6516, 7063}, {7180, 52370}, {9426, 20336}, {21833, 32661}, {22096, 40521}, {22381, 50491}
X(55229) = X(i)-Dao conjugate of X(j) for these {i, j}: {1086, 20975}, {1249, 4079}, {3162, 53581}, {5190, 3124}, {6374, 4064}, {6626, 647}, {6631, 3690}, {9296, 3949}, {9428, 306}, {10001, 2197}, {31998, 71}, {34021, 656}, {36103, 50487}, {36830, 2200}, {36901, 21046}, {39052, 213}, {39053, 181}, {39054, 228}, {39060, 2171}, {39062, 42}, {40589, 3049}, {40592, 810}, {40596, 1918}, {40618, 3269}, {40619, 3708}
X(55229) = X(i)-cross conjugate of X(j) for these {i, j}: {4610, 52612}, {4625, 4623}, {17215, 86}, {46107, 44129}
X(55229) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(86), X(2421)}}, {{A, B, C, X(274), X(4569)}}, {{A, B, C, X(286), X(6335)}}, {{A, B, C, X(514), X(9035)}}, {{A, B, C, X(648), X(811)}}, {{A, B, C, X(670), X(4602)}}, {{A, B, C, X(1459), X(17215)}}, {{A, B, C, X(4563), X(4610)}}, {{A, B, C, X(4623), X(4631)}}, {{A, B, C, X(7260), X(54982)}}
X(55229) = tripole of the mixed polar line of X(2) and X(71) in K002
X(55229) = barycentric product X(i)*X(j) for these (i, j): {4, 52612}, {27, 670}, {28, 4602}, {162, 6385}, {261, 46404}, {264, 4610}, {273, 4631}, {274, 811}, {286, 799}, {305, 52919}, {310, 648}, {1172, 55213}, {1474, 4609}, {1896, 55205}, {1969, 52935}, {4572, 46103}, {4590, 46107}, {4623, 92}, {6331, 86}, {6335, 873}, {15413, 23999}, {16747, 4593}, {17171, 689}, {17206, 6528}, {17924, 24037}, {18020, 3261}, {18021, 653}, {18022, 4556}, {18026, 52379}, {20567, 52914}, {22456, 51370}, {31623, 4625}, {34537, 7649}, {40364, 52920}, {44129, 99}, {44130, 4573}, {46110, 7340}, {46254, 693}, {52608, 8747}
X(55229) = barycentric quotient X(i)/X(j) for these (i, j): {4, 4079}, {19, 50487}, {25, 53581}, {27, 512}, {28, 798}, {29, 3709}, {58, 3049}, {76, 4064}, {81, 810}, {86, 647}, {92, 4705}, {99, 71}, {107, 2333}, {110, 2200}, {112, 1918}, {162, 213}, {190, 3690}, {242, 46390}, {249, 32656}, {250, 32739}, {261, 652}, {264, 4024}, {270, 3063}, {274, 656}, {286, 661}, {310, 525}, {314, 8611}, {423, 17990}, {514, 20975}, {643, 52370}, {645, 2318}, {648, 42}, {653, 181}, {658, 1425}, {662, 228}, {664, 2197}, {668, 3949}, {670, 306}, {693, 3708}, {757, 22383}, {799, 72}, {811, 37}, {823, 1824}, {850, 21046}, {873, 905}, {1396, 51641}, {1414, 1409}, {1444, 822}, {1474, 669}, {1509, 1459}, {1783, 872}, {1790, 39201}, {1839, 8663}, {1848, 42661}, {1896, 55206}, {1897, 1500}, {1919, 23216}, {1969, 4036}, {1978, 3695}, {2185, 1946}, {2203, 1924}, {2322, 4524}, {2326, 8641}, {2973, 21131}, {3261, 125}, {4025, 3269}, {4091, 34980}, {4131, 37754}, {4238, 39258}, {4241, 51436}, {4554, 201}, {4556, 184}, {4558, 4055}, {4561, 52386}, {4563, 3682}, {4569, 37755}, {4572, 26942}, {4573, 73}, {4590, 1331}, {4592, 3990}, {4600, 4574}, {4602, 20336}, {4609, 40071}, {4610, 3}, {4612, 212}, {4616, 52373}, {4620, 23067}, {4623, 63}, {4625, 1214}, {4631, 78}, {4635, 1439}, {4636, 52425}, {4637, 1410}, {6064, 4587}, {6331, 10}, {6335, 756}, {6385, 14208}, {6386, 52369}, {6528, 1826}, {6628, 7254}, {7199, 18210}, {7257, 3694}, {7304, 22090}, {7340, 1813}, {7649, 3124}, {8747, 2489}, {8750, 7109}, {13149, 1254}, {14618, 21043}, {15413, 2632}, {16747, 8061}, {16755, 22094}, {17167, 15451}, {17171, 3005}, {17172, 42665}, {17206, 520}, {17209, 39469}, {17923, 42666}, {17924, 2643}, {17925, 3122}, {18020, 101}, {18021, 6332}, {18022, 52623}, {18026, 2171}, {18155, 53560}, {18200, 22373}, {18653, 9409}, {21178, 38356}, {23582, 8750}, {23989, 21134}, {23999, 1783}, {24006, 21833}, {24037, 1332}, {24041, 906}, {28660, 52355}, {30805, 2972}, {30940, 53556}, {31623, 4041}, {31902, 4826}, {31903, 4832}, {31905, 4455}, {32676, 2205}, {34537, 4561}, {35325, 41267}, {36066, 2196}, {36797, 1334}, {37168, 14407}, {40495, 20902}, {41676, 21035}, {44129, 523}, {44130, 3700}, {44326, 53012}, {44709, 42293}, {46103, 663}, {46107, 115}, {46110, 4092}, {46254, 100}, {46404, 12}, {46406, 6356}, {46541, 52963}, {51370, 684}, {51843, 21056}, {52379, 521}, {52608, 52396}, {52612, 69}, {52619, 4466}, {52914, 41}, {52915, 21034}, {52919, 25}, {52920, 1973}, {52921, 607}, {52935, 48}, {52937, 20618}, {52938, 8736}, {52954, 14398}, {53655, 15377}, {54229, 21823}, {55196, 283}, {55202, 3998}, {55205, 52385}, {55209, 52388}, {55211, 52389}, {55213, 1231}

X(55230) = X(42)X(2433)∩X(72)X(905)

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

X(55230) lies on these lines: {10, 21050}, {37, 3900}, {42, 2433}, {71, 10097}, {72, 905}, {101, 2715}, {190, 53202}, {201, 21134}, {228, 1946}, {386, 52597}, {512, 798}, {525, 656}, {647, 810}, {663, 55210}, {838, 21123}, {878, 2200}, {984, 29037}, {1459, 17976}, {1734, 4522}, {2501, 4024}, {2623, 53562}, {3239, 7654}, {4705, 42666}, {6586, 8676}, {8750, 32695}, {9404, 21761}, {14838, 53521}, {17420, 29142}, {21046, 51404}, {21189, 23877}, {21300, 25258}, {21789, 42662}, {22037, 48018}, {23282, 53424}, {24462, 29051}, {29200, 50350}, {32656, 32662}, {42661, 50487}, {50498, 50509}

X(55230) = reflection of X(i) in X(j) for these {i,j}: {21831, 37}
X(55230) = isotomic conjugate of X(55229)
X(55230) = perspector of circumconic {{A, B, C, X(42), X(71)}}
X(55230) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 52935}, {7, 52914}, {19, 4610}, {25, 4623}, {27, 662}, {28, 99}, {29, 1414}, {31, 55229}, {58, 811}, {60, 18026}, {63, 52919}, {69, 52920}, {77, 52921}, {81, 648}, {86, 162}, {92, 4556}, {107, 1444}, {108, 261}, {110, 286}, {112, 274}, {163, 44129}, {242, 36066}, {249, 17924}, {270, 664}, {273, 4636}, {278, 4612}, {310, 32676}, {422, 17929}, {513, 18020}, {593, 6335}, {608, 4631}, {645, 1396}, {651, 46103}, {653, 2185}, {658, 2326}, {670, 2203}, {685, 51369}, {687, 18609}, {757, 1897}, {799, 1474}, {823, 1790}, {827, 16747}, {873, 8750}, {905, 23582}, {1014, 36797}, {1098, 36118}, {1101, 46107}, {1172, 4573}, {1332, 36419}, {1333, 6331}, {1437, 6528}, {1459, 23999}, {1509, 1783}, {1880, 55196}, {1973, 52612}, {2150, 46404}, {2189, 4554}, {2299, 4625}, {2322, 4637}, {2332, 4635}, {4025, 24000}, {4131, 32230}, {4183, 4616}, {4563, 5317}, {4565, 31623}, {4567, 17925}, {4584, 31905}, {4590, 6591}, {4592, 8747}, {4596, 31900}, {4599, 17171}, {4601, 43925}, {4614, 31903}, {4622, 37168}, {5379, 7192}, {6064, 43923}, {7054, 13149}, {7058, 32714}, {7112, 36071}, {7340, 18344}, {7649, 24041}, {15352, 18604}, {15413, 23964}, {16077, 51420}, {16696, 42396}, {16697, 16813}, {16715, 53657}, {16732, 47443}, {16757, 44183}, {17172, 36095}, {17206, 24019}, {17923, 37140}, {18180, 18831}, {18605, 30450}, {32674, 52379}, {36104, 51370}, {41676, 52376}
X(55230) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55229}, {6, 4610}, {10, 811}, {37, 6331}, {115, 44129}, {125, 86}, {130, 44709}, {226, 4625}, {244, 286}, {523, 46107}, {647, 3261}, {1084, 27}, {3005, 7649}, {3124, 17171}, {3162, 52919}, {5139, 8747}, {5375, 46254}, {6337, 52612}, {6505, 4623}, {6741, 44130}, {15267, 36118}, {15450, 17167}, {15526, 310}, {17423, 58}, {17434, 30805}, {21709, 44143}, {22391, 4556}, {26932, 873}, {30476, 17215}, {34467, 757}, {34591, 274}, {35071, 17206}, {35072, 52379}, {36033, 52935}, {38978, 242}, {38983, 261}, {38985, 1444}, {38986, 28}, {38991, 46103}, {38996, 1474}, {39000, 51370}, {39006, 1509}, {39025, 270}, {39026, 18020}, {40586, 648}, {40591, 99}, {40600, 162}, {40607, 1897}, {40608, 29}, {40626, 18021}, {40627, 17925}, {51574, 799}, {52877, 46541}, {55043, 16747}, {55064, 31623}, {55065, 264}, {55066, 81}
X(55230) = X(i)-Ceva conjugate of X(j) for these {i, j}: {10, 21046}, {101, 2200}, {201, 3708}, {1331, 71}, {1425, 3269}, {3690, 20975}, {4024, 4079}, {4041, 4705}, {8750, 42}, {32739, 21035}
X(55230) = X(i)-cross conjugate of X(j) for these {i, j}: {20975, 3690}
X(55230) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(20666)}}, {{A, B, C, X(10), X(2200)}}, {{A, B, C, X(101), X(21046)}}, {{A, B, C, X(201), X(39258)}}, {{A, B, C, X(306), X(52894)}}, {{A, B, C, X(512), X(525)}}, {{A, B, C, X(656), X(798)}}, {{A, B, C, X(661), X(46382)}}, {{A, B, C, X(905), X(4455)}}, {{A, B, C, X(1425), X(1500)}}, {{A, B, C, X(1897), X(21831)}}, {{A, B, C, X(1946), X(42666)}}, {{A, B, C, X(2054), X(43693)}}, {{A, B, C, X(2333), X(53012)}}, {{A, B, C, X(3690), X(52963)}}, {{A, B, C, X(3695), X(21830)}}, {{A, B, C, X(3709), X(4705)}}, {{A, B, C, X(3900), X(9391)}}, {{A, B, C, X(4064), X(4079)}}, {{A, B, C, X(4574), X(17990)}}, {{A, B, C, X(6356), X(6378)}}, {{A, B, C, X(14407), X(14429)}}
X(55230) = barycentric product X(i)*X(j) for these (i, j): {3, 4024}, {10, 647}, {12, 652}, {37, 656}, {42, 525}, {65, 8611}, {100, 3708}, {101, 125}, {110, 21046}, {115, 1331}, {181, 6332}, {184, 52623}, {190, 20975}, {201, 650}, {210, 51664}, {283, 55197}, {304, 50487}, {305, 53581}, {306, 512}, {307, 3709}, {321, 810}, {337, 46390}, {523, 71}, {661, 72}, {756, 905}, {1018, 18210}, {1089, 22383}, {1109, 906}, {1214, 4041}, {1252, 21134}, {1332, 2643}, {1334, 17094}, {1365, 4587}, {1400, 52355}, {1409, 4086}, {1425, 3239}, {1439, 4171}, {1459, 594}, {1500, 4025}, {1577, 228}, {1783, 2632}, {1796, 6367}, {1807, 2610}, {1813, 4092}, {1824, 24018}, {1826, 520}, {1897, 3269}, {1918, 3267}, {1946, 6358}, {2171, 521}, {2197, 522}, {2200, 850}, {2318, 7178}, {2333, 3265}, {2489, 52396}, {2501, 3682}, {3049, 313}, {3064, 7066}, {3120, 4574}, {3122, 52609}, {3124, 4561}, {3270, 4605}, {3690, 514}, {3694, 4017}, {3695, 649}, {3700, 73}, {3710, 7180}, {3937, 4103}, {3942, 40521}, {3949, 513}, {4036, 48}, {4064, 6}, {4077, 52370}, {4079, 69}, {4091, 7140}, {4466, 4557}, {4551, 53560}, {4705, 63}, {6356, 657}, {6535, 7254}, {10097, 4062}, {10099, 3930}, {14208, 213}, {14618, 4055}, {15232, 52310}, {15413, 872}, {15526, 8750}, {20336, 798}, {20618, 4105}, {20902, 692}, {21011, 23286}, {21012, 39180}, {21035, 4580}, {21043, 4558}, {21044, 23067}, {21050, 51336}, {21056, 3504}, {21833, 4592}, {21859, 7004}, {22080, 31010}, {22086, 4013}, {24006, 3990}, {25098, 7148}, {26942, 663}, {32656, 338}, {32674, 7068}, {32739, 339}, {37755, 3900}, {40071, 669}, {41013, 822}, {42666, 52351}, {52335, 52610}, {52369, 667}, {52385, 55206}, {52386, 7649}, {52387, 6591}, {52388, 55210}, {52389, 55212}, {52431, 6370}, {53010, 6129}, {53012, 6587}
X(55230) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55229}, {3, 4610}, {10, 6331}, {12, 46404}, {25, 52919}, {37, 811}, {41, 52914}, {42, 648}, {48, 52935}, {63, 4623}, {69, 52612}, {71, 99}, {72, 799}, {73, 4573}, {78, 4631}, {100, 46254}, {101, 18020}, {115, 46107}, {125, 3261}, {181, 653}, {184, 4556}, {201, 4554}, {212, 4612}, {213, 162}, {228, 662}, {283, 55196}, {306, 670}, {512, 27}, {520, 17206}, {521, 52379}, {523, 44129}, {525, 310}, {607, 52921}, {647, 86}, {652, 261}, {656, 274}, {661, 286}, {663, 46103}, {669, 1474}, {684, 51370}, {756, 6335}, {798, 28}, {810, 81}, {822, 1444}, {872, 1783}, {905, 873}, {906, 24041}, {1214, 4625}, {1231, 55213}, {1254, 13149}, {1331, 4590}, {1332, 24037}, {1334, 36797}, {1409, 1414}, {1410, 4637}, {1425, 658}, {1439, 4635}, {1459, 1509}, {1500, 1897}, {1783, 23999}, {1813, 7340}, {1824, 823}, {1826, 6528}, {1918, 112}, {1924, 2203}, {1946, 2185}, {1973, 52920}, {2171, 18026}, {2196, 36066}, {2197, 664}, {2200, 110}, {2205, 32676}, {2318, 645}, {2333, 107}, {2489, 8747}, {2632, 15413}, {2643, 17924}, {2972, 30805}, {3005, 17171}, {3049, 58}, {3063, 270}, {3122, 17925}, {3124, 7649}, {3269, 4025}, {3682, 4563}, {3690, 190}, {3694, 7257}, {3695, 1978}, {3700, 44130}, {3708, 693}, {3709, 29}, {3949, 668}, {3990, 4592}, {3998, 55202}, {4024, 264}, {4036, 1969}, {4041, 31623}, {4055, 4558}, {4064, 76}, {4079, 4}, {4092, 46110}, {4455, 31905}, {4466, 52619}, {4524, 2322}, {4561, 34537}, {4574, 4600}, {4587, 6064}, {4705, 92}, {4826, 31902}, {4832, 31903}, {6332, 18021}, {6356, 46406}, {7109, 8750}, {7254, 6628}, {8061, 16747}, {8611, 314}, {8641, 2326}, {8663, 1839}, {8736, 52938}, {8750, 23582}, {9409, 18653}, {14208, 6385}, {14398, 52954}, {14407, 37168}, {15377, 53655}, {15451, 17167}, {17990, 423}, {18210, 7199}, {20336, 4602}, {20618, 52937}, {20902, 40495}, {20975, 514}, {21034, 52915}, {21035, 41676}, {21043, 14618}, {21046, 850}, {21056, 51843}, {21131, 2973}, {21134, 23989}, {21823, 54229}, {21833, 24006}, {22090, 7304}, {22094, 16755}, {22373, 18200}, {22383, 757}, {23067, 4620}, {23216, 1919}, {26942, 4572}, {32656, 249}, {32739, 250}, {34980, 4091}, {37754, 4131}, {37755, 4569}, {38356, 21178}, {39201, 1790}, {39258, 4238}, {39469, 17209}, {40071, 4609}, {41267, 35325}, {42293, 44709}, {42661, 1848}, {42665, 17172}, {42666, 17923}, {46390, 242}, {50487, 19}, {51436, 4241}, {51641, 1396}, {52355, 28660}, {52369, 6386}, {52370, 643}, {52373, 4616}, {52385, 55205}, {52386, 4561}, {52388, 55209}, {52389, 55211}, {52396, 52608}, {52425, 4636}, {52623, 18022}, {52963, 46541}, {53012, 44326}, {53556, 30940}, {53560, 18155}, {53581, 25}, {55206, 1896}
X(55230) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 3900, 21831}

X(55231) = TRILINEAR POLE OF LINE {28, 242}

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

X(55231) lies on these lines: {99, 36077}, {162, 799}, {648, 670}, {1897, 4639}, {4554, 4612}, {4610, 4625}, {4623, 55196}, {4634, 46254}, {18020, 52914}, {30938, 52955}, {40874, 44330}, {52920, 52935}

X(55231) = trilinear pole of line {28, 242}
X(55231) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 4079}, {6, 55230}, {10, 3049}, {32, 4064}, {37, 810}, {42, 647}, {48, 4705}, {63, 50487}, {69, 53581}, {71, 512}, {72, 798}, {73, 3709}, {101, 20975}, {115, 32656}, {125, 32739}, {181, 652}, {184, 4024}, {201, 3063}, {213, 656}, {228, 661}, {295, 46390}, {306, 669}, {520, 2333}, {523, 2200}, {525, 1918}, {649, 3690}, {657, 1425}, {663, 2197}, {667, 3949}, {692, 3708}, {756, 22383}, {822, 1824}, {872, 905}, {906, 2643}, {1084, 4561}, {1331, 3124}, {1402, 8611}, {1409, 4041}, {1410, 4171}, {1459, 1500}, {1576, 21046}, {1796, 8663}, {1826, 39201}, {1919, 3695}, {1924, 20336}, {1946, 2171}, {1978, 23216}, {1980, 52369}, {2196, 4155}, {2205, 14208}, {2318, 7180}, {2359, 42661}, {2489, 3682}, {2501, 4055}, {3122, 4574}, {3269, 8750}, {3694, 51641}, {4017, 52370}, {4025, 7109}, {4036, 9247}, {4092, 32660}, {4103, 22096}, {4524, 52373}, {4575, 21833}, {4580, 41267}, {6378, 22090}, {8641, 37755}, {9426, 40071}, {10099, 39258}, {14575, 52623}, {15389, 21056}, {21043, 32661}, {21134, 23990}, {21834, 22381}, {22341, 55206}, {42666, 52431}, {52065, 55202}
X(55231) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 55230}, {136, 21833}, {1015, 20975}, {1086, 3708}, {1249, 4705}, {3162, 50487}, {4858, 21046}, {5190, 2643}, {5375, 3690}, {5521, 3124}, {6376, 4064}, {6626, 656}, {6631, 3949}, {9296, 3695}, {9428, 20336}, {10001, 201}, {26932, 3269}, {31998, 72}, {34021, 525}, {34961, 52370}, {36103, 4079}, {36830, 228}, {39052, 42}, {39053, 2171}, {39054, 71}, {39060, 12}, {39062, 37}, {40589, 810}, {40592, 647}, {40596, 213}, {40605, 8611}, {40618, 2632}, {40619, 125}, {40620, 18210}, {40625, 53560}
X(55231) = X(i)-cross conjugate of X(j) for these {i, j}: {811, 55229}, {4573, 4610}, {15413, 274}, {17924, 286}, {46103, 18020}, {52935, 4623}
X(55231) = intersection, other than A, B, C, of circumconics {{A, B, C, X(27), X(1897)}}, {{A, B, C, X(81), X(2421)}}, {{A, B, C, X(86), X(658)}}, {{A, B, C, X(162), X(648)}}, {{A, B, C, X(310), X(52937)}}, {{A, B, C, X(513), X(9035)}}, {{A, B, C, X(670), X(799)}}, {{A, B, C, X(811), X(6331)}}, {{A, B, C, X(4563), X(4573)}}, {{A, B, C, X(4594), X(37215)}}, {{A, B, C, X(4610), X(4631)}}, {{A, B, C, X(13486), X(43190)}}, {{A, B, C, X(44129), X(46404)}}, {{A, B, C, X(46103), X(52914)}}
X(55231) = tripole of the mixed polar line of X(2) and X(72) in K002
X(55231) = barycentric product X(i)*X(j) for these (i, j): {1, 55229}, {4, 4623}, {19, 52612}, {27, 799}, {28, 670}, {29, 4625}, {108, 18021}, {112, 6385}, {162, 310}, {250, 40495}, {264, 52935}, {270, 4572}, {274, 648}, {278, 4631}, {286, 99}, {304, 52919}, {305, 52920}, {331, 4612}, {811, 86}, {1414, 44130}, {1444, 6528}, {1474, 4602}, {1509, 6335}, {1897, 873}, {1969, 4556}, {2185, 46404}, {2203, 4609}, {2299, 55213}, {2322, 4635}, {2326, 46406}, {4554, 46103}, {4610, 92}, {6331, 81}, {13149, 7058}, {15413, 23582}, {16697, 42405}, {16703, 42396}, {16747, 4577}, {17171, 4593}, {17206, 823}, {17924, 4590}, {17925, 4601}, {18020, 693}, {18026, 261}, {22456, 51369}, {23999, 4025}, {24037, 7649}, {24041, 46107}, {31623, 4573}, {31905, 4639}, {34537, 6591}, {36066, 40717}, {37168, 4634}, {40149, 55196}, {41083, 55211}, {44129, 662}, {44426, 7340}, {46254, 514}, {52379, 653}, {52608, 5317}, {52619, 5379}, {52914, 6063}, {52921, 7182}, {55202, 8747}, {55205, 8748}
X(55231) = barycentric quotient X(i)/X(j) for these (i, j): {1, 55230}, {4, 4705}, {19, 4079}, {25, 50487}, {27, 661}, {28, 512}, {29, 4041}, {58, 810}, {60, 1946}, {75, 4064}, {81, 647}, {86, 656}, {92, 4024}, {99, 72}, {100, 3690}, {107, 1824}, {108, 181}, {110, 228}, {112, 213}, {162, 42}, {163, 2200}, {190, 3949}, {242, 4155}, {249, 906}, {250, 692}, {261, 521}, {264, 4036}, {270, 663}, {274, 525}, {286, 523}, {310, 14208}, {314, 52355}, {333, 8611}, {422, 17989}, {513, 20975}, {514, 3708}, {593, 22383}, {643, 2318}, {645, 3694}, {648, 37}, {651, 2197}, {653, 2171}, {658, 37755}, {662, 71}, {664, 201}, {668, 3695}, {670, 20336}, {693, 125}, {757, 1459}, {763, 7254}, {799, 306}, {811, 10}, {823, 1826}, {873, 4025}, {905, 3269}, {934, 1425}, {1101, 32656}, {1111, 21134}, {1172, 3709}, {1332, 52386}, {1333, 3049}, {1396, 7180}, {1414, 73}, {1434, 51664}, {1437, 39201}, {1444, 520}, {1474, 798}, {1509, 905}, {1577, 21046}, {1783, 1500}, {1790, 822}, {1829, 42661}, {1870, 42666}, {1897, 756}, {1969, 52623}, {1973, 53581}, {1978, 52369}, {1980, 23216}, {2185, 652}, {2189, 3063}, {2201, 46390}, {2203, 669}, {2322, 4171}, {2326, 657}, {2355, 8663}, {2421, 42702}, {2501, 21833}, {2906, 42653}, {3261, 20902}, {4025, 2632}, {4091, 37754}, {4131, 2972}, {4183, 4524}, {4206, 50494}, {4211, 50490}, {4230, 5360}, {4235, 21839}, {4238, 20683}, {4246, 51377}, {4248, 4729}, {4554, 26942}, {4556, 48}, {4558, 3990}, {4560, 53560}, {4561, 52387}, {4563, 3998}, {4565, 1409}, {4567, 4574}, {4569, 6356}, {4573, 1214}, {4575, 4055}, {4590, 1332}, {4592, 3682}, {4601, 52609}, {4602, 40071}, {4610, 63}, {4612, 219}, {4616, 1439}, {4623, 69}, {4625, 307}, {4631, 345}, {4636, 212}, {4637, 52373}, {5088, 9391}, {5317, 2489}, {5379, 4557}, {5546, 52370}, {6064, 4571}, {6331, 321}, {6335, 594}, {6385, 3267}, {6516, 7066}, {6528, 41013}, {6591, 3124}, {7192, 18210}, {7199, 4466}, {7257, 3710}, {7304, 25098}, {7340, 6516}, {7649, 2643}, {8748, 55206}, {8750, 872}, {13149, 6354}, {14004, 21727}, {14014, 50495}, {15149, 24290}, {15413, 15526}, {15742, 40521}, {16697, 17434}, {16703, 2525}, {16741, 14417}, {16747, 826}, {16750, 21107}, {16757, 38356}, {17171, 8061}, {17206, 24018}, {17515, 53562}, {17923, 2610}, {17924, 115}, {17925, 3125}, {17926, 36197}, {18020, 100}, {18021, 35518}, {18026, 12}, {18180, 15451}, {18604, 32320}, {18605, 30451}, {18609, 686}, {18653, 2631}, {23224, 34980}, {23582, 1783}, {23999, 1897}, {24000, 8750}, {24006, 21043}, {24019, 2333}, {24037, 4561}, {24041, 1331}, {30576, 22086}, {30606, 14418}, {30939, 14429}, {30940, 24459}, {31623, 3700}, {31900, 4983}, {31901, 48053}, {31902, 48005}, {31903, 4822}, {31905, 21832}, {32676, 1918}, {33295, 53556}, {35325, 21814}, {35360, 21807}, {35518, 7068}, {36066, 295}, {36118, 1254}, {36419, 6591}, {36797, 210}, {36838, 20618}, {37140, 52431}, {37168, 4730}, {40149, 55197}, {40495, 339}, {41083, 55212}, {41676, 3954}, {42396, 18098}, {43925, 3121}, {44129, 1577}, {44130, 4086}, {44327, 53010}, {44426, 4092}, {46102, 21859}, {46103, 650}, {46107, 1109}, {46254, 190}, {46404, 6358}, {46541, 21805}, {51369, 684}, {51420, 9409}, {52379, 6332}, {52612, 304}, {52890, 14404}, {52913, 3198}, {52914, 55}, {52919, 19}, {52920, 25}, {52921, 33}, {52935, 3}, {52955, 14398}, {54229, 21725}, {54240, 8736}, {55196, 1812}, {55202, 52396}, {55205, 52565}, {55224, 42699}, {55227, 42700}, {55229, 75}

X(55232) = X(10)X(3239)∩X(71)X(652)

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

X(55232) lies on these lines: {10, 3239}, {37, 2433}, {42, 4105}, {71, 652}, {72, 10097}, {100, 2715}, {228, 878}, {306, 4025}, {321, 43665}, {424, 2501}, {512, 661}, {521, 2522}, {525, 14208}, {647, 656}, {649, 832}, {650, 15313}, {668, 53202}, {906, 32662}, {1459, 2523}, {1783, 32695}, {2533, 6590}, {2610, 4024}, {2616, 2623}, {2968, 22432}, {3063, 46380}, {3125, 21961}, {3738, 46383}, {3900, 6591}, {4086, 21719}, {4120, 21720}, {4171, 55212}, {7068, 38356}, {7234, 8646}, {7252, 8674}, {7253, 26080}, {8062, 24960}, {14399, 16612}, {21046, 53560}, {21054, 36197}, {42664, 50330}, {43060, 50350}, {47136, 48269}

X(55232) = reflection of X(i) in X(j) for these {i,j}: {22383, 2522}
X(55232) = isotomic conjugate of X(55231)
X(55232) = trilinear pole of line {3708, 20975}
X(55232) = perspector of circumconic {{A, B, C, X(12), X(37)}}
X(55232) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 52919}, {4, 4556}, {19, 52935}, {25, 4610}, {27, 110}, {28, 662}, {29, 4565}, {31, 55231}, {32, 55229}, {34, 4612}, {57, 52914}, {58, 648}, {60, 653}, {63, 52920}, {81, 162}, {86, 112}, {99, 1474}, {107, 1790}, {108, 2185}, {109, 46103}, {163, 286}, {222, 52921}, {249, 7649}, {261, 32674}, {270, 651}, {274, 32676}, {278, 4636}, {423, 17940}, {593, 1897}, {643, 1396}, {649, 18020}, {664, 2189}, {667, 46254}, {685, 17209}, {757, 1783}, {799, 2203}, {811, 1333}, {823, 1437}, {827, 17171}, {849, 6335}, {905, 24000}, {933, 17167}, {934, 2326}, {1019, 5379}, {1098, 32714}, {1101, 17924}, {1172, 1414}, {1304, 18653}, {1331, 36419}, {1395, 4631}, {1412, 36797}, {1444, 24019}, {1459, 23582}, {1509, 8750}, {1576, 44129}, {1839, 6578}, {1870, 37140}, {1973, 4623}, {1974, 52612}, {2150, 18026}, {2201, 36066}, {2204, 4625}, {2206, 6331}, {2299, 4573}, {2332, 4616}, {2905, 53628}, {3120, 47443}, {4025, 23964}, {4091, 32230}, {4183, 4637}, {4558, 8747}, {4561, 36420}, {4570, 17925}, {4591, 37168}, {4592, 5317}, {4600, 43925}, {4627, 31903}, {4629, 31900}, {4872, 36071}, {6591, 24041}, {7054, 36118}, {7112, 32673}, {10423, 17172}, {15388, 21178}, {16747, 34072}, {16813, 44709}, {17187, 42396}, {17206, 32713}, {17923, 36069}, {18604, 36126}, {18609, 36114}, {22383, 23999}, {23357, 46107}, {32696, 51370}, {35325, 52394}, {36104, 51369}, {44698, 46639}, {44769, 52954}
X(55232) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55231}, {6, 52935}, {10, 648}, {11, 46103}, {37, 811}, {115, 286}, {125, 81}, {226, 4573}, {244, 27}, {523, 17924}, {525, 15413}, {647, 693}, {1084, 28}, {2972, 16697}, {3005, 6591}, {3162, 52920}, {4075, 6335}, {4858, 44129}, {5139, 5317}, {5375, 18020}, {5452, 52914}, {5521, 36419}, {6337, 4623}, {6376, 55229}, {6505, 4610}, {6631, 46254}, {6741, 31623}, {7358, 7058}, {11517, 4612}, {14714, 2326}, {15267, 32714}, {15449, 16747}, {15450, 18180}, {15526, 274}, {17423, 1333}, {17434, 4131}, {20975, 16716}, {23285, 40495}, {26932, 1509}, {34467, 593}, {34591, 86}, {35071, 1444}, {35072, 261}, {36033, 4556}, {36103, 52919}, {38966, 36421}, {38978, 2201}, {38982, 17923}, {38983, 2185}, {38985, 1790}, {38986, 1474}, {38991, 270}, {38996, 2203}, {39000, 51369}, {39005, 18609}, {39006, 757}, {39025, 2189}, {40586, 162}, {40591, 662}, {40599, 36797}, {40600, 112}, {40603, 6331}, {40607, 1783}, {40608, 1172}, {40618, 873}, {40626, 52379}, {46093, 18604}, {47413, 16715}, {50330, 17925}, {50497, 43925}, {51574, 99}, {55043, 17171}, {55059, 31926}, {55060, 1396}, {55064, 29}, {55065, 92}, {55066, 58}
X(55232) = X(i)-Ceva conjugate of X(j) for these {i, j}: {71, 53560}, {100, 228}, {306, 18210}, {525, 4064}, {656, 55230}, {692, 3954}, {1332, 72}, {1783, 37}, {3695, 20975}, {3700, 4024}, {3949, 3708}, {4036, 4705}, {4559, 21810}, {21721, 21720}, {21859, 2197}, {21958, 21056}, {26942, 125}, {37755, 2632}, {41506, 4516}, {41508, 115}
X(55232) = X(i)-cross conjugate of X(j) for these {i, j}: {3269, 2197}, {3708, 3949}, {20975, 3695}
X(55232) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(46536)}}, {{A, B, C, X(3), X(424)}}, {{A, B, C, X(72), X(21839)}}, {{A, B, C, X(125), X(24290)}}, {{A, B, C, X(228), X(321)}}, {{A, B, C, X(512), X(525)}}, {{A, B, C, X(594), X(2197)}}, {{A, B, C, X(652), X(2610)}}, {{A, B, C, X(656), X(661)}}, {{A, B, C, X(756), X(37755)}}, {{A, B, C, X(810), X(50488)}}, {{A, B, C, X(905), X(4983)}}, {{A, B, C, X(2171), X(53010)}}, {{A, B, C, X(3239), X(4605)}}, {{A, B, C, X(3690), X(20683)}}, {{A, B, C, X(3695), X(52959)}}, {{A, B, C, X(3708), X(4730)}}, {{A, B, C, X(3949), X(21805)}}, {{A, B, C, X(4024), X(4041)}}, {{A, B, C, X(4025), X(18210)}}, {{A, B, C, X(4079), X(50494)}}, {{A, B, C, X(4822), X(51664)}}, {{A, B, C, X(14404), X(20975)}}, {{A, B, C, X(15413), X(50497)}}, {{A, B, C, X(17989), X(52609)}}, {{A, B, C, X(20336), X(52893)}}, {{A, B, C, X(21107), X(50490)}}, {{A, B, C, X(21810), X(22123)}}, {{A, B, C, X(41508), X(52386)}}
X(55232) = barycentric product X(i)*X(j) for these (i, j): {1, 4064}, {3, 4036}, {10, 656}, {12, 521}, {37, 525}, {48, 52623}, {100, 125}, {101, 20902}, {108, 7068}, {115, 1332}, {181, 35518}, {190, 3708}, {201, 522}, {213, 3267}, {226, 8611}, {228, 850}, {304, 4079}, {305, 50487}, {306, 661}, {307, 4041}, {313, 810}, {321, 647}, {337, 4155}, {338, 906}, {339, 692}, {523, 72}, {594, 905}, {1018, 4466}, {1089, 1459}, {1109, 1331}, {1214, 3700}, {1231, 3709}, {1365, 4571}, {1425, 4397}, {1500, 15413}, {1565, 40521}, {1577, 71}, {1807, 6370}, {1812, 55197}, {1824, 3265}, {1826, 24018}, {1897, 2632}, {1946, 34388}, {2171, 6332}, {2197, 4391}, {2318, 4077}, {2321, 51664}, {2501, 3998}, {2610, 52351}, {2623, 42698}, {2643, 4561}, {3125, 52609}, {3239, 37755}, {3269, 6335}, {3690, 693}, {3694, 7178}, {3695, 513}, {3710, 4017}, {3900, 6356}, {3942, 4103}, {3949, 514}, {3954, 4580}, {4013, 53532}, {4024, 63}, {4025, 756}, {4086, 73}, {4092, 6516}, {4131, 7140}, {4552, 53560}, {4705, 69}, {5379, 5489}, {6358, 652}, {10097, 42713}, {10099, 3932}, {14208, 42}, {14429, 4674}, {14582, 42701}, {14618, 3990}, {14837, 53010}, {14977, 21839}, {15419, 762}, {15420, 21810}, {15526, 1783}, {16732, 4574}, {17094, 210}, {17879, 8750}, {17898, 53012}, {17924, 52386}, {18098, 2525}, {18210, 3952}, {20336, 512}, {20618, 4130}, {20948, 2200}, {20975, 668}, {21043, 4592}, {21046, 662}, {21050, 9255}, {21134, 765}, {21833, 4563}, {21859, 26932}, {22383, 28654}, {23224, 7141}, {23994, 32656}, {24006, 3682}, {26942, 650}, {27801, 3049}, {31010, 3958}, {34591, 4605}, {40071, 798}, {40364, 53581}, {41013, 520}, {42702, 43665}, {42703, 878}, {42717, 51404}, {43534, 53556}, {44426, 7066}, {52355, 65}, {52369, 649}, {52387, 7649}, {52565, 55206}, {55230, 75}
X(55232) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55231}, {3, 52935}, {10, 811}, {12, 18026}, {19, 52919}, {25, 52920}, {33, 52921}, {37, 648}, {42, 162}, {48, 4556}, {55, 52914}, {63, 4610}, {69, 4623}, {71, 662}, {72, 99}, {73, 1414}, {75, 55229}, {100, 18020}, {115, 17924}, {125, 693}, {181, 108}, {190, 46254}, {201, 664}, {210, 36797}, {212, 4636}, {213, 112}, {219, 4612}, {228, 110}, {295, 36066}, {304, 52612}, {306, 799}, {307, 4625}, {321, 6331}, {339, 40495}, {345, 4631}, {512, 28}, {520, 1444}, {521, 261}, {523, 286}, {525, 274}, {594, 6335}, {647, 81}, {650, 46103}, {652, 2185}, {656, 86}, {657, 2326}, {661, 27}, {663, 270}, {669, 2203}, {684, 51369}, {686, 18609}, {692, 250}, {756, 1897}, {798, 1474}, {810, 58}, {822, 1790}, {826, 16747}, {872, 8750}, {905, 1509}, {906, 249}, {1109, 46107}, {1214, 4573}, {1254, 36118}, {1331, 24041}, {1332, 4590}, {1409, 4565}, {1425, 934}, {1439, 4616}, {1459, 757}, {1500, 1783}, {1577, 44129}, {1783, 23582}, {1812, 55196}, {1824, 107}, {1826, 823}, {1897, 23999}, {1918, 32676}, {1946, 60}, {2171, 653}, {2197, 651}, {2200, 163}, {2318, 643}, {2333, 24019}, {2489, 5317}, {2525, 16703}, {2610, 17923}, {2631, 18653}, {2632, 4025}, {2643, 7649}, {2972, 4131}, {3049, 1333}, {3063, 2189}, {3121, 43925}, {3124, 6591}, {3125, 17925}, {3198, 52913}, {3267, 6385}, {3269, 905}, {3682, 4592}, {3690, 100}, {3694, 645}, {3695, 668}, {3700, 31623}, {3708, 514}, {3709, 1172}, {3710, 7257}, {3949, 190}, {3954, 41676}, {3990, 4558}, {3998, 4563}, {4024, 92}, {4025, 873}, {4036, 264}, {4041, 29}, {4055, 4575}, {4064, 75}, {4079, 19}, {4086, 44130}, {4092, 44426}, {4155, 242}, {4171, 2322}, {4466, 7199}, {4524, 4183}, {4557, 5379}, {4561, 24037}, {4571, 6064}, {4574, 4567}, {4705, 4}, {4729, 4248}, {4730, 37168}, {4822, 31903}, {4983, 31900}, {5360, 4230}, {6332, 52379}, {6354, 13149}, {6356, 4569}, {6358, 46404}, {6516, 7340}, {6591, 36419}, {7066, 6516}, {7068, 35518}, {7180, 1396}, {7254, 763}, {8061, 17171}, {8611, 333}, {8663, 2355}, {8736, 54240}, {8750, 24000}, {9391, 5088}, {9409, 51420}, {14208, 310}, {14398, 52955}, {14404, 52890}, {14417, 16741}, {14418, 30606}, {14429, 30939}, {15451, 18180}, {15526, 15413}, {17434, 16697}, {17989, 422}, {18098, 42396}, {18210, 7192}, {20336, 670}, {20618, 36838}, {20683, 4238}, {20902, 3261}, {20975, 513}, {21043, 24006}, {21046, 1577}, {21107, 16750}, {21134, 1111}, {21725, 54229}, {21727, 14004}, {21805, 46541}, {21807, 35360}, {21814, 35325}, {21832, 31905}, {21833, 2501}, {21839, 4235}, {21859, 46102}, {22086, 30576}, {22383, 593}, {23216, 1980}, {24018, 17206}, {24290, 15149}, {24459, 30940}, {25098, 7304}, {26942, 4554}, {30451, 18605}, {32320, 18604}, {32656, 1101}, {34980, 23224}, {35518, 18021}, {36197, 17926}, {37754, 4091}, {37755, 658}, {38356, 16757}, {39201, 1437}, {40071, 4602}, {40521, 15742}, {41013, 6528}, {42653, 2906}, {42661, 1829}, {42666, 1870}, {42699, 55224}, {42700, 55227}, {42702, 2421}, {46390, 2201}, {48005, 31902}, {48053, 31901}, {50487, 25}, {50490, 4211}, {50494, 4206}, {50495, 14014}, {51377, 4246}, {51664, 1434}, {52355, 314}, {52369, 1978}, {52370, 5546}, {52373, 4637}, {52386, 1332}, {52387, 4561}, {52396, 55202}, {52431, 37140}, {52565, 55205}, {52609, 4601}, {52623, 1969}, {53010, 44327}, {53556, 33295}, {53560, 4560}, {53562, 17515}, {53581, 1973}, {55197, 40149}, {55206, 8748}, {55212, 41083}, {55230, 1}
X(55232) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {521, 2522, 22383}, {656, 8611, 647}, {3700, 21721, 4036}

X(55233) = TRILINEAR POLE OF LINE {29, 332}

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

X(55233) lies on these lines: {648, 670}, {799, 823}, {4554, 41207}, {4610, 46254}, {4636, 35519}, {52612, 55205}

X(55233) = trilinear pole of line {29, 332}
X(55233) = X(i)-isoconjugate-of-X(j) for these {i, j}: {65, 3049}, {71, 51641}, {73, 798}, {77, 53581}, {181, 22383}, {201, 1919}, {222, 50487}, {228, 7180}, {307, 1924}, {512, 1409}, {603, 4079}, {604, 55230}, {647, 1402}, {667, 2197}, {669, 1214}, {810, 1400}, {1084, 6516}, {1231, 9426}, {1332, 1356}, {1397, 55232}, {1410, 3709}, {1415, 20975}, {1425, 3063}, {1880, 39201}, {1918, 51664}, {1980, 26942}, {2200, 4017}, {2205, 17094}, {2333, 51640}, {2489, 22341}, {2643, 32660}, {3121, 23067}, {3124, 36059}, {4055, 55208}, {4554, 23216}, {4705, 52411}, {7250, 52370}, {21859, 22096}
X(55233) = X(i)-Dao conjugate of X(j) for these {i, j}: {1146, 20975}, {3161, 55230}, {6631, 2197}, {7952, 4079}, {9296, 201}, {9428, 307}, {10001, 1425}, {20620, 3124}, {31998, 73}, {34021, 51664}, {34961, 2200}, {39052, 1402}, {39054, 1409}, {39060, 1254}, {39062, 1400}, {40582, 810}, {40602, 3049}, {40605, 647}, {40624, 3708}, {40626, 3269}
X(55233) = X(i)-cross conjugate of X(j) for these {i, j}: {799, 4631}, {46110, 44130}, {52379, 46254}
X(55233) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(314), X(4554)}}, {{A, B, C, X(333), X(2421)}}, {{A, B, C, X(522), X(9035)}}, {{A, B, C, X(648), X(823)}}, {{A, B, C, X(799), X(4563)}}, {{A, B, C, X(4610), X(52379)}}, {{A, B, C, X(4631), X(52612)}}
X(55233) = tripole of the mixed polar line of X(2) and X(73) in K002
X(55233) = barycentric product X(i)*X(j) for these (i, j): {29, 670}, {162, 40072}, {270, 6386}, {281, 52612}, {286, 7257}, {305, 52921}, {310, 36797}, {312, 55231}, {314, 811}, {318, 4623}, {332, 6528}, {333, 6331}, {1172, 4602}, {1896, 55202}, {1969, 4612}, {1978, 46103}, {2299, 4609}, {3064, 34537}, {4183, 55213}, {4391, 46254}, {4590, 46110}, {4610, 7017}, {4631, 92}, {18020, 35519}, {18021, 1897}, {18022, 4636}, {23999, 35518}, {24037, 44426}, {28660, 648}, {31623, 799}, {44129, 645}, {44130, 99}, {46107, 6064}, {46404, 7058}, {52379, 6335}, {52608, 8748}, {52914, 561}, {55229, 8}
X(55233) = barycentric quotient X(i)/X(j) for these (i, j): {8, 55230}, {21, 810}, {27, 7180}, {28, 51641}, {29, 512}, {33, 50487}, {99, 73}, {162, 1402}, {190, 2197}, {249, 32660}, {261, 1459}, {270, 667}, {274, 51664}, {281, 4079}, {283, 39201}, {284, 3049}, {286, 4017}, {310, 17094}, {312, 55232}, {314, 656}, {318, 4705}, {332, 520}, {333, 647}, {415, 17992}, {522, 20975}, {607, 53581}, {643, 228}, {645, 71}, {646, 3949}, {648, 1400}, {662, 1409}, {664, 1425}, {668, 201}, {670, 307}, {799, 1214}, {811, 65}, {823, 1880}, {1098, 1946}, {1172, 798}, {1414, 1410}, {1444, 51640}, {1812, 822}, {1897, 181}, {1978, 26942}, {2185, 22383}, {2189, 1919}, {2204, 1924}, {2299, 669}, {2322, 3709}, {2326, 3063}, {3064, 3124}, {3596, 4064}, {3699, 3690}, {4391, 3708}, {4554, 37755}, {4556, 52411}, {4561, 7066}, {4563, 40152}, {4572, 6356}, {4573, 52373}, {4590, 1813}, {4592, 22341}, {4600, 23067}, {4602, 1231}, {4610, 222}, {4612, 48}, {4620, 52610}, {4623, 77}, {4625, 1439}, {4631, 63}, {4636, 184}, {5081, 42666}, {5546, 2200}, {6064, 1331}, {6331, 226}, {6332, 3269}, {6335, 2171}, {6514, 32320}, {6516, 7138}, {6528, 225}, {7017, 4024}, {7058, 652}, {7256, 2318}, {7257, 72}, {7258, 3694}, {7259, 52370}, {8748, 2489}, {13149, 7147}, {14006, 7234}, {14024, 4455}, {18020, 109}, {18021, 4025}, {18026, 1254}, {18155, 18210}, {23582, 32674}, {23999, 108}, {24037, 6516}, {24041, 36059}, {28660, 525}, {30606, 22086}, {31623, 661}, {34387, 21134}, {35518, 2632}, {35519, 125}, {36118, 7143}, {36797, 42}, {40072, 14208}, {44129, 7178}, {44130, 523}, {44426, 2643}, {46103, 649}, {46107, 1365}, {46110, 115}, {46254, 651}, {46404, 6354}, {46406, 20618}, {46878, 42661}, {47389, 6517}, {51382, 9409}, {52379, 905}, {52608, 52565}, {52612, 348}, {52616, 2972}, {52914, 31}, {52919, 608}, {52920, 1395}, {52921, 25}, {52935, 603}, {52956, 14398}, {55196, 1790}, {55202, 52385}, {55207, 3998}, {55211, 52037}, {55229, 7}, {55231, 57}
X(55233) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6331, 55231, 55229}

X(55234) = X(12)X(21721)∩X(65)X(650)

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

X(55234) lies on these lines: {12, 21721}, {65, 650}, {73, 10097}, {109, 2715}, {226, 43665}, {512, 810}, {525, 8611}, {647, 822}, {652, 17975}, {656, 52310}, {661, 2501}, {664, 53202}, {1214, 25098}, {1400, 2433}, {1402, 8641}, {1409, 22383}, {1441, 21438}, {2171, 4024}, {2623, 21828}, {3239, 21957}, {4017, 42664}, {6589, 53262}, {11375, 24961}, {25667, 44733}, {32660, 32662}, {32674, 32695}

X(55234) = isotomic conjugate of X(55233)
X(55234) = perspector of circumconic {{A, B, C, X(73), X(201)}}
X(55234) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 52914}, {4, 4612}, {21, 648}, {25, 4631}, {27, 643}, {28, 645}, {29, 662}, {31, 55233}, {33, 4610}, {41, 55229}, {55, 55231}, {60, 6335}, {63, 52921}, {78, 52919}, {81, 36797}, {92, 4636}, {99, 1172}, {100, 46103}, {107, 1812}, {108, 7058}, {110, 31623}, {112, 314}, {162, 333}, {163, 44130}, {190, 270}, {249, 44426}, {250, 4391}, {261, 1783}, {281, 52935}, {283, 823}, {284, 811}, {286, 5546}, {318, 4556}, {332, 24019}, {345, 52920}, {521, 23582}, {607, 4623}, {650, 18020}, {652, 23999}, {653, 1098}, {663, 46254}, {664, 2326}, {668, 2189}, {670, 2204}, {799, 2299}, {931, 44734}, {1101, 46110}, {1396, 7256}, {1414, 2322}, {1474, 7257}, {1824, 55196}, {1896, 4558}, {1897, 2185}, {2193, 6528}, {2194, 6331}, {2212, 52612}, {2332, 4625}, {3064, 24041}, {4183, 4573}, {4560, 5379}, {4571, 36419}, {4584, 14024}, {4590, 18344}, {4592, 8748}, {4603, 14006}, {5081, 37140}, {6061, 13149}, {6064, 6591}, {6332, 24000}, {6514, 36126}, {6516, 36421}, {7054, 18026}, {8750, 52379}, {14395, 42308}, {15146, 41206}, {16077, 52949}, {17515, 47318}, {23964, 35518}, {28660, 32676}
X(55234) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55233}, {115, 44130}, {125, 333}, {223, 55231}, {226, 799}, {244, 31623}, {523, 46110}, {647, 35519}, {1084, 29}, {1214, 6331}, {3005, 3064}, {3160, 55229}, {3162, 52921}, {5139, 8748}, {6505, 4631}, {8054, 46103}, {15267, 653}, {15526, 28660}, {17423, 284}, {17434, 52616}, {22391, 4636}, {26932, 52379}, {32664, 52914}, {34467, 2185}, {34591, 314}, {35071, 332}, {36033, 4612}, {38983, 7058}, {38985, 1812}, {38986, 1172}, {38996, 2299}, {39006, 261}, {39025, 2326}, {40586, 36797}, {40590, 811}, {40591, 645}, {40608, 2322}, {40611, 648}, {40618, 18021}, {40622, 44129}, {46093, 6514}, {47345, 6528}, {51574, 7257}, {55053, 270}, {55060, 27}, {55065, 7017}, {55066, 21}
X(55234) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1425, 20975}, {1813, 73}, {2171, 3708}, {32674, 1400}
X(55234) = X(i)-cross conjugate of X(j) for these {i, j}: {20975, 1425}
X(55234) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(512), X(525)}}, {{A, B, C, X(661), X(810)}}, {{A, B, C, X(1459), X(4064)}}, {{A, B, C, X(1938), X(9391)}}, {{A, B, C, X(3708), X(4024)}}, {{A, B, C, X(4079), X(8611)}}, {{A, B, C, X(7180), X(17094)}}, {{A, B, C, X(17992), X(52610)}}, {{A, B, C, X(51641), X(51664)}}
X(55234) = barycentric product X(i)*X(j) for these (i, j): {12, 1459}, {37, 51664}, {57, 55232}, {65, 656}, {71, 7178}, {108, 2632}, {109, 125}, {115, 1813}, {181, 4025}, {201, 513}, {222, 4024}, {225, 520}, {226, 647}, {228, 4077}, {306, 7180}, {307, 512}, {348, 4079}, {523, 73}, {1020, 53560}, {1042, 52355}, {1109, 36059}, {1214, 661}, {1231, 798}, {1254, 521}, {1331, 1365}, {1367, 8750}, {1400, 525}, {1402, 14208}, {1409, 1577}, {1410, 4086}, {1415, 20902}, {1425, 522}, {1427, 8611}, {1439, 4041}, {1441, 810}, {1790, 55197}, {1807, 51663}, {1880, 24018}, {1937, 9391}, {2171, 905}, {2197, 514}, {2489, 52565}, {2501, 40152}, {2643, 6516}, {2972, 36127}, {3049, 349}, {3269, 653}, {3669, 3949}, {3676, 3690}, {3694, 7216}, {3695, 43924}, {3700, 52373}, {3708, 651}, {3710, 7250}, {3998, 55208}, {4017, 72}, {4036, 603}, {4064, 56}, {4091, 8736}, {4466, 4559}, {4574, 53545}, {4605, 7117}, {4705, 77}, {6354, 652}, {6356, 663}, {6517, 8754}, {7066, 7649}, {10397, 13853}, {15526, 32674}, {17094, 42}, {18210, 4551}, {20336, 51641}, {20618, 657}, {20975, 664}, {21044, 52610}, {21046, 4565}, {21131, 44717}, {21134, 59}, {21859, 3942}, {22341, 24006}, {22383, 6358}, {23067, 3120}, {26942, 649}, {32660, 338}, {34980, 52938}, {37754, 54240}, {37755, 650}, {40149, 822}, {40160, 52310}, {41013, 51640}, {42666, 52392}, {43923, 52387}, {44426, 7138}, {50487, 7182}, {52037, 55212}, {52391, 53527}, {52411, 52623}, {55230, 7}
X(55234) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55233}, {7, 55229}, {25, 52921}, {31, 52914}, {42, 36797}, {48, 4612}, {57, 55231}, {63, 4631}, {65, 811}, {71, 645}, {72, 7257}, {73, 99}, {77, 4623}, {108, 23999}, {109, 18020}, {115, 46110}, {125, 35519}, {181, 1897}, {184, 4636}, {201, 668}, {222, 4610}, {225, 6528}, {226, 6331}, {228, 643}, {307, 670}, {348, 52612}, {512, 29}, {520, 332}, {523, 44130}, {525, 28660}, {603, 52935}, {608, 52919}, {647, 333}, {649, 46103}, {651, 46254}, {652, 7058}, {656, 314}, {661, 31623}, {667, 270}, {669, 2299}, {798, 1172}, {810, 21}, {822, 1812}, {905, 52379}, {1214, 799}, {1231, 4602}, {1254, 18026}, {1331, 6064}, {1365, 46107}, {1395, 52920}, {1400, 648}, {1402, 162}, {1409, 662}, {1410, 1414}, {1425, 664}, {1439, 4625}, {1459, 261}, {1790, 55196}, {1813, 4590}, {1880, 823}, {1919, 2189}, {1924, 2204}, {1946, 1098}, {2171, 6335}, {2197, 190}, {2200, 5546}, {2318, 7256}, {2489, 8748}, {2632, 35518}, {2643, 44426}, {2972, 52616}, {3049, 284}, {3063, 2326}, {3124, 3064}, {3269, 6332}, {3690, 3699}, {3694, 7258}, {3708, 4391}, {3709, 2322}, {3949, 646}, {3998, 55207}, {4017, 286}, {4024, 7017}, {4025, 18021}, {4064, 3596}, {4079, 281}, {4455, 14024}, {4705, 318}, {6354, 46404}, {6356, 4572}, {6516, 24037}, {6517, 47389}, {7066, 4561}, {7138, 6516}, {7143, 36118}, {7147, 13149}, {7178, 44129}, {7180, 27}, {7234, 14006}, {9409, 51382}, {14208, 40072}, {14398, 52956}, {17094, 310}, {17992, 415}, {18210, 18155}, {20618, 46406}, {20975, 522}, {21134, 34387}, {22086, 30606}, {22341, 4592}, {22383, 2185}, {23067, 4600}, {26942, 1978}, {32320, 6514}, {32660, 249}, {32674, 23582}, {36059, 24041}, {37755, 4554}, {39201, 283}, {40152, 4563}, {42661, 46878}, {42666, 5081}, {50487, 33}, {51640, 1444}, {51641, 28}, {51664, 274}, {52037, 55211}, {52370, 7259}, {52373, 4573}, {52385, 55202}, {52411, 4556}, {52565, 52608}, {52610, 4620}, {53581, 607}, {55230, 8}, {55232, 312}

X(55235) = TRILINEAR POLE OF LINE {35, 319}

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

X(55235) lies on these lines: {86, 33115}, {99, 8652}, {100, 17934}, {190, 4610}, {319, 21054}, {645, 651}, {1978, 4601}, {3699, 4600}, {3952, 5468}, {4572, 55209}, {17935, 36863}, {33948, 52935}, {37783, 52137}

X(55235) = trilinear pole of line {35, 319}
X(55235) = X(i)-isoconjugate-of-X(j) for these {i, j}: {79, 798}, {512, 2160}, {661, 6186}, {667, 8818}, {669, 30690}, {1919, 6757}, {1924, 20565}, {2489, 7100}, {3063, 52382}, {3121, 6742}, {3124, 13486}, {3709, 52372}, {4079, 52375}, {4117, 55209}, {7073, 7180}, {7110, 51641}, {7113, 15475}, {8606, 55208}, {11060, 53527}, {50487, 52393}
X(55235) = X(i)-Dao conjugate of X(j) for these {i, j}: {1100, 4983}, {6631, 8818}, {8287, 3125}, {9296, 6757}, {9428, 20565}, {10001, 52382}, {14838, 21131}, {31998, 79}, {36830, 6186}, {39054, 2160}, {40604, 21828}
X(55235) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4601, 33939}
X(55235) = X(i)-cross conjugate of X(j) for these {i, j}: {7265, 319}, {16755, 34016}, {42033, 4600}
X(55235) = intersection, other than A, B, C, of circumconics {{A, B, C, X(651), X(4629)}}, {{A, B, C, X(1978), X(33939)}}, {{A, B, C, X(3699), X(42033)}}, {{A, B, C, X(4554), X(4632)}}, {{A, B, C, X(7265), X(21054)}}
X(55235) = tripole of the mixed polar line of X(2) and X(79) in K002
X(55235) = barycentric product X(i)*X(j) for these (i, j): {35, 670}, {190, 34016}, {319, 99}, {1016, 16755}, {1442, 7257}, {1978, 40214}, {2174, 4602}, {3219, 799}, {3578, 4632}, {3678, 4623}, {3969, 4610}, {4420, 4625}, {4467, 4600}, {4563, 52412}, {4590, 7265}, {10411, 20566}, {14838, 4601}, {16577, 4631}, {17095, 645}, {17104, 6386}, {18160, 4567}, {21054, 31614}, {33939, 662}, {34537, 55210}, {35193, 4572}, {42033, 4573}, {47318, 7799}, {52421, 643}, {55202, 6198}
X(55235) = barycentric quotient X(i)/X(j) for these (i, j): {35, 512}, {80, 15475}, {99, 79}, {110, 6186}, {190, 8818}, {319, 523}, {323, 21828}, {643, 7073}, {645, 7110}, {662, 2160}, {664, 52382}, {668, 6757}, {670, 20565}, {799, 30690}, {1399, 51641}, {1414, 52372}, {1442, 4017}, {2003, 7180}, {2174, 798}, {2605, 3122}, {3219, 661}, {3578, 4988}, {3647, 4983}, {3678, 4705}, {3969, 4024}, {4420, 4041}, {4467, 3120}, {4554, 43682}, {4561, 52388}, {4563, 52381}, {4573, 52374}, {4592, 7100}, {4600, 6742}, {4601, 15455}, {4610, 52393}, {4620, 38340}, {6516, 52390}, {7257, 52344}, {7265, 115}, {7799, 4707}, {8287, 21131}, {10411, 36}, {11107, 18344}, {14590, 52413}, {14616, 43082}, {14838, 3125}, {16755, 1086}, {17095, 7178}, {17104, 667}, {17190, 4979}, {18160, 16732}, {20566, 10412}, {21054, 8029}, {24041, 13486}, {33939, 1577}, {34016, 514}, {34537, 55209}, {35057, 4516}, {35192, 3063}, {35193, 663}, {35195, 42649}, {40214, 649}, {42033, 3700}, {42701, 2610}, {47318, 1989}, {52351, 14582}, {52405, 3709}, {52408, 810}, {52412, 2501}, {52421, 4077}, {52603, 52434}, {52935, 52375}, {53542, 8034}, {55210, 3124}
X(55235) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {645, 4563, 799}, {4601, 4631, 1978}

X(55236) = X(649)X(2160)∩X(661)X(1637)

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

X(55236) lies on these lines: {79, 49284}, {649, 2160}, {650, 4802}, {661, 1637}, {2610, 3700}, {3676, 21141}, {4041, 4838}, {4391, 4707}, {4521, 7110}, {9090, 26700}, {20509, 48094}, {21209, 52393}, {23755, 47915}, {30690, 47676}

X(55236) = isotomic conjugate of X(55235)
X(55236) = perspector of circumconic {{A, B, C, X(79), X(6757)}}
X(55236) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55235}, {35, 662}, {99, 2174}, {100, 40214}, {110, 3219}, {163, 319}, {190, 17104}, {643, 2003}, {645, 1399}, {648, 52408}, {651, 35193}, {664, 35192}, {692, 34016}, {1101, 7265}, {1110, 16755}, {1414, 52405}, {1442, 5546}, {1576, 33939}, {1807, 14590}, {1813, 11107}, {2161, 10411}, {2594, 4612}, {2605, 4567}, {3647, 4629}, {3678, 4556}, {4420, 4565}, {4558, 6198}, {4563, 14975}, {4570, 14838}, {4575, 52412}, {4596, 17454}, {4636, 16577}, {6149, 47318}, {6516, 41502}, {8701, 17190}, {17402, 46073}, {17403, 46077}, {18315, 35194}, {18359, 52603}, {24041, 55210}, {35057, 52378}, {36069, 42701}
X(55236) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55235}, {115, 319}, {136, 52412}, {244, 3219}, {514, 16755}, {523, 7265}, {1084, 35}, {1086, 34016}, {3005, 55210}, {3120, 3578}, {4858, 33939}, {4988, 4467}, {6741, 42033}, {8054, 40214}, {14993, 47318}, {38982, 42701}, {38986, 2174}, {38991, 35193}, {39025, 35192}, {40584, 10411}, {40608, 52405}, {40622, 17095}, {40627, 2605}, {50330, 14838}, {55053, 17104}, {55060, 2003}, {55064, 4420}, {55065, 3969}, {55066, 52408}
X(55236) = X(i)-Ceva conjugate of X(j) for these {i, j}: {52374, 3120}
X(55236) = X(i)-cross conjugate of X(j) for these {i, j}: {3125, 2160}, {4983, 523}
X(55236) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(46554)}}, {{A, B, C, X(512), X(23875)}}, {{A, B, C, X(513), X(31947)}}, {{A, B, C, X(514), X(4024)}}, {{A, B, C, X(523), X(4802)}}, {{A, B, C, X(649), X(2610)}}, {{A, B, C, X(650), X(661)}}, {{A, B, C, X(663), X(55210)}}, {{A, B, C, X(693), X(18014)}}, {{A, B, C, X(1400), X(52413)}}, {{A, B, C, X(1577), X(48275)}}, {{A, B, C, X(1637), X(3064)}}, {{A, B, C, X(2433), X(7252)}}, {{A, B, C, X(3120), X(3676)}}, {{A, B, C, X(4017), X(51648)}}, {{A, B, C, X(4036), X(43927)}}, {{A, B, C, X(4077), X(47887)}}, {{A, B, C, X(4521), X(21950)}}, {{A, B, C, X(4765), X(23755)}}, {{A, B, C, X(4813), X(4983)}}, {{A, B, C, X(5466), X(7192)}}, {{A, B, C, X(7649), X(23752)}}, {{A, B, C, X(8599), X(47885)}}, {{A, B, C, X(12071), X(17422)}}, {{A, B, C, X(18015), X(43931)}}, {{A, B, C, X(21124), X(49293)}}, {{A, B, C, X(21832), X(47676)}}, {{A, B, C, X(25576), X(48266)}}, {{A, B, C, X(35352), X(48103)}}
X(55236) = barycentric product X(i)*X(j) for these (i, j): {513, 6757}, {514, 8818}, {522, 52382}, {523, 79}, {1109, 13486}, {1577, 2160}, {1989, 4707}, {2166, 53527}, {2501, 52381}, {3120, 6742}, {3124, 55209}, {3700, 52374}, {4017, 52344}, {4024, 52393}, {4036, 52375}, {4077, 7073}, {4086, 52372}, {6186, 850}, {7110, 7178}, {10412, 36}, {14582, 17923}, {14592, 52413}, {15455, 3125}, {15475, 320}, {20565, 512}, {21044, 38340}, {21828, 94}, {24006, 7100}, {30690, 661}, {43082, 758}, {43682, 650}, {44426, 52390}, {52388, 7649}
X(55236) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55235}, {36, 10411}, {79, 99}, {115, 7265}, {512, 35}, {514, 34016}, {523, 319}, {649, 40214}, {661, 3219}, {663, 35193}, {667, 17104}, {798, 2174}, {810, 52408}, {1086, 16755}, {1577, 33939}, {1989, 47318}, {2160, 662}, {2501, 52412}, {2610, 42701}, {3063, 35192}, {3120, 4467}, {3122, 2605}, {3124, 55210}, {3125, 14838}, {3700, 42033}, {3709, 52405}, {4017, 1442}, {4024, 3969}, {4041, 4420}, {4077, 52421}, {4516, 35057}, {4705, 3678}, {4707, 7799}, {4979, 17190}, {4983, 3647}, {4988, 3578}, {6186, 110}, {6742, 4600}, {6757, 668}, {7073, 643}, {7100, 4592}, {7110, 645}, {7178, 17095}, {7180, 2003}, {8029, 21054}, {8034, 53542}, {8818, 190}, {10412, 20566}, {13486, 24041}, {14582, 52351}, {15455, 4601}, {15475, 80}, {16732, 18160}, {18344, 11107}, {20565, 670}, {21131, 8287}, {21828, 323}, {30690, 799}, {38340, 4620}, {42649, 35195}, {43082, 14616}, {43682, 4554}, {51641, 1399}, {52344, 7257}, {52372, 1414}, {52374, 4573}, {52375, 52935}, {52381, 4563}, {52382, 664}, {52388, 4561}, {52390, 6516}, {52393, 4610}, {52413, 14590}, {52434, 52603}, {55209, 34537}

X(55237) = TRILINEAR POLE OF LINE {36, 320}

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

X(55237) lies on these lines: {81, 239}, {86, 1647}, {99, 4588}, {645, 651}, {4556, 4610}, {4615, 4638}, {4619, 55194}, {4631, 55209}, {4634, 47318}, {5108, 24505}, {5468, 7192}, {22128, 40075}

X(55237) = trilinear pole of line {36, 320}
X(55237) = X(i)-isoconjugate-of-X(j) for these {i, j}: {80, 798}, {512, 2161}, {649, 34857}, {661, 6187}, {669, 18359}, {759, 4079}, {1168, 14407}, {1411, 3709}, {1807, 2489}, {1919, 15065}, {1924, 20566}, {2174, 15475}, {3063, 52383}, {3121, 51562}, {4516, 32675}, {4705, 34079}, {7180, 52371}, {14560, 21824}, {14582, 14975}, {14616, 53581}, {21043, 32671}, {21833, 36069}, {24624, 50487}, {36910, 51641}
X(55237) = X(i)-Dao conjugate of X(j) for these {i, j}: {44, 4730}, {3936, 4120}, {5375, 34857}, {9296, 15065}, {9428, 20566}, {10001, 52383}, {31998, 80}, {34586, 4079}, {35069, 4705}, {35128, 4516}, {35204, 3709}, {36830, 6187}, {38982, 21833}, {39054, 2161}, {40584, 512}, {40604, 55210}, {40612, 661}, {51583, 4024}
X(55237) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4634, 99}
X(55237) = X(i)-cross conjugate of X(j) for these {i, j}: {4707, 320}
X(55237) = intersection, other than A, B, C, of circumconics {{A, B, C, X(81), X(651)}}, {{A, B, C, X(239), X(3218)}}, {{A, B, C, X(274), X(4554)}}, {{A, B, C, X(320), X(16741)}}, {{A, B, C, X(645), X(7058)}}, {{A, B, C, X(758), X(8682)}}, {{A, B, C, X(799), X(52379)}}, {{A, B, C, X(873), X(4625)}}, {{A, B, C, X(1509), X(4573)}}, {{A, B, C, X(4242), X(26643)}}, {{A, B, C, X(4359), X(8052)}}, {{A, B, C, X(4707), X(4750)}}
X(55237) = tripole of the mixed polar line of X(2) and X(80) in K002
X(55237) = barycentric product X(i)*X(j) for these (i, j): {36, 670}, {110, 40075}, {214, 4634}, {274, 4585}, {320, 99}, {323, 55209}, {1227, 4622}, {1443, 7257}, {1870, 55202}, {1983, 6385}, {2245, 52612}, {2361, 55213}, {3218, 799}, {3904, 4620}, {3936, 4610}, {3960, 4601}, {4453, 4600}, {4511, 4625}, {4590, 4707}, {4602, 7113}, {4609, 52434}, {4615, 51583}, {4623, 758}, {10411, 20565}, {17078, 645}, {17923, 4563}, {18593, 4631}, {20924, 662}, {21828, 34537}, {22128, 6331}, {24037, 53527}, {27950, 4639}, {32851, 4573}, {35550, 52935}, {52413, 52608}
X(55237) = barycentric quotient X(i)/X(j) for these (i, j): {36, 512}, {79, 15475}, {99, 80}, {100, 34857}, {110, 6187}, {214, 4730}, {314, 52356}, {320, 523}, {323, 55210}, {643, 52371}, {645, 36910}, {662, 2161}, {664, 52383}, {668, 15065}, {670, 20566}, {758, 4705}, {799, 18359}, {1414, 1411}, {1443, 4017}, {1983, 213}, {2245, 4079}, {2323, 3709}, {2610, 21833}, {3218, 661}, {3268, 21054}, {3724, 50487}, {3738, 4516}, {3904, 21044}, {3936, 4024}, {3960, 3125}, {4242, 1824}, {4282, 3063}, {4453, 3120}, {4511, 4041}, {4556, 34079}, {4558, 52431}, {4563, 52351}, {4573, 2006}, {4585, 37}, {4590, 47318}, {4592, 1807}, {4600, 51562}, {4601, 36804}, {4610, 24624}, {4612, 2341}, {4620, 655}, {4622, 1168}, {4623, 14616}, {4625, 18815}, {4707, 115}, {4867, 4770}, {4880, 48005}, {4881, 4729}, {4973, 4983}, {4996, 53562}, {6370, 21043}, {6516, 52391}, {7113, 798}, {7257, 52409}, {7799, 7265}, {10411, 35}, {17078, 7178}, {17191, 1635}, {17455, 14407}, {17515, 18344}, {17923, 2501}, {20565, 10412}, {20924, 1577}, {21758, 3121}, {21828, 3124}, {22128, 647}, {27757, 4931}, {27950, 21832}, {32679, 21824}, {32851, 3700}, {35550, 4036}, {40075, 850}, {41801, 30572}, {51583, 4120}, {52378, 32675}, {52381, 14582}, {52407, 810}, {52413, 2489}, {52434, 669}, {52440, 51641}, {52935, 759}, {53314, 3122}, {53527, 2643}, {55209, 94}, {55235, 41226}
X(55237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {799, 4563, 55235}, {4563, 4573, 799}

X(55238) = X(37)X(650)∩X(321)X(4391)

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

X(55238) lies on these lines: {37, 650}, {226, 21141}, {321, 4391}, {335, 18359}, {522, 32917}, {594, 3700}, {649, 5341}, {661, 2171}, {756, 4041}, {759, 53686}, {1255, 8045}, {1824, 18344}, {2161, 46457}, {2222, 9090}, {2262, 21353}, {2501, 8736}, {4120, 24078}, {6354, 7178}, {14582, 55236}, {18011, 42759}, {21209, 33133}, {21828, 30572}, {36910, 45344}

X(55238) = isotomic conjugate of X(55237)
X(55238) = trilinear pole of line {4516, 4705}
X(55238) = perspector of circumconic {{A, B, C, X(80), X(15065)}}
X(55238) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55237}, {36, 662}, {58, 4585}, {86, 1983}, {99, 7113}, {110, 3218}, {162, 22128}, {163, 320}, {214, 4591}, {249, 53527}, {323, 13486}, {645, 52440}, {648, 52407}, {664, 4282}, {758, 4556}, {799, 52434}, {901, 17191}, {1101, 4707}, {1414, 2323}, {1443, 5546}, {1464, 4612}, {1576, 20924}, {1790, 4242}, {1813, 17515}, {1870, 4558}, {2160, 10411}, {2245, 52935}, {2361, 4573}, {3724, 4610}, {3738, 52378}, {3960, 4570}, {4511, 4565}, {4567, 53314}, {4575, 17923}, {4592, 52413}, {4600, 21758}, {4620, 8648}, {4622, 17455}, {4625, 52426}, {4629, 4973}, {4636, 18593}, {7100, 14590}, {17402, 39153}, {17403, 39152}, {21828, 24041}, {30690, 52603}
X(55238) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55237}, {10, 4585}, {115, 320}, {125, 22128}, {136, 17923}, {244, 3218}, {523, 4707}, {1084, 36}, {3005, 21828}, {4858, 20924}, {4988, 4453}, {5139, 52413}, {6741, 32851}, {15898, 662}, {36901, 40075}, {36909, 645}, {38979, 17191}, {38986, 7113}, {38996, 52434}, {39025, 4282}, {40600, 1983}, {40608, 2323}, {40622, 17078}, {40627, 53314}, {50330, 3960}, {50497, 21758}, {55064, 4511}, {55065, 3936}, {55066, 52407}
X(55238) = X(i)-Ceva conjugate of X(j) for these {i, j}: {47318, 80}
X(55238) = X(i)-cross conjugate of X(j) for these {i, j}: {4730, 523}
X(55238) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(46555)}}, {{A, B, C, X(10), X(18011)}}, {{A, B, C, X(37), X(321)}}, {{A, B, C, X(512), X(23876)}}, {{A, B, C, X(523), X(4777)}}, {{A, B, C, X(650), X(661)}}, {{A, B, C, X(1018), X(35354)}}, {{A, B, C, X(1577), X(47874)}}, {{A, B, C, X(2433), X(4559)}}, {{A, B, C, X(3064), X(12077)}}, {{A, B, C, X(3952), X(5466)}}, {{A, B, C, X(4024), X(31010)}}, {{A, B, C, X(4049), X(4120)}}, {{A, B, C, X(4551), X(35347)}}, {{A, B, C, X(4707), X(4730)}}, {{A, B, C, X(7265), X(55210)}}, {{A, B, C, X(18014), X(35353)}}, {{A, B, C, X(21719), X(23685)}}, {{A, B, C, X(21828), X(53045)}}, {{A, B, C, X(23757), X(30572)}}, {{A, B, C, X(35307), X(35361)}}
X(55238) = barycentric product X(i)*X(j) for these (i, j): {115, 47318}, {522, 52383}, {523, 80}, {1411, 4086}, {1577, 2161}, {1807, 24006}, {1989, 7265}, {2006, 3700}, {2501, 52351}, {3120, 51562}, {3125, 36804}, {3678, 43082}, {4017, 52409}, {4036, 759}, {4077, 52371}, {6187, 850}, {10412, 35}, {14582, 52412}, {14616, 4705}, {14618, 52431}, {15065, 513}, {15475, 319}, {18359, 661}, {18815, 4041}, {20566, 512}, {21044, 655}, {21054, 476}, {21824, 32680}, {24624, 4024}, {30572, 36590}, {34079, 52623}, {34857, 693}, {35174, 4516}, {35352, 36815}, {36910, 7178}, {41226, 55236}, {44426, 52391}, {52356, 65}, {55210, 94}
X(55238) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55237}, {35, 10411}, {37, 4585}, {80, 99}, {94, 55209}, {115, 4707}, {213, 1983}, {512, 36}, {523, 320}, {647, 22128}, {655, 4620}, {661, 3218}, {669, 52434}, {759, 52935}, {798, 7113}, {810, 52407}, {850, 40075}, {1168, 4622}, {1411, 1414}, {1577, 20924}, {1635, 17191}, {1807, 4592}, {1824, 4242}, {2006, 4573}, {2161, 662}, {2341, 4612}, {2489, 52413}, {2501, 17923}, {2643, 53527}, {3063, 4282}, {3120, 4453}, {3121, 21758}, {3122, 53314}, {3124, 21828}, {3125, 3960}, {3700, 32851}, {3709, 2323}, {4017, 1443}, {4024, 3936}, {4036, 35550}, {4041, 4511}, {4079, 2245}, {4120, 51583}, {4516, 3738}, {4705, 758}, {4729, 4881}, {4730, 214}, {4770, 4867}, {4931, 27757}, {4983, 4973}, {6187, 110}, {7178, 17078}, {7265, 7799}, {10412, 20565}, {14407, 17455}, {14582, 52381}, {14616, 4623}, {15065, 668}, {15475, 79}, {18344, 17515}, {18359, 799}, {18815, 4625}, {20566, 670}, {21043, 6370}, {21044, 3904}, {21054, 3268}, {21824, 32679}, {21832, 27950}, {21833, 2610}, {24624, 4610}, {30572, 41801}, {32675, 52378}, {34079, 4556}, {34857, 100}, {36804, 4601}, {36910, 645}, {41226, 55235}, {47318, 4590}, {48005, 4880}, {50487, 3724}, {51562, 4600}, {51641, 52440}, {52351, 4563}, {52356, 314}, {52371, 643}, {52383, 664}, {52391, 6516}, {52409, 7257}, {52431, 4558}, {53562, 4996}, {55210, 323}

X(55239) = X(75)X(1581)∩X(99)X(831)

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

X(55239) lies on these lines: {75, 1581}, {99, 831}, {274, 27191}, {304, 20941}, {310, 30997}, {662, 799}, {668, 53649}, {670, 4033}, {873, 18052}, {1740, 18058}, {4553, 4576}, {16571, 18069}, {16741, 17374}, {17149, 36289}, {17466, 18156}, {18051, 40364}, {18070, 37134}, {18079, 33760}, {18133, 34022}, {18137, 20452}, {18143, 55081}, {18150, 40017}, {21582, 33806}, {24004, 36860}, {30938, 52043}, {39995, 40874}

X(55239) = trilinear pole of line {38, 1930}
X(55239) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 18105}, {82, 798}, {83, 669}, {110, 51906}, {115, 4630}, {213, 18108}, {251, 512}, {308, 9426}, {523, 46288}, {560, 18070}, {661, 46289}, {667, 18098}, {688, 52395}, {689, 9427}, {733, 5027}, {827, 3124}, {872, 39179}, {1084, 4577}, {1176, 2489}, {1501, 52618}, {1576, 34294}, {1918, 10566}, {1919, 18082}, {1924, 3112}, {1974, 4580}, {2422, 51862}, {2501, 10547}, {2643, 34072}, {3049, 32085}, {3122, 4628}, {3288, 42288}, {4117, 4593}, {6573, 38996}, {17997, 46286}, {22105, 32740}, {39182, 40981}, {50487, 52376}, {52394, 53581}
X(55239) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 18105}, {39, 661}, {141, 798}, {244, 51906}, {339, 1109}, {4858, 34294}, {6374, 18070}, {6626, 18108}, {6631, 18098}, {6665, 8061}, {9296, 18082}, {9428, 3112}, {15449, 2643}, {31998, 82}, {34021, 10566}, {34452, 1924}, {36830, 46289}, {39054, 251}, {40585, 512}, {55043, 3124}, {55050, 4117}
X(55239) = X(i)-Ceva conjugate of X(j) for these {i, j}: {24041, 304}
X(55239) = X(i)-cross conjugate of X(j) for these {i, j}: {2084, 38}, {4568, 4576}, {8061, 75}
X(55239) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(75), X(37204)}}, {{A, B, C, X(141), X(3570)}}, {{A, B, C, X(662), X(831)}}, {{A, B, C, X(799), X(1934)}}, {{A, B, C, X(1930), X(24039)}}, {{A, B, C, X(2643), X(8061)}}, {{A, B, C, X(4576), X(4610)}}, {{A, B, C, X(4593), X(18062)}}
X(55239) = tripole of the mixed polar line of X(2) and X(82) in K002
X(55239) = barycentric product X(i)*X(j) for these (i, j): {38, 670}, {39, 4602}, {141, 799}, {163, 52568}, {274, 4568}, {304, 41676}, {310, 4553}, {427, 55202}, {662, 8024}, {1235, 4592}, {1634, 561}, {1926, 46161}, {1930, 99}, {1964, 4609}, {2084, 44168}, {2525, 46254}, {3665, 7257}, {3688, 55213}, {3703, 4625}, {3933, 811}, {3954, 52612}, {4576, 75}, {4593, 7794}, {4600, 48084}, {15523, 4623}, {16696, 1978}, {16703, 190}, {16720, 7260}, {16747, 4561}, {16887, 668}, {16892, 4601}, {17187, 6386}, {17442, 52608}, {20883, 4563}, {20898, 35137}, {21336, 35567}, {23285, 24041}, {24037, 826}, {24039, 31125}, {34537, 8061}, {35325, 40364}, {35540, 37134}, {36036, 51371}, {37204, 8041}, {40072, 46153}, {46148, 6385}
X(55239) = barycentric quotient X(i)/X(j) for these (i, j): {1, 18105}, {38, 512}, {39, 798}, {76, 18070}, {86, 18108}, {99, 82}, {110, 46289}, {141, 661}, {163, 46288}, {190, 18098}, {249, 34072}, {274, 10566}, {304, 4580}, {561, 52618}, {661, 51906}, {662, 251}, {668, 18082}, {670, 3112}, {688, 4117}, {799, 83}, {811, 32085}, {826, 2643}, {1101, 4630}, {1235, 24006}, {1401, 51641}, {1509, 39179}, {1577, 34294}, {1634, 31}, {1923, 9426}, {1930, 523}, {1964, 669}, {2084, 1084}, {2236, 5027}, {2396, 3405}, {2525, 3708}, {2530, 3122}, {3051, 1924}, {3404, 2422}, {3665, 4017}, {3703, 4041}, {3917, 810}, {3933, 656}, {3954, 4079}, {4020, 3049}, {4553, 42}, {4554, 18097}, {4563, 34055}, {4567, 4628}, {4568, 37}, {4575, 10547}, {4576, 1}, {4590, 4599}, {4592, 1176}, {4593, 52395}, {4602, 308}, {4609, 18833}, {4610, 52376}, {4623, 52394}, {4884, 4729}, {7794, 8061}, {7813, 2642}, {8024, 1577}, {8033, 18111}, {8041, 2084}, {8061, 3124}, {14210, 22105}, {15523, 4705}, {16696, 649}, {16703, 514}, {16747, 7649}, {16887, 513}, {16892, 3125}, {17171, 6591}, {17187, 667}, {17442, 2489}, {17457, 8664}, {17799, 17997}, {18155, 18101}, {18183, 50486}, {18715, 2492}, {18829, 43763}, {20883, 2501}, {20898, 7927}, {21035, 50487}, {21123, 3121}, {21336, 2514}, {21424, 47126}, {21814, 53581}, {23285, 1109}, {24037, 4577}, {24039, 52898}, {24041, 827}, {31008, 18107}, {31125, 23894}, {33299, 3709}, {34022, 18106}, {34537, 4593}, {35309, 1500}, {35319, 2179}, {35325, 1973}, {35335, 52020}, {36827, 923}, {37134, 733}, {41676, 19}, {44168, 37204}, {46148, 213}, {46151, 1096}, {46153, 1402}, {46159, 875}, {46161, 1967}, {46254, 42396}, {48084, 3120}, {48278, 4516}, {52568, 20948}, {55202, 1799}
X(55239) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 18060, 2643}, {662, 55202, 24039}, {662, 799, 18062}, {4033, 7199, 670}, {18062, 24039, 662}

X(55240) = X(1)X(2084)∩X(83)X(1019)

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

X(55240) lies on these lines: {1, 2084}, {82, 23894}, {83, 1019}, {512, 2295}, {514, 23804}, {649, 23791}, {661, 830}, {798, 812}, {1015, 4367}, {4024, 4039}, {4129, 4375}, {4455, 4705}, {4580, 47679}, {4593, 24037}, {4599, 36085}, {8061, 34054}, {16552, 29534}, {32678, 34072}, {33793, 38847}, {39179, 47947}, {39577, 51862}

X(55240) = isotomic conjugate of X(55239)
X(55240) = trilinear pole of line {2643, 4117}
X(55240) = perspector of circumconic {{A, B, C, X(82), X(3112)}}
X(55240) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 1634}, {3, 41676}, {6, 4576}, {31, 55239}, {38, 662}, {39, 99}, {58, 4568}, {69, 35325}, {81, 4553}, {86, 46148}, {95, 35319}, {100, 16696}, {101, 16887}, {110, 141}, {112, 3933}, {163, 1930}, {190, 17187}, {249, 826}, {250, 2525}, {323, 46155}, {333, 46153}, {385, 46161}, {394, 46151}, {427, 4558}, {524, 36827}, {645, 1401}, {648, 3917}, {670, 3051}, {688, 34537}, {691, 7813}, {692, 16703}, {732, 805}, {757, 35309}, {799, 1964}, {811, 4020}, {827, 7794}, {906, 16747}, {907, 8362}, {1235, 32661}, {1331, 17171}, {1414, 33299}, {1576, 8024}, {1812, 46152}, {1843, 4563}, {1923, 4602}, {2084, 24037}, {2236, 37134}, {2396, 51869}, {2407, 46147}, {2421, 20021}, {2530, 4567}, {2715, 51371}, {3005, 4590}, {3313, 44766}, {3570, 46159}, {3665, 5546}, {3688, 4573}, {3703, 4565}, {3787, 35136}, {3954, 52935}, {4556, 15523}, {4570, 16892}, {4575, 20883}, {4577, 8041}, {4585, 46160}, {4592, 17442}, {4600, 21123}, {4601, 50521}, {4609, 41331}, {4610, 21035}, {4623, 21814}, {4625, 40972}, {5467, 31125}, {5468, 46154}, {6292, 7953}, {6331, 20775}, {8061, 24041}, {8115, 46167}, {8116, 46166}, {8623, 18829}, {9019, 17708}, {9145, 23297}, {9146, 30489}, {9150, 52961}, {9494, 44168}, {10007, 43357}, {10330, 52554}, {11205, 35137}, {11794, 41328}, {14570, 16030}, {14574, 52568}, {14994, 26714}, {14999, 46157}, {16704, 46162}, {17938, 35540}, {18206, 35333}, {19609, 55085}, {23285, 23357}, {23342, 46156}, {25424, 32449}, {27369, 52608}, {27374, 55218}, {28469, 41657}, {30941, 46163}, {34211, 46164}, {35334, 54308}, {39639, 41622}, {41267, 52612}, {44769, 51360}, {48278, 52378}
X(55240) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55239}, {9, 4576}, {10, 4568}, {115, 1930}, {136, 20883}, {244, 141}, {512, 2084}, {1015, 16887}, {1084, 38}, {1086, 16703}, {3005, 8061}, {4858, 8024}, {4988, 48084}, {5099, 18715}, {5139, 17442}, {5190, 16747}, {5521, 17171}, {8054, 16696}, {15527, 20898}, {17423, 4020}, {32664, 1634}, {34294, 20889}, {34591, 3933}, {36103, 41676}, {38986, 39}, {38996, 1964}, {40586, 4553}, {40600, 46148}, {40607, 35309}, {40608, 33299}, {40627, 2530}, {41884, 799}, {50330, 16892}, {50497, 21123}, {55043, 7794}, {55053, 17187}, {55064, 3703}, {55066, 3917}
X(55240) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4593, 1}, {4599, 82}, {18108, 18105}, {37204, 3112}
X(55240) = X(i)-cross conjugate of X(j) for these {i, j}: {661, 18070}, {1109, 19}
X(55240) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1580)}}, {{A, B, C, X(2), X(46573)}}, {{A, B, C, X(4), X(46501)}}, {{A, B, C, X(19), X(16568)}}, {{A, B, C, X(25), X(46497)}}, {{A, B, C, X(37), X(36954)}}, {{A, B, C, X(213), X(20372)}}, {{A, B, C, X(427), X(46500)}}, {{A, B, C, X(512), X(812)}}, {{A, B, C, X(513), X(4040)}}, {{A, B, C, X(523), X(830)}}, {{A, B, C, X(649), X(4063)}}, {{A, B, C, X(661), X(1577)}}, {{A, B, C, X(798), X(1924)}}, {{A, B, C, X(921), X(2129)}}, {{A, B, C, X(923), X(1821)}}, {{A, B, C, X(1024), X(4041)}}, {{A, B, C, X(1500), X(14991)}}, {{A, B, C, X(1973), X(16564)}}, {{A, B, C, X(2085), X(33793)}}, {{A, B, C, X(2333), X(20605)}}, {{A, B, C, X(2489), X(47127)}}, {{A, B, C, X(3405), X(46289)}}, {{A, B, C, X(4017), X(35355)}}, {{A, B, C, X(4103), X(4129)}}, {{A, B, C, X(4375), X(40623)}}, {{A, B, C, X(4593), X(18111)}}, {{A, B, C, X(4613), X(7255)}}, {{A, B, C, X(10566), X(18105)}}, {{A, B, C, X(23892), X(51641)}}, {{A, B, C, X(27809), X(27810)}}, {{A, B, C, X(43671), X(52030)}}, {{A, B, C, X(47679), X(48395)}}
X(55240) = barycentric product X(i)*X(j) for these (i, j): {10, 18108}, {19, 4580}, {31, 52618}, {115, 4599}, {308, 798}, {338, 34072}, {523, 82}, {661, 83}, {1084, 37204}, {1109, 827}, {1176, 24006}, {1577, 251}, {1924, 40016}, {1953, 39182}, {2395, 3405}, {2492, 37221}, {2501, 34055}, {2643, 4577}, {3112, 512}, {3124, 4593}, {3708, 42396}, {4024, 52376}, {4117, 42371}, {4705, 52394}, {10566, 37}, {16606, 18107}, {16732, 4628}, {17500, 2616}, {18070, 6}, {18082, 513}, {18097, 650}, {18098, 514}, {18101, 4551}, {18105, 75}, {18111, 52651}, {18833, 669}, {20948, 46288}, {22105, 897}, {23894, 52898}, {23994, 4630}, {32085, 656}, {34294, 662}, {39179, 594}, {43763, 804}, {46104, 810}, {46289, 850}, {51906, 799}, {52395, 8061}
X(55240) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4576}, {2, 55239}, {19, 41676}, {31, 1634}, {37, 4568}, {42, 4553}, {82, 99}, {83, 799}, {213, 46148}, {251, 662}, {308, 4602}, {512, 38}, {513, 16887}, {514, 16703}, {523, 1930}, {649, 16696}, {656, 3933}, {661, 141}, {667, 17187}, {669, 1964}, {733, 37134}, {798, 39}, {810, 3917}, {827, 24041}, {875, 46159}, {923, 36827}, {1084, 2084}, {1096, 46151}, {1109, 23285}, {1176, 4592}, {1402, 46153}, {1500, 35309}, {1577, 8024}, {1799, 55202}, {1924, 3051}, {1967, 46161}, {1973, 35325}, {2084, 8041}, {2179, 35319}, {2422, 3404}, {2489, 17442}, {2492, 18715}, {2501, 20883}, {2514, 21336}, {2642, 7813}, {2643, 826}, {3049, 4020}, {3112, 670}, {3120, 48084}, {3121, 21123}, {3122, 2530}, {3124, 8061}, {3125, 16892}, {3405, 2396}, {3708, 2525}, {3709, 33299}, {4017, 3665}, {4041, 3703}, {4079, 3954}, {4117, 688}, {4516, 48278}, {4577, 24037}, {4580, 304}, {4593, 34537}, {4599, 4590}, {4628, 4567}, {4630, 1101}, {4705, 15523}, {4729, 4884}, {5027, 2236}, {6591, 17171}, {7649, 16747}, {7927, 20898}, {8061, 7794}, {8664, 17457}, {9426, 1923}, {10547, 4575}, {10566, 274}, {17997, 17799}, {18070, 76}, {18082, 668}, {18097, 4554}, {18098, 190}, {18101, 18155}, {18105, 1}, {18106, 34022}, {18107, 31008}, {18108, 86}, {18111, 8033}, {18833, 4609}, {20948, 52568}, {22105, 14210}, {23894, 31125}, {24006, 1235}, {32085, 811}, {34055, 4563}, {34072, 249}, {34294, 1577}, {37204, 44168}, {39179, 1509}, {42396, 46254}, {43763, 18829}, {46288, 163}, {46289, 110}, {47126, 21424}, {50486, 18183}, {50487, 21035}, {51641, 1401}, {51906, 661}, {52020, 35335}, {52376, 4610}, {52394, 4623}, {52395, 4593}, {52618, 561}, {52898, 24039}, {53581, 21814}

X(55241) = TRILINEAR POLE OF LINE {40, 322}

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

X(55241) lies on these lines: {274, 26591}, {645, 651}, {662, 21580}, {811, 1897}, {4601, 55207}, {7258, 44326}, {21404, 25533}, {44327, 55202}

X(55241) = trilinear pole of line {40, 322}
X(55241) = X(i)-isoconjugate-of-X(j) for these {i, j}: {84, 798}, {189, 669}, {282, 51641}, {309, 1924}, {647, 7151}, {649, 2357}, {661, 2208}, {667, 1903}, {810, 7129}, {1413, 3709}, {1433, 2489}, {1919, 39130}, {1946, 2358}, {2188, 55208}, {2192, 7180}, {3049, 40836}, {3063, 52384}, {3121, 13138}, {3122, 36049}, {3125, 32652}, {4017, 7118}, {4117, 55211}, {4524, 6612}, {7250, 7367}, {9426, 44190}
X(55241) = X(i)-Dao conjugate of X(j) for these {i, j}: {57, 7180}, {5375, 2357}, {5514, 3122}, {6631, 1903}, {9296, 39130}, {9428, 309}, {10001, 52384}, {16596, 3125}, {31998, 84}, {34961, 7118}, {36830, 2208}, {39052, 7151}, {39053, 2358}, {39054, 1436}, {39062, 7129}
X(55241) = X(i)-Ceva conjugate of X(j) for these {i, j}: {55202, 7257}
X(55241) = intersection, other than A, B, C, of circumconics {{A, B, C, X(651), X(1897)}}, {{A, B, C, X(811), X(4573)}}, {{A, B, C, X(4563), X(7257)}}, {{A, B, C, X(4625), X(6331)}}
X(55241) = tripole of the mixed polar line of X(2) and X(84) in K002
X(55241) = barycentric product X(i)*X(j) for these (i, j): {40, 670}, {196, 55207}, {198, 4602}, {322, 99}, {329, 799}, {347, 7257}, {668, 8822}, {1817, 1978}, {2187, 4609}, {2331, 52608}, {2360, 6386}, {4625, 7080}, {14256, 7258}, {14837, 4601}, {17896, 4600}, {21075, 4623}, {21871, 52612}, {27398, 4554}, {34537, 55212}, {40702, 645}, {55116, 55205}, {55202, 7952}, {55213, 7074}
X(55241) = barycentric quotient X(i)/X(j) for these (i, j): {40, 512}, {99, 84}, {100, 2357}, {110, 2208}, {162, 7151}, {190, 1903}, {196, 55208}, {198, 798}, {221, 51641}, {223, 7180}, {322, 523}, {329, 661}, {347, 4017}, {643, 2192}, {645, 282}, {648, 7129}, {653, 2358}, {662, 1436}, {664, 52384}, {668, 39130}, {670, 309}, {799, 189}, {811, 40836}, {1332, 41087}, {1414, 1413}, {1817, 649}, {1819, 1946}, {2187, 669}, {2324, 3709}, {2331, 2489}, {2360, 667}, {3699, 53013}, {4554, 8808}, {4561, 52389}, {4563, 41081}, {4567, 36049}, {4570, 32652}, {4573, 1422}, {4592, 1433}, {4600, 13138}, {4601, 44327}, {4602, 44190}, {4620, 37141}, {4625, 1440}, {4637, 6612}, {5546, 7118}, {6129, 3122}, {7078, 810}, {7080, 4041}, {7257, 280}, {7259, 7367}, {8058, 4516}, {8822, 513}, {14256, 7216}, {14837, 3125}, {17896, 3120}, {21075, 4705}, {21871, 4079}, {27398, 650}, {34537, 55211}, {36797, 7008}, {40702, 7178}, {41083, 6591}, {52609, 53010}, {55112, 8611}, {55116, 55206}, {55205, 34400}, {55207, 44189}, {55212, 3124}
X(55241) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {645, 4554, 799}, {811, 4561, 7257}, {55202, 55224, 55211}

X(55242) = X(650)X(1459)∩X(656)X(3700)

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

X(55242) lies on these lines: {647, 4041}, {649, 18344}, {650, 1459}, {656, 3700}, {2358, 55208}, {2501, 4017}, {4025, 4391}, {7151, 43925}, {8059, 9090}, {55214, 55238}

X(55242) = isotomic conjugate of X(55241)
X(55242) = perspector of circumconic {{A, B, C, X(84), X(309)}}
X(55242) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55241}, {40, 662}, {99, 198}, {100, 1817}, {101, 8822}, {109, 27398}, {110, 329}, {163, 322}, {190, 2360}, {221, 645}, {223, 643}, {227, 4612}, {347, 5546}, {648, 7078}, {653, 1819}, {799, 2187}, {1331, 41083}, {1332, 3194}, {1414, 2324}, {2199, 7257}, {2331, 4592}, {3195, 4563}, {4556, 21075}, {4558, 7952}, {4565, 7080}, {4567, 6129}, {4570, 14837}, {4573, 7074}, {4616, 7368}, {6611, 7256}, {7011, 36797}, {8058, 52378}, {21871, 52935}, {24041, 55212}, {36841, 41088}
X(55242) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55241}, {11, 27398}, {115, 322}, {244, 329}, {1015, 8822}, {1084, 40}, {3005, 55212}, {3341, 645}, {4988, 17896}, {5139, 2331}, {5521, 41083}, {8054, 1817}, {38986, 198}, {38996, 2187}, {40608, 2324}, {40622, 40702}, {40627, 6129}, {50330, 14837}, {55053, 2360}, {55060, 223}, {55064, 7080}, {55066, 7078}
X(55242) = X(i)-cross conjugate of X(j) for these {i, j}: {3125, 2358}, {7180, 661}
X(55242) = intersection, other than A, B, C, of circumconics {{A, B, C, X(42), X(26001)}}, {{A, B, C, X(244), X(43925)}}, {{A, B, C, X(647), X(649)}}, {{A, B, C, X(650), X(661)}}, {{A, B, C, X(2357), X(8808)}}, {{A, B, C, X(2395), X(21960)}}, {{A, B, C, X(3572), X(25008)}}, {{A, B, C, X(4077), X(35348)}}, {{A, B, C, X(6587), X(6591)}}, {{A, B, C, X(7180), X(14837)}}, {{A, B, C, X(8611), X(40628)}}
X(55242) = barycentric product X(i)*X(j) for these (i, j): {189, 661}, {280, 4017}, {282, 7178}, {309, 512}, {522, 52384}, {523, 84}, {525, 7129}, {650, 8808}, {1021, 13853}, {1413, 4086}, {1422, 3700}, {1433, 24006}, {1436, 1577}, {1440, 4041}, {1903, 514}, {2192, 4077}, {2208, 850}, {2357, 693}, {2358, 6332}, {2501, 41081}, {3064, 52037}, {3124, 55211}, {3125, 44327}, {3676, 53013}, {4516, 53642}, {13138, 3120}, {14208, 7151}, {16732, 36049}, {17094, 7008}, {17924, 41087}, {17925, 53010}, {21044, 37141}, {21207, 32652}, {34400, 55206}, {34404, 7180}, {39130, 513}, {40117, 4466}, {40836, 656}, {44189, 55208}, {44190, 798}, {51664, 7003}, {52389, 7649}, {55110, 8611}
X(55242) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55241}, {84, 99}, {189, 799}, {280, 7257}, {282, 645}, {309, 670}, {512, 40}, {513, 8822}, {523, 322}, {649, 1817}, {650, 27398}, {661, 329}, {667, 2360}, {669, 2187}, {798, 198}, {810, 7078}, {1413, 1414}, {1422, 4573}, {1433, 4592}, {1436, 662}, {1440, 4625}, {1903, 190}, {1946, 1819}, {2192, 643}, {2208, 110}, {2357, 100}, {2358, 653}, {2489, 2331}, {3120, 17896}, {3122, 6129}, {3124, 55212}, {3125, 14837}, {3709, 2324}, {4017, 347}, {4041, 7080}, {4079, 21871}, {4516, 8058}, {4705, 21075}, {6591, 41083}, {6612, 4637}, {7008, 36797}, {7118, 5546}, {7129, 648}, {7151, 162}, {7178, 40702}, {7180, 223}, {7216, 14256}, {7367, 7259}, {8611, 55112}, {8808, 4554}, {13138, 4600}, {32652, 4570}, {34400, 55205}, {36049, 4567}, {37141, 4620}, {39130, 668}, {40836, 811}, {41081, 4563}, {41087, 1332}, {44189, 55207}, {44190, 4602}, {44327, 4601}, {51641, 221}, {52384, 664}, {52389, 4561}, {53010, 52609}, {53013, 3699}, {55206, 55116}, {55208, 196}, {55211, 34537}
X(55242) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {656, 6587, 55212}

X(55243) = X(1)X(75)∩X(99)X(100)

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

X(55243) lies on these lines: {1, 75}, {8, 3110}, {76, 16376}, {99, 100}, {148, 25685}, {646, 662}, {670, 4597}, {689, 29189}, {1019, 23891}, {1023, 24004}, {3227, 37128}, {4256, 18140}, {4560, 42720}, {4618, 4634}, {24617, 30866}, {24962, 26072}

X(55243) = trilinear pole of line {44, 4358}
X(55243) = perspector of circumconic {{A, B, C, X(799), X(4601)}}
X(55243) = X(i)-isoconjugate-of-X(j) for these {i, j}: {32, 4049}, {42, 23345}, {88, 798}, {106, 512}, {213, 1022}, {647, 8752}, {661, 9456}, {667, 4674}, {669, 903}, {810, 36125}, {901, 3122}, {1084, 4615}, {1320, 51641}, {1402, 23838}, {1417, 4041}, {1797, 2489}, {1918, 6548}, {1919, 4080}, {1924, 20568}, {2226, 14407}, {2316, 7180}, {2501, 32659}, {2712, 17991}, {3049, 6336}, {3120, 32719}, {3121, 3257}, {3124, 4591}, {3125, 32665}, {4117, 4634}, {4120, 41935}, {4557, 43922}, {8034, 9268}, {18105, 46150}, {21950, 32645}
X(55243) = X(i)-Dao conjugate of X(j) for these {i, j}: {44, 21828}, {214, 512}, {519, 4730}, {3936, 53527}, {4370, 661}, {6376, 4049}, {6626, 1022}, {6631, 4674}, {9296, 4080}, {9428, 20568}, {31998, 88}, {34021, 6548}, {35092, 3125}, {36830, 9456}, {36912, 4770}, {38979, 3122}, {39052, 8752}, {39054, 106}, {39062, 36125}, {40592, 23345}, {40605, 23838}, {51402, 4516}, {52659, 4017}, {52871, 4041}, {52872, 4705}, {52877, 50487}, {55055, 3121}
X(55243) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4601, 16729}, {4634, 799}
X(55243) = X(i)-cross conjugate of X(j) for these {i, j}: {4922, 519}, {16729, 4601}
X(55243) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(100)}}, {{A, B, C, X(44), X(2234)}}, {{A, B, C, X(75), X(668)}}, {{A, B, C, X(86), X(99)}}, {{A, B, C, X(274), X(799)}}, {{A, B, C, X(314), X(7257)}}, {{A, B, C, X(519), X(740)}}, {{A, B, C, X(664), X(4360)}}, {{A, B, C, X(900), X(2787)}}, {{A, B, C, X(1010), X(46541)}}, {{A, B, C, X(1043), X(7256)}}, {{A, B, C, X(1319), X(2703)}}, {{A, B, C, X(1733), X(38462)}}, {{A, B, C, X(1964), X(29189)}}, {{A, B, C, X(2087), X(4448)}}, {{A, B, C, X(2251), X(51907)}}, {{A, B, C, X(2415), X(25590)}}, {{A, B, C, X(3227), X(3570)}}, {{A, B, C, X(3264), X(35550)}}, {{A, B, C, X(3886), X(30731)}}, {{A, B, C, X(3952), X(46895)}}, {{A, B, C, X(4236), X(37168)}}, {{A, B, C, X(4358), X(14210)}}, {{A, B, C, X(4555), X(17160)}}, {{A, B, C, X(4589), X(16704)}}, {{A, B, C, X(4596), X(54308)}}, {{A, B, C, X(4634), X(30939)}}, {{A, B, C, X(4730), X(4922)}}, {{A, B, C, X(5209), X(17935)}}, {{A, B, C, X(10436), X(32042)}}, {{A, B, C, X(18792), X(52680)}}
X(55243) = tripole of the mixed polar line of X(2) and X(88) in K002
X(55243) = barycentric product X(i)*X(j) for these (i, j): {44, 670}, {190, 30939}, {304, 46541}, {519, 799}, {1023, 310}, {1227, 47318}, {1877, 55207}, {1978, 52680}, {2251, 4609}, {2325, 4625}, {3264, 662}, {3285, 6386}, {3762, 4600}, {3911, 7257}, {3943, 4623}, {3977, 811}, {3992, 4610}, {4169, 873}, {4358, 99}, {4370, 4634}, {4432, 4639}, {4434, 7260}, {4573, 4723}, {4592, 46109}, {4601, 900}, {4602, 902}, {4615, 4738}, {4620, 4768}, {4632, 4975}, {4633, 4742}, {5440, 6331}, {14429, 46254}, {16704, 668}, {16729, 4555}, {17780, 274}, {21805, 52612}, {23344, 6385}, {23703, 28660}, {24004, 86}, {24037, 4120}, {24039, 52747}, {27808, 30576}, {34537, 4730}, {36791, 4622}, {38462, 4563}, {40663, 4631}, {51975, 55237}, {55202, 8756}
X(55243) = barycentric quotient X(i)/X(j) for these (i, j): {44, 512}, {75, 4049}, {81, 23345}, {86, 1022}, {99, 88}, {110, 9456}, {162, 8752}, {190, 4674}, {214, 21828}, {274, 6548}, {333, 23838}, {519, 661}, {643, 2316}, {645, 1320}, {648, 36125}, {662, 106}, {668, 4080}, {670, 20568}, {678, 14407}, {799, 903}, {811, 6336}, {900, 3125}, {902, 798}, {1019, 43922}, {1023, 42}, {1227, 4707}, {1319, 7180}, {1404, 51641}, {1635, 3122}, {1639, 4516}, {1877, 55208}, {1960, 3121}, {2087, 8034}, {2251, 669}, {2325, 4041}, {3264, 1577}, {3285, 667}, {3689, 3709}, {3762, 3120}, {3911, 4017}, {3943, 4705}, {3977, 656}, {3992, 4024}, {4033, 4013}, {4120, 2643}, {4169, 756}, {4358, 523}, {4370, 4730}, {4432, 21832}, {4448, 39786}, {4487, 14321}, {4528, 36197}, {4555, 30575}, {4558, 36058}, {4565, 1417}, {4567, 901}, {4570, 32665}, {4575, 32659}, {4590, 4622}, {4592, 1797}, {4600, 3257}, {4601, 4555}, {4615, 679}, {4622, 2226}, {4634, 54974}, {4700, 4822}, {4723, 3700}, {4727, 48005}, {4730, 3124}, {4738, 4120}, {4742, 4841}, {4768, 21044}, {4908, 4770}, {4922, 16592}, {4969, 4983}, {4975, 4988}, {5235, 23352}, {5440, 647}, {7199, 6549}, {7257, 4997}, {9459, 1924}, {14429, 3708}, {16704, 513}, {16729, 900}, {16948, 2441}, {17191, 53314}, {17780, 37}, {21805, 4079}, {22356, 810}, {23202, 3049}, {23344, 213}, {23703, 1400}, {24004, 10}, {24037, 4615}, {24039, 52759}, {24041, 4591}, {30576, 3733}, {30606, 3737}, {30725, 53540}, {30731, 210}, {30939, 514}, {31059, 9508}, {34537, 4634}, {37168, 6591}, {38462, 2501}, {40988, 42666}, {46109, 24006}, {46541, 19}, {47318, 1168}, {51583, 53527}, {51975, 55238}, {52680, 649}, {52747, 23894}, {52924, 28658}, {52963, 50487}, {52964, 50491}, {53582, 21805}, {55237, 52553}
X(55243) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 7257, 668}

X(55244) = X(1)X(513)∩X(10)X(523)

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

X(55244) lies on these lines: {1, 513}, {10, 523}, {19, 4394}, {37, 661}, {65, 4017}, {75, 693}, {82, 18108}, {88, 897}, {106, 759}, {512, 53114}, {514, 4364}, {522, 596}, {536, 4444}, {876, 19945}, {891, 14315}, {900, 21630}, {901, 1290}, {903, 18827}, {994, 4083}, {1247, 31947}, {1320, 7984}, {1577, 4377}, {1647, 42754}, {1910, 9456}, {2166, 43082}, {2214, 4790}, {2217, 51648}, {2218, 6129}, {2403, 28195}, {2642, 9278}, {3257, 37135}, {3667, 22791}, {3733, 5563}, {4010, 4080}, {4145, 4674}, {4369, 17382}, {4555, 35147}, {4802, 31359}, {4833, 16484}, {4926, 34860}, {4945, 45342}, {5620, 6089}, {6003, 10222}, {6370, 34895}, {6545, 23757}, {6549, 23822}, {7192, 17320}, {8702, 11524}, {9013, 49465}, {9268, 39154}, {13476, 50359}, {14286, 21222}, {14434, 48030}, {14475, 25034}, {23598, 28151}, {28165, 39708}, {28205, 39711}, {29144, 39712}, {30572, 52383}, {36053, 36058}, {36119, 36125}, {51658, 52384}

X(55244) = midpoint of X(i) and X(j) for these {i,j}: {1022, 23352}, {14286, 21222}, {23345, 23838}, {764, 24457}
X(55244) = isotomic conjugate of X(55243)
X(55244) = trilinear pole of line {661, 3125}
X(55244) = perspector of circumconic {{A, B, C, X(88), X(4080)}}
X(55244) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 46541}, {21, 23703}, {31, 55243}, {44, 662}, {58, 17780}, {81, 1023}, {86, 23344}, {99, 902}, {100, 52680}, {101, 16704}, {110, 519}, {112, 3977}, {162, 5440}, {163, 4358}, {190, 3285}, {249, 4120}, {250, 14429}, {593, 4169}, {643, 1319}, {645, 1404}, {648, 22356}, {670, 9459}, {678, 4622}, {692, 30939}, {799, 2251}, {811, 23202}, {900, 4570}, {1017, 4615}, {1018, 30576}, {1331, 37168}, {1333, 24004}, {1412, 30731}, {1414, 3689}, {1576, 3264}, {1635, 4567}, {1639, 52378}, {1960, 4600}, {2325, 4565}, {2415, 33628}, {2429, 41629}, {2702, 31059}, {3911, 5546}, {3943, 4556}, {4141, 11636}, {4370, 4591}, {4558, 8756}, {4559, 30606}, {4575, 38462}, {4590, 14407}, {4610, 52963}, {4627, 4700}, {4629, 4969}, {4636, 40663}, {4653, 52924}, {4730, 24041}, {5379, 53532}, {5467, 52747}, {16729, 32665}, {17455, 47318}, {21805, 52935}, {32661, 46109}, {37140, 40988}
X(55244) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55243}, {10, 17780}, {37, 24004}, {115, 4358}, {125, 5440}, {136, 38462}, {244, 519}, {1015, 16704}, {1084, 44}, {1086, 30939}, {3005, 4730}, {3120, 4975}, {4369, 4922}, {4858, 3264}, {4988, 3762}, {5521, 37168}, {6741, 4723}, {8054, 52680}, {9460, 799}, {17423, 23202}, {34591, 3977}, {35092, 16729}, {36103, 46541}, {38986, 902}, {38996, 2251}, {40586, 1023}, {40594, 99}, {40595, 662}, {40599, 30731}, {40600, 23344}, {40608, 3689}, {40611, 23703}, {40627, 1635}, {50330, 900}, {50497, 1960}, {55053, 3285}, {55056, 4742}, {55059, 4702}, {55060, 1319}, {55064, 2325}, {55065, 3992}, {55066, 22356}, {55067, 30606}
X(55244) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4622, 88}, {6548, 4049}, {30575, 3125}
X(55244) = X(i)-cross conjugate of X(j) for these {i, j}: {3125, 30575}, {4730, 661}, {53527, 513}
X(55244) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(4), X(13744)}}, {{A, B, C, X(28), X(36155)}}, {{A, B, C, X(56), X(43692)}}, {{A, B, C, X(81), X(50773)}}, {{A, B, C, X(313), X(24399)}}, {{A, B, C, X(512), X(4770)}}, {{A, B, C, X(513), X(523)}}, {{A, B, C, X(514), X(4828)}}, {{A, B, C, X(522), X(4132)}}, {{A, B, C, X(536), X(3948)}}, {{A, B, C, X(649), X(47894)}}, {{A, B, C, X(656), X(4394)}}, {{A, B, C, X(679), X(17960)}}, {{A, B, C, X(758), X(1319)}}, {{A, B, C, X(764), X(35352)}}, {{A, B, C, X(798), X(50335)}}, {{A, B, C, X(1019), X(31010)}}, {{A, B, C, X(1022), X(4049)}}, {{A, B, C, X(1577), X(3669)}}, {{A, B, C, X(1647), X(30572)}}, {{A, B, C, X(2489), X(47131)}}, {{A, B, C, X(2642), X(9508)}}, {{A, B, C, X(3120), X(24457)}}, {{A, B, C, X(3122), X(36848)}}, {{A, B, C, X(3125), X(14421)}}, {{A, B, C, X(3251), X(4730)}}, {{A, B, C, X(3952), X(23836)}}, {{A, B, C, X(4010), X(19945)}}, {{A, B, C, X(4080), X(52900)}}, {{A, B, C, X(4139), X(4926)}}, {{A, B, C, X(4378), X(4411)}}, {{A, B, C, X(4551), X(14812)}}, {{A, B, C, X(4618), X(18011)}}, {{A, B, C, X(4790), X(4815)}}, {{A, B, C, X(4802), X(8672)}}, {{A, B, C, X(6089), X(8674)}}, {{A, B, C, X(6129), X(51658)}}, {{A, B, C, X(6548), X(23345)}}, {{A, B, C, X(6757), X(20615)}}, {{A, B, C, X(7180), X(47754)}}, {{A, B, C, X(7649), X(48281)}}, {{A, B, C, X(9510), X(46275)}}, {{A, B, C, X(17161), X(50344)}}, {{A, B, C, X(17356), X(27727)}}, {{A, B, C, X(28658), X(40878)}}, {{A, B, C, X(30575), X(51908)}}, {{A, B, C, X(30591), X(50330)}}, {{A, B, C, X(42754), X(42768)}}, {{A, B, C, X(42757), X(42759)}}
X(55244) = barycentric product X(i)*X(j) for these (i, j): {1, 4049}, {10, 1022}, {37, 6548}, {106, 1577}, {115, 4622}, {226, 23838}, {523, 88}, {661, 903}, {850, 9456}, {1018, 6549}, {1019, 4013}, {1109, 4591}, {1168, 4707}, {1320, 7178}, {1797, 24006}, {2316, 4077}, {2643, 4615}, {3120, 3257}, {3124, 4634}, {3125, 4555}, {4017, 4997}, {4033, 43922}, {4080, 513}, {4120, 679}, {4582, 53540}, {4674, 514}, {4730, 54974}, {6336, 656}, {14208, 8752}, {14618, 36058}, {16732, 901}, {18070, 46150}, {20568, 512}, {21207, 32665}, {23345, 321}, {23352, 30588}, {23598, 53114}, {23894, 52759}, {30575, 900}, {35353, 52900}, {36125, 525}, {40833, 4770}, {52553, 55238}
X(55244) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55243}, {10, 24004}, {19, 46541}, {37, 17780}, {42, 1023}, {88, 99}, {106, 662}, {210, 30731}, {213, 23344}, {512, 44}, {513, 16704}, {514, 30939}, {523, 4358}, {647, 5440}, {649, 52680}, {656, 3977}, {661, 519}, {667, 3285}, {669, 2251}, {679, 4615}, {756, 4169}, {798, 902}, {810, 22356}, {900, 16729}, {901, 4567}, {903, 799}, {1022, 86}, {1168, 47318}, {1320, 645}, {1400, 23703}, {1417, 4565}, {1577, 3264}, {1797, 4592}, {1924, 9459}, {2226, 4622}, {2316, 643}, {2441, 16948}, {2501, 38462}, {2643, 4120}, {3049, 23202}, {3120, 3762}, {3121, 1960}, {3122, 1635}, {3124, 4730}, {3125, 900}, {3257, 4600}, {3700, 4723}, {3708, 14429}, {3709, 3689}, {3733, 30576}, {3737, 30606}, {4013, 4033}, {4017, 3911}, {4024, 3992}, {4041, 2325}, {4049, 75}, {4079, 21805}, {4080, 668}, {4120, 4738}, {4516, 1639}, {4555, 4601}, {4591, 24041}, {4615, 24037}, {4622, 4590}, {4634, 34537}, {4674, 190}, {4705, 3943}, {4707, 1227}, {4730, 4370}, {4770, 4908}, {4822, 4700}, {4841, 4742}, {4983, 4969}, {4988, 4975}, {4997, 7257}, {6336, 811}, {6548, 274}, {6549, 7199}, {6591, 37168}, {7180, 1319}, {8034, 2087}, {8752, 162}, {9456, 110}, {9508, 31059}, {14321, 4487}, {14407, 678}, {16592, 4922}, {20568, 670}, {21044, 4768}, {21805, 53582}, {21828, 214}, {21832, 4432}, {23345, 81}, {23352, 5235}, {23838, 333}, {23894, 52747}, {24006, 46109}, {28658, 52924}, {30575, 4555}, {32659, 4575}, {32665, 4570}, {36058, 4558}, {36125, 648}, {36197, 4528}, {39786, 4448}, {42666, 40988}, {43922, 1019}, {48005, 4727}, {50487, 52963}, {50491, 52964}, {51641, 1404}, {52553, 55237}, {52759, 24039}, {53314, 17191}, {53527, 51583}, {53540, 30725}, {54974, 4634}, {55208, 1877}, {55238, 51975}
X(55244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1022, 23352, 513}, {1022, 23838, 23345}, {23345, 23352, 23838}

X(55245) = X(99)X(100)∩X(645)X(1016)

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

X(55245) lies on these lines: {99, 100}, {314, 24297}, {645, 1016}, {662, 4482}, {670, 4555}, {1509, 24524}, {4792, 4793}, {14061, 25685}, {14616, 20937}, {25278, 34016}, {25303, 32014}, {33908, 37128}, {35957, 36800}

X(55245) = trilinear pole of line {45, 4671}
X(55245) = X(i)-isoconjugate-of-X(j) for these {i, j}: {89, 798}, {512, 2163}, {649, 28658}, {661, 28607}, {667, 53114}, {669, 39704}, {1918, 52620}, {1919, 30588}, {1924, 20569}, {2320, 51641}, {2364, 7180}, {3121, 4604}, {3122, 4588}, {3125, 34073}
X(55245) = X(i)-Dao conjugate of X(j) for these {i, j}: {4850, 48350}, {5375, 28658}, {6631, 53114}, {9296, 30588}, {9428, 20569}, {31998, 89}, {34021, 52620}, {36830, 28607}, {36911, 661}, {36912, 4730}, {39054, 2163}, {40587, 512}, {55045, 3122}
X(55245) = X(i)-cross conjugate of X(j) for these {i, j}: {4774, 3679}, {4833, 5235}
X(55245) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(4634)}}, {{A, B, C, X(100), X(4555)}}, {{A, B, C, X(668), X(36804)}}, {{A, B, C, X(2787), X(4777)}}, {{A, B, C, X(4671), X(42721)}}, {{A, B, C, X(4770), X(4774)}}
X(55245) = tripole of the mixed polar line of X(2) and X(89) in K002
X(55245) = barycentric product X(i)*X(j) for these (i, j): {45, 670}, {274, 4767}, {310, 4752}, {1978, 4653}, {2177, 4602}, {3679, 799}, {3940, 6331}, {4125, 4610}, {4273, 6386}, {4554, 4720}, {4600, 4791}, {4601, 4777}, {4625, 4873}, {4632, 4717}, {4634, 4908}, {4639, 4693}, {4671, 99}, {4945, 55243}, {5219, 7257}, {5235, 668}, {24037, 4931}, {31625, 4833}, {34537, 4770}, {47683, 7035}
X(55245) = barycentric quotient X(i)/X(j) for these (i, j): {45, 512}, {99, 89}, {100, 28658}, {110, 28607}, {190, 53114}, {274, 52620}, {643, 2364}, {645, 2320}, {662, 2163}, {668, 30588}, {670, 20569}, {799, 39704}, {1405, 51641}, {2099, 7180}, {2177, 798}, {3679, 661}, {3711, 3709}, {3940, 647}, {4125, 4024}, {4273, 667}, {4567, 4588}, {4570, 34073}, {4600, 4604}, {4601, 4597}, {4634, 40833}, {4653, 649}, {4671, 523}, {4693, 21832}, {4717, 4988}, {4720, 650}, {4752, 42}, {4767, 37}, {4770, 3124}, {4774, 16592}, {4775, 3121}, {4777, 3125}, {4791, 3120}, {4800, 39786}, {4803, 4893}, {4833, 1015}, {4867, 21828}, {4873, 4041}, {4893, 3122}, {4908, 4730}, {4931, 2643}, {4933, 2642}, {4944, 4516}, {4945, 55244}, {5219, 4017}, {5235, 513}, {7257, 30608}, {17196, 48335}, {17553, 4790}, {27757, 53527}, {43052, 53540}, {47683, 244}, {49280, 18210}
X(55245) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {668, 55243, 799}, {668, 7257, 99}, {799, 7257, 55243}

X(55246) = X(89)X(4784)∩X(693)X(900)

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

X(55246) lies on these lines: {89, 4784}, {512, 53114}, {513, 1960}, {514, 23809}, {523, 4707}, {661, 14407}, {693, 900}, {1019, 2163}, {1290, 1633}, {2320, 4367}, {4597, 35147}, {4604, 37135}, {4790, 6591}, {4806, 30588}, {6006, 23796}, {19654, 24328}, {28217, 40086}, {28601, 28871}

X(55246) = isotomic conjugate of X(55245)
X(55246) = perspector of circumconic {{A, B, C, X(89), X(20569)}}
X(55246) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55245}, {45, 662}, {58, 4767}, {81, 4752}, {99, 2177}, {100, 4653}, {101, 5235}, {109, 4720}, {110, 3679}, {162, 3940}, {163, 4671}, {190, 4273}, {249, 4931}, {643, 2099}, {645, 1405}, {691, 4933}, {765, 4833}, {1252, 47683}, {1414, 3711}, {4565, 4873}, {4567, 4893}, {4570, 4777}, {4588, 4803}, {4591, 4908}, {4600, 4775}, {4770, 24041}, {4944, 52378}, {5219, 5546}, {8694, 17553}, {52680, 52925}
X(55246) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55245}, {10, 4767}, {11, 4720}, {115, 4671}, {125, 3940}, {244, 3679}, {513, 4833}, {661, 47683}, {1015, 5235}, {1084, 45}, {3005, 4770}, {3120, 4717}, {4369, 4774}, {4988, 4791}, {8054, 4653}, {38986, 2177}, {40586, 4752}, {40608, 3711}, {40627, 4893}, {50330, 4777}, {50497, 4775}, {55045, 4803}, {55053, 4273}, {55060, 2099}, {55064, 4873}, {55065, 4125}
X(55246) = X(i)-cross conjugate of X(j) for these {i, j}: {48350, 523}
X(55246) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(37), X(3246)}}, {{A, B, C, X(65), X(5126)}}, {{A, B, C, X(512), X(900)}}, {{A, B, C, X(513), X(523)}}, {{A, B, C, X(594), X(3551)}}, {{A, B, C, X(649), X(47755)}}, {{A, B, C, X(656), X(4790)}}, {{A, B, C, X(798), X(50359)}}, {{A, B, C, X(840), X(2245)}}, {{A, B, C, X(1019), X(1020)}}, {{A, B, C, X(1464), X(10428)}}, {{A, B, C, X(1577), X(48074)}}, {{A, B, C, X(1633), X(48403)}}, {{A, B, C, X(1769), X(2486)}}, {{A, B, C, X(2489), X(47132)}}, {{A, B, C, X(2642), X(4784)}}, {{A, B, C, X(3120), X(14315)}}, {{A, B, C, X(3123), X(21051)}}, {{A, B, C, X(3125), X(14422)}}, {{A, B, C, X(3700), X(23838)}}, {{A, B, C, X(3733), X(7250)}}, {{A, B, C, X(4132), X(28217)}}, {{A, B, C, X(4406), X(4761)}}, {{A, B, C, X(4770), X(23352)}}, {{A, B, C, X(4840), X(50330)}}, {{A, B, C, X(4897), X(6083)}}, {{A, B, C, X(4977), X(8672)}}, {{A, B, C, X(7180), X(23345)}}, {{A, B, C, X(8818), X(41439)}}, {{A, B, C, X(9510), X(18823)}}, {{A, B, C, X(30588), X(52901)}}, {{A, B, C, X(47842), X(50525)}}, {{A, B, C, X(50354), X(51662)}}
X(55246) = barycentric product X(i)*X(j) for these (i, j): {37, 52620}, {514, 53114}, {523, 89}, {1577, 2163}, {2320, 7178}, {2364, 4077}, {3120, 4604}, {3125, 4597}, {16732, 4588}, {20569, 512}, {21207, 34073}, {28607, 850}, {28658, 693}, {30588, 513}, {30608, 4017}, {35353, 52901}, {39704, 661}, {40426, 48350}, {40833, 4730}
X(55246) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55245}, {37, 4767}, {42, 4752}, {89, 99}, {244, 47683}, {512, 45}, {513, 5235}, {523, 4671}, {647, 3940}, {649, 4653}, {650, 4720}, {661, 3679}, {667, 4273}, {798, 2177}, {1015, 4833}, {2163, 662}, {2320, 645}, {2364, 643}, {2642, 4933}, {2643, 4931}, {3120, 4791}, {3121, 4775}, {3122, 4893}, {3124, 4770}, {3125, 4777}, {3709, 3711}, {4017, 5219}, {4024, 4125}, {4041, 4873}, {4516, 4944}, {4588, 4567}, {4597, 4601}, {4604, 4600}, {4730, 4908}, {4790, 17553}, {4893, 4803}, {4988, 4717}, {7180, 2099}, {16592, 4774}, {18210, 49280}, {20569, 670}, {21828, 4867}, {21832, 4693}, {28607, 110}, {28658, 100}, {30588, 668}, {30608, 7257}, {34073, 4570}, {39704, 799}, {39786, 4800}, {40833, 4634}, {48335, 17196}, {51641, 1405}, {52620, 274}, {53114, 190}, {53527, 27757}, {53540, 43052}, {55244, 4945}

X(55247) = X(645)X(651)∩X(6742)X(7257)

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

X(55247) lies on these lines: {645, 651}, {1978, 55202}, {6742, 7257}, {15418, 36860}

X(55247) = trilinear pole of line {46, 20930}
X(55247) = X(i)-isoconjugate-of-X(j) for these {i, j}: {90, 798}, {669, 2994}, {1069, 2489}, {1924, 20570}, {3049, 7040}, {7072, 7180}
X(55247) = X(i)-Dao conjugate of X(j) for these {i, j}: {63, 647}, {9428, 20570}, {31998, 90}, {39054, 2164}
X(55247) = X(i)-Ceva conjugate of X(j) for these {i, j}: {6331, 799}
X(55247) = intersection, other than A, B, C, of circumconics {{A, B, C, X(651), X(6742)}}
X(55247) = tripole of the mixed polar line of X(2) and X(90) in K002
X(55247) = barycentric product X(i)*X(j) for these (i, j): {46, 670}, {1068, 55202}, {2178, 4602}, {3193, 4572}, {4625, 5552}, {5905, 799}, {6331, 6505}, {20930, 99}, {21077, 4623}, {21188, 4601}, {21853, 52612}, {31631, 4554}, {34537, 55214}, {52033, 52608}
X(55247) = barycentric quotient X(i)/X(j) for these (i, j): {46, 512}, {99, 90}, {643, 7072}, {662, 2164}, {670, 20570}, {799, 2994}, {811, 7040}, {1406, 51641}, {1800, 1946}, {2178, 798}, {3157, 810}, {3193, 663}, {3559, 18344}, {4563, 6513}, {4592, 1069}, {4625, 7318}, {5552, 4041}, {5905, 661}, {6505, 647}, {6511, 822}, {7257, 36626}, {20930, 523}, {21077, 4705}, {21188, 3125}, {21853, 4079}, {31631, 650}, {51648, 3122}, {52033, 2489}, {55214, 3124}
X(55247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4554, 4563, 799}

X(55248) = X(650)X(2605)∩X(4391)X(4467)

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

X(55248) lies on these lines: {650, 2605}, {1069, 23090}, {2501, 55214}, {2994, 17498}, {4017, 55236}, {4041, 21831}, {4391, 4467}, {7178, 21117}, {9090, 36082}, {16612, 46038}, {18344, 50501}, {21828, 55242}, {55206, 55216}, {55212, 55238}

X(55248) = isotomic conjugate of X(55247)
X(55248) = trilinear pole of line {4516, 20982}
X(55248) = perspector of circumconic {{A, B, C, X(90), X(20570)}}
X(55248) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55247}, {46, 662}, {99, 2178}, {107, 6511}, {109, 31631}, {110, 5905}, {162, 6505}, {163, 20930}, {645, 1406}, {648, 3157}, {651, 3193}, {653, 1800}, {1068, 4558}, {1813, 3559}, {4556, 21077}, {4565, 5552}, {4567, 51648}, {4570, 21188}, {4592, 52033}, {21853, 52935}, {24041, 55214}
X(55248) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55247}, {11, 31631}, {115, 20930}, {125, 6505}, {244, 5905}, {1084, 46}, {3005, 55214}, {5139, 52033}, {38985, 6511}, {38986, 2178}, {38991, 3193}, {40627, 51648}, {50330, 21188}, {55064, 5552}, {55066, 3157}
X(55248) = X(i)-Ceva conjugate of X(j) for these {i, j}: {1069, 2310}
X(55248) = X(i)-cross conjugate of X(j) for these {i, j}: {647, 661}
X(55248) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(650), X(661)}}, {{A, B, C, X(2310), X(23090)}}, {{A, B, C, X(2605), X(4017)}}, {{A, B, C, X(3709), X(17412)}}, {{A, B, C, X(4077), X(35347)}}, {{A, B, C, X(8611), X(21044)}}, {{A, B, C, X(17498), X(21832)}}, {{A, B, C, X(17899), X(21831)}}
X(55248) = barycentric product X(i)*X(j) for these (i, j): {523, 90}, {656, 7040}, {1021, 7363}, {1069, 24006}, {1577, 2164}, {2501, 6513}, {2994, 661}, {4041, 7318}, {4077, 7072}, {20570, 512}, {36626, 4017}
X(55248) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55247}, {90, 99}, {512, 46}, {523, 20930}, {647, 6505}, {650, 31631}, {661, 5905}, {663, 3193}, {798, 2178}, {810, 3157}, {822, 6511}, {1069, 4592}, {1946, 1800}, {2164, 662}, {2489, 52033}, {2994, 799}, {3122, 51648}, {3124, 55214}, {3125, 21188}, {4041, 5552}, {4079, 21853}, {4705, 21077}, {6513, 4563}, {7040, 811}, {7072, 643}, {7318, 4625}, {18344, 3559}, {20570, 670}, {36626, 7257}, {51641, 1406}

X(55249) = X(162)X(24041)∩X(662)X(799)

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

X(55249) lies on these lines: {162, 24041}, {662, 799}, {4592, 36134}, {4620, 55247}, {6507, 20641}

X(55249) = trilinear pole of line {47, 44179}
X(55249) = X(i)-isoconjugate-of-X(j) for these {i, j}: {68, 2489}, {91, 798}, {96, 55219}, {115, 32734}, {512, 2165}, {647, 14593}, {669, 5392}, {847, 3049}, {925, 3124}, {1084, 46134}, {1924, 20571}, {2351, 2501}, {2643, 36145}, {4117, 55215}, {4580, 27367}, {12077, 41271}, {32692, 41221}
X(55249) = X(i)-Dao conjugate of X(j) for these {i, j}: {577, 810}, {9428, 20571}, {31998, 91}, {34116, 798}, {39013, 2643}, {39052, 14593}, {39054, 2165}
X(55249) = X(i)-cross conjugate of X(j) for these {i, j}: {1748, 24041}
X(55249) = intersection, other than A, B, C, of circumconics {{A, B, C, X(162), X(1748)}}, {{A, B, C, X(662), X(36134)}}, {{A, B, C, X(799), X(36105)}}, {{A, B, C, X(1993), X(3570)}}, {{A, B, C, X(24039), X(44179)}}
X(55249) = tripole of the mixed polar line of X(2) and X(91) in K002
X(55249) = barycentric product X(i)*X(j) for these (i, j): {24, 55202}, {47, 670}, {304, 41679}, {317, 4592}, {662, 7763}, {811, 9723}, {1748, 4563}, {1993, 799}, {2180, 55218}, {4602, 571}, {18605, 1978}, {24037, 924}, {24041, 6563}, {34537, 55216}, {36036, 51439}, {42700, 4610}, {44179, 99}, {46254, 52584}, {55227, 63}
X(55249) = barycentric quotient X(i)/X(j) for these (i, j): {47, 512}, {99, 91}, {162, 14593}, {249, 36145}, {317, 24006}, {563, 3049}, {571, 798}, {662, 2165}, {670, 20571}, {799, 5392}, {811, 847}, {924, 2643}, {1101, 32734}, {1147, 810}, {1748, 2501}, {1993, 661}, {2180, 55219}, {4558, 1820}, {4575, 2351}, {4592, 68}, {6563, 1109}, {7763, 1577}, {9723, 656}, {17881, 23105}, {18315, 2168}, {18605, 649}, {24037, 46134}, {24041, 925}, {34537, 55215}, {34948, 3122}, {36134, 41271}, {39113, 2618}, {41679, 19}, {42700, 4024}, {44179, 523}, {46254, 30450}, {52436, 1924}, {52584, 3708}, {52917, 1096}, {55202, 20563}, {55216, 3124}, {55227, 92}

X(55250) = X(661)X(2618)∩X(822)X(1820)

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

X(55250) lies on these lines: {91, 23894}, {661, 2618}, {822, 1820}, {4444, 5392}, {24006, 55216}, {32678, 36145}

X(55250) = isotomic conjugate of X(55249)
X(55250) = perspector of circumconic {{A, B, C, X(91), X(20571)}}
X(55250) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 41679}, {24, 4558}, {31, 55249}, {47, 662}, {52, 18315}, {99, 571}, {100, 18605}, {110, 1993}, {112, 9723}, {163, 44179}, {184, 55227}, {249, 924}, {250, 52584}, {317, 32661}, {394, 52917}, {467, 15958}, {563, 811}, {648, 1147}, {670, 52436}, {933, 52032}, {1576, 7763}, {1748, 4575}, {2715, 51439}, {4230, 51776}, {4563, 44077}, {4567, 34948}, {4590, 34952}, {5961, 14590}, {6331, 52435}, {6563, 23357}, {14586, 39113}, {14966, 31635}, {15329, 52505}, {15423, 44174}, {18020, 30451}, {18883, 52603}, {24041, 55216}, {39295, 44808}, {43755, 52000}, {44769, 51393}
X(55250) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55249}, {115, 44179}, {136, 1748}, {244, 1993}, {1084, 47}, {3005, 55216}, {4858, 7763}, {8054, 18605}, {17423, 563}, {34591, 9723}, {34853, 662}, {36103, 41679}, {37864, 163}, {38986, 571}, {40627, 34948}, {55065, 42700}, {55066, 1147}
X(55250) = X(i)-cross conjugate of X(j) for these {i, j}: {810, 24006}, {3708, 1820}
X(55250) = intersection, other than A, B, C, of circumconics {{A, B, C, X(661), X(1577)}}, {{A, B, C, X(822), X(3708)}}, {{A, B, C, X(1109), X(14208)}}, {{A, B, C, X(2156), X(6521)}}, {{A, B, C, X(2618), X(24006)}}, {{A, B, C, X(8611), X(21044)}}
X(55250) = barycentric product X(i)*X(j) for these (i, j): {338, 36145}, {523, 91}, {656, 847}, {1109, 925}, {1577, 2165}, {2618, 96}, {2643, 46134}, {3124, 55215}, {5392, 661}, {14208, 14593}, {14618, 1820}, {18314, 2168}, {20571, 512}, {23994, 32734}, {24006, 68}, {30450, 3708}
X(55250) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55249}, {19, 41679}, {68, 4592}, {91, 99}, {92, 55227}, {512, 47}, {523, 44179}, {649, 18605}, {656, 9723}, {661, 1993}, {798, 571}, {810, 1147}, {847, 811}, {925, 24041}, {1096, 52917}, {1109, 6563}, {1577, 7763}, {1820, 4558}, {1924, 52436}, {2165, 662}, {2168, 18315}, {2351, 4575}, {2501, 1748}, {2618, 39113}, {2643, 924}, {3049, 563}, {3122, 34948}, {3124, 55216}, {3708, 52584}, {4024, 42700}, {5392, 799}, {14593, 162}, {20563, 55202}, {20571, 670}, {23105, 17881}, {24006, 317}, {30450, 46254}, {32734, 1101}, {36145, 249}, {41271, 36134}, {46134, 24037}, {55215, 34537}, {55219, 2180}

X(55251) = X(1879)X(12077)∩X(2081)X(2501)

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

X(55251) lies on these lines: {1879, 12077}, {2081, 2501}, {14618, 41078}, {15422, 47230}

X(55251) = perspector of circumconic {{A, B, C, X(93), X(20572)}}
X(55251) = X(i)-isoconjugate-of-X(j) for these {i, j}: {49, 662}, {163, 44180}, {1994, 4575}, {2964, 4558}, {2965, 4592}
X(55251) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 44180}, {136, 1994}, {1084, 49}, {5139, 2965}, {21975, 4558}, {38970, 51440}, {46604, 32661}
X(55251) = X(i)-Ceva conjugate of X(j) for these {i, j}: {38342, 93}
X(55251) = X(i)-cross conjugate of X(j) for these {i, j}: {14270, 10412}
X(55251) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(1879)}}, {{A, B, C, X(115), X(1625)}}, {{A, B, C, X(2501), X(14618)}}
X(55251) = isotomic conjugate of the tripole of the mixed polar line of X(2) and X(93) in K002
X(55251) = barycentric product X(i)*X(j) for these (i, j): {115, 38342}, {523, 93}, {2970, 930}, {3124, 55217}, {10412, 562}, {11140, 2501}, {14618, 2963}, {20572, 512}, {23290, 252}, {24006, 2962}, {46139, 8754}
X(55251) = barycentric quotient X(i)/X(j) for these (i, j): {93, 99}, {512, 49}, {523, 44180}, {562, 10411}, {2489, 2965}, {2501, 1994}, {2962, 4592}, {2963, 4558}, {2970, 41298}, {8741, 52606}, {8742, 52605}, {8754, 1510}, {11140, 4563}, {14618, 7769}, {16230, 51440}, {20572, 670}, {20975, 37084}, {32737, 47390}, {38342, 4590}, {46139, 47389}, {51513, 143}, {55217, 34537}

X(55252) = X(99)X(110)∩X(317)X(34338)

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

X(55252) lies on these lines: {99, 110}, {317, 34338}, {6331, 30450}, {7763, 18883}, {14570, 35319}, {41679, 55227}

X(55252) = trilinear pole of line {52, 34835}
X(55252) = X(i)-isoconjugate-of-X(j) for these {i, j}: {96, 798}, {512, 2168}, {661, 41271}, {1924, 34385}, {2643, 32692}, {54034, 55250}
X(55252) = X(i)-Dao conjugate of X(j) for these {i, j}: {139, 8754}, {343, 647}, {9428, 34385}, {31998, 96}, {36830, 41271}, {39054, 2168}, {47421, 20975}
X(55252) = intersection, other than A, B, C, of circumconics {{A, B, C, X(52), X(5118)}}, {{A, B, C, X(110), X(14570)}}, {{A, B, C, X(317), X(42405)}}, {{A, B, C, X(467), X(4226)}}, {{A, B, C, X(933), X(11547)}}, {{A, B, C, X(5027), X(52317)}}, {{A, B, C, X(5468), X(39113)}}, {{A, B, C, X(6563), X(53331)}}, {{A, B, C, X(7763), X(10411)}}
X(55252) = tripole of the mixed polar line of X(2) and X(96) in K002
X(55252) = barycentric product X(i)*X(j) for these (i, j): {52, 670}, {343, 55227}, {2180, 4602}, {4563, 467}, {14213, 55249}, {14570, 7763}, {14576, 52608}, {27362, 42297}, {28706, 41679}, {34537, 52317}, {39113, 99}, {52032, 6331}
X(55252) = barycentric quotient X(i)/X(j) for these (i, j): {52, 512}, {99, 96}, {110, 41271}, {249, 32692}, {467, 2501}, {662, 2168}, {670, 34385}, {1993, 2623}, {2180, 798}, {3133, 34952}, {6563, 8901}, {7763, 15412}, {9723, 23286}, {11547, 15422}, {14213, 55250}, {14570, 2165}, {14576, 2489}, {23181, 2351}, {35360, 14593}, {39113, 523}, {41679, 8882}, {44179, 2616}, {52032, 647}, {52317, 3124}, {55227, 275}, {55249, 2167}

X(55253) = X(68)X(17434)∩X(96)X(5466)

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

X(55253) lies on these lines: {68, 17434}, {96, 5466}, {476, 32692}, {523, 2623}, {850, 15412}, {2165, 10412}, {2395, 41271}, {2501, 34952}, {6753, 15422}, {12077, 50946}, {15328, 46088}

X(55253) = isotomic conjugate of X(55252)
X(55253) = perspector of circumconic {{A, B, C, X(96), X(34385)}}
X(55253) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55252}, {47, 14570}, {51, 55249}, {52, 662}, {99, 2180}, {162, 52032}, {163, 39113}, {467, 4575}, {1625, 44179}, {1748, 23181}, {1993, 2617}, {4592, 14576}, {24041, 52317}, {41679, 44706}
X(55253) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55252}, {115, 39113}, {125, 52032}, {136, 467}, {1084, 52}, {3005, 52317}, {5139, 14576}, {34853, 14570}, {37864, 1625}, {38986, 2180}
X(55253) = X(i)-Ceva conjugate of X(j) for these {i, j}: {32692, 2165}
X(55253) = X(i)-cross conjugate of X(j) for these {i, j}: {647, 2623}, {20975, 68}
X(55253) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(115), X(52742)}}, {{A, B, C, X(393), X(11079)}}, {{A, B, C, X(476), X(523)}}, {{A, B, C, X(647), X(6753)}}, {{A, B, C, X(2165), X(37802)}}, {{A, B, C, X(2623), X(15412)}}, {{A, B, C, X(8901), X(52932)}}, {{A, B, C, X(16040), X(47230)}}, {{A, B, C, X(17434), X(20975)}}
X(55253) = barycentric product X(i)*X(j) for these (i, j): {136, 52932}, {523, 96}, {1577, 2168}, {2167, 55250}, {2616, 91}, {2623, 5392}, {8901, 925}, {15412, 2165}, {15422, 52350}, {23286, 847}, {32692, 338}, {34385, 512}, {41271, 850}
X(55253) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55252}, {96, 99}, {275, 55227}, {512, 52}, {523, 39113}, {647, 52032}, {798, 2180}, {2165, 14570}, {2167, 55249}, {2168, 662}, {2351, 23181}, {2489, 14576}, {2501, 467}, {2616, 44179}, {2623, 1993}, {3124, 52317}, {8882, 41679}, {8901, 6563}, {14593, 35360}, {15412, 7763}, {15422, 11547}, {23286, 9723}, {32692, 249}, {34385, 670}, {34952, 3133}, {41271, 110}, {55250, 14213}

X(55254) = X(2)X(39)∩X(653)X(799)

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

X(55254) lies on these lines: {2, 39}, {99, 7450}, {325, 3137}, {653, 799}, {1978, 4563}, {44327, 55202}, {53811, 55237}

X(55254) = trilinear pole of line {35516, 515}
X(55254) = X(i)-isoconjugate-of-X(j) for these {i, j}: {102, 798}, {512, 32677}, {669, 36100}, {1402, 2432}, {1924, 34393}, {2489, 36055}, {3049, 36121}, {4516, 32643}, {15629, 51641}
X(55254) = X(i)-Dao conjugate of X(j) for these {i, j}: {9428, 34393}, {23986, 512}, {31998, 102}, {39054, 32677}, {40605, 2432}, {51221, 2489}
X(55254) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(653)}}, {{A, B, C, X(76), X(46404)}}, {{A, B, C, X(305), X(4572)}}, {{A, B, C, X(515), X(538)}}, {{A, B, C, X(2182), X(2229)}}, {{A, B, C, X(3266), X(35516)}}, {{A, B, C, X(3291), X(8755)}}, {{A, B, C, X(6331), X(28660)}}
X(55254) = tripole of the mixed polar line of X(2) and X(102) in K002
X(55254) = barycentric product X(i)*X(j) for these (i, j): {274, 42718}, {305, 7452}, {515, 670}, {2182, 4602}, {2406, 28660}, {35516, 99}, {51361, 55213}, {51368, 55233}, {52608, 8755}
X(55254) = barycentric quotient X(i)/X(j) for these (i, j): {99, 102}, {333, 2432}, {515, 512}, {645, 15629}, {662, 32677}, {670, 34393}, {799, 36100}, {811, 36121}, {1455, 51641}, {2182, 798}, {2406, 1400}, {4576, 46359}, {4592, 36055}, {6331, 52780}, {7452, 25}, {8755, 2489}, {14304, 4516}, {24035, 1880}, {28660, 2399}, {34050, 7180}, {35516, 523}, {42718, 37}, {42755, 42752}, {44130, 53152}, {46974, 810}, {51368, 55234}, {52378, 32643}, {53522, 3122}

X(55255) = X(2)X(2399)∩X(6)X(652)

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

X(55255) lies on these lines: {2, 2399}, {6, 652}, {25, 663}, {37, 8611}, {102, 111}, {393, 3064}, {647, 1400}, {661, 1880}, {694, 46359}, {1427, 51664}, {1976, 5075}, {3228, 34393}, {16081, 52780}, {32677, 34079}, {32683, 53939}, {36100, 37128}

X(55255) = isotomic conjugate of X(55254)
X(55255) = perspector of circumconic {{A, B, C, X(102), X(34393)}}
X(55255) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 2406}, {31, 55254}, {58, 42718}, {63, 7452}, {99, 2182}, {163, 35516}, {283, 24035}, {314, 2425}, {515, 662}, {643, 34050}, {645, 1455}, {648, 46974}, {1812, 23987}, {4567, 53522}, {4573, 51361}, {4592, 8755}, {4612, 51421}, {11700, 47318}, {14304, 52378}, {51368, 52914}
X(55255) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55254}, {10, 42718}, {115, 35516}, {1084, 515}, {3162, 7452}, {5139, 8755}, {38986, 2182}, {40611, 2406}, {40627, 53522}, {55060, 34050}, {55066, 46974}
X(55255) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}}, {{A, B, C, X(468), X(7439)}}, {{A, B, C, X(523), X(8999)}}, {{A, B, C, X(647), X(652)}}, {{A, B, C, X(649), X(2501)}}, {{A, B, C, X(690), X(2819)}}, {{A, B, C, X(885), X(52931)}}, {{A, B, C, X(1459), X(24006)}}, {{A, B, C, X(2399), X(2432)}}, {{A, B, C, X(3569), X(5075)}}, {{A, B, C, X(7180), X(14837)}}, {{A, B, C, X(21828), X(53045)}}
X(55255) = barycentric product X(i)*X(j) for these (i, j): {102, 523}, {226, 2432}, {1400, 2399}, {1577, 32677}, {15629, 7178}, {15633, 53321}, {24006, 36055}, {34393, 512}, {36100, 661}, {36121, 656}, {52780, 647}, {53152, 73}
X(55255) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55254}, {25, 7452}, {37, 42718}, {102, 99}, {512, 515}, {523, 35516}, {798, 2182}, {810, 46974}, {1400, 2406}, {1880, 24035}, {2399, 28660}, {2432, 333}, {2489, 8755}, {3122, 53522}, {4516, 14304}, {7180, 34050}, {15629, 645}, {32643, 52378}, {32677, 662}, {34393, 670}, {36055, 4592}, {36100, 799}, {36121, 811}, {42752, 42755}, {46359, 4576}, {51641, 1455}, {52780, 6331}, {53152, 44130}, {55234, 51368}

X(55256) = X(2)X(39)∩X(99)X(4243)

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

X(55256) lies on these lines: {2, 39}, {99, 4243}, {325, 3138}, {645, 4572}, {658, 799}, {670, 32040}, {811, 1897}, {4563, 31624}

X(55256) = trilinear pole of line {35517, 516}
X(55256) = X(i)-isoconjugate-of-X(j) for these {i, j}: {103, 798}, {213, 2424}, {512, 911}, {669, 36101}, {677, 3121}, {1924, 18025}, {2205, 2400}, {2338, 51641}, {2489, 36056}, {3049, 36122}, {3122, 36039}, {3125, 32642}
X(55256) = X(i)-Dao conjugate of X(j) for these {i, j}: {1566, 3122}, {6626, 2424}, {9428, 18025}, {20622, 2489}, {23972, 512}, {31998, 103}, {39054, 911}, {46095, 3049}, {50441, 3709}
X(55256) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(658)}}, {{A, B, C, X(76), X(31624)}}, {{A, B, C, X(274), X(811)}}, {{A, B, C, X(305), X(1978)}}, {{A, B, C, X(310), X(6331)}}, {{A, B, C, X(516), X(538)}}, {{A, B, C, X(910), X(2229)}}, {{A, B, C, X(1886), X(3291)}}, {{A, B, C, X(3266), X(35517)}}, {{A, B, C, X(3926), X(4561)}}, {{A, B, C, X(3948), X(30807)}}, {{A, B, C, X(4352), X(23973)}}, {{A, B, C, X(26006), X(36212)}}
X(55256) = tripole of the mixed polar line of X(2) and X(103) in K002
X(55256) = barycentric product X(i)*X(j) for these (i, j): {274, 42719}, {305, 4241}, {516, 670}, {1886, 52608}, {2398, 310}, {4602, 910}, {14953, 1978}, {17747, 52612}, {26006, 6331}, {30807, 799}, {35517, 99}, {41339, 55213}, {51366, 55229}
X(55256) = barycentric quotient X(i)/X(j) for these (i, j): {86, 2424}, {99, 103}, {310, 2400}, {516, 512}, {645, 2338}, {662, 911}, {670, 18025}, {676, 3122}, {799, 36101}, {811, 36122}, {910, 798}, {1456, 51641}, {1886, 2489}, {2398, 42}, {2426, 1918}, {3234, 51436}, {4241, 25}, {4558, 32657}, {4563, 1815}, {4567, 36039}, {4570, 32642}, {4592, 36056}, {4600, 677}, {4625, 43736}, {6331, 52781}, {14953, 649}, {17747, 4079}, {23973, 1042}, {24015, 1427}, {26006, 647}, {28346, 17990}, {30807, 661}, {35517, 523}, {40869, 3709}, {41321, 2333}, {42719, 37}, {42756, 42752}, {43035, 7180}, {44129, 53150}, {51366, 55230}, {51406, 14407}, {51435, 4455}, {51436, 53581}, {52619, 15634}
X(55256) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6331, 55241, 1978}

X(55257) = X(2)X(2400)∩X(6)X(657)

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

X(55257) lies on these lines: {2, 2400}, {6, 657}, {25, 649}, {37, 656}, {42, 647}, {103, 111}, {393, 7649}, {661, 1427}, {911, 34079}, {1400, 3709}, {1815, 2987}, {1880, 4017}, {1976, 5029}, {1989, 47234}, {2054, 3569}, {2509, 39798}, {3228, 18025}, {14910, 32657}, {16081, 52781}, {32684, 53940}, {36101, 37128}

X(55257) = isotomic conjugate of X(55256)
X(55257) = perspector of circumconic {{A, B, C, X(103), X(18025)}}
X(55257) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55256}, {58, 42719}, {63, 4241}, {81, 2398}, {99, 910}, {100, 14953}, {110, 30807}, {162, 26006}, {163, 35517}, {274, 2426}, {516, 662}, {643, 43035}, {645, 1456}, {676, 4567}, {1414, 40869}, {1444, 41321}, {1886, 4592}, {2287, 23973}, {2328, 24015}, {4573, 41339}, {4584, 51435}, {4616, 51418}, {4622, 51406}, {4623, 51436}, {5379, 39470}, {17747, 52935}
X(55257) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55256}, {10, 42719}, {115, 35517}, {125, 26006}, {244, 30807}, {1084, 516}, {3162, 4241}, {5139, 1886}, {8054, 14953}, {36908, 24015}, {38986, 910}, {40586, 2398}, {40608, 40869}, {40627, 676}, {55060, 43035}
X(55257) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}}, {{A, B, C, X(101), X(4049)}}, {{A, B, C, X(468), X(7432)}}, {{A, B, C, X(523), X(9000)}}, {{A, B, C, X(647), X(649)}}, {{A, B, C, X(657), X(661)}}, {{A, B, C, X(663), X(7178)}}, {{A, B, C, X(690), X(2824)}}, {{A, B, C, X(1020), X(1024)}}, {{A, B, C, X(1042), X(45276)}}, {{A, B, C, X(1055), X(1464)}}, {{A, B, C, X(2333), X(45282)}}, {{A, B, C, X(2400), X(2424)}}, {{A, B, C, X(2501), X(6586)}}, {{A, B, C, X(3569), X(5029)}}, {{A, B, C, X(7180), X(7658)}}, {{A, B, C, X(47230), X(47234)}}
X(55257) = barycentric product X(i)*X(j) for these (i, j): {10, 2424}, {103, 523}, {1577, 911}, {1815, 2501}, {2338, 7178}, {2400, 42}, {3120, 677}, {3709, 52156}, {4041, 43736}, {4049, 45144}, {14618, 32657}, {15634, 4557}, {16732, 36039}, {18025, 512}, {21045, 35184}, {21207, 32642}, {24006, 36056}, {24016, 52335}, {24290, 9503}, {36101, 661}, {36122, 656}, {40116, 4466}, {52781, 647}, {53150, 71}
X(55257) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55256}, {25, 4241}, {37, 42719}, {42, 2398}, {103, 99}, {512, 516}, {523, 35517}, {647, 26006}, {649, 14953}, {661, 30807}, {677, 4600}, {798, 910}, {911, 662}, {1042, 23973}, {1427, 24015}, {1815, 4563}, {1918, 2426}, {2333, 41321}, {2338, 645}, {2400, 310}, {2424, 86}, {2489, 1886}, {3122, 676}, {3709, 40869}, {4079, 17747}, {4455, 51435}, {7180, 43035}, {14407, 51406}, {15634, 52619}, {17990, 28346}, {18025, 670}, {32642, 4570}, {32657, 4558}, {36039, 4567}, {36056, 4592}, {36101, 799}, {36122, 811}, {42752, 42756}, {43736, 4625}, {51436, 3234}, {51641, 1456}, {52781, 6331}, {53150, 44129}, {53581, 51436}, {55230, 51366}

X(55258) = X(2)X(39)∩X(99)X(3658)

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

X(55258) lies on these lines: {2, 39}, {99, 3658}, {325, 3139}, {645, 651}, {2481, 30992}, {6331, 6335}

X(55258) = trilinear pole of line {3262, 17139}
X(55258) = X(i)-isoconjugate-of-X(j) for these {i, j}: {42, 2423}, {104, 798}, {512, 909}, {661, 34858}, {667, 2250}, {669, 34234}, {1795, 2489}, {1918, 2401}, {1919, 38955}, {1924, 18816}, {2200, 43933}, {2342, 7180}, {3049, 36123}, {3121, 36037}, {3122, 32641}, {4516, 32669}, {10428, 14407}, {51641, 52663}
X(55258) = X(i)-Dao conjugate of X(j) for these {i, j}: {908, 21828}, {1145, 3709}, {3259, 3121}, {6631, 2250}, {9296, 38955}, {9428, 18816}, {16586, 661}, {23980, 512}, {25640, 2489}, {31998, 104}, {34021, 2401}, {36830, 34858}, {39054, 909}, {40592, 2423}, {40613, 798}, {40620, 15635}, {46398, 3125}, {55153, 4516}
X(55258) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(651)}}, {{A, B, C, X(76), X(4554)}}, {{A, B, C, X(274), X(4573)}}, {{A, B, C, X(305), X(6386)}}, {{A, B, C, X(310), X(4625)}}, {{A, B, C, X(517), X(538)}}, {{A, B, C, X(799), X(28660)}}, {{A, B, C, X(908), X(3948)}}, {{A, B, C, X(980), X(23981)}}, {{A, B, C, X(2183), X(2229)}}, {{A, B, C, X(2427), X(5283)}}, {{A, B, C, X(3262), X(3266)}}, {{A, B, C, X(3291), X(14571)}}, {{A, B, C, X(36212), X(42717)}}
X(55258) = tripole of the mixed polar line of X(2) and X(104) in K002
X(55258) = barycentric product X(i)*X(j) for these (i, j): {305, 4246}, {517, 670}, {799, 908}, {1145, 4634}, {1785, 55202}, {2183, 4602}, {2397, 274}, {2427, 6385}, {3262, 99}, {4625, 6735}, {4639, 51381}, {6386, 859}, {10015, 4601}, {14571, 52608}, {17139, 668}, {17757, 4623}, {21801, 52612}, {22464, 7257}, {23788, 7035}, {23981, 40072}, {24029, 28660}, {36038, 4600}, {51367, 55231}
X(55258) = barycentric quotient X(i)/X(j) for these (i, j): {81, 2423}, {99, 104}, {110, 34858}, {190, 2250}, {274, 2401}, {286, 43933}, {314, 43728}, {332, 37628}, {517, 512}, {643, 2342}, {645, 52663}, {662, 909}, {668, 38955}, {670, 18816}, {799, 34234}, {811, 36123}, {859, 667}, {908, 661}, {1145, 4730}, {1457, 51641}, {1465, 7180}, {1769, 3122}, {2183, 798}, {2397, 37}, {2427, 213}, {2804, 4516}, {3262, 523}, {3310, 3121}, {3658, 51824}, {4246, 25}, {4558, 14578}, {4567, 32641}, {4573, 34051}, {4592, 1795}, {4600, 36037}, {4601, 13136}, {4620, 37136}, {4622, 10428}, {5379, 14776}, {6331, 16082}, {6735, 4041}, {7192, 15635}, {7257, 51565}, {10015, 3125}, {14571, 2489}, {15507, 4455}, {15632, 51377}, {16586, 21828}, {17139, 513}, {17757, 4705}, {21801, 4079}, {22350, 810}, {22464, 4017}, {23788, 244}, {23981, 1402}, {24029, 1400}, {36038, 3120}, {42753, 8034}, {42757, 42752}, {51362, 4770}, {51367, 55232}, {51377, 50487}, {51380, 4524}, {51381, 21832}, {51390, 24290}, {51409, 4983}, {51423, 4822}, {51433, 4729}, {52378, 32669}, {53151, 1824}, {55243, 36944}, {55245, 36921}
X(55258) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {799, 55241, 4563}, {799, 55247, 4573}

X(55259) = X(2)X(905)∩X(6)X(650)

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

X(55259) lies on these lines: {2, 905}, {6, 650}, {25, 667}, {37, 647}, {42, 810}, {104, 111}, {393, 6591}, {513, 46018}, {661, 1400}, {851, 10099}, {909, 34079}, {941, 43728}, {1427, 7178}, {1880, 2501}, {1976, 5040}, {1989, 47227}, {2165, 6588}, {2250, 21894}, {2350, 4893}, {2720, 9090}, {3228, 18816}, {3239, 25078}, {3310, 53522}, {3572, 15635}, {8749, 47235}, {13136, 42717}, {14578, 14910}, {16081, 16082}, {21828, 30572}, {32685, 53941}, {34234, 37128}

X(55259) = isotomic conjugate of X(55258)
X(55259) = trilinear pole of line {4516, 512}
X(55259) = perspector of circumconic {{A, B, C, X(104), X(2250)}}
X(55259) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 24029}, {31, 55258}, {58, 2397}, {63, 4246}, {86, 2427}, {99, 2183}, {110, 908}, {163, 3262}, {190, 859}, {333, 23981}, {517, 662}, {643, 1465}, {645, 1457}, {648, 22350}, {1145, 4591}, {1252, 23788}, {1769, 4567}, {1785, 4558}, {1790, 53151}, {1812, 23706}, {2804, 52378}, {3310, 4600}, {4556, 17757}, {4565, 6735}, {4570, 10015}, {4584, 15507}, {4592, 14571}, {4610, 51377}, {4619, 14010}, {4620, 53549}, {4627, 51423}, {4629, 51409}, {4637, 51380}, {5546, 22464}, {21801, 52935}, {34586, 47318}
X(55259) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55258}, {10, 2397}, {115, 3262}, {244, 908}, {661, 23788}, {1015, 17139}, {1084, 517}, {3162, 4246}, {4988, 36038}, {5139, 14571}, {38986, 2183}, {40600, 2427}, {40611, 24029}, {40627, 1769}, {50330, 10015}, {50497, 3310}, {55053, 859}, {55060, 1465}, {55064, 6735}, {55066, 22350}
X(55259) = X(i)-Ceva conjugate of X(j) for these {i, j}: {34234, 15635}
X(55259) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}}, {{A, B, C, X(100), X(35353)}}, {{A, B, C, X(468), X(7423)}}, {{A, B, C, X(513), X(51659)}}, {{A, B, C, X(523), X(9001)}}, {{A, B, C, X(647), X(667)}}, {{A, B, C, X(649), X(2623)}}, {{A, B, C, X(650), X(661)}}, {{A, B, C, X(690), X(2830)}}, {{A, B, C, X(851), X(1876)}}, {{A, B, C, X(1402), X(5662)}}, {{A, B, C, X(1465), X(44113)}}, {{A, B, C, X(1635), X(21894)}}, {{A, B, C, X(1637), X(47235)}}, {{A, B, C, X(1647), X(30572)}}, {{A, B, C, X(2401), X(2423)}}, {{A, B, C, X(2424), X(53321)}}, {{A, B, C, X(2489), X(40134)}}, {{A, B, C, X(2616), X(7649)}}, {{A, B, C, X(3139), X(7435)}}, {{A, B, C, X(3569), X(5040)}}, {{A, B, C, X(3657), X(53406)}}, {{A, B, C, X(3669), X(44550)}}, {{A, B, C, X(4049), X(35354)}}, {{A, B, C, X(4551), X(35348)}}, {{A, B, C, X(6588), X(6753)}}, {{A, B, C, X(16082), X(34858)}}, {{A, B, C, X(38955), X(45145)}}, {{A, B, C, X(41933), X(52499)}}, {{A, B, C, X(47227), X(47230)}}
X(55259) = barycentric product X(i)*X(j) for these (i, j): {104, 523}, {225, 37628}, {1309, 18210}, {1577, 909}, {1795, 24006}, {2250, 514}, {2342, 4077}, {2401, 37}, {2423, 321}, {3120, 36037}, {4017, 51565}, {4516, 54953}, {13136, 3125}, {14266, 3657}, {14578, 14618}, {15635, 3952}, {16082, 647}, {16732, 32641}, {18816, 512}, {21044, 37136}, {34051, 3700}, {34234, 661}, {34858, 850}, {35353, 45145}, {36123, 656}, {36795, 7180}, {36921, 55246}, {36944, 55244}, {38955, 513}, {40437, 53527}, {43728, 65}, {43933, 72}, {52663, 7178}, {53566, 53702}
X(55259) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55258}, {25, 4246}, {37, 2397}, {104, 99}, {213, 2427}, {244, 23788}, {512, 517}, {513, 17139}, {523, 3262}, {661, 908}, {667, 859}, {798, 2183}, {810, 22350}, {909, 662}, {1400, 24029}, {1402, 23981}, {1795, 4592}, {1824, 53151}, {2250, 190}, {2342, 643}, {2401, 274}, {2423, 81}, {2489, 14571}, {3120, 36038}, {3121, 3310}, {3122, 1769}, {3125, 10015}, {4017, 22464}, {4041, 6735}, {4079, 21801}, {4455, 15507}, {4516, 2804}, {4524, 51380}, {4705, 17757}, {4729, 51433}, {4730, 1145}, {4770, 51362}, {4822, 51423}, {4983, 51409}, {7180, 1465}, {8034, 42753}, {10428, 4622}, {13136, 4601}, {14578, 4558}, {14776, 5379}, {15635, 7192}, {16082, 6331}, {18816, 670}, {21828, 16586}, {21832, 51381}, {24290, 51390}, {32641, 4567}, {32669, 52378}, {34051, 4573}, {34234, 799}, {34858, 110}, {36037, 4600}, {36123, 811}, {36921, 55245}, {36944, 55243}, {37136, 4620}, {37628, 332}, {38955, 668}, {42752, 42757}, {43728, 314}, {43933, 286}, {50487, 51377}, {51377, 15632}, {51565, 7257}, {51641, 1457}, {51824, 3658}, {52663, 645}, {55232, 51367}

X(55260) = X(2)X(39)∩X(99)X(100)

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

X(55260) lies on these lines: {2, 39}, {75, 46912}, {86, 24487}, {99, 100}, {190, 55239}, {314, 14947}, {325, 3140}, {645, 55202}, {646, 670}, {1978, 54118}, {3799, 4576}, {4554, 4602}, {4573, 55207}, {4625, 7258}, {7192, 23354}, {7199, 24004}, {16728, 46802}, {16741, 17310}, {17217, 53340}, {18829, 53216}, {30866, 40017}, {31615, 55194}

X(55260) = trilinear pole of line {3263, 18157}
X(55260) = perspector of circumconic {{A, B, C, X(670), X(4601)}}
X(55260) = X(i)-isoconjugate-of-X(j) for these {i, j}: {42, 43929}, {105, 798}, {213, 1027}, {294, 51641}, {512, 1438}, {667, 18785}, {669, 673}, {810, 8751}, {884, 1400}, {919, 3122}, {1024, 1402}, {1416, 3709}, {1919, 13576}, {1924, 2481}, {1973, 10099}, {2195, 7180}, {2489, 36057}, {3049, 36124}, {3121, 36086}, {3125, 32666}, {4455, 51866}, {9426, 18031}
X(55260) = X(i)-Dao conjugate of X(j) for these {i, j}: {2238, 4455}, {3912, 21832}, {6184, 512}, {6337, 10099}, {6626, 1027}, {6631, 18785}, {9296, 13576}, {9428, 2481}, {17755, 661}, {20621, 2489}, {27918, 39786}, {31998, 105}, {35094, 3125}, {36905, 4017}, {38980, 3122}, {38989, 3121}, {39046, 798}, {39054, 1438}, {39062, 8751}, {39063, 7180}, {40582, 884}, {40592, 43929}, {40605, 1024}, {40609, 3709}, {40620, 43921}
X(55260) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(100)}}, {{A, B, C, X(76), X(668)}}, {{A, B, C, X(99), X(274)}}, {{A, B, C, X(310), X(799)}}, {{A, B, C, X(518), X(538)}}, {{A, B, C, X(646), X(28809)}}, {{A, B, C, X(672), X(2229)}}, {{A, B, C, X(883), X(34284)}}, {{A, B, C, X(918), X(2787)}}, {{A, B, C, X(980), X(2283)}}, {{A, B, C, X(1018), X(27040)}}, {{A, B, C, X(1978), X(18152)}}, {{A, B, C, X(2223), X(3229)}}, {{A, B, C, X(2284), X(5283)}}, {{A, B, C, X(3263), X(3266)}}, {{A, B, C, X(3291), X(5089)}}, {{A, B, C, X(3912), X(3948)}}, {{A, B, C, X(3978), X(53216)}}, {{A, B, C, X(4236), X(15149)}}, {{A, B, C, X(4352), X(41353)}}, {{A, B, C, X(4573), X(16750)}}, {{A, B, C, X(4602), X(7257)}}, {{A, B, C, X(6335), X(30830)}}, {{A, B, C, X(9072), X(9465)}}, {{A, B, C, X(18829), X(40874)}}, {{A, B, C, X(25083), X(36212)}}, {{A, B, C, X(46108), X(51481)}}
X(55260) = tripole of the mixed polar line of X(2) and X(105) in K002
X(55260) = barycentric product X(i)*X(j) for these (i, j): {274, 42720}, {305, 4238}, {314, 883}, {518, 670}, {1025, 28660}, {1026, 310}, {1861, 55202}, {2223, 4609}, {2283, 40072}, {2284, 6385}, {2340, 55213}, {3263, 99}, {3286, 6386}, {3717, 4625}, {3912, 799}, {3930, 52612}, {3932, 4623}, {4563, 46108}, {4601, 918}, {4602, 672}, {5089, 52608}, {5236, 55207}, {7257, 9436}, {16728, 36803}, {17755, 4639}, {18157, 190}, {18206, 1978}, {23829, 7035}, {24037, 4088}, {24290, 34537}, {25083, 6331}, {30941, 668}, {40704, 645}, {54353, 561}
X(55260) = barycentric quotient X(i)/X(j) for these (i, j): {21, 884}, {69, 10099}, {81, 43929}, {86, 1027}, {99, 105}, {190, 18785}, {241, 7180}, {314, 885}, {332, 23696}, {333, 1024}, {518, 512}, {643, 2195}, {645, 294}, {648, 8751}, {662, 1438}, {665, 3121}, {668, 13576}, {670, 2481}, {672, 798}, {799, 673}, {811, 36124}, {883, 65}, {918, 3125}, {1025, 1400}, {1026, 42}, {1414, 1416}, {1458, 51641}, {1818, 810}, {2223, 669}, {2254, 3122}, {2283, 1402}, {2284, 213}, {3263, 523}, {3286, 667}, {3675, 8034}, {3693, 3709}, {3717, 4041}, {3912, 661}, {3930, 4079}, {3932, 4705}, {4088, 2643}, {4238, 25}, {4437, 24290}, {4447, 7234}, {4558, 32658}, {4563, 1814}, {4567, 919}, {4570, 32666}, {4573, 1462}, {4576, 46149}, {4584, 51866}, {4589, 52030}, {4592, 36057}, {4600, 36086}, {4601, 666}, {4602, 18031}, {4620, 36146}, {4639, 52209}, {4684, 4822}, {4899, 4729}, {4966, 4983}, {5089, 2489}, {5236, 55208}, {6331, 54235}, {7192, 43921}, {7256, 28071}, {7257, 14942}, {7258, 6559}, {8299, 4455}, {9436, 4017}, {9454, 1924}, {9455, 9426}, {14439, 14407}, {15149, 6591}, {16728, 665}, {17755, 21832}, {18157, 514}, {18206, 649}, {20683, 50487}, {20752, 3049}, {23829, 244}, {24290, 3124}, {25083, 647}, {30941, 513}, {34855, 7250}, {39258, 53581}, {40704, 7178}, {40773, 29956}, {41353, 1042}, {41610, 2440}, {42720, 37}, {42758, 42752}, {43042, 53540}, {46108, 2501}, {50333, 4516}, {53553, 4128}, {54325, 1918}, {54353, 31}, {55202, 31637}

X(55261) = X(2)X(650)∩X(6)X(513)

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

X(55261) lies on these lines: {2, 650}, {6, 513}, {25, 884}, {37, 523}, {42, 661}, {105, 111}, {251, 18108}, {263, 9010}, {354, 5098}, {514, 39957}, {649, 2350}, {665, 6084}, {666, 35147}, {673, 24617}, {694, 46149}, {798, 1400}, {804, 54980}, {812, 39979}, {885, 941}, {905, 39981}, {919, 1290}, {1427, 7180}, {1438, 34079}, {1814, 2987}, {1880, 2489}, {1989, 43082}, {2248, 54254}, {2481, 3228}, {3572, 27846}, {3669, 42290}, {3700, 3967}, {3737, 16503}, {4049, 16611}, {4394, 39966}, {4790, 39965}, {6588, 8770}, {7199, 16706}, {8749, 8751}, {8791, 47235}, {13576, 21894}, {14910, 32658}, {16081, 54235}, {16606, 21949}, {18785, 55244}, {21448, 40134}, {21832, 22319}, {28658, 55246}, {28840, 50114}, {29226, 52660}, {29362, 39798}, {36086, 37135}, {39961, 48026}

X(55261) = isotomic conjugate of X(55260)
X(55261) = trilinear pole of line {3125, 512}
X(55261) = perspector of circumconic {{A, B, C, X(105), X(2481)}}
X(55261) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 54353}, {21, 1025}, {31, 55260}, {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}, {274, 54325}, {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}, {1332, 54407}, {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(55261) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55260}, {10, 42720}, {115, 3263}, {125, 25083}, {136, 46108}, {244, 3912}, {661, 23829}, {1015, 30941}, {1084, 518}, {1086, 18157}, {3005, 24290}, {3162, 4238}, {5139, 5089}, {5521, 15149}, {8054, 18206}, {17423, 20752}, {32664, 54353}, {33675, 670}, {38986, 672}, {38989, 16728}, {38996, 2223}, {40586, 1026}, {40590, 883}, {40600, 2284}, {40608, 3693}, {40611, 1025}, {40622, 40704}, {40627, 2254}, {50330, 918}, {50497, 665}, {55053, 3286}, {55060, 241}, {55064, 3717}, {55066, 1818}
X(55261) = X(i)-Ceva conjugate of X(j) for these {i, j}: {673, 43921}
X(55261) = X(i)-cross conjugate of X(j) for these {i, j}: {4455, 513}, {39786, 37}
X(55261) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}}, {{A, B, C, X(65), X(5091)}}, {{A, B, C, X(213), X(5701)}}, {{A, B, C, X(468), X(7458)}}, {{A, B, C, X(512), X(3669)}}, {{A, B, C, X(513), X(523)}}, {{A, B, C, X(514), X(55240)}}, {{A, B, C, X(647), X(8642)}}, {{A, B, C, X(649), X(17494)}}, {{A, B, C, X(650), X(798)}}, {{A, B, C, X(690), X(2837)}}, {{A, B, C, X(1018), X(1022)}}, {{A, B, C, X(1643), X(3125)}}, {{A, B, C, X(2402), X(2440)}}, {{A, B, C, X(2423), X(43991)}}, {{A, B, C, X(2485), X(26217)}}, {{A, B, C, X(2492), X(47235)}}, {{A, B, C, X(2501), X(26546)}}, {{A, B, C, X(3140), X(4244)}}, {{A, B, C, X(3768), X(21894)}}, {{A, B, C, X(4024), X(27712)}}, {{A, B, C, X(4041), X(7216)}}, {{A, B, C, X(4049), X(23894)}}, {{A, B, C, X(4132), X(29362)}}, {{A, B, C, X(4140), X(28006)}}, {{A, B, C, X(4455), X(7212)}}, {{A, B, C, X(4580), X(21005)}}, {{A, B, C, X(4885), X(20980)}}, {{A, B, C, X(4988), X(27610)}}, {{A, B, C, X(7199), X(18071)}}, {{A, B, C, X(9010), X(23878)}}, {{A, B, C, X(9034), X(55122)}}, {{A, B, C, X(9278), X(24617)}}, {{A, B, C, X(12030), X(36150)}}, {{A, B, C, X(13576), X(52902)}}, {{A, B, C, X(14119), X(37014)}}, {{A, B, C, X(14273), X(47227)}}, {{A, B, C, X(18154), X(22044)}}, {{A, B, C, X(20979), X(27346)}}, {{A, B, C, X(21832), X(27846)}}, {{A, B, C, X(22105), X(42721)}}, {{A, B, C, X(25423), X(29226)}}, {{A, B, C, X(31150), X(46001)}}, {{A, B, C, X(36227), X(52208)}}, {{A, B, C, X(41934), X(46784)}}
X(55261) = barycentric product X(i)*X(j) for these (i, j): {10, 1027}, {65, 885}, {105, 523}, {210, 43930}, {225, 23696}, {294, 7178}, {321, 43929}, {525, 8751}, {661, 673}, {1024, 226}, {1416, 4086}, {1427, 28132}, {1438, 1577}, {1441, 884}, {1462, 3700}, {1814, 2501}, {2195, 4077}, {2481, 512}, {3120, 36086}, {3121, 36803}, {3122, 51560}, {3125, 666}, {3657, 52456}, {3952, 43921}, {4010, 52030}, {4088, 51838}, {4516, 927}, {6559, 7216}, {10099, 4}, {13576, 513}, {14618, 32658}, {14625, 47915}, {14942, 4017}, {16732, 919}, {18031, 798}, {18785, 514}, {21044, 36146}, {21052, 51845}, {21207, 32666}, {21832, 52209}, {21945, 36041}, {24006, 36057}, {24290, 6185}, {34018, 3709}, {35353, 52902}, {36124, 656}, {36796, 7180}, {36802, 53540}, {54235, 647}
X(55261) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55260}, {25, 4238}, {31, 54353}, {37, 42720}, {42, 1026}, {65, 883}, {105, 99}, {213, 2284}, {244, 23829}, {294, 645}, {512, 518}, {513, 30941}, {514, 18157}, {523, 3263}, {647, 25083}, {649, 18206}, {661, 3912}, {665, 16728}, {666, 4601}, {667, 3286}, {669, 2223}, {673, 799}, {798, 672}, {810, 1818}, {884, 21}, {885, 314}, {919, 4567}, {1024, 333}, {1027, 86}, {1042, 41353}, {1400, 1025}, {1402, 2283}, {1416, 1414}, {1438, 662}, {1462, 4573}, {1814, 4563}, {1918, 54325}, {1924, 9454}, {2195, 643}, {2440, 41610}, {2481, 670}, {2489, 5089}, {2501, 46108}, {2643, 4088}, {3049, 20752}, {3121, 665}, {3122, 2254}, {3124, 24290}, {3125, 918}, {3709, 3693}, {4017, 9436}, {4041, 3717}, {4079, 3930}, {4128, 53553}, {4455, 8299}, {4516, 50333}, {4705, 3932}, {4729, 4899}, {4822, 4684}, {4983, 4966}, {6559, 7258}, {6591, 15149}, {7178, 40704}, {7180, 241}, {7234, 4447}, {7250, 34855}, {8034, 3675}, {8751, 648}, {9426, 9455}, {10099, 69}, {13576, 668}, {14407, 14439}, {14942, 7257}, {18031, 4602}, {18785, 190}, {21832, 17755}, {23696, 332}, {24290, 4437}, {28071, 7256}, {29956, 40773}, {31637, 55202}, {32658, 4558}, {32666, 4570}, {36057, 4592}, {36086, 4600}, {36124, 811}, {36146, 4620}, {42752, 42758}, {43921, 7192}, {43929, 81}, {46149, 4576}, {50487, 20683}, {51641, 1458}, {51866, 4584}, {52030, 4589}, {52209, 4639}, {53540, 43042}, {53581, 39258}, {54235, 6331}, {55208, 5236}
X(55261) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1024, 1027, 43929}

X(55262) = X(2)X(39)∩X(190)X(670)

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

X(55262) lies on these lines: {2, 39}, {99, 9059}, {190, 670}, {325, 3141}, {886, 53195}, {3264, 4141}, {4576, 36863}, {4601, 55237}, {7192, 41314}, {7257, 51564}, {8033, 41242}, {16729, 46797}, {17780, 55243}, {18827, 31002}, {30939, 36872}, {33296, 46126}

X(55262) = trilinear pole of line {3264, 4783}
X(55262) = X(i)-isoconjugate-of-X(j) for these {i, j}: {32, 55244}, {88, 669}, {106, 798}, {213, 23345}, {512, 9456}, {560, 4049}, {810, 8752}, {901, 3121}, {903, 1924}, {1022, 1918}, {1084, 4622}, {1417, 3709}, {1919, 4674}, {1980, 4080}, {2205, 6548}, {2316, 51641}, {2489, 36058}, {3049, 36125}, {3122, 32665}, {3125, 32719}, {4117, 4615}, {4634, 9427}, {4730, 41935}, {9426, 20568}
X(55262) = X(i)-Dao conjugate of X(j) for these {i, j}: {214, 798}, {519, 14407}, {3936, 21828}, {4370, 512}, {6374, 4049}, {6376, 55244}, {6544, 8034}, {6626, 23345}, {9296, 4674}, {9428, 903}, {20619, 2489}, {31998, 106}, {34021, 1022}, {35085, 17991}, {35092, 3122}, {38979, 3121}, {39054, 9456}, {39062, 8752}, {40620, 43922}, {52659, 7180}, {52871, 3709}, {52872, 4079}, {52877, 53581}
X(55262) = X(i)-cross conjugate of X(j) for these {i, j}: {14407, 519}, {24004, 55243}
X(55262) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(190)}}, {{A, B, C, X(39), X(46148)}}, {{A, B, C, X(44), X(2229)}}, {{A, B, C, X(76), X(1978)}}, {{A, B, C, X(99), X(16712)}}, {{A, B, C, X(274), X(799)}}, {{A, B, C, X(310), X(670)}}, {{A, B, C, X(519), X(538)}}, {{A, B, C, X(874), X(31002)}}, {{A, B, C, X(902), X(3229)}}, {{A, B, C, X(980), X(23703)}}, {{A, B, C, X(1023), X(5283)}}, {{A, B, C, X(1645), X(14407)}}, {{A, B, C, X(3264), X(3266)}}, {{A, B, C, X(3291), X(8756)}}, {{A, B, C, X(3948), X(4358)}}, {{A, B, C, X(3977), X(36212)}}, {{A, B, C, X(4141), X(39785)}}, {{A, B, C, X(4169), X(16589)}}, {{A, B, C, X(4554), X(18140)}}, {{A, B, C, X(4610), X(18600)}}, {{A, B, C, X(4615), X(16711)}}, {{A, B, C, X(4632), X(16705)}}, {{A, B, C, X(4639), X(30939)}}, {{A, B, C, X(27162), X(37215)}}, {{A, B, C, X(27523), X(30731)}}, {{A, B, C, X(31008), X(36860)}}, {{A, B, C, X(46109), X(51481)}}
X(55262) = tripole of the mixed polar line of X(2) and X(106) in K002
X(55262) = barycentric product X(i)*X(j) for these (i, j): {44, 4602}, {305, 46541}, {519, 670}, {1023, 6385}, {3264, 99}, {3689, 55213}, {3762, 4601}, {3943, 52612}, {3977, 6331}, {3992, 4623}, {4358, 799}, {4563, 46109}, {4609, 902}, {4625, 4723}, {4634, 4738}, {14407, 44168}, {16704, 1978}, {17780, 310}, {23703, 40072}, {24004, 274}, {30939, 668}, {34537, 4120}, {36791, 4615}, {37790, 55207}, {38462, 55202}, {52608, 8756}, {52680, 6386}, {55243, 75}
X(55262) = barycentric quotient X(i)/X(j) for these (i, j): {44, 798}, {75, 55244}, {76, 4049}, {86, 23345}, {99, 106}, {274, 1022}, {310, 6548}, {314, 23838}, {519, 512}, {645, 2316}, {648, 8752}, {662, 9456}, {668, 4674}, {670, 903}, {799, 88}, {811, 36125}, {900, 3122}, {902, 669}, {1023, 213}, {1227, 53527}, {1319, 51641}, {1414, 1417}, {1635, 3121}, {1647, 8034}, {1978, 4080}, {2251, 1924}, {2325, 3709}, {2796, 17991}, {3264, 523}, {3285, 1919}, {3762, 3125}, {3911, 7180}, {3943, 4079}, {3977, 647}, {3992, 4705}, {4120, 3124}, {4141, 17414}, {4169, 1500}, {4358, 661}, {4370, 14407}, {4432, 4455}, {4434, 7234}, {4487, 4729}, {4558, 32659}, {4563, 1797}, {4567, 32665}, {4570, 32719}, {4576, 46150}, {4590, 4591}, {4591, 41935}, {4592, 36058}, {4600, 901}, {4601, 3257}, {4602, 20568}, {4615, 2226}, {4634, 679}, {4700, 4832}, {4723, 4041}, {4727, 4826}, {4738, 4730}, {4742, 4822}, {4768, 4516}, {4783, 4155}, {4922, 4128}, {4975, 4983}, {5440, 810}, {6331, 6336}, {7192, 43922}, {7257, 1320}, {8756, 2489}, {9459, 9426}, {14407, 1084}, {14408, 21835}, {14429, 20975}, {16704, 649}, {16729, 1635}, {17191, 21758}, {17195, 6085}, {17780, 42}, {21805, 50487}, {22356, 3049}, {23344, 1918}, {23703, 1402}, {23757, 42752}, {24004, 37}, {24037, 4622}, {27808, 4013}, {30606, 7252}, {30731, 1334}, {30939, 513}, {31059, 5029}, {34537, 4615}, {36791, 4120}, {37790, 55208}, {41629, 2441}, {46109, 2501}, {46541, 25}, {51583, 21828}, {52619, 6549}, {52680, 667}, {52747, 9178}, {52963, 53581}, {53582, 52963}, {55237, 40215}, {55243, 1}, {55245, 4792}, {55258, 52031}
X(55262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {55254, 55258, 55256}

X(55263) = X(2)X(514)∩X(6)X(649)

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

X(55263) lies on these lines: {2, 514}, {6, 649}, {25, 8643}, {37, 661}, {42, 512}, {88, 37128}, {106, 111}, {351, 2054}, {513, 39974}, {650, 39798}, {694, 46150}, {740, 35353}, {798, 28658}, {876, 899}, {901, 2702}, {903, 3228}, {941, 4813}, {1019, 17012}, {1326, 43926}, {1400, 7180}, {1427, 7216}, {1635, 39982}, {1646, 3572}, {1797, 2987}, {1880, 55208}, {2087, 42753}, {3310, 6085}, {3752, 8042}, {4080, 27809}, {4145, 21894}, {4394, 39984}, {4555, 53195}, {4615, 39292}, {4674, 21832}, {4988, 14624}, {6336, 16081}, {8749, 8752}, {9456, 34079}, {14407, 21828}, {14437, 23352}, {14910, 32659}, {20979, 46018}, {30834, 30835}, {31147, 31179}, {31207, 31229}, {32686, 53942}

X(55263) = isotomic conjugate of X(55262)
X(55263) = trilinear pole of line {3122, 17991}
X(55263) = perspector of circumconic {{A, B, C, X(106), X(903)}}
X(55263) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 55243}, {31, 55262}, {44, 99}, {58, 24004}, {63, 46541}, {81, 17780}, {86, 1023}, {100, 16704}, {101, 30939}, {110, 4358}, {162, 3977}, {163, 3264}, {190, 52680}, {214, 47318}, {274, 23344}, {333, 23703}, {519, 662}, {643, 3911}, {645, 1319}, {648, 5440}, {668, 3285}, {670, 2251}, {678, 4615}, {757, 4169}, {799, 902}, {811, 22356}, {900, 4567}, {901, 16729}, {1014, 30731}, {1017, 4634}, {1332, 37168}, {1404, 7257}, {1414, 2325}, {1635, 4600}, {1960, 4601}, {2415, 16948}, {3689, 4573}, {3762, 4570}, {3943, 52935}, {3952, 30576}, {3992, 4556}, {4120, 24041}, {4370, 4622}, {4432, 4584}, {4434, 4603}, {4551, 30606}, {4558, 38462}, {4565, 4723}, {4575, 46109}, {4590, 4730}, {4591, 4738}, {4592, 8756}, {4596, 4969}, {4602, 9459}, {4610, 21805}, {4612, 40663}, {4614, 4700}, {4620, 4895}, {4623, 52963}, {4627, 4742}, {4629, 4975}, {4768, 52378}, {5235, 52924}, {6331, 23202}, {14407, 24037}, {17191, 51562}, {23889, 52747}, {31059, 37135}, {40172, 55237}
X(55263) = X(i)-vertex conjugate of X(j) for these {i, j}: {902, 17969}
X(55263) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55262}, {9, 55243}, {10, 24004}, {115, 3264}, {125, 3977}, {136, 46109}, {244, 4358}, {512, 14407}, {1015, 30939}, {1084, 519}, {3005, 4120}, {3162, 46541}, {5139, 8756}, {8054, 16704}, {9460, 670}, {17413, 4141}, {17423, 22356}, {38979, 16729}, {38986, 44}, {38996, 902}, {40586, 17780}, {40594, 799}, {40595, 99}, {40600, 1023}, {40607, 4169}, {40608, 2325}, {40627, 900}, {50330, 3762}, {50497, 1635}, {52877, 53582}, {55053, 52680}, {55060, 3911}, {55064, 4723}, {55066, 5440}
X(55263) = X(i)-Ceva conjugate of X(j) for these {i, j}: {88, 43922}, {1022, 55244}, {4591, 106}, {4615, 46150}
X(55263) = X(i)-cross conjugate of X(j) for these {i, j}: {14407, 512}, {21828, 649}, {42752, 1042}
X(55263) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(6)}}, {{A, B, C, X(10), X(46126)}}, {{A, B, C, X(106), X(52759)}}, {{A, B, C, X(351), X(5029)}}, {{A, B, C, X(468), X(7448)}}, {{A, B, C, X(512), X(514)}}, {{A, B, C, X(513), X(47780)}}, {{A, B, C, X(523), X(9002)}}, {{A, B, C, X(647), X(8643)}}, {{A, B, C, X(650), X(47793)}}, {{A, B, C, X(690), X(2843)}}, {{A, B, C, X(740), X(899)}}, {{A, B, C, X(798), X(4893)}}, {{A, B, C, X(876), X(35353)}}, {{A, B, C, X(1027), X(4551)}}, {{A, B, C, X(1042), X(38941)}}, {{A, B, C, X(1404), X(2245)}}, {{A, B, C, X(1635), X(4169)}}, {{A, B, C, X(1646), X(14404)}}, {{A, B, C, X(1918), X(46125)}}, {{A, B, C, X(2087), X(21828)}}, {{A, B, C, X(2226), X(17953)}}, {{A, B, C, X(2403), X(2441)}}, {{A, B, C, X(2423), X(4559)}}, {{A, B, C, X(2489), X(47766)}}, {{A, B, C, X(3121), X(52745)}}, {{A, B, C, X(3122), X(14475)}}, {{A, B, C, X(3952), X(43928)}}, {{A, B, C, X(4017), X(21183)}}, {{A, B, C, X(4120), X(21129)}}, {{A, B, C, X(4557), X(31992)}}, {{A, B, C, X(4638), X(17998)}}, {{A, B, C, X(4674), X(52755)}}, {{A, B, C, X(4841), X(42664)}}, {{A, B, C, X(6544), X(14407)}}, {{A, B, C, X(6545), X(8034)}}, {{A, B, C, X(6548), X(23345)}}, {{A, B, C, X(6591), X(47796)}}, {{A, B, C, X(8752), X(52753)}}, {{A, B, C, X(14752), X(24003)}}, {{A, B, C, X(18015), X(35352)}}, {{A, B, C, X(18105), X(47773)}}, {{A, B, C, X(30575), X(46795)}}, {{A, B, C, X(42753), X(42768)}}, {{A, B, C, X(46001), X(47771)}}
X(55263) = barycentric product X(i)*X(j) for these (i, j): {1, 55244}, {10, 23345}, {42, 6548}, {106, 523}, {115, 4591}, {512, 903}, {525, 8752}, {661, 88}, {1022, 37}, {1168, 53527}, {1318, 30572}, {1320, 4017}, {1417, 4086}, {1577, 9456}, {1635, 30575}, {1797, 2501}, {2226, 4120}, {2316, 7178}, {2433, 52753}, {2441, 4052}, {2643, 4622}, {3120, 901}, {3122, 4555}, {3124, 4615}, {3125, 3257}, {3733, 4013}, {3952, 43922}, {4049, 6}, {4080, 649}, {4557, 6549}, {4674, 513}, {4730, 679}, {4792, 55246}, {4997, 7180}, {6336, 647}, {14407, 54974}, {14618, 32659}, {16732, 32665}, {17991, 35153}, {18005, 2712}, {20568, 798}, {21207, 32719}, {23352, 53114}, {23598, 28658}, {23838, 65}, {24006, 36058}, {36125, 656}, {40215, 55238}, {52031, 55259}, {52759, 9178}, {53545, 5548}
X(55263) = barycentric quotient X(i)/X(j) for these (i, j): {1, 55243}, {2, 55262}, {25, 46541}, {37, 24004}, {42, 17780}, {88, 799}, {106, 99}, {213, 1023}, {512, 519}, {513, 30939}, {523, 3264}, {647, 3977}, {649, 16704}, {661, 4358}, {667, 52680}, {669, 902}, {679, 4634}, {798, 44}, {810, 5440}, {901, 4600}, {903, 670}, {1022, 274}, {1084, 14407}, {1320, 7257}, {1334, 30731}, {1402, 23703}, {1417, 1414}, {1500, 4169}, {1635, 16729}, {1797, 4563}, {1918, 23344}, {1919, 3285}, {1924, 2251}, {2226, 4615}, {2316, 645}, {2441, 41629}, {2489, 8756}, {2501, 46109}, {3049, 22356}, {3121, 1635}, {3122, 900}, {3124, 4120}, {3125, 3762}, {3257, 4601}, {3709, 2325}, {4013, 27808}, {4041, 4723}, {4049, 76}, {4079, 3943}, {4080, 1978}, {4120, 36791}, {4128, 4922}, {4155, 4783}, {4455, 4432}, {4516, 4768}, {4591, 4590}, {4615, 34537}, {4622, 24037}, {4674, 668}, {4705, 3992}, {4729, 4487}, {4730, 4738}, {4792, 55245}, {4822, 4742}, {4826, 4727}, {4832, 4700}, {4983, 4975}, {5029, 31059}, {6085, 17195}, {6336, 6331}, {6548, 310}, {6549, 52619}, {7180, 3911}, {7234, 4434}, {7252, 30606}, {8034, 1647}, {8752, 648}, {9178, 52747}, {9426, 9459}, {9456, 662}, {14407, 4370}, {17414, 4141}, {17991, 2796}, {20568, 4602}, {20975, 14429}, {21758, 17191}, {21828, 51583}, {21835, 14408}, {23345, 86}, {23838, 314}, {32659, 4558}, {32665, 4567}, {32719, 4570}, {36058, 4592}, {36125, 811}, {40215, 55237}, {41935, 4591}, {42752, 23757}, {43922, 7192}, {46150, 4576}, {50487, 21805}, {51641, 1319}, {52031, 55258}, {52963, 53582}, {53527, 1227}, {53581, 52963}, {55208, 37790}, {55244, 75}

X(55264) = X(16077)X(18878)∩X(31621)X(32833)

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

X(55264) lies on these lines: {16077, 18878}, {31621, 32833}

X(55264) = trilinear pole of line {1494, 7799}
X(55264) = X(i)-isoconjugate-of-X(j) for these {i, j}: {113, 798}, {1725, 14398}, {2173, 21731}, {2631, 44084}, {9406, 55121}
X(55264) = X(i)-Dao conjugate of X(j) for these {i, j}: {9410, 55121}, {31998, 113}, {36896, 21731}
X(55264) = intersection, other than A, B, C, of circumconics {{A, B, C, X(76), X(4563)}}, {{A, B, C, X(99), X(32833)}}, {{A, B, C, X(670), X(6035)}}, {{A, B, C, X(6331), X(40830)}}, {{A, B, C, X(15066), X(15329)}}, {{A, B, C, X(16077), X(31621)}}, {{A, B, C, X(34405), X(35136)}}
X(55264) = tripole of the mixed polar line of X(2) and X(113) in K002
X(55264) = barycentric product X(i)*X(j) for these (i, j): {1494, 18878}, {10419, 670}, {40388, 52608}, {40423, 99}, {40832, 44769}
X(55264) = barycentric quotient X(i)/X(j) for these (i, j): {74, 21731}, {99, 113}, {687, 1990}, {1304, 44084}, {1494, 55121}, {2986, 1637}, {4558, 47405}, {5504, 9409}, {10419, 512}, {10420, 1495}, {14910, 14398}, {14919, 686}, {16077, 403}, {16080, 47236}, {18878, 30}, {18879, 2420}, {32708, 14581}, {39988, 55141}, {40388, 2489}, {40423, 523}, {40832, 41079}, {43755, 3284}, {44769, 3003}, {52505, 14397}

X(55265) = X(6)X(2501)∩X(51)X(512)

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

X(55265) lies on these lines: {6, 2501}, {51, 512}, {523, 2433}, {647, 800}, {686, 12828}, {1636, 1637}, {1648, 3258}, {1899, 3566}, {5466, 14853}, {6792, 52472}, {10097, 45088}, {10279, 10982}, {16220, 16657}

X(55265) = isotomic conjugate of X(55264)
X(55265) = perspector of circumconic {{A, B, C, X(30), X(113)}}
X(55265) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55264}, {163, 40423}, {662, 10419}, {687, 35200}, {2159, 18878}, {2349, 10420}, {2986, 36034}, {4592, 40388}, {14919, 36114}, {36053, 44769}, {36119, 43755}
X(55265) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55264}, {113, 44769}, {115, 40423}, {133, 687}, {1084, 10419}, {1511, 43755}, {3003, 99}, {3163, 18878}, {3258, 2986}, {5139, 40388}, {11064, 4563}, {16178, 16080}, {39005, 14919}, {39021, 1494}
X(55265) = X(i)-Ceva conjugate of X(j) for these {i, j}: {523, 21731}, {2501, 1637}, {36789, 3258}
X(55265) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(47405)}}, {{A, B, C, X(113), X(5642)}}, {{A, B, C, X(403), X(1651)}}, {{A, B, C, X(512), X(52743)}}, {{A, B, C, X(686), X(1636)}}, {{A, B, C, X(1637), X(15475)}}, {{A, B, C, X(1640), X(41512)}}, {{A, B, C, X(2420), X(14397)}}, {{A, B, C, X(2433), X(21731)}}, {{A, B, C, X(2501), X(39021)}}, {{A, B, C, X(3163), X(14583)}}, {{A, B, C, X(9033), X(14582)}}, {{A, B, C, X(14254), X(34104)}}, {{A, B, C, X(14391), X(35361)}}
X(55265) = barycentric product X(i)*X(j) for these (i, j): {30, 55121}, {113, 523}, {403, 9033}, {1637, 3580}, {1725, 36035}, {1990, 6334}, {3003, 41079}, {3258, 41512}, {11064, 47236}, {14397, 52504}, {14618, 47405}, {15328, 34104}, {21731, 3260}, {39985, 55141}, {44138, 9409}, {46106, 686}
X(55265) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55264}, {30, 18878}, {113, 99}, {403, 16077}, {512, 10419}, {523, 40423}, {686, 14919}, {1495, 10420}, {1637, 2986}, {1990, 687}, {2420, 18879}, {2489, 40388}, {3003, 44769}, {3284, 43755}, {9409, 5504}, {14397, 52505}, {14398, 14910}, {14581, 32708}, {21731, 74}, {41079, 40832}, {44084, 1304}, {47236, 16080}, {47405, 4558}, {55121, 1494}, {55141, 39988}
X(55265) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1637, 52743, 14401}

X(55266) = TRILINEAR POLE OF LINE {98, 325}

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

X(55266) lies on these lines: {2, 40812}, {76, 34536}, {99, 41173}, {685, 877}, {868, 6394}, {1316, 47736}, {2396, 2966}, {6037, 10425}, {9154, 34229}, {14960, 32697}

X(55266) = trilinear pole of line {98, 325}
X(55266) = X(i)-isoconjugate-of-X(j) for these {i, j}: {114, 798}, {512, 17462}, {661, 51335}, {1733, 2491}, {1755, 55122}, {1959, 42663}, {3569, 8772}, {32676, 41181}
X(55266) = X(i)-Dao conjugate of X(j) for these {i, j}: {15526, 41181}, {31998, 114}, {36830, 51335}, {36899, 55122}, {39054, 17462}
X(55266) = X(i)-cross conjugate of X(j) for these {i, j}: {525, 35142}, {4563, 43187}, {6563, 18024}
X(55266) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(925)}}, {{A, B, C, X(3), X(14960)}}, {{A, B, C, X(76), X(99)}}, {{A, B, C, X(276), X(52608)}}, {{A, B, C, X(525), X(868)}}, {{A, B, C, X(648), X(46606)}}, {{A, B, C, X(685), X(2966)}}, {{A, B, C, X(689), X(31614)}}, {{A, B, C, X(930), X(30530)}}, {{A, B, C, X(4235), X(35922)}}, {{A, B, C, X(4558), X(40812)}}, {{A, B, C, X(5468), X(34229)}}
X(55266) = tripole of the mixed polar line of X(2) and X(114) in K002
X(55266) = barycentric product X(i)*X(j) for these (i, j): {336, 36105}, {2065, 670}, {2966, 8781}, {2987, 43187}, {10425, 290}, {17932, 35142}, {22456, 43705}, {36036, 8773}, {40428, 99}
X(55266) = barycentric quotient X(i)/X(j) for these (i, j): {98, 55122}, {99, 114}, {110, 51335}, {525, 41181}, {662, 17462}, {685, 460}, {1976, 42663}, {2065, 512}, {2715, 1692}, {2966, 230}, {2987, 3569}, {3563, 17994}, {4558, 47406}, {8781, 2799}, {10425, 511}, {17932, 3564}, {22456, 44145}, {32654, 2491}, {32696, 44099}, {32697, 232}, {35142, 16230}, {35364, 44114}, {36036, 1733}, {36084, 8772}, {36105, 240}, {39291, 47734}, {40428, 523}, {41173, 51820}, {42065, 39469}, {43187, 51481}, {43705, 684}, {43754, 52144}, {51455, 55143}, {52091, 41167}

X(55267) = X(2)X(2501)∩X(6)X(523)

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

X(55267) lies on these lines: {2, 2501}, {3, 39078}, {6, 523}, {216, 2489}, {647, 1196}, {868, 41172}, {877, 14960}, {1560, 2967}, {1637, 1649}, {1648, 3258}, {2485, 40939}, {2492, 8562}, {2799, 3569}, {3005, 8029}, {3163, 9475}, {3566, 44526}, {5466, 14494}, {5477, 42663}, {6587, 10190}, {6753, 40938}, {8430, 14356}, {8968, 14333}, {9168, 9209}, {14401, 31945}, {18311, 24975}, {21196, 40940}, {23992, 55152}, {31947, 40941}, {32320, 34966}, {36875, 52450}, {38652, 47230}, {39874, 50644}, {40179, 47122}, {44538, 44680}, {50330, 55195}

X(55267) = isotomic conjugate of X(55266)
X(55267) = complement of isotomic conjugate of X(4226)
X(55267) = perspector of circumconic {{A, B, C, X(98), X(114)}}
X(55267) = center of circumconic {{A, B, C, X(338), X(523)}}
X(55267) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55266}, {163, 40428}, {248, 36105}, {293, 32697}, {662, 2065}, {1910, 10425}, {2715, 8773}, {2966, 36051}, {2987, 36084}, {32654, 36036}, {36104, 43705}
X(55267) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55266}, {114, 2966}, {115, 40428}, {132, 32697}, {230, 99}, {868, 2}, {1084, 2065}, {2679, 32654}, {11672, 10425}, {35067, 17932}, {35088, 8781}, {36212, 4563}, {38970, 35142}, {38987, 2987}, {39000, 43705}, {39001, 248}, {39039, 36105}, {39069, 36084}, {39072, 2715}, {41172, 52091}, {41181, 6394}, {55152, 98}
X(55267) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2, 868}, {523, 55122}, {648, 3564}, {925, 237}, {2501, 3569}, {4563, 2450}, {9307, 51610}
X(55267) = X(i)-complementary conjugate of X(j) for these {i, j}: {31, 868}, {163, 44377}, {230, 21253}, {1101, 55122}, {1692, 8287}, {1733, 53575}, {4226, 2887}, {8772, 125}, {17462, 36471}, {23995, 6132}, {32676, 3564}, {42663, 24040}, {52035, 21256}, {52144, 34846}
X(55267) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(36790)}}, {{A, B, C, X(114), X(5477)}}, {{A, B, C, X(230), X(34369)}}, {{A, B, C, X(232), X(52515)}}, {{A, B, C, X(868), X(879)}}, {{A, B, C, X(1316), X(14265)}}, {{A, B, C, X(2395), X(2799)}}, {{A, B, C, X(2422), X(3569)}}, {{A, B, C, X(3564), X(6530)}}, {{A, B, C, X(15595), X(51820)}}, {{A, B, C, X(35906), X(51389)}}, {{A, B, C, X(48452), X(51481)}}
X(55267) = barycentric product X(i)*X(j) for these (i, j): {114, 523}, {230, 2799}, {325, 55122}, {460, 6333}, {1577, 17462}, {3569, 51481}, {4226, 868}, {14265, 41167}, {14618, 47406}, {16230, 3564}, {41181, 648}, {44145, 684}, {51335, 850}, {51429, 52035}
X(55267) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55266}, {114, 99}, {230, 2966}, {232, 32697}, {240, 36105}, {460, 685}, {511, 10425}, {512, 2065}, {523, 40428}, {684, 43705}, {1692, 2715}, {1733, 36036}, {2491, 32654}, {2799, 8781}, {3564, 17932}, {3569, 2987}, {8772, 36084}, {16230, 35142}, {17462, 662}, {17994, 3563}, {39469, 42065}, {41167, 52091}, {41181, 525}, {42663, 1976}, {44099, 32696}, {44114, 35364}, {44145, 22456}, {47406, 4558}, {47734, 39291}, {51335, 110}, {51481, 43187}, {51820, 41173}, {52144, 43754}, {55122, 98}, {55143, 51455}

X(55268) = X(3926)X(23582)∩X(6526)X(44181)

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

X(55268) lies on these lines: {3926, 23582}, {6526, 44181}, {18020, 53050}, {41174, 52581}

X(55268) = trilinear pole of line {15384, 18020}
X(55268) = X(i)-isoconjugate-of-X(j) for these {i, j}: {122, 798}, {810, 1562}, {3708, 42658}, {37754, 44705}
X(55268) = X(i)-Dao conjugate of X(j) for these {i, j}: {31998, 122}, {39062, 1562}
X(55268) = X(i)-cross conjugate of X(j) for these {i, j}: {36841, 18020}
X(55268) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(34211)}}, {{A, B, C, X(99), X(3926)}}, {{A, B, C, X(648), X(18848)}}, {{A, B, C, X(6331), X(40830)}}, {{A, B, C, X(34403), X(44326)}}, {{A, B, C, X(36841), X(53050)}}, {{A, B, C, X(52581), X(53639)}}
X(55268) = tripole of the mixed polar line of X(2) and X(122) in K002
X(55268) = barycentric product X(i)*X(j) for these (i, j): {15384, 670}, {18020, 53639}, {23582, 44326}, {31614, 6526}, {44181, 99}, {47443, 52581}
X(55268) = barycentric quotient X(i)/X(j) for these (i, j): {99, 122}, {250, 42658}, {253, 5489}, {648, 1562}, {1301, 20975}, {4558, 47409}, {4590, 20580}, {6526, 8029}, {15384, 512}, {18020, 8057}, {23582, 6587}, {23999, 17898}, {32230, 44705}, {34403, 23616}, {36841, 39020}, {44181, 523}, {44326, 15526}, {46639, 3269}, {47443, 15905}, {53639, 125}

X(55269) = X(393)X(523)∩X(647)X(800)

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

X(55269) lies on these lines: {253, 43673}, {393, 523}, {525, 40995}, {647, 800}, {1249, 6587}, {2501, 41489}, {5489, 21134}, {8057, 15905}, {14380, 45801}, {39201, 40947}

X(55269) = isotomic conjugate of X(55268)
X(55269) = perspector of circumconic {{A, B, C, X(122), X(125)}}
X(55269) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55268}, {163, 44181}, {662, 15384}, {24000, 46639}
X(55269) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55268}, {115, 44181}, {122, 23582}, {525, 44326}, {647, 53639}, {1084, 15384}, {6587, 99}, {8057, 36841}, {39020, 18020}, {45248, 47443}, {52613, 4563}
X(55269) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2501, 3269}, {6587, 1562}, {20580, 122}, {23616, 5489}
X(55269) = intersection, other than A, B, C, of circumconics {{A, B, C, X(393), X(15526)}}, {{A, B, C, X(1249), X(1562)}}, {{A, B, C, X(3269), X(41489)}}, {{A, B, C, X(15905), X(41172)}}
X(55269) = barycentric product X(i)*X(j) for these (i, j): {20, 5489}, {115, 20580}, {122, 523}, {125, 8057}, {339, 42658}, {1249, 23616}, {1367, 14308}, {1562, 525}, {14618, 47409}, {15526, 6587}, {17898, 2632}, {23105, 35602}, {23107, 3172}
X(55269) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55268}, {122, 99}, {125, 53639}, {512, 15384}, {523, 44181}, {1562, 648}, {3269, 46639}, {5489, 253}, {6587, 23582}, {8029, 6526}, {8057, 18020}, {15526, 44326}, {15905, 47443}, {17898, 23999}, {20580, 4590}, {20975, 1301}, {23616, 34403}, {39020, 36841}, {42658, 250}, {44705, 32230}, {47409, 4558}

X(55270) = X(4)X(18020)∩X(76)X(249)

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

X(55270) lies on these lines: {4, 18020}, {76, 249}, {250, 44162}, {877, 55226}, {2396, 4235}, {3552, 23357}, {3926, 4590}, {7769, 39295}, {7782, 14366}, {30247, 45773}, {31632, 40890}

X(55270) = trilinear pole of line {250, 325}
X(55270) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 8029}, {63, 22260}, {115, 810}, {125, 798}, {213, 21134}, {228, 21131}, {304, 23099}, {339, 1924}, {512, 3708}, {647, 2643}, {656, 3124}, {661, 20975}, {667, 21046}, {669, 20902}, {822, 8754}, {1084, 14208}, {1109, 3049}, {1459, 21833}, {1973, 5489}, {2489, 2632}, {2971, 24018}, {3121, 4064}, {3122, 55232}, {3125, 55230}, {3267, 4117}, {3949, 8034}, {4079, 18210}, {4466, 50487}, {4516, 55234}, {9247, 23105}, {20948, 23216}, {21043, 22383}, {23610, 40364}, {33919, 36060}
X(55270) = X(i)-Dao conjugate of X(j) for these {i, j}: {1249, 8029}, {1560, 33919}, {3162, 22260}, {6337, 5489}, {6338, 23616}, {6626, 21134}, {6631, 21046}, {9428, 339}, {31998, 125}, {36830, 20975}, {39052, 2643}, {39054, 3708}, {39062, 115}, {40596, 3124}, {48317, 42344}
X(55270) = X(i)-cross conjugate of X(j) for these {i, j}: {648, 18020}, {4563, 4590}, {16237, 42308}, {55225, 34537}, {55226, 52940}
X(55270) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(2421)}}, {{A, B, C, X(4), X(648)}}, {{A, B, C, X(76), X(99)}}, {{A, B, C, X(276), X(6331)}}, {{A, B, C, X(3115), X(52936)}}, {{A, B, C, X(3926), X(4563)}}, {{A, B, C, X(4230), X(50437)}}, {{A, B, C, X(14590), X(38936)}}, {{A, B, C, X(18878), X(43187)}}, {{A, B, C, X(31614), X(52940)}}, {{A, B, C, X(44767), X(53202)}}
X(55270) = tripole of the mixed polar line of X(2) and X(125) in K002
X(55270) = barycentric product X(i)*X(j) for these (i, j): {107, 47389}, {112, 34537}, {162, 24037}, {249, 6331}, {250, 670}, {2421, 41174}, {4235, 52940}, {4567, 55231}, {4570, 55229}, {4590, 648}, {4623, 5379}, {14273, 42370}, {18020, 99}, {23582, 4563}, {23964, 52608}, {23999, 4592}, {24000, 55202}, {24041, 811}, {31614, 4}, {36797, 7340}, {37669, 55268}, {44146, 45773}, {44183, 55225}, {46102, 55196}, {46103, 55194}, {46254, 662}, {47443, 76}, {52378, 55233}
X(55270) = barycentric quotient X(i)/X(j) for these (i, j): {4, 8029}, {25, 22260}, {27, 21131}, {69, 5489}, {86, 21134}, {99, 125}, {107, 8754}, {110, 20975}, {112, 3124}, {162, 2643}, {190, 21046}, {249, 647}, {250, 512}, {264, 23105}, {468, 33919}, {648, 115}, {662, 3708}, {670, 339}, {685, 51441}, {799, 20902}, {811, 1109}, {877, 868}, {892, 51258}, {1101, 810}, {1783, 21833}, {1897, 21043}, {1974, 23099}, {2421, 41172}, {2966, 51404}, {3926, 23616}, {4230, 44114}, {4235, 1648}, {4558, 3269}, {4563, 15526}, {4567, 55232}, {4570, 55230}, {4590, 525}, {4592, 2632}, {4600, 4064}, {4610, 4466}, {4611, 38356}, {4612, 53560}, {5095, 14443}, {5379, 4705}, {6064, 52355}, {6331, 338}, {6528, 2970}, {7340, 17094}, {7473, 51428}, {10411, 16186}, {14273, 42344}, {14574, 23216}, {14590, 2088}, {16077, 12079}, {18020, 523}, {18831, 8901}, {23357, 3049}, {23582, 2501}, {23964, 2489}, {23999, 24006}, {24037, 14208}, {24041, 656}, {31614, 69}, {32696, 15630}, {32713, 2971}, {33799, 34953}, {34537, 3267}, {35360, 41221}, {36306, 30452}, {36309, 30453}, {36797, 4092}, {36841, 1562}, {37669, 55269}, {38861, 34982}, {39295, 14582}, {41174, 43665}, {41676, 39691}, {41679, 47421}, {42308, 18808}, {42396, 34294}, {44162, 23610}, {45773, 895}, {46102, 55197}, {46103, 55195}, {46254, 1577}, {47389, 3265}, {47390, 39201}, {47443, 6}, {52378, 55234}, {52608, 36793}, {52914, 4516}, {52935, 18210}, {52940, 14977}, {54108, 34978}, {55194, 26942}, {55196, 26932}, {55202, 17879}, {55225, 127}, {55229, 21207}, {55231, 16732}, {55268, 459}

X(55271) = X(2)X(523)∩X(69)X(3566)

Barycentrics    (b-c)*(b+c)*(-2*a^2+b^2+c^2)*(b^4-4*b^2*c^2+c^4+a^2*(b^2+c^2)) : :
X(55271) = -2*X[351]+X[14272]

X(55271) lies on these lines: {2, 523}, {69, 3566}, {126, 9134}, {351, 14272}, {804, 6148}, {826, 13232}, {1499, 44206}, {2482, 55122}, {2501, 21448}, {2799, 14443}, {5099, 48317}, {5181, 36790}, {6088, 14277}, {6131, 7664}, {9723, 22089}, {11634, 53367}, {14424, 35522}, {23992, 55152}, {33921, 54274}, {48393, 55195}

X(55271) = reflection of X(i) in X(j) for these {i,j}: {14272, 351}, {14424, 35522}, {351, 47139}, {9131, 6131}, {9178, 18310}
X(55271) = perspector of circumconic {{A, B, C, X(126), X(671)}}
X(55271) = center of circumconic {{A, B, C, X(2501), X(9134)}}
X(55271) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 44182}, {662, 15387}, {36142, 41909}
X(55271) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 44182}, {126, 691}, {1084, 15387}, {1648, 34161}, {3291, 99}, {6390, 4563}, {21906, 6}, {23992, 41909}, {48317, 2374}
X(55271) = X(i)-Ceva conjugate of X(j) for these {i, j}: {76, 1648}, {2501, 690}, {35136, 524}
X(55271) = X(i)-complementary conjugate of X(j) for these {i, j}: {896, 5139}, {922, 15525}, {3565, 4892}, {35136, 21256}, {38252, 1648}
X(55271) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(126)}}, {{A, B, C, X(690), X(2408)}}, {{A, B, C, X(3291), X(46783)}}, {{A, B, C, X(5466), X(9134)}}, {{A, B, C, X(8681), X(55131)}}, {{A, B, C, X(9178), X(11634)}}, {{A, B, C, X(9214), X(36874)}}, {{A, B, C, X(14977), X(52628)}}, {{A, B, C, X(17948), X(47286)}}
X(55271) = isotomic conjugate of the tripole of the mixed polar line of X(2) and X(126) in K002
X(55271) = barycentric product X(i)*X(j) for these (i, j): {126, 523}, {524, 9134}, {1577, 17466}, {1648, 53367}, {2501, 52881}, {3291, 35522}, {11634, 52628}, {14263, 52629}, {14618, 47412}, {21905, 76}, {45807, 5140}, {47286, 690}
X(55271) = barycentric quotient X(i)/X(j) for these (i, j): {126, 99}, {512, 15387}, {523, 44182}, {690, 41909}, {1649, 34161}, {3291, 691}, {9134, 671}, {14263, 34574}, {14273, 2374}, {17466, 662}, {21905, 6}, {47286, 892}, {47412, 4558}, {52881, 4563}, {53367, 52940}, {55140, 52141}
X(55271) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {351, 55135, 14272}, {523, 18310, 9178}, {9178, 18310, 8371}, {47139, 55135, 351}

X(55272) = X(250)X(305)∩X(1289)X(45773)

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

X(55272) lies on these lines: {250, 305}, {1289, 45773}, {13854, 44183}, {18020, 34254}

X(55272) = trilinear pole of line {249, 15388}
X(55272) = X(i)-isoconjugate-of-X(j) for these {i, j}: {127, 798}, {661, 38356}, {810, 53569}, {2485, 3708}, {2643, 8673}, {4079, 18187}
X(55272) = X(i)-Dao conjugate of X(j) for these {i, j}: {31998, 127}, {36830, 38356}, {39062, 53569}
X(55272) = X(i)-cross conjugate of X(j) for these {i, j}: {1289, 44183}, {4563, 18020}
X(55272) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(305)}}, {{A, B, C, X(648), X(34405)}}, {{A, B, C, X(1289), X(13854)}}, {{A, B, C, X(4563), X(34254)}}, {{A, B, C, X(18018), X(44766)}}, {{A, B, C, X(31614), X(45773)}}
X(55272) = tripole of the mixed polar line of X(2) and X(127) in K002
X(55272) = barycentric product X(i)*X(j) for these (i, j): {1289, 4590}, {13854, 31614}, {15388, 670}, {18018, 47443}, {18020, 44766}, {44183, 99}, {55270, 66}
X(55272) = barycentric quotient X(i)/X(j) for these (i, j): {99, 127}, {110, 38356}, {249, 8673}, {250, 2485}, {648, 53569}, {1289, 115}, {4558, 47413}, {13854, 8029}, {14376, 5489}, {15388, 512}, {18020, 33294}, {31614, 34254}, {43678, 23105}, {44183, 523}, {44766, 125}, {47443, 22}, {52935, 18187}, {55270, 315}

X(55273) = X(22)X(33294)∩X(25)X(523)

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

X(55273) lies on these lines: {22, 33294}, {25, 523}, {125, 23616}, {525, 1899}, {647, 1196}, {826, 55265}, {868, 5489}, {2485, 40938}, {2501, 13854}, {2799, 42665}, {3265, 30771}, {6353, 47216}, {6587, 37453}, {9979, 47205}, {14420, 42659}

X(55273) = isotomic conjugate of X(55272)
X(55273) = perspector of circumconic {{A, B, C, X(127), X(338)}}
X(55273) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55272}, {163, 44183}, {662, 15388}, {1101, 1289}, {2156, 47443}
X(55273) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55272}, {115, 44183}, {127, 250}, {523, 1289}, {647, 44766}, {1084, 15388}, {2485, 99}, {3265, 4563}, {55047, 249}
X(55273) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2501, 125}, {33294, 38356}, {34212, 868}
X(55273) = intersection, other than A, B, C, of circumconics {{A, B, C, X(22), X(868)}}, {{A, B, C, X(25), X(339)}}, {{A, B, C, X(125), X(13854)}}, {{A, B, C, X(127), X(34254)}}
X(55273) = barycentric product X(i)*X(j) for these (i, j): {125, 33294}, {127, 523}, {338, 8673}, {525, 53569}, {2485, 339}, {14618, 47413}, {17907, 5489}, {18187, 4036}, {20806, 23105}, {21046, 21178}, {21134, 4150}, {23616, 52448}, {34254, 8029}, {38356, 850}
X(55273) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55272}, {22, 47443}, {115, 1289}, {125, 44766}, {127, 99}, {315, 55270}, {512, 15388}, {523, 44183}, {2485, 250}, {5489, 14376}, {8029, 13854}, {8673, 249}, {18187, 52935}, {23105, 43678}, {33294, 18020}, {34254, 31614}, {38356, 110}, {47413, 4558}, {53569, 648}

X(55274) = X(2396)X(2419)∩X(3265)X(41173)

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

X(55274) lies on these lines: {2396, 2419}, {3265, 41173}, {9476, 55266}

X(55274) = trilinear pole of line {6393, 15407}
X(55274) = X(i)-isoconjugate-of-X(j) for these {i, j}: {132, 798}, {2312, 17994}
X(55274) = X(i)-Dao conjugate of X(j) for these {i, j}: {31998, 132}
X(55274) = X(i)-cross conjugate of X(j) for these {i, j}: {20580, 6394}
X(55274) = intersection, other than A, B, C, of circumconics {{A, B, C, X(99), X(3926)}}, {{A, B, C, X(287), X(41173)}}, {{A, B, C, X(305), X(2396)}}, {{A, B, C, X(394), X(4230)}}, {{A, B, C, X(6340), X(44326)}}, {{A, B, C, X(40830), X(52608)}}
X(55274) = tripole of the mixed polar line of X(2) and X(132) in K002
X(55274) = barycentric product X(i)*X(j) for these (i, j): {4563, 9476}, {15407, 670}, {17932, 35140}
X(55274) = barycentric quotient X(i)/X(j) for these (i, j): {99, 132}, {1297, 17994}, {2419, 868}, {2435, 44114}, {2715, 51437}, {2966, 16318}, {4558, 9475}, {4563, 15595}, {9476, 2501}, {15407, 512}, {17932, 1503}, {35140, 16230}, {43754, 42671}, {44770, 34854}, {55202, 17875}

X(55275) = X(25)X(669)∩X(393)X(523)

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

X(55275) lies on these lines: {25, 669}, {393, 523}, {800, 2489}, {868, 41172}, {1609, 47125}, {2409, 23977}, {2485, 14576}, {5489, 27376}, {6353, 6587}, {12077, 55273}, {47138, 51334}

X(55275) = isotomic conjugate of X(55274)
X(55275) = perspector of circumconic {{A, B, C, X(132), X(6531)}}
X(55275) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55274}, {662, 15407}, {4575, 9476}, {6394, 36046}
X(55275) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55274}, {136, 9476}, {232, 99}, {441, 4563}, {1084, 15407}, {23976, 17932}, {33504, 6394}, {38970, 35140}, {39073, 4558}, {50938, 2966}, {55267, 2419}
X(55275) = X(i)-Ceva conjugate of X(j) for these {i, j}: {523, 17994}
X(55275) = intersection, other than A, B, C, of circumconics {{A, B, C, X(868), X(2395)}}, {{A, B, C, X(878), X(17994)}}, {{A, B, C, X(15595), X(51820)}}, {{A, B, C, X(23977), X(53149)}}
X(55275) = barycentric product X(i)*X(j) for these (i, j): {132, 523}, {1503, 16230}, {2409, 868}, {14618, 9475}, {15595, 2501}, {16318, 2799}, {17994, 30737}, {41167, 52641}
X(55275) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55274}, {132, 99}, {512, 15407}, {868, 2419}, {1503, 17932}, {2501, 9476}, {9475, 4558}, {15595, 4563}, {16230, 35140}, {16318, 2966}, {17875, 55202}, {17994, 1297}, {34854, 44770}, {42671, 43754}, {44114, 2435}, {51437, 2715}

X(55276) = X(393)X(2433)∩X(1990)X(14401)

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

X(55276) lies on these lines: {393, 2433}, {1990, 14401}, {6524, 44705}, {8029, 51513}, {8745, 30442}, {12077, 55269}

X(55276) = perspector of circumconic {{A, B, C, X(133), X(47111)}}
X(55276) = X(i)-isoconjugate-of-X(j) for these {i, j}: {662, 15404}
X(55276) = X(i)-Dao conjugate of X(j) for these {i, j}: {1084, 15404}, {1990, 99}, {44436, 4563}, {50937, 44769}
X(55276) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2433), X(2442)}}, {{A, B, C, X(6529), X(14401)}}, {{A, B, C, X(18808), X(53159)}}
X(55276) = isotomic conjugate of the tripole of the mixed polar line of X(2) and X(133) in K002
X(55276) = barycentric product X(i)*X(j) for these (i, j): {133, 523}, {1637, 51358}, {14618, 47433}, {51385, 9033}
X(55276) = barycentric quotient X(i)/X(j) for these (i, j): {133, 99}, {512, 15404}, {47433, 4558}, {51385, 16077}

X(55277) = (name pending)

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

X(55277) lies on these lines: {7763, 47389}

X(55277) = isotomic conjugate of X(55278)
X(55277) = trilinear pole of line {44174, 51458}
X(55277) = X(i)-isoconjugate-of-X(j) for these {i, j}: {136, 798}, {1748, 22260}, {2643, 6753}, {6754, 55250}, {8754, 55216}
X(55277) = X(i)-Dao conjugate of X(j) for these {i, j}: {31998, 136}
X(55277) = X(i)-cross conjugate of X(j) for these {i, j}: {99, 47389}
X(55277) = intersection, other than A, B, C, of circumconics {{A, B, C, X(54), X(4558)}}, {{A, B, C, X(76), X(4563)}}, {{A, B, C, X(99), X(7763)}}, {{A, B, C, X(40830), X(52608)}}
X(55277) = tripole of the mixed polar line of X(2) and X(136) in K002
X(55277) = barycentric product X(i)*X(j) for these (i, j): {31614, 68}, {44174, 670}, {47389, 925}, {52350, 55270}
X(55277) = barycentric quotient X(i)/X(j) for these (i, j): {68, 8029}, {99, 136}, {249, 6753}, {925, 8754}, {2351, 22260}, {4558, 47421}, {20563, 23105}, {31614, 317}, {32734, 2971}, {44174, 512}, {46134, 2970}, {47389, 6563}, {47390, 34952}, {47443, 8745}, {55202, 17881}, {55270, 11547}

X(55278) = X(6)X(2501)∩X(523)X(2165)

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

X(55278) lies on these lines: {6, 2501}, {233, 55267}, {311, 14618}, {523, 2165}, {800, 2489}, {924, 50647}, {6753, 14576}

X(55278) = isotomic conjugate of X(55277)
X(55278) = perspector of circumconic {{A, B, C, X(136), X(1300)}}
X(55278) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55277}, {662, 44174}
X(55278) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55277}, {135, 249}, {1084, 44174}, {2501, 99}, {52584, 4563}
X(55278) = X(i)-Ceva conjugate of X(j) for these {i, j}: {523, 8754}, {2501, 47421}
X(55278) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(47421)}}, {{A, B, C, X(136), X(317)}}, {{A, B, C, X(2165), X(8754)}}, {{A, B, C, X(8029), X(35361)}}, {{A, B, C, X(15328), X(23105)}}
X(55278) = barycentric product X(i)*X(j) for these (i, j): {136, 523}, {317, 8029}, {338, 6753}, {2970, 924}, {6563, 8754}, {14618, 47421}, {23105, 24}, {35235, 43088}
X(55278) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55277}, {136, 99}, {317, 31614}, {512, 44174}, {2970, 46134}, {2971, 32734}, {6563, 47389}, {6753, 249}, {8029, 68}, {8745, 47443}, {8754, 925}, {11547, 55270}, {17881, 55202}, {22260, 2351}, {23105, 20563}, {34952, 47390}, {47421, 4558}

X(55279) = TRILINEAR POLE OF LINE {69, 576}

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

X(55279) lies on these lines: {99, 33513}, {8781, 39284}, {10330, 17932}, {30786, 37454}, {31626, 39998}

X(55279) = trilinear pole of line {69, 576}
X(55279) = X(i)-isoconjugate-of-X(j) for these {i, j}: {140, 798}, {213, 21103}, {512, 17438}, {661, 13366}, {667, 21012}, {669, 20879}, {810, 6748}, {1232, 1924}, {2643, 35324}, {17168, 50487}
X(55279) = X(i)-Dao conjugate of X(j) for these {i, j}: {6626, 21103}, {6631, 21012}, {9428, 1232}, {31998, 140}, {36830, 13366}, {39054, 17438}, {39062, 6748}, {52032, 35441}
X(55279) = X(i)-cross conjugate of X(j) for these {i, j}: {343, 18020}, {7769, 4590}, {39183, 40410}
X(55279) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(20189)}}, {{A, B, C, X(99), X(4554)}}, {{A, B, C, X(925), X(42396)}}, {{A, B, C, X(930), X(2966)}}, {{A, B, C, X(2396), X(10330)}}, {{A, B, C, X(4235), X(37454)}}, {{A, B, C, X(4576), X(9133)}}, {{A, B, C, X(6758), X(28654)}}, {{A, B, C, X(7372), X(23989)}}, {{A, B, C, X(16077), X(42405)}}, {{A, B, C, X(24041), X(31619)}}, {{A, B, C, X(35137), X(43187)}}, {{A, B, C, X(35178), X(44766)}}, {{A, B, C, X(43188), X(43351)}}, {{A, B, C, X(46144), X(55034)}}
X(55279) = tripole of the mixed polar line of X(2) and X(140) in K002
X(55279) = barycentric product X(i)*X(j) for these (i, j): {1173, 670}, {14570, 31617}, {31626, 6331}, {33513, 69}, {33631, 52608}, {39183, 4590}, {39284, 4563}, {39289, 4576}, {40410, 99}
X(55279) = barycentric quotient X(i)/X(j) for these (i, j): {86, 21103}, {99, 140}, {110, 13366}, {190, 21012}, {249, 35324}, {288, 2623}, {343, 35441}, {648, 6748}, {662, 17438}, {670, 1232}, {799, 20879}, {1173, 512}, {4558, 22052}, {4610, 17168}, {6331, 40684}, {6528, 44732}, {14570, 233}, {18020, 35311}, {23181, 32078}, {31610, 12077}, {31617, 15412}, {31626, 647}, {33513, 4}, {33631, 2489}, {35360, 53386}, {39180, 20975}, {39183, 115}, {39284, 2501}, {40410, 523}

X(55280) = X(230)X(231)∩X(826)X(3288)

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

X(55280) lies on these lines: {230, 231}, {593, 7372}, {826, 3288}, {850, 14417}, {1109, 46101}, {1252, 6758}, {2081, 46384}, {2395, 3108}, {2525, 6563}, {2793, 44445}, {2799, 31296}, {3005, 55122}, {3569, 7927}, {3804, 6562}, {5466, 10185}, {6368, 32320}, {9033, 17434}, {12075, 17414}, {14480, 23357}, {15412, 44427}, {18808, 40402}, {21103, 35441}, {21828, 55197}, {33294, 41300}, {47669, 55212}, {55195, 55210}

X(55280) = midpoint of X(i) and X(j) for these {i,j}: {31296, 41298}
X(55280) = reflection of X(i) in X(j) for these {i,j}: {12077, 647}, {2525, 6563}, {3804, 6562}, {33294, 41300}, {47254, 47627}, {647, 47122}
X(55280) = isotomic conjugate of X(55279)
X(55280) = complement of isotomic conjugate of X(20189)
X(55280) = perspector of circumconic {{A, B, C, X(4), X(140)}}
X(55280) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 55279}, {48, 33513}, {162, 31626}, {163, 40410}, {288, 2617}, {662, 1173}, {1101, 39183}, {4575, 39284}, {4592, 33631}, {31610, 36134}, {39178, 52377}
X(55280) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55279}, {115, 40410}, {125, 31626}, {136, 39284}, {137, 31610}, {140, 14570}, {233, 99}, {523, 39183}, {1084, 1173}, {1249, 33513}, {1493, 4558}, {5139, 33631}, {11792, 2}, {33549, 648}, {35442, 343}
X(55280) = X(i)-Ceva conjugate of X(j) for these {i, j}: {2, 11792}, {53, 3269}, {275, 125}, {648, 34564}, {2963, 115}, {35311, 13366}, {35324, 233}
X(55280) = X(i)-complementary conjugate of X(j) for these {i, j}: {31, 11792}, {20189, 2887}, {32676, 46084}
X(55280) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {45857, 21294}
X(55280) = intersection, other than A, B, C, of circumconics {{A, B, C, X(125), X(45259)}}, {{A, B, C, X(140), X(468)}}, {{A, B, C, X(232), X(3108)}}, {{A, B, C, X(233), X(11062)}}, {{A, B, C, X(1990), X(6748)}}, {{A, B, C, X(2963), X(36422)}}, {{A, B, C, X(3003), X(22052)}}, {{A, B, C, X(3064), X(35308)}}, {{A, B, C, X(7649), X(21103)}}, {{A, B, C, X(8756), X(21012)}}, {{A, B, C, X(11792), X(20189)}}, {{A, B, C, X(12077), X(15412)}}, {{A, B, C, X(16230), X(31065)}}, {{A, B, C, X(35324), X(47230)}}, {{A, B, C, X(42293), X(46088)}}
X(55280) = barycentric product X(i)*X(j) for these (i, j): {10, 21103}, {125, 35311}, {140, 523}, {275, 35441}, {338, 35324}, {525, 6748}, {1232, 512}, {1577, 17438}, {11792, 20189}, {13366, 850}, {14618, 22052}, {14978, 23286}, {15412, 233}, {17168, 4024}, {20879, 661}, {21012, 514}, {35318, 53576}, {36422, 39183}, {40684, 647}, {44732, 520}
X(55280) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55279}, {4, 33513}, {115, 39183}, {140, 99}, {233, 14570}, {512, 1173}, {523, 40410}, {647, 31626}, {1232, 670}, {2489, 33631}, {2501, 39284}, {2623, 288}, {6748, 648}, {12077, 31610}, {13366, 110}, {15412, 31617}, {17168, 4610}, {17438, 662}, {20879, 799}, {20975, 39180}, {21012, 190}, {21103, 86}, {22052, 4558}, {32078, 23181}, {35311, 18020}, {35324, 249}, {35441, 343}, {40684, 6331}, {44732, 6528}, {53386, 35360}
X(55280) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 47122, 647}, {523, 47627, 47254}, {523, 647, 12077}, {647, 12077, 1637}, {6563, 23878, 2525}, {31296, 41298, 2799}

X(55281) = X(99)X(883)∩X(643)X(4625)

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

X(55281) lies on these lines: {99, 883}, {643, 4625}, {645, 42720}, {4572, 54440}

X(55281) = trilinear pole of line {333, 1174}
X(55281) = X(i)-isoconjugate-of-X(j) for these {i, j}: {42, 48151}, {65, 2488}, {142, 798}, {213, 21104}, {354, 512}, {513, 52020}, {649, 21808}, {656, 40983}, {661, 1475}, {667, 3925}, {669, 20880}, {1015, 35310}, {1042, 6608}, {1212, 7180}, {1233, 1924}, {1400, 21127}, {1402, 6362}, {1418, 3709}, {1427, 10581}, {2084, 18087}, {2293, 4017}, {3059, 7250}, {3063, 52023}, {3122, 35338}, {3125, 35326}, {3669, 21795}, {4079, 18164}, {4847, 51641}, {7178, 20229}, {7216, 8012}, {16708, 53581}, {17169, 50487}, {21039, 43924}
X(55281) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 21808}, {6626, 21104}, {6631, 3925}, {9428, 1233}, {10001, 52023}, {31998, 142}, {34961, 2293}, {36830, 1475}, {39026, 52020}, {39054, 354}, {40582, 21127}, {40592, 48151}, {40596, 40983}, {40602, 2488}, {40605, 6362}
X(55281) = X(i)-cross conjugate of X(j) for these {i, j}: {274, 4600}, {2287, 4620}
X(55281) = intersection, other than A, B, C, of circumconics {{A, B, C, X(75), X(190)}}, {{A, B, C, X(99), X(645)}}, {{A, B, C, X(648), X(51563)}}, {{A, B, C, X(664), X(42362)}}, {{A, B, C, X(1414), X(4627)}}, {{A, B, C, X(4552), X(51614)}}, {{A, B, C, X(4577), X(4610)}}, {{A, B, C, X(4632), X(6331)}}, {{A, B, C, X(32736), X(36086)}}
X(55281) = tripole of the mixed polar line of X(2) and X(142) in K002
X(55281) = barycentric product X(i)*X(j) for these (i, j): {333, 6606}, {1170, 7257}, {1174, 670}, {2346, 799}, {4625, 6605}, {10509, 7256}, {21453, 645}, {28660, 53243}, {31618, 643}, {32008, 99}, {42311, 7259}, {47487, 6331}
X(55281) = barycentric quotient X(i)/X(j) for these (i, j): {21, 21127}, {81, 48151}, {86, 21104}, {99, 142}, {100, 21808}, {101, 52020}, {110, 1475}, {112, 40983}, {190, 3925}, {284, 2488}, {333, 6362}, {643, 1212}, {644, 21039}, {645, 4847}, {662, 354}, {664, 52023}, {670, 1233}, {765, 35310}, {799, 20880}, {1170, 4017}, {1174, 512}, {1414, 1418}, {2287, 6608}, {2328, 10581}, {2346, 661}, {3939, 21795}, {4558, 22053}, {4567, 35338}, {4570, 35326}, {4573, 10481}, {4577, 18087}, {4589, 53239}, {4610, 17169}, {4612, 17194}, {4615, 53240}, {4620, 35312}, {4623, 16708}, {4635, 53242}, {5546, 2293}, {6605, 4041}, {6606, 226}, {7256, 51972}, {7257, 1229}, {7259, 3059}, {10482, 3709}, {21453, 7178}, {31618, 4077}, {32008, 523}, {36797, 1855}, {40443, 51664}, {47487, 647}, {52612, 53236}, {52935, 18164}, {53243, 1400}

X(55282) = X(1)X(514)∩X(523)X(656)

Barycentrics    (b-c)*(b+c)*(-(b-c)^2+a*(b+c)) : :
X(55282) = -2*X[2530]+3*X[6545]

X(55282) lies on these lines: {1, 514}, {512, 23755}, {523, 656}, {525, 4804}, {647, 4988}, {661, 48403}, {693, 23877}, {784, 16892}, {826, 4024}, {830, 47680}, {905, 47887}, {918, 48264}, {1577, 4088}, {2530, 6545}, {2826, 23738}, {3776, 48410}, {3810, 4801}, {4064, 30591}, {4142, 17494}, {4151, 4707}, {4379, 24892}, {4458, 4560}, {4705, 21674}, {4802, 6129}, {4823, 48272}, {4824, 27577}, {4893, 29661}, {4959, 28292}, {4977, 53532}, {4978, 23887}, {6362, 6608}, {6546, 29689}, {6591, 21108}, {7192, 29118}, {7662, 48300}, {8045, 47834}, {11125, 50349}, {21106, 48281}, {21111, 28175}, {21112, 28179}, {21119, 28147}, {21125, 23753}, {21188, 47828}, {23770, 48131}, {23815, 48414}, {28470, 47722}, {29017, 48120}, {29021, 47703}, {29051, 47695}, {29082, 48301}, {29094, 48291}, {29098, 48101}, {29102, 48305}, {29116, 49292}, {29162, 50523}, {29240, 48322}, {29288, 47705}, {29304, 48339}, {29664, 44435}, {29681, 47771}, {33142, 47780}, {47132, 48299}, {47700, 48395}, {47719, 48399}, {47819, 48415}, {47872, 48056}, {47918, 48400}, {47934, 48402}, {48082, 48267}, {48121, 49295}, {48122, 48398}, {48407, 50453}, {50351, 52601}

X(55282) = midpoint of X(i) and X(j) for these {i,j}: {17166, 49303}, {21118, 47704}, {23755, 53558}
X(55282) = reflection of X(i) in X(j) for these {i,j}: {17494, 4142}, {21105, 48282}, {21106, 48281}, {21118, 49300}, {21124, 3801}, {21132, 21118}, {4024, 48393}, {4041, 7178}, {4064, 30591}, {4088, 1577}, {4560, 4458}, {4724, 21185}, {47700, 48395}, {47701, 47712}, {47719, 48399}, {47918, 48400}, {47934, 48402}, {47970, 21201}, {48082, 48267}, {48121, 49295}, {48122, 48398}, {48131, 23770}, {48151, 21104}, {48272, 4823}, {48278, 693}, {48299, 47132}, {48300, 7662}, {48407, 50453}, {48410, 3776}, {50351, 52601}, {661, 48403}, {663, 47123}
X(55282) = isotomic conjugate of X(55281)
X(55282) = perspector of circumconic {{A, B, C, X(142), X(226)}}
X(55282) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 53243}, {31, 55281}, {110, 2346}, {162, 47487}, {163, 32008}, {662, 1174}, {1170, 5546}, {1414, 10482}, {2194, 6606}, {4565, 6605}, {41610, 53244}
X(55282) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55281}, {115, 32008}, {125, 47487}, {142, 643}, {244, 2346}, {1084, 1174}, {1111, 274}, {1212, 99}, {1214, 6606}, {3119, 2287}, {40606, 662}, {40608, 10482}, {40611, 53243}, {40622, 21453}, {55064, 6605}
X(55282) = X(i)-Ceva conjugate of X(j) for these {i, j}: {37, 3120}, {1446, 21044}
X(55282) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(21808)}}, {{A, B, C, X(523), X(885)}}, {{A, B, C, X(656), X(21127)}}, {{A, B, C, X(1027), X(4017)}}, {{A, B, C, X(1111), X(47970)}}, {{A, B, C, X(1577), X(23599)}}, {{A, B, C, X(3120), X(35310)}}, {{A, B, C, X(3925), X(40663)}}, {{A, B, C, X(4040), X(24290)}}, {{A, B, C, X(4041), X(4077)}}, {{A, B, C, X(4088), X(4724)}}, {{A, B, C, X(7178), X(21104)}}, {{A, B, C, X(7235), X(20880)}}, {{A, B, C, X(18006), X(35312)}}, {{A, B, C, X(51421), X(51424)}}
X(55282) = barycentric product X(i)*X(j) for these (i, j): {10, 21104}, {142, 523}, {210, 23599}, {226, 6362}, {321, 48151}, {1111, 35310}, {1212, 4077}, {1229, 4017}, {1233, 512}, {1418, 4086}, {1441, 21127}, {1446, 6608}, {1475, 850}, {1577, 354}, {2488, 349}, {3261, 52020}, {3267, 40983}, {3925, 514}, {4010, 53239}, {4049, 51463}, {4064, 53238}, {4079, 53236}, {4088, 53241}, {4120, 53240}, {4171, 53242}, {4847, 7178}, {10481, 3700}, {14618, 22053}, {16708, 4705}, {16732, 35338}, {17094, 1855}, {17169, 4024}, {18087, 826}, {18164, 4036}, {20880, 661}, {21039, 24002}, {21044, 35312}, {21207, 35326}, {21795, 52621}, {21808, 693}, {52023, 522}, {53237, 8611}
X(55282) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55281}, {142, 99}, {226, 6606}, {354, 662}, {512, 1174}, {523, 32008}, {647, 47487}, {661, 2346}, {1212, 643}, {1229, 7257}, {1233, 670}, {1400, 53243}, {1418, 1414}, {1475, 110}, {1855, 36797}, {2293, 5546}, {2488, 284}, {3059, 7259}, {3709, 10482}, {3925, 190}, {4017, 1170}, {4041, 6605}, {4077, 31618}, {4847, 645}, {6362, 333}, {6608, 2287}, {7178, 21453}, {10481, 4573}, {10581, 2328}, {16708, 4623}, {17169, 4610}, {17194, 4612}, {18087, 4577}, {18164, 52935}, {20880, 799}, {21039, 644}, {21104, 86}, {21127, 21}, {21795, 3939}, {21808, 100}, {22053, 4558}, {35310, 765}, {35312, 4620}, {35326, 4570}, {35338, 4567}, {40983, 112}, {48151, 81}, {51664, 40443}, {51972, 7256}, {52020, 101}, {52023, 664}, {53236, 52612}, {53239, 4589}, {53240, 4615}, {53242, 4635}
X(55282) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {514, 21185, 4724}, {514, 21201, 47970}, {514, 47123, 663}, {514, 47712, 47701}, {514, 48282, 21105}, {514, 49300, 21118}, {523, 3801, 21124}, {523, 7178, 4041}, {693, 23877, 48278}, {826, 48393, 4024}, {4041, 7178, 30574}, {6362, 21104, 48151}, {17166, 49303, 514}, {23755, 53558, 512}, {47704, 49300, 21132}

X(55283) = TRILINEAR POLE OF LINE {95, 252}

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

X(55283) lies on these lines: {10411, 18831}, {11140, 34384}, {42405, 55217}

X(55283) = trilinear pole of line {95, 252}
X(55283) = X(i)-isoconjugate-of-X(j) for these {i, j}: {143, 798}, {560, 20577}, {810, 14577}, {1510, 2179}, {2964, 55219}, {32676, 47424}
X(55283) = X(i)-Dao conjugate of X(j) for these {i, j}: {2963, 42650}, {6374, 20577}, {15526, 47424}, {21975, 55219}, {31998, 143}, {36901, 137}, {39062, 14577}
X(55283) = X(i)-cross conjugate of X(j) for these {i, j}: {850, 34384}
X(55283) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4563), X(10411)}}, {{A, B, C, X(18831), X(41208)}}, {{A, B, C, X(35137), X(43187)}}
X(55283) = tripole of the mixed polar line of X(2) and X(143) in K002
X(55283) = barycentric product X(i)*X(j) for these (i, j): {252, 670}, {2963, 55218}, {34384, 930}, {34386, 38342}, {46139, 95}, {55217, 97}
X(55283) = barycentric quotient X(i)/X(j) for these (i, j): {76, 20577}, {93, 51513}, {95, 1510}, {99, 143}, {252, 512}, {525, 47424}, {648, 14577}, {850, 137}, {930, 51}, {2963, 55219}, {3519, 15451}, {6331, 14129}, {11140, 12077}, {18315, 2965}, {18831, 3518}, {20572, 23290}, {21975, 42650}, {32737, 40981}, {34384, 41298}, {36148, 2179}, {38342, 53}, {46139, 5}, {55217, 324}, {55218, 7769}

X(55284) = X(99)X(53622)∩X(4616)X(7253)

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

X(55284) lies on these lines: {99, 53622}, {4616, 7253}

X(55284) = trilinear pole of line {333, 5792}
X(55284) = X(i)-isoconjugate-of-X(j) for these {i, j}: {144, 798}, {165, 512}, {213, 7658}, {649, 21872}, {661, 3207}, {667, 21060}, {669, 16284}, {1419, 3709}, {4524, 17106}
X(55284) = X(i)-Dao conjugate of X(j) for these {i, j}: {5375, 21872}, {6626, 7658}, {6631, 21060}, {31998, 144}, {36830, 3207}, {39054, 165}
X(55284) = X(i)-cross conjugate of X(j) for these {i, j}: {4573, 99}
X(55284) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(86), X(648)}}, {{A, B, C, X(99), X(645)}}, {{A, B, C, X(927), X(44765)}}, {{A, B, C, X(4569), X(44327)}}, {{A, B, C, X(6335), X(35157)}}, {{A, B, C, X(6606), X(13136)}}, {{A, B, C, X(8706), X(18830)}}, {{A, B, C, X(28626), X(38340)}}, {{A, B, C, X(35179), X(37205)}}
X(55284) = tripole of the mixed polar line of X(2) and X(144) in K002
X(55284) = barycentric product X(i)*X(j) for these (i, j): {333, 53640}, {3062, 799}, {10405, 99}, {11051, 670}, {19605, 4625}, {28660, 53622}, {36620, 645}, {44186, 662}
X(55284) = barycentric quotient X(i)/X(j) for these (i, j): {86, 7658}, {99, 144}, {100, 21872}, {110, 3207}, {190, 21060}, {662, 165}, {799, 16284}, {1414, 1419}, {3062, 661}, {4558, 22117}, {4569, 50562}, {4573, 3160}, {4616, 9533}, {4625, 31627}, {4635, 50561}, {4637, 17106}, {7253, 13609}, {10405, 523}, {11051, 512}, {19605, 4041}, {36620, 7178}, {44186, 1577}, {53622, 1400}, {53640, 226}

X(55285) = X(1)X(41800)∩X(10)X(525)

Barycentrics    (b-c)*(b+c)*(-3*a^2+(b-c)^2+2*a*(b+c)) : :
X(55285) = -X[1]+3*X[41800], -X[3700]+3*X[21052], -X[4088]+3*X[44729], -X[4162]+3*X[47800], -X[4504]+3*X[45674], -X[4879]+3*X[47799]

X(55285) lies on these lines: {1, 41800}, {10, 525}, {523, 656}, {676, 3900}, {905, 6366}, {918, 4147}, {1499, 4129}, {1577, 4843}, {1638, 4449}, {1734, 6362}, {1869, 44705}, {2254, 21120}, {2487, 4367}, {2490, 47835}, {2826, 48018}, {2977, 29082}, {3566, 14321}, {3700, 21052}, {3800, 4807}, {3810, 4925}, {3907, 17069}, {3910, 17072}, {4036, 17898}, {4088, 44729}, {4162, 47800}, {4462, 50357}, {4504, 45674}, {4730, 48403}, {4761, 48402}, {4879, 47799}, {4977, 47921}, {6332, 53573}, {6587, 55232}, {7655, 47136}, {9511, 44408}, {14077, 21188}, {14838, 28473}, {21189, 42337}, {21302, 50347}, {21944, 45741}, {22089, 52139}, {28209, 47929}, {28902, 48607}, {29162, 50501}, {29240, 50504}, {35057, 39540}, {35347, 41501}, {39510, 39583}, {47837, 48290}, {48179, 48338}, {48245, 48323}, {48400, 50355}

X(55285) = midpoint of X(i) and X(j) for these {i,j}: {1734, 10015}, {2254, 21120}, {21302, 50347}, {4041, 7178}, {4462, 50357}, {4730, 48403}, {4761, 48402}, {4807, 50453}, {48400, 50355}, {7655, 47136}
X(55285) = reflection of X(i) in X(j) for these {i,j}: {14321, 21051}, {3801, 7657}, {4367, 2487}, {48299, 2490}, {676, 14837}, {6332, 53573}
X(55285) = isotomic conjugate of X(55284)
X(55285) = perspector of circumconic {{A, B, C, X(144), X(226)}}
X(55285) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 53622}, {31, 55284}, {110, 3062}, {163, 10405}, {662, 11051}, {1576, 44186}, {2194, 53640}, {4565, 19605}
X(55285) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 55284}, {7, 4573}, {115, 10405}, {244, 3062}, {1084, 11051}, {1214, 53640}, {4858, 44186}, {7658, 7253}, {13609, 86}, {40611, 53622}, {40622, 36620}, {55064, 19605}
X(55285) = X(i)-Ceva conjugate of X(j) for these {i, j}: {3700, 523}, {21052, 21051}
X(55285) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3160), X(41501)}}, {{A, B, C, X(7178), X(7658)}}, {{A, B, C, X(7235), X(16284)}}, {{A, B, C, X(21060), X(40663)}}
X(55285) = barycentric product X(i)*X(j) for these (i, j): {10, 7658}, {144, 523}, {1419, 4086}, {1577, 165}, {3064, 50563}, {3160, 3700}, {3207, 850}, {3709, 50560}, {3900, 50562}, {4171, 50561}, {13609, 4566}, {14618, 22117}, {16284, 661}, {21060, 514}, {21872, 693}, {31627, 4041}
X(55285) = barycentric quotient X(i)/X(j) for these (i, j): {2, 55284}, {144, 99}, {165, 662}, {226, 53640}, {512, 11051}, {523, 10405}, {661, 3062}, {1400, 53622}, {1419, 1414}, {1577, 44186}, {3160, 4573}, {3207, 110}, {4041, 19605}, {7178, 36620}, {7658, 86}, {9533, 4616}, {13609, 7253}, {16284, 799}, {17106, 4637}, {21060, 190}, {21872, 100}, {22117, 4558}, {31627, 4625}, {50561, 4635}, {50562, 4569}
X(55285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 7657, 3801}, {3566, 21051, 14321}, {3900, 14837, 676}, {4041, 30574, 7178}, {4041, 7178, 523}, {4807, 50453, 3800}, {47835, 48299, 2490}

X(55286) = X(3)X(74)∩X(51)X(550)

Barycentrics    a^8*(b^2+c^2)-3*a^6*(b^4-6*b^2*c^2+c^4)-a^2*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)+3*a^4*(b^6-6*b^4*c^2-6*b^2*c^4+c^6) : :
X(55286) = 3*X[20]+5*X[15026], X[143]+3*X[376], X[185]+3*X[54044], X[1657]+3*X[13364], X[5446]+3*X[15690], -X[5447]+3*X[15759], -X[5562]+9*X[45759], X[5889]+15*X[14093], -X[6101]+9*X[10304], -X[10263]+9*X[20791], X[10575]+7*X[44682], -X[10627]+5*X[46853], -X[11793]+3*X[14891], -X[12162]+9*X[17504], X[12279]+15*X[15693], X[13421]+3*X[36987], X[13598]+3*X[15691]

X(55286) lies on these lines: {3, 74}, {4, 12046}, {20, 15026}, {30, 11695}, {51, 550}, {140, 11017}, {143, 376}, {185, 54044}, {389, 548}, {549, 11381}, {631, 32137}, {974, 21660}, {1154, 13348}, {1657, 13364}, {3522, 6243}, {3528, 6102}, {3534, 9781}, {3537, 32140}, {5446, 15690}, {5447, 15759}, {5562, 45759}, {5888, 16835}, {5889, 14093}, {5946, 15696}, {6101, 10304}, {8703, 10625}, {9729, 44245}, {9730, 16982}, {10095, 12103}, {10124, 46849}, {10263, 20791}, {10295, 11576}, {10575, 44682}, {10627, 46853}, {11439, 15701}, {11451, 49139}, {11465, 49134}, {11793, 14891}, {11812, 44870}, {12100, 14128}, {12108, 14915}, {12162, 17504}, {12279, 15693}, {13363, 15704}, {13421, 36987}, {13598, 15691}, {14855, 15712}, {15043, 15689}, {15058, 15700}, {15060, 15717}, {15714, 45957}, {15720, 52093}, {15739, 34152}, {16981, 37481}, {19708, 34783}, {21735, 54042}, {27355, 35404}, {32136, 37480}, {32184, 32903}, {34200, 40647}, {37490, 41463}, {40280, 50693}

X(55286) = midpoint of X(i) and X(j) for these {i,j}: {10095, 12103}, {14128, 46850}, {32184, 32903}, {550, 12006}, {9729, 44245}
X(55286) = reflection of X(i) in X(j) for these {i,j}: {11017, 140}, {11592, 3}, {4, 12046}
X(55286) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2693), X(11592)}}
X(55286) = radical center of circles (A, d(X(5),BC)), ...
X(55286) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5663, 11592}, {12100, 46850, 14128}, {12103, 16836, 10095}, {14855, 15712, 45959}

X(55287) = X(3)X(1616)∩X(55)X(945)

Barycentrics    a^2*(-4*a^5*b*c*(b+c)+a^6*(b^2+c^2)-4*a*b*(b-c)^2*c*(b^3-3*b^2*c-3*b*c^2+c^3)+8*a^3*b*c*(b^3-2*b^2*c-2*b*c^2+c^3)+a^4*(-3*b^4+4*b^3*c+16*b^2*c^2+4*b*c^3-3*c^4)-(b^2-c^2)^2*(b^4-4*b^3*c+8*b^2*c^2-4*b*c^3+c^4)+a^2*(b-c)^2*(3*b^4-2*b^3*c-18*b^2*c^2-2*b*c^3+3*c^4)) : :

X(55287) lies on these lines: {3, 1616}, {55, 945}, {389, 517}, {1480, 11430}, {2818, 3057}, {2841, 5882}, {3877, 11793}, {9729, 25413}, {12672, 13474}, {16836, 37562}, {31787, 55166}

X(55287) = reflection of X(i) in X(j) for these {i,j}: {13474, 12672}, {25413, 9729}
X(55287) = radical center of circles (A, d(X(8),BC)), ...

X(55288) = X(1)X(3)∩X(9)X(2808)

Barycentrics    a*(a^7-3*a^6*(b+c)-(b-c)^4*(b+c)^3+a^5*(5*b^2+2*b*c+5*c^2)+a^4*(-3*b^3+7*b^2*c+7*b*c^2-3*c^3)+a^2*(b-c)^2*(7*b^3+9*b^2*c+9*b*c^2+7*c^3)-a*(b-c)^2*(b^4+6*b^2*c^2+c^4)-a^3*(5*b^4+4*b^3*c+6*b^2*c^2+4*b*c^3+5*c^4)) : :

X(55288) lies on these lines: {1, 3}, {9, 2808}, {20, 27000}, {2257, 50658}, {3523, 26658}, {6908, 41785}, {9944, 54424}, {20328, 38122}, {31435, 46850}, {39156, 52155}

X(55288) = radical center of circles (A, d(X(9),BC)), ...

X(55289) = X(3)X(595)∩X(960)X(2808)

Barycentrics    a^2*(-2*a^5*b*c*(b+c)+a^6*(b^2+c^2)-2*a*b*(b-c)^2*c*(b^3-3*b^2*c-3*b*c^2+c^3)+4*a^3*b*c*(b^3-2*b^2*c-2*b*c^2+c^3)+a^4*(-3*b^4+2*b^3*c+20*b^2*c^2+2*b*c^3-3*c^4)-(b^2-c^2)^2*(b^4-2*b^3*c+4*b^2*c^2-2*b*c^3+c^4)+a^2*(3*b^6-4*b^5*c-19*b^4*c^2+16*b^3*c^3-19*b^2*c^4-4*b*c^5+3*c^6)) : :

X(55289) lies on these lines: {3, 595}, {392, 46850}, {517, 6744}, {960, 2808}, {2818, 13624}, {5731, 29958}, {6000, 31838}, {9729, 31786}, {12109, 14110}, {18481, 44865}, {31788, 53790}

X(55289) = midpoint of X(i) and X(j) for these {i,j}: {12109, 14110}, {18481, 44865}, {9729, 31786}
X(55289) = radical center of circles (A, d(X(10),BC)), ...
X(55289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9729, 31786, 45955}

X(55290) = X(3)X(618)∩X(5)X(47853)

Barycentrics    6*(2*a^6+a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-4*a^2*(b^2+c^2)^2)*S-(sqrt(3)*(2*a^8+(b^2-c^2)^4-15*a^6*(b^2+c^2)+a^4*(17*b^4+14*b^2*c^2+17*c^4)+a^2*(-5*b^6+13*b^4*c^2+13*b^2*c^4-5*c^6))) : :

X(55290) lies on these lines: {3, 618}, {5, 47853}, {6115, 14538}, {6771, 47857}, {11179, 13084}, {14904, 41045}, {32552, 33389}, {36383, 49961}, {37340, 41071}, {38412, 54569}

X(55290) = midpoint of X(i) and X(j) for these {i,j}: {6115, 14538}
X(55290) = reflection of X(i) in X(j) for these {i,j}: {47853, 5}, {47857, 6771}
X(55290) = radical center of circles (A, d(X(15),BC)), ...

X(55291) = X(3)X(619)∩X(5)X(47854)

Barycentrics    6*(2*a^6+a^4*(b^2+c^2)+(b^2-c^2)^2*(b^2+c^2)-4*a^2*(b^2+c^2)^2)*S+sqrt(3)*(2*a^8+(b^2-c^2)^4-15*a^6*(b^2+c^2)+a^4*(17*b^4+14*b^2*c^2+17*c^4)+a^2*(-5*b^6+13*b^4*c^2+13*b^2*c^4-5*c^6)) : :

X(55291) lies on these lines: {3, 619}, {5, 47854}, {6114, 14539}, {6774, 47858}, {11179, 13083}, {14905, 41044}, {32553, 33388}, {36382, 49962}, {37341, 41070}

X(55291) = midpoint of X(i) and X(j) for these {i,j}: {6114, 14539}
X(55291) = reflection of X(i) in X(j) for these {i,j}: {47854, 5}, {47858, 6774}
X(55291) = radical center of circles (A, d(X(16),BC)), ...

X(55292) = X(3)X(35217)∩X(389)X(18583)

Barycentrics    2*a^16-7*a^14*(b^2+c^2)+9*a^10*(b^2-c^2)^2*(b^2+c^2)+(b^2-c^2)^6*(b^2+c^2)^2-5*a^2*(b^2-c^2)^4*(b^2+c^2)^3+a^12*(5*b^4+22*b^2*c^2+5*c^4)+3*a^6*(b^2-c^2)^2*(b^6+11*b^4*c^2+11*b^2*c^4+c^6)+a^4*(b^2-c^2)^2*(7*b^8+8*b^6*c^2-6*b^4*c^4+8*b^2*c^6+7*c^8)-a^8*(15*b^8+28*b^6*c^2-30*b^4*c^4+28*b^2*c^6+15*c^8) : :

X(55292) lies on these lines: {3, 35217}, {389, 18583}, {1503, 11430}, {5663, 23292}, {11438, 38317}, {13394, 47090}, {18388, 52262}, {18390, 45303}, {18580, 52019}

X(55292) = radical center of circles (A, d(X(22),BC)), ...

X(55293) = X(3)X(35218)∩X(468)X(1514)

Barycentrics    2*a^16-7*a^14*(b^2+c^2)+(b^2-c^2)^6*(b^2+c^2)^2+a^12*(5*b^4+38*b^2*c^2+5*c^4)+a^6*(b^2-c^2)^2*(3*b^6+80*b^4*c^2+80*b^2*c^4+3*c^6)-a^2*(b^2-c^2)^4*(5*b^6+11*b^4*c^2+11*b^2*c^4+5*c^6)+a^10*(9*b^6-40*b^4*c^2-40*b^2*c^4+9*c^6)+7*a^4*(b^2-c^2)^2*(b^8-3*b^6*c^2-10*b^4*c^4-3*b^2*c^6+c^8)-a^8*(15*b^8+35*b^6*c^2-126*b^4*c^4+35*b^2*c^6+15*c^8) : :

X(55293) lies on these lines: {3, 35218}, {125, 35484}, {140, 38791}, {389, 2781}, {468, 1514}, {541, 15122}, {576, 20126}, {5972, 55166}, {10293, 15131}, {10294, 17854}, {10721, 41448}, {10990, 37118}, {13293, 35485}, {16534, 46850}, {41359, 52546}

X(55293) = radical center of circles (A, d(X(23),BC)), ...

X(55294) = X(3)X(32125)∩X(10257)X(22802)

Barycentrics    2*a^16-7*a^14*(b^2+c^2)+(b^2-c^2)^6*(b^2+c^2)^2+a^12*(5*b^4+38*b^2*c^2+5*c^4)-a^2*(b^2-c^2)^4*(5*b^6+7*b^4*c^2+7*b^2*c^4+5*c^6)+a^10*(9*b^6-49*b^4*c^2-49*b^2*c^4+9*c^6)-3*a^8*(5*b^8+4*b^6*c^2-42*b^4*c^4+4*b^2*c^6+5*c^8)+a^4*(b^2-c^2)^2*(7*b^8-24*b^6*c^2-54*b^4*c^4-24*b^2*c^6+7*c^8)+a^6*(3*b^10+59*b^8*c^2-78*b^6*c^4-78*b^4*c^6+59*b^2*c^8+3*c^10) : :

X(55294) lies on these lines: {3, 32125}, {10257, 22802}, {13346, 47090}, {13383, 37853}, {15122, 22660}, {15311, 16196}, {23336, 55292}, {32205, 44236}

X(55294) = radical center of circles (A, d(X(24),BC)), ...

X(55295) = X(140)X(43577)∩X(156)X(47090)

Barycentrics    2*a^16-7*a^14*(b^2+c^2)+(b^2-c^2)^6*(b^2+c^2)^2+5*a^12*(b^4+6*b^2*c^2+c^4)-5*a^8*(b^2-c^2)^2*(3*b^4+10*b^2*c^2+3*c^4)-a^2*(b^2-c^2)^4*(5*b^6+11*b^4*c^2+11*b^2*c^4+5*c^6)+a^10*(9*b^6-29*b^4*c^2-29*b^2*c^4+9*c^6)+a^4*(b^2-c^2)^2*(7*b^8-8*b^6*c^2-34*b^4*c^4-8*b^2*c^6+7*c^8)+a^6*(3*b^10+43*b^8*c^2-42*b^6*c^4-42*b^4*c^6+43*b^2*c^8+3*c^10) : :

X(55295) lies on these lines: {140, 43577}, {156, 47090}, {389, 44236}, {5448, 23336}, {5663, 15115}, {12084, 32125}, {13352, 32358}, {14156, 46850}, {32210, 52262}, {44232, 46686}

X(55295) = radical center of circles (A, d(X(26),BC)), ...

X(55296) = X(1)X(31659)∩X(3)X(2886)

Barycentrics    2*a^10-4*a^9*(b+c)+(b-c)^6*(b+c)^4+a^8*(-5*b^2+8*b*c-5*c^2)-2*a*(b-c)^4*(b+c)^3*(b^2-b*c+c^2)-2*a^2*(b-c)^4*(b+c)^2*(2*b^2+b*c+2*c^2)+14*a^7*(b^3+c^3)+2*a^6*(b^4-7*b^3*c+14*b^2*c^2-7*b*c^3+c^4)+2*a^3*(b-c)^2*(5*b^5+2*b^4*c+5*b^3*c^2+5*b^2*c^3+2*b*c^4+5*c^5)-2*a^5*(9*b^5-8*b^4*c+7*b^3*c^2+7*b^2*c^3-8*b*c^4+9*c^5)+2*a^4*(2*b^6+b^5*c-12*b^4*c^2+14*b^3*c^3-12*b^2*c^4+b*c^5+2*c^6) : :

X(55296) lies on these lines: {1, 31659}, {3, 2886}, {12, 6863}, {140, 3753}, {952, 6734}, {2975, 6825}, {3585, 5841}, {5433, 10267}, {5840, 14794}, {6713, 10902}, {6923, 30264}, {6928, 24953}, {6954, 10527}, {6958, 31260}, {12704, 37701}, {15325, 24299}, {24474, 37737}, {26286, 26481}, {26332, 38109}, {26437, 26487}, {26475, 32613}, {45630, 52837}

X(55296) = radical center of circles (A, d(X(35),BC)), ...
X(55296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10959, 21155, 10267}

X(55297) = X(1)X(6713)∩X(3)X(119)

Barycentrics    2*a^10-4*a^9*(b+c)+(b-c)^6*(b+c)^4+a^8*(-5*b^2+16*b*c-5*c^2)-2*a*(b-c)^4*(b+c)^3*(b^2-3*b*c+c^2)-2*a^2*(b-c)^4*(b+c)^2*(2*b^2+5*b*c+2*c^2)+2*a^7*(7*b^3-2*b^2*c-2*b*c^2+7*c^3)+2*a^6*(b^4-19*b^3*c+14*b^2*c^2-19*b*c^3+c^4)+a^5*(-18*b^5+28*b^4*c+6*b^3*c^2+6*b^2*c^3+28*b*c^4-18*c^5)+2*a^4*(2*b^6+13*b^5*c-20*b^4*c^2+6*b^3*c^3-20*b^2*c^4+13*b*c^5+2*c^6)+2*a^3*(5*b^7-14*b^6*c+9*b^4*c^3+9*b^3*c^4-14*b*c^6+5*c^7) : :

X(55297) lies on these lines: {1, 6713}, {2, 12775}, {3, 119}, {11, 6958}, {100, 6891}, {104, 5552}, {140, 392}, {952, 5440}, {1387, 23340}, {1537, 13747}, {2077, 3583}, {2818, 22102}, {3576, 12749}, {5432, 10269}, {6684, 55296}, {6691, 25413}, {6827, 34474}, {6863, 31235}, {6922, 33814}, {6928, 24466}, {10265, 12437}, {10270, 15017}, {10531, 31272}, {10738, 35251}, {10915, 11715}, {10942, 38602}, {12115, 38693}, {12608, 46684}, {12703, 16173}, {12751, 15015}, {13913, 19048}, {13977, 19047}, {15296, 38122}, {19914, 20418}, {23513, 26333}, {25438, 37726}, {26285, 26476}, {26358, 26492}, {26482, 32612}, {31659, 37561}, {45631, 52836}

X(55297) = midpoint of X(i) and X(j) for these {i,j}: {2077, 39692}
X(55297) = radical center of circles (A, d(X(36),BC)), ...
X(55297) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {119, 38761, 6256}, {10956, 21154, 10269}, {26364, 48695, 119}

X(55298) = X(1)X(6958)∩X(3)X(960)

Barycentrics    a*(a^9+12*a^7*b*c-3*a^8*(b+c)+(b-c)^4*(b+c)^3*(b^2+c^2)-a*(b-c)^4*(b+c)^2*(3*b^2-2*b*c+3*c^2)+2*a^6*(4*b^3-5*b^2*c-5*b*c^2+4*c^3)-2*a^2*b*(b-c)^2*c*(7*b^3+b^2*c+b*c^2+7*c^3)-2*a^5*(3*b^4+8*b^3*c-16*b^2*c^2+8*b*c^3+3*c^4)-2*a^4*(3*b^5-14*b^4*c+7*b^3*c^2+7*b^2*c^3-14*b*c^4+3*c^5)+4*a^3*(2*b^6-b^5*c-7*b^4*c^2+10*b^3*c^3-7*b^2*c^4-b*c^5+2*c^6)) : :

X(55298) lies on these lines: {1, 6958}, {3, 960}, {78, 952}, {140, 19861}, {474, 37562}, {496, 37533}, {1837, 6882}, {1898, 50371}, {3811, 33956}, {4511, 6891}, {6265, 55297}, {6326, 10085}, {6961, 21740}, {9614, 37531}, {12740, 24914}, {17615, 37700}, {17857, 37611}, {26446, 55296}

X(55298) = radical center of circles (A, d(X(46),BC)), ...

X(55299) = X(3)X(128)∩X(30)X(13565)

Barycentrics    2*a^16-4*a^14*(b^2+c^2)+(b^2-c^2)^6*(b^4+b^2*c^2+c^4)-4*a^12*(2*b^4+b^2*c^2+2*c^4)-7*a^2*(b^2-c^2)^4*(b^6+2*b^4*c^2+2*b^2*c^4+c^6)+a^10*(29*b^6+27*b^4*c^2+27*b^2*c^4+29*c^6)+a^4*(b^2-c^2)^2*(14*b^8+25*b^6*c^2+28*b^4*c^4+25*b^2*c^6+14*c^8)-a^8*(25*b^8+16*b^6*c^2-4*b^4*c^4+16*b^2*c^6+25*c^8)-a^6*(2*b^10+9*b^8*c^2+25*b^6*c^4+25*b^4*c^6+9*b^2*c^8+2*c^10) : :

X(55299) lies on these lines: {3, 128}, {30, 13565}, {140, 34768}, {3530, 32744}, {11592, 31379}, {15307, 34598}, {15327, 23281}, {15619, 38429}

X(55299) = radical center of circles (A, d(X(54),BC)), ...

X(55300) = X(1)X(52265)∩X(3)X(1602)

Barycentrics    2*a^10-4*a^9*(b+c)+(b-c)^6*(b+c)^4+a^8*(-5*b^2+4*b*c-5*c^2)-2*a*(b-c)^4*(b+c)^3*(b^2+c^2)-2*a^2*(b-c)^4*(b+c)^2*(2*b^2-b*c+2*c^2)+2*a^7*(7*b^3+b^2*c+b*c^2+7*c^3)+2*a^6*(b^4-b^3*c+20*b^2*c^2-b*c^3+c^4)+2*a^3*(b-c)^2*(5*b^5+5*b^4*c+14*b^3*c^2+14*b^2*c^3+5*b*c^4+5*c^5)-2*a^5*(9*b^5-5*b^4*c+12*b^3*c^2+12*b^2*c^3-5*b*c^4+9*c^5)+2*a^4*(2*b^6-5*b^5*c-14*b^4*c^2+18*b^3*c^3-14*b^2*c^4-5*b*c^5+2*c^6) : :

X(55300) lies on these lines: {1, 52265}, {3, 1602}, {140, 31786}, {495, 6825}, {952, 4847}, {956, 6908}, {1478, 3428}, {4316, 30264}, {5251, 31789}, {5771, 31788}, {6922, 19854}, {6954, 15325}, {10268, 24953}, {15931, 21154}, {20418, 43175}, {47742, 55298}

X(55300) = radical center of circles (A, d(X(55),BC)), ...

X(55301) = X(3)X(1603)∩X(496)X(6891)

Barycentrics    2*a^10-4*a^9*(b+c)+(b-c)^6*(b+c)^4-5*a^8*(b^2-4*b*c+c^2)-2*a*(b-c)^4*(b+c)^3*(b^2-4*b*c+c^2)-2*a^2*(b-c)^4*(b+c)^2*(2*b^2+7*b*c+2*c^2)+2*a^7*(7*b^3-3*b^2*c-3*b*c^2+7*c^3)+2*a^6*(b^4-25*b^3*c+20*b^2*c^2-25*b*c^3+c^4)+2*a^3*(b-c)^2*(5*b^5-7*b^4*c-22*b^3*c^2-22*b^2*c^3-7*b*c^4+5*c^5)-2*a^5*(9*b^5-17*b^4*c-8*b^3*c^2-8*b^2*c^3-17*b*c^4+9*c^5)+a^4*(4*b^6+38*b^5*c-60*b^4*c^2+4*b^3*c^3-60*b^2*c^4+38*b*c^5+4*c^6) : :

X(55301) lies on these lines: {3, 1603}, {140, 31788}, {496, 6891}, {952, 6736}, {1479, 6922}, {3035, 6260}, {3359, 52264}, {4324, 24466}, {5432, 37526}, {5687, 6926}, {6001, 6700}, {6684, 55300}, {10270, 12679}, {31775, 41698}, {37560, 52265}

X(55301) = radical center of circles (A, d(X(56),BC)), ...

X(55302) = X(1)X(6891)∩X(3)X(9)

Barycentrics    a*(a^9+12*a^7*b*c-3*a^8*(b+c)+8*a^6*(b-c)^2*(b+c)+(b-c)^4*(b+c)^5-a*(b-c)^4*(b+c)^2*(3*b^2+2*b*c+3*c^2)-2*a^5*(3*b^4+10*b^3*c-18*b^2*c^2+10*b*c^3+3*c^4)-16*a^2*b*c*(b^5-b^4*c-b*c^4+c^5)-2*a^4*(3*b^5-13*b^4*c+2*b^3*c^2+2*b^2*c^3-13*b*c^4+3*c^5)+4*a^3*(2*b^6+b^5*c-10*b^4*c^2+6*b^3*c^3-10*b^2*c^4+b*c^5+2*c^6)) : :

X(55302) lies on these lines: {1, 6891}, {3, 9}, {78, 5768}, {140, 8583}, {200, 952}, {944, 2057}, {1750, 6948}, {1768, 52050}, {3359, 6911}, {3586, 6282}, {5534, 30283}, {5722, 6922}, {6769, 51785}, {6954, 30503}, {6961, 8726}, {12120, 35252}, {12650, 34918}, {16408, 31788}, {26446, 55300}, {37514, 37554}, {45770, 55301}

X(55302) = intersection, other than A, B, C, of circumconics
X(55302) = radical center of circles (A, d(X(57),BC)), ...
X(55302) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5720, 7171, 1490}

X(55303) = X(3)X(6)∩X(55)X(2818)

Barycentrics    a^2*(a^8-a^6*(b-c)^2-2*a^7*(b+c)+a^2*(b^2-c^2)^2*(5*b^2-2*b*c+5*c^2)+2*a*(b+c)*(b^3-b^2*c+b*c^2-c^3)^2+2*a^5*(3*b^3+b^2*c+b*c^2+3*c^3)-2*(b^2-c^2)^2*(b^4-b^3*c+b^2*c^2-b*c^3+c^4)-a^4*(3*b^4+2*b^3*c-4*b^2*c^2+2*b*c^3+3*c^4)-2*a^3*(3*b^5-b^4*c+2*b^3*c^2+2*b^2*c^3-b*c^4+3*c^5)) : :

X(55303) lies on these lines: {3, 6}, {55, 2818}, {1204, 7421}, {3145, 6759}, {3295, 55287}, {3357, 37195}, {5562, 20846}, {6923, 53794}, {7510, 17056}, {11344, 11793}, {11695, 37282}

X(55303) = intersection, other than A, B, C, of circumconics
X(55303) = radical center of circles (A, d(X(63),BC)), ...
X(55303) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 581, 578}

X(55304) = X(3)X(1033)∩X(30)X(155)

Barycentrics    2*a^16+(b^2-c^2)^8-7*a^14*(b^2+c^2)-a^2*(b^2-c^2)^6*(b^2+c^2)+a^12*(b^4+38*b^2*c^2+c^4)-a^8*(b^2-c^2)^2*(55*b^4+114*b^2*c^2+55*c^4)+a^10*(29*b^6-45*b^4*c^2-45*b^2*c^4+29*c^6)+a^6*(b^2-c^2)^2*(43*b^6+101*b^4*c^2+101*b^2*c^4+43*c^6)-a^4*(b^2-c^2)^2*(13*b^8+20*b^6*c^2+62*b^4*c^4+20*b^2*c^6+13*c^8) : :

X(55304) lies on these lines: {3, 1033}, {5, 1073}, {30, 155}, {140, 14363}, {578, 41369}, {1620, 16303}, {1990, 52543}, {5656, 13155}, {5709, 47848}, {7330, 47850}, {13157, 40686}, {14216, 15238}, {15644, 53795}

X(55304) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1217), X(3344)}}
X(55304) = radical center of circles (A, d(X(64),BC)), ...
X(55304) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1249, 3346, 3}

X(55305) = X(1)X(6922)∩X(3)X(1610)

Barycentrics    2*a^10-6*a^9*(b+c)+14*a^7*(b-c)^2*(b+c)-(b-c)^6*(b+c)^4+4*a*(b-c)^4*(b+c)^3*(b^2-b*c+c^2)+a^8*(b^2+16*b*c+c^2)-2*a^2*(b-c)^4*(b+c)^2*(2*b^2-5*b*c+2*c^2)-2*a^5*(b-c)^2*(3*b^3-13*b^2*c-13*b*c^2+3*c^3)-2*a^6*(7*b^4+5*b^3*c-28*b^2*c^2+5*b*c^3+7*c^4)-2*a^3*(b-c)^2*(3*b^5+11*b^4*c-6*b^3*c^2-6*b^2*c^3+11*b*c^4+3*c^5)+2*a^4*(8*b^6-13*b^5*c-20*b^4*c^2+34*b^3*c^3-20*b^2*c^4-13*b*c^5+8*c^6) : :

X(55305) lies on these lines: {1, 6922}, {3, 1610}, {10, 55300}, {944, 1260}, {952, 6737}, {1864, 10572}, {6827, 37730}, {31788, 37281}

X(55305) = radical center of circles (A, d(X(65),BC)), ...

X(55306) = X(3)X(1196)∩X(30)X(143)

Barycentrics    a^2*(a^10*(b^2+c^2)+a^2*(b^2-c^2)^2*(b^2+c^2)^3-a^8*(b^4+4*b^2*c^2+c^4)-2*a^6*(b^6-7*b^4*c^2-7*b^2*c^4+c^6)+2*a^4*(b^8-8*b^6*c^2-14*b^4*c^4-8*b^2*c^6+c^8)-(b^2-c^2)^2*(b^8-2*b^6*c^2+10*b^4*c^4-2*b^2*c^6+c^8)) : :
X(55306) = -X[5562]+3*X[32986], X[5889]+3*X[33272]

X(55306) lies on these lines: {3, 1196}, {30, 143}, {511, 2549}, {2782, 14913}, {5140, 9744}, {5562, 32986}, {5889, 33272}, {5907, 37242}, {5943, 35930}, {7739, 44495}, {9729, 14135}, {11286, 11695}, {11287, 11793}, {19161, 44526}, {40250, 46847}

X(55306) = midpoint of X(i) and X(j) for these {i,j}: {19161, 44526}
X(55306) = reflection of X(i) in X(j) for these {i,j}: {5907, 37242}
X(55306) = radical center of circles (A, d(X(69),BC)), ...

X(55307) = X(3)X(1612)∩X(389)X(5762)

Barycentrics    2*a^10-2*a^9*(b+c)-(b-c)^6*(b+c)^4-3*a^8*(b^2+c^2)+2*a^3*(b-c)^2*(b+c)^3*(b^2+c^2)-2*a^6*(b-c)^2*(b^2+3*b*c+c^2)-2*a^2*b*c*(b^2-c^2)^2*(3*b^2-2*b*c+3*c^2)+6*a^7*(b^3+b^2*c+b*c^2+c^3)+2*a^4*(b-c)^2*(2*b^4+7*b^3*c+6*b^2*c^2+7*b*c^3+2*c^4)-2*a^5*(3*b^5+3*b^4*c+2*b^3*c^2+2*b^2*c^3+3*b*c^4+3*c^5) : :

X(55307) lies on these lines: {3, 1612}, {389, 5762}, {517, 55305}, {2834, 12675}, {3663, 19904}, {9729, 29243}, {9825, 29010}, {11745, 29069}, {17704, 29339}

X(55307) = radical center of circles (A, d(X(72),BC)), ...

X(55308) = X(2)X(6070)∩X(3)X(31378)

Barycentrics    2*a^12-4*a^10*(b^2+c^2)-2*a^8*(b^4-8*b^2*c^2+c^4)+(b^2-c^2)^4*(b^4+b^2*c^2+c^4)-a^2*(b^2-c^2)^2*(b^6-6*b^4*c^2-6*b^2*c^4+c^6)+a^6*(9*b^6-13*b^4*c^2-13*b^2*c^4+9*c^6)-a^4*(5*b^8+4*b^6*c^2-20*b^4*c^4+4*b^2*c^6+5*c^8) : :

X(55308) lies on these lines: {2, 6070}, {3, 31378}, {30, 15152}, {110, 3258}, {113, 14934}, {125, 14611}, {146, 38701}, {477, 1553}, {511, 16319}, {523, 5972}, {542, 3154}, {632, 18285}, {1138, 38677}, {2072, 34147}, {2777, 47084}, {3090, 5627}, {3292, 47348}, {5609, 16340}, {5642, 7471}, {5663, 31379}, {6723, 12079}, {7480, 14920}, {10272, 16168}, {11064, 47148}, {11800, 12052}, {14643, 25641}, {15063, 36164}, {16163, 46045}, {16760, 47200}, {20957, 32609}, {23583, 44560}, {30714, 36184}, {34150, 36518}, {35282, 46634}, {38729, 40630}, {38793, 46632}, {44234, 44674}

X(55308) = midpoint of X(i) and X(j) for these {i,j}: {110, 3258}, {113, 14934}, {125, 14611}, {11064, 47148}, {12079, 30221}, {15063, 36164}, {16163, 46045}, {3292, 47348}, {30714, 36184}, {477, 1553}, {5609, 16340}, {6070, 14480}
X(55308) = reflection of X(i) in X(j) for these {i,j}: {11800, 12052}, {12079, 6723}, {22104, 5972}, {5972, 31945}
X(55308) = complement of X(6070)
X(55308) = X(i)-complementary conjugate of X(j) for these {i, j}: {1101, 25641}, {30528, 21253}
X(55308) = radical center of circles (A, d(X(74),BC)), ...
X(55308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14480, 6070}, {523, 31945, 5972}, {523, 5972, 22104}, {5609, 45694, 16340}

X(55309) = X(3)X(33786)∩X(7709)X(9292)

Barycentrics    a^2*(-2*b^6*c^6*(b^2-c^2)^2+a^10*(b^6+c^6)+a^8*(-3*b^8+3*b^6*c^2+8*b^4*c^4+3*b^2*c^6-3*c^8)+a^6*(3*b^10-6*b^8*c^2-5*b^6*c^4-5*b^4*c^6-6*b^2*c^8+3*c^10)-a^4*(b^12-3*b^10*c^2+11*b^8*c^4+12*b^6*c^6+11*b^4*c^8-3*b^2*c^10+c^12)) : :
X(55309) = X[6241]+3*X[22678]

X(55309) lies on these lines: {3, 33786}, {6241, 22678}, {7709, 9292}, {9821, 40254}, {15072, 40253}, {32516, 53797}

X(55309) = radical center of circles (A, d(X(76),BC)), ...

X(55310) = X(3)X(17054)∩X(57)X(389)

Barycentrics    a*(a^9-a^8*(b+c)-(b-c)^6*(b+c)^3+a^7*(-3*b^2+4*b*c-3*c^2)-2*a*b*c*(b^2-c^2)^2*(2*b^2-3*b*c+2*c^2)+4*a^6*(b^3+c^3)+4*a^2*(b-c)^4*(b^3+2*b^2*c+2*b*c^2+c^3)-a^3*(b-c)^2*(b^4-10*b^3*c-6*b^2*c^2-10*b*c^3+c^4)+3*a^5*(b^4-4*b^3*c+4*b^2*c^2-4*b*c^3+c^4)-6*a^4*(b^5-b^4*c-b*c^4+c^5)) : :

X(55310) lies on these lines: {3, 17054}, {57, 389}, {578, 3752}, {2999, 37505}, {3359, 55287}, {9940, 55303}, {37560, 55166}

X(55310) = radical center of circles (A, d(X(78),BC)), ...

X(55311) = X(1)X(945)∩X(3)X(223)

Barycentrics    a*(a^9-a^8*(b+c)-(b-c)^6*(b+c)^3+8*a^3*(b^2-c^2)^2*(b^2+c^2)+4*a^6*(b^3+c^3)+4*a^2*(b-c)^4*(b^3+2*b^2*c+2*b*c^2+c^3)+a^5*(-6*b^4+4*b^2*c^2-6*c^4)-a*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4)-6*a^4*(b^5-b^4*c-b*c^4+c^5)) : :

X(55311) lies on these lines: {1, 945}, {3, 223}, {40, 1745}, {57, 389}, {102, 21147}, {282, 6918}, {513, 49171}, {517, 1490}, {610, 37623}, {1427, 9786}, {1697, 55287}, {1750, 1872}, {1753, 2635}, {1763, 5709}, {2184, 5777}, {2817, 6261}, {3149, 14557}, {3465, 7982}, {3468, 3576}, {3601, 55303}, {5908, 19541}, {7580, 52097}, {9121, 22770}, {15951, 37531}, {16389, 49163}, {20764, 40212}, {22350, 36986}, {39585, 51759}

X(55311) = intersection, other than A, B, C, of circumconics
X(55311) = radical center of circles (A, d(X(84),BC)), ...

X(55312) = X(2)X(6071)∩X(99)X(2679)

Barycentrics    a^2*(2*a^8*b^2*c^2+a^6*(b^6-5*b^4*c^2-5*b^2*c^4+c^6)+b^2*c^2*(b^8+c^8)-a^4*(b^8-6*b^6*c^2-2*b^4*c^4-6*b^2*c^6+c^8)-a^2*(3*b^8*c^2+b^6*c^4+b^4*c^6+3*b^2*c^8)) : :

X(55312) lies on these lines: {2, 6071}, {99, 2679}, {511, 6390}, {512, 620}, {2698, 6072}, {3111, 7820}, {5976, 32484}, {6786, 12833}, {7891, 38527}, {8724, 33755}, {14001, 34238}, {14113, 34383}, {15561, 33330}, {33512, 51427}

X(55312) = midpoint of X(i) and X(j) for these {i,j}: {2698, 6072}, {5976, 32484}, {6071, 14509}, {99, 2679}
X(55312) = reflection of X(i) in X(j) for these {i,j}: {22103, 620}
X(55312) = complement of X(6071)
X(55312) = X(i)-complementary conjugate of X(j) for these {i, j}: {24037, 33330}, {46142, 24040}
X(55312) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2143), X(38241)}}
X(55312) = radical center of circles (A, d(X(98),BC)), ...
X(55312) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14509, 6071}, {512, 620, 22103}

X(55313) = X(2)X(6072)∩X(3)X(33704)

Barycentrics    a^2*(2*a^12*b^2*c^2+a^10*(b^6-5*b^4*c^2-5*b^2*c^4+c^6)-a^2*b^2*c^2*(b^2-c^2)^2*(5*b^6-b^4*c^2-b^2*c^4+5*c^6)+a^8*(-3*b^8+8*b^6*c^2+2*b^4*c^4+8*b^2*c^6-3*c^8)+b^2*c^2*(b^2-c^2)^2*(b^8-4*b^6*c^2+4*b^4*c^4-4*b^2*c^6+c^8)+a^6*(3*b^10-12*b^8*c^2+5*b^6*c^4+5*b^4*c^6-12*b^2*c^8+3*c^10)-a^4*(b^12-11*b^10*c^2+15*b^8*c^4-12*b^6*c^6+15*b^4*c^8-11*b^2*c^10+c^12)) : :
X(55313) = X[31513]+3*X[34473], -X[33330]+3*X[38224]

X(55313) lies on these lines: {2, 6072}, {3, 33704}, {98, 2679}, {230, 511}, {512, 11623}, {2698, 6071}, {2782, 55312}, {6784, 13137}, {7755, 31850}, {31513, 34473}, {33330, 38224}, {40254, 41330}, {44127, 53766}

X(55313) = midpoint of X(i) and X(j) for these {i,j}: {2698, 6071}, {6072, 14510}, {98, 2679}
X(55313) = reflection of X(i) in X(j) for these {i,j}: {22103, 6036}
X(55313) = complement of X(6072)
X(55313) = radical center of circles (A, d(X(99),BC)), ...
X(55313) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14510, 6072}, {511, 6036, 22103}, {2698, 14651, 6071}

X(55314) = X(2)X(6073)∩X(3)X(37815)

Barycentrics    2*a^10-4*a^9*(b+c)-18*a^5*(b-c)^4*(b+c)-2*a*(b-c)^6*(b+c)^3+(b-c)^6*(b+c)^4-4*a^8*(b^2-5*b*c+c^2)+2*a^3*(b-c)^4*(5*b^3+b^2*c+b*c^2+5*c^3)+2*a^7*(7*b^3-9*b^2*c-9*b*c^2+7*c^3)-a^6*(b^4+34*b^3*c-72*b^2*c^2+34*b*c^3+c^4)-a^2*(b^2-c^2)^2*(5*b^4-10*b^3*c+12*b^2*c^2-10*b*c^3+5*c^4)+a^4*(b-c)^2*(7*b^4+20*b^3*c-30*b^2*c^2+20*b*c^3+7*c^4) : :
X(55314) = X[31512]+3*X[38693]

X(55314) lies on these lines: {2, 6073}, {3, 37815}, {104, 3259}, {149, 38707}, {513, 20418}, {517, 1387}, {953, 6075}, {1125, 40531}, {1484, 38617}, {2818, 14115}, {10246, 34232}, {11373, 55310}, {31512, 38693}, {39756, 43043}

X(55314) = midpoint of X(i) and X(j) for these {i,j}: {104, 3259}, {1484, 38617}, {6073, 14511}, {953, 6075}
X(55314) = reflection of X(i) in X(j) for these {i,j}: {22102, 6713}
X(55314) = complement of X(6073)
X(55314) = radical center of circles (A, d(X(100),BC)), ...
X(55314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14511, 6073}, {517, 6713, 22102}

X(55315) = X(2)X(52108)∩X(109)X(10017)

Barycentrics    2*a^12-4*a^11*(b+c)+(b-c)^6*(b+c)^4*(b^2+c^2)-2*a^10*(b^2-8*b*c+c^2)-6*a^2*b*(b-c)^4*c*(b+c)^2*(2*b^2-b*c+2*c^2)+4*a^9*(3*b^3-4*b^2*c-4*b*c^2+3*c^3)-2*a^7*(b-c)^2*(5*b^3-18*b^2*c-18*b*c^2+5*c^3)-2*a*(b-c)^4*(b+c)^3*(b^4-3*b^3*c+2*b^2*c^2-3*b*c^3+c^4)+2*a^6*(b-c)^2*(9*b^4+8*b^3*c-25*b^2*c^2+8*b*c^3+9*c^4)-a^8*(9*b^4+22*b^3*c-64*b^2*c^2+22*b*c^3+9*c^4)-2*a^5*(b-c)^2*(b^5+22*b^4*c-9*b^3*c^2-9*b^2*c^3+22*b*c^4+c^5)+2*a^3*(b-c)^4*(3*b^5+10*b^4*c+3*b^3*c^2+3*b^2*c^3+10*b*c^4+3*c^5)-2*a^4*(b-c)^2*(5*b^6-10*b^5*c-12*b^4*c^2+22*b^3*c^3-12*b^2*c^4-10*b*c^5+5*c^6) : :

X(55315) lies on these lines: {2, 52108}, {109, 10017}, {522, 6718}, {952, 39762}, {1155, 1785}, {2734, 52109}, {15325, 51616}, {24025, 40531}, {39546, 55314}

X(55315) = midpoint of X(i) and X(j) for these {i,j}: {109, 10017}, {2734, 52109}
X(55315) = reflection of X(i) in X(j) for these {i,j}: {40558, 6718}
X(55315) = complement of X(52108)
X(55315) = X(i)-complementary conjugate of X(j) for these {i, j}: {24027, 39535}
X(55315) = radical center of circles (A, d(X(102),BC)), ...
X(55315) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {522, 6718, 40558}

X(55316) = X(2)X(14505)∩X(101)X(1566)

Barycentrics    2*a^8-4*a^7*(b+c)+(b-c)^4*(b+c)^2*(b^2+c^2)+2*a^6*(b^2+4*b*c+c^2)-4*a^5*(b^3+c^3)-2*a*(b-c)^4*(b^3+2*b^2*c+2*b*c^2+c^3)+a^4*(9*b^4-6*b^3*c-4*b^2*c^2-6*b*c^3+9*c^4)-6*a^3*(b^5-b^3*c^2-b^2*c^3+c^5)+2*a^2*(b^6-2*b^4*c^2+2*b^3*c^3-2*b^2*c^4+c^6) : :
X(55316) = -X[34805]+3*X[51406]

X(55316) lies on these lines: {2, 14505}, {101, 1566}, {514, 6710}, {952, 44012}, {2724, 6074}, {33331, 38764}, {34805, 51406}

X(55316) = midpoint of X(i) and X(j) for these {i,j}: {101, 1566}, {2724, 6074}
X(55316) = reflection of X(i) in X(j) for these {i,j}: {40554, 6710}
X(55316) = complement of X(14505)
X(55316) = X(i)-complementary conjugate of X(j) for these {i, j}: {1110, 33331}
X(55316) = radical center of circles (A, d(X(103),BC)), ...
X(55316) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {514, 6710, 40554}

X(55317) = X(2)X(6075)∩X(100)X(3259)

Barycentrics    2*a^6+12*a^4*b*c-4*a^5*(b+c)+(b-c)^4*(b+c)^2-2*a*(b-c)^2*(b^3-3*b^2*c-3*b*c^2+c^3)+2*a^3*(3*b^3-5*b^2*c-5*b*c^2+3*c^3)-a^2*(3*b^4+6*b^3*c-20*b^2*c^2+6*b*c^3+3*c^4) : :

X(55317) lies on these lines: {2, 6075}, {100, 3259}, {153, 38707}, {513, 3035}, {517, 6745}, {908, 53792}, {952, 55314}, {953, 6073}, {1054, 43909}, {1145, 53799}, {1319, 5121}, {2810, 14115}, {3814, 37370}, {5123, 50752}, {5972, 40531}, {6550, 10196}, {7336, 17719}, {10428, 17567}, {11698, 38617}, {17044, 44432}, {29349, 44013}, {31841, 38752}, {34123, 52478}, {40540, 47778}, {51419, 53801}

X(55317) = midpoint of X(i) and X(j) for these {i,j}: {100, 3259}, {11698, 38617}, {6075, 14513}, {953, 6073}
X(55317) = reflection of X(i) in X(j) for these {i,j}: {22102, 3035}
X(55317) = complement of X(6075)
X(55317) = X(i)-complementary conjugate of X(j) for these {i, j}: {765, 31841}
X(55317) = radical center of circles (A, d(X(104),BC)), ...
X(55317) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14513, 6075}, {513, 3035, 22102}

X(55318) = X(2)X(52109)∩X(102)X(10017)

Barycentrics    2*a^16-4*a^15*(b+c)+(b-c)^8*(b+c)^6*(b^2+c^2)-2*a^14*(b^2-8*b*c+c^2)+4*a^13*(4*b^3-5*b^2*c-5*b*c^2+4*c^3)-2*a^11*(b-c)^2*(9*b^3-34*b^2*c-34*b*c^2+9*c^3)-2*a*(b-c)^6*(b+c)^5*(b^4-3*b^3*c+2*b^2*c^2-3*b*c^3+c^4)+6*a^10*(b-c)^2*(9*b^4+8*b^3*c-17*b^2*c^2+8*b*c^3+9*c^4)-a^12*(19*b^4+26*b^3*c-92*b^2*c^2+26*b*c^3+19*c^4)-2*a^9*(b-c)^2*(5*b^5+74*b^4*c-29*b^3*c^2-29*b^2*c^3+74*b*c^4+5*c^5)-2*a^2*(b^2-c^2)^4*(3*b^6-2*b^5*c+2*b^4*c^2-2*b^3*c^3+2*b^2*c^4-2*b*c^5+3*c^6)+2*a^3*(b-c)^4*(b+c)^3*(7*b^6-17*b^5*c+21*b^4*c^2-30*b^3*c^3+21*b^2*c^4-17*b*c^5+7*c^6)+a^4*(b-c)^4*(b+c)^2*(7*b^6+56*b^5*c-37*b^4*c^2+124*b^3*c^3-37*b^2*c^4+56*b*c^5+7*c^6)-a^8*(b-c)^2*(55*b^6-68*b^5*c-83*b^4*c^2+248*b^3*c^3-83*b^2*c^4-68*b*c^5+55*c^6)-4*a^5*(b-c)^4*(9*b^7+17*b^6*c+3*b^5*c^2+27*b^4*c^3+27*b^3*c^4+3*b^2*c^5+17*b*c^6+9*c^7)+4*a^7*(b-c)^2*(10*b^7+23*b^6*c-43*b^5*c^2+38*b^4*c^3+38*b^3*c^4-43*b^2*c^5+23*b*c^6+10*c^7)+2*a^6*(b-c)^2*(9*b^8-58*b^7*c+26*b^6*c^2+62*b^5*c^3-126*b^4*c^4+62*b^3*c^5+26*b^2*c^6-58*b*c^7+9*c^8) : :

X(55318) lies on these lines: {2, 52109}, {102, 10017}, {515, 6711}, {1319, 55314}, {2734, 52108}, {2818, 55315}, {38776, 39535}

X(55318) = midpoint of X(i) and X(j) for these {i,j}: {102, 10017}, {2734, 52108}
X(55318) = reflection of X(i) in X(j) for these {i,j}: {40558, 6711}
X(55318) = complement of X(52109)
X(55318) = radical center of circles (A, d(X(109),BC)), ...
X(55318) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {515, 6711, 40558}

X(55319) = X(2)X(1553)∩X(3)X(30715)

Barycentrics    2*a^16-4*a^14*(b^2+c^2)+(b^2-c^2)^6*(b^4+b^2*c^2+c^4)-4*a^12*(2*b^4-7*b^2*c^2+2*c^4)-7*a^2*(b^2-c^2)^4*(b^6+2*b^4*c^2+2*b^2*c^4+c^6)-a^6*(b^2-c^2)^2*(2*b^6-63*b^4*c^2-63*b^2*c^4+2*c^6)+a^10*(29*b^6-33*b^4*c^2-33*b^2*c^4+29*c^6)+a^4*(b^2-c^2)^2*(14*b^8-11*b^6*c^2-48*b^4*c^4-11*b^2*c^6+14*c^8)-a^8*(25*b^8+28*b^6*c^2-108*b^4*c^4+28*b^2*c^6+25*c^8) : :
X(55319) = -X[399]+3*X[31378], X[3448]+3*X[38701], -X[7471]+3*X[38727], -X[14989]+5*X[15081], -X[36193]+5*X[38728]

X(55319) lies on these lines: {2, 1553}, {3, 30715}, {30, 6699}, {74, 3258}, {125, 34150}, {187, 6128}, {399, 31378}, {477, 6070}, {523, 20417}, {542, 47084}, {2133, 52546}, {2777, 3154}, {3233, 48378}, {3448, 38701}, {5663, 31379}, {5667, 43911}, {6000, 16319}, {6053, 31945}, {6723, 36169}, {7471, 38727}, {10193, 36178}, {10264, 38610}, {10990, 46045}, {11807, 12052}, {12041, 16340}, {14356, 47050}, {14934, 16003}, {14989, 15081}, {15041, 20957}, {15055, 17511}, {15059, 36172}, {15061, 25641}, {16111, 36184}, {20396, 21316}, {25563, 36179}, {36193, 38728}, {47220, 50401}

X(55319) = midpoint of X(i) and X(j) for these {i,j}: {125, 36164}, {10264, 38610}, {1553, 14508}, {10990, 46045}, {12041, 16340}, {14934, 16003}, {16111, 36184}, {477, 6070}, {74, 3258}
X(55319) = reflection of X(i) in X(j) for these {i,j}: {11807, 12052}, {21316, 20396}, {22104, 6699}, {3233, 48378}, {36169, 6723}, {6053, 31945}, {55308, 31379}
X(55319) = complement of X(1553)
X(55319) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2133), X(41522)}}
X(55319) = radical center of circles (A, d(X(110),BC)), ...
X(55319) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14508, 1553}, {30, 6699, 22104}, {74, 3258, 32417}, {5663, 31379, 55308}

X(55320) = X(3)X(11451)∩X(143)X(15692)

Barycentrics    a^8*(b^2+c^2)+a^6*(-3*b^4+50*b^2*c^2-3*c^4)-a^2*(b^2-c^2)^2*(b^4-5*b^2*c^2+c^4)+a^4*(3*b^6-58*b^4*c^2-58*b^2*c^4+3*c^6) : :
X(55320) = 49*X[3]+15*X[11451], X[143]+15*X[15692], -X[5876]+33*X[15718], X[12006]+7*X[44682], -X[14128]+9*X[41983], X[44863]+3*X[46332]

X(55320) lies on these lines: {3, 11451}, {143, 15692}, {389, 12100}, {548, 12046}, {549, 11381}, {631, 11017}, {3523, 15060}, {3524, 32142}, {3530, 5663}, {3917, 11592}, {5876, 15718}, {5889, 15700}, {6101, 15717}, {10299, 37484}, {11812, 46849}, {12006, 44682}, {12290, 33879}, {14128, 41983}, {14869, 32062}, {15026, 15705}, {15759, 18874}, {19711, 45957}, {44863, 46332}

X(55320) = midpoint of X(i) and X(j) for these {i,j}: {548, 12046}
X(55320) = radical center of circles (A, d(X(140),BC)), ...





leftri  Touchpoints conics: X(55321) - X(55384)  rightri

This preamble and centers X(ini)-X(end) were contributed by César Eliud Lozada, August 5, 2023.

Let's denote as q(P) the circumconic of ABC with perspector P with respect to ABC.

Let's consider two circumconics q' = q(P') and q" = q(P"). If P' and P" lie both in the interior of ABC, these conics have four real intersections {A, B, C, D} (D being the tripole of the line P'P") and four common tangents. Assume P' = U' : V' : W' and P" = U" : V" : W" (trilinears, for simpler expressions). The following results were algebraically found:

a) The common tangents of q' and q" are:

  1. tA = (v' w" - v" w')2 : (u' w" + w' u")2 : (u' v" + v' u")2
  2. tB = (v' w" + v" w')2 : (u' w" - w' u")2 : (u' v" + v' u")2
  3. tC = (v' w" + v" w')2 : (u' w" + w' u")2 : (u' v" - v' u")2
  4. tD = (v' w" - v" w')2 : (u' w" - w' u")2 : (u' v" - v' u")2.
where u' = sqrt(U'), v' = sqrt(V'), w' = sqrt(W') and u" = sqrt(U"), v" = sqrt(V"), w" = sqrt(W").

It can be conjectured that tA, tB, tC, tD are each the closest tangent line to A, B, C, D, respectively.

Note: If P' and P" are triangle centers then tD is a central line, here referred as the D-tangent of q' and q".


b) Let A*B*C* be the triangle bounded by lines tA, tB and tC. Then:

  1. A* = -(u'2 v" w" + u"2 v' w')/(v' w" + v" w') : v' v" : w' w", and cyclically B* and C*.
  2. ABC and A*B*C* are perspective with perspector P* = u' u" : v' v" : w' w"
The triangle A*B*C* is introduced here as the circumscribing triangle of q' and q".


c) Let A', A" be the points at which tA touchs q' and q", respectively, and denote B', B", C', C", D', D" similarly.

  1. A' = u'/(v' w" - v" w') : -v'/(w' u" + w" u') : w'/(u' v" + u" v'),
    B' = u'/(v' w" + v" w') : v'/(w' u" - w" u') : -w'/(u' v" + u" v'),
    C' = -u'/(v' w" + v" w') : v'/(w' u" + w" u') : w'/(u' v" - v' u")
  2. A" = u"/(v' w" - v" w') : v"/(w' u" + w" u') : -w"/(u' v" + u" v'),
    B" = -u"/(v' w" + v" w') : v"/(w' u" - w" u') : w"/(u' v" + u" v'),
    C" = u"/(v' w" + v" w') : -v"/(w' u" + w" u') : w"/(u' v" - v' u")
  3. D' = u'/(v' w" - v" w') : v'/(w' u" - u' w") : w'/(u' v" - v' u"),
    D" = u"/(v' w" - v" w') : v"/(w' u" - u' w") : w"/(u' v" - v' u")

    Note: If P' and P" are triangle centers then D' and D" are also triangle centers.

  4. The eight points A', B', C', D', A", B", C", D" lie on a conic 𝒞(q', q"), here named the touchpoints conic of q' and q", and having:

    • trilinear equation: ∑ [ ((v' w")2 - (v" w')2)2 u2 + 2 (u'2 v"2 + u"2 v'2) (u'2 w"2 + u"2 w'2) v w ] = 0
    • center: O* = u'2 u"2 (v'2 w"2 + v"2 w'2) ((u'4 v"2 w"2 + u"4 v'2 w'2) a - v'2 v"2 (u'2 w"2 + u"2 w'2) b - w'2 w"2 (u'2 v"2 + u"2 v'2) c) : :
    • perspector: Q* = u'2 u"2 (v'2 w"2 + v"2 w'2) : : (This perspector is the crosspoint of P' and P")

    𝒞(q', q") results to be the bicevian conic of P' and P" with respect to the circumscribing triangle A*B*C* of q' and q".

In centers X(55321) - X(55384), an unnamed circumconic with perspector P will be denoted as CCP(P), instead of circumconic with perspector P (just for shortening the length of its name). Please remember that the perspectors of the Steiner circumellipse, the MacBeath circumconic and the circumcircle of ABC are X(2), X(3) and X(6), respectively.

A sketch of this configuration and a table of related centers can be downloaded from here.

underbar

X(55321) = TOUCHPOINT OF CCP( X(1) ) AND THE D-TANGENT TO THE STEINER CIRCUMELLIPSE

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

X(55321) lies on these lines: {2, 364}, {9, 20534}, {88, 40378}, {100, 55326}, {1156, 4180}, {20332, 52866}

X(55321) = X(i)-aleph conjugate of-X(j) for these (i, j): (4181, 2958), (40378, 1052), (55322, 9), (55325, 43), (55326, 1740), (55376, 10860), (55377, 2951)
X(55321) = X(190)-Ceva conjugate of-X(55322)
X(55321) = X(20527)-Dao conjugate of-X(514)
X(55321) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4180, 522), (20779, 1459), (40378, 514), (52866, 649), (55322, 18297), (55325, 366), (55326, 1), (55377, 8)
X(55321) = X(366)-zayin conjugate of-X(649)
X(55321) = trilinear pole of line {1, 366}
X(55321) = pole of line {55322, 55377} wrt Steiner circumellipse
X(55321) = pole of line {365, 366} wrt Yff parabola
X(55321) = barycentric product of X(i) and X(j) for these {i, j}: {7, 55377}, {75, 55326}, {190, 40378}, {366, 55322}, {664, 4180}
X(55321) = trilinear product of X(i) and X(j) for these {i, j}: {2, 55326}, {57, 55377}, {100, 40378}, {365, 55322}, {366, 55325}
X(55321) = trilinear quotient X(i)/X(j) for these (i, j): (4180, 650), (20779, 22383), (40378, 513), (52866, 667)

X(55322) = TOUCHPOINT OF THE STEINER CIRCUMELLIPSE AND THE D-TANGENT TO CCP( X(1) )

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

X(55322) lies on Steiner circumellipse and these lines: {1, 40383}, {190, 55325}, {192, 40375}, {367, 3227}, {903, 20527}, {1121, 4181}, {3226, 20664}, {18297, 40374}, {18825, 52865}, {18827, 20682}

X(55322) = X(190)-Ceva conjugate of-X(55321)
X(55322) = X(40378)-Dao conjugate of-X(514)
X(55322) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (367, 513), (4181, 522), (20527, 514), (20664, 649), (20682, 661), (20751, 1459), (52865, 667), (55321, 366), (55325, 1), (55326, 365), (55376, 8), (55377, 4182)
X(55322) = X(365)-zayin conjugate of-X(649)
X(55322) = trilinear pole of line {2, 366}
X(55322) = touchpoint of Steiner circumellipse and line {55321, 55322}
X(55322) = pole of line {366, 18297} wrt Yff parabola
X(55322) = barycentric product of X(i) and X(j) for these {i, j}: {7, 55376}, {75, 55325}, {190, 20527}, {367, 668}, {664, 4181}
X(55322) = trilinear product of X(i) and X(j) for these {i, j}: {2, 55325}, {57, 55376}, {99, 20682}, {100, 20527}, {190, 367}
X(55322) = trilinear quotient X(i)/X(j) for these (i, j): (367, 649), (4181, 650), (20527, 513), (20664, 667), (20682, 512)

X(55323) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(1) ) AND THE MACBEATH CIRCUMCONIC

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

X(55323) lies on these lines: {1, 14749}, {6, 41}, {9, 37523}, {37, 1409}, {65, 8898}, {81, 20028}, {86, 651}, {109, 55100}, {222, 226}, {225, 608}, {284, 1415}, {572, 22118}, {573, 16678}, {603, 2268}, {992, 5433}, {1108, 2288}, {1195, 8608}, {1319, 2300}, {1388, 21769}, {1397, 44115}, {1950, 36075}, {2003, 40153}, {2092, 2594}, {2182, 14597}, {2197, 2245}, {2278, 52411}, {2305, 5172}, {2975, 46879}, {5114, 52410}, {5783, 37660}, {5930, 12573}, {8609, 21770}, {14829, 17074}, {16679, 51657}, {19701, 34048}, {20986, 55349}, {21061, 37558}, {26580, 26625}, {46882, 54339}, {51645, 52023}, {52087, 52139}, {54359, 54400}

X(55323) = isogonal conjugate of X(46880)
X(55323) = cross-difference of every pair of points on the line X(522)X(14310)
X(55323) = crosspoint of X(59) and X(6648)
X(55323) = crosssum of X(i) and X(j) for these {i,j}: {11, 52326}, {37, 51870}, {46880, 46880}
X(55323) = X(21061)-beth conjugate of-X(21061)
X(55323) = X(i)-Ceva conjugate of-X(j) for these (i, j): (81, 65), (651, 21173), (1476, 1402), (17074, 37558), (37558, 52139)
X(55323) = X(i)-Dao conjugate of-X(j) for these (i, j): (3, 46880), (12, 321), (478, 20028), (1193, 3687), (21796, 20895), (34589, 4391), (40590, 54121), (40611, 2051), (53566, 3910)
X(55323) = X(i)-isoconjugate of-X(j) for these {i, j}: {8, 53083}, {9, 20028}, {21, 2051}, {284, 54121}, {312, 52150}, {333, 34434}, {2185, 51870}, {3687, 40453}
X(55323) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (56, 20028), (65, 54121), (181, 51870), (572, 333), (604, 53083), (1397, 52150), (1400, 2051), (1402, 34434), (2975, 314), (11109, 44130), (14829, 28660), (14973, 3701), (17074, 274), (17751, 3596), (20617, 1441), (20986, 21), (21061, 312), (21173, 18155), (22118, 1812), (37558, 75), (51662, 693), (52087, 3687), (52139, 8), (52357, 313), (52358, 76), (53566, 34387), (55362, 17183)
X(55323) = X(4560)-zayin conjugate of-X(650)
X(55323) = pole of line {56, 24220} wrt circumhyperbola dual of Yff parabola
X(55323) = pole of line {1402, 12723} wrt Feuerbach circumhyperbola
X(55323) = pole of line {333, 46879} wrt Stammler hyperbola
X(55323) = pole of line {6589, 21186} wrt Steiner inellipse
X(55323) = pole of line {28660, 46880} wrt Steiner-Wallace hyperbola
X(55323) = barycentric product of X(i) and X(j) for these {i, j}: {1, 37558}, {6, 52358}, {7, 52139}, {21, 20617}, {37, 17074}
X(55323) = trilinear product of X(i) and X(j) for these {i, j}: {6, 37558}, {31, 52358}, {42, 17074}, {56, 21061}, {57, 52139}
X(55323) = trilinear quotient X(i)/X(j) for these (i, j): (56, 53083), (57, 20028), (65, 2051), (226, 54121), (572, 21)
X(55323) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (37, 1409, 4559), (73, 1400, 40590), (2067, 6502, 23361)

X(55324) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(1) ) AND CCP( X(4) )

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

X(55324) lies on these lines: {6, 19}, {9, 47345}, {37, 2358}, {71, 53009}, {108, 37508}, {109, 41364}, {196, 41342}, {573, 14257}, {1214, 1767}, {2357, 53011}, {3213, 22341}, {32431, 38949}, {34030, 34266}

X(55324) = X(i)-Ceva conjugate of-X(j) for these (i, j): (40444, 225), (41083, 73)

X(55325) = TOUCHPOINT OF CCP( X(1) ) AND THE D-TANGENT TO THE CIRCUMCIRCLE

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

X(55325) lies on these lines: {6, 40375}, {88, 367}, {190, 55322}, {673, 20527}, {897, 20682}, {4166, 40374}, {4181, 20751}, {20332, 52865}, {20664, 37129}

X(55325) = X(i)-aleph conjugate of-X(j) for these (i, j): (367, 1052), (4180, 2958), (55321, 9), (55322, 63), (55326, 43), (55377, 10860)
X(55325) = X(55376)-beth conjugate of-X(55376)
X(55325) = X(100)-Ceva conjugate of-X(55326)
X(55325) = X(40378)-Dao conjugate of-X(693)
X(55325) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (367, 514), (4181, 4391), (20527, 693), (20664, 513), (20682, 523), (20751, 905), (52865, 649), (55321, 18297), (55322, 75), (55326, 366), (55376, 312)
X(55325) = X(365)-zayin conjugate of-X(513)
X(55325) = trilinear pole of line {1, 364}
X(55325) = barycentric product of X(i) and X(j) for these {i, j}: {1, 55322}, {57, 55376}, {99, 20682}, {100, 20527}, {190, 367}
X(55325) = trilinear product of X(i) and X(j) for these {i, j}: {6, 55322}, {56, 55376}, {100, 367}, {101, 20527}, {109, 4181}
X(55325) = trilinear quotient X(i)/X(j) for these (i, j): (367, 513), (4181, 522), (20527, 514), (20664, 649), (20682, 661)

X(55326) = TOUCHPOINT OF THE CIRCUMCIRCLE AND THE D-TANGENT TO CCP( X(1) )

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

X(55326) lies on circumcircle and these lines: {1, 20673}, {35, 20695}, {55, 364}, {100, 55321}, {104, 4180}, {105, 40378}, {739, 52866}

X(55326) = X(55377)-beth conjugate of-X(55377)
X(55326) = X(100)-Ceva conjugate of-X(55325)
X(55326) = X(20527)-Dao conjugate of-X(693)
X(55326) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4180, 4391), (20779, 905), (40378, 693), (52866, 513), (55321, 75), (55325, 18297), (55377, 312)
X(55326) = X(366)-zayin conjugate of-X(513)
X(55326) = trilinear pole of line {6, 365}
X(55326) = touchpoint of circumcircle and line {55325, 55326}
X(55326) = barycentric product of X(i) and X(j) for these {i, j}: {1, 55321}, {57, 55377}, {100, 40378}, {365, 55322}, {366, 55325}
X(55326) = trilinear product of X(i) and X(j) for these {i, j}: {6, 55321}, {56, 55377}, {101, 40378}, {109, 4180}, {190, 52866}
X(55326) = trilinear quotient X(i)/X(j) for these (i, j): (4180, 522), (20779, 1459), (40378, 514), (52866, 649)

X(55327) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(1) ) AND CCP( X(7) )

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

X(55327) lies on these lines: {1, 3}, {3730, 9533}, {8545, 53242}

X(55327) = X(23618)-Ceva conjugate of-X(10481)

X(55328) = TOUCHPOINT OF CCP( X(1) ) AND THE D-TANGENT TO CCP( X(7) )

Barycentrics    (a+b-c)*(a-b+c)*(-(b*(b-c)*c)+(b-c)*(a^2-b*c-a*(b+c))*sin(A/2)+a*(a^2+(3*b-2*c)*c-a*(b+c))*sin(B/2)-a*(a^2-a*(b+c)+b*(-2*b+3*c))*sin(C/2)) : :

X(55328) lies on these lines: {7, 173}, {57, 18886}, {88, 14596}, {100, 13444}, {176, 3645}, {177, 1156}, {673, 18888}, {7022, 8078}, {16016, 36101}, {45876, 55331}

X(55328) = cevapoint of X(i) and X(j) for these {i,j}: {174, 10492}, {650, 10500}, {7707, 10495}
X(55328) = X(i)-aleph conjugate of-X(j) for these (i, j): (234, 2957), (13444, 1740), (14596, 1052), (43192, 1742), (55329, 57), (55341, 40), (55342, 2951)
X(55328) = X(658)-Ceva conjugate of-X(55329)
X(55328) = X(10492)-cross conjugate of-X(174)
X(55328) = X(i)-Dao conjugate of-X(j) for these (i, j): (178, 3239), (223, 10492), (10493, 6730)
X(55328) = X(i)-isoconjugate of-X(j) for these {i, j}: {55, 10492}, {259, 10495}, {260, 650}, {7028, 45878}, {45877, 53119}
X(55328) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (57, 10492), (109, 260), (177, 522), (266, 10495), (7707, 6730), (10490, 6728), (13444, 1), (14596, 514), (16012, 3900), (16016, 3239), (18888, 650), (43192, 188), (45874, 53119), (45875, 7028), (45876, 53123), (55329, 4146), (55341, 556), (55342, 8)
X(55328) = X(i)-zayin conjugate of-X(j) for these (i, j): (174, 657), (503, 10495)
X(55328) = trilinear pole of line {1, 167}
X(55328) = barycentric product of X(i) and X(j) for these {i, j}: {7, 55342}, {75, 13444}, {174, 55341}, {177, 664}, {188, 55329}
X(55328) = trilinear product of X(i) and X(j) for these {i, j}: {2, 13444}, {57, 55342}, {100, 14596}, {174, 43192}, {177, 651}
X(55328) = trilinear quotient X(i)/X(j) for these (i, j): (7, 10492), (174, 10495), (177, 650), (178, 6730), (234, 6728)

X(55329) = TOUCHPOINT OF CCP( X(7) ) AND THE D-TANGENT TO CCP( X(1) )

Barycentrics    (a+b-c)*(a-b+c)*(2*b*c*sin(A/2)+a*(-a+b+c-2*c*sin(B/2)-2*b*sin(C/2))) : :

X(55329) lies on these lines: {7, 10491}, {177, 10498}, {178, 52156}, {279, 7022}, {503, 31526}, {555, 2089}, {658, 43192}, {664, 55341}, {934, 10496}, {10490, 34018}

X(55329) = cevapoint of X(i) and X(j) for these {i,j}: {174, 10495}, {177, 10492}, {514, 10499}
X(55329) = X(658)-Ceva conjugate of-X(55328)
X(55329) = X(i)-cross conjugate of-X(j) for these (i, j): (10495, 174), (43192, 55341)
X(55329) = X(i)-Dao conjugate of-X(j) for these (i, j): (223, 10495), (10493, 3900), (16016, 3239)
X(55329) = X(55)-isoconjugate of-X(10495)
X(55329) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (57, 10495), (177, 6730), (178, 3239), (234, 522), (7371, 10492), (7707, 3900), (10490, 650), (13444, 259), (14596, 6728), (43192, 9), (55328, 188), (55341, 8), (55342, 6731)
X(55329) = X(i)-zayin conjugate of-X(j) for these (i, j): (259, 657), (1742, 10495)
X(55329) = trilinear pole of line {7, 174}
X(55329) = barycentric product of X(i) and X(j) for these {i, j}: {7, 55341}, {85, 43192}, {178, 658}, {234, 664}, {555, 55342}
X(55329) = trilinear product of X(i) and X(j) for these {i, j}: {7, 43192}, {57, 55341}, {174, 55328}, {178, 934}, {234, 651}
X(55329) = trilinear quotient X(i)/X(j) for these (i, j): (7, 10495), (178, 3900), (234, 650), (555, 10492), (7707, 657)

X(55330) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(1) ) AND CCP( X(8) )

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

X(55330) lies on these lines: {9, 3057}, {63, 4358}, {573, 3161}, {1697, 45193}, {15273, 21061}

X(55330) = X(333)-Ceva conjugate of-X(6736)
X(55330) = X(21031)-Dao conjugate of-X(226)
X(55330) = barycentric product of X(17183) and X(55375)
X(55330) = trilinear product of X(18163) and X(55375)

X(55331) = TOUCHPOINT OF CCP( X(1) ) AND THE D-TANGENT TO CCP( X(8) )

Barycentrics    a*(-a^2+b^2+c^2+2*b*c*sin(A/2)-2*b*c*sin(B/2)-2*b*c*sin(C/2)) : :

X(55331) lies on these lines: {2, 258}, {8, 164}, {9, 7048}, {63, 16017}, {88, 8126}, {100, 3659}, {145, 8078}, {174, 39121}, {236, 1488}, {1156, 42017}, {2091, 43760}, {16011, 37129}, {43192, 55342}, {45876, 55328}

X(55331) = isotomic conjugate of the anticomplement of X(10492)
X(55331) = anticomplement of X(21623)
X(55331) = cevapoint of X(i) and X(j) for these {i, j}: {258, 10492}, {15997, 45877}
X(55331) = crosssum of X(649) and X(6729)
X(55331) = X(i)-aleph conjugate of-X(j) for these (i, j): (2090, 2957), (3659, 1740), (16015, 1052), (45875, 978), (45876, 57), (55332, 40), (55363, 1742)
X(55331) = X(i)-Ceva conjugate of-X(j) for these (i, j): (190, 55332), (45876, 55342)
X(55331) = X(10492)-cross conjugate of-X(2)
X(55331) = X(i)-Dao conjugate of-X(j) for these (i, j): (2090, 514), (10494, 6732), (21623, 21623)
X(55331) = X(i)-isoconjugate of-X(j) for these {i, j}: {174, 45878}, {266, 45877}, {10492, 42622}
X(55331) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (258, 10492), (259, 45877), (2091, 3676), (3659, 1), (10492, 21623), (10495, 6732), (15997, 6728), (16011, 513), (16015, 514), (42017, 522), (43192, 2089), (45874, 266), (45875, 174), (45876, 4146), (53119, 10495), (55328, 18886), (55332, 556), (55342, 7057), (55363, 188)
X(55331) = X(i)-zayin conjugate of-X(j) for these (i, j): (188, 649), (361, 45877)
X(55331) = trilinear pole of line {1, 188}
X(55331) = perspector of inconic with center X(10492)
X(55331) = pole of line {55332, 55342} wrt Steiner circumellipse
X(55331) = pole of line {174, 188} wrt Yff parabola
X(55331) = barycentric product of X(i) and X(j) for these {i, j}: {75, 3659}, {174, 55332}, {188, 45876}, {190, 16015}, {556, 45875}
X(55331) = trilinear product of X(i) and X(j) for these {i, j}: {2, 3659}, {100, 16015}, {174, 55363}, {188, 45875}, {190, 16011}
X(55331) = trilinear quotient X(i)/X(j) for these (i, j): (188, 45877), (259, 45878), (2090, 6728), (2091, 3669), (7028, 10495)

X(55332) = TOUCHPOINT OF CCP( X(8) ) AND THE D-TANGENT TO CCP( X(1) )

Barycentrics    (a-b)*(a-c)*(sin(B/2)+sin(C/2)) : :

X(55332) lies on these lines: {190, 45875}, {361, 19582}, {556, 7028}, {2090, 4997}, {3699, 55363}, {6731, 53123}, {7048, 21623}, {8707, 45874}, {15997, 36798}, {16018, 30568}, {36805, 41799}

X(55332) = cevapoint of X(188) and X(45877)
X(55332) = X(190)-Ceva conjugate of-X(55331)
X(55332) = X(i)-cross conjugate of-X(j) for these (i, j): (45877, 188), (55363, 45876)
X(55332) = X(i)-Dao conjugate of-X(j) for these (i, j): (1, 45877), (5452, 45878), (16015, 514), (39121, 10492)
X(55332) = X(i)-isoconjugate of-X(j) for these {i, j}: {56, 45877}, {57, 45878}
X(55332) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (9, 45877), (55, 45878), (2090, 514), (3659, 266), (7028, 10492), (15997, 513), (41799, 3669), (42017, 6728), (45874, 56), (45875, 57), (45876, 7), (55331, 174), (55341, 18886), (55342, 2089), (55363, 1)
X(55332) = X(i)-zayin conjugate of-X(j) for these (i, j): (266, 649), (978, 45877)
X(55332) = trilinear pole of line {8, 188}
X(55332) = pole of line {188, 556} wrt Yff parabola
X(55332) = barycentric product of X(i) and X(j) for these {i, j}: {8, 45876}, {75, 55363}, {190, 2090}, {312, 45875}, {556, 55331}
X(55332) = trilinear product of X(i) and X(j) for these {i, j}: {2, 55363}, {8, 45875}, {9, 45876}, {100, 2090}, {188, 55331}
X(55332) = trilinear quotient X(i)/X(j) for these (i, j): (8, 45877), (9, 45878), (2090, 513), (15997, 649), (41799, 43924)

X(55333) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(1) ) AND CCP( X(10) )

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

X(55333) lies on these lines: {9, 24067}, {37, 65}, {1999, 3219}, {2269, 21810}, {2347, 21879}, {3294, 16824}

X(55333) = X(i)-Ceva conjugate of-X(j) for these (i, j): (190, 50346), (1255, 1193), (40435, 20653)
X(55333) = X(960)-Dao conjugate of-X(55090)
X(55333) = X(2363)-isoconjugate of-X(55090)
X(55333) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2092, 55090), (40966, 55091), (55095, 40827), (55100, 14534)
X(55333) = pole of line {2185, 55090} wrt Stammler hyperbola
X(55333) = barycentric product of X(i) and X(j) for these {i, j}: {1211, 55100}, {2092, 55095}, {2292, 5260}, {3704, 55101}, {40966, 55096}
X(55333) = trilinear product of X(i) and X(j) for these {i, j}: {2092, 5260}, {2292, 55100}, {3725, 55095}, {21033, 55101}
X(55333) = trilinear quotient X(i)/X(j) for these (i, j): (2292, 55090), (5260, 14534), (21033, 55091), (55100, 2363)

X(55334) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(1) ) AND CCP( X(11) )

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

X(55334) lies on these lines: {657, 2170}

X(55334) = crosssum of X(650) and X(43947)

X(55335) = PERSPECTOR OF THE TOUCHPOINTS-CONIC OF CCP( X(1) ) AND CCP( X(11) )

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

X(55335) lies on these lines: {1, 59}, {11, 523}, {36, 2071}, {55, 38863}, {244, 6129}, {496, 45238}, {513, 2310}, {655, 40450}, {657, 2170}, {672, 8609}, {774, 31849}, {1279, 5048}, {1618, 16560}, {1647, 35014}, {3025, 53524}, {3120, 3326}, {3259, 18210}, {3675, 43909}, {4336, 5091}, {4516, 7336}, {7004, 14115}, {20294, 24026}, {34949, 45234}, {37722, 51879}, {46101, 52316}, {52305, 55359}

X(55335) = reflection of X(1090) in X(11)
X(55335) = cross-difference of every pair of points on the line X(1983)X(46384)
X(55335) = crosspoint of X(1) and X(11)
X(55335) = crosssum of X(1) and X(59)
X(55335) = X(522)-beth conjugate of-X(1090)
X(55335) = X(i)-Ceva conjugate of-X(j) for these (i, j): (655, 46384), (29374, 513)
X(55335) = X(i)-Dao conjugate of-X(j) for these (i, j): (6615, 40450), (16578, 75)
X(55335) = X(59)-isoconjugate of-X(40450)
X(55335) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1830, 46102), (2170, 40450), (14740, 1016), (16578, 4998), (21742, 59), (22346, 44717)
X(55335) = pole of line {2254, 3722} wrt Feuerbach circumhyperbola
X(55335) = barycentric product of X(i) and X(j) for these {i, j}: {11, 16578}, {1086, 14740}, {1830, 26932}, {21742, 34387}
X(55335) = trilinear product of X(i) and X(j) for these {i, j}: {244, 14740}, {1830, 7004}, {2170, 16578}, {4858, 21742}, {17197, 21797}
X(55335) = trilinear quotient X(i)/X(j) for these (i, j): (11, 40450), (1830, 7012), (14740, 765), (16578, 4564), (21742, 2149)
X(55335) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 2957, 59), (55370, 55380, 55359)

X(55336) = PERSPECTOR OF ABC AND THE CIRCUMSCRIBING TRIANGLE OF THE STEINER CIRCUMELLIPSE AND CCP( X(8) )

Barycentrics    sqrt(-a+b+c) : :

X(55336) lies on these lines: {8, 14218}, {508, 509}, {17277, 55339}

X(55336) = isotomic conjugate of X(508)
X(55336) = crosspoint of X(190) and X(55339)
X(55336) = X(14218)-cross conjugate of-X(2)
X(55336) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 508), (9, 509), (236, 366), (40374, 174)
X(55336) = X(i)-isoconjugate of-X(j) for these {i, j}: {6, 509}, {31, 508}, {174, 18753}, {266, 365}, {4166, 7370}
X(55336) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 509), (2, 508), (188, 366), (259, 365), (365, 266), (366, 174), (508, 7), (509, 57), (556, 18297), (4166, 259), (4179, 6724), (4182, 188), (6725, 4179), (6726, 4166), (6731, 4182), (7025, 507), (18297, 4146)
X(55336) = perspector of inconic with center X(14218)
X(55336) = pole of the tripolar of X(55339) wrt Yff parabola
X(55336) = barycentric product of X(i) and X(j) for these {i, j}: {8, 508}, {188, 18297}, {312, 509}, {366, 556}, {4146, 4182}
X(55336) = trilinear product of X(i) and X(j) for these {i, j}: {8, 509}, {9, 508}, {174, 4182}, {188, 366}, {259, 18297}
X(55336) = trilinear quotient X(i)/X(j) for these (i, j): (2, 509), (75, 508), (188, 365), (259, 18753), (312, 55336)

X(55337) = CENTER OF THE TOUCHPOINTS-CONIC OF THE STEINER CIRCUMELLIPSE AND CCP( X(8) )

Barycentrics    a*(-a+b+c)*(a^2+b^2+c^2-2*a*(b+c)) : :
X(62325) = -3*X[2]+2*X[24181]

X(55337) lies on K971 and these lines: {1, 644}, {2, 24181}, {3, 41391}, {8, 9}, {37, 37549}, {40, 39570}, {41, 4587}, {45, 3959}, {55, 30618}, {57, 29627}, {63, 3730}, {75, 32008}, {78, 220}, {85, 190}, {101, 4855}, {145, 16572}, {169, 1018}, {200, 6605}, {218, 3870}, {318, 6559}, {321, 3294}, {344, 1445}, {894, 27253}, {1025, 7177}, {1083, 23102}, {1212, 3872}, {1281, 3501}, {1723, 3950}, {1743, 3915}, {1766, 48890}, {2292, 3731}, {2324, 27396}, {2348, 3913}, {3158, 8647}, {3160, 28981}, {3177, 40872}, {3219, 29616}, {3306, 16549}, {3578, 17294}, {3663, 25880}, {3681, 15490}, {3729, 20880}, {3811, 5526}, {3951, 50995}, {3970, 11520}, {3984, 54330}, {4437, 39273}, {4488, 32086}, {4515, 37658}, {4578, 47375}, {4652, 42316}, {5552, 40869}, {6332, 53583}, {6554, 6735}, {6557, 51780}, {6558, 44720}, {6684, 26258}, {7308, 8055}, {9310, 14439}, {9312, 28961}, {9436, 28740}, {9581, 26074}, {9593, 26242}, {10826, 21090}, {12514, 17744}, {12649, 21096}, {16284, 17336}, {16552, 49451}, {16593, 30617}, {16601, 19860}, {16823, 19582}, {17107, 35160}, {17234, 32007}, {17261, 33890}, {17277, 32088}, {17339, 17741}, {19861, 25066}, {20269, 40534}, {21371, 29966}, {25083, 25930}, {25237, 26653}, {25728, 30625}, {27068, 31434}, {27384, 27514}, {27420, 27544}, {27538, 28058}, {28742, 40719}, {29001, 34059}, {29007, 31994}, {32003, 37787}, {36846, 43065}, {52963, 54406}

X(55337) = isogonal conjugate of X(17107)
X(55337) = anticomplement of X(24181)
X(55337) = cevapoint of X(9) and X(24771)
X(55337) = cross-difference of every pair of points on the line X(43924)X(48032)
X(55337) = crosspoint of X(i) and X(j) for these {i, j}: {75, 21609}, {3870, 27819}
X(55337) = crosssum of X(i) and X(j) for these {i, j}: {649, 53538}, {17107, 17107}
X(55337) = X(i)-beth conjugate of-X(j) for these (i, j): (644, 169), (7259, 1)
X(55337) = X(i)-Ceva conjugate of-X(j) for these (i, j): (75, 200), (190, 4468), (344, 3870), (30701, 78), (32008, 8)
X(55337) = X(i)-cross conjugate of-X(j) for these (i, j): (3309, 644), (6600, 3870)
X(55337) = X(i)-Dao conjugate of-X(j) for these (i, j): (1, 277), (3, 17107), (9, 40154), (220, 1), (1040, 4000), (4847, 142), (4904, 514), (5452, 2191), (5519, 53544), (24152, 24154), (24153, 24155), (24181, 24181), (24771, 6601)
X(55337) = X(i)-isoconjugate of-X(j) for these {i, j}: {6, 40154}, {56, 277}, {57, 2191}, {1292, 3669}, {1407, 6601}, {2428, 43930}, {32644, 43042}, {36041, 53544}, {37206, 43924}
X(55337) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 40154), (9, 277), (55, 2191), (200, 6601), (218, 57), (344, 85), (644, 37206), (1445, 279), (1617, 269), (3309, 3676), (3699, 54987), (3870, 7), (3939, 1292), (3991, 226), (4350, 479), (4468, 24002), (4878, 65), (6600, 1), (6604, 1088), (7719, 278), (8642, 43924), (15185, 10481), (17093, 23062), (21059, 56), (23144, 7177), (24152, 24155), (24153, 24154), (27819, 27818), (31638, 34018), (38375, 1086), (41539, 3668), (41610, 1434), (44448, 693), (51378, 22464), (51652, 43932), (52927, 36041)
X(55337) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3309)}}, {{A, B, C, X(8), X(1280)}}, {{A, B, C, X(9), X(218)}}, {{A, B, C, X(21), X(390)}}, {{A, B, C, X(55), X(2082)}}, {{A, B, C, X(85), X(4468)}}, {{A, B, C, X(200), X(21609)}}, {{A, B, C, X(318), X(3717)}}, {{A, B, C, X(344), X(346)}}, {{A, B, C, X(391), X(41610)}}, {{A, B, C, X(452), X(4233)}}, {{A, B, C, X(1261), X(17093)}}, {{A, B, C, X(1617), X(1697)}}, {{A, B, C, X(2269), X(21059)}}, {{A, B, C, X(2321), X(3991)}}, {{A, B, C, X(2339), X(33950)}}, {{A, B, C, X(2346), X(7674)}}, {{A, B, C, X(3161), X(27819)}}, {{A, B, C, X(3174), X(24181)}}, {{A, B, C, X(3692), X(6559)}}, {{A, B, C, X(4530), X(38375)}}, {{A, B, C, X(4866), X(24393)}}, {{A, B, C, X(5665), X(12625)}}, {{A, B, C, X(5686), X(32635)}}, {{A, B, C, X(6065), X(7131)}}, {{A, B, C, X(7162), X(54236)}}, {{A, B, C, X(8647), X(17107)}}, {{A, B, C, X(10005), X(43533)}}, {{A, B, C, X(12640), X(45830)}}, {{A, B, C, X(15185), X(42015)}}, {{A, B, C, X(52653), X(62286)}}
X(55337) = X(i)-zayin conjugate of-X(j) for these (i, j): (3676, 649), (4943, 4498)
X(55337) = perspector of circumconic {{A, B, C, X(3699), X(53653)}}
X(55337) = pole of line {200, 4859} wrt circumhyperbola dual of Yff parabola
X(55337) = pole of line {1412, 17107} wrt Stammler hyperbola
X(55337) = pole of line {1434, 17107} wrt Steiner-Wallace hyperbola
X(55337) = pole of line {644, 3939} wrt Yff parabola
X(55337) = KP4(X(9)) OF X(8) AND X(7)
X(55337) = barycentric product of X(i) and X(j) for these {i, j}: {8, 3870}, {9, 344}, {75, 6600}, {100, 44448}, {200, 6604}
X(55337) = trilinear product of X(i) and X(j) for these {i, j}: {2, 6600}, {8, 218}, {9, 3870}, {21, 3991}, {55, 344}
X(55337) = trilinear quotient X(i)/X(j) for these (i, j): (2, 40154), (8, 277), (9, 2191), (218, 56), (344, 7)
X(55337) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 4936, 644), (9, 728, 8), (9, 1334, 5250), (9, 1697, 33950), (9, 3208, 2082), (218, 3991, 3870), (220, 3693, 78), (644, 25082, 1), (1212, 4513, 3872), (2082, 3208, 3895), (3730, 17742, 63), (16284, 17336, 32024)

X(55338) = TOUCHPOINT OF THE STEINER CIRCUMELLIPSE AND THE D-TANGENT TO CCP( X(8) )

Barycentrics    -a+b+c+2*sqrt(b*c)*sin(A/2)-2*sqrt(a*c)*sin(B/2)-2*sqrt(a*b)*sin(C/2) : :

X(55338) lies on Incircle Of Anticomplementary Triangle, Steiner circumellipse and these lines: {2, 5997}

X(55338) = anticomplement of X(5997)
X(55338) = X(55339)-anticomplementary conjugate of-X(6327)
X(55338) = X(55339)-Ceva conjugate of-X(2)
X(55338) = X(2)-cross conjugate of-X(55339)
X(55338) = X(i)-Dao conjugate of-X(j) for these (i, j): (5997, 5997), (14218, 514)
X(55338) = trilinear pole of line {2, 55336}
X(55338) = touchpoint of Steiner circumellipse and the tripolar of X(55339)
X(55338) = pole of line {508, 509} wrt Yff parabola

X(55339) = TRIPOLE OF THE D-TANGENT OF THE STEINER CIRCUMELLIPSE AND CCP( X(8) )

Barycentrics    (b-2*sqrt(a*c)*sin(B/2))*(c-2*sqrt(a*b)*sin(C/2)) : :

X(55339) lies on these lines: {17277, 55336}

X(55339) = isotomic conjugate of X(5997)
X(55339) = cevapoint of X(2) and X(55338)
X(55339) = X(i)-cross conjugate of-X(j) for these (i, j): (2, 55338), (55336, 190)
X(55339) = X(2)-Dao conjugate of-X(5997)
X(55339) = X(31)-isoconjugate of-X(5997)
X(55339) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2, 5997), (5998, 1086)
X(55339) = perspector of inconic through X(2) and X(8)
X(55339) = barycentric product of X(1016) and X(5998)
X(55339) = trilinear product of X(765) and X(5998)
X(55339) = trilinear quotient X(i)/X(j) for these (i, j): (75, 5997), (5998, 244)

X(55340) = CENTER OF THE TOUCHPOINTS-CONIC OF THE STEINER CIRCUMELLIPSE AND CCP( X(9) )

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

X(55340) lies on these lines: {1, 6}, {48, 52015}, {57, 16688}, {77, 4666}, {86, 2481}, {105, 284}, {142, 2293}, {354, 17194}, {551, 1064}, {663, 23810}, {664, 31618}, {991, 38053}, {1026, 17263}, {1125, 1818}, {1621, 55086}, {1742, 6173}, {2340, 6666}, {2346, 3939}, {3616, 25521}, {3622, 10571}, {3720, 20335}, {3946, 4343}, {3957, 17121}, {4069, 25101}, {4318, 37558}, {4667, 20978}, {5144, 22054}, {7032, 24333}, {7191, 54308}, {7671, 24554}, {8053, 20367}, {8299, 17049}, {10025, 29817}, {10857, 15506}, {11025, 24635}, {11712, 17438}, {16574, 23407}, {21320, 29740}, {24388, 25935}, {27918, 29820}, {29814, 30946}, {48897, 51706}

X(55340) = crosspoint of X(1621) and X(55082)
X(55340) = X(i)-Ceva conjugate of-X(j) for these (i, j): (86, 142), (664, 17494), (32008, 8012)
X(55340) = X(i)-Dao conjugate of-X(j) for these (i, j): (142, 55076), (1212, 40216), (3925, 10), (40606, 17758)
X(55340) = X(i)-isoconjugate of-X(j) for these {i, j}: {1174, 17758}, {2346, 13476}, {2350, 32008}
X(55340) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (142, 40216), (354, 17758), (1212, 55076), (1475, 13476), (1621, 32008), (4251, 2346), (17169, 40004), (18164, 39734), (33765, 42311), (35338, 54118), (38859, 10509), (43915, 226), (55082, 31618), (55086, 1170)
X(55340) = X(1621)-waw conjugate of-X(3294)
X(55340) = pole of line {81, 2346} wrt Stammler hyperbola
X(55340) = barycentric product of X(i) and X(j) for these {i, j}: {142, 1621}, {333, 43915}, {354, 17277}, {1212, 55082}, {1229, 55086}
X(55340) = trilinear product of X(i) and X(j) for these {i, j}: {21, 43915}, {142, 4251}, {354, 1621}, {1475, 17277}, {2293, 55082}
X(55340) = trilinear quotient X(i)/X(j) for these (i, j): (142, 17758), (354, 13476), (1475, 2350), (1621, 2346), (4251, 1174)
X(55340) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 5259, 3191), (142, 2293, 35338), (1212, 8551, 9)

X(55341) = TOUCHPOINT OF THE STEINER CIRCUMELLIPSE AND THE D-TANGENT TO CCP( X(9) )

Barycentrics    (a-b)*(a-c)*(a+b-c)*(a-b+c)*((a-b+c)*sin(B/2)+(a+b-c)*sin(C/2)) : :

X(55341) lies on Steiner circumellipse and these lines: {9, 16019}, {145, 7022}, {178, 1121}, {190, 43192}, {234, 903}, {236, 4146}, {664, 55329}, {2481, 7707}, {3227, 10490}, {45876, 55328}

X(55341) = X(664)-Ceva conjugate of-X(55342)
X(55341) = X(i)-cross conjugate of-X(j) for these (i, j): (43192, 55329), (55342, 45876)
X(55341) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 10495), (178, 6730), (10493, 650), (10494, 10501), (13443, 45877), (15495, 10492), (16016, 522)
X(55341) = X(i)-isoconjugate of-X(j) for these {i, j}: {6, 10495}, {258, 45878}, {260, 6729}
X(55341) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 10495), (173, 45877), (174, 10492), (177, 6728), (178, 522), (234, 514), (3659, 53119), (6733, 260), (7707, 650), (10490, 513), (10495, 10501), (13444, 266), (16016, 6730), (18888, 6729), (42622, 45878), (43192, 1), (45875, 258), (45876, 7048), (55328, 174), (55329, 7), (55331, 7028), (55342, 188)
X(55341) = X(i)-zayin conjugate of-X(j) for these (i, j): (43, 10495), (12518, 649)
X(55341) = trilinear pole of line {2, 178}
X(55341) = touchpoint of Steiner circumellipse and line {55341, 55342}
X(55341) = barycentric product of X(i) and X(j) for these {i, j}: {8, 55329}, {75, 43192}, {178, 664}, {190, 234}, {556, 55328}
X(55341) = trilinear product of X(i) and X(j) for these {i, j}: {2, 43192}, {9, 55329}, {100, 234}, {173, 45876}, {174, 55342}
X(55341) = trilinear quotient X(i)/X(j) for these (i, j): (2, 10495), (173, 45878), (177, 6729), (178, 650), (234, 513)

X(55342) = TOUCHPOINT OF CCP( X(9) ) AND THE D-TANGENT TO THE STEINER CIRCUMELLIPSE

Barycentrics    a*(a-b)*(a-c)*(a+b-c)*(a-b+c)*(c*sin(B/2)+b*sin(C/2)) : :

X(55342) lies on these lines: {1, 7057}, {8, 13443}, {100, 13444}, {177, 1320}, {1280, 14596}, {2089, 12646}, {3870, 18886}, {9837, 12539}, {11690, 42017}, {14942, 16012}, {16016, 41798}, {43192, 55331}

X(55342) = cevapoint of X(10492) and X(45707)
X(55342) = crosspoint of X(45876) and X(55341)
X(55342) = crosssum of X(663) and X(6729)
X(55342) = X(i)-Ceva conjugate of-X(j) for these (i, j): (664, 55341), (45876, 55331)
X(55342) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 10492), (178, 522), (10493, 6728), (21623, 10491), (39026, 260)
X(55342) = X(i)-isoconjugate of-X(j) for these {i, j}: {6, 10492}, {260, 513}, {266, 10495}, {289, 45877}, {1488, 45878}, {6732, 45874}, {10501, 13444}
X(55342) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 10492), (101, 260), (177, 514), (259, 10495), (3659, 258), (7707, 6728), (10492, 10491), (13444, 57), (14596, 3676), (16012, 650), (16016, 522), (18888, 513), (43192, 174), (45874, 289), (45875, 1488), (45877, 6732), (53118, 45877), (55328, 7), (55329, 555), (55331, 7048), (55332, 53123), (55341, 4146), (55363, 7028)
X(55342) = X(361)-zayin conjugate of-X(10495)
X(55342) = trilinear pole of line {9, 173}
X(55342) = pole of line {45876, 55328} wrt Steiner circumellipse
X(55342) = barycentric product of X(i) and X(j) for these {i, j}: {8, 55328}, {177, 190}, {188, 55341}, {236, 45876}, {312, 13444}
X(55342) = trilinear product of X(i) and X(j) for these {i, j}: {8, 13444}, {9, 55328}, {100, 177}, {173, 55331}, {178, 6733}
X(55342) = trilinear quotient X(i)/X(j) for these (i, j): (2, 10492), (100, 260), (177, 513), (178, 6728), (188, 10495)

X(55343) = CENTER OF THE TOUCHPOINTS-CONIC OF THE STEINER CIRCUMELLIPSE AND CCP( X(10) )

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

X(55343) lies on these lines: {10, 37}, {190, 32014}, {551, 21879}, {1125, 4115}, {1698, 24044}, {3219, 3294}, {3578, 29574}, {3634, 4037}, {3636, 21839}, {3730, 27268}, {3828, 52579}, {9780, 24049}, {18827, 32009}, {22011, 40774}, {22047, 32004}, {24075, 46932}, {24081, 29610}, {33766, 33770}, {49737, 50262}, {52745, 53587}

X(55343) = X(i)-Ceva conjugate of-X(j) for these (i, j): (190, 31290), (1268, 8013), (32009, 1125)
X(55343) = X(24185)-Dao conjugate of-X(514)
X(55343) = X(1171)-isoconjugate of-X(34585)
X(55343) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1962, 34585), (33774, 52558)
X(55343) = pole of line {3739, 8013} wrt circumhyperbola dual of Yff parabola
X(55343) = barycentric product of X(i) and X(j) for these {i, j}: {4115, 31290}, {8013, 33770}, {21816, 33779}, {33774, 52576}
X(55343) = trilinear product of X(i) and X(j) for these {i, j}: {8013, 33766}, {21816, 33770}
X(55343) = trilinear quotient X(i)/X(j) for these (i, j): (1213, 34585), (33766, 52558)
X(55343) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (10, 37, 24051), (1125, 21816, 4115)

X(55344) = CENTER OF THE TOUCHPOINTS-CONIC OF THE STEINER CIRCUMELLIPSE AND CCP( X(11) )

Barycentrics    (b-c)*(-a+b+c)*(a^4-b*(b-c)^2*c-a^3*(b+c)+3*a*(b-c)^2*(b+c)+a^2*(-3*b^2+7*b*c-3*c^2))*(2*a^3-2*a^2*(b+c)+(b-c)^2*(b+c)-a*(b^2-4*b*c+c^2)) : :

X(55344) lies on these lines: {11, 650}, {666, 31619}

X(55344) = X(30610)-Ceva conjugate of-X(3035)
X(55344) = X(11124)-reciprocal conjugate of-X(43946)

X(55345) = CENTER OF THE TOUCHPOINTS-CONIC OF THE MACBEATH CIRCUMCONIC AND CCP( X(4) )

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

X(55345) lies on these lines: {6, 64}, {800, 16035}, {1181, 17807}, {1993, 46106}, {8743, 46375}

X(55345) = X(275)-Ceva conjugate of-X(235)
X(55345) = X(44079)-reciprocal conjugate of-X(17703)
X(55345) = barycentric product of X(19166) and X(55354)

X(55346) = TRIPOLE OF THE D-TANGENT OF THE MACBEATH CIRCUMCONIC AND CCP( X(4) )

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

X(55346) lies on these lines: {7, 7339}, {108, 927}, {243, 24032}, {278, 7115}, {648, 1020}, {651, 36054}, {653, 3064}, {658, 1897}, {693, 934}, {908, 4564}, {1262, 14953}, {1275, 5379}, {1936, 7012}, {1981, 23890}, {3262, 4998}, {5088, 38461}, {6354, 23979}, {7056, 23586}, {16090, 52889}, {23706, 41353}, {23999, 52240}, {39294, 50442}

X(55346) = polar conjugate of X(1146)
X(55346) = isotomic conjugate of X(2968)
X(55346) = isogonal conjugate of X(3270)
X(55346) = cevapoint of X(i) and X(j) for these {i, j}: {1, 1020}, {2, 1897}, {3, 651}, {4, 653}, {7, 934}, {100, 329}, {108, 278}, {1119, 36118}, {1398, 32714}, {1783, 7071}, {1813, 3561}, {2283, 39063}, {2406, 38554}, {4566, 6356}, {6354, 53321}, {7012, 7128}
X(55346) = crosssum of X(3270) and X(3270)
X(55346) = X(i)-cross conjugate of-X(j) for these (i, j): (1, 648), (2, 658), (3, 651), (4, 653), (5, 38340), (7, 18026), (20, 190), (30, 655), (278, 13149), (347, 664), (411, 662), (412, 823), (1068, 54240), (1119, 36118), (1262, 1275), (1398, 32714), (1593, 36099), (3007, 4555), (3100, 666), (3149, 37141), (4192, 37137), (4219, 162), (4220, 36098), (4296, 6648), (4329, 668), (5999, 37207), (6356, 4566), (6905, 37136), (6909, 3257), (6996, 34085), (7012, 46102), (7071, 1783), (7580, 100), (7952, 6335), (15252, 2), (17080, 4573), (17134, 99), (17220, 6528), (17221, 18831), (18655, 53639), (18658, 46134), (18659, 670), (18661, 16077), (20291, 6540), (20764, 1813), (23171, 110), (23512, 799), (33557, 37212), (36002, 37139), (37022, 27834)
X(55346) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 2968), (3, 3270), (6, 35072), (9, 34591), (57, 53557), (223, 7004), (281, 5514), (478, 7117), (517, 41215), (1249, 1146), (1465, 10017), (2245, 38353), (3160, 26932), (3162, 14936), (5190, 42462), (6337, 23983), (6505, 24031), (6523, 42069), (6609, 3937), (7952, 4081), (9296, 15416), (10001, 6332), (15267, 20975), (17113, 1565), (20620, 23615), (22391, 39687), (23050, 24010), (31998, 15411), (36033, 2638), (36103, 2310), (36830, 23090), (36908, 18210), (39052, 1021), (39053, 522), (39060, 4391), (39062, 7253), (40590, 53560), (40593, 17880), (40596, 21789), (40837, 11), (45245, 40616), (47345, 21044)
X(55346) = X(i)-isoconjugate of-X(j) for these {i, j}: {3, 2310}, {4, 2638}, {6, 34591}, {9, 7117}, {11, 212}, {19, 35072}, {25, 24031}, {31, 2968}, {33, 1364}, {41, 26932}, {48, 1146}, {55, 7004}, {63, 14936}, {77, 3022}, {78, 3271}, {84, 47432}, {92, 39687}, {184, 24026}, {200, 3937}, {219, 2170}, {220, 3942}, {222, 3119}, {244, 1260}, {255, 42069}, {283, 4516}, {284, 53560}, {341, 22096}, {521, 663}, {522, 1946}, {603, 4081}, {647, 1021}, {650, 652}, {656, 21789}, {657, 905}, {661, 23090}, {798, 15411}, {810, 7253}, {822, 17926}, {906, 42462}, {926, 23696}, {1015, 3692}, {1040, 14935}, {1086, 1802}, {1098, 20975}, {1253, 1565}, {1265, 3248}, {1437, 52335}, {1459, 3900}, {1790, 36197}, {1792, 3122}
X(55346) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 34591), (2, 2968), (3, 35072), (4, 1146), (7, 26932), (19, 2310), (20, 40616), (25, 14936), (33, 3119), (34, 2170), (48, 2638), (56, 7117), (57, 7004), (59, 219), (63, 24031), (65, 53560), (69, 23983), (85, 17880), (92, 24026), (99, 15411), (107, 17926), (108, 650), (109, 652), (110, 23090), (112, 21789), (162, 1021), (184, 39687), (196, 38357), (198, 47432), (222, 1364), (223, 53557), (225, 21044), (250, 7054), (264, 23978), (269, 3942), (273, 4858), (278, 11), (279, 1565), (281, 4081), (329, 7358), (331, 34387), (347, 16596), (393, 42069), (607, 3022), (608, 3271), (648, 7253), (651, 521), (653, 522), (658, 4025), (664, 6332)
X(55346) = X(i)-zayin conjugate of-X(j) for these (i, j): (2636, 650), (9355, 652)
X(55346) = trilinear pole of line {651, 653}
X(55346) = perspector of the inconic with center X(15252)
X(55346) = pole of line {23615, 33573} wrt polar circle
X(55346) = pole of line {3270, 35072} wrt Stammler hyperbola
X(55346) = pole of line {2968, 3270} wrt Steiner-Wallace hyperbola
X(55346) = barycentric product of X(i) and X(j) for these {i, j}: {4, 1275}, {7, 46102}, {59, 331}, {63, 24032}, {69, 23984}
X(55346) = trilinear product of X(i) and X(j) for these {i, j}: {2, 7128}, {3, 24032}, {4, 7045}, {7, 7012}, {19, 1275}
X(55346) = trilinear quotient X(i)/X(j) for these (i, j): (2, 34591), (3, 2638), (4, 2310), (7, 7004), (19, 14936)

X(55347) = CENTER OF THE TOUCHPOINTS-CONIC OF THE MACBEATH CIRCUMCONIC AND CCP( X(7) )

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

X(55347) lies on these lines: {55, 103}

X(55348) = CENTER OF THE TOUCHPOINTS-CONIC OF THE MACBEATH CIRCUMCONIC AND CCP( X(8) )

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

X(55348) lies on these lines: {219, 4266}

X(55349) = CENTER OF THE TOUCHPOINTS-CONIC OF THE MACBEATH CIRCUMCONIC AND CCP( X(9) )

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

X(55349) lies on these lines: {6, 31}, {20986, 55323}, {21770, 40974}

X(55349) = X(i)-isoconjugate of-X(j) for these {i, j}: {947, 54121}, {34434, 40417}
X(55349) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (572, 40417), (2262, 54121)
X(55349) = pole of line {86, 40417} wrt Stammler hyperbola
X(55349) = barycentric product of X(i) and X(j) for these {i, j}: {572, 946}, {2262, 2975}, {11109, 22063}
X(55349) = trilinear product of X(i) and X(j) for these {i, j}: {572, 2262}, {946, 20986}, {17074, 40957}
X(55349) = trilinear quotient X(i)/X(j) for these (i, j): (946, 54121), (2262, 2051), (2975, 40417), (20986, 947)

X(55350) = CENTER OF THE TOUCHPOINTS-CONIC OF THE MACBEATH CIRCUMCONIC AND CCP( X(10) )

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

X(55350) lies on these lines: {71, 213}

X(55350) = X(40394)-Ceva conjugate of-X(21670)
X(55350) = barycentric product of X(42440) and X(55098)

X(55351) = PERSPECTOR OF THE TOUCHPOINTS-CONIC OF THE MACBEATH CIRCUMCONIC AND CCP( X(10) )

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

X(55351) lies on these lines: {10, 7141}, {71, 213}, {73, 22069}, {185, 216}, {201, 1834}, {212, 52544}, {656, 18641}, {3269, 47407}, {4303, 22084}, {7066, 40591}, {13754, 44709}, {22059, 22073}, {22072, 22076}

X(55351) = crosspoint of X(3) and X(10)
X(55351) = crosssum of X(i) and X(j) for these {i, j}: {4, 58}, {404, 3193}
X(55351) = X(i)-Ceva conjugate of-X(j) for these (i, j): (10, 21670), (40518, 647), (44765, 52310)
X(55351) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (42440, 92), (42450, 27)
X(55351) = pole of line {418, 22341} wrt Jerabek circumhyperbola
X(55351) = pole of line {21011, 21670} wrt Kiepert circumhyperbola
X(55351) = barycentric product of X(i) and X(j) for these {i, j}: {63, 42440}, {306, 42450}, {1790, 21670}
X(55351) = trilinear product of X(i) and X(j) for these {i, j}: {3, 42440}, {72, 42450}, {1437, 21670}
X(55351) = trilinear quotient X(i)/X(j) for these (i, j): (21670, 41013), (42440, 4), (42450, 28)

X(55352) = CENTER OF THE TOUCHPOINTS-CONIC OF THE MACBEATH CIRCUMCONIC AND CCP( X(11) )

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

X(55352) lies on these lines: {3063, 7117}

X(55353) = PERSPECTOR OF THE TOUCHPOINTS-CONIC OF THE MACBEATH CIRCUMCONIC AND CCP( X(11) )

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

X(55353) lies on these lines: {3063, 7117}, {6075, 18210}, {55359, 55366}

X(55353) = crosspoint of X(3) and X(11)
X(55353) = crosssum of X(4) and X(59)

X(55354) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(4) ) AND THE CIRCUMCIRCLE

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

X(55354) lies on these lines: {3, 14363}, {6, 25}, {160, 6525}, {378, 13450}, {418, 52604}, {1597, 8887}, {6638, 15274}, {40641, 41334}

X(55354) = X(1105)-Ceva conjugate of-X(53)
X(55354) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3199, 17703), (55345, 19166)
X(55354) = trilinear quotient of X(2181) and X(17703)

X(55355) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(4) ) AND CCP( X(7) )

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

X(55355) lies on these lines: {278, 1456}

X(55356) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(4) ) AND CCP( X(8) )

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

X(55356) lies on these lines: {281, 1837}

X(55357) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(4) ) AND CCP( X(9) )

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

X(55357) lies on these lines: {6, 33}, {1108, 23204}, {1249, 3190}, {3191, 15500}

X(55357) = crosssum of X(1459) and X(40527)
X(55357) = trilinear product of X(40979) and X(55324)

X(55358) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(4) ) AND CCP( X(10) )

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

X(55358) lies on these lines: {1826, 1834}

X(55358) = X(40447)-Ceva conjugate of-X(1842)

X(55359) = PERSPECTOR OF THE TOUCHPOINTS-CONIC OF CCP( X(4) ) AND CCP( X(11) )

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

X(55359) lies on these lines: {4, 52109}, {11, 513}, {125, 13999}, {657, 1566}, {971, 1519}, {1456, 1877}, {1565, 31605}, {1876, 6001}, {2310, 4017}, {3270, 15313}, {3309, 34949}, {3330, 52413}, {3583, 47379}, {3738, 46100}, {5521, 35580}, {13136, 44184}, {23593, 39026}, {42069, 54239}, {46101, 46384}, {52305, 55335}, {55353, 55366}

X(55359) = crosspoint of X(4) and X(11)
X(55359) = crosssum of X(3) and X(59)
X(55359) = X(36949)-Dao conjugate of-X(69)
X(55359) = X(36949)-reciprocal conjugate of-X(4998)
X(55359) = pole of line {900, 1830} wrt Feuerbach circumhyperbola
X(55359) = pole of line {4530, 14393} wrt orthic inconic
X(55359) = barycentric product of X(i) and X(j) for these {i, j}: {11, 36949}, {2170, 18689}
X(55359) = trilinear product of X(i) and X(j) for these {i, j}: {2170, 36949}, {3271, 18689}
X(55359) = trilinear quotient X(i)/X(j) for these (i, j): (18689, 4998), (36949, 4564)
X(55359) = (X(55370), X(55380))-harmonic conjugate of X(55335)

X(55360) = CENTER OF THE TOUCHPOINTS-CONIC OF THE CIRCUMCIRCLE AND CCP( X(7) )

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

X(55360) lies on these lines: {56, 991}

X(55361) = CENTER OF THE TOUCHPOINTS-CONIC OF THE CIRCUMCIRCLE AND CCP( X(8) )

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

X(55361) lies on these lines: {55, 2316}

X(55362) = CENTER OF THE TOUCHPOINTS-CONIC OF THE CIRCUMCIRCLE AND CCP( X(9) )

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

X(55362) lies on these lines: {1, 7428}, {3, 519}, {6, 41}, {21, 1634}, {36, 3293}, {81, 52150}, {100, 1222}, {104, 7421}, {228, 37605}, {529, 19513}, {535, 19648}, {855, 37722}, {859, 5563}, {958, 3831}, {999, 15654}, {1071, 53292}, {1319, 22345}, {1385, 53303}, {1420, 3185}, {1470, 2933}, {1473, 10966}, {1626, 26357}, {2392, 22765}, {2975, 14829}, {3057, 22344}, {3304, 18613}, {3813, 37331}, {3827, 18183}, {3878, 23169}, {4057, 53535}, {4225, 41629}, {4267, 37617}, {4857, 13744}, {5258, 16374}, {5289, 20805}, {5298, 28238}, {5434, 27622}, {7419, 42028}, {7987, 15624}, {8071, 23843}, {11236, 19549}, {11260, 37619}, {12607, 19514}, {15888, 28349}, {16678, 20040}, {16823, 53261}, {17448, 37575}, {17674, 53572}, {18162, 18166}, {20999, 37564}, {22458, 30144}, {23205, 37568}, {24328, 28383}, {28385, 37662}, {28386, 37646}, {31157, 37225}

X(55362) = crosssum of X(513) and X(40451)
X(55362) = X(i)-Ceva conjugate of-X(j) for these (i, j): (81, 20228), (100, 21173), (1476, 45219)
X(55362) = X(i)-Dao conjugate of-X(j) for these (i, j): (3452, 54121), (21796, 321), (24237, 693)
X(55362) = X(i)-isoconjugate of-X(j) for these {i, j}: {1222, 34434}, {2051, 23617}, {51476, 54121}
X(55362) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (572, 1222), (1201, 2051), (2975, 32017), (3752, 54121), (20228, 34434), (20986, 23617), (21796, 51870)
X(55362) = pole of line {663, 3667} wrt circumcircle
X(55362) = pole of line {333, 1222} wrt Stammler hyperbola
X(55362) = pole of line {20028, 28660} wrt Steiner-Wallace hyperbola
X(55362) = barycentric product of X(i) and X(j) for these {i, j}: {572, 3663}, {1201, 14829}, {2975, 3752}, {3057, 17074}, {17183, 55323}
X(55362) = trilinear product of X(i) and X(j) for these {i, j}: {572, 3752}, {1201, 2975}, {2347, 17074}, {3663, 20986}, {11109, 22344}
X(55362) = trilinear quotient X(i)/X(j) for these (i, j): (572, 23617), (1201, 34434), (2975, 1222), (3663, 54121), (3752, 2051)
X(55362) = (X(i), X(j))-harmonic conjugate of X(k) for these (i, j, k): (1, 23206, 23844), (3, 3913, 15625), (3, 12513, 15621), (56, 23361, 20470), (999, 15654, 23383), (1319, 22345, 23846), (1470, 8192, 2933), (3057, 22344, 23845), (3304, 28348, 18613)

X(55363) = TOUCHPOINT OF CCP( X(9) ) AND THE D-TANGENT TO THE CIRCUMCIRCLE

Barycentrics    a*(a-b)*(a-c)*(sin(B/2)+sin(C/2)) : :

X(55363) lies on these lines: {100, 6733}, {164, 11527}, {188, 6732}, {266, 12646}, {361, 3913}, {664, 45876}, {1280, 41799}, {1320, 15997}, {2090, 14942}, {3699, 55332}, {6726, 7028}, {39121, 53118}, {43192, 55331}

X(55363) = cevapoint of X(i) and X(j) for these {i, j}: {259, 45878}, {10495, 53119}
X(55363) = crosspoint of X(45876) and X(55332)
X(55363) = X(i)-Ceva conjugate of-X(j) for these (i, j): (100, 3659), (45876, 45875)
X(55363) = X(i)-cross conjugate of-X(j) for these (i, j): (10495, 188), (45877, 258), (45878, 259)
X(55363) = X(i)-Dao conjugate of-X(j) for these (i, j): (5452, 45877), (10494, 21623), (16015, 693)
X(55363) = X(i)-isoconjugate of-X(j) for these {i, j}: {7, 45878}, {57, 45877}, {6732, 13444}, {10504, 45874}
X(55363) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (41, 45878), (55, 45877), (2090, 693), (3659, 174), (10495, 21623), (15997, 514), (41799, 3676), (43192, 18886), (45874, 57), (45875, 7), (45876, 85), (45877, 10504), (53119, 10492), (55331, 4146), (55332, 75)
X(55363) = X(i)-zayin conjugate of-X(j) for these (i, j): (266, 513), (1743, 45877)
X(55363) = trilinear pole of line {9, 259}
X(55363) = barycentric product of X(i) and X(j) for these {i, j}: {1, 55332}, {8, 45875}, {9, 45876}, {100, 2090}, {188, 55331}
X(55363) = trilinear product of X(i) and X(j) for these {i, j}: {6, 55332}, {8, 45874}, {9, 45875}, {55, 45876}, {100, 15997}
X(55363) = trilinear quotient X(i)/X(j) for these (i, j): (9, 45877), (55, 45878), (2090, 514), (3659, 266), (7028, 10492)

X(55364) = CENTER OF THE TOUCHPOINTS-CONIC OF THE CIRCUMCIRCLE AND CCP( X(10) )

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

X(55364) lies on these lines: {42, 181}

X(55364) = X(40986)-reciprocal conjugate of-X(55089)
X(55364) = barycentric product of X(i) and X(j) for these {i, j}: {4016, 55098}, {40986, 55094}
X(55364) = trilinear product of X(20966) and X(55098)
X(55364) = trilinear quotient of X(20966) and X(55089)

X(55365) = CENTER OF THE TOUCHPOINTS-CONIC OF THE CIRCUMCIRCLE AND CCP( X(11) )

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

X(55365) lies on these lines: {1946, 3271}

X(55366) = PERSPECTOR OF THE TOUCHPOINTS-CONIC OF THE CIRCUMCIRCLE AND CCP( X(11) )

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

X(55366) lies on these lines: {11, 47394}, {663, 42771}, {667, 7117}, {1946, 3271}, {2170, 4041}, {2223, 51377}, {4516, 41218}, {41333, 52426}, {55353, 55359}

X(55366) = isogonal conjugate of the isotomic conjugate of X(46100)
X(55366) = crosspoint of X(6) and X(11)
X(55366) = crosssum of X(2) and X(59)
X(55366) = X(i)-Ceva conjugate of-X(j) for these (i, j): (929, 52331), (34179, 663), (34189, 649)
X(55366) = X(i)-Dao conjugate of-X(j) for these (i, j): (13006, 76), (46100, 4998)
X(55366) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (13006, 4998), (23198, 44717), (46100, 76)
X(55366) = pole of line {4530, 14393} wrt Brocard inellipse
X(55366) = barycentric product of X(i) and X(j) for these {i, j}: {6, 46100}, {11, 13006}, {4516, 16701}
X(55366) = trilinear product of X(i) and X(j) for these {i, j}: {31, 46100}, {2170, 13006}
X(55366) = trilinear quotient X(i)/X(j) for these (i, j): (13006, 4564), (16701, 4620), (46100, 75)

X(55367) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(7) ) AND CCP( X(8) )

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

X(55367) lies on these lines: {2, 11}

X(55368) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(7) ) AND CCP( X(9) )

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

X(55368) lies on these lines: {1, 971}, {3870, 25716}, {4326, 7955}

X(55369) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(7) ) AND CCP( X(10) )

Barycentrics    (a+b-c)*(a-b+c)*(b+c)*(2*a^2+(b-c)^2+a*(b+c))*(3*a^4-b*(b-c)^2*c-a^3*(b+c)+a^2*(b^2+9*b*c+c^2)-a*(b+c)*(3*b^2+4*b*c+3*c^2)) : :

X(55369) lies on these lines: {226, 4356}

X(55370) = PERSPECTOR OF THE TOUCHPOINTS-CONIC OF CCP( X(7) ) AND CCP( X(11) )

Barycentrics    (b-c)^2*(-a+b+c)*(2*a^4-2*a^3*(b+c)+(b-c)^2*(b^2+c^2)-a^2*(b^2-4*b*c+c^2)) : :
X(55370) = 2*X(11)+X(3328) = 4*X(1387)-X(3322)

X(55370) lies on these lines: {11, 514}, {57, 2958}, {497, 38941}, {516, 1319}, {1086, 55372}, {1358, 14116}, {1387, 3322}, {1464, 45272}, {1565, 3022}, {1566, 2170}, {2310, 48151}, {2530, 42771}, {4449, 42770}, {4534, 44012}, {5433, 31852}, {5540, 55316}, {7354, 31851}, {10896, 18328}, {16173, 53801}, {17761, 44043}, {46101, 52334}, {52305, 55335}

X(55370) = midpoint of X(3328) and X(5532)
X(55370) = reflection of X(5532) in X(11)
X(55370) = crosspoint of X(7) and X(11)
X(55370) = crosssum of X(55) and X(59)
X(55370) = X(11)-daleth conjugate of-X(514)
X(55370) = X(17044)-Dao conjugate of-X(8)
X(55370) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (17044, 4998), (23730, 664)
X(55370) = X(11)-waw conjugate of-X(42462)
X(55370) = pole of line {4530, 14393} wrt incircle
X(55370) = pole of line {3887, 5083} wrt Feuerbach circumhyperbola
X(55370) = barycentric product of X(i) and X(j) for these {i, j}: {11, 17044}, {522, 23730}, {17197, 21914}
X(55370) = trilinear product of X(i) and X(j) for these {i, j}: {650, 23730}, {2170, 17044}, {18191, 21914}
X(55370) = trilinear quotient X(i)/X(j) for these (i, j): (17044, 4564), (23730, 651)
X(55370) = (X(55335), X(55359))-harmonic conjugate of X(55380)

X(55371) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(7) ) AND CCP( X(11) )

Barycentrics    (b-c)*(2*a^4-2*a^3*(b+c)+(b-c)^2*(b^2+c^2)-a^2*(b^2-4*b*c+c^2))*(3*a^6+11*a^4*b*c+b*(b-c)^4*c-5*a^5*(b+c)-2*a^3*b*c*(b+c)+a^2*(b-c)^2*(5*b^2+2*b*c+5*c^2)-3*a*(b-c)*(b^4-c^4)) : :

X(55371) lies on these lines: {1086, 55370}

X(55372) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(8) ) AND CCP( X(9) )

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

X(55372) lies on these lines: {9, 55}, {42, 4029}, {3701, 3872}, {3714, 4915}, {4666, 46897}, {16576, 29821}, {37558, 52353}

X(55372) = X(1222)-Ceva conjugate of-X(2321)
X(55372) = X(21031)-Dao conjugate of-X(3663)
X(55372) = X(55330)-reciprocal conjugate of-X(17183)

X(55373) = TOUCHPOINT OF CCP( X(8) ) AND THE D-TANGENT TO CCP( X(9) )

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

X(55373) lies on these lines: {190, 55322}, {367, 36805}, {4181, 4997}, {20527, 36807}

X(55373) = X(3699)-Ceva conjugate of-X(55374)
X(55373) = X(40378)-Dao conjugate of-X(3676)
X(55373) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (367, 3669), (4181, 514), (20527, 3676), (20664, 43924), (20682, 4017), (55322, 7), (55325, 57), (55374, 366)
X(55373) = trilinear pole of line {8, 4181}
X(55373) = barycentric product of X(i) and X(j) for these {i, j}: {8, 55322}, {190, 4181}, {312, 55325}, {367, 646}, {3699, 20527}
X(55373) = trilinear product of X(i) and X(j) for these {i, j}: {8, 55325}, {9, 55322}, {100, 4181}, {366, 55374}, {367, 3699}
X(55373) = trilinear quotient X(i)/X(j) for these (i, j): (367, 43924), (4181, 513), (20527, 3669), (20682, 7180)

X(55374) = TOUCHPOINT OF CCP( X(9) ) AND THE D-TANGENT TO CCP( X(8) )

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

X(55374) lies on these lines: {100, 55321}, {1280, 40378}, {1320, 4180}

X(55374) = X(3699)-Ceva conjugate of-X(55373)
X(55374) = X(20527)-Dao conjugate of-X(3676)
X(55374) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4180, 514), (40378, 3676), (52866, 43924), (55321, 7), (55326, 57), (55373, 18297)
X(55374) = trilinear pole of line {9, 4180}
X(55374) = barycentric product of X(i) and X(j) for these {i, j}: {8, 55321}, {190, 4180}, {312, 55326}, {366, 55373}, {3699, 40378}
X(55374) = trilinear product of X(i) and X(j) for these {i, j}: {8, 55326}, {9, 55321}, {100, 4180}, {365, 55373}, {644, 40378}
X(55374) = trilinear quotient X(i)/X(j) for these (i, j): (4180, 513), (40378, 3669)

X(55375) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(8) ) AND CCP( X(10) )

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

X(55375) lies on these lines: {321, 54357}, {2321, 21677}

X(55375) = X(30710)-Ceva conjugate of-X(6737)

X(55376) = PERSPECTOR OF THE TOUCHPOINTS-CONIC OF CCP( X(8) ) AND CCP( X(11) )

Barycentrics    (b-c)^2*(-a+b+c)*(2*a^2+b^2+c^2-2*a*(b+c)) : :
X(55376) = 2*X(11)+X(4542)

X(55376) lies on these lines: {8, 4076}, {11, 522}, {149, 39185}, {521, 3271}, {900, 43909}, {1086, 4926}, {1146, 55377}, {2170, 4171}, {2310, 6615}, {2325, 4119}, {3022, 34949}, {3323, 31605}, {3717, 3880}, {4422, 46973}, {5853, 38211}, {6547, 33905}, {17059, 24840}, {21044, 52946}, {46101, 52338}, {52305, 55335}

X(55376) = midpoint of X(i) and X(j) for these {i, j}: {149, 39185}, {4542, 7336}
X(55376) = reflection of X(i) in X(j) for these (i, j): (7336, 11), (46973, 4422)
X(55376) = crosspoint of X(8) and X(11)
X(55376) = crosssum of X(56) and X(59)
X(55376) = X(7253)-beth conjugate of-X(7336)
X(55376) = X(i)-Ceva conjugate of-X(j) for these (i, j): (1862, 6161), (4582, 52338), (40520, 42462)
X(55376) = X(11)-daleth conjugate of-X(522)
X(55376) = X(i)-Dao conjugate of-X(j) for these (i, j): (4422, 7), (6547, 4998), (6615, 46972), (21204, 17089), (40468, 664)
X(55376) = X(59)-isoconjugate of-X(46972)
X(55376) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1862, 46102), (2170, 46972), (3722, 4564), (4422, 4998), (6161, 651), (6546, 664), (6547, 7), (46973, 31615)
X(55376) = X(11)-waw conjugate of-X(21132)
X(55376) = pole of line {10015, 28890} wrt circumhyperbola dual of Yff parabola
X(55376) = pole of line {3738, 14740} wrt Feuerbach circumhyperbola
X(55376) = pole of line {4530, 14393} wrt Mandart inellipse
X(55376) = barycentric product of X(i) and X(j) for these {i, j}: {8, 6547}, {11, 4422}, {522, 6546}, {1862, 26932}, {2170, 4986}
X(55376) = trilinear product of X(i) and X(j) for these {i, j}: {9, 6547}, {11, 3722}, {522, 6161}, {650, 6546}, {1862, 7004}
X(55376) = trilinear quotient X(i)/X(j) for these (i, j): (11, 46972), (1862, 7012), (3722, 59), (4422, 4564), (4986, 4998)
X(55376) = (X(55335), X(55359))-harmonic conjugate of X(55370)

X(55377) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(8) ) AND CCP( X(11) )

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

X(55377) lies on these lines: {1146, 55376}

X(55377) = X(6161)-Dao conjugate of-X(3669)

X(55378) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(9) ) AND CCP( X(10) )

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

X(55378) lies on these lines: {37, 42}

X(55378) = X(1220)-Ceva conjugate of-X(21675)
X(55378) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (40952, 55090), (55100, 40412)
X(55378) = barycentric product of X(i) and X(j) for these {i, j}: {442, 55100}, {2294, 5260}, {40952, 55095}
X(55378) = trilinear product of X(i) and X(j) for these {i, j}: {2294, 55100}, {5260, 40952}, {40967, 55101}, {40978, 55095}
X(55378) = trilinear quotient X(i)/X(j) for these (i, j): (2294, 55090), (5260, 40412), (40967, 55091)

X(55379) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(9) ) AND CCP( X(11) )

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

X(55379) lies on these lines: {663, 2310}

X(55379) = crosssum of X(3669) and X(43947)
X(55379) = trilinear product of X(1618) and X(55380)

X(55380) = PERSPECTOR OF THE TOUCHPOINTS-CONIC OF CCP( X(9) ) AND CCP( X(11) )

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

X(55380) lies on these lines: {9, 6065}, {11, 6362}, {663, 2310}, {826, 2611}, {1146, 44729}, {1566, 5532}, {2170, 3900}, {3309, 45234}, {3777, 17463}, {4516, 4542}, {52305, 55335}

X(55380) = crosspoint of X(9) and X(11)
X(55380) = crosssum of X(i) and X(j) for these {i, j}: {57, 59}, {651, 3315}
X(55380) = X(24036)-Dao conjugate of-X(85)
X(55380) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (5083, 1275), (24036, 4998)
X(55380) = pole of line {654, 14418} wrt Feuerbach circumhyperbola
X(55380) = barycentric product of X(i) and X(j) for these {i, j}: {11, 24036}, {1146, 5083}
X(55380) = trilinear product of X(i) and X(j) for these {i, j}: {2170, 24036}, {2310, 5083}, {43974, 55379}
X(55380) = trilinear quotient X(i)/X(j) for these (i, j): (5083, 7045), (24036, 4564)

X(55381) = CENTER OF THE TOUCHPOINTS-CONIC OF CCP( X(10) ) AND CCP( X(11) )

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

X(55381) lies on these lines: {3709, 21044}

X(55382) = PERSPECTOR OF THE TOUCHPOINTS-CONIC OF CCP( X(10) ) AND CCP( X(11) )

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

X(55382) lies on these lines: {11, 17420}, {656, 3120}, {3709, 21044}, {46101, 46384}

X(55382) = crosspoint of X(10) and X(11)
X(55382) = crosssum of X(58) and X(59)
X(55382) = X(i)-Ceva conjugate of-X(j) for these (i, j): (10, 21676), (40520, 55195), (50039, 52341)
X(55382) = pole of line {21013, 21676} wrt Kiepert circumhyperbola
X(55382) = barycentric product of X(17197) and X(21676)
X(55382) = trilinear product of X(18191) and X(21676)

X(55383) = CENTER OF THE TOUCHPOINTS-CONIC OF THE CIRCUMCIRCLE AND CCP( X(115) )

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

X(55383) lies on these lines: {647, 3124}, {9033, 12310}, {41512, 50947}

X(55384) = PERSPECTOR OF THE TOUCHPOINTS-CONIC OF THE CIRCUMCIRCLE AND CCP( X(115) )

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

X(55384) lies on these lines: {6, 23357}, {115, 12077}, {647, 3124}, {669, 20975}, {1084, 47415}, {1112, 47635}, {1648, 1650}, {3003, 20977}, {5661, 20859}, {8779, 14567}, {15527, 23992}, {30442, 47414}, {36830, 39024}, {37183, 41336}

X(55384) = cross-difference of every pair of points on the line X(4226)X(14366)
X(55384) = crosspoint of X(6) and X(115)
X(55384) = crosssum of X(2) and X(249)
X(55384) = X(3447)-Ceva conjugate of-X(512)
X(55384) = X(34990)-Dao conjugate of-X(76)
X(55384) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1112, 18020), (20975, 46087), (34990, 4590)
X(55384) = perspector of the inconic through X(6328) and X(10412)
X(55384) = pole of line {1648, 8029} wrt Brocard inellipse
X(55384) = pole of line {14769, 45147} wrt Kiepert circumhyperbola
X(55384) = barycentric product of X(i) and X(j) for these {i, j}: {115, 34990}, {125, 1112}, {868, 47635}, {2970, 23217}, {16734, 21833}
X(55384) = trilinear product of X(i) and X(j) for these {i, j}: {1112, 3708}, {2643, 34990}
X(55384) = trilinear quotient X(i)/X(j) for these (i, j): (3708, 46087), (34990, 24041)

X(55385) = BARYCENTRIC QUOTIENT X(1584)/X(1)

Barycentrics    Cos[A] - Csc[A] : :
Barycentrics    a*(2*b^2*c^2 + (a^2 - b^2 - c^2)*S) : :

X(55385) lies on these lines: {7, 55387}, {8, 55388}, {9, 1267}, {19, 27}, {57, 5391}, {326, 55397}, {491, 52419}, {1930, 3377}, {1958, 19216}, {3218, 32794}, {3219, 32793}, {3305, 32791}, {3306, 32792}, {3928, 32798}, {3929, 32797}, {5437, 32796}, {7308, 32795}, {19215, 52134}, {27003, 32800}, {27065, 32799}, {55393, 55395}, {55394, 55396}

X(55385) = isotomic conjugate of the polar conjugate of X(55389)
X(55385) = barycentric product X(i)*X(j) for these {i,j}: {69, 55389}, {75, 1584}, {304, 3093}
X(55385) = barycentric quotient X(i)/X(j) for these {i,j}: {1584, 1}, {3093, 19}, {55389, 4}
X(55385) = {X(63),X(75)}-harmonic conjugate of X(55386)

X(55386) = BARYCENTRIC QUOTIENT X(1583)/X(1)

Barycentrics    Cos[A] + Csc[A] : :
Barycentrics    a*(2*b^2*c^2 - (a^2 - b^2 - c^2)*S) : :

X(55386) lies on these lines: {7, 55388}, {8, 55387}, {9, 5391}, {19, 27}, {57, 1267}, {326, 55398}, {492, 52420}, {1930, 3378}, {1958, 19215}, {3218, 32793}, {3219, 32794}, {3305, 32792}, {3306, 32791}, {3928, 32797}, {3929, 32798}, {5437, 32795}, {7308, 32796}, {19216, 52134}, {27003, 32799}, {27065, 32800}, {55393, 55396}, {55394, 55395}

X(55386) = isotomic conjugate of the polar conjugate of X(55390)
X(55386) = barycentric product X(i)*X(j) for these {i,j}: {69, 55390}, {75, 1583}, {304, 3092}
X(55386) = barycentric quotient X(i)/X(j) for these {i,j}: {1583, 1}, {3092, 19}, {55390, 4}
X(55386) = {X(63),X(75)}-harmonic conjugate of X(55385)

X(55387) = X(7)X(55385)∩X(63)X(69)

Barycentrics    Cos[A] - Cot[A] : :
Barycentrics    a*(a^2 - b^2 - c^2)*(b*c - S) : :

X(55387) lies on these lines: {7, 55385}, {8, 55386}, {9, 492}, {40, 490}, {57, 491}, {63, 69}, {84, 489}, {264, 55396}, {317, 55395}, {488, 55104}, {606, 3084}, {637, 7330}, {638, 5709}, {1270, 3219}, {1271, 3218}, {3305, 32805}, {3306, 32806}, {3593, 27065}, {3595, 27003}, {3928, 32809}, {3929, 32808}, {5391, 7183}, {6213, 17206}, {7308, 32807}, {19216, 20769}, {37534, 45509}, {55391, 55397}, {55392, 55398}

X(55387) = isotomic conjugate of the polar conjugate of X(3084)
X(55387) = X(i)-isoconjugate of X(j) for these (i,j): {25, 1336}, {33, 13460}, {34, 13427}, {393, 34125}, {605, 6520}, {607, 13459}, {608, 13426}, {1096, 6212}, {1124, 6524}, {1267, 52439}, {2207, 13386}, {6136, 6591}
X(55387) = X(i)-Dao conjugate of X(j) for these (i,j): {6338, 46744}, {6503, 6212}, {6505, 1336}, {11517, 13427}, {37867, 605}
X(55387) = barycentric product X(i)*X(j) for these {i,j}: {63, 5391}, {69, 3084}, {77, 13458}, {78, 13436}, {304, 1335}, {305, 606}, {326, 13387}, {345, 52420}, {394, 46745}, {1102, 1123}, {3926, 6213}, {4561, 6365}, {13435, 55388}
X(55387) = barycentric quotient X(i)/X(j) for these {i,j}: {63, 1336}, {77, 13459}, {78, 13426}, {219, 13427}, {222, 13460}, {255, 34125}, {326, 13386}, {394, 6212}, {606, 25}, {1092, 605}, {1102, 1267}, {1123, 6520}, {1331, 6136}, {1335, 19}, {3084, 4}, {3926, 46744}, {3964, 3083}, {5391, 92}, {6213, 393}, {6365, 7649}, {6507, 1124}, {13387, 158}, {13436, 273}, {13458, 318}, {34121, 1096}, {46745, 2052}, {52420, 278}, {55388, 13424}
X(55387) = {X(63),X(69)}-harmonic conjugate of X(55388)

X(55388) = X(7)X(55386)∩X(63)X(69)

Barycentrics    Cos[A] + Cot[A] : :
Barycentrics    a*(a^2 - b^2 - c^2)*(b*c + S) : :

X(55388) lies on these lines: {7, 55386}, {8, 55385}, {9, 491}, {40, 489}, {57, 492}, {63, 69}, {84, 490}, {264, 55395}, {317, 55396}, {487, 55104}, {605, 3083}, {637, 5709}, {638, 7330}, {1267, 7183}, {1270, 3218}, {1271, 3219}, {3305, 32806}, {3306, 32805}, {3593, 27003}, {3595, 27065}, {3928, 32808}, {3929, 32809}, {5437, 32807}, {6212, 17206}, {19215, 20769}, {37534, 45508}, {55391, 55398}, {55392, 55397}

X(55388) = isotomic conjugate of the polar conjugate of X(3083)
X(55388) = X(i)-isoconjugate of X(j) for these (i,j): {25, 1123}, {33, 13438}, {34, 13456}, {393, 34121}, {606, 6520}, {607, 13437}, {608, 13454}, {1096, 6213}, {1335, 6524}, {2207, 13387}, {5391, 52439}, {6135, 6591}
X(55388) = X(i)-Dao conjugate of X(j) for these (i,j): {6338, 46745}, {6503, 6213}, {6505, 1123}, {11517, 13456}, {37867, 606}
X(55388) = barycentric product X(i)*X(j) for these {i,j}: {63, 1267}, {69, 3083}, {77, 13425}, {78, 13453}, {304, 1124}, {305, 605}, {326, 13386}, {345, 52419}, {394, 46744}, {1102, 1336}, {3926, 6212}, {4561, 6364}, {13424, 55387}
X(55388) = barycentric quotient X(i)/X(j) for these {i,j}: {63, 1123}, {77, 13437}, {78, 13454}, {219, 13456}, {222, 13438}, {255, 34121}, {326, 13387}, {394, 6213}, {605, 25}, {1092, 606}, {1102, 5391}, {1124, 19}, {1267, 92}, {1331, 6135}, {1336, 6520}, {3083, 4}, {3926, 46745}, {3964, 3084}, {6212, 393}, {6364, 7649}, {6507, 1335}, {13386, 158}, {13425, 318}, {13453, 273}, {34125, 1096}, {46744, 2052}, {52419, 278}, {55387, 13435}
X(55388) = {X(63),X(69)}-harmonic conjugate of X(55387)

X(55389) = X(1)X(29)∩X(19)X(19216)

Barycentrics    Sec[A] - Sin[A] : :
Barycentrics    a*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*b^2*c^2 + (a^2 - b^2 - c^2)*S) : :

X(55389) lies on these lines: {1, 29}, {19, 19216}, {33, 13386}, {34, 13387}, {278, 3084}, {281, 3083}, {1659, 30687}, {1859, 45714}, {7133, 55396}, {16232, 55395}

X(55389) = polar conjugate of the isotomic conjugate of X(55385)
X(55389) = barycentric product X(i)*X(j) for these {i,j}: {4, 55385}, {75, 3093}, {92, 1584}
X(55389) = barycentric quotient X(i)/X(j) for these {i,j}: {1584, 63}, {3093, 1}, {55385, 69}, {55414, 55390}
X(55389) = {X(1),X(92)}-harmonic conjugate of X(55390)

X(55390) = X(1)X(29)∩X(19)X(19215)

Barycentrics    Sec[A] + Sin[A] : :
Barycentrics    a*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*b^2*c^2 - (a^2 - b^2 - c^2)*S) : :

X(55390) lies on these lines: {1, 29}, {19, 19215}, {33, 13387}, {34, 13386}, {278, 3083}, {281, 3084}, {1859, 45713}, {2362, 55396}, {13390, 30687}, {42013, 55395}

X(55390) = polar conjugate of the isotomic conjugate of X(55386)
X(55390) = barycentric product X(i)*X(j) for these {i,j}: {4, 55386}, {75, 3092}, {92, 1583}
X(55390) = barycentric quotient X(i)/X(j) for these {i,j}: {1583, 63}, {3092, 1}, {55386, 69}, {55414, 55389}
X(55390) = {X(1),X(92)}-harmonic conjugate of X(55389)

X(55391) = X(1)X(69)∩X(2)X(3553)

Barycentrics    Cot[A] - Sin[A] : :
Barycentrics    a*(2*b*c*(a^2 - b^2 - c^2) + 4*S^2) : :

X(55391) lies on these lines: {1, 69}, {2, 3553}, {7, 326}, {8, 7269}, {19, 20769}, {33, 264}, {34, 317}, {36, 9723}, {56, 3964}, {63, 18162}, {75, 78}, {77, 320}, {86, 19861}, {183, 612}, {193, 3554}, {200, 42696}, {224, 18655}, {253, 9538}, {311, 3760}, {319, 3872}, {322, 3870}, {325, 614}, {344, 2324}, {491, 3084}, {492, 3083}, {648, 7129}, {969, 37607}, {997, 10436}, {1007, 5272}, {1040, 40680}, {1060, 41008}, {1062, 41005}, {1232, 3761}, {1442, 21296}, {1444, 3576}, {1870, 32001}, {1909, 44149}, {1959, 7289}, {2171, 25940}, {2257, 41610}, {2287, 24554}, {2331, 17907}, {3100, 6527}, {3191, 20336}, {3262, 3811}, {3622, 54303}, {3663, 22836}, {3664, 30144}, {3672, 34772}, {3869, 54404}, {3912, 28420}, {3920, 15589}, {4328, 42697}, {4417, 5256}, {4420, 32087}, {4861, 32099}, {5224, 19860}, {5227, 52134}, {5268, 34229}, {5287, 14829}, {5310, 15574}, {5736, 24547}, {6198, 32000}, {6261, 10444}, {7191, 37668}, {7280, 44180}, {7291, 18713}, {8822, 10884}, {10477, 46475}, {10513, 17024}, {16284, 17393}, {17019, 37655}, {17134, 20347}, {17234, 25930}, {17298, 53996}, {17322, 54392}, {17377, 36846}, {17441, 22263}, {17880, 33808}, {18147, 35516}, {18194, 39099}, {18455, 40995}, {20905, 27381}, {23151, 40937}, {23681, 24439}, {24328, 43216}, {25527, 54369}, {26006, 28753}, {27384, 37788}, {27507, 48381}, {28739, 28922}, {28793, 53816}, {55387, 55397}, {55388, 55398}

X(55391) = isotomic conjugate of the isogonal conjugate of X(602)
X(55391) = barycentric product X(i)*X(j) for these {i,j}: {63, 55393}, {75, 55399}, {76, 602}, {304, 11398}
X(55391) = barycentric quotient X(i)/X(j) for these {i,j}: {602, 6}, {11398, 19}, {55393, 92}, {55399, 1}
X(55391) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 69, 55392}, {7, 4511, 326}, {78, 7190, 75}, {193, 26639, 3554}, {320, 44179, 77}

X(55392) = X(1)X(69)∩X(2)X(3554)

Barycentrics    Cot[A] + Sin[A] : :
Barycentrics    a*(2*b*c*(a^2 - b^2 - c^2) - 4*S^2) : :

X(55392) lies on these lines: {1, 69}, {2, 3554}, {6, 25099}, {7, 4861}, {8, 326}, {9, 1332}, {33, 317}, {34, 264}, {35, 9723}, {40, 1444}, {55, 3964}, {63, 18161}, {75, 77}, {78, 319}, {86, 322}, {145, 54303}, {183, 614}, {193, 3553}, {239, 27305}, {269, 42697}, {309, 7210}, {311, 3761}, {320, 7190}, {325, 612}, {350, 44149}, {491, 3083}, {492, 3084}, {643, 35258}, {648, 2331}, {997, 17270}, {1007, 5268}, {1038, 40680}, {1060, 41005}, {1062, 41008}, {1232, 3760}, {1443, 31995}, {1870, 32000}, {1959, 5227}, {2099, 54344}, {2191, 3226}, {2324, 54280}, {2893, 18446}, {2975, 54404}, {3262, 10436}, {3620, 26639}, {3663, 22837}, {3672, 38460}, {3870, 17377}, {3920, 37668}, {4296, 6527}, {4341, 9312}, {4360, 36846}, {4384, 53996}, {4417, 5287}, {4511, 32099}, {4853, 42696}, {4909, 30143}, {5010, 44180}, {5224, 19861}, {5256, 14829}, {5271, 6505}, {5272, 34229}, {5279, 18713}, {5322, 15574}, {6198, 32001}, {7129, 17907}, {7191, 15589}, {7269, 21296}, {7289, 52134}, {8557, 15988}, {10513, 29815}, {11260, 24471}, {11679, 45126}, {14544, 26227}, {16284, 17394}, {17011, 37655}, {17206, 37529}, {17277, 25930}, {18230, 28982}, {18261, 50092}, {18447, 40995}, {25303, 44133}, {25935, 28753}, {39113, 54401}, {55387, 55398}, {55388, 55397}

X(55392) = isotomic conjugate of the isogonal conjugate of X(601)
X(55392) = barycentric product X(i)*X(j) for these {i,j}: {63, 55394}, {75, 55400}, {76, 601}, {304, 11399}
X(55392) = barycentric quotient X(i)/X(j) for these {i,j}: {601, 6}, {11399, 19}, {55394, 92}, {55400, 1}
X(55392) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 69, 55391}, {8, 1442, 326}, {77, 3872, 75}, {319, 44179, 78}

X(55393) = X(4)X(75)∩X(34)X(326)

Barycentrics    Csc[A] - Tan[A] : :
Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*b*c*(a^2 - b^2 - c^2) + 4*S^2) : :

X(55393) lies on these lines: {4, 75}, {7, 317}, {8, 264}, {34, 326}, {53, 4361}, {69, 273}, {86, 34231}, {92, 14555}, {239, 393}, {278, 4417}, {281, 17277}, {297, 4000}, {318, 42696}, {319, 32000}, {320, 1119}, {340, 21296}, {342, 6604}, {344, 26003}, {345, 37279}, {458, 2345}, {894, 3087}, {1249, 3759}, {1267, 1585}, {1478, 17859}, {1479, 17858}, {1586, 5391}, {1785, 3875}, {1851, 40703}, {1857, 40717}, {1870, 44179}, {1948, 53994}, {3535, 32791}, {3536, 32792}, {3583, 18691}, {3758, 40065}, {4360, 7952}, {4363, 6748}, {4644, 27377}, {4699, 54372}, {5222, 17907}, {5564, 7046}, {5749, 36794}, {5839, 9308}, {6820, 54284}, {7282, 42697}, {11393, 18695}, {16706, 52283}, {17121, 40138}, {17289, 52288}, {17321, 17555}, {17917, 41878}, {17923, 30828}, {20927, 46108}, {30854, 55116}, {31995, 32002}, {32099, 44134}, {55385, 55395}, {55386, 55396}

X(55393) = isotomic conjugate of the isogonal conjugate of X(11398)
X(55393) = polar conjugate of the isogonal conjugate of X(55399)
X(55393) = cevapoint of X(11398) and X(55399)
X(55393) = barycentric product X(i)*X(j) for these {i,j}: {76, 11398}, {92, 55391}, {264, 55399}, {602, 1969}
X(55393) = barycentric quotient X(i)/X(j) for these {i,j}: {602, 48}, {11398, 6}, {55391, 63}, {55399, 3}
X(55393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 75, 55394}, {273, 5081, 69}, {1119, 32001, 320}

X(55394) = X(4)X(75)∩X(33)X(326)

Barycentrics    Csc[A] + Tan[A] : :
Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*b*c*(a^2 - b^2 - c^2) - 4*S^2) : :

X(55394) lies on these lines: {4, 75}, {7, 264}, {8, 317}, {33, 326}, {53, 4363}, {69, 318}, {86, 7952}, {92, 54113}, {190, 281}, {192, 54372}, {239, 3087}, {273, 42697}, {297, 2345}, {319, 7046}, {320, 32000}, {329, 31623}, {340, 32099}, {344, 37448}, {393, 894}, {445, 17776}, {458, 4000}, {1119, 7321}, {1249, 3758}, {1267, 1586}, {1478, 17858}, {1479, 17859}, {1585, 5391}, {1753, 54404}, {1785, 10436}, {2322, 54280}, {3535, 32792}, {3536, 32791}, {3585, 18691}, {3759, 40065}, {4360, 34231}, {4361, 6748}, {4644, 9308}, {5081, 42696}, {5222, 36794}, {5749, 17907}, {5839, 27377}, {6198, 44179}, {6819, 54284}, {7102, 40703}, {10538, 40680}, {11109, 17321}, {11392, 18695}, {16706, 52288}, {17120, 40138}, {17289, 52283}, {18679, 26065}, {18743, 37276}, {21296, 44134}, {32002, 32087}, {37235, 44140}, {55385, 55396}, {55386, 55395}

X(55394) = isotomic conjugate of the isogonal conjugate of X(11399)
X(55394) = polar conjugate of the isogonal conjugate of X(55400)
X(55394) = cevapoint of X(11399) and X(55400)
X(55394) = barycentric product X(i)*X(j) for these {i,j}: {76, 11399}, {92, 55392}, {264, 55400}, {601, 1969}
X(55394) = barycentric quotient X(i)/X(j) for these {i,j}: {601, 48}, {11399, 6}, {55392, 63}, {55400, 3}
X(55394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 75, 55393}, {318, 7282, 69}, {7046, 32001, 319}, {10538, 53821, 40680}

X(55395) = X(4)X(63)∩X(9)X(1585)

Barycentrics    Cos[A] - Tan[A] : :
Barycentrics    a*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*((a^2 - b^2 - c^2)^2 - 4*b*c*S) : :

X(55395) lies on these lines: {4, 63}, {9, 1585}, {19, 13387}, {33, 55398}, {34, 55397}, {57, 1586}, {92, 6212}, {219, 55412}, {222, 55411}, {264, 55388}, {317, 55387}, {427, 16028}, {1748, 6213}, {3077, 55403}, {3092, 55400}, {3093, 55399}, {3305, 3535}, {3306, 3536}, {16232, 55389}, {42013, 55390}, {55385, 55393}, {55386, 55394}

X(55395) = isotomic conjugate of the polar conjugate of X(55403)
X(55395) = polar conjugate of the isogonal conjugate of X(3077)
X(55395) = barycentric product X(i)*X(j) for these {i,j}: {69, 55403}, {92, 55409}, {264, 3077}
X(55395) = barycentric quotient X(i)/X(j) for these {i,j}: {3077, 3}, {55403, 4}, {55409, 63}, {55413, 55396}
X(55395) = {X(4),X(63)}-harmonic conjugate of X(55396)

X(55396) = X(4)X(63)∩X(9)X(1586)

Barycentrics    Cos[A] + Tan[A] : :
Barycentrics    a*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*((a^2 - b^2 - c^2)^2 + 4*b*c*S) : :

X(55396) lies on these lines: {4, 63}, {9, 1586}, {19, 13386}, {33, 55397}, {34, 55398}, {57, 1585}, {92, 6213}, {219, 55411}, {222, 55412}, {235, 16028}, {264, 55387}, {317, 55388}, {1748, 6212}, {2362, 55390}, {3076, 55404}, {3092, 55399}, {3093, 55400}, {3305, 3536}, {3306, 3535}, {7133, 55389}, {55385, 55394}, {55386, 55393}

X(55396) = isotomic conjugate of the polar conjugate of X(55404)
X(55396) = polar conjugate of the isogonal conjugate of X(3076)
X(55396) = barycentric product X(i)*X(j) for these {i,j}: {69, 55404}, {92, 55410}, {264, 3076}
X(55396) = barycentric quotient X(i)/X(j) for these {i,j}: {3076, 3}, {55404, 4}, {55410, 63}, {55413, 55395}
X(55396) = {X(4),X(63)}-harmonic conjugate of X(55395)

X(55397) = X(1)X(21)∩X(2)X(176)

Barycentrics    Cos[A] - Sin[A] : :
Barycentrics    a*(a^2 - b^2 - c^2 + 2*S) : :

X(55397) lies on these lines: {1, 21}, {2, 176}, {9, 3083}, {12, 16028}, {19, 19216}, {33, 55396}, {34, 55395}, {42, 45427}, {55, 45431}, {57, 3084}, {145, 46421}, {175, 9965}, {193, 13386}, {219, 55410}, {222, 55409}, {326, 55385}, {372, 42700}, {482, 5249}, {491, 13461}, {908, 5405}, {1124, 55400}, {1335, 55399}, {2994, 14121}, {3052, 45477}, {3218, 13388}, {3219, 30556}, {3297, 55406}, {3298, 55405}, {3299, 54444}, {3434, 52805}, {3641, 3870}, {3666, 7969}, {3744, 5605}, {4641, 7968}, {5256, 18991}, {5273, 17805}, {5905, 13390}, {6213, 16440}, {7411, 31564}, {10910, 25466}, {11220, 31563}, {15891, 41798}, {16441, 24611}, {17599, 45398}, {17740, 35774}, {17802, 28610}, {20292, 30426}, {24477, 26517}, {24987, 31533}, {25568, 26523}, {25722, 30355}, {30334, 36845}, {31538, 54357}, {31546, 41717}, {32912, 45426}, {44447, 52808}, {55387, 55391}, {55388, 55392}, {55401, 55403}, {55402, 55404}

X(55397) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1333, 175}, {1806, 4329}, {2066, 52364}, {2194, 46421}, {2299, 13387}, {6502, 2897}, {14121, 21287}, {16232, 2893}, {32676, 54019}, {42013, 1330}, {53064, 3152}, {53065, 3151}
X(55397) = X(92)-Ceva conjugate of X(55398)
X(55397) = X(i)-isoconjugate of X(j) for these (i,j): {2, 8576}, {3, 41516}, {4, 6414}, {6, 486}, {25, 11091}, {32, 34392}, {51, 16037}, {68, 5413}, {371, 2165}, {393, 26922}, {485, 44193}, {512, 54030}, {523, 39384}, {589, 8036}, {847, 8911}, {1322, 6416}, {1505, 18820}, {1585, 2351}, {5408, 14593}, {6413, 13429}, {8577, 13428}, {8770, 8940}, {8946, 24245}, {10666, 41515}, {24243, 53061}, {32734, 54029}
X(55397) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 486}, {5408, 63}, {6376, 34392}, {6505, 11091}, {10960, 1}, {10962, 3378}, {24246, 91}, {32664, 8576}, {36033, 6414}, {36103, 41516}, {39054, 54030}
X(55397) = cevapoint of X(1) and X(19216)
X(55397) = barycentric product X(i)*X(j) for these {i,j}: {1, 491}, {31, 45806}, {47, 34391}, {57, 13461}, {63, 1586}, {75, 372}, {92, 5409}, {304, 5412}, {485, 44179}, {492, 3377}, {662, 54028}, {1748, 11090}, {1969, 26920}, {13439, 55398}
X(55397) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 486}, {19, 41516}, {31, 8576}, {47, 371}, {48, 6414}, {63, 11091}, {75, 34392}, {163, 39384}, {255, 26922}, {371, 3378}, {372, 1}, {485, 91}, {491, 75}, {563, 8911}, {662, 54030}, {1586, 92}, {1707, 8940}, {1748, 1585}, {1993, 55398}, {2167, 16037}, {3377, 485}, {5409, 63}, {5412, 19}, {6413, 1820}, {13461, 312}, {19216, 24245}, {26920, 48}, {34391, 20571}, {39383, 36145}, {44179, 492}, {45806, 561}, {54028, 1577}, {55398, 13428}
X(55397) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 63, 55398}, {31, 1959, 55398}, {38, 52134, 55398}, {81, 3869, 55398}, {255, 45224, 55398}, {1621, 24635, 55398}, {2975, 28606, 55398}, {5248, 16585, 55398}, {13389, 30557, 2}

X(55398) = X(1)X(21)∩X(2)X(175)

Barycentrics    Cos[A] + Sin[A] : :
Barycentrics    a*(a^2 - b^2 - c^2 - 2*S) : :

X(55398) lies on these lines: {1, 21}, {2, 175}, {9, 3084}, {11, 16028}, {19, 19215}, {33, 55395}, {34, 55396}, {42, 45426}, {55, 45430}, {57, 3083}, {145, 46422}, {176, 9965}, {193, 7133}, {219, 55409}, {222, 55410}, {326, 55386}, {371, 42700}, {481, 5249}, {908, 5393}, {1124, 55399}, {1335, 55400}, {1659, 5905}, {2994, 7090}, {3052, 45476}, {3218, 13389}, {3219, 30557}, {3297, 55405}, {3298, 55406}, {3301, 54444}, {3434, 52808}, {3640, 3870}, {3666, 7968}, {3744, 5604}, {4641, 7969}, {5256, 18992}, {5273, 17802}, {6212, 16441}, {7411, 31563}, {8225, 41717}, {10911, 25466}, {11220, 31564}, {15892, 41798}, {16440, 24611}, {17599, 45399}, {17740, 35775}, {17805, 28610}, {20292, 30425}, {24477, 26522}, {24987, 31532}, {25568, 26518}, {25722, 30354}, {30333, 36845}, {31539, 54357}, {32912, 45427}, {44447, 52805}, {55387, 55392}, {55388, 55391}, {55401, 55404}, {55402, 55403}

X(55398) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1333, 176}, {1805, 4329}, {2067, 2897}, {2194, 46422}, {2299, 13386}, {2362, 2893}, {5414, 52364}, {7090, 21287}, {7133, 1330}, {32676, 54017}, {53063, 3152}, {53066, 3151}
X(55398) = X(92)-Ceva conjugate of X(55397)
X(55398) = X(i)-isoconjugate of X(j) for these (i,j): {2, 8577}, {3, 41515}, {4, 6413}, {6, 485}, {25, 11090}, {32, 34391}, {51, 16032}, {57, 13455}, {68, 5412}, {372, 2165}, {486, 44192}, {512, 54031}, {523, 39383}, {588, 8035}, {847, 26920}, {1321, 6415}, {1504, 18819}, {1586, 2351}, {5409, 14593}, {6414, 13440}, {8576, 13439}, {8770, 8944}, {8948, 24246}, {10665, 41516}, {24244, 53060}, {32734, 54028}
X(55398) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 485}, {5409, 63}, {5452, 13455}, {6376, 34391}, {6505, 11090}, {10960, 3377}, {10962, 1}, {24245, 91}, {32664, 8577}, {36033, 6413}, {36103, 41515}, {39054, 54031}
X(55398) = cevapoint of X(1) and X(19215)
X(55398) = barycentric product X(i)*X(j) for these {i,j}: {1, 492}, {31, 45805}, {47, 34392}, {63, 1585}, {75, 371}, {92, 5408}, {304, 5413}, {486, 44179}, {491, 3378}, {662, 54029}, {1748, 11091}, {1969, 8911}, {3083, 13457}, {13428, 55397}
X(55398) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 485}, {19, 41515}, {31, 8577}, {47, 372}, {48, 6413}, {55, 13455}, {63, 11090}, {75, 34391}, {163, 39383}, {371, 1}, {372, 3377}, {486, 91}, {492, 75}, {563, 26920}, {662, 54031}, {1585, 92}, {1707, 8944}, {1748, 1586}, {1993, 55397}, {2167, 16032}, {3378, 486}, {5408, 63}, {5413, 19}, {6414, 1820}, {8911, 48}, {19215, 24246}, {34392, 20571}, {39384, 36145}, {44179, 491}, {45805, 561}, {54029, 1577}, {55397, 13439}
X(55398) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 63, 55397}, {31, 1959, 55397}, {38, 52134, 55397}, {81, 3869, 55397}, {255, 45224, 55397}, {1621, 24635, 55397}, {2975, 28606, 55397}, {5248, 16585, 55397}, {13388, 30556, 2}

X(55399) = X(2)X(219)∩X(6)X(63)

Barycentrics    Cos[A] - Sin[A]^2 : :
Barycentrics    a^2*(b*c*(a^2 - b^2 - c^2) + 2*S^2) : :

X(55399) lies on these lines: {2, 219}, {3, 26889}, {6, 63}, {9, 10601}, {25, 7193}, {31, 613}, {38, 611}, {48, 11350}, {51, 24320}, {55, 5135}, {57, 394}, {72, 36754}, {78, 36745}, {81, 5744}, {92, 239}, {155, 37532}, {162, 7151}, {182, 7085}, {184, 37581}, {191, 16472}, {193, 26871}, {209, 36741}, {218, 329}, {220, 3305}, {222, 1993}, {223, 23144}, {241, 6505}, {321, 28916}, {323, 23140}, {485, 16028}, {511, 1473}, {580, 1259}, {582, 11517}, {604, 6507}, {608, 1748}, {610, 39592}, {651, 9965}, {674, 37577}, {908, 2911}, {956, 44414}, {1040, 16465}, {1062, 14054}, {1124, 55398}, {1181, 5709}, {1191, 11682}, {1203, 12526}, {1332, 18141}, {1335, 55397}, {1350, 7293}, {1351, 26892}, {1407, 22128}, {1429, 27659}, {1451, 37248}, {1465, 3173}, {1471, 25941}, {1818, 37309}, {1936, 19354}, {1944, 54284}, {1959, 16502}, {1998, 7070}, {2003, 3928}, {2207, 55401}, {2256, 5287}, {2975, 19767}, {2990, 43043}, {3061, 36504}, {3092, 55396}, {3093, 55395}, {3167, 26884}, {3190, 13329}, {3193, 41344}, {3211, 11347}, {3219, 5422}, {3220, 33586}, {3306, 17811}, {3556, 41580}, {3682, 37282}, {3690, 43650}, {3744, 12595}, {3759, 18750}, {3781, 7484}, {3784, 26866}, {3796, 5285}, {3868, 7078}, {3869, 5262}, {3870, 7074}, {3916, 36742}, {3927, 37509}, {3955, 11402}, {4361, 14213}, {4363, 20879}, {4652, 36746}, {5020, 26885}, {5050, 26890}, {5085, 5314}, {5157, 12329}, {5228, 5249}, {5299, 51304}, {5706, 6734}, {5708, 22136}, {5739, 23151}, {5748, 37680}, {5783, 19822}, {5905, 34048}, {6511, 52032}, {6515, 26932}, {6763, 16473}, {7225, 28388}, {7308, 52405}, {7330, 10982}, {8745, 55407}, {9729, 26935}, {9776, 37659}, {11064, 20266}, {11329, 22127}, {11349, 22153}, {11433, 27509}, {13346, 26927}, {13388, 55409}, {13389, 55410}, {14547, 20835}, {15066, 27003}, {16059, 17976}, {16412, 22126}, {16697, 18206}, {17011, 54358}, {17277, 27287}, {17301, 17781}, {17796, 30852}, {17862, 28950}, {18603, 46885}, {18607, 45126}, {19349, 37591}, {19350, 24310}, {20760, 37510}, {20818, 37269}, {22060, 37474}, {22464, 34032}, {23061, 26910}, {24467, 36747}, {25885, 42289}, {26921, 36752}, {26923, 37491}, {27174, 46882}, {27623, 30007}, {34234, 37683}, {37034, 42463}, {37514, 55104}, {52134, 54416}, {54301, 54422}, {55402, 55415}

X(55399) = isotomic conjugate of the polar conjugate of X(11398)
X(55399) = isogonal conjugate of the polar conjugate of X(55393)
X(55399) = X(55393)-Ceva conjugate of X(11398)
X(55399) = barycentric product X(i)*X(j) for these {i,j}: {1, 55391}, {3, 55393}, {69, 11398}, {75, 602}
X(55399) = barycentric quotient X(i)/X(j) for these {i,j}: {602, 1}, {11398, 4}, {55391, 75}, {55393, 264}
X(55399) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 63, 55400}, {6, 55405, 63}, {6, 55406, 54444}, {9, 52423, 10601}, {57, 2323, 394}, {63, 54444, 55406}, {219, 52424, 2}, {220, 17825, 3305}, {1407, 37672, 22128}, {1993, 3218, 222}, {2003, 3928, 22129}, {26889, 26893, 3}, {54444, 55406, 55400}

X(55400) = X(2)X(222)∩X(6)X(63)

Barycentrics    Cos[A] + Sin[A]^2 : :
Barycentrics    a^2*(b*c*(a^2 - b^2 - c^2) - 2*S^2) : :

X(55400) lies on these lines: {2, 222}, {3, 26890}, {6, 63}, {9, 394}, {21, 7078}, {25, 3955}, {31, 611}, {38, 613}, {41, 6507}, {51, 37581}, {55, 1331}, {57, 10601}, {72, 36742}, {73, 37248}, {78, 36746}, {81, 329}, {86, 27287}, {92, 608}, {144, 37685}, {162, 3195}, {182, 1473}, {184, 24320}, {189, 5749}, {191, 16473}, {193, 26872}, {198, 1790}, {212, 20835}, {218, 24635}, {219, 1993}, {220, 37672}, {221, 19860}, {228, 37474}, {255, 11344}, {405, 3157}, {442, 8757}, {452, 3562}, {486, 16028}, {500, 11517}, {511, 7085}, {581, 1259}, {607, 1748}, {612, 17615}, {908, 940}, {914, 32777}, {1069, 35194}, {1124, 55397}, {1181, 7330}, {1335, 55398}, {1350, 5314}, {1351, 26893}, {1406, 3812}, {1407, 3306}, {1708, 18607}, {1745, 37229}, {1762, 19350}, {1812, 54280}, {1864, 2000}, {1935, 19349}, {1959, 54416}, {2162, 27442}, {2183, 11350}, {2207, 55402}, {2267, 22097}, {2323, 3929}, {2478, 41344}, {2911, 16585}, {2975, 16466}, {3092, 55395}, {3093, 55396}, {3167, 26885}, {3173, 40937}, {3218, 5422}, {3220, 3796}, {3305, 17811}, {3436, 5711}, {3556, 55098}, {3744, 12594}, {3758, 18750}, {3781, 26867}, {3784, 7484}, {3869, 17015}, {3916, 36754}, {3927, 36750}, {3928, 52423}, {3937, 43650}, {3940, 51340}, {4303, 37282}, {4361, 20879}, {4363, 14213}, {4652, 36745}, {4855, 37501}, {5020, 26884}, {5050, 26889}, {5085, 7293}, {5249, 6180}, {5280, 51304}, {5285, 33586}, {5546, 40214}, {5709, 10982}, {5739, 51407}, {5744, 32911}, {5748, 37633}, {5905, 37543}, {6350, 15988}, {6505, 25091}, {6512, 52032}, {6515, 26942}, {6763, 16472}, {7074, 35258}, {7123, 40781}, {7169, 41580}, {7193, 11402}, {8745, 55408}, {9347, 11678}, {9370, 24987}, {9729, 26927}, {11108, 23070}, {11427, 27509}, {11681, 26131}, {12059, 30142}, {13323, 29958}, {13346, 26935}, {13615, 22117}, {14557, 24611}, {15018, 23958}, {15066, 23140}, {15805, 37612}, {16058, 22161}, {16293, 23072}, {16418, 23071}, {16502, 52134}, {17862, 28968}, {18652, 25019}, {18662, 32933}, {19354, 24430}, {19735, 30035}, {19861, 34046}, {20266, 37648}, {20332, 37206}, {22053, 37309}, {23061, 26911}, {23151, 28922}, {24467, 36752}, {25875, 37523}, {26059, 40435}, {26921, 36747}, {26924, 37491}, {30513, 54451}, {30556, 55410}, {30557, 55409}, {30852, 37674}, {31424, 54301}, {32773, 33650}, {34035, 54425}, {37284, 52408}, {37498, 55104}, {37584, 44413}, {40571, 46882}, {44547, 54289}, {55401, 55415}

X(55400) = isotomic conjugate of the polar conjugate of X(11399)
X(55400) = isogonal conjugate of the polar conjugate of X(55394)
X(55400) = X(55394)-Ceva conjugate of X(11399)
X(55400) = crossdifference of every pair of points on line {8678, 53549}
X(55400) = barycentric product X(i)*X(j) for these {i,j}: {1, 55392}, {3, 55394}, {69, 11399}, {75, 601}
X(55400) = barycentric quotient X(i)/X(j) for these {i,j}: {601, 1}, {11399, 4}, {55392, 75}, {55394, 264}
X(55400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 63, 55399}, {6, 55406, 63}, {9, 2003, 394}, {63, 54444, 6}, {1407, 17825, 3306}, {1993, 3219, 219}, {3218, 5422, 52424}, {3305, 22128, 17811}, {10601, 22129, 57}, {26890, 26892, 3}, {54444, 55406, 55399}

X(55401) = X(63)X(393)∩X(222)X(55413)

Barycentrics    Cos[A] - Tan[A]^2 : :
Barycentrics    a*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*((-a^2 + b^2 + c^2)^3 - 8*b*c*S^2) : :

X(55401) lies on these lines: {9, 2052}, {57, 11547}, {63, 393}, {219, 55414}, {222, 55413}, {2207, 55399}, {5437, 14165}, {7330, 41365}, {55397, 55403}, {55398, 55404}, {55400, 55415}

X(55401) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 393, 55402}, {393, 55407, 63}

X(55402) = X(63)X(393)∩X(222)X(55414)

Barycentrics    Cos[A] + Tan[A]^2 : :
Barycentrics    a*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*((-a^2 + b^2 + c^2)^3 + 8*b*c*S^2) : :

X(55402) lies on these lines: {9, 11547}, {57, 2052}, {63, 393}, {219, 55413}, {222, 55414}, {2207, 55400}, {5709, 41365}, {7308, 14165}, {8745, 54444}, {55397, 55404}, {55398, 55403}, {55399, 55415}

X(55402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 393, 55401}, {393, 55408, 63}

X(55403) = X(1)X(393)∩X(1096)X(1123)

Barycentrics    Sin[A] - Tan[A]^2 : :
Barycentrics    a*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*((a^2 - b^2 - c^2)^2 - 4*b*c*S) : :

X(55403) lies on these lines: {1, 393}, {1096, 1123}, {1124, 55415}, {1335, 2207}, {2052, 3083}, {3077, 55395}, {3084, 11547}, {3301, 8745}, {55397, 55401}, {55398, 55402}, {55409, 55413}, {55410, 55414}

X(55403) = polar conjugate of the isotomic conjugate of X(55395)
X(55403) = barycentric product X(i)*X(j) for these {i,j}: {4, 55395}, {158, 55409}, {2052, 3077}
X(55403) = barycentric quotient X(i)/X(j) for these {i,j}: {3077, 394}, {55395, 69}, {55409, 326}
X(55403) = {X(1),X(393)}-harmonic conjugate of X(55404)

X(55404) = X(1)X(393)∩X(1096)X(1336)

Barycentrics    Sin[A] + Tan[A]^2 : :
Barycentrics    a*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*((a^2 - b^2 - c^2)^2 + 4*b*c*S) : :

X(55404) lies on these lines: {1, 393}, {1096, 1336}, {1124, 2207}, {1335, 55415}, {2052, 3084}, {3076, 55396}, {3083, 11547}, {3299, 8745}, {55397, 55402}, {55398, 55401}, {55409, 55414}, {55410, 55413}

X(55404) = polar conjugate of the isotomic conjugate of X(55396)
X(55404) = barycentric product X(i)*X(j) for these {i,j}: {4, 55396}, {158, 55410}, {2052, 3076}
X(55404) = barycentric quotient X(i)/X(j) for these {i,j}: {3076, 394}, {55396, 69}, {55410, 326}
X(55404) = {X(1),X(393)}-harmonic conjugate of X(55403)

X(55405) = X(2)X(220)∩X(6)X(63)

Barycentrics    2*Cos[A] - Sin[A]^2 : :
Barycentrics    a^2*(b*c*(a^2 - b^2 - c^2) + S^2) : :

X(55405) lies on these lines: {2, 220}, {3, 3190}, {6, 63}, {8, 37537}, {9, 17825}, {27, 5792}, {56, 25941}, {57, 219}, {72, 36745}, {81, 46889}, {92, 4361}, {101, 37269}, {141, 26872}, {144, 32911}, {154, 7193}, {189, 5839}, {218, 2999}, {221, 37591}, {222, 2323}, {239, 18750}, {329, 3782}, {394, 1407}, {517, 21370}, {518, 1040}, {524, 26871}, {527, 34048}, {613, 1707}, {651, 28610}, {908, 24789}, {910, 39592}, {940, 2256}, {970, 42461}, {1191, 3869}, {1260, 13329}, {1350, 1473}, {1445, 25091}, {1498, 5709}, {1611, 16514}, {1616, 11682}, {1936, 2192}, {1959, 16781}, {1993, 22129}, {2175, 54326}, {2207, 55407}, {2911, 3752}, {2975, 17018}, {3008, 35599}, {3052, 12595}, {3173, 34042}, {3195, 23052}, {3197, 15509}, {3207, 11350}, {3210, 54107}, {3219, 10601}, {3297, 55398}, {3298, 55397}, {3670, 16471}, {3687, 23151}, {3690, 7484}, {3916, 36746}, {3917, 26866}, {3927, 36754}, {3929, 52423}, {3955, 17809}, {4513, 34255}, {4640, 45728}, {4652, 37501}, {5085, 7085}, {5220, 24434}, {5314, 53094}, {5435, 25934}, {5437, 52405}, {5526, 23511}, {5745, 37543}, {5773, 19645}, {6180, 9965}, {6507, 7113}, {6508, 7124}, {6509, 7011}, {6617, 35072}, {7050, 17126}, {7078, 54422}, {7151, 8765}, {7293, 31884}, {9776, 25878}, {10025, 20921}, {11347, 20367}, {11477, 26892}, {11684, 17025}, {12526, 16466}, {13567, 27509}, {14213, 17119}, {15066, 23958}, {15644, 26928}, {16028, 42265}, {16502, 51304}, {17011, 24635}, {17080, 23144}, {17118, 20879}, {17259, 27287}, {17781, 49747}, {17810, 24320}, {17814, 37532}, {18206, 18603}, {19725, 24633}, {20223, 42051}, {21454, 37659}, {22145, 36100}, {22149, 37510}, {22276, 22769}, {24467, 37498}, {25930, 45227}, {26005, 27540}, {26011, 27411}, {26867, 43650}, {26890, 53093}, {26911, 40916}, {26921, 37514}, {26938, 37515}, {34046, 54320}, {37597, 54369}, {37687, 46873}, {55408, 55415}

X(55405) = crossdifference of every pair of points on line {2488, 8678}
X(55405) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 63, 55406}, {9, 52424, 17825}, {57, 219, 17811}, {63, 55399, 6}, {222, 2323, 37672}, {394, 3218, 1407}, {1473, 26893, 1350}, {2323, 3928, 222}, {7085, 26889, 5085}, {7193, 37581, 154}

X(55406) = X(2)X(1407)∩X(6)X(63)

Barycentrics    2*Cos[A] + Sin[A]^2 : :
Barycentrics    a^2*(b*c*(a^2 - b^2 - c^2) - S^2) : :

X(55406) lies on these lines: {2, 1407}, {3, 29958}, {6, 63}, {9, 222}, {57, 17825}, {72, 36746}, {77, 25091}, {78, 37501}, {81, 144}, {92, 4363}, {141, 26871}, {154, 3955}, {189, 2345}, {219, 2003}, {220, 394}, {221, 958}, {223, 25939}, {268, 6509}, {329, 940}, {524, 26872}, {527, 37543}, {611, 1707}, {651, 5273}, {894, 18750}, {908, 37674}, {954, 17194}, {960, 34046}, {991, 1260}, {1038, 1413}, {1071, 54305}, {1191, 2975}, {1214, 34052}, {1331, 20835}, {1350, 7085}, {1473, 5085}, {1498, 7330}, {1762, 3197}, {1778, 40153}, {1790, 3207}, {2174, 6507}, {2192, 24430}, {2207, 55408}, {2286, 6508}, {2328, 22117}, {3052, 12594}, {3157, 31445}, {3177, 54107}, {3195, 8765}, {3218, 10601}, {3271, 54326}, {3297, 55397}, {3298, 55398}, {3436, 49745}, {3713, 14552}, {3916, 36745}, {3917, 26867}, {3920, 7050}, {3927, 36742}, {3928, 52424}, {3937, 7484}, {4306, 37244}, {4383, 5744}, {4640, 7074}, {4670, 19727}, {5228, 9965}, {5234, 34043}, {5297, 11678}, {5314, 31884}, {5687, 48897}, {5711, 12527}, {5745, 34042}, {5748, 17775}, {5791, 8757}, {5942, 19822}, {6350, 44416}, {7078, 31424}, {7151, 23052}, {7193, 17809}, {7293, 53094}, {10319, 34371}, {11477, 26893}, {12572, 41344}, {13323, 42461}, {14213, 17118}, {15644, 26938}, {15668, 27287}, {15823, 19349}, {16028, 42262}, {16058, 22148}, {16781, 23538}, {17074, 18228}, {17119, 20879}, {17810, 37581}, {19734, 20245}, {19735, 24612}, {20760, 37474}, {22097, 54322}, {23154, 37246}, {23292, 27509}, {24467, 37514}, {26866, 43650}, {26889, 53093}, {26910, 40916}, {26921, 37498}, {26928, 37515}, {30852, 37682}, {32782, 37781}, {37619, 47041}, {51304, 54416}, {55407, 55415}

X(55406) = crossdifference of every pair of points on line {2520, 8678}
X(55406) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 22129, 1407}, {6, 63, 55405}, {9, 222, 17811}, {63, 54444, 55399}, {63, 55400, 6}, {219, 2003, 37672}, {394, 3219, 220}, {1473, 26890, 5085}, {2003, 3929, 219}, {3955, 24320, 154}, {4640, 45729, 7074}, {7085, 26892, 1350}, {17074, 18228, 25934}, {54444, 55399, 6}, {55399, 55400, 54444}

X(55407) = X(63)X(393)∩X(2052)X(3219)

Barycentrics    2*Cos[A] - Tan[A]^2 : :
Barycentrics    a*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*((a^2 - b^2 - c^2)^3 + 4*b*c*S^2) : :

X(55407) lies on these lines: {63, 393}, {1947, 28731}, {2052, 3219}, {2202, 6508}, {2207, 55405}, {3218, 11547}, {8745, 55399}, {14165, 27003}, {22129, 55413}, {55406, 55415}

X(55407) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 393, 55408}, {63, 55401, 393}

X(55408) = X(63)X(393)∩X(2052)X(3218)

Barycentrics    2*Cos[A] + Tan[A]^2 : :
Barycentrics    a*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*((a^2 - b^2 - c^2)^3 - 4*b*c*S^2) : :

X(55408) lies on these lines: {63, 393}, {2052, 3218}, {2207, 55406}, {3219, 11547}, {6508, 7120}, {8745, 55400}, {14165, 27065}, {22129, 55414}, {52418, 54444}, {55405, 55415}

X(55408) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 393, 55407}, {63, 55402, 393}

X(55409) = X(1)X(394)∩X(35)X(5406)

Barycentrics    Cos[A]^2 - Sin[A] : :
Barycentrics    a^2*((a^2 - b^2 - c^2)^2 - 4*b*c*S) : :

X(55409) lies on these lines: {1, 394}, {2, 1124}, {6, 3084}, {33, 55412}, {34, 55411}, {35, 5406}, {36, 5407}, {55, 5408}, {56, 5409}, {210, 45424}, {219, 55398}, {222, 55397}, {354, 45423}, {612, 45490}, {614, 45493}, {940, 19050}, {1335, 1993}, {1583, 2066}, {1584, 6502}, {1591, 31472}, {1592, 44624}, {3083, 3297}, {3298, 37672}, {3299, 10601}, {4383, 19047}, {6347, 17275}, {6805, 31408}, {8962, 31459}, {10931, 17597}, {13388, 55399}, {30557, 55400}, {55403, 55413}, {55404, 55414}

X(55409) = barycentric product X(i)*X(j) for these {i,j}: {63, 55395}, {75, 3077}, {326, 55403}
X(55409) = barycentric quotient X(i)/X(j) for these {i,j}: {3077, 1}, {55395, 92}, {55403, 158}
X(55409) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 394, 55410}, {3297, 17811, 3083}

X(55410) = X(1)X(394)∩X(35)X(5407)

Barycentrics    Cos[A]^2 + Sin[A] : :
Barycentrics    a^2*((a^2 - b^2 - c^2)^2 + 4*b*c*S) : :

X(55410) lies on these lines: {1, 394}, {2, 1335}, {6, 3083}, {33, 55411}, {34, 55412}, {35, 5407}, {36, 5406}, {55, 5409}, {56, 5408}, {210, 45425}, {219, 55397}, {222, 55398}, {354, 45422}, {612, 45491}, {614, 45492}, {940, 19049}, {1124, 1993}, {1583, 2067}, {1584, 5414}, {1591, 44623}, {1592, 44622}, {3084, 3298}, {3297, 37672}, {3301, 10601}, {4383, 19048}, {6348, 17275}, {10932, 17597}, {13389, 55399}, {30556, 55400}, {55403, 55414}, {55404, 55413}

X(55410) = barycentric product X(i)*X(j) for these {i,j}: {63, 55396}, {75, 3076}, {326, 55404}
X(55410) = barycentric quotient X(i)/X(j) for these {i,j}: {3076, 1}, {55396, 92}, {55404, 158}
X(55410) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 394, 55409}, {3298, 17811, 3084}

X(55411) = X(4)X(394)∩X(6)X(1586)

Barycentrics    Cos[A]^2 - Tan[A] : :
Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*((a^2 - b^2 - c^2)^3 + 8*b^2*c^2*S) : :

X(55411) lies on these lines: {2, 1579}, {4, 394}, {6, 1586}, {24, 5407}, {25, 5409}, {33, 55410}, {34, 55409}, {219, 55396}, {222, 55395}, {371, 15199}, {372, 15201}, {378, 5406}, {427, 6289}, {1151, 15203}, {1152, 15205}, {1583, 11473}, {1584, 5413}, {1585, 17811}, {1593, 5408}, {1993, 3093}, {3536, 10601}, {5411, 15213}, {6409, 15207}, {6410, 15209}, {10881, 15217}, {15200, 35765}, {45400, 50645}, {49087, 52077}

X(55411) = {X(4),X(394)}-harmonic conjugate of X(55412)

X(55412) = X(4)X(394)∩X(6)X(1585)

Barycentrics    Cos[A]^2 + Tan[A] : :
Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*((a^2 - b^2 - c^2)^3 - 8*b^2*c^2*S) : :

X(55412) lies on these lines: {2, 1578}, {4, 394}, {6, 1585}, {24, 5406}, {25, 5408}, {33, 55409}, {34, 55410}, {219, 55395}, {222, 55396}, {371, 15198}, {372, 15200}, {378, 5407}, {427, 6290}, {1151, 15202}, {1152, 15204}, {1583, 5412}, {1584, 11474}, {1586, 17811}, {1593, 5409}, {1993, 3092}, {3535, 10601}, {5410, 15210}, {6409, 15206}, {6410, 15208}, {10880, 15214}, {15199, 35764}, {45401, 50645}, {49086, 52077}

X(55412) = {X(4),X(394)}-harmonic conjugate of X(55411)

X(55413) = X(222)X(55401)∩X(393)X(394)

Barycentrics    Cos[A]^2 - Tan[A]^2 : :
Barycentrics    a^2*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*((a^2 - b^2 - c^2)^4 - 16*b^2*c^2*S^2) : :

X(55413) lies on these lines: {2, 55415}, {6, 11547}, {219, 55402}, {222, 55401}, {393, 394}, {1993, 2207}, {2052, 17811}, {14165, 17825}, {17814, 41365}, {22129, 55407}, {37778, 41244}, {55403, 55409}, {55404, 55410}

X(55413) = barycentric product X(55395)*X(55396)
X(55413) = {X(393),X(394)}-harmonic conjugate of X(55414)

X(55414) = X(222)X(55402)∩X(393)X(394)

Barycentrics    Cos[A]^2 + Tan[A]^2 : :
Barycentrics    a^2*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*((a^2 - b^2 - c^2)^4 + 16*b^2*c^2*S^2) : :

X(55414) lies on these lines: {2, 2207}, {6, 275}, {219, 55401}, {222, 55402}, {393, 394}, {1941, 37498}, {1993, 55415}, {8745, 10601}, {11547, 17811}, {22129, 55408}, {27376, 37192}, {55403, 55410}, {55404, 55409}

X(55414) = barycentric product X(55389)*X(55390)
X(55414) = {X(393),X(394)}-harmonic conjugate of X(55413)

X(55415) = X(2)X(55413)∩X(4)X(6)

Barycentrics    Sin[A]^2 + Tan[A]^2 : :
Barycentrics    a^2*(a^2 + b^2 - c^2)^2*(a^2 - b^2 + c^2)^2*((a^2 - b^2 - c^2)^2 + 2*S^2) : :

X(55415) lies on these lines: {2, 55413}, {4, 6}, {19, 8898}, {24, 10608}, {25, 800}, {32, 1033}, {232, 5020}, {264, 41235}, {394, 801}, {458, 21447}, {577, 21312}, {1096, 1827}, {1124, 55403}, {1184, 16318}, {1335, 55404}, {1593, 5065}, {1843, 52439}, {1968, 15905}, {1993, 55414}, {2138, 3575}, {2202, 2286}, {2331, 54416}, {2356, 6059}, {3199, 46432}, {6995, 52223}, {7120, 7124}, {7129, 16502}, {7487, 42458}, {8749, 34818}, {10601, 11547}, {11381, 14642}, {11413, 41890}, {12167, 34854}, {13342, 36417}, {13567, 46741}, {17811, 32000}, {26206, 43981}, {31829, 42459}, {36416, 52433}, {37174, 40318}, {38292, 52950}, {40801, 50666}, {55399, 55402}, {55400, 55401}, {55405, 55408}, {55406, 55407}

X(55415) = reflection of X(55415) in the van Aubel line
X(55415) = polar conjugate of X(40032)
X(55415) = polar conjugate of the isotomic conjugate of X(1593)
X(55415) = X(i)-isoconjugate of X(j) for these (i,j): {48, 40032}, {63, 15740}, {255, 37874}, {326, 52223}
X(55415) = X(i)-Dao conjugate of X(j) for these (i,j): {1249, 40032}, {3162, 15740}, {6523, 37874}, {15259, 52223}
X(55415) = crossdifference of every pair of points on line {520, 20580}
X(55415) = barycentric product X(i)*X(j) for these {i,j}: {4, 1593}, {25, 32000}, {158, 1496}, {393, 17811}, {1093, 43652}, {2052, 5065}, {2207, 32830}, {26224, 27376}
X(55415) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 40032}, {25, 15740}, {393, 37874}, {1496, 326}, {1593, 69}, {2207, 52223}, {5065, 394}, {17811, 3926}, {32000, 305}, {43652, 3964}
X(55415) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 393, 2207}, {25, 41489, 800}, {53, 53420, 4}

X(55416) = X(2)X(55418)∩X(63)X(76)

Barycentrics    2*Cos[A] - Csc[A]^2 : :
Barycentrics    a*((a^2 - b^2 - c^2)^3 - 4*b^2*c^2*(a^2 - b^2 + b*c - c^2)) : :

X(55416) lies on these lines: {2, 55418}, {9, 32832}, {40, 14907}, {57, 7763}, {63, 76}, {183, 26921}, {315, 5709}, {320, 51612}, {325, 37532}, {350, 920}, {1078, 55104}, {1102, 20924}, {1975, 24467}, {3218, 3926}, {3219, 32828}, {3306, 7769}, {3928, 32833}, {6337, 26877}, {7330, 11185}, {7750, 37584}, {17206, 42467}, {23958, 32831}, {26878, 34229}, {27003, 32829}, {27065, 32838}, {32830, 55419}, {32867, 35595}

X(55416) = {X(63),X(76)}-harmonic conjugate of X(55417)

X(55417) = X(2)X(55419)∩X(63)X(76)

Barycentrics    2*Cos[A] + Csc[A]^2 : :
Barycentrics    a*((a^2 - b^2 - c^2)^3 - 4*b^2*c^2*(a^2 - b^2 - b*c - c^2)) : :

X(55417) lies on these lines: {2, 55419}, {9, 7763}, {57, 32832}, {63, 76}, {84, 14907}, {99, 55104}, {183, 24467}, {315, 7330}, {920, 1909}, {1102, 33939}, {1975, 26921}, {3218, 32828}, {3219, 3926}, {3305, 7769}, {3929, 32833}, {5709, 11185}, {6337, 26878}, {26877, 34229}, {27003, 32838}, {27065, 32829}, {32819, 37584}, {32830, 55418}, {32839, 35595}, {37612, 37688}

X(55417) = {X(63),X(76)}-harmonic conjugate of X(55416)

X(55418) = X(2)X(55416)∩X(63)X(3926)

Barycentrics    2*Cos[A] - Cot[A]^2 : :
Barycentrics    a*(a^2 - b^2 - c^2)*(b*c*(a^2 - b^2 - c^2) + 4*S^2) : :

X(55418) lies on these lines: {2, 55416}, {9, 32828}, {57, 32829}, {63, 3926}, {69, 26921}, {76, 3219}, {183, 26878}, {1007, 37532}, {3218, 7763}, {3305, 32838}, {3306, 32839}, {3785, 55104}, {3928, 32837}, {3929, 32836}, {5709, 32816}, {6337, 24467}, {7289, 10008}, {7308, 32867}, {7330, 32815}, {7769, 27003}, {23958, 32835}, {27065, 32832}, {28706, 28731}, {32006, 37584}, {32830, 55417}

X(55418) = {X(63),X(3926)}-harmonic conjugate of X(55419)

X(55419) = X(2)X(55417)∩X(63)X(3926)

Barycentrics    2*Cos[A] + Cot[A]^2 : :
Barycentrics    a*(a^2 - b^2 - c^2)*(b*c*(a^2 - b^2 - c^2) - 4*S^2) : :

X(55419) lies on these lines: {2, 55417}, {9, 32829}, {57, 32828}, {63, 3926}, {69, 24467}, {76, 3218}, {183, 26877}, {3219, 7763}, {3305, 32839}, {3306, 32838}, {3928, 32836}, {3929, 32837}, {5227, 10008}, {5437, 32867}, {5709, 32815}, {6337, 26921}, {7330, 32816}, {7769, 27065}, {23958, 32834}, {27003, 32832}, {32830, 55416}, {34229, 37612}

X(55419) = barycentric product X(i)*X(j) for these {i,j}: {63, 54443}, {304, 54444}
X(55419) = barycentric quotient X(i)/X(j) for these {i,j}: {54428, 1096}, {54443, 92}, {54444, 19}
X(55419) = {X(63),X(3926)}-harmonic conjugate of X(55418)

X(55420) = X(2)X(55385)∩X(9)X(75)

Barycentrics    1 + Cos[A] - Csc[A] : :

X(55420) lies on these lines: {2, 55385}, {7, 55422}, {8, 55423}, {9, 75}, {57, 32792}, {63, 5391}, {326, 30557}, {1267, 3305}, {3218, 32800}, {3219, 32794}, {3306, 32796}, {3929, 32802}, {5437, 32804}, {6213, 54404}, {7308, 32791}, {27065, 32793}, {32799, 35595}, {32803, 51780}, {32806, 52419}, {55393, 55430}, {55394, 55431}, {55395, 55428}, {55396, 55459}

X(55420) = barycentric product X(13387)*X(55426)
X(55420) = barycentric quotient X(55426)/X(13386)
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55385, 55450}, {9, 75, 55421}, {63, 5391, 55451}, {3219, 32794, 55386}

X(55421) = X(2)X(55386)∩X(9)X(75)

Barycentrics    1 + Cos[A] + Csc[A] : :

X(55421) lies on these lines: {2, 55386}, {7, 55423}, {8, 55422}, {9, 75}, {57, 32791}, {63, 1267}, {326, 30556}, {3218, 32799}, {3219, 32793}, {3305, 5391}, {3306, 32795}, {3929, 32801}, {5437, 32803}, {6212, 54404}, {7308, 32792}, {27065, 32794}, {32800, 35595}, {32804, 51780}, {32805, 52420}, {55393, 55431}, {55394, 55430}, {55395, 55429}, {55396, 55458}

X(55421) = barycentric product X(13386)*X(55456)
X(55421) = barycentric quotient X(55456)/X(13387)
X(55421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55386, 55451}, {9, 75, 55420}, {63, 1267, 55450}, {3219, 32793, 55385}

X(55422) = X(2)X(55387)∩X(9)X(69)

Barycentrics    1 + Cos[A] - Cot[A] : :

X(55422) lies on these lines: {2, 55387}, {7, 55420}, {8, 55421}, {9, 69}, {40, 12323}, {57, 32806}, {63, 491}, {264, 55431}, {317, 55430}, {487, 7330}, {492, 3305}, {638, 55104}, {1270, 27065}, {1271, 3219}, {1444, 32555}, {3218, 3595}, {3593, 35595}, {3929, 32811}, {5437, 32813}, {7308, 32805}, {30556, 55392}, {30557, 55391}, {32792, 52420}, {32812, 51780}, {55397, 55426}, {55398, 55457}

X(55422) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55387, 55452}, {9, 69, 55423}, {63, 491, 55453}, {1271, 3219, 55388}

X(55423) = X(2)X(55388)∩X(9)X(69)

Barycentrics    1 + Cos[A] + Cot[A] : :

X(55423) lies on these lines: {2, 55388}, {7, 55421}, {8, 55420}, {9, 69}, {40, 12322}, {57, 32805}, {63, 492}, {264, 55430}, {317, 55431}, {488, 7330}, {491, 3305}, {637, 55104}, {1270, 3219}, {1271, 27065}, {1444, 32556}, {3218, 3593}, {3306, 32807}, {3595, 35595}, {3929, 32810}, {5437, 32812}, {7308, 32806}, {30556, 55391}, {30557, 55392}, {32791, 52419}, {32813, 51780}, {55397, 55427}, {55398, 55456}

X(55423) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55388, 55453}, {9, 69, 55422}, {63, 492, 55452}, {1270, 3219, 55387}

X(55424) = X(1)X(4)∩X29)X(55389)

Barycentrics    1 - Sec[A] + Sin[A] : :

X(55424) lies on these lines: {1, 4}, {2, 55389}, {19, 13389}, {92, 3083}, {1214, 16432}, {1435, 13388}, {3084, 17923}, {7133, 55461}, {16232, 55460}, {30333, 37104}, {37543, 39794}

X(55424) = barycentric product X(7)*X(55430)
X(55424) = barycentric quotient X(55430)/X(8)
X(55424) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 278, 55455}, {2, 55389, 55454}, {92, 3083, 55425}

X(55425) = X(1)X(281)∩X29)X(55390)

Barycentrics    1 + Sec[A] + Sin[A] : :

X(55425) lies on these lines: {1, 281}, {2, 55390}, {19, 30556}, {33, 7090}, {34, 14121}, {92, 3083}, {1783, 18991}, {2362, 55431}, {3084, 52412}, {6212, 37305}, {7079, 30557}, {7119, 31453}, {13390, 30686}, {15210, 55460}, {42013, 55430}

X(55425) = barycentric product X(8)*X(55460)
X(55425) = barycentric quotient X(55460)/X(7)
X(55425) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 281, 55454}, {2, 55390, 55455}, {92, 3083, 55424}

X(55426) = X(1)X(491)∩X69)X(3083)

Barycentrics    1 - Cot[A] + Sin[A] : :

X(55426) lies on these lines: {1, 491}, {2, 3553}, {69, 3083}, {78, 1267}, {1271, 55392}, {3084, 32806}, {3760, 34391}, {5391, 7190}, {6516, 52419}, {13389, 55387}, {30556, 55388}, {31637, 46744}, {55397, 55422}, {55398, 55453}

X(55426) = barycentric product X(13386)*X(55420)
X(55426) = barycentric quotient X(55420)/X(13387)
X(55426) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 491, 55457}, {2, 55391, 55456}, {69, 3083, 55427}

X(55427) = X(1)X(492)∩X69)X(3083)

Barycentrics    1 + Cot[A] + Sin[A] : :

X(55427) lies on these lines: {1, 492}, {2, 3554}, {69, 3083}, {77, 1267}, {1270, 55391}, {3084, 32805}, {3761, 34392}, {3872, 5391}, {13389, 55388}, {30556, 55387}, {55397, 55423}, {55398, 55452}

X(55427) = barycentric product X(13386)*X(55451)
X(55427) = barycentric quotient X(55451)/X(13387)
X(55427) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 492, 55456}, {2, 55392, 55457}, {69, 3083, 55426}

X(55428) = X(2)X(55393)∩X(75)X(1585)

Barycentrics    1 - Csc[A] + Tan[A] : :

X(55428) lies on these lines: {2, 55393}, {4, 5391}, {75, 1585}, {273, 491}, {492, 5081}, {1267, 3535}, {1586, 32792}, {3536, 32796}, {32794, 55394}, {55385, 55460}, {55386, 55431}, {55395, 55420}, {55396, 55451}

X(55428) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55393, 55458}, {4, 5391, 55459}, {75, 1585, 55429}

X(55429) = X(2)X(55394)∩X(75)X(1585)

Barycentrics    1 + Csc[A] + Tan[A] : :

X(55429) lies on these lines: {2, 55394}, {4, 1267}, {75, 1585}, {318, 491}, {492, 7282}, {1586, 32791}, {3535, 5391}, {3536, 32795}, {32793, 55393}, {55385, 55431}, {55386, 55460}, {55395, 55421}, {55396, 55450}

X(55429) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55394, 55459}, {4, 1267, 55458}, {75, 1585, 55428}

X(55430) = X(2)X(55395)∩X(4)X(9)

Barycentrics    1 + Cos[A] - Tan[A] : :

X(55430) lies on these lines: {2, 55395}, {4, 9}, {33, 30556}, {34, 30557}, {57, 3536}, {63, 1586}, {208, 6203}, {219, 3093}, {222, 55443}, {264, 55423}, {317, 55422}, {1172, 31438}, {1585, 3305}, {1712, 3069}, {3092, 55432}, {3219, 55396}, {3535, 7308}, {4183, 15892}, {4194, 30412}, {4200, 30413}, {7008, 7348}, {7412, 32555}, {16232, 55454}, {32556, 37305}, {42013, 55425}, {55385, 55458}, {55386, 55459}, {55393, 55420}, {55394, 55421}, {55400, 55411}

X(55430) = barycentric product X(8)*X(55424)
X(55430) = barycentric quotient X(55424)/X(7)
X(55430) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55395, 55460}, {4, 9, 55431}, {63, 1586, 55461}

X(55431) = X(2)X(55396)∩X(4)X(9)

Barycentrics    1 + Cos[A] + Tan[A] : :

X(55431) lies on these lines: {2, 55396}, {4, 9}, {33, 30557}, {34, 30556}, {57, 3535}, {63, 1585}, {208, 6204}, {219, 3092}, {222, 55444}, {264, 55422}, {317, 55423}, {1586, 3305}, {1712, 3068}, {2362, 55425}, {3093, 55432}, {3219, 55395}, {3536, 7308}, {4183, 15891}, {4194, 30413}, {4200, 30412}, {7008, 7347}, {7133, 55454}, {7412, 32556}, {8957, 51359}, {32555, 37305}, {55385, 55429}, {55386, 55428}, {55393, 55421}, {55394, 55420}, {55400, 55412}

X(55431) = barycentric product X(8)*X(55455)
X(55431) = barycentric quotient X(55455)/X(7)
X(55431) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55396, 55461}, {4, 9, 55430}, {63, 1585, 55460}

X(55432) = X(1)X(6)∩X(2)X(222)

Barycentrics    1 + Cos[A] + Sin[A]^2 : :

X(55432) lies on these lines: {1, 6}, {2, 222}, {3, 2183}, {10, 5782}, {19, 31788}, {25, 26890}, {51, 7085}, {55, 2316}, {56, 5053}, {57, 17825}, {63, 10601}, {71, 3527}, {73, 37244}, {81, 18228}, {101, 23073}, {142, 6180}, {169, 374}, {182, 24320}, {197, 375}, {198, 572}, {212, 13615}, {241, 8257}, {255, 16293}, {281, 608}, {282, 1413}, {294, 34919}, {329, 37543}, {391, 7080}, {394, 3305}, {442, 3330}, {458, 1948}, {474, 1745}, {478, 2122}, {527, 5228}, {573, 10310}, {579, 1466}, {604, 41426}, {607, 33950}, {610, 37526}, {672, 1405}, {692, 35273}, {894, 26659}, {909, 10269}, {936, 36746}, {940, 3452}, {965, 6700}, {966, 5783}, {1146, 17369}, {1213, 45886}, {1260, 14547}, {1351, 3781}, {1376, 35338}, {1377, 14121}, {1378, 7090}, {1400, 5120}, {1404, 9310}, {1407, 5437}, {1442, 26669}, {1473, 43650}, {1480, 40587}, {1482, 21801}, {1766, 2262}, {1935, 19520}, {1944, 3758}, {1993, 27065}, {2003, 7308}, {2178, 4268}, {2207, 55434}, {2238, 31497}, {2245, 32561}, {2250, 22758}, {2261, 9940}, {2265, 19350}, {2268, 2347}, {2270, 37413}, {2287, 27383}, {2293, 6600}, {2310, 28125}, {2317, 20818}, {2325, 4513}, {2330, 7083}, {2344, 9365}, {2345, 53994}, {2348, 17603}, {2551, 5711}, {2635, 37240}, {3092, 55430}, {3093, 55431}, {3157, 11108}, {3196, 34544}, {3217, 21748}, {3219, 5422}, {3220, 5085}, {3241, 36916}, {3306, 22129}, {3562, 5129}, {3618, 27509}, {3660, 22163}, {3686, 3713}, {3690, 15004}, {3707, 6745}, {3752, 10900}, {3784, 16419}, {3929, 52423}, {3937, 22112}, {3955, 5020}, {4271, 54285}, {4303, 16410}, {4363, 4858}, {4383, 5745}, {4413, 45885}, {4503, 30827}, {4512, 7074}, {4517, 8540}, {4579, 26241}, {4644, 52457}, {4670, 34852}, {4682, 18227}, {4877, 46889}, {5044, 36742}, {5050, 7193}, {5084, 41344}, {5158, 35072}, {5257, 55323}, {5268, 18236}, {5273, 32911}, {5285, 17810}, {5314, 33586}, {5316, 25934}, {5328, 37633}, {5362, 30414}, {5367, 30415}, {5438, 37501}, {5480, 50861}, {5537, 42316}, {5706, 12572}, {5710, 5795}, {5776, 6260}, {5781, 43177}, {5832, 53599}, {5943, 37581}, {6181, 20331}, {6510, 25930}, {6554, 7359}, {6617, 53819}, {6666, 25878}, {7069, 19354}, {7079, 52413}, {7169, 45979}, {7330, 37514}, {7484, 26892}, {8583, 34046}, {8728, 8757}, {9355, 24341}, {9364, 17754}, {9441, 24708}, {9596, 34261}, {9777, 26867}, {9843, 40942}, {10319, 14557}, {10982, 55104}, {11284, 26884}, {11402, 26885}, {11424, 26935}, {11433, 26942}, {14260, 40595}, {14853, 26939}, {15066, 35595}, {15733, 28043}, {15805, 24467}, {15817, 36743}, {15988, 26685}, {16283, 20972}, {16608, 28739}, {16853, 23070}, {16857, 23071}, {17023, 40880}, {17073, 25019}, {17120, 27420}, {17263, 28965}, {17338, 26657}, {17349, 26059}, {18230, 37659}, {19349, 37224}, {19716, 27413}, {19784, 20306}, {19860, 34040}, {20905, 28968}, {21362, 24328}, {23151, 54280}, {23344, 23855}, {24266, 24336}, {24388, 30620}, {24482, 36086}, {24554, 29007}, {24635, 37787}, {25067, 53996}, {25091, 45126}, {26540, 28780}, {26911, 53863}, {26933, 54012}, {30265, 51489}, {31424, 36745}, {31445, 36754}, {32777, 45206}, {34619, 37654}, {34894, 40779}, {37566, 54405}, {40065, 55116}, {41006, 50115}, {52978, 55337}, {55401, 55447}, {55415, 55462}

X(55432) = complement of the isotomic conjugate of X(30513)
X(55432) = isogonal conjugate of the isotomic conjugate of X(28808)
X(55432) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 52148}, {663, 53837}, {998, 2886}, {9058, 17072}, {30513, 2887}
X(55432) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 52148}, {2320, 55}, {3306, 999}, {5744, 3428}, {9104, 667}, {36091, 53286}
X(55432) = X(i)-isoconjugate of X(j) for these (i,j): {34, 30680}, {57, 1000}, {85, 34446}, {269, 36916}, {279, 52429}, {3669, 51564}, {7091, 14556}, {7190, 52188}
X(55432) = X(i)-Dao conjugate of X(j) for these (i,j): {3753, 26580}, {5452, 1000}, {6600, 36916}, {11517, 30680}, {31397, 26591}, {52148, 2}
X(55432) = crossdifference of every pair of points on line {513, 30725}
X(55432) = barycentric product X(i)*X(j) for these {i,j}: {1, 3872}, {6, 28808}, {8, 999}, {9, 3306}, {21, 3753}, {41, 20925}, {55, 42697}, {72, 17519}, {75, 52428}, {220, 17079}, {281, 22129}, {284, 4054}, {522, 35281}, {2320, 40587}, {3939, 21183}, {30513, 52148}
X(55432) = barycentric quotient X(i)/X(j) for these {i,j}: {55, 1000}, {219, 30680}, {220, 36916}, {999, 7}, {1253, 52429}, {2175, 34446}, {3306, 85}, {3753, 1441}, {3872, 75}, {3939, 51564}, {4054, 349}, {17519, 286}, {20925, 20567}, {21183, 52621}, {22129, 348}, {28808, 76}, {35281, 664}, {42697, 6063}, {52428, 1}
X(55432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55400, 222}, {6, 9, 219}, {6, 44, 218}, {6, 220, 2323}, {6, 16885, 2911}, {9, 1449, 2324}, {9, 2323, 220}, {44, 1212, 9}, {63, 10601, 52424}, {220, 2323, 219}, {374, 2182, 169}, {1146, 17369, 54283}, {2003, 7308, 17811}, {2003, 17811, 23140}, {2183, 2267, 3}, {2268, 2347, 4254}, {3219, 5422, 55399}, {3305, 54444, 394}, {3758, 30854, 1944}, {3929, 52423, 55405}, {9777, 26867, 26893}, {10601, 55438, 63}, {17825, 55406, 57}, {30556, 30557, 392}

X(55433) = X(2)X(55401)∩X(63)X(1947)

Barycentrics    1 - Cos[A] + Tan[A]^2 : :

X(55433) lies on these lines: {2, 55401}, {9, 55407}, {19, 40573}, {57, 393}, {63, 1947}, {158, 1753}, {219, 55446}, {222, 55415}, {2207, 52424}, {3218, 55402}, {3305, 55467}, {3306, 11547}, {3928, 55408}, {8745, 52423}, {13388, 55404}, {13389, 55403}, {55397, 55435}, {55398, 55436}, {55399, 55414}, {55400, 55447}

X(55433) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55401, 55462}, {57, 393, 55463}, {63, 2052, 55434}, {2052, 55439, 63}

X(55434) = X(2)X(55402)∩X(63)X(1947)

Barycentrics    1 + Cos[A] + Tan[A]^2 : :

X(55434) lies on these lines: {2, 55402}, {9, 393}, {19, 2250}, {57, 55408}, {63, 1947}, {219, 55415}, {222, 55446}, {281, 40131}, {1752, 51282}, {2207, 55432}, {3219, 55401}, {3305, 11547}, {3306, 55468}, {3929, 55407}, {30556, 55403}, {30557, 55404}, {41365, 55104}, {55397, 55436}, {55398, 55435}, {55399, 55447}, {55400, 55414}

X(55434) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55402, 55463}, {9, 393, 55462}, {63, 2052, 55433}, {2052, 55440, 63}

X(55435) = X(1)X(2052)∩X(2)X(55403)

Barycentrics    1 - Sin[A] + Tan[A]^2 : :

X(55435) lies on these lines: {1, 2052}, {2, 55403}, {393, 3084}, {1124, 55447}, {1335, 55414}, {13388, 55402}, {30557, 55401}, {55397, 55433}, {55398, 55434}, {55409, 55415}, {55410, 55446}, {55413, 55441}

X(55435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2052, 55436}, {2, 55403, 55464}, {393, 3084, 55465}

X(55436) = X(1)X(2052)∩X(2)X(55404)

Barycentrics    1 + Sin[A] + Tan[A]^2 : :

X(55436) lies on these lines: {1, 2052}, {2, 55404}, {393, 3083}, {1124, 55414}, {1335, 55447}, {13389, 55402}, {30556, 55401}, {55397, 55434}, {55398, 55433}, {55409, 55446}, {55410, 55415}, {55413, 55442}

X(55436) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2052, 55435}, {2, 55404, 55465}, {393, 3083, 55464}

X(55437) = X(2)X(220)∩X(63)X(10601)

Barycentrics    1 - 2*Cos[A] + Sin[A]^2 : :

X(55437) lies on these lines: {2, 220}, {6, 2243}, {57, 394}, {63, 10601}, {219, 3306}, {511, 26866}, {651, 2094}, {1086, 4383}, {1155, 45728}, {1181, 37532}, {1351, 3937}, {1407, 1993}, {1465, 23144}, {1473, 33586}, {1947, 41244}, {2207, 55439}, {2256, 37633}, {2911, 16610}, {2999, 17745}, {3066, 24320}, {3190, 37309}, {3219, 17825}, {3690, 16419}, {3796, 26889}, {3868, 36745}, {3873, 7074}, {3928, 52423}, {5256, 18607}, {5422, 55406}, {5526, 54390}, {7011, 46832}, {7193, 35259}, {9965, 32911}, {10982, 24467}, {12595, 37540}, {12649, 37537}, {14997, 20059}, {16471, 24046}, {17811, 27003}, {20142, 40461}, {26724, 31053}, {26877, 37498}, {26928, 45186}, {27509, 37648}, {55408, 55447}, {55415, 55468}

X(55437) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55405, 55466}, {6, 3218, 22129}, {57, 55399, 394}, {63, 10601, 55438}, {63, 52424, 10601}, {1993, 23958, 1407}, {3928, 52423, 55400}, {26889, 37581, 3796}

X(55438) = X(2)X(1407)∩X(63)X(10601)

Barycentrics    1 + 2*Cos[A] + Sin[A]^2 : :

X(55438) lies on these lines: {2, 1407}, {6, 3219}, {9, 394}, {63, 10601}, {219, 54444}, {220, 1993}, {221, 5260}, {222, 3305}, {268, 46832}, {511, 26867}, {594, 2994}, {940, 7277}, {958, 7299}, {1331, 13615}, {1351, 3690}, {1948, 41244}, {2207, 55440}, {2256, 33761}, {3066, 37581}, {3218, 17825}, {3683, 45729}, {3758, 19716}, {3796, 24320}, {3876, 36746}, {3929, 55399}, {3937, 16419}, {3955, 35259}, {5228, 20078}, {5422, 55405}, {7085, 33586}, {10982, 26921}, {17781, 37543}, {17811, 27065}, {26878, 37498}, {26938, 45186}, {27131, 37674}, {27509, 37649}, {29958, 37246}, {34048, 54357}, {55407, 55447}, {55415, 55467}

X(55438) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55406, 22129}, {6, 3219, 55466}, {9, 55400, 394}, {63, 10601, 55437}, {63, 55432, 10601}, {24320, 26890, 3796}

X(55439) = X(2)X(55407)∩X(63)X(1947)

Barycentrics    1 - 2*Cos[A] + Tan[A]^2 : :

X(55439) lies on these lines: {2, 55407}, {27, 21370}, {57, 11547}, {63, 1947}, {393, 3218}, {653, 1708}, {1407, 55413}, {2207, 55437}, {3306, 14165}, {3928, 55402}, {18027, 55417}, {22129, 55415}, {24467, 41365}, {55405, 55414}, {55406, 55447}, {55446, 55466}

X(55439) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55407, 55467}, {57, 55401, 11547}, {63, 2052, 55440}, {63, 55433, 2052}, {393, 3218, 55468}, {3306, 55462, 14165}

X(55440) = X(2)X(55408)∩X(63)X(1947)

Barycentrics    1 + 2*Cos[A] + Tan[A]^2 : :

X(55440) lies on these lines: {2, 55408}, {9, 11547}, {63, 1947}, {220, 55413}, {393, 3219}, {2207, 55438}, {3305, 14165}, {3929, 55401}, {18027, 55416}, {22129, 55446}, {26921, 41365}, {55405, 55447}, {55406, 55414}, {55415, 55466}

X(55440) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55408, 55468}, {9, 55402, 11547}, {63, 2052, 55439}, {63, 55434, 2052}, {393, 3219, 55467}, {3305, 55463, 14165}

X(55441) = X(1)X(17811)∩X(2)X(1124)

Barycentrics    1 + Cos[A]^2 - Sin[A] : :

X(55441) lies on these lines: {1, 17811}, {2, 1124}, {33, 55444}, {34, 55443}, {219, 13388}, {222, 30557}, {394, 1335}, {3299, 17825}, {3301, 37672}, {3539, 31408}, {3686, 31473}, {3740, 45424}, {3742, 45423}, {5268, 45490}, {5272, 45493}, {5405, 25934}, {15066, 55410}, {15235, 44624}, {15236, 31472}, {19047, 37679}, {19050, 37674}, {55403, 55445}, {55404, 55446}, {55413, 55435}, {55414, 55465}

X(55441) = X(1096)-isoconjugate of X(38488)
X(55441) = X(6503)-Dao conjugate of X(38488)
X(55441) = barycentric product X(i)*X(j) for these {i,j}: {1335, 32793}, {3297, 5391}
X(55441) = barycentric quotient X(i)/X(j) for these {i,j}: {394, 38488}, {3297, 1336}
X(55441) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17811, 55442}, {2, 55409, 1124}, {394, 3084, 1335}

X(55442) = X(1)X(17811)∩X(2)X(1335)

Barycentrics    1 + Cos[A]^2 + Sin[A] : :

X(55442) lies on these lines: {1, 17811}, {2, 1335}, {33, 55443}, {34, 55444}, {219, 13389}, {222, 30556}, {394, 1124}, {3299, 37672}, {3301, 17825}, {3740, 45425}, {3742, 45422}, {5257, 31473}, {5268, 45491}, {5272, 45492}, {5393, 25934}, {15066, 55409}, {15235, 44622}, {15236, 44623}, {19048, 37679}, {19049, 37674}, {55403, 55446}, {55404, 55445}, {55413, 55436}, {55414, 55464}

X(55442) = barycentric product X(i)*X(j) for these {i,j}: {1124, 32794}, {1267, 3298}
X(55442) = barycentric quotient X(3298)/X(1123)
X(55442) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17811, 55441}, {2, 55410, 1335}, {394, 3083, 1124}

X(55443) = X(2)X(1579)∩X(4)X(17811)

Barycentrics    1 + Cos[A]^2 - Tan[A] : :

X(55443) lies on these lines: {2, 1579}, {4, 17811}, {6, 3536}, {25, 11824}, {33, 55442}, {34, 55441}, {219, 55461}, {222, 55430}, {371, 15211}, {372, 15213}, {394, 638}, {427, 10515}, {1151, 15215}, {1152, 15217}, {2063, 12323}, {5406, 15205}, {5407, 15203}, {5408, 15201}, {5409, 15199}, {6409, 15219}, {6410, 15221}, {15066, 55412}, {15212, 35765}

X(55443) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55411, 3092}, {4, 17811, 55444}, {394, 1586, 3093}

X(55444) = X(2)X(1578)∩X(4)X(17811)

Barycentrics    1 + Cos[A]^2 + Tan[A] : :

X(55444) lies on these lines: {2, 1578}, {4, 17811}, {6, 3535}, {25, 11825}, {33, 55441}, {34, 55442}, {219, 55460}, {222, 55431}, {371, 15210}, {372, 15212}, {394, 637}, {427, 10514}, {1151, 15214}, {1152, 15216}, {2063, 12322}, {3162, 8968}, {5406, 15204}, {5407, 15202}, {5408, 15200}, {5409, 15198}, {6409, 15218}, {6410, 15220}, {15066, 55411}, {15211, 35764}

X(55444) = polar conjugate of the isogonal conjugate of X(9686)
X(55444) = barycentric product X(264)*X(9686)
X(55444) = barycentric quotient X(9686)/X(3)
X(55444) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55412, 3093}, {4, 17811, 55443}, {394, 1585, 3092}

X(55445) = X(2)X(53413)∩X(6)X(53506)

Barycentrics    1 + Cos[A]^2 - Tan[A]^2 : :

X(55445) lies on these lines: {2, 55413}, {6, 53506}, {219, 55463}, {220, 55408}, {222, 55462}, {297, 315}, {393, 17811}, {1407, 55407}, {8745, 37672}, {10601, 14165}, {15066, 55414}, {22129, 55467}, {55403, 55441}, {55404, 55442}, {55409, 55464}, {55410, 55465}, {55466, 55468}

X(55445) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55413, 55415}, {393, 17811, 55446}, {394, 11547, 2207}

X(55446) = X(2)X(2207)∩X(6)X(14361)

Barycentrics    1 + Cos[A]^2 + Tan[A]^2 : :

X(554) lies on these lines: {2, 2207}, {6, 14361}, {219, 55433}, {220, 55407}, {222, 55434}, {393, 17811}, {394, 801}, {436, 1181}, {1407, 55408}, {1498, 6618}, {1968, 6617}, {1993, 55447}, {6820, 27376}, {8745, 17825}, {15066, 55413}, {22129, 55440}, {55403, 55442}, {55404, 55441}, {55409, 55436}, {55410, 55435}, {55439, 55466}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55414, 2207}, {393, 17811, 55445}, {394, 2052, 55415}

X(55447) = X(2)X(55413)∩X(6)X(275)

Barycentrics    1 + Sin[A]^2 + Tan[A]^2 : :

X(55447) lies on these lines: {2, 55413}, {6, 275}, {324, 41238}, {393, 6819}, {1124, 55435}, {1335, 55436}, {1993, 55446}, {2207, 5422}, {11547, 17825}, {37514, 41365}, {52424, 55402}, {55399, 55434}, {55400, 55433}, {55401, 55432}, {55405, 55440}, {55406, 55439}, {55407, 55438}, {55408, 55437}

X(55447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55415, 55413}, {6, 2052, 55414}

X(55448) = X(2)X(55416)∩X(63)X(32828)

Barycentrics    1 - 2*Cos[A] + Csc[A]^2 : :

X(55448) lies on these lines: {2, 55416}, {9, 32838}, {57, 3926}, {63, 32828}, {69, 37532}, {76, 3218}, {84, 32826}, {1975, 26877}, {3219, 32832}, {3305, 32867}, {3306, 32829}, {3785, 5709}, {3928, 46951}, {3929, 32885}, {5437, 32839}, {6337, 37612}, {7308, 32883}, {7763, 27003}, {18027, 55408}, {23958, 32830}, {26878, 37688}, {26921, 34229}, {32834, 55417}

X(55448) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55416, 55418}, {63, 32828, 55449}, {76, 3218, 55419}, {23958, 32830, 55470}

X(55449) = X(2)X(55417)∩X(63)X(32828)

Barycentrics    1 + 2*Cos[A] + Csc[A]^2 : :

X(55449) lies on these lines: {2, 55417}, {9, 3926}, {40, 32826}, {57, 32838}, {63, 32828}, {76, 3219}, {1975, 26878}, {3218, 32832}, {3305, 32829}, {3306, 32867}, {3785, 7330}, {3928, 32885}, {3929, 46951}, {5437, 32883}, {7308, 32839}, {7763, 27065}, {7769, 35595}, {18027, 55407}, {23958, 32870}, {24467, 34229}, {26877, 37688}, {32815, 55104}, {32830, 55469}, {32834, 55416}, {32884, 51780}

X(55449) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55417, 55419}, {63, 32828, 55448}, {76, 3219, 55418}

X(55450) = X(2)X(55385)∩X(57)X(75)

Barycentrics    1 - Cos[A] + Csc[A] : :

X(55450) lies on these lines: {2, 55385}, {7, 55452}, {8, 55453}, {9, 32791}, {57, 75}, {63, 1267}, {69, 52419}, {326, 13389}, {3218, 32793}, {3219, 32799}, {3305, 32795}, {3306, 5391}, {3928, 32801}, {5437, 32792}, {7308, 32803}, {27003, 32794}, {42697, 52420}, {55393, 55460}, {55394, 55461}, {55395, 55458}, {55396, 55429}

X(55450) = barycentric product X(13386)*X(55457)
X(55450) = barycentric quotient X(55457)/X(13387)
X(55450) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55385, 55420}, {57, 75, 55451}, {63, 1267, 55421}, {3218, 32793, 55386}

X(55451) = X(2)X(55386)∩X(57)X(75)

Barycentrics    1 - Cos[A] - Csc[A] : :

X(55451) lies on these lines: {2, 55386}, {7, 55453}, {8, 55452}, {9, 32792}, {57, 75}, {63, 5391}, {69, 52420}, {326, 13388}, {1267, 3306}, {3218, 32794}, {3219, 32800}, {3305, 32796}, {3928, 32802}, {5437, 32791}, {7308, 32804}, {27003, 32793}, {42697, 52419}, {55393, 55461}, {55394, 55460}, {55395, 55459}, {55396, 55428}

X(55451) = barycentric product X(13387)*X(55427)
X(55451) = barycentric quotient X(55427)/X(13386)
X(55451) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55386, 55421}, {57, 75, 55450}, {63, 5391, 55420}, {3218, 32794, 55385}

X(55452) = X(2)X(55387)∩X(57)X(69)

Barycentrics    1 - Cos[A] + Cot[A] : :

X(55452) lies on these lines: {2, 55387}, {7, 55450}, {8, 55451}, {9, 32805}, {57, 69}, {63, 492}, {75, 52420}, {84, 12322}, {264, 55461}, {317, 55460}, {320, 52419}, {487, 37534}, {488, 5709}, {491, 3306}, {1270, 3218}, {1271, 27003}, {3219, 3593}, {3305, 32807}, {3928, 32810}, {5437, 32806}, {7308, 32812}, {13388, 55392}, {13389, 55391}, {23958, 32814}, {45508, 55104}, {55397, 55456}, {55398, 55427}

X(55452) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55387, 55422}, {57, 69, 55453}, {63, 492, 55423}, {1270, 3218, 55388}

X(55453) = X(2)X(55388)∩X(57)X(69)

Barycentrics    1 - Cos[A] - Cot[A] : :

X(55453) lies on these lines: {2, 55388}, {7, 55451}, {8, 55450}, {9, 32806}, {57, 69}, {63, 491}, {75, 52419}, {84, 12323}, {264, 55460}, {317, 55461}, {320, 52420}, {487, 5709}, {488, 37534}, {492, 3306}, {1270, 27003}, {1271, 3218}, {3219, 3595}, {3928, 32811}, {5437, 32805}, {7308, 32813}, {13388, 55391}, {13389, 55392}, {45509, 55104}, {55397, 55457}, {55398, 55426}

X(55453) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55388, 55423}, {57, 69, 55452}, {63, 491, 55422}, {1271, 3218, 55387}

X(55454) = X(1)X(281)∩X(2)X(55389)

Barycentrics    1 + Sec[A] - Sin[A] : :

X(55454) lies on these lines: {1, 281}, {2, 55389}, {19, 30557}, {33, 14121}, {34, 7090}, {92, 3084}, {587, 8583}, {1659, 30686}, {1783, 18992}, {3083, 52412}, {6213, 37305}, {7079, 30556}, {7133, 55431}, {15213, 55461}, {16232, 55430}

X(55454) = barycentric product X(8)*X(55461)
X(55454) = barycentric quotient X(55461)/X(7)
X(55454) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 281, 55425}, {2, 55389, 55424}, {92, 3084, 55455}

X(55455) = X(1)X(4)∩X(2)X(55390)

Barycentrics    1 - Sec[A] - Sin[A] : :

X(55455) lies on these lines: {1, 4}, {2, 55390}, {19, 13388}, {92, 3084}, {1214, 16433}, {1435, 13389}, {2362, 55461}, {3083, 17923}, {30334, 37104}, {37543, 39795}, {42013, 55460}

X(55455) = barycentric product X(7)*X(55431)
X(55455) = barycentric quotient X(55431)/X(8)
X(55455) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 278, 55424}, {2, 55390, 55425}, {92, 3084, 55454}

X(55456) = X(1)X(492)∩X(69)X(3084)

Barycentrics    1 + Cot[A] - Sin[A] : :

X(55456) lies on these lines: {1, 492}, {2, 3553}, {69, 3084}, {78, 5391}, {1267, 7190}, {1270, 55392}, {3083, 32805}, {3760, 34392}, {6516, 52420}, {13388, 55388}, {30557, 55387}, {31637, 46745}, {55397, 55452}, {55398, 55423}

X(55456) = barycentric product X(13387)*X(55421)
X(55456) = barycentric quotient X(55421)/X(13386)
X(55456) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 492, 55427}, {2, 55391, 55426}, {69, 3084, 55457}

X(55457) = X(1)X(491)∩X(69)X(3084)

Barycentrics    1 - Cot[A] - Sin[A] : :

X(55457) lies on these lines: {1, 491}, {2, 3554}, {69, 3084}, {77, 5391}, {1267, 3872}, {1271, 55391}, {3083, 32806}, {3761, 34391}, {13388, 55387}, {30557, 55388}, {55397, 55453}, {55398, 55422}

X(55457) = barycentric product X(13387)*X(55450)
X(55457) = barycentric quotient X(55450)/X(13386)
X(55457) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 491, 55426}, {2, 55392, 55427}, {69, 3084, 55456}

X(55458) = X(2)X(55393)∩X(75)X(1586)

Barycentrics    1 + Csc[A] - Tan[A] : :

X(55458) lies on these lines: {2, 55393}, {4, 1267}, {75, 1586}, {273, 492}, {491, 5081}, {1585, 32791}, {3535, 32795}, {3536, 5391}, {32793, 55394}, {55385, 55430}, {55386, 55461}, {55395, 55450}, {55396, 55421}

X(55458) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55393, 55428}, {4, 1267, 55429}, {75, 1586, 55459}

X(55459) = X(2)X(55394)∩X(75)X(1586)

Barycentrics    1 - Csc[A] - Tan[A] : :

X(55459) lies on these lines: {2, 55394}, {4, 5391}, {75, 1586}, {318, 492}, {491, 7282}, {1267, 3536}, {1585, 32792}, {3535, 32796}, {32794, 55393}, {55385, 55461}, {55386, 55430}, {55395, 55451}, {55396, 55420}

X(55459) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55394, 55429}, {4, 5391, 55428}, {75, 1586, 55458}

X(55460) = X(2)X(55395)∩X(4)X(57)

Barycentrics    1 - Cos[A] + Tan[A] : :

X(55460) lies on these lines: {2, 55395}, {4, 57}, {9, 3535}, {19, 1659}, {33, 13388}, {34, 13389}, {63, 1585}, {219, 55444}, {222, 3092}, {264, 55453}, {273, 52419}, {278, 6212}, {317, 55452}, {1172, 51841}, {1435, 13390}, {1586, 3306}, {1767, 13437}, {1905, 54462}, {3093, 52424}, {3218, 55396}, {3536, 5437}, {5307, 13460}, {7282, 52420}, {15210, 55425}, {16232, 55424}, {40397, 46433}, {42013, 55455}, {55385, 55428}, {55386, 55429}, {55393, 55450}, {55394, 55451}, {55399, 55412}

X(55460) = barycentric product X(7)*X(55425)
X(55460) = barycentric quotient X(55425)/X(8)
X(55460) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55395, 55430}, {4, 57, 55461}, {63, 1585, 55431}

X(55461) = X(2)X(55396)∩X(4)X(57)

Barycentrics    1 - Cos[A] - Tan[A] : :

X(55461) lies on these lines: {2, 55396}, {4, 57}, {9, 3536}, {19, 3069}, {33, 13389}, {34, 13388}, {63, 1586}, {219, 55443}, {222, 3093}, {264, 55452}, {273, 52420}, {278, 6213}, {317, 55453}, {1172, 51842}, {1435, 1659}, {1585, 3306}, {1767, 13459}, {2362, 55455}, {3092, 52424}, {3218, 55395}, {3535, 5437}, {5307, 13438}, {7133, 55424}, {7282, 52419}, {15213, 55454}, {40397, 46434}, {55385, 55459}, {55386, 55458}, {55393, 55451}, {55394, 55450}, {55399, 55411}

X(55461) = barycentric product X(7)*X(55454)
X(55461) = barycentric quotient X(55454)/X(8)
X(55461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55396, 55431}, {4, 57, 55460}, {63, 1586, 55430}

X(55462) = X(2)X(55401)∩X(63)X(11547)

Barycentrics    1 + Cos[A] - Tan[A]^2 : :

X(55462) lies on these lines: {2, 55401}, {9, 393}, {19, 1881}, {57, 55407}, {63, 11547}, {219, 2207}, {222, 55445}, {281, 54359}, {1948, 21447}, {2052, 3305}, {2323, 8745}, {3219, 55402}, {3306, 14165}, {3929, 55408}, {30556, 55404}, {30557, 55403}, {55397, 55464}, {55398, 55465}, {55400, 55413}, {55415, 55432}

X(55462) = barycentric product X(i)*X(j) for these {i,j}: {33, 55393}, {318, 11398}, {1857, 55391}
X(55462) = barycentric quotient X(i)/X(j) for these {i,j}: {602, 1804}, {11398, 77}, {55391, 7055}, {55393, 7182}, {55399, 7183}
X(55462) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55401, 55433}, {9, 393, 55434}, {63, 11547, 55463}, {11547, 55467, 63}, {14165, 55439, 3306}

X(55463) = X(2)X(55402)∩X(63)X(11547)

Barycentrics    1 - Cos[A] - Tan[A]^2 : :

X(55463) lies on these lines: {2, 55402}, {9, 55408}, {57, 393}, {63, 11547}, {108, 1096}, {208, 8747}, {219, 55445}, {222, 2207}, {223, 5317}, {232, 53819}, {1947, 21447}, {2003, 8745}, {2052, 3306}, {3218, 55401}, {3305, 14165}, {3928, 55407}, {13388, 55403}, {13389, 55404}, {52424, 55415}, {55397, 55465}, {55398, 55464}, {55399, 55413}

X(55463) = barycentric product X(i)*X(j) for these {i,j}: {34, 55394}, {273, 11399}, {1118, 55392}
X(55463) = barycentric quotient X(i)/X(j) for these {i,j}: {601, 1259}, {11399, 78}, {55392, 1264}, {55394, 3718}, {55400, 3719}
X(55463) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55402, 55434}, {57, 393, 55433}, {63, 11547, 55462}, {11547, 55468, 63}, {14165, 55440, 3305}

X(55464) = X(1)X(11547)∩X(2)X(55403)

Barycentrics    1 + Sin[A] - Tan[A]^2 : :

X(55464) lies on these lines: {1, 11547}, {2, 55403}, {393, 3083}, {1124, 55413}, {2207, 55410}, {13389, 55401}, {30556, 55402}, {55397, 55462}, {55398, 55463}, {55409, 55445}, {55414, 55442}

X(55464) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11547, 55465}, {2, 55403, 55435}, {393, 3083, 55436}

X(55465) = X(1)X(11547)∩X(2)X(55404)

Barycentrics    1 - Sin[A] - Tan[A]^2 : :

X(55465) lies on these lines: {1, 11547}, {2, 55404}, {393, 3084}, {1335, 55413}, {2207, 55409}, {13388, 55401}, {30557, 55402}, {55397, 55463}, {55398, 55462}, {55410, 55445}, {55414, 55441}

X(55465) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11547, 55464}, {2, 55404, 55436}, {393, 3084, 55435}

X(55466) = X(2)X(220)∩X(3)X(1796)

Barycentrics    1 + 2*Cos[A] - Sin[A]^2 : :

X(55466) lies on these lines: {2, 220}, {3, 1796}, {6, 3219}, {9, 10601}, {57, 52405}, {63, 77}, {72, 1062}, {81, 2256}, {101, 11350}, {182, 26867}, {218, 5256}, {221, 11684}, {306, 23151}, {329, 37800}, {343, 26872}, {644, 34255}, {965, 19822}, {967, 2242}, {1181, 26921}, {1184, 16514}, {1191, 17024}, {1407, 15066}, {1473, 3781}, {1790, 20818}, {1812, 30680}, {1993, 55406}, {2207, 55467}, {2221, 2273}, {2323, 3929}, {2911, 3666}, {2994, 17362}, {2999, 5526}, {3100, 3681}, {3190, 20835}, {3207, 11340}, {3218, 17811}, {3305, 7190}, {3672, 32911}, {3683, 45728}, {3796, 7085}, {3819, 26866}, {3876, 36745}, {3927, 23071}, {3951, 7078}, {4383, 4415}, {5220, 24431}, {5222, 35599}, {5905, 52023}, {6180, 20078}, {6512, 10607}, {7011, 44436}, {7050, 30652}, {7361, 20477}, {7381, 17747}, {7485, 26911}, {7509, 26915}, {9965, 37659}, {10984, 26938}, {11341, 40447}, {16438, 20367}, {17781, 22464}, {17825, 24554}, {22076, 42461}, {22132, 23114}, {22139, 22149}, {23112, 23122}, {24320, 26893}, {24547, 26223}, {24556, 27334}, {26657, 26840}, {26878, 37514}, {26885, 35259}, {26942, 37638}, {27131, 33129}, {27420, 54284}, {27926, 40461}, {37543, 54357}, {40571, 46889}, {40966, 54312}, {55407, 55414}, {55408, 55413}, {55415, 55440}, {55439, 55446}, {55445, 55468}

X(55466) = isotomic conjugate of the polar conjugate of X(3295)
X(55466) = isogonal conjugate of the polar conjugate of X(42696)
X(55466) = X(42696)-Ceva conjugate of X(3295)
X(55466) = X(i)-isoconjugate of X(j) for these (i,j): {19, 3296}, {1096, 30679}
X(55466) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 3296}, {6503, 30679}
X(55466) = crossdifference of every pair of points on line {2488, 18344}
X(55466) = barycentric product X(i)*X(j) for these {i,j}: {3, 42696}, {63, 3305}, {69, 3295}, {78, 7190}, {219, 52422}, {222, 42032}, {345, 52424}, {1331, 48268}, {1332, 47965}, {1444, 3697}, {4561, 48340}
X(55466) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 3296}, {394, 30679}, {3295, 4}, {3305, 92}, {3697, 41013}, {7190, 273}, {42032, 7017}, {42696, 264}, {47965, 17924}, {48268, 46107}, {48340, 7649}, {52422, 331}, {52424, 278}
X(55466) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55405, 55437}, {6, 3219, 55438}, {9, 55399, 10601}, {63, 219, 394}, {63, 394, 22129}, {220, 55405, 2}, {2323, 3929, 55400}, {7085, 7193, 3796}, {24320, 26893, 33586}, {26872, 27509, 343}, {26885, 37581, 35259}

X(55467) = X(2)X(55407)∩X(63)X(11547)

Barycentrics    1 + 2*Cos[A] - Tan[A]^2 : :

X(55467) lies on these lines: {2, 55407}, {9, 2052}, {57, 14165}, {63, 11547}, {220, 55414}, {393, 3219}, {2207, 55466}, {3305, 55433}, {3929, 55402}, {22129, 55445}, {55406, 55413}, {55415, 55438}

X(55467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55407, 55439}, {9, 55401, 2052}, {63, 11547, 55468}, {63, 55462, 11547}, {393, 3219, 55440}

X(55468) = X(2)X(55408)∩X(63)X(11547)

Barycentrics    1 - 2*Cos[A] - Tan[A]^2 : :

X(55468) lies on these lines: {2, 55408}, {9, 14165}, {57, 2052}, {63, 11547}, {393, 3218}, {1407, 55414}, {2207, 22129}, {3306, 55434}, {3928, 55401}, {37532, 41365}, {55405, 55413}, {55415, 55437}, {55445, 55466}

X(55468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55408, 55440}, {57, 55402, 2052}, {63, 11547, 55467}, {63, 55463, 11547}, {393, 3218, 55439}

X(55469) = X(9)X(76)∩X(63)X(7763)

Barycentrics    1 + 2*Cos[A] - Cot[A]^2 : :

X(55469) lies on these lines: {2, 55416}, {9, 76}, {40, 316}, {57, 7769}, {63, 7763}, {69, 26878}, {84, 7782}, {99, 7330}, {315, 55104}, {325, 26921}, {3218, 32829}, {3219, 3926}, {3305, 32832}, {3587, 7802}, {3719, 33939}, {3929, 7799}, {5709, 7752}, {7773, 37584}, {26941, 34386}, {27003, 32839}, {27065, 32828}, {32830, 55449}, {32831, 55419}, {32838, 35595}

X(55469) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55418, 55416}, {63, 7763, 55470}, {3219, 3926, 55417}

X(55470) = X(57)X(76)∩X(63)X(7763)

Barycentrics    1 - 2*Cos[A] - Cot[A]^2 : :

X(55470) lies on these lines: {2, 55417}, {9, 7769}, {40, 7782}, {57, 76}, {63, 7763}, {69, 26877}, {84, 316}, {99, 5709}, {183, 37612}, {325, 24467}, {350, 17437}, {1078, 37534}, {1909, 17700}, {1975, 37532}, {3218, 3926}, {3219, 32829}, {3306, 32832}, {3928, 7799}, {5152, 24469}, {7171, 7802}, {7183, 20924}, {7330, 7752}, {7771, 37526}, {17699, 25303}, {23958, 32830}, {26931, 34386}, {27003, 32828}, {27065, 32839}, {32831, 55418}

X(55470) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55419, 55417}, {63, 7763, 55469}, {3218, 3926, 55416}, {23958, 32830, 55448}

X(55471) = X(2)X(371)∩X(68)X(140)

Barycentrics    1 + Cos[A]/(Cos[A] - Sin[A]) : :

X(55471) lies on these lines: {2, 371}, {68, 140}, {343, 5420}, {485, 52350}, {640, 1590}, {1322, 3536}, {1584, 9682}, {2165, 8253}, {3128, 45499}, {3155, 10514}, {3535, 26362}, {5392, 10195}, {5591, 6414}, {6281, 10133}, {6290, 8964}, {6389, 24245}, {8223, 42060}, {8968, 13430}, {10666, 17811}, {11090, 37802}, {11316, 13567}, {12123, 32587}

X(55471) = isotomic conjugate of the polar conjugate of X(1322)
X(55471) = X(i)-Dao conjugate of X(j) for these (i,j): {3069, 39388}, {24245, 1132}
X(55471) = barycentric product X(i)*X(j) for these {i,j}: {69, 1322}, {486, 1271}, {1152, 34392}, {3536, 11091}
X(55471) = barycentric quotient X(i)/X(j) for these {i,j}: {486, 1132}, {1152, 372}, {1271, 491}, {1322, 4}, {3536, 1586}, {5410, 5412}, {6414, 6416}, {33365, 39388}
X(55471) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11091, 486}, {2, 13428, 55477}, {11091, 55477, 13428}, {13428, 55477, 486}

X(55472) = X(2)X(19)∩X(9)X(92)

Barycentrics    1 + Cos[A] - Sec[A] : :

X(55472) lies on these lines: {1, 54343}, {2, 19}, {4, 5250}, {9, 92}, {27, 10444}, {28, 19861}, {29, 31435}, {33, 1621}, {34, 3869}, {40, 5125}, {57, 1748}, {63, 278}, {78, 41227}, {165, 35994}, {196, 1445}, {204, 17127}, {238, 1096}, {240, 614}, {243, 30223}, {281, 3305}, {297, 25894}, {390, 40971}, {392, 7497}, {394, 608}, {405, 1871}, {412, 12705}, {607, 10601}, {748, 2181}, {960, 54394}, {962, 1753}, {997, 54368}, {1001, 1859}, {1013, 4512}, {1430, 1707}, {1435, 3218}, {1585, 6212}, {1586, 6213}, {1591, 16027}, {1592, 16033}, {1659, 55395}, {1697, 5174}, {1699, 37371}, {1767, 5435}, {1838, 12514}, {1852, 5794}, {1861, 3434}, {1993, 52413}, {2002, 18652}, {2082, 11433}, {2257, 41083}, {2285, 11427}, {2331, 32911}, {2362, 55475}, {3306, 17917}, {3576, 17515}, {3928, 52414}, {4219, 35258}, {4233, 54348}, {4383, 14571}, {5236, 5905}, {5272, 51288}, {5338, 35973}, {6857, 55105}, {7079, 27065}, {7133, 55482}, {7191, 23052}, {7297, 26958}, {7308, 52412}, {7501, 35262}, {7713, 17555}, {7719, 26003}, {8583, 37253}, {11114, 15942}, {11547, 27659}, {13386, 55431}, {13387, 55430}, {13390, 55396}, {14013, 24556}, {15149, 17167}, {15199, 34121}, {15200, 34125}, {16031, 16032}, {16036, 16037}, {16232, 55481}, {17903, 26723}, {18417, 46883}, {21482, 40937}, {30556, 55390}, {30557, 55389}, {30852, 37799}, {42013, 55476}, {55397, 55424}, {55398, 55455}

X(55472) = polar conjugate of the isotomic conjugate of X(55391)
X(55472) = polar conjugate of the isogonal conjugate of X(602)
X(55472) = barycentric product X(i)*X(j) for these {i,j}: {1, 55393}, {4, 55391}, {75, 11398}, {92, 55399}, {264, 602}, {348, 55462}
X(55472) = barycentric quotient X(i)/X(j) for these {i,j}: {602, 3}, {11398, 1}, {55391, 69}, {55393, 75}, {55399, 63}, {55462, 281}
X(55472) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 19, 55478}, {1748, 17923, 57}, {9816, 30674, 2}

X(55473) = X(2)X(95)∩X(4)X(487)

Barycentrics    1 - Cot[A] + Tan[A] : :

X(55473) lies on these lines: {2, 95}, {4, 487}, {7, 55428}, {8, 55429}, {33, 55457}, {34, 55426}, {53, 1991}, {69, 1585}, {264, 1271}, {297, 3068}, {340, 1270}, {458, 5591}, {492, 3535}, {1249, 45420}, {1267, 5081}, {1586, 32806}, {1590, 45198}, {3069, 27377}, {3595, 32002}, {3964, 15200}, {5391, 7282}, {5861, 9308}, {6748, 45473}, {7585, 17907}, {9723, 15204}, {13639, 37765}, {15208, 44180}, {24244, 38294}, {32000, 32809}, {34391, 44146}, {55387, 55460}, {55388, 55431}, {55391, 55481}, {55392, 55476}, {55395, 55422}, {55396, 55453}

X(55473) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 317, 55479}, {4, 491, 55480}, {69, 1585, 55474}, {3535, 32001, 492}

X(55474) = X(2)X(216)∩X(4)X(488)

Barycentrics    1 + Cot[A] + Tan[A] : :

X(55474) lies on these lines: {2, 216}, {4, 488}, {7, 55429}, {8, 55428}, {33, 55456}, {34, 55427}, {53, 45472}, {69, 1585}, {273, 1267}, {278, 46744}, {281, 46745}, {297, 5590}, {317, 1270}, {318, 5391}, {340, 32814}, {458, 3069}, {491, 3535}, {591, 6748}, {648, 7585}, {1235, 13429}, {1271, 44134}, {1586, 32805}, {1589, 20477}, {3068, 9308}, {3536, 32807}, {3964, 15198}, {5860, 27377}, {6776, 55020}, {7586, 36794}, {9723, 15202}, {15206, 44180}, {23291, 55021}, {32001, 32808}, {32806, 52710}, {34391, 44131}, {40065, 45421}, {55387, 55431}, {55388, 55460}, {55391, 55476}, {55392, 55481}, {55395, 55423}, {55396, 55452}

X(55474) = isotomic conjugate of the isogonal conjugate of X(3092)
X(55474) = polar conjugate of the isogonal conjugate of X(1583)
X(55474) = cevapoint of X(1583) and X(3092)
X(55474) = barycentric product X(i)*X(j) for these {i,j}: {75, 55390}, {76, 3092}, {92, 55386}, {264, 1583}
X(55474) = barycentric quotient X(i)/X(j) for these {i,j}: {1583, 3}, {3092, 6}, {55386, 63}, {55390, 1}, {55414, 3093}
X(55474) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 264, 55480}, {4, 492, 55479}, {69, 1585, 55473}, {3535, 32000, 491}

X(55475) = X(1)X(1586)∩X(2)X(34)

Barycentrics    1 + Sin[A] - Tan[A] : :

X(55475) lies on these lines: {1, 1586}, {2, 34}, {4, 3083}, {35, 15205}, {36, 15203}, {55, 15201}, {56, 15199}, {264, 55427}, {317, 55426}, {326, 55458}, {475, 6348}, {1124, 55411}, {1398, 15211}, {1584, 11398}, {1600, 52427}, {1841, 31473}, {1870, 3084}, {2202, 7348}, {2331, 7586}, {2362, 55472}, {3093, 55410}, {5010, 15209}, {7090, 55389}, {7280, 15207}, {13386, 55425}, {13387, 55424}, {13389, 55395}, {13390, 30687}, {16232, 55478}, {30556, 55396}, {55391, 55479}, {55392, 55480}, {55397, 55430}, {55398, 55461}, {55409, 55443}, {55412, 55442}

X(55475) = polar conjugate of the isotomic conjugate of X(55453)
X(55475) = barycentric product X(4)*X(55453)
X(55475) = barycentric quotient X(55453)/X(69)
X(55475) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1586, 55482}, {2, 34, 55481}, {4, 3083, 55476}, {1870, 3536, 3084}

X(55476) = X(1)X(1585)∩X(2)X(33)

Barycentrics    1 + Sin[A] + Tan[A] : :

X(55476) lies on these lines: {1, 1585}, {2, 33}, {4, 3083}, {35, 15204}, {36, 15202}, {55, 15200}, {56, 15198}, {264, 55426}, {317, 55427}, {326, 55429}, {406, 6348}, {1124, 55412}, {1583, 11399}, {1659, 55390}, {1753, 16440}, {1872, 16432}, {3084, 3535}, {3092, 55410}, {5010, 15208}, {6204, 7120}, {7071, 15212}, {7129, 7585}, {7133, 55478}, {7280, 15206}, {13386, 55424}, {13387, 55425}, {13389, 55396}, {14121, 55389}, {15188, 52427}, {15203, 54428}, {30556, 55395}, {42013, 55472}, {55391, 55474}, {55392, 55473}, {55397, 55431}, {55398, 55460}, {55409, 55444}, {55411, 55442}

X(55476) = polar conjugate of the isotomic conjugate of X(55423)
X(55476) = barycentric product X(4)*X(55423)
X(55476) = barycentric quotient X(55423)/X(69)
X(55476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1585, 55481}, {2, 33, 55482}, {4, 3083, 55475}, {3535, 6198, 3084}

X(55477) = X(2)X(371)∩X(5)X(10133)

Barycentrics    1 - Sin[A]/(Cos[A] - Sin[A]) : :

X(55477) lies on these lines: {2, 371}, {5, 10133}, {68, 1656}, {343, 13951}, {394, 32490}, {494, 615}, {1322, 1585}, {1584, 44193}, {1586, 41516}, {1589, 24245}, {3536, 13429}, {5392, 10194}, {5420, 32575}, {6414, 10963}, {10601, 10666}, {13430, 32812}, {16037, 19188}, {32587, 49103}, {32807, 34392}, {37342, 52144}

X(55477) = X(24245)-Dao conjugate of X(3317)
X(55477) = barycentric product X(i)*X(j) for these {i,j}: {486, 32806}, {3312, 34392}
X(55477) = barycentric quotient X(i)/X(j) for these {i,j}: {486, 3317}, {3312, 372}, {5407, 5409}, {32806, 491}
X(55477) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 486, 11091}, {2, 13428, 55471}, {486, 8940, 8036}, {486, 55471, 13428}, {13428, 55471, 11091}

X(55478) = X(2)X(19)∩X(29)X(40)

Barycentrics    1 - Cos[A] + Sec[A] : :

X(55478) lies on these lines: {1, 37253}, {2, 19}, {4, 3359}, {7, 1767}, {9, 1748}, {25, 37619}, {28, 19860}, {29, 40}, {33, 100}, {46, 37235}, {57, 92}, {63, 281}, {81, 2331}, {107, 14006}, {165, 1013}, {171, 1096}, {204, 17126}, {240, 612}, {278, 3306}, {394, 607}, {412, 37560}, {443, 55105}, {445, 24347}, {474, 1871}, {517, 37393}, {608, 10601}, {750, 2181}, {940, 14571}, {1158, 39574}, {1376, 1859}, {1435, 27003}, {1452, 54396}, {1585, 6213}, {1586, 6212}, {1591, 16033}, {1592, 16027}, {1706, 5174}, {1707, 7076}, {1709, 39531}, {1753, 4194}, {1784, 17699}, {1844, 3811}, {1891, 5554}, {1940, 37550}, {2082, 11427}, {2285, 11433}, {2362, 55481}, {3219, 7079}, {3576, 37304}, {3579, 54299}, {3753, 7497}, {3812, 54394}, {3920, 23052}, {3929, 52414}, {4183, 35258}, {4200, 11024}, {5250, 6197}, {5268, 51288}, {5281, 40971}, {5341, 26958}, {5422, 52413}, {5437, 17923}, {7017, 19811}, {7090, 55395}, {7133, 55476}, {7518, 11471}, {7521, 24541}, {7532, 8251}, {7713, 11109}, {7719, 37448}, {8141, 52260}, {8557, 18679}, {12705, 52248}, {13386, 55461}, {13387, 55460}, {13388, 55390}, {13389, 55389}, {14121, 55396}, {14923, 40399}, {15199, 34125}, {15200, 34121}, {15942, 17579}, {16031, 16037}, {16032, 16036}, {16232, 55475}, {26446, 37321}, {30503, 37258}, {31266, 37799}, {40117, 41081}, {41227, 54392}, {42013, 55482}, {54318, 54368}, {55397, 55454}, {55398, 55425}

X(55478) = polar conjugate of the isotomic conjugate of X(55392)
X(55478) = polar conjugate of the isogonal conjugate of X(601)
X(55478) = barycentric product X(i)*X(j) for these {i,j}: {1, 55394}, {4, 55392}, {75, 11399}, {92, 55400}, {264, 601}, {345, 55463}
X(55478) = barycentric quotient X(i)/X(j) for these {i,j}: {601, 3}, {11399, 1}, {55392, 69}, {55394, 75}, {55400, 63}, {55463, 278}
X(55478) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 19, 55472}, {2, 3101, 30675}, {1748, 52412, 9}, {6197, 7498, 5250}

X(55479) = X(2)X(95)∩X(4)X(488)

Barycentrics    1 + Cot[A] - Tan[A] : :

X(55479) lies on these lines: {2, 95}, {4, 488}, {7, 55458}, {8, 55459}, {33, 55427}, {34, 55456}, {53, 591}, {69, 1586}, {264, 1270}, {297, 3069}, {340, 1271}, {458, 5590}, {491, 3536}, {1249, 45421}, {1267, 7282}, {1585, 32805}, {1589, 45198}, {3068, 27377}, {3535, 32807}, {3593, 32002}, {3964, 15199}, {5081, 5391}, {5860, 9308}, {6748, 45472}, {7586, 17907}, {9723, 15203}, {13759, 37765}, {15207, 44180}, {24243, 38294}, {32000, 32808}, {32814, 44134}, {34392, 44146}, {55387, 55430}, {55388, 55461}, {55391, 55475}, {55392, 55482}, {55395, 55452}, {55396, 55423}

X(55479) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 317, 55473}, {4, 492, 55474}, {69, 1586, 55480}, {3536, 32001, 491}

X(55480) = X(2)X(216)∩X(4)X(487)

Barycentrics    1 - Cot[A] - Tan[A] : :

X(55480) lies on these lines: {2, 216}, {4, 487}, {7, 55459}, {8, 55458}, {33, 55426}, {34, 55457}, {53, 45473}, {69, 1586}, {273, 5391}, {278, 46745}, {281, 46744}, {297, 5591}, {317, 1271}, {318, 1267}, {458, 3068}, {492, 3536}, {648, 7586}, {1235, 13440}, {1270, 44134}, {1585, 32806}, {1590, 20477}, {1991, 6748}, {3069, 9308}, {3964, 15201}, {5861, 27377}, {6776, 55021}, {7585, 36794}, {9723, 15205}, {15209, 44180}, {23291, 55020}, {32001, 32809}, {32805, 52710}, {34392, 44131}, {40065, 45420}, {55387, 55461}, {55388, 55430}, {55391, 55482}, {55392, 55475}, {55395, 55453}, {55396, 55422}

X(55480) = isotomic conjugate of the isogonal conjugate of X(3093)
X(55480) = polar conjugate of the isogonal conjugate of X(1584)
X(55480) = cevapoint of X(1584) and X(3093)
X(55480) = barycentric product X(i)*X(j) for these {i,j}: {75, 55389}, {76, 3093}, {92, 55385}, {264, 1584}
X(55480) = barycentric quotient X(i)/X(j) for these {i,j}: {1584, 3}, {3093, 6}, {55385, 63}, {55389, 1}, {55414, 3092}
X(55480) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 264, 55474}, {4, 491, 55473}, {69, 1586, 55479}, {3536, 32000, 492}

X(55481) = X(1)X(1585)∩X(2)X(34)

Barycentrics    1 - Sin[A] + Tan[A] : :

X(55481) lies on these lines: {1, 1585}, {2, 34}, {4, 3084}, {35, 15202}, {36, 15204}, {55, 15198}, {56, 15200}, {264, 55457}, {317, 55456}, {326, 55428}, {475, 6347}, {1335, 55412}, {1398, 15212}, {1583, 11398}, {1599, 52427}, {1659, 30687}, {1870, 3083}, {2202, 7347}, {2331, 7585}, {2362, 55478}, {3092, 55409}, {5010, 15206}, {7280, 15208}, {13386, 55455}, {13387, 55454}, {13388, 55396}, {14121, 55390}, {16232, 55472}, {30557, 55395}, {55391, 55473}, {55392, 55474}, {55397, 55460}, {55398, 55431}, {55410, 55444}, {55411, 55441}

X(55481) = polar conjugate of the isotomic conjugate of X(55452)
X(55481) = barycentric product X(4)*X(55452)
X(55481) = barycentric quotient X(55452)/X(69)
X(55481) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1585, 55476}, {2, 34, 55475}, {4, 3084, 55482}, {1870, 3535, 3083}

X(55482) = X(1)X(1586)∩X(2)X(33)

Barycentrics    1 - Sin[A] - Tan[A] : :

X(55482) lies on these lines: {1, 1586}, {2, 33}, {4, 3084}, {35, 15203}, {36, 15205}, {55, 15199}, {56, 15201}, {264, 55456}, {317, 55457}, {326, 55459}, {406, 6347}, {1335, 55411}, {1584, 11399}, {1753, 16441}, {1872, 16433}, {3083, 3536}, {3093, 55409}, {5010, 15207}, {6203, 7120}, {7071, 15211}, {7090, 55390}, {7129, 7586}, {7133, 55472}, {7280, 15209}, {13386, 55454}, {13387, 55455}, {13388, 55395}, {13390, 55389}, {15187, 52427}, {15204, 54428}, {30557, 55396}, {42013, 55478}, {55391, 55480}, {55392, 55479}, {55397, 55461}, {55398, 55430}, {55410, 55443}, {55412, 55441}

X(55482) = polar conjugate of the isotomic conjugate of X(55422)
X(55482) = barycentric product X(4)*X(55422)
X(55482) = barycentric quotient X(55422)/X(69)
X(55482) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1586, 55475}, {2, 33, 55476}, {4, 3084, 55481}, {3536, 6198, 3083}





leftri  Centers on the cubic K005: X(55483) - X(55495)  rightri

Centers X(55483)-X(55495) were contributed by César Eliud Lozada, August 9, 2023.

Mostly of these centers are the 3rd intersection of K005 and the line {P, Q}, where P and Q lie on K005.

underbar

X(55483) = X(1)X(627)∩X(61)X(6192)

Barycentrics    a*((a^6+(b+c)*a^5-(b^2+3*b*c+c^2)*a^4-2*(b+c)*(b^2+b*c+c^2)*a^3-(b^2+c^2)*(b^2-4*b*c+c^2)*a^2+(b^2-c^2)*(b-c)*(b^2+4*b*c+c^2)*a+(b^2-c^2)*(b-c)*(b^3+c^3))*sqrt(3)+2*S*(a^4-3*(b+c)*a^3-(2*b^2+3*b*c+2*c^2)*a^2-3*(b^2-c^2)*(b-c)*a+(b^2+4*b*c+c^2)*(b^2-b*c+c^2))) : :

X(55483) lies on the cubics K005, K1075 and these lines: {1, 627}, {3, 8433}, {4, 8435}, {5, 55484}, {18, 48797}, {61, 6192}, {3336, 39261}, {3460, 3490}, {3467, 55489}, {3468, 38931}, {6191, 55490}, {7345, 8837}, {33429, 51749}

X(55483) = isogonal conjugate of X(55484)
X(55483) = X(1652)-isoconjugate of-X(7088)
X(55483) = trilinear product X(1653)*X(7089)
X(55483) = trilinear quotient X(i)/X(j) for these (i, j): (1653, 1652), (7089, 7088)

X(55484) = X(1)X(628) ∩ X(62)X(6191)

Barycentrics    a*((a^6+(b+c)*a^5-(b^2+3*b*c+c^2)*a^4-2*(b+c)*(b^2+b*c+c^2)*a^3-(b^2+c^2)*(b^2-4*b*c+c^2)*a^2+(b^2-c^2)*(b-c)*(b^2+4*b*c+c^2)*a+(b^2-c^2)*(b-c)*(b^3+c^3))*sqrt(3)-2*S*(a^4-3*(b+c)*a^3-(2*b^2+3*b*c+2*c^2)*a^2-3*(b^2-c^2)*(b-c)*a+(b^2+4*b*c+c^2)*(b^2-b*c+c^2))) : :

X(55484) lies on the cubics K005, K1075 and these lines: {1, 628}, {3, 8434}, {4, 8436}, {5, 55483}, {17, 48795}, {62, 6191}, {3336, 39262}, {3460, 3489}, {3467, 55488}, {3468, 38932}, {6192, 55491}, {7344, 8839}, {33428, 51750}

X(55484) = isogonal conjugate of X(55483)
X(55484) = X(1653)-isoconjugate of-X(7089)
X(55484) = trilinear product X(1652)*X(7088)
X(55484) = trilinear quotient X(i)/X(j) for these (i, j): (1652, 1653), (7088, 7089)

X(55485) = X(1)X(3459)∩X(3)X(3461)

Barycentrics    a*(a^3-(b-c)*a^2-(b^2+b*c+c^2)*a+(b+c)*(b^2-c^2))*(a^3+(b-c)*a^2-(b^2+b*c+c^2)*a-(b+c)*(b^2-c^2))*(a^15-6*(b^2+c^2)*a^13-(b+c)*(b^2+c^2)*a^12+(15*b^4+15*c^4-2*(b^2-10*b*c+c^2)*b*c)*a^11+(b+c)*(6*b^4+6*c^4-(3*b^2-8*b*c+3*c^2)*b*c)*a^10-2*(10*b^6+10*c^6-(4*b^4+4*c^4-(11*b^2-4*b*c+11*c^2)*b*c)*b*c)*a^9-(b+c)*(15*b^6+15*c^6-(13*b^2+6*b*c+13*c^2)*(b-c)^2*b*c)*a^8+(15*b^8+15*c^8-(12*b^6+12*c^6-(5*b^4+5*c^4-(6*b^2-5*b*c+6*c^2)*b*c)*b*c)*b*c)*a^7+(b+c)*(20*b^8+20*c^8-(22*b^6+22*c^6-(17*b^4+17*c^4-(13*b^2-14*b*c+13*c^2)*b*c)*b*c)*b*c)*a^6-(b^2-c^2)^2*(6*b^6+6*c^6-(8*b^4+8*c^4-5*b*c*(b-c)^2)*b*c)*a^5-(b^2-c^2)*(b-c)*(15*b^8+15*c^8+(12*b^6+12*c^6+b*c*(5*b^2-2*b*c+5*c^2)*(b+c)^2)*b*c)*a^4+(b^8+c^8-(2*b^6+2*c^6+(3*b^4+3*c^4-b*c*(4*b^2-b*c+4*c^2))*b*c)*b*c)*(b^2-c^2)^2*a^3+(b^2-c^2)^3*(b-c)*(6*b^6+6*c^6+(5*b^4+5*c^4+b*c*(3*b^2+5*b*c+3*c^2))*b*c)*a^2+(b^2-c^2)^4*(b-c)^2*b^2*c^2*a-(b^3+c^3)*(b^2-c^2)^6) : :

X(55485) lies on the cubic K005 and these lines: {1, 3459}, {3, 3461}, {4, 5685}, {5, 34305}, {54, 3467}, {2121, 3468}, {3463, 46037}, {3469, 3471}, {7344, 55493}, {7345, 55492}

X(55485) = X(i)-Ceva conjugate of-X(j) for these (i, j): (5, 3467), (34305, 3483)

X(55486) = X(18)X(6192) ∩ X(627)X(3467)

Barycentrics    a*(2*a^12+(b+c)*a^11-5*(b^2+c^2)*a^10+(b+c)*(b^2-9*b*c+c^2)*a^9+2*(2*b^4+2*c^4-3*(b^2-3*b*c+c^2)*b*c)*a^8-(b+c)*(8*b^4+8*c^4-3*(7*b^2-5*b*c+7*c^2)*b*c)*a^7+3*(2*b^4+2*c^4-(13*b^2-28*b*c+13*c^2)*b*c)*b*c*a^6+(b+c)*(8*b^6+8*c^6-3*(6*b^4+6*c^4-(10*b^2-19*b*c+10*c^2)*b*c)*b*c)*a^5-(b^4+c^4-3*b*c*(b^2+c^2))*(4*b^4+4*c^4+(3*b^2-20*b*c+3*c^2)*b*c)*a^4-(b+c)*(b^8+c^8-(9*b^6+9*c^6-(43*b^4+43*c^4-b*c*(111*b^2-140*b*c+111*c^2))*b*c)*b*c)*a^3+(b^2-c^2)^2*(5*b^6+5*c^6-2*(6*b^4+6*c^4+b*c*(b^2+3*b*c+c^2))*b*c)*a^2-(b^2-c^2)^2*(b+c)*(b^6+c^6+(3*b^4+3*c^4-5*b*c*(5*b^2-9*b*c+5*c^2))*b*c)*a-(b^2-c^2)^3*(b+c)*(b-2*c)*(2*b-c)*(b^3-c^3)+2*S*sqrt(3)*((b+c)*a^9-(b^2+c^2)*a^8-(b+c)*(2*b^2-b*c+2*c^2)*a^7+(3*b^4+3*c^4-2*(3*b^2-4*b*c+3*c^2)*b*c)*a^6+7*(b+c)*b^2*c^2*a^5-3*(b^6+c^6-2*(b^2-c^2)^2*b*c)*a^4+(b+c)*(2*b^6+2*c^6-(6*b^4+6*c^4-(11*b^2-19*b*c+11*c^2)*b*c)*b*c)*a^3+(b^2-b*c+c^2)*(b^6+c^6-(2*b^4+2*c^4+(b^2-10*b*c+c^2)*b*c)*b*c)*a^2-(b^2-c^2)*(b-c)*(b^6+c^6-(3*b^4+3*c^4+b*c*(3*b^2-17*b*c+3*c^2))*b*c)*a+3*(b^2-c^2)^2*(b-c)*b*c*(b^3-c^3))) : :

X(55486) lies on the cubic K005 and these lines: {1, 39261}, {3, 8434}, {4, 8502}, {18, 6192}, {627, 3467}, {3468, 3490}, {3471, 55487}, {7345, 8918}, {38931, 46037}, {48797, 55493}

X(55487) = X(17)X(6191)∩X(628)X(3467)

Barycentrics    a*(2*a^12+(b+c)*a^11-5*(b^2+c^2)*a^10+(b+c)*(b^2-9*b*c+c^2)*a^9+2*(2*b^4+2*c^4-3*(b^2-3*b*c+c^2)*b*c)*a^8-(b+c)*(8*b^4+8*c^4-3*(7*b^2-5*b*c+7*c^2)*b*c)*a^7+3*(2*b^4+2*c^4-(13*b^2-28*b*c+13*c^2)*b*c)*b*c*a^6+(b+c)*(8*b^6+8*c^6-3*(6*b^4+6*c^4-(10*b^2-19*b*c+10*c^2)*b*c)*b*c)*a^5-(b^4+c^4-3*b*c*(b^2+c^2))*(4*b^4+4*c^4+(3*b^2-20*b*c+3*c^2)*b*c)*a^4-(b+c)*(b^8+c^8-(9*b^6+9*c^6-(43*b^4+43*c^4-b*c*(111*b^2-140*b*c+111*c^2))*b*c)*b*c)*a^3+(b^2-c^2)^2*(5*b^6+5*c^6-2*(6*b^4+6*c^4+b*c*(b^2+3*b*c+c^2))*b*c)*a^2-(b^2-c^2)^2*(b+c)*(b^6+c^6+(3*b^4+3*c^4-5*b*c*(5*b^2-9*b*c+5*c^2))*b*c)*a-(b^2-c^2)^3*(b+c)*(b-2*c)*(2*b-c)*(b^3-c^3)-2*S*sqrt(3)*((b+c)*a^9-(b^2+c^2)*a^8-(b+c)*(2*b^2-b*c+2*c^2)*a^7+(3*b^4+3*c^4-2*(3*b^2-4*b*c+3*c^2)*b*c)*a^6+7*(b+c)*b^2*c^2*a^5-3*(b^6+c^6-2*(b^2-c^2)^2*b*c)*a^4+(b+c)*(2*b^6+2*c^6-(6*b^4+6*c^4-(11*b^2-19*b*c+11*c^2)*b*c)*b*c)*a^3+(b^2-b*c+c^2)*(b^6+c^6-(2*b^4+2*c^4+(b^2-10*b*c+c^2)*b*c)*b*c)*a^2-(b^2-c^2)*(b-c)*(b^6+c^6-(3*b^4+3*c^4+b*c*(3*b^2-17*b*c+3*c^2))*b*c)*a+3*(b^2-c^2)^2*(b-c)*b*c*(b^3-c^3))) : :

X(55487) lies on the cubic K005 and these lines: {1, 39262}, {3, 8433}, {4, 8501}, {17, 6191}, {628, 3467}, {3468, 3489}, {3471, 55486}, {7344, 8919}, {38932, 46037}, {48795, 55492}

X(55488) = X(3)X(1338)∩X(627)X(3459)

Barycentrics    a^2*(-2*(a^8-4*(b^2+c^2)*a^6+(6*b^4+5*b^2*c^2+6*c^4)*a^4-(b^2+c^2)*(4*b^4-11*b^2*c^2+4*c^4)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S+sqrt(3)*(a^10-3*(b^2+c^2)*a^8+(2*b^4+b^2*c^2+2*c^4)*a^6+2*(b^2+c^2)^3*a^4-(b^2-c^2)^2*(3*b^4+7*b^2*c^2+3*c^4)*a^2+(b^4-c^4)*(b^2-c^2)^3))*(sqrt(3)*b^2-2*S)*(sqrt(3)*c^2-2*S) : :

X(55488) lies on the cubic K005 and these lines: {3, 1338}, {4, 5675}, {18, 6151}, {54, 39261}, {61, 55493}, {627, 3459}, {3467, 55484}, {3471, 38931}, {8918, 55495}, {55490, 55492}

X(55488) = X(5)-Ceva conjugate of-X(39261)

X(55489) = X(3)X(1337)∩X(17)X(2981)

Barycentrics    a^2*(2*(a^8-4*(b^2+c^2)*a^6+(6*b^4+5*b^2*c^2+6*c^4)*a^4-(b^2+c^2)*(4*b^4-11*b^2*c^2+4*c^4)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S+sqrt(3)*(a^10-3*(b^2+c^2)*a^8+(2*b^4+b^2*c^2+2*c^4)*a^6+2*(b^2+c^2)^3*a^4-(b^2-c^2)^2*(3*b^4+7*b^2*c^2+3*c^4)*a^2+(b^4-c^4)*(b^2-c^2)^3))*(sqrt(3)*b^2+2*S)*(sqrt(3)*c^2+2*S) : :

X(55489) lies on the cubic K005 and these lines: {3, 1337}, {4, 5674}, {17, 2981}, {54, 39262}, {62, 55492}, {628, 3459}, {3467, 55483}, {3471, 38932}, {8919, 55494}, {55491, 55493}

X(55489) = X(5)-Ceva conjugate of-X(39262)

X(55490) = X(3)X(8450)∩X(17)X(628)

Barycentrics    a^2*(2*(a^6-3*(b^2+c^2)*a^4-(3*b^4-11*b^2*c^2+3*c^4)*a^2-2*(b^2+c^2)*(2*b^4-7*b^2*c^2+2*c^4))*S+sqrt(3)*(a^8-2*(b^2+c^2)*a^6-b^2*c^2*a^4-(b^2+c^2)*(b^2+3*b*c+c^2)*(b^2-3*b*c+c^2)*a^2+2*c^8-2*(3*b^2+b*c-3*c^2)*(3*b^2-b*c-3*c^2)*b^2*c^2+2*b^8)) : :

X(55490) lies on the cubic K005 and these lines: {3, 8450}, {4, 8470}, {17, 628}, {62, 16459}, {3489, 8839}, {6191, 55483}, {8919, 38932}, {55488, 55492}

X(55491) = X(3)X(8450)∩X(18)X(627)

Barycentrics    a^2*(-2*(a^6-3*(b^2+c^2)*a^4-(3*b^4-11*b^2*c^2+3*c^4)*a^2-2*(b^2+c^2)*(2*b^4-7*b^2*c^2+2*c^4))*S+sqrt(3)*(a^8-2*(b^2+c^2)*a^6-b^2*c^2*a^4-(b^2+c^2)*(b^2+3*b*c+c^2)*(b^2-3*b*c+c^2)*a^2+2*c^8-2*(3*b^2+b*c-3*c^2)*(3*b^2-b*c-3*c^2)*b^2*c^2+2*b^8)) : :

X(55491) lies on the cubic K005 and these lines: {3, 8450}, {4, 8478}, {18, 627}, {61, 16460}, {3490, 8837}, {6192, 55484}, {8918, 38931}, {55489, 55493}

X(55492) = X(4)X(8172)∩X(61)X(195)

Barycentrics    a^2*(-2*(a^12-2*(b^2+c^2)*a^10-(5*b^4+8*b^2*c^2+5*c^4)*a^8+2*(b^2+c^2)*(10*b^4+7*b^2*c^2+10*c^4)*a^6-(25*b^8+25*c^8+17*(2*b^4+b^2*c^2+2*c^4)*b^2*c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)*(7*b^4+11*b^2*c^2+7*c^4)*a^2-(b^2-c^2)^4*(3*b^2+c^2)*(b^2+3*c^2))*S+sqrt(3)*(a^14-7*(b^2+c^2)*a^12+7*(3*b^4+4*b^2*c^2+3*c^4)*a^10-(b^2+c^2)*(35*b^4+2*b^2*c^2+35*c^4)*a^8+(35*b^8+35*c^8+(4*b^4+3*b^2*c^2+4*c^4)*b^2*c^2)*a^6-(b^2+c^2)*(21*b^8+21*c^8-(56*b^4-43*b^2*c^2+56*c^4)*b^2*c^2)*a^4+(7*b^8+7*c^8-2*(9*b^4+11*b^2*c^2+9*c^4)*b^2*c^2)*(b^2-c^2)^2*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^4-c^4)*(b^2-c^2)^3)) : :

X(55492) lies on the cubic K005 and these lines: {3, 8446}, {4, 8172}, {5, 8929}, {15, 50213}, {17, 13483}, {18, 38935}, {61, 195}, {62, 55489}, {627, 8930}, {3336, 48797}, {3470, 8837}, {6192, 47307}, {7345, 55485}, {8918, 47305}, {48795, 55487}, {55488, 55490}

X(55492) = reflection of X(15) in X(50213)
X(55492) = isogonal conjugate of X(8929)
X(55492) = crosssum of X(8929) and X(8929)
X(55492) = X(37848)-cross conjugate of-X(15)
X(55492) = X(i)-Dao conjugate of-X(j) for these (i, j): (3, 8929), (40580, 51271)
X(55492) = X(2153)-isoconjugate of-X(51271)
X(55492) = X(15)-reciprocal conjugate of-X(51271)
X(55492) = pole of line {8929, 51271} with respect to Stammler hyperbola

X(55493) = X(4)X(8173)∩X(62)X(195)

Barycentrics    a^2*(2*(a^12-2*(b^2+c^2)*a^10-(5*b^4+8*b^2*c^2+5*c^4)*a^8+2*(b^2+c^2)*(10*b^4+7*b^2*c^2+10*c^4)*a^6-(25*b^8+25*c^8+17*(2*b^4+b^2*c^2+2*c^4)*b^2*c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)*(7*b^4+11*b^2*c^2+7*c^4)*a^2-(b^2-c^2)^4*(3*b^2+c^2)*(b^2+3*c^2))*S+sqrt(3)*(a^14-7*(b^2+c^2)*a^12+7*(3*b^4+4*b^2*c^2+3*c^4)*a^10-(b^2+c^2)*(35*b^4+2*b^2*c^2+35*c^4)*a^8+(35*b^8+35*c^8+(4*b^4+3*b^2*c^2+4*c^4)*b^2*c^2)*a^6-(b^2+c^2)*(21*b^8+21*c^8-(56*b^4-43*b^2*c^2+56*c^4)*b^2*c^2)*a^4+(7*b^8+7*c^8-2*(9*b^4+11*b^2*c^2+9*c^4)*b^2*c^2)*(b^2-c^2)^2*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^4-c^4)*(b^2-c^2)^3)) : :

X(55493) lies on the cubic K005 and these lines: {3, 8456}, {4, 8173}, {5, 8930}, {16, 50214}, {17, 38935}, {18, 13484}, {61, 55488}, {62, 195}, {628, 8929}, {3336, 48795}, {3470, 8839}, {6191, 47307}, {7344, 55485}, {8919, 47305}, {48797, 55486}, {55489, 55491}

X(55493) = reflection of X(16) in X(50214)
X(55493) = isogonal conjugate of X(8930)
X(55493) = X(37850)-cross conjugate of-X(16)
X(55493) = X(40581)-Dao conjugate of-X( 51264)
X(55493) = X(2154)-isoconjugate of-X(51264)
X(55493) = X(16)-reciprocal conjugate of-X(51264)
X(55493) = pole of line {8930, 51264} with respect to Stammler hyperbola

X(55494) = X(18)X(2120)∩X(61)X(3462)

Barycentrics    (2*sqrt(3)*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)*b^2)*(a^2+b^2-c^2)*S+a^8-(2*b^2+c^2)*a^6+(b^2-c^2)*(2*b^2+3*c^2)*a^4-(b^2-c^2)*(2*b^4+b^2*c^2+5*c^4)*a^2+(b^2+2*c^2)*(b^2-c^2)^3)*(2*sqrt(3)*(a^4-(b^2+2*c^2)*a^2-(b^2-c^2)*c^2)*(a^2-b^2+c^2)*S+a^8-(b^2+2*c^2)*a^6-(b^2-c^2)*(3*b^2+2*c^2)*a^4+(b^2-c^2)*(5*b^4+b^2*c^2+2*c^4)*a^2-(2*b^2+c^2)*(b^2-c^2)^3) : :

X(55494) lies on the cubic K005 and these lines: {3, 8174}, {4, 8471}, {5, 8837}, {18, 2120}, {61, 3462}, {195, 8918}, {627, 8839}, {3460, 6192}, {3468, 48797}, {8919, 55489}, {8929, 38933}, {46754, 46755}

X(55494) = isogonal conjugate of X(8837)
X(55494) = isotomic conjugate of X(46753)
X(55494) = polar conjugate of X(51273)
X(55494) = X(54)-cross conjugate of-X(18)
X(55494) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 46753), (1249, 51273)
X(55494) = X(i)-isoconjugate of-X(j) for these {i, j}: {31, 46753}, {48, 51273}
X(55494) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2, 46753), (4, 51273)
X(55494) = pole of the tripolar of X(51273) with respect to polar circle
X(55494) = pole of line {8837, 46753} with respect to Steiner-Wallace hyperbola
X(55494) = trilinear quotient X(i)/X(j) for these (i, j): (75, 46753), (92, 51273)

X(55495) = X(17)X(2120)∩X(62)X(3462)

Barycentrics    (-2*sqrt(3)*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)*b^2)*(a^2+b^2-c^2)*S+a^8-(2*b^2+c^2)*a^6+(b^2-c^2)*(2*b^2+3*c^2)*a^4-(b^2-c^2)*(2*b^4+b^2*c^2+5*c^4)*a^2+(b^2+2*c^2)*(b^2-c^2)^3)*(-2*sqrt(3)*(a^4-(b^2+2*c^2)*a^2-(b^2-c^2)*c^2)*(a^2-b^2+c^2)*S+a^8-(b^2+2*c^2)*a^6-(b^2-c^2)*(3*b^2+2*c^2)*a^4+(b^2-c^2)*(5*b^4+b^2*c^2+2*c^4)*a^2-(2*b^2+c^2)*(b^2-c^2)^3) : :

X(55495) lies on the cubic K005 and these lines: {3, 8175}, {4, 8479}, {5, 8839}, {17, 2120}, {62, 3462}, {195, 8919}, {628, 8837}, {3460, 6191}, {3468, 48795}, {8918, 55488}, {8930, 38933}, {46753, 46756}

X(55495) = isogonal conjugate of X(8839)
X(55495) = isotomic conjugate of X(46754)
X(55495) = polar conjugate of X(51266)
X(55495) = X(54)-cross conjugate of-X(17)
X(55495) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 46754), (1249, 51266)
X(55495) = X(i)-isoconjugate of-X(j) for these {i, j}: {31, 46754}, {48, 51266}
X(55495) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2, 46754), (4, 51266)
X(55495) = pole of the tripolar of X(51266) with respect to polar circle
X(55495) = pole of line {8839, 46754} with respect to Steiner-Wallace hyperbola
X(55495) = trilinear quotient X(i)/X(j) for these (i, j): (75, 46754), (92, 51266)



leftri  Centers on the cubic K006: X(55496) - X(55528)  rightri

Centers X(55496)-X(55528) were contributed by César Eliud Lozada, August 9, 2023.

Mostly of these centers are the 3rd intersection of K006 and the line {P, Q}, where P and Q lie on K006.

underbar

X(55496) = X(1)X(254)∩X(3)X(90)

Barycentrics    a*(a^9-(b+c)*a^8-2*(2*b^2+b*c+2*c^2)*a^7+4*(b^3+c^3)*a^6+2*(3*b^2+4*b*c+3*c^2)*(b^2-b*c+c^2)*a^5-2*(b+c)*(3*b^4+3*c^4-4*b*c*(b^2-b*c+c^2))*a^4-2*(2*b^6+2*c^6-(b^2-c^2)^2*b*c)*a^3+4*(b^2-c^2)*(b-c)*(b^4+c^4+b*c*(b^2+b*c+c^2))*a^2+(b^4-c^4)*(b^2-c^2)*(b-c)^2*a-(b^2-c^2)^4*(b+c))*(a^3-(b-c)*a^2-(b^2+c^2)*a+(b+c)*(b^2-c^2))*(a^3+(b-c)*a^2-(b^2+c^2)*a-(b+c)*(b^2-c^2)) : :

X(55496) lies on the cubic K006 and these lines: {1, 254}, {3, 90}, {485, 55506}, {486, 55505}, {6212, 55510}, {6213, 55509}, {6513, 21616}, {8946, 55508}, {8948, 55507}

X(55496) = X(4)-Ceva conjugate of-X(90)
X(55496) = (orthic)-isogonal conjugate-of-X(90)
X(55496) = X(6513)-Dao conjugate of-X(69)

X(55497) = X(1)X(485)∩X(90)X(372)

Barycentrics    a*(4*a*(b+c)*(a^4-2*(b^2+c^2)*a^2+b^4+c^4)*S+(a+b+c)*(a^7-(b+c)*a^6-(3*b^2+2*b*c+3*c^2)*a^5+3*(b+c)*(b^2+c^2)*a^4+(3*b^4-2*b^2*c^2+3*c^4)*a^3-(b+c)*(3*b^4-2*b^2*c^2+3*c^4)*a^2-(b^2-c^2)^2*(b-c)^2*a+(b^4-c^4)*(b^2-c^2)*(b+c))) : :
X(55497) = a*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(b*c + S)*(a*b*c + (-a + b + c)*S) : :

X(55497) lies on the cubic K006 and these lines: {1, 485}, {3, 6212}, {4, 55505}, {46, 55509}, {90, 372}, {254, 1826}, {371, 55508}, {486, 8945}, {487, 13386}, {997, 14121}, {1824, 6213}, {2960, 32555}, {3083, 31591}, {8946, 55515}, {8947, 55511}, {31574, 41860}, {55499, 55510}, {55507, 55513}, {55512, 55524}, {55516, 55525}, {55523, 55527}

X(55497) = isogonal conjugate of X(55505)
X(55497) = X(4)-Ceva conjugate of-X(6212)
X(55497) = X(3083)-Dao conjugate of-X(69)
X(55497) = X(44590)-reciprocal conjugate of-X(6213)
X(55497) = barycentric product X(44590)*X(46744)
X(55497) = trilinear product X(13386)*X(44590)
X(55497) = (orthic)-isogonal conjugate-of-X(6212)
X(55497) = trilinear quotient X(44590)/X(34121)

X(55498) = X(1)X(486)∩X(3)X(6213)

Barycentrics    a*(-4*a*(b+c)*(a^4-2*(b^2+c^2)*a^2+b^4+c^4)*S+(a+b+c)*(a^7-(b+c)*a^6-(3*b^2+2*b*c+3*c^2)*a^5+3*(b+c)*(b^2+c^2)*a^4+(3*b^4-2*b^2*c^2+3*c^4)*a^3-(b+c)*(3*b^4-2*b^2*c^2+3*c^4)*a^2-(b^2-c^2)^2*(b-c)^2*a+(b^4-c^4)*(b^2-c^2)*(b+c))) : :
X(55498) = a*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(b*c - S)*(a*b*c - (-a + b + c)*S) : :

X(55498) lies on the cubic K006 and these lines: {1, 486}, {3, 6213}, {4, 55506}, {46, 55510}, {90, 371}, {254, 1826}, {372, 55507}, {485, 8941}, {488, 13387}, {997, 7090}, {1824, 6212}, {2960, 32556}, {3084, 31590}, {8948, 55516}, {8949, 55512}, {31573, 41860}, {55500, 55509}, {55508, 55514}, {55511, 55523}, {55515, 55526}, {55524, 55528}

X(55498) = isogonal conjugate of X(55506)
X(55498) = X(4)-Ceva conjugate of-X(6213)
X(55498) = X(3084)-Dao conjugate of-X(69)
X(55498) = X(44591)-reciprocal conjugate of-X(6212)
X(55498) = barycentric product X(44591)*X(46745)
X(55498) = trilinear product X(13387)*X(44591)
X(55498) = (orthic)-isogonal conjugate-of-X(6213)
X(55498) = trilinear quotient X(44591)/X(34125)

X(55499) = X(1)X(8946)∩X(3)X(8947)

Barycentrics    a*(a^9+(b+c)*a^8-2*(b+c)^2*a^7-2*(b+c)*(b^2+3*b*c+c^2)*a^6+4*(b^2-b*c+c^2)*b*c*a^5+2*(b+c)*(7*b^2-6*b*c+7*c^2)*b*c*a^4+2*(b^2+4*b*c+c^2)*(b^4+c^4-2*b*c*(b^2-3*b*c+c^2))*a^3+2*(b^2-c^2)*(b-c)*(b^4+c^4-3*b*c*(b^2+c^2))*a^2-(b^2-c^2)^2*(b^4+c^4+2*b*c*(2*b^2-3*b*c+2*c^2))*a-(b^4-c^4)*(b^2-c^2)^2*(b-c)+4*S*((b+c)*a^6+(b^2+b*c+c^2)*a^5-(b+c)*b*c*a^4-6*(b^2+c^2)*b*c*a^3-(b+c)*(b^4+c^4)*a^2-(b^6+c^6-(b^4+c^4+b*c*(b^2-6*b*c+c^2))*b*c)*a+(b^4-c^4)*b*c*(b-c))) : :

X(55499) lies on the cubic K006 and these lines: {1, 8946}, {3, 8947}, {4, 55507}, {90, 488}, {254, 55500}, {371, 55506}, {485, 55516}, {486, 6213}, {6212, 55512}, {8948, 55523}, {8949, 55526}, {55497, 55510}, {55505, 55514}, {55508, 55521}, {55509, 55519}, {55515, 55528}

X(55499) = isogonal conjugate of X(55507)
X(55499) = X(4)-Ceva conjugate of-X(8947)
X(55499) = trilinear product X(7348)*X(8942)
X(55499) = (orthic)-isogonal conjugate-of-X(8947)
X(55499) = trilinear quotient X(8942)/X(6203)

X(55500) = X(1)X(8948)∩X(3)X(8949)

Barycentrics    a*(a^9+(b+c)*a^8-2*(b+c)^2*a^7-2*(b+c)*(b^2+3*b*c+c^2)*a^6+4*(b^2-b*c+c^2)*b*c*a^5+2*(b+c)*(7*b^2-6*b*c+7*c^2)*b*c*a^4+2*(b^2+4*b*c+c^2)*(b^4+c^4-2*b*c*(b^2-3*b*c+c^2))*a^3+2*(b^2-c^2)*(b-c)*(b^4+c^4-3*b*c*(b^2+c^2))*a^2-(b^2-c^2)^2*(b^4+c^4+2*b*c*(2*b^2-3*b*c+2*c^2))*a-(b^4-c^4)*(b^2-c^2)^2*(b-c)-4*S*((b+c)*a^6+(b^2+b*c+c^2)*a^5-(b+c)*b*c*a^4-6*(b^2+c^2)*b*c*a^3-(b+c)*(b^4+c^4)*a^2-(b^6+c^6-(b^4+c^4+b*c*(b^2-6*b*c+c^2))*b*c)*a+(b^4-c^4)*b*c*(b-c))) : :

X(55500) lies on the cubic K006 and these lines: {1, 8948}, {3, 8949}, {4, 55508}, {90, 487}, {254, 55499}, {372, 55505}, {485, 6212}, {486, 55515}, {6213, 55511}, {8946, 55524}, {8947, 55525}, {55498, 55509}, {55506, 55513}, {55507, 55522}, {55510, 55520}, {55516, 55527}

X(55500) = isogonal conjugate of X(55508)
X(55500) = X(4)-Ceva conjugate of-X(8949)
X(55500) = trilinear product X(7347)*X(8938)
X(55500) = (orthic)-isogonal conjugate-of-X(8949)
X(55500) = trilinear quotient X(8938)/X(6204)

X(55501) = X(3)X(485)∩X(254)X(372)

Barycentrics    (a^8-2*(3*b^4+2*b^2*c^2+3*c^4)*a^4+4*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^2-(3*b^4-2*b^2*c^2+3*c^4)*(b^2-c^2)^2)*a^2+2*(2*a^8-5*(b^2+c^2)*a^6+(3*b^4-2*b^2*c^2+3*c^4)*a^4+(b^4-c^4)*(b^2-c^2)*a^2-(b^2-c^2)^4)*S : :

X(55501) lies on the cubic K006 and these lines: {1, 55505}, {3, 485}, {4, 55509}, {90, 3377}, {254, 372}, {486, 8944}, {487, 13439}, {639, 11090}, {1321, 35820}, {1588, 21463}, {5446, 6561}, {6213, 55508}, {6460, 13440}, {8946, 55511}, {8949, 55506}, {47731, 55502}, {55507, 55515}, {55512, 55525}, {55526, 55527}

X(55501) = isogonal conjugate of X(55509)
X(55501) = X(4)-Ceva conjugate of-X(485)
X(55501) = X(i)-Dao conjugate of-X(j) for these (i, j): (11090, 69)
X(55501) = X(8909)-reciprocal conjugate of-X(5408)
X(55501) = X(46433)-of-orthic triangle, when ABC is acute
X(55501) = (orthic)-isogonal conjugate-of-X(485)
X(55501) = pole of line {1599, 55509} with respect to Stammler hyperbola

X(55502) = X(3)X(486)∩X(254)X(371)

Barycentrics    (a^8-2*(3*b^4+2*b^2*c^2+3*c^4)*a^4+4*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^2-(3*b^4-2*b^2*c^2+3*c^4)*(b^2-c^2)^2)*a^2-2*(2*a^8-5*(b^2+c^2)*a^6+(3*b^4-2*b^2*c^2+3*c^4)*a^4+(b^4-c^4)*(b^2-c^2)*a^2-(b^2-c^2)^4)*S : :

X(55502) lies on the cubic K006 and these lines: {1, 55506}, {3, 486}, {4, 55510}, {90, 3378}, {254, 371}, {485, 8940}, {488, 13428}, {640, 11091}, {1322, 35821}, {1587, 21464}, {5446, 6560}, {6212, 55507}, {6459, 13429}, {8947, 55505}, {8948, 55512}, {47731, 55501}, {55508, 55516}, {55511, 55526}, {55525, 55528}

X(55502) = isogonal conjugate of X(55510)
X(55502) = X(4)-Ceva conjugate of-X(486)
X(55502) = X(i)-Dao conjugate of-X(j) for these (i, j): (11091, 69)
X(55502) = X(46434)-of-orthic triangle, when ABC is acute
X(55502) = (orthic)-isogonal conjugate-of-X(486)
X(55502) = pole of line {1600, 55510} with respect to Stammler hyperbola

X(55503) = X(254)X(488)∩X(486)X(494)

Barycentrics    a^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^10-5*(b^2+c^2)*a^8+2*(5*b^4+6*b^2*c^2+5*c^4)*a^6-2*(b^2+c^2)*(5*b^4-8*b^2*c^2+5*c^4)*a^4+(5*b^4-38*b^2*c^2+5*c^4)*(b^2+c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)*((b^2+c^2)^2-16*b^2*c^2)+4*S*((b^2+c^2)*a^6-(3*b^4+8*b^2*c^2+3*c^4)*a^4+(3*b^2+c^2)*(b^2+3*c^2)*(b^2+c^2)*a^2-b^8-c^8-2*b^2*c^2*((b^2+c^2)^2-9*b^2*c^2))) : :
X(55503) = a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(b^2 - S)*(c^2 - S)*(b^2*c^2 (a^2 - 2*S) + (-a^2 + b^2 + c^2)*S^2) : :

X(55503) lies on the cubic K006 and these lines: {1, 55507}, {3, 6406}, {90, 8947}, {254, 488}, {371, 55510}, {485, 55512}, {486, 494}, {6213, 19217}, {8948, 55526}, {12232, 53062}, {45599, 55509}, {55505, 55516}, {55508, 55523}, {55511, 55528}

X(55503) = X(4)-Ceva conjugate of-X(8946)
X(55503) = X(494)-Dao conjugate of-X(69)
X(55503) = X(8943)-reciprocal conjugate of-X(487)
X(55503) = barycentric product X(8943)*X(24243)
X(55503) = trilinear product X(8943)*X(19217)
X(55503) = (orthic)-isogonal conjugate-of-X(8946)
X(55503) = trilinear quotient X(8943)/X(19216)

X(55504) = X(254)X(487)∩X(485)X(493)

Barycentrics    a^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^10-5*(b^2+c^2)*a^8+2*(5*b^4+6*b^2*c^2+5*c^4)*a^6-2*(b^2+c^2)*(5*b^4-8*b^2*c^2+5*c^4)*a^4+(5*b^4-38*b^2*c^2+5*c^4)*(b^2+c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)*((b^2+c^2)^2-16*b^2*c^2)-4*S*((b^2+c^2)*a^6-(3*b^4+8*b^2*c^2+3*c^4)*a^4+(3*b^2+c^2)*(b^2+3*c^2)*(b^2+c^2)*a^2-b^8-c^8-2*b^2*c^2*((b^2+c^2)^2-9*b^2*c^2))) : :
X(55504) = a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(b^2 + S)*(c^2 + S)*(b^2*c^2 (a^2 + 2*S) + (-a^2 + b^2 + c^2)*S^2) : :

X(55504) lies on the cubic K006 and these lines: {1, 55508}, {3, 6291}, {90, 8949}, {254, 487}, {372, 55509}, {485, 493}, {486, 55511}, {6212, 19218}, {8946, 55525}, {8950, 12231}, {45600, 55510}, {55506, 55515}, {55507, 55524}, {55512, 55527}

X(55504) = X(4)-Ceva conjugate of-X(8948)
X(55504) = X(493)-Dao conjugate of-X(69)
X(55504) = X(8939)-reciprocal conjugate of-X(488)
X(55504) = barycentric product X(8939)*X(24244)
X(55504) = trilinear product X(8939)*X(19218)
X(55504) = (orthic)-isogonal conjugate-of-X(8948)
X(55504) = trilinear quotient X(8939)/X(19215)

X(55505) = X(46)X(371)∩X(155)X(6213)

Barycentrics    a*(-4*b*c*(2*a^7+3*(b+c)*a^6+4*b*c*a^5-(b+c)*(3*b^2-2*b*c+3*c^2)*a^4-2*(b^2+c^2)*(b+c)^2*a^3+(b+c)*(b^2+c^2)*(b^2-4*b*c+c^2)*a^2-(b^2-c^2)^3*(b-c))*S+(a+b+c)*(a^10-(3*b^2-4*b*c+3*c^2)*a^8-2*(b+c)*b*c*a^7+2*(b^2+c^2)*(b^2-5*b*c+c^2)*a^6+6*(b^2-c^2)*(b-c)*b*c*a^5+2*(b^2+4*b*c+c^2)*(b^2-b*c+c^2)*(b^2+c^2)*a^4-2*(b+c)*(b^2+c^2)*(3*b^2-8*b*c+3*c^2)*b*c*a^3-(b^2-c^2)^2*(3*b^4+3*c^4-2*b*c*(b^2-b*c+c^2))*a^2+2*(b^2-c^2)^3*(b-c)*b*c*a+(b^2-c^2)^4*(b-c)^2)) : :

X(55505) lies on the cubic K006 and these lines: {1, 55501}, {4, 55497}, {46, 371}, {155, 6213}, {372, 55500}, {486, 55496}, {487, 55519}, {488, 13387}, {6212, 19218}, {8947, 55502}, {8949, 55517}, {31387, 55506}, {55499, 55514}, {55503, 55516}, {55518, 55523}, {55520, 55521}

X(55505) = isogonal conjugate of X(55497)
X(55505) = X(3)-cross conjugate of-X(6213)
X(55505) = X(13386)-isoconjugate of-X(44590)
X(55505) = trilinear quotient X(34121)/X(44590)

X(55506) = X(46)X(372)∩X(155)X(6212)

Barycentrics    a*(4*b*c*(2*a^7+3*(b+c)*a^6+4*b*c*a^5-(b+c)*(3*b^2-2*b*c+3*c^2)*a^4-2*(b^2+c^2)*(b+c)^2*a^3+(b+c)*(b^2+c^2)*(b^2-4*b*c+c^2)*a^2-(b^2-c^2)^3*(b-c))*S+(a+b+c)*(a^10-(3*b^2-4*b*c+3*c^2)*a^8-2*(b+c)*b*c*a^7+2*(b^2+c^2)*(b^2-5*b*c+c^2)*a^6+6*(b^2-c^2)*(b-c)*b*c*a^5+2*(b^2+4*b*c+c^2)*(b^2-b*c+c^2)*(b^2+c^2)*a^4-2*(b+c)*(b^2+c^2)*(3*b^2-8*b*c+3*c^2)*b*c*a^3-(b^2-c^2)^2*(3*b^4+3*c^4-2*b*c*(b^2-b*c+c^2))*a^2+2*(b^2-c^2)^3*(b-c)*b*c*a+(b^2-c^2)^4*(b-c)^2)) : :

X(55506) lies on the cubic K006 and these lines: {1, 55502}, {4, 55498}, {46, 372}, {155, 6212}, {371, 55499}, {485, 55496}, {487, 13386}, {488, 55520}, {6213, 19217}, {8947, 55518}, {8949, 55501}, {31387, 55505}, {55500, 55513}, {55504, 55515}, {55517, 55524}, {55519, 55522}

X(55506) = isogonal conjugate of X(55498)
X(55506) = X(3)-cross conjugate of-X(6212)
X(55506) = X(13387)-isoconjugate of-X(44591)
X(55506) = trilinear quotient X(34125)/X(44591)

X(55507) = X(46)X(487)∩X(155)X(8949)

Barycentrics    a*(2*b*c*(a^10-(b^2-6*b*c+c^2)*a^8-2*(b^4+c^4+4*b*c*(b^2+b*c+c^2))*a^6+2*(b^3-c^3-b*c*(3*b+c))*(b^3-c^3+b*c*(b+3*c))*a^4+(b^4+c^4+2*b*c*(4*b^2+5*b*c+4*c^2))*(b^2-c^2)^2*a^2-(b^2-c^2)^4*(b+c)^2)-S*(a^10-(b-c)^2*a^8-2*(b^4+c^4+6*b*c*(b^2-b*c+c^2))*a^6+2*(b^6+c^6-b^2*c^2*(23*b^2+4*b*c+23*c^2))*a^4+(b^8+c^8+6*(2*b^6+2*c^6+(2*b^4+2*c^4-b*c*(2*b^2+7*b*c+2*c^2))*b*c)*b*c)*a^2+(b^2-c^2)^2*(b+c)^2*(4*b^2*c^2-(b^2-c^2)^2))) : :

X(55507) lies on the cubic K006 and these lines: {1, 55503}, {4, 55499}, {46, 487}, {155, 8949}, {371, 55520}, {372, 55498}, {6212, 55502}, {6213, 55518}, {8948, 55496}, {55497, 55513}, {55500, 55522}, {55501, 55515}, {55504, 55524}

X(55507) = isogonal conjugate of X(55499)
X(55507) = X(3)-cross conjugate of-X(8949)
X(55507) = X(7348)-isoconjugate of-X(8942)
X(55507) = trilinear quotient X(6203)/X(8942)

X(55508) = X(46)X(488)∩X(155)X(8947)

Barycentrics    a*(2*b*c*(a^10-(b^2-6*b*c+c^2)*a^8-2*(b^4+c^4+4*b*c*(b^2+b*c+c^2))*a^6+2*(b^3-c^3-b*c*(3*b+c))*(b^3-c^3+b*c*(b+3*c))*a^4+(b^4+c^4+2*b*c*(4*b^2+5*b*c+4*c^2))*(b^2-c^2)^2*a^2-(b^2-c^2)^4*(b+c)^2)+S*(a^10-(b-c)^2*a^8-2*(b^4+c^4+6*b*c*(b^2-b*c+c^2))*a^6+2*(b^6+c^6-b^2*c^2*(23*b^2+4*b*c+23*c^2))*a^4+(b^8+c^8+6*(2*b^6+2*c^6+(2*b^4+2*c^4-b*c*(2*b^2+7*b*c+2*c^2))*b*c)*b*c)*a^2+(b^2-c^2)^2*(b+c)^2*(4*b^2*c^2-(b^2-c^2)^2))) : :

X(55508) lies on the cubic K006 and these lines: {1, 55504}, {4, 55500}, {46, 488}, {155, 8947}, {371, 55497}, {372, 55519}, {6212, 55517}, {6213, 55501}, {8946, 55496}, {55498, 55514}, {55499, 55521}, {55502, 55516}, {55503, 55523}

X(55508) = isogonal conjugate of X(55500)
X(55508) = X(3)-cross conjugate of-X(8947)
X(55508) = X(7347)-isoconjugate of-X(8938)
X(55508) = trilinear quotient X(6204)/X(8938)

X(55509) = X(155)X(371)∩X(488)X(13428)

Barycentrics    a^2*((-a^2+b^2+c^2)*(a^12-6*(b^2+c^2)*a^10+5*(3*b^4+2*b^2*c^2+3*c^4)*a^8-4*(b^2+c^2)*(5*b^4-6*b^2*c^2+5*c^4)*a^6+(15*b^8+15*c^8-2*(14*b^4-5*b^2*c^2+14*c^4)*b^2*c^2)*a^4-2*(b^4-c^4)*(b^2-c^2)*(3*b^4-14*b^2*c^2+3*c^4)*a^2+(b^4-10*b^2*c^2+c^4)*(b^2-c^2)^4)+2*S*(a^12-2*(b^2+c^2)*a^10-(5*b^4-2*b^2*c^2+5*c^4)*a^8+4*(b^2+c^2)*(5*b^4-4*b^2*c^2+5*c^4)*a^6-(25*b^8+25*c^8+2*(2*b^2-c^2)*(b^2-2*c^2)*b^2*c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)*(7*b^4+6*b^2*c^2+7*c^4)*a^2-(b^2-c^2)^4*(3*b^2+c^2)*(b^2+3*c^2))) : :

X(55509) lies on the cubic K006 and these lines: {4, 55501}, {46, 55497}, {155, 371}, {372, 55504}, {487, 55517}, {488, 13428}, {6213, 55496}, {45599, 55503}, {55498, 55500}, {55499, 55519}, {55518, 55521}

X(55509) = isogonal conjugate of X(55501)
X(55509) = X(3)-cross conjugate of-X(371)
X(55509) = X(8911)-reciprocal conjugate of-X(8909)

X(55510) = X(155)X(372)∩X(487)X(13439)

Barycentrics    a^2*((-a^2+b^2+c^2)*(a^12-6*(b^2+c^2)*a^10+5*(3*b^4+2*b^2*c^2+3*c^4)*a^8-4*(b^2+c^2)*(5*b^4-6*b^2*c^2+5*c^4)*a^6+(15*b^8+15*c^8-2*(14*b^4-5*b^2*c^2+14*c^4)*b^2*c^2)*a^4-2*(b^4-c^4)*(b^2-c^2)*(3*b^4-14*b^2*c^2+3*c^4)*a^2+(b^4-10*b^2*c^2+c^4)*(b^2-c^2)^4)-2*S*(a^12-2*(b^2+c^2)*a^10-(5*b^4-2*b^2*c^2+5*c^4)*a^8+4*(b^2+c^2)*(5*b^4-4*b^2*c^2+5*c^4)*a^6-(25*b^8+25*c^8+2*(2*b^2-c^2)*(b^2-2*c^2)*b^2*c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)*(7*b^4+6*b^2*c^2+7*c^4)*a^2-(b^2-c^2)^4*(3*b^2+c^2)*(b^2+3*c^2))) : :

X(55510) lies on the cubic K006 and these lines: {4, 55502}, {46, 55498}, {155, 372}, {371, 55503}, {487, 13439}, {488, 55518}, {6212, 55496}, {45600, 55504}, {55497, 55499}, {55500, 55520}, {55517, 55522}

X(55510) = isogonal conjugate of X(55502)
X(55510) = X(3)-cross conjugate of-X(372)

X(55511) = X(193)X(371)∩X(486)X(55504)

Barycentrics    (3*a^2-b^2-c^2)*(3*(b^2+c^2)*a^6-(b^4+22*b^2*c^2+c^4)*a^4+2*(a^2+b^2+c^2)*(a^2-3*b^2-3*c^2)*S*a^2-(b^2+c^2)*(3*b^4-2*b^2*c^2+3*c^4)*a^2+(b^4-c^4)^2) : :

X(55511) lies on the cubic K006 and these lines: {1, 55519}, {3, 55517}, {4, 55514}, {46, 55516}, {155, 55512}, {193, 371}, {372, 55521}, {486, 55504}, {6213, 55500}, {8946, 55501}, {8947, 55497}, {55498, 55523}, {55502, 55526}, {55503, 55528}

X(55511) = isogonal conjugate of X(55514)
X(55511) = X(4)-Ceva conjugate of-X(55517)
X(55511) = X(3)-cross conjugate of-X(55512)
X(55511) = X(8769)-isoconjugate of-X(8854)
X(55511) = X(3053)-reciprocal conjugate of-X(8854)
X(55511) = pole of line {8854, 55514} with respect to Stammler hyperbola
X(55511) = (orthic)-isogonal conjugate-of-X(55517)
X(55511) = trilinear quotient X(1707)/X(8854)

X(55512) = X(193)X(372)∩X(485)X(55503)

Barycentrics    (3*a^2-b^2-c^2)*(3*(b^2+c^2)*a^6-(b^4+22*b^2*c^2+c^4)*a^4-2*(a^2+b^2+c^2)*(a^2-3*b^2-3*c^2)*S*a^2-(b^2+c^2)*(3*b^4-2*b^2*c^2+3*c^4)*a^2+(b^4-c^4)^2) : :

X(55512) lies on the cubic K006 and these lines: {1, 55520}, {3, 55518}, {4, 55513}, {46, 55515}, {155, 55511}, {193, 372}, {371, 55522}, {485, 55503}, {6212, 55499}, {8948, 55502}, {8949, 55498}, {55497, 55524}, {55501, 55525}, {55504, 55527}

X(55512) = isogonal conjugate of X(55513)
X(55512) = X(4)-Ceva conjugate of-X(55518)
X(55512) = X(3)-cross conjugate of-X(55511)
X(55512) = X(8769)-isoconjugate of-X(8855)
X(55512) = X(3053)-reciprocal conjugate of-X(8855)
X(55512) = pole of line {8855, 55513} with respect to Stammler hyperbola
X(55512) = (orthic)-isogonal conjugate-of-X(55518)
X(55512) = trilinear quotient X(1707)/X(8855)

X(55513) = X(3)X(8770)∩X(486)X(488)

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

X(55513) lies on the cubic K006 and these lines: {1, 55516}, {3, 8770}, {4, 55512}, {90, 55519}, {254, 55517}, {371, 8946}, {372, 55526}, {485, 55521}, {486, 488}, {487, 55528}, {6212, 19213}, {6213, 8769}, {6391, 35841}, {34208, 39660}, {45600, 55504}, {55497, 55507}, {55500, 55506}

X(55513) = isogonal conjugate of X(55512)
X(55513) = X(4)-Ceva conjugate of-X(55514)
X(55513) = X(8855)-reciprocal conjugate of-X(193)
X(55513) = pole of line {439, 55512} with respect to Stammler hyperbola
X(55513) = barycentric product X(2996)*X(8855)
X(55513) = trilinear product X(8769)*X(8855)
X(55513) = (orthic)-isogonal conjugate-of-X(55514)
X(55513) = trilinear quotient X(8855)/X(1707)

X(55514) = X(3)X(8770)∩X(485)X(487)

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

X(55514) lies on the cubic K006 and these lines: {1, 55515}, {3, 8770}, {4, 55511}, {90, 55520}, {254, 55518}, {371, 55525}, {372, 8948}, {485, 487}, {486, 55522}, {488, 55527}, {6212, 8769}, {6213, 19213}, {6391, 35840}, {34208, 39661}, {45599, 55503}, {55498, 55508}, {55499, 55505}

X(55514) = isogonal conjugate of X(55511)
X(55514) = X(4)-Ceva conjugate of-X(55513)
X(55514) = X(8854)-reciprocal conjugate of-X(193)
X(55514) = pole of line {439, 55511} with respect to Stammler hyperbola
X(55514) = barycentric product X(2996)*X(8854)
X(55514) = trilinear product X(8769)*X(8854)
X(55514) = (orthic)-isogonal conjugate-of-X(55513)
X(55514) = trilinear quotient X(8854)/X(1707)

X(55515) = X(488)X(2128)∩X(2129)X(6212)

Barycentrics    a*(2*(a^9+3*(b+c)*a^8-12*b*c*a^7+4*(b+c)*(2*b^2-3*b*c+2*c^2)*a^6-2*(3*b^4+3*c^4-2*b*c*(7*b^2+b*c+7*c^2))*a^5+2*(3*b-c)*(b-3*c)*(b+c)*(b^2+c^2)*a^4-4*(2*b^6+2*c^6-(7*b^4+7*c^4+2*b*c*(b^2-17*b*c+c^2))*b*c)*a^3-4*(b+c)*(b^2+c^2)^2*b*c*a^2-(b^2+c^2)*(b^2+4*b*c+c^2)*(b^2-3*c^2)*(3*b^2-c^2)*a-(b+c)*(b^2-4*b*c+c^2)*(b^2+c^2)^3)*S+(a^2+b^2+c^2)*(a^9-3*(b+c)*a^8-2*(b^2+3*b*c+c^2)*a^7-2*(b+c)*(b^2-15*b*c+c^2)*a^6-2*(2*b^4+2*c^4-b*c*(7*b^2+8*b*c+7*c^2))*a^5+2*(b+c)*(2*b^4+2*c^4-5*b*c*(7*b^2-8*b*c+7*c^2))*a^4+2*(b^6+c^6+b*c*(7*b^2+16*b*c+7*c^2)*(b^2-3*b*c+c^2))*a^3+2*(b+c)*(b^2+c^2)*(b^4+c^4+b*c*(13*b^2-22*b*c+13*c^2))*a^2+(b^2-4*b*c+c^2)*(b^2-3*c^2)*(3*b^2-c^2)*(b+c)^2*a-(b^4-c^4)*(b^2+c^2)*(b-c)*(b^2+4*b*c+c^2))) : :

X(55515) lies on the cubic K006 and these lines: {1, 55514}, {3, 55519}, {4, 55516}, {46, 55512}, {90, 55517}, {371, 8947}, {372, 55523}, {486, 55500}, {488, 2128}, {2129, 6212}, {8946, 55497}, {55498, 55526}, {55499, 55528}, {55501, 55507}, {55504, 55506}

X(55515) = isogonal conjugate of X(55516)
X(55515) = (orthic)-isogonal conjugate-of-X(55519)
X(55515) = X(4)-Ceva conjugate of-X(55519)

X(55516) = X(487)X(2128)∩X(2129)X(6213)

Barycentrics    a*(-2*(a^9+3*(b+c)*a^8-12*b*c*a^7+4*(b+c)*(2*b^2-3*b*c+2*c^2)*a^6-2*(3*b^4+3*c^4-2*b*c*(7*b^2+b*c+7*c^2))*a^5+2*(3*b-c)*(b-3*c)*(b+c)*(b^2+c^2)*a^4-4*(2*b^6+2*c^6-(7*b^4+7*c^4+2*b*c*(b^2-17*b*c+c^2))*b*c)*a^3-4*(b+c)*(b^2+c^2)^2*b*c*a^2-(b^2+c^2)*(b^2+4*b*c+c^2)*(b^2-3*c^2)*(3*b^2-c^2)*a-(b+c)*(b^2-4*b*c+c^2)*(b^2+c^2)^3)*S+(a^2+b^2+c^2)*(a^9-3*(b+c)*a^8-2*(b^2+3*b*c+c^2)*a^7-2*(b+c)*(b^2-15*b*c+c^2)*a^6-2*(2*b^4+2*c^4-b*c*(7*b^2+8*b*c+7*c^2))*a^5+2*(b+c)*(2*b^4+2*c^4-5*b*c*(7*b^2-8*b*c+7*c^2))*a^4+2*(b^6+c^6+b*c*(7*b^2+16*b*c+7*c^2)*(b^2-3*b*c+c^2))*a^3+2*(b+c)*(b^2+c^2)*(b^4+c^4+b*c*(13*b^2-22*b*c+13*c^2))*a^2+(b^2-4*b*c+c^2)*(b^2-3*c^2)*(3*b^2-c^2)*(b+c)^2*a-(b^4-c^4)*(b^2+c^2)*(b-c)*(b^2+4*b*c+c^2))) : :

X(55516) lies on the cubic K006 and these lines: {1, 55513}, {3, 55520}, {4, 55515}, {46, 55511}, {90, 55518}, {371, 55524}, {372, 8949}, {485, 55499}, {487, 2128}, {2129, 6213}, {8948, 55498}, {55497, 55525}, {55500, 55527}, {55502, 55508}, {55503, 55505}

X(55516) = isogonal conjugate of X(55515)
X(55516) = (orthic)-isogonal conjugate-of-X(55520)
X(55516) = X(4)-Ceva conjugate of-X(55520)

X(55517) = X(3)X(55511)∩X(485)X(8948)

Barycentrics    2*(a^2+b^2+c^2)*(2*a^12-25*(b^2+c^2)*a^10+(59*b^4+158*b^2*c^2+59*c^4)*a^8-2*(b^2+c^2)*(23*b^4+48*b^2*c^2+23*c^4)*a^6+4*(b^8+c^8-2*(b^4+13*b^2*c^2+c^4)*b^2*c^2)*a^4+(b^4-c^4)*(b^2-c^2)*(7*b^4+6*b^2*c^2+7*c^4)*a^2-(b^4-c^4)^2*(b^2-c^2)^2)*S+a^2*(3*a^14-7*(b^2+c^2)*a^12-(25*b^4+106*b^2*c^2+25*c^4)*a^10+(b^2+c^2)*(69*b^4+334*b^2*c^2+69*c^4)*a^8-(23*b^8+23*c^8+154*(2*b^4+b^2*c^2+2*c^4)*b^2*c^2)*a^6-(b^2+c^2)*(53*b^8+53*c^8-14*(2*b^4-41*b^2*c^2+2*c^4)*b^2*c^2)*a^4+(45*b^8+45*c^8-2*(30*b^4-7*b^2*c^2+30*c^4)*b^2*c^2)*(b^2+c^2)^2*a^2-(b^4-c^4)^2*(b^2+c^2)*(9*(b^2-c^2)^2-4*b^2*c^2)) : :

X(55517) lies on the cubic K006 and these lines: {3, 55511}, {90, 55515}, {254, 55513}, {485, 8948}, {486, 55525}, {487, 55509}, {6212, 55508}, {8946, 55527}, {8949, 55505}, {55506, 55524}, {55510, 55522}

X(55517) = (orthic)-isogonal conjugate-of-X(55511)
X(55517) = X(4)-Ceva conjugate of-X(55511)

X(55518) = X(3)X(55512)∩X(486)X(8946)

Barycentrics    -2*(a^2+b^2+c^2)*(2*a^12-25*(b^2+c^2)*a^10+(59*b^4+158*b^2*c^2+59*c^4)*a^8-2*(b^2+c^2)*(23*b^4+48*b^2*c^2+23*c^4)*a^6+4*(b^8+c^8-2*(b^4+13*b^2*c^2+c^4)*b^2*c^2)*a^4+(b^4-c^4)*(b^2-c^2)*(7*b^4+6*b^2*c^2+7*c^4)*a^2-(b^4-c^4)^2*(b^2-c^2)^2)*S+a^2*(3*a^14-7*(b^2+c^2)*a^12-(25*b^4+106*b^2*c^2+25*c^4)*a^10+(b^2+c^2)*(69*b^4+334*b^2*c^2+69*c^4)*a^8-(23*b^8+23*c^8+154*(2*b^4+b^2*c^2+2*c^4)*b^2*c^2)*a^6-(b^2+c^2)*(53*b^8+53*c^8-14*(2*b^4-41*b^2*c^2+2*c^4)*b^2*c^2)*a^4+(45*b^8+45*c^8-2*(30*b^4-7*b^2*c^2+30*c^4)*b^2*c^2)*(b^2+c^2)^2*a^2-(b^4-c^4)^2*(b^2+c^2)*(9*(b^2-c^2)^2-4*b^2*c^2)) : :

X(55518) lies on the cubic K006 and these lines: {3, 55512}, {90, 55516}, {254, 55514}, {485, 55526}, {486, 8946}, {488, 55510}, {6213, 55507}, {8947, 55506}, {8948, 55528}, {55505, 55523}, {55509, 55521}

X(55518) = (orthic)-isogonal conjugate-of-X(55512)
X(55518) = X(4)-Ceva conjugate of-X(55512)

X(55519) = X(485)X(8949)∩X(6212)X(8948)

Barycentrics    a*(a^2-b^2+c^2)*(a^2+b^2-c^2)*((b+c)*a^10-(b^2+b*c+c^2)*a^9-6*(b+c)*b*c*a^8+8*(2*b^2-b*c+2*c^2)*b*c*a^7-2*(b^2-c^2)*(b-c)^3*a^6+2*(b^4+c^4-2*b*c*(7*b^2+b*c+7*c^2))*(b^2-b*c+c^2)*a^5+4*(b+c)*(b^4+c^4+4*b*c*(b^2+c^2))*b*c*a^4+16*(b^2-b*c+c^2)*(b^4+c^4+b*c*(b-c)^2)*b*c*a^3+(b+c)*(b^2+c^2)*(b^6+c^6-(8*b^4+8*c^4+5*b*c*(b^2+c^2))*b*c)*a^2-(b^6+c^6+(b^4+c^4-b*c*(b^2+6*b*c+c^2))*b*c)*(b^2+c^2)^2*a+2*(b^4-c^4)^2*b*c*(b+c)-S*(a^9-(b+c)*a^8-8*b*c*a^7+16*(b+c)*b*c*a^6-2*(b^4+c^4-6*b*c*(b^2-b*c+c^2))*a^5+2*(b+c)*(b^4+c^4-2*b*c*(8*b^2-3*b*c+8*c^2))*a^4+16*(b^4+c^4-3*b*c*(b-c)^2)*b*c*a^3+16*(b^3+c^3)*(b^2+c^2)*b*c*a^2+(b^4+c^4-2*b*c*(2*b^2+3*b*c+2*c^2))*(b^2+c^2)^2*a-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)^2*(b+c))) : :

X(55519) lies on the cubic K006 and these lines: {1, 55511}, {3, 55515}, {90, 55513}, {254, 55520}, {372, 55508}, {485, 8949}, {486, 55524}, {487, 55505}, {6212, 8948}, {6213, 55525}, {8947, 55527}, {55499, 55509}, {55506, 55522}

X(55519) = (orthic)-isogonal conjugate-of-X(55515)
X(55519) = X(4)-Ceva conjugate of-X(55515)

X(55520) = X(486)X(8947)∩X(6213)X(8946)

Barycentrics    a*(a^2-b^2+c^2)*(a^2+b^2-c^2)*((b+c)*a^10-(b^2+b*c+c^2)*a^9-6*(b+c)*b*c*a^8+8*(2*b^2-b*c+2*c^2)*b*c*a^7-2*(b^2-c^2)*(b-c)^3*a^6+2*(b^4+c^4-2*b*c*(7*b^2+b*c+7*c^2))*(b^2-b*c+c^2)*a^5+4*(b+c)*(b^4+c^4+4*b*c*(b^2+c^2))*b*c*a^4+16*(b^2-b*c+c^2)*(b^4+c^4+b*c*(b-c)^2)*b*c*a^3+(b+c)*(b^2+c^2)*(b^6+c^6-(8*b^4+8*c^4+5*b*c*(b^2+c^2))*b*c)*a^2-(b^6+c^6+(b^4+c^4-b*c*(b^2+6*b*c+c^2))*b*c)*(b^2+c^2)^2*a+2*(b^4-c^4)^2*b*c*(b+c)+S*(a^9-(b+c)*a^8-8*b*c*a^7+16*(b+c)*b*c*a^6-2*(b^4+c^4-6*b*c*(b^2-b*c+c^2))*a^5+2*(b+c)*(b^4+c^4-2*b*c*(8*b^2-3*b*c+8*c^2))*a^4+16*(b^4+c^4-3*b*c*(b-c)^2)*b*c*a^3+16*(b^3+c^3)*(b^2+c^2)*b*c*a^2+(b^4+c^4-2*b*c*(2*b^2+3*b*c+2*c^2))*(b^2+c^2)^2*a-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)^2*(b+c))) : :

X(55520) lies on the cubic K006 and these lines: {1, 55512}, {3, 55516}, {90, 55514}, {254, 55519}, {371, 55507}, {485, 55523}, {486, 8947}, {488, 55506}, {6212, 55526}, {6213, 8946}, {8949, 55528}, {55500, 55510}, {55505, 55521}

X(55520) = (orthic)-isogonal conjugate-of-X(55516)
X(55520) = X(4)-Ceva conjugate of-X(55516)

X(55521) = X(487)X(8948)∩X(2129)X(6212)

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

X(55521) lies on the cubic K006 and these lines: {1, 55524}, {3, 15369}, {4, 55525}, {371, 55527}, {372, 55511}, {485, 55513}, {487, 8948}, {2129, 6212}, {55499, 55508}, {55505, 55520}, {55509, 55518}

X(55521) = isogonal conjugate of X(55525)
X(55521) = X(4)-Ceva conjugate of-X(55522)
X(55521) = X(6462)-reciprocal conjugate of-X(19583)
X(55521) = barycentric product X(6462)*X(55023)
X(55521) = trilinear product X(2129)*X(6462)
X(55521) = (orthic)-isogonal conjugate-of-X(55522)
X(55521) = trilinear quotient X(6462)/X(2128)

X(55522) = X(488)X(8946)∩X(2129)X(6213)

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

X(55522) lies on the cubic K006 and these lines: {1, 55523}, {3, 15369}, {4, 55526}, {371, 55512}, {372, 55528}, {486, 55514}, {488, 8946}, {2129, 6213}, {55500, 55507}, {55506, 55519}, {55510, 55517}

X(55522) = isogonal conjugate of X(55526)
X(55522) = X(4)-Ceva conjugate of-X(55521)
X(55522) = X(6463)-reciprocal conjugate of-X(19583)
X(55522) = barycentric product X(6463)*X(55023)
X(55522) = trilinear product X(2129)*X(6463)
X(55522) = (orthic)-isogonal conjugate-of-X(55521)
X(55522) = trilinear quotient X(6463)/X(2128)

X(55523) = X(487)X(8949)∩X(6212)X(19213)

Barycentrics    a*(-(a^16+8*(b^2+c^2)*a^14+4*(7*b^4-58*b^2*c^2+7*c^4)*a^12+8*(b^2+c^2)*(7*b^4+22*b^2*c^2+7*c^4)*a^10+2*(35*b^8+35*c^8+2*b^2*c^2*(78*b^4-359*b^2*c^2+78*c^4))*a^8+8*(b^2+c^2)*(7*b^8+7*c^8-2*b^2*c^2*(58*b^4-101*b^2*c^2+58*c^4))*a^6+4*(7*b^12+7*c^12-(142*b^8+142*c^8-5*b^2*c^2*(117*b^4-116*b^2*c^2+117*c^4))*b^2*c^2)*a^4+8*(b^8+c^8+6*b^2*c^2*(2*b^4-7*b^2*c^2+2*c^4))*(b^2+c^2)^3*a^2+(b^4+c^4+2*b*c*(2*b+c)*(b-2*c))*(b^4+c^4-2*b*c*(b+2*c)*(2*b-c))*(b^2+c^2)^4)*S+4*b*c*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4-2*(3*b^2-c^2)*a^2+(b^2+c^2)^2)*(a^4+2*(b^2+c^2)*a^2-4*b^2*c^2+(b^2-c^2)^2)*(a^4+2*(b^2-3*c^2)*a^2+(b^2+c^2)^2)) : :

X(55523) lies on the cubic K006 and these lines: {1, 55522}, {4, 55524}, {46, 55525}, {372, 55515}, {485, 55520}, {487, 8949}, {6212, 19213}, {6213, 19214}, {8948, 55499}, {55497, 55527}, {55498, 55511}, {55503, 55508}, {55505, 55518}

X(55523) = isogonal conjugate of X(55524)

X(55524) = X(488)X(8947)∩X(6212)X(19214)

Barycentrics    a*((a^16+8*(b^2+c^2)*a^14+4*(7*b^4-58*b^2*c^2+7*c^4)*a^12+8*(b^2+c^2)*(7*b^4+22*b^2*c^2+7*c^4)*a^10+2*(35*b^8+35*c^8+2*b^2*c^2*(78*b^4-359*b^2*c^2+78*c^4))*a^8+8*(b^2+c^2)*(7*b^8+7*c^8-2*b^2*c^2*(58*b^4-101*b^2*c^2+58*c^4))*a^6+4*(7*b^12+7*c^12-(142*b^8+142*c^8-5*b^2*c^2*(117*b^4-116*b^2*c^2+117*c^4))*b^2*c^2)*a^4+8*(b^8+c^8+6*b^2*c^2*(2*b^4-7*b^2*c^2+2*c^4))*(b^2+c^2)^3*a^2+(b^4+c^4+2*b*c*(2*b+c)*(b-2*c))*(b^4+c^4-2*b*c*(b+2*c)*(2*b-c))*(b^2+c^2)^4)*S+4*b*c*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^4-2*(3*b^2-c^2)*a^2+(b^2+c^2)^2)*(a^4+2*(b^2+c^2)*a^2-4*b^2*c^2+(b^2-c^2)^2)*(a^4+2*(b^2-3*c^2)*a^2+(b^2+c^2)^2)) : :

X(55524) lies on the cubic K006 and these lines: {1, 55521}, {4, 55523}, {46, 55526}, {371, 55516}, {486, 55519}, {488, 8947}, {6212, 19214}, {6213, 19213}, {8946, 55500}, {55497, 55512}, {55498, 55528}, {55504, 55507}, {55506, 55517}

X(55524) = isogonal conjugate of X(55523)

X(55525) = X(4)X(55521)∩X(488)X(19583)

Barycentrics    a^2*(-a^2+b^2+c^2)*(a^4+2*(b^2+c^2)*a^2-4*b^2*c^2+(b^2-c^2)^2)*(a^8-4*(b^2+c^2)*a^6-2*(5*b^4-6*b^2*c^2+5*c^4)*a^4-4*(b^2+c^2)*((b^2+c^2)^2-16*b^2*c^2)*a^2+(b^4+c^4+2*b*c*(2*b+c)*(b-2*c))*(b^4+c^4-2*b*c*(b+2*c)*(2*b-c))-8*S*((b^2+c^2)*a^4+(-4*b^2*c^2+(b^2-c^2)^2)*(2*a^2+b^2+c^2))) : :

X(55525) lies on the cubic K006 and these lines: {4, 55521}, {46, 55523}, {155, 55526}, {371, 55514}, {486, 55517}, {488, 19583}, {6213, 55519}, {8946, 55504}, {8947, 55500}, {55497, 55516}, {55501, 55512}, {55502, 55528}

X(55525) = isogonal conjugate of X(55521)
X(55525) = X(3)-cross conjugate of-X(55526)
X(55525) = X(2129)-isoconjugate of-X(6462)
X(55525) = X(19588)-reciprocal conjugate of-X(6462)
X(55525) = trilinear quotient X(2128)/X(6462)

X(55526) = X(4)X(55522)∩X(487)X(19583)

Barycentrics    a^2*(-a^2+b^2+c^2)*(a^4+2*(b^2+c^2)*a^2-4*b^2*c^2+(b^2-c^2)^2)*(a^8-4*(b^2+c^2)*a^6-2*(5*b^4-6*b^2*c^2+5*c^4)*a^4-4*(b^2+c^2)*((b^2+c^2)^2-16*b^2*c^2)*a^2+(b^4+c^4+2*b*c*(2*b+c)*(b-2*c))*(b^4+c^4-2*b*c*(b+2*c)*(2*b-c))+8*S*((b^2+c^2)*a^4+(-4*b^2*c^2+(b^2-c^2)^2)*(2*a^2+b^2+c^2))) : :

X(55526) lies on the cubic K006 and these lines: {4, 55522}, {46, 55524}, {155, 55525}, {372, 55513}, {485, 55518}, {487, 19583}, {6212, 55520}, {8948, 55503}, {8949, 55499}, {55498, 55515}, {55501, 55527}, {55502, 55511}

X(55526) = isogonal conjugate of X(55522)
X(55526) = X(3)-cross conjugate of-X(55525)
X(55526) = X(2129)-isoconjugate of-X(6463)
X(55526) = X(19588)-reciprocal conjugate of-X(6463)
X(55526) = trilinear quotient X(2128)/X(6463)

X(55527) = X(371)X(55521)∩X(488)X(55514)

Barycentrics    (5*a^6-5*(b^2+c^2)*a^4-(9*b^4-14*b^2*c^2+9*c^4)*a^2+(b^2+c^2)^3)*(5*(b^2+c^2)*a^14+5*(b^4-26*b^2*c^2+c^4)*a^12-(b^2+c^2)*(19*b^4-258*b^2*c^2+19*c^4)*a^10-(27*b^8+27*c^8+2*(104*b^4-75*b^2*c^2+104*c^4)*b^2*c^2)*a^8+(b^2+c^2)*(7*b^8+7*c^8-2*(314*b^4-389*b^2*c^2+314*c^4)*b^2*c^2)*a^6+(23*b^12+23*c^12-(10*b^8+10*c^8+(759*b^4-2644*b^2*c^2+759*c^4)*b^2*c^2)*b^2*c^2)*a^4+2*(a^12-6*(b^2+c^2)*a^10-(29*b^4-70*b^2*c^2+29*c^4)*a^8-4*(b^2+c^2)*(3*b^2-8*b*c+3*c^2)*(3*b^2+8*b*c+3*c^2)*a^6-(9*b^8+9*c^8+2*(210*b^4-101*b^2*c^2+210*c^4)*b^2*c^2)*a^4+2*(b^2+c^2)*(5*b^8+5*c^8-2*(118*b^4-271*b^2*c^2+118*c^4)*b^2*c^2)*a^2+5*(b^2+c^2)^6)*S*a^2+(7*b^4-10*b^2*c^2+7*c^4)*(b^2+c^2)^5*a^2-(b^2-c^2)^2*(b^2+c^2)^6) : :

X(55527) lies on the cubic K006 and these lines: {155, 55528}, {371, 55521}, {488, 55514}, {8946, 55517}, {8947, 55519}, {55497, 55523}, {55500, 55516}, {55501, 55526}, {55504, 55512}

X(55527) = X(3)-cross conjugate of-X(55528)

X(55528) = X(372)X(55522)∩X(487)X(55513)

Barycentrics    (5*a^6-5*(b^2+c^2)*a^4-(9*b^4-14*b^2*c^2+9*c^4)*a^2+(b^2+c^2)^3)*(5*(b^2+c^2)*a^14+5*(b^4-26*b^2*c^2+c^4)*a^12-(b^2+c^2)*(19*b^4-258*b^2*c^2+19*c^4)*a^10-(27*b^8+27*c^8+2*(104*b^4-75*b^2*c^2+104*c^4)*b^2*c^2)*a^8+(b^2+c^2)*(7*b^8+7*c^8-2*(314*b^4-389*b^2*c^2+314*c^4)*b^2*c^2)*a^6+(23*b^12+23*c^12-(10*b^8+10*c^8+(759*b^4-2644*b^2*c^2+759*c^4)*b^2*c^2)*b^2*c^2)*a^4-2*(a^12-6*(b^2+c^2)*a^10-(29*b^4-70*b^2*c^2+29*c^4)*a^8-4*(b^2+c^2)*(3*b^2-8*b*c+3*c^2)*(3*b^2+8*b*c+3*c^2)*a^6-(9*b^8+9*c^8+2*(210*b^4-101*b^2*c^2+210*c^4)*b^2*c^2)*a^4+2*(b^2+c^2)*(5*b^8+5*c^8-2*(118*b^4-271*b^2*c^2+118*c^4)*b^2*c^2)*a^2+5*(b^2+c^2)^6)*S*a^2+(7*b^4-10*b^2*c^2+7*c^4)*(b^2+c^2)^5*a^2-(b^2-c^2)^2*(b^2+c^2)^6) : :

X(55528) lies on the cubic K006 and these lines: {155, 55527}, {372, 55522}, {487, 55513}, {8948, 55518}, {8949, 55520}, {55498, 55524}, {55499, 55515}, {55502, 55525}, {55503, 55511}

X(55528) = X(3)-cross conjugate of-X(55527)

X(55529) = X(311)X(491)∩X(324)X(1586)

Barycentrics    1/(Cos[2*A] - Sin[2*A]) : :

X(55529) lies on these lines: {3, 55530}, {264, 55567}, {311, 491}, {324, 1586}, {338, 1599}, {637, 13439}, {1600, 45793}, {1993, 55543}, {5392, 16032}, {13428, 55021}

X(55529) = isotomic conjugate of X(55566)
X(55529) = polar conjugate of X(10881)
X(55529) = polar conjugate of the isogonal conjugate of X(55533)
X(55529) = X(i)-isoconjugate of X(j) for these (i,j): {31, 55566}, {48, 10881}
X(55529) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 55566}, {1249, 10881}
X(55529) = cevapoint of X(338) and X(54029)
X(55529) = trilinear pole of line {18314, 54028}
X(55529) = barycentric product X(i)*X(j) for these {i,j}: {264, 55533}, {317, 55535}, {5392, 55531}, {55530, 55537}, {55541, 55566}
X(55529) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55566}, {4, 10881}, {1586, 15208}, {3387, 3386}, {3388, 3385}, {55530, 55538}, {55531, 1993}, {55533, 3}, {55535, 68}, {55537, 55567}, {55543, 55531}, {55545, 55533}, {55566, 55539}

X(55530) = X(311)X(492)∩X(324)X(1585)

Barycentrics    1/(Cos[2*A] + Sin[2*A]) : :

X(55530) lies on these lines: {3, 55529}, {264, 55566}, {311, 492}, {324, 1585}, {338, 1600}, {638, 13428}, {1599, 45793}, {1993, 55544}, {5392, 16037}, {13439, 55020}

X(55530) = isotomic conjugate of X(55567)
X(55530) = polar conjugate of X(10880)
X(55530) = polar conjugate of the isogonal conjugate of X(55534)
X(55530) = X(i)-isoconjugate of X(j) for these (i,j): {31, 55567}, {48, 10880}
X(55530) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 55567}, {1249, 10880}
X(55530) = cevapoint of X(338) and X(54028)
X(55530) = trilinear pole of line {18314, 54029}
X(55530) = barycentric product X(i)*X(j) for these {i,j}: {264, 55534}, {317, 55536}, {5392, 55532}, {55529, 55538}, {55542, 55567}
X(55530) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55567}, {4, 10880}, {1585, 15207}, {3373, 3372}, {3374, 3371}, {55529, 55537}, {55532, 1993}, {55534, 3}, {55536, 68}, {55538, 55566}, {55544, 55532}, {55546, 55534}, {55567, 55540}

X(55531) = X(2)X(55533)∩X(311)X(491)

Barycentrics    Cos[2*A]/(Cos[2*A] - Sin[2*A]) : :

X(55531) lies on these lines: {2, 55533}, {311, 491}, {642, 1600}, {1147, 43973}, {1993, 8968}, {55031, 55473}, {55534, 55542}

X(55531) = X(1820)-isoconjugate of X(10881)
X(55531) = barycentric product X(i)*X(j) for these {i,j}: {317, 55533}, {1993, 55529}, {55532, 55537}, {55535, 55551}, {55543, 55566}
X(55531) = barycentric quotient X(i)/X(j) for these {i,j}: {24, 10881}, {1993, 55566}, {43973, 55534}, {55529, 5392}, {55532, 55538}, {55533, 68}, {55543, 55529}, {55545, 55535}
X(55531) = {X(2),X(55537)}-harmonic conjugate of X(55533)

X(55532) = X(2)X(55534)∩X(311)X(492)

Barycentrics    Cos[2*A]/(Cos[2*A] + Sin[2*A]) : :

X(55532) lies on these lines: {2, 55534}, {311, 492}, {641, 1599}, {1147, 43973}, {55031, 55479}, {55533, 55541}

X(55532) = X(1820)-isoconjugate of X(10880)
X(55532) = barycentric product X(i)*X(j) for these {i,j}: {317, 55534}, {1993, 55530}, {55531, 55538}, {55536, 55551}, {55544, 55567}
X(55532) = barycentric quotient X(i)/X(j) for these {i,j}: {24, 10880}, {1993, 55567}, {43973, 55533}, {55530, 5392}, {55531, 55537}, {55534, 68}, {55544, 55530}, {55546, 55536}
X(55532) = {X(2),X(55538)}-harmonic conjugate of X(55534)

X(55533) = X(2)X(55531)∩X(5)X(372)

Barycentrics    Sin[2*A]/(Cos[2*A] - Sin[2*A]) : :

X(55533) lies on these lines: {2, 55531}, {3, 26950}, {5, 372}, {216, 13970}, {324, 1586}, {343, 5409}, {494, 13951}, {577, 5449}, {3284, 13909}, {3549, 26873}, {5576, 26894}, {6458, 10024}, {6639, 26920}, {8908, 10116}, {8911, 25738}, {10898, 20303}, {11090, 55535}, {26912, 26917}, {55532, 55541}

X(55533) = isogonal conjugate of X(10881)
X(55533) = isogonal conjugate of the polar conjugate of X(55529)
X(55533) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10881}, {19, 55566}
X(55533) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 10881}, {6, 55566}, {10960, 15208}
X(55533) = barycentric product X(i)*X(j) for these {i,j}: {3, 55529}, {68, 55531}, {1993, 55535}, {55534, 55537}, {55545, 55566}
X(55533) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 55566}, {6, 10881}, {372, 15208}, {43973, 55532}, {55529, 264}, {55531, 317}, {55534, 55538}, {55535, 5392}, {55545, 55529}
X(55533) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55537, 55531}, {577, 5449, 55534}

X(55534) = X(2)X(55532)∩X(5)X(371)

Barycentrics    Sin[2*A]/(Cos[2*A] + Sin[2*A]) : :

X(55534) lies on these lines: {2, 55532}, {3, 26951}, {5, 371}, {216, 13909}, {324, 1585}, {343, 5408}, {493, 8976}, {577, 5449}, {2072, 26922}, {3284, 13970}, {3549, 26945}, {5576, 26919}, {6457, 10024}, {6639, 8911}, {8908, 44516}, {10897, 20303}, {11091, 55536}, {11799, 26918}, {13371, 26875}, {23293, 26916}, {25738, 26920}, {55531, 55542}

X(55534) = isogonal conjugate of X(10880)
X(55534) = isogonal conjugate of the polar conjugate of X(55530)
X(55534) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10880}, {19, 55567}
X(55534) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 10880}, {6, 55567}, {10962, 15207}
X(55534) = barycentric product X(i)*X(j) for these {i,j}: {3, 55530}, {68, 55532}, {1993, 55536}, {55533, 55538}, {55546, 55567}
X(55534) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 55567}, {6, 10880}, {371, 15207}, {43973, 55531}, {55530, 264}, {55532, 317}, {55533, 55537}, {55536, 5392}, {55546, 55530}
X(55534) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 55538, 55532}, {577, 5449, 55533}

X(55535) = X(3)X(55545)∩X(5392)X(16032)

Barycentrics    Tan[2*A]/(Cos[2*A] - Sin[2*A]) : :

X(55389) lies on these lines: {3, 55545}, {5392, 16032}, {11090, 55533}, {55536, 55549}

X(55535) = X(47)-isoconjugate of X(10881)
X(55535) = X(i)-Dao conjugate of X(j) for these (i,j): {24246, 15208}, {34853, 10881}
X(55535) = barycentric product X(i)*X(j) for these {i,j}: {68, 55529}, {5392, 55533}, {55536, 55537}
X(55535) = barycentric quotient X(i)/X(j) for these {i,j}: {68, 55566}, {485, 15208}, {2165, 10881}, {55529, 317}, {55531, 55551}, {55533, 1993}, {55536, 55538}, {55545, 55531}

X(55536) = X(3)X(55546)∩X(5392)X(16037)

Barycentrics    Tan[2*A]/(Cos[2*A] + Sin[2*A]) : :

X(55536) lies on these lines: {3, 55546}, {5392, 16037}, {11091, 55534}, {55535, 55549}

X(55536) = X(47)-isoconjugate of X(10880)
X(55536) = X(i)-Dao conjugate of X(j) for these (i,j): {24245, 15207}, {34853, 10880}
X(55536) = barycentric product X(i)*X(j) for these {i,j}: {68, 55530}, {5392, 55534}, {55535, 55538}
X(55536) = barycentric quotient X(i)/X(j) for these {i,j}: {68, 55567}, {486, 15207}, {2165, 10880}, {55530, 317}, {55532, 55551}, {55534, 1993}, {55535, 55537}, {55546, 55532}

X(55537) = X(2)X(55531)∩X(68)X(43973)

Barycentrics    (Cos[2*A] + Sin[2*A])/(Cos[2*A] - Sin[2*A]) : :

X(55537) lies on these lines: {2, 55531}, {68, 43973}, {317, 55541}, {637, 13439}, {13428, 13579}

X(55537) = isotomic conjugate of X(55538)
X(55537) = X(55535)-anticomplementary conjugate of X(4329)
X(55537) = X(31)-isoconjugate of X(55538)
X(55537) = X(2)-Dao conjugate of X(55538)
X(55537) = barycentric product X(i)*X(j) for these {i,j}: {55529, 55567}, {55538, 55547}
X(55537) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55538}, {10880, 10881}, {55529, 55530}, {55531, 55532}, {55533, 55534}, {55535, 55536}, {55538, 55548}, {55567, 55566}
X(55537) = {X(55531),X(55533)}-harmonic conjugate of X(2)

X(55538) = X(2)X(55532)∩X(68)X(43973)

Barycentrics    (Cos[2*A] - Sin[2*A])/(Cos[2*A] + Sin[2*A]) : :

X(55538) lies on these lines: {2, 55532}, {68, 43973}, {317, 55542}, {638, 13428}, {13439, 13579}

X(55538) = isotomic conjugate of X(55537)
X(55538) = X(55536)-anticomplementary conjugate of X(4329)
X(55538) = X(31)-isoconjugate of X(55537)
X(55538) = X(2)-Dao conjugate of X(55537)
X(55538) = barycentric product X(i)*X(j) for these {i,j}: {55530, 55566}, {55537, 55548}
X(55538) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55537}, {10881, 10880}, {55530, 55529}, {55532, 55531}, {55534, 55533}, {55536, 55535}, {55537, 55547}, {55566, 55567}
X(55538) = {X(55532),X(55534)}-harmonic conjugate of X(2)

X(55539) = X(2)X(54)∩X(49)X(1600)

Barycentrics    (Cos[2*A] - Sin[2*A])^2 : :

X(55539) lies on these lines: {2, 54}, {49, 1600}, {184, 12975}, {1584, 9703}, {1591, 40111}, {1599, 22115}, {3043, 3535}, {15192, 52432}, {15204, 52416}

X(55539) = isotomic conjugate of X(55541)
X(55539) = X(i)-isoconjugate of X(j) for these (i,j): {19, 55545}, {31, 55541}
X(55539) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 55541}, {6, 55545}
X(55539) = barycentric product X(i)*X(j) for these {i,j}: {55540, 55548}, {55566, 55566}
X(55539) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55541}, {3, 55545}, {1993, 55543}, {55540, 55547}, {55548, 55542}, {55566, 55529}
X(55539) = {X(2),X(1147)}-harmonic conjugate of X(55540)

X(55540) = X(2)X(54)∩X(49)X(1599)

Barycentrics    (Cos[2*A] + Sin[2*A])^2 : :

X(55540) lies on these lines: {2, 54}, {49, 1599}, {184, 12974}, {1583, 9703}, {1592, 40111}, {1600, 22115}, {3043, 3536}, {9676, 55566}, {15191, 52432}, {15203, 52416}

X(55540) = isotomic conjugate of X(55542)
X(55540) = X(i)-isoconjugate of X(j) for these (i,j): {19, 55546}, {31, 55542}
X(55540) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 55542}, {6, 55546}
X(55540) = barycentric product X(i)*X(j) for these {i,j}: {55539, 55547}, {55567, 55567}
X(55540) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55542}, {3, 55546}, {1993, 55544}, {55539, 55548}, {55547, 55541}, {55567, 55530}
X(55540) = {X(2),X(1147)}-harmonic conjugate of X(55539)

X(55541) = X(2)X(55547)∩X(317)X(55537)

Barycentrics    (Cos[2*A] - Sin[2*A])^(-2) : :

X(55541) lies on these lines: {2, 55547}, {317, 55537}, {467, 55545}, {5449, 55542}, {39113, 55543}, {55532, 55533}

X(55541) = isotomic conjugate of X(55539)
X(55541) = polar conjugate of the isogonal conjugate of X(55545)
X(55541) = X(31)-isoconjugate of X(55539)
X(55541) = X(2)-Dao conjugate of X(55539)
X(55541) = barycentric product X(i)*X(j) for these {i,j}: {264, 55545}, {5392, 55543}, {55529, 55529}, {55542, 55547}
X(55541) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55539}, {55529, 55566}, {55542, 55548}, {55543, 1993}, {55545, 3}, {55547, 55540}

X(55542) = X(2)X(55548)∩X(317)X(55538)

Barycentrics    (Cos[2*A] + Sin[2*A])^(-2) : :

X(55542) lies on these lines: {2, 55548}, {317, 55538}, {467, 55546}, {5449, 55541}, {39113, 55544}, {55531, 55534}

X(55542) = isotomic conjugate of X(55540)
X(55542) = polar conjugate of the isogonal conjugate of X(55546)
X(55542) = X(31)-isoconjugate of X(55540)
X(55542) = X(2)-Dao conjugate of X(55540)
X(55542) = barycentric product X(i)*X(j) for these {i,j}: {264, 55546}, {5392, 55544}, {55530, 55530}, {55541, 55548}
X(55542) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55540}, {55530, 55567}, {55541, 55547}, {55544, 1993}, {55546, 3}, {55548, 55539}

X(55543) = X(1993)X(55529)∩X(39113)X(55541)

Barycentrics    Cos[2*A]/(Cos[2*A] - Sin[2*A])^2 : :

X(55543) lies on these lines: {1993, 55529}, {39113, 55541}

X(55543) = barycentric product X(i)*X(j) for these {i,j}: {317, 55545}, {1993, 55541}, {55529, 55531}, {55544, 55547}
X(55543) = barycentric quotient X(i)/X(j) for these {i,j}: {1993, 55539}, {55531, 55566}, {55541, 5392}, {55544, 55548}, {55545, 68}

X(55544) = X(1993)X(55530)∩X(39113)X(55542)

Barycentrics    Cos[2*A]/(Cos[2*A] + Sin[2*A])^2 : :

X(55544) lies on these lines: {1993, 55530}, {39113, 55542}

X(55544) = barycentric product X(i)*X(j) for these {i,j}: {317, 55546}, {1993, 55542}, {55530, 55532}, {55543, 55548}
X(55544) = barycentric quotient X(i)/X(j) for these {i,j}: {1993, 55540}, {55532, 55567}, {55542, 5392}, {55543, 55547}, {55546, 68}

X(55545) = X(3)X(55535)∩X(467)X(55541)

Barycentrics    Sin[2*A]/(Cos[2*A] - Sin[2*A])^2 : :

X(55545) lies on these lines: {3, 55535}, {467, 55541}, {1993, 55529}

X(55545) = isogonal conjugate of the polar conjugate of X(55541)
X(55545) = X(19)-isoconjugate of X(55539)
X(55545) = X(6)-Dao conjugate of X(55539)
X(55545) = barycentric product X(i)*X(j) for these {i,j}: {3, 55541}, {68, 55543}, {55529, 55533}, {55531, 55535}, {55546, 55547}
X(55545) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 55539}, {55533, 55566}, {55541, 264}, {55543, 317}, {55546, 55548}

X(55546) = X(3)X(55536)∩X(467)X(55542)

Barycentrics    Sin[2*A]/(Cos[2*A] + Sin[2*A])^2 : :

X(55546) lies on these lines: {3, 55536}, {467, 55542}, {1993, 55530}

X(55546) = isogonal conjugate of the polar conjugate of X(55542)
X(55546) = X(19)-isoconjugate of X(55540)
X(55546) = X(6)-Dao conjugate of X(55540)
X(55546) = barycentric product X(i)*X(j) for these {i,j}: {3, 55542}, {68, 55544}, {55530, 55534}, {55532, 55536}, {55545, 55548}
X(55546) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 55540}, {55534, 55567}, {55542, 264}, {55544, 317}, {55545, 55547}

X(55547) = BARYCENTRIC QUOTIENT X(2)/X(55548)

Barycentrics    (Cos[2*A] + Sin[2*A])^2/(Cos[2*A] - Sin[2*A])^2 : :

X(55547) lies on this line: {2, 55541}

X(55547) = isotomic conjugate of X(55548)
X(55547) = X(31)-isoconjugate of X(55548)
X(55547) = X(2)-Dao conjugate of X(55548)
X(55547) = barycentric product X(i)*X(j) for these {i,j}: {55537, 55537}, {55540, 55541}
X(55547) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55548}, {55537, 55538}, {55540, 55539}, {55541, 55542}, {55543, 55544}, {55545, 55546}

X(55548) = BARYCENTRIC QUOTIENT X(2)/X(55547)

Barycentrics    (Cos[2*A] - Sin[2*A])^2/(Cos[2*A] + Sin[2*A])^2 : :

X(55548) lies on these lines: {2, 55542}

X(55548) = isotomic conjugate of X(55547)
X(55548) = X(31)-isoconjugate of X(55547)
X(55548) = X(2)-Dao conjugate of X(55547)
X(55548) = barycentric product X(i)*X(j) for these {i,j}: {55538, 55538}, {55539, 55542}
X(55548) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55547}, {55538, 55537}, {55539, 55540}, {55542, 55541}, {55544, 55543}, {55546, 55545}

X(55549) = X(1)X(14533)∩X(5)X(6)

Barycentrics    Cos[2*A] - Sec[2*A] : :

X(55549) lies on these lines: {3, 14533}, {5, 6}, {53, 12134}, {96, 7592}, {159, 2871}, {184, 216}, {264, 275}, {287, 20563}, {393, 41757}, {394, 6389}, {570, 1147}, {571, 13754}, {577, 5562}, {847, 40402}, {925, 26717}, {1409, 1820}, {1609, 9908}, {1625, 8746}, {1879, 9927}, {3284, 8798}, {3289, 41168}, {3292, 33926}, {5158, 43844}, {5647, 11402}, {5889, 8882}, {6662, 16266}, {8439, 39849}, {8553, 32661}, {8745, 11441}, {9833, 17849}, {10539, 14576}, {12038, 14806}, {12359, 53414}, {13428, 55565}, {13439, 55564}, {15066, 37802}, {15905, 18877}, {18401, 32692}, {22052, 31504}, {42466, 46200}, {55535, 55536}, {55558, 55566}, {55559, 55567}

X(55549) = isogonal conjugate of X(11547)
X(55549) = isogonal conjugate of the isotomic conjugate of X(52350)
X(55549) = isotomic conjugate of the polar conjugate of X(2351)
X(55549) = isogonal conjugate of the polar conjugate of X(68)
X(55549) = polar conjugate of the isotomic conjugate of X(16391)
X(55549) = X(42376)-complementary conjugate of X(20305)
X(55549) = X(i)-Ceva conjugate of X(j) for these (i,j): {68, 2351}, {5392, 3}, {52350, 16391}
X(55549) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11547}, {4, 1748}, {19, 317}, {24, 92}, {47, 2052}, {75, 8745}, {158, 1993}, {393, 44179}, {467, 2190}, {811, 6753}, {823, 924}, {1096, 7763}, {1147, 6521}, {1577, 52917}, {1969, 44077}, {2180, 8795}, {6520, 9723}, {6528, 55216}, {6563, 24019}, {8747, 42700}, {14576, 40440}, {17881, 23964}, {20571, 36416}, {23999, 47421}, {24006, 41679}, {36126, 52584}, {52414, 52415}
X(55549) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 11547}, {5, 467}, {6, 317}, {130, 52317}, {206, 8745}, {577, 55551}, {1147, 1993}, {6503, 7763}, {17423, 6753}, {22391, 24}, {34853, 2052}, {35071, 6563}, {36033, 1748}, {37864, 393}, {37867, 9723}, {46093, 52584}
X(55549) = cevapoint of X(i) and X(j) for these (i,j): {6, 17849}, {3269, 32320}
X(55549) = trilinear pole of line {17434, 39201}
X(55549) = crossdifference of every pair of points on line {924, 52000}
X(55549) = barycentric product X(i)*X(j) for these {i,j}: {3, 68}, {4, 16391}, {6, 52350}, {63, 1820}, {69, 2351}, {91, 255}, {96, 5562}, {125, 44174}, {155, 32132}, {184, 20563}, {394, 2165}, {418, 34385}, {485, 26922}, {520, 925}, {577, 5392}, {847, 1092}, {3265, 32734}, {3964, 14593}, {6413, 11091}, {6414, 11090}, {15316, 34853}, {20571, 52430}, {23606, 55553}, {24018, 36145}, {30450, 32320}, {37802, 50433}, {39201, 46134}, {41271, 52347}
X(55549) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 317}, {6, 11547}, {32, 8745}, {48, 1748}, {68, 264}, {96, 8795}, {184, 24}, {216, 467}, {217, 14576}, {255, 44179}, {394, 7763}, {418, 52}, {520, 6563}, {577, 1993}, {925, 6528}, {1092, 9723}, {1147, 55551}, {1576, 52917}, {1820, 92}, {2165, 2052}, {2351, 4}, {2632, 17881}, {3049, 6753}, {3990, 42700}, {4558, 55227}, {5392, 18027}, {5562, 39113}, {6413, 1586}, {6414, 1585}, {6751, 27362}, {14575, 44077}, {14585, 571}, {14593, 1093}, {16391, 69}, {17974, 31635}, {20563, 18022}, {20975, 136}, {23606, 1147}, {26922, 492}, {30451, 15423}, {32132, 46746}, {32320, 52584}, {32661, 41679}, {32692, 16813}, {32734, 107}, {36145, 823}, {39201, 924}, {39643, 41770}, {40348, 47392}, {41212, 55073}, {41271, 8884}, {42293, 52317}, {44174, 18020}, {50433, 18883}, {51477, 14111}, {52153, 52415}, {52350, 76}, {52430, 47}, {52435, 52432}, {52436, 36416}
X(55549) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1993, 5392, 55550}, {6413, 6414, 2351}, {10665, 10666, 68}

X(55550) = X68)X(4271)∩X(264)X(275)

Barycentrics    Cos[2*A] + Sec[2*A] : :

X(55550) lies on these lines: {3, 41271}, {6, 52350}, {68, 427}, {264, 275}, {394, 2165}, {511, 2351}, {578, 16391}, {5422, 37802}, {13428, 55564}, {13439, 55565}, {55558, 55567}, {55559, 55566}

X(55550) = {X(1993),X(5392)}-harmonic conjugate of X(55549)

X(55551) = X(3)X(95)∩X(69)X(186)

Barycentrics    Csc[2*A] - Sin[2*A] : :

X(55551) lies on these lines: {3, 95}, {4, 44180}, {24, 317}, {25, 32002}, {69, 186}, {99, 39437}, {193, 41758}, {250, 19118}, {325, 21213}, {339, 20564}, {340, 3515}, {393, 35296}, {491, 15208}, {492, 15207}, {648, 1609}, {1270, 15195}, {1271, 15196}, {1658, 41008}, {2351, 55562}, {4996, 55393}, {6530, 52278}, {6644, 45198}, {7279, 55394}, {7529, 54105}, {8553, 9308}, {8745, 41679}, {8797, 35500}, {11547, 39114}, {15191, 55479}, {15192, 55473}, {15219, 32805}, {15220, 32806}, {16391, 55563}, {17506, 52710}, {17907, 52275}, {20987, 36176}, {21844, 32000}, {22467, 40680}, {32001, 44879}, {32534, 44134}, {35302, 37765}, {37814, 41005}, {44077, 51439}, {44131, 44269}, {55554, 55566}, {55555, 55567}

X(55551) = isotomic conjugate of the isogonal conjugate of X(52432)
X(55551) = X(i)-isoconjugate of X(j) for these (i,j): {91, 2351}, {1820, 2165}
X(55551) = X(i)-Dao conjugate of X(j) for these (i,j): {134, 15451}, {577, 55549}, {924, 20975}, {34116, 2351}
X(55551) = cevapoint of X(15423) and X(34338)
X(55551) = barycentric product X(i)*X(j) for these {i,j}: {24, 7763}, {76, 52432}, {99, 15423}, {276, 3133}, {305, 36416}, {317, 1993}, {924, 55227}, {1748, 44179}, {4590, 34338}, {6563, 41679}, {6754, 34537}, {9723, 11547}
X(55551) = barycentric quotient X(i)/X(j) for these {i,j}: {24, 2165}, {47, 1820}, {317, 5392}, {571, 2351}, {1147, 55549}, {1748, 91}, {1993, 68}, {3133, 216}, {6754, 3124}, {7763, 20563}, {8745, 14593}, {9723, 52350}, {11547, 847}, {15423, 523}, {18315, 52932}, {34338, 115}, {35603, 47731}, {36416, 25}, {39013, 20975}, {41222, 24862}, {41679, 925}, {52432, 6}, {55227, 46134}, {55531, 55535}, {55532, 55536}
X(55551) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 44180, 55560}, {24, 9723, 317}, {69, 186, 55561}

X(55552) = X(4)X(55562)∩X(68)X(317)

Barycentrics    Cot[2*A] - Tan[2*A] : :

X(55552) lies on these lines: {4, 55562}, {68, 317}, {69, 55563}, {264, 5962}, {340, 20563}, {847, 32002}, {2351, 55560}, {13428, 55557}, {13439, 55556}, {16391, 55561}, {44128, 46134}

X(55552) = isotomic conjugate of X(43973)
X(55552) = X(31)-isoconjugate of X(43973)
X(55552) = X(2)-Dao conjugate of X(43973)
X(55552) = barycentric quotient X(2)/X(43973)
X(55552) = {X(68),X(317)}-harmonic conjugate of X(55553)

X(55553) = X(4)X(55563)∩X(68)X(317)

Barycentrics    Cot[2*A] + Tan[2*A] : :

X(55553) lies on these lines: {4, 55563}, {68, 317}, {69, 46134}, {76, 46746}, {264, 847}, {467, 2052}, {925, 46724}, {2165, 16081}, {2351, 16089}, {5962, 32002}, {9291, 16391}, {10550, 14593}, {13428, 55556}, {13439, 55557}, {20477, 46200}

X(55553) = isogonal conjugate of X(52435)
X(55553) = isotomic conjugate of X(1147)
X(55553) = polar conjugate of X(571)
X(55553) = isotomic conjugate of the anticomplement of X(5449)
X(55553) = isotomic conjugate of the complement of X(68)
X(55553) = isotomic conjugate of the isogonal conjugate of X(847)
X(55553) = polar conjugate of the isogonal conjugate of X(5392)
X(55553) = X(i)-isoconjugate of X(j) for these (i,j): {1, 52435}, {6, 563}, {24, 52430}, {31, 1147}, {47, 184}, {48, 571}, {63, 52436}, {163, 30451}, {255, 44077}, {560, 9723}, {1748, 14585}, {1993, 9247}, {2180, 14533}, {2200, 18605}, {4100, 8745}, {4575, 34952}, {9417, 51776}, {14575, 44179}, {32656, 34948}, {32661, 55216}
X(55553) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 1147}, {3, 52435}, {9, 563}, {115, 30451}, {136, 34952}, {1249, 571}, {2501, 39013}, {3162, 52436}, {6374, 9723}, {6523, 44077}, {24245, 8911}, {24246, 26920}, {34853, 184}, {36901, 52584}, {37864, 14575}, {39058, 51776}
X(55553) = cevapoint of X(i) and X(j) for these (i,j): {2, 68}, {136, 14618}, {847, 5392}, {2970, 18314}, {34391, 34392}
X(55553) = trilinear pole of line {6334, 14618}
X(55553) = barycentric product X(i)*X(j) for these {i,j}: {68, 18027}, {76, 847}, {91, 1969}, {92, 20571}, {264, 5392}, {324, 34385}, {850, 30450}, {1502, 14593}, {2052, 20563}, {2165, 18022}, {5962, 20573}, {14618, 46134}, {18817, 37802}, {24006, 55215}, {39116, 46746}
X(55553) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 563}, {2, 1147}, {4, 571}, {6, 52435}, {25, 52436}, {68, 577}, {76, 9723}, {91, 48}, {92, 47}, {94, 5961}, {96, 14533}, {136, 39013}, {264, 1993}, {286, 18605}, {290, 51776}, {311, 52032}, {324, 52}, {393, 44077}, {467, 3133}, {485, 26920}, {486, 8911}, {523, 30451}, {847, 6}, {850, 52584}, {925, 32661}, {1093, 8745}, {1820, 52430}, {1969, 44179}, {2052, 24}, {2165, 184}, {2351, 14585}, {2501, 34952}, {2970, 47421}, {5392, 3}, {5962, 50}, {6528, 41679}, {11547, 52432}, {13450, 14576}, {14165, 52416}, {14593, 32}, {14618, 924}, {15352, 52917}, {17924, 34948}, {18022, 7763}, {18027, 317}, {18817, 18883}, {20563, 394}, {20571, 63}, {23290, 52317}, {24006, 55216}, {27367, 41331}, {30450, 110}, {34385, 97}, {34391, 5409}, {34392, 5408}, {37802, 22115}, {39116, 155}, {44132, 51439}, {44427, 44808}, {46106, 51393}, {46134, 4558}, {51833, 5063}, {52350, 1092}, {52504, 13754}, {52661, 52952}, {55215, 4592}, {55250, 810}, {55549, 23606}
X(55553) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {68, 317, 55552}, {69, 51833, 55562}, {847, 20563, 264}

X(55554) = X(264)X(275)∩X(323)X(55474)

Barycentrics    Cos[2*A] - Csc[2*A] : :

X(55554) lies on these lines: {264, 275}, {323, 55474}, {1994, 55480}, {55551, 55566}, {55562, 55564}, {55563, 55565}

X(55554) = barycentric product X(317)*X(55558)
X(55554) = barycentric quotient X(55558)/X(68)
X(55554) = {X(264),X(1993)}-harmonic conjugate of X(55555)

X(55555) = X(264)X(275)∩X(323)X(55480)

Barycentrics    Cos[2*A] + Csc[2*A] : :

X(55555) lies on these lines: {264, 275}, {323, 55480}, {1994, 55474}, {55551, 55567}, {55562, 55565}, {55563, 55564}

X(55555) = barycentric product X(317)*X(55559)
X(55555) = barycentric quotient X(55559)/X(68)
X(55555) = {X(264),X(1993)}-harmonic conjugate of X(55554)

X(55556) = X(317)X(5392)∩X(13428)X(55553)

Barycentrics    Cot[2*A] - Sec[2*A] : :

X(55556) lies on these lines: {317, 5392}, {13428, 55553}, {13439, 55552}, {34391, 55563}, {55558, 55560}, {55559, 55561}

X(55556) = polar conjugate of the isogonal conjugate of X(55564)
X(55556) = barycentric product X(264)*X(55564)
X(55556) = barycentric quotient X(55564)/X(3)
X(55556) = {X(317),X(5392)}-harmonic conjugate of X(55557)

X(55557) = X(317)X(5392)∩X(13428)X(55552)

Barycentrics    Cot[2*A] + Sec[2*A] : :

X(55557) lies on these lines: {317, 5392}, {13428, 55552}, {13439, 55553}, {34392, 55563}, {55558, 55561}, {55559, 55560}

X(55557) = polar conjugate of the isogonal conjugate of X(55565)
X(55557) = barycentric product X(264)*X(55565)
X(55557) = barycentric quotient X(55565)/X(3)
X(55557) = {X(317),X(5392)}-harmonic conjugate of X(55556)

X(55558) = X(3)X(96)∩X(1583)X(37802)

Barycentrics    Sec[2*A] - Sin[2*A] : :

X(55558) lies on these lines: {3, 96}, {1583, 37802}, {1599, 52350}, {1600, 2165}, {2351, 8982}, {6414, 55564}, {13428, 16391}, {55549, 55566}, {55550, 55567}, {55556, 55560}, {55557, 55561}

X(55558) = barycentric product X(68)*X(55554)
X(55558) = barycentric quotient X(55554)/X(317)
X(55558) = {X(3),X(5392)}-harmonic conjugate of X(55559)

X(55559) = X(3)X(96)∩X(1584)X(37802)

Barycentrics    Sec[2*A] + Sin[2*A] : :

X(55559) lies on these lines: {3, 96}, {1584, 37802}, {1599, 2165}, {1600, 52350}, {2351, 13428}, {6413, 55565}, {13439, 16391}, {26922, 55564}, {55549, 55567}, {55550, 55566}, {55556, 55561}, {55557, 55560}

X(55559) = barycentric product X(68)*X(55555)
X(55559) = barycentric quotient X(55555)/X(317)
X(55559) = {X(3),X(5392)}-harmonic conjugate of X(55558)

X(55560) = X(3)X(317)∩X(25)X(37647)

Barycentrics    Cot[2*A] - Sin[2*A] : :

X(55560) lies on these lines: {3, 317}, {4, 44180}, {6, 41679}, {24, 32002}, {25, 37647}, {69, 3520}, {95, 7503}, {99, 264}, {340, 35477}, {491, 15209}, {492, 15206}, {1270, 15194}, {1271, 15197}, {1995, 54105}, {2071, 40680}, {2351, 55552}, {3087, 35296}, {3516, 3964}, {4996, 55394}, {7279, 55393}, {7509, 54412}, {7526, 44138}, {8553, 27377}, {9291, 16391}, {9308, 41677}, {11250, 41005}, {11413, 46724}, {12084, 20477}, {15190, 55474}, {15193, 55480}, {15218, 32805}, {15221, 32806}, {18570, 41008}, {32000, 35475}, {32001, 35473}, {35478, 52710}, {36794, 52275}, {55556, 55558}, {55557, 55559}

X(55560) = barycentric product X(1993)*X(55562)
X(55560) = barycentric quotient X(55562)/X(5392)
X(55560) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 317, 55561}, {4, 44180, 55551}, {378, 9723, 264}

X(55561) = X(3)X(317)∩X(24)X(264)

Barycentrics    Cot[2*A] + Sin[2*A] : :

X(55561) lies on these lines: {2, 41758}, {3, 317}, {22, 46724}, {24, 264}, {25, 37688}, {26, 20477}, {69, 186}, {95, 17928}, {183, 21213}, {297, 8553}, {340, 9723}, {378, 32002}, {491, 15207}, {492, 15208}, {1270, 15196}, {1271, 15195}, {1609, 17907}, {1658, 41005}, {2351, 16089}, {3515, 44134}, {3964, 15750}, {7488, 40680}, {10323, 54412}, {15191, 55480}, {15192, 55474}, {15219, 32806}, {15220, 32805}, {16391, 55552}, {21844, 32001}, {32000, 44879}, {37814, 41008}, {55556, 55559}, {55557, 55558}

X(55561) = barycentric product X(1993)*X(55563)
X(55561) = barycentric quotient X(55563)/X(5392)
X(55561) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 317, 55560}, {69, 186, 55551}, {21844, 32001, 44180}

X(55562) = X(4)X(55552)∩X(68)X(264)

Barycentrics    Csc[2*A] - Tan[2*A] : :

X(55562) lies on these lines: {4, 55552}, {68, 264}, {69, 46134}, {95, 34853}, {317, 847}, {648, 2165}, {2351, 55551}, {14593, 32002}, {20563, 44134}, {55554, 55564}, {55555, 55565}

X(55562) = barycentric product X(5392)*X(55560)
X(55562) = barycentric quotient X(55560)/X(1993)
X(55562) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {68, 264, 55563}, {69, 51833, 55553}

X(55563) = X(4)X(55553)∩X(68)X(264)

Barycentrics    Csc[2*A] + Tan[2*A] : :

X(55563) lies on these lines: {4, 55553}, {68, 264}, {69, 55552}, {317, 5962}, {2165, 36794}, {16391, 55551}, {34391, 55556}, {34392, 55557}, {34853, 46724}, {40814, 47731}, {55554, 55565}, {55555, 55564}

X(55563) = barycentric product X(5392)*X(55561)
X(55563) = barycentric quotient X(55561)/X(1993)
X(55563) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {68, 264, 55562}, {5962, 20563, 317}

X(55564) = X(68)X(1594)∩X(2351)X(55566)

Barycentrics    Cos[2*A] - Tan[2*A] : :

X(55564) lies on these lines: {68, 1594}, {2351, 55566}, {5392, 10666}, {6414, 55558}, {13428, 55550}, {13439, 55549}, {16391, 55567}, {26922, 55559}, {55554, 55562}, {55555, 55563}

X(55564) = isogonal conjugate of the polar conjugate of X(55556)
X(55564) = barycentric product X(3)*X(55556)
X(55564) = barycentric quotient X(55556)/X(264)
X(55564) = {X(68),X(1993)}-harmonic conjugate of X(55565)

X(55565) = X(68)X(1594)∩X(2351)X(55522)

Barycentrics    Cos[2*A] + Tan[2*A] : :

X(555) lies on these lines: {68, 1594}, {2351, 55567}, {5392, 10665}, {6413, 55559}, {13428, 55549}, {13439, 55550}, {16391, 55566}, {55554, 55563}, {55555, 55562}

isogonal conjugate of the polar conjugate of X(55557)
barycentric product X(3)*X(55557)
barycentric quotient X(55557)/X(264)
{X(68),X(1993)}-harmonic conjugate of X(55564)

X(55566) = X(2)X(371)∩X(3)X(54)

Barycentrics    Cos[2*A] - Sin[2*A] : :

X(55566) lies on these lines: {2, 371}, {3, 54}, {6, 589}, {22, 9732}, {25, 6239}, {110, 3155}, {111, 493}, {184, 9738}, {193, 11513}, {264, 55530}, {323, 5408}, {372, 1994}, {394, 1151}, {485, 13579}, {491, 44128}, {588, 12962}, {590, 15234}, {1180, 6422}, {1350, 13617}, {1370, 12257}, {1583, 6221}, {1584, 3311}, {1586, 10880}, {1589, 6515}, {1590, 37645}, {1591, 8981}, {1592, 42215}, {1627, 6424}, {2351, 55564}, {3060, 3156}, {3071, 15233}, {3092, 15188}, {3093, 15189}, {3364, 52349}, {3389, 52348}, {3580, 18457}, {3592, 10601}, {3796, 12306}, {3917, 43120}, {5392, 16032}, {5406, 6409}, {5410, 15201}, {5413, 15192}, {6396, 11004}, {6413, 11417}, {6419, 34545}, {6425, 17811}, {6636, 11824}, {7485, 43119}, {8911, 11418}, {9676, 55540}, {10665, 26916}, {10881, 15208}, {10960, 26919}, {11002, 35300}, {11003, 45499}, {11090, 45794}, {11474, 15193}, {13366, 43121}, {15186, 55412}, {15187, 55411}, {15246, 45553}, {16391, 55565}, {34565, 43143}, {34986, 43144}, {39648, 52275}, {55549, 55558}, {55550, 55559}, {55551, 55554}

X(55566) = isotomic conjugate of X(55529)
X(55566) = anticomplement of the isotomic conjugate of X(16032)
X(55566) = isotomic conjugate of the polar conjugate of X(10881)
X(55566) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2148, 488}, {2168, 638}, {16032, 6327}
X(55566) = X(i)-Ceva conjugate of X(j) for these (i,j): {5392, 55567}, {16032, 2}
X(55566) = X(i)-isoconjugate of X(j) for these (i,j): {19, 55533}, {31, 55529}
X(55566) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 55529}, {6, 55533}
X(55566) = barycentric product X(i)*X(j) for these {i,j}: {69, 10881}, {11091, 15208}, {55529, 55539}, {55538, 55567}
X(55566) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55529}, {3, 55533}, {68, 55535}, {1993, 55531}, {3385, 3388}, {3386, 3387}, {10881, 4}, {15208, 1586}, {55529, 55541}, {55531, 55543}, {55533, 55545}, {55538, 55530}, {55567, 55537}
X(55566) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 43134, 13428}, {3, 1993, 55567}, {6, 5407, 1600}, {97, 5889, 55567}, {371, 5409, 2}, {394, 1151, 1599}, {1584, 3311, 5422}, {3156, 45489, 3060}, {3796, 12306, 13616}, {6409, 37672, 5406}, {6413, 26875, 11417}, {9732, 10132, 22}

X(55567) = X(2)X(372)∩X(3)X(54)

Barycentrics    Cos[2*A] + Sin[2*A] : :

X(55567) lies on these lines: {2, 372}, {3, 54}, {6, 588}, {22, 9733}, {25, 6400}, {110, 3156}, {111, 494}, {184, 9739}, {193, 11514}, {264, 55529}, {323, 5409}, {371, 1994}, {394, 1152}, {486, 13579}, {492, 44128}, {589, 12969}, {615, 15233}, {1180, 6421}, {1350, 13616}, {1370, 12256}, {1583, 3312}, {1584, 6398}, {1585, 10881}, {1589, 37645}, {1590, 6515}, {1591, 42216}, {1592, 13966}, {1627, 6423}, {2351, 55565}, {3060, 3155}, {3070, 15234}, {3092, 15186}, {3093, 15187}, {3365, 52349}, {3390, 52348}, {3580, 18459}, {3594, 10601}, {3796, 12305}, {3917, 43121}, {5062, 8962}, {5392, 16037}, {5407, 6410}, {5411, 15198}, {5412, 15191}, {6200, 11004}, {6414, 11418}, {6420, 34545}, {6426, 17811}, {6636, 11825}, {7485, 43118}, {10880, 15207}, {10962, 26894}, {11002, 35299}, {11003, 45498}, {11091, 45794}, {11417, 26920}, {11473, 15190}, {11917, 21097}, {13366, 43120}, {15188, 55412}, {15189, 55411}, {15246, 45552}, {16391, 55564}, {34565, 43145}, {34986, 43141}, {39679, 52275}, {55549, 55559}, {55550, 55558}, {55551, 55555}

X(55567) = isotomic conjugate of X(55530)
X(55567) = anticomplement of the isotomic conjugate of X(16037)
X(55567) = isotomic conjugate of the polar conjugate of X(10880)
X(55567) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2148, 487}, {2168, 637}, {16037, 6327}
X(55567) = X(i)-Ceva conjugate of X(j) for these (i,j): {5392, 55566}, {16037, 2}
X(55567) = X(i)-isoconjugate of X(j) for these (i,j): {19, 55534}, {31, 55530}
X(55567) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 55530}, {6, 55534}
X(55567) = barycentric product X(i)*X(j) for these {i,j}: {69, 10880}, {11090, 15207}, {55530, 55540}, {55537, 55566}
X(55567) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 55530}, {3, 55534}, {68, 55536}, {1993, 55532}, {3371, 3374}, {3372, 3373}, {10880, 4}, {15207, 1585}, {55530, 55542}, {55532, 55544}, {55534, 55546}, {55537, 55529}, {55566, 55538}
X(55567) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 43133, 13439}, {3, 1993, 55566}, {6, 5406, 1599}, {97, 5889, 55566}, {372, 5408, 2}, {394, 1152, 1600}, {1583, 3312, 5422}, {3155, 45488, 3060}, {3796, 12305, 13617}, {6410, 37672, 5407}, {9733, 10133, 22}

X(55568) = X(4)-CEVA CONJUGATE OF X(254)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 3*a^4*c^2 + 2*a^2*b^2*c^2 - 3*b^4*c^2 + 3*a^2*c^4 + 3*b^2*c^4 - c^6)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - a^4*c^2 + 2*a^2*b^2*c^2 + 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6)*(3*a^12 - 14*a^10*b^2 + 25*a^8*b^4 - 20*a^6*b^6 + 5*a^4*b^8 + 2*a^2*b^10 - b^12 - 14*a^10*c^2 + 38*a^8*b^2*c^2 - 36*a^6*b^4*c^2 + 20*a^4*b^6*c^2 - 14*a^2*b^8*c^2 + 6*b^10*c^2 + 25*a^8*c^4 - 36*a^6*b^2*c^4 - 2*a^4*b^4*c^4 + 12*a^2*b^6*c^4 - 15*b^8*c^4 - 20*a^6*c^6 + 20*a^4*b^2*c^6 + 12*a^2*b^4*c^6 + 20*b^6*c^6 + 5*a^4*c^8 - 14*a^2*b^2*c^8 - 15*b^4*c^8 + 2*a^2*c^10 + 6*b^2*c^10 - c^12) : :

X(55568) lies on the cubic K006 and these lines: {3, 254}, {90, 921}, {485, 55510}, {486, 55509}, {6504, 12359}, {31387, 55505}, {34756, 36752}, {55507, 55508}

X(55568) = orthic-isogonal conjugate of X(254)
X(55568) = X(4)-Ceva conjugate of X(254)
X(55568) = X(6504)-Dao conjugate of X(69)

X(55569) = X(2)X(3)∩X(33)X(55475)

Barycentrics    1 - 2*Tan[A] : :

X(55569) lies on these lines: {2, 3}, {33, 55475}, {34, 55482}, {53, 3069}, {154, 14230}, {193, 13439}, {264, 1270}, {275, 1131}, {317, 1271}, {343, 12322}, {393, 589}, {394, 12323}, {459, 43561}, {486, 8796}, {1132, 2052}, {1322, 13428}, {1853, 14233}, {1990, 19053}, {1993, 3093}, {3068, 6748}, {3070, 11427}, {3071, 11433}, {3087, 7585}, {3092, 5422}, {3218, 55395}, {3219, 55396}, {3591, 39284}, {3593, 55474}, {3595, 32002}, {4994, 16032}, {5407, 32806}, {5409, 35764}, {5412, 55566}, {6239, 47328}, {6515, 12221}, {6749, 19054}, {7090, 13386}, {8962, 33843}, {8968, 42269}, {10192, 14235}, {10194, 54893}, {10195, 54892}, {11206, 13749}, {11474, 55567}, {12601, 41588}, {13387, 13390}, {13567, 23261}, {13748, 32064}, {14165, 43507}, {14239, 23332}, {15066, 55412}, {16080, 43567}, {17810, 45863}, {18290, 35830}, {23251, 23292}, {27003, 55460}, {27065, 55431}, {32000, 32814}, {32793, 55394}, {32794, 55393}, {32799, 55429}, {32800, 55428}, {32808, 52710}, {37643, 42283}, {43462, 43508}, {43530, 43566}

X(55569) = anticomplement of X(1590)
X(55569) = polar conjugate of X(3317)
X(55569) = polar conjugate of the isotomic conjugate of X(32806)
X(55569) = polar conjugate of the isogonal conjugate of X(3312)
X(55569) = X(i)-isoconjugate of X(j) for these (i,j): {48, 3317}, {8908, 46218}
X(55569) = X(1249)-Dao conjugate of X(3317)
X(55569) = barycentric product X(i)*X(j) for these {i,j}: {4, 32806}, {264, 3312}, {1586, 55477}, {2052, 5407}
X(55569) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 3317}, {3312, 3}, {5407, 394}, {32806, 69}, {55477, 11091}
X(55569) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15187, 15191}, {3, 15189, 15193}, {3, 15191, 15195}, {3, 15193, 15197}, {4, 1586, 2}, {4, 3128, 7378}, {4, 3536, 1585}, {4, 5200, 6995}, {4, 6353, 52286}, {4, 8889, 32588}, {5, 1589, 2}, {25, 1600, 15192}, {25, 15201, 1600}, {264, 55479, 1270}, {317, 55480, 1271}, {1583, 1597, 15186}, {1584, 1598, 15188}, {1585, 1586, 3536}, {1585, 3536, 2}, {1591, 11292, 2}, {1593, 1599, 15190}, {1593, 15199, 1599}, {3093, 55411, 1993}, {3518, 15221, 15208}, {5198, 15213, 15200}, {6805, 7388, 2}, {10594, 15217, 15204}, {11403, 15211, 15198}, {14865, 15219, 15206}, {15187, 15189, 3}, {15187, 15193, 15195}, {15189, 15191, 15197}, {15191, 15193, 3}, {15195, 15197, 3}, {15215, 35502, 15202}, {24243, 44638, 193}, {32587, 52287, 4}, {55393, 55459, 32794}, {55394, 55458, 32793}, {55395, 55461, 3218}, {55396, 55430, 3219}, {55412, 55443, 15066}

X(55570) = X(2)X(3)∩X(54)X(44731)

Barycentrics    (2 - 7*Cos[A]^2)*Tan[A] : :
3 X[4] - 7 X[6622], 13 X[5079] - 21 X[21974]

X(55570) lies on these lines: {2, 3}, {54, 44731}, {1181, 44108}, {1192, 10282}, {1204, 32063}, {1351, 12038}, {1452, 37606}, {1495, 12315}, {1620, 6000}, {1968, 15655}, {2931, 12309}, {3092, 6455}, {3093, 6456}, {3199, 5210}, {3527, 11430}, {5412, 6450}, {5413, 6449}, {5878, 15448}, {6199, 10881}, {6395, 10880}, {6403, 12006}, {6411, 35765}, {6412, 35764}, {6451, 11473}, {6452, 11474}, {6749, 31450}, {6759, 37487}, {7713, 17502}, {7716, 17508}, {8537, 53091}, {8780, 12163}, {9707, 43602}, {9786, 11202}, {9932, 19588}, {10605, 14530}, {11204, 15811}, {11426, 34565}, {11432, 13367}, {11438, 17821}, {11449, 12160}, {11470, 33878}, {12164, 51393}, {12174, 26882}, {13093, 21663}, {13148, 15039}, {13474, 41424}, {14157, 34469}, {15083, 51933}, {18440, 44158}, {19128, 44456}, {19357, 44109}, {19504, 38638}, {21309, 39575}, {25563, 36990}, {26864, 43596}, {26883, 35450}, {26944, 34782}, {26958, 34785}, {33556, 44102}, {37483, 43898}, {40909, 43839}

X(55570) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 24, 1598}, {3, 2070, 39568}, {3, 3517, 1597}, {3, 7517, 54992}, {3, 10244, 20}, {3, 10245, 11414}, {3, 11484, 54994}, {3, 18535, 3516}, {3, 20850, 12085}, {3, 35501, 35477}, {3, 45735, 5020}, {3, 51519, 47527}, {4, 52297, 5079}, {24, 186, 15750}, {24, 1598, 3517}, {24, 3520, 25}, {24, 15750, 3}, {24, 21844, 1593}, {24, 32534, 3520}, {25, 3515, 44879}, {25, 32534, 3}, {186, 3515, 3}, {186, 35479, 3515}, {186, 37957, 37934}, {186, 44879, 32534}, {186, 44880, 21844}, {1593, 15750, 21844}, {1593, 21844, 3}, {3515, 15750, 24}, {3516, 3518, 18535}, {3516, 35472, 3}, {3518, 35472, 3516}, {3520, 44879, 24}, {3528, 4232, 13488}, {3542, 37931, 1657}, {3575, 35486, 3526}, {5198, 35477, 35501}, {6240, 37453, 3851}, {6642, 18324, 3}, {7395, 10298, 3}, {7505, 37196, 3843}, {7517, 37955, 3}, {9715, 22467, 3}, {9818, 15331, 3}, {10018, 12173, 5055}, {10243, 14070, 16195}, {10295, 37197, 17800}, {10594, 17506, 11410}, {11410, 17506, 3}, {11414, 15078, 3}, {11438, 17821, 19347}, {12085, 15646, 3}, {14070, 37814, 3}, {21844, 44880, 24}, {32534, 44879, 25}, {35477, 47485, 5198}, {35502, 47486, 25}, {37922, 37973, 7575}, {38438, 44802, 54994}, {38438, 54994, 3}, {42789, 42790, 49138}, {44802, 54994, 11484}

X(55571) = X(2)X(3)∩X(6)X(3357)

Barycentrics    (2 + 3*Cos[A]^2)*Tan[A] : :
X(55571) = X[4] - 3 X[3088], 4 X[140] - 3 X[3547], 7 X[3523] - 3 X[52404]

X(55571) lies on these lines: {2, 3}, {6, 3357}, {54, 12174}, {64, 578}, {74, 22233}, {112, 43136}, {154, 13474}, {184, 12315}, {185, 11426}, {389, 10606}, {1033, 5702}, {1112, 15041}, {1147, 11472}, {1181, 13093}, {1192, 10110}, {1204, 10982}, {1351, 12163}, {1398, 6767}, {1498, 3426}, {1853, 13403}, {1902, 10246}, {1968, 9605}, {1993, 15062}, {2207, 5024}, {2935, 20417}, {3053, 33843}, {3092, 6398}, {3093, 6221}, {3167, 12162}, {3199, 15815}, {3311, 11474}, {3312, 11473}, {3527, 3532}, {3867, 48873}, {3964, 32824}, {5050, 12294}, {5093, 6102}, {5412, 6449}, {5413, 6450}, {5447, 32620}, {5644, 12006}, {5878, 23292}, {5890, 34469}, {5895, 18388}, {5907, 37497}, {6000, 11425}, {6090, 15058}, {6241, 11402}, {6407, 10880}, {6408, 10881}, {6409, 35764}, {6410, 35765}, {6696, 39571}, {6749, 8573}, {7071, 7373}, {7592, 43596}, {7689, 44413}, {7713, 31663}, {7716, 14810}, {8567, 11438}, {8778, 21309}, {8780, 12038}, {9707, 11455}, {9919, 32607}, {10060, 19365}, {10076, 11429}, {10282, 15811}, {10575, 37506}, {10605, 11424}, {10620, 13148}, {10986, 15603}, {10990, 19457}, {11381, 19357}, {11427, 12250}, {11470, 53092}, {11475, 11486}, {11476, 11485}, {11623, 39841}, {12118, 18440}, {12133, 32609}, {12164, 13352}, {12233, 20427}, {12241, 26944}, {12242, 32345}, {12300, 55039}, {12302, 16534}, {12308, 15463}, {12324, 31804}, {12897, 14852}, {13367, 14530}, {15030, 35602}, {15105, 46373}, {15473, 38788}, {15515, 33842}, {16657, 26937}, {18390, 40686}, {19467, 34780}, {22334, 50414}, {22655, 52854}, {25563, 26958}, {27371, 44526}, {32138, 39522}, {34785, 36990}, {37476, 46850}, {38723, 46682}, {39588, 44456}, {39899, 43595}, {42021, 43690}, {43600, 52719}, {43689, 45034}

X(55571) = reflection of X(19347) in X(11425)
X(55571) = orthocentroidal-circle-inverse of X(44960)
X(55571) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 44960}, {3, 4, 3517}, {3, 382, 9909}, {3, 1593, 1597}, {3, 1597, 1598}, {3, 3830, 9714}, {3, 10245, 38444}, {3, 11484, 17928}, {3, 18534, 16195}, {3, 18535, 24}, {3, 20850, 1658}, {3, 35501, 1593}, {3, 44454, 2937}, {3, 47527, 39568}, {4, 378, 3516}, {4, 3516, 3}, {4, 3517, 1598}, {4, 3520, 32534}, {4, 3522, 37458}, {4, 3523, 21841}, {4, 5056, 37984}, {4, 5094, 3851}, {4, 10299, 4232}, {4, 32534, 25}, {4, 35477, 3515}, {4, 35478, 35477}, {4, 35483, 3522}, {4, 35487, 37197}, {4, 35491, 37196}, {4, 37119, 35487}, {4, 37460, 7715}, {20, 1595, 18494}, {20, 54994, 3}, {24, 378, 35475}, {24, 11403, 18535}, {24, 11410, 3}, {24, 13596, 11403}, {24, 26863, 25}, {24, 35475, 11410}, {25, 1593, 35502}, {25, 3515, 47486}, {25, 3520, 3}, {378, 1593, 3}, {378, 1885, 47524}, {378, 13596, 11410}, {378, 14865, 1593}, {378, 35477, 35478}, {378, 35501, 1597}, {378, 35502, 3520}, {381, 47524, 3}, {1593, 3516, 4}, {1593, 11403, 13596}, {1593, 11410, 11403}, {1593, 14865, 35501}, {1593, 35475, 18535}, {1593, 54994, 1595}, {1594, 44438, 3843}, {1597, 3517, 4}, {1885, 3541, 381}, {3515, 3516, 35477}, {3515, 35477, 3}, {3520, 13596, 26863}, {3520, 35502, 25}, {6642, 11250, 3}, {7387, 18570, 3}, {7395, 11413, 3}, {7503, 12086, 21312}, {7503, 21312, 3}, {7507, 18560, 3830}, {7526, 12085, 3}, {7527, 11413, 7395}, {7715, 33923, 37460}, {9818, 12084, 3}, {9909, 11479, 10024}, {10110, 11204, 1192}, {10594, 35473, 15750}, {10605, 11424, 11432}, {11250, 31861, 6642}, {11381, 19357, 32063}, {11403, 11410, 24}, {11403, 35475, 3}, {11410, 13596, 18535}, {11414, 14118, 3}, {11426, 35450, 185}, {12173, 35481, 17800}, {13488, 44960, 4}, {13596, 18535, 1597}, {13596, 35475, 24}, {15186, 15193, 1584}, {15189, 15190, 1583}, {15559, 35481, 12173}, {15750, 35473, 3}, {23040, 52294, 35479}, {26863, 35502, 11403}, {32534, 35502, 4}, {32534, 47486, 3515}, {35477, 35478, 3516}, {35478, 47486, 3520}, {35484, 35491, 4}, {35490, 52295, 18386}, {35921, 37198, 3}, {37119, 37197, 5055}, {37199, 37337, 11286}, {42789, 42790, 3525}, {42807, 42808, 6677}

X(55572) = X(2)X(3)∩X(6)X(11202)

Barycentrics    5*Cos[A]*Sin[A] - 2*Tan[A] : :
X(55572) = X[4] - 5 X[6353], 3 X[4] - 5 X[6623], X[4] + 5 X[37460], 7 X[3526] - 5 X[30771], 3 X[6353] - X[6623], 5 X[6353] - 2 X[44957], X[6623] + 3 X[37460], 5 X[6623] - 6 X[44957], 5 X[7396] - 13 X[10303], 5 X[37460] + 2 X[44957]

X(55572) lies on these lines: {2, 3}, {6, 11202}, {53, 21843}, {64, 44763}, {154, 11438}, {185, 14530}, {232, 1384}, {371, 43955}, {389, 17809}, {999, 52427}, {1112, 15040}, {1181, 44110}, {1192, 6759}, {1204, 12315}, {1351, 44102}, {1495, 10605}, {1511, 19118}, {1609, 2079}, {1620, 3357}, {1843, 5892}, {1853, 44673}, {1905, 37606}, {1974, 33878}, {2931, 19588}, {3053, 14581}, {3092, 6449}, {3093, 6450}, {3167, 37489}, {3199, 5023}, {3426, 10606}, {3527, 11425}, {5024, 10311}, {5050, 8541}, {5092, 7716}, {5093, 19128}, {5217, 54428}, {5410, 6395}, {5411, 6199}, {5412, 6398}, {5413, 6221}, {5446, 15010}, {5621, 13289}, {5890, 26864}, {5946, 6403}, {6000, 37487}, {6409, 35765}, {6410, 35764}, {6417, 10881}, {6418, 10880}, {6455, 11473}, {6456, 11474}, {6800, 15053}, {7713, 13624}, {8276, 43430}, {8277, 43431}, {8567, 13474}, {8588, 33842}, {8739, 11485}, {8740, 11486}, {8780, 13754}, {9126, 17994}, {9703, 34397}, {9786, 10282}, {9833, 26944}, {10641, 42115}, {10642, 42116}, {10986, 53026}, {11179, 41585}, {11216, 51733}, {11363, 12702}, {11402, 11464}, {11426, 13367}, {11430, 17810}, {11432, 13366}, {11820, 32237}, {12007, 15577}, {12024, 13567}, {13093, 26883}, {13419, 40686}, {13884, 18512}, {13937, 18510}, {14528, 37505}, {14657, 34131}, {14826, 44683}, {15463, 38638}, {15473, 38794}, {15603, 33885}, {18400, 26958}, {18451, 32110}, {19132, 21851}, {19596, 39879}, {21309, 45141}, {21663, 35450}, {22115, 44077}, {22550, 32048}, {23329, 36990}, {26937, 34780}, {27371, 44535}, {32267, 44750}, {33582, 39857}, {33586, 51394}, {33843, 53095}, {34513, 39588}, {37624, 41722}, {38728, 46682}, {39575, 43136}, {39899, 41584}, {41597, 51933}, {43691, 43719}, {44086, 51340}, {48378, 48910}, {51140, 53019}

X(55572) = midpoint of X(i) and X(j) for these {i,j}: {3, 20850}, {6353, 37460}
X(55572) = reflection of X(4) in X(44957)
X(55572) = circumcircle-inverse of X(37984)
X(55572) = tangential-circle-inverse of X(37933)
X(55572) = barycentric product X(25)*X(32837)
X(55572) = barycentric quotient X(32837)/X(305)
X(55572) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 37458, 18494}, {2, 44239, 18536}, {3, 24, 3517}, {3, 25, 1597}, {3, 2070, 9909}, {3, 3517, 1598}, {3, 7506, 11479}, {3, 9714, 39568}, {3, 10244, 11414}, {3, 10245, 22}, {3, 11484, 7503}, {3, 18378, 47527}, {3, 18534, 54992}, {3, 18535, 378}, {3, 35501, 11410}, {3, 37956, 44457}, {3, 44454, 18859}, {3, 51519, 18534}, {4, 186, 35472}, {4, 3542, 45004}, {4, 11410, 35501}, {4, 15750, 3}, {4, 35472, 11410}, {4, 35479, 15750}, {4, 35501, 1597}, {4, 37453, 5055}, {4, 37931, 3534}, {4, 44879, 44880}, {4, 44880, 35479}, {23, 15078, 21312}, {24, 186, 25}, {24, 378, 47485}, {24, 3515, 3}, {24, 10594, 47486}, {24, 21213, 2070}, {24, 32534, 3518}, {24, 35479, 4}, {24, 44878, 186}, {24, 44879, 3515}, {24, 44880, 15750}, {25, 186, 3}, {25, 378, 18535}, {25, 1597, 1598}, {25, 3515, 186}, {25, 11410, 4}, {25, 15750, 11410}, {25, 35472, 35501}, {186, 3518, 35473}, {186, 13596, 21844}, {186, 35472, 15750}, {186, 35473, 32534}, {186, 37951, 44281}, {186, 44281, 37955}, {186, 44878, 3515}, {186, 44879, 44878}, {186, 45173, 7502}, {186, 47485, 378}, {186, 47486, 13596}, {376, 4232, 1596}, {378, 18535, 1597}, {378, 37969, 12083}, {378, 47485, 25}, {403, 37196, 3830}, {427, 35486, 5054}, {468, 18533, 381}, {1113, 1114, 37984}, {1495, 10605, 32063}, {1593, 32534, 3}, {1596, 37934, 376}, {1597, 3517, 25}, {1658, 6642, 3}, {1995, 10298, 54994}, {2070, 37958, 44265}, {3131, 3132, 26865}, {3147, 3575, 1656}, {3515, 15750, 35479}, {3516, 21844, 3}, {3518, 32534, 1593}, {3530, 7715, 3088}, {6644, 7575, 14070}, {6644, 14070, 3}, {7387, 37814, 3}, {7395, 38444, 3}, {7484, 44837, 3}, {7505, 12173, 3851}, {7507, 10018, 5070}, {7517, 18859, 44454}, {7577, 52292, 15703}, {9715, 17928, 3}, {9786, 10282, 19347}, {9818, 18324, 3}, {10295, 44438, 15681}, {10298, 54994, 3}, {10594, 21844, 3516}, {11410, 15750, 35472}, {11410, 35472, 3}, {11414, 22467, 3}, {12106, 18324, 9818}, {15078, 21312, 3}, {21844, 47486, 10594}, {26255, 44285, 381}, {34484, 35477, 11403}, {35471, 37197, 5073}, {35472, 35479, 186}, {35479, 44880, 3515}, {37458, 37935, 2}, {37489, 51393, 3167}, {37904, 37953, 2070}, {38444, 44802, 7395}, {42789, 42790, 11001}, {44233, 49669, 381}, {44268, 47093, 20}

X(55573) = X(2)X(3)∩X(33)X(55481)

Barycentrics    1 + 2*Tan[A] : :

X(55573) lies on these lines: {2, 3}, {33, 55481}, {34, 55476}, {53, 3068}, {154, 14233}, {193, 13428}, {264, 1271}, {275, 1132}, {317, 1270}, {343, 12323}, {393, 588}, {394, 12322}, {459, 43560}, {485, 8796}, {1131, 2052}, {1321, 13439}, {1659, 13386}, {1853, 14230}, {1990, 19054}, {1993, 3092}, {3069, 6748}, {3070, 11433}, {3071, 11427}, {3087, 7586}, {3093, 5422}, {3199, 8962}, {3218, 55396}, {3219, 55395}, {3590, 39284}, {3593, 32002}, {3595, 55480}, {4994, 16037}, {5406, 32805}, {5408, 35765}, {5413, 55567}, {6400, 47328}, {6515, 12222}, {6561, 8968}, {6749, 19053}, {10192, 14239}, {10194, 54892}, {10195, 54893}, {11206, 13748}, {11473, 55566}, {12602, 41588}, {13387, 14121}, {13567, 23251}, {13749, 32064}, {14165, 43508}, {14235, 23332}, {15066, 55411}, {16080, 43566}, {17810, 45862}, {18289, 35831}, {23261, 23292}, {27003, 55461}, {27065, 55430}, {32001, 32814}, {32793, 55393}, {32794, 55394}, {32799, 55458}, {32800, 55459}, {32809, 52710}, {37643, 42284}, {43462, 43507}, {43530, 43567}

X(55573) = anticomplement of X(1589)
X(55573) = polar conjugate of X(3316)
X(55573) = polar conjugate of the isotomic conjugate of X(32805)
X(55573) = polar conjugate of the isogonal conjugate of X(3311)
X(55573) = X(48)-isoconjugate of X(3316)
X(55573) = X(1249)-Dao conjugate of X(3316)
X(55573) = barycentric product X(i)*X(j) for these {i,j}: {4, 32805}, {264, 3311}, {2052, 5406}, {8908, 18027}
X(55573) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 3316}, {3311, 3}, {5406, 394}, {8908, 577}, {32805, 69}
X(55573) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15186, 15190}, {3, 15188, 15192}, {3, 15190, 15194}, {3, 15192, 15196}, {4, 1585, 2}, {4, 3127, 7378}, {4, 3535, 1586}, {4, 6353, 52287}, {4, 8889, 32587}, {4, 52291, 6995}, {5, 1590, 2}, {25, 1599, 15191}, {25, 15198, 1599}, {264, 55473, 1271}, {317, 55474, 1270}, {1583, 1598, 15187}, {1584, 1597, 15189}, {1585, 1586, 3535}, {1586, 3535, 2}, {1592, 11291, 2}, {1593, 1600, 15193}, {1593, 15200, 1600}, {3092, 55412, 1993}, {3518, 15218, 15207}, {5198, 15210, 15199}, {6806, 7389, 2}, {10594, 15214, 15203}, {11403, 15212, 15201}, {14865, 15220, 15209}, {15186, 15188, 3}, {15186, 15192, 15194}, {15188, 15190, 15196}, {15190, 15192, 3}, {15194, 15196, 3}, {15216, 35502, 15205}, {24244, 44637, 193}, {32588, 52286, 4}, {55393, 55429, 32793}, {55394, 55428, 32794}, {55395, 55431, 3219}, {55396, 55460, 3218}, {55411, 55444, 15066}

X(55574) = X(2)X(3)∩X(389)X(14528)

Barycentrics    (2 - 9*Cos[A]^2)*Tan[A] : :
X(55574) = 5 X[3522] - 3 X[45771]

X(55574) lies on these lines: {2, 3}, {389, 14528}, {1192, 11202}, {1204, 14530}, {1495, 13093}, {1614, 43902}, {1620, 6759}, {1986, 38638}, {2207, 15655}, {3092, 6451}, {3093, 6452}, {3426, 8567}, {3532, 6000}, {5410, 6408}, {5411, 6407}, {5412, 6456}, {5413, 6455}, {6496, 11473}, {6497, 11474}, {7689, 8780}, {9908, 12893}, {10282, 37487}, {11430, 41447}, {11432, 44111}, {12164, 32110}, {12292, 38633}, {12315, 21663}, {13148, 32609}, {13754, 51933}, {15448, 20427}, {15471, 37491}, {16879, 33556}, {17845, 44673}, {37486, 43898}

X(55574) = reflection of X(43719) in X(3532)
X(55574) = barycentric product X(25)*X(32876)
X(55574) = barycentric quotient X(32876)/X(305)
X(55574) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 24, 1597}, {3, 3515, 3517}, {3, 9714, 54992}, {3, 10244, 21312}, {3, 10245, 20}, {3, 11484, 14118}, {3, 18535, 3520}, {3, 20850, 12084}, {3, 37922, 9714}, {3, 43809, 16419}, {3, 45735, 11479}, {24, 14865, 25}, {24, 17506, 3516}, {24, 32534, 17506}, {24, 35473, 5198}, {25, 21844, 3}, {140, 550, 6643}, {140, 18420, 1656}, {186, 15750, 3}, {186, 18571, 37933}, {186, 21844, 35479}, {186, 32534, 3515}, {389, 14528, 43908}, {468, 10295, 31726}, {1192, 11202, 19347}, {1593, 35472, 3}, {1656, 1657, 18404}, {1657, 31726, 5073}, {3147, 37931, 382}, {3515, 3516, 24}, {3515, 15750, 32534}, {3515, 32534, 3}, {3516, 17506, 3}, {3522, 3523, 3538}, {3522, 35513, 550}, {3523, 6803, 140}, {6642, 15331, 3}, {6803, 37460, 37458}, {7387, 15646, 3}, {7395, 38438, 3}, {9715, 15078, 3}, {10018, 37196, 3851}, {14865, 35477, 3516}, {21844, 35479, 25}, {32534, 35477, 21844}, {32534, 35479, 35477}, {35243, 43615, 3}, {35471, 37453, 3843}, {35472, 44879, 1593}, {35486, 37460, 18420}, {35503, 37197, 15681}, {38448, 54994, 3}, {42789, 42790, 11541}, {44879, 52294, 24}

X(55575) = X(2)X(3)∩X(6)X(44763)

Barycentrics    (2 + 5*Cos[A]^2)*Tan[A] : :

X(55575) lies on these lines: {2, 3}, {6, 44763}, {64, 11430}, {184, 13093}, {389, 8567}, {578, 10606}, {1181, 35450}, {1204, 11432}, {1351, 7689}, {1968, 5024}, {3092, 6450}, {3093, 6449}, {3199, 53095}, {3357, 11425}, {3426, 6759}, {3527, 11438}, {5023, 33843}, {5050, 11470}, {5410, 6407}, {5411, 6408}, {5412, 6455}, {5413, 6456}, {5422, 43603}, {5925, 18388}, {6221, 11474}, {6398, 11473}, {6411, 35764}, {6412, 35765}, {6445, 10880}, {6446, 10881}, {6696, 26944}, {7592, 34469}, {8537, 44456}, {8778, 43136}, {9683, 43337}, {9786, 11204}, {10110, 37487}, {10605, 11426}, {10982, 21663}, {11202, 15811}, {11381, 14530}, {11402, 43602}, {11424, 44107}, {11440, 12160}, {11472, 12038}, {11475, 42115}, {11476, 42116}, {12007, 44883}, {12017, 12294}, {12133, 15040}, {12290, 26864}, {12301, 19588}, {12315, 19357}, {13367, 32063}, {13403, 40686}, {13474, 17821}, {13630, 53091}, {14581, 22332}, {15041, 15472}, {15579, 32621}, {18916, 43903}, {19124, 33878}, {20427, 23292}, {23328, 39571}, {26869, 43607}, {27371, 44519}, {32210, 39522}, {43691, 43908}

X(55575) = barycentric product X(25)*X(32875)
X(55575) = barycentric quotient X(32875)/X(305)
X(55575) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 382, 16195}, {3, 1593, 1598}, {3, 1597, 3517}, {3, 10244, 38444}, {3, 18535, 3515}, {3, 35501, 4}, {3, 47527, 9909}, {4, 10303, 37942}, {4, 11410, 3}, {4, 35479, 25}, {25, 35477, 3}, {64, 11430, 19347}, {378, 3516, 3}, {378, 3520, 1593}, {378, 11410, 35501}, {378, 35475, 3516}, {378, 35477, 14865}, {550, 3088, 18494}, {1593, 1598, 1597}, {1593, 3516, 3520}, {1593, 3520, 3}, {1593, 11410, 15750}, {1593, 15750, 4}, {2071, 7395, 3}, {3515, 35473, 3}, {3515, 35502, 18535}, {3520, 14865, 21844}, {3520, 21844, 35477}, {3520, 34484, 35473}, {3575, 35485, 15696}, {5094, 18560, 3843}, {7506, 35498, 3}, {7507, 35481, 5073}, {9818, 11250, 3}, {11413, 54994, 3}, {12083, 18364, 3}, {12085, 18570, 3}, {12173, 35491, 15681}, {13596, 32534, 5198}, {14118, 21312, 3}, {14130, 47524, 3}, {14865, 35477, 25}, {18535, 34484, 1598}, {21844, 35479, 15750}, {35472, 44880, 15750}, {35473, 35502, 3515}, {35475, 35478, 378}, {37118, 37197, 5070}, {37119, 44438, 3851}, {42789, 42790, 5067}

X(55576) = X(2)X(3)∩X(74)X(32063)

Barycentrics    7*Cos[A]*Sin[A] - Tan[A] : :
X(55576) = X[4] - 7 X[35486], 2 X[4] - 7 X[37453]

X(55576) lies on these lines: {2, 3}, {74, 32063}, {112, 15655}, {154, 21663}, {159, 5621}, {182, 11405}, {184, 37487}, {185, 1620}, {187, 45141}, {232, 5210}, {1033, 8553}, {1112, 15036}, {1192, 13367}, {1204, 17821}, {1350, 44102}, {1398, 7280}, {1495, 10606}, {1511, 12165}, {1902, 16192}, {1986, 54048}, {2207, 15513}, {3098, 19118}, {3172, 5023}, {3431, 44731}, {5010, 7071}, {5024, 53026}, {5050, 15053}, {5085, 8541}, {5092, 12167}, {5206, 8778}, {5410, 6396}, {5411, 6200}, {5412, 6412}, {5413, 6411}, {6449, 10881}, {6450, 10880}, {6759, 34469}, {8567, 26883}, {8739, 11480}, {8740, 11481}, {8744, 15603}, {9541, 13937}, {9777, 11430}, {9786, 13366}, {10282, 12174}, {10311, 53095}, {10605, 11202}, {10610, 12175}, {10645, 11409}, {10646, 11408}, {10985, 15433}, {11363, 35242}, {11396, 13624}, {11402, 11438}, {11425, 15004}, {11449, 12164}, {11454, 35264}, {11468, 13093}, {12038, 12160}, {12039, 53094}, {12315, 26882}, {13148, 15020}, {13340, 52000}, {14157, 35450}, {15010, 41427}, {15051, 33878}, {16226, 52719}, {18396, 44673}, {19459, 35228}, {23328, 31383}, {32062, 41424}, {32110, 47391}, {34417, 41447}, {34780, 43607}, {34781, 43903}, {36987, 44084}, {37493, 43394}

X(55576) = reflection of X(37453) in X(35486)
X(55576) = isogonal conjugate of X(43699)
X(55576) = X(1)-isoconjugate of X(43699)
X(55576) = X(3)-Dao conjugate of X(43699)
X(55576) = barycentric quotient X(6)/X(43699)
X(55576) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 37196, 18386}, {2, 37931, 37196}, {2, 38446, 3}, {3, 24, 3516}, {3, 25, 11410}, {3, 186, 25}, {3, 1597, 35473}, {3, 1598, 35477}, {3, 1658, 11414}, {3, 3515, 1593}, {3, 3517, 3520}, {3, 6644, 54994}, {3, 7488, 37198}, {3, 9714, 11250}, {3, 9909, 2071}, {3, 14070, 21312}, {3, 15750, 3515}, {3, 16195, 11413}, {3, 32534, 15750}, {3, 35479, 11403}, {3, 47527, 10226}, {4, 186, 44878}, {4, 3542, 44996}, {4, 5054, 52298}, {20, 38282, 10151}, {22, 37941, 3}, {24, 378, 52294}, {24, 1597, 25}, {24, 3516, 5198}, {24, 17506, 3}, {24, 35473, 1597}, {25, 186, 3515}, {25, 1597, 5198}, {25, 3516, 1597}, {25, 11410, 1593}, {25, 15750, 186}, {186, 13596, 44879}, {186, 17506, 35473}, {186, 21844, 35472}, {186, 35472, 3}, {186, 35473, 24}, {186, 37941, 44281}, {186, 44281, 37917}, {186, 44832, 45173}, {376, 468, 44438}, {378, 47485, 18535}, {378, 52294, 1597}, {549, 18533, 5094}, {549, 37934, 18533}, {550, 3147, 37197}, {1596, 34200, 35485}, {1597, 35473, 3516}, {3515, 5198, 24}, {3515, 11410, 25}, {3516, 5198, 1593}, {3516, 35473, 11410}, {3517, 3520, 11403}, {3520, 35479, 3517}, {3524, 37460, 427}, {5004, 5005, 30769}, {6644, 54994, 11284}, {8703, 37935, 4}, {10018, 35503, 382}, {10154, 47114, 20}, {10298, 15078, 3}, {10298, 37952, 15078}, {10605, 11202, 26864}, {12084, 37936, 44454}, {15646, 18324, 3}, {15693, 18494, 37118}, {15750, 17506, 5198}, {15750, 35472, 11410}, {17928, 38448, 3}, {18535, 47485, 25}, {18560, 44962, 4}, {21844, 32534, 3}, {22467, 38438, 3}, {32534, 35472, 186}, {35473, 52294, 378}, {35477, 44879, 1598}, {42789, 42790, 15682}

X(55577) = X(2)X(3)∩X(6)X(8820)

Barycentrics    2 - Cos[A]*Sin[A] : :

X(55577) lies on these lines: {2, 3}, {6, 8820}, {51, 1161}, {154, 45552}, {184, 26341}, {371, 17825}, {372, 17811}, {394, 3312}, {487, 18928}, {590, 8943}, {615, 8573}, {999, 3084}, {1160, 3917}, {1609, 8252}, {1993, 6418}, {1994, 6501}, {3083, 3295}, {3167, 45410}, {3311, 5409}, {3819, 9733}, {3964, 32806}, {4254, 31473}, {5024, 8962}, {5406, 6450}, {5407, 6221}, {5408, 6398}, {5413, 55443}, {5414, 55442}, {5422, 6417}, {5544, 45579}, {5591, 19006}, {5646, 45498}, {5651, 10133}, {5943, 9732}, {6199, 55566}, {6347, 9708}, {6348, 9709}, {6395, 15066}, {6420, 37672}, {6500, 34545}, {6502, 55441}, {6688, 9738}, {8400, 32575}, {8416, 8577}, {8855, 39648}, {8903, 45429}, {8904, 31521}, {8939, 32789}, {9306, 43118}, {9723, 32813}, {9777, 11916}, {10132, 26348}, {10219, 43144}, {11091, 37648}, {11474, 55444}, {11824, 17810}, {13889, 45473}, {17809, 45550}, {18997, 21640}, {25893, 31546}, {34417, 35246}

X(55577) = complement of X(6806)
X(55577) = orthocentroidal-circle-inverse of X(15235)
X(55577) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 15235}, {2, 20, 3540}, {2, 1584, 3}, {2, 1586, 11314}, {2, 1591, 1656}, {2, 1600, 1583}, {2, 3539, 15236}, {2, 6805, 5}, {1583, 1584, 1600}, {1583, 1600, 3}, {1585, 15201, 1597}, {1586, 15200, 1598}, {3156, 7484, 3}, {3535, 15217, 1593}, {3536, 15216, 25}, {5409, 10601, 3311}, {10132, 43650, 26348}, {15199, 15204, 3517}, {15212, 15213, 4}, {15214, 15221, 3516}, {15215, 15220, 3515}

X(55578) = X(2)X(3)∩X(51)X(17821)

Barycentrics    5*Cos[A]*Sin[A] - 3*Tan[A] : :

X(55578) lies on these lines: {2, 3}, {51, 17821}, {61, 11409}, {62, 11408}, {64, 43691}, {389, 26864}, {575, 12167}, {576, 19118}, {1112, 15034}, {1173, 11426}, {1181, 50414}, {1192, 26883}, {1350, 44091}, {1351, 19122}, {1493, 12175}, {1495, 9786}, {1498, 44082}, {1620, 22334}, {1843, 53093}, {1974, 11477}, {2207, 35007}, {3092, 6453}, {3093, 6454}, {3167, 15801}, {3172, 22331}, {3199, 8778}, {3303, 52427}, {3527, 38848}, {3592, 5413}, {3594, 5412}, {3746, 11399}, {5007, 45141}, {5013, 10985}, {5093, 9545}, {5410, 6420}, {5411, 6419}, {5563, 11398}, {5609, 12165}, {5640, 11576}, {5889, 8780}, {5890, 14530}, {6090, 17834}, {6152, 13321}, {6403, 11482}, {6427, 10880}, {6428, 10881}, {7071, 54428}, {7713, 30389}, {7716, 10541}, {7786, 22480}, {7982, 11363}, {8192, 13607}, {8276, 35815}, {8277, 35814}, {8567, 32062}, {9590, 11365}, {9707, 11423}, {9777, 19357}, {9815, 13394}, {9833, 26869}, {10282, 11402}, {10641, 22238}, {10642, 22236}, {10982, 11202}, {10986, 30435}, {11381, 37487}, {11387, 15024}, {11388, 45502}, {11389, 45503}, {11396, 15178}, {11405, 22234}, {11424, 52518}, {11425, 34417}, {11438, 12174}, {12007, 15582}, {12017, 15028}, {12024, 34782}, {12133, 15021}, {12140, 15027}, {12160, 41597}, {12164, 35264}, {13367, 17810}, {15083, 37489}, {15473, 38795}, {15811, 21663}, {16035, 51877}, {16835, 35450}, {19128, 53092}, {19347, 26882}, {26377, 34486}, {35259, 46730}, {37486, 43586}, {38729, 46682}, {44102, 53858}

X(55578) = X(54867)-Ceva conjugate of X(6)
X(55578) = barycentric product X(25)*X(32835)
X(55578) = barycentric quotient X(32835)/X(305)
X(55578) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 25, 5198}, {3, 1597, 35475}, {3, 1598, 35502}, {3, 3517, 3518}, {3, 3518, 25}, {3, 5198, 1593}, {3, 9714, 17714}, {3, 10594, 11403}, {3, 17714, 11414}, {3, 35479, 15750}, {3, 35502, 3516}, {4, 11410, 1593}, {4, 15750, 11410}, {4, 35479, 3}, {4, 44880, 35472}, {4, 44957, 37197}, {24, 25, 3515}, {24, 3517, 25}, {24, 3518, 3}, {24, 10594, 44879}, {24, 47485, 3517}, {25, 3515, 1593}, {25, 3516, 1598}, {25, 11403, 10594}, {25, 15750, 4}, {140, 37122, 5064}, {186, 1598, 3516}, {186, 35502, 3}, {468, 7487, 7507}, {1192, 41424, 26883}, {1598, 35501, 4}, {1658, 7529, 54994}, {2070, 6642, 9715}, {3147, 6756, 5094}, {3515, 5198, 3}, {3515, 11410, 15750}, {3518, 37953, 7487}, {3518, 44879, 10594}, {3523, 7714, 1907}, {3542, 37458, 12173}, {6642, 9715, 7484}, {6644, 9714, 11414}, {6644, 17714, 3}, {7487, 30734, 5198}, {7502, 13154, 3}, {7506, 14070, 7395}, {7575, 13861, 3}, {7715, 37935, 3541}, {9909, 17928, 37198}, {10323, 37939, 10244}, {10594, 11403, 5198}, {10594, 44879, 3}, {13595, 38444, 11479}, {18533, 21841, 37197}, {32534, 34484, 1597}, {32534, 35475, 3}, {45735, 51519, 7387}, {47485, 47486, 24}

X(55579) = X(2)X(3)∩X(6)X(8821)

Barycentrics    2 + Cos[A]*Sin[A] : :

X(55579) lies on these lines: {2, 3}, {6, 8821}, {51, 1160}, {154, 45553}, {184, 26348}, {371, 17811}, {372, 17825}, {394, 3311}, {488, 18928}, {590, 8573}, {615, 8939}, {999, 3083}, {1161, 3917}, {1609, 8253}, {1993, 6417}, {1994, 6500}, {2066, 55441}, {2067, 55442}, {3084, 3295}, {3167, 45411}, {3312, 5408}, {3819, 9732}, {3964, 32805}, {5120, 31473}, {5406, 6398}, {5407, 6449}, {5409, 6221}, {5412, 55444}, {5422, 6418}, {5544, 45578}, {5590, 19005}, {5646, 45499}, {5651, 10132}, {5943, 9733}, {6199, 15066}, {6347, 9709}, {6348, 9708}, {6395, 55567}, {6419, 37672}, {6501, 34545}, {6688, 9739}, {8225, 25893}, {8396, 8576}, {8407, 32568}, {8854, 39679}, {8903, 31521}, {8904, 45428}, {8943, 32790}, {8962, 9605}, {8968, 13889}, {9306, 43119}, {9723, 32812}, {9777, 11917}, {10133, 26341}, {10219, 43141}, {11090, 37648}, {11473, 55443}, {11825, 17810}, {13943, 45472}, {17809, 45551}, {18998, 21641}, {31474, 55409}, {34417, 35247}, {44193, 55471}

X(55579) = complement of X(6805)
X(55579) = orthocentroidal-circle-inverse of X(15236)
X(55579) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 15236}, {2, 20, 3539}, {2, 1583, 3}, {2, 1585, 11313}, {2, 1592, 1656}, {2, 1599, 1584}, {2, 3540, 15235}, {2, 6806, 5}, {1583, 1584, 1599}, {1584, 1599, 3}, {1585, 15199, 1598}, {1586, 15198, 1597}, {3155, 7484, 3}, {3535, 15215, 25}, {3536, 15214, 1593}, {5408, 10601, 3312}, {10133, 43650, 26341}, {15200, 15203, 3517}, {15210, 15211, 4}, {15216, 15219, 3515}, {15217, 15218, 3516}

X(55580) = X(3)X(6)∩X(23)X(8780)

Barycentrics    a^2*(a^4-13*b^4-2*b^2*c^2-13*c^4+12*a^2*(b^2+c^2)) : :
X(55580) = -7*X[3]+6*X[6], -X[4]+3*X[54174], -16*X[5]+15*X[50963], -5*X[20]+3*X[50974], -3*X[69]+2*X[3627], -4*X[140]+3*X[54132], -12*X[141]+11*X[5072], -3*X[193]+5*X[17538], -7*X[381]+8*X[50991], -2*X[382]+3*X[50955], -4*X[546]+3*X[51212], -4*X[548]+3*X[1992] and many others

X(55580) lies on these lines: {3, 6}, {4, 54174}, {5, 50963}, {20, 50974}, {22, 9716}, {23, 8780}, {30, 50992}, {69, 3627}, {140, 54132}, {141, 5072}, {193, 17538}, {381, 50991}, {382, 50955}, {524, 1657}, {542, 17800}, {546, 51212}, {548, 1992}, {550, 54170}, {599, 3843}, {631, 14848}, {632, 14853}, {895, 44763}, {1352, 5076}, {1353, 44245}, {1503, 49137}, {1656, 54173}, {2393, 13093}, {2781, 12315}, {2979, 11284}, {3090, 21850}, {3091, 48876}, {3146, 18440}, {3167, 23061}, {3292, 9909}, {3526, 20423}, {3528, 50979}, {3529, 3564}, {3618, 12108}, {3619, 12812}, {3628, 10519}, {3830, 34507}, {3850, 21356}, {3851, 40107}, {3853, 50978}, {3857, 40330}, {5032, 21735}, {5070, 50977}, {5073, 15069}, {5079, 5480}, {5446, 33540}, {5476, 46219}, {5544, 11002}, {5609, 7387}, {5643, 21766}, {5921, 11541}, {5943, 14924}, {5965, 48872}, {6144, 48898}, {6391, 13452}, {6403, 11403}, {6776, 12103}, {7484, 12834}, {7496, 9777}, {7776, 51438}, {8537, 11410}, {8550, 15696}, {8584, 14093}, {9019, 33541}, {9925, 12082}, {9968, 32063}, {9970, 15039}, {9972, 12307}, {10303, 18583}, {10606, 34788}, {11160, 33703}, {11405, 35477}, {11645, 49139}, {11898, 29181}, {12167, 14865}, {12282, 14984}, {14530, 15582}, {14893, 50990}, {15022, 38136}, {15034, 45016}, {15533, 15684}, {15534, 15689}, {15579, 34777}, {15693, 41153}, {15704, 34380}, {15718, 51185}, {15720, 54169}, {15722, 46267}, {16419, 21969}, {16475, 31666}, {18358, 50689}, {18404, 47558}, {18553, 51024}, {19118, 35479}, {20080, 49140}, {20582, 51173}, {21734, 50966}, {22165, 38335}, {23046, 50994}, {25556, 38638}, {29317, 40341}, {32135, 38635}, {32284, 36987}, {35001, 35450}, {37669, 47316}, {38064, 50970}, {39899, 48873}, {44246, 47546}, {45760, 50981}, {48906, 50693}, {49134, 50973}, {49138, 51179}, {50692, 50985}

X(55580) = reflection of X(i) in X(j) for these {i,j}: {193, 48874}, {1351, 33878}, {11477, 52987}, {15684, 15533}, {3, 53097}, {39899, 48873}, {44456, 1350}, {48662, 40341}, {5073, 15069}, {6144, 48898}
X(55580) = center of Tucker-Hagos(-12) circle
X(55580) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(187), X(44763)}}, {{A, B, C, X(3053), X(13452)}}, {{A, B, C, X(14489), X(53093)}}, {{A, B, C, X(40801), X(53092)}}
X(55580) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 11482}, {3, 1351, 53092}, {3, 5093, 53093}, {3, 53091, 20190}, {3, 53092, 12017}, {3, 53097, 33878}, {511, 1350, 44456}, {511, 52987, 11477}, {1350, 11477, 10541}, {1350, 44456, 5050}, {5050, 33878, 1350}, {5864, 5865, 5171}, {9821, 40268, 10983}, {10541, 11477, 576}, {11173, 44453, 9605}, {11477, 11482, 1351}, {11477, 52987, 3}, {11477, 53097, 52987}, {12313, 12314, 2080}, {15069, 19924, 5073}, {15696, 50962, 8550}, {20190, 37517, 53858}, {20190, 53858, 53091}, {29317, 40341, 48662}, {40107, 54131, 3851}

X(55581) = X(3)X(6)∩X(69)X(46851)

Barycentrics    a^6+11*a^4*(b^2+c^2)-2*a^2*(6*b^4+b^2*c^2+6*c^4) : :
X(55581) = -13*X[3]+11*X[6], -11*X[1352]+9*X[50687], -3*X[1992]+4*X[33751], -51*X[3854]+55*X[40330], -11*X[5476]+12*X[47598], -11*X[5480]+12*X[10109], -33*X[10519]+29*X[46935], -11*X[11178]+10*X[41099], -10*X[14893]+11*X[47354], -2*X[24206]+3*X[50967], -4*X[25565]+5*X[54173], -9*X[33699]+11*X[39884] and many others

X(55581) lies on these lines: {3, 6}, {69, 46851}, {524, 44903}, {1352, 50687}, {1992, 33751}, {2979, 16187}, {3854, 40330}, {5476, 47598}, {5480, 10109}, {5921, 29317}, {5965, 14927}, {10519, 46935}, {11178, 41099}, {11645, 51175}, {14893, 47354}, {19924, 51023}, {21766, 21969}, {24206, 50967}, {25565, 54173}, {33699, 39884}, {34507, 51163}, {38071, 48876}, {44882, 51140}, {46333, 48873}, {48662, 50973}, {48884, 50691}, {48885, 54170}, {48942, 50955}, {50978, 51165}, {51028, 51141}

X(55581) = reflection of X(i) in X(j) for these {i,j}: {3098, 53097}, {37517, 52987}, {576, 33878}
X(55581) = center of Tucker-Hagos(-11) circle
X(55581) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(46851)}}, {{A, B, C, X(20190), X(40803)}}
X(55581) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 1351, 15520}, {511, 33878, 576}, {511, 52987, 37517}, {576, 3098, 5085}, {1350, 53091, 14810}, {1351, 3098, 182}, {5085, 53097, 33878}, {15520, 52987, 3098}, {33878, 53091, 1350}

X(55582) = X(3)X(6)∩X(4)X(3631)

Barycentrics    a^2*(a^4-11*b^4-2*b^2*c^2-11*c^4+10*a^2*(b^2+c^2)) : :
X(55582) = -6*X[3]+5*X[6], -3*X[4]+4*X[3631], -3*X[20]+X[11008], -5*X[69]+3*X[3543], -10*X[141]+9*X[3545], -2*X[193]+3*X[43273], -3*X[376]+2*X[3629], -24*X[547]+25*X[3763], -10*X[597]+11*X[15719], -5*X[599]+4*X[3845], -5*X[1352]+4*X[3853], -15*X[1656]+14*X[42785] and many others

X(55582) lies on these lines: {2, 54521}, {3, 6}, {4, 3631}, {20, 11008}, {30, 40341}, {64, 44668}, {69, 3543}, {141, 3545}, {154, 323}, {193, 43273}, {376, 3629}, {394, 15107}, {524, 11001}, {547, 3763}, {597, 15719}, {599, 3845}, {1154, 35237}, {1352, 3853}, {1503, 5059}, {1656, 42785}, {1657, 5965}, {2071, 43713}, {2781, 9924}, {2979, 10545}, {3060, 5888}, {3066, 33884}, {3242, 11278}, {3522, 12007}, {3524, 6329}, {3533, 14853}, {3564, 48872}, {3589, 15702}, {3618, 15708}, {3619, 5056}, {3620, 3832}, {3630, 15069}, {3796, 11004}, {3818, 38335}, {3830, 43150}, {3839, 50982}, {3850, 48876}, {5067, 10519}, {5476, 15723}, {5640, 5646}, {5645, 7496}, {6144, 15686}, {8705, 11738}, {10304, 51132}, {10601, 41462}, {10606, 34777}, {11179, 50968}, {11180, 51025}, {11531, 16496}, {11539, 20423}, {11812, 47352}, {11898, 29317}, {12087, 15580}, {12121, 16176}, {12220, 41468}, {13192, 33979}, {13421, 15805}, {13595, 15066}, {13620, 35228}, {13754, 33534}, {14483, 34817}, {14561, 16239}, {15080, 17809}, {15271, 33706}, {15533, 18440}, {15534, 15690}, {15689, 51140}, {15710, 51138}, {16200, 49465}, {16491, 30392}, {16981, 21766}, {17811, 34417}, {17813, 44883}, {17825, 21969}, {18325, 47445}, {19130, 21358}, {19708, 20583}, {19711, 51185}, {20806, 37940}, {25331, 34153}, {26864, 37672}, {32366, 36987}, {32455, 50965}, {33533, 44413}, {33537, 45186}, {34380, 48873}, {34778, 37944}, {35478, 39588}, {36990, 43621}, {39899, 48880}, {41982, 50979}, {42815, 54140}, {42816, 54141}, {46333, 51178}, {47452, 47468}, {48884, 50955}, {48891, 51187}, {49505, 51120}, {50630, 53089}, {50962, 50976}

X(55582) = reflection of X(i) in X(j) for these {i,j}: {193, 48881}, {1350, 53097}, {1351, 52987}, {11477, 1350}, {16176, 12121}, {39899, 48880}, {43273, 54170}, {44439, 10625}, {44456, 3098}, {48910, 69}, {51028, 54169}, {54131, 50967}, {6, 33878}, {6144, 46264}, {55580, 55581}
X(55582) = isogonal conjugate of X(54866)
X(55582) = center of Tucker-Hagos(-10) circle
X(55582) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(14490)}}, {{A, B, C, X(64), X(35007)}}, {{A, B, C, X(1384), X(11738)}}, {{A, B, C, X(5206), X(43713)}}, {{A, B, C, X(14483), X(30435)}}, {{A, B, C, X(14528), X(53096)}}, {{A, B, C, X(39561), X(40801)}}
X(55582) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 39561}, {6, 31884, 5092}, {6, 37517, 5102}, {6, 53097, 33878}, {69, 48910, 47353}, {193, 48881, 43273}, {193, 54170, 48881}, {394, 15107, 41424}, {511, 10625, 44439}, {511, 1350, 11477}, {511, 3098, 44456}, {511, 52987, 1351}, {511, 55581, 55580}, {1350, 11477, 5085}, {1350, 5102, 3}, {1350, 53093, 31884}, {1351, 31884, 53093}, {1351, 5092, 6}, {3098, 37517, 50664}, {3545, 51166, 54131}, {3763, 21850, 38072}, {5093, 14810, 10541}, {15066, 33586, 31860}, {17834, 37483, 37487}, {21850, 54173, 3763}, {31884, 52987, 1350}, {33878, 44456, 3098}

X(55583) = X(3)X(6)∩X(4)X(50990)

Barycentrics    a^6+9*a^4*(b^2+c^2)-2*a^2*(5*b^4+b^2*c^2+5*c^4) : :
X(55583) = -11*X[3]+9*X[6], -11*X[4]+15*X[50990], -11*X[5]+12*X[51143], -9*X[141]+8*X[12811], -X[193]+2*X[48885], -8*X[546]+9*X[11178], -10*X[632]+9*X[5476], -9*X[1352]+7*X[50688], -7*X[3090]+9*X[54173], -5*X[3091]+6*X[40107], -5*X[3146]+9*X[11180], -5*X[3522]+4*X[33749] and many others

X(55583) lies on these lines: {3, 6}, {4, 50990}, {5, 51143}, {69, 46848}, {141, 12811}, {193, 48885}, {524, 15704}, {542, 3529}, {546, 11178}, {632, 5476}, {1092, 37953}, {1352, 50688}, {2979, 16042}, {3090, 54173}, {3091, 40107}, {3146, 11180}, {3522, 33749}, {3525, 20423}, {3544, 24206}, {3564, 48879}, {3627, 34507}, {3628, 50977}, {3818, 12102}, {3853, 22165}, {3857, 48876}, {3858, 50991}, {5072, 54131}, {5073, 15533}, {5076, 18553}, {5095, 35503}, {5480, 12812}, {5643, 16981}, {5965, 48896}, {7946, 50639}, {8541, 35475}, {8550, 44245}, {8584, 33923}, {9544, 23061}, {9716, 35268}, {10303, 25555}, {10519, 46936}, {11412, 37946}, {11470, 44879}, {11541, 29317}, {11645, 49137}, {12103, 51136}, {12108, 54169}, {12584, 17714}, {14831, 41463}, {14848, 51141}, {14869, 50984}, {14984, 38626}, {15020, 25556}, {15022, 19130}, {15069, 49136}, {15534, 15696}, {15582, 34779}, {17538, 54170}, {18800, 33254}, {21969, 40916}, {29012, 49140}, {29323, 40341}, {31670, 50689}, {32273, 37444}, {34380, 48880}, {35403, 51189}, {39899, 48920}, {49138, 50992}, {50693, 50975}, {50970, 50988}

X(55583) = midpoint of X(i) and X(j) for these {i,j}: {53097, 55580}
X(55583) = reflection of X(i) in X(j) for these {i,j}: {182, 33878}, {193, 48885}, {37517, 1350}, {39899, 48920}, {44456, 14810}, {48904, 69}, {576, 52987}, {52987, 53097}, {55581, 55582}
X(55583) = center of Tucker-Hagos(-9) circle
X(55583) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(46848)}}, {{A, B, C, X(1173), X(14075)}}
X(55583) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 22330}, {3, 22330, 182}, {61, 62, 14075}, {182, 11477, 576}, {182, 37517, 5093}, {511, 1350, 37517}, {511, 14810, 44456}, {511, 53097, 52987}, {511, 55582, 55581}, {576, 17508, 575}, {1350, 17508, 3098}, {1350, 37517, 17508}, {5093, 33878, 1350}, {6419, 6420, 34571}, {11477, 31884, 53092}, {11477, 53097, 33878}, {14810, 44456, 15520}, {53097, 55580, 511}, {53097, 55582, 55580}

X(55584) = X(3)X(6)∩X(69)X(382)

Barycentrics    a^2*(a^4-9*b^4-2*b^2*c^2-9*c^4+8*a^2*(b^2+c^2)) : :
X(55584) = -5*X[3]+4*X[6], -8*X[141]+7*X[3851], -3*X[376]+2*X[1353], -5*X[381]+6*X[21356], -4*X[546]+5*X[3620], -8*X[547]+7*X[51173], -4*X[548]+3*X[14912], -8*X[597]+9*X[15707], -4*X[599]+3*X[14269], -2*X[895]+3*X[15041], -4*X[1352]+3*X[3830], -5*X[1656]+6*X[10519] and many others

X(55584) lies on these lines: {3, 6}, {20, 34380}, {30, 5921}, {51, 5544}, {69, 382}, {110, 9909}, {141, 3851}, {193, 550}, {376, 1353}, {381, 21356}, {394, 20850}, {524, 15681}, {542, 15685}, {546, 3620}, {547, 51173}, {548, 14912}, {549, 51028}, {597, 15707}, {599, 14269}, {895, 15041}, {1352, 3830}, {1469, 6767}, {1503, 17800}, {1597, 6403}, {1598, 6101}, {1656, 10519}, {1657, 3564}, {1992, 15688}, {1993, 6030}, {2104, 28448}, {2105, 28447}, {2781, 12308}, {2979, 5020}, {3056, 7373}, {3060, 16419}, {3066, 3917}, {3167, 44110}, {3524, 51732}, {3526, 14853}, {3528, 51170}, {3529, 20080}, {3530, 51171}, {3531, 14926}, {3534, 6776}, {3543, 50978}, {3618, 15720}, {3619, 5079}, {3843, 31670}, {5026, 38635}, {5032, 34200}, {5054, 18583}, {5055, 5480}, {5070, 51128}, {5073, 18440}, {5095, 38723}, {5181, 38789}, {5477, 38731}, {5644, 7484}, {5646, 5943}, {5651, 33586}, {5965, 48905}, {6090, 15107}, {6391, 12163}, {6593, 38638}, {7776, 51374}, {8547, 53019}, {8705, 33887}, {8780, 32237}, {9924, 12315}, {10168, 15722}, {10245, 22115}, {10602, 32608}, {10620, 14984}, {10752, 32609}, {11179, 15695}, {11216, 15578}, {11270, 38263}, {11284, 33884}, {11410, 41398}, {11412, 39568}, {11645, 50973}, {11737, 51184}, {11799, 47447}, {11820, 13754}, {12007, 50965}, {12041, 39562}, {12272, 16835}, {12294, 18535}, {12310, 32235}, {14093, 50979}, {14530, 34779}, {14532, 32515}, {14561, 46219}, {14645, 38741}, {14848, 15701}, {14994, 48663}, {15069, 29317}, {15683, 51179}, {15684, 19924}, {15686, 50974}, {15687, 50954}, {15689, 44882}, {15691, 50986}, {15694, 20423}, {15696, 48906}, {15700, 51172}, {15703, 50977}, {15704, 39874}, {15715, 50987}, {15718, 50970}, {15988, 17571}, {16187, 17810}, {16981, 40916}, {18325, 47446}, {18358, 51538}, {18534, 41716}, {19149, 50461}, {19154, 43574}, {19588, 52100}, {19709, 24206}, {21358, 50963}, {21735, 33748}, {21968, 53857}, {21969, 22112}, {23061, 26864}, {26516, 43413}, {26521, 43414}, {28343, 38639}, {29012, 40341}, {32217, 37922}, {33851, 45016}, {34507, 48910}, {34788, 52028}, {35403, 48889}, {37944, 41428}, {38335, 51537}, {38636, 51157}, {38743, 50567}, {38755, 51007}, {40107, 53023}, {43273, 48885}, {43576, 54992}, {44668, 54202}, {46475, 46845}, {47353, 48904}, {47451, 47468}

X(55584) = midpoint of X(i) and X(j) for these {i,j}: {15683, 51179}, {3529, 20080}, {33878, 55580}, {53097, 55582}
X(55584) = reflection of X(i) in X(j) for these {i,j}: {193, 550}, {1351, 1350}, {11477, 3098}, {12315, 9924}, {15684, 50955}, {18438, 10625}, {3, 33878}, {381, 50967}, {382, 69}, {3534, 54170}, {3543, 50978}, {33878, 53097}, {39874, 15704}, {39899, 20}, {44456, 3}, {48662, 11898}, {48910, 34507}, {5073, 18440}, {50962, 376}, {50974, 15686}, {50986, 15691}, {51028, 549}, {51212, 48876}, {6, 52987}, {6243, 37511}, {6391, 12163}, {6776, 48874}, {55580, 55582}, {55582, 55583}
X(55584) = inverse of X(18860) in Stammler Circle
X(55584) = center of Tucker-Hagos(-8) circle
X(55584) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1297), X(44456)}}, {{A, B, C, X(3053), X(43719)}}, {{A, B, C, X(3531), X(5008)}}, {{A, B, C, X(5023), X(11270)}}, {{A, B, C, X(5085), X(40803)}}, {{A, B, C, X(14810), X(40802)}}, {{A, B, C, X(16835), X(22331)}}, {{A, B, C, X(40801), X(53091)}}
X(55584) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 53091}, {3, 511, 44456}, {6, 1350, 14810}, {20, 34380, 39899}, {30, 11898, 48662}, {511, 10625, 18438}, {511, 3098, 11477}, {511, 37511, 6243}, {511, 53097, 33878}, {511, 55582, 55580}, {511, 55583, 55582}, {576, 31884, 12017}, {1350, 11477, 53094}, {1350, 53094, 3098}, {1351, 33878, 1350}, {1351, 53091, 5093}, {3098, 11477, 5050}, {3619, 38136, 5079}, {5032, 50966, 34200}, {5085, 37517, 11482}, {5092, 5102, 53092}, {5097, 14810, 20190}, {6449, 6450, 5206}, {6776, 48874, 3534}, {6776, 54170, 48874}, {10519, 21850, 1656}, {11477, 53094, 5097}, {11485, 11486, 5008}, {11824, 12314, 3}, {18440, 29181, 5073}, {19924, 50955, 15684}, {33878, 55580, 511}, {38596, 38597, 18860}, {44456, 53091, 1351}, {48876, 51212, 381}, {50967, 51212, 48876}

X(55585) = X(3)X(6)∩X(30)X(3630)

Barycentrics    a^6+7*a^4*(b^2+c^2)-2*a^2*(4*b^4+b^2*c^2+4*c^4) : :
X(55585) = -9*X[3]+7*X[6], -7*X[141]+6*X[5066], -7*X[193]+15*X[15697], -7*X[597]+8*X[44580], -3*X[599]+2*X[48895], -7*X[1352]+5*X[17578], -3*X[3534]+X[6144], -14*X[3589]+15*X[15713], -49*X[3619]+45*X[5071], -35*X[3620]+27*X[3839], -4*X[3631]+3*X[3818], -11*X[3855]+14*X[40107] and many others

X(55585) lies on these lines: {2, 54734}, {3, 6}, {30, 3630}, {69, 13603}, {141, 5066}, {193, 15697}, {323, 26881}, {524, 19710}, {542, 15683}, {597, 44580}, {599, 48895}, {1352, 17578}, {2979, 34417}, {3056, 37602}, {3534, 6144}, {3564, 48896}, {3589, 15713}, {3619, 5071}, {3620, 3839}, {3631, 3818}, {3855, 40107}, {3858, 48876}, {3861, 18358}, {4550, 13391}, {5068, 24206}, {5476, 10124}, {5480, 35018}, {5651, 48912}, {5888, 11002}, {5965, 39874}, {7485, 44107}, {7486, 10519}, {7712, 23061}, {8703, 32455}, {9037, 41454}, {9306, 15107}, {10110, 33540}, {10168, 51028}, {10545, 16187}, {11008, 46264}, {11179, 50969}, {11412, 12112}, {11470, 44880}, {11645, 40341}, {11898, 29323}, {12834, 41462}, {13102, 42901}, {13103, 42900}, {14491, 41435}, {14912, 33751}, {15691, 48881}, {15699, 21850}, {15709, 20423}, {15721, 54132}, {16981, 22112}, {19140, 20773}, {20425, 42895}, {20426, 42894}, {29012, 49138}, {29317, 49135}, {34380, 48898}, {34507, 48904}, {39899, 48891}, {43150, 48910}, {47353, 48943}, {48906, 50971}, {50970, 51137}, {51141, 54169}

X(55585) = midpoint of X(i) and X(j) for these {i,j}: {1350, 55580}, {33878, 55582}, {52987, 55581}, {53097, 55584}
X(55585) = reflection of X(i) in X(j) for these {i,j}: {182, 52987}, {193, 48892}, {11178, 50967}, {11477, 14810}, {3098, 33878}, {37517, 3098}, {39899, 48891}, {44456, 5092}, {48884, 69}, {48904, 34507}, {48910, 43150}, {576, 1350}, {51028, 10168}, {51212, 40107}, {55581, 55583}, {55583, 55584}
X(55585) = isogonal conjugate of X(54851)
X(55585) = center of Tucker-Hagos(-7) circle
X(55585) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(13603)}}, {{A, B, C, X(3431), X(31652)}}, {{A, B, C, X(5007), X(14491)}}, {{A, B, C, X(15513), X(20421)}}
X(55585) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 19924, 48884}, {511, 14810, 11477}, {511, 3098, 37517}, {511, 55583, 55581}, {511, 55584, 55583}, {576, 15516, 15520}, {576, 55583, 55580}, {1350, 44456, 5092}, {1350, 5092, 3098}, {1350, 55580, 511}, {1351, 17508, 22234}, {3098, 33878, 52987}, {5092, 44456, 576}, {5092, 50664, 10541}, {6200, 6396, 15513}, {11477, 14810, 39561}, {17508, 22234, 182}, {21850, 34573, 42785}, {33878, 44456, 1350}, {33878, 55580, 44456}, {33878, 55584, 55582}, {42115, 42116, 15603}, {42785, 50977, 34573}, {53097, 55582, 33878}

X(55586) = X(3)X(6)∩X(51)X(5888)

Barycentrics    a^2*(2*a^4-13*b^4-4*b^2*c^2-13*c^4+11*a^2*(b^2+c^2)) : :
X(55586) = -15*X[3]+11*X[6], -11*X[141]+9*X[38071], -7*X[193]+15*X[50975], -5*X[3620]+3*X[48901], -4*X[3631]+3*X[18553], -11*X[3818]+9*X[50687], -8*X[3856]+11*X[40107], -12*X[10109]+11*X[19130], -9*X[10519]+7*X[42786], -9*X[14893]+11*X[18358], X[20080]+3*X[48873], -6*X[21356]+5*X[25561] and many others

X(55586) lies on circumconic {{A, B, C, X(5008), X(14487)}} and on these lines: {3, 6}, {51, 5888}, {141, 38071}, {193, 50975}, {323, 44110}, {524, 48891}, {542, 44903}, {2979, 44106}, {3620, 48901}, {3630, 29012}, {3631, 18553}, {3818, 50687}, {3856, 40107}, {3917, 10545}, {5965, 48920}, {6030, 34986}, {10109, 19130}, {10168, 50970}, {10519, 42786}, {11160, 11645}, {14531, 43612}, {14893, 18358}, {19924, 22165}, {20080, 48873}, {21356, 25561}, {21850, 51128}, {21969, 41462}, {34507, 43621}, {35434, 48910}, {39874, 46333}, {40341, 48879}, {42785, 46935}, {46264, 54174}, {47598, 51127}, {48881, 51136}, {48905, 51188}

X(55586) = midpoint of X(i) and X(j) for these {i,j}: {182, 55580}, {1350, 55583}, {3, 55581}, {3098, 55582}, {33878, 55585}, {40341, 48879}, {52987, 55584}
X(55586) = reflection of X(i) in X(j) for these {i,j}: {10168, 50970}, {14810, 52987}, {44456, 50664}, {48942, 34507}, {48943, 43150}, {575, 1350}
X(55586) = center of Tucker-Hagos(-11/2) circle
X(55586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14810, 5092}, {6, 33878, 52987}, {511, 1350, 575}, {511, 50664, 44456}, {511, 52987, 14810}, {575, 14810, 17508}, {1350, 12017, 3098}, {1350, 55583, 511}, {3098, 37517, 12017}, {3098, 44456, 50664}, {3098, 55585, 55582}, {17508, 37517, 6}, {17508, 52987, 1350}, {19924, 43150, 48943}, {33878, 53097, 55585}, {37517, 55585, 55583}

X(55587) = X(3)X(6)∩X(20)X(5965)

Barycentrics    a^6+5*a^4*(b^2+c^2)-2*a^2*(3*b^4+b^2*c^2+3*c^4) : :
X(55587) = -7*X[3]+5*X[6], -5*X[141]+4*X[3850], -6*X[547]+5*X[5480], -5*X[597]+6*X[41983], -5*X[599]+3*X[38335], -5*X[1352]+3*X[3543], -5*X[1386]+6*X[31662], -17*X[3533]+15*X[14561], -9*X[3545]+10*X[24206], -8*X[3628]+7*X[42785], -5*X[3818]+4*X[3853], -7*X[3832]+5*X[31670] and many others

X(55587) lies on these lines: {3, 6}, {4, 32027}, {20, 5965}, {22, 44108}, {51, 21766}, {69, 29317}, {110, 37913}, {141, 3850}, {376, 51140}, {382, 43150}, {394, 32237}, {524, 15686}, {542, 11001}, {547, 5480}, {548, 3629}, {549, 50970}, {597, 41983}, {599, 38335}, {621, 51020}, {622, 51021}, {1154, 8717}, {1293, 28551}, {1352, 3543}, {1386, 31662}, {1503, 48879}, {1657, 40341}, {2781, 15580}, {2979, 5651}, {3060, 22112}, {3066, 3819}, {3357, 44668}, {3533, 14561}, {3545, 24206}, {3564, 48880}, {3627, 3631}, {3628, 42785}, {3818, 3853}, {3832, 31670}, {3845, 11178}, {3917, 16187}, {5056, 10519}, {5059, 5921}, {5476, 11539}, {5646, 6688}, {6101, 46261}, {6329, 15712}, {6403, 13596}, {6771, 49862}, {6774, 49861}, {6776, 48885}, {7916, 40278}, {8550, 41981}, {8584, 46332}, {8703, 12007}, {10168, 15719}, {10250, 15578}, {11003, 55038}, {11008, 17538}, {11179, 33751}, {11645, 11898}, {11649, 37944}, {11812, 18583}, {15069, 29323}, {15533, 48662}, {15681, 50973}, {15683, 50961}, {15687, 50982}, {15690, 44882}, {15691, 51136}, {15702, 20423}, {15708, 54132}, {15714, 51138}, {16163, 41731}, {16239, 38317}, {16981, 41462}, {18440, 49133}, {18553, 48910}, {19124, 35478}, {19711, 41153}, {20583, 45759}, {23061, 35268}, {29181, 34507}, {32271, 38792}, {33884, 34417}, {34200, 51132}, {34380, 48881}, {34788, 44883}, {35400, 50955}, {35404, 50958}, {36990, 50989}, {37925, 41716}, {38136, 42786}, {41982, 51737}, {42528, 51209}, {42529, 51208}, {44903, 50985}, {47352, 51141}, {47353, 48942}, {50978, 51025}, {51028, 51137}

X(55587) = midpoint of X(i) and X(j) for these {i,j}: {182, 55581}, {1350, 55584}, {1657, 40341}, {11898, 48872}, {15681, 50973}, {15683, 50961}, {3, 55582}, {3098, 55583}, {33878, 53097}, {44903, 50985}, {52987, 55585}, {6, 55580}
X(55587) = reflection of X(i) in X(j) for these {i,j}: {182, 1350}, {1351, 14810}, {11477, 5092}, {15687, 50982}, {382, 43150}, {3098, 52987}, {3627, 3631}, {3629, 548}, {31670, 40107}, {34788, 44883}, {35404, 50958}, {37517, 3}, {41731, 16163}, {44456, 575}, {48673, 43147}, {48884, 34507}, {48896, 48873}, {48898, 48874}, {48901, 48876}, {48904, 1352}, {48910, 18553}, {549, 50970}, {576, 3098}, {51132, 34200}, {51136, 15691}, {51140, 376}, {51166, 547}, {51212, 24206}, {52987, 33878}, {53097, 55586}, {6776, 48885}, {55581, 55584}, {55583, 55585}, {55585, 53097}
X(55587) = center of Tucker-Hagos(-5) circle
X(55587) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1297), X(37517)}}, {{A, B, C, X(5092), X(40803)}}, {{A, B, C, X(13452), X(35007)}}, {{A, B, C, X(28551), X(33628)}}
X(55587) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5102, 50664}, {3, 511, 37517}, {182, 1350, 3098}, {182, 15520, 53091}, {182, 37517, 5097}, {182, 5097, 39561}, {182, 52987, 1350}, {182, 55585, 55581}, {511, 14810, 1351}, {511, 33878, 52987}, {511, 43147, 48673}, {511, 5092, 11477}, {511, 575, 44456}, {511, 55585, 55583}, {511, 55586, 53097}, {524, 48874, 48898}, {542, 48873, 48896}, {576, 3098, 17508}, {1350, 1351, 14810}, {1350, 53097, 55584}, {1350, 55584, 511}, {1351, 14810, 182}, {1351, 53094, 15516}, {1352, 19924, 48904}, {3098, 39561, 3}, {5092, 11477, 15520}, {8722, 47618, 9737}, {9821, 47618, 8722}, {10625, 37494, 37480}, {11898, 48872, 11645}, {14810, 15516, 53094}, {29181, 34507, 48884}, {31884, 44456, 575}, {33878, 55586, 55585}, {37480, 37494, 46730}, {37517, 39561, 576}, {37517, 55585, 55582}, {48876, 48901, 11178}, {51212, 54173, 24206}

X(55588) = X(3)X(6)∩X(4)X(50994)

Barycentrics    a^2*(2*a^4-11*b^4-4*b^2*c^2-11*c^4+9*a^2*(b^2+c^2)) : :
X(55588) = -13*X[3]+9*X[6], -13*X[4]+21*X[50994], -9*X[69]+X[11541], -9*X[141]+7*X[3857], -8*X[546]+9*X[25561], -9*X[599]+5*X[5076], -55*X[632]+63*X[50981], -7*X[3090]+9*X[50977], -5*X[3091]+9*X[54173], -X[3146]+3*X[34507], -7*X[3523]+6*X[46267], -11*X[3525]+9*X[5476] and many others

X(55588) lies on these lines: {3, 6}, {4, 50994}, {69, 11541}, {141, 3857}, {524, 12103}, {542, 15704}, {546, 25561}, {599, 5076}, {632, 50981}, {1352, 48943}, {2781, 38632}, {2854, 38626}, {2979, 14002}, {3090, 50977}, {3091, 54173}, {3146, 34507}, {3292, 26881}, {3523, 46267}, {3525, 5476}, {3529, 11645}, {3544, 51212}, {3564, 48920}, {3627, 18553}, {3629, 33751}, {3818, 50688}, {3861, 50991}, {3917, 16042}, {5079, 54131}, {5562, 37946}, {5965, 48874}, {5969, 38627}, {6101, 37967}, {7492, 34986}, {7496, 12834}, {7530, 15606}, {8584, 46853}, {8703, 33749}, {9024, 38631}, {9976, 15021}, {10303, 20423}, {10519, 15022}, {11470, 35479}, {11898, 48879}, {12088, 12584}, {12102, 48889}, {12108, 50970}, {12294, 26863}, {12811, 24206}, {12812, 19130}, {14869, 25555}, {15069, 49137}, {15533, 17800}, {17538, 50974}, {21849, 40916}, {25565, 51166}, {29181, 43150}, {29323, 49140}, {30734, 33586}, {34380, 48885}, {40341, 48896}, {41989, 50959}, {44245, 50971}, {48876, 48895}, {48901, 50689}, {50693, 54174}, {50965, 51180}

X(55588) = midpoint of X(i) and X(j) for these {i,j}: {182, 55582}, {1350, 55585}, {11898, 48879}, {3, 55583}, {3098, 55584}, {33878, 55587}, {40341, 48896}, {576, 55580}, {52987, 53097}, {6, 55581}
X(55588) = reflection of X(i) in X(j) for these {i,j}: {11477, 20190}, {3629, 33751}, {44456, 15516}, {48891, 48874}, {48895, 48876}, {48942, 43150}, {48943, 1352}, {5092, 1350}, {5097, 3098}, {51166, 25565}, {55586, 55587}
X(55588) = center of Tucker-Hagos(-9/2) circle
X(55588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 22234}, {3, 22234, 20190}, {3, 53097, 55583}, {3, 53858, 182}, {511, 1350, 5092}, {511, 15516, 44456}, {511, 20190, 11477}, {511, 55587, 55586}, {576, 10541, 15516}, {576, 52987, 1350}, {1350, 5050, 3098}, {1350, 53097, 55580}, {1350, 55585, 511}, {3098, 22234, 3}, {5092, 5097, 5050}, {5092, 55586, 55585}, {5097, 20190, 575}, {5965, 48874, 48891}, {10541, 44456, 576}, {11477, 20190, 5097}, {11477, 53097, 55584}, {29181, 43150, 48942}, {33878, 53097, 52987}, {52987, 55587, 53097}

X(55589) = X(3)X(6)∩X(141)X(3856)

Barycentrics    3*a^6+11*a^4*(b^2+c^2)-2*a^2*(7*b^4+3*b^2*c^2+7*c^4) : :
X(55589) = -17*X[3]+11*X[6], -11*X[141]+8*X[3856], -11*X[599]+5*X[35434], -11*X[1352]+5*X[50691], -17*X[3854]+11*X[31670], -X[5476]+4*X[50970], -8*X[10109]+11*X[50977], -11*X[11178]+8*X[14893], -7*X[38110]+8*X[51139], -11*X[38317]+12*X[47598], -15*X[41099]+11*X[51538], -14*X[50969]+5*X[51140] and many others

X(55589) lies on these lines: {3, 6}, {141, 3856}, {542, 46333}, {599, 35434}, {1352, 50691}, {1503, 44903}, {3854, 31670}, {5476, 50970}, {10109, 50977}, {11178, 14893}, {12834, 16981}, {19924, 50687}, {29012, 50967}, {29181, 33699}, {29317, 54170}, {38110, 51139}, {38317, 47598}, {40341, 48920}, {41099, 51538}, {50969, 51140}, {50971, 50986}

X(55589) = midpoint of X(i) and X(j) for these {i,j}: {39561, 55583}, {5085, 55584}, {5093, 55582}
X(55589) = reflection of X(i) in X(j) for these {i,j}: {15520, 31884}, {37517, 5085}, {39561, 3098}, {5093, 14810}
X(55589) = center of Tucker-Hagos(-11/3) circle
X(55589) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 55586, 55581}, {182, 37517, 11482}, {511, 14810, 5093}, {511, 3098, 39561}, {511, 31884, 15520}, {511, 5085, 37517}, {576, 17508, 5050}, {1350, 33878, 55588}, {1350, 53097, 44456}, {1350, 55580, 5092}, {1350, 55582, 10541}, {1350, 55584, 15516}, {1350, 55585, 576}, {1350, 55588, 55585}, {3098, 55587, 55583}, {5050, 44456, 5102}, {15520, 31884, 17508}, {33878, 52987, 55587}, {52987, 55585, 1350}, {52987, 55587, 3098}

X(55590) = X(3)X(6)∩X(141)X(3858)

Barycentrics    a^2*(2*a^4-9*b^4-4*b^2*c^2-9*c^4+7*a^2*(b^2+c^2)) : :
X(55590) = -11*X[3]+7*X[6], -7*X[141]+5*X[3858], -3*X[599]+X[48904], -7*X[1352]+3*X[15682], -7*X[3818]+5*X[17578], -6*X[3839]+7*X[25561], -11*X[3855]+7*X[31670], -4*X[3861]+7*X[40107], -6*X[5066]+7*X[24206], -13*X[5068]+21*X[10519], -5*X[5071]+7*X[50977], -7*X[5476]+9*X[15709] and many others

X(55590) lies on these lines: {3, 6}, {69, 29323}, {141, 3858}, {524, 15691}, {542, 19710}, {599, 48904}, {1352, 15682}, {1353, 33751}, {3564, 48891}, {3630, 15704}, {3818, 17578}, {3839, 25561}, {3855, 31670}, {3861, 40107}, {5066, 24206}, {5068, 10519}, {5071, 50977}, {5476, 15709}, {5480, 15699}, {5646, 10219}, {5921, 11645}, {5943, 21766}, {5965, 48881}, {6144, 15696}, {6776, 15697}, {10124, 50970}, {10168, 44580}, {11898, 48896}, {12294, 52294}, {14927, 48880}, {15069, 48879}, {15606, 46261}, {15687, 19924}, {15713, 38079}, {15721, 20423}, {16187, 33586}, {18553, 29181}, {19130, 35018}, {21849, 22112}, {29317, 39884}, {32237, 35264}, {32455, 33923}, {34380, 48892}, {34507, 49135}

X(55590) = midpoint of X(i) and X(j) for these {i,j}: {182, 55584}, {1350, 55587}, {1351, 55581}, {11898, 48896}, {15069, 48879}, {3, 55585}, {3098, 53097}, {3630, 15704}, {33878, 52987}, {37517, 55580}, {576, 55582}, {6, 55583}
X(55590) = reflection of X(i) in X(j) for these {i,j}: {1353, 33751}, {11477, 50664}, {14810, 1350}, {25561, 54173}, {32455, 33923}, {37517, 20190}, {44456, 22330}, {48889, 48876}, {48895, 40107}, {48920, 48874}, {48942, 1352}, {48943, 18553}, {575, 3098}, {5097, 14810}, {55586, 55588}, {55588, 33878}
X(55590) = center of Tucker-Hagos(-7/2) circle
X(55590) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(14075), X(14491)}}, {{A, B, C, X(17508), X(40803)}}
X(55590) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 55587, 55584}, {511, 1350, 14810}, {511, 14810, 5097}, {511, 22330, 44456}, {511, 33878, 55588}, {511, 50664, 11477}, {511, 55588, 55586}, {542, 48874, 48920}, {575, 55588, 53097}, {1350, 1351, 3098}, {1350, 33878, 55587}, {1350, 53097, 1351}, {1350, 55582, 53094}, {1350, 55584, 182}, {1350, 55585, 15516}, {1350, 55587, 511}, {1351, 53091, 53858}, {1351, 53097, 55581}, {1353, 50965, 33751}, {3098, 15520, 3}, {5097, 14810, 5092}, {17508, 44456, 22330}, {18553, 29181, 48943}, {19924, 48876, 48889}, {20190, 53858, 575}, {31884, 37517, 20190}, {31884, 55580, 37517}, {52987, 55587, 1350}, {52987, 55589, 33878}, {53097, 53858, 55580}

X(55591) = X(2)X(50970)∩X(3)X(6)

Barycentrics    a^2*(3*a^4-13*b^4-6*b^2*c^2-13*c^4+10*a^2*(b^2+c^2)) : :
X(55591) = -X[2]+4*X[50970], -8*X[3]+5*X[6], 5*X[69]+X[5059], -10*X[141]+7*X[3832], -6*X[547]+5*X[38136], -5*X[599]+2*X[3543], -5*X[1498]+8*X[15580], -X[3146]+4*X[3631], -5*X[3242]+2*X[11531], -5*X[3522]+2*X[3629], -7*X[3528]+4*X[12007], -3*X[3545]+5*X[10519] and many others

X(55591) lies on these lines: {2, 50970}, {3, 6}, {20, 16775}, {30, 47445}, {69, 5059}, {141, 3832}, {159, 51959}, {394, 35265}, {547, 38136}, {599, 3543}, {611, 51817}, {1498, 15580}, {1503, 11001}, {2979, 35259}, {3066, 33879}, {3146, 3631}, {3242, 11531}, {3522, 3629}, {3528, 12007}, {3534, 5965}, {3545, 10519}, {3564, 15686}, {3620, 51163}, {3630, 14927}, {3763, 5056}, {3796, 55038}, {3845, 10516}, {3850, 31670}, {3853, 48876}, {5067, 5480}, {5073, 43150}, {5650, 17810}, {6144, 44882}, {6194, 8556}, {6329, 15717}, {6800, 37672}, {7736, 46944}, {7998, 33586}, {8567, 34777}, {8705, 37944}, {8716, 22676}, {9756, 33706}, {9924, 30443}, {10242, 19924}, {10601, 16981}, {10606, 44668}, {11002, 17825}, {11008, 50693}, {11459, 15811}, {11539, 14561}, {11812, 20423}, {11898, 48880}, {13595, 17811}, {14853, 15702}, {15069, 48873}, {15072, 16936}, {15103, 34787}, {15534, 25406}, {15640, 50958}, {15682, 50982}, {15690, 34380}, {15695, 51140}, {15697, 51136}, {15708, 21167}, {15719, 54132}, {15723, 38317}, {16163, 16176}, {16239, 21850}, {19708, 51132}, {19710, 50961}, {22165, 51025}, {29317, 47353}, {29323, 50955}, {30392, 38315}, {33703, 36990}, {34507, 49133}, {38110, 41983}, {39899, 48885}, {41981, 48906}, {46332, 50979}, {47358, 51120}, {47448, 47468}, {48662, 48879}, {48874, 48905}, {50781, 50868}, {50782, 50864}, {50783, 50871}, {50784, 50862}, {50787, 51119}, {50791, 50865}, {50966, 51737}, {50989, 51023}, {50990, 51022}, {50991, 51165}, {51026, 51142}, {51028, 51185}

X(55591) = midpoint of X(i) and X(j) for these {i,j}: {15520, 55583}, {17508, 55585}, {25406, 54174}, {31884, 53097}, {5050, 55584}, {5102, 55582}, {52987, 55589}
X(55591) = reflection of X(i) in X(j) for these {i,j}: {1351, 17508}, {10516, 54173}, {11477, 5050}, {14853, 54169}, {15520, 14810}, {15534, 25406}, {25406, 50965}, {31884, 1350}, {33878, 55589}, {44456, 15520}, {5050, 3098}, {5102, 3}, {51024, 10516}, {51538, 141}, {53023, 10519}, {6, 31884}, {55589, 55590}
X(55591) = center of Tucker-Hagos(-10/3) circle
X(55591) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1297), X(5102)}}, {{A, B, C, X(14490), X(21309)}}, {{A, B, C, X(35007), X(43691)}}, {{A, B, C, X(40801), X(50664)}}
X(55591) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 50664}, {3, 33878, 55587}, {3, 39561, 5085}, {3, 511, 5102}, {3, 55587, 55582}, {182, 55586, 55580}, {511, 1350, 31884}, {511, 14810, 15520}, {511, 17508, 1351}, {511, 3098, 5050}, {511, 55589, 33878}, {511, 55590, 55589}, {1350, 11477, 3098}, {1350, 55582, 3}, {1350, 55584, 53094}, {1350, 55585, 10541}, {3098, 55584, 11477}, {3098, 55588, 55584}, {5085, 5102, 39561}, {5097, 50664, 22234}, {10519, 53023, 21358}, {11477, 53094, 6}, {11477, 55588, 53097}, {14810, 44456, 53093}, {14810, 55583, 44456}, {15520, 55583, 511}, {33878, 52987, 1350}, {33878, 55584, 55588}, {50965, 54174, 15534}, {51024, 54173, 50993}

X(55592) = X(3)X(6)∩X(599)X(48942)

Barycentrics    a^2*(4*a^4-15*b^4-8*b^2*c^2-15*c^4+11*a^2*(b^2+c^2)) : :
X(55592) = -19*X[3]+11*X[6], -3*X[599]+X[48942], -17*X[3854]+33*X[10519], X[5921]+3*X[48880], 3*X[11180]+5*X[48873], -11*X[14927]+27*X[46333], -11*X[18553]+5*X[50691], -11*X[24206]+9*X[38071], -3*X[33699]+11*X[48876], -15*X[35434]+11*X[48904], -3*X[40107]+X[51163], -5*X[40330]+3*X[48895] and many others

X(55592) lies on these lines: {3, 6}, {599, 48942}, {2979, 32237}, {3854, 10519}, {5921, 48880}, {6688, 21766}, {11180, 48873}, {11645, 44903}, {14893, 19924}, {14927, 46333}, {18553, 50691}, {24206, 38071}, {33699, 48876}, {35434, 48904}, {40107, 51163}, {40330, 48895}, {41099, 48901}, {43150, 50692}, {48889, 50687}, {48898, 50967}, {50977, 51211}

X(55592) = midpoint of X(i) and X(j) for these {i,j}: {1350, 55590}, {14810, 55587}, {3, 55586}, {3098, 55588}, {575, 55585}, {5092, 53097}, {5097, 55584}
X(55592) = reflection of X(i) in X(j) for these {i,j}: {15516, 14810}, {20190, 3098}
X(55592) = center of Tucker-Hagos(-11/4) circle
X(55592) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 55589, 55586}, {182, 11477, 5097}, {511, 14810, 15516}, {511, 3098, 20190}, {1350, 33878, 182}, {1350, 52987, 55590}, {1350, 55584, 3098}, {1350, 55587, 14810}, {1350, 55590, 511}, {1350, 55591, 55584}, {3098, 52987, 55591}, {3098, 55591, 55588}, {5093, 33878, 53097}, {5097, 14810, 53094}, {11477, 20190, 22330}, {11477, 55591, 33878}, {14810, 55590, 55587}, {31884, 33878, 55583}

X(55593) = X(2)X(50981)∩X(3)X(6)

Barycentrics    a^2*(3*a^4-11*b^4-6*b^2*c^2-11*c^4+8*a^2*(b^2+c^2)) : :
X(55593) = -11*X[2]+14*X[50981], -7*X[3]+4*X[6], -8*X[141]+5*X[3843], -X[193]+4*X[548], -X[382]+4*X[48876], -4*X[550]+X[39899], -8*X[597]+11*X[15718], -4*X[599]+X[15684], -4*X[1352]+X[5073], -5*X[1656]+4*X[38136], -2*X[1992]+5*X[14093], -7*X[3526]+4*X[21850] and many others

X(55593) lies on these lines: {2, 50981}, {3, 6}, {20, 11898}, {25, 33884}, {69, 1657}, {141, 3843}, {159, 47748}, {193, 548}, {376, 34380}, {381, 10519}, {382, 48876}, {524, 15689}, {550, 39899}, {597, 15718}, {599, 15684}, {1352, 5073}, {1353, 3522}, {1503, 15681}, {1598, 15067}, {1656, 38136}, {1992, 14093}, {2979, 6090}, {3060, 5644}, {3167, 35268}, {3517, 10627}, {3526, 21850}, {3534, 3564}, {3619, 5072}, {3620, 3627}, {3830, 29181}, {3851, 31670}, {5020, 7998}, {5032, 45759}, {5054, 14853}, {5070, 5480}, {5076, 18358}, {5181, 38790}, {5640, 16419}, {5650, 33586}, {5921, 15704}, {6391, 7689}, {6776, 15696}, {7484, 11002}, {7485, 16981}, {8703, 14912}, {8705, 35452}, {9924, 13093}, {10516, 14269}, {10752, 15040}, {11001, 50978}, {11160, 15686}, {11178, 35403}, {11188, 47527}, {11459, 39568}, {12100, 51028}, {12101, 51184}, {12103, 39874}, {12283, 34469}, {14561, 15694}, {14645, 38742}, {14848, 15707}, {14984, 15041}, {15055, 39562}, {15069, 48880}, {15082, 17810}, {15682, 50954}, {15685, 29012}, {15688, 25406}, {15690, 50974}, {15693, 38110}, {15695, 50965}, {15697, 51179}, {15701, 20423}, {15703, 25565}, {15712, 51171}, {15716, 51172}, {15717, 51732}, {15720, 18583}, {17538, 20080}, {17800, 18440}, {18325, 47468}, {19708, 33748}, {19709, 50977}, {20850, 35259}, {21356, 38335}, {21735, 51170}, {30734, 48912}, {33750, 50979}, {33851, 48679}, {34382, 36987}, {34507, 48872}, {36990, 49134}, {37955, 52238}, {38638, 45016}, {38744, 50567}, {38756, 51007}, {39260, 46475}, {39884, 49136}, {40107, 48910}, {40341, 44796}, {48661, 49511}, {50957, 50993}, {50968, 51174}, {50976, 51187}

X(55593) = midpoint of X(i) and X(j) for these {i,j}: {1350, 55591}, {10519, 54170}, {14912, 54174}, {39561, 55585}, {5085, 53097}, {5093, 55584}
X(55593) = reflection of X(i) in X(j) for these {i,j}: {1351, 5085}, {11477, 39561}, {14561, 54169}, {14912, 8703}, {20423, 21167}, {381, 10519}, {33878, 55591}, {38335, 21356}, {39561, 14810}, {39562, 15055}, {44456, 5093}, {5032, 45759}, {5050, 31884}, {5085, 3098}, {5093, 3}, {5102, 17508}, {50962, 14912}, {51212, 38136}, {53023, 50977}, {54132, 38110}, {55591, 52987}
X(55593) = center of Tucker-Hagos(-8/3) circle
X(55593) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1297), X(5093)}}, {{A, B, C, X(3053), X(44763)}}, {{A, B, C, X(13452), X(22331)}}
X(55593) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 33878, 55584}, {3, 44456, 53091}, {3, 511, 5093}, {3, 55584, 44456}, {6, 55587, 55580}, {69, 1657, 48662}, {69, 48874, 1657}, {182, 55588, 55582}, {511, 14810, 39561}, {511, 17508, 5102}, {511, 3098, 5085}, {511, 52987, 55591}, {1350, 52987, 33878}, {1350, 53097, 3098}, {1350, 55589, 5050}, {1350, 55590, 1351}, {1350, 55591, 511}, {1351, 33878, 53097}, {1351, 5050, 15520}, {3098, 52987, 55590}, {3098, 55581, 575}, {5102, 31884, 17508}, {6455, 6456, 15513}, {8703, 54174, 50962}, {11477, 14810, 12017}, {12017, 14810, 3}, {12017, 33878, 55585}, {14810, 55585, 11477}, {18440, 48873, 17800}, {33878, 55580, 55587}, {37517, 53094, 53092}, {50966, 54174, 8703}

X(55594) = X(2)X(42785)∩X(3)X(6)

Barycentrics    a^2*(2*a^4-7*b^4-4*b^2*c^2-7*c^4+5*a^2*(b^2+c^2)) : :
X(55594) = -9*X[2]+7*X[42785], -9*X[3]+5*X[6], 5*X[69]+3*X[11001], -5*X[141]+3*X[3845], -9*X[376]+X[11008], -6*X[547]+5*X[19130], -5*X[597]+7*X[19711], -3*X[599]+X[48884], -5*X[1352]+X[33703], -17*X[3533]+15*X[38317], 3*X[3534]+X[40341], -9*X[3543]+25*X[3620] and many others

X(55594) lies on these lines: {2, 42785}, {3, 6}, {30, 3631}, {51, 41462}, {69, 11001}, {74, 36987}, {141, 3845}, {373, 5888}, {376, 11008}, {524, 15690}, {542, 3630}, {547, 19130}, {550, 5965}, {597, 19711}, {599, 48884}, {1352, 33703}, {1495, 2979}, {1503, 48920}, {1843, 13596}, {1974, 44878}, {2810, 41454}, {3056, 37587}, {3292, 7712}, {3533, 38317}, {3534, 40341}, {3543, 3620}, {3545, 3619}, {3564, 48885}, {3589, 11812}, {3618, 15719}, {3629, 8703}, {3819, 34417}, {3832, 10519}, {3850, 24206}, {3853, 18358}, {3917, 13595}, {4550, 43129}, {5056, 42786}, {5059, 29323}, {5067, 51212}, {5476, 15702}, {5562, 12112}, {5645, 16981}, {5650, 10545}, {6329, 12100}, {6636, 44109}, {7998, 48912}, {8550, 33751}, {10168, 41983}, {10546, 33884}, {10627, 43586}, {10752, 13620}, {11004, 22352}, {11178, 38335}, {11179, 50966}, {11204, 34777}, {11278, 49465}, {11539, 21850}, {12007, 33923}, {12219, 41464}, {12220, 41471}, {12294, 34484}, {14483, 41435}, {14492, 16988}, {14855, 52099}, {15018, 21969}, {15051, 34155}, {15068, 15606}, {15069, 48896}, {15080, 34986}, {15580, 34146}, {15688, 51140}, {15689, 50973}, {15708, 20423}, {15759, 20583}, {18440, 48879}, {18553, 29317}, {20080, 46264}, {20301, 38725}, {21167, 25555}, {25565, 51128}, {29012, 48874}, {32414, 37688}, {32455, 46332}, {34380, 41981}, {35400, 47353}, {36990, 49133}, {38723, 41731}, {39874, 48898}, {41455, 45955}, {44091, 47485}, {45759, 51132}, {46267, 54132}, {47598, 51130}, {48905, 51027}, {48906, 50965}

X(55594) = midpoint of X(i) and X(j) for these {i,j}: {182, 53097}, {1350, 52987}, {1351, 55583}, {11477, 55581}, {14810, 55588}, {15069, 48896}, {18440, 48879}, {3, 55587}, {3098, 33878}, {34507, 48873}, {37517, 55582}, {576, 55584}, {5092, 55586}, {50977, 54170}, {6, 55585}, {69, 48880}
X(55594) = reflection of X(i) in X(j) for these {i,j}: {1351, 20190}, {11477, 15516}, {12007, 33923}, {18553, 48876}, {20583, 15759}, {37517, 50664}, {48889, 40107}, {48891, 48881}, {48895, 141}, {48942, 18553}, {48943, 3818}, {575, 14810}, {5092, 3098}, {5097, 3}, {52987, 55592}, {54132, 46267}, {55586, 33878}, {55588, 55590}, {55590, 52987}, {8550, 33751}
X(55594) = isogonal conjugate of X(54608)
X(55594) = center of Tucker-Hagos(-5/2) circle
X(55594) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(11738)}}, {{A, B, C, X(74), X(35007)}}, {{A, B, C, X(842), X(35006)}}, {{A, B, C, X(1297), X(5097)}}, {{A, B, C, X(3431), X(53096)}}, {{A, B, C, X(5007), X(14483)}}, {{A, B, C, X(5206), X(20421)}}, {{A, B, C, X(34567), X(41940)}}
X(55594) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 33878, 55582}, {3, 37517, 50664}, {3, 50664, 5092}, {3, 5102, 182}, {3, 511, 5097}, {3, 55582, 37517}, {3, 55591, 55587}, {6, 33878, 55585}, {15, 16, 35007}, {69, 48880, 11645}, {141, 19924, 48895}, {141, 48895, 25561}, {182, 52987, 55589}, {182, 55589, 53097}, {511, 14810, 575}, {511, 20190, 1351}, {542, 48881, 48891}, {1350, 33878, 3098}, {1350, 55590, 14810}, {1350, 55591, 3}, {1350, 55592, 55590}, {1350, 55593, 52987}, {3098, 52987, 33878}, {3098, 55585, 6}, {3620, 43621, 3818}, {5092, 55590, 55586}, {6200, 6396, 5206}, {11477, 17508, 15516}, {11477, 55581, 511}, {12017, 33878, 55584}, {17508, 55581, 11477}, {18553, 29317, 48942}, {29181, 40107, 48889}, {29317, 48876, 18553}, {31884, 55584, 576}, {33878, 55586, 55588}, {34507, 48873, 29323}, {34754, 34755, 5008}, {51166, 54169, 11539}, {52987, 55587, 55591}, {52987, 55593, 55592}

X(55595) = X(3)X(6)∩X(4)X(50957)

Barycentrics    a^2*(5*a^4-17*b^4-10*b^2*c^2-17*c^4+12*a^2*(b^2+c^2)) : :
X(55595) = -11*X[3]+6*X[6], -16*X[4]+21*X[50957], 2*X[5]+3*X[54170], 3*X[69]+2*X[15704], -11*X[381]+16*X[51143], -X[382]+6*X[54173], -4*X[546]+9*X[10519], 2*X[550]+3*X[50967], -6*X[599]+X[5073], -6*X[1352]+X[49136], -4*X[1656]+3*X[50963], 2*X[1657]+3*X[50955] and many others

X(55595) lies on these lines: {3, 6}, {4, 50957}, {5, 54170}, {30, 50990}, {69, 15704}, {381, 51143}, {382, 54173}, {524, 15696}, {546, 10519}, {550, 50967}, {599, 5073}, {1352, 49136}, {1656, 50963}, {1657, 50955}, {1992, 33923}, {2781, 14530}, {2979, 8780}, {3146, 48876}, {3522, 50966}, {3523, 14848}, {3525, 21850}, {3526, 54169}, {3528, 54174}, {3529, 18440}, {3530, 54132}, {3564, 17538}, {3619, 12811}, {3627, 51537}, {3628, 51212}, {3830, 40107}, {3843, 19924}, {3851, 50977}, {3853, 21356}, {3857, 51538}, {5070, 54131}, {5072, 31670}, {5076, 29181}, {5643, 7484}, {6776, 44245}, {7998, 30734}, {8550, 15688}, {9976, 38633}, {10299, 51028}, {11414, 14094}, {11541, 39884}, {11898, 48881}, {12167, 35475}, {12315, 15581}, {13093, 34787}, {14853, 14869}, {14984, 15021}, {15020, 45016}, {15039, 33851}, {15069, 15681}, {15684, 18553}, {15691, 50992}, {15701, 25555}, {15720, 20423}, {17800, 34507}, {18358, 50688}, {21735, 50979}, {35403, 50993}, {35404, 50994}, {38136, 46936}, {40341, 48885}, {41981, 50969}, {47353, 49134}, {48662, 48880}, {48873, 49137}, {50965, 51174}

X(55595) = midpoint of X(i) and X(j) for these {i,j}: {53093, 53097}
X(55595) = reflection of X(i) in X(j) for these {i,j}: {1351, 12017}, {11477, 22234}, {11482, 3}, {35403, 50993}, {53094, 3098}
X(55595) = center of Tucker-Hagos(-12/5) circle
X(55595) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1297), X(11482)}}, {{A, B, C, X(3527), X(14075)}}, {{A, B, C, X(10541), X(14489)}}
X(55595) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 5050}, {3, 11482, 12017}, {3, 33878, 55580}, {3, 44456, 575}, {3, 5093, 10541}, {3, 511, 11482}, {3, 55580, 1351}, {3, 55584, 11477}, {3, 55593, 52987}, {511, 3098, 53094}, {1350, 55591, 3098}, {1350, 55593, 33878}, {1350, 55594, 55593}, {3098, 55592, 55591}, {10541, 14810, 3}, {11477, 53094, 22234}, {11477, 55588, 55584}, {11477, 55591, 55588}, {11482, 53093, 53092}, {12017, 53092, 53093}, {14810, 55582, 5093}, {14810, 55589, 55582}, {31884, 55587, 44456}, {52987, 55583, 55590}, {53093, 53094, 20190}, {53093, 53097, 511}

X(55596) = X(3)X(6)∩X(141)X(3861)

Barycentrics    3*a^6+7*a^4*(b^2+c^2)-2*a^2*(5*b^4+3*b^2*c^2+5*c^4) : :
X(55596) = -13*X[3]+7*X[6], 2*X[69]+X[48896], -7*X[141]+4*X[3861], -X[193]+4*X[33751], -7*X[1352]+X[49135], -3*X[3839]+7*X[10519], -11*X[3855]+14*X[24206], -10*X[3858]+7*X[48901], -4*X[5066]+7*X[50977], -13*X[5068]+7*X[31670], 5*X[5071]+7*X[54170], -7*X[5476]+10*X[15713] and many others

X(55596) lies on circumconic {{A, B, C, X(1297), X(15520)}} and on these lines: {3, 6}, {69, 48896}, {141, 3861}, {193, 33751}, {1352, 49135}, {1503, 19710}, {1974, 44880}, {2979, 35265}, {3564, 15691}, {3630, 12103}, {3839, 10519}, {3855, 24206}, {3858, 48901}, {5066, 50977}, {5068, 31670}, {5071, 54170}, {5476, 15713}, {5480, 48154}, {5965, 15697}, {7486, 19130}, {9544, 35268}, {10124, 38317}, {11178, 15687}, {11180, 15683}, {11898, 48891}, {14561, 15709}, {14853, 15721}, {15069, 48920}, {15082, 33586}, {15682, 29317}, {15699, 38136}, {17578, 40107}, {25406, 50966}, {32455, 46853}, {34380, 50965}, {34507, 48874}, {43150, 48872}, {48873, 49138}, {48876, 48884}, {51137, 54132}

X(55596) = midpoint of X(i) and X(j) for these {i,j}: {1350, 55593}, {15520, 55585}, {17508, 55587}, {3098, 55589}, {31884, 33878}, {5050, 53097}, {5102, 55584}
X(55596) = reflection of X(i) in X(j) for these {i,j}: {182, 31884}, {15520, 3}, {17508, 3098}, {37517, 5050}, {38317, 54169}, {5050, 14810}, {576, 17508}, {5102, 5092}, {51140, 25406}, {51538, 24206}, {52987, 55593}, {55587, 55589}, {55589, 52987}, {55593, 55594}
X(55596) = center of Tucker-Hagos(-7/3) circle
X(55596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 15520}, {3, 55590, 55585}, {6, 55588, 55581}, {182, 33878, 55583}, {182, 37517, 22330}, {182, 5093, 39561}, {182, 52987, 33878}, {511, 14810, 5050}, {511, 3098, 17508}, {511, 5092, 5102}, {511, 55594, 55593}, {1350, 52987, 3098}, {1350, 55592, 182}, {1350, 55593, 511}, {1350, 55594, 52987}, {1350, 55595, 55594}, {3098, 52987, 55587}, {3098, 55587, 576}, {14810, 53097, 37517}, {33878, 53092, 55584}, {34507, 48874, 48879}

X(55597) = X(3)X(6)∩X(30)X(41152)

Barycentrics    a^2*(4*a^4-13*b^4-8*b^2*c^2-13*c^4+9*a^2*(b^2+c^2)) : :
X(55597) = -17*X[3]+9*X[6], -9*X[599]+X[49136], -5*X[632]+9*X[54169], -9*X[1352]+X[11541], 7*X[3090]+9*X[54170], -5*X[3091]+9*X[50977], -X[3146]+3*X[18553], X[3529]+3*X[34507], -4*X[3530]+3*X[46267], -17*X[3544]+9*X[31670], -X[3627]+3*X[40107], -10*X[3628]+9*X[25565] and many others

X(55597) lies on circumconics {{A, B, C, X(1297), X(22330)}} and on these lines: {3, 6}, {30, 41152}, {69, 48920}, {524, 44245}, {542, 12103}, {546, 19924}, {599, 49136}, {632, 54169}, {1216, 37967}, {1352, 11541}, {2781, 50414}, {3090, 54170}, {3091, 50977}, {3146, 18553}, {3529, 34507}, {3530, 46267}, {3544, 31670}, {3627, 40107}, {3628, 25565}, {3819, 16042}, {3856, 51143}, {3857, 24206}, {3917, 14002}, {5076, 11178}, {5476, 10303}, {5907, 37946}, {7496, 21849}, {10519, 48895}, {10627, 12105}, {11645, 15704}, {12045, 21766}, {12102, 29181}, {12108, 25555}, {14869, 38079}, {29323, 48874}, {33749, 33923}, {41149, 41982}, {43150, 48873}, {48889, 50688}, {50693, 50967}

X(55597) = midpoint of X(i) and X(j) for these {i,j}: {182, 55586}, {1350, 55594}, {14810, 33878}, {3, 55588}, {3098, 55590}, {43150, 48873}, {575, 53097}, {5092, 55587}, {5097, 55585}, {69, 48920}
X(55597) = reflection of X(i) in X(j) for these {i,j}: {22330, 3}, {33749, 33923}, {50664, 14810}, {55592, 55594}
X(55597) = center of Tucker-Hagos(-9/4) circle
X(55597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 22330, 20190}, {3, 511, 22330}, {3, 52987, 55588}, {182, 55591, 55586}, {511, 14810, 50664}, {511, 55594, 55592}, {576, 52987, 33878}, {1350, 55593, 3098}, {1350, 55594, 511}, {1350, 55595, 52987}, {1350, 55596, 55594}, {3098, 5085, 14810}, {3098, 52987, 53097}, {3098, 53097, 575}, {3098, 55581, 5085}, {3098, 55587, 15520}, {3098, 55593, 55590}, {11477, 53091, 576}, {14540, 14541, 18860}, {14810, 55590, 55581}, {31884, 55585, 5097}, {52987, 55596, 55595}, {55590, 55594, 55593}

X(55598) = X(3)X(6)∩X(141)X(14893)

Barycentrics    5*a^6+11*a^4*(b^2+c^2)-2*a^2*(8*b^4+5*b^2*c^2+8*c^4) : :
X(55598) = -21*X[3]+11*X[6], 11*X[69]+9*X[46333], -11*X[141]+6*X[14893], -11*X[1352]+X[50692], -16*X[3589]+21*X[51141], 2*X[3630]+3*X[48898], 2*X[3631]+3*X[48874], -11*X[3818]+6*X[33699], -17*X[3854]+22*X[24206], -16*X[3856]+11*X[48901], -72*X[10109]+77*X[42786], -11*X[11178]+6*X[50687] and many others

X(55598) lies on these lines: {3, 6}, {69, 46333}, {141, 14893}, {1352, 50692}, {3589, 51141}, {3620, 29317}, {3630, 48898}, {3631, 48874}, {3818, 33699}, {3854, 24206}, {3856, 48901}, {10109, 42786}, {11178, 50687}, {11645, 50989}, {16187, 48912}, {18358, 48904}, {19130, 54170}, {19924, 41099}, {38071, 50977}, {39874, 48885}, {40107, 43621}, {44903, 48880}, {45760, 51126}, {46264, 50992}, {47598, 54169}, {48884, 54173}, {48892, 50967}

X(55598) = midpoint of X(i) and X(j) for these {i,j}: {1350, 55595}, {53091, 53097}
X(55598) = reflection of X(i) in X(j) for these {i,j}: {576, 53094}, {51537, 40107}, {53093, 14810}
X(55598) = center of Tucker-Hagos(-11/5) circle
X(55598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 55589, 55581}, {3, 55592, 55589}, {511, 14810, 53093}, {511, 53094, 576}, {1350, 55594, 3098}, {1350, 55595, 511}, {1350, 55596, 52987}, {1350, 55597, 55596}, {3098, 33878, 37517}, {3098, 52987, 55585}, {3098, 55585, 182}, {3098, 55587, 6}, {3098, 55596, 55594}, {14810, 55583, 15520}, {14810, 55591, 55583}, {37517, 52987, 33878}, {55586, 55594, 55592}

X(55599) = X(3)X(6)∩X(3856)X(24206)

Barycentrics    a^2*(6*a^4-17*b^4-12*b^2*c^2-17*c^4+11*a^2*(b^2+c^2)) : :
X(55599) = -23*X[3]+11*X[6], -11*X[3818]+5*X[50691], -17*X[3854]+11*X[48901], -8*X[3856]+11*X[24206], -14*X[10109]+11*X[50959], -11*X[10519]+3*X[50687], -11*X[11178]+5*X[35434], -8*X[14893]+11*X[25561], -5*X[21167]+3*X[38079], -6*X[25565]+5*X[38136], -4*X[40107]+X[48942], -5*X[41099]+11*X[50977] and many others

X(55599) lies on these lines: {3, 6}, {3818, 50691}, {3854, 48901}, {3856, 24206}, {5965, 50965}, {10109, 50959}, {10519, 50687}, {11178, 35434}, {11645, 46333}, {12045, 33586}, {14893, 25561}, {18553, 48874}, {19924, 38071}, {21167, 38079}, {25565, 38136}, {29012, 44903}, {29317, 33699}, {29323, 54173}, {34380, 50970}, {38317, 54170}, {40107, 48942}, {41099, 50977}, {48873, 50692}, {50961, 50966}

X(55599) = midpoint of X(i) and X(j) for these {i,j}: {15520, 53097}, {17508, 33878}, {3, 55589}, {3098, 55593}, {31884, 52987}, {38317, 54170}, {5050, 55587}, {5102, 55585}
X(55599) = reflection of X(i) in X(j) for these {i,j}: {5092, 31884}, {5097, 17508}, {5102, 20190}, {55586, 55589}, {55589, 55592}, {55590, 55593}, {55593, 55597}
X(55599) = center of Tucker-Hagos(-11/6) circle
X(55599) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55598}, {3, 55592, 55586}, {511, 17508, 5097}, {511, 20190, 5102}, {511, 31884, 5092}, {511, 55597, 55593}, {575, 3098, 14810}, {1350, 3098, 55597}, {1351, 5085, 39561}, {1351, 5092, 575}, {3098, 52987, 1351}, {3098, 55581, 3}, {3098, 55597, 55590}, {5092, 5097, 53093}, {14810, 55594, 55588}, {15520, 53097, 511}, {39561, 55596, 52987}, {55586, 55598, 55594}

X(55600) = X(3)X(6)∩X(30)X(51142)

Barycentrics    5*a^6+9*a^4*(b^2+c^2)-2*a^2*(7*b^4+5*b^2*c^2+7*c^4) : :
X(55600) = -19*X[3]+9*X[6], -9*X[141]+4*X[12102], -4*X[546]+9*X[50977], 9*X[599]+X[49137], -7*X[632]+9*X[50980], 9*X[1352]+X[49140], -X[3146]+6*X[40107], 11*X[3525]+9*X[54170], X[3529]+9*X[54173], -4*X[3627]+9*X[11178], -4*X[3628]+9*X[54169], -14*X[3857]+9*X[48901] and many others

X(55600) lies on circumconics {{A, B, C, X(1297), X(22234)}} and on these lines: {3, 6}, {30, 51142}, {141, 12102}, {542, 17538}, {546, 50977}, {599, 49137}, {632, 50980}, {1352, 49140}, {3091, 19924}, {3146, 40107}, {3525, 54170}, {3529, 54173}, {3627, 11178}, {3628, 54169}, {3819, 30734}, {3857, 48901}, {5476, 14869}, {10304, 33749}, {10519, 48904}, {11541, 48873}, {12584, 38632}, {15022, 31670}, {15058, 37946}, {15704, 34507}, {18553, 49136}, {19130, 46936}, {29317, 51537}, {32273, 47528}, {37957, 43652}, {44245, 50965}, {48874, 48884}, {48876, 48879}, {50970, 50986}

X(55600) = midpoint of X(i) and X(j) for these {i,j}: {11482, 53097}, {33878, 53094}
X(55600) = reflection of X(i) in X(j) for these {i,j}: {12017, 14810}, {22234, 3}, {37517, 53091}, {52987, 55595}, {55598, 1350}
X(55600) = center of Tucker-Hagos(-9/5) circle
X(55600) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55597}, {3, 511, 22234}, {3, 52987, 55583}, {3, 53858, 20190}, {3, 55580, 53858}, {3, 55597, 52987}, {182, 52987, 53097}, {182, 55594, 55589}, {511, 1350, 55598}, {511, 14810, 12017}, {1350, 3098, 55596}, {3098, 39561, 14810}, {3098, 55583, 3}, {3098, 55587, 17508}, {3098, 55589, 182}, {3098, 55596, 55587}, {5092, 55591, 55581}, {11477, 39561, 576}, {11482, 53097, 511}, {14540, 14541, 8722}, {14810, 55585, 39561}, {14810, 55593, 55585}, {20190, 55580, 37517}, {20190, 55590, 55580}, {52987, 55598, 55595}

X(55601) = X(3)X(6)∩X(323)X(6030)

Barycentrics    a^2*(4*a^4-11*b^4-8*b^2*c^2-11*c^4+7*a^2*(b^2+c^2)) : :
X(55601) = -15*X[3]+7*X[6], -7*X[141]+3*X[15687], 3*X[550]+X[3630], 3*X[599]+X[48879], 7*X[1352]+X[49138], -49*X[3619]+33*X[3855], -5*X[3620]+3*X[18553], -11*X[3629]+15*X[51180], -7*X[3818]+3*X[15682], -9*X[3839]+7*X[48895], -5*X[3858]+7*X[24206], -15*X[5071]+7*X[31670] and many others

X(55601) lies on these lines: {3, 6}, {69, 48891}, {141, 15687}, {323, 6030}, {542, 15691}, {550, 3630}, {599, 48879}, {1352, 49138}, {2979, 7712}, {3619, 3855}, {3620, 18553}, {3629, 51180}, {3631, 29012}, {3818, 15682}, {3819, 15107}, {3839, 48895}, {3858, 24206}, {3861, 29181}, {3917, 10546}, {5066, 19924}, {5071, 31670}, {5476, 15721}, {5650, 48912}, {5943, 41462}, {6144, 15688}, {10124, 51127}, {10219, 33586}, {10519, 17578}, {10545, 15082}, {11160, 15697}, {11178, 48943}, {11645, 19710}, {15066, 44082}, {15246, 44107}, {15683, 43150}, {15699, 19130}, {15709, 54170}, {15713, 21850}, {18358, 29317}, {25561, 48910}, {29323, 48876}, {32237, 33884}, {32455, 34200}, {33751, 34380}, {34507, 48920}, {34573, 35018}, {39899, 51188}, {40107, 48874}, {42785, 51212}, {44091, 47486}, {48892, 50965}, {49832, 49833}

X(55601) = midpoint of X(i) and X(j) for these {i,j}: {182, 55588}, {14810, 52987}, {18553, 48873}, {3, 55590}, {3098, 55594}, {34507, 48920}, {40107, 48874}, {43150, 48880}, {575, 55587}, {5092, 33878}, {5097, 53097}, {6, 55586}, {69, 48891}
X(55601) = reflection of X(i) in X(j) for these {i,j}: {15516, 3}, {20190, 14810}, {55592, 55597}, {55597, 1350}
X(55601) = isogonal conjugate of X(54934)
X(55601) = center of Tucker-Hagos(-7/4) circle
X(55601) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1297), X(15516)}}, {{A, B, C, X(5008), X(13603)}}
X(55601) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55596}, {3, 511, 15516}, {6, 20190, 50664}, {6, 3098, 14810}, {182, 55593, 55588}, {511, 1350, 55597}, {511, 14810, 20190}, {511, 55597, 55592}, {1350, 3098, 55594}, {1350, 31884, 55595}, {1350, 33878, 55598}, {1350, 55600, 55599}, {3098, 33878, 5092}, {3098, 55585, 3}, {3098, 55596, 55585}, {3098, 55598, 33878}, {14810, 52987, 511}, {14810, 55586, 6}, {14810, 55594, 55586}, {17508, 52987, 55584}, {20190, 55597, 52987}, {31884, 55587, 575}, {31884, 55595, 55587}, {48880, 54173, 43150}

X(55602) = X(3)X(6)∩X(141)X(5076)

Barycentrics    a^2*(7*a^4-19*b^4-14*b^2*c^2-19*c^4+12*a^2*(b^2+c^2)) : :
X(55602) = -13*X[3]+6*X[6], 4*X[20]+3*X[50955], 3*X[69]+4*X[12103], 4*X[140]+3*X[54170], -12*X[141]+5*X[5076], -5*X[382]+12*X[47354], 4*X[548]+3*X[50967], 6*X[599]+X[17800], -25*X[631]+18*X[38079], -10*X[632]+3*X[51212], 6*X[1352]+X[49137], -5*X[1656]+12*X[54169] and many others

X(55602) lies on these lines: {3, 6}, {20, 50955}, {30, 50994}, {69, 12103}, {140, 54170}, {141, 5076}, {382, 47354}, {548, 50967}, {599, 17800}, {631, 38079}, {632, 51212}, {1352, 49137}, {1656, 54169}, {1657, 54173}, {1992, 46853}, {2781, 15039}, {3146, 48874}, {3167, 7492}, {3526, 51173}, {3529, 48876}, {3530, 14848}, {3564, 50693}, {3619, 3857}, {3620, 11541}, {3627, 10519}, {3843, 50977}, {3851, 19924}, {5070, 25565}, {5073, 40107}, {5079, 31670}, {5159, 33522}, {5544, 41462}, {6144, 33751}, {8550, 50970}, {9715, 15034}, {9968, 14530}, {10303, 21850}, {11284, 44299}, {12102, 40330}, {12108, 14853}, {12811, 51538}, {15054, 32254}, {15107, 30734}, {15582, 32063}, {15681, 34507}, {15696, 50965}, {15704, 18440}, {15712, 54132}, {18553, 49134}, {21734, 50979}, {21735, 54174}, {34787, 35450}, {35407, 48884}, {39884, 49140}, {44903, 50990}, {46219, 54131}, {47353, 49139}, {48873, 49136}

X(55602) = midpoint of X(i) and X(j) for these {i,j}: {53097, 53858}
X(55602) = reflection of X(i) in X(j) for these {i,j}: {53092, 3}
X(55602) = center of Tucker-Hagos(-12/7) circle
X(55602) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1297), X(53092)}}, {{A, B, C, X(14489), X(20190)}}
X(55602) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55595}, {3, 5093, 20190}, {3, 511, 53092}, {3, 576, 12017}, {3, 55580, 11482}, {3, 55584, 576}, {3, 55593, 53097}, {6, 1350, 55596}, {575, 55597, 52987}, {1350, 3098, 55593}, {1350, 31884, 55594}, {1350, 53097, 55597}, {1350, 55591, 55598}, {1351, 53092, 53858}, {3098, 15520, 14810}, {3098, 55590, 5085}, {3098, 55596, 55581}, {3098, 55599, 1350}, {10541, 53858, 575}, {11482, 33878, 55580}, {12017, 55594, 33878}, {14810, 53093, 3}, {14810, 55583, 53093}, {14810, 55591, 44456}, {14810, 55598, 55591}, {15520, 44456, 1351}, {31884, 55594, 55584}, {53093, 55591, 55583}

X(55603) = X(3)X(6)∩X(141)X(3853)

Barycentrics    3*a^6+5*a^4*(b^2+c^2)-2*a^2*(4*b^4+3*b^2*c^2+4*c^4) : :
X(55603) = -11*X[3]+5*X[6], X[69]+2*X[48885], -5*X[141]+2*X[3853], -2*X[547]+5*X[54169], -10*X[632]+7*X[42785], 5*X[1352]+X[5059], -17*X[3533]+5*X[51212], 5*X[3534]+X[51027], -X[3543]+5*X[10519], -X[3629]+4*X[33923], -7*X[3832]+10*X[24206], -8*X[3850]+5*X[48901] and many others

X(55603) lies on these lines: {3, 6}, {69, 48885}, {141, 3853}, {376, 5965}, {547, 54169}, {599, 29323}, {632, 42785}, {1352, 5059}, {1503, 15686}, {1657, 43150}, {2979, 35268}, {3533, 51212}, {3534, 51027}, {3543, 10519}, {3545, 19924}, {3564, 15690}, {3629, 33923}, {3631, 15704}, {3818, 48874}, {3832, 24206}, {3845, 29181}, {3850, 48901}, {5056, 31670}, {5067, 19130}, {5476, 11812}, {5480, 16239}, {6036, 46944}, {6329, 44682}, {6403, 35478}, {7998, 13595}, {8703, 50970}, {9306, 33884}, {10516, 38335}, {11001, 29012}, {11204, 44668}, {11539, 38317}, {12007, 46853}, {12045, 17810}, {14561, 15702}, {14853, 15708}, {14912, 51214}, {15069, 48891}, {15107, 16187}, {15578, 34788}, {15695, 50973}, {15696, 40341}, {15697, 50961}, {15714, 20583}, {15719, 20423}, {15723, 54131}, {15759, 51132}, {16981, 43650}, {18440, 48920}, {18553, 48872}, {19710, 50982}, {19711, 38110}, {33703, 40107}, {33750, 54174}, {33851, 52098}, {33879, 34417}, {34507, 48881}, {38726, 41731}, {41981, 44882}, {46332, 51737}, {48876, 48880}

X(55603) = midpoint of X(i) and X(j) for these {i,j}: {14561, 54170}, {17508, 55589}, {3, 55591}, {3098, 55596}, {31884, 55593}, {39561, 55587}, {5085, 33878}, {5093, 53097}
X(55603) = reflection of X(i) in X(j) for these {i,j}: {1350, 55599}, {11178, 10519}, {15520, 17508}, {17508, 31884}, {37517, 39561}, {39561, 3}, {576, 5085}, {5085, 14810}, {5093, 5092}, {5476, 21167}, {52987, 55596}, {55587, 55591}, {55589, 55593}, {55591, 55594}, {55596, 1350}, {55599, 55601}
X(55603) = center of Tucker-Hagos(-5/3) circle
X(55603) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1297), X(39561)}}, {{A, B, C, X(14075), X(14483)}}
X(55603) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55594}, {3, 511, 39561}, {3, 55582, 5097}, {3, 55587, 37517}, {3, 55594, 55587}, {6, 1350, 55595}, {6, 55590, 55583}, {6, 55595, 55590}, {182, 52987, 55585}, {511, 1350, 55596}, {511, 14810, 5085}, {511, 5092, 5093}, {511, 55601, 55599}, {576, 3098, 14810}, {1350, 3098, 52987}, {1350, 31884, 55593}, {1350, 33878, 55597}, {1350, 52987, 55598}, {1350, 55601, 55600}, {1350, 55602, 55601}, {3098, 17508, 31884}, {3098, 55589, 17508}, {3098, 55592, 22234}, {3098, 55593, 15520}, {3098, 55597, 55581}, {3098, 55600, 1350}, {10519, 29317, 11178}, {11812, 51166, 5476}, {14810, 33878, 576}, {14810, 50664, 3}, {14810, 55581, 182}, {14810, 55597, 33878}, {15520, 37517, 5102}, {17508, 55589, 511}, {17508, 55596, 55589}, {22234, 52987, 53097}, {34507, 48881, 48896}, {39561, 55596, 55591}, {40107, 48873, 48884}

X(55604) = X(3)X(6)∩X(30)X(3620)

Barycentrics    a^2*(5*a^4-13*b^4-10*b^2*c^2-13*c^4+8*a^2*(b^2+c^2)) : :
X(55604) = -9*X[3]+4*X[6], 4*X[20]+X[48662], 2*X[69]+3*X[3534], -8*X[141]+3*X[3830], -X[193]+6*X[8703], 9*X[376]+X[20080], -9*X[381]+14*X[3619], -X[382]+6*X[10519], 4*X[550]+X[11898], 4*X[599]+X[15685], 4*X[1352]+X[17800], -2*X[1353]+7*X[3528] and many others

X(55604) lies on these lines: {2, 54707}, {3, 6}, {20, 48662}, {30, 3620}, {69, 3534}, {141, 3830}, {193, 8703}, {376, 20080}, {381, 3619}, {382, 10519}, {524, 15695}, {550, 11898}, {599, 15685}, {1352, 17800}, {1353, 3528}, {1597, 33533}, {1657, 48876}, {1843, 35501}, {2979, 26864}, {3522, 34380}, {3526, 51212}, {3531, 41435}, {3564, 15696}, {3589, 15701}, {3618, 15693}, {3630, 15689}, {3631, 15681}, {3763, 19709}, {3818, 15684}, {3819, 31860}, {3843, 29181}, {3917, 20850}, {5020, 15107}, {5032, 15759}, {5054, 21850}, {5055, 31670}, {5072, 51538}, {5073, 48873}, {5076, 40330}, {5480, 46219}, {5644, 7485}, {5921, 12103}, {8148, 49465}, {9039, 41454}, {9909, 15066}, {9924, 35450}, {9970, 38638}, {10299, 51732}, {10304, 50962}, {10545, 21766}, {11008, 15688}, {11160, 15690}, {11179, 50970}, {11284, 48912}, {11414, 12112}, {11451, 16419}, {11539, 51173}, {11579, 38633}, {12100, 51171}, {12177, 38635}, {12702, 16496}, {14269, 48910}, {14848, 15718}, {14853, 15720}, {14912, 33923}, {14997, 21487}, {15058, 39568}, {15069, 48885}, {15694, 51126}, {15700, 54132}, {15703, 19130}, {15707, 20423}, {15722, 47352}, {17504, 51028}, {18325, 47449}, {19588, 52099}, {19708, 51170}, {20421, 38263}, {21358, 48895}, {30771, 33522}, {34200, 54174}, {36990, 49139}, {39884, 49137}, {40107, 48872}, {40341, 48892}, {42785, 54131}, {42786, 53023}, {47353, 48879}, {48905, 50955}, {50969, 51175}

X(55604) = midpoint of X(i) and X(j) for these {i,j}: {12017, 33878}, {22234, 55587}, {3098, 55598}
X(55604) = reflection of X(i) in X(j) for these {i,j}: {1350, 55600}, {1351, 53093}, {11482, 53094}, {382, 51537}, {5076, 40330}, {53091, 3}, {55595, 1350}
X(55604) = isogonal conjugate of X(54612)
X(55604) = center of -8/5-Tucker-Hagos ci
rcleX(55604) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(74), X(22331)}}, {{A, B, C, X(1297), X(53091)}}, {{A, B, C, X(3431), X(22332)}}, {{A, B, C, X(3531), X(5007)}}, {{A, B, C, X(5023), X(20421)}}, {{A, B, C, X(7772), X(44731)}}, {{A, B, C, X(40802), X(55594)}}
X(55604) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55593}, {3, 33878, 44456}, {3, 511, 53091}, {3, 55584, 5093}, {3, 55593, 55584}, {6, 1350, 55594}, {15, 16, 22331}, {182, 55591, 55580}, {182, 55597, 55591}, {511, 1350, 55595}, {511, 53094, 11482}, {1350, 31884, 52987}, {1350, 53097, 55596}, {1350, 55591, 55597}, {1350, 55603, 55602}, {1351, 31884, 3}, {1351, 33878, 55582}, {1351, 5050, 22330}, {1351, 55602, 55599}, {1384, 5024, 13357}, {3098, 37517, 14810}, {3098, 5092, 31884}, {3098, 52987, 5092}, {3098, 55594, 6}, {3098, 55596, 37517}, {3098, 55600, 55598}, {3098, 55601, 1350}, {3098, 55603, 55601}, {5092, 53093, 12017}, {6199, 6395, 43136}, {6200, 6396, 5023}, {6221, 6398, 32}, {6411, 9601, 6200}, {6451, 6452, 8588}, {10519, 48874, 382}, {10645, 10646, 5585}, {11485, 11486, 5007}, {12017, 33878, 511}, {12017, 55595, 33878}, {14810, 53097, 5050}, {14810, 55596, 53097}, {18440, 48881, 15681}, {31884, 52987, 1351}, {33878, 55580, 55586}, {42115, 42116, 187}, {48881, 54173, 18440}, {55595, 55602, 55600}

X(55605) = X(3)X(6)∩X(1353)X(50970)

Barycentrics    7*a^6+11*a^4*(b^2+c^2)-2*a^2*(9*b^4+7*b^2*c^2+9*c^4) : :
X(55605) = -25*X[3]+11*X[6], X[1353]+6*X[50970], -11*X[5480]+18*X[47598], X[5921]+6*X[48885], -4*X[10109]+11*X[54169], -33*X[10519]+5*X[50691], -11*X[11178]+4*X[33699], -4*X[14893]+11*X[50977], -22*X[19130]+29*X[46935], -22*X[20582]+15*X[38071], 9*X[21356]+5*X[48873], -22*X[24206]+15*X[41099] and many others

X(55605) lies on these lines: {3, 6}, {1353, 50970}, {5480, 47598}, {5921, 48885}, {6723, 33522}, {10109, 54169}, {10519, 50691}, {11178, 33699}, {14893, 50977}, {16187, 44106}, {19130, 46935}, {19924, 50964}, {20582, 38071}, {21356, 48873}, {24206, 41099}, {33751, 50967}, {35434, 48889}, {38317, 45760}, {39884, 48879}, {40107, 50692}, {40330, 48904}, {44903, 48876}, {46333, 48896}

X(55605) = midpoint of X(i) and X(j) for these {i,j}: {10541, 33878}
X(55605) = reflection of X(i) in X(j) for these {i,j}: {37517, 53092}, {53858, 5092}
X(55605) = center of Tucker-Hagos(-11/7) circle
X(55605) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55592}, {3, 55592, 55581}, {3, 55598, 55589}, {182, 52987, 55584}, {511, 5092, 53858}, {511, 53092, 37517}, {1350, 1351, 55594}, {1350, 14810, 52987}, {1350, 3098, 55587}, {1350, 53094, 55593}, {1350, 55587, 55596}, {1350, 55592, 55598}, {3098, 52987, 17508}, {3098, 55589, 3}, {3098, 55596, 576}, {3098, 55603, 55600}, {10541, 33878, 511}, {14810, 55584, 182}, {14810, 55601, 1350}, {20190, 52987, 55583}, {31884, 55597, 55585}, {52987, 55603, 55601}

X(55606) = X(3)X(6)∩X(23)X(3917)

Barycentrics    a^2*(2*a^4-5*b^4-4*b^2*c^2-5*c^4+3*a^2*(b^2+c^2)) : :
X(55606) = -7*X[3]+3*X[6], -2*X[4]+3*X[25561], 5*X[20]+3*X[11180], -5*X[140]+6*X[50984], -3*X[141]+X[3627], 7*X[376]+X[50992], -X[382]+3*X[11178], -2*X[546]+3*X[24206], -3*X[549]+2*X[25555], -3*X[597]+5*X[15712], 3*X[599]+X[1657], -5*X[631]+3*X[5476] and many others

X(55606) lies on these lines: {3, 6}, {4, 25561}, {5, 19924}, {20, 11180}, {23, 3917}, {30, 18553}, {51, 5643}, {69, 13452}, {140, 50984}, {141, 3627}, {315, 51397}, {373, 41462}, {376, 50992}, {382, 11178}, {524, 548}, {542, 550}, {546, 24206}, {549, 25555}, {597, 15712}, {599, 1657}, {629, 51161}, {630, 51162}, {631, 5476}, {632, 5480}, {1352, 3529}, {1386, 31666}, {1495, 33884}, {1503, 12103}, {1843, 14865}, {1974, 35479}, {1992, 21735}, {1995, 3819}, {2393, 15579}, {2781, 7555}, {2930, 10575}, {2979, 3292}, {3066, 12045}, {3090, 31670}, {3091, 48901}, {3146, 3818}, {3357, 34787}, {3518, 12294}, {3522, 50967}, {3523, 20423}, {3524, 46267}, {3525, 38317}, {3526, 54131}, {3528, 11179}, {3530, 10168}, {3534, 15069}, {3544, 51538}, {3564, 44245}, {3589, 12108}, {3620, 49140}, {3628, 19130}, {3763, 5072}, {3843, 21358}, {3850, 20582}, {3851, 51024}, {5076, 10516}, {5079, 53023}, {5182, 33276}, {5447, 12106}, {5562, 8718}, {5609, 33851}, {5650, 15107}, {5891, 37924}, {5907, 12082}, {5943, 40916}, {5965, 44882}, {5969, 7780}, {6000, 15581}, {6403, 35475}, {6636, 23061}, {6688, 33586}, {7464, 36987}, {7470, 38664}, {7485, 21849}, {7488, 9970}, {7530, 11793}, {7550, 45186}, {7575, 54042}, {7689, 8681}, {7691, 15021}, {7749, 53505}, {7750, 50567}, {7756, 15993}, {7768, 52088}, {7895, 40278}, {7998, 14002}, {8541, 35477}, {8542, 12084}, {8549, 11204}, {8550, 8703}, {8584, 45759}, {9716, 15080}, {9968, 15577}, {9976, 15055}, {10219, 17810}, {10249, 34788}, {10299, 38064}, {10303, 14561}, {10628, 32367}, {11160, 50969}, {11416, 35497}, {11422, 22352}, {11470, 32534}, {11649, 37950}, {12086, 41714}, {12100, 41153}, {12105, 43586}, {12122, 23235}, {12812, 34573}, {13564, 52098}, {13857, 52300}, {14093, 15534}, {14831, 44832}, {14848, 51137}, {14869, 21167}, {14893, 51143}, {15019, 15246}, {15022, 42786}, {15023, 34155}, {15027, 32273}, {15030, 37946}, {15034, 19140}, {15039, 51941}, {15066, 32237}, {15067, 37967}, {15073, 21663}, {15074, 43604}, {15082, 21766}, {15533, 15689}, {15582, 34146}, {15684, 50993}, {15686, 22165}, {15704, 29012}, {15706, 51185}, {15717, 54132}, {15826, 34152}, {16010, 33542}, {16051, 33522}, {16187, 30734}, {16661, 45187}, {16789, 32257}, {16982, 32191}, {17800, 47353}, {18440, 48896}, {19596, 47748}, {20301, 20397}, {21243, 46517}, {21356, 33703}, {21734, 54174}, {21844, 44102}, {22486, 33004}, {29113, 49560}, {31099, 43653}, {32271, 38795}, {32449, 32523}, {32521, 51523}, {33749, 46853}, {33751, 48906}, {33879, 48912}, {33923, 50970}, {35018, 50959}, {36990, 48879}, {37455, 44422}, {37465, 52658}, {38072, 46219}, {38079, 51166}, {38335, 51186}, {40330, 43621}, {41149, 46332}, {41981, 50971}, {46264, 50693}, {46333, 50990}, {47316, 53415}, {48872, 48884}, {50985, 51134}, {51393, 54047}

X(55606) = midpoint of X(i) and X(j) for these {i,j}: {141, 48874}, {182, 33878}, {1350, 3098}, {1351, 55585}, {1352, 48880}, {11477, 55583}, {14810, 55594}, {15686, 22165}, {17508, 55591}, {18440, 48896}, {20, 34507}, {3, 52987}, {3357, 34787}, {3818, 48873}, {31884, 55596}, {35456, 52993}, {36990, 48879}, {37517, 55584}, {43150, 48920}, {44456, 55581}, {48872, 48884}, {48876, 48881}, {575, 55588}, {576, 53097}, {5085, 55589}, {5092, 55590}, {5097, 55586}, {5476, 54170}, {6, 55587}, {69, 48898}, {9821, 52996}
X(55606) = reflection of X(i) in X(j) for these {i,j}: {1350, 55601}, {1351, 50664}, {11477, 22330}, {14810, 3098}, {14893, 51143}, {18553, 40107}, {25561, 50977}, {33878, 55592}, {37517, 15516}, {43150, 48876}, {48889, 141}, {48891, 48885}, {48895, 24206}, {48906, 33751}, {48920, 48881}, {48942, 3818}, {48943, 48889}, {575, 3}, {576, 20190}, {5092, 14810}, {5097, 5092}, {52987, 55597}, {55586, 55590}, {55588, 52987}, {55590, 55594}, {55594, 1350}, {55599, 55603}, {9968, 50414}
X(55606) = isogonal conjugate of X(54857)
X(55606) = center of Tucker-Hagos(-3/2) circle
X(55606) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(32), X(13452)}}, {{A, B, C, X(575), X(1297)}}, {{A, B, C, X(1384), X(44763)}}, {{A, B, C, X(10541), X(40801)}}
X(55606) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10541, 17508}, {3, 11477, 182}, {3, 11482, 5085}, {3, 1350, 52987}, {3, 47066, 21402}, {3, 47068, 21401}, {3, 575, 5092}, {3, 576, 20190}, {3, 55580, 6}, {3, 55584, 11482}, {3, 55593, 55580}, {3, 55595, 53097}, {3, 55602, 1350}, {3, 55604, 55602}, {6, 1350, 55593}, {6, 55593, 55587}, {20, 34507, 11645}, {20, 54173, 34507}, {30, 40107, 18553}, {141, 29317, 48889}, {141, 48874, 29317}, {182, 11477, 22330}, {182, 1350, 55592}, {182, 3098, 31884}, {182, 576, 53092}, {182, 55583, 11477}, {187, 44453, 44499}, {511, 3098, 14810}, {1350, 14810, 55590}, {1350, 31884, 33878}, {1350, 33878, 55596}, {1350, 52987, 55597}, {1350, 53097, 55595}, {1350, 55593, 55598}, {1350, 55601, 55599}, {1350, 55602, 55600}, {1350, 55603, 55601}, {1350, 55604, 55603}, {1351, 10541, 22234}, {1351, 55591, 55585}, {1352, 48880, 29323}, {1503, 48885, 48891}, {2979, 7492, 3292}, {5085, 37517, 15516}, {5085, 55584, 37517}, {5092, 55594, 55586}, {5351, 5352, 15513}, {6455, 6456, 15603}, {9968, 15577, 50414}, {10519, 48873, 3818}, {10541, 22234, 50664}, {11477, 31884, 3}, {11477, 33878, 55583}, {11477, 53092, 576}, {11477, 55583, 511}, {11477, 55592, 55588}, {11824, 11825, 8722}, {14540, 14541, 5188}, {14810, 55588, 575}, {14810, 55590, 5097}, {14810, 55599, 55594}, {17508, 22234, 10541}, {17508, 55585, 1351}, {21766, 34417, 15082}, {24206, 29181, 48895}, {29012, 48876, 43150}, {29012, 48881, 48920}, {29317, 48889, 48943}, {37517, 55589, 55584}, {39561, 55581, 44456}, {43150, 48920, 29012}, {44456, 53094, 39561}, {55603, 55605, 55604}

X(55607) = X(3)X(6)∩X(20)X(3631)

Barycentrics    a^2*(7*a^4-17*b^4-14*b^2*c^2-17*c^4+10*a^2*(b^2+c^2)) : :
X(55607) = -12*X[3]+5*X[6], 3*X[20]+4*X[3631], -10*X[141]+3*X[3543], 6*X[376]+X[40341], -12*X[547]+5*X[31670], 5*X[599]+2*X[11001], -15*X[3522]+X[11008], -3*X[3526]+2*X[42785], -17*X[3533]+10*X[5480], -18*X[3545]+25*X[3763], -20*X[3589]+27*X[15708], -5*X[3619]+3*X[3832] and many others

X(55607) lies on these lines: {3, 6}, {20, 3631}, {69, 41467}, {141, 3543}, {376, 40341}, {394, 7712}, {547, 31670}, {599, 11001}, {3066, 5888}, {3522, 11008}, {3526, 42785}, {3532, 7691}, {3533, 5480}, {3545, 3763}, {3589, 15708}, {3619, 3832}, {3620, 5059}, {3629, 10304}, {3818, 50993}, {3839, 51165}, {3845, 21358}, {3853, 10516}, {3917, 41424}, {5056, 34573}, {5562, 46207}, {6144, 50967}, {6329, 15692}, {7488, 15748}, {9973, 36987}, {10519, 33703}, {10546, 17811}, {10605, 46945}, {11179, 41982}, {11531, 49465}, {11539, 54131}, {11645, 51189}, {11812, 21850}, {12007, 21735}, {14490, 34817}, {15042, 34155}, {15066, 37913}, {15080, 37672}, {15107, 44299}, {15533, 15690}, {15681, 43150}, {15686, 48905}, {15688, 50973}, {15702, 47355}, {15710, 51132}, {15719, 47352}, {15723, 38072}, {16176, 38726}, {18358, 48873}, {19924, 42786}, {20080, 44882}, {20423, 41983}, {21766, 48912}, {32455, 54174}, {33522, 47296}, {33586, 41462}, {35400, 48884}, {37689, 46944}, {38335, 50977}, {43273, 51183}, {47353, 48880}, {48891, 50955}, {48892, 50968}, {51126, 51212}

X(55607) = reflection of X(i) in X(j) for these {i,j}: {1350, 55602}, {55602, 55605}, {55605, 55606}
X(55607) = center of Tucker-Hagos(-10/7) circle
X(55607) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3532), X(35007)}}, {{A, B, C, X(11738), X(21309)}}, {{A, B, C, X(14483), X(43136)}}, {{A, B, C, X(14490), X(30435)}}
X(55607) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55591}, {3, 33878, 37517}, {3, 5097, 5085}, {3, 55587, 5102}, {3, 55594, 55582}, {3, 55603, 1350}, {6, 3098, 31884}, {182, 55599, 55595}, {511, 55605, 55602}, {511, 55606, 55605}, {1151, 1152, 35007}, {1350, 11477, 55593}, {1350, 31884, 53097}, {1350, 5085, 52987}, {1350, 55582, 55594}, {3098, 55585, 14810}, {3098, 55598, 5092}, {3098, 55601, 33878}, {3098, 55606, 55604}, {5092, 55601, 55598}, {6437, 6438, 5008}, {11477, 12017, 6}, {11480, 11481, 5206}, {11824, 35247, 6411}, {11825, 35246, 6412}, {12017, 55585, 11477}, {12017, 55593, 55585}, {12017, 55604, 55600}, {14810, 39561, 3}, {14810, 55585, 12017}, {15708, 54170, 51166}, {17508, 55592, 55580}, {31884, 53097, 53094}, {33878, 55604, 55601}, {50664, 55594, 55587}

X(55608) = X(3)X(6)∩X(542)X(15697)

Barycentrics    5*a^6+7*a^4*(b^2+c^2)-2*a^2*(6*b^4+5*b^2*c^2+6*c^4) : :
X(55608) = -17*X[3]+7*X[6], 3*X[599]+2*X[48920], 7*X[1352]+3*X[15683], X[3630]+4*X[44245], -9*X[3839]+14*X[24206], -12*X[3861]+7*X[51163], -12*X[5066]+7*X[48901], -7*X[5480]+12*X[10124], -17*X[7486]+7*X[31670], -6*X[10519]+X[48884], -7*X[11178]+2*X[15682] and many others

X(55608) lies on these lines: {3, 6}, {542, 15697}, {599, 48920}, {1352, 15683}, {3630, 44245}, {3839, 24206}, {3858, 29181}, {3861, 51163}, {5066, 48901}, {5071, 19924}, {5480, 10124}, {7486, 31670}, {10519, 48884}, {11178, 15682}, {14927, 48885}, {15687, 48874}, {15691, 48898}, {15709, 51212}, {15721, 51141}, {17578, 29317}, {18583, 44580}, {19710, 41152}, {39884, 48880}, {40107, 48879}

X(55608) = midpoint of X(i) and X(j) for these {i,j}: {3098, 55600}, {33878, 53093}, {48873, 51537}
X(55608) = reflection of X(i) in X(j) for these {i,j}: {11482, 5092}, {37517, 22234}, {576, 12017}, {52987, 55598}, {53094, 14810}, {55598, 55600}, {55600, 55604}, {55604, 55606}
X(55608) = center of Tucker-Hagos(-7/5) circle
X(55608) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55590}, {6, 55597, 55589}, {182, 1350, 52987}, {182, 55581, 37517}, {182, 55603, 1350}, {511, 14810, 53094}, {511, 5092, 11482}, {511, 55604, 55600}, {511, 55606, 55604}, {576, 3098, 31884}, {1350, 1351, 55592}, {1350, 14810, 55587}, {1350, 3098, 182}, {1350, 31884, 55584}, {1350, 55584, 55594}, {1350, 55590, 55596}, {1350, 55605, 55603}, {1350, 55606, 55605}, {3098, 55587, 14810}, {3098, 55600, 511}, {3098, 55604, 55598}, {5092, 55593, 55583}, {14810, 15516, 3}, {14810, 55590, 15516}, {14810, 55592, 1351}, {15520, 52987, 55585}, {15520, 55590, 55581}, {31884, 55594, 576}, {48874, 50977, 48904}, {53093, 55604, 55599}

X(55609) = X(3)X(6)∩X(141)X(33699)

Barycentrics    a^2*(8*a^4-19*b^4-16*b^2*c^2-19*c^4+11*a^2*(b^2+c^2)) : :
X(55609) = -27*X[3]+11*X[6], -11*X[141]+3*X[33699], -77*X[3619]+45*X[41099], 5*X[3620]+3*X[48880], X[3630]+3*X[48892], -33*X[10519]+X[50692], -13*X[11178]+5*X[51167], X[31670]+15*X[50966], -15*X[35434]+11*X[48943], -3*X[38071]+11*X[54169], 11*X[43150]+9*X[46333], -11*X[43621]+27*X[50687] and many others

X(55609) lies on circumconic {{A, B, C, X(5007), X(14487)}} and on these lines: {3, 6}, {141, 33699}, {3619, 41099}, {3620, 48880}, {3630, 48892}, {3631, 11645}, {3856, 29181}, {5888, 12045}, {6688, 41462}, {10109, 19924}, {10519, 50692}, {11178, 51167}, {14487, 41435}, {15082, 48912}, {31670, 50966}, {35434, 48943}, {38071, 54169}, {43150, 46333}, {43621, 50687}, {44903, 48881}, {46264, 50969}, {48873, 50691}, {48891, 54173}, {48906, 51182}

X(55609) = midpoint of X(i) and X(j) for these {i,j}: {14810, 55597}, {15516, 55588}, {20190, 55590}, {22330, 55587}, {3, 55592}, {3098, 55601}, {33878, 50664}
X(55609) = center of Tucker-Hagos(-11/8) circle
X(55609) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55589}, {3, 55598, 55586}, {3, 55599, 55592}, {3, 55605, 55599}, {576, 55589, 55581}, {576, 55603, 1350}, {1350, 3098, 5092}, {1350, 31884, 55580}, {1350, 5050, 52987}, {1350, 55585, 55594}, {3098, 33878, 14810}, {3098, 37517, 31884}, {3098, 55598, 3}, {3098, 55600, 37517}, {3098, 55603, 33878}, {3098, 55605, 55598}, {3098, 55606, 55601}, {3098, 55607, 55606}, {3098, 55608, 55607}, {5092, 44456, 15516}, {5092, 55588, 44456}, {5092, 55594, 55585}, {14810, 33878, 50664}, {14810, 55590, 53091}, {14810, 55597, 511}, {14810, 55603, 55597}, {14810, 55606, 55603}, {31884, 55590, 20190}, {31884, 55600, 55590}, {55594, 55606, 55604}, {55599, 55606, 55605}

X(55610) = X(3)X(6)∩X(69)X(550)

Barycentrics    a^2*(3*a^4-7*b^4-6*b^2*c^2-7*c^4+4*a^2*(b^2+c^2)) : :
X(55610) = -3*X[2]+2*X[38136], -5*X[3]+2*X[6], X[4]+2*X[48874], -4*X[140]+X[51212], -4*X[141]+X[382], -4*X[159]+X[12315], -X[193]+7*X[3528], -5*X[381]+8*X[20582], -X[399]+4*X[33851], -4*X[546]+7*X[3619], -4*X[548]+X[6776] and many others

X(55610) lies on these lines: {2, 38136}, {3, 6}, {4, 48874}, {5, 51538}, {20, 18440}, {22, 6090}, {25, 7998}, {30, 10519}, {69, 550}, {140, 51212}, {141, 382}, {159, 12315}, {193, 3528}, {373, 16419}, {376, 3564}, {381, 20582}, {394, 35268}, {399, 33851}, {524, 15688}, {542, 15689}, {546, 3619}, {548, 6776}, {549, 14853}, {597, 15700}, {599, 15681}, {631, 21850}, {732, 51122}, {1352, 1657}, {1353, 33923}, {1368, 33522}, {1503, 3534}, {1511, 48679}, {1597, 32620}, {1598, 10170}, {1656, 31670}, {1975, 12122}, {1992, 33750}, {2781, 32609}, {2854, 15041}, {2979, 3167}, {3146, 18358}, {3357, 9924}, {3516, 6403}, {3517, 5447}, {3520, 12167}, {3522, 48906}, {3523, 18583}, {3524, 14848}, {3526, 5480}, {3527, 7516}, {3529, 3620}, {3530, 3618}, {3589, 15720}, {3627, 40330}, {3751, 31663}, {3763, 3851}, {3818, 5073}, {3830, 10516}, {3843, 24206}, {3917, 9909}, {4316, 39891}, {4324, 39892}, {5020, 5650}, {5032, 15710}, {5054, 14561}, {5055, 19924}, {5070, 19130}, {5076, 43621}, {5079, 34573}, {5181, 20127}, {5476, 15701}, {5544, 40916}, {5621, 38633}, {5640, 7484}, {5644, 21849}, {5663, 35243}, {5878, 15585}, {5921, 17538}, {5965, 15695}, {6101, 19347}, {6391, 11270}, {7373, 10387}, {7387, 15067}, {7485, 11002}, {7492, 26864}, {7689, 33543}, {8547, 33544}, {8703, 25406}, {8705, 18859}, {9155, 38873}, {9777, 15246}, {9970, 15040}, {10109, 50981}, {10168, 15718}, {10299, 51171}, {10300, 37643}, {10304, 14912}, {10323, 12164}, {10620, 32254}, {10627, 41716}, {11178, 15684}, {11179, 14093}, {11180, 15686}, {11188, 12085}, {11204, 52028}, {11284, 15107}, {11410, 39588}, {11414, 11459}, {11799, 47451}, {11820, 33532}, {11898, 15696}, {12100, 54132}, {12103, 14927}, {12121, 32306}, {12163, 19588}, {12174, 16661}, {12308, 12584}, {12601, 23275}, {12602, 21737}, {12902, 49116}, {13093, 34778}, {13564, 14530}, {14070, 54042}, {14269, 21358}, {14907, 51374}, {14984, 15055}, {15030, 39568}, {15035, 45016}, {15069, 48898}, {15072, 37198}, {15533, 50968}, {15574, 51383}, {15578, 34777}, {15646, 52238}, {15685, 29323}, {15690, 50969}, {15693, 20423}, {15694, 38317}, {15698, 51028}, {15706, 38064}, {15707, 47352}, {15708, 38079}, {15716, 50983}, {15988, 19535}, {16187, 31860}, {16434, 37687}, {16475, 17502}, {16835, 41464}, {17800, 36990}, {17811, 20850}, {17821, 34779}, {18325, 47569}, {18553, 48879}, {19118, 32534}, {19274, 25898}, {19708, 50979}, {19709, 51024}, {19710, 51023}, {21970, 30739}, {23039, 32063}, {25561, 35403}, {32247, 34153}, {32608, 32621}, {34469, 39874}, {34507, 48662}, {34609, 43653}, {35498, 40929}, {36701, 49029}, {36703, 49028}, {36987, 54992}, {37899, 54013}, {38040, 54445}, {38638, 52697}, {38741, 50567}, {38753, 51007}, {39899, 44882}, {40132, 40911}, {41149, 50962}, {43150, 48896}, {44682, 51732}, {44833, 52301}, {46332, 51214}, {46336, 47582}, {47446, 47468}, {48884, 49134}, {50954, 50991}, {50956, 51143}, {50961, 50972}, {50971, 51175}, {50975, 50992}, {50984, 51173}, {50985, 51177}, {50994, 51184}

X(55610) = midpoint of X(i) and X(j) for these {i,j}: {182, 55589}, {1350, 31884}, {14853, 54170}, {15520, 55587}, {17508, 52987}, {25406, 50967}, {3, 55593}, {3098, 55603}, {5050, 33878}, {5085, 55591}, {5102, 53097}
X(55610) = reflection of X(i) in X(j) for these {i,j}: {1350, 55603}, {1351, 5050}, {10516, 50977}, {1597, 32620}, {11477, 15520}, {14269, 21358}, {14561, 21167}, {14848, 3524}, {14853, 549}, {15520, 5092}, {16475, 17502}, {17508, 14810}, {25406, 8703}, {3, 31884}, {3830, 10516}, {31884, 3098}, {33878, 55593}, {44456, 5102}, {45016, 15035}, {5050, 3}, {5093, 5085}, {5102, 182}, {51538, 5}, {52028, 11204}, {52238, 15646}, {53097, 55589}, {54131, 38317}, {6, 17508}, {55589, 55594}, {55591, 55596}, {55593, 1350}, {55596, 55599}, {55603, 55606}
X(55610) = isogonal conjugate of X(54845)
X(55610) = anticomplement of X(38136)
X(55610) = inverse of isogonal conjugate of X(52519) in First Brocard Circle
X(55610) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 54845}, {38136, 38136}
X(55610) = center of Tucker-Hagos(-4/3) circle
X(55610) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(6), X(52519)}}, {{A, B, C, X(32), X(43719)}}, {{A, B, C, X(1297), X(5050)}}, {{A, B, C, X(3053), X(11270)}}, {{A, B, C, X(3426), X(5008)}}, {{A, B, C, X(5041), X(43908)}}, {{A, B, C, X(5085), X(14489)}}, {{A, B, C, X(12017), X(40801)}}, {{A, B, C, X(40802), X(52987)}}
X(55610) = barycentric quotient X(i)/X(j) for these (i, j): {6, 54845}
X(55610) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 12017}, {3, 37484, 11426}, {3, 44456, 182}, {3, 47618, 5024}, {3, 5093, 5085}, {3, 511, 5050}, {3, 53091, 5092}, {20, 48876, 18440}, {22, 33884, 6090}, {141, 48873, 382}, {182, 44456, 11482}, {182, 511, 5102}, {182, 53097, 44456}, {182, 55594, 53097}, {511, 14810, 17508}, {511, 3098, 31884}, {511, 5092, 15520}, {511, 55594, 55589}, {511, 55606, 55603}, {575, 55592, 55585}, {576, 55590, 55582}, {1350, 14810, 55584}, {1350, 3098, 3}, {1350, 31884, 511}, {1350, 5085, 55591}, {1350, 53094, 55590}, {1350, 53097, 55594}, {1350, 55591, 55596}, {1350, 55604, 55602}, {1350, 55606, 55604}, {1350, 55607, 55606}, {1351, 12017, 53092}, {1351, 33878, 55580}, {1351, 55595, 33878}, {1352, 48881, 1657}, {3098, 52987, 14810}, {3098, 55609, 55607}, {3529, 3620, 39884}, {3534, 54173, 50955}, {3763, 48901, 3851}, {3818, 48872, 5073}, {5092, 11477, 53091}, {5092, 55587, 11477}, {5092, 55597, 55587}, {8703, 34380, 25406}, {10516, 29317, 3830}, {10983, 50685, 1351}, {11482, 55600, 55595}, {11898, 15696, 46264}, {14561, 21167, 5054}, {14810, 52987, 6}, {14810, 55586, 20190}, {14810, 55601, 52987}, {14810, 55605, 1350}, {14810, 55606, 55601}, {15107, 21766, 11284}, {24206, 48910, 3843}, {29317, 50977, 10516}, {31884, 55596, 5093}, {31884, 55603, 55593}, {34507, 48885, 48905}, {34507, 48905, 48662}, {34778, 39879, 13093}, {36990, 48880, 17800}, {40107, 48880, 36990}, {50965, 54173, 3534}, {53094, 55582, 576}, {55596, 55603, 55599}, {55601, 55606, 55605}, {55606, 55609, 55608}

X(55611) = X(3)X(6)∩X(542)X(50693)

Barycentrics    7*a^6+9*a^4*(b^2+c^2)-2*a^2*(8*b^4+7*b^2*c^2+8*c^4) : :
X(55611) = -23*X[3]+9*X[6], -2*X[546]+9*X[54169], -2*X[3146]+9*X[11178], 11*X[3525]+45*X[50966], X[3529]+6*X[40107], -2*X[3627]+9*X[50977], -9*X[5476]+16*X[12108], 6*X[10519]+X[48879], -2*X[11541]+9*X[48884], -16*X[12102]+9*X[48904], 4*X[12103]+3*X[34507], -16*X[12811]+9*X[48901] and many others

X(55611) lies on these lines: {3, 6}, {542, 50693}, {546, 54169}, {3090, 19924}, {3146, 11178}, {3525, 50966}, {3529, 40107}, {3627, 50977}, {3857, 29181}, {5476, 12108}, {10519, 48879}, {11541, 48884}, {12102, 48904}, {12103, 34507}, {12811, 48901}, {14869, 51141}, {16042, 44299}, {17538, 54173}, {18553, 49137}, {20582, 41991}, {21735, 33749}, {24206, 50689}, {25555, 54170}, {29317, 50688}, {31670, 46936}, {33851, 38632}, {49134, 50993}

X(55611) = midpoint of X(i) and X(j) for these {i,j}: {3098, 55605}
X(55611) = reflection of X(i) in X(j) for these {i,j}: {576, 10541}, {55602, 55606}, {55605, 55607}
X(55611) = center of Tucker-Hagos(-9/7) circle
X(55611) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55588}, {3, 53097, 22330}, {3, 55583, 22234}, {3, 55600, 52987}, {3, 55606, 55600}, {182, 55603, 55598}, {511, 55606, 55602}, {511, 55607, 55605}, {575, 55601, 55595}, {575, 55606, 55601}, {576, 52987, 55585}, {576, 55589, 55580}, {1350, 31884, 44456}, {1350, 5092, 55589}, {1350, 55610, 55609}, {3098, 55587, 31884}, {3098, 55596, 14810}, {3098, 55603, 182}, {3098, 55605, 511}, {3098, 55608, 55603}, {3098, 55610, 55608}, {5050, 55604, 1350}, {11477, 15516, 576}, {14810, 22330, 3}, {14810, 55596, 37517}, {14810, 55604, 55596}, {17508, 55594, 55581}, {22234, 52987, 55583}, {31884, 55595, 575}, {31884, 55601, 55587}, {37517, 52987, 53097}, {52987, 55608, 55606}, {53858, 55602, 55597}

X(55612) = X(3)X(6)∩X(20)X(43150)

Barycentrics    a^2*(4*a^4-9*b^4-8*b^2*c^2-9*c^4+5*a^2*(b^2+c^2)) : :
X(55612) = -13*X[3]+5*X[6], 7*X[376]+X[50961], -5*X[549]+X[51166], 3*X[599]+X[48896], 5*X[1352]+3*X[11001], -11*X[3525]+7*X[42785], -9*X[3543]+25*X[40330], -9*X[3545]+5*X[48901], -X[3629]+5*X[46853], -5*X[3818]+X[33703], -7*X[3832]+5*X[48895], -3*X[3845]+5*X[24206] and many others

X(55612) lies on circumconic {{A, B, C, X(1297), X(50664)}} and on these lines: {3, 6}, {20, 43150}, {376, 50961}, {524, 33751}, {542, 15690}, {547, 19924}, {548, 5965}, {549, 51166}, {599, 48896}, {1352, 11001}, {1469, 51817}, {3060, 5645}, {3066, 10219}, {3525, 42785}, {3543, 40330}, {3545, 48901}, {3564, 41981}, {3629, 46853}, {3631, 12103}, {3818, 33703}, {3819, 13595}, {3832, 48895}, {3845, 24206}, {3850, 29181}, {3853, 29317}, {3917, 32237}, {5059, 10519}, {5067, 31670}, {5476, 15708}, {5480, 11539}, {5921, 48898}, {6000, 15580}, {10168, 19711}, {10516, 48943}, {11178, 48872}, {11645, 15686}, {12007, 34200}, {12294, 47485}, {14093, 51140}, {14927, 34507}, {15036, 34155}, {15082, 15107}, {15691, 50982}, {15702, 50966}, {15714, 51132}, {15719, 54170}, {18583, 41983}, {22352, 55038}, {25561, 38335}, {25565, 41985}, {29323, 39884}, {36987, 41714}, {36990, 50954}, {38136, 41992}, {42786, 51538}, {48884, 49133}

X(55612) = midpoint of X(i) and X(j) for these {i,j}: {182, 55590}, {1350, 14810}, {1352, 48920}, {15691, 50982}, {18553, 48880}, {20, 43150}, {24206, 48874}, {3, 55594}, {3098, 55606}, {3631, 12103}, {31884, 55599}, {34200, 50970}, {34507, 48891}, {40107, 48881}, {48872, 48942}, {48873, 48889}, {48876, 48885}, {575, 33878}, {576, 55586}, {5092, 52987}, {5097, 55587}, {6, 55588}, {9821, 43147}
X(55612) = reflection of X(i) in X(j) for these {i,j}: {22330, 5092}, {50664, 3}, {55592, 1350}, {55597, 55601}, {55601, 55606}, {55606, 55609}
X(55612) = isogonal conjugate of X(54891)
X(55612) = center of Tucker-Hagos(-5/4) circle
X(55612) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55587}, {3, 33878, 5102}, {3, 39561, 5092}, {3, 511, 50664}, {3, 55591, 37517}, {3, 55607, 55603}, {3, 55610, 55607}, {6, 55596, 55588}, {6, 55602, 55596}, {182, 1350, 55590}, {182, 55608, 55605}, {511, 1350, 55592}, {511, 5092, 22330}, {575, 55606, 55600}, {576, 55593, 55586}, {1350, 1351, 52987}, {1350, 14810, 511}, {1350, 3098, 14810}, {1350, 31884, 1351}, {1350, 53094, 33878}, {1350, 55587, 55594}, {1350, 55592, 55597}, {1350, 55608, 55606}, {1350, 55610, 55608}, {1351, 39561, 5097}, {1351, 55604, 1350}, {3098, 52987, 31884}, {3098, 55603, 3}, {3098, 55609, 55601}, {3098, 55611, 55610}, {5085, 55595, 55585}, {5092, 55606, 55599}, {10519, 48880, 18553}, {11178, 48872, 48942}, {14810, 55590, 182}, {14810, 55592, 15516}, {17508, 55598, 53097}, {22330, 50664, 39561}, {39561, 52987, 55582}, {40107, 48881, 29323}, {48873, 50977, 48889}, {48874, 54169, 24206}, {48876, 48885, 11645}, {48876, 50965, 48885}, {55582, 55607, 55604}, {55588, 55606, 55602}, {55606, 55610, 55609}

X(55613) = X(3)X(6)∩X(5480)X(45760)

Barycentrics    9*a^6+11*a^4*(b^2+c^2)-2*a^2*(10*b^4+9*b^2*c^2+10*c^4) : :
X(55613) = -29*X[3]+11*X[6], -11*X[5480]+20*X[45760], -11*X[10516]+5*X[35434], X[14561]+5*X[50966], -2*X[14893]+11*X[54169], -11*X[31670]+29*X[46935], -2*X[33699]+11*X[50977], -5*X[38317]+8*X[50984], -11*X[48884]+2*X[50692], 20*X[50972]+7*X[50978]

X(55613) lies on these lines: {3, 6}, {5480, 45760}, {10516, 35434}, {14561, 50966}, {14893, 54169}, {29012, 46333}, {29181, 38071}, {29317, 50687}, {31670, 46935}, {33699, 50977}, {38317, 50984}, {48884, 50692}, {50972, 50978}

X(55613) = center of Tucker-Hagos(-11/9) circle
X(55613) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55586}, {3, 55599, 55589}, {3, 55605, 55598}, {3, 55609, 55605}, {182, 55585, 11477}, {182, 55592, 55581}, {182, 55603, 55596}, {1350, 31884, 5093}, {1350, 37517, 52987}, {3098, 55596, 31884}, {3098, 55600, 14810}, {3098, 55605, 3}, {3098, 55606, 182}, {3098, 55610, 55603}, {3098, 55611, 55608}, {3098, 55612, 55611}, {11477, 55606, 55600}, {12017, 55585, 37517}, {14810, 55593, 39561}, {14810, 55600, 55585}, {17508, 39561, 12017}, {17508, 55596, 55583}, {22234, 55608, 55604}, {31884, 55610, 55606}, {39561, 55600, 55593}, {55589, 55596, 55592}, {55589, 55605, 55599}, {55593, 55610, 55607}

X(55614) = X(3)X(6)∩X(20)X(599)

Barycentrics    a^2*(5*a^4-11*b^4-10*b^2*c^2-11*c^4+6*a^2*(b^2+c^2)) : :
X(55614) = -8*X[3]+3*X[6], -4*X[4]+9*X[21358], -26*X[5]+21*X[50964], 2*X[20]+3*X[599], -8*X[140]+3*X[54131], -6*X[141]+X[3146], -9*X[154]+4*X[9968], 4*X[376]+X[15533], -X[382]+6*X[50977], 2*X[546]+3*X[48874], -8*X[548]+3*X[43273], 4*X[550]+X[15069] and many others

X(55614) lies on these lines: {3, 6}, {4, 21358}, {5, 50964}, {20, 599}, {23, 17811}, {30, 47448}, {69, 43691}, {140, 54131}, {141, 3146}, {154, 9968}, {376, 15533}, {382, 50977}, {394, 7492}, {524, 3522}, {542, 15696}, {546, 48874}, {548, 43273}, {550, 15069}, {597, 15717}, {631, 50966}, {1352, 15704}, {1498, 15582}, {1503, 17538}, {1656, 19924}, {1657, 40107}, {1992, 21734}, {2393, 8567}, {2781, 15034}, {2854, 15021}, {2930, 15054}, {3066, 41462}, {3090, 53023}, {3091, 3763}, {3242, 7991}, {3304, 10387}, {3523, 47352}, {3525, 5480}, {3526, 38072}, {3528, 8550}, {3529, 10519}, {3530, 20423}, {3534, 34507}, {3543, 51186}, {3619, 50689}, {3627, 10516}, {3628, 31670}, {3631, 14927}, {3796, 23061}, {3818, 49136}, {3832, 20582}, {4663, 16192}, {5059, 21356}, {5072, 48901}, {5073, 11178}, {5076, 29317}, {5476, 15720}, {5493, 47358}, {5609, 35218}, {5646, 34417}, {5648, 10990}, {5650, 30734}, {5999, 8556}, {6144, 25406}, {6593, 38444}, {6636, 9716}, {6698, 15044}, {7467, 36650}, {7486, 50959}, {7496, 17825}, {7716, 11403}, {7735, 46944}, {8703, 51187}, {9588, 38087}, {9589, 51003}, {9925, 12163}, {10299, 54132}, {10303, 21167}, {10304, 15534}, {10605, 41463}, {10606, 34787}, {11160, 50971}, {11179, 33923}, {11414, 19596}, {11451, 33586}, {11898, 48892}, {12007, 33750}, {12082, 15058}, {12102, 43621}, {12103, 48876}, {12108, 21850}, {12329, 44844}, {14094, 33851}, {14561, 14869}, {14924, 17810}, {15020, 52697}, {15022, 34573}, {15023, 52699}, {15156, 15162}, {15157, 15163}, {15581, 34778}, {15683, 50991}, {15692, 51185}, {15697, 50989}, {15850, 40248}, {15993, 44519}, {16010, 33543}, {16042, 21766}, {16661, 35707}, {17800, 18553}, {18374, 43652}, {18440, 48885}, {21735, 51737}, {22334, 34817}, {22828, 22972}, {26958, 33522}, {30389, 38315}, {33703, 47354}, {33749, 50962}, {37751, 38675}, {38064, 44682}, {40258, 54202}, {40341, 44882}, {43653, 46517}, {44245, 46264}, {44535, 53505}, {46853, 51180}, {47114, 47546}, {47445, 47468}, {48154, 50980}, {48662, 48891}, {48880, 49137}, {50687, 51143}, {50692, 51022}, {50969, 51027}

X(55614) = midpoint of X(i) and X(j) for these {i,j}: {3, 55595}, {3098, 55608}, {33878, 53091}
X(55614) = reflection of X(i) in X(j) for these {i,j}: {1350, 55604}, {11477, 11482}, {51185, 15692}, {51537, 141}, {53093, 3}, {6, 53094}, {55595, 55600}, {55600, 55606}, {55604, 55608}
X(55614) = center of Tucker-Hagos(-6/5) circle
X(55614) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(52443)}}, {{A, B, C, X(32), X(43691)}}, {{A, B, C, X(54), X(22246)}}, {{A, B, C, X(64), X(21309)}}, {{A, B, C, X(69), X(33636)}}, {{A, B, C, X(1297), X(53093)}}, {{A, B, C, X(1384), X(3532)}}, {{A, B, C, X(8573), X(34437)}}, {{A, B, C, X(20190), X(40801)}}, {{A, B, C, X(22334), X(30435)}}, {{A, B, C, X(43136), X(52518)}}
X(55614) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 10541}, {3, 1351, 20190}, {3, 53092, 5092}, {3, 53093, 53094}, {3, 55580, 575}, {3, 55584, 53092}, {3, 55588, 53858}, {3, 55595, 511}, {3, 55610, 55606}, {6, 1350, 55591}, {182, 55593, 55582}, {511, 55606, 55600}, {511, 55608, 55604}, {550, 54173, 15069}, {575, 52987, 55580}, {576, 55611, 55609}, {1151, 1152, 1384}, {1350, 11477, 52987}, {1350, 3098, 31884}, {1350, 5085, 33878}, {1350, 55582, 55593}, {1350, 55610, 55607}, {1351, 55605, 1350}, {1657, 40107, 47353}, {3098, 55603, 14810}, {3098, 55606, 3}, {3098, 55612, 55610}, {3098, 55613, 55612}, {3528, 50967, 8550}, {5092, 55584, 5102}, {5092, 55596, 55584}, {6409, 6410, 5210}, {10519, 48881, 36990}, {10541, 11477, 6}, {10541, 53097, 11477}, {10541, 55607, 55602}, {11477, 52987, 53097}, {11477, 53093, 11482}, {11480, 11481, 15655}, {11482, 55602, 55595}, {12017, 22234, 53093}, {12017, 55604, 55598}, {14810, 33878, 5085}, {14810, 55597, 576}, {14810, 55606, 55597}, {14810, 55609, 55603}, {17508, 55590, 44456}, {20190, 55583, 1351}, {20190, 55594, 55583}, {21167, 51212, 47355}, {22236, 22238, 30435}, {36836, 36843, 3053}, {55588, 55606, 55601}, {55604, 55610, 55608}, {55606, 55612, 55611}

X(55615) = X(3)X(6)∩X(141)X(48942)

Barycentrics    a^2*(6*a^4-13*b^4-12*b^2*c^2-13*c^4+7*a^2*(b^2+c^2)) : :
X(55615) = -19*X[3]+7*X[6], -4*X[141]+X[48942], -7*X[3818]+X[49135], 5*X[3858]+7*X[48874], -4*X[3861]+7*X[24206], -13*X[5068]+7*X[48901], -15*X[5071]+7*X[51538], X[5476]+5*X[50966], 7*X[10519]+X[15683], -7*X[14561]+11*X[15721], -X[15682]+7*X[50977], -4*X[15687]+7*X[25561] and many others

X(55615) lies on these lines: {3, 6}, {141, 48942}, {1503, 15691}, {3564, 50971}, {3818, 49135}, {3858, 48874}, {3861, 24206}, {5066, 29181}, {5068, 48901}, {5071, 51538}, {5476, 50966}, {10519, 15683}, {12294, 47486}, {14561, 15721}, {15682, 50977}, {15687, 25561}, {15697, 50969}, {15699, 19924}, {15709, 38317}, {15713, 21167}, {17578, 48873}, {18553, 48881}, {19130, 48154}, {19710, 29012}, {26881, 33884}, {40107, 48920}, {43150, 48885}, {48876, 48891}, {48880, 49138}

X(55615) = midpoint of X(i) and X(j) for these {i,j}: {182, 55591}, {14810, 55599}, {17508, 55593}, {3, 55596}, {3098, 55610}, {31884, 55603}, {33878, 39561}, {5050, 55589}, {5085, 52987}, {5093, 55587}
X(55615) = reflection of X(i) in X(j) for these {i,j}: {5093, 20190}, {5097, 5085}, {55586, 55591}, {55590, 55596}, {55591, 55597}, {55594, 55599}, {55596, 55601}, {55599, 55606}, {55606, 55610}, {55610, 55612}
X(55615) = center of Tucker-Hagos(-7/6) circle
X(55615) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55585}, {3, 55608, 55601}, {6, 55600, 55592}, {182, 55597, 55586}, {182, 55604, 55597}, {511, 20190, 5093}, {511, 5085, 5097}, {511, 55597, 55591}, {511, 55606, 55599}, {1350, 10541, 33878}, {1350, 15516, 55590}, {1350, 31884, 5050}, {1350, 44456, 52987}, {1350, 5050, 55589}, {1350, 5092, 55588}, {1350, 55588, 55594}, {1350, 55609, 55606}, {1350, 55611, 55609}, {3098, 55603, 31884}, {3098, 55606, 14810}, {3098, 55608, 3}, {3098, 55611, 1350}, {3098, 55613, 55610}, {3098, 55614, 55612}, {14810, 55588, 5092}, {14810, 55594, 575}, {14810, 55599, 511}, {15520, 55603, 55596}, {15520, 55608, 55603}, {17508, 55603, 55593}, {31884, 55593, 17508}, {55585, 55611, 55608}, {55609, 55612, 55611}, {55610, 55614, 55613}

X(55616) = X(3)X(6)∩X(141)X(5073)

Barycentrics    a^2*(7*a^4-15*b^4-14*b^2*c^2-15*c^4+8*a^2*(b^2+c^2)) : :
X(55616) = -11*X[3]+4*X[6], 2*X[69]+5*X[15696], -8*X[141]+X[5073], -X[193]+8*X[33923], 6*X[376]+X[11898], 3*X[381]+4*X[48874], -3*X[382]+10*X[40330], -8*X[548]+X[39899], 2*X[549]+5*X[50966], 6*X[550]+X[5921], 3*X[599]+4*X[48885], 4*X[1352]+3*X[15681] and many others

X(55616) lies on circumconic {{A, B, C, X(3531), X(14075)}} and on these lines: {3, 6}, {69, 15696}, {141, 5073}, {193, 33923}, {376, 11898}, {381, 48874}, {382, 40330}, {548, 39899}, {549, 50966}, {550, 5921}, {599, 48885}, {1352, 15681}, {1353, 10304}, {1657, 10519}, {3528, 34380}, {3534, 11180}, {3620, 15704}, {3818, 49134}, {3830, 48873}, {3843, 51163}, {3851, 29181}, {5020, 21766}, {5032, 15714}, {5054, 51212}, {5070, 31670}, {5079, 51538}, {5480, 15694}, {5544, 33586}, {5651, 20850}, {6776, 15688}, {12308, 33851}, {14093, 50967}, {14269, 24206}, {14891, 51028}, {14912, 46853}, {15042, 52699}, {15585, 48672}, {15683, 50954}, {15684, 48872}, {15685, 36990}, {15689, 54173}, {15692, 51732}, {15693, 18583}, {15695, 44882}, {15700, 50988}, {15702, 51173}, {15703, 19924}, {15706, 54132}, {15718, 20423}, {15720, 21850}, {17800, 48881}, {18358, 49136}, {19130, 46215}, {19709, 48901}, {21358, 35403}, {34200, 50962}, {35400, 47354}, {38638, 48679}, {39874, 44245}, {40911, 44212}, {41716, 54047}, {44682, 51171}, {45759, 54174}, {47353, 48920}, {48880, 49139}, {48898, 50955}

X(55616) = midpoint of X(i) and X(j) for these {i,j}: {3098, 55611}, {33878, 53092}
X(55616) = reflection of X(i) in X(j) for these {i,j}: {1350, 55605}, {51171, 44682}, {51173, 15702}, {55602, 55607}, {55607, 55611}
X(55616) = center of Tucker-Hagos(-8/7) circle
X(55616) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55584}, {3, 33878, 5093}, {3, 55593, 44456}, {3, 55610, 55604}, {6, 1350, 55590}, {182, 5093, 53091}, {511, 55611, 55607}, {1350, 14810, 1351}, {1350, 31884, 182}, {1350, 53094, 55587}, {1350, 55584, 55593}, {1350, 55590, 55595}, {1350, 55605, 55602}, {1350, 55607, 55605}, {1350, 55612, 55610}, {1350, 55614, 55612}, {1351, 14810, 3}, {3098, 55606, 31884}, {3098, 55608, 14810}, {3098, 55611, 511}, {3098, 55613, 55606}, {3098, 55615, 55614}, {3311, 3312, 34571}, {3534, 48876, 48662}, {5085, 55594, 55580}, {5092, 55600, 55591}, {11477, 55596, 33878}, {11485, 11486, 14075}, {14810, 55587, 53094}, {14810, 55606, 55592}, {14810, 55608, 1350}, {14810, 55612, 55608}, {17508, 55582, 11482}, {17508, 55597, 55582}

X(55617) = X(3)X(6)∩X(546)X(20582)

Barycentrics    a^2*(8*a^4-17*b^4-16*b^2*c^2-17*c^4+9*a^2*(b^2+c^2)) : :
X(55617) = -25*X[3]+9*X[6], -5*X[382]+21*X[51186], -5*X[546]+9*X[20582], 5*X[550]+3*X[22165], -X[3146]+9*X[50977], -17*X[3544]+9*X[48901], -X[3627]+9*X[54169], -9*X[3818]+X[11541], 7*X[3857]+9*X[48874], -5*X[5076]+9*X[25561], 3*X[10519]+X[48920], 7*X[11160]+25*X[50975] and many others

X(55617) lies on circumconic {{A, B, C, X(5008), X(16835)}} and on these lines: {3, 6}, {382, 51186}, {542, 44245}, {546, 20582}, {550, 22165}, {3146, 50977}, {3292, 6030}, {3529, 7936}, {3544, 48901}, {3627, 54169}, {3628, 19924}, {3818, 11541}, {3819, 14002}, {3857, 48874}, {5076, 25561}, {5447, 12105}, {7492, 44110}, {10519, 48920}, {11160, 50975}, {11178, 49136}, {11645, 12103}, {11793, 37967}, {12045, 41462}, {12102, 29317}, {12584, 16661}, {12811, 29181}, {14869, 48310}, {15688, 51188}, {15704, 40107}, {15712, 46267}, {16042, 44106}, {17538, 34507}, {33749, 34200}, {37946, 44870}, {48873, 50688}, {48880, 49140}, {49139, 50993}, {50693, 54173}, {51136, 51183}

X(55617) = midpoint of X(i) and X(j) for these {i,j}: {14810, 55601}, {15516, 33878}, {20190, 52987}, {22330, 55588}, {3, 55597}, {3098, 55612}, {5092, 55592}, {50664, 55590}
X(55617) = reflection of X(i) in X(j) for these {i,j}: {55609, 55612}
X(55617) = center of Tucker-Hagos(-9/8) circle
X(55617) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55583}, {3, 22234, 5092}, {3, 33878, 53858}, {3, 53097, 22234}, {3, 55583, 575}, {3, 55588, 22330}, {3, 55606, 55597}, {3, 55611, 55606}, {3, 55614, 55611}, {6, 55610, 55605}, {182, 55607, 55599}, {511, 55612, 55609}, {576, 52987, 55584}, {576, 55608, 55602}, {1350, 17508, 55586}, {1350, 31884, 12017}, {3098, 55608, 31884}, {3098, 55610, 14810}, {3098, 55611, 3}, {3098, 55613, 1350}, {3098, 55615, 55612}, {3098, 55616, 55615}, {5092, 55603, 55592}, {5237, 5238, 187}, {6453, 6454, 32}, {14810, 52987, 20190}, {14810, 55586, 17508}, {14810, 55601, 511}, {14810, 55606, 52987}, {14810, 55610, 55601}, {17508, 55613, 55610}, {22330, 55597, 55588}, {31884, 55602, 576}, {31884, 55608, 55594}, {35007, 53096, 13357}, {55588, 55606, 55600}, {55606, 55615, 55614}

X(55618) = X(3)X(6)∩X(141)X(33703)

Barycentrics    a^2*(9*a^4-19*b^4-18*b^2*c^2-19*c^4+10*a^2*(b^2+c^2)) : :
X(55618) = -14*X[3]+5*X[6], -10*X[141]+X[33703], -8*X[547]+5*X[53023], 8*X[548]+X[40341], 5*X[599]+4*X[15686], -2*X[3543]+5*X[10516], -2*X[3629]+11*X[21735], 4*X[3631]+5*X[17538], -25*X[3763]+16*X[3850], -10*X[3818]+X[49133], -14*X[3832]+5*X[48910], 4*X[3853]+5*X[48873] and many others

X(55618) lies on these lines: {3, 6}, {141, 33703}, {154, 33884}, {547, 53023}, {548, 40341}, {599, 15686}, {3543, 10516}, {3545, 29181}, {3629, 21735}, {3631, 17538}, {3763, 3850}, {3818, 49133}, {3832, 48910}, {3853, 48873}, {5056, 51538}, {5059, 48881}, {5646, 15107}, {5965, 15688}, {8703, 50973}, {10519, 11001}, {11178, 35400}, {11539, 38072}, {11812, 14561}, {12007, 21734}, {14853, 15719}, {15533, 50976}, {15534, 46332}, {15580, 34778}, {15690, 50968}, {15697, 50982}, {15702, 21167}, {16239, 38136}, {19708, 50970}, {19711, 20423}, {21358, 29317}, {21766, 31860}, {22165, 50969}, {25561, 35401}, {31662, 38315}, {34380, 41982}, {35259, 37913}, {41153, 54132}, {41983, 47352}, {43273, 50992}, {51214, 51737}

X(55618) = midpoint of X(i) and X(j) for these {i,j}: {3098, 55613}
X(55618) = reflection of X(i) in X(j) for these {i,j}: {55610, 55613}, {55613, 55615}
X(55618) = center of Tucker-Hagos(-10/9) circle
X(55618) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55582}, {3, 33878, 5097}, {3, 50664, 53094}, {3, 55587, 6}, {3, 55591, 5102}, {3, 55607, 1350}, {3, 55610, 55603}, {3, 55612, 55607}, {182, 55609, 55602}, {511, 55615, 55613}, {1350, 31884, 5085}, {1350, 5102, 55591}, {1350, 53093, 33878}, {3098, 55610, 31884}, {3098, 55611, 14810}, {3098, 55613, 511}, {3098, 55615, 55610}, {3098, 55616, 55614}, {3098, 55617, 55616}, {5092, 55605, 55595}, {5097, 55612, 55608}, {14810, 37517, 3}, {14810, 55596, 5050}, {14810, 55604, 53097}, {14810, 55611, 55604}, {15690, 54173, 51027}, {17508, 55608, 55599}, {31884, 55599, 53093}, {37517, 55603, 55596}, {39561, 55603, 55594}, {53097, 55614, 55611}, {55593, 55610, 55606}, {55607, 55614, 55612}, {55610, 55616, 55615}

X(55619) = X(3)X(6)∩X(1352)X(46333)

Barycentrics    a^2*(10*a^4-21*b^4-20*b^2*c^2-21*c^4+11*a^2*(b^2+c^2)) : :
X(55619) = -31*X[3]+11*X[6], 11*X[1352]+9*X[46333], -11*X[3818]+X[50692], -16*X[3856]+11*X[48895], -6*X[14893]+11*X[24206], -7*X[18583]+12*X[51139], 3*X[25561]+2*X[48873], -6*X[33699]+11*X[48889], 9*X[38071]+11*X[48874], 11*X[39884]+9*X[44903], -11*X[40330]+3*X[50691], -X[48942]+6*X[50977]

X(55619) lies on these lines: {3, 6}, {1352, 46333}, {3818, 50692}, {3856, 48895}, {14893, 24206}, {18583, 51139}, {19924, 50980}, {25561, 48873}, {33699, 48889}, {38071, 48874}, {39884, 44903}, {40330, 50691}, {48942, 50977}

X(55619) = midpoint of X(i) and X(j) for these {i,j}: {12017, 52987}, {22234, 33878}, {3, 55598}, {3098, 55614}
X(55619) = reflection of X(i) in X(j) for these {i,j}: {48942, 51537}, {55594, 55600}, {55595, 55601}, {55608, 55612}
X(55619) = center of Tucker-Hagos(-11/10) circle
X(55619) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55581}, {3, 55609, 55599}, {3, 55613, 55609}, {182, 5102, 15516}, {182, 55587, 44456}, {182, 55608, 55600}, {511, 55601, 55595}, {511, 55612, 55608}, {1350, 14810, 5097}, {1350, 5097, 55590}, {1350, 55581, 55592}, {3098, 55611, 31884}, {3098, 55612, 14810}, {3098, 55613, 3}, {3098, 55617, 55615}, {3098, 55618, 55617}, {5097, 55606, 1350}, {11482, 53094, 182}, {11482, 55610, 55604}, {12017, 52987, 511}, {14810, 55590, 5092}, {14810, 55605, 55586}, {14810, 55612, 55606}, {14810, 55615, 55612}, {31884, 55601, 575}, {31884, 55611, 55601}, {44456, 55601, 55594}, {55589, 55600, 55598}, {55589, 55613, 55610}, {55592, 55609, 55605}, {55595, 55614, 55611}, {55599, 55615, 55613}, {55612, 55617, 55616}

X(55620) = X(3)X(6)∩X(69)X(44245)

Barycentrics    a^2*(11*a^4-23*b^4-22*b^2*c^2-23*c^4+12*a^2*(b^2+c^2)) : :
X(55620) = -17*X[3]+6*X[6], 3*X[69]+8*X[44245], -12*X[141]+X[49136], -X[382]+12*X[54169], 8*X[550]+3*X[50955], -35*X[1656]+24*X[50959], 7*X[1657]+15*X[50954], 5*X[3091]+6*X[48874], -25*X[3522]+3*X[50974], 7*X[3523]+15*X[50966], 8*X[3530]+3*X[54170] and many others

X(55620) lies on these lines: {3, 6}, {69, 44245}, {141, 49136}, {382, 54169}, {550, 50955}, {1656, 50959}, {1657, 50954}, {3091, 48874}, {3522, 50974}, {3523, 50966}, {3530, 54170}, {3534, 41152}, {5070, 19924}, {5072, 29181}, {5073, 50977}, {5076, 48873}, {8550, 14093}, {10300, 33522}, {10519, 15704}, {11178, 49134}, {11405, 23040}, {11541, 18358}, {12103, 18440}, {12812, 51538}, {13093, 15581}, {14848, 15712}, {14869, 51212}, {15020, 48679}, {15069, 15689}, {15681, 40107}, {15685, 18553}, {15696, 54173}, {15707, 25555}, {17538, 48876}, {21766, 30734}, {32254, 51522}, {33923, 50967}, {35434, 51143}, {41981, 50978}, {44682, 54132}, {46219, 50963}, {47354, 49133}, {48881, 49137}, {50961, 50971}

X(55620) = center of Tucker-Hagos(-12/11) circle
X(55620) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55580}, {3, 33878, 11482}, {3, 44456, 10541}, {3, 52987, 1351}, {3, 53097, 53092}, {3, 55584, 575}, {3, 55606, 55595}, {3, 55610, 55602}, {3, 55614, 55610}, {3, 55616, 55614}, {6, 1350, 55589}, {576, 5092, 53093}, {576, 55611, 55606}, {1350, 10541, 55588}, {1350, 31884, 5092}, {1350, 5050, 33878}, {1350, 55614, 55611}, {1351, 12017, 39561}, {1351, 5092, 5050}, {1351, 55610, 55604}, {3098, 55612, 31884}, {3098, 55613, 14810}, {3098, 55615, 1350}, {3098, 55618, 55616}, {3098, 55619, 55618}, {5092, 55615, 55612}, {10541, 55588, 44456}, {11477, 14810, 3}, {11477, 55600, 55593}, {11477, 55607, 55600}, {14810, 55593, 12017}, {14810, 55600, 11477}, {14810, 55613, 55607}, {22330, 52987, 55582}, {22330, 55599, 52987}, {53092, 55595, 53097}, {55614, 55618, 55617}

X(55621) = X(3)X(6)∩X(3564)X(51135)

Barycentrics    a^2*(12*a^4-23*b^4-24*b^2*c^2-23*c^4+11*a^2*(b^2+c^2)) : :
X(55621) = -35*X[3]+11*X[6], -17*X[3854]+11*X[48895], -5*X[14893]+11*X[20582], 11*X[21356]+5*X[46333], -11*X[25561]+5*X[35434], X[33699]+11*X[50965], -25*X[45760]+22*X[51127], 5*X[48874]+7*X[51128], 11*X[48880]+X[50692], -11*X[48889]+5*X[50691], 13*X[50992]+35*X[51176]

X(55621) lies on these lines: {3, 6}, {3564, 51135}, {3854, 48895}, {6030, 44108}, {10109, 29181}, {14893, 20582}, {15082, 44106}, {19924, 47598}, {21356, 46333}, {25561, 35434}, {29012, 50991}, {29323, 44903}, {33699, 50965}, {33884, 44110}, {45760, 51127}, {48874, 51128}, {48880, 50692}, {48889, 50691}, {50992, 51176}

X(55621) = midpoint of X(i) and X(j) for these {i,j}: {14810, 55610}, {3, 55599}, {31884, 55615}, {39561, 55590}, {575, 55591}, {5085, 55594}, {5092, 55596}, {5093, 55588}
X(55621) = reflection of X(i) in X(j) for these {i,j}: {22330, 5085}, {55592, 55599}, {55599, 55609}, {55601, 55610}, {55610, 55617}
X(55621) = center of Tucker-Hagos(-11/12) circle
X(55621) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3098, 55619}, {3, 55605, 55586}, {3, 55609, 55592}, {3, 55613, 55599}, {3, 55619, 55609}, {182, 3098, 55620}, {511, 5085, 22330}, {511, 55617, 55610}, {3098, 14810, 55617}, {3098, 31884, 55615}, {5102, 53092, 15520}, {14810, 55586, 3}, {14810, 55601, 20190}, {14810, 55606, 6}, {14810, 55610, 511}, {14810, 55617, 55601}, {14810, 55619, 55605}, {17508, 31884, 14810}, {17508, 55605, 55589}, {31884, 55610, 17508}, {31884, 55614, 5102}, {31884, 55618, 55593}, {55592, 55619, 55612}, {55599, 55619, 55613}

X(55622) = X(3)X(6)∩X(141)X(5059)

Barycentrics    a^2*(11*a^4-21*b^4-22*b^2*c^2-21*c^4+10*a^2*(b^2+c^2)) : :
X(55622) = -16*X[3]+5*X[6], 10*X[141]+X[5059], 7*X[376]+4*X[50982], 6*X[547]+5*X[48874], 9*X[599]+2*X[14927], 5*X[1352]+6*X[15686], 10*X[3522]+X[40341], -4*X[3543]+15*X[21358], -2*X[3629]+13*X[21734], 4*X[3631]+7*X[50693], -25*X[3763]+14*X[3832], 6*X[3845]+5*X[48873] and many others

X(55622) lies on these lines: {3, 6}, {141, 5059}, {376, 50982}, {547, 48874}, {599, 14927}, {1352, 15686}, {2916, 51959}, {3522, 40341}, {3543, 21358}, {3629, 21734}, {3631, 50693}, {3763, 3832}, {3845, 48873}, {3850, 48910}, {5056, 29181}, {5067, 53023}, {5306, 46944}, {5480, 15702}, {5645, 15246}, {11001, 36990}, {11179, 46332}, {11812, 54131}, {12007, 19708}, {13595, 21766}, {14093, 50973}, {15533, 44882}, {15690, 48876}, {15708, 51212}, {15723, 19924}, {16239, 31670}, {17811, 37913}, {18583, 19711}, {21356, 51025}, {24206, 38335}, {33703, 40330}, {34778, 35446}, {41981, 46264}, {47352, 51139}, {47353, 48885}, {48880, 49133}, {48898, 50968}, {51186, 51537}

X(55622) = reflection of X(i) in X(j) for these {i,j}: {55620, 3098}
X(55622) = center of Tucker-Hagos(-10/11) circle
X(55622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3098, 55618}, {3, 33878, 39561}, {3, 37517, 5085}, {3, 55591, 6}, {3, 55603, 55582}, {3, 55607, 55591}, {3, 55610, 55594}, {182, 1350, 53097}, {182, 3098, 55619}, {182, 55619, 55610}, {511, 3098, 55620}, {1350, 11477, 55590}, {1350, 14810, 53094}, {1350, 5085, 55584}, {1350, 55612, 55607}, {1350, 55618, 55612}, {1351, 55608, 1350}, {1351, 55616, 55608}, {3098, 14810, 55616}, {3098, 31884, 55614}, {5092, 55613, 55602}, {5097, 55612, 55603}, {6409, 6410, 5206}, {11482, 37517, 5102}, {14810, 55587, 3}, {14810, 55606, 15516}, {14810, 55608, 1351}, {14810, 55612, 55587}, {17508, 55609, 55595}, {31884, 53094, 14810}, {36836, 36843, 35007}, {44456, 55610, 55600}

X(55623) = X(3)X(6)∩X(632)X(19924)

Barycentrics    a^2*(10*a^4-19*b^4-20*b^2*c^2-19*c^4+9*a^2*(b^2+c^2)) : :
X(55623) = -29*X[3]+9*X[6], X[3529]+9*X[50977], -4*X[3627]+9*X[25561], -14*X[3628]+9*X[50959], 9*X[3818]+X[49140], -14*X[3857]+9*X[48895], 9*X[11178]+X[49137], X[11541]+9*X[48880], -4*X[12102]+9*X[24206], 2*X[12103]+3*X[40107], -19*X[15022]+9*X[48901], 2*X[15704]+3*X[18553] and many others

X(55623) lies on these lines: {3, 6}, {542, 51134}, {632, 19924}, {3529, 50977}, {3627, 25561}, {3628, 50959}, {3818, 49140}, {3857, 48895}, {11178, 49137}, {11541, 48880}, {11645, 17538}, {12102, 24206}, {12103, 40107}, {12812, 29181}, {15022, 48901}, {15704, 18553}, {15717, 46267}, {25565, 41992}, {34507, 50693}, {48873, 50689}, {48881, 48942}, {48943, 50688}, {49133, 51186}, {50961, 51177}

X(55623) = midpoint of X(i) and X(j) for these {i,j}: {3, 55600}, {48880, 51537}, {52987, 53093}, {53094, 55598}
X(55623) = reflection of X(i) in X(j) for these {i,j}: {11482, 20190}, {5097, 12017}, {55590, 55598}, {55604, 55612}, {55606, 55614}, {55619, 3098}
X(55623) = center of Tucker-Hagos(-9/10) circle
X(55623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3098, 55617}, {3, 52987, 22330}, {3, 55600, 511}, {3, 55606, 55588}, {3, 55611, 55597}, {3, 55617, 55606}, {182, 3098, 55618}, {182, 55618, 55609}, {511, 12017, 5097}, {511, 20190, 11482}, {511, 3098, 55619}, {511, 55598, 55590}, {511, 55612, 55604}, {576, 52987, 55582}, {3098, 14810, 55615}, {3098, 31884, 55612}, {3098, 52987, 55620}, {3098, 55622, 55621}, {5092, 31884, 14810}, {5092, 55612, 55599}, {11482, 53093, 39561}, {14810, 55588, 3}, {14810, 55599, 5092}, {14810, 55606, 575}, {14810, 55615, 55594}, {17508, 55607, 55592}, {22234, 55611, 55600}, {31884, 55614, 53093}, {31884, 55620, 52987}, {53094, 55610, 55598}, {55595, 55614, 55608}, {55597, 55617, 55611}, {55604, 55620, 55614}

X(55624) = X(3)X(6)∩X(141)X(17800)

Barycentrics    a^2*(9*a^4-17*b^4-18*b^2*c^2-17*c^4+8*a^2*(b^2+c^2)) : :
X(55624) = -13*X[3]+4*X[6], 8*X[141]+X[17800], -X[193]+10*X[46853], 8*X[548]+X[11898], 8*X[550]+X[48662], -2*X[1353]+11*X[21735], 5*X[1656]+4*X[48874], -10*X[3522]+X[39899], -7*X[3526]+4*X[38136], -14*X[3619]+5*X[5076], 5*X[3620]+4*X[12103], 8*X[3818]+X[49139] and many others

X(55624) lies on these lines: {3, 6}, {141, 17800}, {193, 46853}, {548, 11898}, {550, 48662}, {1353, 21735}, {1503, 15689}, {1656, 48874}, {2781, 38638}, {2854, 38633}, {3522, 39899}, {3526, 38136}, {3534, 10519}, {3564, 15688}, {3619, 5076}, {3620, 12103}, {3818, 49139}, {3830, 50956}, {3843, 48873}, {5020, 33879}, {5055, 29181}, {5073, 48881}, {5476, 15722}, {5644, 11002}, {5921, 44245}, {5969, 38634}, {6090, 26881}, {7666, 41716}, {7998, 9909}, {8703, 50974}, {9024, 38637}, {10304, 34380}, {10516, 15684}, {11812, 51173}, {12100, 50966}, {14093, 25406}, {14269, 29317}, {14561, 15701}, {14853, 15693}, {14912, 34200}, {15681, 54169}, {15685, 50977}, {15694, 21167}, {15695, 50971}, {15696, 48876}, {15700, 38110}, {15703, 53023}, {15710, 33748}, {15711, 51028}, {15716, 54132}, {15720, 51212}, {15759, 54174}, {16261, 39568}, {18358, 49137}, {19708, 50962}, {19710, 50954}, {31670, 46219}, {33751, 40341}, {35384, 51217}, {37897, 40911}, {37910, 44833}, {40330, 49136}, {41099, 50981}, {48880, 49134}, {49133, 51537}

X(55624) = midpoint of X(i) and X(j) for these {i,j}: {31884, 55618}
X(55624) = reflection of X(i) in X(j) for these {i,j}: {55610, 55618}, {55618, 3098}
X(55624) = center of Tucker-Hagos(-8/9) circle
X(55624) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 44456}, {3, 3098, 55616}, {3, 33878, 53091}, {3, 55593, 5093}, {3, 55604, 55584}, {3, 55610, 55593}, {3, 55616, 55604}, {6, 1350, 55588}, {6, 55612, 55602}, {182, 3098, 55617}, {182, 55607, 55595}, {182, 55617, 55607}, {511, 3098, 55618}, {1350, 10541, 55585}, {1350, 3098, 55620}, {1350, 5092, 55580}, {1350, 55614, 55609}, {1350, 55615, 55610}, {3098, 14810, 55614}, {3098, 52987, 55619}, {3098, 55623, 55622}, {5050, 55610, 1350}, {5085, 31884, 14810}, {10541, 55585, 1351}, {14810, 33878, 3}, {14810, 55603, 5085}, {14810, 55606, 50664}, {14810, 55609, 576}, {14810, 55612, 55581}, {14810, 55614, 33878}, {17508, 55606, 55591}, {31884, 55615, 5050}, {31884, 55618, 511}, {33878, 55610, 55603}, {55580, 55620, 55611}, {55581, 55603, 55596}, {55610, 55620, 55615}

X(55625) = X(3)X(6)∩X(5480)X(15713)

Barycentrics    a^2*(8*a^4-15*b^4-16*b^2*c^2-15*c^4+7*a^2*(b^2+c^2)) : :
X(55625) = -23*X[3]+7*X[6], 7*X[3818]+X[49138], 9*X[3839]+7*X[48873], -11*X[3855]+7*X[48895], -15*X[3858]+7*X[51163], -15*X[5071]+7*X[48901], -7*X[5480]+15*X[15713], 3*X[10519]+X[48891], 7*X[11180]+25*X[15697], X[14927]+3*X[43150], -3*X[15682]+7*X[48889], -3*X[15683]+7*X[48920] and many others

X(55625) lies on these lines: {3, 6}, {3818, 49138}, {3839, 48873}, {3855, 48895}, {3858, 51163}, {3861, 29317}, {5071, 48901}, {5480, 15713}, {10124, 19924}, {10519, 48891}, {11180, 15697}, {11645, 15691}, {12045, 15107}, {14927, 43150}, {15682, 48889}, {15683, 48920}, {15687, 24206}, {15699, 48874}, {19710, 39884}, {25561, 48872}, {29181, 35018}, {34573, 41989}, {40330, 48880}, {44882, 50978}, {46267, 50988}, {48662, 50968}

X(55625) = midpoint of X(i) and X(j) for these {i,j}: {182, 55592}, {14810, 55612}, {15516, 55590}, {20190, 55594}, {22330, 33878}, {3, 55601}, {5092, 55597}, {50664, 52987}
X(55625) = reflection of X(i) in X(j) for these {i,j}: {55609, 55617}, {55617, 3098}
X(55625) = center of Tucker-Hagos(-7/8) circle
X(55625) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15520, 5092}, {3, 3098, 55615}, {6, 55611, 55599}, {182, 3098, 55616}, {182, 31884, 14810}, {182, 55583, 1351}, {182, 55587, 11477}, {182, 55608, 55596}, {182, 55616, 55606}, {511, 3098, 55617}, {511, 55617, 55609}, {1350, 3098, 55619}, {1350, 53091, 55587}, {1350, 55619, 55612}, {1351, 55605, 55594}, {1351, 55614, 55605}, {3098, 52987, 55618}, {3098, 55603, 55620}, {3098, 55623, 55621}, {3098, 55624, 55623}, {5085, 55600, 55586}, {11477, 55606, 55597}, {14810, 55590, 3}, {14810, 55605, 20190}, {14810, 55606, 182}, {14810, 55608, 15516}, {14810, 55612, 511}, {14810, 55615, 55590}, {14810, 55616, 55592}, {14810, 55619, 1350}, {15516, 55612, 55601}, {17508, 55604, 55588}, {31884, 55618, 5093}, {55590, 55615, 55608}

X(55626) = X(3)X(6)∩X(4)X(20582)

Barycentrics    a^2*(7*a^4-13*b^4-14*b^2*c^2-13*c^4+6*a^2*(b^2+c^2)) : :
X(55626) = -10*X[3]+3*X[6], -5*X[4]+12*X[20582], 3*X[64]+4*X[15581], -16*X[140]+9*X[38072], 6*X[141]+X[3529], 6*X[376]+X[15069], -2*X[382]+9*X[21358], -8*X[546]+15*X[3763], 4*X[548]+3*X[54173], 4*X[550]+3*X[599], -6*X[597]+13*X[10299], -25*X[631]+18*X[48310] and many others

X(55626) lies on these lines: {3, 6}, {4, 20582}, {20, 11164}, {30, 51186}, {64, 15581}, {140, 38072}, {141, 3529}, {154, 7492}, {376, 15069}, {382, 21358}, {394, 6030}, {524, 3528}, {542, 50976}, {546, 3763}, {548, 54173}, {550, 599}, {597, 10299}, {631, 48310}, {632, 31670}, {1352, 12103}, {1503, 50693}, {1656, 51024}, {1657, 50977}, {1995, 44299}, {2781, 15020}, {2930, 51522}, {3066, 14924}, {3090, 29181}, {3091, 48910}, {3146, 7928}, {3522, 11160}, {3525, 21167}, {3526, 19924}, {3530, 47352}, {3533, 50984}, {3534, 40107}, {3544, 34573}, {3619, 50688}, {3627, 48872}, {3628, 48874}, {3629, 33750}, {3818, 49137}, {5059, 47354}, {5076, 24206}, {5079, 48901}, {5480, 10303}, {5563, 10387}, {5643, 7485}, {5646, 41462}, {7496, 33586}, {7512, 45248}, {7716, 35502}, {7998, 41424}, {8550, 10304}, {8567, 15579}, {8584, 15710}, {8703, 51188}, {10300, 26958}, {10323, 14094}, {10519, 17538}, {11178, 17800}, {11179, 46853}, {11284, 44106}, {11541, 40330}, {12108, 14561}, {14002, 21766}, {14869, 47355}, {15021, 16010}, {15023, 38438}, {15034, 51941}, {15054, 33851}, {15162, 30525}, {15163, 30524}, {15533, 15688}, {15534, 34200}, {15582, 16661}, {15681, 18553}, {15693, 25555}, {15696, 34507}, {15704, 36990}, {15712, 20423}, {15717, 54170}, {15826, 37948}, {16042, 31860}, {16835, 34817}, {17504, 51185}, {17809, 23061}, {17810, 40916}, {17811, 44082}, {19708, 41149}, {21734, 51737}, {21735, 50967}, {33751, 39899}, {33923, 50973}, {35018, 50980}, {35407, 48942}, {37751, 51535}, {41398, 43713}, {41981, 51027}, {44245, 48876}, {44904, 50964}, {46936, 51538}, {48880, 49136}

X(55626) = midpoint of X(i) and X(j) for these {i,j}: {3, 55602}
X(55626) = reflection of X(i) in X(j) for these {i,j}: {1350, 55607}, {10541, 3}, {11477, 53858}, {53858, 10541}, {55602, 55611}, {55607, 55616}, {55616, 3098}
X(55626) = center of Tucker-Hagos(-6/7) circle
X(55626) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(64), X(5008)}}, {{A, B, C, X(1297), X(10541)}}, {{A, B, C, X(1384), X(11270)}}, {{A, B, C, X(16835), X(30435)}}, {{A, B, C, X(21309), X(43719)}}
X(55626) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 5085}, {3, 11482, 5092}, {3, 1350, 11477}, {3, 3098, 55614}, {3, 33878, 575}, {3, 511, 10541}, {3, 575, 53094}, {3, 55580, 182}, {3, 55593, 11482}, {3, 55595, 576}, {3, 55602, 511}, {6, 31884, 14810}, {182, 3098, 55615}, {182, 55604, 55591}, {182, 55615, 55604}, {511, 10541, 53858}, {511, 3098, 55616}, {511, 55616, 55607}, {576, 55606, 55595}, {1350, 3098, 55618}, {1350, 5085, 55582}, {1350, 5102, 33878}, {1350, 53093, 53097}, {3098, 14810, 55610}, {3098, 52987, 55617}, {3098, 55603, 55619}, {3098, 55606, 55620}, {3098, 55624, 55622}, {3098, 55625, 55624}, {5092, 55608, 55593}, {10541, 53092, 53093}, {10541, 55611, 1350}, {10541, 55614, 55602}, {11482, 55593, 55583}, {12305, 12306, 8722}, {14810, 52987, 3}, {14810, 55601, 17508}, {14810, 55606, 20190}, {14810, 55610, 6}, {14810, 55615, 55586}, {14810, 55617, 52987}, {14810, 55621, 3098}, {17508, 55601, 55584}, {20190, 55617, 55606}, {33878, 53094, 5102}, {52987, 55611, 55605}, {53093, 53858, 53092}, {53094, 55614, 55600}, {55580, 55604, 55597}, {55584, 55610, 55601}, {55602, 55616, 55611}, {55610, 55624, 55621}

X(55627) = X(3)X(6)∩X(141)X(48920)

Barycentrics    a^2*(6*a^4-11*b^4-12*b^2*c^2-11*c^4+5*a^2*(b^2+c^2)) : :
X(55627) = -17*X[3]+5*X[6], 2*X[141]+X[48920], 2*X[550]+X[43150], -17*X[3533]+5*X[31670], -2*X[3543]+5*X[25561], 5*X[3818]+X[5059], 7*X[3832]+5*X[48873], -8*X[3850]+5*X[48895], -2*X[3853]+5*X[24206], -11*X[5056]+5*X[48901], -5*X[5066]+2*X[51165], -13*X[5067]+5*X[51538] and many others

X(55627) lies on these lines: {3, 6}, {141, 48920}, {524, 41982}, {547, 29181}, {550, 43150}, {1503, 15690}, {1843, 35478}, {3533, 31670}, {3543, 25561}, {3631, 44245}, {3818, 5059}, {3832, 48873}, {3845, 29317}, {3850, 48895}, {3853, 24206}, {3917, 35265}, {5056, 48901}, {5066, 51165}, {5067, 51538}, {5476, 15719}, {5650, 13595}, {5965, 8703}, {7998, 37913}, {10303, 42785}, {10516, 51167}, {10519, 11645}, {11001, 29323}, {11539, 19924}, {14561, 15708}, {15686, 29012}, {15702, 38317}, {15759, 50970}, {16239, 19130}, {18553, 48885}, {19708, 51214}, {19711, 51166}, {25406, 51179}, {33703, 48880}, {34380, 46332}, {40107, 48891}, {41991, 51163}, {46267, 54170}, {48879, 49133}, {48881, 48889}, {50975, 51215}, {51180, 51737}

X(55627) = midpoint of X(i) and X(j) for these {i,j}: {182, 55593}, {1350, 17508}, {14810, 55615}, {15520, 33878}, {3, 55603}, {3098, 31884}, {39561, 55591}, {5050, 52987}, {5085, 55596}, {5102, 55587}, {6, 55589}
X(55627) = reflection of X(i) in X(j) for these {i,j}: {14810, 31884}, {15520, 20190}, {3098, 55621}, {575, 17508}, {5102, 50664}, {55588, 55593}, {55589, 55597}, {55593, 55601}, {55594, 55603}, {55599, 55610}, {55603, 55612}, {55606, 55615}, {55615, 3098}, {55621, 55625}
X(55627) = center of Tucker-Hagos(-5/6) circle
X(55627) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 37517}, {3, 3098, 55612}, {3, 55582, 182}, {3, 55587, 50664}, {3, 55591, 39561}, {3, 55607, 55587}, {3, 55610, 55591}, {3, 55612, 55594}, {3, 55618, 55603}, {6, 55608, 55597}, {6, 55620, 55608}, {182, 3098, 55614}, {182, 55601, 55588}, {182, 55614, 55601}, {511, 17508, 575}, {511, 20190, 15520}, {511, 31884, 14810}, {511, 50664, 5102}, {511, 55597, 55589}, {511, 55601, 55593}, {576, 55604, 55592}, {1350, 12017, 55583}, {1350, 17508, 511}, {1350, 3098, 55617}, {3098, 14810, 55606}, {3098, 17508, 55613}, {3098, 52987, 55616}, {3098, 55603, 55618}, {3098, 55606, 55619}, {3098, 55608, 55620}, {3098, 55624, 55621}, {3098, 55625, 55623}, {3098, 55626, 55625}, {5085, 55610, 55596}, {5102, 55618, 55607}, {14810, 55594, 3}, {14810, 55606, 5092}, {14810, 55612, 5097}, {14810, 55617, 55586}, {14810, 55619, 55590}, {14810, 55623, 3098}, {17508, 55613, 1350}, {31884, 55621, 55615}, {31884, 55626, 55624}, {37517, 39561, 5093}, {39561, 55612, 55599}, {52987, 55616, 55609}, {53094, 55585, 22330}, {53094, 55602, 55585}, {55591, 55618, 55610}, {55612, 55625, 55622}

X(55628) = X(3)X(6)∩X(546)X(50965)

Barycentrics    11*a^6+9*a^4*(b^2+c^2)-2*a^2*(10*b^4+11*b^2*c^2+10*c^4) : :
X(55628) = -31*X[3]+9*X[6], 2*X[546]+9*X[50965], -25*X[632]+36*X[50984], 2*X[3529]+9*X[11178], -85*X[5076]+63*X[51164], -52*X[10303]+63*X[51141], 9*X[11180]+35*X[50693], 2*X[11541]+9*X[48879], 2*X[12103]+9*X[54169], -20*X[12812]+9*X[48901], 2*X[15704]+9*X[50977], 5*X[17538]+6*X[40107] and many others

X(55628) lies on these lines: {3, 6}, {546, 50965}, {632, 50984}, {3525, 19924}, {3529, 11178}, {5076, 51164}, {10303, 51141}, {11180, 50693}, {11541, 48879}, {12103, 54169}, {12812, 48901}, {15704, 50977}, {17538, 40107}, {19708, 33749}, {22165, 41981}, {24206, 50688}, {29317, 50689}, {33851, 38626}, {34507, 44245}, {48884, 49140}, {50978, 51135}

X(55628) = reflection of X(i) in X(j) for these {i,j}: {3098, 55622}
X(55628) = center of Tucker-Hagos(-9/11) circle
X(55628) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3098, 55611}, {3, 52987, 22234}, {3, 53858, 5092}, {3, 55583, 182}, {3, 55595, 53858}, {3, 55606, 55583}, {3, 55614, 55597}, {3, 55617, 55600}, {3, 55626, 55623}, {182, 3098, 55613}, {182, 55603, 33878}, {182, 55606, 52987}, {575, 55606, 55592}, {576, 3098, 55614}, {576, 52987, 55581}, {1350, 55621, 3098}, {3098, 14810, 55603}, {3098, 17508, 55612}, {3098, 55587, 55615}, {3098, 55596, 55616}, {3098, 55600, 55617}, {3098, 55605, 55618}, {5092, 55618, 55605}, {11477, 55606, 55596}, {11477, 55616, 55606}, {14810, 55597, 3}, {14810, 55609, 5085}, {14810, 55612, 53091}, {14810, 55614, 576}, {17508, 55612, 55598}, {20190, 55602, 55587}, {20190, 55615, 55602}, {31884, 33878, 14810}, {55614, 55626, 55624}

X(55629) = X(3)X(6)∩X(69)X(548)

Barycentrics    a^2*(5*a^4-9*b^4-10*b^2*c^2-9*c^4+4*a^2*(b^2+c^2)) : :
X(55629) = 3*X[2]+2*X[48874], -7*X[3]+2*X[6], 3*X[20]+2*X[39884], X[69]+4*X[548], 4*X[74]+X[32254], 4*X[141]+X[1657], 4*X[159]+X[13093], -X[193]+11*X[21735], 9*X[376]+X[5921], 3*X[381]+2*X[48873], X[382]+4*X[48881], -6*X[549]+X[51212] and many others

X(55629) lies on these lines: {2, 48874}, {3, 6}, {20, 39884}, {25, 21766}, {30, 40330}, {69, 548}, {74, 32254}, {141, 1657}, {159, 13093}, {193, 21735}, {376, 5921}, {381, 48873}, {382, 48881}, {394, 44108}, {524, 14093}, {542, 15695}, {549, 51212}, {550, 10519}, {597, 15706}, {599, 15689}, {1352, 3534}, {1353, 34200}, {1503, 15696}, {1656, 29181}, {1992, 45759}, {2781, 15040}, {3066, 16419}, {3167, 6636}, {3426, 33532}, {3522, 3564}, {3523, 21850}, {3524, 18583}, {3525, 38136}, {3526, 21167}, {3528, 48906}, {3529, 18358}, {3530, 14853}, {3618, 15712}, {3619, 3627}, {3620, 17538}, {3628, 51538}, {3763, 3843}, {3818, 17800}, {3819, 20850}, {3830, 24206}, {3851, 48910}, {3917, 8780}, {5054, 5480}, {5055, 48901}, {5070, 53023}, {5071, 50980}, {5072, 34573}, {5073, 10516}, {5181, 38788}, {5476, 15707}, {5544, 7484}, {5651, 9909}, {6090, 7492}, {6403, 11410}, {6776, 8703}, {7689, 19588}, {10007, 14535}, {10620, 33851}, {10691, 33522}, {11178, 15685}, {11180, 15690}, {11284, 41462}, {11414, 15058}, {11645, 50968}, {11820, 35243}, {11898, 15688}, {12007, 50962}, {12100, 14848}, {12167, 35477}, {12315, 34778}, {14269, 48904}, {14530, 34146}, {14561, 15720}, {14893, 50981}, {14912, 21734}, {15035, 48679}, {15069, 48892}, {15082, 31860}, {15577, 32063}, {15585, 20427}, {15681, 36990}, {15684, 21358}, {15686, 21356}, {15691, 51023}, {15692, 50966}, {15694, 19924}, {15700, 20423}, {15701, 54131}, {15703, 51024}, {15710, 54174}, {15715, 51028}, {15716, 38064}, {15717, 38110}, {15718, 47352}, {15719, 38079}, {15723, 50984}, {16163, 32306}, {16491, 31666}, {17504, 51732}, {17811, 32237}, {19118, 21844}, {19130, 46219}, {19140, 38638}, {20582, 38335}, {20987, 47748}, {21970, 46336}, {22112, 33586}, {25406, 33923}, {26864, 33884}, {30734, 33879}, {32217, 37955}, {32305, 38633}, {33751, 43273}, {34380, 46853}, {35434, 50956}, {35450, 39879}, {35485, 39871}, {37198, 52093}, {38742, 50567}, {38754, 51007}, {40107, 48905}, {41716, 54042}, {43576, 54994}, {47353, 48896}, {48310, 51173}, {48879, 49134}, {48884, 49139}

X(55629) = midpoint of X(i) and X(j) for these {i,j}: {1350, 53094}, {11482, 33878}, {12017, 55595}, {14810, 55619}, {15692, 50966}, {3, 55604}, {3620, 17538}
X(55629) = reflection of X(i) in X(j) for these {i,j}: {1350, 55608}, {1351, 53091}, {11482, 12017}, {12017, 3}, {16491, 31666}, {22234, 5092}, {3098, 55623}, {3618, 15712}, {3843, 3763}, {33878, 55595}, {35434, 50956}, {5071, 50980}, {50963, 15694}, {53091, 53094}, {55595, 55604}, {55598, 55606}, {55604, 55614}, {55608, 55619}, {55614, 3098}
X(55629) = center of Tucker-Hagos(-4/5) circle
X(55629) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(32), X(44763)}}, {{A, B, C, X(1297), X(12017)}}, {{A, B, C, X(5092), X(14489)}}, {{A, B, C, X(31884), X(40803)}}
X(55629) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 40268, 12054}, {3, 44456, 5085}, {3, 5093, 5092}, {3, 511, 12017}, {3, 52987, 53092}, {3, 55593, 6}, {3, 55606, 55580}, {6, 1350, 55587}, {6, 55618, 55606}, {6, 55626, 55621}, {182, 1350, 55584}, {182, 3098, 55612}, {182, 55605, 55590}, {511, 3098, 55614}, {511, 5092, 22234}, {511, 55606, 55598}, {550, 10519, 18440}, {575, 55596, 55582}, {575, 55609, 55596}, {576, 3098, 55613}, {576, 55601, 55591}, {576, 55613, 55601}, {599, 48898, 48662}, {1151, 43127, 3}, {1350, 3098, 55616}, {1350, 31884, 14810}, {1350, 53097, 55592}, {1350, 55587, 55593}, {1350, 55608, 55604}, {1350, 55614, 55608}, {1350, 55616, 55610}, {1350, 55622, 3098}, {1350, 55626, 55622}, {1351, 12017, 53091}, {1351, 53091, 11482}, {1351, 53092, 5097}, {1351, 55610, 1350}, {3098, 17508, 55611}, {3098, 35248, 35456}, {3098, 52987, 55615}, {3098, 55603, 55617}, {3098, 55606, 55618}, {3098, 55610, 55620}, {3098, 55626, 55624}, {3098, 55627, 55626}, {3098, 55628, 55627}, {3763, 29317, 3843}, {5085, 52987, 44456}, {5085, 55607, 52987}, {5092, 53097, 5093}, {5092, 55603, 53097}, {5092, 55617, 55603}, {10516, 48880, 5073}, {11482, 12017, 5050}, {11482, 33878, 511}, {11482, 55614, 55602}, {11898, 15688, 44882}, {12017, 55604, 33878}, {12017, 55610, 55595}, {12100, 54170, 14848}, {14810, 55608, 53094}, {14810, 55612, 182}, {14810, 55616, 1351}, {14810, 55623, 55619}, {14810, 55627, 55625}, {15516, 55581, 11477}, {15516, 55594, 55581}, {15684, 21358, 50957}, {15689, 48662, 48898}, {15694, 19924, 50963}, {17508, 55581, 15516}, {17508, 55611, 55594}, {20190, 55585, 5102}, {20190, 55599, 55585}, {21356, 50969, 15686}, {24206, 48872, 3830}, {36990, 48885, 15681}, {44882, 54173, 11898}, {48885, 50977, 36990}, {52987, 55615, 55607}, {53093, 55614, 55600}, {55590, 55612, 55605}, {55614, 55626, 55623}

X(55630) = X(3)X(6)∩X(3839)X(29317)

Barycentrics    9*a^6+7*a^4*(b^2+c^2)-2*a^2*(8*b^4+9*b^2*c^2+8*c^4) : :
X(55630) = -25*X[3]+7*X[6], 11*X[3855]+7*X[48873], -16*X[3861]+7*X[48904], 2*X[5066]+7*X[50965], -7*X[5476]+16*X[44580], -4*X[10124]+7*X[21167], 7*X[10519]+5*X[15697], 7*X[11178]+2*X[15683], -5*X[15687]+14*X[20582], 2*X[15691]+7*X[54169], -10*X[15713]+7*X[38317], -5*X[17578]+14*X[24206] and many others

X(55630) lies on these lines: {3, 6}, {3839, 29317}, {3855, 48873}, {3861, 48904}, {5066, 50965}, {5476, 44580}, {6030, 33884}, {7998, 44082}, {10124, 21167}, {10519, 15697}, {11178, 15683}, {15687, 20582}, {15691, 54169}, {15699, 29181}, {15709, 19924}, {15713, 38317}, {17578, 24206}, {19710, 50977}, {21356, 29012}, {22165, 51134}, {35018, 48901}, {38136, 51127}, {41989, 42786}, {48879, 49135}, {48884, 49138}, {51177, 54173}

X(55630) = midpoint of X(i) and X(j) for these {i,j}: {31884, 55624}
X(55630) = reflection of X(i) in X(j) for these {i,j}: {3098, 55624}, {55603, 55613}, {55613, 3098}, {55624, 55627}
X(55630) = center of Tucker-Hagos(-7/9) circle
X(55630) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3098, 55608}, {3, 55585, 182}, {3, 55596, 15520}, {6, 55617, 55605}, {182, 3098, 55611}, {182, 55611, 55598}, {511, 3098, 55613}, {511, 55627, 55624}, {576, 3098, 55612}, {1350, 55623, 3098}, {3098, 55587, 55614}, {3098, 55596, 55615}, {3098, 55600, 55616}, {3098, 55605, 55617}, {3098, 55629, 55628}, {5050, 55599, 55587}, {5050, 55614, 55599}, {5085, 55589, 37517}, {5085, 55606, 55589}, {5092, 55600, 55581}, {5092, 55616, 55600}, {14810, 55601, 3}, {14810, 55610, 17508}, {14810, 55617, 6}, {14810, 55621, 55610}, {14810, 55627, 55621}, {15520, 55596, 55585}, {15520, 55608, 55596}, {15520, 55615, 55603}, {17508, 39561, 20190}, {17508, 55610, 52987}, {31884, 55610, 14810}, {31884, 55622, 5085}, {31884, 55623, 39561}, {31884, 55624, 511}, {31884, 55629, 55627}, {37517, 52987, 55584}, {52987, 55608, 55601}, {52987, 55628, 55626}, {55615, 55627, 55625}

X(55631) = X(3)X(6)∩X(23)X(3819)

Barycentrics    a^2*(4*a^4-7*b^4-8*b^2*c^2-7*c^4+3*a^2*(b^2+c^2)) : :
X(55631) = -11*X[3]+3*X[6], X[5]+3*X[50965], 3*X[141]+X[15704], 3*X[376]+X[34507], -X[382]+3*X[25561], -3*X[597]+7*X[44682], 3*X[599]+5*X[15696], -5*X[632]+3*X[19130], 3*X[1352]+5*X[17538], X[1657]+3*X[11178], -7*X[3090]+3*X[48901], 5*X[3091]+3*X[48873] and many others

X(55631) lies on these lines: {3, 6}, {5, 50965}, {20, 18553}, {23, 3819}, {30, 51143}, {140, 19924}, {141, 15704}, {376, 34507}, {382, 25561}, {524, 33923}, {542, 548}, {546, 29317}, {550, 11645}, {597, 44682}, {599, 15696}, {632, 19130}, {1216, 5609}, {1352, 17538}, {1503, 32903}, {1657, 11178}, {1843, 35475}, {2979, 9716}, {3090, 48901}, {3091, 48873}, {3146, 48880}, {3292, 6636}, {3522, 54173}, {3523, 5476}, {3525, 31670}, {3528, 50974}, {3529, 3818}, {3530, 25555}, {3544, 42786}, {3564, 33751}, {3627, 24206}, {3628, 29181}, {3763, 48904}, {3853, 20582}, {3857, 51163}, {3917, 7492}, {5070, 51024}, {5072, 48910}, {5073, 21358}, {5076, 48872}, {5447, 7555}, {5480, 14869}, {5650, 14002}, {5943, 7496}, {6000, 15582}, {6688, 40916}, {7393, 52163}, {7464, 43130}, {7512, 15034}, {7550, 13598}, {7689, 9925}, {7750, 51397}, {7998, 32237}, {8550, 46853}, {8584, 15714}, {9968, 10282}, {10168, 15712}, {10170, 37967}, {10299, 54170}, {10303, 38317}, {10516, 48879}, {10519, 41482}, {10752, 15023}, {11179, 21735}, {11204, 34787}, {11470, 35472}, {12045, 34417}, {12082, 44870}, {12086, 43129}, {12100, 46267}, {12103, 29012}, {12294, 44879}, {12584, 15054}, {12811, 34573}, {12834, 15246}, {14924, 16419}, {15020, 19140}, {15039, 52098}, {15082, 16042}, {15691, 50991}, {15717, 20423}, {15720, 54131}, {16239, 25565}, {17506, 44102}, {18571, 54044}, {20301, 38729}, {21734, 50967}, {22352, 23061}, {22486, 33022}, {22676, 35951}, {33851, 51522}, {34146, 50414}, {37946, 46847}, {37957, 43811}, {38064, 50966}, {38072, 51141}, {40330, 49140}, {41435, 46848}, {43621, 50689}, {48154, 50959}, {48876, 48892}, {48884, 49137}, {51524, 54224}

X(55631) = midpoint of X(i) and X(j) for these {i,j}: {141, 48885}, {182, 55594}, {1350, 5092}, {1351, 55586}, {1352, 48891}, {15691, 50991}, {17508, 55599}, {19130, 48874}, {20, 18553}, {20190, 55597}, {24206, 48881}, {3, 55606}, {3098, 14810}, {3818, 48920}, {31884, 55627}, {43150, 48898}, {48872, 48943}, {48873, 48895}, {48876, 48892}, {48879, 48942}, {48880, 48889}, {550, 40107}, {575, 52987}, {576, 55588}, {5097, 33878}, {50664, 55592}, {6, 55590}
X(55631) = reflection of X(i) in X(j) for these {i,j}: {1350, 55609}, {15516, 5092}, {20190, 3}, {22330, 20190}, {25555, 3530}, {25565, 50984}, {3098, 55625}, {46267, 12100}, {55592, 55601}, {55597, 55606}, {55601, 55612}, {55606, 55617}, {55612, 3098}, {55621, 55627}
X(55631) = center of Tucker-Hagos(-3/4) circle
X(55631) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(14075)}}, {{A, B, C, X(1173), X(34571)}}, {{A, B, C, X(1297), X(20190)}}, {{A, B, C, X(5007), X(46848)}}
X(55631) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 33878, 53093}, {3, 53092, 53094}, {3, 53093, 17508}, {3, 55580, 10541}, {3, 55593, 53092}, {3, 55595, 6}, {3, 55597, 22330}, {3, 55602, 11477}, {3, 55611, 55588}, {3, 55616, 55595}, {3, 55624, 55620}, {3, 55628, 55623}, {3, 55629, 55626}, {6, 55595, 55583}, {6, 55603, 55590}, {6, 55616, 55603}, {20, 50977, 18553}, {61, 62, 34571}, {141, 48885, 29323}, {182, 11482, 575}, {182, 3098, 55610}, {182, 55600, 53097}, {182, 55622, 55619}, {371, 372, 14075}, {511, 5092, 15516}, {550, 40107, 11645}, {550, 54169, 40107}, {576, 55628, 55624}, {1350, 10541, 55580}, {1350, 3098, 55615}, {1350, 44456, 55589}, {1350, 5050, 55585}, {1350, 5092, 511}, {1350, 55589, 55594}, {1350, 55611, 55606}, {1350, 55615, 55609}, {1350, 55620, 55611}, {1350, 55624, 3098}, {1351, 55596, 55586}, {1351, 55607, 55596}, {3098, 17508, 55608}, {3098, 31884, 14810}, {3098, 52987, 55614}, {3098, 55587, 55613}, {3098, 55603, 55616}, {3098, 55608, 55618}, {3098, 55625, 55621}, {3098, 55629, 55627}, {3098, 55630, 55629}, {5085, 55604, 55587}, {5104, 37512, 44500}, {5206, 44499, 38010}, {10516, 48879, 48942}, {10519, 48898, 43150}, {10541, 55580, 576}, {10541, 55614, 1350}, {11477, 55602, 52987}, {11477, 55614, 55602}, {11482, 55580, 44456}, {11482, 55614, 55600}, {14810, 55606, 3}, {14810, 55615, 5092}, {14810, 55617, 20190}, {14810, 55619, 182}, {14810, 55621, 55601}, {14810, 55625, 55612}, {14810, 55626, 55617}, {14810, 55629, 55625}, {15513, 44453, 2030}, {17508, 33878, 5097}, {17508, 55608, 33878}, {17508, 55618, 55599}, {20190, 22330, 50664}, {20190, 55612, 55597}, {21167, 48874, 19130}, {22330, 55606, 55592}, {37517, 55605, 55593}, {39561, 55598, 55584}, {53094, 55593, 37517}, {55587, 55613, 55604}, {55594, 55627, 55622}, {55626, 55629, 55628}

X(55632) = X(3)X(6)∩X(69)X(15688)

Barycentrics    a^2*(11*a^4-19*b^4-22*b^2*c^2-19*c^4+8*a^2*(b^2+c^2)) : :
X(55632) = -15*X[3]+4*X[6], 2*X[69]+9*X[15688], 8*X[141]+3*X[15681], -X[193]+12*X[34200], -3*X[382]+14*X[3619], -12*X[548]+X[39874], 6*X[550]+5*X[3620], -2*X[1353]+13*X[21734], 3*X[1657]+8*X[18358], 10*X[3522]+X[11898], 7*X[3526]+4*X[48874], 21*X[3528]+X[20080] and many others

X(55632) lies on these lines: {3, 6}, {69, 15688}, {141, 15681}, {193, 34200}, {382, 3619}, {548, 39874}, {550, 3620}, {1353, 21734}, {1657, 18358}, {3522, 11898}, {3526, 48874}, {3528, 20080}, {3534, 21356}, {3589, 15707}, {3618, 15700}, {3763, 14269}, {3818, 15685}, {3830, 20582}, {3843, 43621}, {3851, 34573}, {5020, 41462}, {5055, 50964}, {5070, 29181}, {6030, 26864}, {8703, 11160}, {9909, 10546}, {10304, 51179}, {10516, 49134}, {10519, 15696}, {10752, 15042}, {14093, 48906}, {15107, 16419}, {15684, 48880}, {15689, 18440}, {15693, 21850}, {15694, 31670}, {15695, 22165}, {15701, 48310}, {15706, 54170}, {15708, 51173}, {15710, 51170}, {15714, 54174}, {17504, 50966}, {18325, 47451}, {18551, 44457}, {19709, 42786}, {21167, 46219}, {21358, 48879}, {21735, 34380}, {33539, 41435}, {40330, 49137}, {41982, 50974}, {45759, 50962}, {48891, 50968}, {48892, 50955}, {50687, 50981}

X(55632) = reflection of X(i) in X(j) for these {i,j}: {55620, 55622}, {55622, 55628}
X(55632) = center of Tucker-Hagos(-8/11) circle
X(55632) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5041), X(44731)}}, {{A, B, C, X(11270), X(22331)}}
X(55632) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 5093}, {3, 3098, 55604}, {3, 55593, 53091}, {3, 55604, 44456}, {3, 55610, 55584}, {3, 55616, 55593}, {3, 55624, 55616}, {3, 55629, 55624}, {6, 1350, 55586}, {6, 17508, 12017}, {6, 55626, 3098}, {182, 3098, 55609}, {182, 55618, 55602}, {182, 55623, 55618}, {511, 55622, 55620}, {511, 55628, 55622}, {1350, 37517, 33878}, {1350, 55617, 55610}, {1351, 55629, 55625}, {3098, 5092, 55607}, {3098, 55585, 55612}, {3098, 55594, 55614}, {5085, 55612, 55595}, {6221, 6398, 5008}, {6449, 6450, 35007}, {10519, 15696, 48662}, {12017, 33878, 37517}, {14810, 55610, 3}, {14810, 55617, 17508}, {14810, 55621, 52987}, {14810, 55625, 55605}, {14810, 55627, 55617}, {14810, 55630, 55626}, {14810, 55631, 55630}, {17508, 55586, 6}, {17508, 55605, 55583}, {17508, 55617, 1350}, {17508, 55630, 55627}, {31884, 55626, 14810}, {31884, 55631, 55629}, {33878, 55610, 55601}, {53094, 55603, 55580}

X(55633) = X(3)X(6)∩X(3528)X(5965)

Barycentrics    7*a^6+5*a^4*(b^2+c^2)-2*a^2*(6*b^4+7*b^2*c^2+6*c^4) : :
X(55633) = -19*X[3]+5*X[6], -12*X[547]+5*X[48901], -11*X[549]+4*X[51130], -17*X[3533]+10*X[19130], -3*X[3543]+10*X[24206], 9*X[3545]+5*X[48873], -12*X[3845]+5*X[48904], -12*X[3850]+5*X[51163], 2*X[3853]+5*X[48881], 3*X[5059]+25*X[40330], -5*X[5476]+12*X[41983], -5*X[5480]+12*X[11812] and many others

X(55633) lies on these lines: {3, 6}, {547, 48901}, {549, 51130}, {3528, 5965}, {3533, 19130}, {3543, 24206}, {3545, 48873}, {3832, 29317}, {3845, 48904}, {3850, 51163}, {3853, 48881}, {5059, 40330}, {5476, 41983}, {5480, 11812}, {5645, 43650}, {5651, 37913}, {5921, 48892}, {10516, 49133}, {11001, 11178}, {11539, 48874}, {12007, 45759}, {12294, 44878}, {13595, 16187}, {14869, 42785}, {14927, 40107}, {15686, 39884}, {15690, 48898}, {15696, 43150}, {15702, 19924}, {15714, 50970}, {15719, 51212}, {16239, 21167}, {18583, 51137}, {21358, 35400}, {32273, 38725}, {33703, 48879}, {33751, 54173}, {34200, 51140}, {34507, 41981}, {38335, 48872}, {50980, 51165}

X(55633) = midpoint of X(i) and X(j) for these {i,j}: {3, 55607}, {33878, 53858}
X(55633) = reflection of X(i) in X(j) for these {i,j}: {3098, 55626}, {42785, 14869}, {53092, 5092}, {55605, 55616}, {55611, 3098}
X(55633) = center of Tucker-Hagos(-5/7) circle
X(55633) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 5097}, {3, 3098, 55603}, {3, 50664, 17508}, {3, 5102, 5092}, {3, 55591, 50664}, {3, 55594, 39561}, {3, 55610, 55582}, {3, 55618, 55594}, {3, 55629, 55622}, {6, 55615, 55600}, {182, 1350, 55581}, {182, 3098, 55608}, {182, 55585, 1351}, {182, 55587, 37517}, {511, 3098, 55611}, {511, 5092, 53092}, {575, 55604, 55589}, {576, 3098, 55610}, {576, 55610, 55598}, {1350, 5097, 55587}, {1350, 55581, 52987}, {1350, 55625, 3098}, {1350, 55629, 55625}, {1351, 17508, 182}, {1351, 55629, 55624}, {3098, 17508, 55606}, {3098, 52987, 55613}, {3098, 55596, 55614}, {3098, 55600, 55615}, {3098, 55605, 55616}, {3098, 55630, 55628}, {3098, 55631, 55630}, {5085, 55601, 55583}, {5085, 55620, 55601}, {5092, 55614, 55596}, {10541, 55607, 55591}, {14810, 55612, 3}, {14810, 55621, 55584}, {14810, 55623, 55590}, {14810, 55625, 1350}, {14810, 55626, 55605}, {14810, 55627, 55612}, {14810, 55631, 55629}, {17508, 55585, 22234}, {17508, 55606, 55585}, {31884, 55629, 14810}, {31884, 55632, 55631}, {53094, 55590, 576}, {53094, 55629, 55623}, {55603, 55611, 55607}, {55603, 55630, 55627}, {55616, 55629, 55626}

X(55634) = X(3)X(6)∩X(141)X(19710)

Barycentrics    a^2*(10*a^4-17*b^4-20*b^2*c^2-17*c^4+7*a^2*(b^2+c^2)) : :
X(55634) = -27*X[3]+7*X[6], 7*X[141]+3*X[19710], -7*X[3589]+12*X[44580], -49*X[3619]+9*X[15682], X[3630]+9*X[8703], 2*X[3631]+3*X[48892], 7*X[3818]+3*X[15683], -27*X[3839]+7*X[43621], -9*X[5066]+14*X[34573], -39*X[5068]+49*X[42786], -17*X[7486]+7*X[48901], -12*X[10124]+7*X[19130] and many others

X(55634) lies on circumconic {{A, B, C, X(5007), X(13603)}} and on these lines: {3, 6}, {141, 19710}, {3589, 44580}, {3619, 15682}, {3620, 11645}, {3630, 8703}, {3631, 48892}, {3818, 15683}, {3839, 43621}, {3858, 29317}, {5066, 34573}, {5068, 42786}, {7486, 48901}, {10124, 19130}, {12294, 44880}, {13603, 41435}, {15687, 48881}, {15691, 48891}, {15699, 50965}, {15709, 31670}, {15713, 19924}, {15721, 42785}, {15759, 32455}, {18358, 48885}, {29181, 48154}, {43150, 54169}, {48906, 51183}, {48942, 49135}, {49138, 51537}

X(55634) = midpoint of X(i) and X(j) for these {i,j}: {182, 55595}, {12017, 55598}, {14810, 55623}, {3, 55608}, {52987, 53091}, {53094, 55600}
X(55634) = reflection of X(i) in X(j) for these {i,j}: {575, 53094}, {55594, 55604}, {55600, 55612}, {55606, 55619}, {55619, 55623}, {55623, 55629}, {55629, 55631}
X(55634) = center of Tucker-Hagos(-7/10) circle
X(55634) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 15520}, {3, 3098, 55601}, {3, 55596, 15516}, {3, 55630, 55625}, {6, 3098, 55609}, {182, 3098, 55607}, {182, 55617, 55599}, {182, 55624, 55617}, {511, 53094, 575}, {511, 55604, 55594}, {511, 55612, 55600}, {511, 55629, 55623}, {511, 55631, 55629}, {1350, 55628, 55621}, {3098, 14810, 5092}, {3098, 33878, 55612}, {3098, 37517, 55610}, {3098, 55598, 55614}, {3098, 55632, 55631}, {3098, 55633, 55632}, {5085, 55611, 55592}, {5092, 55586, 5097}, {5092, 55606, 55586}, {6451, 6452, 15603}, {10645, 10646, 15513}, {12017, 55598, 511}, {12017, 55614, 55598}, {14810, 55615, 3}, {14810, 55625, 55590}, {14810, 55627, 55606}, {14810, 55629, 55619}, {14810, 55631, 55627}, {15520, 55621, 55615}, {17508, 55616, 55597}, {31884, 55631, 14810}, {31884, 55632, 3098}, {53091, 55629, 55622}, {55590, 55619, 55608}, {55595, 55629, 55624}, {55625, 55631, 55630}

X(55635) = X(3)X(6)∩X(1352)X(15697)

Barycentrics    11*a^6+7*a^4*(b^2+c^2)-2*a^2*(9*b^4+11*b^2*c^2+9*c^4) : :
X(55635) = -29*X[3]+7*X[6], 7*X[1352]+15*X[15697], -18*X[3839]+7*X[48904], 4*X[3861]+7*X[48881], -18*X[5066]+7*X[51163], 15*X[5071]+7*X[48873], 4*X[10124]+7*X[50965], 7*X[11178]+4*X[19710], -3*X[15682]+14*X[24206], 9*X[15683]+35*X[40330], -17*X[15687]+28*X[50960], 4*X[15691]+7*X[50977] and many others

X(55635) lies on these lines: {3, 6}, {1352, 15697}, {3839, 48904}, {3855, 29317}, {3861, 48881}, {5066, 51163}, {5071, 48873}, {10124, 50965}, {11178, 19710}, {15682, 24206}, {15683, 40330}, {15687, 50960}, {15691, 50977}, {15699, 48901}, {15713, 48874}, {15721, 19924}, {21167, 48154}, {33751, 51215}, {48876, 50971}, {48889, 51167}

X(55635) = reflection of X(i) in X(j) for these {i,j}: {3098, 55628}, {55628, 55632}
X(55635) = center of Tucker-Hagos(-7/11) circle
X(55635) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 15516}, {3, 3098, 55596}, {3, 31884, 55634}, {3, 55601, 15520}, {3, 55634, 55630}, {6, 55623, 55613}, {182, 3098, 55605}, {182, 55605, 55587}, {182, 55608, 55590}, {182, 55633, 55629}, {511, 55632, 55628}, {1350, 1351, 55588}, {1350, 15516, 55585}, {1350, 53094, 44456}, {1350, 55615, 55608}, {1350, 55616, 55609}, {1350, 55622, 55620}, {1351, 55619, 55603}, {1351, 55626, 55619}, {3098, 17508, 55600}, {3098, 39561, 55606}, {3098, 55583, 55610}, {3098, 55589, 55611}, {5050, 44456, 53858}, {5050, 55609, 52987}, {5085, 55617, 55598}, {5092, 55611, 55589}, {5092, 55631, 55624}, {10541, 55583, 576}, {14810, 31884, 55633}, {14810, 55625, 3}, {14810, 55629, 182}, {14810, 55631, 1350}, {14810, 55633, 3098}, {14810, 55634, 55625}, {15516, 55625, 55615}, {53094, 55581, 39561}, {53094, 55606, 55581}, {55588, 55631, 55626}, {55609, 55631, 55627}, {55615, 55634, 55631}

X(55636) = X(3)X(6)∩X(548)X(3631)

Barycentrics    a^2*(8*a^4-13*b^4-16*b^2*c^2-13*c^4+5*a^2*(b^2+c^2)) : :
X(55636) = -21*X[3]+5*X[6], 11*X[69]+21*X[51177], 5*X[141]+3*X[15686], 3*X[376]+X[43150], 3*X[548]+X[3631], -15*X[631]+7*X[42785], 3*X[3543]+5*X[48880], -27*X[3545]+35*X[42786], -5*X[3589]+9*X[41983], 5*X[3620]+3*X[48898], -X[3629]+9*X[45759], -25*X[3763]+9*X[38335] and many others

X(55636) lies on these lines: {3, 6}, {69, 51177}, {141, 15686}, {376, 43150}, {524, 46332}, {548, 3631}, {631, 42785}, {1503, 41981}, {3543, 48880}, {3545, 42786}, {3589, 41983}, {3619, 7910}, {3620, 48898}, {3629, 45759}, {3763, 38335}, {3818, 11001}, {3819, 10546}, {3832, 43621}, {3845, 48881}, {3850, 29317}, {3917, 7712}, {5056, 48873}, {5059, 48920}, {5067, 48901}, {5965, 33923}, {6329, 14891}, {6636, 44108}, {6688, 15107}, {10168, 51166}, {10219, 34417}, {10304, 51178}, {10545, 12045}, {11008, 21735}, {11539, 19130}, {11645, 15690}, {11812, 19924}, {13595, 41462}, {14093, 40341}, {15688, 51027}, {15702, 31670}, {15708, 51211}, {16239, 29181}, {18358, 29323}, {19711, 21850}, {25561, 48879}, {41985, 50984}, {48874, 51126}, {48891, 50977}, {48892, 51134}, {48942, 49133}, {49881, 49882}

X(55636) = midpoint of X(i) and X(j) for these {i,j}: {182, 55597}, {1350, 20190}, {14810, 55631}, {15516, 52987}, {22330, 55590}, {3, 55612}, {575, 55592}, {5092, 55601}, {50664, 55594}
X(55636) = reflection of X(i) in X(j) for these {i,j}: {55609, 3098}, {55617, 55625}, {55625, 55631}
X(55636) = isogonal conjugate of X(54852)
X(55636) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 54852}
X(55636) = center of Tucker-Hagos(-5/8) circle
X(55636) = barycentric quotient X(i)/X(j) for these (i, j): {6, 54852}
X(55636) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 39561}, {3, 3098, 55594}, {3, 31884, 55633}, {3, 37517, 5092}, {3, 55591, 182}, {3, 55594, 50664}, {3, 55603, 5097}, {3, 55607, 37517}, {3, 55618, 55587}, {3, 55622, 55603}, {3, 55629, 55618}, {3, 55633, 55627}, {6, 3098, 55606}, {182, 3098, 55604}, {182, 55604, 55586}, {182, 55615, 55597}, {182, 55626, 55615}, {511, 3098, 55609}, {511, 55631, 55625}, {575, 55610, 55592}, {576, 55616, 55599}, {1350, 20190, 511}, {1350, 55630, 55623}, {3098, 31884, 55634}, {3098, 37517, 55607}, {3098, 55585, 55610}, {3098, 55609, 55617}, {5085, 55608, 55588}, {5097, 55594, 55582}, {14810, 31884, 55631}, {14810, 55627, 3}, {14810, 55630, 20190}, {14810, 55632, 55601}, {14810, 55633, 55612}, {14810, 55634, 3098}, {15516, 55631, 55624}, {17508, 55590, 22330}, {17508, 55614, 55590}, {52987, 55624, 55619}, {53094, 55620, 55596}, {55586, 55594, 55591}, {55587, 55633, 55629}, {55597, 55631, 55626}, {55606, 55629, 55621}

X(55637) = X(3)X(6)∩X(20)X(11178)

Barycentrics    5*a^6+3*a^4*(b^2+c^2)-2*a^2*(4*b^4+5*b^2*c^2+4*c^4) : :
X(55637) = -13*X[3]+3*X[6], 2*X[20]+3*X[11178], X[69]+4*X[33751], 2*X[140]+3*X[50965], 3*X[141]+2*X[12103], 3*X[376]+2*X[40107], 2*X[546]+3*X[48881], 4*X[548]+X[34507], -7*X[550]+12*X[50972], 3*X[1352]+7*X[50693], 7*X[3090]+3*X[48873], -X[3146]+6*X[24206] and many others

X(55637) lies on circumconic {{A, B, C, X(14075), X(46851)}} and on these lines: {3, 6}, {20, 11178}, {69, 33751}, {140, 50965}, {141, 12103}, {376, 40107}, {524, 46853}, {542, 3522}, {546, 48881}, {548, 34507}, {550, 50972}, {631, 19924}, {632, 29181}, {1352, 50693}, {3090, 48873}, {3091, 29317}, {3146, 24206}, {3357, 15581}, {3524, 25555}, {3525, 19130}, {3528, 54173}, {3529, 48884}, {3530, 5476}, {3533, 25565}, {3534, 18553}, {3619, 11541}, {3627, 48880}, {3628, 21167}, {3763, 5076}, {3818, 15704}, {3857, 34573}, {3858, 50980}, {5059, 50969}, {5072, 48895}, {5073, 25561}, {5079, 48910}, {5480, 12108}, {7492, 9306}, {7496, 11451}, {7525, 52098}, {8550, 34200}, {9968, 35228}, {10168, 15717}, {10299, 20423}, {10303, 31670}, {10516, 48920}, {10519, 48892}, {11179, 21734}, {11204, 15579}, {11470, 17506}, {11645, 15696}, {12294, 35479}, {12584, 51522}, {12811, 42786}, {14002, 16187}, {14869, 38317}, {15020, 43652}, {15023, 15462}, {15036, 25556}, {15069, 15688}, {15082, 30734}, {15706, 46267}, {15712, 51137}, {17538, 29012}, {17800, 21358}, {20397, 32273}, {21735, 51179}, {22676, 35950}, {33923, 51136}, {44245, 48898}, {44903, 51143}, {46219, 51024}, {48889, 49136}, {50691, 50956}

X(55637) = midpoint of X(i) and X(j) for these {i,j}: {182, 55598}, {1350, 12017}, {14810, 55634}, {22234, 52987}, {3, 55614}, {53093, 55595}, {53094, 55604}
X(55637) = reflection of X(i) in X(j) for these {i,j}: {3098, 55629}, {48884, 51537}, {576, 53093}, {52987, 55600}, {53091, 5092}, {55595, 55606}, {55598, 55608}, {55600, 55614}, {55604, 55619}, {55608, 3098}, {55614, 55623}, {55623, 55631}, {55629, 55634}
X(55637) = center of Tucker-Hagos(-3/5) circle
X(55637) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 5092}, {3, 11482, 53094}, {3, 31884, 55631}, {3, 33878, 10541}, {3, 53097, 20190}, {3, 55580, 5085}, {3, 55595, 53093}, {3, 55600, 22234}, {3, 55602, 6}, {3, 55604, 11482}, {3, 55610, 11477}, {3, 55617, 55583}, {3, 55624, 55602}, {3, 55626, 55606}, {3, 55629, 55614}, {6, 55596, 55581}, {6, 55612, 55596}, {182, 3098, 55603}, {182, 55603, 55585}, {511, 3098, 55608}, {511, 5092, 53091}, {511, 55606, 55595}, {511, 55619, 55604}, {511, 55631, 55623}, {511, 55634, 55629}, {548, 54169, 34507}, {575, 55627, 55617}, {1350, 12017, 511}, {1350, 17508, 37517}, {1350, 3098, 55613}, {1350, 31884, 55632}, {1350, 5093, 55586}, {1350, 55583, 52987}, {1350, 55627, 3098}, {1350, 55632, 55627}, {1351, 55601, 55589}, {1351, 55618, 55601}, {3098, 17508, 1350}, {3098, 39561, 55605}, {3098, 55587, 55610}, {3098, 55596, 55612}, {3098, 55605, 55615}, {3098, 55631, 55628}, {3098, 55633, 55630}, {5050, 55607, 55590}, {5085, 55580, 22330}, {5085, 55616, 55594}, {5092, 55587, 15520}, {5097, 55609, 55593}, {11477, 55597, 55587}, {11477, 55610, 55597}, {11482, 55619, 55600}, {14810, 55631, 3}, {14810, 55632, 17508}, {14810, 55633, 182}, {14810, 55635, 55633}, {14810, 55636, 31884}, {17508, 55583, 575}, {20190, 53097, 576}, {20190, 55606, 53097}, {22234, 55614, 55598}, {22234, 55623, 55611}, {22330, 55594, 55580}, {22330, 55631, 55621}, {31884, 55629, 55634}, {31884, 55636, 55635}, {39561, 55605, 33878}, {50664, 55599, 55584}, {52987, 55581, 55588}, {53094, 55629, 55619}, {53097, 55626, 55620}, {55588, 55631, 55624}, {55594, 55621, 55616}, {55597, 55631, 55625}, {55606, 55631, 55626}

X(55638) = X(3)X(6)∩X(5066)X(29317)

Barycentrics    a^2*(12*a^4-19*b^4-24*b^2*c^2-19*c^4+7*a^2*(b^2+c^2)) : :
X(55638) = -31*X[3]+7*X[6], 5*X[3858]+7*X[48881], -13*X[5068]+7*X[48895], 17*X[7486]+7*X[48873], -10*X[10124]+7*X[25565], -11*X[15682]+35*X[50956], 5*X[15697]+7*X[50977], -3*X[15699]+7*X[21167], -15*X[15713]+7*X[38136], -11*X[15721]+7*X[38317], 5*X[17578]+7*X[48880] and many others

X(55638) lies on these lines: {3, 6}, {3858, 48881}, {5066, 29317}, {5068, 48895}, {7486, 48873}, {10124, 25565}, {15682, 50956}, {15691, 29012}, {15697, 50977}, {15699, 21167}, {15713, 38136}, {15721, 38317}, {17578, 48880}, {19710, 29323}, {44580, 51130}, {48889, 49135}, {48920, 49138}

X(55638) = midpoint of X(i) and X(j) for these {i,j}: {14810, 31884}, {15520, 55590}, {17508, 55606}, {3, 55615}, {5050, 55594}, {575, 55593}, {5085, 55599}, {5092, 55603}, {5097, 55589}, {5102, 55588}
X(55638) = reflection of X(i) in X(j) for these {i,j}: {31884, 55636}, {50664, 17508}, {55592, 55603}, {55601, 55615}, {55603, 55617}, {55612, 55621}, {55615, 55625}, {55621, 55631}, {55631, 31884}
X(55638) = center of Tucker-Hagos(-7/12) circle
X(55638) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3098, 55590}, {3, 31884, 55630}, {3, 55601, 15516}, {3, 55625, 55601}, {3, 55630, 55615}, {3, 55635, 55634}, {6, 55628, 55619}, {182, 3098, 55602}, {182, 55623, 55609}, {182, 55632, 55623}, {511, 17508, 50664}, {511, 55617, 55603}, {511, 55631, 55621}, {511, 55636, 31884}, {1351, 3098, 55606}, {3098, 5085, 55599}, {5050, 55613, 55594}, {5050, 55626, 55613}, {5085, 53097, 5093}, {5085, 55591, 1351}, {5092, 55617, 55592}, {5092, 55629, 55617}, {14810, 31884, 511}, {14810, 55634, 3}, {14810, 55635, 55625}, {14810, 55636, 55631}, {14810, 55637, 55636}, {15516, 55625, 55612}, {15520, 55630, 3098}, {17508, 55633, 55624}, {31884, 55618, 55632}, {31884, 55624, 55633}, {50664, 55601, 55585}, {53094, 55611, 55586}, {55585, 55596, 55591}, {55590, 55599, 55596}, {55590, 55601, 55597}, {55591, 55633, 55627}

X(55639) = X(3)X(6)∩X(30)X(3619)

Barycentrics    a^2*(7*a^4-11*b^4-14*b^2*c^2-11*c^4+4*a^2*(b^2+c^2)) : :
X(55639) = -9*X[3]+2*X[6], 3*X[20]+4*X[18358], X[69]+6*X[8703], 4*X[141]+3*X[3534], 4*X[159]+3*X[35450], -X[193]+15*X[19708], 9*X[376]+5*X[3620], -9*X[381]+16*X[34573], 4*X[548]+3*X[10519], -4*X[597]+11*X[15716], 2*X[599]+5*X[15695], 5*X[631]+2*X[48874] and many others

X(55639) lies on these lines: {3, 6}, {20, 18358}, {25, 41462}, {30, 3619}, {69, 8703}, {141, 3534}, {159, 35450}, {193, 19708}, {376, 3620}, {381, 34573}, {548, 10519}, {597, 15716}, {599, 15695}, {631, 48874}, {632, 51538}, {1352, 15696}, {1353, 33750}, {1598, 33540}, {1656, 21167}, {1992, 15759}, {3167, 15080}, {3426, 33533}, {3522, 39874}, {3524, 21850}, {3526, 29181}, {3528, 3564}, {3530, 51212}, {3579, 16496}, {3589, 15693}, {3618, 12100}, {3630, 14093}, {3631, 15688}, {3763, 3830}, {3818, 15681}, {3819, 41424}, {3839, 50980}, {3843, 48872}, {3851, 29317}, {5054, 31670}, {5055, 48910}, {5070, 48901}, {5072, 51163}, {5073, 24206}, {5476, 15718}, {5480, 15720}, {5544, 7496}, {5888, 11284}, {6090, 7712}, {6391, 20421}, {6636, 26864}, {6776, 33923}, {7467, 8617}, {7484, 15107}, {7716, 35501}, {8780, 15066}, {9924, 11204}, {10299, 38110}, {10303, 38136}, {10304, 20080}, {10323, 12112}, {10516, 17800}, {10546, 21766}, {10691, 37643}, {11008, 34200}, {11178, 50968}, {11179, 51174}, {12167, 35473}, {12315, 15577}, {12601, 36701}, {12602, 36703}, {12702, 49465}, {13624, 16491}, {14848, 15692}, {14853, 15712}, {14855, 46202}, {14891, 54132}, {14927, 44245}, {15041, 32254}, {15042, 15462}, {15051, 45016}, {15684, 48879}, {15685, 21358}, {15689, 48905}, {15690, 21356}, {15694, 19130}, {15698, 51171}, {15701, 19924}, {15704, 40330}, {15705, 50966}, {15706, 20423}, {15707, 54131}, {15710, 50979}, {15717, 18583}, {15988, 19704}, {16010, 38633}, {16419, 34417}, {17504, 54170}, {17538, 39884}, {18325, 47452}, {19118, 35472}, {19709, 48895}, {21312, 41464}, {21487, 37680}, {21970, 43957}, {25406, 46853}, {32063, 34778}, {32306, 38723}, {35403, 48943}, {35485, 41584}, {36702, 49028}, {36717, 49029}, {38638, 51941}, {40107, 48662}, {40916, 48912}, {41982, 50978}, {42144, 44465}, {42145, 44461}, {45759, 50967}, {46219, 53023}, {47353, 48891}, {48889, 49134}, {48920, 49139}, {50954, 50972}

X(55639) = midpoint of X(i) and X(j) for these {i,j}: {1350, 10541}, {3, 55616}
X(55639) = reflection of X(i) in X(j) for these {i,j}: {1350, 55611}, {1351, 53092}, {53858, 182}, {55602, 55616}, {55607, 3098}, {55616, 55626}, {55626, 55633}
X(55639) = center of Tucker-Hagos(-4/7) circle
X(55639) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3053), X(20421)}}, {{A, B, C, X(3426), X(5007)}}, {{A, B, C, X(14489), X(53094)}}, {{A, B, C, X(22331), X(43713)}}, {{A, B, C, X(40802), X(55585)}}, {{A, B, C, X(41940), X(43908)}}
X(55639) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 5050}, {3, 31884, 55629}, {3, 33878, 12017}, {3, 44456, 5092}, {3, 5093, 53094}, {3, 53091, 17508}, {3, 55584, 5085}, {3, 55593, 182}, {3, 55602, 53092}, {3, 55604, 6}, {3, 55606, 11482}, {3, 55626, 55602}, {182, 3098, 55601}, {182, 511, 53858}, {182, 55601, 55582}, {182, 55627, 55614}, {511, 3098, 55607}, {511, 55633, 55626}, {575, 55608, 55591}, {575, 55621, 55608}, {1350, 10541, 511}, {1350, 15516, 55584}, {1350, 31884, 55631}, {1350, 5092, 44456}, {1350, 55588, 55593}, {1350, 55609, 55604}, {1350, 55624, 55620}, {1351, 55610, 55595}, {3098, 17508, 55598}, {3098, 31884, 55632}, {3098, 37517, 55606}, {3098, 55585, 55609}, {3098, 55607, 55616}, {3098, 55637, 55636}, {3763, 48880, 3830}, {5050, 11482, 15516}, {5085, 31884, 55630}, {5092, 55609, 55585}, {6200, 6396, 3053}, {6200, 6422, 6221}, {6221, 6398, 30435}, {6396, 6421, 6398}, {6451, 6452, 15655}, {10516, 48885, 17800}, {10541, 55602, 55580}, {10541, 55626, 55611}, {10541, 55633, 55624}, {10645, 10646, 5210}, {11482, 55622, 55610}, {12017, 33878, 1351}, {12017, 55610, 33878}, {12305, 43126, 3}, {14810, 55635, 1350}, {14810, 55636, 3098}, {14810, 55637, 31884}, {14810, 55638, 55637}, {15041, 33851, 32254}, {15516, 55606, 55589}, {15688, 54169, 50955}, {17508, 53097, 53091}, {17508, 55612, 53097}, {17508, 55628, 55612}, {20190, 55619, 55596}, {21167, 48873, 1656}, {31884, 55626, 55633}, {33533, 35243, 3426}, {34573, 43621, 381}, {34573, 48881, 43621}, {42115, 42116, 1384}, {52987, 53094, 5093}, {52987, 55625, 55618}, {53094, 55618, 52987}, {55585, 55635, 55634}, {55589, 55631, 55622}

X(55640) = X(3)X(6)∩X(547)X(21167)

Barycentrics    9*a^6+5*a^4*(b^2+c^2)-2*a^2*(7*b^4+9*b^2*c^2+7*c^4) : :
X(55640) = -23*X[3]+5*X[6], -2*X[547]+5*X[21167], 5*X[3357]+4*X[15580], -17*X[3533]+5*X[51538], -14*X[3832]+5*X[48904], -7*X[3845]+25*X[50980], 4*X[3850]+5*X[48881], 4*X[3853]+5*X[48880], -X[5059]+10*X[48885], 13*X[5067]+5*X[48873], -5*X[5476]+14*X[19711], 7*X[8703]+2*X[50982] and many others

X(55640) lies on these lines: {3, 6}, {547, 21167}, {3357, 15580}, {3533, 51538}, {3545, 29317}, {3564, 41982}, {3832, 48904}, {3845, 50980}, {3850, 48881}, {3853, 48880}, {5059, 48885}, {5067, 48873}, {5476, 19711}, {5965, 10304}, {8703, 50982}, {11178, 15686}, {11539, 29181}, {11812, 38317}, {12100, 51166}, {12108, 42785}, {13595, 33879}, {14561, 15719}, {14853, 51137}, {15690, 50977}, {15708, 19924}, {15723, 53023}, {19708, 51140}, {24206, 33703}, {25561, 35400}, {34573, 41991}, {48889, 49133}, {51176, 54173}

X(55640) = midpoint of X(i) and X(j) for these {i,j}: {3, 55618}
X(55640) = reflection of X(i) in X(j) for these {i,j}: {3098, 55630}, {55603, 55618}, {55613, 55624}, {55618, 55627}, {55630, 31884}
X(55640) = center of Tucker-Hagos(-5/9) circle
X(55640) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 50664}, {3, 3098, 55587}, {3, 31884, 55627}, {3, 39561, 17508}, {3, 55594, 182}, {3, 55607, 5097}, {3, 55610, 5102}, {3, 55612, 37517}, {3, 55618, 511}, {3, 55622, 55594}, {3, 55627, 55603}, {3, 55629, 55607}, {3, 55636, 55633}, {6, 55625, 55611}, {182, 3098, 55600}, {182, 52987, 44456}, {182, 55610, 55589}, {182, 55633, 55622}, {511, 31884, 55630}, {511, 55624, 55613}, {511, 55627, 55618}, {575, 55616, 55598}, {576, 3098, 55605}, {1350, 55628, 3098}, {1350, 55634, 55628}, {3098, 17508, 55596}, {3098, 55583, 55608}, {3098, 55589, 55610}, {3098, 55637, 55635}, {5085, 31884, 55629}, {5085, 55615, 52987}, {5085, 55629, 55615}, {5092, 55608, 55583}, {5097, 50664, 53092}, {11482, 55610, 55593}, {14810, 55636, 3}, {14810, 55638, 31884}, {14810, 55639, 55637}, {15520, 50664, 39561}, {17508, 55596, 576}, {20190, 55604, 55581}, {31884, 55610, 55631}, {31884, 55639, 55638}, {37517, 55603, 55591}, {50664, 55636, 55634}, {55613, 55630, 55624}, {55633, 55637, 55636}

X(55641) = X(3)X(6)∩X(548)X(599)

Barycentrics    a^2*(11*a^4-17*b^4-22*b^2*c^2-17*c^4+6*a^2*(b^2+c^2)) : :
X(55641) = -14*X[3]+3*X[6], 5*X[20]+6*X[47354], 3*X[64]+8*X[15582], 6*X[141]+5*X[17538], 7*X[376]+4*X[50991], 8*X[546]+3*X[48872], 8*X[548]+3*X[599], 8*X[550]+3*X[47353], -20*X[631]+9*X[38072], -20*X[632]+9*X[53023], 3*X[1352]+8*X[44245], 2*X[1657]+9*X[21358] and many others

X(55641) lies on these lines: {3, 6}, {20, 47354}, {64, 15582}, {141, 17538}, {376, 50991}, {524, 21735}, {546, 48872}, {548, 599}, {550, 47353}, {631, 38072}, {632, 53023}, {1352, 44245}, {1657, 21358}, {3090, 21167}, {3091, 48881}, {3522, 15069}, {3523, 54131}, {3525, 29181}, {3526, 25565}, {3528, 43273}, {3529, 10516}, {3530, 38079}, {3544, 51163}, {3619, 49140}, {3627, 3763}, {3628, 48873}, {3796, 9716}, {3857, 43621}, {3861, 50980}, {5067, 50984}, {5072, 29317}, {5076, 48880}, {5646, 16042}, {7492, 35264}, {7496, 17810}, {7525, 51933}, {7716, 14865}, {8550, 21734}, {8703, 50989}, {9924, 15579}, {9968, 17821}, {10304, 50992}, {12082, 33537}, {12103, 36990}, {12108, 47355}, {13452, 34817}, {14093, 15533}, {14869, 31670}, {14891, 51185}, {14924, 40916}, {15020, 51941}, {15021, 33851}, {15534, 45759}, {15686, 51186}, {15688, 34507}, {15689, 50993}, {15696, 50977}, {15698, 41153}, {15712, 47352}, {15720, 19924}, {20423, 44682}, {20582, 33703}, {21766, 41424}, {24206, 49136}, {25561, 49134}, {31447, 38087}, {31666, 38315}, {33923, 54173}, {46332, 51188}, {46333, 51143}, {46853, 51183}, {48885, 49137}, {48905, 50693}

X(55641) = midpoint of X(i) and X(j) for these {i,j}: {3, 55620}
X(55641) = reflection of X(i) in X(j) for these {i,j}: {55620, 55628}, {55622, 55632}, {55632, 55635}
X(55641) = center of Tucker-Hagos(-6/11) circle
X(55641) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(13452), X(30435)}}, {{A, B, C, X(21309), X(44763)}}
X(55641) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 53093}, {3, 31884, 55626}, {3, 33878, 20190}, {3, 52987, 10541}, {3, 53092, 17508}, {3, 53097, 5085}, {3, 576, 53094}, {3, 55595, 182}, {3, 55602, 575}, {3, 55606, 6}, {3, 55610, 576}, {3, 55620, 511}, {3, 55629, 55606}, {3, 55632, 55620}, {3, 55639, 55637}, {6, 31884, 55629}, {6, 55629, 55618}, {182, 3098, 55599}, {182, 55617, 55595}, {182, 55624, 55607}, {182, 55634, 55624}, {511, 55632, 55622}, {576, 55633, 55623}, {1350, 53858, 53097}, {3098, 55590, 55610}, {3522, 54169, 15069}, {5085, 53097, 53858}, {5085, 55618, 55593}, {5092, 55616, 55591}, {5092, 55630, 55616}, {10541, 52987, 11477}, {10541, 55614, 52987}, {11477, 55614, 1350}, {11477, 55626, 55614}, {14810, 55637, 3}, {14810, 55638, 3098}, {14810, 55639, 31884}, {14810, 55640, 55639}, {17508, 55588, 53092}, {17508, 55625, 55604}, {20190, 55611, 33878}, {20190, 55627, 55611}, {31884, 55591, 55630}, {31884, 55614, 55631}, {31884, 55622, 55632}, {53092, 55604, 55588}, {53094, 55610, 55582}, {53097, 55614, 55602}, {55595, 55624, 55617}, {55620, 55632, 55628}, {55628, 55637, 55635}

X(55642) = X(3)X(6)∩X(141)X(15690)

Barycentrics    11*a^6+5*a^4*(b^2+c^2)-2*a^2*(8*b^4+11*b^2*c^2+8*c^4) : :
X(55642) = -27*X[3]+5*X[6], 5*X[141]+6*X[15690], 6*X[547]+5*X[48881], -18*X[549]+7*X[42785], 17*X[3533]+5*X[48873], 6*X[3543]+5*X[48879], -27*X[3545]+5*X[43621], -10*X[3589]+21*X[19711], 35*X[3619]+9*X[11001], 5*X[3620]+6*X[48892], -X[3629]+12*X[15759], 5*X[3630]+72*X[46332] and many others

X(55642) lies on these lines: {3, 6}, {141, 15690}, {547, 48881}, {549, 42785}, {3533, 48873}, {3543, 48879}, {3545, 43621}, {3589, 19711}, {3619, 11001}, {3620, 48892}, {3629, 15759}, {3630, 46332}, {3631, 8703}, {3818, 15686}, {3845, 34573}, {3850, 21167}, {5056, 29317}, {5059, 24206}, {5965, 21735}, {6329, 15711}, {10304, 50961}, {11008, 19708}, {11539, 50959}, {11738, 41435}, {11812, 51126}, {15688, 43150}, {15699, 51165}, {15702, 19130}, {15708, 31670}, {15710, 51214}, {15719, 19924}, {16239, 48901}, {18358, 48896}, {21850, 51137}, {33703, 48885}, {33751, 39874}, {37913, 41462}, {41981, 48898}, {41982, 54169}, {41983, 50965}, {44091, 44878}, {45759, 51140}, {48905, 50954}, {48920, 49133}

X(55642) = midpoint of X(i) and X(j) for these {i,j}: {3, 55622}
X(55642) = reflection of X(i) in X(j) for these {i,j}: {3098, 55632}, {55628, 55635}, {55635, 55641}, {55641, 14810}
X(55642) = center of Tucker-Hagos(-5/11) circle
X(55642) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5007), X(11738)}}, {{A, B, C, X(20421), X(35007)}}
X(55642) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14810, 55640}, {3, 3098, 37517}, {3, 31884, 55612}, {3, 5097, 17508}, {3, 55582, 5092}, {3, 55603, 182}, {3, 55607, 50664}, {3, 55612, 39561}, {3, 55618, 5097}, {3, 55622, 511}, {3, 55627, 55587}, {3, 55629, 55591}, {3, 55633, 55603}, {3, 55636, 3098}, {3, 55640, 55633}, {6, 55639, 55634}, {182, 3098, 55598}, {182, 55630, 55611}, {182, 55637, 55630}, {511, 14810, 55641}, {511, 55641, 55635}, {575, 55624, 55605}, {576, 3098, 55601}, {1351, 31884, 55623}, {3098, 17508, 33878}, {3098, 5092, 52987}, {3098, 55587, 55607}, {3098, 55601, 55613}, {3098, 55632, 55628}, {3098, 55635, 55632}, {3098, 55640, 55636}, {5085, 55625, 55600}, {5097, 55631, 55618}, {6200, 6396, 35007}, {6480, 6481, 5008}, {10645, 10646, 5206}, {17508, 55631, 55608}, {20190, 55616, 55589}, {37517, 52987, 55582}, {37517, 55594, 55585}, {39561, 55640, 31884}, {50664, 55636, 55627}, {52987, 55608, 55599}, {52987, 55628, 55620}, {53094, 55615, 55583}, {55582, 55604, 55594}, {55594, 55612, 55604}, {55628, 55641, 55637}

X(55643) = X(3)X(6)∩X(25)X(33879)

Barycentrics    a^2*(9*a^4-13*b^4-18*b^2*c^2-13*c^4+4*a^2*(b^2+c^2)) : :
X(55643) = -11*X[3]+2*X[6], X[69]+8*X[33923], -4*X[140]+X[51538], 4*X[141]+5*X[15696], -X[381]+4*X[21167], 8*X[548]+X[18440], -5*X[631]+2*X[38136], 5*X[1656]+4*X[48881], -X[1992]+10*X[15714], 7*X[3523]+2*X[48874], -5*X[3524]+2*X[38079], 7*X[3526]+2*X[48873] and many others

X(55643) lies on these lines: {3, 6}, {25, 33879}, {69, 33923}, {140, 51538}, {141, 15696}, {381, 21167}, {542, 38633}, {548, 18440}, {631, 38136}, {1503, 15688}, {1656, 48881}, {1992, 15714}, {3167, 33884}, {3523, 48874}, {3524, 38079}, {3526, 48873}, {3528, 48876}, {3534, 47354}, {3564, 10304}, {3618, 44682}, {3619, 15704}, {3763, 5073}, {3843, 48880}, {3845, 50969}, {3851, 48872}, {5054, 29181}, {5055, 29317}, {5070, 48910}, {5072, 43621}, {5079, 51163}, {5447, 51933}, {5544, 15107}, {5650, 9909}, {5888, 30734}, {6090, 6636}, {6593, 15042}, {6776, 46853}, {7998, 35264}, {8703, 10519}, {8780, 35268}, {10299, 18583}, {10516, 15681}, {11414, 16261}, {11820, 33533}, {12041, 32254}, {12100, 14853}, {12103, 40330}, {13093, 15577}, {14093, 54169}, {14530, 34778}, {14561, 15693}, {14848, 17504}, {14891, 54170}, {15051, 48679}, {15062, 35253}, {15069, 33751}, {15682, 50980}, {15685, 50957}, {15689, 29012}, {15692, 38110}, {15694, 25565}, {15695, 50977}, {15701, 38317}, {15707, 19924}, {15711, 54132}, {15712, 51212}, {15716, 20423}, {15717, 21850}, {15718, 54131}, {15720, 31670}, {15759, 50967}, {17506, 19118}, {17538, 18358}, {17800, 24206}, {19708, 51179}, {21358, 29323}, {21735, 48906}, {25406, 34200}, {32306, 38726}, {33750, 34380}, {37968, 52238}, {39884, 50693}, {46219, 48901}, {46332, 50978}, {48662, 48892}, {48889, 49139}, {48920, 49134}, {51136, 51175}

X(55643) = midpoint of X(i) and X(j) for these {i,j}: {17508, 55613}, {3, 55624}
X(55643) = reflection of X(i) in X(j) for these {i,j}: {1350, 55613}, {31884, 55640}, {33750, 45759}, {55610, 55624}, {55613, 55627}, {55618, 55630}, {55624, 31884}, {55640, 14810}
X(55643) = center of Tucker-Hagos(-4/9) circle
X(55643) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3426), X(14075)}}, {{A, B, C, X(3527), X(34571)}}, {{A, B, C, X(14489), X(17508)}}
X(55643) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 12017}, {3, 14810, 55639}, {3, 3098, 1351}, {3, 44456, 53094}, {3, 5093, 17508}, {3, 55584, 5092}, {3, 55593, 5085}, {3, 55604, 182}, {3, 55614, 53092}, {3, 55616, 6}, {3, 55620, 11482}, {3, 55631, 55595}, {6, 1350, 55583}, {6, 55631, 55616}, {182, 3098, 55597}, {182, 55604, 55580}, {182, 55615, 55591}, {182, 55626, 55604}, {182, 55636, 55626}, {511, 14810, 55640}, {511, 31884, 55624}, {511, 55627, 55613}, {511, 55630, 55618}, {576, 55625, 55607}, {1350, 17508, 5093}, {1350, 31884, 55627}, {1351, 12017, 575}, {1351, 3098, 55602}, {1351, 5085, 5050}, {1351, 55602, 33878}, {1351, 55610, 55593}, {3098, 14810, 55641}, {3098, 15520, 55599}, {3098, 55581, 55606}, {3098, 55638, 31884}, {3763, 48885, 5073}, {5085, 31884, 3098}, {5085, 53097, 15520}, {5092, 55596, 5102}, {5092, 55614, 55584}, {5092, 55621, 55596}, {5092, 55633, 55614}, {5102, 31884, 55621}, {12017, 55637, 55629}, {12017, 55639, 55632}, {15062, 37198, 35253}, {15520, 55599, 53097}, {17508, 55613, 511}, {17508, 55627, 1350}, {17508, 55632, 55610}, {20190, 55608, 55582}, {31884, 55618, 55630}, {31884, 55641, 55638}, {33878, 55629, 55620}, {34380, 45759, 33750}, {52987, 55634, 55622}, {53092, 55639, 55633}, {53094, 55606, 44456}, {55583, 55637, 55631}, {55586, 55627, 55615}, {55595, 55610, 55603}

X(55644) = X(3)X(6)∩X(5)X(50984)

Barycentrics    7*a^6+3*a^4*(b^2+c^2)-2*a^2*(5*b^4+7*b^2*c^2+5*c^4) : :
X(55644) = -17*X[3]+3*X[6], -5*X[5]+12*X[50984], 3*X[141]+4*X[44245], -2*X[546]+9*X[21167], 4*X[548]+3*X[50977], 4*X[550]+3*X[11178], -10*X[632]+3*X[48901], -10*X[3091]+3*X[48904], X[3146]+6*X[48885], 3*X[3357]+4*X[15582], 25*X[3522]+3*X[11180], 11*X[3525]+3*X[48873] and many others

X(55644) lies on these lines: {3, 6}, {5, 50984}, {23, 44299}, {141, 44245}, {542, 3528}, {546, 21167}, {548, 50977}, {550, 11178}, {632, 48901}, {3090, 29317}, {3091, 48904}, {3146, 48885}, {3357, 15582}, {3522, 11180}, {3523, 19924}, {3525, 48873}, {3526, 51141}, {3529, 24206}, {3530, 50965}, {3544, 43621}, {3627, 48879}, {3628, 48881}, {3763, 48920}, {3818, 12103}, {3832, 50969}, {3857, 42786}, {5072, 48872}, {5079, 48895}, {5476, 15712}, {8541, 23040}, {8703, 34507}, {9968, 11202}, {10168, 10299}, {10303, 19130}, {10519, 33751}, {12108, 38317}, {12812, 51163}, {14869, 29181}, {15034, 52098}, {15696, 18553}, {15704, 48884}, {15716, 46267}, {15717, 25555}, {17538, 48896}, {17800, 25561}, {21734, 51178}, {21735, 54173}, {22165, 41982}, {29012, 50693}, {32273, 38729}, {33749, 50967}, {33923, 54169}, {34778, 50414}, {44682, 50988}, {46853, 50978}, {48889, 49137}, {50692, 50956}

X(55644) = midpoint of X(i) and X(j) for these {i,j}: {10541, 55602}, {3, 55626}
X(55644) = reflection of X(i) in X(j) for these {i,j}: {3098, 55633}, {52987, 55602}, {55605, 3098}, {55611, 55626}, {55633, 55639}, {55639, 14810}
X(55644) = center of Tucker-Hagos(-3/7) circle
X(55644) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 20190}, {3, 14810, 55637}, {3, 53097, 5092}, {3, 576, 17508}, {3, 55595, 5085}, {3, 55602, 10541}, {3, 55606, 182}, {3, 55610, 53093}, {3, 55614, 575}, {3, 55617, 22234}, {3, 55620, 6}, {3, 55632, 55595}, {3, 55639, 55626}, {6, 55608, 55589}, {6, 55620, 55597}, {182, 3098, 55596}, {182, 52987, 11477}, {182, 55613, 33878}, {182, 55628, 55606}, {182, 55633, 55616}, {182, 55637, 55628}, {511, 14810, 55639}, {511, 3098, 55605}, {511, 55639, 55633}, {575, 55631, 55614}, {576, 3098, 55600}, {1350, 55630, 3098}, {1350, 55636, 55630}, {1351, 55615, 55598}, {3098, 14810, 55640}, {3098, 17508, 55587}, {3098, 55589, 55608}, {3098, 55640, 55635}, {5050, 55601, 55581}, {5050, 55622, 55601}, {5085, 55612, 55585}, {5085, 55632, 55612}, {5092, 14810, 55638}, {5092, 55592, 5093}, {5092, 55629, 55603}, {5097, 55621, 55604}, {10541, 11477, 53092}, {10541, 55602, 511}, {10541, 55626, 55602}, {10541, 55631, 55611}, {10541, 55639, 55631}, {11477, 52987, 55583}, {11477, 55606, 52987}, {11477, 55641, 31884}, {12017, 55618, 55590}, {14810, 55631, 55641}, {14810, 55643, 55642}, {15717, 25555, 51137}, {17508, 55600, 576}, {20190, 55623, 1350}, {20190, 55636, 55623}, {22234, 55603, 53097}, {22234, 55637, 55629}, {31884, 33878, 55625}, {33878, 55625, 55613}, {50664, 55619, 55593}, {53093, 55588, 37517}, {53093, 55610, 55588}, {53094, 55594, 15520}, {53094, 55624, 55594}, {53097, 55629, 55617}, {53858, 55626, 55607}, {55597, 55627, 55620}

X(55645) = X(3)X(6)∩X(547)X(29317)

Barycentrics    a^2*(12*a^4-17*b^4-24*b^2*c^2-17*c^4+5*a^2*(b^2+c^2)) : :
X(55645) = -29*X[3]+5*X[6], 5*X[3522]+X[43150], -17*X[3533]+5*X[48901], -25*X[3763]+X[49133], 7*X[3832]+5*X[48880], -X[3845]+5*X[21167], -11*X[5056]+5*X[48895], X[5059]+5*X[48889], -21*X[15702]+5*X[51538], -9*X[15708]+5*X[38317], 7*X[19711]+5*X[50965], X[33703]+5*X[48920], -5*X[38110]+X[51166]

X(55645) lies on these lines: {3, 6}, {542, 41982}, {547, 29317}, {3522, 43150}, {3533, 48901}, {3564, 46332}, {3763, 49133}, {3832, 48880}, {3845, 21167}, {5056, 48895}, {5059, 48889}, {5650, 37913}, {5965, 34200}, {11812, 29181}, {13595, 15082}, {15686, 29323}, {15690, 29012}, {15702, 51538}, {15708, 38317}, {19711, 50965}, {19924, 41983}, {33703, 48920}, {38110, 51166}

X(55645) = midpoint of X(i) and X(j) for these {i,j}: {182, 55599}, {17508, 55615}, {3, 55627}, {39561, 55594}, {575, 55596}, {5085, 55606}, {5092, 55610}, {5093, 55590}, {5097, 55591}
X(55645) = reflection of X(i) in X(j) for these {i,j}: {15516, 5085}, {55596, 55609}, {55597, 55610}, {55599, 55617}, {55610, 55625}, {55612, 55627}, {55621, 31884}, {55627, 55636}, {55631, 55638}, {55638, 14810}
X(55645) = center of Tucker-Hagos(-5/12) circle
X(55645) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14810, 55636}, {3, 3098, 5097}, {3, 31884, 55603}, {3, 5102, 17508}, {3, 55587, 5092}, {3, 55607, 182}, {3, 55612, 50664}, {3, 55618, 39561}, {3, 55622, 37517}, {3, 55629, 55582}, {3, 55633, 55594}, {3, 55636, 55612}, {3, 55639, 55622}, {3, 55640, 55627}, {3, 55642, 14810}, {6, 55635, 55623}, {182, 3098, 55595}, {182, 55624, 55599}, {182, 55634, 55617}, {182, 55641, 55634}, {511, 14810, 55638}, {511, 31884, 55621}, {511, 5085, 15516}, {511, 55609, 55596}, {511, 55625, 55610}, {575, 55629, 55609}, {576, 55632, 55619}, {3098, 20190, 55592}, {3098, 22234, 1350}, {3098, 53094, 55588}, {3098, 55584, 55606}, {5050, 11477, 15520}, {5050, 31884, 3098}, {5092, 14810, 55637}, {5092, 55625, 55597}, {5092, 55637, 55625}, {14810, 55606, 55639}, {14810, 55627, 55640}, {14810, 55634, 55641}, {15516, 55638, 55630}, {15516, 55639, 55631}, {15520, 55603, 55587}, {17508, 31884, 55615}, {17508, 55603, 5102}, {17508, 55615, 511}, {20190, 55597, 11477}, {37517, 55603, 55589}, {39561, 55633, 55618}, {39561, 55640, 55633}, {55599, 55634, 55624}, {55603, 55640, 31884}

X(55646) = X(3)X(6)∩X(141)X(376)

Barycentrics    a^2*(5*a^4-7*b^4-10*b^2*c^2-7*c^4+2*a^2*(b^2+c^2)) : :
X(55646) = -6*X[3]+X[6], -X[4]+6*X[21167], -6*X[5]+X[43621], 3*X[20]+7*X[3619], 3*X[40]+2*X[49465], X[64]+4*X[15577], X[67]+4*X[38726], X[69]+9*X[10304], 4*X[140]+X[48873], 2*X[141]+3*X[376], 2*X[159]+3*X[10606], 9*X[165]+X[16496] and many others

X(55646) lies on these lines: {2, 31860}, {3, 6}, {4, 21167}, {5, 43621}, {20, 3619}, {22, 10546}, {30, 3763}, {36, 10387}, {40, 49465}, {64, 15577}, {67, 38726}, {69, 10304}, {74, 907}, {140, 48873}, {141, 376}, {154, 6636}, {159, 10606}, {165, 16496}, {193, 51737}, {323, 3796}, {378, 7716}, {381, 42786}, {382, 48885}, {394, 15080}, {518, 35242}, {524, 19708}, {542, 14093}, {548, 1352}, {549, 31670}, {550, 18358}, {597, 15698}, {599, 8703}, {631, 29181}, {1495, 17811}, {1503, 3522}, {1656, 29317}, {1657, 24206}, {1843, 11410}, {1995, 5646}, {2781, 15051}, {2916, 33533}, {2930, 12041}, {2979, 17809}, {3066, 7496}, {3090, 51163}, {3242, 3579}, {3515, 44091}, {3523, 5480}, {3524, 3589}, {3526, 48901}, {3528, 3631}, {3530, 14561}, {3534, 3818}, {3545, 50969}, {3564, 46853}, {3618, 15692}, {3629, 15710}, {3630, 6776}, {3654, 49690}, {3655, 49679}, {3830, 48879}, {3851, 48904}, {3917, 26864}, {4550, 20987}, {5054, 19130}, {5055, 48895}, {5073, 48920}, {5476, 15700}, {6144, 11179}, {6210, 8692}, {6329, 15715}, {6593, 15036}, {6684, 38144}, {6697, 18405}, {7386, 47296}, {7484, 34417}, {7485, 11451}, {7492, 21766}, {7687, 18536}, {7987, 16491}, {8547, 20421}, {8550, 11008}, {8617, 33979}, {9039, 12329}, {9412, 38553}, {9924, 44883}, {9969, 36987}, {10168, 15706}, {10299, 14853}, {10303, 51538}, {10323, 15058}, {10545, 40916}, {10605, 44832}, {10691, 26958}, {11001, 20582}, {11178, 15689}, {11180, 50971}, {11331, 42854}, {11413, 41464}, {11414, 33537}, {11464, 45248}, {11645, 15695}, {11646, 38736}, {12100, 21850}, {12108, 38136}, {12294, 15750}, {12584, 15041}, {13624, 38315}, {13634, 15668}, {13635, 17259}, {14269, 48943}, {14650, 37751}, {14891, 38064}, {14982, 37853}, {15035, 51941}, {15042, 45016}, {15055, 16010}, {15162, 35232}, {15163, 35231}, {15246, 33586}, {15504, 40251}, {15533, 39899}, {15534, 15759}, {15578, 34787}, {15681, 48884}, {15685, 25561}, {15688, 18440}, {15690, 51186}, {15693, 19924}, {15696, 29012}, {15702, 51127}, {15705, 50983}, {15709, 50959}, {15711, 51185}, {15717, 51212}, {15719, 48310}, {15720, 38317}, {16063, 18382}, {16674, 46475}, {17504, 20423}, {17538, 40330}, {17800, 48889}, {17821, 34146}, {18583, 44682}, {19121, 38446}, {19459, 21663}, {20080, 21734}, {21487, 37679}, {21737, 42284}, {22352, 37672}, {22769, 41454}, {23249, 36703}, {23259, 36701}, {23267, 36702}, {23273, 36717}, {23328, 36851}, {24471, 30282}, {25335, 34153}, {26206, 37941}, {32254, 38633}, {32620, 33532}, {33751, 34507}, {33923, 48876}, {34200, 40341}, {35255, 38425}, {35256, 38426}, {35260, 40911}, {38723, 49116}, {39884, 44245}, {41982, 51027}, {42096, 44465}, {42097, 44461}, {44519, 53475}, {46333, 51022}, {46950, 47609}, {47599, 50964}, {48942, 49139}, {49681, 51705}, {49923, 49924}, {52055, 52099}, {52162, 54439}

X(55646) = midpoint of X(i) and X(j) for these {i,j}: {182, 55600}, {1350, 53093}, {12017, 55604}, {17538, 40330}, {20, 51537}, {3, 55629}, {53091, 55595}, {53094, 55614}
X(55646) = reflection of X(i) in X(j) for these {i,j}: {1350, 55614}, {1351, 22234}, {11482, 182}, {3098, 55634}, {33878, 55598}, {53093, 53094}, {53094, 3}, {6, 12017}, {55595, 55608}, {55600, 55619}, {55604, 3098}, {55608, 55623}, {55614, 55629}, {55619, 55631}, {55629, 55637}, {55637, 14810}
X(55646) = isogonal conjugate of X(54519)
X(55646) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 54519}
X(55646) = center of Tucker-Hagos(-2/5) circle
X(55646) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(32), X(43713)}}, {{A, B, C, X(64), X(5007)}}, {{A, B, C, X(74), X(30435)}}, {{A, B, C, X(907), X(2420)}}, {{A, B, C, X(1297), X(53094)}}, {{A, B, C, X(1384), X(20421)}}, {{A, B, C, X(3284), X(34817)}}, {{A, B, C, X(3426), X(43136)}}, {{A, B, C, X(3431), X(9605)}}, {{A, B, C, X(7772), X(14528)}}, {{A, B, C, X(15905), X(41435)}}, {{A, B, C, X(17508), X(40801)}}, {{A, B, C, X(40802), X(55582)}}
X(55646) = barycentric quotient X(i)/X(j) for these (i, j): {6, 54519}
X(55646) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 48881, 48910}, {3, 1350, 5085}, {3, 1351, 17508}, {3, 33878, 5092}, {3, 35246, 6200}, {3, 35247, 6396}, {3, 511, 53094}, {3, 55602, 20190}, {3, 55604, 12017}, {3, 55610, 182}, {3, 55616, 5050}, {3, 55620, 575}, {3, 55632, 33878}, {3, 55636, 55607}, {3, 55639, 3098}, {3, 55640, 55622}, {3, 55643, 14810}, {6, 15815, 12055}, {15, 16, 30435}, {140, 48873, 53023}, {141, 376, 48905}, {141, 48905, 47353}, {182, 3098, 55594}, {182, 511, 11482}, {182, 53097, 5102}, {182, 55594, 44456}, {182, 55640, 55631}, {511, 14810, 55637}, {511, 55608, 55595}, {511, 55619, 55600}, {511, 55623, 55608}, {511, 55631, 55619}, {549, 31670, 47355}, {575, 55603, 55584}, {575, 55625, 55603}, {576, 55612, 55593}, {576, 55630, 55612}, {1350, 31884, 55626}, {1350, 5085, 11477}, {1350, 55626, 55618}, {1350, 55641, 31884}, {1351, 17508, 10541}, {1351, 50664, 6}, {1351, 55606, 55591}, {1351, 55624, 55606}, {3098, 14810, 55639}, {3098, 17508, 55585}, {3098, 37517, 55601}, {3098, 52987, 55609}, {3098, 55609, 55616}, {3098, 55636, 55632}, {3098, 55637, 55634}, {3098, 55644, 55642}, {3524, 50965, 54131}, {3528, 10519, 44882}, {3530, 48874, 14561}, {3631, 44882, 39874}, {4550, 35243, 33534}, {5050, 55616, 52987}, {5092, 14810, 55636}, {5092, 55601, 37517}, {5097, 55596, 55580}, {5097, 55617, 55596}, {5102, 55594, 55582}, {6200, 35246, 12306}, {6200, 6396, 1384}, {6396, 35247, 12305}, {6411, 6412, 5210}, {7492, 21766, 35259}, {10304, 54169, 43273}, {10519, 44882, 15069}, {10541, 22234, 53093}, {10541, 55591, 1351}, {10541, 55624, 1350}, {10645, 10646, 15655}, {11480, 11481, 3053}, {11482, 55600, 53097}, {11482, 55629, 55610}, {11482, 55631, 55614}, {12017, 55604, 511}, {12017, 55629, 55604}, {12017, 55639, 55629}, {12305, 12306, 5188}, {14810, 31884, 55641}, {14810, 55606, 55638}, {14810, 55631, 55640}, {14810, 55644, 55643}, {14810, 55645, 55644}, {15055, 33851, 16010}, {15516, 55599, 55583}, {15520, 55605, 55588}, {15578, 34787, 52028}, {15688, 18440, 48892}, {15705, 54170, 50983}, {17508, 55585, 50664}, {17508, 55638, 55624}, {20190, 55587, 5093}, {20190, 55615, 55587}, {20190, 55628, 55602}, {31670, 47355, 38072}, {33878, 55604, 55598}, {34778, 35228, 154}, {39561, 55611, 55590}, {48892, 50977, 18440}, {52987, 55635, 55627}, {53094, 55591, 22234}, {55587, 55628, 55615}, {55590, 55621, 55611}, {55603, 55625, 55620}, {55606, 55638, 55633}

X(55647) = X(3)X(6)∩X(140)X(25565)

Barycentrics    a^2*(8*a^4-11*b^4-16*b^2*c^2-11*c^4+3*a^2*(b^2+c^2)) : :
X(55647) = -19*X[3]+3*X[6], -5*X[140]+3*X[25565], 3*X[376]+X[18553], 5*X[550]+3*X[47354], 5*X[632]+3*X[48881], X[1657]+3*X[25561], -7*X[3090]+3*X[48895], 5*X[3091]+3*X[48880], X[3146]+3*X[48920], 5*X[3522]+3*X[50977], -11*X[3525]+3*X[48901], 7*X[3528]+X[34507] and many others

X(55647) lies on these lines: {3, 6}, {140, 25565}, {376, 18553}, {542, 33923}, {548, 11645}, {550, 47354}, {632, 48881}, {1657, 25561}, {3090, 48895}, {3091, 48880}, {3146, 48920}, {3522, 50977}, {3525, 48901}, {3528, 34507}, {3529, 48889}, {3530, 19924}, {3627, 21167}, {3628, 29317}, {3763, 48942}, {3818, 17538}, {3819, 7492}, {3850, 50984}, {5056, 50969}, {5072, 48904}, {5073, 50968}, {5076, 48879}, {5079, 48872}, {5476, 15717}, {5643, 15246}, {6688, 7496}, {8550, 45759}, {8703, 40107}, {9970, 15023}, {10168, 44682}, {10219, 40916}, {10303, 48873}, {11178, 15696}, {12100, 25555}, {12102, 34573}, {12103, 29323}, {12108, 29181}, {12584, 15021}, {14002, 15082}, {14093, 15069}, {14869, 19130}, {15022, 43621}, {15704, 24206}, {15712, 38079}, {17504, 46267}, {21734, 54173}, {21735, 50961}, {29012, 44245}, {32237, 41462}, {35228, 50414}, {46219, 51141}, {46853, 54169}, {48891, 50693}

X(55647) = midpoint of X(i) and X(j) for these {i,j}: {182, 55601}, {1350, 50664}, {15516, 55594}, {20190, 55606}, {22330, 52987}, {3, 55631}, {575, 55597}, {5092, 55612}, {6, 55592}
X(55647) = reflection of X(i) in X(j) for these {i,j}: {55609, 55625}, {55617, 55631}, {55625, 55636}, {55636, 14810}
X(55647) = center of Tucker-Hagos(-3/8) circle
X(55647) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 17508}, {3, 14810, 55631}, {3, 52987, 5092}, {3, 55580, 53094}, {3, 55602, 5085}, {3, 55606, 20190}, {3, 55610, 10541}, {3, 55614, 182}, {3, 55623, 22330}, {3, 55624, 11482}, {3, 55626, 576}, {3, 55632, 55580}, {3, 55639, 55614}, {3, 55643, 55641}, {3, 55644, 14810}, {3, 55646, 55644}, {6, 55615, 55592}, {6, 55633, 55615}, {182, 3098, 55593}, {182, 53858, 575}, {182, 55614, 55588}, {182, 55627, 55601}, {182, 55639, 55627}, {511, 14810, 55636}, {511, 55625, 55609}, {511, 55631, 55617}, {511, 55636, 55625}, {575, 55606, 53097}, {576, 55637, 55626}, {1350, 50664, 511}, {1350, 55634, 55621}, {1350, 55640, 55634}, {1351, 3098, 55599}, {1351, 31884, 3098}, {1351, 55593, 55582}, {3098, 14810, 55638}, {3098, 15520, 1350}, {3098, 17508, 55581}, {3098, 5085, 55590}, {5050, 55608, 55586}, {5092, 14810, 31884}, {5092, 55599, 1351}, {5097, 14810, 55635}, {10541, 55583, 5097}, {10541, 55610, 55583}, {11477, 55611, 55594}, {11477, 55629, 55611}, {12017, 55622, 55596}, {14810, 55606, 55637}, {14810, 55627, 55639}, {14810, 55634, 55640}, {14810, 55646, 55645}, {17508, 55594, 15516}, {17508, 55611, 11477}, {20190, 22330, 53093}, {20190, 55631, 55606}, {22330, 55612, 52987}, {22330, 55631, 55612}, {31884, 52987, 55623}, {31884, 53093, 55620}, {33878, 55630, 55619}, {52987, 55599, 55597}, {53094, 55632, 55603}, {55612, 55645, 55642}, {55621, 55631, 55628}, {55638, 55645, 55643}

X(55648) = X(3)X(6)∩X(69)X(46853)

Barycentrics    a^2*(11*a^4-15*b^4-22*b^2*c^2-15*c^4+4*a^2*(b^2+c^2)) : :
X(55648) = -13*X[3]+2*X[6], X[69]+10*X[46853], 9*X[376]+2*X[39884], -5*X[381]+16*X[50984], -X[382]+12*X[21167], 4*X[547]+7*X[50969], -12*X[548]+X[14927], -16*X[549]+5*X[50963], 6*X[550]+5*X[40330], 3*X[599]+8*X[33751], 2*X[1352]+9*X[15688], -X[1353]+12*X[15759] and many others

X(55648) lies on these lines: {3, 6}, {69, 46853}, {376, 39884}, {381, 50984}, {382, 21167}, {547, 50969}, {548, 14927}, {549, 50963}, {550, 40330}, {599, 33751}, {1352, 15688}, {1353, 15759}, {1656, 51163}, {2930, 38633}, {3522, 18440}, {3524, 48874}, {3526, 48881}, {3528, 5921}, {3564, 21735}, {3619, 12103}, {3763, 17800}, {3830, 48885}, {3851, 48880}, {5054, 48873}, {5055, 48872}, {5070, 29317}, {5076, 34573}, {5079, 43621}, {5480, 15693}, {5544, 7485}, {6636, 8780}, {6776, 34200}, {8703, 11180}, {9970, 15042}, {10299, 21850}, {10304, 48876}, {10519, 33923}, {11898, 54169}, {12083, 14926}, {12100, 51212}, {14093, 44882}, {14530, 35228}, {14848, 15698}, {14853, 44682}, {14869, 51538}, {15036, 45016}, {15577, 35450}, {15681, 24206}, {15683, 50980}, {15684, 48920}, {15685, 48889}, {15686, 51537}, {15689, 36990}, {15692, 18583}, {15694, 48901}, {15695, 48898}, {15700, 50965}, {15711, 51732}, {15714, 50967}, {15718, 19924}, {15720, 29181}, {15722, 38072}, {16187, 20850}, {18358, 50693}, {19709, 48904}, {21358, 48896}, {21734, 48906}, {41716, 54044}, {46219, 48910}, {48662, 50977}

X(55648) = midpoint of X(i) and X(j) for these {i,j}: {3, 55632}
X(55648) = reflection of X(i) in X(j) for these {i,j}: {55620, 55632}, {55622, 55635}, {55632, 55641}, {55635, 14810}, {55641, 55642}
X(55648) = center of Tucker-Hagos(-4/11) circle
X(55648) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3098, 5050}, {3, 44456, 17508}, {3, 55584, 53094}, {3, 55593, 5092}, {3, 55604, 5085}, {3, 55610, 12017}, {3, 55624, 6}, {3, 55626, 11482}, {3, 55632, 511}, {3, 55637, 55602}, {3, 55641, 55620}, {3, 55646, 55643}, {6, 1350, 55581}, {182, 1351, 53092}, {182, 14810, 31884}, {182, 3098, 55592}, {182, 55592, 11477}, {182, 55608, 55583}, {182, 55613, 55587}, {182, 55616, 33878}, {182, 55625, 1350}, {182, 55644, 14810}, {511, 14810, 55635}, {511, 55635, 55622}, {575, 55630, 55607}, {576, 55634, 55618}, {1350, 31884, 55625}, {1350, 53094, 5097}, {1350, 55625, 55616}, {1351, 55629, 55610}, {1351, 55639, 55629}, {3098, 20190, 55591}, {3098, 5050, 55595}, {5085, 31884, 55613}, {5085, 55631, 55604}, {5092, 55626, 55593}, {5092, 55640, 55626}, {11477, 31884, 3098}, {11477, 53094, 182}, {11477, 55592, 55584}, {11482, 55629, 55608}, {12017, 55610, 55580}, {14810, 55590, 55636}, {14810, 55612, 55637}, {14810, 55629, 55639}, {14810, 55635, 55641}, {15516, 55605, 53097}, {15516, 55627, 55605}, {17508, 55614, 44456}, {17508, 55636, 55614}, {31884, 55596, 55624}, {31884, 55628, 55632}, {31884, 55646, 55644}, {33878, 55602, 55596}

X(55649) = X(2)X(29317)∩X(3)X(6)

Barycentrics    3*a^6+a^4*(b^2+c^2)-2*a^2*(2*b^4+3*b^2*c^2+2*c^4) : :
X(55649) = -7*X[3]+X[6], 2*X[4]+X[48879], 2*X[5]+X[48880], X[20]+2*X[24206], X[69]+11*X[21735], 2*X[140]+X[48881], X[141]+2*X[548], 2*X[376]+X[11178], X[382]+2*X[48920], -4*X[546]+7*X[42786], 2*X[550]+X[3818], -X[597]+4*X[14891] and many others

X(55649) lies on these lines: {2, 29317}, {3, 6}, {4, 48879}, {5, 48880}, {20, 24206}, {22, 5650}, {23, 16187}, {25, 15082}, {30, 21167}, {69, 21735}, {140, 48881}, {141, 548}, {184, 33884}, {373, 7485}, {376, 11178}, {382, 48920}, {524, 45759}, {542, 10304}, {546, 42786}, {549, 29181}, {550, 3818}, {597, 14891}, {599, 14093}, {631, 19130}, {1352, 3522}, {1495, 21766}, {1503, 8703}, {1511, 52098}, {1656, 48872}, {1657, 3763}, {1843, 35477}, {1974, 21844}, {2781, 23042}, {2916, 33541}, {3090, 43621}, {3357, 15577}, {3523, 31670}, {3524, 14561}, {3526, 48910}, {3528, 33751}, {3530, 5480}, {3534, 10516}, {3564, 34200}, {3589, 15712}, {3619, 17538}, {3627, 34573}, {3628, 51163}, {3819, 35259}, {3830, 50968}, {3843, 48943}, {3845, 50984}, {3850, 51128}, {3917, 6800}, {5054, 53023}, {5476, 12100}, {5640, 15246}, {5651, 7492}, {5888, 14002}, {5965, 19708}, {6636, 7998}, {6697, 34786}, {6699, 32273}, {6759, 15067}, {6776, 21734}, {7387, 33540}, {7496, 34417}, {7667, 45303}, {7689, 52016}, {7869, 40278}, {8567, 39879}, {8705, 34152}, {8717, 33533}, {9970, 15036}, {10168, 14853}, {10282, 34778}, {10299, 25555}, {10323, 15030}, {11002, 12834}, {11179, 33750}, {11202, 34146}, {11250, 32600}, {11414, 46847}, {11645, 15688}, {11649, 37948}, {12041, 12584}, {12045, 16419}, {12108, 51126}, {12220, 35497}, {12294, 32534}, {13452, 41435}, {14134, 35687}, {14907, 51371}, {14912, 15710}, {15042, 48679}, {15107, 22112}, {15681, 25561}, {15686, 20582}, {15689, 21358}, {15690, 47354}, {15695, 47353}, {15696, 36990}, {15698, 20423}, {15700, 54131}, {15701, 51024}, {15702, 25565}, {15705, 38064}, {15706, 47352}, {15707, 38072}, {15711, 41153}, {15713, 50959}, {15715, 54170}, {15722, 50963}, {15759, 34380}, {17504, 38110}, {17782, 37619}, {17800, 48942}, {18358, 44245}, {18553, 48905}, {18906, 43459}, {19124, 35473}, {19137, 37814}, {19710, 50972}, {20301, 38728}, {21850, 44682}, {22165, 46332}, {28146, 48811}, {32223, 46336}, {32271, 48378}, {32305, 33851}, {32620, 35243}, {33923, 34507}, {34817, 44763}, {35479, 44091}, {38703, 38704}, {38726, 49116}, {38942, 43652}, {40330, 50693}, {41983, 48310}, {43273, 50989}, {46853, 48876}, {50976, 50993}, {50981, 51143}, {50990, 51177}, {51135, 51184}

X(55649) = midpoint of X(i) and X(j) for these {i,j}: {182, 55603}, {1350, 5050}, {15520, 52987}, {15689, 21358}, {25406, 54173}, {3, 31884}, {3098, 17508}, {3534, 10516}, {32620, 35243}, {39242, 54374}, {39561, 55596}, {48873, 51538}, {576, 55589}, {5085, 55610}, {5092, 55615}, {5093, 55591}, {5102, 33878}, {6, 55593}
X(55649) = reflection of X(i) in X(j) for these {i,j}: {182, 17508}, {1350, 55615}, {14810, 55645}, {14853, 10168}, {15520, 182}, {17508, 3}, {3098, 31884}, {31884, 14810}, {37517, 15520}, {38317, 549}, {39561, 5085}, {48310, 41983}, {5050, 5092}, {576, 5050}, {5102, 575}, {51538, 19130}, {52987, 55603}, {55585, 55589}, {55587, 55593}, {55589, 1350}, {55591, 55599}, {55593, 55606}, {55596, 55610}, {55603, 3098}, {55606, 55621}, {55610, 55627}, {55613, 55630}, {55615, 55631}, {55621, 55636}, {55627, 55638}, {55630, 55640}, {55640, 55643}, {55645, 55647}
X(55649) = center of Tucker-Hagos(-1/3) circle
X(55649) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1297), X(17508)}}, {{A, B, C, X(5007), X(13452)}}, {{A, B, C, X(30435), X(44763)}}, {{A, B, C, X(40803), X(55612)}}
X(55649) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 5092}, {3, 3098, 182}, {3, 33878, 53094}, {3, 35248, 30270}, {3, 46728, 13347}, {3, 511, 17508}, {3, 55614, 20190}, {3, 55616, 12017}, {3, 55620, 10541}, {3, 55626, 575}, {3, 55629, 6}, {3, 55636, 55587}, {3, 55638, 55596}, {3, 55639, 1350}, {3, 55641, 55606}, {3, 55643, 31884}, {3, 55646, 14810}, {4, 48885, 48879}, {5, 48880, 48904}, {6, 1350, 55580}, {6, 3098, 55598}, {6, 31884, 55618}, {20, 24206, 48884}, {140, 48881, 48901}, {141, 548, 48898}, {182, 14810, 55633}, {182, 37517, 22234}, {182, 55608, 55581}, {511, 575, 5102}, {511, 55606, 55593}, {511, 55647, 55645}, {549, 29181, 38317}, {550, 3818, 48896}, {574, 2076, 5039}, {575, 14810, 55634}, {631, 48873, 19130}, {1350, 10541, 44456}, {1350, 14810, 55635}, {1350, 3098, 55611}, {1350, 31884, 55624}, {1350, 5050, 511}, {1350, 55585, 52987}, {1350, 55620, 55609}, {1350, 55624, 55615}, {1350, 55631, 3098}, {1350, 55639, 55631}, {1351, 55594, 55583}, {1351, 55614, 55594}, {1351, 55625, 55605}, {1351, 55632, 55614}, {1352, 3522, 48892}, {1656, 48872, 48895}, {1657, 3763, 48889}, {3094, 5206, 41412}, {3098, 55596, 55610}, {3098, 55600, 55612}, {3528, 46264, 33751}, {3534, 10516, 29323}, {5050, 55615, 55589}, {5085, 55591, 5093}, {5093, 55610, 55591}, {5097, 55623, 55601}, {5476, 12100, 51137}, {6636, 7998, 35268}, {7492, 41462, 5651}, {7998, 35268, 9306}, {9735, 9736, 5171}, {10541, 44456, 15516}, {10541, 55588, 576}, {10541, 55620, 55588}, {11477, 55604, 55590}, {11477, 55622, 55604}, {12017, 53097, 5097}, {12017, 55616, 53097}, {12100, 50965, 5476}, {12974, 12975, 13335}, {14810, 17508, 55630}, {14810, 20190, 55632}, {14810, 31884, 55640}, {14810, 55606, 55636}, {14810, 55627, 55638}, {14810, 55631, 55639}, {14810, 55636, 55641}, {14810, 55644, 55642}, {14810, 55645, 55643}, {14810, 55646, 55644}, {14810, 55647, 55646}, {15520, 55630, 55608}, {15520, 55633, 55613}, {15520, 55640, 55628}, {15696, 36990, 48891}, {15712, 48874, 3589}, {17508, 31884, 55603}, {17508, 39561, 5085}, {17508, 55589, 5050}, {17508, 55596, 39561}, {17508, 55603, 15520}, {17508, 55613, 37517}, {17508, 55624, 55585}, {17508, 55643, 55637}, {20190, 55594, 1351}, {25406, 54173, 5965}, {31884, 55593, 55621}, {31884, 55610, 55627}, {31884, 55618, 55629}, {33751, 40107, 46264}, {33878, 55612, 55600}, {43126, 43127, 3}, {50664, 55590, 11477}, {53091, 55602, 55582}, {53093, 55607, 55584}, {53094, 55626, 33878}, {55582, 55602, 55592}, {55584, 55607, 55597}, {55588, 55631, 55620}, {55591, 55610, 55599}, {55597, 55619, 55607}, {55601, 55623, 55616}, {55604, 55622, 55617}, {55612, 55634, 55626}, {55614, 55632, 55625}, {55646, 55648, 55647}

X(55650) = X(3)X(6)∩X(20)X(25561)

Barycentrics    a^2*(10*a^4-13*b^4-20*b^2*c^2-13*c^4+3*a^2*(b^2+c^2)) : :
X(55650) = -23*X[3]+3*X[6], 2*X[20]+3*X[25561], 2*X[546]+3*X[48885], 4*X[548]+X[18553], 7*X[3090]+3*X[48880], 7*X[3528]+3*X[50977], 2*X[3529]+3*X[48942], 2*X[3627]+3*X[48920], -8*X[3628]+3*X[48895], 3*X[3818]+7*X[50693], X[3843]+3*X[50968], -X[3853]+6*X[50984] and many others

X(55650) lies on these lines: {3, 6}, {20, 25561}, {542, 46853}, {546, 48885}, {548, 18553}, {632, 29317}, {3090, 48880}, {3522, 11645}, {3528, 50977}, {3529, 48942}, {3627, 48920}, {3628, 48895}, {3818, 50693}, {3843, 50968}, {3853, 50984}, {5070, 51141}, {5079, 48904}, {5476, 10299}, {9716, 22352}, {10303, 48901}, {10304, 34507}, {12103, 24206}, {12108, 19130}, {14869, 48881}, {15698, 46267}, {15704, 21167}, {15712, 19924}, {17538, 29323}, {25555, 44682}, {33751, 43150}, {33923, 40107}, {41991, 51128}, {42786, 50689}, {43621, 46936}, {44245, 48891}

X(55650) = midpoint of X(i) and X(j) for these {i,j}: {182, 55604}, {11482, 52987}, {12017, 55608}, {22234, 55595}, {3, 55637}, {3098, 53094}, {5092, 55619}, {53091, 55598}, {53093, 55600}
X(55650) = reflection of X(i) in X(j) for these {i,j}: {14810, 55646}, {22234, 20190}, {55588, 55595}, {55594, 55608}, {55598, 55612}, {55606, 55623}, {55614, 55631}, {55619, 55634}, {55623, 55637}, {55634, 14810}
X(55650) = center of Tucker-Hagos(-3/10) circle
X(55650) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14810, 55606}, {3, 31884, 576}, {3, 53097, 17508}, {3, 55595, 53094}, {3, 55606, 5092}, {3, 55620, 5085}, {3, 55626, 182}, {3, 55629, 53093}, {3, 55632, 53092}, {3, 55643, 55626}, {3, 55644, 55631}, {3, 55647, 14810}, {3, 55649, 55647}, {6, 55625, 55599}, {6, 55640, 55625}, {182, 3098, 55591}, {182, 55615, 55586}, {182, 55626, 55597}, {182, 55636, 55615}, {511, 14810, 55634}, {511, 20190, 22234}, {511, 55608, 55594}, {511, 55612, 55598}, {511, 55631, 55614}, {511, 55634, 55619}, {511, 55637, 55623}, {1350, 55642, 55638}, {1351, 55630, 55609}, {3098, 20190, 55588}, {3098, 5050, 55592}, {3098, 55648, 55645}, {3098, 55649, 55648}, {5085, 55620, 55583}, {5085, 55633, 55601}, {5092, 14810, 55627}, {5092, 55627, 55590}, {11477, 20190, 575}, {11477, 55591, 55580}, {11477, 55614, 55595}, {11477, 55648, 55644}, {11482, 52987, 511}, {11482, 55614, 52987}, {12017, 31884, 55608}, {12017, 55637, 55617}, {14810, 55594, 31884}, {14810, 55615, 55636}, {14810, 55623, 55637}, {17508, 55598, 53091}, {17508, 55628, 53097}, {17508, 55639, 55612}, {20190, 55588, 5097}, {20190, 55617, 55584}, {22234, 53094, 20190}, {22234, 55637, 3098}, {22330, 55647, 55642}, {33878, 55635, 55621}, {44682, 50965, 25555}, {52987, 55644, 55641}, {53093, 55629, 55600}, {53094, 55614, 11477}, {53097, 55639, 55628}, {55583, 55633, 55620}, {55597, 55647, 55643}, {55600, 55637, 55629}

X(55651) = X(3)X(6)∩X(20)X(3763)

Barycentrics    a^2*(7*a^4-9*b^4-14*b^2*c^2-9*c^4+2*a^2*(b^2+c^2)) : :
X(55651) = 6*X[2]+X[48872], -8*X[3]+X[6], 2*X[20]+5*X[3763], X[69]+13*X[21734], -8*X[140]+X[48910], 2*X[141]+5*X[3522], 2*X[159]+5*X[8567], 6*X[165]+X[3242], 4*X[376]+3*X[21358], 3*X[381]+4*X[48885], 6*X[548]+X[39884], 6*X[549]+X[48873] and many others

X(55651) lies on these lines: {2, 48872}, {3, 6}, {20, 3763}, {22, 44299}, {25, 5646}, {69, 21734}, {140, 48910}, {141, 3522}, {159, 8567}, {165, 3242}, {376, 21358}, {381, 48885}, {518, 16192}, {542, 51189}, {548, 39884}, {549, 48873}, {550, 10516}, {597, 15705}, {599, 5921}, {631, 48881}, {1352, 8703}, {1353, 15714}, {1498, 35228}, {1503, 3528}, {1656, 48880}, {2781, 15036}, {2916, 15062}, {2930, 15055}, {3066, 7485}, {3070, 36702}, {3071, 36717}, {3146, 34573}, {3516, 7716}, {3523, 29181}, {3524, 5480}, {3526, 29317}, {3530, 31670}, {3532, 34817}, {3534, 24206}, {3543, 50984}, {3589, 15717}, {3619, 50693}, {3628, 43621}, {3818, 15696}, {3830, 48920}, {3832, 51128}, {3843, 48879}, {4220, 37682}, {5032, 50970}, {5054, 25565}, {5055, 48904}, {5070, 48895}, {5204, 10387}, {5476, 15706}, {5621, 33851}, {5650, 41424}, {6636, 17811}, {6776, 15533}, {7987, 38315}, {8550, 33750}, {9909, 16187}, {10007, 22676}, {10168, 15716}, {10323, 15811}, {10519, 21735}, {10606, 15577}, {11003, 37672}, {11178, 15695}, {11179, 15759}, {11204, 39879}, {11440, 41435}, {11645, 50976}, {12007, 50967}, {12100, 38079}, {14093, 33751}, {14561, 15712}, {14891, 20423}, {15051, 52697}, {15069, 46853}, {15162, 38709}, {15163, 38708}, {15246, 17825}, {15681, 48889}, {15683, 50972}, {15685, 48942}, {15688, 47353}, {15689, 48896}, {15691, 50980}, {15692, 47352}, {15693, 38072}, {15700, 19924}, {15702, 50969}, {15703, 51141}, {15710, 51737}, {15711, 38064}, {15715, 50983}, {15720, 19130}, {15721, 50959}, {17504, 18583}, {17810, 22112}, {17821, 34778}, {20582, 51537}, {20987, 37198}, {21356, 50971}, {23040, 39588}, {23251, 36703}, {23261, 36701}, {24273, 54993}, {25406, 40341}, {32217, 37941}, {32620, 33534}, {33923, 46264}, {34200, 43273}, {35259, 41462}, {37751, 38698}, {38638, 52098}, {43174, 49690}, {44903, 50956}, {45759, 54173}, {51126, 51538}, {51185, 54170}

X(55651) = midpoint of X(i) and X(j) for these {i,j}: {182, 55605}, {10541, 55607}, {15702, 50969}, {3, 55639}, {3619, 50693}
X(55651) = reflection of X(i) in X(j) for these {i,j}: {1350, 55616}, {15703, 51141}, {3832, 51128}, {47355, 3523}, {6, 10541}, {55602, 3098}, {55607, 55626}, {55616, 55633}, {55626, 55639}, {55633, 14810}, {55639, 55644}
X(55651) = center of Tucker-Hagos(-2/7) circle
X(55651) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(64), X(43136)}}, {{A, B, C, X(3431), X(22246)}}, {{A, B, C, X(3532), X(30435)}}, {{A, B, C, X(5007), X(43691)}}, {{A, B, C, X(21309), X(43713)}}, {{A, B, C, X(33636), X(41435)}}, {{A, B, C, X(34817), X(38292)}}, {{A, B, C, X(40803), X(55610)}}
X(55651) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 53094}, {3, 3098, 5085}, {3, 33878, 17508}, {3, 55610, 5092}, {3, 55624, 12017}, {3, 55626, 10541}, {3, 55629, 182}, {3, 55632, 5050}, {3, 55637, 11477}, {3, 55640, 55582}, {3, 55642, 55618}, {3, 55647, 55641}, {6, 55614, 55591}, {182, 14810, 55629}, {182, 3098, 55590}, {182, 55612, 55584}, {182, 55633, 55605}, {182, 55635, 55612}, {511, 14810, 55633}, {511, 3098, 55602}, {575, 3098, 55593}, {576, 55627, 55604}, {631, 48881, 53023}, {1151, 1152, 30435}, {1350, 11477, 55587}, {1350, 14810, 31884}, {1350, 31884, 55622}, {1350, 5085, 1351}, {1350, 53094, 6}, {1350, 55618, 55608}, {1350, 55622, 55614}, {1350, 55626, 55616}, {1350, 55646, 14810}, {1351, 3098, 1350}, {1351, 53091, 15520}, {1351, 55593, 55581}, {1351, 55648, 55643}, {3098, 15520, 55597}, {3098, 55597, 55610}, {3098, 55649, 55647}, {3523, 29181, 47355}, {5050, 55632, 55606}, {5092, 14810, 55625}, {5092, 55587, 53091}, {5093, 55620, 55594}, {6409, 6410, 3053}, {6411, 6412, 15655}, {10541, 31884, 55607}, {10541, 53097, 53858}, {10541, 55607, 511}, {11477, 55597, 53097}, {11480, 11481, 1384}, {12017, 52987, 5102}, {12017, 55624, 52987}, {14810, 55612, 55635}, {14810, 55619, 55636}, {14810, 55625, 55637}, {14810, 55633, 55639}, {14810, 55648, 55646}, {14810, 55649, 55648}, {15516, 55636, 55619}, {15520, 55637, 3098}, {15692, 50965, 47352}, {17508, 33878, 53093}, {17508, 55608, 5097}, {17508, 55631, 33878}, {17508, 55642, 55631}, {20190, 55603, 44456}, {20190, 55634, 55603}, {37517, 55615, 55595}, {39561, 55601, 55580}, {39561, 55628, 55601}, {50664, 55623, 55596}, {52987, 55636, 55624}, {55593, 55643, 55638}, {55594, 55630, 55620}, {55599, 55647, 55642}, {55606, 55640, 55632}, {55616, 55648, 55644}

X(55652) = X(3)X(6)∩X(548)X(11178)

Barycentrics    11*a^6+3*a^4*(b^2+c^2)-2*a^2*(7*b^4+11*b^2*c^2+7*c^4) : :
X(55652) = -25*X[3]+3*X[6], 8*X[546]+3*X[48879], 8*X[548]+3*X[11178], 5*X[550]+6*X[20582], -10*X[1656]+21*X[51141], -14*X[3090]+3*X[48904], 5*X[3091]+6*X[48885], 35*X[3528]+9*X[21356], -20*X[3530]+9*X[48310], 8*X[3628]+3*X[48880], 3*X[3818]+8*X[44245], 7*X[3851]+15*X[50968] and many others

X(55652) lies on circumconic {{A, B, C, X(5008), X(11270)}} and on these lines: {3, 6}, {542, 21735}, {546, 48879}, {548, 11178}, {550, 20582}, {1656, 51141}, {3090, 48904}, {3091, 48885}, {3525, 29317}, {3528, 21356}, {3530, 48310}, {3628, 48880}, {3818, 44245}, {3851, 50968}, {5076, 48920}, {5476, 44682}, {7492, 44082}, {8550, 15759}, {10299, 51137}, {10304, 13399}, {11204, 15581}, {12103, 21167}, {12108, 48881}, {14869, 48901}, {15020, 52098}, {15688, 18553}, {15692, 25555}, {15712, 51139}, {15717, 19924}, {17538, 24206}, {22165, 34200}, {25565, 50969}, {33923, 50977}, {34507, 46853}, {40916, 44106}, {41981, 47354}, {48896, 50693}

X(55652) = midpoint of X(i) and X(j) for these {i,j}: {3, 55641}
X(55652) = reflection of X(i) in X(j) for these {i,j}: {3098, 55635}, {55628, 55641}, {55632, 14810}, {55635, 55642}, {55642, 55648}
X(55652) = center of Tucker-Hagos(-3/11) circle
X(55652) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 31884, 575}, {3, 52987, 17508}, {3, 55602, 53094}, {3, 55614, 5092}, {3, 55626, 20190}, {3, 55629, 10541}, {3, 55631, 182}, {3, 55639, 11477}, {3, 55641, 511}, {3, 55643, 55614}, {3, 55646, 55631}, {3, 55648, 55641}, {3, 55649, 55644}, {3, 55650, 55649}, {3, 55651, 55650}, {6, 14810, 55630}, {182, 3098, 55589}, {182, 53097, 576}, {182, 55619, 55587}, {182, 55631, 55600}, {182, 55646, 55640}, {182, 55649, 55646}, {511, 14810, 55632}, {511, 55641, 55628}, {511, 55642, 55635}, {511, 55648, 55642}, {576, 55635, 55620}, {1351, 55634, 55613}, {5050, 55625, 55598}, {5085, 55636, 55608}, {5092, 14810, 55621}, {5092, 55621, 55584}, {5092, 55633, 55596}, {5237, 5238, 32}, {6449, 6450, 21309}, {6453, 6454, 5007}, {10541, 55597, 37517}, {10541, 55629, 55597}, {11477, 55623, 55603}, {11477, 55639, 55623}, {12017, 55615, 55581}, {14810, 17508, 3098}, {14810, 20190, 55626}, {14810, 55584, 55633}, {14810, 55601, 31884}, {14810, 55626, 55637}, {17508, 55605, 6}, {17508, 55640, 55610}, {20190, 55626, 52987}, {20190, 55647, 14810}, {22330, 55602, 55585}, {22330, 55627, 55602}, {31884, 44456, 55619}, {44456, 55595, 53097}, {44456, 55631, 55611}, {52987, 55617, 55605}, {52987, 55630, 55617}, {53094, 55602, 22330}, {55610, 55632, 55622}, {55637, 55649, 55647}, {55642, 55649, 55648}

X(55653) = X(2)X(43621)∩X(3)X(6)

Barycentrics    a^2*(4*a^4-5*b^4-8*b^2*c^2-5*c^4+a^2*(b^2+c^2)) : :
X(55653) = -9*X[2]+X[43621], -9*X[3]+X[6], -3*X[4]+7*X[42786], X[5]+X[48885], X[20]+X[48889], X[69]+15*X[19708], X[141]+3*X[8703], X[159]+3*X[11204], 9*X[376]+7*X[3619], 3*X[381]+X[48879], 3*X[548]+X[18358], -3*X[549]+X[19130] and many others

X(55653) lies on these lines: {2, 43621}, {3, 6}, {4, 42786}, {5, 48885}, {20, 48889}, {23, 5888}, {30, 34573}, {69, 19708}, {74, 7953}, {140, 29317}, {141, 8703}, {159, 11204}, {186, 44091}, {323, 22352}, {373, 48912}, {376, 3619}, {381, 48879}, {524, 15759}, {542, 3631}, {548, 18358}, {549, 19130}, {550, 21167}, {597, 15711}, {631, 48901}, {632, 51163}, {1352, 3528}, {1495, 3819}, {1503, 33751}, {1656, 48904}, {1657, 48942}, {1843, 35473}, {1974, 35472}, {2071, 32600}, {2916, 52099}, {2979, 44109}, {3431, 54041}, {3522, 18553}, {3523, 38317}, {3524, 31670}, {3526, 48872}, {3530, 29181}, {3534, 3763}, {3579, 49465}, {3589, 12100}, {3618, 15698}, {3620, 10304}, {3630, 45759}, {3845, 51128}, {3917, 9544}, {5054, 48910}, {5055, 50968}, {5476, 15692}, {5480, 15712}, {5650, 7492}, {5907, 8718}, {5943, 15107}, {6000, 33533}, {6403, 23040}, {6688, 7485}, {6723, 10300}, {7484, 10219}, {7496, 10545}, {7525, 43586}, {7712, 7998}, {7782, 14994}, {7849, 42787}, {7897, 9774}, {8177, 46893}, {9822, 18570}, {10168, 17504}, {10193, 23300}, {10323, 44870}, {10516, 15696}, {10519, 21734}, {10691, 47296}, {11008, 11179}, {11178, 15688}, {11202, 34778}, {11464, 43896}, {11812, 25565}, {12045, 40916}, {12220, 35493}, {12294, 21844}, {12584, 15055}, {12900, 25337}, {13474, 33539}, {14093, 18440}, {14561, 15717}, {14891, 46267}, {14892, 51026}, {15018, 21849}, {15040, 52098}, {15051, 19140}, {15690, 20582}, {15693, 47355}, {15695, 21358}, {15705, 20423}, {15706, 51137}, {15707, 51024}, {15708, 50969}, {15714, 51737}, {15715, 38064}, {15716, 47352}, {15718, 38072}, {15720, 53023}, {16419, 31860}, {16496, 35242}, {19711, 48310}, {20080, 54173}, {20301, 38727}, {21735, 34507}, {21766, 35268}, {32142, 50414}, {32223, 43957}, {32273, 38728}, {36489, 48940}, {36699, 48938}, {36705, 48902}, {40107, 44882}, {41982, 50971}, {42112, 44465}, {42113, 44461}, {43584, 45308}, {43934, 44673}, {44682, 48874}, {45757, 51131}, {46333, 50956}, {50981, 51134}

X(55653) = midpoint of X(i) and X(j) for these {i,j}: {141, 48892}, {182, 55606}, {10168, 50965}, {1351, 55588}, {1657, 48942}, {15516, 55597}, {15690, 20582}, {17508, 55627}, {18553, 48898}, {19130, 48881}, {20, 48889}, {20190, 55612}, {22330, 55592}, {3, 14810}, {3098, 5092}, {3534, 25561}, {3818, 48891}, {37517, 55586}, {4, 48920}, {40107, 44882}, {43150, 46264}, {48879, 48943}, {48880, 48895}, {5, 48885}, {5050, 55599}, {550, 24206}, {575, 1350}, {576, 55590}, {5085, 55615}, {5097, 52987}, {50664, 55601}, {53094, 55623}, {6, 55594}
X(55653) = reflection of X(i) in X(j) for these {i,j}: {1350, 55617}, {14810, 55647}, {15516, 20190}, {22330, 182}, {25565, 11812}, {3098, 55636}, {33751, 33923}, {50664, 5092}, {55592, 55606}, {55594, 55609}, {55597, 55612}, {55601, 3098}, {55606, 55625}, {55612, 55631}, {55621, 55638}, {55631, 14810}, {55638, 55645}, {55645, 55649}
X(55653) = complement of X(48895)
X(55653) = isogonal conjugate of X(54477)
X(55653) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 54477}
X(55653) = center of Tucker-Hagos(-1/4) circle
X(55653) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(32), X(20421)}}, {{A, B, C, X(54), X(41940)}}, {{A, B, C, X(74), X(5007)}}, {{A, B, C, X(1176), X(15860)}}, {{A, B, C, X(2420), X(7953)}}, {{A, B, C, X(3284), X(41435)}}, {{A, B, C, X(3431), X(7772)}}, {{A, B, C, X(12055), X(14388)}}, {{A, B, C, X(14487), X(34571)}}
X(55653) = barycentric quotient X(i)/X(j) for these (i, j): {6, 54477}
X(55653) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 48880, 48895}, {3, 1350, 17508}, {3, 35248, 39}, {3, 43128, 13355}, {3, 55610, 53094}, {3, 55629, 5085}, {3, 55631, 20190}, {3, 55636, 50664}, {3, 55638, 15516}, {3, 55639, 6}, {3, 55640, 5097}, {3, 55641, 576}, {3, 55642, 55594}, {3, 55647, 55631}, {3, 55652, 55650}, {6, 55604, 55585}, {15, 16, 5007}, {141, 48892, 11645}, {141, 8703, 48892}, {182, 14810, 55625}, {182, 3098, 33878}, {182, 511, 22330}, {182, 55596, 11477}, {182, 55625, 55592}, {182, 55637, 55613}, {182, 55648, 14810}, {182, 55649, 55644}, {187, 574, 13357}, {376, 3818, 48891}, {381, 48879, 48943}, {549, 48881, 19130}, {550, 21167, 24206}, {550, 24206, 29323}, {576, 3098, 55598}, {576, 55641, 55623}, {1350, 12017, 37517}, {1350, 37517, 55586}, {1350, 5093, 55583}, {1350, 55627, 55617}, {1350, 55632, 3098}, {1350, 55637, 55627}, {1351, 55588, 511}, {1351, 55603, 55588}, {1351, 55626, 55603}, {1351, 55635, 55619}, {1503, 33923, 33751}, {3098, 14810, 55636}, {3098, 52987, 55607}, {3098, 55585, 55604}, {3098, 55594, 55609}, {3098, 55598, 55610}, {3098, 55607, 55615}, {3098, 55649, 55646}, {3523, 48873, 38317}, {3534, 3763, 48884}, {3763, 48884, 25561}, {5050, 55614, 55587}, {5050, 55630, 55599}, {5092, 55623, 55582}, {5097, 14810, 55629}, {5102, 55595, 55581}, {5650, 7492, 32237}, {6200, 45512, 6221}, {6200, 6396, 32}, {6221, 6398, 43136}, {6396, 45513, 6398}, {6411, 6412, 5023}, {6636, 41462, 1495}, {8160, 8161, 9821}, {10516, 15696, 48896}, {10541, 55584, 15520}, {10541, 55618, 55584}, {10645, 10646, 187}, {11477, 31884, 55616}, {11477, 55616, 55596}, {11477, 55628, 55606}, {11480, 11481, 22331}, {12017, 17508, 5092}, {12017, 33878, 5093}, {12017, 37517, 575}, {12017, 55632, 1350}, {12017, 55643, 55632}, {12017, 55646, 55637}, {14810, 20190, 55621}, {14810, 55590, 55633}, {14810, 55594, 55634}, {14810, 55606, 31884}, {14810, 55619, 55635}, {14810, 55631, 55638}, {14810, 55634, 55639}, {14810, 55647, 55645}, {14810, 55649, 55647}, {14810, 55650, 55649}, {15516, 55621, 55597}, {17508, 37517, 12017}, {17508, 55583, 182}, {17508, 55649, 55643}, {18860, 35422, 50652}, {20190, 55638, 55612}, {31884, 55616, 55628}, {33878, 53092, 44456}, {39561, 55608, 53097}, {42115, 42116, 21309}, {43141, 43144, 5171}, {44456, 55607, 52987}, {44456, 55646, 55640}, {46264, 50977, 43150}, {50664, 55631, 55601}, {53091, 55620, 55591}, {53093, 55622, 55593}, {53094, 55633, 55590}, {53097, 55624, 55608}, {55582, 55646, 55641}, {55584, 55618, 55600}, {55587, 55630, 55614}, {55591, 55620, 55605}, {55593, 55622, 55611}, {55639, 55646, 55642}, {55644, 55649, 55648}, {55649, 55652, 55651}

X(55654) = X(2)X(50968)∩X(3)X(6)

Barycentrics    a^2*(9*a^4-11*b^4-18*b^2*c^2-11*c^4+2*a^2*(b^2+c^2)) : :
X(55654) = 4*X[2]+5*X[50968], -10*X[3]+X[6], -5*X[4]+14*X[51128], X[64]+8*X[35228], 8*X[140]+X[48872], 2*X[141]+7*X[3528], 2*X[376]+X[10516], 8*X[548]+X[36990], -4*X[549]+X[53023], 4*X[550]+5*X[3763], -2*X[597]+11*X[15715], X[599]+8*X[34200] and many others

X(55654) lies on these lines: {2, 50968}, {3, 6}, {4, 51128}, {22, 33879}, {23, 5646}, {64, 35228}, {140, 48872}, {141, 3528}, {154, 6030}, {376, 10516}, {524, 15710}, {548, 36990}, {549, 53023}, {550, 3763}, {597, 15715}, {599, 34200}, {631, 48910}, {632, 43621}, {1352, 33923}, {1503, 10304}, {1656, 48885}, {3242, 31663}, {3520, 7716}, {3522, 48905}, {3523, 48881}, {3524, 29181}, {3525, 51163}, {3526, 48880}, {3529, 34573}, {3530, 38136}, {3564, 45759}, {3589, 10299}, {3796, 33884}, {3843, 48920}, {3851, 48879}, {3860, 51164}, {5054, 29317}, {5070, 48904}, {5076, 42786}, {5476, 15716}, {5480, 15717}, {5650, 44082}, {6090, 44110}, {6636, 35259}, {7280, 10387}, {7484, 44106}, {7492, 41424}, {8567, 15577}, {8703, 47353}, {8705, 37948}, {9909, 15082}, {9924, 15578}, {10164, 38144}, {10323, 16261}, {10519, 19708}, {10545, 14924}, {11001, 50984}, {11160, 25406}, {11179, 15714}, {11270, 34817}, {11540, 50964}, {12100, 14561}, {14853, 15698}, {14891, 38110}, {15051, 51941}, {15069, 21734}, {15246, 17810}, {15534, 51180}, {15682, 50972}, {15688, 21358}, {15689, 29323}, {15692, 54131}, {15693, 38317}, {15696, 24206}, {15706, 19924}, {15711, 20423}, {15712, 31670}, {15719, 50969}, {15720, 48901}, {15759, 50985}, {17502, 38315}, {17504, 47352}, {17811, 35268}, {18440, 33751}, {19709, 51141}, {21735, 44882}, {21766, 35265}, {23253, 36703}, {23263, 36701}, {23269, 36702}, {23275, 36717}, {31860, 40916}, {41149, 50967}, {44541, 53475}, {46219, 48895}, {46264, 46853}, {50973, 51737}, {50975, 50991}, {51134, 51143}

X(55654) = midpoint of X(i) and X(j) for these {i,j}: {17508, 55630}, {3, 55643}, {5085, 55618}
X(55654) = reflection of X(i) in X(j) for these {i,j}: {1350, 55618}, {31884, 55643}, {55610, 55630}, {55618, 31884}, {55624, 55640}, {55630, 14810}, {55643, 55649}
X(55654) = center of Tucker-Hagos(-2/9) circle
X(55654) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5008), X(43713)}}, {{A, B, C, X(5041), X(14528)}}, {{A, B, C, X(11270), X(30435)}}, {{A, B, C, X(43136), X(43719)}}
X(55654) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3098, 53094}, {3, 31884, 5085}, {3, 55610, 17508}, {3, 55629, 5092}, {3, 55637, 10541}, {3, 55639, 182}, {3, 55641, 53093}, {3, 55644, 53097}, {3, 55645, 55591}, {3, 55646, 1350}, {3, 55651, 55646}, {3, 55653, 55651}, {6, 53094, 20190}, {6, 55607, 55586}, {182, 3098, 55588}, {182, 55582, 53858}, {182, 55627, 55593}, {182, 55639, 55614}, {182, 55647, 55639}, {376, 21167, 10516}, {511, 14810, 55630}, {511, 31884, 55618}, {511, 55640, 55624}, {511, 55649, 55643}, {575, 55633, 55604}, {576, 55636, 55616}, {1350, 5085, 5102}, {1350, 53858, 55582}, {1350, 55646, 55641}, {1351, 55631, 55607}, {3098, 20190, 55584}, {3098, 22234, 55592}, {3098, 5097, 55595}, {3098, 55649, 55645}, {3098, 55650, 55648}, {3530, 48873, 47355}, {5050, 5093, 22234}, {5085, 11477, 5050}, {5092, 14810, 55617}, {5092, 55638, 55603}, {5092, 55644, 55629}, {8703, 47353, 50976}, {10541, 55622, 33878}, {14810, 17508, 55610}, {14810, 20190, 3098}, {14810, 52987, 55632}, {14810, 55586, 55631}, {14810, 55610, 31884}, {14810, 55653, 55652}, {15520, 55649, 55642}, {17508, 55605, 39561}, {17508, 55610, 6}, {17508, 55617, 5093}, {17508, 55630, 511}, {17508, 55649, 14810}, {17508, 55652, 55649}, {22234, 53097, 11477}, {31884, 55610, 55626}, {31884, 55614, 55627}, {33878, 55637, 55622}, {37517, 55625, 55602}, {39561, 55637, 55615}, {50664, 55608, 55580}, {55587, 55634, 55620}, {55588, 55650, 55647}, {55592, 55645, 55638}, {55593, 55610, 55601}, {55603, 55649, 55644}, {55610, 55632, 55621}, {55624, 55643, 55640}

X(55655) = X(2)X(48885)∩X(3)X(6)

Barycentrics    5*a^6+a^4*(b^2+c^2)-2*a^2*(3*b^4+5*b^2*c^2+3*c^4) : :
X(55655) = 3*X[2]+2*X[48885], -11*X[3]+X[6], 4*X[5]+X[48879], 4*X[140]+X[48880], X[141]+4*X[33923], 3*X[376]+2*X[24206], 3*X[381]+2*X[48920], 4*X[548]+X[3818], -6*X[549]+X[48901], 4*X[550]+X[48884], X[1352]+9*X[10304], X[3357]+4*X[35228], -7*X[3523]+2*X[19130] and many others

X(55655) lies on these lines: {2, 48885}, {3, 6}, {5, 48879}, {22, 16187}, {110, 29322}, {140, 48880}, {141, 33923}, {376, 24206}, {381, 48920}, {524, 15714}, {542, 19708}, {548, 3818}, {549, 48901}, {550, 48884}, {631, 29317}, {1352, 10304}, {1503, 46853}, {1974, 17506}, {3357, 35228}, {3522, 29012}, {3523, 19130}, {3524, 48873}, {3525, 43621}, {3526, 48895}, {3528, 14927}, {3530, 38317}, {3534, 48889}, {3589, 44682}, {3627, 42786}, {3763, 15696}, {3851, 48943}, {3853, 51128}, {5054, 48872}, {5476, 17504}, {5480, 12100}, {5646, 9909}, {5651, 6636}, {5921, 21734}, {6723, 7386}, {6776, 50961}, {8703, 11178}, {9306, 21766}, {9813, 37283}, {10168, 15698}, {10299, 14561}, {10516, 48891}, {11204, 15577}, {11451, 15246}, {11645, 14093}, {12045, 31860}, {12294, 35472}, {14891, 18583}, {15035, 52098}, {15042, 52697}, {15681, 48942}, {15686, 50984}, {15687, 50972}, {15688, 36990}, {15689, 25561}, {15692, 19924}, {15694, 50968}, {15704, 34573}, {15708, 25565}, {15710, 54173}, {15712, 29181}, {15715, 20423}, {15716, 54131}, {15717, 31670}, {15718, 51024}, {15720, 48910}, {15759, 54169}, {21735, 46264}, {32217, 37968}, {32271, 48375}, {32273, 38727}, {32903, 34775}, {34200, 44882}, {35268, 41462}, {45759, 48876}

X(55655) = midpoint of X(i) and X(j) for these {i,j}: {182, 55608}, {1350, 53091}, {12017, 55614}, {15694, 50968}, {22234, 55598}, {3, 55646}, {3763, 15696}, {5092, 55623}, {53093, 55604}, {53094, 55629}, {6, 55595}
X(55655) = reflection of X(i) in X(j) for these {i,j}: {182, 53094}, {1350, 55619}, {22234, 12017}, {3098, 55637}, {37517, 11482}, {51137, 15692}, {51537, 24206}, {52987, 55604}, {53093, 5092}, {55598, 55614}, {55600, 3098}, {55604, 55623}, {55608, 55629}, {55614, 55634}, {55629, 14810}, {55637, 55646}, {55646, 55650}, {55650, 55653}
X(55655) = isogonal conjugate of X(54917)
X(55655) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 54917}
X(55655) = center of Tucker-Hagos(-1/5) circle
X(55655) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(34571)}}, {{A, B, C, X(6), X(29322)}}, {{A, B, C, X(74), X(14075)}}, {{A, B, C, X(40803), X(55606)}}
X(55655) = barycentric quotient X(i)/X(j) for these (i, j): {6, 54917}
X(55655) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 48885, 48904}, {3, 3098, 17508}, {3, 31884, 5092}, {3, 35248, 37479}, {3, 43126, 7692}, {3, 43127, 7690}, {3, 55629, 53094}, {3, 55639, 5085}, {3, 55641, 20190}, {3, 55643, 6}, {3, 55652, 55644}, {3, 55654, 55653}, {6, 55616, 55590}, {15, 16, 14075}, {182, 1351, 39561}, {182, 37517, 15516}, {182, 52987, 1351}, {182, 55587, 576}, {182, 55616, 55583}, {182, 55622, 55589}, {182, 55628, 55592}, {182, 55633, 1350}, {371, 372, 34571}, {376, 24206, 48896}, {511, 12017, 22234}, {511, 14810, 55629}, {511, 3098, 55600}, {511, 5092, 53093}, {511, 55650, 55646}, {511, 55653, 55650}, {548, 21167, 3818}, {575, 55610, 55585}, {575, 55636, 55610}, {1350, 14810, 55633}, {1350, 5097, 55581}, {1350, 53094, 53091}, {1350, 55619, 55608}, {1350, 55629, 55619}, {1350, 55633, 3098}, {1350, 55648, 14810}, {1350, 55651, 55648}, {1351, 31884, 55612}, {1351, 5092, 182}, {1351, 55612, 52987}, {1351, 55629, 55604}, {1351, 55651, 55647}, {1352, 10304, 33751}, {3098, 14810, 55635}, {3098, 55583, 55603}, {3098, 55589, 55606}, {3530, 48881, 38317}, {3763, 15696, 29323}, {5050, 55626, 55594}, {5050, 55638, 55613}, {5092, 55599, 22330}, {5093, 55607, 55588}, {5097, 14810, 55625}, {5102, 55602, 55586}, {11477, 55624, 55601}, {12017, 55614, 511}, {12017, 55634, 55598}, {12017, 55646, 55634}, {14810, 15516, 55622}, {14810, 17508, 55605}, {14810, 55584, 55630}, {14810, 55590, 55631}, {14810, 55612, 31884}, {14810, 55629, 55637}, {14810, 55635, 55640}, {14810, 55651, 55649}, {14810, 55653, 55651}, {15516, 55584, 37517}, {15516, 55606, 55584}, {15520, 55611, 33878}, {17508, 55635, 55587}, {17508, 55640, 55596}, {20190, 33878, 15520}, {20190, 55641, 55611}, {22234, 55637, 55614}, {22330, 55599, 55582}, {31884, 55582, 55620}, {31884, 55604, 55623}, {31884, 55647, 55642}, {33878, 55641, 55627}, {44456, 55618, 55597}, {45498, 45499, 5188}, {50664, 55615, 53097}, {53097, 55632, 55615}, {55582, 55620, 55599}, {55588, 55621, 55607}, {55590, 55631, 55616}, {55594, 55638, 55626}, {55603, 55649, 55643}, {55606, 55645, 55639}, {55610, 55636, 55628}, {55630, 55649, 55645}, {55649, 55653, 55652}

X(55656) = X(3)X(6)∩X(22)X(5888)

Barycentrics    a^2*(11*a^4-13*b^4-22*b^2*c^2-13*c^4+2*a^2*(b^2+c^2)) : :
X(55656) = -12*X[3]+X[6], 3*X[20]+8*X[34573], -12*X[140]+X[43621], 2*X[141]+9*X[10304], 9*X[165]+2*X[49465], 6*X[376]+5*X[3763], -3*X[382]+14*X[42786], 8*X[548]+3*X[10516], -12*X[549]+X[48910], X[599]+10*X[19708], 10*X[631]+X[48872], X[1352]+10*X[46853] and many others

X(55656) lies on these lines: {3, 6}, {20, 34573}, {22, 5888}, {140, 43621}, {141, 10304}, {165, 49465}, {376, 3763}, {382, 42786}, {548, 10516}, {549, 48910}, {599, 19708}, {631, 48872}, {1352, 46853}, {1503, 21735}, {2916, 46945}, {3242, 35242}, {3522, 3619}, {3523, 51126}, {3524, 47355}, {3526, 48885}, {3532, 41435}, {3543, 51128}, {3589, 15692}, {3618, 15705}, {3620, 21734}, {3630, 25406}, {3818, 15688}, {3839, 50972}, {3851, 48920}, {5054, 48880}, {5055, 48879}, {5480, 10299}, {6144, 51737}, {6329, 54170}, {7484, 31860}, {7485, 10545}, {7712, 21766}, {7716, 11410}, {8703, 18358}, {10303, 51163}, {10606, 35228}, {11178, 50976}, {11456, 46207}, {12100, 31670}, {14093, 47353}, {14269, 51141}, {14561, 44682}, {14891, 21850}, {15036, 52697}, {15042, 19140}, {15107, 17825}, {15246, 48912}, {15533, 15759}, {15689, 48884}, {15693, 19130}, {15694, 48895}, {15695, 48891}, {15698, 47352}, {15700, 38072}, {15708, 51127}, {15710, 40341}, {15712, 48873}, {15714, 54173}, {15716, 19924}, {15717, 29181}, {15720, 29317}, {15750, 44091}, {16192, 16496}, {17504, 54131}, {17811, 26881}, {18440, 50993}, {19121, 38441}, {19709, 48943}, {23249, 36702}, {23259, 36717}, {34200, 46264}, {34817, 43713}, {36701, 42283}, {36703, 42284}, {43273, 45759}, {46219, 48904}, {49679, 51705}

X(55656) = midpoint of X(i) and X(j) for these {i,j}: {3, 55648}
X(55656) = reflection of X(i) in X(j) for these {i,j}: {1350, 55620}, {55620, 55635}, {55622, 55641}, {55628, 14810}, {55632, 55642}, {55641, 55648}, {55648, 55652}
X(55656) = isogonal conjugate of X(54815)
X(55656) = center of Tucker-Hagos(-2/11) circle
X(55656) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(74), X(43136)}}, {{A, B, C, X(3532), X(5007)}}, {{A, B, C, X(20421), X(21309)}}, {{A, B, C, X(30435), X(43713)}}, {{A, B, C, X(38292), X(41435)}}
X(55656) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14810, 5085}, {3, 31884, 53094}, {3, 55629, 17508}, {3, 55639, 5092}, {3, 55643, 182}, {3, 55644, 53093}, {3, 55648, 511}, {3, 55652, 55641}, {3, 55653, 55646}, {3, 55654, 55651}, {3, 55655, 55654}, {6, 5092, 10541}, {15, 16, 43136}, {182, 3098, 55586}, {182, 55615, 55580}, {182, 55636, 55604}, {182, 55643, 55626}, {182, 55650, 55643}, {511, 14810, 55628}, {511, 55642, 55632}, {511, 55652, 55648}, {575, 55640, 55616}, {576, 55649, 14810}, {1151, 1152, 5007}, {1350, 5085, 576}, {1350, 55580, 55591}, {1350, 55624, 55614}, {1350, 55626, 55615}, {1350, 55635, 55622}, {1350, 55646, 55639}, {1351, 55637, 55618}, {3098, 12017, 55582}, {3098, 50664, 33878}, {3098, 5092, 44456}, {3522, 21167, 36990}, {3524, 48881, 47355}, {5092, 55585, 5050}, {5092, 55631, 55585}, {5092, 55634, 55588}, {5092, 55642, 55620}, {5092, 55653, 55649}, {5097, 55630, 55602}, {6200, 6396, 21309}, {6409, 6410, 22331}, {6411, 6412, 187}, {6411, 6444, 6200}, {6412, 6443, 6396}, {10541, 31884, 1350}, {10541, 55639, 55607}, {11480, 11481, 32}, {12017, 55582, 6}, {14810, 50664, 3098}, {14810, 55581, 55629}, {14810, 55614, 31884}, {17508, 55611, 15516}, {17508, 55629, 11477}, {20190, 55633, 55593}, {31884, 53094, 53097}, {33878, 55604, 55597}, {33878, 55624, 55609}, {33878, 55639, 55624}, {37517, 55634, 55610}, {37517, 55644, 55634}, {39561, 55625, 55595}, {47355, 48881, 51024}, {55604, 55643, 55636}, {55632, 55639, 55635}, {55632, 55648, 55642}, {55636, 55653, 55650}, {55646, 55654, 55653}

X(55657) = X(3)X(6)∩X(5)X(48920)

Barycentrics    a^2*(6*a^4-7*b^4-12*b^2*c^2-7*c^4+a^2*(b^2+c^2)) : :
X(55657) = -13*X[3]+X[6], X[141]+2*X[33751], -5*X[549]+2*X[25565], 5*X[631]+X[48880], X[1352]+11*X[21735], 5*X[1656]+X[48879], -X[3146]+7*X[42786], 5*X[3522]+X[3818], -7*X[3523]+X[48901], -3*X[3524]+X[38317], -7*X[3526]+X[48904], -7*X[3528]+X[48898] and many others

X(55657) lies on circumconic {{A, B, C, X(34571), X(46851)}} and on these lines: {3, 6}, {5, 48920}, {20, 48942}, {22, 15082}, {140, 48885}, {141, 33751}, {373, 15246}, {376, 25561}, {542, 45759}, {548, 24206}, {549, 25565}, {550, 48889}, {631, 48880}, {698, 46893}, {1352, 21735}, {1503, 34200}, {1656, 48879}, {3146, 42786}, {3522, 3818}, {3523, 48901}, {3524, 38317}, {3526, 48904}, {3528, 48898}, {3530, 19130}, {3564, 15759}, {3763, 48896}, {3819, 35264}, {3830, 51141}, {5066, 50972}, {5476, 15698}, {5480, 44682}, {5650, 6636}, {5965, 15714}, {7484, 12045}, {7492, 33879}, {8703, 21167}, {9751, 44422}, {10168, 14891}, {10299, 31670}, {10303, 43621}, {10304, 11645}, {10323, 46847}, {10516, 15688}, {11178, 14093}, {12100, 29181}, {12103, 34573}, {12294, 17506}, {14561, 15692}, {14853, 15705}, {14869, 51163}, {15036, 19140}, {15042, 51941}, {15690, 50984}, {15693, 53023}, {15696, 48884}, {15701, 50968}, {15710, 25406}, {15711, 38110}, {15712, 38136}, {15715, 46267}, {15716, 51137}, {15717, 48873}, {15720, 48872}, {17504, 19924}, {18553, 33923}, {19708, 50977}, {21734, 46264}, {22352, 33884}, {25555, 48874}, {32903, 51756}, {33750, 51178}, {35265, 41462}, {43150, 44882}, {44580, 50959}, {46332, 50971}, {50986, 51737}

X(55657) = midpoint of X(i) and X(j) for these {i,j}: {182, 55610}, {1350, 39561}, {15520, 55593}, {17508, 31884}, {3, 55649}, {3098, 5085}, {38110, 50965}, {38136, 48881}, {5050, 55603}, {575, 55599}, {576, 55591}, {5092, 55627}, {5093, 52987}, {5102, 55589}, {6, 55596}, {8703, 21167}
X(55657) = reflection of X(i) in X(j) for these {i,j}: {14810, 55649}, {3098, 55638}, {31884, 55645}, {39561, 20190}, {575, 5085}, {5093, 50664}, {55588, 55596}, {55590, 55599}, {55591, 55601}, {55594, 55610}, {55596, 55612}, {55599, 3098}, {55603, 55621}, {55606, 55627}, {55610, 55631}, {55615, 31884}, {55627, 14810}, {55638, 55647}, {55649, 55653}
X(55657) = center of Tucker-Hagos(-1/6) circle
X(55657) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14810, 5092}, {3, 31884, 17508}, {3, 43126, 43144}, {3, 43127, 43141}, {3, 55639, 53094}, {3, 55644, 20190}, {3, 55647, 575}, {3, 55648, 6}, {3, 55650, 55606}, {3, 55653, 14810}, {3, 55654, 55649}, {3, 55655, 55653}, {3, 55656, 55655}, {5, 48920, 48943}, {6, 55648, 55637}, {140, 48885, 48895}, {141, 46853, 33751}, {182, 14810, 55619}, {182, 3098, 53097}, {182, 55589, 5102}, {182, 55600, 44456}, {182, 55631, 55594}, {182, 55640, 55610}, {182, 55649, 55640}, {182, 55652, 55646}, {511, 20190, 39561}, {511, 50664, 5093}, {511, 55596, 55588}, {511, 55601, 55591}, {511, 55612, 55596}, {548, 24206, 48891}, {576, 55629, 55601}, {576, 55642, 55629}, {1350, 39561, 511}, {1350, 55636, 55623}, {1350, 55644, 55636}, {1351, 3098, 55597}, {1351, 55641, 3098}, {3098, 15520, 55593}, {3098, 17508, 15520}, {3098, 55581, 55602}, {3098, 55602, 55612}, {3098, 55643, 55638}, {3098, 55649, 55643}, {3098, 55651, 55647}, {5050, 31884, 55603}, {5085, 55624, 55581}, {5085, 55654, 55651}, {5092, 55606, 5097}, {5092, 55634, 55586}, {5093, 55639, 55618}, {8703, 21167, 29012}, {11477, 55632, 55608}, {11482, 55644, 55631}, {12017, 55587, 22330}, {12017, 55626, 55587}, {14810, 55606, 55634}, {14810, 55615, 31884}, {14810, 55653, 55650}, {15516, 55617, 33878}, {15520, 17508, 5085}, {15520, 55615, 55590}, {15520, 55638, 55615}, {15520, 55651, 55645}, {17508, 55589, 182}, {17508, 55603, 5050}, {17508, 55640, 55589}, {20190, 55636, 1350}, {22234, 55605, 55582}, {31884, 55603, 55621}, {31884, 55615, 55627}, {33878, 55633, 55617}, {37517, 55614, 55592}, {37517, 55635, 55614}, {39561, 55644, 55630}, {44456, 55622, 55600}, {50664, 55625, 52987}, {52987, 53094, 50664}, {52987, 55639, 55625}, {53091, 55607, 55583}, {53093, 55616, 55585}, {55587, 55626, 55609}, {55591, 55629, 55613}, {55596, 55637, 55624}, {55597, 55647, 55641}, {55610, 55654, 55652}, {55613, 55649, 55642}, {55630, 55649, 55644}, {55649, 55655, 55654}

X(55658) = X(2)X(48879)∩X(3)X(6)

Barycentrics    7*a^6+a^4*(b^2+c^2)-2*a^2*(4*b^4+7*b^2*c^2+4*c^4) : :
X(55658) = 6*X[2]+X[48879], -15*X[3]+X[6], X[69]+27*X[15710], -8*X[140]+X[48904], X[141]+6*X[34200], 6*X[376]+X[48884], -8*X[548]+X[48896], 6*X[549]+X[48880], 3*X[550]+4*X[34573], -15*X[631]+X[43621], X[1352]+13*X[21734], 5*X[1656]+2*X[48920] and many others

X(55658) lies on these lines: {2, 48879}, {3, 6}, {30, 42786}, {69, 15710}, {140, 48904}, {141, 34200}, {376, 48884}, {548, 48896}, {549, 48880}, {550, 34573}, {631, 43621}, {1352, 21734}, {1656, 48920}, {3522, 24206}, {3523, 29317}, {3524, 19130}, {3528, 3619}, {3530, 48901}, {3589, 17504}, {3618, 15715}, {3763, 15688}, {3818, 8703}, {5054, 48895}, {5055, 48943}, {5476, 14891}, {5888, 7492}, {6030, 7712}, {6636, 10546}, {7485, 44106}, {10168, 15705}, {10299, 48873}, {10304, 11178}, {11204, 35228}, {11270, 41435}, {11645, 51186}, {12100, 48310}, {12108, 51163}, {14093, 48905}, {15066, 44110}, {15246, 34417}, {15646, 19137}, {15692, 31670}, {15693, 48910}, {15695, 25561}, {15696, 48889}, {15698, 19924}, {15699, 50972}, {15700, 47355}, {15707, 50968}, {15709, 41448}, {15711, 21850}, {15712, 38317}, {15714, 48906}, {15719, 25565}, {15759, 22165}, {18358, 21167}, {19124, 23040}, {19708, 21356}, {20080, 33750}, {21735, 33751}, {22112, 48912}, {29181, 42785}, {31663, 49465}, {32534, 44091}, {39874, 40107}, {41982, 47354}, {45759, 50977}

X(55658) = midpoint of X(i) and X(j) for these {i,j}: {182, 55611}, {1350, 53092}, {10541, 55616}, {3, 55651}
X(55658) = reflection of X(i) in X(j) for these {i,j}: {3098, 55639}, {52987, 55605}, {55605, 55626}, {55611, 55633}, {55626, 14810}, {55633, 55644}, {55644, 55651}
X(55658) = center of Tucker-Hagos(-1/7) circle
X(55658) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3431), X(5041)}}, {{A, B, C, X(5007), X(11270)}}, {{A, B, C, X(5008), X(20421)}}
X(55658) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14810, 17508}, {3, 43126, 12974}, {3, 43127, 12975}, {3, 55643, 53094}, {3, 55646, 5092}, {3, 55648, 5085}, {3, 55656, 55653}, {3, 55657, 55655}, {6, 55610, 55586}, {6, 55656, 55654}, {182, 3098, 55585}, {182, 55637, 55603}, {511, 14810, 55626}, {511, 55633, 55611}, {511, 55651, 55644}, {575, 55609, 55582}, {575, 55629, 55596}, {575, 55645, 55629}, {1350, 55634, 3098}, {1350, 55640, 55628}, {1350, 55647, 55640}, {1351, 55627, 55600}, {3098, 37517, 55598}, {3098, 55587, 55604}, {3098, 55594, 55608}, {3098, 55596, 55609}, {3098, 55604, 55613}, {3098, 55640, 55634}, {3098, 55644, 55639}, {3098, 55649, 55642}, {3763, 15688, 48891}, {5050, 55612, 55583}, {5050, 55641, 55612}, {5085, 55587, 22234}, {5085, 55648, 55631}, {5092, 14810, 55601}, {5092, 55636, 33878}, {5092, 55653, 55646}, {5093, 55622, 55597}, {5097, 55614, 55589}, {5097, 55638, 55614}, {5102, 55620, 55592}, {6200, 6396, 5008}, {10541, 55616, 511}, {12017, 31884, 55594}, {12017, 55584, 6}, {12017, 55594, 576}, {12017, 55639, 55602}, {14810, 17508, 52987}, {14810, 20190, 55610}, {14810, 52987, 55630}, {14810, 55601, 55632}, {14810, 55605, 55633}, {14810, 55617, 31884}, {14810, 55630, 55637}, {14810, 55652, 55649}, {14810, 55654, 55652}, {15516, 55623, 55593}, {15520, 55628, 1350}, {17508, 52987, 182}, {17508, 55621, 15520}, {17508, 55632, 37517}, {17508, 55652, 14810}, {21167, 33923, 48898}, {22234, 55613, 55587}, {22330, 55619, 55591}, {31884, 55584, 55617}, {33878, 55646, 55636}, {37517, 55633, 55607}, {39561, 55606, 55581}, {39561, 55635, 55606}, {50664, 55653, 55647}, {53091, 55618, 55588}, {53093, 55624, 55590}, {53094, 55606, 39561}, {53858, 55651, 55643}, {55584, 55654, 55650}, {55606, 55643, 55635}, {55626, 55654, 55651}, {55653, 55657, 55656}

X(55659) = X(2)X(48920)∩X(3)X(6)

Barycentrics    a^2*(8*a^4-9*b^4-16*b^2*c^2-9*c^4+a^2*(b^2+c^2)) : :
X(55659) = 3*X[2]+X[48920], -17*X[3]+X[6], 3*X[376]+X[48889], 3*X[549]+X[48885], -5*X[631]+X[48895], X[1352]+15*X[19708], -5*X[1656]+X[48943], -5*X[3522]+X[48891], 7*X[3523]+X[48880], -9*X[3524]+X[48901], 7*X[3526]+X[48879], 7*X[3528]+X[3818] and many others

X(55659) lies on these lines: {2, 48920}, {3, 6}, {376, 48889}, {542, 15759}, {548, 29323}, {549, 48885}, {631, 48895}, {1352, 19708}, {1656, 48943}, {1843, 23040}, {3522, 48891}, {3523, 48880}, {3524, 48901}, {3526, 48879}, {3528, 3818}, {3529, 42786}, {3530, 29317}, {3534, 48942}, {3819, 26881}, {5054, 48904}, {5476, 15705}, {5480, 17504}, {5921, 50977}, {6636, 32237}, {6688, 15246}, {6697, 32903}, {6723, 10691}, {7485, 10219}, {7492, 15082}, {7496, 12045}, {8703, 24206}, {10124, 50972}, {10168, 15711}, {10304, 40330}, {11645, 33751}, {13570, 54006}, {14093, 36990}, {14891, 19924}, {14927, 18553}, {15681, 51141}, {15688, 25561}, {15692, 48873}, {15693, 48872}, {15712, 19130}, {15714, 48876}, {15717, 38317}, {15718, 50968}, {20582, 41982}, {21167, 39884}, {25565, 41983}, {29012, 33923}, {34573, 44245}, {36705, 48940}, {44682, 48881}, {44882, 45759}, {46267, 50965}

X(55659) = midpoint of X(i) and X(j) for these {i,j}: {182, 55612}, {10124, 50972}, {1350, 15516}, {17508, 55638}, {22330, 55594}, {3, 55653}, {3098, 20190}, {34573, 44245}, {46267, 50965}, {575, 55601}, {5085, 55621}, {5092, 55631}, {5097, 55592}, {50664, 55606}, {6, 55597}, {6697, 32903}
X(55659) = reflection of X(i) in X(j) for these {i,j}: {55609, 55631}, {55617, 55636}, {55625, 14810}, {55636, 55647}, {55647, 55653}
X(55659) = center of Tucker-Hagos(-1/8) circle
X(55659) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 55646, 17508}, {3, 55648, 53094}, {3, 55650, 20190}, {3, 55651, 182}, {3, 55652, 575}, {3, 55656, 55649}, {3, 55658, 55657}, {6, 55620, 55589}, {6, 55627, 55597}, {6, 55644, 55627}, {182, 14810, 55612}, {182, 3098, 55584}, {182, 55629, 55590}, {182, 55649, 55635}, {182, 55655, 55651}, {511, 14810, 55625}, {511, 55631, 55609}, {511, 55636, 55617}, {511, 55653, 55647}, {576, 55639, 55615}, {576, 55649, 55639}, {1350, 10541, 1351}, {1350, 14810, 55631}, {1350, 15516, 511}, {1350, 44456, 55587}, {1350, 5092, 15516}, {1350, 53094, 5050}, {1350, 55588, 55592}, {1350, 55620, 55608}, {1350, 55649, 14810}, {1351, 22234, 5097}, {1351, 55624, 1350}, {1351, 55633, 55606}, {1351, 55646, 55633}, {3098, 17508, 22234}, {3098, 22234, 55591}, {3098, 55654, 55650}, {5050, 55595, 44456}, {5085, 55594, 22330}, {5092, 55615, 576}, {10541, 17508, 5092}, {10541, 55624, 55585}, {10541, 55646, 55624}, {12017, 55641, 55603}, {14810, 55590, 55629}, {14810, 55619, 31884}, {14810, 55625, 55636}, {14810, 55633, 55638}, {14810, 55648, 55645}, {14810, 55650, 55648}, {14810, 55655, 55653}, {14810, 55657, 55655}, {17508, 55585, 10541}, {17508, 55606, 50664}, {20190, 55631, 55588}, {20190, 55645, 3098}, {21167, 46853, 48892}, {22330, 55621, 55594}, {31884, 44456, 55611}, {31884, 55587, 55619}, {33878, 55640, 55623}, {37517, 55626, 55599}, {39561, 55614, 55586}, {50664, 55653, 55646}, {52987, 55643, 55634}, {53091, 55622, 52987}, {53091, 55643, 55622}, {53093, 55632, 55596}, {55587, 55655, 55652}, {55594, 55637, 55621}, {55597, 55631, 55620}

X(55660) = X(3)X(6)∩X(140)X(48879)

Barycentrics    9*a^6+a^4*(b^2+c^2)-2*a^2*(5*b^4+9*b^2*c^2+5*c^4) : :
X(55660) = -19*X[3]+X[6], 8*X[140]+X[48879], 8*X[548]+X[48884], -10*X[631]+X[48904], -10*X[3522]+X[48896], 7*X[3523]+2*X[48885], 7*X[3526]+2*X[48920], 7*X[3528]+2*X[24206], 8*X[3530]+X[48880], 2*X[3534]+7*X[51141], X[3818]+8*X[33923], -11*X[5070]+2*X[48943] and many others

X(55660) lies on these lines: {3, 6}, {140, 48879}, {542, 15710}, {548, 48884}, {631, 48904}, {1503, 45759}, {3522, 48896}, {3523, 48885}, {3524, 29317}, {3526, 48920}, {3528, 24206}, {3530, 48880}, {3534, 51141}, {3818, 33923}, {5070, 48943}, {5476, 15711}, {5965, 33750}, {6636, 33879}, {8703, 50984}, {10168, 15715}, {10299, 51538}, {10304, 29012}, {10516, 14093}, {10519, 51215}, {11178, 21167}, {12100, 38317}, {14561, 15698}, {15051, 52098}, {15688, 29323}, {15700, 53023}, {15704, 42786}, {15705, 19924}, {15712, 48901}, {15713, 50972}, {15717, 19130}, {15720, 48895}, {15759, 50977}, {17504, 29181}, {19708, 51023}, {19711, 51165}, {21734, 33751}, {21735, 48892}, {38136, 44682}, {46332, 47354}, {46853, 48898}

X(55660) = midpoint of X(i) and X(j) for these {i,j}: {182, 55613}, {17508, 55640}, {3, 55654}, {5085, 55624}
X(55660) = reflection of X(i) in X(j) for these {i,j}: {3098, 55640}, {55596, 55613}, {55603, 55624}, {55613, 31884}, {55624, 14810}, {55630, 55643}, {55640, 55649}, {55649, 55654}, {55654, 55657}
X(55660) = center of Tucker-Hagos(-1/9) circle
X(55660) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 55649, 17508}, {3, 55651, 5092}, {3, 55656, 14810}, {3, 55658, 55655}, {3, 55659, 55658}, {6, 55633, 55600}, {6, 55647, 55633}, {182, 3098, 55583}, {182, 33878, 576}, {182, 37517, 53092}, {182, 55628, 33878}, {182, 55633, 55592}, {182, 55649, 31884}, {182, 55653, 55644}, {511, 14810, 55624}, {511, 31884, 55613}, {511, 55643, 55630}, {511, 55649, 55640}, {511, 55657, 55654}, {575, 55621, 55591}, {575, 55639, 55608}, {576, 17508, 5085}, {576, 55635, 55609}, {1350, 55650, 55642}, {1351, 55636, 55611}, {3098, 17508, 39561}, {3098, 39561, 55589}, {3098, 55655, 55652}, {5050, 55627, 52987}, {5050, 55649, 55635}, {5085, 14810, 55603}, {5085, 55597, 15520}, {5092, 14810, 55597}, {5092, 55597, 53091}, {5093, 31884, 55606}, {5097, 55626, 55598}, {5102, 55629, 55599}, {10541, 55632, 55590}, {11477, 31884, 55610}, {14810, 33878, 55628}, {14810, 50664, 55614}, {15520, 55610, 55587}, {15520, 55625, 55596}, {15520, 55649, 55637}, {17508, 55596, 182}, {17508, 55640, 511}, {17508, 55649, 3098}, {17508, 55655, 55649}, {20190, 55599, 5102}, {20190, 55629, 55585}, {31884, 55610, 55625}, {31884, 55616, 55627}, {33878, 53091, 11477}, {33878, 55656, 55653}, {37517, 55631, 55605}, {50664, 55614, 55581}, {53094, 55631, 37517}, {55587, 55655, 55651}, {55591, 55639, 55621}, {55592, 55653, 55647}, {55606, 55653, 55648}, {55610, 55651, 55645}, {55630, 55649, 55643}, {55649, 55658, 55657}

X(55661) = X(2)X(48943)∩X(3)X(6)

Barycentrics    a^2*(10*a^4-11*b^4-20*b^2*c^2-11*c^4+a^2*(b^2+c^2)) : :
X(55661) = -6*X[2]+X[48943], -21*X[3]+X[6], 3*X[20]+7*X[42786], 4*X[140]+X[48920], X[141]+9*X[45759], 3*X[548]+2*X[34573], -6*X[549]+X[48895], 4*X[550]+X[48942], -21*X[3523]+X[43621], 9*X[3524]+X[48880], 7*X[3528]+X[51537], 4*X[3530]+X[48885] and many others

X(55661) lies on these lines: {2, 48943}, {3, 6}, {20, 42786}, {140, 48920}, {141, 45759}, {542, 15714}, {548, 34573}, {549, 48895}, {550, 48942}, {3522, 29323}, {3523, 43621}, {3524, 48880}, {3528, 51537}, {3530, 48885}, {3589, 14891}, {3619, 21735}, {3763, 14093}, {3818, 10304}, {5054, 48879}, {5476, 15715}, {5888, 6636}, {8703, 25561}, {10219, 31860}, {10299, 38317}, {10545, 15246}, {11451, 48912}, {11645, 19708}, {12100, 19130}, {15080, 44108}, {15686, 51128}, {15688, 48884}, {15689, 51141}, {15698, 31670}, {15700, 48910}, {15706, 47355}, {15710, 39874}, {15711, 19924}, {15712, 29317}, {15717, 48901}, {15720, 48904}, {15759, 43150}, {17504, 48881}, {18358, 34200}, {18553, 21167}, {19711, 25565}, {20582, 46332}, {21844, 44091}, {24206, 33923}, {29012, 46853}, {35497, 41464}, {41982, 50984}, {41983, 51127}, {42785, 48873}, {50985, 54169}

X(55661) = midpoint of X(i) and X(j) for these {i,j}: {182, 55614}, {1350, 22234}, {3, 55655}, {3098, 12017}, {5092, 55634}, {53091, 55600}, {53093, 55608}, {53094, 55637}, {6, 55598}
X(55661) = reflection of X(i) in X(j) for these {i,j}: {14810, 55650}, {5097, 53093}, {53091, 20190}, {55590, 55600}, {55595, 55612}, {55606, 55629}, {55608, 55631}, {55619, 55637}, {55623, 14810}, {55634, 55646}, {55646, 55653}, {55650, 55655}
X(55661) = center of Tucker-Hagos(-1/10) circle
X(55661) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 55651, 17508}, {3, 55653, 5092}, {3, 55654, 182}, {3, 55657, 14810}, {3, 55658, 55653}, {3, 55659, 55657}, {3, 55660, 55659}, {6, 55629, 55598}, {6, 55646, 55629}, {6, 55649, 55636}, {182, 3098, 55582}, {182, 55627, 55588}, {182, 55639, 55601}, {182, 55654, 55647}, {511, 14810, 55623}, {511, 20190, 53091}, {511, 55612, 55595}, {511, 55629, 55606}, {511, 55631, 55608}, {511, 55637, 55619}, {511, 55653, 55646}, {511, 55655, 55650}, {575, 14810, 55615}, {576, 55643, 55625}, {1350, 22234, 511}, {1350, 55652, 55645}, {1351, 55640, 55617}, {3098, 50664, 55586}, {3098, 55658, 55656}, {5050, 55633, 55597}, {5085, 55632, 55585}, {5085, 55644, 55612}, {5092, 55586, 50664}, {5092, 55594, 575}, {5092, 55606, 6}, {5092, 55642, 55599}, {5092, 55650, 55634}, {12017, 55646, 3098}, {14810, 55588, 55627}, {14810, 55599, 55631}, {17508, 55608, 53093}, {17508, 55631, 5097}, {17508, 55642, 33878}, {17508, 55649, 55618}, {20190, 31884, 55590}, {20190, 55609, 37517}, {21167, 33751, 18553}, {31884, 37517, 55609}, {31884, 53091, 55600}, {33878, 55599, 55594}, {33878, 55651, 55642}, {39561, 55626, 55592}, {52987, 55648, 55638}, {53094, 55646, 55604}, {55585, 55644, 55632}, {55587, 55641, 55621}, {55587, 55649, 55641}, {55593, 55629, 55614}, {55593, 55654, 55649}, {55601, 55647, 55639}, {55604, 55646, 55637}, {55608, 55655, 55651}, {55627, 55657, 55654}, {55650, 55657, 55655}, {55653, 55659, 55658}

X(55662) = X(3)X(6)∩X(376)X(51141)

Barycentrics    11*a^6+a^4*(b^2+c^2)-2*a^2*(6*b^4+11*b^2*c^2+6*c^4) : :
X(55662) = -23*X[3]+X[6], 4*X[376]+7*X[51141], -12*X[549]+X[48904], 10*X[631]+X[48879], 7*X[1352]+15*X[50975], 10*X[3522]+X[48884], -15*X[3524]+4*X[25565], -12*X[3530]+X[51163], X[3818]+10*X[46853], 9*X[5054]+2*X[48920], -X[5480]+12*X[14891], -12*X[8703]+X[48896] and many others

X(55662) lies on circumconic {{A, B, C, X(40803), X(55601)}} and on these lines: {3, 6}, {376, 51141}, {549, 48904}, {631, 48879}, {1352, 50975}, {3522, 48884}, {3524, 25565}, {3530, 51163}, {3818, 46853}, {5054, 48920}, {5480, 14891}, {6636, 16187}, {8703, 48896}, {10299, 19130}, {10304, 24206}, {11178, 14927}, {12100, 48901}, {12103, 42786}, {15688, 48889}, {15689, 48942}, {15698, 48873}, {15700, 48872}, {15711, 38079}, {15712, 48880}, {15714, 50977}, {15715, 19924}, {15717, 29317}, {15759, 44882}, {21734, 40330}, {21735, 29012}, {34200, 47354}, {38317, 44682}, {46219, 48943}

X(55662) = midpoint of X(i) and X(j) for these {i,j}: {3, 55656}
X(55662) = reflection of X(i) in X(j) for these {i,j}: {3098, 55641}, {55622, 14810}, {55628, 55642}, {55635, 55648}, {55642, 55652}, {55652, 55656}
X(55662) = center of Tucker-Hagos(-1/11) circle
X(55662) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 55653, 17508}, {3, 55654, 5092}, {3, 55656, 511}, {3, 55660, 55658}, {3, 55661, 55660}, {6, 55650, 55640}, {182, 14810, 55608}, {182, 3098, 55581}, {182, 55581, 15520}, {182, 55585, 5097}, {182, 55633, 52987}, {182, 55637, 1350}, {182, 55648, 55628}, {182, 55655, 55649}, {182, 55658, 55655}, {511, 14810, 55622}, {511, 55652, 55642}, {511, 55656, 55652}, {575, 55657, 55653}, {576, 3098, 55593}, {576, 55646, 55630}, {1350, 17508, 182}, {1350, 55629, 55617}, {1350, 55651, 55643}, {1351, 14810, 3098}, {1351, 55651, 14810}, {3098, 17508, 575}, {3098, 53097, 55603}, {3098, 55599, 55611}, {3098, 55644, 55638}, {3098, 55655, 55651}, {5050, 55636, 55600}, {5092, 14810, 55592}, {5092, 55603, 22234}, {5092, 55638, 53097}, {5092, 55654, 55644}, {5097, 31884, 55605}, {5097, 55605, 55585}, {12017, 55627, 55583}, {14810, 15516, 55616}, {14810, 53094, 55587}, {14810, 55592, 55629}, {14810, 55608, 55633}, {14810, 55622, 55635}, {17508, 55583, 12017}, {17508, 55637, 37517}, {17508, 55649, 55613}, {17508, 55652, 55632}, {17508, 55653, 55637}, {20190, 55639, 55596}, {22234, 37517, 5093}, {39561, 55631, 55598}, {50664, 55626, 55589}, {53094, 55616, 15516}, {55586, 55653, 55646}, {55632, 55643, 55641}, {55635, 55652, 55648}, {55638, 55657, 55654}, {55642, 55658, 55656}, {55655, 55660, 55659}

X(55663) = X(3)X(6)∩X(3819)X(6030)

Barycentrics    a^2*(12*a^4-13*b^4-24*b^2*c^2-13*c^4+a^2*(b^2+c^2)) : :
X(55663) = -25*X[3]+X[6], 5*X[550]+7*X[51128], 5*X[631]+X[48920], 5*X[3522]+X[48889], -7*X[3523]+X[48895], -7*X[3526]+X[48943], -7*X[3528]+X[48891], -5*X[3530]+2*X[51127], X[3818]+11*X[21735], -13*X[10299]+X[48901], X[11160]+15*X[33750], 5*X[14093]+X[25561] and many others

X(55663) lies on these lines: {3, 6}, {550, 51128}, {631, 48920}, {1503, 15759}, {3522, 48889}, {3523, 48895}, {3526, 48943}, {3528, 48891}, {3530, 51127}, {3818, 21735}, {3819, 6030}, {6636, 15082}, {7485, 12045}, {7998, 44110}, {8703, 29323}, {10299, 48901}, {11160, 33750}, {11645, 21167}, {12100, 29317}, {14093, 25561}, {14561, 15705}, {14891, 29181}, {15042, 52098}, {15246, 44106}, {15692, 38317}, {15695, 51141}, {15696, 48942}, {15706, 53023}, {15710, 21356}, {15712, 48885}, {15717, 48880}, {15720, 48879}, {17504, 38136}, {17538, 42786}, {19130, 44682}, {20582, 29012}, {21734, 48898}, {22165, 51184}, {24206, 46853}, {25406, 50961}, {32237, 33879}, {44580, 50972}, {46332, 50984}, {50954, 51186}

X(55663) = midpoint of X(i) and X(j) for these {i,j}: {182, 55615}, {14810, 17508}, {15520, 55594}, {20190, 55621}, {3, 55657}, {39561, 55599}, {5050, 55606}, {575, 55603}, {5085, 55627}, {5092, 31884}, {5097, 55593}, {5102, 55590}
X(55663) = reflection of X(i) in X(j) for these {i,j}: {20190, 17508}, {31884, 55647}, {55593, 55609}, {55597, 55615}, {55601, 55621}, {55603, 55625}, {55612, 31884}, {55615, 55636}, {55621, 14810}, {55631, 55645}, {55638, 55649}, {55645, 55653}, {55653, 55657}, {55657, 55659}
X(55663) = center of Tucker-Hagos(-1/12) circle
X(55663) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 55654, 17508}, {3, 55655, 5092}, {3, 55656, 182}, {3, 55659, 55653}, {3, 55660, 55657}, {3, 55661, 55659}, {3, 55662, 55661}, {6, 14810, 55617}, {182, 3098, 55580}, {182, 55636, 55597}, {182, 55643, 55615}, {182, 55656, 55650}, {511, 14810, 55621}, {511, 17508, 20190}, {511, 55609, 55593}, {511, 55625, 55603}, {511, 55649, 55638}, {576, 55648, 55634}, {1351, 55642, 55623}, {5050, 55640, 55606}, {5050, 55651, 55640}, {5085, 55649, 55627}, {5092, 14810, 52987}, {5092, 55599, 39561}, {5092, 55623, 1351}, {5092, 55647, 55612}, {5092, 55655, 55647}, {5097, 55637, 55609}, {5102, 55613, 55590}, {5102, 55639, 55613}, {5206, 37512, 13357}, {5237, 5238, 5007}, {6449, 6450, 43136}, {12017, 55633, 55588}, {14810, 17508, 511}, {14810, 20190, 55601}, {14810, 55584, 55625}, {14810, 55586, 55626}, {14810, 55601, 55631}, {14810, 55606, 55632}, {14810, 55626, 55636}, {14810, 55657, 55654}, {15520, 55624, 55594}, {15520, 55644, 55624}, {17508, 55630, 6}, {17508, 55643, 55586}, {17508, 55649, 55610}, {17508, 55652, 55630}, {17508, 55654, 14810}, {17508, 55660, 55658}, {20190, 52987, 22330}, {20190, 55654, 55645}, {31884, 39561, 55599}, {37517, 55641, 55619}, {39561, 55649, 31884}, {39561, 55655, 55649}, {50664, 55631, 55592}, {52987, 55658, 55655}, {53094, 55624, 15520}, {55597, 55612, 55604}, {55615, 55650, 55643}, {55657, 55661, 55660}

X(55664) = X(3)X(6)∩X(22)X(12045)

Barycentrics    a^2*(12*a^4-11*b^4-24*b^2*c^2-11*c^4-a^2*(b^2+c^2)) : :
X(55664) = 23*X[3]+X[6], 5*X[631]+X[48891], 5*X[3522]+X[48895], -7*X[3523]+X[48889], -7*X[3526]+X[48942], -7*X[3528]+X[48920], 2*X[3530]+X[33751], 17*X[3534]+7*X[51164], -X[3818]+13*X[10299], 5*X[5476]+7*X[50969], X[10168]+5*X[15714], 3*X[10304]+X[38317] and many others

X(55664) lies on these lines: {3, 6}, {22, 12045}, {549, 29323}, {631, 48891}, {1503, 14891}, {3522, 48895}, {3523, 48889}, {3526, 48942}, {3528, 48920}, {3530, 33751}, {3534, 51164}, {3818, 10299}, {5476, 50969}, {5650, 26881}, {10168, 15714}, {10304, 38317}, {10516, 15706}, {11645, 17504}, {12100, 29012}, {15082, 15246}, {15696, 48943}, {15698, 51023}, {15700, 25561}, {15711, 21167}, {15712, 48892}, {15717, 48898}, {15720, 48896}, {15722, 50976}, {15759, 29181}, {19130, 46853}, {19708, 51538}, {21734, 48880}, {21735, 48901}, {24206, 44682}, {29317, 34200}, {32600, 45308}, {33750, 50977}, {38136, 48885}, {46332, 51165}, {50985, 51737}, {51137, 53023}

X(55664) = midpoint of X(i) and X(j) for these {i,j}: {182, 55627}, {17508, 55657}, {20190, 55638}, {38136, 48885}, {39561, 55606}, {5050, 55615}, {575, 55610}, {5085, 14810}, {5092, 55649}, {5093, 55594}, {5097, 55596}, {6, 55599}
X(55664) = reflection of X(i) in X(j) for these {i,j}: {50664, 5085}, {55592, 55610}, {55596, 55617}, {55599, 55625}, {55601, 55627}, {55610, 55636}, {55612, 55638}, {55621, 55645}, {55627, 55647}, {55631, 55649}, {55638, 55653}, {55645, 55657}, {55649, 55659}, {55653, 55663}, {55663, 3}
X(55664) = inverse of X(55662) in First Brocard Circle
X(55664) = center of Tucker-Hagos(1/12) circle
X(55664) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 17508, 55657}, {3, 182, 55661}, {3, 5085, 55660}, {3, 5092, 55659}, {3, 511, 55663}, {3, 53094, 55658}, {3, 6, 55662}, {6, 55650, 55625}, {6, 55662, 55650}, {182, 55639, 55588}, {182, 55647, 55601}, {182, 55654, 55627}, {182, 55661, 55647}, {511, 55610, 55592}, {511, 55625, 55599}, {511, 55636, 55610}, {511, 55653, 55638}, {511, 55659, 55649}, {511, 55663, 55653}, {576, 55581, 44456}, {1351, 55652, 55634}, {5050, 17508, 5092}, {5050, 31884, 55589}, {5050, 55639, 55593}, {5050, 55659, 55645}, {5085, 55624, 576}, {5085, 55643, 55581}, {5085, 55654, 55614}, {5085, 55656, 55624}, {5085, 55660, 14810}, {5092, 55588, 182}, {5092, 55609, 50664}, {5092, 55631, 15516}, {5092, 55656, 55609}, {5092, 55661, 55639}, {5093, 55630, 55594}, {5093, 55651, 55630}, {5097, 55646, 55617}, {11477, 55642, 55619}, {12017, 55644, 55590}, {14810, 50664, 55597}, {14810, 55609, 55631}, {14810, 55628, 55636}, {17508, 55603, 5085}, {17508, 55621, 20190}, {17508, 55649, 5050}, {17508, 55657, 511}, {17508, 55660, 55603}, {17508, 55663, 55621}, {20190, 55653, 55612}, {22330, 50664, 53091}, {31884, 55589, 55615}, {37517, 55648, 55623}, {39561, 55643, 55606}, {39561, 55658, 55643}, {53093, 55633, 55586}, {53094, 55643, 39561}, {55589, 55649, 31884}, {55599, 55650, 55640}, {55601, 55663, 55654}, {55649, 55660, 55656}

X(55665) = X(3)X(6)∩X(141)X(14891)

Barycentrics    11*a^6-a^4*(b^2+c^2)-2*a^2*(5*b^4+11*b^2*c^2+5*c^4) : :
X(55665) = 21*X[3]+X[6], -X[141]+12*X[14891], 6*X[548]+5*X[51126], -18*X[549]+7*X[42786], 10*X[631]+X[48896], 10*X[3522]+X[48904], 7*X[3523]+4*X[33751], 9*X[3524]+2*X[48892], 21*X[3528]+X[43621], 2*X[3589]+9*X[45759], -5*X[3763]+27*X[15706], -X[3818]+12*X[12100] and many others

X(55665) lies on circumconic {{A, B, C, X(13452), X(41940)}} and on these lines: {3, 6}, {141, 14891}, {542, 15715}, {548, 51126}, {549, 42786}, {631, 48896}, {3522, 48904}, {3523, 33751}, {3524, 48892}, {3528, 43621}, {3589, 45759}, {3763, 15706}, {3818, 12100}, {5054, 48891}, {5476, 15714}, {5888, 35268}, {8703, 48879}, {9544, 41462}, {10168, 15710}, {10299, 24206}, {10304, 19130}, {10546, 15246}, {11178, 17504}, {11180, 15705}, {11645, 15716}, {14093, 47355}, {15066, 44108}, {15686, 51127}, {15688, 48895}, {15689, 48943}, {15698, 46264}, {15700, 48905}, {15711, 50991}, {15712, 34573}, {15717, 29012}, {15720, 29323}, {15759, 48881}, {21734, 48885}, {21735, 29317}, {33750, 40107}, {33923, 38317}, {34200, 48880}, {35477, 44091}, {39899, 50989}, {41983, 51128}, {46219, 48942}, {46332, 48310}, {46853, 48901}, {47598, 51134}

X(55665) = midpoint of X(i) and X(j) for these {i,j}: {182, 55628}
X(55665) = reflection of X(i) in X(j) for these {i,j}: {3098, 55642}, {55620, 14810}, {55628, 55648}, {55635, 55652}, {55642, 55656}, {55652, 55662}, {55662, 3}
X(55665) = inverse of X(55661) in First Brocard Circle
X(55665) = center of Tucker-Hagos(1/11) circle
X(55665) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55663}, {3, 17508, 55655}, {3, 182, 55660}, {3, 5085, 55659}, {3, 5092, 55658}, {3, 511, 55662}, {3, 53094, 55657}, {3, 6, 55661}, {6, 3098, 55587}, {6, 55656, 55641}, {6, 55661, 55649}, {182, 31884, 55583}, {182, 52987, 5093}, {182, 55613, 11477}, {182, 55628, 511}, {182, 55649, 55606}, {182, 55660, 55644}, {182, 55662, 55648}, {511, 14810, 55620}, {511, 55648, 55628}, {511, 55662, 55652}, {575, 55633, 55589}, {575, 55654, 55633}, {576, 55640, 55605}, {576, 55655, 55640}, {1351, 55650, 55630}, {3098, 55589, 55604}, {3098, 55642, 55635}, {3098, 55652, 55642}, {3098, 55660, 55653}, {5050, 55647, 55608}, {5085, 55616, 22330}, {5085, 55659, 55637}, {5092, 55646, 37517}, {5092, 55661, 55636}, {5097, 55643, 55611}, {11477, 14810, 55613}, {11477, 55607, 33878}, {12017, 14810, 55585}, {12017, 55585, 39561}, {12017, 55593, 6}, {14810, 39561, 55600}, {14810, 55585, 3098}, {17508, 55644, 182}, {17508, 55655, 576}, {17508, 55660, 55596}, {20190, 55634, 44456}, {20190, 55651, 55603}, {22330, 55606, 55580}, {31884, 53092, 55592}, {33878, 55606, 55598}, {33878, 55648, 55632}, {37517, 55658, 55646}, {44456, 55651, 55634}, {50664, 55639, 52987}, {50664, 55653, 55625}, {50664, 55657, 55639}, {53093, 55627, 55581}, {53094, 55639, 50664}, {55587, 55600, 55593}, {55606, 55621, 55616}, {55606, 55625, 55618}, {55642, 55662, 55656}

X(55666) = X(2)X(48942)∩X(3)X(6)

Barycentrics    a^2*(10*a^4-9*b^4-20*b^2*c^2-9*c^4-a^2*(b^2+c^2)) : :
X(55666) = -6*X[2]+X[48942], 19*X[3]+X[6], 4*X[140]+X[48891], 13*X[376]+7*X[50964], 4*X[548]+X[48895], 3*X[549]+2*X[33751], 4*X[550]+X[48943], -X[1352]+21*X[15698], -6*X[3524]+X[25561], 7*X[3528]+3*X[38317], 4*X[3530]+X[48892], -X[3818]+11*X[15717] and many others

X(55666) lies on these lines: {2, 48942}, {3, 6}, {140, 48891}, {376, 50964}, {542, 15711}, {548, 48895}, {549, 33751}, {550, 48943}, {631, 29323}, {1352, 15698}, {3524, 25561}, {3528, 38317}, {3530, 48892}, {3818, 15717}, {5054, 48896}, {5476, 15710}, {5480, 45759}, {5921, 15705}, {7485, 32237}, {8703, 48920}, {10168, 15759}, {10299, 14927}, {10304, 48901}, {11178, 15716}, {11645, 15692}, {12100, 24206}, {14093, 51137}, {14891, 50958}, {15688, 48904}, {15691, 51139}, {15700, 36990}, {15712, 29012}, {15714, 19924}, {15715, 50977}, {15720, 48884}, {17504, 44882}, {19130, 33923}, {21167, 43150}, {21735, 48880}, {29317, 46853}, {33750, 34507}, {34200, 48885}, {39884, 44682}, {41435, 43814}, {46267, 51212}, {48876, 51136}

X(55666) = midpoint of X(i) and X(j) for these {i,j}: {182, 55629}, {11482, 55598}, {12017, 55637}, {14093, 51137}, {22234, 55604}, {3098, 53093}, {48898, 51537}, {5092, 55650}, {53091, 55608}, {53094, 55655}, {6, 55600}
X(55666) = reflection of X(i) in X(j) for these {i,j}: {11482, 50664}, {14810, 55655}, {575, 12017}, {55588, 55598}, {55594, 55614}, {55604, 55631}, {55606, 55634}, {55619, 14810}, {55623, 55646}, {55634, 55650}, {55637, 55653}, {55650, 55661}, {55661, 3}
X(55666) = inverse of X(55660) in First Brocard Circle
X(55666) = center of Tucker-Hagos(1/10) circle
X(55666) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55662}, {3, 182, 55659}, {3, 3098, 55663}, {3, 5085, 55658}, {3, 5092, 55657}, {3, 511, 55661}, {3, 6, 55660}, {3, 55665, 55664}, {6, 55633, 55592}, {6, 55647, 55615}, {6, 55660, 55647}, {182, 14810, 55590}, {182, 55590, 5097}, {182, 55605, 1351}, {182, 55635, 55584}, {182, 55649, 55605}, {182, 55651, 55612}, {182, 55655, 55629}, {511, 14810, 55619}, {511, 50664, 11482}, {511, 55631, 55604}, {511, 55646, 55623}, {511, 55653, 55637}, {549, 33751, 48889}, {575, 17508, 5092}, {576, 55636, 55599}, {576, 55654, 55636}, {1350, 1351, 55583}, {1350, 14810, 55627}, {1350, 53094, 12017}, {1350, 55653, 14810}, {1350, 55662, 55653}, {1351, 55625, 55594}, {1351, 55632, 1350}, {1351, 55649, 55625}, {5050, 55622, 55581}, {5050, 55644, 55601}, {5085, 55604, 22234}, {5085, 55648, 55587}, {5085, 55658, 55631}, {5092, 55590, 182}, {5092, 55653, 55586}, {5092, 55657, 55606}, {5093, 12017, 53093}, {11477, 55640, 55609}, {11482, 31884, 55598}, {11482, 55598, 511}, {14810, 55615, 55633}, {14810, 55619, 55634}, {14810, 55655, 55650}, {14810, 55661, 55655}, {17508, 55613, 5085}, {17508, 55632, 20190}, {17508, 55653, 575}, {31884, 50664, 55588}, {33878, 55652, 55638}, {37517, 55643, 55617}, {39561, 55639, 55597}, {52987, 55656, 55645}, {53091, 55646, 55608}, {53094, 55646, 53091}, {53097, 55642, 55621}, {55581, 55644, 55622}, {55583, 55637, 55614}, {55583, 55649, 55632}, {55584, 55651, 55635}, {55587, 55658, 55648}, {55608, 55655, 55646}, {55612, 55659, 55651}, {55617, 55653, 55643}

X(55667) = X(3)X(6)∩X(140)X(48896)

Barycentrics    9*a^6-a^4*(b^2+c^2)-2*a^2*(4*b^4+9*b^2*c^2+4*c^4) : :
X(55667) = 17*X[3]+X[6], 8*X[140]+X[48896], 5*X[376]+4*X[25565], 8*X[548]+X[48904], 5*X[631]+4*X[33751], -10*X[3522]+X[48879], 7*X[3523]+2*X[48892], 7*X[3526]+2*X[48891], 7*X[3528]+2*X[19130], 8*X[3530]+X[48898], -X[3818]+10*X[15712], -11*X[5070]+2*X[48942] and many others

X(55667) lies on these lines: {3, 6}, {140, 48896}, {376, 25565}, {542, 15705}, {548, 48904}, {631, 33751}, {1503, 17504}, {1974, 23040}, {3522, 48879}, {3523, 48892}, {3524, 29012}, {3526, 48891}, {3528, 19130}, {3530, 48898}, {3818, 15712}, {5054, 29323}, {5070, 48942}, {5476, 15759}, {5650, 35264}, {8703, 38317}, {9909, 12045}, {10109, 51134}, {10304, 29317}, {10516, 15700}, {10519, 50961}, {11178, 15692}, {11645, 15706}, {12100, 47354}, {12108, 42786}, {14093, 53023}, {14561, 19708}, {14891, 21167}, {15246, 33879}, {15710, 19924}, {15711, 41152}, {15714, 38110}, {15715, 25406}, {15716, 50954}, {15717, 24206}, {15718, 25561}, {15720, 48889}, {19710, 51139}, {19711, 50971}, {21735, 48885}, {29181, 38079}, {33923, 48901}, {38136, 46853}, {41982, 48310}, {44245, 51126}, {47355, 48920}

X(55667) = midpoint of X(i) and X(j) for these {i,j}: {182, 55630}, {17508, 55660}, {5050, 55618}, {5085, 55643}
X(55667) = reflection of X(i) in X(j) for these {i,j}: {3098, 55643}, {55596, 55618}, {55603, 55630}, {55613, 55640}, {55618, 14810}, {55630, 55649}, {55640, 55654}, {55643, 55657}, {55649, 55660}, {55660, 3}
X(55667) = inverse of X(55659) in First Brocard Circle
X(55667) = center of Tucker-Hagos(1/9) circle
X(55667) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55661}, {3, 182, 55658}, {3, 3098, 55662}, {3, 31884, 55663}, {3, 5085, 55657}, {3, 5092, 55655}, {3, 511, 55660}, {3, 53094, 55653}, {3, 6, 55659}, {3, 55666, 55665}, {6, 55627, 55589}, {6, 55659, 55644}, {182, 55598, 576}, {182, 55611, 37517}, {182, 55637, 55585}, {182, 55649, 55603}, {182, 55658, 55637}, {511, 14810, 55618}, {511, 55640, 55613}, {511, 55649, 55630}, {511, 55654, 55640}, {511, 55657, 55643}, {575, 3098, 55581}, {575, 55657, 55638}, {576, 3098, 55590}, {576, 55633, 55598}, {631, 33751, 48884}, {1350, 55661, 55652}, {1351, 3098, 52987}, {1351, 31884, 55599}, {1351, 39561, 15520}, {1351, 55604, 53097}, {1351, 55647, 3098}, {3098, 17508, 5085}, {3098, 55587, 55602}, {3098, 55597, 55608}, {3098, 55641, 55633}, {3098, 55655, 55647}, {5085, 31884, 1351}, {5085, 53097, 5050}, {5085, 55593, 575}, {5085, 55651, 55593}, {5092, 14810, 22330}, {5092, 55612, 53093}, {5092, 55653, 55582}, {5092, 55659, 55620}, {5093, 55646, 55615}, {5097, 55639, 55600}, {10541, 55648, 55594}, {11477, 55636, 55605}, {14810, 22330, 55604}, {14810, 37517, 55611}, {15520, 55662, 55649}, {17508, 39561, 5092}, {17508, 55649, 182}, {17508, 55655, 39561}, {17508, 55660, 511}, {20190, 55615, 5093}, {20190, 55646, 55587}, {22330, 31884, 55596}, {31884, 55582, 55610}, {31884, 55610, 55623}, {31884, 55620, 55627}, {31884, 55649, 55642}, {33878, 55650, 55635}, {39561, 55655, 31884}, {50664, 55629, 55583}, {53092, 55622, 55586}, {55581, 55662, 55651}, {55587, 55646, 55628}, {55590, 55653, 55641}, {55640, 55660, 55654}

X(55668) = X(2)X(48891)∩X(3)X(6)

Barycentrics    a^2*(8*a^4-7*b^4-16*b^2*c^2-7*c^4-a^2*(b^2+c^2)) : :
X(55668) = 3*X[2]+X[48891], 15*X[3]+X[6], -X[69]+33*X[15715], -X[141]+9*X[17504], 3*X[376]+X[48895], 3*X[549]+X[48892], 3*X[550]+5*X[51126], -15*X[631]+7*X[42786], -5*X[1656]+X[48942], 5*X[3522]+3*X[38317], 7*X[3523]+X[48898], -9*X[3524]+X[3818] and many others

X(55668) lies on these lines: {2, 48891}, {3, 6}, {22, 10219}, {23, 12045}, {30, 51127}, {69, 15715}, {140, 29323}, {141, 17504}, {376, 48895}, {542, 14891}, {549, 48892}, {550, 51126}, {631, 42786}, {1495, 5888}, {1656, 48942}, {3520, 44091}, {3522, 38317}, {3523, 48898}, {3524, 3818}, {3526, 48896}, {3528, 48901}, {3530, 29012}, {3534, 48943}, {3589, 34200}, {3618, 15710}, {3619, 10299}, {3620, 33750}, {3763, 15700}, {3819, 15080}, {5054, 48884}, {5621, 15042}, {5650, 7712}, {5943, 48912}, {6636, 6688}, {7485, 44082}, {7496, 32237}, {8703, 19130}, {9822, 15646}, {10168, 45759}, {10304, 48880}, {10546, 15082}, {11178, 15706}, {11645, 12100}, {12294, 23040}, {14093, 48910}, {14561, 21734}, {14855, 52055}, {14890, 50960}, {15036, 32305}, {15688, 47355}, {15690, 25565}, {15692, 46264}, {15693, 25561}, {15698, 21356}, {15705, 50977}, {15711, 22165}, {15712, 24206}, {15714, 21850}, {15716, 18440}, {15759, 19924}, {17502, 49465}, {19708, 31670}, {20300, 32903}, {21735, 42785}, {22352, 41462}, {29317, 33923}, {36699, 48940}, {38071, 51134}, {38448, 41464}, {40291, 44321}, {41983, 50971}, {44682, 44882}, {46853, 48885}, {50986, 54169}

X(55668) = midpoint of X(i) and X(j) for these {i,j}: {140, 33751}, {182, 55631}, {1350, 22330}, {14810, 20190}, {15516, 55606}, {15690, 25565}, {17508, 55663}, {20300, 32903}, {3098, 50664}, {575, 55612}, {576, 55592}, {5085, 55645}, {5092, 55653}, {5097, 55597}, {6, 55601}
X(55668) = reflection of X(i) in X(j) for these {i,j}: {55609, 55636}, {55617, 14810}, {55625, 55647}, {55636, 55653}, {55647, 55659}, {55659, 3}
X(55668) = inverse of X(55658) in First Brocard Circle
X(55668) = isogonal conjugate of X(54717)
X(55668) = center of Tucker-Hagos(1/8) circle
X(55668) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(74), X(5041)}}, {{A, B, C, X(7772), X(11270)}}, {{A, B, C, X(16835), X(41940)}}
X(55668) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12017, 55656}, {3, 1350, 55660}, {3, 14810, 55663}, {3, 182, 55657}, {3, 3098, 55661}, {3, 31884, 55662}, {3, 5085, 55655}, {3, 511, 55659}, {3, 53094, 55649}, {3, 6, 55658}, {3, 55666, 55664}, {3, 55667, 55666}, {6, 17508, 5092}, {6, 3098, 55586}, {6, 55632, 52987}, {6, 55654, 55632}, {15, 16, 5041}, {140, 33751, 29323}, {182, 3098, 44456}, {182, 5102, 575}, {182, 55589, 11482}, {182, 55600, 5102}, {182, 55640, 53097}, {182, 55646, 55594}, {182, 55649, 55600}, {182, 55652, 55610}, {182, 55655, 55622}, {511, 14810, 55617}, {511, 55647, 55625}, {511, 55653, 55636}, {511, 55659, 55647}, {575, 55634, 33878}, {576, 55627, 55592}, {576, 55651, 55627}, {1350, 22330, 511}, {1350, 55650, 55638}, {1350, 55660, 55650}, {1351, 55644, 55615}, {3098, 5092, 50664}, {3522, 38317, 48920}, {5050, 55637, 55590}, {5085, 55606, 15516}, {5085, 55639, 37517}, {5092, 55642, 22330}, {5092, 55659, 55609}, {5097, 14810, 55605}, {5097, 31884, 55597}, {8160, 8161, 48673}, {9738, 9739, 40268}, {10541, 55643, 55587}, {11477, 55633, 55599}, {11482, 55610, 55584}, {11482, 55622, 55589}, {12017, 55656, 3098}, {14810, 17508, 20190}, {14810, 52987, 55621}, {14810, 55606, 55630}, {14810, 55610, 55631}, {14810, 55657, 55652}, {14810, 55658, 55653}, {15516, 55645, 55606}, {15688, 47355, 48879}, {17508, 55630, 5085}, {17508, 55652, 182}, {17508, 55658, 6}, {20190, 55653, 55601}, {20190, 55663, 14810}, {22234, 55635, 55593}, {22330, 55638, 1350}, {33878, 55634, 55612}, {33878, 55649, 55634}, {37517, 55655, 55639}, {39561, 55629, 55588}, {48879, 51137, 47355}, {53091, 55641, 55596}, {53092, 55618, 55581}, {53093, 55648, 55603}, {53097, 55640, 55619}, {55587, 55643, 55623}, {55589, 55657, 55645}, {55594, 55657, 55646}, {55621, 55663, 55654}

X(55669) = X(2)X(33751)∩X(3)X(6)

Barycentrics    7*a^6-a^4*(b^2+c^2)-2*a^2*(3*b^4+7*b^2*c^2+3*c^4) : :
X(55669) = 3*X[2]+4*X[33751], 13*X[3]+X[6], -8*X[140]+X[48884], 6*X[376]+X[48904], 4*X[548]+3*X[38317], 6*X[549]+X[48898], 5*X[631]+2*X[48892], -X[1352]+15*X[15692], 5*X[1656]+2*X[48891], 5*X[3522]+2*X[19130], 27*X[3524]+X[14927], -8*X[3530]+X[3818] and many others

X(55669) lies on these lines: {2, 33751}, {3, 6}, {140, 48884}, {376, 48904}, {542, 15036}, {548, 38317}, {549, 48898}, {631, 48892}, {1352, 15692}, {1503, 44682}, {1656, 48891}, {3522, 19130}, {3523, 29012}, {3524, 14927}, {3526, 29323}, {3528, 29317}, {3530, 3818}, {3589, 46853}, {5054, 48889}, {5055, 48942}, {5476, 45759}, {5480, 34200}, {5651, 15246}, {5921, 33750}, {6636, 22112}, {6723, 7494}, {6776, 15705}, {7484, 32237}, {7485, 16187}, {8703, 48901}, {10168, 19708}, {10193, 36989}, {10299, 46264}, {10304, 48885}, {11178, 12100}, {11202, 15578}, {11645, 15700}, {12103, 51126}, {14093, 48872}, {14561, 21735}, {14869, 42786}, {14891, 50977}, {14893, 51134}, {15042, 16010}, {15055, 52098}, {15687, 51139}, {15688, 48920}, {15693, 36990}, {15696, 48895}, {15703, 50976}, {15707, 25561}, {15710, 51212}, {15711, 48876}, {15712, 39884}, {15714, 48874}, {15715, 50974}, {15717, 40330}, {15719, 51537}, {15759, 18583}, {17506, 19124}, {19924, 50969}, {21734, 31670}, {21766, 22352}, {32600, 46261}, {33923, 48880}, {50965, 51732}

X(55669) = midpoint of X(i) and X(j) for these {i,j}: {182, 55633}, {10541, 55639}, {15703, 50976}, {53092, 55607}, {6, 55602}
X(55669) = reflection of X(i) in X(j) for these {i,j}: {10541, 5092}, {3098, 55644}, {37517, 53858}, {42786, 14869}, {51141, 15700}, {52987, 55607}, {55605, 55633}, {55611, 55639}, {55616, 14810}, {55633, 55651}, {55644, 55658}, {55658, 3}
X(55669) = inverse of X(55657) in First Brocard Circle
X(55669) = center of Tucker-Hagos(1/7) circle
X(55669) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5481), X(55655)}}, {{A, B, C, X(40803), X(55594)}}
X(55669) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 33751, 48896}, {3, 12017, 55654}, {3, 1350, 55659}, {3, 14810, 55662}, {3, 3098, 55660}, {3, 31884, 55661}, {3, 5050, 55656}, {3, 5085, 55653}, {3, 511, 55658}, {3, 6, 55657}, {3, 55646, 55663}, {3, 55667, 55665}, {3, 55668, 55667}, {6, 55657, 55637}, {182, 37517, 53091}, {182, 52987, 5097}, {182, 55581, 6}, {182, 55608, 1351}, {182, 55637, 55581}, {182, 55648, 55596}, {511, 14810, 55616}, {511, 5092, 10541}, {511, 55639, 55611}, {511, 55658, 55644}, {548, 38317, 48879}, {575, 55625, 55584}, {575, 55646, 55603}, {575, 55663, 55646}, {576, 17508, 5092}, {576, 3098, 55589}, {576, 55600, 55580}, {1350, 5092, 182}, {1350, 55580, 55590}, {1350, 55611, 55605}, {1350, 55624, 55612}, {1350, 55629, 55615}, {1350, 55635, 3098}, {1350, 55649, 55635}, {1350, 55651, 55639}, {1350, 55659, 55649}, {1351, 14810, 55608}, {1351, 55608, 55587}, {1351, 55622, 55592}, {3098, 39561, 55583}, {3098, 55660, 55652}, {5050, 55631, 55585}, {5050, 55656, 55631}, {5085, 55607, 53092}, {5092, 14810, 15516}, {5092, 55631, 5050}, {5092, 55653, 44456}, {5092, 55657, 55588}, {5092, 55663, 55620}, {5093, 55641, 55601}, {5097, 55653, 55629}, {5102, 55632, 55597}, {10541, 55611, 576}, {10541, 55639, 511}, {10541, 55651, 1350}, {10541, 55659, 55633}, {11477, 55627, 55598}, {11482, 55618, 55586}, {11645, 15700, 51141}, {12017, 55606, 15520}, {12017, 55654, 55606}, {14810, 55592, 55622}, {14810, 55662, 55655}, {15516, 55659, 14810}, {17508, 55640, 5085}, {17508, 55660, 39561}, {17508, 55665, 3}, {20190, 31884, 37517}, {20190, 55661, 31884}, {22234, 55630, 33878}, {22330, 55634, 55593}, {31884, 37517, 55600}, {31884, 55580, 55609}, {33878, 55647, 55630}, {44456, 55615, 52987}, {44456, 55639, 55607}, {50664, 55650, 55610}, {52987, 55653, 55640}, {53093, 55643, 55594}, {53097, 55636, 55613}, {55584, 55646, 55625}, {55588, 55659, 55648}, {55594, 55643, 55628}, {55602, 55639, 55624}, {55606, 55654, 55642}, {55633, 55658, 55651}, {55649, 55667, 55664}

X(55670) = X(2)X(29323)∩X(3)X(6)

Barycentrics    a^2*(6*a^4-5*b^4-12*b^2*c^2-5*c^4-a^2*(b^2+c^2)) : :
X(55670) = 11*X[3]+X[6], -4*X[140]+X[48889], -4*X[549]+X[25561], X[597]+5*X[15714], 5*X[631]+X[48898], -X[1352]+13*X[10299], 5*X[1656]+X[48896], -X[2930]+13*X[15042], 5*X[3522]+X[48901], -7*X[3523]+X[3818], -7*X[3526]+X[48884], -7*X[3528]+X[48880] and many others

X(55670) lies on these lines: {2, 29323}, {3, 6}, {5, 33751}, {20, 48943}, {25, 12045}, {140, 48889}, {141, 30507}, {373, 6636}, {376, 38317}, {542, 17504}, {548, 19130}, {549, 25561}, {550, 48895}, {597, 15714}, {631, 48898}, {732, 46893}, {1352, 10299}, {1495, 33879}, {1503, 10193}, {1656, 48896}, {1843, 17506}, {2930, 15042}, {3522, 48901}, {3523, 3818}, {3524, 11645}, {3526, 48884}, {3528, 48880}, {3530, 24206}, {3534, 51137}, {3564, 14891}, {3589, 33923}, {3819, 6800}, {3853, 51127}, {5066, 51139}, {5476, 19708}, {5480, 46853}, {5650, 15246}, {5965, 15711}, {7485, 15082}, {7509, 46847}, {7998, 9544}, {8703, 29317}, {8705, 37968}, {8718, 15030}, {9909, 10219}, {10168, 29181}, {10282, 15578}, {10303, 42786}, {10304, 14561}, {10516, 15693}, {10519, 15705}, {11178, 15700}, {11179, 15715}, {11180, 15692}, {11204, 23041}, {11812, 50971}, {12584, 15036}, {14853, 46267}, {14994, 43459}, {15051, 32305}, {15462, 43391}, {15686, 25565}, {15688, 53023}, {15696, 47355}, {15698, 25406}, {15704, 51126}, {15710, 38064}, {15712, 18553}, {15716, 43273}, {15717, 46264}, {15720, 48905}, {15759, 50983}, {18382, 32903}, {19124, 35472}, {19709, 50976}, {19711, 47354}, {19924, 38110}, {20301, 38726}, {21734, 48873}, {21735, 31670}, {25555, 48881}, {32237, 40916}, {33699, 51134}, {33884, 34986}, {35475, 44091}, {47353, 51141}

X(55670) = midpoint of X(i) and X(j) for these {i,j}: {182, 31884}, {1350, 15520}, {1351, 55589}, {11204, 23041}, {20190, 55645}, {25406, 50977}, {3, 17508}, {376, 38317}, {3098, 5050}, {38225, 52995}, {39561, 55610}, {48880, 51538}, {575, 55615}, {576, 55593}, {5085, 55649}, {5092, 55657}, {5093, 55596}, {5102, 52987}, {50664, 55621}, {6, 55603}
X(55670) = reflection of X(i) in X(j) for these {i,j}: {1350, 55621}, {14810, 55657}, {14853, 46267}, {15520, 50664}, {3, 55664}, {3098, 55645}, {31884, 55653}, {5050, 20190}, {5092, 17508}, {5097, 5050}, {5102, 15516}, {55586, 55593}, {55589, 55601}, {55590, 55603}, {55593, 55612}, {55594, 55615}, {55599, 55627}, {55603, 55631}, {55606, 31884}, {55610, 55638}, {55615, 14810}, {55621, 55647}, {55627, 55649}, {55645, 55659}, {55649, 55663}, {55657, 3}, {55664, 55668}
X(55670) = inverse of X(55655) in First Brocard Circle
X(55670) = center of Tucker-Hagos(1/6) circle
X(55670) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55655)}}, {{A, B, C, X(6), X(54917)}}, {{A, B, C, X(54), X(34571)}}, {{A, B, C, X(3431), X(14075)}}, {{A, B, C, X(5481), X(55653)}}, {{A, B, C, X(40801), X(55656)}}, {{A, B, C, X(41940), X(46848)}}
X(55670) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10541, 55652}, {3, 12017, 55651}, {3, 1350, 55658}, {3, 1351, 55656}, {3, 14810, 55661}, {3, 182, 55653}, {3, 20190, 55650}, {3, 3098, 55659}, {3, 45552, 43127}, {3, 45553, 43126}, {3, 5050, 55654}, {3, 5085, 55649}, {3, 5092, 14810}, {3, 6, 55655}, {3, 55646, 55662}, {3, 55649, 55663}, {3, 55667, 55664}, {3, 55668, 55666}, {3, 55669, 55668}, {5, 33751, 48891}, {5, 48891, 48942}, {6, 55655, 55631}, {140, 48892, 48889}, {182, 3098, 11477}, {182, 33878, 22330}, {182, 53092, 50664}, {182, 55583, 6}, {182, 55592, 5097}, {182, 55596, 5093}, {182, 55644, 33878}, {182, 55648, 55592}, {182, 55649, 55596}, {182, 55653, 55606}, {182, 55655, 55616}, {182, 55658, 55628}, {511, 14810, 55615}, {511, 50664, 15520}, {511, 55593, 55586}, {511, 55603, 55590}, {511, 55612, 55593}, {511, 55631, 55603}, {548, 19130, 48920}, {576, 55646, 55612}, {576, 55662, 55646}, {1350, 15520, 511}, {1350, 55640, 55621}, {1350, 55647, 55634}, {1350, 55658, 55647}, {1351, 55618, 55589}, {1351, 55637, 55601}, {1351, 55656, 55637}, {3098, 22234, 55584}, {3589, 33923, 48885}, {5050, 55643, 55595}, {5085, 55591, 5050}, {5085, 55610, 39561}, {5085, 55654, 55591}, {5085, 55657, 55599}, {5092, 55661, 55594}, {5102, 55651, 55624}, {5116, 15513, 41413}, {10541, 55629, 37517}, {10541, 55652, 55597}, {11477, 55595, 55583}, {11477, 55606, 55588}, {11477, 55648, 3098}, {11477, 55654, 31884}, {11477, 55660, 55645}, {11482, 55607, 55581}, {12017, 52987, 15516}, {12017, 55624, 5102}, {12017, 55651, 52987}, {14810, 55594, 55623}, {14810, 55599, 55627}, {15516, 55651, 55619}, {15520, 55640, 1350}, {15520, 55658, 55640}, {15696, 47355, 48904}, {17508, 55649, 5085}, {17508, 55654, 20190}, {17508, 55660, 182}, {17508, 55664, 55657}, {17508, 55665, 55660}, {17508, 55667, 3}, {17508, 55669, 55667}, {20190, 53094, 5092}, {20190, 55588, 575}, {21158, 21159, 21163}, {22330, 55653, 55625}, {31884, 33878, 55613}, {31884, 55654, 55648}, {37517, 55652, 55629}, {39561, 55649, 55610}, {44456, 55641, 55608}, {53091, 55626, 55585}, {53093, 55639, 55587}, {53097, 55633, 55609}, {55587, 55639, 55617}, {55589, 55637, 55618}, {55590, 55657, 55643}, {55593, 55646, 55630}, {55610, 55649, 55638}, {55625, 55653, 55644}, {55653, 55668, 55665}

X(55671) = X(3)X(6)∩X(4)X(51127)

Barycentrics    a^2*(11*a^4-9*b^4-22*b^2*c^2-9*c^4-2*a^2*(b^2+c^2)) : :
X(55671) = 10*X[3]+X[6], -5*X[4]+16*X[51127], -2*X[141]+13*X[10299], 5*X[376]+6*X[48310], 3*X[381]+8*X[33751], 8*X[548]+3*X[53023], -12*X[549]+X[36990], 4*X[550]+7*X[47355], 2*X[597]+9*X[15710], -X[599]+12*X[17504], 10*X[631]+X[48905], -X[1352]+12*X[12100] and many others

X(55671) lies on these lines: {3, 6}, {4, 51127}, {141, 10299}, {154, 15246}, {376, 48310}, {381, 33751}, {524, 15715}, {542, 15716}, {548, 53023}, {549, 36990}, {550, 47355}, {597, 15710}, {599, 17504}, {631, 48905}, {1352, 12100}, {1353, 50973}, {1503, 15717}, {3066, 6636}, {3242, 17502}, {3522, 48910}, {3523, 10516}, {3524, 20582}, {3526, 48892}, {3528, 3589}, {3529, 51126}, {3530, 3763}, {3796, 21766}, {3851, 48891}, {5054, 48898}, {5055, 48896}, {5070, 29323}, {5071, 51139}, {5480, 10304}, {5646, 6030}, {5921, 15692}, {5925, 31267}, {6776, 15698}, {7484, 44082}, {7492, 31860}, {7716, 32534}, {8567, 23041}, {8703, 38072}, {11160, 15705}, {11179, 15711}, {11645, 15718}, {11737, 51167}, {12584, 15042}, {14093, 48885}, {14561, 33923}, {14891, 48876}, {14982, 48375}, {15051, 16010}, {15069, 21167}, {15681, 51137}, {15688, 48901}, {15689, 48904}, {15693, 24206}, {15694, 48889}, {15695, 48920}, {15696, 38317}, {15700, 21358}, {15702, 50971}, {15708, 51537}, {15712, 46264}, {15714, 20423}, {15720, 29012}, {15759, 38064}, {16419, 32237}, {17811, 44110}, {18583, 45759}, {19708, 54131}, {19709, 48942}, {21734, 48881}, {21735, 29181}, {22112, 44106}, {23253, 36701}, {23263, 36703}, {23269, 36717}, {23275, 36702}, {31663, 38315}, {31670, 46853}, {32217, 37948}, {32600, 52100}, {34200, 47352}, {35228, 52028}, {38079, 46332}, {38633, 52098}, {40916, 41424}, {46219, 48884}, {50983, 51212}

X(55671) = midpoint of X(i) and X(j) for these {i,j}: {182, 55635}
X(55671) = reflection of X(i) in X(j) for these {i,j}: {1350, 55622}, {3, 55665}, {55620, 55642}, {55622, 55648}, {55632, 55652}, {55641, 55656}, {55648, 55662}, {55656, 3}
X(55671) = inverse of X(55654) in First Brocard Circle
X(55671) = center of Tucker-Hagos(2/11) circle
X(55671) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(64), X(5041)}}, {{A, B, C, X(1297), X(55656)}}, {{A, B, C, X(9605), X(11270)}}, {{A, B, C, X(40801), X(55655)}}
X(55671) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12017, 55649}, {3, 182, 55651}, {3, 33878, 55657}, {3, 5050, 55653}, {3, 5085, 55646}, {3, 511, 55656}, {3, 6, 55654}, {3, 55610, 55658}, {3, 55629, 55659}, {3, 55639, 55660}, {3, 55643, 55661}, {3, 55648, 55662}, {182, 14810, 55584}, {182, 55635, 511}, {182, 55655, 55612}, {182, 55662, 55635}, {182, 55669, 55666}, {511, 55652, 55632}, {575, 55639, 55591}, {575, 55660, 55639}, {576, 55643, 55607}, {576, 55661, 55643}, {1350, 1351, 55582}, {1350, 14810, 55626}, {1350, 53093, 1351}, {1350, 53094, 5085}, {1350, 55641, 55622}, {1350, 55654, 14810}, {1351, 31884, 1350}, {1351, 53091, 22330}, {1351, 55648, 55620}, {1351, 55655, 31884}, {3098, 10541, 5102}, {5050, 55653, 55614}, {5085, 55646, 11477}, {5092, 55612, 182}, {5092, 55647, 39561}, {5092, 55663, 52987}, {5097, 14810, 55601}, {5097, 55649, 55616}, {10541, 22330, 53093}, {11477, 55646, 55618}, {12017, 55601, 6}, {12017, 55616, 5097}, {12017, 55649, 53097}, {14810, 55605, 55629}, {14810, 55617, 55633}, {14810, 55652, 55648}, {14810, 55663, 55655}, {15516, 55633, 33878}, {15520, 55636, 55595}, {17508, 52987, 5092}, {17508, 55658, 20190}, {17508, 55665, 55652}, {17508, 55667, 55663}, {17508, 55668, 3}, {20190, 55658, 55610}, {31884, 55642, 55641}, {34200, 47352, 50968}, {37517, 55650, 55624}, {39561, 55647, 55604}, {50664, 55644, 55593}, {55584, 55629, 55605}, {55655, 55669, 55667}

X(55672) = X(2)X(48884)∩X(3)X(6)

Barycentrics    5*a^6-a^4*(b^2+c^2)-2*a^2*(2*b^4+5*b^2*c^2+2*c^4) : :
X(55672) = -6*X[2]+X[48884], 9*X[3]+X[6], X[4]+4*X[33751], 4*X[5]+X[48896], -X[66]+6*X[10193], -X[69]+21*X[15698], -12*X[140]+7*X[42786], -X[141]+6*X[12100], 2*X[206]+3*X[11204], 3*X[376]+2*X[19130], 3*X[381]+2*X[48891], 4*X[548]+X[48901] and many others

X(55672) lies on these lines: {2, 48884}, {3, 6}, {4, 33751}, {5, 48896}, {30, 51126}, {66, 10193}, {69, 15698}, {74, 7954}, {140, 42786}, {141, 12100}, {184, 41462}, {206, 11204}, {376, 19130}, {378, 44091}, {381, 48891}, {524, 15711}, {542, 3620}, {548, 48901}, {549, 3818}, {550, 38317}, {597, 15759}, {599, 15716}, {631, 29012}, {1176, 20421}, {1352, 15717}, {1495, 7485}, {1503, 15712}, {1656, 29323}, {1843, 35472}, {1974, 35473}, {2777, 31267}, {3431, 41435}, {3506, 54439}, {3522, 29317}, {3523, 24206}, {3524, 3619}, {3526, 48889}, {3528, 14561}, {3530, 18358}, {3534, 47355}, {3589, 8703}, {3618, 19708}, {3630, 14891}, {3631, 17504}, {3763, 11645}, {3819, 26864}, {3845, 51127}, {3851, 48942}, {3867, 37934}, {4550, 32600}, {5054, 48905}, {5476, 34200}, {5480, 33923}, {5651, 5888}, {6636, 11451}, {6688, 31860}, {6759, 15578}, {7492, 10545}, {7496, 10546}, {7896, 42787}, {7931, 9774}, {9306, 15080}, {10168, 10304}, {10219, 20850}, {10298, 41464}, {10299, 39874}, {11001, 25565}, {11008, 15715}, {11179, 15705}, {11202, 44883}, {11539, 50971}, {11812, 51128}, {12041, 52098}, {12112, 15058}, {13624, 49465}, {14269, 50976}, {14458, 16988}, {15066, 22352}, {15107, 43650}, {15681, 48943}, {15688, 48910}, {15690, 48310}, {15699, 51139}, {15700, 18440}, {15701, 25561}, {15706, 43150}, {15710, 20423}, {15718, 47353}, {15720, 36990}, {16192, 38029}, {16419, 41424}, {16491, 35242}, {18570, 19137}, {19121, 35493}, {19124, 21844}, {19128, 23040}, {19711, 20582}, {20301, 38723}, {21167, 34507}, {21735, 25555}, {21850, 45759}, {25406, 40107}, {25563, 36989}, {29181, 46853}, {32068, 33522}, {32273, 38726}, {37126, 52093}, {41454, 43149}, {41983, 47354}, {42112, 44461}, {42113, 44465}, {44245, 51163}, {46945, 54992}, {47598, 51022}, {48920, 53023}, {50988, 51165}, {51140, 54169}

X(55672) = midpoint of X(i) and X(j) for these {i,j}: {182, 55637}, {1350, 11482}, {12017, 55646}, {22234, 55608}, {3, 53094}, {575, 55619}, {5092, 55661}, {53091, 55614}, {53093, 55629}, {6, 55604}
X(55672) = reflection of X(i) in X(j) for these {i,j}: {1350, 55623}, {12017, 5092}, {22234, 182}, {3, 55666}, {3098, 55646}, {576, 53091}, {52987, 55608}, {55587, 55595}, {55595, 55619}, {55598, 3098}, {55600, 55629}, {55604, 55634}, {55608, 55637}, {55614, 14810}, {55629, 55650}, {55634, 55653}, {55637, 55655}, {55646, 55661}, {55655, 3}
X(55672) = inverse of X(55653) in First Brocard Circle
X(55672) = isogonal conjugate of X(54582)
X(55672) = center of Tucker-Hagos(1/5) circle
X(55672) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55653)}}, {{A, B, C, X(4), X(41940)}}, {{A, B, C, X(6), X(54477)}}, {{A, B, C, X(39), X(20421)}}, {{A, B, C, X(69), X(15860)}}, {{A, B, C, X(74), X(7772)}}, {{A, B, C, X(1297), X(55655)}}, {{A, B, C, X(2420), X(7954)}}, {{A, B, C, X(3431), X(5007)}}, {{A, B, C, X(5041), X(11738)}}, {{A, B, C, X(5158), X(41435)}}
X(55672) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 48892, 48884}, {3, 10541, 55647}, {3, 12017, 55646}, {3, 1350, 55657}, {3, 1351, 55654}, {3, 14810, 55660}, {3, 31884, 55659}, {3, 33878, 55656}, {3, 43118, 43127}, {3, 43119, 43126}, {3, 5050, 55651}, {3, 5085, 14810}, {3, 511, 55655}, {3, 53093, 55650}, {3, 575, 55652}, {3, 6, 55653}, {3, 55646, 55661}, {3, 55649, 55662}, {3, 55651, 55663}, {3, 55668, 55665}, {3, 55670, 55669}, {3, 55671, 55670}, {6, 55639, 55594}, {15, 16, 7772}, {182, 14810, 55581}, {182, 52987, 15520}, {182, 55603, 576}, {182, 55642, 55585}, {182, 55662, 55633}, {187, 574, 13356}, {371, 372, 41940}, {376, 19130, 48879}, {511, 14810, 55614}, {511, 5092, 12017}, {511, 55619, 55595}, {511, 55629, 55600}, {511, 55634, 55604}, {511, 55650, 55629}, {511, 55653, 55634}, {550, 38317, 48904}, {575, 55659, 31884}, {576, 55669, 55664}, {1350, 20190, 39561}, {1350, 55657, 55644}, {1351, 55607, 55586}, {1351, 55631, 55596}, {1351, 55654, 55631}, {3098, 55587, 55601}, {3098, 55596, 55607}, {3098, 55601, 55611}, {3098, 55640, 55632}, {3098, 55644, 55636}, {3098, 55653, 55642}, {3524, 11178, 51141}, {3528, 14561, 48885}, {3534, 47355, 48895}, {3589, 8703, 48880}, {5050, 55632, 55582}, {5050, 55651, 55606}, {5050, 55663, 55640}, {5085, 33878, 50664}, {5092, 55659, 44456}, {5092, 55670, 55668}, {5093, 55626, 55590}, {5097, 55647, 55610}, {5102, 55616, 55588}, {5116, 5206, 5039}, {5888, 7712, 5651}, {6200, 6396, 39}, {6411, 12963, 6200}, {6411, 6412, 15815}, {6412, 12968, 6396}, {7496, 35268, 16187}, {10541, 55610, 5097}, {10541, 55647, 55583}, {10645, 10646, 574}, {10645, 41407, 42116}, {10646, 41406, 42115}, {11477, 55612, 55589}, {11477, 55643, 55612}, {11480, 11481, 22332}, {11482, 55655, 55630}, {12017, 33878, 53091}, {12017, 53094, 5092}, {12017, 55598, 22234}, {12017, 55604, 6}, {12017, 55637, 37517}, {12017, 55646, 511}, {12017, 55655, 55598}, {12017, 55658, 55608}, {12017, 55661, 3098}, {12974, 12975, 13334}, {14810, 50664, 33878}, {14810, 55597, 55624}, {14810, 55603, 55628}, {14810, 55664, 3}, {15516, 55627, 53097}, {15516, 55648, 55605}, {15520, 55633, 52987}, {15520, 55649, 55613}, {15717, 33750, 1352}, {17508, 55660, 5085}, {17508, 55664, 55603}, {17508, 55666, 55637}, {17508, 55667, 55649}, {17508, 55668, 55658}, {17508, 55670, 55667}, {20190, 39561, 182}, {20190, 55623, 11482}, {20190, 55657, 1350}, {22330, 55615, 55584}, {31884, 55595, 55619}, {39561, 55655, 55623}, {44456, 55601, 55587}, {50664, 55653, 55609}, {53097, 55648, 55627}, {55580, 55622, 55599}, {55584, 55641, 55615}, {55588, 55638, 55616}, {55590, 55645, 55626}, {55594, 55653, 55639}, {55610, 55647, 55635}, {55655, 55669, 55666}

X(55673) = X(2)X(50960)∩X(3)X(6)

Barycentrics    a^2*(9*a^4-7*b^4-18*b^2*c^2-7*c^4-2*a^2*(b^2+c^2)) : :
X(55673) = -17*X[2]+8*X[50960], 8*X[3]+X[6], 2*X[20]+7*X[47355], 8*X[140]+X[48905], -2*X[141]+11*X[15717], 4*X[206]+5*X[8567], X[382]+8*X[33751], -4*X[549]+X[10516], -X[599]+10*X[15692], -10*X[631]+X[36990], -X[1352]+10*X[15712], 2*X[1386]+7*X[16192] and many others

X(55673) lies on these lines: {2, 50960}, {3, 6}, {20, 47355}, {140, 48905}, {141, 15717}, {154, 5650}, {165, 38315}, {206, 8567}, {376, 53023}, {382, 33751}, {524, 15705}, {542, 15706}, {548, 38136}, {549, 10516}, {599, 15692}, {631, 36990}, {1352, 15712}, {1386, 16192}, {1495, 5646}, {1498, 15578}, {1503, 3524}, {1656, 48892}, {2916, 17928}, {2930, 15051}, {3070, 36717}, {3071, 36702}, {3146, 51126}, {3242, 7987}, {3522, 3589}, {3523, 3763}, {3526, 48898}, {3528, 5480}, {3530, 46264}, {3534, 38317}, {3564, 17504}, {3618, 21734}, {3796, 7998}, {3818, 15720}, {3830, 50976}, {3832, 51127}, {3843, 48891}, {3851, 48896}, {5054, 29012}, {5055, 29323}, {5070, 48884}, {5476, 50968}, {5621, 15035}, {5895, 31267}, {6090, 22352}, {6636, 17825}, {6800, 15246}, {7464, 46945}, {7484, 35268}, {7485, 26881}, {7503, 16936}, {7509, 15811}, {7516, 33540}, {7716, 15750}, {8703, 14561}, {8705, 37941}, {10168, 14093}, {10304, 29181}, {10519, 15533}, {10606, 23041}, {11178, 15718}, {11179, 14891}, {11645, 15707}, {12100, 43273}, {12834, 33586}, {13910, 42637}, {13972, 42638}, {14853, 19708}, {14912, 15715}, {14927, 34573}, {15055, 52697}, {15069, 44682}, {15688, 29317}, {15690, 50988}, {15693, 47353}, {15696, 19130}, {15697, 50959}, {15711, 50986}, {15716, 50977}, {15719, 47354}, {15740, 16775}, {15759, 20423}, {16776, 38444}, {17821, 44883}, {19649, 37682}, {20780, 42316}, {21735, 48881}, {22112, 31860}, {23251, 36701}, {23261, 36703}, {31670, 33923}, {32600, 33541}, {33534, 49671}, {33884, 37672}, {34200, 38110}, {38064, 45759}, {38079, 41982}, {38942, 45308}, {41106, 51167}, {43174, 49679}, {43621, 44245}, {46219, 48889}, {46853, 48873}, {50693, 51163}, {50965, 51185}, {50984, 51186}, {50989, 51136}, {51128, 51537}, {51138, 54174}

X(55673) = midpoint of X(i) and X(j) for these {i,j}: {182, 55640}, {17508, 55667}, {3524, 33750}, {39561, 55613}, {5050, 55624}, {5085, 55654}
X(55673) = reflection of X(i) in X(j) for these {i,j}: {1350, 55624}, {3, 55667}, {31884, 55654}, {55593, 55613}, {55610, 55640}, {55613, 14810}, {55618, 55643}, {55624, 55649}, {55640, 55657}, {55643, 55660}, {55654, 3}, {55667, 55670}
X(55673) = inverse of X(55651) in First Brocard Circle
X(55673) = isogonal conjugate of X(54706)
X(55673) = center of Tucker-Hagos(2/9) circle
X(55673) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(74), X(22246)}}, {{A, B, C, X(3532), X(9605)}}, {{A, B, C, X(5481), X(55646)}}, {{A, B, C, X(7772), X(43691)}}, {{A, B, C, X(14528), X(43136)}}, {{A, B, C, X(15851), X(34817)}}, {{A, B, C, X(34130), X(38010)}}, {{A, B, C, X(40801), X(55653)}}
X(55673) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11482, 55652}, {3, 12017, 14810}, {3, 1350, 55656}, {3, 1351, 55653}, {3, 17508, 5085}, {3, 182, 55646}, {3, 20190, 55641}, {3, 33878, 55655}, {3, 511, 55654}, {3, 53092, 55650}, {3, 6, 55651}, {3, 55610, 55657}, {3, 55629, 55658}, {3, 55639, 55659}, {3, 55643, 55660}, {3, 55648, 55661}, {3, 55672, 55671}, {15, 16, 22246}, {182, 55594, 11482}, {182, 55610, 5102}, {182, 55619, 1351}, {182, 55631, 44456}, {182, 55649, 55589}, {182, 55652, 55594}, {511, 14810, 55613}, {511, 55643, 55618}, {511, 55649, 55624}, {511, 55657, 55640}, {511, 55660, 55643}, {511, 55670, 55667}, {575, 55629, 55582}, {575, 55645, 55596}, {575, 55658, 55629}, {576, 55649, 55615}, {576, 55659, 55639}, {1151, 1152, 9605}, {1350, 11477, 55585}, {1350, 5085, 5050}, {1350, 5092, 10541}, {1350, 55646, 55631}, {1350, 55649, 31884}, {1350, 55671, 55669}, {1351, 55653, 55626}, {3098, 15516, 55580}, {3522, 3589, 48872}, {3524, 33750, 1503}, {5050, 5093, 15516}, {5085, 17508, 53094}, {5085, 5102, 182}, {5092, 55585, 12017}, {5092, 55659, 576}, {5092, 55670, 55664}, {5097, 55644, 55604}, {5102, 55622, 55591}, {6409, 6410, 5013}, {10541, 53094, 5092}, {10541, 55656, 1350}, {11477, 14810, 55607}, {11477, 55600, 53097}, {11480, 11481, 5024}, {12017, 14810, 11477}, {12017, 55593, 39561}, {12017, 55607, 6}, {14810, 39561, 55593}, {14810, 55585, 55620}, {14810, 55665, 3}, {15516, 55664, 55663}, {15520, 55627, 33878}, {15520, 55649, 55611}, {15520, 55655, 55627}, {15692, 25406, 21167}, {17508, 55666, 5093}, {17508, 55667, 511}, {17508, 55668, 55610}, {17508, 55669, 55649}, {17508, 55672, 55670}, {20190, 55627, 15520}, {31884, 55591, 55614}, {31884, 55610, 55622}, {37517, 55647, 55616}, {50664, 55584, 53858}, {50664, 55637, 55584}, {52987, 55661, 55648}, {53092, 55632, 55587}, {55587, 55650, 55632}, {55588, 55653, 55635}, {55593, 55610, 55600}, {55657, 55670, 55668}

X(55674) = X(2)X(32237)∩X(3)X(6)

Barycentrics    a^2*(4*a^4-3*b^4-8*b^2*c^2-3*c^4-a^2*(b^2+c^2)) : :
X(55674) = 7*X[3]+X[6], X[20]+3*X[38317], -X[141]+5*X[15712], 3*X[376]+X[48901], 3*X[381]+X[48896], X[597]+3*X[45759], -X[599]+9*X[15706], -5*X[631]+X[3818], -X[1352]+9*X[3524], X[1353]+15*X[15711], -5*X[1656]+X[48884], X[1657]+7*X[47355] and many others

X(55674) lies on these lines: {2, 32237}, {3, 6}, {4, 48891}, {5, 29323}, {20, 38317}, {22, 6688}, {25, 10219}, {30, 25565}, {110, 3819}, {140, 17712}, {141, 15712}, {184, 21766}, {373, 7492}, {376, 48901}, {381, 48896}, {524, 14891}, {542, 12100}, {547, 50971}, {548, 3589}, {549, 11645}, {550, 19130}, {597, 45759}, {599, 15706}, {631, 3818}, {1352, 3524}, {1353, 15711}, {1495, 7496}, {1503, 3530}, {1656, 48884}, {1657, 47355}, {1843, 21844}, {1974, 35477}, {1995, 12045}, {2393, 37283}, {2916, 43809}, {3292, 41462}, {3357, 23041}, {3522, 14561}, {3523, 18553}, {3525, 42786}, {3526, 48905}, {3528, 31670}, {3534, 48904}, {3618, 21735}, {3627, 51126}, {3850, 51127}, {3917, 11003}, {5054, 25561}, {5476, 10304}, {5480, 8703}, {5621, 15040}, {5650, 15080}, {5651, 7485}, {5888, 35265}, {5921, 15717}, {5943, 6636}, {5965, 54201}, {5972, 43957}, {5999, 9751}, {6000, 15578}, {6676, 6723}, {6776, 15692}, {6781, 53484}, {7484, 16187}, {7509, 44870}, {7514, 8717}, {7516, 46261}, {7525, 11695}, {7550, 46847}, {7712, 33879}, {7771, 14994}, {7793, 41622}, {7915, 40278}, {9822, 37814}, {10124, 51139}, {10282, 44883}, {10299, 25406}, {10516, 15720}, {11178, 15693}, {11179, 15698}, {11204, 19149}, {11579, 15036}, {11649, 37968}, {11898, 15716}, {12083, 13570}, {12108, 34573}, {12215, 43459}, {12294, 35473}, {12584, 15051}, {13367, 45308}, {14093, 47352}, {14853, 21734}, {14865, 44091}, {14926, 54006}, {15035, 32305}, {15041, 52098}, {15055, 19140}, {15062, 32600}, {15684, 50976}, {15686, 48310}, {15688, 48872}, {15691, 50959}, {15695, 38072}, {15696, 48879}, {15700, 43273}, {15702, 51537}, {15705, 54173}, {15707, 47353}, {15714, 50965}, {15718, 21358}, {15721, 50975}, {15759, 41153}, {16163, 20301}, {16165, 44321}, {16197, 44862}, {17504, 48876}, {18583, 19924}, {19121, 35497}, {19124, 32534}, {19708, 38064}, {20582, 41983}, {20791, 41398}, {21167, 40107}, {22467, 43129}, {22712, 32429}, {22802, 31267}, {23042, 34778}, {23329, 36989}, {24256, 32456}, {24295, 29113}, {25555, 29181}, {31666, 49465}, {32149, 35925}, {32217, 34152}, {32273, 38723}, {32416, 47342}, {33749, 34380}, {33884, 44109}, {34236, 37184}, {35242, 38029}, {35268, 40916}, {36201, 46265}, {36697, 48940}, {36699, 48902}, {36705, 48938}, {38110, 46853}, {42421, 44562}, {42785, 51538}, {43576, 44832}, {43621, 50693}, {44903, 51134}

X(55674) = midpoint of X(i) and X(j) for these {i,j}: {182, 14810}, {10282, 44883}, {1350, 5097}, {1351, 55590}, {1657, 48943}, {11477, 55586}, {12017, 55650}, {15516, 55612}, {15520, 55599}, {15691, 50959}, {16163, 20301}, {17508, 55670}, {18553, 46264}, {20, 48895}, {20190, 55653}, {22330, 55601}, {24206, 44882}, {3, 5092}, {34200, 50983}, {37517, 55588}, {39561, 55615}, {4, 48891}, {40107, 48906}, {48889, 48898}, {48896, 48942}, {48901, 48920}, {5, 48892}, {547, 50971}, {548, 3589}, {5050, 55627}, {550, 19130}, {575, 3098}, {576, 55594}, {5085, 55657}, {5188, 44423}, {5480, 48885}, {50664, 55631}, {53091, 55619}, {53093, 55634}, {53094, 55666}, {6, 55606}, {8703, 10168}
X(55674) = reflection of X(i) in X(j) for these {i,j}: {10124, 51139}, {1350, 55625}, {14810, 55659}, {15516, 182}, {20190, 5092}, {22330, 50664}, {3, 55668}, {3098, 55647}, {3850, 51127}, {34573, 12108}, {46267, 50983}, {50664, 20190}, {52987, 55609}, {55592, 55612}, {55594, 55617}, {55597, 3098}, {55601, 55631}, {55606, 55636}, {55612, 14810}, {55621, 55649}, {55631, 55653}, {55638, 55657}, {55645, 55663}, {55653, 3}, {55663, 55664}, {55664, 55670}
X(55674) = inverse of X(55649) in First Brocard Circle
X(55674) = complement of X(48889)
X(55674) = isogonal conjugate of X(54890)
X(55674) = center of Tucker-Hagos(1/4) circle
X(55674) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(29316)}}, {{A, B, C, X(1297), X(55653)}}, {{A, B, C, X(5481), X(14810)}}, {{A, B, C, X(7772), X(13452)}}, {{A, B, C, X(9605), X(44763)}}, {{A, B, C, X(40803), X(52987)}}
X(55674) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 48898, 48889}, {3, 10541, 55637}, {3, 11477, 55652}, {3, 12017, 31884}, {3, 1350, 55655}, {3, 3098, 55657}, {3, 31884, 55658}, {3, 33878, 55654}, {3, 371, 43126}, {3, 372, 43127}, {3, 5050, 55646}, {3, 50664, 55645}, {3, 53091, 55648}, {3, 53093, 55644}, {3, 576, 55650}, {3, 6, 55649}, {3, 55610, 55656}, {3, 55646, 55660}, {3, 55649, 55661}, {3, 55668, 55664}, {3, 55673, 55672}, {5, 48892, 29323}, {6, 55618, 55580}, {20, 38317, 48895}, {182, 1350, 5097}, {182, 1351, 575}, {182, 15516, 50664}, {182, 17508, 53094}, {182, 3098, 1351}, {182, 511, 15516}, {182, 53094, 5092}, {182, 55587, 6}, {182, 55592, 22330}, {182, 55649, 55587}, {182, 55655, 1350}, {182, 55658, 55608}, {182, 55660, 55616}, {182, 55667, 55662}, {182, 55672, 55669}, {376, 48901, 48920}, {381, 48896, 48942}, {511, 3098, 55597}, {511, 55649, 55621}, {548, 3589, 29317}, {549, 44882, 24206}, {575, 55650, 55602}, {1350, 1351, 55581}, {1350, 14810, 55625}, {1350, 55581, 55590}, {1350, 55625, 55612}, {1350, 55633, 55619}, {1350, 55648, 55633}, {1350, 55655, 14810}, {1351, 5085, 182}, {1351, 55602, 55584}, {1351, 55629, 55593}, {1351, 55651, 3098}, {1351, 55659, 55638}, {1351, 55671, 55667}, {1495, 7496, 15082}, {3098, 15520, 53097}, {3098, 55593, 55606}, {3098, 55649, 55641}, {3522, 14561, 48880}, {3523, 33750, 46264}, {5050, 55646, 52987}, {5050, 55660, 55627}, {5085, 55643, 15520}, {5085, 55646, 53858}, {5092, 55594, 12017}, {5093, 55614, 55585}, {5102, 55604, 55583}, {5206, 50659, 41413}, {5351, 5352, 31652}, {5480, 8703, 48885}, {8160, 8161, 3095}, {10168, 48885, 5480}, {10541, 33878, 39561}, {10541, 55654, 33878}, {11477, 55586, 511}, {11477, 55603, 55586}, {11477, 55639, 55603}, {11477, 55652, 55623}, {11482, 55632, 55591}, {12017, 31884, 576}, {12017, 55658, 55594}, {13349, 13350, 13334}, {14810, 15516, 55592}, {14810, 55584, 55617}, {14810, 55606, 55629}, {14810, 55612, 55631}, {14810, 55627, 55635}, {14810, 55629, 55636}, {14810, 55651, 55647}, {14810, 55657, 55651}, {14810, 55659, 55653}, {14810, 55666, 3}, {14810, 55670, 55666}, {14810, 55671, 55668}, {15516, 55664, 55659}, {15516, 55666, 55663}, {15520, 55643, 55599}, {15686, 50988, 48310}, {15696, 53023, 48879}, {15718, 21358, 51141}, {17508, 55667, 5085}, {17508, 55668, 20190}, {17508, 55673, 55670}, {19924, 50983, 46267}, {20190, 55663, 55601}, {22234, 55596, 44456}, {22234, 55642, 55596}, {24206, 44882, 11645}, {33878, 55622, 55605}, {33878, 55637, 55615}, {34200, 50983, 19924}, {37517, 55610, 55588}, {37517, 55644, 55610}, {37517, 55656, 55634}, {38110, 46853, 48881}, {43141, 43144, 9737}, {44682, 48906, 21167}, {45498, 45499, 30270}, {52987, 55627, 55609}, {53092, 55624, 55582}, {53093, 55610, 37517}, {53094, 55673, 55671}, {55580, 55618, 55598}, {55582, 55624, 55600}, {55583, 55630, 55604}, {55585, 55640, 55614}, {55589, 55628, 55607}, {55591, 55632, 55611}, {55596, 55642, 55626}, {55599, 55657, 55643}, {55603, 55652, 55639}, {55605, 55637, 55622}, {55606, 55670, 55665}

X(55675) = X(3)X(6)∩X(5)X(50971)

Barycentrics    11*a^6-3*a^4*(b^2+c^2)-2*a^2*(4*b^4+11*b^2*c^2+4*c^4) : :
X(55675) = 19*X[3]+3*X[6], 5*X[5]+6*X[50971], 8*X[546]+3*X[48896], -14*X[3090]+3*X[48884], 5*X[3091]+6*X[48892], 5*X[3522]+6*X[10168], -14*X[3523]+3*X[11178], 7*X[3528]+4*X[25555], -X[3529]+12*X[33751], -32*X[3530]+21*X[51141], 8*X[3628]+3*X[48898], -3*X[3818]+14*X[14869] and many others

X(55675) lies on these lines: {3, 6}, {5, 50971}, {542, 15717}, {546, 48896}, {3090, 48884}, {3091, 48892}, {3522, 10168}, {3523, 11178}, {3525, 29012}, {3528, 25555}, {3529, 33751}, {3530, 51141}, {3628, 48898}, {3818, 14869}, {5072, 29323}, {5076, 48891}, {5476, 33923}, {7496, 26881}, {9968, 11204}, {10299, 40107}, {11579, 15023}, {11645, 15720}, {12100, 34507}, {12102, 51126}, {12103, 48904}, {12108, 44882}, {15704, 38317}, {17538, 19130}, {19924, 21735}, {21734, 38064}, {24206, 33750}, {25565, 33703}, {41462, 43814}, {44245, 48901}, {44682, 50977}, {46853, 50983}, {47355, 49137}, {48879, 50693}, {49134, 50976}

X(55675) = midpoint of X(i) and X(j) for these {i,j}: {182, 55642}
X(55675) = reflection of X(i) in X(j) for these {i,j}: {3098, 55648}, {55628, 55652}, {55635, 55656}, {55642, 55662}, {55652, 3}, {55662, 55665}, {55665, 55671}
X(55675) = inverse of X(55647) in First Brocard Circle
X(55675) = center of Tucker-Hagos(3/11) circle
X(55675) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10541, 55631}, {3, 11477, 55650}, {3, 182, 55637}, {3, 5085, 55606}, {3, 511, 55652}, {3, 53092, 55646}, {3, 53093, 14810}, {3, 53094, 20190}, {3, 53097, 55653}, {3, 575, 55644}, {3, 6, 55647}, {3, 55595, 55654}, {3, 55606, 55655}, {3, 55620, 55656}, {3, 55626, 55657}, {3, 55647, 55660}, {3, 55652, 55662}, {6, 55647, 55600}, {6, 55660, 55633}, {182, 55598, 15520}, {182, 55642, 511}, {182, 55658, 55603}, {182, 55667, 55658}, {182, 55672, 55667}, {511, 55652, 55628}, {511, 55656, 55635}, {511, 55662, 55642}, {511, 55671, 55665}, {575, 55631, 55580}, {576, 55583, 44456}, {576, 55652, 55620}, {1351, 55661, 55640}, {3098, 11477, 52987}, {3098, 17508, 53094}, {3098, 20190, 22234}, {3098, 55655, 55645}, {5050, 55639, 55584}, {5050, 55673, 55670}, {5085, 55639, 15516}, {5092, 15516, 5085}, {5092, 55609, 12017}, {5092, 55631, 10541}, {5092, 55664, 1350}, {5092, 55666, 55615}, {5092, 55668, 55639}, {5092, 55670, 55659}, {5092, 55673, 55669}, {5092, 55674, 55673}, {10541, 11477, 5050}, {10541, 55580, 575}, {10541, 55631, 576}, {11477, 55650, 3098}, {11482, 55584, 11477}, {11482, 55631, 55589}, {12017, 55626, 22330}, {12017, 55657, 55587}, {12974, 12975, 52771}, {14810, 15520, 55598}, {14810, 53093, 55583}, {15516, 55589, 37517}, {15516, 55630, 55585}, {17508, 55669, 5092}, {17508, 55672, 182}, {17508, 55673, 55649}, {17508, 55674, 55672}, {20190, 55659, 55588}, {20190, 55670, 3}, {22330, 55657, 55626}, {37517, 55655, 55630}, {37517, 55672, 55668}, {39561, 55653, 55608}, {50664, 55651, 55596}, {52987, 55631, 55611}, {53092, 55646, 55597}, {53094, 55671, 55648}, {55584, 55648, 55622}, {55656, 55673, 55671}

X(55676) = X(2)X(41424)∩X(3)X(6)

Barycentrics    a^2*(7*a^4-5*b^4-14*b^2*c^2-5*c^4-2*a^2*(b^2+c^2)) : :
X(55676) = 6*X[3]+X[6], -3*X[4]+10*X[51126], -X[64]+8*X[15578], -X[69]+15*X[15692], -8*X[140]+X[36990], -2*X[141]+9*X[3524], 9*X[165]+5*X[16491], X[193]+27*X[15705], 4*X[206]+3*X[10606], 3*X[376]+4*X[3589], 3*X[381]+4*X[48892], 4*X[548]+3*X[14561] and many others

X(55676) lies on these lines: {2, 41424}, {3, 6}, {4, 51126}, {22, 10545}, {30, 47355}, {64, 15578}, {69, 15692}, {140, 36990}, {141, 3524}, {154, 5888}, {165, 16491}, {186, 7716}, {193, 15705}, {206, 10606}, {323, 17809}, {376, 3589}, {381, 48892}, {394, 41462}, {524, 15698}, {542, 15700}, {548, 14561}, {549, 3763}, {550, 43621}, {597, 19708}, {599, 12100}, {631, 10516}, {1176, 43713}, {1352, 3530}, {1386, 35242}, {1495, 7484}, {1503, 3523}, {1511, 5621}, {1593, 44091}, {1656, 48898}, {1657, 33751}, {1974, 11410}, {2854, 15036}, {2916, 6644}, {3066, 7492}, {3242, 13624}, {3431, 34817}, {3522, 5480}, {3526, 29012}, {3528, 29181}, {3534, 19130}, {3545, 50971}, {3564, 44682}, {3576, 49465}, {3579, 38315}, {3618, 10304}, {3620, 7891}, {3629, 15715}, {3630, 10519}, {3631, 6776}, {3654, 49679}, {3655, 49690}, {3796, 9544}, {3818, 5054}, {3830, 48891}, {3843, 48896}, {3851, 29323}, {3867, 37460}, {4297, 38144}, {5010, 10387}, {5055, 48884}, {5070, 48889}, {5476, 14093}, {5596, 23328}, {5646, 7496}, {6034, 38736}, {6144, 14891}, {6329, 15710}, {6636, 17810}, {7494, 47296}, {7495, 34775}, {7509, 8718}, {7514, 35237}, {7987, 16496}, {8177, 8716}, {8550, 20080}, {8567, 19149}, {8703, 31670}, {9541, 13972}, {9751, 13860}, {9756, 37455}, {9818, 33534}, {9924, 10249}, {10168, 15688}, {10193, 34776}, {10303, 14927}, {10546, 40916}, {10601, 15107}, {11001, 48310}, {11178, 15707}, {11179, 17504}, {11645, 15701}, {12041, 52697}, {12108, 39884}, {12220, 38446}, {12512, 38035}, {13634, 17259}, {13635, 15668}, {14528, 41435}, {14853, 21735}, {14982, 48378}, {15018, 33586}, {15035, 16010}, {15040, 32305}, {15055, 51941}, {15533, 15716}, {15534, 15711}, {15577, 52028}, {15681, 48895}, {15685, 48943}, {15689, 48879}, {15693, 18440}, {15696, 48901}, {15702, 51128}, {15706, 39899}, {15708, 47354}, {15709, 50975}, {15719, 20582}, {15720, 24206}, {15750, 19124}, {15759, 51185}, {15812, 16976}, {16677, 46475}, {17506, 39588}, {17538, 51163}, {17811, 22352}, {17825, 34417}, {18583, 46853}, {19125, 21663}, {19132, 34778}, {19711, 51186}, {20423, 45759}, {21312, 31521}, {21487, 37674}, {21734, 51212}, {21737, 42283}, {21850, 34200}, {23046, 51167}, {23249, 36701}, {23259, 36703}, {23267, 36717}, {23273, 36702}, {25330, 34153}, {29317, 42785}, {31663, 38029}, {32233, 38727}, {32455, 50967}, {32600, 52055}, {33923, 38110}, {35602, 45308}, {36989, 40686}, {37672, 44109}, {38136, 44245}, {38444, 41464}, {40670, 44878}, {42096, 44461}, {42097, 44465}, {43150, 50993}, {46333, 51134}, {47598, 50956}, {49688, 51705}

X(55676) = midpoint of X(i) and X(j) for these {i,j}: {182, 55644}, {1350, 53858}, {10541, 55651}, {53092, 55616}, {6, 55607}
X(55676) = reflection of X(i) in X(j) for these {i,j}: {1350, 55626}, {3, 55669}, {53092, 182}, {55602, 55633}, {55607, 55639}, {55611, 14810}, {55616, 55644}, {55626, 55651}, {55639, 55658}, {55651, 3}
X(55676) = inverse of X(55646) in First Brocard Circle
X(55676) = isogonal conjugate of X(54520)
X(55676) = center of Tucker-Hagos(2/7) circle
X(55676) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55646)}}, {{A, B, C, X(6), X(54519)}}, {{A, B, C, X(39), X(43713)}}, {{A, B, C, X(64), X(7772)}}, {{A, B, C, X(74), X(9605)}}, {{A, B, C, X(3431), X(30435)}}, {{A, B, C, X(5007), X(14528)}}, {{A, B, C, X(5024), X(20421)}}, {{A, B, C, X(5041), X(14490)}}, {{A, B, C, X(5158), X(34817)}}, {{A, B, C, X(5481), X(31884)}}, {{A, B, C, X(41940), X(52518)}}
X(55676) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10541, 55626}, {3, 11482, 55647}, {3, 12017, 3098}, {3, 12313, 43126}, {3, 12314, 43127}, {3, 13347, 1192}, {3, 1350, 55654}, {3, 17508, 53094}, {3, 17704, 1620}, {3, 182, 31884}, {3, 45552, 12305}, {3, 45553, 12306}, {3, 5050, 14810}, {3, 5093, 55648}, {3, 511, 55651}, {3, 53091, 55643}, {3, 53092, 55644}, {3, 6, 55646}, {3, 55580, 55652}, {3, 55610, 55655}, {3, 55629, 55657}, {3, 55639, 55658}, {3, 55643, 55659}, {3, 55648, 55660}, {3, 55673, 55671}, {3, 55674, 55673}, {15, 16, 9605}, {182, 22330, 5050}, {182, 511, 53092}, {182, 55596, 22330}, {182, 55606, 5093}, {182, 55613, 576}, {182, 55625, 1351}, {182, 55649, 55583}, {182, 55653, 33878}, {182, 55655, 55592}, {182, 55660, 55606}, {182, 55665, 55653}, {182, 55672, 55665}, {376, 3589, 48910}, {511, 14810, 55611}, {511, 55633, 55602}, {511, 55639, 55607}, {548, 14561, 48872}, {549, 46264, 3763}, {575, 55655, 55610}, {576, 55629, 55591}, {576, 55642, 55601}, {576, 55657, 55629}, {631, 33750, 44882}, {631, 44882, 10516}, {1350, 53093, 5102}, {1350, 55654, 55641}, {1351, 55632, 55594}, {1351, 55649, 55614}, {3098, 50664, 44456}, {3098, 5092, 12017}, {3098, 55672, 55668}, {3524, 11180, 50984}, {3589, 48910, 38072}, {3618, 10304, 48881}, {3763, 46264, 47353}, {5050, 55604, 37517}, {5085, 11477, 182}, {5092, 55594, 20190}, {5092, 55639, 10541}, {5092, 55664, 55585}, {5092, 55669, 55639}, {5092, 55674, 55672}, {5092, 8588, 35423}, {5097, 55637, 55593}, {5097, 55663, 55637}, {6200, 6396, 5024}, {6221, 6398, 22246}, {6411, 6412, 53095}, {6776, 10299, 21167}, {10168, 15688, 51024}, {10249, 35228, 9924}, {10304, 50983, 54131}, {10304, 54131, 50968}, {10541, 53858, 53093}, {10541, 55607, 6}, {10541, 55626, 53858}, {10541, 55644, 11477}, {10541, 55651, 511}, {10541, 55673, 55669}, {11477, 31884, 1350}, {11480, 11481, 5013}, {11482, 55624, 55587}, {12017, 44456, 50664}, {12017, 55656, 55582}, {12017, 55668, 55656}, {14810, 22330, 55596}, {14810, 37517, 55604}, {14810, 53097, 55618}, {14810, 55667, 3}, {15516, 55650, 55603}, {15520, 55612, 55580}, {15520, 55652, 55612}, {15578, 23041, 64}, {17508, 55672, 5092}, {17508, 55673, 5085}, {17508, 55675, 55674}, {20190, 55666, 55649}, {22234, 55640, 55590}, {31884, 55591, 55613}, {31884, 55614, 55625}, {31884, 55673, 55670}, {33751, 38317, 1657}, {33878, 55639, 55616}, {33923, 38110, 48873}, {37517, 55604, 53097}, {37517, 55672, 55667}, {39561, 55631, 55584}, {39561, 55662, 55631}, {48881, 50983, 3618}, {50664, 55668, 55661}, {52987, 55643, 55622}, {53091, 55643, 52987}, {55583, 55653, 55632}, {55585, 55655, 55636}, {55587, 55647, 55624}, {55590, 55640, 55620}, {55601, 55657, 55642}

X(55677) = X(3)X(6)∩X(140)X(25561)

Barycentrics    a^2*(10*a^4-7*b^4-20*b^2*c^2-7*c^4-3*a^2*(b^2+c^2)) : :
X(55677) = 17*X[3]+3*X[6], -8*X[140]+3*X[25561], 2*X[546]+3*X[48892], 2*X[548]+3*X[10168], -6*X[549]+X[18553], -X[1656]+3*X[51137], 7*X[3090]+3*X[48898], -11*X[3525]+3*X[51537], 7*X[3528]+3*X[5476], X[3529]+9*X[38317], 3*X[3589]+2*X[44245], 2*X[3627]+3*X[48891] and many others

X(55677) lies on these lines: {3, 6}, {140, 25561}, {542, 15712}, {546, 48892}, {548, 10168}, {549, 18553}, {631, 11645}, {632, 29012}, {1656, 51137}, {3090, 48898}, {3091, 29323}, {3525, 51537}, {3528, 5476}, {3529, 38317}, {3589, 44245}, {3627, 48891}, {3628, 48889}, {3818, 10303}, {3850, 50971}, {5079, 48884}, {5643, 6636}, {7492, 11451}, {8550, 17504}, {8703, 25555}, {10282, 15579}, {10299, 50977}, {10304, 46267}, {12045, 30734}, {12100, 40107}, {12103, 19130}, {12108, 24206}, {14869, 44882}, {15020, 32305}, {15069, 15700}, {15704, 33751}, {15717, 34507}, {19924, 46853}, {21735, 38064}, {23040, 44102}, {25565, 50988}, {33749, 54169}, {33923, 50983}, {44682, 51737}, {44883, 50414}, {47355, 49136}, {48901, 50693}, {49139, 50976}

X(55677) = midpoint of X(i) and X(j) for these {i,j}: {182, 55646}, {11482, 55600}, {12017, 55655}, {22234, 55614}, {3098, 53091}, {575, 55623}, {576, 55595}, {5092, 55666}, {53093, 55637}, {53094, 55672}, {6, 55608}
X(55677) = reflection of X(i) in X(j) for these {i,j}: {14810, 55661}, {5092, 53094}, {53093, 20190}, {55590, 55604}, {55594, 55619}, {55600, 55631}, {55606, 55637}, {55619, 55646}, {55623, 55650}, {55629, 55653}, {55634, 55655}, {55650, 3}, {55661, 55666}, {55666, 55672}, {55672, 55674}
X(55677) = inverse of X(55644) in First Brocard Circle
X(55677) = center of Tucker-Hagos(3/10) circle
X(55677) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10541, 3098}, {3, 11477, 55649}, {3, 11482, 55646}, {3, 182, 55631}, {3, 20190, 55606}, {3, 5050, 55641}, {3, 5085, 52987}, {3, 511, 55650}, {3, 52987, 55653}, {3, 53093, 55637}, {3, 575, 14810}, {3, 576, 55647}, {3, 6, 55644}, {3, 55580, 55651}, {3, 55602, 55654}, {3, 55614, 55655}, {3, 55641, 55658}, {3, 55644, 55659}, {3, 55650, 55661}, {3, 55676, 55675}, {6, 55644, 55597}, {6, 55659, 55627}, {182, 3098, 5102}, {182, 55589, 6}, {182, 55600, 11482}, {182, 55640, 44456}, {182, 55652, 53097}, {182, 55657, 55594}, {182, 55668, 55657}, {182, 55673, 55668}, {511, 20190, 53093}, {511, 55646, 55619}, {511, 55653, 55629}, {511, 55655, 55634}, {511, 55672, 55666}, {511, 55674, 55672}, {575, 14810, 55588}, {576, 55637, 55595}, {1350, 55665, 55663}, {1351, 55660, 55636}, {3098, 10541, 22330}, {3098, 55671, 55664}, {5050, 55641, 55583}, {5085, 44456, 182}, {5085, 55653, 5097}, {5092, 5097, 5085}, {5092, 55606, 20190}, {5092, 55634, 12017}, {5092, 55669, 55615}, {5092, 55674, 55670}, {10541, 55671, 3}, {11477, 55617, 55590}, {11477, 55649, 55617}, {11482, 55600, 511}, {11482, 55646, 55600}, {11482, 55657, 55623}, {12017, 55614, 22234}, {15516, 31884, 55586}, {15520, 55639, 55592}, {17508, 55672, 53094}, {17508, 55674, 5092}, {17508, 55676, 55674}, {20190, 55606, 575}, {20190, 55647, 576}, {20190, 55668, 55652}, {22234, 55655, 55614}, {33878, 55662, 55645}, {37517, 55654, 55625}, {39561, 55628, 55580}, {39561, 55651, 55601}, {44456, 55673, 55669}, {50664, 55617, 11477}, {53094, 55671, 53091}, {55580, 55651, 55628}, {55585, 55648, 55621}, {55587, 55656, 55638}, {55606, 55627, 55620}, {55608, 55672, 55667}, {55617, 55631, 55622}, {55629, 55646, 55640}, {55668, 55674, 55673}

X(55678) = X(3)X(6)∩X(5)X(33750)

Barycentrics    a^2*(11*a^4-7*b^4-22*b^2*c^2-7*c^4-4*a^2*(b^2+c^2)) : :
X(55678) = 9*X[3]+2*X[6], 2*X[5]+9*X[33750], -X[69]+12*X[12100], -4*X[141]+15*X[15693], X[193]+21*X[15698], 8*X[206]+3*X[35450], 5*X[376]+6*X[38079], -9*X[381]+20*X[51126], -18*X[549]+7*X[3619], -15*X[631]+4*X[18358], 10*X[632]+X[14927], X[1992]+10*X[15711] and many others

X(55678) lies on these lines: {3, 6}, {5, 33750}, {69, 12100}, {141, 15693}, {193, 15698}, {206, 35450}, {376, 38079}, {381, 51126}, {524, 15716}, {542, 15718}, {549, 3619}, {631, 18358}, {632, 14927}, {1495, 16419}, {1503, 15720}, {1593, 35253}, {1597, 44091}, {1992, 15711}, {3167, 15246}, {3426, 7514}, {3522, 38110}, {3523, 39874}, {3524, 3620}, {3526, 44882}, {3528, 18583}, {3530, 25406}, {3534, 3589}, {3545, 50988}, {3564, 15717}, {3579, 16491}, {3618, 8703}, {3630, 11179}, {3631, 15700}, {3763, 15701}, {3818, 15694}, {3830, 25565}, {3851, 48898}, {5054, 34573}, {5055, 48905}, {5070, 29012}, {5073, 38317}, {5544, 10545}, {5888, 6800}, {6776, 15712}, {7484, 15080}, {7485, 26864}, {7509, 12112}, {7712, 40916}, {8177, 51122}, {8567, 23042}, {8780, 22352}, {10168, 15689}, {10299, 48876}, {10303, 39884}, {10304, 21850}, {10519, 44682}, {11008, 17504}, {11180, 41983}, {11204, 19132}, {11898, 21167}, {12108, 40330}, {12167, 35472}, {12315, 23041}, {13624, 16496}, {14093, 38064}, {14561, 15696}, {14848, 34200}, {14853, 33923}, {15035, 32254}, {15681, 19130}, {15684, 48891}, {15685, 48895}, {15688, 31670}, {15692, 20080}, {15695, 47352}, {15699, 50975}, {15705, 50979}, {15707, 43273}, {15714, 54132}, {15722, 21358}, {15988, 19705}, {16010, 38638}, {16239, 51537}, {17538, 38136}, {19118, 35473}, {19708, 51171}, {19709, 48884}, {19711, 21356}, {21487, 37633}, {21734, 48874}, {31521, 52099}, {32063, 44883}, {32306, 38727}, {33751, 53023}, {36990, 42786}, {38072, 48879}, {38335, 50971}, {38633, 51941}, {42144, 44461}, {42145, 44465}, {44245, 51538}, {46853, 51212}, {50957, 51137}, {50987, 54170}

X(55678) = midpoint of X(i) and X(j) for these {i,j}: {182, 55652}
X(55678) = reflection of X(i) in X(j) for these {i,j}: {1350, 55628}, {3, 55671}, {55620, 55648}, {55622, 55652}, {55632, 55656}, {55641, 55662}, {55648, 3}, {55656, 55665}, {55671, 55675}
X(55678) = inverse of X(55639) in First Brocard Circle
X(55678) = center of Tucker-Hagos(4/11) circle
X(55678) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3426), X(7772)}}, {{A, B, C, X(3527), X(41940)}}, {{A, B, C, X(5013), X(20421)}}, {{A, B, C, X(5481), X(55610)}}, {{A, B, C, X(6391), X(15860)}}, {{A, B, C, X(14489), X(14810)}}, {{A, B, C, X(22332), X(43713)}}, {{A, B, C, X(41435), X(52703)}}
X(55678) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10541, 55595}, {3, 1351, 55643}, {3, 182, 55610}, {3, 20190, 55580}, {3, 5050, 55629}, {3, 5085, 1351}, {3, 5092, 12017}, {3, 5093, 14810}, {3, 511, 55648}, {3, 6, 55639}, {3, 55584, 55649}, {3, 55593, 55651}, {3, 55604, 55653}, {3, 55616, 55654}, {3, 55624, 55655}, {3, 55632, 55656}, {6, 55646, 55594}, {6, 55653, 55604}, {6, 55676, 55672}, {182, 17508, 55677}, {182, 55631, 5102}, {182, 55652, 511}, {182, 55668, 55646}, {182, 55677, 55673}, {511, 55652, 55622}, {511, 55675, 55671}, {575, 55638, 55581}, {575, 55674, 55667}, {576, 55654, 55616}, {1350, 55670, 3}, {1351, 3098, 33878}, {1351, 53092, 15520}, {1351, 55610, 53097}, {1351, 55643, 55602}, {3098, 37517, 55590}, {3098, 5092, 5085}, {3098, 55597, 55607}, {3098, 55641, 55632}, {3098, 55658, 55647}, {3098, 55665, 55662}, {5085, 53097, 182}, {5085, 55651, 575}, {5085, 55667, 55593}, {5085, 55671, 55641}, {5085, 55673, 55657}, {5092, 17508, 55676}, {5092, 55661, 20190}, {5092, 55670, 50664}, {5092, 55677, 55668}, {5097, 55660, 55626}, {6200, 6396, 5013}, {6200, 6424, 6221}, {6221, 6398, 9605}, {6396, 6423, 6398}, {10168, 15689, 50963}, {10541, 14810, 5093}, {10645, 10646, 53095}, {11477, 55655, 55624}, {11482, 33878, 44456}, {12017, 33878, 5050}, {12017, 55639, 6}, {12017, 55646, 11482}, {12017, 55665, 55620}, {15516, 55644, 55591}, {15520, 55647, 1350}, {15520, 55658, 3098}, {15520, 55662, 55628}, {20190, 31884, 53091}, {20190, 55661, 37517}, {20190, 55669, 31884}, {37517, 55669, 55661}, {39561, 55659, 55614}, {42115, 42116, 5024}, {47355, 48892, 3830}, {50664, 55670, 55658}, {53093, 55649, 55584}, {53094, 55676, 5092}, {55580, 55639, 55609}, {55590, 55674, 55669}, {55594, 55609, 55600}, {55639, 55648, 55642}, {55642, 55672, 55665}, {55646, 55656, 55652}, {55647, 55674, 55670}, {55657, 55677, 55674}

X(55679) = X(3)X(6)∩X(23)X(6688)

Barycentrics    a^2*(8*a^4-5*b^4-16*b^2*c^2-5*c^4-3*a^2*(b^2+c^2)) : :
X(55679) = 13*X[3]+3*X[6], -5*X[5]+21*X[50988], X[550]+3*X[10168], 3*X[597]+5*X[46853], -5*X[631]+X[18553], 5*X[632]+3*X[44882], -7*X[3090]+3*X[48889], 5*X[3091]+27*X[33750], -X[3146]+9*X[38317], 5*X[3522]+3*X[5476], -35*X[3523]+3*X[11180], -9*X[3524]+X[34507] and many others

X(55679) lies on circumconic {{A, B, C, X(5481), X(55606)}} and on these lines: {3, 6}, {5, 50988}, {23, 6688}, {140, 11645}, {542, 3530}, {546, 29323}, {548, 25555}, {550, 10168}, {597, 46853}, {631, 18553}, {632, 44882}, {1503, 12108}, {1995, 10219}, {3090, 48889}, {3091, 33750}, {3146, 38317}, {3292, 15246}, {3522, 5476}, {3523, 11180}, {3524, 34507}, {3525, 3818}, {3526, 25561}, {3528, 38064}, {3529, 48895}, {3589, 12103}, {3627, 48892}, {3628, 29012}, {3819, 9544}, {3853, 25565}, {3857, 51126}, {3917, 9716}, {5072, 48884}, {5076, 47355}, {5079, 48905}, {5609, 11793}, {5621, 15039}, {5943, 7492}, {7486, 50975}, {7496, 22352}, {7550, 8718}, {7555, 11695}, {8550, 44682}, {8703, 46267}, {9976, 15036}, {10299, 11179}, {10303, 46264}, {11178, 15720}, {12045, 16042}, {13570, 37924}, {14561, 48920}, {14869, 24206}, {14927, 42786}, {15021, 19140}, {15034, 32305}, {15054, 37126}, {15080, 15082}, {15331, 32154}, {15579, 50414}, {15704, 19130}, {15712, 40107}, {15717, 50977}, {17538, 48901}, {19124, 35479}, {19924, 33923}, {20423, 21734}, {25406, 43150}, {29317, 44245}, {38110, 48885}, {44300, 47313}, {48943, 49137}

X(55679) = midpoint of X(i) and X(j) for these {i,j}: {182, 55653}, {14810, 50664}, {15579, 50414}, {22330, 55606}, {25565, 50971}, {3, 20190}, {3098, 15516}, {3589, 33751}, {39561, 55621}, {548, 25555}, {5050, 55638}, {575, 55631}, {576, 55597}, {5085, 55664}, {5092, 55674}, {5097, 55601}, {6, 55612}, {8703, 46267}
X(55679) = reflection of X(i) in X(j) for these {i,j}: {55609, 14810}, {55617, 55647}, {55625, 55653}, {55636, 55659}, {55647, 3}, {55659, 55668}, {55668, 55674}
X(55679) = inverse of X(55637) in First Brocard Circle
X(55679) = center of Tucker-Hagos(3/8) circle
X(55679) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 55644}, {3, 11482, 55641}, {3, 12017, 53097}, {3, 17508, 55677}, {3, 5050, 55626}, {3, 5092, 20190}, {3, 511, 55647}, {3, 52987, 55650}, {3, 576, 14810}, {3, 6, 55637}, {3, 55595, 55651}, {3, 55620, 55654}, {3, 55626, 55655}, {3, 55637, 55657}, {3, 55647, 55659}, {3, 55677, 55674}, {6, 55624, 55581}, {6, 55648, 55596}, {182, 17508, 55676}, {182, 3098, 5093}, {182, 55583, 53092}, {182, 55596, 6}, {182, 55606, 22330}, {182, 55628, 576}, {182, 55644, 11477}, {182, 55665, 31884}, {182, 55669, 55648}, {182, 55672, 55660}, {511, 14810, 55609}, {511, 55653, 55625}, {511, 55659, 55636}, {511, 55674, 55668}, {548, 50983, 25555}, {575, 55657, 55602}, {576, 55624, 55588}, {1350, 55661, 55645}, {1350, 55667, 55661}, {1351, 55658, 55627}, {3098, 55666, 55663}, {5085, 55656, 53091}, {5092, 14810, 5085}, {5092, 55673, 15516}, {5097, 55649, 55601}, {8160, 8161, 32447}, {10541, 52987, 575}, {10541, 55641, 11482}, {11477, 55614, 33878}, {11477, 55644, 55606}, {11477, 55675, 55670}, {11482, 55641, 52987}, {12017, 55649, 5097}, {12017, 55671, 55649}, {14810, 50664, 511}, {14810, 55581, 55612}, {14810, 55606, 55628}, {14810, 55614, 55631}, {14810, 55660, 55653}, {14810, 55672, 55664}, {15516, 55631, 55580}, {15516, 55663, 3098}, {15516, 55674, 55666}, {15520, 55629, 55586}, {17508, 53094, 5092}, {20190, 22330, 182}, {20190, 55597, 50664}, {20190, 55645, 22234}, {20190, 55664, 55597}, {20190, 55668, 55617}, {20190, 55674, 3}, {22234, 55652, 1350}, {22234, 55667, 55652}, {31884, 53092, 55583}, {33878, 55648, 55624}, {33878, 55676, 55672}, {37517, 55651, 55615}, {39561, 55646, 55590}, {47066, 47068, 40268}, {53091, 55656, 55603}, {53094, 55678, 17508}, {53097, 55649, 55623}, {55583, 55606, 55592}, {55585, 55643, 55619}, {55587, 55654, 55634}, {55590, 55646, 55621}, {55594, 55655, 55638}, {55597, 55631, 55614}, {55606, 55623, 55616}, {55612, 55674, 55669}

X(55680) = X(3)X(6)∩X(3533)X(3818)

Barycentrics    a^2*(12*a^4-7*b^4-24*b^2*c^2-7*c^4-5*a^2*(b^2+c^2)) : :
X(55680) = 19*X[3]+5*X[6], -7*X[3523]+X[43150], -17*X[3533]+5*X[3818], X[3543]+15*X[33750], 7*X[3832]+5*X[48898], -11*X[5056]+5*X[48889], X[5059]+5*X[48895], 5*X[10168]+X[15686], -X[10516]+5*X[51137], 23*X[11001]+25*X[51029], 2*X[11540]+X[51135], -25*X[15693]+X[51027] and many others

X(55680) lies on circumconic {{A, B, C, X(5481), X(55594)}} and on these lines: {3, 6}, {373, 37913}, {542, 41983}, {547, 29012}, {1503, 11812}, {3523, 43150}, {3533, 3818}, {3543, 33750}, {3832, 48898}, {3845, 29323}, {5056, 48889}, {5059, 48895}, {5965, 12100}, {10168, 15686}, {10516, 51137}, {11001, 51029}, {11539, 11645}, {11540, 51135}, {12045, 35268}, {15082, 22352}, {15690, 29317}, {15693, 51027}, {15716, 51140}, {15719, 25406}, {15723, 25561}, {17538, 42785}, {19124, 44878}, {19711, 50980}, {19924, 41982}, {25555, 41981}, {29181, 46267}, {33703, 48891}, {47355, 48942}, {48920, 51538}

X(55680) = midpoint of X(i) and X(j) for these {i,j}: {182, 55657}, {15516, 55621}, {15520, 55606}, {20190, 55664}, {39561, 55627}, {48920, 51538}, {5050, 14810}, {575, 31884}, {5085, 55670}, {5092, 17508}, {5093, 55599}, {5097, 55603}, {5102, 55594}, {50664, 55645}, {6, 55615}
X(55680) = reflection of X(i) in X(j) for these {i,j}: {17508, 55679}, {22330, 5050}, {31884, 55659}, {55592, 55615}, {55593, 55617}, {55597, 55621}, {55601, 31884}, {55603, 55636}, {55612, 55645}, {55615, 55647}, {55621, 55653}, {55631, 55657}, {55638, 55663}, {55645, 3}, {55653, 55664}, {55657, 55668}, {55663, 55670}, {55664, 55674}, {55674, 17508}
X(55680) = inverse of X(55633) in First Brocard Circle
X(55680) = center of Tucker-Hagos(5/12) circle
X(55680) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 182, 55594}, {3, 37517, 14810}, {3, 39561, 55627}, {3, 5050, 55618}, {3, 50664, 55612}, {3, 5085, 39561}, {3, 5097, 55636}, {3, 5102, 55640}, {3, 511, 55645}, {3, 6, 55633}, {3, 55591, 55649}, {6, 55666, 55647}, {6, 55675, 55666}, {182, 17508, 55673}, {182, 3098, 11482}, {182, 44456, 575}, {182, 55600, 6}, {182, 55622, 5097}, {182, 55640, 5102}, {182, 55652, 44456}, {182, 55668, 55631}, {182, 55672, 55652}, {182, 55673, 55657}, {182, 55677, 55668}, {511, 31884, 55601}, {511, 5050, 22330}, {511, 55615, 55592}, {511, 55617, 55593}, {511, 55636, 55603}, {511, 55647, 55615}, {511, 55653, 55621}, {511, 55659, 31884}, {511, 55670, 55663}, {511, 55674, 55664}, {511, 55679, 17508}, {575, 55672, 55659}, {576, 55661, 55625}, {576, 55671, 55661}, {1351, 55650, 55609}, {1351, 55665, 55650}, {5050, 55676, 55667}, {5085, 17508, 55670}, {5085, 55610, 182}, {5085, 55673, 55610}, {5085, 55674, 55638}, {5092, 53094, 55679}, {5092, 55670, 5085}, {5092, 55674, 20190}, {5092, 55679, 55674}, {5093, 55649, 55599}, {11477, 55662, 55634}, {12017, 55654, 15520}, {12017, 55669, 55606}, {15516, 55621, 511}, {15516, 55653, 55597}, {15520, 55669, 55654}, {17508, 55660, 55675}, {17508, 55667, 55676}, {17508, 55673, 55677}, {20190, 55612, 50664}, {20190, 55653, 15516}, {20190, 55674, 55653}, {22330, 55631, 53097}, {37517, 55611, 55587}, {39561, 55596, 37517}, {39561, 55649, 55591}, {44456, 55652, 55619}, {50664, 55674, 3}, {53091, 55644, 55586}, {53093, 55658, 55590}, {53097, 55610, 55596}, {55603, 55640, 55622}, {55615, 55666, 55660}, {55619, 55677, 55672}

X(55681) = X(3)X(6)∩X(4)X(25565)

Barycentrics    7*a^6-3*a^4*(b^2+c^2)-2*a^2*(2*b^4+7*b^2*c^2+2*c^4) : :
X(55681) = 11*X[3]+3*X[6], -5*X[4]+12*X[25565], X[20]+6*X[10168], -10*X[140]+3*X[47354], 3*X[376]+4*X[25555], 4*X[546]+3*X[48898], 4*X[548]+3*X[5476], -11*X[549]+4*X[51143], 5*X[550]+9*X[38079], 3*X[597]+4*X[33923], -10*X[631]+3*X[11178], -10*X[632]+3*X[3818], -10*X[3091]+3*X[48884] and many others

X(55681) lies on these lines: {3, 6}, {4, 25565}, {20, 10168}, {140, 47354}, {376, 25555}, {524, 44682}, {542, 3523}, {546, 48898}, {548, 5476}, {549, 51143}, {550, 38079}, {597, 33923}, {631, 11178}, {632, 3818}, {1503, 14869}, {1974, 35475}, {3090, 29012}, {3091, 48884}, {3146, 33750}, {3522, 38064}, {3524, 40107}, {3525, 46264}, {3526, 11645}, {3528, 19924}, {3529, 19130}, {3530, 34507}, {3589, 15704}, {3618, 48885}, {3627, 38317}, {3628, 44882}, {3853, 48310}, {5054, 18553}, {5068, 50975}, {5072, 48905}, {5079, 48889}, {5182, 33022}, {5480, 44245}, {5622, 15023}, {5643, 7492}, {6759, 15579}, {7496, 9306}, {8541, 17506}, {8550, 12100}, {9716, 41462}, {9968, 15578}, {10303, 24206}, {10984, 14094}, {11179, 15717}, {11202, 15581}, {12045, 41424}, {12103, 48901}, {12811, 51126}, {14002, 22112}, {14561, 17538}, {15021, 15462}, {15069, 15693}, {15080, 16187}, {15688, 46267}, {15696, 47352}, {15712, 50977}, {15720, 43273}, {15826, 37968}, {16042, 35268}, {19124, 44879}, {20423, 21735}, {22352, 35264}, {23049, 32903}, {25561, 46219}, {29317, 50693}, {29323, 47355}, {30734, 32237}, {33749, 54173}, {38110, 48880}, {46935, 50956}, {48891, 49136}, {48895, 49137}, {50690, 50964}, {51522, 52098}

X(55681) = midpoint of X(i) and X(j) for these {i,j}: {182, 55658}, {3, 10541}, {53092, 55626}, {53858, 55602}, {6, 55616}
X(55681) = reflection of X(i) in X(j) for these {i,j}: {3098, 55651}, {576, 53092}, {52987, 55611}, {53858, 575}, {55605, 55639}, {55607, 14810}, {55611, 55644}, {55633, 55658}, {55644, 3}, {55658, 55669}, {55669, 55676}
X(55681) = inverse of X(55631) in First Brocard Circle
X(55681) = center of Tucker-Hagos(3/7) circle
X(55681) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(54), X(14075)}}, {{A, B, C, X(5481), X(52987)}}, {{A, B, C, X(7772), X(46848)}}, {{A, B, C, X(13472), X(34571)}}
X(55681) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11482, 31884}, {3, 12017, 11477}, {3, 1351, 55641}, {3, 17508, 55675}, {3, 22234, 55628}, {3, 5050, 55614}, {3, 511, 55644}, {3, 53092, 55626}, {3, 53093, 55606}, {3, 53094, 55679}, {3, 576, 55637}, {3, 6, 55631}, {3, 55580, 55646}, {3, 55602, 55651}, {3, 55606, 55652}, {3, 55614, 55653}, {3, 55631, 55655}, {3, 55641, 55657}, {3, 55644, 55658}, {3, 55679, 17508}, {182, 17508, 55672}, {182, 3098, 15520}, {182, 55603, 6}, {182, 55637, 576}, {182, 55658, 511}, {182, 55662, 55581}, {182, 55669, 55633}, {511, 14810, 55607}, {511, 55639, 55605}, {511, 55676, 55669}, {575, 55597, 1351}, {575, 55643, 55583}, {1350, 55638, 3098}, {1350, 55660, 55642}, {1350, 55668, 55660}, {1351, 55641, 55597}, {3098, 17508, 55674}, {3098, 55587, 55599}, {3098, 55590, 55603}, {3098, 55655, 55643}, {3098, 55674, 55667}, {3530, 51737, 34507}, {5050, 55653, 55587}, {5085, 53094, 55678}, {5085, 53858, 10541}, {5085, 55673, 55593}, {5092, 55674, 5085}, {5092, 55677, 20190}, {5092, 55680, 53094}, {5093, 55656, 55612}, {5097, 55617, 55580}, {5097, 55646, 55596}, {5102, 55648, 55601}, {10541, 55602, 575}, {10541, 55626, 53092}, {10541, 55633, 22234}, {10541, 55651, 53858}, {10541, 55669, 55611}, {10541, 55676, 3}, {11477, 14810, 55600}, {11477, 55600, 55585}, {11482, 31884, 55588}, {12017, 14810, 39561}, {12017, 39561, 182}, {12017, 55673, 14810}, {14561, 33751, 48879}, {14810, 55585, 55613}, {14810, 55673, 55665}, {15516, 55661, 55610}, {15520, 55581, 37517}, {15520, 55667, 55649}, {15520, 55672, 55662}, {17508, 39561, 55673}, {17508, 55669, 55676}, {20190, 55606, 53093}, {20190, 55670, 55595}, {20190, 55674, 55647}, {20190, 55679, 55677}, {22234, 55649, 52987}, {22330, 55650, 1350}, {22330, 55668, 55650}, {33878, 55659, 55640}, {37517, 55649, 55608}, {50664, 55588, 11482}, {53091, 55654, 55594}, {53097, 55595, 55590}, {53097, 55626, 55602}, {53858, 55626, 53097}, {55580, 55646, 55617}, {55583, 55644, 55616}, {55587, 55653, 55630}, {55594, 55654, 55635}, {55607, 55626, 55620}, {55616, 55676, 55670}, {55638, 55674, 55668}

X(55682) = X(2)X(50957)∩X(3)X(6)

Barycentrics    a^2*(9*a^4-5*b^4-18*b^2*c^2-5*c^4-4*a^2*(b^2+c^2)) : :
X(55682) = -16*X[2]+7*X[50957], 7*X[3]+2*X[6], X[20]+2*X[38136], -X[69]+10*X[15712], 8*X[206]+X[13093], X[376]+2*X[38110], 4*X[548]+5*X[3618], -10*X[549]+X[11180], 4*X[597]+5*X[14093], -2*X[599]+11*X[15718], -10*X[631]+X[18440], -2*X[1352]+11*X[15720] and many others

X(55682) lies on these lines: {2, 50957}, {3, 6}, {20, 38136}, {23, 5544}, {30, 33750}, {69, 15712}, {154, 15082}, {206, 13093}, {373, 9909}, {376, 38110}, {524, 15706}, {542, 15707}, {548, 3618}, {549, 11180}, {550, 51538}, {597, 14093}, {599, 15718}, {631, 18440}, {1176, 44763}, {1352, 15720}, {1503, 5054}, {1656, 44882}, {1657, 3589}, {1992, 14891}, {3167, 7998}, {3522, 18583}, {3523, 48906}, {3524, 3564}, {3525, 39884}, {3526, 46264}, {3528, 21850}, {3530, 6776}, {3534, 14561}, {3619, 12108}, {3628, 14927}, {3763, 48662}, {3796, 5650}, {3818, 46219}, {3830, 38317}, {3843, 47355}, {3851, 48905}, {5020, 35268}, {5055, 29012}, {5066, 50975}, {5070, 36990}, {5072, 51126}, {5073, 48892}, {5476, 15695}, {5480, 15696}, {6090, 7485}, {6800, 7484}, {7395, 8718}, {7496, 26864}, {8703, 14853}, {8705, 37955}, {9778, 38040}, {10168, 15681}, {10303, 18358}, {10304, 14848}, {10516, 15694}, {10519, 12100}, {10606, 23042}, {10627, 43908}, {11179, 15700}, {11202, 52028}, {11402, 33884}, {11410, 19128}, {11820, 49671}, {12167, 21844}, {12315, 44883}, {12601, 36703}, {12602, 36701}, {14269, 29323}, {14869, 40330}, {14912, 15692}, {15040, 32254}, {15041, 15462}, {15042, 33851}, {15055, 45016}, {15067, 19347}, {15688, 29181}, {15689, 29317}, {15693, 50955}, {15698, 50979}, {15701, 43273}, {15705, 33748}, {15711, 50967}, {15713, 51023}, {15714, 54170}, {15716, 51174}, {15717, 48876}, {15759, 50987}, {16419, 22352}, {17504, 34380}, {17800, 19130}, {19118, 35477}, {20423, 41153}, {21356, 41983}, {21735, 48874}, {23041, 32063}, {25555, 48872}, {32306, 38728}, {33751, 48910}, {33923, 51212}, {34152, 52238}, {35265, 40916}, {36702, 49029}, {36717, 49028}, {38335, 48310}, {46332, 50969}, {46853, 51732}, {47353, 51137}, {48891, 49134}, {48895, 49139}, {50954, 51139}, {50977, 50989}, {50981, 50990}, {50993, 51141}

X(55682) = midpoint of X(i) and X(j) for these {i,j}: {182, 55660}, {39561, 55630}, {5050, 55643}, {5085, 55673}, {6, 55618}
X(55682) = reflection of X(i) in X(j) for these {i,j}: {1350, 55630}, {3, 55673}, {31884, 55660}, {55593, 55618}, {55610, 55643}, {55618, 55649}, {55624, 55654}, {55630, 55657}, {55643, 3}, {55654, 55667}, {55660, 55670}, {55673, 17508}
X(55682) = inverse of X(55629) in First Brocard Circle
X(55682) = center of Tucker-Hagos(4/9) circle
X(55682) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(39), X(44763)}}, {{A, B, C, X(5481), X(33878)}}, {{A, B, C, X(14489), X(31884)}}
X(55682) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12054, 10983}, {3, 1351, 55639}, {3, 20190, 11482}, {3, 33878, 55648}, {3, 44456, 14810}, {3, 511, 55643}, {3, 53094, 55678}, {3, 575, 55620}, {3, 6, 55629}, {3, 55584, 55646}, {3, 55593, 55649}, {3, 55604, 55651}, {3, 55616, 55653}, {3, 55624, 55654}, {3, 55632, 55655}, {6, 55641, 55587}, {6, 55676, 55665}, {182, 17508, 55670}, {182, 3098, 22330}, {182, 31884, 5093}, {182, 55606, 6}, {182, 55648, 1351}, {182, 55653, 11477}, {182, 55660, 511}, {182, 55665, 55606}, {182, 55667, 55613}, {182, 55669, 55625}, {182, 55670, 31884}, {182, 55672, 55644}, {511, 17508, 55673}, {511, 55649, 55618}, {511, 55657, 55630}, {511, 55670, 55660}, {575, 55646, 55584}, {575, 55663, 55603}, {576, 55651, 55604}, {1351, 55639, 55595}, {3098, 10541, 53091}, {3098, 55677, 55671}, {5050, 5085, 12017}, {5050, 55649, 55580}, {5085, 5102, 10541}, {5085, 53094, 17508}, {5085, 55671, 5102}, {5085, 55674, 55593}, {5092, 17508, 5085}, {5097, 55638, 55589}, {5097, 55658, 55614}, {10541, 55671, 3098}, {10541, 55677, 3}, {11477, 31884, 55596}, {11477, 55616, 33878}, {11477, 55653, 55616}, {11482, 55657, 55610}, {12017, 53092, 182}, {12017, 55610, 5050}, {12017, 55648, 53092}, {14810, 15520, 55591}, {14810, 44456, 55602}, {14810, 53093, 44456}, {15516, 55637, 55582}, {15520, 55649, 55598}, {15693, 51737, 50955}, {15759, 50987, 54132}, {17508, 39561, 55672}, {17508, 55649, 55674}, {17508, 55670, 55676}, {17508, 55680, 53094}, {17508, 55681, 55680}, {20190, 55657, 39561}, {20190, 55672, 1350}, {20190, 55674, 55636}, {21735, 51171, 48874}, {22330, 55679, 55677}, {31884, 55613, 55624}, {37517, 55659, 55626}, {39561, 55672, 55657}, {47355, 48898, 3843}, {50664, 55655, 53097}, {52987, 55666, 55656}, {53093, 55591, 15520}, {53094, 55676, 55679}, {53097, 55655, 55632}, {53858, 55622, 55585}, {55585, 55650, 55622}, {55587, 55649, 55621}, {55587, 55661, 55641}, {55589, 55658, 55638}, {55603, 55669, 55663}, {55654, 55673, 55667}

X(55683) = X(3)X(6)∩X(542)X(15719)

Barycentrics    11*a^6-5*a^4*(b^2+c^2)-2*a^2*(3*b^4+11*b^2*c^2+3*c^4) : :
X(55683) = 17*X[3]+5*X[6], 6*X[547]+5*X[44882], -13*X[549]+2*X[50958], 5*X[597]+6*X[41982], -5*X[1352]+27*X[15708], 17*X[3533]+5*X[46264], 6*X[3543]+5*X[48896], -5*X[3818]+16*X[16239], 6*X[3845]+5*X[48898], -16*X[3850]+5*X[48884], -4*X[3853]+15*X[38317], X[5059]+10*X[19130] and many others

X(55683) lies on these lines: {3, 6}, {542, 15719}, {547, 44882}, {549, 50958}, {597, 41982}, {1352, 15708}, {1974, 35478}, {3533, 46264}, {3543, 48896}, {3818, 16239}, {3845, 48898}, {3850, 48884}, {3853, 38317}, {5056, 29012}, {5059, 19130}, {5067, 14927}, {5480, 15690}, {5965, 15717}, {10168, 11001}, {11178, 11812}, {11202, 15580}, {11539, 39884}, {11645, 15723}, {12007, 17504}, {12103, 42785}, {13595, 22112}, {15686, 48901}, {15692, 51140}, {15702, 24206}, {16187, 22352}, {19711, 41152}, {33703, 48892}, {34200, 51166}, {38064, 48885}, {41981, 48880}, {41983, 51737}, {41992, 42786}, {46332, 51732}, {47352, 48920}, {48891, 49133}, {50988, 51025}, {51027, 51141}

X(55683) = midpoint of X(i) and X(j) for these {i,j}: {182, 55662}, {6, 55620}
X(55683) = reflection of X(i) in X(j) for these {i,j}: {3098, 55652}, {55628, 55656}, {55635, 55662}, {55642, 3}, {55652, 55665}, {55662, 55671}, {55665, 55675}, {55675, 55678}
X(55683) = inverse of X(55627) in First Brocard Circle
X(55683) = center of Tucker-Hagos(5/11) circle
X(55683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12017, 5102}, {3, 182, 55587}, {3, 37517, 55640}, {3, 5050, 55607}, {3, 50664, 55603}, {3, 5085, 50664}, {3, 5097, 55633}, {3, 5102, 55636}, {3, 511, 55642}, {3, 6, 55627}, {3, 55582, 55645}, {3, 55618, 55653}, {3, 55645, 55658}, {6, 55644, 55589}, {6, 55667, 55644}, {6, 55677, 55667}, {182, 14810, 576}, {182, 17508, 55669}, {182, 53094, 17508}, {182, 55581, 53091}, {182, 55587, 39561}, {182, 55608, 6}, {182, 55633, 5097}, {182, 55649, 1351}, {182, 55662, 511}, {182, 55667, 55608}, {182, 55669, 3098}, {182, 55672, 14810}, {182, 55674, 55655}, {182, 55675, 55662}, {182, 55681, 53094}, {511, 55656, 55628}, {511, 55665, 55652}, {511, 55675, 55665}, {575, 55645, 55582}, {575, 55658, 55596}, {576, 55644, 55597}, {1351, 55605, 55583}, {1351, 55649, 55605}, {1351, 55666, 55649}, {1351, 55676, 55666}, {5050, 55668, 55637}, {5085, 17508, 55660}, {5085, 55676, 55614}, {5085, 55679, 55672}, {5092, 55679, 5085}, {5092, 55680, 3}, {5092, 55682, 55681}, {5093, 55647, 55598}, {10541, 55653, 15520}, {11477, 55661, 55630}, {12017, 15516, 182}, {12017, 55651, 15516}, {12017, 55670, 52987}, {14810, 55609, 55629}, {14810, 55628, 55635}, {15516, 55670, 55651}, {15520, 55653, 55600}, {17508, 55596, 55673}, {17508, 55655, 55674}, {17508, 55665, 55675}, {20190, 55674, 55625}, {44456, 55650, 55613}, {50664, 55680, 55679}, {53093, 55657, 55585}, {53094, 55671, 55678}, {55587, 55605, 55594}, {55587, 55640, 55612}, {55589, 55669, 55659}, {55597, 55679, 55677}, {55632, 55678, 55676}, {55635, 55655, 55648}, {55652, 55660, 55656}, {55662, 55675, 55671}

X(55684) = X(3)X(6)∩X(22)X(5643)

Barycentrics    a^2*(11*a^4-5*b^4-22*b^2*c^2-5*c^4-6*a^2*(b^2+c^2)) : :
X(55684) = 8*X[3]+3*X[6], 7*X[4]+15*X[50975], 2*X[20]+9*X[47352], 8*X[140]+3*X[43273], -X[382]+12*X[10168], 8*X[546]+3*X[48905], 8*X[548]+3*X[54131], -12*X[549]+X[15069], 2*X[550]+9*X[38064], 6*X[597]+5*X[3522], -3*X[599]+14*X[3523], -25*X[631]+3*X[11180] and many others

X(55684) lies on these lines: {3, 6}, {4, 50975}, {20, 47352}, {22, 5643}, {23, 17825}, {140, 43273}, {382, 10168}, {524, 15717}, {542, 15720}, {546, 48905}, {548, 54131}, {549, 15069}, {550, 38064}, {597, 3522}, {599, 3523}, {631, 11180}, {632, 10516}, {895, 15023}, {1176, 43691}, {1352, 14869}, {1498, 7550}, {1503, 3525}, {1657, 38072}, {2930, 15020}, {3090, 36990}, {3091, 44882}, {3146, 3589}, {3242, 30389}, {3524, 8550}, {3526, 47353}, {3529, 53023}, {3530, 11179}, {3533, 47354}, {3534, 25555}, {3618, 48872}, {3628, 46264}, {3763, 10303}, {3796, 40916}, {3832, 48310}, {3854, 51022}, {5059, 50971}, {5070, 11645}, {5072, 29012}, {5076, 48898}, {5476, 15696}, {5480, 17538}, {5493, 38023}, {5621, 7509}, {5646, 26864}, {6593, 15021}, {7492, 10601}, {7496, 9544}, {7555, 15805}, {7991, 38315}, {8556, 37455}, {8567, 19153}, {8584, 15705}, {8718, 15811}, {8719, 35950}, {9588, 50783}, {9716, 21766}, {9968, 19132}, {10249, 15581}, {10299, 51179}, {10304, 51185}, {11284, 22352}, {12100, 51187}, {12103, 38110}, {12108, 48906}, {14561, 15704}, {14848, 50968}, {14924, 22112}, {14927, 15022}, {15054, 52697}, {15246, 37672}, {15462, 51522}, {15534, 15692}, {15689, 46267}, {15693, 40107}, {15694, 18553}, {15708, 51186}, {15712, 50978}, {15826, 37941}, {16936, 38402}, {19130, 49136}, {20397, 32233}, {20423, 33923}, {21167, 40341}, {22334, 31521}, {31670, 44245}, {43174, 51000}, {44682, 54173}, {48892, 49137}, {49135, 50959}, {51127, 51537}

X(55684) = midpoint of X(i) and X(j) for these {i,j}: {182, 55665}, {6, 55622}
X(55684) = reflection of X(i) in X(j) for these {i,j}: {1350, 55632}, {3, 55675}, {55620, 55652}, {55622, 55656}, {55632, 55662}, {55641, 3}, {55648, 55665}, {55656, 55671}, {55671, 55678}, {55678, 55683}, {55683, 5092}
X(55684) = inverse of X(55614) in First Brocard Circle
X(55684) = center of Tucker-Hagos(6/11) circle
X(55684) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(22246)}}, {{A, B, C, X(39), X(43691)}}, {{A, B, C, X(1176), X(33636)}}, {{A, B, C, X(3532), X(5024)}}, {{A, B, C, X(5481), X(11477)}}, {{A, B, C, X(9605), X(22334)}}, {{A, B, C, X(14528), X(21309)}}
X(55684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11482, 3098}, {3, 1351, 55631}, {3, 5050, 52987}, {3, 511, 55641}, {3, 52987, 55646}, {3, 53091, 55602}, {3, 576, 55626}, {3, 6, 55614}, {3, 55580, 14810}, {3, 55595, 55647}, {3, 55602, 55649}, {3, 55610, 55650}, {3, 55614, 55651}, {3, 55620, 55652}, {3, 55641, 55656}, {3, 55678, 55675}, {3, 55682, 55679}, {6, 53094, 55673}, {6, 55651, 55591}, {182, 17508, 55653}, {182, 5092, 55682}, {182, 55583, 575}, {182, 55592, 53091}, {182, 55644, 22330}, {182, 55653, 5093}, {182, 55665, 511}, {182, 55670, 33878}, {182, 55672, 55596}, {182, 55674, 55616}, {182, 55675, 55628}, {182, 55682, 55676}, {371, 372, 22246}, {511, 5092, 55683}, {511, 55652, 55620}, {511, 55656, 55622}, {511, 55683, 55678}, {575, 55617, 37517}, {575, 55666, 55617}, {576, 55647, 55595}, {576, 55681, 55677}, {1151, 1152, 5024}, {1350, 11477, 55583}, {1350, 5085, 12017}, {1350, 55646, 55627}, {1350, 55653, 31884}, {1350, 55671, 55662}, {1351, 55654, 55607}, {1351, 55672, 55654}, {5050, 52987, 53858}, {5085, 5092, 53094}, {5085, 53093, 20190}, {5092, 20190, 55681}, {5093, 55682, 17508}, {5097, 55667, 55639}, {6409, 6410, 53095}, {10541, 53094, 3}, {10541, 53097, 53093}, {11477, 53093, 53092}, {11477, 55606, 53097}, {12017, 17508, 1350}, {12017, 55678, 55632}, {14810, 22234, 55580}, {14924, 41424, 30734}, {15516, 55658, 55593}, {15520, 55659, 55604}, {15815, 39560, 6}, {17508, 37517, 55666}, {17508, 55613, 55670}, {17508, 55632, 55671}, {20190, 53093, 10541}, {20190, 55606, 182}, {20190, 55677, 576}, {20190, 55679, 55606}, {22112, 30734, 14924}, {22234, 55580, 5102}, {22236, 22238, 9605}, {22330, 33878, 11477}, {22330, 55670, 55644}, {31884, 55656, 55648}, {36836, 36843, 5013}, {37517, 55666, 55643}, {39561, 55668, 55629}, {44456, 55655, 55618}, {50664, 55669, 55610}, {53091, 55649, 55582}, {55583, 55644, 55613}, {55606, 55653, 55637}, {55616, 55648, 55635}, {55628, 55675, 55665}, {55635, 55665, 55660}

X(55685) = X(2)X(54891)∩X(3)X(6)

Barycentrics    9*a^6-5*a^4*(b^2+c^2)-2*a^2*(2*b^4+9*b^2*c^2+2*c^4) : :
X(55685) = 13*X[3]+5*X[6], -X[3543]+10*X[10168], 8*X[3589]+X[48896], 5*X[3618]+4*X[33751], -14*X[3832]+5*X[48884], -2*X[3845]+5*X[38317], 4*X[3850]+5*X[44882], 4*X[3853]+5*X[48898], -X[5059]+10*X[48892], 13*X[5067]+5*X[46264], 5*X[5476]+4*X[15690], 4*X[6329]+5*X[46853] and many others

X(55685) lies on these lines: {2, 54891}, {3, 6}, {542, 15708}, {1428, 51817}, {1503, 11539}, {3524, 5965}, {3543, 10168}, {3545, 29012}, {3564, 41983}, {3589, 48896}, {3618, 33751}, {3796, 15082}, {3832, 48884}, {3845, 38317}, {3850, 44882}, {3853, 48898}, {5059, 48892}, {5067, 46264}, {5476, 15690}, {5645, 15107}, {6329, 46853}, {9306, 33879}, {10516, 15723}, {11001, 14561}, {11178, 15702}, {11812, 51137}, {12007, 44682}, {12100, 51140}, {13595, 35268}, {14853, 51211}, {15686, 38110}, {15698, 51214}, {15704, 42785}, {15711, 51138}, {15719, 50994}, {15720, 43150}, {16187, 35265}, {18583, 41981}, {19124, 47485}, {19130, 33703}, {19710, 51165}, {19711, 50977}, {25555, 48879}, {29317, 33750}, {29323, 38335}, {33884, 55038}, {37913, 43650}, {38136, 48904}, {39884, 41992}, {44580, 51136}, {46332, 51166}, {48895, 49133}

X(55685) = midpoint of X(i) and X(j) for these {i,j}: {182, 55667}, {15520, 55613}, {33750, 38064}, {39561, 55640}, {5050, 55654}, {5085, 55682}, {6, 55624}
X(55685) = reflection of X(i) in X(j) for these {i,j}: {17508, 55682}, {3098, 55654}, {52987, 55613}, {55596, 55624}, {55603, 55640}, {55613, 55649}, {55624, 55657}, {55630, 55660}, {55640, 3}, {55649, 55667}, {55654, 55670}, {55660, 55673}, {55667, 17508}, {55682, 5092}
X(55685) = inverse of X(55612) in First Brocard Circle
X(55685) = center of Tucker-Hagos(5/9) circle
X(55685) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55612)}}, {{A, B, C, X(6), X(54891)}}, {{A, B, C, X(5481), X(37517)}}
X(55685) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 182, 37517}, {3, 37517, 55633}, {3, 39561, 55603}, {3, 5050, 55591}, {3, 50664, 55587}, {3, 5092, 55683}, {3, 5102, 55627}, {3, 511, 55640}, {3, 6, 55612}, {3, 55587, 55642}, {3, 55622, 55653}, {3, 55636, 55655}, {3, 55680, 17508}, {182, 3098, 22234}, {182, 5092, 55681}, {182, 55585, 575}, {182, 55603, 39561}, {182, 55637, 6}, {182, 55649, 15520}, {182, 55669, 55581}, {182, 55674, 55608}, {182, 55676, 55628}, {511, 17508, 55667}, {511, 5092, 55682}, {511, 55624, 55596}, {511, 55649, 55613}, {511, 55657, 55624}, {511, 55660, 55630}, {511, 55670, 55654}, {511, 55673, 55660}, {575, 55655, 55585}, {575, 55664, 55610}, {576, 3098, 55584}, {576, 55674, 55658}, {1350, 55677, 55665}, {1351, 55644, 55598}, {1351, 55668, 55644}, {3098, 17508, 55670}, {3098, 20190, 182}, {3098, 55648, 55637}, {5050, 5085, 20190}, {5050, 55595, 5093}, {5085, 31884, 12017}, {5092, 20190, 53094}, {5093, 14810, 55589}, {5097, 55650, 55594}, {10541, 55678, 14810}, {11477, 55659, 3098}, {12017, 53094, 55650}, {12017, 55674, 576}, {15516, 55646, 55583}, {15520, 55613, 511}, {15520, 55649, 52987}, {15520, 55672, 55649}, {17508, 39561, 3}, {17508, 55596, 55669}, {17508, 55649, 55672}, {17508, 55660, 55673}, {17508, 55670, 55675}, {17508, 55683, 55680}, {20190, 55670, 5050}, {20190, 55679, 55588}, {20190, 55680, 55645}, {22234, 37517, 5097}, {33750, 38064, 29317}, {33878, 55666, 55652}, {39561, 55587, 5102}, {44456, 55647, 55605}, {52987, 55672, 55662}, {53092, 55656, 55590}, {53094, 55584, 55674}, {53097, 55661, 55635}, {55588, 55670, 55657}, {55594, 55612, 55602}, {55603, 55630, 55618}, {55608, 55649, 31884}, {55610, 55676, 55664}

X(55686) = X(3)X(6)∩X(1503)X(10124)

Barycentrics    a^2*(12*a^4-5*b^4-24*b^2*c^2-5*c^4-7*a^2*(b^2+c^2)) : :
X(55686) = 17*X[3]+7*X[6], 5*X[3618]+X[48920], -3*X[3839]+7*X[38317], 5*X[3858]+7*X[44882], -13*X[5068]+7*X[48889], 7*X[5476]+5*X[15697], 17*X[7486]+7*X[46264], -7*X[10168]+X[15687], -7*X[11180]+55*X[15721], 7*X[14561]+X[15683], 9*X[15709]+7*X[25406], -25*X[15713]+49*X[50988] and many others

X(55686) lies on these lines: {3, 6}, {1503, 10124}, {3564, 41152}, {3618, 48920}, {3839, 38317}, {3858, 44882}, {5066, 29012}, {5068, 48889}, {5476, 15697}, {5650, 9544}, {6688, 35268}, {7486, 46264}, {8718, 46847}, {10168, 15687}, {11180, 15721}, {11645, 15699}, {14561, 15683}, {15691, 29317}, {15709, 25406}, {15713, 50988}, {17578, 48898}, {19710, 38110}, {21167, 50978}, {38064, 51538}, {38136, 48892}, {48891, 49138}, {48895, 49135}

X(55686) = midpoint of X(i) and X(j) for these {i,j}: {182, 55670}, {14810, 39561}, {15516, 55638}, {15520, 55615}, {20190, 55680}, {38136, 48892}, {5050, 55657}, {575, 55649}, {576, 55599}, {5085, 5092}, {5093, 55606}, {5097, 55610}, {50664, 55663}, {6, 55627}
X(55686) = reflection of X(i) in X(j) for these {i,j}: {20190, 5085}, {55591, 55609}, {55596, 55625}, {55597, 55627}, {55599, 55636}, {55601, 55638}, {55610, 55647}, {55612, 55649}, {55621, 55657}, {55627, 55659}, {55631, 55663}, {55638, 3}, {55645, 55664}, {55649, 55668}, {55653, 55670}, {55663, 55674}, {55664, 17508}, {55670, 55679}, {55674, 55680}, {55680, 5092}
X(55686) = inverse of X(55608) in First Brocard Circle
X(55686) = center of Tucker-Hagos(7/12) circle
X(55686) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15516, 55601}, {3, 511, 55638}, {3, 6, 55608}, {6, 55677, 55659}, {6, 55683, 55677}, {182, 17508, 31884}, {182, 22330, 50664}, {182, 3098, 53092}, {182, 33878, 575}, {182, 5092, 55679}, {182, 55625, 15516}, {182, 55644, 6}, {182, 55653, 22330}, {182, 55660, 5093}, {182, 55665, 11477}, {182, 55672, 55583}, {182, 55674, 55592}, {182, 55676, 55606}, {182, 55679, 55653}, {182, 55681, 55665}, {182, 55684, 5092}, {511, 17508, 55664}, {511, 5085, 20190}, {511, 5092, 55680}, {511, 55609, 55591}, {511, 55625, 55596}, {511, 55627, 55597}, {511, 55636, 55599}, {511, 55647, 55610}, {511, 55649, 55612}, {511, 55657, 55621}, {511, 55659, 55627}, {511, 55668, 55649}, {511, 55674, 55663}, {575, 5092, 53094}, {575, 53094, 55668}, {576, 55666, 55636}, {576, 55678, 55666}, {1351, 55661, 55617}, {1351, 55675, 55661}, {5050, 17508, 55657}, {5085, 55673, 12017}, {5085, 55684, 55682}, {5092, 14810, 55681}, {5092, 55677, 55683}, {5093, 55676, 55660}, {5093, 55682, 55676}, {5097, 55672, 55647}, {5102, 31884, 33878}, {10541, 55672, 5097}, {11477, 12017, 182}, {11477, 31884, 55593}, {11477, 55665, 14810}, {12017, 53094, 55600}, {12017, 55673, 39561}, {14810, 39561, 511}, {15516, 55664, 55615}, {15520, 17508, 3}, {17508, 31884, 55670}, {17508, 55589, 55667}, {17508, 55664, 55674}, {22234, 55651, 55586}, {31884, 55593, 55613}, {31884, 55615, 55625}, {31884, 55653, 55645}, {31884, 55682, 17508}, {37517, 55671, 55650}, {39561, 55667, 55620}, {39561, 55681, 55673}, {44456, 55662, 55623}, {50664, 55674, 55631}, {53091, 55658, 55588}, {53093, 55669, 55594}, {55599, 55666, 55654}

X(55687) = X(3)X(6)∩X(4)X(10168)

Barycentrics    5*a^6-3*a^4*(b^2+c^2)-2*a^2*(b^4+5*b^2*c^2+c^4) : :
X(55687) = 7*X[3]+3*X[6], -X[4]+6*X[10168], -17*X[5]+12*X[50960], X[20]+4*X[25555], -8*X[140]+3*X[11178], -3*X[141]+8*X[12108], 3*X[206]+2*X[15579], -4*X[546]+9*X[38317], 2*X[548]+3*X[597], -6*X[549]+X[34507], 2*X[550]+3*X[5476], -2*X[599]+7*X[51141] and many others

X(55687) lies on these lines: {2, 54857}, {3, 6}, {4, 10168}, {5, 50960}, {20, 25555}, {23, 11451}, {140, 11178}, {141, 12108}, {184, 7496}, {206, 15579}, {518, 31666}, {524, 15712}, {542, 631}, {546, 38317}, {548, 597}, {549, 34507}, {550, 5476}, {599, 51141}, {632, 1503}, {698, 32523}, {1176, 13452}, {1352, 10303}, {1656, 11645}, {1657, 47352}, {1843, 35479}, {1974, 14865}, {1995, 22352}, {3090, 46264}, {3091, 29012}, {3146, 19130}, {3292, 7485}, {3357, 9968}, {3431, 43812}, {3518, 19124}, {3522, 19924}, {3523, 11179}, {3524, 50992}, {3525, 24206}, {3526, 18553}, {3528, 20423}, {3529, 14561}, {3530, 8550}, {3534, 46267}, {3544, 14927}, {3589, 3627}, {3618, 17538}, {3628, 3818}, {3832, 25565}, {3850, 48310}, {3856, 51022}, {5012, 9716}, {5020, 14924}, {5026, 7815}, {5070, 25561}, {5072, 47355}, {5076, 29323}, {5079, 36990}, {5182, 33004}, {5480, 12103}, {5609, 32305}, {5643, 34417}, {6329, 48874}, {6800, 16187}, {7387, 52163}, {7527, 52093}, {7550, 10984}, {7555, 51739}, {7991, 38029}, {8541, 21844}, {8546, 10610}, {8584, 14891}, {8703, 41153}, {9039, 43146}, {9306, 40916}, {9813, 32154}, {9925, 12038}, {10249, 10282}, {10299, 54173}, {10356, 12252}, {11202, 15582}, {11204, 34117}, {11422, 15246}, {11470, 35473}, {11579, 15020}, {11649, 37952}, {12812, 51126}, {14002, 35268}, {14093, 51185}, {14853, 48885}, {14869, 48906}, {14928, 32832}, {15039, 16010}, {15054, 15462}, {15055, 25556}, {15069, 15720}, {15080, 16042}, {15082, 26864}, {15533, 15718}, {15534, 15706}, {15578, 34779}, {15693, 50989}, {15704, 38110}, {15717, 33749}, {16239, 47354}, {17578, 50975}, {17800, 38072}, {18583, 44245}, {19128, 35475}, {19140, 51522}, {20582, 50988}, {20583, 51181}, {21766, 44109}, {22165, 41983}, {22486, 33276}, {23041, 50414}, {23042, 44883}, {28538, 31447}, {31166, 52102}, {31455, 53499}, {31670, 33750}, {32135, 34473}, {32599, 43652}, {35477, 44102}, {38079, 50971}, {39884, 42786}, {42785, 51163}, {44682, 50979}, {46219, 47353}, {46853, 50987}, {48881, 51732}, {48891, 49137}, {48895, 49136}

X(55687) = midpoint of X(i) and X(j) for these {i,j}: {182, 55672}, {11482, 55614}, {12017, 53094}, {14093, 51185}, {22234, 55637}, {3, 53093}, {46264, 51537}, {575, 55650}, {576, 55600}, {53091, 55646}, {6, 55629}
X(55687) = reflection of X(i) in X(j) for these {i,j}: {182, 12017}, {1350, 55634}, {11482, 575}, {22234, 53093}, {3, 55677}, {3098, 55655}, {576, 22234}, {52987, 55614}, {53094, 5092}, {55587, 55598}, {55595, 55623}, {55598, 55629}, {55600, 55637}, {55604, 14810}, {55608, 55646}, {55614, 55650}, {55619, 55653}, {55629, 55661}, {55637, 3}, {55646, 55666}, {55655, 55672}, {55661, 55674}, {55672, 53094}
X(55687) = inverse of X(55606) in First Brocard Circle
X(55687) = center of Tucker-Hagos(3/5) circle
X(55687) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55606)}}, {{A, B, C, X(6), X(54857)}}, {{A, B, C, X(39), X(13452)}}, {{A, B, C, X(576), X(5481)}}, {{A, B, C, X(5024), X(44763)}}
X(55687) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 55631}, {3, 1350, 55647}, {3, 1351, 55626}, {3, 20190, 182}, {3, 3098, 55652}, {3, 5085, 20190}, {3, 5093, 55620}, {3, 53091, 55595}, {3, 53094, 55677}, {3, 53097, 14810}, {3, 53858, 55617}, {3, 6, 55606}, {3, 55580, 55641}, {3, 55595, 55646}, {3, 55606, 55649}, {3, 55620, 55651}, {3, 55679, 55675}, {20, 38064, 25555}, {182, 15520, 50664}, {182, 3098, 39561}, {182, 37517, 5050}, {182, 5092, 17508}, {182, 55608, 53091}, {182, 55628, 53092}, {182, 55633, 15516}, {182, 55649, 6}, {182, 55662, 5097}, {182, 55667, 37517}, {182, 55674, 55587}, {182, 55681, 3}, {182, 55683, 55669}, {182, 55685, 5092}, {511, 14810, 55604}, {511, 5092, 53094}, {511, 575, 11482}, {511, 55629, 55598}, {511, 55646, 55608}, {511, 55653, 55619}, {511, 55674, 55661}, {575, 20190, 10541}, {575, 5092, 55679}, {575, 55631, 11477}, {1350, 50664, 15520}, {1350, 55640, 3098}, {1350, 55647, 55628}, {1350, 55658, 55640}, {1350, 55670, 55658}, {1350, 55678, 55670}, {1351, 55626, 55588}, {1351, 55653, 55603}, {1351, 55673, 55653}, {3523, 11179, 40107}, {3526, 43273, 18553}, {3530, 8550, 50977}, {5085, 53094, 12017}, {5085, 55686, 55685}, {5092, 14810, 55680}, {5092, 17508, 55683}, {5092, 50664, 55678}, {5092, 55674, 55682}, {5093, 55651, 55594}, {5093, 55664, 55630}, {5097, 31884, 55585}, {5097, 55668, 31884}, {5102, 55639, 55590}, {5102, 55663, 55613}, {5351, 5352, 15515}, {10541, 53094, 55614}, {10541, 55614, 53093}, {10541, 55675, 576}, {10541, 55679, 52987}, {10541, 55681, 55644}, {11482, 53093, 575}, {11482, 55614, 511}, {11482, 55629, 55580}, {11482, 55675, 55655}, {12017, 55677, 22234}, {12017, 55681, 55600}, {12017, 55682, 55629}, {14561, 48892, 48904}, {14810, 22330, 53097}, {14810, 37517, 55596}, {14810, 53097, 55611}, {14810, 55676, 55667}, {14810, 55680, 55676}, {15516, 55657, 33878}, {15516, 55671, 55633}, {15520, 55658, 1350}, {17508, 39561, 55660}, {17508, 55587, 55665}, {17508, 55605, 55668}, {17508, 55655, 55672}, {17508, 55665, 55674}, {20190, 55680, 22330}, {20190, 55683, 55583}, {20190, 55684, 55681}, {22234, 55672, 55637}, {22234, 55675, 55650}, {31670, 33750, 33751}, {31884, 55585, 55605}, {31884, 55668, 55662}, {33878, 55671, 55657}, {38317, 44882, 48884}, {39561, 55660, 55589}, {43120, 43121, 52771}, {44456, 55654, 55612}, {45552, 45553, 21163}, {50664, 55674, 55621}, {53091, 53094, 55666}, {55581, 55642, 55610}, {55582, 55648, 55615}, {55584, 55656, 55627}, {55586, 55645, 55616}, {55590, 55663, 55639}, {55595, 55646, 55623}, {55603, 55653, 55635}, {55604, 55629, 55618}, {55610, 55659, 55642}, {55628, 55637, 55634}

X(55688) = X(3)X(6)∩X(51)X(5645)

Barycentrics    a^2*(8*a^4-3*b^4-16*b^2*c^2-3*c^4-5*a^2*(b^2+c^2)) : :
X(55688) = 11*X[3]+5*X[6], 7*X[549]+X[51136], 3*X[597]+X[48885], -5*X[631]+X[43150], -5*X[1352]+21*X[15702], X[3529]+7*X[42785], -17*X[3533]+5*X[18553], 3*X[3543]+5*X[48898], 27*X[3545]+5*X[14927], -5*X[3589]+X[3853], X[3629]+7*X[44682] and many others

X(55688) lies on these lines: {3, 6}, {51, 5645}, {110, 34468}, {542, 11812}, {547, 11645}, {549, 51136}, {597, 48885}, {631, 43150}, {1352, 15702}, {1495, 12045}, {1503, 16239}, {3529, 42785}, {3530, 5965}, {3533, 18553}, {3543, 48898}, {3545, 14927}, {3589, 3853}, {3629, 44682}, {3796, 16187}, {3818, 5067}, {3819, 11003}, {3832, 38317}, {3845, 10168}, {3850, 29012}, {5056, 46264}, {5059, 14561}, {5476, 48920}, {5480, 15686}, {5943, 37913}, {6329, 33923}, {6688, 13595}, {6776, 15708}, {8681, 37283}, {10193, 41729}, {10219, 22112}, {11001, 38064}, {11179, 15719}, {11539, 24206}, {11737, 51135}, {12007, 12100}, {12107, 40284}, {14891, 51138}, {15246, 55038}, {15690, 18583}, {15700, 51140}, {15723, 43273}, {19128, 35478}, {19711, 48876}, {19924, 50972}, {21766, 34986}, {29181, 41981}, {33703, 48895}, {33750, 48880}, {37126, 43612}, {38110, 48892}, {38335, 48942}, {47352, 48904}, {48874, 50987}, {48943, 49133}, {51027, 51137}

X(55688) = midpoint of X(i) and X(j) for these {i,j}: {182, 55674}, {1351, 55592}, {11737, 51135}, {14810, 15516}, {14891, 51138}, {18583, 33751}, {3, 50664}, {3098, 22330}, {39561, 55645}, {5050, 55663}, {575, 55653}, {576, 55601}, {5085, 55686}, {5092, 20190}, {5097, 55612}, {6, 55631}, {6329, 33923}
X(55688) = reflection of X(i) in X(j) for these {i,j}: {55609, 55647}, {55617, 55653}, {55625, 55659}, {55636, 3}, {55647, 55668}, {55659, 55674}, {55668, 55679}, {55679, 5092}
X(55688) = inverse of X(55603) in First Brocard Circle
X(55688) = center of Tucker-Hagos(5/8) circle
X(55688) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1297), X(55636)}}, {{A, B, C, X(5097), X(5481)}}, {{A, B, C, X(34567), X(34571)}}, {{A, B, C, X(40803), X(55585)}}
X(55688) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 55622}, {3, 182, 5097}, {3, 37517, 55627}, {3, 39561, 55594}, {3, 5050, 55582}, {3, 5092, 55680}, {3, 511, 55636}, {3, 6, 55603}, {3, 55582, 55640}, {3, 55591, 55642}, {3, 55594, 55645}, {3, 55607, 55649}, {3, 55642, 55657}, {182, 14810, 15516}, {182, 17508, 1350}, {182, 5097, 50664}, {182, 55633, 39561}, {182, 55655, 6}, {182, 55675, 55581}, {182, 55678, 55619}, {182, 55679, 55625}, {182, 55681, 55655}, {182, 55685, 55683}, {511, 5092, 55679}, {511, 55647, 55609}, {511, 55653, 55617}, {511, 55668, 55647}, {511, 55674, 55659}, {575, 55586, 5093}, {576, 55642, 55591}, {576, 55657, 55601}, {1350, 17508, 55666}, {1350, 55583, 55590}, {1350, 55627, 55612}, {1350, 55629, 55613}, {1350, 55651, 55632}, {1350, 55662, 14810}, {1350, 55666, 55653}, {1351, 14810, 55592}, {1351, 53094, 55669}, {1351, 55592, 511}, {1351, 55622, 55587}, {3098, 55677, 55664}, {3098, 55682, 55677}, {5050, 55672, 55606}, {5085, 5092, 20190}, {5085, 55684, 12017}, {5092, 14810, 53094}, {5092, 55670, 55681}, {5092, 55677, 55682}, {5092, 55687, 55686}, {5093, 55637, 55586}, {10541, 53091, 182}, {10541, 55671, 53091}, {10541, 55677, 22330}, {10541, 55682, 3098}, {11477, 55658, 55615}, {11482, 55656, 55596}, {12017, 17508, 575}, {12017, 55684, 17508}, {14810, 53094, 55674}, {14810, 55590, 55616}, {14810, 55616, 55631}, {14810, 55666, 55662}, {15516, 55592, 1351}, {15520, 55646, 55588}, {17508, 37517, 3}, {17508, 55617, 55668}, {17508, 55643, 55670}, {17508, 55684, 5092}, {20190, 22330, 10541}, {22234, 55665, 55610}, {33878, 55650, 55621}, {33878, 55667, 55650}, {37517, 55603, 55583}, {44456, 55644, 55599}, {50664, 55653, 37517}, {52987, 55661, 55638}, {52987, 55673, 55661}, {53091, 55682, 55671}, {53092, 55654, 55585}, {53097, 55660, 55634}, {55584, 55619, 55597}, {55585, 55654, 55623}, {55606, 55672, 55663}, {55612, 55645, 55633}, {55631, 55653, 55643}, {55653, 55686, 55684}, {55680, 55686, 55685}

X(55689) = X(2)X(54934)∩X(3)X(6)

Barycentrics    11*a^6-7*a^4*(b^2+c^2)-2*a^2*(2*b^4+11*b^2*c^2+2*c^4) : :
X(55689) = 15*X[3]+7*X[6], -4*X[141]+15*X[51137], -12*X[3530]+X[3630], -14*X[3589]+3*X[15687], 10*X[3618]+X[48879], -7*X[3818]+18*X[15699], -3*X[3839]+14*X[10168], -10*X[3858]+21*X[38317], 4*X[3861]+7*X[44882], -10*X[5066]+21*X[48310], 15*X[5071]+7*X[46264], 7*X[5476]+4*X[15691] and many others

X(55689) lies on these lines: {2, 54934}, {3, 6}, {141, 51137}, {184, 5888}, {542, 15721}, {3530, 3630}, {3589, 15687}, {3618, 48879}, {3818, 15699}, {3839, 10168}, {3855, 29012}, {3858, 38317}, {3861, 44882}, {5066, 48310}, {5071, 46264}, {5476, 15691}, {6030, 10545}, {6144, 15700}, {6329, 50987}, {7712, 22112}, {10124, 18358}, {11008, 33749}, {11178, 15709}, {11179, 51141}, {14561, 49138}, {15080, 44082}, {15682, 19130}, {15683, 38064}, {15697, 31670}, {15713, 20582}, {17504, 32455}, {22165, 44580}, {25555, 43621}, {35018, 51126}, {38110, 42785}, {42786, 48154}, {43150, 51186}, {46267, 48910}, {47352, 48891}

X(55689) = midpoint of X(i) and X(j) for these {i,j}: {182, 55675}, {6, 55632}
X(55689) = reflection of X(i) in X(j) for these {i,j}: {3098, 55656}, {55628, 55662}, {55635, 3}, {55642, 55665}, {55652, 55671}, {55662, 55675}, {55665, 55678}, {55675, 55683}, {55678, 5092}, {55683, 55684}
X(55689) = inverse of X(55601) in First Brocard Circle
X(55689) = center of Tucker-Hagos(7/11) circle
X(55689) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55601)}}, {{A, B, C, X(6), X(54934)}}, {{A, B, C, X(5041), X(14491)}}, {{A, B, C, X(5481), X(15520)}}, {{A, B, C, X(11270), X(31652)}}, {{A, B, C, X(15602), X(20421)}}
X(55689) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15516, 55596}, {3, 15520, 55608}, {3, 182, 15520}, {3, 511, 55635}, {3, 6, 55601}, {3, 55638, 55655}, {6, 5092, 17508}, {6, 55654, 33878}, {6, 55671, 55632}, {182, 17508, 52987}, {182, 53094, 55633}, {182, 55603, 575}, {182, 55649, 22234}, {182, 55658, 6}, {182, 55667, 576}, {182, 55675, 511}, {182, 55679, 55613}, {182, 55681, 55649}, {182, 55683, 55662}, {182, 55685, 55681}, {182, 55687, 55685}, {511, 5092, 55678}, {511, 55662, 55628}, {511, 55678, 55665}, {575, 55663, 55584}, {575, 55669, 55603}, {575, 55682, 55669}, {576, 3098, 55582}, {1351, 55660, 55611}, {1351, 55677, 55660}, {3098, 17508, 55668}, {3098, 55582, 55598}, {3098, 55656, 55642}, {3098, 55665, 55656}, {3098, 55668, 55658}, {5085, 55688, 55687}, {5092, 50664, 55676}, {5092, 55594, 55679}, {5092, 55653, 53094}, {5092, 55678, 55683}, {5093, 55659, 55600}, {5097, 55673, 55644}, {6200, 6396, 15602}, {10541, 39561, 182}, {10541, 55674, 39561}, {11477, 55666, 55640}, {12017, 55676, 50664}, {15520, 55585, 37517}, {17508, 39561, 55654}, {17508, 55610, 55667}, {17508, 55652, 55671}, {17508, 55658, 55672}, {17508, 55671, 55675}, {20190, 55684, 55652}, {22234, 55649, 55581}, {22330, 55651, 55589}, {37517, 55608, 55585}, {39561, 55674, 55637}, {44456, 55661, 3098}, {44456, 55676, 55661}, {50664, 55661, 44456}, {50664, 55668, 55586}, {52987, 55633, 55610}, {53091, 55657, 55583}, {53093, 55670, 55587}, {55585, 55598, 55590}, {55585, 55658, 55630}, {55598, 55667, 55653}, {55615, 55674, 3}, {55620, 55671, 55663}, {55672, 55685, 5092}

X(55690) = X(3)X(6)∩X(110)X(44321)

Barycentrics    a^2*(10*a^4-3*b^4-20*b^2*c^2-3*c^4-7*a^2*(b^2+c^2)) : :
X(55690) = 13*X[3]+7*X[6], 3*X[597]+2*X[33751], -7*X[1352]+27*X[15709], -7*X[3589]+2*X[3861], -7*X[3818]+17*X[7486], 33*X[3855]+7*X[14927], -2*X[5066]+7*X[10168], 13*X[5068]+7*X[46264], 7*X[5480]+3*X[19710], 7*X[6776]+33*X[15721], -12*X[10124]+7*X[24206], 13*X[11179]+7*X[50994] and many others

X(55690) lies on circumconic {{A, B, C, X(5481), X(15516)}} and on these lines: {3, 6}, {110, 44321}, {542, 15713}, {597, 33751}, {1352, 15709}, {1503, 48154}, {1843, 44880}, {3589, 3861}, {3818, 7486}, {3855, 14927}, {3858, 29012}, {5066, 10168}, {5068, 46264}, {5071, 11645}, {5480, 19710}, {6776, 15721}, {10124, 24206}, {11179, 50994}, {11451, 22352}, {14561, 48943}, {15682, 38064}, {15683, 46267}, {15687, 44882}, {15691, 18583}, {15699, 25561}, {17578, 29323}, {19924, 50987}, {21167, 33749}, {25555, 48891}, {32237, 43650}, {38110, 48895}, {47352, 48896}, {48885, 51732}

X(55690) = midpoint of X(i) and X(j) for these {i,j}: {182, 53094}, {12017, 55687}, {22234, 55646}, {3098, 11482}, {575, 55661}, {576, 55604}, {5097, 55619}, {53091, 55655}, {53093, 55672}, {6, 55637}
X(55690) = reflection of X(i) in X(j) for these {i,j}: {12017, 20190}, {14810, 55666}, {22234, 50664}, {5092, 55687}, {5097, 53091}, {55586, 55595}, {55590, 55608}, {55594, 55623}, {55598, 55631}, {55606, 55646}, {55614, 55653}, {55619, 55655}, {55623, 55661}, {55634, 3}, {55650, 55672}, {55655, 55674}, {55661, 55677}, {55666, 53094}, {55677, 5092}
X(55690) = inverse of X(55596) in First Brocard Circle
X(55690) = center of Tucker-Hagos(7/10) circle
X(55690) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 15520, 55601}, {3, 182, 15516}, {3, 5085, 55689}, {3, 511, 55634}, {3, 6, 55596}, {3, 55585, 55638}, {3, 55630, 55653}, {3, 55689, 55686}, {6, 55648, 55581}, {6, 55679, 55657}, {182, 14810, 575}, {182, 17508, 1351}, {182, 5085, 55688}, {182, 5092, 14810}, {182, 55587, 5050}, {182, 55655, 53091}, {182, 55662, 39561}, {182, 55669, 6}, {182, 55674, 5097}, {182, 55681, 55587}, {182, 55682, 55592}, {182, 55683, 1350}, {182, 55685, 55669}, {182, 55687, 53094}, {182, 55688, 5092}, {511, 20190, 12017}, {511, 50664, 22234}, {511, 5092, 55677}, {511, 55623, 55594}, {511, 55631, 55598}, {511, 55653, 55614}, {511, 55661, 55623}, {511, 55672, 55650}, {511, 55674, 55655}, {575, 5092, 55670}, {576, 55668, 55627}, {576, 55682, 55668}, {1350, 55683, 55674}, {1351, 17508, 55659}, {1351, 55638, 55590}, {1351, 55659, 55606}, {3098, 55684, 55680}, {5085, 12017, 55687}, {5092, 55606, 17508}, {5092, 55657, 55679}, {5093, 55658, 55597}, {5097, 55648, 55588}, {5097, 55666, 55619}, {10541, 17508, 50664}, {11477, 55667, 55636}, {12017, 53094, 182}, {12017, 55687, 511}, {12017, 55688, 55666}, {14810, 55588, 55612}, {14810, 55590, 55615}, {14810, 55666, 55661}, {15516, 55659, 55585}, {15516, 55674, 55625}, {17508, 22234, 55646}, {17508, 55585, 3}, {22330, 55649, 55586}, {33878, 55675, 55663}, {37517, 55673, 55647}, {39561, 55662, 55584}, {39561, 55676, 55631}, {44456, 55660, 55617}, {50664, 55679, 55624}, {52987, 55678, 55664}, {53093, 53094, 55629}, {53094, 55614, 55671}, {53094, 55629, 55672}, {53097, 55665, 55645}, {55581, 55669, 55648}, {55583, 55656, 55621}, {55584, 55676, 55662}, {55590, 55634, 55608}, {55592, 55668, 55651}, {55612, 55688, 55685}, {55624, 55646, 55637}, {55625, 55638, 55633}

X(55691) = X(2)X(54608)∩X(3)X(6)

Barycentrics    7*a^6-5*a^4*(b^2+c^2)-2*a^2*(b^4+7*b^2*c^2+c^4) : :
X(55691) = 9*X[3]+5*X[6], -5*X[69]+33*X[15719], -5*X[141]+12*X[11812], -12*X[547]+5*X[3818], -9*X[549]+2*X[3631], 5*X[597]+2*X[15690], 27*X[3524]+X[11008], -3*X[3543]+10*X[19130], -10*X[3589]+3*X[3845], 25*X[3618]+3*X[11001], 5*X[3620]+9*X[11179], X[3629]+6*X[12100] and many others

X(55691) lies on these lines: {2, 54608}, {3, 6}, {30, 42785}, {69, 15719}, {141, 11812}, {184, 44299}, {524, 19711}, {542, 3619}, {547, 3818}, {549, 3631}, {597, 15690}, {1176, 11738}, {1503, 42786}, {1843, 44878}, {1974, 13596}, {2330, 37587}, {3523, 5965}, {3524, 11008}, {3533, 23294}, {3543, 19130}, {3545, 7919}, {3589, 3845}, {3618, 11001}, {3620, 11179}, {3629, 12100}, {3630, 41983}, {3832, 29012}, {3850, 38317}, {3853, 44882}, {5054, 43150}, {5059, 25555}, {5067, 25406}, {5476, 15686}, {5645, 7492}, {5888, 11003}, {6329, 8703}, {6688, 41424}, {7485, 44109}, {10250, 35228}, {10519, 33749}, {10545, 35268}, {10546, 22112}, {10984, 12112}, {11178, 11539}, {11204, 41593}, {11531, 38029}, {11645, 47355}, {12007, 15712}, {13595, 15080}, {14561, 33703}, {14853, 33751}, {15693, 40341}, {15711, 20583}, {15723, 18440}, {16239, 18358}, {17504, 51138}, {19124, 34484}, {19924, 51171}, {21850, 50987}, {23046, 51135}, {33750, 48885}, {34417, 37913}, {35400, 38072}, {38110, 48898}, {38335, 48905}, {38727, 41731}, {41462, 55038}, {41981, 51732}, {41982, 51166}, {41985, 47354}, {46267, 48891}, {47352, 48895}, {49133, 53023}

X(55691) = midpoint of X(i) and X(j) for these {i,j}: {182, 55681}, {576, 55605}, {53092, 55651}, {53858, 55616}, {6, 55639}
X(55691) = reflection of X(i) in X(j) for these {i,j}: {182, 10541}, {3098, 55658}, {52987, 55616}, {55602, 14810}, {55605, 55644}, {55611, 55651}, {55633, 3}, {55644, 55669}, {55658, 55676}, {55669, 55681}, {55676, 5092}
X(55691) = inverse of X(55594) in First Brocard Circle
X(55691) = isogonal conjugate of X(54643)
X(55691) = center of Tucker-Hagos(5/7) circle
X(55691) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55594)}}, {{A, B, C, X(6), X(54608)}}, {{A, B, C, X(39), X(11738)}}, {{A, B, C, X(74), X(53096)}}, {{A, B, C, X(3431), X(35007)}}, {{A, B, C, X(5481), X(39561)}}, {{A, B, C, X(7772), X(14483)}}, {{A, B, C, X(20421), X(37512)}}
X(55691) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55645}, {3, 1351, 55618}, {3, 182, 39561}, {3, 5085, 55688}, {3, 5097, 55603}, {3, 5102, 55612}, {3, 511, 55633}, {3, 6, 55594}, {3, 55582, 55636}, {3, 55594, 55642}, {3, 55612, 55649}, {3, 55640, 55655}, {3, 55688, 55685}, {6, 55653, 55585}, {6, 55676, 55639}, {6, 55678, 55653}, {15, 16, 53096}, {182, 15520, 53093}, {182, 17508, 576}, {182, 37517, 50664}, {182, 5085, 55687}, {182, 52987, 5050}, {182, 55649, 575}, {182, 55662, 53091}, {182, 55667, 22234}, {182, 55672, 6}, {182, 55681, 511}, {182, 55683, 55587}, {182, 55684, 55660}, {182, 55687, 17508}, {182, 55688, 55683}, {182, 55689, 5092}, {511, 14810, 55602}, {511, 55644, 55605}, {511, 55651, 55611}, {575, 55612, 5102}, {575, 55668, 33878}, {576, 55655, 55596}, {1350, 55667, 55652}, {1350, 55679, 55667}, {1351, 55637, 55589}, {1351, 55656, 55601}, {1351, 55670, 55637}, {3098, 17508, 55665}, {3098, 33878, 55600}, {3098, 55646, 55635}, {3098, 55660, 55646}, {3098, 55669, 55658}, {5050, 55674, 52987}, {5050, 55684, 55674}, {5085, 20190, 182}, {5085, 5092, 55689}, {5092, 20190, 12017}, {5092, 55586, 55677}, {5092, 55653, 55678}, {5092, 55661, 55679}, {5092, 55668, 53094}, {5092, 55676, 55681}, {5093, 55631, 55581}, {5093, 55671, 55631}, {6200, 6396, 37512}, {10541, 55684, 53858}, {10541, 55687, 55644}, {11477, 55657, 55608}, {11482, 55654, 55590}, {12017, 55688, 37517}, {12017, 55689, 3098}, {14810, 15520, 55583}, {14810, 44456, 55598}, {14810, 53093, 15520}, {14810, 55682, 55675}, {15516, 55677, 31884}, {15520, 55598, 44456}, {15520, 55675, 14810}, {17508, 39561, 55640}, {17508, 55587, 3}, {17508, 55644, 55669}, {20190, 55690, 5085}, {22234, 55667, 1350}, {22330, 55666, 55610}, {33878, 53094, 55668}, {37517, 55603, 55582}, {37517, 55658, 55607}, {50664, 55636, 5097}, {53091, 55673, 55606}, {53094, 55634, 55672}, {53097, 55659, 55630}, {55584, 55647, 55613}, {55590, 55654, 55628}, {55594, 55627, 55609}, {55600, 55644, 55626}, {55601, 55670, 55656}, {55603, 55685, 55680}, {55606, 55673, 55662}, {55626, 55639, 55634}, {55627, 55688, 55684}

X(55692) = X(2)X(48662)∩X(3)X(6)

Barycentrics    a^2*(11*a^4-3*b^4-22*b^2*c^2-3*c^4-8*a^2*(b^2+c^2)) : :
X(55692) = -12*X[2]+X[48662], 7*X[3]+4*X[6], -12*X[140]+X[5921], X[193]+10*X[15712], X[376]+10*X[50987], 9*X[381]+2*X[14927], -X[382]+12*X[38110], 4*X[548]+7*X[51171], -12*X[549]+X[11898], 8*X[597]+3*X[15689], 10*X[631]+X[39899], 10*X[632]+X[39874] and many others

X(55692) lies on these lines: {2, 48662}, {3, 6}, {22, 5644}, {110, 16419}, {140, 5921}, {193, 15712}, {376, 50987}, {381, 14927}, {382, 38110}, {524, 15718}, {548, 51171}, {549, 11898}, {597, 15689}, {631, 39899}, {632, 39874}, {1176, 33541}, {1352, 15694}, {1353, 3524}, {1503, 5070}, {1656, 25406}, {1657, 3618}, {1992, 15706}, {3066, 20850}, {3526, 40330}, {3530, 14912}, {3534, 18583}, {3564, 15720}, {3589, 3843}, {3620, 12108}, {3796, 22112}, {3830, 38064}, {3851, 46264}, {5020, 26881}, {5032, 14891}, {5054, 6776}, {5055, 51737}, {5073, 14561}, {5480, 15681}, {5544, 43650}, {5622, 15040}, {5651, 44108}, {7484, 11003}, {7712, 30734}, {8148, 38029}, {8780, 16187}, {10124, 50954}, {10168, 19709}, {10299, 33748}, {11160, 41983}, {11179, 15701}, {11402, 21766}, {12308, 15462}, {12315, 23042}, {13093, 19132}, {14093, 48874}, {14530, 52028}, {14848, 15695}, {14853, 15696}, {14893, 51177}, {15684, 47352}, {15685, 48901}, {15686, 51173}, {15688, 51212}, {15692, 50962}, {15693, 48876}, {15700, 50979}, {15703, 43273}, {15714, 51028}, {15717, 34380}, {15722, 50989}, {17800, 51163}, {17825, 32237}, {18440, 46219}, {18525, 38118}, {19123, 34469}, {19154, 54992}, {21356, 50988}, {21850, 33750}, {25555, 49139}, {32217, 35452}, {32300, 38788}, {32621, 37283}, {33751, 54131}, {38049, 48661}, {38072, 48896}, {38119, 48680}, {38136, 49136}, {38633, 48679}, {46267, 48904}, {49134, 53023}

X(55692) = midpoint of X(i) and X(j) for these {i,j}: {182, 55683}, {6, 55641}
X(55692) = reflection of X(i) in X(j) for these {i,j}: {1350, 55635}, {3, 55678}, {55620, 55656}, {55622, 55662}, {55632, 3}, {55641, 55665}, {55648, 55671}, {55656, 55675}, {55671, 55683}, {55675, 5092}, {55678, 55684}, {55684, 55689}
X(55692) = inverse of X(55593) in First Brocard Circle
X(55692) = center of Tucker-Hagos(8/11) circle
X(55692) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5013), X(44763)}}, {{A, B, C, X(5481), X(53091)}}, {{A, B, C, X(13452), X(22332)}}, {{A, B, C, X(14489), X(55604)}}, {{A, B, C, X(40803), X(55582)}}
X(55692) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 55616}, {3, 182, 53091}, {3, 44456, 55624}, {3, 5050, 44456}, {3, 5093, 55604}, {3, 511, 55632}, {3, 6, 55593}, {6, 5085, 55687}, {6, 55676, 55636}, {6, 55687, 55682}, {182, 1350, 5050}, {182, 17508, 5097}, {182, 5097, 53093}, {182, 55655, 575}, {182, 55674, 6}, {182, 55683, 511}, {182, 55684, 55648}, {182, 55685, 55655}, {182, 55687, 55674}, {182, 55688, 53094}, {182, 55689, 55683}, {182, 55690, 5085}, {182, 55691, 55690}, {511, 5092, 55675}, {511, 55665, 55641}, {511, 55683, 55671}, {511, 55689, 55684}, {575, 5092, 55664}, {575, 55664, 55585}, {575, 55676, 55610}, {576, 5092, 55673}, {1350, 10541, 182}, {1350, 15516, 1351}, {1350, 44456, 55584}, {1350, 53094, 55669}, {1350, 55635, 55620}, {1350, 55649, 55629}, {1350, 55651, 55631}, {1350, 55656, 55635}, {1350, 55659, 55639}, {1350, 55671, 55656}, {1350, 55673, 55659}, {1351, 5050, 15516}, {1351, 55629, 55587}, {1351, 55678, 55662}, {5050, 12017, 10541}, {5050, 55624, 5093}, {5050, 55639, 576}, {5050, 55682, 55649}, {5085, 20190, 12017}, {5085, 53094, 55688}, {5085, 55684, 55689}, {5092, 55585, 55676}, {5092, 55631, 17508}, {5092, 55656, 55678}, {5097, 17508, 55651}, {5102, 55653, 55595}, {6455, 6456, 15515}, {10541, 55687, 55580}, {11477, 55672, 55643}, {11482, 55681, 3}, {14891, 51181, 5032}, {15516, 55664, 55592}, {15516, 55669, 1350}, {15516, 55675, 55622}, {15516, 55688, 5092}, {15520, 55668, 55614}, {17508, 53093, 33878}, {22234, 55657, 55582}, {22330, 55658, 55591}, {31884, 50664, 11482}, {37517, 55654, 55602}, {37517, 55677, 55654}, {39561, 55679, 55646}, {45578, 45579, 10983}, {50664, 55681, 31884}, {53093, 53094, 55608}, {55608, 55662, 55642}, {55628, 55689, 55685}, {55642, 55665, 55661}, {55649, 55675, 55665}

X(55693) = X(3)X(6)∩X(154)X(12045)

Barycentrics    9*a^6-7*a^4*(b^2+c^2)-2*a^2*(b^4+9*b^2*c^2+c^4) : :
X(55693) = 11*X[3]+7*X[6], 7*X[597]+2*X[15691], -14*X[3589]+5*X[3858], -10*X[3618]+X[48904], -7*X[3818]+16*X[35018], 11*X[3855]+7*X[46264], -16*X[3861]+7*X[48884], -4*X[5066]+7*X[38317], -5*X[5071]+14*X[10168], 7*X[5476]+2*X[19710], -16*X[10124]+7*X[11178], 7*X[11179]+11*X[15721] and many others

X(55693) lies on these lines: {3, 6}, {154, 12045}, {184, 33879}, {542, 15709}, {597, 15691}, {1503, 15699}, {3589, 3858}, {3618, 48904}, {3818, 35018}, {3839, 29012}, {3855, 46264}, {3861, 48884}, {5066, 38317}, {5071, 10168}, {5476, 19710}, {10124, 11178}, {10519, 51140}, {10984, 16261}, {11179, 15721}, {11224, 38029}, {14561, 15682}, {14853, 15697}, {15687, 38110}, {15713, 50983}, {17578, 19130}, {18583, 48879}, {19124, 52294}, {19924, 33750}, {22112, 35265}, {25555, 48896}, {26881, 43650}, {29323, 47352}, {32455, 44682}, {38136, 48898}, {44580, 50977}, {46267, 53023}, {48880, 51732}, {48885, 51171}, {48892, 51538}, {50974, 50990}

X(55693) = midpoint of X(i) and X(j) for these {i,j}: {182, 55685}, {15520, 55630}, {39561, 55660}, {5050, 55673}, {5093, 55618}, {6, 55643}
X(55693) = reflection of X(i) in X(j) for these {i,j}: {17508, 55685}, {3098, 55660}, {52987, 55618}, {55596, 55630}, {55603, 55643}, {55613, 55654}, {55618, 55657}, {55630, 3}, {55640, 55667}, {55643, 55670}, {55649, 55673}, {55660, 17508}, {55667, 55682}, {55673, 5092}, {55685, 5085}
X(55693) = inverse of X(55590) in First Brocard Circle
X(55693) = center of Tucker-Hagos(7/9) circle
X(55693) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5085, 55686}, {3, 511, 55630}, {3, 6, 55590}, {3, 55585, 55635}, {3, 55690, 55689}, {6, 55688, 55681}, {182, 17508, 39561}, {182, 20190, 55691}, {182, 37517, 53093}, {182, 52987, 50664}, {182, 55649, 5050}, {182, 55672, 575}, {182, 55681, 6}, {182, 55686, 55596}, {182, 55688, 55655}, {182, 55691, 55687}, {511, 17508, 55660}, {511, 5085, 55685}, {511, 5092, 55673}, {511, 55643, 55603}, {511, 55654, 55613}, {511, 55657, 55618}, {511, 55667, 55640}, {511, 55670, 55643}, {575, 5092, 55659}, {575, 55659, 44456}, {575, 55680, 31884}, {576, 55631, 55583}, {576, 55644, 55588}, {1350, 5092, 55675}, {1350, 55664, 55649}, {1351, 55658, 55600}, {1351, 55679, 55658}, {3098, 55687, 55683}, {5050, 55615, 15520}, {5050, 55639, 5093}, {5050, 55682, 55624}, {5085, 5102, 55684}, {5092, 20190, 55692}, {5092, 50664, 55639}, {5092, 55609, 55676}, {5093, 53094, 55657}, {5097, 55663, 55593}, {5097, 55676, 55637}, {10541, 55690, 55585}, {10541, 55691, 55669}, {10541, 55692, 5092}, {11477, 55668, 55633}, {12017, 20190, 182}, {12017, 55692, 10541}, {15516, 55585, 576}, {15520, 55630, 511}, {15520, 55686, 17508}, {17508, 39561, 3098}, {17508, 55596, 3}, {17508, 55640, 55667}, {17508, 55655, 55670}, {17508, 55691, 5085}, {22330, 55646, 55581}, {31884, 55680, 55672}, {33878, 55677, 55662}, {37517, 55674, 55644}, {39561, 55669, 55589}, {44456, 55611, 55587}, {44456, 55659, 55611}, {50664, 53094, 52987}, {52987, 53094, 55665}, {53092, 55671, 55594}, {53093, 55674, 37517}, {53097, 55666, 55642}, {53858, 55648, 55586}, {55584, 55661, 55628}, {55585, 55649, 55615}, {55587, 55672, 55652}, {55588, 55674, 55656}, {55590, 55601, 55595}, {55590, 55690, 55688}, {55593, 55676, 55663}, {55601, 55686, 55680}, {55603, 55649, 55631}, {55613, 55667, 55654}, {55649, 55675, 55664}, {55667, 55685, 55682}

X(55694) = X(3)X(6)∩X(542)X(3525)

Barycentrics    11*a^6-9*a^4*(b^2+c^2)-2*a^2*(b^4+11*b^2*c^2+c^4) : :
X(55694) = 13*X[3]+9*X[6], -X[382]+12*X[46267], 2*X[546]+9*X[51737], 9*X[597]+2*X[12103], -65*X[631]+21*X[50994], -20*X[632]+9*X[11178], -7*X[3090]+18*X[10168], -25*X[3091]+36*X[25565], -X[3146]+12*X[25555], 7*X[3523]+4*X[33749], 17*X[3544]+27*X[25406], -18*X[3589]+7*X[3857] and many others

X(55694) lies on these lines: {3, 6}, {382, 46267}, {542, 3525}, {546, 51737}, {597, 12103}, {631, 50994}, {632, 11178}, {3090, 10168}, {3091, 25565}, {3146, 25555}, {3523, 33749}, {3544, 25406}, {3589, 3857}, {3618, 11541}, {3627, 38079}, {3628, 47354}, {3796, 30734}, {3818, 12812}, {5026, 38627}, {5072, 11645}, {5076, 47352}, {5079, 43273}, {5476, 15704}, {5643, 35268}, {6593, 38626}, {8550, 12108}, {10303, 11179}, {12811, 38317}, {14869, 34507}, {15021, 25556}, {16042, 43650}, {16189, 38029}, {18800, 33001}, {19124, 26863}, {19130, 50688}, {29012, 50689}, {33751, 51171}, {38110, 48884}, {38631, 51157}, {40107, 50961}, {48904, 49140}, {51141, 51175}

X(55694) = midpoint of X(i) and X(j) for these {i,j}: {182, 55689}, {6, 55648}
X(55694) = reflection of X(i) in X(j) for these {i,j}: {3098, 55662}, {52987, 55620}, {55628, 3}, {55635, 55665}, {55642, 55671}, {55652, 55675}, {55662, 55678}, {55665, 55683}, {55671, 5092}, {55675, 55684}, {55683, 55689}, {55689, 55692}
X(55694) = inverse of X(55588) in First Brocard Circle
X(55694) = center of Tucker-Hagos(9/11) circle
X(55694) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 55617}, {3, 22234, 55583}, {3, 511, 55628}, {3, 53093, 22330}, {3, 53858, 55597}, {3, 576, 55600}, {3, 6, 55588}, {3, 55588, 55637}, {3, 55600, 55644}, {3, 55628, 55652}, {182, 12017, 55693}, {182, 20190, 55687}, {182, 5092, 39561}, {182, 52987, 53093}, {182, 55649, 50664}, {182, 55672, 5050}, {182, 55685, 6}, {182, 55689, 511}, {182, 55690, 55669}, {182, 55691, 17508}, {182, 55692, 55683}, {182, 55693, 55691}, {511, 5092, 55671}, {511, 55665, 55635}, {511, 55678, 55662}, {511, 55692, 55689}, {575, 20190, 5085}, {575, 53097, 15520}, {575, 55597, 53858}, {575, 55674, 53097}, {575, 55677, 55590}, {575, 55679, 55602}, {576, 55644, 55587}, {1351, 5085, 5092}, {1351, 5092, 55667}, {1351, 53093, 575}, {1351, 55612, 55581}, {1351, 55647, 52987}, {1351, 55667, 3098}, {3098, 39561, 1351}, {3098, 55581, 55596}, {3098, 55593, 55605}, {3098, 55651, 55640}, {3098, 55652, 55641}, {3098, 55667, 55655}, {3098, 55669, 55657}, {3098, 55687, 55681}, {5050, 55688, 55672}, {5085, 55641, 55684}, {5085, 55657, 55685}, {5092, 50664, 55604}, {5092, 55599, 55674}, {5092, 55620, 55675}, {5093, 55668, 55608}, {5097, 55658, 55589}, {5097, 55682, 55658}, {5102, 55659, 55598}, {10541, 12017, 20190}, {10541, 20190, 182}, {10541, 55693, 576}, {11477, 55677, 55649}, {15516, 55676, 55603}, {15520, 55667, 55599}, {17508, 55600, 3}, {17508, 55635, 55665}, {20190, 55679, 55690}, {37517, 53094, 55660}, {39561, 55683, 55642}, {44456, 55666, 55630}, {50664, 55677, 11477}, {52987, 55637, 55612}, {52987, 55642, 55620}, {52987, 55667, 55647}, {53091, 55670, 55585}, {53092, 53094, 55631}, {53092, 55631, 37517}, {53093, 55623, 22234}, {55596, 55665, 55648}, {55597, 55647, 55623}, {55632, 55671, 55663}, {55637, 55685, 55679}, {55640, 55691, 55688}, {55641, 55684, 55678}

X(55695) = X(2)X(44108)∩X(3)X(6)

Barycentrics    a^2*(6*a^4-b^4-12*b^2*c^2-c^4-5*a^2*(b^2+c^2)) : :
X(55695) = 7*X[3]+5*X[6], -4*X[140]+X[43150], 5*X[597]+X[15686], -5*X[1352]+17*X[3533], -X[3146]+7*X[42785], -X[3543]+5*X[14561], -5*X[3589]+2*X[3850], -25*X[3618]+X[33703], X[3629]+5*X[15712], -X[3631]+4*X[12108], -5*X[3818]+11*X[5056], 7*X[3832]+5*X[46264] and many others

X(55695) lies on these lines: {2, 44108}, {3, 6}, {140, 43150}, {154, 10219}, {184, 15082}, {373, 13595}, {518, 31662}, {524, 41983}, {542, 11539}, {547, 1503}, {548, 6329}, {549, 5965}, {597, 15686}, {1352, 3533}, {3146, 42785}, {3530, 12007}, {3543, 14561}, {3545, 11645}, {3564, 11812}, {3589, 3850}, {3618, 33703}, {3629, 15712}, {3631, 12108}, {3796, 6688}, {3818, 5056}, {3832, 46264}, {3845, 29012}, {3853, 19130}, {3917, 55038}, {5012, 5650}, {5059, 48901}, {5476, 11001}, {5480, 48891}, {5622, 17701}, {5640, 22352}, {5892, 34513}, {5943, 35268}, {6800, 43650}, {7496, 44109}, {7998, 34986}, {8584, 51181}, {8703, 51166}, {9977, 43804}, {10249, 23042}, {10282, 15580}, {10984, 46847}, {11003, 33879}, {11178, 15723}, {11179, 15702}, {11540, 50958}, {11695, 43129}, {12045, 35259}, {12100, 51138}, {12101, 51135}, {12294, 35478}, {13366, 33884}, {13561, 16239}, {13596, 19128}, {14891, 20583}, {14912, 15719}, {15055, 34155}, {15533, 51141}, {15690, 29181}, {15693, 51140}, {15711, 51132}, {15713, 51136}, {16200, 38029}, {18553, 44516}, {18583, 48892}, {19711, 21167}, {20423, 33750}, {21850, 33751}, {22165, 50988}, {25555, 38136}, {25563, 41729}, {33748, 54173}, {33749, 48876}, {38118, 38155}, {38335, 47352}, {38728, 41731}, {39588, 44878}, {41981, 48885}, {44580, 50982}, {48896, 49133}, {48920, 51732}, {50989, 51137}

X(55695) = midpoint of X(i) and X(j) for these {i,j}: {182, 5085}, {10249, 23042}, {1351, 55596}, {14912, 50977}, {15055, 34155}, {15516, 55663}, {15520, 31884}, {21167, 50979}, {22330, 55638}, {25406, 38317}, {3, 39561}, {3098, 5093}, {37517, 55591}, {38110, 51737}, {38136, 44882}, {5050, 17508}, {575, 55670}, {576, 55610}, {5097, 55627}, {5102, 55603}, {50664, 55680}, {6, 55649}
X(55695) = reflection of X(i) in X(j) for these {i,j}: {1350, 55638}, {14561, 46267}, {14810, 55670}, {17508, 55686}, {3, 55680}, {3098, 55663}, {31884, 55664}, {38136, 25555}, {39561, 50664}, {48895, 38136}, {5085, 20190}, {5092, 5085}, {5093, 15516}, {5097, 39561}, {55586, 55596}, {55588, 55599}, {55590, 55610}, {55591, 55612}, {55593, 55621}, {55594, 55627}, {55596, 55631}, {55599, 14810}, {55603, 55645}, {55606, 55649}, {55610, 55653}, {55615, 55657}, {55627, 3}, {55638, 55668}, {55649, 55674}, {55657, 17508}, {55663, 55679}, {55670, 5092}, {55680, 55688}
X(55695) = inverse of X(55587) in First Brocard Circle
X(55695) = center of Tucker-Hagos(5/6) circle
X(55695) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5481), X(50664)}}, {{A, B, C, X(13452), X(53096)}}, {{A, B, C, X(37512), X(46123)}}
X(55695) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55642}, {3, 1351, 55607}, {3, 182, 50664}, {3, 37517, 55612}, {3, 5050, 5102}, {3, 5085, 55685}, {3, 5097, 55594}, {3, 511, 55627}, {3, 6, 55587}, {3, 55582, 55633}, {3, 55587, 55636}, {3, 55591, 55640}, {3, 55603, 55645}, {3, 55618, 55649}, {3, 55633, 55653}, {3, 55645, 55657}, {3, 55685, 55680}, {6, 17508, 55621}, {6, 5085, 55682}, {6, 5092, 55661}, {6, 53094, 55641}, {182, 17508, 5050}, {182, 3098, 53093}, {182, 5092, 575}, {182, 55685, 39561}, {182, 55687, 6}, {182, 55688, 5097}, {182, 55689, 576}, {182, 55690, 14810}, {182, 55692, 55674}, {182, 55693, 5085}, {182, 55694, 12017}, {511, 14810, 55599}, {511, 15516, 5093}, {511, 55599, 55588}, {511, 55610, 55590}, {511, 55649, 55606}, {511, 55653, 55610}, {576, 55689, 53094}, {1350, 55660, 55638}, {1350, 55668, 55650}, {1350, 55681, 55668}, {1351, 55596, 511}, {1351, 55631, 55586}, {1351, 55654, 55596}, {1351, 55672, 55631}, {1351, 55684, 55672}, {3098, 53093, 15516}, {3098, 55673, 55663}, {3098, 55679, 55666}, {5050, 31884, 15520}, {5050, 5092, 55615}, {5050, 55682, 55593}, {5085, 12017, 55693}, {5085, 17508, 55686}, {5085, 53093, 55673}, {5085, 55654, 55684}, {5085, 55682, 55687}, {5092, 14810, 55677}, {5092, 20190, 55690}, {5092, 55634, 55676}, {5092, 55666, 55679}, {10541, 12017, 182}, {10541, 55694, 20190}, {11477, 55655, 55601}, {11477, 55678, 55655}, {11482, 55651, 55585}, {15516, 55679, 3098}, {15520, 17508, 31884}, {17508, 31884, 55664}, {17508, 39561, 55603}, {17508, 55603, 3}, {17508, 55657, 55670}, {17508, 55686, 5092}, {20190, 50664, 55688}, {20190, 55688, 55691}, {22234, 55669, 33878}, {22330, 55668, 1350}, {25406, 38064, 38317}, {25406, 38317, 11645}, {25555, 44882, 48895}, {29323, 46267, 14561}, {33878, 55647, 55619}, {33878, 55669, 55647}, {37517, 55640, 55591}, {38110, 51737, 29012}, {39561, 55640, 37517}, {39561, 55667, 55582}, {44456, 55637, 55592}, {44456, 55671, 55637}, {52987, 55659, 55634}, {52987, 55676, 55659}, {53091, 55676, 52987}, {53092, 55675, 55597}, {53094, 55610, 55667}, {53097, 55658, 55625}, {55584, 55644, 55609}, {55585, 55651, 55617}, {55587, 55649, 55618}, {55590, 55606, 55598}, {55590, 55653, 55623}, {55596, 55672, 55654}, {55612, 55688, 55683}, {55638, 55668, 55660}, {55641, 55692, 55689}, {55649, 55693, 55692}

X(55696) = X(2)X(54851)∩X(3)X(6)

Barycentrics    a^2*(8*a^4-b^4-16*b^2*c^2-c^4-7*a^2*(b^2+c^2)) : :
X(55696) = 9*X[3]+7*X[6], -7*X[141]+15*X[15713], -9*X[549]+X[3630], 7*X[597]+X[19710], -7*X[3589]+3*X[5066], -35*X[3618]+3*X[15682], 7*X[3619]+9*X[11179], -35*X[3620]+99*X[15721], -X[3631]+9*X[50983], -7*X[3818]+15*X[5071], 9*X[3839]+7*X[46264], 11*X[3855]+21*X[25406] and many others

X(55696) lies on these lines: {2, 54851}, {3, 6}, {141, 15713}, {373, 7712}, {524, 44580}, {542, 10124}, {549, 3630}, {597, 19710}, {1176, 13603}, {1495, 6688}, {1503, 35018}, {2330, 37602}, {3292, 5888}, {3589, 5066}, {3618, 15682}, {3619, 11179}, {3620, 15721}, {3631, 50983}, {3818, 5071}, {3819, 44109}, {3839, 46264}, {3855, 25406}, {3858, 38110}, {3861, 29012}, {5068, 38317}, {5476, 15683}, {5943, 15080}, {6144, 15693}, {6329, 19924}, {6636, 44107}, {10168, 15699}, {10219, 35264}, {10545, 32237}, {11003, 15082}, {12100, 32455}, {12112, 44870}, {13366, 41462}, {14561, 17578}, {14853, 48920}, {15018, 22352}, {15301, 44224}, {15687, 19130}, {15697, 48880}, {18358, 48154}, {18553, 39874}, {20080, 50977}, {25555, 29323}, {25561, 47355}, {29317, 51732}, {44091, 52294}, {47352, 48884}, {48898, 49135}, {48901, 49138}, {48910, 51173}, {51137, 51175}, {51181, 54169}

X(55696) = midpoint of X(i) and X(j) for these {i,j}: {182, 20190}, {1351, 55597}, {14810, 22330}, {15520, 55638}, {3, 15516}, {39561, 55664}, {46267, 51737}, {5050, 55680}, {575, 55674}, {576, 55612}, {5092, 50664}, {5093, 55621}, {5097, 55631}, {6, 55653}
X(55696) = reflection of X(i) in X(j) for these {i,j}: {55609, 55653}, {55617, 55659}, {55625, 3}, {55636, 55668}, {55647, 55674}, {55659, 55679}, {55668, 5092}, {55679, 55688}, {55688, 20190}
X(55696) = inverse of X(55585) in First Brocard Circle
X(55696) = isogonal conjugate of X(54734)
X(55696) = center of Tucker-Hagos(7/8) circle
X(55696) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55585)}}, {{A, B, C, X(6), X(54851)}}, {{A, B, C, X(39), X(13603)}}, {{A, B, C, X(74), X(31652)}}, {{A, B, C, X(7772), X(14491)}}, {{A, B, C, X(15515), X(20421)}}
X(55696) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 55625}, {3, 6, 55585}, {3, 55590, 55638}, {3, 55634, 55653}, {6, 12017, 55691}, {6, 5085, 55678}, {6, 55672, 55594}, {6, 55676, 55604}, {15, 16, 31652}, {182, 10541, 55695}, {182, 12017, 5092}, {182, 17508, 53093}, {182, 37479, 39515}, {182, 5085, 575}, {182, 5092, 50664}, {182, 55687, 5050}, {182, 55690, 15516}, {182, 55691, 6}, {182, 55695, 20190}, {511, 20190, 55688}, {511, 5092, 55668}, {511, 55653, 55609}, {511, 55659, 55617}, {511, 55674, 55647}, {511, 55679, 55659}, {575, 55657, 1351}, {576, 55646, 55586}, {576, 55662, 55593}, {576, 55670, 55612}, {1350, 55677, 55663}, {1350, 55685, 55677}, {1351, 5085, 55681}, {1351, 55597, 511}, {1351, 55657, 55597}, {1351, 55681, 55657}, {3098, 33878, 55599}, {3098, 37517, 53097}, {3098, 5092, 55674}, {3098, 55590, 55601}, {3098, 55647, 55636}, {3098, 55658, 55643}, {3098, 55662, 55646}, {5050, 14810, 22330}, {5050, 5085, 55667}, {5050, 55676, 37517}, {5085, 53093, 55651}, {5092, 44456, 55664}, {5092, 55586, 55670}, {5092, 55594, 55672}, {5092, 55661, 17508}, {5092, 55668, 55679}, {5092, 55695, 12017}, {5093, 55655, 55588}, {5097, 55661, 33878}, {6200, 6396, 15515}, {11477, 55669, 55627}, {11482, 55671, 55603}, {12017, 33878, 55692}, {14810, 55618, 55631}, {14810, 55687, 55680}, {15516, 20190, 55686}, {15516, 55674, 55590}, {15516, 55686, 3}, {15520, 55667, 55596}, {15520, 55678, 55634}, {15520, 55693, 5085}, {17508, 33878, 55661}, {17508, 53093, 5097}, {20190, 22330, 55687}, {20190, 55601, 55689}, {20190, 55686, 55690}, {22234, 55683, 31884}, {22330, 55680, 14810}, {33878, 55651, 3098}, {37517, 55687, 55676}, {39561, 53094, 55606}, {39561, 55581, 53858}, {39561, 55658, 44456}, {39874, 42786, 18553}, {44456, 53094, 55658}, {52987, 55666, 55645}, {52987, 55682, 55666}, {53091, 55684, 55649}, {53092, 55673, 55587}, {53097, 55651, 55618}, {53858, 55643, 55581}, {55583, 55654, 55619}, {55584, 55660, 55623}, {55585, 55642, 55608}, {55587, 55673, 55650}, {55588, 55655, 55621}, {55612, 55674, 55662}, {55631, 55653, 55642}

X(55697) = X(2)X(50954)∩X(3)X(6)

Barycentrics    a^2*(9*a^4-b^4-18*b^2*c^2-c^4-8*a^2*(b^2+c^2)) : :
X(55697) = -14*X[2]+5*X[50954], 5*X[3]+4*X[6], X[20]+8*X[51732], -2*X[69]+11*X[15720], 8*X[140]+X[39899], X[193]+8*X[3530], X[381]+2*X[25406], -X[382]+10*X[3618], -10*X[549]+X[11160], 2*X[550]+7*X[51171], 8*X[597]+X[15681], -10*X[631]+X[11898] and many others

X(55697) lies on these lines: {2, 50954}, {3, 6}, {20, 51732}, {69, 15720}, {140, 39899}, {193, 3530}, {373, 3796}, {381, 25406}, {382, 3618}, {524, 15707}, {549, 11160}, {550, 51171}, {597, 15681}, {631, 11898}, {632, 5921}, {1176, 52100}, {1352, 46219}, {1353, 3523}, {1428, 6767}, {1495, 5544}, {1503, 5055}, {1597, 19128}, {1656, 48662}, {1657, 18583}, {1992, 15700}, {2330, 7373}, {2781, 38633}, {2854, 38638}, {3167, 5650}, {3517, 13363}, {3524, 33748}, {3526, 6776}, {3531, 37924}, {3534, 14853}, {3564, 5054}, {3589, 3851}, {3620, 14869}, {3628, 39874}, {3830, 14561}, {3843, 46264}, {5012, 6090}, {5020, 6800}, {5032, 17504}, {5070, 18440}, {5073, 44882}, {5079, 39884}, {5447, 43908}, {5476, 15685}, {5480, 17800}, {5622, 32609}, {5640, 5644}, {5790, 38118}, {5969, 38635}, {6329, 48873}, {6391, 12038}, {6467, 33556}, {7998, 11402}, {8705, 37922}, {9024, 38636}, {9751, 14614}, {10168, 10516}, {10170, 19347}, {10247, 38029}, {10299, 51170}, {10519, 15693}, {10601, 20850}, {11001, 51173}, {11179, 15694}, {11180, 15723}, {11284, 35265}, {11479, 16261}, {11812, 50974}, {12006, 12220}, {12100, 50962}, {12315, 19132}, {13903, 39875}, {13961, 39876}, {14269, 29012}, {14848, 15689}, {15035, 39562}, {15041, 52699}, {15533, 51137}, {15684, 53023}, {15688, 33750}, {15695, 20423}, {15696, 21850}, {15701, 22165}, {15711, 54174}, {15716, 50967}, {15718, 21167}, {15719, 50978}, {15722, 50977}, {15759, 51028}, {15988, 17573}, {18535, 19124}, {18859, 52238}, {19709, 38317}, {20127, 32300}, {20806, 43845}, {23042, 32063}, {25555, 48905}, {29323, 38072}, {33699, 51177}, {33749, 40341}, {34513, 39588}, {35259, 43650}, {35403, 46267}, {35452, 51733}, {36177, 47283}, {38079, 38335}, {38115, 51514}, {38116, 51515}, {38117, 51516}, {38119, 51517}, {38120, 51518}, {39568, 43651}, {40647, 43719}, {41149, 51138}, {43815, 47527}, {44214, 47447}, {44457, 51739}, {44580, 50986}, {48898, 49134}, {48901, 49139}, {50955, 51186}, {50980, 50992}, {50988, 51175}

X(55697) = midpoint of X(i) and X(j) for these {i,j}: {182, 55693}, {15520, 55640}, {3524, 33748}, {39561, 55667}, {5050, 55682}, {576, 55613}, {5093, 55624}, {6, 55654}
X(55697) = reflection of X(i) in X(j) for these {i,j}: {1350, 55640}, {15688, 33750}, {3, 55682}, {31884, 55667}, {5085, 55693}, {55591, 55613}, {55593, 55624}, {55610, 55654}, {55613, 55657}, {55618, 55660}, {55624, 3}, {55640, 55670}, {55643, 55673}, {55654, 17508}, {55667, 5092}, {55673, 55685}, {55682, 5085}, {55693, 55695}
X(55697) = inverse of X(55584) in First Brocard Circle
X(55697) = center of Tucker-Hagos(8/9) circle
X(55697) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(5008), X(44731)}}, {{A, B, C, X(5013), X(43719)}}, {{A, B, C, X(11270), X(15815)}}, {{A, B, C, X(16835), X(22332)}}, {{A, B, C, X(40801), X(55604)}}
X(55697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12017, 55692}, {3, 1351, 55604}, {3, 22246, 47618}, {3, 44456, 55616}, {3, 5050, 5093}, {3, 5093, 55593}, {3, 511, 55624}, {3, 53091, 44456}, {3, 6, 55584}, {3, 55584, 55632}, {6, 53094, 55626}, {6, 55676, 55601}, {182, 10541, 12017}, {182, 13336, 19129}, {182, 20190, 6}, {182, 5085, 5050}, {182, 5092, 53093}, {182, 55687, 50664}, {182, 55691, 575}, {182, 55692, 53091}, {182, 55694, 5092}, {182, 55696, 10541}, {511, 17508, 55654}, {511, 5085, 55682}, {511, 5092, 55667}, {511, 55613, 55591}, {511, 55657, 55613}, {511, 55660, 55618}, {511, 55670, 55640}, {511, 55673, 55643}, {511, 55685, 55673}, {511, 55695, 55693}, {575, 5092, 55612}, {576, 55676, 55629}, {1350, 50664, 53092}, {1350, 55621, 55610}, {1350, 55687, 55678}, {1351, 5050, 39561}, {1351, 55620, 55582}, {1351, 55678, 55647}, {1656, 48906, 48662}, {3098, 55690, 55684}, {3311, 3312, 5041}, {3524, 33748, 34380}, {5085, 10541, 55695}, {5085, 5102, 53094}, {5085, 53093, 31884}, {5085, 53094, 55686}, {5085, 55673, 55685}, {5092, 22330, 55655}, {5092, 55623, 55674}, {5092, 55642, 55676}, {5092, 55663, 17508}, {5097, 55646, 55580}, {5097, 55664, 55596}, {5097, 55681, 55646}, {5102, 53094, 55649}, {5102, 55649, 33878}, {6449, 6450, 37512}, {10541, 53093, 55694}, {11477, 55674, 55639}, {11482, 12017, 55690}, {11482, 55684, 3}, {12017, 33878, 55691}, {14810, 20190, 55689}, {15516, 55672, 53097}, {15520, 17508, 55621}, {15520, 55640, 511}, {15520, 55670, 1350}, {15520, 55687, 55670}, {17508, 20190, 5085}, {17508, 39561, 52987}, {17508, 52987, 55663}, {17508, 55649, 55668}, {17508, 55663, 55671}, {20190, 55601, 55688}, {22330, 55582, 1351}, {23042, 52028, 32063}, {25406, 38110, 381}, {31884, 55582, 55599}, {31884, 55599, 55620}, {37517, 55651, 55595}, {37517, 55679, 55651}, {39561, 55612, 5102}, {50664, 55670, 15520}, {52987, 55652, 55623}, {52987, 55694, 20190}, {53097, 55672, 55648}, {53858, 55656, 55587}, {55583, 55661, 55622}, {55585, 55666, 55641}, {55586, 55674, 55652}, {55587, 55677, 55656}, {55591, 55676, 55657}, {55596, 55681, 55664}, {55610, 55643, 55630}, {55612, 55647, 55634}, {55618, 55673, 55660}, {55621, 55670, 55658}

X(55698) = X(3)X(6)∩X(4)X(46267)

Barycentrics    a^2*(10*a^4-b^4-20*b^2*c^2-c^4-9*a^2*(b^2+c^2)) : :
X(55698) = 11*X[3]+9*X[6], -X[4]+6*X[46267], -11*X[140]+6*X[51143], -31*X[546]+36*X[51131], 3*X[549]+2*X[33749], 9*X[597]+X[15704], -11*X[631]+3*X[50990], -14*X[3090]+9*X[25561], 11*X[3525]+9*X[11179], X[3529]+9*X[5476], -17*X[3544]+27*X[38317], -9*X[3589]+4*X[12811] and many others

X(55698) lies on these lines: {3, 6}, {4, 46267}, {140, 51143}, {542, 632}, {546, 51131}, {549, 33749}, {597, 15704}, {631, 50990}, {1176, 46848}, {1503, 12812}, {3090, 25561}, {3091, 11645}, {3525, 11179}, {3529, 5476}, {3544, 38317}, {3589, 12811}, {3618, 29323}, {3627, 25555}, {3628, 10168}, {3818, 15022}, {3857, 38110}, {5072, 43273}, {5076, 51167}, {6329, 48885}, {6688, 30734}, {7496, 34986}, {8550, 14869}, {8584, 44682}, {9976, 15020}, {10303, 34507}, {11451, 14002}, {11541, 48898}, {12045, 26864}, {12102, 19130}, {12108, 40107}, {14561, 48942}, {15691, 41153}, {15696, 51185}, {18583, 48891}, {20791, 35499}, {35407, 50963}, {35475, 44102}, {37946, 43651}, {44882, 48943}, {46264, 50689}, {48892, 51732}, {48901, 49140}

X(55698) = midpoint of X(i) and X(j) for these {i,j}: {182, 12017}, {1351, 55598}, {11482, 55637}, {3, 22234}, {575, 55677}, {576, 55614}, {5097, 55634}, {53091, 55672}, {53093, 55687}, {6, 55655}
X(55698) = reflection of X(i) in X(j) for these {i,j}: {14810, 55672}, {575, 53093}, {5092, 55690}, {53091, 50664}, {55588, 55600}, {55594, 55629}, {55595, 55631}, {55606, 55650}, {55608, 55653}, {55619, 55661}, {55623, 3}, {55634, 55666}, {55646, 55674}, {55650, 55677}, {55661, 53094}, {55666, 5092}, {55677, 55687}, {55687, 20190}, {55690, 12017}
X(55698) = inverse of X(55583) in First Brocard Circle
X(55698) = center of Tucker-Hagos(9/10) circle
X(55698) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(39), X(46848)}}, {{A, B, C, X(13472), X(14075)}}
X(55698) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10541, 55694}, {3, 11477, 55611}, {3, 22330, 55588}, {3, 5050, 53858}, {3, 511, 55623}, {3, 53093, 22234}, {3, 53858, 52987}, {3, 576, 55597}, {3, 6, 55583}, {3, 55583, 55631}, {3, 55597, 14810}, {3, 55623, 55650}, {182, 20190, 575}, {182, 5085, 50664}, {182, 55687, 53093}, {182, 55691, 5050}, {182, 55693, 6}, {182, 55695, 5092}, {182, 55697, 55696}, {511, 50664, 53091}, {511, 5092, 55666}, {511, 53094, 55661}, {511, 55631, 55595}, {511, 55650, 55606}, {511, 55653, 55608}, {511, 55666, 55634}, {511, 55674, 55646}, {575, 55588, 22330}, {575, 55606, 5097}, {575, 55681, 55590}, {576, 55675, 55624}, {1350, 55689, 55680}, {1351, 55668, 55615}, {1351, 55685, 55668}, {3098, 55692, 55686}, {5050, 5085, 55660}, {5050, 55691, 55674}, {5085, 33878, 55683}, {5085, 53091, 55672}, {5085, 53093, 55614}, {5092, 5097, 55657}, {5092, 55590, 55670}, {5093, 55669, 55601}, {5097, 55657, 55586}, {5102, 55658, 55592}, {10541, 20190, 55695}, {10541, 53093, 12017}, {11477, 17508, 55647}, {11477, 55647, 55594}, {11482, 53094, 55637}, {11482, 55637, 511}, {11482, 55677, 55619}, {12017, 53091, 5085}, {12017, 53093, 55687}, {12017, 55646, 55691}, {12017, 55687, 20190}, {14810, 55609, 55627}, {15516, 55647, 11477}, {15520, 55652, 55580}, {15520, 55676, 55612}, {17508, 55581, 55656}, {17508, 55611, 3}, {20190, 50664, 55679}, {20190, 53093, 55677}, {20190, 55631, 55688}, {20190, 55687, 55690}, {20190, 55696, 10541}, {22330, 55679, 55628}, {33878, 55683, 55664}, {37517, 55659, 55599}, {37517, 55682, 55659}, {39561, 55675, 53097}, {44456, 55667, 55625}, {44483, 44484, 44504}, {50664, 55679, 576}, {50664, 55688, 55603}, {52987, 55691, 55684}, {53093, 53094, 11482}, {53097, 55675, 55653}, {55580, 55676, 55652}, {55582, 55662, 55621}, {55584, 55665, 55638}, {55585, 55671, 55645}, {55587, 55678, 55663}, {55588, 55623, 55600}, {55603, 55616, 55609}, {55603, 55672, 55655}, {55631, 55688, 55681}, {55637, 55687, 53094}, {55670, 55695, 55693}

X(55699) = X(2)X(54866)∩X(3)X(6)

Barycentrics    a^2*(11*a^4-b^4-22*b^2*c^2-c^4-10*a^2*(b^2+c^2)) : :
X(55699) = 6*X[3]+5*X[6], -5*X[69]+27*X[15708], -10*X[141]+21*X[15702], 3*X[376]+8*X[6329], -3*X[382]+14*X[42785], -4*X[547]+15*X[38064], -12*X[549]+X[40341], 10*X[597]+X[11001], -5*X[599]+16*X[11812], -15*X[631]+4*X[3631], -5*X[1352]+16*X[16239], 21*X[3523]+X[11008] and many others

X(55699) lies on these lines: {2, 54866}, {3, 6}, {69, 15708}, {141, 15702}, {154, 10546}, {376, 6329}, {382, 42785}, {524, 15719}, {542, 15723}, {547, 38064}, {549, 40341}, {597, 11001}, {599, 11812}, {631, 3631}, {1176, 14490}, {1352, 16239}, {1495, 17825}, {1503, 5056}, {3523, 11008}, {3524, 3629}, {3533, 6776}, {3543, 3618}, {3545, 3589}, {3619, 15069}, {3620, 8550}, {3630, 14912}, {3763, 11179}, {3796, 7712}, {3832, 7923}, {3845, 46264}, {3850, 36990}, {3853, 14561}, {5059, 5480}, {5067, 10516}, {5645, 48912}, {5892, 9973}, {5965, 15720}, {6144, 41983}, {7484, 44109}, {7485, 55038}, {7716, 47485}, {10168, 18440}, {10249, 19132}, {10387, 51817}, {10601, 15080}, {10606, 41593}, {11180, 51128}, {11278, 38315}, {11456, 33537}, {11531, 16491}, {14848, 48880}, {15018, 17810}, {15045, 17710}, {15066, 17809}, {15534, 19711}, {15580, 23041}, {15686, 31670}, {15690, 21850}, {15694, 43150}, {15698, 20583}, {15705, 51132}, {15707, 51140}, {15709, 51136}, {16176, 38728}, {16496, 30392}, {17813, 35228}, {18583, 43621}, {19130, 38335}, {21358, 39899}, {26864, 43650}, {33179, 38029}, {33703, 44882}, {37944, 51733}, {41981, 48873}, {46267, 48884}, {46333, 51130}, {48892, 51024}, {48898, 49133}, {48943, 50963}, {50968, 51166}, {50975, 51165}, {50976, 51171}, {51170, 51214}

X(55699) = midpoint of X(i) and X(j) for these {i,j}: {182, 55694}, {6, 55656}
X(55699) = reflection of X(i) in X(j) for these {i,j}: {1350, 55641}, {3, 55683}, {55620, 55662}, {55622, 3}, {55632, 55665}, {55641, 55671}, {55648, 55675}, {55656, 55678}, {55665, 5092}, {55671, 55684}, {55678, 55689}, {55684, 55692}, {55692, 55694}
X(55699) = inverse of X(55582) in First Brocard Circle
X(55699) = isogonal conjugate of X(54521)
X(55699) = center of Tucker-Hagos(10/11) circle
X(55699) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55582)}}, {{A, B, C, X(6), X(54866)}}, {{A, B, C, X(39), X(14490)}}, {{A, B, C, X(64), X(53096)}}, {{A, B, C, X(5024), X(11738)}}, {{A, B, C, X(9605), X(14483)}}, {{A, B, C, X(14528), X(35007)}}, {{A, B, C, X(37512), X(43713)}}
X(55699) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12017, 55691}, {3, 1351, 55603}, {3, 33878, 55636}, {3, 37517, 55607}, {3, 5050, 5097}, {3, 5097, 55591}, {3, 511, 55622}, {3, 6, 55582}, {3, 55587, 31884}, {3, 55607, 55646}, {3, 55627, 55651}, {3, 55642, 55656}, {3, 55685, 53094}, {6, 53094, 3098}, {182, 10541, 5085}, {182, 12017, 6}, {182, 20190, 5050}, {182, 5085, 53093}, {182, 55691, 50664}, {182, 55693, 575}, {182, 55694, 511}, {182, 55696, 12017}, {182, 55698, 55697}, {511, 5092, 55665}, {511, 55662, 55620}, {511, 55665, 55632}, {511, 55684, 55671}, {575, 5092, 55601}, {575, 55672, 44456}, {576, 55690, 55682}, {1351, 55673, 55626}, {1351, 55687, 55673}, {3098, 55592, 55604}, {3098, 55650, 55639}, {3098, 55672, 55659}, {3098, 55691, 55685}, {3618, 48905, 38072}, {3618, 51737, 48905}, {5050, 53094, 11477}, {5050, 55584, 22234}, {5050, 55692, 55675}, {5085, 55671, 55684}, {5092, 50664, 37517}, {5092, 55601, 55672}, {5092, 55646, 55676}, {5092, 55665, 55678}, {5093, 55674, 55614}, {5097, 55659, 55587}, {5097, 55683, 55648}, {5097, 55695, 20190}, {10541, 55684, 55694}, {10601, 15080, 31860}, {11179, 11539, 51027}, {11477, 53094, 55654}, {11477, 55626, 55588}, {11477, 55654, 1350}, {11477, 55675, 55641}, {12017, 55604, 55690}, {12017, 55678, 55692}, {12017, 55696, 10541}, {12017, 55697, 55696}, {15516, 55681, 55610}, {15520, 55679, 55629}, {17508, 53091, 53097}, {17508, 55612, 3}, {20190, 55588, 55687}, {20190, 55645, 55688}, {22234, 55670, 55584}, {22330, 55669, 55593}, {37513, 37514, 37487}, {37517, 55636, 33878}, {37517, 55691, 5092}, {38064, 48906, 47355}, {39561, 55618, 5102}, {39561, 55685, 55645}, {39874, 51126, 10516}, {44456, 55678, 55652}, {47355, 48906, 47353}, {50664, 55594, 39561}, {50664, 55688, 55594}, {50664, 55696, 55695}, {55582, 55671, 55642}, {55591, 55645, 55618}, {55604, 55682, 55668}, {55642, 55689, 55683}, {55678, 55692, 55689}, {55680, 55695, 55693}

X(55700) = X(3)X(6)∩X(373)X(26881)

Barycentrics    a^2*(12*a^4-b^4-24*b^2*c^2-c^4-11*a^2*(b^2+c^2)) : :
X(55700) = 13*X[3]+11*X[6], 11*X[597]+X[44903], -17*X[3854]+11*X[48889], 7*X[5476]+5*X[50975], -11*X[14561]+3*X[50687], -11*X[18553]+29*X[46935], 11*X[25406]+5*X[41099], -11*X[48895]+5*X[50691], 11*X[48898]+X[50692], 13*X[50974]+35*X[50994], 35*X[50987]+X[51136]

X(55700) lies on circumconic {{A, B, C, X(39), X(46851)}} and on these lines: {3, 6}, {373, 26881}, {542, 47598}, {597, 44903}, {1176, 46851}, {1503, 10109}, {3854, 48889}, {5012, 15082}, {5476, 50975}, {5965, 50983}, {6329, 33751}, {6688, 6800}, {10219, 35259}, {11645, 38071}, {12045, 43650}, {12834, 22352}, {14561, 50687}, {14893, 29012}, {18553, 46935}, {25406, 41099}, {29317, 50971}, {29323, 33699}, {34380, 51138}, {48891, 51538}, {48895, 50691}, {48898, 50692}, {50974, 50994}, {50987, 51136}

X(55700) = midpoint of X(i) and X(j) for these {i,j}: {182, 55695}, {14810, 15520}, {15516, 55664}, {22330, 55645}, {39561, 55670}, {48891, 51538}, {5050, 5092}, {575, 17508}, {576, 55615}, {5093, 55627}, {5097, 31884}, {5102, 55606}, {50664, 55686}, {6, 55657}
X(55700) = reflection of X(i) in X(j) for these {i,j}: {15516, 5050}, {17508, 55688}, {20190, 55695}, {31884, 55668}, {55589, 55609}, {55592, 55621}, {55593, 55625}, {55597, 31884}, {55601, 55645}, {55603, 55647}, {55612, 55657}, {55615, 55659}, {55621, 3}, {55631, 55664}, {55638, 55670}, {55645, 55674}, {55653, 17508}, {55657, 55679}, {55663, 55680}, {55664, 5092}, {55674, 55686}, {55680, 5085}, {55686, 20190}, {55695, 55696}
X(55700) = inverse of X(55581) in First Brocard Circle
X(55700) = center of Tucker-Hagos(11/12) circle
X(55700) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 55621}, {3, 6, 55581}, {182, 12017, 575}, {182, 20190, 50664}, {182, 55691, 53093}, {182, 55693, 5050}, {182, 55694, 6}, {182, 55698, 55696}, {182, 55699, 55698}, {511, 17508, 55653}, {511, 5085, 55680}, {511, 5092, 55664}, {511, 55609, 55589}, {511, 55621, 55592}, {511, 55625, 55593}, {511, 55647, 55603}, {511, 55657, 55612}, {511, 55659, 55615}, {511, 55668, 31884}, {511, 55670, 55638}, {511, 55674, 55645}, {511, 55679, 55657}, {511, 55680, 55663}, {575, 5092, 1350}, {575, 55627, 5093}, {575, 55666, 37517}, {576, 5092, 55659}, {1350, 10541, 12017}, {1350, 44456, 55583}, {1350, 55649, 55627}, {1350, 55653, 55631}, {1351, 55677, 55636}, {1351, 55689, 55677}, {5050, 10541, 55693}, {5050, 5085, 55649}, {5050, 55673, 576}, {5050, 55682, 44456}, {5050, 55685, 55588}, {5050, 55692, 55673}, {5050, 55697, 10541}, {5085, 39561, 55670}, {5085, 5093, 17508}, {5085, 53093, 55591}, {5092, 14810, 55675}, {5092, 55585, 55668}, {5092, 55588, 55669}, {5092, 55669, 55679}, {5097, 55668, 55597}, {5102, 55667, 55606}, {10541, 55693, 55695}, {11477, 55683, 55661}, {12017, 55637, 55690}, {12017, 55688, 20190}, {14810, 15520, 511}, {15516, 20190, 5092}, {15516, 55693, 55686}, {15520, 55682, 14810}, {15520, 55691, 55682}, {17508, 37517, 55643}, {17508, 55613, 3}, {17508, 55643, 55666}, {20190, 50664, 55674}, {20190, 55597, 55687}, {20190, 55653, 55688}, {20190, 55680, 5085}, {22234, 55676, 55590}, {22330, 55674, 55601}, {37517, 55666, 55617}, {50664, 55631, 15516}, {53091, 55681, 55594}, {53093, 55682, 15520}, {55583, 55637, 55602}, {55586, 55627, 55599}, {55588, 55657, 55624}, {55591, 55602, 55596}, {55592, 55631, 55609}, {55599, 55627, 55613}, {55612, 55653, 55637}, {55657, 55690, 55685}, {55695, 55698, 55697}

X(55701) = X(3)X(6)∩X(4)X(54639)

Barycentrics    a^2*(11*a^4+b^4-22*b^2*c^2+c^4-12*a^2*(b^2+c^2)) : :
X(55701) = 5*X[3]+6*X[6], -32*X[5]+21*X[50957], 2*X[20]+9*X[14848], -3*X[69]+14*X[14869], -20*X[140]+9*X[21356], -X[382]+12*X[597], -4*X[546]+15*X[3618], 3*X[599]+8*X[33749], -25*X[631]+3*X[11160], -5*X[1352]+16*X[51127], 3*X[1353]+8*X[12108], 5*X[1656]+6*X[11179] and many others

X(55701) lies on these lines: {3, 6}, {4, 54639}, {5, 50957}, {20, 14848}, {69, 14869}, {140, 21356}, {382, 597}, {524, 15720}, {542, 5070}, {546, 3618}, {599, 33749}, {631, 11160}, {1352, 51127}, {1353, 12108}, {1503, 5072}, {1598, 52163}, {1656, 11179}, {1657, 51737}, {1992, 3530}, {3090, 18440}, {3091, 48906}, {3146, 18583}, {3292, 16419}, {3525, 3564}, {3526, 8550}, {3529, 51171}, {3544, 39884}, {3589, 5079}, {3627, 25406}, {3628, 6776}, {3796, 44106}, {3832, 38079}, {3843, 25555}, {3851, 47352}, {5012, 8780}, {5020, 44110}, {5032, 10299}, {5054, 22165}, {5073, 5476}, {5076, 46264}, {5182, 51523}, {5198, 19128}, {5422, 6030}, {5480, 49136}, {5544, 16042}, {5609, 5622}, {5643, 6800}, {6636, 52719}, {7484, 11422}, {7492, 9777}, {7526, 43697}, {7550, 12164}, {7666, 32154}, {7947, 10303}, {8584, 15700}, {9716, 11402}, {9968, 10249}, {10168, 15069}, {10250, 17821}, {10300, 11427}, {10601, 44082}, {11405, 32534}, {12102, 14927}, {12167, 44879}, {12315, 19153}, {14853, 15704}, {15022, 39874}, {15039, 15462}, {15045, 15074}, {15054, 45016}, {15534, 15707}, {15681, 51185}, {15693, 41149}, {15694, 34507}, {15696, 20423}, {15701, 51188}, {17538, 21850}, {18358, 46936}, {19118, 35502}, {19709, 46267}, {33748, 48876}, {33923, 54132}, {34117, 35450}, {37924, 51733}, {38136, 50688}, {38317, 48662}, {39899, 51128}, {43238, 51203}, {43239, 51200}, {44214, 47446}, {44245, 51212}, {44682, 50967}, {44882, 49137}, {50692, 51177}, {50983, 51174}, {51165, 51173}, {51522, 52699}

X(55701) = midpoint of X(i) and X(j) for these {i,j}: {576, 55628}, {6, 55671}
X(55701) = reflection of X(i) in X(j) for these {i,j}: {1350, 55642}, {3, 55684}, {55620, 3}, {55622, 55665}, {55632, 55671}, {55641, 55675}, {55648, 55678}, {55656, 55683}, {55662, 5092}, {55671, 55689}, {55678, 55692}, {55684, 55694}, {55692, 55699}, {55699, 182}
X(55701) = center of Tucker-Hagos(12/11) circle
X(55701) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(574), X(43719)}}, {{A, B, C, X(5008), X(43908)}}, {{A, B, C, X(5013), X(16835)}}, {{A, B, C, X(11270), X(53095)}}, {{A, B, C, X(14489), X(53097)}}, {{A, B, C, X(15602), X(44763)}}
X(55701) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 55602}, {3, 1351, 55595}, {3, 44456, 55606}, {3, 5050, 53092}, {3, 5093, 53097}, {3, 511, 55620}, {3, 53093, 5050}, {3, 53097, 55629}, {3, 575, 11482}, {3, 576, 33878}, {3, 55584, 55626}, {3, 55593, 55637}, {3, 55606, 55643}, {3, 55616, 55647}, {3, 55620, 55648}, {3, 55632, 55652}, {3, 55684, 55678}, {6, 17508, 55584}, {6, 182, 55697}, {6, 5085, 14810}, {6, 55699, 55689}, {182, 3098, 55700}, {182, 39561, 55696}, {182, 5050, 12017}, {182, 511, 55699}, {182, 575, 10541}, {182, 576, 55698}, {511, 5092, 55662}, {511, 55665, 55622}, {511, 55671, 55632}, {511, 55675, 55641}, {575, 20190, 52987}, {575, 52987, 6}, {575, 55650, 22330}, {575, 55695, 55650}, {576, 55628, 511}, {576, 55672, 55597}, {576, 55683, 55628}, {1351, 12017, 55682}, {1351, 55682, 55639}, {3526, 8550, 50955}, {5050, 33878, 53091}, {5050, 55643, 39561}, {5085, 55614, 55679}, {5085, 55656, 55683}, {5097, 55676, 55593}, {5097, 55693, 55676}, {5102, 55674, 55604}, {8550, 38064, 3526}, {10541, 11477, 55687}, {10541, 53093, 575}, {10541, 55614, 5085}, {10541, 55675, 55692}, {11477, 55602, 55580}, {11477, 55687, 3}, {11482, 55580, 1351}, {11482, 55602, 11477}, {14810, 33878, 55610}, {14810, 52987, 55614}, {14810, 55664, 55658}, {14810, 55668, 55660}, {14810, 55683, 55671}, {14810, 55698, 20190}, {15516, 55691, 31884}, {15520, 55688, 55646}, {20190, 22234, 55654}, {20190, 22330, 55668}, {20190, 55617, 5092}, {20190, 55652, 55684}, {22234, 53097, 5093}, {22234, 55603, 576}, {22330, 55681, 1350}, {22330, 55695, 55681}, {25555, 43273, 3843}, {33878, 55629, 55603}, {33878, 55678, 55656}, {37517, 55673, 55616}, {37517, 55690, 55673}, {39561, 53094, 44456}, {39561, 55696, 53094}, {43118, 43119, 47113}, {52987, 55644, 55617}, {52987, 55689, 55675}, {53858, 55684, 55635}, {55603, 55660, 55638}, {55638, 55650, 55644}, {55684, 55699, 55694}

X(55702) = X(3)X(6)∩X(1176)X(14487)

Barycentrics    a^2*(10*a^4+b^4-20*b^2*c^2+c^4-11*a^2*(b^2+c^2)) : :
X(55702) = 9*X[3]+11*X[6], -11*X[597]+X[33699], -11*X[3589]+6*X[10109], -7*X[3619]+27*X[38064], X[3630]+9*X[50979], -X[3818]+6*X[46267], -16*X[3856]+11*X[48889], -6*X[5476]+X[48943], 4*X[6329]+X[48892], 3*X[6776]+7*X[42786], -9*X[10168]+4*X[34573], X[11008]+9*X[50977] and many others

X(55702) lies on these lines: {3, 6}, {542, 51126}, {597, 33699}, {1176, 14487}, {1495, 11451}, {3564, 45760}, {3589, 10109}, {3618, 11645}, {3619, 38064}, {3630, 50979}, {3818, 46267}, {3856, 48889}, {5476, 48943}, {6329, 48892}, {6688, 26864}, {6776, 42786}, {10168, 34573}, {11008, 50977}, {12112, 43651}, {14848, 48879}, {14893, 19130}, {15052, 46865}, {18553, 38110}, {29323, 50691}, {31670, 46333}, {38071, 48906}, {38317, 39874}, {42785, 46264}, {43621, 51171}, {44903, 48891}, {48901, 50692}, {48942, 51732}

X(55702) = midpoint of X(i) and X(j) for these {i,j}: {182, 53093}, {1351, 55600}, {11482, 55655}, {22234, 53094}, {575, 55690}, {576, 55629}, {5097, 55650}, {53091, 55687}, {6, 55672}
X(55702) = reflection of X(i) in X(j) for these {i,j}: {11482, 15516}, {14810, 55677}, {5092, 12017}, {5097, 22234}, {53094, 20190}, {55586, 55598}, {55590, 55614}, {55594, 55634}, {55604, 55653}, {55606, 55655}, {55619, 3}, {55623, 55666}, {55634, 55672}, {55637, 55674}, {55650, 53094}, {55661, 5092}, {55666, 55687}, {55677, 55690}, {55690, 55698}, {55698, 182}
X(55702) = center of Tucker-Hagos(11/10) circle
X(55702) = intersection, other than A, B, C, of circumconics {{A, B, C, X(39), X(14487)}}, {{A, B, C, X(30535), X(55696)}}
X(55702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 182, 55700}, {3, 511, 55619}, {3, 55581, 55621}, {3, 55599, 14810}, {6, 182, 55696}, {6, 5085, 55639}, {6, 55678, 55585}, {6, 55691, 55653}, {182, 3098, 55699}, {182, 39561, 10541}, {182, 5050, 20190}, {182, 50664, 5092}, {182, 511, 55698}, {182, 575, 55695}, {182, 576, 55697}, {511, 15516, 11482}, {511, 20190, 53094}, {511, 5092, 55661}, {511, 55598, 55586}, {511, 55634, 55594}, {511, 55653, 55604}, {511, 55666, 55623}, {511, 55672, 55634}, {511, 55674, 55637}, {511, 55687, 55666}, {576, 55688, 55657}, {576, 55697, 55688}, {1350, 55694, 55686}, {1351, 55679, 55627}, {1351, 55693, 55679}, {3098, 37517, 55584}, {3098, 5092, 55670}, {3098, 55591, 55601}, {5050, 5097, 575}, {5050, 53094, 22234}, {5050, 55595, 53091}, {5050, 55654, 39561}, {5050, 55675, 15516}, {5050, 55697, 55591}, {5085, 11482, 55655}, {5085, 37517, 55668}, {5085, 55584, 55675}, {5092, 12017, 55690}, {5092, 55634, 55672}, {5092, 55657, 55676}, {5092, 55661, 55677}, {5092, 55698, 12017}, {5093, 55681, 55612}, {5097, 55670, 55588}, {5102, 55669, 55597}, {10541, 33878, 55689}, {10541, 39561, 55674}, {10541, 55622, 5085}, {11477, 55685, 55659}, {11482, 55655, 511}, {12017, 53091, 55646}, {12017, 55646, 55687}, {15516, 20190, 55645}, {15516, 55584, 5097}, {15516, 55668, 37517}, {15520, 55665, 55582}, {17508, 22330, 55590}, {17508, 44456, 55636}, {20190, 22234, 55650}, {20190, 55659, 55685}, {22234, 55687, 55595}, {22330, 55636, 44456}, {33878, 55654, 3098}, {37517, 55668, 55606}, {39561, 55689, 33878}, {52987, 55692, 55680}, {53093, 53094, 5050}, {53097, 55683, 55663}, {55582, 55665, 55631}, {55583, 55671, 55638}, {55585, 55691, 55678}, {55587, 55684, 55664}, {55588, 55599, 55592}, {55589, 55639, 55609}, {55594, 55609, 55599}, {55606, 55622, 55615}, {55615, 55670, 55654}, {55653, 55696, 55691}

X(55703) = X(3)X(6)∩X(154)X(373)

Barycentrics    a^2*(9*a^4+b^4-18*b^2*c^2+c^4-10*a^2*(b^2+c^2)) : :
X(55703) = -13*X[2]+4*X[50958], 4*X[3]+5*X[6], X[20]+8*X[6329], X[64]+8*X[41593], -8*X[547]+5*X[10516], -10*X[597]+X[3543], 5*X[631]+4*X[12007], -10*X[1386]+X[11531], 7*X[3523]+2*X[3629], -34*X[3533]+25*X[3763], -20*X[3589]+11*X[5056], -25*X[3618]+7*X[3832] and many others

X(55703) lies on these lines: {2, 50958}, {3, 6}, {20, 6329}, {23, 5645}, {64, 41593}, {154, 373}, {518, 30392}, {524, 15708}, {547, 10516}, {597, 3543}, {599, 14912}, {611, 37587}, {631, 12007}, {1181, 46207}, {1386, 11531}, {1498, 16261}, {1503, 3545}, {1992, 21167}, {3167, 15082}, {3292, 5646}, {3523, 3629}, {3532, 10574}, {3533, 3763}, {3564, 11539}, {3589, 5056}, {3618, 3832}, {3631, 10303}, {3796, 5640}, {3845, 14561}, {3850, 48906}, {3853, 38136}, {5012, 17825}, {5054, 5965}, {5059, 44882}, {5067, 6776}, {5076, 42785}, {5422, 37913}, {5480, 33703}, {5621, 52699}, {5622, 52697}, {5650, 11402}, {5921, 51126}, {6090, 17809}, {6699, 16176}, {6800, 10601}, {7503, 43612}, {7998, 37672}, {8549, 15580}, {8556, 9755}, {8584, 51214}, {8705, 37940}, {10168, 15723}, {10519, 15534}, {11001, 14853}, {11424, 16936}, {11812, 15533}, {11898, 33749}, {13196, 15271}, {14528, 32366}, {14848, 29317}, {15028, 41579}, {15041, 34155}, {15043, 17710}, {15045, 44668}, {15069, 16239}, {15576, 37124}, {15640, 51135}, {15686, 54131}, {15690, 20423}, {15692, 20583}, {15693, 50973}, {15698, 51132}, {15701, 51140}, {15713, 50961}, {15722, 51174}, {15748, 17928}, {16200, 38315}, {17810, 35268}, {17811, 33879}, {18583, 48905}, {19153, 52028}, {19711, 50987}, {29012, 38072}, {34380, 41983}, {37925, 51733}, {37944, 52238}, {38047, 38155}, {38317, 47353}, {39588, 47485}, {40686, 41729}, {41153, 51165}, {43150, 46219}, {43576, 46945}, {44214, 47445}, {47466, 47468}, {48901, 49133}, {50972, 51166}, {50974, 51186}, {50977, 51187}

X(55703) = midpoint of X(i) and X(j) for these {i,j}: {15520, 55660}, {39561, 55685}, {5050, 55697}, {576, 55630}, {5093, 55643}, {5102, 55618}, {6, 55673}
X(55703) = reflection of X(i) in X(j) for these {i,j}: {1350, 55643}, {3, 55685}, {31884, 55673}, {5085, 55697}, {55591, 55618}, {55593, 55630}, {55610, 55660}, {55618, 3}, {55624, 55667}, {55630, 55670}, {55643, 17508}, {55654, 55682}, {55660, 5092}, {55673, 5085}, {55682, 55693}, {55685, 55695}, {55697, 182}
X(55703) = center of Tucker-Hagos(10/9) circle
X(55703) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2065), X(38010)}}, {{A, B, C, X(3532), X(37512)}}, {{A, B, C, X(5024), X(14490)}}, {{A, B, C, X(5481), X(55699)}}, {{A, B, C, X(10541), X(30535)}}, {{A, B, C, X(22334), X(53096)}}, {{A, B, C, X(34567), X(43136)}}, {{A, B, C, X(40801), X(55594)}}
X(55703) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12017, 55688}, {3, 1351, 55594}, {3, 182, 55699}, {3, 33878, 55633}, {3, 39561, 5102}, {3, 5050, 39561}, {3, 5097, 55582}, {3, 511, 55618}, {3, 55582, 55622}, {3, 55591, 31884}, {3, 55610, 55645}, {3, 55612, 55646}, {3, 55640, 55654}, {6, 182, 10541}, {6, 53094, 53097}, {6, 55614, 1351}, {182, 17508, 55700}, {182, 3098, 55698}, {182, 39561, 55695}, {182, 511, 55697}, {182, 576, 55696}, {182, 55702, 55701}, {511, 17508, 55643}, {511, 5085, 55673}, {511, 5092, 55660}, {511, 55630, 55593}, {511, 55667, 55624}, {511, 55670, 55630}, {511, 55695, 55685}, {575, 55696, 55662}, {576, 55662, 55586}, {597, 25406, 53023}, {1151, 1152, 37512}, {1350, 12017, 55684}, {1350, 5085, 17508}, {1350, 55632, 55614}, {1351, 20190, 55676}, {1351, 55632, 55583}, {1351, 55666, 1350}, {3098, 55698, 55692}, {5050, 5093, 575}, {5050, 55610, 53091}, {5085, 15520, 55651}, {5085, 31884, 53094}, {5085, 53858, 55657}, {5085, 55654, 55682}, {5092, 15520, 55610}, {5093, 55682, 55613}, {5097, 55695, 55680}, {6431, 6432, 5041}, {10541, 31884, 5085}, {10542, 39764, 6}, {11179, 38110, 10516}, {11477, 55645, 55591}, {11477, 55676, 55625}, {12017, 53091, 55637}, {15516, 33878, 53858}, {15516, 55687, 33878}, {15520, 55610, 11477}, {15520, 55660, 511}, {17508, 37517, 55627}, {17508, 39561, 37517}, {17508, 55583, 55649}, {17508, 55627, 3}, {17508, 55649, 55666}, {17508, 55662, 55670}, {17508, 55700, 12017}, {20190, 55594, 55683}, {20190, 55625, 5092}, {22234, 55674, 44456}, {22236, 22238, 53096}, {22330, 55672, 55584}, {26341, 45551, 1151}, {26348, 45550, 1152}, {31884, 55591, 55607}, {33878, 55687, 55671}, {37517, 55637, 55587}, {39561, 50664, 5050}, {39561, 55587, 15520}, {39561, 55603, 5097}, {39561, 55627, 5093}, {39561, 55691, 55603}, {39561, 55693, 55640}, {44456, 55674, 55626}, {51185, 51737, 51024}, {52987, 55690, 55678}, {53092, 55692, 3098}, {53094, 53097, 55656}, {55581, 55661, 55620}, {55582, 55699, 55691}, {55583, 55666, 55632}, {55584, 55672, 55641}, {55585, 55677, 55648}, {55589, 55663, 55629}, {55589, 55681, 55663}, {55624, 55682, 55667}, {55682, 55697, 55693}

X(55704) = X(3)X(6)∩X(5)X(46267)

Barycentrics    a^2*(8*a^4+b^4-16*b^2*c^2+c^4-9*a^2*(b^2+c^2)) : :
X(55704) = 7*X[3]+9*X[6], -X[5]+3*X[46267], -9*X[597]+X[3627], -35*X[631]+3*X[50992], 5*X[632]+3*X[8550], X[1657]+15*X[51185], 7*X[3090]+9*X[11179], -X[3146]+9*X[5476], -11*X[3525]+3*X[34507], -17*X[3544]+9*X[3818], -9*X[3589]+5*X[12812], -5*X[3618]+X[48889] and many others

X(55704) lies on circumconic {{A, B, C, X(574), X(13452)}} and on these lines: {3, 6}, {5, 46267}, {23, 12834}, {30, 41153}, {110, 12045}, {140, 33749}, {184, 10219}, {524, 12108}, {542, 3628}, {546, 11645}, {597, 3627}, {631, 50992}, {632, 8550}, {1495, 5643}, {1503, 12811}, {1657, 51185}, {3090, 11179}, {3146, 5476}, {3292, 43810}, {3525, 34507}, {3544, 3818}, {3589, 12812}, {3618, 48889}, {3819, 11422}, {3857, 48906}, {4663, 31666}, {5012, 6688}, {5054, 50989}, {5072, 47352}, {5079, 25561}, {5462, 12105}, {5622, 46865}, {5650, 9716}, {5943, 14002}, {6329, 29317}, {6776, 46936}, {7492, 21849}, {7496, 13366}, {8541, 35479}, {8584, 15712}, {8593, 16922}, {8681, 32154}, {9976, 15034}, {10110, 37967}, {10610, 15826}, {11541, 48901}, {11649, 12006}, {12102, 29012}, {12103, 50971}, {13160, 20301}, {13452, 43697}, {14561, 50689}, {14853, 48891}, {14865, 44102}, {14869, 40107}, {14890, 41152}, {14927, 42785}, {15018, 32237}, {15019, 22352}, {15022, 38317}, {15082, 44109}, {15083, 40258}, {15579, 41593}, {15606, 36153}, {15704, 51737}, {18583, 29323}, {18800, 32992}, {19128, 26863}, {19924, 44245}, {20423, 50693}, {25406, 48895}, {25556, 51522}, {32135, 51523}, {32171, 40284}, {32305, 35500}, {34986, 40916}, {38079, 41991}, {41149, 41983}, {43651, 44870}, {45760, 51143}, {46264, 50688}, {48898, 49140}

X(55704) = midpoint of X(i) and X(j) for these {i,j}: {140, 33749}, {182, 50664}, {1351, 55601}, {15520, 55663}, {3, 22330}, {37517, 55592}, {39561, 55686}, {5050, 55700}, {575, 20190}, {576, 55631}, {5092, 15516}, {5093, 55645}, {5097, 55653}, {6, 55674}
X(55704) = reflection of X(i) in X(j) for these {i,j}: {55609, 55659}, {55617, 3}, {55625, 55668}, {55636, 55674}, {55647, 55679}, {55659, 5092}, {55668, 55688}, {55679, 20190}, {55688, 55696}, {55696, 182}
X(55704) = center of Tucker-Hagos(9/8) circle
X(55704) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 55600}, {3, 182, 55698}, {3, 511, 55617}, {3, 53097, 55628}, {3, 53858, 55583}, {3, 575, 22330}, {3, 576, 55588}, {3, 55583, 55623}, {3, 55617, 55647}, {6, 12017, 55665}, {6, 182, 55695}, {6, 5085, 55629}, {6, 55618, 1351}, {6, 55682, 55587}, {182, 17508, 55699}, {182, 22234, 55694}, {182, 3098, 55697}, {182, 39561, 12017}, {182, 5092, 55700}, {182, 511, 55696}, {182, 53093, 575}, {182, 575, 20190}, {182, 576, 10541}, {182, 55703, 55702}, {511, 20190, 55679}, {511, 5092, 55659}, {511, 55659, 55609}, {511, 55668, 55625}, {511, 55674, 55636}, {575, 5097, 53092}, {575, 53093, 50664}, {575, 55694, 55597}, {576, 55649, 55580}, {576, 55675, 1350}, {576, 55687, 55649}, {576, 55693, 55675}, {1350, 5092, 55664}, {1351, 55601, 511}, {1351, 55656, 55589}, {1351, 55670, 55601}, {1351, 55691, 55670}, {3098, 55690, 55680}, {3098, 55697, 55690}, {5050, 5092, 15516}, {5050, 55639, 53091}, {5050, 55673, 39561}, {5050, 55692, 6}, {5085, 5097, 55653}, {5085, 52987, 55677}, {5085, 53092, 52987}, {5092, 14810, 55673}, {5092, 55609, 55668}, {5092, 55649, 55674}, {5092, 55695, 55692}, {5093, 55672, 55590}, {5097, 55615, 44456}, {5102, 55655, 55586}, {10541, 53092, 55669}, {10541, 53093, 5050}, {10541, 55580, 55687}, {11477, 12017, 55681}, {11477, 55620, 55585}, {11477, 55665, 55606}, {11477, 55673, 55620}, {11477, 55681, 14810}, {11482, 55684, 3098}, {11482, 55697, 55684}, {12017, 14810, 55686}, {12017, 55585, 5092}, {14810, 55620, 55631}, {15516, 55631, 576}, {15520, 53094, 55594}, {17508, 53097, 55650}, {17508, 55628, 3}, {20190, 55679, 55688}, {22234, 55583, 53858}, {33878, 55666, 55638}, {33878, 55685, 55666}, {37517, 55657, 55592}, {39560, 44500, 38010}, {39561, 55607, 5097}, {39561, 55681, 11477}, {44456, 55669, 55615}, {53091, 55699, 17508}, {53093, 55701, 182}, {53093, 55703, 55701}, {53094, 55594, 55663}, {53097, 55650, 55612}, {55580, 55620, 55593}, {55582, 55660, 55619}, {55584, 55667, 55634}, {55587, 55661, 55621}, {55587, 55682, 55661}, {55589, 55649, 55618}, {55590, 55672, 55645}, {55593, 55629, 55607}, {55597, 55631, 55611}, {55606, 55661, 55641}, {55664, 55700, 55693}

X(55705) = X(2)X(21968)∩X(3)X(6)

Barycentrics    a^2*(7*a^4+b^4-14*b^2*c^2+c^4-8*a^2*(b^2+c^2)) : :
X(55705) = 3*X[3]+4*X[6], -X[4]+8*X[51732], 6*X[5]+X[39874], -2*X[69]+9*X[5054], -12*X[140]+5*X[3620], -8*X[141]+15*X[15694], X[193]+6*X[549], -3*X[381]+10*X[3618], -X[382]+8*X[18583], X[399]+6*X[5622], -8*X[597]+X[3830], 5*X[631]+2*X[1353] and many others

X(55705) lies on these lines: {2, 21968}, {3, 6}, {4, 51732}, {5, 39874}, {25, 5644}, {30, 51171}, {69, 5054}, {140, 3620}, {141, 15694}, {193, 549}, {323, 7484}, {381, 3618}, {382, 18583}, {399, 5622}, {524, 15701}, {542, 15703}, {597, 3830}, {631, 1353}, {895, 15040}, {1176, 3531}, {1352, 5070}, {1386, 8148}, {1428, 7373}, {1482, 16491}, {1495, 10601}, {1503, 3851}, {1511, 39562}, {1597, 19118}, {1598, 19128}, {1656, 6776}, {1657, 14853}, {1974, 18535}, {1992, 15693}, {2330, 6767}, {3060, 52719}, {3167, 43650}, {3431, 38263}, {3517, 39588}, {3523, 34380}, {3524, 50962}, {3526, 3564}, {3534, 21850}, {3545, 41450}, {3589, 5055}, {3628, 5921}, {3629, 15707}, {3630, 12007}, {3653, 49505}, {3763, 10168}, {3796, 20850}, {3818, 19709}, {3843, 14561}, {4550, 21637}, {5012, 5020}, {5032, 12100}, {5072, 39884}, {5073, 5480}, {5076, 14927}, {5095, 38728}, {5182, 12188}, {5422, 9909}, {5476, 15684}, {5477, 38739}, {5544, 35259}, {5621, 25556}, {5790, 39870}, {5888, 11422}, {5892, 6467}, {5899, 51733}, {5943, 41424}, {5946, 12220}, {6144, 50977}, {6329, 14848}, {6391, 47391}, {6403, 12006}, {6593, 12308}, {6723, 32272}, {6771, 43028}, {6774, 43029}, {6800, 10545}, {7395, 15032}, {7485, 11004}, {7529, 43815}, {7728, 32300}, {7806, 40248}, {8252, 39893}, {8253, 39894}, {8550, 34573}, {8780, 17825}, {8976, 49229}, {9714, 15047}, {9777, 15107}, {9924, 10250}, {10246, 16496}, {10249, 41593}, {10540, 19137}, {10620, 52699}, {11003, 11284}, {11008, 15720}, {11160, 11812}, {11216, 35228}, {11230, 39878}, {11402, 15066}, {11424, 35253}, {11441, 46865}, {11456, 11479}, {11539, 50974}, {11799, 47456}, {12174, 19123}, {12283, 15028}, {12315, 52028}, {12702, 16475}, {12902, 15118}, {13635, 37677}, {13951, 49228}, {14093, 54132}, {14269, 19130}, {14530, 23042}, {14891, 54174}, {14996, 16434}, {14997, 19544}, {15046, 41737}, {15087, 20806}, {15492, 46475}, {15534, 15722}, {15685, 48910}, {15689, 20423}, {15695, 48881}, {15696, 51212}, {15699, 50954}, {15706, 50967}, {15708, 50978}, {15718, 32455}, {15805, 43586}, {15988, 16417}, {17800, 43621}, {18325, 47457}, {18493, 38049}, {18551, 19153}, {19127, 44457}, {19132, 32063}, {19136, 44454}, {19139, 43845}, {19154, 39568}, {21487, 37685}, {25555, 36990}, {29012, 42785}, {30734, 35265}, {31479, 39901}, {31723, 41256}, {31724, 41257}, {32234, 34128}, {33586, 44107}, {33750, 48874}, {34718, 49684}, {34748, 49688}, {34779, 35450}, {35001, 52238}, {35403, 38072}, {35501, 44102}, {36696, 38593}, {37451, 37689}, {37624, 38029}, {37643, 45298}, {41987, 51216}, {43697, 52055}, {43704, 43725}, {44214, 47279}, {44455, 47373}, {45018, 49102}, {45759, 51028}, {46267, 47353}, {48891, 51024}, {48892, 54131}, {48895, 50963}, {48898, 49139}, {48901, 49134}, {49137, 51538}, {51137, 51174}, {51172, 54170}

X(55705) = midpoint of X(i) and X(j) for these {i,j}: {1351, 55602}, {576, 55633}, {53858, 55651}, {6, 55676}
X(55705) = reflection of X(i) in X(j) for these {i,j}: {1350, 55644}, {1351, 53858}, {10541, 182}, {33878, 55607}, {55602, 55651}, {55607, 55658}, {55616, 3}, {55626, 55669}, {55639, 55676}, {55651, 55681}, {55658, 5092}, {55676, 55691}
X(55705) = inverse of X(44456) in First Brocard Circle
X(55705) = isogonal conjugate of X(54523)
X(55705) = center of Tucker-Hagos(8/7) circle
X(55705) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(44456)}}, {{A, B, C, X(4), X(22332)}}, {{A, B, C, X(32), X(44731)}}, {{A, B, C, X(39), X(3531)}}, {{A, B, C, X(54), X(22331)}}, {{A, B, C, X(74), X(15815)}}, {{A, B, C, X(3426), X(5013)}}, {{A, B, C, X(3431), X(5023)}}, {{A, B, C, X(5158), X(38263)}}, {{A, B, C, X(6391), X(52703)}}, {{A, B, C, X(11063), X(43725)}}, {{A, B, C, X(12017), X(30535)}}, {{A, B, C, X(34207), X(50660)}}
X(55705) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 55593}, {3, 182, 55697}, {3, 33878, 55632}, {3, 5050, 53091}, {3, 5093, 55584}, {3, 511, 55616}, {3, 53091, 5093}, {3, 55584, 55624}, {6, 5033, 1384}, {6, 53093, 50664}, {6, 55582, 576}, {6, 55646, 37517}, {15, 16, 15815}, {140, 14912, 11898}, {182, 15520, 55694}, {182, 17508, 55698}, {182, 19131, 37471}, {182, 22234, 55693}, {182, 3098, 55696}, {182, 39561, 20190}, {182, 5034, 12054}, {182, 50664, 6}, {182, 5092, 55699}, {182, 511, 10541}, {182, 53091, 55692}, {182, 53093, 5050}, {182, 576, 55695}, {182, 55687, 55700}, {182, 55703, 55701}, {182, 55704, 55703}, {371, 372, 22332}, {511, 5092, 55658}, {511, 55651, 55602}, {511, 55669, 55626}, {575, 53858, 53092}, {575, 55674, 15520}, {575, 55695, 55590}, {575, 55700, 55662}, {576, 55653, 55582}, {631, 33748, 1353}, {1350, 20190, 55682}, {1350, 39561, 11482}, {1350, 55623, 55610}, {1351, 12017, 55678}, {1351, 5050, 575}, {1351, 55602, 511}, {1351, 55629, 55581}, {1351, 55643, 53097}, {1351, 55678, 3098}, {2030, 2456, 9301}, {3098, 55585, 55597}, {3098, 55653, 55641}, {3098, 55667, 55653}, {3098, 55672, 55657}, {3311, 3312, 7772}, {3589, 11179, 18440}, {3589, 18440, 5055}, {3618, 48906, 381}, {5050, 55682, 39561}, {5050, 55701, 182}, {5085, 15520, 55643}, {5085, 53858, 55651}, {5085, 55641, 53094}, {5092, 37517, 55646}, {5092, 55601, 55665}, {5092, 55658, 55676}, {5097, 55668, 55585}, {5097, 55687, 31884}, {5097, 55700, 55687}, {6221, 6398, 574}, {6329, 31670, 14848}, {6329, 51737, 31670}, {6776, 38110, 1656}, {10541, 53092, 3}, {10541, 53858, 55681}, {10541, 55651, 5085}, {10541, 55676, 55691}, {10541, 55691, 12017}, {11477, 17508, 55629}, {11477, 55656, 55594}, {11482, 12017, 55672}, {11482, 55682, 1350}, {11485, 11486, 39}, {12017, 33878, 5092}, {12017, 53091, 55604}, {12017, 53092, 55639}, {14810, 22234, 5102}, {14810, 55693, 55684}, {14848, 51737, 15681}, {14927, 38136, 5076}, {15516, 17508, 11477}, {15516, 55698, 17508}, {15520, 53097, 1351}, {15520, 55694, 55674}, {17508, 55581, 55647}, {17508, 55594, 55656}, {18583, 25406, 382}, {22234, 55684, 55580}, {22234, 55693, 14810}, {22330, 55690, 55649}, {33878, 55610, 55598}, {33878, 55639, 55607}, {37517, 55646, 33878}, {37517, 55665, 55601}, {42115, 42116, 8589}, {50664, 55704, 55702}, {52987, 55673, 55648}, {52987, 55688, 55673}, {53092, 55602, 53858}, {53094, 55641, 55667}, {55583, 55659, 55618}, {55585, 55687, 55668}, {55587, 55654, 55620}, {55587, 55679, 55654}, {55588, 55660, 55622}, {55590, 55657, 55623}, {55590, 55696, 55689}, {55598, 55658, 55633}, {55606, 55685, 55671}

X(55706) = X(3)X(6)∩X(51)X(6030)

Barycentrics    a^2*(6*a^4+b^4-12*b^2*c^2+c^4-7*a^2*(b^2+c^2)) : :
X(55706) = 5*X[3]+7*X[6], -7*X[597]+X[15687], -4*X[3589]+X[18553], -35*X[3618]+11*X[3855], -X[3630]+7*X[14869], -7*X[3818]+13*X[5068], -5*X[3858]+14*X[25555], -4*X[3861]+7*X[19130], 5*X[5071]+7*X[11179], -7*X[5476]+X[15682], -4*X[5480]+X[48943], -X[5921]+7*X[42786] and many others

X(55706) lies on these lines: {3, 6}, {51, 6030}, {141, 33749}, {373, 5012}, {542, 15699}, {597, 15687}, {1428, 37602}, {1503, 5066}, {1843, 47486}, {3292, 33879}, {3530, 32455}, {3564, 10124}, {3589, 18553}, {3618, 3855}, {3630, 14869}, {3818, 5068}, {3839, 11645}, {3858, 25555}, {3861, 19130}, {5071, 11179}, {5422, 35268}, {5476, 15682}, {5480, 48943}, {5640, 44106}, {5650, 34986}, {5921, 42786}, {5943, 6800}, {5965, 15713}, {6144, 15720}, {6329, 48891}, {6688, 35259}, {6776, 7486}, {7492, 44107}, {7805, 49112}, {7998, 13366}, {8550, 43150}, {8584, 50987}, {9306, 12045}, {10250, 23041}, {10282, 13363}, {11002, 22352}, {11160, 15721}, {12007, 40107}, {14853, 15683}, {14912, 15709}, {15030, 43651}, {15082, 43650}, {15246, 44111}, {15491, 35021}, {15534, 51137}, {15691, 29181}, {15697, 20423}, {16981, 34565}, {17578, 46264}, {18583, 48895}, {19128, 52294}, {19710, 29317}, {21850, 48920}, {24206, 48154}, {34380, 41149}, {37527, 37687}, {37947, 51733}, {48898, 49138}, {48901, 49135}, {51140, 51188}

X(55706) = midpoint of X(i) and X(j) for these {i,j}: {182, 5050}, {10250, 23041}, {1351, 55603}, {11179, 38317}, {11477, 55589}, {15516, 55686}, {22330, 55664}, {3, 15520}, {3098, 5102}, {37517, 55593}, {48898, 51538}, {575, 55695}, {576, 31884}, {5085, 39561}, {5093, 55649}, {5097, 55657}, {5476, 25406}, {6, 17508}
X(55706) = reflection of X(i) in X(j) for these {i,j}: {1350, 55645}, {14810, 17508}, {15520, 15516}, {17508, 20190}, {25561, 38317}, {3, 55686}, {3098, 55664}, {31884, 55674}, {38317, 46267}, {5050, 50664}, {575, 5050}, {5085, 55700}, {5092, 55695}, {5102, 22330}, {52987, 55621}, {55588, 55603}, {55589, 55612}, {55590, 55615}, {55593, 55631}, {55594, 31884}, {55596, 55638}, {55599, 55649}, {55603, 55653}, {55606, 55657}, {55610, 55663}, {55615, 3}, {55621, 55668}, {55627, 55670}, {55645, 55679}, {55649, 55680}, {55657, 5092}, {55664, 55688}, {55670, 5085}, {55686, 55696}, {55695, 182}
X(55706) = isogonal conjugate of X(54920)
X(55706) = center of Tucker-Hagos(7/6) circle
X(55706) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(74), X(15602)}}, {{A, B, C, X(5481), X(55696)}}, {{A, B, C, X(11270), X(15515)}}, {{A, B, C, X(16835), X(31652)}}, {{A, B, C, X(20190), X(30535)}}
X(55706) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 182, 55696}, {3, 55585, 55625}, {3, 55590, 55634}, {3, 55596, 55638}, {3, 55601, 14810}, {3, 55693, 55686}, {6, 10541, 55671}, {6, 12017, 55658}, {6, 5092, 55586}, {6, 55584, 576}, {6, 55626, 1351}, {15, 16, 15602}, {182, 15516, 55690}, {182, 15520, 55693}, {182, 17508, 55697}, {182, 22234, 55691}, {182, 3098, 10541}, {182, 37517, 55694}, {182, 39561, 5085}, {182, 50664, 575}, {182, 5085, 55700}, {182, 5092, 55698}, {182, 511, 55695}, {182, 53091, 55688}, {182, 53093, 50664}, {182, 576, 12017}, {182, 55687, 55699}, {182, 55704, 55702}, {182, 55705, 55704}, {511, 22330, 5102}, {511, 31884, 55594}, {511, 50664, 5050}, {511, 5092, 55657}, {511, 55621, 52987}, {511, 55663, 55610}, {511, 55668, 55621}, {511, 55674, 31884}, {575, 55699, 55619}, {576, 55658, 55584}, {1350, 55667, 55645}, {1350, 55679, 55661}, {1350, 55691, 55679}, {1351, 55653, 55588}, {1351, 55673, 55603}, {1351, 55687, 55653}, {1351, 55699, 55687}, {3098, 53091, 22330}, {3098, 55682, 55664}, {5050, 5085, 39561}, {5050, 55682, 53091}, {5050, 55693, 15516}, {5050, 55697, 6}, {5050, 55703, 182}, {5050, 55705, 55703}, {5085, 5093, 55649}, {5085, 55610, 17508}, {5085, 55649, 55680}, {5092, 55606, 55666}, {5093, 55680, 55599}, {5102, 10541, 55682}, {5476, 25406, 29323}, {10541, 22330, 55677}, {10541, 53091, 3098}, {11179, 46267, 25561}, {11477, 55589, 511}, {11477, 55643, 55589}, {11477, 55672, 55612}, {11477, 55692, 55672}, {11482, 55676, 55587}, {12017, 31884, 55685}, {12017, 55594, 5092}, {14810, 55586, 55606}, {14810, 55594, 55617}, {14810, 55610, 55627}, {14810, 55615, 55630}, {14810, 55658, 55650}, {14810, 55661, 55652}, {14810, 55670, 55663}, {15516, 20190, 55601}, {15516, 55590, 5097}, {15516, 55690, 55590}, {15516, 55693, 55615}, {15516, 55696, 3}, {15520, 55685, 55608}, {17508, 52987, 55654}, {17508, 55605, 55660}, {17508, 55652, 55667}, {17508, 55654, 55668}, {17508, 55663, 55670}, {17508, 55693, 55689}, {17508, 55697, 20190}, {20190, 55704, 55701}, {22234, 55691, 1350}, {25555, 48906, 48889}, {31884, 55685, 55674}, {33878, 55659, 55623}, {33878, 55681, 55659}, {37517, 53094, 55631}, {37517, 55660, 55593}, {37517, 55694, 53094}, {39561, 55596, 15520}, {39561, 55649, 5093}, {39561, 55693, 55596}, {44456, 55655, 55597}, {44456, 55684, 55655}, {44483, 44484, 44508}, {53092, 53094, 37517}, {53097, 55669, 55636}, {55583, 55651, 55609}, {55587, 55676, 55647}, {55589, 55672, 55643}, {55603, 55687, 55673}

X(55707) = X(3)X(6)∩X(141)X(45760)

Barycentrics    9*a^6-11*a^4*(b^2+c^2)+2*a^2*(b^4-9*b^2*c^2+c^4) : :
X(55707) = 7*X[3]+11*X[6], -11*X[141]+20*X[45760], -11*X[597]+2*X[14893], -11*X[1352]+29*X[46935], -17*X[3854]+44*X[25555], -2*X[3856]+11*X[51732], -11*X[5476]+2*X[33699], 8*X[6329]+X[48898], -8*X[10109]+11*X[38317], 2*X[10168]+X[14912], -X[10516]+4*X[46267], -2*X[10519]+5*X[51137] and many others

X(55707) lies on these lines: {3, 6}, {141, 45760}, {373, 35264}, {597, 14893}, {1352, 46935}, {1503, 38071}, {3564, 47598}, {3854, 25555}, {3856, 51732}, {5476, 33699}, {5965, 33748}, {6329, 48898}, {10109, 38317}, {10168, 14912}, {10516, 46267}, {10519, 51137}, {11178, 38110}, {11179, 25565}, {11402, 15082}, {11695, 51933}, {14561, 41099}, {15534, 51141}, {29012, 50687}, {29317, 46333}, {33879, 43650}, {35434, 53023}, {38136, 48884}, {41149, 50988}, {48896, 51538}, {48904, 50692}, {50691, 51171}, {50979, 50991}, {50989, 51175}, {50992, 51140}, {51173, 51185}

X(55707) = midpoint of X(i) and X(j) for these {i,j}: {15520, 55667}, {33748, 38064}, {39561, 55693}, {5050, 55703}, {576, 55640}, {5093, 55654}, {5102, 55624}, {6, 55682}
X(55707) = reflection of X(i) in X(j) for these {i,j}: {182, 55703}, {17508, 55693}, {3098, 55667}, {52987, 55624}, {55589, 55613}, {55596, 55640}, {55603, 55654}, {55613, 3}, {55624, 55670}, {55630, 55673}, {55640, 17508}, {55649, 55682}, {55654, 5092}, {55660, 55685}, {55667, 5085}, {55682, 55695}, {55685, 55697}, {55693, 182}, {55703, 55706}
X(55707) = center of Tucker-Hagos(11/9) circle
X(55707) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 55613}, {3, 55702, 182}, {6, 12017, 55636}, {6, 182, 55687}, {6, 5085, 55593}, {6, 55692, 55606}, {182, 22234, 5092}, {182, 3098, 55694}, {182, 37517, 20190}, {182, 39561, 17508}, {182, 5050, 39561}, {182, 511, 55693}, {182, 52987, 12017}, {182, 53091, 55669}, {182, 576, 55691}, {182, 55649, 55695}, {182, 55672, 10541}, {182, 55681, 55696}, {182, 55685, 55697}, {182, 55689, 55698}, {511, 17508, 55640}, {511, 5085, 55667}, {511, 5092, 55654}, {511, 55640, 55596}, {511, 55670, 55624}, {511, 55673, 55630}, {511, 55685, 55660}, {511, 55695, 55682}, {511, 55697, 55685}, {511, 55706, 55703}, {575, 53097, 22234}, {575, 55696, 1351}, {1350, 55698, 55689}, {1351, 5085, 55657}, {1351, 55681, 3098}, {1351, 55696, 55681}, {3098, 39561, 15520}, {3098, 55590, 55600}, {3098, 55647, 55635}, {3098, 55660, 55643}, {3098, 55662, 55644}, {3098, 55687, 55674}, {5050, 5085, 575}, {5050, 53093, 55706}, {5085, 5093, 55638}, {5085, 5102, 55651}, {5085, 53858, 31884}, {5092, 5093, 55603}, {5092, 53097, 55662}, {5092, 55592, 3}, {5097, 10541, 55672}, {5097, 55672, 55583}, {5097, 55686, 55610}, {5102, 12017, 55670}, {10541, 55610, 55686}, {11477, 55688, 55658}, {12017, 15516, 52987}, {12017, 52987, 55683}, {15516, 55670, 5102}, {15520, 55667, 511}, {17508, 39561, 576}, {17508, 55587, 55649}, {17508, 55596, 55655}, {17508, 55649, 55665}, {17508, 55694, 5085}, {20190, 53091, 37517}, {20190, 55590, 55678}, {22234, 55603, 5093}, {22330, 53094, 55585}, {33748, 38064, 5965}, {33878, 55690, 55675}, {39561, 55695, 55587}, {44456, 55679, 55633}, {53091, 55580, 6}, {53091, 55678, 53858}, {53092, 55699, 14810}, {53094, 55585, 55652}, {53858, 55678, 55590}, {55582, 55666, 55628}, {55584, 55677, 55642}, {55591, 55664, 55637}, {55593, 55599, 55598}, {55593, 55643, 55618}, {55598, 55649, 55621}, {55600, 55609, 55605}, {55603, 55649, 55629}, {55630, 55685, 55673}, {55695, 55706, 55704}

X(55708) = X(2)X(33749)∩X(3)X(6)

Barycentrics    7*a^6-9*a^4*(b^2+c^2)+2*a^2*(b^4-7*b^2*c^2+c^4) : :
X(55708) = 3*X[2]+4*X[33749], 5*X[3]+9*X[6], -10*X[140]+3*X[22165], -X[382]+15*X[51185], -2*X[546]+9*X[597], 5*X[549]+2*X[41149], -25*X[632]+18*X[20582], -9*X[1352]+23*X[46936], -5*X[1656]+12*X[46267], 2*X[1992]+5*X[51137], 5*X[3091]+9*X[11179], -5*X[3526]+3*X[51186] and many others

X(55708) lies on these lines: {2, 33749}, {3, 6}, {140, 22165}, {184, 16042}, {382, 51185}, {524, 14869}, {542, 3090}, {546, 597}, {549, 41149}, {632, 20582}, {1352, 46936}, {1503, 3857}, {1656, 46267}, {1974, 26863}, {1992, 51137}, {1995, 44110}, {3091, 11179}, {3525, 7909}, {3526, 51186}, {3530, 8584}, {3544, 3618}, {3564, 51128}, {3627, 5476}, {3628, 8550}, {3818, 12811}, {5012, 14002}, {5026, 38628}, {5054, 51188}, {5076, 43273}, {5079, 18553}, {5422, 44106}, {5622, 52098}, {5643, 11003}, {6030, 15019}, {6329, 48901}, {6593, 38632}, {6776, 15022}, {7492, 15004}, {7808, 51523}, {7936, 41137}, {8541, 44879}, {8546, 9813}, {8549, 50414}, {8593, 33002}, {10169, 34785}, {10303, 11160}, {10359, 32135}, {10601, 30734}, {10984, 37946}, {11422, 43650}, {11470, 35475}, {11541, 25406}, {11649, 15043}, {12102, 18583}, {12103, 51737}, {12105, 51733}, {12108, 50977}, {12812, 38317}, {13366, 40916}, {14848, 49137}, {14853, 48896}, {15054, 25556}, {15534, 15720}, {15579, 34779}, {15581, 23042}, {15687, 41153}, {15704, 51138}, {16187, 44109}, {16835, 43697}, {16924, 18800}, {17538, 20423}, {19130, 50689}, {19662, 32976}, {19924, 50693}, {20583, 50987}, {21849, 52719}, {29012, 50688}, {31401, 41672}, {35502, 44102}, {38110, 51127}, {38629, 51157}, {43651, 43810}

X(55708) = midpoint of X(i) and X(j) for these {i,j}: {1351, 55607}, {10541, 53092}, {3, 53858}, {576, 55644}
X(55708) = reflection of X(i) in X(j) for these {i,j}: {182, 55705}, {3098, 55669}, {52987, 55626}, {53092, 575}, {55605, 55658}, {55611, 3}, {55633, 55676}, {55644, 55681}, {55651, 5092}, {55669, 55691}, {55681, 10541}, {55691, 182}
X(55708) = center of Tucker-Hagos(9/7) circle
X(55708) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(574), X(16835)}}, {{A, B, C, X(5008), X(13472)}}, {{A, B, C, X(8589), X(11270)}}, {{A, B, C, X(13452), X(15602)}}, {{A, B, C, X(17508), X(30535)}}
X(55708) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 55597}, {3, 511, 55611}, {3, 53093, 55704}, {3, 53097, 55623}, {3, 575, 22234}, {3, 55588, 55628}, {3, 55597, 55637}, {3, 55623, 55649}, {6, 12017, 55601}, {6, 55654, 1351}, {6, 55697, 14810}, {182, 15516, 55655}, {182, 15520, 5092}, {182, 3098, 55693}, {182, 39561, 3098}, {182, 50664, 55707}, {182, 52987, 20190}, {182, 53092, 55644}, {182, 55581, 55692}, {182, 55649, 12017}, {182, 55672, 55695}, {182, 55681, 10541}, {182, 55685, 55696}, {182, 55689, 55697}, {511, 5092, 55651}, {511, 575, 53092}, {511, 55626, 52987}, {511, 55658, 55605}, {511, 55676, 55633}, {575, 50664, 53093}, {575, 55606, 15516}, {575, 55698, 22330}, {1350, 55685, 55665}, {1350, 55696, 55685}, {1351, 55654, 55586}, {1351, 55672, 55596}, {1351, 55684, 55631}, {1351, 55695, 55672}, {3098, 55693, 55683}, {5050, 53093, 575}, {5050, 55707, 39561}, {5093, 55674, 55585}, {5097, 55679, 53097}, {5102, 55653, 55581}, {5102, 55692, 55653}, {6419, 6420, 5041}, {6453, 6454, 37512}, {10541, 53092, 511}, {10541, 53093, 55705}, {10541, 53858, 3}, {10541, 55607, 55684}, {10541, 55644, 55687}, {10541, 55681, 55691}, {11477, 15520, 576}, {11477, 53093, 55703}, {11477, 55637, 55587}, {11482, 20190, 55630}, {11482, 53093, 55702}, {11482, 55606, 37517}, {12017, 53097, 55679}, {14810, 55689, 17508}, {14810, 55697, 55689}, {15516, 55606, 11482}, {15516, 55702, 5085}, {15520, 55637, 11477}, {17508, 52987, 55652}, {17508, 55596, 55654}, {17508, 55605, 55658}, {17508, 55610, 55660}, {17508, 55655, 55668}, {17508, 55658, 55669}, {17508, 55707, 55706}, {20190, 22330, 55617}, {20190, 55584, 55675}, {20190, 55626, 55681}, {20190, 55701, 182}, {20190, 55706, 55701}, {22234, 55611, 53858}, {22234, 55694, 55583}, {22234, 55698, 55600}, {22234, 55704, 55694}, {22330, 55704, 55698}, {33878, 55667, 55635}, {33878, 55688, 55667}, {37517, 55630, 55584}, {37517, 55655, 55589}, {37517, 55675, 55606}, {39561, 55660, 15520}, {44456, 55670, 55608}, {52987, 55658, 55626}, {53091, 55610, 6}, {53094, 55580, 55647}, {55580, 55647, 55603}, {55582, 55659, 55613}, {55585, 55674, 55640}, {55589, 55669, 55639}, {55590, 55673, 55642}, {55594, 55682, 55662}, {55639, 55651, 55645}

X(55709) = X(3)X(6)∩X(110)X(6688)

Barycentrics    a^2*(8*a^4+3*b^4-16*b^2*c^2+3*c^4-11*a^2*(b^2+c^2)) : :
X(55709) = 5*X[3]+11*X[6], -11*X[597]+3*X[38071], X[1353]+3*X[10168], -5*X[3618]+X[18553], -17*X[3854]+33*X[14561], -11*X[5476]+3*X[50687], -11*X[5480]+3*X[33699], -X[5921]+9*X[38317], 11*X[11179]+5*X[41099], -5*X[11898]+21*X[51186], 5*X[12007]+3*X[20582], -9*X[14848]+X[48904] and many others

X(55709) lies on circumconic {{A, B, C, X(14810), X(30535)}} and on these lines: {3, 6}, {110, 6688}, {542, 10109}, {597, 38071}, {1353, 10168}, {1503, 3856}, {3564, 51127}, {3589, 15806}, {3618, 18553}, {3854, 14561}, {5012, 32237}, {5422, 44082}, {5476, 50687}, {5480, 33699}, {5544, 17809}, {5651, 10219}, {5921, 38317}, {5943, 11003}, {5965, 45760}, {6030, 34545}, {6329, 15807}, {6723, 45298}, {11179, 41099}, {11402, 16187}, {11422, 15082}, {11645, 14893}, {11793, 36153}, {11898, 51186}, {12007, 20582}, {14848, 48904}, {14853, 50692}, {14912, 43150}, {14927, 48895}, {15246, 34566}, {19924, 51138}, {20423, 48920}, {21356, 50961}, {22112, 34986}, {24206, 46267}, {33748, 40330}, {35434, 43273}, {38110, 51128}, {44882, 44903}, {46264, 50691}, {47352, 50954}, {48901, 51029}

X(55709) = midpoint of X(i) and X(j) for these {i,j}: {182, 15516}, {1351, 55612}, {15520, 55680}, {3589, 33749}, {37517, 55597}, {46267, 50979}, {575, 50664}, {576, 55653}, {5092, 22330}, {5093, 55664}, {5097, 55674}, {5102, 55638}, {6, 20190}
X(55709) = reflection of X(i) in X(j) for these {i,j}: {55609, 3}, {55617, 55668}, {55625, 55674}, {55636, 55679}, {55647, 5092}, {55659, 55688}, {55668, 20190}, {55679, 55696}, {55688, 182}, {55696, 55704}, {55704, 50664}
X(55709) = center of Tucker-Hagos(11/8) circle
X(55709) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 55609}, {3, 55581, 55619}, {3, 55702, 55700}, {3, 55707, 55702}, {6, 5050, 55708}, {6, 53093, 55697}, {6, 55610, 576}, {6, 55705, 55689}, {182, 1350, 55690}, {182, 14810, 20190}, {182, 15520, 55669}, {182, 22234, 55587}, {182, 3098, 55692}, {182, 39561, 1351}, {182, 511, 55688}, {182, 53094, 55695}, {182, 575, 15516}, {182, 576, 53094}, {182, 55587, 5085}, {182, 55608, 55691}, {182, 55662, 55693}, {182, 55669, 12017}, {182, 55688, 55696}, {182, 55692, 55698}, {511, 20190, 55668}, {511, 50664, 55704}, {511, 5092, 55647}, {511, 55668, 55617}, {511, 55674, 55625}, {511, 55679, 55636}, {575, 5050, 50664}, {575, 5092, 39561}, {575, 5097, 53091}, {575, 55698, 53092}, {576, 55667, 55582}, {1350, 55690, 55674}, {1351, 5092, 55612}, {1351, 53093, 182}, {1351, 55612, 511}, {1351, 55667, 55590}, {1351, 55671, 52987}, {1351, 55697, 55671}, {3098, 55698, 55686}, {5085, 55587, 55666}, {5092, 55582, 55653}, {5092, 55599, 3}, {5092, 55620, 55664}, {5092, 55623, 55667}, {5093, 55687, 55594}, {5097, 55690, 1350}, {5097, 55695, 55633}, {5102, 55672, 55588}, {10541, 37517, 55670}, {11477, 55691, 55657}, {11482, 55699, 55649}, {12017, 15520, 55606}, {12017, 55606, 55680}, {12017, 55642, 5092}, {14810, 55584, 55601}, {14810, 55586, 55605}, {14810, 55590, 55610}, {14810, 55605, 55621}, {14810, 55666, 55658}, {14810, 55668, 55659}, {14810, 55671, 55663}, {15516, 55612, 22330}, {15516, 55674, 5097}, {17508, 55584, 14810}, {20190, 50664, 55706}, {20190, 55601, 17508}, {20190, 55617, 55679}, {33878, 55677, 55645}, {33878, 55693, 55677}, {37517, 55670, 55597}, {39561, 52987, 6}, {39561, 55705, 55623}, {44456, 55681, 55627}, {50664, 55653, 55705}, {52987, 55708, 53093}, {53091, 53093, 55655}, {53092, 55703, 3098}, {53097, 55685, 55661}, {53858, 55682, 55585}, {55581, 55619, 55592}, {55581, 55633, 55598}, {55585, 55682, 55650}, {55587, 55666, 55631}, {55588, 55672, 55638}, {55592, 55612, 55599}

X(55710) = X(2)X(54644)∩X(3)X(6)

Barycentrics    5*a^6-7*a^4*(b^2+c^2)+2*a^2*(b^4-5*b^2*c^2+c^4) : :
X(55710) = 3*X[3]+7*X[6], -X[69]+6*X[10168], -6*X[140]+X[3630], -7*X[141]+12*X[10124], 7*X[193]+33*X[15721], 2*X[206]+3*X[10250], 3*X[549]+2*X[32455], -6*X[597]+X[3818], -7*X[1352]+17*X[7486], 3*X[1353]+2*X[3631], -8*X[3589]+3*X[11178], 2*X[3629]+3*X[50977], 3*X[3839]+7*X[11179] and many others

X(55710) lies on these lines: {2, 54644}, {3, 6}, {22, 44107}, {69, 10168}, {140, 3630}, {141, 10124}, {184, 10546}, {193, 15721}, {206, 10250}, {323, 43650}, {524, 15713}, {542, 3618}, {549, 32455}, {597, 3818}, {1176, 14491}, {1352, 7486}, {1353, 3631}, {1495, 5422}, {1503, 3858}, {1974, 52294}, {3564, 48154}, {3589, 11178}, {3620, 5965}, {3629, 50977}, {3796, 52719}, {3839, 11179}, {3855, 14561}, {3861, 18583}, {5012, 7712}, {5054, 6144}, {5068, 6776}, {5476, 6329}, {5622, 25556}, {5892, 22829}, {5943, 26864}, {6403, 44880}, {6688, 17809}, {6771, 11489}, {6774, 11488}, {7485, 44111}, {8550, 18358}, {8584, 44580}, {9039, 43149}, {9306, 44109}, {9873, 51860}, {10545, 11003}, {11422, 22112}, {11423, 54434}, {11424, 52093}, {11645, 51185}, {12007, 34507}, {12834, 44082}, {13366, 15066}, {13603, 43697}, {14848, 48905}, {14853, 48904}, {14912, 24206}, {14997, 37527}, {15004, 15107}, {15019, 35268}, {15032, 15058}, {15080, 34545}, {15682, 46264}, {15683, 31670}, {15691, 48880}, {15697, 19924}, {17578, 29012}, {19710, 21850}, {20080, 40107}, {20415, 42114}, {20416, 42111}, {20423, 48892}, {25406, 43621}, {39588, 44091}, {39899, 47352}, {43150, 46267}, {43273, 48895}, {48891, 54131}, {51137, 51170}, {52098, 52699}

X(55710) = midpoint of X(i) and X(j) for these {i,j}: {182, 22234}, {1351, 55614}, {11482, 53094}, {37517, 55598}, {576, 55655}, {5097, 55677}, {53091, 53093}, {6, 12017}
X(55710) = reflection of X(i) in X(j) for these {i,j}: {182, 53093}, {1350, 55650}, {12017, 55702}, {22234, 53091}, {3, 55690}, {3098, 55672}, {52987, 55629}, {53091, 575}, {53094, 55698}, {55587, 55600}, {55595, 14810}, {55598, 55646}, {55600, 55655}, {55604, 55661}, {55608, 3}, {55614, 55666}, {55623, 55674}, {55629, 55677}, {55637, 53094}, {55646, 5092}, {55655, 55687}, {55666, 20190}, {55672, 12017}, {55687, 182}, {55702, 50664}
X(55710) = isogonal conjugate of X(54645)
X(55710) = center of Tucker-Hagos(7/5) circle
X(55710) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(31652)}}, {{A, B, C, X(39), X(14491)}}, {{A, B, C, X(74), X(15515)}}, {{A, B, C, X(574), X(13603)}}, {{A, B, C, X(3098), X(30535)}}, {{A, B, C, X(3431), X(15513)}}, {{A, B, C, X(11738), X(15602)}}
X(55710) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55638}, {3, 511, 55608}, {3, 55590, 55630}, {3, 55596, 55635}, {6, 10485, 5033}, {6, 12055, 5028}, {6, 5050, 50664}, {6, 55582, 5093}, {6, 55656, 5102}, {6, 55676, 1351}, {6, 55701, 55668}, {15, 16, 15515}, {182, 1351, 55683}, {182, 17508, 55694}, {182, 5050, 55708}, {182, 5097, 55669}, {182, 52987, 5085}, {182, 575, 39561}, {182, 576, 17508}, {182, 55581, 55688}, {182, 55585, 55689}, {182, 55608, 55690}, {182, 55633, 55692}, {182, 55672, 12017}, {182, 55685, 10541}, {182, 55708, 55707}, {371, 372, 31652}, {511, 14810, 55595}, {511, 20190, 55666}, {511, 5092, 55646}, {511, 53091, 22234}, {511, 575, 53091}, {511, 55600, 55587}, {511, 55655, 55600}, {511, 55666, 55614}, {511, 55674, 55623}, {511, 55677, 55629}, {569, 15037, 11438}, {575, 55704, 53092}, {575, 55709, 5050}, {1350, 55642, 3098}, {1350, 55668, 55642}, {1350, 55681, 55660}, {1350, 55695, 55681}, {1350, 55701, 55695}, {1351, 20190, 55649}, {1351, 55649, 55583}, {1351, 55676, 55594}, {1351, 55683, 55605}, {1351, 55703, 20190}, {1352, 33748, 33749}, {3098, 5092, 55665}, {3098, 55652, 55639}, {3098, 55653, 55640}, {3098, 55669, 55653}, {3098, 55687, 55672}, {5050, 53091, 53093}, {5085, 53092, 5097}, {5085, 55629, 55677}, {5092, 33878, 55658}, {5092, 50664, 55705}, {5093, 10541, 14810}, {5093, 55678, 55582}, {5093, 55685, 55589}, {5097, 55607, 37517}, {5097, 55653, 44456}, {5102, 55700, 55667}, {5476, 48906, 48884}, {6329, 48906, 5476}, {8550, 51732, 38317}, {10541, 14810, 55685}, {10541, 55582, 55678}, {11179, 51171, 19130}, {11477, 55639, 55586}, {11477, 55674, 55603}, {11477, 55697, 55674}, {11482, 12017, 55604}, {11482, 53093, 55698}, {11482, 53094, 511}, {11482, 55698, 55637}, {12007, 38110, 34507}, {12017, 53091, 6}, {12017, 53093, 55702}, {12017, 55604, 53094}, {12017, 55646, 5092}, {12017, 55672, 55687}, {12017, 55687, 55691}, {12017, 55702, 182}, {14075, 37479, 9301}, {15516, 50664, 55696}, {15516, 55638, 22330}, {15516, 55693, 576}, {15516, 55704, 55615}, {15516, 55706, 3}, {15520, 55689, 55585}, {15520, 55693, 55596}, {15520, 55706, 55693}, {17508, 55587, 55644}, {17508, 55600, 55655}, {20190, 55594, 55676}, {22234, 55608, 15520}, {22234, 55637, 11482}, {22330, 55695, 1350}, {31884, 55688, 55675}, {33878, 55705, 55699}, {37517, 55658, 33878}, {37517, 55672, 55598}, {43150, 46267, 47355}, {44456, 55653, 52987}, {50664, 55594, 55703}, {50664, 55653, 55704}, {50664, 55696, 55706}, {53092, 55705, 55607}, {53094, 55604, 55661}, {53097, 55670, 55633}, {53097, 55692, 55670}, {55580, 55671, 55627}, {55581, 55675, 31884}, {55584, 55657, 55611}, {55584, 55684, 55657}, {55585, 55672, 55634}, {55588, 55651, 55613}, {55588, 55680, 55651}, {55593, 55659, 55628}, {55598, 55608, 55601}, {55603, 55674, 55652}, {55610, 55679, 55662}, {55614, 55646, 55632}

X(55711) = X(2)X(12007)∩X(3)X(6)

Barycentrics    a^2*(7*a^4+3*b^4-14*b^2*c^2+3*c^4-10*a^2*(b^2+c^2)) : :
X(55711) = 3*X[2]+4*X[12007], 2*X[3]+5*X[6], -X[4]+8*X[6329], -5*X[67]+12*X[38725], -8*X[140]+X[40341], -10*X[141]+17*X[3533], -X[376]+8*X[51138], -12*X[547]+5*X[1352], -8*X[549]+X[50973], -10*X[597]+3*X[3545], 3*X[599]+4*X[1353], 5*X[631]+2*X[3629] and many others

X(55711) lies on these lines: {2, 12007}, {3, 6}, {4, 6329}, {51, 52719}, {54, 45248}, {64, 13434}, {67, 38725}, {110, 10601}, {140, 40341}, {141, 3533}, {154, 3066}, {155, 36153}, {376, 51138}, {394, 5646}, {458, 15576}, {524, 15702}, {547, 1352}, {549, 50973}, {597, 3545}, {599, 1353}, {631, 3629}, {1386, 16200}, {1498, 41593}, {1503, 3832}, {1853, 41729}, {1992, 15708}, {1994, 21766}, {3167, 16187}, {3329, 9756}, {3524, 20583}, {3525, 3631}, {3526, 5965}, {3543, 5480}, {3564, 47355}, {3567, 17710}, {3589, 5067}, {3618, 5056}, {3751, 30392}, {3763, 16239}, {3796, 34545}, {3845, 11179}, {3850, 14561}, {3853, 48906}, {5012, 17810}, {5032, 50983}, {5059, 25406}, {5070, 43150}, {5071, 51136}, {5462, 9973}, {5476, 38335}, {5544, 9306}, {5622, 51941}, {5640, 41424}, {5651, 11402}, {6403, 44878}, {6771, 49906}, {6774, 49905}, {6800, 31860}, {7708, 33979}, {7716, 19128}, {8547, 47485}, {8549, 19132}, {8584, 15719}, {10124, 50961}, {10168, 15533}, {10169, 36989}, {10250, 39879}, {10264, 25331}, {10303, 11008}, {10359, 13196}, {10519, 32455}, {10620, 34155}, {11001, 44882}, {11284, 44109}, {11531, 16475}, {11646, 38735}, {11812, 15534}, {11898, 15723}, {12039, 32621}, {12177, 44000}, {12283, 16776}, {13366, 17811}, {14490, 43697}, {14848, 48901}, {14853, 33703}, {14982, 32300}, {15018, 35259}, {15024, 41579}, {15043, 44668}, {15061, 16176}, {15577, 17813}, {15686, 20423}, {15690, 48873}, {15692, 51132}, {15694, 51140}, {15715, 50970}, {15721, 50982}, {16010, 52699}, {16241, 51209}, {16242, 51208}, {17821, 34777}, {18440, 25555}, {19924, 50976}, {26516, 41964}, {26521, 41963}, {28461, 51729}, {32217, 37925}, {33179, 38315}, {33749, 38317}, {34117, 52028}, {34484, 39588}, {34567, 34817}, {35400, 48904}, {35401, 50963}, {37672, 43650}, {37940, 51733}, {38144, 39870}, {41983, 54173}, {46267, 50955}, {48310, 50974}, {48874, 50968}, {48898, 51024}, {51212, 51737}

X(55711) = midpoint of X(i) and X(j) for these {i,j}: {1351, 55616}, {576, 55658}, {53092, 55705}, {53858, 55676}, {6, 10541}
X(55711) = reflection of X(i) in X(j) for these {i,j}: {1350, 55651}, {10541, 55705}, {3, 55691}, {33878, 55611}, {53858, 6}, {6, 53092}, {55602, 55658}, {55607, 3}, {55616, 55669}, {55626, 55676}, {55639, 55681}, {55644, 5092}, {55676, 10541}, {55705, 55708}
X(55711) = inverse of X(5102) in First Brocard Circle
X(55711) = center of Tucker-Hagos(10/7) circle
X(55711) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(5102)}}, {{A, B, C, X(3), X(18843)}}, {{A, B, C, X(64), X(37512)}}, {{A, B, C, X(574), X(14490)}}, {{A, B, C, X(1350), X(30535)}}, {{A, B, C, X(2987), X(53858)}}, {{A, B, C, X(5024), X(14483)}}, {{A, B, C, X(5206), X(14528)}}, {{A, B, C, X(10542), X(11175)}}, {{A, B, C, X(30435), X(34567)}}, {{A, B, C, X(40803), X(44456)}}, {{A, B, C, X(52518), X(53096)}}
X(55711) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12017, 55685}, {3, 1351, 55587}, {3, 33878, 55627}, {3, 37517, 55591}, {3, 5050, 50664}, {3, 50664, 55703}, {3, 511, 55607}, {3, 6, 5102}, {3, 55582, 55618}, {3, 55594, 31884}, {3, 55610, 55642}, {3, 55645, 55656}, {3, 55703, 55699}, {6, 15815, 5111}, {6, 31884, 576}, {6, 50659, 10542}, {182, 14810, 55692}, {182, 15516, 1351}, {182, 15520, 55655}, {182, 3098, 55690}, {182, 37517, 55683}, {182, 575, 53091}, {182, 55581, 55687}, {182, 55633, 55691}, {182, 55655, 20190}, {182, 55674, 12017}, {182, 55683, 55695}, {182, 55690, 55697}, {182, 55709, 5050}, {182, 55710, 55709}, {511, 5092, 55644}, {511, 55658, 55602}, {511, 55669, 55616}, {511, 55681, 55639}, {511, 55705, 10541}, {567, 36752, 37475}, {567, 37475, 11425}, {575, 50664, 39561}, {575, 55708, 53092}, {576, 55685, 55594}, {1350, 5085, 55671}, {1350, 53093, 182}, {1350, 55654, 55629}, {1350, 55671, 55646}, {1350, 55676, 55651}, {1351, 15516, 6}, {1351, 53091, 15516}, {1351, 55616, 511}, {1351, 55662, 53097}, {1351, 55688, 55622}, {1351, 55692, 14810}, {1352, 51732, 47352}, {3066, 11003, 154}, {3589, 14912, 15069}, {3618, 33748, 8550}, {3618, 8550, 10516}, {5050, 5093, 55707}, {5050, 53092, 55705}, {5050, 55705, 55708}, {5085, 55626, 55676}, {5092, 22234, 5093}, {5092, 53097, 55654}, {5092, 55592, 55662}, {5093, 12017, 55617}, {5097, 55612, 37517}, {5097, 55685, 55584}, {5102, 55582, 11477}, {5422, 11003, 3066}, {5645, 11003, 13595}, {6419, 26341, 12306}, {6420, 26348, 12305}, {10541, 53092, 53858}, {10541, 53858, 55626}, {10541, 55676, 5085}, {10541, 55708, 53093}, {11179, 18583, 36990}, {11179, 51185, 38072}, {11477, 55618, 55582}, {11477, 55671, 1350}, {11482, 55697, 3098}, {11482, 55704, 55684}, {11842, 52771, 3053}, {12017, 55584, 55674}, {12017, 55608, 53094}, {15516, 50664, 55688}, {15516, 55688, 5097}, {15516, 55706, 55608}, {15520, 20190, 33878}, {17508, 22330, 44456}, {17508, 44456, 55614}, {17508, 55590, 55648}, {17508, 55636, 3}, {20190, 33878, 55673}, {22234, 55707, 5092}, {22330, 55702, 17508}, {33749, 38317, 39899}, {33878, 55673, 55641}, {36990, 51185, 18583}, {37517, 55683, 55612}, {39561, 55707, 55603}, {44456, 55648, 55590}, {44505, 44506, 44508}, {47352, 51027, 547}, {50664, 55603, 55701}, {50664, 55636, 55702}, {50664, 55680, 55704}, {50979, 51732, 1352}, {52987, 55696, 55682}, {53091, 55629, 22234}, {53094, 55651, 55669}, {55581, 55659, 55610}, {55581, 55687, 55659}, {55583, 55668, 55624}, {55585, 55679, 55643}, {55586, 55660, 55620}, {55587, 55603, 55592}, {55587, 55669, 55633}, {55588, 55667, 55632}, {55606, 55693, 55678}, {55658, 55708, 55706}

X(55712) = X(3)X(6)∩X(184)X(10545)

Barycentrics    a^2*(7*a^4+4*b^4-14*b^2*c^2+4*c^4-11*a^2*(b^2+c^2)) : :
X(55712) = 3*X[3]+11*X[6], -11*X[141]+18*X[47598], X[193]+6*X[10168], -11*X[597]+4*X[10109], 3*X[1353]+4*X[34573], -10*X[3618]+3*X[11178], -11*X[3630]+60*X[45760], -2*X[3631]+9*X[38110], -5*X[3763]+12*X[46267], -X[3818]+8*X[6329], 17*X[3854]+11*X[6776], -4*X[3856]+11*X[18583], -11*X[5476]+4*X[14893] and many others

X(55712) lies on these lines: {3, 6}, {141, 47598}, {184, 10545}, {193, 10168}, {323, 44299}, {542, 51171}, {597, 10109}, {1353, 34573}, {1503, 42785}, {3564, 42786}, {3618, 11178}, {3619, 5965}, {3630, 45760}, {3631, 38110}, {3763, 46267}, {3818, 6329}, {3854, 6776}, {3856, 18583}, {5012, 48912}, {5422, 44109}, {5476, 14893}, {5888, 11004}, {5943, 52719}, {6759, 36153}, {7485, 34566}, {7712, 15019}, {9306, 15018}, {9976, 19137}, {10169, 34776}, {10250, 41593}, {11008, 40107}, {11179, 48884}, {11202, 39125}, {11422, 16187}, {12007, 38317}, {14487, 43697}, {14561, 33749}, {14848, 35434}, {14853, 50691}, {14912, 25555}, {15004, 15080}, {18440, 51185}, {19130, 39874}, {20415, 42111}, {20416, 42114}, {20423, 46333}, {21850, 44903}, {24206, 46935}, {26881, 34417}, {32068, 37643}, {32455, 50977}, {33699, 48906}, {34507, 51126}, {38064, 51170}, {38942, 43584}, {43150, 47352}, {48880, 50971}

X(55712) = midpoint of X(i) and X(j) for these {i,j}: {1351, 55626}, {576, 55669}, {53092, 55711}, {6, 55705}
X(55712) = reflection of X(i) in X(j) for these {i,j}: {182, 55708}, {3098, 55676}, {52987, 55633}, {55587, 55602}, {55605, 3}, {55611, 55669}, {55633, 55681}, {55639, 5092}, {55658, 55691}, {55669, 10541}, {55681, 182}, {55691, 55705}, {55708, 55711}, {55711, 575}
X(55712) = center of Tucker-Hagos(11/7) circle
X(55712) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(574), X(14487)}}, {{A, B, C, X(30535), X(37517)}}
X(55712) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 55605}, {3, 55586, 3098}, {3, 55709, 55707}, {6, 33878, 5097}, {6, 55607, 53858}, {6, 55646, 5093}, {6, 55699, 1351}, {182, 15520, 52987}, {182, 22234, 15520}, {182, 3098, 55689}, {182, 37517, 55672}, {182, 39561, 22234}, {182, 5093, 55628}, {182, 5097, 55608}, {182, 52987, 55685}, {182, 55637, 5085}, {182, 55658, 55691}, {182, 55667, 20190}, {511, 5092, 55639}, {511, 575, 55711}, {511, 55669, 55611}, {511, 55711, 55708}, {575, 53091, 39561}, {576, 3098, 44456}, {576, 39561, 15516}, {576, 55693, 1350}, {576, 55708, 10541}, {1350, 5050, 55704}, {1350, 55675, 55649}, {1350, 55693, 55675}, {1350, 55704, 55693}, {1351, 55626, 511}, {1351, 55673, 55588}, {1351, 55687, 55603}, {1351, 55699, 55653}, {1351, 55706, 55687}, {3098, 17508, 55661}, {3098, 55586, 55598}, {3098, 55676, 55658}, {3098, 55691, 55676}, {3098, 55710, 50664}, {5050, 55639, 55705}, {5050, 55673, 55706}, {5050, 55692, 53093}, {5085, 55580, 55659}, {5092, 55609, 3}, {5092, 55653, 55673}, {5092, 55696, 55692}, {5092, 55702, 55700}, {5093, 20190, 55587}, {5097, 55696, 33878}, {5102, 55674, 55583}, {5102, 55701, 55674}, {6329, 50979, 3818}, {10541, 55611, 55681}, {10541, 55639, 5092}, {10541, 55711, 5050}, {11477, 55678, 55601}, {11477, 55695, 55655}, {11482, 55703, 14810}, {12017, 44456, 55656}, {12017, 55582, 55668}, {14810, 55703, 55694}, {15516, 55710, 55585}, {15516, 55711, 55669}, {15520, 55672, 37517}, {17508, 33878, 55642}, {17508, 53093, 182}, {20190, 55587, 55667}, {22234, 37517, 6}, {22234, 55709, 55613}, {22330, 55580, 576}, {33878, 53093, 55696}, {33878, 55696, 17508}, {37517, 55691, 55633}, {52987, 55685, 55662}, {53097, 55688, 55660}, {55583, 55674, 55630}, {55584, 55679, 55640}, {55585, 55598, 55589}, {55588, 55673, 55635}, {55590, 55682, 55652}, {55594, 55665, 55637}, {55601, 55695, 55678}, {55606, 55697, 55683}, {55608, 55649, 55631}, {55642, 55658, 55651}, {55653, 55706, 55699}

X(55713) = X(2)X(34566)∩X(3)X(6)

Barycentrics    a^2*(6*a^4+5*b^4-12*b^2*c^2+5*c^4-11*a^2*(b^2+c^2)) : :
X(55713) = X[3]+11*X[6], X[1353]+2*X[25555], X[1992]+2*X[46267], -11*X[3818]+17*X[3854], 4*X[3856]+11*X[12007], -4*X[6329]+X[24206], -X[11180]+5*X[14561], -X[18553]+4*X[18583], X[20423]+3*X[33748], -5*X[21167]+7*X[50988], -11*X[25406]+3*X[46333],-11*X[34507]+29*X[46935] and many others

X(55713) lies on these lines: {2, 34566}, {3, 6}, {373, 34545}, {524, 47598}, {542, 38071}, {597, 5965}, {1199, 15030}, {1353, 25555}, {1503, 14893}, {1992, 46267}, {1993, 15082}, {1994, 5650}, {2548, 14162}, {3564, 10109}, {3818, 3854}, {3856, 12007}, {5305, 51520}, {5476, 14912}, {5480, 33749}, {5640, 9544}, {6090, 6688}, {6329, 24206}, {6800, 15004}, {7592, 46847}, {7753, 14160}, {8550, 38136}, {8584, 38110}, {10168, 20583}, {10282, 39125}, {10601, 12045}, {11002, 34565}, {11003, 44107}, {11004, 33879}, {11179, 29323}, {11180, 14561}, {11216, 23042}, {11645, 14853}, {15019, 35265}, {15035, 16226}, {16981, 22352}, {18553, 18583}, {20423, 33748}, {21167, 50988}, {21849, 35268}, {23515, 45967}, {25406, 46333}, {29012, 33699}, {29317, 44903}, {32455, 40107}, {34507, 46935}, {46264, 50692}, {47462, 47569}, {48901, 50691}, {51140, 51185}, {51142, 51182}

X(55713) = midpoint of X(i) and X(j) for these {i,j}: {182, 5093}, {1351, 55649}, {11216, 23042}, {11477, 55596}, {37517, 55610}, {5050, 15520}, {576, 5085}, {5097, 55706}, {5102, 17508}, {5476, 14912}, {6, 39561}, {8550, 38136}, {8584, 38110}
X(55713) = reflection of X(i) in X(j) for these {i,j}: {1350, 55663}, {14810, 5085}, {25561, 14561}, {3, 55700}, {3098, 55680}, {31884, 55686}, {39561, 15516}, {48889, 38136}, {575, 39561}, {5085, 50664}, {5092, 55706}, {5093, 22330}, {52987, 55638}, {55586, 55599}, {55588, 55610}, {55589, 55621}, {55590, 55627}, {55591, 55631}, {55593, 55645}, {55594, 55649}, {55596, 55653}, {55599, 3}, {55603, 55664}, {55606, 55670}, {55610, 55674}, {55615, 17508}, {55627, 5092}, {55638, 55688}, {55649, 20190}, {55657, 55695}, {55663, 55696}, {55670, 182}, {55680, 55704}, {55695, 5050}, {55700, 55709}, {55706, 575}
X(55713) = center of Tucker-Hagos(11/6) circle
X(55713) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(8589), X(14487)}}, {{A, B, C, X(22330), X(30535)}}
X(55713) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 55599}, {3, 55581, 55609}, {3, 55586, 55619}, {3, 55589, 55621}, {3, 55609, 14810}, {3, 55707, 55700}, {3, 55709, 55702}, {3, 55712, 55709}, {6, 182, 22330}, {6, 22234, 15516}, {6, 39764, 44500}, {6, 5050, 15520}, {6, 575, 5097}, {6, 55711, 11482}, {182, 11477, 55653}, {182, 1351, 55625}, {182, 3098, 55684}, {182, 31884, 55686}, {182, 33878, 55679}, {182, 37517, 55644}, {182, 511, 55670}, {182, 576, 33878}, {182, 55583, 55676}, {182, 55596, 55682}, {182, 55648, 55688}, {182, 55660, 5085}, {182, 55686, 55695}, {511, 15516, 39561}, {511, 17508, 55615}, {511, 22330, 5093}, {511, 5092, 55627}, {511, 55599, 55586}, {511, 55621, 55589}, {511, 55627, 55590}, {511, 55631, 55591}, {511, 55638, 52987}, {511, 55645, 55593}, {511, 55663, 1350}, {511, 55688, 55638}, {575, 14810, 50664}, {575, 55588, 53093}, {575, 55599, 55707}, {575, 55677, 55708}, {576, 55701, 55597}, {576, 55710, 55683}, {1350, 55685, 55663}, {1350, 55696, 55677}, {1350, 55708, 55696}, {1351, 20190, 55594}, {1351, 55676, 55583}, {1351, 55703, 55649}, {1351, 55710, 20190}, {1353, 25555, 43150}, {3098, 55697, 55680}, {3098, 55704, 55690}, {3098, 55711, 55704}, {5050, 31884, 182}, {5050, 5093, 31884}, {5050, 5102, 17508}, {5050, 55695, 55706}, {5085, 55603, 55664}, {5085, 55624, 55672}, {5092, 55590, 55650}, {5092, 55619, 3}, {5093, 55682, 11477}, {5097, 55666, 1351}, {10541, 55587, 55668}, {11477, 55596, 511}, {11477, 55682, 55596}, {11482, 55711, 3098}, {12017, 55591, 55667}, {14810, 33878, 55606}, {14810, 50664, 55698}, {14810, 55594, 55614}, {14810, 55664, 55657}, {14810, 55670, 55660}, {14810, 55683, 55666}, {14810, 55698, 5092}, {15520, 17508, 5102}, {15520, 39561, 5050}, {15520, 55603, 576}, {17508, 55593, 55645}, {22330, 53092, 575}, {31884, 33878, 55603}, {33878, 53092, 53091}, {34545, 44111, 34986}, {37517, 53093, 55674}, {37517, 55674, 55588}, {37517, 55693, 55610}, {39561, 55707, 55712}, {44456, 55687, 55612}, {52987, 55688, 55661}, {53091, 55614, 55710}, {53093, 55610, 55693}, {53097, 55691, 55659}, {55582, 55669, 55617}, {55584, 55681, 55636}, {55587, 55668, 55623}, {55588, 55674, 55634}, {55591, 55667, 55631}, {55592, 55625, 55605}, {55596, 55660, 55628}, {55638, 55688, 55673}, {55649, 55710, 55703}, {55663, 55696, 55685}, {55680, 55704, 55697}

X(55714) = X(3)X(6)∩X(22)X(34566)

Barycentrics    a^2*(5*a^4+6*b^4-10*b^2*c^2+6*c^4-11*a^2*(b^2+c^2)) : :
X(55714) = -X[3]+11*X[6], X[193]+4*X[25555], -11*X[597]+6*X[47598], X[1352]+9*X[5032], 2*X[1353]+3*X[5476], 3*X[1992]+2*X[24206], 2*X[3629]+3*X[38317], -11*X[3818]+16*X[3856], -51*X[3854]+11*X[5921], X[6759]+4*X[39125], 11*X[6776]+9*X[50687], 4*X[8550]+X[48884] and many others

X(55714) lies on these lines: {3, 6}, {22, 34566}, {110, 15004}, {193, 25555}, {542, 41099}, {597, 47598}, {1352, 5032}, {1353, 5476}, {1992, 24206}, {1993, 16187}, {1994, 5651}, {3066, 34986}, {3629, 38317}, {3818, 3856}, {3854, 5921}, {5480, 13687}, {5544, 37672}, {5965, 40330}, {6723, 11433}, {6759, 39125}, {6776, 50687}, {7894, 10358}, {8550, 48884}, {8584, 10109}, {9306, 34565}, {9813, 19150}, {11003, 53863}, {11179, 48896}, {11402, 32237}, {11645, 35434}, {12007, 33699}, {14927, 20423}, {19924, 50975}, {22112, 34545}, {23048, 41729}, {29012, 50691}, {31670, 33749}, {32455, 34507}, {34380, 45760}, {34788, 41593}, {38079, 41149}, {40107, 51171}, {44903, 48898}, {46267, 50962}, {46333, 51212}, {48874, 50972}, {48885, 54132}, {50977, 51732}

X(55714) = midpoint of X(i) and X(j) for these {i,j}: {1351, 53094}, {11477, 55604}, {37517, 55637}, {576, 55710}, {6, 11482}
X(55714) = reflection of X(i) in X(j) for these {i,j}: {182, 53091}, {1350, 55666}, {12017, 575}, {22234, 6}, {3, 55702}, {3098, 55687}, {33878, 55623}, {52987, 55646}, {55585, 55595}, {55587, 55608}, {55595, 55661}, {55598, 3}, {55600, 55672}, {55604, 55677}, {55608, 53094}, {55614, 5092}, {55629, 55690}, {55634, 20190}, {55637, 12017}, {55646, 55698}, {55655, 182}, {55672, 53093}, {55677, 50664}, {55687, 55710}, {55710, 22234}
X(55714) = inverse of X(55713) in First Brocard Circle
X(55714) = center of Tucker-Hagos(11/5) circle
X(55714) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2987), X(22234)}}, {{A, B, C, X(8588), X(14487)}}
X(55714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 55598}, {3, 6, 55713}, {3, 55586, 55613}, {3, 55713, 55712}, {6, 1351, 15516}, {6, 22330, 15520}, {6, 511, 22234}, {182, 1351, 55587}, {182, 15520, 5097}, {182, 22234, 53091}, {182, 3098, 55683}, {182, 37517, 1350}, {182, 511, 55655}, {182, 52987, 55674}, {182, 55581, 3}, {182, 55633, 5092}, {182, 55672, 55690}, {182, 55674, 55691}, {182, 55683, 55693}, {182, 55709, 55707}, {511, 20190, 55634}, {511, 50664, 55677}, {511, 5092, 55614}, {511, 53093, 55672}, {511, 53094, 55608}, {511, 575, 12017}, {511, 55595, 55585}, {511, 55623, 33878}, {511, 55646, 52987}, {511, 55661, 55595}, {511, 55672, 55600}, {511, 55677, 55604}, {511, 55690, 55629}, {511, 55698, 55646}, {575, 5093, 37517}, {575, 55653, 55703}, {576, 55694, 11477}, {576, 55712, 55589}, {1350, 12017, 55666}, {1350, 55613, 55605}, {1350, 55632, 55612}, {1350, 55666, 55637}, {1350, 55688, 55662}, {1351, 15516, 182}, {1351, 5050, 55616}, {1351, 53091, 53094}, {1351, 55711, 14810}, {3098, 39561, 55708}, {5050, 55646, 55698}, {5085, 55585, 55644}, {5085, 55595, 55661}, {5092, 55584, 55633}, {5092, 55596, 55652}, {5093, 55643, 5102}, {5097, 15516, 1351}, {10541, 55594, 55667}, {11477, 50664, 55649}, {11477, 55604, 511}, {11482, 12017, 5093}, {11482, 22234, 576}, {12017, 17508, 55687}, {12017, 53094, 55688}, {12017, 55637, 17508}, {14810, 15516, 55711}, {15516, 55592, 55709}, {15516, 55608, 55710}, {15516, 55688, 575}, {17508, 37517, 55583}, {17508, 55583, 3098}, {17508, 55596, 55643}, {17508, 55627, 55660}, {17508, 55662, 55669}, {17508, 55691, 55684}, {17508, 55707, 55700}, {20190, 44456, 55603}, {20190, 55603, 55665}, {22234, 55710, 39561}, {31884, 55704, 55689}, {33878, 55681, 55640}, {33878, 55706, 55681}, {39561, 55660, 5050}, {44473, 44474, 44500}, {50664, 55649, 55694}, {52987, 55674, 55635}, {53091, 55629, 53093}, {53097, 55695, 55658}, {55580, 55699, 55657}, {55582, 55670, 55611}, {55582, 55701, 55670}, {55583, 55589, 55586}, {55584, 55633, 55596}, {55586, 55666, 55619}, {55587, 55605, 55592}, {55588, 55676, 55630}, {55591, 55668, 55628}, {55593, 55679, 55642}, {55598, 55712, 55702}, {55606, 55705, 55685}, {55610, 55696, 55675}

X(55715) = X(3)X(6)∩X(51)X(10546)

Barycentrics    a^2*(4*a^4+7*b^4-8*b^2*c^2+7*c^4-11*a^2*(b^2+c^2)) : :
X(55715) = -3*X[3]+11*X[6], -3*X[69]+7*X[42786], -5*X[141]+9*X[38079], X[193]+3*X[5476], -3*X[1352]+7*X[42785], 3*X[1992]+X[3818], -5*X[3620]+9*X[38317], X[3629]+X[19130], -X[3630]+3*X[24206], -X[3631]+3*X[18583], 5*X[3763]+3*X[50962], -17*X[3854]+33*X[14853] and many others

X(55715) lies on these lines: {3, 6}, {51, 10546}, {69, 42786}, {141, 38079}, {193, 5476}, {323, 5943}, {524, 10109}, {542, 14893}, {895, 14487}, {1173, 54434}, {1352, 42785}, {1495, 1994}, {1992, 3818}, {3060, 7712}, {3292, 10545}, {3564, 3856}, {3589, 46114}, {3620, 38317}, {3629, 19130}, {3630, 24206}, {3631, 18583}, {3763, 50962}, {3819, 15018}, {3854, 14853}, {5032, 46264}, {5965, 11803}, {6000, 39125}, {6144, 11178}, {6329, 46267}, {6636, 34566}, {6688, 15004}, {6776, 50691}, {7766, 44422}, {8550, 29323}, {8584, 11645}, {9969, 11702}, {10168, 50980}, {11008, 34507}, {11179, 46333}, {11216, 34779}, {11422, 32237}, {12007, 29317}, {13366, 15107}, {13598, 15032}, {14561, 20080}, {14848, 40341}, {15080, 21969}, {15082, 23061}, {15534, 25561}, {15988, 17547}, {16001, 42101}, {16002, 42102}, {18440, 51140}, {19140, 43129}, {19150, 44091}, {19924, 20583}, {20423, 48895}, {22856, 22900}, {25555, 34380}, {29181, 33749}, {34417, 34986}, {35434, 48884}, {39874, 48901}, {40107, 51126}, {43621, 50692}, {44106, 55038}, {44903, 48906}, {47281, 47581}, {48880, 54132}, {48892, 50979}, {48943, 54131}, {50977, 51171}, {50978, 51128}

X(55715) = midpoint of X(i) and X(j) for these {i,j}: {193, 43150}, {10168, 51132}, {11477, 14810}, {15534, 25561}, {3629, 19130}, {44456, 55594}, {575, 1351}, {576, 5097}, {5092, 37517}
X(55715) = reflection of X(i) in X(j) for these {i,j}: {1350, 55679}, {14810, 55704}, {15516, 22330}, {20190, 15516}, {22330, 5097}, {3, 55709}, {3098, 55696}, {33878, 55636}, {50664, 6}, {52987, 55659}, {55586, 55609}, {55587, 55617}, {55588, 55625}, {55590, 55647}, {55592, 3}, {55594, 55668}, {55597, 55674}, {55601, 5092}, {55606, 55688}, {55612, 20190}, {55621, 55700}, {55631, 182}, {55645, 55706}, {55653, 50664}, {55663, 5050}, {55674, 575}, {55686, 39561}, {55700, 55713}
X(55715) = inverse of X(55712) in First Brocard Circle
X(55715) = center of Tucker-Hagos(11/4) circle
X(55715) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(187), X(14487)}}, {{A, B, C, X(2987), X(50664)}}
X(55715) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 55592}, {3, 6, 55712}, {3, 55581, 55599}, {3, 55586, 55609}, {3, 55589, 55619}, {3, 55592, 55621}, {3, 55709, 55700}, {3, 55712, 55702}, {3, 55713, 55709}, {6, 12017, 39561}, {6, 15514, 12055}, {6, 33878, 55710}, {6, 55582, 5050}, {6, 55676, 53091}, {182, 3098, 55678}, {182, 44456, 55594}, {182, 511, 55631}, {182, 53097, 55657}, {182, 576, 5102}, {182, 55589, 3}, {182, 55594, 55668}, {182, 55600, 55673}, {182, 55610, 55677}, {182, 55631, 55680}, {182, 55680, 20190}, {193, 5476, 43150}, {323, 44107, 5943}, {323, 53863, 44107}, {511, 20190, 55612}, {511, 22330, 15516}, {511, 5050, 55663}, {511, 5097, 22330}, {511, 55609, 55586}, {511, 55617, 55587}, {511, 55625, 55588}, {511, 55647, 55590}, {511, 55659, 52987}, {511, 55674, 55597}, {511, 55679, 1350}, {511, 55688, 55606}, {511, 55696, 3098}, {575, 5092, 55705}, {575, 55590, 5085}, {1350, 22234, 55706}, {1350, 55679, 55645}, {1350, 55691, 55661}, {1350, 55706, 55679}, {1351, 15520, 575}, {1351, 5093, 53858}, {1351, 53858, 15520}, {1351, 55593, 11477}, {1351, 55678, 44456}, {3098, 55585, 55593}, {3098, 55643, 55634}, {3098, 55653, 55638}, {3098, 55672, 55651}, {3098, 55674, 55653}, {3098, 55691, 55667}, {3098, 55694, 55672}, {5050, 55606, 55688}, {5050, 55651, 55694}, {5085, 55590, 55647}, {5085, 55602, 55662}, {5092, 33878, 55636}, {5092, 55594, 55646}, {5102, 53097, 1351}, {6435, 6436, 14075}, {10541, 55603, 55666}, {11477, 12017, 55585}, {11477, 14810, 511}, {11477, 39561, 14810}, {11482, 44456, 6}, {12017, 55607, 55665}, {12017, 55665, 5092}, {14810, 39561, 55704}, {14810, 55704, 55686}, {15516, 55653, 50664}, {15520, 53858, 5097}, {17508, 55588, 55625}, {20190, 55612, 55664}, {20190, 55638, 55674}, {22330, 55592, 55713}, {22856, 22900, 39590}, {31884, 55708, 55690}, {33878, 55636, 55601}, {33878, 55699, 55658}, {37517, 39561, 55607}, {37517, 55710, 33878}, {37517, 55712, 55598}, {39561, 55585, 12017}, {39561, 55600, 182}, {44456, 55678, 53097}, {44497, 44498, 44500}, {50664, 55645, 55691}, {50664, 55674, 55696}, {52987, 53091, 55695}, {52987, 55695, 55659}, {53093, 55587, 55670}, {53093, 55639, 55689}, {53094, 55583, 55615}, {53097, 53858, 11482}, {55580, 55703, 55655}, {55581, 55681, 55613}, {55584, 55687, 55627}, {55586, 55594, 55589}, {55587, 55670, 55617}, {55587, 55689, 55639}, {55591, 55669, 55623}, {55591, 55701, 55669}, {55599, 55713, 55707}, {55601, 55663, 55632}, {55607, 55705, 55681}, {55632, 55646, 55640}, {55634, 55695, 55676}, {55649, 55711, 55698}, {55658, 55710, 55699}

X(55716) = X(3)X(6)∩X(51)X(323)

Barycentrics    a^2*(2*a^4+5*b^4-4*b^2*c^2+5*c^4-7*a^2*(b^2+c^2)) : :
X(55716) = -3*X[3]+7*X[6], -3*X[5]+X[3630], -X[66]+3*X[23048], -7*X[69]+15*X[5071], -7*X[141]+9*X[15699], 3*X[381]+X[6144], -7*X[597]+5*X[15713], -7*X[1352]+11*X[3855], -7*X[3589]+6*X[10124], -35*X[3618]+27*X[15709], -7*X[3619]+9*X[38317], -35*X[3620]+51*X[7486] and many others

X(55716) lies on these lines: {2, 44107}, {3, 6}, {5, 3630}, {30, 32455}, {51, 323}, {66, 23048}, {69, 5071}, {74, 14831}, {141, 15699}, {143, 43586}, {193, 3818}, {195, 13433}, {373, 23061}, {381, 6144}, {385, 44422}, {524, 5066}, {542, 1539}, {597, 15713}, {895, 13603}, {1352, 3855}, {1353, 29012}, {1495, 3060}, {1503, 48942}, {1843, 2914}, {1974, 52416}, {1992, 11645}, {1993, 21849}, {1994, 15107}, {2781, 39125}, {2967, 10985}, {2979, 34565}, {3167, 31860}, {3292, 10546}, {3564, 3861}, {3589, 10124}, {3618, 15709}, {3619, 38317}, {3620, 7486}, {3631, 24206}, {3763, 14848}, {3819, 15004}, {3858, 5480}, {3917, 5888}, {4550, 39522}, {5032, 15697}, {5068, 14853}, {5650, 15019}, {5943, 15066}, {6033, 41750}, {6329, 10168}, {6403, 44091}, {6467, 37945}, {6636, 44111}, {6688, 9777}, {6776, 29323}, {7712, 11422}, {7805, 14881}, {7837, 9993}, {7890, 44230}, {8537, 12294}, {8540, 37602}, {8550, 29317}, {8584, 19710}, {8681, 43129}, {8718, 15032}, {9976, 10752}, {10110, 15068}, {10250, 34778}, {10754, 41622}, {11178, 40341}, {11179, 48880}, {11456, 13598}, {11649, 37947}, {12007, 48920}, {12160, 44870}, {12221, 22819}, {12222, 22820}, {13366, 15080}, {14160, 18424}, {14912, 48898}, {14984, 25556}, {14997, 37521}, {15052, 15801}, {15534, 18440}, {15683, 46264}, {15691, 48892}, {15721, 46267}, {15988, 16861}, {16001, 42102}, {16002, 42101}, {16808, 20426}, {16809, 20425}, {17578, 48901}, {18583, 34573}, {19128, 44880}, {19149, 34788}, {22165, 25565}, {22329, 32414}, {25555, 48876}, {29301, 49489}, {33694, 38730}, {33749, 44882}, {34545, 41462}, {34777, 34779}, {38079, 51128}, {39523, 41455}, {39899, 48884}, {42117, 47863}, {42118, 47864}, {42283, 49028}, {42284, 49029}, {43273, 48879}, {44056, 44668}, {44110, 55038}, {47279, 47581}, {47281, 47571}, {47456, 47569}, {48881, 50979}, {49138, 51212}, {50988, 54169}, {51129, 51182}

X(55716) = midpoint of X(i) and X(j) for these {i,j}: {182, 11477}, {193, 3818}, {11178, 50962}, {19149, 34788}, {3098, 44456}, {3629, 21850}, {34777, 34779}, {39899, 48884}, {576, 1351}, {51140, 54131}, {6, 37517}, {9976, 10752}
X(55716) = reflection of X(i) in X(j) for these {i,j}: {182, 22330}, {1350, 20190}, {14810, 575}, {18553, 5480}, {22165, 25565}, {3, 15516}, {3098, 50664}, {33878, 55653}, {40107, 18583}, {43147, 44423}, {43150, 19130}, {44882, 33749}, {48876, 25555}, {48891, 48906}, {48895, 21850}, {48943, 31670}, {575, 5097}, {5092, 6}, {5097, 576}, {52987, 55674}, {53097, 55612}, {54173, 46267}, {6, 55715}, {55583, 55592}, {55584, 55597}, {55585, 55601}, {55586, 3098}, {55587, 55631}, {55588, 14810}, {55589, 55663}, {55590, 3}, {55591, 55664}, {55592, 55679}, {55593, 55680}, {55594, 5092}, {55596, 55686}, {55597, 55688}, {55599, 55695}, {55601, 55696}, {55603, 55700}, {55606, 182}, {55612, 55704}, {55615, 55706}, {55619, 53093}, {55627, 5050}, {55631, 55709}, {55634, 55710}, {55650, 53091}, {55657, 39561}, {55666, 22234}, {55670, 55713}, {55698, 55714}, {55706, 15520}, {55713, 5093}
X(55716) = inverse of X(55710) in First Brocard Circle
X(55716) = inverse of X(35006) in Cosine Circle
X(55716) = isogonal conjugate of X(54644)
X(55716) = center of Tucker-Hagos(7/2) circle
X(55716) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55710)}}, {{A, B, C, X(6), X(54645)}}, {{A, B, C, X(32), X(14491)}}, {{A, B, C, X(54), X(31652)}}, {{A, B, C, X(74), X(15513)}}, {{A, B, C, X(187), X(13603)}}, {{A, B, C, X(842), X(15514)}}, {{A, B, C, X(2987), X(5092)}}, {{A, B, C, X(3431), X(15515)}}, {{A, B, C, X(40802), X(55705)}}
X(55716) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55630}, {3, 15516, 55706}, {3, 182, 55686}, {3, 511, 55590}, {3, 55590, 55615}, {3, 55601, 55634}, {3, 55608, 55638}, {3, 55615, 14810}, {6, 11173, 41412}, {6, 12017, 55712}, {6, 1351, 37517}, {6, 55607, 53093}, {6, 55632, 55708}, {6, 55699, 53091}, {15, 16, 15513}, {182, 11477, 511}, {182, 3098, 55676}, {182, 31884, 55679}, {182, 33878, 55653}, {182, 5093, 22330}, {182, 52987, 55660}, {182, 576, 5093}, {182, 55583, 31884}, {182, 55587, 55648}, {182, 55596, 3}, {182, 55606, 55670}, {182, 55616, 55674}, {182, 55628, 17508}, {182, 55644, 55682}, {193, 20423, 3818}, {511, 14810, 55588}, {511, 20190, 1350}, {511, 44423, 43147}, {511, 5050, 55627}, {511, 53093, 55619}, {511, 55597, 55584}, {511, 55612, 53097}, {511, 55631, 55587}, {511, 55653, 33878}, {511, 55663, 55589}, {511, 55664, 55591}, {511, 55674, 52987}, {511, 55680, 55593}, {511, 55686, 55596}, {511, 55688, 55597}, {511, 55700, 55603}, {524, 19130, 43150}, {542, 21850, 48895}, {575, 5092, 55702}, {576, 52987, 53858}, {1350, 11482, 39561}, {1350, 20190, 55657}, {1350, 39561, 20190}, {1350, 55657, 55623}, {1350, 55672, 55636}, {1350, 55705, 55672}, {1351, 5093, 11477}, {1351, 5102, 576}, {1495, 11004, 34986}, {1666, 1667, 35006}, {1994, 15107, 44109}, {3060, 11004, 1495}, {3098, 12017, 55668}, {3098, 37517, 44456}, {3098, 5092, 55661}, {3098, 55586, 55594}, {3098, 55710, 55689}, {3098, 55712, 12017}, {3620, 14561, 42786}, {3629, 21850, 542}, {5008, 35002, 13335}, {5050, 53858, 55714}, {5050, 55646, 55691}, {5050, 55674, 55698}, {5085, 22234, 55709}, {5085, 55587, 55631}, {5085, 55604, 55658}, {5085, 55631, 55666}, {5092, 55702, 55695}, {5093, 22330, 5097}, {5111, 51206, 44498}, {5111, 51207, 44497}, {5480, 5965, 18553}, {6221, 6398, 15603}, {10541, 55593, 55655}, {10541, 55655, 55680}, {11477, 11482, 55644}, {11477, 15520, 55625}, {11477, 22330, 55606}, {11477, 53092, 55583}, {11477, 53858, 55684}, {11482, 55630, 15516}, {11482, 55705, 6}, {11645, 31670, 48943}, {12017, 44456, 55582}, {12017, 55582, 3098}, {12017, 55668, 5092}, {12017, 55712, 50664}, {14810, 55588, 55599}, {14810, 55695, 55677}, {15516, 55590, 55690}, {15516, 55601, 55696}, {15516, 55625, 182}, {15516, 55696, 55710}, {15516, 55706, 575}, {15520, 37517, 55585}, {15520, 55686, 55713}, {17508, 53091, 55704}, {17508, 53097, 55612}, {17508, 55598, 55639}, {17508, 55612, 55650}, {19130, 43150, 25561}, {19924, 48906, 48891}, {21969, 44109, 15107}, {22234, 55587, 5085}, {22330, 55679, 53092}, {31884, 55583, 55592}, {33878, 55648, 55604}, {33878, 55660, 55609}, {36241, 36242, 13349}, {36243, 36244, 13350}, {39561, 55672, 55705}, {39899, 54131, 48884}, {44456, 50664, 55586}, {44497, 44498, 44499}, {51170, 54132, 46264}, {51206, 51207, 5052}, {52987, 55660, 55616}, {52987, 55691, 55646}, {52987, 55714, 5050}, {53091, 55639, 55699}, {53093, 55584, 55649}, {53093, 55607, 55678}, {53093, 55649, 55688}, {53094, 55603, 55647}, {53094, 55708, 55700}, {55581, 55711, 55659}, {55584, 55678, 55607}, {55589, 55681, 55629}, {55589, 55703, 55663}, {55591, 55707, 55664}, {55593, 55655, 55617}, {55595, 55673, 55633}, {55600, 55651, 55621}, {55600, 55685, 55651}, {55602, 55671, 55640}, {55603, 55708, 53094}, {55605, 55675, 55643}, {55606, 55650, 55628}, {55610, 55711, 55687}, {55611, 55683, 55654}, {55614, 55669, 55645}, {55614, 55697, 55669}, {55626, 55692, 55667}, {55633, 55694, 55673}, {55651, 55701, 55685}, {55653, 55679, 55665}

X(55717) = X(3)X(6)∩X(184)X(16981)

Barycentrics    a^2*(3*a^4+8*b^4-6*b^2*c^2+8*c^4-11*a^2*(b^2+c^2)) : :
X(55717) = -5*X[3]+11*X[6], -11*X[1352]+17*X[3854], -X[3357]+4*X[39125], -8*X[3856]+11*X[5480], -11*X[5476]+8*X[10109], 11*X[6776]+X[50692], -4*X[8550]+X[48896], -2*X[11160]+5*X[11178], -4*X[12007]+X[48880], -5*X[14561]+3*X[21356], X[15534]+5*X[51172], -10*X[18583]+7*X[51128] and many others

X(55717) lies on circumconic {{A, B, C, X(2987), X(17508)}} and on these lines: {3, 6}, {184, 16981}, {524, 38071}, {542, 50687}, {1352, 3854}, {1503, 33699}, {1992, 29012}, {1993, 44106}, {1994, 35268}, {3060, 35265}, {3357, 39125}, {3564, 14893}, {3629, 48901}, {3856, 5480}, {5476, 10109}, {5965, 20423}, {6144, 18553}, {6776, 50692}, {6800, 21969}, {7998, 15004}, {8550, 48896}, {9306, 11002}, {10516, 50962}, {11160, 11178}, {12007, 48880}, {12160, 46847}, {13102, 43399}, {13103, 43400}, {14561, 21356}, {14912, 19924}, {15534, 51172}, {16187, 23061}, {18583, 51128}, {20582, 38317}, {21849, 35259}, {29181, 44903}, {29317, 54132}, {31670, 50691}, {33749, 48873}, {33884, 53863}, {35434, 54131}, {41153, 50980}, {47446, 47581}, {47598, 48310}, {48876, 51127}, {48879, 51170}, {48884, 51538}, {50963, 51187}

X(55717) = midpoint of X(i) and X(j) for these {i,j}: {1351, 5102}, {10516, 50962}, {15520, 37517}, {31884, 44456}, {5050, 11477}
X(55717) = reflection of X(i) in X(j) for these {i,j}: {182, 15520}, {1350, 55695}, {11178, 14853}, {15520, 576}, {17508, 6}, {3, 55713}, {3098, 5050}, {31884, 575}, {33878, 55657}, {39561, 5093}, {48884, 51538}, {5050, 5097}, {576, 5102}, {5102, 55716}, {52987, 17508}, {53097, 55615}, {55581, 55589}, {55583, 55593}, {55585, 55603}, {55586, 55621}, {55587, 31884}, {55588, 55645}, {55589, 3}, {55590, 55664}, {55591, 55670}, {55593, 5092}, {55594, 55686}, {55596, 5085}, {55599, 55700}, {55603, 182}, {55610, 55706}, {55613, 55707}, {55615, 50664}, {55621, 55709}, {55649, 39561}, {55657, 15516}, {55695, 22330}, {55713, 55715}
X(55717) = inverse of X(55709) in First Brocard Circle
X(55717) = inverse of the isogonal conjugate of X(42010) in Cosine Circle
X(55717) = center of Tucker-Hagos(11/3) circle
X(55717) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 55589}, {3, 6, 55709}, {3, 55586, 55605}, {3, 55715, 55714}, {6, 11477, 55584}, {6, 1350, 55701}, {6, 14810, 55708}, {6, 44456, 55601}, {6, 55632, 50664}, {182, 3098, 55675}, {182, 511, 55603}, {182, 55585, 55637}, {182, 55598, 3}, {182, 55611, 55672}, {511, 22330, 55695}, {511, 31884, 55587}, {511, 50664, 55615}, {511, 5085, 55596}, {511, 5092, 55593}, {511, 575, 31884}, {511, 55589, 55581}, {511, 55593, 55583}, {511, 55603, 55585}, {511, 55615, 53097}, {511, 55621, 55586}, {511, 55645, 55588}, {511, 55657, 33878}, {511, 55664, 55590}, {511, 55670, 55591}, {511, 55686, 55594}, {511, 55695, 1350}, {511, 55700, 55599}, {511, 55706, 55610}, {511, 55715, 55713}, {511, 55716, 5102}, {575, 55659, 55699}, {576, 1351, 37517}, {576, 3098, 5097}, {576, 39561, 5093}, {576, 55583, 11482}, {576, 55687, 53858}, {1350, 22330, 55710}, {1350, 55650, 3098}, {1350, 55681, 55642}, {1350, 55695, 55660}, {1350, 55701, 55668}, {1350, 55710, 55681}, {1351, 5102, 511}, {1351, 55716, 576}, {3098, 17508, 55654}, {3098, 55584, 52987}, {3098, 55587, 55595}, {5050, 55591, 55670}, {5050, 55659, 55693}, {5085, 55610, 55663}, {5092, 55583, 55608}, {5092, 55593, 55640}, {5093, 39561, 15520}, {5093, 55610, 6}, {10541, 55612, 55665}, {12017, 55590, 55644}, {12017, 55618, 55664}, {14810, 55697, 17508}, {14810, 55708, 55689}, {15516, 33878, 55687}, {15516, 55633, 182}, {15516, 55657, 55703}, {15520, 55581, 55707}, {15520, 55613, 55712}, {15520, 55649, 39561}, {15520, 55685, 22234}, {17508, 20190, 55685}, {17508, 39561, 55706}, {17508, 52987, 55630}, {17508, 55586, 55613}, {17508, 55589, 55621}, {17508, 55610, 55649}, {17508, 55630, 55658}, {17508, 55708, 55697}, {20190, 55595, 55652}, {20190, 55601, 55659}, {20190, 55709, 55702}, {22234, 52987, 20190}, {22234, 55685, 5050}, {33878, 53858, 15516}, {33878, 55671, 55617}, {33878, 55687, 55633}, {33878, 55703, 55657}, {37517, 55672, 44456}, {39561, 55587, 55680}, {39561, 55596, 5085}, {50664, 53097, 55655}, {50664, 55615, 55682}, {52987, 55652, 55611}, {52987, 55689, 14810}, {53091, 55606, 55691}, {53092, 55582, 55674}, {53093, 55594, 55669}, {53093, 55643, 55686}, {55580, 55711, 55653}, {55582, 55674, 55600}, {55590, 55664, 55618}, {55592, 55659, 55619}, {55594, 55669, 55628}, {55594, 55686, 55643}, {55597, 55676, 55635}, {55599, 55713, 55700}, {55606, 55691, 55662}, {55631, 55705, 55683}, {55653, 55711, 55694}

X(55718) = X(3)X(6)∩X(4)X(11054)

Barycentrics    a^2*(2*a^4+7*b^4-4*b^2*c^2+7*c^4-9*a^2*(b^2+c^2)) : :
X(55718) = -5*X[3]+9*X[6], -5*X[5]+3*X[22165], -9*X[69]+17*X[3544],-5*X[381]+X[51188], X[382]+3*X[15534], -X[550]+3*X[8584], -9*X[597]+7*X[14869], -9*X[599]+13*X[5079], -5*X[631]+6*X[46267], -5*X[632]+6*X[25555], -25*X[1656]+21*X[51186], -9*X[1992]+X[3529] and many others

X(55718) lies on these lines: {3, 6}, {4, 11054}, {5, 22165}, {23, 21969}, {30, 41149}, {51, 16042}, {69, 3544}, {193, 48901}, {381, 51188}, {382, 15534}, {394, 30734}, {518, 26200}, {524, 546}, {542, 3627}, {550, 8584}, {597, 14869}, {599, 5079}, {631, 46267}, {632, 25555}, {895, 16835}, {1353, 29317}, {1495, 9716}, {1503, 48943}, {1656, 51186}, {1843, 26863}, {1992, 3529}, {1993, 44082}, {1994, 6030}, {1995, 21849}, {2781, 38626}, {2810, 38630}, {2854, 38632}, {3060, 3292}, {3090, 5476}, {3091, 7946}, {3146, 11645}, {3357, 11216}, {3518, 12584}, {3525, 50977}, {3564, 12102}, {3628, 20582}, {3629, 29012}, {3630, 38136}, {3746, 19369}, {3818, 50689}, {3851, 15533}, {3855, 50992}, {3857, 5480}, {3917, 15019}, {5072, 11178}, {5076, 54131}, {5095, 6240}, {5349, 16002}, {5350, 16001}, {5563, 8540}, {5609, 12061}, {5643, 5650}, {5965, 21850}, {5969, 38628}, {6102, 15826}, {6776, 49140}, {7464, 14831}, {7492, 13366}, {7496, 53863}, {7527, 14531}, {7555, 13421}, {7805, 51523}, {7863, 41146}, {7982, 9355}, {7998, 44107}, {8537, 14865}, {8541, 35502}, {8542, 40247}, {8550, 15704}, {8593, 19696}, {8681, 15083}, {9024, 38629}, {9820, 47451}, {9970, 15801}, {9976, 15054}, {10168, 12108}, {10169, 25563}, {10263, 11649}, {10282, 12105}, {10303, 54173}, {10594, 11470}, {10752, 11381}, {11161, 14044}, {11179, 17538}, {11541, 29323}, {12007, 48892}, {12086, 32305}, {12103, 51135}, {12811, 19130}, {12812, 24206}, {13102, 43400}, {13103, 43399}, {13371, 20301}, {14269, 51187}, {14561, 46936}, {14853, 15022}, {14912, 48880}, {14984, 16982}, {15004, 40916}, {15069, 50962}, {15720, 51185}, {15850, 38227}, {15988, 17543}, {18583, 51127}, {18800, 33250}, {21663, 35499}, {25565, 50978}, {31670, 48942}, {31724, 32273}, {32455, 48891}, {34117, 50414}, {34148, 37957}, {35018, 50991}, {37946, 45186}, {38079, 41992}, {39899, 48904}, {40330, 42785}, {41152, 47478}, {41991, 47354}, {43697, 53860}, {44102, 44879}, {47278, 47571}, {47447, 47581}, {48873, 51170}, {48876, 51128}, {48906, 48920}, {49136, 51140}, {50693, 51028}

X(55718) = midpoint of X(i) and X(j) for these {i,j}: {182, 44456}, {193, 48901}, {1351, 37517}, {39899, 48904}, {576, 11477}
X(55718) = reflection of X(i) in X(j) for these {i,j}: {182, 55715}, {1350, 50664}, {14810, 6}, {25561, 20423}, {3, 22330}, {3098, 15516}, {33878, 55674}, {43150, 5480}, {48889, 21850}, {48892, 12007}, {48920, 48906}, {48942, 31670}, {550, 33749}, {575, 576}, {5092, 5097}, {5097, 55716}, {50978, 25565}, {52987, 20190}, {53097, 55631}, {55582, 55592}, {55583, 55597}, {55584, 55601}, {55585, 55612}, {55586, 14810}, {55587, 55653}, {55588, 3}, {55589, 55680}, {55590, 5092}, {55591, 55686}, {55592, 55696}, {55593, 55700}, {55594, 182}, {55597, 55704}, {55599, 5050}, {55601, 55709}, {55606, 575}, {55615, 39561}, {55623, 22234}, {55627, 55713}, {55661, 55714}, {55670, 15520}, {55677, 11482}, {55695, 5093}, {55716, 1351}
X(55718) = inverse of X(55708) in First Brocard Circle
X(55718) = center of Tucker-Hagos(9/2) circle
X(55718) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(187), X(16835)}}, {{A, B, C, X(1173), X(5008)}}, {{A, B, C, X(2987), X(14810)}}, {{A, B, C, X(8588), X(11270)}}, {{A, B, C, X(15655), X(43719)}}
X(55718) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55628}, {3, 511, 55588}, {3, 52987, 55617}, {3, 53097, 55600}, {3, 55583, 55597}, {3, 55597, 55623}, {6, 1350, 55697}, {6, 1351, 55717}, {6, 17508, 55709}, {6, 55584, 17508}, {6, 55671, 5050}, {61, 62, 5008}, {182, 3098, 55673}, {182, 5102, 55715}, {182, 511, 55594}, {182, 52987, 55652}, {182, 53097, 55631}, {182, 576, 11482}, {182, 55589, 55646}, {182, 55600, 3}, {182, 55610, 55668}, {182, 55631, 55677}, {182, 55640, 55678}, {182, 55646, 55680}, {511, 1351, 55716}, {511, 14810, 55586}, {511, 15516, 3098}, {511, 20190, 52987}, {511, 5050, 55599}, {511, 50664, 1350}, {511, 5092, 55590}, {511, 55592, 55582}, {511, 55597, 55583}, {511, 55601, 55584}, {511, 55612, 55585}, {511, 55653, 55587}, {511, 55674, 33878}, {511, 55680, 55589}, {511, 55686, 55591}, {511, 55696, 55592}, {511, 55700, 55593}, {576, 22234, 53858}, {576, 37517, 11477}, {576, 55644, 55714}, {576, 55687, 15520}, {1350, 15520, 50664}, {1350, 50664, 55670}, {1350, 53092, 55687}, {1350, 55658, 55621}, {1350, 55670, 55634}, {1350, 55678, 55640}, {1350, 55687, 55647}, {1350, 55697, 55658}, {1351, 11477, 576}, {1351, 37517, 511}, {1351, 44456, 5102}, {3098, 15516, 55695}, {3098, 5093, 15516}, {3098, 55695, 55666}, {5050, 55587, 55653}, {5050, 55614, 55681}, {5050, 55653, 55690}, {5085, 55585, 55612}, {5085, 55595, 55644}, {5085, 55612, 55661}, {5092, 5097, 55713}, {5092, 55590, 55627}, {5092, 55606, 55650}, {5097, 55586, 55706}, {5097, 55706, 6}, {5102, 55594, 5097}, {5102, 55673, 5093}, {5107, 13330, 44499}, {5965, 21850, 48889}, {6453, 6454, 5206}, {10541, 33878, 55637}, {10541, 53097, 55622}, {10541, 55637, 55674}, {10541, 55689, 20190}, {11477, 53097, 44456}, {11477, 55716, 55606}, {11482, 44456, 53097}, {11482, 53097, 182}, {11482, 55631, 575}, {11482, 55678, 53092}, {12017, 55603, 55659}, {14810, 55594, 55610}, {14810, 55668, 55657}, {14810, 55690, 55671}, {14810, 55706, 5092}, {15516, 55679, 53093}, {17508, 52987, 55626}, {17508, 55584, 55601}, {17508, 55601, 14810}, {20190, 55663, 55679}, {20190, 55709, 55701}, {22234, 53858, 22330}, {22234, 55611, 55694}, {22234, 55623, 55698}, {22330, 55597, 55704}, {22330, 55617, 55708}, {22330, 55704, 22234}, {31884, 55710, 55688}, {33878, 55654, 55605}, {33878, 55674, 55615}, {39561, 55605, 55689}, {39561, 55637, 10541}, {39561, 55674, 55702}, {52987, 53093, 55663}, {52987, 55681, 55630}, {53091, 55582, 55649}, {53091, 55602, 55684}, {53091, 55649, 55696}, {53094, 55596, 55636}, {55581, 55710, 31884}, {55582, 55684, 55602}, {55583, 55694, 55611}, {55585, 55644, 55595}, {55585, 55714, 5085}, {55587, 55681, 55614}, {55591, 55655, 55609}, {55591, 55705, 55655}, {55593, 55672, 55625}, {55593, 55711, 55672}, {55594, 55657, 55619}, {55596, 55712, 53094}, {55598, 55693, 55651}, {55604, 55669, 55638}, {55604, 55703, 55669}, {55605, 55689, 55654}, {55607, 55692, 55660}, {55608, 55676, 55645}, {55608, 55707, 55676}, {55616, 55699, 55667}, {55629, 55691, 55664}, {55655, 55705, 55686}, {55672, 55711, 55700}

X(55719) = X(3)X(6)∩X(110)X(21969)

Barycentrics    a^2*(2*a^4+9*b^4-4*b^2*c^2+9*c^4-11*a^2*(b^2+c^2)) : :
X(55719) = -7*X[3]+11*X[6], -11*X[1352]+15*X[41099], -11*X[1992]+3*X[46333], -11*X[3589]+10*X[45760], -17*X[3854]+11*X[34507], -15*X[5032]+7*X[50969], -4*X[5480]+3*X[25561], -X[5921]+3*X[48901], -3*X[8584]+X[48874], -12*X[10109]+11*X[24206], -7*X[10168]+8*X[41153], -7*X[11178]+5*X[50989] and many others

X(55719) lies on these lines: {3, 6}, {110, 21969}, {193, 48943}, {524, 14893}, {542, 33699}, {1352, 41099}, {1353, 19924}, {1992, 46333}, {1993, 32237}, {3292, 16981}, {3589, 45760}, {3629, 29317}, {3854, 34507}, {3856, 34380}, {3917, 12834}, {5032, 50969}, {5480, 25561}, {5651, 21849}, {5921, 48901}, {5965, 39884}, {6723, 41588}, {8550, 48891}, {8584, 48874}, {10109, 24206}, {10168, 41153}, {11178, 50989}, {11645, 50974}, {12007, 48885}, {14561, 46935}, {14831, 43576}, {15004, 21766}, {18553, 21850}, {18583, 47598}, {20423, 40330}, {26881, 34986}, {29323, 50692}, {33749, 48881}, {33751, 50979}, {33884, 44107}, {35434, 36990}, {46267, 50967}, {48873, 51028}

X(55719) = midpoint of X(i) and X(j) for these {i,j}: {11477, 37517}, {576, 44456}
X(55719) = reflection of X(i) in X(j) for these {i,j}: {1350, 15516}, {14810, 5097}, {18553, 21850}, {3, 55715}, {3098, 22330}, {33878, 20190}, {48881, 33749}, {48885, 12007}, {48891, 8550}, {575, 55716}, {5092, 576}, {5097, 1351}, {50967, 46267}, {52987, 50664}, {53097, 55653}, {55581, 55592}, {55582, 55597}, {55583, 55601}, {55584, 55612}, {55585, 55631}, {55586, 3}, {55587, 55674}, {55588, 5092}, {55589, 55700}, {55590, 182}, {55592, 55709}, {55594, 575}, {55599, 55713}, {55606, 6}, {55619, 55714}, {55627, 15520}, {55634, 11482}, {55657, 5093}, {55706, 5102}, {55713, 55717}, {55716, 55718}, {55718, 37517}
X(55719) = inverse of X(55707) in First Brocard Circle
X(55719) = center of Tucker-Hagos(11/2) circle
X(55719) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2987), X(55606)}}, {{A, B, C, X(39561), X(40803)}}
X(55719) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 511, 55586}, {3, 6, 55707}, {3, 55586, 55599}, {3, 55589, 55609}, {3, 55598, 55621}, {3, 55713, 55702}, {3, 55715, 55713}, {6, 1350, 55692}, {6, 511, 55606}, {6, 55593, 55687}, {182, 1350, 55659}, {182, 3098, 55671}, {182, 511, 55590}, {182, 55581, 55605}, {182, 55587, 55629}, {182, 55612, 55666}, {182, 55671, 55688}, {511, 20190, 33878}, {511, 22330, 3098}, {511, 37517, 55718}, {511, 50664, 52987}, {511, 5092, 55588}, {511, 575, 55594}, {511, 55592, 55581}, {511, 55597, 55582}, {511, 55601, 55583}, {511, 55612, 55584}, {511, 55631, 55585}, {511, 55653, 53097}, {576, 55585, 5050}, {576, 55649, 6}, {1350, 1351, 576}, {1350, 14810, 55615}, {1350, 5050, 55669}, {1350, 5092, 14810}, {1350, 53094, 55639}, {1350, 55580, 55587}, {1350, 55589, 55592}, {1350, 55624, 55608}, {1350, 55635, 55612}, {1350, 55669, 55631}, {1350, 55692, 55649}, {1350, 55711, 55673}, {1350, 55714, 55700}, {1351, 44456, 1350}, {1351, 5097, 55716}, {1351, 53091, 5102}, {1351, 55581, 55715}, {3098, 10541, 55664}, {3098, 22330, 55706}, {3098, 5102, 22330}, {3098, 55706, 55677}, {5085, 55583, 55601}, {5085, 55601, 55650}, {5092, 5097, 15516}, {5092, 55704, 55695}, {5092, 55706, 10541}, {5093, 52987, 50664}, {5097, 55713, 55714}, {5097, 55718, 1351}, {10541, 55664, 5092}, {11477, 37517, 511}, {11482, 55582, 17508}, {12017, 55596, 55647}, {14810, 55599, 55619}, {14810, 55674, 55661}, {14810, 55690, 55670}, {14810, 55695, 55674}, {14810, 55716, 5097}, {15516, 55615, 55690}, {15516, 55625, 55693}, {15516, 55659, 182}, {15516, 55674, 55704}, {15516, 55700, 55709}, {15516, 55709, 55712}, {15520, 33878, 20190}, {15520, 55655, 55711}, {17508, 55582, 55597}, {17508, 55597, 55634}, {20190, 33878, 55627}, {22234, 31884, 55696}, {22330, 55677, 575}, {22330, 55688, 53091}, {33878, 55673, 55611}, {33878, 55711, 55655}, {39561, 53097, 55653}, {39561, 55653, 55698}, {50664, 52987, 55657}, {50664, 55625, 53094}, {52987, 53094, 55625}, {52987, 55665, 55618}, {53092, 55591, 55672}, {53093, 55603, 55668}, {53858, 55610, 55710}, {55586, 55718, 55717}, {55591, 55672, 55617}, {55593, 55687, 55636}, {55594, 55670, 55623}, {55595, 55703, 55658}, {55600, 55676, 55638}, {55602, 55699, 55660}, {55604, 55681, 55645}, {55607, 55701, 55667}, {55610, 55710, 55679}, {55612, 55659, 55635}, {55614, 55691, 55663}, {55637, 55705, 55680}, {55646, 55708, 55686}, {55674, 55688, 55682}

X(55720) = X(2)X(54920)∩X(3)X(6)

Barycentrics    a^2*(a^4+6*b^4-2*b^2*c^2+6*c^4-7*a^2*(b^2+c^2)) : :
X(55720) = -5*X[3]+7*X[6], -7*X[69]+11*X[3855], -7*X[141]+8*X[35018], -7*X[1352]+9*X[3839], -7*X[1353]+3*X[19710], -3*X[1992]+X[48873], -4*X[3629]+X[48879], -2*X[3631]+3*X[38136], -7*X[3818]+8*X[3861], -5*X[3858]+7*X[21850], -6*X[5066]+7*X[5480], -13*X[5068]+14*X[19130] and many others

X(55720) lies on these lines: {2, 54920}, {3, 6}, {51, 16187}, {69, 3855}, {110, 44082}, {141, 35018}, {193, 29012}, {382, 6144}, {524, 15687}, {542, 10721}, {546, 3630}, {550, 32455}, {1147, 13421}, {1352, 3839}, {1353, 19710}, {1469, 37602}, {1974, 47486}, {1992, 48873}, {1993, 44110}, {2979, 22112}, {3060, 5651}, {3066, 21849}, {3564, 48884}, {3629, 48879}, {3631, 38136}, {3818, 3861}, {3858, 21850}, {5066, 5480}, {5068, 19130}, {5071, 20423}, {5476, 15699}, {5921, 5965}, {6030, 11003}, {6403, 52294}, {6771, 49813}, {6774, 49812}, {6776, 15683}, {7486, 14853}, {8550, 48880}, {8717, 13391}, {9306, 21969}, {10124, 18583}, {10263, 46261}, {10519, 25555}, {10752, 52098}, {11004, 35268}, {11179, 15697}, {11645, 50962}, {11649, 37945}, {11898, 48889}, {12007, 48874}, {13111, 17130}, {14912, 48892}, {14926, 23039}, {14927, 29317}, {15069, 48895}, {15691, 44882}, {15709, 54173}, {15721, 50967}, {16981, 23061}, {18553, 40341}, {29323, 39899}, {32237, 33586}, {33749, 51170}, {33851, 34155}, {34146, 34788}, {34779, 44668}, {37521, 37687}, {38317, 48154}, {40916, 44107}, {43150, 53023}, {43273, 48920}, {43399, 54138}, {43400, 54139}, {44580, 51732}, {46267, 51141}, {47352, 51172}, {47447, 47571}, {47451, 47581}, {48662, 48942}, {51026, 51182}, {51214, 51537}

X(55720) = midpoint of X(i) and X(j) for these {i,j}: {11477, 44456}, {382, 6144}
X(55720) = reflection of X(i) in X(j) for these {i,j}: {182, 1351}, {1350, 5097}, {1351, 55719}, {11898, 48889}, {15069, 48895}, {17508, 55717}, {3, 55716}, {3098, 576}, {3630, 546}, {33878, 575}, {34507, 21850}, {37517, 11477}, {40341, 18553}, {48662, 48942}, {48874, 12007}, {48880, 8550}, {48896, 6776}, {48898, 1353}, {48904, 51212}, {550, 32455}, {576, 37517}, {52098, 10752}, {52987, 6}, {52996, 35439}, {53097, 5092}, {6, 55718}, {55580, 55594}, {55581, 1350}, {55582, 55606}, {55583, 3098}, {55584, 14810}, {55585, 3}, {55586, 20190}, {55587, 182}, {55588, 50664}, {55589, 39561}, {55590, 15516}, {55591, 55713}, {55594, 22330}, {55596, 15520}, {55598, 11482}, {55603, 5093}, {55606, 55715}, {55649, 5102}
X(55720) = inverse of X(55706) in First Brocard Circle
X(55720) = center of Tucker-Hagos(7) circle
X(55720) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(55706)}}, {{A, B, C, X(6), X(54920)}}, {{A, B, C, X(575), X(40803)}}, {{A, B, C, X(1297), X(55585)}}, {{A, B, C, X(2987), X(52987)}}, {{A, B, C, X(3431), X(15602)}}, {{A, B, C, X(5008), X(14491)}}, {{A, B, C, X(11270), X(15513)}}
X(55720) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55625}, {3, 511, 55585}, {3, 55585, 55596}, {3, 55634, 55649}, {6, 33878, 55668}, {6, 55580, 55621}, {6, 55582, 55632}, {6, 55610, 20190}, {6, 55654, 55701}, {182, 1350, 55655}, {182, 14810, 17508}, {182, 15516, 55710}, {182, 15520, 15516}, {182, 22234, 55711}, {182, 3098, 55669}, {182, 37517, 1351}, {182, 53094, 55691}, {182, 55581, 1350}, {182, 55592, 55644}, {182, 55603, 55662}, {182, 55616, 55665}, {182, 55649, 53094}, {182, 55655, 55683}, {182, 55662, 5092}, {182, 55669, 55687}, {182, 55672, 55688}, {182, 55681, 55692}, {182, 55688, 55694}, {511, 1350, 55581}, {511, 14810, 55584}, {511, 15516, 55590}, {511, 20190, 55586}, {511, 3098, 55583}, {511, 35439, 52996}, {511, 50664, 55588}, {511, 5092, 53097}, {511, 575, 33878}, {511, 55594, 55580}, {511, 55606, 55582}, {511, 55713, 55591}, {542, 51212, 48904}, {576, 52987, 55708}, {1350, 1351, 5097}, {1350, 5097, 182}, {1350, 53091, 55674}, {1350, 55581, 55587}, {1350, 55625, 55608}, {1350, 55648, 55619}, {1350, 55655, 3098}, {1350, 55674, 55633}, {1351, 11477, 55719}, {1351, 55584, 6}, {1351, 55587, 55714}, {1351, 55590, 15520}, {1351, 55629, 5093}, {1351, 55651, 55715}, {1351, 55719, 37517}, {3098, 17508, 55652}, {3098, 55583, 55589}, {3098, 55687, 55660}, {5050, 55582, 55606}, {5050, 55606, 55672}, {5085, 22330, 55712}, {5085, 55580, 55594}, {5085, 55616, 55659}, {5092, 5093, 22234}, {5092, 53097, 55603}, {5092, 55617, 55654}, {5097, 14810, 55709}, {5097, 55674, 53091}, {5102, 33878, 575}, {6776, 19924, 48896}, {10541, 55604, 55657}, {11477, 44456, 511}, {11482, 31884, 50664}, {11482, 55588, 55681}, {11898, 54131, 48889}, {12017, 53858, 55713}, {12017, 55591, 55631}, {12017, 55631, 55667}, {14810, 20190, 55671}, {14810, 52987, 55605}, {14810, 55584, 52987}, {14810, 55590, 55601}, {14810, 55612, 55626}, {14810, 55617, 55629}, {14810, 55630, 55635}, {14810, 55663, 55651}, {14810, 55671, 55658}, {14810, 55719, 55718}, {15516, 55584, 55630}, {15516, 55612, 55686}, {15516, 55625, 55690}, {15516, 55635, 55693}, {15520, 52987, 55689}, {15520, 55630, 55706}, {15520, 55638, 55707}, {15520, 55693, 39561}, {15520, 55716, 576}, {16981, 23061, 34417}, {17508, 55605, 14810}, {17508, 55640, 55663}, {20190, 55586, 55610}, {22234, 55585, 55638}, {22330, 55580, 55637}, {31884, 55588, 55598}, {31884, 55692, 55666}, {33878, 53094, 55612}, {33878, 55649, 55600}, {37517, 52987, 55717}, {37517, 55585, 55716}, {48662, 51024, 48942}, {50664, 55588, 31884}, {53092, 55597, 55675}, {53092, 55646, 55695}, {53093, 55593, 55653}, {53093, 55653, 55685}, {53097, 55629, 55592}, {53097, 55701, 55617}, {53858, 55591, 12017}, {55593, 55653, 55611}, {55594, 55659, 55616}, {55595, 55676, 55627}, {55597, 55646, 55613}, {55597, 55695, 55646}, {55599, 55679, 55639}, {55601, 55668, 55634}, {55602, 55673, 55636}, {55604, 55657, 55628}, {55606, 55672, 55640}, {55606, 55715, 5050}, {55607, 55682, 55647}, {55609, 55677, 55643}, {55614, 55670, 55642}, {55614, 55705, 55670}, {55618, 55678, 55650}, {55619, 55674, 55648}, {55623, 55680, 55656}, {55624, 55684, 55661}, {55627, 55704, 55676}, {55636, 55698, 55673}, {55639, 55703, 55679}, {55643, 55699, 55677}, {55647, 55702, 55682}, {55650, 55700, 55678}, {55668, 55718, 5102}

X(55721) = X(3)X(6)∩X(4)X(50992)

Barycentrics    a^2*(a^4+8*b^4-2*b^2*c^2+8*c^4-9*a^2*(b^2+c^2)) : :
X(55721) = -7*X[3]+9*X[6], -7*X[4]+3*X[50992], -7*X[5]+6*X[50991], -9*X[141]+10*X[12812], -3*X[376]+4*X[33749], -7*X[381]+5*X[50989], -4*X[546]+3*X[34507], -2*X[548]+3*X[8584], -7*X[549]+8*X[41153], -9*X[597]+8*X[12108], -9*X[599]+11*X[5072], -25*X[632]+27*X[38079] and many others

X(55721) lies on these lines: {3, 6}, {4, 50992}, {5, 50991}, {69, 15031}, {141, 12812}, {193, 29317}, {376, 33749}, {381, 50989}, {524, 3627}, {542, 3146}, {546, 34507}, {548, 8584}, {549, 41153}, {597, 12108}, {599, 5072}, {632, 38079}, {895, 13452}, {1147, 12105}, {1352, 50689}, {1353, 48880}, {1657, 15534}, {1992, 17538}, {1993, 44108}, {1995, 21969}, {2781, 34788}, {3060, 16042}, {3090, 20423}, {3091, 11178}, {3292, 35264}, {3518, 11470}, {3525, 25555}, {3529, 19924}, {3544, 19130}, {3564, 48904}, {3628, 5476}, {3629, 48898}, {3843, 15533}, {3850, 22165}, {3857, 21850}, {5076, 15069}, {5095, 35471}, {5365, 16002}, {5366, 16001}, {5480, 12811}, {5643, 33884}, {5651, 16981}, {5965, 48884}, {6403, 26863}, {6759, 37967}, {6776, 48879}, {7496, 15004}, {8537, 35475}, {8541, 14865}, {8550, 12103}, {9306, 14002}, {9716, 15107}, {9968, 44668}, {9976, 51522}, {10168, 54174}, {10303, 50967}, {10752, 26883}, {11002, 16187}, {11179, 50693}, {11284, 21849}, {11541, 29012}, {11645, 49136}, {11649, 37946}, {11663, 14094}, {11898, 48895}, {12086, 32599}, {12102, 34380}, {12106, 13421}, {12584, 37440}, {14449, 40929}, {14853, 46936}, {14892, 51142}, {14912, 48885}, {14984, 15083}, {15022, 24206}, {15034, 25556}, {15581, 34779}, {15684, 51187}, {15686, 41149}, {15704, 51140}, {15720, 46267}, {17131, 22728}, {18553, 54131}, {18569, 32273}, {18800, 33244}, {19662, 32980}, {21766, 44107}, {25561, 50973}, {31670, 50688}, {32455, 48874}, {34787, 50414}, {35479, 44102}, {38335, 51188}, {40341, 48889}, {44245, 51132}, {48662, 48943}, {49137, 50962}

X(55721) = midpoint of X(i) and X(j) for these {i,j}: {15684, 51187}
X(55721) = reflection of X(i) in X(j) for these {i,j}: {182, 37517}, {1350, 55716}, {11178, 54132}, {11898, 48895}, {15686, 41149}, {3, 55718}, {3098, 1351}, {33878, 5097}, {37517, 55720}, {40341, 48889}, {40929, 14449}, {48662, 48943}, {48874, 32455}, {48879, 6776}, {48880, 1353}, {48884, 51212}, {48898, 3629}, {576, 11477}, {50973, 25561}, {52987, 576}, {53097, 575}, {54174, 10168}, {6, 55719}, {55580, 55606}, {55581, 3098}, {55582, 14810}, {55583, 3}, {55584, 5092}, {55585, 182}, {55586, 15516}, {55587, 6}, {55588, 22330}, {55589, 5093}, {55590, 55715}, {55596, 5102}, {55603, 55717}, {55720, 44456}
X(55721) = inverse of X(55704) in First Brocard Circle
X(55721) = center of Tucker-Hagos(9) circle
X(55721) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(187), X(13452)}}, {{A, B, C, X(15655), X(44763)}}, {{A, B, C, X(40801), X(53858)}}
X(55721) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 11477, 55718}, {3, 1350, 55623}, {3, 1351, 53858}, {3, 22330, 55708}, {3, 511, 55583}, {3, 53097, 55597}, {3, 575, 55694}, {3, 6, 55704}, {3, 55583, 52987}, {3, 55588, 55600}, {6, 1350, 55682}, {6, 33878, 55661}, {6, 511, 55587}, {6, 53097, 55641}, {6, 55584, 55621}, {6, 55618, 55692}, {6, 55629, 55695}, {182, 3098, 55667}, {182, 37517, 55717}, {182, 511, 55585}, {182, 52987, 55637}, {182, 55585, 55603}, {182, 55603, 55658}, {182, 55611, 3}, {182, 55637, 55675}, {182, 55642, 17508}, {511, 14810, 55582}, {511, 15516, 55586}, {511, 22330, 55588}, {511, 3098, 55581}, {511, 44456, 55720}, {511, 5092, 55584}, {511, 5097, 33878}, {511, 575, 53097}, {511, 55606, 55580}, {511, 55715, 55590}, {511, 55716, 1350}, {511, 55720, 37517}, {575, 20190, 55705}, {575, 55647, 5085}, {576, 55708, 22330}, {576, 55720, 11477}, {1350, 11482, 20190}, {1350, 20190, 55644}, {1350, 39561, 55672}, {1350, 55657, 3098}, {1350, 55672, 55630}, {1350, 55682, 55636}, {1351, 3098, 15520}, {1351, 5085, 55715}, {1351, 53097, 575}, {1351, 55581, 182}, {1351, 55593, 6}, {1351, 55651, 5097}, {1351, 55678, 5093}, {3098, 17508, 55651}, {3098, 5085, 55662}, {3098, 55587, 55593}, {3098, 55643, 55633}, {3098, 55655, 55638}, {3098, 55707, 55674}, {3098, 55710, 55678}, {5050, 55594, 55655}, {5050, 55626, 55679}, {5050, 55655, 55689}, {5085, 53097, 55602}, {5085, 55602, 55647}, {5092, 5102, 55714}, {5092, 55584, 55596}, {5092, 55614, 55652}, {5093, 14810, 55710}, {5093, 55595, 10541}, {5097, 17508, 55712}, {5097, 55631, 53093}, {5102, 55584, 5092}, {5102, 55614, 53092}, {5965, 51212, 48884}, {10541, 55582, 55595}, {10541, 55595, 14810}, {11477, 53097, 1351}, {11482, 20190, 39561}, {11482, 53097, 55657}, {11482, 55716, 576}, {12017, 55612, 55660}, {14810, 55582, 55589}, {14810, 55710, 55685}, {15516, 31884, 55691}, {15516, 55586, 31884}, {15516, 55677, 55701}, {15520, 52987, 55681}, {15520, 55608, 55696}, {15520, 55649, 55707}, {17508, 33878, 55608}, {17508, 55608, 55642}, {17508, 55618, 55649}, {20190, 55682, 55687}, {20190, 55716, 11482}, {22234, 55583, 55611}, {22330, 55583, 55628}, {22330, 55617, 55698}, {22330, 55708, 22234}, {31884, 55701, 55677}, {33878, 53093, 55631}, {33878, 55651, 55599}, {33878, 55692, 55618}, {37517, 55633, 5102}, {37517, 55672, 55716}, {47066, 47068, 9734}, {50664, 55610, 55669}, {50664, 55650, 55684}, {52987, 55606, 55598}, {52987, 55649, 55606}, {52987, 55689, 55626}, {53091, 55591, 55653}, {53091, 55653, 55693}, {53092, 55584, 55614}, {53094, 55601, 55640}, {55587, 55720, 55719}, {55588, 55698, 55617}, {55591, 55653, 55605}, {55592, 55706, 55646}, {55594, 55655, 55613}, {55601, 55713, 53094}, {55604, 55670, 55635}, {55604, 55711, 55670}, {55607, 55697, 55659}, {55609, 55690, 55654}, {55610, 55684, 55650}, {55615, 55709, 55676}, {55616, 55703, 55668}, {55624, 55699, 55666}, {55625, 55702, 55673}, {55629, 55695, 55665}, {55634, 55700, 55671}, {55646, 55706, 55683}

X(55722) = X(3)X(6)∩X(20)X(3629)

Barycentrics    a^2*(a^4+9*b^4-2*b^2*c^2+9*c^4-10*a^2*(b^2+c^2)) : :
X(55722) = -4*X[3]+5*X[6], -5*X[69]+7*X[3832], -10*X[141]+11*X[5056], -5*X[193]+X[5059], -3*X[376]+4*X[12007], -4*X[547]+5*X[20423], -10*X[597]+9*X[15708], -5*X[599]+6*X[3545], -5*X[1352]+6*X[3845], -5*X[1353]+3*X[15686], -10*X[1386]+9*X[30392], -3*X[1992]+2*X[44882] and many others

X(55722) lies on these lines: {3, 6}, {4, 40341}, {20, 3629}, {22, 55038}, {64, 14531}, {69, 3832}, {110, 33586}, {141, 5056}, {183, 44434}, {193, 5059}, {376, 12007}, {381, 50973}, {382, 5965}, {394, 13595}, {516, 49680}, {518, 3062}, {524, 3543}, {542, 51187}, {547, 20423}, {597, 15708}, {599, 3545}, {613, 37587}, {1154, 11472}, {1352, 3845}, {1353, 15686}, {1386, 30392}, {1498, 44668}, {1503, 6144}, {1992, 44882}, {1993, 37913}, {2104, 15163}, {2105, 15162}, {2781, 12284}, {2930, 10752}, {2979, 17825}, {3060, 3066}, {3091, 3631}, {3146, 11008}, {3167, 32237}, {3242, 16200}, {3292, 41424}, {3416, 38155}, {3515, 15748}, {3523, 6329}, {3527, 15606}, {3533, 10519}, {3564, 48910}, {3763, 5067}, {3819, 5544}, {3843, 43150}, {3850, 10516}, {3853, 15069}, {3917, 5646}, {5032, 50965}, {5071, 50982}, {5079, 42785}, {5181, 38792}, {5645, 10601}, {5651, 17810}, {6090, 31860}, {6776, 11001}, {7798, 14532}, {8584, 54170}, {9777, 22112}, {9973, 15811}, {10263, 17814}, {10304, 20583}, {10605, 43576}, {10765, 37751}, {11160, 51537}, {11178, 51189}, {11179, 15690}, {11180, 51188}, {11539, 18583}, {11645, 35400}, {11799, 47445}, {11898, 38335}, {12111, 22334}, {12164, 46207}, {12383, 25331}, {14893, 50985}, {14912, 48881}, {14984, 51941}, {15035, 41447}, {15040, 34155}, {15066, 16981}, {15480, 53015}, {15576, 35474}, {15580, 19149}, {15681, 51140}, {15683, 51136}, {15684, 51174}, {15687, 50961}, {15692, 50970}, {15702, 47352}, {15723, 50977}, {16176, 17702}, {16187, 21849}, {16936, 32366}, {17813, 32127}, {17847, 32235}, {18358, 41991}, {19139, 37936}, {19588, 51959}, {19711, 38064}, {19924, 50962}, {20080, 51538}, {21167, 51171}, {23061, 35259}, {24206, 38072}, {25330, 32247}, {25406, 32455}, {28538, 50871}, {29012, 49133}, {29317, 39899}, {32217, 37940}, {33751, 50968}, {33851, 44878}, {34628, 51155}, {34632, 51124}, {35402, 51175}, {36967, 51208}, {36968, 51209}, {38021, 50791}, {38074, 50782}, {38076, 50784}, {38746, 50567}, {38758, 51007}, {41983, 51732}, {43453, 53017}, {43574, 51730}, {47450, 47571}, {47453, 47468}, {48662, 48904}, {48889, 50955}

X(55722) = midpoint of X(i) and X(j) for these {i,j}: {15684, 51174}, {3146, 11008}, {3543, 51214}
X(55722) = reflection of X(i) in X(j) for these {i,j}: {182, 55719}, {1350, 1351}, {1351, 55720}, {11477, 44456}, {11898, 48901}, {14532, 7798}, {15069, 31670}, {15162, 2105}, {15163, 2104}, {15533, 54131}, {15681, 51140}, {15683, 51136}, {20, 3629}, {2930, 10752}, {3, 37517}, {376, 51132}, {3098, 55718}, {3543, 51166}, {33878, 576}, {34628, 51155}, {34632, 51124}, {36990, 51212}, {37751, 10765}, {40341, 4}, {44456, 55721}, {48662, 48904}, {48872, 6776}, {48873, 1353}, {599, 54132}, {5921, 51163}, {50961, 15687}, {50973, 381}, {50985, 14893}, {51027, 3543}, {51188, 11180}, {52987, 55716}, {53097, 6}, {54170, 8584}, {54174, 597}, {6, 11477}, {64, 34777}, {55580, 3098}, {55581, 14810}, {55582, 3}, {55583, 5092}, {55584, 182}, {55585, 575}, {55586, 22330}, {55587, 5097}, {55588, 55715}, {55591, 5102}, {55593, 55717}, {9973, 45186}
X(55722) = inverse of X(55703) in First Brocard Circle
X(55722) = center of Tucker-Hagos(10) circle
X(55722) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(1297), X(55582)}}, {{A, B, C, X(1384), X(14490)}}, {{A, B, C, X(2987), X(53097)}}, {{A, B, C, X(3062), X(33628)}}, {{A, B, C, X(3532), X(5206)}}, {{A, B, C, X(5050), X(40803)}}, {{A, B, C, X(5097), X(40801)}}, {{A, B, C, X(14483), X(21309)}}, {{A, B, C, X(22334), X(35007)}}, {{A, B, C, X(35006), X(36616)}}, {{A, B, C, X(40802), X(53094)}}
X(55722) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12017, 55680}, {3, 1350, 55622}, {3, 1351, 5097}, {3, 33878, 55603}, {3, 39561, 55699}, {3, 5050, 55691}, {3, 511, 55582}, {3, 6, 55703}, {3, 55594, 55618}, {3, 55610, 55636}, {3, 55627, 55646}, {3, 55685, 55676}, {6, 31884, 10541}, {6, 511, 53097}, {182, 1350, 55651}, {182, 3098, 55666}, {182, 511, 55584}, {182, 52987, 55635}, {182, 55587, 55612}, {182, 55605, 55659}, {182, 55629, 55671}, {182, 55651, 53094}, {182, 55720, 55719}, {511, 14810, 55581}, {511, 22330, 55586}, {511, 3098, 55580}, {511, 5092, 55583}, {511, 575, 55585}, {511, 55715, 55588}, {511, 55716, 52987}, {511, 55721, 44456}, {524, 51163, 5921}, {524, 51166, 3543}, {524, 51212, 36990}, {575, 55585, 55610}, {575, 55655, 55692}, {576, 52987, 55698}, {576, 55585, 55664}, {576, 55597, 55701}, {576, 55628, 575}, {576, 55672, 55713}, {1151, 1152, 5206}, {1350, 11477, 1351}, {1350, 1351, 6}, {1350, 14810, 55614}, {1350, 15516, 55673}, {1350, 5085, 14810}, {1350, 5102, 55711}, {1350, 53094, 31884}, {1350, 55582, 55587}, {1350, 55587, 55591}, {1350, 55622, 55607}, {1350, 55626, 55608}, {1350, 55646, 55616}, {1350, 55671, 55629}, {1350, 55711, 3}, {1350, 55714, 55684}, {1351, 33878, 53091}, {1351, 44456, 55720}, {1351, 53091, 576}, {1351, 55581, 5085}, {1351, 55584, 182}, {1351, 55616, 55714}, {1351, 55648, 11482}, {1351, 55674, 53858}, {1351, 55720, 11477}, {1353, 48873, 43273}, {3098, 5093, 53093}, {3098, 55718, 5093}, {3543, 51214, 524}, {5085, 55614, 55656}, {5092, 55583, 55593}, {5092, 55608, 55648}, {5093, 33878, 55679}, {5097, 14810, 50664}, {5097, 55592, 55685}, {5097, 55688, 39561}, {5097, 55695, 15516}, {5102, 11477, 37517}, {5921, 51212, 51163}, {11477, 53093, 55718}, {11477, 55582, 5102}, {11482, 55583, 55626}, {11482, 55593, 5092}, {11824, 11917, 3594}, {11825, 11916, 3592}, {11898, 48901, 47353}, {12017, 55606, 55654}, {12305, 45489, 6425}, {12306, 45488, 6426}, {14810, 33878, 1350}, {14810, 50664, 55683}, {14810, 55581, 33878}, {14810, 55664, 55655}, {14810, 55674, 55660}, {14810, 55698, 55674}, {15520, 55606, 12017}, {15520, 55669, 55709}, {15534, 48872, 6776}, {17508, 55588, 55604}, {17508, 55604, 55641}, {17508, 55715, 53092}, {20190, 55596, 55639}, {20190, 55619, 55662}, {22234, 55589, 55653}, {22234, 55653, 55697}, {22236, 22238, 35007}, {22330, 55586, 55649}, {22330, 55649, 55705}, {31670, 34380, 15069}, {33878, 55624, 55597}, {33878, 55701, 55624}, {36990, 51212, 51024}, {37517, 55691, 55716}, {39561, 55587, 55633}, {39561, 55633, 55688}, {50664, 55679, 55695}, {51028, 51214, 51166}, {51166, 51214, 51027}, {52987, 55660, 55609}, {52987, 55691, 55627}, {52987, 55716, 5050}, {53092, 55604, 17508}, {55582, 55699, 55594}, {55584, 55629, 55590}, {55585, 55655, 55592}, {55586, 55649, 55595}, {55589, 55653, 55602}, {55590, 55659, 55605}, {55596, 55662, 55619}, {55597, 55713, 55672}, {55598, 55657, 55620}, {55598, 55708, 55657}, {55599, 55704, 55658}, {55600, 55670, 55632}, {55600, 55712, 55670}, {55601, 55687, 55643}, {55606, 55680, 55642}, {55606, 55709, 55669}, {55611, 55707, 55668}, {55613, 55694, 55661}, {55617, 55702, 55667}, {55623, 55700, 55665}, {55631, 55710, 55682}

X(55723) = X(3)X(6)∩X(69)X(14487)

Barycentrics    a^6-11*a^4*(b^2+c^2)+2*a^2*(5*b^4-b^2*c^2+5*c^4) : :
X(55723) = -9*X[3]+11*X[6], -11*X[141]+12*X[10109], -3*X[1992]+2*X[48892], -7*X[3619]+9*X[20423], -5*X[3620]+6*X[19130],-2*X[3630]+3*X[3818], -8*X[3631]+9*X[11178], -12*X[3856]+11*X[18358], -9*X[5476]+8*X[34573], -9*X[11180]+5*X[20080], -3*X[11204]+4*X[39125], -33*X[14853]+29*X[46935] and many others

X(55723) lies on these lines: {3, 6}, {69, 14487}, {141, 10109}, {193, 19924}, {524, 33699}, {542, 11008}, {1992, 48892}, {3619, 20423}, {3620, 19130}, {3629, 48880}, {3630, 3818}, {3631, 11178}, {3856, 18358}, {5476, 34573}, {5965, 48904}, {6144, 11645}, {9544, 15107}, {10545, 16981}, {11180, 20080}, {11204, 39125}, {14853, 46935}, {15004, 41462}, {15066, 21969}, {18440, 35434}, {18583, 45760}, {23061, 48912}, {29012, 50692}, {29317, 39874}, {40341, 48895}, {42786, 48876}, {43150, 50954}, {44903, 48879}, {46264, 46333}, {47598, 50977}, {48905, 50962}, {48906, 51135}, {51141, 51172}

X(55723) = midpoint of X(i) and X(j) for these {i,j}: {11008, 43621}
X(55723) = reflection of X(i) in X(j) for these {i,j}: {182, 11477}, {1350, 55718}, {3, 55719}, {3098, 37517}, {33878, 55716}, {37517, 44456}, {40341, 48895}, {48880, 3629}, {576, 55720}, {52987, 1351}, {53097, 5097}, {55580, 14810}, {55581, 3}, {55582, 5092}, {55583, 182}, {55584, 575}, {55585, 6}, {55586, 55715}, {55587, 576}, {55589, 55717}, {55720, 55721}, {55721, 55722}
X(55723) = inverse of X(55702) in First Brocard Circle
X(55723) = center of Tucker-Hagos(11) circle
X(55723) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(14487)}}, {{A, B, C, X(2987), X(55585)}}
X(55723) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1350, 55621}, {3, 511, 55581}, {3, 6, 55702}, {3, 55581, 55589}, {3, 55586, 55598}, {3, 55589, 55605}, {3, 55592, 55613}, {3, 55714, 55707}, {3, 55715, 55712}, {3, 55717, 55714}, {6, 511, 55585}, {6, 55594, 55672}, {6, 55639, 55696}, {182, 15520, 53092}, {182, 3098, 55665}, {182, 511, 55583}, {182, 52987, 31884}, {182, 55581, 55592}, {182, 55583, 55596}, {182, 55596, 55644}, {182, 55606, 55660}, {182, 55613, 3}, {182, 55625, 55669}, {182, 55644, 17508}, {182, 55649, 55679}, {511, 14810, 55580}, {511, 5092, 55582}, {511, 575, 55584}, {511, 576, 55587}, {511, 55715, 55586}, {511, 55718, 1350}, {511, 55722, 55721}, {575, 55584, 55603}, {575, 55625, 55682}, {575, 55646, 55689}, {576, 3098, 55710}, {1350, 15520, 55687}, {1350, 50664, 55658}, {1350, 53092, 55670}, {1350, 55658, 3098}, {1350, 55670, 55628}, {1350, 55678, 55634}, {1350, 55687, 55640}, {1350, 55697, 55647}, {1350, 55718, 15520}, {1351, 31884, 22330}, {1351, 52987, 39561}, {1351, 55604, 6}, {1351, 55671, 5097}, {3098, 5092, 55655}, {3098, 55583, 33878}, {3098, 55652, 55636}, {3098, 55669, 55646}, {5050, 55590, 55637}, {5050, 55607, 55668}, {5050, 55637, 55683}, {5085, 55588, 55608}, {5085, 55608, 55652}, {5092, 50664, 55697}, {5092, 55582, 52987}, {5092, 55586, 55599}, {5093, 33878, 55676}, {5097, 55601, 12017}, {5097, 55649, 55708}, {5102, 14810, 22234}, {5102, 55580, 14810}, {6435, 6436, 34571}, {11008, 43621, 542}, {11477, 31884, 1351}, {11477, 33878, 55716}, {11477, 53092, 55718}, {11477, 55583, 576}, {11477, 55592, 55717}, {11477, 55716, 37517}, {11482, 55591, 55674}, {12017, 33878, 55616}, {12017, 53097, 55601}, {12017, 55601, 55649}, {12017, 55671, 5092}, {14810, 22234, 55693}, {15516, 55610, 55681}, {15516, 55661, 55699}, {15520, 55628, 182}, {15520, 55658, 50664}, {17508, 55587, 55600}, {17508, 55600, 55635}, {20190, 55593, 55633}, {22330, 55709, 55713}, {31884, 55616, 55623}, {31884, 55620, 55625}, {31884, 55653, 55642}, {31884, 55682, 55663}, {33878, 44456, 11477}, {33878, 55676, 55606}, {37517, 44456, 55720}, {37517, 55598, 55715}, {37517, 55721, 44456}, {39561, 55655, 55694}, {50664, 55634, 55678}, {52987, 55642, 55604}, {52987, 55667, 55612}, {52987, 55717, 55709}, {53091, 55631, 55685}, {53093, 55612, 55667}, {53094, 55597, 55630}, {53858, 55629, 55706}, {55585, 55672, 55594}, {55585, 55712, 55609}, {55590, 55668, 55607}, {55591, 55674, 55611}, {55594, 55696, 55639}, {55595, 55711, 55657}, {55602, 55703, 55659}, {55606, 55686, 55648}, {55610, 55699, 55661}, {55614, 55695, 55662}, {55618, 55701, 55666}, {55629, 55706, 55675}, {55714, 55720, 55719}

X(55724) = X(3)X(6)∩X(69)X(546)

Barycentrics    a^2*(a^4+11*b^4-2*b^2*c^2+11*c^4-12*a^2*(b^2+c^2)) : :
X(55724) = -5*X[3]+6*X[6], -5*X[4]+3*X[11160], -10*X[5]+9*X[21356], -3*X[69]+4*X[546], -8*X[140]+9*X[14848], -12*X[141]+13*X[5079], -3*X[193]+X[3529], -5*X[381]+4*X[22165], -4*X[548]+3*X[54170], -2*X[550]+3*X[1992], -12*X[597]+11*X[15720], -6*X[599]+7*X[3851] and many others

X(55724) lies on these lines: {3, 6}, {4, 11160}, {5, 21356}, {23, 3167}, {25, 23061}, {64, 34788}, {69, 546}, {140, 14848}, {141, 5079}, {193, 3529}, {381, 22165}, {382, 524}, {394, 44106}, {542, 5073}, {548, 54170}, {550, 1992}, {597, 15720}, {599, 3851}, {631, 54174}, {632, 10519}, {895, 12085}, {1353, 12103}, {1503, 49136}, {1656, 20423}, {1657, 50962}, {2104, 30525}, {2105, 30524}, {2393, 12315}, {2781, 13093}, {2979, 5643}, {3060, 11284}, {3090, 48876}, {3091, 7939}, {3146, 3564}, {3292, 8780}, {3357, 17813}, {3515, 15020}, {3516, 8537}, {3517, 11470}, {3520, 11405}, {3522, 50979}, {3525, 18583}, {3526, 48310}, {3527, 6101}, {3528, 5032}, {3533, 38079}, {3534, 8550}, {3544, 3620}, {3618, 14869}, {3627, 18440}, {3628, 14853}, {3629, 48873}, {3830, 15069}, {3843, 34507}, {3850, 50978}, {3853, 11180}, {5020, 21969}, {5055, 40107}, {5059, 50974}, {5070, 5476}, {5072, 5480}, {5076, 11898}, {5198, 6403}, {5544, 7998}, {5609, 10752}, {5965, 48662}, {6030, 11422}, {6090, 14002}, {6144, 29012}, {6391, 16835}, {6515, 46517}, {6642, 13421}, {6776, 15704}, {7484, 15019}, {7492, 11402}, {7517, 9970}, {7525, 43908}, {8549, 35450}, {8567, 10250}, {8584, 15688}, {9019, 52100}, {9716, 26864}, {9777, 40916}, {9909, 44110}, {9968, 39879}, {10170, 52163}, {10300, 11433}, {10753, 51524}, {10754, 51523}, {10755, 51529}, {10756, 51528}, {10757, 51534}, {10758, 51526}, {10759, 51525}, {10764, 51527}, {11179, 15696}, {11216, 32608}, {11270, 37784}, {11645, 49134}, {11737, 50994}, {11799, 47446}, {12082, 12160}, {12102, 51538}, {12164, 12271}, {12167, 35502}, {12601, 23263}, {12602, 23253}, {12811, 40330}, {13391, 15073}, {14269, 15533}, {14530, 34787}, {14561, 51128}, {14912, 48874}, {14924, 15082}, {15066, 30734}, {15074, 43612}, {15083, 19588}, {15360, 52292}, {15534, 15681}, {15579, 32599}, {15581, 32063}, {15687, 50992}, {15694, 25555}, {15707, 51185}, {15826, 18859}, {15988, 19526}, {16042, 16981}, {16051, 41588}, {16266, 45016}, {17538, 48906}, {17800, 19924}, {19118, 44879}, {20080, 39884}, {20850, 37672}, {23048, 40686}, {23269, 49028}, {23275, 49029}, {25406, 44245}, {29181, 39899}, {31856, 44569}, {32306, 34725}, {33556, 44102}, {34797, 54216}, {38071, 50990}, {38731, 41672}, {39874, 49140}, {40341, 48901}, {41614, 45034}, {43193, 51203}, {43194, 51200}, {46219, 50977}, {47451, 47571}, {50690, 51215}, {50957, 50973}, {50972, 51132}, {51166, 51175}

X(55724) = reflection of X(i) in X(j) for these {i,j}: {1350, 37517}, {1351, 44456}, {11477, 55721}, {11898, 31670}, {15681, 15534}, {18440, 51212}, {20080, 39884}, {3, 11477}, {3098, 55719}, {32254, 48679}, {33878, 1351}, {37484, 50649}, {40341, 48901}, {44456, 55722}, {47618, 8586}, {48662, 48910}, {48873, 3629}, {50992, 15687}, {52987, 55718}, {53097, 576}, {6, 55720}, {64, 34788}, {55580, 3}, {55581, 5092}, {55582, 182}, {55583, 575}, {55584, 6}, {55585, 5097}, {55587, 55716}, {55722, 55723}
X(55724) = inverse of X(55701) in First Brocard Circle
X(55724) = inverse of X(38225) in Stammler Circle
X(55724) = center of Tucker-Hagos(12) circle
X(55724) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(187), X(43719)}}, {{A, B, C, X(575), X(14489)}}, {{A, B, C, X(3053), X(16835)}}, {{A, B, C, X(3527), X(5008)}}, {{A, B, C, X(5210), X(11270)}}, {{A, B, C, X(11482), X(40801)}}, {{A, B, C, X(17508), X(40802)}}
X(55724) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10541, 55682}, {3, 11477, 1351}, {3, 44456, 11477}, {3, 511, 55580}, {3, 53091, 10541}, {3, 6, 55701}, {3, 55580, 33878}, {3, 55595, 55620}, {3, 55602, 55629}, {3, 55616, 55641}, {3, 55624, 55644}, {3, 55631, 55648}, {3, 55692, 55679}, {3, 55705, 55687}, {6, 14810, 55697}, {6, 5085, 55709}, {6, 511, 55584}, {6, 55582, 55601}, {6, 55671, 55706}, {182, 3098, 55664}, {182, 511, 55582}, {182, 55582, 55593}, {182, 55588, 55614}, {182, 55593, 55639}, {511, 50649, 37484}, {511, 5092, 55581}, {511, 5097, 55585}, {511, 575, 55583}, {511, 576, 53097}, {511, 55716, 55587}, {511, 55719, 3098}, {511, 55723, 55722}, {511, 8586, 47618}, {575, 55588, 55627}, {575, 55597, 55662}, {575, 55617, 17508}, {576, 52987, 20190}, {576, 55606, 53093}, {1160, 9301, 12314}, {1161, 9301, 12313}, {1350, 12017, 55643}, {1350, 17508, 55632}, {1350, 5093, 12017}, {1350, 55613, 55604}, {1350, 55632, 55610}, {1350, 55703, 55653}, {1351, 33878, 5050}, {1351, 55595, 53092}, {1351, 55610, 6}, {3098, 55719, 5102}, {5050, 55629, 55678}, {5092, 55581, 55591}, {5092, 55591, 55616}, {5097, 31884, 55705}, {5097, 55585, 31884}, {5102, 10541, 22330}, {5102, 53097, 55677}, {5864, 5865, 9737}, {5965, 48910, 48662}, {9732, 9733, 9734}, {10541, 22330, 53091}, {11477, 53097, 576}, {11477, 55580, 11482}, {11477, 55582, 53858}, {11477, 55583, 5093}, {11477, 55721, 44456}, {11477, 55722, 55721}, {11482, 33878, 3}, {11482, 55580, 55602}, {12017, 55595, 55637}, {12017, 55682, 55688}, {14984, 48679, 32254}, {15516, 55603, 55676}, {15516, 55650, 55694}, {15520, 55594, 53094}, {15520, 55644, 55704}, {17508, 20190, 55684}, {17508, 52987, 55617}, {17508, 55583, 52987}, {17508, 55586, 1350}, {17508, 55627, 55654}, {17508, 55658, 55666}, {17508, 55662, 55668}, {17508, 55720, 37517}, {20190, 52987, 55626}, {20190, 55584, 55595}, {20190, 55601, 55647}, {20190, 55606, 55652}, {22234, 52987, 55658}, {22234, 55587, 55631}, {22234, 55631, 5085}, {22330, 52987, 55671}, {22330, 55688, 575}, {34380, 51212, 18440}, {34507, 54131, 3843}, {38596, 38597, 38225}, {39561, 55590, 55646}, {39561, 55646, 55692}, {50664, 55596, 55651}, {50664, 55623, 55675}, {52987, 55583, 55586}, {52987, 55605, 55597}, {52987, 55630, 55600}, {52987, 55652, 55606}, {52987, 55708, 14810}, {52987, 55717, 55708}, {52987, 55720, 55718}, {52987, 55721, 55720}, {53094, 55594, 55624}, {53858, 55614, 182}, {55580, 55639, 55588}, {55586, 55700, 55605}, {55586, 55709, 55613}, {55589, 55674, 55607}, {55590, 55679, 55611}, {55592, 55672, 55618}, {55596, 55675, 55623}, {55598, 55670, 55622}, {55603, 55694, 55650}, {55608, 55695, 55656}, {55612, 55710, 55673}, {55631, 55716, 22234}, {55649, 55715, 55711}, {55653, 55714, 55703}, {55655, 55713, 55699}

X(55725) = X(631)X(50990)∩X(1078)X(51186)

Barycentrics    80*a^4-10*b^4-101*b^2*c^2-10*c^4-92*a^2*(b^2+c^2) : :

X(55725) lies on these lines: {631, 50990}, {1078, 51186}, {7786, 8584}, {8703, 22712}

X(55725) = isogonal conjugate of perspector of Tucker-Hagos(-9) circle

X(55726) = X(2)X(3793)∩X(3)X(47586)

Barycentrics    35*a^4-7*b^4-50*b^2*c^2-7*c^4-44*a^2*(b^2+c^2) : :

X(55726) lies on these lines: {2, 3793}, {3, 47586}, {376, 9466}, {599, 631}, {1078, 33197}, {1992, 7786}, {2482, 10299}, {3090, 7810}, {3533, 7821}, {3545, 11168}, {8556, 15682}, {8596, 33226}, {9740, 14482}, {15598, 53142}, {16241, 43275}, {16242, 43274}, {20081, 33215}, {20194, 21358}, {23055, 33196}

X(55726) = isogonal conjugate of perspector of Tucker-Hagos(-6) circle
X(55726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 21309, 54616}

X(55727) = X(550)X(22712)∩X(3629)X(7786)

Barycentrics    24*a^4-6*b^4-37*b^2*c^2-6*c^4-32*a^2*(b^2+c^2) : :

X(55727) lies on these lines: {550, 22712}, {631, 55695}, {3629, 7786}

X(55727) = isogonal conjugate of perspector of Tucker-Hagos(-5) circle

X(55728) = X(631)X(50994)∩X(1078)X(51143)

Barycentrics    77*a^4-22*b^4-125*b^2*c^2-22*c^4-107*a^2*(b^2+c^2) : :

X(55728) lies on these lines: {631, 50994}, {1078, 51143}, {3534, 22712}, {7786, 15534}, {21358, 55725}

X(55728) = isogonal conjugate of perspector of Tucker-Hagos(-9/2) circle

X(55729) = X(20)X(6248)∩X(193)X(7786)

Barycentrics    15*a^4-5*b^4-26*b^2*c^2-5*c^4-22*a^2*(b^2+c^2) : :

X(55729) lies on these lines: {20, 6248}, {69, 31492}, {193, 7786}, {538, 32990}, {631, 3564}, {2896, 7486}, {3785, 5395}, {5032, 32960}, {7810, 32987}, {7876, 37667}, {7904, 17578}, {8556, 32982}, {9606, 20080}, {11160, 11285}, {11168, 52250}, {14069, 55726}, {15589, 33258}, {15717, 16990}, {33023, 42850}, {33238, 41895}

X(55729) = isogonal conjugate of perspector of Tucker-Hagos(-4) circle

X(55730) = X(2)X(5008)∩X(3)X(10302)

Barycentrics    8*a^4-4*b^4-17*b^2*c^2-4*c^4-14*a^2*(b^2+c^2) : :
X(55730) = X[76]+4*X[15810], X[598]+4*X[7810], X[9939]+4*X[14762]

X(55730) lies on these lines: {2, 5008}, {3, 10302}, {30, 7697}, {76, 15810}, {524, 7786}, {598, 7810}, {631, 7870}, {632, 7922}, {1078, 8366}, {1656, 7883}, {2896, 8176}, {3091, 7936}, {3314, 7619}, {3619, 55726}, {5485, 7847}, {6179, 47352}, {7610, 31168}, {7618, 16990}, {7831, 42850}, {7854, 41136}, {7934, 11168}, {7948, 8859}, {8556, 9166}, {8724, 46941}, {9939, 14762}, {11164, 15696}, {12042, 15693}, {26613, 47005}, {31276, 32479}

X(55730) = isogonal conjugate of perspector of Tucker-Hagos(-3) circle

X(55731) = X(3)X(54608)∩X(382)X(22712)

Barycentrics    21*a^4-14*b^4-53*b^2*c^2-14*c^4-43*a^2*(b^2+c^2) : :

X(55731) lies on these lines: {3, 54608}, {382, 22712}, {631, 55691}, {7786, 40341}, {33217, 55730}

X(55731) = isogonal conjugate of perspector of Tucker-Hagos(-5/2) circle

X(55732) = X(2)X(7762)∩X(3)X(3424)

Barycentrics    3*a^4-3*b^4-10*b^2*c^2-3*c^4-8*a^2*(b^2+c^2) : :

X(55732) lies on circumconic {{A, B, C, X(18841), X(34285)}} and on these lines: {2, 7762}, {3, 3424}, {4, 3934}, {69, 7786}, {76, 32474}, {141, 631}, {183, 32956}, {194, 16043}, {230, 33194}, {315, 32957}, {599, 31400}, {626, 5067}, {1078, 3619}, {1285, 3785}, {2896, 32968}, {3090, 9752}, {3096, 32951}, {3314, 32978}, {3524, 7795}, {3525, 7815}, {3533, 7778}, {3545, 7784}, {3620, 11285}, {3734, 17538}, {3767, 33230}, {3788, 15702}, {5071, 7865}, {5418, 5591}, {5420, 5590}, {6292, 7735}, {7736, 7854}, {7763, 21356}, {7789, 10299}, {7791, 52713}, {7819, 46453}, {7825, 41106}, {7830, 11001}, {7849, 37690}, {7868, 33189}, {7887, 52718}, {7896, 9770}, {7904, 14033}, {7922, 34803}, {7928, 16041}, {7931, 32977}, {7938, 32969}, {7942, 23055}, {8356, 32822}, {8359, 9741}, {8362, 15589}, {8364, 37689}, {8556, 33196}, {10130, 51508}, {10351, 33000}, {10513, 31406}, {11008, 55085}, {11165, 32879}, {11287, 32834}, {11318, 32870}, {12040, 32881}, {14001, 16986}, {17008, 33221}, {17128, 33226}, {20582, 55726}, {21358, 33197}, {21843, 33236}, {26100, 51665}, {31168, 32832}, {31268, 41623}, {31276, 32986}, {32001, 37125}, {32817, 32990}, {32828, 33190}, {32831, 33685}, {32880, 51122}, {32882, 52229}, {32955, 37688}, {32985, 46226}, {33217, 55729}

X(55732) = isogonal conjugate of perspector of Tucker-Hagos(-2) circle
X(55732) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 30435, 18841}, {2, 7879, 32823}, {631, 53033, 39142}, {1078, 3619, 14069}, {3096, 34229, 32951}, {3785, 16045, 1285}

X(55733) = X(3)X(54934)∩X(631)X(55689)

Barycentrics    33*a^4-44*b^4-137*b^2*c^2-44*c^4-109*a^2*(b^2+c^2) : :

X(55733) lies on these lines: {3, 54934}, {631, 55689}, {3843, 22712}, {33217, 55727}

X(55733) = isogonal conjugate of perspector of Tucker-Hagos(-7/4) circle

X(55734) = X(3)X(54857)∩X(542)X(631)

Barycentrics    5*a^4-10*b^4-29*b^2*c^2-10*c^4-23*a^2*(b^2+c^2) : :
X(55734) =

X(55734) lies on these lines: {3, 54857}, {381, 22712}, {542, 631}, {599, 7786}, {671, 7872}, {1078, 20582}, {3763, 55730}, {7883, 31239}, {7944, 8860}, {11160, 55085}

X(55734) = isogonal conjugate of perspector of Tucker-Hagos(-3/2) circle

X(55735) = X(3)X(54845)∩X(631)X(5921)

Barycentrics    7*a^4-21*b^4-58*b^2*c^2-21*c^4-46*a^2*(b^2+c^2) : :

X(55735) lies on these lines: {3, 54845}, {631, 5921}, {2996, 9466}, {3091, 22712}, {3522, 16986}, {3620, 7786}, {3763, 55729}

X(55735) = isogonal conjugate of perspector of Tucker-Hagos(-4/3) circle

X(55736) = X(3)X(54891)∩X(631)X(55685)

Barycentrics    9*a^4-36*b^4-97*b^2*c^2-36*c^4-77*a^2*(b^2+c^2) : :

X(55736) lies on these lines: {3, 54891}, {631, 55685}, {3763, 55727}, {3851, 22712}

X(55736) = isogonal conjugate of perspector of Tucker-Hagos(-5/4) circle

X(55737) = X(631)X(11180)∩X(3545)X(22682)

Barycentrics    11*a^4-55*b^4-146*b^2*c^2-55*c^4-116*a^2*(b^2+c^2) : :

X(55737) lies on these lines: {631, 11180}, {3545, 22682}, {3763, 55726}, {7786, 21356}, {15810, 21735}

X(55737) = isogonal conjugate of perspector of Tucker-Hagos(-6/5) circle

X(55738) = X(2)X(5007)∩X(5)X(3096)

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

X(55738) lies on these lines: {2, 5007}, {3, 10159}, {5, 3096}, {6, 31268}, {20, 7831}, {24, 53025}, {32, 16896}, {76, 4045}, {141, 7786}, {183, 7943}, {316, 33269}, {382, 7910}, {598, 7873}, {599, 55085}, {631, 1352}, {1078, 3763}, {3314, 9698}, {3526, 7868}, {3530, 7835}, {3620, 7905}, {3843, 7911}, {3934, 7933}, {3972, 7800}, {5070, 7899}, {5319, 7859}, {6683, 7871}, {6704, 7893}, {7617, 33284}, {7751, 16897}, {7757, 8362}, {7766, 39784}, {7770, 7936}, {7771, 7822}, {7782, 46226}, {7795, 33258}, {7799, 31450}, {7807, 20582}, {7808, 7850}, {7810, 16895}, {7815, 7930}, {7828, 33221}, {7836, 31457}, {7846, 34573}, {7860, 7865}, {7870, 11285}, {7879, 7926}, {7881, 31492}, {7894, 51860}, {7914, 7942}, {7918, 31276}, {7938, 31239}, {7944, 15271}, {7949, 11174}, {11307, 16241}, {11308, 16242}, {14067, 34506}, {14568, 32956}, {15810, 33014}, {19692, 47101}, {31470, 32821}, {33020, 48913}, {33198, 51224}

X(55738) = isogonal conjugate of perspector of Tucker-Hagos(-1) circle
X(55738) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3763), X(7849)}}, {{A, B, C, X(39955), X(42006)}}
X(55738) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5007, 43527}, {2, 7849, 7814}, {2, 7854, 7878}, {3, 10159, 47005}, {6292, 16986, 76}, {7814, 7849, 7922}, {11174, 32027, 7949}

X(55739) = X(631)X(18440)∩X(5056)X(22712)

Barycentrics    9*a^4+45*b^4+106*b^2*c^2+45*c^4+86*a^2*(b^2+c^2) : :

X(55739) lies on these lines: {631, 18440}, {5056, 22712}, {7846, 55736}, {34573, 55735}

X(55739) = isogonal conjugate of perspector of Tucker-Hagos(-4/5) circle

X(55740) = X(2)X(14075)∩X(631)X(11178)

Barycentrics    7*a^4+28*b^4+65*b^2*c^2+28*c^4+53*a^2*(b^2+c^2) : :

X(55740) lies on these lines: {2, 14075}, {631, 11178}, {5055, 22712}, {7786, 21358}, {7846, 55735}, {10302, 20081}, {21356, 31268}, {34573, 55734}

X(55740) = isogonal conjugate of perspector of Tucker-Hagos(-3/4) circle

X(55741) = X(2)X(43136)∩X(631)X(1503)

Barycentrics    5*a^4+15*b^4+34*b^2*c^2+15*c^4+28*a^2*(b^2+c^2) : :

X(55741) lies on these lines: {2, 43136}, {376, 6292}, {538, 18840}, {631, 1503}, {3090, 22712}, {3619, 7786}, {7822, 10299}, {7823, 16045}, {7846, 55734}, {10159, 32817}, {31276, 32956}, {34573, 55732}

X(55741) = isogonal conjugate of perspector of Tucker-Hagos(-2/3) circle

X(55742) = X(547)X(22712)∩X(631)X(18553)

Barycentrics    16*a^4+40*b^4+89*b^2*c^2+40*c^4+74*a^2*(b^2+c^2) : :

X(55742) lies on these lines: {547, 22712}, {631, 18553}, {7786, 20582}, {34573, 55730}

X(55742) = isogonal conjugate of perspector of Tucker-Hagos(-3/5) circle

X(55743) = X(2)X(7826)∩X(194)X(10159)

Barycentrics    3*a^4+6*b^4+13*b^2*c^2+6*c^4+11*a^2*(b^2+c^2) : :

X(55743) lies on these lines: {2, 7826}, {194, 10159}, {631, 17508}, {732, 3763}, {1078, 34573}, {1656, 7944}, {3619, 55085}, {3843, 7937}, {3934, 7919}, {5071, 10357}, {5346, 16986}, {6292, 19689}, {7846, 55732}, {7930, 15694}

X(55743) = isogonal conjugate of perspector of Tucker-Hagos(-1/2) circle

X(55744) = X(3)X(54519)∩X(631)X(10516)

Barycentrics    21*a^4+35*b^4+74*b^2*c^2+35*c^4+64*a^2*(b^2+c^2) : :

X(55744) lies on these lines: {3, 54519}, {631, 10516}, {1285, 16896}, {5067, 22712}, {7786, 41622}, {7846, 55731}, {51128, 55741}

X(55744) = isogonal conjugate of perspector of Tucker-Hagos(-2/5) circle

X(55745) = X(2)X(7882)∩X(631)X(3818)

Barycentrics    8*a^4+12*b^4+25*b^2*c^2+12*c^4+22*a^2*(b^2+c^2) : :

X(55745) lies on these lines: {2, 7882}, {631, 3818}, {1078, 44000}, {3628, 22712}, {6179, 55743}, {7786, 32449}, {7846, 55730}, {51128, 55738}

X(55745) = isogonal conjugate of perspector of Tucker-Hagos(-1/3) circle

X(55746) = X(3)X(54477)∩X(631)X(29012)

Barycentrics    15*a^4+20*b^4+41*b^2*c^2+20*c^4+37*a^2*(b^2+c^2) : :

X(55746) lies on these lines: {3, 54477}, {631, 29012}, {1078, 51128}, {5070, 22712}, {6179, 55742}, {7846, 55729}, {7905, 34573}

X(55746) = isogonal conjugate of perspector of Tucker-Hagos(-1/4) circle

X(55747) = X(2)X(34571)∩X(3)X(54917)

Barycentrics    24*a^4+30*b^4+61*b^2*c^2+30*c^4+56*a^2*(b^2+c^2) : :

X(55747) lies on these lines: {2, 34571}, {3, 54917}, {631, 48898}, {6179, 55741}, {7786, 41747}, {7846, 55727}

X(55747) = isogonal conjugate of perspector of Tucker-Hagos(-1/5) circle

X(55748) = X(631)X(48895)∩X(6179)X(55736)

Barycentrics    80*a^4+72*b^4+145*b^2*c^2+72*c^4+154*a^2*(b^2+c^2) : :

X(55748) lies on these lines: {631, 48895}, {6179, 55736}, {31268, 55728}, {51126, 55747}, {51127, 55745}

X(55748) = isogonal conjugate of perspector of Tucker-Hagos(1/9) circle

X(55749) = X(3)X(54717)∩X(631)X(43621)

Barycentrics    63*a^4+56*b^4+113*b^2*c^2+56*c^4+121*a^2*(b^2+c^2) : :

X(55749) lies on these lines: {3, 54717}, {631, 43621}, {31268, 55729}, {47355, 55747}, {51126, 55746}, {51127, 55743}

X(55749) = isogonal conjugate of perspector of Tucker-Hagos(1/8) circle

X(55750) = X(631)X(48880)∩X(3589)X(55747)

Barycentrics    48*a^4+42*b^4+85*b^2*c^2+42*c^4+92*a^2*(b^2+c^2) : :

X(55750) lies on these lines: {631, 48880}, {3589, 55747}, {6179, 55735}, {47355, 55746}, {51126, 55745}, {51127, 55738}

X(55750) = isogonal conjugate of perspector of Tucker-Hagos(1/7) circle

X(55751) = X(6)X(55747)∩X(631)X(29317)

Barycentrics    35*a^4+30*b^4+61*b^2*c^2+30*c^4+67*a^2*(b^2+c^2) : :

X(55751) lies on these lines: {6, 55747}, {631, 29317}, {1078, 51127}, {3589, 55746}, {5055, 22803}, {31268, 55730}, {47355, 55745}, {51126, 55743}

X(55751) = isogonal conjugate of perspector of Tucker-Hagos(1/6) circle

X(55752) = X(69)X(55747)∩X(631)X(48910)

Barycentrics    117*a^4+99*b^4+202*b^2*c^2+99*c^4+224*a^2*(b^2+c^2) : :

X(55752) lies on these lines: {69, 55747}, {631, 48910}, {3618, 55746}, {47355, 55744}, {51126, 55741}

X(55752) = isogonal conjugate of perspector of Tucker-Hagos(2/11) circle

X(55753) = X(2)X(41940)∩X(3)X(54582)

Barycentrics    24*a^4+20*b^4+41*b^2*c^2+20*c^4+46*a^2*(b^2+c^2) : :

X(55753) lies on these lines: {2, 41940}, {3, 54582}, {6, 55746}, {141, 55747}, {631, 48901}, {3589, 55745}, {6179, 55734}, {7786, 51127}, {16239, 22712}, {31268, 55731}, {47355, 55743}, {51126, 55738}

X(55753) = isogonal conjugate of perspector of Tucker-Hagos(1/5) circle

X(55754) = X(3)X(54706)∩X(69)X(55746)

Barycentrics    77*a^4+63*b^4+130*b^2*c^2+63*c^4+148*a^2*(b^2+c^2) : :

X(55754) lies on these lines: {3, 54706}, {69, 55746}, {631, 48881}, {3589, 55744}, {3618, 55745}, {3619, 55747}, {21735, 39784}, {47355, 55741}, {51126, 55732}

X(55754) = isogonal conjugate of perspector of Tucker-Hagos(2/9) circle

X(55755) = X(2)X(5368)∩X(3)X(54890)

Barycentrics    15*a^4+12*b^4+25*b^2*c^2+12*c^4+29*a^2*(b^2+c^2) : :

X(55755) lies on these lines: {2, 5368}, {3, 54890}, {6, 55745}, {141, 55746}, {631, 19130}, {1078, 51126}, {3589, 55743}, {3618, 55744}, {3763, 55747}, {22712, 46219}, {31268, 41623}, {47355, 55738}, {48310, 55740}

X(55755) = isogonal conjugate of perspector of Tucker-Hagos(1/4) circle

X(55756) = X(524)X(55745)∩X(631)X(55647)

Barycentrics    112*a^4+88*b^4+185*b^2*c^2+88*c^4+218*a^2*(b^2+c^2) : :

X(55756) lies on these lines: {524, 55745}, {631, 55647}, {3589, 55742}, {6179, 55733}, {21358, 55746}, {22712, 47598}, {47352, 55743}, {47355, 55734}, {48310, 55738}

X(55756) = isogonal conjugate of perspector of Tucker-Hagos(3/11) circle

X(55757) = X(3)X(54520)∩X(6)X(55744)

Barycentrics    45*a^4+35*b^4+74*b^2*c^2+35*c^4+88*a^2*(b^2+c^2) : :

X(55757) lies on these lines: {3, 54520}, {6, 55744}, {69, 55745}, {631, 29181}, {3589, 55741}, {3618, 55743}, {3619, 55746}, {7796, 55755}, {31268, 55733}, {47355, 55732}, {48310, 55737}

X(55757) = isogonal conjugate of perspector of Tucker-Hagos(2/7) circle

X(55758) = X(597)X(55743)∩X(599)X(55745)

Barycentrics    91*a^4+70*b^4+149*b^2*c^2+70*c^4+179*a^2*(b^2+c^2) : :

X(55758) lies on these lines: {597, 55743}, {599, 55745}, {631, 55644}, {1992, 55744}, {3589, 55740}, {15723, 22712}, {20582, 55746}, {47352, 55742}, {47355, 55730}, {48310, 55734}, {55085, 55757}

X(55758) = isogonal conjugate of perspector of Tucker-Hagos(3/10) circle

X(55759) = X(2)X(5041)∩X(3)X(14488)

Barycentrics    8*a^4+6*b^4+13*b^2*c^2+6*c^4+16*a^2*(b^2+c^2) : :

X(55759) lies on these lines: {2, 5041}, {3, 14488}, {6, 55743}, {69, 55744}, {141, 55745}, {597, 55742}, {631, 14810}, {632, 22712}, {698, 7786}, {1078, 47355}, {1656, 7943}, {3589, 55738}, {3618, 55741}, {3763, 55746}, {6179, 55732}, {7782, 19689}, {7787, 39784}, {7796, 55753}, {7808, 7934}, {31268, 55734}, {34573, 55747}, {47352, 55740}, {48310, 55730}, {55085, 55755}

X(55759) = isogonal conjugate of perspector of Tucker-Hagos(1/3) circle

X(55760) = X(193)X(55743)∩X(631)X(48874)

Barycentrics    105*a^4+77*b^4+170*b^2*c^2+77*c^4+214*a^2*(b^2+c^2) : :

X(55760) lies on these lines: {193, 55743}, {631, 48874}, {3589, 55735}, {3618, 55739}, {3620, 55744}, {7796, 55751}, {51171, 55741}

X(55760) = isogonal conjugate of perspector of Tucker-Hagos(4/11) circle

X(55761) = X(6)X(55742)∩X(631)X(19924)

Barycentrics    55*a^4+40*b^4+89*b^2*c^2+40*c^4+113*a^2*(b^2+c^2) : :

X(55761) lies on these lines: {6, 55742}, {524, 55743}, {597, 55740}, {631, 19924}, {1078, 48310}, {3589, 55734}, {7881, 55759}, {21356, 55744}, {21358, 55745}, {31268, 55735}, {47352, 55738}, {51127, 55758}, {55085, 55753}

X(55761) = isogonal conjugate of perspector of Tucker-Hagos(3/8) circle

X(55762) = X(3)X(43951)∩X(6)X(55741)

Barycentrics    21*a^4+15*b^4+34*b^2*c^2+15*c^4+44*a^2*(b^2+c^2) : :

X(55762) lies on these lines: {3, 43951}, {6, 55741}, {69, 55743}, {140, 46944}, {141, 55744}, {631, 5480}, {1992, 55742}, {3090, 7710}, {3525, 9748}, {3533, 22712}, {3589, 55732}, {3618, 55738}, {3619, 55745}, {7796, 55749}, {7864, 16045}, {7889, 10299}, {31268, 55736}, {32818, 55759}, {32879, 51588}, {47352, 55737}, {51126, 53033}, {51127, 55757}, {51171, 55739}, {55085, 55751}

X(55762) = isogonal conjugate of perspector of Tucker-Hagos(2/5) circle

X(55763) = X(631)X(55633)∩X(3589)X(55731)

Barycentrics    119*a^4+84*b^4+193*b^2*c^2+84*c^4+253*a^2*(b^2+c^2) : :

X(55763) lies on these lines: {631, 55633}, {3589, 55731}, {3631, 55743}, {31268, 55737}, {55085, 55750}

X(55763) = isogonal conjugate of perspector of Tucker-Hagos(5/12) circle

X(55764) = X(6)X(55740)∩X(524)X(55742)

Barycentrics    40*a^4+28*b^4+65*b^2*c^2+28*c^4+86*a^2*(b^2+c^2) : :

X(55764) lies on these lines: {6, 55740}, {524, 55742}, {597, 55738}, {599, 55743}, {631, 55631}, {1992, 55741}, {3589, 55730}, {3618, 55737}, {6179, 55731}, {10124, 22712}, {20582, 55745}, {47352, 55734}, {51127, 55756}, {55085, 55749}

X(55764) = isogonal conjugate of perspector of Tucker-Hagos(3/7) circle

X(55765) = X(6)X(55739)∩X(193)X(55741)

Barycentrics    65*a^4+45*b^4+106*b^2*c^2+45*c^4+142*a^2*(b^2+c^2) : :

X(55765) lies on these lines: {6, 55739}, {193, 55741}, {631, 55629}, {3589, 55729}, {3618, 55735}, {3620, 55743}, {5032, 55740}, {11160, 55742}, {32818, 55757}, {51171, 55738}

X(55765) = isogonal conjugate of perspector of Tucker-Hagos(4/9) circle

X(55766) = X(631)X(55627)∩X(3589)X(55727)

Barycentrics    96*a^4+66*b^4+157*b^2*c^2+66*c^4+212*a^2*(b^2+c^2) : :

X(55766) lies on these lines: {631, 55627}, {3589, 55727}, {6329, 55738}, {7881, 55755}, {11008, 55741}

X(55766) = isogonal conjugate of perspector of Tucker-Hagos(5/11) circle

X(55767) = X(2)X(3108)∩X(5)X(7859)

Barycentrics    3*a^4+2*b^4+5*b^2*c^2+2*c^4+7*a^2*(b^2+c^2) : :

X(55767) lies on these lines: {2, 3108}, {3, 14492}, {5, 7859}, {6, 31268}, {39, 16896}, {69, 55741}, {83, 7761}, {99, 16898}, {114, 5067}, {141, 55743}, {193, 55739}, {382, 49112}, {524, 55740}, {597, 55734}, {599, 55742}, {631, 3098}, {1078, 3589}, {3329, 7849}, {3526, 11272}, {3618, 55732}, {3619, 55744}, {3763, 55745}, {3843, 7918}, {5041, 16988}, {5070, 7942}, {6179, 47352}, {6292, 33686}, {6329, 55736}, {6683, 16987}, {6694, 11308}, {6695, 11307}, {6704, 7765}, {7752, 33221}, {7786, 24256}, {7790, 33269}, {7807, 48310}, {7808, 7933}, {7814, 7944}, {7832, 9606}, {7835, 31450}, {7878, 31168}, {7881, 55753}, {7883, 16897}, {7889, 33225}, {7892, 31457}, {7905, 34573}, {7936, 12156}, {7943, 33218}, {8362, 12150}, {9166, 32968}, {14907, 18841}, {19694, 44562}, {32818, 55754}, {33198, 52691}, {33258, 43459}, {51127, 55755}, {51171, 55735}

X(55767) = isogonal conjugate of perspector of Tucker-Hagos(1/2) circle
X(55767) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7772, 10159}

X(55768) = X(2)X(22246)∩X(6)X(55737)

Barycentrics    85*a^4+55*b^4+146*b^2*c^2+55*c^4+212*a^2*(b^2+c^2) : :

X(55768) lies on these lines: {2, 22246}, {6, 55737}, {69, 55740}, {597, 55732}, {599, 55741}, {631, 50966}, {1992, 55738}, {3618, 55730}, {7832, 55766}, {7905, 55745}, {11160, 55739}, {20582, 55744}, {21356, 55742}, {32818, 55751}, {47352, 55726}

X(55768) = isogonal conjugate of perspector of Tucker-Hagos(6/11) circle

X(55769) = X(6)X(55736)∩X(631)X(55612)

Barycentrics    56*a^4+36*b^4+97*b^2*c^2+36*c^4+142*a^2*(b^2+c^2) : :

X(55769) lies on these lines: {6, 55736}, {631, 55612}, {3629, 55738}, {7832, 55765}, {7870, 55768}, {51126, 55766}

X(55769) = isogonal conjugate of perspector of Tucker-Hagos(5/9) circle

X(55770) = X(3)X(52519)∩X(6)X(55735)

Barycentrics    33*a^4+21*b^4+58*b^2*c^2+21*c^4+86*a^2*(b^2+c^2) : :

X(55770) lies on these lines: {3, 52519}, {6, 55735}, {69, 55739}, {193, 55738}, {631, 21850}, {3618, 55729}, {3620, 55741}, {5032, 55737}, {7832, 55764}, {51126, 55765}, {51171, 55732}, {53033, 55767}

X(55770) = isogonal conjugate of perspector of Tucker-Hagos(4/7) circle

X(55771) = X(6)X(55734)∩X(631)X(5476)

Barycentrics    16*a^4+10*b^4+29*b^2*c^2+10*c^4+44*a^2*(b^2+c^2) : :

X(55771) lies on these lines: {6, 55734}, {141, 55742}, {381, 9774}, {524, 55738}, {597, 55730}, {598, 7842}, {599, 55740}, {631, 5476}, {1078, 9731}, {1992, 55737}, {3618, 55726}, {5032, 55735}, {6179, 55729}, {7763, 55770}, {7786, 48310}, {7832, 55762}, {7870, 55767}, {11539, 22712}, {21356, 55741}, {21358, 55743}, {51126, 55764}, {55085, 55746}

X(55771) = isogonal conjugate of perspector of Tucker-Hagos(3/5) circle

X(55772) = X(631)X(55603)∩X(3629)X(55736)

Barycentrics    39*a^4+24*b^4+73*b^2*c^2+24*c^4+113*a^2*(b^2+c^2) : :

X(55772) lies on these lines: {631, 55603}, {3629, 55736}, {6329, 55731}, {7763, 55768}, {7832, 55761}, {7905, 55743}, {20583, 55734}, {31268, 55739}, {40341, 55738}, {51126, 55763}, {53033, 55765}, {55085, 55745}

X(55772) = isogonal conjugate of perspector of Tucker-Hagos(5/8) circle

X(55773) = X(6)X(55733)∩X(631)X(55601)

Barycentrics    72*a^4+44*b^4+137*b^2*c^2+44*c^4+214*a^2*(b^2+c^2) : :

X(55773) lies on these lines: {6, 55733}, {631, 55601}, {3630, 55738}, {6179, 55728}, {7796, 55747}, {7832, 55760}, {9606, 55759}, {22712, 45760}

X(55773) = isogonal conjugate of perspector of Tucker-Hagos(7/11) circle

X(55774) = X(2)X(3933)∩X(4)X(4045)

Barycentrics    5*a^4+3*b^4+10*b^2*c^2+3*c^4+16*a^2*(b^2+c^2) : :

X(55774) lies on these lines: {2, 3933}, {3, 14484}, {4, 4045}, {6, 55732}, {69, 55738}, {140, 40268}, {141, 55741}, {193, 55735}, {524, 55737}, {597, 55726}, {631, 1350}, {1078, 3618}, {1285, 7787}, {1975, 16045}, {1992, 55734}, {2548, 33230}, {3090, 39646}, {3146, 14535}, {3525, 6683}, {3619, 55085}, {3620, 55739}, {3763, 55744}, {3815, 33194}, {5067, 7834}, {6179, 55727}, {6680, 15702}, {6704, 9741}, {7736, 7821}, {7763, 55767}, {7782, 14039}, {7786, 14069}, {7796, 55746}, {7803, 32957}, {7804, 17538}, {7832, 55759}, {7859, 32951}, {7861, 41106}, {7870, 55764}, {7875, 32978}, {7905, 55742}, {7914, 9770}, {7943, 34803}, {9606, 55757}, {11008, 55736}, {11174, 32816}, {21356, 31268}, {31400, 47355}, {31401, 32952}, {31404, 33196}, {39668, 44442}, {51126, 53033}, {51127, 55754}, {51171, 55729}

X(55774) = isogonal conjugate of perspector of Tucker-Hagos(2/3) circle
X(55774) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9605, 18840}

X(55775) = X(631)X(55596)∩X(7832)X(55758)

Barycentrics    51*a^4+30*b^4+109*b^2*c^2+30*c^4+179*a^2*(b^2+c^2) : :

X(55775) lies on these lines: {631, 55596}, {7832, 55758}, {32455, 55733}, {47355, 55773}, {53033, 55760}, {55085, 55741}

X(55775) = isogonal conjugate of perspector of Tucker-Hagos(7/10) circle

X(55776) = X(3)X(54643)∩X(6)X(55731)

Barycentrics    24*a^4+14*b^4+53*b^2*c^2+14*c^4+88*a^2*(b^2+c^2) : :

X(55776) lies on these lines: {3, 54643}, {6, 55731}, {631, 55594}, {3631, 55738}, {6179, 55726}, {6329, 55727}, {7763, 55765}, {7796, 55745}, {7832, 55757}, {7870, 55761}, {9606, 55753}, {40341, 55736}, {47355, 55772}, {55085, 55740}

X(55776) = isogonal conjugate of perspector of Tucker-Hagos(5/7) circle

X(55777) = X(631)X(55593)∩X(7763)X(55764)

Barycentrics    57*a^4+33*b^4+130*b^2*c^2+33*c^4+218*a^2*(b^2+c^2) : :

X(55777) lies on these lines: {631, 55593}, {7763, 55764}, {7832, 55756}, {20080, 55735}, {31400, 55771}, {51170, 55732}, {53033, 55759}

X(55777) = isogonal conjugate of perspector of Tucker-Hagos(8/11) circle

X(55778) = X(2)X(5355)∩X(6)X(55730)

Barycentrics    7*a^4+4*b^4+17*b^2*c^2+4*c^4+29*a^2*(b^2+c^2) : :

X(55778) lies on these lines: {2, 5355}, {6, 55730}, {69, 55737}, {76, 51588}, {141, 55740}, {524, 55734}, {597, 1078}, {599, 55085}, {631, 20423}, {671, 7864}, {1656, 23234}, {1992, 55732}, {2482, 19689}, {5969, 7786}, {7763, 55762}, {7796, 55744}, {7802, 18842}, {7832, 55755}, {7870, 55759}, {9606, 55749}, {11160, 55735}, {15694, 22712}, {20582, 55743}, {20583, 55731}, {21358, 55742}, {31268, 55741}, {31400, 55770}, {33217, 55776}, {47355, 55771}, {51126, 55761}, {51185, 55725}

X(55778) = isogonal conjugate of perspector of Tucker-Hagos(3/4) circle

X(55779) = X(631)X(55590)∩X(6144)X(55733)

Barycentrics    32*a^4+18*b^4+85*b^2*c^2+18*c^4+148*a^2*(b^2+c^2) : :

X(55779) lies on these lines: {631, 55590}, {6144, 55733}, {7763, 55760}, {7832, 55754}, {7870, 55758}, {55085, 55736}

X(55779) = isogonal conjugate of perspector of Tucker-Hagos(7/9) circle

X(55780) = X(2)X(9606)∩X(20)X(10358)

Barycentrics    9*a^4+5*b^4+26*b^2*c^2+5*c^4+46*a^2*(b^2+c^2) : :

X(55780) lies on these lines: {2, 9606}, {6, 55729}, {20, 10358}, {69, 55735}, {141, 55739}, {193, 55732}, {631, 18583}, {1078, 51171}, {2996, 7765}, {3620, 7905}, {5032, 55730}, {6179, 55725}, {7763, 55759}, {7796, 55743}, {7832, 55753}, {7870, 55756}, {11160, 55085}, {31400, 55767}, {32960, 55726}, {33217, 55774}, {33238, 53101}, {37667, 51860}, {47355, 55770}, {51126, 55760}, {53033, 55755}

X(55780) = isogonal conjugate of perspector of Tucker-Hagos(4/5) circle

X(55781) = X(6)X(55728)∩X(631)X(55588)

Barycentrics    40*a^4+22*b^4+125*b^2*c^2+22*c^4+224*a^2*(b^2+c^2) : :

X(55781) lies on these lines: {6, 55728}, {631, 55588}, {1078, 51185}, {7832, 55752}, {7870, 55755}, {8584, 55730}, {15533, 55734}, {50990, 55737}, {50991, 55738}, {51186, 55740}, {55085, 55733}

X(55781) = isogonal conjugate of perspector of Tucker-Hagos(9/11) circle

X(55782) = X(6)X(55727)∩X(1078)X(6329)

Barycentrics    11*a^4+6*b^4+37*b^2*c^2+6*c^4+67*a^2*(b^2+c^2) : :

X(55782) lies on these lines: {6, 55727}, {550, 18502}, {631, 55587}, {1078, 6329}, {3629, 55731}, {3631, 55736}, {7763, 55757}, {7832, 55751}, {11008, 55085}, {31268, 55742}, {31400, 55765}, {33217, 55773}, {47355, 55769}

X(55782) = isogonal conjugate of perspector of Tucker-Hagos(5/6) circle

X(55783) = X(2)X(14482)∩X(3)X(54616)

Barycentrics    13*a^4+7*b^4+50*b^2*c^2+7*c^4+92*a^2*(b^2+c^2) : :

X(55783) lies on these lines: {2, 14482}, {3, 54616}, {6, 55726}, {69, 55734}, {524, 55732}, {599, 55737}, {631, 47352}, {1992, 55730}, {3545, 15428}, {3619, 55742}, {5032, 32960}, {7763, 55755}, {7786, 33197}, {7832, 55750}, {7870, 55753}, {14069, 55780}, {15709, 22712}, {21356, 55738}, {21358, 55741}, {31400, 55762}, {32474, 44562}, {32818, 55745}, {33194, 41133}, {47355, 55768}, {48310, 55774}, {53033, 55752}, {55085, 55731}

X(55783) = isogonal conjugate of perspector of Tucker-Hagos(6/7) circle

X(55784) = X(3)X(54734)∩X(631)X(55585)

Barycentrics    15*a^4+8*b^4+65*b^2*c^2+8*c^4+121*a^2*(b^2+c^2) : :

X(55784) lies on these lines: {3, 54734}, {631, 55585}, {3630, 55733}, {7763, 55754}, {7796, 55741}, {7832, 55749}, {9606, 55746}, {31400, 55760}, {31492, 55776}, {33217, 55771}, {55085, 55730}

X(55784) = isogonal conjugate of perspector of Tucker-Hagos(7/8) circle

X(55785) = X(631)X(55584)∩X(7763)X(55753)

Barycentrics    17*a^4+9*b^4+82*b^2*c^2+9*c^4+154*a^2*(b^2+c^2) : :

X(55785) lies on these lines: {631, 55584}, {7763, 55753}, {7832, 55748}, {8366, 55783}, {20080, 55732}, {31400, 55759}, {32818, 55744}, {51170, 55729}, {53033, 55750}

X(55785) = isogonal conjugate of perspector of Tucker-Hagos(8/9) circle

X(55786) = X(6)X(55725)∩X(631)X(55583)

Barycentrics    19*a^4+10*b^4+101*b^2*c^2+10*c^4+191*a^2*(b^2+c^2) : :

X(55786) lies on these lines: {6, 55725}, {631, 55583}, {7763, 55752}, {7870, 55750}, {7881, 55745}, {8584, 55728}, {15534, 55730}, {22165, 55734}, {50992, 55732}, {50993, 55738}, {50994, 55737}, {51143, 55740}, {55085, 55729}

X(55786) = isogonal conjugate of perspector of Tucker-Hagos(9/10) circle

X(55787) = X(3)X(54521)∩X(631)X(55582)

Barycentrics    21*a^4+11*b^4+122*b^2*c^2+11*c^4+232*a^2*(b^2+c^2) : :

X(55787) lies on these lines: {3, 54521}, {631, 55582}, {7763, 55751}, {7796, 55740}, {9606, 55744}, {11008, 55731}, {14069, 55778}, {20583, 55726}, {31400, 55757}, {31492, 55774}, {32960, 55730}, {33217, 55770}, {40341, 55732}, {55085, 55728}

X(55787) = isogonal conjugate of perspector of Tucker-Hagos(10/11) circle

X(55788) = X(3)X(54639)∩X(1078)X(5032)

Barycentrics    23*a^4+11*b^4-122*b^2*c^2+11*c^4-254*a^2*(b^2+c^2) : :

X(55788) lies on these lines: {3, 54639}, {193, 55726}, {524, 55729}, {631, 54174}, {1078, 5032}, {3620, 55734}, {7763, 55747}, {7807, 55787}, {7881, 55741}, {8366, 55774}, {11160, 55730}, {21356, 55735}, {21358, 55739}, {31400, 55743}, {48310, 55770}

X(55788) = isogonal conjugate of perspector of Tucker-Hagos(12/11) circle

X(55789) = X(631)X(55723)∩X(7796)X(55735)

Barycentrics    21*a^4+10*b^4-101*b^2*c^2+10*c^4-211*a^2*(b^2+c^2) : :

X(55789) lies on these lines: {631, 55723}, {7796, 55735}, {7807, 55786}, {7846, 55787}, {9606, 55731}, {11285, 55725}, {31492, 55753}, {33217, 55764}

X(55789) = isogonal conjugate of perspector of Tucker-Hagos(11/10) circle

X(55790) = X(69)X(55731)∩X(631)X(55722)

Barycentrics    19*a^4+9*b^4-82*b^2*c^2+9*c^4-172*a^2*(b^2+c^2) : :

X(55790) lies on these lines: {69, 55731}, {631, 55722}, {3589, 55787}, {3631, 55732}, {7763, 55746}, {7807, 55785}, {7846, 55786}, {7905, 55730}, {11008, 55727}, {14069, 55770}, {31400, 55741}, {32818, 55738}, {32960, 55735}, {33197, 55778}

X(55790) = isogonal conjugate of perspector of Tucker-Hagos(10/9) circle

X(55791) = X(2)X(14148)∩X(1078)X(8584)

Barycentrics    17*a^4+8*b^4-65*b^2*c^2+8*c^4-137*a^2*(b^2+c^2) : :

X(55791) lies on these lines: {2, 14148}, {524, 55728}, {631, 55721}, {1078, 8584}, {3589, 55786}, {7807, 55784}, {7846, 55785}, {7870, 55747}, {8366, 55773}, {15031, 32532}, {15533, 55730}, {15534, 55725}, {31400, 55739}, {50990, 55732}, {50991, 55734}, {51186, 55738}

X(55791) = isogonal conjugate of perspector of Tucker-Hagos(9/8) circle

X(55792) = X(2)X(9607)∩X(3)X(54523)

Barycentrics    15*a^4+7*b^4-50*b^2*c^2+7*c^4-106*a^2*(b^2+c^2) : :

X(55792) lies on these lines: {2, 9607}, {3, 54523}, {631, 44456}, {1078, 51170}, {3589, 55785}, {7763, 55745}, {7796, 55734}, {7807, 55783}, {7846, 55784}, {9606, 20080}, {11285, 55726}, {14069, 55768}, {31400, 55738}, {32960, 55737}, {33217, 55762}, {53033, 55747}

X(55792) = isogonal conjugate of perspector of Tucker-Hagos(8/7) circle

X(55793) = X(3)X(54920)∩X(1078)X(32455)

Barycentrics    13*a^4+6*b^4-37*b^2*c^2+6*c^4-79*a^2*(b^2+c^2) : :

X(55793) lies on these lines: {3, 54920}, {631, 55720}, {1078, 32455}, {3589, 55784}, {7763, 55744}, {7807, 55782}, {7846, 55783}, {8366, 55771}, {11285, 55727}, {31400, 55735}, {32818, 55737}

X(55793) = isogonal conjugate of perspector of Tucker-Hagos(7/6) circle

X(55794) = X(2)X(2418)∩X(3)X(18842)

Barycentrics    11*a^4+5*b^4-26*b^2*c^2+5*c^4-56*a^2*(b^2+c^2) : :

X(55794) lies on these lines: {2, 2418}, {3, 18842}, {69, 55730}, {140, 51588}, {141, 55737}, {376, 42849}, {524, 55726}, {597, 631}, {599, 31400}, {1078, 1992}, {3090, 40925}, {3524, 8722}, {3589, 55783}, {3619, 55740}, {5067, 5461}, {7610, 14482}, {7763, 55743}, {7796, 55733}, {7807, 55780}, {7823, 33215}, {7832, 55747}, {7846, 55782}, {7870, 55745}, {8366, 55770}, {8591, 32968}, {9770, 15482}, {11160, 11285}, {14069, 55767}, {15491, 53142}, {15702, 22712}, {20582, 55741}, {21356, 55734}, {31401, 33230}, {31492, 55744}, {32818, 55735}, {32960, 55738}, {32989, 55792}, {33197, 55774}, {33217, 55760}, {39142, 55762}, {48310, 55768}, {50992, 55728}

X(55794) = isogonal conjugate of perspector of Tucker-Hagos(6/5) circle
X(55794) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5024, 5485}

X(55795) = X(2)X(7765)∩X(3)X(53102)

Barycentrics    9*a^4+4*b^4-17*b^2*c^2+4*c^4-37*a^2*(b^2+c^2) : :

X(55795) lies on these lines: {2, 7765}, {3, 53102}, {141, 55736}, {631, 37517}, {1078, 3629}, {3530, 32134}, {3589, 55782}, {3631, 55731}, {7763, 55741}, {7796, 55732}, {7807, 55778}, {7832, 55746}, {7846, 55780}, {7881, 31492}, {11285, 55730}, {31268, 55744}, {31400, 55729}, {32989, 55788}, {33217, 55759}, {40341, 55727}, {47355, 55766}

X(55795) = isogonal conjugate of perspector of Tucker-Hagos(5/4) circle
X(55795) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 53096, 43676}

X(55796) = X(2)X(32457)∩X(1078)X(15534)

Barycentrics    32*a^4+14*b^4-53*b^2*c^2+14*c^4-116*a^2*(b^2+c^2) : :

X(55796) lies on these lines: {2, 32457}, {524, 55725}, {631, 46267}, {1078, 15534}, {3589, 55781}, {7763, 55739}, {7807, 55776}, {7846, 55779}, {7870, 55743}, {8366, 55767}, {11285, 55731}, {15533, 55728}, {15713, 22712}, {22165, 55730}, {31492, 55733}, {47352, 55791}, {50992, 55726}, {50993, 55734}, {50994, 55732}, {51143, 55738}

X(55796) = isogonal conjugate of perspector of Tucker-Hagos(9/7) circle

X(55797) = X(2)X(1975)∩X(3)X(5395)

Barycentrics    7*a^4+3*b^4-10*b^2*c^2+3*c^4-22*a^2*(b^2+c^2) : :

X(55797) lies on these lines: {2, 1975}, {3, 5395}, {69, 31492}, {141, 55735}, {193, 1078}, {574, 32826}, {631, 1351}, {1506, 33272}, {3055, 52250}, {3523, 5171}, {3589, 55780}, {3619, 55739}, {3620, 11285}, {7748, 41895}, {7761, 31401}, {7763, 55738}, {7765, 32883}, {7770, 51579}, {7782, 32971}, {7786, 32989}, {7796, 55731}, {7807, 55774}, {7808, 32973}, {7832, 55745}, {7839, 33001}, {7846, 55778}, {7870, 55742}, {7881, 55737}, {7901, 32898}, {7905, 55725}, {7931, 32873}, {9606, 51170}, {10303, 22712}, {11160, 55726}, {14069, 55762}, {15482, 32829}, {15815, 32979}, {17005, 33025}, {31450, 32828}, {31455, 32972}, {31467, 33215}, {31489, 32982}, {32838, 53096}, {32960, 55741}, {33012, 37665}, {33188, 37689}, {33197, 55768}, {33217, 55757}, {39142, 55752}, {47352, 55788}, {47355, 55765}, {53033, 55743}

X(55797) = isogonal conjugate of perspector of Tucker-Hagos(4/3) circle
X(55797) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5013, 2996}

X(55798) = X(631)X(55717)∩X(7763)X(55737)

Barycentrics    57*a^4+24*b^4-73*b^2*c^2+24*c^4-161*a^2*(b^2+c^2) : :

X(55798) lies on these lines: {631, 55717}, {7763, 55737}, {7807, 55772}, {7846, 55777}, {8366, 55764}

X(55798) = isogonal conjugate of perspector of Tucker-Hagos(11/8) circle

X(55799) = X(2)X(31457)∩X(3)X(54645)

Barycentrics    24*a^4+10*b^4-29*b^2*c^2+10*c^4-64*a^2*(b^2+c^2) : :

X(55799) lies on these lines: {2, 31457}, {3, 54645}, {631, 55716}, {1078, 6144}, {3589, 55779}, {7763, 55735}, {7796, 55730}, {7807, 55771}, {7832, 55744}, {7846, 55776}, {7870, 55740}, {11285, 55734}, {33217, 55755}

X(55799) = isogonal conjugate of perspector of Tucker-Hagos(7/5) circle

X(55800) = X(2)X(32822)∩X(3)X(18843)

Barycentrics    51*a^4+21*b^4-58*b^2*c^2+21*c^4-128*a^2*(b^2+c^2) : :

X(55800) lies on these lines: {2, 32822}, {3, 18843}, {69, 55727}, {631, 5102}, {1078, 11008}, {3618, 55795}, {7763, 55734}, {7807, 55770}, {7846, 55775}, {11285, 55735}, {14069, 55759}, {32960, 55743}, {32989, 55785}, {53033, 55741}

X(55800) = isogonal conjugate of perspector of Tucker-Hagos(10/7) circle

X(55801) = X(2)X(99)∩X(3)X(598)

Barycentrics    5*a^4+2*b^4-5*b^2*c^2+2*c^4-11*a^2*(b^2+c^2) : :

X(55801) lies on these lines: {2, 99}, {3, 598}, {39, 1153}, {69, 55726}, {76, 11165}, {83, 10484}, {140, 7827}, {141, 55734}, {384, 14762}, {524, 1078}, {549, 2080}, {576, 631}, {597, 8586}, {599, 55730}, {3055, 8352}, {3094, 7606}, {3589, 55778}, {3618, 55794}, {3763, 55742}, {3815, 51224}, {3849, 33273}, {3972, 42849}, {5024, 8860}, {5032, 31400}, {5054, 22712}, {5116, 9830}, {5215, 44562}, {5485, 32832}, {5661, 53199}, {6179, 31492}, {7603, 8597}, {7610, 7757}, {7752, 33215}, {7760, 34506}, {7763, 21356}, {7769, 8359}, {7771, 11163}, {7775, 33004}, {7782, 11164}, {7786, 22486}, {7796, 55729}, {7799, 12040}, {7801, 10302}, {7802, 23334}, {7807, 48310}, {7809, 11184}, {7810, 7917}, {7811, 9770}, {7812, 8182}, {7813, 33689}, {7821, 7824}, {7828, 41139}, {7831, 22110}, {7832, 55743}, {7833, 8176}, {7846, 55774}, {7856, 10303}, {7870, 11285}, {7878, 15720}, {8356, 9771}, {8366, 55759}, {8589, 9855}, {9698, 34604}, {9761, 47067}, {9763, 47069}, {10150, 14046}, {11054, 37688}, {11148, 32828}, {11151, 11317}, {11171, 32469}, {11645, 37334}, {14069, 55757}, {14568, 15597}, {15031, 15815}, {15491, 35954}, {15533, 55725}, {16241, 45880}, {16242, 45879}, {16921, 34504}, {16922, 47617}, {17005, 31173}, {19905, 39498}, {20582, 55740}, {22165, 55728}, {31268, 55745}, {31450, 33188}, {31457, 33015}, {31489, 35955}, {32479, 33013}, {32960, 55744}, {32989, 55780}, {33001, 34511}, {33197, 55762}, {33217, 55753}, {33220, 50571}, {37118, 37765}, {40246, 43457}, {47355, 55764}, {51126, 55758}, {53033, 55739}

X(55801) = inverse of isotomic conjugate of X(15464) in Kiepert Hyperbola
X(55801) = isogonal conjugate of perspector of Tucker-Hagos(3/2) circle
X(55801) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2482), X(15464)}}, {{A, B, C, X(5461), X(42286)}}, {{A, B, C, X(7608), X(42008)}}, {{A, B, C, X(10484), X(31125)}}
X(55801) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 32480, 7617}, {2, 52691, 9166}, {2, 574, 671}, {2, 7622, 41134}, {39, 1153, 8859}, {574, 7617, 32480}, {671, 41134, 19911}, {44453, 47352, 42536}

X(55802) = X(7796)X(55727)∩X(7807)X(55764)

Barycentrics    72*a^4+28*b^4-65*b^2*c^2+28*c^4-142*a^2*(b^2+c^2) : :

X(55802) lies on these lines: {7796, 55727}, {7807, 55764}, {7846, 55773}, {7870, 55737}, {11285, 55740}, {33217, 55751}

X(55802) = isogonal conjugate of perspector of Tucker-Hagos(11/7) circle

X(55803) = X(2)X(15815)∩X(3)X(10155)

Barycentrics    39*a^4+15*b^4-34*b^2*c^2+15*c^4-74*a^2*(b^2+c^2) : :

X(55803) lies on these lines: {2, 15815}, {3, 10155}, {631, 5093}, {1078, 20080}, {3589, 55777}, {3618, 55792}, {7763, 55730}, {7807, 55762}, {7832, 55742}, {7846, 55772}, {7881, 55732}, {11285, 55741}, {14069, 55754}, {32989, 55774}, {39142, 55744}, {53033, 55738}

X(55803) = isogonal conjugate of perspector of Tucker-Hagos(8/5) circle
X(55803) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15815, 38259}

X(55804) = X(2)X(7748)∩X(3)X(11669)

Barycentrics    16*a^4+6*b^4-13*b^2*c^2+6*c^4-28*a^2*(b^2+c^2) : :

X(55804) lies on these lines: {2, 7748}, {3, 11669}, {76, 51587}, {631, 5097}, {1078, 40341}, {3589, 55776}, {3618, 55790}, {3631, 55727}, {7763, 55729}, {7807, 55759}, {7832, 55741}, {7846, 55771}, {7870, 55734}, {11285, 55743}, {14069, 55752}, {14869, 22712}, {32818, 55726}, {32989, 55770}, {33217, 55749}, {47355, 55763}

X(55804) = isogonal conjugate of perspector of Tucker-Hagos(5/3) circle
X(55804) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 37512, 53105}

X(55805) = X(2)X(11147)∩X(3)X(53098)

Barycentrics    95*a^4+35*b^4-74*b^2*c^2+35*c^4-158*a^2*(b^2+c^2) : :

X(55805) lies on these lines: {2, 11147}, {3, 53098}, {597, 55797}, {599, 55729}, {631, 11482}, {1078, 11160}, {3618, 55788}, {3620, 55730}, {7763, 55727}, {7807, 55757}, {8366, 55752}, {11285, 55744}, {15721, 22712}, {20582, 55739}, {32989, 55767}, {33197, 55754}, {51171, 55801}, {53033, 55736}

X(55805) = isogonal conjugate of perspector of Tucker-Hagos(12/7) circle
X(55805) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 53095, 41895}

X(55806) = X(2)X(7756)∩X(3)X(53107)

Barycentrics    33*a^4+12*b^4-25*b^2*c^2+12*c^4-53*a^2*(b^2+c^2) : :

X(55806) lies on these lines: {2, 7756}, {3, 53107}, {141, 55733}, {631, 15520}, {1078, 3630}, {3589, 55775}, {7763, 55726}, {7807, 55755}, {7832, 55740}, {7846, 55770}, {11285, 55745}, {32989, 55765}, {53033, 55735}, {55085, 55804}

X(55806) = isogonal conjugate of perspector of Tucker-Hagos(7/4) circle
X(55806) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15515, 53106}

X(55807) = X(2)X(8589)∩X(3)X(45103)

Barycentrics    56*a^4+20*b^4-41*b^2*c^2+20*c^4-86*a^2*(b^2+c^2) : :

X(55807) lies on these lines: {2, 8589}, {3, 45103}, {597, 55796}, {599, 55728}, {631, 22330}, {1078, 15533}, {7807, 55753}, {7832, 55739}, {7846, 55769}, {7870, 55732}, {8366, 55749}, {11285, 55746}, {11812, 22712}, {22165, 55725}, {32989, 55760}, {47352, 55786}, {50990, 55726}, {50991, 55730}, {51185, 55801}, {51186, 55734}, {51237, 55806}

X(55807) = isogonal conjugate of perspector of Tucker-Hagos(9/5) circle
X(55807) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8589, 17503}

X(55808) = X(631)X(55714)∩X(7807)X(55751)

Barycentrics    85*a^4+30*b^4-61*b^2*c^2+30*c^4-127*a^2*(b^2+c^2) : :

X(55808) lies on these lines: {631, 55714}, {7807, 55751}, {7846, 55768}, {7881, 55730}, {11285, 55747}, {51237, 55805}, {55085, 55803}

X(55808) = isogonal conjugate of perspector of Tucker-Hagos(11/6) circle

X(55809) = X(6)X(55808)∩X(631)X(55713)

Barycentrics    96*a^4+30*b^4-61*b^2*c^2+30*c^4-116*a^2*(b^2+c^2) : :

X(55809) lies on these lines: {6, 55808}, {631, 55713}, {7807, 55747}, {7832, 55737}, {7846, 55766}, {7870, 55728}, {11285, 55751}, {51237, 55791}

X(55809) = isogonal conjugate of perspector of Tucker-Hagos(11/5) circle

X(55810) = X(2)X(6781)∩X(3)X(10185)

Barycentrics    65*a^4+20*b^4-41*b^2*c^2+20*c^4-77*a^2*(b^2+c^2) : :

X(55810) lies on these lines: {2, 6781}, {3, 10185}, {6, 55807}, {597, 55791}, {599, 55725}, {631, 22234}, {1078, 12151}, {1153, 51584}, {7786, 51237}, {7807, 55746}, {7832, 55736}, {7846, 55765}, {7870, 55727}, {11285, 55753}, {15701, 22712}, {47352, 55781}, {50991, 55728}, {50993, 55730}, {50994, 55726}, {51143, 55734}, {51185, 55796}, {55085, 55799}

X(55810) = isogonal conjugate of perspector of Tucker-Hagos(9/4) circle
X(55810) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8588, 45103}

X(55811) = X(2)X(7842)∩X(3)X(11668)

Barycentrics    40*a^4+12*b^4-25*b^2*c^2+12*c^4-46*a^2*(b^2+c^2) : :

X(55811) lies on these lines: {2, 7842}, {3, 11668}, {6, 55806}, {631, 15516}, {3589, 55773}, {7807, 55745}, {7832, 55735}, {7846, 55764}, {7870, 55726}, {11285, 55755}, {12108, 22712}, {32989, 55739}, {51237, 55778}, {55085, 55798}

X(55811) = isogonal conjugate of perspector of Tucker-Hagos(7/3) circle
X(55811) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15513, 53107}

X(55812) = X(2)X(5210)∩X(3)X(41895)

Barycentrics    119*a^4+35*b^4-74*b^2*c^2+35*c^4-134*a^2*(b^2+c^2) : :

X(55812) lies on these lines: {2, 5210}, {3, 41895}, {6, 55805}, {597, 55788}, {631, 5032}, {1153, 35287}, {3523, 32480}, {3620, 55726}, {7807, 55744}, {7846, 55763}, {11285, 55757}, {15708, 22712}, {21356, 55729}, {21358, 55735}, {31400, 55806}, {32989, 55738}, {47352, 55780}, {48310, 55765}, {51171, 55794}, {51237, 55767}

X(55812) = isogonal conjugate of perspector of Tucker-Hagos(12/5) circle
X(55812) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5210, 53101}

X(55813) = X(2)X(5206)∩X(3)X(53104)

Barycentrics    21*a^4+6*b^4-13*b^2*c^2+6*c^4-23*a^2*(b^2+c^2) : :

X(55813) lies on these lines: {2, 5206}, {3, 53104}, {6, 55804}, {141, 55731}, {631, 39561}, {1078, 3631}, {3589, 55772}, {3618, 55787}, {6036, 10299}, {6179, 55811}, {6329, 55795}, {7807, 55743}, {7832, 55734}, {7846, 55762}, {7870, 55725}, {11285, 55759}, {15720, 22712}, {17004, 43676}, {31268, 55747}, {31400, 55805}, {32960, 55752}, {32989, 55735}, {53033, 55729}, {55085, 55797}

X(55813) = isogonal conjugate of perspector of Tucker-Hagos(5/2) circle
X(55813) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5206, 53109}

X(55814) = X(2)X(5023)∩X(3)X(38259)

Barycentrics    55*a^4+15*b^4-34*b^2*c^2+15*c^4-58*a^2*(b^2+c^2) : :

X(55814) lies on these lines: {2, 5023}, {3, 38259}, {6, 55803}, {631, 34380}, {3618, 55785}, {6179, 55809}, {7807, 55741}, {7839, 15708}, {7846, 55761}, {11285, 55762}, {31400, 55804}, {32960, 55754}, {32989, 55732}, {51171, 55792}, {51237, 55734}, {53033, 55727}

X(55814) = isogonal conjugate of perspector of Tucker-Hagos(8/3) circle
X(55814) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5023, 18845}

X(55815) = X(6)X(55802)∩X(631)X(55712)

Barycentrics    105*a^4+28*b^4-65*b^2*c^2+28*c^4-109*a^2*(b^2+c^2) : :

X(55815) lies on these lines: {6, 55802}, {631, 55712}, {7807, 55740}, {7832, 55733}, {7846, 55760}, {11285, 55764}, {31492, 55804}, {33217, 55747}, {51237, 55730}, {55085, 55796}

X(55815) = isogonal conjugate of perspector of Tucker-Hagos(11/4) circle

X(55816) = X(2)X(18843)∩X(6)X(55800)

Barycentrics    91*a^4+21*b^4-58*b^2*c^2+21*c^4-88*a^2*(b^2+c^2) : :

X(55816) lies on these lines: {2, 18843}, {6, 55800}, {631, 3629}, {3618, 55782}, {3619, 55736}, {3631, 39142}, {6329, 55790}, {7807, 55735}, {7846, 55758}, {11008, 55813}, {11285, 55770}, {14069, 55743}, {22712, 32450}, {32960, 55759}

X(55816) = isogonal conjugate of perspector of Tucker-Hagos(10/3) circle

X(55817) = X(3)X(54644)∩X(6)X(55799)

Barycentrics    45*a^4+10*b^4-29*b^2*c^2+10*c^4-43*a^2*(b^2+c^2) : :

X(55817) lies on these lines: {3, 54644}, {6, 55799}, {631, 55710}, {6144, 55811}, {6179, 55807}, {7763, 55816}, {7807, 55734}, {7832, 55731}, {7846, 55757}, {9606, 55801}, {11285, 55771}, {22712, 32520}, {31492, 55802}, {32455, 55806}, {33217, 55745}, {55085, 55794}

X(55817) = isogonal conjugate of perspector of Tucker-Hagos(7/2) circle

X(55818) = X(6)X(55798)∩X(631)X(55709)

Barycentrics    112*a^4+24*b^4-73*b^2*c^2+24*c^4-106*a^2*(b^2+c^2) : :

X(55818) lies on these lines: {6, 55798}, {631, 55709}, {6179, 55806}, {7846, 55756}, {8366, 55740}, {11285, 55772}

X(55818) = isogonal conjugate of perspector of Tucker-Hagos(11/3) circle

X(55819) = X(2)X(3053)∩X(3)X(2996)

Barycentrics    15*a^4+3*b^4-10*b^2*c^2+3*c^4-14*a^2*(b^2+c^2) : :

X(55819) lies on these lines: {2, 3053}, {3, 2996}, {6, 55797}, {69, 33684}, {76, 51579}, {141, 55729}, {187, 32987}, {193, 631}, {194, 3523}, {439, 34229}, {487, 5420}, {488, 5418}, {524, 55812}, {1078, 3620}, {1992, 55805}, {3054, 52250}, {3091, 9754}, {3522, 17004}, {3524, 6392}, {3589, 55770}, {3618, 55780}, {3619, 55735}, {3763, 55739}, {3767, 5569}, {3785, 7821}, {3832, 17006}, {3934, 21843}, {4045, 32990}, {5023, 32979}, {5032, 31400}, {5052, 7786}, {5206, 32838}, {5265, 31999}, {5281, 32095}, {5304, 33012}, {6179, 55804}, {7486, 14712}, {7746, 33272}, {7747, 32883}, {7749, 32972}, {7762, 15702}, {7763, 11160}, {7771, 32974}, {7793, 10303}, {7796, 55817}, {7807, 55732}, {7832, 55730}, {7840, 32873}, {7846, 55755}, {7905, 55809}, {7941, 32898}, {8588, 32826}, {11285, 55774}, {11361, 32897}, {14069, 55741}, {14907, 32988}, {15589, 33259}, {15717, 17008}, {19661, 54639}, {19687, 52718}, {20080, 55814}, {32818, 55816}, {32828, 34506}, {32830, 33274}, {32832, 35927}, {32870, 33007}, {32960, 55762}, {32981, 37688}, {32982, 37637}, {33004, 37689}, {33197, 55737}, {33206, 37668}, {33217, 55744}, {47355, 55760}, {51170, 55803}, {55085, 55793}

X(55819) = isogonal conjugate of perspector of Tucker-Hagos(4) circle
X(55819) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3053, 5395}, {1078, 32989, 3620}

X(55820) = X(6)X(55796)∩X(76)X(51589)

Barycentrics    77*a^4+14*b^4-53*b^2*c^2+14*c^4-71*a^2*(b^2+c^2) : :

X(55820) lies on these lines: {6, 55796}, {76, 51589}, {141, 55728}, {524, 55810}, {597, 55786}, {631, 55708}, {1078, 50991}, {6055, 13172}, {6179, 55802}, {7786, 51185}, {7807, 55731}, {7846, 55754}, {8366, 55738}, {8584, 55801}, {11054, 15712}, {11055, 15693}, {11285, 55776}, {15534, 55807}, {50993, 55725}, {51186, 55730}, {51237, 55819}, {55085, 55792}

X(55820) = isogonal conjugate of perspector of Tucker-Hagos(9/2) circle

X(55821) = X(2)X(7843)∩X(3)X(43676)

Barycentrics    24*a^4+4*b^4-17*b^2*c^2+4*c^4-22*a^2*(b^2+c^2) : :

X(55821) lies on these lines: {2, 7843}, {3, 43676}, {6, 55795}, {69, 55816}, {76, 51581}, {141, 55727}, {631, 7905}, {3530, 22712}, {3589, 55769}, {3629, 55804}, {6179, 31492}, {6329, 7786}, {7763, 55814}, {7771, 7872}, {7807, 55730}, {7832, 55729}, {7846, 55753}, {9606, 55799}, {11285, 55778}, {16241, 22844}, {16242, 22845}, {17004, 53105}, {33217, 55743}, {33257, 34506}, {40341, 55813}, {55085, 55791}

X(55821) = isogonal conjugate of perspector of Tucker-Hagos(5) circle
X(55821) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 35007, 53102}

X(55822) = X(631)X(55707)∩X(7832)X(55728)

Barycentrics    117*a^4+18*b^4-85*b^2*c^2+18*c^4-107*a^2*(b^2+c^2) : :

X(55822) lies on these lines: {631, 55707}, {7832, 55728}, {7846, 55752}, {11285, 55779}, {55085, 55790}

X(55822) = isogonal conjugate of perspector of Tucker-Hagos(11/2) circle

X(55823) = X(2)X(1285)∩X(3)X(5485)

Barycentrics    35*a^4+5*b^4-26*b^2*c^2+5*c^4-32*a^2*(b^2+c^2) : :
X(55823) = 4*X[3]+X[5485], -3*X[4]+8*X[7617], X[20]+4*X[16509], X[376]+4*X[7610], 4*X[549]+X[9740], -16*X[1153]+11*X[3525], -7*X[3090]+2*X[23334], -7*X[3523]+2*X[11165], 21*X[3528]+4*X[53143], -3*X[3545]+8*X[15597], -13*X[5067]+8*X[8176], -X[5503]+6*X[38737], 4*X[7615]+X[11001], -8*X[7619]+3*X[9770], 4*X[8667]+11*X[15719], 3*X[10304]+2*X[40727], -X[11148]+11*X[15717], -4*X[11184]+9*X[15709], -X[11541]+16*X[47617], -4*X[12040]+9*X[15708], 8*X[13468]+7*X[15698], 11*X[21735]+4*X[34505], 7*X[41106]+8*X[47101]

X(55823) lies on these lines: {2, 1285}, {3, 5485}, {4, 7617}, {6, 55794}, {20, 16509}, {76, 11147}, {141, 55726}, {193, 55805}, {376, 7610}, {524, 631}, {538, 3524}, {543, 19708}, {549, 9740}, {597, 55783}, {1078, 21356}, {1153, 3525}, {1992, 55801}, {3090, 23334}, {3523, 11165}, {3528, 53143}, {3545, 15597}, {3589, 55768}, {3618, 55778}, {3619, 55734}, {3785, 41133}, {3849, 5071}, {5032, 55797}, {5067, 8176}, {5215, 33231}, {5418, 33364}, {5420, 33365}, {5503, 38737}, {6179, 55799}, {7386, 42008}, {7615, 11001}, {7619, 9770}, {7763, 55813}, {7771, 23055}, {7786, 44500}, {7796, 55815}, {7807, 55729}, {7832, 55727}, {7846, 55751}, {7864, 8859}, {7870, 55821}, {7883, 32959}, {8366, 55735}, {8667, 15719}, {10304, 40727}, {11148, 15717}, {11160, 55812}, {11164, 32828}, {11184, 15709}, {11285, 55780}, {11541, 47617}, {12040, 15708}, {13468, 15698}, {14039, 26613}, {14069, 55738}, {14907, 23053}, {15692, 52229}, {15810, 33230}, {17008, 32480}, {17538, 32479}, {20582, 55737}, {21358, 33197}, {21735, 34505}, {21843, 42850}, {31276, 32985}, {31400, 55800}, {32818, 55814}, {32960, 55767}, {39142, 55819}, {41106, 47101}, {47352, 55774}, {48310, 55762}, {50990, 55820}, {50992, 55810}, {51237, 55817}, {55085, 55789}

X(55823) = isogonal conjugate of perspector of Tucker-Hagos(6) circle
X(55823) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1384, 18842}

X(55824) = X(6)X(55793)∩X(76)X(51585)

Barycentrics    48*a^4+6*b^4-37*b^2*c^2+6*c^4-44*a^2*(b^2+c^2) : :

X(55824) lies on these lines: {6, 55793}, {76, 51585}, {631, 55706}, {3630, 55811}, {6144, 55806}, {6179, 55797}, {7763, 55812}, {7807, 55727}, {7832, 55726}, {7846, 55750}, {7870, 55820}, {8366, 55734}, {11285, 55782}, {15712, 22712}, {32455, 55799}

X(55824) = isogonal conjugate of perspector of Tucker-Hagos(7) circle

X(55825) = X(2)X(22331)∩X(3)X(43681)

Barycentrics    63*a^4+7*b^4-50*b^2*c^2+7*c^4-58*a^2*(b^2+c^2) : :

X(55825) lies on these lines: {2, 22331}, {3, 43681}, {6, 55792}, {69, 55814}, {193, 55803}, {439, 9466}, {631, 1353}, {3618, 55777}, {3832, 32152}, {6179, 55796}, {7763, 55811}, {7796, 55813}, {7807, 55726}, {7846, 55749}, {9606, 51170}, {11285, 55783}, {14069, 55737}, {15717, 20081}, {31400, 55799}, {32960, 55768}, {32989, 55823}, {33217, 55741}, {34506, 52250}, {51171, 55785}, {53033, 55824}

X(55825) = isogonal conjugate of perspector of Tucker-Hagos(8) circle

X(55826) = X(6)X(55791)∩X(76)X(51584)

Barycentrics    80*a^4+8*b^4-65*b^2*c^2+8*c^4-74*a^2*(b^2+c^2) : :

X(55826) lies on these lines: {6, 55791}, {76, 51584}, {141, 55725}, {524, 55807}, {597, 55781}, {599, 55820}, {631, 50992}, {1078, 50993}, {6179, 55795}, {7846, 55748}, {7870, 55819}, {8366, 55733}, {8584, 55796}, {11285, 55784}, {12100, 22712}, {15533, 55810}, {15534, 55801}, {50994, 55823}, {51143, 55730}, {51185, 55786}, {51186, 55728}

X(55826) = isogonal conjugate of perspector of Tucker-Hagos(9) circle

X(55827) = X(6)X(55790)∩X(69)X(55813)

Barycentrics    99*a^4+9*b^4-82*b^2*c^2+9*c^4-92*a^2*(b^2+c^2) : :

X(55827) lies on these lines: {6, 55790}, {69, 55813}, {631, 12007}, {3529, 9756}, {3618, 55776}, {3629, 55800}, {3631, 39142}, {6329, 55787}, {7763, 55810}, {7832, 55725}, {7881, 55819}, {10299, 22712}, {11008, 55804}, {11285, 55785}, {14069, 55735}, {20583, 55794}, {32818, 55811}, {32960, 55770}, {33197, 55730}, {53033, 55823}

X(55827) = isogonal conjugate of perspector of Tucker-Hagos(10) circle

X(55828) = X(6)X(55789)∩X(631)X(55702)

Barycentrics    120*a^4+10*b^4-101*b^2*c^2+10*c^4-112*a^2*(b^2+c^2) : :

X(55828) lies on these lines: {6, 55789}, {631, 55702}, {6179, 55794}, {7796, 55811}, {7807, 55725}, {11285, 55786}, {22712, 44682}, {33217, 55740}

X(55828) = isogonal conjugate of perspector of Tucker-Hagos(11) circle

X(55829) = X(2)X(54639)∩X(6)X(55788)

Barycentrics    143*a^4+11*b^4-122*b^2*c^2+11*c^4-134*a^2*(b^2+c^2) : :

X(55829) lies on these lines: {2, 54639}, {6, 55788}, {69, 55812}, {193, 55801}, {524, 55805}, {597, 55780}, {599, 55819}, {631, 11160}, {1992, 55797}, {3620, 55823}, {5032, 55794}, {7763, 55809}, {7870, 55818}, {7905, 55804}, {8366, 55732}, {11285, 55787}, {15692, 22712}, {20582, 55735}, {31400, 55798}, {32989, 55821}, {51171, 55783}, {53033, 55822}

X(55829) = isogonal conjugate of perspector of Tucker-Hagos(12) circle





leftri  Centers on the cubic K007: X(55830) - X(55837)  rightri

Centers X(55830)-X(55837) were contributed by César Eliud Lozada, August 12, 2023.

underbar

X(55830) = ANTICOMPLEMENT OF X(3349)

Barycentrics    (a^8-4*(b^2-c^2)*a^6+2*(b^2-c^2)*(3*b^2+5*c^2)*a^4-4*(b^4-c^4)*(b^2+c^2)*a^2+(b^2-c^2)^4)*(a^8+4*(b^2-c^2)*a^6-2*(b^2-c^2)*(5*b^2+3*c^2)*a^4+4*(b^4-c^4)*(b^2+c^2)*a^2+(b^2-c^2)^4)*(-a^2+b^2+c^2)*(a^16-8*(b^2+c^2)*a^14+4*(7*b^4-10*b^2*c^2+7*c^4)*a^12-56*(b^4-c^4)*(b^2-c^2)*a^10+2*(b^2-c^2)^2*(35*b^4+114*b^2*c^2+35*c^4)*a^8-8*(b^4-c^4)*(b^2-c^2)*(7*b^4+18*b^2*c^2+7*c^4)*a^6+4*(b^2-c^2)^2*(b^4+7*c^4)*(7*b^4+c^4)*a^4-8*(b^2-c^2)^6*(b^2+c^2)*a^2+(b^4+14*b^2*c^2+c^4)*(b^2-c^2)^6) : :

X(55830) lies on the cubic K007 and these lines: {2, 3349}, {4, 1032}, {7, 41080}, {8, 55836}, {20, 3355}, {69, 55833}, {189, 1034}, {253, 3346}

X(55830) = anticomplement of X(3349)
X(55830) = anticomplementary conjugate of X(14365)
X(55830) = cyclocevian conjugate of the isotomic conjugate of X(55832)
X(55830) = isotomic conjugate of X(55833)
X(55830) = cevapoint of X(3350) and X(3355)
X(55830) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1, 14365), (3350, 8)
X(55830) = X(69)-Ceva conjugate of-X(1032)
X(55830) = X(14481)-cross conjugate of-X(2)
X(55830) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 55833), (3344, 3356), (3346, 4), (3349, 3349), (3350, 2131)
X(55830) = X(31)-isoconjugate of-X(55833)
X(55830) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2, 55833), (2130, 3343), (3344, 2131), (3350, 3356), (14481, 3349), (17833, 1033), (28782, 6)
X(55830) = perspector of the inconic with center X(14481)
X(55830) = barycentric product X(i)*X(j) for these {i, j}: {76, 28782}, {2130, 47633}
X(55830) = trilinear product X(75)*X(28782)
X(55830) = trilinear quotient X(i)/X(j) for these (i, j): (75, 55833), (28782, 31)
X(55830) = (X(3350), X(31943))-harmonic conjugate of X(2)

X(55831) = ANTICOMPLEMENT OF X(3352)

Barycentrics    (a^6-2*(b-c)*a^5-(b-c)^2*a^4+4*(b^3-c^3)*a^3-(b^2-c^2)^2*a^2-2*(b^4-c^4)*(b+c)*a+(b^2-c^2)^2*(b-c)^2)*(a^6+2*(b-c)*a^5-(b-c)^2*a^4-4*(b^3-c^3)*a^3-(b^2-c^2)^2*a^2+2*(b^4-c^4)*(b+c)*a+(b^2-c^2)^2*(b-c)^2)*(a^15-3*(b+c)*a^14-3*(b+c)^2*a^13+(b+c)*(17*b^2-18*b*c+17*c^2)*a^12-(3*b-c)*(b-3*c)*(b+c)^2*a^11-(b+c)*(39*b^4+39*c^4-2*b*c*(30*b^2-29*b*c+30*c^2))*a^10+(25*b^2+38*b*c+25*c^2)*(b^2-c^2)^2*a^9+(b^2-c^2)*(b-c)*(45*b^4+45*c^4+2*b*c*(14*b^2+39*b*c+14*c^2))*a^8-(b^2-c^2)^2*(45*b^4+45*c^4+2*b*c*(36*b^2+35*b*c+36*c^2))*a^7-(b^2-c^2)*(b-c)*(25*b^6+25*c^6+(42*b^4+42*c^4+b*c*(87*b^2+76*b*c+87*c^2))*b*c)*a^6+(b^2-c^2)^2*(b+c)^2*(39*b^4+39*c^4-2*b*c*(20*b^2-57*b*c+20*c^2))*a^5+(b^2-c^2)^2*(b+c)^3*(3*b^4+3*c^4+2*b*c*(6*b^2-7*b*c+6*c^2))*a^4-(b^2-c^2)^2*(b+c)^2*(17*b^6+17*c^6-(38*b^4+38*c^4-b*c*(95*b^2-84*b*c+95*c^2))*b*c)*a^3+(b^2-c^2)^5*(b-c)*(3*b^2+2*b*c+3*c^2)*a^2+(b^2-c^2)^4*(b-c)^2*(3*b^2+c^2)*(b^2+3*c^2)*a-(b^2-c^2)^6*(b+c)^3) : :

X(55831) lies on the cubic K007 and these lines: {2, 3351}, {4, 1034}, {7, 1032}, {8, 14365}, {20, 3472}, {69, 55836}, {189, 253}, {329, 55833}

X(55831) = anticomplement of X(3352)
X(55831) = anticomplementary conjugate of X(41080)
X(55831) = isotomic conjugate of X(55836)
X(55831) = cyclocevian conjugate of the isotomic conjugate of X(55837)
X(55831) = cevapoint of X(3351) and X(3472)
X(55831) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1, 41080), (3351, 8), (47440, 192), (47851, 34162)
X(55831) = X(69)-Ceva conjugate of-X(1034)
X(55831) = X(46978)-cross conjugate of-X(2)
X(55831) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 55836), (3342, 46979), (3351, 3354), (3352, 3352), (40838, 4)
X(55831) = X(31)-isoconjugate of-X(55836)
X(55831) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2, 55836), (3342, 3354), (3351, 46979), (3353, 3341), (46978, 3352)
X(55831) = perspector of the inconic with center X(46978)
X(55831) = barycentric product X(3353)*X(47634)
X(55831) = trilinear quotient X(75)/X(55836)

X(55832) = ANTICOMPLEMENT OF X(3356)

Barycentrics    (a^12+6*(b^2-c^2)*a^10-(b^2-c^2)*(29*b^2+15*c^2)*a^8+4*(b^2-c^2)*(9*b^4+10*b^2*c^2+5*c^4)*a^6-(b^2-c^2)*(9*b^6+15*c^6+5*(3*b-c)*(3*b+c)*b^2*c^2)*a^4-2*(b^2-c^2)^4*(5*b^2+3*c^2)*a^2+(5*b^4+10*b^2*c^2+c^4)*(b^2-c^2)^4)*(7*a^24-28*(b^2+c^2)*a^22-14*(3*b^4-14*b^2*c^2+3*c^4)*a^20+4*(b^2+c^2)*(121*b^4-250*b^2*c^2+121*c^4)*a^18-3*(b^2-c^2)^2*(437*b^4+726*b^2*c^2+437*c^4)*a^16+24*(b^4-c^4)*(b^2-c^2)*(75*b^4+106*b^2*c^2+75*c^4)*a^14-12*(b^2-c^2)^2*(105*b^8+105*c^8+2*(210*b^4+211*b^2*c^2+210*c^4)*b^2*c^2)*a^12+8*(b^4-c^4)*(b^2-c^2)*(21*b^8+21*c^8+10*(42*b^4-5*b^2*c^2+42*c^4)*b^2*c^2)*a^10+(b^2-c^2)^2*(7*b^4-30*b^2*c^2+7*c^4)*(63*b^8+63*c^8+2*(42*b^4-19*b^2*c^2+42*c^4)*b^2*c^2)*a^8-28*(b^2-c^2)^6*(b^2+c^2)*(13*b^4+38*b^2*c^2+13*c^4)*a^6+2*(b^2-c^2)^6*(59*b^8+59*c^8+2*(166*b^4+313*b^2*c^2+166*c^4)*b^2*c^2)*a^4-4*(b^2-c^2)^6*(3*b^2+c^2)*(b^2+3*c^2)*(b^2+c^2)*(b^4+6*b^2*c^2+c^4)*a^2-(b^2-c^2)^12)*(a^12-6*(b^2-c^2)*a^10+(b^2-c^2)*(15*b^2+29*c^2)*a^8-4*(b^2-c^2)*(5*b^4+10*b^2*c^2+9*c^4)*a^6+(b^2-c^2)*(15*b^6+9*c^6-5*(b-3*c)*(b+3*c)*b^2*c^2)*a^4-2*(b^2-c^2)^4*(3*b^2+5*c^2)*a^2+(b^4+10*b^2*c^2+5*c^4)*(b^2-c^2)^4) : :

X(55832) lies on the cubic K007 and these lines: {2, 3356}, {4, 14365}, {7, 55836}, {189, 41080}, {253, 1032}

X(55832) = anticomplement of X(3356)
X(55832) = isotomic conjugate of the cyclocevian conjugate of X(55830)
X(55832) = anticomplementary conjugate of X(55833)
X(55832) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1, 55833), (14481, 8)
X(55832) = X(69)-Ceva conjugate of-X(14365)
X(55832) = X(i)-Dao conjugate of-X(j) for these (i, j): (3356, 3356), (14481, 3637)
X(55832) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3349, 3637), (3355, 3350)

X(55833) = ANTICOMPLEMENT OF X(14481)

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^16+8*(b^2-c^2)*a^14-4*(b^2-c^2)*(17*b^2+7*c^2)*a^12+8*(b^2-c^2)*(23*b^4+14*b^2*c^2+7*c^4)*a^10-2*(b^2-c^2)*(125*b^6+35*c^6+3*(35*b^2-3*c^2)*b^2*c^2)*a^8+8*(b^2-c^2)*(23*b^8+7*c^8+2*(14*b^4-11*b^2*c^2-2*c^4)*b^2*c^2)*a^6-4*(b^2-c^2)^2*(17*b^8-7*c^8+2*(2*b^2-c^2)*(13*b^2+14*c^2)*b^2*c^2)*a^4+8*(b^4-c^4)^2*(b^2-c^2)*(b^4+6*b^2*c^2+c^4)*a^2+(b^2-c^2)^8)*(a^16-8*(b^2-c^2)*a^14+4*(b^2-c^2)*(7*b^2+17*c^2)*a^12-8*(b^2-c^2)*(7*b^4+14*b^2*c^2+23*c^4)*a^10+2*(b^2-c^2)*(35*b^6+125*c^6-3*(3*b^2-35*c^2)*b^2*c^2)*a^8-8*(b^2-c^2)*(7*b^8+23*c^8-2*(2*b^4+11*b^2*c^2-14*c^4)*b^2*c^2)*a^6+4*(b^2-c^2)^2*(7*b^8-17*c^8+2*(14*b^2+13*c^2)*(b^2-2*c^2)*b^2*c^2)*a^4-8*(b^4-c^4)^2*(b^2-c^2)*(b^4+6*b^2*c^2+c^4)*a^2+(b^2-c^2)^8)*(a^8-4*(b^2+c^2)*a^6+2*(3*b^4-2*b^2*c^2+3*c^4)*a^4-4*(b^4-c^4)*(b^2-c^2)*a^2+(b^4+6*b^2*c^2+c^4)*(b^2-c^2)^2) : :

X(55833) lies on the cubic K007 and these lines: {2, 3356}, {8, 55837}, {20, 2130}, {69, 55830}, {329, 55831}, {5932, 34162}

X(55833) = cyclocevian conjugate of X(14362)
X(55833) = anticomplement of X(14481)
X(55833) = isogonal conjugate of X(28782)
X(55833) = isotomic conjugate of X(55830)
X(55833) = anticomplementary conjugate of X(55832)
X(55833) = cevapoint of X(2131) and X(3356)
X(55833) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1, 55832), (3356, 8)
X(55833) = X(i)-cross conjugate of-X(j) for these (i, j): (4, 14361), (3349, 2)
X(55833) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 55830), (1073, 2130), (3356, 3355), (14481, 14481)
X(55833) = X(i)-isoconjugate of-X(j) for these {i, j}: {31, 55830}, {17833, 47849}
X(55833) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2, 55830), (1033, 17833), (2131, 3344), (3343, 2130), (3349, 14481), (3356, 3350)
X(55833) = perspector of the inconic with center X(3349)
X(55833) = pole of line {28782, 55830} with respect to Steiner-Wallace hyperbola
X(55833) = barycentric product X(2131)*X(47435)
X(55833) = trilinear quotient X(i)/X(j) for these (i, j): (75, 55830), (1712, 17833)

X(55834) = ANTICOMPLEMENT OF X(40991)

Barycentrics    sqrt(2*OH^2*sqrt(-3*S^2+SW^2)-3*S^2-18*R^2*SW+5*SW^2)*S^2*(sqrt(-3*S^2+SW^2)+2*SA-SW)-SA*(S^2-3*SB*SC)*sqrt(-3*S^2+SW^2)+S^2*(SW*(-3*SW+12*R^2+2*SA)-3*SA^2) : :

X(55834) lies on the cubic K007 and these lines: {2, 40989}, {4, 39159}, {253, 55835}

X(55834) = isotomic conjugate of the cyclocevian conjugate of X(39158)
X(55834) = anticomplement of X(40991)
X(55834) = anticomplementary conjugate of X(42428)
X(55834) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1, 42428), (40989, 8)
X(55834) = X(69)-Ceva conjugate of-X(39159)
X(55834) = X(i)-Dao conjugate of-X(j) for these (i, j): (40989, 40993), (40991, 40991)
X(55834) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (39163, 40993), (40851, 39162)

X(55835) = ANTICOMPLEMENT OF X(40992)

Barycentrics    -sqrt(2*OH^2*sqrt(-3*S^2+SW^2)-3*S^2-18*R^2*SW+5*SW^2)*S^2*(sqrt(-3*S^2+SW^2)+2*SA-SW)-SA*(S^2-3*SB*SC)*sqrt(-3*S^2+SW^2)+S^2*(SW*(-3*SW+12*R^2+2*SA)-3*SA^2) : :

X(55835) lies on the cubic K007 and these lines: {2, 40990}, {4, 39158}, {253, 55834}

X(55835) = isotomic conjugate of the cyclocevian conjugate of X(39159)
X(55835) = anticomplement of X(40992)
X(55835) = anticomplementary conjugate of X(42427)
X(55835) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1, 42427), (40990, 8)
X(55835) = X(69)-Ceva conjugate of-X(39158)
X(55835) = X(i)-Dao conjugate of-X(j) for these (i, j): (40990, 40994), (40992, 40992)
X(55835) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (39162, 40994), (40852, 39163)

X(55836) = ANTICOMPLEMENT OF X(46978)

Barycentrics    (a^15-3*(b-c)*a^14-3*(b-c)^2*a^13+(b-c)*(17*b^2+18*b*c+17*c^2)*a^12-(b+3*c)*(3*b+c)*(b-c)^2*a^11-(b-c)*(39*b^4+39*c^4+2*b*c*(30*b^2+29*b*c+30*c^2))*a^10+(25*b^2-38*b*c+25*c^2)*(b^2-c^2)^2*a^9+(b^2-c^2)*(b+c)*(45*b^4+45*c^4-2*b*c*(14*b^2-39*b*c+14*c^2))*a^8-(b^2-c^2)^2*(45*b^4+45*c^4-2*b*c*(36*b^2-35*b*c+36*c^2))*a^7-(b^2-c^2)*(b+c)*(25*b^6+25*c^6-(42*b^4+42*c^4-b*c*(87*b^2-76*b*c+87*c^2))*b*c)*a^6+(b^2-c^2)^2*(b-c)^2*(39*b^4+39*c^4+2*b*c*(20*b^2+57*b*c+20*c^2))*a^5+(b^2-c^2)^2*(b-c)^3*(3*b^4+3*c^4-2*b*c*(6*b^2+7*b*c+6*c^2))*a^4-(b^2-c^2)^2*(b-c)^2*(17*b^6+17*c^6+(38*b^4+38*c^4+b*c*(95*b^2+84*b*c+95*c^2))*b*c)*a^3+(b^2-c^2)^5*(b+c)*(3*b^2-2*b*c+3*c^2)*a^2+(b^2-c^2)^4*(b+c)^2*(3*b^2+c^2)*(b^2+3*c^2)*a-(b^2-c^2)^6*(b-c)^3)*(a^15+3*(b-c)*a^14-3*(b-c)^2*a^13-(b-c)*(17*b^2+18*b*c+17*c^2)*a^12-(b+3*c)*(3*b+c)*(b-c)^2*a^11+(b-c)*(39*b^4+39*c^4+2*b*c*(30*b^2+29*b*c+30*c^2))*a^10+(25*b^2-38*b*c+25*c^2)*(b^2-c^2)^2*a^9-(b^2-c^2)*(b+c)*(45*b^4+45*c^4-2*b*c*(14*b^2-39*b*c+14*c^2))*a^8-(b^2-c^2)^2*(45*b^4+45*c^4-2*b*c*(36*b^2-35*b*c+36*c^2))*a^7+(b^2-c^2)*(b+c)*(25*b^6+25*c^6-(42*b^4+42*c^4-b*c*(87*b^2-76*b*c+87*c^2))*b*c)*a^6+(b^2-c^2)^2*(b-c)^2*(39*b^4+39*c^4+2*b*c*(20*b^2+57*b*c+20*c^2))*a^5-(b^2-c^2)^2*(b-c)^3*(3*b^4+3*c^4-2*b*c*(6*b^2+7*b*c+6*c^2))*a^4-(b^2-c^2)^2*(b-c)^2*(17*b^6+17*c^6+(38*b^4+38*c^4+b*c*(95*b^2+84*b*c+95*c^2))*b*c)*a^3-(b^2-c^2)^5*(b+c)*(3*b^2-2*b*c+3*c^2)*a^2+(b^2-c^2)^4*(b+c)^2*(3*b^2+c^2)*(b^2+3*c^2)*a+(b^2-c^2)^6*(b-c)^3)*(a^6-2*(b+c)*a^5-(b+c)^2*a^4+4*(b^3+c^3)*a^3-(b^2-c^2)^2*a^2-2*(b^4-c^4)*(b-c)*a+(b^2-c^2)^2*(b+c)^2) : :

X(55836) lies on the cubic K007 and these lines: {2, 46978}, {7, 55832}, {8, 55830}, {20, 3353}, {69, 55831}, {329, 14362}, {5932, 14361}

X(55836) = cyclocevian conjugate of X(34162)
X(55836) = anticomplement of X(46978)
X(55836) = isotomic conjugate of X(55831)
X(55836) = anticomplementary conjugate of X(55837)
X(55836) = cevapoint of X(3354) and X(46979)
X(55836) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1, 55837), (46979, 8)
X(55836) = X(i)-cross conjugate of-X(j) for these (i, j): (4, 5932), (3352, 2)
X(55836) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 55831), (282, 3353), (46978, 46978), (46979, 3472)
X(55836) = X(31)-isoconjugate of-X(55831)
X(55836) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2, 55831), (3341, 3353), (3352, 46978), (3354, 3342), (46979, 3351)
X(55836) = perspector of the inconic with center X(3352)
X(55836) = barycentric product X(3354)*X(47436)
X(55836) = trilinear quotient X(75)/X(55831)

X(55837) = ANTICOMPLEMENT OF X(46979)

Barycentrics    (a+b-c)*(a-b+c)*(a^9+3*(b-c)*a^8-4*(b-c)*(2*b^2+3*b*c+2*c^2)*a^6-6*(b^2-c^2)^2*a^5+2*(b^2-c^2)*(b+c)*(3*b^2+4*b*c+3*c^2)*a^4+8*(b^4-c^4)*(b^2-c^2)*a^3-4*(b^2-c^2)*(b+c)^3*b*c*a^2-(b^2-c^2)^2*(3*b^2+c^2)*(b^2+3*c^2)*a-(b^2-c^2)^3*(b+c)^3)*(a^9-3*(b-c)*a^8+4*(b-c)*(2*b^2+3*b*c+2*c^2)*a^6-6*(b^2-c^2)^2*a^5-2*(b^2-c^2)*(b+c)*(3*b^2+4*b*c+3*c^2)*a^4+8*(b^4-c^4)*(b^2-c^2)*a^3+4*(b^2-c^2)*(b+c)^3*b*c*a^2-(b^2-c^2)^2*(3*b^2+c^2)*(b^2+3*c^2)*a+(b^2-c^2)^3*(b+c)^3)*(a^21+3*(b+c)*a^20-6*(b+c)^2*a^19-2*(b+c)*(13*b^2-18*b*c+13*c^2)*a^18+(9*b^2+2*b*c+9*c^2)*(b+c)^2*a^17+(b+c)*(99*b^4+99*c^4-26*(6*b^2-5*b*c+6*c^2)*b*c)*a^16+8*(3*b^4+3*c^4+4*(b^2-4*b*c+c^2)*b*c)*(b+c)^2*a^15-8*(b^2-c^2)*(b-c)*(27*b^4+27*c^4+4*(7*b^2+15*b*c+7*c^2)*b*c)*a^14-2*(b^2-c^2)^2*(63*b^4+63*c^4+2*b*c*(60*b^2+37*b*c+60*c^2))*a^13+2*(b^2-c^2)*(b-c)*(147*b^6+147*c^6+(302*b^4+302*c^4+b*c*(565*b^2+532*b*c+565*c^2))*b*c)*a^12+4*(b^2-c^2)^2*(63*b^6+63*c^6+(38*b^4+38*c^4+b*c*(61*b^2+188*b*c+61*c^2))*b*c)*a^11-4*(b^2-c^2)*(b-c)*(63*b^8+63*c^8+2*(96*b^6+96*c^6+(172*b^4+172*c^4+3*b*c*(72*b^2+83*b*c+72*c^2))*b*c)*b*c)*a^10-2*(b^2-c^2)^2*(b+c)^2*(147*b^6+147*c^6-(370*b^4+370*c^4-b*c*(709*b^2-684*b*c+709*c^2))*b*c)*a^9+2*(b^2-c^2)^2*(b+c)^3*(63*b^6+63*c^6-(34*b^4+34*c^4-b*c*(169*b^2-76*b*c+169*c^2))*b*c)*a^8+8*(b^2-c^2)^2*(b+c)^2*(27*b^8+27*c^8-2*(42*b^6+42*c^6-(83*b^4+83*c^4-3*b*c*(42*b^2-53*b*c+42*c^2))*b*c)*b*c)*a^7-8*(b^2-c^2)^2*(b+c)^3*(3*b^8+3*c^8-2*(4*b^6+4*c^6-(17*b^4+17*c^4-b*c*(16*b^2-19*b*c+16*c^2))*b*c)*b*c)*a^6-(b^2-c^2)^4*(b-c)^2*(99*b^6+99*c^6+(118*b^4+118*c^4+b*c*(493*b^2+308*b*c+493*c^2))*b*c)*a^5-(b^2-c^2)^5*(b-c)*(9*b^6+9*c^6+(66*b^4+66*c^4+b*c*(71*b^2+92*b*c+71*c^2))*b*c)*a^4+2*(b^2-c^2)^4*(b-c)^2*(13*b^8+13*c^8+2*(18*b^6+18*c^6+(62*b^4+62*c^4+b*c*(78*b^2+119*b*c+78*c^2))*b*c)*b*c)*a^3+2*(b^2-c^2)^6*(b+c)^3*(3*b^4+3*c^4-2*b*c*(2*b-c)*(b-2*c))*a^2-(b^2-c^2)^6*(b+c)^4*(3*b^2+c^2)*(b^2+3*c^2)*a-(b^2-c^2)^9*(b-c)^3) : :

X(55837) lies on the cubic K007 and these lines: {2, 46978}, {4, 41080}, {7, 14365}, {8, 55833}, {189, 1032}, {253, 1034}

X(55837) = anticomplement of X(46979)
X(55837) = isotomic conjugate of the cyclocevian conjugate of X(55831)
X(55837) = anticomplementary conjugate of X(55836)
X(55837) = X(i)-anticomplementary conjugate of-X(j) for these (i, j): (1, 55836), (46978, 8)
X(55837) = X(69)-Ceva conjugate of-X(41080)
X(55837) = X(i)-Dao conjugate of-X(j) for these (i, j): (46978, 3473), (46979, 46979)
X(55837) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3352, 3473), (3472, 3351)



leftri  Centers on the cubic K008: X(55838) - X(55855)  rightri

Centers X(55838)-X(55855) were contributed by César Eliud Lozada, August 12, 2023.

underbar

X(55838) = X(2)X(8877)∩X(67)X(671)

Barycentrics    (a^2+c^2-2*b^2)*(a^2+b^2-2*c^2)*(3*a^12-4*(b^2+c^2)*a^10-(3*b^4-8*b^2*c^2+3*c^4)*a^8+2*(b^2+c^2)*(5*b^4-7*b^2*c^2+5*c^4)*a^6-(b^4+11*b^2*c^2+c^4)*(b^4-b^2*c^2+c^4)*a^4-2*(b^2+c^2)*(3*b^8+3*c^8-7*(b^4-b^2*c^2+c^4)*b^2*c^2)*a^2+(b^4-c^4)^2*(b^2+c^2)^2) : :

X(55838) lies on the cubic K008 and these lines: {2, 8877}, {4, 55851}, {67, 671}, {69, 14364}, {524, 55854}, {2373, 34166}, {7883, 39061}, {55848, 55855}

X(55838) = isotomic conjugate of the antigonal conjugate of X(41498)
X(55838) = X(897)-anticomplementary conjugate of-X(13574)
X(55838) = X(316)-Ceva conjugate of-X(671)
X(55838) = X(10415)-Dao conjugate of-X(67)

X(55839) = X(4)X(13574)∩X(671)X(2373)

Barycentrics    (a^4-c^2*a^2+c^4-b^4)*(a^4-b^2*a^2+b^4-c^4)*(a^16-4*(b^4+c^4)*a^12+6*(b^2+c^2)*b^2*c^2*a^10+(6*b^8+6*c^8-(2*b^4+11*b^2*c^2+2*c^4)*b^2*c^2)*a^8-2*(b^2+c^2)*(5*b^4-9*b^2*c^2+5*c^4)*b^2*c^2*a^6-(4*b^12+4*c^12-(6*b^8+6*c^8+(9*b^4-20*b^2*c^2+9*c^4)*b^2*c^2)*b^2*c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)*(b^2-2*c^2)*(2*b^2-c^2)*b^2*c^2*a^2+(b^8+c^8-4*(b^2-c^2)^2*b^2*c^2)*(b^4-c^4)^2) : :

X(55839) lies on the cubic K008 and these lines: {2, 14364}, {4, 13574}, {671, 2373}, {39157, 55854}, {55848, 55851}

X(55839) = X(897)-anticomplementary conjugate of-X(14364)
X(55839) = X(316)-Ceva conjugate of-X(67)

X(55840) = X(4)X(2373)∩X(14364)X(39157)

Barycentrics    (a^6-(3*b^2+c^2)*a^4-(b^2-c^2)^2*a^2+(b^4-c^4)*(3*b^2-c^2))*(a^6-(b^2+3*c^2)*a^4-(b^2-c^2)^2*a^2+(b^4-c^4)*(b^2-3*c^2))*(a^18+(b^2+c^2)*a^16-(6*b^4+7*b^2*c^2+6*c^4)*a^14-2*(b^2+c^2)*(b^2+3*b*c+c^2)*(b^2-3*b*c+c^2)*a^12+(12*b^8+12*c^8+(3*b^4-26*b^2*c^2+3*c^4)*b^2*c^2)*a^10-4*(b^2+c^2)*(6*b^4-11*b^2*c^2+6*c^4)*b^2*c^2*a^8-(b^2-c^2)^2*(10*b^8+10*c^8+(5*b^4-18*b^2*c^2+5*c^4)*b^2*c^2)*a^6+2*(b^4-c^4)*(b^2-c^2)*(b^8+c^8+5*(b^2-c^2)^2*b^2*c^2)*a^4+(3*b^8+3*c^8-(11*b^4-20*b^2*c^2+11*c^4)*b^2*c^2)*(b^4-c^4)^2*a^2-(b^2+c^2)^3*(b^2-c^2)^6) : :

X(55840) lies on the cubic K008 and these lines: {4, 2373}, {67, 55848}, {13574, 55849}, {14364, 39157}

X(55840) = X(316)-Ceva conjugate of-X(55848)

X(55841) = X(4)X(14364)∩X(67)X(2373)

Barycentrics    (a^6-c^2*a^4-(b^2-c^2)^2*a^2-(b^4-c^4)*c^2)*(a^6-b^2*a^4-(b^2-c^2)^2*a^2+(b^4-c^4)*b^2)*(a^20-4*(b^2+c^2)*a^18+(b^4+16*b^2*c^2+c^4)*a^16+2*(b^2+c^2)*(5*b^4-13*b^2*c^2+5*c^4)*a^14-(8*b^8+8*c^8+(14*b^4-37*b^2*c^2+14*c^4)*b^2*c^2)*a^12-6*(b^2+c^2)*(b^8+c^8-(7*b^4-11*b^2*c^2+7*c^4)*b^2*c^2)*a^10+2*(4*b^12+4*c^12-(9*b^4-16*b^2*c^2+9*c^4)*(b^4+3*b^2*c^2+c^4)*b^2*c^2)*a^8-2*(b^4-c^4)*(b^2-c^2)*(b^8+c^8+(5*b^4-14*b^2*c^2+5*c^4)*b^2*c^2)*a^6-(b^4-c^4)^2*(b^8+c^8-7*(2*b^4-3*b^2*c^2+2*c^4)*b^2*c^2)*a^4+2*(b^4-c^4)^2*(b^2+c^2)*(b^8+c^8-(5*b^4-7*b^2*c^2+5*c^4)*b^2*c^2)*a^2-(b^2+c^2)^4*(b^2-c^2)^6) : :

X(55841) lies on the cubic K008 and these lines: {4, 14364}, {67, 2373}, {13574, 55848}, {55849, 55854}

X(55841) = X(316)-Ceva conjugate of-X(2373)

X(55842) = X(4)X(34164)∩X(524)X(39157)

Barycentrics    (a^6-3*(2*b-c)*(2*b+c)*a^4-3*(3*b^4-10*b^2*c^2-c^4)*a^2+(b^2+c^2)*(2*b^2-3*b*c-c^2)*(2*b^2+3*b*c-c^2))*(a^6+3*(b-2*c)*(b+2*c)*a^4+3*(b^4+10*b^2*c^2-3*c^4)*a^2+(b^2+c^2)*(b^2+3*b*c-2*c^2)*(b^2-3*b*c-2*c^2))*(3*a^8-8*(b^2+c^2)*a^6-2*(b^4-12*b^2*c^2+c^4)*a^4+8*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^2-(b^4-c^4)^2) : :

X(55842) lies on the cubic K008 and these lines: {2, 55850}, {4, 34164}, {67, 55853}, {316, 55849}, {524, 39157}, {2373, 55846}, {14360, 55848}

X(55842) = isotomic conjugate of X(55849)
X(55842) = X(897)-anticomplementary conjugate of-X(55850)
X(55842) = X(316)-Ceva conjugate of-X(55853)
X(55842) = X(2)-Dao conjugate of-X(55849)
X(55842) = X(31)-isoconjugate of-X(55849)
X(55842) = X(2)-reciprocal conjugate of-X(55849)
X(55842) = trilinear quotient X(75)/X(55849)

X(55843) = X(4)X(39157)∩X(2373)X(34164)

Barycentrics    (a^6+(b-3*c)*(b+3*c)*a^4-(b^4-26*b^2*c^2+9*c^4)*a^2-(b^4-c^4)*(b^2+c^2))*(a^6-(3*b-c)*(3*b+c)*a^4-(9*b^4-26*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2+c^2))*(a^12-2*(b^2+c^2)*a^10-((b^2-c^2)^2-4*b^2*c^2)*a^8+4*(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^6-((b^2-c^2)^2-4*b^2*c^2)*(b^4+6*b^2*c^2+c^4)*a^4-2*(b^4-c^4)*(b^2-c^2)*(b^4-8*b^2*c^2+c^4)*a^2+((b^2-c^2)^2-4*b^2*c^2)*(b^4-c^4)^2) : :

X(55843) lies on the cubic K008 and these lines: {2, 55849}, {4, 39157}, {67, 55850}, {524, 55848}, {2373, 34164}, {14364, 55853}

X(55843) = X(897)-anticomplementary conjugate of-X(55849)
X(55843) = X(316)-Ceva conjugate of-X(55850)

X(55844) = X(67)X(13574)∩X(671)X(14364)

Barycentrics    (a^6+(b^2-3*c^2)*a^4-(b^4-5*b^2*c^2+3*c^4)*a^2-(b^4-c^4)*(b^2+c^2))*(a^6-(3*b^2-c^2)*a^4-(3*b^4-5*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2+c^2))*(a^20+2*(b^2+c^2)*a^18-(3*b^4+31*b^2*c^2+3*c^4)*a^16-(b^2+c^2)*(8*b^4-57*b^2*c^2+8*c^4)*a^14+(2*b^8+2*c^8+b^2*c^2*(17*b^4-103*b^2*c^2+17*c^4))*a^12+(b^2+c^2)*(12*b^8+12*c^8-b^2*c^2*(95*b^4-158*b^2*c^2+95*c^4))*a^10+(2*b^12+2*c^12+(47*b^8+47*c^8+b^2*c^2*(56*b^4-149*b^2*c^2+56*c^4))*b^2*c^2)*a^8-(b^2+c^2)*(8*b^12+8*c^12-(15*b^8+15*c^8-b^2*c^2*(116*b^4-199*b^2*c^2+116*c^4))*b^2*c^2)*a^6-(3*b^12+3*c^12+(19*b^8+19*c^8-2*b^2*c^2*(49*b^4-75*b^2*c^2+49*c^4))*b^2*c^2)*(b^2+c^2)^2*a^4+(b^4-c^4)^2*(b^2+c^2)*(2*b^8+2*c^8+b^2*c^2*(23*b^4-30*b^2*c^2+23*c^4))*a^2+(b^4-c^4)^2*(b^2+c^2)^2*(b^8+c^8-2*(5*b^4-7*b^2*c^2+5*c^4)*b^2*c^2)) : :

X(55844) lies on the cubic K008 and these lines: {4, 55854}, {67, 13574}, {671, 14364}, {2373, 55851}

X(55844) = X(316)-Ceva conjugate of-X(13574)

X(55845) = X(67)X(14364)∩X(2373)X(13574)

Barycentrics    (a^8-2*b^2*a^6+(2*b^4+b^2*c^2-2*c^4)*a^4+(b^2-c^2)*(2*b^2-c^2)*b^2*a^2-(b^4-c^4)*(3*b^4-2*b^2*c^2+c^4))*(a^8-2*c^2*a^6-(2*b^4-b^2*c^2-2*c^4)*a^4+(b^2-c^2)*(b^2-2*c^2)*c^2*a^2+(b^4-c^4)*(b^4-2*b^2*c^2+3*c^4))*(5*a^24-10*(b^2+c^2)*a^22-(6*b^4-31*b^2*c^2+6*c^4)*a^20+(b^2+c^2)*(34*b^4-55*b^2*c^2+34*c^4)*a^18-(25*b^8+25*c^8+(52*b^4-89*b^2*c^2+52*c^4)*b^2*c^2)*a^16-4*(b^2+c^2)*(9*b^8+9*c^8-(37*b^4-51*b^2*c^2+37*c^4)*b^2*c^2)*a^14+(60*b^12+60*c^12-(30*b^8+30*c^8+(123*b^4-191*b^2*c^2+123*c^4)*b^2*c^2)*b^2*c^2)*a^12+(b^2+c^2)*(4*b^12+4*c^12-(114*b^8+114*c^8-(292*b^4-371*b^2*c^2+292*c^4)*b^2*c^2)*b^2*c^2)*a^10-(45*b^16+45*c^16-(92*b^12+92*c^12-(7*b^8+7*c^8+(145*b^4-214*b^2*c^2+145*c^4)*b^2*c^2)*b^2*c^2)*b^2*c^2)*a^8+(b^4-c^4)*(b^2-c^2)*(14*b^12+14*c^12+(32*b^8+32*c^8-(62*b^4-83*b^2*c^2+62*c^4)*b^2*c^2)*b^2*c^2)*a^6+(10*b^12+10*c^12-(41*b^8+41*c^8-(73*b^4-76*b^2*c^2+73*c^4)*b^2*c^2)*b^2*c^2)*(b^4-c^4)^2*a^4-(b^4-c^4)^2*(b^2+c^2)*(6*b^12+6*c^12-(17*b^8+17*c^8-2*(11*b^4-9*b^2*c^2+11*c^4)*b^2*c^2)*b^2*c^2)*a^2+(b^4-c^4)^6) : :

X(55845) lies on the cubic K008 and these lines: {67, 14364}, {2373, 13574}, {55848, 55854}

X(55845) = X(316)-Ceva conjugate of-X(14364)

X(55846) = X(67)X(34166)∩X(69)X(13574)

Barycentrics    (a^2+3*c*a+b^2+c^2)*(a^2+3*b*a+b^2+c^2)*(a^2-3*c*a+b^2+c^2)*(a^2-3*b*a+b^2+c^2)*(a^12+4*(b^2+c^2)*a^10+(5*b^4-44*b^2*c^2+5*c^4)*a^8+18*(b^2+c^2)*b^2*c^2*a^6-(5*b^8+5*c^8-b^2*c^2*(34*b^4-57*b^2*c^2+34*c^4))*a^4-2*(b^2+c^2)*(2*b^8+2*c^8+b^2*c^2*(8*b^4-15*b^2*c^2+8*c^4))*a^2-(b^8+c^8-2*b^2*c^2*(7*b^4-12*b^2*c^2+7*c^4))*(b^2+c^2)^2) : :

X(55846) lies on the cubic K008 and these lines: {2, 55851}, {4, 55855}, {67, 34166}, {69, 13574}, {316, 55854}, {671, 34898}, {2373, 55842}, {14364, 34165}

X(55846) = isotomic conjugate of X(55854)
X(55846) = X(897)-anticomplementary conjugate of-X(55851)
X(55846) = X(316)-Ceva conjugate of-X(34166)
X(55846) = X(2)-Dao conjugate of-X(55854)
X(55846) = X(31)-isoconjugate of-X(55854)
X(55846) = X(2)-reciprocal conjugate of-X(55854)
X(55846) = trilinear quotient X(75)/X(55854)

X(55847) = X(4)X(2393)∩X(524)X(2373)

Barycentrics    (a^4-4*c^2*a^2-b^4+c^4)*(a^4-4*b^2*a^2+b^4-c^4)*(a^12-2*(b^2+c^2)*a^10-(b^4-9*b^2*c^2+c^4)*a^8+4*(b^4-c^4)*(b^2-c^2)*a^6-(b^8+c^8+2*b^2*c^2*(3*b^4-5*b^2*c^2+3*c^4))*a^4-2*(b^4-c^4)*(b^2-c^2)^3*a^2+(b^4-3*b^2*c^2+c^4)*(b^4-c^4)^2) : :

X(55847) lies on the cubic K008 and these lines: {2, 55848}, {4, 2393}, {67, 39157}, {524, 2373}, {671, 55849}, {13574, 55850}, {14364, 34164}

X(55847) = X(897)-anticomplementary conjugate of-X(55848)
X(55847) = X(316)-Ceva conjugate of-X(39157)

X(55848) = X(69)X(858)∩X(317)X(671)

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

X(55848) lies on the cubics K008, K1315 and these lines: {2, 55847}, {67, 55840}, {69, 858}, {316, 34165}, {317, 671}, {524, 55843}, {11061, 34166}, {13574, 55841}, {14360, 55842}, {55838, 55855}, {55839, 55851}, {55845, 55854}

X(55848) = isotomic conjugate of X(34165)
X(55848) = isogonal conjugate of X(38532)
X(55848) = X(897)-anticomplementary conjugate of-X(55847)
X(55848) = X(316)-Ceva conjugate of-X(55840)
X(55848) = X(i)-cross conjugate of-X(j) for these (i, j): (67, 55851), (13608, 2)
X(55848) = X(i)-Dao conjugate of-X(j) for these (i, j): (2, 34165), (11147, 7493)
X(55848) = X(31)-isoconjugate of-X(34165)
X(55848) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2, 34165), (1384, 19153), (1992, 7493), (4232, 41370)
X(55848) = perspector of the inconic with center X(13608)
X(55848) = pole of line {19153, 38532} with respect to Stammler hyperbola
X(55848) = pole of line {7493, 34165} with respect to Steiner-Wallace hyperbola
X(55848) = trilinear quotient X(i)/X(j) for these (i, j): (75, 34165), (36277, 19153)

X(55849) = X(69)X(34165)∩X(858)X(34166)

Barycentrics    (a^8-8*b^2*a^6+2*(b^4+8*b^2*c^2-c^4)*a^4+8*(b^2-c^2)*(b^2-2*c^2)*b^2*a^2-(b^4-c^4)*(3*b^4-8*b^2*c^2+c^4))*(a^8-8*c^2*a^6-2*(b^4-8*b^2*c^2-c^4)*a^4+8*(b^2-c^2)*(2*b^2-c^2)*c^2*a^2+(b^4-c^4)*(b^4-8*b^2*c^2+3*c^4))*(4*a^6-9*(b^2+c^2)*a^4-6*(2*b^2-c^2)*(b^2-2*c^2)*a^2+(b^2+c^2)^3) : :

X(55849) lies on the cubic K008 and these lines: {2, 55843}, {69, 34165}, {316, 55842}, {671, 55847}, {858, 34166}, {11061, 55855}, {13574, 55840}, {34163, 55851}, {55841, 55854}

X(55849) = isotomic conjugate of X(55842)
X(55849) = X(897)-anticomplementary conjugate of-X(55843)
X(55849) = X(2)-Dao conjugate of-X(55842)
X(55849) = X(31)-isoconjugate of-X(55842)
X(55849) = X(2)-reciprocal conjugate of-X(55842)
X(55849) = trilinear quotient X(75)/X(55842)

X(55850) = X(69)X(34166)∩X(671)X(34165)

Barycentrics    (a^6+(b-3*c)*(b+3*c)*a^4-(b^4-26*b^2*c^2+9*c^4)*a^2-(b^4-c^4)*(b^2+c^2))*(a^6-(3*b-c)*(3*b+c)*a^4-(9*b^4-26*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2+c^2))*(a^8+4*(b^2+c^2)*a^6+3*(2*b^4-29*b^2*c^2+2*c^4)*a^4+(b^2+c^2)*(4*b^4+53*b^2*c^2+4*c^4)*a^2+(b^4-16*b^2*c^2+c^4)*(b^2+c^2)^2) : :

X(55850) lies on the cubic K008 and these lines: {2, 55842}, {67, 55843}, {69, 34166}, {316, 55855}, {671, 34165}, {858, 55851}, {13574, 55847}, {34163, 55854}

X(55850) = isotomic conjugate of X(55855)
X(55850) = X(897)-anticomplementary conjugate of-X(55842)
X(55850) = X(316)-Ceva conjugate of-X(55843)
X(55850) = X(2)-Dao conjugate of-X(55855)
X(55850) = X(31)-isoconjugate of-X(55855)
X(55850) = X(2)-reciprocal conjugate of-X(55855)
X(55850) = trilinear quotient X(75)/X(55855)

X(55851) = X(524)X(14360)∩X(6093)X(14654)

Barycentrics    (a^6-3*(3*b^2-c^2)*a^4-3*(b^4-3*b^2*c^2-c^4)*a^2+(b^2+c^2)*(7*b^4-10*b^2*c^2+c^4))*(a^6+3*(b^2-3*c^2)*a^4+3*(b^4+3*b^2*c^2-c^4)*a^2+(b^2+c^2)*(b^4-10*b^2*c^2+7*c^4))*(5*a^2-b^2-c^2) : :

X(55851) lies on the cubic K008 and these lines: {2, 55846}, {4, 55838}, {67, 55852}, {69, 55853}, {316, 34164}, {524, 14360}, {858, 55850}, {2373, 55844}, {6093, 14654}, {8182, 34161}, {11061, 39157}, {22100, 52474}, {27088, 38533}, {34163, 55849}, {55839, 55848}

X(55851) = antigonal conjugate of the isogonal conjugate of X(10354)
X(55851) = isogonal conjugate of X(10355)
X(55851) = isotomic conjugate of X(34164)
X(55851) = cevapoint of X(1499) and X(31654)
X(55851) = X(897)-anticomplementary conjugate of-X(55846)
X(55851) = X(316)-Ceva conjugate of-X(55852)
X(55851) = X(i)-cross conjugate of-X(j) for these (i, j): (67, 55848), (34581, 2)
X(55851) = X(2)-Dao conjugate of-X(34164)
X(55851) = X(31)-isoconjugate of-X(34164)
X(55851) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (2, 34164), (38533, 6)
X(55851) = perspector of the inconic with center X(34581)
X(55851) = pole of line {10355, 34164} with respect to Steiner-Wallace hyperbola
X(55851) = barycentric product X(76)*X(38533)
X(55851) = trilinear product X(75)*X(38533)
X(55851) = trilinear quotient X(i)/X(j) for these (i, j): (75, 34164), (38533, 31)

X(55852) = X(671)X(13574)∩X(14364)X(34166)

Barycentrics    (a^6-3*(3*b^2-c^2)*a^4-3*(b^4-3*b^2*c^2-c^4)*a^2+(b^2+c^2)*(7*b^4-10*b^2*c^2+c^4))*(a^6+3*(b^2-3*c^2)*a^4+3*(b^4+3*b^2*c^2-c^4)*a^2+(b^2+c^2)*(b^4-10*b^2*c^2+7*c^4))*(9*a^18-11*(b^2+c^2)*a^16-(54*b^4-67*b^2*c^2+54*c^4)*a^14+2*(b^2+c^2)*(7*b^4+37*b^2*c^2+7*c^4)*a^12+(80*b^8+80*c^8-b^2*c^2*(127*b^4+171*b^2*c^2+127*c^4))*a^10-(b^2+c^2)*(12*b^8+12*c^8+11*b^2*c^2*(8*b^4-23*b^2*c^2+8*c^4))*a^8-(50*b^12+50*c^12-(101*b^8+101*c^8+5*b^2*c^2*(5*b^2-3*b*c-5*c^2)*(5*b^2+3*b*c-5*c^2))*b^2*c^2)*a^6+(b^2+c^2)*(10*b^12+10*c^12+(18*b^8+18*c^8-b^2*c^2*(261*b^4-434*b^2*c^2+261*c^4))*b^2*c^2)*a^4+(15*b^12+15*c^12-(71*b^8+71*c^8-b^2*c^2*(229*b^4-342*b^2*c^2+229*c^4))*b^2*c^2)*(b^2+c^2)^2*a^2-(b^2-c^2)^2*(b^2+c^2)^7) : :

X(55852) lies on the cubic K008 and these lines: {2, 55854}, {67, 55851}, {671, 13574}, {2373, 55855}, {14364, 34166}

X(55852) = X(897)-anticomplementary conjugate of-X(55854)
X(55852) = X(316)-Ceva conjugate of-X(55851)

X(55853) = X(671)X(34166)∩X(13574)X(34165)

Barycentrics    (a^6-3*(2*b-c)*(2*b+c)*a^4-3*(3*b^4-10*b^2*c^2-c^4)*a^2+(b^2+c^2)*(2*b^2-3*b*c-c^2)*(2*b^2+3*b*c-c^2))*(a^6+3*(b-2*c)*(b+2*c)*a^4+3*(b^4+10*b^2*c^2-3*c^4)*a^2+(b^2+c^2)*(b^2+3*b*c-2*c^2)*(b^2-3*b*c-2*c^2))*(5*a^12-12*(b^2+c^2)*a^10-9*(5*b^4-8*b^2*c^2+5*c^4)*a^8-2*(b^2+c^2)*(7*b^4-67*b^2*c^2+7*c^4)*a^6+3*(b^4-b^2*c^2-11*c^4)*(11*b^4+b^2*c^2-c^4)*a^4+18*(b^2+c^2)*(b^8+c^8-5*(b^4-3*b^2*c^2+c^4)*b^2*c^2)*a^2-(b^2+c^2)^6) : :

X(55853) lies on the cubic K008 and these lines: {2, 55855}, {67, 55842}, {69, 55851}, {671, 34166}, {858, 55854}, {13574, 34165}, {14364, 55843}

X(55853) = X(897)-anticomplementary conjugate of-X(55855)
X(55853) = X(316)-Ceva conjugate of-X(55842)

X(55854) = X(11061)X(34164)∩X(14360)X(23106)

Barycentrics    (a^12+4*(b^2-3*c^2)*a^10+(5*b^4+20*b^2*c^2-3*c^4)*a^8-2*(17*b^2-10*c^2)*(b^2+c^2)*c^2*a^6-(5*b^8+3*c^8+(18*b^4-57*b^2*c^2+14*c^4)*b^2*c^2)*a^4-2*(b^2+c^2)*(2*b^8+6*c^8-b^2*c^2*(24*b^4-33*b^2*c^2+16*c^4))*a^2-(b^2-c^2)*(b^2+c^2)^5)*(a^12-4*(3*b^2-c^2)*a^10-(3*b^4-20*b^2*c^2-5*c^4)*a^8+2*(10*b^2-17*c^2)*(b^2+c^2)*b^2*a^6-(3*b^8+5*c^8+b^2*c^2*(14*b^4-57*b^2*c^2+18*c^4))*a^4-2*(b^2+c^2)*(6*b^8+2*c^8-b^2*c^2*(16*b^4-33*b^2*c^2+24*c^4))*a^2+(b^2-c^2)*(b^2+c^2)^5)*(a^2+b^2+3*b*c+c^2)*(a^2+b^2-3*b*c+c^2) : :

X(55854) lies on the cubic K008 and these lines: {2, 55852}, {4, 55844}, {316, 55846}, {524, 55838}, {858, 55853}, {11061, 34164}, {14360, 23106}, {34163, 55850}, {39157, 55839}, {55841, 55849}, {55845, 55848}

X(55854) = isotomic conjugate of X(55846)
X(55854) = X(897)-anticomplementary conjugate of-X(55852)
X(55854) = X(67)-cross conjugate of-X(39157)
X(55854) = X(2)-Dao conjugate of-X(55846)
X(55854) = X(31)-isoconjugate of-X(55846)
X(55854) = X(2)-reciprocal conjugate of-X(55846)
X(55854) = trilinear quotient X(75)/X(55846)

X(55855) = X(524)X(13492)∩X(14360)X(39157)

Barycentrics    (a^8+2*(2*b^2-7*c^2)*a^6+3*(b^2+10*c^2)*(2*b^2-c^2)*a^4+(4*b^6-14*c^6-3*b^2*c^2*(29*b^2-19*c^2))*a^2+(b^2+c^2)^4)*(a^8-2*(7*b^2-2*c^2)*a^6-3*(10*b^2+c^2)*(b^2-2*c^2)*a^4-(14*b^6-4*c^6-3*b^2*c^2*(19*b^2-29*c^2))*a^2+(b^2+c^2)^4)*(a^6+(b^2+c^2)*a^4-(b^4+26*b^2*c^2+c^4)*a^2-(b^2+c^2)*(b^4-10*b^2*c^2+c^4)) : :

X(55855) lies on the cubic K008 and these lines: {2, 55853}, {4, 55846}, {316, 55850}, {524, 13492}, {2373, 55852}, {11061, 55849}, {14360, 39157}, {55838, 55848}

X(55855) = isotomic conjugate of X(55850)
X(55855) = X(897)-anticomplementary conjugate of-X(55853)
X(55855) = X(2)-Dao conjugate of-X(55850)
X(55855) = X(31)-isoconjugate of-X(55850)
X(55855) = X(2)-reciprocal conjugate of-X(55850)
X(55855) = trilinear quotient X(75)/X(55850)

X(55856) = X(2)X(3)∩X(6)X(10194)

Barycentrics    8*Cos[A]*Sin[A] + 5*Sin[2*B] + 5*Sin[2*C] : :
Barycentrics    4*a^4 - 9*a^2*b^2 + 5*b^4 - 9*a^2*c^2 - 10*b^2*c^2 + 5*c^4 : :
X(55856) = 15 X[2] - X[3], 27 X[2] + X[4], 6 X[2] + X[5], 57 X[2] - X[20], 9 X[2] - 2 X[140], 29 X[2] - X[376], 13 X[2] + X[381], 69 X[2] + X[382], 33 X[2] + 2 X[546], 5 X[2] + 2 X[547], 51 X[2] - 2 X[548], 8 X[2] - X[549], 36 X[2] - X[550], 33 X[2] - 5 X[631], 12 X[2] - 5 X[632], 9 X[2] + 5 X[1656], 99 X[2] - X[1657], 3 X[2] + X[3090], 51 X[2] + 5 X[3091], and many others

X(55856) lies on these lines: {2, 3}, {6, 10194}, {10, 10283}, {12, 37587}, {15, 42949}, {16, 42948}, {17, 10187}, {18, 10188}, {39, 12815}, {51, 13421}, {52, 32205}, {61, 43199}, {62, 43200}, {83, 10185}, {141, 5097}, {143, 373}, {156, 43650}, {182, 51127}, {195, 15018}, {233, 6749}, {252, 40634}, {265, 22251}, {355, 30315}, {395, 42488}, {396, 42489}, {397, 16966}, {398, 16967}, {399, 13393}, {511, 51128}, {517, 51073}, {542, 51181}, {551, 38081}, {568, 11465}, {569, 40111}, {575, 48310}, {576, 20582}, {590, 19116}, {597, 50986}, {599, 51183}, {615, 8960}, {620, 38229}, {625, 38230}, {952, 3624}, {1001, 38170}, {1007, 32883}, {1125, 1483}, {1131, 6408}, {1132, 6407}, {1147, 16187}, {1216, 6688}, {1353, 3589}, {1385, 10172}, {1482, 19877}, {1484, 6667}, {1487, 21975}, {1503, 42786}, {1506, 3054}, {1698, 5901}, {3055, 7746}, {3068, 13993}, {3069, 13925}, {3070, 6481}, {3071, 6480}, {3316, 6418}, {3317, 6417}, {3519, 8254}, {3564, 47355}, {3579, 10171}, {3590, 7581}, {3591, 7582}, {3592, 42603}, {3594, 42602}, {3619, 34380}, {3634, 5690}, {3636, 38176}, {3653, 37714}, {3763, 5102}, {3815, 5041}, {3816, 20104}, {3819, 10263}, {3826, 38043}, {3828, 10222}, {3833, 5694}, {3844, 38040}, {3917, 10095}, {3933, 37647}, {3968, 10284}, {4423, 32141}, {4698, 51046}, {4755, 51047}, {4857, 5432}, {5219, 34753}, {5270, 5433}, {5305, 31489}, {5318, 42793}, {5321, 42794}, {5326, 7741}, {5339, 42092}, {5340, 42089}, {5343, 42116}, {5344, 42115}, {5349, 10645}, {5350, 10646}, {5351, 42501}, {5352, 42500}, {5418, 6437}, {5420, 6438}, {5439, 31835}, {5447, 15082}, {5461, 51524}, {5462, 15067}, {5493, 9955}, {5550, 5790}, {5562, 13363}, {5609, 45311}, {5640, 14449}, {5642, 20396}, {5650, 10627}, {5651, 32046}, {5734, 38066}, {5844, 9780}, {5876, 5892}, {5882, 9956}, {5886, 11531}, {5891, 12006}, {5907, 45956}, {5943, 6101}, {5946, 10219}, {6070, 18285}, {6102, 10170}, {6118, 45872}, {6119, 45871}, {6243, 11451}, {6247, 14862}, {6425, 43254}, {6426, 43255}, {6429, 35255}, {6430, 35256}, {6431, 7584}, {6432, 7583}, {6433, 42274}, {6434, 42277}, {6445, 23275}, {6446, 23269}, {6447, 43413}, {6448, 31414}, {6451, 23263}, {6452, 23253}, {6482, 41945}, {6483, 41946}, {6486, 6565}, {6487, 6564}, {6496, 52666}, {6497, 52667}, {6666, 38171}, {6683, 32448}, {6684, 38034}, {6689, 36966}, {6721, 11623}, {6722, 38735}, {6723, 10264}, {7294, 7951}, {7607, 43527}, {7608, 10159}, {7749, 18907}, {7752, 14929}, {7762, 17006}, {7764, 9771}, {7768, 37688}, {7769, 32820}, {7780, 15597}, {7781, 12040}, {7808, 44381}, {7815, 32134}, {7821, 11168}, {7867, 20576}, {7869, 44377}, {7886, 15491}, {7988, 40273}, {7989, 28186}, {8151, 10189}, {8550, 24206}, {8976, 32786}, {8981, 10577}, {9342, 11849}, {9624, 19876}, {9681, 43433}, {9705, 46865}, {9729, 15060}, {9730, 14128}, {9781, 44299}, {9786, 33540}, {10110, 54042}, {10173, 31744}, {10175, 31662}, {10182, 41362}, {10190, 10280}, {10192, 32767}, {10193, 51491}, {10198, 32214}, {10200, 32213}, {10247, 46933}, {10272, 15059}, {10539, 22112}, {10576, 13966}, {10589, 15172}, {10595, 46931}, {10610, 43586}, {10619, 13565}, {10625, 13364}, {10738, 26060}, {10992, 31274}, {10993, 31235}, {11017, 11381}, {11231, 22791}, {11272, 31239}, {11362, 50822}, {11480, 42920}, {11481, 42921}, {11482, 21356}, {11488, 42628}, {11489, 42627}, {11522, 19872}, {11542, 42149}, {11543, 42152}, {11614, 53418}, {11698, 20418}, {11801, 38794}, {12002, 15644}, {12046, 14845}, {12161, 17825}, {12242, 13567}, {12245, 46930}, {12645, 46934}, {12900, 20417}, {13372, 25147}, {13392, 38724}, {13411, 15935}, {13451, 37484}, {13571, 17005}, {13582, 48155}, {13846, 43885}, {13847, 43886}, {13886, 13961}, {13903, 13939}, {13951, 32785}, {14483, 26861}, {14643, 40685}, {14677, 36518}, {14693, 31275}, {14762, 34510}, {14848, 51214}, {14864, 23332}, {14971, 38751}, {15024, 16881}, {15028, 18436}, {15048, 31455}, {15058, 40280}, {15068, 15805}, {15088, 38793}, {15092, 38748}, {15178, 19883}, {15580, 23300}, {15602, 39565}, {15806, 43866}, {16192, 28182}, {16241, 41971}, {16242, 41972}, {16644, 42590}, {16645, 42591}, {16768, 38429}, {16772, 37835}, {16773, 37832}, {16808, 42907}, {16809, 42906}, {16962, 42592}, {16963, 42593}, {16964, 43101}, {16965, 43104}, {18357, 54447}, {18362, 31457}, {18553, 44516}, {18581, 42923}, {18582, 42922}, {18841, 53859}, {18874, 45186}, {19860, 19907}, {20107, 25466}, {20190, 47354}, {20195, 38111}, {20252, 36770}, {20299, 44762}, {20304, 30714}, {20379, 38795}, {20399, 49102}, {20414, 35885}, {20415, 48311}, {20416, 48312}, {20424, 32396}, {20575, 31237}, {20583, 51182}, {21401, 48313}, {21402, 48314}, {22165, 22330}, {22236, 42910}, {22238, 42911}, {22247, 38734}, {22331, 31417}, {23237, 34837}, {23515, 34153}, {24470, 31231}, {24953, 31263}, {25440, 52795}, {25502, 37698}, {25681, 38045}, {26921, 51780}, {28174, 31423}, {28194, 50826}, {30308, 31425}, {31188, 37545}, {31401, 43291}, {31415, 44535}, {31657, 38318}, {31658, 38137}, {31834, 37481}, {32140, 54012}, {32817, 32898}, {32818, 32897}, {32821, 32832}, {32825, 32867}, {32871, 52713}, {32904, 35728}, {33416, 42118}, {33417, 42117}, {33545, 46266}, {33814, 38319}, {34573, 37517}, {35719, 44914}, {35812, 43880}, {35813, 43879}, {35814, 42558}, {35815, 42557}, {35822, 41968}, {35823, 41967}, {36153, 41597}, {36836, 43417}, {36843, 43416}, {37471, 43598}, {37476, 51933}, {37509, 37687}, {37680, 45931}, {37734, 43731}, {38083, 50824}, {40693, 42634}, {40694, 42633}, {41121, 43100}, {41122, 43107}, {41943, 42953}, {41944, 42952}, {41953, 41963}, {41954, 41964}, {41975, 42647}, {41976, 42648}, {42085, 42773}, {42086, 42774}, {42095, 42150}, {42098, 42151}, {42107, 42432}, {42110, 42431}, {42111, 42122}, {42114, 42123}, {42126, 42776}, {42127, 42775}, {42129, 42999}, {42130, 42473}, {42131, 42472}, {42132, 42998}, {42135, 42157}, {42138, 42158}, {42144, 42918}, {42145, 42919}, {42147, 42580}, {42148, 42581}, {42153, 42912}, {42156, 42913}, {42159, 42490}, {42162, 42491}, {42268, 42600}, {42269, 42601}, {42433, 42595}, {42434, 42594}, {42568, 43523}, {42569, 43524}, {42598, 42992}, {42599, 42993}, {42684, 42798}, {42685, 42797}, {42813, 43244}, {42814, 43245}, {42815, 43464}, {42816, 43463}, {42873, 53025}, {42904, 43294}, {42905, 43295}, {42950, 43198}, {42951, 43197}, {42956, 43010}, {42957, 43011}, {43014, 43027}, {43015, 43026}, {43018, 43031}, {43019, 43030}, {43246, 43424}, {43247, 43425}, {43328, 43440}, {43329, 43441}, {43442, 43773}, {43443, 43774}, {43467, 43776}, {43468, 43775}, {43505, 43890}, {43506, 43889}, {45310, 51525}, {51027, 53093}, {51186, 53858}

X(55856) = midpoint of X(i) and X(j) for these {i,j}: {2, 15703}, {3, 3832}, {5, 14869}, {140, 44904}, {381, 15698}, {3090, 3526}, {3523, 3851}, {3857, 44682}, {15700, 41106}
X(55856) = reflection of X(i) in X(j) for these {i,j}: {5, 3090}, {3523, 140}, {3830, 45762}, {3851, 44904}, {3857, 5}, {8703, 15700}, {14869, 3526}, {19711, 15702}, {44682, 14869}
X(55856) = complement of X(3526)
X(55856) = orthocentroidal-circle-inverse of X(46219)
X(55856) = polar conjugate of X(54791)
X(55856) = X(48)-isoconjugate of X(54791)
X(55856) = X(1249)-Dao conjugate of X(54791)
X(55856) = barycentric quotient X(4)/X(54791)
X(55856) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 16239}, {2, 4, 46219}, {2, 5, 632}, {2, 381, 47598}, {2, 547, 11539}, {2, 1656, 140}, {2, 3090, 3526}, {2, 3545, 15723}, {2, 3628, 5}, {2, 5055, 10124}, {2, 5056, 3533}, {2, 5067, 3}, {2, 5070, 3628}, {2, 7486, 3525}, {2, 7504, 13747}, {2, 15694, 41984}, {2, 15699, 549}, {2, 16239, 41992}, {2, 16922, 7807}, {2, 32975, 32954}, {2, 32976, 7866}, {2, 32998, 11285}, {2, 32999, 33233}, {2, 33249, 8362}, {2, 33270, 33003}, {2, 46935, 4}, {2, 46936, 631}, {3, 5, 3845}, {3, 381, 33703}, {3, 547, 5}, {3, 631, 41983}, {3, 1656, 5056}, {3, 3526, 15702}, {3, 3533, 140}, {3, 3545, 3853}, and many other

X(55857) = X(2)X(3)∩X(17)X(42610)

Barycentrics    5*Sin[2*A] + 6*Sin[2*B] + 6*Sin[2*C] : :
Barycentrics    5*a^4 - 11*a^2*b^2 + 6*b^4 - 11*a^2*c^2 - 12*b^2*c^2 + 6*c^4 : :
X(55857) = 18 X[2] - X[3], 33 X[2] + X[4], 15 X[2] + 2 X[5], 69 X[2] - X[20], 21 X[2] - 4 X[140], 35 X[2] - X[376], 16 X[2] + X[381], 84 X[2] + X[382], 81 X[2] + 4 X[546], 13 X[2] + 4 X[547], 123 X[2] - 4 X[548], 19 X[2] - 2 X[549], 87 X[2] - 2 X[550], 39 X[2] - 5 X[631], 27 X[2] - 10 X[632], 12 X[2] + 5 X[1656], 120 X[2] - X[1657], and many others

X(55857) lies on these lines: {2, 3}, {17, 42610}, {18, 42611}, {61, 42129}, {62, 42132}, {141, 11482}, {195, 10601}, {355, 19878}, {373, 6243}, {389, 12045}, {399, 6723}, {517, 19872}, {569, 16187}, {575, 47355}, {576, 3763}, {590, 6427}, {597, 51175}, {599, 22330}, {615, 6428}, {1125, 12645}, {1154, 11465}, {1173, 53124}, {1216, 13321}, {1351, 34573}, {1352, 51127}, {1482, 3634}, {1511, 15025}, {1649, 10280}, {1698, 10222}, {1853, 50414}, {2979, 16982}, {3054, 30435}, {3055, 9605}, {3070, 6522}, {3071, 6519}, {3304, 31479}, {3311, 32789}, {3312, 32790}, {3411, 10187}, {3412, 10188}, {3589, 11898}, {3592, 10577}, {3594, 10576}, {3619, 5093}, {3622, 51515}, {3624, 5790}, {3653, 50797}, {3828, 50805}, {3933, 32867}, {3934, 32520}, {5007, 37637}, {5050, 51126}, {5085, 42786}, {5206, 11614}, {5237, 42098}, {5238, 42095}, {5339, 43305}, {5340, 43304}, {5351, 42127}, {5352, 42126}, {5418, 6447}, {5420, 6448}, {5446, 54047}, {5544, 37493}, {5550, 37624}, {5609, 15059}, {5640, 32142}, {5650, 37484}, {5651, 13353}, {5844, 46932}, {5881, 38083}, {5886, 51073}, {5891, 15012}, {5901, 19877}, {5972, 15027}, {6101, 11451}, {6221, 42566}, {6398, 42567}, {6407, 42561}, {6408, 31412}, {6417, 32785}, {6418, 32786}, {6419, 8253}, {6420, 8252}, {6425, 13785}, {6426, 13665}, {6449, 42274}, {6450, 42277}, {6451, 42268}, {6452, 42269}, {6453, 42262}, {6454, 42265}, {6455, 42270}, {6456, 42273}, {6496, 42283}, {6497, 42284}, {6500, 8972}, {6501, 13925}, {6667, 12331}, {6683, 13108}, {6688, 54048}, {6689, 21968}, {6699, 15046}, {6721, 12188}, {6722, 13188}, {7603, 44535}, {7746, 31467}, {7749, 15484}, {7758, 9771}, {7772, 31489}, {7786, 32519}, {7858, 8860}, {7886, 15850}, {7982, 11230}, {7988, 48661}, {7991, 11231}, {7998, 10095}, {7999, 15026}, {8167, 37621}, {8981, 45385}, {9624, 34718}, {9641, 9817}, {9703, 43651}, {9730, 40247}, {9780, 10247}, {9781, 33879}, {9956, 18526}, {10170, 37481}, {10194, 32787}, {10195, 32788}, {10219, 16625}, {10246, 19862}, {10283, 46933}, {10516, 20190}, {10541, 18440}, {10595, 46930}, {10620, 12900}, {10625, 15082}, {10627, 44299}, {10653, 42948}, {10654, 42949}, {11017, 12279}, {11258, 38807}, {11412, 32205}, {11423, 26869}, {11432, 47296}, {11444, 13363}, {11477, 38317}, {11480, 42963}, {11481, 42962}, {11485, 42599}, {11486, 42598}, {11488, 42590}, {11489, 42591}, {11591, 15028}, {11695, 18436}, {11801, 38638}, {11999, 43601}, {12295, 15042}, {12307, 32396}, {12308, 40685}, {12355, 22247}, {12429, 43839}, {12902, 15020}, {13464, 38066}, {13881, 53096}, {13966, 45384}, {14023, 15597}, {14061, 51524}, {14128, 15045}, {14530, 23332}, {14561, 51128}, {14627, 15066}, {14643, 20397}, {14848, 40107}, {14926, 37475}, {14978, 52147}, {15024, 15067}, {15029, 38789}, {15034, 20304}, {15040, 23515}, {15041, 38791}, {15044, 15088}, {15047, 17825}, {15054, 34128}, {15057, 38626}, {15561, 20398}, {15805, 43845}, {16001, 36770}, {16189, 19876}, {16644, 42489}, {16645, 42488}, {16772, 42910}, {16773, 42911}, {16964, 42997}, {16965, 42996}, {16966, 22238}, {16967, 22236}, {18350, 43650}, {18525, 30389}, {18543, 34486}, {19106, 42499}, {19107, 42498}, {19883, 37727}, {20399, 38224}, {20582, 50962}, {20791, 45958}, {21309, 31404}, {21358, 25555}, {22112, 37471}, {22234, 47352}, {22332, 31455}, {23302, 42818}, {23303, 42817}, {24206, 39899}, {24470, 31188}, {24844, 40480}, {25563, 48672}, {26446, 31253}, {28204, 30315}, {31272, 51525}, {31273, 51526}, {31274, 38734}, {31399, 50798}, {31454, 42603}, {31859, 50570}, {32046, 46865}, {32609, 36253}, {32883, 34803}, {32898, 52713}, {33416, 36843}, {33417, 36836}, {34126, 38669}, {34127, 38664}, {34754, 43467}, {34755, 43468}, {36969, 42774}, {36970, 42773}, {37532, 51780}, {37640, 42984}, {37641, 42985}, {37679, 45931}, {37832, 43239}, {37835, 43238}, {38064, 50954}, {38068, 50806}, {38112, 46931}, {38319, 38762}, {38572, 38775}, {38573, 38787}, {38627, 48657}, {39601, 44519}, {41347, 41872}, {42089, 42166}, {42092, 42163}, {42107, 43780}, {42110, 43779}, {42111, 42164}, {42114, 42165}, {42115, 42162}, {42116, 42159}, {42150, 43101}, {42151, 43104}, {42153, 42936}, {42156, 42937}, {42157, 42596}, {42158, 42597}, {42160, 42692}, {42161, 42693}, {42215, 42571}, {42216, 42570}, {42492, 42628}, {42493, 42627}, {42508, 43422}, {42509, 43423}, {42600, 43796}, {42601, 43795}, {42797, 42891}, {42798, 42890}, {42813, 43646}, {42814, 43645}, {42916, 42987}, {42917, 42986}, {42964, 43241}, {42965, 43240}, {42978, 49948}, {42979, 49947}, {42982, 43198}, {42983, 43197}, {43342, 43888}, {43343, 43887}, {43428, 43878}, {43429, 43877}, {43483, 43776}, {43484, 43775}, {50800, 51080}, {50957, 51135}, {50970, 51173}

X(55857) = midpoint of X(3533) and X(7486)
X(55857) = reflection of X(3854) in X(5)
X(55857) = complement of X(3533)
X(55857) = orthocentroidal-circle-inverse of X(16239)
X(55857) = X(54893)-complementary conjugate of X(20305)
X(55857) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 16239}, {2, 5, 46219}, {2, 1656, 3526}, {2, 3090, 632}, {2, 3628, 3}, {2, 5055, 15723}, {2, 5067, 140}, {2, 5070, 1656}, {2, 5071, 47598}, {2, 7486, 3533}, {2, 15699, 15694}, {2, 15702, 41984}, {2, 15703, 5054}, {2, 16922, 33233}, {2, 32958, 8364}, {2, 32976, 8362}, {2, 46935, 631}, {2, 46936, 3525}, {2, 47599, 15703}, {3, 381, 49136}, {3, 546, 49137}, {3, 1656, 5079}, {3, 3090, 5072}, {3, 3091, 382}, {3, 3525, 5054}, {3, 3627, 3534}, {3, 3628, 1656}, {3, 3830, 12103}, {3, 3843, 3529}, {3, 3851, 3627}, {3, 5055, 3091}, {3, 5070, 3628}, {3, 5072, 5076}, and many others

X(55858) = X(2)X(3)∩X(6)X(43370)

Barycentrics    7*Sin[2*A] + 6*Sin[2*B] + 6*Sin[2*C] : :
Barycentrics    7*a^4 - 13*a^2*b^2 + 6*b^4 - 13*a^2*c^2 - 12*b^2*c^2 + 6*c^4 : :
X(55858) = 18 X[2] + X[3], 39 X[2] - X[4], 21 X[2] - 2 X[5], 75 X[2] + X[20], 15 X[2] + 4 X[140], 37 X[2] + X[376], 20 X[2] - X[381], 96 X[2] - X[382], 99 X[2] - 4 X[546], 23 X[2] - 4 X[547], 129 X[2] + 4 X[548], 17 X[2] + 2 X[549], 93 X[2] + 2 X[550], 33 X[2] + 5 X[631], 9 X[2] + 10 X[632], 24 X[2] - 5 X[1656], 132 X[2] + X[1657], and many others

X(55858) lies on these lines: {2, 3}, {6, 43370}, {13, 42597}, {14, 42596}, {15, 42951}, {16, 42950}, {32, 11614}, {52, 15082}, {61, 42818}, {62, 42817}, {125, 15039}, {141, 53092}, {195, 17811}, {355, 31253}, {373, 37484}, {394, 15047}, {397, 42595}, {398, 42594}, {399, 20397}, {485, 6448}, {486, 6447}, {569, 11935}, {575, 3763}, {576, 47355}, {590, 6428}, {597, 51174}, {599, 22234}, {615, 6427}, {999, 7294}, {1209, 22333}, {1350, 42785}, {1351, 51126}, {1385, 19872}, {1482, 19862}, {1483, 46932}, {1506, 22331}, {1698, 12645}, {2979, 32205}, {3054, 9605}, {3055, 30435}, {3295, 5326}, {3311, 32790}, {3312, 32789}, {3398, 15850}, {3411, 49905}, {3412, 49906}, {3582, 31480}, {3589, 11482}, {3592, 13951}, {3594, 8976}, {3619, 53091}, {3624, 10222}, {3634, 10246}, {3653, 31399}, {3828, 50804}, {3934, 32519}, {5007, 31489}, {5050, 34573}, {5237, 42128}, {5238, 42125}, {5309, 31470}, {5351, 42098}, {5352, 42095}, {5355, 31455}, {5418, 18510}, {5420, 18512}, {5462, 54048}, {5493, 50806}, {5550, 10247}, {5563, 31479}, {5587, 31666}, {5640, 16982}, {5646, 37486}, {5650, 6243}, {5651, 37471}, {5892, 45187}, {6053, 15061}, {6101, 11465}, {6147, 31188}, {6221, 53516}, {6390, 32867}, {6398, 53513}, {6407, 18762}, {6408, 18538}, {6417, 32786}, {6418, 32785}, {6419, 8252}, {6420, 8253}, {6425, 10577}, {6426, 10576}, {6445, 42561}, {6446, 31412}, {6449, 42583}, {6450, 42582}, {6451, 42270}, {6452, 42273}, {6453, 13785}, {6454, 13665}, {6455, 42274}, {6456, 42277}, {6496, 42268}, {6497, 42269}, {6500, 13941}, {6501, 8972}, {6519, 41953}, {6522, 41954}, {6688, 54047}, {6723, 15027}, {7585, 43506}, {7586, 43505}, {7746, 22332}, {7758, 15597}, {7772, 31467}, {7786, 32520}, {7982, 11231}, {7991, 11230}, {7998, 15026}, {7999, 13363}, {8167, 11849}, {9540, 45385}, {9691, 23273}, {9771, 14023}, {9780, 37624}, {9956, 30389}, {10194, 31454}, {10195, 41968}, {10541, 24206}, {10627, 11451}, {10645, 43782}, {10646, 43781}, {11426, 47296}, {11480, 42580}, {11481, 42581}, {11695, 23039}, {12041, 15029}, {12045, 15644}, {12188, 20399}, {12331, 31235}, {12773, 20400}, {12815, 31457}, {12900, 15041}, {12902, 15025}, {13108, 31239}, {13188, 20398}, {13336, 16187}, {13353, 22112}, {13847, 31487}, {13881, 31652}, {13886, 43881}, {13935, 45384}, {13939, 43882}, {14094, 34128}, {14643, 38729}, {15012, 18436}, {15020, 20304}, {15021, 38789}, {15024, 32142}, {15028, 15067}, {15034, 38724}, {15046, 38728}, {15081, 38638}, {15087, 15805}, {15484, 35007}, {15513, 18584}, {15561, 38740}, {16189, 34718}, {16644, 42592}, {16645, 42593}, {16772, 43774}, {16773, 43773}, {16966, 36843}, {16967, 36836}, {18440, 20190}, {18493, 31423}, {18526, 51073}, {19877, 38028}, {19878, 26446}, {20401, 38574}, {20415, 36770}, {20582, 50961}, {21401, 40334}, {21402, 40335}, {22236, 33417}, {22238, 33416}, {22330, 47352}, {23235, 34127}, {26958, 37505}, {30531, 54202}, {31447, 38021}, {34126, 38665}, {34754, 42613}, {34755, 42612}, {34780, 50414}, {34783, 40247}, {36253, 38794}, {37612, 51780}, {37682, 45931}, {37832, 41972}, {37835, 41971}, {38064, 50958}, {38066, 51077}, {38068, 51075}, {38079, 51172}, {38083, 50797}, {38112, 46934}, {38224, 38751}, {38317, 53097}, {38734, 38750}, {38739, 38745}, {39899, 51128}, {40107, 50962}, {40693, 42948}, {40694, 42949}, {41943, 42978}, {41944, 42979}, {41963, 42603}, {41964, 42602}, {42089, 42598}, {42092, 42599}, {42115, 42166}, {42116, 42163}, {42121, 42590}, {42124, 42591}, {42130, 42914}, {42131, 42915}, {42143, 43772}, {42146, 43771}, {42150, 42500}, {42151, 42501}, {42153, 43776}, {42156, 43775}, {42160, 42963}, {42161, 42962}, {42488, 42974}, {42489, 42975}, {42522, 43517}, {42523, 43518}, {42627, 43464}, {42628, 43463}, {42773, 42814}, {42774, 42813}, {42786, 53094}, {42797, 43244}, {42798, 43245}, {42892, 43025}, {42893, 43024}, {42910, 42945}, {42911, 42944}, {42932, 43557}, {42933, 43556}, {42946, 43467}, {42947, 43468}, {42986, 43198}, {42987, 43197}, {43479, 43543}, {43480, 43542}, {46933, 51515}

X(55858) = orthocentroidal-circle-inverse of X(48154)
X(55858) = X(54892)-complementary conjugate of X(20305)
X(55858) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 48154}, {2, 140, 5070}, {2, 632, 3}, {2, 3525, 3628}, {2, 3526, 1656}, {2, 3533, 5}, {2, 5071, 41985}, {2, 10124, 5055}, {2, 11539, 15703}, {2, 15702, 47599}, {2, 15723, 5054}, {2, 16239, 46219}, {2, 33003, 33249}, {2, 46219, 3526}, {2, 47598, 15694}, {3, 5, 5076}, and many others

X(55859) = X(2)X(3)∩X(17)X(42121)

Barycentrics    8*Sin[2*A] + 7*Sin[2*B] + 7*Sin[2*C] : :
Barycentrics   8*a^4 - 15*a^2*b^2 + 7*b^4 - 15*a^2*c^2 - 14*b^2*c^2 + 7*c^4 : :
X(55859) = 21 X[2] + X[3], 45 X[2] - X[4], 12 X[2] - X[5], 87 X[2] + X[20], 9 X[2] + 2 X[140], 43 X[2] + X[376], 23 X[2] - X[381], 111 X[2] - X[382], 57 X[2] - 2 X[546], 13 X[2] - 2 X[547], 75 X[2] + 2 X[548], 10 X[2] + X[549], 54 X[2] + X[550], 39 X[2] + 5 X[631], 6 X[2] + 5 X[632], 27 X[2] - 5 X[1656], 153 X[2] + X[1657], and many others

X(55859) lies on these lines: {2, 3}, {17, 42121}, {18, 42124}, {61, 10187}, {62, 10188}, {141, 15516}, {143, 5650}, {373, 10627}, {397, 33416}, {398, 33417}, {495, 7294}, {496, 5326}, {499, 8162}, {551, 50830}, {576, 50982}, {590, 35814}, {597, 50985}, {599, 51182}, {615, 35815}, {1125, 38112}, {1151, 42600}, {1152, 42601}, {1353, 3763}, {1385, 31253}, {1483, 1698}, {1484, 31235}, {1506, 11614}, {1587, 43414}, {1588, 43413}, {3054, 7755}, {3411, 42592}, {3412, 42593}, {3567, 44324}, {3589, 15520}, {3590, 18512}, {3591, 18510}, {3619, 51732}, {3624, 10283}, {3634, 13607}, {3819, 15026}, {3828, 51087}, {3917, 13421}, {5237, 43640}, {5238, 43639}, {5254, 12815}, {5349, 42914}, {5350, 42915}, {5351, 43104}, {5352, 43101}, {5418, 42579}, {5420, 42578}, {5446, 10219}, {5462, 15082}, {5493, 38034}, {5550, 5844}, {5690, 19862}, {5882, 38042}, {5888, 38848}, {5901, 11224}, {6243, 44299}, {6468, 18762}, {6469, 18538}, {6470, 7584}, {6471, 7583}, {6486, 53520}, {6487, 53517}, {6666, 38111}, {6688, 10263}, {6689, 21357}, {7764, 15597}, {7768, 37647}, {7780, 9771}, {7781, 16509}, {7998, 14449}, {7999, 16881}, {8252, 19116}, {8253, 19117}, {8550, 43150}, {8583, 19907}, {8960, 13966}, {8972, 43506}, {8981, 32790}, {9692, 14226}, {9780, 51700}, {10159, 53104}, {10170, 13382}, {10185, 10302}, {10192, 14864}, {10222, 50827}, {10576, 41964}, {10577, 41963}, {10653, 42610}, {10654, 42611}, {10992, 38229}, {11017, 14855}, {11230, 43174}, {11231, 13464}, {11362, 38022}, {11465, 33879}, {11488, 42917}, {11489, 42916}, {11542, 42492}, {11543, 42493}, {11669, 43527}, {11694, 15027}, {11695, 15067}, {12007, 34507}, {12046, 54044}, {12645, 46931}, {13431, 21230}, {13571, 17006}, {13886, 43564}, {13939, 43565}, {13941, 43505}, {14128, 45956}, {14848, 51184}, {15045, 31834}, {15105, 25563}, {16241, 42594}, {16242, 42595}, {16534, 34128}, {16772, 42993}, {16773, 42992}, {16964, 42500}, {16965, 42501}, {16966, 41974}, {16967, 41973}, {18357, 30315}, {19872, 37705}, {19876, 37727}, {20582, 51140}, {22112, 32046}, {22234, 50991}, {22247, 51524}, {22251, 30714}, {23302, 42937}, {23303, 42936}, {23332, 45185}, {25339, 38706}, {25555, 48876}, {25561, 50988}, {26614, 38745}, {31238, 51046}, {31239, 32448}, {32062, 55286}, {32871, 52718}, {34598, 35885}, {34754, 43774}, {34755, 43773}, {37624, 46932}, {37832, 42597}, {37835, 42596}, {38082, 43177}, {40107, 48310}, {40693, 42590}, {40694, 42591}, {42087, 42908}, {42088, 42909}, {42089, 42924}, {42092, 42925}, {42115, 42494}, {42116, 42495}, {42117, 42498}, {42118, 42499}, {42122, 42773}, {42123, 42774}, {42139, 42688}, {42142, 42689}, {42143, 42150}, {42146, 42151}, {42149, 43029}, {42152, 43028}, {42157, 42684}, {42158, 42685}, {42163, 43032}, {42166, 43033}, {42435, 43549}, {42436, 43548}, {42472, 42889}, {42473, 42888}, {42488, 43484}, {42489, 43483}, {42490, 42910}, {42491, 42911}, {42627, 42998}, {42628, 42999}, {42633, 42978}, {42634, 42979}, {42694, 42940}, {42695, 42941}, {42817, 43198}, {42818, 43197}, {42942, 42959}, {42943, 42958}, {43026, 43874}, {43027, 43873}, {43143, 45872}, {43145, 45871}, {43254, 43569}, {43255, 43568}, {43342, 43438}, {43343, 43439}, {43374, 43882}, {43375, 43881}, {43376, 43510}, {43377, 43509}, {46025, 46831}, {46266, 52681}, {50986, 53092}

X(55859) = midpoint of X(i) and X(j) for these {i,j}: {2, 15723}, {3, 3855}, {3525, 5070}, {5056, 15720}, {5072, 15717}
X(55859) = reflection of X(i) in X(j) for these {i,j}: {550, 21735}, {15720, 140}, {41991, 5}
X(55859) = complement of X(5070)
X(55859) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 48154}, {2, 381, 41985}, {2, 632, 5}, {2, 3525, 5070}, {2, 3526, 3628}, {2, 3533, 1656}, {2, 10124, 15699}, {2, 15694, 47599}, {2, 16239, 632}, {2, 46219, 140}, {2, 47598, 549}, {3, 5, 15687}, {3, 381, 49138}, {3, 382, 15697}, {3, 631, 44580}, {3, 1656, 5068}, and many others

X(55860) = X(2)X(3)∩X(6)X(42978)

Barycentrics    7*Sin[2*A] + 8*Sin[2*B] + 8*Sin[2*C] : :
Barycentrics    7*a^4 - 15*a^2*b^2 + 8*b^4 - 15*a^2*c^2 - 16*b^2*c^2 + 8*c^4 : :
X(55860) = 24 X[2] - X[3], 45 X[2] + X[4], 21 X[2] + 2 X[5], 93 X[2] - X[20], 27 X[2] - 4 X[140], 47 X[2] - X[376], 22 X[2] + X[381], 114 X[2] + X[382], 111 X[2] + 4 X[546], 19 X[2] + 4 X[547], 165 X[2] - 4 X[548], 25 X[2] - 2 X[549], 117 X[2] - 2 X[550], 51 X[2] - 5 X[631], 33 X[2] - 10 X[632], 18 X[2] + 5 X[1656], 162 X[2] - X[1657], 39 X[2] + 7 X[3090], and many others

X(55860) lies on these lines: {2, 3}, {6, 42978}, {15, 42690}, {16, 42691}, {17, 43028}, {18, 43029}, {52, 10219}, {61, 42611}, {62, 42610}, {395, 42984}, {396, 42985}, {485, 43514}, {486, 43513}, {568, 12045}, {590, 6500}, {615, 6501}, {1385, 30315}, {1506, 21309}, {1698, 10247}, {3055, 22246}, {3070, 43415}, {3071, 9690}, {3411, 43426}, {3412, 43427}, {3616, 51515}, {3624, 37624}, {3763, 5093}, {3933, 32883}, {5050, 43150}, {5326, 9669}, {5339, 33417}, {5340, 33416}, {5550, 12645}, {5640, 13421}, {5651, 9704}, {5790, 13607}, {5844, 46931}, {5882, 19878}, {5886, 31253}, {6199, 10577}, {6243, 6688}, {6390, 32884}, {6395, 10576}, {6407, 42262}, {6408, 42265}, {6417, 8253}, {6418, 8252}, {6431, 42557}, {6432, 42558}, {6472, 35255}, {6473, 35256}, {6474, 42215}, {6475, 42216}, {6564, 43338}, {6565, 43339}, {6721, 52090}, {7294, 9654}, {7755, 31489}, {7999, 13321}, {8148, 11230}, {8254, 13432}, {8550, 51127}, {8976, 32790}, {9624, 38066}, {9691, 42583}, {9781, 54047}, {10145, 42561}, {10146, 31412}, {10159, 11669}, {10171, 48661}, {10172, 18525}, {10187, 16645}, {10188, 16644}, {10222, 19876}, {10246, 34595}, {10263, 44299}, {10283, 46932}, {10627, 33879}, {11231, 11522}, {11451, 32142}, {11465, 15067}, {11480, 42688}, {11481, 42689}, {11482, 21358}, {11485, 42936}, {11486, 42937}, {11614, 15655}, {11623, 14692}, {12007, 51126}, {12017, 18553}, {12242, 26958}, {12815, 31455}, {13393, 20125}, {13464, 51073}, {13665, 41964}, {13785, 41963}, {13951, 32789}, {14530, 14864}, {14627, 17811}, {14848, 50982}, {14862, 40686}, {15026, 54048}, {15039, 20396}, {15603, 18584}, {16267, 42593}, {16268, 42592}, {16808, 42774}, {16809, 42773}, {16966, 42895}, {16967, 42894}, {18230, 51514}, {18493, 43174}, {18581, 42949}, {18582, 42948}, {19116, 43564}, {19117, 43565}, {19130, 46215}, {19883, 34748}, {20195, 51516}, {22235, 43464}, {22236, 43483}, {22237, 43463}, {22238, 43484}, {22330, 50993}, {23269, 43382}, {23275, 43383}, {23302, 42989}, {23303, 42988}, {31235, 51517}, {31239, 32447}, {31260, 51518}, {31274, 38732}, {32785, 43882}, {32786, 43881}, {33606, 42991}, {33607, 42990}, {34507, 47355}, {36750, 37682}, {37637, 43136}, {37640, 42590}, {37641, 42591}, {37832, 42935}, {37835, 42934}, {38112, 46930}, {38317, 44456}, {38319, 48680}, {38740, 48657}, {42115, 43300}, {42116, 43301}, {42121, 42950}, {42122, 42776}, {42123, 42775}, {42124, 42951}, {42125, 42945}, {42126, 42684}, {42127, 42685}, {42128, 42944}, {42129, 42152}, {42132, 42149}, {42150, 42687}, {42151, 42686}, {42160, 42500}, {42161, 42501}, {42258, 42600}, {42259, 42601}, {42476, 43014}, {42477, 43015}, {42488, 43024}, {42489, 43025}, {42490, 42580}, {42491, 42581}, {42492, 43446}, {42493, 43447}, {42694, 42908}, {42695, 42909}, {42795, 43194}, {42796, 43193}, {42813, 42958}, {42814, 42959}, {42815, 43102}, {42816, 43103}, {42916, 43445}, {42917, 43444}, {42968, 43403}, {42969, 43404}, {43006, 43013}, {43007, 43012}, {43254, 53516}, {43255, 53513}, {43258, 51849}, {43259, 51850}, {43527, 53104}, {43540, 43635}, {43541, 43634}, {51140, 53092}

X(55860) = anticomplement of X(41992)
X(55860) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 41984}, {2, 1656, 46219}, {2, 3090, 16239}, {2, 3628, 3526}, {2, 5067, 632}, {2, 5070, 3}, {2, 15699, 15723}, {2, 46935, 3533}, {2, 47599, 381}, {3, 5, 14269}, {3, 381, 49134}, {3, 3843, 15685}, {3, 5070, 15703}, {3, 35403, 20}, {4, 550, 49136}, {4, 1656, 5055}, and many others

X(55861) = X(2)X(3)∩X(6)X(42492)

Barycentrics    8*Sin[2*A] + 9*Sin[2*B] + 9*Sin[2*C] : :
Barycentrics    8*a^4 - 17*a^2*b^2 + 9*b^4 - 17*a^2*c^2 - 18*b^2*c^2 + 9*c^4 : :
X(55861) = 27 X[2] - X[3], 51 X[2] + X[4], 12 X[2] + X[5], 105 X[2] - X[20], 15 X[2] - 2 X[140], 53 X[2] - X[376], 25 X[2] + X[381], 129 X[2] + X[382], 63 X[2] + 2 X[546], 11 X[2] + 2 X[547], 93 X[2] - 2 X[548], 14 X[2] - X[549], 66 X[2] - X[550], 57 X[2] - 5 X[631], 18 X[2] - 5 X[632], 21 X[2] + 5 X[1656], 183 X[2] - X[1657], and many others

X(55861) lies on these lines: {2, 3}, {6, 42492}, {17, 42593}, {18, 42592}, {49, 46865}, {141, 22330}, {156, 22112}, {373, 32142}, {397, 43020}, {398, 43021}, {575, 51126}, {576, 34573}, {952, 34595}, {1125, 38176}, {1151, 43792}, {1152, 43791}, {1216, 10219}, {1353, 47355}, {1483, 3624}, {1484, 38629}, {1493, 15605}, {1698, 10283}, {3054, 5007}, {3055, 7772}, {3589, 22234}, {3619, 11482}, {3634, 10222}, {3653, 30315}, {3763, 53858}, {3815, 5368}, {3917, 16982}, {5326, 10593}, {5351, 42138}, {5352, 42135}, {5355, 31406}, {5493, 50825}, {5609, 6723}, {5650, 10095}, {5690, 51073}, {5844, 19877}, {5892, 40247}, {5901, 16189}, {6053, 20397}, {6101, 6688}, {6419, 32789}, {6420, 32790}, {6425, 18762}, {6426, 18538}, {6427, 13993}, {6428, 13925}, {6453, 42583}, {6454, 42582}, {6519, 42561}, {6522, 31412}, {6667, 51525}, {6721, 51523}, {6722, 51524}, {7294, 10592}, {7917, 37688}, {7982, 19872}, {8252, 19117}, {8253, 19116}, {8981, 43880}, {9607, 12815}, {10170, 15012}, {10172, 34773}, {10247, 46931}, {10264, 38632}, {10541, 18358}, {11230, 31253}, {11451, 14449}, {11465, 16881}, {11698, 38631}, {11801, 15020}, {12006, 45187}, {12045, 15067}, {12900, 51522}, {13966, 43879}, {14094, 40685}, {15025, 38794}, {15178, 19862}, {16772, 43776}, {16773, 43775}, {16964, 43639}, {16965, 43640}, {17337, 45942}, {17852, 42265}, {18357, 30389}, {18510, 43883}, {18512, 43884}, {19876, 50823}, {19878, 38028}, {20304, 22251}, {20399, 34127}, {20400, 34126}, {21230, 37648}, {22236, 43103}, {22238, 43102}, {22332, 43291}, {23251, 42601}, {23261, 42600}, {23332, 50414}, {24954, 38045}, {25565, 50980}, {31274, 38229}, {31275, 38230}, {31399, 50824}, {32523, 40108}, {33416, 42166}, {33417, 42163}, {33879, 37484}, {36836, 42143}, {36843, 42146}, {36969, 42595}, {36970, 42594}, {37832, 42948}, {37835, 42949}, {38021, 50826}, {38022, 51077}, {38072, 50981}, {38076, 50833}, {38079, 40107}, {38081, 50804}, {38083, 50801}, {38110, 51127}, {38626, 38729}, {38627, 38740}, {38628, 38751}, {38630, 38775}, {39884, 42786}, {42101, 43647}, {42102, 43648}, {42108, 43293}, {42109, 43292}, {42111, 43630}, {42114, 43631}, {42115, 43771}, {42116, 43772}, {42117, 42580}, {42118, 42581}, {42121, 42598}, {42124, 42599}, {42149, 42610}, {42152, 42611}, {42164, 42914}, {42165, 42915}, {42262, 43318}, {42435, 43441}, {42436, 43440}, {42490, 43417}, {42491, 43416}, {42500, 42814}, {42501, 42813}, {42627, 42917}, {42628, 42916}, {42785, 52987}, {42892, 42936}, {42893, 42937}, {42910, 42925}, {42911, 42924}, {42950, 43464}, {42951, 43463}, {42978, 43228}, {42979, 43229}, {43004, 43306}, {43005, 43307}, {43014, 43873}, {43015, 43874}, {43022, 43372}, {43023, 43373}, {43105, 43241}, {43106, 43240}, {48876, 51128}

X(55861) = midpoint of X(i) and X(j) for these {i,j}: {5067, 46219}, {5079, 10303}
X(55861) = reflection of X(550) in X(21734)
X(55861) = complement of X(46219)
X(55861) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 381, 41984}, {2, 632, 41992}, {2, 1656, 16239}, {2, 3628, 632}, {2, 5067, 46219}, {2, 5070, 140}, {2, 15703, 47598}, {2, 47599, 549}, {3, 381, 11541}, {3, 1656, 15022}, {3, 3090, 12811}, {3, 3544, 12102}, {3, 5072, 50688}, {3, 11541, 44245}, {3, 12811, 3627}, and many others

X(55862) = X(2)X(3)∩X(61)X(42591)

Barycentrics    10*Sin[2*A] + 9*Sin[2*B] + 9*Sin[2*C] : :
Barycentrics    10*a^4 - 19*a^2*b^2 + 9*b^4 - 19*a^2*c^2 - 18*b^2*c^2 + 9*c^4 : :
X(55862) = 27 X[2] + X[3], 57 X[2] - X[4], 15 X[2] - X[5], 111 X[2] + X[20], 6 X[2] + X[140], 55 X[2] + X[376], 29 X[2] - X[381], 141 X[2] - X[382], 36 X[2] - X[546], 8 X[2] - X[547], 48 X[2] + X[548], 13 X[2] + X[549], 69 X[2] + X[550], 51 X[2] + 5 X[631], 9 X[2] + 5 X[632], 33 X[2] - 5 X[1656], 195 X[2] + X[1657], 9 X[2] - X[3090], and many others

X(55862) lies on these lines: {2, 3}, {61, 42591}, {62, 42590}, {141, 22234}, {156, 16187}, {230, 41940}, {371, 42566}, {372, 42567}, {395, 42593}, {396, 42592}, {575, 34573}, {576, 51126}, {952, 51073}, {1209, 20585}, {1483, 19877}, {1698, 51700}, {3054, 7772}, {3055, 5007}, {3316, 43884}, {3317, 43883}, {3564, 51128}, {3589, 22330}, {3619, 53092}, {3624, 5844}, {3634, 15178}, {3746, 5326}, {3763, 51732}, {3819, 14449}, {5237, 42146}, {5238, 42143}, {5351, 44015}, {5352, 44016}, {5447, 10219}, {5462, 44324}, {5550, 38112}, {5563, 7294}, {5609, 40685}, {5650, 15026}, {5690, 16189}, {5892, 31834}, {5901, 19878}, {5943, 16982}, {6243, 33879}, {6419, 13993}, {6420, 13925}, {6427, 32786}, {6428, 32785}, {6453, 18762}, {6454, 18538}, {6688, 10627}, {7697, 32523}, {7871, 37688}, {8254, 53415}, {8960, 43212}, {10147, 42262}, {10148, 42265}, {10175, 31666}, {10187, 41943}, {10188, 41944}, {10222, 19862}, {10272, 20397}, {11485, 42493}, {11486, 42492}, {11591, 15012}, {11614, 35007}, {11694, 20396}, {12046, 13598}, {12645, 46930}, {13363, 16625}, {13392, 15059}, {13630, 40247}, {13903, 43505}, {13961, 43506}, {15025, 34153}, {15029, 38728}, {15082, 32142}, {16960, 42946}, {16961, 42947}, {18356, 54012}, {18358, 20190}, {18583, 51127}, {19872, 38042}, {20398, 38628}, {20399, 38627}, {20400, 38631}, {22250, 32423}, {23302, 43014}, {23303, 43015}, {25542, 33814}, {25561, 51135}, {28212, 31423}, {28224, 30389}, {30531, 54201}, {31235, 51525}, {31274, 51524}, {31399, 51082}, {33416, 42598}, {33417, 42599}, {34089, 42523}, {34091, 42522}, {34126, 38763}, {34127, 38751}, {34128, 38795}, {34380, 47355}, {35255, 53516}, {35256, 53513}, {36836, 43296}, {36843, 43297}, {37505, 47296}, {37624, 46931}, {37832, 42595}, {37835, 42594}, {41963, 42573}, {41964, 42572}, {42122, 42692}, {42123, 42693}, {42136, 43638}, {42137, 43643}, {42149, 42496}, {42152, 42497}, {42215, 42568}, {42216, 42569}, {42435, 43489}, {42436, 43490}, {42488, 42913}, {42489, 42912}, {42498, 42580}, {42499, 42581}, {42557, 43880}, {42558, 43879}, {42596, 42945}, {42597, 42944}, {42612, 43773}, {42613, 43774}, {42793, 42973}, {42794, 42972}, {42922, 42950}, {42923, 42951}, {42938, 43544}, {42939, 43545}, {42990, 43100}, {42991, 43107}, {43030, 43873}, {43031, 43874}, {43101, 43645}, {43104, 43646}, {43291, 53096}, {43558, 43885}, {43559, 43886}, {46847, 55286}

X(55862) = midpoint of X(i) and X(j) for these {i,j}: {3, 3857}, {5, 3523}, {3090, 14869}, {3851, 44682}
X(55862) = reflection of X(i) in X(j) for these {i,j}: {140, 3526}, {3090, 3628}, {8703, 45761}, {14893, 41106}, {15700, 11812}, {34200, 19711}, {45762, 5066}
X(55862) = X(54791)-complementary conjugate of X(20305)
X(55862) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 140, 48154}, {2, 549, 41985}, {2, 632, 3628}, {2, 3533, 5070}, {2, 10124, 47599}, {2, 15723, 15699}, {2, 16239, 140}, {2, 46219, 5}, {2, 47598, 547}, {3, 5, 12102}, {3, 381, 49140}, {3, 1656, 3544}, {3, 3090, 3857}, {3, 3544, 3627}, {3, 3628, 12812}, {3, 5079, 50689}, and many others

X(55863) = X(2)X(3)∩X(6)X(42938)

Barycentrics    9*Sin[2*A] + 4*Sin[2*B] + 4*Sin[2*C] : :
Barycentrics    9*a^4 - 13*a^2*b^2 + 4*b^4 - 13*a^2*c^2 - 8*b^2*c^2 + 4*c^4 : :
X(55863) = 12 X[2] + 5 X[3], 39 X[2] - 5 X[4], 27 X[2] - 10 X[5], 63 X[2] + 5 X[20], 3 X[2] - 20 X[140], 29 X[2] + 5 X[376], 22 X[2] - 5 X[381], 18 X[2] - X[382], 21 X[2] - 4 X[546], 37 X[2] - 20 X[547], 99 X[2] + 20 X[548], 7 X[2] + 10 X[549], 15 X[2] + 2 X[550], 9 X[2] + 25 X[631], 33 X[2] - 50 X[632], 42 X[2] - 25 X[1656], and many others

X(55863) lies on these lines: {2, 3}, {6, 42938}, {11, 38636}, {13, 42774}, {14, 42773}, {69, 32887}, {113, 38633}, {114, 38634}, {115, 38635}, {119, 38637}, {125, 38638}, {127, 38639}, {137, 38640}, {143, 54047}, {216, 36431}, {230, 31450}, {399, 15057}, {485, 6446}, {486, 6445}, {568, 15606}, {599, 33749}, {615, 9680}, {1151, 45385}, {1152, 45384}, {1153, 7751}, {1384, 31455}, {1482, 9588}, {1588, 9691}, {3035, 31458}, {3055, 31417}, {3167, 52104}, {3244, 26446}, {3311, 35813}, {3312, 35812}, {3411, 16241}, {3412, 16242}, {3624, 31425}, {3626, 10165}, {3629, 53091}, {3632, 10246}, {3636, 10247}, {3653, 34641}, {3763, 33386}, {3819, 37481}, {4031, 11374}, {4309, 52793}, {4317, 31479}, {4999, 31494}, {5010, 9671}, {5024, 7749}, {5050, 40107}, {5092, 48662}, {5093, 6329}, {5237, 43418}, {5238, 43419}, {5319, 31470}, {5326, 9654}, {5339, 42798}, {5340, 42797}, {5351, 42984}, {5352, 42985}, {5368, 9605}, {5418, 6418}, {5420, 6417}, {5432, 7373}, {5433, 6767}, {5585, 39590}, {5646, 43807}, {5650, 18436}, {5690, 20057}, {5881, 11231}, {5892, 14531}, {6337, 32886}, {6407, 13951}, {6408, 8976}, {6448, 8960}, {6449, 8252}, {6450, 8253}, {6451, 42262}, {6452, 42265}, {6455, 10577}, {6456, 10576}, {6472, 9692}, {6473, 43797}, {6474, 13939}, {6475, 13886}, {6486, 42557}, {6487, 42558}, {6496, 6565}, {6497, 6564}, {6500, 13966}, {6501, 8981}, {6519, 35823}, {6522, 35822}, {6684, 8148}, {6689, 54202}, {6699, 12308}, {7280, 9656}, {7294, 9669}, {7619, 7759}, {7765, 37637}, {7829, 51588}, {7998, 12006}, {9167, 52090}, {9540, 13961}, {9541, 43435}, {9589, 11230}, {9624, 12702}, {9681, 13785}, {9690, 32786}, {9698, 30435}, {9703, 37471}, {9704, 13336}, {10095, 54041}, {10113, 15042}, {10164, 18493}, {10168, 53092}, {10182, 40686}, {10194, 41945}, {10195, 41946}, {10256, 50774}, {10540, 13347}, {10541, 50955}, {10627, 13321}, {10653, 42949}, {10654, 42948}, {11432, 44673}, {11465, 13391}, {11480, 42489}, {11481, 42488}, {11482, 50977}, {11485, 42490}, {11486, 42491}, {11591, 44299}, {11695, 37484}, {11793, 40280}, {12017, 15069}, {12162, 15082}, {12164, 20191}, {12315, 25563}, {12316, 32348}, {12433, 31188}, {12902, 48378}, {13624, 37714}, {13903, 13935}, {13925, 43510}, {13993, 43509}, {14128, 20791}, {14530, 23329}, {14627, 15805}, {14981, 35021}, {15024, 54042}, {15035, 20396}, {15040, 34128}, {15043, 54048}, {15045, 32142}, {15061, 24981}, {15063, 38728}, {15066, 43845}, {15178, 34747}, {15819, 32450}, {16003, 38794}, {16267, 42612}, {16268, 42613}, {16644, 42990}, {16645, 42991}, {16772, 42089}, {16773, 42092}, {16881, 33884}, {16964, 42597}, {16965, 42596}, {16966, 43193}, {16967, 43194}, {17704, 18439}, {18525, 31399}, {18526, 54445}, {18553, 51137}, {19116, 42643}, {19117, 42644}, {19872, 28160}, {19876, 51084}, {20190, 21358}, {20379, 32609}, {21309, 31467}, {22236, 42780}, {22238, 42779}, {22246, 31400}, {23236, 38793}, {26614, 38664}, {26864, 43608}, {28208, 30315}, {28224, 46932}, {30389, 50798}, {31235, 38755}, {31239, 48663}, {31274, 38743}, {31401, 43136}, {31663, 34595}, {32063, 52102}, {32785, 43415}, {32789, 43791}, {32790, 43792}, {33416, 42116}, {33417, 42115}, {33533, 43597}, {33540, 33887}, {35022, 38750}, {35023, 37726}, {35024, 38774}, {36748, 52704}, {36836, 42937}, {36843, 42936}, {36948, 41005}, {37514, 50461}, {37606, 37721}, {38021, 51088}, {38072, 51141}, {38074, 50833}, {38138, 46931}, {38226, 51587}, {38751, 48657}, {41107, 42592}, {41108, 42593}, {41943, 42636}, {41944, 42635}, {42093, 43327}, {42094, 43326}, {42095, 42434}, {42098, 42433}, {42099, 42499}, {42100, 42498}, {42119, 42951}, {42120, 42950}, {42125, 43105}, {42128, 43106}, {42129, 42147}, {42132, 42148}, {42149, 42501}, {42152, 42500}, {42154, 43547}, {42155, 43546}, {42270, 43516}, {42273, 43515}, {42415, 43869}, {42416, 43870}, {42512, 43773}, {42513, 43774}, {42582, 42600}, {42583, 42601}, {42590, 43403}, {42591, 43404}, {42602, 43570}, {42603, 43571}, {42610, 42813}, {42611, 42814}, {42633, 43479}, {42634, 43480}, {42815, 43103}, {42816, 43102}, {42914, 43196}, {42915, 43195}, {42932, 43555}, {42933, 43554}, {42944, 42974}, {42945, 42975}, {43018, 43233}, {43019, 43232}, {43177, 51516}, {43523, 52045}, {43524, 52046}, {46267, 53858}, {48873, 51127}

X(55863) = complement of X(3544)
X(55863) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 3851}, {2, 376, 47478}, {2, 546, 1656}, {2, 549, 15688}, {2, 550, 5079}, {2, 631, 3530}, {2, 3523, 3529}, {2, 3524, 15687}, {2, 3528, 5}, {2, 3529, 35018}, {2, 3530, 382}, {2, 10299, 546}, {2, 14869, 15720}, {2, 15681, 5055}, {2, 15700, 14269}, {2, 15707, 15681}, {2, 15708, 15715}, {2, 15710, 11737}, {2, 15715, 38071}, {2, 15720, 3}, {2, 17504, 381}, {2, 49135, 3090}, {3, 4, 15689}, {3, 5, 17800}, {3, 140, 15694}, {3, 1656, 3830}, {3, 3517, 34006}, {3, 3526, 5070}, {3, 3851, 15681}, {3, 5055, 5073}, {3, 5056, 35400}, {3, 5070, 3843}, and many others

X(55864) = X(1)X(31188)∩X(2)X(3)

Barycentrics    9*Sin[2*A] + 5*Sin[2*B] + 5*Sin[2*C] : :
Barycentrics    9*a^4 - 14*a^2*b^2 + 5*b^4 - 14*a^2*c^2 - 10*b^2*c^2 + 5*c^4 : :
X(55864) =15 X[2] + 4 X[3], 21 X[2] - 2 X[4], 27 X[2] - 8 X[5], 18 X[2] + X[20], 3 X[2] + 16 X[140], 17 X[2] + 2 X[376], 23 X[2] - 4 X[381], 99 X[2] - 4 X[382], 111 X[2] - 16 X[546], 35 X[2] - 16 X[547], 117 X[2] + 16 X[548], 11 X[2] + 8 X[549], 87 X[2] + 8 X[550], 9 X[2] + 10 X[631], 21 X[2] - 40 X[632], 39 X[2] - 20 X[1656], and many others

X(55864) lies on these lines: {1, 31188}, {2, 3}, {10, 30392}, {15, 42597}, {16, 42596}, {17, 42800}, {18, 42799}, {32, 31407}, {36, 31410}, {61, 43200}, {62, 43199}, {99, 32867}, {146, 38792}, {147, 31274}, {148, 38735}, {152, 38770}, {153, 31235}, {165, 19878}, {182, 9706}, {183, 32835}, {185, 15082}, {187, 31417}, {193, 39561}, {230, 31492}, {325, 32871}, {355, 46931}, {388, 5326}, {390, 37720}, {485, 6481}, {486, 6480}, {497, 7294}, {498, 5265}, {499, 5281}, {575, 11160}, {597, 51214}, {633, 33404}, {634, 33405}, {944, 31662}, {946, 31425}, {962, 19862}, {1007, 32898}, {1078, 32839}, {1125, 5734}, {1131, 6396}, {1132, 6200}, {1152, 31414}, {1153, 7759}, {1385, 46933}, {1588, 9542}, {1698, 38155}, {1975, 32870}, {1994, 15805}, {2979, 11695}, {2996, 11668}, {3054, 7738}, {3068, 6432}, {3069, 6431}, {3086, 31452}, {3087, 52704}, {3316, 6398}, {3317, 6221}, {3411, 42152}, {3412, 42149}, {3448, 38725}, {3567, 33884}, {3576, 19877}, {3590, 35822}, {3591, 35823}, {3593, 45509}, {3595, 45508}, {3600, 37719}, {3616, 11362}, {3617, 11231}, {3618, 5102}, {3619, 15069}, {3620, 33748}, {3622, 26446}, {3623, 38028}, {3624, 4301}, {3634, 5731}, {3763, 5921}, {3767, 31457}, {3785, 7814}, {3819, 14531}, {3828, 30389}, {3911, 11036}, {3916, 46873}, {3917, 15028}, {4297, 19872}, {4309, 5274}, {4317, 5261}, {4325, 10590}, {4330, 10591}, {4661, 13373}, {4678, 10246}, {5008, 31455}, {5041, 5304}, {5097, 51171}, {5218, 37722}, {5237, 43403}, {5238, 43404}, {5286, 31450}, {5305, 31470}, {5318, 42610}, {5319, 7616}, {5321, 42611}, {5334, 42489}, {5335, 42488}, {5339, 43421}, {5340, 43420}, {5343, 5352}, {5344, 5351}, {5365, 42580}, {5366, 42581}, {5395, 53108}, {5418, 7586}, {5420, 7585}, {5432, 14986}, {5447, 15024}, {5550, 6684}, {5562, 44299}, {5650, 5889}, {5656, 25563}, {5657, 11278}, {5691, 31253}, {5703, 31231}, {5704, 37723}, {5818, 46930}, {5881, 9780}, {5886, 31447}, {5892, 7999}, {5972, 15057}, {5984, 38739}, {6194, 6683}, {6419, 43255}, {6420, 43254}, {6427, 43212}, {6428, 43211}, {6429, 8252}, {6430, 8253}, {6433, 6459}, {6434, 6460}, {6437, 32786}, {6438, 32785}, {6453, 10194}, {6454, 10195}, {6455, 23275}, {6456, 23269}, {6484, 43512}, {6485, 43511}, {6486, 9681}, {6487, 10576}, {6488, 42417}, {6489, 42418}, {6500, 42541}, {6501, 42542}, {6700, 31446}, {7288, 15888}, {7619, 7751}, {7735, 9606}, {7736, 44535}, {7748, 11614}, {7752, 32884}, {7769, 37668}, {7796, 15589}, {7982, 38068}, {7987, 51073}, {7991, 19883}, {7998, 15606}, {8550, 51215}, {8591, 20398}, {8972, 13935}, {8976, 43510}, {9143, 20397}, {9167, 38664}, {9540, 13941}, {9543, 23273}, {9544, 13336}, {9589, 10164}, {9607, 37637}, {9657, 10588}, {9670, 10589}, {9693, 42215}, {9698, 37665}, {9705, 11003}, {9711, 30478}, {9748, 16987}, {9779, 35242}, {10141, 43886}, {10142, 43885}, {10171, 16192}, {10187, 41108}, {10188, 41107}, {10519, 37517}, {10541, 20582}, {10625, 11465}, {10645, 42890}, {10646, 42891}, {11177, 20399}, {11180, 20190}, {11185, 32883}, {11451, 15644}, {11488, 16773}, {11489, 16772}, {11522, 51120}, {11793, 33879}, {12383, 20396}, {13340, 32205}, {13434, 22112}, {13886, 35256}, {13903, 43374}, {13939, 35255}, {13951, 43509}, {13961, 43375}, {13966, 31487}, {13971, 31440}, {14683, 20379}, {15020, 45311}, {15056, 16836}, {15108, 18951}, {15178, 31145}, {15305, 17704}, {15325, 31480}, {15602, 43448}, {16187, 43614}, {16189, 51108}, {16241, 42999}, {16242, 42998}, {16511, 53021}, {16964, 42902}, {16965, 42903}, {16966, 43465}, {16967, 43466}, {17749, 22392}, {18230, 43177}, {18581, 43243}, {18582, 43242}, {18840, 54921}, {20014, 37624}, {20052, 38112}, {20057, 38127}, {20094, 38750}, {20095, 38762}, {20096, 38774}, {20099, 38806}, {21356, 53093}, {21843, 31404}, {22235, 43548}, {22236, 42500}, {22237, 43549}, {22238, 42501}, {23236, 34128}, {23241, 36520}, {23302, 42491}, {23303, 42490}, {23958, 26878}, {25406, 34573}, {25440, 31420}, {25555, 50967}, {26040, 31260}, {26614, 52090}, {27065, 37534}, {27385, 54398}, {30340, 37731}, {31436, 44675}, {31465, 44595}, {31494, 47742}, {31884, 51127}, {32817, 32872}, {32818, 32873}, {32820, 32874}, {32827, 43459}, {32830, 37688}, {32831, 34229}, {33416, 34754}, {33417, 34755}, {33650, 38782}, {33749, 38064}, {35260, 40686}, {36746, 37687}, {36836, 42932}, {36843, 42933}, {36948, 45198}, {37640, 43239}, {37641, 43238}, {38069, 38665}, {38072, 51211}, {38076, 50863}, {38110, 51170}, {38740, 41134}, {40170, 45255}, {40329, 40896}, {41973, 49873}, {41974, 49874}, {42089, 42896}, {42090, 43365}, {42091, 43364}, {42092, 42897}, {42111, 43632}, {42114, 43633}, {42121, 43463}, {42124, 43464}, {42129, 43329}, {42132, 43328}, {42133, 42434}, {42134, 42433}, {42139, 43194}, {42142, 43193}, {42143, 52079}, {42146, 52080}, {42147, 43028}, {42148, 43029}, {42157, 43440}, {42158, 43441}, {42163, 42773}, {42166, 42774}, {42225, 43561}, {42226, 43560}, {42494, 42943}, {42495, 42942}, {42582, 42637}, {42583, 42638}, {42594, 42775}, {42595, 42776}, {42924, 43542}, {42925, 43543}, {42936, 42990}, {42937, 42991}, {42952, 49826}, {42953, 49827}, {42960, 49907}, {42961, 49908}, {42992, 54593}, {42993, 54594}, {42994, 49903}, {42995, 49904}, {43174, 50872}, {43316, 43505}, {43317, 43506}, {43442, 43486}, {43443, 43485}, {43527, 54522}, {43544, 43775}, {43545, 43776}, {43816, 54012}, {44732, 46921}, {48310, 53097}, {51126, 51212}, {51128, 53094}

X(55864) =complement of X(15022)
X(55864) =orthocentroidal-circle-inverse of X(46936)
X(55864) =ninepoint-circle-of-medial-triangle-inverse of X(47094)
X(55864) =X(54892)-anticomplementary conjugate of X(21270)
X(55864) ={X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 5056}, {2, 4, 46936}, {2, 20, 7486}, {2, 140, 10303}, {2, 439, 16921}, {2, 549, 3839}, {2, 631, 20}, {2, 3091, 46935}, {2, 3146, 1656}, {2, 3522, 3090}, {2, 3523, 3091}, {2, 3832, 5067}, {2, 5054, 15692}, {2, 5068, 3628}, {2, 6910, 5129}, {2, 6921, 17580}, {2, 6926, 6884}, and many others

X(55865) = X(2)X(3)∩X(184)X(49104)

Barycentrics    2 + 4*Cos[A]*Sin[A] + Sin[2*B] + Sin[2*C] : :
Barycentrics    2*a^2*b^2*c^2 + S*(a^2*(-a^2 + b^2 + c^2) + 4*S^2) : :

X(55865) lies on these lines: {2, 3}, {184, 49104}, {230, 8962}, {343, 641}, {394, 5418}, {485, 5406}, {590, 5408}, {1993, 8981}, {3035, 6347}, {3083, 5433}, {3084, 5432}, {4999, 6348}, {5420, 10601}, {5422, 13966}, {7583, 55567}, {11091, 45472}, {11245, 48772}, {12239, 23292}, {35255, 55566}, {43650, 49103}, {52348, 53456}, {52349, 53467}

X(55865) = complement of X(15234)
X(55865) = ninepoint-circle-of-medial-triangle-inverse of X(47632)
X(55865) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 1591}, {2, 631, 1584}, {2, 1583, 1592}, {2, 1599, 5}, {2, 1600, 15236}, {2, 3523, 6805}, {2, 15233, 3628}, {549, 15236, 1600}, {632, 15235, 2}, {3526, 55579, 2}, {3533, 3540, 2}

X(55866) = X(2)X(3)∩X(15)X(42611)

Barycentrics    9*Sin[2*A] + 8*Sin[2*B] + 8*Sin[2*C] : :
Barycentrics   9*a^4 - 17*a^2*b^2 + 8*b^4 - 17*a^2*c^2 - 16*b^2*c^2 + 8*c^4 : :
X(55866) = 24 X[2] + X[3], 51 X[2] - X[4], 27 X[2] - 2 X[5], 99 X[2] + X[20], 21 X[2] + 4 X[140], 49 X[2] + X[376], 26 X[2] - X[381], 126 X[2] - X[382], 129 X[2] - 4 X[546], 29 X[2] - 4 X[547], 171 X[2] + 4 X[548], 23 X[2] + 2 X[549], 123 X[2] + 2 X[550], 9 X[2] + X[631], 3 X[2] + 2 X[632], 6 X[2] - X[1656], 174 X[2] + X[1657],

X(55866) lies on these lines: {2, 3}, {15, 42611}, {16, 42610}, {49, 22112}, {143, 44299}, {298, 33405}, {299, 33404}, {499, 31480}, {590, 6501}, {615, 6500}, {1384, 11614}, {1482, 34595}, {1483, 46931}, {1698, 37624}, {3054, 5319}, {3070, 42601}, {3071, 42600}, {3411, 16644}, {3412, 16645}, {3624, 10247}, {3634, 37727}, {3763, 5965}, {3767, 31470}, {3933, 32884}, {5093, 40107}, {5326, 31452}, {5346, 9698}, {5418, 41947}, {5420, 41948}, {5644, 41586}, {5790, 51073}, {5881, 19872}, {6101, 33879}, {6390, 32883}, {6407, 43318}, {6408, 43319}, {6417, 8252}, {6418, 8253}, {6445, 42262}, {6446, 42265}, {6472, 42215}, {6473, 42216}, {6474, 35255}, {6475, 31414}, {6688, 37484}, {6723, 23236}, {7294, 31479}, {7583, 43881}, {7584, 43882}, {7746, 31492}, {7747, 15603}, {7749, 21309}, {7998, 32205}, {8148, 9624}, {8227, 31447}, {9588, 11230}, {9680, 9691}, {9681, 42583}, {9704, 43650}, {9780, 51515}, {9955, 31425}, {10095, 54047}, {10187, 16962}, {10188, 16963}, {10219, 10625}, {10653, 42595}, {10654, 42594}, {10983, 39784}, {11362, 19878}, {11465, 13321}, {11485, 42489}, {11486, 42488}, {12045, 13340}, {12308, 34128}, {12645, 19877}, {13665, 41962}, {13881, 31457}, {13903, 32786}, {13951, 31454}, {13961, 32785}, {14627, 17825}, {15024, 54048}, {15047, 15066}, {15082, 15606}, {15178, 19876}, {15805, 50461}, {15905, 52704}, {16187, 18350}, {16772, 42129}, {16773, 42132}, {16960, 43029}, {16961, 43028}, {16964, 42498}, {16965, 42499}, {16966, 42491}, {16967, 42490}, {17851, 18538}, {18493, 28228}, {18874, 54041}, {19862, 28234}, {20304, 38638}, {20396, 32609}, {21358, 53092}, {22234, 50993}, {22236, 41978}, {22238, 41977}, {26364, 31494}, {28236, 31253}, {30389, 38083}, {31489, 43136}, {32898, 52718}, {33416, 42156}, {33417, 42153}, {33749, 50955}, {37509, 37682}, {42111, 42682}, {42114, 42683}, {42149, 42512}, {42152, 42513}, {42159, 42500}, {42162, 42501}, {42496, 43447}, {42497, 43446}, {42590, 42998}, {42591, 42999}, {42592, 49905}, {42593, 49906}, {42777, 42948}, {42778, 42949}, {42801, 43490}, {42802, 43489}, {42813, 43240}, {42814, 43241}, {42817, 43102}, {42818, 43103}, {42990, 43239}, {42991, 43238}, {43024, 43373}, {43025, 43372}, {43254, 43880}, {43255, 43879}, {43525, 43570}, {43526, 43571}, {43634, 43869}, {43635, 43870}, {46932, 51700}

X(55866) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 41985}, {2, 631, 48154}, {2, 632, 1656}, {2, 3526, 5070}, {2, 3533, 3628}, {2, 15723, 5055}, {2, 16239, 3526}, {2, 46219, 3}, {2, 47598, 381}, {3, 381, 49139}, {3, 1656, 19709}, {3, 3091, 35407}, {3, 3851, 15684}, {4, 632, 35381}, {4, 15701, 3}, {5, 140, 15717}, and many others

X(55867) = X(1)X(54288)∩X(2)X(7)

Barycentrics    3*Cos[A] + 2*Cos[B] + 2*Cos[C] : :
X(55867) = 3 X[1] + 4 X[54288], 6 X[2] + X[63], 9 X[2] - 2 X[226], 3 X[2] + 4 X[5745], 15 X[2] - X[5905], 27 X[2] + X[20078], 8 X[2] - X[31164], 12 X[2] - 5 X[31266], 3 X[63] + 4 X[226], X[63] - 8 X[5745], 5 X[63] + 2 X[5905], 9 X[63] - 2 X[20078], 4 X[63] + 3 X[31164], 2 X[63] + 5 X[31266], X[226] + 6 X[5745], and many others

X(55867) lies on these lines: {1, 54288}, {2, 7}, {5, 21165}, {10, 3612}, {21, 3586}, {40, 6888}, {78, 5791}, {140, 18446}, {165, 33108}, {404, 993}, {442, 4652}, {515, 3523}, {535, 19876}, {631, 51755}, {758, 3624}, {912, 3526}, {968, 33140}, {997, 5444}, {1376, 34879}, {1478, 3634}, {1621, 5231}, {1707, 33105}, {2476, 31424}, {2886, 35258}, {3476, 24987}, {3488, 6734}, {3619, 9028}, {3628, 37826}, {3666, 31187}, {3677, 29681}, {3749, 29690}, {3751, 29678}, {3870, 6690}, {3876, 18389}, {3916, 18541}, {3951, 11374}, {3969, 11679}, {3984, 13411}, {4001, 30828}, {4197, 15803}, {4413, 37309}, {4414, 17064}, {4438, 29828}, {4512, 11680}, {4640, 31245}, {4751, 8680}, {4850, 25080}, {4999, 19861}, {5122, 44217}, {5218, 25006}, {5234, 11681}, {5235, 40214}, {5250, 26363}, {5256, 35466}, {5269, 29664}, {5271, 32851}, {5287, 37646}, {5307, 52412}, {5361, 27757}, {5372, 17296}, {5436, 15674}, {5438, 37291}, {5709, 6852}, {5722, 15670}, {5737, 41243}, {6675, 41574}, {6679, 29826}, {6682, 29855}, {6684, 6890}, {6705, 37112}, {6853, 7330}, {6862, 55104}, {6933, 12572}, {7174, 29665}, {7288, 24564}, {7290, 29680}, {9352, 38052}, {9581, 16865}, {9843, 31259}, {10039, 31458}, {10585, 12527}, {11231, 22758}, {11375, 18253}, {11682, 24541}, {12514, 18393}, {14829, 30608}, {15844, 44256}, {16475, 29688}, {16570, 24725}, {16585, 17080}, {16815, 24268}, {17227, 17785}, {17272, 30831}, {17580, 19877}, {17594, 24892}, {17783, 49515}, {17796, 37674}, {18229, 32779}, {19804, 31205}, {19860, 24953}, {22060, 47522}, {24580, 24603}, {25681, 31260}, {26034, 50752}, {26098, 36277}, {28595, 29857}, {28846, 31207}, {29607, 46180}, {29626, 43984}, {31261, 34176}, {31508, 49719}, {33110, 35445}, {33142, 37553}, {34377, 47355}, {40482, 40843}, {45939, 54287}, {50393, 51073}

X(55867) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9, 30852}, {2, 63, 31266}, {2, 3218, 25525}, {2, 3219, 5219}, {2, 5273, 908}, {2, 5744, 5249}, {2, 5745, 63}, {2, 27003, 41867}, {2, 27065, 30827}, {2, 35595, 20196}, {2, 54357, 3305}, {10, 6910, 4855}, {63, 31266, 31164}, {5791, 7483, 78}, {24953, 26066, 19860}

X(55868) = X(2)X(7)∩X(8)X(35)

Barycentrics    3*Cos[A] + Cos[B] + Cos[C] : :
X(55868) = 3 X[2] + 2 X[63], 9 X[2] - 4 X[226], 3 X[2] - 8 X[5745], 6 X[2] - X[5905], 9 X[2] + X[20078], 7 X[2] - 2 X[31164], 3 X[63] + 2 X[226], X[63] + 4 X[5745], 4 X[63] + X[5905], 6 X[63] - X[20078], 7 X[63] + 3 X[31164], X[226] - 6 X[5745], 8 X[226] - 3 X[5905], 4 X[226] + X[20078], 14 X[226] - 9 X[31164], and many others

X(55868) lies on these lines: {2, 7}, {8, 35}, {10, 4190}, {20, 21165}, {21, 3488}, {38, 26228}, {45, 37634}, {56, 18253}, {69, 33113}, {72, 6910}, {165, 25006}, {191, 11415}, {333, 2164}, {345, 1150}, {377, 3916}, {442, 18541}, {515, 3522}, {517, 6974}, {631, 912}, {758, 3616}, {846, 11269}, {896, 26098}, {938, 16865}, {940, 55466}, {956, 12648}, {958, 5554}, {962, 24468}, {1006, 5770}, {1012, 5771}, {1376, 36003}, {1473, 7465}, {1478, 5445}, {1479, 3647}, {1621, 24477}, {1698, 50237}, {1707, 29639}, {1788, 5260}, {1796, 6539}, {2478, 31445}, {2886, 44447}, {2895, 24616}, {2975, 3476}, {2999, 31326}, {3035, 3715}, {3090, 37826}, {3173, 15066}, {3210, 25254}, {3361, 24564}, {3434, 4640}, {3436, 26066}, {3474, 33108}, {3485, 11684}, {3523, 18446}, {3554, 17011}, {3586, 6734}, {3601, 20013}, {3618, 34377}, {3620, 9028}, {3666, 24597}, {3681, 5218}, {3690, 37521}, {3782, 31187}, {3822, 19877}, {3868, 6857}, {3869, 30478}, {3927, 7483}, {3935, 5281}, {3940, 37298}, {3951, 13411}, {3977, 11679}, {4228, 37581}, {4307, 29664}, {4310, 29681}, {4329, 34176}, {4344, 30652}, {4383, 55438}, {4389, 41806}, {4414, 33137}, {4419, 33133}, {4428, 51463}, {4430, 10578}, {4438, 26034}, {4512, 26015}, {4679, 10584}, {4699, 8680}, {4748, 31247}, {4847, 20075}, {4921, 5839}, {5044, 6921}, {5175, 15680}, {5187, 12572}, {5220, 5432}, {5234, 24982}, {5250, 10529}, {5278, 51583}, {5289, 31157}, {5302, 24914}, {5307, 8756}, {5358, 17521}, {5372, 32849}, {5439, 31259}, {5444, 5692}, {5552, 41229}, {5559, 20050}, {5657, 6909}, {5659, 9778}, {5690, 35251}, {5698, 11680}, {5703, 18389}, {5704, 37162}, {5705, 6871}, {5709, 6837}, {5716, 16948}, {5722, 31156}, {5737, 19822}, {5739, 32851}, {5741, 54280}, {5758, 6888}, {5768, 37106}, {5777, 6962}, {5811, 6960}, {5812, 6860}, {5818, 5841}, {5903, 31458}, {6327, 30741}, {6763, 10198}, {6824, 55109}, {6832, 37532}, {6833, 26921}, {6835, 37623}, {6838, 7330}, {6878, 10202}, {6889, 24467}, {6890, 55104}, {6891, 26878}, {6977, 31837}, {6988, 12528}, {6989, 26877}, {7081, 53661}, {7085, 37449}, {7361, 18667}, {8609, 28606}, {9352, 26040}, {9945, 19704}, {10430, 35986}, {10527, 12514}, {10586, 31435}, {11608, 20094}, {12115, 26446}, {12433, 19526}, {12526, 24541}, {12647, 17010}, {14552, 33077}, {14829, 17776}, {15254, 17728}, {15670, 15934}, {15672, 15933}, {15673, 15935}, {15803, 31446}, {16434, 26867}, {16455, 22458}, {16570, 41011}, {16816, 24268}, {16842, 34753}, {16885, 37663}, {17020, 37681}, {17052, 26783}, {17316, 31039}, {17529, 37545}, {17696, 26634}, {17768, 31245}, {18249, 19861}, {18359, 20881}, {18607, 25939}, {19785, 35466}, {20076, 24987}, {20242, 30943}, {20760, 30944}, {20805, 37225}, {21061, 25601}, {21319, 22149}, {22001, 31025}, {22060, 35980}, {23085, 47521}, {24248, 24892}, {24320, 35996}, {24695, 33105}, {26062, 46933}, {26070, 37653}, {26745, 42326}, {26911, 33852}, {27013, 28846}, {27383, 37291}, {27549, 53673}, {29590, 46180}, {30828, 32859}, {31204, 33146}, {31276, 46179}, {32858, 37655}, {32916, 33163}, {33119, 50295}, {33144, 36263}, {34772, 54398}, {36004, 53620}, {37265, 40571}, {37462, 37582}, {37652, 41243}, {37660, 44416}, {50043, 55095}

X(55868) = midpoint of X(63) and X(31266)
X(55868) = anticomplement of X(31266)
X(55868) = X(6)-isoconjugate of X(17098)
X(55868) = X(9)-Dao conjugate of X(17098)
X(55868) = barycentric product X(75)*X(3612)
X(55868) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17098}, {3612, 1}
X(55868) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 63, 5905}, {2, 144, 31053}, {2, 3219, 31018}, {2, 9965, 31019}, {2, 17484, 5226}, {2, 20078, 226}, {2, 21454, 27186}, {2, 23958, 9776}, {2, 26792, 5748}, {10, 4652, 4190}, {57, 54357, 2}, {63, 226, 20078}, {63, 5745, 2}, {191, 26363, 11415}, {226, 20078, 5905}, {3218, 27186, 21454}, {3305, 3911, 2}, {3911, 5325, 3305}, {3916, 5791, 377}, {4847, 35258, 20075}, {5273, 5744, 2}, {5316, 31224, 2}, {5361, 33168, 8}, {5372, 32849, 34255}, {5748, 6172, 26792}, {6734, 31424, 6872}, {17338, 27002, 2}, {21165, 51755, 20}

X(55869) = X(1)X(16579)∩X(2)X(7)

Barycentrics    1 + Cos[A]^2 + Cos[A]*Cos[B] + Cos[A]*Cos[C] : :

X(55869) lies on these lines: {1, 16579}, {2, 7}, {3, 960}, {10, 5709}, {19, 1764}, {40, 5837}, {46, 443}, {65, 19520}, {69, 45206}, {84, 6987}, {191, 15803}, {210, 11502}, {219, 3666}, {220, 37597}, {224, 20846}, {255, 54305}, {277, 39947}, {284, 1812}, {333, 39943}, {394, 45126}, {405, 15823}, {497, 42012}, {610, 10856}, {920, 6857}, {936, 6905}, {940, 40937}, {942, 958}, {993, 18443}, {1001, 11018}, {1006, 8726}, {1040, 2328}, {1155, 37270}, {1212, 5021}, {1214, 17811}, {1329, 5791}, {1697, 12437}, {1709, 5698}, {1711, 24210}, {1723, 37642}, {1728, 5084}, {1737, 2551}, {1762, 21370}, {1763, 22097}, {1768, 10857}, {1836, 37363}, {2082, 18163}, {2095, 9708}, {2182, 16435}, {2323, 5256}, {2550, 41338}, {2886, 5805}, {2900, 41228}, {2975, 34489}, {3229, 6171}, {3338, 30478}, {3358, 51090}, {3587, 50808}, {3601, 4511}, {3654, 28452}, {3683, 17603}, {3687, 3719}, {3715, 18236}, {3820, 5771}, {3878, 37531}, {3916, 37249}, {4428, 5289}, {4512, 10383}, {4641, 55432}, {4643, 41883}, {4652, 37300}, {4679, 7082}, {4847, 54408}, {4858, 5271}, {5044, 6911}, {5119, 34607}, {5234, 6763}, {5251, 30274}, {5302, 5708}, {5705, 6829}, {5737, 6708}, {5743, 5755}, {5784, 7580}, {5794, 20420}, {5795, 18391}, {6245, 6827}, {6358, 20223}, {6505, 15066}, {6675, 25681}, {6700, 6954}, {6824, 21616}, {6869, 17647}, {6878, 26877}, {6880, 26878}, {6883, 9940}, {8557, 39595}, {8624, 16283}, {8727, 24703}, {8728, 26066}, {8730, 40659}, {9352, 35985}, {9710, 12516}, {9946, 51506}, {10319, 15830}, {10391, 13615}, {10393, 11344}, {10479, 54396}, {10900, 37650}, {12436, 18249}, {12704, 19843}, {14552, 53994}, {15298, 25568}, {15299, 26105}, {15481, 18227}, {15836, 17814}, {16293, 44547}, {17073, 53415}, {17074, 24635}, {17080, 37659}, {18231, 37436}, {19861, 37583}, {21233, 24310}, {21621, 24316}, {26363, 55108}, {30223, 40998}, {31631, 37265}, {34281, 54421}, {39585, 55105}, {39980, 52705}, {44734, 46884}, {45039, 50700}

X(55869) = X(55105)-complementary conjugate of X(16608)
X(55869) = X(13395)-Ceva conjugate of X(521)
X(55869) = crossdifference of every pair of points on line {663, 6588}
X(55869) = barycentric product X(i)*X(j) for these {i,j}: {75, 26357}, {3718, 22479}
X(55869) = barycentric quotient X(i)/X(j) for these {i,j}: {22479, 34}, {26357, 1}
X(55869) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 63, 1708}, {2, 1708, 8257}, {9, 57, 5745}, {9, 30827, 3305}, {57, 41867, 3306}, {1214, 17811, 53996}, {3218, 9776, 57}, {3219, 18228, 9}

X(55870) = X(2)X(7)∩X(35)X(997)

Barycentrics    2 + Cos[A]^2 + Cos[A]*Cos[B] + Cos[A]*Cos[C] : :

X(55870) lies on these lines: {2, 7}, {35, 997}, {46, 37462}, {84, 6992}, {224, 11344}, {404, 12514}, {960, 11509}, {1158, 3523}, {1727, 6910}, {2164, 2339}, {3916, 50204}, {4640, 37309}, {4652, 37249}, {4666, 42842}, {4679, 15842}, {5258, 18398}, {5287, 8609}, {5709, 6854}, {5791, 50208}, {6505, 17811}, {6878, 37534}, {6911, 55104}, {6947, 7330}, {15066, 45126}, {15823, 25875}, {19804, 40435}, {19861, 37579}, {24175, 39947}, {24564, 37550}, {25006, 54408}

X(55871) = X(2)X(7)∩X(6)X(6505)

Barycentrics    2 - Cos[A]^2 - Cos[A]*Cos[B] - Cos[A]*Cos[C] : :

X(55871) lies on these lines: {2, 7}, {6, 6505}, {40, 6992}, {46, 2478}, {65, 25875}, {72, 50204}, {77, 54444}, {78, 14054}, {169, 21367}, {224, 37282}, {241, 55400}, {354, 42885}, {377, 1728}, {914, 11433}, {920, 2476}, {997, 3984}, {999, 51379}, {1004, 1864}, {1006, 37531}, {1158, 3091}, {1210, 43740}, {1214, 10601}, {1748, 26003}, {1836, 15297}, {1993, 53996}, {2182, 16438}, {2287, 46885}, {2990, 16578}, {2999, 16586}, {3434, 15299}, {3618, 6349}, {3870, 33925}, {3873, 20588}, {3876, 5253}, {3970, 42700}, {4511, 41863}, {4666, 18839}, {4855, 10399}, {5047, 12514}, {5250, 5259}, {5271, 20928}, {5422, 45126}, {5439, 26921}, {5536, 31249}, {5709, 6947}, {5729, 37270}, {5880, 7082}, {6350, 18928}, {6513, 7131}, {6840, 41869}, {6854, 7330}, {6880, 37534}, {6883, 24474}, {6905, 41854}, {6911, 40263}, {7672, 54348}, {8557, 26723}, {9352, 36002}, {10391, 37309}, {10393, 37301}, {10394, 35977}, {10900, 24597}, {15842, 17728}, {17073, 37649}, {17700, 41540}, {18607, 55432}, {19861, 26437}, {20292, 54370}, {24982, 37550}, {25091, 55399}, {34789, 41858}, {39947, 40940}, {49719, 54286}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1708, 63}, {9, 57, 5905}, {1708, 8257, 2}, {3305, 3306, 31266}, {37282, 44547, 224}

X(55872) = X(2)X(7)∩X(90)X(52126)

Barycentrics    1 + 2*Cos[A]^2 + 2*Cos[A]*Cos[B] + 2*Cos[A]*Cos[C] : :

X(55872) lies on these lines: {2, 7}, {90, 52126}, {149, 42012}, {191, 997}, {323, 45126}, {1006, 24467}, {1062, 35193}, {1158, 3522}, {1214, 15066}, {1711, 33134}, {1727, 3612}, {1728, 37162}, {1812, 27174}, {2994, 14552}, {3719, 33077}, {3868, 37306}, {3876, 6905}, {3916, 37300}, {4640, 34879}, {5220, 11502}, {5709, 6839}, {6763, 54318}, {6829, 37532}, {6840, 7330}, {6954, 26878}, {11101, 39598}, {11679, 18359}, {17796, 55466}, {28920, 42700}, {33110, 41338}, {45206, 45794}, {54302, 54392}

X(55872) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {997, 4652, 27086}, {3218, 27186, 57}, {3219, 27131, 9}

X(55873) = X(2)X(7)∩X(40)X(20066)

Barycentrics    1 - 2*Cos[A]^2 - 2*Cos[A]*Cos[B] - 2*Cos[A]*Cos[C] : :

X(55873) lies on these lines: {2, 7}, {40, 20066}, {46, 2475}, {72, 37300}, {78, 27086}, {149, 41338}, {191, 54318}, {323, 6505}, {914, 45794}, {920, 6872}, {997, 3951}, {1006, 3868}, {1158, 3146}, {1214, 1993}, {1711, 33131}, {1728, 5046}, {1748, 40149}, {1776, 44447}, {1994, 45126}, {3151, 21221}, {3187, 17479}, {3719, 32858}, {3895, 50817}, {3927, 37249}, {4053, 42700}, {4511, 37618}, {4641, 18607}, {4652, 54432}, {4661, 20588}, {5057, 7082}, {5432, 41571}, {5709, 6840}, {5928, 46487}, {6349, 37645}, {6350, 6515}, {6360, 37652}, {6830, 37532}, {6839, 7330}, {6905, 12528}, {6954, 26877}, {6987, 12649}, {9928, 37115}, {10394, 35989}, {12514, 16865}, {13100, 54290}, {13388, 55566}, {13389, 55567}, {15836, 43605}, {20060, 41229}, {20846, 44547}, {21368, 24310}, {21907, 39947}, {25440, 31938}, {26066, 41697}, {33110, 42012}, {34772, 37106}, {37644, 45206}, {39772, 54430}

X(55873) = barycentric product X(75)*X(36152)
X(55873) = barycentric quotient X(36152)/X(1)
X(55873) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 57, 31266}, {63, 1708, 2}, {3218, 3219, 5905}

X(55874) = X(2)X(7)∩X(4)X(34822)

Barycentrics    Sec[B]*Sec[C]*(1 + Sec[A]^2 + Sec[A]*Sec[B] + Sec[A]*Sec[C]) : :

X(55874) lies on these lines: {2, 7}, {4, 34822}, {19, 6708}, {72, 41344}, {92, 30675}, {278, 30674}, {281, 10319}, {405, 1712}, {452, 10538}, {936, 7549}, {940, 9119}, {960, 5706}, {1040, 4183}, {1435, 17073}, {1715, 12514}, {1763, 20262}, {1868, 37257}, {2339, 8748}, {3194, 47512}, {4640, 21160}, {5084, 40836}, {7079, 30810}, {7567, 55104}, {8807, 34042}, {17917, 25915}, {18679, 55462}, {24611, 37185}, {26165, 54359}, {31424, 37275}, {31435, 51616}, {37179, 46878}, {41004, 41883}

X(55875) = X(2)X(7)∩X(3)X(33)

Barycentrics    Sec[B]*Sec[C]*(-1 + Sec[A]^2 + Sec[A]*Sec[B] + Sec[A]*Sec[C]) : :

X(55875) lies on these lines: {1, 37275}, {2, 7}, {3, 33}, {19, 1214}, {28, 1038}, {34, 7535}, {40, 40960}, {55, 21160}, {56, 43214}, {169, 223}, {208, 442}, {278, 9816}, {443, 44696}, {474, 52389}, {610, 21370}, {942, 7078}, {1073, 1767}, {1435, 37695}, {1439, 34048}, {1452, 54346}, {1748, 30675}, {1817, 46884}, {1859, 30265}, {2082, 45126}, {4219, 9817}, {5252, 15940}, {6349, 55472}, {6350, 55478}, {6904, 10538}, {7011, 40937}, {7131, 16054}, {7549, 15803}, {8270, 51687}, {9940, 21484}, {10383, 11028}, {16577, 26215}, {16870, 37526}, {18588, 31261}, {18679, 55463}, {20613, 37075}, {37264, 54320}, {37543, 54385}, {39943, 40407}, {52373, 54324}

X(55875) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 57, 40152}, {6203, 6204, 5746}

X(55876) = X(1)X(2)∩X(63)X(1659)

Barycentrics    Cos[A] + Cos[B] + Cos[C] + Sin[A] : :

X(55876) lies on these lines: {1, 2}, {63, 1659}, {81, 26458}, {149, 31568}, {176, 5744}, {225, 1585}, {226, 55398}, {481, 31019}, {482, 3218}, {590, 8609}, {908, 30556}, {940, 19049}, {1068, 3535}, {1072, 7389}, {1583, 37579}, {1584, 26357}, {1586, 40950}, {1590, 54320}, {1592, 26481}, {1599, 36152}, {2094, 21169}, {2975, 31533}, {2990, 3300}, {3068, 8557}, {4383, 19050}, {5249, 13388}, {5604, 17724}, {5718, 7968}, {5745, 55397}, {7133, 31484}, {7969, 35466}, {10267, 16433}, {10680, 21548}, {10902, 16441}, {11012, 16440}, {11249, 16432}, {12001, 21550}, {13390, 31266}, {16202, 21547}, {16586, 31535}, {17718, 45713}, {17723, 45399}, {18991, 24597}, {21553, 34486}, {21561, 35252}, {25094, 31583}, {25939, 38487}, {26464, 32911}, {30557, 54357}, {31187, 44635}, {35258, 52805}, {37674, 44646}, {37679, 44645}

X(55877) = X(1)X(2)∩X(63)X(13390)

Barycentrics    Cos[A] + Cos[B] + Cos[C] - Sin[A] : :

X(55877) lies on these lines: {1, 2}, {63, 13390}, {81, 26464}, {149, 31567}, {175, 5744}, {225, 1586}, {226, 55397}, {481, 3218}, {482, 31019}, {615, 8609}, {908, 30557}, {940, 19050}, {1068, 3536}, {1072, 7388}, {1583, 26357}, {1584, 37579}, {1585, 40950}, {1589, 54320}, {1591, 26481}, {1600, 36152}, {1659, 31266}, {2975, 31532}, {2990, 3302}, {3069, 8557}, {4383, 19049}, {5249, 13389}, {5333, 39312}, {5605, 17724}, {5718, 7969}, {5745, 55398}, {7968, 35466}, {10267, 16432}, {10680, 21547}, {10902, 16440}, {11012, 16441}, {11249, 16433}, {12001, 21545}, {16202, 21548}, {16586, 31534}, {17718, 45714}, {17723, 45398}, {18992, 24597}, {21492, 34486}, {21558, 35252}, {25094, 31582}, {26458, 32911}, {30556, 54357}, {31187, 44636}, {35258, 52808}, {37674, 44645}, {37679, 44646}

X(55878) = X(2)X(3)∩X(184)X(49103)

Barycentrics    2 - 4*Cos[A]*Sin[A] - Sin[2*B] - Sin[2*C] : :
Barycentrics    2*a^2*b^2*c^2 - S*(a^2*(-a^2 + b^2 + c^2) + 4*S^2) : :

X(55878) lies on these lines; {2, 3}, {184, 49103}, {343, 642}, {394, 5420}, {486, 5407}, {615, 5409}, {1993, 13966}, {3035, 6348}, {3083, 5432}, {3084, 5433}, {4999, 6347}, {5418, 10601}, {5422, 8981}, {7584, 55566}, {11090, 45473}, {11245, 48773}, {12240, 23292}, {35256, 55567}, {37638, 55471}, {43650, 49104}, {52348, 53457}, {52349, 53468}

X(55878) = complement of X(15233)
X(55878) = ninepoint-circle-of-medial-triangle-inverse of X(47631)
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 1592}, {2, 140, 55866}, {2, 631, 1583}, {2, 1584, 1591}, {2, 1599, 15235}, {2, 1600, 5}, {2, 3523, 6806}, {2, 15234, 3628}, {549, 15235, 1599}, {632, 15236, 2}, {3526, 55577, 2}, {3533, 3539, 2}

X(55879) = X(2)X(3)∩X(33)X(55876)

Barycentrics    Cos[A] + Cos[B] + Cos[C] - Tan[A] : :

X(55879) lies on these lines; {2, 3}, {33, 55876}, {34, 55877}, {226, 55395}, {908, 55430}, {940, 55411}, {5249, 55460}, {5393, 55482}, {5405, 55475}, {5745, 55396}, {6212, 30687}, {54357, 55431}

X(55880) = X(2)X(3)∩X(33)X(55877)

Barycentrics    Cos[A] + Cos[B] + Cos[C] + Tan[A] : :

X(55880) lies on these lines; {2, 3}, {33, 55877}, {34, 55876}, {226, 55396}, {908, 55431}, {940, 55412}, {5249, 55461}, {5393, 55481}, {5405, 55476}, {5745, 55395}, {6213, 30687}, {54357, 55430}

X(55881) = X(2)X(3)∩X(485)X(8968)

Barycentrics    1 + 2*Tan[A] + Tan[B] + Tan[C] : :

X(55881) lies on these lines; {2, 3}, {485, 11433}, {486, 8968}, {638, 34836}, {3083, 19372}, {3084, 9817}, {3618, 18923}, {4993, 16037}, {5408, 10963}, {5409, 12322}, {5591, 14767}, {6289, 14826}, {6413, 10961}, {8797, 11091}, {11090, 12323}, {11206, 48466}, {12964, 17825}, {13567, 42265}, {16028, 27509}, {17810, 45861}, {17811, 23311}, {23292, 42262}, {32064, 48467}, {37643, 42277}, {45198, 55474}

orthocentroidal-circle-inverse of X(1589)
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 1589}, {2, 1585, 1590}, {2, 3091, 1586}, {2, 32489, 6805}, {2, 55573, 3}, {486, 8968, 11427}, {3090, 3535, 2}, {11313, 15235, 2}, {32491, 55579, 2}

X(55882) = X(2)X(3)∩X(485)X(11427)

Barycentrics    1 - 2*Tan[A] - Tan[B] - Tan[C] : :

X(55882) lies on these lines; {2, 3}, {485, 11427}, {486, 11433}, {637, 34836}, {3083, 9817}, {3084, 19372}, {3618, 18924}, {4993, 16032}, {5408, 12323}, {5409, 10961}, {5590, 14767}, {6290, 14826}, {6414, 10963}, {8797, 11090}, {8968, 42277}, {11091, 12322}, {11206, 48467}, {12970, 17825}, {13567, 42262}, {17810, 45860}, {17811, 23312}, {23292, 42265}, {32064, 48466}, {37643, 42274}, {45198, 55480}

X(55882) = orthocentroidal-circle-inverse of X(1590)
X(55882) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 1590}, {2, 1586, 1589}, {2, 3091, 1585}, {2, 32488, 6806}, {2, 55569, 3}, {3090, 3536, 2}, {11314, 15236, 2}, {32490, 55577, 2}

X(55883) = X(2)X(3)∩X(175)X(6360)

Barycentrics    1 - Tan[A] + Tan[B] + Tan[C] : :

X(55883) lies on these lines; {2, 3}, {175, 6360}, {184, 8982}, {193, 18923}, {253, 32814}, {343, 489}, {394, 490}, {488, 46717}, {491, 5407}, {492, 20477}, {637, 11090}, {638, 5409}, {1038, 55482}, {1040, 55475}, {1270, 6527}, {1578, 55411}, {1588, 32589}, {1899, 26441}, {1993, 43133}, {3164, 26873}, {6413, 11417}, {6458, 55567}, {6459, 11433}, {6460, 11427}, {6515, 43134}, {7585, 26868}, {8968, 35820}, {10132, 45407}, {11418, 26894}, {13440, 26916}, {13441, 44128}, {13567, 42258}, {13935, 32575}, {13941, 13960}, {23292, 42259}, {40680, 55479}, {41761, 44196}, {41914, 51952}, {42329, 45510}

X(55883) = anticomplement of X(1585)
X(55883) = anticomplement of the isogonal conjugate of X(6413)
X(55883) = anticomplement of the isotomic conjugate of X(11090)
X(55883) = isotomic conjugate of the isogonal conjugate of X(10533)
X(55883) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 488}, {485, 21270}, {1820, 638}, {6413, 8}, {8577, 5905}, {11090, 6327}, {39383, 7253}, {41515, 5906}, {54031, 21300}
X(55883) = X(11090)-Ceva conjugate of X(2)
X(55883) = barycentric product X(76)*X(10533)
X(55883) = barycentric quotient X(10533)/X(6)
X(55883) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 55573}, {3, 1586, 2}, {4, 1589, 2}, {175, 46422, 6360}, {376, 3536, 1590}, {1584, 7388, 2}, {1590, 3536, 2}, {1591, 39387, 2}, {6805, 11292, 2}

X(55884) = X(2)X(3)∩X(95)X(491)

Barycentrics    1 + Tan[A] + 2*Tan[B] + 2*Tan[C] : :

X(55884) lies on these lines; {2, 3}, {95, 491}, {343, 45509}, {394, 45508}, {492, 5409}, {637, 5407}, {5418, 46760}, {5420, 8954}, {6396, 8968}, {8966, 32785}, {9540, 11433}, {10132, 45510}, {11427, 13935}, {45472, 55020}

X(55884) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 1585}, {2, 1589, 1586}, {2, 1600, 7389}, {2, 3523, 1590}, {2, 11294, 1592}, {2, 55569, 3090}, {3525, 3536, 2}, {11315, 55577, 2}

X(55885) = X(2)X(3)∩X(69)X(6415)

Barycentrics    2 + Tan[B] + Tan[C] : :

X(55885) lies on these lines; {2, 3}, {69, 6415}, {141, 10960}, {216, 615}, {343, 5409}, {371, 13567}, {372, 23292}, {394, 10665}, {488, 37669}, {491, 41008}, {492, 41005}, {577, 590}, {641, 6509}, {1060, 3084}, {1062, 3083}, {1151, 26958}, {1214, 31534}, {1270, 40995}, {1578, 17811}, {1579, 17825}, {1899, 10132}, {3068, 15905}, {3070, 8968}, {3284, 32787}, {3311, 11433}, {3312, 11427}, {3580, 18457}, {3589, 11514}, {5158, 32788}, {5393, 46974}, {5405, 17102}, {5407, 11091}, {5408, 11064}, {5590, 20208}, {6200, 47296}, {6221, 37643}, {6306, 40682}, {6307, 40683}, {6389, 24246}, {6413, 26950}, {7585, 38292}, {7586, 15851}, {8252, 36751}, {8253, 36748}, {8962, 14961}, {10898, 37649}, {10979, 32790}, {12257, 23291}, {13389, 17073}, {13441, 52347}, {13847, 52703}, {13889, 23298}, {14389, 18459}, {16032, 19210}, {18289, 39648}, {19355, 26873}, {22052, 32789}, {22401, 32497}, {30412, 42018}, {32805, 40680}, {32808, 40996}, {35300, 45303}, {37565, 55877}, {37696, 55482}, {37697, 55475}, {41588, 45489}, {42353, 45554}, {45298, 45411}

X(55885) = complement of X(1585)
X(55885) = complement of the isogonal conjugate of X(6413)
X(55885) = complement of the isotomic conjugate of X(11090)
X(55885) = isotomic conjugate of the isogonal conjugate of X(21640)
X(55885) = isotomic conjugate of the polar conjugate of X(3070)
X(55885) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 8968}, {48, 641}, {485, 20305}, {1820, 640}, {6413, 10}, {8577, 226}, {11090, 2887}, {13455, 41883}, {39383, 8062}, {54031, 21259}
X(55885) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 8968}, {54031, 525}
X(55885) = X(8968)-Dao conjugate of X(2)
X(55885) = barycentric product X(i)*X(j) for these {i,j}: {69, 3070}, {76, 21640}, {8968, 11090}
X(55885) = barycentric quotient X(i)/X(j) for these {i,j}: {3070, 4}, {8968, 1585}, {21640, 6}, {21659, 3071}
X(55885) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 3535}, {2, 1586, 5}, {2, 1589, 3}, {2, 1591, 32491}, {2, 6805, 11313}, {2, 7388, 15235}, {2, 11292, 55579}, {3, 23258, 418}, {3, 38283, 23246}, {427, 3156, 36714}, {5407, 37638, 11091}

X(55886) = X(2)X(3)∩X(1994)X(10666)

Barycentrics    1 + 3*Tan[A] + Tan[B] + Tan[C] : :

X(55886) lies on these lines; {2, 3}, {1994, 10666}, {3068, 44633}, {5406, 32807}, {6565, 8968}, {9817, 55481}, {10601, 12964}, {10962, 26894}, {11427, 42561}, {11433, 31412}, {13567, 42273}, {14826, 26468}, {18923, 51171}, {19372, 55476}, {23292, 42270}, {31610, 55534}

X(55886) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3832, 55569}, {5, 1585, 2}, {1590, 3090, 2}, {1592, 7389, 2}

X(55887) = X(2)X(3)∩X(6)X(8966)

Barycentrics    2 + 2*Tan[A] + Tan[B] + Tan[C] : :
X(55887) = 3 X[2] + X[55573]

X(55887) lies on these lines; {2, 3}, {6, 8966}, {154, 48466}, {485, 13567}, {486, 23292}, {639, 17811}, {1060, 55481}, {1062, 55476}, {1853, 48467}, {3083, 37697}, {3084, 37696}, {3167, 49355}, {5408, 34836}, {6214, 14826}, {6289, 9306}, {6290, 21243}, {6415, 55020}, {7583, 11433}, {7584, 11427}, {8797, 32813}, {8954, 10576}, {10961, 15896}, {10963, 45472}, {14767, 45473}, {16032, 19176}, {18538, 37643}, {23311, 53415}, {26868, 44633}, {26958, 42265}, {34986, 49317}, {41005, 55474}, {41008, 55473}, {42277, 47296}

X(55887) = midpoint of X(1589) and X(55573)
X(55887) = complement of X(1589)
X(55887) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1583, 11315}, {2, 1585, 3}, {2, 1590, 140}, {2, 1592, 11314}, {2, 3091, 3536}, {2, 7389, 55577}, {2, 55573, 1589}

X(55888) = X(2)X(3)∩X(176)X(6360)

Barycentrics    1 + Tan[A] - Tan[B] - Tan[C] : :

X(55888) lies on these lines; {2, 3}, {176, 6360}, {184, 26441}, {193, 18924}, {343, 490}, {394, 489}, {487, 46717}, {491, 20477}, {492, 5406}, {637, 5408}, {638, 11091}, {1038, 55476}, {1040, 55481}, {1271, 6527}, {1579, 55412}, {1587, 8954}, {1899, 8982}, {1993, 43134}, {3164, 26945}, {6200, 8968}, {6414, 11418}, {6457, 55566}, {6459, 11427}, {6460, 11433}, {6515, 43133}, {8966, 8972}, {9540, 32568}, {10133, 45406}, {11417, 26919}, {13430, 44128}, {13567, 42259}, {23292, 42258}, {40680, 55473}, {41761, 44199}, {41914, 51953}, {42329, 45511}

X(55888) = anticomplement of X(1586)
X(55888) = anticomplement of the isogonal conjugate of X(6414)
X(55888) = anticomplement of the isotomic conjugate of X(11091)
X(55888) = isotomic conjugate of the isogonal conjugate of X(10534)
X(55888) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 487}, {486, 21270}, {1820, 637}, {6414, 8}, {8576, 5905}, {11091, 6327}, {26922, 4329}, {39384, 7253}, {41516, 5906}, {54030, 21300}
X(55888) = X(11091)-Ceva conjugate of X(2)
X(55888) = barycentric product X(76)*X(10534)
X(55888) = barycentric quotient X(10534)/X(6)
X(55888) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 55569}, {3, 1585, 2}, {4, 1590, 2}, {176, 46421, 6360}, {376, 3535, 1589}, {1583, 7389, 2}, {1589, 3535, 2}, {1592, 39388, 2}, {6806, 11291, 2}

X(55889) = X(2)X(3)∩X(95)X(492)

Barycentrics    1 - Tan[A] - 2*Tan[B] - 2*Tan[C] : :

X(55889) lies on these lines; {2, 3}, {95, 492}, {343, 45508}, {394, 45509}, {491, 5408}, {638, 5406}, {3069, 26868}, {5418, 32589}, {5420, 46760}, {8962, 13638}, {9540, 11427}, {10133, 45511}, {11433, 13935}, {13960, 32786}, {45473, 55021}

X(55889) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 1586}, {2, 1590, 1585}, {2, 1599, 7388}, {2, 3523, 1589}, {2, 11293, 1591}, {2, 55573, 3090}, {3525, 3535, 2}, {11316, 55579, 2}

X(55890) = X(2)X(3)∩X(69)X(6416)

Barycentrics    2 - Tan[B] - Tan[C] : :

X(55890) lies on these lines; {2, 3}, {69, 6416}, {141, 10962}, {216, 590}, {343, 5408}, {371, 23292}, {372, 13567}, {394, 10666}, {487, 37669}, {491, 41005}, {492, 41008}, {577, 615}, {642, 6509}, {1060, 3083}, {1062, 3084}, {1152, 26958}, {1214, 31535}, {1271, 40995}, {1578, 17825}, {1579, 17811}, {1899, 10133}, {3069, 15905}, {3284, 32788}, {3311, 11427}, {3312, 11433}, {3580, 18459}, {3589, 11513}, {5158, 32787}, {5393, 17102}, {5405, 46974}, {5406, 11090}, {5409, 11064}, {5591, 20208}, {6302, 40682}, {6303, 40683}, {6389, 24245}, {6396, 47296}, {6398, 37643}, {6414, 26951}, {7585, 15851}, {7586, 38292}, {8252, 36748}, {8253, 36751}, {8961, 46832}, {10897, 37649}, {10979, 32789}, {12256, 23291}, {13388, 17073}, {13430, 52347}, {13846, 52703}, {13943, 23299}, {14389, 18457}, {16037, 19210}, {18290, 39679}, {19356, 26945}, {22052, 32790}, {22401, 32494}, {30413, 42018}, {32806, 40680}, {32809, 40996}, {35299, 45303}, {37565, 55876}, {37696, 55476}, {37697, 55481}, {41588, 45488}, {42353, 45555}, {45298, 45410}

X(55890) = complement of X(1586)
X(55890) = complement of the isogonal conjugate of X(6414)
X(55890) = complement of the isotomic conjugate of X(11091)
X(55890) = isotomic conjugate of the isogonal conjugate of X(21641)
X(55890) = isotomic conjugate of the polar conjugate of X(3071)
X(55890) = X(i)-complementary conjugate of X(j) for these (i,j): {48, 642}, {486, 20305}, {1820, 639}, {6414, 10}, {8576, 226}, {11091, 2887}, {26922, 18589}, {39384, 8062}, {54030, 21259}
X(55890) = X(54030)-Ceva conjugate of X(525)
X(55890) = barycentric product X(i)*X(j) for these {i,j}: {69, 3071}, {76, 21641}
X(55890) = barycentric quotient X(i)/X(j) for these {i,j}: {3071, 4}, {21641, 6}, {21659, 3070}
X(55890) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 3536}, {2, 1585, 5}, {2, 1590, 3}, {2, 1592, 32490}, {2, 6806, 11314}, {2, 7389, 15236}, {2, 11291, 55577}, {3, 23248, 418}, {3, 38283, 23256}, {427, 3155, 36709}, {1368, 8964, 3}, {5406, 37638, 11090}

X(55891) = X(2)X(3)∩X(1994)X(10665)

Barycentrics    1 - 3*Tan[A] - Tan[B] - Tan[C] : :

X(55891) lies on these lines; {2, 3}, {1994, 10665}, {3069, 44634}, {9817, 55475}, {10601, 12970}, {10960, 26919}, {11427, 31412}, {11433, 42561}, {13567, 42270}, {14826, 26469}, {18924, 51171}, {19372, 55482}, {23292, 42273}, {31610, 55533}

X(55891) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3832, 55573}, {5, 1586, 2}, {1589, 3090, 2}, {1591, 7388, 2}

X(55892) = X(2)X(3)∩X(6)X(8969)

Barycentrics    2 - 2*Tan[A] - Tan[B] - Tan[C] : :
X(55892) = 3 X[2] + X[55569]

X(55892) lies on these lines; {2, 3}, {6, 8969}, {154, 48467}, {485, 23292}, {486, 13567}, {590, 26868}, {640, 17811}, {1060, 55475}, {1062, 55482}, {1853, 48466}, {3083, 37696}, {3084, 37697}, {3167, 49356}, {5409, 34836}, {6215, 14826}, {6289, 21243}, {6290, 9306}, {6416, 55021}, {7583, 11427}, {7584, 11433}, {8797, 32812}, {8968, 42265}, {10577, 32589}, {10961, 26875}, {10963, 15895}, {14767, 45472}, {16037, 19176}, {18762, 37643}, {23312, 53415}, {26953, 44638}, {26958, 42262}, {34986, 49318}, {41005, 55480}, {41008, 55479}, {42274, 47296}
X(55892) = midpoint of X(1590) and X(55569)
X(55892) = complement of X(1590)
X(55892) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1584, 11316}, {2, 1586, 3}, {2, 1589, 140}, {2, 1591, 11313}, {2, 3091, 3535}, {2, 7388, 55579}, {2, 55569, 1590}

X(55893) = X(2)X(3)∩X(69)X(5407)

Barycentrics    1 + 2*Tan[B] + 2*Tan[C] : :

X(55893) lies on these lines; {2, 3}, {69, 5407}, {95, 55480}, {97, 43133}, {193, 11513}, {216, 7586}, {487, 11090}, {488, 5409}, {577, 7585}, {1151, 11433}, {1152, 11427}, {1270, 40680}, {1578, 1993}, {1579, 5422}, {3068, 36748}, {3069, 36751}, {5406, 37669}, {5590, 34828}, {6409, 13567}, {6410, 23292}, {6411, 37643}, {8968, 42261}, {8972, 22052}, {10132, 12256}, {10979, 13941}, {11514, 51171}, {12306, 33522}, {13439, 24246}, {19053, 52703}, {19420, 44192}, {32814, 41005}, {46724, 55474}

X(55893) = isotomic conjugate of the polar conjugate of X(7581)
X(55893) = X(34089)-complementary conjugate of X(20305)
X(55893) = barycentric product X(69)*X(7581)
X(55893) = barycentric quotient X(7581)/X(4)
X(55893) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 55573}, {3, 1589, 2}, {3, 23272, 418}, {631, 1586, 2}, {1584, 11292, 2}, {3156, 21736, 6995}, {6805, 39387, 2}

X(55894) = X(2)X(3)∩X(253)X(1270)

Barycentrics    2 - Tan[A] + Tan[B] + Tan[C] : :

X(55894) lies on these lines; {2, 3}, {253, 1270}, {347, 46422}, {487, 41914}, {490, 37669}, {492, 6527}, {494, 13949}, {1271, 5409}, {1578, 55443}, {3083, 3100}, {3084, 4296}, {6459, 13567}, {6460, 23292}, {8968, 23249}, {8974, 10313}, {16032, 43768}, {20477, 32805}, {23291, 26441}, {26958, 42258}

X(55894) = anticomplement of X(3535)
X(55894) = anticomplement of the isogonal conjugate of X(6415)
X(55894) = isotomic conjugate of the isogonal conjugate of X(17819)
X(55894) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 51953}, {1131, 21270}, {6415, 8}
X(55894) = barycentric product X(76)*X(17819)
X(55894) = barycentric quotient X(17819)/X(6)
X(55894) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 1585}, {2, 3522, 1590}, {2, 55569, 3091}, {3, 3536, 2}, {1586, 1589, 2}, {3128, 3156, 7000}, {7376, 55577, 2}

X(55895) = X(2)X(3)∩X(95)X(32806)

Barycentrics    2 + Tan[A] + 2*Tan[B] + 2*Tan[C] : :

X(55895) lies on these lines; {2, 3}, {95, 32806}, {141, 18923}, {3917, 10518}, {5409, 46621}, {5590, 6413}, {5591, 26873}, {6458, 33364}, {6460, 8968}, {9540, 13567}, {10132, 10784}, {10517, 43653}, {13935, 23292}, {37669, 45508}

X(55895) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 3535}, {2, 1584, 7375}, {2, 1586, 3090}, {2, 1589, 4}, {2, 11292, 3540}

X(55896) = X(2)X(3)∩X(1588)X(8968)

Barycentrics    2 + 3*Tan[A] + Tan[B] + Tan[C] : :

X(55896) lies on these lines; {2, 3}, {1588, 8968}, {3593, 5408}, {3595, 11091}, {7585, 19040}, {8962, 15355}, {9306, 26468}, {13567, 31412}, {21243, 26469}, {23292, 42561}, {26958, 42273}

X(55896) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 1589}, {2, 3832, 1586}, {2, 55573, 20}, {5, 3535, 2}, {3540, 11313, 2}, {7375, 15235, 2}

X(55897) = X(2)X(3)∩X(69)X(5406)

Barycentrics    1 - 2*Tan[B] - 2*Tan[C] : :

X(55897) lies on these lines; {2, 3}, {69, 5406}, {95, 55474}, {97, 43134}, {193, 11514}, {216, 7585}, {487, 5408}, {488, 11091}, {577, 7586}, {1151, 11427}, {1152, 11433}, {1271, 40680}, {1578, 5422}, {1579, 1993}, {3068, 36751}, {3069, 36748}, {5407, 37669}, {5591, 34828}, {6409, 23292}, {6410, 13567}, {6412, 37643}, {8972, 10979}, {10133, 12257}, {11513, 51171}, {12305, 33522}, {13428, 24245}, {13941, 22052}, {19054, 52703}, {19421, 44193}, {26899, 26912}, {32814, 41008}, {46724, 55480}

X(55897) = isotomic conjugate of the polar conjugate of X(7582)
X(55897) = X(34091)-complementary conjugate of X(20305)
X(55897) = barycentric product X(69)*X(7582)
X(55897) = barycentric quotient X(7582)/X(4)
X(55897) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 55569}, {3, 1590, 2}, {3, 8964, 7494}, {3, 23266, 418}, {631, 1585, 2}, {1583, 11291, 2}, {6806, 39388, 2}

X(55898) = X(2)X(3)∩X(253)X(1271)

Barycentrics    2 + Tan[A] - Tan[B] - Tan[C] : :

X(55898) lies on these lines; {2, 3}, {253, 1271}, {347, 46421}, {488, 41914}, {489, 37669}, {491, 6527}, {493, 8975}, {1270, 5408}, {1579, 55444}, {3083, 4296}, {3084, 3100}, {6459, 23292}, {6460, 13567}, {8962, 22240}, {8968, 9540}, {8969, 8972}, {8982, 23291}, {10313, 13950}, {16037, 43768}, {20477, 32806}, {26958, 42259}

X(55898) = anticomplement of X(3536)
X(55898) = anticomplement of the isogonal conjugate of X(6416)
X(55898) = isotomic conjugate of the isogonal conjugate of X(17820)
X(55898) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 51952}, {1132, 21270}, {6416, 8}
X(55898) = barycentric product X(76)*X(17820)
X(55898) = barycentric quotient X(17820)/X(6)
X(55898) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 1586}, {2, 3522, 1589}, {2, 55573, 3091}, {3, 3535, 2}, {1585, 1590, 2}, {3127, 3155, 7374}, {7375, 55579, 2}

X(55899) = X(2)X(3)∩X(95)X(32805)

Barycentrics    2 - Tan[A] - 2*Tan[B] - 2*Tan[C] : :

X(55899) lies on these lines; {2, 3}, {95, 32805}, {141, 18924}, {3917, 10517}, {5408, 46622}, {5590, 26945}, {5591, 6414}, {6457, 33365}, {8968, 32785}, {9540, 23292}, {10133, 10783}, {10518, 43653}, {13567, 13935}, {37669, 45509}

X(55899) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 3536}, {2, 1583, 7376}, {2, 1585, 3090}, {2, 1590, 4}, {2, 11291, 3539}

X(55900) = X(2)X(7)∩X(4)X(7293)

Barycentrics    Cos[A] - Sin[A]^2 - Sin[B]^2 - Sin[C]^2 : :

X(55900) lies on these lines: {2, 7}, {4, 7293}, {5, 1473}, {31, 499}, {38, 498}, {92, 16706}, {140, 7085}, {141, 55399}, {222, 37649}, {343, 52424}, {631, 5314}, {914, 5256}, {1352, 26889}, {2221, 37646}, {2345, 20879}, {2975, 19784}, {3220, 6997}, {3541, 37534}, {3589, 55400}, {3618, 26871}, {3619, 26872}, {3763, 55405}, {3869, 19836}, {4000, 14213}, {5709, 7383}, {6515, 52423}, {7485, 50861}, {7499, 37581}, {7539, 26866}, {10072, 17469}, {10601, 26932}, {11313, 16028}, {11427, 22128}, {12526, 19881}, {14561, 26892}, {14786, 24467}, {15474, 24773}, {16419, 21015}, {17370, 18750}, {19854, 32781}, {24320, 37439}, {26034, 26363}, {26364, 33163}, {26942, 55437}, {47355, 55406}

X(55900) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9965, 28780}, {2, 27003, 20266}, {2, 27509, 3305}, {3618, 26871, 54444}

X(55901) = X(2)X(7)∩X(5)X(7293)

Barycentrics    Cos[A] - 2*Sin[A]^2 - 2*Sin[B]^2 - 2*Sin[C]^2 : :

X(55901) lies on these lines: {2, 7}, {5, 7293}, {92, 17370}, {140, 5314}, {1473, 1656}, {3220, 37990}, {3526, 7085}, {3582, 17469}, {3589, 54444}, {3763, 55399}, {3869, 19881}, {11548, 26933}, {11682, 19836}, {14213, 16706}, {17289, 20879}, {22128, 37649}, {24206, 26889}, {26892, 38317}, {37636, 52423}, {47355, 55400}

X(55902) = X(2)X(7)∩X(4)X(5314)

Barycentrics    Cos[A] + Sin[A]^2 + Sin[B]^2 + Sin[C]^2 : :

X(55902) lies on these lines: {2, 7}, {4, 5314}, {5, 7085}, {31, 498}, {38, 499}, {69, 54444}, {92, 17289}, {140, 1473}, {141, 55400}, {219, 37649}, {343, 55432}, {631, 7293}, {958, 25963}, {1211, 45886}, {1352, 26890}, {2221, 37662}, {2345, 14213}, {2975, 19836}, {3589, 55399}, {3618, 26872}, {3619, 26871}, {3763, 55406}, {3869, 19784}, {4000, 20879}, {5133, 50861}, {5233, 19795}, {5285, 6997}, {7330, 7383}, {7404, 55104}, {7499, 24320}, {7539, 26867}, {10056, 17469}, {10601, 26942}, {11314, 16028}, {11517, 50324}, {14552, 28813}, {14561, 26893}, {14786, 26921}, {16419, 26933}, {17371, 18750}, {19854, 26061}, {26028, 26034}, {26363, 33163}, {26932, 55438}, {30854, 52412}, {37439, 37581}, {47355, 55405}

X(55902) = {X(2),X(28739)}-harmonic conjugate of X(5249)

X(55903) = X(2)X(7)∩X(5)X(5314)

Barycentrics    Cos[A] + 2*Sin[A]^2 + 2*Sin[B]^2 + 2*Sin[C]^2 : :

X(55903) lies on these lines: {2, 7}, {5, 5314}, {92, 17371}, {140, 7293}, {141, 54444}, {1211, 45883}, {1473, 3526}, {1656, 7085}, {2975, 19881}, {3584, 17469}, {3763, 55400}, {5285, 37990}, {11548, 21015}, {11682, 19784}, {14213, 17289}, {14786, 55104}, {16706, 20879}, {24206, 26890}, {26893, 38317}, {47355, 55399}

X(55903) = {X(2),X(28780)}-harmonic conjugate of X(5249)

X(55904) = X(2)X(7)∩X(498)X(17469)

Barycentrics    Cos[A] + 3*Sin[A]^2 + 3*Sin[B]^2 + 3*Sin[C]^2 : :

X(55904) lies on these lines: {2, 7}, {498, 17469}, {632, 1473}, {3090, 5314}, {3525, 7293}, {3619, 54444}, {3628, 7085}, {7383, 18540}, {7571, 50861}, {34573, 55400}, {51126, 55399}

X(55905) = X(2)X(7)∩X(4)X(1473)

Barycentrics    2*Cos[A] - Sin[A]^2 - Sin[B]^2 - Sin[C]^2 : :

X(55905) lies on these lines: {2, 7}, {4, 1473}, {6, 26871}, {20, 7293}, {31, 3075}, {38, 3085}, {56, 25876}, {69, 55399}, {92, 4000}, {141, 26872}, {145, 33178}, {189, 5222}, {222, 11427}, {241, 6349}, {281, 54284}, {343, 55437}, {427, 26866}, {499, 1707}, {631, 7085}, {938, 27505}, {1210, 4194}, {1407, 23292}, {1595, 26928}, {2221, 34234}, {3220, 6995}, {3423, 14004}, {3436, 4202}, {3523, 5314}, {3541, 26877}, {3546, 37612}, {3547, 37532}, {3589, 55406}, {3618, 55400}, {3666, 6350}, {4200, 4292}, {5262, 52366}, {5709, 7400}, {6776, 26889}, {6836, 23542}, {7011, 26906}, {7146, 45224}, {7193, 14826}, {7365, 17923}, {7392, 24320}, {7404, 24467}, {7484, 26939}, {7494, 37581}, {8889, 26933}, {10519, 26893}, {10527, 37530}, {11031, 27531}, {11433, 26932}, {12526, 19836}, {12610, 21370}, {14853, 26892}, {16706, 18750}, {17740, 23600}, {18141, 28420}, {19843, 26034}, {19855, 32781}, {22129, 37649}, {34120, 37545}, {51171, 54444}

X(55905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9965, 28739}, {141, 55405, 26872}, {427, 26866, 26929}, {26932, 52424, 11433}

X(55906) = X(2)X(7)∩X(30)X(1473)

Barycentrics    3*Cos[A] - Sin[A]^2 - Sin[B]^2 - Sin[C]^2 : :

X(55906) lies on these lines: {2, 7}, {30, 1473}, {31, 10072}, {38, 10056}, {92, 37756}, {376, 7293}, {498, 36263}, {499, 896}, {524, 55399}, {549, 7085}, {597, 55400}, {599, 55405}, {1707, 3582}, {1992, 26871}, {3086, 36277}, {3524, 5314}, {4000, 14206}, {11179, 26889}, {11684, 19836}, {13633, 20760}, {20423, 26892}, {21356, 26872}, {26866, 31152}, {26890, 38064}, {26893, 54173}, {26932, 55437}, {37581, 44210}, {47352, 55406}

X(55907) = X(2)X(7)∩X(20)X(1473)

Barycentrics    4*Cos[A] - Sin[A]^2 - Sin[B]^2 - Sin[C]^2 : :

X(55907) lies on these lines: {2, 7}, {20, 1473}, {31, 14986}, {69, 55405}, {145, 54295}, {189, 239}, {193, 26871}, {499, 16570}, {1407, 37669}, {1707, 3086}, {2221, 37666}, {3088, 24467}, {3089, 37532}, {3522, 7293}, {3523, 7085}, {3618, 55406}, {3620, 26872}, {4000, 18750}, {4383, 54113}, {5314, 15717}, {5709, 52404}, {7386, 26866}, {7396, 26929}, {7398, 24320}, {10565, 37581}, {11427, 22129}, {11433, 55437}, {20110, 32863}, {24177, 41785}, {26928, 52398}, {51171, 55400}

X(55907) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 27509, 2}, {3911, 27539, 2}, {5435, 27540, 2}, {26871, 55399, 193}

X(55908) = X(2)X(7)∩X(376)X(1473)

Barycentrics    6*Cos[A] - Sin[A]^2 - Sin[B]^2 - Sin[C]^2 : :

X(55908) = X[26871] + 2 X[55405]

X(55908) lies on these lines: {2, 7}, {376, 1473}, {524, 26871}, {597, 55406}, {599, 26872}, {896, 3086}, {1707, 10072}, {1992, 55399}, {3085, 36263}, {3436, 17679}, {3524, 7085}, {3582, 16570}, {5314, 15692}, {5709, 34621}, {7293, 10304}, {13633, 22149}, {14986, 36277}, {18750, 37756}, {26866, 26939}, {26892, 54132}, {26893, 50967}, {26929, 31152}

X(55909) = X(2)X(7)∩X(1473)X(3522)

Barycentrics    8*Cos[A] - Sin[A]^2 - Sin[B]^2 - Sin[C]^2 : :

X(55909) lies on these lines: {2, 7}, {193, 55405}, {1473, 3522}, {1707, 14986}, {3086, 16570}, {4359, 30694}, {7085, 15717}, {7293, 21734}, {20080, 26871}, {23089, 36698}, {24177, 30625}, {51170, 55399}, {51171, 55406}

X(55910) = X(2)X(7)∩X(631)X(1473)

Barycentrics    2*Cos[A] + Sin[A]^2 + Sin[B]^2 + Sin[C]^2 : :

X(55910) lies on these lines: {2, 7}, {4, 7085}, {6, 26872}, {8, 54305}, {10, 4200}, {20, 5314}, {31, 3074}, {38, 3086}, {69, 55400}, {92, 2345}, {141, 26871}, {189, 29611}, {193, 54444}, {219, 11427}, {220, 23292}, {268, 26906}, {343, 55438}, {427, 26867}, {464, 54322}, {498, 1707}, {631, 1473}, {964, 3436}, {1211, 3330}, {1595, 26938}, {2551, 11109}, {2975, 17526}, {3061, 45224}, {3088, 55104}, {3101, 5813}, {3523, 7293}, {3541, 26878}, {3589, 55405}, {3618, 55399}, {3920, 5807}, {3955, 14826}, {4194, 12572}, {5285, 6995}, {5739, 23600}, {6349, 25091}, {6350, 32777}, {6554, 52412}, {6776, 26890}, {7123, 40435}, {7330, 7400}, {7378, 50861}, {7392, 37581}, {7404, 26921}, {7484, 26929}, {7494, 24320}, {8889, 21015}, {10519, 26892}, {11433, 26942}, {12526, 19784}, {14552, 28795}, {14853, 26893}, {17289, 18750}, {17555, 40444}, {17776, 25082}, {18540, 34621}, {18652, 25930}, {19795, 28807}, {19808, 20921}, {19843, 33163}, {19855, 26061}, {24635, 28769}, {26027, 26034}, {37649, 55466}

X(55910) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3219, 27509}, {2, 31018, 27539}, {141, 55406, 26871}, {427, 26867, 26939}, {5273, 28780, 2}, {7308, 20266, 2}, {26942, 55432, 11433}

X(55911) = X(2)X(7)∩X(549)X(1473)

Barycentrics    3*Cos[A] + Sin[A]^2 + Sin[B]^2 + Sin[C]^2 : :

X(55911) lies on these lines: {2, 7}, {30, 7085}, {31, 10056}, {38, 10072}, {376, 5314}, {498, 896}, {499, 36263}, {524, 55400}, {549, 1473}, {597, 55399}, {599, 55406}, {1707, 3584}, {1992, 26872}, {2345, 14206}, {3085, 36277}, {3524, 7293}, {11179, 26890}, {11684, 19784}, {13632, 20760}, {14210, 16585}, {20423, 26893}, {21356, 26871}, {24320, 44210}, {26867, 31152}, {26889, 38064}, {26892, 54173}, {26942, 55438}, {31133, 50861}, {37645, 52405}, {47352, 55405}

X(55912) = X(2)X(7)∩X(1473)X(3523)

Barycentrics    4*Cos[A] + Sin[A]^2 + Sin[B]^2 + Sin[C]^2 : :

X(55912) lies on these lines: {2, 7}, {20, 7085}, {38, 14986}, {69, 55406}, {189, 3661}, {193, 26872}, {220, 37669}, {348, 25091}, {498, 16570}, {1211, 54113}, {1260, 36706}, {1473, 3523}, {1707, 3085}, {2345, 18750}, {3088, 26921}, {3436, 50408}, {3522, 5314}, {3618, 55405}, {3620, 26871}, {4416, 23600}, {5278, 26961}, {7123, 8816}, {7293, 15717}, {7330, 52404}, {7386, 26867}, {7396, 26939}, {7398, 37581}, {8165, 25983}, {10565, 24320}, {11427, 55466}, {11433, 55438}, {17776, 24635}, {18652, 26658}, {19822, 30807}, {20110, 37685}, {26034, 26050}, {26938, 52398}, {51170, 54444}, {51171, 55399}

X(55912) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5273, 28739, 2}, {26872, 55400, 193}

X(55913) = X(2)X(7)∩X(1473)X(3524)

Barycentrics    6*Cos[A] + Sin[A]^2 + Sin[B]^2 + Sin[C]^2 : :
X(55913) = X[26872] + 2 X[55406]

X(55913) lies on these lines: {2, 7}, {376, 7085}, {524, 26872}, {597, 55405}, {599, 26871}, {896, 3085}, {1473, 3524}, {1707, 10056}, {1992, 55400}, {3086, 36263}, {3436, 50171}, {3584, 16570}, {5032, 54444}, {5314, 10304}, {6350, 50104}, {7293, 15692}, {7330, 34621}, {13632, 22149}, {26034, 26056}, {26867, 26929}, {26892, 50967}, {26893, 54132}, {26939, 31152}

X(55914) = X(2)X(7)∩X(1473)X(15717)

Barycentrics    8*Cos[A] + Sin[A]^2 + Sin[B]^2 + Sin[C]^2 : :

X(55914) lies on these lines: {2, 7}, {81, 20111}, {193, 55406}, {1473, 15717}, {3085, 16570}, {3436, 50431}, {3522, 7085}, {5314, 21734}, {19822, 30694}, {20080, 26872}, {51170, 55400}, {51171, 55405}

X(55915) = X(2)X(7)∩X(381)X(15717)

Barycentrics    3*Cos[A] - 2*Sin[A]^2 - 2*Sin[B]^2 - 2*Sin[C]^2 : :

X(55915) lies on these lines: {2, 7}, {30, 7293}, {31, 3582}, {38, 3584}, {228, 13633}, {381, 1473}, {499, 36277}, {542, 26889}, {549, 5314}, {597, 54444}, {599, 55399}, {5054, 7085}, {5476, 26892}, {10168, 26890}, {11684, 19881}, {13632, 22060}, {14206, 16706}, {14213, 37756}, {14787, 24467}, {18281, 37612}, {21358, 55405}, {26893, 50977}, {47352, 55400}

X(55916) = X(2)X(7)∩X(1473)X(5054)

Barycentrics    3*Cos[A] + 2*Sin[A]^2 + 2*Sin[B]^2 + 2*Sin[C]^2 : :

X(55916) lies on these lines: {2, 7}, {30, 5314}, {31, 3584}, {38, 3582}, {228, 13632}, {381, 7085}, {498, 36277}, {524, 54444}, {542, 26890}, {549, 7293}, {599, 55400}, {1211, 3013}, {1473, 5054}, {5476, 26893}, {10168, 26889}, {13633, 22060}, {14206, 17289}, {14389, 52405}, {14787, 26921}, {16585, 24036}, {20879, 37756}, {21358, 55406}, {26892, 50977}, {47352, 55399}



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Kimberling-Pavlov conjugates: X(55917)-X(56365)

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This preamble and centers X(55917)-X(56365) were contributed by Ivan Pavlov, August 14, 2023.

Let P1={a1,a2,a3} and P2={b1, b2, b3) be arbitrary points and let (cc) be the circumconic with perspector X={u,v,w}. Let A1, B1, C1 and A2, B2, C2 be the traces on (cc) of P1 and P2, respectively.

The lines A1A2, B1B2, C1C2 form a triangle perspective to ABC. The perspector has the following barycentrics:

u/(u^2/(a1*b1)-(v/a2+w/a3)*(v/b2+w/b3)) : v/(v^2/(a2*b2)-(u/a1+w/a3)*(u/b1+w/b3)) : w/(w^2/(a3*b3)-(u/a1+v/a2)*(u/b1+v/b2))

This point is here introduced as the Kimberling-Pavlov X-conjugate of P1 and P2. It is obviously symmetric and involutory (i.e., it is a conjugation). In his article "Mappings Associated with Vertex Triangles" (Forum Geometricorum, 9 (2009) 27-39), Clark Kimberling discusses this mapping for the case X=X(6), and he denotes the mapping by M1. He also proposes variations denoted by M2, M3, and M4.

Here, these mappings are generalized for any point X, and the equivalent of formula (6) on p.34 of the cited article gives the following barycentrics:

(KP2(X) of P1 and P2) = u/(u^2/(a1*b1)-(v/a2-w/a3)*(v/b2-w/b3)) : v/(v^2/(a2*b2)-(u/a1-w/a3)*(u/b1-w/b3)) : w/(w^2/(a3*b3)-(u/a1-v/a2)*(u/b1-v/b2))
(KP3(X) of P1 and P2) = u/(u^2/(a1*b1)+(v/a2+w/a3)*(v/b2+w/b3)) : v/(v^2/(a2*b2)+(u/a1+w/a3)*(u/b1+w/b3)) : w/(w^2/(a3*b3)+(u/a1+v/a2)*(u/b1+v/b2))
(KP4(X) of P1 and P2) = u/(u^2/(a1*b1)+(v/a2-w/a3)*(v/b2-w/b3)) : v/(v^2/(a2*b2)+(u/a1-w/a3)*(u/b1-w/b3)) : w/(w^2/(a3*b3)+(u/a1-v/a2)*(u/b1-v/b2))

Stated below are a few properties of these points:

Theorem 1.
Let I=X(1) and
P'= cevapoint of I and the isogonal conjugate of P
Q'= cevapoint of I and the isogonal conjugate of Q.

Then the Kimberling-Pavlov I-conjugate of P and Q is the intersection, other than A,B,C, of the conics {{A,B,C,P,Q'}} and {{A,B,C,P',Q}}.

Theorem 2.
In the limiting case, where P=Q, the Kimberling-Pavlov I-conjugate of P and P is the cross-conjugate of I and the the isogonal conjugate of P(P).
Generally, the Kimberling-Pavlov X-conjugate of P and P is the cross conjugate of the X^2-reciprocal conjugate of P and P, where " ^ " denotes barycentric square.

Theorem 3.
The Kimberling-Pavlov X(6)-conjugate of P and Q is the P-vertex conjugate of Q.

Theorem 4.
Let 𝓒 be a circumconic through I. If P lies on 𝓒, then the Kimberling-Pavlov I-conjugate of I and P also lies on 𝓒.

Theorem 5.
The Kimberling-Pavlov G-conjugate of P and Q is the isotomic conjugate of the midpoint of the barycentric quotients P/G and Q/G.



X(55917) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(3)

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

X(55917) lies on these lines: {3, 2635}, {4, 23707}, {77, 37697}, {283, 52889}, {296, 36279}, {1794, 11499}, {1795, 5398}, {1807, 9642}, {3362, 7524}, {7163, 10037}

X(55917) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3)}}, {{A, B, C, X(4), X(650)}}, {{A, B, C, X(55), X(5397)}}, {{A, B, C, X(1159), X(51281)}}, {{A, B, C, X(1816), X(7524)}}, {{A, B, C, X(1936), X(36279)}}, {{A, B, C, X(2173), X(50349)}}, {{A, B, C, X(3075), X(12702)}}, {{A, B, C, X(3426), X(36123)}}, {{A, B, C, X(3579), X(41344)}}, {{A, B, C, X(5398), X(39173)}}, {{A, B, C, X(7241), X(24298)}}, {{A, B, C, X(34234), X(39963)}}, {{A, B, C, X(37697), X(52371)}}

X(55918) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(4)

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

X(55918) lies on the Feuerbach Hyperbola and these lines: {1, 1776}, {3, 1156}, {4, 1155}, {7, 5886}, {8, 11111}, {9, 4262}, {21, 37606}, {79, 499}, {80, 4302}, {90, 6875}, {392, 2320}, {652, 23893}, {920, 17098}, {938, 22936}, {956, 1320}, {1000, 37740}, {1159, 3560}, {1389, 11496}, {1392, 3869}, {1476, 32153}, {1896, 52891}, {2346, 40269}, {3062, 52027}, {3065, 17009}, {3254, 5698}, {3485, 5557}, {3486, 5559}, {3487, 34917}, {3579, 7319}, {3647, 6598}, {3680, 12514}, {3911, 5561}, {5204, 10308}, {5220, 34894}, {5550, 10266}, {5556, 37582}, {5560, 18395}, {5603, 34485}, {5744, 11604}, {6876, 36599}, {6912, 36279}, {6950, 7082}, {8166, 38306}, {10572, 43731}, {11114, 12019}, {12047, 43732}, {15254, 34919}, {15558, 24302}, {16615, 37567}, {17501, 37572}, {32636, 43733}, {33576, 35242}, {37568, 43734}

X(55918) = isogonal conjugate of X(36279)
X(55918) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36279}, {6, 31164}
X(55918) = X(i)-vertex conjugate of X(j) for these {i, j}: {1000, 1436}
X(55918) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 36279}, {9, 31164}
X(55918) = X(i)-cross conjugate of X(j) for these {i, j}: {37600, 1}
X(55918) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(50105)}}, {{A, B, C, X(3), X(652)}}, {{A, B, C, X(28), X(11111)}}, {{A, B, C, X(44), X(956)}}, {{A, B, C, X(45), X(392)}}, {{A, B, C, X(58), X(2291)}}, {{A, B, C, X(65), X(37606)}}, {{A, B, C, X(88), X(44178)}}, {{A, B, C, X(89), X(14377)}}, {{A, B, C, X(277), X(37131)}}, {{A, B, C, X(499), X(4420)}}, {{A, B, C, X(759), X(9309)}}, {{A, B, C, X(896), X(51290)}}, {{A, B, C, X(957), X(2161)}}, {{A, B, C, X(1037), X(28173)}}, {{A, B, C, X(1057), X(34820)}}, {{A, B, C, X(1098), X(1776)}}, {{A, B, C, X(1159), X(2646)}}, {{A, B, C, X(1167), X(10623)}}, {{A, B, C, X(1175), X(1436)}}, {{A, B, C, X(1247), X(9395)}}, {{A, B, C, X(1411), X(9353)}}, {{A, B, C, X(1443), X(4302)}}, {{A, B, C, X(2224), X(7349)}}, {{A, B, C, X(3219), X(15474)}}, {{A, B, C, X(3316), X(30556)}}, {{A, B, C, X(3317), X(30557)}}, {{A, B, C, X(3431), X(36052)}}, {{A, B, C, X(3478), X(28219)}}, {{A, B, C, X(3559), X(6875)}}, {{A, B, C, X(3579), X(5204)}}, {{A, B, C, X(3617), X(30144)}}, {{A, B, C, X(3621), X(22837)}}, {{A, B, C, X(3647), X(41547)}}, {{A, B, C, X(3935), X(45700)}}, {{A, B, C, X(4567), X(39721)}}, {{A, B, C, X(5217), X(37582)}}, {{A, B, C, X(5220), X(43065)}}, {{A, B, C, X(5886), X(52371)}}, {{A, B, C, X(12514), X(16948)}}, {{A, B, C, X(12702), X(37605)}}, {{A, B, C, X(13472), X(52185)}}, {{A, B, C, X(13624), X(37567)}}, {{A, B, C, X(14121), X(38234)}}, {{A, B, C, X(17595), X(37589)}}, {{A, B, C, X(24914), X(34259)}}, {{A, B, C, X(36100), X(39963)}}, {{A, B, C, X(36279), X(37600)}}, {{A, B, C, X(37540), X(37599)}}, {{A, B, C, X(52680), X(52746)}}
X(55918) = barycentric quotient X(i)/X(j) for these (i, j): {1, 31164}, {6, 36279}

X(55919) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(6)

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

X(55919) lies on these lines: {1, 536}, {2, 37129}, {6, 750}, {44, 2279}, {45, 292}, {56, 52896}, {58, 25524}, {87, 15668}, {106, 1001}, {238, 2163}, {513, 23892}, {870, 41847}, {996, 50302}, {1015, 4492}, {1120, 5263}, {1126, 5711}, {1438, 2278}, {1474, 52890}, {1740, 39972}, {2234, 25426}, {2309, 10013}, {3240, 46922}, {3445, 10448}, {4724, 23345}, {5204, 52150}, {6329, 25571}, {7240, 17255}, {7292, 26240}, {8053, 34445}, {16477, 37522}, {17259, 25528}, {17262, 24661}, {17325, 53541}, {17379, 40433}, {17595, 17954}, {20992, 34444}, {24441, 24722}, {27846, 31139}, {42083, 49721}

X(55919) = isogonal conjugate of X(3240)
X(55919) = trilinear pole of line {649, 4378}
X(55919) = perspector of circumconic {{A, B, C, X(29351), X(37209)}}
X(55919) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3240}, {2, 54981}, {6, 4664}, {100, 29350}, {101, 4776}
X(55919) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 3240}, {9, 4664}, {1015, 4776}, {8054, 29350}, {32664, 54981}
X(55919) = X(i)-cross conjugate of X(j) for these {i, j}: {30950, 1}
X(55919) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(2), X(513)}}, {{A, B, C, X(7), X(7241)}}, {{A, B, C, X(28), X(16394)}}, {{A, B, C, X(37), X(9309)}}, {{A, B, C, X(44), X(1001)}}, {{A, B, C, X(45), X(238)}}, {{A, B, C, X(55), X(3737)}}, {{A, B, C, X(75), X(49493)}}, {{A, B, C, X(88), X(750)}}, {{A, B, C, X(89), X(4670)}}, {{A, B, C, X(105), X(40401)}}, {{A, B, C, X(256), X(30598)}}, {{A, B, C, X(277), X(1242)}}, {{A, B, C, X(291), X(31178)}}, {{A, B, C, X(523), X(32023)}}, {{A, B, C, X(650), X(34919)}}, {{A, B, C, X(673), X(4413)}}, {{A, B, C, X(741), X(28607)}}, {{A, B, C, X(751), X(30571)}}, {{A, B, C, X(873), X(2162)}}, {{A, B, C, X(876), X(20569)}}, {{A, B, C, X(896), X(50349)}}, {{A, B, C, X(903), X(52654)}}, {{A, B, C, X(941), X(34585)}}, {{A, B, C, X(1002), X(39982)}}, {{A, B, C, X(1014), X(2214)}}, {{A, B, C, X(1156), X(5695)}}, {{A, B, C, X(1178), X(34819)}}, {{A, B, C, X(1218), X(39746)}}, {{A, B, C, X(1221), X(34816)}}, {{A, B, C, X(1246), X(43733)}}, {{A, B, C, X(1255), X(9348)}}, {{A, B, C, X(1268), X(3551)}}, {{A, B, C, X(2161), X(39954)}}, {{A, B, C, X(2234), X(4784)}}, {{A, B, C, X(2278), X(3286)}}, {{A, B, C, X(2296), X(39966)}}, {{A, B, C, X(3000), X(10004)}}, {{A, B, C, X(3214), X(5550)}}, {{A, B, C, X(3240), X(30950)}}, {{A, B, C, X(3242), X(16786)}}, {{A, B, C, X(3617), X(28352)}}, {{A, B, C, X(3634), X(17749)}}, {{A, B, C, X(3720), X(39961)}}, {{A, B, C, X(3736), X(41847)}}, {{A, B, C, X(4448), X(24482)}}, {{A, B, C, X(4782), X(40720)}}, {{A, B, C, X(5061), X(17595)}}, {{A, B, C, X(5204), X(37558)}}, {{A, B, C, X(5221), X(37522)}}, {{A, B, C, X(5556), X(15320)}}, {{A, B, C, X(5711), X(32636)}}, {{A, B, C, X(5936), X(41439)}}, {{A, B, C, X(6063), X(40086)}}, {{A, B, C, X(6180), X(31618)}}, {{A, B, C, X(8053), X(20992)}}, {{A, B, C, X(9462), X(32020)}}, {{A, B, C, X(9780), X(27627)}}, {{A, B, C, X(10308), X(50044)}}, {{A, B, C, X(10448), X(16948)}}, {{A, B, C, X(13476), X(30712)}}, {{A, B, C, X(15668), X(27644)}}, {{A, B, C, X(15808), X(50575)}}, {{A, B, C, X(16468), X(16672)}}, {{A, B, C, X(16477), X(16777)}}, {{A, B, C, X(17318), X(20332)}}, {{A, B, C, X(17379), X(18166)}}, {{A, B, C, X(19604), X(23051)}}, {{A, B, C, X(24696), X(51333)}}, {{A, B, C, X(25508), X(27623)}}, {{A, B, C, X(27164), X(28365)}}, {{A, B, C, X(37142), X(55918)}}, {{A, B, C, X(39740), X(53677)}}, {{A, B, C, X(40148), X(43924)}}, {{A, B, C, X(40737), X(50344)}}
X(55919) = barycentric product X(i)*X(j) for these (i, j): {1, 36871}, {29351, 514}, {37209, 513}
X(55919) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4664}, {6, 3240}, {31, 54981}, {513, 4776}, {649, 29350}, {29351, 190}, {36871, 75}, {37209, 668}

X(55920) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(7)

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

X(55920) lies on the Feuerbach Hyperbola and these lines: {1, 37787}, {2, 3254}, {4, 5766}, {7, 1155}, {8, 4702}, {9, 3935}, {21, 5220}, {44, 40779}, {45, 294}, {55, 1156}, {79, 3085}, {80, 390}, {100, 15346}, {104, 37606}, {144, 3255}, {516, 5561}, {518, 2320}, {657, 23893}, {885, 4777}, {943, 5729}, {954, 1159}, {1000, 8236}, {1001, 1320}, {1445, 10390}, {1621, 34894}, {2550, 11604}, {3062, 29007}, {3296, 5703}, {3523, 5557}, {3579, 43733}, {3617, 6598}, {3680, 16859}, {4724, 23838}, {5424, 18412}, {5551, 37582}, {5556, 37568}, {5560, 10039}, {6172, 34919}, {6601, 18230}, {7284, 15298}, {8544, 37105}, {8545, 35445}, {9780, 43740}, {12848, 34917}, {15175, 41700}, {15180, 52769}, {16676, 42317}, {18490, 31658}, {18810, 42311}, {24297, 53055}, {30353, 31507}, {30424, 43732}, {30513, 52653}, {42082, 54474}

X(55920) = isogonal conjugate of X(4860)
X(55920) = trilinear pole of line {650, 4794}
X(55920) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4860}, {6, 6173}, {55, 21314}, {56, 5231}, {57, 34522}, {269, 42014}, {279, 32578}, {658, 17425}
X(55920) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 5231}, {3, 4860}, {9, 6173}, {223, 21314}, {5452, 34522}, {6594, 44785}, {6600, 42014}
X(55920) = X(i)-cross conjugate of X(j) for these {i, j}: {7671, 7}, {14077, 100}
X(55920) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(2), X(765)}}, {{A, B, C, X(6), X(15254)}}, {{A, B, C, X(37), X(5220)}}, {{A, B, C, X(44), X(1001)}}, {{A, B, C, X(45), X(518)}}, {{A, B, C, X(55), X(59)}}, {{A, B, C, X(77), X(30332)}}, {{A, B, C, X(88), X(39273)}}, {{A, B, C, X(89), X(673)}}, {{A, B, C, X(105), X(47357)}}, {{A, B, C, X(144), X(29007)}}, {{A, B, C, X(390), X(1443)}}, {{A, B, C, X(480), X(15837)}}, {{A, B, C, X(517), X(37606)}}, {{A, B, C, X(1002), X(2161)}}, {{A, B, C, X(1037), X(34820)}}, {{A, B, C, X(1159), X(24929)}}, {{A, B, C, X(1280), X(36588)}}, {{A, B, C, X(1445), X(18230)}}, {{A, B, C, X(1621), X(54128)}}, {{A, B, C, X(3085), X(4420)}}, {{A, B, C, X(3240), X(26227)}}, {{A, B, C, X(3617), X(34772)}}, {{A, B, C, X(3692), X(5766)}}, {{A, B, C, X(3746), X(13472)}}, {{A, B, C, X(3811), X(9780)}}, {{A, B, C, X(4076), X(40419)}}, {{A, B, C, X(4248), X(16859)}}, {{A, B, C, X(4689), X(37540)}}, {{A, B, C, X(5217), X(37568)}}, {{A, B, C, X(5218), X(28071)}}, {{A, B, C, X(5223), X(16676)}}, {{A, B, C, X(5729), X(40937)}}, {{A, B, C, X(6172), X(8545)}}, {{A, B, C, X(7269), X(30340)}}, {{A, B, C, X(9095), X(37129)}}, {{A, B, C, X(9353), X(41439)}}, {{A, B, C, X(10509), X(32088)}}, {{A, B, C, X(14077), X(15346)}}, {{A, B, C, X(14191), X(52746)}}, {{A, B, C, X(15481), X(16672)}}, {{A, B, C, X(15733), X(28537)}}, {{A, B, C, X(17718), X(52371)}}, {{A, B, C, X(18359), X(27475)}}, {{A, B, C, X(23617), X(28626)}}, {{A, B, C, X(32008), X(43762)}}, {{A, B, C, X(33635), X(37741)}}, {{A, B, C, X(36101), X(40434)}}, {{A, B, C, X(39954), X(40400)}}, {{A, B, C, X(39963), X(43760)}}
X(55920) = barycentric product X(i)*X(j) for these (i, j): {18810, 220}, {34521, 480}
X(55920) = barycentric quotient X(i)/X(j) for these (i, j): {1, 6173}, {6, 4860}, {9, 5231}, {55, 34522}, {57, 21314}, {220, 42014}, {1253, 32578}, {6603, 44785}, {8641, 17425}, {46003, 21104}

X(55921) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(8)

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

X(55921) lies on the Feuerbach Hyperbola and these lines: {4, 31776}, {8, 1155}, {9, 1055}, {56, 1156}, {79, 14986}, {80, 4293}, {649, 23893}, {943, 37606}, {1000, 5731}, {1159, 1389}, {1210, 5560}, {1392, 3889}, {2320, 10179}, {3218, 4900}, {3254, 11240}, {3522, 5559}, {3579, 7317}, {3616, 34919}, {4188, 4866}, {5128, 31509}, {5204, 32635}, {5708, 16615}, {6224, 12641}, {6904, 34918}, {7319, 32636}, {11570, 24302}, {16174, 46435}, {24297, 36279}, {30340, 34917}, {37582, 43734}

X(55921) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 31142}
X(55921) = X(i)-vertex conjugate of X(j) for these {i, j}: {2320, 3433}
X(55921) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 31142}
X(55921) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(19), X(8686)}}, {{A, B, C, X(27), X(37313)}}, {{A, B, C, X(45), X(10179)}}, {{A, B, C, X(56), X(649)}}, {{A, B, C, X(60), X(963)}}, {{A, B, C, X(88), X(7131)}}, {{A, B, C, X(89), X(1434)}}, {{A, B, C, X(279), X(18450)}}, {{A, B, C, X(280), X(37769)}}, {{A, B, C, X(284), X(28227)}}, {{A, B, C, X(936), X(5550)}}, {{A, B, C, X(942), X(37606)}}, {{A, B, C, X(945), X(15339)}}, {{A, B, C, X(957), X(2718)}}, {{A, B, C, X(961), X(34610)}}, {{A, B, C, X(1036), X(38451)}}, {{A, B, C, X(1159), X(1385)}}, {{A, B, C, X(1411), X(41439)}}, {{A, B, C, X(1443), X(4293)}}, {{A, B, C, X(2137), X(15728)}}, {{A, B, C, X(2334), X(52792)}}, {{A, B, C, X(3422), X(28173)}}, {{A, B, C, X(3478), X(15337)}}, {{A, B, C, X(3935), X(11240)}}, {{A, B, C, X(4188), X(31903)}}, {{A, B, C, X(4420), X(14986)}}, {{A, B, C, X(4860), X(37600)}}, {{A, B, C, X(4887), X(18467)}}, {{A, B, C, X(4996), X(52178)}}, {{A, B, C, X(5126), X(36279)}}, {{A, B, C, X(5204), X(32636)}}, {{A, B, C, X(5221), X(37605)}}, {{A, B, C, X(5563), X(13452)}}, {{A, B, C, X(5708), X(13624)}}, {{A, B, C, X(9780), X(19861)}}, {{A, B, C, X(14953), X(37304)}}, {{A, B, C, X(20050), X(36846)}}, {{A, B, C, X(28193), X(37741)}}, {{A, B, C, X(36101), X(44559)}}, {{A, B, C, X(37223), X(46962)}}
X(55921) = barycentric quotient X(i)/X(j) for these (i, j): {1, 31142}

X(55922) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(9)

Barycentrics    a*(a^2-2*a*b+b^2+4*a*c+4*b*c-5*c^2)*(a^2+4*a*b-5*b^2-2*a*c+4*b*c+c^2) : :
X(55922) = -3*X[6173]+2*X[34919]

X(55922) lies on the Feuerbach Hyperbola and these lines: {1, 6610}, {4, 30424}, {8, 527}, {9, 1155}, {21, 8544}, {57, 1156}, {80, 4312}, {104, 11372}, {294, 16670}, {513, 23893}, {516, 1000}, {518, 4900}, {885, 6006}, {943, 43178}, {971, 1159}, {1320, 3243}, {1706, 4866}, {1836, 3254}, {2320, 18450}, {2801, 24297}, {3000, 16676}, {3065, 15299}, {3158, 5528}, {3296, 21625}, {3680, 15733}, {5059, 7320}, {5128, 32635}, {5221, 33576}, {5542, 18490}, {5557, 9614}, {5558, 12053}, {5559, 9613}, {5572, 45834}, {5729, 38271}, {5732, 37606}, {5805, 46435}, {5856, 12641}, {6173, 34919}, {7285, 32636}, {8545, 35445}, {10309, 18483}, {10390, 14100}, {10483, 13606}, {14496, 30329}, {30330, 31507}

X(55922) = isogonal conjugate of X(35445)
X(55922) = trilinear pole of line {650, 14413}
X(55922) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 35445}, {6, 6172}, {101, 46919}, {1253, 47374}, {7045, 23056}
X(55922) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 35445}, {9, 6172}, {1015, 46919}, {17113, 47374}, {17115, 23056}, {25411, 36973}
X(55922) = X(i)-cross conjugate of X(j) for these {i, j}: {4860, 1}, {23056, 650}
X(55922) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(19), X(19604)}}, {{A, B, C, X(27), X(37240)}}, {{A, B, C, X(44), X(3243)}}, {{A, B, C, X(45), X(38316)}}, {{A, B, C, X(57), X(513)}}, {{A, B, C, X(77), X(30424)}}, {{A, B, C, X(88), X(4454)}}, {{A, B, C, X(89), X(36101)}}, {{A, B, C, X(103), X(2364)}}, {{A, B, C, X(269), X(41439)}}, {{A, B, C, X(279), X(30353)}}, {{A, B, C, X(518), X(6006)}}, {{A, B, C, X(522), X(1088)}}, {{A, B, C, X(673), X(4413)}}, {{A, B, C, X(903), X(39959)}}, {{A, B, C, X(969), X(1449)}}, {{A, B, C, X(1001), X(16676)}}, {{A, B, C, X(1002), X(50835)}}, {{A, B, C, X(1159), X(3576)}}, {{A, B, C, X(1440), X(7110)}}, {{A, B, C, X(1443), X(4312)}}, {{A, B, C, X(2137), X(34434)}}, {{A, B, C, X(2161), X(51102)}}, {{A, B, C, X(2191), X(41441)}}, {{A, B, C, X(2297), X(4373)}}, {{A, B, C, X(2316), X(52013)}}, {{A, B, C, X(2827), X(5856)}}, {{A, B, C, X(3000), X(4724)}}, {{A, B, C, X(3158), X(3667)}}, {{A, B, C, X(3247), X(15254)}}, {{A, B, C, X(3668), X(8544)}}, {{A, B, C, X(3738), X(5851)}}, {{A, B, C, X(3935), X(31146)}}, {{A, B, C, X(4321), X(4346)}}, {{A, B, C, X(4328), X(30340)}}, {{A, B, C, X(4492), X(25430)}}, {{A, B, C, X(4860), X(35445)}}, {{A, B, C, X(5128), X(32636)}}, {{A, B, C, X(5708), X(35242)}}, {{A, B, C, X(6173), X(8545)}}, {{A, B, C, X(7190), X(43180)}}, {{A, B, C, X(7271), X(30332)}}, {{A, B, C, X(9579), X(52372)}}, {{A, B, C, X(9814), X(36620)}}, {{A, B, C, X(10579), X(33635)}}, {{A, B, C, X(11529), X(37606)}}, {{A, B, C, X(12127), X(20050)}}, {{A, B, C, X(14377), X(43762)}}, {{A, B, C, X(14554), X(27475)}}, {{A, B, C, X(15601), X(51058)}}, {{A, B, C, X(23062), X(31391)}}, {{A, B, C, X(23617), X(36606)}}, {{A, B, C, X(34916), X(39273)}}
X(55922) = barycentric quotient X(i)/X(j) for these (i, j): {1, 6172}, {6, 35445}, {279, 47374}, {513, 46919}, {14936, 23056}

X(55923) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(19)

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

X(55923) lies on these lines: {1, 17959}, {10, 4419}, {19, 896}, {37, 4413}, {63, 897}, {65, 9004}, {75, 17897}, {656, 23894}, {759, 1296}, {2186, 2234}, {4674, 5223}, {4784, 23835}, {17872, 23051}, {18827, 35179}, {23052, 36119}, {39238, 40747}, {42285, 50314}

X(55923) = isogonal conjugate of X(36277)
X(55923) = trilinear pole of line {661, 48332}
X(55923) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36277}, {2, 1384}, {3, 4232}, {6, 1992}, {32, 11059}, {74, 35266}, {99, 8644}, {100, 30234}, {110, 1499}, {111, 27088}, {163, 14207}, {187, 52141}, {249, 6791}, {476, 9126}, {691, 9125}, {895, 15471}, {1176, 41585}, {1333, 42724}, {1383, 11165}, {1976, 51438}, {1995, 13608}, {2408, 5467}, {2444, 5468}, {3167, 52454}, {11422, 22100}, {11580, 34581}, {37745, 52230}
X(55923) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 36277}, {9, 1992}, {37, 42724}, {115, 14207}, {244, 1499}, {1015, 4786}, {6376, 11059}, {8054, 30234}, {32664, 1384}, {36103, 4232}, {38986, 8644}, {39040, 51438}
X(55923) = X(i)-cross conjugate of X(j) for these {i, j}: {36263, 1}
X(55923) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(9), X(7241)}}, {{A, B, C, X(44), X(5223)}}, {{A, B, C, X(57), X(4492)}}, {{A, B, C, X(63), X(656)}}, {{A, B, C, X(88), X(4419)}}, {{A, B, C, X(89), X(4748)}}, {{A, B, C, X(105), X(36588)}}, {{A, B, C, X(204), X(17898)}}, {{A, B, C, X(513), X(8056)}}, {{A, B, C, X(522), X(9004)}}, {{A, B, C, X(523), X(6057)}}, {{A, B, C, X(561), X(24006)}}, {{A, B, C, X(673), X(4413)}}, {{A, B, C, X(903), X(39954)}}, {{A, B, C, X(1820), X(19611)}}, {{A, B, C, X(2161), X(39959)}}, {{A, B, C, X(2173), X(23052)}}, {{A, B, C, X(2191), X(4373)}}, {{A, B, C, X(2234), X(3403)}}, {{A, B, C, X(2616), X(3223)}}, {{A, B, C, X(3062), X(39798)}}, {{A, B, C, X(3551), X(7312)}}, {{A, B, C, X(4000), X(4461)}}, {{A, B, C, X(9348), X(39980)}}, {{A, B, C, X(36263), X(36277)}}
X(55923) = barycentric product X(i)*X(j) for these (i, j): {1, 5485}, {1296, 1577}, {17959, 5503}, {21448, 75}, {23894, 2418}, {35179, 661}, {35522, 36045}, {37216, 523}, {39238, 561}
X(55923) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1992}, {6, 36277}, {10, 42724}, {19, 4232}, {31, 1384}, {75, 11059}, {513, 4786}, {523, 14207}, {649, 30234}, {661, 1499}, {798, 8644}, {896, 27088}, {897, 52141}, {1296, 662}, {1959, 51438}, {2173, 35266}, {2418, 24039}, {2434, 23889}, {2624, 9126}, {2642, 9125}, {2643, 6791}, {5485, 75}, {17442, 41585}, {17959, 22329}, {21448, 1}, {23894, 2408}, {32648, 36142}, {35179, 799}, {36045, 691}, {36263, 11165}, {37216, 99}, {39238, 31}

X(55924) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(21)

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

X(55924) lies on the Feuerbach Hyperbola and on these lines: {1, 36002}, {4, 1159}, {7, 12943}, {8, 10895}, {21, 1155}, {65, 1156}, {79, 6738}, {84, 31870}, {153, 24298}, {314, 30806}, {411, 37606}, {495, 1000}, {515, 34485}, {661, 23893}, {950, 34917}, {1320, 41701}, {3062, 30329}, {3065, 12736}, {3296, 18990}, {3485, 7320}, {3486, 5558}, {3617, 52255}, {3621, 15998}, {3869, 4866}, {4345, 37703}, {5229, 43740}, {5557, 10572}, {5559, 12047}, {6912, 36279}, {6982, 7317}, {10308, 31794}, {11114, 34919}, {11684, 15910}, {12019, 52269}, {15935, 18490}

X(55924) = isogonal conjugate of X(37600)
X(55924) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(3), X(1159)}}, {{A, B, C, X(28), X(17577)}}, {{A, B, C, X(29), X(24032)}}, {{A, B, C, X(58), X(52792)}}, {{A, B, C, X(65), X(661)}}, {{A, B, C, X(81), X(1121)}}, {{A, B, C, X(85), X(88)}}, {{A, B, C, X(89), X(10405)}}, {{A, B, C, X(105), X(31140)}}, {{A, B, C, X(284), X(15337)}}, {{A, B, C, X(947), X(15339)}}, {{A, B, C, X(961), X(11236)}}, {{A, B, C, X(994), X(1014)}}, {{A, B, C, X(1037), X(54446)}}, {{A, B, C, X(1168), X(18821)}}, {{A, B, C, X(1170), X(37131)}}, {{A, B, C, X(1220), X(51567)}}, {{A, B, C, X(2191), X(41446)}}, {{A, B, C, X(3426), X(37741)}}, {{A, B, C, X(3579), X(31794)}}, {{A, B, C, X(3615), X(40446)}}, {{A, B, C, X(3869), X(5342)}}, {{A, B, C, X(4420), X(6738)}}, {{A, B, C, X(5221), X(37567)}}, {{A, B, C, X(5708), X(12702)}}, {{A, B, C, X(6932), X(17519)}}, {{A, B, C, X(11684), X(46441)}}, {{A, B, C, X(13404), X(41432)}}, {{A, B, C, X(14191), X(14584)}}, {{A, B, C, X(14483), X(36052)}}, {{A, B, C, X(16835), X(52185)}}, {{A, B, C, X(24624), X(32008)}}, {{A, B, C, X(30556), X(43561)}}, {{A, B, C, X(30557), X(43560)}}, {{A, B, C, X(37582), X(50193)}}
X(55924) = barycentric quotient X(i)/X(j) for these (i, j): {6, 37600}

X(55925) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(37)

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

X(55925) lies on these lines: {1, 16702}, {10, 524}, {37, 896}, {65, 51653}, {75, 16741}, {81, 897}, {513, 23894}, {4649, 4674}, {4784, 55244}, {9278, 16666}, {41683, 52757}, {42285, 50293}

X(55925) = isogonal conjugate of X(31144)
X(55925) = trilinear pole of line {661, 14419}
X(55925) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 31144}, {101, 46915}
X(55925) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 31144}, {1015, 46915}
X(55925) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(6), X(4663)}}, {{A, B, C, X(7), X(67)}}, {{A, B, C, X(42), X(17162)}}, {{A, B, C, X(44), X(4649)}}, {{A, B, C, X(81), X(513)}}, {{A, B, C, X(88), X(4472)}}, {{A, B, C, X(89), X(4670)}}, {{A, B, C, X(256), X(1100)}}, {{A, B, C, X(274), X(50163)}}, {{A, B, C, X(741), X(28658)}}, {{A, B, C, X(757), X(7312)}}, {{A, B, C, X(985), X(50299)}}, {{A, B, C, X(1155), X(50349)}}, {{A, B, C, X(1757), X(16666)}}, {{A, B, C, X(2160), X(34585)}}, {{A, B, C, X(2234), X(4782)}}, {{A, B, C, X(2298), X(34893)}}, {{A, B, C, X(4492), X(25417)}}, {{A, B, C, X(4690), X(39720)}}, {{A, B, C, X(5061), X(37520)}}, {{A, B, C, X(5221), X(37594)}}, {{A, B, C, X(9348), X(39948)}}, {{A, B, C, X(10308), X(49718)}}, {{A, B, C, X(17012), X(49995)}}, {{A, B, C, X(25498), X(28604)}}, {{A, B, C, X(32636), X(37559)}}, {{A, B, C, X(34914), X(41311)}}, {{A, B, C, X(39734), X(43927)}}, {{A, B, C, X(39974), X(50309)}}, {{A, B, C, X(41847), X(43997)}}, {{A, B, C, X(43712), X(43733)}}, {{A, B, C, X(49743), X(52372)}}, {{A, B, C, X(50228), X(52376)}}
X(55925) = barycentric quotient X(i)/X(j) for these (i, j): {1, 31144}, {513, 46915}

X(55926) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(58)

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

X(55926) lies on these lines: {1, 3994}, {6, 52959}, {10, 37129}, {56, 19241}, {58, 899}, {86, 6381}, {106, 5251}, {661, 23892}, {2163, 37680}, {23345, 50349}, {40433, 49482}

X(55926) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(4), X(29352)}}, {{A, B, C, X(10), X(661)}}, {{A, B, C, X(29), X(19241)}}, {{A, B, C, X(44), X(5251)}}, {{A, B, C, X(80), X(39798)}}, {{A, B, C, X(83), X(88)}}, {{A, B, C, X(291), X(31161)}}, {{A, B, C, X(759), X(23617)}}, {{A, B, C, X(994), X(39956)}}, {{A, B, C, X(3214), X(3634)}}, {{A, B, C, X(3617), X(17749)}}, {{A, B, C, X(3625), X(28352)}}, {{A, B, C, X(3626), X(27627)}}, {{A, B, C, X(4276), X(5053)}}, {{A, B, C, X(4653), X(40400)}}, {{A, B, C, X(5235), X(37680)}}, {{A, B, C, X(5550), X(50575)}}, {{A, B, C, X(5561), X(7241)}}, {{A, B, C, X(32014), X(40434)}}, {{A, B, C, X(34234), X(39963)}}, {{A, B, C, X(40401), X(48826)}}, {{A, B, C, X(43734), X(55036)}}

X(55927) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(75)

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

X(55927) lies on these lines: {1, 922}, {10, 598}, {31, 897}, {37, 1383}, {65, 43697}, {75, 896}, {759, 11636}, {798, 23894}, {876, 46001}, {1581, 36289}, {1760, 23051}, {1966, 46300}, {2166, 4008}, {2173, 2186}, {2234, 51844}, {4674, 16468}, {4782, 55244}, {18827, 35138}, {39712, 41847}

X(55927) = isogonal conjugate of X(36263)
X(55927) = trilinear pole of line {661, 4794}
X(55927) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 36263}, {2, 574}, {3, 5094}, {6, 599}, {32, 9464}, {39, 10130}, {67, 10510}, {69, 8541}, {74, 13857}, {99, 17414}, {106, 4141}, {110, 3906}, {111, 39785}, {187, 42008}, {249, 8288}, {512, 9146}, {513, 3908}, {523, 9145}, {524, 42007}, {690, 32583}, {1177, 19510}, {1976, 51397}, {3917, 32581}, {5467, 23288}, {5486, 8542}, {9872, 34898}, {11165, 21448}, {12074, 17436}, {15810, 39389}
X(55927) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 36263}, {9, 599}, {214, 4141}, {244, 3906}, {6376, 9464}, {32664, 574}, {36103, 5094}, {38986, 17414}, {39026, 3908}, {39040, 51397}, {39054, 9146}
X(55927) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(4), X(17513)}}, {{A, B, C, X(6), X(10987)}}, {{A, B, C, X(9), X(757)}}, {{A, B, C, X(31), X(798)}}, {{A, B, C, X(44), X(4759)}}, {{A, B, C, X(57), X(765)}}, {{A, B, C, X(88), X(17354)}}, {{A, B, C, X(89), X(673)}}, {{A, B, C, X(92), X(16568)}}, {{A, B, C, X(105), X(39704)}}, {{A, B, C, X(270), X(341)}}, {{A, B, C, X(513), X(28562)}}, {{A, B, C, X(552), X(4076)}}, {{A, B, C, X(679), X(55922)}}, {{A, B, C, X(727), X(46018)}}, {{A, B, C, X(749), X(983)}}, {{A, B, C, X(751), X(985)}}, {{A, B, C, X(1088), X(7012)}}, {{A, B, C, X(1929), X(40401)}}, {{A, B, C, X(1966), X(36289)}}, {{A, B, C, X(2234), X(52138)}}, {{A, B, C, X(2244), X(51312)}}, {{A, B, C, X(2298), X(30598)}}, {{A, B, C, X(3113), X(37132)}}, {{A, B, C, X(4676), X(37129)}}, {{A, B, C, X(5263), X(41847)}}, {{A, B, C, X(9258), X(39725)}}, {{A, B, C, X(17472), X(20904)}}, {{A, B, C, X(27641), X(29423)}}, {{A, B, C, X(39727), X(39733)}}
X(55927) = barycentric product X(i)*X(j) for these (i, j): {1, 598}, {31, 40826}, {662, 8599}, {1383, 75}, {1821, 52692}, {10511, 16568}, {11636, 1577}, {18818, 896}, {23287, 36085}, {23297, 82}, {30489, 3112}, {30491, 811}, {35138, 661}, {43697, 92}, {46001, 799}, {51541, 897}
X(55927) = barycentric quotient X(i)/X(j) for these (i, j): {1, 599}, {6, 36263}, {19, 5094}, {31, 574}, {44, 4141}, {75, 9464}, {82, 10130}, {101, 3908}, {163, 9145}, {598, 75}, {661, 3906}, {662, 9146}, {798, 17414}, {896, 39785}, {897, 42008}, {923, 42007}, {1383, 1}, {1959, 51397}, {1973, 8541}, {2173, 13857}, {2643, 8288}, {8599, 1577}, {11636, 662}, {18669, 19510}, {18818, 46277}, {20380, 24038}, {23297, 1930}, {23894, 23288}, {30489, 38}, {30491, 656}, {35138, 799}, {36142, 32583}, {36277, 11165}, {40826, 561}, {43697, 63}, {46001, 661}, {51541, 14210}, {52692, 1959}

X(55928) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(79)

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

X(55928) lies on the Feuerbach Hyperbola and on these lines: {4, 11661}, {7, 37701}, {35, 1156}, {79, 1155}, {80, 38176}, {140, 43732}, {1159, 15173}, {1320, 5251}, {1392, 3884}, {2320, 5692}, {2346, 41700}, {3254, 15254}, {3647, 10266}, {5556, 37572}, {5560, 6284}, {5561, 7951}, {6595, 35204}, {6702, 11604}, {9404, 23893}, {15446, 37606}, {17501, 37568}, {23838, 50349}, {37524, 43733}, {41872, 43740}

X(55928) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(35), X(1155)}}, {{A, B, C, X(44), X(5251)}}, {{A, B, C, X(45), X(5692)}}, {{A, B, C, X(89), X(43758)}}, {{A, B, C, X(1159), X(37571)}}, {{A, B, C, X(1212), X(41700)}}, {{A, B, C, X(2911), X(41872)}}, {{A, B, C, X(3245), X(37600)}}, {{A, B, C, X(3422), X(34820)}}, {{A, B, C, X(3647), X(45065)}}, {{A, B, C, X(3683), X(51476)}}, {{A, B, C, X(5217), X(37572)}}, {{A, B, C, X(5526), X(15254)}}, {{A, B, C, X(5903), X(37606)}}, {{A, B, C, X(33635), X(36052)}}, {{A, B, C, X(37131), X(42326)}}, {{A, B, C, X(37701), X(52371)}}

X(55929) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(80)

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

X(55929) lies on the Feuerbach Hyperbola and on these lines: {1, 51529}, {4, 11219}, {7, 16173}, {8, 4781}, {9, 15015}, {11, 5561}, {36, 1156}, {80, 1155}, {100, 51570}, {550, 43731}, {654, 23893}, {1000, 7972}, {1392, 3874}, {1768, 3577}, {2346, 10058}, {2771, 5424}, {2800, 14497}, {3065, 5427}, {3245, 24297}, {3254, 28534}, {3680, 6763}, {4900, 16558}, {5560, 10483}, {7161, 12738}, {7319, 37524}, {10129, 10199}, {10265, 23959}, {13606, 32900}, {14315, 23838}, {15175, 37606}, {17057, 30513}, {17501, 37582}, {25557, 38026}, {34919, 38025}, {35596, 50891}, {36005, 37006}, {37572, 43734}, {43732, 52783}, {46821, 52371}

X(55929) = reflection of X(i) in X(j) for these {i,j}: {100, 51570}, {5561, 11}
X(55929) = isogonal conjugate of X(3245)
X(55929) = trilinear pole of line {650, 16666}
X(55929) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3245}, {106, 50841}
X(55929) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 3245}, {214, 50841}
X(55929) = X(i)-cross conjugate of X(j) for these {i, j}: {5126, 1}
X(55929) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(28), X(37299)}}, {{A, B, C, X(36), X(103)}}, {{A, B, C, X(59), X(28211)}}, {{A, B, C, X(88), X(15015)}}, {{A, B, C, X(89), X(24616)}}, {{A, B, C, X(100), X(4622)}}, {{A, B, C, X(102), X(15227)}}, {{A, B, C, X(291), X(14191)}}, {{A, B, C, X(765), X(24858)}}, {{A, B, C, X(900), X(14315)}}, {{A, B, C, X(1159), X(37525)}}, {{A, B, C, X(1443), X(4316)}}, {{A, B, C, X(2161), X(2718)}}, {{A, B, C, X(2163), X(28535)}}, {{A, B, C, X(3245), X(5126)}}, {{A, B, C, X(3738), X(28160)}}, {{A, B, C, X(3887), X(28534)}}, {{A, B, C, X(5204), X(37524)}}, {{A, B, C, X(5902), X(37606)}}, {{A, B, C, X(6763), X(16948)}}, {{A, B, C, X(10428), X(28471)}}, {{A, B, C, X(15337), X(28219)}}, {{A, B, C, X(16173), X(52371)}}, {{A, B, C, X(17548), X(31901)}}, {{A, B, C, X(28159), X(32899)}}, {{A, B, C, X(28193), X(36052)}}, {{A, B, C, X(34234), X(51636)}}, {{A, B, C, X(34578), X(37131)}}, {{A, B, C, X(37129), X(39445)}}, {{A, B, C, X(37138), X(39444)}}, {{A, B, C, X(40110), X(55919)}}, {{A, B, C, X(51529), X(51565)}}
X(55929) = barycentric quotient X(i)/X(j) for these (i, j): {6, 3245}, {44, 50841}

X(55930) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(82)

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

X(55930) lies on these lines: {10, 10302}, {37, 7292}, {38, 897}, {75, 18075}, {82, 896}, {759, 12074}, {5263, 39697}, {8061, 23894}, {17160, 39712}, {18827, 42367}, {32922, 42285}, {49675, 53114}

X(55930) = trilinear pole of line {661, 2832}
X(55930) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 5008}, {3, 10301}, {6, 597}, {32, 26235}, {110, 12073}, {523, 35357}, {1383, 15810}, {1976, 51396}, {11636, 17436}
X(55930) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 597}, {244, 12073}, {6376, 26235}, {32664, 5008}, {36103, 10301}, {39040, 51396}, {39054, 35356}
X(55930) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(7292)}}, {{A, B, C, X(38), X(896)}}, {{A, B, C, X(45), X(49675)}}, {{A, B, C, X(88), X(17305)}}, {{A, B, C, X(256), X(34893)}}, {{A, B, C, X(291), X(34916)}}, {{A, B, C, X(673), X(40434)}}, {{A, B, C, X(679), X(55919)}}, {{A, B, C, X(751), X(39959)}}, {{A, B, C, X(757), X(7241)}}, {{A, B, C, X(765), X(4492)}}, {{A, B, C, X(903), X(1390)}}, {{A, B, C, X(2191), X(28650)}}, {{A, B, C, X(2298), X(39710)}}, {{A, B, C, X(3112), X(18075)}}, {{A, B, C, X(5263), X(17160)}}, {{A, B, C, X(7312), X(39798)}}, {{A, B, C, X(15570), X(16676)}}, {{A, B, C, X(36917), X(55920)}}
X(55930) = barycentric product X(i)*X(j) for these (i, j): {1, 10302}, {12074, 1577}, {39389, 75}, {42367, 661}
X(55930) = barycentric quotient X(i)/X(j) for these (i, j): {1, 597}, {19, 10301}, {31, 5008}, {75, 26235}, {163, 35357}, {661, 12073}, {662, 35356}, {1959, 51396}, {10302, 75}, {12074, 662}, {36263, 15810}, {39389, 1}, {42367, 799}

X(55931) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(84)

Barycentrics    a*(a^3+b^3-a^2*(b-5*c)+5*b^2*c-b*c^2-5*c^3-a*(b^2+6*b*c+c^2))*(a^3-5*b^3+a^2*(5*b-c)-b^2*c+5*b*c^2+c^3-a*(b^2+6*b*c+c^2)) : :

X(55931) lies on the Feuerbach Hyperbola and on these lines: {1, 18908}, {7, 5587}, {10, 34919}, {40, 1156}, {84, 1155}, {104, 52026}, {936, 37606}, {1000, 5727}, {1159, 5665}, {1210, 3296}, {1512, 10307}, {3062, 41700}, {3254, 12019}, {3579, 7285}, {3680, 34790}, {4900, 5692}, {5056, 5558}, {5128, 10308}, {5219, 18490}, {5290, 5557}, {6918, 7091}, {10429, 31673}, {12702, 33576}, {14298, 23893}, {18412, 45834}, {36798, 51284}

X(55931) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 2094}
X(55931) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 2094}
X(55931) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(40), X(1155)}}, {{A, B, C, X(44), X(36925)}}, {{A, B, C, X(88), X(41790)}}, {{A, B, C, X(318), X(18908)}}, {{A, B, C, X(899), X(51284)}}, {{A, B, C, X(936), X(3617)}}, {{A, B, C, X(979), X(9361)}}, {{A, B, C, X(998), X(41441)}}, {{A, B, C, X(1159), X(3601)}}, {{A, B, C, X(3340), X(37606)}}, {{A, B, C, X(3531), X(13404)}}, {{A, B, C, X(3579), X(5128)}}, {{A, B, C, X(3621), X(12629)}}, {{A, B, C, X(3625), X(36846)}}, {{A, B, C, X(3626), X(19861)}}, {{A, B, C, X(5251), X(16676)}}, {{A, B, C, X(5587), X(7079)}}, {{A, B, C, X(5692), X(16670)}}, {{A, B, C, X(34234), X(39963)}}, {{A, B, C, X(34525), X(43533)}}, {{A, B, C, X(34820), X(54446)}}, {{A, B, C, X(35242), X(37567)}}, {{A, B, C, X(35445), X(36279)}}, {{A, B, C, X(36629), X(52409)}}
X(55931) = barycentric quotient X(i)/X(j) for these (i, j): {1, 2094}

X(55932) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(86)

Barycentrics    a*(b*c+a*(4*b+c))*(b*c+a*(b+4*c)) : :

X(55932) lies on these lines: {1, 4753}, {6, 30653}, {42, 37129}, {44, 25426}, {86, 899}, {106, 4649}, {238, 41434}, {292, 16666}, {798, 23892}, {870, 17160}, {1126, 16477}, {3240, 46922}, {4784, 23345}, {10013, 17277}, {33882, 40746}

X(55932) = isogonal conjugate of X(30950)
X(55932) = trilinear pole of line {649, 4794}
X(55932) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 30950}, {2, 16971}, {6, 4688}, {56, 4519}
X(55932) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 4519}, {3, 30950}, {9, 4688}, {32664, 16971}
X(55932) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(2), X(51488)}}, {{A, B, C, X(28), X(51595)}}, {{A, B, C, X(42), X(798)}}, {{A, B, C, X(44), X(4649)}}, {{A, B, C, X(59), X(21453)}}, {{A, B, C, X(81), X(765)}}, {{A, B, C, X(88), X(39971)}}, {{A, B, C, X(89), X(673)}}, {{A, B, C, X(238), X(16666)}}, {{A, B, C, X(256), X(39710)}}, {{A, B, C, X(291), X(39974)}}, {{A, B, C, X(749), X(941)}}, {{A, B, C, X(751), X(903)}}, {{A, B, C, X(757), X(2346)}}, {{A, B, C, X(1100), X(16477)}}, {{A, B, C, X(1174), X(4570)}}, {{A, B, C, X(1246), X(7319)}}, {{A, B, C, X(1386), X(16786)}}, {{A, B, C, X(2364), X(14942)}}, {{A, B, C, X(3736), X(17160)}}, {{A, B, C, X(3935), X(17012)}}, {{A, B, C, X(9309), X(39739)}}, {{A, B, C, X(13476), X(49449)}}, {{A, B, C, X(14621), X(30653)}}, {{A, B, C, X(15320), X(17501)}}, {{A, B, C, X(18082), X(28625)}}, {{A, B, C, X(23617), X(40438)}}, {{A, B, C, X(24297), X(40110)}}, {{A, B, C, X(30571), X(39982)}}, {{A, B, C, X(30598), X(39975)}}, {{A, B, C, X(31637), X(43697)}}, {{A, B, C, X(32008), X(40408)}}, {{A, B, C, X(37128), X(40434)}}, {{A, B, C, X(37142), X(55924)}}, {{A, B, C, X(39737), X(39956)}}, {{A, B, C, X(39952), X(42335)}}, {{A, B, C, X(39961), X(40418)}}, {{A, B, C, X(40401), X(50283)}}
X(55932) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4688}, {6, 30950}, {9, 4519}, {31, 16971}

X(55933) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(87)

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

X(55933) lies on these lines: {1, 4759}, {43, 37129}, {56, 16477}, {87, 899}, {106, 16468}, {238, 41436}, {292, 16670}, {4782, 23345}, {20979, 23892}, {22343, 39972}

X(55933) = trilinear pole of line {649, 25569}
X(55933) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4740}
X(55933) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 4740}
X(55933) = X(i)-cross conjugate of X(j) for these {i, j}: {3240, 1}
X(55933) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(2), X(9333)}}, {{A, B, C, X(9), X(16477)}}, {{A, B, C, X(43), X(899)}}, {{A, B, C, X(44), X(4759)}}, {{A, B, C, X(57), X(9282)}}, {{A, B, C, X(75), X(9343)}}, {{A, B, C, X(88), X(39952)}}, {{A, B, C, X(89), X(20332)}}, {{A, B, C, X(238), X(16670)}}, {{A, B, C, X(256), X(39975)}}, {{A, B, C, X(291), X(36588)}}, {{A, B, C, X(749), X(3551)}}, {{A, B, C, X(751), X(39982)}}, {{A, B, C, X(985), X(40400)}}, {{A, B, C, X(2316), X(7220)}}, {{A, B, C, X(3223), X(39965)}}, {{A, B, C, X(3751), X(16786)}}, {{A, B, C, X(4663), X(16779)}}, {{A, B, C, X(9309), X(9338)}}, {{A, B, C, X(9325), X(55922)}}, {{A, B, C, X(17038), X(39956)}}, {{A, B, C, X(18793), X(28658)}}, {{A, B, C, X(37128), X(39963)}}
X(55933) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4740}

X(55934) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(90)

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

X(55934) lies on the Feuerbach Hyperbola and on these lines: {46, 1156}, {90, 1155}, {1000, 37708}, {1159, 1898}, {1699, 34485}, {5558, 12047}, {6261, 37518}, {7285, 37524}, {7320, 10572}, {9612, 34917}, {23893, 46389}

X(55934) = X(i)-cross conjugate of X(j) for these {i, j}: {36279, 1}
X(55934) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(46), X(1155)}}, {{A, B, C, X(1159), X(3612)}}, {{A, B, C, X(2635), X(51282)}}, {{A, B, C, X(3362), X(9394)}}, {{A, B, C, X(3426), X(36052)}}, {{A, B, C, X(5128), X(37524)}}, {{A, B, C, X(14483), X(37741)}}, {{A, B, C, X(24624), X(39963)}}, {{A, B, C, X(52185), X(52518)}}

X(55935) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(1) AND X(105)

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

X(55935) lies on these lines: {1, 4752}, {2, 4126}, {44, 105}, {57, 53397}, {88, 518}, {89, 100}, {244, 39963}, {274, 55245}, {279, 43038}, {537, 24408}, {1002, 20331}, {1022, 2254}, {2401, 36921}, {3315, 40434}, {4555, 36593}, {4712, 16676}, {9451, 39958}, {34578, 49772}, {34892, 49768}

X(55935) = isogonal conjugate of X(3246)
X(55935) = trilinear pole of line {45, 513}
X(55935) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3246}, {6, 41140}, {101, 6009}, {190, 8658}
X(55935) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 3246}, {9, 41140}, {1015, 6009}, {55053, 8658}
X(55935) = X(i)-cross conjugate of X(j) for these {i, j}: {48244, 100}
X(55935) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(8), X(52429)}}, {{A, B, C, X(44), X(518)}}, {{A, B, C, X(80), X(8047)}}, {{A, B, C, X(100), X(4555)}}, {{A, B, C, X(650), X(1320)}}, {{A, B, C, X(678), X(36924)}}, {{A, B, C, X(679), X(24841)}}, {{A, B, C, X(753), X(1126)}}, {{A, B, C, X(903), X(40400)}}, {{A, B, C, X(1120), X(7035)}}, {{A, B, C, X(1252), X(28535)}}, {{A, B, C, X(1438), X(28539)}}, {{A, B, C, X(2113), X(9325)}}, {{A, B, C, X(2334), X(6187)}}, {{A, B, C, X(2346), X(7241)}}, {{A, B, C, X(3676), X(8686)}}, {{A, B, C, X(3935), X(49772)}}, {{A, B, C, X(4126), X(32635)}}, {{A, B, C, X(4663), X(49515)}}, {{A, B, C, X(4724), X(20331)}}, {{A, B, C, X(4998), X(9093)}}, {{A, B, C, X(7292), X(49768)}}, {{A, B, C, X(15323), X(16615)}}, {{A, B, C, X(23617), X(39742)}}, {{A, B, C, X(28317), X(41434)}}, {{A, B, C, X(55920), X(55923)}}
X(55935) = barycentric product X(i)*X(j) for these (i, j): {6017, 693}, {39428, 4671}
X(55935) = barycentric quotient X(i)/X(j) for these (i, j): {1, 41140}, {6, 3246}, {513, 6009}, {667, 8658}, {6017, 100}, {39428, 89}

X(55936) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(2) AND X(4)

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

X(55936) lies on these lines: {2, 1748}, {9, 52351}, {21, 1061}, {35, 78}, {55, 41740}, {57, 52381}, {63, 1993}, {280, 6872}, {345, 3219}, {348, 3218}, {1791, 3869}, {1812, 27174}, {7131, 30675}, {24611, 46487}, {26703, 36076}, {28807, 31018}

X(55936) = trilinear pole of line {2605, 521}
X(55936) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 1478}, {19, 1060}, {56, 54283}, {1400, 11103}, {2161, 4351}
X(55936) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 54283}, {6, 1060}, {9, 1478}, {40582, 11103}, {40584, 4351}
X(55936) = X(i)-cross conjugate of X(j) for these {i, j}: {2278, 1}
X(55936) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5692)}}, {{A, B, C, X(2), X(21)}}, {{A, B, C, X(4), X(81)}}, {{A, B, C, X(8), X(2990)}}, {{A, B, C, X(9), X(1021)}}, {{A, B, C, X(19), X(30650)}}, {{A, B, C, X(27), X(20846)}}, {{A, B, C, X(35), X(57)}}, {{A, B, C, X(85), X(2349)}}, {{A, B, C, X(87), X(9395)}}, {{A, B, C, X(88), X(44178)}}, {{A, B, C, X(92), X(2185)}}, {{A, B, C, X(97), X(3719)}}, {{A, B, C, X(275), X(7058)}}, {{A, B, C, X(312), X(2167)}}, {{A, B, C, X(333), X(1748)}}, {{A, B, C, X(394), X(39167)}}, {{A, B, C, X(588), X(7347)}}, {{A, B, C, X(589), X(7348)}}, {{A, B, C, X(893), X(2156)}}, {{A, B, C, X(1000), X(31018)}}, {{A, B, C, X(1005), X(14953)}}, {{A, B, C, X(1013), X(26647)}}, {{A, B, C, X(1062), X(1214)}}, {{A, B, C, X(1176), X(37741)}}, {{A, B, C, X(1817), X(6872)}}, {{A, B, C, X(1952), X(34289)}}, {{A, B, C, X(2006), X(15446)}}, {{A, B, C, X(2161), X(34446)}}, {{A, B, C, X(2184), X(30690)}}, {{A, B, C, X(2320), X(50442)}}, {{A, B, C, X(3869), X(17185)}}, {{A, B, C, X(3928), X(27065)}}, {{A, B, C, X(3929), X(27003)}}, {{A, B, C, X(5392), X(7108)}}, {{A, B, C, X(6512), X(45127)}}, {{A, B, C, X(7019), X(18018)}}, {{A, B, C, X(7183), X(14919)}}, {{A, B, C, X(7474), X(16367)}}, {{A, B, C, X(14621), X(37142)}}, {{A, B, C, X(14956), X(21511)}}, {{A, B, C, X(17097), X(25417)}}, {{A, B, C, X(17098), X(39948)}}, {{A, B, C, X(17512), X(46487)}}, {{A, B, C, X(18206), X(27486)}}, {{A, B, C, X(26637), X(28807)}}, {{A, B, C, X(34919), X(36101)}}, {{A, B, C, X(36599), X(39980)}}, {{A, B, C, X(36605), X(55924)}}, {{A, B, C, X(37870), X(40447)}}, {{A, B, C, X(43757), X(48360)}}
X(55936) = barycentric product X(i)*X(j) for these (i, j): {1061, 69}, {3422, 75}, {35518, 36076}
X(55936) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1478}, {3, 1060}, {9, 54283}, {21, 11103}, {36, 4351}, {1061, 4}, {1062, 18531}, {3422, 1}, {18532, 1063}, {36076, 108}

X(55937) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(2) AND X(9)

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

X(55937) lies on cubic K295 and on these lines: {2, 165}, {4, 42073}, {7, 1419}, {9, 5936}, {57, 36620}, {75, 144}, {86, 14953}, {142, 28626}, {145, 335}, {239, 4373}, {390, 15569}, {514, 2400}, {527, 36588}, {675, 26716}, {903, 1992}, {1001, 42335}, {1088, 9533}, {1268, 17354}, {2989, 54233}, {3146, 27000}, {3622, 26839}, {3886, 29616}, {4312, 5222}, {4779, 20533}, {4786, 6548}, {5435, 38254}, {5805, 24604}, {5905, 42361}, {7318, 8732}, {7613, 53602}, {9309, 31391}, {10136, 52511}, {10405, 36101}, {11372, 24590}, {12848, 18815}, {15717, 27183}, {17578, 26531}, {17738, 39570}, {20043, 39700}, {24599, 39721}, {26626, 30712}, {27381, 40424}, {40039, 41316}

X(55937) = isotomic conjugate of X(29616)
X(55937) = isogonal conjugate of X(42316)
X(55937) = trilinear pole of line {676, 28843}
X(55937) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 42316}, {6, 5223}, {31, 29616}, {1253, 10004}
X(55937) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 29616}, {3, 42316}, {9, 5223}, {17113, 10004}
X(55937) = X(i)-cross conjugate of X(j) for these {i, j}: {4312, 7}, {5222, 2}
X(55937) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(4), X(279)}}, {{A, B, C, X(6), X(35270)}}, {{A, B, C, X(8), X(1434)}}, {{A, B, C, X(9), X(81)}}, {{A, B, C, X(19), X(1462)}}, {{A, B, C, X(57), X(144)}}, {{A, B, C, X(79), X(277)}}, {{A, B, C, X(80), X(50836)}}, {{A, B, C, X(83), X(1219)}}, {{A, B, C, X(84), X(1170)}}, {{A, B, C, X(85), X(5556)}}, {{A, B, C, X(88), X(4454)}}, {{A, B, C, X(92), X(9812)}}, {{A, B, C, X(98), X(49631)}}, {{A, B, C, X(145), X(239)}}, {{A, B, C, X(189), X(9778)}}, {{A, B, C, X(263), X(649)}}, {{A, B, C, X(278), X(1699)}}, {{A, B, C, X(330), X(5395)}}, {{A, B, C, X(390), X(3886)}}, {{A, B, C, X(513), X(42290)}}, {{A, B, C, X(518), X(6008)}}, {{A, B, C, X(527), X(6006)}}, {{A, B, C, X(528), X(6009)}}, {{A, B, C, X(596), X(18841)}}, {{A, B, C, X(671), X(49630)}}, {{A, B, C, X(900), X(5845)}}, {{A, B, C, X(957), X(1019)}}, {{A, B, C, X(959), X(3500)}}, {{A, B, C, X(996), X(18842)}}, {{A, B, C, X(1001), X(15569)}}, {{A, B, C, X(1002), X(27484)}}, {{A, B, C, X(1121), X(44559)}}, {{A, B, C, X(1255), X(10390)}}, {{A, B, C, X(1445), X(9965)}}, {{A, B, C, X(1509), X(32022)}}, {{A, B, C, X(1817), X(6994)}}, {{A, B, C, X(1839), X(41325)}}, {{A, B, C, X(1890), X(2550)}}, {{A, B, C, X(1992), X(4786)}}, {{A, B, C, X(2006), X(7988)}}, {{A, B, C, X(2051), X(3817)}}, {{A, B, C, X(2346), X(25417)}}, {{A, B, C, X(2996), X(39724)}}, {{A, B, C, X(3187), X(20043)}}, {{A, B, C, X(3218), X(12848)}}, {{A, B, C, X(3296), X(38059)}}, {{A, B, C, X(3424), X(9746)}}, {{A, B, C, X(3427), X(38009)}}, {{A, B, C, X(3431), X(40076)}}, {{A, B, C, X(3577), X(34056)}}, {{A, B, C, X(3617), X(26626)}}, {{A, B, C, X(3798), X(40819)}}, {{A, B, C, X(3946), X(6601)}}, {{A, B, C, X(4025), X(42287)}}, {{A, B, C, X(4312), X(10004)}}, {{A, B, C, X(4384), X(29624)}}, {{A, B, C, X(4667), X(24624)}}, {{A, B, C, X(4750), X(5967)}}, {{A, B, C, X(4779), X(5853)}}, {{A, B, C, X(5222), X(29616)}}, {{A, B, C, X(5228), X(40779)}}, {{A, B, C, X(5435), X(20059)}}, {{A, B, C, X(5558), X(32008)}}, {{A, B, C, X(5561), X(34578)}}, {{A, B, C, X(5905), X(8732)}}, {{A, B, C, X(6553), X(17743)}}, {{A, B, C, X(6654), X(41845)}}, {{A, B, C, X(7317), X(9328)}}, {{A, B, C, X(7319), X(9311)}}, {{A, B, C, X(8056), X(31507)}}, {{A, B, C, X(9214), X(18653)}}, {{A, B, C, X(9779), X(50442)}}, {{A, B, C, X(10164), X(10307)}}, {{A, B, C, X(10171), X(45098)}}, {{A, B, C, X(10308), X(44178)}}, {{A, B, C, X(16816), X(29585)}}, {{A, B, C, X(17209), X(52765)}}, {{A, B, C, X(17316), X(24599)}}, {{A, B, C, X(17397), X(46933)}}, {{A, B, C, X(17495), X(41316)}}, {{A, B, C, X(17758), X(38204)}}, {{A, B, C, X(18845), X(54120)}}, {{A, B, C, X(20332), X(39975)}}, {{A, B, C, X(20533), X(52210)}}, {{A, B, C, X(21160), X(55105)}}, {{A, B, C, X(23958), X(41563)}}, {{A, B, C, X(25430), X(45834)}}, {{A, B, C, X(26003), X(26827)}}, {{A, B, C, X(26745), X(43760)}}, {{A, B, C, X(28534), X(28910)}}, {{A, B, C, X(29576), X(46934)}}, {{A, B, C, X(29583), X(29590)}}, {{A, B, C, X(29609), X(46931)}}, {{A, B, C, X(30275), X(31019)}}, {{A, B, C, X(34244), X(48580)}}, {{A, B, C, X(34917), X(43758)}}, {{A, B, C, X(42326), X(43732)}}, {{A, B, C, X(43951), X(44431)}}, {{A, B, C, X(47386), X(47787)}}, {{A, B, C, X(50865), X(52374)}}
X(55937) = barycentric product X(i)*X(j) for these (i, j): {26716, 3261}, {32040, 514}, {42317, 85}, {54668, 86}
X(55937) = barycentric quotient X(i)/X(j) for these (i, j): {1, 5223}, {2, 29616}, {6, 42316}, {279, 10004}, {26716, 101}, {32040, 190}, {32721, 32642}, {36136, 36039}, {42317, 9}, {54668, 10}

X(55938) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(2) AND X(21)

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

X(55938) lies on these lines: {2, 46014}, {21, 40}, {27, 196}, {81, 223}, {270, 3194}, {329, 333}, {1434, 14256}, {1817, 2185}, {2262, 36100}, {24624, 41572}

X(55938) = trilinear pole of line {3737, 6129}
X(55938) = X(i)-isoconjugate-of-X(j) for these {i, j}: {37, 3576}, {42, 5744}, {71, 34231}, {28658, 36922}, {37410, 41087}
X(55938) = X(i)-Dao conjugate of X(j) for these {i, j}: {40589, 3576}, {40592, 5744}
X(55938) = X(i)-cross conjugate of X(j) for these {i, j}: {15239, 8822}
X(55938) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(17097)}}, {{A, B, C, X(4), X(40)}}, {{A, B, C, X(21), X(27)}}, {{A, B, C, X(85), X(88)}}, {{A, B, C, X(90), X(39980)}}, {{A, B, C, X(286), X(1014)}}, {{A, B, C, X(829), X(19607)}}, {{A, B, C, X(1021), X(1172)}}, {{A, B, C, X(1170), X(34234)}}, {{A, B, C, X(1171), X(1790)}}, {{A, B, C, X(1389), X(2006)}}, {{A, B, C, X(1396), X(53083)}}, {{A, B, C, X(1476), X(2990)}}, {{A, B, C, X(2982), X(13478)}}, {{A, B, C, X(3218), X(41572)}}, {{A, B, C, X(3577), X(50442)}}, {{A, B, C, X(8056), X(17098)}}, {{A, B, C, X(14377), X(34051)}}, {{A, B, C, X(16704), X(41610)}}, {{A, B, C, X(37142), X(42302)}}
X(55938) = barycentric product X(i)*X(j) for these (i, j): {3577, 86}, {40438, 44730}, {50442, 81}
X(55938) = barycentric quotient X(i)/X(j) for these (i, j): {28, 34231}, {58, 3576}, {81, 5744}, {3194, 37410}, {3577, 10}, {4653, 36922}, {36925, 3992}, {44730, 4647}, {50442, 321}

X(55939) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(2) AND X(28)

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

X(55939) lies on these lines: {28, 3218}, {57, 40571}, {88, 2287}, {278, 41804}, {279, 16704}, {307, 2006}, {333, 15474}, {404, 51223}, {1021, 1022}, {2401, 17498}, {24632, 34578}, {39698, 45744}

X(55939) = X(i)-isoconjugate-of-X(j) for these {i, j}: {37, 37817}, {42, 24597}
X(55939) = X(i)-Dao conjugate of X(j) for these {i, j}: {40589, 37817}, {40592, 24597}
X(55939) = X(i)-cross conjugate of X(j) for these {i, j}: {997, 86}
X(55939) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(286), X(39695)}}, {{A, B, C, X(307), X(1444)}}, {{A, B, C, X(331), X(39700)}}, {{A, B, C, X(333), X(40571)}}, {{A, B, C, X(1021), X(2287)}}, {{A, B, C, X(1751), X(40406)}}, {{A, B, C, X(2994), X(34406)}}, {{A, B, C, X(5125), X(27174)}}, {{A, B, C, X(5317), X(39956)}}, {{A, B, C, X(7466), X(26643)}}, {{A, B, C, X(13583), X(21739)}}, {{A, B, C, X(17495), X(45744)}}, {{A, B, C, X(24624), X(40403)}}
X(55939) = barycentric quotient X(i)/X(j) for these (i, j): {58, 37817}, {81, 24597}

X(55940) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(2) AND X(31)

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

X(55940) lies on these lines: {2, 1911}, {6, 350}, {31, 239}, {604, 1447}, {1333, 33295}, {2203, 31905}, {3112, 31317}, {9456, 27922}, {20172, 23538}, {30667, 41527}

X(55940) = trilinear pole of line {667, 48273}
X(55940) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 12782}, {190, 1912}
X(55940) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 12782}, {55053, 1912}
X(55940) = X(i)-cross conjugate of X(j) for these {i, j}: {24631, 2}
X(55940) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(16476)}}, {{A, B, C, X(2), X(239)}}, {{A, B, C, X(6), X(31)}}, {{A, B, C, X(38), X(31317)}}, {{A, B, C, X(57), X(2665)}}, {{A, B, C, X(83), X(985)}}, {{A, B, C, X(87), X(38810)}}, {{A, B, C, X(88), X(4713)}}, {{A, B, C, X(89), X(37132)}}, {{A, B, C, X(105), X(17743)}}, {{A, B, C, X(189), X(1821)}}, {{A, B, C, X(333), X(16998)}}, {{A, B, C, X(673), X(3113)}}, {{A, B, C, X(894), X(9309)}}, {{A, B, C, X(1218), X(27483)}}, {{A, B, C, X(1580), X(8033)}}, {{A, B, C, X(1999), X(26626)}}, {{A, B, C, X(2995), X(27447)}}, {{A, B, C, X(3114), X(34252)}}, {{A, B, C, X(3187), X(17397)}}, {{A, B, C, X(3759), X(39737)}}, {{A, B, C, X(4601), X(55919)}}, {{A, B, C, X(6063), X(19975)}}, {{A, B, C, X(6650), X(7224)}}, {{A, B, C, X(7307), X(51321)}}, {{A, B, C, X(17103), X(39933)}}, {{A, B, C, X(38275), X(39980)}}
X(55940) = barycentric quotient X(i)/X(j) for these (i, j): {1, 12782}, {667, 1912}

X(55941) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(2) AND X(55)

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

X(55941) lies on these lines: {2, 9441}, {7, 2280}, {55, 27475}, {75, 10025}, {335, 3870}, {673, 1836}, {1088, 5228}, {2400, 17494}, {14004, 52781}, {14953, 39734}

X(55941) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(25), X(1462)}}, {{A, B, C, X(55), X(81)}}, {{A, B, C, X(57), X(6185)}}, {{A, B, C, X(83), X(39959)}}, {{A, B, C, X(239), X(3870)}}, {{A, B, C, X(279), X(36124)}}, {{A, B, C, X(514), X(28854)}}, {{A, B, C, X(1170), X(3423)}}, {{A, B, C, X(1275), X(55922)}}, {{A, B, C, X(1280), X(17743)}}, {{A, B, C, X(1434), X(14942)}}, {{A, B, C, X(14004), X(14953)}}, {{A, B, C, X(14377), X(34018)}}, {{A, B, C, X(17758), X(42409)}}, {{A, B, C, X(36601), X(39980)}}, {{A, B, C, X(42309), X(52507)}}

X(55942) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(2) AND X(58)

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

X(55942) lies on these lines: {2, 1412}, {8, 58}, {81, 312}, {85, 26627}, {86, 4997}, {92, 1396}, {257, 3218}, {333, 593}, {741, 4518}, {894, 18359}, {975, 15376}, {1150, 5035}, {1171, 4102}, {1509, 28660}, {2399, 17498}, {2975, 31359}, {4234, 36596}, {4921, 42030}, {5235, 30608}, {6557, 8025}, {14942, 29835}, {17587, 18163}, {24556, 42339}, {26541, 40011}, {26638, 32008}

X(55942) = isotomic conjugate of X(26580)
X(55942) = trilinear pole of line {3733, 15571}
X(55942) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4424}, {31, 26580}, {37, 995}, {42, 4850}, {65, 4266}, {101, 48350}, {213, 4389}, {692, 50453}, {872, 16712}, {1018, 9002}, {1400, 3877}, {1402, 5233}, {1826, 23206}, {1918, 33934}, {3949, 4247}, {4557, 48335}, {17461, 28658}, {20973, 53114}, {21042, 28607}
X(55942) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 26580}, {9, 4424}, {1015, 48350}, {1086, 50453}, {6626, 4389}, {34021, 33934}, {36911, 21042}, {40582, 3877}, {40589, 995}, {40592, 4850}, {40602, 4266}, {40605, 5233}, {40620, 44435}
X(55942) = X(i)-cross conjugate of X(j) for these {i, j}: {4833, 99}
X(55942) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(46638)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(9), X(26627)}}, {{A, B, C, X(27), X(11115)}}, {{A, B, C, X(57), X(5264)}}, {{A, B, C, X(58), X(81)}}, {{A, B, C, X(83), X(88)}}, {{A, B, C, X(86), X(4600)}}, {{A, B, C, X(89), X(3758)}}, {{A, B, C, X(239), X(5297)}}, {{A, B, C, X(274), X(24624)}}, {{A, B, C, X(284), X(1252)}}, {{A, B, C, X(332), X(30680)}}, {{A, B, C, X(335), X(33170)}}, {{A, B, C, X(673), X(39706)}}, {{A, B, C, X(675), X(870)}}, {{A, B, C, X(873), X(40415)}}, {{A, B, C, X(894), X(3218)}}, {{A, B, C, X(975), X(3187)}}, {{A, B, C, X(996), X(40426)}}, {{A, B, C, X(1016), X(40434)}}, {{A, B, C, X(1222), X(39698)}}, {{A, B, C, X(1255), X(2985)}}, {{A, B, C, X(3450), X(34051)}}, {{A, B, C, X(3912), X(29835)}}, {{A, B, C, X(4803), X(5235)}}, {{A, B, C, X(4921), X(5333)}}, {{A, B, C, X(5437), X(26688)}}, {{A, B, C, X(8025), X(41629)}}, {{A, B, C, X(14954), X(16054)}}, {{A, B, C, X(16713), X(26638)}}, {{A, B, C, X(17023), X(50000)}}, {{A, B, C, X(17495), X(29705)}}, {{A, B, C, X(27003), X(27064)}}, {{A, B, C, X(27483), X(46918)}}, {{A, B, C, X(34537), X(38810)}}, {{A, B, C, X(36604), X(39980)}}, {{A, B, C, X(37633), X(41434)}}
X(55942) = barycentric product X(i)*X(j) for these (i, j): {86, 996}, {274, 40401}, {7192, 9059}, {40426, 5235}
X(55942) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4424}, {2, 26580}, {21, 3877}, {58, 995}, {81, 4850}, {86, 4389}, {274, 33934}, {284, 4266}, {333, 5233}, {513, 48350}, {514, 50453}, {996, 10}, {1019, 48335}, {1437, 23206}, {1509, 16712}, {3679, 21042}, {3733, 9002}, {4273, 20973}, {4653, 17461}, {7192, 44435}, {9059, 3952}, {40401, 37}, {40426, 30588}, {47683, 21130}

X(55943) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(2) AND X(59)

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

X(55943) lies on these lines: {59, 5773}, {666, 1814}, {673, 909}, {1462, 54235}, {1936, 2342}, {2401, 2402}, {5138, 51832}, {33676, 36819}, {34018, 34051}, {53214, 54953}

X(55943) = isotomic conjugate of X(51390)
X(55943) = trilinear pole of line {104, 105}
X(55943) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 53548}, {31, 51390}, {101, 42758}, {517, 672}, {518, 2183}, {859, 3930}, {908, 2223}, {926, 24029}, {1025, 53549}, {1026, 3310}, {1110, 42770}, {1457, 3693}, {1465, 2340}, {1769, 2284}, {1785, 20752}, {1818, 14571}, {2254, 2427}, {2283, 46393}, {3252, 15507}, {3262, 9454}, {3286, 21801}, {4564, 42771}, {4712, 51987}, {5089, 22350}, {6184, 54364}, {6735, 52635}, {10015, 54325}, {14260, 14439}, {17139, 39258}, {18206, 51377}, {23980, 36819}, {40730, 51381}
X(55943) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 51390}, {478, 53548}, {514, 42770}, {1015, 42758}, {33675, 3262}
X(55943) = X(i)-cross conjugate of X(j) for these {i, j}: {51832, 18816}, {51987, 105}, {52456, 2481}
X(55943) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(24002)}}, {{A, B, C, X(57), X(1936)}}, {{A, B, C, X(59), X(81)}}, {{A, B, C, X(83), X(9311)}}, {{A, B, C, X(189), X(48070)}}, {{A, B, C, X(514), X(46102)}}, {{A, B, C, X(666), X(6185)}}, {{A, B, C, X(673), X(14942)}}, {{A, B, C, X(801), X(42304)}}, {{A, B, C, X(909), X(2342)}}, {{A, B, C, X(1275), X(37131)}}, {{A, B, C, X(1462), X(1814)}}, {{A, B, C, X(1509), X(5385)}}, {{A, B, C, X(2401), X(40437)}}, {{A, B, C, X(2989), X(43760)}}, {{A, B, C, X(3286), X(5138)}}, {{A, B, C, X(4391), X(34529)}}, {{A, B, C, X(4590), X(14534)}}, {{A, B, C, X(4998), X(53219)}}, {{A, B, C, X(13136), X(36037)}}, {{A, B, C, X(14621), X(39273)}}, {{A, B, C, X(18816), X(34234)}}, {{A, B, C, X(32230), X(40395)}}
X(55943) = barycentric product X(i)*X(j) for these (i, j): {104, 2481}, {105, 18816}, {1462, 36795}, {2401, 666}, {2423, 36803}, {16082, 1814}, {18031, 909}, {31637, 36123}, {34018, 52663}, {34051, 36796}, {34234, 673}, {43728, 927}, {54953, 885}
X(55943) = barycentric quotient X(i)/X(j) for these (i, j): {2, 51390}, {56, 53548}, {104, 518}, {105, 517}, {513, 42758}, {666, 2397}, {673, 908}, {884, 53549}, {885, 2804}, {909, 672}, {919, 2427}, {1024, 46393}, {1027, 1769}, {1086, 42770}, {1416, 1457}, {1438, 2183}, {1462, 1465}, {1795, 1818}, {2250, 3930}, {2342, 2340}, {2401, 918}, {2423, 665}, {2481, 3262}, {2720, 2283}, {3271, 42771}, {6654, 51381}, {8751, 14571}, {10428, 34230}, {13136, 42720}, {13576, 17757}, {14578, 20752}, {14942, 6735}, {15635, 3675}, {16082, 46108}, {18785, 21801}, {18816, 3263}, {28071, 51380}, {32641, 2284}, {32735, 23981}, {34051, 241}, {34234, 3912}, {34858, 2223}, {36037, 1026}, {36057, 22350}, {36123, 1861}, {36124, 1785}, {36146, 24029}, {36819, 4712}, {37136, 1025}, {38955, 3932}, {41934, 51987}, {43728, 50333}, {43921, 42753}, {43929, 3310}, {51565, 3717}, {51832, 120}, {51838, 54364}, {51987, 23980}, {52210, 51419}, {52456, 119}, {52663, 3693}, {54364, 24028}, {54953, 883}, {55259, 24290}

X(55944) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(2) AND X(90)

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

X(55944) lies on the Kiepert Hyperbola and on these lines: {10, 4302}, {193, 4080}, {321, 54280}, {1029, 37666}, {2996, 16704}, {3091, 5397}, {3543, 54528}, {3798, 4049}, {3839, 54679}, {6870, 54972}, {6871, 43531}, {6994, 40149}, {7406, 54739}, {7612, 8229}, {11114, 54786}, {17577, 54624}, {36002, 45097}, {52269, 54790}

X(55944) = trilinear pole of line {51725, 523}
X(55944) = X(i)-cross conjugate of X(j) for these {i, j}: {24597, 2}
X(55944) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(21), X(6994)}}, {{A, B, C, X(27), X(2994)}}, {{A, B, C, X(57), X(36599)}}, {{A, B, C, X(81), X(90)}}, {{A, B, C, X(84), X(2990)}}, {{A, B, C, X(189), X(37203)}}, {{A, B, C, X(277), X(43758)}}, {{A, B, C, X(279), X(4302)}}, {{A, B, C, X(391), X(14996)}}, {{A, B, C, X(469), X(6871)}}, {{A, B, C, X(1255), X(17098)}}, {{A, B, C, X(2006), X(5560)}}, {{A, B, C, X(2895), X(37666)}}, {{A, B, C, X(3218), X(41563)}}, {{A, B, C, X(7319), X(18359)}}, {{A, B, C, X(8046), X(42483)}}, {{A, B, C, X(8229), X(37174)}}, {{A, B, C, X(10405), X(21907)}}, {{A, B, C, X(14552), X(37685)}}, {{A, B, C, X(17097), X(27789)}}, {{A, B, C, X(26745), X(36100)}}, {{A, B, C, X(31042), X(37371)}}, {{A, B, C, X(37142), X(39952)}}, {{A, B, C, X(37279), X(50695)}}

X(55945) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(1) AND X(7)

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

X(55945) lies on these lines: {10, 3761}, {19, 18206}, {37, 980}, {63, 18785}, {65, 7223}, {86, 39737}, {225, 9436}, {274, 31359}, {596, 32104}, {876, 50339}, {3875, 13476}, {4360, 39739}, {4510, 4674}, {7245, 17294}, {10447, 42027}, {17038, 25590}, {17143, 34860}, {17144, 39702}, {17151, 39742}, {17155, 39714}, {42285, 52716}

X(55945) = isotomic conjugate of X(49470)
X(55945) = trilinear pole of line {661, 4379}
X(55945) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 37657}, {31, 49470}, {32, 30830}, {692, 48080}
X(55945) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 49470}, {9, 37657}, {1086, 48080}, {6376, 30830}
X(55945) = X(i)-cross conjugate of X(j) for these {i, j}: {3696, 2}
X(55945) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}}, {{A, B, C, X(2), X(16831)}}, {{A, B, C, X(7), X(274)}}, {{A, B, C, X(8), X(49495)}}, {{A, B, C, X(57), X(310)}}, {{A, B, C, X(63), X(4025)}}, {{A, B, C, X(76), X(7233)}}, {{A, B, C, X(86), X(14377)}}, {{A, B, C, X(239), X(17294)}}, {{A, B, C, X(269), X(24214)}}, {{A, B, C, X(291), X(2279)}}, {{A, B, C, X(292), X(7241)}}, {{A, B, C, X(330), X(2481)}}, {{A, B, C, X(514), X(40028)}}, {{A, B, C, X(561), X(4077)}}, {{A, B, C, X(870), X(903)}}, {{A, B, C, X(1266), X(30181)}}, {{A, B, C, X(2665), X(3551)}}, {{A, B, C, X(3226), X(17262)}}, {{A, B, C, X(3696), X(49470)}}, {{A, B, C, X(3875), X(17143)}}, {{A, B, C, X(4360), X(32104)}}, {{A, B, C, X(4384), X(17316)}}, {{A, B, C, X(4492), X(25426)}}, {{A, B, C, X(5936), X(32009)}}, {{A, B, C, X(6384), X(8056)}}, {{A, B, C, X(10447), X(33296)}}, {{A, B, C, X(16833), X(49765)}}, {{A, B, C, X(17144), X(17151)}}, {{A, B, C, X(25590), X(31997)}}, {{A, B, C, X(30710), X(39741)}}, {{A, B, C, X(30712), X(39736)}}, {{A, B, C, X(31002), X(39963)}}, {{A, B, C, X(32010), X(39980)}}, {{A, B, C, X(34409), X(54119)}}, {{A, B, C, X(35175), X(48321)}}, {{A, B, C, X(36531), X(48822)}}, {{A, B, C, X(36606), X(39740)}}, {{A, B, C, X(39700), X(40216)}}
X(55945) = barycentric product X(i)*X(j) for these (i, j): {1, 40030}, {39981, 75}
X(55945) = barycentric quotient X(i)/X(j) for these (i, j): {1, 37657}, {2, 49470}, {75, 30830}, {514, 48080}, {39981, 1}, {40030, 75}

X(55946) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(1) AND X(85)

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

X(55946) lies on these lines: {8, 334}, {75, 1001}, {76, 3975}, {85, 239}, {286, 14024}, {331, 40864}, {870, 20880}, {2481, 16825}, {4051, 35167}, {10030, 42309}

X(55946) = trilinear pole of line {693, 3716}
X(55946) = isotomic conjugate of X(51058)
X(55946) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(673)}}, {{A, B, C, X(2), X(16823)}}, {{A, B, C, X(8), X(239)}}, {{A, B, C, X(19), X(25426)}}, {{A, B, C, X(75), X(76)}}, {{A, B, C, X(277), X(52209)}}, {{A, B, C, X(279), X(41527)}}, {{A, B, C, X(292), X(3500)}}, {{A, B, C, X(314), X(7209)}}, {{A, B, C, X(348), X(40864)}}, {{A, B, C, X(596), X(3912)}}, {{A, B, C, X(1121), X(5695)}}, {{A, B, C, X(1821), X(10405)}}, {{A, B, C, X(6063), X(40845)}}, {{A, B, C, X(16833), X(49451)}}, {{A, B, C, X(29484), X(29756)}}, {{A, B, C, X(49488), X(50095)}}
X(55946) = barycentric quotient X(i)/X(j) for these (i, j): {2, 51058}

X(55947) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(1) AND X(86)

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

X(55947) lies on these lines: {86, 192}, {274, 1698}, {1434, 3212}, {1509, 4658}, {2368, 43077}, {3226, 24165}, {7192, 21128}, {7245, 18827}, {16709, 40780}, {24621, 37678}, {32014, 34475}, {51311, 52136}

X(55947) = isotomic conjugate of X(3993)
X(55947) = trilinear pole of line {3835, 4379}
X(55947) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 21904}, {31, 3993}, {37, 21793}, {42, 16468}, {213, 4393}, {692, 4806}, {756, 34476}, {1824, 23095}, {1918, 30963}, {2205, 10009}, {4557, 4782}, {40733, 40747}
X(55947) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 3993}, {9, 21904}, {1086, 4806}, {6626, 4393}, {34021, 30963}, {40589, 21793}, {40592, 16468}, {40620, 4785}
X(55947) = X(i)-cross conjugate of X(j) for these {i, j}: {30966, 86}
X(55947) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1268)}}, {{A, B, C, X(2), X(29570)}}, {{A, B, C, X(7), X(39740)}}, {{A, B, C, X(75), X(192)}}, {{A, B, C, X(86), X(274)}}, {{A, B, C, X(239), X(29615)}}, {{A, B, C, X(310), X(7192)}}, {{A, B, C, X(333), X(6064)}}, {{A, B, C, X(334), X(596)}}, {{A, B, C, X(870), X(903)}}, {{A, B, C, X(2481), X(39710)}}, {{A, B, C, X(3227), X(39717)}}, {{A, B, C, X(4384), X(29605)}}, {{A, B, C, X(5936), X(38247)}}, {{A, B, C, X(17210), X(39950)}}, {{A, B, C, X(21128), X(24165)}}, {{A, B, C, X(25426), X(40775)}}, {{A, B, C, X(27483), X(31308)}}, {{A, B, C, X(28650), X(39738)}}, {{A, B, C, X(30598), X(39736)}}, {{A, B, C, X(30710), X(32011)}}, {{A, B, C, X(31002), X(39706)}}, {{A, B, C, X(40773), X(42302)}}, {{A, B, C, X(51449), X(52654)}}
X(55947) = barycentric product X(i)*X(j) for these (i, j): {274, 52654}, {1509, 34475}, {27494, 86}, {40735, 6385}, {43077, 52619}, {51449, 76}, {53648, 7192}
X(55947) = barycentric quotient X(i)/X(j) for these (i, j): {1, 21904}, {2, 3993}, {58, 21793}, {81, 16468}, {86, 4393}, {274, 30963}, {310, 10009}, {514, 4806}, {593, 34476}, {1019, 4782}, {1790, 23095}, {3736, 40733}, {7192, 4785}, {8025, 4991}, {16704, 4759}, {27494, 10}, {30966, 27481}, {34475, 594}, {40735, 213}, {40773, 3795}, {40780, 20691}, {43077, 4557}, {51449, 6}, {52654, 37}, {53648, 3952}

X(55948) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(8)

Barycentrics    (a^2-2*a*b+b^2+4*a*c+4*b*c-5*c^2)*(a^2+4*a*b-5*b^2-2*a*c+4*b*c+c^2) : :
X(55948) = -7*X[9780]+4*X[42050]

X(55948) lies on these lines: {2, 1323}, {7, 1121}, {8, 527}, {11, 44559}, {92, 38461}, {312, 30806}, {514, 9779}, {3161, 25411}, {3241, 14942}, {4997, 29627}, {9780, 42050}, {10405, 32086}, {17079, 52156}, {28610, 42030}, {30711, 50095}, {31994, 32008}, {32098, 36605}, {38093, 41006}, {44664, 53620}

X(55948) = isotomic conjugate of X(6172)
X(55948) = trilinear pole of line {1638, 44551}
X(55948) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 35445}, {31, 6172}, {692, 46919}, {1262, 23056}, {14827, 47374}
X(55948) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 6172}, {9, 35445}, {1086, 46919}
X(55948) = X(i)-cross conjugate of X(j) for these {i, j}: {6173, 2}
X(55948) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(4), X(27818)}}, {{A, B, C, X(7), X(514)}}, {{A, B, C, X(9), X(52705)}}, {{A, B, C, X(57), X(55924)}}, {{A, B, C, X(75), X(52715)}}, {{A, B, C, X(80), X(42318)}}, {{A, B, C, X(277), X(7319)}}, {{A, B, C, X(279), X(5556)}}, {{A, B, C, X(281), X(5199)}}, {{A, B, C, X(519), X(29627)}}, {{A, B, C, X(598), X(35158)}}, {{A, B, C, X(658), X(9779)}}, {{A, B, C, X(903), X(4454)}}, {{A, B, C, X(1219), X(40014)}}, {{A, B, C, X(1222), X(40026)}}, {{A, B, C, X(1320), X(21446)}}, {{A, B, C, X(1392), X(7131)}}, {{A, B, C, X(2051), X(8051)}}, {{A, B, C, X(2094), X(31164)}}, {{A, B, C, X(2320), X(36101)}}, {{A, B, C, X(2481), X(4659)}}, {{A, B, C, X(3161), X(4462)}}, {{A, B, C, X(3241), X(3912)}}, {{A, B, C, X(3577), X(43760)}}, {{A, B, C, X(3616), X(17294)}}, {{A, B, C, X(3669), X(41439)}}, {{A, B, C, X(3762), X(52746)}}, {{A, B, C, X(4654), X(28610)}}, {{A, B, C, X(4762), X(44664)}}, {{A, B, C, X(5435), X(45098)}}, {{A, B, C, X(5558), X(9311)}}, {{A, B, C, X(5665), X(39980)}}, {{A, B, C, X(6172), X(6173)}}, {{A, B, C, X(7320), X(17758)}}, {{A, B, C, X(9309), X(47915)}}, {{A, B, C, X(9579), X(52374)}}, {{A, B, C, X(9780), X(50095)}}, {{A, B, C, X(14377), X(36621)}}, {{A, B, C, X(16284), X(32086)}}, {{A, B, C, X(17079), X(30807)}}, {{A, B, C, X(17097), X(41790)}}, {{A, B, C, X(17274), X(35578)}}, {{A, B, C, X(18025), X(39704)}}, {{A, B, C, X(18101), X(21139)}}, {{A, B, C, X(18230), X(38093)}}, {{A, B, C, X(20568), X(39749)}}, {{A, B, C, X(20880), X(31994)}}, {{A, B, C, X(27475), X(50835)}}, {{A, B, C, X(29611), X(50310)}}, {{A, B, C, X(29616), X(38314)}}, {{A, B, C, X(32631), X(43052)}}, {{A, B, C, X(34914), X(55022)}}, {{A, B, C, X(36889), X(46137)}}, {{A, B, C, X(42304), X(45100)}}, {{A, B, C, X(42326), X(43734)}}
X(55948) = barycentric product X(i)*X(j) for these (i, j): {55922, 75}
X(55948) = barycentric quotient X(i)/X(j) for these (i, j): {1, 35445}, {2, 6172}, {514, 46919}, {1088, 47374}, {2310, 23056}, {55922, 1}

X(55949) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(10)

Barycentrics    (2*a^2+2*b^2+3*b*c-c^2+3*a*(b+c))*(2*a^2-b^2+3*b*c+2*c^2+3*a*(b+c)) : :
X(55949) = -4*X[3634]+X[50276], 2*X[3828]+X[50258]

X(55949) lies on the Kiepert Hyperbola and on these lines: {2, 6629}, {10, 524}, {30, 54668}, {86, 671}, {226, 7181}, {321, 14210}, {514, 5466}, {538, 34475}, {543, 551}, {1916, 17180}, {2786, 9180}, {2789, 43667}, {3120, 44572}, {3634, 50276}, {3667, 43674}, {3828, 50258}, {3849, 50180}, {4049, 28840}, {4052, 50223}, {4080, 16826}, {6539, 29615}, {6542, 27797}, {6703, 54553}, {11611, 50116}, {17132, 43677}, {22007, 40515}, {28470, 43668}

X(55949) = isotomic conjugate of X(31144)
X(55949) = trilinear pole of line {4750, 31148}
X(55949) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 31144}, {692, 46915}
X(55949) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 31144}, {1086, 46915}
X(55949) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4663)}}, {{A, B, C, X(2), X(4)}}, {{A, B, C, X(37), X(47947)}}, {{A, B, C, X(80), X(42335)}}, {{A, B, C, X(86), X(514)}}, {{A, B, C, X(256), X(48587)}}, {{A, B, C, X(257), X(1125)}}, {{A, B, C, X(274), X(43972)}}, {{A, B, C, X(310), X(50163)}}, {{A, B, C, X(519), X(4753)}}, {{A, B, C, X(538), X(4785)}}, {{A, B, C, X(543), X(2786)}}, {{A, B, C, X(551), X(6542)}}, {{A, B, C, X(903), X(4472)}}, {{A, B, C, X(1220), X(34892)}}, {{A, B, C, X(2690), X(53224)}}, {{A, B, C, X(3667), X(52229)}}, {{A, B, C, X(3849), X(30519)}}, {{A, B, C, X(4670), X(18827)}}, {{A, B, C, X(6002), X(17132)}}, {{A, B, C, X(14621), X(50299)}}, {{A, B, C, X(15309), X(17133)}}, {{A, B, C, X(16611), X(37675)}}, {{A, B, C, X(17234), X(47352)}}, {{A, B, C, X(17283), X(48310)}}, {{A, B, C, X(17381), X(21358)}}, {{A, B, C, X(17392), X(46922)}}, {{A, B, C, X(19883), X(51353)}}, {{A, B, C, X(29619), X(51103)}}, {{A, B, C, X(29639), X(37854)}}, {{A, B, C, X(34585), X(47915)}}, {{A, B, C, X(35141), X(55948)}}, {{A, B, C, X(37128), X(53114)}}, {{A, B, C, X(37631), X(42028)}}, {{A, B, C, X(42025), X(42045)}}, {{A, B, C, X(42285), X(50309)}}, {{A, B, C, X(49743), X(52374)}}, {{A, B, C, X(50228), X(52394)}}
X(55949) = barycentric product X(i)*X(j) for these (i, j): {55925, 75}
X(55949) = barycentric quotient X(i)/X(j) for these (i, j): {2, 31144}, {514, 46915}, {55925, 1}

X(55950) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(17)

Barycentrics    13*a^4-25*a^2*(b^2+c^2)+8*(2*b^4-5*b^2*c^2+2*c^4)+6*sqrt(3)*(a^2-2*(b^2+c^2))*S : :

X(55950) lies on the Kiepert Hyperbola and on these lines: {13, 8176}, {14, 9886}, {17, 524}, {18, 7619}, {30, 54669}, {98, 9760}, {302, 671}, {530, 54571}, {533, 53104}, {543, 11602}, {1153, 5464}, {5466, 23872}, {5858, 54593}, {7607, 34508}, {7610, 21359}, {8182, 50855}, {8587, 33376}, {9763, 43544}, {11165, 42035}, {11489, 18842}, {12154, 42063}, {12817, 49901}, {13084, 54861}, {16509, 42036}, {16646, 40672}, {16967, 42536}, {22490, 43539}, {33375, 40671}, {33459, 33607}, {33475, 43548}, {33610, 54580}, {33623, 54581}, {37785, 42062}

X(55950) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(302), X(524)}}

X(55951) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(18)

Barycentrics    13*a^4-25*a^2*(b^2+c^2)+8*(2*b^4-5*b^2*c^2+2*c^4)-6*sqrt(3)*(a^2-2*(b^2+c^2))*S : :

X(55951) lies on the Kiepert Hyperbola and on these lines: {13, 9885}, {14, 8176}, {17, 7619}, {18, 524}, {30, 54670}, {98, 9762}, {303, 671}, {531, 54572}, {532, 53104}, {543, 11603}, {1153, 5463}, {5466, 23873}, {5859, 54594}, {7607, 34509}, {7610, 21360}, {8182, 50858}, {8587, 33377}, {9761, 43545}, {11165, 42036}, {11488, 18842}, {12155, 42062}, {12816, 49902}, {13083, 54860}, {16509, 42035}, {16647, 40671}, {16966, 42536}, {22489, 43538}, {33374, 40672}, {33458, 33606}, {33474, 43549}, {33611, 54581}, {33625, 54580}, {37786, 42063}

X(55951) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(303), X(524)}}

X(55952) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(57)

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

X(55952) lies on these lines: {1, 4009}, {57, 536}, {81, 50127}, {291, 31137}, {312, 3227}, {519, 957}, {522, 43928}, {3175, 39980}, {17294, 17946}, {25417, 27064}, {31142, 33908}, {35652, 39948}, {36603, 42051}, {37870, 51488}

X(55952) = trilinear pole of line {14430, 513}
X(55952) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(226), X(41683)}}, {{A, B, C, X(239), X(31137)}}, {{A, B, C, X(312), X(522)}}, {{A, B, C, X(903), X(7033)}}, {{A, B, C, X(3175), X(42034)}}, {{A, B, C, X(3680), X(36795)}}, {{A, B, C, X(4052), X(42471)}}, {{A, B, C, X(4654), X(27064)}}, {{A, B, C, X(6384), X(18822)}}, {{A, B, C, X(14554), X(34860)}}, {{A, B, C, X(16833), X(29824)}}, {{A, B, C, X(16834), X(30942)}}, {{A, B, C, X(17294), X(17763)}}, {{A, B, C, X(17342), X(50103)}}, {{A, B, C, X(20942), X(42051)}}, {{A, B, C, X(26227), X(29573)}}, {{A, B, C, X(29574), X(29828)}}, {{A, B, C, X(29580), X(29825)}}, {{A, B, C, X(29584), X(29827)}}, {{A, B, C, X(31142), X(40862)}}, {{A, B, C, X(31993), X(51488)}}, {{A, B, C, X(35652), X(42029)}}, {{A, B, C, X(42032), X(42047)}}

X(55953) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(81)

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

X(55953) lies on these lines: {1, 3994}, {81, 536}, {89, 17160}, {274, 35543}, {291, 31136}, {321, 3227}, {523, 43928}, {959, 10944}, {1002, 28503}, {4921, 53083}, {14829, 26745}, {17946, 31143}, {25417, 46922}, {39948, 42044}, {39980, 50106}

X(55953) = trilinear pole of line {14431, 31149}
X(55953) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}}, {{A, B, C, X(239), X(31136)}}, {{A, B, C, X(310), X(18822)}}, {{A, B, C, X(321), X(523)}}, {{A, B, C, X(335), X(31161)}}, {{A, B, C, X(596), X(18359)}}, {{A, B, C, X(903), X(3112)}}, {{A, B, C, X(996), X(48826)}}, {{A, B, C, X(1120), X(5235)}}, {{A, B, C, X(1222), X(24624)}}, {{A, B, C, X(2787), X(33908)}}, {{A, B, C, X(3175), X(4980)}}, {{A, B, C, X(4762), X(28503)}}, {{A, B, C, X(4921), X(14829)}}, {{A, B, C, X(5333), X(46922)}}, {{A, B, C, X(9456), X(39960)}}, {{A, B, C, X(9462), X(18825)}}, {{A, B, C, X(17160), X(36594)}}, {{A, B, C, X(17281), X(50102)}}, {{A, B, C, X(17743), X(43758)}}, {{A, B, C, X(18816), X(36588)}}, {{A, B, C, X(18823), X(19623)}}, {{A, B, C, X(19819), X(42032)}}, {{A, B, C, X(29584), X(30970)}}, {{A, B, C, X(29615), X(50756)}}, {{A, B, C, X(42029), X(42044)}}, {{A, B, C, X(42034), X(50106)}}, {{A, B, C, X(42047), X(50043)}}
X(55953) = barycentric product X(i)*X(j) for these (i, j): {55926, 75}
X(55953) = barycentric quotient X(i)/X(j) for these (i, j): {55926, 1}

X(55954) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(85)

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

X(55954) lies on these lines: {2, 6603}, {8, 4702}, {9, 1121}, {85, 527}, {312, 50095}, {333, 17294}, {3679, 14942}, {3912, 30608}, {4384, 4997}, {4518, 50310}, {10405, 32100}, {17281, 17947}, {17330, 52517}, {17776, 30711}, {18359, 30854}, {32015, 38093}

X(55954) = isotomic conjugate of X(6173)
X(55954) = trilinear pole of line {14392, 30565}
X(55954) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4860}, {31, 6173}, {41, 21314}, {56, 34522}, {269, 32578}, {604, 5231}, {934, 17425}, {1407, 42014}
X(55954) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 34522}, {2, 6173}, {9, 4860}, {3160, 21314}, {3161, 5231}, {6600, 32578}, {14714, 17425}, {24771, 42014}
X(55954) = X(i)-cross conjugate of X(j) for these {i, j}: {47787, 190}
X(55954) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(15254)}}, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(9), X(527)}}, {{A, B, C, X(10), X(17294)}}, {{A, B, C, X(75), X(1016)}}, {{A, B, C, X(80), X(27475)}}, {{A, B, C, X(239), X(50310)}}, {{A, B, C, X(277), X(7317)}}, {{A, B, C, X(519), X(4384)}}, {{A, B, C, X(598), X(2481)}}, {{A, B, C, X(673), X(1000)}}, {{A, B, C, X(1120), X(39721)}}, {{A, B, C, X(1222), X(32022)}}, {{A, B, C, X(1255), X(55924)}}, {{A, B, C, X(1434), X(7320)}}, {{A, B, C, X(2718), X(7349)}}, {{A, B, C, X(3679), X(3912)}}, {{A, B, C, X(4866), X(7131)}}, {{A, B, C, X(4971), X(29051)}}, {{A, B, C, X(5325), X(28609)}}, {{A, B, C, X(5559), X(9311)}}, {{A, B, C, X(6559), X(36916)}}, {{A, B, C, X(6666), X(38093)}}, {{A, B, C, X(10302), X(35158)}}, {{A, B, C, X(13606), X(14377)}}, {{A, B, C, X(16823), X(29617)}}, {{A, B, C, X(16833), X(49466)}}, {{A, B, C, X(17078), X(30854)}}, {{A, B, C, X(17758), X(43731)}}, {{A, B, C, X(17776), X(42029)}}, {{A, B, C, X(18025), X(36889)}}, {{A, B, C, X(30701), X(40023)}}, {{A, B, C, X(31169), X(40864)}}, {{A, B, C, X(32019), X(40014)}}, {{A, B, C, X(32088), X(42311)}}, {{A, B, C, X(33116), X(42034)}}, {{A, B, C, X(35160), X(36588)}}, {{A, B, C, X(35176), X(55952)}}, {{A, B, C, X(36807), X(40029)}}, {{A, B, C, X(39970), X(46187)}}, {{A, B, C, X(39980), X(45830)}}, {{A, B, C, X(42318), X(50839)}}, {{A, B, C, X(50093), X(50127)}}
X(55954) = barycentric product X(i)*X(j) for these (i, j): {18810, 200}, {34521, 728}, {55920, 75}
X(55954) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4860}, {2, 6173}, {7, 21314}, {8, 5231}, {9, 34522}, {200, 42014}, {220, 32578}, {657, 17425}, {6745, 44785}, {18810, 1088}, {34521, 23062}, {46003, 48151}, {55920, 1}

X(55955) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(86)

Barycentrics    (a+4*b+c)*(a+b+4*c) : :

X(55955) lies on these lines: {2, 3943}, {7, 11237}, {10, 903}, {27, 8756}, {69, 50951}, {75, 3992}, {86, 519}, {190, 16590}, {310, 3264}, {320, 4745}, {335, 4688}, {523, 6548}, {536, 27483}, {545, 6650}, {673, 41138}, {675, 28210}, {1266, 51069}, {1268, 17320}, {3679, 17360}, {4357, 39710}, {4360, 25055}, {4363, 17488}, {4373, 5224}, {4389, 36588}, {4460, 28626}, {4472, 40891}, {4677, 41847}, {4945, 31025}, {5936, 50101}, {17251, 39720}, {17274, 39707}, {17378, 30712}, {19883, 28653}, {27475, 38093}, {27790, 41816}, {29593, 31139}, {32025, 38098}

X(55955) = reflection of X(i) in X(j) for these {i,j}: {31332, 2}
X(55955) = isogonal conjugate of X(21747)
X(55955) = isotomic conjugate of X(551)
X(55955) = trilinear pole of line {4120, 17310}
X(55955) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 21747}, {6, 16666}, {19, 22357}, {31, 551}, {32, 24589}, {41, 4031}, {58, 21806}, {89, 21754}, {213, 26860}, {604, 3707}, {667, 4781}, {692, 28209}, {1397, 3902}, {2206, 4714}, {2251, 42026}, {14435, 32665}, {16590, 28607}
X(55955) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 551}, {3, 21747}, {6, 22357}, {9, 16666}, {10, 21806}, {1086, 28209}, {3160, 4031}, {3161, 3707}, {6376, 24589}, {6626, 26860}, {6631, 4781}, {9460, 42026}, {27481, 4407}, {35092, 14435}, {36911, 16590}, {40603, 4714}, {40615, 30722}
X(55955) = X(i)-cross conjugate of X(j) for these {i, j}: {3828, 2}, {4777, 190}, {47780, 668}, {52620, 53659}
X(55955) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(16672)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(10), X(519)}}, {{A, B, C, X(256), X(9343)}}, {{A, B, C, X(274), X(17160)}}, {{A, B, C, X(291), X(39974)}}, {{A, B, C, X(313), X(4967)}}, {{A, B, C, X(333), X(17271)}}, {{A, B, C, X(334), X(4665)}}, {{A, B, C, X(350), X(4688)}}, {{A, B, C, X(513), X(28554)}}, {{A, B, C, X(514), X(28309)}}, {{A, B, C, X(536), X(28840)}}, {{A, B, C, X(545), X(2786)}}, {{A, B, C, X(551), X(3828)}}, {{A, B, C, X(870), X(17119)}}, {{A, B, C, X(897), X(1390)}}, {{A, B, C, X(996), X(3679)}}, {{A, B, C, X(1220), X(5560)}}, {{A, B, C, X(1441), X(5564)}}, {{A, B, C, X(1494), X(40417)}}, {{A, B, C, X(1698), X(25055)}}, {{A, B, C, X(2481), X(10302)}}, {{A, B, C, X(3226), X(9462)}}, {{A, B, C, X(3227), X(39717)}}, {{A, B, C, X(3596), X(4102)}}, {{A, B, C, X(3626), X(38098)}}, {{A, B, C, X(3634), X(19883)}}, {{A, B, C, X(3668), X(4909)}}, {{A, B, C, X(3952), X(27812)}}, {{A, B, C, X(4359), X(17320)}}, {{A, B, C, X(4360), X(43260)}}, {{A, B, C, X(4479), X(4699)}}, {{A, B, C, X(4492), X(37129)}}, {{A, B, C, X(4669), X(4745)}}, {{A, B, C, X(4677), X(51066)}}, {{A, B, C, X(4777), X(16590)}}, {{A, B, C, X(4980), X(28653)}}, {{A, B, C, X(5224), X(41629)}}, {{A, B, C, X(5235), X(36594)}}, {{A, B, C, X(7241), X(17038)}}, {{A, B, C, X(9780), X(38314)}}, {{A, B, C, X(13377), X(17269)}}, {{A, B, C, X(17274), X(31231)}}, {{A, B, C, X(17395), X(34578)}}, {{A, B, C, X(17731), X(18823)}}, {{A, B, C, X(18025), X(36889)}}, {{A, B, C, X(18082), X(46772)}}, {{A, B, C, X(18821), X(32008)}}, {{A, B, C, X(19797), X(20336)}}, {{A, B, C, X(19804), X(50101)}}, {{A, B, C, X(20566), X(40216)}}, {{A, B, C, X(24589), X(52620)}}, {{A, B, C, X(24857), X(39697)}}, {{A, B, C, X(24858), X(36440)}}, {{A, B, C, X(26234), X(37756)}}, {{A, B, C, X(27742), X(27760)}}, {{A, B, C, X(30761), X(37792)}}, {{A, B, C, X(31359), X(36610)}}, {{A, B, C, X(32089), X(40438)}}, {{A, B, C, X(34892), X(39712)}}, {{A, B, C, X(34914), X(39714)}}, {{A, B, C, X(36804), X(53226)}}, {{A, B, C, X(36910), X(55076)}}, {{A, B, C, X(38093), X(40719)}}, {{A, B, C, X(39742), X(39983)}}, {{A, B, C, X(48809), X(50287)}}, {{A, B, C, X(51067), X(51070)}}, {{A, B, C, X(51068), X(51072)}}, {{A, B, C, X(51069), X(51071)}}
X(55955) = barycentric product X(i)*X(j) for these (i, j): {27797, 86}, {28210, 3261}, {40434, 75}, {41434, 76}
X(55955) = barycentric quotient X(i)/X(j) for these (i, j): {1, 16666}, {2, 551}, {3, 22357}, {6, 21747}, {7, 4031}, {8, 3707}, {37, 21806}, {75, 24589}, {86, 26860}, {190, 4781}, {312, 3902}, {321, 4714}, {514, 28209}, {900, 14435}, {903, 42026}, {2177, 21754}, {3661, 4407}, {3676, 30722}, {3679, 16590}, {3699, 30727}, {4671, 4793}, {5219, 39782}, {27797, 10}, {28210, 101}, {40434, 1}, {41434, 6}
X(55955) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 28309, 31332}

X(55956) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(92)

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

X(55956) lies on these lines: {2, 6510}, {8, 11111}, {63, 1121}, {92, 527}, {312, 17346}, {4677, 36596}, {4921, 19607}, {4997, 17360}, {5739, 6557}, {29617, 52517}, {30711, 33168}

X(55956) = isotomic conjugate of X(31164)
X(55956) = trilinear pole of line {14414, 45316}
X(55956) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 36279}, {31, 31164}
X(55956) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 31164}, {9, 36279}
X(55956) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(27), X(11111)}}, {{A, B, C, X(63), X(521)}}, {{A, B, C, X(75), X(50105)}}, {{A, B, C, X(81), X(751)}}, {{A, B, C, X(84), X(31445)}}, {{A, B, C, X(519), X(55952)}}, {{A, B, C, X(903), X(13577)}}, {{A, B, C, X(1751), X(34578)}}, {{A, B, C, X(2094), X(6172)}}, {{A, B, C, X(3928), X(17781)}}, {{A, B, C, X(4417), X(4921)}}, {{A, B, C, X(4600), X(40028)}}, {{A, B, C, X(4725), X(28623)}}, {{A, B, C, X(5205), X(29617)}}, {{A, B, C, X(5739), X(41629)}}, {{A, B, C, X(9311), X(24624)}}, {{A, B, C, X(14554), X(43731)}}, {{A, B, C, X(14616), X(39704)}}, {{A, B, C, X(16833), X(49991)}}, {{A, B, C, X(17294), X(26015)}}, {{A, B, C, X(18821), X(34409)}}, {{A, B, C, X(33168), X(42029)}}, {{A, B, C, X(34393), X(36588)}}, {{A, B, C, X(34860), X(46638)}}, {{A, B, C, X(35145), X(36871)}}, {{A, B, C, X(35511), X(53193)}}, {{A, B, C, X(38271), X(39980)}}
X(55956) = barycentric product X(i)*X(j) for these (i, j): {55918, 75}
X(55956) = barycentric quotient X(i)/X(j) for these (i, j): {1, 36279}, {2, 31164}, {55918, 1}

X(55957) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(94)

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

X(55957) lies on the Kiepert Hyperbola and on these lines: {4, 5609}, {6, 54807}, {94, 524}, {98, 10989}, {148, 54918}, {323, 671}, {526, 5466}, {598, 54395}, {1993, 54927}, {1994, 54864}, {7608, 16042}, {10302, 41254}, {18366, 46723}, {34545, 54926}, {37672, 54801}, {41135, 54925}

X(55957) = isotomic conjugate of X(44555)
X(55957) = trilinear pole of line {549, 9175}
X(55957) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 44555}, {2173, 39239}
X(55957) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 44555}, {36896, 39239}
X(55957) = X(i)-cross conjugate of X(j) for these {i, j}: {40112, 2}
X(55957) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(30), X(46789)}}, {{A, B, C, X(265), X(5655)}}, {{A, B, C, X(287), X(9143)}}, {{A, B, C, X(290), X(9141)}}, {{A, B, C, X(297), X(10989)}}, {{A, B, C, X(323), X(524)}}, {{A, B, C, X(1494), X(13485)}}, {{A, B, C, X(1972), X(43768)}}, {{A, B, C, X(5609), X(14919)}}, {{A, B, C, X(5641), X(18019)}}, {{A, B, C, X(10294), X(11564)}}, {{A, B, C, X(15066), X(21399)}}, {{A, B, C, X(16042), X(52281)}}, {{A, B, C, X(23236), X(34897)}}, {{A, B, C, X(41079), X(46809)}}
X(55957) = barycentric quotient X(i)/X(j) for these (i, j): {2, 44555}, {74, 39239}, {381, 15362}, {10295, 10294}, {52173, 381}

X(55958) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(95)

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

X(55958) lies on these lines: {2, 36430}, {5, 1494}, {30, 95}, {69, 1568}, {264, 5055}, {287, 597}, {328, 49674}, {340, 5066}, {3524, 36948}, {3830, 52712}, {5054, 46724}, {5071, 36889}, {6148, 15031}, {6368, 34767}, {14767, 44579}, {15699, 40410}, {19307, 44135}, {21358, 42313}, {23046, 32002}, {30786, 37647}, {31360, 33219}, {34573, 44576}, {36412, 44577}, {37765, 42330}, {38071, 54105}, {45198, 47478}

X(55958) = isogonal conjugate of X(44109)
X(55958) = isotomic conjugate of X(549)
X(55958) = polar conjugate of X(6749)
X(55958) = trilinear pole of line {14391, 40885}
X(55958) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 44109}, {31, 549}, {48, 6749}, {560, 44148}
X(55958) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 549}, {3, 44109}, {1249, 6749}, {6374, 44148}
X(55958) = X(i)-cross conjugate of X(j) for these {i, j}: {547, 2}
X(55958) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}}, {{A, B, C, X(3), X(5055)}}, {{A, B, C, X(4), X(3545)}}, {{A, B, C, X(5), X(30)}}, {{A, B, C, X(6), X(37517)}}, {{A, B, C, X(67), X(53104)}}, {{A, B, C, X(83), X(5641)}}, {{A, B, C, X(98), X(11178)}}, {{A, B, C, X(140), X(15699)}}, {{A, B, C, X(183), X(21358)}}, {{A, B, C, X(186), X(49674)}}, {{A, B, C, X(262), X(17983)}}, {{A, B, C, X(276), X(31621)}}, {{A, B, C, X(290), X(10302)}}, {{A, B, C, X(325), X(597)}}, {{A, B, C, X(327), X(671)}}, {{A, B, C, X(376), X(5071)}}, {{A, B, C, X(381), X(36430)}}, {{A, B, C, X(523), X(7608)}}, {{A, B, C, X(524), X(37647)}}, {{A, B, C, X(546), X(38071)}}, {{A, B, C, X(547), X(549)}}, {{A, B, C, X(550), X(47478)}}, {{A, B, C, X(598), X(35142)}}, {{A, B, C, X(632), X(47599)}}, {{A, B, C, X(1007), X(5032)}}, {{A, B, C, X(1138), X(9221)}}, {{A, B, C, X(1656), X(5054)}}, {{A, B, C, X(1989), X(3613)}}, {{A, B, C, X(2165), X(14458)}}, {{A, B, C, X(2963), X(43458)}}, {{A, B, C, X(3090), X(3524)}}, {{A, B, C, X(3091), X(3839)}}, {{A, B, C, X(3363), X(37350)}}, {{A, B, C, X(3627), X(14892)}}, {{A, B, C, X(3628), X(11539)}}, {{A, B, C, X(3830), X(19709)}}, {{A, B, C, X(3845), X(5066)}}, {{A, B, C, X(3851), X(14269)}}, {{A, B, C, X(5056), X(10304)}}, {{A, B, C, X(5067), X(15709)}}, {{A, B, C, X(5068), X(50687)}}, {{A, B, C, X(5072), X(38335)}}, {{A, B, C, X(5079), X(15688)}}, {{A, B, C, X(5094), X(47597)}}, {{A, B, C, X(5486), X(11669)}}, {{A, B, C, X(5503), X(9462)}}, {{A, B, C, X(6662), X(26861)}}, {{A, B, C, X(6856), X(17561)}}, {{A, B, C, X(7486), X(15708)}}, {{A, B, C, X(7578), X(44135)}}, {{A, B, C, X(7770), X(33219)}}, {{A, B, C, X(7788), X(47355)}}, {{A, B, C, X(7841), X(44543)}}, {{A, B, C, X(7887), X(33220)}}, {{A, B, C, X(8370), X(33228)}}, {{A, B, C, X(8703), X(10109)}}, {{A, B, C, X(8781), X(40826)}}, {{A, B, C, X(8884), X(16837)}}, {{A, B, C, X(9290), X(46270)}}, {{A, B, C, X(10153), X(13377)}}, {{A, B, C, X(10155), X(51179)}}, {{A, B, C, X(10159), X(14387)}}, {{A, B, C, X(10185), X(30542)}}, {{A, B, C, X(11058), X(45838)}}, {{A, B, C, X(11082), X(54561)}}, {{A, B, C, X(11087), X(54562)}}, {{A, B, C, X(11112), X(17533)}}, {{A, B, C, X(11113), X(17530)}}, {{A, B, C, X(11284), X(32216)}}, {{A, B, C, X(11286), X(11318)}}, {{A, B, C, X(11737), X(15687)}}, {{A, B, C, X(12812), X(45759)}}, {{A, B, C, X(13481), X(18361)}}, {{A, B, C, X(14033), X(32984)}}, {{A, B, C, X(14041), X(33013)}}, {{A, B, C, X(14226), X(24244)}}, {{A, B, C, X(14241), X(24243)}}, {{A, B, C, X(14483), X(19307)}}, {{A, B, C, X(14494), X(52188)}}, {{A, B, C, X(14843), X(18854)}}, {{A, B, C, X(14860), X(32533)}}, {{A, B, C, X(14938), X(15319)}}, {{A, B, C, X(15318), X(46412)}}, {{A, B, C, X(15694), X(15703)}}, {{A, B, C, X(15712), X(45757)}}, {{A, B, C, X(16041), X(32983)}}, {{A, B, C, X(16774), X(46217)}}, {{A, B, C, X(16857), X(50740)}}, {{A, B, C, X(16924), X(33251)}}, {{A, B, C, X(17504), X(35018)}}, {{A, B, C, X(17532), X(17556)}}, {{A, B, C, X(17577), X(37375)}}, {{A, B, C, X(18317), X(36439)}}, {{A, B, C, X(18816), X(55955)}}, {{A, B, C, X(18850), X(36436)}}, {{A, B, C, X(27124), X(27177)}}, {{A, B, C, X(30775), X(40132)}}, {{A, B, C, X(32961), X(33255)}}, {{A, B, C, X(32962), X(33278)}}, {{A, B, C, X(32963), X(33187)}}, {{A, B, C, X(32994), X(33264)}}, {{A, B, C, X(33005), X(33017)}}, {{A, B, C, X(33006), X(33016)}}, {{A, B, C, X(33237), X(33240)}}, {{A, B, C, X(33606), X(41897)}}, {{A, B, C, X(33607), X(41898)}}, {{A, B, C, X(34208), X(52187)}}, {{A, B, C, X(34573), X(37671)}}, {{A, B, C, X(36438), X(36456)}}, {{A, B, C, X(37439), X(43957)}}, {{A, B, C, X(37688), X(50991)}}, {{A, B, C, X(39704), X(46136)}}, {{A, B, C, X(41099), X(41106)}}, {{A, B, C, X(43084), X(52094)}}, {{A, B, C, X(43726), X(46204)}}, {{A, B, C, X(44556), X(53099)}}, {{A, B, C, X(44576), X(52289)}}, {{A, B, C, X(46104), X(46138)}}
X(55958) = barycentric product X(i)*X(j) for these (i, j): {14483, 76}
X(55958) = barycentric quotient X(i)/X(j) for these (i, j): {2, 549}, {4, 6749}, {6, 44109}, {76, 44148}, {14483, 6}, {19307, 52154}

X(55959) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(2) AND X(111)

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

X(55959) lies on these lines: {6, 9146}, {25, 51122}, {99, 1383}, {111, 538}, {3228, 3266}, {9147, 34204}, {9148, 9178}, {10717, 14948}, {11175, 12036}, {18818, 53080}

X(55959) = trilinear pole of line {599, 34364}
X(55959) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}}, {{A, B, C, X(99), X(5503)}}, {{A, B, C, X(524), X(5971)}}, {{A, B, C, X(538), X(690)}}, {{A, B, C, X(671), X(34537)}}, {{A, B, C, X(2770), X(41909)}}, {{A, B, C, X(4590), X(6325)}}, {{A, B, C, X(8781), X(10415)}}, {{A, B, C, X(9870), X(22105)}}, {{A, B, C, X(10511), X(36953)}}, {{A, B, C, X(18880), X(45096)}}, {{A, B, C, X(34087), X(35146)}}

X(55960) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(4) AND X(7)

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

X(55960) lies on the Feuerbach Hyperbola and on these lines: {4, 37787}, {7, 1776}, {63, 3254}, {79, 54370}, {104, 12669}, {943, 10394}, {1156, 7082}, {3065, 5732}, {3681, 34894}, {4197, 15297}, {5698, 43740}, {7675, 15175}, {8545, 34917}, {30513, 38057}, {41228, 45393}

X(55960) = X(i)-cross conjugate of X(j) for these {i, j}: {34879, 1}
X(55960) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(63), X(37787)}}, {{A, B, C, X(1013), X(7474)}}, {{A, B, C, X(1776), X(6061)}}, {{A, B, C, X(2161), X(3423)}}, {{A, B, C, X(2287), X(7318)}}, {{A, B, C, X(7411), X(52891)}}, {{A, B, C, X(24624), X(39273)}}, {{A, B, C, X(36100), X(42318)}}, {{A, B, C, X(37741), X(39943)}}

X(55961) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(4) AND X(8)

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

X(55961) lies on the Feuerbach Hyperbola and on these lines: {8, 1776}, {80, 54286}, {404, 1156}, {936, 3467}, {1000, 11111}, {3306, 46435}, {3895, 12641}, {5559, 12514}, {10394, 34894}, {14923, 24297}, {15446, 19861}

X(55961) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(60), X(1776)}}, {{A, B, C, X(285), X(36626)}}, {{A, B, C, X(404), X(52891)}}, {{A, B, C, X(936), X(27529)}}, {{A, B, C, X(2185), X(55956)}}, {{A, B, C, X(6603), X(15297)}}, {{A, B, C, X(11111), X(17519)}}, {{A, B, C, X(14584), X(45824)}}, {{A, B, C, X(26285), X(37612)}}

X(55962) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(4) AND X(57)

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

X(55962) lies on the Kiepert Hyperbola and on these lines: {4, 35466}, {10, 3486}, {21, 43533}, {144, 4080}, {226, 4644}, {321, 5273}, {376, 54528}, {3090, 5397}, {3424, 8229}, {3545, 54679}, {3929, 4052}, {4049, 7658}, {4383, 45098}, {6855, 54972}, {6856, 43531}, {7397, 54739}, {7490, 40149}, {13576, 30943}, {14554, 37650}, {17577, 54623}, {18840, 37660}, {50739, 54786}

X(55962) = isotomic conjugate of X(30828)
X(55962) = X(i)-cross conjugate of X(j) for these {i, j}: {31187, 2}
X(55962) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(8), X(2006)}}, {{A, B, C, X(21), X(57)}}, {{A, B, C, X(27), X(6857)}}, {{A, B, C, X(69), X(17094)}}, {{A, B, C, X(80), X(50442)}}, {{A, B, C, X(85), X(43759)}}, {{A, B, C, X(88), X(44178)}}, {{A, B, C, X(90), X(8056)}}, {{A, B, C, X(144), X(3911)}}, {{A, B, C, X(189), X(37887)}}, {{A, B, C, X(272), X(1119)}}, {{A, B, C, X(277), X(34234)}}, {{A, B, C, X(278), X(333)}}, {{A, B, C, X(469), X(6856)}}, {{A, B, C, X(673), X(4644)}}, {{A, B, C, X(967), X(1175)}}, {{A, B, C, X(1150), X(24597)}}, {{A, B, C, X(1156), X(21446)}}, {{A, B, C, X(1249), X(14331)}}, {{A, B, C, X(2321), X(51316)}}, {{A, B, C, X(3618), X(37660)}}, {{A, B, C, X(3929), X(5435)}}, {{A, B, C, X(4373), X(43948)}}, {{A, B, C, X(6336), X(55956)}}, {{A, B, C, X(6837), X(37276)}}, {{A, B, C, X(6988), X(37279)}}, {{A, B, C, X(8229), X(52283)}}, {{A, B, C, X(14555), X(37646)}}, {{A, B, C, X(15149), X(30943)}}, {{A, B, C, X(17097), X(25430)}}, {{A, B, C, X(18359), X(43734)}}, {{A, B, C, X(24580), X(52891)}}, {{A, B, C, X(30101), X(30712)}}, {{A, B, C, X(30809), X(37371)}}, {{A, B, C, X(30811), X(31232)}}, {{A, B, C, X(30828), X(31187)}}, {{A, B, C, X(37142), X(39981)}}
X(55962) = barycentric quotient X(i)/X(j) for these (i, j): {2, 30828}

X(55963) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(4) AND X(63)

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

X(55963) lies on these lines: {4, 78}, {20, 53813}, {21, 8747}, {27, 1812}, {63, 278}, {92, 345}, {264, 36795}, {280, 6837}, {281, 52351}, {329, 40573}, {348, 1847}, {948, 40843}, {1013, 36124}, {1118, 37248}, {1791, 54343}, {1857, 37358}, {5249, 41081}, {17917, 52381}, {36100, 37800}, {37302, 51410}

X(55963) = isogonal conjugate of X(19350)
X(55963) = isotomic conjugate of X(6350)
X(55963) = polar conjugate of X(18391)
X(55963) = trilinear pole of line {7649, 10015}
X(55963) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 19350}, {3, 8557}, {6, 18446}, {31, 6350}, {48, 18391}, {212, 54366}, {647, 54442}, {1512, 14578}
X(55963) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 6350}, {3, 19350}, {9, 18446}, {1249, 18391}, {36103, 8557}, {39052, 54442}, {40837, 54366}
X(55963) = X(i)-cross conjugate of X(j) for these {i, j}: {1012, 7}, {1074, 75}, {37695, 2}, {41389, 46133}
X(55963) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(21)}}, {{A, B, C, X(4), X(27)}}, {{A, B, C, X(7), X(264)}}, {{A, B, C, X(57), X(37531)}}, {{A, B, C, X(84), X(1217)}}, {{A, B, C, X(90), X(2184)}}, {{A, B, C, X(189), X(15474)}}, {{A, B, C, X(243), X(948)}}, {{A, B, C, X(272), X(8048)}}, {{A, B, C, X(277), X(34234)}}, {{A, B, C, X(281), X(2326)}}, {{A, B, C, X(318), X(52780)}}, {{A, B, C, X(329), X(5249)}}, {{A, B, C, X(379), X(14956)}}, {{A, B, C, X(464), X(25516)}}, {{A, B, C, X(1013), X(15149)}}, {{A, B, C, X(1105), X(10429)}}, {{A, B, C, X(1435), X(41505)}}, {{A, B, C, X(1817), X(6837)}}, {{A, B, C, X(2322), X(40838)}}, {{A, B, C, X(2349), X(55918)}}, {{A, B, C, X(3423), X(40801)}}, {{A, B, C, X(4000), X(42709)}}, {{A, B, C, X(4080), X(52575)}}, {{A, B, C, X(6349), X(6708)}}, {{A, B, C, X(6350), X(37695)}}, {{A, B, C, X(7474), X(14021)}}, {{A, B, C, X(9965), X(30852)}}, {{A, B, C, X(10305), X(18853)}}, {{A, B, C, X(10405), X(21907)}}, {{A, B, C, X(10883), X(14953)}}, {{A, B, C, X(14016), X(37181)}}, {{A, B, C, X(17917), X(52412)}}, {{A, B, C, X(18359), X(43740)}}, {{A, B, C, X(34402), X(44186)}}, {{A, B, C, X(37448), X(52891)}}, {{A, B, C, X(40431), X(40836)}}
X(55963) = barycentric quotient X(i)/X(j) for these (i, j): {1, 18446}, {2, 6350}, {4, 18391}, {6, 19350}, {19, 8557}, {162, 54442}, {278, 54366}, {1785, 1512}

X(55964) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(4) AND X(84)

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

X(55964) lies on the Feuerbach Hyperbola and on these lines: {9, 4304}, {20, 1156}, {84, 1776}, {1210, 5665}, {1323, 8809}, {3486, 7160}, {4866, 10572}, {5723, 36121}, {5784, 34919}, {6601, 30305}, {6837, 17097}, {12245, 24297}, {14331, 23893}

X(55964) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(20), X(1323)}}, {{A, B, C, X(27), X(11111)}}, {{A, B, C, X(103), X(51497)}}, {{A, B, C, X(277), X(34234)}}, {{A, B, C, X(279), X(4304)}}, {{A, B, C, X(759), X(1119)}}, {{A, B, C, X(957), X(3423)}}, {{A, B, C, X(1043), X(40836)}}, {{A, B, C, X(1210), X(20007)}}, {{A, B, C, X(1295), X(39943)}}, {{A, B, C, X(1751), X(41514)}}, {{A, B, C, X(2994), X(34056)}}, {{A, B, C, X(4313), X(21314)}}, {{A, B, C, X(4350), X(30305)}}, {{A, B, C, X(4845), X(7046)}}, {{A, B, C, X(6740), X(7318)}}, {{A, B, C, X(6743), X(14986)}}, {{A, B, C, X(6764), X(12629)}}, {{A, B, C, X(34578), X(34701)}}

X(55965) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(4) AND X(85)

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

X(55965) lies on these lines: {9, 7183}, {63, 7079}, {85, 8558}, {220, 394}, {283, 11107}, {333, 44331}, {480, 1259}, {728, 3719}, {2365, 52776}, {5282, 6559}, {54966, 54968}

X(55965) = trilinear pole of line {4105, 35057}
X(55965) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 1836}, {19, 20277}, {25, 17073}, {56, 46835}, {57, 4336}, {393, 53847}, {604, 17860}, {651, 2520}, {1400, 17188}, {1474, 21912}, {8643, 27833}, {8750, 23727}, {34079, 51462}
X(55965) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 46835}, {6, 20277}, {9, 1836}, {3161, 17860}, {5452, 4336}, {6505, 17073}, {26932, 23727}, {35069, 51462}, {38991, 2520}, {40582, 17188}, {51574, 21912}
X(55965) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1121)}}, {{A, B, C, X(2), X(2349)}}, {{A, B, C, X(3), X(44331)}}, {{A, B, C, X(6), X(3497)}}, {{A, B, C, X(8), X(4564)}}, {{A, B, C, X(9), X(220)}}, {{A, B, C, X(21), X(85)}}, {{A, B, C, X(27), X(37285)}}, {{A, B, C, X(56), X(3512)}}, {{A, B, C, X(57), X(3929)}}, {{A, B, C, X(58), X(7096)}}, {{A, B, C, X(63), X(271)}}, {{A, B, C, X(72), X(349)}}, {{A, B, C, X(75), X(33298)}}, {{A, B, C, X(76), X(4567)}}, {{A, B, C, X(84), X(1434)}}, {{A, B, C, X(90), X(673)}}, {{A, B, C, X(104), X(9311)}}, {{A, B, C, X(189), X(2185)}}, {{A, B, C, X(249), X(34016)}}, {{A, B, C, X(277), X(37131)}}, {{A, B, C, X(348), X(1098)}}, {{A, B, C, X(514), X(15446)}}, {{A, B, C, X(672), X(5282)}}, {{A, B, C, X(765), X(30701)}}, {{A, B, C, X(943), X(27475)}}, {{A, B, C, X(987), X(39957)}}, {{A, B, C, X(1043), X(8777)}}, {{A, B, C, X(1110), X(3730)}}, {{A, B, C, X(1156), X(1170)}}, {{A, B, C, X(1247), X(39981)}}, {{A, B, C, X(1257), X(40023)}}, {{A, B, C, X(1392), X(36605)}}, {{A, B, C, X(1812), X(34404)}}, {{A, B, C, X(2053), X(9322)}}, {{A, B, C, X(2161), X(39970)}}, {{A, B, C, X(2167), X(2994)}}, {{A, B, C, X(2284), X(16552)}}, {{A, B, C, X(2320), X(10405)}}, {{A, B, C, X(2339), X(40420)}}, {{A, B, C, X(2990), X(55956)}}, {{A, B, C, X(2991), X(34860)}}, {{A, B, C, X(3065), X(14377)}}, {{A, B, C, X(5692), X(24433)}}, {{A, B, C, X(6172), X(37787)}}, {{A, B, C, X(9328), X(15180)}}, {{A, B, C, X(15175), X(17758)}}, {{A, B, C, X(15315), X(40398)}}, {{A, B, C, X(21446), X(32015)}}, {{A, B, C, X(27509), X(28731)}}, {{A, B, C, X(30608), X(36100)}}, {{A, B, C, X(31359), X(34863)}}, {{A, B, C, X(32635), X(55954)}}, {{A, B, C, X(34398), X(34409)}}, {{A, B, C, X(34402), X(40443)}}, {{A, B, C, X(34406), X(34411)}}, {{A, B, C, X(36800), X(40011)}}, {{A, B, C, X(37214), X(40411)}}, {{A, B, C, X(40399), X(42030)}}
X(55965) = barycentric product X(i)*X(j) for these (i, j): {1, 34409}, {34398, 78}, {37741, 75}, {52616, 52776}
X(55965) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1836}, {3, 20277}, {8, 17860}, {9, 46835}, {21, 17188}, {55, 4336}, {63, 17073}, {72, 21912}, {255, 53847}, {663, 2520}, {758, 51462}, {905, 23727}, {27834, 27833}, {34398, 273}, {34409, 75}, {37741, 1}, {52776, 36127}, {54968, 52938}

X(55966) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(4) AND X(104)

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

X(55966) lies on the Feuerbach Hyperbola and on these lines: {7, 14878}, {9, 10050}, {80, 5537}, {100, 30513}, {104, 1776}, {1156, 6909}, {3254, 30384}, {10090, 46435}, {10309, 40293}, {10427, 37249}, {10572, 34918}, {10707, 43740}, {11501, 37725}

X(55966) = X(i)-cross conjugate of X(j) for these {i, j}: {50371, 1}
X(55966) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4)}}, {{A, B, C, X(36), X(972)}}, {{A, B, C, X(100), X(32641)}}, {{A, B, C, X(105), X(10426)}}, {{A, B, C, X(1295), X(36052)}}, {{A, B, C, X(2316), X(2716)}}, {{A, B, C, X(6909), X(52891)}}, {{A, B, C, X(10058), X(24624)}}, {{A, B, C, X(10310), X(40293)}}

X(55967) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(6) AND X(7)

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

X(55967) lies on these lines: {2, 2280}, {6, 27475}, {7, 238}, {9, 335}, {75, 1001}, {86, 47595}, {142, 14621}, {183, 40027}, {242, 273}, {673, 17278}, {1088, 1447}, {2346, 40732}, {5272, 7249}, {5936, 8236}, {6384, 16992}, {7179, 21453}, {17277, 36807}, {18230, 39749}, {18815, 36815}, {20142, 51194}, {25269, 27494}, {28542, 36588}, {28640, 42335}, {31002, 37670}

X(55967) = trilinear pole of line {4435, 23781}
X(55967) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 51058}
X(55967) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 51058}
X(55967) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(16503)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(6), X(105)}}, {{A, B, C, X(8), X(16020)}}, {{A, B, C, X(9), X(87)}}, {{A, B, C, X(21), X(949)}}, {{A, B, C, X(77), X(14189)}}, {{A, B, C, X(85), X(7261)}}, {{A, B, C, X(95), X(2862)}}, {{A, B, C, X(98), X(3062)}}, {{A, B, C, X(142), X(7179)}}, {{A, B, C, X(262), X(15909)}}, {{A, B, C, X(277), X(7233)}}, {{A, B, C, X(518), X(29362)}}, {{A, B, C, X(552), X(39948)}}, {{A, B, C, X(614), X(3757)}}, {{A, B, C, X(870), X(17743)}}, {{A, B, C, X(1156), X(5695)}}, {{A, B, C, X(1383), X(9094)}}, {{A, B, C, X(1390), X(10013)}}, {{A, B, C, X(1441), X(47595)}}, {{A, B, C, X(2191), X(52030)}}, {{A, B, C, X(3263), X(17278)}}, {{A, B, C, X(3286), X(37741)}}, {{A, B, C, X(3598), X(18230)}}, {{A, B, C, X(3616), X(39581)}}, {{A, B, C, X(4384), X(6185)}}, {{A, B, C, X(4518), X(6601)}}, {{A, B, C, X(4604), X(9086)}}, {{A, B, C, X(4998), X(39963)}}, {{A, B, C, X(5272), X(7081)}}, {{A, B, C, X(6006), X(28542)}}, {{A, B, C, X(7292), X(26227)}}, {{A, B, C, X(7612), X(10307)}}, {{A, B, C, X(8056), X(40419)}}, {{A, B, C, X(9082), X(21448)}}, {{A, B, C, X(9095), X(37129)}}, {{A, B, C, X(9108), X(10390)}}, {{A, B, C, X(9110), X(39389)}}, {{A, B, C, X(9436), X(42409)}}, {{A, B, C, X(13478), X(32021)}}, {{A, B, C, X(16992), X(27644)}}, {{A, B, C, X(17000), X(33295)}}, {{A, B, C, X(17279), X(26234)}}, {{A, B, C, X(24695), X(34919)}}, {{A, B, C, X(26229), X(29007)}}, {{A, B, C, X(32008), X(41527)}}, {{A, B, C, X(32019), X(39714)}}, {{A, B, C, X(32023), X(37887)}}, {{A, B, C, X(37128), X(39273)}}, {{A, B, C, X(37670), X(52897)}}, {{A, B, C, X(39981), X(43760)}}, {{A, B, C, X(40435), X(54128)}}
X(55967) = barycentric product X(i)*X(j) for these (i, j): {1, 55946}
X(55967) = barycentric quotient X(i)/X(j) for these (i, j): {1, 51058}, {55946, 75}

X(55968) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(6) AND X(27)

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

X(55968) lies on these lines: {2, 37502}, {7, 16752}, {27, 238}, {72, 335}, {75, 24424}, {86, 20769}, {273, 16609}, {333, 6384}, {978, 45965}, {1246, 27623}, {8049, 27643}, {14621, 16054}

X(55968) = trilinear pole of line {514, 53556}
X(55968) = X(i)-isoconjugate-of-X(j) for these {i, j}: {37, 37507}, {213, 30962}
X(55968) = X(i)-Dao conjugate of X(j) for these {i, j}: {6626, 30962}, {40589, 37507}
X(55968) = X(i)-cross conjugate of X(j) for these {i, j}: {37555, 81}
X(55968) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7)}}, {{A, B, C, X(6), X(40435)}}, {{A, B, C, X(58), X(37502)}}, {{A, B, C, X(72), X(238)}}, {{A, B, C, X(87), X(1751)}}, {{A, B, C, X(239), X(16827)}}, {{A, B, C, X(277), X(44129)}}, {{A, B, C, X(333), X(27644)}}, {{A, B, C, X(1258), X(5331)}}, {{A, B, C, X(4225), X(26003)}}, {{A, B, C, X(16054), X(31909)}}, {{A, B, C, X(16752), X(28660)}}, {{A, B, C, X(19810), X(40941)}}, {{A, B, C, X(27643), X(29767)}}, {{A, B, C, X(28621), X(39736)}}, {{A, B, C, X(34234), X(39981)}}, {{A, B, C, X(37870), X(40409)}}
X(55968) = barycentric quotient X(i)/X(j) for these (i, j): {58, 37507}, {86, 30962}

X(55969) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(6) AND X(36)

Barycentrics    a*(b-c)*(a^3-b*c*(b+c)-a*(b^2+c^2)) : :
X(55969) = -X[4063]+3*X[53390], -3*X[11125]+X[21118], -X[20293]+3*X[48204], -2*X[20316]+3*X[48205], -X[21302]+3*X[26078], -3*X[45686]+X[48264], -X[47694]+3*X[47845], -3*X[47794]+2*X[53574], -2*X[48330]+3*X[53315]

X(55969) lies on these lines: {1, 4777}, {6, 650}, {36, 238}, {42, 48225}, {43, 48213}, {86, 693}, {87, 16495}, {514, 21112}, {521, 34975}, {522, 2605}, {523, 1459}, {612, 48200}, {614, 48211}, {659, 9002}, {663, 900}, {814, 14288}, {1001, 24457}, {1491, 5040}, {1638, 4724}, {1734, 8674}, {1740, 50335}, {2504, 50348}, {3287, 6586}, {3667, 48306}, {3720, 48189}, {3738, 14838}, {3920, 48187}, {4041, 53532}, {4063, 53390}, {4145, 48333}, {4411, 10436}, {4508, 27485}, {4778, 21188}, {4794, 6006}, {4802, 48281}, {4828, 41847}, {4885, 15668}, {4926, 48307}, {4977, 7178}, {5263, 47729}, {5427, 14315}, {6003, 50350}, {7191, 48223}, {7649, 21111}, {8053, 8641}, {8062, 50327}, {8675, 53550}, {8760, 37474}, {11125, 21118}, {14299, 51659}, {14812, 16468}, {15485, 23838}, {17019, 48423}, {17259, 31287}, {17277, 31209}, {17349, 27115}, {17379, 17494}, {18154, 20150}, {20293, 48204}, {20316, 48205}, {21102, 21106}, {21103, 21119}, {21302, 26078}, {23806, 34830}, {25508, 25511}, {26102, 48202}, {26777, 37677}, {27623, 27674}, {27644, 27648}, {28151, 48282}, {28161, 48292}, {28165, 48293}, {28169, 48287}, {28175, 48342}, {28183, 48303}, {28217, 48340}, {28220, 47970}, {28221, 42312}, {28365, 28374}, {29066, 50302}, {29580, 50763}, {31150, 46922}, {32941, 48285}, {33682, 48284}, {37129, 37222}, {43997, 47724}, {45686, 48264}, {47694, 47845}, {47794, 53574}, {48330, 53315}

X(55969) = midpoint of X(i) and X(j) for these {i,j}: {1459, 17418}, {14299, 51659}, {21102, 21106}, {21103, 21119}, {3737, 21173}, {4041, 53532}, {43924, 46385}, {48281, 50346}, {50349, 53314}
X(55969) = reflection of X(i) in X(j) for these {i,j}: {21111, 7649}, {21189, 31947}, {4491, 48331}, {48283, 1459}, {48297, 3737}, {48302, 2605}, {50327, 8062}, {53527, 905}
X(55969) = perspector of circumconic {{A, B, C, X(81), X(104)}}
X(55969) = X(i)-isoconjugate-of-X(j) for these {i, j}: {100, 994}, {110, 45095}, {190, 46018}
X(55969) = X(i)-Dao conjugate of X(j) for these {i, j}: {244, 45095}, {8054, 994}, {55053, 46018}
X(55969) = X(i)-Ceva conjugate of X(j) for these {i, j}: {4588, 1}
X(55969) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(859)}}, {{A, B, C, X(36), X(86)}}, {{A, B, C, X(87), X(993)}}, {{A, B, C, X(513), X(51659)}}, {{A, B, C, X(523), X(21189)}}, {{A, B, C, X(650), X(14299)}}, {{A, B, C, X(1019), X(48321)}}, {{A, B, C, X(1150), X(37222)}}, {{A, B, C, X(2278), X(3286)}}, {{A, B, C, X(2423), X(3733)}}, {{A, B, C, X(3737), X(43927)}}, {{A, B, C, X(7178), X(14349)}}, {{A, B, C, X(16695), X(23345)}}, {{A, B, C, X(23800), X(40086)}}
X(55969) = barycentric product X(i)*X(j) for these (i, j): {1, 48321}, {333, 51659}, {514, 993}, {1150, 513}, {2278, 693}, {3669, 49492}, {5136, 905}, {14299, 34234}
X(55969) = barycentric quotient X(i)/X(j) for these (i, j): {649, 994}, {661, 45095}, {667, 46018}, {993, 190}, {1150, 668}, {2278, 100}, {5136, 6335}, {14299, 908}, {48321, 75}, {49492, 646}, {51659, 226}
X(55969) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {513, 31947, 21189}, {513, 3737, 48297}, {513, 48331, 4491}, {513, 905, 53527}, {522, 2605, 48302}, {523, 1459, 48283}, {1459, 17418, 523}, {3737, 21173, 513}, {43924, 46385, 4977}, {48281, 50346, 4802}, {50349, 53314, 514}

X(55970) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(6) AND X(75)

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

X(55970) lies on these lines: {2, 1914}, {6, 335}, {7, 1428}, {75, 238}, {86, 5009}, {310, 33295}, {1268, 5263}, {4000, 6650}, {4362, 40033}, {6384, 34252}, {14621, 16706}, {16503, 17394}, {17350, 27494}, {20172, 27483}, {29852, 52394}, {39749, 50030}

X(55970) = isotomic conjugate of X(29674)
X(55970) = trilinear pole of line {8632, 50458}
X(55970) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 49509}, {31, 29674}, {41, 36482}, {101, 50454}, {213, 30965}
X(55970) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 29674}, {9, 49509}, {1015, 50454}, {3160, 36482}, {6626, 30965}
X(55970) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(16825)}}, {{A, B, C, X(2), X(7)}}, {{A, B, C, X(4), X(18032)}}, {{A, B, C, X(6), X(82)}}, {{A, B, C, X(10), X(29646)}}, {{A, B, C, X(19), X(87)}}, {{A, B, C, X(28), X(37100)}}, {{A, B, C, X(57), X(40415)}}, {{A, B, C, X(83), X(870)}}, {{A, B, C, X(89), X(4600)}}, {{A, B, C, X(261), X(52652)}}, {{A, B, C, X(552), X(2985)}}, {{A, B, C, X(897), X(55919)}}, {{A, B, C, X(977), X(1244)}}, {{A, B, C, X(1001), X(16503)}}, {{A, B, C, X(1014), X(3113)}}, {{A, B, C, X(1447), X(3407)}}, {{A, B, C, X(1751), X(32010)}}, {{A, B, C, X(2214), X(40748)}}, {{A, B, C, X(2248), X(43761)}}, {{A, B, C, X(3226), X(17743)}}, {{A, B, C, X(4000), X(20947)}}, {{A, B, C, X(4362), X(29821)}}, {{A, B, C, X(4676), X(37129)}}, {{A, B, C, X(5263), X(16709)}}, {{A, B, C, X(6628), X(25417)}}, {{A, B, C, X(7261), X(39724)}}, {{A, B, C, X(14377), X(18827)}}, {{A, B, C, X(15320), X(43534)}}, {{A, B, C, X(15474), X(51865)}}, {{A, B, C, X(15523), X(29852)}}, {{A, B, C, X(16706), X(33931)}}, {{A, B, C, X(17017), X(32914)}}, {{A, B, C, X(17103), X(41534)}}, {{A, B, C, X(20541), X(20629)}}, {{A, B, C, X(20553), X(20643)}}, {{A, B, C, X(20570), X(40845)}}, {{A, B, C, X(29654), X(32778)}}, {{A, B, C, X(40409), X(40412)}}
X(55970) = barycentric quotient X(i)/X(j) for these (i, j): {1, 49509}, {2, 29674}, {7, 36482}, {86, 30965}, {513, 50454}

X(55971) = KIMBERLING-PAVLOV X(1)-CONJUGATE OF X(6) AND X(81)

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

X(55971) lies on these lines: {43, 81}, {86, 192}, {87, 22174}, {274, 20899}, {757, 27644}, {873, 5333}, {1014, 1423}, {4469, 16726}, {16604, 20332}, {17038, 25528}, {37128, 41531}, {37673, 39952}, {40439, 42025}, {40773, 40780}

X(55971) = trilinear pole of line {1019, 4378}
X(55971) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 21904}, {6, 3993}, {10, 21793}, {37, 16468}, {42, 4393}, {101, 4806}, {213, 30963}, {594, 34476}, {1018, 4782}, {1826, 23095}, {1918, 10009}, {3690, 31912}, {3795, 40747}, {4557, 4785}, {4991, 52555}, {20691, 40753}, {40718, 40733}
X(55971) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 21904}, {9, 3993}, {1015, 4806}, {6626, 30963}, {34021, 10009}, {40589, 16468}, {40592, 4393}
X(55971) = X(i)-cross conjugate of X(j) for these {i, j}: {40773, 81}, {52654, 55947}
X(55971) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(29570)}}, {{A, B, C, X(2), X(43)}}, {{A, B, C, X(6), X(1255)}}, {{A, B, C, X(10), X(27646)}}, {{A, B, C, X(21), X(423)}}, {{A, B, C, X(57), X(37604)}}, {{A, B, C, X(58), X(32014)}}, {{A, B, C, X(81), X(86)}}, {{A, B, C, X(88), X(750)}}, {{A, B, C, X(257), X(47915)}}, {{A, B, C, X(274), X(1019)}}, {{A, B, C, X(321), X(28244)}}, {{A, B, C, X(335), X(39798)}}, {{A, B, C, X(513), X(27483)}}, {{A, B, C, X(673), X(39962)}}, {{A, B, C, X(979), X(39738)}}, {{A, B, C, X(1258), X(43531)}}, {{A, B, C, X(3500), X(39736)}}, {{A, B, C, X(3736), X(40734)}}, {{A, B, C, X(4469), X(4481)}}, {{A, B, C, X(4833), X(5235)}}, {{A, B, C, X(7153), X(39740)}}, {{A, B, C, X(16604), X(20899)}}, {{A, B, C, X(16710), X(39747)}}, {{A, B, C, X(16826), X(25426)}}, {{A, B, C, X(18166), X(42025)}}, {{A, B, C, X(25430), X(36598)}}, {{A, B, C, X(25508), X(32911)}}, {{A, B, C, X(27475), X(36494)}}, {{A, B, C, X(27494), X(52654)}}, {{A, B, C, X(27789), X(39972)}}, {{A, B, C, X(30571), X(31308)}}, {{A, B, C, X(32009), X(39748)}}, {{A, B, C, X(37129), X(39971)}}
X(55971) = barycentric product X(i)*X(j) for these (i, j): {1, 55947}, {310, 40735}, {1019, 53648}, {27494, 81}, {34475, 757}, {43077, 7199}, {51449, 75}, {52654, 86}
X(55971) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3993}, {6, 21904}, {58, 16468}, {81, 4393}, {86, 30963}, {274, 10009}, {513, 4806}, {849, 34476}, {1019, 4785}, {1333, 21793}, {1437, 23095}, {3733, 4782}, {3736, 3795}, {16744, 25376}, {27494, 321}, {34475, 1089}, {40735, 42}, {40773, 27481}, {40780, 3971}, {43077, 1018}, {51449, 1}, {52654, 10}, {52680, 4759}, {53648, 4033}, {55947, 75}

X(55972) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(4) AND X(69)

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

X(55972) lies on these lines: {2, 6394}, {4, 325}, {69, 297}, {76, 1093}, {183, 52283}, {225, 52565}, {290, 23291}, {315, 8884}, {316, 16263}, {317, 20022}, {327, 40330}, {458, 1007}, {467, 40123}, {847, 1235}, {1300, 35575}, {1826, 52396}, {5641, 11180}, {5921, 45031}, {6526, 34403}, {6776, 54124}, {6820, 45201}, {10002, 18906}, {11331, 34229}, {14826, 34405}, {17983, 44134}, {32000, 34208}, {32006, 37200}, {32829, 37124}, {34803, 52289}, {37174, 37668}, {41013, 42703}

X(55972) = isotomic conjugate of X(6776)
X(55972) = polar conjugate of X(7735)
X(55972) = trilinear pole of line {2501, 3265}
X(55972) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 6776}, {48, 7735}, {63, 40825}, {184, 4008}, {255, 6620}, {810, 35278}, {1973, 37188}, {9247, 40814}, {32676, 47194}, {43976, 52430}
X(55972) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 6776}, {1249, 7735}, {3162, 40825}, {6337, 37188}, {6523, 6620}, {15526, 47194}, {39062, 35278}, {52032, 42353}
X(55972) = X(i)-cross conjugate of X(j) for these {i, j}: {1352, 2}, {23878, 6331}, {40802, 40824}
X(55972) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(297)}}, {{A, B, C, X(4), X(93)}}, {{A, B, C, X(69), X(76)}}, {{A, B, C, X(83), X(8797)}}, {{A, B, C, X(94), X(41896)}}, {{A, B, C, X(95), X(18840)}}, {{A, B, C, X(182), X(40330)}}, {{A, B, C, X(183), X(37668)}}, {{A, B, C, X(253), X(290)}}, {{A, B, C, X(311), X(315)}}, {{A, B, C, X(316), X(44135)}}, {{A, B, C, X(317), X(1235)}}, {{A, B, C, X(337), X(34401)}}, {{A, B, C, X(458), X(37174)}}, {{A, B, C, X(459), X(40413)}}, {{A, B, C, X(511), X(43718)}}, {{A, B, C, X(542), X(11180)}}, {{A, B, C, X(598), X(32827)}}, {{A, B, C, X(671), X(32815)}}, {{A, B, C, X(801), X(6340)}}, {{A, B, C, X(1352), X(6776)}}, {{A, B, C, X(1494), X(5485)}}, {{A, B, C, X(1899), X(14826)}}, {{A, B, C, X(3091), X(37200)}}, {{A, B, C, X(3260), X(11185)}}, {{A, B, C, X(3399), X(46952)}}, {{A, B, C, X(5392), X(13575)}}, {{A, B, C, X(5395), X(7773)}}, {{A, B, C, X(6504), X(18018)}}, {{A, B, C, X(6524), X(47847)}}, {{A, B, C, X(7620), X(16093)}}, {{A, B, C, X(7788), X(15589)}}, {{A, B, C, X(8796), X(46104)}}, {{A, B, C, X(9306), X(23291)}}, {{A, B, C, X(9513), X(39265)}}, {{A, B, C, X(10159), X(32825)}}, {{A, B, C, X(10513), X(37671)}}, {{A, B, C, X(10603), X(16080)}}, {{A, B, C, X(14387), X(32819)}}, {{A, B, C, X(14484), X(42299)}}, {{A, B, C, X(15164), X(50944)}}, {{A, B, C, X(15165), X(50945)}}, {{A, B, C, X(18841), X(32823)}}, {{A, B, C, X(18842), X(55958)}}, {{A, B, C, X(19222), X(46142)}}, {{A, B, C, X(20563), X(40009)}}, {{A, B, C, X(27354), X(27356)}}, {{A, B, C, X(27376), X(46701)}}, {{A, B, C, X(32000), X(54412)}}, {{A, B, C, X(32820), X(35510)}}, {{A, B, C, X(32826), X(53105)}}, {{A, B, C, X(34285), X(43696)}}, {{A, B, C, X(34393), X(40028)}}, {{A, B, C, X(40799), X(40803)}}, {{A, B, C, X(40810), X(51334)}}, {{A, B, C, X(43678), X(46746)}}, {{A, B, C, X(43711), X(53200)}}, {{A, B, C, X(44133), X(52713)}}, {{A, B, C, X(44134), X(44146)}}
X(55972) = barycentric product X(i)*X(j) for these (i, j): {4, 40824}, {264, 40802}, {2799, 41074}, {14618, 35575}, {18022, 40799}, {40801, 76}, {40803, 44144}, {40823, 44161}
X(55972) = barycentric quotient X(i)/X(j) for these (i, j): {2, 6776}, {4, 7735}, {25, 40825}, {69, 37188}, {92, 4008}, {264, 40814}, {297, 1513}, {343, 42353}, {393, 6620}, {458, 9755}, {525, 47194}, {648, 35278}, {2052, 43976}, {14618, 30735}, {18022, 40822}, {35575, 4558}, {37174, 9752}, {40799, 184}, {40801, 6}, {40802, 3}, {40803, 43718}, {40811, 20794}, {40823, 14575}, {40824, 69}, {41074, 2966}, {43727, 51336}, {52283, 7710}

X(55973) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(4) AND X(94)

Barycentrics    b^2*c^2*(a^6+(b^2-c^2)^2*(b^2+c^2)-a^4*(4*b^2+c^2)-a^2*(4*b^4-9*b^2*c^2+c^4))*(a^6+(b^2-c^2)^2*(b^2+c^2)-a^4*(b^2+4*c^2)-a^2*(b^4-9*b^2*c^2+4*c^4)) : :

X(55973) lies on the Kiepert Hyperbola and on these lines: {2, 44468}, {4, 2854}, {30, 54671}, {94, 47286}, {98, 2696}, {338, 5485}, {671, 3260}, {2394, 35522}, {5466, 41079}, {16080, 44146}, {30735, 43667}, {34289, 54395}, {46105, 53474}

X(55973) = isotomic conjugate of X(41617)
X(55973) = polar conjugate of X(37962)
X(55973) = trilinear pole of line {30739, 523}
X(55973) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 41617}, {48, 37962}, {163, 2780}, {36060, 41618}
X(55973) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 41617}, {115, 2780}, {1249, 37962}, {1560, 41618}
X(55973) = X(i)-cross conjugate of X(j) for these {i, j}: {47097, 264}
X(55973) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(4)}}, {{A, B, C, X(265), X(14982)}}, {{A, B, C, X(290), X(3260)}}, {{A, B, C, X(297), X(7464)}}, {{A, B, C, X(525), X(895)}}, {{A, B, C, X(2987), X(48362)}}, {{A, B, C, X(5505), X(41617)}}, {{A, B, C, X(5523), X(15262)}}, {{A, B, C, X(6344), X(40832)}}, {{A, B, C, X(9227), X(15412)}}, {{A, B, C, X(14364), X(35142)}}, {{A, B, C, X(14618), X(18023)}}, {{A, B, C, X(44427), X(47286)}}
X(55973) = barycentric product X(i)*X(j) for these (i, j): {2696, 850}
X(55973) = barycentric quotient X(i)/X(j) for these (i, j): {2, 41617}, {4, 37962}, {468, 41618}, {523, 2780}, {2696, 110}, {5485, 52496}

X(55974) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(6) AND X(23)

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

X(55974) lies on these lines: {4, 13239}, {6, 525}, {23, 385}, {141, 9210}, {308, 44173}, {647, 35522}, {850, 2492}, {2395, 9462}, {2485, 23285}, {2998, 9178}, {3569, 9030}, {3906, 23287}, {8266, 39201}, {9209, 15271}, {11174, 30474}, {18487, 23878}, {22089, 41328}, {25054, 44373}, {50547, 55121}

X(55974) = reflection of X(i) in X(j) for these {i,j}: {23285, 2485}, {35522, 647}, {669, 22105}, {850, 2492}
X(55974) = perspector of circumconic {{A, B, C, X(83), X(2373)}}
X(55974) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 45096}
X(55974) = X(i)-Dao conjugate of X(j) for these {i, j}: {115, 45096}
X(55974) = X(i)-Ceva conjugate of X(j) for these {i, j}: {11636, 2}
X(55974) = X(i)-complementary conjugate of X(j) for these {i, j}: {1973, 17413}
X(55974) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {1383, 21294}, {11636, 6327}, {35138, 21275}
X(55974) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(23), X(308)}}, {{A, B, C, X(2998), X(26233)}}, {{A, B, C, X(9462), X(19127)}}
X(55974) = barycentric product X(i)*X(j) for these (i, j): {19127, 850}, {26233, 523}
X(55974) = barycentric quotient X(i)/X(j) for these (i, j): {523, 45096}, {19127, 110}, {26233, 99}
X(55974) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {523, 22105, 669}

X(55975) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(6) AND X(75)

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

X(55975) lies on these lines: {1, 1921}, {6, 350}, {56, 10030}, {58, 30940}, {75, 292}, {183, 34445}, {870, 18170}, {2279, 3729}, {2665, 18194}, {5378, 31625}, {16525, 39044}, {20148, 30963}, {20475, 34444}, {21788, 26687}, {37678, 40433}

X(55975) = isotomic conjugate of X(12782)
X(55975) = trilinear pole of line {649, 3766}
X(55975) = X(i)-isoconjugate-of-X(j) for these {i, j}: {31, 12782}, {100, 1912}
X(55975) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 12782}, {8054, 1912}
X(55975) = X(i)-cross conjugate of X(j) for these {i, j}: {12263, 2}
X(55975) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(6)}}, {{A, B, C, X(2), X(17027)}}, {{A, B, C, X(7), X(2998)}}, {{A, B, C, X(75), X(308)}}, {{A, B, C, X(183), X(40417)}}, {{A, B, C, X(290), X(309)}}, {{A, B, C, X(673), X(7033)}}, {{A, B, C, X(903), X(4713)}}, {{A, B, C, X(1268), X(34816)}}, {{A, B, C, X(1909), X(9311)}}, {{A, B, C, X(2481), X(3114)}}, {{A, B, C, X(3112), X(14621)}}, {{A, B, C, X(3223), X(51333)}}, {{A, B, C, X(3228), X(39704)}}, {{A, B, C, X(3551), X(35166)}}, {{A, B, C, X(8033), X(52175)}}, {{A, B, C, X(8053), X(20475)}}, {{A, B, C, X(12263), X(12782)}}, {{A, B, C, X(17028), X(17029)}}, {{A, B, C, X(17030), X(17034)}}, {{A, B, C, X(17033), X(26801)}}, {{A, B, C, X(18166), X(37678)}}, {{A, B, C, X(18170), X(40728)}}, {{A, B, C, X(18194), X(21788)}}, {{A, B, C, X(29433), X(29742)}}, {{A, B, C, X(30598), X(39968)}}, {{A, B, C, X(30712), X(38262)}}, {{A, B, C, X(39746), X(54456)}}, {{A, B, C, X(39914), X(46281)}}
X(55975) = barycentric product X(i)*X(j) for these (i, j): {55940, 75}
X(55975) = barycentric quotient X(i)/X(j) for these (i, j): {2, 12782}, {649, 1912}, {55940, 1}

X(55976) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(3) AND X(4)

Barycentrics    a^2*(a^2-b^2-c^2)*(2*a^6-(b^2-2*c^2)*(b^2-c^2)^2-a^4*(5*b^2+2*c^2)+a^2*(4*b^4+6*b^2*c^2-2*c^4))*(2*a^6+(b^2-c^2)^2*(2*b^2-c^2)-a^4*(2*b^2+5*c^2)+a^2*(-2*b^4+6*b^2*c^2+4*c^4)) : :

X(55976) lies on the Jerabek Hyperbola and on these lines: {4, 3292}, {20, 10293}, {64, 7464}, {68, 16051}, {74, 37480}, {323, 3426}, {631, 5486}, {895, 1092}, {1173, 53860}, {1177, 7556}, {1243, 16428}, {1995, 3527}, {3090, 14457}, {3431, 16836}, {3519, 3546}, {3529, 43695}, {5656, 11744}, {9716, 38323}, {10097, 32320}, {10297, 21400}, {11413, 43719}, {13452, 45187}, {17928, 43908}, {18436, 43720}, {31371, 43844}, {37645, 45088}

X(55976) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(4)}}, {{A, B, C, X(20), X(7464)}}, {{A, B, C, X(24), X(16051)}}, {{A, B, C, X(254), X(15398)}}, {{A, B, C, X(305), X(46259)}}, {{A, B, C, X(376), X(34570)}}, {{A, B, C, X(631), X(1995)}}, {{A, B, C, X(858), X(7556)}}, {{A, B, C, X(1006), X(16428)}}, {{A, B, C, X(1092), X(3292)}}, {{A, B, C, X(1141), X(44156)}}, {{A, B, C, X(1294), X(41894)}}, {{A, B, C, X(2986), X(34386)}}, {{A, B, C, X(3090), X(17928)}}, {{A, B, C, X(3284), X(37480)}}, {{A, B, C, X(3518), X(3546)}}, {{A, B, C, X(3525), X(6642)}}, {{A, B, C, X(3529), X(11413)}}, {{A, B, C, X(5158), X(16836)}}, {{A, B, C, X(5656), X(15262)}}, {{A, B, C, X(5879), X(18849)}}, {{A, B, C, X(5897), X(18847)}}, {{A, B, C, X(7512), X(31099)}}, {{A, B, C, X(10297), X(21844)}}, {{A, B, C, X(10422), X(43537)}}, {{A, B, C, X(11585), X(44879)}}, {{A, B, C, X(12085), X(17538)}}, {{A, B, C, X(15318), X(18019)}}, {{A, B, C, X(18401), X(35510)}}, {{A, B, C, X(18852), X(41890)}}, {{A, B, C, X(18854), X(45301)}}
X(55976) = barycentric product X(i)*X(j) for these (i, j): {3, 54774}
X(55976) = barycentric quotient X(i)/X(j) for these (i, j): {54774, 264}

X(55977) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(3) AND X(6)

Barycentrics    a^2*(a^2+b^2-5*c^2)*(a^2-b^2-c^2)*(a^2-5*b^2+c^2) : :
X(55977) = -3*X[599]+2*X[5486], -6*X[9813]+5*X[11482], -8*X[16511]+9*X[21358]

X(55977) lies on the Jerabek Hyperbola and on these lines: {3, 8681}, {4, 524}, {6, 373}, {54, 32154}, {64, 2393}, {65, 9004}, {66, 40341}, {67, 15533}, {74, 1296}, {141, 17040}, {154, 1177}, {265, 11898}, {290, 35179}, {394, 895}, {511, 3426}, {520, 10097}, {542, 10293}, {575, 43908}, {576, 3527}, {599, 5486}, {879, 9007}, {1173, 53858}, {1351, 3531}, {1352, 45088}, {1503, 35512}, {3431, 5085}, {3564, 4846}, {3630, 16774}, {5050, 44731}, {5102, 14483}, {5210, 9145}, {6144, 43726}, {6391, 11511}, {6413, 19409}, {6414, 19408}, {6467, 34817}, {8538, 38260}, {8547, 20421}, {8675, 35364}, {8705, 11738}, {9003, 51480}, {9019, 16835}, {9023, 17999}, {9051, 10099}, {9813, 11482}, {9924, 34207}, {9925, 40441}, {10510, 17813}, {10541, 14528}, {10765, 46949}, {13623, 39899}, {14924, 47352}, {14984, 34802}, {15066, 52496}, {15453, 47343}, {15531, 40916}, {15534, 38005}, {15740, 53021}, {16511, 21358}, {17430, 43716}, {17810, 52174}, {22334, 45187}, {31884, 43713}, {33878, 46202}, {34382, 34801}, {34383, 54998}, {35259, 41617}, {37142, 37216}, {41614, 43697}, {43718, 52703}, {43719, 52987}

X(55977) = isogonal conjugate of X(4232)
X(55977) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 4232}, {4, 36277}, {19, 1992}, {82, 41585}, {92, 1384}, {112, 14207}, {162, 1499}, {811, 8644}, {897, 15471}, {1474, 42724}, {1707, 52454}, {1783, 4786}, {1897, 30234}, {1973, 11059}, {9126, 36129}, {27088, 36128}, {35266, 36119}
X(55977) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 4232}, {6, 1992}, {125, 1499}, {141, 41585}, {1511, 35266}, {6337, 11059}, {6593, 15471}, {10354, 37855}, {17423, 8644}, {22391, 1384}, {34467, 30234}, {34591, 14207}, {36033, 36277}, {39006, 4786}, {51574, 42724}
X(55977) = X(i)-Ceva conjugate of X(j) for these {i, j}: {5485, 21448}
X(55977) = X(i)-cross conjugate of X(j) for these {i, j}: {10602, 6}
X(55977) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(11284)}}, {{A, B, C, X(3), X(4)}}, {{A, B, C, X(22), X(46517)}}, {{A, B, C, X(23), X(31152)}}, {{A, B, C, X(25), X(40126)}}, {{A, B, C, X(77), X(34916)}}, {{A, B, C, X(78), X(34893)}}, {{A, B, C, X(154), X(2393)}}, {{A, B, C, X(159), X(9924)}}, {{A, B, C, X(182), X(52703)}}, {{A, B, C, X(216), X(53093)}}, {{A, B, C, X(287), X(5651)}}, {{A, B, C, X(305), X(523)}}, {{A, B, C, X(373), X(42286)}}, {{A, B, C, X(394), X(520)}}, {{A, B, C, X(511), X(9007)}}, {{A, B, C, X(518), X(9051)}}, {{A, B, C, X(521), X(9004)}}, {{A, B, C, X(525), X(9027)}}, {{A, B, C, X(575), X(36751)}}, {{A, B, C, X(576), X(36748)}}, {{A, B, C, X(577), X(11477)}}, {{A, B, C, X(599), X(8542)}}, {{A, B, C, X(684), X(45809)}}, {{A, B, C, X(1238), X(9925)}}, {{A, B, C, X(1350), X(3284)}}, {{A, B, C, X(1494), X(40801)}}, {{A, B, C, X(1995), X(30739)}}, {{A, B, C, X(2351), X(33585)}}, {{A, B, C, X(2854), X(9033)}}, {{A, B, C, X(3053), X(11511)}}, {{A, B, C, X(3504), X(9225)}}, {{A, B, C, X(3525), X(11484)}}, {{A, B, C, X(3564), X(8675)}}, {{A, B, C, X(3613), X(40032)}}, {{A, B, C, X(3718), X(7241)}}, {{A, B, C, X(3917), X(30489)}}, {{A, B, C, X(3933), X(46154)}}, {{A, B, C, X(4492), X(7182)}}, {{A, B, C, X(5085), X(5158)}}, {{A, B, C, X(5181), X(51253)}}, {{A, B, C, X(6090), X(14919)}}, {{A, B, C, X(6464), X(34386)}}, {{A, B, C, X(7716), X(19459)}}, {{A, B, C, X(8585), X(30786)}}, {{A, B, C, X(9000), X(9028)}}, {{A, B, C, X(9001), X(34381)}}, {{A, B, C, X(9003), X(14984)}}, {{A, B, C, X(9026), X(9031)}}, {{A, B, C, X(9139), X(54172)}}, {{A, B, C, X(9186), X(43754)}}, {{A, B, C, X(9289), X(25322)}}, {{A, B, C, X(9307), X(34818)}}, {{A, B, C, X(11180), X(17974)}}, {{A, B, C, X(11898), X(52437)}}, {{A, B, C, X(13481), X(20563)}}, {{A, B, C, X(14489), X(36889)}}, {{A, B, C, X(15069), X(15394)}}, {{A, B, C, X(15406), X(38951)}}, {{A, B, C, X(15533), X(22151)}}, {{A, B, C, X(15905), X(53097)}}, {{A, B, C, X(17702), X(47343)}}, {{A, B, C, X(17810), X(32621)}}, {{A, B, C, X(17811), X(53021)}}, {{A, B, C, X(17813), X(19153)}}, {{A, B, C, X(17968), X(17979)}}, {{A, B, C, X(19132), X(34777)}}, {{A, B, C, X(20806), X(40341)}}, {{A, B, C, X(21448), X(32133)}}, {{A, B, C, X(22052), X(53858)}}, {{A, B, C, X(31637), X(55919)}}, {{A, B, C, X(32740), X(40319)}}, {{A, B, C, X(34285), X(41489)}}, {{A, B, C, X(35510), X(41890)}}, {{A, B, C, X(47353), X(50433)}}, {{A, B, C, X(52013), X(52392)}}, {{A, B, C, X(54032), X(54132)}}
X(55977) = barycentric product X(i)*X(j) for these (i, j): {3, 5485}, {305, 39238}, {1296, 525}, {10097, 2418}, {14977, 2434}, {17979, 5503}, {21448, 69}, {32133, 41614}, {32648, 45807}, {35179, 647}, {37216, 656}, {55923, 63}
X(55977) = barycentric quotient X(i)/X(j) for these (i, j): {3, 1992}, {6, 4232}, {39, 41585}, {48, 36277}, {69, 11059}, {72, 42724}, {184, 1384}, {187, 15471}, {647, 1499}, {656, 14207}, {895, 52141}, {1296, 648}, {1459, 4786}, {2434, 4235}, {3049, 8644}, {3284, 35266}, {3292, 27088}, {5485, 264}, {8770, 52454}, {10097, 2408}, {17979, 22329}, {20975, 6791}, {21448, 4}, {22383, 30234}, {35179, 6331}, {36212, 51438}, {37216, 811}, {38532, 41370}, {39238, 25}, {40349, 53778}, {52477, 37778}, {55923, 92}
X(55977) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5485, 34165, 52477}, {6090, 32127, 6}

X(55978) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(3) AND X(54)

Barycentrics    a^2*(a^2-b^2-c^2)*(a^6+a^4*(2*b^2-c^2)+(b^2-c^2)^2*(4*b^2+c^2)-a^2*(7*b^4+c^4))*(a^6-a^4*(b^2-2*c^2)+(b^2-c^2)^2*(b^2+4*c^2)-a^2*(b^4+7*c^4)) : :

X(55978) lies on the Jerabek Hyperbola and on these lines: {4, 41586}, {6, 11459}, {54, 3292}, {64, 12082}, {895, 5562}, {1173, 45187}, {1177, 14094}, {3426, 15107}, {3519, 12362}, {3527, 5889}, {3532, 10323}, {5907, 32599}, {6823, 14861}, {7395, 11422}, {7509, 14528}, {8718, 34437}, {8795, 44146}, {10097, 17434}, {10293, 15054}, {11414, 43719}, {12024, 13622}, {12358, 43704}, {16835, 37946}, {34483, 44076}, {34664, 41724}

X(55978) = isogonal conjugate of X(37458)
X(55978) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(4)}}, {{A, B, C, X(5), X(7550)}}, {{A, B, C, X(20), X(12082)}}, {{A, B, C, X(76), X(11459)}}, {{A, B, C, X(96), X(15398)}}, {{A, B, C, X(97), X(671)}}, {{A, B, C, X(394), X(5485)}}, {{A, B, C, X(550), X(37946)}}, {{A, B, C, X(598), X(31626)}}, {{A, B, C, X(2351), X(8753)}}, {{A, B, C, X(2373), X(40448)}}, {{A, B, C, X(2996), X(43756)}}, {{A, B, C, X(3090), X(7395)}}, {{A, B, C, X(3091), X(7509)}}, {{A, B, C, X(3146), X(10323)}}, {{A, B, C, X(3292), X(5562)}}, {{A, B, C, X(3470), X(12358)}}, {{A, B, C, X(3518), X(12362)}}, {{A, B, C, X(3525), X(11479)}}, {{A, B, C, X(3529), X(11414)}}, {{A, B, C, X(5641), X(50464)}}, {{A, B, C, X(6823), X(14865)}}, {{A, B, C, X(7399), X(35500)}}, {{A, B, C, X(7400), X(35502)}}, {{A, B, C, X(8718), X(38946)}}, {{A, B, C, X(8798), X(11793)}}, {{A, B, C, X(14789), X(49671)}}, {{A, B, C, X(14979), X(16934)}}, {{A, B, C, X(17538), X(39568)}}, {{A, B, C, X(18401), X(41890)}}, {{A, B, C, X(38933), X(50188)}}
X(55978) = barycentric quotient X(i)/X(j) for these (i, j): {6, 37458}

X(55979) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(3) AND X(63)

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

X(55979) lies on these lines: {3, 22067}, {27, 39704}, {48, 1797}, {57, 89}, {58, 2163}, {63, 22356}, {84, 2320}, {103, 4588}, {967, 28658}, {2221, 28607}, {3423, 41341}, {4604, 17277}, {9037, 23859}, {13478, 30588}, {17191, 17274}, {22129, 23073}, {30589, 31019}

X(55979) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 45}, {19, 3679}, {25, 4671}, {33, 5219}, {34, 4873}, {92, 2177}, {108, 4944}, {162, 4931}, {278, 3711}, {281, 2099}, {318, 1405}, {393, 3940}, {648, 4770}, {653, 4814}, {1474, 4125}, {1783, 4777}, {1824, 5235}, {1826, 4653}, {1880, 4720}, {1897, 4893}, {2489, 55245}, {4273, 41013}, {4752, 7649}, {4767, 6591}, {4775, 6335}, {4791, 8750}, {4792, 8756}, {4908, 36125}, {4933, 36128}, {14571, 36921}
X(55979) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 3679}, {125, 4931}, {6505, 4671}, {11517, 4873}, {22391, 2177}, {26932, 4791}, {34467, 4893}, {36033, 45}, {38983, 4944}, {39006, 4777}, {51574, 4125}, {55066, 4770}
X(55979) = X(i)-Ceva conjugate of X(j) for these {i, j}: {39704, 2163}
X(55979) = X(i)-cross conjugate of X(j) for these {i, j}: {22357, 3}
X(55979) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(27)}}, {{A, B, C, X(48), X(1404)}}, {{A, B, C, X(77), X(1443)}}, {{A, B, C, X(78), X(17012)}}, {{A, B, C, X(223), X(40257)}}, {{A, B, C, X(348), X(21907)}}, {{A, B, C, X(394), X(42028)}}, {{A, B, C, X(1812), X(37685)}}, {{A, B, C, X(1814), X(43697)}}, {{A, B, C, X(2982), X(13472)}}, {{A, B, C, X(6336), X(44759)}}, {{A, B, C, X(14919), X(41081)}}, {{A, B, C, X(22357), X(22372)}}, {{A, B, C, X(22370), X(23092)}}
X(55979) = barycentric product X(i)*X(j) for these (i, j): {3, 39704}, {63, 89}, {222, 30608}, {1331, 52620}, {1444, 53114}, {1459, 4597}, {1790, 30588}, {2163, 69}, {2320, 77}, {2364, 348}, {3942, 5385}, {4025, 4588}, {4592, 55246}, {4604, 905}, {15413, 34073}, {17206, 28658}, {20569, 48}, {22356, 40833}, {28607, 304}
X(55979) = barycentric quotient X(i)/X(j) for these (i, j): {3, 3679}, {48, 45}, {63, 4671}, {72, 4125}, {89, 92}, {184, 2177}, {212, 3711}, {219, 4873}, {222, 5219}, {255, 3940}, {283, 4720}, {603, 2099}, {647, 4931}, {652, 4944}, {810, 4770}, {905, 4791}, {906, 4752}, {1331, 4767}, {1437, 4653}, {1459, 4777}, {1790, 5235}, {1795, 36921}, {1797, 4945}, {1946, 4814}, {2163, 4}, {2320, 318}, {2364, 281}, {3292, 4933}, {3916, 4717}, {3942, 4957}, {4091, 49280}, {4588, 1897}, {4592, 55245}, {4604, 6335}, {7193, 4693}, {7254, 47683}, {20569, 1969}, {22093, 4774}, {22128, 27757}, {22350, 51362}, {22356, 4908}, {22357, 16590}, {22383, 4893}, {22384, 4800}, {23073, 36911}, {23206, 17461}, {28607, 19}, {28658, 1826}, {30608, 7017}, {34073, 1783}, {36058, 4792}, {39704, 264}, {52407, 4867}, {52411, 1405}, {52620, 46107}, {53114, 41013}, {55246, 24006}
X(55979) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 23082, 22372}

X(55980) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(3) AND X(68)

Barycentrics    a^2*(a^2-b^2-c^2)*(2*a^6+(b^2-c^2)^2*(2*b^2-c^2)-a^4*(2*b^2+5*c^2)-2*a^2*(b^4-2*c^4))*(2*a^6-(b^2-2*c^2)*(b^2-c^2)^2-a^4*(5*b^2+2*c^2)+a^2*(4*b^4-2*c^4)) : :

X(55980) lies on the Jerabek Hyperbola and on these lines: {4, 11422}, {6, 12106}, {64, 12161}, {67, 18281}, {68, 3292}, {74, 11004}, {140, 47552}, {265, 5654}, {575, 5486}, {576, 1177}, {895, 1147}, {1173, 14002}, {1493, 6145}, {3090, 45736}, {3431, 9730}, {3519, 6640}, {3521, 19467}, {3525, 13418}, {3527, 7545}, {3532, 11250}, {5889, 11270}, {6776, 45835}, {9716, 11564}, {10097, 30451}, {10116, 31857}, {10564, 20421}, {11443, 43586}, {11559, 19456}, {13452, 53860}, {14457, 37505}, {14528, 37814}, {15073, 43697}, {15077, 41597}, {16266, 32599}, {19151, 32046}, {21400, 44076}, {32533, 43844}, {33565, 37645}, {34148, 48362}, {34351, 47280}, {34783, 43720}, {37497, 43713}, {43908, 45735}

X(55980) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(12106)}}, {{A, B, C, X(3), X(4)}}, {{A, B, C, X(23), X(18281)}}, {{A, B, C, X(140), X(14002)}}, {{A, B, C, X(576), X(14961)}}, {{A, B, C, X(631), X(7545)}}, {{A, B, C, X(1147), X(3292)}}, {{A, B, C, X(1166), X(32132)}}, {{A, B, C, X(3090), X(45735)}}, {{A, B, C, X(3091), X(37814)}}, {{A, B, C, X(3146), X(11250)}}, {{A, B, C, X(3284), X(13352)}}, {{A, B, C, X(3471), X(11004)}}, {{A, B, C, X(3518), X(6640)}}, {{A, B, C, X(3525), X(13621)}}, {{A, B, C, X(5158), X(9730)}}, {{A, B, C, X(5654), X(38936)}}, {{A, B, C, X(7555), X(31857)}}, {{A, B, C, X(7772), X(37511)}}, {{A, B, C, X(10255), X(44879)}}, {{A, B, C, X(11422), X(19210)}}, {{A, B, C, X(12086), X(34350)}}, {{A, B, C, X(15860), X(37470)}}, {{A, B, C, X(18565), X(35475)}}, {{A, B, C, X(20251), X(42313)}}
X(55980) = barycentric product X(i)*X(j) for these (i, j): {3, 54913}
X(55980) = barycentric quotient X(i)/X(j) for these (i, j): {54913, 264}

X(55981) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(3) AND X(74)

Barycentrics    a^2*(a^2-b^2-c^2)*(5*a^6+(b^2-c^2)^2*(2*b^2+5*c^2)-a^4*(8*b^2+5*c^2)+a^2*(b^4+12*b^2*c^2-5*c^4))*(5*a^6+(b^2-c^2)^2*(5*b^2+2*c^2)-a^4*(5*b^2+8*c^2)+a^2*(-5*b^4+12*b^2*c^2+c^4)) : :

X(55981) lies on the Jerabek Hyperbola and on these lines: {4, 5642}, {6, 15035}, {64, 14094}, {68, 20397}, {69, 38727}, {74, 3292}, {110, 3426}, {265, 5159}, {895, 51394}, {1177, 43574}, {1511, 3531}, {1636, 10097}, {3431, 15036}, {3527, 15020}, {4846, 38726}, {10293, 40112}, {14861, 44247}, {15021, 44763}, {15054, 43719}, {22115, 43720}

X(55981) = isogonal conjugate of X(37984)
X(55981) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 37984}, {19, 44569}
X(55981) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 37984}, {6, 44569}
X(55981) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(3), X(4)}}, {{A, B, C, X(186), X(5159)}}, {{A, B, C, X(249), X(14919)}}, {{A, B, C, X(1636), X(3292)}}, {{A, B, C, X(2693), X(34570)}}, {{A, B, C, X(3563), X(10419)}}, {{A, B, C, X(5961), X(20397)}}, {{A, B, C, X(13530), X(46087)}}, {{A, B, C, X(14865), X(44247)}}, {{A, B, C, X(34210), X(52437)}}, {{A, B, C, X(38727), X(52153)}}
X(55981) = barycentric quotient X(i)/X(j) for these (i, j): {3, 44569}, {6, 37984}

X(55982) = KIMBERLING-PAVLOV X(3)-CONJUGATE OF X(3) AND X(97)

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

X(55982) lies on these lines: {2, 36430}, {3, 5640}, {4, 46412}, {23, 5481}, {97, 3284}, {216, 14919}, {276, 46106}, {394, 52703}, {549, 18317}, {632, 14938}, {1217, 10303}, {1297, 7496}, {3090, 22270}, {3628, 22268}, {5158, 11004}, {17974, 54375}, {40801, 40916}

X(55982) = isogonal conjugate of X(6749)
X(55982) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 6749}, {19, 549}, {92, 44109}, {1973, 44148}
X(55982) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 6749}, {6, 549}, {6337, 44148}, {22391, 44109}
X(55982) = X(i)-Ceva conjugate of X(j) for these {i, j}: {55958, 14483}
X(55982) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3)}}, {{A, B, C, X(6), X(52703)}}, {{A, B, C, X(54), X(16080)}}, {{A, B, C, X(74), X(43530)}}, {{A, B, C, X(83), X(55978)}}, {{A, B, C, X(94), X(36952)}}, {{A, B, C, X(111), X(43718)}}, {{A, B, C, X(216), X(3284)}}, {{A, B, C, X(248), X(39389)}}, {{A, B, C, X(251), X(52153)}}, {{A, B, C, X(275), X(16835)}}, {{A, B, C, X(343), X(10095)}}, {{A, B, C, X(441), X(7496)}}, {{A, B, C, X(459), X(13472)}}, {{A, B, C, X(895), X(5640)}}, {{A, B, C, X(1173), X(2052)}}, {{A, B, C, X(1176), X(15107)}}, {{A, B, C, X(1795), X(40434)}}, {{A, B, C, X(2351), X(3108)}}, {{A, B, C, X(2981), X(36297)}}, {{A, B, C, X(2987), X(43697)}}, {{A, B, C, X(3090), X(37068)}}, {{A, B, C, X(3521), X(13582)}}, {{A, B, C, X(5158), X(18479)}}, {{A, B, C, X(6151), X(36296)}}, {{A, B, C, X(6504), X(31371)}}, {{A, B, C, X(7578), X(34802)}}, {{A, B, C, X(8796), X(52518)}}, {{A, B, C, X(11004), X(37638)}}, {{A, B, C, X(11538), X(17505)}}, {{A, B, C, X(15024), X(37874)}}, {{A, B, C, X(17572), X(21482)}}, {{A, B, C, X(25909), X(37312)}}, {{A, B, C, X(26235), X(36212)}}, {{A, B, C, X(37188), X(40916)}}
X(55982) = barycentric product X(i)*X(j) for these (i, j): {3, 55958}, {14483, 69}
X(55982) = barycentric quotient X(i)/X(j) for these (i, j): {3, 549}, {6, 6749}, {69, 44148}, {184, 44109}, {14483, 4}, {55958, 264}

X(55983) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(8) AND X(75)

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

X(55983) lies on these lines: {8, 40023}, {75, 144}, {76, 4301}, {85, 3160}, {331, 5342}, {334, 18743}, {350, 40014}, {767, 26716}, {1699, 18025}, {2481, 16834}, {24603, 30854}, {30806, 40029}

X(55983) = isotomic conjugate of X(5223)
X(55983) = trilinear pole of line {693, 4765}
X(55983) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 42316}, {31, 5223}, {32, 29616}, {10004, 14827}
X(55983) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 5223}, {9, 42316}, {6376, 29616}
X(55983) = X(i)-cross conjugate of X(j) for these {i, j}: {5542, 2}, {54668, 55937}
X(55983) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(4), X(5819)}}, {{A, B, C, X(7), X(144)}}, {{A, B, C, X(8), X(86)}}, {{A, B, C, X(75), X(76)}}, {{A, B, C, X(92), X(693)}}, {{A, B, C, X(189), X(21453)}}, {{A, B, C, X(269), X(4301)}}, {{A, B, C, X(309), X(42311)}}, {{A, B, C, X(350), X(18743)}}, {{A, B, C, X(479), X(45100)}}, {{A, B, C, X(513), X(2186)}}, {{A, B, C, X(903), X(4454)}}, {{A, B, C, X(3226), X(39702)}}, {{A, B, C, X(3598), X(43951)}}, {{A, B, C, X(3912), X(16834)}}, {{A, B, C, X(4384), X(24603)}}, {{A, B, C, X(5223), X(5542)}}, {{A, B, C, X(10980), X(21060)}}, {{A, B, C, X(18810), X(18816)}}, {{A, B, C, X(27475), X(27484)}}, {{A, B, C, X(28650), X(32015)}}, {{A, B, C, X(28809), X(30854)}}, {{A, B, C, X(30598), X(32008)}}, {{A, B, C, X(30712), X(36605)}}, {{A, B, C, X(30806), X(35175)}}, {{A, B, C, X(35160), X(39707)}}, {{A, B, C, X(39741), X(42304)}}, {{A, B, C, X(44733), X(54128)}}
X(55983) = barycentric product X(i)*X(j) for these (i, j): {274, 54668}, {26716, 40495}, {32040, 693}, {42317, 6063}, {55937, 75}
X(55983) = barycentric quotient X(i)/X(j) for these (i, j): {1, 42316}, {2, 5223}, {75, 29616}, {1088, 10004}, {26716, 692}, {32040, 100}, {36136, 32642}, {42317, 55}, {54668, 37}, {55937, 1}

X(55984) = KIMBERLING-PAVLOV X(2)-CONJUGATE OF X(8) AND X(92)

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

X(55984) lies on these lines: {2, 30806}, {8, 10394}, {75, 1121}, {85, 30379}, {189, 4359}, {1311, 14074}, {3872, 14942}, {4384, 34234}, {4997, 30854}, {10405, 20880}, {16284, 17335}, {18031, 20925}, {30807, 50442}

X(55983) = isotomic conjugate of X(8545)
X(55984) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 37541}, {31, 8545}, {1397, 50107}, {1415, 14077}, {1996, 2175}, {14827, 47386}, {30181, 32739}
X(55984) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 8545}, {9, 37541}, {1146, 14077}, {40593, 1996}, {40619, 30181}, {40624, 47787}
X(55984) = X(i)-cross conjugate of X(j) for these {i, j}: {5231, 75}
X(55984) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(9), X(514)}}, {{A, B, C, X(21), X(1847)}}, {{A, B, C, X(75), X(4391)}}, {{A, B, C, X(274), X(318)}}, {{A, B, C, X(522), X(36871)}}, {{A, B, C, X(673), X(30513)}}, {{A, B, C, X(1320), X(27475)}}, {{A, B, C, X(1422), X(12711)}}, {{A, B, C, X(2481), X(18810)}}, {{A, B, C, X(3680), X(17758)}}, {{A, B, C, X(3872), X(3912)}}, {{A, B, C, X(4384), X(6735)}}, {{A, B, C, X(4723), X(30854)}}, {{A, B, C, X(5081), X(20924)}}, {{A, B, C, X(5665), X(55090)}}, {{A, B, C, X(16284), X(20880)}}, {{A, B, C, X(20569), X(36796)}}, {{A, B, C, X(23062), X(44559)}}, {{A, B, C, X(40505), X(47915)}}, {{A, B, C, X(42015), X(43971)}}, {{A, B, C, X(44733), X(55924)}}
X(55984) = barycentric product X(i)*X(j) for these (i, j): {14074, 35519}, {34919, 75}
X(55984) = barycentric quotient X(i)/X(j) for these (i, j): {1, 37541}, {2, 8545}, {85, 1996}, {312, 50107}, {522, 14077}, {693, 30181}, {1088, 47386}, {1121, 46644}, {4391, 47787}, {5231, 15346}, {14074, 109}, {34919, 1}

X(55985) = KP2(X(1)) OF X(2) AND X(4)

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

X(55985) lies on these lines: {9, 52381}, {21, 1060}, {36, 78}, {57, 52351}, {63, 15066}, {280, 4190}, {345, 3218}, {348, 3219}, {1019, 1726}, {1708, 6513}, {5905, 28753}

X(55985) = trilinear pole of line {7629, 50350}
X(55985) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 1479}, {19, 1062}, {37, 5358}, {1172, 54360}, {1400, 17584}, {2160, 4354}, {2299, 18588}
X(55985) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 1062}, {9, 1479}, {226, 18588}, {40582, 17584}, {40589, 5358}
X(55985) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5904)}}, {{A, B, C, X(2), X(21)}}, {{A, B, C, X(4), X(1708)}}, {{A, B, C, X(9), X(3219)}}, {{A, B, C, X(19), X(30651)}}, {{A, B, C, X(27), X(37301)}}, {{A, B, C, X(36), X(57)}}, {{A, B, C, X(43), X(9395)}}, {{A, B, C, X(81), X(3296)}}, {{A, B, C, X(85), X(2167)}}, {{A, B, C, X(88), X(42467)}}, {{A, B, C, X(92), X(4564)}}, {{A, B, C, X(97), X(7183)}}, {{A, B, C, X(104), X(15474)}}, {{A, B, C, X(189), X(2990)}}, {{A, B, C, X(191), X(1698)}}, {{A, B, C, X(275), X(1275)}}, {{A, B, C, X(292), X(2156)}}, {{A, B, C, X(312), X(2349)}}, {{A, B, C, X(333), X(15066)}}, {{A, B, C, X(337), X(18018)}}, {{A, B, C, X(404), X(26830)}}, {{A, B, C, X(443), X(27174)}}, {{A, B, C, X(588), X(6204)}}, {{A, B, C, X(589), X(6203)}}, {{A, B, C, X(758), X(43682)}}, {{A, B, C, X(1020), X(1726)}}, {{A, B, C, X(1060), X(1214)}}, {{A, B, C, X(1445), X(9965)}}, {{A, B, C, X(1759), X(16549)}}, {{A, B, C, X(1817), X(4190)}}, {{A, B, C, X(1952), X(5392)}}, {{A, B, C, X(2184), X(18359)}}, {{A, B, C, X(2994), X(6601)}}, {{A, B, C, X(3719), X(14919)}}, {{A, B, C, X(3868), X(46885)}}, {{A, B, C, X(3873), X(18206)}}, {{A, B, C, X(3928), X(27003)}}, {{A, B, C, X(3929), X(27065)}}, {{A, B, C, X(6504), X(34401)}}, {{A, B, C, X(6757), X(16577)}}, {{A, B, C, X(7108), X(34289)}}, {{A, B, C, X(8817), X(43363)}}, {{A, B, C, X(14953), X(35977)}}, {{A, B, C, X(24624), X(39947)}}, {{A, B, C, X(25417), X(39273)}}, {{A, B, C, X(28753), X(40571)}}, {{A, B, C, X(30701), X(40406)}}, {{A, B, C, X(31900), X(37312)}}
X(55985) = barycentric product X(i)*X(j) for these (i, j): {1063, 69}, {7163, 75}
X(55985) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1479}, {3, 1062}, {21, 17584}, {35, 4354}, {58, 5358}, {73, 54360}, {1060, 18531}, {1063, 4}, {1214, 18588}, {7163, 1}, {18532, 1061}

X(55986) = KP2(X(1)) OF X(2) AND X(9)

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

X(55986) lies on these lines: {78, 5223}, {144, 348}, {280, 3522}, {329, 52381}, {345, 29616}, {910, 10405}, {3177, 17496}, {3207, 36101}, {3219, 41081}, {3730, 4091}, {4209, 41321}, {5744, 52351}, {6350, 52500}, {14953, 31623}

X(55986) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 1699}, {56, 23058}
X(55986) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 23058}, {9, 1699}
X(55986) = X(i)-cross conjugate of X(j) for these {i, j}: {4130, 100}
X(55986) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5223)}}, {{A, B, C, X(2), X(21)}}, {{A, B, C, X(3), X(1262)}}, {{A, B, C, X(8), X(4564)}}, {{A, B, C, X(9), X(144)}}, {{A, B, C, X(57), X(7987)}}, {{A, B, C, X(76), X(5385)}}, {{A, B, C, X(81), X(7091)}}, {{A, B, C, X(84), X(1170)}}, {{A, B, C, X(85), X(2320)}}, {{A, B, C, X(89), X(1434)}}, {{A, B, C, X(92), X(27789)}}, {{A, B, C, X(101), X(3730)}}, {{A, B, C, X(104), X(279)}}, {{A, B, C, X(189), X(2167)}}, {{A, B, C, X(220), X(51418)}}, {{A, B, C, X(277), X(15446)}}, {{A, B, C, X(329), X(3219)}}, {{A, B, C, X(330), X(2975)}}, {{A, B, C, X(672), X(2053)}}, {{A, B, C, X(910), X(3207)}}, {{A, B, C, X(932), X(3177)}}, {{A, B, C, X(957), X(7096)}}, {{A, B, C, X(959), X(3497)}}, {{A, B, C, X(1121), X(1392)}}, {{A, B, C, X(1219), X(40403)}}, {{A, B, C, X(1255), X(2184)}}, {{A, B, C, X(1320), X(36605)}}, {{A, B, C, X(1376), X(4640)}}, {{A, B, C, X(1476), X(39273)}}, {{A, B, C, X(1809), X(7183)}}, {{A, B, C, X(1817), X(3522)}}, {{A, B, C, X(2217), X(42290)}}, {{A, B, C, X(2346), X(42483)}}, {{A, B, C, X(2349), X(50442)}}, {{A, B, C, X(2359), X(41894)}}, {{A, B, C, X(2371), X(10482)}}, {{A, B, C, X(2991), X(6553)}}, {{A, B, C, X(3218), X(5744)}}, {{A, B, C, X(4184), X(4209)}}, {{A, B, C, X(4188), X(35935)}}, {{A, B, C, X(4189), X(16054)}}, {{A, B, C, X(4225), X(37416)}}, {{A, B, C, X(4567), X(30701)}}, {{A, B, C, X(5553), X(34529)}}, {{A, B, C, X(6350), X(37798)}}, {{A, B, C, X(6904), X(27174)}}, {{A, B, C, X(7132), X(9309)}}, {{A, B, C, X(11115), X(11343)}}, {{A, B, C, X(16053), X(16865)}}, {{A, B, C, X(17521), X(37280)}}, {{A, B, C, X(19308), X(35915)}}, {{A, B, C, X(27818), X(37131)}}, {{A, B, C, X(30711), X(40399)}}, {{A, B, C, X(31015), X(36017)}}, {{A, B, C, X(34056), X(41790)}}, {{A, B, C, X(39749), X(40436)}}, {{A, B, C, X(42467), X(44794)}}
X(55986) = barycentric quotient X(i)/X(j) for these (i, j): {1, 1699}, {9, 23058}, {19605, 24856}

X(55987) = KP2(X(1)) OF X(2) AND X(21)

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

X(55987) lies on these lines: {2, 7011}, {3, 280}, {9, 7125}, {21, 40396}, {63, 2324}, {78, 947}, {92, 11349}, {144, 30679}, {189, 198}, {329, 348}, {345, 5744}, {908, 52381}, {1214, 36100}, {1817, 31623}, {6350, 34277}, {6909, 36984}, {13138, 40945}, {16440, 46422}, {16441, 46421}, {21482, 41514}

X(55987) = trilinear pole of line {1734, 21173}
X(55987) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 2262}, {4, 22063}, {6, 946}, {7, 40957}, {19, 17102}, {56, 20262}, {84, 40943}, {222, 1856}, {278, 40945}, {604, 23528}, {7129, 52097}
X(55987) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 20262}, {3, 2262}, {6, 17102}, {9, 946}, {3161, 23528}, {36033, 22063}
X(55987) = X(i)-cross conjugate of X(j) for these {i, j}: {3239, 100}, {4091, 651}, {10397, 13138}, {12675, 7}
X(55987) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(189)}}, {{A, B, C, X(2), X(21)}}, {{A, B, C, X(3), X(1817)}}, {{A, B, C, X(9), X(329)}}, {{A, B, C, X(27), X(1170)}}, {{A, B, C, X(57), X(104)}}, {{A, B, C, X(81), X(1476)}}, {{A, B, C, X(92), X(1255)}}, {{A, B, C, X(95), X(1444)}}, {{A, B, C, X(100), X(4619)}}, {{A, B, C, X(144), X(3305)}}, {{A, B, C, X(198), X(54322)}}, {{A, B, C, X(223), X(18283)}}, {{A, B, C, X(278), X(44178)}}, {{A, B, C, X(333), X(4564)}}, {{A, B, C, X(394), X(1809)}}, {{A, B, C, X(404), X(27174)}}, {{A, B, C, X(908), X(3219)}}, {{A, B, C, X(911), X(34429)}}, {{A, B, C, X(936), X(31424)}}, {{A, B, C, X(943), X(2184)}}, {{A, B, C, X(961), X(967)}}, {{A, B, C, X(963), X(8828)}}, {{A, B, C, X(971), X(31658)}}, {{A, B, C, X(1000), X(34546)}}, {{A, B, C, X(1029), X(55924)}}, {{A, B, C, X(1105), X(1796)}}, {{A, B, C, X(1214), X(24018)}}, {{A, B, C, X(1252), X(1261)}}, {{A, B, C, X(1262), X(1790)}}, {{A, B, C, X(1320), X(2994)}}, {{A, B, C, X(1396), X(2224)}}, {{A, B, C, X(1931), X(11688)}}, {{A, B, C, X(2185), X(40420)}}, {{A, B, C, X(2335), X(7097)}}, {{A, B, C, X(2338), X(4183)}}, {{A, B, C, X(2349), X(40434)}}, {{A, B, C, X(2359), X(41890)}}, {{A, B, C, X(2982), X(13478)}}, {{A, B, C, X(2991), X(39694)}}, {{A, B, C, X(3417), X(7130)}}, {{A, B, C, X(3497), X(43071)}}, {{A, B, C, X(3929), X(5748)}}, {{A, B, C, X(4184), X(11349)}}, {{A, B, C, X(4233), X(14021)}}, {{A, B, C, X(4567), X(32017)}}, {{A, B, C, X(4640), X(43946)}}, {{A, B, C, X(5044), X(31445)}}, {{A, B, C, X(5481), X(36057)}}, {{A, B, C, X(5732), X(21153)}}, {{A, B, C, X(6557), X(45393)}}, {{A, B, C, X(8056), X(15446)}}, {{A, B, C, X(10397), X(40945)}}, {{A, B, C, X(10405), X(27789)}}, {{A, B, C, X(11350), X(37402)}}, {{A, B, C, X(13388), X(46421)}}, {{A, B, C, X(13389), X(46422)}}, {{A, B, C, X(13577), X(43736)}}, {{A, B, C, X(13588), X(21511)}}, {{A, B, C, X(13614), X(21482)}}, {{A, B, C, X(15179), X(39948)}}, {{A, B, C, X(15474), X(43760)}}, {{A, B, C, X(16452), X(27651)}}, {{A, B, C, X(17781), X(27065)}}, {{A, B, C, X(30710), X(40403)}}, {{A, B, C, X(32008), X(40444)}}, {{A, B, C, X(32625), X(34867)}}, {{A, B, C, X(35981), X(36016)}}
X(55987) = barycentric product X(i)*X(j) for these (i, j): {1, 40417}, {75, 947}, {40396, 69}
X(55987) = barycentric quotient X(i)/X(j) for these (i, j): {1, 946}, {3, 17102}, {6, 2262}, {8, 23528}, {9, 20262}, {33, 1856}, {41, 40957}, {48, 22063}, {198, 40943}, {212, 40945}, {947, 1}, {7078, 52097}, {40396, 4}, {40417, 75}

X(55988) = KP2(X(1)) OF X(2) AND X(56)

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

X(55988) lies on these lines: {2, 7225}, {8, 748}, {29, 5101}, {85, 27064}, {189, 26685}, {257, 3305}, {312, 4361}, {333, 17279}, {614, 4518}, {3772, 4997}, {6557, 37759}, {17338, 40435}, {18359, 26688}

X(55988) = trilinear pole of line {4808, 522}
X(55988) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3976}
X(55988) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 3976}
X(55988) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}}, {{A, B, C, X(9), X(27064)}}, {{A, B, C, X(27), X(39703)}}, {{A, B, C, X(56), X(4383)}}, {{A, B, C, X(57), X(1016)}}, {{A, B, C, X(80), X(40012)}}, {{A, B, C, X(81), X(37679)}}, {{A, B, C, X(83), X(25430)}}, {{A, B, C, X(226), X(32019)}}, {{A, B, C, X(239), X(614)}}, {{A, B, C, X(279), X(42360)}}, {{A, B, C, X(321), X(5101)}}, {{A, B, C, X(329), X(26685)}}, {{A, B, C, X(673), X(39694)}}, {{A, B, C, X(748), X(1255)}}, {{A, B, C, X(894), X(3305)}}, {{A, B, C, X(992), X(2277)}}, {{A, B, C, X(1722), X(1999)}}, {{A, B, C, X(1751), X(32012)}}, {{A, B, C, X(2006), X(34523)}}, {{A, B, C, X(2051), X(36954)}}, {{A, B, C, X(2985), X(8056)}}, {{A, B, C, X(3218), X(26688)}}, {{A, B, C, X(3772), X(4358)}}, {{A, B, C, X(3911), X(27130)}}, {{A, B, C, X(4057), X(32911)}}, {{A, B, C, X(4076), X(30568)}}, {{A, B, C, X(5249), X(17338)}}, {{A, B, C, X(13478), X(36805)}}, {{A, B, C, X(17353), X(27184)}}, {{A, B, C, X(18228), X(26065)}}, {{A, B, C, X(18743), X(37759)}}, {{A, B, C, X(21454), X(35577)}}, {{A, B, C, X(26047), X(29616)}}, {{A, B, C, X(26223), X(27065)}}, {{A, B, C, X(26745), X(46638)}}, {{A, B, C, X(30906), X(32782)}}
X(55988) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3976}

X(55989) = KP2(X(1)) OF X(2) AND X(57)

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

X(55989) lies on these lines: {9, 1404}, {44, 346}, {200, 902}, {281, 26793}, {1743, 36846}, {2287, 3285}, {5749, 7110}, {16704, 34523}, {17350, 18811}, {26685, 37781}, {36910, 53994}

X(55989) = trilinear pole of line {1960, 2516}
X(55989) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 32577}, {6, 4862}, {55, 47444}, {56, 30827}, {57, 2098}, {75, 34543}, {269, 34524}, {664, 17424}
X(55989) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 30827}, {9, 4862}, {206, 34543}, {223, 47444}, {5452, 2098}, {6600, 34524}, {32664, 32577}, {39025, 17424}
X(55989) = X(i)-cross conjugate of X(j) for these {i, j}: {4162, 100}, {26690, 2}
X(55989) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3621)}}, {{A, B, C, X(2), X(9)}}, {{A, B, C, X(6), X(44)}}, {{A, B, C, X(7), X(765)}}, {{A, B, C, X(8), X(52442)}}, {{A, B, C, X(19), X(26745)}}, {{A, B, C, X(37), X(16885)}}, {{A, B, C, X(45), X(15492)}}, {{A, B, C, X(57), X(1743)}}, {{A, B, C, X(84), X(6553)}}, {{A, B, C, X(86), X(55920)}}, {{A, B, C, X(88), X(41441)}}, {{A, B, C, X(90), X(1219)}}, {{A, B, C, X(145), X(1476)}}, {{A, B, C, X(348), X(26793)}}, {{A, B, C, X(391), X(26637)}}, {{A, B, C, X(672), X(17350)}}, {{A, B, C, X(941), X(17299)}}, {{A, B, C, X(983), X(7194)}}, {{A, B, C, X(996), X(55918)}}, {{A, B, C, X(1156), X(4373)}}, {{A, B, C, X(1257), X(38271)}}, {{A, B, C, X(1280), X(3062)}}, {{A, B, C, X(1903), X(4080)}}, {{A, B, C, X(2161), X(39956)}}, {{A, B, C, X(2298), X(5839)}}, {{A, B, C, X(2345), X(33168)}}, {{A, B, C, X(2346), X(30712)}}, {{A, B, C, X(2348), X(6180)}}, {{A, B, C, X(2991), X(55937)}}, {{A, B, C, X(2995), X(36798)}}, {{A, B, C, X(3219), X(5749)}}, {{A, B, C, X(3623), X(11519)}}, {{A, B, C, X(4866), X(46872)}}, {{A, B, C, X(5296), X(27065)}}, {{A, B, C, X(7091), X(35577)}}, {{A, B, C, X(7319), X(40436)}}, {{A, B, C, X(34234), X(52549)}}, {{A, B, C, X(39694), X(43739)}}, {{A, B, C, X(40779), X(54120)}}
X(55989) = barycentric product X(i)*X(j) for these (i, j): {18811, 55}, {34523, 6}, {46004, 8706}
X(55989) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4862}, {9, 30827}, {31, 32577}, {32, 34543}, {55, 2098}, {57, 47444}, {220, 34524}, {3063, 17424}, {3689, 44784}, {18811, 6063}, {34523, 76}, {52804, 15347}

X(55990) = KP2(X(1)) OF X(2) AND X(58)

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

X(55990) lies on these lines: {8, 40091}, {85, 26223}, {257, 27065}, {312, 26688}, {333, 17285}, {2994, 26685}, {4518, 7191}, {4997, 33133}, {17342, 42030}, {17353, 40394}, {27064, 30690}, {27643, 28660}, {29679, 52133}

X(55990) = trilinear pole of line {4491, 522}
X(55990) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3953}
X(55990) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 3953}
X(55990) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(8)}}, {{A, B, C, X(6), X(27643)}}, {{A, B, C, X(9), X(26223)}}, {{A, B, C, X(27), X(39698)}}, {{A, B, C, X(57), X(26688)}}, {{A, B, C, X(58), X(32911)}}, {{A, B, C, X(80), X(40013)}}, {{A, B, C, X(81), X(1016)}}, {{A, B, C, X(83), X(1255)}}, {{A, B, C, X(86), X(27807)}}, {{A, B, C, X(88), X(2985)}}, {{A, B, C, X(226), X(36954)}}, {{A, B, C, X(239), X(7191)}}, {{A, B, C, X(321), X(33157)}}, {{A, B, C, X(335), X(55027)}}, {{A, B, C, X(673), X(35058)}}, {{A, B, C, X(675), X(7033)}}, {{A, B, C, X(894), X(27065)}}, {{A, B, C, X(1222), X(39747)}}, {{A, B, C, X(1230), X(36934)}}, {{A, B, C, X(2221), X(4383)}}, {{A, B, C, X(2341), X(23617)}}, {{A, B, C, X(3219), X(27064)}}, {{A, B, C, X(3661), X(29679)}}, {{A, B, C, X(4358), X(33133)}}, {{A, B, C, X(4600), X(32011)}}, {{A, B, C, X(5222), X(19993)}}, {{A, B, C, X(5294), X(26580)}}, {{A, B, C, X(5905), X(26685)}}, {{A, B, C, X(6539), X(17285)}}, {{A, B, C, X(7035), X(40415)}}, {{A, B, C, X(7308), X(26627)}}, {{A, B, C, X(14534), X(40434)}}, {{A, B, C, X(14621), X(27789)}}, {{A, B, C, X(17184), X(17353)}}, {{A, B, C, X(17277), X(27163)}}, {{A, B, C, X(17338), X(27186)}}, {{A, B, C, X(17342), X(28605)}}, {{A, B, C, X(24624), X(32017)}}, {{A, B, C, X(26065), X(31018)}}, {{A, B, C, X(30701), X(39700)}}, {{A, B, C, X(30710), X(32012)}}
X(55990) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3953}

X(55991) = KP2(X(1)) OF X(2) AND X(82)

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

X(55991) lies on these lines: {31, 341}, {44, 2220}, {404, 513}, {519, 595}, {960, 1319}, {1417, 5253}, {1877, 5294}, {3073, 33118}, {3145, 24482}, {3871, 46187}, {4357, 17095}, {14584, 41226}, {18360, 25965}, {46877, 52680}

X(55991) = isogonal conjugate of X(24443)
X(55991) = trilinear pole of line {1635, 13256}
X(55991) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 24443}, {2, 17053}, {4, 23154}, {6, 3782}, {7, 23638}, {8, 17114}, {37, 16700}, {56, 1329}, {57, 17452}, {65, 18178}, {86, 21936}, {109, 21119}, {190, 23751}, {264, 23196}, {278, 22071}, {604, 20237}, {1400, 17182}, {1412, 21030}, {34079, 51465}
X(55991) = X(i)-vertex conjugate of X(j) for these {i, j}: {1222, 1408}
X(55991) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 1329}, {3, 24443}, {9, 3782}, {11, 21119}, {3161, 20237}, {5452, 17452}, {32664, 17053}, {35069, 51465}, {36033, 23154}, {40582, 17182}, {40589, 16700}, {40599, 21030}, {40600, 21936}, {40602, 18178}, {55053, 23751}
X(55991) = X(i)-cross conjugate of X(j) for these {i, j}: {4768, 36037}, {48307, 100}
X(55991) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(44)}}, {{A, B, C, X(2), X(2349)}}, {{A, B, C, X(4), X(26751)}}, {{A, B, C, X(6), X(987)}}, {{A, B, C, X(8), X(52442)}}, {{A, B, C, X(9), X(341)}}, {{A, B, C, X(10), X(3467)}}, {{A, B, C, X(19), X(39946)}}, {{A, B, C, X(21), X(1220)}}, {{A, B, C, X(27), X(40406)}}, {{A, B, C, X(28), X(13735)}}, {{A, B, C, X(29), X(45393)}}, {{A, B, C, X(54), X(4570)}}, {{A, B, C, X(56), X(983)}}, {{A, B, C, X(58), X(82)}}, {{A, B, C, X(60), X(1252)}}, {{A, B, C, X(63), X(5294)}}, {{A, B, C, X(72), X(40715)}}, {{A, B, C, X(75), X(90)}}, {{A, B, C, X(78), X(24982)}}, {{A, B, C, X(83), X(4567)}}, {{A, B, C, X(84), X(34860)}}, {{A, B, C, X(86), X(943)}}, {{A, B, C, X(87), X(2218)}}, {{A, B, C, X(100), X(404)}}, {{A, B, C, X(104), X(1222)}}, {{A, B, C, X(285), X(14942)}}, {{A, B, C, X(405), X(1982)}}, {{A, B, C, X(596), X(3065)}}, {{A, B, C, X(673), X(40403)}}, {{A, B, C, X(727), X(1408)}}, {{A, B, C, X(759), X(39748)}}, {{A, B, C, X(775), X(1167)}}, {{A, B, C, X(903), X(10308)}}, {{A, B, C, X(961), X(40400)}}, {{A, B, C, X(977), X(9309)}}, {{A, B, C, X(979), X(2217)}}, {{A, B, C, X(996), X(15446)}}, {{A, B, C, X(1043), X(52663)}}, {{A, B, C, X(1120), X(1476)}}, {{A, B, C, X(1156), X(1257)}}, {{A, B, C, X(1247), X(39798)}}, {{A, B, C, X(1434), X(2991)}}, {{A, B, C, X(2167), X(40394)}}, {{A, B, C, X(2190), X(36052)}}, {{A, B, C, X(2298), X(5331)}}, {{A, B, C, X(3497), X(39979)}}, {{A, B, C, X(3871), X(5253)}}, {{A, B, C, X(4564), X(17743)}}, {{A, B, C, X(6597), X(55076)}}, {{A, B, C, X(7042), X(30598)}}, {{A, B, C, X(7161), X(42285)}}, {{A, B, C, X(7284), X(39702)}}, {{A, B, C, X(7285), X(39959)}}, {{A, B, C, X(15175), X(40430)}}, {{A, B, C, X(17350), X(27678)}}, {{A, B, C, X(36037), X(38541)}}, {{A, B, C, X(36604), X(52375)}}
X(55991) = barycentric product X(i)*X(j) for these (i, j): {1, 2985}, {312, 3450}
X(55991) = barycentric quotient X(i)/X(j) for these (i, j): {1, 3782}, {6, 24443}, {8, 20237}, {9, 1329}, {21, 17182}, {31, 17053}, {41, 23638}, {48, 23154}, {55, 17452}, {58, 16700}, {210, 21030}, {212, 22071}, {213, 21936}, {284, 18178}, {604, 17114}, {650, 21119}, {667, 23751}, {758, 51465}, {2985, 75}, {3450, 57}, {9247, 23196}

X(55992) = KP2(X(1)) OF X(2) AND X(88)

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

X(55992) lies on these lines: {9, 14151}, {44, 38460}, {200, 678}, {346, 4370}, {644, 3973}, {1635, 2827}, {2287, 15492}, {3928, 27834}, {4921, 16729}, {7110, 50115}

X(55992) = trilinear pole of line {3158, 3251}
X(55992) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4887}, {57, 5048}
X(55992) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 4887}, {5452, 5048}
X(55992) = X(i)-cross conjugate of X(j) for these {i, j}: {4895, 100}
X(55992) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31145)}}, {{A, B, C, X(2), X(9)}}, {{A, B, C, X(6), X(4921)}}, {{A, B, C, X(37), X(15492)}}, {{A, B, C, X(44), X(88)}}, {{A, B, C, X(81), X(37654)}}, {{A, B, C, X(100), X(14193)}}, {{A, B, C, X(104), X(519)}}, {{A, B, C, X(105), X(7312)}}, {{A, B, C, X(294), X(17439)}}, {{A, B, C, X(644), X(27834)}}, {{A, B, C, X(765), X(903)}}, {{A, B, C, X(1252), X(2316)}}, {{A, B, C, X(1255), X(40401)}}, {{A, B, C, X(1311), X(4076)}}, {{A, B, C, X(1743), X(3973)}}, {{A, B, C, X(2298), X(17362)}}, {{A, B, C, X(2346), X(39704)}}, {{A, B, C, X(3065), X(24858)}}, {{A, B, C, X(3219), X(50115)}}, {{A, B, C, X(6553), X(7285)}}, {{A, B, C, X(9432), X(28583)}}, {{A, B, C, X(32635), X(55991)}}, {{A, B, C, X(34056), X(35168)}}
X(55992) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4887}, {55, 5048}

X(55993) = KP2(X(1)) OF X(2) AND X(89)

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

X(55993) lies on these lines: {9, 1319}, {44, 200}, {281, 1877}, {346, 519}, {513, 2441}, {2287, 3973}, {4370, 4936}, {14584, 36910}, {20942, 30939}, {36796, 50127}

X(55993) = trilinear pole of line {1635, 8643}
X(55993) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 4346}, {56, 5328}, {57, 7962}
X(55993) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 5328}, {9, 4346}, {5452, 7962}
X(55993) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(44)}}, {{A, B, C, X(2), X(9)}}, {{A, B, C, X(6), X(1743)}}, {{A, B, C, X(19), X(36603)}}, {{A, B, C, X(37), X(3973)}}, {{A, B, C, X(57), X(40400)}}, {{A, B, C, X(63), X(50115)}}, {{A, B, C, X(89), X(16670)}}, {{A, B, C, X(269), X(983)}}, {{A, B, C, X(672), X(50127)}}, {{A, B, C, X(903), X(3062)}}, {{A, B, C, X(997), X(3679)}}, {{A, B, C, X(1156), X(36588)}}, {{A, B, C, X(1219), X(7285)}}, {{A, B, C, X(1252), X(2364)}}, {{A, B, C, X(1257), X(33576)}}, {{A, B, C, X(1275), X(17743)}}, {{A, B, C, X(1280), X(55922)}}, {{A, B, C, X(1757), X(36404)}}, {{A, B, C, X(1903), X(4052)}}, {{A, B, C, X(2161), X(8056)}}, {{A, B, C, X(2192), X(2983)}}, {{A, B, C, X(2298), X(39948)}}, {{A, B, C, X(2316), X(7123)}}, {{A, B, C, X(3731), X(16885)}}, {{A, B, C, X(3870), X(31146)}}, {{A, B, C, X(3929), X(5749)}}, {{A, B, C, X(4234), X(37391)}}, {{A, B, C, X(7284), X(24858)}}, {{A, B, C, X(9353), X(23051)}}, {{A, B, C, X(16833), X(41276)}}, {{A, B, C, X(29649), X(42043)}}, {{A, B, C, X(36406), X(39252)}}, {{A, B, C, X(39594), X(42042)}}, {{A, B, C, X(39956), X(41441)}}, {{A, B, C, X(40218), X(52556)}}
X(55993) = barycentric quotient X(i)/X(j) for these (i, j): {1, 4346}, {9, 5328}, {55, 7962}

X(55994) = KP2(X(1)) OF X(2) AND X(92)

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

X(55994) lies on these lines: {9, 17555}, {19, 3692}, {25, 1260}, {63, 1435}, {219, 608}, {268, 37248}, {1474, 2327}, {1897, 40968}, {2322, 54324}, {21811, 37295}

X(55994) = polar conjugate of X(17861)
X(55994) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 26934}, {3, 3772}, {6, 41004}, {48, 17861}, {63, 3924}, {71, 17189}, {77, 40968}, {78, 36570}, {222, 1837}, {228, 16749}, {278, 53850}, {905, 53279}, {1214, 40980}, {1790, 21935}
X(55994) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 26934}, {9, 41004}, {1249, 17861}, {3162, 3924}, {36103, 3772}
X(55994) = X(i)-cross conjugate of X(j) for these {i, j}: {663, 1897}, {54247, 162}
X(55994) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(40445)}}, {{A, B, C, X(2), X(5279)}}, {{A, B, C, X(4), X(5174)}}, {{A, B, C, X(7), X(82)}}, {{A, B, C, X(9), X(63)}}, {{A, B, C, X(19), X(25)}}, {{A, B, C, X(21), X(318)}}, {{A, B, C, X(71), X(54324)}}, {{A, B, C, X(75), X(26703)}}, {{A, B, C, X(84), X(106)}}, {{A, B, C, X(92), X(1172)}}, {{A, B, C, X(169), X(1766)}}, {{A, B, C, X(264), X(5379)}}, {{A, B, C, X(272), X(1311)}}, {{A, B, C, X(281), X(2326)}}, {{A, B, C, X(284), X(7094)}}, {{A, B, C, X(309), X(8759)}}, {{A, B, C, X(346), X(41514)}}, {{A, B, C, X(415), X(1013)}}, {{A, B, C, X(663), X(40968)}}, {{A, B, C, X(775), X(7219)}}, {{A, B, C, X(915), X(53813)}}, {{A, B, C, X(1043), X(40457)}}, {{A, B, C, X(1988), X(2161)}}, {{A, B, C, X(2167), X(2335)}}, {{A, B, C, X(2287), X(36100)}}, {{A, B, C, X(3731), X(5730)}}, {{A, B, C, X(5282), X(28287)}}, {{A, B, C, X(6336), X(7129)}}, {{A, B, C, X(7097), X(34234)}}, {{A, B, C, X(8748), X(37203)}}, {{A, B, C, X(16547), X(16548)}}, {{A, B, C, X(41502), X(52414)}}
X(55994) = barycentric product X(i)*X(j) for these (i, j): {1, 34406}, {4, 40436}, {33, 34399}
X(55994) = barycentric quotient X(i)/X(j) for these (i, j): {1, 41004}, {4, 17861}, {6, 26934}, {19, 3772}, {25, 3924}, {27, 16749}, {28, 17189}, {33, 1837}, {212, 53850}, {607, 40968}, {608, 36570}, {1824, 21935}, {2299, 40980}, {8750, 53279}, {34399, 7182}, {34406, 75}, {40436, 69}, {52775, 36118}

X(55995) = KP2(X(1)) OF X(2) AND X(104)

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

X(55995) lies on these lines: {3, 42070}, {63, 16578}, {78, 214}, {280, 4188}, {345, 21488}, {348, 31018}, {1812, 17191}, {1813, 6513}, {3452, 52381}, {3911, 52351}, {6985, 13397}

X(55995) = trilinear pole of line {3157, 3913}
X(55995) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 30384}
X(55995) = X(i)-Dao conjugate of X(j) for these {i, j}: {9, 30384}
X(55995) = X(i)-cross conjugate of X(j) for these {i, j}: {1639, 100}
X(55995) = intersection, other than A, B, C, of circumconics, {{A, B, C, X(2), X(21)}}, {{A, B, C, X(9), X(31018)}}, {{A, B, C, X(28), X(21488)}}, {{A, B, C, X(44), X(42070)}}, {{A, B, C, X(57), X(37618)}}, {{A, B, C, X(81), X(8666)}}, {{A, B, C, X(88), X(104)}}, {{A, B, C, X(89), X(1476)}}, {{A, B, C, X(189), X(1392)}}, {{A, B, C, X(474), X(27174)}}, {{A, B, C, X(645), X(27834)}}, {{A, B, C, X(943), X(40434)}}, {{A, B, C, X(1255), X(17758)}}, {{A, B, C, X(1320), X(21739)}}, {{A, B, C, X(1809), X(14919)}}, {{A, B, C, X(1813), X(13397)}}, {{A, B, C, X(1817), X(4188)}}, {{A, B, C, X(2167), X(40420)}}, {{A, B, C, X(2178), X(36743)}}, {{A, B, C, X(2349), X(4997)}}, {{A, B, C, X(2990), X(4564)}}, {{A, B, C, X(2991), X(39698)}}, {{A, B, C, X(2994), X(3680)}}, {{A, B, C, X(3219), X(3452)}}, {{A, B, C, X(3912), X(37782)}}, {{A, B, C, X(4567), X(36805)}}, {{A, B, C, X(4998), X(43363)}}, {{A, B, C, X(5905), X(36599)}}, {{A, B, C, X(6336), X(37131)}}, {{A, B, C, X(8047), X(43736)}}, {{A, B, C, X(10074), X(34051)}}, {{A, B, C, X(11329), X(35997)}}, {{A, B, C, X(14740), X(16578)}}, {{A, B, C, X(15446), X(39963)}}, {{A, B, C, X(21495), X(33325)}}, {{A, B, C, X(21511), X(35983)}}, {{A, B, C, X(21907), X(43760)}}, {{A, B, C, X(32017), X(40406)}}, {{A, B, C, X(37312), X(52012)}}
X(55995) = barycentric quotient X(i)/X(j) for these (i, j): {1, 30384}

X(55996) = KP2(X(1)) OF X(2) AND X(109)

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

X(55996) lies on the MacBeath circumconic and on these lines: {2, 1797}, {110, 32704}, {394, 36791}, {458, 2989}, {651, 26693}, {895, 52747}, {1331, 17780}, {1332, 24004}, {1814, 26651}, {1993, 46638}, {2415, 25268}, {3667, 15403}, {4563, 55262}, {9059, 35186}

X(55996) = trilinear pole of line {3, 3654}
X(55996) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 32475}, {649, 14923}, {661, 7419}, {4394, 14261}, {5510, 34080}, {9456, 55134}
X(55996) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 32475}, {4370, 55134}, {5375, 14923}, {36830, 7419}, {40621, 5510}
X(55996) = X(i)-anticomplementary conjugate of X(j) for these {i, j}: {15403, 4329}
X(55996) = X(i)-cross conjugate of X(j) for these {i, j}: {6, 15403}, {2429, 6079}
X(55996) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(190)}}, {{A, B, C, X(81), X(38828)}}, {{A, B, C, X(83), X(28564)}}, {{A, B, C, X(110), X(287)}}, {{A, B, C, X(394), X(40518)}}, {{A, B, C, X(458), X(4243)}}, {{A, B, C, X(645), X(27834)}}, {{A, B, C, X(666), X(29227)}}, {{A, B, C, X(1025), X(26651)}}, {{A, B, C, X(3699), X(25268)}}, {{A, B, C, X(3939), X(23617)}}, {{A, B, C, X(7123), X(40523)}}, {{A, B, C, X(26685), X(53337)}}, {{A, B, C, X(35008), X(35137)}}, {{A, B, C, X(43531), X(44876)}}
X(55996) = barycentric product X(i)*X(j) for these (i, j): {3264, 35186}, {32704, 69}, {53647, 54237}
X(55996) = barycentric quotient X(i)/X(j) for these (i, j): {3, 32475}, {100, 14923}, {110, 7419}, {519, 55134}, {1293, 14261}, {3667, 5510}, {15403, 1293}, {32704, 4}, {32705, 8752}, {35186, 106}, {36112, 36125}, {54237, 3667}

X(55997) = KP2(X(2)) OF X(1) AND X(86)

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

X(55997) lies on these lines: {1, 8026}, {43, 4360}, {190, 21757}, {192, 2162}, {669, 27804}, {726, 51449}, {727, 3993}, {893, 17319}, {2176, 4393}, {3009, 32928}, {3226, 3971}, {3995, 20332}, {4598, 17459}, {6043, 38832}, {17318, 21780}, {32925, 40735}, {34064, 51973}

X(55997) = isotomic conjugate of X(24165)
X(55997) = trilinear pole of line {4063, 4785}
X(55997) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 21757}, {4, 22378}, {6, 16604}, {31, 24165}, {81, 21827}, {87, 20971}, {213, 16710}, {692, 48406}, {2162, 17459}, {2209, 52573}, {7121, 34832}
X(55997) = X(i)-Dao conjugate of X(j) for these {i, j}: {2, 24165}, {9, 16604}, {75, 20899}, {1086, 48406}, {6377, 21128}, {6626, 16710}, {32664, 21757}, {36033, 22378}, {40586, 21827}, {40598, 34832}
X(55997) = X(i)-cross conjugate of X(j) for these {i, j}: {667, 190}, {25142, 4598}
X(55997) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43)}}, {{A, B, C, X(2), X(3226)}}, {{A, B, C, X(6), X(33784)}}, {{A, B, C, X(42), X(669)}}, {{A, B, C, X(75), X(39694)}}, {{A, B, C, X(81), X(7035)}}, {{A, B, C, X(86), X(1255)}}, {{A, B, C, X(192), X(8026)}}, {{A, B, C, X(257), X(40033)}}, {{A, B, C, X(310), X(27807)}}, {{A, B, C, X(330), X(32095)}}, {{A, B, C, X(667), X(21757)}}, {{A, B, C, X(726), X(3971)}}, {{A, B, C, X(740), X(52208)}}, {{A, B, C, X(870), X(25430)}}, {{A, B, C, X(873), X(40434)}}, {{A, B, C, X(894), X(17319)}}, {{A, B, C, X(1016), X(40415)}}, {{A, B, C, X(1174), X(5378)}}, {{A, B, C, X(1215), X(9281)}}, {{A, B, C, X(1222), X(1390)}}, {{A, B, C, X(1897), X(29363)}}, {{A, B, C, X(2296), X(27789)}}, {{A, B, C, X(3952), X(27804)}}, {{A, B, C, X(4876), X(39924)}}, {{A, B, C, X(6384), X(39703)}}, {{A, B, C, X(7018), X(39714)}}, {{A, B, C, X(17459), X(25142)}}, {{A, B, C, X(18082), X(32928)}}, {{A, B, C, X(30710), X(39717)}}, {{A, B, C, X(31002), X(55026)}}, {{A, B, C, X(32010), X(32017)}}, {{A, B, C, X(33152), X(33164)}}, {{A, B, C, X(34064), X(40164)}}, {{A, B, C, X(34248), X(40433)}}, {{A, B, C, X(40027), X(54128)}}, {{A, B, C, X(55953), X(55955)}}
X(55997) = barycentric product X(i)*X(j) for these (i, j): {35572, 3835}
X(55997) = barycentric quotient X(i)/X(j) for these (i, j): {1, 16604}, {2, 24165}, {31, 21757}, {42, 21827}, {43, 17459}, {48, 22378}, {86, 16710}, {192, 34832}, {330, 52573}, {514, 48406}, {2176, 20971}, {3835, 21128}, {3971, 21040}, {6376, 20899}, {20760, 22081}, {35572, 4598}

X(55998) = KP2(X(2)) OF X(1) AND X(145)

Barycentrics    a^2+4*b*c-3*a*(b+c) : :
X(55998) = -X[7]+2*X[3950], -4*X[4078]+3*X[38052], -3*X[6173]+4*X[17243], -4*X[7263]+5*X[20195]

X(55998) lies on these lines: {1, 87}, {2, 31326}, {6, 4718}, {7, 3950}, {9, 536}, {10, 4461}, {37, 4659}, {45, 4686}, {57, 3175}, {63, 42044}, {75, 3731}, {141, 4873}, {142, 28301}, {144, 519}, {145, 4488}, {165, 4434}, {190, 1743}, {193, 3633}, {200, 32925}, {239, 3973}, {269, 4552}, {319, 49748}, {321, 18229}, {344, 1266}, {346, 3663}, {522, 3174}, {527, 17314}, {545, 4851}, {740, 5223}, {903, 17241}, {936, 3159}, {1001, 28555}, {1018, 1423}, {1100, 49721}, {1125, 7229}, {1278, 4384}, {1449, 17318}, {1654, 4668}, {1992, 4464}, {2321, 4419}, {2325, 4000}, {2550, 28557}, {2901, 35629}, {2999, 17147}, {3008, 3161}, {3062, 28850}, {3169, 21362}, {3177, 11519}, {3187, 25734}, {3210, 23511}, {3242, 49522}, {3243, 28582}, {3247, 4363}, {3305, 50106}, {3452, 42049}, {3632, 4416}, {3664, 4454}, {3672, 17355}, {3677, 4387}, {3679, 4431}, {3707, 4371}, {3739, 16676}, {3751, 49452}, {3760, 17787}, {3869, 12546}, {3879, 4898}, {3886, 49447}, {3912, 4862}, {3943, 17276}, {3946, 54389}, {3970, 7201}, {3971, 8580}, {3995, 17022}, {4007, 4478}, {4021, 5749}, {4029, 4648}, {4032, 4099}, {4034, 17332}, {4052, 5226}, {4058, 5232}, {4072, 29616}, {4078, 38052}, {4098, 5308}, {4312, 28526}, {4346, 21255}, {4357, 50107}, {4360, 16667}, {4373, 29627}, {4389, 17286}, {4398, 17264}, {4432, 16487}, {4440, 4902}, {4460, 4856}, {4512, 32936}, {4664, 10436}, {4677, 17333}, {4688, 16675}, {4693, 16496}, {4704, 16831}, {4726, 17259}, {4727, 40341}, {4740, 17260}, {4747, 4909}, {4764, 17277}, {4821, 16815}, {4852, 16670}, {4853, 25237}, {4865, 50865}, {4869, 4887}, {4884, 24392}, {4888, 17316}, {4908, 17267}, {4910, 32455}, {4918, 9578}, {4929, 5853}, {5220, 28484}, {5268, 31087}, {5294, 50071}, {5437, 35652}, {5695, 7174}, {5697, 43216}, {5745, 42047}, {5839, 17133}, {5880, 28556}, {5942, 49169}, {6172, 28313}, {6173, 17243}, {6646, 17294}, {6765, 24068}, {7227, 41312}, {7263, 20195}, {7290, 49453}, {7308, 42051}, {8056, 18743}, {9055, 51194}, {9623, 25255}, {10022, 28640}, {10442, 29069}, {10582, 17155}, {16469, 32921}, {16569, 17759}, {16669, 50120}, {16677, 31238}, {16814, 17119}, {16834, 17350}, {17160, 17336}, {17229, 17255}, {17231, 49747}, {17233, 17274}, {17235, 17269}, {17237, 53664}, {17239, 24441}, {17246, 17281}, {17247, 17308}, {17248, 19875}, {17258, 17270}, {17275, 49742}, {17280, 17304}, {17299, 17334}, {17301, 17340}, {17309, 17345}, {17317, 49722}, {17323, 17359}, {17344, 50087}, {17353, 50101}, {17364, 29605}, {17376, 28322}, {17389, 31300}, {17487, 34747}, {17495, 54390}, {17776, 23681}, {18044, 24004}, {18065, 39995}, {18186, 30939}, {20078, 50292}, {20080, 49761}, {20171, 20881}, {21296, 49765}, {24070, 27557}, {24280, 49476}, {24398, 42720}, {24514, 42043}, {24778, 28778}, {24821, 49469}, {25101, 31183}, {25256, 36846}, {25527, 42033}, {29571, 31995}, {29649, 53056}, {30350, 42055}, {31302, 49451}, {33165, 50080}, {36404, 49533}, {39126, 51302}, {42696, 50093}, {49448, 49507}, {49456, 50314}, {49460, 49513}, {49474, 49516}

X(55998) = reflection of X(i) in X(j) for these {i,j}: {17151, 9}, {7, 3950}, {9, 17262}
X(55998) = anticomplement of X(53594)
X(55998) = X(i)-Dao conjugate of X(j) for these {i, j}: {53594, 53594}
X(55998) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 3950, 29573}, {9, 17151, 16833}, {9, 536, 17151}, {37, 4659, 25590}, {75, 3731, 16832}, {190, 3644, 3875}, {190, 3875, 1743}, {192, 3729, 1}, {239, 25269, 25728}, {346, 3663, 17284}, {536, 17262, 9}, {1278, 17261, 4384}, {2321, 4419, 17272}, {2901, 54422, 35629}, {3161, 4452, 3008}, {3210, 30568, 23511}, {3672, 17355, 29598}, {3950, 17132, 7}, {4021, 50118, 5749}, {4072, 53598, 29616}, {4360, 50127, 16667}, {4363, 4681, 3247}, {4398, 17264, 17282}, {4431, 17257, 3679}, {4431, 50090, 17257}, {4440, 17242, 17298}, {4440, 17298, 4902}, {4664, 10436, 16673}, {4693, 49517, 16496}, {4704, 17116, 16831}, {4788, 25269, 239}, {5695, 49523, 7174}, {7263, 41313, 20195}, {17246, 17281, 17306}, {17318, 17351, 1449}, {49507, 49514, 49448}

X(55999) = KP2(X(3)) OF X(2) AND X(6)

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

X(55999) lies on these lines: {24, 1351}, {32, 14253}, {193, 1692}, {372, 8913}, {1147, 3563}, {1993, 3053}, {2396, 47733}, {2996, 47735}, {3167, 14248}, {3425, 9545}, {5889, 47113}, {9292, 34986}, {9737, 34148}, {11004, 52505}, {11547, 37174}, {12221, 13429}, {12222, 13440}, {18883, 37645}, {21874, 42700}

X(55999) = isogonal conjugate of X(13881)
X(55999) = trilinear pole of line {6132, 8651}
X(55999) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 13881}, {6, 17890}
X(55999) = X(i)-Dao conjugate of X(j) for these {i, j}: {3, 13881}, {9, 17890}
X(55999) = X(i)-cross conjugate of X(j) for these {i, j}: {2489, 110}, {44680, 99}
X(55999) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(24)}}, {{A, B, C, X(3), X(1351)}}, {{A, B, C, X(4), X(249)}}, {{A, B, C, X(6), X(193)}}, {{A, B, C, X(25), X(32989)}}, {{A, B, C, X(32), X(1692)}}, {{A, B, C, X(59), X(54123)}}, {{A, B, C, X(64), X(41895)}}, {{A, B, C, X(74), X(38259)}}, {{A, B, C, X(76), X(3431)}}, {{A, B, C, X(83), X(13472)}}, {{A, B, C, X(89), X(28527)}}, {{A, B, C, X(97), X(43670)}}, {{A, B, C, X(194), X(2396)}}, {{A, B, C, X(251), X(6423)}}, {{A, B, C, X(263), X(14370)}}, {{A, B, C, X(279), X(3450)}}, {{A, B, C, X(323), X(37645)}}, {{A, B, C, X(394), X(41899)}}, {{A, B, C, X(511), X(9737)}}, {{A, B, C, X(576), X(47113)}}, {{A, B, C, X(588), X(8946)}}, {{A, B, C, X(589), X(8948)}}, {{A, B, C, X(598), X(11588)}}, {{A, B, C, X(671), X(11270)}}, {{A, B, C, X(1173), X(18845)}}, {{A, B, C, X(1176), X(6339)}}, {{A, B, C, X(1297), X(9732)}}, {{A, B, C, X(1379), X(3557)}}, {{A, B, C, X(1380), X(3558)}}, {{A, B, C, X(1383), X(14659)}}, {{A, B, C, X(1992), X(37784)}}, {{A, B, C, X(1994), X(6515)}}, {{A, B, C, X(2986), X(34386)}}, {{A, B, C, X(3095), X(35383)}}, {{A, B, C, X(3407), X(6179)}}, {{A, B, C, X(3527), X(53101)}}, {{A, B, C, X(3580), X(11004)}}, {{A, B, C, X(3926), X(5504)}}, {{A, B, C, X(5649), X(46639)}}, {{A, B, C, X(9306), X(34986)}}, {{A, B, C, X(11736), X(33698)}}, {{A, B, C, X(11738), X(53106)}}, {{A, B, C, X(11741), X(17503)}}, {{A, B, C, X(13452), X(32901)}}, {{A, B, C, X(14376), X(16867)}}, {{A, B, C, X(14491), X(53109)}}, {{A, B, C, X(14528), X(40802)}}, {{A, B, C, X(15316), X(28724)}}, {{A, B, C, X(15317), X(18876)}}, {{A, B, C, X(16835), X(21399)}}, {{A, B, C, X(20251), X(43527)}}, {{A, B, C, X(30535), X(43908)}}, {{A, B, C, X(30541), X(43681)}}, {{A, B, C, X(34148), X(54114)}}, {{A, B, C, X(37685), X(40571)}}, {{A, B, C, X(38534), X(52583)}}, {{A, B, C, X(40318), X(51170)}}, {{A, B, C, X(41909), X(43697)}}
X(55999) = barycentric quotient X(i)/X(j) for these (i, j): {1, 17890}, {6, 13881}

X(56000) = KP2(X(3)) OF X(2) AND X(27)

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

X(56000) lies on these lines: {2, 6}, {9, 54356}, {19, 41723}, {21, 219}, {22, 44101}, {27, 17220}, {28, 3211}, {48, 4225}, {58, 2327}, {60, 283}, {71, 4184}, {77, 18206}, {110, 1474}, {511, 44093}, {572, 34148}, {573, 5889}, {593, 6514}, {648, 2989}, {651, 52673}, {859, 20818}, {916, 7431}, {1100, 16699}, {1172, 3193}, {1396, 3173}, {1409, 4296}, {1778, 2911}, {1815, 46639}, {2194, 3056}, {2264, 18178}, {2268, 9637}, {2293, 2328}, {2322, 3562}, {3060, 44103}, {3187, 31623}, {3218, 14597}, {3990, 34772}, {4877, 52405}, {5208, 20752}, {5746, 36428}, {6505, 46885}, {7253, 23145}, {7419, 22356}, {7453, 40954}, {9028, 17171}, {11110, 22126}, {16049, 19350}, {17976, 36015}, {21270, 31909}, {22127, 37442}, {32431, 50435}, {40572, 51574}

X(56000) = perspector of circumconic {{A, B, C, X(99), X(4636)}}
X(56000) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 28786}, {34, 40161}, {57, 41506}, {65, 1751}, {201, 40574}, {213, 15467}, {226, 2218}, {272, 2171}, {661, 1305}, {1020, 23289}, {1400, 2997}, {1402, 40011}, {7180, 51566}
X(56000) = X(i)-Dao conjugate of X(j) for these {i, j}: {6, 28786}, {72, 26942}, {5452, 41506}, {6626, 15467}, {11517, 40161}, {36830, 1305}, {40582, 2997}, {40602, 1751}, {40605, 40011}
X(56000) = X(i)-Ceva conjugate of X(j) for these {i, j}: {40414, 3}, {44129, 4184}, {46103, 21}
X(56000) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5736)}}, {{A, B, C, X(2), X(284)}}, {{A, B, C, X(7), X(51893)}}, {{A, B, C, X(9), X(5278)}}, {{A, B, C, X(55), X(19732)}}, {{A, B, C, X(60), X(86)}}, {{A, B, C, X(69), X(283)}}, {{A, B, C, X(71), X(14053)}}, {{A, B, C, X(81), X(2150)}}, {{A, B, C, X(209), X(1211)}}, {{A, B, C, X(325), X(20294)}}, {{A, B, C, X(333), X(7054)}}, {{A, B, C, X(394), X(2989)}}, {{A, B, C, X(524), X(8676)}}, {{A, B, C, X(940), X(2352)}}, {{A, B, C, X(949), X(965)}}, {{A, B, C, X(966), X(41320)}}, {{A, B, C, X(1172), X(40571)}}, {{A, B, C, X(1252), X(8748)}}, {{A, B, C, X(1815), X(37669)}}, {{A, B, C, X(2316), X(19742)}}, {{A, B, C, X(2323), X(3936)}}, {{A, B, C, X(2364), X(19684)}}, {{A, B, C, X(3945), X(4306)}}, {{A, B, C, X(4876), X(29964)}}, {{A, B, C, X(5125), X(35196)}}, {{A, B, C, X(5738), X(51496)}}, {{A, B, C, X(17056), X(21748)}}, {{A, B, C, X(17379), X(55999)}}, {{A, B, C, X(35466), X(43060)}}
X(56000) = barycentric product X(i)*X(j) for these (i, j): {21, 3868}, {110, 20294}, {209, 261}, {283, 5125}, {333, 579}, {1043, 4306}, {2185, 22021}, {2198, 52379}, {2352, 314}, {3190, 86}, {8676, 99}, {17206, 41320}, {18134, 284}, {23800, 643}, {27396, 81}, {43060, 645}, {46103, 51574}
X(56000) = barycentric quotient X(i)/X(j) for these (i, j): {3, 28786}, {21, 2997}, {55, 41506}, {60, 272}, {86, 15467}, {110, 1305}, {209, 12}, {219, 40161}, {284, 1751}, {333, 40011}, {579, 226}, {643, 51566}, {2189, 40574}, {2194, 2218}, {2198, 2171}, {2352, 65}, {3190, 10}, {3868, 1441}, {4306, 3668}, {8676, 523}, {14053, 3136}, {18134, 349}, {20294, 850}, {21789, 23289}, {22021, 6358}, {23800, 4077}, {27396, 321}, {41320, 1826}, {43060, 7178}, {51574, 26942}
X(56000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {48, 4269, 4225}, {81, 37659, 86}, {219, 46882, 21}, {283, 284, 7054}

This is the end of PART 28: Centers X(54001) - X(56000)

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)