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This is PART 22: Centers X(42001) - X(44000)

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(42001) = X(13)X(5916)∩X(62)X(21466)

Barycentrics    (S*(Sqrt[3]*a^2 + S) + 3*SB*SC)*(Sqrt[3]*S*(-a^2 + 2*SA) + 3*(a^2*SA - 2*SB*SC))^2 : :

X(42001) lies on the 1st Simmons inconic and these lines: {13, 5916}, {62, 21466}, {546, 11555}, {8014, 18777}, {11537, 30467}, {20578, 30466}, {23283, 30454}, {30460, 31945}

X(42001) = X(i)-Ceva conjugate of X(j) for these (i,j): {13, 11537}, {36839, 9200}
X(42001) = crosspoint of X(13) and X(11537)
X(42001) = barycentric product X(i)*X(j) for these {i,j}: {13, 13, 520}, {530, 11537}, {11078, 30469}
X(42001) = barycentric quotient X(30469)/X(11092)

X(42002) = X(14)X(5917)∩X(61)X(21467)

Barycentrics    (S*(Sqrt[3]*a^2 - S) - 3*SB*SC)*(Sqrt[3]*S*(-a^2 + 2*SA) - 3*(a^2*SA - 2*SB*SC))^2 : :

X(42002) lies on the 2nd Simmons inconic and these lines: {14, 5917}, {61, 21467}, {546, 11556}, {8015, 18776}, {11549, 30470}, {20579, 30469}, {23284, 30455}, {30463, 31945}

X(42002) = X(i)-Ceva conjugate of X(j) for these (i,j): {14, 11549}, {36840, 9201}
X(42002) = crosspoint of X(14) and X(11549)
X(42002) = barycentric product X(i)*X(j) for these {i,j}: {14, 14, 530}, {531, 11549}, {11092, 30466}
X(42002) = barycentric quotient X(30466)/X(11078)

X(42003) = X(13)X(11600)∩X(323)X(532)

Barycentrics    (a^2*SA + Sqrt[3]*S*(-a^2 + 2*SA) - 2*SB*SC)^2*(S*(Sqrt[3]*a^2 + S) + 3*SB*SC) : :

X(42003) lies on the 1st Simmons inconic and these lines: {13, 11600}, {323, 532}, {11542, 30465}, {14446, 18803}, {30452, 34325}

X(42003) = barycentric product X(i)*X(j) for these {i,j}: {13, 13, 532}, {11078, 30462}
X(42003) = barycentric quotient X(30462)/X(11092)

X(42004) = X(14)X(11601)∩X(323)X(533)

Barycentrics    (a^2*SA - Sqrt[3]*S*(-a^2 + 2*SA) - 2*SB*SC)^2(S*(Sqrt[3]*a^2 - S) - 3*SB*SC) : :

X(42004) lies on the 2nd Simmons inconic and these lines: {14, 11601}, {323, 533}, {11543, 30468}, {14447, 18804}, {30453, 34326}

X(42004) = barycentric product X(i)*X(j) for these {i,j}: {14, 14, 532}, {11079, 30459}
X(42004) = barycentric quotient X(30459)/X(11078)

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Perpsectors associated with inverse triangles: X(42005)-X(42066)

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This preamble is contributed by Clark Kimberling and Peter Moses, March 18, 2021.

Suppose that A'B'C' is a triangle with vertices A', B', C' represented in normalized barycentric coordinates. Let M be the matrix representation of A'B'C', and let inv(M) denote the inverse of M. Then the rows of inv(M), interpreted as vertices of a triangle, define the inverse triangle of A'B'C'. The row sums of the inverse triangle are all 1, so that this triangle is "automatically" normalized.

Let P = p : q : r be a point, and let A'B'C' be the cevian triangle of P, given by A ' = 0 : q : r, with B' and C' determined cycllically from A'. The inverse triangle of A'B'C' is the triangle A''B''C'' given by A'' = - q - r : q + r : p + q, with B'' and C'' determined cyclically from A''; thus, A''B''C'' is the anticevian triangle of the point q + r : r + p : p + q.

Here, let A'B'C' be the cevian triangle of P. The inverse of A'B'C' is the triangle A''B''C'' given by A'' = 0 : p - q + r : p + q - r, with B'' and C'' determined cyclically from A''; thus A''B''C'' is the cevian triangle of the point - p + q + r ; p - q + r : p + q - r.

A triangle A'B'C' is inscribed in ABC if and only if its inverse circumscribes ABC.

See the preambles just before X(43280), X(43344), and X(46961).

X(42005) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-FEUERBACH

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

X(42005) lies on these lines: {8, 79}, {10, 1109}, {12, 1089}, {75, 267}, {274, 20951}, {321, 21081}, {349, 23994}, {523, 24390}, {1125, 20886}, {1325, 2975}, {1365, 34829}, {1577, 23105}, {1631, 2915}, {1733, 24640}, {1930, 20437}, {2611, 24387}, {2643, 23626}, {3992, 27690}, {4858, 4999}, {4975, 37737}, {5506, 18151}, {17874, 31880}, {17886, 20880}, {18698, 19854}, {20236, 25650}, {20634, 20913}, {25446, 28611}

X(42005) = Feuerbach-to-ABC barycentric image of X(12)

X(42006) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-2ND-NEUBERG

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

Let A' be the apex of the isosceles triangle BCA' constructed inward on BC such that angle(A'BC) = angle(A'CB) = ω. Define B' and C' cyclically. Let KA be the symmedian point of BCA', and define KB and KC cyclically. The lines AKA, BKB, CKC concur in X(42006). (Randy Hutson, May 31, 2021)

The trilinear polar of X(42006) meets the line at infinity at X(523).

X(42006) lies on the Kiepert hyperbola and these lines: {2, 732}, {4, 2896}, {6, 33686}, {10, 33891}, {39, 10159}, {76, 4045}, {83, 385}, {98, 5092}, {141, 1916}, {183, 3407}, {194, 18840}, {262, 3314}, {321, 21817}, {384, 6308}, {511, 14492}, {538, 10302}, {598, 754}, {671, 7924}, {1447, 17741}, {1799, 40163}, {2023, 35005}, {2782, 9302}, {3329, 14994}, {3399, 32515}, {3406, 9755}, {3620, 14484}, {5395, 15589}, {5466, 31950}, {5976, 11606}, {6248, 12122}, {6704, 7755}, {7608, 7925}, {7766, 40332}, {7770, 12206}, {7787, 41650}, {7794, 32190}, {7836, 40108}, {7879, 22728}, {7885, 22682}, {7904, 22676}, {7931, 8781}, {8024, 31630}, {8587, 11168}, {8992, 19092}, {9866, 24256}, {12216, 32149}, {12263, 12783}, {13983, 19091}, {14458, 22712}, {14603, 39998}, {16987, 31239}, {16989, 18841}, {22706, 30998}, {26235, 34087}, {33278, 41895}, {40022, 40162}

X(42006) = isogonal conjugate of X(12212)
X(42006) = isotomic conjugate of X(3329)

X(42007) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-2ND-BROCARD

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

X(42007) lies on these lines: {6, 110}, {53, 17983}, {69, 31125}, {141, 30786}, {187, 2393}, {316, 524}, {511, 9186}, {526, 5505}, {574, 8542}, {576, 30498}, {599, 8288}, {691, 5104}, {2444, 6088}, {2871, 11173}, {3569, 9023}, {5024, 15268}, {5107, 9027}, {5585, 6091}, {5648, 41939}, {6784, 22111}, {8430, 8675}, {8546, 10485}, {8681, 9132}, {8869, 17710}, {9019, 41404}, {9225, 15398}, {9486, 20975}, {9872, 10510}, {10417, 32260}, {10602, 21448}, {12367, 32729}, {13192, 41617}, {13330, 14246}, {14609, 30495}, {15993, 16092}, {18023, 33769}, {20977, 41936}, {25052, 31128}, {25322, 41909}

X(42007) = isogonal conjugate of isotomic conjugate of X(42008)
X(42007) = trilinear pole of line X(574)X(17414)
X(42007) = perspector of ABC and cross-triangle of ABC and 2nd Ehrmann triangle
X(42007) = barycentric product X(6)*X(42008)
X(42007) = barycentric quotient X(42008)/X(76)

X(42008) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-4TH-BROCARD

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

X(42008) lies on these lines: {2, 99}, {23, 32479}, {67, 524}, {110, 9830}, {316, 41404}, {325, 9187}, {381, 9775}, {427, 8753}, {523, 34206}, {542, 10554}, {598, 9515}, {599, 8288}, {625, 10630}, {691, 3849}, {850, 10562}, {892, 7840}, {897, 25383}, {1153, 7496}, {1641, 11646}, {2770, 36196}, {2782, 9759}, {2799, 5466}, {3266, 18023}, {3268, 14977}, {5094, 11165}, {5169, 8176}, {5189, 10416}, {5468, 11161}, {5485, 16051}, {5968, 11184}, {5971, 17964}, {6032, 11163}, {6321, 14694}, {7610, 30542}, {7775, 14246}, {8182, 16063}, {8430, 31174}, {8597, 26276}, {8877, 31074}, {9133, 41133}, {9148, 9178}, {9213, 23878}, {9214, 9770}, {9741, 30775}, {9766, 11058}, {9829, 35955}, {10130, 15810}, {10302, 31078}, {10488, 39689}, {10557, 30789}, {10561, 30476}, {11148, 30769}, {11318, 14263}, {11645, 32729}, {12036, 19662}, {13857, 32583}, {14908, 31152}, {15398, 30745}, {16509, 30739}, {18818, 23297}, {23334, 31099}, {32216, 40727}, {34169, 37350}, {34806, 37746}, {39061, 41136}

X(42008) = isotomic conjugate of isogonal conjugate of X(42007)
X(42008) = trilinear pole of line X(599)X(3906) (the line through X(599) parallel to the trilinear polar of X(599))
X(42008) = barycentric product X(76)*X(42007)
X(42008) = barycentric quotient X(42007)/X(6)

d

X(42009) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-LUCAS-TANGENT

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

X(42009) lies on these lines: {2, 13880}, {20, 488}, {32, 591}, {69, 485}, {76, 6228}, {99, 32437}, {193, 19103}, {298, 6305}, {299, 6304}, {315, 32421}, {325, 35685}, {371, 492}, {486, 10008}, {491, 6118}, {511, 6289}, {599, 626}, {638, 6250}, {1078, 13088}, {1504, 7888}, {3620, 13834}, {3788, 8997}, {3933, 32497}, {5591, 32955}, {6337, 13701}, {6680, 13847}, {8180, 35812}, {9893, 9939}, {10519, 14229}, {12222, 32814}, {13651, 20080}, {13873, 32458}, {32436, 35820}

X(42010) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-McCAY

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

X(42010) lies on these lines: {4, 8591}, {76, 5461}, {98, 7840}, {99, 8786}, {114, 14488}, {148, 32532}, {524, 8587}, {543, 17503}, {598, 2482}, {625, 671}, {1916, 22110}, {3314, 11167}, {3407, 11163}, {5503, 7925}, {5969, 15814}, {7607, 40107}, {7608, 15850}, {7931, 10302}, {8289, 9770}, {8592, 10811}, {8596, 41895}, {8859, 10153}, {10484, 10487}

X(42010) = isotomic conjugate of X(8859)

X(42011) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-ANTI-McCAY

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

X(42011) lies on these lines: {4, 7618}, {6, 10153}, {76, 16509}, {98, 8600}, {262, 9771}, {524, 7607}, {598, 11149}, {671, 11165}, {1007, 11172}, {2996, 11148}, {5485, 39785}, {7612, 9770}, {7777, 8587}, {11167, 22110}, {11668, 15597}, {12040, 17503}

X(42011) = isotomic conjugate of X(8860)

X(42012) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-APUS

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

X(420) lies on these lines: {1, 394}, {2, 15299}, {8, 90}, {9, 55}, {10, 1728}, {31, 1723}, {40, 1726}, {46, 6734}, {56, 18251}, {57, 2886}, {63, 516}, {72, 11496}, {78, 5248}, {84, 3428}, {405, 12710}, {517, 3927}, {528, 3929}, {674, 5227}, {758, 3872}, {936, 8069}, {956, 6001}, {958, 12711}, {968, 3190}, {1617, 5784}, {1621, 41228}, {1698, 17699}, {1708, 2550}, {1763, 6210}, {1824, 12549}, {1836, 5857}, {2099, 6762}, {2308, 28125}, {2328, 4319}, {2968, 3966}, {2975, 10085}, {3305, 6745}, {3338, 10044}, {3358, 10860}, {3436, 12617}, {3650, 7701}, {3680, 6597}, {3719, 3886}, {3740, 15297}, {3870, 15298}, {3928, 31140}, {4295, 9965}, {4314, 5250}, {4430, 4861}, {4652, 12511}, {5172, 5438}, {5173, 12560}, {5220, 17658}, {5269, 8557}, {5271, 17860}, {5437, 31245}, {5696, 15931}, {5709, 37820}, {6067, 11246}, {6690, 7308}, {6736, 18249}, {7411, 25722}, {8257, 26040}, {10582, 11018}, {10679, 34790}, {11679, 17738}, {12513, 12709}, {12527, 21628}, {12704, 24390}, {15503, 26885}, {15587, 37270}, {17742, 21369}, {18499, 37584}, {24929, 31435}, {31424, 40292}

X(42013) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-2ND-PAMFILOS-ZHOU

Barycentrics    a (-a+b+c)*((2*a^4-4*(b+c)*a^3-4*(b+c)^2*a^2+4*(b^2-c^2)*(b-c)*a+2*(b^2-c^2)^2)*S-(a+b-c)*(a-b+c)*(a^4+2*(b+c)*a^3-2*(b+c)^2*a^2-2*(b+c)^3*a+(b^2-c^2)^2)) : :
Barycentrics    a*(a*(a - b - c)*(a + b + c) + 2*(b + c)*S) : :
Barycentrics    Sin[A]/(1 + Cot[A] - Csc[A]) : :
Trilinears    1/(1 - tan(A/2)) : :
Trilinears    (tan A) (1 + cot(A/2)) : :

X(42013) lies on the Feuerbach circumhyperbola, the cubics K233 and K631, and these lines: {1, 371}, {4, 1336}, {6, 9043}, {7, 13389}, {8, 14121}, {9, 5414}, {19, 25}, {21, 1805}, {44, 19037}, {57, 30279}, {65, 13460}, {79, 30426}, {80, 30432}, {84, 6502}, {90, 372}, {104, 18460}, {177, 21465}, {193, 13386}, {256, 30361}, {281, 13454}, {497, 6352}, {1100, 19038}, {1108, 18999}, {1124, 36742}, {1703, 38271}, {1721, 6203}, {1826, 41516}, {1904, 13973}, {3062, 30289}, {3295, 8965}, {3296, 30342}, {3297, 34046}, {3302, 7741}, {3303, 38487}, {3553, 5415}, {4194, 7090}, {5218, 6351}, {5405, 7595}, {5416, 8557}, {7162, 35809}, {7284, 35769}, {13388, 16441}

X(42013) = isogonal conjugate of X(13388)
X(42013) = isogonal conjugate of the complement of X(13386)
X(42013) = polar conjugate of the isotomic conjugate of X(30556)
X(42013) = X(i)-Ceva conjugate of X(j) for these (i,j): {281, 7133}, {6136, 650}, {13390, 16232}
X(42013) = X(i)-cross conjugate of X(j) for these (i,j): {6, 7133}, {650, 6136}, {30376, 7}
X(42013) = X(i)-isoconjugate of X(j) for these (i,j): {1, 13388}, {2, 2067}, {3, 1659}, {7, 5414}, {57, 30557}, {63, 2362}, {77, 7133}, {222, 7090}, {226, 1805}, {1335, 13390}, {3084, 16232}, {6213, 13389}, {6502, 13387}
X(42013) = cevapoint of X(6) and X(34125)
X(42013) = crosspoint of X(i) and X(j) for these (i,j): {1, 15891}, {281, 13426}, {13390, 14121}
X(42013) = crosssum of X(2067) and X(5414)
X(42013) = crossdifference of every pair of points on line {905, 6365}
X(42013) = barycentric product X(i)*X(j) for these {i,j}: {1, 14121}, {4, 30556}, {8, 16232}, {9, 13390}, {92, 2066}, {281, 13389}, {318, 6502}, {1336, 30557}, {1806, 41013}, {6212, 7090}, {7133, 13386}, {13388, 13426}
X(42013) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 13388}, {19, 1659}, {25, 2362}, {31, 2067}, {33, 7090}, {41, 5414}, {55, 30557}, {607, 7133}, {1806, 1444}, {2066, 63}, {2194, 1805}, {5414, 3084}, {6502, 77}, {7133, 13387}, {13388, 13436}, {13389, 348}, {13390, 85}, {13427, 14121}, {14121, 75}, {16232, 7}, {30556, 69}, {30557, 5391}, {34125, 13389}
X(42013) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 6212, 16232}, {1, 32556, 2067}, {19, 33, 7133}, {37, 55, 7133}, {4319, 40131, 7133}, {5089, 7071, 7133}, {5275, 11997, 7133}

X(42014) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-4TH-MIXTILINEAR

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

X(42014) lies on these lines: {2, 8255}, {3, 5696}, {6, 28125}, {7, 2886}, {8, 190}, {9, 55}, {10, 5729}, {44, 28043}, {45, 2340}, {56, 5784}, {63, 15726}, {78, 15254}, {100, 32076}, {142, 17728}, {144, 3434}, {220, 2310}, {329, 7965}, {391, 4012}, {516, 3419}, {517, 4915}, {518, 2099}, {527, 1836}, {956, 2801}, {958, 10394}, {971, 3428}, {1001, 4511}, {1376, 37787}, {1445, 15587}, {2098, 4516}, {2550, 12848}, {3035, 18801}, {3062, 41338}, {3189, 5766}, {3679, 41700}, {3927, 41869}, {3928, 30353}, {3957, 30628}, {3962, 4853}, {4312, 4880}, {4413, 8257}, {4416, 30620}, {4423, 10177}, {4666, 5572}, {4860, 5231}, {5221, 5880}, {5228, 24341}, {5759, 5842}, {5762, 37820}, {5817, 7680}, {6690, 18230}, {8543, 12635}, {10059, 15298}, {10387, 40968}, {10527, 25557}, {11018, 30330}, {11194, 18450}, {11260, 30318}, {11495, 25722}, {16885, 19624}, {17275, 23529}, {17330, 28118}, {17335, 28058}, {17718, 41570}, {18407, 31671}, {21168, 37000}, {28124, 37654}, {29007, 34784}

X(42014) = isogonal conjugate of X(7)-vertex conjugate of X(55)
X(42014) = isotomic conjugate of X(18810)
X(42014) = anticomplement of X(8255)

X(42015) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-HUTSON-EXTOUCH

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

X(42015) lies on the Feuerbach hyperbola and these lines: {1, 3059}, {4, 5223}, {7, 4847}, {8, 9898}, {21, 4326}, {84, 2951}, {104, 6575}, {200, 2346}, {480, 30393}, {516, 10429}, {518, 5665}, {1389, 12654}, {3062, 41338}, {3296, 12864}, {3577, 4915}, {4853, 11526}, {4882, 7160}, {5220, 33576}, {6067, 10980}, {6737, 7320}, {7091, 15587}, {8001, 9874}, {10390, 15185}

X(42016) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-3RD-HATZIPOLAKIS

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

X(42016) lies on these lines: {3, 40632}, {4, 22972}, {54, 2929}, {195, 3521}, {1154, 22549}, {2888, 23308}, {3574, 22971}, {10619, 19460}, {11744, 14049}, {12307, 22978}, {14483, 22750}, {16665, 22962}, {18550, 36747}, {22533, 33565}, {22538, 22585}

X(42017) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-INNER-TANGENTIAL-MID-ARC

Barycentrics    Cos[A/2]*(Sin[B/2] + Sin[C/2]) : :

X(42017) lies on the Feuerbach circumhyperbola and these lines: {1, 188}, {3, 10023}, {4, 12694}, {7, 2091}, {8, 7027}, {9, 6731}, {84, 164}, {104, 3659}, {177, 178}, {3577, 11528}, {7707, 16016}, {8372, 17623}

X(42017) = midpoint of X(7057) and X(11691)
X(42017) = reflection of X(i) in X(j) for these {i,j}: {177, 178}, {188, 18258}
X(42017) = X(i)-Ceva conjugate of X(j) for these (i,j): {188, 15997}, {2090, 16016}, {7048, 2090}
X(42017) = crosspoint of X(i) and X(j) for these (i,j): {8, 188}, {7028, 7048}
X(42017) = crosssum of X(56) and X(266)
X(42017) = trilinear pole of line {650, 6730}
X(42017) = barycentric product X(i)*X(j) for these {i,j}: {8, 16015}, {178, 7028}, {188, 2090}, {312, 16011}, {346, 2091}, {556, 15997}, {3659, 4391}, {7027, 41799}, {7048, 16016}
X(42017) = barycentric quotient X(i)/X(j) for these {i,j}: {177, 18886}, {2090, 4146}, {2091, 279}, {3659, 651}, {7707, 2089}, {15997, 174}, {16011, 57}, {16012, 173}, {16015, 7}, {16016, 7057}, {18887, 177}, {41799, 7371}

X(42018) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-2ND-HATZIPOLAKIS

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

X(42018) lies on these lines: {1, 15851}, {2, 1119}, {3, 9}, {5, 281}, {19, 19541}, {44, 15905}, {45, 216}, {144, 25932}, {219, 1807}, {344, 41005}, {346, 2968}, {440, 18228}, {441, 26685}, {577, 16885}, {1062, 2324}, {1214, 7308}, {1249, 15252}, {1743, 38292}, {1863, 33306}, {2257, 38288}, {3452, 17279}, {3715, 23207}, {3731, 17102}, {3912, 40995}, {4422, 6389}, {5158, 16777}, {5273, 7536}, {6554, 21530}, {6666, 17073}, {7079, 11108}, {7515, 27382}, {8558, 37500}, {10254, 15833}, {11374, 40942}, {15526, 17267}, {17350, 21940}, {20226, 37694}, {20263, 21068}, {20818, 37700}, {21482, 27065}, {21499, 28731}, {25087, 30457}, {34524, 35072}

X(42019) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-MANDART-EXCIRCLES

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

X(42019) lies on these lines: {1, 10601}, {6, 1497}, {8, 36123}, {34, 517}, {46, 269}, {56, 1066}, {58, 8069}, {86, 3085}, {200, 1256}, {219, 7129}, {221, 24028}, {255, 1413}, {521, 5687}, {837, 3436}, {1124, 37885}, {1411, 2098}, {1474, 22132}, {2829, 9370}, {5534, 19354}, {11507, 41442}, {22117, 35448}, {24928, 36754}

X(42019) = isogonal conjugate of X(3086)
X(42019) = cevapoint of X(1124) and X(1335)
X(42019) = perspector of ABC and unary cofactor triangle of Mandart-excircles triangle

X(42020) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-INNER-MIXTILINEAR-TANGENTS

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

X(42020) lies on these lines: {2, 1222}, {4, 10744}, {8, 210}, {10, 11512}, {69, 3264}, {145, 3699}, {345, 6736}, {668, 6604}, {1330, 3421}, {1654, 4461}, {1997, 36846}, {3617, 5484}, {3621, 6555}, {3913, 4571}, {4487, 12649}, {4738, 10573}, {4853, 28808}, {4997, 18220}, {5554, 20905}, {6735, 34823}, {7774, 39354}, {12607, 30828}, {12640, 30568}, {14548, 24524}, {32850, 41772}

X(42021) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-ANTI-INCIRCLE-CIRCLES

Barycentrics    (a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - 4*a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - 4*a^2*b^2 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4) : :
X(42021) = (a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - 4*a^2*c^2 - 2*b^2*c^2 + c^4)*(a^4 - 4*a^2*b^2 + b^4 - 2*a^2*c^2 - 2*b^2*c^2 + c^4) : :
X(42021) = Cot[A]/(2 + Csc[A]^2) : :

X(42021) lies on the Jerabek circumhyperbola, the cubics K471 and K917, and these lines: {2, 1173}, {3, 9936}, {4, 1216}, {6, 140}, {20, 16835}, {30, 22334}, {54, 3523}, {64, 550}, {65, 10044}, {66, 14864}, {68, 3917}, {69, 5447}, {70, 16063}, {71, 24467}, {74, 3522}, {265, 41673}, {343, 38260}, {376, 13452}, {394, 34002}, {599, 23335}, {631, 13472}, {633, 41897}, {634, 41898}, {895, 3546}, {1092, 40441}, {1147, 1176}, {1352, 10627}, {1656, 3527}, {1657, 3426}, {1899, 3519}, {3431, 10299}, {3521, 23039}, {3531, 3851}, {3532, 33923}, {3564, 34817}, {3800, 35364}, {3854, 14487}, {4846, 5562}, {5056, 14483}, {5504, 38727}, {5921, 17712}, {6145, 14791}, {6391, 12359}, {6643, 15077}, {6776, 41435}, {6816, 18555}, {7525, 34437}, {9813, 40107}, {9927, 15749}, {11270, 21735}, {11457, 15108}, {11821, 17702}, {11850, 12164}, {12118, 34801}, {12325, 18368}, {13421, 22336}, {13623, 34783}, {13754, 15740}, {14528, 15712}, {14861, 18436}, {15577, 34207}, {15606, 18420}, {17505, 18404}, {18531, 32533}, {18532, 32534}, {27866, 38534}, {32142, 39571}

X(42021) = isogonal conjugate of X(10594)
X(42021) = isotomic conjugate of the anticomplement of X(10979)
X(42021) = X(10979)-cross conjugate of X(2)
X(42021) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10594}, {19, 5422}, {92, 13345}, {1973, 32832}
X(42021) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 5422}, {6, 10594}, {69, 32832}, {184, 13345}

X(42022) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-LUCAS-ANTIPODAL

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

X(42022) lies on these lines: {155, 1351}, {371, 19442}, {487, 19464}, {494, 3167}, {1147, 26507}, {1161, 12164}, {1993, 26374}, {3564, 5491}, {5200, 26503}, {6193, 24243}, {6391, 10666}, {6406, 19461}, {8681, 9975}, {17839, 17843}, {26461, 30435}

X(42023) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-3RD-TRI-SQUARES

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

X(42023) lies on these lines: {2, 13834}, {4, 5860}, {30, 14232}, {83, 19102}, {262, 9768}, {485, 1991}, {488, 1132}, {524, 1327}, {543, 13712}, {591, 1328}, {598, 12159}, {599, 42024}, {637, 1131}, {641, 3317}, {671, 32808}, {5861, 14241}, {6118, 34089}, {6279, 14238}, {6289, 36723}, {10195, 11313}, {12124, 14229}, {13468, 13835}, {13850, 40727}, {14237, 36719}, {14244, 32419}, {18842, 19053}, {22563, 22645}

X(42023) = isogonal conjugate of X(41411)

X(42024) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-4TH-TRI-SQUARES

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

X(42024) lies on these lines: {2, 13711}, {4, 5861}, {30, 14237}, {83, 19105}, {262, 9767}, {486, 591}, {487, 1131}, {524, 1328}, {543, 13835}, {598, 12158}, {599, 42023}, {638, 1132}, {642, 3316}, {671, 32809}, {1327, 1991}, {5860, 14226}, {6119, 34091}, {6280, 14234}, {6290, 36726}, {10194, 11314}, {12123, 14244}, {13468, 13712}, {13932, 40727}, {14229, 32421}, {14232, 36733}, {18842, 19054}, {22562, 22616}

X(42024) = isogonal conjugate of X(41410)

X(42025) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-11

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

X(42025) lies on these lines: {1, 39711}, {2, 6}, {21, 551}, {58, 17553}, {63, 17207}, {99, 28330}, {274, 29584}, {314, 4980}, {519, 25526}, {553, 1014}, {593, 41311}, {894, 1255}, {903, 17587}, {1010, 3241}, {1281, 3315}, {1408, 4870}, {1412, 4654}, {1509, 30581}, {1790, 6173}, {1817, 17168}, {3175, 4670}, {3187, 41847}, {3218, 37869}, {3219, 28639}, {3616, 16948}, {3656, 4221}, {3679, 4658}, {3828, 17551}, {3929, 18164}, {4034, 28651}, {4184, 4428}, {4225, 40726}, {4234, 38314}, {4361, 25417}, {4418, 5625}, {4496, 7303}, {4954, 18792}, {5253, 35206}, {5284, 33682}, {5287, 41242}, {16046, 16712}, {16052, 26131}, {16700, 25060}, {16753, 25059}, {16826, 32090}, {16834, 17175}, {17045, 26842}, {17169, 35935}, {17376, 41850}, {17557, 28620}, {17589, 31145}, {18185, 35983}, {18200, 31147}, {18601, 25058}, {19290, 19767}, {19796, 37095}, {26643, 33955}, {26840, 41820}, {28194, 37402}, {29570, 32933}, {29574, 33953}, {29586, 33947}, {29597, 40773}, {29615, 33770}, {30599, 30939}, {34914, 40143}

X(42025) = isotomic conjugate of polar conjugate of X(31901)

X(42026) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-14

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

X(42026) lies on these lines: {2, 45}, {89, 40833}, {106, 38314}, {519, 4674}, {551, 4781}, {679, 20072}, {812, 6548}, {1320, 9945}, {2094, 2316}, {2226, 4615}, {3218, 21372}, {3241, 4792}, {3257, 35596}, {4049, 4750}, {4555, 40891}, {4850, 39704}, {6336, 7490}, {6549, 41140}, {10707, 19636}, {14953, 16088}, {16590, 24589}, {17488, 24620}, {17537, 24046}, {24184, 30564}, {25055, 26627}, {31145, 36593}

X(42027) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-16

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

X(42027) lies on these lines: {1, 87}, {2, 17038}, {10, 3728}, {19, 2319}, {37, 714}, {42, 25295}, {65, 740}, {75, 982}, {76, 18832}, {82, 34252}, {244, 20892}, {256, 1221}, {291, 17787}, {313, 3122}, {314, 18827}, {321, 22167}, {335, 1581}, {518, 34434}, {519, 994}, {522, 876}, {536, 13476}, {537, 31165}, {700, 40881}, {730, 21746}, {756, 27438}, {759, 932}, {897, 4598}, {899, 25277}, {984, 7275}, {1278, 4365}, {1400, 4039}, {1655, 25421}, {1740, 24351}, {1910, 34071}, {1999, 13610}, {2053, 2218}, {2162, 2214}, {2217, 23086}, {2228, 18040}, {2321, 21100}, {3121, 22218}, {3596, 17065}, {3644, 39739}, {3663, 39712}, {3701, 22220}, {3840, 20891}, {3842, 27432}, {3948, 21095}, {3997, 21752}, {4043, 22045}, {4044, 22214}, {4135, 22016}, {4377, 21238}, {4664, 39737}, {4674, 4709}, {4704, 32925}, {4735, 28593}, {4788, 17146}, {4871, 20923}, {6385, 23824}, {7209, 39126}, {8769, 11679}, {9902, 21299}, {10009, 33789}, {10479, 39708}, {16571, 24621}, {16888, 21927}, {17063, 30090}, {17279, 24653}, {17793, 28366}, {18785, 21061}, {18833, 21443}, {20688, 22036}, {20876, 23853}, {20917, 41886}, {21219, 26069}, {21278, 23633}, {21435, 23680}, {21759, 40747}, {22316, 40504}, {23051, 29652}, {24225, 39714}, {24325, 27455}, {25120, 28244}, {25121, 30473}, {27450, 31323}, {27478, 40775}, {28358, 30982}, {28522, 35633}, {32039, 35143}, {33296, 40409}, {36494, 40783}

X(42027) = isogonal conjugate of X(38832)
X(42027) = isotomic conjugate of X(33296)

X(42028) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-21

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

X(42028) lies on these lines: {1, 4234}, {2, 6}, {21, 3304}, {27, 39704}, {57, 17207}, {58, 551}, {63, 17394}, {99, 17223}, {110, 9105}, {190, 17019}, {191, 41815}, {274, 16834}, {354, 3794}, {519, 1010}, {552, 553}, {593, 30593}, {846, 5625}, {894, 3175}, {999, 19247}, {1043, 3241}, {1444, 2094}, {1449, 4771}, {1961, 4096}, {1999, 4670}, {3210, 16884}, {3284, 25908}, {3286, 4428}, {3616, 4831}, {3622, 16948}, {3664, 19786}, {3679, 25526}, {3699, 4682}, {3758, 5287}, {3829, 14009}, {3879, 19808}, {3928, 17185}, {3929, 18206}, {4001, 17322}, {4038, 32942}, {4052, 14534}, {4102, 40438}, {4267, 40726}, {4349, 4514}, {4421, 13588}, {4641, 16826}, {4649, 4685}, {4667, 33066}, {4785, 18200}, {4980, 30599}, {5271, 41847}, {5294, 17317}, {8822, 17320}, {9534, 19332}, {11110, 25055}, {14007, 19875}, {16046, 17103}, {16054, 33955}, {16477, 25501}, {16696, 25058}, {16700, 25059}, {16723, 25536}, {16833, 17175}, {17045, 26840}, {17326, 41850}, {17377, 19822}, {17389, 33954}, {17391, 32777}, {18172, 29580}, {18601, 25060}, {18602, 18603}, {18646, 37265}, {19336, 19767}, {19819, 37095}, {19883, 28620}, {23140, 25521}, {23812, 33135}, {24841, 29816}, {26626, 33947}, {29573, 33953}, {29574, 33770}, {29584, 33296}, {29615, 32004}, {30606, 37756}, {31162, 37422}, {34632, 37402}, {37869, 38000}, {37870, 39980}, {39914, 39915}

X(42028) = isotomic conjugate of polar conjugate of X(31903)

X(42029) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-23

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

X(42029) lies on these lines: {2, 37}, {8, 1836}, {10, 33154}, {76, 30713}, {85, 4102}, {92, 1839}, {190, 5271}, {226, 4431}, {274, 29597}, {304, 29574}, {319, 5905}, {322, 31164}, {329, 4886}, {333, 3729}, {519, 17789}, {527, 20920}, {553, 39126}, {594, 27184}, {940, 17116}, {1089, 19875}, {1930, 29573}, {1999, 4363}, {2321, 18134}, {3187, 3758}, {3241, 4673}, {3247, 25507}, {3661, 3782}, {3679, 4385}, {3681, 17163}, {3696, 32937}, {3702, 38314}, {3706, 24349}, {3757, 4428}, {3759, 26223}, {3769, 4418}, {3773, 17889}, {3790, 3925}, {3828, 4066}, {3875, 41823}, {3928, 4659}, {3969, 31019}, {3994, 26037}, {4009, 26038}, {4052, 34258}, {4054, 4417}, {4361, 27064}, {4365, 32771}, {4383, 17117}, {4384, 32088}, {4387, 16823}, {4415, 4665}, {4421, 32932}, {4442, 29667}, {4656, 4967}, {4669, 4737}, {4676, 32914}, {4677, 4692}, {4693, 29651}, {4762, 21438}, {4785, 20952}, {4935, 31145}, {5249, 17233}, {5256, 17160}, {5278, 17336}, {5564, 5739}, {6535, 25957}, {7206, 41859}, {7283, 16418}, {10436, 34064}, {10447, 30710}, {10449, 24473}, {14213, 20921}, {14555, 32087}, {16708, 40493}, {16817, 16857}, {16833, 32104}, {16834, 17143}, {17019, 41847}, {17144, 19722}, {17184, 17228}, {17227, 33146}, {17240, 18139}, {17241, 27186}, {17261, 19732}, {17276, 37653}, {17286, 23681}, {17299, 17778}, {17310, 20432}, {17319, 19701}, {17351, 37652}, {17354, 26723}, {17360, 32859}, {17361, 17483}, {17389, 17762}, {17393, 19684}, {17592, 28522}, {18141, 31995}, {19876, 28611}, {20236, 31142}, {20237, 28609}, {20888, 20917}, {20909, 31147}, {20913, 29577}, {20919, 33941}, {20943, 29593}, {21020, 32925}, {21085, 33101}, {21605, 34284}, {21611, 31150}, {21615, 40087}, {25385, 32855}, {26792, 41821}, {28654, 30596}, {29580, 31997}, {30599, 30939}

X(42029) = isotomic conjugate of X(39948)

X(42030) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-24

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

X(42030) lies on these lines: {2, 319}, {8, 3683}, {9, 4102}, {75, 3578}, {85, 553}, {92, 1839}, {257, 29617}, {312, 3686}, {333, 4034}, {345, 30711}, {519, 31359}, {1121, 3929}, {1220, 3679}, {1311, 8652}, {3687, 30608}, {4384, 32015}, {4997, 11679}, {6557, 14555}, {17281, 34527}, {17294, 32008}, {17363, 37631}, {17743, 19723}, {26860, 28651}, {34234, 37211}

X(42030) = isotomic conjugate of X(4654)

X(42031) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-26

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

X(42031) lies on these lines: {1, 4365}, {3, 29347}, {8, 3585}, {10, 321}, {75, 1125}, {192, 19858}, {226, 21081}, {306, 11263}, {312, 3634}, {341, 4745}, {519, 17789}, {551, 3702}, {594, 22036}, {758, 5295}, {1269, 40034}, {1698, 4671}, {1909, 31013}, {2321, 12609}, {3244, 4968}, {3263, 39580}, {3625, 4692}, {3626, 4385}, {3635, 4673}, {3671, 6358}, {3678, 3696}, {3695, 3841}, {3704, 3822}, {3706, 3874}, {3714, 3754}, {3739, 27784}, {3743, 31993}, {3840, 24176}, {3919, 17751}, {3967, 4015}, {3995, 16828}, {4084, 17164}, {4133, 18697}, {4134, 17163}, {4358, 28611}, {4359, 19862}, {4461, 19843}, {4519, 5439}, {4669, 4696}, {4686, 37592}, {4720, 41696}, {4737, 4746}, {4975, 15808}, {5248, 5695}, {6533, 19883}, {6743, 17860}, {8714, 23685}, {10447, 17733}, {12447, 20320}, {16825, 32104}, {17019, 41812}, {17147, 19863}, {17495, 19864}, {18743, 31253}, {19789, 19836}, {19804, 19878}, {19881, 33150}, {20888, 33930}, {21071, 24044}, {24160, 33160}, {24167, 30942}, {33066, 41814}

X(42032) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-35

Barycentrics    (a - b - c)*(a^2 - b^2 - 4*b*c - c^2) : :
Barycentrics    (a - b - c)*(a^2 - b^2 - 4*b*c - c^2) : :
Barycentrics    (2 + Cos[A])*Csc[A/2]^2 : :

X(42032) lies on these lines: {2, 37}, {8, 3058}, {69, 17781}, {85, 32869}, {190, 34255}, {304, 17079}, {306, 36889}, {329, 17233}, {333, 3161}, {348, 32833}, {376, 7283}, {381, 3695}, {497, 3790}, {553, 3729}, {1043, 36624}, {1089, 10056}, {1479, 7206}, {2321, 14555}, {2325, 5325}, {2899, 3704}, {3543, 7270}, {3685, 3974}, {3687, 4873}, {3703, 11238}, {3706, 27549}, {3782, 29579}, {3886, 4082}, {3912, 4654}, {3969, 31018}, {3994, 33171}, {3996, 5423}, {4135, 33144}, {4415, 17269}, {4431, 7308}, {4656, 17286}, {4754, 17316}, {4854, 9780}, {4942, 4966}, {5233, 8055}, {5309, 7230}, {5712, 17242}, {5749, 34064}, {6541, 26098}, {14552, 17336}, {17078, 32830}, {17314, 27064}, {17340, 26065}, {17361, 20214}, {20925, 32892}, {28809, 30713}, {29616, 33066}

X(42032) = X(i)-isoconjugate of X(j) for these (i,j): {604, 3296}, {1395, 30679}
X(42032) = barycentric product X(i)*X(j) for these {i,j}: {312, 3305}, {314, 3697}, {341, 7190}, {3295, 3596}
X(42032) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 3296}, {345, 30679}, {3295, 56}, {3305, 57}, {3697, 65}, {4917, 1420}, {7190, 269}
X(42032) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 346, 42033}, {2, 42033, 345}, {304, 32836, 17079}, {312, 345, 28808}, {312, 346, 345}, {312, 42033, 2}, {2321, 30568, 14555}, {4387, 6057, 8}, {17264, 42034, 2}, {17279, 22034, 30699}, {17281, 35652, 2}

X(42033) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-37

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

X(42033) lies on these lines: {2, 37}, {8, 3683}, {9, 4886}, {30, 3695}, {35, 7206}, {55, 3790}, {63, 17233}, {81, 17315}, {85, 32836}, {171, 6541}, {190, 306}, {304, 17078}, {319, 3219}, {320, 32858}, {333, 2321}, {341, 36626}, {519, 595}, {553, 3912}, {644, 1812}, {646, 30713}, {726, 33124}, {728, 3719}, {740, 33118}, {846, 3773}, {894, 37631}, {940, 17242}, {1043, 3710}, {1089, 3584}, {1211, 17261}, {1999, 3943}, {2185, 2329}, {2325, 3687}, {2363, 4234}, {2901, 3017}, {3058, 3685}, {3161, 14555}, {3262, 20919}, {3692, 17346}, {3699, 4082}, {3705, 4387}, {3712, 4995}, {3717, 3996}, {3729, 4654}, {3896, 33166}, {3923, 33073}, {3932, 32932}, {3950, 34064}, {3961, 4439}, {3971, 33160}, {3977, 14829}, {3986, 41817}, {3993, 32780}, {3994, 29846}, {4001, 17295}, {4011, 32855}, {4054, 41878}, {4062, 32938}, {4135, 17719}, {4360, 5294}, {4365, 33115}, {4383, 17339}, {4385, 10056}, {4427, 33078}, {4432, 32866}, {4442, 29873}, {4513, 17389}, {4564, 7364}, {4641, 6542}, {4656, 30832}, {4676, 33088}, {4693, 29673}, {4872, 7788}, {4873, 11679}, {4970, 33159}, {5233, 30568}, {5256, 17354}, {5278, 5564}, {5695, 29641}, {5739, 17336}, {6535, 32917}, {7321, 18139}, {7799, 16577}, {11648, 34542}, {15523, 24723}, {17079, 21605}, {17160, 26723}, {17229, 37653}, {17231, 26840}, {17256, 33761}, {17258, 32782}, {17262, 27184}, {17266, 40688}, {17299, 37652}, {17314, 26065}, {17340, 27064}, {17347, 25734}, {17351, 17778}, {17361, 20078}, {17368, 20182}, {17600, 24295}, {19723, 29617}, {21070, 24053}, {28516, 33147}, {28522, 33132}, {29574, 33770}, {29674, 32934}, {29687, 32845}, {32848, 32930}, {32850, 32862}, {32915, 33121}, {32925, 33126}

X(42033) = X(i)-Ceva conjugate of X(j) for these (i,j): {4600, 3699}, {33939, 319}
X(42033) = X(4420)-cross conjugate of X(319)
X(42033) = X(i)-isoconjugate of X(j) for these (i,j): {56, 2160}, {57, 6186}, {79, 604}, {608, 7100}, {649, 26700}, {667, 38340}, {1106, 7110}, {1397, 30690}, {1407, 7073}, {1408, 8818}, {1435, 8606}, {1443, 11060}, {3122, 35049}, {6757, 16947}, {7180, 13486}, {14399, 36064}
X(42033) = crossdifference of every pair of points on line {667, 23751}
X(42033) = barycentric product X(i)*X(j) for these {i,j}: {8, 319}, {9, 33939}, {35, 3596}, {75, 4420}, {261, 7206}, {312, 3219}, {313, 35193}, {314, 3678}, {333, 3969}, {341, 1442}, {346, 17095}, {644, 18160}, {645, 7265}, {646, 14838}, {668, 35057}, {1043, 40999}, {1265, 7282}, {1978, 9404}, {2174, 28659}, {2321, 34016}, {3578, 4102}, {3699, 4467}, {3718, 6198}, {4600, 6741}, {6064, 21054}, {7799, 36910}, {11107, 20336}, {16755, 30730}, {27801, 35192}, {30713, 40214}, {31938, 40422}, {32851, 41226}, {40071, 41502}, {40713, 40714}
X(42033) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 79}, {9, 2160}, {35, 56}, {55, 6186}, {78, 7100}, {100, 26700}, {190, 38340}, {200, 7073}, {312, 30690}, {319, 7}, {346, 7110}, {643, 13486}, {646, 15455}, {1043, 3615}, {1260, 8606}, {1399, 1106}, {1442, 269}, {1792, 1789}, {1825, 1426}, {2003, 1407}, {2174, 604}, {2321, 8818}, {2594, 1042}, {3219, 57}, {3578, 553}, {3596, 20565}, {3647, 32636}, {3678, 65}, {3699, 6742}, {3701, 6757}, {3969, 226}, {4420, 1}, {4467, 3676}, {4567, 35049}, {6198, 34}, {6741, 3120}, {7186, 7248}, {7206, 12}, {7265, 7178}, {7282, 1119}, {7799, 17078}, {9404, 649}, {11107, 28}, {14838, 3669}, {14975, 1395}, {15742, 34922}, {16577, 1427}, {16755, 17096}, {17095, 279}, {17104, 1408}, {18160, 24002}, {21054, 1365}, {22342, 1410}, {31938, 942}, {33939, 85}, {34016, 1434}, {35057, 513}, {35192, 1333}, {35193, 58}, {35194, 1393}, {36910, 1989}, {40214, 1412}, {40713, 554}, {40714, 1081}, {40999, 3668}, {41226, 2006}, {41502, 1474}, {41562, 37566}
X(42033) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 346, 42032}, {2, 42032, 312}, {190, 306, 33066}, {192, 32777, 19786}, {304, 32833, 17078}, {312, 345, 32851}, {321, 32849, 33116}, {345, 346, 312}, {345, 42032, 2}, {1278, 24789, 19820}, {3219, 3969, 319}, {3685, 3703, 4514}, {3695, 7283, 7270}, {3712, 6057, 7081}, {3923, 33092, 33073}, {15523, 32936, 24723}, {17147, 33157, 16706}, {29674, 32934, 33068}, {32848, 32930, 33071}, {32858, 32933, 320}, {32862, 32929, 32850}, {32915, 33161, 33121}, {32925, 33156, 33126}

X(42034) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-40

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

X(42034) lies on these lines: {2, 37}, {8, 3967}, {76, 4052}, {92, 4102}, {190, 3929}, {226, 17233}, {304, 29573}, {314, 41629}, {319, 329}, {320, 34255}, {333, 17336}, {341, 1089}, {519, 4066}, {984, 4135}, {1999, 3758}, {2064, 17378}, {2321, 4417}, {2886, 3790}, {2999, 17160}, {3187, 41242}, {3241, 3702}, {3452, 4431}, {3661, 4415}, {3685, 4428}, {3696, 27538}, {3705, 3829}, {3706, 32937}, {3729, 3928}, {3740, 4903}, {3757, 4387}, {3759, 27064}, {3769, 3923}, {3773, 3944}, {3782, 17227}, {3869, 14973}, {3966, 17777}, {3969, 31053}, {3974, 32850}, {3994, 31330}, {4044, 6376}, {4054, 17240}, {4125, 4745}, {4362, 4676}, {4365, 32931}, {4421, 5695}, {4442, 29679}, {4519, 10453}, {4647, 19875}, {4654, 17297}, {4656, 5224}, {4659, 30567}, {4669, 4717}, {4677, 4737}, {4693, 29670}, {4696, 31145}, {4734, 28484}, {4762, 21611}, {4886, 31018}, {4968, 38314}, {5249, 17241}, {5256, 41823}, {5271, 17335}, {5287, 41847}, {5564, 14555}, {5712, 17315}, {5737, 17261}, {5905, 17361}, {6057, 29641}, {6382, 21615}, {6535, 25760}, {6541, 33111}, {7283, 16370}, {7321, 18141}, {8055, 32087}, {16284, 17294}, {16817, 17542}, {16833, 17143}, {16834, 17144}, {17056, 17242}, {17116, 37674}, {17117, 37679}, {17158, 33941}, {17228, 27184}, {17262, 38000}, {17277, 30568}, {17283, 23681}, {17285, 25527}, {17310, 17789}, {17329, 37653}, {17351, 37683}, {17354, 40940}, {17360, 33066}, {17369, 29841}, {17386, 17778}, {17394, 34064}, {17591, 28516}, {17781, 18750}, {17786, 27792}, {18145, 33935}, {18150, 36791}, {18156, 29574}, {20888, 29600}, {20911, 33780}, {20913, 29582}, {20917, 29577}, {20927, 31142}, {20952, 31147}, {21093, 33084}, {21600, 39996}, {25385, 33092}, {29597, 31997}, {30710, 39948}, {30854, 33938}, {32017, 36603}, {34284, 40023}

X(42034) = isotomic conjugate of X(39980)

X(42035) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-7th-FERMAT-DAO

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

Let A' be the orthocenter of triangle BCX(13), and define B' and C' cyclically. Then X(42035) is the orthocenter of triangle A'B'C'. (Randy Hutson, May 31, 2021)

X(42035) lies on these lines: {2, 22574}, {4, 530}, {13, 524}, {14, 543}, {17, 9763}, {18, 9885}, {98, 531}, {99, 40672}, {115, 599}, {262, 9762}, {298, 671}, {538, 21359}, {598, 12155}, {633, 22235}, {1992, 9112}, {2482, 16645}, {3424, 41022}, {5464, 7610}, {5466, 23870}, {5469, 5969}, {5470, 14645}, {5472, 15534}, {5858, 12816}, {5859, 33607}, {5862, 33602}, {5863, 33604}, {6114, 9877}, {6115, 9770}, {6777, 9830}, {7607, 13083}, {7612, 21156}, {7620, 31710}, {8587, 8594}, {9113, 18800}, {9114, 9886}, {9166, 40706}, {9180, 23871}, {9741, 38412}, {9760, 36776}, {10754, 22573}, {11121, 14904}, {11122, 41135}, {11180, 41045}, {12817, 33459}, {18842, 37641}, {22570, 36967}, {33603, 35690}, {33605, 35691}, {33606, 35696}, {35304, 36772}, {36316, 40709}

X(42035) = isogonal conjugate of X(41406)
X(42035) = isotomic conjugate of X(37786)
X(42035) = {X(599),X(40727)}-harmonic conjugate of X(42036)

X(42036) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-8th-FERMAT-DAO

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

Let A' be the orthocenter of triangle BCX(14), and define B' and C' cyclically. Then X(42036) is the orthocenter of triangle A'B'C'. (Randy Hutson, May 31, 2021)

X(42036) lies on these lines: {2, 22573}, {4, 531}, {13, 543}, {14, 524}, {17, 9886}, {18, 9761}, {98, 530}, {99, 40671}, {115, 599}, {262, 9760}, {299, 671}, {538, 21360}, {598, 12154}, {634, 22237}, {1992, 9113}, {2482, 16644}, {3424, 41023}, {5463, 7610}, {5466, 23871}, {5469, 14645}, {5470, 5969}, {5471, 15534}, {5858, 33606}, {5859, 12817}, {5862, 33605}, {5863, 33603}, {6114, 9770}, {6115, 9877}, {6778, 9830}, {7607, 13084}, {7612, 21157}, {7620, 31709}, {8587, 8595}, {9112, 18800}, {9116, 9885}, {9166, 40707}, {9180, 23870}, {10754, 22574}, {11121, 41135}, {11122, 14905}, {11180, 41044}, {12816, 33458}, {18842, 37640}, {22568, 36968}, {33602, 35694}, {33604, 35695}, {33607, 35692}, {36317, 40710}

X(42036) = isogonal conjugate of X(41407)
X(42036) = isotomic conjugate of X(37785)
X(42036) = {X(599),X(40727)}-harmonic conjugate of X(42035)

X(42037) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-42

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

X(42037) lies on these lines: {2, 32}, {6, 16276}, {22, 7878}, {82, 17264}, {308, 14614}, {384, 19568}, {428, 32085}, {598, 16277}, {1176, 34608}, {3108, 35929}, {5007, 16950}, {7394, 7856}, {7760, 16932}, {7827, 34603}, {8667, 18092}, {9870, 34482}, {10191, 35277}, {16275, 18907}, {17409, 36794}, {30435, 40022}, {38817, 39927}

X(42038) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-49

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

X(42038) lies on these lines: {1, 4757}, {2, 38}, {31, 3677}, {42, 4003}, {201, 5298}, {354, 1962}, {519, 3670}, {524, 18183}, {536, 4022}, {551, 2292}, {614, 3929}, {678, 3938}, {750, 18193}, {846, 3315}, {896, 7191}, {976, 16371}, {986, 3241}, {1086, 29690}, {1089, 6534}, {1201, 31165}, {1254, 5434}, {1393, 11237}, {1647, 4415}, {1739, 4745}, {2310, 11238}, {2650, 24473}, {3058, 7004}, {3218, 9340}, {3666, 17449}, {3679, 24443}, {3681, 36634}, {3720, 3999}, {3722, 17596}, {3728, 4688}, {3741, 4980}, {3742, 3989}, {3752, 21805}, {3782, 3829}, {3828, 24167}, {3840, 3994}, {3873, 17591}, {3920, 18201}, {3957, 17593}, {3976, 38314}, {3987, 34641}, {4414, 4428}, {4640, 29818}, {4650, 17024}, {4664, 21330}, {4669, 4695}, {4683, 5211}, {4697, 29823}, {4722, 29821}, {4860, 5311}, {4884, 29687}, {5293, 36006}, {5573, 17125}, {7174, 17124}, {9345, 10980}, {11194, 37549}, {12782, 29577}, {16418, 28082}, {17446, 37756}, {17450, 28606}, {17483, 17722}, {17716, 23958}, {17721, 33098}, {19875, 24046}, {20942, 32925}, {21020, 24165}, {24231, 33105}, {24239, 32856}, {24477, 33128}, {24627, 32923}, {25557, 29682}, {26015, 33145}, {26840, 32844}, {29668, 32933}, {29676, 33146}, {29680, 33103}, {29816, 37520}, {29840, 33067}, {29844, 32950}, {31148, 40471}, {33595, 37599}

X(42038) = {X(2),X(38)}-harmonic conjugate of X(42039)

X(42039) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-50

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

X(42039) lies on these lines: {1, 4127}, {2, 38}, {10, 6534}, {31, 3929}, {44, 29819}, {63, 9340}, {201, 5434}, {518, 1962}, {519, 2292}, {536, 3728}, {612, 3928}, {678, 3961}, {726, 4980}, {846, 3722}, {896, 3920}, {976, 16370}, {1254, 11237}, {2310, 3058}, {3175, 31136}, {3219, 17469}, {3666, 21805}, {3670, 3828}, {3677, 17125}, {3679, 4642}, {3717, 32781}, {3741, 3994}, {3938, 4428}, {3953, 19883}, {3967, 31241}, {3987, 38098}, {4022, 4755}, {4357, 33162}, {4364, 29685}, {4389, 33117}, {4414, 4421}, {4415, 29690}, {4419, 33094}, {4424, 4669}, {4641, 29816}, {4643, 32854}, {4661, 17592}, {4664, 22167}, {4695, 4745}, {4703, 29832}, {4850, 36634}, {4921, 35623}, {4971, 23928}, {4995, 7004}, {5220, 17017}, {5293, 13587}, {6646, 33072}, {7069, 11238}, {7262, 29815}, {7322, 17124}, {10385, 24430}, {15170, 35194}, {15254, 29818}, {16830, 32940}, {16857, 28082}, {17133, 23668}, {17163, 28516}, {17184, 21026}, {17258, 32947}, {17261, 32943}, {17301, 21039}, {17598, 27065}, {17722, 26792}, {18183, 20582}, {19875, 24443}, {19876, 24046}, {20942, 30942}, {21342, 30950}, {21806, 28606}, {24697, 33090}, {25006, 33145}, {28840, 40471}, {29664, 33101}, {31145, 37598}, {32927, 38000}, {32933, 36480}

X(42039) = {X(2),X(38)}-harmonic conjugate of X(42038)

X(42040) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-53

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

X(42040) lies on these lines: {1, 9352}, {2, 38}, {31, 18193}, {42, 3999}, {57, 17469}, {88, 3961}, {519, 3953}, {536, 21330}, {551, 3670}, {597, 18183}, {614, 896}, {748, 3929}, {750, 3677}, {774, 10072}, {899, 21342}, {902, 4906}, {976, 16417}, {986, 38314}, {1155, 29818}, {1193, 24473}, {1393, 5434}, {1401, 21969}, {1646, 22199}, {1647, 3782}, {1739, 4669}, {1962, 17591}, {2292, 25055}, {3120, 3829}, {3241, 3976}, {3315, 17596}, {3666, 17450}, {3679, 24046}, {3720, 4003}, {3722, 4421}, {3752, 17449}, {3924, 11194}, {3994, 20942}, {4022, 4688}, {4428, 17595}, {4677, 4695}, {4740, 22167}, {4745, 24168}, {4860, 17017}, {4980, 24165}, {5211, 33067}, {5272, 36263}, {6384, 20889}, {7004, 11238}, {7191, 18201}, {9340, 23958}, {9350, 16496}, {11019, 33145}, {12782, 29582}, {16370, 28082}, {17301, 21346}, {17533, 28096}, {17593, 29817}, {17598, 27003}, {17722, 26842}, {17728, 33143}, {17872, 37756}, {18173, 18601}, {21805, 36634}, {24177, 33136}, {24440, 31145}, {25557, 29688}, {27002, 32927}, {29690, 40688}, {29819, 37520}, {37549, 40726}

X(42040) = {X(2),X(38)}-harmonic conjugate of X(42041)

X(42041) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-54

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

X(42041) lies on these lines: {1, 3988}, {2, 38}, {9, 17469}, {10, 4980}, {44, 29816}, {45, 3938}, {201, 11237}, {210, 3989}, {519, 14020}, {612, 896}, {748, 7174}, {750, 3928}, {774, 10056}, {976, 16418}, {1962, 3681}, {2292, 3679}, {2308, 15481}, {2310, 10385}, {3058, 7069}, {3688, 21969}, {3715, 17017}, {3722, 4428}, {3728, 4664}, {3828, 24443}, {3829, 29690}, {3961, 33761}, {3967, 30970}, {3971, 4981}, {3994, 31330}, {4009, 31241}, {4078, 33081}, {4104, 32848}, {4113, 4681}, {4126, 4364}, {4422, 29686}, {4424, 4745}, {4656, 33136}, {4722, 5220}, {4755, 21330}, {4995, 24431}, {5268, 36263}, {5293, 17549}, {6376, 20889}, {10459, 31165}, {16675, 41711}, {16830, 32938}, {17257, 33074}, {17258, 32948}, {17260, 32923}, {17261, 32945}, {17542, 28082}, {17598, 35595}, {19346, 34247}, {21020, 32925}, {21026, 27184}, {21805, 28606}, {24697, 33091}, {31136, 35652}

X(42041) = {X(2),X(38)}-harmonic conjugate of X(42040)

X(42042) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-59

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

X(42042) lies on these lines: {1, 2}, {6, 3750}, {30, 37529}, {35, 19346}, {55, 4649}, {81, 2177}, {85, 25721}, {87, 40433}, {100, 37604}, {165, 1002}, {171, 4421}, {192, 36645}, {291, 5269}, {381, 37699}, {518, 17592}, {527, 4335}, {536, 3510}, {553, 4334}, {581, 28194}, {672, 16667}, {846, 3751}, {902, 37685}, {968, 1757}, {984, 37593}, {986, 24473}, {1011, 3746}, {1051, 9052}, {1100, 17716}, {1126, 5248}, {1376, 4038}, {1386, 17715}, {1449, 2276}, {1468, 17549}, {1575, 16884}, {1621, 16468}, {1962, 3681}, {1985, 37721}, {2108, 3722}, {2238, 3247}, {2334, 19765}, {2356, 7714}, {2667, 4664}, {3136, 37719}, {3158, 35104}, {3242, 17600}, {3303, 16058}, {3304, 16059}, {3475, 33147}, {3656, 5396}, {3689, 37595}, {3723, 37673}, {3729, 40721}, {3731, 37657}, {3737, 4948}, {3755, 17889}, {3829, 17717}, {3873, 17591}, {3875, 37632}, {3896, 4980}, {3913, 11358}, {3928, 17594}, {3989, 4661}, {3993, 32937}, {4021, 30946}, {4026, 33084}, {4085, 18134}, {4090, 41839}, {4191, 5563}, {4192, 7982}, {4199, 11523}, {4255, 40726}, {4300, 34632}, {4343, 6172}, {4360, 4479}, {4383, 16484}, {4512, 40774}, {4650, 4689}, {4658, 8715}, {4660, 17778}, {4663, 7262}, {4734, 24165}, {4785, 23655}, {4849, 15569}, {4851, 33079}, {4854, 33101}, {4870, 37694}, {4883, 17063}, {4921, 10458}, {4954, 18792}, {4966, 33174}, {4970, 24349}, {5247, 16418}, {5264, 16395}, {5331, 39969}, {5710, 16396}, {5712, 33109}, {5718, 33141}, {7196, 25716}, {7991, 37400}, {9909, 37580}, {10107, 31503}, {10222, 19540}, {10385, 14547}, {11518, 16056}, {11520, 37467}, {11522, 22392}, {13587, 37608}, {15485, 32911}, {15621, 18185}, {16189, 19647}, {16370, 37573}, {16371, 37607}, {16496, 37676}, {16777, 21904}, {17056, 32865}, {17317, 24760}, {17379, 36646}, {17393, 24766}, {17718, 33135}, {18140, 25287}, {18169, 41629}, {18173, 25059}, {19684, 32945}, {20182, 41711}, {21223, 25264}, {21746, 21849}, {21806, 28606}, {21838, 24528}, {23638, 39543}, {24217, 37662}, {24524, 31008}, {25074, 40133}, {27804, 32925}, {31034, 32947}, {31165, 37548}, {32921, 41823}, {33158, 38047}, {33771, 37603}, {34612, 37631}, {37355, 37722}, {37365, 37727}, {37370, 37724}, {37732, 38021}

X(42042) = {X(2),X(42)}-harmonic conjugate of X(42043)
X(42042) = {X(42),X(17018)}-harmonic conjugate of X(1)

X(42043) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-60

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

X(42043) lies on these lines: {1, 2}, {6, 3550}, {9, 21904}, {30, 37699}, {39, 24528}, {55, 16468}, {100, 28523}, {165, 511}, {192, 4090}, {210, 17592}, {238, 4428}, {291, 39980}, {381, 37529}, {518, 17591}, {549, 37698}, {672, 31508}, {726, 4734}, {872, 4096}, {984, 4849}, {1002, 36603}, {1126, 25440}, {1376, 4649}, {1449, 1575}, {1468, 13587}, {1743, 2276}, {1757, 3929}, {2177, 8616}, {2238, 3731}, {2258, 18793}, {2663, 16571}, {3052, 16477}, {3158, 3795}, {3247, 37673}, {3304, 16409}, {3501, 20970}, {3510, 41142}, {3654, 5396}, {3666, 21870}, {3689, 17716}, {3711, 20182}, {3736, 18192}, {3746, 16058}, {3750, 4383}, {3751, 3928}, {3755, 3944}, {3829, 33141}, {3875, 4479}, {3896, 32931}, {3973, 37657}, {3984, 11533}, {3993, 27538}, {3996, 25496}, {4038, 4413}, {4085, 4417}, {4192, 7991}, {4203, 8715}, {4234, 4281}, {4255, 11194}, {4272, 17281}, {4335, 6172}, {4551, 4654}, {4641, 17601}, {4650, 4663}, {4689, 7262}, {4857, 6818}, {4863, 17722}, {4866, 16850}, {4921, 18169}, {4970, 32937}, {4980, 32860}, {5010, 19346}, {5247, 16370}, {5264, 16396}, {5270, 6817}, {5400, 30308}, {5563, 16059}, {5718, 32865}, {5881, 37365}, {7196, 25721}, {7714, 40976}, {7982, 19540}, {9342, 9345}, {9350, 37633}, {9548, 14636}, {9909, 37576}, {16189, 19546}, {16371, 37608}, {16417, 37607}, {16418, 37573}, {16484, 37679}, {16667, 17754}, {17379, 39972}, {17598, 41711}, {17718, 33132}, {21805, 28606}, {21849, 23638}, {24217, 37663}, {24524, 34020}, {25075, 40133}, {25264, 41840}, {25286, 30964}, {25287, 31008}, {25568, 33152}, {25590, 37632}, {31034, 32948}, {31162, 37732}, {31165, 37598}, {32926, 41823}, {33160, 38047}, {36646, 37677}, {37355, 37720}, {37370, 37721}

X(42043) = {X(2),X(42)}-harmonic conjugate of X(42042)
X(42043) = {X(42),X(43)}-harmonic conjugate of X(1)

X(42044) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-68

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

X(42044) lies on these lines: {2, 37}, {43, 3994}, {81, 3729}, {190, 3187}, {210, 28484}, {306, 33151}, {354, 28555}, {519, 3869}, {528, 34603}, {538, 17389}, {553, 28301}, {726, 3873}, {740, 3681}, {984, 4365}, {1255, 10436}, {1717, 3811}, {1836, 33093}, {1999, 32933}, {2171, 4654}, {2292, 3679}, {2321, 32782}, {2325, 26723}, {2895, 17299}, {2901, 3868}, {3058, 28503}, {3120, 33092}, {3159, 3876}, {3219, 17262}, {3240, 3967}, {3247, 5333}, {3305, 17151}, {3416, 33100}, {3578, 17333}, {3663, 33172}, {3685, 3891}, {3703, 33134}, {3706, 7226}, {3712, 29665}, {3760, 20889}, {3769, 4427}, {3773, 32776}, {3782, 3943}, {3790, 4972}, {3875, 32911}, {3896, 32937}, {3912, 33146}, {3914, 32862}, {3920, 5695}, {3923, 32928}, {3929, 4921}, {3932, 33131}, {3938, 4693}, {3944, 32848}, {3950, 5249}, {3969, 27184}, {3971, 28522}, {3993, 32771}, {4011, 32924}, {4062, 33101}, {4102, 17271}, {4110, 40603}, {4135, 4970}, {4360, 26223}, {4361, 27065}, {4362, 32936}, {4363, 17019}, {4387, 7191}, {4415, 33077}, {4418, 9347}, {4430, 28582}, {4439, 33117}, {4442, 29641}, {4659, 5287}, {4661, 28581}, {4676, 17150}, {4851, 17483}, {4854, 29667}, {4956, 11235}, {4967, 28651}, {5057, 33088}, {5256, 41242}, {5271, 33761}, {5278, 17261}, {5905, 17314}, {6057, 29679}, {6535, 32784}, {6541, 25957}, {6542, 32859}, {9352, 29649}, {10129, 29671}, {11238, 21333}, {11246, 28556}, {15523, 33154}, {16727, 40493}, {17011, 17318}, {17144, 31036}, {17155, 28516}, {17175, 29597}, {17184, 17233}, {17242, 18139}, {17243, 27186}, {17276, 32863}, {17319, 19684}, {17336, 19742}, {17351, 37685}, {17361, 31011}, {17393, 19717}, {17763, 32934}, {18145, 28659}, {19738, 29584}, {19875, 39708}, {20017, 33066}, {20691, 31060}, {24210, 33089}, {24248, 33078}, {24703, 32842}, {25269, 37652}, {29674, 33145}, {29687, 33149}, {30568, 37680}, {32846, 33098}, {32847, 33094}, {32852, 33099}, {32854, 33095}, {32921, 32930}, {32926, 32929}, {33128, 33164}, {33135, 33161}, {33143, 33158}, {33152, 33156}

X(42044) = anticomplement of X(42051)

X(42045) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-69

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

X(42045) lies on these lines: {1, 540}, {2, 6}, {30, 944}, {72, 10108}, {306, 4667}, {320, 17011}, {321, 3879}, {376, 41810}, {445, 648}, {511, 3873}, {519, 2650}, {538, 17389}, {551, 41815}, {553, 41801}, {754, 29584}, {894, 3969}, {903, 41823}, {1100, 17184}, {1171, 25536}, {1230, 30939}, {1449, 32774}, {1959, 3970}, {1962, 17770}, {2092, 18601}, {2308, 24542}, {3664, 4359}, {3679, 41812}, {3758, 32858}, {3759, 27186}, {3782, 24724}, {3909, 40952}, {3989, 17771}, {3995, 17390}, {4026, 20290}, {4038, 32843}, {4062, 4697}, {4357, 41820}, {4360, 17483}, {4363, 20017}, {4393, 33146}, {4421, 41811}, {4442, 33097}, {4450, 17018}, {4478, 6539}, {4644, 32933}, {4649, 4972}, {4658, 5051}, {4722, 29653}, {4754, 6542}, {4851, 26223}, {4854, 17491}, {4938, 21085}, {4981, 34379}, {5625, 6536}, {13745, 38314}, {14544, 41571}, {16477, 29851}, {17019, 33066}, {17020, 24183}, {17120, 33157}, {17121, 26724}, {17147, 17365}, {17317, 27065}, {17344, 37869}, {17364, 28606}, {17377, 28605}, {17484, 34064}, {17768, 27804}, {20072, 33761}, {21020, 23812}, {23731, 28840}, {23905, 31064}, {25056, 27782}, {26580, 37595}, {33081, 33682}

X(42046) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-72

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

X(42046) lies on these lines: {1, 190}, {2, 292}, {31, 4586}, {37, 20141}, {239, 20331}, {664, 36276}, {716, 1966}, {2279, 3226}, {3768, 28840}, {4465, 16826}, {16522, 20176}, {16526, 17261}, {16827, 28283}, {17475, 29584}, {29580, 39916}

X(42046) = reflection of X(43270) in X(2)

X(42047) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-76

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

X(42047) lies on these lines: {2, 37}, {4, 519}, {8, 4415}, {165, 28557}, {226, 17314}, {329, 5839}, {527, 10442}, {545, 19645}, {726, 24477}, {740, 25568}, {940, 7222}, {964, 38314}, {966, 4656}, {1266, 30567}, {1766, 3928}, {1999, 4644}, {2298, 35578}, {2901, 3487}, {3241, 5716}, {3452, 17151}, {3474, 17763}, {3475, 32915}, {3729, 37642}, {3769, 24280}, {3782, 34255}, {3914, 3974}, {3950, 25525}, {3971, 38057}, {4054, 5712}, {4080, 20017}, {4220, 4421}, {4361, 18228}, {4362, 5698}, {4371, 14555}, {4402, 8055}, {4419, 11679}, {4442, 10327}, {4659, 39595}, {4873, 20106}, {4891, 11038}, {4916, 17778}, {5016, 31145}, {5241, 41915}, {5273, 17262}, {5658, 29016}, {5743, 32087}, {5846, 9812}, {6703, 7229}, {9778, 28530}, {9779, 28472}, {11194, 37399}, {11235, 28503}, {17233, 26132}, {17276, 37655}, {17351, 37666}, {17390, 41825}, {21949, 39570}, {25055, 37037}, {28580, 34607}, {30568, 37650}, {31995, 37674}

X(42048) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-77

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

X(42048) lies on these lines: {2, 85}, {7, 1146}, {196, 1855}, {220, 31994}, {344, 18159}, {481, 7090}, {482, 14121}, {514, 5603}, {527, 1478}, {544, 34627}, {1111, 4000}, {1360, 5434}, {1699, 2391}, {1737, 7960}, {3241, 14942}, {3474, 28118}, {3476, 9318}, {3732, 5819}, {4419, 31397}, {4421, 9305}, {4644, 18391}, {7223, 40127}, {10481, 23058}, {21258, 32086}, {24477, 35102}, {28609, 29594}, {28610, 28638}

X(42049) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-78

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

X(42049) lies on these lines: {2, 37}, {8, 4884}, {40, 376}, {57, 17314}, {63, 5839}, {333, 4371}, {524, 28610}, {726, 25568}, {740, 24477}, {1699, 28557}, {2325, 23511}, {3161, 37679}, {3241, 5710}, {3474, 32845}, {3475, 17155}, {3687, 4419}, {3875, 37642}, {3913, 37328}, {3929, 37654}, {3950, 5437}, {4035, 4862}, {4361, 5273}, {4398, 26132}, {4421, 28503}, {4641, 20043}, {4644, 32939}, {4851, 21454}, {4852, 37666}, {5325, 16833}, {5698, 32934}, {5712, 7222}, {5737, 32087}, {5745, 17151}, {5846, 9778}, {7228, 41825}, {9812, 28530}, {10445, 17132}, {10856, 17133}, {16046, 41629}, {17056, 31995}, {17262, 18228}, {17299, 37655}, {17595, 34255}, {19732, 41915}, {22145, 37672}, {24165, 38053}, {24248, 32855}, {24280, 33071}, {24621, 24654}

X(42050) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-79

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

X(42050) lies on these lines: {1, 527}, {2, 85}, {7, 34522}, {9, 1323}, {77, 34526}, {142, 21314}, {144, 6603}, {165, 2391}, {220, 651}, {277, 34578}, {514, 5657}, {518, 11200}, {544, 944}, {1121, 33298}, {1642, 38941}, {2094, 5228}, {2124, 3929}, {3474, 28125}, {3496, 3928}, {4971, 6764}, {5088, 5819}, {5222, 17595}, {5723, 5744}, {5731, 5845}, {6173, 10481}, {7181, 40127}, {11201, 15726}, {16020, 26273}, {17301, 40133}, {17762, 25242}, {25568, 35102}, {26658, 32024}

X(42051) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-80

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

X(42051) lies on these lines: {1, 19276}, {2, 37}, {8, 33068}, {38, 3696}, {43, 4706}, {44, 32933}, {57, 17151}, {63, 4361}, {65, 519}, {81, 4852}, {210, 726}, {239, 4641}, {244, 4365}, {306, 1086}, {314, 16700}, {319, 26840}, {333, 17117}, {354, 740}, {518, 17155}, {527, 14557}, {528, 7667}, {535, 34666}, {537, 4685}, {545, 17781}, {551, 4065}, {614, 5695}, {899, 3967}, {940, 3875}, {966, 41915}, {980, 32104}, {982, 3706}, {986, 3679}, {1155, 4362}, {1211, 3663}, {1266, 3687}, {1269, 21857}, {1279, 32929}, {1386, 4418}, {1738, 3703}, {1812, 16759}, {1999, 17160}, {2321, 24177}, {2895, 17345}, {2901, 5439}, {2999, 4659}, {3006, 21949}, {3058, 28580}, {3219, 17348}, {3305, 17262}, {3670, 5295}, {3681, 28582}, {3683, 16825}, {3689, 32920}, {3697, 24068}, {3704, 23536}, {3714, 24443}, {3729, 4383}, {3740, 28555}, {3741, 4003}, {3742, 28484}, {3744, 32922}, {3745, 3980}, {3757, 4689}, {3773, 24169}, {3823, 32862}, {3834, 32858}, {3838, 29849}, {3840, 4519}, {3844, 33125}, {3873, 28581}, {3886, 17597}, {3896, 17140}, {3912, 40688}, {3928, 24310}, {3929, 16552}, {3966, 24248}, {3969, 17231}, {3971, 28516}, {3991, 14746}, {3999, 10453}, {4001, 17362}, {4009, 16569}, {4052, 14554}, {4054, 37662}, {4096, 28554}, {4135, 24003}, {4360, 37595}, {4363, 5256}, {4371, 14552}, {4387, 5272}, {4395, 26723}, {4398, 27184}, {4440, 33066}, {4496, 7019}, {4527, 24200}, {4640, 32845}, {4644, 20043}, {4646, 4968}, {4647, 37592}, {4656, 5241}, {4660, 4914}, {4663, 32940}, {4670, 17011}, {4682, 32928}, {4693, 29820}, {4696, 21896}, {4716, 32913}, {4762, 16892}, {4849, 17165}, {4860, 39594}, {4884, 25006}, {4886, 6646}, {4906, 32943}, {4970, 24325}, {5249, 7263}, {5271, 17119}, {5287, 17318}, {5294, 17366}, {5325, 21233}, {5564, 37653}, {5712, 31995}, {5739, 17276}, {5839, 9965}, {5847, 11246}, {5880, 33088}, {5918, 28850}, {6603, 28951}, {7283, 33309}, {7321, 17778}, {9776, 17314}, {10167, 29016}, {10436, 20182}, {11679, 17595}, {15254, 32936}, {16834, 20963}, {16885, 25734}, {17020, 41242}, {17045, 41850}, {17135, 21342}, {17143, 37596}, {17144, 24621}, {17229, 33172}, {17235, 32782}, {17254, 41816}, {17351, 32911}, {17372, 32863}, {17374, 20017}, {17376, 26842}, {17600, 24342}, {17733, 32636}, {17889, 32855}, {19701, 25590}, {20292, 32842}, {20508, 23878}, {20691, 20913}, {23681, 30811}, {24715, 32866}, {25125, 31060}, {28557, 40998}, {29584, 33296}, {32778, 33149}, {32857, 32861}, {33075, 33102}, {33077, 33146}, {33089, 33131}, {33132, 33167}, {33147, 33160}, {34728, 34742}, {36871, 39948}, {37631, 39774}

X(42051) = complement of X(42044)
X(42051) = anticomplement of X(35652)

X(42052) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-83

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

Let LA be the radical axis of the circumcircle and reflected A-Neuberg circle, and define LB and LC cyclically. Let A' = LB∩LC, and define B' and C' cyclically. A'B'C' is homothetic to ABC at X(251). X(42052) = X(2)-of-A'B'C'. (Randy Hutson, May 31, 2021)

X(42052) lies on these lines: {2, 32}, {69, 41464}, {311, 34603}, {428, 7767}, {524, 23642}, {1180, 7893}, {1225, 30737}, {2979, 3852}, {3108, 33021}, {3266, 10691}, {6636, 7768}, {7750, 8024}, {7779, 38862}, {7788, 9723}, {7794, 35929}, {7826, 8267}, {7854, 16932}, {7860, 37353}, {20063, 40002}

X(42053) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-89

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

X(42053) lies on these lines: {2, 38}, {10, 21342}, {354, 740}, {519, 942}, {545, 25371}, {551, 3743}, {553, 752}, {614, 4672}, {726, 3742}, {1086, 29655}, {1125, 39544}, {3175, 28554}, {3306, 32920}, {3315, 4418}, {3678, 6532}, {3679, 28611}, {3741, 3999}, {3757, 18201}, {3829, 20256}, {3846, 24231}, {3848, 28582}, {3980, 17597}, {4085, 24177}, {4090, 16602}, {4359, 4732}, {4362, 4860}, {4363, 29668}, {4432, 29820}, {4434, 27003}, {4666, 32934}, {4685, 22295}, {4688, 24182}, {4697, 7191}, {4883, 4970}, {4891, 28522}, {4974, 32913}, {5211, 33097}, {5272, 32935}, {5625, 17600}, {5880, 29844}, {7292, 32940}, {7321, 33106}, {11246, 28494}, {17147, 17450}, {17155, 28516}, {17595, 29651}, {17726, 23812}, {17767, 40998}, {18193, 32916}, {25351, 29673}, {25557, 29671}, {26842, 32844}, {29817, 32845}, {29843, 33149}

X(42053) = complement of X(42054)

X(42054) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-91

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

X(42054) lies on these lines: {1, 33309}, {2, 38}, {8, 4703}, {9, 32920}, {10, 3782}, {37, 22199}, {45, 29651}, {63, 4434}, {72, 519}, {190, 3961}, {200, 32934}, {210, 726}, {306, 4439}, {329, 4865}, {518, 3971}, {536, 4685}, {545, 24336}, {551, 27784}, {612, 4697}, {740, 3681}, {752, 17781}, {1757, 3791}, {2667, 4664}, {2796, 34612}, {2886, 21093}, {2887, 3717}, {3187, 4753}, {3219, 32927}, {3242, 4011}, {3666, 4090}, {3678, 24068}, {3679, 4385}, {3699, 17596}, {3706, 4135}, {3715, 16825}, {3718, 17274}, {3740, 24165}, {3741, 3967}, {3749, 25728}, {3750, 17261}, {3790, 33084}, {3840, 4009}, {3874, 4075}, {3891, 4974}, {3920, 4672}, {3932, 33064}, {3935, 32936}, {3938, 4432}, {3994, 17135}, {4003, 6686}, {4113, 4709}, {4362, 5220}, {4415, 29673}, {4421, 20760}, {4422, 29672}, {4655, 10327}, {4660, 30615}, {4661, 32915}, {4679, 29844}, {4683, 33091}, {4732, 28605}, {4756, 32930}, {4849, 4970}, {4871, 21342}, {4892, 29641}, {4899, 24210}, {5223, 32853}, {5297, 32940}, {6646, 33079}, {7174, 25496}, {8616, 17336}, {9954, 21084}, {16496, 30568}, {17147, 21805}, {17330, 40085}, {17350, 17716}, {17484, 33072}, {20834, 24820}, {20942, 31137}, {24821, 32939}, {24841, 29820}, {25351, 33146}, {26580, 33162}, {26792, 32844}, {27065, 32923}, {27184, 28595}, {28516, 32860}, {29819, 41241}, {32847, 33066}, {32850, 33099}, {32862, 33065}, {33117, 33151}, {33118, 33152}, {33126, 33164}

X(42054) = anticomplement of X(42053)

X(42055) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-92

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

X(42055) lies on these lines: {1, 4234}, {2, 38}, {7, 4865}, {10, 40688}, {57, 4434}, {65, 519}, {75, 39742}, {190, 29820}, {320, 32866}, {321, 17449}, {354, 726}, {518, 4685}, {527, 24180}, {536, 13476}, {545, 24424}, {551, 6051}, {614, 32935}, {740, 3873}, {894, 17598}, {903, 40038}, {976, 19336}, {1086, 29673}, {1836, 29844}, {1930, 17179}, {2275, 28592}, {2796, 3058}, {2887, 24231}, {3218, 32923}, {3241, 17480}, {3242, 3980}, {3315, 32930}, {3662, 28595}, {3677, 25496}, {3705, 4892}, {3741, 21342}, {3742, 3971}, {3782, 29655}, {3791, 32913}, {3816, 21093}, {3840, 3999}, {3923, 17597}, {3957, 32845}, {3961, 24841}, {3967, 4871}, {3993, 4883}, {3995, 17450}, {4003, 6685}, {4052, 11019}, {4090, 16610}, {4363, 29652}, {4430, 32860}, {4432, 32933}, {4440, 33095}, {4514, 32857}, {4672, 7191}, {4860, 29649}, {4884, 25557}, {4891, 28555}, {4906, 17351}, {4921, 32914}, {4974, 32912}, {4980, 31136}, {4987, 17362}, {5211, 33096}, {7081, 18201}, {7292, 32938}, {7321, 33109}, {8666, 37227}, {8669, 32636}, {8720, 37080}, {11246, 17766}, {11346, 28082}, {16711, 17141}, {16825, 19723}, {17017, 19738}, {17146, 17147}, {17483, 32844}, {17595, 29670}, {17599, 19722}, {20834, 24826}, {25351, 33117}, {26840, 33076}, {26842, 33072}, {27003, 32927}, {28516, 32915}, {29817, 32936}, {29835, 33145}, {29840, 33097}, {29843, 33154}, {33067, 33090}, {33069, 33089}, {33120, 33146}, {33121, 33147}, {33124, 33167}

X(42055) = anticomplement of X(4096)

X(42056) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-94

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

X(42056) lies on these lines: {2, 38}, {9, 4434}, {10, 4009}, {43, 4664}, {210, 392}, {312, 3679}, {321, 4937}, {536, 3740}, {551, 4090}, {3626, 4519}, {3706, 4669}, {3715, 29649}, {3826, 21093}, {3828, 31993}, {3967, 4688}, {3985, 17281}, {4023, 6541}, {4104, 29594}, {4113, 34641}, {4126, 29655}, {4358, 31136}, {4533, 35633}, {4671, 4732}, {4672, 5297}, {4685, 35652}, {4697, 5268}, {4740, 26038}, {4865, 18228}, {5293, 13735}, {7308, 32920}, {7322, 25496}, {8580, 32934}, {16833, 30393}, {17271, 20947}, {17274, 30758}, {17338, 17725}, {18743, 31137}, {19875, 27798}, {21060, 29600}, {21805, 31035}, {25351, 33151}, {28554, 32925}, {29577, 33084}, {32927, 35595}

X(42057) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-99

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

X(42057) lies on these lines: {1, 2}, {30, 12545}, {38, 3993}, {81, 32943}, {149, 32949}, {244, 3896}, {320, 33095}, {333, 16484}, {350, 3879}, {354, 740}, {376, 10476}, {497, 32946}, {515, 39550}, {516, 10439}, {518, 3971}, {527, 35645}, {528, 38484}, {536, 13476}, {537, 3175}, {553, 7248}, {672, 3950}, {726, 3873}, {752, 3058}, {902, 37639}, {940, 32941}, {982, 4970}, {1001, 32853}, {1011, 8666}, {1015, 21877}, {1269, 4479}, {1279, 3791}, {1575, 17388}, {1621, 32919}, {2321, 24512}, {2796, 5208}, {2887, 4966}, {2901, 3881}, {3136, 24387}, {3304, 11358}, {3315, 32924}, {3550, 37684}, {3663, 30941}, {3664, 4441}, {3685, 32913}, {3706, 4883}, {3742, 28581}, {3750, 14829}, {3751, 4011}, {3755, 24169}, {3769, 17715}, {3875, 30962}, {3886, 3980}, {3913, 16059}, {3946, 30945}, {3995, 17145}, {3996, 17122}, {4038, 5263}, {4090, 4358}, {4135, 17165}, {4191, 8715}, {4192, 5882}, {4359, 4709}, {4360, 17598}, {4365, 17140}, {4387, 32935}, {4417, 24217}, {4421, 23853}, {4430, 32925}, {4432, 4641}, {4514, 32846}, {4649, 32942}, {4667, 24330}, {4684, 24210}, {4688, 25124}, {4693, 32939}, {4715, 24705}, {4780, 24177}, {4849, 24003}, {4851, 4865}, {4852, 4906}, {4856, 37657}, {4889, 20530}, {5247, 33309}, {5284, 32864}, {5563, 13588}, {6682, 37593}, {8616, 37683}, {8731, 24391}, {10222, 37365}, {10441, 28194}, {10465, 34628}, {10471, 17180}, {11246, 17764}, {12437, 16056}, {12513, 16058}, {12536, 37110}, {12607, 37355}, {15485, 37652}, {17056, 21242}, {17147, 17449}, {17151, 30350}, {17155, 28522}, {17231, 28595}, {17233, 33169}, {17234, 32865}, {17300, 33109}, {17314, 17754}, {17315, 37686}, {17318, 24691}, {17377, 30963}, {17390, 21264}, {17448, 21838}, {17597, 32921}, {17778, 33106}, {17781, 35614}, {18059, 21443}, {18134, 21241}, {18139, 33136}, {19540, 37727}, {20162, 24586}, {20963, 21071}, {22214, 24513}, {24552, 33682}, {24692, 33094}, {27269, 41912}, {28562, 34611}, {30986, 37730}, {32773, 33087}, {32863, 32947}, {32945, 37633}, {33069, 33134}, {33121, 33158}, {33124, 33135}, {34379, 40998}, {34612, 35626}, {38832, 41629}

X(42058) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-103

Barycentrics    5*a^3 - b^3 - c^3 : :

X(42058) lies on these lines: {2, 31}, {209, 34607}, {519, 32912}, {545, 3891}, {674, 1992}, {744, 4740}, {758, 3241}, {896, 29832}, {902, 31034}, {1617, 41801}, {1621, 17378}, {2094, 2835}, {2390, 11206}, {3006, 36277}, {3187, 28580}, {3744, 4715}, {3920, 17333}, {4217, 17751}, {4651, 37654}, {4655, 29831}, {4660, 21747}, {5055, 20575}, {5711, 14020}, {7357, 33767}, {10304, 30269}, {16704, 21283}, {17342, 33078}, {17382, 32950}, {17486, 39347}, {17491, 26228}, {20045, 24695}, {21282, 24597}, {26065, 28599}, {27754, 33073}, {28494, 33128}, {28498, 33156}, {28503, 32933}, {28508, 33143}, {28512, 33161}, {28566, 33114}, {28570, 33122}, {31303, 32941}, {34611, 41629}

X(42058) = anticomplement of X(31134)

X(42059) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-HATZIPOLAKIS-MOSES

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

X(42059) lies on the Jerabek hyperbola and these lines: {4, 17824}, {68, 10224}, {74, 6799}, {195, 265}, {1199, 38006}, {1498, 18550}, {2917, 5944}, {3519, 14076}, {3521, 18400}, {3574, 22466}, {5900, 17823}, {6143, 13418}, {10274, 13621}, {10628, 11559}, {13423, 37932}, {21400, 36749}, {32351, 33565}

X(42059) = isogonal conjugate of anticomplement of X(6143)

X(42060) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-2ND-INNER-VECTEN

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

X(42060) lies on these lines: {2, 13921}, {20, 487}, {32, 1991}, {69, 486}, {76, 6229}, {99, 32434}, {193, 19104}, {298, 6301}, {299, 6300}, {315, 32419}, {325, 35684}, {372, 491}, {485, 10008}, {492, 6119}, {511, 6290}, {599, 626}, {637, 6251}, {1078, 13087}, {1505, 7888}, {3620, 13711}, {3788, 13989}, {3933, 32494}, {5590, 32955}, {6337, 13821}, {6680, 13846}, {8184, 35813}, {9891, 9939}, {10519, 14244}, {13770, 20080}, {13926, 32458}, {32433, 35821}

X(42061) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-3RD-BROCARD

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

X(42061) lies on these lines: {32, 8789}, {39, 695}, {76, 115}, {511, 694}, {736, 18829}, {737, 805}, {2458, 9467}, {3094, 19602}, {3199, 17980}, {3721, 3865}, {5167, 16068}, {11654, 18872}

X(42061) = X(i)-isoconjugate of X(j) for these (i,j): {385, 3113}, {1580, 3114}, {1926, 18898}, {1966, 3407}
X(42061) = barycentric product X(i)*X(j) for these {i,j}: {694, 3094}, {1581, 3116}, {1916, 3117}, {3314, 9468}, {3862, 3863}, {5117, 17970}, {17415, 18829}, {18896, 18899}
X(42061) = barycentric quotient X(i)/X(j) for these {i,j}: {694, 3114}, {1967, 3113}, {3094, 3978}, {3116, 1966}, {3117, 385}, {3314, 14603}, {8789, 18898}, {9006, 5027}, {9468, 3407}, {14251, 8840}, {17415, 804}, {17938, 33514}, {18829, 9063}, {18899, 1691}
X(42061) = {X(9468),X(17970)}-harmonic conjugate of X(32)

X(42062) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-4TH-INNER-FERMAT-DAO-NHI

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

X(42062) lies on these lines: {2, 5472}, {4, 20415}, {13, 35931}, {14, 5459}, {17, 530}, {18, 22489}, {76, 9763}, {99, 40671}, {396, 671}, {524, 40707}, {531, 11602}, {543, 11122}, {597, 11161}, {5466, 9194}, {8595, 23302}, {8838, 36316}, {12821, 35019}, {33475, 40706}, {33602, 33623}, {33604, 33610}

X(42062) = isotomic conjugate of complement of X(37786)

X(42063) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-4TH-OUTER-FERMAT-DAO-NHI

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

X(42063) lies on these lines: {2, 5471}, {4, 20416}, {13, 5460}, {14, 35932}, {17, 22490}, {18, 531}, {76, 9761}, {99, 40672}, {395, 671}, {524, 40706}, {530, 11603}, {543, 11121}, {597, 11161}, {5466, 9195}, {8594, 23303}, {8836, 36317}, {12820, 35020}, {33474, 40707}, {33603, 33625}, {33605, 33611}

X(42063) = isotomic conjugate of complement of X(37785)

X(42064) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-K721-OSCULATING

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

X(42064) lies on these lines: {1, 528}, {33, 8735}, {55, 2170}, {103, 517}, {200, 1146}, {220, 2310}, {664, 3957}, {1121, 3935}, {1212, 3939}, {1642, 2161}, {2342, 41339}, {4511, 14942}, {4666, 17044}, {4845, 6603}, {5527, 38454}

X(42064) = isogonal conjugate of X(38459)

X(42065) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-7TH-BROCARD

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

X(42065) lies on these lines: {25, 110}, {32, 1147}, {49, 10547}, {98, 325}, {155, 2353}, {184, 23217}, {394, 2351}, {487, 6402}, {488, 6401}, {511, 39644}, {684, 878}, {1092, 40319}, {1402, 36051}, {1570, 34382}, {3289, 14600}, {3455, 13754}, {3456, 41597}, {5504, 9517}, {6193, 32816}, {8884, 18831}, {9149, 9925}, {10723, 33803}, {14601, 23098}, {14908, 22115}, {17702, 39838}, {33581, 41619}, {35456, 41533}, {40352, 41615}

X(42065) = isogonal conjugate of X(44145)
X(42065) = trilinear pole of line X(577)X(3049)
X(42065) = cevapoint of X(184) and X(3289)
X(42065) = crosspoint of X(2987) and X(43705)
X(42065) = crosssum of X(230) and X(460)
X(42065) = trilinear product X(i)*X(j) for these {i,j}: {3, 36051}, {31, 43705}, {48, 2987}, {63, 32654}, {184, 8773}, {255, 3563}, {293, 34157}, {810, 10425}, {822, 32697}, {4575, 35364}, {8781, 9247}, {36105, 39201}

X(42066) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-APOLLONIUS

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

X(42066) lies on these lines: {1, 21}, {2, 20360}, {42, 23928}, {65, 6042}, {181, 756}, {192, 20536}, {210, 2643}, {321, 1109}, {740, 4388}, {2611, 21333}, {2632, 4094}, {3725, 4016}, {3728, 26893}, {5202, 26885}, {17476, 21342}, {21020, 25760}, {21254, 33124}, {21805, 24048}, {23913, 26037}

X(42067) = X(4)X(6335)∩X(19)X(1843)

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

X(42067) lies on the orthic inconic and these lines: {4, 6335}, {19, 1843}, {25, 3052}, {28, 17946}, {34, 9432}, {125, 5521}, {607, 8541}, {608, 1974}, {1015, 22096}, {1086, 2969}, {1331, 24822}, {1474, 17962}, {1829, 2836}, {1880, 2880}, {2082, 40673}, {2310, 14935}, {2393, 7297}, {3125, 3271}, {3270, 11918}, {5139, 5517}, {5190, 5509}, {5341, 9969}, {6212, 6291}, {6213, 6406}, {7300, 32366}, {8735, 8754}, {9822, 27059}, {11574, 26998}, {14936, 20975}

X(42067) = polar conjugate of X(31625)
X(42067) = isogonal conjugate of the isotomic conjugate of X(2969)
X(42067) = polar conjugate of the isotomic conjugate of X(1015)
X(42067) = polar conjugate of the isogonal conjugate of X(1977)
X(42067) = orthic-isogonal conjugate of X(6591)
X(42067) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 6591}, {19, 2489}, {915, 3310}, {2969, 1015}
X(42067) = X(1977)-cross conjugate of X(1015)
X(42067) = X(i)-isoconjugate of X(j) for these (i,j): {3, 7035}, {48, 31625}, {59, 3718}, {63, 1016}, {69, 765}, {71, 4601}, {72, 4600}, {77, 4076}, {78, 4998}, {100, 4561}, {190, 1332}, {201, 6064}, {304, 1252}, {305, 1110}, {306, 4567}, {326, 15742}, {345, 4564}, {646, 1813}, {664, 4571}, {668, 1331}, {799, 4574}, {905, 6632}, {906, 1978}, {1018, 4563}, {1264, 7012}, {1265, 7045}, {1275, 3692}, {3690, 24037}, {3694, 4620}, {3695, 24041}, {3699, 6516}, {3949, 4590}, {3952, 4592}, {3977, 5376}, {4033, 4558}, {4158, 23999}, {4554, 4587}, {4570, 20336}, {4575, 27808}, {4619, 15416}, {5383, 22370}, {6065, 7182}, {6332, 31615}, {6386, 32656}, {7257, 23067}, {23990, 40364}
X(42067) = crosspoint of X(4) and X(6591)
X(42067) = crosssum of X(i) and X(j) for these (i,j): {3, 1332}, {69, 4561}, {100, 17776}, {345, 4571}
X(42067) = crossdifference of every pair of points on line {1332, 4561}
X(42067) = barycentric product X(i)*X(j) for these {i,j}: {4, 1015}, {6, 2969}, {11, 608}, {19, 244}, {25, 1086}, {27, 3122}, {28, 3125}, {32, 2973}, {34, 2170}, {56, 8735}, {92, 3248}, {125, 36420}, {264, 1977}, {278, 3271}, {281, 1357}, {286, 3121}, {393, 3937}, {512, 17925}, {513, 6591}, {593, 8754}, {607, 1358}, {648, 8034}, {649, 7649}, {667, 17924}, {764, 1783}, {1096, 3942}, {1111, 1973}, {1118, 7117}, {1119, 14936}, {1146, 1398}, {1365, 2189}, {1395, 4858}, {1396, 4516}, {1435, 2310}, {1436, 38362}, {1474, 3120}, {1509, 2971}, {1565, 2207}, {1647, 8752}, {1824, 16726}, {1880, 18191}, {1897, 21143}, {1974, 23989}, {2052, 22096}, {2087, 36125}, {2203, 16732}, {2333, 17205}, {2423, 39534}, {2489, 7192}, {2501, 3733}, {3669, 18344}, {3675, 8751}, {5317, 18210}, {6335, 8027}, {6545, 8750}, {7115, 7336}, {7154, 38374}, {7215, 36434}, {7250, 17926}, {7337, 26932}, {14571, 15635}, {20975, 36419}, {21132, 32674}
X(42067) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 31625}, {19, 7035}, {25, 1016}, {28, 4601}, {244, 304}, {607, 4076}, {608, 4998}, {649, 4561}, {667, 1332}, {669, 4574}, {764, 15413}, {1015, 69}, {1084, 3690}, {1086, 305}, {1111, 40364}, {1356, 2197}, {1357, 348}, {1395, 4564}, {1398, 1275}, {1474, 4600}, {1919, 1331}, {1973, 765}, {1974, 1252}, {1977, 3}, {1980, 906}, {2170, 3718}, {2189, 6064}, {2203, 4567}, {2207, 15742}, {2489, 3952}, {2501, 27808}, {2969, 76}, {2971, 594}, {2973, 1502}, {3022, 30681}, {3063, 4571}, {3120, 40071}, {3121, 72}, {3122, 306}, {3124, 3695}, {3125, 20336}, {3248, 63}, {3249, 1459}, {3271, 345}, {3733, 4563}, {3937, 3926}, {4128, 4019}, {6591, 668}, {7117, 1264}, {7649, 1978}, {8027, 905}, {8034, 525}, {8735, 3596}, {8750, 6632}, {8754, 28654}, {14936, 1265}, {17924, 6386}, {17925, 670}, {18344, 646}, {21143, 4025}, {21762, 20760}, {22096, 394}, {23560, 22149}, {23989, 40050}, {36420, 18020}, {38986, 22370}

X(42068) = X(4)X(6331)∩X(25)X(694)

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

X(42068) lies on the orthic inconic and these lines: {4, 6331}, {25, 694}, {125, 5139}, {136, 2679}, {512, 6388}, {1084, 23216}, {1112, 1843}, {1974, 32740}, {2872, 6784}, {2971, 3124}, {5167, 32269}, {6786, 41360}, {6995, 25046}, {11332, 23584}, {16240, 40325}, {34383, 36898}, {34417, 40951}, {34980, 38356}

X(42068) = isogonal conjugate of the isotomic conjugate of X(2971)
X(42068) = polar conjugate of X(44168)
X(42068) = polar conjugate of the isotomic conjugate of X(1084)
X(42068) = polar conjugate of the isogonal conjugate of X(9427)
X(42068) = orthic-isogonal conjugate of X(2489)
X(42068) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 2489}, {2971, 1084}, {3563, 2491}
X(42068) = X(9427)-cross conjugate of X(1084)
X(42068) = X(i)-isoconjugate of X(j) for these (i,j): {63, 34537}, {69, 24037}, {249, 40364}, {304, 4590}, {305, 24041}, {670, 4592}, {799, 4563}, {1101, 40050}, {3718, 7340}, {4176, 23999}, {4558, 4602}, {4561, 4623}, {4575, 4609}, {4601, 17206}, {6064, 7182}, {14208, 31614}, {23995, 40360}
X(42068) = crosspoint of X(4) and X(2489)
X(42068) = crosssum of X(3) and X(4563)
X(42068) = crossdifference of every pair of points on line {4563, 24284}
X(42068) = polar conjugate of barycentric square of X(670)
X(42068) = pole wrt polar circle of line X(670)X(888) (the tangent to the Steiner circumellipse at X(670))
X(42068) = barycentric product X(i)*X(j) for these {i,j}: {4, 1084}, {6, 2971}, {25, 3124}, {32, 8754}, {92, 4117}, {112, 22260}, {115, 1974}, {125, 36417}, {232, 15630}, {264, 9427}, {278, 7063}, {281, 1356}, {470, 41993}, {471, 41994}, {512, 2489}, {648, 23099}, {669, 2501}, {1501, 2970}, {1824, 3121}, {1924, 24006}, {1973, 2643}, {1977, 7140}, {2052, 23216}, {2086, 17980}, {2203, 21833}, {2207, 20975}, {2333, 3122}, {2422, 17994}, {2969, 7109}, {6331, 23610}, {8753, 21906}, {9426, 14618}, {27369, 34294}, {34980, 36434}
X(42068) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 34537}, {115, 40050}, {338, 40360}, {669, 4563}, {1084, 69}, {1356, 348}, {1924, 4592}, {1973, 24037}, {1974, 4590}, {2489, 670}, {2501, 4609}, {2643, 40364}, {2970, 40362}, {2971, 76}, {3124, 305}, {4117, 63}, {7063, 345}, {8754, 1502}, {9426, 4558}, {9427, 3}, {22260, 3267}, {23099, 525}, {23216, 394}, {23610, 647}, {36417, 18020}, {41993, 40709}, {41994, 40710}

X(42069) = X(3)X(7040)∩X(4)X(653)

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

X(42069) lies on the orthic inconic and these lines: {3, 7040}, {4, 653}, {11, 2969}, {25, 1857}, {29, 17947}, {33, 7140}, {118, 4605}, {125, 20620}, {158, 235}, {243, 468}, {281, 1863}, {430, 1859}, {1086, 7649}, {1118, 37197}, {1146, 3270}, {1398, 40836}, {1461, 18328}, {1824, 1856}, {1826, 1827}, {1885, 1940}, {1892, 39531}, {1984, 40616}, {2310, 8735}, {2355, 16240}, {2501, 2643}, {2968, 14010}, {3022, 4092}, {3120, 38362}, {3271, 5532}, {4081, 5514}, {5095, 40950}, {5190, 15607}, {6335, 34337}, {6555, 7046}, {9669, 31387}, {12138, 36123}, {32706, 38554}

X(42069) = polar conjugate of X(1275)
X(42069) = isogonal conjugate of the isotomic conjugate of X(21666)
X(42069) = polar conjugate of the isotomic conjugate of X(1146)
X(42069) = polar conjugate of the isogonal conjugate of X(14936)
X(42069) = orthic-isogonal conjugate of X(3064)
X(42069) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 3064}, {158, 2501}, {1857, 18344}, {7040, 650}, {21666, 1146}, {40836, 6591}
X(42069) = X(i)-cross conjugate of X(j) for these (i,j): {4516, 2310}, {14936, 1146}
X(42069) = pole wrt polar circle of trilinear polar of X(1275) (line X(100)X(658))
X(42069) = trilinear pole, wrt orthic triangle, of line X(1)X(4)
X(42069) = crosspoint of X(i) and X(j) for these (i,j): {4, 3064}, {90, 1021}, {393, 7649}, {3900, 41509}
X(42069) = crosssum of X(i) and X(j) for these (i,j): {3, 1813}, {46, 1020}, {222, 36059}, {394, 1331}, {651, 3562}, {1461, 4306}
X(42069) = crossdifference of every pair of points on line {906, 1813}
X(42069) = X(i)-isoconjugate of X(j) for these (i,j): {3, 7045}, {48, 1275}, {59, 77}, {63, 1262}, {69, 24027}, {78, 7339}, {108, 6517}, {109, 6516}, {222, 4564}, {249, 37755}, {304, 23979}, {348, 2149}, {394, 7128}, {603, 4998}, {651, 1813}, {658, 906}, {664, 36059}, {765, 7053}, {905, 4619}, {934, 1331}, {1016, 7099}, {1020, 4558}, {1092, 24032}, {1101, 6356}, {1102, 23985}, {1110, 7056}, {1252, 7177}, {1260, 24013}, {1332, 1461}, {1409, 4620}, {1410, 4600}, {1414, 23067}, {1425, 24041}, {1439, 4570}, {1802, 23586}, {1804, 7012}, {3692, 23971}, {3964, 24033}, {4554, 32660}, {4566, 4575}, {4569, 32656}, {4571, 6614}, {4574, 4637}, {4587, 4617}, {6507, 23984}, {7115, 7183}, {7138, 18020}
X(42069) = barycentric product X(i)*X(j) for these {i,j}: {4, 1146}, {6, 21666}, {8, 8735}, {11, 281}, {19, 24026}, {25, 23978}, {29, 21044}, {33, 4858}, {92, 2310}, {125, 36421}, {158, 34591}, {220, 2973}, {244, 7101}, {264, 14936}, {273, 3119}, {278, 4081}, {286, 36197}, {318, 2170}, {331, 3022}, {346, 2969}, {393, 2968}, {522, 3064}, {523, 17926}, {607, 34387}, {653, 23615}, {1021, 24006}, {1086, 7046}, {1093, 35072}, {1109, 2326}, {1111, 7079}, {1119, 23970}, {1847, 24010}, {1857, 26932}, {2052, 3270}, {2322, 3120}, {2332, 21207}, {2501, 7253}, {2638, 6521}, {2970, 7054}, {3239, 7649}, {3271, 7017}, {3900, 17924}, {4183, 16732}, {4391, 18344}, {4397, 6591}, {4516, 31623}, {5514, 40836}, {6506, 7040}, {6520, 24031}, {6524, 23983}, {6526, 40616}, {7003, 38357}, {7058, 8754}, {7071, 23989}, {7140, 26856}, {8755, 15633}, {14618, 21789}, {23104, 32674}
X(42069) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 1275}, {11, 348}, {19, 7045}, {25, 1262}, {29, 4620}, {33, 4564}, {115, 6356}, {244, 7177}, {281, 4998}, {607, 59}, {608, 7339}, {650, 6516}, {652, 6517}, {657, 1331}, {663, 1813}, {1015, 7053}, {1021, 4592}, {1086, 7056}, {1096, 7128}, {1119, 23586}, {1146, 69}, {1358, 30682}, {1365, 20618}, {1398, 23971}, {1435, 24013}, {1847, 24011}, {1973, 24027}, {1974, 23979}, {2170, 77}, {2212, 2149}, {2310, 63}, {2322, 4600}, {2326, 24041}, {2332, 4570}, {2501, 4566}, {2638, 6507}, {2643, 37755}, {2968, 3926}, {2969, 279}, {3022, 219}, {3063, 36059}, {3064, 664}, {3119, 78}, {3121, 1410}, {3124, 1425}, {3125, 1439}, {3239, 4561}, {3248, 7099}, {3270, 394}, {3271, 222}, {3709, 23067}, {3900, 1332}, {4081, 345}, {4092, 26942}, {4105, 4587}, {4130, 4571}, {4183, 4567}, {4516, 1214}, {4524, 4574}, {4858, 7182}, {5532, 26932}, {6059, 7115}, {6520, 24032}, {6524, 23984}, {6591, 934}, {7004, 7183}, {7046, 1016}, {7071, 1252}, {7079, 765}, {7101, 7035}, {7117, 1804}, {7253, 4563}, {7649, 658}, {8641, 906}, {8735, 7}, {8750, 4619}, {8754, 6354}, {14936, 3}, {17924, 4569}, {17925, 4616}, {17926, 99}, {18344, 651}, {21044, 307}, {21666, 76}, {21789, 4558}, {23615, 6332}, {23970, 1265}, {23978, 305}, {23983, 4176}, {24010, 3692}, {24012, 1802}, {24026, 304}, {24031, 1102}, {26932, 7055}, {34591, 326}, {35072, 3964}, {35508, 1260}, {36197, 72}, {36421, 18020}, {38362, 14256}, {39014, 20776}, {39687, 1092}
X(42069) = {X(281),X(1863)}-harmonic conjugate of X(7071)

X(42070) = X(4)X(145)∩X(25)X(23858)

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

X(42070) lies on the orthic inconic and these lines: {4, 145}, {25, 23858}, {33, 7140}, {125, 1834}, {430, 8754}, {468, 5205}, {1830, 17660}, {1864, 3270}, {3689, 3943}, {4120, 4895}, {4370, 22371}, {4742, 38462}, {7071, 34446}, {14191, 41556}

X(42070) = isogonal conjugate of isotomic conjugate of polar conjugate of X(2226)
X(42070) = pole wrt polar circle of line X(900)X(903)
X(42070) = polar conjugate of the isotomic conjugate of X(4370)
X(42070) = polar conjugate of the isogonal conjugate of X(1017)
X(42070) = orthic-isogonal conjugate of X(8756)
X(42070) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 8756}, {32704, 14425}
X(42070) = X(1017)-cross conjugate of X(4370)
X(42070) = cevapoint of X(3251) and X(4542)
X(42070) = crosspoint of X(4) and X(8756)
X(42070) = crosssum of X(3) and X(1797)
X(42070) = crossdifference of every pair of points on line {1797, 22086} (the tangent to the MacBeath circumconic at X(1797))
X(42070) = X(i)-isoconjugate of X(j) for these (i,j): {3, 679}, {63, 2226}, {77, 1318}, {88, 1797}, {304, 41935}, {903, 36058}, {905, 4638}, {1459, 4618}, {1790, 30575}, {20568, 32659}
X(42070) = barycentric product X(i)*X(j) for these {i,j}: {4, 4370}, {19, 4738}, {25, 36791}, {44, 38462}, {92, 678}, {264, 1017}, {278, 4152}, {281, 1317}, {286, 21821}, {519, 8756}, {653, 4543}, {1824, 16729}, {1877, 2325}, {1897, 6544}, {2052, 22371}, {3251, 6335}, {3689, 37790}, {3943, 37168}, {6336, 8028}, {15742, 35092}
X(42070) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 679}, {25, 2226}, {607, 1318}, {678, 63}, {902, 1797}, {1017, 3}, {1317, 348}, {1783, 4618}, {1824, 30575}, {1974, 41935}, {2251, 36058}, {3251, 905}, {4152, 345}, {4370, 69}, {4542, 26932}, {4543, 6332}, {4738, 304}, {6544, 4025}, {8028, 3977}, {8750, 4638}, {8756, 903}, {9459, 32659}, {21821, 72}, {22371, 394}, {35092, 1565}, {36791, 305}, {38462, 20568}
X(42070) = {X(1862),X(1897)}-harmonic conjugate of X(2969)

X(42071) = X(6)X(3270)∩X(19)X(1843)

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

X(42071) lies on the orthic inconic and these lines: {6, 3270}, {19, 1843}, {25, 20468}, {31, 14935}, {125, 15904}, {184, 40141}, {518, 1861}, {692, 1974}, {926, 20455}, {1783, 5185}, {1814, 2808}, {1824, 1830}, {1826, 1827}, {1865, 2870}, {1897, 32029}, {2356, 20683}, {2807, 3751}, {2875, 8541}, {4437, 34337}, {5095, 8674}, {6184, 20776}, {13476, 21252}, {16973, 23050}, {18026, 36215}

X(42071) = reflection of X(3270) in X(6)
X(42071) = isogonal conjugate of the isotomic conjugate of X(34337)
X(42071) = polar conjugate of the isotomic conjugate of X(6184)
X(42071) = polar conjugate of the isogonal conjugate of X(39686)
X(42071) = orthic-isogonal conjugate of X(5089)
X(42071) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 5089}, {34337, 6184}
X(42071) = X(39686)-cross conjugate of X(6184)
X(42071) = X(i)-isoconjugate of X(j) for these (i,j): {63, 6185}, {105, 31637}, {304, 41934}, {673, 1814}, {927, 23696}, {2481, 36057}, {18031, 32658}
X(42071) = crosspoint of X(4) and X(5089)
X(42071) = crosssum of X(3) and X(1814)
X(42071) = crossdifference of every pair of points on line {1814, 39470}
X(42071) = barycentric product X(i)*X(j) for these {i,j}: {4, 6184}, {6, 34337}, {19, 4712}, {25, 4437}, {264, 39686}, {281, 1362}, {518, 5089}, {672, 1861}, {1783, 3126}, {1824, 16728}, {1876, 3693}, {2052, 20776}, {2340, 5236}, {2356, 3912}, {4238, 24290}, {8751, 23102}, {15149, 20683}, {15742, 35505}
X(42071) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 6185}, {672, 31637}, {1362, 348}, {1861, 18031}, {1876, 34018}, {1974, 41934}, {2223, 1814}, {2356, 673}, {3126, 15413}, {4437, 305}, {4712, 304}, {5089, 2481}, {6184, 69}, {9454, 36057}, {9455, 32658}, {15615, 7117}, {20776, 394}, {23612, 25083}, {34337, 76}, {35505, 1565}, {39014, 3270}, {39686, 3}

X(42072) = X(4)X(957)∩X(33)X(51)

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

X(42072) lies on the orthic inconic and these lines: {4, 957}, {25, 3052}, {33, 51}, {108, 3937}, {125, 429}, {184, 3195}, {208, 1425}, {225, 1828}, {1824, 1856}, {3259, 20621}, {21664, 26611}, {34980, 40952}

X(42072) = isogonal conjugate of the isotomic conjugate of X(21664)
X(42072) = polar conjugate of the isotomic conjugate of X(23980)
X(42072) = orthic-isogonal conjugate of X(14571)
X(42072) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 14571}, {108, 3310}, {21664, 23980}
X(42072) = X(i)-isoconjugate of X(j) for these (i,j): {304, 41933}, {1795, 18816}
X(42072) = crosspoint of X(4) and X(14571)
X(42072) = barycentric product X(i)*X(j) for these {i,j}: {4, 23980}, {6, 21664}, {19, 24028}, {25, 26611}, {281, 1361}, {517, 14571}, {1785, 2183}, {2427, 39534}, {3326, 7115}, {6591, 15632}, {23984, 41215}
X(42072) = barycentric quotient X(i)/X(j) for these {i,j}: {1361, 348}, {1974, 41933}, {14571, 18816}, {21664, 76}, {23980, 69}, {24028, 304}, {26611, 305}, {41215, 23983}

X(42073) = X(25)X(105)∩X(125)X(430)

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

X(42073) lies on the orthic inconic and these lines: {25, 105}, {125, 430}, {1565, 26705}, {1827, 2262}, {34980, 40954}

X(42073) = isogonal conjugate of the isotomic conjugate of X(21665)
X(42073) = polar conjugate of the isotomic conjugate of X(23972)
X(42073) = orthic-isogonal conjugate of X(1886)
X(42073) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 1886}, {21665, 23972}, {26705, 676}
X(42073) = X(i)-isoconjugate of X(j) for these (i,j): {1815, 36101}, {18025, 36056}
X(42073) = crosspoint of X(4) and X(1886)
X(42073) = crosssum of X(3) and X(1815)
X(42073) = crossdifference of every pair of points on the tangent to the MacBeath circumconic at X(1815)
X(42073) = barycentric product X(i)*X(j) for these {i,j}: {4, 23972}, {6, 21665}, {19, 24014}, {281, 1360}, {516, 1886}, {676, 41321}, {3234, 7649}
X(42073) = barycentric quotient X(i)/X(j) for these {i,j}: {1360, 348}, {1886, 18025}, {3234, 4561}, {21665, 76}, {23972, 69}, {24014, 304}

leftri

Points on the Hofstadter inellipse: X(42074)-X(42084)

rightri

These points are contributed by Peter Moses, March 20, 2021.

The Hofstadter inellipse is introduced at X(359), where it is denoted by E(1/2).

The Hofstadter inellipse is also the incentral inellipse, the trilinear square of the antiorthic axis, the X(1)-Ceva conjugate of the antiorthic axis, the barycentric product X(1)*[Steiner inellipse], the barycentric product X(9)*[incircle], and the locus of trilinear poles, wrt the incentral triangle, of lines passing through X(1). (Randy Hutson, May 31, 2021)

X(42074) = X(1)-CEVA CONJUGATE OF X(2173)

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

X(42074) lies on the Hofstadter inellipse and these lines: {1, 162}, {31, 2153}, {204, 32676}, {244, 1104}, {2308, 2310}, {2631, 14399}, {2638, 14547}, {3163, 6062}


X(42074) = isogonal conjugate of the isotomic conjugate of X(1099)
X(42074) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 2173}, {162, 2631}
X(42074) = X(i)-isoconjugate of X(j) for these (i,j): {2, 40384}, {6, 31621}, {74, 1494}, {76, 40353}, {525, 34568}, {1304, 34767}, {2159, 33805}, {9139, 36890}, {14264, 40423}, {14380, 16077}, {14919, 16080}, {16076, 41433}
X(42074) = crosspoint of X(i) and X(j) for these (i,j): {1, 2173}, {1354, 3163}
X(42074) = crosssum of X(1) and X(2349)
X(42074) = crossdifference of every pair of points on line {2349, 2631}
X(42074) = trilinear square of X(2173)
X(42074) = trilinear pole, wrt incentral triangle, of line X(1)X(656)
X(42074) = barycentric product X(i)*X(j) for these {i,j}: {1, 3163}, {6, 1099}, {9, 1354}, {19, 16163}, {30, 2173}, {31, 36789}, {48, 34334}, {57, 6062}, {63, 16240}, {75, 9408}, {162, 14401}, {610, 38956}, {661, 3233}, {1495, 14206}, {1553, 36151}, {1784, 3284}, {2159, 23097}, {2349, 3081}, {2420, 36035}, {2631, 4240}, {3260, 9406}, {9409, 24001}, {24000, 39008}
X(42074) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 31621}, {30, 33805}, {31, 40384}, {560, 40353}, {1099, 76}, {1354, 85}, {1495, 2349}, {2173, 1494}, {2631, 34767}, {3081, 14206}, {3163, 75}, {3233, 799}, {6062, 312}, {9406, 74}, {9407, 2159}, {9408, 1}, {14401, 14208}, {14581, 36119}, {16163, 304}, {16240, 92}, {32676, 34568}, {34334, 1969}, {36435, 1099}, {36789, 561}, {39008, 17879}

X(42075) = X(1)-CEVA CONJUGATE OF X(1755)

Barycentrics    a^5*(a^2*b^2 - b^4 + a^2*c^2 - c^4)^2 : :
Trilinears    a^2 cos^2(A + ω) : :

X(42075) lies on the Hofstadter inellipse and these lines: {1, 1821}, {31, 1927}, {38, 2632}, {240, 1959}, {244, 8850}, {560, 563}, {1953, 1964}, {2260, 3248}, {2269, 2638}, {2309, 2310}, {7062, 11672}, {16725, 23996}

X(42075) = isogonal conjugate of the isotomic conjugate of X(23996)
X(42075) = X(1)-Ceva conjugate of X(1755)
X(42075) = X(i)-isoconjugate of X(j) for these (i,j): {2, 34536}, {76, 41932}, {98, 290}, {287, 16081}, {336, 36120}, {850, 41173}, {879, 22456}, {1976, 18024}, {14265, 40428}, {14295, 18858}, {14382, 36897}
X(42075) = crosspoint of X(i) and X(j) for these (i,j): {1, 1755}, {1355, 11672}
X(42075) = crosssum of X(1) and X(1821)
X(42075) = trilinear square of X(1755)
X(42075) = trilinear pole, wrt incentral triangle, of line X(1)X(810)
X(42075) = barycentric product X(i)*X(j) for these {i,j}: {1, 11672}, {6, 23996}, {9, 1355}, {31, 36790}, {42, 16725}, {48, 2967}, {57, 7062}, {75, 9419}, {163, 41167}, {237, 1959}, {240, 3289}, {325, 9417}, {511, 1755}, {560, 32458}, {561, 36425}, {798, 15631}, {1821, 23611}, {1910, 23098}, {3569, 23997}, {5360, 17209}, {17462, 34157}, {23995, 35088}
X(42075) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 34536}, {237, 1821}, {560, 41932}, {1355, 85}, {1755, 290}, {1959, 18024}, {2211, 36120}, {2967, 1969}, {3289, 336}, {7062, 312}, {9417, 98}, {9418, 1910}, {9419, 1}, {11672, 75}, {14966, 36036}, {15631, 4602}, {16725, 310}, {23611, 1959}, {23996, 76}, {32458, 1928}, {36425, 31}, {36790, 561}, {41167, 20948}
{X(1),X(39342)}-harmonic conjugate of X(1821)

X(42076) = X(1)-CEVA CONJUGATE OF X(2182)

Barycentrics    a*(2*a^4 - a^3*b - a^2*b^2 + a*b^3 - b^4 - a^3*c + 2*a^2*b*c - a*b^2*c - a^2*c^2 - a*b*c^2 + 2*b^2*c^2 + a*c^3 - c^4)^2 : :
Trilinears    a^2 ((b + c) sec A - b sec B - c sec C)^2 : :

X(42076) lies on the Hofstadter inellipse and these lines: {1, 36100}, {31, 33}, {42, 2638}, {56, 244}, {2632, 2650}, {3248, 40958}, {24031, 36050}

X(42076) = isogonal conjugate of the isotomic conjugate of X(24034)
X(42076) = X(1)-Ceva conjugate of X(2182)
X(42076) = X(102)-isoconjugate of X(34393)
X(42076) = crosspoint of X(i) and X(j) for these (i,j): {1, 2182}, {1359, 23986}
X(42076) = crosssum of X(1) and X(36100)
X(42076) = trilinear square of X(2182)
X(42076) = trilinear pole, wrt incentral triangle, of line X(1)X(521)
X(42076) = barycentric product X(i)*X(j) for these {i,j}: {1, 23986}, {6, 24034}, {9, 1359}, {19, 38554}, {515, 2182}, {2425, 14304}
X(42076) = barycentric quotient X(i)/X(j) for these {i,j}: {1359, 85}, {2182, 34393}, {23986, 75}, {24034, 76}, {38554, 304}

X(42077) = X(1)-CEVA CONJUGATE OF X(910)

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

X(42077) lies on the Hofstadter inellipse and these lines: {1, 36101}, {6, 2310}, {31, 57}, {42, 24012}, {678, 14392}, {756, 3195}, {1253, 2331}, {1783, 24010}, {1962, 2632}, {2293, 2638}, {2643, 40977}, {3248, 20978}, {4617, 34033}, {16469, 24644}

X(42077) = isogonal conjugate of the isotomic conjugate of X(24014)
X(42077) = X(1)-Ceva conjugate of X(910)
X(42077) = X(i)-isoconjugate of X(j) for these (i,j): {103, 18025}, {677, 2400}
X(42077) = crosspoint of X(i) and X(j) for these (i,j): {1, 910}, {1360, 23972}
X(42077) = crosssum of X(1) and X(36101)
X(42077) = trilinear square of X(910)
X(42077) = trilinear pole, wrt incentral triangle, of line X(1)X(905)
X(42077) = barycentric product X(i)*X(j) for these {i,j}: {1, 23972}, {6, 24014}, {9, 1360}, {48, 21665}, {513, 3234}, {516, 910}, {1456, 40869}
X(42077) = barycentric quotient X(i)/X(j) for these {i,j}: {910, 18025}, {1360, 85}, {3234, 668}, {21665, 1969}, {23972, 75}, {24014, 76}

X(42078) = X(1)-CEVA CONJUGATE OF X(2183)

Barycentrics    a^3*(a^2*b - b^3 + a^2*c - 2*a*b*c + b^2*c + b*c^2 - c^3)^2 : :
Trilinears    ((a - c) cos B + (a - b) cos C)^2 : :

X(42078) lies on the Hofstadter inellipse and these lines: {1, 34234}, {31, 692}, {42, 1864}, {55, 2638}, {65, 244}, {221, 7138}, {872, 34857}, {2177, 24012}, {2292, 2632}, {2643, 3725}, {3878, 24025}, {4088, 23757}, {14571, 21801}

X(42078) = isogonal conjugate of the isotomic conjugate of X(24028)
X(42078) = X(1)-Ceva conjugate of X(2183)
X(42078) = X(i)-isoconjugate of X(j) for these (i,j): {76, 41933}, {104, 18816}, {2401, 13136}, {34051, 36795}
X(42078) = crosspoint of X(i) and X(j) for these (i,j): {1, 2183}, {1361, 23980}
X(42078) = crosssum of X(1) and X(34234)
X(42078) = crossdifference of every pair of points on line {3762, 24618}
X(42078) = trilinear square of X(2183)
X(42078) = trilinear pole, wrt incentral triangle, of line X(1)X(522)
X(42078) = barycentric product X(i)*X(j) for these {i,j}: {1, 23980}, {6, 24028}, {9, 1361}, {31, 26611}, {48, 21664}, {517, 2183}, {649, 15632}, {859, 21801}, {909, 23101}, {1769, 2427}, {2149, 3326}, {7128, 41215}, {14571, 22350}
X(42078) = barycentric quotient X(i)/X(j) for these {i,j}: {560, 41933}, {1361, 85}, {2183, 18816}, {15632, 1978}, {21664, 1969}, {23980, 75}, {24028, 76}, {26611, 561}

X(42079) = X(1)-CEVA CONJUGATE OF X(672)

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

X(42079) lies on the Hofstadter inellipse and these lines: {1, 673}, {6, 292}, {37, 2293}, {42, 244}, {48, 692}, {55, 20995}, {75, 39775}, {101, 2195}, {200, 14829}, {241, 518}, {560, 21059}, {664, 35961}, {665, 926}, {756, 38358}, {900, 20681}, {922, 19624}, {984, 991}, {1026, 17755}, {1088, 36905}, {1279, 3009}, {1962, 14746}, {2223, 9454}, {2294, 2643}, {3010, 6603}, {3725, 4117}, {4712, 16728}, {21805, 38980}, {23612, 39686}, {33701, 39044}

X(42079) = reflection of X(2310) in X(37)
X(42079) = isogonal conjugate of the isotomic conjugate of X(4712)
X(42079) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 672}, {3252, 39258}
X(42079) = X(i)-isoconjugate of X(j) for these (i,j): {2, 6185}, {76, 41934}, {105, 2481}, {294, 34018}, {885, 927}, {1024, 34085}, {1438, 18031}, {1462, 36796}, {31637, 36124}
X(42079) = crosspoint of X(i) and X(j) for these (i,j): {1, 672}, {1362, 6184}, {2223, 40730}, {9436, 17758}
X(42079) = crosssum of X(i) and X(j) for these (i,j): {1, 673}, {2195, 4251}
X(42079) = crossdifference of every pair of points on line {673, 812}
X(42079) = Hofstadter-inellipse antipode of X(2310)
X(42079) = trilinear square of X(672)
X(42079) = trilinear pole, wrt incentral triangle, of line X(1)X(514)
X(42079) = barycentric product X(i)*X(j) for these {i,j}: {1, 6184}, {6, 4712}, {9, 1362}, {31, 4437}, {42, 16728}, {48, 34337}, {75, 39686}, {92, 20776}, {101, 3126}, {241, 2340}, {518, 672}, {665, 1026}, {673, 23612}, {765, 35505}, {926, 1025}, {1110, 35094}, {1438, 23102}, {1458, 3693}, {1818, 5089}, {1861, 20752}, {2223, 3912}, {2254, 2284}, {2356, 25083}, {3252, 8299}, {3263, 9454}, {3286, 3930}, {7084, 17060}, {14439, 34230}, {17464, 34159}, {17755, 40730}, {18206, 20683}, {30941, 39258}, {33570, 37138}, {33700, 39341}
X(42079) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 6185}, {518, 18031}, {560, 41934}, {672, 2481}, {1026, 36803}, {1362, 85}, {1458, 34018}, {2223, 673}, {2283, 34085}, {2340, 36796}, {3126, 3261}, {4437, 561}, {4712, 76}, {6184, 75}, {8638, 1024}, {9454, 105}, {9455, 1438}, {15615, 2170}, {16728, 310}, {20752, 31637}, {20776, 63}, {23612, 3912}, {34337, 1969}, {35505, 1111}, {39014, 2310}, {39258, 13576}, {39686, 1}
X(42079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 39341, 673}, {673, 37138, 39341}

X(42080) = X(1)-CEVA CONJUGATE OF X(823)

Barycentrics    a^5*(b - c)^2*(b + c)^2*(a^2 - b^2 - c^2)^4 : :
Trilinears    1/(sec^2 B - sec^2 C)^2 : :
Trilinears    1/(csc B/2 - csc C/2)^2 : :
Trilinears    1/(csc 2B - csc 2C)^2 : :

X(42080) lies on the Hofstadter inellipse and these lines: {1, 823}, {73, 2660}, {244, 38985}, {836, 4094}, {2638, 38344}, {7065, 35071}

X(42080) = isogonal conjugate of the polar conjugate of X(37754)
X(42080) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 822}, {1248, 652}
X(42080) = X(i)-isoconjugate of X(j) for these (i,j): {2, 34538}, {75, 24021}, {76, 23590}, {107, 6528}, {158, 23999}, {264, 32230}, {561, 24022}, {648, 15352}, {811, 36126}, {1093, 18020}, {1502, 23975}, {2052, 23582}, {6331, 6529}, {18027, 23964}, {34537, 36434}
X(42080) = crosspoint of X(i) and X(j) for these (i,j): {1, 822}, {1363, 35071}
X(42080) = crosssum of X(i) and X(j) for these (i,j): {1, 823}, {6521, 36126}
X(42080) = trilinear square of X(823)
X(42080) = trilinear pole, wrt incentral triangle, of line X(1)X(29)
X(42080) = barycentric product X(i)*X(j) for these {i,j}: {1, 35071}, {3, 37754}, {9, 1363}, {32, 24020}, {42, 16730}, {48, 2972}, {57, 7065}, {63, 34980}, {125, 4100}, {255, 3269}, {520, 822}, {560, 23974}, {577, 2632}, {656, 32320}, {823, 23613}, {1092, 3708}, {2167, 41219}, {6507, 20975}, {7138, 35072}, {14585, 17879}, {20902, 23606}, {23103, 24019}, {23994, 36433}, {24018, 39201}
X(42080) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 34538}, {32, 24021}, {560, 23590}, {577, 23999}, {810, 15352}, {822, 6528}, {1363, 85}, {1501, 24022}, {1917, 23975}, {2632, 18027}, {2972, 1969}, {3049, 36126}, {4100, 18020}, {4117, 36434}, {7065, 312}, {9247, 32230}, {14585, 24000}, {16730, 310}, {20975, 6521}, {23613, 24018}, {23974, 1928}, {24020, 1502}, {32320, 811}, {34980, 92}, {35071, 75}, {36433, 1101}, {37754, 264}, {39201, 823}, {41219, 14213}

X(42081) = X(1)-CEVA CONJUGATE OF X(897)

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

X(42081) lies on the Hofstadter inellipse and these lines: {1, 662}, {44, 39256}, {48, 2157}, {214, 238}, {244, 1100}, {501, 6042}, {560, 4575}, {678, 9508}, {896, 922}, {1193, 3248}, {1964, 4117}, {2173, 17462}, {2310, 2646}, {2482, 7067}, {2642, 14419}, {4094, 38348}, {5550, 26081}, {16733, 24038}

X(42081) = isogonal conjugate of the isotomic conjugate of X(24038)
X(42081) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 896}, {662, 2642}, {24041, 23889}
X(42081) = X(i)-isoconjugate of X(j) for these (i,j): {2, 10630}, {4, 15398}, {76, 41936}, {111, 671}, {115, 34539}, {523, 34574}, {691, 5466}, {892, 9178}, {895, 17983}, {5968, 9154}, {8753, 30786}, {9139, 9214}, {9979, 39413}, {10415, 14246}, {18023, 32740}, {23894, 36085}
X(42081) = crosspoint of X(i) and X(j) for these (i,j): {1, 896}, {1366, 2482}, {23889, 24041}
X(42081) = crosssum of X(i) and X(j) for these (i,j): {1, 897}, {2643, 23894}
X(42081) = crossdifference of every pair of points on line {897, 2642}
X(42081) = trilinear square of X(897)
X(42081) = trilinear pole, wrt incentral triangle, of line X(1)X(661)
X(42081) = barycentric product X(i)*X(j) for these {i,j}: {1, 2482}, {6, 24038}, {9, 1366}, {31, 36792}, {42, 16733}, {48, 34336}, {57, 7067}, {63, 5095}, {75, 39689}, {187, 14210}, {351, 24039}, {524, 896}, {662, 1649}, {690, 23889}, {897, 8030}, {922, 3266}, {923, 23106}, {2642, 5468}, {4062, 16702}, {6629, 21839}, {17466, 34161}, {20380, 36263}, {23992, 24041}, {33915, 36085}
X(42081) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 10630}, {48, 15398}, {163, 34574}, {187, 897}, {351, 23894}, {560, 41936}, {896, 671}, {922, 111}, {1101, 34539}, {1366, 85}, {1649, 1577}, {2482, 75}, {2642, 5466}, {5095, 92}, {5467, 36085}, {7067, 312}, {8030, 14210}, {14210, 18023}, {14567, 923}, {16733, 310}, {23200, 36060}, {23889, 892}, {23992, 1109}, {24038, 76}, {34336, 1969}, {36792, 561}, {39689, 1}
X(42081) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 39339, 897}, {662, 897, 39339}, {662, 17467, 2643}

X(42082) = X(1)-CEVA CONJUGATE OF X(1155)

Barycentrics    a*(2*a^2 - b^2 + 2*b*c - c^2 - a*(b + c))^2 : :
Trilinears    (2 cos A - cos B - cos C)^2 : :

X(42082) lies on the Hofstadter inellipse and these lines: {1, 651}, {6, 244}, {44, 9502}, {73, 2638}, {106, 16469}, {109, 1253}, {580, 1106}, {678, 2254}, {1155, 6610}, {1201, 3248}, {1254, 3157}, {1458, 5126}, {2293, 24012}, {2632, 18675}, {2643, 2650}, {3245, 6126}, {3945, 17719}, {4349, 24222}, {4585, 4712}, {6068, 35110}, {6594, 35293}, {15346, 28125}, {24980, 41801}

X(42082) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 1155}, {7045, 23890}
X(42082) = crosspoint of X(i) and X(j) for these (i,j): {1, 1155}, {3321, 35110}, {7045, 23890}
X(42082) = crosssum of X(i) and X(j) for these (i,j): {1, 1156}, {2310, 23893}
X(42082) = crossdifference of every pair of points on line {1156, 3887}
X(42082) = trilinear square of X(1155)
X(42082) = trilinear pole, wrt incentral triangle, of line X(1)X(650)
X(42082) = X(i)-isoconjugate of X(j) for these (i,j): {1121, 2291}, {23351, 35157}, {23893, 37139}, {34056, 41798}
X(42082) = barycentric product X(i)*X(j) for these {i,j}: {1, 35110}, {9, 3321}, {57, 6068}, {527, 1155}, {1055, 30806}, {1323, 6603}, {3328, 4564}, {5528, 15729}, {6366, 23890}, {6510, 23710}, {6610, 6745}, {7045, 35091}
X(42082) = barycentric quotient X(i)/X(j) for these {i,j}: {1055, 1156}, {1155, 1121}, {3321, 85}, {3328, 4858}, {6068, 312}, {6139, 23893}, {23346, 37139}, {23890, 35157}, {35091, 24026}, {35110, 75}

X(42083) = X(1)-CEVA CONJUGATE OF X(899)

Barycentrics    a*(a*b + a*c - 2*b*c)^2 : :
X(42083) = 3 X[4664] - X[41683], 5 X[4704] - X[17154]

X(42083) lies on the inellipse centered at X(24003) (the trilinear square of the Nagel line).

X(42083) lies on the Hofstadter inellipse and these lines: {1, 190}, {37, 244}, {44, 17475}, {75, 24003}, {88, 24419}, {192, 872}, {292, 16672}, {518, 17460}, {536, 899}, {644, 36267}, {659, 678}, {726, 34587}, {740, 4738}, {891, 3768}, {900, 20681}, {984, 2802}, {1964, 17262}, {2234, 39916}, {2292, 2643}, {2310, 3057}, {2632, 18674}, {2667, 4117}, {3123, 40521}, {3799, 24338}, {4088, 23757}, {4094, 4145}, {4319, 24012}, {4370, 27846}, {4704, 17154}, {5550, 26076}, {6533, 25079}, {8683, 34247}, {16676, 24578}, {17160, 39044}, {17261, 17445}, {17464, 21801}, {17487, 24722}, {17793, 24004}, {19582, 25268}

X(42083) = midpoint of X(192) and X(3952)
X(42083) = reflection of X(i) in X(j) for these {i,j}: {75, 24003}, {244, 37}, {2667, 14752}
X(42083) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 899}, {190, 3768}, {7035, 23891}
X(42083) = X(i)-isoconjugate of X(j) for these (i,j): {739, 3227}, {889, 23349}, {4607, 23892}
X(42083) = crosspoint of X(i) and X(j) for these (i,j): {1, 899}, {7035, 23891}
X(42083) = crosssum of X(i) and X(j) for these (i,j): {1, 37129}, {3248, 23892}
X(42083) = crossdifference of every pair of points on line {3768, 23892}
X(42083) = antipode of X(75) in the inellipse centered at X(24003)
X(42083) = antipode of X(244) in the Hofstadter inellipse
X(42083) = trilinear square of X(899)
X(42083) = trilinear pole, wrt incentral triangle, of line X(1)X(649)
X(42083) = barycentric product X(i)*X(j) for these {i,j}: {1, 13466}, {190, 14434}, {536, 899}, {891, 23891}, {3230, 6381}, {3768, 41314}, {4728, 23343}, {7035, 39011}, {8031, 37129}
X(42083) = barycentric quotient X(i)/X(j) for these {i,j}: {536, 31002}, {890, 23892}, {899, 3227}, {3230, 37129}, {8031, 6381}, {13466, 75}, {14434, 514}, {14441, 21143}, {23343, 4607}, {23891, 889}, {39011, 244}

X(42084) = X(1)-CEVA CONJUGATE OF X(1635)

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

X(42084) lies on the Hofstadter inellipse and these lines: {1, 3257}, {31, 40172}, {44, 678}, {214, 238}, {244, 513}, {512, 2643}, {518, 17460}, {663, 3248}, {679, 9325}, {765, 9282}, {984, 24482}, {2087, 3251}, {2310, 4162}, {3122, 4983}, {4542, 33922}, {7208, 28886}, {7290, 36267}, {16507, 38348}, {17145, 20072}, {19945, 38989}

X(42084) = midpoint of X(17145) and X(20072)
X(42084) = reflection of X(21805) in X(44)
X(42084) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 1635}, {244, 2087}, {678, 3251}, {4738, 6544}, {9282, 44}, {9325, 513}, {39771, 14442}, {40172, 1960}
X(42084) = crosspoint of X(i) and X(j) for these (i,j): {1, 1635}, {44, 513}, {244, 2087}, {678, 3251}, {4738, 6544}, {14027, 35092}
X(42084) = crosssum of X(i) and X(j) for these (i,j): {1, 3257}, {88, 100}, {679, 4618}, {765, 5376}
X(42084) = crossdifference of every pair of points on line {1022, 1023}
X(42084) = trilinear square of X(1635)
X(42084) = trilinear pole, wrt incentral triangle, of line X(1)X(88)
X(42084) = X(i)-isoconjugate of X(j) for these (i,j): {88, 5376}, {100, 4618}, {190, 4638}, {679, 765}, {901, 4555}, {903, 9268}, {1016, 2226}, {1318, 4998}, {4567, 30575}, {6548, 6551}, {6635, 23345}, {17780, 39414}, {31625, 41935}
X(42084) = barycentric product X(i)*X(j) for these {i,j}: {1, 35092}, {9, 14027}, {44, 1647}, {57, 4542}, {100, 14442}, {244, 4370}, {513, 6544}, {514, 3251}, {519, 2087}, {650, 39771}, {678, 1086}, {900, 1635}, {1015, 4738}, {1017, 1111}, {1022, 33922}, {1023, 6550}, {1317, 2170}, {1319, 4530}, {1960, 3762}, {3122, 16729}, {3248, 36791}, {3669, 4543}, {3942, 42070}, {4895, 30725}, {8661, 24004}, {17205, 21821}
X(42084) = barycentric quotient X(i)/X(j) for these {i,j}: {649, 4618}, {667, 4638}, {678, 1016}, {902, 5376}, {1015, 679}, {1017, 765}, {1023, 6635}, {1635, 4555}, {1647, 20568}, {1960, 3257}, {2087, 903}, {2251, 9268}, {3122, 30575}, {3248, 2226}, {3251, 190}, {4370, 7035}, {4542, 312}, {4543, 646}, {4738, 31625}, {4895, 4582}, {6544, 668}, {8661, 1022}, {14027, 85}, {14442, 693}, {14637, 1635}, {14835, 4370}, {33922, 24004}, {35092, 75}, {39771, 4554}
X(42084) = {X(1),X(39343)}-harmonic conjugate of X(3257)

leftri

Gibert (i,j,k) points: X(42085)-X(42284)

rightri

This preamble is contributed by Peter Moses, March 22, 2021.

Bernard Gibert has noted a set of points in connecton with the cubic K1191. These points are given by the combo

SW*X[6]*i + Sqrt[3]*S*(j*X[4] + k*X[3]) where (i,j,k) are constants or other 0-degree functions of a,b,c.

See K1191 .

X(42085) = GIBERT(1,-1,1) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 6*SB*SC : :

X(42085) is the intersection of the tangents to conic {{X(4),X(13),X(14),X(15),X(16)}} at X(13) and X(16). (Randy Hutson, May 31, 2021)

X(42085) lies on these lines: {2, 10645}, {3, 5321}, {4, 15}, {5, 11480}, {6, 30}, {13, 3543}, {14, 376}, {16, 20}, {18, 3522}, {61, 3146}, {62, 3529}, {69, 531}, {141, 11295}, {146, 10657}, {193, 530}, {302, 22491}, {381, 23302}, {382, 5318}, {393, 6110}, {395, 3534}, {396, 3830}, {397, 5073}, {398, 1657}, {532, 11008}, {533, 20080}, {546, 36836}, {550, 5339}, {616, 6777}, {617, 7898}, {619, 37171}, {621, 34540}, {622, 40901}, {623, 37172}, {631, 16967}, {1249, 6111}, {1250, 4302}, {1478, 10638}, {1479, 7051}, {1656, 5349}, {2041, 35820}, {2042, 35821}, {2043, 6396}, {2044, 6200}, {3090, 5352}, {3091, 5238}, {3098, 22512}, {3180, 19569}, {3389, 35732}, {3523, 5365}, {3524, 37835}, {3545, 16241}, {3589, 11296}, {3619, 3642}, {3620, 3643}, {3627, 11542}, {3767, 19781}, {3839, 37832}, {3843, 16772}, {3845, 16644}, {4299, 19373}, {5059, 41973}, {5237, 16961}, {5357, 10483}, {5362, 11114}, {5367, 17579}, {5473, 6782}, {5474, 6114}, {5878, 10675}, {6108, 37689}, {6115, 36772}, {6411, 34551}, {6412, 34552}, {6564, 36455}, {6565, 36437}, {6770, 23005}, {6783, 36962}, {7519, 37776}, {7735, 41409}, {8588, 25164}, {8703, 16645}, {9736, 16002}, {9833, 10676}, {10304, 16242}, {10633, 35471}, {10642, 18533}, {10643, 18537}, {10658, 12383}, {10662, 12118}, {10678, 12254}, {11001, 34755}, {11297, 34573}, {11409, 37196}, {12103, 36843}, {12816, 33604}, {14538, 33518}, {15640, 41107}, {15682, 36969}, {15696, 16773}, {15704, 22238}, {16063, 37775}, {16635, 18424}, {16802, 16804}, {16960, 17578}, {16965, 33703}, {19708, 41122}, {22531, 22856}, {22843, 31706}, {23013, 39874}, {23334, 36775}, {32785, 36445}, {32786, 36463}, {33517, 36994}, {35695, 36330}, {41035, 41038}

X(42085) = reflection of X(42086) in X(6)

X(42086) = GIBERT(1,1,-1) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 6*SB*SC : :

X(42086) is the intersection of the tangents to conic {{X(4),X(13),X(14),X(15),X(16)}} at X(14) and X(15). (Randy Hutson, May 31, 2021)

X(42086) lies on these lines: {2, 10646}, {3, 5318}, {4, 16}, {5, 11481}, {6, 30}, {13, 376}, {14, 3543}, {15, 20}, {17, 3522}, {61, 3529}, {62, 3146}, {69, 530}, {141, 11296}, {146, 10658}, {193, 531}, {303, 22492}, {381, 23303}, {382, 5321}, {393, 6111}, {395, 3830}, {396, 3534}, {397, 1657}, {398, 5073}, {532, 20080}, {533, 11008}, {546, 36843}, {550, 5340}, {616, 7898}, {617, 6778}, {618, 37170}, {621, 40900}, {622, 34541}, {624, 37173}, {631, 16966}, {1249, 6110}, {1250, 1478}, {1479, 19373}, {1656, 5350}, {2041, 35821}, {2042, 35820}, {2043, 6200}, {2044, 6396}, {3090, 5351}, {3091, 5237}, {3098, 22513}, {3181, 19569}, {3365, 35732}, {3523, 5366}, {3524, 37832}, {3545, 16242}, {3589, 11295}, {3619, 3643}, {3620, 3642}, {3627, 11543}, {3767, 19780}, {3839, 37835}, {3843, 16773}, {3845, 16645}, {4299, 7051}, {4302, 10638}, {5059, 41974}, {5238, 16960}, {5353, 10483}, {5362, 17579}, {5367, 11114}, {5473, 6115}, {5474, 6783}, {5878, 10676}, {6109, 37689}, {6114, 36962}, {6411, 34552}, {6412, 34551}, {6564, 36437}, {6565, 36455}, {6773, 23004}, {6782, 36961}, {7519, 37775}, {7735, 41408}, {8588, 25154}, {8703, 16644}, {9735, 16001}, {9833, 10675}, {10304, 16241}, {10632, 35471}, {10641, 18533}, {10644, 18537}, {10657, 12383}, {10661, 12118}, {10677, 12254}, {11001, 34754}, {11298, 34573}, {11408, 37196}, {12103, 36836}, {12817, 33605}, {14136, 36772}, {14539, 33517}, {15640, 41108}, {15682, 36970}, {15696, 16772}, {15704, 22236}, {16063, 37776}, {16634, 18424}, {16803, 16805}, {16961, 17578}, {16964, 33703}, {19708, 41121}, {22532, 22900}, {22890, 31705}, {23006, 39874}, {23249, 35731}, {32785, 36463}, {32786, 36445}, {33518, 36992}, {35691, 35752}, {41034, 41039}

X(42086) = reflection of X(42085) in X(6)

X(42087) = GIBERT(1,-1,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*a^2*SA - 6*SB*SC : :

X(42087) lies on these lines: {3, 5321}, {4, 11480}, {5, 10645}, {6, 20}, {13, 15}, {14, 8703}, {16, 398}, {18, 33923}, {61, 15704}, {62, 12103}, {140, 5349}, {376, 395}, {382, 16772}, {397, 1657}, {531, 15300}, {546, 5352}, {548, 10646}, {549, 16967}, {621, 35931}, {623, 35304}, {1250, 15338}, {1503, 36993}, {1885, 10641}, {2883, 30402}, {3146, 11488}, {3479, 35725}, {3522, 5339}, {3529, 5335}, {3530, 33416}, {3534, 10654}, {3543, 16644}, {3575, 11475}, {3627, 5238}, {3845, 16241}, {4316, 5357}, {4324, 5353}, {5059, 5340}, {5073, 5350}, {5254, 19781}, {5305, 41409}, {5343, 21735}, {5351, 16961}, {5362, 15680}, {5365, 10299}, {5367, 37256}, {5474, 22512}, {5895, 17826}, {6284, 7051}, {6671, 31693}, {7354, 10638}, {8175, 40668}, {8550, 36995}, {10187, 15712}, {10295, 10633}, {10304, 16645}, {10632, 18560}, {10653, 15681}, {10658, 34153}, {10675, 15311}, {10676, 34782}, {11515, 31829}, {11812, 12817}, {12100, 37835}, {15326, 19373}, {15683, 37640}, {15686, 36968}, {15687, 37832}, {15690, 41108}, {15695, 41113}, {15696, 40694}, {15759, 41122}, {15768, 30465}, {16242, 34200}, {16965, 34754}, {17538, 22238}, {17800, 40693}, {19708, 33603}, {19710, 41101}, {33518, 36755}, {35404, 41943}, {37776, 37900}, {41035, 41056}, {41977, 41981}

X(42087) = {X(6),X(20)}-harmonic conjugate of X(42088)

X(42088) = GIBERT(1,1,-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*a^2*SA + 6*SB*SC : :

X(42088) lies on these lines: {3, 5318}, {4, 11481}, {5, 10646}, {6, 20}, {13, 8703}, {14, 16}, {15, 397}, {17, 33923}, {61, 12103}, {62, 15704}, {140, 5350}, {376, 396}, {382, 16773}, {398, 1657}, {530, 15300}, {546, 5351}, {548, 10645}, {549, 16966}, {622, 35932}, {624, 35303}, {1250, 7354}, {1503, 36995}, {1885, 10642}, {2883, 30403}, {3146, 11489}, {3480, 35726}, {3522, 5340}, {3529, 5334}, {3530, 33417}, {3534, 10653}, {3543, 16645}, {3575, 11476}, {3627, 5237}, {3845, 16242}, {4316, 5353}, {4324, 5357}, {5059, 5339}, {5073, 5349}, {5254, 19780}, {5305, 41408}, {5344, 21735}, {5352, 16960}, {5362, 37256}, {5366, 10299}, {5367, 15680}, {5473, 22513}, {5895, 17827}, {6284, 19373}, {6672, 31694}, {7051, 15326}, {8174, 40667}, {8550, 36993}, {10188, 15712}, {10295, 10632}, {10304, 16644}, {10633, 18560}, {10638, 15338}, {10654, 15681}, {10657, 34153}, {10675, 34782}, {10676, 15311}, {11516, 31829}, {11812, 12816}, {12100, 37832}, {15683, 37641}, {15686, 36967}, {15687, 37835}, {15690, 41107}, {15695, 41112}, {15696, 40693}, {15759, 41121}, {15769, 30468}, {16241, 34200}, {16964, 34755}, {17538, 22236}, {17800, 40694}, {19708, 33602}, {19710, 41100}, {33517, 36756}, {35404, 41944}, {37775, 37900}, {41034, 41057}, {41978, 41981}

X(42088) = {X(6),X(20)}-harmonic conjugate of X(42087)

X(42089) = GIBERT(-1,1,3) POINT

Barycentrics    Sqrt[3]*a^2*S - 9*a^2*SA - 6*SB*SC : :

X(42089) lies on these lines: {2, 13}, {3, 5321}, {4, 10187}, {5, 11481}, {6, 140}, {14, 3524}, {15, 631}, {17, 3533}, {18, 3523}, {20, 16809}, {61, 10303}, {62, 3525}, {376, 19107}, {395, 5054}, {396, 15694}, {398, 15720}, {498, 19373}, {499, 1250}, {549, 10654}, {574, 40921}, {623, 37173}, {627, 34541}, {628, 40900}, {629, 22907}, {632, 11542}, {1656, 5318}, {2045, 6200}, {2046, 6396}, {2548, 19780}, {3090, 5237}, {3091, 5351}, {3147, 10641}, {3526, 11486}, {3541, 10642}, {3542, 11476}, {3545, 36968}, {3546, 11516}, {3548, 10635}, {3618, 6671}, {3628, 36843}, {5024, 40922}, {5067, 16965}, {5071, 36969}, {5339, 15712}, {5362, 17566}, {6114, 21157}, {6640, 18470}, {6674, 22862}, {6782, 21156}, {7404, 10644}, {8252, 34552}, {8253, 34551}, {10304, 36970}, {10633, 37119}, {11268, 18281}, {11539, 16644}, {12100, 41120}, {12108, 36836}, {14216, 30403}, {14869, 22236}, {15692, 36967}, {15693, 41113}, {15698, 33603}, {15702, 16241}, {15708, 16268}, {15709, 16963}, {15717, 16964}, {15719, 41108}, {17827, 40686}, {19781, 21843}, {21158, 33518}, {33884, 36981}

X(42089) = {X(3),X(5321)}-harmonic conjugate of X(42090)
X(42089) = {X(4),X(10646)}-harmonic conjugate of X(42091)
X(42089) = {X(6),X(140)}-harmonic conjugate of X(42092)

X(42090) = GIBERT(1,-1,3) POINT

Barycentrics    Sqrt[3]*a^2*S + 9*a^2*SA - 6*SB*SC : :

X(42090) lies on these lines: {2, 12821}, {3, 5321}, {4, 10188}, {6, 550}, {13, 11001}, {14, 10304}, {15, 20}, {16, 376}, {17, 5059}, {18, 21735}, {30, 11480}, {61, 17538}, {382, 23302}, {395, 15688}, {396, 15681}, {548, 11481}, {631, 16809}, {1657, 5318}, {2041, 35786}, {2042, 35787}, {2549, 19781}, {3091, 33417}, {3146, 5352}, {3522, 5334}, {3523, 16967}, {3524, 33416}, {3528, 11489}, {3529, 5238}, {3534, 10653}, {3543, 16241}, {4299, 10638}, {4302, 7051}, {5286, 41409}, {5339, 33923}, {5349, 15720}, {5878, 30402}, {5925, 17826}, {8703, 11543}, {10632, 35481}, {10633, 35503}, {10657, 12244}, {10675, 20427}, {11267, 34350}, {11475, 18533}, {11486, 15696}, {11542, 15704}, {12103, 22236}, {12817, 15719}, {15682, 37832}, {15683, 36969}, {15685, 41119}, {15692, 37835}, {15697, 41101}, {16242, 19708}, {16645, 34200}, {16772, 17800}, {19710, 41112}, {22843, 22861}

X(42090) = {X(3),X(5321)}-harmonic conjugate of X(42089)
X(42090) = {X(4),X(10645)}-harmonic conjugate of X(42092)
X(42090) = {X(6),X(550)}-harmonic conjugate of X(42091)

X(42091) = GIBERT(1,1,-3) POINT

Barycentrics    Sqrt[3]*a^2*S - 9*a^2*SA + 6*SB*SC : :

X(42091) lies on these lines: {2, 12820}, {3, 5318}, {4, 10187}, {6, 550}, {13, 10304}, {14, 11001}, {15, 376}, {16, 20}, {17, 21735}, {18, 5059}, {30, 11481}, {62, 17538}, {382, 23303}, {395, 15681}, {396, 15688}, {548, 11480}, {631, 16808}, {1250, 4299}, {1657, 5321}, {2041, 35787}, {2042, 35786}, {2549, 19780}, {3091, 33416}, {3146, 5351}, {3522, 5335}, {3523, 16966}, {3524, 33417}, {3528, 11488}, {3529, 5237}, {3534, 10654}, {3543, 16242}, {4302, 19373}, {5286, 41408}, {5340, 33923}, {5350, 15720}, {5878, 30403}, {5925, 17827}, {8703, 11542}, {10632, 35503}, {10633, 35481}, {10658, 12244}, {10676, 20427}, {11268, 34350}, {11476, 18533}, {11485, 15696}, {11543, 15704}, {12103, 22238}, {12816, 15719}, {13939, 35739}, {15682, 37835}, {15683, 36970}, {15685, 41120}, {15692, 37832}, {15697, 41100}, {16241, 19708}, {16644, 34200}, {16773, 17800}, {19710, 41113}, {22890, 22907}

X(42091) = {X(3),X(5318)}-harmonic conjugate of X(42092)
X(42091) = {X(4),X(10646)}-harmonic conjugate of X(42089)
X(42091) = {X(6),X(550)}-harmonic conjugate of X(42090)

X(42092) = GIBERT(1,1,3) POINT

Barycentrics    Sqrt[3]*a^2*S + 9*a^2*SA + 6*SB*SC : :

X(42092) lies on these lines: {2, 14}, {3, 5318}, {4, 10188}, {5, 11480}, {6, 140}, {13, 3524}, {16, 631}, {17, 3523}, {18, 3533}, {20, 16808}, {61, 3525}, {62, 10303}, {376, 19106}, {395, 15694}, {396, 5054}, {397, 15720}, {498, 7051}, {499, 10638}, {549, 10653}, {574, 40922}, {624, 37172}, {627, 40901}, {628, 34540}, {630, 22861}, {632, 11543}, {1656, 5321}, {2045, 6396}, {2046, 6200}, {2548, 19781}, {3090, 5238}, {3091, 5352}, {3147, 10642}, {3526, 11485}, {3541, 10641}, {3542, 11475}, {3545, 36967}, {3546, 11515}, {3548, 10634}, {3618, 6672}, {3628, 36836}, {5024, 40921}, {5067, 16964}, {5071, 36970}, {5340, 15712}, {5367, 17566}, {6108, 36764}, {6115, 21156}, {6640, 18468}, {6673, 22906}, {6770, 36766}, {6782, 36770}, {6783, 21157}, {7404, 10643}, {8252, 34551}, {8253, 34552}, {10304, 36969}, {10632, 37119}, {11267, 18281}, {11539, 16645}, {12100, 41119}, {12108, 36843}, {14216, 30402}, {14869, 22238}, {15692, 36968}, {15693, 41112}, {15698, 33602}, {15702, 16242}, {15708, 16267}, {15709, 16962}, {15717, 16965}, {15719, 41107}, {17826, 40686}, {19780, 21843}, {21159, 33517}, {33884, 36979}

X(42092) = {X(3),X(5318)}-harmonic conjugate of X(42091)
X(42092) = {X(4),X(10645)}-harmonic conjugate of X(42090)
X(42092) = {X(6),X(140)}-harmonic conjugate of X(42089)

X(42093) = GIBERT(-1,2,0) POINT

Barycentrics    Sqrt[3]*a^2*S - 12*SB*SC : :

X(42093) lies on these lines: {3, 16809}, {4, 6}, {5, 11480}, {13, 12821}, {14, 3830}, {15, 381}, {16, 382}, {18, 5073}, {20, 23303}, {30, 11481}, {62, 5076}, {115, 36961}, {187, 36992}, {383, 37637}, {395, 3543}, {396, 3839}, {462, 41424}, {463, 31860}, {472, 26958}, {546, 18582}, {599, 621}, {622, 40341}, {623, 11295}, {1080, 31489}, {1250, 12953}, {1351, 16002}, {1656, 10645}, {1657, 10646}, {2043, 8252}, {2044, 8253}, {3091, 23302}, {3146, 11489}, {3366, 35821}, {3367, 35820}, {3412, 3843}, {3426, 11138}, {3531, 11139}, {3534, 37835}, {3627, 11543}, {3763, 11304}, {3832, 11488}, {3845, 10654}, {3851, 16966}, {3853, 40694}, {3855, 16772}, {3861, 40693}, {5024, 41024}, {5055, 33417}, {5072, 5238}, {5079, 5352}, {5093, 16001}, {5210, 41034}, {5353, 18514}, {5357, 18513}, {5471, 36962}, {5479, 16942}, {6409, 35732}, {6411, 14813}, {6412, 14814}, {6425, 35740}, {6777, 13103}, {7051, 10896}, {7507, 11475}, {9735, 14162}, {10516, 20428}, {10632, 35488}, {10633, 35480}, {10638, 10895}, {10641, 37197}, {10642, 12173}, {10653, 15687}, {10657, 38789}, {10658, 12902}, {10662, 12293}, {11302, 33561}, {11646, 41060}, {12101, 41113}, {12943, 19373}, {13881, 19781}, {15069, 20429}, {15305, 36980}, {15681, 16242}, {15684, 36968}, {16241, 19709}, {16773, 33703}, {17845, 30403}, {18584, 41040}, {19364, 21659}, {22615, 35738}, {22795, 22906}, {22797, 23013}, {22971, 22974}, {25164, 33518}, {31133, 37775}, {33699, 41120}, {36969, 38335}

X(42093) = {X(4),X(6)}-harmonic conjugate of X(42094)
X(42093) = {X(42095),X(42096)}-harmonic conjugate of X(3)
X(42093) = {X(42175),X(42176)}-harmonic conjugate of X(3)

X(42094) = GIBERT(1,2,0) POINT

Barycentrics    Sqrt[3]*a^2*S + 12*SB*SC : :

X(42094) lies on these lines: {3, 16808}, {4, 6}, {5, 11481}, {13, 3830}, {14, 12820}, {15, 382}, {16, 381}, {17, 5073}, {20, 23302}, {30, 11480}, {61, 5076}, {115, 36962}, {187, 36994}, {383, 31489}, {395, 3839}, {396, 3543}, {462, 31860}, {463, 41424}, {473, 26958}, {546, 18581}, {599, 622}, {621, 40341}, {624, 11296}, {1080, 37637}, {1250, 10895}, {1351, 16001}, {1656, 10646}, {1657, 10645}, {2043, 8253}, {2044, 8252}, {3091, 23303}, {3146, 11488}, {3391, 35821}, {3392, 35820}, {3411, 3843}, {3426, 11139}, {3531, 11138}, {3534, 37832}, {3627, 11542}, {3763, 11303}, {3832, 11489}, {3845, 10653}, {3851, 16967}, {3853, 40693}, {3855, 16773}, {3861, 40694}, {5024, 41025}, {5055, 33416}, {5072, 5237}, {5079, 5351}, {5093, 16002}, {5210, 41035}, {5353, 18513}, {5357, 18514}, {5472, 36961}, {5478, 16943}, {6409, 35740}, {6410, 35732}, {6411, 14814}, {6412, 14813}, {6778, 13102}, {7051, 12943}, {7507, 11476}, {9736, 14162}, {10516, 20429}, {10632, 35480}, {10633, 35488}, {10638, 12953}, {10641, 12173}, {10642, 37197}, {10654, 15687}, {10657, 12902}, {10658, 38789}, {10661, 12293}, {10896, 19373}, {11301, 33560}, {11646, 41061}, {12101, 41112}, {13881, 19780}, {15069, 20428}, {15305, 36978}, {15681, 16241}, {15684, 36967}, {16242, 19709}, {16772, 33703}, {17845, 30402}, {18584, 41041}, {19363, 21659}, {22644, 35738}, {22794, 22862}, {22796, 23006}, {22971, 22975}, {25154, 33517}, {31133, 37776}, {33699, 41119}, {36970, 38335}

X(42094) = {X(4),X(6)}-harmonic conjugate of X(42093)
X(42094) = {X(42097),X(42098)}-harmonic conjugate of X(3)
X(42094) = {X(42177),X(42178)}-harmonic conjugate of X(3)

X(42095) = GIBERT(-1,2,2) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*a^2*SA - 12*SB*SC : :

X(42095) lies on these lines: {2, 5321}, {3, 16809}, {4, 11481}, {5, 6}, {13, 16961}, {14, 5055}, {15, 1656}, {16, 381}, {18, 3851}, {61, 5079}, {62, 5072}, {115, 36765}, {382, 10646}, {395, 3545}, {396, 5071}, {397, 5068}, {398, 5056}, {546, 36843}, {547, 10654}, {599, 624}, {622, 9761}, {623, 3763}, {1250, 10896}, {1853, 10676}, {2041, 6412}, {2042, 6411}, {3090, 5334}, {3091, 5318}, {3523, 5349}, {3526, 10645}, {3533, 5365}, {3628, 36836}, {3830, 16242}, {3832, 16773}, {3843, 19106}, {3854, 5350}, {5050, 20416}, {5054, 36970}, {5066, 10653}, {5070, 16964}, {5076, 5351}, {5094, 11475}, {5141, 5367}, {5154, 5362}, {5617, 33517}, {6114, 31489}, {6144, 34509}, {6409, 35738}, {6560, 34562}, {6561, 34559}, {6670, 11298}, {6672, 11296}, {7486, 16772}, {7507, 10642}, {7547, 10633}, {7685, 41040}, {8252, 18587}, {8253, 18586}, {9113, 10612}, {10109, 41120}, {10658, 38724}, {10895, 19373}, {11297, 33561}, {11301, 16942}, {11476, 37197}, {12817, 15701}, {14269, 36968}, {15694, 36967}, {15703, 16241}, {19781, 31706}, {32395, 32398}, {34508, 40341}, {36990, 41041}, {37464, 41038}, {37832, 41122}

X(42095) = {X(3),X(42093)}-harmonic conjugate of X(42096)
X(42095) = {X(4),X(11481)}-harmonic conjugate of X(42097)
X(42095) = {X(5),X(6)}-harmonic conjugate of X(42098)

X(42096) = GIBERT(1,-2,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*a^2*SA - 12*SB*SC : :

X(42096) lies on these lines: {3, 16809}, {4, 11480}, {6, 30}, {13, 15684}, {14, 15681}, {15, 382}, {16, 1657}, {20, 5321}, {376, 23303}, {381, 10645}, {395, 11001}, {396, 15682}, {398, 5059}, {530, 6144}, {531, 40341}, {550, 18581}, {1546, 30402}, {2043, 6412}, {2044, 6411}, {3146, 5318}, {3522, 5349}, {3529, 5334}, {3534, 10646}, {3543, 11488}, {3627, 18582}, {3763, 11295}, {3830, 16644}, {3843, 16966}, {3851, 33417}, {5073, 5340}, {5076, 5238}, {5335, 33703}, {5895, 10675}, {7051, 12953}, {10632, 35490}, {10638, 12943}, {10642, 37196}, {10657, 38790}, {10676, 17845}, {11475, 12173}, {11486, 16964}, {11543, 15704}, {12817, 15695}, {14269, 16241}, {15640, 37640}, {15685, 36968}, {15688, 37835}, {15689, 16242}, {16772, 17578}, {32789, 36445}, {32790, 36463}, {34754, 36969}, {35434, 41943}, {36761, 39838}, {36993, 41039}, {37832, 38335}

X(42096) = reflection of X(42097) in X(6)
X(42096) = {X(3),X(42093)}-harmonic conjugate of X(42095)
X(42096) = {X(4),X(11480)}-harmonic conjugate of X(42098)

X(42097) = GIBERT(1,2,-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*a^2*SA + 12*SB*SC : :

X(42097) lies on these lines: {3, 16808}, {4, 11481}, {6, 30}, {13, 15681}, {14, 15684}, {15, 1657}, {16, 382}, {20, 5318}, {376, 23302}, {381, 10646}, {395, 15682}, {396, 11001}, {397, 5059}, {530, 40341}, {531, 6144}, {550, 18582}, {1250, 12943}, {1545, 30403}, {2043, 6411}, {2044, 6412}, {3146, 5321}, {3522, 5350}, {3529, 5335}, {3534, 10645}, {3543, 11489}, {3627, 18581}, {3763, 11296}, {3830, 16645}, {3843, 16967}, {3851, 33416}, {5073, 5339}, {5076, 5237}, {5334, 33703}, {5895, 10676}, {10633, 35490}, {10641, 37196}, {10658, 38790}, {10675, 17845}, {11476, 12173}, {11485, 16965}, {11542, 15704}, {12816, 15695}, {12953, 19373}, {14269, 16242}, {15640, 37641}, {15685, 36967}, {15688, 37832}, {15689, 16241}, {16773, 17578}, {32789, 36463}, {32790, 36445}, {34755, 36970}, {35434, 41944}, {36995, 41038}, {37835, 38335}, {39838, 41458}

X(42097) = reflection of X(42096) in X(6)
X(42097) = {X(3),X(42094)}-harmonic conjugate of X(42098)
X(42097) = {X(4),X(11481)}-harmonic conjugate of X(42095)

X(42098) = GIBERT(1,2,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*a^2*SA + 12*SB*SC : :

X(42098) lies on these lines: {2, 5318}, {3, 16808}, {4, 11480}, {5, 6}, {13, 5055}, {14, 16960}, {15, 381}, {16, 1656}, {17, 3851}, {61, 5072}, {62, 5079}, {115, 36771}, {382, 10645}, {395, 5071}, {396, 3545}, {397, 5056}, {398, 5068}, {546, 36836}, {547, 10653}, {599, 623}, {621, 9763}, {624, 3763}, {1853, 10675}, {2041, 6411}, {2042, 6412}, {3090, 5335}, {3091, 5321}, {3523, 5350}, {3526, 10646}, {3533, 5366}, {3628, 36843}, {3830, 16241}, {3832, 16772}, {3843, 19107}, {3854, 5349}, {5050, 20415}, {5054, 36969}, {5066, 10654}, {5070, 16965}, {5076, 5352}, {5094, 11476}, {5141, 5362}, {5154, 5367}, {5472, 36765}, {5613, 33518}, {6115, 31489}, {6144, 34508}, {6410, 35738}, {6560, 34559}, {6561, 34562}, {6669, 11297}, {6671, 11295}, {7051, 10895}, {7486, 16773}, {7507, 10641}, {7547, 10632}, {7684, 41041}, {8252, 18586}, {8253, 18587}, {9112, 10611}, {10109, 41119}, {10638, 10896}, {10657, 38724}, {11298, 33560}, {11302, 16943}, {11475, 37197}, {12816, 15701}, {13103, 36766}, {14269, 36967}, {15694, 36968}, {15703, 16242}, {19780, 31705}, {22892, 36772}, {32395, 32397}, {34509, 40341}, {36990, 41040}, {37463, 41039}, {37835, 41121}

X(42098) = {X(3),X(42094)}-harmonic conjugate of X(42097)
X(42098) = {X(4),X(11480)}-harmonic conjugate of X(42096)
X(42098) = {X(5),X(6)}-harmonic conjugate of X(42095)

X(42099) = GIBERT(1,-2,3) POINT

Barycentrics    Sqrt[3]*a^2*S + 9*a^2*SA - 12*SB*SC : :

X(42099) lies on these lines: {3, 16809}, {4, 10188}, {6, 1657}, {13, 15}, {14, 3534}, {16, 20}, {17, 5073}, {18, 550}, {61, 3529}, {62, 15704}, {74, 8173}, {376, 16242}, {381, 33417}, {382, 11480}, {395, 15686}, {398, 34755}, {531, 35751}, {548, 23303}, {621, 5463}, {623, 35931}, {1250, 4324}, {2777, 10657}, {3146, 5238}, {3206, 8718}, {3543, 37832}, {3627, 5352}, {3830, 16241}, {4316, 19373}, {5059, 5335}, {5237, 11543}, {5254, 41409}, {5339, 16961}, {5349, 33923}, {5351, 11489}, {5473, 6777}, {6240, 11475}, {6781, 19780}, {7748, 19781}, {8703, 12817}, {10483, 10638}, {10633, 13619}, {10641, 18560}, {10642, 35471}, {10653, 15683}, {10654, 11001}, {10658, 12121}, {10676, 34785}, {11476, 35481}, {11485, 16965}, {11486, 15681}, {11488, 33703}, {12821, 15707}, {15072, 36981}, {15640, 41121}, {15684, 16644}, {15685, 41101}, {15689, 16645}, {15690, 41122}, {15691, 41944}, {18468, 18565}, {19710, 41108}, {20063, 37776}, {22802, 30402}, {22843, 36756}, {22855, 36993}, {25166, 33518}, {25236, 41023}, {35304, 40334}, {36766, 36961}, {36992, 41024}

X(42099) = {X(6),X(1657)}-harmonic conjugate of X(42100)

X(42100) = GIBERT(1,2,-3) POINT

Barycentrics    Sqrt[3]*a^2*S - 9*a^2*SA + 12*SB*SC : :

X(42100) lies on these lines: {3, 16808}, {4, 10187}, {6, 1657}, {13, 3534}, {14, 16}, {15, 20}, {17, 550}, {18, 5073}, {61, 15704}, {62, 3529}, {74, 8172}, {376, 16241}, {381, 33416}, {382, 11481}, {396, 15686}, {397, 34754}, {530, 36329}, {548, 23302}, {622, 5464}, {624, 35932}, {1250, 10483}, {2777, 10658}, {3146, 5237}, {3205, 8718}, {3543, 37835}, {3627, 5351}, {3830, 16242}, {4316, 7051}, {4324, 10638}, {5059, 5334}, {5238, 11542}, {5254, 41408}, {5340, 16960}, {5350, 33923}, {5352, 11488}, {5474, 6778}, {6240, 11476}, {6781, 19781}, {7748, 19780}, {8703, 12816}, {10632, 13619}, {10641, 35471}, {10642, 18560}, {10653, 11001}, {10654, 15683}, {10657, 12121}, {10675, 34785}, {11475, 35481}, {11485, 15681}, {11486, 16964}, {11489, 33703}, {12820, 15707}, {15072, 36979}, {15640, 41122}, {15684, 16645}, {15685, 41100}, {15689, 16644}, {15690, 41121}, {15691, 41943}, {18470, 18565}, {19710, 41107}, {20063, 37775}, {22802, 30403}, {22890, 36755}, {22901, 36995}, {25156, 33517}, {25235, 41022}, {35303, 40335}, {36994, 41025}

X(42100) = {X(6),X(1657)}-harmonic conjugate of X(42099)

X(42101) = GIBERT(-1,3,0) POINT

Barycentrics    Sqrt[3]*a^2*S - 18*SB*SC : :

X(42101) lies on these lines: {3, 42103}, {4, 6}, {5, 10645}, {13, 14893}, {14, 12821}, {15, 546}, {16, 3627}, {18, 41977}, {30, 10646}, {62, 12102}, {381, 23302}, {382, 16773}, {383, 3054}, {395, 3830}, {396, 3845}, {548, 33416}, {550, 16967}, {621, 3631}, {622, 3630}, {1080, 3055}, {2043, 32790}, {2044, 32789}, {3091, 11480}, {3146, 11481}, {3411, 3853}, {3543, 11489}, {3832, 16772}, {3839, 11488}, {3843, 18582}, {3850, 16966}, {3857, 5238}, {3861, 11542}, {5066, 36967}, {5076, 11486}, {5352, 12811}, {6221, 35740}, {6411, 35732}, {8588, 41034}, {8589, 41035}, {10151, 10641}, {10653, 38335}, {10654, 14269}, {11138, 13603}, {11139, 14487}, {11304, 34573}, {11475, 23047}, {12101, 12817}, {15682, 16645}, {16194, 36980}, {16241, 38071}, {16539, 32062}, {16644, 41099}, {16962, 41987}, {18323, 18470}, {18358, 20428}, {18424, 41017}, {21850, 25164}, {22512, 41408}, {23046, 37832}, {33699, 36968}

X(42101) = {X(4),X(6)}-harmonic conjugate of X(42102)
X(42101) = {X(42103),X(42104)}-harmonic conjugate of X(3)
X(42101) = {X(42107),X(42108)}-harmonic conjugate of X(3)
X(42101) = {X(42183),X(42184)}-harmonic conjugate of X(3)

X(42102) = GIBERT(1,3,0) POINT

Barycentrics    Sqrt[3]*a^2*S + 18*SB*SC : :

X(42102) lies on these lines: {3, 42105}, {4, 6}, {5, 10646}, {13, 12820}, {14, 14893}, {15, 3627}, {16, 546}, {17, 41978}, {30, 10645}, {61, 12102}, {381, 23303}, {382, 16772}, {383, 3055}, {395, 3845}, {396, 3830}, {548, 33417}, {550, 16966}, {621, 3630}, {622, 3631}, {1080, 3054}, {2043, 32789}, {2044, 32790}, {3091, 11481}, {3146, 11480}, {3412, 3853}, {3543, 11488}, {3832, 16773}, {3839, 11489}, {3843, 18581}, {3850, 16967}, {3857, 5237}, {3861, 11543}, {5066, 36968}, {5076, 11485}, {5351, 12811}, {6200, 35740}, {6412, 35732}, {8588, 41035}, {8589, 41034}, {10151, 10642}, {10653, 14269}, {10654, 38335}, {11138, 14487}, {11139, 13603}, {11303, 34573}, {11476, 23047}, {12101, 12816}, {15682, 16644}, {16194, 36978}, {16242, 38071}, {16538, 32062}, {16645, 41099}, {16963, 41987}, {18323, 18468}, {18358, 20429}, {18424, 41016}, {21850, 25154}, {22513, 41409}, {23046, 37835}, {33699, 36967}

X(42102) = {X(4),X(6)}-harmonic conjugate of X(42101)
X(42102) = {X(42105),X(42106)}-harmonic conjugate of X(3)
X(42102) = {X(42109),X(42110)}-harmonic conjugate of X(3)
X(42102) = {X(42113),X(42114)}-harmonic conjugate of X(3)
X(42102) = {X(42185),X(42186)}-harmonic conjugate of X(3)

X(42103) = GIBERT(-1,3,1) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA - 18*SB*SC : :

X(42103) lies on these lines: {2, 12821}, {3,42102}, {4, 16}, {5, 11480}, {6, 546}, {13, 33603}, {14, 3839}, {15, 3091}, {17, 3854}, {20, 16967}, {376, 33416}, {381, 396}, {382, 23303}, {395, 14269}, {622, 22491}, {3090, 10645}, {3146, 10646}, {3543, 37835}, {3544, 5238}, {3545, 16966}, {3627, 11481}, {3832, 5334}, {3843, 5318}, {3845, 10653}, {3851, 5349}, {3855, 11488}, {3857, 22236}, {3858, 5339}, {3860, 41119}, {5056, 33417}, {5071, 36967}, {5352, 15022}, {7394, 37776}, {11268, 18568}, {12102, 36843}, {12811, 36836}, {12817, 37832}, {15682, 16242}, {15687, 16645}, {16644, 38071}, {16961, 36969}, {22795, 22907}, {33517, 41042}, {33518, 41036}, {33607, 41108}

X(42103) = {X(3),X(42101)}-harmonic conjugate of X(42104)
X(42103) = {X(4),X(16)}-harmonic conjugate of X(42105)
X(42103) = {X(6),X(546)}-harmonic conjugate of X(42106)

X(42104) = GIBERT(1,-3,1) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 18*SB*SC : :

X(42104) lies on these lines: {3, 42101), {4, 15}, {6, 3627}, {14, 15682}, {16, 3146}, {20, 16809}, {30, 11481}, {376, 16967}, {382, 5321}, {395, 15684}, {396, 38335}, {546, 11480}, {1657, 23303}, {3091, 10645}, {3522, 33416}, {3529, 10646}, {3543, 5334}, {3545, 33417}, {3830, 5318}, {3832, 16966}, {3839, 36967}, {3843, 23302}, {3853, 40693}, {5073, 5349}, {5076, 11485}, {5237, 11541}, {5335, 16964}, {5344, 41973}, {7391, 37775}, {11001, 37835}, {11489, 33703}, {11542, 15687}, {12102, 22236}, {12817, 15640}, {14893, 16644}, {15683, 16242}, {16241, 41099}, {16960, 41119}, {33625, 36326}, {33699, 41113}

X(42104) = {X(3),X(42101)}-harmonic conjugate of X(42103)
X(42104) = {X(4),X(15)}-harmonic conjugate of X(42106)
X(42104) = {X(6),X(3627)}-harmonic conjugate of X(42105)

X(42105) = GIBERT(1,3,-1) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 18*SB*SC : :

X(42105) lies on these lines: {3,42102}, {4, 16}, {6, 3627}, {13, 15682}, {15, 3146}, {20, 16808}, {30, 11480}, {376, 16966}, {382, 5318}, {395, 38335}, {396, 15684}, {546, 11481}, {1657, 23302}, {3091, 10646}, {3522, 33417}, {3529, 10645}, {3543, 5335}, {3545, 33416}, {3830, 5321}, {3832, 16967}, {3839, 36968}, {3843, 23303}, {3853, 40694}, {5073, 5350}, {5076, 11486}, {5238, 11541}, {5334, 16965}, {5343, 41974}, {7391, 37776}, {11001, 37832}, {11488, 33703}, {11543, 15687}, {12102, 22238}, {12816, 15640}, {14893, 16645}, {15683, 16241}, {16242, 41099}, {16961, 41120}, {33623, 36324}, {33699, 41112}

X(42105) = {X(3),X(42102)}-harmonic conjugate of X(42106)
X(42105) = {X(4),X(16)}-harmonic conjugate of X(42103)
X(42105) = {X(6),X(3627)}-harmonic conjugate of X(42104)

X(42106) = GIBERT(1,3,1) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 18*SB*SC : :

X(42106) lies on these lines: {2, 12820}, {3,42102}, {4, 15}, {5, 11481}, {6, 546}, {13, 3839}, {14, 33602}, {16, 3091}, {18, 3854}, {20, 16966}, {376, 33417}, {381, 395}, {382, 23302}, {396, 14269}, {621, 22492}, {3090, 10646}, {3146, 10645}, {3543, 37832}, {3544, 5237}, {3545, 16967}, {3627, 11480}, {3832, 5335}, {3843, 5321}, {3845, 10654}, {3851, 5350}, {3855, 11489}, {3857, 22238}, {3858, 5340}, {3860, 41120}, {5056, 33416}, {5071, 36968}, {5351, 15022}, {7394, 37775}, {11267, 18568}, {12102, 36836}, {12811, 36843}, {12816, 37835}, {15682, 16241}, {15687, 16644}, {16645, 38071}, {16960, 36970}, {22794, 22861}, {33517, 41037}, {33518, 41043}, {33606, 41107}

X(42106) = {X(3),X(42102)}-harmonic conjugate of X(42105)
X(42106) = {X(4),X(15)}-harmonic conjugate of X(42104)
X(42106) = {X(6),X(546)}-harmonic conjugate of X(42103)

X(42107) = GIBERT(-1,3,2) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*a^2*SA - 18*SB*SC : :

X(42107) lies on these lines: {3,42101}, {4, 11481}, {5, 15}, {6, 3091}, {13, 38071}, {14, 5066}, {16, 546}, {18, 3858}, {30, 16967}, {61, 12811}, {62, 3857}, {140, 19107}, {381, 395}, {396, 3545}, {397, 3850}, {398, 3851}, {547, 33417}, {550, 33416}, {623, 31694}, {1656, 5349}, {3090, 11480}, {3544, 22236}, {3614, 10638}, {3627, 10646}, {3628, 10645}, {3832, 11489}, {3839, 16645}, {3843, 16773}, {3845, 19106}, {3854, 5340}, {3855, 5335}, {3856, 16965}, {3859, 16961}, {5068, 5339}, {5072, 11485}, {5133, 37775}, {5238, 12812}, {5351, 12102}, {6777, 20252}, {7051, 7173}, {10109, 16241}, {10151, 11476}, {10297, 10635}, {10632, 35487}, {10642, 23047}, {10654, 19709}, {10658, 11801}, {11737, 37832}, {14893, 36968}, {15022, 36836}, {15687, 16242}, {15699, 36967}, {16626, 18358}, {22513, 22847}, {23046, 36969}, {30403, 41362}, {32789, 35732}, {33561, 37352}, {34755, 41991}

X(42107) = {X(3),X(42101)}-harmonic conjugate of X(42108)
X(42107) = {X(4),X(11481)}-harmonic conjugate of X(42109)
X(42107) = {X(6),X(3091)}-harmonic conjugate of X(42110)

X(42108) = GIBERT(1,-3,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*a^2*SA - 18*SB*SC : :

X(42108) lies on these lines: {3, 42101}, {4, 11480}, {6, 3146}, {13, 33699}, {14, 16}, {15, 3627}, {20, 23303}, {382, 5318}, {396, 3543}, {397, 19106}, {398, 5073}, {546, 10645}, {548, 16967}, {550, 16809}, {622, 36331}, {1657, 5349}, {3529, 11481}, {3830, 18582}, {3845, 16966}, {3850, 33417}, {3853, 16772}, {5059, 11489}, {5238, 12102}, {5334, 33703}, {5335, 15682}, {5350, 11542}, {5893, 30402}, {6108, 41151}, {8703, 33416}, {10646, 15704}, {10654, 15684}, {11488, 17578}, {11541, 22238}, {12101, 37832}, {14893, 16241}, {15683, 16645}, {15686, 37835}, {15687, 36967}, {16242, 19710}, {16773, 17800}, {34603, 37776}, {35404, 36969}

X(42108) = {X(3),X(42101)}-harmonic conjugate of X(42107)
X(42108) = {X(4),X(11480)}-harmonic conjugate of X(42110)
X(42108) = {X(6),X(3146)}-harmonic conjugate of X(42109)

X(42109) = GIBERT(1,3,-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*a^2*SA + 18*SB*SC : :

X(42109) lies on these lines: {3,42102}, {4, 11481}, {6, 3146}, {13, 15}, {14, 33699}, {16, 3627}, {20, 23302}, {382, 5321}, {395, 3543}, {397, 5073}, {398, 19107}, {546, 10646}, {548, 16966}, {550, 16808}, {621, 35750}, {623, 36768}, {1657, 5350}, {3529, 11480}, {3830, 18581}, {3845, 16967}, {3850, 33416}, {3853, 16773}, {5059, 11488}, {5237, 12102}, {5334, 15682}, {5335, 33703}, {5349, 11543}, {5893, 30403}, {6109, 41151}, {8703, 33417}, {10645, 15704}, {10653, 15684}, {11489, 17578}, {11541, 22236}, {12101, 37835}, {14893, 16242}, {15683, 16644}, {15686, 37832}, {15687, 36968}, {16241, 19710}, {16772, 17800}, {34603, 37775}, {35404, 36970}

X(42109) = {X(3),X(42102)}-harmonic conjugate of X(42110)
X(42109) = {X(4),X(11481)}-harmonic conjugate of X(42107)
X(42109) = {X(6),X(3146)}-harmonic conjugate of X(42108)

X(42110) = GIBERT(1,3,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*a^2*SA + 18*SB*SC : :

X(42110) lies on these lines: {3,42102}, {4, 11480}, {5, 16}, {6, 3091}, {13, 5066}, {14, 38071}, {15, 546}, {17, 3858}, {30, 16966}, {61, 3857}, {62, 12811}, {140, 19106}, {381, 396}, {395, 3545}, {397, 3851}, {398, 3850}, {547, 33416}, {550, 33417}, {624, 31693}, {1250, 3614}, {1656, 5350}, {3090, 11481}, {3544, 22238}, {3627, 10645}, {3628, 10646}, {3832, 11488}, {3839, 16644}, {3843, 16772}, {3845, 19107}, {3854, 5339}, {3855, 5334}, {3856, 16964}, {3859, 16960}, {5068, 5340}, {5072, 11486}, {5133, 37776}, {5237, 12812}, {5352, 12102}, {6778, 20253}, {7173, 19373}, {10109, 16242}, {10151, 11475}, {10297, 10634}, {10633, 35487}, {10641, 23047}, {10653, 19709}, {10657, 11801}, {11737, 37835}, {14893, 36967}, {15022, 36843}, {15687, 16241}, {15699, 36968}, {16627, 18358}, {22512, 22893}, {23046, 36970}, {30402, 41362}, {32790, 35732}, {33560, 37351}, {34754, 41991}

X(42110) = {X(3),X(42102)}-harmonic conjugate of X(42109)
X(42110) = {X(4),X(11480)}-harmonic conjugate of X(42108)
X(42110) = {X(6),X(3091)}-harmonic conjugate of X(42107)

X(42111) = GIBERT(-1,3,3) POINT

Barycentrics    Sqrt[3]*a^2*S - 9*a^2*SA - 18*SB*SC : :

X(42111) lies on these lines: {2, 10645}, {3,42101}, {4, 10187}, {5, 6}, {14, 5071}, {15, 3090}, {16, 3091}, {18, 5068}, {20, 33416}, {61, 15022}, {62, 3544}, {303, 22491}, {381, 23303}, {395, 19709}, {396, 41120}, {546, 11481}, {623, 3619}, {624, 3620}, {631, 19107}, {1656, 5321}, {3545, 10653}, {3618, 5460}, {3628, 11480}, {3832, 19106}, {3839, 16242}, {3851, 5318}, {3857, 36843}, {5055, 10654}, {5056, 5334}, {5066, 16645}, {5067, 33417}, {5072, 11486}, {5079, 11485}, {5339, 35018}, {6411, 35738}, {6670, 37170}, {7486, 16964}, {10109, 16644}, {10658, 15081}, {11008, 34509}, {11306, 34573}, {12811, 22238}, {12812, 22236}, {18586, 32789}, {18587, 32790}, {20080, 34508}, {22907, 41409}, {31706, 41407}, {32785, 35731}, {36968, 41099}, {36969, 41106}, {37640, 41122}, {37641, 41119}

X(42111) = {X(3),X(42101)}-harmonic conjugate of X(42112)
X(42111) = {X(4),X(10646)}-harmonic conjugate of X(42113)
X(42111) = {X(5),X(6)}-harmonic conjugate of X(42114)

X(42112) = GIBERT(1,-3,3) POINT

Barycentrics    Sqrt[3]*a^2*S + 9*a^2*SA - 18*SB*SC : :

X(42112) lies on these lines: {3,42101}, {4, 10188}, {6, 30}, {14, 15683}, {15, 3146}, {16, 3529}, {20, 10646}, {61, 11541}, {376, 16809}, {382, 16772}, {395, 15685}, {530, 11008}, {531, 20080}, {1657, 5321}, {3522, 16967}, {3528, 33416}, {3534, 23303}, {3543, 16808}, {3627, 11480}, {3830, 23302}, {3832, 33417}, {5059, 5334}, {5073, 5318}, {5343, 16961}, {6110, 33630}, {11001, 11489}, {11295, 34573}, {11481, 15704}, {11488, 15682}, {15640, 36969}, {16644, 33699}, {16645, 19710}, {17800, 40694}, {19106, 33703}, {36968, 41113}

X(42112) = reflection of X(42113) in X(6)
X(42112) = {X(3),X(42101)}-harmonic conjugate of X(42111)
X(42112) = {X(4),X(10645)}-harmonic conjugate of X(42114)

X(42113) = GIBERT(1,3,-3) POINT

Barycentrics    Sqrt[3]*a^2*S - 9*a^2*SA + 18*SB*SC : :

X(42113) lies on these lines: {3,42102, {4, 10187}, {6, 30}, {13, 15683}, {15, 3529}, {16, 3146}, {20, 10645}, {62, 11541}, {376, 16808}, {382, 16773}, {396, 15685}, {530, 20080}, {531, 11008}, {1657, 5318}, {3522, 16966}, {3528, 33417}, {3534, 23302}, {3543, 16809}, {3627, 11481}, {3830, 23303}, {3832, 33416}, {5059, 5335}, {5073, 5321}, {5344, 16960}, {6111, 33630}, {11001, 11488}, {11296, 34573}, {11480, 15704}, {11489, 15682}, {15640, 36970}, {16644, 19710}, {16645, 33699}, {17800, 40693}, {19107, 33703}, {36967, 41112}

X(42113) = reflection of X(42112) in X(6)
X(42113) = {X(3),X(42102)}-harmonic conjugate of X(42114)
X(42113) = {X(4),X(10646)}-harmonic conjugate of X(42111)

X(42114) = GIBERT(1,3,3) POINT

Barycentrics    Sqrt[3]*a^2*S + 9*a^2*SA + 18*SB*SC : :

X(42114) lies on these lines: {2, 10646}, {3, 42102}, {4, 10188}, {5, 6}, {13, 5071}, {15, 3091}, {16, 3090}, {17, 5068}, {20, 33417}, {61, 3544}, {62, 15022}, {302, 22492}, {381, 23302}, {395, 41119}, {396, 19709}, {546, 11480}, {623, 3620}, {624, 3619}, {631, 19106}, {1656, 5318}, {3545, 10654}, {3618, 5459}, {3628, 11481}, {3832, 19107}, {3839, 16241}, {3851, 5321}, {3857, 36836}, {5055, 10653}, {5056, 5335}, {5066, 16644}, {5067, 33416}, {5072, 11485}, {5079, 11486}, {5340, 35018}, {6412, 35738}, {6669, 37171}, {7486, 16965}, {10109, 16645}, {10657, 15081}, {11008, 34508}, {11305, 34573}, {12811, 22236}, {12812, 22238}, {18586, 32790}, {18587, 32789}, {20080, 34509}, {22861, 41408}, {31705, 41406}, {36967, 41099}, {36970, 41106}, {37640, 41120}, {37641, 41121}

X(42114) = {X(3),X(42102)}-harmonic conjugate of X(42113)
X(42114) = {X(4),X(10645)}-harmonic conjugate of X(42112)
X(42114) = {X(5),X(6)}-harmonic conjugate of X(42111)

X(42115) = GIBERT(-2,0,3) POINT

Barycentrics    a^2*(2*Sqrt[3]*S - 9*SA) : :
Barycentrics    a^2*(2*Sqrt[3]*S - 9*SA) : :
Barycentrics    (3*Sqrt[3]*Cos[A] - 2*Sin[A])*Sin[A] : :

X(42115) lies on these lines: {2, 33602}, {3, 6}, {4, 42121}, {5, 42120}, {13, 15694}, {14, 15681}, {18, 5073}, {20, 11543}, {30, 11489}, {69, 35303}, {140, 5335}, {186, 11408}, {302, 11296}, {376, 42117}, {378, 11409}, {381, 23303}, {382, 16773}, {395, 3534}, {396, 15693}, {397, 15720}, {398, 42090}, {466, 37643}, {546, 42141}, {548, 42119}, {549, 11488}, {550, 5334}, {616, 11302}, {631, 11542}, {999, 1250}, {1593, 10633}, {1597, 10642}, {1598, 11476}, {1656, 5318}, {1657, 5321}, {2041, 18762}, {2042, 18538}, {2043, 42225}, {2044, 42226}, {2045, 42202}, {2046, 42201}, {3068, 15764}, {3070, 42198}, {3071, 42196}, {3090, 42138}, {3091, 42137}, {3132, 26864}, {3146, 42135}, {3295, 19373}, {3426, 32586}, {3522, 42122}, {3523, 42124}, {3526, 18582}, {3529, 42136}, {3544, 42591}, {3618, 35304}, {3619, 37341}, {3620, 37173}, {3627, 42139}, {3628, 42142}, {3763, 5463}, {3830, 16645}, {3843, 19106}, {3851, 16967}, {3858, 42473}, {5054, 10653}, {5055, 16242}, {5070, 16965}, {5072, 42106}, {5076, 42103}, {5079, 42110}, {5204, 5353}, {5217, 5357}, {5339, 16961}, {5340, 16966}, {5362, 16371}, {5366, 35018}, {5367, 16370}, {5464, 40341}, {6000, 17827}, {8703, 37641}, {9541, 36457}, {10605, 21648}, {10632, 15750}, {10654, 15688}, {10675, 14530}, {10676, 13093}, {11202, 17826}, {11244, 35450}, {11268, 12085}, {11300, 34540}, {11421, 21312}, {12100, 37640}, {12812, 42493}, {14269, 37835}, {14813, 23249}, {14814, 23259}, {14869, 42627}, {14891, 42633}, {15684, 41944}, {15685, 36970}, {15686, 42497}, {15689, 16963}, {15695, 36967}, {15696, 40694}, {15701, 16644}, {15704, 42140}, {15707, 16241}, {15714, 42517}, {15723, 42501}, {15765, 32785}, {17538, 42585}, {17800, 19107}, {18424, 22862}, {18585, 32786}, {19709, 36969}, {21475, 37633}, {21476, 37680}, {23267, 42224}, {23273, 42222}, {30403, 32063}, {33417, 42156}, {34200, 42634}, {35255, 36437}, {35256, 36455}, {35400, 42429}, {35434, 42513}, {35732, 42213}, {36995, 41041}, {42104, 42163}, {42105, 42107}, {42108, 42159}, {42187, 42193}, {42188, 42250}, {42189, 42191}, {42190, 42252}, {42192, 42246}, {42194, 42248}, {42195, 42256}, {42197, 42254}, {42211, 42282}, {42217, 42280}, {42219, 42281}, {42498, 42505}

X(42115) = isogonal conjugate of X(33603)
X(42115) = isogonal conjugate of the anticomplement of X(33618)
X(42115) = X(1)-isoconjugate of X(33603)
X(42115) = Brocard-circle-inverse of X(42116)
X(42115) = Schoute-circle-inverse of X(22238)
X(42115) = barycentric quotient X(6)/X(33603)
X(42115) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42118, 42128}, {3, 6, 42116}, {3, 16, 11486}, {3, 11486, 11485}, {4, 42121, 42129}, {4, 42123, 42131}, {5, 42120, 42127}, {6, 10646, 3}, {6, 11480, 34754}, {6, 11481, 10646}, {6, 41408, 21309}, {6, 42116, 11485}, {14, 42625, 15681}, {15, 16, 22238}, {16, 5237, 11481}, {16, 5351, 15}, {16, 10645, 34755}, {16, 10646, 6}, {16, 11481, 3}, {18, 42100, 42093}, {20, 11543, 42126}, {61, 35739, 1152}, {62, 34754, 6}, {140, 5335, 42132}, {550, 5334, 42130}, {1350, 21159, 3}, {3365, 35739, 6454}, {3627, 42628, 42139}, {5237, 36843, 3}, {5318, 42089, 1656}, {5321, 42091, 1657}, {5351, 22238, 3}, {6200, 6396, 11481}, {6200, 6445, 42116}, {6221, 6398, 11486}, {6221, 6451, 42116}, {6396, 6446, 42116}, {6398, 6452, 42116}, {6410, 17851, 42116}, {10645, 34755, 6}, {10646, 34755, 10645}, {11481, 36843, 16}, {11486, 42116, 6}, {15655, 33878, 42116}, {16242, 42155, 5055}, {16645, 36968, 3830}, {16645, 42097, 16809}, {16773, 42088, 18581}, {16809, 36968, 42097}, {16809, 42097, 3830}, {16961, 42099, 5339}, {16963, 42528, 42154}, {16965, 33416, 42098}, {16965, 42491, 5070}, {16967, 42094, 3851}, {16967, 42158, 42094}, {18581, 42088, 382}, {18581, 42113, 42101}, {19106, 42095, 3843}, {23303, 42086, 381}, {23303, 42102, 42111}, {33416, 42098, 5070}, {42086, 42111, 42102}, {42088, 42101, 42113}, {42089, 42151, 5318}, {42091, 42149, 5321}, {42093, 42100, 5073}, {42098, 42491, 33416}, {42101, 42113, 382}, {42102, 42111, 381}, {42103, 42109, 5076}, {42109, 42599, 42103}, {42121, 42123, 4}, {42121, 42145, 42143}, {42123, 42143, 42145}, {42129, 42131, 4}, {42135, 42584, 3146}, {42143, 42145, 4}, {42153, 42433, 17800}, {42154, 42528, 15689}, {42195, 42256, 42284}, {42195, 42284, 42279}, {42197, 42254, 42283}, {42197, 42283, 42278}, {42221, 42223, 4}

X(42116) = GIBERT(2,0,3) POINT

Barycentrics    a^2*(2*Sqrt[3]*S + 9*SA) : :
Barycentrics    a^2*(2*Sqrt[3]*S + 9*SA) : :
Barycentrics    Sin[A]*(3*Sqrt[3]*Cos[A] + 2*Sin[A]) : :

X(42116) lies on these lines: {2, 33603}, {3, 6}, {4, 42122}, {5, 42119}, {13, 15681}, {14, 15694}, {17, 5073}, {20, 11542}, {30, 11488}, {69, 35304}, {140, 5334}, {186, 11409}, {303, 11295}, {376, 42118}, {378, 11408}, {381, 23302}, {382, 16772}, {395, 15693}, {396, 3534}, {397, 42091}, {398, 15720}, {465, 37643}, {546, 42140}, {548, 42120}, {549, 11489}, {550, 5335}, {617, 11301}, {631, 11543}, {999, 10638}, {1593, 10632}, {1597, 10641}, {1598, 11475}, {1656, 5321}, {1657, 5318}, {2041, 18538}, {2042, 18762}, {2043, 42226}, {2044, 42225}, {2045, 42199}, {2046, 42200}, {3069, 15764}, {3070, 42197}, {3071, 42195}, {3090, 42135}, {3091, 42136}, {3131, 26864}, {3146, 42138}, {3295, 7051}, {3426, 32585}, {3522, 42123}, {3523, 42121}, {3526, 18581}, {3529, 42137}, {3544, 42590}, {3618, 35303}, {3619, 37340}, {3620, 37172}, {3627, 42142}, {3628, 42139}, {3763, 5464}, {3830, 16644}, {3843, 19107}, {3851, 16966}, {3858, 42472}, {5054, 10654}, {5055, 16241}, {5070, 16964}, {5072, 42103}, {5076, 42106}, {5079, 42107}, {5204, 5357}, {5217, 5353}, {5339, 16967}, {5340, 16960}, {5362, 16370}, {5365, 35018}, {5367, 16371}, {5463, 40341}, {6000, 17826}, {6771, 36772}, {8703, 37640}, {9541, 36439}, {10605, 21647}, {10633, 15750}, {10653, 15688}, {10675, 13093}, {10676, 14530}, {11202, 17827}, {11243, 35450}, {11267, 12085}, {11299, 34541}, {11420, 21312}, {12100, 37641}, {12812, 42492}, {14269, 37832}, {14813, 23259}, {14814, 23249}, {14869, 42628}, {14891, 42634}, {15684, 41943}, {15685, 36969}, {15686, 42496}, {15689, 16962}, {15695, 36968}, {15696, 40693}, {15701, 16645}, {15704, 42141}, {15707, 16242}, {15714, 42516}, {15723, 42500}, {15765, 32786}, {17538, 42584}, {17800, 19106}, {18424, 22906}, {18585, 32785}, {19709, 36970}, {21475, 37680}, {21476, 37633}, {23267, 42223}, {23273, 42221}, {30402, 32063}, {33416, 42153}, {34200, 42633}, {35255, 36455}, {35256, 36437}, {35400, 42430}, {35434, 42512}, {35732, 42212}, {36993, 41040}, {42104, 42110}, {42105, 42166}, {42109, 42162}, {42187, 42251}, {42188, 42194}, {42189, 42253}, {42190, 42192}, {42191, 42247}, {42193, 42249}, {42196, 42257}, {42198, 42255}, {42214, 42282}, {42218, 42281}, {42220, 42280}, {42499, 42504}

X(42116) = reflection of X(42116) in Brocard axis
X(42116) = isogonal conjugate of X(33602)
X(42116) = isogonal conjugate of the anticomplement of X(33619)
X(42116) = Brocard-circle-inverse of X(42115)
X(42116) = Schoute-circle-inverse of X(22236)
X(42116) = X(1)-isoconjugate of X(33602)
X(42116) = barycentric quotient X(6)/X(33602)
X(42116) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42117, 42125}, {3, 6, 42115}, {3, 15, 11485}, {3, 11485, 11486}, {4, 42122, 42130}, {4, 42124, 42132}, {5, 42119, 42126}, {6, 10645, 3}, {6, 11480, 10645}, {6, 11481, 34755}, {6, 41409, 21309}, {6, 42115, 11486}, {13, 42626, 15681}, {15, 16, 22236}, {15, 5238, 11480}, {15, 5352, 16}, {15, 10645, 6}, {15, 10646, 34754}, {15, 11480, 3}, {17, 42099, 42094}, {20, 11542, 42127}, {61, 34755, 6}, {140, 5334, 42129}, {550, 5335, 42131}, {1350, 21158, 3}, {3627, 42627, 42142}, {5238, 36836, 3}, {5318, 42090, 1657}, {5321, 42092, 1656}, {5352, 22236, 3}, {6200, 6396, 11480}, {6200, 6445, 42115}, {6221, 6398, 11485}, {6221, 6451, 42115}, {6396, 6446, 42115}, {6398, 6452, 42115}, {6410, 17851, 42115}, {10645, 34754, 10646}, {10646, 34754, 6}, {11480, 36836, 15}, {11485, 42115, 6}, {15655, 33878, 42115}, {16241, 42154, 5055}, {16644, 36967, 3830}, {16644, 42096, 16808}, {16772, 42087, 18582}, {16808, 36967, 42096}, {16808, 42096, 3830}, {16960, 42100, 5340}, {16962, 42529, 42155}, {16964, 33417, 42095}, {16964, 42490, 5070}, {16966, 42093, 3851}, {16966, 42157, 42093}, {18582, 42087, 382}, {18582, 42112, 42102}, {19107, 42098, 3843}, {23302, 42085, 381}, {23302, 42101, 42114}, {33417, 42095, 5070}, {42085, 42114, 42101}, {42087, 42102, 42112}, {42090, 42152, 5318}, {42092, 42150, 5321}, {42094, 42099, 5073}, {42095, 42490, 33417}, {42101, 42114, 381}, {42102, 42112, 382}, {42106, 42108, 5076}, {42108, 42598, 42106}, {42122, 42124, 4}, {42122, 42146, 42144}, {42124, 42144, 42146}, {42130, 42132, 4}, {42138, 42585, 3146}, {42144, 42146, 4}, {42155, 42529, 15689}, {42156, 42434, 17800}, {42196, 42257, 42284}, {42196, 42284, 42278}, {42198, 42255, 42283}, {42198, 42283, 42279}, {42222, 42224, 4}

X(42117) = GIBERT(2,-1,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*a^2*SA - 6*SB*SC : :

X(42117) is the intersection of the tangents to the Evans conic at X(14) and X(15). (Randy Hutson, May 31, 2021)

X(42117) lies on these lines: {2, 33603}, {3, 5334}, {4, 11408}, {5, 15}, {6, 30}, {13, 12820}, {14, 549}, {16, 398}, {17, 3858}, {18, 15712}, {20, 11486}, {53, 6110}, {61, 3627}, {62, 15704}, {69, 11295}, {140, 5339}, {141, 531}, {235, 10632}, {302, 35304}, {303, 31694}, {381, 11488}, {382, 5335}, {395, 8703}, {396, 3845}, {397, 19106}, {495, 10638}, {496, 7051}, {530, 3629}, {533, 3630}, {546, 18582}, {548, 11481}, {617, 37351}, {618, 35022}, {621, 37340}, {632, 5238}, {1546, 21647}, {1595, 11475}, {1596, 10641}, {1656, 5343}, {2043, 6398}, {2044, 6221}, {3054, 6109}, {3534, 37641}, {3618, 11296}, {3619, 11297}, {3628, 36836}, {3631, 3643}, {3642, 34573}, {3830, 37640}, {3851, 5365}, {3853, 40693}, {5066, 16644}, {5352, 14869}, {5353, 6284}, {5357, 7354}, {5362, 11113}, {5367, 11112}, {5617, 36772}, {6200, 34551}, {6396, 34552}, {6823, 10634}, {8972, 36445}, {10299, 22237}, {10301, 37776}, {10642, 37458}, {10678, 36966}, {11299, 34540}, {11304, 34541}, {11409, 18533}, {11539, 37835}, {11812, 41120}, {12100, 16645}, {12103, 22238}, {13350, 16002}, {13665, 36455}, {13785, 36437}, {13941, 36463}, {15686, 34755}, {15699, 16241}, {15713, 41122}, {15714, 41944}, {15760, 18468}, {15765, 18762}, {16242, 17504}, {16773, 16961}, {16962, 23046}, {18538, 18585}, {18586, 23259}, {18587, 23249}, {19710, 36968}, {22512, 22906}, {30739, 37775}, {33699, 36969}, {35255, 36439}, {35256, 36457}, {36993, 41034}, {37832, 38071}, {41943, 41971}

X(42117) = reflection of X(42118) in X(6)

X(42118) = GIBERT(2,1,-1) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*a^2*SA + 6*SB*SC : :

X(42118) is the intersection of the tangents to the Evans conic at X(13) and X(16). (Randy Hutson, May 31, 2021)

X(42118) lies on these lines: {2, 33602}, {3, 5335}, {4, 11409}, {5, 16}, {6, 30}, {13, 549}, {14, 12821}, {15, 397}, {17, 15712}, {18, 3858}, {20, 11485}, {53, 6111}, {61, 15704}, {62, 3627}, {69, 11296}, {140, 5340}, {141, 530}, {235, 10633}, {302, 31693}, {303, 35303}, {381, 11489}, {382, 5334}, {395, 3845}, {396, 8703}, {398, 19107}, {495, 1250}, {496, 19373}, {531, 3629}, {532, 3630}, {546, 18581}, {548, 11480}, {616, 37352}, {619, 35022}, {622, 37341}, {632, 5237}, {1545, 21648}, {1595, 11476}, {1596, 10642}, {1656, 5344}, {2043, 6221}, {2044, 6398}, {3054, 6108}, {3365, 35740}, {3534, 37640}, {3618, 11295}, {3619, 11298}, {3628, 36843}, {3631, 3642}, {3643, 34573}, {3830, 37641}, {3851, 5366}, {3853, 40694}, {5066, 16645}, {5351, 14869}, {5353, 7354}, {5357, 6284}, {5362, 11112}, {5367, 11113}, {6200, 34552}, {6396, 34551}, {6823, 10635}, {8972, 36463}, {10299, 22235}, {10301, 37775}, {10641, 37458}, {10677, 36966}, {11300, 34541}, {11303, 34540}, {11408, 18533}, {11539, 37832}, {11812, 41119}, {12100, 16644}, {12103, 22236}, {13349, 16001}, {13665, 36437}, {13785, 36455}, {13941, 36445}, {15686, 34754}, {15699, 16242}, {15713, 41121}, {15714, 41943}, {15760, 18470}, {15765, 18538}, {16241, 17504}, {16772, 16960}, {16963, 23046}, {18585, 18762}, {18586, 23249}, {18587, 23259}, {19710, 36967}, {22513, 22862}, {30739, 37776}, {33699, 36970}, {35255, 36457}, {35256, 36439}, {36995, 41035}, {37835, 38071}, {41944, 41972}

X(42118) = reflection of X(42117) in X(6)

X(42119) = GIBERT(2,-1,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 3*SB*SC : :

X(42119) lies on these lines: {2, 5321}, {3, 5334}, {4, 15}, {6, 20}, {13, 15682}, {14, 3524}, {16, 376}, {18, 10299}, {30, 5335}, {61, 3529}, {62, 17538}, {140, 5343}, {185, 18929}, {382, 11542}, {388, 10638}, {395, 10304}, {396, 3543}, {397, 5059}, {398, 3522}, {497, 7051}, {550, 11486}, {616, 5862}, {617, 7865}, {621, 37172}, {622, 3849}, {631, 10645}, {1656, 5365}, {1885, 11408}, {2041, 23249}, {2042, 23259}, {2044, 9541}, {2883, 17826}, {3090, 5238}, {3091, 23302}, {3146, 5318}, {3523, 5339}, {3525, 5352}, {3528, 10646}, {3545, 16966}, {3832, 16772}, {3839, 16644}, {4190, 5367}, {4299, 5357}, {4302, 5353}, {5067, 33417}, {5068, 5349}, {5071, 16241}, {5073, 5344}, {5350, 22235}, {5362, 6872}, {6225, 10675}, {6770, 33517}, {6773, 23013}, {7735, 19781}, {10653, 11001}, {10676, 11206}, {10996, 11515}, {11420, 37201}, {12820, 16962}, {14912, 36995}, {15692, 16645}, {15698, 16242}, {15702, 37835}, {15710, 16268}, {15719, 41120}, {16773, 21734}, {16961, 19708}, {18930, 19467}, {19106, 33703}, {19772, 37643}, {21735, 41973}, {36327, 36521}, {36771, 41030}, {36772, 41022}, {36968, 41972}, {37832, 41099}, {41107, 41971}

X(42119) = {X(6),X(20)}-harmonic conjugate of X(42120)

X(42120) = GIBERT(2,1,-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 3*SB*SC : :

X(42120) lies on these lines: {2, 5318}, {3, 5335}, {4, 16}, {6, 20}, {13, 3524}, {14, 15682}, {15, 376}, {17, 10299}, {30, 5334}, {61, 17538}, {62, 3529}, {140, 5344}, {185, 18930}, {382, 11543}, {388, 1250}, {395, 3543}, {396, 10304}, {397, 3522}, {398, 5059}, {497, 19373}, {550, 11485}, {616, 7865}, {617, 5863}, {621, 3849}, {622, 37173}, {631, 10646}, {1656, 5366}, {1885, 11409}, {2041, 23259}, {2042, 23249}, {2043, 9541}, {2883, 17827}, {3090, 5237}, {3091, 23303}, {3146, 5321}, {3523, 5340}, {3525, 5351}, {3528, 10645}, {3545, 16967}, {3832, 16773}, {3839, 16645}, {4190, 5362}, {4299, 5353}, {4302, 5357}, {5067, 33416}, {5068, 5350}, {5071, 16242}, {5073, 5343}, {5349, 22237}, {5367, 6872}, {6225, 10676}, {6770, 23006}, {6773, 33518}, {7735, 19780}, {10654, 11001}, {10675, 11206}, {10996, 11516}, {11421, 37201}, {12821, 16963}, {14912, 36993}, {15692, 16644}, {15698, 16241}, {15702, 37832}, {15710, 16267}, {15719, 41119}, {16772, 21734}, {16960, 19708}, {18929, 19467}, {19107, 33703}, {19773, 37643}, {21735, 41974}, {31412, 35740}, {35749, 36521}, {36967, 41971}, {37835, 41099}, {41108, 41972}

X(42120) = {X(6),X(20)}-harmonic conjugate of X(42119)

X(42121) = GIBERT(-2,1,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 9*a^2*SA - 6*SB*SC : :

X(42121) lies on these lines: {2, 11486}, {3, 5334}, {4,42115}, {5, 16}, {6, 140}, {13, 15699}, {14, 8703}, {15, 395}, {18, 550}, {30, 11481}, {61, 14869}, {62, 632}, {141, 6672}, {302, 37341}, {396, 11539}, {397, 16966}, {398, 10645}, {427, 10633}, {495, 19373}, {496, 1250}, {546, 36843}, {547, 10653}, {590, 34551}, {597, 6671}, {615, 34552}, {619, 33459}, {621, 35303}, {623, 3849}, {631, 11485}, {1368, 10635}, {1595, 10642}, {1596, 11476}, {1656, 5335}, {2045, 6221}, {2046, 6398}, {3054, 14139}, {3147, 11408}, {3411, 16772}, {3526, 11488}, {3530, 11480}, {3541, 11409}, {3627, 5237}, {3628, 18582}, {3845, 19106}, {5054, 37641}, {5339, 33923}, {5340, 35018}, {5351, 15704}, {5353, 5433}, {5357, 5432}, {5362, 13747}, {5367, 7483}, {6114, 22848}, {6774, 36755}, {10124, 16644}, {10654, 12100}, {11267, 34351}, {11268, 23335}, {11308, 34540}, {11585, 18470}, {12108, 22236}, {14216, 17827}, {14813, 18538}, {14814, 18762}, {15686, 36970}, {15687, 36968}, {15690, 41120}, {15694, 37640}, {15711, 41108}, {15713, 16241}, {15759, 41113}, {15765, 35255}, {16239, 40693}, {16268, 17504}, {18585, 35256}, {18907, 19780}, {18914, 19364}, {18930, 26944}, {19710, 41122}, {19711, 41101}, {20252, 23006}, {21735, 22237}, {22847, 23005}, {35734, 36446}, {36969, 38071}, {41974, 41977}

X(42121) = {X(3),X(5334)}-harmonic conjugate of X(42122)
X(42121) = {X(4),X(42115)}-harmonic conjugate of X(42123)
X(42121) = {X(6),X(140)}-harmonic conjugate of X(42124)

X(42122) = GIBERT(2,-1,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 9*a^2*SA - 6*SB*SC : :

X(42122) lies on these lines: {3, 5334}, {4,42116}, {5, 11480}, {6, 550}, {13, 15}, {14, 12100}, {16, 548}, {17, 41978}, {20, 11485}, {61, 12103}, {140, 5321}, {376, 11486}, {382, 11488}, {395, 34200}, {397, 34754}, {398, 10646}, {531, 36521}, {546, 5238}, {547, 33417}, {549, 18581}, {621, 35304}, {1657, 5335}, {1885, 10632}, {3530, 16964}, {3627, 18582}, {3628, 5352}, {3850, 16966}, {3853, 16772}, {5066, 16241}, {5305, 19781}, {5339, 15712}, {5343, 15720}, {5349, 35018}, {5353, 15338}, {5357, 15326}, {5878, 17826}, {6756, 11475}, {7051, 15171}, {8703, 10654}, {10633, 37931}, {10634, 31829}, {10638, 18990}, {10641, 13488}, {10653, 15686}, {11812, 37835}, {12108, 33416}, {14891, 16242}, {14893, 37832}, {15681, 37640}, {15687, 16644}, {15688, 37641}, {15690, 41101}, {15691, 36968}, {15698, 33605}, {15704, 22236}, {15711, 41113}, {15759, 41108}, {16645, 17504}, {16961, 41973}, {16963, 41982}, {19711, 41120}, {34755, 41981}, {36993, 41035}, {37776, 37899}

X(42122) = {X(3),X(5334)}-harmonic conjugate of X(42121)
X(42122) = {X(4),X(42116)}-harmonic conjugate of X(42124)
X(42122) = {X(6),X(550)}-harmonic conjugate of X(42123)

X(42123) = GIBERT(2,1,-3) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 9*a^2*SA + 6*SB*SC : :

X(42123) lies on these lines: {3, 5335}, {4,42115}, {5, 11481}, {6, 550}, {13, 12100}, {14, 16}, {15, 548}, {18, 41977}, {20, 11486}, {62, 12103}, {140, 5318}, {376, 11485}, {382, 11489}, {396, 34200}, {397, 10645}, {398, 34755}, {530, 36521}, {546, 5237}, {547, 33416}, {549, 18582}, {622, 35303}, {1250, 18990}, {1657, 5334}, {1885, 10633}, {3530, 16965}, {3627, 18581}, {3628, 5351}, {3850, 16967}, {3853, 16773}, {5066, 16242}, {5305, 19780}, {5340, 15712}, {5344, 15720}, {5350, 35018}, {5353, 15326}, {5357, 15338}, {5878, 17827}, {6756, 11476}, {8703, 10653}, {10632, 37931}, {10635, 31829}, {10642, 13488}, {10654, 15686}, {11812, 37832}, {12108, 33417}, {14891, 16241}, {14893, 37835}, {15171, 19373}, {15681, 37641}, {15687, 16645}, {15688, 37640}, {15690, 41100}, {15691, 36967}, {15698, 33604}, {15704, 22238}, {15711, 41112}, {15759, 41107}, {16644, 17504}, {16960, 41974}, {16962, 41982}, {19711, 41119}, {34754, 41981}, {36995, 41034}, {37775, 37899}

X(42123) = {X(3),X(5335)}-harmonic conjugate of X(42124)
X(42123) = {X(4),X(42115)}-harmonic conjugate of X(42121)
X(42123) = {X(6),X(550)}-harmonic conjugate of X(42122)

X(42124) = GIBERT(2,1,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 9*a^2*SA + 6*SB*SC : :

X(42124) lies on these lines: {2, 11485}, {3, 5335}, {4,42116}, {5, 15}, {6, 140}, {13, 8703}, {14, 15699}, {16, 396}, {17, 550}, {30, 11480}, {61, 632}, {62, 14869}, {141, 6671}, {303, 37340}, {395, 11539}, {397, 10646}, {398, 16967}, {427, 10632}, {495, 7051}, {496, 10638}, {546, 36836}, {547, 10654}, {590, 34552}, {597, 6672}, {615, 34551}, {618, 33458}, {622, 35304}, {624, 3849}, {631, 11486}, {1368, 10634}, {1595, 10641}, {1596, 11475}, {1656, 5334}, {2045, 6398}, {2046, 6221}, {3054, 14138}, {3147, 11409}, {3412, 16773}, {3526, 11489}, {3530, 11481}, {3541, 11408}, {3627, 5238}, {3628, 18581}, {3845, 19107}, {5054, 37640}, {5339, 35018}, {5340, 33923}, {5352, 15704}, {5353, 5432}, {5357, 5433}, {5362, 7483}, {5367, 13747}, {6115, 22892}, {6771, 36756}, {10124, 16645}, {10653, 12100}, {11267, 23335}, {11268, 34351}, {11307, 34541}, {11585, 18468}, {12108, 22238}, {14216, 17826}, {14813, 18762}, {14814, 18538}, {15686, 36969}, {15687, 36967}, {15690, 41119}, {15694, 37641}, {15711, 41107}, {15713, 16242}, {15759, 41112}, {15765, 35256}, {16239, 40694}, {16267, 17504}, {18585, 35255}, {18907, 19781}, {18914, 19363}, {18929, 26944}, {19710, 41121}, {19711, 41100}, {20253, 23013}, {21735, 22235}, {22513, 36763}, {22893, 23004}, {35734, 36447}, {36970, 38071}, {41973, 41978}

X(42124) = {X(3),X(5335)}-harmonic conjugate of X(42123)
X(42124) = {X(4),X(42116)}-harmonic conjugate of X(42122)
X(42124) = {X(6),X(140)}-harmonic conjugate of X(42121)

X(42125) = GIBERT(-2,2,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*a^2*SA - 12*SB*SC : :

X(42125) lies on these lines: {2, 33603}, {3, 5321}, {4, 11409}, {5, 5334}, {6, 13}, {15, 1656}, {16, 382}, {18, 1657}, {30, 11489}, {61, 5072}, {69, 31694}, {140, 5343}, {141, 22491}, {302, 11295}, {395, 3830}, {396, 19709}, {398, 3851}, {403, 11408}, {546, 5335}, {550, 5365}, {617, 31684}, {621, 11306}, {1250, 9668}, {1384, 37332}, {2043, 18762}, {2044, 18538}, {3091, 11542}, {3526, 11480}, {3534, 10646}, {3618, 31693}, {3619, 37351}, {3620, 37171}, {3629, 22492}, {3843, 5318}, {3845, 37641}, {5024, 37333}, {5054, 10645}, {5055, 10654}, {5066, 37640}, {5073, 5349}, {5076, 16961}, {5079, 16966}, {5094, 37775}, {5353, 10896}, {5357, 10895}, {5362, 17556}, {5367, 17532}, {5611, 33518}, {5869, 22831}, {6114, 13102}, {6144, 22496}, {6221, 18586}, {6398, 18587}, {6437, 35731}, {6782, 13103}, {7685, 41038}, {8972, 36454}, {9655, 19373}, {9761, 35697}, {10187, 15720}, {10612, 22862}, {10633, 12173}, {10638, 31479}, {10642, 18494}, {10653, 14269}, {10662, 12429}, {10676, 34780}, {11165, 22568}, {11304, 34540}, {11516, 18536}, {12817, 36968}, {13941, 36436}, {15688, 16242}, {15693, 36967}, {15765, 23259}, {16268, 34755}, {16628, 31706}, {16644, 34754}, {16773, 17800}, {16942, 22861}, {17827, 18400}, {18396, 21648}, {18585, 23249}, {32785, 36439}, {32786, 36457}, {32789, 36456}, {32790, 36438}, {33417, 36836}, {35749, 37785}, {36990, 41037}, {41041, 41054}

X(42125) = {X(3),X(5321)}-harmonic conjugate of X(42126)
X(42125) = {X(4),X(11486)}-harmonic conjugate of X(42127)
X(42125) = {X(6),X(381)}-harmonic conjugate of X(42128)

X(42126) = GIBERT(2,-2,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*a^2*SA - 12*SB*SC : :

X(42126) lies on these lines: {3, 5321}, {4, 11408}, {6, 382}, {13, 38335}, {14, 3534}, {15, 381}, {16, 1657}, {20, 11543}, {30, 5334}, {61, 5076}, {140, 5365}, {395, 15681}, {396, 14269}, {398, 5073}, {546, 11488}, {550, 5343}, {621, 11295}, {1656, 11480}, {2043, 35256}, {2044, 35255}, {3526, 10645}, {3627, 5335}, {3830, 5318}, {3843, 18582}, {3851, 5349}, {5054, 16967}, {5072, 16966}, {5079, 5238}, {5340, 41973}, {5353, 12953}, {5357, 12943}, {6240, 11409}, {7051, 9669}, {9654, 10638}, {10632, 37197}, {10633, 37196}, {10646, 15696}, {10653, 15684}, {12817, 16241}, {13102, 22512}, {14093, 16242}, {15685, 41113}, {15687, 37640}, {15688, 16645}, {15693, 37835}, {15695, 41120}, {16808, 22236}, {16960, 41101}, {16961, 36843}, {17800, 40694}, {17827, 34785}, {22796, 36772}, {31152, 37775}, {36993, 41041}

X(42126) = {X(3),X(5321)}-harmonic conjugate of X(42125)
X(42126) = {X(4),X(11485)}-harmonic conjugate of X(42128)
X(42126) = {X(6),X(382)}-harmonic conjugate of X(42127)

X(42127) = GIBERT(2,2,-1) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*a^2*SA + 12*SB*SC : :

X(42127) lies on these lines: {3, 5318}, {4, 11409}, {6, 382}, {13, 3534}, {14, 38335}, {15, 1657}, {16, 381}, {20, 11542}, {30, 5335}, {62, 5076}, {140, 5366}, {395, 14269}, {396, 15681}, {397, 5073}, {546, 11489}, {550, 5344}, {622, 11296}, {1250, 9654}, {1656, 11481}, {2043, 35255}, {2044, 35256}, {3526, 10646}, {3627, 5334}, {3830, 5321}, {3843, 18581}, {3851, 5350}, {5054, 16966}, {5072, 16967}, {5079, 5237}, {5339, 41974}, {5353, 12943}, {5357, 12953}, {6240, 11408}, {9669, 19373}, {10632, 37196}, {10633, 37197}, {10645, 15696}, {10654, 15684}, {12816, 16242}, {13103, 22513}, {14093, 16241}, {15685, 41112}, {15687, 37641}, {15688, 16644}, {15693, 37832}, {15695, 41119}, {16809, 22238}, {16960, 36836}, {16961, 41100}, {17800, 40693}, {17826, 34785}, {31152, 37776}, {36995, 41040}

X(42127) = {X(3),X(5318)}-harmonic conjugate of X(42128)
X(42127) = {X(4),X(11486)}-harmonic conjugate of X(42125)
X(42127) = {X(6),X(382)}-harmonic conjugate of X(42126)

X(42128) = GIBERT(2,2,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*a^2*SA + 12*SB*SC : :

X(42128) lies on these lines: {2, 33602}, {3, 5318}, {4, 11408}, {5, 5335}, {6, 13}, {15, 382}, {16, 1656}, {17, 1657}, {30, 11488}, {62, 5072}, {69, 31693}, {140, 5344}, {141, 22492}, {303, 11296}, {395, 19709}, {396, 3830}, {397, 3851}, {403, 11409}, {546, 5334}, {550, 5366}, {616, 31683}, {622, 11305}, {1250, 31479}, {1384, 37333}, {2043, 18538}, {2044, 18762}, {3091, 11543}, {3526, 11481}, {3534, 10645}, {3618, 31694}, {3619, 37352}, {3620, 37170}, {3629, 22491}, {3843, 5321}, {3845, 37640}, {5024, 37332}, {5054, 10646}, {5055, 10653}, {5066, 37641}, {5073, 5350}, {5076, 16960}, {5079, 16967}, {5094, 37776}, {5353, 10895}, {5357, 10896}, {5362, 17532}, {5367, 17556}, {5615, 33517}, {5868, 22832}, {6115, 13103}, {6144, 22495}, {6221, 18587}, {6398, 18586}, {6409, 35730}, {6411, 35731}, {6783, 13102}, {7051, 9655}, {7684, 41039}, {8972, 36436}, {9668, 10638}, {9763, 35693}, {10188, 15720}, {10611, 22906}, {10632, 12173}, {10641, 18494}, {10654, 14269}, {10661, 12429}, {10675, 34780}, {11165, 22570}, {11303, 34541}, {11515, 18536}, {12816, 36967}, {13941, 36454}, {15688, 16241}, {15693, 36968}, {15765, 23249}, {16267, 34754}, {16629, 31705}, {16645, 34755}, {16772, 17800}, {16943, 22907}, {17826, 18400}, {18396, 21647}, {18585, 23259}, {32785, 36457}, {32786, 36439}, {32789, 36438}, {32790, 36456}, {33416, 36843}, {36327, 37786}, {36990, 41036}, {41040, 41055}

X(42128) = {X(3),X(5318)}-harmonic conjugate of X(42127)
X(42128) = {X(4),X(11485)}-harmonic conjugate of X(42126)
X(42128) = {X(6),X(381)}-harmonic conjugate of X(42125)

X(42129) = GIBERT(-2,2,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 9*a^2*SA - 12*SB*SC : :

X(42129) lies on these lines: {2, 11485}, {3, 5321}, {4,42115}, {5, 5335}, {6, 17}, {14, 5054}, {15, 3526}, {16, 381}, {62, 5079}, {140, 5334}, {302, 11306}, {382, 11481}, {395, 5055}, {396, 15703}, {547, 37641}, {599, 40335}, {618, 35697}, {624, 9761}, {1250, 9669}, {1594, 11409}, {1657, 10646}, {2045, 18762}, {2046, 18538}, {3090, 11542}, {3533, 22237}, {3534, 12817}, {3628, 11488}, {3843, 16773}, {3851, 5318}, {5070, 23302}, {5072, 16808}, {5076, 5237}, {5339, 10645}, {5340, 34755}, {5343, 15712}, {5365, 33923}, {5460, 9886}, {7505, 11408}, {7507, 10633}, {7615, 33474}, {9541, 15765}, {9654, 19373}, {10612, 23013}, {10632, 37453}, {10653, 19709}, {10654, 15694}, {11297, 30472}, {14813, 32785}, {14814, 32786}, {15300, 22578}, {15688, 36970}, {15693, 41122}, {15699, 37640}, {15700, 36967}, {15701, 41120}, {15723, 16241}, {16268, 16644}, {17827, 18381}, {19106, 36843}, {22236, 33417}, {36968, 38335}, {41108, 41971}

X(42129) = {X(3),X(5321)}-harmonic conjugate of X(42130)
X(42129) = {X(4),X(42115)}-harmonic conjugate of X(42131)
X(42129) = {X(6),X(1656)}-harmonic conjugate of X(42132)

X(42130) = GIBERT(2,-2,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 9*a^2*SA - 12*SB*SC : :

X(42130) lies on these lines: {3, 5321}, {4,42116}, {6, 1657}, {14, 15688}, {15, 382}, {16, 3534}, {20, 11486}, {30, 5335}, {376, 11543}, {381, 11480}, {395, 15689}, {396, 15684}, {548, 11489}, {550, 5334}, {1656, 10645}, {3146, 11542}, {3526, 16809}, {3627, 11488}, {3830, 18582}, {3843, 23302}, {5054, 36970}, {5072, 5352}, {5073, 5318}, {5076, 16808}, {5079, 33417}, {5339, 10646}, {5340, 34754}, {5343, 33923}, {5365, 15712}, {7051, 9668}, {9655, 10638}, {10653, 15685}, {10654, 15681}, {11408, 18560}, {11409, 35471}, {11475, 18494}, {11481, 15696}, {14093, 16645}, {15686, 37641}, {15693, 33416}, {15700, 37835}, {15720, 16967}, {16644, 38335}, {17826, 22802}, {19106, 22236}, {34755, 41973}

X(42130) = {X(3),X(5321)}-harmonic conjugate of X(42129)
X(42130) = {X(4),X(42116)}-harmonic conjugate of X(42132)
X(42130) = {X(6),X(1657)}-harmonic conjugate of X(42131)

X(42131) = GIBERT(2,2,-3) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 9*a^2*SA + 12*SB*SC : :

X(42131) lies on these lines: {3, 5318}, {4,42115}, {6, 1657}, {13, 15688}, {15, 3534}, {16, 382}, {20, 11485}, {30, 5334}, {376, 11542}, {381, 11481}, {395, 15684}, {396, 15689}, {548, 11488}, {550, 5335}, {1250, 9655}, {1656, 10646}, {3146, 11543}, {3526, 16808}, {3627, 11489}, {3830, 18581}, {3843, 23303}, {5054, 36969}, {5072, 5351}, {5073, 5321}, {5076, 16809}, {5079, 33416}, {5339, 34755}, {5340, 10645}, {5344, 33923}, {5366, 15712}, {9668, 19373}, {10653, 15681}, {10654, 15685}, {11408, 35471}, {11409, 18560}, {11476, 18494}, {11480, 15696}, {14093, 16644}, {15686, 37640}, {15693, 33417}, {15700, 37832}, {15720, 16966}, {16645, 38335}, {17827, 22802}, {19107, 22238}, {34754, 41974}

X(42131) = {X(3),X(5318)}-harmonic conjugate of X(42132)
X(42131) = {X(4),X(42115)}-harmonic conjugate of X(42129)
X(42131) = {X(6),X(1657)}-harmonic conjugate of X(42130)

X(42132) = GIBERT(2,2,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 9*a^2*SA + 12*SB*SC : :

X(42132) lies on these lines: {2, 11486}, {3, 5318}, {4,42116}, {5, 5334}, {6, 17}, {13, 5054}, {15, 381}, {16, 3526}, {61, 5079}, {115, 36763}, {140, 5335}, {303, 11305}, {382, 11480}, {395, 15703}, {396, 5055}, {547, 37640}, {599, 40334}, {619, 35693}, {623, 9763}, {1594, 11408}, {1657, 10645}, {2045, 18538}, {2046, 18762}, {3090, 11543}, {3533, 22235}, {3534, 12816}, {3628, 11489}, {3843, 16772}, {3851, 5321}, {5070, 23303}, {5072, 16809}, {5076, 5238}, {5339, 34754}, {5340, 10646}, {5344, 15712}, {5366, 33923}, {5459, 9885}, {6771, 36771}, {7051, 9654}, {7505, 11409}, {7507, 10632}, {7615, 33475}, {9541, 18585}, {9669, 10638}, {10611, 23006}, {10633, 37453}, {10653, 15694}, {10654, 19709}, {11298, 30471}, {14813, 32786}, {14814, 32785}, {15300, 22577}, {15688, 36969}, {15693, 41121}, {15699, 37641}, {15700, 36968}, {15701, 41119}, {15723, 16242}, {16267, 16645}, {17826, 18381}, {19107, 36836}, {22238, 33416}, {36967, 38335}, {41107, 41972}

X(42132) = {X(3),X(5318)}-harmonic conjugate of X(42131)
X(42132) = {X(4),X(42116)}-harmonic conjugate of X(42130)
X(42132) = {X(6),X(1656)}-harmonic conjugate of X(42129)

X(42133) = GIBERT(-2,3,0) POINT

Barycentrics    Sqrt[3]*a^2*S - 9*SB*SC : :

X(42133) lies on these lines: {2, 10645}, {3,42135}, {4, 6}, {14, 3543}, {15, 3091}, {16, 3146}, {18, 5059}, {20, 10646}, {30, 11489}, {193, 22575}, {376, 23303}, {381, 11488}, {382, 11543}, {383, 16942}, {395, 15682}, {396, 41099}, {472, 37643}, {546, 11485}, {621, 3620}, {622, 20080}, {2043, 32786}, {2044, 32785}, {3090, 11480}, {3523, 16967}, {3529, 11481}, {3544, 36836}, {3545, 23302}, {3619, 11304}, {3627, 11486}, {3830, 37641}, {3832, 16964}, {3839, 10654}, {3843, 11542}, {3845, 37640}, {5068, 16966}, {5238, 15022}, {5471, 31684}, {5479, 37689}, {6200, 35732}, {6437, 35740}, {6451, 14813}, {6452, 14814}, {6623, 10641}, {7051, 10591}, {7486, 33417}, {9541, 36454}, {10151, 11408}, {10304, 37835}, {10590, 10638}, {11001, 16645}, {11138, 11738}, {11541, 36843}, {15640, 36968}, {15655, 41034}, {15717, 33416}, {16002, 37517}, {16644, 41106}, {16960, 41973}, {16961, 22237}, {17578, 19106}, {25164, 31670}, {31099, 37775}, {36969, 41113}

X(42133) = {X(4),X(6)}-harmonic conjugate of X(42134)
X(42133) = {X(42135),X(42136)}-harmonic conjugate of X(3)
X(42133) = {X(42139),X(42140)}-harmonic conjugate of X(3)

X(42134) = GIBERT(2,3,0) POINT

Barycentrics    Sqrt[3]*a^2*S + 9*SB*SC : :

X(42134) lies on these lines: {2, 10646}, {3,42137}, {4, 6}, {13, 3543}, {15, 3146}, {16, 3091}, {17, 5059}, {20, 10645}, {30, 11488}, {193, 22576}, {376, 23302}, {381, 11489}, {382, 11542}, {395, 41099}, {396, 15682}, {473, 37643}, {546, 11486}, {621, 20080}, {622, 3620}, {1080, 16943}, {1250, 10590}, {2043, 32785}, {2044, 32786}, {3090, 11481}, {3523, 16966}, {3529, 11480}, {3544, 36843}, {3545, 23303}, {3619, 11303}, {3627, 11485}, {3830, 37640}, {3832, 16965}, {3839, 10653}, {3843, 11543}, {3845, 37641}, {5068, 16967}, {5237, 15022}, {5472, 31683}, {5478, 37689}, {6396, 35732}, {6411, 35740}, {6451, 14814}, {6452, 14813}, {6623, 10642}, {7486, 33416}, {9541, 36436}, {10151, 11409}, {10304, 37832}, {10591, 19373}, {11001, 16644}, {11139, 11738}, {11541, 36836}, {15640, 36967}, {15655, 41035}, {15717, 33417}, {16001, 37517}, {16645, 41106}, {16960, 22235}, {16961, 41974}, {17578, 19107}, {25154, 31670}, {31099, 37776}, {36970, 41112}

X(42134) = {X(4),X(6)}-harmonic conjugate of X(42133)
X(42134) = {X(42137),X(42138)}-harmonic conjugate of X(3)
X(42134) = {X(42141),X(42142)}-harmonic conjugate of X(3)

X(42135) = GIBERT(-2,3,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*a^2*SA - 18*SB*SC : :

X(42135) lies on these lines: {3,42133}, {4, 11409}, {5, 15}, {6, 546}, {13, 23046}, {14, 3845}, {16, 3627}, {30, 11481}, {61, 3857}, {381, 5334}, {382, 11489}, {395, 15687}, {396, 38071}, {398, 3858}, {427, 37775}, {549, 16967}, {550, 5349}, {621, 31694}, {632, 10645}, {1656, 5365}, {3091, 11485}, {3628, 11480}, {3843, 5335}, {3850, 5339}, {3851, 5343}, {3856, 40693}, {3860, 41113}, {3861, 40694}, {5066, 10654}, {7051, 10593}, {8703, 12817}, {9541, 18586}, {10592, 10638}, {10646, 15704}, {10653, 14893}, {11539, 36967}, {11737, 16644}, {12101, 41120}, {12102, 22238}, {12811, 22236}, {12812, 36836}, {14269, 37641}, {15686, 16242}, {15699, 33417}, {15712, 33416}, {16960, 41108}, {20253, 22512}, {33699, 41122}, {35404, 36968}

X(42135) = {X(3),X(42133)}-harmonic conjugate of X(42136)
X(42135) = {X(4),X(11486)}-harmonic conjugate of X(42137)
X(42135) = {X(6),X(546)}-harmonic conjugate of X(42138)

X(42136) = GIBERT(2,-3,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*a^2*SA - 18*SB*SC : :

X(42136) lies on these lines: {3,42133}, {4, 11408}, {5, 11480}, {6, 3627}, {13, 12101}, {14, 16}, {15, 546}, {61, 12102}, {140, 5349}, {382, 5334}, {396, 14893}, {398, 19106}, {428, 37776}, {547, 36967}, {548, 23303}, {550, 18581}, {622, 36327}, {1657, 5365}, {3146, 11486}, {3530, 16967}, {3628, 10645}, {3830, 5335}, {3843, 11488}, {3845, 18582}, {3850, 23302}, {3853, 5318}, {3856, 16772}, {3857, 36836}, {3860, 37832}, {3861, 16808}, {5066, 16966}, {5073, 5343}, {5238, 12811}, {5350, 41973}, {5352, 12812}, {10151, 10632}, {10646, 12103}, {10653, 33699}, {10654, 15687}, {11481, 15704}, {11737, 16241}, {12100, 12817}, {15684, 37641}, {15686, 16645}, {15690, 16242}, {16644, 23046}, {33417, 35018}, {34200, 37835}, {37640, 38335}

X(42136) = {X(3),X(42133)}-harmonic conjugate of X(42135)
X(42136) = {X(4),X(11485)}-harmonic conjugate of X(42138)
X(42136) = {X(6),X(3627)}-harmonic conjugate of X(42137)

X(42137) = GIBERT(2,3,-1) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*a^2*SA + 18*SB*SC : :

X(42137) lies on these lines: {3,42134}, {4, 11409}, {5, 11481}, {6, 3627}, {13, 15}, {14, 12101}, {16, 546}, {62, 12102}, {140, 5350}, {382, 5335}, {395, 14893}, {397, 19107}, {428, 37775}, {547, 36968}, {548, 23302}, {550, 18582}, {621, 35749}, {623, 36769}, {1657, 5366}, {3146, 11485}, {3530, 16966}, {3628, 10646}, {3830, 5334}, {3843, 11489}, {3845, 18581}, {3850, 23303}, {3853, 5321}, {3856, 16773}, {3857, 36843}, {3860, 37835}, {3861, 16809}, {5066, 16967}, {5073, 5344}, {5237, 12811}, {5349, 41974}, {5351, 12812}, {10151, 10633}, {10645, 12103}, {10653, 15687}, {10654, 33699}, {11480, 15704}, {11737, 16242}, {12100, 12816}, {15684, 37640}, {15686, 16644}, {15690, 16241}, {16645, 23046}, {33416, 35018}, {34200, 37832}, {37641, 38335}

X(42137) = {X(3),X(42134)}-harmonic conjugate of X(42138)
X(42137) = {X(4),X(11486)}-harmonic conjugate of X(42135)
X(42137) = {X(6),X(3627)}-harmonic conjugate of X(42136)

X(42138) = GIBERT(2,3,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*a^2*SA + 18*SB*SC : :

X(42138) lies on these lines: {3,42134}, {4, 11408}, {5, 16}, {6, 546}, {13, 3845}, {14, 23046}, {15, 3627}, {30, 11480}, {62, 3857}, {381, 5335}, {382, 11488}, {395, 38071}, {396, 15687}, {397, 3858}, {427, 37776}, {549, 16966}, {550, 5350}, {622, 31693}, {632, 10646}, {1250, 10592}, {1656, 5366}, {3091, 11486}, {3628, 11481}, {3843, 5334}, {3850, 5340}, {3851, 5344}, {3856, 40694}, {3860, 41112}, {3861, 40693}, {5066, 10653}, {8703, 12816}, {9541, 18587}, {10593, 19373}, {10645, 15704}, {10654, 14893}, {11539, 36968}, {11737, 16645}, {12101, 41119}, {12102, 22236}, {12811, 22238}, {12812, 36843}, {14269, 37640}, {15686, 16241}, {15699, 33416}, {15712, 33417}, {16961, 41107}, {20252, 22513}, {33699, 41121}, {35404, 36967}

X(42138) = {X(3),X(42134)}-harmonic conjugate of X(42137)
X(42138) = {X(4),X(11485)}-harmonic conjugate of X(42136)
X(42138) = {X(6),X(546)}-harmonic conjugate of X(42135)

X(42139) = GIBERT(-2,3,2) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA - 9*SB*SC : :

X(42139) lies on these lines: {2, 5321}, {3,42133}, {4, 16}, {5, 5334}, {6, 3091}, {13, 33605}, {14, 3545}, {15, 3090}, {20, 23303}, {61, 3544}, {140, 5365}, {376, 19107}, {381, 5335}, {395, 3839}, {397, 3854}, {398, 5068}, {546, 11486}, {621, 625}, {622, 7615}, {624, 22491}, {631, 16967}, {1250, 5225}, {1656, 5343}, {3146, 11481}, {3522, 5349}, {3524, 33416}, {3525, 10645}, {3529, 10646}, {3543, 16645}, {3832, 5318}, {3851, 11542}, {3855, 16808}, {3858, 5344}, {5056, 5339}, {5067, 16964}, {5071, 10654}, {5187, 5362}, {5229, 19373}, {5351, 11541}, {5367, 6871}, {5863, 33627}, {6622, 10641}, {6997, 37776}, {7051, 10589}, {8889, 11475}, {10588, 10638}, {10653, 12816}, {10676, 32064}, {11001, 16242}, {11008, 22114}, {11299, 16942}, {11409, 23047}, {12817, 19708}, {15022, 22236}, {15702, 36967}, {16773, 17578}, {16963, 41972}, {17827, 41362}, {18586, 35255}, {18587, 35256}, {18945, 19364}, {22856, 41094}, {23013, 31684}, {32785, 35732}, {33412, 37178}, {33603, 41101}, {37832, 41113}

X(42139) = {X(3),X(42133)}-harmonic conjugate of X(42140)
X(42139) = {X(4),X(16)}-harmonic conjugate of X(42141)
X(42139) = {X(6),X(3091)}-harmonic conjugate of X(42142)

X(42140) = GIBERT(2,-3,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 9*SB*SC : :

X(42140) lies on these lines: {3,42133}, {4, 15}, {6, 3146}, {14, 11001}, {16, 3529}, {20, 5321}, {30, 5334}, {62, 11541}, {376, 16242}, {382, 5335}, {395, 15683}, {550, 5365}, {631, 16809}, {1327, 36446}, {1328, 36465}, {1370, 37775}, {1657, 5343}, {3090, 10645}, {3091, 11480}, {3522, 23303}, {3523, 5349}, {3524, 16967}, {3543, 5318}, {3544, 5352}, {3545, 36967}, {3627, 11485}, {3830, 11542}, {3832, 23302}, {3855, 16966}, {5059, 5339}, {5071, 33417}, {5225, 7051}, {5229, 10638}, {5367, 31295}, {5862, 36352}, {5893, 17826}, {10299, 33416}, {10646, 17538}, {10654, 15682}, {12817, 15698}, {16241, 41106}, {16964, 33703}, {18930, 21659}, {19708, 37835}, {33442, 36360}, {33443, 36361}

X(42140) = {X(3),X(42133)}-harmonic conjugate of X(42139)
X(42140) = {X(4),X(15)}-harmonic conjugate of X(42142)
X(42140) = {X(6),X(3146)}-harmonic conjugate of X(42141)

X(42141) = GIBERT(2,3,-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 9*SB*SC : :

X(42141) lies on these lines: {3,42134}, {4, 16}, {6, 3146}, {13, 11001}, {15, 3529}, {20, 5318}, {30, 5335}, {61, 11541}, {376, 16241}, {382, 5334}, {396, 15683}, {550, 5366}, {631, 16808}, {1250, 5229}, {1327, 36464}, {1328, 36447}, {1370, 37776}, {1657, 5344}, {3090, 10646}, {3091, 11481}, {3522, 23302}, {3523, 5350}, {3524, 16966}, {3543, 5321}, {3544, 5351}, {3545, 36968}, {3627, 11486}, {3830, 11543}, {3832, 23303}, {3855, 16967}, {5059, 5340}, {5071, 33416}, {5225, 19373}, {5362, 31295}, {5863, 36346}, {5893, 17827}, {10299, 33417}, {10645, 17538}, {10653, 15682}, {12816, 15698}, {16242, 41106}, {16965, 33703}, {18929, 21659}, {19708, 37832}, {32785, 35740}, {33440, 36353}, {33441, 36355}

X(42141) = {X(3),X(42134)}-harmonic conjugate of X(42142)
X(42141) = {X(4),X(16)}-harmonic conjugate of X(42139)
X(42141) = {X(6),X(3146)}-harmonic conjugate of X(42140)

X(42142) = GIBERT(2,3,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 9*SB*SC : :

X(42142) lies on these lines: {2, 5318}, {3,42134}, {4, 15}, {5, 5335}, {6, 3091}, {13, 3545}, {14, 33604}, {16, 3090}, {20, 23302}, {62, 3544}, {140, 5366}, {376, 19106}, {381, 5334}, {396, 3839}, {397, 5068}, {398, 3854}, {546, 11485}, {621, 7615}, {622, 625}, {623, 22492}, {631, 16966}, {1250, 10588}, {1656, 5344}, {3146, 11480}, {3522, 5350}, {3524, 33417}, {3525, 10646}, {3529, 10645}, {3543, 16644}, {3832, 5321}, {3851, 11543}, {3855, 16809}, {3858, 5343}, {5056, 5340}, {5067, 16965}, {5071, 10653}, {5187, 5367}, {5225, 10638}, {5229, 7051}, {5352, 11541}, {5362, 6871}, {5478, 36771}, {5862, 33626}, {6622, 10642}, {6997, 37775}, {8889, 11476}, {10589, 19373}, {10654, 12817}, {10675, 32064}, {11001, 16241}, {11008, 22113}, {11300, 16943}, {11408, 23047}, {12816, 19708}, {15022, 22238}, {15702, 36968}, {16772, 17578}, {16962, 41971}, {17826, 41362}, {18586, 35256}, {18587, 35255}, {18945, 19363}, {22900, 41098}, {23006, 31683}, {32786, 35732}, {33413, 37177}, {33602, 41100}, {37835, 41112}

X(42142) = {X(3),X(42134)}-harmonic conjugate of X(42141)
X(42142) = {X(4),X(15)}-harmonic conjugate of X(42140)
X(42142) = {X(6),X(3091)}-harmonic conjugate of X(42139)

X(42143) = GIBERT(-2,3,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 9*a^2*SA - 18*SB*SC : :

X(42143) lies on these lines: {2, 33603}, {5, 6}, {13, 11737}, {14, 547}, {15, 3628}, {16, 546}, {18, 3850}, {30, 10646}, {61, 12812}, {62, 12811}, {140, 5321}, {187, 31706}, {302, 31694}, {381, 11489}, {395, 5066}, {396, 10109}, {397, 16961}, {398, 16966}, {548, 19107}, {623, 34573}, {624, 3631}, {632, 11480}, {1656, 5334}, {2041, 6452}, {2042, 6451}, {3055, 6114}, {3090, 11485}, {3091, 11486}, {3530, 33416}, {3589, 5460}, {3614, 5357}, {3619, 11306}, {3627, 11481}, {3630, 34508}, {3845, 16645}, {3851, 5335}, {3857, 22238}, {3859, 16965}, {3860, 36969}, {3861, 16773}, {5055, 11488}, {5237, 12102}, {5349, 33923}, {5353, 7173}, {5362, 17533}, {5365, 15720}, {5367, 17530}, {5459, 6329}, {6200, 35738}, {6669, 35020}, {6782, 20252}, {6783, 10612}, {10297, 18470}, {10633, 23047}, {10641, 37942}, {10653, 38071}, {10654, 15699}, {11812, 36967}, {12100, 36970}, {12101, 36968}, {12817, 15759}, {14892, 16268}, {16239, 16964}, {16626, 41407}, {16644, 41120}, {18586, 32785}, {18587, 32786}, {19709, 37641}, {37454, 37775}

X(42143) = {X(5),X(6)}-harmonic conjugate of X(42146)

X(42144) = GIBERT(2,-3,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 9*a^2*SA - 18*SB*SC : :

X(42144) lies on these lines: {5, 10645}, {6, 30}, {13, 35404}, {14, 15686}, {15, 3627}, {16, 15704}, {18, 550}, {20, 11543}, {382, 11542}, {395, 19710}, {396, 12816}, {531, 3630}, {546, 11480}, {548, 18581}, {549, 16809}, {1657, 5334}, {2043, 6452}, {2044, 6451}, {3146, 11485}, {3529, 11486}, {3534, 11489}, {3619, 11295}, {3830, 11488}, {3845, 23302}, {3853, 18582}, {3857, 5352}, {3858, 16966}, {5073, 5335}, {5318, 34754}, {5349, 15712}, {5350, 16960}, {8703, 23303}, {11481, 12103}, {12101, 16644}, {12102, 36836}, {12817, 15711}, {15685, 37641}, {15687, 16808}, {15690, 16645}, {16241, 23046}, {16964, 34755}

X(42144) = reflection of X(42145) in X(6)

X(42145) = GIBERT(2,3,-3) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 9*a^2*SA + 18*SB*SC : :

X(42145) lies on these lines: {5, 10646}, {6, 30}, {13, 15686}, {14, 35404}, {15, 15704}, {16, 3627}, {17, 550}, {20, 11542}, {382, 11543}, {395, 12817}, {396, 19710}, {530, 3630}, {546, 11481}, {548, 18582}, {549, 16808}, {1657, 5335}, {2043, 6451}, {2044, 6452}, {3146, 11486}, {3529, 11485}, {3534, 11488}, {3619, 11296}, {3830, 11489}, {3845, 23303}, {3853, 18581}, {3857, 5351}, {3858, 16967}, {5073, 5334}, {5321, 34755}, {5349, 16961}, {5350, 15712}, {8703, 23302}, {11480, 12103}, {12101, 16645}, {12102, 36843}, {12816, 15711}, {15685, 37640}, {15687, 16809}, {15690, 16644}, {16242, 23046}, {16965, 34754}

X(42145) = reflection of X(42144) in X(6)

X(42146) = GIBERT(2,3,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 9*a^2*SA + 18*SB*SC : :

X(42146) lies on these lines: {2, 33602}, {5, 6}, {13, 547}, {14, 11737}, {15, 546}, {16, 3628}, {17, 3850}, {30, 10645}, {61, 12811}, {62, 12812}, {140, 5318}, {187, 31705}, {303, 31693}, {381, 11488}, {395, 10109}, {396, 5066}, {397, 16967}, {398, 16960}, {548, 19106}, {623, 3631}, {624, 34573}, {632, 11481}, {1656, 5335}, {2041, 6451}, {2042, 6452}, {3055, 6115}, {3090, 11486}, {3091, 11485}, {3530, 33417}, {3589, 5459}, {3614, 5353}, {3619, 11305}, {3627, 11480}, {3630, 34509}, {3845, 16644}, {3851, 5334}, {3857, 22236}, {3859, 16964}, {3860, 36970}, {3861, 16772}, {5055, 11489}, {5238, 12102}, {5350, 33923}, {5357, 7173}, {5362, 17530}, {5366, 15720}, {5367, 17533}, {5460, 6329}, {6396, 35738}, {6670, 35019}, {6782, 10611}, {6783, 20253}, {10297, 18468}, {10632, 23047}, {10642, 37942}, {10653, 15699}, {10654, 38071}, {11812, 36968}, {12100, 36969}, {12101, 36967}, {12816, 15759}, {14892, 16267}, {16239, 16965}, {16627, 41406}, {16645, 41119}, {18586, 32786}, {18587, 32785}, {19709, 37640}, {37454, 37776}

X(42146) = {X(5),X(6)}-harmonic conjugate of X(42143)

X(42147) = GIBERT(3,-1,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 2*a^2*SA - 2*SB*SC : :

X(42147) lies on these lines: {2, 5339}, {3, 395}, {4, 396}, {5, 15}, {6, 20}, {13, 3627}, {14, 140}, {16, 548}, {17, 546}, {18, 549}, {30, 61}, {62, 550}, {203, 15171}, {298, 32820}, {376, 22238}, {381, 5349}, {382, 5318}, {383, 22532}, {389, 36980}, {531, 635}, {617, 11290}, {621, 11307}, {628, 11304}, {631, 5334}, {632, 37835}, {633, 11299}, {1327, 18587}, {1328, 18586}, {1657, 10653}, {1885, 8740}, {1906, 10641}, {1907, 11475}, {2041, 3070}, {2042, 3071}, {2043, 41946}, {2044, 41945}, {2307, 6284}, {2883, 11243}, {3090, 5343}, {3091, 16644}, {3104, 32448}, {3106, 32516}, {3146, 5340}, {3411, 10646}, {3412, 3853}, {3522, 36843}, {3523, 16645}, {3526, 18581}, {3528, 11481}, {3530, 10645}, {3545, 5365}, {3628, 16241}, {3832, 11488}, {3843, 18582}, {3845, 16962}, {3850, 37832}, {3861, 16808}, {4325, 5357}, {4330, 5353}, {5054, 41113}, {5066, 41943}, {5237, 8703}, {5305, 41407}, {5335, 33703}, {5344, 15682}, {5351, 33923}, {5460, 6674}, {5471, 37512}, {5479, 22893}, {5480, 36993}, {6109, 16002}, {6561, 35740}, {6694, 37352}, {6772, 41020}, {7005, 18990}, {7051, 37722}, {7127, 15338}, {7685, 10616}, {8259, 10613}, {8260, 22843}, {8359, 12154}, {8918, 11549}, {8929, 11586}, {10617, 21158}, {10638, 15888}, {11137, 34148}, {11486, 15696}, {11489, 15717}, {11539, 41122}, {11626, 16836}, {12007, 36995}, {12100, 16268}, {12103, 36968}, {12817, 38071}, {13567, 19772}, {14138, 22795}, {14892, 41978}, {14893, 41121}, {15684, 41112}, {15686, 41100}, {15687, 16267}, {15694, 41120}, {15712, 16242}, {16239, 16967}, {16963, 34200}, {17504, 41944}, {19773, 23292}, {20415, 31710}, {20429, 22906}, {21156, 22847}, {21850, 36757}, {22114, 33459}, {33387, 36330}, {34153, 36209}, {34508, 35304}, {38335, 41119}, {41021, 41746}

X(42147) = {X(6),X(20)}-harmonic conjugate of X(42148)

X(42148) = GIBERT(3,1,-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*a^2*SA + 2*SB*SC : :

X(42148) lies on these lines: {2, 5340}, {3, 396}, {4, 395}, {5, 16}, {6, 20}, {13, 140}, {14, 3627}, {15, 548}, {17, 549}, {18, 546}, {30, 62}, {61, 550}, {202, 15171}, {299, 32820}, {376, 22236}, {381, 5350}, {382, 5321}, {389, 36978}, {530, 636}, {616, 11289}, {622, 11308}, {627, 11303}, {631, 5335}, {632, 37832}, {634, 11300}, {1080, 22531}, {1250, 15888}, {1327, 18586}, {1328, 18587}, {1657, 10654}, {1885, 8739}, {1906, 10642}, {1907, 11476}, {2041, 3071}, {2042, 3070}, {2043, 41945}, {2044, 41946}, {2307, 15326}, {2883, 11244}, {3090, 5344}, {3091, 16645}, {3105, 32448}, {3107, 32516}, {3146, 5339}, {3411, 3853}, {3412, 10645}, {3522, 36836}, {3523, 16644}, {3526, 18582}, {3528, 11480}, {3530, 10646}, {3545, 5366}, {3628, 16242}, {3832, 11489}, {3843, 18581}, {3845, 16963}, {3850, 37835}, {3861, 16809}, {4325, 5353}, {4330, 5357}, {5054, 41112}, {5066, 41944}, {5238, 8703}, {5305, 41406}, {5334, 33703}, {5343, 15682}, {5352, 33923}, {5459, 6673}, {5472, 37512}, {5478, 22847}, {5480, 36995}, {6108, 16001}, {6695, 37351}, {6775, 41021}, {7006, 18990}, {7127, 7354}, {7684, 10617}, {8259, 22890}, {8260, 10614}, {8359, 12155}, {8919, 11537}, {8930, 15743}, {10616, 21159}, {11134, 34148}, {11485, 15696}, {11488, 15717}, {11539, 41121}, {11624, 16836}, {12007, 36993}, {12100, 16267}, {12103, 36967}, {12816, 38071}, {13567, 19773}, {14139, 22794}, {14892, 41977}, {14893, 41122}, {15684, 41113}, {15686, 41101}, {15687, 16268}, {15694, 41119}, {15712, 16241}, {16239, 16966}, {16962, 34200}, {17504, 41943}, {19373, 37722}, {19772, 23292}, {20416, 31709}, {20428, 22862}, {21157, 22893}, {21850, 36758}, {22113, 33458}, {33386, 35752}, {34153, 36208}, {34509, 35303}, {38335, 41120}, {41020, 41745}

X(42148) = {X(6),X(20)}-harmonic conjugate of X(42147)

X(42149) = GIBERT(-3,1,3) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA - 2*SB*SC : :

X(42149) lies on these lines: {2, 17}, {3, 395}, {4, 16}, {5, 5340}, {6, 140}, {13, 3090}, {14, 20}, {15, 3523}, {30, 36843}, {39, 22714}, {61, 631}, {69, 6672}, {202, 3085}, {203, 7288}, {298, 11308}, {302, 315}, {371, 2045}, {372, 2046}, {376, 5351}, {381, 5350}, {396, 3526}, {397, 1656}, {471, 11547}, {485, 14813}, {486, 14814}, {499, 7127}, {547, 41119}, {549, 22236}, {550, 5339}, {616, 22511}, {617, 22114}, {618, 37177}, {621, 39554}, {628, 3181}, {632, 16644}, {633, 7793}, {635, 37178}, {1657, 5321}, {2041, 35813}, {2042, 35812}, {2043, 36452}, {2044, 36470}, {3068, 3390}, {3069, 3389}, {3086, 7006}, {3091, 5366}, {3104, 6194}, {3106, 12251}, {3146, 36968}, {3147, 8740}, {3205, 11003}, {3364, 9540}, {3365, 13935}, {3522, 5334}, {3524, 5238}, {3525, 37640}, {3528, 36967}, {3529, 36970}, {3530, 36836}, {3533, 11488}, {3541, 8739}, {3543, 41122}, {3545, 41100}, {3618, 6694}, {3832, 36969}, {3851, 5318}, {5054, 16772}, {5055, 41112}, {5056, 5335}, {5059, 5365}, {5067, 37832}, {5068, 5344}, {5071, 41107}, {5073, 5349}, {5206, 5471}, {5218, 7005}, {5352, 15717}, {5463, 36251}, {5611, 10617}, {5613, 22848}, {5862, 33386}, {5868, 41034}, {6114, 41021}, {6770, 16530}, {6775, 20416}, {6782, 41020}, {7803, 11290}, {9744, 37464}, {9753, 37463}, {9761, 37341}, {10187, 22235}, {10299, 10645}, {10303, 16241}, {10304, 41108}, {10359, 36759}, {10614, 37825}, {11244, 14216}, {11302, 33459}, {11305, 33474}, {11480, 15712}, {11485, 15720}, {11626, 13340}, {12154, 35287}, {13084, 37172}, {13103, 22847}, {13846, 34551}, {13847, 34552}, {14136, 36770}, {14137, 14541}, {15444, 36300}, {15445, 36305}, {15692, 41101}, {15702, 16962}, {15709, 41943}, {16529, 40898}, {16630, 33412}, {20081, 32466}, {20415, 41745}, {21735, 41973}, {22491, 35230}, {33389, 39647}, {34508, 37173}, {36980, 37484}

X(42149) = {X(6),X(140)}-harmonic conjugate of X(42152)
X(42149) = {X(3),X(398)}-harmonic conjugate of X(42150)
X(42149) = {X(4),X(16)}-harmonic conjugate of X(42151)

X(42150) = GIBERT(3,-1,3) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 2*SB*SC : :

X(42150) lies on these lines: {2, 5238}, {3, 395}, {4, 15}, {5, 36836}, {6, 550}, {13, 3146}, {14, 631}, {16, 3522}, {18, 3523}, {20, 61}, {30, 5340}, {62, 376}, {140, 5339}, {203, 4294}, {381, 16772}, {382, 396}, {397, 1657}, {531, 37172}, {546, 16644}, {548, 22238}, {549, 41113}, {634, 9939}, {1656, 5321}, {2307, 4302}, {3090, 16241}, {3091, 36970}, {3104, 7709}, {3106, 32522}, {3364, 6460}, {3365, 6459}, {3389, 9541}, {3411, 21734}, {3412, 33703}, {3524, 41108}, {3525, 37835}, {3528, 5237}, {3529, 16965}, {3530, 16645}, {3533, 16967}, {3543, 16962}, {3642, 37177}, {3832, 37832}, {3839, 41943}, {3851, 5349}, {4293, 7005}, {5054, 41120}, {5056, 5365}, {5059, 5335}, {5068, 16966}, {5073, 5318}, {5286, 41407}, {5344, 19106}, {5351, 10304}, {5471, 15515}, {5862, 22844}, {5868, 8721}, {5878, 11243}, {6111, 15005}, {6560, 14814}, {6561, 14813}, {6695, 37173}, {8703, 36843}, {9754, 37464}, {10299, 11489}, {10646, 21735}, {11481, 33923}, {11543, 15712}, {12154, 33215}, {12244, 36208}, {15682, 16267}, {15683, 41107}, {15692, 16268}, {15698, 41944}, {15702, 41122}, {15717, 16242}, {15720, 23303}, {16960, 22235}, {16963, 19708}, {17538, 36968}, {36772, 41020}, {36980, 37481}

X(42150) = {X(6),X(550)}-harmonic conjugate of X(42151)
X(42150) = {X(3),X(398)}-harmonic conjugate of X(42149)
X(42150) = {X(4),X(15)}-harmonic conjugate of X(42152)

X(42151) = GIBERT(3,1,-3) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 2*SB*SC : :

X(42151) lies on these lines: {2, 5237}, {3, 396}, {4, 16}, {5, 36843}, {6, 550}, {13, 631}, {14, 3146}, {15, 3522}, {17, 3523}, {20, 62}, {30, 5339}, {61, 376}, {140, 5340}, {202, 4294}, {381, 16773}, {382, 395}, {398, 1657}, {530, 37173}, {546, 16645}, {548, 22236}, {549, 41112}, {633, 9939}, {1656, 5318}, {3090, 16242}, {3091, 36969}, {3105, 7709}, {3107, 32522}, {3364, 9541}, {3389, 6460}, {3390, 6459}, {3411, 33703}, {3412, 21734}, {3524, 41107}, {3525, 37832}, {3528, 5238}, {3529, 16964}, {3530, 16644}, {3533, 16966}, {3543, 16963}, {3643, 37178}, {3832, 37835}, {3839, 41944}, {3851, 5350}, {4293, 7006}, {4299, 7127}, {5054, 41119}, {5056, 5366}, {5059, 5334}, {5068, 16967}, {5073, 5321}, {5286, 41406}, {5343, 19107}, {5352, 10304}, {5472, 15515}, {5863, 22845}, {5869, 8721}, {5878, 11244}, {6110, 15005}, {6560, 14813}, {6561, 14814}, {6694, 37172}, {8703, 36836}, {9754, 37463}, {10299, 11488}, {10645, 21735}, {11480, 33923}, {11542, 15712}, {12155, 33215}, {12244, 36209}, {15682, 16268}, {15683, 41108}, {15692, 16267}, {15698, 41943}, {15702, 41121}, {15717, 16241}, {15720, 23302}, {16961, 22237}, {16962, 19708}, {17538, 36967}, {36978, 37481}

X(42151) = {X(6),X(550)}-harmonic conjugate of X(42150)
X(42151) = {X(3),X(397)}-harmonic conjugate of X(42152)
X(42151) = {X(4),X(16)}-harmonic conjugate of X(42149)

X(42152) = GIBERT(3,1,3) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 2*SB*SC : :

X(42152) lies on these lines: {2, 18}, {3, 396}, {4, 15}, {5, 5339}, {6, 140}, {13, 20}, {14, 3090}, {16, 3523}, {30, 36836}, {39, 22715}, {62, 631}, {69, 6671}, {202, 7288}, {203, 3085}, {299, 11307}, {303, 315}, {371, 2046}, {372, 2045}, {376, 5352}, {381, 5349}, {395, 3526}, {398, 1656}, {470, 11547}, {485, 14814}, {486, 14813}, {498, 2307}, {547, 41120}, {549, 22238}, {550, 5340}, {616, 22113}, {617, 22510}, {619, 37178}, {622, 39555}, {627, 3180}, {632, 16645}, {634, 7793}, {636, 37177}, {1657, 5318}, {2041, 35812}, {2042, 35813}, {2043, 36453}, {2044, 36469}, {3068, 3365}, {3069, 3364}, {3086, 7005}, {3091, 5365}, {3105, 6194}, {3107, 12251}, {3146, 36967}, {3147, 8739}, {3206, 11003}, {3389, 9540}, {3390, 13935}, {3522, 5335}, {3524, 5237}, {3525, 37641}, {3528, 36968}, {3529, 36969}, {3530, 36843}, {3533, 11489}, {3541, 8740}, {3543, 41121}, {3545, 41101}, {3618, 6695}, {3832, 36970}, {3851, 5321}, {5054, 16773}, {5055, 41113}, {5056, 5334}, {5059, 5366}, {5067, 37835}, {5068, 5343}, {5071, 41108}, {5073, 5350}, {5206, 5472}, {5218, 7006}, {5351, 15717}, {5464, 36252}, {5615, 10616}, {5617, 22892}, {5863, 33387}, {5869, 41035}, {6115, 41020}, {6772, 20415}, {6773, 16529}, {6783, 41021}, {7803, 11289}, {9744, 37463}, {9753, 37464}, {9763, 37340}, {10188, 22237}, {10299, 10646}, {10303, 16242}, {10304, 41107}, {10359, 36760}, {10613, 37824}, {11243, 14216}, {11301, 33458}, {11306, 33475}, {11481, 15712}, {11486, 15720}, {11624, 13340}, {12155, 35287}, {13083, 37173}, {13102, 22893}, {13846, 34552}, {13847, 34551}, {14136, 14540}, {15444, 36304}, {15445, 36301}, {15692, 41100}, {15702, 16963}, {15709, 41944}, {16530, 40899}, {16631, 33413}, {20081, 32465}, {20416, 41746}, {21735, 41974}, {22492, 35229}, {33388, 39647}, {34509, 37172}, {36763, 41022}, {36978, 37484}

X(42152) = {X(6),X(140)}-harmonic conjugate of X(42149)
X(42152) = {X(3),X(397)}-harmonic conjugate of X(42151)
X(42152) = {X(4),X(15)}-harmonic conjugate of X(42150)

X(42153) = GIBERT(-3,2,2) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*a^2*SA - 4*SB*SC : :

X(42153) lies on these lines: {2, 398}, {3, 14}, {4, 395}, {5, 6}, {13, 3851}, {15, 3526}, {16, 382}, {17, 5055}, {20, 5321}, {30, 36843}, {61, 1656}, {62, 381}, {140, 10654}, {202, 9654}, {299, 22114}, {302, 1975}, {376, 5343}, {383, 5868}, {396, 3090}, {397, 3091}, {546, 10653}, {549, 41113}, {569, 11137}, {599, 636}, {619, 11310}, {621, 11308}, {623, 11311}, {624, 33464}, {627, 9761}, {629, 11301}, {631, 5334}, {634, 5858}, {635, 3763}, {1151, 2042}, {1152, 2041}, {1250, 9670}, {1657, 5237}, {3106, 13108}, {3146, 5349}, {3364, 8976}, {3365, 13951}, {3366, 35812}, {3367, 35813}, {3389, 13785}, {3390, 13665}, {3411, 3843}, {3412, 16966}, {3529, 5365}, {3534, 5351}, {3643, 35020}, {3830, 16963}, {3832, 5318}, {3839, 5350}, {3855, 5335}, {5054, 5238}, {5056, 37640}, {5067, 23302}, {5070, 11485}, {5073, 36968}, {5079, 37832}, {5352, 15720}, {5366, 41099}, {5464, 33386}, {5471, 7746}, {5617, 36251}, {5865, 20426}, {5869, 6773}, {6114, 37637}, {6425, 35738}, {6695, 11298}, {6770, 22847}, {7005, 31479}, {7006, 9669}, {7127, 10896}, {7486, 11488}, {7507, 8739}, {7685, 36990}, {8260, 41039}, {8836, 37638}, {8919, 18777}, {9657, 19373}, {9781, 36978}, {10539, 11134}, {10613, 40334}, {10614, 41037}, {10617, 36993}, {10646, 15696}, {11315, 33444}, {11316, 33445}, {11412, 36980}, {11459, 11626}, {11737, 41119}, {12817, 15684}, {13103, 16530}, {13846, 18586}, {13847, 18587}, {14137, 37825}, {14269, 41100}, {15534, 34509}, {15694, 41101}, {15702, 33605}, {15703, 16962}, {17800, 19107}, {18440, 36758}, {19780, 20428}, {20429, 31706}, {21360, 36368}, {22491, 37341}, {22845, 33415}, {33459, 37171}, {33474, 37172}, {36209, 38724}, {36436, 41951}, {36454, 41952}, {38071, 41112}

X(42153) = {X(3),X(5339)}-harmonic conjugate of X(42154)
X(42153) = {X(4),X(22238)}-harmonic conjugate of X(42155)
X(42153) = {X(5),X(6)}-harmonic conjugate of X(42156)
X(42153) = {X(14),X(16645)}-harmonic conjugate of X(42154)

X(42154) = GIBERT(3,-2,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 2*a^2*SA - 4*SB*SC : :

X(42154) lies on these lines: {2, 5321}, {3, 14}, {4, 396}, {5, 36836}, {6, 30}, {13, 3830}, {15, 381}, {16, 3534}, {17, 3843}, {20, 398}, {61, 382}, {62, 1657}, {203, 9668}, {298, 1975}, {376, 395}, {383, 36993}, {397, 3146}, {530, 15534}, {531, 599}, {532, 6144}, {533, 40341}, {542, 23013}, {549, 18581}, {550, 36843}, {590, 36445}, {615, 36463}, {616, 5858}, {617, 7784}, {619, 11306}, {621, 11299}, {622, 5859}, {623, 11301}, {631, 5343}, {1080, 41038}, {1151, 2044}, {1152, 2043}, {1525, 11243}, {1656, 5238}, {2307, 12953}, {3090, 5365}, {3091, 5349}, {3107, 22728}, {3180, 7823}, {3522, 16773}, {3524, 23303}, {3526, 5352}, {3543, 5318}, {3545, 23302}, {3627, 40693}, {3642, 3763}, {3818, 22906}, {3839, 11488}, {3845, 18582}, {5054, 10645}, {5055, 16241}, {5064, 11475}, {5073, 16965}, {5077, 12154}, {5237, 15696}, {5335, 15682}, {5350, 17578}, {5463, 15300}, {5473, 9115}, {5479, 41041}, {5890, 36980}, {5978, 7778}, {5979, 9766}, {6108, 19781}, {6109, 25164}, {6409, 34551}, {6410, 34552}, {6770, 41039}, {6772, 36990}, {7005, 9655}, {7051, 11238}, {8703, 11543}, {8739, 37196}, {9117, 41043}, {9749, 41060}, {9761, 35931}, {10304, 11489}, {10613, 36992}, {10638, 11237}, {10646, 15688}, {11092, 37638}, {11137, 13352}, {11486, 15681}, {11542, 15687}, {12100, 41120}, {12101, 41119}, {12817, 16966}, {14093, 41944}, {14269, 16808}, {15684, 19106}, {15685, 41100}, {15689, 16963}, {15693, 41122}, {15694, 16967}, {15695, 16961}, {15701, 33416}, {15703, 33417}, {16267, 34754}, {16960, 35403}, {18586, 23261}, {18587, 23251}, {19708, 33605}, {21467, 36185}, {21734, 22237}, {22491, 35304}, {22532, 22893}, {22891, 35229}, {33517, 36383}, {33699, 41112}, {36208, 38790}, {36772, 41042}, {36962, 41020}, {41023, 41746}, {41121, 41971}

X(42154) = reflection of X(42155) in X(6)
X(42154) = {X(3),X(5339)}-harmonic conjugate of X(42153)
X(42154) = {X(4),X(22236)}-harmonic conjugate of X(42156)
X(42154) = {X(14),X(16645)}-harmonic conjugate of X(42153)

X(42155) = GIBERT(3,2,-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*a^2*SA + 4*SB*SC : :

X(42155) lies on these lines: {2, 5318}, {3, 13}, {4, 395}, {5, 36843}, {6, 30}, {14, 3830}, {15, 3534}, {16, 381}, {18, 3843}, {20, 397}, {61, 1657}, {62, 382}, {202, 9668}, {299, 1975}, {376, 396}, {383, 41039}, {398, 3146}, {530, 599}, {531, 15534}, {532, 40341}, {533, 6144}, {542, 23006}, {549, 18582}, {550, 36836}, {590, 36463}, {615, 36445}, {616, 7784}, {617, 5859}, {618, 11305}, {621, 5858}, {622, 11300}, {624, 11302}, {631, 5344}, {1080, 36995}, {1151, 2043}, {1152, 2044}, {1250, 11237}, {1524, 11244}, {1656, 5237}, {3090, 5366}, {3091, 5350}, {3106, 22728}, {3181, 7823}, {3522, 16772}, {3524, 23302}, {3526, 5351}, {3543, 5321}, {3545, 23303}, {3627, 40694}, {3643, 3763}, {3818, 22862}, {3839, 11489}, {3845, 18581}, {5054, 10646}, {5055, 16242}, {5064, 11476}, {5073, 16964}, {5077, 12155}, {5238, 15696}, {5334, 15682}, {5349, 17578}, {5464, 15300}, {5474, 9117}, {5478, 41040}, {5890, 36978}, {5978, 9766}, {5979, 7778}, {6108, 25154}, {6109, 19780}, {6409, 34552}, {6410, 34551}, {6773, 41038}, {6775, 36990}, {7006, 9655}, {7127, 12943}, {8703, 11542}, {8740, 37196}, {9115, 41042}, {9750, 41061}, {9763, 35932}, {10304, 11488}, {10614, 36994}, {10645, 15688}, {11078, 37638}, {11134, 13352}, {11238, 19373}, {11485, 15681}, {11543, 15687}, {12100, 41119}, {12101, 41120}, {12816, 16967}, {14093, 41943}, {14269, 16809}, {15684, 19107}, {15685, 41101}, {15689, 16962}, {15693, 41121}, {15694, 16966}, {15695, 16960}, {15701, 33417}, {15703, 33416}, {16268, 34755}, {16961, 35403}, {18586, 23251}, {18587, 23261}, {19708, 33604}, {21466, 36186}, {21734, 22235}, {22492, 35303}, {22531, 22847}, {22846, 35230}, {33518, 36382}, {33699, 41113}, {36209, 38790}, {36961, 41021}, {41022, 41745}, {41122, 41972}

X(42155) = reflection of X(42154) in X(6)
X(42155) = {X(3),X(5340)}-harmonic conjugate of X(42156)
X(42155) = {X(4),X(22238)}-harmonic conjugate of X(42153)
X(42155) = {X(13),X(16644)}-harmonic conjugate of X(42156)

X(42156) = GIBERT(3,2,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 2*a^2*SA + 4*SB*SC : :

X(42156) lies on these lines: {2, 397}, {3, 13}, {4, 396}, {5, 6}, {14, 3851}, {15, 382}, {16, 3526}, {18, 5055}, {20, 5318}, {30, 36836}, {61, 381}, {62, 1656}, {140, 10653}, {203, 9654}, {298, 22113}, {303, 1975}, {376, 5344}, {395, 3090}, {398, 3091}, {546, 10654}, {549, 41112}, {569, 11134}, {599, 635}, {615, 35740}, {618, 11309}, {622, 11307}, {623, 33465}, {624, 11312}, {628, 9763}, {630, 11302}, {631, 5335}, {633, 5859}, {636, 3763}, {1080, 5869}, {1151, 2041}, {1152, 2042}, {1657, 5238}, {2307, 10895}, {3107, 13108}, {3146, 5350}, {3364, 13785}, {3365, 13665}, {3389, 8976}, {3390, 13951}, {3391, 35812}, {3392, 35813}, {3411, 16967}, {3412, 3843}, {3529, 5366}, {3534, 5352}, {3642, 35019}, {3830, 16962}, {3832, 5321}, {3839, 5349}, {3855, 5334}, {5054, 5237}, {5056, 37641}, {5067, 23303}, {5070, 11486}, {5073, 36967}, {5079, 37835}, {5351, 15720}, {5365, 41099}, {5463, 33387}, {5472, 7746}, {5613, 36252}, {5864, 20425}, {5868, 6770}, {6115, 37637}, {6426, 35738}, {6694, 11297}, {6773, 22893}, {7005, 9669}, {7006, 31479}, {7051, 9657}, {7486, 11489}, {7507, 8740}, {7684, 36990}, {8259, 41038}, {8838, 37638}, {8918, 18776}, {9670, 10638}, {9781, 36980}, {10539, 11137}, {10613, 41036}, {10614, 40335}, {10616, 36995}, {10645, 15696}, {11315, 33446}, {11316, 33447}, {11412, 36978}, {11459, 11624}, {11737, 41120}, {12816, 15684}, {13102, 16529}, {13846, 18587}, {13847, 18586}, {14136, 37824}, {14269, 41101}, {15534, 34508}, {15694, 41100}, {15702, 33604}, {15703, 16963}, {17800, 19106}, {18440, 36757}, {19781, 20429}, {20428, 31705}, {21359, 36366}, {22492, 37340}, {22844, 33414}, {33458, 37170}, {33475, 37173}, {36208, 38724}, {36436, 41952}, {36454, 41951}, {38071, 41113}

X(42156) = {X(3),X(5340)}-harmonic conjugate of X(42155)
X(42156) = {X(4),X(22236)}-harmonic conjugate of X(42154)
X(42156) = {X(5),X(6)}-harmonic conjugate of X(42153)
X(42156) = {X(13),X(16644)}-harmonic conjugate of X(42155)

X(42157) = GIBERT(3,-2,3) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 4*SB*SC : :

X(42157) lies on these lines: {2, 5352}, {3, 14}, {4, 15}, {5, 5238}, {6, 1657}, {13, 382}, {16, 398}, {20, 62}, {30, 61}, {140, 5321}, {202, 4299}, {203, 6284}, {376, 5237}, {381, 36836}, {395, 548}, {396, 3627}, {531, 633}, {546, 16772}, {616, 22844}, {617, 636}, {628, 21360}, {631, 37835}, {635, 11299}, {1607, 3439}, {1614, 3201}, {1656, 11480}, {2777, 36208}, {2794, 5869}, {3104, 11257}, {3105, 22696}, {3146, 5344}, {3205, 34148}, {3364, 6560}, {3365, 6561}, {3389, 14813}, {3390, 14814}, {3411, 15696}, {3522, 5334}, {3523, 5343}, {3524, 41122}, {3529, 10653}, {3534, 22238}, {3543, 12816}, {3830, 16962}, {3843, 16644}, {3845, 41943}, {3850, 23302}, {3851, 16966}, {3855, 12821}, {4302, 7006}, {4324, 7127}, {4857, 7051}, {5055, 12817}, {5059, 41974}, {5073, 5340}, {5254, 41407}, {5270, 10638}, {5318, 34754}, {5350, 11542}, {5464, 11304}, {5470, 9880}, {5473, 5864}, {6102, 36981}, {6694, 11303}, {6777, 13188}, {6780, 37825}, {7005, 7354}, {7755, 19781}, {7814, 30471}, {7833, 12154}, {8172, 10263}, {8175, 15445}, {8703, 16268}, {8739, 35471}, {8740, 18560}, {10187, 15720}, {10304, 41113}, {10619, 10678}, {10658, 30714}, {11082, 32535}, {11137, 37495}, {11243, 22802}, {11295, 36329}, {11489, 21735}, {11543, 33923}, {12121, 36209}, {12203, 36760}, {13630, 36980}, {14862, 30402}, {15681, 41100}, {15687, 41121}, {15692, 41120}, {15712, 23303}, {16529, 36962}, {17538, 37641}, {19778, 40712}, {22796, 36782}, {31670, 36757}, {33703, 37640}, {34508, 35931}

X(42157) = {X(6),X(1657)}-harmonic conjugate of X(421

X(42158) = GIBERT(3,2,-3) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 4*SB*SC : :

X(42158) lies on these lines: {2, 5351}, {3, 13}, {4, 16}, {5, 5237}, {6, 1657}, {14, 382}, {15, 397}, {20, 61}, {30, 62}, {140, 5318}, {202, 6284}, {203, 4299}, {376, 5238}, {381, 36843}, {395, 3627}, {396, 548}, {530, 634}, {546, 16773}, {616, 635}, {617, 22845}, {627, 21359}, {631, 37832}, {636, 11300}, {1250, 5270}, {1608, 3438}, {1614, 3200}, {1656, 11481}, {2307, 4316}, {2777, 36209}, {2794, 5868}, {3104, 22695}, {3105, 11257}, {3146, 5343}, {3206, 34148}, {3364, 14814}, {3365, 14813}, {3366, 35740}, {3389, 6560}, {3390, 6561}, {3412, 15696}, {3522, 5335}, {3523, 5344}, {3524, 41121}, {3529, 10654}, {3534, 22236}, {3543, 12817}, {3830, 16963}, {3843, 16645}, {3845, 41944}, {3850, 23303}, {3851, 16967}, {3855, 12820}, {4302, 7005}, {4857, 19373}, {5055, 12816}, {5059, 41973}, {5073, 5339}, {5254, 41406}, {5321, 34755}, {5349, 11543}, {5463, 11303}, {5469, 9880}, {5474, 5865}, {6102, 36979}, {6695, 11304}, {6778, 13188}, {6779, 37824}, {7006, 7354}, {7127, 10483}, {7755, 19780}, {7814, 30472}, {7833, 12155}, {8173, 10263}, {8174, 15444}, {8703, 16267}, {8739, 18560}, {8740, 35471}, {10188, 15720}, {10304, 41112}, {10619, 10677}, {10657, 30714}, {11087, 32535}, {11134, 37495}, {11244, 22802}, {11296, 35751}, {11488, 21735}, {11542, 33923}, {12121, 36208}, {12203, 36759}, {13630, 36978}, {14862, 30403}, {15681, 41101}, {15687, 41122}, {15692, 41119}, {15712, 23302}, {16530, 36961}, {17538, 37640}, {19779, 40711}, {31670, 36758}, {33352, 38400}, {33703, 37641}, {34504, 36775}, {34509, 35752}, {35256, 35739}

X(42158) = {X(6),X(1657)}-harmonic conjugate of X(42157)

X(42159) = GIBERT(-3,3,1) POINT

Barycentrics    Sqrt[3]*a^2*S - a^2*SA - 6*SB*SC : :

X(42159) lies on these lines: {2, 5238}, {3, 5321}, {4, 14}, {5, 5339}, {6, 546}, {13, 3832}, {15, 3090}, {16, 3146}, {17, 3545}, {18, 20}, {30, 36843}, {61, 3091}, {202, 5229}, {203, 10591}, {376, 41122}, {381, 398}, {382, 395}, {396, 3851}, {397, 3843}, {550, 16645}, {621, 7938}, {622, 22114}, {623, 37177}, {629, 11147}, {631, 37835}, {632, 11480}, {636, 37171}, {1327, 18585}, {1328, 15765}, {1657, 16773}, {3364, 31412}, {3366, 9540}, {3367, 13935}, {3389, 23259}, {3390, 23249}, {3411, 17578}, {3522, 16242}, {3523, 36967}, {3525, 5352}, {3529, 5237}, {3543, 12817}, {3544, 11488}, {3627, 11543}, {3628, 36836}, {3839, 41112}, {3845, 5340}, {3855, 37640}, {3857, 11542}, {5055, 16772}, {5056, 41973}, {5067, 16241}, {5068, 37832}, {5071, 41101}, {5072, 11485}, {5076, 11486}, {5079, 23302}, {5225, 7006}, {5350, 14269}, {5366, 41107}, {5460, 37173}, {5868, 41017}, {6561, 35738}, {7005, 10590}, {7685, 33420}, {10303, 10645}, {10646, 17538}, {11001, 41944}, {11304, 22491}, {11481, 15704}, {12154, 32984}, {14539, 31706}, {15022, 16966}, {15682, 16963}, {16267, 41106}, {16627, 16635}, {18436, 36980}, {18586, 41945}, {18587, 41946}, {20416, 22512}, {22113, 22492}, {25164, 40921}, {33703, 36968}, {36251, 41042}

X(42159) = {X(3),X(5321)}-harmonic conjugate of X(42160)
X(42159) = {X(4),X(62)}-harmonic conjugate of X(42161)
X(42159) = {X(6),X(546)}-harmonic conjugate of X(42162)

X(42160) = GIBERT(3,-3,1) POINT

Barycentrics    Sqrt[3]*a^2*S + a^2*SA - 6*SB*SC : :

X(42160) lies on these lines: {2, 5352}, {3, 5321}, {4, 13}, {5, 36836}, {6, 3627}, {14, 20}, {15, 3091}, {16, 3529}, {17, 3832}, {18, 376}, {30, 5339}, {62, 3146}, {203, 5225}, {381, 5349}, {382, 398}, {395, 1657}, {396, 3843}, {397, 3830}, {546, 18582}, {548, 16645}, {631, 36967}, {3090, 5238}, {3364, 23249}, {3365, 23259}, {3523, 10187}, {3525, 10645}, {3528, 16242}, {3534, 16773}, {3543, 16965}, {3544, 16966}, {3545, 12817}, {3628, 11480}, {3839, 41101}, {3850, 16644}, {3851, 16772}, {3853, 5340}, {3855, 37832}, {5056, 16241}, {5059, 36968}, {5072, 23302}, {5076, 5318}, {5229, 7005}, {5351, 11489}, {6694, 37170}, {8596, 22114}, {8721, 41038}, {9541, 35732}, {10303, 16967}, {10304, 41122}, {11001, 16268}, {11481, 12103}, {11543, 15704}, {14269, 41119}, {14540, 22861}, {14927, 36758}, {15683, 16963}, {15687, 41112}, {16002, 22512}, {16962, 41099}, {17578, 36969}, {23261, 35738}, {33703, 37641}, {34508, 36769}, {34783, 36980}, {35229, 36993}, {37333, 40922}, {41106, 41943}

X(42160) = {X(3),X(5321)}-harmonic conjugate of X(42159)
X(42160) = {X(4),X(61)}-harmonic conjugate of X(42162)
X(42160) = {X(6),X(3627)}-harmonic conjugate of X(42161)

X(42161) = GIBERT(3,3,-1) POINT

Barycentrics    Sqrt[3]*a^2*S - a^2*SA + 6*SB*SC : :

X(42161) lies on these lines: {2, 5351}, {3, 5318}, {4, 14}, {5, 36843}, {6, 3627}, {13, 20}, {15, 3529}, {16, 3091}, {17, 376}, {18, 3832}, {30, 5340}, {61, 3146}, {202, 5225}, {381, 5350}, {382, 397}, {395, 3843}, {396, 1657}, {398, 3830}, {546, 18581}, {548, 16644}, {631, 36968}, {3090, 5237}, {3389, 23249}, {3390, 23259}, {3523, 10188}, {3525, 10646}, {3528, 16241}, {3534, 16772}, {3543, 16964}, {3544, 16967}, {3545, 12816}, {3628, 11481}, {3839, 41100}, {3850, 16645}, {3851, 16773}, {3853, 5339}, {3855, 37835}, {5056, 16242}, {5059, 36967}, {5072, 23303}, {5076, 5321}, {5229, 7006}, {5352, 11488}, {6695, 37171}, {8596, 22113}, {8721, 41039}, {10303, 16966}, {10304, 41121}, {11001, 16267}, {11480, 12103}, {11542, 15704}, {14269, 41120}, {14541, 22907}, {14927, 36757}, {15683, 16962}, {15687, 41113}, {16001, 22513}, {16963, 41099}, {17578, 36970}, {23251, 35738}, {33703, 37640}, {34783, 36978}, {35230, 36995}, {37332, 40921}, {41106, 41944}

X(42161) = {X(3),X(5318)}-harmonic conjugate of X(42162)
X(42161) = {X(4),X(62)}-harmonic conjugate of X(42159)
X(42161) = {X(6),X(3627)}-harmonic conjugate of X(42160)

X(42162) = GIBERT(3,3,1) POINT

Barycentrics    Sqrt[3]*a^2*S + a^2*SA + 6*SB*SC : :

X(42162) lies on these lines: {2, 5237}, {3, 5318}, {4, 13}, {5, 5340}, {6, 546}, {14, 3832}, {15, 3146}, {16, 3090}, {17, 20}, {18, 3545}, {30, 36836}, {62, 3091}, {202, 10591}, {203, 5229}, {376, 41121}, {381, 397}, {382, 396}, {395, 3851}, {398, 3843}, {550, 16644}, {621, 22113}, {622, 7938}, {624, 37178}, {630, 11147}, {631, 37832}, {632, 11481}, {635, 37170}, {1327, 15765}, {1328, 18585}, {1657, 16772}, {3364, 23259}, {3365, 23249}, {3389, 31412}, {3391, 9540}, {3392, 13935}, {3412, 17578}, {3522, 16241}, {3523, 36968}, {3525, 5351}, {3529, 5238}, {3543, 12816}, {3544, 11489}, {3627, 11542}, {3628, 36843}, {3839, 41113}, {3845, 5339}, {3855, 37641}, {3857, 11543}, {5055, 16773}, {5056, 41974}, {5067, 16242}, {5068, 37835}, {5071, 41100}, {5072, 11486}, {5076, 11485}, {5079, 23303}, {5225, 7005}, {5349, 14269}, {5365, 41108}, {5459, 37172}, {5869, 41016}, {6560, 35738}, {7006, 10590}, {7684, 33421}, {10303, 10646}, {10645, 17538}, {11001, 41943}, {11303, 22492}, {11480, 15704}, {12155, 32984}, {14538, 31705}, {15022, 16967}, {15682, 16962}, {16268, 41106}, {16626, 16634}, {18436, 36978}, {18586, 41946}, {18587, 41945}, {20415, 22513}, {22114, 22491}, {25154, 40922}, {33703, 36967}, {36252, 41043}

X(42162) = {X(3),X(5318)}-harmonic conjugate of X(42161)
X(42162) = {X(4),X(61)}-harmonic conjugate of X(42160)
X(42162) = {X(6),X(546)}-harmonic conjugate of X(42159)

X(42163) = GIBERT(-3,3,2) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*a^2*SA - 6*SB*SC : :

X(42163) lies on these lines: {2, 5339}, {3, 5321}, {4, 395}, {5, 14}, {6, 3091}, {13, 3850}, {15, 3628}, {16, 3627}, {18, 30}, {20, 16645}, {62, 546}, {140, 5352}, {203, 10593}, {302, 32819}, {376, 5365}, {381, 397}, {511, 31706}, {524, 22114}, {531, 630}, {532, 33464}, {547, 41108}, {548, 16242}, {550, 36970}, {590, 35732}, {621, 33412}, {631, 5343}, {632, 5238}, {635, 37351}, {636, 33561}, {1656, 10654}, {2307, 7173}, {3090, 5334}, {3146, 11489}, {3364, 18538}, {3365, 18762}, {3411, 3861}, {3525, 11480}, {3529, 11481}, {3530, 36967}, {3564, 16627}, {3629, 22113}, {3832, 5340}, {3843, 5350}, {3845, 16268}, {3851, 40693}, {3857, 16808}, {5055, 41113}, {5056, 16644}, {5068, 37640}, {5072, 18582}, {5079, 11485}, {5344, 41099}, {5351, 15704}, {5460, 37341}, {5464, 33415}, {5471, 39565}, {5478, 41056}, {5562, 36980}, {6114, 16002}, {6695, 35020}, {6782, 16001}, {7005, 10592}, {8260, 10612}, {8739, 23047}, {10109, 16962}, {10110, 36978}, {10645, 14869}, {10646, 12103}, {10677, 30531}, {11137, 13434}, {11244, 41362}, {11306, 22491}, {11488, 15022}, {11542, 12811}, {11626, 15030}, {11737, 16267}, {11801, 36209}, {12102, 19106}, {12108, 33416}, {12812, 16966}, {14893, 41100}, {15619, 36301}, {15687, 16963}, {15699, 41101}, {15702, 33603}, {16241, 41971}, {16960, 41989}, {20415, 38735}, {22847, 41022}, {22882, 32421}, {22883, 32419}, {23046, 41107}, {31694, 34508}, {36758, 39884}

X(42163) = {X(3),X(5321)}-harmonic conjugate of X(42164)
X(42163) = {X(4),X(22238)}-harmonic conjugate of X(42165)
X(42163) = {X(6),X(3091)}-harmonic conjugate of X(42166)

X(42164) = GIBERT(3,-3,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 2*a^2*SA - 6*SB*SC : :

X(42164) lies on these lines: {3, 5321}, {4, 396}, {5, 5238}, {6, 3146}, {13, 3853}, {14, 550}, {15, 546}, {16, 15704}, {17, 3845}, {18, 548}, {20, 395}, {30, 62}, {61, 3627}, {140, 36967}, {185, 36980}, {376, 5343}, {381, 16772}, {382, 397}, {547, 12817}, {629, 35304}, {631, 5365}, {632, 10645}, {1657, 40694}, {3090, 11480}, {3091, 23302}, {3522, 16645}, {3529, 5334}, {3530, 37835}, {3543, 5340}, {3628, 5352}, {3830, 5350}, {3832, 16644}, {3858, 37832}, {5059, 37641}, {5073, 10653}, {5076, 11485}, {5237, 11543}, {5893, 11243}, {10616, 41037}, {11481, 17538}, {11542, 12102}, {12101, 16267}, {12811, 16966}, {13598, 36978}, {14540, 22512}, {14869, 16967}, {14893, 16962}, {15681, 41113}, {15686, 16268}, {15687, 41101}, {15688, 41120}, {15690, 41944}, {16242, 33923}, {16963, 19710}, {16965, 41973}, {17578, 37640}, {22844, 36330}, {23046, 41943}, {34200, 41122}, {35403, 41119}, {35404, 41107}

X(42164) = {X(3),X(5321)}-harmonic conjugate of X(42163)
X(42164) = {X(4),X(22236)}-harmonic conjugate of X(42166)
X(42164) = {X(6),X(3146)}-harmonic conjugate of X(42165)

X(42165) = GIBERT(3,3,-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*a^2*SA + 6*SB*SC : :

X(42165) lies on these lines: {3, 5318}, {4, 395}, {5, 5237}, {6, 3146}, {13, 550}, {14, 3853}, {15, 15704}, {16, 546}, {17, 548}, {18, 3845}, {20, 396}, {30, 61}, {62, 3627}, {140, 36968}, {185, 36978}, {376, 5344}, {381, 16773}, {382, 398}, {547, 12816}, {630, 35303}, {631, 5366}, {632, 10646}, {1657, 40693}, {3090, 11481}, {3091, 23303}, {3522, 16644}, {3529, 5335}, {3530, 37832}, {3543, 5339}, {3628, 5351}, {3830, 5349}, {3832, 16645}, {3858, 37835}, {5059, 37640}, {5073, 10654}, {5076, 11486}, {5238, 11542}, {5893, 11244}, {10617, 41036}, {11480, 17538}, {11543, 12102}, {12101, 16268}, {12811, 16967}, {13598, 36980}, {14541, 22513}, {14869, 16966}, {14893, 16963}, {15681, 41112}, {15686, 16267}, {15687, 41100}, {15688, 41119}, {15690, 41943}, {16241, 33923}, {16962, 19710}, {16964, 41974}, {17578, 37641}, {22845, 35752}, {23046, 41944}, {34200, 41121}, {35403, 41120}, {35404, 41108}

X(42165) = {X(3),X(5318)}-harmonic conjugate of X(42166)
X(42165) = {X(4),X(22238)}-harmonic conjugate of X(42163)
X(42165) = {X(6),X(3146)}-harmonic conjugate of X(42164)

X(42166) = GIBERT(3,3,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 2*a^2*SA + 6*SB*SC : :

X(42166) lies on these lines: {2, 5340}, {3, 5318}, {4, 396}, {5, 13}, {6, 3091}, {14, 3850}, {15, 3627}, {16, 3628}, {17, 30}, {20, 16644}, {61, 546}, {140, 5351}, {202, 10593}, {303, 32819}, {376, 5366}, {381, 398}, {511, 31705}, {524, 22113}, {530, 629}, {533, 33465}, {547, 41107}, {548, 16241}, {550, 36969}, {615, 35732}, {622, 33413}, {631, 5344}, {632, 5237}, {635, 33560}, {636, 37352}, {1656, 10653}, {3090, 5335}, {3146, 11488}, {3389, 18538}, {3390, 18762}, {3412, 3861}, {3525, 11481}, {3529, 11480}, {3530, 36968}, {3564, 16626}, {3614, 7127}, {3629, 22114}, {3832, 5339}, {3843, 5349}, {3845, 16267}, {3851, 40694}, {3857, 16809}, {5055, 41112}, {5056, 16645}, {5068, 37641}, {5072, 18581}, {5079, 11486}, {5343, 41099}, {5352, 15704}, {5459, 37340}, {5463, 33414}, {5472, 39565}, {5479, 41057}, {5562, 36978}, {6115, 16001}, {6694, 35019}, {6783, 16002}, {7006, 10592}, {8259, 10611}, {8740, 23047}, {10109, 16963}, {10110, 36980}, {10645, 12103}, {10646, 14869}, {10678, 30531}, {11134, 13434}, {11243, 41362}, {11305, 22492}, {11489, 15022}, {11543, 12811}, {11624, 15030}, {11737, 16268}, {11801, 36208}, {12102, 19107}, {12108, 33417}, {12812, 16967}, {14893, 41101}, {15619, 36300}, {15687, 16962}, {15699, 41100}, {15702, 33602}, {16242, 41972}, {16961, 41989}, {20416, 38735}, {22893, 41023}, {22927, 32421}, {22928, 32419}, {23046, 41108}, {31693, 34509}, {36757, 39884}

X(42166) = {X(3),X(5318)}-harmonic conjugate of X(42165)
X(42166) = {X(4),X(22236)}-harmonic conjugate of X(42164)
X(42166) = {X(6),X(3091)}-harmonic conjugate of X(42163)

X(42167) = GIBERT(-1,1,2*SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*Sqrt[3]*a^2*SA - 6*SB*SC : :

X(42167) lies on these lines: {3, 5321}, {4, 6412}, {6, 42170}, {15, 7584}, {16, 34551}, {397, 6398}, {398, 6200}, {615, 11480}, {1152, 5335}, {2042, 23302}, {5318, 6396}, {5334, 6411}, {5340, 6434}, {6410, 35732}, {10653, 35735}, {16773, 35812}, {16966, 35738}, {19107, 34552}

X(42167) = {X(3),X(5321)}-harmonic conjugate of X(42168)
X(42167) = {X(4),X(6412)}-harmonic conjugate of X(42169)

X(42168) = GIBERT(1,-1,2*SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*Sqrt[3]*a^2*SA - 6*SB*SC : :

X(42168) lies on these lines: {3, 5321}, {4, 6411}, {{6, 42169}, 15, 7583}, {16, 34552}, {397, 6221}, {398, 6396}, {590, 11480}, {1151, 5335}, {2041, 23302}, {5318, 6200}, {5334, 6412}, {5340, 6433}, {6409, 35740}, {16773, 35813}, {19107, 34551}

X(42168) = {X(3),X(5321)}-harmonic conjugate of X(42167)
X(42168) = {X(4),X(6411)}-harmonic conjugate of X(42170)

X(42169) = GIBERT(1,1,-2*SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*Sqrt[3]*a^2*SA + 6*SB*SC : :

X(42169) lies on these lines: {3, 5318}, {4, 6412}, {6, 42168}, {15, 34552}, {16, 7584}, {397, 6200}, {398, 6398}, {615, 11481}, {1152, 5334}, {2041, 23303}, {5321, 6396}, {5335, 6411}, {5339, 6434}, {16772, 35812}, {19106, 34551}

X(42169) = {X(3),X(5318)}-harmonic conjugate of X(42170)
X(42169) = {X(4),X(6412)}-harmonic conjugate of X(42167)

X(42170) = GIBERT(1,1,2*SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*Sqrt[3]*a^2*SA + 6*SB*SC : :

X(42170) lies on these lines: {3, 5318}, {4, 6411}, {6, 42167}, {15, 34551}, {16, 7583}, {397, 6396}, {398, 6221}, {590, 11481}, {1151, 5334}, {2042, 23303}, {5321, 6200}, {5335, 6412}, {5339, 6433}, {6409, 35732}, {10654, 35735}, {11542, 35731}, {16772, 35813}, {16960, 35739}, {16967, 35738}, {19106, 34552}, {33518, 35748}

X(42170) = {X(3),X(5318)}-harmonic conjugate of X(42169)
X(42170) = {X(4),X(6411)}-harmonic conjugate of X(42168)

X(42171) = GIBERT(-1,1,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA - 6*SB*SC : :

X(42171) lies on these lines: {3, 5321}, {4, 5420}, {6, 14813}, {15, 486}, {16, 2044}, {18, 5418}, {372, 5335}, {376, 36470}, {397, 6395}, {398, 6221}, {485, 11489}, {615, 18582}, {2041, 16809}, {2043, 19107}, {2045, 10645}, {2046, 16967}, {3312, 35740}, {3364, 16961}, {3390, 16966}, {5318, 6398}, {5334, 6200}, {5339, 6411}, {5340, 6438}, {5366, 6477}, {6412, 14814}, {8252, 11480}, {10654, 41945}, {11485, 18510}, {11543, 34551}, {16645, 36439}, {22644, 35739}, {31454, 40694}, {36437, 36967}, {36455, 37835}

X(42171) = {X(3),X(5321)}-harmonic conjugate of X(42172)
X(42171) = {X(4),X(6396)}-harmonic conjugate of X(42173)
X(42171) = {X(6),X(14813)}-harmonic conjugate of X(42174)

X(42172) = GIBERT(1,-1,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA - 6*SB*SC : :

X(42172) lies on these lines: {3, 5321}, {4, 5418}, {6, 14814}, {5, 42188}, {15, 485}, {16, 2043}, {18, 5420}, {371, 5335}, {376, 36452}, {397, 6199}, {398, 6398}, {486, 11489}, {590, 18582}, {2042, 16809}, {2044, 19107}, {2045, 16967}, {2046, 10645}, {3365, 16961}, {3389, 16966}, {5318, 6221}, {5334, 6396}, {5339, 6412}, {5340, 6437}, {5350, 9690}, {5366, 6476}, {6411, 14813}, {6449, 35740}, {8253, 11480}, {10654, 41946}, {11485, 18512}, {11543, 34552}, {16645, 36457}, {31487, 40693}, {36437, 37835}, {36455, 36967}

X(42172) = {X(3),X(5321)}-harmonic conjugate of X(42171)
X(42172) = {X(4),X(6200)}-harmonic conjugate of X(42174)
X(42172) = {X(6),X(14814)}-harmonic conjugate of X(42173)

X(42173) = GIBERT(1,1,-SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA + 6*SB*SC : :

X(42173) lies on these lines: {3, 5318}, {4, 5420}, {5, 42189}, {6, 14814}, {15, 2043}, {16, 486}, {17, 5418}, {372, 5334}, {376, 36453}, {397, 6221}, {398, 6395}, {485, 11488}, {615, 18581}, {2042, 16808}, {2044, 19106}, {2045, 16966}, {2046, 10646}, {3365, 16967}, {3389, 16960}, {5321, 6398}, {5335, 6200}, {5339, 6438}, {5340, 6411}, {5365, 6477}, {6412, 14813}, {8252, 11481}, {10653, 41945}, {11486, 18510}, {11542, 34552}, {16644, 36457}, {31454, 40693}, {36437, 37832}, {36455, 36968}

X(42173) = {X(3),X(5318)}-harmonic conjugate of X(42174)
X(42173) = {X(4),X(6396)}-harmonic conjugate of X(42171)
X(42173) = {X(6),X(14814)}-harmonic conjugate of X(42172)

X(42174) = GIBERT(1,1,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA + 6*SB*SC : :

X(42174) lies on these lines: {3, 5318}, {4, 5418}, {5, 42187}, {6, 14813}, {15, 2044}, {16, 485}, {17, 5420}, {371, 5334}, {376, 36469}, {397, 6398}, {398, 6199}, {486, 11488}, {590, 18581}, {623, 35741}, {2041, 16808}, {2043, 19106}, {2045, 10646}, {2046, 16966}, {3364, 16967}, {3390, 16960}, {5321, 6221}, {5335, 6396}, {5339, 6437}, {5340, 6412}, {5349, 9690}, {5365, 6476}, {6411, 14814}, {8253, 11481}, {10653, 41946}, {11486, 18512}, {11542, 34551}, {16644, 36439}, {31487, 40694}, {36437, 36968}, {36455, 37832}

X(42174) = {X(3),X(5318)}-harmonic conjugate of X(42173)
X(42174) = {X(4),X(6200)}-harmonic conjugate of X(42172)
X(42174) = {X(6),X(14813)}-harmonic conjugate of X(42171)

X(42175) = GIBERT(-1,2,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA - 12*SB*SC : :

X(42175) lies on these lines: {3, 16809}, {4, 5420}, {5, 42194}, {6, 42178}, {14, 13846}, {15, 6565}, {16, 35820}, {18, 23251}, {371, 5334}, {372, 5318}, {382, 3392}, {2042, 35821}, {2044, 6564}, {3367, 11480}, {5321, 6200}, {5339, 6221}, {5340, 6395}, {6419, 35740}, {22880, 31706}, {35823, 36454}, {36448, 41107}

X(42175) = {X(3),X(42093)}-harmonic conjugate of X(42176)
X(42175) = {X(4),X(6396)}-harmonic conjugate of X(42177)
X(42175) = {X(6),X(42279)}-harmonic conjugate of X(42178)

X(42176) = GIBERT(1,-2,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA - 12*SB*SC : :

X(42176) lies on these lines: {3, 16809}, {4, 5418}, {14, 13847}, {5, 42192}, {15, 6564}, {16, 35821}, {18, 23261}, {371, 5318}, {372, 5334}, {382, 3391}, {2041, 35820}, {2043, 6565}, {3366, 11480}, {5321, 6396}, {5339, 6398}, {5340, 6199}, {22881, 31706}, {35822, 36436}, {36466, 41107}

X(42176) = {X(3),X(42093)}-harmonic conjugate of X(42175)
X(42176) = {X(4),X(6200)}-harmonic conjugate of X(42178)
X(42176) = {X(6),X(42278)}-harmonic conjugate of X(42177)

X(42177) = GIBERT(1,2,-SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA + 12*SB*SC : :

X(42177) lies on these lines: {3, 16808}, {4, 5420}, {5, 42193}, {13, 13846}, {15, 35820}, {16, 6565}, {17, 23251}, {371, 5335}, {372, 5321}, {382, 3367}, {2041, 35821}, {2043, 6564}, {3392, 11481}, {5318, 6200}, {5339, 6395}, {5340, 6221}, {22925, 31705}, {35823, 36436}, {36466, 41108}

X(42177) = {X(3),X(42094)}-harmonic conjugate of X(42178)
X(42177) = {X(4),X(6396)}-harmonic conjugate of X(42175)
X(42177) = {X(6),X(42278)}-harmonic conjugate of X(42176)

X(42178) = GIBERT(1,2,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA + 12*SB*SC : :

X(42178) lies on these lines: {3, 16808}, {4, 5418}, {5, 42191}, {6, 42175}, {13, 13847}, {15, 35821}, {16, 6564}, {17, 23261}, {371, 5321}, {372, 5335}, {382, 3366}, {2042, 35820}, {2044, 6565}, {3391, 11481}, {5318, 6396}, {5339, 6199}, {5340, 6398}, {19107, 35731}, {22926, 31705}, {35822, 36454}, {36448, 41108}

X(42178) = {X(3),X(42094)}-harmonic conjugate of X(42177)
X(42178) = {X(4),X(6200)}-harmonic conjugate of X(42176)
X(42178) = {X(6),X(42279)}-harmonic conjugate of X(42175)

X(42179) = GIBERT(-1,2*SQRT(3),1) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA - 12*Sqrt[3]*SB*SC : :

X(42179) lies on these lines: {3, 42180}, ,{4, 16}, {6, 42182}, {13, 1328}, {61, 23259}, {382, 3392}, {546, 3364}, {2043, 33416}, {2044, 16966}, {3365, 3627}, {3366, 35821}, {3367, 16808}, {3389, 22615}, {3391, 3843}, {5318, 7584}, {10645, 35732}, {11485, 23261}, {18586, 19107}, {22597, 22855}, {36454, 36967}

X(42179) = {X(4),X(16)}-harmonic conjugate of X(42181)

X(42180) = GIBERT(1,-2*SQRT(3),1) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 12*Sqrt[3]*SB*SC : :

X(42180) lies on these lines: {3, 42179}, {4, 15}, {6, 42181}, {14, 1328}, {62, 23259}, {382, 3367}, {546, 3389}, {2043, 16967}, {2044, 33417}, {3146, 35739}, {3364, 22615}, {3366, 3843}, {3390, 3627}, {3391, 35821}, {3392, 16809}, {5321, 7584}, {11486, 23261}, {18587, 19106}, {22599, 22901}, {35255, 35731}, {36436, 36968}

X(42180) = {X(4),X(15)}-harmonic conjugate of X(42182)

X(42181) = GIBERT(1,2*SQRT(3),-1) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 12*Sqrt[3]*SB*SC : :

X(42181) lies on these lines: {3, 42182},, {4, 16}, {6, 42180}, {13, 1327}, {61, 23249}, {382, 3391}, {546, 3365}, {2043, 16966}, {2044, 33416}, {3364, 3627}, {3366, 16808}, {3367, 35820}, {3390, 22644}, {3392, 3843}, {5318, 7583}, {11485, 23251}, {18587, 19107}, {22626, 22855}, {36436, 36967}

X(42181) = {X(4),X(16)}-harmonic conjugate of X(42179)

X(42182) = GIBERT(1,2*SQRT(3),1) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 12*Sqrt[3]*SB*SC : :

X(42182) lies on these lines: {3, 42181}, {4, 15}, {6, 42179}, {14, 1327}, {62, 23249}, {382, 3366}, {546, 3390}, {2043, 33417}, {2044, 16967}, {3091, 35739}, {3365, 22644}, {3367, 3843}, {3389, 3627}, {3391, 16809}, {3392, 35820}, {5321, 7583}, {10646, 35732}, {11486, 23251}, {18586, 19106}, {22628, 22901}, {36454, 36968}

X(42182) = {X(4),X(15)}-harmonic conjugate of X(42180)

X(42183) = GIBERT(-1,3,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA - 18*SB*SC : :

X(42183) lies on these lines: {3, 42101}, {4, 5420}, {6, 42186}, {16, 22644}, {1327, 33606}, {2042, 19107}, {2044, 16809}, {5318, 6395}, {5321, 6221}, {6199, 35740}, {6200, 35732}, {6411, 14813}, {6560, 36969}, {6561, 36454}, {32787, 36448}

X(42183) = {X(3),X(42101)}-harmonic conjugate of X(42184)
X(42183) = {X(4),X(6396)}-harmonic conjugate of X(42185)
X(42183) = {X(6),X(42281)}-harmonic conjugate of X(42186)

X(42184) = GIBERT(1,-3,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA - 18*SB*SC : :

X(42184) lies on these lines: {3, 42101}, {4, 5418}, {6, 42185}, {16, 22615}, {1328, 33606}, {2041, 19107}, {2043, 16809}, {5318, 6199}, {5321, 6398}, {6412, 14814}, {6445, 35740}, {6560, 36436}, {6561, 36969}, {32788, 36466}

X(42184) = {X(3),X(42101)}-harmonic conjugate of X(42183)
X(42184) = {X(4),X(6200)}-harmonic conjugate of X(42186)
X(42184) = {X(6),X(42280)}-harmonic conjugate of X(42185)

X(42185) = GIBERT(1,3,-SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA + 18*SB*SC : :

X(42185) lies on these lines: {3, 42102}, {4, 5420}, {6, 42184}, {15, 22644}, {1327, 33607}, {2041, 19106}, {2043, 16808}, {5318, 6221}, {5321, 6395}, {6411, 14814}, {6451, 35740}, {6560, 36970}, {6561, 36436}, {32787, 36466}

X(42185) = {X(3),X(42102)}-harmonic conjugate of X(42186)
X(42185) = {X(4),X(6396)}-harmonic conjugate of X(42183)
X(42185) = {X(6),X(42280)}-harmonic conjugate of X(42184)

X(42186) = GIBERT(1,3,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA + 18*SB*SC : :

X(42186) lies on these lines: {3, 42102}, {4, 5418}, {6, 42183}, {15, 22615}, {1328, 33607}, {2042, 19106}, {2044, 16808}, {5318, 6398}, {5321, 6199}, {6221, 35740}, {6396, 35732}, {6412, 14813}, {6560, 36454}, {6561, 36970}, {32788, 36448}

X(42186) = {X(3),X(42102)}-harmonic conjugate of X(42185)
X(42186) = {X(4),X(6200)}-harmonic conjugate of X(42184)
X(42186) = {X(6),X(42281)}-harmonic conjugate of X(42183)

X(42187) = GIBERT(-1,SQRT(3),1) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42187) lies on these lines: {3, 22615}, {4, 16}, {5, 42174}, {6, 42183}, {13, 14226}, {14, 13703}, {15, 23259}, {20, 3392}, {61, 23273}, {62, 23249}, {486, 5318}, {2041, 35787}, {2042, 35821}, {2044, 6565}, {3071, 11485}, {3091, 3364}, {3146, 3365}, {3366, 6459}, {3391, 3832}, {5321, 6561}, {5335, 7586}, {10653, 36467}, {10654, 36454}, {11480, 14813}, {32488, 33359}

X(42187) = {X(3),X(42283)}-harmonic conjugate of X(42188)
X(42187) = {X(4),X(16)}-harmonic conjugate of X(42189)
X(42187) = {X(6),X(42281)}-harmonic conjugate of X(42190)

X(42188) = GIBERT(1,-SQRT(3),1) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42188) lies on these lines: {3, 22615}, {4, 15}, {5, 42172}, {6, 42184}, {13, 13705}, {14, 14226}, {16, 23259}, {20, 3367}, {61, 23249}, {62, 23273}, {486, 5321}, {2041, 35821}, {2042, 35787}, {2043, 6565}, {3071, 11486}, {3091, 3389}, {3146, 3390}, {3366, 3832}, {3391, 6459}, {3529, 35739}, {5318, 6561}, {5334, 7586}, {10645, 35732}, {10653, 36436}, {10654, 36449}, {11481, 14814}, {32488, 33361}

X(42188) = {X(3),X(42283)}-harmonic conjugate of X(42187)
X(42188) = {X(4),X(15)}-harmonic conjugate of X(42190)
X(42188) = {X(6),X(42280)}-harmonic conjugate of X(42189)

X(42189) = GIBERT(1,SQRT(3),-1) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 6*Sqrt[3]*SB*SC : :

X(42189) lies on these lines: {3, 22644}, {4, 16}, {5, 42173}, {6, 42184}, {13, 14241}, {14, 13823}, {15, 23249}, {20, 3391}, {61, 23267}, {62, 23259}, {485, 5318}, {2041, 35820}, {2042, 35786}, {2043, 6564}, {3070, 11485}, {3091, 3365}, {3146, 3364}, {3367, 6460}, {3389, 31412}, {3392, 3832}, {5321, 6560}, {5335, 7585}, {10646, 35732}, {10653, 36450}, {10654, 36436}, {11480, 14814}, {31414, 40693}, {32489, 33360}

X(42189) = {X(3),X(42284)}-harmonic conjugate of X(42190)
X(42189) = {X(4),X(16)}-harmonic conjugate of X(42187)
X(42189) = {X(6),X(42280)}-harmonic conjugate of X(42188)

X(42190) = GIBERT(1,SQRT(3),1) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 6*Sqrt[3]*SB*SC : :

X(42190) lies on these lines: {3, 22644}, {4, 15}, {5, 42171}, {6, 42183}, {13, 13825}, {14, 14241}, {16, 23249}, {20, 3366}, {61, 23259}, {62, 23267}, {485, 5321}, {2041, 35786}, {2042, 35820}, {2044, 6564}, {3070, 11486}, {3090, 35739}, {3091, 3390}, {3146, 3389}, {3364, 31412}, {3367, 3832}, {3392, 6460}, {5318, 6560}, {5334, 7585}, {10653, 36454}, {10654, 36468}, {11481, 14813}, {31414, 40694}, {32489, 33358}

X(42190) = {X(3),X(42284)}-harmonic conjugate of X(42189)
X(42190) = {X(4),X(15)}-harmonic conjugate of X(42188)
X(42190) = {X(6),X(42281)}-harmonic conjugate of X(42187)

X(42191) = GIBERT(-1,SQRT(3),2) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42191) lies on these lines: {3, 22615}, {4, 11481}, {5, 42178}, {6, 35732}, {15, 3071}, {395, 36454}, {590, 18581}, {615, 2044}, {1328, 35735}, {2042, 5321}, {3070, 11486}, {3366, 31454}, {6200, 35738}, {6565, 34551}, {8960, 11543}, {11480, 23259}, {15765, 16967}, {18585, 19106}, {22236, 23273}, {22238, 23249}, {36439, 37832}

X(42191) = {X(3),X(42283)}-harmonic conjugate of X(42192)
X(42191) = {X(4),X(11481)}-harmonic conjugate of X(42193)
X(42191) = {X(6),X(35732)}-harmonic conjugate of X(42194)

X(42192) = GIBERT(1,-SQRT(3),2) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42192) lies on these lines: {3, 22615}, {4, 11480}, {5, 42176}, {16, 3071}, {396, 36436}, {590, 18582}, {615, 2043}, {2041, 5318}, {3070, 11485}, {3391, 31454}, {6565, 34552}, {8960, 11542}, {11481, 23259}, {15765, 19107}, {16966, 18585}, {22236, 23249}, {22238, 23273}, {36457, 37835}

X(42192) = {X(3),X(42283)}-harmonic conjugate of X(42191)
X(42192) = {X(4),X(11480)}-harmonic conjugate of X(42194)
X(42192) = {X(6),X(42282)}-harmonic conjugate of X(42193)

X(42193) = GIBERT(1,SQRT(3),-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*a^2*SA + 6*Sqrt[3]*SB*SC : :

X(42193) lies on these lines: {3, 22644}, {4, 11481}, {5, 42177}, {15, 3070}, {395, 36436}, {590, 2043}, {615, 18581}, {2041, 5321}, {3071, 11486}, {6564, 34552}, {11480, 23249}, {15765, 19106}, {16967, 18585}, {22236, 23267}, {22238, 23259}, {32785, 35740}, {36457, 37832}

X(42193) = {X(3),X(42284)}-harmonic conjugate of X(42194)
X(42193) = {X(4),X(11481)}-harmonic conjugate of X(42191)
X(42193) = {X(6),X(42282)}-harmonic conjugate of X(42192)

X(42194) = GIBERT(1,SQRT(3),2) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*a^2*SA + 6*Sqrt[3]*SB*SC : :

X(42194) lies on these lines: {3, 22644}, {4, 11480}, {5, 42175}, {6, 35732}, {16, 3070}, {396, 36454}, {590, 2044}, {615, 18582}, {1327, 35735}, {2042, 5318}, {3071, 11485}, {6396, 35738}, {6564, 34551}, {11481, 23249}, {15765, 16966}, {18585, 19107}, {22236, 23259}, {22238, 23267}, {36439, 37835}

X(42194) = {X(3),X(42284)}-harmonic conjugate of X(42193)
X(42194) = {X(4),X(11480)}-harmonic conjugate of X(42192)
X(42194) = {X(6),X(35732)}-harmonic conjugate of X(42191)

X(42195) = GIBERT(-1,SQRT(3),3) POINT

Barycentrics    Sqrt[3]*a^2*S - 9*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42195) lies on these lines: {3, 22615}, {4, 10187}, {6, 14813}, {15, 23273}, {16, 23249}, {486, 16772}, {1588, 34754}, {2042, 6200}, {2044, 6396}, {3364, 32785}, {3366, 8972}, {3390, 13941}, {3392, 18582}, {5318, 5420}, {6411, 15765}, {8252, 36439}, {10645, 23259}, {13785, 35735}, {18586, 23303}, {18762, 34551}, {23267, 34755}, {35814, 40693}

X(42196) = GIBERT(1,-SQRT(3),3) POINT

Barycentrics    Sqrt[3]*a^2*S + 9*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42196) lies on these lines: {3, 22615}, {4, 10188}, {6, 14814}, {15, 23249}, {16, 23273}, {486, 16773}, {1588, 34755}, {2041, 6200}, {2043, 6396}, {3365, 13941}, {3367, 18581}, {3389, 32785}, {3391, 8972}, {5321, 5420}, {6411, 18585}, {8252, 36457}, {10646, 23259}, {18587, 23302}, {18762, 34552}, {23267, 34754}, {35814, 40694}

X(42197) = GIBERT(1,SQRT(3),-3) POINT

Barycentrics    Sqrt[3]*a^2*S - 9*a^2*SA + 6*Sqrt[3]*SB*SC : :

X(42197) lies on these lines: {3, 22644}, {4, 10187}, {6, 14814}, {15, 23267}, {16, 23259}, {485, 16772}, {1587, 34754}, {2041, 6396}, {2043, 6200}, {3365, 32786}, {3367, 13941}, {3389, 8972}, {3391, 18582}, {5318, 5418}, {6412, 18585}, {8253, 36457}, {10645, 23249}, {18538, 34552}, {18587, 23303}, {23273, 34755}, {35815, 40693}

X(42198) = GIBERT(1,SQRT(3),3) POINT

Barycentrics    Sqrt[3]*a^2*S + 9*a^2*SA + 6*Sqrt[3]*SB*SC : :

X(42198) lies on these lines: {3, 22644}, {4, 10188}, {6, 14813}, {15, 23259}, {16, 23267}, {485, 16773}, {1587, 34755}, {2042, 6396}, {2044, 6200}, {3364, 8972}, {3366, 18581}, {3390, 32786}, {3392, 13941}, {5321, 5418}, {6412, 15765}, {8253, 36439}, {10646, 23249}, {13665, 35735}, {18538, 34551}, {18586, 23302}, {23273, 34754}, {35815, 40694}

X(42199) = GIBERT(-2,1,SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA - 6*SB*SC : :

X(42199) lies on these lines: {3, 5334}, {4, 3591}, {6, 14813}, {15, 615}, {18, 3070}, {372, 5318}, {395, 35822}, {398, 6200}, {2042, 7584}, {2043, 35256}, {2044, 11486}, {2046, 18538}, {3069, 11542}, {3312, 35732}, {3390, 16967}, {3392, 3412}, {5321, 6396}, {5335, 6395}, {5339, 6412}, {6420, 35740}, {6560, 18581}, {9680, 40694}, {10654, 15764}, {13993, 35738}

X(42200) = GIBERT(2,-1,SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA - 6*SB*SC : :

X(42200) lies on these lines: {3, 5334}, {4, 3590}, {6, 14814}, {14, 15764}, {15, 590}, {18, 3071}, {371, 5318}, {395, 35823}, {398, 6396}, {2041, 7583}, {2043, 11486}, {2044, 35255}, {2045, 18762}, {3068, 11542}, {3389, 16967}, {3391, 3412}, {5321, 6200}, {5335, 6199}, {5339, 6411}, {6449, 35732}, {6453, 35740}, {6561, 15765}, {9541, 18586}

X(42201) = GIBERT(2,1,-SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA + 6*SB*SC : :

X(42201) lies on these lines: {3, 5335}, {4, 3591}, {6, 14814}, {13, 15764}, {16, 615}, {17, 3070}, {372, 5321}, {396, 35822}, {397, 6200}, {2041, 7584}, {2043, 11485}, {2044, 35256}, {2045, 18538}, {3069, 11543}, {3365, 16966}, {3367, 3411}, {5318, 6396}, {5334, 6395}, {5340, 6412}, {6450, 35732}, {6560, 15765}, {9680, 40693}

X(42202) = GIBERT(2,1,SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA + 6*SB*SC : :

X(42202) lies on these lines: {3, 5335}, {4, 3590}, {6, 14813}, {16, 590}, {17, 3071}, {371, 5321}, {396, 35823}, {397, 6396}, {2042, 7583}, {2043, 35255}, {2044, 11485}, {2046, 18762}, {3068, 11543}, {3311, 35732}, {3364, 16966}, {3366, 3411}, {5318, 6200}, {5334, 6199}, {5340, 6411}, {6561, 18582}, {9541, 18587}, {10653, 15764}, {13925, 35738}

X(42203) = GIBERT(-2,2,SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA - 12*SB*SC : :

X(42203) lies on these lines: {3, 5321}, {4, 3591}, {398, 6199}, {2044, 11543}, {3311, 35732}, {3312, 5335}, {5318, 6395}, {5334, 6221}, {5339, 6200}, {6417, 35740}, {6452, 14814}, {6565, 19107}, {11485, 13785}, {16809, 35820}

X(42204) = GIBERT(2,-2,SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA - 12*SB*SC : :

X(42204) lies on these lines: {3, 5321}, {4, 3590}, {398, 6395}, {2043, 11543}, {3311, 5335}, {5318, 6199}, {5334, 6398}, {5339, 6396}, {6407, 35740}, {6451, 14813}, {6455, 35732}, {6564, 19107}, {11485, 13665}, {16809, 35821}

X(42205) = GIBERT(2,2,-SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA + 12*SB*SC : :

X(42205) lies on these lines: {3, 5318}, {4, 3591}, {397, 6199}, {2043, 11542}, {3312, 5334}, {5321, 6395}, {5335, 6221}, {5340, 6200}, {6452, 14813}, {6456, 35732}, {6565, 19106}, {11486, 13785}, {16808, 35820}

X(42206) = GIBERT(2,2,SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA + 12*SB*SC : :

X(42206) lies on these lines: {3, 5318}, {4, 3590}, {397, 6395}, {2044, 11542}, {3311, 5334}, {3312, 35732}, {5321, 6199}, {5335, 6398}, {5340, 6396}, {6451, 14814}, {6564, 19106}, {11486, 13665}, {16808, 35821}, {31412, 35738}

X(42207) = GIBERT(-2,3,SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA - 18*SB*SC : :

X(42207) lies on these lines: {4, 3591}, {396, 6565}, {397, 6436}, {1327, 41120}, {2044, 18538}, {3392, 19107}, {3830, 36465}, {5321, 6200}, {5334, 6199}, {5339, 6437}, {5340, 6442}, {5343, 9690}, {6221, 35732}, {6412, 14814}, {8253, 36439}, {11543, 23249}, {15764, 36970}, {16809, 18585}, {18586, 23259}, {19054, 36448}

X(42208) = GIBERT(2,-3,SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA - 18*SB*SC : :

X(42208) lies on these lines: {4, 3590}, {396, 6564}, {397, 6435}, {1328, 41120}, {2043, 18762}, {3391, 19107}, {3830, 36446}, {5321, 6396}, {5334, 6395}, {5339, 6438}, {5340, 6441}, {6411, 14813}, {6451, 35732}, {6480, 35740}, {8252, 36457}, {11543, 23259}, {15765, 16809}, {18587, 23249}, {19053, 36466}

X(42209) = GIBERT(2,3,-SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*Sqrt[3]*a^2*SA + 18*SB*SC : :

X(42209) lies on these lines: {4, 3591}, {395, 6565}, {398, 6436}, {1327, 41119}, {2043, 18538}, {3367, 19106}, {3830, 36447}, {5318, 6200}, {5335, 6199}, {5339, 6442}, {5340, 6437}, {5344, 9690}, {6412, 14813}, {6452, 35732}, {8253, 36457}, {11542, 23249}, {15765, 16808}, {18587, 23259}, {19054, 36466}

X(42210) = GIBERT(2,3,SQRT(3)) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*Sqrt[3]*a^2*SA + 18*SB*SC : :

X(42210) lies on these lines: {4, 3590}, {395, 6564}, {398, 6435}, {1328, 41119}, {2044, 18762}, {3366, 19106}, {3830, 36464}, {5318, 6396}, {5335, 6395}, {5339, 6441}, {5340, 6438}, {6200, 35740}, {6398, 35732}, {6411, 14814}, {8252, 36439}, {11542, 23259}, {15764, 36969}, {16808, 18585}, {18586, 23249}, {19053, 36448}

X(42211) = GIBERT(-2,SQRT(3),1) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42211) lies on these lines: {3, 18762}, {4, 11409}, {14, 32787}, {15, 3071}, {2044, 11542}, {5318, 6565}, {5321, 35821}, {5334, 18586}, {5335, 7584}, {6561, 15765}, {11481, 14814}, {11485, 23273}, {16242, 36457}, {16644, 36439}, {18539, 37332}

X(42212) = GIBERT(2,-SQRT(3),1) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42212) lies on these lines: {3, 18762}, {4, 11408}, {13, 32787}, {16, 3071}, {1328, 15764}, {2043, 11543}, {5318, 35821}, {5321, 6565}, {5334, 7584}, {5335, 18587}, {6561, 18582}, {11480, 14813}, {11486, 23273}, {16241, 36439}, {16645, 36457}, {18539, 37333}

X(42213) = GIBERT(2,SQRT(3),-1) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*a^2*SA + 6*Sqrt[3]*SB*SC : :

X(42213) lies on these lines: {3, 18538}, {4, 11409}, {14, 32788}, {15, 3070}, {1327, 15764}, {2043, 11542}, {5318, 6564}, {5321, 35820}, {5334, 18587}, {5335, 7583}, {6560, 18581}, {11481, 14813}, {11485, 23267}, {16242, 36439}, {16644, 36457}, {26438, 37332}

X(42214) = GIBERT(2,SQRT(3),1) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*a^2*SA + 6*Sqrt[3]*SB*SC : :

X(42214) lies on these lines: {3, 18538}, {4, 11408}, {13, 32788}, {16, 3070}, {2044, 11543}, {5318, 35820}, {5321, 6564}, {5334, 7583}, {5335, 18586}, {6560, 15765}, {11480, 14814}, {11486, 23267}, {16241, 36457}, {16645, 36439}, {26438, 37333}

X(42215) = GIBERT(2*SQRT(3),-1,1) POINT

Barycentrics    2*a^2*S + a^2*SA - 2*SB*SC : :

X(42215) lies on these lines: {2, 6221}, {3, 1588}, {4, 1131}, {5, 371}, {6, 30}, {10, 31439}, {15, 34551}, {16, 34552}, {20, 3312}, {35, 19027}, {36, 19029}, {74, 19051}, {140, 486}, {141, 32419}, {143, 12239}, {182, 9687}, {186, 13937}, {230, 9675}, {235, 10880}, {265, 19060}, {355, 1702}, {372, 550}, {376, 6398}, {381, 3068}, {382, 1587}, {388, 31474}, {397, 3364}, {398, 3389}, {403, 13884}, {485, 546}, {487, 11314}, {492, 6390}, {495, 2066}, {496, 2067}, {547, 6437}, {548, 1152}, {549, 615}, {576, 12598}, {631, 6449}, {632, 6453}, {639, 7915}, {952, 35775}, {1124, 18990}, {1132, 3090}, {1270, 26619}, {1327, 6441}, {1328, 5066}, {1335, 15171}, {1351, 39876}, {1353, 35841}, {1478, 19038}, {1479, 18996}, {1483, 35642}, {1504, 7745}, {1595, 11473}, {1596, 5412}, {1656, 9540}, {1657, 6418}, {2043, 11486}, {2044, 11485}, {2460, 38230}, {2550, 31485}, {3070, 3627}, {3091, 8976}, {3092, 6756}, {3093, 13488}, {3102, 32448}, {3146, 6427}, {3298, 15172}, {3299, 7354}, {3301, 6284}, {3316, 5068}, {3317, 9543}, {3522, 6450}, {3523, 6455}, {3524, 6451}, {3525, 6519}, {3526, 6407}, {3528, 6456}, {3529, 6428}, {3530, 5420}, {3534, 6395}, {3543, 23267}, {3545, 8972}, {3579, 13936}, {3583, 19030}, {3585, 19028}, {3594, 12103}, {3628, 5418}, {3629, 32421}, {3818, 36723}, {3830, 18512}, {3832, 13886}, {3843, 23263}, {3845, 6564}, {3850, 13925}, {3851, 13903}, {3853, 6431}, {3857, 35815}, {3858, 8960}, {3861, 6470}, {4299, 18995}, {4302, 19037}, {5010, 13958}, {5054, 6445}, {5055, 32785}, {5058, 5254}, {5073, 6500}, {5076, 23253}, {5092, 13972}, {5204, 13962}, {5217, 13963}, {5305, 6424}, {5326, 31500}, {5334, 18586}, {5335, 18587}, {5409, 15235}, {5411, 18533}, {5413, 37458}, {5414, 9660}, {5591, 26289}, {5787, 19068}, {5870, 36711}, {5886, 9583}, {6033, 19109}, {6202, 36712}, {6214, 37343}, {6215, 8396}, {6250, 14239}, {6290, 13650}, {6321, 19056}, {6396, 8703}, {6410, 33923}, {6411, 12100}, {6412, 34200}, {6420, 15704}, {6429, 9680}, {6430, 41981}, {6433, 11812}, {6435, 33699}, {6438, 15690}, {6439, 11540}, {6446, 15688}, {6452, 10304}, {6468, 10124}, {6476, 41951}, {6480, 11539}, {6496, 15717}, {6497, 21735}, {6501, 17800}, {6502, 9647}, {6699, 13979}, {6823, 10897}, {7280, 18966}, {7388, 7879}, {7485, 9695}, {7525, 9683}, {7687, 13915}, {7715, 35765}, {7728, 19111}, {7741, 18965}, {7951, 13901}, {7968, 34773}, {7969, 22791}, {8276, 13861}, {8725, 19091}, {8983, 9955}, {8991, 20299}, {8994, 20304}, {9582, 13947}, {9585, 34595}, {9602, 37637}, {9616, 26446}, {9646, 10592}, {9655, 31408}, {9661, 10593}, {9676, 40111}, {9682, 12106}, {9690, 15694}, {9821, 19089}, {9956, 13912}, {10272, 10819}, {10283, 35763}, {10386, 35809}, {10733, 19052}, {10738, 19082}, {10742, 19113}, {10749, 19094}, {10895, 13905}, {10896, 13904}, {11292, 12221}, {11313, 12322}, {11542, 18585}, {11543, 15765}, {12121, 19110}, {12163, 19061}, {12240, 13630}, {12257, 36655}, {12293, 19062}, {12515, 19077}, {12699, 18991}, {12702, 19065}, {12918, 19115}, {12971, 36966}, {13624, 13971}, {13748, 36658}, {13759, 26615}, {13763, 33878}, {13881, 22617}, {13883, 18480}, {13902, 18493}, {13910, 19130}, {13911, 18357}, {13975, 31663}, {14216, 19088}, {14830, 19057}, {14880, 18994}, {15484, 31403}, {15686, 41946}, {15687, 35822}, {15699, 32789}, {15760, 18457}, {15800, 19096}, {16232, 37730}, {17578, 23269}, {18481, 18992}, {18525, 19066}, {18534, 19006}, {18581, 34559}, {18582, 34562}, {18583, 19145}, {19004, 41869}, {19055, 38741}, {19059, 20127}, {19081, 38753}, {19087, 20427}, {19108, 38730}, {21737, 26348}, {26288, 26340}, {26441, 36714}, {28174, 35774}, {31419, 31453}, {31859, 35949}, {32810, 32896}, {35771, 35820}, {35777, 37440}, {35788, 38138}, {35789, 38112}, {35814, 41964}, {36490, 36553}, {36492, 36551}, {36512, 36585}, {41949, 41969}, {41953, 41963}

X(42216) = GIBERT(2*SQRT(3),1,-1) POINT

Barycentrics    2*a^2*S - a^2*SA + 2*SB*SC : :

X(42216) lies on these lines: {2, 6398}, {3, 1587}, {4, 1132}, {5, 372}, {6, 30}, {15, 34552}, {16, 34551}, {20, 3311}, {35, 19028}, {36, 19030}, {74, 19052}, {140, 485}, {141, 32421}, {143, 12240}, {182, 13030}, {186, 13884}, {235, 10881}, {265, 19059}, {355, 1703}, {371, 550}, {376, 6221}, {381, 3069}, {382, 1588}, {397, 3365}, {398, 3390}, {403, 13937}, {486, 546}, {488, 11313}, {491, 6390}, {495, 5414}, {496, 6502}, {547, 6438}, {548, 1151}, {549, 590}, {576, 12597}, {631, 6450}, {632, 6454}, {640, 7915}, {952, 35774}, {1124, 15171}, {1131, 3090}, {1160, 21737}, {1271, 26620}, {1327, 5066}, {1328, 6442}, {1335, 18990}, {1351, 39875}, {1353, 35840}, {1478, 19037}, {1479, 18995}, {1483, 35641}, {1505, 7745}, {1595, 11474}, {1596, 5413}, {1656, 13935}, {1657, 6417}, {2043, 11485}, {2044, 11486}, {2362, 37730}, {2459, 38230}, {3071, 3627}, {3091, 13951}, {3092, 13488}, {3093, 6756}, {3103, 32448}, {3146, 6428}, {3295, 31408}, {3297, 15172}, {3299, 6284}, {3301, 7354}, {3316, 10303}, {3317, 5068}, {3522, 6449}, {3523, 6456}, {3524, 6452}, {3525, 6522}, {3526, 6408}, {3528, 6455}, {3529, 6427}, {3530, 5418}, {3534, 6199}, {3543, 23273}, {3545, 13941}, {3579, 13883}, {3583, 19029}, {3585, 19027}, {3592, 12103}, {3628, 5420}, {3629, 32419}, {3818, 36726}, {3830, 18510}, {3832, 13939}, {3843, 23253}, {3845, 6565}, {3850, 13993}, {3851, 13961}, {3853, 6432}, {3857, 35814}, {3858, 35786}, {3861, 6471}, {4294, 31474}, {4299, 18996}, {4302, 19038}, {5010, 13901}, {5013, 31411}, {5024, 31403}, {5054, 6446}, {5055, 32786}, {5062, 5254}, {5073, 6501}, {5076, 23263}, {5092, 13910}, {5204, 13904}, {5217, 13905}, {5305, 6423}, {5334, 18587}, {5335, 18586}, {5408, 15236}, {5410, 18533}, {5412, 37458}, {5590, 26288}, {5787, 19067}, {5871, 36712}, {6033, 19108}, {6200, 8703}, {6201, 36711}, {6214, 8416}, {6215, 37342}, {6251, 14235}, {6289, 13771}, {6321, 19055}, {6409, 33923}, {6411, 34200}, {6412, 12100}, {6419, 15704}, {6429, 41981}, {6430, 16239}, {6434, 11812}, {6436, 33699}, {6437, 15690}, {6440, 11540}, {6445, 15688}, {6451, 10304}, {6469, 10124}, {6477, 41952}, {6481, 11539}, {6496, 21735}, {6497, 15717}, {6500, 17800}, {6699, 13915}, {6823, 10898}, {7280, 18965}, {7389, 7879}, {7687, 13979}, {7715, 35764}, {7728, 19110}, {7741, 18966}, {7951, 13958}, {7968, 22791}, {7969, 34773}, {8277, 13861}, {8725, 19092}, {8960, 15712}, {8982, 36709}, {8983, 13624}, {9690, 15695}, {9708, 31413}, {9821, 19090}, {9955, 13971}, {9956, 13975}, {10272, 10820}, {10283, 35762}, {10386, 35808}, {10733, 19051}, {10738, 19081}, {10742, 19112}, {10749, 19093}, {10895, 13963}, {10896, 13962}, {11291, 12222}, {11314, 12323}, {11542, 15765}, {11543, 18585}, {12121, 19111}, {12163, 19062}, {12239, 13630}, {12256, 36656}, {12293, 19061}, {12515, 19078}, {12699, 18992}, {12702, 19066}, {12918, 19114}, {12965, 36966}, {13639, 26616}, {13644, 33878}, {13749, 36657}, {13881, 22646}, {13912, 31663}, {13936, 18480}, {13959, 18493}, {13969, 20304}, {13972, 19130}, {13973, 18357}, {13980, 20299}, {14216, 19087}, {14830, 19058}, {14880, 18993}, {15686, 41945}, {15687, 35823}, {15699, 32790}, {15760, 18459}, {15800, 19095}, {17578, 23275}, {18481, 18991}, {18525, 19065}, {18534, 19005}, {18581, 34562}, {18582, 34559}, {18583, 19146}, {19003, 41869}, {19056, 38741}, {19060, 20127}, {19082, 38753}, {19088, 20427}, {19109, 38730}, {26289, 26339}, {28174, 35775}, {31439, 31730}, {31859, 35948}, {32811, 32896}, {35770, 35821}, {35776, 37440}, {35788, 38112}, {35789, 38138}, {35815, 41963}, {36490, 36552}, {36491, 36551}, {36512, 36584}, {41950, 41970}, {41954, 41964}

X(42217) = GIBERT(-2, SQRT(3),2) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA - 3*Sqrt[3]*SB*SC : :

X(42217) lies on these lines: {3, 18762}, {4, 16}, {6, 35732}, {13, 36447}, {15, 23273}, {62, 23267}, {486, 11488}, {631, 3392}, {1588, 11485}, {2042, 5334}, {2044, 3069}, {3068, 11543}, {3071, 11480}, {3090, 3364}, {3365, 3529}, {3390, 13939}, {3391, 3855}, {6221, 35738}, {9541, 15765}, {11486, 23249}, {13785, 34551}, {14226, 35737}, {14814, 23263}, {35822, 36454}

X(42218) = GIBERT(2, -SQRT(3),2) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 3*Sqrt[3]*SB*SC : :

X(42218) lies on these lines: {3, 18762}, {4, 15}, {14, 36465}, {16, 23273}, {61, 23267}, {486, 11489}, {631, 3367}, {1588, 11486}, {2041, 5335}, {2043, 3069}, {3068, 11542}, {3071, 11481}, {3090, 3389}, {3365, 13939}, {3366, 3855}, {3390, 3529}, {9541, 18585}, {11480, 35732}, {11485, 23249}, {13785, 34552}, {14813, 23263}, {17538, 35739}, {35822, 36436}

X(42219) = GIBERT(2, SQRT(3),-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 3*Sqrt[3]*SB*SC : :

X(42219) lies on these lines: {3, 18538}, {4, 16}, {13, 36464}, {15, 23267}, {62, 23273}, {485, 11488}, {631, 3391}, {1587, 11485}, {2041, 5334}, {2043, 3068}, {3069, 11543}, {3070, 11480}, {3090, 3365}, {3364, 3529}, {3389, 13886}, {3392, 3855}, {11481, 35732}, {11486, 23259}, {13665, 34552}, {14813, 23253}, {35823, 36436}

X(42220) = GIBERT(2, SQRT(3),2) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 3*Sqrt[3]*SB*SC : :

X(42220) lies on these lines: {3, 18538}, {4, 15}, {6, 35732}, {14, 36446}, {16, 23267}, {61, 23273}, {485, 11489}, {631, 3366}, {1587, 11486}, {2042, 5335}, {2044, 3068}, {3069, 11542}, {3070, 11481}, {3090, 3390}, {3364, 13886}, {3367, 3855}, {3389, 3529}, {3525, 35739}, {6398, 35738}, {11485, 23259}, {13665, 34551}, {14241, 35737}, {14814, 23253}, {35823, 36454}

X(42221) = GIBERT(-2, SQRT(3),3) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 9*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42221) lies on these lines: {3, 18762}, {6, 14813}, {13, 615}, {18, 41963}, {2042, 6221}, {2044, 6398}, {2045, 6451}, {3070, 34755}, {3071, 10645}, {3364, 32789}, {3392, 32790}, {5318, 10577}, {5335, 13966}, {6200, 15765}, {6561, 15764}, {10646, 14814}, {11486, 23267}, {11489, 18538}, {11542, 13941}, {18510, 35735}

X(42222) = GIBERT(2, -SQRT(3),3) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 9*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42222) lies on these lines: {3, 18762}, {6, 14814}, {14, 615}, {17, 41963}, {2041, 6221}, {2043, 6398}, {2046, 6451}, {3070, 34754}, {3071, 10646}, {3367, 32790}, {3389, 32789}, {5321, 10577}, {5334, 13966}, {6200, 18585}, {6565, 15764}, {10645, 14813}, {11485, 23267}, {11488, 18538}, {11543, 13941}

X(42223) = GIBERT(2, SQRT(3),-3) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 9*a^2*SA + 6*Sqrt[3]*SB*SC : :

X(42223) lies on these lines: {3, 18538}, {6, 14814}, {13, 590}, {18, 41964}, {2041, 6398}, {2043, 6221}, {2046, 6452}, {3070, 10645}, {3071, 34755}, {3365, 32790}, {3391, 32789}, {5318, 10576}, {5335, 8981}, {6396, 18585}, {6564, 15764}, {8972, 11542}, {10646, 14813}, {11486, 23273}, {11489, 18587}

X(42224) = GIBERT(2, SQRT(3),3) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 9*a^2*SA + 6*Sqrt[3]*SB*SC : :

X(42224) lies on these lines: {3, 18538}, {6, 14813}, {14, 590}, {17, 41964}, {2042, 6398}, {2044, 6221}, {2045, 6452}, {3070, 10646}, {3071, 34754}, {3366, 32789}, {3390, 32790}, {5321, 10576}, {5334, 8981}, {6396, 15765}, {6560, 15764}, {8972, 11543}, {10645, 14814}, {11485, 23273}, {11488, 18586}, {18512, 35735}

X(42225) = GIBERT(2*SQRT(3),-3,3) POINT

Barycentrics    2*a^2*S + 3*a^2*SA - 6*SB*SC : :

X(42225) lies on these lines: {2, 6451}, {3, 18762}, {4, 3590}, {5, 6200}, {6, 30}, {15, 35730}, {20, 6398}, {140, 6411}, {371, 3627}, {372, 15704}, {376, 6452}, {381, 6445}, {382, 6199}, {485, 3853}, {486, 548}, {495, 9660}, {496, 9647}, {546, 1151}, {549, 6565}, {550, 3071}, {590, 3845}, {615, 8703}, {1131, 31487}, {1132, 3528}, {1152, 12103}, {1328, 8252}, {1587, 5073}, {1588, 1657}, {1656, 23263}, {3068, 3830}, {3069, 3534}, {3090, 6455}, {3091, 6449}, {3146, 3311}, {3312, 3529}, {3316, 9543}, {3317, 21734}, {3522, 13951}, {3525, 6496}, {3543, 13665}, {3592, 22644}, {3593, 26615}, {3628, 6409}, {3630, 32419}, {3843, 9540}, {3850, 5418}, {3856, 9680}, {3858, 10576}, {3861, 6468}, {4316, 19029}, {4324, 19027}, {5059, 7582}, {5066, 8253}, {5076, 31412}, {5420, 33923}, {6410, 13993}, {6425, 12102}, {6427, 11541}, {6447, 13886}, {6450, 17538}, {6456, 13939}, {6460, 17800}, {6476, 35812}, {6481, 15686}, {6484, 41991}, {6564, 15687}, {7585, 15682}, {7586, 11001}, {8991, 18383}, {10295, 13937}, {10577, 15712}, {10645, 34551}, {10646, 34552}, {12101, 13846}, {13847, 15690}, {13883, 33697}, {13901, 18513}, {13935, 15696}, {13979, 37853}, {15681, 18510}, {15684, 18512}, {15685, 19053}, {18514, 18965}, {19117, 35820}, {19710, 32788}, {28178, 35774}, {28186, 35775}, {31439, 31673}, {31454, 35786}, {32787, 33699}, {32805, 33457}, {35404, 35822}, {35610, 37705}, {35777, 37814}

X(42226) = GIBERT(2*SQRT(3),3,-3) POINT

Barycentrics    2*a^2*S - 3*a^2*SA + 6*SB*SC : :

X(42226) lies on these lines: {2, 6452}, {3, 18538}, {4, 3591}, {5, 6396}, {6, 30}, {20, 6221}, {140, 6412}, {371, 15704}, {372, 3627}, {376, 6451}, {381, 6446}, {382, 6395}, {485, 548}, {486, 3853}, {546, 1152}, {549, 6564}, {550, 3070}, {590, 8703}, {615, 3845}, {1131, 3528}, {1151, 12103}, {1327, 8253}, {1587, 1657}, {1588, 5073}, {1656, 23253}, {3068, 3534}, {3069, 3830}, {3090, 6456}, {3091, 6450}, {3146, 3312}, {3311, 3529}, {3316, 21734}, {3522, 8976}, {3525, 6497}, {3543, 13785}, {3594, 22615}, {3595, 26616}, {3628, 6410}, {3630, 32421}, {3843, 13935}, {3850, 5420}, {3858, 10577}, {3861, 6469}, {4316, 19030}, {4324, 19028}, {5059, 7581}, {5066, 8252}, {5418, 33923}, {6409, 13925}, {6426, 12102}, {6428, 11541}, {6448, 13939}, {6449, 17538}, {6455, 13886}, {6459, 17800}, {6477, 35813}, {6480, 15686}, {6485, 41991}, {6565, 15687}, {7585, 11001}, {7586, 15682}, {9540, 15696}, {9541, 15681}, {10295, 13884}, {10576, 15712}, {10645, 34552}, {10646, 34551}, {12101, 13847}, {13846, 15690}, {13903, 31414}, {13915, 37853}, {13936, 33697}, {13958, 18513}, {13980, 18383}, {14269, 17851}, {15684, 18510}, {15685, 19054}, {18514, 18966}, {19116, 35821}, {19710, 32787}, {21737, 35247}, {28178, 35775}, {28186, 35774}, {32788, 33699}, {32806, 33456}, {35404, 35823}, {35611, 37705}, {35776, 37814}

X(42227) = GIBERT(-3,1,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - Sqrt[3]*a^2*SA - 2*SB*SC : :

X(42227) lies on these lines: {3, 395}, {4, 372}, {6, 14813}, {14, 2041}, {15, 2045}, {18, 485}, {61, 2042}, {62, 2044}, {397, 3312}, {462, 10133}, {1152, 5339}, {2043, 16964}, {3070, 18581}, {3365, 6561}, {3366, 10194}, {3594, 5340}, {5318, 6395}, {5321, 6398}, {5334, 6396}, {5343, 6454}, {5418, 11489}, {5868, 36714}, {6418, 35740}, {6420, 35732}, {13847, 15765}, {13951, 18582}, {16268, 36455}, {18586, 32788}, {18587, 41946}, {33353, 33439}, {33367, 33443}, {33369, 33437}, {36437, 41101}, {37342, 37824}, {39679, 41034}

X(42228) = GIBERT(3,-1,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + Sqrt[3]*a^2*SA - 2*SB*SC : :

X(42228) lies on these lines: {3, 395}, {4, 371}, {6, 14814}, {14, 2042}, {15, 2046}, {18, 486}, {61, 2041}, {62, 2043}, {397, 3311}, {462, 10132}, {1151, 5339}, {2044, 16964}, {3071, 18581}, {3364, 6560}, {3367, 10195}, {3592, 5340}, {5318, 6199}, {5321, 6221}, {5334, 6200}, {5343, 6453}, {5349, 35740}, {5420, 11489}, {5868, 36709}, {8976, 18582}, {13846, 18585}, {16268, 36437}, {18586, 41945}, {18587, 32787}, {33350, 33438}, {33366, 33436}, {33368, 33442}, {36455, 41101}, {37343, 37824}, {39648, 41034}

X(42229) = GIBERT(3,1,-SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - Sqrt[3]*a^2*SA + 2*SB*SC : :

X(42229) lies on these lines: {3, 396}, {4, 372}, {6, 14814}, {13, 2042}, {16, 2046}, {17, 485}, {61, 2043}, {62, 2041}, {398, 3312}, {463, 10133}, {1152, 5340}, {2044, 16965}, {3070, 18582}, {3390, 6561}, {3391, 10194}, {3594, 5339}, {5318, 6398}, {5321, 6395}, {5335, 6396}, {5344, 6454}, {5418, 11488}, {5869, 36714}, {6450, 35740}, {13847, 18585}, {13951, 18581}, {16267, 36437}, {18586, 41946}, {18587, 32788}, {33351, 33437}, {33367, 33439}, {33369, 33441}, {35739, 41974}, {36455, 41100}, {37342, 37825}, {39679, 41035}

X(42230) = GIBERT(3,1,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + Sqrt[3]*a^2*SA + 2*SB*SC : :

X(42230) lies on these lines: {3, 396}, {4, 371}, {6, 14813}, {13, 2041}, {16, 2045}, {17, 486}, {18, 35730}, {61, 2044}, {62, 2042}, {398, 3311}, {463, 10132}, {1151, 5340}, {2043, 16965}, {3071, 18582}, {3389, 6560}, {3392, 10195}, {3592, 5339}, {5318, 6221}, {5321, 6199}, {5335, 6200}, {5344, 6453}, {5420, 11488}, {5869, 36709}, {6419, 35732}, {8976, 18581}, {13846, 15765}, {16267, 36455}, {18586, 32787}, {18587, 41945}, {33352, 33436}, {33366, 33440}, {33368, 33438}, {36437, 41100}, {37343, 37825}, {39648, 41035}

X(42231) = GIBERT(-3,2,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - Sqrt[3]*a^2*SA - 4*SB*SC : :

X(42231) lies on these lines: {3, 14}, {4, 372}, {15, 10577}, {61, 18586}, {299, 33436}, {371, 398}, {397, 6420}, {485, 22237}, {491, 33451}, {1152, 3367}, {1656, 3366}, {2042, 10654}, {2044, 35822}, {2046, 10576}, {3070, 11543}, {3312, 5340}, {3364, 8960}, {3365, 35821}, {3389, 41973}, {3390, 6564}, {3392, 13785}, {5321, 6396}, {5334, 6200}, {5349, 6454}, {6301, 33369}, {6419, 35732}, {16809, 23251}, {19107, 23261}, {22114, 22874}, {22598, 33353}, {33445, 39388}, {34551, 36470}, {34559, 36453}, {35740, 35771}, {35813, 36970}, {36455, 41120}

X(42232) = GIBERT(3,-2,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + Sqrt[3]*a^2*SA - 4*SB*SC : :

X(42232) lies on these lines: {3, 14}, {4, 371}, {15, 10576}, {61, 18587}, {299, 33437}, {372, 398}, {397, 6419}, {486, 22237}, {492, 33450}, {1151, 3366}, {1656, 3367}, {2041, 10654}, {2043, 35823}, {2045, 10577}, {3071, 11543}, {3311, 5340}, {3364, 35820}, {3389, 6565}, {3390, 41973}, {3391, 13665}, {5321, 6200}, {5334, 6396}, {5349, 6453}, {5365, 35732}, {6305, 33366}, {16809, 23261}, {19107, 23251}, {22114, 22872}, {22627, 33350}, {33444, 39387}, {34552, 36452}, {34562, 36469}, {35812, 36970}, {36437, 41120}

X(42233) = GIBERT(3,2,-SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - Sqrt[3]*a^2*SA + 4*SB*SC : :

X(42233) lies on these lines: {3, 13}, {4, 372}, {16, 10577}, {62, 18587}, {298, 33438}, {371, 397}, {398, 6420}, {485, 22235}, {491, 33449}, {1152, 3392}, {1656, 3391}, {2041, 10653}, {2043, 35822}, {2045, 10576}, {3070, 11542}, {3312, 5339}, {3364, 41974}, {3365, 6564}, {3367, 13785}, {3389, 8960}, {3390, 35821}, {5318, 6396}, {5335, 6200}, {5350, 6454}, {5366, 35732}, {6300, 33367}, {16808, 23251}, {19106, 23261}, {22113, 22919}, {22600, 33351}, {33447, 39388}, {34552, 36453}, {34562, 36470}, {35813, 36969}, {36437, 41119}

X(42234) = GIBERT(3,2,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + Sqrt[3]*a^2*SA + 4*SB*SC : :

X(42234) lies on these lines: {3, 13}, {4, 371}, {16, 10576}, {62, 18586}, {298, 33439}, {372, 397}, {398, 6419}, {486, 22235}, {492, 33448}, {1151, 3391}, {1656, 3392}, {2042, 10653}, {2044, 35823}, {2046, 10577}, {3071, 11542}, {3311, 5339}, {3364, 6565}, {3365, 41974}, {3366, 13665}, {3389, 35820}, {5318, 6200}, {5335, 6396}, {5350, 6453}, {6304, 33368}, {6420, 35732}, {16808, 23261}, {19106, 23251}, {22113, 22917}, {22629, 33352}, {33446, 39387}, {34551, 36469}, {34559, 36452}, {35812, 36969}, {36455, 41119}

X(42235) = GIBERT(-3,2*SQRT(3),3) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA - 4*Sqrt[3]*SB*SC : :

X(42235) lies on these lines: {2, 33361}, {3, 3367}, {4, 16}, {5, 3364}, {13, 486}, {14, 371}, {15, 3071}, {30, 3365}, {61, 1588}, {62, 3070}, {372, 16965}, {381, 3391}, {615, 35739}, {621, 33353}, {2042, 3389}, {2043, 16242}, {2045, 33416}, {2046, 16966}, {3105, 41018}, {5238, 23275}, {5318, 18762}, {6200, 16967}, {6777, 33431}, {10645, 23259}, {10646, 14814}, {11486, 23251}, {13749, 41021}, {14233, 41034}, {15765, 37835}, {18585, 36969}, {18587, 35787}, {19054, 36454}, {23273, 34754}, {25559, 35759}, {33436, 40901}

X(42236) = GIBERT(3,-2*SQRT(3),3) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 4*Sqrt[3]*SB*SC : :

X(42236) lies on these lines: {2, 33359}, {3, 3367}, {4, 15}, {5, 3389}, {13, 371}, {14, 486}, {16, 3071}, {20, 35739}, {30, 3390}, {61, 3070}, {62, 1588}, {372, 16964}, {381, 3366}, {622, 33351}, {2041, 3364}, {2044, 16241}, {2045, 16967}, {2046, 33417}, {5237, 23275}, {5321, 18762}, {5352, 35732}, {6200, 16966}, {6778, 33431}, {10645, 14813}, {10646, 23259}, {11485, 23251}, {13749, 41020}, {14233, 41035}, {15765, 36970}, {18585, 35731}, {18586, 35787}, {19054, 36436}, {23273, 34755}, {33438, 40900}

X(42237) = GIBERT(3,2*SQRT(3),-3) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 4*Sqrt[3]*SB*SC : :

X(42) lies on these lines: {2, 33358}, {3, 3366}, {4, 16}, {5, 3365}, {13, 485}, {14, 372}, {15, 3070}, {30, 3364}, {61, 1587}, {62, 3071}, {371, 16965}, {381, 3392}, {621, 33350}, {2041, 3390}, {2044, 16242}, {2045, 16966}, {2046, 33416}, {5238, 23269}, {5318, 18538}, {5340, 8960}, {5351, 35732}, {6396, 16967}, {6777, 33430}, {10645, 23249}, {10646, 14813}, {11486, 23261}, {13748, 41021}, {14230, 41034}, {15765, 36969}, {18585, 35739}, {18586, 35786}, {19053, 36436}, {23267, 34754}, {33437, 40901}

X(42238) = GIBERT(3,2*SQRT(3),3) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 4*Sqrt[3]*SB*SC : :

X(42238) lies on these lines: {2, 33360}, {3, 3366}, {4, 15}, {5, 3390}, {13, 372}, {14, 485}, {16, 3070}, {30, 3389}, {61, 3071}, {62, 1587}, {371, 16964}, {381, 3367}, {622, 33352}, {2042, 3365}, {2043, 16241}, {2045, 33417}, {2046, 16967}, {5237, 23269}, {5321, 18538}, {5339, 8960}, {6396, 16966}, {6778, 33430}, {10645, 14814}, {10646, 23249}, {11485, 23261}, {13748, 41020}, {14230, 41035}, {15765, 37832}, {18585, 36970}, {18587, 35786}, {19053, 36454}, {23267, 34755}, {33439, 40900}

X(42239) = GIBERT(-3,3,2*SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*Sqrt[3]*a^2*SA - 6*SB*SC : :

X(42239) lies on these lines: {3, 5321}, {4, 615}, {5, 3390}, {6, 35732}, {14, 34551}, {15, 18762}, {30, 3365}, {371, 398}, {372, 5318}, {395, 2044}, {396, 486}, {397, 3312}, {639, 6303}, {1151, 5334}, {2042, 3071}, {3364, 11543}, {3366, 37835}, {3594, 5335}, {5339, 6409}, {5349, 14814}, {5471, 35742}, {5480, 41018}, {6114, 35759}, {10577, 15765}, {11480, 32790}, {12256, 41039}, {15764, 36470}, {16809, 35739}, {18585, 35820}, {22856, 35746}, {32788, 36454}, {34552, 36970}, {35734, 41120}, {35735, 41113}

X(42240) = GIBERT(3,-3,2*SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + 2*Sqrt[3]*a^2*SA - 6*SB*SC : :

X(42240) lies on these lines: {3, 5321}, {4, 590}, {5, 3389}, {14, 34552}, {15, 18538}, {30, 3364}, {371, 5318}, {372, 398}, {395, 2043}, {396, 485}, {397, 3311}, {640, 6307}, {1152, 5334}, {2041, 3070}, {3365, 11543}, {3367, 37835}, {3592, 5335}, {3845, 35731}, {5339, 6410}, {5349, 14813}, {6409, 35732}, {10576, 18585}, {11480, 32789}, {12257, 41039}, {15765, 35821}, {16809, 35738}, {16964, 35739}, {21736, 41038}, {32787, 36436}, {34551, 36970}

X(42241) = GIBERT(3,3,-2*SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*Sqrt[3]*a^2*SA + 6*SB*SC : :

X(42241) lies on these lines: {3, 5318}, {4, 615}, {5, 3365}, {13, 34552}, {16, 18762}, {30, 3390}, {371, 397}, {372, 5321}, {395, 486}, {396, 2043}, {398, 3312}, {639, 6302}, {1151, 5335}, {2041, 3071}, {3389, 11542}, {3391, 37832}, {3594, 5334}, {5340, 6409}, {5350, 14813}, {6410, 35732}, {10577, 18585}, {11481, 32790}, {12256, 41038}, {15765, 35820}, {16808, 35738}, {19106, 35739}, {32788, 36436}, {34551, 36969}

X(42242) = GIBERT(-3,3,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - Sqrt[3]*a^2*SA - 6*SB*SC : :

X(42242) lies on these lines: {3, 5321}, {4, 372}, {14, 485}, {371, 5334}, {397, 6418}, {398, 3311}, {489, 33353}, {1151, 5339}, {1327, 36445}, {1328, 3392}, {2041, 35739}, {2042, 3389}, {2043, 3367}, {2046, 3366}, {3070, 40694}, {3071, 10654}, {3312, 5318}, {3365, 19107}, {3390, 16809}, {5335, 6420}, {5340, 6432}, {5349, 6450}, {6410, 14814}, {9738, 16002}, {13785, 40693}, {18585, 23251}, {20428, 37342}, {33603, 35737}, {35731, 41108}, {36714, 41038}

X(42243) = GIBERT(3,-3,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + Sqrt[3]*a^2*SA - 6*SB*SC : :

X(42243) lies on these lines: {3, 5321}, {4, 371}, {14, 486}, {372, 5334}, {397, 6417}, {398, 3312}, {490, 33350}, {1152, 5339}, {1327, 3391}, {1328, 36463}, {2041, 3390}, {2044, 3366}, {2045, 3367}, {3070, 10654}, {3071, 40694}, {3311, 5318}, {3364, 19107}, {3389, 16809}, {5335, 6419}, {5340, 6431}, {5349, 6449}, {6200, 35732}, {6221, 35740}, {6409, 14813}, {9739, 16002}, {13665, 40693}, {15765, 23261}, {20428, 37343}, {36709, 41038}

X(42244) = GIBERT(3,3,-SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S - Sqrt[3]*a^2*SA + 6*SB*SC : :

X(42244) lies on these lines: {3, 5318}, {4, 372}, {13, 485}, {371, 5335}, {397, 3311}, {398, 6418}, {489, 33351}, {1151, 5340}, {1327, 36463}, {1328, 3367}, {2041, 3364}, {2044, 3392}, {2045, 3391}, {3070, 40693}, {3071, 10653}, {3312, 5321}, {3365, 16808}, {3390, 19106}, {5334, 6420}, {5339, 6432}, {5350, 6450}, {6396, 35732}, {6410, 14813}, {9738, 16001}, {13785, 40694}, {15765, 23251}, {20429, 37342}, {36714, 41039}

X(42245) = GIBERT(3,3,SQRT(3)) POINT

Barycentrics    Sqrt[3]*a^2*S + Sqrt[3]*a^2*SA + 6*SB*SC : :

X(42245) lies on these lines: {3, 5318}, {4, 371}, {13, 486}, {372, 5335}, {397, 3312}, {398, 6417}, {490, 33352}, {1152, 5340}, {1327, 3366}, {1328, 36445}, {2042, 3365}, {2043, 3391}, {2046, 3392}, {3070, 10653}, {3071, 40693}, {3311, 5321}, {3364, 16808}, {3389, 19106}, {5334, 6419}, {5339, 6431}, {5350, 6449}, {6409, 14814}, {9739, 16001}, {13665, 40694}, {18585, 23261}, {20429, 37343}, {33602, 35737}, {36709, 41039}

X(42246) = GIBERT(-3,SQRT(3),1) POINT

Barycentrics    Sqrt[3]*a^2*S - a^2*SA - 2*Sqrt[3]*SB*SC : :

X(42246) lies on these lines: {2, 33367}, {3, 486}, {4, 14}, {15, 23273}, {16, 23259}, {17, 14226}, {61, 1588}, {371, 18581}, {398, 18586}, {488, 22882}, {640, 22598}, {1132, 3367}, {1328, 18587}, {2042, 10654}, {2043, 36452}, {2044, 35823}, {3364, 18582}, {3389, 5334}, {3390, 5335}, {3392, 6459}, {5237, 23275}, {5321, 22615}, {5340, 18585}, {11294, 33440}, {12322, 37178}, {13939, 35739}, {14813, 22236}, {14814, 36843}, {22238, 23261}, {36437, 41113}, {36445, 41112}

X(42247) = GIBERT(3,-SQRT(3),1) POINT

Barycentrics    Sqrt[3]*a^2*S + a^2*SA - 2*Sqrt[3]*SB*SC : :

X(42247) lies on these lines: {2, 33369}, {3, 486}, {4, 13}, {15, 23259}, {16, 23273}, {18, 14226}, {62, 1588}, {371, 18582}, {397, 18587}, {488, 22927}, {640, 22600}, {1132, 3392}, {1328, 18586}, {2041, 10653}, {2043, 35823}, {2044, 36469}, {3364, 5335}, {3365, 5334}, {3367, 6459}, {3389, 18581}, {5238, 23275}, {5318, 22615}, {5339, 15765}, {11294, 33442}, {11488, 35730}, {12322, 37177}, {14813, 36836}, {14814, 22238}, {22236, 23261}, {36455, 41112}, {36463, 41113}

X(42248) = GIBERT(3,SQRT(3),-1) POINT

Barycentrics    Sqrt[3]*a^2*S - a^2*SA + 2*Sqrt[3]*SB*SC : :

X(42248) lies on these lines: {2, 33368}, {3, 485}, {4, 14}, {15, 23267}, {16, 23249}, {17, 14241}, {61, 1587}, {372, 18581}, {398, 18587}, {487, 22883}, {639, 22627}, {1131, 3366}, {1327, 18586}, {2041, 10654}, {2043, 35822}, {2044, 36470}, {3365, 18582}, {3389, 5335}, {3390, 5334}, {3391, 6460}, {5237, 23269}, {5321, 22644}, {5340, 15765}, {11293, 33441}, {12323, 37178}, {14540, 21737}, {14813, 36843}, {14814, 22236}, {22238, 23251}, {36455, 41113}, {36463, 41112}

X(42249) = GIBERT(3,SQRT(3),1) POINT

Barycentrics    Sqrt[3]*a^2*S + a^2*SA + 2*Sqrt[3]*SB*SC : :

X(42249) lies on these lines: {2, 33366}, {3, 485}, {4, 13}, {15, 23249}, {16, 23267}, {18, 14241}, {62, 1587}, {372, 18582}, {397, 18586}, {487, 22928}, {639, 22629}, {1131, 3391}, {1327, 18587}, {2042, 10653}, {2043, 36453}, {2044, 35822}, {3364, 5334}, {3365, 5335}, {3366, 6460}, {3390, 18581}, {5238, 23269}, {5318, 22644}, {5339, 18585}, {11293, 33443}, {12323, 37177}, {14541, 21737}, {14813, 22238}, {14814, 36836}, {22236, 23251}, {36437, 41112}, {36445, 41113}

X(42250) = GIBERT(-3,SQRT(3),2) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*a^2*SA - 2*Sqrt[3]*SB*SC : :

X(42250) lies on these lines: {3, 486}, {4, 395}, {6, 35732}, {18, 15765}, {61, 14813}, {62, 3070}, {371, 11543}, {397, 2044}, {398, 2042}, {1151, 23303}, {1588, 22236}, {2043, 16773}, {3364, 16966}, {5237, 14814}, {5335, 13939}, {6303, 22882}, {11480, 23273}, {11481, 23259}, {16267, 36439}, {16965, 18585}, {18586, 32787}, {23261, 36843}, {31414, 37641}, {32490, 33445}, {33395, 33424}, {34551, 35823}, {34559, 36470}, {35746, 35849}, {36455, 41951}

X(42251) = GIBERT(3,-SQRT(3),2) POINT

Barycentrics    Sqrt[3]*a^2*S + 2*a^2*SA - 2*Sqrt[3]*SB*SC : :

X(42251) lies on these lines: {3, 486}, {4, 396}, {17, 18585}, {61, 3070}, {62, 14814}, {371, 11542}, {397, 2041}, {398, 2043}, {1151, 23302}, {1588, 22238}, {2044, 16772}, {3389, 16967}, {5238, 14813}, {5334, 13939}, {6302, 22927}, {6565, 35738}, {11480, 23259}, {11481, 23273}, {11488, 35740}, {15765, 16964}, {16268, 36457}, {18587, 32787}, {23261, 35732}, {31414, 37640}, {32490, 33447}, {33392, 33427}, {34552, 35823}, {34562, 36453}, {36437, 41951}

X(42252) = GIBERT(3,SQRT(3),-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*a^2*SA + 2*Sqrt[3]*SB*SC : :

X(42252) lies on these lines: {3, 485}, {4, 395}, {18, 18585}, {61, 14814}, {62, 3071}, {372, 11543}, {397, 2043}, {398, 2041}, {1152, 23303}, {1587, 22236}, {2044, 16773}, {3365, 16966}, {5237, 14813}, {5335, 13886}, {6307, 22883}, {6564, 35738}, {11480, 23267}, {11481, 23249}, {15765, 16965}, {16267, 36457}, {18587, 32788}, {23251, 35732}, {31412, 35740}, {32491, 33444}, {33393, 33426}, {34552, 35822}, {34562, 36452}, {36437, 41952}

X(42253) = GIBERT(3,SQRT(3),2) POINT

Barycentrics    Sqrt[3]*a^2*S + 2*a^2*SA + 2*Sqrt[3]*SB*SC : :

X(42253) lies on these lines: {3, 485}, {4, 396}, {6, 35732}, {17, 15765}, {61, 3071}, {62, 14813}, {372, 11542}, {397, 2042}, {398, 2044}, {1152, 23302}, {1587, 22238}, {2043, 16772}, {3365, 35730}, {3390, 16967}, {5238, 14814}, {5334, 13886}, {6306, 22928}, {11480, 23249}, {11481, 23267}, {16268, 36439}, {16964, 18585}, {18586, 32788}, {23251, 36836}, {32491, 33446}, {33394, 33425}, {34551, 35822}, {34559, 36469}, {35746, 35846}, {36455, 41952}

X(42254) = GIBERT(-3,SQRT(3),3) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA - 2*Sqrt[3]*SB*SC : :

X(42254) lies on these lines: {2, 3364}, {3, 486}, {4, 16}, {6, 14813}, {13, 3317}, {15, 1588}, {20, 3365}, {61, 7582}, {62, 1587}, {371, 2042}, {372, 2044}, {376, 36465}, {395, 485}, {488, 6303}, {638, 33353}, {640, 6301}, {1151, 15765}, {2041, 6565}, {2043, 35821}, {2045, 6200}, {2046, 10577}, {3068, 3366}, {3069, 3390}, {3070, 11486}, {3091, 3391}, {3389, 6459}, {5237, 23263}, {5335, 13941}, {5418, 23303}, {5871, 41021}, {7584, 34551}, {8981, 35738}, {10194, 23302}, {10645, 23273}, {10646, 23259}, {10784, 41020}, {11481, 14814}, {12322, 37173}, {13748, 41034}, {13847, 36439}, {13935, 35739}, {16773, 22615}, {22238, 23251}, {23249, 34755}, {35733, 37640}

X(42255) = GIBERT(3,-SQRT(3),3) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 2*Sqrt[3]*SB*SC : :

X(42255) lies on these lines: {2, 3367}, {3, 486}, {4, 15}, {6, 14814}, {14, 3317}, {16, 1588}, {20, 3390}, {61, 1587}, {62, 7582}, {371, 2041}, {372, 2043}, {376, 35739}, {396, 485}, {488, 6302}, {638, 33351}, {640, 6300}, {1151, 16644}, {2042, 6565}, {2044, 35821}, {2045, 10577}, {2046, 6200}, {3068, 3391}, {3069, 3365}, {3070, 11485}, {3091, 3366}, {3364, 6459}, {5238, 23263}, {5334, 13941}, {5418, 23302}, {5871, 41020}, {7584, 34552}, {10194, 23303}, {10645, 23259}, {10646, 23273}, {10784, 41021}, {11480, 14813}, {12322, 37172}, {13748, 41035}, {13847, 36457}, {13935, 36967}, {16772, 22615}, {22236, 23251}, {23249, 34754}, {35731, 36445}

X(42256) = GIBERT(3,SQRT(3),-3) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 2*Sqrt[3]*SB*SC : :

X(42256) lies on these lines: {2, 3365}, {3, 485}, {4, 16}, {6, 14814}, {13, 3316}, {15, 1587}, {20, 3364}, {61, 7581}, {62, 1588}, {371, 2043}, {372, 2041}, {376, 36446}, {395, 486}, {487, 6307}, {637, 33350}, {639, 6305}, {1152, 16645}, {2042, 6564}, {2044, 35820}, {2045, 10576}, {2046, 6396}, {3068, 3389}, {3069, 3367}, {3071, 11486}, {3091, 3392}, {3366, 31412}, {3390, 6460}, {5237, 23253}, {5335, 8972}, {5420, 23303}, {5870, 41021}, {7583, 34552}, {9540, 36968}, {10195, 23302}, {10645, 23267}, {10646, 23249}, {10783, 41020}, {11481, 14813}, {12323, 37173}, {13749, 41034}, {13846, 36457}, {14538, 21737}, {16773, 22644}, {22238, 23261}, {23259, 34755}

X(42257) = GIBERT(3,SQRT(3),3) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 2*Sqrt[3]*SB*SC : :

X(42257) lies on these lines: {2, 3366}, {3, 485}, {4, 15}, {6, 14813}, {14, 3316}, {16, 1587}, {20, 3389}, {61, 1588}, {62, 7581}, {371, 2044}, {372, 2042}, {376, 36464}, {396, 486}, {487, 6306}, {631, 35739}, {637, 33352}, {639, 6304}, {1152, 15765}, {2041, 6564}, {2043, 35820}, {2045, 6396}, {2046, 10576}, {3068, 3364}, {3069, 3392}, {3071, 11485}, {3091, 3367}, {3365, 6460}, {3391, 31412}, {5238, 23253}, {5334, 8972}, {5420, 23302}, {5870, 41020}, {6561, 35740}, {7583, 34551}, {9540, 36967}, {10195, 23303}, {10645, 23249}, {10646, 23267}, {10783, 41021}, {11480, 14814}, {12323, 37172}, {13749, 41035}, {13846, 36439}, {13966, 35738}, {14539, 21737}, {16772, 22644}, {22236, 23261}, {23259, 34754}, {35944, 36762}

X(42258) = GIBERT(SQRT(3),-1,2) POINT

Barycentrics    a^2*S + 2*a^2*SA - 2*SB*SC : :

X(42258) lies on these lines: {1, 9647}, {2, 6409}, {3, 486}, {4, 590}, {5, 6200}, {6, 20}, {30, 371}, {140, 6565}, {141, 489}, {156, 9676}, {165, 13973}, {372, 550}, {376, 1152}, {381, 5418}, {382, 485}, {490, 524}, {516, 7969}, {546, 10576}, {548, 6396}, {549, 10577}, {591, 12221}, {631, 6411}, {637, 35949}, {952, 35610}, {1086, 31550}, {1124, 4299}, {1131, 3068}, {1132, 15717}, {1160, 12124}, {1327, 15684}, {1328, 5054}, {1335, 4302}, {1503, 26441}, {1587, 3529}, {1656, 6455}, {1657, 3311}, {1699, 9615}, {1885, 5412}, {1991, 12323}, {2041, 5318}, {2042, 5321}, {2066, 7354}, {2067, 6284}, {2548, 9600}, {2549, 6424}, {2883, 10533}, {3069, 3522}, {3090, 23263}, {3091, 8253}, {3092, 18533}, {3297, 4293}, {3298, 4294}, {3299, 4316}, {3301, 4324}, {3312, 3534}, {3364, 14814}, {3365, 36967}, {3371, 41980}, {3372, 41979}, {3389, 14813}, {3390, 36968}, {3523, 8252}, {3524, 23275}, {3526, 6451}, {3528, 6412}, {3530, 18762}, {3543, 6429}, {3575, 11473}, {3583, 9661}, {3585, 9646}, {3589, 11293}, {3590, 10139}, {3594, 7582}, {3627, 6453}, {3830, 6407}, {3832, 6433}, {3843, 6445}, {3845, 6484}, {3850, 6486}, {3853, 6480}, {4190, 31473}, {4297, 7968}, {5058, 7756}, {5059, 7585}, {5062, 6781}, {5073, 13665}, {5076, 6519}, {5254, 12963}, {5305, 41410}, {5414, 15338}, {5475, 9674}, {5587, 9582}, {5691, 9616}, {5870, 15428}, {5895, 17819}, {6199, 17800}, {6398, 15696}, {6417, 15681}, {6419, 15704}, {6420, 12103}, {6422, 7737}, {6426, 7586}, {6431, 7581}, {6437, 23249}, {6439, 9692}, {6450, 18510}, {6452, 13961}, {6456, 15688}, {6468, 8972}, {6470, 15683}, {6478, 35404}, {6485, 41962}, {6502, 15326}, {6644, 35777}, {6811, 10838}, {7517, 9682}, {7728, 10819}, {7748, 9675}, {7951, 31499}, {8276, 18534}, {8407, 36733}, {8550, 8982}, {8703, 13966}, {8855, 10691}, {8980, 39809}, {8991, 41362}, {8994, 12295}, {8997, 39838}, {8998, 13202}, {9583, 41869}, {9631, 18455}, {9649, 18965}, {9662, 13901}, {9686, 26883}, {9695, 35502}, {9778, 19065}, {9812, 13902}, {9975, 11179}, {10264, 35835}, {10295, 10881}, {10304, 13847}, {10519, 12509}, {10748, 11835}, {10820, 38723}, {10880, 18560}, {11513, 31829}, {11541, 23269}, {11836, 38798}, {12257, 13749}, {12296, 13881}, {12305, 35945}, {12376, 34153}, {12512, 13936}, {12943, 31472}, {12964, 15311}, {12968, 35947}, {12970, 34782}, {13488, 35764}, {13748, 21736}, {13883, 28164}, {13886, 15682}, {13912, 31673}, {13939, 21735}, {13941, 21734}, {13947, 16192}, {13993, 34200}, {14226, 15715}, {14677, 35827}, {15171, 35768}, {15325, 35803}, {15686, 35770}, {15692, 41951}, {15698, 41947}, {15765, 37835}, {17365, 31549}, {17845, 19088}, {18289, 34609}, {18481, 35775}, {18585, 35731}, {18990, 35808}, {19051, 38788}, {19089, 22676}, {19145, 31670}, {22791, 35763}, {23311, 39387}, {28160, 31439}, {28174, 35641}, {28224, 35842}, {32423, 35826}, {32497, 36709}, {32521, 35867}, {33923, 35256}, {34380, 39893}, {34773, 35642}, {35765, 37458}, {36711, 39649}

X(42259) = GIBERT(SQRT(3),1,-2) POINT

Barycentrics    a^2*S - 2*a^2*SA + 2*SB*SC : :

X(42259) lies on these lines: {2, 6410}, {3, 485}, {4, 615}, {5, 6396}, {6, 20}, {30, 372}, {140, 6564}, {141, 490}, {165, 13911}, {371, 550}, {376, 1151}, {381, 5420}, {382, 486}, {489, 524}, {516, 7968}, {546, 10577}, {548, 6200}, {549, 10576}, {591, 12322}, {631, 6412}, {638, 35948}, {952, 35611}, {1086, 31549}, {1124, 4302}, {1131, 15717}, {1132, 3069}, {1161, 12123}, {1327, 5054}, {1328, 15684}, {1335, 4299}, {1503, 8982}, {1588, 3529}, {1656, 6456}, {1657, 3312}, {1885, 5413}, {1991, 12222}, {2041, 5321}, {2042, 5318}, {2066, 15338}, {2067, 15326}, {2549, 6423}, {2883, 10534}, {3068, 3522}, {3090, 23253}, {3091, 8252}, {3093, 18533}, {3297, 4294}, {3298, 4293}, {3299, 4324}, {3301, 4316}, {3311, 3534}, {3364, 36967}, {3365, 14813}, {3385, 41980}, {3386, 41979}, {3389, 36968}, {3390, 14814}, {3523, 8253}, {3524, 23269}, {3526, 6452}, {3528, 6411}, {3530, 18538}, {3543, 6430}, {3575, 11474}, {3589, 11294}, {3591, 10140}, {3592, 7581}, {3627, 6454}, {3830, 6408}, {3832, 6434}, {3843, 6446}, {3845, 6485}, {3850, 6487}, {3853, 6481}, {4297, 7969}, {5010, 9646}, {5058, 6781}, {5059, 7586}, {5062, 7756}, {5073, 13785}, {5076, 6522}, {5217, 31472}, {5254, 12968}, {5305, 41411}, {5414, 7354}, {5691, 13973}, {5871, 15428}, {5895, 17820}, {6199, 9681}, {6221, 15696}, {6284, 6502}, {6395, 17800}, {6418, 15681}, {6419, 12103}, {6420, 15704}, {6421, 7737}, {6425, 7585}, {6432, 7582}, {6438, 23259}, {6445, 31487}, {6449, 18512}, {6451, 9680}, {6455, 15688}, {6469, 13941}, {6471, 15683}, {6479, 35404}, {6484, 41961}, {6644, 35776}, {6813, 10837}, {6872, 31473}, {7280, 9661}, {7728, 10820}, {8277, 18534}, {8400, 36719}, {8550, 26441}, {8703, 8981}, {8854, 10691}, {8960, 33923}, {8972, 21734}, {9600, 31411}, {9778, 19066}, {9812, 13959}, {9974, 11179}, {10264, 35834}, {10295, 10880}, {10304, 13846}, {10519, 12510}, {10748, 11836}, {10819, 38723}, {10881, 18560}, {11514, 31829}, {11541, 23275}, {11835, 38798}, {12256, 13748}, {12295, 13969}, {12297, 13881}, {12305, 21737}, {12306, 35944}, {12375, 34153}, {12512, 13883}, {12963, 35946}, {12964, 34782}, {12970, 15311}, {13202, 13990}, {13488, 35765}, {13886, 21735}, {13893, 16192}, {13925, 34200}, {13936, 28164}, {13939, 15682}, {13967, 39809}, {13975, 31673}, {13980, 41362}, {13989, 39838}, {14241, 15715}, {14677, 35826}, {15171, 35769}, {15325, 35802}, {15515, 31481}, {15686, 35771}, {15692, 41952}, {15698, 41948}, {15765, 37832}, {15815, 31463}, {17365, 31550}, {17845, 19087}, {18290, 34609}, {18481, 35774}, {18585, 35739}, {18990, 35809}, {19052, 38788}, {19090, 22676}, {19146, 31670}, {22791, 35762}, {23312, 39388}, {28174, 35642}, {28224, 35843}, {32423, 35827}, {32494, 36714}, {32521, 35866}, {34380, 39894}, {34773, 35641}, {35764, 37458}, {36712, 39658}

X(42260) = GIBERT(SQRT(3),-1,3) POINT

Barycentrics    a^2*S + 3*a^2*SA - 2*SB*SC : :

X(42260) lies on these lines: {1, 9631}, {2, 12819}, {3, 486}, {4, 5418}, {5, 6409}, {6, 550}, {20, 371}, {30, 485}, {55, 9647}, {56, 9660}, {140, 6411}, {372, 376}, {381, 6455}, {382, 590}, {488, 13712}, {489, 35949}, {491, 7802}, {492, 7782}, {511, 12124}, {546, 8253}, {548, 1152}, {549, 1328}, {631, 6565}, {641, 11147}, {944, 35610}, {962, 35763}, {1124, 15326}, {1131, 9542}, {1132, 15692}, {1335, 15338}, {1370, 18289}, {1504, 6781}, {1588, 3522}, {1614, 9676}, {1656, 6451}, {1657, 3070}, {2043, 3364}, {2044, 3389}, {2045, 33416}, {2046, 33417}, {2066, 4299}, {2067, 4302}, {2549, 12963}, {2777, 10819}, {3068, 3529}, {3069, 3528}, {3090, 35787}, {3102, 35946}, {3146, 6564}, {3311, 3534}, {3312, 15696}, {3317, 15698}, {3523, 10577}, {3526, 6496}, {3530, 8252}, {3543, 6486}, {3592, 12103}, {3627, 35255}, {3851, 32789}, {4293, 35808}, {4294, 35768}, {4297, 35775}, {5059, 6480}, {5073, 6445}, {5218, 35801}, {5286, 41410}, {5691, 9582}, {5731, 35642}, {5878, 10533}, {5925, 17819}, {6194, 35867}, {6361, 35641}, {6407, 13665}, {6408, 15695}, {6410, 7584}, {6412, 13966}, {6418, 15689}, {6419, 6460}, {6425, 7583}, {6426, 19116}, {6432, 15690}, {6433, 18538}, {6438, 41981}, {6447, 18512}, {6450, 15688}, {6452, 41964}, {6454, 7586}, {6456, 18510}, {6484, 31412}, {6497, 13961}, {6519, 13903}, {7288, 35803}, {7387, 9682}, {7388, 7937}, {7745, 9600}, {7747, 9674}, {7756, 9675}, {8276, 39568}, {8854, 34608}, {8972, 23253}, {8983, 28150}, {9543, 15683}, {9615, 41869}, {9646, 12943}, {9649, 19030}, {9661, 12953}, {9662, 19028}, {9677, 34148}, {9691, 15685}, {9693, 31414}, {9778, 35611}, {9862, 35878}, {10147, 12818}, {10194, 15712}, {10299, 23275}, {10304, 13935}, {10483, 31472}, {10820, 38726}, {10880, 35481}, {10881, 35503}, {10895, 31499}, {11001, 35822}, {11265, 34350}, {11473, 18533}, {11825, 35945}, {11835, 23699}, {11836, 38803}, {12082, 35776}, {12148, 12171}, {12244, 12375}, {12248, 35882}, {12253, 35880}, {12257, 22592}, {12383, 35826}, {12962, 19103}, {12964, 20427}, {12968, 19102}, {13172, 35824}, {13199, 35856}, {13200, 35828}, {13847, 34200}, {13911, 28160}, {13912, 28164}, {13939, 19708}, {13973, 31663}, {15681, 32787}, {15684, 41948}, {15686, 19117}, {15720, 32790}, {17928, 35777}, {18587, 35740}, {19145, 29181}, {21734, 35813}, {21735, 23273}, {22484, 41490}, {25406, 35841}, {26295, 36701}, {26441, 40274}, {31730, 35774}, {34781, 35864}, {35400, 41952}, {35731, 36455}

X(42261) = GIBERT(SQRT(3),1,-3) POINT

Barycentrics    a^2*S - 3*a^2*SA + 2*SB*SC : :

X(42261) lies on these lines: {2, 12818}, {3, 485}, {4, 5420}, {5, 6410}, {6, 550}, {20, 372}, {30, 486}, {140, 6412}, {371, 376}, {381, 6456}, {382, 615}, {487, 13835}, {490, 35948}, {491, 7782}, {492, 7802}, {511, 12123}, {546, 8252}, {548, 1151}, {549, 1327}, {631, 6564}, {642, 11147}, {944, 35611}, {962, 35762}, {1038, 9632}, {1124, 15338}, {1131, 15692}, {1335, 15326}, {1370, 18290}, {1505, 6781}, {1587, 3522}, {1656, 6452}, {1657, 3071}, {2041, 35739}, {2043, 3390}, {2044, 3365}, {2045, 33417}, {2046, 33416}, {2549, 12968}, {2777, 10820}, {3068, 3528}, {3069, 3529}, {3090, 35786}, {3103, 35947}, {3146, 6565}, {3311, 9681}, {3312, 3534}, {3316, 15698}, {3523, 10576}, {3524, 31412}, {3526, 6497}, {3530, 8253}, {3543, 6487}, {3594, 12103}, {3627, 35256}, {3851, 32790}, {4293, 35809}, {4294, 35769}, {4297, 35774}, {4299, 5414}, {4302, 6502}, {5010, 31472}, {5059, 6481}, {5073, 6446}, {5218, 35800}, {5267, 31484}, {5286, 41411}, {5731, 35641}, {5878, 10534}, {5925, 17820}, {6194, 35866}, {6361, 35642}, {6407, 15695}, {6408, 13785}, {6409, 7583}, {6411, 8981}, {6417, 15689}, {6419, 9541}, {6420, 6459}, {6425, 19117}, {6426, 7584}, {6431, 15690}, {6434, 18762}, {6437, 41981}, {6448, 18510}, {6449, 15688}, {6451, 41963}, {6453, 7585}, {6455, 18512}, {6485, 33703}, {6496, 13903}, {6522, 13961}, {7288, 35802}, {7389, 7937}, {8277, 39568}, {8589, 31481}, {8855, 34608}, {8960, 21735}, {8982, 40275}, {9540, 10304}, {9647, 19037}, {9660, 18995}, {9683, 35243}, {9778, 35610}, {9862, 35879}, {10148, 12819}, {10195, 15712}, {10299, 23269}, {10819, 38726}, {10880, 35503}, {10881, 35481}, {11001, 35823}, {11266, 34350}, {11474, 18533}, {11824, 35944}, {11835, 38803}, {11836, 23699}, {12082, 35777}, {12147, 12172}, {12244, 12376}, {12248, 35883}, {12253, 35881}, {12256, 22591}, {12383, 35827}, {12963, 19105}, {12969, 19104}, {12970, 20427}, {13172, 35825}, {13199, 35857}, {13200, 35829}, {13846, 34200}, {13886, 19708}, {13911, 31663}, {13941, 23263}, {13971, 28150}, {13973, 28160}, {13975, 28164}, {15681, 32788}, {15683, 35814}, {15684, 41947}, {15686, 19116}, {15720, 32789}, {17928, 35776}, {19146, 29181}, {21734, 35812}, {22485, 41491}, {25406, 35840}, {26294, 36703}, {31463, 37512}, {31730, 35775}, {34781, 35865}, {35400, 41951}

X(42262) = GIBERT(-SQRT(3),2,2) POINT

Barycentrics    a^2*S - 2*a^2*SA - 4*SB*SC : :

X(42262) lies on these lines: {2, 489}, {3, 3367}, {4, 615}, {5, 6}, {11, 3298}, {12, 3297}, {20, 6412}, {30, 5420}, {69, 23312}, {115, 6421}, {140, 6409}, {230, 26468}, {371, 1656}, {372, 381}, {376, 23263}, {382, 6396}, {387, 36680}, {394, 15233}, {403, 3093}, {492, 32488}, {546, 6426}, {547, 8981}, {549, 1328}, {550, 10194}, {590, 1588}, {591, 638}, {599, 640}, {631, 6411}, {639, 3763}, {946, 13973}, {999, 35801}, {1124, 7951}, {1131, 6442}, {1270, 32872}, {1327, 38071}, {1335, 7741}, {1377, 25639}, {1378, 3814}, {1482, 35789}, {1504, 7603}, {1505, 39565}, {1506, 6422}, {1578, 15760}, {1579, 11585}, {1587, 3545}, {1591, 17825}, {1592, 17811}, {1594, 3092}, {1699, 13947}, {1834, 36690}, {1853, 12970}, {2041, 11481}, {2042, 11480}, {2362, 17605}, {2476, 31473}, {3053, 37342}, {3068, 5056}, {3069, 3070}, {3102, 7697}, {3167, 35837}, {3295, 35803}, {3311, 5055}, {3312, 3851}, {3316, 6441}, {3364, 37832}, {3366, 11485}, {3389, 37835}, {3391, 11486}, {3525, 9541}, {3526, 6200}, {3544, 7581}, {3591, 3854}, {3614, 19029}, {3627, 35256}, {3628, 5418}, {3817, 13936}, {3818, 19146}, {3830, 6450}, {3832, 6438}, {3839, 41946}, {3843, 6398}, {3845, 6430}, {3850, 13993}, {3853, 6434}, {3855, 23249}, {3861, 6469}, {5013, 37343}, {5020, 8281}, {5066, 6471}, {5067, 6437}, {5068, 7586}, {5070, 6221}, {5071, 7582}, {5072, 6420}, {5073, 6456}, {5079, 6419}, {5087, 30557}, {5094, 11473}, {5286, 36664}, {5413, 7507}, {5414, 10896}, {5448, 13970}, {5475, 6423}, {5476, 9974}, {5587, 7968}, {5790, 35642}, {5893, 13980}, {5907, 12240}, {5943, 9823}, {6119, 11316}, {6199, 35812}, {6251, 13934}, {6395, 35814}, {6408, 14269}, {6417, 8960}, {6418, 19709}, {6424, 7746}, {6429, 35255}, {6433, 9681}, {6452, 17800}, {6455, 15694}, {6468, 9680}, {6470, 35018}, {6485, 38335}, {6486, 15723}, {6497, 15681}, {6502, 10895}, {6721, 13873}, {6813, 9756}, {7173, 19027}, {7486, 31454}, {7516, 9683}, {7547, 10881}, {7585, 15022}, {7687, 13990}, {7969, 8227}, {7988, 18991}, {7989, 18992}, {8277, 9818}, {8414, 32491}, {8983, 10171}, {9600, 31455}, {9615, 34595}, {9654, 35769}, {9669, 35809}, {9677, 13353}, {9738, 12601}, {9824, 14913}, {9955, 35774}, {9956, 35775}, {9975, 34507}, {10109, 13925}, {10113, 10820}, {10139, 41985}, {10148, 12102}, {10172, 13912}, {10175, 13911}, {10247, 35843}, {10601, 15234}, {10653, 34562}, {10654, 34559}, {10671, 20428}, {10672, 20429}, {11294, 32807}, {11474, 37197}, {11479, 13943}, {11548, 18289}, {12221, 32806}, {12256, 14230}, {12314, 22810}, {12376, 38724}, {12645, 35811}, {12963, 37637}, {13913, 38319}, {13937, 23047}, {13971, 19925}, {13975, 18483}, {14226, 34089}, {15884, 35830}, {16232, 17606}, {16644, 18586}, {16645, 18587}, {18393, 38235}, {18493, 35641}, {18512, 35770}, {18525, 35762}, {19145, 38317}, {21736, 32494}, {23253, 41947}, {23269, 41106}, {31479, 35808}, {32385, 32395}, {32447, 35867}, {32609, 35835}, {35731, 36456}, {35738, 36836}, {35825, 38743}, {35827, 38789}, {35857, 38755}, {35879, 38732}, {36655, 36990}

X(42263) = GIBERT(SQRT(3),-2,2) POINT

Barycentrics    a^2*S + 2*a^2*SA - 4*SB*SC : :

X(42263) lies on these lines: {2, 6411}, {3, 3367}, {4, 590}, {5, 6409}, {6, 30}, {20, 1152}, {115, 36719}, {371, 382}, {372, 1657}, {376, 615}, {381, 6200}, {485, 3627}, {486, 550}, {546, 5418}, {548, 5420}, {631, 23263}, {1124, 10483}, {1132, 41953}, {1327, 33699}, {1328, 8703}, {1478, 9660}, {1479, 9647}, {1539, 10819}, {1579, 12605}, {1587, 6431}, {1588, 3529}, {1656, 35787}, {2043, 11481}, {2044, 11480}, {2066, 12943}, {2067, 12953}, {3068, 3543}, {3070, 3146}, {3092, 6240}, {3093, 18560}, {3297, 7354}, {3298, 6284}, {3311, 5073}, {3312, 17800}, {3524, 32790}, {3534, 6396}, {3545, 32789}, {3830, 6221}, {3839, 32785}, {3843, 6449}, {3845, 6433}, {3851, 6455}, {3853, 6429}, {3861, 9680}, {5055, 6451}, {5059, 6432}, {5070, 6496}, {5076, 6453}, {5413, 37196}, {5475, 9600}, {5895, 12964}, {6144, 32421}, {6199, 15684}, {6395, 15685}, {6398, 15681}, {6407, 35812}, {6408, 35814}, {6421, 7756}, {6422, 7747}, {6424, 7748}, {6426, 7584}, {6434, 15686}, {6438, 11001}, {6439, 12101}, {6441, 15640}, {6445, 14269}, {6447, 35815}, {6452, 15689}, {6456, 35813}, {6468, 15687}, {6469, 19710}, {6471, 19116}, {6480, 38335}, {7526, 9683}, {7530, 9682}, {7581, 11541}, {7582, 41955}, {7583, 22644}, {7586, 15683}, {7969, 41869}, {9582, 18492}, {9655, 35808}, {9668, 35768}, {9674, 39590}, {9676, 10540}, {9677, 37472}, {9690, 35403}, {9739, 12601}, {10304, 32786}, {10620, 35835}, {10880, 35490}, {11473, 12173}, {12103, 13966}, {12239, 13598}, {12257, 14230}, {12375, 38790}, {12819, 14869}, {12902, 35826}, {12970, 17845}, {13473, 13884}, {13749, 26441}, {13911, 31673}, {13935, 17538}, {13939, 41964}, {13951, 15696}, {13973, 31730}, {14233, 21736}, {15484, 36734}, {15682, 23249}, {17578, 31412}, {17579, 31473}, {18525, 35610}, {19107, 35731}, {23302, 36445}, {23303, 36463}, {26617, 32805}, {28146, 35774}, {28160, 35775}, {31439, 33697}, {32419, 40341}, {34780, 35864}, {35824, 38733}, {35878, 38744}, {35882, 38756}, {36718, 41410}

X(42264) = GIBERT(SQRT(3),2,-2) POINT

Barycentrics    a^2*S - 2*a^2*SA + 4*SB*SC : :

X(42264) lies on these lines: {2, 6412}, {3, 3366}, {4, 615}, {5, 6410}, {6, 30}, {20, 1151}, {115, 36733}, {371, 1657}, {372, 382}, {376, 590}, {381, 6396}, {485, 550}, {486, 3627}, {546, 5420}, {548, 5418}, {631, 23253}, {1131, 41954}, {1327, 8703}, {1328, 33699}, {1335, 10483}, {1539, 10820}, {1578, 12605}, {1587, 3529}, {1588, 6432}, {1656, 35786}, {2043, 11480}, {2044, 11481}, {3069, 3543}, {3071, 3146}, {3092, 18560}, {3093, 6240}, {3297, 6284}, {3298, 7354}, {3311, 17800}, {3312, 5073}, {3522, 31412}, {3524, 32789}, {3534, 6200}, {3545, 32790}, {3830, 6398}, {3839, 32786}, {3843, 6450}, {3845, 6434}, {3851, 6456}, {3853, 6430}, {5055, 6452}, {5059, 6431}, {5070, 6497}, {5076, 6454}, {5412, 37196}, {5414, 12943}, {5475, 36719}, {5895, 12970}, {6144, 32419}, {6199, 15685}, {6221, 15681}, {6395, 15684}, {6407, 35815}, {6408, 35813}, {6421, 7747}, {6422, 7756}, {6423, 7748}, {6425, 7583}, {6433, 15686}, {6437, 9541}, {6440, 12101}, {6442, 15640}, {6444, 31403}, {6446, 14269}, {6448, 35814}, {6449, 8960}, {6451, 15689}, {6455, 35812}, {6468, 19710}, {6469, 15687}, {6470, 19117}, {6481, 38335}, {6502, 12953}, {7581, 41956}, {7582, 11541}, {7584, 22615}, {7585, 15683}, {7968, 41869}, {8976, 15696}, {8981, 12103}, {8982, 13748}, {9540, 17538}, {9601, 22646}, {9655, 35809}, {9668, 35769}, {9676, 37477}, {9680, 13925}, {9738, 12602}, {10304, 32785}, {10620, 35834}, {10881, 35490}, {11114, 31473}, {11474, 12173}, {12102, 17852}, {12240, 13598}, {12256, 14233}, {12376, 38790}, {12818, 14869}, {12902, 35827}, {12964, 17845}, {13473, 13937}, {13886, 41963}, {13911, 31730}, {13973, 31673}, {15338, 31472}, {15484, 36718}, {15682, 23259}, {18525, 35611}, {23302, 36463}, {23303, 36445}, {26618, 32806}, {28146, 35775}, {28160, 35774}, {32421, 40341}, {34780, 35865}, {35825, 38733}, {35879, 38744}, {35883, 38756}, {36734, 41411}

X(42265) = GIBERT(SQRT(3),2,2) POINT

Barycentrics    a^2*S + 2*a^2*SA + 4*SB*SC : :

X(42265) lies on these lines: {2, 490}, {3, 3366}, {4, 590}, {5, 6}, {11, 3297}, {12, 3298}, {20, 6411}, {30, 5418}, {69, 23311}, {115, 6422}, {140, 6410}, {230, 26469}, {371, 381}, {372, 1656}, {376, 23253}, {382, 6200}, {387, 36681}, {394, 15234}, {403, 3092}, {491, 32489}, {546, 6425}, {547, 13966}, {549, 1327}, {550, 10195}, {599, 639}, {615, 1587}, {631, 6412}, {637, 1991}, {640, 3763}, {946, 13911}, {999, 35800}, {1124, 7741}, {1132, 6441}, {1271, 32872}, {1328, 38071}, {1329, 31484}, {1335, 7951}, {1377, 3814}, {1378, 25639}, {1478, 9661}, {1479, 9646}, {1482, 35788}, {1504, 39565}, {1505, 7603}, {1506, 6421}, {1578, 11585}, {1579, 15760}, {1588, 3545}, {1591, 17811}, {1592, 17825}, {1594, 3093}, {1699, 13893}, {1834, 36691}, {1853, 12964}, {2041, 11480}, {2042, 11481}, {2066, 10896}, {2067, 10895}, {2362, 17606}, {3053, 37343}, {3068, 3071}, {3069, 5056}, {3103, 7697}, {3167, 35836}, {3295, 35802}, {3311, 3851}, {3312, 5055}, {3317, 6442}, {3365, 37832}, {3367, 11485}, {3390, 37835}, {3392, 11486}, {3525, 23269}, {3526, 6396}, {3544, 7582}, {3590, 3854}, {3614, 19030}, {3627, 35255}, {3628, 5420}, {3817, 13883}, {3818, 19145}, {3830, 6449}, {3832, 6437}, {3839, 41945}, {3843, 6221}, {3845, 6429}, {3850, 13925}, {3853, 6433}, {3855, 23259}, {3861, 6468}, {4193, 31473}, {4302, 31499}, {5013, 37342}, {5020, 8280}, {5066, 6470}, {5067, 6438}, {5068, 7585}, {5070, 6398}, {5071, 7581}, {5072, 6419}, {5073, 6455}, {5079, 6420}, {5087, 30556}, {5094, 11474}, {5254, 31463}, {5286, 36665}, {5412, 7507}, {5448, 13909}, {5475, 6424}, {5476, 9975}, {5587, 7969}, {5790, 35641}, {5893, 8991}, {5907, 12239}, {5943, 9824}, {6118, 11315}, {6199, 35815}, {6250, 13882}, {6395, 35813}, {6407, 14269}, {6417, 19709}, {6423, 7746}, {6430, 35256}, {6434, 16239}, {6451, 17800}, {6456, 15694}, {6471, 35018}, {6484, 38335}, {6487, 15723}, {6496, 15681}, {6721, 13926}, {6811, 9756}, {7173, 19028}, {7486, 31414}, {7526, 9682}, {7530, 9683}, {7547, 10880}, {7586, 15022}, {7687, 8998}, {7748, 9600}, {7968, 8227}, {7988, 18992}, {7989, 18991}, {8276, 9818}, {8406, 32490}, {8909, 9927}, {8983, 19925}, {9583, 18492}, {9654, 35768}, {9669, 35808}, {9675, 39590}, {9676, 37472}, {9677, 10540}, {9739, 12602}, {9823, 14913}, {9955, 35775}, {9956, 35774}, {9974, 34507}, {10109, 13993}, {10113, 10819}, {10140, 41985}, {10147, 12102}, {10171, 13971}, {10172, 13975}, {10175, 13973}, {10247, 35842}, {10589, 31408}, {10601, 15233}, {10653, 34559}, {10654, 34562}, {10667, 20428}, {10668, 20429}, {11473, 37197}, {11479, 13889}, {11548, 18290}, {12222, 32805}, {12257, 14233}, {12313, 22809}, {12375, 38724}, {12645, 35810}, {12968, 37637}, {13884, 23047}, {13912, 18483}, {13977, 38319}, {14230, 21736}, {14241, 34091}, {15883, 35831}, {16232, 17605}, {16644, 18587}, {16645, 18586}, {18395, 38235}, {18493, 35642}, {18510, 35771}, {18525, 35763}, {19146, 38317}, {23263, 41948}, {23275, 41106}, {31474, 35803}, {31479, 35809}, {32384, 32395}, {32447, 35866}, {32609, 35834}, {35738, 36843}, {35824, 38743}, {35826, 38789}, {35856, 38755}, {35878, 38732}, {36656, 36990}

X(42266) = GIBERT(SQRT(3),-2,3) POINT

Barycentrics    a^2*S + 3*a^2*SA - 4*SB*SC : :

X(42266) lies on these lines: {2, 22615}, {3, 3367}, {4, 5418}, {6, 1657}, {20, 372}, {30, 371}, {35, 35801}, {36, 35803}, {74, 35835}, {376, 486}, {378, 9683}, {381, 6409}, {382, 1151}, {485, 3146}, {490, 32419}, {511, 39893}, {515, 35610}, {516, 35641}, {548, 615}, {550, 3071}, {590, 3627}, {639, 35949}, {962, 35810}, {1131, 6478}, {1152, 3534}, {1327, 13886}, {1328, 10304}, {1503, 35864}, {1587, 5059}, {1656, 6411}, {1870, 9631}, {1885, 35764}, {2066, 10483}, {2362, 4333}, {2460, 35831}, {2777, 12375}, {2794, 35828}, {2829, 35882}, {3068, 9681}, {3069, 17538}, {3092, 37196}, {3311, 17800}, {3312, 15681}, {3522, 5420}, {3523, 23263}, {3529, 6419}, {3543, 6484}, {3579, 35789}, {3830, 6449}, {3843, 6455}, {3850, 32789}, {3851, 6451}, {3853, 6486}, {4297, 35762}, {4299, 35769}, {4302, 35809}, {4316, 6502}, {4324, 5414}, {5055, 6496}, {5073, 6221}, {5254, 41410}, {5412, 18560}, {5413, 35471}, {5691, 35788}, {5840, 35856}, {6240, 11473}, {6284, 9647}, {6407, 13846}, {6410, 13785}, {6412, 13951}, {6417, 15685}, {6420, 15704}, {6425, 13665}, {6426, 18510}, {6429, 13903}, {6454, 7584}, {6456, 13847}, {6460, 11001}, {6480, 8981}, {6481, 23273}, {6759, 9676}, {6781, 12968}, {7354, 9660}, {7391, 8280}, {7500, 8854}, {7667, 8855}, {7748, 12963}, {7969, 28146}, {8725, 35869}, {9677, 13352}, {9680, 17578}, {9821, 35867}, {10533, 22802}, {10721, 10819}, {10734, 11835}, {10881, 13619}, {11474, 35481}, {12121, 12376}, {12163, 35837}, {12203, 35766}, {12240, 14855}, {12305, 38738}, {12515, 35853}, {12699, 35763}, {12702, 35843}, {12943, 35800}, {12953, 35802}, {12970, 34785}, {13883, 28172}, {13993, 15690}, {14241, 35409}, {14830, 35699}, {15682, 31412}, {15686, 32788}, {15712, 32790}, {16772, 35740}, {17702, 35826}, {18457, 18565}, {18481, 35642}, {18533, 35765}, {18538, 41948}, {18762, 33923}, {19116, 19710}, {20127, 35827}, {20427, 35865}, {21735, 32786}, {23698, 35824}, {26615, 33364}, {28168, 31439}, {29181, 35840}, {31454, 41954}, {34773, 35811}, {35730, 36836}, {35731, 36967}, {35776, 39568}, {35825, 38741}, {35857, 38753}, {35879, 38730}, {41947, 41949}

X(42267) = GIBERT(SQRT(3),2,-3) POINT

Barycentrics    a^2*S - 3*a^2*SA + 4*SB*SC : :

X(42267) lies on these lines: {2, 22644}, {3, 3366}, {4, 5420}, {6, 1657}, {20, 371}, {30, 372}, {35, 35800}, {36, 35802}, {74, 35834}, {376, 485}, {381, 6410}, {382, 1152}, {486, 3146}, {489, 32421}, {511, 39894}, {515, 35611}, {516, 35642}, {548, 590}, {550, 3070}, {615, 3627}, {640, 35948}, {962, 35811}, {1132, 6479}, {1151, 3534}, {1327, 10304}, {1328, 13939}, {1503, 35865}, {1588, 5059}, {1656, 6412}, {1885, 35765}, {2066, 4324}, {2067, 4316}, {2459, 35830}, {2777, 12376}, {2794, 35829}, {2829, 35883}, {3068, 17538}, {3069, 22615}, {3093, 37196}, {3311, 15681}, {3312, 17800}, {3522, 5418}, {3523, 23253}, {3528, 31412}, {3529, 6420}, {3543, 6485}, {3579, 35788}, {3830, 6450}, {3843, 6456}, {3850, 32790}, {3851, 6452}, {3853, 6487}, {4297, 35763}, {4299, 35768}, {4302, 35808}, {4333, 16232}, {5055, 6497}, {5073, 6398}, {5254, 41411}, {5412, 35471}, {5413, 18560}, {5414, 10483}, {5691, 35789}, {5840, 35857}, {6240, 11474}, {6284, 35769}, {6408, 13847}, {6409, 13665}, {6411, 8976}, {6418, 15685}, {6419, 15704}, {6425, 18512}, {6426, 13785}, {6429, 31487}, {6430, 13961}, {6453, 7583}, {6455, 13846}, {6459, 11001}, {6480, 23267}, {6481, 13966}, {6484, 31454}, {6781, 12963}, {7354, 35809}, {7391, 8281}, {7500, 8855}, {7667, 8854}, {7748, 12968}, {7968, 28146}, {8725, 35868}, {9680, 13886}, {9683, 33524}, {9821, 35866}, {10534, 22802}, {10721, 10820}, {10734, 11836}, {10880, 13619}, {11473, 35481}, {12121, 12375}, {12124, 21737}, {12163, 35836}, {12203, 35767}, {12239, 14855}, {12306, 38738}, {12515, 35852}, {12699, 35762}, {12702, 35842}, {12943, 35801}, {12953, 35803}, {12964, 34785}, {13925, 15690}, {13936, 28172}, {14226, 35409}, {14830, 35698}, {15686, 32787}, {15712, 32789}, {17702, 35827}, {18459, 18565}, {18481, 35641}, {18533, 35764}, {18538, 33923}, {18587, 35739}, {18762, 41947}, {19117, 19710}, {20127, 35826}, {20427, 35864}, {21735, 32785}, {23698, 35825}, {26616, 33365}, {29181, 35841}, {34773, 35810}, {35777, 39568}, {35824, 38741}, {35856, 38753}, {35878, 38730}, {41948, 41950}, {41953, 41970}

X(42268) = GIBERT(-SQRT(3),3,1) POINT

Barycentrics    a^2*S - a^2*SA - 6*SB*SC : :

X(42268) lies on these lines: {2, 12819}, {3, 22615}, {4, 372}, {5, 1151}, {6, 546}, {20, 10577}, {30, 5420}, {32, 13834}, {262, 32470}, {371, 3091}, {381, 485}, {382, 615}, {388, 35803}, {428, 18290}, {497, 35801}, {550, 8252}, {590, 3851}, {632, 6411}, {640, 12322}, {962, 35789}, {1132, 1327}, {1152, 3627}, {1588, 3832}, {1597, 8277}, {1656, 6455}, {1657, 6497}, {2043, 3392}, {2044, 3367}, {3068, 3855}, {3070, 3843}, {3090, 6200}, {3092, 23047}, {3093, 10151}, {3146, 6396}, {3317, 15682}, {3364, 16808}, {3389, 16809}, {3529, 32786}, {3543, 6485}, {3544, 6453}, {3545, 6459}, {3592, 3857}, {3628, 6409}, {3830, 6408}, {3845, 6432}, {3850, 13925}, {3853, 6430}, {3854, 8960}, {3858, 7583}, {3861, 6471}, {5056, 6486}, {5058, 18424}, {5066, 8981}, {5068, 9540}, {5072, 6221}, {5076, 6398}, {5079, 6449}, {5133, 18289}, {5225, 35809}, {5229, 35769}, {5480, 9974}, {5818, 35610}, {6250, 14853}, {6290, 22617}, {6412, 15704}, {6419, 23273}, {6420, 23249}, {6424, 13711}, {6425, 12811}, {6426, 12102}, {6431, 41991}, {6454, 13941}, {6468, 41989}, {6500, 13665}, {6623, 35764}, {6995, 8281}, {7378, 8855}, {7395, 9683}, {7503, 35777}, {7529, 9682}, {7582, 35822}, {7586, 23253}, {9677, 13434}, {9691, 19709}, {9812, 35611}, {10590, 35808}, {10591, 35768}, {10819, 36518}, {10820, 12295}, {11266, 18568}, {12602, 22591}, {13846, 38071}, {13847, 15687}, {13911, 38140}, {13961, 38335}, {13973, 22793}, {14233, 36655}, {14269, 32788}, {15081, 35826}, {17578, 35813}, {18440, 22596}, {18483, 35774}, {19053, 23269}, {19102, 39590}, {19117, 23046}, {19925, 35775}, {22587, 22588}, {22592, 35833}, {23267, 35770}, {32499, 39876}, {33355, 33356}, {33359, 33361}, {33457, 41491}, {35403, 41951}

X(42269) = GIBERT(SQRT(3),3,1) POINT

Barycentrics    a^2*S + a^2*SA + 6*SB*SC : :

X(42269) lies on these lines: {2, 12818}, {3, 22644}, {4, 371}, {5, 1152}, {6, 546}, {20, 10576}, {30, 5418}, {32, 13711}, {34, 9632}, {262, 32471}, {372, 3091}, {381, 486}, {382, 590}, {388, 35802}, {428, 18289}, {497, 35800}, {550, 8253}, {615, 3851}, {632, 6412}, {639, 12323}, {962, 35788}, {1131, 1328}, {1151, 3627}, {1587, 3832}, {1593, 9682}, {1597, 8276}, {1656, 6456}, {1657, 6496}, {2043, 3366}, {2044, 3391}, {3069, 3855}, {3071, 3843}, {3090, 6396}, {3092, 10151}, {3093, 23047}, {3146, 6200}, {3316, 15682}, {3365, 16808}, {3390, 16809}, {3529, 32785}, {3543, 6484}, {3544, 6454}, {3545, 6460}, {3583, 31472}, {3590, 9542}, {3594, 3857}, {3628, 6410}, {3830, 6407}, {3845, 6431}, {3850, 13993}, {3853, 6429}, {3858, 7584}, {3861, 6470}, {5056, 6487}, {5062, 18424}, {5066, 13966}, {5068, 10194}, {5072, 6398}, {5076, 6221}, {5079, 6450}, {5133, 18290}, {5225, 35808}, {5229, 35768}, {5480, 9975}, {5818, 35611}, {6251, 14853}, {6289, 22646}, {6411, 15704}, {6419, 23259}, {6420, 23267}, {6423, 13834}, {6425, 12102}, {6426, 12811}, {6432, 41991}, {6453, 8972}, {6469, 41989}, {6501, 13785}, {6623, 35765}, {6995, 8280}, {7378, 8854}, {7503, 35776}, {7581, 35823}, {7582, 31414}, {7585, 23263}, {7748, 31463}, {9541, 9692}, {9646, 12953}, {9647, 13898}, {9660, 13897}, {9661, 12943}, {9677, 14157}, {9683, 18534}, {9812, 35610}, {10590, 35809}, {10591, 35769}, {10819, 12295}, {10820, 36518}, {11265, 18568}, {12601, 22592}, {13846, 15687}, {13847, 38071}, {13903, 38335}, {13911, 22793}, {13973, 38140}, {14230, 36656}, {14269, 32787}, {15081, 35827}, {18440, 22625}, {18483, 35775}, {19054, 23275}, {19105, 39590}, {19116, 23046}, {19709, 41946}, {19925, 35774}, {22591, 35832}, {22618, 22619}, {23273, 35771}, {31408, 35803}, {32498, 39875}, {33354, 33357}, {33358, 33360}, {33456, 41490}, {35403, 41952}

X(42270) = GIBERT(-SQRT(3),3,2) POINT

Barycentrics    a^2*S - 2*a^2*SA - 6*SB*SC : :

X(42270) lies on these lines: {2, 6409}, {3, 22615}, {4, 615}, {5, 371}, {6, 3091}, {20, 8252}, {30, 10577}, {140, 35821}, {141, 32488}, {372, 546}, {381, 486}, {382, 5420}, {485, 3851}, {495, 35803}, {496, 35801}, {547, 6484}, {591, 12323}, {631, 23263}, {637, 23312}, {1131, 19053}, {1132, 3068}, {1151, 3090}, {1328, 5055}, {1352, 9975}, {1505, 18424}, {1587, 3855}, {1588, 3545}, {1656, 6449}, {1699, 13973}, {1991, 12221}, {2066, 3614}, {2067, 7173}, {3069, 3832}, {3146, 6410}, {3297, 10590}, {3298, 10591}, {3311, 5072}, {3365, 16809}, {3367, 14813}, {3390, 16808}, {3392, 14814}, {3525, 6411}, {3526, 6496}, {3529, 6412}, {3544, 3592}, {3589, 32489}, {3594, 13939}, {3627, 6396}, {3628, 6200}, {3817, 7969}, {3839, 6460}, {3843, 6560}, {3845, 13966}, {3850, 6564}, {3853, 6487}, {3854, 7586}, {3857, 6420}, {3858, 35786}, {3861, 35813}, {5056, 6429}, {5066, 7583}, {5067, 9541}, {5071, 9540}, {5073, 10194}, {5076, 6450}, {5079, 6221}, {5413, 23047}, {6251, 32494}, {6398, 22644}, {6419, 12811}, {6422, 31415}, {6425, 15022}, {6426, 13941}, {6432, 23267}, {6453, 12812}, {6501, 13665}, {6813, 14233}, {6871, 31473}, {7374, 26331}, {7388, 23311}, {7514, 35777}, {7581, 41106}, {7968, 19925}, {7989, 13911}, {8976, 19709}, {8982, 14235}, {9779, 19065}, {10146, 41962}, {10151, 11474}, {10272, 35835}, {10297, 10898}, {10516, 26468}, {10534, 41362}, {10592, 35808}, {10593, 35768}, {10880, 35487}, {11801, 12376}, {12240, 15030}, {12571, 13936}, {12819, 15720}, {13834, 30435}, {13983, 22682}, {15069, 26469}, {15765, 36970}, {18357, 35642}, {18358, 35841}, {18510, 41953}, {18585, 36969}, {19054, 41952}, {19116, 35822}, {22791, 35789}, {23046, 35814}, {23253, 41099}, {23302, 35732}, {32498, 37342}, {35018, 35255}, {35610, 38042}, {35611, 40273}, {35641, 38034}, {35811, 37705}, {35824, 38229}, {35840, 38136}, {35842, 38138}

X(42271) = GIBERT(SQRT(3),-3,2) POINT

Barycentrics    a^2*S + 2*a^2*SA - 6*SB*SC : :

X(42271) lies on these lines: {3, 22615}, {4, 590}, {6, 3146}, {20, 615}, {30, 372}, {140, 35787}, {371, 3627}, {376, 23263}, {381, 6455}, {382, 3070}, {485, 3830}, {486, 1657}, {546, 6200}, {548, 10577}, {550, 6565}, {1132, 13847}, {1152, 3529}, {1328, 13951}, {1587, 15682}, {1588, 6432}, {3068, 17578}, {3069, 5059}, {3090, 6411}, {3091, 6409}, {3364, 19106}, {3389, 19107}, {3522, 8252}, {3534, 5420}, {3543, 6459}, {3583, 9647}, {3585, 9660}, {3592, 23249}, {3594, 11541}, {3832, 8253}, {3843, 5418}, {3845, 6486}, {3853, 6564}, {3861, 35255}, {5072, 6451}, {5073, 6418}, {5076, 6221}, {5079, 6496}, {5893, 10533}, {6396, 15704}, {6408, 13785}, {6412, 17538}, {6425, 31412}, {6429, 8972}, {6431, 23267}, {6437, 13886}, {6453, 12102}, {6460, 6471}, {6479, 35814}, {6485, 13966}, {6492, 41952}, {6500, 15684}, {6811, 14239}, {7968, 28164}, {8976, 9681}, {8981, 15687}, {9542, 10139}, {9543, 41948}, {9646, 18513}, {9661, 18514}, {9974, 31670}, {10145, 35403}, {10248, 13902}, {11001, 13935}, {12084, 35777}, {12103, 18762}, {12819, 15688}, {13936, 28158}, {14230, 26441}, {19117, 35404}, {22728, 32470}, {23311, 35949}, {28178, 35611}, {28186, 35642}, {28212, 35843}, {31295, 31473}, {32497, 36711}, {33699, 35822}, {35763, 40273}, {35771, 35820}

X(42272) = GIBERT(SQRT(3),3,-2) POINT

Barycentrics    a^2*S - 2*a^2*SA + 6*SB*SC : :

X(42272) lies on these lines: {3, 22644}, {4, 615}, {6, 3146}, {20, 590}, {30, 371}, {140, 35786}, {372, 3627}, {376, 23253}, {381, 6456}, {382, 3071}, {485, 1657}, {486, 3830}, {546, 6396}, {548, 10576}, {550, 6564}, {1131, 13846}, {1151, 3529}, {1327, 8976}, {1587, 6431}, {1588, 15682}, {3068, 5059}, {3069, 17578}, {3090, 6412}, {3091, 6410}, {3365, 19106}, {3390, 19107}, {3522, 8253}, {3534, 5418}, {3543, 6460}, {3592, 11541}, {3594, 23259}, {3832, 8252}, {3843, 5420}, {3845, 6487}, {3853, 6565}, {3861, 35256}, {4316, 9661}, {4324, 9646}, {5072, 6452}, {5073, 6417}, {5076, 6398}, {5079, 6497}, {5893, 10534}, {6200, 15704}, {6407, 13665}, {6411, 17538}, {6430, 13941}, {6432, 23273}, {6438, 13939}, {6454, 12102}, {6459, 6470}, {6478, 35815}, {6484, 8981}, {6493, 41951}, {6501, 15684}, {6813, 14235}, {7969, 28164}, {8982, 14233}, {9540, 11001}, {9541, 23269}, {9975, 31670}, {10146, 35403}, {10248, 13959}, {12084, 35776}, {12103, 18538}, {12818, 15688}, {13883, 28158}, {13951, 41949}, {13966, 15687}, {19116, 35404}, {22728, 32471}, {23312, 35948}, {28178, 35610}, {28186, 35641}, {28212, 35842}, {32494, 36712}, {33699, 35823}, {35762, 40273}, {35770, 35821}

X(42273) = GIBERT(SQRT(3),3,2) POINT

Barycentrics    a^2*S + 2*a^2*SA + 6*SB*SC : :

X(42273) lies on these lines: {2, 6410}, {3, 22644}, {4, 590}, {5, 372}, {6, 3091}, {20, 8253}, {30, 10576}, {140, 35820}, {141, 32489}, {371, 546}, {381, 485}, {382, 5418}, {486, 3851}, {495, 35802}, {496, 35800}, {547, 6485}, {591, 12222}, {631, 23253}, {638, 23311}, {1131, 3069}, {1132, 19054}, {1152, 3090}, {1327, 5055}, {1352, 9974}, {1504, 18424}, {1587, 3545}, {1588, 3855}, {1656, 6450}, {1699, 13911}, {1991, 12322}, {3068, 3832}, {3146, 6409}, {3297, 10591}, {3298, 10590}, {3312, 5072}, {3364, 16809}, {3366, 14814}, {3389, 16808}, {3391, 14813}, {3525, 6412}, {3526, 6497}, {3529, 6411}, {3544, 3594}, {3583, 9646}, {3585, 9661}, {3589, 32488}, {3592, 13886}, {3614, 5414}, {3627, 6200}, {3628, 6396}, {3817, 7968}, {3839, 6459}, {3843, 6561}, {3845, 8981}, {3850, 6565}, {3853, 6486}, {3854, 7585}, {3857, 6419}, {3858, 8960}, {3861, 35812}, {5056, 6430}, {5066, 7584}, {5071, 13935}, {5073, 10195}, {5076, 6449}, {5079, 6398}, {5187, 31473}, {5412, 23047}, {6221, 22615}, {6250, 32497}, {6420, 12811}, {6421, 31415}, {6425, 8972}, {6426, 15022}, {6431, 23273}, {6454, 12812}, {6500, 13785}, {6502, 7173}, {6811, 14230}, {7000, 26330}, {7389, 23312}, {7514, 35776}, {7582, 41106}, {7586, 31414}, {7969, 19925}, {7989, 13973}, {8992, 22682}, {9543, 10139}, {9647, 18513}, {9660, 18514}, {9691, 14269}, {9779, 19066}, {10145, 41961}, {10151, 11473}, {10272, 35834}, {10297, 10897}, {10516, 26469}, {10533, 41362}, {10592, 35809}, {10593, 35769}, {10881, 35487}, {10896, 31472}, {11801, 12375}, {12239, 15030}, {12571, 13883}, {12818, 15720}, {13711, 30435}, {13951, 19709}, {14239, 26441}, {15069, 26468}, {15765, 36969}, {18357, 35641}, {18358, 35840}, {18512, 41954}, {18585, 36970}, {19053, 41951}, {19117, 35823}, {22791, 35788}, {23046, 35815}, {23263, 41099}, {23303, 35732}, {32499, 37343}, {35018, 35256}, {35610, 40273}, {35611, 38042}, {35642, 38034}, {35810, 37705}, {35825, 38229}, {35841, 38136}, {35843, 38138}

X(42274) = GIBERT(-SQRT(3),3,3) POINT

Barycentrics    a^2*S - 3*a^2*SA - 6*SB*SC : :

X(42274) lies on these lines: {2, 1328}, {3, 22615}, {4, 5420}, {5, 6}, {20, 35787}, {30, 6412}, {140, 6411}, {187, 37342}, {371, 3090}, {372, 3091}, {381, 615}, {382, 6452}, {492, 41483}, {546, 1152}, {547, 6437}, {574, 37343}, {590, 5055}, {631, 35821}, {632, 6409}, {639, 3619}, {640, 3620}, {642, 12322}, {1124, 3614}, {1132, 7486}, {1151, 3628}, {1327, 5066}, {1335, 7173}, {1587, 5068}, {1588, 5056}, {1656, 3071}, {1659, 8973}, {2041, 3392}, {2042, 3367}, {2043, 16809}, {2044, 16808}, {2045, 16967}, {2046, 16966}, {3055, 9600}, {3068, 5071}, {3069, 3545}, {3070, 3851}, {3085, 35803}, {3086, 35801}, {3297, 10592}, {3298, 10593}, {3311, 5079}, {3312, 5072}, {3316, 35815}, {3317, 3855}, {3366, 34754}, {3391, 34755}, {3523, 23263}, {3526, 6451}, {3530, 12819}, {3544, 6420}, {3592, 12812}, {3594, 12811}, {3627, 6410}, {3631, 23312}, {3817, 35774}, {3832, 6481}, {3843, 6446}, {3845, 6434}, {3850, 6438}, {3854, 23253}, {3857, 6426}, {3858, 6469}, {5020, 9682}, {5067, 6459}, {5070, 6445}, {5076, 6456}, {5603, 35789}, {5818, 35642}, {6119, 11291}, {6248, 32471}, {6251, 21736}, {6419, 15022}, {6430, 41991}, {6431, 13925}, {6435, 7582}, {6436, 7586}, {6440, 23046}, {6442, 11737}, {6468, 15699}, {6622, 35764}, {6997, 18290}, {7392, 8281}, {7393, 9683}, {7509, 35777}, {7539, 18289}, {7603, 31463}, {7687, 10820}, {8276, 11484}, {8277, 11479}, {8940, 22590}, {8981, 10195}, {9582, 19872}, {9632, 9817}, {9690, 15703}, {9780, 35610}, {9955, 13973}, {10109, 13846}, {10175, 35775}, {10588, 35808}, {10589, 35768}, {10590, 35769}, {10591, 35809}, {10595, 35843}, {10819, 12900}, {11272, 32470}, {11314, 23311}, {11480, 35738}, {12376, 15081}, {12571, 13975}, {13653, 23234}, {13665, 19709}, {13880, 32499}, {13886, 35771}, {14494, 33344}, {15066, 15233}, {17530, 31473}, {18510, 32787}, {18586, 23302}, {18587, 23303}, {32419, 32806}, {32813, 41491}, {35841, 40330}, {36450, 41121}, {36468, 41122}, {41950, 41951}

X(42275) = GIBERT(SQRT(3),-3,3) POINT

Barycentrics    a^2*S + 3*a^2*SA - 6*SB*SC : :

X(42275) lies on these lines: {3, 22615}, {4, 5418}, {5, 6411}, {6, 30}, {20, 486}, {34, 9631}, {187, 13834}, {371, 3146}, {372, 3529}, {376, 6565}, {381, 6451}, {382, 485}, {492, 13712}, {546, 6409}, {550, 5420}, {590, 3830}, {615, 1328}, {631, 35787}, {1131, 35815}, {1151, 3627}, {1152, 15704}, {1327, 3068}, {1588, 5059}, {1593, 9683}, {1657, 3071}, {2041, 19106}, {2042, 19107}, {2043, 10646}, {2044, 10645}, {3069, 6481}, {3070, 5073}, {3522, 10577}, {3528, 12819}, {3543, 6480}, {3845, 8253}, {3853, 6433}, {5072, 6496}, {5076, 6449}, {6395, 17800}, {6410, 12103}, {6419, 11541}, {6429, 13925}, {6434, 13966}, {6436, 7582}, {6437, 23251}, {6438, 7584}, {6441, 19117}, {6446, 13785}, {6453, 31412}, {6459, 23267}, {6468, 8981}, {6477, 35814}, {7391, 18289}, {7585, 15640}, {8252, 8703}, {8960, 23253}, {8976, 9690}, {9540, 17578}, {9647, 12953}, {9660, 12943}, {9676, 14157}, {9682, 18534}, {9778, 35789}, {9812, 35763}, {10819, 13202}, {11008, 32421}, {11413, 35777}, {12240, 14641}, {12244, 35835}, {13651, 22646}, {13665, 15684}, {13770, 32492}, {13846, 33699}, {13847, 19710}, {13911, 33697}, {14927, 35841}, {15683, 35823}, {15685, 32788}, {15686, 35256}, {15687, 35255}, {16808, 36455}, {16809, 36437}, {18510, 41946}, {20070, 35843}, {20080, 32419}, {22591, 22809}, {26361, 26615}, {28150, 35774}, {28164, 35775}

X(42276) = GIBERT(SQRT(3),3,-3) POINT

Barycentrics    a^2*S - 3*a^2*SA + 6*SB*SC : :

X(42276) lies on these lines: {3, 22644}, {4, 5420}, {5, 6412}, {6, 30}, {20, 485}, {187, 13711}, {371, 3529}, {372, 3146}, {376, 6564}, {381, 6452}, {382, 486}, {491, 13835}, {546, 6410}, {550, 5418}, {590, 1327}, {615, 3830}, {631, 35786}, {1132, 35814}, {1151, 15704}, {1152, 3627}, {1328, 3069}, {1587, 5059}, {1657, 3070}, {2041, 19107}, {2042, 19106}, {2043, 10645}, {2044, 10646}, {3068, 6480}, {3071, 5073}, {3522, 10576}, {3528, 12818}, {3543, 6481}, {3845, 8252}, {3853, 6434}, {4324, 31472}, {5072, 6497}, {5076, 6450}, {6199, 17800}, {6409, 12103}, {6420, 11541}, {6430, 13993}, {6433, 8981}, {6435, 7581}, {6437, 7583}, {6438, 23261}, {6442, 19116}, {6445, 13665}, {6460, 23273}, {6469, 13966}, {6476, 31414}, {7391, 18290}, {7586, 15640}, {8253, 8703}, {8718, 9677}, {8960, 23269}, {9541, 15683}, {9682, 21312}, {9690, 31454}, {9778, 35788}, {9812, 35762}, {10820, 13202}, {11008, 32419}, {11413, 35776}, {12239, 14641}, {12244, 35834}, {13651, 32495}, {13770, 22617}, {13785, 15684}, {13846, 19710}, {13847, 33699}, {13935, 17578}, {13973, 33697}, {14927, 35840}, {15685, 32787}, {15686, 35255}, {15687, 35256}, {16808, 36437}, {16809, 36455}, {17538, 31412}, {18512, 41945}, {20070, 35842}, {20080, 32421}, {22592, 22810}, {26362, 26616}, {28150, 35775}, {28164, 35774}

X(42277) = GIBERT(SQRT(3),3,3) POINT

Barycentrics    a^2*S + 3*a^2*SA + 6*SB*SC : :

X(42277) lies on these lines: {2, 1327}, {3, 22644}, {4, 5418}, {5, 6}, {20, 35786}, {30, 6411}, {115, 31463}, {140, 6412}, {187, 37343}, {371, 3091}, {372, 3090}, {381, 590}, {382, 6451}, {491, 41484}, {546, 1151}, {547, 6438}, {574, 37342}, {615, 5055}, {631, 35820}, {632, 6410}, {639, 3620}, {640, 3619}, {641, 12323}, {1124, 7173}, {1131, 7486}, {1152, 3628}, {1328, 5066}, {1335, 3614}, {1587, 5056}, {1588, 5068}, {1598, 9683}, {1656, 3070}, {2041, 3366}, {2042, 3391}, {2043, 16808}, {2044, 16809}, {2045, 16966}, {2046, 16967}, {3068, 3545}, {3069, 5071}, {3071, 3851}, {3085, 35802}, {3086, 35800}, {3297, 10593}, {3298, 10592}, {3311, 5072}, {3312, 5079}, {3316, 3855}, {3317, 35814}, {3367, 34754}, {3392, 34755}, {3523, 23253}, {3526, 6452}, {3530, 12818}, {3544, 6419}, {3592, 12811}, {3594, 12812}, {3627, 6409}, {3631, 23311}, {3814, 31484}, {3817, 35775}, {3832, 6480}, {3839, 9541}, {3843, 6445}, {3845, 6433}, {3850, 6437}, {3854, 23263}, {3857, 6425}, {3858, 6468}, {5067, 6460}, {5070, 6446}, {5076, 6455}, {5603, 35788}, {5818, 35641}, {6118, 11292}, {6248, 32470}, {6420, 15022}, {6429, 41991}, {6432, 13993}, {6435, 7585}, {6436, 7581}, {6439, 23046}, {6441, 11737}, {6469, 15699}, {6622, 35765}, {6997, 18289}, {7392, 8280}, {7509, 35776}, {7539, 18290}, {7687, 10819}, {7741, 31472}, {8276, 11479}, {8277, 11484}, {8944, 22621}, {9632, 37697}, {9646, 10896}, {9661, 10895}, {9676, 15033}, {9682, 9818}, {9690, 41963}, {9780, 35611}, {9955, 13911}, {10109, 13847}, {10175, 35774}, {10194, 13966}, {10588, 35809}, {10589, 35769}, {10590, 35768}, {10591, 35808}, {10595, 35842}, {10820, 12900}, {11272, 32471}, {11313, 23312}, {11481, 35738}, {12375, 15081}, {12571, 13912}, {12953, 31499}, {13773, 23234}, {13785, 19709}, {13921, 32498}, {13939, 35770}, {14494, 33345}, {15066, 15234}, {15703, 41946}, {17533, 31473}, {18512, 32788}, {18586, 23303}, {18587, 23302}, {31481, 39565}, {32421, 32805}, {32812, 41490}, {35840, 40330}, {36449, 41122}, {36467, 41121}, {41949, 41952}

X(42278) = GIBERT(0,-2,SQRT(3)) POINT

Barycentrics    3*Sqrt[3]*a^2*SA - 12*SB*SC : :

X(42278) lies on thesse lines: {2, 3}, {6, 42176}, {13, 8960}, {15, 23251}, {16, 23261}, {17, 6564}, {18, 6565}, {371, 5340}, {372, 5339}, {397, 3311}, {398, 3312}, {1151, 3391}, {1152, 3367}, {1587, 42213}, {1588, 42212}, {3070, 11485}, {3071, 11486}, {3364, 42263}, {3365, 42262}, {3389, 42265}, {3390, 42264}, {5318, 6221}, {5321, 6398}, {5334, 6395}, {5335, 6199}, {5349, 6450}, {5350, 6449}, {5365, 6408}, {5366, 6407}, {5611, 12602}, {5615, 12601}, {6200, 42094}, {6289, 33450}, {6290, 33449}, {6396, 42093}, {6411, 42178}, {6412, 42175}, {6445, 42134}, {6446, 42133}, {6451, 42102}, {6452, 42101}, {6455, 35740}, {6456, 42239}, {8976, 42128}, {10576, 16808}, {10577, 16809}, {11480, 42181}, {11481, 42180}, {13951, 42125}, {16628, 22882}, {16629, 22928}, {19106, 42266}, {19107, 42267}, {23249, 42222}, {23253, 42214}, {23259, 42223}, {23263, 42211}, {35820, 42157}, {35821, 42158}, {42115, 42197}, {42116, 42196}, {42167, 42183}, {42170, 42186}, {42247, 42252}, {42248, 42251}

X(42278) = reflection of X(42279) in X(5073)
X(42278) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 4, 42279), (5, 3851, 42279), (140, 3843, 42279), (381, 1656, 42279), (382, 1657, 42279), (550, 3830, 42279), (42176, 42177, 6)

X(42279) = GIBERT(0,2,SQRT(3)) POINT

Barycentrics    3*Sqrt[3]*a^2*SA + 12*SB*SC : :

X(42279) lies on thesse lines: {2, 3}, {6, 42175}, {14, 8960}, {15, 23261}, {16, 23251}, {17, 6565}, {18, 6564}, {371, 5339}, {372, 5340}, {397, 3312}, {398, 3311}, {1151, 3366}, {1152, 3392}, {1587, 42214}, {1588, 42211}, {3070, 11486}, {3071, 11485}, {3364, 42265}, {3365, 42264}, {3389, 42263}, {3390, 42262}, {5318, 6398}, {5321, 6221}, {5334, 6199}, {5335, 6395}, {5349, 6449}, {5350, 6450}, {5365, 6407}, {5366, 6408}, {5611, 12601}, {5615, 12602}, {6200, 42093}, {6289, 33448}, {6290, 33451}, {6396, 42094}, {6411, 42176}, {6412, 42177}, {6445, 42133}, {6446, 42134}, {6451, 42101}, {6452, 42102}, {6455, 42240}, {6456, 42241}, {8252, 35739}, {8976, 42125}, {10576, 16809}, {10577, 16808}, {11480, 42179}, {11481, 42182}, {13951, 42128}, {16628, 22883}, {16629, 22927}, {16964, 35731}, {19106, 42267}, {19107, 42266}, {23249, 42221}, {23253, 42213}, {23259, 42224}, {23263, 42212}, {35820, 42158}, {35821, 42157}, {42115, 42195}, {42116, 42198}, {42168, 42184}, {42169, 42185}, {42246, 42253}, {42249, 42250}

X(42279) = reflection of X(42278) in X(5073)
X(42279) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 4, 42278), (5, 3851, 42278), (140, 3843, 42278), (381, 1656, 42278), (382, 1657, 42278), (550, 3830, 42278), (42175, 42178, 6)

X(42280) = GIBERT(0,-3,SQRT(3)) POINT

Barycentrics    3*Sqrt[3]*a^2*SA - 18*SB*SC : :

X(42280) lies on thesse lines: {2, 3}, {6, 42184}, {15, 42181}, {16, 42180}, {61, 3070}, {62, 3071}, {371, 5318}, {372, 5321}, {397, 6419}, {398, 6420}, {485, 42162}, {486, 42159}, {590, 35730}, {1151, 42094}, {1152, 42093}, {3311, 5335}, {3312, 5334}, {3364, 19106}, {3365, 16809}, {3367, 42259}, {3389, 16808}, {3390, 19107}, {3391, 42258}, {3592, 5340}, {3594, 5339}, {5237, 42235}, {5238, 42238}, {5349, 6454}, {5350, 6453}, {5365, 6448}, {5366, 6447}, {6200, 35740}, {6221, 42134}, {6250, 7684}, {6251, 7685}, {6396, 42101}, {6398, 42133}, {6409, 42174}, {6410, 42171}, {6411, 42186}, {6412, 42183}, {6425, 42230}, {6426, 42227}, {6449, 42206}, {6450, 42203}, {6560, 42160}, {6561, 42161}, {6564, 42166}, {6565, 42163}, {10645, 42182}, {10646, 42179}, {11480, 42190}, {11481, 42187}, {11485, 23249}, {11486, 23259}, {18538, 42138}, {18581, 42268}, {18582, 42269}, {18762, 42135}, {22236, 23251}, {22238, 23261}, {22615, 42086}, {22644, 42085}, {31412, 42128}, {34560, 38042}, {35820, 42164}, {35821, 42165}, {36836, 42257}, {36843, 42254}, {42103, 42274}, {42104, 42276}, {42105, 42275}, {42106, 42277}, {42115, 42217}, {42116, 42220}, {42136, 42226}, {42137, 42225}, {42168, 42178}, {42169, 42175}

X(42280) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 4, 42281), (5, 546, 42281), (20, 5076, 42281), (381, 3091, 42281), (382, 3146, 42281), (550, 12102, 42281), (42184, 42185, 6)

X(42281) = GIBERT(0,3,SQRT(3)) POINT

Barycentrics    3*Sqrt[3]*a^2*SA + 18*SB*SC : :

X(42281) lies on thesse lines: {2, 3}, {6, 42183}, {15, 42179}, {16, 42182}, {61, 3071}, {62, 3070}, {371, 5321}, {372, 5318}, {397, 6420}, {398, 6419}, {485, 42159}, {486, 42162}, {1151, 42093}, {1152, 42094}, {3311, 5334}, {3312, 5335}, {3364, 16809}, {3365, 19106}, {3366, 42258}, {3389, 19107}, {3390, 16808}, {3392, 42259}, {3592, 5339}, {3594, 5340}, {5237, 42237}, {5238, 42236}, {5349, 6453}, {5350, 6454}, {5365, 6447}, {5366, 6448}, {5479, 35742}, {6200, 42101}, {6221, 42133}, {6250, 7685}, {6251, 7684}, {6396, 42102}, {6398, 42134}, {6409, 42172}, {6410, 42173}, {6411, 42184}, {6412, 42185}, {6425, 42228}, {6426, 42229}, {6449, 42204}, {6450, 42205}, {6560, 42161}, {6561, 42160}, {6564, 42163}, {6565, 42166}, {10645, 42180}, {10646, 42181}, {11480, 42188}, {11481, 42189}, {11485, 23259}, {11486, 23249}, {16964, 35730}, {18538, 42135}, {18581, 42269}, {18582, 42268}, {18762, 42138}, {22236, 23261}, {22238, 23251}, {22615, 42085}, {22644, 42086}, {22795, 35747}, {22797, 35759}, {28178, 34560}, {31412, 42125}, {32789, 35733}, {35731, 36970}, {35820, 42165}, {35821, 42164}, {36836, 42255}, {36843, 42256}, {42103, 42277}, {42104, 42275}, {42105, 42276}, {42106, 42274}, {42115, 42219}, {42116, 42218}, {42136, 42225}, {42137, 42226}, {42167, 42177}, {42170, 42176}

X(42281) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (3, 4, 42280), (5, 546, 42280), (20, 5076, 42280), (381, 3091, 42280), (382, 3146, 42280), (550, 12102, 42280), (42183, 42186, 6), (42187, 42190, 6)

X(42282) = GIBERT(0,-SQRT(3),2) POINT

Barycentrics    6*a^2*SA - 6*Sqrt[3]*SB*SC : :

X(42282) lies on thesse lines: {2, 3}, {6, 42192}, {15, 23249}, {16, 23259}, {61, 1587}, {62, 1588}, {371, 5335}, {372, 5334}, {397, 3592}, {398, 3594}, {487, 622}, {488, 621}, {590, 42166}, {615, 42163}, {1151, 5318}, {1152, 5321}, {3070, 22236}, {3071, 22238}, {3311, 42200}, {3312, 42201}, {3364, 42086}, {3365, 18581}, {3367, 13935}, {3389, 18582}, {3390, 42085}, {3391, 9540}, {4301, 36458}, {4857, 36442}, {5237, 23263}, {5238, 23253}, {5270, 36443}, {5339, 6426}, {5340, 6425}, {5343, 6454}, {5344, 6453}, {5351, 42235}, {5352, 42238}, {5365, 42231}, {5366, 42234}, {5870, 33350}, {5871, 33351}, {6200, 42134}, {6221, 42209}, {6396, 42133}, {6398, 42208}, {6409, 35740}, {6410, 42093}, {6411, 42102}, {6412, 42101}, {6419, 42228}, {6420, 42229}, {6449, 42202}, {6450, 42199}, {6451, 42210}, {6452, 42207}, {6455, 42206}, {6456, 42203}, {9541, 42161}, {9671, 36459}, {10645, 42181}, {10646, 42180}, {11480, 42220}, {11481, 42217}, {11485, 23267}, {11486, 23273}, {11488, 31412}, {11542, 13886}, {11543, 13939}, {18435, 34553}, {19107, 35739}, {23251, 36836}, {23261, 36843}, {23302, 42273}, {23303, 42270}, {32785, 42142}, {32786, 42139}, {32789, 42110}, {32790, 42107}, {35742, 36962}, {42087, 42272}, {42088, 42271}, {42115, 42211}, {42116, 42214}, {42164, 42259}, {42165, 42258}, {42179, 42195}, {42182, 42198}

X(42282) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2, 3091, 35732), (3, 4, 35732), (5, 3090, 35732), (20, 3146, 35732), (376, 3627, 35732), (381, 3525, 35732), (382, 17538, 35732), (546, 631, 35732), (42192, 42193, 6)

X(42283) = GIBERT(-1,SQRT(3),0) POINT

Barycentrics    -(Sqrt[3]*a^2*S) + 6*Sqrt[3]*SB*SC : :

X(42283) lies on thesse lines: {2, 6411}, {3, 22615}, {4, 6}, {5, 6200}, {15, 42179}, {16, 42180}, {20, 6412}, {30, 615}, {61, 42182}, {62, 42181}, {115, 13807}, {140, 42266}, {187, 6251}, {371, 546}, {372, 3627}, {376, 8252}, {381, 590}, {382, 486}, {485, 3843}, {489, 23312}, {542, 26438}, {550, 10577}, {574, 36709}, {637, 3631}, {638, 3630}, {1132, 6460}, {1151, 3091}, {1152, 2672}, {1327, 18512}, {1328, 3830}, {1384, 13834}, {1656, 6451}, {1657, 5420}, {1991, 33457}, {2041, 42088}, {2042, 42087}, {2043, 23303}, {2044, 23302}, {2045, 42168}, {2046, 42170}, {3054, 6813}, {3055, 6811}, {3068, 3839}, {3069, 3543}, {3090, 6409}, {3297, 5229}, {3298, 5225}, {3311, 42269}, {3312, 5076}, {3367, 19106}, {3392, 19107}, {3529, 6410}, {3545, 6433}, {3592, 31412}, {3620, 12322}, {3818, 18539}, {3832, 6437}, {3845, 6564}, {3850, 6480}, {3851, 5418}, {3853, 7584}, {3855, 6468}, {3856, 35812}, {3857, 6453}, {3858, 8981}, {3859, 6476}, {3861, 7583}, {5024, 36711}, {5066, 35255}, {5072, 6449}, {5073, 6446}, {5079, 6455}, {5200, 31860}, {5412, 10151}, {6420, 12102}, {6426, 13939}, {6434, 13935}, {6435, 14893}, {6436, 19116}, {6439, 41106}, {6441, 7585}, {6454, 13993}, {6469, 13847}, {6477, 35404}, {6481, 13966}, {7388, 34573}, {7526, 35777}, {7741, 9647}, {7951, 9660}, {7968, 31673}, {7969, 18483}, {9600, 31415}, {9675, 18424}, {9681, 9690}, {10645, 14813}, {10646, 14814}, {11008, 12221}, {11294, 23311}, {11381, 12240}, {11473, 23047}, {11480, 35732}, {11481, 42217}, {11485, 42190}, {11486, 42189}, {11801, 35826}, {12323, 20080}, {13665, 14269}, {13846, 41099}, {13911, 18492}, {13973, 41869}, {14234, 14236}, {15171, 35801}, {15492, 31561}, {15684, 41951}, {15687, 35823}, {15765, 16809}, {16808, 18585}, {16814, 31562}, {18323, 18459}, {18357, 35610}, {18510, 38335}, {18581, 42184}, {18582, 42186}, {18586, 42085}, {18587, 42086}, {18990, 35803}, {22236, 42220}, {22238, 42219}, {22591, 22810}, {22596, 32492}, {22625, 32497}, {26617, 32812}, {28174, 35789}, {28186, 35762}, {28224, 35811}, {32494, 32498}, {34754, 42238}, {34755, 42237}, {35641, 40273}, {35738, 42136}, {35740, 42110}, {35763, 38034}, {35841, 39884}, {36657, 41410}, {41950, 41957}, {41952, 41955}, {41959, 41967}, {41961, 41965}, {42103, 42243}, {42104, 42242}, {42105, 42244}, {42106, 42245}, {42107, 42240}, {42108, 42239}, {42109, 42241}, {42111, 42172}, {42112, 42171}, {42113, 42173}, {42114, 42174}, {42115, 42197}, {42116, 42198}, {42143, 42176}, {42144, 42175}, {42145, 42177}, {42146, 42178}

X(42283) = {X(4),X(6)}-harmonic conjugate of X(42284)
X(42283) = {X(42187),X(42188)}-harmonic conjugate of X(3)
X(42283) = {X(42191),X(42192)}-harmonic conjugate of X(3)

X(42284) = GIBERT(1,SQRT(3),0) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*Sqrt[3]*SB*SC : :

X(42284) lies on thesse lines: {2, 6412}, {3, 22644}, {4, 6}, {5, 6396}, {15, 42181}, {16, 42182}, {20, 6411}, {30, 590}, {61, 42180}, {62, 42179}, {115, 13687}, {140, 42267}, {187, 6250}, {371, 3627}, {372, 546}, {376, 8253}, {381, 615}, {382, 485}, {486, 3843}, {490, 23311}, {542, 18539}, {550, 10576}, {574, 36714}, {591, 33456}, {637, 3630}, {638, 3631}, {1131, 6459}, {1151, 2671}, {1152, 3091}, {1327, 3830}, {1328, 18510}, {1384, 13711}, {1656, 6452}, {1657, 5418}, {2041, 42087}, {2042, 42088}, {2043, 23302}, {2044, 23303}, {2045, 42169}, {2046, 42167}, {3054, 6811}, {3055, 6813}, {3068, 3543}, {3069, 3839}, {3090, 6410}, {3297, 5225}, {3298, 5229}, {3311, 5076}, {3312, 42268}, {3366, 19106}, {3391, 19107}, {3529, 6409}, {3545, 6434}, {3620, 12323}, {3818, 26438}, {3832, 6438}, {3845, 6565}, {3850, 6481}, {3851, 5420}, {3853, 7583}, {3855, 6469}, {3856, 35813}, {3857, 6454}, {3858, 13966}, {3859, 6477}, {3861, 7584}, {4324, 31499}, {5024, 36712}, {5066, 35256}, {5072, 6450}, {5073, 6445}, {5079, 6456}, {5200, 41424}, {5210, 21736}, {5413, 10151}, {6419, 12102}, {6425, 13886}, {6433, 9540}, {6435, 19117}, {6436, 14893}, {6440, 41106}, {6441, 31414}, {6442, 7586}, {6453, 13925}, {6468, 9541}, {6476, 35404}, {6480, 8981}, {7389, 34573}, {7526, 35776}, {7968, 18483}, {7969, 31673}, {9661, 10483}, {9690, 15684}, {10645, 14814}, {10646, 14813}, {11008, 12222}, {11293, 23312}, {11381, 12239}, {11474, 23047}, {11480, 42220}, {11481, 35732}, {11485, 42188}, {11486, 42187}, {11801, 35827}, {12322, 20080}, {12953, 31472}, {13785, 14269}, {13847, 41099}, {13911, 41869}, {13973, 18492}, {14238, 14240}, {15171, 35800}, {15492, 31562}, {15687, 35822}, {15765, 16808}, {16809, 18585}, {16814, 31561}, {17851, 41970}, {18323, 18457}, {18357, 35611}, {18512, 38335}, {18581, 42183}, {18582, 42185}, {18586, 42086}, {18587, 42085}, {18990, 35802}, {22236, 42218}, {22238, 42217}, {22592, 22809}, {22596, 32494}, {22625, 32495}, {26618, 32813}, {28174, 35788}, {28186, 35763}, {28224, 35810}, {31415, 36655}, {32497, 32499}, {34754, 42236}, {34755, 42235}, {35642, 40273}, {35738, 42137}, {35740, 42109}, {35762, 38034}, {35840, 39884}, {36658, 41411}, {41949, 41958}, {41951, 41956}, {41960, 41968}, {41962, 41966}, {42103, 42242}, {42104, 42243}, {42105, 42245}, {42106, 42244}, {42107, 42239}, {42108, 42240}, {42110, 42241}, {42111, 42171}, {42112, 42172}, {42113, 42174}, {42114, 42173}, {42115, 42195}, {42116, 42196}, {42143, 42175}, {42144, 42176}, {42145, 42178}, {42146, 42177}

X(42284) = {X(4),X(6)}-harmonic conjugate of X(42283)
X(42284) = {X(42189),X(42190)}-harmonic conjugate of X(3)
X(42284) = {X(42193),X(42194)}-harmonic conjugate of X(3)

leftri

Perpsectors associated with product triangles: X(42285)-X(42286)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, March 23, 2021.

Let T1 = A1B1C1 be a triangle, and let M1 be the matrix whose rows are the normalized barycentrics of A1, B1, C1, respectively.
Let T2 = A2B2C2 be a triangle, and let M2 be the matrix whose rows are the normalized barycentrics of A2, B2, C2, respectively.
Let M be the matrix sum M1 + M2. The triangle sum T1 + T2 is here defined as the triangle whose vertices are given by the rows of M1 + M2. (Note that triangle sum is non-associative and that there is no additive identity, hence no additive inverses.)

In this section "cevian(P)" means the cevian triangle of P, and "anticevian U" means the anticevian triangle of U.

cevian(P)+anticevian(U) is perspective to both cevian(P) and anticevian(U), and the perspector is the P-Ceva conjugate of U, given by

u (-u/p + v/q + w/r) : v (-v/q + w/r + u/p) w (-w/r + u/p + v/q).

If P = X(1), then cevian(P) + anticevian(U) is perspective to ABC for U on a certain cubic through X(1), X(10), and X(1125). If U = X(1), the perspector is X(42285); if U = X(1125), the perspector is X(551).

If P = X(6), then cevian(P) + anticevian(U) is perspective to ABC for U on a certain cubic through X(1), X(141), and X(3589). If U = X(141), the perspector is X(42286).

X(42285) = PERSPECTOR OF THESE TRIANGLES: ABC AND CEVIAN(X(1)) + ANTICEVIAN(X(10))

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

X(42285) lies on these lines: {1,16704}, {2,4674}, {8,31011}, {10,3702}, {19,37168}, {37,519}, {38,39697}, {45,996}, {65,392}, {82,40091}, {225,11105}, {261,40438}, {514,4364}, {517,4698}, {551,17450}, {595,2363}, {596,2292}, {756,4738}, {758,13476}, {759,1621}, {876,30580}, {897,5263}, {984,41683}, {986,6532}, {994,3877}, {1953,3986}, {2214,16685}, {2217,5248}, {2802,3842}, {3230,40747}, {3636,31503}, {3679,31035}, {3828,30818}, {3884,34434}, {3919,25501}, {4370,21822}, {4389,20569}, {4424,24589}, {4425,5620}, {4792,32013}, {6630,24864}, {6690,11734}, {9978,33337}, {14210,39712}, {17057,25378}, {18785,36480}, {18833,40089}, {27268,30116}, {29655,34895}, {31339,39708}

X(42286) = PERSPECTOR OF THESE TRIANGLES: ABC AND CEVIAN(X(6)) + ANTICEVIAN(X(141))

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

X(42286) lies on these lines: {2,17413}, {39,524}, {69,31068}, {141,3266}, {373,468}, {523,4045}, {574,9516}, {597,13410}, {599,31088}, {732,41440}, {2393,6683}, {2854,10007}, {4062,21035}, {5967,8546}, {6329,31506}, {6664,23642}, {7790,40826}, {7919,40429}, {8041,36792}, {8542,15482}, {9019,27375}, {9045,32450}, {15464,17430}, {20582,30749}, {20859,25322}, {25334,33798}, {27376,37778}

leftri

Polarologic and Polelogic centers & T-isogonal-axes: X(42287)-X(42410)

rightri

This preamble and centers X(42287)-X(42410) were contributed by César Eliud Lozada, March 24, 2021.

Let T ' = A1B1C1 and T" = A2B2C2 be two distinct scalene triangles. Let (a'), (b'), (c') be the trilinear polars of the vertices of T ' with respect to T" and let A', B', C' be the trilinear poles of the sidelines of T ' with respect to T". Inversely, let (a"), (b"), (c") be the trilinear polars of the vertices of T" with respect to T ' and A", B", C" the trilinear poles of the sidelines of T" with respect to T '. Then:

  1.  If (a'), (b'), (c') concur in a point P' then (a"), (b"), (c") also concur in a point P".
  2.  If A', B', C' are collinear on a line ℓ' then A", B", C" are also collinear on a line ℓ".
  3.  If T ' and T" satisfy one of the properties (1) or (2), then they satisfy the other property.

T ' and T" have the concurrences in (1) and the collinearities in (2) if the isogonal conjugates of the vertices of T ' with respect to T" are collinear on a line 𝓂'. In this case, the isogonal conjugates of the vertices of T" with respect to T ' are also collinear on a line 𝓂".

Here, points P' and P" are named the polarologic centers of (T ' to T") and (T" to T ') and the tripoles of lines ℓ' and ℓ" are referred as the polelogic centers of (T ' to T") and (T" to T ') . Also, the lines 𝓂' and 𝓂" are introduced as the T-isogonal-axes of (T ' wrt T") and (T" wrt T ').

The appearance of (T, [i, j], [m, n]) in the following list means that triangles ABC and T have polarologic centers X(i), X(j) and polelogic centers X(m), X(n):

(ABC-X3 reflections, [1350, 6], [42287, 69]), (1st anti-circumperp, [20477, 6], [30441, 670]), (anti-Honsberger, [182, 32], [42288, 83]), (anti-tangential-midarc, [42289, 1400], [42290, 7]), (anti-Ursa minor, [42291, 826], [42292, 83]), (anti-Wasat, [1510, 42293], [2963, 8795]), (Aries, [42294, 42295], [42296, 42297]), (9th Brocard, [37174, 2], [42298, 2052]), (circummedial, [183, 6], [42299, 308]), (circumnormal, [3, 6], [275, 95]), (circumorthic, [33971, 6], [42300, 8795]), (1st circumperp, [11495, 6], [42301, 190]), (2nd circumperp, [1001, 6], [42302, 86]), (circumsymmedial, [6, 6], [6, 6]), (circumtangential, [3, 6], [648, 99]), (inner-Conway, [30625, 1], [42303, 668]), (outer-Garcia, [3696, 37], [27475, 75]), (Garcia-reflection, [4106, 650], [42304, 1088]), (Gossard, [42305, 42306], [42307, 42308]), (Honsberger, [42309, 1], [42310, 42311]), (intangents, [42312, 657], [39956, 7]), (Johnson, [39530, 216], [42313, 264]), (3rd mixtilinear, [42314, 6], [42315, 269]), (4th mixtilinear, [42316, 6], [42317, 9]), (5th mixtilinear, [3243, 9], [42318, 7]), (1st Schiffler, [42319, 650], [42320, 42321]), (2nd Schiffler, [42322, 650], [42323, 42324]), (tangential-midarc, [--, 7707], [--, 7]), (2nd tangential-midarc, [--, 10495], [--, 7]), (Ursa-minor, [42325, 10581], [42326, 42311]), (Wasat, [42327, 523], [42328, 86])

The appearance of (T, [i, j], [m, n]) in the following list means that triangles ANTICOMPLEMENTARY and T have polarologic centers X(i), X(j) and polelogic centers X(m), X(n):

(anti-Euler, [42329, 264], [42330, 95]), (3rd anti-Euler, [1510, 42331], [42332, 42333]), (Aquila, [42334, 86], [42335, 1268]), (Bevan antipodal, [42336, 42337], [42338, 42339]), (excentral, [798, 523], [40433, 1268]), (Pelletier, [42340, 42341], [42342, 42343]), (Schroeter, [42344, 690], [42345, 99]), (Soddy, [3669, 3900], [1434, 32008]), (Stammler, [1510, 41298], [40393, 40410]), (tangential, [9494, 826], [42346, 10159]), (X-parabola-tangential, [42347, 33906], [42348, 42349]), (X3-ABC reflections, [42350, 95], [42351, 40410])

The appearance of (T, [i, j], [m, n]) in the following list means that triangles MEDIAL and T have polarologic centers X(i), X(j) and polelogic centers X(m), X(n):

(anti-Aquila, [15569, 3739], [39721, 7]), (Euler, [5480, 141], [42352, 253]), (2nd Euler, [42353, 141], [42354, 42355]), (3rd Euler, [42356, 141], [42357, 190]), (4th Euler, [3826, 141], [42358, 75]), (5th Euler, [3815, 141], [42359, 6]), (excenters-midpoints, [4394, 4885], [42360, 42361]), (extouch, [2321, 142], [646, 4569]), (Feuerbach, [5949, 141], [42362, 42363]), (2nd Hatzipolakis, [42364, --], [--, --]), (incentral, [1100, 3739], [662, 670]), (intouch, [10481, 10], [36838, 668]), (Lemoine, [42365, 20582], [42366, 42367]), (Macbeath, [42368, 140], [42369, 18831]), (orthic, [53, 141], [15352, 670]), (Steiner, [14588, 523], [42370, 892]), (symmedial, [5007, 3934], [827, 42371]), (Yff contact, [32094, 514], [42372, 4555])

The appearance of (T, [i, j], [m, n]) in the following list means that triangles ORTHIC and T have polarologic centers X(i), X(j) and polelogic centers X(m), X(n):

(anti-excenters-reflections, [36990, 6], [42373, 393]), (Euler, [5480, 53], [42374, 6]), (2nd Euler, [42353, 53], [42375, 42376]), (3rd Euler, [42356, 53], [--, --]), (4th Euler, [3826, 53], [--, --]), (5th Euler, [3815, 53], [42377, 34208]), (extouch, [42378, 42379], [42380, 42381]), (Feuerbach, [5949, 53], [--, --]), (2nd Hatzipolakis, [42382, 5101], [42383, 42384]), (incentral, [2646, 42385], [662, 15352]), (intouch, [42386, 42387], [42388, 42389]), (Lemoine, [42390, 42391], [42392, 42393]), (Macbeath, [42394, 428], [42395, 42396]), (Mandart-incircle, [42397, 42385], [--, --]), (medial, [141, 53], [670, 15352]), (Steiner, [42398, 42399], [--, --]), (symmedial, [13366, 42400], [933, 42401]), (Yff contact, [42402, 42403], [--, --])

The appearance of (T, i, j) in the following list means that the tripoles of the T-isogonal-axes of triangles ABC and T are X(i) and X(j):

(ABC-X3 reflections, 2, 2), (1st anti-circumperp, 2, 2), (anti-Honsberger, 3407, 76), (anti-tangential-midarc, 40420, 333), (anti-Ursa minor, 41676, 827), (anti-Wasat, 42404, 42405), (Aries, 42406, 42407), (9th Brocard, --, 6), (circummedial, 2, 2), (circumnormal, 2, 2), (circumorthic, 2, 2), (1st circumperp, 2, 2), (2nd circumperp, 2, 2), (circumsymmedial, 2, 2), (circumtangential, 2, 2), (inner-Conway, 32019, 1), (outer-Garcia, 32017, 81), (Garcia-reflection, 42408, 651), (Gossard, --, --), (Honsberger, 42409, 1), (intangents, 658, 658), (Johnson, 42410, 275), (3rd mixtilinear, 2, 2), (4th mixtilinear, 2, 2), (5th mixtilinear, 8056, 57), (1st Schiffler, --, 651), (2nd Schiffler, --, 651), (tangential-midarc, --, --), (2nd tangential-midarc, --, --), (Ursa minor, --, --), (Wasat, --, 110)

X(42287) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO ABC-X3 REFLECTIONS

Barycentrics    (-a^2+b^2+c^2)*(3*a^4-2*(b^2-c^2)*a^2-(b^2-c^2)*(b^2+3*c^2))*(3*a^4+2*(b^2-c^2)*a^2+(b^2-c^2)*(3*b^2+c^2)) : :
X(42287) = 2*X(6)+X(253) = X(69)-4*X(20208) = 4*X(182)-X(41374) = 2*X(1249)-5*X(3618) = 5*X(3618)-X(31887) = 7*X(3619)-10*X(20200)

The reciprocal polelogic center of these triangles is X(69)

X(42287) lies on the cubics K295, K677 and these lines: {2, 154}, {4, 6330}, {6, 253}, {69, 441}, {95, 3619}, {182, 41374}, {193, 35510}, {264, 1249}, {287, 34156}, {305, 37669}, {438, 35711}, {458, 10002}, {459, 34407}, {525, 2419}, {1441, 5749}, {1494, 1992}, {2373, 37643}, {6225, 26218}, {6337, 40708}, {6340, 12215}, {8797, 20204}, {11427, 18018}, {11433, 13575}, {14853, 15312}, {15594, 31360}, {15740, 33198}, {18019, 37645}, {18918, 37073}, {20563, 28708}, {30786, 36894}, {31886, 36889}, {37188, 42313}

X(42287) = reflection of X(31887) in X(1249)
X(42287) = isotomic conjugate of the polar conjugate of X(3424)
X(42287) = polar conjugate of X(10002)
X(42287) = barycentric product X(69)*X(3424)
X(42287) = barycentric quotient X(i)/X(j) for these (i, j): (3, 1350), (4, 10002), (69, 37668), (1073, 40813), (1503, 1529)
X(42287) = trilinear product X(63)*X(3424)
X(42287) = trilinear quotient X(i)/X(j) for these (i, j): (63, 1350), (92, 10002), (304, 37668)
X(42287) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(69)}} and {{A, B, C, X(3), X(5085)}}
X(42287) = Cevapoint of X(525) and X(12037)
X(42287) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 1350}, {48, 10002}, {204, 40813}, {1973, 37668}
X(42287) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 1350), (4, 10002), (69, 37668), (1073, 40813)

X(42288) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO ANTI-HONSBERGER

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

The reciprocal polelogic center of these triangles is X(83)

X(42288) lies on these lines: {3, 83}, {98, 32085}, {184, 251}, {228, 18098}, {733, 17970}, {878, 18105}, {5171, 26224}, {10547, 39674}, {38834, 40319}

X(42288) = complement of the anticomplementary conjugate of X(32451)
X(42288) = isogonal conjugate of X(14994)
X(42288) = barycentric product X(i)*X(j) for these {i, j}: {6, 42299}, {51, 39283}, {82, 2186}, {83, 263}, {251, 262}
X(42288) = barycentric quotient X(i)/X(j) for these (i, j): (32, 14096), (82, 3403), (83, 20023), (251, 183), (262, 8024), (263, 141)
X(42288) = trilinear product X(i)*X(j) for these {i, j}: {31, 42299}, {82, 263}, {83, 3402}, {251, 2186}, {2179, 39283}
X(42288) = trilinear quotient X(i)/X(j) for these (i, j): (31, 14096), (82, 183), (83, 3403), (262, 1930), (263, 38), (2186, 141)
X(42288) = trilinear pole of the line {3049, 18105}
X(42288) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(7786)}} and {{A, B, C, X(3), X(25)}}
X(42288) = X(263)-cross conjugate of-X(42299)
X(42288) = X(i)-isoconjugate-of-X(j) for these {i, j}: {38, 183}, {39, 3403}, {75, 14096}, {182, 1930}
X(42288) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (32, 14096), (82, 3403), (83, 20023), (251, 183)
X(42288) = X(2)-vertex conjugate of-X(83)

X(42289) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO ANTI-TANGENTIAL-MIDARC

Barycentrics    a*(a^2-(b+c)*a-2*b*c)*(b+c)*(a-b+c)*(a+b-c) : :
X(42289) = 5*X(17609)-4*X(40636)

The reciprocal polarologic center of these triangles is X(1400)

X(42289) lies on these lines: {1, 7}, {8, 26125}, {10, 21931}, {12, 3214}, {31, 37543}, {34, 1839}, {37, 65}, {38, 5173}, {42, 226}, {43, 5226}, {45, 41712}, {56, 7225}, {57, 968}, {72, 21039}, {73, 3649}, {181, 28387}, {238, 8543}, {241, 15569}, {256, 17097}, {354, 7004}, {651, 4649}, {674, 1469}, {740, 1441}, {750, 37541}, {756, 41539}, {774, 942}, {916, 7352}, {934, 28842}, {940, 9316}, {941, 5665}, {954, 1253}, {976, 28081}, {984, 7672}, {1001, 1471}, {1064, 39542}, {1066, 6147}, {1100, 1456}, {1125, 17077}, {1193, 3485}, {1201, 30097}, {1214, 1962}, {1245, 28786}, {1254, 3931}, {1386, 34253}, {1402, 39793}, {1411, 32259}, {1423, 3340}, {1427, 37593}, {1450, 15950}, {1457, 17301}, {1463, 4864}, {1736, 30329}, {1738, 21617}, {1757, 29007}, {1818, 5880}, {1834, 21955}, {1836, 14547}, {1854, 2654}, {1892, 2356}, {1953, 3827}, {2310, 5728}, {2318, 3925}, {2340, 2550}, {2647, 17016}, {2650, 12709}, {2772, 5425}, {3293, 3947}, {3487, 37529}, {3660, 17450}, {3682, 12609}, {3685, 41246}, {3751, 8545}, {3812, 25067}, {3869, 24554}, {3870, 30699}, {3883, 17152}, {3886, 4441}, {3911, 30950}, {3993, 4552}, {4038, 17074}, {4365, 6358}, {4658, 34043}, {4848, 21803}, {4854, 6354}, {5249, 25941}, {5263, 10030}, {5311, 8270}, {5435, 26102}, {5714, 37699}, {6051, 37544}, {7073, 10118}, {7237, 15556}, {7613, 30275}, {7677, 16484}, {7986, 15934}, {9364, 37633}, {9791, 17950}, {10460, 40940}, {10474, 39780}, {11246, 22053}, {11375, 17278}, {11518, 18216}, {11526, 16496}, {11529, 33536}, {14942, 21453}, {17017, 34036}, {17080, 17592}, {17257, 19860}, {17609, 40636}, {18421, 30116}, {21454, 29814}, {24341, 41228}, {24789, 28253}, {25453, 28776}, {28082, 28089}, {28774, 29635}, {28780, 29633}, {29640, 37797}, {33128, 37695}, {40934, 41003}, {40958, 41011}

X(42289) = reflection of X(2293) in X(1)
X(42289) = barycentric product X(i)*X(j) for these {i, j}: {10, 5228}, {37, 40719}, {56, 4044}, {57, 3696}, {63, 1893}, {65, 4384}
X(42289) = barycentric quotient X(i)/X(j) for these (i, j): (42, 40779), (56, 42302), (65, 27475), (1001, 333), (1042, 42290), (1400, 1002)
X(42289) = trilinear product X(i)*X(j) for these {i, j}: {3, 1893}, {10, 1471}, {37, 5228}, {42, 40719}, {56, 3696}, {65, 1001}
X(42289) = trilinear quotient X(i)/X(j) for these (i, j): (37, 40779), (57, 42302), (65, 1002), (226, 27475), (1001, 21), (1400, 2279)
X(42289) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(1334)}} and {{A, B, C, X(7), X(37)}}
X(42289) = crosssum of X(1) and X(991)
X(42289) = X(1)-Beth conjugate of-X(1400)
X(42289) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 42302}, {21, 1002}, {81, 40779}, {284, 27475}
X(42289) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (42, 40779), (56, 42302), (65, 27475), (1001, 333)
X(42289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 7, 1458), (1, 1721, 7675), (1, 3671, 1042), (1, 4295, 4300), (1, 4298, 4322), (1, 4312, 991), (1, 4328, 4327), (1, 5018, 1442), (1, 7274, 4321), (1, 11552, 4337), (1, 12560, 2263), (65, 1284, 1400), (991, 4312, 3000), (1001, 5228, 1471), (3671, 4356, 3668), (4318, 7269, 1)

X(42290) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO ANTI-TANGENTIAL-MIDARC

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

The reciprocal polelogic center of these triangles is X(7)

X(42290) lies on these lines: {6, 1014}, {7, 37}, {25, 1396}, {42, 57}, {56, 1462}, {269, 1400}, {393, 37102}, {479, 1427}, {940, 7411}, {941, 980}, {1119, 1880}, {1423, 19604}, {2054, 2114}, {4334, 5223}, {4344, 37596}, {5228, 42314}, {5435, 16606}, {6610, 28658}, {7268, 16975}, {8693, 15728}, {14624, 31643}, {17245, 39983}, {34253, 37138}, {37650, 39798}, {37681, 39956}

X(42290) = isogonal conjugate of X(37658)
X(42290) = isotomic conjugate of X(28809)
X(42290) = barycentric product X(i)*X(j) for these {i, j}: {7, 1002}, {57, 27475}, {85, 2279}, {226, 42302}, {279, 40779}, {1418, 42310}
X(42290) = barycentric quotient X(i)/X(j) for these (i, j): (1, 3886), (7, 4441), (25, 28044), (56, 1001), (57, 4384), (65, 3696)
X(42290) = trilinear product X(i)*X(j) for these {i, j}: {7, 2279}, {56, 27475}, {57, 1002}, {65, 42302}, {269, 40779}
X(42290) = trilinear quotient X(i)/X(j) for these (i, j): (2, 3886), (7, 4384), (19, 28044), (56, 2280), (57, 1001), (77, 23151)
X(42290) = trilinear pole of the line {512, 3669}
X(42290) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(5308)}} and {{A, B, C, X(2), X(6)}}
X(42290) = X(1469)-cross conjugate of-X(7)
X(42290) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3886}, {8, 2280}, {9, 1001}, {33, 23151}
X(42290) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 3886), (7, 4441), (25, 28044), (56, 1001)

X(42291) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO ANTI-URSA MINOR

Barycentrics    ((b^4+b^2*c^2+c^4)*a^4-b^4*c^4)*(b^2-c^2) : :
X(42291) = X(9491)-5*X(31279)

The reciprocal polarologic center of these triangles is X(826)

X(42291) lies on these lines: {2, 9494}, {141, 9005}, {512, 625}, {804, 34964}, {881, 7752}, {3934, 8711}, {6292, 9498}, {9491, 31279}, {30217, 39511}

X(42291) = complement of X(9494)
X(42291) = complementary conjugate of the complement of X(42371)
X(42291) = barycentric quotient X(523)/X(42292)
X(42291) = trilinear quotient X(1577)/X(42292)
X(42291) = X(i)-complementary conjugate of-X(j) for these (i, j): (75, 35971), (308, 16592), (561, 15449), (670, 16587)
X(42291) = X(163)-isoconjugate-of-X(42292)
X(42291) = X(523)-reciprocal conjugate of-X(42292)

X(42292) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO ANTI-URSA MINOR

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

The reciprocal polelogic center of these triangles is X(83)

X(42292) lies on these lines: {194, 40382}, {6374, 7786}

X(42292) = barycentric quotient X(523)/X(42291)
X(42292) = trilinear quotient X(1577)/X(42291)
X(42292) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(7786)}} and {{A, B, C, X(39), X(308)}}
X(42292) = X(163)-isoconjugate-of-X(42291)
X(42292) = X(523)-reciprocal conjugate of-X(42291)

X(42293) = POLAROLOGIC CENTER OF THESE TRIANGLES: ANTI-WASAT TO ABC

Barycentrics    a^4*(-a^2+b^2+c^2)^2*((b^2+c^2)*a^2-(b^2-c^2)^2)*(b^2-c^2) : :
Trilinears    cos B sec C csc^2 C - cos C sec B csc^2 B : :
Trilinears    sin^2 A cos A (cos^2 2B - cos^2 2C) : :

The reciprocal polarologic center of these triangles is X(1510)

X(42293) lies on these lines: {2, 42331}, {6, 23286}, {216, 6368}, {230, 231}, {577, 37084}, {3049, 23200}, {15450, 20975}

X(42293) is the intersection of the isogonal conjugate of the polar conjugate of the Lemoine axis (i.e., line X(3049)X(39201)), and the polar conjugate of the isogonal conjugate of the Lemoine axis (i.e., line X(230)X(231)). (Randy Hutson, June 30, 2021)

X(42293) = complement of X(42331)
X(42293) = isogonal conjugate of X(42405)
X(42293) = barycentric product X(i)*X(j) for these {i, j}: {3, 15451}, {5, 39201}, {6, 17434}, {51, 520}, {53, 32320}, {54, 34983}
X(42293) = barycentric quotient X(i)/X(j) for these (i, j): (32, 16813), (51, 6528), (130, 42331), (184, 18831), (216, 6331), (217, 648)
X(42293) = trilinear product X(i)*X(j) for these {i, j}: {31, 17434}, {48, 15451}, {51, 822}, {216, 810}, {217, 656}, {418, 661}
X(42293) = trilinear quotient X(i)/X(j) for these (i, j): (31, 16813), (48, 18831), (51, 823), (158, 42401), (216, 811), (217, 162)
X(42293) = crossdifference of every pair of points on line {X(3), X(95)}
X(42293) = crosspoint of X(i) and X(j) for these (i, j): {2, 1303}, {4, 42401}, {184, 14586}, {647, 39201}
X(42293) = crosssum of X(i) and X(j) for these (i, j): {264, 18314}, {648, 6528}, {850, 40684}
X(42293) = X(i)-Ceva conjugate of-X(j) for these (i, j): (2, 130), (6, 34980), (647, 15451)
X(42293) = X(i)-complementary conjugate of-X(j) for these (i, j): (31, 130), (1303, 2887)
X(42293) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 16813}, {92, 18831}, {95, 823}, {162, 276}
X(42293) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (32, 16813), (51, 6528), (130, 42331), (184, 18831)
X(42293) = pole wrt polar circle of line X(2)X(276)
X(42293) = perspector of hyperbola {{A,B,C,X(4),X(51)}}
X(42293) = perspector of ABC and orthocevian triangle of X(1303)
X(42293) = X(798)-of-orthic-triangle, if ABC is acute

X(42294) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO ARIES

Barycentrics    (a^16-6*(b^2+c^2)*a^14+4*(4*b^4+b^2*c^2+4*c^4)*a^12-2*(b^2+c^2)*(13*b^4-14*b^2*c^2+13*c^4)*a^10+6*(5*b^8+5*c^8+2*(b^4-5*b^2*c^2+c^4)*b^2*c^2)*a^8-2*(b^4-c^4)*(b^2-c^2)*(13*b^4+14*b^2*c^2+13*c^4)*a^6+4*(b^2-c^2)^2*(4*b^8+4*c^8+3*(b^2+c^2)^2*b^2*c^2)*a^4-6*(b^4-c^4)^3*(b^2-c^2)*a^2+(b^8+c^8+2*(4*b^4+3*b^2*c^2+4*c^4)*b^2*c^2)*(b^2-c^2)^4)*a^2 : :

The reciprocal polarologic center of these triangles is X(42295)

X(42294) lies on this line: {20, 394}

X(42294) = barycentric quotient X(110)/X(42296)
X(42294) = trilinear quotient X(662)/X(42296)
X(42294) = X(661)-isoconjugate-of-X(42296)
X(42294) = X(110)-reciprocal conjugate of-X(42296)

X(42295) = POLAROLOGIC CENTER OF THESE TRIANGLES: ARIES TO ABC

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

The reciprocal polarologic center of these triangles is X(42294)

X(42295) lies on these lines: {2, 6}, {3, 20859}, {22, 1691}, {25, 1501}, {32, 51}, {115, 11550}, {154, 14567}, {182, 1194}, {184, 1196}, {251, 5640}, {419, 3168}, {549, 39524}, {800, 19031}, {1495, 34481}, {1570, 3787}, {1627, 3060}, {1853, 39691}, {1899, 2450}, {1915, 1995}, {1974, 40146}, {2021, 41275}, {2052, 6531}, {2175, 21813}, {2207, 6524}, {2211, 3162}, {2422, 8029}, {2502, 8780}, {3053, 20977}, {3094, 7485}, {3155, 6423}, {3156, 6424}, {3167, 20976}, {3224, 33336}, {3291, 9306}, {3788, 4121}, {3917, 5028}, {4563, 35294}, {5012, 9465}, {5033, 22352}, {5052, 15004}, {6034, 31133}, {6353, 41363}, {6660, 38905}, {6800, 35006}, {7484, 8041}, {7592, 37446}, {8569, 11328}, {8586, 41394}, {8627, 9909}, {8770, 35259}, {10329, 39560}, {11060, 14583}, {11402, 40126}, {13366, 39764}, {13410, 30435}, {14713, 40947}, {16949, 33798}, {16951, 18906}, {18374, 40366}, {20998, 35264}, {21849, 41413}, {23291, 34137}

X(42295) = isogonal conjugate of X(42407)
X(42295) = polar conjugate of the isotomic conjugate of X(40947)
X(42295) = barycentric product X(i)*X(j) for these {i, j}: {3, 41762}, {4, 40947}, {6, 3767}, {19, 2083}, {25, 1899}, {31, 17871}
X(42295) = barycentric quotient X(i)/X(j) for these (i, j): (25, 34405), (110, 42297), (426, 4176), (1632, 670), (1899, 305), (2083, 304)
X(42295) = trilinear product X(i)*X(j) for these {i, j}: {19, 40947}, {25, 2083}, {31, 3767}, {32, 17871}, {48, 41762}, {560, 41760}
X(42295) = trilinear quotient X(i)/X(j) for these (i, j): (19, 34405), (426, 1102), (662, 42297), (1632, 799), (1899, 304), (2083, 69)
X(42295) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(3767)}} and {{A, B, C, X(25), X(325)}}
X(42295) = crossdifference of every pair of points on line {X(512), X(6333)}
X(42295) = crosspoint of X(6) and X(2207)
X(42295) = crosssum of X(2) and X(3926)
X(42295) = X(i)-Ceva conjugate of-X(j) for these (i, j): (2, 14713), (6, 39643), (83, 41761), (107, 669)
X(42295) = X(31)-complementary conjugate of-X(14713)
X(42295) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 34405}, {661, 42297}
X(42295) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 34405), (110, 42297), (426, 4176), (1632, 670)
X(42295) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 1184, 3051), (6, 1611, 394), (6, 1613, 1993), (6, 10601, 20965), (25, 40825, 1501), (394, 1611, 3231), (1196, 1692, 184), (1501, 3124, 25), (1627, 3060, 5017), (1627, 39024, 3060), (1691, 3981, 22), (5359, 5422, 6), (8576, 8577, 3148), (19031, 19034, 800)

X(42296) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO ARIES

Barycentrics    (a^16-2*(3*b^2-2*c^2)*a^14+2*(8*b^4+3*b^2*c^2-10*c^4)*a^12-2*(b^2-c^2)*(13*b^4+23*b^2*c^2+14*c^4)*a^10+2*(b^2-c^2)*(15*b^6+13*c^6+2*(7*b^2+11*c^2)*b^2*c^2)*a^8-2*(b^2-c^2)*(13*b^8+14*c^8+(7*b^4-7*b^2*c^2+5*c^4)*b^2*c^2)*a^6+2*(b^2-c^2)^3*(8*b^6+10*c^6+(25*b^2+21*c^2)*b^2*c^2)*a^4-2*(b^4-c^4)*(b^2-c^2)^2*(3*b^2+c^2)*(b^4+b^2*c^2+2*c^4)*a^2+(b^4+c^4)*(b^2-c^2)^6)*(a^2-c^2)*(a^16+2*(2*b^2-3*c^2)*a^14-2*(10*b^4-3*b^2*c^2-8*c^4)*a^12+2*(b^2-c^2)*(14*b^4+23*b^2*c^2+13*c^4)*a^10-2*(b^2-c^2)*(13*b^6+15*c^6+2*(11*b^2+7*c^2)*b^2*c^2)*a^8+2*(b^2-c^2)*(14*b^8+13*c^8+(5*b^4-7*b^2*c^2+7*c^4)*b^2*c^2)*a^6-2*(b^2-c^2)^3*(10*b^6+8*c^6+(21*b^2+25*c^2)*b^2*c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)^2*(b^2+3*c^2)*(2*b^4+b^2*c^2+c^4)*a^2+(b^4+c^4)*(b^2-c^2)^6)*(a^2-b^2) : :

The reciprocal polelogic center of these triangles is X(42297)

X(42296) lies on these lines: {}

X(42296) = barycentric quotient X(110)/X(42294)
X(42296) = trilinear quotient X(662)/X(42294)
X(42296) = X(661)-isoconjugate-of-X(42294)
X(42296) = X(110)-reciprocal conjugate of-X(42294)

X(42297) = POLELOGIC CENTER OF THESE TRIANGLES: ARIES TO ABC

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

The reciprocal polelogic center of these triangles is X(42296)

X(42297) lies on the circumcircle and these lines: {98, 305}, {111, 42407}, {112, 2396}, {670, 925}, {2715, 4563}, {3563, 34405}, {4609, 22456}, {14659, 37803}

X(42297) = isogonal conjugate of the circumtangential-isogonal conjugate of X(42297)
X(42297) = circumtangential-isogonal conjugate of the isogonal conjugate of X(42297)
X(42297) = barycentric product X(99)*X(42407)
X(42297) = barycentric quotient X(i)/X(j) for these (i, j): (99, 3767), (110, 42295), (648, 41762), (670, 41760), (799, 17871)
X(42297) = trilinear product X(662)*X(42407)
X(42297) = trilinear quotient X(i)/X(j) for these (i, j): (662, 42295), (670, 17871), (799, 3767), (811, 41762)
X(42297) = Collings transform of X(7887)
X(42297) = trilinear pole of the line {6, 6393}
X(42297) = intersection, other than A,B,C, of circumcircle and conic {{A, B, C, X(305), X(2396)}}
X(42297) = Cevapoint of X(523) and X(7887)
X(42297) = X(i)-cross conjugate of-X(j) for these (i, j): (315, 4590), (394, 34537)
X(42297) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 42295}, {669, 17871}, {798, 3767}, {810, 41762}
X(42297) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (99, 3767), (110, 42295), (648, 41762), (670, 41760)

X(42298) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO 9th BROCARD

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

The reciprocal polelogic center of these triangles is X(2052)

X(42298) lies on these lines: {193, 264}, {2052, 6353}, {14265, 16081}, {40814, 40819}

X(42298) = polar conjugate of X(1351)
X(42298) = barycentric product X(264)*X(7612)
X(42298) = barycentric quotient X(i)/X(j) for these (i, j): (4, 1351), (76, 10008), (264, 1007), (2052, 37174)
X(42298) = trilinear product X(92)*X(7612)
X(42298) = trilinear quotient X(i)/X(j) for these (i, j): (92, 1351), (561, 10008), (1969, 1007)
X(42298) = trilinear pole of the line {3566, 14618}
X(42298) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(193)}} and {{A, B, C, X(76), X(847)}}
X(42298) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 1351}, {560, 10008}, {1007, 9247}
X(42298) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 1351), (76, 10008), (264, 1007)

X(42299) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO CIRCUMMEDIAL

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

The reciprocal polelogic center of these triangles is X(308)

X(42299) lies on the Jerabek hyperbola and these lines: {3, 83}, {6, 32085}, {51, 290}, {54, 9418}, {66, 10550}, {69, 263}, {71, 18082}, {73, 18097}, {74, 32581}, {248, 251}, {695, 7745}, {3527, 39646}, {8795, 34854}, {14970, 36214}, {18092, 34817}, {26714, 39427}, {32451, 42359}, {40425, 41435}

X(42299) = isogonal conjugate of X(14096)
X(42299) = isotomic conjugate of X(14994)
X(42299) = polar conjugate of the complement of X(22240)
X(42299) = barycentric product X(i)*X(j) for these {i, j}: {5, 39283}, {76, 42288}, {83, 262}, {251, 327}, {263, 308}
X(42299) = barycentric quotient X(i)/X(j) for these (i, j): (83, 183), (251, 182), (262, 141), (263, 39), (308, 20023), (327, 8024)
X(42299) = trilinear product X(i)*X(j) for these {i, j}: {75, 42288}, {82, 262}, {83, 2186}, {263, 3112}, {308, 3402}
X(42299) = trilinear quotient X(i)/X(j) for these (i, j): (82, 182), (262, 38), (263, 1964), (308, 3403), (327, 1930)
X(42299) = trilinear pole of the line {647, 4108}
X(42299) = intersection, other than A,B,C, of conic {{A, B, C, X(2), X(11174)}} and Jerabek hyperbola
X(42299) = Cevapoint of X(i) and X(j) for these (i, j): {2, 32451}, {262, 263}
X(42299) = X(263)-cross conjugate of-X(42288)
X(42299) = X(i)-isoconjugate-of-X(j) for these {i, j}: {38, 182}, {183, 1964}, {458, 4020}
X(42299) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (83, 183), (251, 182), (262, 141), (263, 39)

X(42300) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO CIRCUMORTHIC

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

The reciprocal polelogic center of these triangles is X(8795)

X(42300) lies on these lines: {2, 34384}, {6, 95}, {25, 262}, {39, 276}, {54, 1976}, {97, 251}, {111, 4993}, {263, 9792}, {308, 36212}, {327, 2165}, {393, 8795}, {2395, 15412}, {7786, 34386}, {8576, 16037}, {8577, 16032}, {8770, 19188}, {11427, 37872}, {33631, 39286}, {34079, 39277}

X(42300) = polar conjugate of X(39530)
X(42300) = barycentric product X(i)*X(j) for these {i, j}: {54, 327}, {95, 262}, {141, 39283}, {263, 34384}, {275, 42313}
X(42300) = barycentric quotient X(i)/X(j) for these (i, j): (4, 39530), (54, 182), (95, 183), (262, 5), (263, 51), (275, 458)
X(42300) = trilinear product X(i)*X(j) for these {i, j}: {38, 39283}, {95, 2186}, {262, 2167}, {327, 2148}
X(42300) = trilinear quotient X(i)/X(j) for these (i, j): (92, 39530), (262, 1953), (263, 2179), (327, 14213)
X(42300) = trilinear pole of the line {512, 11674}
X(42300) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(37067)}}
X(42300) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 39530}, {182, 1953}, {183, 2179}
X(42300) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 39530), (54, 182), (95, 183), (262, 5)

X(42301) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO 1st CIRCUMPERP

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

The reciprocal polelogic center of these triangles is X(190)

X(42301) lies on this line: {4105, 4626}

X(42301) = barycentric product X(1)*X(42303)
X(42301) = barycentric quotient X(i)/X(j) for these (i, j): (100, 30625), (101, 11495)
X(42301) = trilinear product X(6)*X(42303)
X(42301) = trilinear quotient X(i)/X(j) for these (i, j): (100, 11495), (190, 30625)
X(42301) = trilinear pole of the line {165, 170}
X(42301) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(4626)}} and {{A, B, C, X(2), X(42357)}}
X(42301) = Cevapoint of X(1) and X(4105)
X(42301) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 11495}, {649, 30625}
X(42301) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (100, 30625), (101, 11495)

X(42302) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO 2nd CIRCUMPERP

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

The reciprocal polelogic center of these triangles is X(86)

X(42302) lies on these lines: {6, 1014}, {9, 86}, {55, 81}, {58, 2195}, {284, 757}, {333, 873}, {673, 1434}, {1019, 1024}, {1174, 1412}, {2160, 7291}, {2258, 2274}, {2319, 2669}, {4663, 7077}, {4833, 23351}, {15569, 40773}, {18166, 34820}, {33635, 40438}, {37657, 39981}, {40439, 42028}

X(42302) = isotomic conjugate of X(4044)
X(42302) = barycentric product X(i)*X(j) for these {i, j}: {81, 27475}, {86, 1002}, {274, 2279}, {333, 42290}, {1019, 32041}, {1434, 40779}
X(42302) = barycentric quotient X(i)/X(j) for these (i, j): (1, 3696), (21, 3886), (34, 1893), (56, 42289), (58, 1001), (81, 4384)
X(42302) = trilinear product X(i)*X(j) for these {i, j}: {21, 42290}, {58, 27475}, {81, 1002}, {86, 2279}, {1014, 40779}, {1019, 37138}
X(42302) = trilinear quotient X(i)/X(j) for these (i, j): (2, 3696), (21, 37658), (57, 42289), (58, 2280), (81, 1001), (86, 4384)
X(42302) = trilinear pole of the line {663, 1019}
X(42302) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(16831)}} and {{A, B, C, X(2), X(749)}}
X(42302) = Cevapoint of X(i) and X(j) for these (i, j): {1, 37657}, {1002, 2279}
X(42302) = crosssum of X(9) and X(25427)
X(42302) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3696}, {9, 42289}, {10, 2280}, {37, 1001}
X(42302) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 3696), (21, 3886), (34, 1893), (56, 42289)

X(42303) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO INNER-CONWAY

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

The reciprocal polelogic center of these triangles is X(668)

X(42303) lies on this line: {4130, 36838}

X(42303) = isotomic conjugate of the complement of X(4130)
X(42303) = barycentric product X(75)*X(42301)
X(42303) = barycentric quotient X(i)/X(j) for these (i, j): (100, 11495), (190, 30625)
X(42303) = trilinear product X(2)*X(42301)
X(42303) = trilinear quotient X(i)/X(j) for these (i, j): (190, 11495), (668, 30625)
X(42303) = trilinear pole of the line {144, 3059}
X(42303) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(36838)}} and {{A, B, C, X(344), X(2397)}}
X(42303) = X(i)-isoconjugate-of-X(j) for these {i, j}: {649, 11495}, {667, 30625}
X(42303) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (100, 11495), (190, 30625)

X(42304) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO GARCIA-REFLECTION

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

The reciprocal polelogic center of these triangles is X(1088)

X(42304) lies on these lines: {2, 27823}, {7, 3175}, {34, 4248}, {57, 3759}, {65, 145}, {226, 17234}, {1427, 5435}, {3644, 4032}, {9311, 24177}, {19604, 30568}, {31227, 31231}

X(42304) = isogonal conjugate of X(3217)
X(42304) = isotomic conjugate of X(30568)
X(42304) = barycentric product X(i)*X(j) for these {i, j}: {7, 34860}, {57, 40012}, {85, 39956}
X(42304) = barycentric quotient X(i)/X(j) for these (i, j): (1, 3913), (7, 3875), (34, 4186), (56, 3915), (57, 4383), (65, 3214)
X(42304) = trilinear product X(i)*X(j) for these {i, j}: {7, 39956}, {56, 40012}, {57, 34860}
X(42304) = trilinear quotient X(i)/X(j) for these (i, j): (2, 3913), (7, 4383), (56, 16946), (57, 3915), (85, 3875), (226, 3214)
X(42304) = trilinear pole of the line {3667, 4017}
X(42304) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(34791)}} and {{A, B, C, X(2), X(145)}}
X(42304) = X(i)-cross conjugate of-X(j) for these (i, j): (10, 7), (982, 1088)
X(42304) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3913}, {8, 16946}, {9, 3915}, {41, 3875}
X(42304) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 3913), (7, 3875), (34, 4186), (56, 3915)

X(42305) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO GOSSARD

Barycentrics    (2*a^16-4*(b^2+c^2)*a^14-2*(5*b^4-16*b^2*c^2+5*c^4)*a^12+4*(b^2+c^2)*(8*b^4-17*b^2*c^2+8*c^4)*a^10-(19*b^8+19*c^8+4*(13*b^4-36*b^2*c^2+13*c^4)*b^2*c^2)*a^8-8*(b^4-c^4)*(b^2-c^2)*(2*b^4-11*b^2*c^2+2*c^4)*a^6+4*(b^2-c^2)^2*(5*b^8+5*c^8+(b^4-21*b^2*c^2+c^4)*b^2*c^2)*a^4-4*(b^4-c^4)*(b^2-c^2)^3*(b^4+7*b^2*c^2+c^4)*a^2-(b^2-c^2)^4*(b^8+c^8-4*(b^4+3*b^2*c^2+c^4)*b^2*c^2))*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*(a^8-(b^2+c^2)*a^6-(2*b^2-c^2)*(b^2-2*c^2)*a^4+3*(b^4-c^4)*(b^2-c^2)*a^2-(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2)*(a^2-b^2+c^2)*(a^2-c^2)*(a^2+b^2-c^2)*(a^2-b^2) : :

The reciprocal polarologic center of these triangles is X(42306)

X(42305) lies on these lines: {402, 32750}, {4240, 16077}

X(42305) = midpoint of X(4240) and X(42308)
X(42305) = reflection of X(42306) in X(402)
X(42305) = X(402)-reciprocal conjugate of-X(42307)

X(42306) = POLAROLOGIC CENTER OF THESE TRIANGLES: GOSSARD TO ABC

Barycentrics    (b^2-c^2)^2*(-a^2+b^2+c^2)^2*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)^2*(a^8-(b^2+c^2)*a^6-(2*b^2-c^2)*(b^2-2*c^2)*a^4+3*(b^4-c^4)*(b^2-c^2)*a^2-(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2) : :
X(42306) = X(34767)-3*X(42307)

The reciprocal polarologic center of these triangles is X(42305)

X(42306) lies on these lines: {2, 23582}, {402, 32750}, {1650, 14401}, {3163, 11049}, {14920, 39081}, {16177, 38974}, {34767, 42307}

X(42306) = reflection of X(42305) in X(402)
X(42306) = complement of X(42308)
X(42306) = barycentric product X(402)*X(1650)
X(42306) = barycentric quotient X(402)/X(42308)
X(42306) = center of the circumconic {{ A, B, C, X(648), X(15351), X(39062), X(39352) }}
X(42306) = crosspoint of X(i) and X(j) for these (i, j): {2, 1650}, {402, 38240}
X(42306) = X(2)-Ceva conjugate of-X(402)
X(42306) = X(i)-complementary conjugate of-X(j) for these (i, j): (31, 402), (810, 9033), (1495, 23998), (1636, 4369)
X(42306) = X(402)-reciprocal conjugate of-X(42308)

X(42307) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO GOSSARD

Barycentrics    (b^2-c^2)*(-a^2+b^2+c^2)*(a^16+4*(b^2-2*c^2)*a^14-2*(10*b^4-8*b^2*c^2-5*c^4)*a^12+4*(4*b^6+4*c^6+9*(b^2-2*c^2)*b^2*c^2)*a^10+(19*b^8-38*c^8-4*(26*b^4-18*b^2*c^2-13*c^4)*b^2*c^2)*a^8-4*(b^2-c^2)*(8*b^8+4*c^8-(5*b^4+27*b^2*c^2-17*c^4)*b^2*c^2)*a^6+2*(b^2-c^2)^2*(5*b^8+5*c^8+(28*b^4-21*b^2*c^2-26*c^4)*b^2*c^2)*a^4+4*(b^2-c^2)^3*(b^8+2*c^8-(5*b^2-c^2)*(b^2+2*c^2)*b^2*c^2)*a^2-(b^2-c^2)^4*(2*b^8-c^8+2*(2*b^4-3*b^2*c^2-4*c^4)*b^2*c^2))*(a^16-4*(2*b^2-c^2)*a^14+2*(5*b^4+8*b^2*c^2-10*c^4)*a^12+4*(4*b^6+4*c^6-9*(2*b^2-c^2)*b^2*c^2)*a^10-(38*b^8-19*c^8-4*(13*b^4+18*b^2*c^2-26*c^4)*b^2*c^2)*a^8+4*(b^2-c^2)*(4*b^8+8*c^8+(17*b^4-27*b^2*c^2-5*c^4)*b^2*c^2)*a^6+2*(b^2-c^2)^2*(5*b^8+5*c^8-(26*b^4+21*b^2*c^2-28*c^4)*b^2*c^2)*a^4-4*(b^2-c^2)^3*(2*b^8+c^8+(2*b^2+c^2)*(b^2-5*c^2)*b^2*c^2)*a^2+(b^8-2*c^8+2*(4*b^4+3*b^2*c^2-2*c^4)*b^2*c^2)*(b^2-c^2)^4) : :
X(42307) = X(34767)+2*X(42306)

The reciprocal polelogic center of these triangles is X(42308)

X(42307) lies on this line: {34767, 42306}

X(42307) = barycentric quotient X(402)/X(42305)
X(42307) = X(402)-reciprocal conjugate of-X(42305)

X(42308) = POLELOGIC CENTER OF THESE TRIANGLES: GOSSARD TO ABC

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

The reciprocal polelogic center of these triangles is X(42307)

X(42308) lies on these lines: {2, 23582}, {69, 18020}, {287, 16080}, {648, 14401}, {1304, 22456}, {1494, 1651}, {1972, 14919}, {4240, 16077}, {14977, 15459}, {16076, 34582}, {32230, 36889}, {36831, 41208}

X(42308) = reflection of X(4240) in X(42305)
X(42308) = anticomplement of X(42306)
X(42308) = isotomic conjugate of X(1650)
X(42308) = barycentric product X(i)*X(j) for these {i, j}: {99, 15459}, {648, 16077}, {670, 32695}, {1304, 6331}, {1494, 23582}
X(42308) = barycentric quotient X(i)/X(j) for these (i, j): (30, 39008), (74, 3269), (99, 41077), (107, 1637), (110, 1636), (112, 9409)
X(42308) = trilinear product X(i)*X(j) for these {i, j}: {74, 23999}, {162, 16077}, {662, 15459}, {799, 32695}, {811, 1304}, {1494, 24000}
X(42308) = trilinear quotient X(i)/X(j) for these (i, j): (162, 9409), (648, 2631), (662, 1636), (799, 41077), (811, 9033), (823, 1637)
X(42308) = trilinear pole of the line {525, 648}
X(42308) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(69)}} and {{A, B, C, X(3), X(2430)}}
X(42308) = Cevapoint of X(i) and X(j) for these (i, j): {2, 4240}, {30, 648}, {107, 14165}
X(42308) = X(i)-cross conjugate of-X(j) for these (i, j): (5, 39290), (30, 648), (340, 6528), (402, 2)
X(42308) = X(i)-isoconjugate-of-X(j) for these {i, j}: {647, 2631}, {656, 9409}, {661, 1636}, {798, 41077}
X(42308) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (30, 39008), (74, 3269), (99, 41077), (107, 1637)

X(42309) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO HONSBERGER

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

The reciprocal polarologic center of these triangles is X(1)

X(42309) lies on these lines: {1, 7}, {9, 85}, {57, 658}, {142, 348}, {165, 9446}, {169, 1445}, {226, 17093}, {479, 21454}, {518, 9312}, {527, 17079}, {553, 7056}, {664, 3243}, {738, 1434}, {1001, 40719}, {1111, 15299}, {1565, 5805}, {1996, 3911}, {2346, 30494}, {2550, 9436}, {2809, 7672}, {2898, 11019}, {3306, 37780}, {3729, 40704}, {5219, 37757}, {5437, 31627}, {5686, 31994}, {5853, 6604}, {6063, 11679}, {6173, 17078}, {7177, 14377}, {7223, 8581}, {7676, 30502}, {7677, 38859}, {10389, 21453}, {10980, 31526}, {11246, 30623}, {17095, 20195}, {17181, 38150}, {17732, 41857}, {21609, 30568}, {21617, 34847}, {31507, 38250}, {33298, 38200}

X(42309) = midpoint of X(31565) and X(31566)
X(42309) = reflection of X(i) in X(j) for these (i, j): (7, 10481), (30625, 9)
X(42309) = barycentric product X(i)*X(j) for these {i, j}: {7, 40719}, {85, 5228}, {269, 4441}, {279, 4384}, {479, 3886}, {658, 4762}
X(42309) = barycentric quotient X(i)/X(j) for these (i, j): (57, 40779), (269, 1002), (279, 27475), (658, 32041), (738, 42290), (934, 37138)
X(42309) = trilinear product X(i)*X(j) for these {i, j}: {7, 5228}, {57, 40719}, {85, 1471}, {269, 4384}, {279, 1001}, {479, 37658}
X(42309) = trilinear quotient X(i)/X(j) for these (i, j): (7, 40779), (269, 2279), (279, 1002), (479, 42290), (658, 37138), (934, 8693)
X(42309) = homothetic center of Honsberger triangle and polar triangle of Adams circle
X(42309) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(673)}} and {{A, B, C, X(2), X(11038)}}
X(42309) = X(1434)-Beth conjugate of-X(269)
X(42309) = X(i)-isoconjugate-of-X(j) for these {i, j}: {55, 40779}, {200, 2279}, {220, 1002}, {480, 42290}
X(42309) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (57, 40779), (269, 1002), (279, 27475), (658, 32041)
X(42309) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (7, 3160, 11038), (7, 3188, 7675), (7, 7176, 4321), (7, 14189, 1)

X(42310) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO HONSBERGER

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

The reciprocal polelogic center of these triangles is X(42311)

X(42310) lies on these lines: {1, 31269}, {37, 31618}, {57, 21453}, {81, 6605}, {105, 2346}, {274, 3693}, {279, 27253}, {985, 40739}, {1219, 27109}, {9445, 13405}, {24600, 25430}, {32041, 34578}

X(42310) = barycentric quotient X(i)/X(j) for these (i, j): (1002, 354), (1170, 5228), (1174, 2280)
X(42310) = trilinear product X(1002)*X(32008)
X(42310) = trilinear quotient X(i)/X(j) for these (i, j): (1002, 1475), (1170, 1471)
X(42310) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(37), X(3693)}}
X(42310) = X(i)-isoconjugate-of-X(j) for these {i, j}: {354, 2280}, {1001, 1475}, {1212, 1471}
X(42310) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1002, 354), (1170, 5228), (1174, 2280)

X(42311) = POLELOGIC CENTER OF THESE TRIANGLES: HONSBERGER TO ABC

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

The reciprocal polelogic center of these triangles is X(42310)

X(42311) lies on the Feuerbach hyperbola and these lines: {1, 1088}, {7, 39789}, {8, 6063}, {9, 85}, {75, 42015}, {279, 27253}, {294, 1170}, {479, 5558}, {943, 40443}, {2346, 14189}, {3254, 4569}, {3296, 7056}, {6601, 6604}, {6606, 34894}, {9442, 10481}, {10390, 23062}, {17682, 33765}

X(42311) = isotomic conjugate of X(3059)
X(42311) = barycentric product X(i)*X(j) for these {i, j}: {7, 31618}, {75, 10509}, {85, 21453}, {1088, 32008}, {1170, 6063}
X(42311) = barycentric quotient X(i)/X(j) for these (i, j): (1, 8012), (7, 1212), (55, 8551), (56, 20229), (57, 2293), (65, 21795)
X(42311) = trilinear product X(i)*X(j) for these {i, j}: {2, 10509}, {7, 21453}, {57, 31618}, {85, 1170}, {273, 40443}, {279, 32008}
X(42311) = trilinear quotient X(i)/X(j) for these (i, j): (2, 8012), (7, 2293), (9, 8551), (57, 20229), (77, 22079), (85, 1212)
X(42311) = trilinear pole of the line {650, 24002}
X(42311) = intersection, other than A,B,C, of Feuerbach hyperbola and conic {{A, B, C, X(65), X(34855)}}
X(42311) = Cevapoint of X(i) and X(j) for these (i, j): {2, 30628}, {7, 1088}, {85, 6604}
X(42311) = X(i)-cross conjugate of-X(j) for these (i, j): (7, 21453), (514, 36838)
X(42311) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 8012}, {9, 20229}, {33, 22079}, {41, 1212}
X(42311) = trilinear product of vertices of Honsberger triangle
X(42311) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 8012), (7, 1212), (55, 8551), (56, 20229)
X(42311) = {X(85), X(32008)}-harmonic conjugate of X(31618)

X(42312) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO INTANGENTS

Barycentrics    a*(-a+b+c)*(a^2+(b+c)*a-2*b*c)*(b-c) : :
X(42312) = 3*X(663)-2*X(3737) = 4*X(3737)-3*X(17418) = X(20293)-3*X(27545) = 2*X(20316)-3*X(26144)

The reciprocal polarologic center of these triangles is X(657)

Let H be the {ABC,intangents}-circumconic (the hyperbola that is the isogonal conjugate of the Soddy line). Then X(42312) is the perspector of H wrt the intangents triangle. (Randy Hutson, June 30, 2021)

X(42312) lies on these lines: {1, 3667}, {33, 7649}, {35, 39225}, {55, 4057}, {200, 7628}, {521, 4895}, {522, 663}, {523, 4724}, {900, 1459}, {1040, 20315}, {1392, 23838}, {1769, 15313}, {1919, 2268}, {2269, 20979}, {2293, 29328}, {2310, 34949}, {2605, 4926}, {3063, 4526}, {3309, 4017}, {3601, 8656}, {3709, 4501}, {3716, 4397}, {3887, 21189}, {3907, 4811}, {4040, 28161}, {4139, 4498}, {4162, 4449}, {4375, 7220}, {4474, 4985}, {4786, 5287}, {4959, 35057}, {4962, 21173}, {7004, 14115}, {7190, 31605}, {7741, 39508}, {8058, 21119}, {17452, 17458}, {20293, 27545}, {20316, 26144}, {21348, 21834}

X(42312) = midpoint of X(4895) and X(6615)
X(42312) = reflection of X(i) in X(j) for these (i, j): (4397, 3716), (4474, 4985), (17418, 663)
X(42312) = reflection of X(43924) in the Nagel line
X(42312) = pole of the trilinear polar of X(1019) with respect to Feuerbach hyperbola
X(42312) = crossdifference of every pair of points on line {X(978), X(1400)}
X(42312) = crosspoint of X(i) and X(j) for these (i, j): {1, 3699}, {21, 31343}
X(42312) = X(i)-Ceva conjugate of-X(j) for these (i, j): (1, 17477), (1019, 650)
X(42312) = X(i)-isoconjugate-of-X(j) for these {i, j}: {65, 8690}, {101, 42304}, {109, 34860}, {651, 39956}
X(42312) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (284, 8690), (513, 42304), (522, 40012), (650, 34860)
X(42312) = barycentric product X(i)*X(j) for these {i, j}: {1, 20317}, {8, 4498}, {9, 4106}, {333, 4139}, {513, 30568}, {514, 3913}
X(42312) = barycentric quotient X(i)/X(j) for these (i, j): (284, 8690), (513, 42304), (522, 40012), (650, 34860), (663, 39956)
X(42312) = trilinear product X(i)*X(j) for these {i, j}: {6, 20317}, {9, 4498}, {21, 4139}, {55, 4106}, {513, 3913}, {514, 3217}
X(42312) = trilinear quotient X(i)/X(j) for these (i, j): (21, 8690), (514, 42304), (650, 39956)

X(42313) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO JOHNSON

Barycentrics    (-a^2+b^2+c^2)*((b^2+2*c^2)*a^2-b^4+b^2*c^2)*((2*b^2+c^2)*a^2+b^2*c^2-c^4) : :
Barycentrics    cos A sec(A - ω) : :
X(42313) = X(69)+2*X(216) = 4*X(141)-X(264) = X(1351)-4*X(10003) = 2*X(1352)+X(42329) = X(1972)+2*X(15595) = X(3164)+5*X(3620) = 7*X(3619)-4*X(14767) = 2*X(39530)-5*X(40330)

The reciprocal polelogic center of these triangles is X(264)

X(42313) lies on these lines: {2, 51}, {3, 287}, {6, 95}, {53, 141}, {69, 216}, {76, 18024}, {99, 30541}, {183, 40802}, {249, 7771}, {253, 3164}, {305, 343}, {394, 1799}, {401, 3098}, {458, 1350}, {599, 1494}, {1351, 10003}, {1352, 39682}, {1441, 3662}, {1503, 35937}, {1972, 15595}, {2351, 37068}, {2373, 15066}, {2710, 6037}, {3094, 40814}, {3314, 12037}, {3618, 36948}, {3619, 8797}, {3763, 40410}, {3818, 40853}, {5447, 28407}, {5562, 37186}, {6330, 11331}, {9289, 22416}, {11178, 40885}, {11257, 20021}, {11821, 32971}, {15644, 37337}, {17811, 40413}, {18018, 34138}, {18092, 34817}, {21356, 36889}, {30786, 37638}, {31884, 35941}, {33190, 39908}, {33257, 35240}, {33533, 40856}, {34507, 40867}, {36952, 41009}, {37174, 39530}, {37188, 42287}

X(42313) = isogonal conjugate of X(10311)
X(42313) = isotomic conjugate of X(458)
X(42313) = polar conjugate of X(33971)
X(42313) = polar conjugate of the anticomplement of X(42353)
X(42313) = barycentric product X(i)*X(j) for these {i, j}: {3, 327}, {69, 262}, {263, 305}, {304, 2186}, {343, 42300}
X(42313) = barycentric quotient X(i)/X(j) for these (i, j): (3, 182), (5, 39530), (69, 183), (184, 34396), (262, 4), (263, 25)
X(42313) = trilinear product X(i)*X(j) for these {i, j}: {48, 327}, {63, 262}, {69, 2186}, {263, 304}, {305, 3402}
X(42313) = trilinear quotient X(i)/X(j) for these (i, j): (48, 34396), (63, 182), (262, 19), (263, 1973), (304, 183), (305, 3403)
X(42313) = trilinear pole of the line {525, 684}
X(42313) = intersection, other than A,B,C, of conics {{A, B, C, X(3), X(76)}} and {{A, B, C, X(4), X(14853)}}
X(42313) = Cevapoint of X(6) and X(15577)
X(42313) = crosssum of X(1351) and X(11328)
X(42313) = X(327)-Ceva conjugate of-X(262)
X(42313) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 182}, {92, 34396}, {162, 3288}, {183, 1973}
X(42313) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 182), (5, 39530), (69, 183), (184, 34396)

X(42314) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO 3rd MIXTILINEAR

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

The reciprocal polarologic center of these triangles is X(6)

X(42314) lies on these lines: {1, 1418}, {6, 41}, {37, 4321}, {45, 8581}, {77, 38315}, {109, 1407}, {241, 3242}, {269, 1279}, {388, 17245}, {991, 999}, {1001, 4334}, {1037, 5096}, {1042, 1616}, {1106, 21059}, {1190, 23653}, {1191, 4306}, {1253, 5204}, {1319, 2263}, {2191, 4320}, {2293, 3304}, {2975, 25878}, {3361, 4255}, {3600, 4648}, {4327, 16777}, {4675, 12573}, {5228, 42290}, {5265, 37650}, {6180, 7677}, {6610, 7290}, {7271, 38316}, {7288, 17337}, {9316, 21000}, {20978, 32577}

X(42314) = barycentric product X(i)*X(j) for these {i, j}: {56, 29627}, {57, 3243}, {1407, 10005}
X(42314) = barycentric quotient X(56)/X(42318)
X(42314) = trilinear product X(i)*X(j) for these {i, j}: {56, 3243}, {604, 29627}, {1106, 10005}
X(42314) = trilinear quotient X(i)/X(j) for these (i, j): (57, 42318), (1407, 42315)
X(42314) = intersection, other than A,B,C, of conics {{A, B, C, X(6), X(1477)}} and {{A, B, C, X(41), X(3445)}}
X(42314) = X(21)-Beth conjugate of-X(11495)
X(42314) = X(i)-isoconjugate-of-X(j) for these {i, j}: {9, 42318}, {346, 42315}
X(42314) = X(56)-reciprocal conjugate of-X(42318)
X(42314) = X(6)-of-3rd-mixtilinear-triangle
X(42314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (56, 1458, 6), (269, 1420, 1279), (1407, 1617, 3052)

X(42315) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO 3rd MIXTILINEAR

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

The reciprocal polelogic center of these triangles is X(269)

X(42315) lies on these lines: {6, 19604}, {7, 1743}, {57, 1279}, {1014, 33628}, {3243, 5228}, {4936, 36807}, {8817, 30813}

X(42315) = barycentric product X(57)*X(42318)
X(42315) = barycentric quotient X(i)/X(j) for these (i, j): (1, 10005), (56, 3243), (57, 29627), (1106, 42314)
X(42315) = trilinear product X(56)*X(42318)
X(42315) = trilinear quotient X(i)/X(j) for these (i, j): (2, 10005), (7, 29627), (57, 3243), (1407, 42314)
X(42315) = trilinear pole of the line {3669, 8643}
X(42315) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(1279)}} and {{A, B, C, X(6), X(1743)}}
X(42315) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 10005}, {9, 3243}, {55, 29627}, {346, 42314}
X(42315) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 10005), (56, 3243), (57, 29627), (1106, 42314)

X(42316) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO 4th MIXTILINEAR

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

The reciprocal polarologic center of these triangles is X(6)

X(42316) lies on the cubic K297 and these lines: {1, 5022}, {2, 17747}, {3, 101}, {5, 17732}, {6, 31}, {9, 165}, {19, 7964}, {35, 218}, {36, 34867}, {37, 57}, {39, 1191}, {40, 1212}, {41, 5217}, {45, 1155}, {46, 16601}, {48, 6602}, {56, 1334}, {63, 3693}, {100, 37658}, {105, 6016}, {169, 3579}, {183, 190}, {198, 1615}, {213, 4255}, {219, 15931}, {221, 36074}, {292, 3445}, {346, 14829}, {354, 16777}, {381, 5134}, {386, 31461}, {405, 16549}, {474, 3294}, {517, 34522}, {573, 6244}, {584, 1174}, {595, 9605}, {840, 6017}, {956, 1018}, {958, 3501}, {995, 5024}, {999, 5030}, {1001, 17754}, {1015, 16486}, {1100, 10389}, {1104, 9593}, {1146, 5657}, {1190, 36744}, {1213, 26040}, {1282, 5220}, {1434, 27253}, {1447, 24352}, {1475, 3303}, {1500, 5021}, {1571, 16583}, {1593, 41320}, {1616, 2275}, {1617, 2256}, {1656, 24045}, {1697, 40133}, {1743, 31508}, {1788, 21049}, {1796, 11350}, {1826, 1889}, {2082, 37568}, {2176, 5013}, {2271, 31451}, {2277, 28272}, {2284, 22163}, {2291, 6014}, {2324, 10857}, {2345, 5273}, {2911, 37504}, {2975, 4513}, {3204, 38849}, {3208, 12513}, {3247, 10980}, {3295, 4253}, {3423, 4265}, {3553, 10383}, {3554, 10388}, {3576, 6603}, {3598, 4419}, {3684, 4421}, {3731, 17122}, {3748, 16884}, {3752, 9574}, {3913, 21384}, {3916, 17742}, {4191, 40586}, {4209, 32008}, {4383, 17756}, {4428, 16503}, {4520, 19861}, {4646, 31426}, {4713, 15271}, {4860, 16672}, {4884, 17314}, {5010, 5526}, {5124, 37519}, {5173, 21853}, {5179, 26446}, {5204, 9310}, {5221, 21808}, {5228, 40779}, {5276, 37540}, {5282, 14439}, {5314, 7123}, {5338, 37385}, {5687, 16552}, {5711, 25092}, {5781, 7411}, {5792, 37416}, {5819, 9778}, {7368, 8273}, {7522, 8804}, {7539, 24054}, {8568, 40998}, {9588, 23058}, {10164, 40869}, {10310, 32561}, {11114, 26074}, {12514, 25066}, {14321, 28602}, {15668, 25349}, {15815, 21008}, {15853, 37551}, {16370, 16788}, {16518, 21010}, {17095, 27129}, {17355, 32916}, {17451, 37567}, {17595, 26242}, {17796, 34879}, {21856, 37679}, {22080, 26867}, {27000, 31269}, {28535, 28911}, {30503, 34526}, {31859, 40859}, {40937, 41338}

X(42316) = isogonal conjugate of the isotomic conjugate of X(29616)
X(42316) = barycentric product X(i)*X(j) for these {i, j}: {1, 5223}, {6, 29616}, {220, 10004}
X(42316) = barycentric quotient X(101)/X(32040)
X(42316) = trilinear product X(i)*X(j) for these {i, j}: {6, 5223}, {31, 29616}, {1253, 10004}
X(42316) = trilinear quotient X(i)/X(j) for these (i, j): (55, 42317), (100, 32040), (692, 26716)
X(42316) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(35270)}} and {{A, B, C, X(6), X(103)}}
X(42316) = crossdifference of every pair of points on line {X(514), X(676)}
X(42316) = X(9)-Beth conjugate of-X(57)
X(42316) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 42317}, {513, 32040}, {693, 26716}
X(42316) = X(101)-reciprocal conjugate of X(32040)
X(42316) = X(6)-of-4th-mixtilinear-triangle
X(42316) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 41325, 17747), (3, 220, 3207), (3, 3730, 220), (6, 17735, 3052), (6, 21000, 1914), (9, 165, 910), (35, 218, 4258), (39, 14974, 1191), (55, 672, 6), (165, 2951, 15506), (198, 2272, 1615), (213, 31448, 4255), (672, 41423, 55), (3730, 24047, 3), (9574, 16970, 3752)

X(42317) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO 4th MIXTILINEAR

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

The reciprocal polelogic center of these triangles is X(9)

X(42317) lies on the Feuerbach hyperbola and these lines: {1, 3207}, {4, 1886}, {6, 3062}, {7, 1419}, {8, 23058}, {9, 41339}, {90, 16572}, {104, 26716}, {218, 38271}, {219, 42015}, {220, 4866}, {1000, 8074}, {1156, 16670}, {1699, 23972}, {2338, 19605}, {2346, 3247}, {2481, 16834}, {3158, 4876}, {3680, 3684}, {4900, 6603}, {16667, 31507}, {17745, 36599}

X(42317) = barycentric product X(650)*X(32040)
X(42317) = barycentric quotient X(i)/X(j) for these (i, j): (9, 29616), (41, 42316), (55, 5223), (57, 10004)
X(42317) = trilinear product X(i)*X(j) for these {i, j}: {522, 26716}, {663, 32040}
X(42317) = trilinear quotient X(i)/X(j) for these (i, j): (7, 10004), (8, 29616), (9, 5223), (55, 42316)
X(42317) = intersection, other than A,B,C, of Feuerbach hyperbola and conic {{A, B, C, X(6), X(1419)}}
X(42317) = X(i)-isoconjugate-of-X(j) for these {i, j}: {7, 42316}, {55, 10004}, {56, 29616}, {57, 5223}
X(42317) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (9, 29616), (41, 42316), (55, 5223), (57, 10004)

X(42318) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO 5th MIXTILINEAR

Barycentrics    (3*a^2-2*(2*b+c)*a+(b-c)*(b-3*c))*(3*a^2-2*(b+2*c)*a+(3*b-c)*(b-c)) : :
X(42318) = X(7)-4*X(4859) = 2*X(9)+X(4373) = 2*X(3161)-5*X(18230)

The reciprocal polelogic center of these triangles is X(7)

X(42318) lies on the circumhyperbola dual of Yff parabola and these lines: {2, 3158}, {7, 1743}, {8, 36807}, {9, 4373}, {75, 3161}, {142, 30712}, {144, 36606}, {335, 15590}, {390, 31183}, {673, 30332}, {903, 6172}, {1088, 5435}, {2550, 31189}, {4384, 10005}, {5222, 27475}, {5226, 21453}, {5838, 17278}, {5936, 16832}, {8056, 16078}, {12630, 29627}, {14189, 36620}, {17132, 36588}, {18228, 42361}, {20157, 42335}, {26007, 31188}, {28626, 29598}, {29628, 39721}, {31191, 40333}, {38186, 39704}

X(42318) = isotomic conjugate of X(29627)
X(42318) = barycentric product X(312)*X(42315)
X(42318) = barycentric quotient X(i)/X(j) for these (i, j): (1, 3243), (8, 10005), (56, 42314)
X(42318) = trilinear product X(8)*X(42315)
X(42318) = trilinear quotient X(i)/X(j) for these (i, j): (2, 3243), (57, 42314), (312, 10005)
X(42318) = trilinear pole of the line {514, 4162}
X(42318) = intersection, other than A,B,C, of conic {{A, B, C, X(1), X(38316)}} and circumhyperbola dual of Yff parabola
X(42318) = Cevapoint of X(i) and X(j) for these (i, j): {2, 24599}, {11, 14330}
X(42318) = X(390)-cross conjugate of-X(7)
X(42318) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3243}, {9, 42314}, {604, 10005}
X(42318) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 3243), (8, 10005), (56, 42314)

X(42319) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO 1st SCHIFFLER

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

The reciprocal polarologic center of these triangles is X(650)

X(42319) lies on these lines: {523, 4468}, {2788, 4106}, {3912, 29298}, {3935, 8702}

X(42320) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO 1st SCHIFFLER

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

The reciprocal polelogic center of these triangles is X(42321)

X(42320) lies on these lines: {}

X(42321) = POLELOGIC CENTER OF THESE TRIANGLES: 1st SCHIFFLER TO ABC

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

The reciprocal polelogic center of these triangles is X(42320)

X(42321) lies on these lines: {}

X(42322) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO 2nd SCHIFFLER

Barycentrics    a*(a^4-(4*b^2-3*b*c+4*c^2)*a^2+(b+c)*(4*b^2-5*b*c+4*c^2)*a-b^4-c^4)*(b-c) : :
X(42322) = 2*X(214)-3*X(30234)

The reciprocal polarologic center of these triangles is X(650)

X(42322) lies on these lines: {11, 4106}, {57, 35355}, {80, 28475}, {100, 4394}, {104, 30199}, {149, 4380}, {214, 30234}, {649, 38325}, {900, 4786}, {1155, 3309}, {3218, 13266}, {3667, 3911}, {3669, 3999}, {4905, 18201}, {9048, 10755}, {14947, 34583}, {17660, 17664}

X(42322) = midpoint of X(i) and X(j) for these {i, j}: {149, 4380}, {649, 38325}
X(42322) = reflection of X(i) in X(j) for these (i, j): (100, 4394), (4106, 11)

X(42323) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO 2nd SCHIFFLER

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

The reciprocal polelogic center of these triangles is X(42324)

X(42323) lies on these lines: {}

X(42324) = POLELOGIC CENTER OF THESE TRIANGLES: 2nd SCHIFFLER TO ABC

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

The reciprocal polelogic center of these triangles is X(42323)

X(42324) lies on these lines: {}

X(42325) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO URSA MINOR

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

The reciprocal polarologic center of these triangles is X(10581)

X(42325) lies on these lines: {7, 23599}, {21, 1019}, {30, 511}, {79, 885}, {442, 4129}, {663, 3960}, {667, 39476}, {764, 4879}, {905, 4794}, {1308, 4564}, {1734, 4724}, {2499, 21212}, {3126, 3647}, {3762, 21302}, {3777, 4775}, {3888, 4752}, {4040, 14838}, {4367, 6161}, {4729, 21385}, {4806, 6701}, {4807, 21677}, {4895, 23738}, {5216, 35637}, {7178, 21201}, {11281, 23814}, {14427, 21390}, {21127, 30295}, {38371, 39772}

X(42325) = barycentric product X(i)*X(j) for these {i, j}: {513, 17263}, {514, 3957}, {650, 32007}, {693, 17745}
X(42325) = barycentric quotient X(513)/X(42326)
X(42325) = trilinear product X(i)*X(j) for these {i, j}: {513, 3957}, {514, 17745}, {649, 17263}, {663, 32007}
X(42325) = trilinear quotient X(514)/X(42326)
X(42325) = crosssum of X(i) and X(j) for these (i, j): {55, 21127}, {513, 3748}, {661, 4068}
X(42325) = X(101)-isoconjugate-of-X(42326)
X(42325) = X(513)-reciprocal conjugate of-X(42326)
X(42325) = X(7)-Waw conjugate of-X(5083)
X(42325) = X(i)-Zayin conjugate of-X(j) for these (i, j): (2, 100), (9, 14722), (220, 101)

X(42326) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO URSA MINOR

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

The reciprocal polelogic center of these triangles is X(42311)

X(42326) lies on these lines: {1, 3826}, {2, 7264}, {10, 1280}, {35, 105}, {57, 24796}, {75, 32019}, {81, 3008}, {142, 17745}, {1002, 18398}, {1170, 5526}, {1212, 34578}, {1219, 19855}, {1224, 31238}, {1255, 26724}, {1698, 39959}, {3673, 42409}, {5222, 25417}, {5308, 27789}, {7178, 37626}, {16706, 32009}, {17095, 34018}, {24789, 25430}, {27304, 38247}, {33129, 40434}

X(42326) = isogonal conjugate of X(17745)
X(42326) = isotomic conjugate of X(17263)
X(42326) = barycentric quotient X(i)/X(j) for these (i, j): (1, 3957), (7, 32007), (513, 42325)
X(42326) = trilinear quotient X(i)/X(j) for these (i, j): (2, 3957), (85, 32007), (514, 42325)
X(42326) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(4), X(38200)}}
X(42326) = X(1174)-cross conjugate of-X(15909)
X(42326) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3957}, {41, 32007}, {101, 42325}
X(42326) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 3957), (7, 32007), (513, 42325)

X(42327) = POLAROLOGIC CENTER OF THESE TRIANGLES: ABC TO WASAT

Barycentrics    ((b^2+b*c+c^2)*a^2-b^2*c^2)*(b-c) : :
X(42327) = 3*X(2)+X(17217) = X(3768)-7*X(27138) = 3*X(4728)-X(20954) = 3*X(4927)-X(23743) = X(17458)+3*X(27485) = X(18080)+3*X(21606) = X(20906)-3*X(27485)

The reciprocal polarologic center of these triangles is X(523)

X(42327) lies on these lines: {2, 798}, {6, 23149}, {37, 22046}, {75, 21834}, {86, 20981}, {141, 27854}, {512, 17066}, {514, 4408}, {661, 7199}, {693, 27647}, {786, 3250}, {788, 20549}, {802, 6586}, {812, 14838}, {1001, 23400}, {1577, 4481}, {1919, 24601}, {1924, 29458}, {2484, 17215}, {2605, 4107}, {3572, 17234}, {3661, 21055}, {3716, 3834}, {3733, 15668}, {3739, 4132}, {3766, 21123}, {3768, 27106}, {3912, 21099}, {4079, 4374}, {4083, 25127}, {4106, 30094}, {4129, 28840}, {4406, 4502}, {4411, 21206}, {4728, 20954}, {4826, 17159}, {4927, 23743}, {4992, 9400}, {6003, 24220}, {9286, 21238}, {17458, 20906}, {18080, 21606}, {18137, 20953}, {18155, 28372}, {18196, 21763}, {20295, 27159}, {21211, 28217}, {21389, 24354}, {27855, 29985}

X(42327) = midpoint of X(i) and X(j) for these {i, j}: {75, 21834}, {661, 7199}, {798, 17217}, {1577, 4481}, {3250, 3261}, {3766, 21123}, {3835, 21191}, {4079, 4374}, {4406, 4502}, {4826, 17159}, {17458, 20906}
X(42327) = reflection of X(4411) in X(21206)
X(42327) = complement of X(798)
X(42327) = isotomic conjugate of the isogonal conjugate of X(21763)
X(42327) = polar conjugate of the isogonal conjugate of X(22387)
X(42327) = complementary conjugate of X(16592)
X(42327) = barycentric product X(i)*X(j) for these {i, j}: {76, 21763}, {141, 18106}, {264, 22387}, {274, 21836}, {321, 18196}, {514, 25264}
X(42327) = barycentric quotient X(514)/X(42328)
X(42327) = trilinear product X(i)*X(j) for these {i, j}: {10, 18196}, {38, 18106}, {75, 21763}, {86, 21836}, {92, 22387}, {512, 34022}
X(42327) = trilinear quotient X(693)/X(42328)
X(42327) = crossdifference of every pair of points on line {X(2176), X(20990)}
X(42327) = crosspoint of X(2) and X(4602)
X(42327) = crosssum of X(6) and X(1924)
X(42327) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 16592), (2, 115), (4, 6388), (6, 1084)
X(42327) = X(692)-isoconjugate-of-X(42328)
X(42327) = X(514)-reciprocal conjugate of-X(42328)
X(42327) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 17217, 798), (4369, 8062, 8060), (17458, 27485, 20906)

X(42328) = POLELOGIC CENTER OF THESE TRIANGLES: ABC TO WASAT

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

The reciprocal polelogic center of these triangles is X(86)

X(42328) lies on these lines: {75, 6379}, {192, 714}, {257, 4022}, {872, 19565}, {3121, 6385}, {3212, 17497}, {4687, 6376}, {20963, 33296}, {25264, 40433}

X(42328) = isotomic conjugate of X(25264)
X(42328) = barycentric quotient X(i)/X(j) for these (i, j): (274, 34022), (514, 42327), (649, 21763), (661, 21836), (1019, 18196), (1459, 22387)
X(42328) = trilinear quotient X(i)/X(j) for these (i, j): (310, 34022), (513, 21763), (523, 21836), (693, 42327), (905, 22387)
X(42328) = trilinear pole of the line {3835, 6005}
X(42328) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(1218)}} and {{A, B, C, X(2), X(749)}}
X(42328) = Cevapoint of X(514) and X(3121)
X(42328) = X(i)-isoconjugate-of-X(j) for these {i, j}: {100, 21763}, {110, 21836}, {692, 42327}
X(42328) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (274, 34022), (514, 42327), (649, 21763), (661, 21836)

X(42329) = POLAROLOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO ANTI-EULER

Barycentrics    2*(b^2+c^2)*a^10-(6*b^4+5*b^2*c^2+6*c^4)*a^8+2*(b^2+c^2)*(3*b^4-2*b^2*c^2+3*c^4)*a^6-2*(b^6-c^6)*(b^2-c^2)*a^4-(b^2-c^2)^4*b^2*c^2 : :
X(42329) = 3*X(381)-4*X(10003) = 6*X(549)-5*X(40329) = 5*X(631)-4*X(14767) = 2*X(1352)-3*X(42313)

The reciprocal polarologic center of these triangles is X(264)

X(42329) lies on these lines: {2, 26895}, {3, 95}, {4, 216}, {20, 185}, {22, 98}, {30, 30258}, {182, 401}, {184, 8613}, {262, 22240}, {297, 42353}, {324, 26874}, {381, 10003}, {418, 2052}, {436, 26880}, {542, 1972}, {549, 40329}, {577, 41204}, {631, 14767}, {933, 23606}, {1294, 30247}, {1352, 39682}, {1370, 9744}, {1629, 6641}, {1632, 15577}, {3522, 40896}, {3690, 7361}, {3937, 6360}, {6527, 10519}, {6638, 15466}, {6811, 41515}, {6813, 41516}, {8719, 34808}, {9747, 22655}, {11414, 39646}, {12131, 20885}, {14461, 37648}, {14570, 41716}, {15581, 35226}, {17538, 41374}, {18381, 23719}, {18667, 37521}, {22676, 38553}, {22712, 30737}

X(42329) = midpoint of X(20) and X(3164)
X(42329) = reflection of X(i) in X(j) for these (i, j): (4, 216), (264, 3)
X(42329) = anticomplement of X(39530)
X(42329) = polar conjugate of X(42374)
X(42329) = barycentric quotient X(4)/X(42374)
X(42329) = trilinear quotient X(92)/X(42374)
X(42329) = crossdifference of every pair of points on line {X(2451), X(42293)}
X(42329) = X(48)-isoconjugate-of-X(42374)
X(42329) = X(4)-reciprocal conjugate of-X(42374)
X(42329) = pole wrt polar circle of trilinear polar of X(42374) (line X(15451)X(16229))
X(42329) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (8982, 26441, 19467), (26907, 42400, 2)

X(42330) = POLELOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO ANTI-EULER

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

The reciprocal polelogic center of these triangles is X(95)

X(42330) lies on these lines: {2, 1629}, {5, 6330}, {69, 36794}, {95, 441}, {182, 41374}, {287, 8550}, {458, 1350}, {577, 11348}, {8797, 17907}, {31360, 41235}, {37665, 42373}

X(42330) = isotomic conjugate of the complement of X(458)
X(42330) = polar conjugate of X(5480)
X(42330) = barycentric product X(264)*X(5481)
X(42330) = barycentric quotient X(4)/X(5480)
X(42330) = trilinear product X(92)*X(5481)
X(42330) = trilinear quotient X(92)/X(5480)
X(42330) = trilinear pole of the line {525, 35474}
X(42330) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(69)}} and {{A, B, C, X(4), X(42373)}}
X(42330) = Cevapoint of X(2) and X(458)
X(42330) = X(48)-isoconjugate-of-X(5480)
X(42330) = X(4)-reciprocal conjugate of-X(5480)

X(42331) = POLAROLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-EULER TO ANTICOMPLEMENTARY

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

The reciprocal polarologic center of these triangles is X(1510)

X(42331) lies on these lines: {2, 42293}, {69, 15415}, {95, 37084}, {264, 6368}, {325, 523}

X(42331) = anticomplement of X(42293)
X(42331) = isotomic conjugate of X(1303)
X(42331) = anticomplementary conjugate of the anticomplement of X(42405)
X(42331) = barycentric product X(i)*X(j) for these {i, j}: {436, 3267}, {525, 9291}, {1954, 20948}
X(42331) = barycentric quotient X(i)/X(j) for these (i, j): (130, 42293), (436, 112), (850, 9290), (1577, 9251)
X(42331) = trilinear product X(i)*X(j) for these {i, j}: {436, 14208}, {525, 9252}, {656, 9291}, {850, 1954}
X(42331) = trilinear quotient X(i)/X(j) for these (i, j): (436, 32676), (850, 9251)
X(42331) = crosspoint of X(670) and X(42333)
X(42331) = X(823)-anticomplementary conjugate of-X(17035)
X(42331) = X(130)-cross conjugate of-X(2)
X(42331) = X(1576)-isoconjugate-of-X(9251)
X(42331) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (130, 42293), (436, 112), (850, 9290), (1577, 9251)

X(42332) = POLELOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO 3rd ANTI-EULER

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

The reciprocal polelogic center of these triangles is X(42333)

X(42332) lies on these lines: {251, 17005}, {2963, 7769}, {7930, 24861}, {7940, 34816}

X(42332) = isotomic conjugate of the complement of X(7769)
X(42332) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(95), X(18023)}}
X(42332) = Cevapoint of X(2) and X(7769)
X(42332) = X(1510)-cross conjugate of-X(670)

X(42333) = POLELOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-EULER TO ANTICOMPLEMENTARY

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

The reciprocal polelogic center of these triangles is X(42332)

X(42333) lies on these lines: {69, 18027}, {76, 3964}, {264, 394}, {276, 311}, {1502, 4176}, {5562, 8795}, {11444, 42355}

X(42333) = isotomic conjugate of X(389)
X(42333) = barycentric product X(i)*X(j) for these {i, j}: {76, 40448}, {305, 40402}
X(42333) = barycentric quotient X(i)/X(j) for these (i, j): (95, 19170), (311, 34836), (324, 6750)
X(42333) = trilinear product X(i)*X(j) for these {i, j}: {75, 40448}, {304, 40402}
X(42333) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(8795)}} and {{A, B, C, X(4), X(7395)}}
X(42333) = Cevapoint of X(i) and X(j) for these (i, j): {2, 5562}, {69, 311}
X(42333) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (95, 19170), (311, 34836), (324, 6750)

X(42334) = POLAROLOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO AQUILA

Barycentrics    a^3+(b+c)*a^2-(2*b^2+3*b*c+2*c^2)*a-(b+c)^3 : :
X(42334) = 3*X(8)+X(9791) = 2*X(8)+X(24697) = 4*X(1125)-5*X(31248) = 3*X(1654)-X(9791) = 5*X(1698)-4*X(6707) = 5*X(3617)-X(20090) = 3*X(3679)-2*X(4733) = 3*X(3679)-X(24342) = 2*X(9791)-3*X(24697) = 2*X(24325)-3*X(27483) = 2*X(25354)-3*X(31144)

The reciprocal polarologic center of these triangles is X(86)

X(42334) lies on these lines: {1, 1213}, {2, 5625}, {8, 192}, {10, 86}, {81, 8013}, {238, 3686}, {239, 3775}, {291, 4651}, {333, 8298}, {511, 4111}, {519, 25354}, {524, 3416}, {537, 6650}, {594, 1757}, {726, 5564}, {846, 4046}, {1100, 19856}, {1125, 31248}, {1211, 33135}, {1698, 4851}, {2796, 4669}, {2895, 21020}, {3120, 31143}, {3578, 4418}, {3617, 20090}, {3626, 17770}, {3634, 17317}, {3661, 20142}, {3696, 4690}, {3741, 4886}, {3770, 4647}, {3773, 6651}, {3821, 17271}, {3836, 17287}, {3842, 6542}, {3923, 17346}, {3932, 4478}, {3993, 16358}, {4042, 32778}, {4062, 5235}, {4357, 4716}, {4384, 33087}, {4425, 41816}, {4445, 29674}, {4527, 17261}, {4645, 4732}, {4650, 14552}, {4655, 17343}, {4668, 5223}, {4683, 17163}, {4709, 24723}, {4938, 37635}, {4967, 34379}, {5222, 25539}, {5271, 33084}, {5278, 33158}, {5739, 33096}, {9534, 24520}, {9780, 17373}, {10180, 26044}, {16830, 17772}, {17116, 17771}, {17162, 27081}, {17239, 29633}, {17258, 28522}, {17270, 32784}, {17272, 33149}, {17316, 31336}, {17344, 32857}, {17348, 29637}, {17778, 27798}, {20055, 31308}, {24325, 27483}, {29617, 32921}, {31330, 32861}, {32780, 32864}, {32782, 33132}

X(42334) = midpoint of X(8) and X(1654)
X(42334) = reflection of X(i) in X(j) for these (i, j): (1, 1213), (86, 10), (24342, 4733), (24697, 1654)
X(42334) = anticomplement of X(5625)
X(42334) = intersection, other than A,B,C, of conics {{A, B, C, X(79), X(33770)}} and {{A, B, C, X(256), X(40438)}}
X(42334) = X(8)-Beth conjugate of-X(86)
X(42334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (10, 319, 32846), (333, 21085, 33160), (2895, 21020, 33097), (3679, 24342, 4733), (3696, 4690, 33082), (3696, 33082, 24715), (5271, 33084, 33130)

X(42335) = POLELOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO AQUILA

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

The reciprocal polelogic center of these triangles is X(1268)

X(42335) lies on the circumhyperbola dual of Yff parabola and these lines: {2, 4023}, {6, 28626}, {7, 4364}, {75, 3247}, {86, 4416}, {190, 31336}, {310, 25507}, {335, 29578}, {594, 5308}, {673, 1125}, {1268, 3912}, {3696, 16826}, {3842, 5223}, {5263, 39721}, {5333, 39734}, {5550, 20135}, {14621, 29612}, {17277, 30598}, {17308, 28650}, {20133, 39746}, {20157, 42318}

X(42335) = isotomic conjugate of X(24603)
X(42335) = barycentric quotient X(i)/X(j) for these (i, j): (1, 15569), (10, 4733)
X(42335) = trilinear quotient X(i)/X(j) for these (i, j): (2, 15569), (321, 4733)
X(42335) = intersection, other than A,B,C, of conic {{A, B, C, X(1), X(16831)}} and circumhyperbola dual of Yff parabola
X(42335) = Cevapoint of X(2) and X(16826)
X(42335) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 15569}, {1333, 4733}
X(42335) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 15569), (10, 4733)

X(42336) = POLAROLOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO BEVAN ANTIPODAL

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

The reciprocal polarologic center of these triangles is X(42337)

X(42336) lies on these lines: {663, 855}, {664, 9296}

X(42336) = barycentric product X(i)*X(j) for these {i, j}: {57, 6363}, {649, 1122}, {1201, 3669}, {1357, 21362}, {1407, 6615}
X(42336) = barycentric quotient X(i)/X(j) for these (i, j): (604, 8706), (1122, 1978), (1201, 646), (1919, 1261)
X(42336) = trilinear product X(i)*X(j) for these {i, j}: {56, 6363}, {667, 1122}, {1106, 6615}, {1357, 23845}
X(42336) = trilinear quotient X(i)/X(j) for these (i, j): (56, 8706), (667, 1261), (1122, 668), (1201, 3699)
X(42336) = crossdifference of every pair of points on line {X(9), X(30693)}
X(42336) = crosspoint of X(664) and X(42338)
X(42336) = X(i)-isoconjugate-of-X(j) for these {i, j}: {8, 8706}, {644, 32017}, {646, 23617}, {668, 1261}
X(42336) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (604, 8706), (1122, 1978), (1201, 646)

X(42337) = POLAROLOGIC CENTER OF THESE TRIANGLES: BEVAN ANTIPODAL TO ANTICOMPLEMENTARY

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

The reciprocal polarologic center of these triangles is X(42336)

X(42337) lies on these lines: {11, 35065}, {30, 511}, {676, 21186}, {1043, 7253}, {1834, 23757}, {3704, 4086}, {4105, 40500}, {6615, 14284}

X(42337) = isotomic conjugate of X(6613)
X(42337) = barycentric product X(i)*X(j) for these {i, j}: {8, 21120}, {11, 25268}, {312, 6615}, {514, 6736}, {522, 3452}, {650, 20895}
X(42337) = barycentric quotient X(i)/X(j) for these (i, j): (346, 8706), (522, 40420), (650, 1476), (663, 3451), (1122, 4617), (1201, 1461)
X(42337) = trilinear product X(i)*X(j) for these {i, j}: {8, 6615}, {9, 21120}, {341, 6363}, {513, 6736}, {522, 3057}, {650, 3452}
X(42337) = trilinear quotient X(i)/X(j) for these (i, j): (341, 8706), (522, 1476), (650, 3451), (1122, 6614)
X(42337) = crossdifference of every pair of points on line {X(6), X(1604)}
X(42337) = crosspoint of X(i) and X(j) for these (i, j): {2, 6613}, {522, 4397}, {664, 42339}
X(42337) = X(1476)-anticomplementary conjugate of-X(33650)
X(42337) = X(i)-Ceva conjugate of-X(j) for these (i, j): (57, 5514), (312, 1146), (522, 6615)
X(42337) = X(1476)-complementary conjugate of-X(124)
X(42337) = X(i)-isoconjugate-of-X(j) for these {i, j}: {109, 1476}, {651, 3451}, {1106, 8706}, {1261, 6614}
X(42337) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (346, 8706), (522, 40420), (650, 1476), (663, 3451)

X(42338) = POLELOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO BEVAN ANTIPODAL

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

The reciprocal polelogic center of these triangles is X(42339)

X(42338) lies on these lines: {}

X(42338) = intersection, other than A,B,C, of conics {{A, B, C, X(56), X(57)}} and {{A, B, C, X(81), X(1120)}}

X(42339) = POLELOGIC CENTER OF THESE TRIANGLES: BEVAN ANTIPODAL TO ANTICOMPLEMENTARY

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

The reciprocal polelogic center of these triangles is X(42338)

X(42339) lies on these lines: {2, 34524}, {8, 1997}, {85, 30827}, {312, 20196}, {333, 5316}, {3452, 40420}, {7308, 30608}, {11814, 14942}, {31995, 38255}

X(42339) = isotomic conjugate of X(6692)
X(42339) = barycentric quotient X(1)/X(20323)
X(42339) = trilinear quotient X(2)/X(20323)
X(42339) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(8)}} and {{A, B, C, X(9), X(30827)}}
X(42339) = Cevapoint of X(2) and X(3452)
X(42339) = X(6)-isoconjugate-of-X(20323)
X(42339) = X(1)-reciprocal conjugate of-X(20323)

X(42340) = POLAROLOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO PELLETIER

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

The reciprocal polarologic center of these triangles is X(42341)

X(42340) lies on this line: {926, 2170}

X(42341) = POLAROLOGIC CENTER OF THESE TRIANGLES: PELLETIER TO ANTICOMPLEMENTARY

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

The reciprocal polarologic center of these triangles is X(42340)

X(42341) lies on these lines: {2, 30700}, {30, 511}, {38, 3310}, {63, 6139}, {200, 9511}, {210, 1638}, {354, 1639}, {668, 883}, {1015, 17435}, {2488, 4468}, {3681, 4453}, {3873, 30565}, {4014, 21139}, {4025, 4524}, {4147, 21195}, {4367, 21390}, {4449, 20980}, {4919, 21343}, {14430, 30691}, {21051, 40474}, {22086, 32912}

X(42341) = isotomic conjugate of X(14727)
X(42341) = barycentric product X(i)*X(j) for these {i, j}: {513, 40883}, {518, 4885}, {522, 6168}, {672, 20907}, {918, 1376}, {1026, 21139}
X(42341) = barycentric quotient X(i)/X(j) for these (i, j): (518, 30610), (663, 6169), (665, 9309), (918, 32023), (1376, 666), (2254, 9311)
X(42341) = trilinear product X(i)*X(j) for these {i, j}: {518, 4449}, {649, 40883}, {650, 6168}, {665, 3729}, {672, 4885}, {918, 9310}
X(42341) = trilinear quotient X(i)/X(j) for these (i, j): (650, 6169), (665, 9315), (918, 9311), (926, 9439), (1376, 36086), (2254, 9309)
X(42341) = crossdifference of every pair of points on line {X(6), X(1633)}
X(42341) = crosspoint of X(i) and X(j) for these (i, j): {2, 14727}, {518, 883}
X(42341) = crosssum of X(105) and X(884)
X(42341) = X(919)-anticomplementary conjugate of-X(41792)
X(42341) = X(650)-Ceva conjugate of-X(3126)
X(42341) = X(513)-Daleth conjugate of-X(6004)
X(42341) = X(513)-Hirst inverse of-X(3900)
X(42341) = X(i)-isoconjugate-of-X(j) for these {i, j}: {651, 6169}, {666, 9315}, {919, 9311}, {927, 9439}
X(42341) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (518, 30610), (663, 6169), (665, 9309), (918, 32023)

X(42342) = POLELOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO PELLETIER

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

The reciprocal polelogic center of these triangles is X(42343)

X(42342) lies on these lines: {}

X(42343) = POLELOGIC CENTER OF THESE TRIANGLES: PELLETIER TO ANTICOMPLEMENTARY

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

The reciprocal polelogic center of these triangles is X(42342)

X(42343) lies on these lines: {4554, 31250}, {4885, 30610}, {6667, 14947}, {28743, 32041}

X(42343) = isotomic conjugate of X(31287)
X(42343) = barycentric product X(668)*X(41439)
X(42343) = barycentric quotient X(i)/X(j) for these (i, j): (100, 4421), (190, 25728), (668, 25278)
X(42343) = trilinear product X(190)*X(41439)
X(42343) = trilinear quotient X(i)/X(j) for these (i, j): (190, 4421), (668, 25728)
X(42343) = trilinear pole of the line {518, 1278}
X(42343) = Cevapoint of X(i) and X(j) for these (i, j): {2, 4885}, {650, 5274}
X(42343) = X(i)-isoconjugate-of-X(j) for these {i, j}: {649, 4421}, {667, 25728}
X(42343) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (100, 4421), (190, 25728), (668, 25278)

X(42344) = POLAROLOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO SCHROETER

Barycentrics    (b^2-c^2)^4*(2*a^2-b^2-c^2) : :
X(42344) = 2*X(115)+X(1648) = 8*X(115)+X(14444) = X(1641)-4*X(5461) = 4*X(1648)-X(14444) = 2*X(11053)-5*X(14061) = 2*X(14423)+X(14443)

The reciprocal polarologic center of these triangles is X(690)

X(42344) lies on these lines: {115, 125}, {524, 5103}, {1641, 5461}, {11053, 14061}, {11646, 25328}, {14423, 14443}, {23991, 33921}

X(42344) = isotomic conjugate of X(42370)
X(42344) = barycentric product X(i)*X(j) for these {i, j}: {115, 1648}, {338, 21906}, {351, 23105}, {523, 33919}, {690, 8029}
X(42344) = barycentric quotient X(i)/X(j) for these (i, j): (690, 31614), (1648, 4590)
X(42344) = trilinear product X(i)*X(j) for these {i, j}: {661, 33919}, {1109, 21906}, {1648, 2643}
X(42344) = trilinear quotient X(1648)/X(24041)
X(42344) = tripolar centroid of X(8029)
X(42344) = crosspoint of X(i) and X(j) for these (i, j): {671, 42345}, {1648, 33919}
X(42344) = crosssum of X(110) and X(21906)
X(42344) = X(i)-Ceva conjugate of-X(j) for these (i, j): (115, 14443), (1648, 33919)
X(42344) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (690, 31614), (1648, 4590)
X(42344) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (115, 6388, 16278), (115, 15359, 39691)

X(42345) = POLELOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO SCHROETER

Barycentrics    (b^2-c^2)*(a^4-2*b^2*a^2+c^4-2*b^2*c^2+2*b^4)*(a^4-2*c^2*a^2-2*b^2*c^2+2*c^4+b^4) : :
X(42345) = 9*X(2)-4*X(36955) = X(99)-6*X(8029) = X(148)+4*X(12076) = 4*X(620)-9*X(5466) = 9*X(671)-4*X(9293) = 8*X(10279)-3*X(21166)

The reciprocal polelogic center of these triangles is X(99)

X(42345) lies on the cubic K241 and these lines: {2, 36955}, {99, 8029}, {148, 690}, {523, 14061}, {620, 5466}, {671, 9293}, {10279, 21166}, {21089, 21092}

X(42345) = isotomic conjugate of X(14588)
X(42345) = barycentric product X(i)*X(j) for these {i, j}: {523, 40429}, {1648, 14728}
X(42345) = barycentric quotient X(i)/X(j) for these (i, j): (115, 11123), (512, 20976), (514, 17199), (523, 620), (647, 22085), (661, 17467)
X(42345) = trilinear product X(661)*X(40429)
X(42345) = trilinear quotient X(i)/X(j) for these (i, j): (523, 17467), (656, 22085), (661, 20976), (693, 17199), (850, 20903), (1109, 11123)
X(42345) = trilinear pole of the line {1648, 10278}
X(42345) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(14061)}} and {{A, B, C, X(98), X(3448)}}
X(42345) = Cevapoint of X(523) and X(8029)
X(42345) = crossdifference of every pair of points on line {X(20976), X(22085)}
X(42345) = X(524)-cross conjugate of-X(5466)
X(42345) = X(i)-isoconjugate-of-X(j) for these {i, j}: {110, 17467}, {162, 22085}, {163, 620}, {662, 20976}
X(42345) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (115, 11123), (512, 20976), (514, 17199), (523, 620)

X(42346) = POLELOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO TANGENTIAL

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

The reciprocal polelogic center of these triangles is X(10159)

X(42346) lies on these lines: {2, 10014}, {6, 1078}, {32, 5012}, {83, 3051}, {213, 23475}, {251, 3203}, {1186, 3224}, {1629, 2207}, {1974, 5039}, {2422, 8870}, {3114, 7760}, {5007, 9468}, {7808, 9463}, {12212, 39674}, {14252, 30435}, {18993, 26461}, {18994, 26454}, {39588, 39872}

X(42346) = complement of the anticomplementary conjugate of X(39)
X(42346) = anticomplement of the complementary conjugate of X(6683)
X(42346) = isogonal conjugate of X(3934)
X(42346) = polar conjugate of X(42394)
X(42346) = barycentric product X(i)*X(j) for these {i, j}: {6, 39968}, {32, 31630}, {83, 31613}
X(42346) = barycentric quotient X(i)/X(j) for these (i, j): (1, 20889), (4, 42394), (31, 17445), (32, 20965), (42, 21022), (58, 17176)
X(42346) = trilinear product X(i)*X(j) for these {i, j}: {31, 39968}, {82, 31613}, {560, 31630}, {1923, 31622}
X(42346) = trilinear quotient X(i)/X(j) for these (i, j): (2, 20889), (6, 17445), (31, 20965), (37, 21022), (48, 22062), (81, 17176)
X(42346) = 1st Saragossa point of X(83)
X(42346) = trilinear pole of the line {669, 2513}
X(42346) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(7786)}} and {{A, B, C, X(3), X(5039)}}
X(42346) = Cevapoint of X(i) and X(j) for these (i, j): {6, 3051}, {32, 3203}
X(42346) = X(1207)-cross conjugate of-X(83)
X(42346) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 17445}, {6, 20889}, {37, 17176}, {38, 18092}
X(42346) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 20889), (4, 42394), (31, 17445), (32, 20965)
X(42346) = X(592)-vertex conjugate of-X(1173)
X(42346) = {X(83), X(3051)}-harmonic conjugate of X(38854)

X(42347) = POLAROLOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO X-PARABOLA-TANGENTIAL

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

The reciprocal polarologic center of these triangles is X(33906)

X(42347) lies on this line: {1648, 8029}

X(42347) = crosspoint of X(892) and X(42348)

X(42348) = POLELOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO X-PARABOLA-TANGENTIAL

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

The reciprocal polelogic center of these triangles is X(42349)

X(42348) lies on this line: {115, 33799}

X(42349) = POLELOGIC CENTER OF THESE TRIANGLES: X-PARABOLA-TANGENTIAL TO ANTICOMPLEMENTARY

Barycentrics    (3*a^4-2*(b^2+2*c^2)*a^2+2*b^4-2*b^2*c^2+3*c^4)*(3*a^4-2*(2*b^2+c^2)*a^2+3*b^4-2*b^2*c^2+2*c^4) : :
X(42349) = 5*X(99)+16*X(40511) = 16*X(620)+5*X(40429) = X(4590)+20*X(31274)

The reciprocal polelogic center of these triangles is X(42348)

X(42349) lies on these lines: {99, 40511}, {620, 40429}, {3619, 5967}, {4590, 31274}, {18823, 22247}

X(42349) = isotomic conjugate of X(6722)
X(42349) = trilinear pole of the line {690, 14683}
X(42349) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(468)}} and {{A, B, C, X(115), X(31274)}}
X(42349) = Cevapoint of X(2) and X(620)

X(42350) = POLAROLOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO X3-ABC REFLECTIONS

Barycentrics    a^12-4*(b^2+c^2)*a^10+(4*b^4+5*b^2*c^2+4*c^4)*a^8+3*(b^6+c^6)*a^6-(b^2-c^2)^2*(8*b^4+9*b^2*c^2+8*c^4)*a^4+(b^4-c^4)*(b^2-c^2)*(5*b^4-9*b^2*c^2+5*c^4)*a^2-(b^2-c^2)^6 : :
X(42350) = 6*X(547)-5*X(40331) = 5*X(1656)-4*X(6709) = 5*X(3091)-X(40897)

The reciprocal polarologic center of these triangles is X(95)

X(42350) lies on these lines: {3, 233}, {4, 3164}, {5, 95}, {97, 3078}, {547, 40331}, {1351, 3818}, {1656, 6709}, {2967, 37349}, {3091, 40897}, {6321, 31656}, {9792, 32438}, {10003, 40853}, {13352, 18464}, {14941, 30506}, {19210, 35887}, {34836, 35884}

X(42350) = midpoint of X(4) and X(17035)
X(42350) = reflection of X(i) in X(j) for these (i, j): (3, 233), (95, 5)

X(42351) = POLELOGIC CENTER OF THESE TRIANGLES: ANTICOMPLEMENTARY TO X3-ABC REFLECTIONS

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

The reciprocal polelogic center of these triangles is X(40410)

X(42351) lies on these lines: {2, 39243}, {95, 27377}, {140, 287}, {264, 36751}, {297, 40410}, {577, 36948}, {1351, 10003}, {8797, 36412}

X(42351) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(69)}} and {{A, B, C, X(3), X(37067)}}

X(42352) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO EULER

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

The reciprocal polelogic center of these triangles is X(253)

X(42352) lies on these lines: {20, 287}, {253, 297}, {13575, 20213}

X(42352) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(69)}} and {{A, B, C, X(20), X(297)}}

X(42353) = POLAROLOGIC CENTER OF THESE TRIANGLES: MEDIAL TO 2nd EULER

Barycentrics    (-a^2+b^2+c^2)^2*(3*a^4+(b^2-c^2)^2)*((b^2+c^2)*a^2-(b^2-c^2)^2) : :
X(42353) = 5*X(631)-3*X(20792) = X(18437)+2*X(34828)

The reciprocal polarologic center of these triangles is X(141)

X(42353) lies on these lines: {2, 26870}, {3, 66}, {4, 20477}, {5, 53}, {30, 36988}, {114, 122}, {131, 14672}, {182, 441}, {297, 42329}, {343, 418}, {465, 5617}, {466, 5613}, {511, 41005}, {577, 3564}, {631, 20792}, {852, 37648}, {1353, 3284}, {1513, 40822}, {1576, 41729}, {1594, 40681}, {2871, 9967}, {2980, 34002}, {3164, 6530}, {5158, 18583}, {5480, 30258}, {5562, 6751}, {6146, 40947}, {6248, 6823}, {6638, 13567}, {6643, 41761}, {6676, 26880}, {6755, 34836}, {6776, 37188}, {8573, 39571}, {8800, 27352}, {10516, 36751}, {10608, 18396}, {10749, 31656}, {10979, 18358}, {11411, 18953}, {11585, 23333}, {13562, 26899}, {15069, 36748}, {17814, 17849}, {18380, 18404}, {19131, 19156}, {19179, 19212}, {21243, 26906}, {25150, 27353}, {26874, 37636}, {34507, 41008}, {36245, 41362}

X(42353) = midpoint of X(i) and X(j) for these {i, j}: {3, 18437}, {4, 20477}, {5562, 6751}
X(42353) = reflection of X(i) in X(j) for these (i, j): (3, 34828), (53, 5), (8800, 27352)
X(42353) = complement of X(33971)
X(42353) = X(1350)-of-orthic-triangle
X(42353) = X(6)-of-2nd-Euler-triangle
X(42353) = QA-P21 (Reflection of QA-P16 in QA-P1) of quadrangle ABCX(4)
X(42353) = complement of the polar conjugate of X(42313)
X(42353) = barycentric product X(i)*X(j) for these {i, j}: {5, 37188}, {343, 6776}, {418, 40822}
X(42353) = barycentric quotient X(i)/X(j) for these (i, j): (216, 40801), (418, 40799)
X(42353) = trilinear product X(1953)*X(37188)
X(42353) = intersection, other than A,B,C, of conics {{A, B, C, X(4), X(27354)}} and {{A, B, C, X(5), X(14376)}}
X(42353) = crossdifference of every pair of points on line {X(2485), X(23286)}
X(42353) = X(i)-complementary conjugate of-X(j) for these (i, j): (255, 15819), (263, 24005)
X(42353) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (216, 40801), (418, 40799)
X(42353) = {X(5562), X(8905)}-harmonic conjugate of X(27354)

X(42354) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO 2nd EULER

Barycentrics    (a^6-2*b^2*a^4+(b^2-3*c^2)*b^2*a^2+(b^2-c^2)^2*c^2)*(a^6-2*c^2*a^4-(3*b^2-c^2)*c^2*a^2+(b^2-c^2)^2*b^2)/a^2 : :
Barycentrics    sec(2A + ω) : :

The reciprocal polelogic center of these triangles is X(42355)

X(42354) lies on these lines: {6, 311}, {25, 324}, {76, 2987}, {263, 1352}, {264, 8882}, {1976, 14265}, {5012, 5392}, {30535, 40814}

X(42354) = polar conjugate of X(6403)
X(42354) = barycentric quotient X(i)/X(j) for these (i, j): (4, 6403), (5, 41169)
X(42354) = trilinear quotient X(92)/X(6403)
X(42354) = trilinear pole of the line {512, 13449}
X(42354) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(41231)}}
X(42354) = Cevapoint of X(338) and X(23878)
X(42354) = X(48)-isoconjugate-of-X(6403)
X(42354) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 6403), (5, 41169)

X(42355) = POLELOGIC CENTER OF THESE TRIANGLES: 2nd EULER TO MEDIAL

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

The reciprocal polelogic center of these triangles is X(42354)

X(42355) lies on these lines: {97, 5392}, {264, 34148}, {311, 1975}, {324, 1993}, {5889, 8795}, {11444, 42333}

X(42355) = isotomic conjugate of X(5889)
X(42355) = barycentric product X(76)*X(22261)
X(42355) = trilinear product X(75)*X(22261)
X(42355) = trilinear pole of the line {18314, 30476}
X(42355) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(8795)}} and {{A, B, C, X(3), X(34148)}}
X(42355) = Cevapoint of X(338) and X(520)

X(42356) = POLAROLOGIC CENTER OF THESE TRIANGLES: MEDIAL TO 3rd EULER

Barycentrics    (b^2-4*b*c+c^2)*a^3-3*(b^2-c^2)*(b-c)*a^2+(3*b^2+4*b*c+3*c^2)*(b-c)^2*a-(b^2-c^2)*(b-c)^3 : :
X(42356) = X(4)+3*X(38037) = X(7)-9*X(9779) = X(9)+3*X(1699) = X(142)-3*X(3817) = X(382)+3*X(38031) = X(390)+7*X(3832) = X(962)+3*X(38057) = X(1001)-3*X(38037) = X(1537)+3*X(38159) = X(2550)-5*X(3091) = X(2951)-9*X(7988) = X(2951)-5*X(20195) = X(3062)+3*X(6173) = X(3062)+15*X(30308) = X(3579)-3*X(38318) = 9*X(7988)-5*X(20195) = 9*X(9779)+X(16112) = 4*X(9955)-X(25557) = X(15254)+2*X(18483) = X(20330)-3*X(38034)

The reciprocal polarologic center of these triangles is X(141).

X(42356) lies on these lines: {2, 7965}, {4, 1001}, {5, 516}, {7, 11}, {9, 1699}, {12, 390}, {20, 7958}, {119, 381}, {142, 1538}, {144, 6067}, {226, 5572}, {235, 1890}, {354, 41857}, {382, 38031}, {480, 3434}, {495, 30331}, {496, 5542}, {497, 8232}, {518, 946}, {527, 3829}, {546, 18242}, {673, 7384}, {908, 3059}, {954, 1479}, {962, 9710}, {971, 9955}, {1012, 38759}, {1329, 2550}, {1445, 1836}, {1484, 2801}, {1537, 38159}, {1721, 17278}, {1742, 17245}, {2346, 3058}, {2951, 7988}, {3062, 3255}, {3243, 11522}, {3485, 5809}, {3543, 38025}, {3545, 35514}, {3614, 7679}, {3627, 38043}, {3652, 5805}, {3739, 21629}, {3812, 21628}, {3847, 5880}, {3854, 11681}, {3855, 38149}, {3925, 9812}, {3988, 20117}, {4026, 36652}, {4187, 38052}, {4197, 10248}, {4301, 24393}, {4312, 7741}, {4326, 5219}, {4335, 17717}, {4336, 5723}, {4343, 5718}, {4423, 10431}, {4999, 6837}, {5068, 40333}, {5072, 38121}, {5087, 10863}, {5220, 5817}, {5222, 21955}, {5223, 24390}, {5432, 7676}, {5528, 15017}, {5584, 6886}, {5691, 38316}, {5698, 6828}, {5728, 12047}, {5732, 8227}, {5759, 6990}, {5779, 5852}, {5806, 12617}, {5845, 24682}, {5850, 24387}, {5853, 12607}, {5886, 31672}, {5927, 15185}, {6147, 20116}, {6284, 6894}, {6601, 11235}, {6668, 6848}, {6690, 19541}, {6691, 6847}, {6839, 10724}, {6849, 11496}, {6866, 10893}, {6870, 10896}, {6896, 10310}, {6900, 11826}, {7354, 7677}, {7377, 16593}, {7675, 11375}, {7982, 38154}, {7989, 9711}, {8236, 15888}, {8255, 14100}, {8545, 15845}, {8728, 38059}, {8732, 10589}, {9355, 17365}, {9441, 17337}, {9581, 12560}, {10157, 40659}, {10171, 37364}, {10177, 27869}, {10442, 10886}, {10478, 35892}, {10593, 30424}, {11038, 37722}, {12245, 16615}, {12612, 21077}, {12699, 38108}, {13271, 34894}, {13405, 15006}, {13464, 15570}, {13729, 15843}, {15171, 18782}, {15842, 17618}, {15911, 18233}, {15950, 30284}, {16160, 31657}, {17243, 28850}, {17348, 28849}, {17527, 38204}, {18222, 30827}, {18393, 18412}, {18480, 32213}, {19512, 24309}, {21153, 41869}, {21258, 34848}, {25524, 37434}, {30329, 39542}, {30379, 31391}, {30628, 31053}, {31162, 38075}, {31394, 36654}, {36971, 41563}, {36990, 38048}, {36991, 38053}

X(42356) = midpoint of X(i) and X(j) for these {i, j}: {4, 1001}, {7, 16112}, {4301, 24393}, {5880, 11372}, {13271, 34894}, {20116, 31871}, {22793, 31658}
X(42356) = reflection of X(i) in X(j) for these (i, j): (3826, 5), (15570, 13464)
X(42356) = complement of X(11495)
X(42356) = X(6)-of-3rd-Euler-triangle
X(42356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 38037, 1001), (7, 7678, 11), (144, 11680, 6067), (1699, 8226, 2886), (1699, 41858, 8226), (2951, 7988, 20195), (3817, 8727, 3816), (4301, 38158, 24393), (7678, 30311, 7), (9779, 10883, 11), (11372, 38150, 5880), (12558, 12571, 5), (14100, 17605, 21617), (14100, 21617, 8255), (30306, 30307, 11), (30309, 30310, 11), (31555, 31556, 5)

X(42357) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO 3rd EULER

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

The reciprocal polelogic center of these triangles is X(190)

X(42357) lies on these lines: {}

X(42357) = trilinear pole of the line {2140, 3817}

X(42358) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO 4th EULER

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

The reciprocal polelogic center of these triangles is X(75)

X(42358) lies on these lines: {3995, 17018}, {4687, 17786}

X(42358) = isotomic conjugate of the anticomplement of X(4044)
X(42358) = trilinear pole of the line {4129, 6005}
X(42358) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(749)}} and {{A, B, C, X(75), X(3995)}}

X(42359) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO 5th EULER

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

The reciprocal polelogic center of these triangles is X(6)

X(42359) lies on these lines: {39, 1975}, {141, 33734}, {308, 31360}, {1843, 9308}, {7754, 27375}, {32451, 42299}

X(42359) = isotomic conjugate of X(32451)
X(42359) = trilinear pole of the line {3005, 30476}
X(42359) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(11174)}} and {{A, B, C, X(4), X(308)}}

X(42360) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO EXCENTERS-MIDPOINTS

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

The reciprocal polelogic center of these triangles is X(42361)

X(42360) lies on these lines: {1999, 4460}, {2403, 5905}, {17315, 18743}

X(42360) = isotomic conjugate of the anticomplement of X(30568)
X(42360) = barycentric quotient X(1)/X(11512)
X(42360) = trilinear quotient X(2)/X(11512)
X(42360) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(34260)}} and {{A, B, C, X(2), X(145)}}
X(42360) = X(6)-isoconjugate-of-X(11512)
X(42360) = X(1)-reciprocal conjugate of-X(11512)

X(42361) = POLELOGIC CENTER OF THESE TRIANGLES: EXCENTERS-MIDPOINTS TO MEDIAL

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

The reciprocal polelogic center of these triangles is X(42360)

X(42361) lies on the circumhyperbola dual of Yff parabola and these lines: {2, 24181}, {7, 3174}, {329, 673}, {345, 36807}, {962, 39732}, {1088, 6604}, {1440, 9436}, {9776, 27475}, {11037, 39734}, {18228, 42318}, {24152, 24155}, {24153, 24154}, {26015, 36620}

X(42361) = anticomplement of X(24771)
X(42361) = isogonal conjugate of X(21002)
X(42361) = isotomic conjugate of X(36845)
X(42361) = barycentric quotient X(i)/X(j) for these (i, j): (1, 16572), (3, 22153), (7, 8732), (9, 3174), (10, 21096), (75, 20946)
X(42361) = trilinear quotient X(i)/X(j) for these (i, j): (2, 16572), (8, 3174), (63, 22153), (76, 20946), (85, 8732), (321, 21096)
X(42361) = intersection, other than A,B,C, of circumhyperbola dual of Yff parabola and conic {{A, B, C, X(4), X(39959)}}
X(42361) = Cevapoint of X(i) and X(j) for these (i, j): {2, 20015}, {522, 4904}
X(42361) = X(200)-cross conjugate of-X(2)
X(42361) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 16572}, {19, 22153}, {32, 20946}, {41, 8732}
X(42361) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 16572), (3, 22153), (7, 8732), (9, 3174)

X(42362) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO FEUERBACH

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

The reciprocal polelogic center of these triangles is X(42363)

X(42362) lies on these lines: {}

X(42362) = isotomic conjugate of the anticomplement of X(7265)
X(42362) = trilinear pole of the line {442, 1155}
X(42362) = Cevapoint of X(523) and X(1100)

X(42363) = POLELOGIC CENTER OF THESE TRIANGLES: FEUERBACH TO MEDIAL

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

The reciprocal polelogic center of these triangles is X(42362)

X(42363) lies on these lines: {4436, 16680}, {4623, 17166}, {17159, 21295}, {22280, 22311}

X(42363) = isogonal conjugate of X(16874)
X(42363) = isotomic conjugate of X(17166)
X(42363) = barycentric quotient X(i)/X(j) for these (i, j): (10, 22044), (75, 18154), (514, 23823)
X(42363) = trilinear quotient X(i)/X(j) for these (i, j): (76, 18154), (321, 22044), (693, 23823)
X(42363) = trilinear pole of the line {1211, 3912}
X(42363) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(4623)}} and {{A, B, C, X(7), X(4594)}}
X(42363) = Cevapoint of X(i) and X(j) for these (i, j): {512, 3666}, {513, 17045}, {522, 21233}, {523, 3739}
X(42363) = X(i)-isoconjugate-of-X(j) for these {i, j}: {32, 18154}, {692, 23823}, {1333, 22044}
X(42363) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (10, 22044), (75, 18154), (514, 23823)

X(42364) = POLAROLOGIC CENTER OF THESE TRIANGLES: MEDIAL TO 2nd HATZIPOLAKIS

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

X(42364) lies on this line: {1119, 17054}

X(42364) = barycentric product X(1119)*X(14743)
X(42364) = trilinear product X(1435)*X(14743)

X(42365) = POLAROLOGIC CENTER OF THESE TRIANGLES: MEDIAL TO LEMOINE

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

The reciprocal polarologic center of these triangles is X(20582)

X(42365) lies on these lines: {597, 598}, {20583, 35138}

X(42365) = barycentric product X(598)*X(14762)
X(42365) = pole of the trilinear polar of X(42366) with respect to Kiepert hyperbola
X(42365) = X(598)-Ceva conjugate of-X(32069)

X(42366) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO LEMOINE

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

The reciprocal polelogic center of these triangles is X(42367)

X(42366) lies on these lines: {}

X(42366) = Cevapoint of X(i) and X(j) for these (i, j): {523, 42365}, {598, 17436}

X(42367) = POLELOGIC CENTER OF THESE TRIANGLES: LEMOINE TO MEDIAL

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

The reciprocal polelogic center of these triangles is X(42366)

X(42367) lies on the Steiner circumellipse and these lines: {99, 12074}, {141, 671}, {892, 4576}, {3228, 3329}, {4577, 5468}, {7779, 18823}, {9146, 35138}, {14764, 41624}

X(42367) = isogonal conjugate of the Gibert-circumtangential conjugate of X(12074)
X(42367) = isotomic conjugate of X(12073)
X(42367) = barycentric product X(i)*X(j) for these {i, j}: {76, 12074}, {99, 10302}, {670, 39389}
X(42367) = barycentric quotient X(i)/X(j) for these (i, j): (99, 597), (110, 5008), (249, 35357), (599, 17436), (648, 10301), (670, 26235)
X(42367) = trilinear product X(i)*X(j) for these {i, j}: {75, 12074}, {662, 10302}, {799, 39389}
X(42367) = trilinear quotient X(i)/X(j) for these (i, j): (662, 5008), (799, 597), (811, 10301)
X(42367) = trilinear pole of the line {2, 5355}
X(42367) = intersection, other than A,B,C, of Steiner circumellipse and conic {{A, B, C, X(141), X(4576)}}
X(42367) = Cevapoint of X(i) and X(j) for these (i, j): {2, 12073}, {99, 9146}, {523, 20582}, {525, 10300}
X(42367) = X(599)-cross conjugate of-X(4590)
X(42367) = X(i)-isoconjugate-of-X(j) for these {i, j}: {597, 798}, {661, 5008}, {810, 10301}
X(42367) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (99, 597), (110, 5008), (249, 35357), (599, 17436)

X(42368) = POLAROLOGIC CENTER OF THESE TRIANGLES: MEDIAL TO MACBEATH

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

The reciprocal polarologic center of these triangles is X(140)

X(42368) lies on these lines: {5, 264}, {30, 9291}, {140, 276}, {297, 324}, {339, 14978}, {546, 6528}, {3933, 18022}, {5305, 16081}, {8795, 41008}, {40207, 40684}

X(42368) = isotomic conjugate of the isogonal conjugate of X(42400)
X(42368) = polar conjugate of the isogonal conjugate of X(14767)
X(42368) = barycentric product X(i)*X(j) for these {i, j}: {76, 42400}, {264, 14767}, {276, 11197}
X(42368) = trilinear product X(i)*X(j) for these {i, j}: {75, 42400}, {92, 14767}
X(42368) = X(264)-Ceva conjugate of-X(11197)
X(42368) = X(264)-Waw conjugate of-X(40684)
X(42368) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (264, 18027, 5), (276, 16089, 140)

X(42369) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO MACBEATH

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

The reciprocal polelogic center of these triangles is X(18831)

X(42369) lies on this line: {6331, 42401}

X(42369) = isotomic conjugate of the isogonal conjugate of X(42401)
X(42369) = barycentric product X(76)*X(42401)
X(42369) = barycentric quotient X(i)/X(j) for these (i, j): (276, 32320), (850, 41219)
X(42369) = trilinear product X(75)*X(42401)
X(42369) = trilinear pole of the line {264, 11197}
X(42369) = Cevapoint of X(i) and X(j) for these (i, j): {264, 17434}, {525, 42368}
X(42369) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (276, 32320), (850, 41219)

X(42370) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO STEINER

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

The reciprocal polelogic center of these triangles is X(892)

X(42370) lies on these lines: {620, 4590}, {4600, 21047}, {9170, 31614}, {9293, 14588}

X(42370) = isotomic conjugate of X(42344)
X(42370) = barycentric product X(892)*X(31614)
X(42370) = barycentric quotient X(i)/X(j) for these (i, j): (99, 33919), (249, 21906), (691, 22260), (892, 8029)
X(42370) = trilinear quotient X(799)/X(33919)
X(42370) = trilinear pole of the line {99, 11123}
X(42370) = Cevapoint of X(i) and X(j) for these (i, j): {99, 1648}, {524, 14588}
X(42370) = X(798)-isoconjugate-of-X(33919)
X(42370) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (99, 33919), (249, 21906), (691, 22260), (892, 8029)

X(42371) = POLELOGIC CENTER OF THESE TRIANGLES: SYMMEDIAL TO MEDIAL

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

The reciprocal polelogic center of these triangles is X(827)

X(42371) lies on the Steiner circumellipse and these lines: {32, 39082}, {39, 9495}, {76, 14970}, {83, 3225}, {99, 689}, {190, 37204}, {308, 3228}, {315, 40359}, {316, 18901}, {626, 14946}, {671, 40016}, {782, 880}, {826, 18828}, {827, 9063}, {1502, 7818}, {3112, 18826}, {3934, 31622}, {4562, 4602}, {4586, 4593}, {4630, 33515}, {6528, 42395}, {18827, 18833}, {41073, 41209}

X(42371) = reflection of X(i) in X(j) for these (i, j): (32, 39082), (39, 39076), (14946, 626)
X(42371) = anticomplement of the complementary conjugate of X(42291)
X(42371) = isogonal conjugate of X(9494)
X(42371) = isotomic conjugate of X(688)
X(42371) = barycentric product X(i)*X(j) for these {i, j}: {3, 42395}, {75, 37204}, {76, 689}, {83, 4609}, {99, 40016}, {308, 670}
X(42371) = barycentric quotient X(i)/X(j) for these (i, j): (75, 2084), (76, 3005), (82, 1924), (83, 669), (99, 3051), (110, 41331)
X(42371) = trilinear product X(i)*X(j) for these {i, j}: {2, 37204}, {48, 42395}, {75, 689}, {76, 4593}, {82, 4609}, {83, 4602}
X(42371) = trilinear quotient X(i)/X(j) for these (i, j): (76, 2084), (82, 9426), (83, 1924), (99, 1923), (308, 798), (561, 3005)
X(42371) = trilinear pole of the line {2, 308}
X(42371) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(9062)}} and {{A, B, C, X(6), X(36881)}}
X(42371) = Cevapoint of X(i) and X(j) for these (i, j): {2, 688}, {512, 3934}, {626, 826}, {670, 4609}
X(42371) = X(i)-cross conjugate of-X(j) for these (i, j): (512, 31622), (670, 689), (688, 2)
X(42371) = X(i)-isoconjugate-of-X(j) for these {i, j}: {32, 2084}, {38, 9426}, {39, 1924}, {512, 1923}
X(42371) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (75, 2084), (76, 3005), (82, 1924), (83, 669)

X(42372) = POLELOGIC CENTER OF THESE TRIANGLES: MEDIAL TO YFF CONTACT

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

The reciprocal polelogic center of these triangles is X(4555)

X(42372) lies on these lines: {1016, 4422}, {4555, 6635}, {4589, 4622}, {4607, 32665}, {4986, 7035}, {6551, 8709}

X(42372) = isotomic conjugate of X(24188)
X(42372) = barycentric product X(190)*X(6635)
X(42372) = barycentric quotient X(i)/X(j) for these (i, j): (101, 8661), (190, 6550), (765, 2087), (901, 21143), (1016, 1647)
X(42372) = trilinear product X(i)*X(j) for these {i, j}: {100, 6635}, {668, 6551}, {1016, 5376}
X(42372) = trilinear quotient X(i)/X(j) for these (i, j): (100, 8661), (668, 6550), (901, 8027)
X(42372) = trilinear pole of the line {190, 6546}
X(42372) = Cevapoint of X(i) and X(j) for these (i, j): {190, 1647}, {519, 32094}
X(42372) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 8661}, {667, 6550}, {764, 1960}, {900, 8027}
X(42372) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (101, 8661), (190, 6550), (765, 2087), (901, 21143)

X(42373) = POLELOGIC CENTER OF THESE TRIANGLES: ORTHIC TO ANTI-EXCENTERS-REFLECTIONS

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

The reciprocal polelogic center of these triangles is X(393)

X(42373) lies on these lines: {6, 32000}, {263, 12294}, {1976, 15258}, {37665, 42330}

X(42373) = polar conjugate of the anticomplement of X(1350)
X(42373) = barycentric quotient X(25)/X(41266)
X(42373) = trilinear quotient X(19)/X(41266)
X(42373) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(42330)}}
X(42373) = X(63)-isoconjugate-of-X(41266)
X(42373) = X(25)-reciprocal conjugate of-X(41266)

X(42374) = POLELOGIC CENTER OF THESE TRIANGLES: ORTHIC TO EULER

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

The reciprocal polelogic center of these triangles is X(6)

X(42374) lies on these lines: {216, 9308}, {2351, 19189}

X(42374) = polar conjugate of X(42329)
X(42374) = barycentric quotient X(4)/X(42329)
X(42374) = trilinear quotient X(92)/X(42329)
X(42374) = trilinear pole of the line {15451, 16229}
X(42374) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(8795)}} and {{A, B, C, X(4), X(37067)}}
X(42374) = X(48)-isoconjugate-of-X(42329)
X(42374) = X(4)-reciprocal conjugate of-X(42329)

X(42375) = POLELOGIC CENTER OF THESE TRIANGLES: ORTHIC TO 2nd EULER

Barycentrics    (S^4-(2*R^2*(6*R^2-5*SW+SC)-SC^2+2*SW^2)*S^2-(2*R^2-SW)*(4*R^2-SW)*(SW*(2*R^2-SW)+SC^2))*(S^4-(2*R^2*(6*R^2-5*SW+SB)-SB^2+2*SW^2)*S^2-(2*R^2-SW)*(4*R^2-SW)*(SW*(2*R^2-SW)+SB^2)) : :

The reciprocal polelogic center of these triangles is X(42376)

X(42375) lies on these lines: {}

X(42376) = POLELOGIC CENTER OF THESE TRIANGLES: 2nd EULER TO ORTHIC

Barycentrics    (S^2-2*(4*R^2-SB-2*SW)*R^2-SW^2)*(S^2-2*(4*R^2-SC-2*SW)*R^2-SW^2)*SB^2*SC^2 : :

The reciprocal polelogic center of these triangles is X(42375)

X(42376) lies on this line: {393, 6193}

X(42376) = Cevapoint of X(139) and X(12077)

X(42377) = POLELOGIC CENTER OF THESE TRIANGLES: ORTHIC TO 5th EULER

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

The reciprocal polelogic center of these triangles is X(34208)

X(42377) lies on these lines: {4, 10983}, {297, 34208}, {6353, 6531}

X(42377) = polar conjugate of X(37667)
X(42377) = barycentric quotient X(4)/X(37667)
X(42377) = trilinear quotient X(92)/X(37667)
X(42377) = intersection, other than A,B,C, of conics {{A, B, C, X(4), X(93)}} and {{A, B, C, X(6), X(10983)}}
X(42377) = X(48)-isoconjugate-of-X(37667)
X(42377) = X(4)-reciprocal conjugate of-X(37667)

X(42378) = POLAROLOGIC CENTER OF THESE TRIANGLES: ORTHIC TO EXTOUCH

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

The reciprocal polarologic center of these triangles is X(42379)

X(42378) lies on these lines: {8, 210}, {65, 16086}, {72, 13532}, {145, 33118}, {3246, 3621}, {3703, 6737}, {3712, 12437}, {3717, 10950}, {3932, 41575}, {3962, 7270}, {3967, 5086}, {4030, 5837}, {4126, 5795}, {4387, 12625}, {5015, 31165}, {8258, 37539}, {34406, 42379}

X(42378) = pole of the trilinear polar of X(42380) with respect to Feuerbach hyperbola
X(42378) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (8, 1265, 1837), (1265, 1837, 4009)

X(42379) = POLAROLOGIC CENTER OF THESE TRIANGLES: EXTOUCH TO ORTHIC

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

The reciprocal polarologic center of these triangles is X(42378)

X(42379) lies on these lines: {4, 65}, {29, 17605}, {53, 1839}, {225, 1852}, {1785, 6284}, {1838, 7354}, {1842, 37376}, {1940, 7541}, {3585, 39529}, {3683, 17555}, {3962, 5081}, {5307, 40271}, {7510, 12047}, {7534, 9579}, {10895, 39585}, {17923, 37605}, {34406, 42378}

X(42379) = pole of the trilinear polar of X(42381) with respect to Feuerbach hyperbola
X(42379) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 1118, 1837), (4, 42385, 42387), (1940, 7541, 17606)

X(42380) = POLELOGIC CENTER OF THESE TRIANGLES: ORTHIC TO EXTOUCH

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

The reciprocal polelogic center of these triangles is X(42381)

X(42380) lies on these lines: {}

X(42380) = barycentric quotient X(i)/X(j) for these (i, j): (190, 36570), (646, 3772)
X(42380) = trilinear product X(646)*X(40436)
X(42380) = trilinear quotient X(i)/X(j) for these (i, j): (646, 3924), (668, 36570)
X(42380) = Cevapoint of X(650) and X(42378)
X(42380) = X(667)-isoconjugate-of-X(36570)
X(42380) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (190, 36570), (646, 3772)

X(42381) = POLELOGIC CENTER OF THESE TRIANGLES: EXTOUCH TO ORTHIC

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

The reciprocal polelogic center of these triangles is X(42380)

X(42381) lies on these lines: {}

X(42381) = Cevapoint of X(650) and X(42379)

X(42382) = POLAROLOGIC CENTER OF THESE TRIANGLES: ORTHIC TO 2nd HATZIPOLAKIS

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

The reciprocal polarologic center of these triangles is X(5101)

X(42382) lies on these lines: {279, 2355}, {479, 1119}

X(42382) = barycentric product X(278)*X(30623)
X(42382) = trilinear product X(34)*X(30623)

X(42383) = POLELOGIC CENTER OF THESE TRIANGLES: ORTHIC TO 2nd HATZIPOLAKIS

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

The reciprocal polelogic center of these triangles is X(42384)

X(42383) lies on these lines: {}

X(42384) = POLELOGIC CENTER OF THESE TRIANGLES: 2nd HATZIPOLAKIS TO ORTHIC

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

The reciprocal polelogic center of these triangles is X(42383)

X(42384) lies on these lines: {646, 653}, {648, 7258}, {1978, 13149}, {16082, 30701}

X(42384) = barycentric quotient X(i)/X(j) for these (i, j): (100, 1473), (107, 4211), (190, 7289), (321, 21107), (644, 7124), (646, 27509)
X(42384) = trilinear product X(i)*X(j) for these {i, j}: {646, 1041}, {1897, 30701}
X(42384) = trilinear quotient X(i)/X(j) for these (i, j): (190, 1473), (313, 21107), (646, 1040), (668, 7289), (823, 4211), (1018, 22363)
X(42384) = trilinear pole of the line {4, 341}
X(42384) = X(i)-isoconjugate-of-X(j) for these {i, j}: {614, 22383}, {649, 1473}, {667, 7289}, {822, 4211}
X(42384) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (100, 1473), (107, 4211), (190, 7289), (321, 21107)

X(42385) = POLAROLOGIC CENTER OF THESE TRIANGLES: INCENTRAL TO ORTHIC

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

The reciprocal polarologic center of these triangles is X(2646)

X(42385) lies on these lines: {1, 7524}, {4, 65}, {11, 133}, {12, 1785}, {29, 243}, {33, 1867}, {53, 1826}, {55, 39585}, {92, 3057}, {210, 318}, {225, 235}, {278, 11376}, {354, 1895}, {407, 42069}, {412, 1940}, {942, 1784}, {1842, 1852}, {1872, 41538}, {2262, 6520}, {2264, 8748}, {2654, 2658}, {3486, 7518}, {5125, 17606}, {6708, 40946}, {7497, 22760}, {7510, 10572}, {7531, 37600}, {7952, 17718}, {10895, 39531}, {16141, 31902}, {17728, 40836}, {22768, 37393}

X(42385) = polar conjugate of the isotomic conjugate of X(6708)
X(42385) = barycentric product X(i)*X(j) for these {i, j}: {4, 6708}, {92, 2654}, {1896, 18592}
X(42385) = trilinear product X(i)*X(j) for these {i, j}: {4, 2654}, {19, 6708}, {158, 40946}, {1896, 2658}
X(42385) = Zosma transform of X(73)
X(42385) = intersection, other than A,B,C, of conics {{A, B, C, X(4), X(2654)}} and {{A, B, C, X(65), X(1896)}}
X(42385) = pole of the trilinear polar of X(15352) with respect to Feuerbach hyperbola
X(42385) = crossdifference of every pair of points on line {X(23187), X(36054)}
X(42385) = crosspoint of X(4) and X(1896)
X(42385) = crosssum of X(3) and X(22341)
X(42385) = X(4)-Waw conjugate of-X(40950)
X(42385) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 158, 65), (4, 1118, 1836), (4, 1857, 1837), (4, 40149, 1888), (29, 243, 2646), (412, 1940, 1155), (1785, 39574, 12), (42379, 42387, 4)

X(42386) = POLAROLOGIC CENTER OF THESE TRIANGLES: ORTHIC TO INTOUCH

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

The reciprocal polarologic center of these triangles is X(42387)

X(42386) lies on these lines: {7, 354}, {226, 10136}, {658, 17605}, {3474, 10004}, {3706, 7055}, {4114, 10481}, {10360, 10401}, {34398, 42387}

X(42386) = pole of the trilinear polar of X(42388) with respect to Feuerbach hyperbola

X(42387) = POLAROLOGIC CENTER OF THESE TRIANGLES: INTOUCH TO ORTHIC

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

The reciprocal polarologic center of these triangles is X(42386)

X(42387) lies on these lines: {4, 65}, {53, 1886}, {55, 39531}, {225, 10151}, {243, 17605}, {412, 17606}, {3583, 39529}, {6284, 39574}, {7551, 37600}, {12953, 39585}, {34398, 42386}

X(42387) = Zosma transform of X(20277)
X(42387) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 1857, 1836), (4, 42385, 42379)

X(42388) = POLELOGIC CENTER OF THESE TRIANGLES: ORTHIC TO INTOUCH

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

The reciprocal polelogic center of these triangles is X(42389)

X(42388) lies on these lines: {}

X(42388) = barycentric quotient X(479)/X(2520)
X(42388) = Cevapoint of X(650) and X(42386)
X(42388) = X(479)-reciprocal conjugate of-X(2520)

X(42389) = POLELOGIC CENTER OF THESE TRIANGLES: INTOUCH TO ORTHIC

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

The reciprocal polelogic center of these triangles is X(42388)

X(42389) lies on these lines: {}

X(42389) = Cevapoint of X(650) and X(42387)

X(42390) = POLAROLOGIC CENTER OF THESE TRIANGLES: ORTHIC TO LEMOINE

Barycentrics    (12*a^6-11*(b^2+c^2)*a^4-(13*b^4-4*b^2*c^2+13*c^4)*a^2+2*(b^2+c^2)*(5*b^4-11*b^2*c^2+5*c^4))*(2*a^2+2*c^2-b^2)*(2*a^2+2*b^2-c^2) : :

The reciprocal polarologic center of these triangles is X(42391)

X(42390) lies on this line: {597, 598}

X(42390) = pole of the trilinear polar of X(42392) with respect to Kiepert hyperbola

X(42391) = POLAROLOGIC CENTER OF THESE TRIANGLES: LEMOINE TO ORTHIC

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

The reciprocal polarologic center of these triangles is X(42390)

X(42391) lies on these lines: {4, 6}, {3054, 37196}, {3199, 3861}, {3815, 18386}, {3853, 27371}, {18424, 37458}, {37935, 39601}

X(42391) = pole of the trilinear polar of X(42393) with respect to Kiepert hyperbola

X(42392) = POLELOGIC CENTER OF THESE TRIANGLES: ORTHIC TO LEMOINE

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

The reciprocal polelogic center of these triangles is X(42393)

X(42392) lies on these lines: {}

X(42392) = Cevapoint of X(523) and X(42390)

X(42393) = POLELOGIC CENTER OF THESE TRIANGLES: LEMOINE TO ORTHIC

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

The reciprocal polelogic center of these triangles is X(42392)

X(42393) lies on these lines: {}

X(42393) = Cevapoint of X(523) and X(42391)

X(42394) = POLAROLOGIC CENTER OF THESE TRIANGLES: ORTHIC TO MACBEATH

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

The reciprocal polarologic center of these triangles is X(428)

X(42394) lies on these lines: {264, 305}, {290, 11245}, {297, 324}, {428, 17984}, {5133, 23962}, {14569, 18027}, {14768, 39931}, {37439, 40822}

X(42394) = polar conjugate of X(42346)
X(42394) = barycentric product X(i)*X(j) for these {i, j}: {92, 20889}, {264, 3934}, {1235, 18092}
X(42394) = barycentric quotient X(i)/X(j) for these (i, j): (4, 42346), (264, 39968), (427, 31613)
X(42394) = trilinear product X(i)*X(j) for these {i, j}: {4, 20889}, {92, 3934}, {264, 17445}, {286, 21022}
X(42394) = trilinear quotient X(92)/X(42346)
X(42394) = intersection, other than A,B,C, of conics {{A, B, C, X(305), X(3934)}} and {{A, B, C, X(325), X(20965)}}
X(42394) = X(48)-isoconjugate-of-X(42346)
X(42394) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 42346), (264, 39968), (427, 31613)
X(42394) = pole wrt polar circle of trilinear polar of X(42346) (line X(669)X(2513))
X(42394) = {X(264), X(18022)}-harmonic conjugate of X(427)

X(42395) = POLELOGIC CENTER OF THESE TRIANGLES: ORTHIC TO MACBEATH

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

The reciprocal polelogic center of these triangles is X(42396)

X(42395) lies on these lines: {689, 22456}, {6528, 42371}

X(42395) = polar conjugate of X(9494)
X(42395) = barycentric product X(i)*X(j) for these {i, j}: {264, 42371}, {689, 18022}
X(42395) = barycentric quotient X(i)/X(j) for these (i, j): (4, 9494), (264, 688), (308, 3049), (648, 41331), (670, 20775), (689, 184)
X(42395) = trilinear product X(i)*X(j) for these {i, j}: {92, 42371}, {264, 37204}, {689, 1969}, {811, 40016}
X(42395) = trilinear quotient X(i)/X(j) for these (i, j): (92, 9494), (689, 9247), (811, 41331)
X(42395) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 9494}, {688, 9247}, {810, 41331}
X(42395) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 9494), (264, 688), (308, 3049), (648, 41331)

X(42396) = POLELOGIC CENTER OF THESE TRIANGLES: MACBEATH TO ORTHIC

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

The reciprocal polelogic center of these triangles is X(42395)

X(42396) lies on the circumconic with center X(1249) (the conic {{A,B,C,X(107),X(648)}}) and these lines: {83, 16080}, {107, 827}, {112, 689}, {251, 324}, {297, 40850}, {427, 9483}, {648, 4577}, {653, 4599}, {685, 4630}, {1799, 6330}, {4580, 15459}, {6336, 31915}, {10301, 17983}, {17409, 18022}, {18020, 35325}, {23962, 36415}

X(42396) = isotomic conjugate of X(2525)
X(42396) = polar conjugate of X(826)
X(42396) = barycentric product X(i)*X(j) for these {i, j}: {4, 4577}, {19, 4593}, {25, 689}, {82, 811}, {83, 648}, {92, 4599}
X(42396) = barycentric quotient X(i)/X(j) for these (i, j): (4, 826), (25, 3005), (28, 2530), (82, 656), (83, 525), (99, 3933)
X(42396) = trilinear product X(i)*X(j) for these {i, j}: {4, 4599}, {19, 4577}, {25, 4593}, {82, 648}, {83, 162}, {92, 827}
X(42396) = trilinear quotient X(i)/X(j) for these (i, j): (19, 3005), (25, 2084), (27, 2530), (28, 21123), (82, 647), (83, 656)
X(42396) = Zosma transform of X(39336)
X(42396) = trilinear pole of the line {4, 83}
X(42396) = intersection, other than A,B,C, of conics {{A, B, C, X(25), X(35325)}} and {{A, B, C, X(107), X(648)}}
X(42396) = Cevapoint of X(i) and X(j) for these (i, j): {83, 4580}, {112, 648}, {428, 2501}, {523, 7745}
X(42396) = X(i)-cross conjugate of-X(j) for these (i, j): (25, 18020), (264, 23582), (827, 4577)
X(42396) = X(i)-isoconjugate-of-X(j) for these {i, j}: {38, 647}, {39, 656}, {48, 826}, {63, 3005}
X(42396) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 826), (25, 3005), (28, 2530), (82, 656)
X(42396) = X(2)-vertex conjugate of-X(4630)

X(42397) = POLAROLOGIC CENTER OF THESE TRIANGLES: ORTHIC TO MANDART-INCIRCLE

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

The reciprocal polarologic center of these triangles is X(42385)

X(42397) lies on these lines: {11, 6022}, {55, 213}, {144, 145}, {211, 766}, {497, 17137}, {1912, 4162}, {2646, 40432}, {3022, 10544}, {3271, 4875}, {3688, 4520}, {3693, 4531}, {5836, 20863}

X(42397) = barycentric product X(55)*X(26562)
X(42397) = trilinear product X(41)*X(26562)
X(42397) = pole of the trilinear polar of X(670) with respect to Feuerbach hyperbola
X(42397) = crosssum of X(1402) and X(6180)
X(42397) = X(670)-Ceva conjugate of-X(650)
X(42397) = {X(3056), X(23497)}-harmonic conjugate of X(3057)

X(42398) = POLAROLOGIC CENTER OF THESE TRIANGLES: ORTHIC TO STEINER

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

The reciprocal polarologic center of these triangles is X(42399)

X(42398) lies on these lines: {99, 3566}, {524, 2076}, {9182, 9218}

X(42399) = POLAROLOGIC CENTER OF THESE TRIANGLES: STEINER TO ORTHIC

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

The reciprocal polarologic center of these triangles is X(42398)

X(42399) lies on these lines: {4, 3566}, {133, 16188}, {512, 39533}, {523, 10151}, {1598, 34952}, {2501, 42403}

X(42399) = polar conjugate of the isotomic conjugate of X(14341)
X(42399) = barycentric product X(4)*X(14341)
X(42399) = trilinear product X(19)*X(14341)

X(42400) = POLAROLOGIC CENTER OF THESE TRIANGLES: SYMMEDIAL TO ORTHIC

Barycentrics    ((b^2+c^2)*a^6-2*(b^4+b^2*c^2+c^4)*a^4+(b^4-c^4)*(b^2-c^2)*a^2+2*(b^2-c^2)^2*b^2*c^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
Trilinears    (sec A) (2 csc 2A + csc 2B + csc 2C) : :

The reciprocal polarologic center of these triangles is X(13366)

X(42400) lies on these lines: {2, 26895}, {3, 37871}, {4, 51}, {5, 26905}, {25, 9756}, {53, 232}, {115, 138}, {140, 10184}, {184, 33971}, {186, 19192}, {262, 7378}, {264, 3917}, {275, 13366}, {324, 511}, {373, 15466}, {428, 8902}, {436, 1495}, {467, 21243}, {1199, 4994}, {1216, 14978}, {1352, 37192}, {1594, 6750}, {2450, 27371}, {3199, 37988}, {3819, 40684}, {5133, 39569}, {5480, 14569}, {5943, 30506}, {6146, 35717}, {6248, 37174}, {6748, 11245}, {6755, 13567}, {8795, 21638}, {8884, 13367}, {10151, 16311}, {11197, 14767}, {11424, 41365}, {21849, 35360}, {23719, 32767}, {30739, 37873}, {32165, 35887}, {33843, 39906}, {34965, 36412}

X(42400) = isogonal conjugate of the isotomic conjugate of X(42368)
X(42400) = polar conjugate of the isotomic conjugate of X(14767)
X(42400) = barycentric product X(i)*X(j) for these {i, j}: {4, 14767}, {6, 42368}, {275, 11197}
X(42400) = trilinear product X(i)*X(j) for these {i, j}: {19, 14767}, {31, 42368}
X(42400) = intersection, other than A,B,C, of conics {{A, B, C, X(4), X(31365)}} and {{A, B, C, X(51), X(8795)}}
X(42400) = pole of the trilinear polar of X(42401) with respect to Jerabek hyperbola
X(42400) = crosspoint of X(4) and X(8795)
X(42400) = crosssum of X(3) and X(418)
X(42400) = X(4)-Waw conjugate of-X(6748)
X(42400) = X(42)-of-orthic-triangle if ABC is acute
X(42400) = pole wrt polar circle of line X(520)X(31296)
X(42400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 42329, 26907), (4, 2052, 51), (4, 13450, 10110), (53, 427, 6747), (275, 41204, 13366), (436, 1629, 1495)

X(42401) = POLELOGIC CENTER OF THESE TRIANGLES: SYMMEDIAL TO ORTHIC

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

The reciprocal polelogic center of these triangles is X(933)

X(42401) lies on these lines: {648, 42405}, {6331, 42369}, {8794, 16081}

X(42401) = isogonal conjugate of the isotomic conjugate of X(42369)
X(42401) = polar conjugate of the complementary conjugate of X(38976)
X(42401) = barycentric product X(i)*X(j) for these {i, j}: {6, 42369}, {276, 15352}
X(42401) = barycentric quotient X(i)/X(j) for these (i, j): (107, 418), (275, 32320), (393, 42293), (523, 41219), (933, 23606), (1093, 15451)
X(42401) = trilinear product X(i)*X(j) for these {i, j}: {31, 42369}, {158, 42405}, {276, 36126}, {811, 8794}, {823, 8795}
X(42401) = trilinear quotient X(i)/X(j) for these (i, j): (158, 42293), (823, 418), (1577, 41219)
X(42401) = trilinear pole of the line {4, 6752}
X(42401) = Cevapoint of X(i) and X(j) for these (i, j): {4, 42293}, {647, 42400}
X(42401) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 41219}, {255, 42293}, {418, 822}
X(42401) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (107, 418), (275, 32320), (393, 42293), (523, 41219)

X(42402) = POLAROLOGIC CENTER OF THESE TRIANGLES: ORTHIC TO YFF CONTACT

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

The reciprocal polarologic center of these triangles is X(42403)

X(42402) lies on this line: {6542, 32094}

X(42403) = POLAROLOGIC CENTER OF THESE TRIANGLES: YFF CONTACT TO ORTHIC

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

The reciprocal polarologic center of these triangles is X(42402)

X(42403) lies on these lines: {4, 38360}, {2501, 42399}, {3798, 6994}, {4024, 39532}, {6590, 16228}

X(42404) = TRIPOLE OF THE T-ISOGONAL-AXIS OF THESE TRIANGLES: ABC WRT ANTI-WASAT

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

The correspondent reciprocal tripole of these triangles is X(42405)

X(42404) lies on these lines: {}

X(42404) = trilinear pole of the line {52, 6751}
X(42404) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(35360)}} and {{A, B, C, X(110), X(14570)}}
X(42404) = Cevapoint of X(5) and X(42293)

X(42405) = TRIPOLE OF THE T-ISOGONAL-AXIS OF THESE TRIANGLES: ANTI-WASAT WRT ABC

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

The correspondent reciprocal tripole of these triangles is X(42404)

X(42405) lies on the MacBeath circumconic and these lines: {110, 6528}, {275, 287}, {276, 4993}, {648, 42401}, {895, 8795}, {933, 22456}, {2987, 8794}, {4558, 6331}, {35360, 41208}

X(42405) = complement of the anticomplementary conjugate of X(42331)
X(42405) = isogonal conjugate of X(42293)
X(42405) = isotomic conjugate of X(17434)
X(42405) = polar conjugate of X(15451)
X(42405) = barycentric product X(i)*X(j) for these {i, j}: {76, 16813}, {95, 6528}, {99, 8795}, {107, 34384}, {264, 18831}, {275, 6331}
X(42405) = barycentric quotient X(i)/X(j) for these (i, j): (4, 15451), (5, 34983), (54, 39201), (95, 520), (97, 32320), (99, 5562)
X(42405) = trilinear product X(i)*X(j) for these {i, j}: {75, 16813}, {92, 18831}, {95, 823}, {162, 276}, {255, 42401}, {275, 811}
X(42405) = trilinear quotient X(i)/X(j) for these (i, j): (92, 15451), (95, 822), (107, 2179), (162, 217), (275, 810), (276, 656)
X(42405) = orthocorrespondent of X(130)
X(42405) = trilinear pole of the line {3, 95}
X(42405) = intersection, other than A,B,C, of conic {{A, B, C, X(2), X(35360)}} and MacBeath circumconic
X(42405) = Cevapoint of X(i) and X(j) for these (i, j): {264, 18314}, {648, 6528}, {850, 40684}
X(42405) = X(648)-cross conjugate of-X(18831)
X(42405) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 15451}, {51, 822}, {216, 810}, {217, 656}
X(42405) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 15451), (5, 34983), (54, 39201), (95, 520)

X(42406) = TRIPOLE OF THE T-ISOGONAL-AXIS OF THESE TRIANGLES: ABC WRT ARIES

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

The correspondent reciprocal tripole of these triangles is X(42407)

X(42406) lies on these lines: {2, 311}, {6, 6393}, {114, 41761}, {141, 37067}, {216, 3788}, {230, 34254}, {233, 3734}, {315, 8553}, {325, 1609}, {571, 16925}, {577, 620}, {626, 10979}, {631, 5157}, {1879, 32961}, {1975, 9722}, {3815, 11324}, {7774, 13345}, {7778, 36751}, {7791, 14806}, {7803, 13351}, {7862, 36412}, {11511, 38751}, {14060, 41757}, {17907, 34990}, {36212, 41770}

X(42406) = {X(2), X(40697)}-harmonic conjugate of X(41760)

X(42407) = TRIPOLE OF THE T-ISOGONAL-AXIS OF THESE TRIANGLES: ARIES WRT ABC

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

The correspondent reciprocal tripole of these triangles is X(42406)

X(42407) lies on these lines: {6, 6393}, {25, 317}, {69, 1976}, {76, 2165}, {95, 41271}, {99, 41761}, {111, 42297}, {251, 7774}, {305, 13854}, {308, 7795}, {393, 3926}, {491, 8577}, {492, 8576}, {577, 32458}, {670, 6389}, {1502, 16081}, {1989, 32833}, {2395, 3267}, {2963, 32832}, {2998, 7836}, {3108, 16989}, {6387, 31639}, {7778, 8770}, {7792, 39951}, {7799, 34288}, {17907, 39645}, {31401, 39968}

X(42407) = isogonal conjugate of X(42295)
X(42407) = isotomic conjugate of X(3767)
X(42407) = polar conjugate of X(41762)
X(42407) = barycentric product X(i)*X(j) for these {i, j}: {69, 34405}, {523, 42297}
X(42407) = barycentric quotient X(i)/X(j) for these (i, j): (3, 40947), (4, 41762), (63, 2083), (69, 1899), (75, 17871), (76, 41760)
X(42407) = trilinear product X(i)*X(j) for these {i, j}: {63, 34405}, {661, 42297}
X(42407) = trilinear quotient X(i)/X(j) for these (i, j): (63, 40947), (69, 2083), (76, 17871), (92, 41762), (304, 1899), (326, 39643)
X(42407) = trilinear pole of the line {512, 6333}
X(42407) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(7807)}}
X(42407) = Cevapoint of X(2) and X(3926)
X(42407) = X(520)-cross conjugate of-X(670)
X(42407) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 40947}, {25, 2083}, {32, 17871}, {48, 41762}
X(42407) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 40947), (4, 41762), (63, 2083), (69, 1899)

X(42408) = TRIPOLE OF THE T-ISOGONAL-AXIS OF THESE TRIANGLES: ABC WRT GARCIA-REFLECTION

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

The correspondent reciprocal tripole of these triangles is X(651)

X(42408) lies on these lines: {}

X(42408) = trilinear pole of the line {145, 1837}
X(42408) = Cevapoint of X(650) and X(14923)

X(42409) = TRIPOLE OF THE T-ISOGONAL-AXIS OF THESE TRIANGLES: ABC WRT HONSBERGER

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

The correspondent reciprocal tripole of these triangles is X(1)

X(42409) lies on these lines: {105, 7676}, {3673, 42326}, {3693, 32019}, {17278, 34018}, {31169, 34578}

X(42410) = TRIPOLE OF THE T-ISOGONAL-AXIS OF THESE TRIANGLES: ABC WRT JOHNSON

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

The correspondent reciprocal tripole of these triangles is X(275)

X(42410) lies on the Kiepert hyperbola and these lines: {4, 5449}, {96, 7542}, {262, 31236}, {275, 3580}, {343, 2986}, {801, 37636}, {5392, 37638}, {5961, 18316}, {13567, 40393}, {26958, 34289}

X(42410) = polar conjugate of X(6240)
X(42410) = barycentric quotient X(i)/X(j) for these (i, j): (3, 12038), (4, 6240)
X(42410) = trilinear quotient X(i)/X(j) for these (i, j): (63, 12038), (92, 6240)
X(42410) = trilinear pole of the line {523, 18403}
X(42410) = intersection, other than A,B,C, of Kiepert hyperbola and conic {{A, B, C, X(95), X(18817)}}
X(42410) = Cevapoint of X(6) and X(1658)
X(42410) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 12038}, {48, 6240}
X(42410) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 12038), (4, 6240)

X(42411) = X(3)X(39163) ∩ X(4)X(39162)

Barycentrics    Sqrt(-3*S^2+SW^2)*(S^2-3*SB*SC)+2*(S^2-2*SB*SC)*Sqrt(-3*S^2+2*sqrt(-3*S^2+SW^2)*(9*R^2-2*SW)-18*SW*R^2+5*SW^2)+(3*SA-2*SW)*S^2+3*SB*SC*SW : :
Barycentrics    a^2*SA*(y+z)-SB*SC*x : :, where x : y : z = X(40852)
X(42411) = 4*X(3)-3*X(39163) = 2*X(4)-3*X(39162) = X(3146)-3*X(39158) = 5*X(3522)-3*X(39159) = 3*X(39163)-2*X(40852)

Contributed by César Lozada, March 25, 2021.

X(42411) lies on the cubics K004 (Darboux cubic), K187, K852, K855 and these lines: {3, 39163}, {4, 39162}, {20, 3413}, {30, 40851}, {1498, 40993}, {3146, 39158}, {3522, 39159}

X(42411) = reflection of X(i) in X(j) for these (i, j): (40852, 3), (42412, 20)
X(42411) = isogonal conjugate of X(42412)
X(42411) = X(3)-vertex conjugate of-X(40993)
X(42411) = intersection, other than A,B,C, of conics {{A, B, C, X(3), X(39162)}} and {{A, B, C, X(4), X(39158)}}
X(42411) = {X(3), X(40852)}-harmonic conjugate of X(39163)

X(42412) = X(3)X(39162) ∩ X(4)X(39163)

Barycentrics    sqrt(-3*S^2+SW^2)*(S^2-3*SB*SC)-2*(S^2-2*SB*SC)*sqrt(-3*S^2+2*sqrt(-3*S^2+SW^2)*(9*R^2-2*SW)-18*SW*R^2+5*SW^2)+(3*SA-2*SW)*S^2+3*SB*SC*SW : :
Barycentrics   a^2*SA*(y+z)-SB*SC*x : :, where x : y : z = X(40851)
X(42412) = 4*X(3)-3*X(39162) = 2*X(4)-3*X(39163) = X(3146)-3*X(39159) = 5*X(3522)-3*X(39158) = 3*X(39162)-2*X(40851)

Contributed by César Lozada, March 25, 2021.

X(42412) lies on the cubics K004 (Darboux cubic), K187, K852, K855 and these lines: {3, 39162}, {4, 39163}, {20, 3413}, {30, 40852}, {1498, 40994}, {3146, 39159}, {3522, 39158}

X(42412) = reflection of X(i) in X(j) for these (i, j): (40851, 3), (42411, 20)
X(42412) = isogonal conjugate of X(42411)
X(42412) = X(3)-vertex conjugate of-X(40994)
X(42412) = intersection, other than A,B,C, of conics {{A, B, C, X(3), X(39163)}} and {{A, B, C, X(4), X(32443)}}
X(42412) = {X(3), X(40851)}-harmonic conjugate of X(39162)

leftri

Points on the Cullen cubic: X(42413)-X(42421)

rightri

This preamble and points X(42413)-X(42413) are contributed by Peter Moses, March 25, 2021.

The Cullen cubic is indexed as K369; see K369.

Points (42413)-X(42420) are Gibert points, as in the preamble just before X(42085).

X(42413) = GIBERT(SQRT(3),-5/2,3) POINT

Barycentrics    a^2*S + 3*a^2*SA - 5*SB*SC : :

X(42413) lies on the cubic K369 and these lines: {2, 42271}, {3, 23263}, {4, 5418}, {5, 6496}, {6, 5059}, {20, 1152}, {30, 1587}, {371, 23269}, {372, 11001}, {376, 1328}, {382, 6407}, {485, 15682}, {486, 17538}, {550, 6452}, {590, 17578}, {631, 22615}, {641, 26615}, {1131, 3068}, {1132, 6410}, {1151, 3543}, {1588, 1657}, {1702, 28172}, {3522, 23261}, {3523, 42283}, {3524, 42268}, {3525, 35787}, {3528, 6565}, {3529, 6420}, {3534, 13935}, {3627, 9540}, {3832, 6409}, {3845, 6455}, {3850, 6451}, {3853, 6449}, {3854, 32789}, {5056, 6411}, {5073, 23249}, {5076, 35255}, {6221, 23253}, {6396, 23275}, {6435, 7581}, {6439, 8972}, {6448, 15704}, {6450, 15686}, {6471, 15683}, {6474, 15684}, {6478, 9681}, {6488, 42265}, {6497, 15690}, {6501, 17800}, {7584, 15681}, {7585, 42272}, {8252, 21734}, {9543, 13846}, {9683, 14865}, {10299, 42274}, {10304, 42262}, {10577, 21735}, {11541, 35820}, {12103, 13785}, {12296, 35947}, {12819, 15715}, {13925, 35404}, {15640, 41945}, {15717, 42270}, {18991, 28158}, {19066, 28164}, {23273, 42261}, {29317, 39876}, {35776, 37946}, {42140, 42191}, {42141, 42192}, {42160, 42254}, {42161, 42255}

X(42414) = GIBERT(SQRT(3),5/2,-3) POINT

Barycentrics    a^2*S - 3*a^2*SA + 5*SB*SC : :

X(42414) lies on the cubic K369 and these lines: {2, 42272}, {3, 23253}, {4, 5420}, {5, 6497}, {6, 5059}, {20, 1151}, {30, 1588}, {371, 11001}, {372, 23275}, {376, 1327}, {382, 6408}, {485, 17538}, {486, 15682}, {550, 6451}, {615, 17578}, {631, 22644}, {642, 26616}, {1131, 6409}, {1132, 3069}, {1152, 3543}, {1587, 1657}, {1703, 28172}, {3522, 23251}, {3523, 42284}, {3524, 42269}, {3525, 35786}, {3528, 6564}, {3529, 6419}, {3534, 9540}, {3627, 13935}, {3832, 6410}, {3845, 6456}, {3850, 6452}, {3853, 6450}, {3854, 32790}, {5056, 6412}, {5073, 23259}, {5076, 35256}, {6200, 23269}, {6398, 23263}, {6436, 7582}, {6440, 13941}, {6447, 9541}, {6449, 15686}, {6470, 15683}, {6475, 15684}, {6479, 13939}, {6489, 42262}, {6496, 15690}, {6500, 17800}, {7583, 15681}, {7586, 42271}, {8253, 21734}, {10299, 42277}, {10304, 42265}, {10576, 21735}, {11541, 35821}, {12103, 13665}, {12297, 35946}, {12818, 15715}, {13993, 35404}, {15640, 41946}, {15717, 42273}, {18992, 28158}, {19065, 28164}, {23267, 42260}, {29317, 39875}, {35777, 37946}, {42140, 42193}, {42141, 42194}, {42160, 42256}, {42161, 42257}

X(42415) = GIBERT(20,-7,11) POINT

Barycentrics    (20*a^2*S)/Sqrt[3] + 11*a^2*SA - 14*SB*SC : :

X(42415) lies on the cubic K369 and these lines: {15, 10188}, {546, 18582}, {550, 11486}, {3530, 10645}, {3861, 34754}, {5237, 42122}, {5321, 11737}, {5334, 14869}, {5350, 19107}, {10654, 34200}, {11485, 15687}, {14891, 16961}, {15720, 22237}, {41101, 42136}

X(42416) = GIBERT(20,7,-11) POINT

Barycentrics    (20*a^2*S)/Sqrt[3] - 11*a^2*SA + 14*SB*SC : :

X(42416) lies on the cubic K369 and these lines: {16, 10187}, {546, 18581}, {550, 11485}, {3530, 10646}, {3861, 34755}, {5238, 42123}, {5318, 11737}, {5335, 14869}, {5349, 19106}, {10653, 34200}, {11486, 15687}, {14891, 16960}, {15720, 22235}, {41100, 42137}

X(42417) = GIBERT(9*SQRT(3),-5,8) POINT

Barycentrics    9*a^2*S + 8*a^2*SA - 10*SB*SC : :

X(42417) lies on the cubic K369 and these lines: {2, 489}, {6, 11001}, {30, 6419}, {140, 41951}, {371, 3845}, {372, 15690}, {376, 6426}, {381, 6447}, {486, 15701}, {547, 6453}, {590, 5066}, {615, 6451}, {1327, 3830}, {1328, 6221}, {1384, 19099}, {1588, 19708}, {3070, 6470}, {3312, 3534}, {3316, 23261}, {3522, 6489}, {3533, 10147}, {3543, 3592}, {3545, 6425}, {5054, 9681}, {5055, 41963}, {6200, 11812}, {6396, 8703}, {6408, 15695}, {6409, 15719}, {6420, 15686}, {6429, 23275}, {6441, 15640}, {6476, 6565}, {6482, 41985}, {6500, 15685}, {7584, 15759}, {8396, 13810}, {8960, 14893}, {9541, 13847}, {9680, 15703}, {10109, 42270}, {10577, 11540}, {11917, 13666}, {12100, 13993}, {12101, 35821}, {13663, 33457}, {13786, 26341}, {13846, 41099}, {13951, 15722}, {14269, 41952}, {14891, 35813}, {15697, 19053}, {19710, 42259}, {31487, 35403}, {32789, 41955}, {33699, 35822}, {34200, 41964}, {35737, 36836}, {35812, 38071}, {41100, 42200}, {41101, 42202}

X(42418) = GIBERT(9*SQRT(3),5,-8) POINT

Barycentrics    9*a^2*S - 8*a^2*SA + 10*SB*SC : :

X(42418) lies on the cubic K369 and these lines: {2, 490}, {6, 11001}, {30, 6420}, {140, 41952}, {371, 15690}, {372, 3845}, {376, 6425}, {381, 6448}, {485, 15701}, {547, 6454}, {590, 6452}, {615, 5066}, {1327, 6398}, {1328, 3830}, {1384, 19100}, {1587, 19708}, {3071, 6471}, {3311, 3534}, {3317, 23251}, {3522, 6488}, {3533, 10148}, {3543, 3594}, {3545, 6426}, {5054, 10195}, {5055, 41964}, {5067, 17852}, {6200, 8703}, {6396, 11812}, {6407, 15695}, {6410, 15719}, {6419, 15686}, {6430, 23269}, {6442, 15640}, {6477, 6564}, {6483, 41985}, {6501, 15685}, {7583, 15759}, {8416, 13691}, {8960, 17504}, {8976, 15722}, {10109, 42273}, {10304, 31454}, {10576, 11540}, {11916, 13786}, {12100, 13925}, {12101, 35820}, {13666, 26348}, {13783, 33456}, {13846, 15698}, {13847, 41099}, {14269, 41951}, {14891, 35812}, {15697, 19054}, {15708, 31414}, {17851, 32790}, {19710, 42258}, {33699, 35823}, {34200, 41963}, {35737, 36843}, {35813, 38071}, {41100, 42199}, {41101, 42201}

X(42419) = GIBERT(54,-7,13) POINT

Barycentrics    18*Sqrt[3]*a^2*S + 13*a^2*SA - 14*SB*SC : :

X(42419) lies on the cubic K369 and these lines: {2, 11485}, {6, 19710}, {30, 41974}, {61, 5066}, {398, 10109}, {3412, 14892}, {3830, 5344}, {3845, 40693}, {3860, 11542}, {5238, 12100}, {8703, 22238}, {10646, 15759}, {10654, 33699}, {12101, 12816}, {15690, 41101}, {15713, 22236}, {15716, 37641}, {16268, 41978}, {22235, 41099}, {41107, 42108}, {41112, 42136}, {41113, 42098}, {41990, 42159}

X(42420) = GIBERT(54,7,-13) POINT

Barycentrics    18*Sqrt[3]*a^2*S - 13*a^2*SA + 14*SB*SC : : X(42420) lies on the cubic K369 and these lines: {2, 11486}, {6, 19710}, {30, 41973}, {62, 5066}, {397, 10109}, {3411, 14892}, {3830, 5343}, {3845, 40694}, {3860, 11543}, {5237, 12100}, {8703, 22236}, {10645, 15759}, {10653, 33699}, {12101, 12817}, {15690, 41100}, {15713, 22238}, {15716, 37640}, {16267, 41977}, {22237, 41099}, {41108, 42109}, {41112, 42095}, {41113, 42137}, {41990, 42162}

X(42421) = X(6)X(194)∩X(30)X(182)

Barycentrics    {Sqrt[3]*(1 + 2*Cos[2*w])*Csc[w]*Sec[w], Csc[w]^2, 2*(-1 + Cot[w]^2)} : :
Barycentrics    2*a^6 + 2*a^4*b^2 + a^2*b^4 + 2*a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 : :

X(42421) lies on the cubic K369 and these lines: {5, 39750}, {6, 194}, {30, 182}, {32, 141}, {39, 15870}, {69, 19689}, {81, 19700}, {83, 316}, {187, 10007}, {193, 19692}, {385, 24273}, {511, 32134}, {524, 6661}, {732, 5007}, {736, 7804}, {940, 19670}, {1078, 34573}, {1350, 10788}, {1352, 11842}, {1503, 3398}, {2076, 10346}, {3094, 3972}, {3329, 5116}, {3407, 7792}, {3416, 10789}, {3618, 6655}, {3629, 5039}, {3631, 19702}, {3763, 7793}, {4383, 19669}, {5008, 14994}, {5031, 6680}, {5033, 8357}, {5038, 6329}, {5085, 7470}, {5092, 14881}, {5171, 21167}, {5207, 10583}, {5718, 19683}, {5846, 12194}, {7750, 10345}, {7770, 8177}, {7773, 7948}, {7808, 8364}, {7829, 29012}, {7878, 13331}, {7894, 41747}, {9053, 12195}, {9300, 10352}, {10191, 22352}, {10328, 34482}, {10333, 12206}, {10334, 41624}, {11356, 40825}, {12007, 12177}, {12110, 29181}, {12151, 20583}, {13193, 32242}, {14561, 37243}, {15516, 32135}, {16285, 33786}, {18501, 31670}, {19679, 28369}, {32515, 35426}, {33185, 39603}, {36759, 37341}, {36760, 37340}

X(42421) = 5th-Brocard-to-ABC similarity image of X(141)

leftri

Points on the nine-point circle: X(42422)-X(42426)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, March 26, 2021.

The appearance of {i,j} in the following list means that X(i) and X(j) are a pair of antipodes on the nine-point circle; i.e., each is the reflection of the other in the center, X(5), of the nine-point circle.

{11,119}, {113,125}, {114,115}, {115,114}, {116,118}, {117,124}, {118,116}, {119,11}, {120,5511}, {121,5510}, {122,133}, {123,25640}, {124,117}, {125,113}, {126,5512}, {127,132}, {128,137}, {129,130}, {130,129}, {131,136}, {132,127}, {133,122}, {136,131}, {137,128}, {1312,1313}, {1313,1312}, {1560,14672}, {1566,33331}, {2039,2040}, {2040,2039}, {2679,33330}, {3258,25641}, {3259,31841}, {5099,16188}, {5139,31842}, {5510,121}, {5511,120}, {5512,126}, {5513,25642}, {5520,42422}, {5521,42423}, {5950,5952}, {5952,5950}, {6092,31654}, {10017,39535}, {11569,13994}, {12052,42424}, {12494,13234}, {12624,13249}, {13234,12494}, {13249,12624}, {13994,11569}, {14672,1560}, {16177,18809}, {16188,5099}, {18402,20625}, {18809,16177}, {20625,18402}, {25640,123}, {25641,3258}, {25642,5513}, {25652,42425}, {31654,6092}, {31841,3259}, {31842,5139}, {33330,2679}, {33331,1566}, {33333,35591}, {35591,33333}, {38971,42426}, {39535,10017}, {42422,5520}, {42423,5521}, {42424,12052}, {42425,25652}, {42426,38971}

Theorem (Moses): Suppose that P = p : q : r is a point, and define f(P) = p*((a^2 - b^2 + c^2)*q + (-a^2 - b^2 + c^2)*r)*((-b^2 + c^2)*q*r + p*(c^2*q - b^2*r)) : : . The point f(P) is on the nine-point circle, and f(P) is the center of the rectangular circumhyperbola {{A, B, C, X(4), P}}. The perspector of the hyperbola lies on the orthic axis.

The appearance of {i, {i(1),i(2),...i(n),} {name}} in the following list means that X(i) = f(X(k)) for k = 1,2,...,n, and that the circumhyperbola passing through these points has the indicated name, if there is one:

{11, {1, 4, 7, 8, 9, 21, 79, 80, 84, 90, 104, 177, 256, 294, 314, 885, 941, 943, 981, 983, 987, 989, 1000, 1039, 1041, 1061, 1063, 1156, 1172, 1251, 1320, 1389, 1392, 1476, 1896, 1937, 2298, 2320, 2335, 2344, 2346, 2481, 2648, 2997, 3062, 3065, 3254, 3255, 3296, 3307, 3308, 3427, 3467, 3495, 3551, 3577, 3680, 4180, 4866, 4876, 4900, 5377, 5424, 5551, 5553, 5555, 5556, 5557, 5558, 5559, 5560, 5561, 5665, 6595, 6596, 6597, 6598, 6599, 6601, 7003, 7049, 7091, 7126, 7133, 7149, 7155, 7160, 7161, 7162, 7261, 7284, 7285, 7317, 7319, 7320, 7595, 7707, 8372, 8759, 8809, 9365, 9372, 9442, 10266, 10305, 10307, 10308, 10309, 10390, 10429, 10435, 11279, 11604, 11609, 12641, 12867, 12868, 13143, 13426, 13454, 13602, 13606, 14224, 14496, 14497, 14947, 15173, 15175, 15176, 15179, 15180, 15314, 15315, 15446, 15909, 15910, 15997, 15998, 16005, 16615, 17097, 17098, 17501, 18299, 18490, 19551, 21398, 23836, 23838, 23893, 23959, 24297, 24298, 24300, 24302, 26722, 30479, 30494, 30500, 30513, 31316, 31507, 31509, 32635, 33576, 33653, 33696, 34215, 34216, 34256, 34485, 34894, 34917, 34918, 34919, 35097, 35355, 36121, 36599, 36798, 37518, 38249, 38250, 38251, 38261, 38268, 38270, 38271, 38272, 38274, 38306, 38307, 38308, 39144, 39145, 39768, 40396, 40454, 40565, 40566, 40779, 41527, 42013, 42015, 42017}, {Feuerbach circumhyperbola}}

{113, {4, 110, 14264, 15329, 18881, 39985, 41512}, {}}

{114, {4, 99, 4226, 14265, 34174, 36875, 41173}, {}}

{115, {2, 4, 10, 13, 14, 17, 18, 76, 83, 94, 96, 98, 226, 262, 275, 321, 459, 485, 486, 598, 671, 801, 1029, 1131, 1132, 1139, 1140, 1327, 1328, 1446, 1676, 1677, 1751, 1916, 2009, 2010, 2051, 2052, 2394, 2592, 2593, 2671, 2672, 2986, 2996, 3316, 3317, 3366, 3367, 3370, 3373, 3374, 3381, 3382, 3387, 3388, 3391, 3392, 3397, 3399, 3406, 3407, 3413, 3414, 3424, 3429, 3590, 3591, 3597, 4049, 4052, 4080, 4444, 5392, 5395, 5397, 5401, 5402, 5403, 5404, 5466, 5485, 5487, 5488, 5490, 5491, 5503, 6177, 6178, 6504, 6539, 6568, 6569, 6625, 7578, 7607, 7608, 7612, 8587, 8781, 8796, 8808, 9180, 9221, 9290, 9302, 9381, 10153, 10155, 10159, 10185, 10187, 10188, 10194, 10195, 10290, 10302, 10484, 10511, 11121, 11122, 11140, 11167, 11170, 11172, 11538, 11599, 11602, 11603, 11606, 11608, 11611, 11668, 11669, 12066, 12816, 12817, 12818, 12819, 12820, 12821, 12822, 12823, 13380, 13478, 13576, 13579, 13580, 13581, 13582, 13583, 13584, 13585, 13599, 14223, 14226, 14228, 14229, 14231, 14232, 14234, 14236, 14237, 14238, 14240, 14241, 14243, 14244, 14245, 14458, 14484, 14485, 14488, 14492, 14494, 14534, 14554, 14632, 14633, 16080, 16277, 17503, 17758, 18316, 18366, 18840, 18841, 18842, 18843, 18844, 18845, 21845, 21846, 22235, 22237, 22244, 22245, 24007, 24008, 24624, 27797, 30505, 30588, 31363, 31630, 31943, 32014, 32022, 32130, 32532, 33602, 33603, 33604, 33605, 33606, 33607, 33698, 34087, 34089, 34091, 34258, 34289, 34475, 34899, 35005, 35098, 35353, 36316, 36317, 36907, 37865, 37874, 37892, 38253, 38259, 38309, 39284, 39295, 39641, 39642, 39994, 40012, 40013, 40016, 40017, 40021, 40024, 40030, 40031, 40104, 40105, 40149, 40158, 40159, 40162, 40163, 40167, 40168, 40178, 40393, 40395, 40448, 40515, 40706, 40707, 40718, 40824, 40831, 41194, 41195, 41895, 41899, 42006, 42010, 42011, 42023, 42024, 42035, 42036, 42062, 42063}, {Kiepert circumhyperbola}}

{116, {4, 103, 947, 1002, 1126, 1174, 2141, 3681, 3730, 4184, 7357, 8049, 10623, 13577, 33297, 39961, 39993}, {}}

{117, {4, 109, 7450}, {}}

{118, {4, 101, 4243}, {}}

{119, {4, 100, 3658, 14266, 39991}, {}}

{120, {4, 668, 1292, 4236, 14267}, {}}

{121, {4, 1293, 8050, 39264}, {}}

{122, {4, 20, 253, 1249, 1294, 3346, 3668, 5930, 6188, 8804, 8806, 9307, 10152, 14249, 14615, 14863, 15318, 15319, 16251, 18349, 31361, 33702, 33893, 33897, 35140, 35515, 38808, 39130}, {}}

{123, {4, 961, 998, 1295, 1766, 2995, 3436, 7219, 14257, 16049, 21147, 34263, 39990, 40457, 41364}, {}}

{124, {4, 58, 102, 573, 959, 994, 3417, 3869, 4225, 8048, 9309, 10571, 20028, 34242, 39992}, {}}

{125, {3, 4, 6, 54, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 248, 265, 290, 695, 879, 895, 1173, 1175, 1176, 1177, 1242, 1243, 1244, 1245, 1246, 1439, 1798, 1903, 1942, 1987, 2213, 2435, 2574, 2575, 2992, 2993, 3426, 3431, 3519, 3521, 3527, 3531, 3532, 3657, 4846, 5486, 5504, 5505, 5900, 6145, 6391, 6413, 6414, 6415, 6416, 8044, 8612, 8795, 8811, 8814, 9399, 9513, 10097, 10099, 10100, 10261, 10262, 10293, 10378, 10693, 11138, 11139, 11270, 11559, 11564, 11738, 11744, 12023, 13418, 13452, 13472, 13603, 13622, 13623, 14220, 14374, 14375, 14380, 14457, 14483, 14487, 14490, 14491, 14498, 14528, 14542, 14841, 14843, 14861, 15002, 15077, 15232, 15316, 15317, 15320, 15321, 15328, 15453, 15460, 15461, 15740, 15749, 16000, 16540, 16620, 16623, 16665, 16774, 16835, 16867, 17040, 17505, 17711, 18123, 18124, 18125, 18296, 18363, 18368, 18434, 18532, 18550, 19151, 19222, 20029, 20421, 21400, 22334, 22336, 22466, 26861, 28786, 28787, 28788, 30496, 31366, 31371, 32533, 32585, 32586, 32618, 32619, 33565, 34135, 34136, 34207, 34221, 34222, 34259, 34435, 34436, 34437, 34438, 34439, 34440, 34483, 34567, 34800, 34801, 34802, 34817, 35364, 35373, 35512, 35909, 36214, 36296, 36297, 37142, 38005, 38006, 38257, 38260, 38263, 38264, 38433, 38436, 38439, 38442, 38443, 38445, 38447, 38449, 38534, 38535, 38955, 39372, 39379, 39380, 39381, 39665, 39666, 40048, 40441, 41433, 41435, 41518, 41519, 41897, 41898, 42016, 42021, 42059}, {Jerabek circumhyperbola}}

{126, {4, 670, 1296, 11634, 14263, 14948, 34171, 34574, 36874}, {}}

{127, {4, 22, 251, 315, 1297, 3425, 4456, 4463, 8743, 11605, 11610, 13575, 14495}, {}}

{128, {4, 930}, {}}

{129, {4, 1303, 14586}, {}}

{130, {4, 51, 184, 217, 418, 1298, 5562, 20574, 27372, 31357, 32319}, {}}

{131, {4, 925, 30512}, {}}

{132, {4, 112, 877, 4230, 6528, 35908, 39265}, {}}

{133, {4, 107, 4240}, {}}

{134, {4, 52, 571, 3133, 39110}, {}}

{135, {4, 24, 317, 1299, 5412, 5413, 8745, 8882, 14111, 14518, 34756}, {}}

{136, {4, 93, 225, 254, 264, 393, 847, 1093, 1105, 1179, 1217, 1300, 1826, 6344, 6526, 6531, 8737, 8738, 8741, 8742, 8801, 8884, 14860, 15424, 16263, 17983, 18808, 18846, 18847, 18848, 18849, 18850, 18851, 18852, 18853, 18854, 18855, 24243, 24244, 32085, 34208, 35142, 36611, 36612, 38427, 38428, 40402, 41013, 41515, 41516}, {}}

{137, {4, 5, 53, 311, 327, 1141, 1263, 1487, 2165, 2980, 3459, 3613, 8797, 8800, 10412, 11082, 11087, 11816, 13450, 14225, 15619, 16837, 17500, 17507, 17703, 19712, 19713, 21011, 22261, 22335, 25043, 25148, 27352, 27353, 27356, 27360, 27361, 27364, 32535, 34449, 36300, 36301, 36809, 38305, 38899, 39286, 40449}, {{{A,B,C,X(4),X(5)}}}

{138, {4, 16813, 23232}, {}}

{139, {4, 324, 467, 11547, 14149, 23233, 39114}, {}}

{1312, {4, 1113, 15164, 16071}, {}}

{1313, {4, 1114, 15165, 16070}, {}}

{1560, {4, 648, 4235, 30247}, {}}

{1566, {4, 279, 514, 516, 2724, 6185, 10405, 14377, 14953, 23984, 30807, 34529, 35158}, {}}

{2039, {4, 1380, 3557}, {}}

{2040, {4, 1379, 3558}, {}}

{2679, {4, 32, 237, 263, 511, 512, 2211, 2698, 5360, 9292, 14251, 20022, 27375, 34157, 34214, 34238, 34854, 36892, 37841, 39684, 41520}, {}}

{3258, {4, 30, 477, 523, 1138, 1990, 3260, 3471, 5627, 5641, 6662, 9154, 9214, 11080, 11085, 11815, 13489, 14254, 14387, 14536, 15454, 16104, 19776, 19777, 21765, 32230, 34288, 35906, 36298, 36299, 36889, 36891, 39453, 41522}, {}}

{3259, {4, 56, 513, 517, 859, 945, 953, 957, 1457, 1875, 2183, 10428, 14260, 17101, 17139, 34431, 34434, 38008, 39173}, {}}

{5099, {4, 23, 316, 842, 1383, 8744, 10422, 10561, 10630, 13485, 13574, 14246, 23964, 41896}, {}}

{5139, {4, 25, 683, 1426, 1824, 2207, 2333, 3563, 6524, 8753, 8946, 8948, 14248, 14486, 14593, 15591, 17980, 18384, 31942, 34405, 34428, 36878, 39109, 40801, 41521}, {}}

{5190, {4, 27, 92, 278, 917, 1847, 6336, 8747, 17982, 36124, 36613, 37203, 40444, 40445, 40573, 40574}, {}}

{5509, {4, 31, 4215, 5508, 7139, 26893, 29009}, {}}

{5510, {4, 106, 7419, 14261, 14923, 41439, 41446}, {}}

{5511, {4, 105, 169, 3434, 4228, 14268, 34036, 39732, 40154}, {}}

{5512, {4, 111, 1995, 11185, 14262, 34166, 34241, 38331}, {}}

{5513, {4, 190, 4237}, {}}

{5514, {4, 40, 57, 189, 196, 223, 329, 937, 972, 1817, 2184, 3194, 3345, 8810, 14256, 26735, 34546, 36100, 38009, 40397, 41790}, {}}

{5515, {4, 75, 388, 1010, 1065, 1220, 2345, 4385, 34265, 37842}, {}}

{5516, {4, 145, 519, 3667, 4487}, {}}

{5517, {4, 81, 2994, 5739, 12514, 14258, 27174, 34260}, {}}

{5518, {4, 291, 979, 3223, 3501, 7093, 7224, 7346, 7350, 8817, 8927, 13588, 15323, 32937, 39741, 39976}, {}}

{5519, {4, 218, 518, 3309, 6604, 28914, 34159}, {}}

{5520, {4, 267, 1325, 2687, 4581, 5080, 16548, 29374}, {}}

{5521, {4, 19, 28, 34, 286, 915, 1118, 1119, 5317, 8751, 10977, 14493, 17981, 34406, 34408, 36125, 39267, 41505}, {}}

{5522, {4, 95, 631, 3087, 34285}, {}}

{9151, {4, 13586, 35146, 35511}, {}}

{9193, {4, 8598, 14255, 18823}, {}}

{10017, {4, 280, 515, 522, 2734, 10570, 39457, 40437}, {}}

{11792, {4, 140, 252, 1232, 6748, 11703, 13139, 13381, 13597, 15464, 21012, 22270, 26862, 30102, 36948}, {}}

{13612, {4, 282, 1034, 1490, 3176, 3341, 3347, 5932, 8805, 13614}, {}}

{13613, {4, 1032, 1073, 1498, 3343, 3348, 6617, 8807, 14361, 15324}, {}}

{13994, {4, 6094, 11159, 11568, 13377}, {}}

{13999, {4, 270, 1870, 2190, 5081, 7012, 17515}, {}}

{14672, {4, 2373, 7493, 34165, 41370}, {}}

{15607, {4, 55, 942, 955, 1859, 8021, 14547, 38007, 41509}, {}}

{15608, {4, 59, 7163, 15339}, {}}

{15609, {4, 15, 61, 8446, 11146, 11581, 11600, 13483, 16771, 19778, 34219, 39404, 39407}, {}}

{15610, {4, 16, 62, 8456, 11145, 11582, 11601, 13484, 16770, 19779, 34220, 39405, 39406}, {}}

{15611, {4, 596, 996, 1219, 4373, 4696, 10106, 11115, 17355}, {}}

{15612, {4, 693, 2723, 5179, 14956}, {}}

{16177, {4, 2071, 2693, 10419, 13573, 15262, 15384, 34170, 38937}, {}}

{{16188, {4, 691, 7468, 14221, 18333, 32708, 34175, 35139, 38939}, {}}

{16221, {4, 186, 250, 340, 562, 1825, 1835, 5962, 8739, 8740, 14222, 32710, 38936, 40388}, {}}

{20620, {4, 29, 158, 273, 281, 318, 7040, 8748, 11546, 32706, 36123, 36610, 40446, 40836}, {}}

{20621, {4, 1783, 4238, 18026, 26706}, {}}

{20622, {4, 4241, 26705, 36118, 41321}, {}}

{20625, {4, 1166, 7488, 15620, 18401}, {}}

{31653, {4, 63, 2982, 26872, 40575}, {}}

{31654, {4, 524, 1499, 1992, 6093, 9487, 13608, 15471, 22100, 27088, 34161}, {}}

{31655, {4, 892, 2696, 7472, 34169}, {}}

{31845, {4, 3952, 6011, 13589, 38938}, {}}

{33330, {4, 805, 12833, 13137}, {}}

{33504, {4, 441, 525, 1503, 9476, 14376, 34156, 34403, 36894}, {}}

{35579, {4, 520, 6000, 14379, 36893, 39174}, {}}

{35580, {4, 521, 1433, 6001, 39167, 39175}, {}}

{35581, {4, 526, 5663, 14385, 16169}, {}}

{35582, {4, 542, 690, 1640, 5967, 14357, 36890}, {}}

{35583, {4, 758, 6003, 15556, 27086, 39166}, {}}

{35584, {4, 826, 14378, 29012}, {}}

{35587, {4, 900, 952, 14584, 36944}, {}}

{35588, {4, 924, 1147, 13754}, {}}

{35591, {4, 143, 1154, 1510, 11135, 11136, 15907, 24772, 25044, 27357}, {}}

{35968, {4, 5879, 5897, 11413, 39268}, {}}

{35971, {4, 384, 1031, 2998, 3114, 9230, 14970, 37888, 39953}, {}}

{36471, {4, 2065, 2710, 15388, 37183, 38826, 41363}, {}}

{36472, {4, 249, 14253, 23700, 35296}, {}}

{38957, {4, 78, 18391, 18446}, {}}

{38958, {4, 82, 977, 5015, 11102}, {}}

{38959, {4, 85, 277, 673, 948, 2550, 16054}, {}}

{38960, {4, 86, 966, 3485, 11110, 31359, 40028}, {}}

{38964, {4, 91, 1478, 11103, 18815}, {}}

{38966, {4, 33, 1857, 4183, 7008, 7046, 7079, 34398, 36122, 40169}, {}}

{38967, {4, 37, 405, 1882, 5295, 14549, 41506}, {}}

{38968, {4, 42, 1011, 10449}, {}}

{38970, {4, 297, 6530, 14618, 18027, 23582}, {}}

{38971, {4, 850, 858, 1236, 2697, 5523, 10415, 14364, 21017, 39269, 40421}, {}}

{38974, {4, 401, 15351, 15412, 32545, 34536, 34538, 39682, 40815, 41204}, {}}

The appearance of {i, {i(1),i(2),...i(n),} {name}} in the following list means that X(i) is the perspector of the circumhyperbola passing through the points X(i(k)), and that the hyperbola has indicated name, if there is one:

{230, {4, 99, 4226, 14265, 34174, 36875, 41173}, {}}

{231, {4, 930}, {}}

{232, {4, 112, 877, 4230, 6528, 35908, 39265}, {}}

{468, {4, 648, 4235, 30247}, {}}

{523, {2, 4, 10, 13, 14, 17, 18, 76, 83, 94, 96, 98, 226, 262, 275, 321, 459, 485, 486, 598, 671, 801, 1029, 1131, 1132, 1139, 1140, 1327, 1328, 1446, 1676, 1677, 1751, 1916, 2009, 2010, 2051, 2052, 2394, 2592, 2593, 2671, 2672, 2986, 2996, 3316, 3317, 3366, 3367, 3370, 3373, 3374, 3381, 3382, 3387, 3388, 3391, 3392, 3397, 3399, 3406, 3407, 3413, 3414, 3424, 3429, 3590, 3591, 3597, 4049, 4052, 4080, 4444, 5392, 5395, 5397, 5401, 5402, 5403, 5404, 5466, 5485, 5487, 5488, 5490, 5491, 5503, 6177, 6178, 6504, 6539, 6568, 6569, 6625, 7578, 7607, 7608, 7612, 8587, 8781, 8796, 8808, 9180, 9221, 9290, 9302, 9381, 10153, 10155, 10159, 10185, 10187, 10188, 10194, 10195, 10290, 10302, 10484, 10511, 11121, 11122, 11140, 11167, 11170, 11172, 11538, 11599, 11602, 11603, 11606, 11608, 11611, 11668, 11669, 12066, 12816, 12817, 12818, 12819, 12820, 12821, 12822, 12823, 13380, 13478, 13576, 13579, 13580, 13581, 13582, 13583, 13584, 13585, 13599, 14223, 14226, 14228, 14229, 14231, 14232, 14234, 14236, 14237, 14238, 14240, 14241, 14243, 14244, 14245, 14458, 14484, 14485, 14488, 14492, 14494, 14534, 14554, 14632, 14633, 16080, 16277, 17503, 17758, 18316, 18366, 18840, 18841, 18842, 18843, 18844, 18845, 21845, 21846, 22235, 22237, 22244, 22245, 24007, 24008, 24624, 27797, 30505, 30588, 31363, 31630, 31943, 32014, 32022, 32130, 32532, 33602, 33603, 33604, 33605, 33606, 33607, 33698, 34087, 34089, 34091, 34258, 34289, 34475, 34899, 35005, 35098, 35353, 36316, 36317, 36907, 37865, 37874, 37892, 38253, 38259, 38309, 39284, 39295, 39641, 39642, 39994, 40012, 40013, 40016, 40017, 40021, 40024, 40030, 40031, 40104, 40105, 40149, 40158, 40159, 40162, 40163, 40167, 40168, 40178, 40393, 40395, 40448, 40515, 40706, 40707, 40718, 40824, 40831, 41194, 41195, 41895, 41899, 42006, 42010, 42011, 42023, 42024, 42035, 42036, 42062, 42063}, {Kiepert circumhyperbola}}

{647, {3, 4, 6, 54, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 248, 265, 290, 695, 879, 895, 1173, 1175, 1176, 1177, 1242, 1243, 1244, 1245, 1246, 1439, 1798, 1903, 1942, 1987, 2213, 2435, 2574, 2575, 2992, 2993, 3426, 3431, 3519, 3521, 3527, 3531, 3532, 3657, 4846, 5486, 5504, 5505, 5900, 6145, 6391, 6413, 6414, 6415, 6416, 8044, 8612, 8795, 8811, 8814, 9399, 9513, 10097, 10099, 10100, 10261, 10262, 10293, 10378, 10693, 11138, 11139, 11270, 11559, 11564, 11738, 11744, 12023, 13418, 13452, 13472, 13603, 13622, 13623, 14220, 14374, 14375, 14380, 14457, 14483, 14487, 14490, 14491, 14498, 14528, 14542, 14841, 14843, 14861, 15002, 15077, 15232, 15316, 15317, 15320, 15321, 15328, 15453, 15460, 15461, 15740, 15749, 16000, 16540, 16620, 16623, 16665, 16774, 16835, 16867, 17040, 17505, 17711, 18123, 18124, 18125, 18296, 18363, 18368, 18434, 18532, 18550, 19151, 19222, 20029, 20421, 21400, 22334, 22336, 22466, 26861, 28786, 28787, 28788, 30496, 31366, 31371, 32533, 32585, 32586, 32618, 32619, 33565, 34135, 34136, 34207, 34221, 34222, 34259, 34435, 34436, 34437, 34438, 34439, 34440, 34483, 34567, 34800, 34801, 34802, 34817, 35364, 35373, 35512, 35909, 36214, 36296, 36297, 37142, 38005, 38006, 38257, 38260, 38263, 38264, 38433, 38436, 38439, 38442, 38443, 38445, 38447, 38449, 38534, 38535, 38955, 39372, 39379, 39380, 39381, 39665, 39666, 40048, 40441, 41433, 41435, 41518, 41519, 41897, 41898, 42016, 42021, 42059}, {Jerabek circumhyperbola}}

{650, {1, 4, 7, 8, 9, 21, 79, 80, 84, 90, 104, 177, 256, 294, 314, 885, 941, 943, 981, 983, 987, 989, 1000, 1039, 1041, 1061, 1063, 1156, 1172, 1251, 1320, 1389, 1392, 1476, 1896, 1937, 2298, 2320, 2335, 2344, 2346, 2481, 2648, 2997, 3062, 3065, 3254, 3255, 3296, 3307, 3308, 3427, 3467, 3495, 3551, 3577, 3680, 4180, 4866, 4876, 4900, 5377, 5424, 5551, 5553, 5555, 5556, 5557, 5558, 5559, 5560, 5561, 5665, 6595, 6596, 6597, 6598, 6599, 6601, 7003, 7049, 7091, 7126, 7133, 7149, 7155, 7160, 7161, 7162, 7261, 7284, 7285, 7317, 7319, 7320, 7595, 7707, 8372, 8759, 8809, 9365, 9372, 9442, 10266, 10305, 10307, 10308, 10309, 10390, 10429, 10435, 11279, 11604, 11609, 12641, 12867, 12868, 13143, 13426, 13454, 13602, 13606, 14224, 14496, 14497, 14947, 15173, 15175, 15176, 15179, 15180, 15314, 15315, 15446, 15909, 15910, 15997, 15998, 16005, 16615, 17097, 17098, 17501, 18299, 18490, 19551, 21398, 23836, 23838, 23893, 23959, 24297, 24298, 24300, 24302, 26722, 30479, 30494, 30500, 30513, 31316, 31507, 31509, 32635, 33576, 33653, 33696, 34215, 34216, 34256, 34485, 34894, 34917, 34918, 34919, 35097, 35355, 36121, 36599, 36798, 37518, 38249, 38250, 38251, 38261, 38268, 38270, 38271, 38272, 38274, 38306, 38307, 38308, 39144, 39145, 39768, 40396, 40454, 40565, 40566, 40779, 41527, 42013, 42015, 42017}, {Feuerbach circumhyperbola}}

{676, {4, 279, 514, 516, 2724, 6185, 10405, 14377, 14953, 23984, 30807, 34529, 35158}, {}}

{1637, {4, 30, 477, 523, 1138, 1990, 3260, 3471, 5627, 5641, 6662, 9154, 9214, 11080, 11085, 11815, 13489, 14254, 14387, 14536, 15454, 16104, 19776, 19777, 21765, 32230, 34288, 35906, 36298, 36299, 36889, 36891, 39453, 41522}, {}}

{1886, {4, 4241, 26705, 36118, 41321}, {}}

{2485, {4, 22, 251, 315, 1297, 3425, 4456, 4463, 8743, 11605, 11610, 13575, 14495}, {}}

{2489, {4, 25, 683, 1426, 1824, 2207, 2333, 3563, 6524, 8753, 8946, 8948, 14248, 14486, 14593, 15591, 17980, 18384, 31942, 34405, 34428, 36878, 39109, 40801, 41521}, {}}

{2490, {4, 6553, 17539, 36606, 39697}, {}}

{2491, {4, 32, 237, 263, 511, 512, 2211, 2698, 5360, 9292, 14251, 20022, 27375, 34157, 34214, 34238, 34854, 36892, 37841, 39684, 41520}, {}}

{2492, {4, 23, 316, 842, 1383, 8744, 10422, 10561, 10630, 13485, 13574, 14246, 23964, 41896}, {}}

{2493, {4, 691, 7468, 14221, 18333, 32708, 34175, 35139, 38939}, {}}

{2501, {4, 93, 225, 254, 264, 393, 847, 1093, 1105, 1179, 1217, 1300, 1826, 6344, 6526, 6531, 8737, 8738, 8741, 8742, 8801, 8884, 14860, 15424, 16263, 17983, 18808, 18846, 18847, 18848, 18849, 18850, 18851, 18852, 18853, 18854, 18855, 24243, 24244, 32085, 34208, 35142, 36611, 36612, 38427, 38428, 40402, 41013, 41515, 41516}, {}}

{3003, {4, 110, 14264, 15329, 18881, 39985, 41512}, {}}

{3011, {4, 190, 4237}, {}}

{3012, {4, 658}, {}}

{3018, {4, 476, 7471, 34150}, {}}

{3064, {4, 29, 158, 273, 281, 318, 7040, 8748, 11546, 32706, 36123, 36610, 40446, 40836}, {}}

{3290, {4, 668, 1292, 4236, 14267}, {}}

{3291, {4, 670, 1296, 11634, 14263, 14948, 34171, 34574, 36874}, {}}

{3310, {4, 56, 513, 517, 859, 945, 953, 957, 1457, 1875, 2183, 10428, 14260, 17101, 17139, 34431, 34434, 38008, 39173}, {}}

{3806, {4, 141, 3618, 3867, 8362}, {}}

{4874, {4, 330, 3765, 3923, 6650}, {}}

{5089, {4, 1783, 4238, 18026, 26706}, {}}

{6103, {4, 685, 935, 7473, 16077, 17986, 35907}, {}}

{6129, {4, 40, 57, 189, 196, 223, 329, 937, 972, 1817, 2184, 3194, 3345, 8810, 14256, 26735, 34546, 36100, 38009, 40397, 41790}, {}}

{6130, {4, 401, 15351, 15412, 32545, 34536, 34538, 39682, 40815, 41204}, {}}

{6132, {4, 249, 14253, 23700, 35296}, {}}

{{6586, {4, 103, 947, 1002, 1126, 1174, 2141, 3681, 3730, 4184, 7357, 8049, 10623, 13577, 33297, 39961, 39993}, {}}

{6587, {4, 20, 253, 1249, 1294, 3346, 3668, 5930, 6188, 8804, 8806, 9307, 10152, 14249, 14615, 14863, 15318, 15319, 16251, 18349, 31361, 33702, 33893, 33897, 35140, 35515, 38808, 39130}, {}}

{6588, {4, 961, 998, 1295, 1766, 2995, 3436, 7219, 14257, 16049, 21147, 34263, 39990, 40457, 41364}, {}}

{6589, {4, 58, 102, 573, 959, 994, 3417, 3869, 4225, 8048, 9309, 10571, 20028, 34242, 39992}, {}}

{6590, {4, 75, 388, 1010, 1065, 1220, 2345, 4385, 34265, 37842}, {}}

{6591, {4, 19, 28, 34, 286, 915, 1118, 1119, 5317, 8751, 10977, 14493, 17981, 34406, 34408, 36125, 39267, 41505}, {}}

{6753, {4, 24, 317, 1299, 5412, 5413, 8745, 8882, 14111, 14518, 34756}, {}}

{7649, {4, 27, 92, 278, 917, 1847, 6336, 8747, 17982, 36124, 36613, 37203, 40444, 40445, 40573, 40574}, {}}

{7662, {4, 274, 26643, 39721}, {}}

{8105, {4, 1114, 15165, 16070}, {}}

{8106, {4, 1113, 15164, 16071}, {}}

{8607, {4, 109, 7450}, {}}

{8608, {4, 101, 4243}, {}}

{8609, {4, 100, 3658, 14266, 39991}, {}}

{8610, {4, 1293, 8050, 39264}, {}}

{8755, {4, 7452, 23987, 26704, 36127}, {}}

{8756, {4, 1897, 32704}, {}}

{9125, {4, 524, 1499, 1992, 6093, 9487, 13608, 15471, 22100, 27088, 34161}, {}}

{9189, {4, 8598, 14255, 18823}, {}}

{9209, {4, 376, 1494, 39263, 40138, 40385}, {}}

{10418, {4, 892, 2696, 7472, 34169}, {}}

{11176, {4, 13586, 35146, 35511}, {}}

{{12077, {4, 5, 53, 311, 327, 1141, 1263, 1487, 2165, 2980, 3459, 3613, 8797, 8800, 10412, 11082, 11087, 11816, 13450, 14225, 15619, 16837, 17500, 17507, 17703, 19712, 19713, 21011, 22261, 22335, 25043, 25148, 27352, 27353, 27356, 27360, 27361, 27364, 32535, 34449, 36300, 36301, 36809, 38305, 38899, 39286, 40449}, {{A,B,C,X(4), X(5)}}

{14273, {4, 468, 2501, 5203, 10603, 14052, 18020, 40118}, {}}

{14325, {4, 492, 3068, 18819, 39387}, {}}

{14326, {4, 491, 3069, 18820, 39388}, {}}

{14425, {4, 145, 519, 3667, 4487}, {}}

{14571, {4, 108, 4246, 23706}, {}}

{16040, {4, 1166, 7488, 15620, 18401}, {}}

{16230, {4, 297, 6530, 14618, 18027, 23582}, {}}

{16317, {4, 30256, 35179, 36877}, {}}

{16318, {4, 1289, 2409, 6529, 23977}, {}}

{21348, {4, 291, 979, 3223, 3501, 7093, 7224, 7346, 7350, 8817, 8927, 13588, 15323, 32937, 39741, 39976}, {}}

{33525, {4, 55, 942, 955, 1859, 8021, 14547, 38007, 41509}, {}}

{40134, {4, 3421, 4221, 18816}, {}}

X(42422) = NINE-POINT-CIRCLE ANTIPODE OF X(5520)

Barycentrics    (a^5*b - a^4*b^2 - 2*a^3*b^3 + 2*a^2*b^4 + a*b^5 - b^6 + a^5*c + a^3*b^2*c - 2*a*b^4*c - a^4*c^2 + a^3*b*c^2 - 2*a^2*b^2*c^2 + a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 + a*b^2*c^3 + 2*a^2*c^4 - 2*a*b*c^4 + b^2*c^4 + a*c^5 - c^6)*(a^6*b - a^4*b^3 - a^2*b^5 + b^7 + a^6*c - 2*a^5*b*c + a^3*b^3*c + a*b^5*c - b^6*c + a^2*b^3*c^2 - 3*b^5*c^2 - a^4*c^3 + a^3*b*c^3 + a^2*b^2*c^3 - 2*a*b^3*c^3 + 3*b^4*c^3 + 3*b^3*c^4 - a^2*c^5 + a*b*c^5 - 3*b^2*c^5 - b*c^6 + c^7) : :
X(42422) = X[20] - 3 X[38711], 3 X[381] + X[38588]

X(42422) lies on the nine-point circle and these lines: {2, 2687}, {4, 1290}, {5, 5520}, {11, 30}, {12, 31522}, {20, 38711}, {113, 513}, {114, 7626}, {115, 8609}, {119, 523}, {123, 2072}, {124, 11813}, {125, 517}, {136, 37982}, {381, 14686}, {403, 5146}, {429, 16221}, {431, 16178}, {442, 3258}, {3259, 9955}, {5099, 30444}, {5511, 11799}, {5840, 36167}, {6941, 38514}, {6949, 38570}, {7477, 38952}, {10017, 37565}, {11698, 36909}, {16177, 21530}, {30445, 38971}

X(42422) = midpoint of X(i) and X(j) for these {i,j}: {4, 1290}, {7477, 38952}
X(42422) = reflection of X(5520) in X(5)
X(42422) = reflection of X(119) in the Euler line
X(42422) = complement of X(2687)
X(42422) = orthocentroidal-circle-inverse of X(14686)
X(42422) = complement of the isogonal conjugate of X(2771)
X(42422) = medial-isogonal conjugate of X(2771)
X(42422) = orthic-isogonal conjugate of X(2771)
X(42422) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2771}, {42, 3013}, {2771, 10}, {37966, 8062}
X(42422) = X(4)-Ceva conjugate of X(2771)
X(42422) = X(100)-of-reflection-of-Euler-triangle in Euler line
X(42422) = X(5520)-of-Johnson-triangle

X(42423) = NINE-POINT-CIRCLE ANTIPODE OF X(5521)

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

X(42423) lies on the nine-point circle and these lines: {2, 915}, {3, 11}, {4, 13397}, {5, 5521}, {115, 18591}, {116, 18589}, {119, 34332}, {123, 11585}, {124, 21616}, {125, 21530}, {135, 429}, {136, 442}, {517, 15608}, {1214, 38964}, {1807, 38957}, {2072, 5520}, {5139, 30444}, {5164, 36472}, {5190, 6881}, {5511, 15760}, {5514, 42018}, {6842, 20620}, {6882, 13999}, {6907, 38966}, {16178, 37982}, {16221, 30447}, {20621, 21664}

X(42423) = midpoint of X(4) and X(13397)
X(42423) = reflection of X(5521) in X(5)
X(42423) = complement of X(915)
X(42423) = complement of the isogonal conjugate of X(912)
X(42423) = medial-isogonal conjugate of X(912)
X(42423) = orthic-isogonal conjugate of X(912)
X(42423) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 912}, {656, 3139}, {912, 10}, {914, 141}, {1737, 5}, {1795, 6713}, {1807, 18254}, {2252, 2}, {3658, 8062}, {8609, 226}, {18838, 1210}
X(42423) = X(4)-Ceva conjugate of X(912)
X(42423) = X(5521)-of-Johnson-triangle

X(42424) = NINE-POINT-CIRCLE ANTIPODE OF X(16221)

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

X(42424) lies on the nine-point circle and these lines: {2, 16167}, {3, 3258}, {4, 10420}, {5, 12052}, {30, 136}, {113, 924}, {115, 3284}, {122, 10257}, {125, 1568}, {128, 34333}, {131, 523}, {133, 36169}, {135, 403}, {137, 13557}, {1560, 36170}, {5099, 15760}, {5139, 11799}, {5448, 35588}, {5520, 37361}, {11585, 16177}, {15241, 21268}, {15544, 36472}, {18531, 38971}

X(42424) = midpoint of X(i) and X(j) for these {i,j}: {4, 10420}, {13557, 18403}
X(42424) = reflection of X(i) in X(j) for these {i,j}: {16221, 5}, {21268, 23323}
X(42424) = reflection of X(131) in the Euler line
X(42424) = complement of X(32710)
X(42424) = complement of the isogonal conjugate of X(17702)
X(42424) = orthoptic-circle-of-Steiner-inellipse-inverse of X(16167)
X(42424) = medial-isogonal conjugate of X(17702)
X(42424) = orthic-isogonal conjugate of X(17702)
X(42424) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 17702}, {656, 3154}, {3018, 226}, {7471, 8062}, {17702, 10}, {36062, 31379}
X(42424) = X(4)-Ceva conjugate of X(17702)
X(42424) = X(16221)-of-Johnson-triangle

X(42425) = NINE-POINT-CIRCLE ANTIPODE OF X(31845)

Barycentrics    (b - c)^2*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c - a*b*c - a*c^2 + c^3)*(-a^4 + a^3*b - a*b^3 + b^4 + a^3*c - a^2*b*c - 2*b^2*c^2 - a*c^3 + c^4) : :
X(42425) = 3 X[381] + X[14663], 5 X[1698] - X[34196], 3 X[1699] + X[21381], 3 X[34311] + X[34789]

X(42425) lies on the nine-point circle and these lines: {2, 6011}, {4, 759}, {5, 25652}, {11, 1365}, {12, 34194}, {30, 38612}, {113, 946}, {114, 14680}, {117, 7683}, {119, 6246}, {120, 37360}, {121, 9956}, {124, 38390}, {125, 867}, {381, 14663}, {1283, 8229}, {1698, 34196}, {1699, 21381}, {2051, 6044}, {6003, 8286}, {6941, 38511}, {10113, 16160}, {10478, 38480}, {10883, 19642}, {15763, 25640}, {20621, 37362}, {34311, 34789}

X(42425) = midpoint of X(4) and X(759)
X(42425) = reflection of X(31845) in X(5)
X(42425) = complement of X(6011)
X(42425) = complement of the isogonal conjugate of X(6003)
X(42425) = polar-circle inverse of X(30250)
X(42425) = medial-isogonal conjugate of X(6003)
X(42425) = orthic-isogonal conjugate of X(6003)
X(42425) = X(31845)-of-Johnson-triangle
X(42425) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 6003}, {6, 7178}, {513, 6734}, {2605, 35193}, {5174, 20316}, {6003, 10}, {8286, 125}, {13739, 8062}, {31603, 2886}, {33116, 3835}, {34772, 513}, {37583, 522}
X(42425) = X(4)-Ceva conjugate of X(6003)

X(42426) = NINE-POINT-CIRCLE ANTIPODE OF X(38971)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^6 - 2*a^4*b^2 + a^2*b^4 - b^6 - 2*a^4*c^2 + b^4*c^2 + a^2*c^4 + b^2*c^4 - c^6)*(a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 + a^4*b^4*c^2 - 2*a^2*b^6*c^2 - 2*a^6*c^4 + a^4*b^2*c^4 + b^6*c^4 - 2*a^2*b^2*c^6 + b^4*c^6 + 2*a^2*c^8 - c^10) : :
X(42426) = 3 X[403] - X[5523]

X(42426) lies on the nine-point circle and these lines: {2, 1304}, {4, 842}, {5, 38971}, {23, 14918}, {25, 16221}, {30, 127}, {53, 38970}, {113, 525}, {114, 7630}, {115, 232}, {122, 858}, {125, 468}, {132, 523}, {133, 16229}, {136, 37981}, {147, 250}, {427, 3258}, {647, 1560}, {1554, 2781}, {1843, 2679}, {2453, 37074}, {2715, 36472}, {2967, 39216}, {3818, 16760}, {5094, 14685}, {5139, 10151}, {5159, 35968}, {5512, 37984}, {5520, 37362}, {6103, 17986}, {8705, 12624}, {10152, 39062}, {10632, 15609}, {10633, 15610}, {11799, 14672}, {15451, 18402}, {16188, 18312}, {20389, 41377}, {30716, 36173}, {31842, 36170}, {35583, 41503}, {36183, 38974}, {37937, 40079}

X(42426) = midpoint of X(i) and X(j) for these {i,j}: {4, 935}, {17986, 35907}
X(42426) = reflection of X(38971) in X(5)
X(42426) = reflection of X(132) in the Euler line
X(42426) = complement of X(2697)
X(42426) = complement of the isogonal conjugate of X(2781)
X(42426) = polar-circle-inverse of X(842)
X(42426) = orthoptic-circle-of-Steiner-inellipse-inverse of X(1304)
X(42426) = Moses Radical circle inverse of X(1560)
X(42426) = medial-isogonal conjugate of X(2781)
X(42426) = orthic-isogonal conjugate of X(2781)
X(42426) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2781}, {31, 6103}, {2781, 10}, {37937, 8062}
X(42426) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 6103}, {4, 2781}
X(42426) = barycentric product X(18312)*X(37937)
X(42426) = barycentric quotient X(i)/X(j) for these {i,j}: {6103, 2697}, {37937, 5649}
X(42426) = {X(34366),X(35907)}-harmonic conjugate of X(6103)
X(42426) = X(112)-of-reflection-of-Euler-triangle-in-Euler-line
X(42426) = X(38971)-of-Johnson-triangle

X(42427) = ISOTOMIC CONJUGATE OF X(39159)

Barycentrics   -(sqrt(-3*S^2+SW^2)-6*SA+SW)*sqrt(2*OH^2*sqrt(-3*S^2+SW^2)-3*S^2-18*SW*R^2+5*SW^2)+(3*SA-SW)*sqrt(-3*S^2+SW^2)+3*SA^2+6*SB*SC-SW^2 : :
Barycentrics    y + z - x : :, where x:y:z = X(40990)

Contributed by César Lozada, March 25, 2021.

X(42422) lies on the cubic K007 (Lucas cubic) and these lines: {2, 40990}, {20, 3413}, {69, 39159}, {6190, 39158}

X(42427) = anticomplement of X(40990)
X(42427) = isotomic conjugate of X(39159)
X(42427) = cyclocevian conjugate of X(42428)
X(42427) = anticomplementary conjugate of the anticomplement of X(40992)
X(42427) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(6190)}} and {{A, B, C, X(4), X(32443)}}

X(42428) = ISOTOMIC CONJUGATE OF X(39158)

Barycentrics   (sqrt(-3*S^2+SW^2)-6*SA+SW)*sqrt(2*OH^2*sqrt(-3*S^2+SW^2)-3*S^2-18*SW*R^2+5*SW^2)+(3*SA-SW)*sqrt(-3*S^2+SW^2)+3*SA^2+6*SB*SC-SW^2 : :
Barycentrics    y + z - x : :, where x:y:z = X(40989)

Contributed by César Lozada, March 25, 2021.

X(42428) lies on the cubic K007 (Lucas cubic) and these lines: {2, 40989}, {20, 3413}, {69, 39158}, {6190, 39159}

X(42428) = anticomplement of X(40989)
X(42428) = isotomic conjugate of X(39158)
X(42428) = cyclocevian conjugate of X(42427)
X(42428) = anticomplementary conjugate of the anticomplement of X(40991)
X(42428) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(6190)}} and {{A, B, C, X(4), X(39158)}}

leftri

Gibert points on 7th Evans cubic, K1196: X(42429)-X(42436)

rightri

This preamble and points X(42429)-X(42436) are contributed by Peter Moses, March 29, 2021.

See K1196.



X(42429) = GIBERT(3,10,-13) POINT

Barycentrics    Sqrt[3]*a^2*S - 13*a^2*SA + 20*SB*SC : :

X(42429) lies on the cubic K1196 and these lines: {2, 43226}, {6, 42430}, {13, 15681}, {14, 16}, {15, 11001}, {17, 20}, {62, 5059}, {376, 16808}, {382, 16242}, {396, 15704}, {550, 37832}, {617, 22494}, {621, 36386}, {1657, 16965}, {3412, 42165}, {3529, 10653}, {3534, 12816}, {3543, 10646}, {3830, 16967}, {5073, 16645}, {5237, 33703}, {5318, 19710}, {8703, 33417}, {10304, 42105}, {10645, 15686}, {12820, 15688}, {14269, 33416}, {15640, 18581}, {15682, 37835}, {15683, 42086}, {15684, 16809}, {15685, 41101}, {15689, 42094}, {15691, 23302}, {15695, 42098}, {15697, 42092}, {16267, 42090}, {16962, 42127}, {17800, 42154}, {19708, 42106}, {23263, 35739}, {23303, 35404}, {34200, 42102}, {35400, 42115}, {41100, 42131}, {41107, 42087}, {41108, 41972}, {41121, 42137}, {41122, 42104}

X(42430) = GIBERT(-3,10,-13) POINT

Barycentrics    Sqrt[3]*a^2*S + 13*a^2*SA - 20*SB*SC : :

X(42430) lies on the cubic K1196 and these lines: {2, 43227}, {6, 42429}, {13, 15}, {14, 15681}, {16, 11001}, {18, 20}, {61, 5059}, {376, 16809}, {382, 16241}, {395, 15704}, {550, 37835}, {616, 22493}, {622, 36388}, {1657, 16964}, {3411, 42164}, {3529, 10654}, {3534, 12817}, {3543, 10645}, {3830, 16966}, {5073, 16644}, {5238, 33703}, {5321, 19710}, {8703, 33416}, {10304, 42104}, {10646, 15686}, {12821, 15688}, {14269, 33417}, {15640, 18582}, {15682, 37832}, {15683, 42085}, {15684, 16808}, {15685, 41100}, {15689, 42093}, {15691, 23303}, {15695, 42095}, {15697, 42089}, {16268, 42091}, {16963, 42126}, {17800, 42155}, {19708, 42103}, {23302, 35404}, {34200, 42101}, {35400, 42116}, {35931, 36770}, {41101, 42130}, {41107, 41971}, {41108, 42088}, {41121, 42105}, {41122, 42136}

X(42431) = GIBERT(3,4,-3) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 8*SB*SC : :

X(42431) lies on the cubic K1196 and these lines: {3, 36969}, {4, 16}, {5, 5351}, {6, 5073}, {13, 20}, {14, 3627}, {15, 1657}, {17, 550}, {30, 61}, {62, 382}, {140, 5350}, {202, 12953}, {203, 10483}, {376, 41121}, {381, 5237}, {395, 3853}, {396, 15704}, {398, 19107}, {530, 633}, {548, 16241}, {549, 12816}, {630, 33623}, {1656, 10646}, {3091, 16242}, {3105, 5869}, {3146, 10653}, {3200, 6759}, {3201, 37495}, {3206, 13352}, {3364, 42263}, {3365, 42264}, {3389, 35820}, {3390, 35821}, {3391, 35740}, {3392, 42241}, {3411, 17578}, {3522, 5366}, {3523, 16966}, {3529, 36967}, {3533, 42114}, {3534, 5352}, {3543, 5365}, {3544, 12820}, {3830, 16268}, {3843, 36843}, {3845, 16773}, {3850, 16967}, {3851, 11481}, {3858, 23303}, {5056, 33416}, {5059, 5335}, {5068, 42089}, {5076, 42153}, {5343, 42104}, {5868, 36992}, {7006, 12943}, {7755, 41408}, {8739, 35490}, {8740, 34797}, {10299, 42142}, {10654, 33703}, {10721, 36209}, {11001, 16962}, {11600, 15444}, {12103, 16772}, {12155, 33192}, {13491, 36978}, {14269, 41944}, {15681, 16267}, {15682, 42160}, {15683, 41112}, {15684, 41108}, {15687, 16963}, {15696, 16644}, {15712, 33417}, {15720, 42098}, {16960, 42090}, {16961, 42101}, {17800, 22236}, {21735, 42092}, {22832, 37463}, {23004, 41021}, {23251, 42206}, {23261, 42205}, {23302, 33923}, {32789, 42210}, {32790, 42209}, {34755, 42093}, {34783, 36979}, {38335, 41122}, {42177, 42266}, {42178, 42267}

X(42431) = {X(6),X(5073)}-harmonic conjugate of X(42432)

X(42432) = GIBERT(-3,4,-3) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 8*SB*SC : :

X(42432) lies on the cubic K1196 and these lines: {3, 36970}, {4, 15}, {5, 5352}, {6, 5073}, {13, 3627}, {14, 20}, {16, 1657}, {18, 550}, {30, 62}, {61, 382}, {140, 5349}, {202, 10483}, {203, 12953}, {376, 41122}, {381, 5238}, {395, 15704}, {396, 3853}, {397, 19106}, {531, 634}, {548, 16242}, {549, 12817}, {629, 33625}, {1656, 10645}, {3091, 16241}, {3104, 5868}, {3146, 10654}, {3200, 37495}, {3201, 6759}, {3205, 13352}, {3364, 35820}, {3365, 35821}, {3366, 42240}, {3367, 42239}, {3389, 42263}, {3390, 42264}, {3412, 17578}, {3522, 5365}, {3523, 16967}, {3529, 36968}, {3533, 42111}, {3534, 5351}, {3543, 5366}, {3544, 12821}, {3830, 16267}, {3843, 36836}, {3845, 16772}, {3850, 16966}, {3851, 11480}, {3858, 23302}, {5056, 33417}, {5059, 5334}, {5068, 42092}, {5076, 42156}, {5344, 42105}, {5869, 36994}, {7005, 12943}, {7755, 41409}, {8739, 34797}, {8740, 35490}, {10299, 42139}, {10653, 33703}, {10721, 36208}, {11001, 16963}, {11601, 15445}, {12103, 16773}, {12154, 33192}, {13491, 36980}, {14269, 41943}, {14814, 35739}, {15681, 16268}, {15682, 42161}, {15683, 41113}, {15684, 41107}, {15687, 16962}, {15696, 16645}, {15712, 33416}, {15720, 42095}, {16960, 42102}, {16961, 42091}, {17800, 22238}, {21735, 42089}, {22831, 37464}, {23005, 41020}, {23251, 42204}, {23261, 42203}, {23303, 33923}, {32789, 42208}, {32790, 42207}, {34754, 42094}, {34783, 36981}, {38335, 41121}, {42175, 42266}, {42176, 42267}

X(42432) = {X(6),X(5073)}-harmonic conjugate of X(42431)

X(42433) = GIBERT(3,2,-7) POINT

Barycentrics    Sqrt[3]*a^2*S - 7*a^2*SA + 4*SB*SC : :

X(42433) lies on the cubic K1196 and these lines: {3, 13}, {4, 5351}, {5, 10646}, {6, 15696}, {14, 1657}, {15, 548}, {16, 20}, {18, 30}, {61, 376}, {62, 550}, {140, 36969}, {202, 15338}, {382, 11481}, {395, 15704}, {396, 33923}, {397, 5352}, {398, 12103}, {511, 22843}, {530, 628}, {532, 22845}, {549, 42165}, {624, 33386}, {631, 16966}, {632, 5350}, {635, 5463}, {1250, 4325}, {2041, 42235}, {2042, 42237}, {3366, 42213}, {3367, 42211}, {3389, 42261}, {3390, 42260}, {3412, 11480}, {3522, 5238}, {3523, 10188}, {3524, 42162}, {3526, 16808}, {3528, 10645}, {3529, 36970}, {3530, 5318}, {3534, 22238}, {3627, 37835}, {3832, 42089}, {3843, 16967}, {3853, 23303}, {3855, 42105}, {3861, 42109}, {4330, 19373}, {5059, 42159}, {5067, 42141}, {5070, 42094}, {5073, 16645}, {5319, 41408}, {5335, 21734}, {5339, 15681}, {5344, 15692}, {5474, 5864}, {6777, 38741}, {6779, 41020}, {7006, 15326}, {7486, 42106}, {7765, 19780}, {7860, 30472}, {8739, 35491}, {8740, 35503}, {10304, 41107}, {10654, 17538}, {11001, 16268}, {11296, 36767}, {11305, 33387}, {12816, 15694}, {12820, 35018}, {13630, 36979}, {13966, 35739}, {15683, 33606}, {15686, 41108}, {15688, 36836}, {15689, 41101}, {15705, 41119}, {15712, 42166}, {15717, 18582}, {16111, 36209}, {16239, 42137}, {16267, 34200}, {16772, 16960}, {16961, 42096}, {17578, 42113}, {17800, 19107}, {18581, 33703}, {19708, 41943}, {22531, 41022}, {33414, 33560}, {33417, 42127}, {34755, 42087}, {35751, 35932}, {36208, 38723}, {36447, 42247}, {36464, 42249}, {37641, 41973}, {41971, 42150}

X(42433) = {X(6),X(15696)}-harmonic conjugate of X(42434)

X(42434) = GIBERT(-3,2,-7) POINT

Barycentrics    Sqrt[3]*a^2*S + 7*a^2*SA - 4*SB*SC : :

X(42434) lies on the cubic K1196 and these lines:{3, 14}, {4, 5352}, {5, 10645}, {6, 15696}, {13, 1657}, {15, 20}, {16, 548}, {17, 30}, {61, 550}, {62, 376}, {140, 36970}, {203, 15338}, {382, 11480}, {395, 33923}, {396, 15704}, {397, 12103}, {398, 5351}, {511, 22890}, {531, 627}, {533, 22844}, {549, 42164}, {623, 33387}, {631, 16967}, {632, 5349}, {636, 5464}, {2041, 42238}, {2042, 42236}, {3364, 42261}, {3365, 42260}, {3391, 42214}, {3392, 42212}, {3411, 11481}, {3522, 5237}, {3523, 10187}, {3524, 42159}, {3526, 16809}, {3528, 10646}, {3529, 36969}, {3530, 5321}, {3534, 22236}, {3627, 37832}, {3832, 42092}, {3843, 16966}, {3853, 23302}, {3855, 42104}, {3861, 42108}, {4325, 10638}, {4330, 7051}, {5059, 42162}, {5067, 42140}, {5070, 42093}, {5073, 16644}, {5319, 41409}, {5334, 21734}, {5340, 15681}, {5343, 15692}, {5473, 5865}, {6778, 38741}, {6780, 41021}, {7005, 15326}, {7486, 42103}, {7765, 19781}, {7860, 30471}, {8739, 35503}, {8740, 35491}, {10304, 41108}, {10653, 17538}, {11001, 16267}, {11306, 33386}, {12817, 15694}, {12821, 35018}, {13630, 36981}, {15683, 33607}, {15686, 41107}, {15688, 36843}, {15689, 41100}, {15705, 41120}, {15712, 42163}, {15717, 18581}, {16111, 36208}, {16239, 42136}, {16268, 34200}, {16773, 16961}, {16960, 42097}, {17578, 42112}, {17800, 19106}, {18582, 33703}, {19708, 41944}, {22532, 41023}, {33415, 33561}, {33416, 42126}, {34754, 42088}, {35931, 36329}, {36209, 38723}, {36446, 42248}, {36465, 42246}, {37640, 41974}, {41972, 42151}

X(42434) = {X(6),X(15696)}-harmonic conjugate of X(42433)

X(42435) = GIBERT(21,2,11) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 11*a^2*SA + 4*SB*SC : :

X(42435) lies on the cubic K1196 and these lines: {2, 18}, {6, 31457}, {13, 3627}, {15, 548}, {17, 5072}, {62, 15712}, {396, 3850}, {397, 15686}, {398, 12812}, {1657, 16965}, {3411, 16772}, {3412, 3843}, {5237, 14891}, {5238, 21735}, {11542, 42415}, {12108, 16773}, {12817, 23046}, {12820, 42154}, {14093, 36836}, {14890, 41944}, {14893, 16267}, {15684, 42157}, {15706, 22238}, {17538, 37640}, {19106, 33703}, {32455, 36757}, {38335, 41101}

X(42436) = GIBERT(-21,2,11) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 11*a^2*SA - 4*SB*SC : :

X(42436) lies on the cubic K1196 and these lines: {2, 17}, {6, 31457}, {14, 3627}, {16, 548}, {18, 5072}, {61, 15712}, {395, 3850}, {397, 12812}, {398, 15686}, {1657, 16964}, {3411, 3843}, {3412, 16773}, {5237, 21735}, {5238, 14891}, {11543, 42416}, {12108, 16772}, {12816, 23046}, {12821, 42155}, {14093, 36843}, {14890, 41943}, {14893, 16268}, {15684, 42158}, {15706, 22236}, {17538, 37641}, {19107, 33703}, {32455, 36758}, {38335, 41100}

leftri

Products X(i)*T for selected triangles T: X(42437)-X(42463)

rightri

This preamble and centers X(42437)-(X42463) are contributed by Clark Kimberling and Peter Moses, March 31, 2021.

If X is a normalized triangle center and T a normalized central triangle, then the left-product X*T is a triangle center. Let P = p : q : r be a point. Centers X(42437)-X(42450) are products X(i)*(cevian triangle of P), given by

p (q + r) (p y + q y + p z + r z) : q (p + r) (p x + q x + q z + r z) : (p + q) r (p x + r x + q y + r y).

Centers X(42451)-X(42463) are products X(i)*(anticevian triangle of P), given by p*((p + q - r)*(p - q + r)*x + (p - q - r)*(p + q - r)*y + (p - q - r)*(p - q + r)*z) : :

The appearance of (i,j,k) in the following list means that X(i)*(cevian triangle of X(j) = X(k):

(1,1,2292), (1,2,10), (1,4,65), (1,6,20969), (1,7,1), (1,8,8), (1,20,5930), (2,1,1962), (2,2,2), (2,3,32078), (2,4,51), (2,6,11205), (2,7,354), (2,8,210), (2,20,154), (2,30,3081), (3,2,5), (3,4,4), (3,5,31389), (3,7,946), (3,8,10), (3,20,2883), (4,1,18673), (4,2,3), (4,3,31388), (4,4,185), (4,7,1071), (4,8,72), (4,20,20), (5,2,140), (5,3,3), (5,4,389), (5,7,12005), (5,8,3678), (6,1,4016), (6,2,141), (6,4,6), (6,6,23642), (6,7,3663), (6,8,2321), (7,2,9), (7,7,14100), (7,8,3059), (8,1,2650), (8,2,1), (8,7,65), (8,8,3057), (9,1,2294), (9,2,142), (9,4,2262), (9,7,7), (9,8,9), (10,1,1), (10,2,1125), (10,7,942), (10,8,960), (11,2,3035), (11,7,5083), (11,8,14740), (12,1,2646), (12,2,4999), (13,2,618), (14,2,619), (15,2,623), (15,4,5318), (16,2,624), (16,4,5321), (17,2,629), (18,2,630), (19,1,18674), (19,2,18589), (19,7,41004), (19,8,219), (19,20,8804), (20,2,4), (20,4,11381), (20,7,12688), (20,8,65), (20,20,5895), (21,2,442), (21,7,3649), (21,8,21677), (22,2,427), (22,4,11550), (23,2,858), (24,2,11585), (25,2,1368), (25,4,1899), (26,2,13371), (26,4,18381), (27,2,440), (28,2,21530), (29,2,18641), (29,7,39791), (31,1,4137), (31,2,2887), (31,4,3914), (31,7,3782), (31,8,3703), (32,2,626), (32,4,5254), (32,7,4920), (32,8,4136), (33,2,34822), (33,7,222), (34,2,34823), (35,2,25639), (35,7,12047), (35,8,6734), (36,2,3814), (36,7,30384), (36,8,6735), (37,1,37), (37,2,3739), (37,7,3664), (37,8,3686), (38,2,1215), (38,6,42), (38,8,4030), (39,2,3934), (39,4,7745), (39,6,39), (39,8,4095), (40,2,946), (40,4,12688), (40,7,4), (40,8,1), (41,2,17046), (41,7,3665), (41,8,40997), (42,1,38), (42,2,3741), (42,4,41011), (42,7,3666), (42,8,3706), (43,2,3840), (43,6,23446), (43,7,982), (43,8,312), (44,2,3834), (44,7,4887), (44,8,2325), (45,2,34824), (45,7,4896), (45,8,3707), (46,2,21616), (46,4,1898), (46,7,1479), (46,8,78), (47,2,34825), (48,2,20305), (48,4,1826), (48,7,41007), (49,2,34826), (49,4,1594), (50,2,34827), (51,2,3819), (51,3,3917), (51,4,11245), (52,2,1216), (52,3,5562), (52,4,6146), (53,2,34828), (53,3,577), (54,2,1209), (54,4,3574), (55,2,2886), (55,4,1836), (55,7,226), (55,8,4847), (56,2,1329), (56,4,1837), (56,7,12053), (56,8,6736), (57,2,3452), (57,4,1864), (57,7,497), (57,8,200), (58,2,3454), (58,4,1834), (58,8,3704), (60,2,34829), (61,2,635), (61,4,397), (62,2,636), (62,4,398), (63,2,226), (63,4,1824), (63,7,1836), (63,8,55), (64,2,2883), (64,4,5895), (64,8,5930), (64,20,13155), (65,1,3057), (65,2,960), (65,4,1858), (65,7,950), (65,8,6737), (66,2,206), (67,2,6593), (67,4,40949), (68,2,1147), (68,4,52), (69,2,6), (69,4,1843), (69,6,31390), (69,7,12723), (69,8,40965), (70,2,34116), (71,1,1953), (71,2,34830), (71,4,1839), (71,8,40937), (72,1,65), (72,2,942), (72,4,1829), (72,7,4292), (72,8,950), (73,2,34831), (73,4,40950), (74,2,113), (74,4,13202), (74,8,6739), (75,1,2667), (75,2,37), (75,6,21752), (75,7,21746), (75,8,3688), (76,2,39), (76,4,40951), (76,8,4531), (77,2,20262), (77,4,1827), (78,2,1210), (78,4,1828), (78,7,56), (78,8,1837), (79,2,3647), (79,8,31938), (80,2,214), (80,7,11570), (81,2,1211), (81,4,40952), (81,7,4854), (81,8,4046), (82,2,21249), (83,2,6292), (84,2,6260), (84,4,40953), (84,8,40), (85,2,1212), (85,7,39789), (86,2,1213), (86,4,40954), (86,7,4890), (86,8,4111), (87,2,34832), (87,7,4941), (87,8,4110), (88,2,16594), (88,8,4152), (90,2,41540), (90,7,10052), (92,2,1214), (92,7,39796), (92,20,3198), (93,2,34833), (94,2,34834), (95,2,233), (96,2,34835), (97,2,34836), (98,2,114), (99,2,115), (99,8,40608), (100,1,2611), (100,2,11), (100,4,38389), (100,7,11), (100,8,11), (101,1,3708), (101,2,116), (101,4,1146), (101,7,1565), (101,8,1146), (102,2,117), (103,2,118), (104,2,119), (104,7,1537), (104,8,1145), (105,2,120), (105,8,40609), (106,2,121), (107,2,122), (107,20,122), (108,2,123), (108,8,7358), (109,2,124), (109,4,38357), (109,7,38357), (109,8,2968), (110,2,125), (110,4,125), (110,8,6741), (111,2,126), (112,2,127), (112,4,1562), (112,20,1562),

The appearance of (i,j,k) in the following list means that X(i)*(anticevian triangle of X(j) = X(k):

(1,1,40), (1,2,8), (1,3,3157), (1,6,3556), (1,8,6552), (1,9,1), (1,10,10), (1,11,21132), (2,1,165), (2,2,2), (2,3,3167), (2,6,154), (2,7,32079), (2,9,3158), (2,10,3971), (2,30,34582), (3,1,1158), (3,2,4), (3,3,155), (3,4,6523), (3,5,5), (3,6,3), (3,9,3811), (3,10,21077), (4,1,1490), (4,2,20), (4,3,3), (4,4,3183), (4,5,41481), (4,6,1498), (4,9,40), (4,30,15774), (5,1,6796), (5,2,3), (5,3,1147), (5,5,15912), (5,6,6759), (5,9,8715), (6,1,1766), (6,2,69), (6,3,6), (6,6,159), (6,10,2321), (7,1,2951), (7,2,144), (7,6,3197), (7,7,15913), (7,9,9), (7,10,21084), (8,1,1), (8,2,145), (8,6,221), (8,8,8834), (8,9,2136), (9,1,9), (9,2,7), (9,3,3211), (9,6,18621), (9,7,17113), (9,9,3174), (9,10,3950), (10,1,3), (10,2,1), (10,6,14529), (10,9,3913), (10,10,3159), (11,1,100), (11,2,100), (11,3,36059), (11,9,100), (11,11,15914), (12,1,411), (12,2,2975), (12,9,3871), (13,2,616), (14,2,617), (15,2,621), (15,3,10661), (16,2,622), (16,3,10662), (17,2,627), (18,2,628), (19,2,4329), (19,3,219), (19,10,8804), (20,1,7992), (20,2,3146), (20,3,12164), (20,4,4), (20,6,64), (20,9,11523), (21,1,191), (21,2,2475), (21,10,3178), (22,2,7391), (23,2,5189), (24,2,37444), (25,2,1370), (25,3,394), (25,6,1619), (25,10,21062), (26,2,14790), (26,6,32321), (27,2,3151), (27,3,22139), (28,3,22136), (29,1,2939), (29,2,3152), (31,1,21375), (31,2,6327), (31,3,22130), (31,10,306), (32,2,315), (32,3,23128), (32,10,4153), (33,1,1763), (33,3,222), (33,9,8270), (34,1,16389), (34,3,7078), (36,2,5080), (37,1,573), (37,2,75), (37,6,18611), (37,10,37), (38,2,17165), (38,10,42), (39,2,76), (39,6,15270), (39,10,21067), (40,1,84), (40,2,962), (40,9,6765), (41,1,1759), (41,2,21285), (41,10,21073), (42,1,1764), (42,2,17135), (42,6,23359), (42,10,321), (43,1,20368), (43,2,10453), (43,10,4135), (44,2,320), (44,10,3943), (45,10,4029), (46,2,11415), (46,3,1069), (48,2,21270), (48,6,1631), (48,10,1826), (49,6,2937), (51,2,2979), (51,3,2), (51,6,11206), (52,2,11412), (52,3,68), (52,6,9833), (53,2,20477), (53,3,577), (54,2,2888), (54,3,195), (54,5,15780), (54,6,2917), (55,1,63), (55,2,3434), (55,3,3173), (55,9,3870), (55,10,226), (55,11,40166), (56,2,3436), (56,9,78), (56,10,21075), (57,1,10860), (57,2,329), (57,9,200), (57,10,21060), (58,2,1330), (58,10,21081), (61,2,633), (62,2,634), (63,1,1709), (63,2,5905), (63,6,55), (63,9,2900), (63,10,4028), (64,2,6225), (64,3,1498), (65,1,20), (65,2,3869), (65,3,1), (65,9,8), (65,10,72), (66,2,5596), (66,3,159), (67,2,11061), (67,3,2930), (67,6,15141), (68,2,6193), (68,3,9937), (68,6,155), (69,1,1721), (69,2,193), (69,3,19588), (69,6,6),(71,1,1765), (71,2,17220), (71,5,1953), (71,6,8053), (71,10,22021), (72,1,4), (72,2,3868), (72,6,1), (72,9,3189), (72,10,2901), (73,6,23361), (73,10,41013), (74,2,146), (74,3,399), (74,6,2935), (75,1,1742), (75,2,192), (75,3,23075), (75,6,21767), (75,9,3169), (75,10,21080), (76,1,32462), (76,2,194), (76,3,19597), (76,6,32445), (76,9,32468), (77,2,5942), (77,6,198), (78,1,46), (78,2,12649), (78,6,56), (79,2,3648), (79,9,191), (80,1,6326), (80,2,6224), (80,9,5541), (81,1,2941), (81,2,2895), (81,10,21085), (82,2,21289), (82,10,21083), (83,2,2896), (84,2,6223), (84,6,12335), (84,9,1490), (85,1,170), (85,2,3177), (85,9,3208), (86,1,2938), (86,2,1654), (88,2,30578), (92,1,2947), (92,2,6360), (92,3,20760), (94,2,18301), (95,2,17035), (98,2,147), (99,2,148), (100,1,1768), (100,2,149), (100,10,21093), (100,11,11), (101,2,150), (101,10,21090), (101,11,1146), (102,2,151), (103,2,152), (104,1,2950), (104,2,153), (104,9,6326), (105,2,20344), (106,2,21290), (106,10,21087), (107,2,34186), (108,2,34188), (109,2,33650), (109,11,38357), (110,2,3448), (110,6,10117), (110,10,21098), (111,2,14360), (112,2,13219), (112,3,22146)



X(42437) = X(1)*T, WHERE T = CEVIAN TRIANGLE OF X(1)

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

X(42437) lies on these lines: {1, 41821}, {8, 20090}, {10, 3995}, {442, 20653}, {519, 17589}, {594, 21808}, {1230, 4647}, {2292, 4733}, {2475, 3679}, {3178, 27812}, {3617, 33100}, {3915, 28634}, {4065, 8040}, {4783, 4968}, {5506, 24963}, {6367, 21124}, {27577, 27798}

X(42438) = X(2)*T, WHERE T = CEVIAN TRIANGLE OF X(9)

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

X(42438) lies on these lines: {9, 1174}, {71, 374}, {165, 169}, {198, 1626}, {354, 1212}, {661, 33570}, {1202, 16601}, {2246, 26744}, {2348, 21811}, {3119, 3740}, {5273, 17490}, {5919, 15853}, {8932, 11203}

X(42439) = X(2)*T, WHERE T = CEVIAN TRIANGLE OF X(10)

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

X(42439) lies on these lines: {2, 1051}, {10, 3995}, {210, 21014}, {1046, 9780}, {1213, 1962}, {1698, 2895}, {3120, 27798}, {3828, 23812}, {4977, 6546}, {6367, 8029}, {20966, 21700}, {27790, 28516}

X(42440) = X(3)*T, WHERE T = CEVIAN TRIANGLE OF X(1)

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

] X(42440) lies on these lines: {1, 1437}, {5, 23555}, {12, 17874}, {37, 2333}, {55, 20832}, {65, 21318}, {201, 22300}, {758, 1482}, {774, 1953}, {855, 2292}, {942, 17463}, {1486, 3295}, {1725, 18180}, {1834, 4516}, {1962, 18673}, {2070, 37621}, {2611, 2650}, {3145, 38336}, {3649, 18210}, {3728, 6042}, {3913, 31395}, {4016, 17444}, {4646, 23668}, {4647, 24390}, {10459, 21326}, {11688, 18719}, {15507, 41591}, {16980, 24431}, {18115, 33592}, {18692, 41007}, {20254, 28628}, {23841, 24433}, {28258, 34977}

X(42441) = X(3)*T, WHERE T = CEVIAN TRIANGLE OF X(3)

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

Let A'B'C' be the cevian triangle of X(3). Let A" be the circumcenter of AB'C', and define B" and C" cyclically. Then X(42441) = X(4)-of-A"B"C". (Randy Hutson, July 16, 2021)

X(42441) lies on these lines: {2, 1075}, {3, 54}, {4, 3164}, {5, 324}, {52, 418}, {140, 2972}, {155, 6641}, {216, 217}, {233, 31354}, {264, 13599}, {378, 23709}, {381, 35719}, {417, 9730}, {426, 36752}, {631, 12012}, {648, 40448}, {852, 5462}, {1033, 7395}, {1181, 10608}, {1209, 35442}, {1235, 7399}, {1994, 2055}, {3090, 10184}, {3091, 14635}, {3567, 6638}, {3574, 10600}, {5489, 6368}, {5640, 38281}, {5647, 17814}, {5907, 41212}, {6146, 20975}, {6750, 34836}, {7066, 22350}, {7400, 12251}, {10024, 34333}, {11587, 14118}, {12271, 20794}, {13434, 15781}, {13754, 26897}, {14531, 26907}, {14918, 15780}, {15024, 38283}, {17834, 26898}, {31802, 41169}, {40647, 40948}

X(42441) = isogonal conjugate of polar conjugate of X(34836)
X(42441) = crosspoint of X(3) and X(5)
X(42441) = crosssum of X(4) and X(54)

X(42442) = X(3)*T, WHERE T = CEVIAN TRIANGLE OF X(6)

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

X(42442) lies on these lines: {3, 9019}, {6, 2353}, {32, 23635}, {39, 1843}, {159, 9605}, {184, 3456}, {525, 31869}, {732, 1352}, {826, 3574}, {2971, 39590}, {3001, 7819}, {5007, 20975}, {5041, 9407}, {6292, 22424}, {7794, 16893}, {7822, 20819}, {8362, 16789}, {9971, 20960}, {14660, 14886}, {15861, 28343}, {20967, 20969}

X(42443) = X(5)*T, WHERE T = CEVIAN TRIANGLE OF X(1)

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

X(42443) lies on these lines: {1, 859}, {3, 20718}, {37, 2200}, {65, 3724}, {228, 22300}, {500, 513}, {517, 5496}, {692, 943}, {740, 8669}, {758, 1385}, {851, 11553}, {950, 34969}, {1100, 40955}, {1104, 3725}, {1319, 2650}, {1962, 18673}, {2290, 17438}, {2292, 2646}, {2594, 21319}, {3057, 12081}, {3743, 24929}, {4647, 5440}, {5266, 8618}, {15624, 37529}

X(42444) = X(5)*T, WHERE T = CEVIAN TRIANGLE OF X(6)

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

X(42444) lies on these lines: {6, 27375}, {32, 39684}, {39, 3203}, {54, 826}, {182, 732}, {184, 3456}, {211, 20775}, {576, 8546}, {754, 14133}, {3202, 9605}, {5012, 7760}, {5028, 23642}, {5041, 9418}, {7829, 36213}, {9306, 10191}, {13434, 38664}

X(42445) = X(6)*T, WHERE T = CEVIAN TRIANGLE OF X(3)

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

X(42445) lies on these lines: {3, 14533}, {6, 1154}, {25, 5647}, {53, 14978}, {155, 36751}, {184, 10979}, {216, 217}, {233, 3574}, {570, 1216}, {577, 8565}, {1352, 32428}, {2197, 2252}, {3269, 22052}, {5891, 14576}, {7691, 8882}, {11197, 36412}

X(42445) = isogonal conjugate of polar conjugate of X(1209)
X(42445) = isotomic conjugate of polar conjugate of crosspoint of X(5) and X(6)
X(42445) = isotomic conjugate of polar conjugate of crosssum of X(2) and X(54)

X(42446) = X(7)*T, WHERE T = CEVIAN TRIANGLE OF X(1)

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

X(42446) lies on these lines: {1, 1014}, {9, 24394}, {42, 21871}, {55, 199}, {390, 740}, {497, 21020}, {517, 4343}, {756, 21867}, {758, 4326}, {1108, 35270}, {1253, 3747}, {1334, 21039}, {1621, 17868}, {1697, 2292}, {2269, 2310}, {2293, 2650}, {3882, 10868}, {3958, 14100}, {4433, 21033}, {4516, 21811}, {4642, 40934}, {4647, 12575}, {5274, 27798}, {5281, 10180}, {21346, 37555}, {21673, 38930}

X(42447) = X(7)*T, WHERE T = CEVIAN TRIANGLE OF X(4)

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

X(42447) lies on these lines: {6, 3270}, {7, 2808}, {25, 3197}, {33, 11435}, {41, 8554}, {51, 1824}, {55, 584}, {65, 1827}, {184, 18621}, {185, 1902}, {241, 22440}, {390, 9052}, {511, 10394}, {672, 22079}, {674, 14100}, {916, 5728}, {942, 15030}, {950, 14053}, {1253, 20683}, {1334, 2293}, {1409, 2356}, {1442, 14520}, {1837, 40954}, {1843, 1858}, {1863, 5185}, {2171, 2310}, {2389, 3059}, {2772, 30329}, {2807, 18412}, {2810, 40269}, {3022, 4336}, {3057, 9049}, {3100, 4260}, {3271, 40968}, {3779, 4319}, {3781, 7675}, {3917, 10391}, {3990, 14547}, {5338, 11190}, {5650, 17603}, {6000, 15938}, {6284, 15443}, {7680, 15607}, {10382, 26893}, {10393, 22076}, {11436, 40971}, {11446, 37685}, {18725, 26892}, {21933, 42069}, {22277, 41339}

X(42448) = X(8)*T, WHERE T = CEVIAN TRIANGLE OF X(4)

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

X(42448) lies on these lines: {1, 855}, {4, 151}, {8, 29958}, {19, 3330}, {25, 221}, {31, 8615}, {51, 65}, {52, 14988}, {56, 3937}, {64, 11406}, {109, 37259}, {145, 2810}, {184, 3556}, {185, 1829}, {228, 4300}, {244, 17114}, {373, 3812}, {375, 3698}, {392, 11573}, {427, 20306}, {511, 3869}, {513, 7354}, {517, 16980}, {595, 20999}, {674, 3962}, {774, 18210}, {960, 3917}, {1064, 22345}, {1193, 22344}, {1201, 1401}, {1203, 26889}, {1204, 11383}, {1284, 23440}, {1409, 2354}, {1456, 40985}, {1457, 30493}, {1463, 23675}, {1464, 23383}, {1473, 16466}, {1495, 14529}, {1682, 4414}, {1755, 22070}, {1771, 28077}, {1777, 37397}, {1824, 11381}, {1843, 1858}, {1851, 4295}, {1854, 3270}, {1878, 7686}, {1900, 32062}, {2170, 23630}, {2262, 17634}, {2392, 3878}, {2594, 23844}, {2650, 21746}, {2800, 31825}, {2835, 15556}, {2841, 5903}, {2842, 3874}, {3057, 8679}, {3259, 7681}, {3271, 3924}, {3436, 31785}, {3754, 15049}, {3784, 19861}, {3884, 23156}, {3890, 23155}, {3898, 23157}, {4084, 31757}, {4418, 9565}, {4642, 23638}, {5057, 15488}, {5562, 5887}, {5650, 25917}, {5730, 37482}, {6737, 29353}, {7428, 34586}, {7959, 12174}, {10441, 11415}, {10571, 28348}, {11391, 11550}, {12514, 22076}, {12526, 26893}, {12711, 17441}, {13724, 37558}, {13747, 35059}, {13754, 40266}, {15030, 31937}, {17562, 19368}, {18180, 39542}, {19367, 37254}, {20323, 41682}, {23544, 23636}, {26377, 26883}, {26884, 34043}, {33899, 34462}, {37516, 37614}

X(42449) = X(9)*T, WHERE T = CEVIAN TRIANGLE OF X(9)

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

X(42449) lies on these lines: {7, 3177}, {9, 1174}, {77, 2124}, {664, 1223}, {1202, 5572}, {1212, 2293}, {1441, 41006}, {2082, 4326}, {3119, 6666}, {8012, 15185}, {9502, 40937}, {15837, 38375}

X(42450) = X(10)*T, WHERE T = CEVIAN TRIANGLE OF X(4)

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

X(42450) lies on these lines: {1, 8679}, {4, 12930}, {5, 34825}, {6, 1245}, {10, 375}, {25, 14529}, {31, 23843}, {42, 23844}, {44, 10822}, {47, 11334}, {51, 65}, {52, 5887}, {56, 26892}, {72, 674}, {73, 23383}, {124, 7683}, {143, 14988}, {185, 1839}, {221, 17810}, {354, 23154}, {389, 6001}, {511, 960}, {513, 4292}, {515, 34434}, {516, 22300}, {517, 5446}, {518, 29958}, {551, 23156}, {568, 40266}, {581, 3185}, {601, 2933}, {602, 1626}, {758, 31757}, {859, 37836}, {916, 31732}, {946, 31825}, {959, 9309}, {970, 4640}, {997, 37482}, {999, 41682}, {1064, 23361}, {1066, 18613}, {1104, 3271}, {1125, 2392}, {1191, 1469}, {1203, 3220}, {1265, 25304}, {1399, 37259}, {1425, 1456}, {1486, 7078}, {1593, 34935}, {1695, 24708}, {1824, 1898}, {1829, 1852}, {1854, 11436}, {2179, 8608}, {2183, 4300}, {2361, 3145}, {2650, 20961}, {2654, 14055}, {2771, 11557}, {2778, 11807}, {2779, 18483}, {2800, 31760}, {2807, 9856}, {2810, 34791}, {2818, 7686}, {2835, 12432}, {3057, 16980}, {3060, 3869}, {3157, 11365}, {3555, 9026}, {3622, 23155}, {3636, 23157}, {3683, 22076}, {3784, 25524}, {3812, 5943}, {3827, 9969}, {3868, 30438}, {3917, 25917}, {3937, 32636}, {4303, 20470}, {4337, 16453}, {4642, 20962}, {4646, 23638}, {5057, 41723}, {5348, 28077}, {5462, 34339}, {5480, 20306}, {5752, 12514}, {5777, 40635}, {5836, 23841}, {5892, 40296}, {5904, 9049}, {6684, 38472}, {7299, 13733}, {8614, 26884}, {9119, 34146}, {9729, 9943}, {9961, 10574}, {10176, 31737}, {10178, 17704}, {10441, 24703}, {10571, 20122}, {10693, 13417}, {12047, 18180}, {12572, 22299}, {12711, 14557}, {13754, 31937}, {16466, 22654}, {18178, 24210}, {20727, 24511}, {21616, 37536}, {21969, 31165}, {22053, 28270}, {23630, 40133}, {25681, 37521}

X(42450) = crosspoint of X(4) and X(58)
X(42450) = crosssum of X(3) and X(10)
X(42450) = X(178)-of-orthic-triangle if ABC is acute

X(42451) = X(1)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(4)

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

X(42451) lies on these lines: {1, 196}, {4, 3668}, {158, 278}, {347, 1895}, {459, 39130}, {1068, 18678}, {1214, 3346}, {1498, 32714}, {1854, 4295}, {3176, 5930}, {3182, 8802}, {6223, 36118}

X(42452) = X(2)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(4)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(7*a^8 - 4*a^6*b^2 - 14*a^4*b^4 + 12*a^2*b^6 - b^8 - 4*a^6*c^2 + 28*a^4*b^2*c^2 - 12*a^2*b^4*c^2 - 12*b^6*c^2 - 14*a^4*c^4 - 12*a^2*b^2*c^4 + 26*b^4*c^4 + 12*a^2*c^6 - 12*b^2*c^6 - c^8) : :

X(42452) lies on these lines: {2, 15312}, {4, 64}, {20, 12090}, {107, 3079}, {631, 3346}, {1249, 10192}, {3090, 33546}, {3424, 7714}, {3523, 20329}, {5667, 33702}, {6353, 16318}, {6618, 11245}

X(42452) = X(2)-of-anticevian-triangle-of-X(4)

X(42453) = X(2)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(5)

Barycentrics    (a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + a^6*c^2 + a^4*b^2*c^2 - a^2*b^4*c^2 - 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(42453) lies on these lines: {3, 1075}, {5, 324}, {30, 568}, {51, 32428}, {143, 13322}, {216, 12012}, {418, 35360}, {523, 10192}, {632, 6662}, {1368, 2967}, {1994, 41202}, {2052, 30258}, {2790, 41580}, {3164, 3168}, {5891, 14640}, {6676, 16318}, {9755, 9909}, {10691, 15312}, {12077, 40588}, {18282, 24385}

X(42454) = X(2)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(11)

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

X(42454) lies on these lines: {11, 15914}, {51, 513}, {55, 885}, {210, 522}, {354, 514}, {523, 1962}, {650, 5432}, {693, 3816}, {900, 33519}, {1621, 17494}, {3058, 11193}, {3703, 4391}, {3752, 23811}, {4124, 21132}, {4995, 11124}, {6284, 11247}, {17728, 35348}

X(42454) = X(650)-Ceva conjugate of X(11)

X(42455) = X(3)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(11)

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

X(42455) lies on these lines: {2, 33528}, {4, 513}, {8, 885}, {10, 522}, {85, 693}, {158, 17924}, {341, 4397}, {442, 1577}, {499, 905}, {514, 946}, {521, 6238}, {667, 2217}, {900, 14304}, {1212, 28143}, {1734, 18395}, {2401, 3086}, {2517, 11024}, {3667, 9948}, {3704, 4086}, {3762, 6366}, {4448, 37009}, {4462, 20220}, {6554, 28132}, {11607, 36802}, {14010, 40213}, {14505, 23100}, {16732, 21134}, {21132, 23615}, {30591, 31936}

X(42455) = Kirikami-Euler image of X(11)

X(42456) = X(4)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(10)

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

X(42456) lies on these lines: {10, 201}, {307, 17864}, {522, 31730}, {648, 15796}, {726, 1766}, {758, 2901}, {1125, 22465}, {1745, 6360}, {3159, 3950}, {3178, 3971}, {3678, 21084}, {3682, 4552}, {18477, 27378}, {20222, 22350}, {22381, 42027}

X(42457) = X(5)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(4)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(3*a^12 - 7*a^10*b^2 - 2*a^8*b^4 + 18*a^6*b^6 - 17*a^4*b^8 + 5*a^2*b^10 - 7*a^10*c^2 + 16*a^8*b^2*c^2 - 18*a^6*b^4*c^2 + 12*a^4*b^6*c^2 + a^2*b^8*c^2 - 4*b^10*c^2 - 2*a^8*c^4 - 18*a^6*b^2*c^4 + 10*a^4*b^4*c^4 - 6*a^2*b^6*c^4 + 16*b^8*c^4 + 18*a^6*c^6 + 12*a^4*b^2*c^6 - 6*a^2*b^4*c^6 - 24*b^6*c^6 - 17*a^4*c^8 + a^2*b^2*c^8 + 16*b^4*c^8 + 5*a^2*c^10 - 4*b^2*c^10) : :

X(42457) lies on these lines: {3, 14363}, {4, 64}, {107, 1498}, {140, 15274}, {154, 1075}, {1093, 1192}, {1656, 33546}, {1657, 23240}, {3168, 11425}, {3346, 3523}, {3517, 33582}, {5894, 36876}, {8567, 41372}, {10282, 15576}, {10606, 14249}, {14361, 34782}, {15712, 20329}, {17821, 38808}, {35360, 35602}

X(42458) = X(6)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(4)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^10 + 3*a^8*b^2 - 14*a^6*b^4 + 14*a^4*b^6 - 3*a^2*b^8 - b^10 + 3*a^8*c^2 + 20*a^6*b^2*c^2 - 14*a^4*b^4*c^2 - 12*a^2*b^6*c^2 + 3*b^8*c^2 - 14*a^6*c^4 - 14*a^4*b^2*c^4 + 30*a^2*b^4*c^4 - 2*b^6*c^4 + 14*a^4*c^6 - 12*a^2*b^2*c^6 - 2*b^4*c^6 - 3*a^2*c^8 + 3*b^2*c^8 - c^10) : :

X(42458) lies on these lines: {2, 14091}, {3, 1033}, {4, 41489}, {6, 15311}, {20, 2138}, {112, 36413}, {347, 17903}, {390, 21148}, {393, 800}, {3172, 36965}, {5065, 40138}, {6353, 16318}, {6525, 33581}, {6527, 41678}, {6804, 33546}, {8879, 10565}, {12250, 14642}, {13488, 40065}

X(42458) = polar conjugate of isogonal conjugate of X(1661)
X(42458) = polar conjugate of isotomic conjugate of X(6225)
X(42458) = polar conjugate of cyclocevian conjugate of X(35510)

X(42459) = X(6)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(5)

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

Let E be the inellipse that is the barycentric square of the Euler line, centered at X(23583). Then X(42459) is the intersection of the tangents to E at X(36412) (the barycentric square of X(5)) and X(36413) (the barycentric square of X(20)). (Randy Hutson, July 16, 2021)

X(42459) lies on these lines: {3, 393}, {4, 31363}, {5, 53}, {6, 30}, {20, 1249}, {22, 16318}, {26, 1609}, {140, 36751}, {217, 31802}, {230, 10154}, {232, 1368}, {297, 3164}, {343, 13157}, {376, 33630}, {382, 3087}, {418, 14569}, {427, 22240}, {441, 17907}, {459, 37877}, {548, 36748}, {549, 10979}, {550, 577}, {566, 13371}, {570, 23335}, {800, 5254}, {1033, 11414}, {1074, 40937}, {1108, 23537}, {1172, 37468}, {1350, 15312}, {1657, 38292}, {1658, 8553}, {1865, 8727}, {1907, 26216}, {2052, 26906}, {2070, 41758}, {2165, 13383}, {2207, 12362}, {2794, 34774}, {3146, 40065}, {3163, 15686}, {3284, 15704}, {3627, 5158}, {5059, 5702}, {5112, 41584}, {5179, 40943}, {5286, 39568}, {5304, 34608}, {5305, 7387}, {5359, 34658}, {5721, 40979}, {6527, 20208}, {6530, 42329}, {6747, 26905}, {6823, 27376}, {7735, 9909}, {7736, 34609}, {8703, 18487}, {8745, 12605}, {8963, 15235}, {9308, 41008}, {9605, 34938}, {9607, 13341}, {9722, 15761}, {10226, 15109}, {11063, 12107}, {11563, 16328}, {13155, 20265}, {13322, 41334}, {13406, 18573}, {14091, 40234}, {15355, 30739}, {15466, 20207}, {15594, 30549}, {15681, 33636}, {15699, 36430}, {15912, 41523}, {17849, 23128}, {18591, 37424}, {18643, 37448}, {18685, 36029}, {21309, 34726}, {27377, 40853}, {30435, 31305}, {35007, 40136}, {37201, 41489}, {38920, 41465}, {41480, 41481}

X(42460) = X(7)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(3)

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

X(42460) lies on these lines: {1, 7083}, {3, 77}, {6, 29957}, {55, 15374}, {521, 3126}, {651, 7071}, {912, 6767}, {916, 2293}, {954, 3564}, {1069, 3477}, {1200, 2280}, {3270, 23144}, {3781, 7078}, {5942, 28044}, {13754, 15937}, {17262, 23874}, {18621, 34371}, {20760, 38288}, {22117, 22132}, {23078, 23079}, {36059, 37541}

X(42460) = isogonal conjugate of polar conjugate of X(30694)
X(42460) = isogonal conjugate of X(7)-cross conjugate of X(4)

X(42461) = X(8)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(3)

Barycentrics    a^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(42461) lies on these lines: {1, 7083}, {3, 63}, {6, 29958}, {25, 3868}, {38, 1036}, {56, 4641}, {64, 2808}, {65, 1773}, {101, 4306}, {144, 37399}, {145, 28029}, {155, 10680}, {159, 9021}, {218, 1400}, {219, 23620}, {329, 37415}, {394, 23154}, {404, 26866}, {405, 17257}, {517, 39568}, {518, 3556}, {521, 6161}, {651, 1398}, {758, 9798}, {942, 5020}, {956, 3564}, {958, 4643}, {960, 22769}, {999, 1201}, {1046, 1460}, {1069, 3478}, {1147, 16203}, {1245, 6391}, {1423, 5247}, {1425, 23144}, {1482, 12309}, {1593, 12528}, {1597, 40263}, {1598, 24474}, {1633, 3189}, {1722, 28039}, {1724, 21362}, {1858, 16541}, {2178, 21874}, {2286, 20818}, {2292, 3295}, {2800, 9910}, {3191, 19782}, {3193, 11401}, {3218, 37257}, {3219, 37246}, {3220, 11523}, {3487, 25514}, {3732, 7754}, {3869, 8192}, {3874, 11365}, {3876, 7484}, {3901, 8185}, {3913, 4952}, {4185, 5905}, {4186, 12649}, {4223, 11036}, {5044, 16419}, {5777, 11479}, {5904, 8193}, {6147, 7535}, {6642, 24475}, {6743, 24309}, {7011, 23159}, {7078, 7193}, {7289, 37613}, {7393, 31835}, {7532, 20256}, {9909, 37547}, {10529, 28034}, {10822, 34931}, {12109, 17810}, {12164, 22770}, {12635, 22654}, {15934, 28787}, {16049, 20078}, {20007, 37328}, {20013, 35998}, {22120, 22144}, {22148, 23072}, {23168, 38290}, {36059, 41426}, {37541, 38903}

X(42461) = isogonal conjugate of polar conjugate of X(30699)
X(42461) = isogonal conjugate of X(8)-cross conjugate of X(4)

X(42462) = X(9)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(11)

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

X(42462) is the perspector of the circumhyperbola that is the locus of trilinear products of Feuerbach hyperbola antipodes. (Randy Hutson, July 16, 2021)

X(42462) lies on these lines: {7, 514}, {9, 522}, {19, 649}, {37, 650}, {346, 3239}, {393, 7649}, {513, 2262}, {523, 2294}, {654, 4984}, {661, 1901}, {663, 4336}, {665, 30572}, {693, 20905}, {1086, 21133}, {1278, 25259}, {3059, 3900}, {3700, 21033}, {4000, 21202}, {4171, 42337}, {4391, 20895}, {4500, 27417}, {4530, 14393}, {4534, 14442}, {4820, 40137}, {6545, 23760}, {6546, 9318}, {10006, 14476}, {15914, 38375}, {17412, 17418}, {17420, 24121}, {21131, 23775}, {21143, 23764}, {23615, 33573}, {23748, 24002}, {27486, 31346}, {28161, 31325}

X(42462) = isogonal conjugate of X(4619)

X(42463) = X(10)*T, WHERE T = ANTICEVIAN TRIANGLE OF X(3)

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

X(42463) lies on these lines: {1, 1762}, {3, 48}, {6, 27802}, {56, 3173}, {58, 15376}, {60, 28606}, {63, 1437}, {72, 184}, {101, 580}, {110, 3868}, {154, 37547}, {155, 11249}, {182, 5044}, {206, 518}, {255, 20803}, {354, 28787}, {394, 11573}, {405, 26885}, {474, 26889}, {517, 6759}, {525, 24286}, {578, 5777}, {603, 23169}, {692, 3811}, {758, 14529}, {912, 960}, {942, 9306}, {971, 13346}, {975, 5135}, {999, 1201}, {1036, 1069}, {1071, 1092}, {1098, 18042}, {1125, 9028}, {1193, 22130}, {1386, 5045}, {1420, 36059}, {1451, 4245}, {1714, 5137}, {1780, 2352}, {2174, 19763}, {2175, 5266}, {2217, 9928}, {2323, 5752}, {2915, 26893}, {3045, 12532}, {3215, 23067}, {3220, 37482}, {3292, 23154}, {3564, 15985}, {3876, 5012}, {3927, 3955}, {5138, 37594}, {5439, 5651}, {5767, 27410}, {5769, 34831}, {5791, 37527}, {5927, 11424}, {6638, 20764}, {7113, 19762}, {7535, 37543}, {7561, 26942}, {10539, 24474}, {11363, 14054}, {12233, 31832}, {12514, 20986}, {12528, 34148}, {13352, 40263}, {13754, 35203}, {17220, 31900}, {19365, 34048}, {19597, 23075}, {20739, 23620}, {22276, 39582}, {23072, 23089}, {23074, 23172}, {23383, 35327}, {23841, 39523}, {24320, 36742}, {29958, 34986}, {31835, 32046}

X(42463) = isogonal conjugate of polar conjugate of X(3187)
X(42463) = isogonal conjugate of X(10)-cross conjugate of X(4)
X(42463) = isotomic conjugate of polar conjugate of X(5301)

leftri

Perspectors associated with product triangles: X(42464)-X(42471)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, March 28, 2021.

Let T1 = A1B1C1 be a triangle, and let M1 be the matrix whose rows are the normalized barycentrics of A1, B1, C1, respectively. Let T2 = A2B2C2 be a triangle, and let M2 be the matrix whose rows are the normalized barycentrics of A2, B2, C2, respectively. Let M be the matrix product M1*M2. The triangle product T1*T2 is here defined as the triangle whose vertices are given by the rows of M1*M2. The noncommutative operation denoted by *, here named triangle multiplication, is associative.

Abbreviate the cevian triangle of a pont P = p : q : r as cevian(P) and the anticevian triangle of U = u : v : w as anticevian(U). Let

T1 = A'B'C' = anticevian(P), so that A' = -p : q : r
T2 = A''B''C'' = anticevian triangle(U), so that A'' = -u : v : w.

Then T1*T2 is perspective to ABC, and the perspector, f(P,U), is given by

u (p u^2 - q u^2 + r u^2 - 2 r u v - p v^2 + q v^2 + r v^2 + 2 q u w + 2 p v w - p w^2 - q w^2 - r w^2) (p u^2 + q u^2 - r u^2 + 2 r u v - p v^2 - q v^2 - r v^2 - 2 q u w + 2 p v w - p w^2 + q w^2 + r w^2)
:
-v (p u^2 - q u^2 + r u^2 - 2 r u v - p v^2 + q v^2 + r v^2 + 2 q u w + 2 p v w - p w^2 - q w^2 - r w^2) (p u^2 + q u^2 + r u^2 - 2 r u v - p v^2 - q v^2 + r v^2 - 2 q u w + 2 p v w - p w^2 + q w^2 - r w^2)
:
-w (p u^2 + q u^2 + r u^2 - 2 r u v - p v^2 - q v^2 + r v^2 - 2 q u w + 2 p v w - p w^2 + q w^2 - r w^2) (p u^2 + q u^2 - r u^2 + 2 r u v - p v^2 - q v^2 - r v^2 - 2 q u w + 2 p v w - p w^2 + q w^2 + r w^2)

The appearance of (i,j,k) in the following list means that f(X(i),X(j)) = X(k):

(1,1,84)
(1,2,7)
(1,3,1069)
(1,6,7169)
(1,8,6553)
(1,9,200)
(1,10,10)
(1,11,522)
(2,1,3062)
(2,2,2)
(2,3,6391)
(2,6,64)
(2,9,3680)
(2,10,42027)
(3,1,42464)
(3,2,69)
(3,3,15316)
(3,4,3346)
(3,5,5)
(3,6,25)
(3,11,513)
(4,1,3345)
(4,2,253)
(4,3,3)
(4,4,42465)
(5,2,264)
(5,3,68)
(5,5,42466)
(5,6,32319)
(6,1,42467)
(6,2,4)
(6,3,394)
(6,4,42468)
(6,5,13157)
(6,6,34207)
(6,10,226)
(6,11,4391)
(7,1,8917)
(7,2,10405)
(7,6,7152)
(7,9,9)
(8,1,1)
(8,2,4373)
(8,3,42469)
(8,6,2192)
(9,1,57)
(9,2,8)
(9,9,42470)
(9,10,4052)
(9,11,514)
(10,1,4)
(10,2,75)
(10,10,42471)
(10,11,523)
(11,1,513)
(11,2,693)
(11,3,521)
(11,9,3900)
(11,10,522)
(13,2,19776)
(14,2,19777)
(15,2,2992)
(16,2,2993)
(17,2,19712)
(18,2,19713)
(19,2,7219)
(19,3,222)
(20,2,35510)
(20,4,4)
(20,6,154)

The locus of a point X = x : y : z such that f(P,X) lies on this line: at infinity is the bicevian conic of the points X(2) = 1 : 1 : 1 and -p + q + r : p - q + r : p + q - r, given by

(p - q + r)(p + q - r) x^2 + 2 p (p - q - r) y z + (cyclic) = 0.

This conic, denoted by BC(P), has center q + r : r + p : p+ q and perspector

(p - q - r)/(p^2 - q r - r p - p q) : (q - r - p)/(q^2 - r p - p q - q r) : (r - p - q)/(r^2 - p q - q r - r p)

If P lies inside the medial triangle, then BC(P) is an ellipse. If P lies on the nine-point circle, then BC(P) is a right hyperbola.

The appearance of (i, [name]) in the following list means that BC(X(i)) is the named conic:

(2, Steiner inellipse), (3, nine-point circle), (5, bicevian conic of X(2) and X(3), (10, circumellipse of the medial and incentral triangles [see X(34585)], (115, Kiepert circumhyperbola of the medial triangle) (125, Jerabek circumhyperbola of the medial triangle)

The appearance of (i, {n1, n2, ..., nk}) in the next list means that BC(X(i)) is the conic that passes through the points: X(n1), X(n2), ..., X(nk):

(1, {11, 1145, 1146, 2968, 3756, 4904, 6739, 6741, 7358, 8286, 16613, 38992, 39004, 39050, 40608, 40609})
(4, {122, 3184, 13611, 39020, 40616})
(6, {125, 5181, 6388, 7358, 15526, 15595, 17421, 26932, 40618, 40626})
(9, {11, 1086, 8287, 10427, 13609, 16591, 16592, 16593, 16594, 16595, 16596, 16597, 20343, 21623, 26932, 34846, 38989, 39007, 39063, 40615, 40617, 40622, 40629}
(37, {244, 1086, 2968, 4858, 5515, 6377, 16586, 17755, 38995, 39040, 40619, 40624, 40626})
(39, {115, 339, 3124, 5976, 7664, 21208, 36901, 39000, 40619})
(113, {3, 125, 2088, 3134, 39174, 39987})
(114, {3, 115, 868, 17423, 34156, 34810, 38997, 39078})
(116, {3, 118, 354, 2140, 3136, 3789, 5452, 20970, 32664, 39029, 39046, 40586, 40591})
(118, {3, 116, 3138, 14714, 39006})
(119, {3, 11, 3139, 34467, 39175})
(120, {3, 1015, 3140, 3675, 5511, 34160, 39025})
(122, {3, 4, 133, 800, 1249, 3184, 6523, 14363, 15259, 16253, 20208, 23976, 33549, 33580})
(123, {3, 56, 429, 12610, 25640, 36103, 40590})
(124, {3, 65, 117, 478, 3142, 3454, 24220, 34281, 36033, 39037, 39070, 40611, 40613})
(126, {3, 1084, 3143, 5512, 21906, 34158})
(127, {3, 32, 132, 427, 3162, 21248, 22391, 39045, 39071, 39086, 40588, 40959})
(130, {3, 129, 389, 3819, 21243, 34850})
(132, {3, 127, 3150, 35071, 41172})
(136, {3, 131, 216, 6389, 10600, 24245, 24246, 31377, 33553, 34833, 34851, 34853, 35067, 37565, 37864})
(137, {3, 128, 140, 570, 6592, 8562, 15345, 17707, 21975, 23702, 34828, 39171})
(140, {137, 2972, 6592, 8902, 17433, 35442, 39019})
(141, {125, 1084, 3124, 6593, 7668, 8054, 15450, 17413, 36213, 38987, 38988, 38989, 38990, 38991, 38992, 38993, 38994, 38995, 38996, 38997, 38998, 39067, 39068, 39075, 39079, 39080, 40601})
(142, {11, 3119, 6594, 35508, 38991})
(216, {{136, 338, 2972, 14920, 15526, 34834, 36901, 38987, 40624}})
(226, {6506, 26932, 31653, 34591, 35072, 39006})
(230, {441, 868, 35088, 36212, 38987})
(233, {5522, 15526, 35442, 38997, 39081, 40604})
(244, {10, 37, 960, 1125, 3739, 4075, 16597, 18589, 19563, 20529, 21249, 31845, 34587, 34851, 35068, 40607})

Inverse triangles are introduced in the preamble just before X(42005). If T1 and T2 are triangles and T1 is non-degenerate (so that its matrix is invertible), then there exists a unique triangle T such that T1*T = T2, and the solution is T = inverse(T1)*T2. Likewise, there exists a unique triangle T such that T*T1 = T2, and the solution is T = T2*inverse(T1). Following are eight examples:


1. Let P = p : q : r and U = u : v : w. Let T1 = cevian(P) and T2 = cevian(U). The triangle T = A'B'C' such that T1*T = T2 is given by

A' = u (v + w) (2 p u + q u + r u + p v + r v + p w + q w) : v (u + w) (-q u - r u + p v - r v + p w + q w), (u + v) w (-q u - r u + p v + r v + p w - q w)
B' = u (v + w) (q u - r u - p v - r v + p w + q w) : v (u + w) (q u + r u + p v + 2 q v + r v + p w + q w) : (u + v) w (q u + r u - p v - r v - p w + q w)
C' = u (v + w) (-q u + r u + p v + r v - p w - q w) : -v (u + w) (-q u - r u + p v - r v + p w + q w) : (u + v) w (q u + r u + p v + r v + p w + q w + 2 r w)

The locus of a point U = X = x : y : z such that T is perspective to the medial triangle is the cubic given by

(p + r) (q + r) y^2 z + (p + q) (q + r) y z^2 + (cyclic) + 2 (p^2 + q^2 + r^2 + 3(q r + r p + p q)) x y z = 0.

For P = X(148), this cubic is K185. For P = X(150), the cubic passes through X(i) for i = 7, 8, 80, 320, 42482.


2. Let P = p : q : r and U = u : v : w. Let T1 = cevian(P) and T2 = cevian(U). The triangle T = A'B'C' such that T*T1 = T2 is given by

A' = (q + r) (r v + q w) : (p + r) (-r v + q w) : -(p + q) (-r v + q w)
B' = (q + r) (-r u + p w) : (p + r) (r u + p w) : -(p + q) (-r u + p w)
C' = (q + r) (-q u + p v), -(p + r) (-q u + p v), (p + q) (q u + p v)

The locus of a point U = X = x : y : z such that T is perspective to the medial triangle is the cubic given by

p^2 (r (p+r) (q+r) y^2 z - q (p+q) (q+r) y z^2) + (cyclic) = 0.

This cubic passes through X(2) for every point P. For P = X(4), the cubic is K621. The appearance of (i, {n1, n2, ..., nk}) in the next list means that the cubic passes through the points: X(n1), X(n2), ..., X(nk):

(1, {1,2,6,37,81,3293,17147,39949,39964})
(3, {2,3,97,216,577})
(4, [K621],{2,4,6,24,393,847,2052,6515})
(5,{2,5,233,31610,36412})
(6, {2,6,32,39,251,8267})
(7, {1,2,7,279,1088,1445,36845})
(8, {2,8,9,78,312,318,329,346})
(9, {2,9,220,1212,6605})
(10, {2,10,594,1213,6539})
(20, {2,20,1249,6616,18623,27382,36413,37669,41084})
(63, {2,63,394,1214,1812})
(69, {2,3,69,305,1370,3926,20806})
(74, {2,74,323,3003,10419,14264,14910,40353})
(75, {2,10,75,76,310,4043,17135,40004,40005})
(76, {2,76,141,1502,40016})
(99, {2,99,523,4590,14061,14089,31614})
(100, {2,100,650,1252,31615})
(101, {2,101,6586,14085,23990,31616})
(110, {2,110,647,13198,23357})
(190, {2,190,514,1016,6632,14087,27191})
(192, {2,43,192,6376,41840})
(193, {2,193,439,6337,6353,18287})
(239, {2,239,4366,6654,17755})
(385, {2,385,4027,5976,40820})


3. Let P = p : q : r and U = u : v : w. Let T1 = cevian(P) and T2 = anticevian(U). The triangle T = A'B'C' such that T1*T = T2 is given by

A' = u (p u^2 - p u v - q u v + q v^2 - p u w - r u w - q v w - r v w + r w^2)
: v (q u^2 - p u v - q u v + p v^2 + p u w + r u w + q v w + r v w - p w^2 - q w^2 - r w^2)
: w (r u^2 + p u v + q u v - p v^2 - q v^2 - r v^2 - p u w - r u w + q v w + r v w + p w^2)

B' = u (q u^2 - p u v - q u v + p v^2 + p u w + r u w + q v w + r v w - p w^2 - q w^2 - r w^2)
: v (p u^2 - p u v - q u v + q v^2 - p u w - r u w - q v w - r v w + r w^2)
: w (-p u^2 - q u^2 - r u^2 + p u v + q u v + r v^2 + p u w + r u w - q v w - r v w + q w^2)

C' = u (r u^2 + p u v + q u v - p v^2 - q v^2 - r v^2 - p u w - r u w + q v w + r v w + p w^2)
: v (-p u^2 - q u^2 - r u^2 + p u v + q u v + r v^2 + p u w + r u w - q v w - r v w + q w^2)
: w (p u^2 - p u v - q u v + q v^2 - p u w - r u w - q v w - r v w + r w^2)

The triangle T is perspective to ABC for all P and U. The perspector, denoted here by g(P,U), is given by

g(P,U) = u (r u^2 + p u v + q u v - p v^2 - q v^2 - r v^2 - p u w - r u w + q v w + r v w + p w^2) (q u^2 - p u v - q u v + p v^2 + p u w + r u w + q v w + r v w - p w^2 - q w^2 - r w^2)
: v (-p u^2 - q u^2 - r u^2 + p u v + q u v + r v^2 + p u w + r u w - q v w - r v w + q w^2) (q u^2 - p u v - q u v + p v^2 + p u w + r u w + q v w + r v w - p w^2 - q w^2 - r w^2)
: w (r u^2 + p u v + q u v - p v^2 - q v^2 - r v^2 - p u w - r u w + q v w + r v w + p w^2) (-p u^2 - q u^2 - r u^2 + p u v + q u v + r v^2 + p u w + r u w - q v w - r v w + q w^2).

For U = P, this perspector is

(-p^2 + q^2 - r^2) (p^2 + q^2 - r^2) : (p^2 - q^2 - r^2) (p^2 + q^2 - r^2) : (p^2 - q^2 - r^2) (p^2 - q^2 + r^2)

The appearance of (i,j) in the following list means that g(X(i),X(i)) = nX(j):

(1,4), (2,2), (3,68), (4,3346), (5,6662), (6,66), (7,42483), (8,6553), (9,6601), (10,596), (19,42483), (37,13476), (39,27375), (57,34546), (63,6504), (65,42844), (69,6339), (75,2998), (76,42845), (92,34287), (115,36955), (141,6664), (174,189), (188,8), (216, 42846), (365,7357), (366,7), (508,10405), (509,8048), (556,39694), (1577,15412), (2582,2592), (2583,2593), (4179,27807), (4182,42361), (5374,69)


4. Let P = p : q : r and U = u : v : w. Let T1 = cevian(P) and T2 = anticevian(U). The triangle T A'B'C' such that T*T1 = T2 is given by

A' = u (p u - q v + r v + q w - r w) : -v (-q u + r u + p v - p w) : -w (q u - r u - p v + p w)
B' = u (q u - p v + r v - q w) : -v (-p u + r u + q v + p w - r w) : w (-q u + p v - r v + q w)
C' = u (r u - r v - p w + q w) : v (-r u + r v + p w - q w) : w (p u - q u - p v + q v - r w).

The locus of a point U = X = x : y : z for which the anticomplementary triangle is perspective to T is the union of two cubics, given by

Cubic 4.1: p (- p + q + r) y z (y - z) + q (- q + r + p) z x (z - x) + r (- r + p + q) x y (x - y) = 0, and

Cubic 4.2: p x^3 + q y^3 + r z^3 - (r y + q z) y z - (p z + r x) z x - (q x + p y) x y = 0.

The appearance of {i, [name and/or list of points]} in the following list means that for P = X(i), Cubic 4.1 passes through the listed points:

{1, K1077, {1,2,8,9,188,236,3161,7028,8056,24150,24151,24152,24153,24154,24155,24156,24157,24158,39121}
{3, K002, {1,2,3,4,6,9,57,223,282,1073,1249,3341,3342,3343,3344,3349,3350,3351,3352,3356,14481,39162,39163,39164,39165,40989,40990,40991,40992}
{4, {2,4,20,1249,38253}
{5, K612, {2,3,5,6,216,343,2165,34853,40678}
{6, K168, {2,3,6,69,485,486,5374,5408,5409,6337,8770,13388,13389,24245,24246,30556,30557,30558}
{7, {2,7,144,3160,38254}
{8, {2,8,145,3161,38255}
{9, K363, {1,2,7,9,366,1489,3160,7090,13388,13389,14121,19605,40374,41885}
{10, K345,{1,2,9,10,37,226,281,1214,7952,39131}
{11, {2,11,100,650,5375}
{37, {2,10,37,75,6376,16606}
{39, {2,39,76,141,6374}
{44, {2,44,214,320,5239,5240,36668,36669}
{51, {2,51,2979,40588,41378,41379}
{75, {2,75,192,6376,40027,40598}
{76, {2,76,194,6374,32746}
{111, {2,111,14360,15899,38280}
{113, K489,{2,3,6,74,113,403,1989,3003,3580,14993,34834,36896}
{114, {2,98,114,230,36899}
{115, {2,99,115,523,31998}
{116, {2,101,116,6586,39026}
{119, {1,2,9,104,119,1737,2006,8609}
{121, {2,106,121,8610,40595}
{125, {2,110,125,647,36830}
{126, {2,111,126,3291,15899}
{127, {2,112,127,2485,40596}
{132, {2,132,232,1297,5000,5001,41200,41201}
{133, {2,4,30,133,1249,1294,1990,3163,16080}
{140, {2,5,140,216,233,40684}
{141, K836, {2,3,6,39,141,427,5403,5404,14376,40938}
{142,, {1,2,9,142,277,1212,4847}
{178, {2,178,188,236,2090,5430,16015,16016}
{206, K177, {2,3,6,25,32,66,206,1676,1677,3162,19615,41378,41379}
{214, K453, {1,2,9,44,80,88,214,519,3911,4370,19618,40594}
{216, {2,5,216,264,39641,39642}
{220, {2,220,6600,6604,24152,24153}
{223, K965, {2,57,174,189,223,557,558,1659,13388,13389,13390,15495,15891,15892,16662,16663,16664,39122}
{226, {2,63,226,1214,6505,13388,13389}
{230, {2,114,230,325,5976}
{233, {2,17,18,95,140,233}
{236, {2,188,236,1489,7048,41885}
{239, {2,239,6542,6651,41841}
{325, {2,325,385,5976,8290}
{343, {2,343,1993,5408,5409}
{385, {2,385,7779,8290,39091}
{389, {2,5,216,389,577,1147,5562,34836}
{395, {2,299,395,619,30472}
{396, {2,298,396,618,30471}
{402, {2,402,1650,14401,38240,42306}
{442, {1,2,9,21,442,5249,6734,7110,16585,37887,40582,40937}
{478, {2,56,478,509,2362,8048,13388,13389,16232}

The appearance of {i, [list of points]} in the following list means that for P = X(i), Cubic 4.2 passes through the listed points:

{240, {1,2582,2583}
{403, {125,41077}


5. Let P = p : q : r and U = u : v : w. Let T1 = anticevian(P) and T2 = anticevian(U). The triangle T = A'B'C' such that T1*T = T2 is given by

A' = -(q + r) (q r u + p r v + p q w) : (p + r) (q r u + p r v - p q w) : (p + q) (q r u - p r v + p q w)
B' = -2 q r (q + r) (u + w) (q r u + p r v - p q w) : 2 q r (p + r) (u + w) (q r u + p r v + p q w) : -2 q (p + q) r (u + w) (-q r u + p r v + p q w)
C' = -2 q r (q + r) (u + w) (q r u + p r v - p q w): 2 q r (p + r) (u + w) (q r u + p r v + p q w) : -2 q (p + q) r (u + w) (-q r u + p r v + p q w))


6. Let P = p : q : r and U = u : v : w. Let T1 = anticevian(P) and T2 = anticevian(U). The triangle T = A'B'C' such that T*T1 = T2 is given by

A' = p (-p + q + r) (r v + q w) : q (p - q + r) (-r u + p w) : (p + q - r) r (-q u + p v) :
B' = -p (-p + q + r) (-r v + q w) : -q (p - q + r) (r u + p w) : (p + q - r) r (-q u + p v) :
C' = -p (-p + q + r) (-r v + q w) : -q (p - q + r) (-r u + p w) : (p + q - r) r (q u + p v)

The locus of a point P = X = x : y : z such that the triangle T is perspective to the medial triangle is the union of two cubics:

u y z (y - z) + v z x (z - x) + w x y (x - y) = 0, and

v w (x - y - z) x^2 + w u (y - z - x) y^2 + u v (z - x - y) z^2 = 0.

The locus of a point P = X = x : y : z such that the triangle T is perspective to the anticomplementary triangle is the Steiner inellipse, given by

x^2 + y^2 + z^2 - 2 y z - 2 z x - 2 x y = 0.

The locust of a point U = X = x : y : z such that T is perspective to the anticomplementary triangle is the following cubic:

p^2 (r (p + q - r) y^2 z - q (p - q + r) y z^2) + q^2 (p (q + r - p) z^2 x - r (q - r + p) z x^2) + r^2 (q (q + p - q) x^2 y - p (r - p + q) x y^2) = 0.


7. Let P = p : q : r and U = u : v : w. Let T1 = anticevian(P) and T2 = cevian(U). The triangle T = A'B'C' such that T1*T = T2 is given by

A' = u (2 p u + p v - q v + r v + p w + q w - r w) : (p + q - r) v (u + w) : (p - q + r) (u + v) w
B' = (p + q - r) u (v + w) : v (-p u + q u + r u + 2 q v + p w + q w - r w) : -(p - q - r) (u + v) w
C' = (p - q + r) u (v + w) : -(p - q - r) v (u + w) : w (-p u + q u + r u + p v - q v + r v + 2 r w)

The triangle T is perspective to ABC for all P and U. The perspector if U = P is given by

g(P) = p (q + r) (p - q + r) (p + q - r) : q (r + p) (q - r + p) (q + r - p) : r (p + q)(r - p + q) (r + p - q).

The appearance of (i,j) in thje following list means that g(X(i)) = X(j):

(1,65), (2,2), (3,5562), (4,64), (5,14978), (6,1843), (7,3062), (8,3680), (9,3059), (10,4647), (11,42547), (13,34296), (14,34295), (20,33893), (37,2667), (39,42548), (57,42549), (65,42550), (66,22262), (67,10417), (69,6391), (75,42027), (76,42551), (99,9293), (100,42552), (115,42553), (141,42554), (188,42017), (190,42555), (216,42556), (668,9267).


8. Let P = p : q : r and U = u : v : w. Let T1 = anticevian(P) and T2 = cevian(U). The triangle T = A'B'C' such that T*T1 = T2 is given by

A' = -(p - q - r) (r v + q w) : -q (-p + q - r) w : (p + q - r) r v
B' = -p (p - q - r) w : (p - q + r) (r u + p w) : (p + q - r) r u
C' = -p (p - q - r) v : -q (-p + q - r) u : (p + q - r) (q u + p v)

The triangle T is perspective to ABC for all P and U. The perspector is given by

p (- p + q + r) v w : q (p - q + r) w u : r (p + q - r) u v

The locus of a point P = X = x : y : z such that T is perspective to the medial triangle is the conic given by

u (y - z)(x - y - z) + v (z - x)(y - z - x) + w (x - y)(z - x - y) = 0, or, equivalently,

(v - w)(x^2 + y z) + (w - u)(y^2 + z x) + (u - v)(z^2 + x y) = 0.

Clearly, this conic passes through the centroid and the vertices of the medial triangle. The appearance of {i,{n1, n2, ... ,nk} in the following list mean that for U = X(i), the conic passes through the points X(n1), X(n2), ... , X(nk):

{1,{2,9,37,440,1213,3161,4370,5513,6544,6651,15487,16590,16593,17755,21838,24771,27481,31336,36911,38015,39056,39059,40181,40586,40614,40651,41841}}
{3,{2,6,216,233,1196,1249,1560,3162,3163,8105,8106,8968,14091,14401,15595,18311,32750,37891,37895,39034,39078,39081,40179,40582,40583,40601,40937,40938,40939,40940,40941,40942,42306}}
{6,{2,3,39,114,618,619,629,630,641,642,1125,1649,2482,3413,3414,3666,5664,5745,5976,6292,6337,6503,6509,6626,7710,8290,8299,8786,10291,10335,11147,11165,13701,13821,13882,13934,14713,15349,15810,15814,15819,15850,22848,22892,27929,30471,30472,33364,33365,33614,33615,33616,33617,33618,33619,33620,33621,34452,34834,34835,38998,39090,39091,39094,39096,39098,39100,39102,40125,40592,40604,40605,41820,41849}}
{7,{1,2,223,1212,1214,2582,2583,3160,3752,6505,16585,16586,17056,18641,31534,31535,35110,36905,39035,39046,39047,39066,40611,40612,41771}}
{11,{2,650,2238,3008,3290,5375,5452,16588,27942,35113,40869}}
{12,{2,478,5750,17053,34261,39595}}
{13,{2,396,11127,35444,40578,40581,40696,41888}}
{14,{2,395,11126,35443,40579,40580,40695,41887}}
{17,{2,465,10639,11130,23302}}
{18,{2,466,10640,11131,23303}}
{31,{2,16584,17023,19557,32664,33568,40597}}
{32,{2,206,1194,3589,6676,7664,8265,29654,36213,41884}}
{37,{2,10,120,1211,3452,3789,6376,6552,6554,13466,14434,16589,16594,17793,21530,28651,36912,39028,40598,40603,40609}}
{38,{2,661,1575,3912,16587,19584,35123,36906,40585}}
{39,{2,126,141,1368,3739,3741,6338,6374,6389,10472,20339,21246,21248,27854,32746,34021,35073,39080}}
{45,{2,514,519,3936,6547,6631,9460,16610,27751,35121,40587,40594}}
{51,{2,3117,3815,11672,33569,40588}}
{74,{2,3003,5158,9209,36896}}
{85,{2,142,4000,11019,17073,17113,18635,20206,36908,39063,40593}}
{92,{2,226,442,1210,3772,7952,18592,20621,39036,40837}}
{94,{2,623,624,2072,3580,13162,14993,16188,18314}}
{98,{2,230,441,647,8623,22391,23967,36830,36899,36904,38975,41196,41197}}
{99,{2,523,524,3291,5159,8542,9165,15899,23991,31655,31998,35087,39061}}
{196,{2,860,1465,14837,39053}}
{210,{2,2276,6184,29571,33570,40599,40606}}
{216,{2,5,132,3767,6523,6708,13567,20207,34836}}
{253,{2,4,3343,26958,33537,40839}}
{257,{2,4357,16591,24239,28358,39040,41886}}
{269,{2,5437,14986,40183,40194}}
{290,{2,511,23878,24206,39058}}
{292,{2,1966,3836,9470,19564,24325}}
{308,{2,626,3934,39076,39082}}
{311,{2,343,639,640,1209,7746,11585,31842,34853}}
{319,{2,3647,5325,19862,28606,30563}}
{330,{2,75,3840,20258,20343,34832}}
{371,{2,615,5408,10962,24245}}
{372,{2,590,5409,10960,24246}}
{648,{2,30,525,4550,9410,14918,16253,39062,42426}}
{662,{2,14838,16579,35466,39054}}
{664,{2,522,527,10001,15346}}
{694,{2,325,3005,3229,6682,19602,25666,35077,39092}}
{846,{2,239,4988,10026,35085}}
{1225,{2,635,636,21975,31843,37452,37636}}
{1341,{2,13636,39023,39068,40989,40990}}
{1501,{2,6679,7792,19576,40368,40377}}
{1978,{2,3835,3948,20340,20530,21250}}
{2006,{2,908,1577,1737,17057,36909,36914}}
{2415,{2,8,11530,16602,21129,24151,30827}}
{2481,{2,518,3826,4762,33675}}
{3003,{2,113,5309,15760,37648}}
{3108,{2,6665,10691,31128,34573}}
{4554,{2,2886,4885,20335,34852}}

The locus of a point U = X = x : y : z such that T is perspective to the medial triangle is the circumconic given by p y z + q z x + r x y = 0.


The triangle sum, T1 + T2 of two arbitrary triangles T1 and T2 is defined in the preamble just before X(42285). The two distributive laws hold:; i.e., if T is a triangle, then

T*(T1 + T2) = T*T1 + T*T2)
(T1 + T2)*T = (T1 + T*T2)*T

For arbitrary points P and U, the product triangle cevian(P)*anticevian(U) is perspective to anticevian(U)*cevian(P), and the perspector is the P-Ceva conjugate of U.

The product A'B'C' = cevian(P)*cevian(U) is given by
A' = (q u + r u + q v + r w) : r v (u + w) : q w (u + v)
B' = u (q u + r u + q v + r w) : r v (u + w) : q w (u + v)
C' = q u (v + w) : p v (u + w) : w (p u + q v + p w + q w)

In particular, the square of cevian(P) is given by
A' = p (p q + q^2 + p r + r^2) : q r (p + r) : q r (p + q) :
B' = p r (q + r) : q (p^2 + p q + q r + r^2) : p r (p + q) :
C' = p q (q + r) : p q (p + r) : r (p^2 + q^2 + p r + q r)



X(42464) = PERSPECTOR OF ABC AND THE PRODUCT TRIANGLE ANTICEVIAN(X(3))*ANTICEVIAN(X(1))

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 - 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(42464) lies on these lines: {40, 3436}, {46, 208}, {198, 1766}, {221, 517}, {318, 1158}, {1800, 2360}, {12704, 22464}

X(42465) = PERSPECTOR OF ABC AND THE PRODUCT TRIANGLE ANTICEVIAN((X(4))*ANTICEVIAN(X(4))

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^12 + 6*a^10*b^2 - 29*a^8*b^4 + 36*a^6*b^6 - 9*a^4*b^8 - 10*a^2*b^10 + 5*b^12 - 6*a^10*c^2 + 14*a^8*b^2*c^2 + 4*a^6*b^4*c^2 - 36*a^4*b^6*c^2 + 34*a^2*b^8*c^2 - 10*b^10*c^2 + 15*a^8*c^4 - 20*a^6*b^2*c^4 + 50*a^4*b^4*c^4 - 36*a^2*b^6*c^4 - 9*b^8*c^4 - 20*a^6*c^6 - 20*a^4*b^2*c^6 + 4*a^2*b^4*c^6 + 36*b^6*c^6 + 15*a^4*c^8 + 14*a^2*b^2*c^8 - 29*b^4*c^8 - 6*a^2*c^10 + 6*b^2*c^10 + c^12)*(a^12 - 6*a^10*b^2 + 15*a^8*b^4 - 20*a^6*b^6 + 15*a^4*b^8 - 6*a^2*b^10 + b^12 + 6*a^10*c^2 + 14*a^8*b^2*c^2 - 20*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 - 29*a^8*c^4 + 4*a^6*b^2*c^4 + 50*a^4*b^4*c^4 + 4*a^2*b^6*c^4 - 29*b^8*c^4 + 36*a^6*c^6 - 36*a^4*b^2*c^6 - 36*a^2*b^4*c^6 + 36*b^6*c^6 - 9*a^4*c^8 + 34*a^2*b^2*c^8 - 9*b^4*c^8 - 10*a^2*c^10 - 10*b^2*c^10 + 5*c^12) : :

X(42465) lies on these lines: {20, 3183}, {253, 33546}, {459, 3346}, {1249, 3349}, {1294, 41425}, {3176, 5930}, {8804, 8894}, {10152, 12324}, {15005, 16251}, {15311, 33893}, {28781, 42452}, {33702, 36965}

X(42466) = PERSPECTOR OF ABC AND THE PRODUCT TRIANGLE ANTICEVIAN((X(5))*ANTICEVIAN(X(5))

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

X(42466) lies on these lines: {3, 15912}, {216, 6663}, {324, 6662}

X(42467) = PERSPECTOR OF ABC AND THE PRODUCT TRIANGLE ANTICEVIAN((X(6))*ANTICEVIAN(X(1))

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

X(42467) lies on these lines: {1, 40454}, {3, 960}, {19, 13478}, {57, 1848}, {58, 4227}, {63, 573}, {84, 7713}, {103, 40097}, {222, 3666}, {295, 2807}, {312, 1766}, {572, 2339}, {1395, 7004}, {1707, 1768}, {1708, 5928}, {1709, 26118}, {1748, 21370}, {1790, 17185}, {2051, 2285}, {3218, 36850}, {3674, 7177}, {5450, 16579}

X(42468) = PERSPECTOR OF ABC AND THE PRODUCT TRIANGLE ANTICEVIAN((X(6))*ANTICEVIAN(X(4))

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 + 3*a^8*c^2 + 12*a^6*b^2*c^2 - 30*a^4*b^4*c^2 + 12*a^2*b^6*c^2 + 3*b^8*c^2 - 14*a^6*c^4 + 14*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - 14*b^6*c^4 + 14*a^4*c^6 - 20*a^2*b^2*c^6 + 14*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 - c^10)*(a^10 + 3*a^8*b^2 - 14*a^6*b^4 + 14*a^4*b^6 - 3*a^2*b^8 - b^10 - 3*a^8*c^2 + 12*a^6*b^2*c^2 + 14*a^4*b^4*c^2 - 20*a^2*b^6*c^2 - 3*b^8*c^2 + 2*a^6*c^4 - 30*a^4*b^2*c^4 + 14*a^2*b^4*c^4 + 14*b^6*c^4 + 2*a^4*c^6 + 12*a^2*b^2*c^6 - 14*b^4*c^6 - 3*a^2*c^8 + 3*b^2*c^8 + c^10) : :

X(42468) lies on these lines: {3, 6523}, {394, 14361}, {1093, 3346}, {14919, 20213}, {15466, 42458}

X(42469) = PERSPECTOR OF ABC AND THE PRODUCT TRIANGLE ANTICEVIAN((X(8))*ANTICEVIAN(X(3))

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

X(42469) lies on these lines: {28, 39696}, {56, 4641}, {1472, 3167}, {7053, 20805}

X(42470) = PERSPECTOR OF ABC AND THE PRODUCT TRIANGLE ANTICEVIAN((X(9))*ANTICEVIAN(X(9))

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

X(42470) lies on these lines: {1, 6600}, {4, 5853}, {7, 3174}, {8, 24389}, {9, 10388}, {84, 518}, {90, 5223}, {104, 6282}, {200, 6601}, {294, 2324}, {322, 2481}, {516, 10309}, {519, 3427}, {521, 35355}, {527, 10307}, {885, 8058}, {1000, 6666}, {1001, 7160}, {1156, 34784}, {1476, 7672}, {2136, 5665}, {2801, 34256}, {2951, 5856}, {3062, 15733}, {3158, 8730}, {3243, 7091}, {3577, 3880}, {4326, 34919}, {5732, 10305}, {7320, 19860}, {15998, 21627}, {16005, 17768}, {30500, 37569}, {40659, 42015}

X(42471) = PERSPECTOR OF ABC AND THE PRODUCT TRIANGLE ANTICEVIAN((X(10))*ANTICEVIAN(X(10))

Barycentrics    (b + c)*(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(42471) lies on these lines: {1, 3159}, {19, 17915}, {37, 4075}, {65, 2901}, {75, 24046}, {267, 17763}, {321, 596}, {519, 34434}, {726, 13476}, {740, 40504}, {876, 8714}, {994, 14923}, {2214, 39964}, {2218, 22027}, {3175, 6534}, {3249, 4024}, {3634, 25347}, {4066, 42027}, {4674, 17751}, {4737, 31359}, {6532, 31993}, {21081, 21100}, {21208, 27801}, {22045, 39697}, {30942, 39711}

leftri

Gibert points on the cubic K1200: X(42472)-X(42483)

rightri

This preamble and points X(42472)-X(42483) are contributed by Peter Moses, April 2, 2021. See also the preambles just before X(42085), X(42413), and X(42429).

See K1200.



X(42472) = GIBERT (2,7,6) POINT

Barycentrics    a^2*S/Sqrt[3] + 3*a^2*SA + 7*SB*SC) : :

X(42472) lies on the cubic K1200 and these lines: {2, 42088}, {4, 10188}, {5, 5335}, {6, 5068}, {14, 3545}, {15, 3855}, {16, 5071}, {381, 42119}, {546, 42130}, {547, 42127}, {631, 42100}, {1656, 42123}, {3090, 5237}, {3091, 5321}, {3523, 42102}, {3524, 42105}, {3525, 19106}, {3529, 33417}, {3533, 42091}, {3544, 18581}, {3832, 23302}, {3839, 11480}, {3850, 42132}, {3851, 5334}, {3854, 42093}, {3857, 42126}, {3858, 42116}, {5055, 42138}, {5056, 5318}, {5066, 11485}, {5067, 42086}, {5070, 42137}, {5072, 11542}, {5079, 42118}, {5344, 42121}, {5366, 35018}, {7486, 11481}, {10299, 42113}, {10303, 42097}, {10653, 33602}, {11543, 19709}, {12811, 42125}, {12817, 37832}, {15022, 23303}, {15717, 42109}, {16809, 42435}, {16961, 42111}, {16967, 41974}, {19107, 41099}, {37641, 42095}, {38071, 42415}

X(42473) = GIBERT (-2,7,6) POINT

Barycentrics    -a^2*S/Sqrt[3] + 3*a^2*SA + 7*SB*SC) : :

X(42473) lies on the cubic K1200 and these lines: {2, 42087}, {4, 10187}, {5, 5334}, {6, 5068}, {13, 3545}, {15, 5071}, {16, 3855}, {381, 42120}, {546, 42131}, {547, 42126}, {631, 42099}, {1656, 42122}, {3090, 5238}, {3091, 5318}, {3523, 42101}, {3524, 42104}, {3525, 19107}, {3529, 33416}, {3533, 42090}, {3544, 18582}, {3832, 23303}, {3839, 11481}, {3850, 42129}, {3851, 5335}, {3854, 42094}, {3857, 42127}, {3858, 42115}, {5055, 42135}, {5056, 5321}, {5066, 11486}, {5067, 42085}, {5070, 42136}, {5072, 11543}, {5079, 42117}, {5343, 42124}, {5365, 35018}, {7486, 11480}, {10299, 42112}, {10303, 42096}, {10654, 33603}, {11542, 19709}, {12811, 42128}, {12816, 37835}, {15022, 23302}, {15717, 42108}, {16808, 42436}, {16960, 42114}, {16966, 41973}, {19106, 41099}, {37640, 42098}, {38071, 42416}

X(42474) = GIBERT (3,14,16) POINT

Barycentrics    Sqrt[3]*a^2*S + 16*a^2*SA + 28*SB*SC : :

X(42474) lies on the cubic K1200 and these lines: {2, 42088}, {5, 5339}, {6, 5071}, {13, 5055}, {381, 10645}, {395, 5056}, {547, 42114}, {549, 42113}, {1656, 5237}, {3090, 5340}, {3545, 42093}, {3851, 10188}, {3860, 42090}, {5066, 11480}, {5068, 36836}, {5070, 36968}, {5072, 36970}, {5079, 37835}, {7486, 36843}, {10109, 18582}, {11481, 15699}, {11539, 42106}, {11812, 42105}, {12817, 16966}, {14269, 33417}, {15022, 22237}, {15694, 42097}, {15702, 42102}, {15703, 16808}, {15708, 42109}, {15718, 42429}, {22238, 35018}, {37832, 41122}, {38071, 42092}, {41119, 42420}, {41121, 42129}

X(42475) = GIBERT (-3,14,16) POINT

Barycentrics    Sqrt[3]*a^2*S - 16*a^2*SA - 28*SB*SC : :

X(42475) lies on the cubic K1200 and these lines: {2, 42087}, {5, 5340}, {6, 5071}, {14, 5055}, {381, 10646}, {396, 5056}, {547, 42111}, {549, 42112}, {1656, 5238}, {3090, 5339}, {3545, 42094}, {3851, 10187}, {3860, 42091}, {5066, 11481}, {5068, 36843}, {5070, 36967}, {5072, 36969}, {5079, 37832}, {7486, 36836}, {10109, 18581}, {11480, 15699}, {11539, 42103}, {11812, 42104}, {12816, 16967}, {14269, 33416}, {15022, 22235}, {15694, 42096}, {15702, 42101}, {15703, 16809}, {15708, 42108}, {15718, 42430}, {22236, 35018}, {37835, 41121}, {38071, 42089}, {41120, 42419}, {41122, 42132}

X(42476) = GIBERT (11,26,48) POINT

Barycentrics    11*a^2*S/Sqrt[3] + 48*a^2*SA + 52*SB*SC : :

X(42476) lies on the cubic K1200 and these lines: {5, 11480}, {1656, 41978}, {5318, 15702}, {5351, 42128}, {10188, 16967}, {10299, 42094}, {10304, 42109}, {11481, 11540}, {15681, 33417}, {15693, 42098}, {16645, 41985}, {34755, 42132}

X(42477) = GIBERT (-11,26,48) POINT

Barycentrics    11*a^2*S/Sqrt[3] - 48*a^2*SA - 52*SB*SC : :

X(42476) lies on the cubic K1200 and these lines: {5, 11481}, {1656, 41977}, {5321, 15702}, {5352, 42125}, {10187, 16966}, {10299, 42093}, {10304, 42108}, {11480, 11540}, {15681, 33416}, {15693, 42095}, {16644, 41985}, {34754, 42129}

X(42478) = GIBERT (66,13,2) POINT

Barycentrics    11*Sqrt[3]*a^2*S + a^2*SA + 13*SB*SC : :

X(42478) lies on the cubic K1200 and these lines: {5, 37641}, {5059, 42147}, {5335, 38335}, {5351, 10299}, {6435, 36436}, {6436, 36454}, {10304, 11480}, {10653, 17538}, {10654, 15682}, {11486, 11540}, {11488, 15702}, {15681, 42118}, {15690, 42120}, {16967, 33607}, {19708, 41972}, {41122, 42142}, {42119, 42429}

X(42479) = GIBERT (-66,13,2) POINT

Barycentrics    -11*Sqrt[3]*a^2*S + a^2*SA + 13*SB*SC : :

X(42479) lies on the cubic K1200 and these lines: {5, 37640}, {5059, 42148}, {5334, 38335}, {5352, 10299}, {6435, 36454}, {6436, 36436}, {10304, 11481}, {10653, 15682}, {10654, 17538}, {11485, 11540}, {11489, 15702}, {15681, 42117}, {15690, 42119}, {16966, 33606}, {19708, 41971}, {41121, 42139}, {42120, 42430}

X(42480) = GIBERT (117,14,1) POINT

Barycentrics    39*Sqrt[3]*a^2*S + a^2*SA + 28*SB*SC : :

X(42480) lies on the cubic K1200 and these lines: {5, 16268}, {6, 12816}, {61, 15691}, {62, 15709}, {5237, 15692}, {10645, 15759}, {10653, 11001}, {11486, 15701}, {15684, 16965}, {15688, 22236}, {15723, 16963}, {16772, 41983}, {33603, 41112}, {33607, 37641}, {35408, 42431}, {41107, 42137}

X(42481) = GIBERT (-117,14,1) POINT

Barycentrics    39*Sqrt[3]*a^2*S - a^2*SA - 28*SB*SC : :

X(42481) lies on the cubic K1200 and these lines: {5, 16267}, {6, 12816}, {61, 15709}, {62, 15691}, {5238, 15692}, {10646, 15759}, {10654, 11001}, {11485, 15701}, {15684, 16964}, {15688, 22238}, {15723, 16962}, {16773, 41983}, {33602, 41113}, {33606, 37640}, {35408, 42432}, {41108, 42136}

X(42482) = POINT CURSA

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

X(42482) is one of many points in ETC named for a star; see CURSA

X(42482) lies on this line: {80, 320}

X(42483) = ISOGONAL CONJUGATE OF X(1615)

Barycentrics    (a^4 + 4*a^3*b - 10*a^2*b^2 + 4*a*b^3 + b^4 - 4*a^3*c + 4*a^2*b*c + 4*a*b^2*c - 4*b^3*c + 6*a^2*c^2 - 4*a*b*c^2 + 6*b^2*c^2 - 4*a*c^3 - 4*b*c^3 + c^4)*(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4 + 4*a^3*c + 4*a^2*b*c - 4*a*b^2*c - 4*b^3*c - 10*a^2*c^2 + 4*a*b*c^2 + 6*b^2*c^2 + 4*a*c^3 - 4*b*c^3 + c^4) : :
X(42483) = X[18230] - 3 X[32079]

X(42483 lies on the cubic K202 and these lines: {2, 17113}, {7, 19605}, {9, 2124}, {144, 200}, {346, 16284}, {527, 36627}, {5431, 16016}, {15891, 16663}, {15892, 16662}, {18230, 32079}, {20059, 41798}

X(42483) = reflection of X(15913) in X(9)
X(42483) = isogonal conjugate of X(1615)
X(42483) = isotomic conjugate of X(30695)
X(42483) = anticomplement of X(17113)
X(42483) = cyclocevian conjugate of X(6601)
X(42483) = isotomic conjugate of the anticomplement of X(279)
X(42483) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2125, 3434}, {8917, 6604}
X(42483) = X(i)-cross conjugate of X(j) for these (i,j): {279, 2}, {3062, 7}, {17426, 3900}
X(42483) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1615}, {6, 2951}, {31, 30695}, {41, 31527}, {55, 2124}, {101, 17427}, {1253, 17113}, {17426, 24013}
X(42483) = cevapoint of X(i) and X(j) for these (i,j): {513, 35508}, {514, 13609}, {2125, 8917}, {3900, 17426}, {6362, 38973}
X(42483) = trilinear pole of line {3900, 7658}
X(42483) = barycentric product X(i)*X(j) for these {i,j}: {75, 8917}, {85, 2125}
X(42483) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2951}, {2, 30695}, {6, 1615}, {7, 31527}, {57, 2124}, {279, 17113}, {513, 17427}, {2125, 9}, {8917, 1}, {35508, 17426}

X(42484) = ISOGONAL CONJUGATE OF X(1619)

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

X(42484) lies on these lines: {2, 15259}, {4, 31367}, {20, 159}, {25, 40185}, {1249, 3162}, {1370, 14615}, {5930, 8900}, {6804, 31362}, {6816, 14249}, {18589, 36103}

X(42484) = reflection of X(33584) in X(31367)
X(42484) = isogonal conjugate of X(1619)
X(42484) = anticomplement of X(15259)
X(42484) = cyclocevian conjugate of X(6339)
X(42484) = isotomic conjugate of the anticomplement of X(2207)
X(42484) = polar conjugate of the isotomic conjugate of X(2139)
X(42484) = X(2139)-anticomplementary conjugate of X(5905)
X(42484) = X(2139)-Ceva conjugate of X(40186)
X(42484) = X(i)-cross conjugate of X(j) for these (i,j): {2207, 2}, {34944, 4}
X(42484) = cevapoint of X(122) and X(512)
X(42484) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1619}, {63, 2138}, {326, 15259}
X(42484) = barycentric product X(i)*X(j) for these {i,j}: {4, 2139}, {253, 40186}
X(42484) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 1619}, {25, 2138}, {2139, 69}, {2207, 15259}, {40186, 20}

X(42485) = ISOGONAL CONJUGATE OF X(1610)

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

X(42485) lies on these lines: {2, 15267}, {56, 34279}, {63, 23359}, {65, 19608}, {72, 3588}, {304, 18659}, {306, 22282}, {478, 958}, {960, 40590}, {1214, 12089}, {26702, 41401}

X(42485) = isogonal conjugate of X(1610)
X(42485) = anticomplement of X(15267)
X(42485) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1610}, {6, 23512}, {572, 34267}, {1098, 15267}
X(42485) = cevapoint of X(512) and X(34591)
X(42485) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 23512}, {6, 1610}, {34434, 34267}

X(42486) = ISOGONAL CONJUGATE OF X(33786)

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

X(42486) lies on these lines: {32, 8264}, {39, 6374}, {194, 3051}, {315, 14946}, {3186, 19566}, {16985, 40146}, {21080, 32453}, {21814, 22028}

X(42486) = reflection of X(39468) in X(39)
X(42486) = isogonal conjugate of X(33786)
X(42486) = isotomic conjugate of X(8264)
X(42486) = isotomic conjugate of the anticomplement of X(1502)
X(42486) = isotomic conjugate of the complement of X(40907)
X(42486) = X(1502)-cross conjugate of X(2)
X(42486) = cevapoint of X(2) and X(40907)
X(42486) = trilinear pole of line {688, 21262}
X(42486) = X(i)-isoconjugate of X(j) for these (i,j): {1, 33786}, {6, 33782}, {19, 23173}, {31, 8264}, {32, 33788}, {560, 19562}, {4118, 38838}
X(42486) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 33782}, {2, 8264}, {3, 23173}, {6, 33786}, {75, 33788}, {76, 19562}, {38826, 38838}
X(42486) = {X(32),X(40381)}-harmonic conjugate of X(8264)

X(42487) = ISOGONAL CONJUGATE OF X(1629)

Barycentrics    a^2*(a^2 - b^2 - c^2)^2*(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(42487) = X[216] - 3 X[3917], X[264] + 3 X[2979], X[3164] - 9 X[33884], X[6243] - 5 X[40329]

X(42487) lies on these lines: {5, 141}, {185, 31504}, {216, 3289}, {264, 2979}, {3164, 11794}, {6243, 40329}, {6662, 10627}, {10003, 32142}, {10625, 39530}, {11412, 13599}, {15318, 42329}

X(42487) = midpoint of X(10625) and X(39530)
X(42487) = reflection of X(10003) in X(32142)
X(42487) = isogonal conjugate of X(1629)
X(42487) = isogonal conjugate of the polar conjugate of X(36952)
X(42487) = X(15526)-cross conjugate of X(520)
X(42487) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1629}, {19, 36794}, {92, 10312}, {158, 5012}, {393, 18042}, {823, 3050}, {1078, 1096}, {2190, 30506}, {2207, 33764}, {7668, 24000}, {24019, 31296}, {33778, 36417}
X(42487) = barycentric product X(i)*X(j) for these {i,j}: {3, 36952}, {394, 3613}, {520, 11794}, {3926, 27375}, {15526, 27867}
X(42487) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 36794}, {6, 1629}, {184, 10312}, {216, 30506}, {255, 18042}, {326, 33764}, {394, 1078}, {418, 41334}, {520, 31296}, {577, 5012}, {1364, 27010}, {3269, 7668}, {3613, 2052}, {3917, 37125}, {3926, 33769}, {11794, 6528}, {15526, 36901}, {27375, 393}, {27867, 23582}, {28724, 41296}, {34980, 38352}, {36952, 264}, {39201, 3050}

leftri

Gibert points on cubics K1194-K1201: X(42488)-X(42536)

rightri

This preamble and points X(42488)-X(42536) are contributed by Peter Moses, April 5, 2021

For the relevant cubics, see
K1194
K1195
K1197
K1200
K1201

Gibert points are introduced in the preamble just before X(42085)



X(42488) = GIBERT (3,4,7) POINT

Barycentrics    Sqrt[3]*a^2*S + 7*a^2*SA + 8*SB*SC : :

X(42488) lies on the cubic K1194 and these lines: {2, 17}, {3, 36969}, {4, 5352}, {5, 15}, {6, 5070}, {13, 140}, {14, 3090}, {16, 3526}, {18, 396}, {20, 16808}, {61, 1656}, {303, 635}, {381, 5238}, {382, 10645}, {397, 632}, {398, 547}, {546, 36967}, {548, 19106}, {549, 42158}, {569, 3201}, {623, 628}, {624, 11307}, {630, 6669}, {631, 10646}, {1216, 36979}, {2042, 35739}, {2046, 35731}, {3091, 42157}, {3107, 3934}, {3205, 9306}, {3206, 13353}, {3364, 10577}, {3365, 10576}, {3389, 8253}, {3390, 8252}, {3391, 42173}, {3392, 42174}, {3411, 16960}, {3412, 5067}, {3523, 36968}, {3524, 42161}, {3525, 10653}, {3528, 42100}, {3530, 5318}, {3545, 42150}, {3832, 19107}, {3843, 11480}, {3851, 36836}, {3853, 42099}, {3855, 42085}, {3856, 42122}, {3859, 42101}, {3861, 42087}, {5054, 5340}, {5055, 22236}, {5056, 10654}, {5066, 42164}, {5068, 42160}, {5071, 41101}, {5072, 42154}, {5079, 5339}, {5349, 12811}, {5350, 8703}, {5366, 15692}, {5470, 8591}, {6670, 16529}, {6671, 30560}, {7486, 18581}, {7617, 11305}, {7749, 41406}, {7808, 11312}, {8739, 14940}, {9736, 16629}, {9885, 22489}, {10170, 30439}, {10303, 42151}, {10304, 12816}, {10657, 20379}, {11243, 32767}, {11515, 37452}, {11539, 41100}, {11542, 16239}, {11737, 12817}, {15059, 36208}, {15694, 36843}, {15696, 42094}, {15702, 41119}, {15703, 16268}, {15709, 41112}, {15712, 42165}, {15717, 42086}, {15720, 42155}, {17578, 42090}, {20416, 22997}, {21734, 42134}, {22511, 36763}, {24206, 36757}, {32142, 36978}, {33703, 42106}, {34754, 42095}, {35018, 42163}, {42104, 42472}

X(42488) = {X(6),X(5070)}-harmonic conjugate of X(42489)

X(42489) = GIBERT (-3,4,7) POINT

Barycentrics    -(Sqrt[3]*a^2*S) + 7*a^2*SA + 8*SB*SC : :

X(42489) lies on the cubic K1194 and these lines: {2, 18}, {3, 36970}, {4, 5351}, {5, 16}, {6, 5070}, {13, 3090}, {14, 140}, {15, 3526}, {17, 395}, {20, 16809}, {62, 1656}, {302, 636}, {381, 5237}, {382, 10646}, {397, 547}, {398, 632}, {546, 36968}, {548, 19107}, {549, 42157}, {569, 3200}, {623, 11308}, {624, 627}, {629, 6670}, {631, 10645}, {1216, 36981}, {3091, 42158}, {3106, 3934}, {3205, 13353}, {3206, 9306}, {3364, 8253}, {3365, 8252}, {3366, 42171}, {3367, 42172}, {3389, 10577}, {3390, 10576}, {3411, 5067}, {3412, 16961}, {3523, 36967}, {3524, 42160}, {3525, 10654}, {3528, 42099}, {3530, 5321}, {3545, 42151}, {3832, 19106}, {3843, 11481}, {3851, 36843}, {3853, 42100}, {3855, 42086}, {3856, 42123}, {3859, 42102}, {3861, 42088}, {5054, 5339}, {5055, 22238}, {5056, 10653}, {5066, 42165}, {5068, 42161}, {5071, 41100}, {5072, 42155}, {5079, 5340}, {5349, 8703}, {5350, 12811}, {5365, 15692}, {5469, 8591}, {6669, 16530}, {6672, 30559}, {7486, 18582}, {7617, 11306}, {7749, 41407}, {7808, 11311}, {8740, 14940}, {9735, 16628}, {9886, 22490}, {10170, 30440}, {10303, 42150}, {10304, 12817}, {10658, 20379}, {11244, 32767}, {11516, 37452}, {11539, 41101}, {11543, 16239}, {11737, 12816}, {15059, 36209}, {15694, 36836}, {15696, 42093}, {15702, 41120}, {15703, 16267}, {15709, 41113}, {15712, 42164}, {15717, 42085}, {15720, 42154}, {17578, 42091}, {20415, 22998}, {21734, 42133}, {24206, 36758}, {32142, 36980}, {33703, 42103}, {34755, 42098}, {35018, 42166}, {36251, 36766}, {36770, 37177}, {42105, 42473}

X(42489) = {X(6),X(5070)}-harmonic conjugate of X(42488)

X(42490) = GIBERT (3,2,8) POINT

Barycentrics    Sqrt[3]*a^2*S + 8*a^2*SA + 4*SB*SC : :

X(42490) lies on the cubic K1194 and these lines: {2, 5339}, {3, 13}, {5, 11480}, {6, 631}, {15, 3526}, {18, 15694}, {20, 23302}, {61, 5054}, {62, 15720}, {140, 16645}, {381, 5352}, {382, 10645}, {395, 10303}, {396, 3523}, {397, 3524}, {398, 3525}, {547, 42160}, {548, 18582}, {549, 22238}, {599, 628}, {627, 40341}, {630, 11297}, {632, 10654}, {635, 13083}, {1656, 5238}, {1657, 37832}, {2041, 8253}, {2042, 8252}, {3091, 42474}, {3412, 11486}, {3522, 42166}, {3528, 5318}, {3530, 11481}, {3628, 42150}, {3642, 11309}, {3763, 11307}, {3832, 42087}, {3843, 16966}, {3851, 36967}, {3853, 42090}, {3856, 42104}, {3859, 42144}, {3861, 42114}, {5055, 12817}, {5056, 42164}, {5067, 5321}, {5070, 16964}, {5071, 5349}, {5072, 42432}, {5079, 36970}, {5237, 15693}, {5344, 19708}, {5350, 17538}, {6671, 11311}, {6694, 11302}, {6778, 38634}, {7486, 42119}, {8703, 42162}, {10304, 42165}, {10653, 15712}, {11134, 37515}, {11488, 15717}, {12100, 42151}, {14093, 41121}, {14869, 42149}, {14891, 41112}, {15028, 36980}, {15688, 42431}, {15696, 42097}, {15700, 16267}, {15701, 16962}, {15705, 22235}, {15706, 41107}, {15715, 33604}, {15718, 41100}, {15723, 41108}, {16239, 18581}, {16242, 42435}, {16808, 17800}, {17578, 42110}, {21734, 42088}, {31467, 41407}, {33923, 42161}, {37835, 41971}, {42169, 42219}, {42170, 42217}

X(42490) = {X(6),X(631)}-harmonic conjugate of X(42491)

X(42491) = GIBERT (-3,2,8) POINT

Barycentrics    -(Sqrt[3]*a^2*S) + 8*a^2*SA + 4*SB*SC : :

X(42491) lies on the cubic K1194 and these lines: {2, 5340}, {3, 14}, {5, 11481}, {6, 631}, {16, 3526}, {17, 15694}, {20, 23303}, {61, 15720}, {62, 5054}, {140, 16644}, {381, 5351}, {382, 10646}, {395, 3523}, {396, 10303}, {397, 3525}, {398, 3524}, {547, 42161}, {548, 18581}, {549, 22236}, {599, 627}, {628, 40341}, {629, 11298}, {632, 10653}, {636, 13084}, {1656, 5237}, {1657, 37835}, {2041, 8252}, {2042, 8253}, {3091, 42475}, {3411, 11485}, {3522, 42163}, {3528, 5321}, {3530, 11480}, {3628, 42151}, {3643, 11310}, {3763, 11308}, {3832, 42088}, {3843, 16967}, {3851, 36968}, {3853, 42091}, {3856, 42105}, {3859, 42145}, {3861, 42111}, {5055, 12816}, {5056, 42165}, {5067, 5318}, {5070, 16965}, {5071, 5350}, {5072, 42431}, {5079, 36969}, {5238, 15693}, {5343, 19708}, {5349, 17538}, {6672, 11312}, {6695, 11301}, {6777, 38634}, {7486, 42120}, {8703, 42159}, {10304, 42164}, {10654, 15712}, {11137, 37515}, {11489, 15717}, {12100, 42150}, {14093, 41122}, {14869, 42152}, {14891, 41113}, {15028, 36978}, {15688, 42432}, {15696, 42096}, {15700, 16268}, {15701, 16963}, {15705, 22237}, {15706, 41108}, {15715, 33605}, {15718, 41101}, {15723, 41107}, {16239, 18582}, {16241, 42436}, {16809, 17800}, {17578, 42107}, {21734, 42087}, {31467, 41406}, {33923, 42160}, {37832, 41972}, {42167, 42220}, {42168, 42218}

X(42491) = {X(6),X(631)}-harmonic conjugate of X(42490)

X(42492) = GIBERT (4,9,17) POINT

Barycentrics    (4*a^2*S)/Sqrt[3] + 17*a^2*SA + 18*SB*SC : :

X(42492) lies on the cubic K1194 and these lines: {5, 11480}, {14, 15699}, {16, 632}, {18, 10188}, {30, 42472}, {140, 5344}, {547, 42139}, {549, 16966}, {550, 33417}, {3530, 42141}, {3628, 11485}, {3857, 10645}, {3858, 42108}, {5335, 10124}, {8703, 42105}, {10109, 42119}, {11539, 18582}, {11737, 42130}, {11812, 42127}, {12108, 42142}, {12812, 42116}, {14869, 42146}, {15704, 42114}, {15711, 42100}, {15712, 42098}, {15713, 42123}, {16239, 42132}, {17504, 42094}, {23046, 42090}, {37640, 41985}

X(42493) = GIBERT (-4,9,17) POINT

Barycentrics    (-4*a^2*S)/Sqrt[3] + 17*a^2*SA + 18*SB*SC : :

X(42493) lies on the cubic K1194 and these lines: {5, 11481}, {13, 15699}, {15, 632}, {17, 10187}, {30, 42473}, {140, 5343}, {547, 42142}, {549, 16967}, {550, 33416}, {3530, 42140}, {3628, 11486}, {3857, 10646}, {3858, 42109}, {5334, 10124}, {8703, 42104}, {10109, 42120}, {11539, 18581}, {11737, 42131}, {11812, 42126}, {12108, 42139}, {12812, 42115}, {14869, 42143}, {15704, 42111}, {15711, 42099}, {15712, 42095}, {15713, 42122}, {16239, 42129}, {17504, 42093}, {23046, 42091}, {37641, 41985}

X(42494) = GIBERT (6,7,6) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 7*SB*SC : :

X(42494) lies on the cubic K1194 and these lines: {2, 5340}, {3, 5366}, {4, 15}, {5, 37641}, {6, 5068}, {13, 3090}, {18, 42114}, {20, 5350}, {61, 3855}, {62, 5071}, {140, 5344}, {381, 5343}, {395, 15022}, {396, 3832}, {397, 5056}, {398, 3091}, {550, 42132}, {622, 31275}, {631, 37832}, {1656, 5335}, {1657, 42138}, {3146, 16644}, {3522, 23302}, {3523, 5318}, {3524, 42161}, {3525, 16965}, {3528, 36969}, {3533, 16966}, {3543, 16772}, {3544, 40694}, {3545, 40693}, {3839, 22236}, {3850, 5334}, {3851, 11542}, {3854, 5339}, {3858, 5365}, {5059, 42094}, {5067, 10653}, {5073, 42124}, {5238, 15682}, {5351, 15709}, {5862, 22113}, {7486, 22238}, {10299, 42086}, {10303, 42155}, {10654, 42435}, {11486, 35018}, {15712, 42127}, {15717, 42165}, {16241, 17538}, {16267, 41106}, {16653, 22531}, {16964, 41099}, {17578, 36836}, {21735, 42092}, {41974, 42089}

X(42495) = GIBERT (-6,7,6) POINT

Barycentrics    -Sqrt[3]*a^2*S + 3*a^2*SA + 7*SB*SC : :

X(42495) lies on the cubic K1194 and these lines: {2, 5339}, {3, 5365}, {4, 16}, {5, 37640}, {6, 5068}, {14, 3090}, {17, 42111}, {20, 5349}, {61, 5071}, {62, 3855}, {140, 5343}, {381, 5344}, {395, 3832}, {396, 15022}, {397, 3091}, {398, 5056}, {550, 42129}, {621, 31275}, {631, 37835}, {1656, 5334}, {1657, 42135}, {3146, 16645}, {3522, 23303}, {3523, 5321}, {3524, 42160}, {3525, 16964}, {3528, 36970}, {3533, 16967}, {3543, 16773}, {3544, 40693}, {3545, 40694}, {3839, 22238}, {3850, 5335}, {3851, 11543}, {3854, 5340}, {3858, 5366}, {5059, 42093}, {5067, 10654}, {5073, 42121}, {5237, 15682}, {5352, 15709}, {5863, 22114}, {7486, 22236}, {10299, 42085}, {10303, 42154}, {10653, 42436}, {11485, 35018}, {15712, 42126}, {15717, 42164}, {16242, 17538}, {16268, 41106}, {16652, 22532}, {16965, 41099}, {17578, 36843}, {21735, 42089}, {41973, 42092}

X(42496) = GIBERT (12,5,7) POINT

Barycentrics    4*Sqrt[3]*a^2*S + 7*a^2*SA + 10*SB*SC : :

X(42496) lies on the cubic K1194 and these lines: {5, 37640}, {6, 547}, {13, 15}, {14, 11737}, {16, 11812}, {17, 395}, {61, 3850}, {62, 16239}, {140, 16644}, {382, 22235}, {397, 3530}, {398, 12811}, {524, 6669}, {531, 35019}, {546, 10654}, {548, 42152}, {549, 11488}, {3412, 3861}, {3845, 11485}, {3853, 22236}, {3859, 5339}, {3860, 5321}, {5066, 18582}, {5334, 38071}, {5335, 8703}, {5340, 12103}, {5343, 41991}, {5352, 41981}, {6329, 6670}, {6783, 22566}, {9540, 34552}, {10109, 11543}, {10124, 23302}, {10611, 31710}, {10653, 12100}, {11480, 15690}, {11481, 41983}, {11486, 11539}, {11540, 16242}, {12101, 41119}, {12102, 42147}, {12812, 40694}, {12816, 42108}, {13886, 18587}, {13935, 34551}, {13939, 18586}, {14891, 41943}, {14892, 42098}, {14893, 42117}, {15640, 33604}, {15686, 42116}, {15687, 42128}, {15691, 42086}, {15699, 37641}, {15759, 41107}, {16772, 33923}, {16963, 41984}, {17504, 42416}, {18581, 42474}, {19107, 33607}, {19710, 42127}, {20253, 41621}, {22495, 36770}, {23046, 42142}, {33699, 42119}, {34200, 42118}, {35018, 37835}, {35404, 42134}, {36763, 41745}, {41101, 42136}, {41108, 42110}, {41987, 42093}

X(42496) = {X(6),X(547)}-harmonic conjugate of X(42497)

X(42497) = GIBERT (-12,5,7) POINT

Barycentrics    -4*Sqrt[3]*a^2*S + 7*a^2*SA + 10*SB*SC : :

X(42497) lies on the cubic K1194 and these lines: {5, 37641}, {6, 547}, {13, 11737}, {14, 16}, {15, 11812}, {18, 396}, {61, 16239}, {62, 3850}, {140, 16645}, {382, 22237}, {397, 12811}, {398, 3530}, {524, 6670}, {530, 35020}, {546, 10653}, {548, 42149}, {549, 11489}, {3411, 3861}, {3845, 11486}, {3853, 22238}, {3859, 5340}, {3860, 5318}, {5066, 18581}, {5334, 8703}, {5335, 38071}, {5339, 12103}, {5344, 41991}, {5351, 41981}, {6329, 6669}, {6782, 22566}, {9540, 34551}, {10109, 11542}, {10124, 23303}, {10612, 31709}, {10654, 12100}, {11480, 41983}, {11481, 15690}, {11485, 11539}, {11540, 16241}, {12101, 41120}, {12102, 42148}, {12812, 40693}, {12817, 42109}, {13886, 18586}, {13935, 34552}, {13939, 18587}, {14891, 41944}, {14892, 42095}, {14893, 42118}, {15640, 33605}, {15686, 42115}, {15687, 42125}, {15691, 42085}, {15699, 37640}, {15759, 41108}, {16773, 33923}, {16962, 41984}, {17504, 42415}, {18582, 42475}, {19106, 33606}, {19710, 42126}, {20252, 41620}, {23046, 42139}, {33699, 42120}, {34200, 42117}, {35018, 37832}, {35404, 42133}, {41100, 42137}, {41107, 42107}, {41987, 42094}

X(42497) = {X(6),X(547)}-harmonic conjugate of X(42496)

X(42498) = GIBERT (1,10,23) POINT

Barycentrics    (a^2*S)/Sqrt[3] + 23*a^2*SA + 20*SB*SC : :

X(42498) lies on the cubic K1195 and these lines: {2, 10645}, {6, 15723}, {13, 10124}, {15, 16239}, {16, 3533}, {18, 10187}, {62, 632}, {140, 19106}, {547, 42430}, {3525, 42086}, {3526, 11481}, {3628, 42099}, {5070, 42096}, {5352, 41992}, {10188, 11542}, {10646, 11539}, {11267, 12043}, {11540, 36969}, {15694, 16808}, {15709, 42114}, {15713, 42102}, {15721, 42113}, {16961, 42435}, {16962, 23303}, {16967, 36836}, {41984, 42143}

X(42499) = GIBERT (-1,10,23) POINT

Barycentrics    -((a^2*S)/Sqrt[3]) + 23*a^2*SA + 20*SB*SC : :

X(42499) lies on the cubic K1195 and these lines: {2, 10646}, {6, 15723}, {14, 10124}, {15, 3533}, {16, 16239}, {17, 10188}, {61, 632}, {140, 19107}, {547, 42429}, {3525, 42085}, {3526, 11480}, {3628, 42100}, {5070, 42097}, {5351, 41992}, {10187, 11543}, {10645, 11539}, {11268, 12043}, {11540, 36970}, {15694, 16809}, {15709, 42111}, {15713, 42101}, {15721, 42112}, {16960, 42436}, {16963, 23302}, {16966, 36843}, {41984, 42146}

X(42500) = GIBERT (3,5,16) POINT

Barycentrics    Sqrt[3]*a^2*S + 16*a^2*SA + 10*SB*SC : :

X(42500) lies on the cubic K1195 and these lines: {2, 5321}, {3, 5350}, {4, 42474}, {6, 15702}, {13, 549}, {14, 10124}, {15, 11539}, {16, 11812}, {17, 12108}, {30, 33417}, {61, 140}, {376, 42102}, {381, 42112}, {396, 5054}, {397, 631}, {398, 3525}, {547, 10645}, {616, 33475}, {619, 31274}, {632, 37835}, {3523, 42155}, {3524, 5318}, {3526, 10654}, {3530, 36968}, {3533, 36836}, {3534, 42110}, {3628, 36970}, {3845, 42430}, {5055, 42087}, {5066, 42108}, {5067, 5349}, {5070, 42164}, {5071, 42101}, {5238, 16239}, {5335, 33604}, {6669, 35303}, {8703, 16966}, {10109, 19107}, {10303, 16773}, {10304, 42098}, {10653, 15701}, {11481, 15708}, {11488, 15721}, {11540, 11543}, {12100, 37832}, {12821, 35018}, {14890, 16963}, {14891, 42146}, {15681, 42114}, {15688, 42109}, {15689, 42106}, {15693, 18582}, {15694, 23303}, {15695, 42105}, {15699, 36967}, {15700, 42086}, {15703, 42085}, {15705, 42142}, {15706, 42091}, {15707, 42132}, {15709, 16645}, {15711, 42138}, {15712, 42165}, {15713, 16242}, {15715, 42134}, {15718, 42128}, {15720, 42148}, {15722, 41119}, {15723, 42116}, {15759, 42100}, {16808, 34200}, {16962, 42121}, {17504, 36969}, {19708, 42094}, {19709, 42090}, {30471, 37688}, {38071, 42099}, {41121, 42123}, {42133, 42475}

X(42500) = {X(6),X(15702)}-harmonic conjugate of X(42501)

X(42501) = GIBERT (-3,5,16) POINT

Barycentrics    -(Sqrt[3]*a^2*S) + 16*a^2*SA + 10*SB*SC : :

X(42501) lies on the cubic K1195 and these lines: {2, 5318}, {3, 5349}, {4, 42475}, {6, 15702}, {13, 10124}, {14, 549}, {15, 11812}, {16, 11539}, {18, 12108}, {30, 33416}, {62, 140}, {376, 42101}, {381, 42113}, {395, 5054}, {397, 3525}, {398, 631}, {547, 10646}, {617, 33474}, {618, 31274}, {632, 37832}, {3523, 42154}, {3524, 5321}, {3526, 10653}, {3530, 36967}, {3533, 36843}, {3534, 42107}, {3628, 36969}, {3845, 42429}, {5055, 42088}, {5066, 42109}, {5067, 5350}, {5070, 42165}, {5071, 42102}, {5237, 16239}, {5334, 33605}, {6670, 35304}, {8703, 16967}, {10109, 19106}, {10303, 16772}, {10304, 42095}, {10654, 15701}, {11480, 15708}, {11489, 15721}, {11540, 11542}, {12100, 37835}, {12820, 35018}, {14890, 16962}, {14891, 42143}, {15681, 42111}, {15688, 42108}, {15689, 42103}, {15693, 18581}, {15694, 23302}, {15695, 42104}, {15699, 36968}, {15700, 42085}, {15703, 42086}, {15705, 42139}, {15706, 42090}, {15707, 42129}, {15709, 16644}, {15711, 42135}, {15712, 42164}, {15713, 16241}, {15715, 42133}, {15718, 42125}, {15720, 42147}, {15722, 41120}, {15723, 42115}, {15759, 42099}, {16809, 34200}, {16963, 42124}, {17504, 36970}, {19708, 42093}, {19709, 42091}, {30472, 37688}, {38071, 42100}, {41122, 42122}, {42134, 42474}

X(42501) = {X(6),X(15702)}-harmonic conjugate of X(42500)

X(42502) = GIBERT (27,17,16) POINT

Barycentrics    9*Sqrt[3]*a^2*S + 16*a^2*SA + 34*SB*SC : :

X(42502) lies on the cubic K1195 and these lines: {2, 397}, {13, 8703}, {14, 5066}, {17, 12100}, {61, 3860}, {396, 3830}, {398, 41106}, {549, 41974}, {3412, 14893}, {3534, 16772}, {3628, 42420}, {3845, 16267}, {5318, 11001}, {5321, 41099}, {5335, 33604}, {5340, 19708}, {5350, 15682}, {10188, 11539}, {11488, 15697}, {11812, 23302}, {12101, 42147}, {15685, 42152}, {15690, 41943}, {15693, 41112}, {15698, 16644}, {15701, 42148}, {15722, 42151}, {15759, 16965}, {16962, 33699}, {19709, 40693}, {41101, 42136}, {41113, 42110}, {41973, 41987}

X(42503) = GIBERT (-27,17,16) POINT

Barycentrics    -9*Sqrt[3]*a^2*S + 16*a^2*SA + 34*SB*SC : :

X(42503) lies on the cubic K1195 and these lines: {2, 398}, {13, 5066}, {14, 8703}, {18, 12100}, {62, 3860}, {395, 3830}, {397, 41106}, {549, 41973}, {3411, 14893}, {3534, 16773}, {3628, 42419}, {3845, 16268}, {5318, 41099}, {5321, 11001}, {5334, 33605}, {5339, 19708}, {5349, 15682}, {10187, 11539}, {10612, 36769}, {11489, 15697}, {11812, 23303}, {12101, 42148}, {15685, 42149}, {15690, 41944}, {15693, 41113}, {15698, 16645}, {15701, 42147}, {15722, 42150}, {15759, 16964}, {16963, 33699}, {19709, 40694}, {41100, 42137}, {41112, 42107}, {41974, 41987}

X(42504) = GIBERT (27,10,65) POINT

Barycentrics    9*Sqrt[3]*a^2*S + 65*a^2*SA + 20*SB*SC : :

X(42504) lies on the cubic K1195 and these lines: {2, 5238}, {6, 15693}, {13, 8703}, {15, 11812}, {17, 15695}, {18, 15713}, {61, 15719}, {62, 19711}, {381, 10188}, {549, 3411}, {3412, 15706}, {3830, 16241}, {3845, 5352}, {5066, 36967}, {5237, 12100}, {5349, 10109}, {5350, 19710}, {10645, 11001}, {10654, 33605}, {12108, 42419}, {12817, 42107}, {15640, 37832}, {15697, 41121}, {15698, 41100}, {15711, 16772}, {15722, 16963}, {15759, 16267}, {16966, 41099}, {19708, 41943}, {22165, 36388}, {33416, 33606}

X(42505) = GIBERT (-27,10,65) POINT

Barycentrics    -9*Sqrt[3]*a^2*S + 65*a^2*SA + 20*SB*SC : :

X(42505) lies on the cubic K1195 and these lines: {2, 5237}, {6, 15693}, {14, 8703}, {16, 11812}, {17, 15713}, {18, 15695}, {61, 19711}, {62, 15719}, {381, 10187}, {549, 3412}, {3411, 15706}, {3830, 16242}, {3845, 5351}, {5066, 36968}, {5238, 12100}, {5349, 19710}, {5350, 10109}, {10646, 11001}, {10653, 33604}, {12108, 42420}, {12816, 42110}, {15640, 37835}, {15697, 41122}, {15698, 41101}, {15711, 16773}, {15722, 16962}, {15759, 16268}, {16967, 41099}, {19708, 41944}, {22165, 36386}, {33417, 33607}

X(42506) = GIBERT (27,10,11) POINT

Barycentrics    9*Sqrt[3]*a^2*S + 11*a^2*SA + 20*SB*SC : :

X(42506) lies on the cubic K1195 and these lines: {2, 17}, {6, 25565}, {13, 3830}, {14, 5066}, {15, 11001}, {16, 11812}, {30, 3412}, {61, 3845}, {396, 8703}, {397, 12100}, {546, 42419}, {3107, 11055}, {3411, 15703}, {3534, 16962}, {3860, 42166}, {5237, 15719}, {5238, 15690}, {5335, 15697}, {5340, 15685}, {5351, 19711}, {5469, 10611}, {5470, 14136}, {5858, 22489}, {10109, 16268}, {10304, 41974}, {10653, 15698}, {11481, 15693}, {11540, 42420}, {12821, 33604}, {14893, 41973}, {15640, 36969}, {15682, 42157}, {15695, 42158}, {15711, 42148}, {15759, 16772}, {16529, 36329}, {16808, 37640}, {16961, 37832}, {16966, 42480}, {18582, 41122}, {19708, 42152}, {19709, 42156}, {19710, 42434}, {22510, 36382}, {22571, 35693}, {22602, 36391}, {22631, 36390}, {22688, 36384}, {22846, 33627}, {25151, 36387}, {25157, 36393}, {25158, 36395}, {25159, 36396}, {25160, 36397}, {25217, 36367}, {33605, 42473}, {33606, 42095}, {35384, 42130}, {35730, 35735}, {36763, 36767}, {41020, 41028}, {41971, 42108}

X(42507) = GIBERT (-27,10,11) POINT

Barycentrics    -9*Sqrt[3]*a^2*S + 11*a^2*SA + 20*SB*SC : :

X(42507) lies on the cubic K1195 and these lines: {2, 18}, {6, 25565}, {13, 5066}, {14, 3830}, {15, 11812}, {16, 11001}, {30, 3411}, {62, 3845}, {395, 8703}, {398, 12100}, {546, 42420}, {3106, 11055}, {3412, 15703}, {3534, 16963}, {3860, 42163}, {5237, 15690}, {5238, 15719}, {5334, 15697}, {5339, 15685}, {5352, 19711}, {5469, 14137}, {5470, 10612}, {5859, 22490}, {10109, 16267}, {10304, 41973}, {10654, 15698}, {11480, 15693}, {11540, 42419}, {12820, 33605}, {14893, 41974}, {15640, 36970}, {15682, 42158}, {15695, 42157}, {15711, 42147}, {15759, 16773}, {16530, 35751}, {16809, 37641}, {16960, 37835}, {16967, 42481}, {18581, 41121}, {19708, 42149}, {19709, 42153}, {19710, 42433}, {22511, 36383}, {22572, 35697}, {22604, 36394}, {22633, 36392}, {22690, 36385}, {22891, 33626}, {25161, 36389}, {25167, 36398}, {25168, 36399}, {25169, 36400}, {25170, 36401}, {25214, 36369}, {33604, 42472}, {33607, 42098}, {35384, 42131}, {36402, 41127}, {36403, 41103}, {41021, 41029}, {41972, 42109}

X(42508) = GIBERT (27,10,-16) POINT

Barycentrics    9*Sqrt[3]*a^2*S - 16*a^2*SA + 20*SB*SC : :

X(42508) lies on the cubic K1195 and these lines: {2, 5340}, {6, 11001}, {14, 3830}, {17, 15722}, {61, 3534}, {397, 19708}, {3411, 35403}, {3845, 22238}, {3860, 42161}, {5054, 41974}, {5055, 10187}, {5066, 16645}, {5318, 42475}, {5335, 33604}, {5339, 15682}, {8703, 10653}, {10646, 15693}, {11481, 11812}, {12100, 42151}, {12816, 42095}, {15534, 36331}, {15640, 42108}, {15685, 42158}, {15690, 22236}, {15697, 42120}, {15701, 42156}, {15704, 42419}, {15716, 16267}, {15759, 40693}, {16965, 19709}, {35384, 42126}, {36392, 36394}, {41099, 42094}, {41108, 42097}, {41122, 42127}, {42474, 42477}

X(42509) = GIBERT (-27,10,-16) POINT

Barycentrics    -9*Sqrt[3]*a^2*S - 16*a^2*SA + 20*SB*SC : :

X(42509) lies on the cubic K1195 and these lines: {2, 5339}, {6, 11001}, {13, 3830}, {18, 15722}, {62, 3534}, {398, 19708}, {3412, 35403}, {3845, 22236}, {3860, 42160}, {5054, 41973}, {5055, 10188}, {5066, 16644}, {5321, 42474}, {5334, 33605}, {5340, 15682}, {8703, 10654}, {10645, 15693}, {11480, 11812}, {12100, 42150}, {12817, 42098}, {15534, 35750}, {15640, 42109}, {15685, 42157}, {15690, 22238}, {15697, 42119}, {15701, 42153}, {15704, 42420}, {15716, 16268}, {15759, 40694}, {16964, 19709}, {35384, 42127}, {36390, 36391}, {41099, 42093}, {41107, 42096}, {41121, 42126}, {42475, 42476}

X(42510) = GIBERT (9,1,-7) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 7*a^2*SA + 2*SB*SC : :

X(42510) lies on the cubic K1197 and these lines: {2, 13}, {4, 16963}, {6, 8703}, {14, 15682}, {15, 19708}, {17, 15702}, {18, 3839}, {20, 41973}, {30, 5339}, {61, 10304}, {62, 376}, {202, 10385}, {381, 5350}, {395, 3830}, {396, 15693}, {397, 5054}, {398, 15681}, {532, 37173}, {547, 5340}, {549, 36843}, {631, 16267}, {3090, 10187}, {3107, 36322}, {3146, 3411}, {3412, 10299}, {3523, 41943}, {3524, 5237}, {3534, 10654}, {3543, 12817}, {3545, 16965}, {3845, 18581}, {3860, 42094}, {5055, 16773}, {5066, 16645}, {5071, 41977}, {5318, 19709}, {5351, 15692}, {5352, 15710}, {5464, 5863}, {5859, 34511}, {6200, 36449}, {6396, 36468}, {9115, 36363}, {10109, 42121}, {10646, 15698}, {11001, 34755}, {11296, 33459}, {11480, 15759}, {11481, 12100}, {11489, 36969}, {11539, 42156}, {11542, 15713}, {11543, 33699}, {11812, 16644}, {12101, 42105}, {12816, 37835}, {14269, 42165}, {15640, 36970}, {15683, 16964}, {15685, 42088}, {15687, 42153}, {15689, 42147}, {15690, 42090}, {15697, 36967}, {15700, 16772}, {15701, 42092}, {15703, 42166}, {15709, 33607}, {15711, 42420}, {15719, 16241}, {19710, 42123}, {22236, 34200}, {22907, 36386}, {22998, 36344}, {36436, 42246}, {36448, 42191}, {36454, 42248}, {36466, 42193}, {36962, 41031}, {38335, 42163}, {42140, 42429}, {42416, 42475}, {42432, 42436}

X(42510) = {X(6),X(8703)}-harmonic conjugate of X(42511)

X(42511) = GIBERT (-9,1,-7) POINT

Barycentrics    -3*Sqrt[3]*a^2*S - 7*a^2*SA + 2*SB*SC : :

X(42511) lies on the cubic K1197 and these lines: {2, 14}, {4, 16962}, {6, 8703}, {13, 15682}, {16, 19708}, {17, 3839}, {18, 15702}, {20, 41974}, {30, 5340}, {61, 376}, {62, 10304}, {203, 10385}, {381, 5349}, {395, 15693}, {396, 3830}, {397, 15681}, {398, 5054}, {533, 37172}, {547, 5339}, {549, 36836}, {631, 16268}, {3090, 10188}, {3106, 36323}, {3146, 3412}, {3411, 10299}, {3523, 41944}, {3524, 5238}, {3534, 10653}, {3543, 12816}, {3545, 16964}, {3845, 18582}, {3860, 42093}, {5055, 16772}, {5066, 16644}, {5071, 41978}, {5321, 19709}, {5351, 15710}, {5352, 15692}, {5463, 5862}, {5858, 34511}, {6200, 36467}, {6396, 36450}, {6782, 36767}, {9117, 36362}, {10109, 42124}, {10645, 15698}, {11001, 34754}, {11295, 33458}, {11480, 12100}, {11481, 15759}, {11488, 36970}, {11539, 42153}, {11542, 33699}, {11543, 15713}, {11812, 16645}, {12101, 42104}, {12817, 37832}, {14269, 42164}, {15640, 36969}, {15683, 16965}, {15685, 42087}, {15687, 42156}, {15689, 42148}, {15690, 42091}, {15697, 36968}, {15700, 16773}, {15701, 42089}, {15703, 42163}, {15709, 33606}, {15711, 42419}, {15719, 16242}, {19710, 42122}, {22238, 34200}, {22861, 36388}, {22997, 36319}, {35752, 36772}, {36436, 42249}, {36448, 42194}, {36454, 42247}, {36466, 42192}, {36961, 41030}, {38335, 42166}, {42141, 42430}, {42415, 42474}, {42431, 42435}

X(42511) = {X(6),X(8703)}-harmonic conjugate of X(42510)

X(42512) = GIBERT (15,11,19) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 19*a^2*SA + 22*SB*SC : :

X(42512) lies on the cubic K1197 and these lines: {2, 16960}, {13, 15692}, {14, 5071}, {15, 41099}, {17, 631}, {30, 11480}, {396, 1656}, {632, 40693}, {3091, 5365}, {3146, 12820}, {3522, 42161}, {3843, 42150}, {3858, 42154}, {3859, 42160}, {5076, 16772}, {5318, 15695}, {5339, 41989}, {10654, 19709}, {11542, 15713}, {12812, 42475}, {14093, 42086}, {15693, 41112}, {15694, 23302}, {15696, 42162}, {15697, 41121}, {15711, 42155}, {15712, 42156}, {16241, 19708}, {16267, 42089}, {16961, 37640}, {17538, 36969}, {17578, 36967}, {35434, 42116}, {41943, 42085}

X(42513) = GIBERT (-15,11,19) POINT

Barycentrics    -5*Sqrt[3]*a^2*S + 19*a^2*SA + 22*SB*SC : :

X(42513) lies on the cubic K1197 and these lines: {2, 16961}, {13, 5071}, {14, 15692}, {16, 41099}, {18, 631}, {30, 11481}, {395, 1656}, {632, 40694}, {3091, 5366}, {3146, 12821}, {3522, 42160}, {3843, 42151}, {3858, 42155}, {3859, 42161}, {5076, 16773}, {5321, 15695}, {5340, 41989}, {10653, 19709}, {11543, 15713}, {12812, 42474}, {14093, 42085}, {15693, 41113}, {15694, 23303}, {15696, 42159}, {15697, 41122}, {15711, 42154}, {15712, 42153}, {16242, 19708}, {16268, 42092}, {16960, 37641}, {17538, 36970}, {17578, 36968}, {35434, 42115}, {41944, 42086}

X(42514) = GIBERT (18,65,-50) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 25*a^2*SA + 65*SB*SC : :

X(42514) lies on the cubic K1197 and these lines: {6, 15640}, {14, 15682}, {30, 5344}, {3543, 36843}, {3830, 42143}, {5343, 15684}, {5350, 15683}, {10645, 11001}, {15685, 42124}, {15719, 42429}, {35384, 42117}, {41099, 42113}, {41107, 42141}

X(42515) = GIBERT (-18,65,-50) POINT

Barycentrics    -3*Sqrt[3]*a^2*S - 25*a^2*SA + 65*SB*SC : :

X(42515) lies on the cubic K1197 and these lines: {6, 15640}, {13, 15682}, {30, 5343}, {3543, 36836}, {3830, 42146}, {5344, 15684}, {5349, 15683}, {10646, 11001}, {15685, 42121}, {15719, 42430}, {35384, 42118}, {41099, 42112}, {41108, 42140}

X(42516) = GIBERT (30,1,14) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 7*a^2*SA + SB*SC : :

X(42516) lies on the cubic K1197 and these lines: {6, 9542}, {14, 5071}, {15, 19708}, {30, 5335}, {61, 631}, {376, 34754}, {396, 3091}, {3522, 22236}, {3859, 5343}, {5334, 19709}, {5350, 17578}, {10187, 40694}, {10653, 17538}, {10654, 12817}, {11486, 15711}, {11489, 15694}, {15697, 42120}, {15714, 42116}, {15715, 34755}, {35403, 42117}, {35434, 42134}, {37832, 42435}, {41101, 42140}, {41113, 42473}, {41971, 42112}, {42150, 42429}

X(42517) = GIBERT (-30,1,14) POINT

Barycentrics    -5*Sqrt[3]*a^2*S + 7*a^2*SA + SB*SC : :

X(42517) lies on the cubic K1197 and these lines: {6, 9542}, {13, 5071}, {16, 19708}, {30, 5334}, {62, 631}, {376, 34755}, {395, 3091}, {3522, 22238}, {3859, 5344}, {5335, 19709}, {5349, 17578}, {10188, 40693}, {10653, 12816}, {10654, 17538}, {11485, 15711}, {11488, 15694}, {15697, 42119}, {15714, 42115}, {15715, 34754}, {35403, 42118}, {35434, 42133}, {37835, 42436}, {41100, 42141}, {41112, 42472}, {41972, 42113}, {42151, 42430}

X(42518) = GIBERT (45,26,34) POINT

Barycentrics    15*Sqrt[3]*a^2*S + 34*a^2*SA + 52*SB*SC : :

X(42518) lies on the cubic K1197 and these lines: {3, 33607}, {13, 15695}, {14, 16960}, {17, 15694}, {30, 36836}, {396, 41099}, {1656, 16267}, {3843, 41101}, {5071, 42153}, {5340, 14093}, {10646, 15693}, {11488, 15697}, {11542, 15713}, {15696, 41943}, {15711, 41112}, {16962, 35403}, {19708, 33604}, {41121, 41971}

X(42519) = GIBERT (-45,26,34) POINT

Barycentrics    -15*Sqrt[3]*a^2*S + 34*a^2*SA + 52*SB*SC : :

X(42519) lies on the cubic K1197 and these lines: {3, 33606}, {13, 16961}, {14, 15695}, {18, 15694}, {30, 36843}, {395, 41099}, {1656, 16268}, {3843, 41100}, {5071, 42156}, {5339, 14093}, {10645, 15693}, {11489, 15697}, {11543, 15713}, {15696, 41944}, {15711, 41113}, {16963, 35403}, {19708, 33605}, {41122, 41972}

X(42520) = GIBERT (45,2,13) POINT

Barycentrics    15*Sqrt[3]*a^2*S + 13*a^2*SA + 4*SB*SC : :

X(42520) lies on the cubic K1197 and these lines: {2, 16961}, {6, 15693}, {14, 16960}, {15, 19708}, {16, 15711}, {17, 5071}, {18, 42481}, {30, 61}, {62, 15692}, {381, 33607}, {631, 16963}, {632, 41943}, {1656, 3412}, {1992, 36386}, {3091, 16267}, {3843, 12817}, {5238, 15714}, {5321, 42419}, {8703, 34754}, {10654, 12816}, {11485, 15695}, {14093, 22236}, {15694, 16962}, {15697, 36968}, {15698, 34755}, {15713, 16241}, {16808, 37640}, {16964, 35403}, {19107, 41112}, {33416, 35381}, {41121, 42110}

X(42521) = GIBERT (-45,2,13) POINT

Barycentrics    -15*Sqrt[3]*a^2*S + 13*a^2*SA + 4*SB*SC : :

X(42521) lies on the cubic K1197 and these lines: {2, 16960}, {6, 15693}, {13, 16961}, {15, 15711}, {16, 19708}, {17, 42480}, {18, 5071}, {30, 62}, {61, 15692}, {381, 33606}, {631, 16962}, {632, 41944}, {1656, 3411}, {1992, 36388}, {3091, 16268}, {3843, 12816}, {5237, 15714}, {5318, 42420}, {8703, 34755}, {10653, 12817}, {11486, 15695}, {14093, 22238}, {15694, 16963}, {15697, 36967}, {15698, 34754}, {15713, 16242}, {16809, 37641}, {16965, 35403}, {19106, 41113}, {33417, 35381}, {41122, 42107}

X(42522) = GIBERT (8 Sqrt[3],1,6) POINT

Barycentrics    8*a^2*S + 6*a^2*SA + 2*SB*SC : :

X(42522) lies on the cubic K1201 and these lines: {2, 3311}, {3, 9542}, {4, 6199}, {6, 3523}, {20, 371}, {147, 13653}, {372, 15692}, {376, 9543}, {485, 3839}, {549, 6500}, {576, 26516}, {590, 6470}, {597, 33365}, {631, 6417}, {638, 13639}, {1131, 6561}, {1132, 35815}, {1151, 10304}, {1504, 5304}, {1588, 5056}, {3068, 3071}, {3069, 6431}, {3070, 42413}, {3090, 13903}, {3146, 7583}, {3299, 5265}, {3301, 5281}, {3312, 15717}, {3316, 13785}, {3522, 6221}, {3524, 6418}, {3525, 19116}, {3528, 6407}, {3529, 18512}, {3530, 6501}, {3543, 6459}, {3545, 13925}, {3590, 42277}, {3629, 33364}, {3832, 13886}, {3854, 18538}, {5058, 37665}, {5059, 23267}, {5067, 18510}, {5068, 8976}, {5261, 13905}, {5274, 13904}, {5418, 13941}, {5420, 6419}, {6395, 10299}, {6408, 15698}, {6409, 9692}, {6425, 6460}, {6427, 35255}, {6441, 32786}, {6445, 21735}, {6447, 42216}, {6449, 21734}, {6450, 15705}, {6474, 15688}, {6995, 10880}, {8703, 9691}, {8960, 23259}, {9680, 35770}, {9690, 33923}, {9695, 16661}, {10145, 14093}, {13665, 17578}, {13935, 15708}, {13961, 15702}, {14986, 19038}, {15640, 35822}, {15697, 42259}, {15703, 34089}, {15721, 19053}, {19145, 33748}, {20070, 31439}, {26521, 39561}, {31412, 41955}, {31414, 42263}, {32789, 41947}, {32805, 32898}

X(42522) = {X(6),X(3523)}-harmonic conjugate of X(42523)

X(42523) = GIBERT (-8 Sqrt[3],1,6) POINT

Barycentrics    -8*a^2*S + 6*a^2*SA + 2*SB*SC : :

X(42523) lies on the cubic K1201 and these lines: {2, 3312}, {3, 9543}, {4, 6395}, {6, 3523}, {20, 372}, {147, 13773}, {371, 15692}, {376, 19116}, {486, 3839}, {549, 6501}, {576, 26521}, {597, 33364}, {615, 6471}, {631, 6418}, {637, 13759}, {1131, 35814}, {1132, 6560}, {1152, 10304}, {1505, 5304}, {1587, 5056}, {3068, 6432}, {3069, 3070}, {3071, 42414}, {3090, 13961}, {3146, 7584}, {3299, 5281}, {3301, 5265}, {3311, 9542}, {3317, 13665}, {3522, 6398}, {3524, 6417}, {3525, 19117}, {3528, 6408}, {3529, 18510}, {3530, 6500}, {3543, 6460}, {3545, 13993}, {3591, 42274}, {3629, 33365}, {3832, 13939}, {3854, 18762}, {5059, 23273}, {5062, 37665}, {5067, 18512}, {5068, 13951}, {5261, 13963}, {5274, 13962}, {5418, 6420}, {5420, 8972}, {6199, 10299}, {6407, 15698}, {6426, 6459}, {6428, 35256}, {6442, 32785}, {6446, 21735}, {6448, 42215}, {6449, 15705}, {6450, 21734}, {6454, 9541}, {6475, 15688}, {6485, 9681}, {6995, 10881}, {9540, 15708}, {10146, 14093}, {13785, 17578}, {13847, 31412}, {13903, 15702}, {14986, 19037}, {15640, 35823}, {15697, 42258}, {15703, 34091}, {15721, 19054}, {17554, 31473}, {19146, 33748}, {26516, 39561}, {31414, 41954}, {32790, 41948}, {32806, 32898}

X(42523) = {X(6),X(3523)}-harmonic conjugate of X(42522)

X(42524) = GIBERT (9 Sqrt[3],2,-23) POINT

Barycentrics    9*a^2*S - 23*a^2*SA + 4*SB*SC : :

X(42524) lies on the cubic K1201 and these lines: {2, 1327}, {30, 35813}, {371, 19708}, {372, 8703}, {376, 6454}, {382, 6489}, {397, 15764}, {549, 42418}, {615, 33699}, {1152, 3534}, {1657, 10148}, {3070, 15713}, {3524, 8960}, {3594, 14093}, {3830, 6450}, {3845, 6487}, {5066, 42259}, {5420, 41099}, {6200, 15759}, {6398, 15695}, {6410, 15693}, {6412, 15716}, {6419, 34200}, {6420, 10304}, {6426, 15688}, {6434, 6565}, {6440, 18510}, {6446, 13847}, {6452, 13846}, {6456, 15701}, {6459, 6479}, {6460, 15719}, {6477, 42215}, {6481, 15690}, {6485, 11001}, {6522, 15689}, {7583, 12100}, {9543, 35771}, {12101, 35256}, {13935, 15640}, {14869, 41952}, {15300, 35825}, {15533, 39894}, {15682, 42261}, {15696, 17852}, {15698, 35815}, {15700, 35812}, {15711, 32787}, {19709, 35820}, {19711, 42216}, {34091, 41106}, {41950, 41958}, {41962, 42225}

X(42525) = GIBERT (-9 Sqrt[3],2,-23) POINT

Barycentrics    -9*a^2*S - 23*a^2*SA + 4*SB*SC : :

X(42525) lies on the cubic K1201 and these lines: {2, 1328}, {30, 35812}, {371, 8703}, {372, 19708}, {376, 6453}, {382, 6488}, {398, 15764}, {549, 42417}, {590, 33699}, {1151, 3534}, {1657, 10147}, {3071, 15713}, {3524, 9681}, {3543, 9680}, {3592, 14093}, {3830, 6449}, {3845, 6486}, {4677, 9582}, {5066, 42258}, {5418, 41099}, {6221, 15695}, {6396, 15759}, {6409, 15693}, {6411, 15716}, {6419, 10304}, {6420, 34200}, {6425, 15688}, {6433, 6564}, {6439, 18512}, {6445, 13846}, {6451, 13847}, {6455, 15701}, {6459, 15719}, {6460, 6478}, {6476, 42216}, {6480, 15690}, {6484, 11001}, {6519, 15689}, {7584, 12100}, {8960, 15681}, {9540, 15640}, {10141, 31487}, {12101, 35255}, {14869, 41951}, {15300, 35824}, {15533, 39893}, {15682, 42260}, {15686, 31454}, {15698, 35814}, {15700, 35813}, {15711, 32788}, {19709, 35821}, {19711, 42215}, {34089, 41106}, {41949, 41957}, {41961, 42226}

X(42526) = GIBERT (18 Sqrt[3],22,35) POINT

Barycentrics    18*a^2*S + 35*a^2*SA + 44*SB*SC : :

X(42526) lies on the cubic K1201 and these lines: {2, 3312}, {3, 41952}, {381, 6425}, {485, 15701}, {590, 3830}, {1587, 11540}, {3071, 19709}, {3311, 10109}, {3534, 23251}, {3590, 15702}, {5055, 31487}, {5066, 23259}, {5418, 15695}, {6221, 41099}, {6412, 13665}, {6430, 35822}, {6447, 38071}, {6449, 33699}, {6519, 14893}, {8703, 23249}, {8981, 41106}, {9540, 12101}, {11001, 18538}, {11812, 32785}, {13785, 13846}, {15640, 35255}, {15690, 31412}, {32806, 32892}, {35403, 41963}, {42277, 42417}

X(42527) = GIBERT (-18 Sqrt[3],22,35) POINT

Barycentrics    -18*a^2*S + 35*a^2*SA + 44*SB*SC : :

X(42527) lies on the cubic K1201 and these lines: {2, 3311}, {3, 41951}, {381, 6426}, {486, 15701}, {615, 3830}, {1588, 11540}, {3070, 19709}, {3312, 10109}, {3534, 23261}, {3591, 15702}, {5055, 41952}, {5066, 23249}, {5420, 15695}, {6398, 41099}, {6411, 13785}, {6429, 35823}, {6448, 38071}, {6450, 33699}, {6522, 14893}, {8703, 23259}, {9680, 15694}, {11001, 18762}, {11812, 32786}, {12101, 13935}, {13665, 13847}, {13966, 41106}, {15640, 35256}, {32805, 32892}, {35403, 41964}, {42274, 42418}

X(42528) = GIBERT (3,2,-11) POINT

Barycentrics    Sqrt[3]*a^2*S - 11*a^2*SA + 4*SB*SC : :

X(42528) lies on the cubic K1201 and these lines: {2, 12820}, {3, 13}, {6, 15688}, {14, 3534}, {15, 8703}, {16, 376}, {18, 20}, {30, 10646}, {61, 3522}, {62, 548}, {299, 7782}, {381, 33416}, {395, 550}, {396, 34200}, {549, 16966}, {617, 33622}, {631, 42431}, {3106, 22676}, {3411, 15696}, {3524, 37832}, {3528, 5238}, {3543, 42089}, {3642, 5463}, {3830, 16967}, {3839, 42113}, {5054, 16808}, {5055, 42097}, {5066, 42109}, {5071, 42105}, {5318, 12100}, {5321, 15686}, {5334, 15697}, {5335, 41943}, {5350, 14869}, {5352, 33923}, {5464, 35751}, {6777, 38749}, {7584, 35739}, {7739, 41408}, {10124, 42110}, {10299, 42162}, {10304, 10645}, {11001, 12817}, {11057, 30472}, {11303, 36770}, {11480, 14093}, {11486, 15695}, {11488, 15710}, {11539, 42145}, {11542, 15759}, {11543, 15691}, {11812, 42137}, {12103, 16773}, {12816, 15701}, {13083, 35752}, {15681, 16645}, {15684, 42095}, {15685, 42093}, {15689, 16963}, {15690, 41108}, {15692, 18582}, {15693, 33417}, {15694, 42094}, {15698, 33602}, {15699, 42102}, {15700, 42127}, {15702, 42141}, {15706, 42128}, {15708, 42134}, {15709, 42114}, {15712, 42165}, {15714, 42124}, {15716, 42132}, {15717, 42161}, {15719, 42142}, {16267, 42118}, {16268, 42085}, {16772, 41974}, {16960, 19708}, {17504, 23302}, {17538, 42149}, {19710, 41122}, {21734, 42152}, {21735, 40693}, {22238, 42434}, {22845, 40899}, {33699, 42107}, {35733, 42237}, {36209, 37853}, {36436, 42179}, {36438, 42178}, {36454, 42181}, {36456, 42177}, {41120, 42140}, {41983, 42146}

X(42528) = {X(6),X(15688)}-harmonic conjugate of X(42529)

X(42529) = GIBERT (-3,2,-11) POINT

Barycentrics    -(Sqrt[3]*a^2*S) - 11*a^2*SA + 4*SB*SC : :

X(42529) lies on the cubic K1201 and these lines: {2, 12821}, {3, 14}, {6, 15688}, {13, 3534}, {15, 376}, {16, 8703}, {17, 20}, {30, 10645}, {61, 548}, {62, 3522}, {298, 7782}, {381, 33417}, {395, 34200}, {396, 550}, {549, 16967}, {616, 33624}, {631, 42432}, {3107, 22676}, {3412, 15696}, {3524, 37835}, {3528, 5237}, {3543, 42092}, {3643, 5464}, {3830, 16966}, {3839, 42112}, {5054, 16809}, {5055, 42096}, {5066, 42108}, {5071, 42104}, {5318, 15686}, {5321, 12100}, {5334, 41944}, {5335, 15697}, {5349, 14869}, {5351, 33923}, {5463, 36329}, {6778, 38749}, {7739, 41409}, {10124, 42107}, {10299, 42159}, {10304, 10646}, {11001, 12816}, {11057, 30471}, {11481, 14093}, {11485, 15695}, {11489, 15710}, {11539, 42144}, {11542, 15691}, {11543, 15759}, {11812, 42136}, {12103, 16772}, {12817, 15701}, {13084, 36330}, {15681, 16644}, {15684, 42098}, {15685, 42094}, {15689, 16962}, {15690, 41107}, {15692, 18581}, {15693, 33416}, {15694, 42093}, {15698, 33603}, {15699, 42101}, {15700, 42126}, {15702, 42140}, {15706, 42125}, {15708, 42133}, {15709, 42111}, {15712, 42164}, {15714, 42121}, {15716, 42129}, {15717, 42160}, {15719, 42139}, {16267, 42086}, {16268, 42117}, {16773, 41973}, {16961, 19708}, {17504, 23303}, {17538, 42152}, {19710, 41121}, {21734, 42149}, {21735, 40694}, {22236, 42433}, {22844, 40898}, {33699, 42110}, {36208, 37853}, {36436, 42182}, {36438, 42175}, {36454, 42180}, {36456, 42176}, {41119, 42141}, {41983, 42143}

X(42529) = {X(6),X(15688)}-harmonic conjugate of X(42528)

X(42530) = GIBERT (19,14,23) POINT

Barycentrics    (19*a^2*S)/Sqrt[3] + 23*a^2*SA + 28*SB*SC : :

X(42530) lies on the cubic K1201 and these lines: {13, 15706}, {14, 42132}, {15, 3839}, {16, 17}, {3412, 18581}, {3544, 11488}, {5076, 16808}, {15681, 16644}, {16241, 19708}, {16645, 16960}, {16964, 42098}, {16967, 37640}, {18582, 33703}, {33699, 42087}, {37832, 42135}, {42100, 42162}

X(42531) = GIBERT (-19,14,23) POINT

Barycentrics    (-19*a^2*S)/Sqrt[3] + 23*a^2*SA + 28*SB*SC : :

X(42531) lies on the cubic K1201 and these lines: {13, 42129}, {14, 15706}, {15, 18}, {16, 3839}, {3411, 18582}, {3544, 11489}, {5076, 16809}, {15681, 16645}, {16242, 19708}, {16644, 16961}, {16965, 42095}, {16966, 37641}, {18581, 33703}, {33699, 42088}, {37835, 42138}, {42099, 42159}

X(42532) = GIBERT (27,2,13) POINT

Barycentrics    9*Sqrt[3]*a^2*S + 13*a^2*SA + 4*SB*SC : :

X(42532) lies on the cubic K1201 and these lines: {2, 18}, {6, 15693}, {13, 3830}, {14, 42132}, {15, 8703}, {16, 15698}, {17, 19709}, {62, 12100}, {381, 3412}, {396, 5066}, {397, 19710}, {398, 10109}, {3411, 5054}, {3534, 22236}, {3839, 41973}, {3845, 16267}, {5237, 15711}, {5238, 19708}, {5335, 42430}, {5352, 15759}, {5469, 36330}, {8584, 36757}, {10653, 15697}, {10654, 12817}, {11001, 34754}, {11055, 32465}, {11295, 36366}, {11488, 41120}, {11812, 16242}, {12820, 42104}, {15534, 36386}, {15640, 19106}, {15682, 40693}, {15685, 16965}, {15686, 41974}, {15695, 42433}, {15701, 16963}, {15713, 16772}, {15716, 22238}, {16966, 41122}, {18581, 33605}, {33602, 42140}, {33699, 42147}, {34200, 42420}, {36969, 42144}, {36970, 41119}, {37832, 41113}

X(42533) = GIBERT (-27,2,13) POINT

Barycentrics    -9*Sqrt[3]*a^2*S + 13*a^2*SA + 4*SB*SC : :

X(42533) lies on the cubic K1201 and these lines: {2, 17}, {6, 15693}, {13, 42129}, {14, 3830}, {15, 15698}, {16, 8703}, {18, 19709}, {61, 12100}, {381, 3411}, {395, 5066}, {397, 10109}, {398, 19710}, {3412, 5054}, {3534, 22238}, {3839, 41974}, {3845, 16268}, {5237, 19708}, {5238, 15711}, {5334, 42429}, {5351, 15759}, {5470, 35752}, {8584, 36758}, {10653, 12816}, {10654, 15697}, {11001, 34755}, {11055, 32466}, {11296, 36368}, {11489, 41119}, {11812, 16241}, {12821, 42105}, {15534, 36388}, {15640, 19107}, {15682, 40694}, {15685, 16964}, {15686, 41973}, {15695, 42434}, {15701, 16962}, {15713, 16773}, {15716, 22236}, {16967, 41121}, {18582, 33604}, {33603, 42141}, {33699, 42148}, {34200, 42419}, {36969, 41120}, {36970, 42145}, {37835, 41112}

X(42534) = X(5)X(182)∩X(6)X(76)

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

X(42534) lies on K1200 and these lines: {2, 1501}, {3, 10007}, {5, 182}, {6, 76}, {32, 141}, {39, 4048}, {67, 13193}, {69, 7787}, {98, 10516}, {110, 32242}, {115, 19120}, {287, 39685}, {384, 3094}, {511, 7804}, {518, 10791}, {524, 5039}, {597, 5034}, {599, 12150}, {698, 3734}, {1078, 3763}, {1180, 10328}, {1350, 12110}, {1352, 3398}, {1469, 10797}, {2023, 5026}, {2076, 3972}, {2456, 14561}, {2458, 5103}, {2916, 33717}, {3056, 10798}, {3114, 14603}, {3242, 12195}, {3329, 10334}, {3416, 12194}, {3618, 5038}, {3619, 7793}, {3934, 8177}, {3981, 16950}, {4027, 7875}, {4045, 29012}, {5007, 14994}, {5012, 39668}, {5017, 10350}, {5033, 8361}, {5041, 41622}, {5050, 12177}, {5085, 13860}, {5092, 6683}, {5116, 7786}, {5182, 7884}, {5480, 10358}, {5846, 10800}, {5969, 11286}, {6393, 6661}, {6680, 10104}, {6776, 10359}, {7606, 14762}, {7772, 32449}, {7789, 13356}, {7794, 15870}, {7815, 33185}, {7839, 41747}, {7887, 7943}, {7893, 12206}, {7915, 39603}, {8041, 16949}, {8722, 21167}, {10346, 19689}, {10353, 11606}, {10519, 10788}, {10790, 37485}, {10799, 12589}, {11261, 35375}, {11338, 39080}, {12151, 19570}, {12192, 14982}, {12202, 41735}, {12203, 36990}, {12251, 35427}, {12588, 12835}, {14001, 34870}, {14036, 39652}, {14370, 31360}, {15069, 39872}, {15482, 17508}, {15514, 22486}, {16932, 20859}, {18501, 33878}, {18502, 31670}, {18841, 39874}, {19130, 40279}, {24733, 41259}, {32135, 39515}, {41443, 42286}

X(42534) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 7770, 24256}, {6, 24273, 76}, {69, 7787, 12212}, {141, 42421, 32}, {182, 3818, 14880}, {182, 7808, 3589}, {597, 13196, 5034}, {1676, 1677, 7834}, {3329, 12215, 13331}, {3618, 39141, 5038}, {7878, 32451, 6}, {10358, 13355, 5480}, {24206, 39750, 10104}

X(42535) = X(5)X(32)∩X(6)X(98)

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

X(42535) lies on K1200 and these lines: {2, 1501}, {4, 34870}, {5, 32}, {6, 98}, {39, 14880}, {83, 7887}, {115, 40250}, {182, 3815}, {183, 5017}, {187, 15819}, {385, 13330}, {598, 7610}, {1007, 39141}, {1078, 3053}, {1656, 38905}, {2076, 22712}, {2080, 7737}, {2548, 3398}, {3054, 41412}, {3055, 5033}, {3094, 5999}, {3934, 39603}, {4027, 7777}, {5013, 12203}, {5034, 9300}, {5038, 7736}, {5039, 5306}, {5104, 6194}, {5182, 11184}, {5254, 13356}, {6036, 39750}, {6055, 7753}, {7612, 11170}, {7735, 12212}, {7747, 40279}, {7752, 10349}, {7773, 10350}, {7787, 32961}, {7793, 16924}, {7808, 8361}, {7815, 7819}, {7901, 10345}, {7912, 10333}, {7925, 10334}, {7934, 10347}, {8177, 35432}, {8667, 22486}, {8787, 11163}, {9596, 10799}, {9599, 12835}, {9752, 10788}, {9770, 12151}, {10335, 14931}, {10359, 31404}, {10631, 14537}, {11361, 39652}, {11842, 15484}, {12054, 31401}, {23055, 33005}, {31489, 39560}, {39685, 40814}

X(42535) = crosssum of X(1664) and X(1665)
X(42535) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 13860, 2023}, {32, 5475, 10796}

X(42536) = X(5)X(524)∩X(6)X(598)

Barycentrics    5*a^6 - 15*a^4*b^2 + 9*a^2*b^4 + 2*b^6 - 15*a^4*c^2 - 18*a^2*b^2*c^2 - 3*b^4*c^2 + 9*a^2*c^4 - 3*b^2*c^4 + 2*c^6 : :
X(42536) = 2 X[1153] - 3 X[7606], 3 X[5476] - X[8176], X[8182] + 3 X[20423], X[11165] - 9 X[14848], 9 X[14853] - X[23334]

X(42536) lies on K1200 and these lines: {2, 8586}, {5, 524}, {6, 598}, {262, 7610}, {511, 1153}, {542, 40277}, {543, 10796}, {574, 597}, {575, 32479}, {2080, 8182}, {5026, 11164}, {5038, 7738}, {5475, 8584}, {5485, 11170}, {5969, 11165}, {7608, 42011}, {7619, 25555}, {7777, 10487}, {7786, 22486}, {7899, 21358}, {8859, 13330}, {9855, 10485}, {10166, 13192}, {14853, 23334}, {15019, 42008}

X(42536) = midpoint of X(i) and X(j) for these {i,j}: {576, 7617}, {8584, 20112}
X(42536) = reflection of X(7619) in X(25555)
X(42536) = {X(6),X(11317)}-harmonic conjugate of X(8787)

leftri

Gibert points on the Brocard-Kiepert quartic, Q073: X(42537)-X(42546)

rightri

This preamble and points X(42537)-X(42546) are contributed by Peter Moses, April 6, 2021

Gibert points are introduced in the preamble just before X(42085); for the Brocard-Kiepert quartic, see Q073.



X(42537) = GIBERT (-6 SQRT(3),25,-22) POINT

Barycentrics    -3*a^2*S - 11*a^2*SA + 25*SB*SC : :

X(42537) lies on the curce Q073 and these lines: {30, 1588}, {376, 42268}, {1132, 13847}, {1151, 3543}, {1327, 3068}, {1328, 6396}, {3146, 31414}, {3316, 42266}, {3534, 32786}, {3830, 35255}, {3845, 6451}, {5059, 6426}, {6419, 33703}, {6441, 15640}, {6479, 35821}, {6497, 15686}, {6500, 35400}, {9541, 33699}, {9543, 41952}, {10194, 17538}, {15685, 23259}, {15697, 42283}, {15710, 35787}, {35409, 35820}, {36449, 42141}, {36467, 42140}

X(42538) = GIBERT (6 SQRT(3),25,-22) POINT

Barycentrics    3*a^2*S - 11*a^2*SA + 25*SB*SC : :

X(42538) lies on the curce Q073 and these lines: {30, 1587}, {376, 42269}, {1131, 13846}, {1152, 3543}, {1327, 6200}, {1328, 3069}, {3146, 32788}, {3317, 42267}, {3529, 8960}, {3534, 32785}, {3830, 35256}, {3845, 6452}, {5059, 6425}, {6420, 33703}, {6442, 15640}, {6478, 35820}, {6496, 15686}, {6501, 35400}, {10195, 17538}, {15681, 31412}, {15685, 23249}, {15697, 42284}, {15710, 35786}, {35409, 35821}, {36450, 42140}, {36468, 42141}

X(42539) = GIBERT (-16 SQRT(3),25,2) POINT

Barycentrics    -8*a^2*S + a^2*SA + 25*SB*SC : :

X(42539) lies on the curce Q073 and these lines: {2, 1328}, {4, 6501}, {5, 6474}, {30, 17851}, {615, 42413}, {1131, 3071}, {1132, 1152}, {3068, 3854}, {3091, 13903}, {3146, 6448}, {3311, 3832}, {3317, 3522}, {3543, 6395}, {5056, 6407}, {6420, 23263}, {6471, 7586}, {9542, 15022}, {9543, 42270}, {15705, 42225}

X(42540) = GIBERT (16 SQRT(3),25,2) POINT

Barycentrics    8*a^2*S + a^2*SA + 25*SB*SC : :

X(42540) lies on the curce Q073 and these lines: {2, 1327}, {4, 6500}, {5, 6475}, {590, 42414}, {1131, 1151}, {1132, 3070}, {3069, 3854}, {3091, 13961}, {3146, 6447}, {3312, 3832}, {3316, 3522}, {3543, 6199}, {5056, 6408}, {6419, 23253}, {6470, 7585}, {9542, 14241}, {15705, 42226}, {21734, 31412}

X(42541) = GIBERT (-64 SQRT(3),25,62) POINT

Barycentrics    -32*a^2*S + 31*a^2*SA + 25*SB*SC : :

X(42541) lies on the curce Q073 and these lines: {20, 6408}, {3069, 3839}, {3312, 3317}, {5059, 6475}, {5420, 6419}, {6199, 15708}, {6451, 15692}, {6459, 41964}, {9542, 32788}, {13785, 15640}

X(42542) = GIBERT (64 SQRT(3),25,62) POINT

Barycentrics    32*a^2*S + 31*a^2*SA + 25*SB*SC : :

X(42542) lies on the curce Q073 and these lines: {20, 6407}, {3068, 3839}, {3311, 3316}, {5059, 6474}, {5418, 6420}, {6395, 15708}, {6452, 15692}, {6460, 41963}, {6498, 31487}, {13665, 15640}

X(42543) = GIBERT (-9,98,-155) POINT

Barycentrics    -3*Sqrt[3]*a^2*S - 155*a^2*SA + 196*SB*SC : :

X(42543) lies on the curce Q073 and these lines: {1657, 3412}, {3411, 15704}, {3534, 33416}, {5238, 5366}, {10646, 12817}, {10654, 11001}, {11543, 42430}, {12816, 15685}, {15681, 42153}

X(42544) = GIBERT (9,98,-155) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 155*a^2*SA + 196*SB*SC : :

X(42544) lies on the curce Q073 and these lines: {1657, 3411}, {3412, 15704}, {3534, 33417}, {5237, 5365}, {10645, 12816}, {10653, 11001}, {11542, 42429}, {12817, 15685}, {15681, 42156}

X(42545) = GIBERT (-45,98,-79) POINT

Barycentrics    -15*Sqrt[3]*a^2*S - 79*a^2*SA + 196*SB*SC : :

X(42545) lies on the curce Q073 and these lines: {13, 382}, {546, 10188}, {550, 12817}, {3411, 42088}, {3529, 16268}, {3530, 42099}, {3855, 10645}, {19106, 42415}

X(42546) = GIBERT (45,98,-79) POINT

Barycentrics    15*Sqrt[3]*a^2*S - 79*a^2*SA + 196*SB*SC : :

X(42546) lies on the curve Q073 and these lines: {14, 382}, {546, 10187}, {550, 12816}, {3412, 42087}, {3529, 16267}, {3530, 42100}, {3855, 10646}, {19107, 42416}

X(42547) = X(11)X(15914)∩X(100)X(693)

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

X(42547) lies on these lines: {11, 15914}, {100, 693}, {513, 34789}, {514, 21635}, {2804, 23770}, {3035, 11124}, {3738, 4010}, {4939, 42455}, {6366, 30592}, {11934, 13274}, {35100, 38752}

X(42548) = X(6)X(76)∩X(32)X(39684)

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

X(42548) lies on these lines: {6, 76}, {32, 39684}, {39, 3051}, {99, 42346}, {194, 40382}, {217, 5052}, {385, 1207}, {511, 14133}, {688, 23099}, {1500, 2309}, {1613, 7786}, {2086, 5368}, {3118, 27374}, {3231, 6683}, {3934, 17176}, {5007, 9427}, {5041, 32748}, {6292, 14822}, {6461, 12992}, {7772, 18899}, {7839, 38382}, {9019, 13330}, {9419, 42442}, {9865, 34482}, {10339, 32476}, {13331, 16285}, {14778, 32450}, {17475, 25264}

X(42548) = isogonal conjugate of X(31622)
X(42548) = trilinear product X(19)*X(23210)

X(42549) = X(69)X(189)∩X(84)X(517)

Barycentrics    a*(a*b + b^2 + a*c - 2*b*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)*(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(42549) lies on these lines: {57, 1422}, {65, 1413}, {69, 189}, {84, 517}, {354, 2208}, {1364, 17832}, {1433, 18732}, {2097, 7129}, {2188, 17441}, {2192, 3827}, {5908, 15239}, {8808, 14554}

X(42549) = crosspoint of X(57) and X(34546)
X(42549) = crosssum of X(9) and X(1604)

X(42550) = X(1)X(1437)∩X(65)X(15267)

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

X(42550) lies on these lines: {1, 1437}, {65, 15267}, {72, 1089}, {314, 2995}, {758, 10441}, {960, 19608}, {1409, 2171}, {2292, 22345}, {7015, 10570}, {18697, 41600}, {20653, 22076}

X(42550) = isogonal conjugate of X(40452)
X(42550) = crosspoint of X(65) and X(42485)
X(42550) = crosssum of X(21) and X(1610)

X(42551) = X(2)X(17042)∩X(6)X(194)

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

X(42551) lies on these lines: {2, 17042}, {6, 194}, {39, 4074}, {76, 3981}, {141, 14820}, {525, 882}, {538, 21849}, {695, 9230}, {706, 40951}, {732, 1843}, {755, 3222}, {2353, 3504}, {3094, 31360}, {3934, 41440}, {20081, 20977}, {31506, 41622}

X(42551) = isogonal conjugate of X(38834)
X(42551) = X(i)-isoconjugate-of X(j) for these {i,j}: {82, 1613}, {251, 1740}
X(42551) = crosspoint of X(76) and X(42486)
X(42551) = crosssum of X(32) and X(33786)
X(42551) = trilinear product X(i)*X(j) for these {i,j}: {38, 2998}, {39, 18832}, {141, 3223}, {561, 19606}
X(42551) = trilinear quotient X(i)/X(j) for these (i,j): (1930, 194), (2998, 82), (3223, 251), (3665, 1424), (18832, 83), (19606, 560)

X(42552) = X(11)X(11193)∩X(149)X(693)

Barycentrics    a*(a - b - c)*(b - c)*(a^3 - a^2*b - a*b^2 + b^3 - a^2*c + a*b*c - b^2*c + a*c^2 + b*c^2 - c^3)*(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(42552) lies on these lines: {11, 11193}, {149, 693}, {513, 22321}, {654, 14418}, {900, 1830}, {1768, 3309}, {2254, 3722}, {3446, 15313}, {3738, 14740}, {3887, 5083}, {8760, 12747}, {11247, 37718}, {20095, 30613}

X(42552) = isogonal conjugate of X(40577)
X(42552) = crosssum of X(i) and X(j) for these {i,j}: {513, 38863}, {5540, 11193}
X(42552) = crossdifference of every pair of points on line X(1421)X(5540)
X(42552) = trilinear product X(i)*X(j) for these {i,j}: {109, 34896}, {522, 3446}, {663, 8047}

X(42553) = X(99)X(523)∩X(115)X(8029)

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

X(42553) lies on these lines: {99, 523}, {115, 8029}, {512, 39846}, {620, 11123}, {671, 9293}, {1649, 31274}, {2482, 36955}, {6722, 8371}, {8151, 15561}, {10278, 14061}, {10279, 38224}, {12042, 16220}, {14444, 33919}, {32204, 38750}

X(42554) = X(6)X(76)∩X(69)X(1369)

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

X(42554) lies on these lines: {6, 76}, {69, 1369}, {141, 6665}, {305, 3763}, {339, 11574}, {524, 31390}, {594, 20911}, {826, 22260}, {1235, 3867}, {1799, 2916}, {3266, 34573}, {3313, 14994}, {3589, 11205}, {3619, 9464}, {3631, 36792}, {3926, 13351}, {3933, 42442}, {4509, 23885}, {8788, 26190}, {10191, 40022}, {17949, 40043}, {20898, 21038}, {22289, 22308}, {33907, 35522}, {41256, 41916}

X(42554) = isotomic conjugate of isogonal conjugate of X(6292)

X(42555) = X(190)X(6634)∩X(514)X(4440)

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

X(42555) lies on these lines: {190, 6634}, {514, 4440}, {522, 21100}, {812, 14759}, {900, 3035}, {1086, 21204}, {2786, 3762}, {2796, 5592}, {3667, 9282}, {9262, 18645}, {17197, 21211}, {24821, 32212}, {32094, 42372}

X(42555) = isogonal conjugate of X(41405)
X(42555) = isotomic conjugate of X(6631)

X(42556) = X(3)X(95)∩X(51)X(216)

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

X(42556) lies on these lines: {3, 95}, {51, 216}, {185, 20775}, {511, 42441}, {1033, 26865}, {1075, 26876}, {3164, 26874}, {3611, 23197}, {6638, 12012}, {10263, 30258}, {11197, 14767}, {20975, 31364}, {23209, 40947}, {41212, 42445}

leftri

Gibert points on the KHO quartic Q168: X(42557)-X(42561)

rightri

This preamble and points X(42557)-X(42560) are contributed by Peter Moses, April 7, 2021. See also the preambles just before X(42085), X(42413), and X(42429).

This section gives four new points on the following KHO quartic (using KHO coordinates (x,y,z), introduced at KHO curves.

2*x^4 + 30*x^2*y^2 - 108*y^4 - 27*x^2*y*z + 216*y^3*z - 171*y^2*z^2 + 81*y*z^3 - 18*z^4 = 0.

This quartic passes through X(i) for these i: 2,5,17,18,371,372,1131,1132,3068,3069,3070,3071,8976,13951,31412,39641,39642, 42557, 42558, 42559, 42560.



X(42557) = GIBERT (-5 SQRT(3),8,13) POINT

Barycentrics    5*a^2*S - 13*a^2*SA - 16*SB*SC : :

X(42557) lies on the quartic K168 and these lines: {4, 6487}, {5, 372}, {6, 15703}, {140, 6484}, {376, 6565}, {381, 6481}, {486, 3525}, {1132, 3523}, {1656, 35770}, {1657, 42262}, {3068, 3317}, {3069, 6436}, {3071, 12108}, {3090, 35814}, {3091, 12818}, {3146, 5420}, {3830, 6396}, {3839, 42274}, {3843, 6485}, {3854, 13935}, {5054, 6200}, {5070, 35771}, {6411, 15722}, {6419, 8253}, {6434, 14269}, {6438, 19709}, {6477, 6560}, {6480, 15694}, {7586, 10576}, {8960, 13993}, {10124, 32790}, {12100, 18762}, {12102, 42267}, {13846, 42527}, {13847, 18512}, {13939, 35812}, {13941, 35822}, {14226, 42525}, {14241, 42277}, {14893, 35256}, {15705, 23259}, {19710, 42283}, {21734, 42266}, {33923, 35821}, {35762, 37712}

X(42558) = GIBERT (5 SQRT(3),8,13) POINT

Barycentrics    5*a^2*S + 13*a^2*SA + 16*SB*SC : :

X(42558) lies on the quartic K168 and these lines: {4, 6486}, {5, 371}, {6, 15703}, {140, 6485}, {376, 6564}, {381, 6480}, {485, 3525}, {1131, 3523}, {1656, 35771}, {1657, 42265}, {3068, 6435}, {3069, 3316}, {3070, 12108}, {3090, 35815}, {3091, 12819}, {3146, 5418}, {3830, 6200}, {3839, 9541}, {3843, 6484}, {3854, 9540}, {5054, 6396}, {5070, 35770}, {6412, 15722}, {6420, 8252}, {6433, 14269}, {6437, 19709}, {6476, 6561}, {6481, 15694}, {7585, 10577}, {8972, 35823}, {10124, 32789}, {12100, 18538}, {12102, 42266}, {13846, 18510}, {13847, 42526}, {13886, 35813}, {14226, 42274}, {14241, 42524}, {14893, 35255}, {15705, 23249}, {19710, 42284}, {21734, 42267}, {33923, 35820}, {35763, 37712}

X(42559) = GIBERT (-3/SQRT(2),-1/2,1) POINT

Barycentrics    -Sqrt[3/2]*a^2*S + a^2*SA - SB*SC : :

X(42559) lies on the quartic K168 and these lines: {6, 20}, {17, 14782}, {18, 14783}, {10653, 14784}, {10654, 14785}

X(42560) = GIBERT (3/SQRT(2),-1/2,1) POINT

Barycentrics    Sqrt[3/2]*a^2*S + a^2*SA - SB*SC : :

X(42560) lies on the quartic K168 and these lines:: {6, 20}, {17, 14783}, {18, 14782}, {10653, 14785}, {10654, 14784}

X(42561) = GIBERT (-2 SQRT(3),3,2) POINT

Barycentrics    -a^2*S + a^2*SA + 3*SB*SC : :
X(42561) = 2 X[6450] - 3 X[13935], X[6450] - 3 X[13951], 2 X[6450] + 3 X[23263], 2 X[13951] + X[23263]

X(31412) = the associated Gibert point, (2 SQRT(3),3,2)

X(42561) lies on the curve Q168 and these lines: {2, 489}, {3, 18762}, {4, 372}, {5, 1588}, {6, 3091}, {20, 615}, {30, 6450}, {69, 32488}, {114, 13653}, {140, 6455}, {371, 3090}, {376, 1328}, {378, 8277}, {381, 1587}, {382, 6408}, {485, 3545}, {487, 26362}, {488, 7620}, {491, 12221}, {515, 13959}, {516, 13947}, {546, 3312}, {550, 6497}, {590, 5056}, {626, 637}, {631, 6561}, {632, 6449}, {638, 5860}, {639, 7375}, {641, 26619}, {946, 19065}, {962, 13973}, {1056, 35801}, {1058, 35803}, {1124, 10590}, {1131, 3854}, {1152, 2672}, {1271, 23312}, {1335, 10591}, {1377, 31418}, {1504, 31415}, {1593, 13943}, {1656, 9540}, {1657, 35256}, {1699, 13936}, {1702, 10175}, {1703, 18483}, {2066, 10588}, {2067, 10589}, {3070, 3832}, {3093, 6623}, {3128, 13052}, {3297, 5261}, {3298, 5274}, {3364, 18582}, {3365, 42159}, {3367, 42254}, {3389, 18581}, {3390, 42162}, {3392, 42255}, {3522, 42263}, {3523, 8252}, {3524, 42260}, {3525, 6200}, {3528, 42266}, {3529, 6396}, {3533, 6486}, {3535, 8979}, {3543, 6430}, {3544, 6419}, {3564, 26469}, {3583, 13963}, {3585, 13962}, {3591, 5059}, {3592, 8972}, {3594, 42284}, {3614, 19038}, {3618, 32489}, {3627, 6398}, {3628, 6221}, {3634, 9616}, {3817, 18991}, {3818, 39875}, {3830, 13961}, {3839, 6471}, {3843, 23253}, {3850, 13665}, {3851, 6500}, {3855, 6564}, {3857, 6428}, {5055, 8981}, {5066, 19117}, {5067, 5418}, {5068, 7585}, {5070, 9691}, {5071, 10576}, {5072, 6417}, {5076, 42226}, {5079, 6199}, {5177, 31473}, {5225, 5414}, {5229, 6502}, {5411, 23047}, {5412, 6622}, {5448, 19061}, {5475, 26456}, {5587, 19066}, {5590, 7388}, {5640, 12239}, {5691, 13971}, {5818, 35775}, {5870, 36655}, {5893, 19087}, {5895, 13980}, {6202, 36656}, {6253, 13953}, {6256, 13964}, {6284, 13954}, {6352, 31562}, {6353, 8281}, {6409, 10303}, {6420, 23267}, {6422, 31404}, {6425, 32789}, {6426, 42272}, {6427, 12811}, {6448, 12102}, {6451, 14869}, {6452, 12103}, {6454, 42276}, {6456, 15704}, {6474, 15703}, {6485, 33703}, {6496, 12108}, {6499, 38071}, {7000, 13748}, {7173, 18996}, {7354, 13955}, {7486, 8253}, {7512, 35777}, {7687, 19110}, {7714, 18290}, {7728, 13979}, {7988, 8983}, {7989, 13883}, {8164, 35808}, {8227, 13902}, {8855, 8889}, {8964, 8990}, {9615, 19862}, {9974, 14853}, {10194, 10299}, {10515, 36664}, {10592, 31474}, {10721, 13969}, {10722, 13967}, {10723, 13989}, {10724, 13991}, {10728, 13977}, {10733, 13990}, {10735, 13992}, {10895, 19029}, {10896, 19027}, {11292, 26361}, {11294, 32805}, {11479, 19005}, {11488, 35732}, {11489, 42282}, {12111, 12240}, {12173, 13937}, {12245, 35789}, {12296, 13934}, {12509, 22617}, {12943, 18966}, {12953, 13958}, {12970, 32064}, {13846, 42522}, {13972, 36990}, {13975, 41869}, {13976, 34789}, {13981, 36962}, {13982, 36961}, {14561, 39876}, {14651, 33431}, {14784, 41976}, {14785, 41975}, {15681, 42537}, {15682, 42267}, {15690, 42527}, {17538, 42275}, {17578, 42264}, {17820, 41362}, {18539, 39864}, {18945, 19356}, {18992, 19925}, {19056, 23514}, {19060, 23515}, {19078, 38161}, {19082, 23513}, {19088, 23332}, {19109, 36519}, {19111, 36518}, {21734, 42539}, {22553, 22587}, {23269, 35786}, {26462, 31411}, {33345, 33371}, {35733, 42235}, {35738, 42203}, {35739, 42100}, {35822, 41106}, {41956, 42523}, {42119, 42239}, {42120, 42241}, {42125, 42280}, {42128, 42281}, {42135, 42209}, {42138, 42207}

X(42561) = midpoint of X(13935) and X(23263)
X(42561) = reflection of X(13935) in X(13951)
X(42561) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 489, 33365}, {2, 1132, 3071}, {2, 3071, 6459}, {4, 486, 3069}, {4, 3069, 6460}, {4, 13939, 372}, {5, 1588, 3068}, {5, 13785, 1588}, {6, 3091, 31412}, {6, 42270, 3091}, {371, 3090, 32785}, {371, 42274, 3090}, {372, 486, 13939}, {372, 6565, 42268}, {372, 13939, 3069}, {372, 42268, 4}, {376, 3317, 5420}, {376, 35821, 42413}, {381, 7584, 1587}, {485, 7582, 19054}, {485, 35823, 7582}, {486, 6565, 4}, {486, 32498, 12256}, {486, 42268, 372}, {546, 3312, 23249}, {615, 23261, 20}, {615, 42271, 6410}, {631, 23275, 6561}, {1132, 42262, 6459}, {1152, 42283, 3146}, {1328, 3317, 42413}, {1328, 5420, 35821}, {1587, 7584, 19053}, {1656, 42215, 9540}, {3071, 42262, 2}, {3090, 23273, 371}, {3146, 13941, 1152}, {3544, 13886, 42277}, {3545, 7582, 485}, {3545, 14226, 35823}, {3545, 35823, 19054}, {3627, 13993, 6398}, {3832, 7586, 3070}, {3843, 42216, 23253}, {3850, 19116, 13665}, {3851, 18510, 7583}, {3855, 7581, 6564}, {5068, 7585, 42265}, {5072, 6417, 18538}, {5420, 35821, 376}, {6396, 22615, 3529}, {6409, 32790, 10303}, {6410, 23261, 42271}, {6410, 42271, 20}, {6419, 42277, 13886}, {6420, 42269, 23267}, {6560, 35787, 4}, {6561, 10577, 631}, {6564, 7581, 31414}, {8252, 42258, 3523}, {10895, 19029, 31408}, {11294, 32805, 33364}, {18762, 23259, 32786}, {23269, 41099, 35786}, {23273, 42274, 32785}, {42217, 42218, 32786}, {42242, 42244, 6565}

leftri

Gibert points: X(42562)-X(42593)

rightri

This preamble and points X(42562)-X(42593) are contributed by Peter Moses, April 7, 2021. See also the preambles just before X(42085), X(42413), and X(42429).

Points X(42562)-X(42575) lie on the cubic K458. Points X(42576)-X(42579) lie on the cubic K369.



X(42562) = GIBERT (12-7*SQRT(3), 5-3*SQRT(3), 3-2*SQRT(3)) POINT

Barycentrics    a^2*((-7 + 4*Sqrt[3])*S + (3 - 2*Sqrt[3])*SA) + (10 - 6*Sqrt[3])*SB*SC : :

X(42562) lies on the cubic K458 and these lines: {2, 371}, {5, 3389}, {6, 42565}, {13, 3070}, {14, 34559}, {15, 3071}, {16, 17}, {61, 3392}, {62, 590}, {302, 33351}, {303, 641}, {372, 2042}, {396, 3390}, {615, 3364}, {2044, 42266}, {2045, 10576}, {2046, 6200}, {2460, 6671}, {3102, 33392}, {3103, 22691}, {3367, 42251}, {3391, 37832}, {5318, 42226}, {5335, 6396}, {5420, 11488}, {6449, 36456}, {6564, 42244}, {6565, 42159}, {8253, 42156}, {8981, 23303}, {10195, 22235}, {10645, 42170}, {10646, 42201}, {11303, 33352}, {13993, 41943}, {14814, 16966}, {16809, 42212}, {16960, 42202}, {16965, 35740}, {16967, 18762}, {18586, 23261}, {19106, 42194}, {22615, 36454}, {23259, 42175}, {35732, 35821}, {35770, 36468}, {35814, 36449}, {35820, 36437}, {36439, 42258}, {36463, 42269}, {42113, 42178}, {42130, 42279}, {42150, 42187}, {42152, 42254}, {42177, 42277}, {42179, 42432}, {42219, 42494}, {42228, 42274}, {42245, 42261}

X(42562) = {X(2),X(5418)}-harmonic conjugate of X(42564)
X(42562) = {X(16),X(17)}-harmonic conjugate of X(42563)
X(42562) = {X(371),X(10577)}-harmonic conjugate of X(42564)

X(42563) = GIBERT (12+7*SQRT(3), 5+3*SQRT(3), 3+2*SQRT(3)) POINT

Barycentrics    a^2*((7 + 4*Sqrt[3])*S + (3 + 2*Sqrt[3])*SA) + (10 + 6*Sqrt[3])*SB*SC : :

X(42563) lies on the cubic K458 and these lines: {2, 372}, {5, 3390}, {6, 42564}, {13, 3071}, {14, 34562}, {15, 3070}, {16, 17}, {61, 3391}, {62, 615}, {302, 33352}, {303, 642}, {371, 2041}, {396, 3389}, {549, 35731}, {590, 3365}, {2043, 42267}, {2045, 6396}, {2046, 10577}, {2459, 6671}, {3102, 22691}, {3103, 33394}, {3366, 42253}, {3392, 35740}, {5318, 42225}, {5335, 6200}, {5418, 11488}, {6450, 36438}, {6564, 42159}, {6565, 42245}, {8252, 42156}, {8960, 42152}, {10194, 22235}, {10645, 42169}, {10646, 42202}, {11303, 33351}, {13925, 41943}, {13966, 23303}, {14813, 16966}, {15765, 35739}, {16809, 42214}, {16960, 42201}, {16965, 42241}, {16967, 18538}, {18587, 23251}, {19106, 42192}, {22644, 36436}, {23249, 42176}, {35771, 36449}, {35815, 36468}, {35820, 42282}, {35821, 36455}, {36445, 42268}, {36457, 42259}, {42113, 42177}, {42130, 42278}, {42150, 42189}, {42178, 42274}, {42181, 42432}, {42217, 42494}, {42227, 42277}, {42244, 42260}

X(42563) = {X(2),X(5420)}-harmonic conjugate of X(42565)
X(42563) = {X(16),X(17)}-harmonic conjugate of X(42562)
X(42563) = {X(372),X(10576)}-harmonic conjugate of X(42565)

X(42564) = GIBERT (-12-7*SQRT(3), 5+3*SQRT(3), 3+2*SQRT(3)) POINT

Barycentrics    a^2 ((-7-4 Sqrt[3]) S+(3+2 Sqrt[3]) SA)+(10+6 Sqrt[3]) SB SC : :

X(42564) lies on the cubic K458 and these lines: {2, 371}, {5, 3364}, {6, 42563}, {13, 34562}, {14, 3070}, {15, 18}, {16, 3071}, {61, 590}, {62, 3367}, {302, 641}, {303, 33353}, {372, 2041}, {395, 3365}, {615, 3389}, {2043, 42266}, {2045, 6200}, {2046, 10576}, {2460, 6672}, {3102, 33395}, {3103, 22692}, {3366, 37835}, {3392, 42250}, {5321, 42226}, {5334, 6396}, {5420, 11489}, {6449, 36438}, {6564, 42242}, {6565, 42162}, {8253, 42153}, {8981, 23302}, {10195, 22237}, {10645, 42199}, {10646, 42168}, {11304, 33350}, {13993, 41944}, {14813, 16967}, {16808, 42211}, {16961, 42200}, {16964, 35739}, {16966, 18762}, {18587, 23261}, {19107, 42193}, {22615, 36436}, {23259, 42177}, {35770, 36450}, {35814, 36467}, {35820, 36455}, {35821, 42282}, {36445, 42269}, {36457, 42258}, {42112, 42176}, {42131, 42278}, {42149, 42255}, {42151, 42188}, {42175, 42277}, {42180, 42431}, {42220, 42495}, {42230, 42274}, {42243, 42261}

X(42564) = {X(2),X(5418)}-harmonic conjugate of X(42562)
X(42564) = {X(15),X(18)}-harmonic conjugate of X(42565)
X(42564) = {X(371),X(10577)}-harmonic conjugate of X(42562)

X(42565) = GIBERT (-12+7*SQRT(3), 5-3*SQRT(3), 3-2*SQRT(3)) POINT

Barycentrics    a^2*((7 - 4*Sqrt[3])*S + (3 - 2*Sqrt[3])*SA) + (10 - 6*Sqrt[3])*SB*SC : :

X(42565) lies on the cubic K458 and these lines: {2, 372}, {5, 3365}, {6, 42562}, {13, 34559}, {14, 3071}, {15, 18}, {16, 3070}, {61, 615}, {62, 3366}, {302, 642}, {303, 33350}, {371, 2042}, {395, 3364}, {590, 3390}, {2044, 42267}, {2045, 10577}, {2046, 6396}, {2459, 6672}, {3102, 22692}, {3103, 33393}, {3367, 37835}, {3391, 42252}, {5321, 42225}, {5334, 6200}, {5418, 11489}, {6450, 36456}, {6564, 42162}, {6565, 42243}, {8252, 42153}, {8960, 42149}, {10194, 22237}, {10645, 42200}, {10646, 42167}, {11304, 33353}, {13925, 41944}, {13966, 23302}, {14814, 16967}, {16242, 35739}, {16808, 42213}, {16961, 42199}, {16964, 42239}, {16966, 18538}, {18586, 23251}, {19107, 42191}, {22644, 36454}, {23249, 42178}, {25189, 35757}, {32787, 35731}, {35732, 35820}, {35771, 36467}, {35815, 36450}, {35821, 36437}, {36439, 42259}, {36463, 42268}, {42112, 42175}, {42131, 42279}, {42151, 42190}, {42176, 42274}, {42182, 42431}, {42218, 42495}, {42229, 42277}, {42242, 42260}

X(42565) = {X(2),X(5420)}-harmonic conjugate of X(42563)
X(42565) = {X(15),X(18)}-harmonic conjugate of X(42564)
X(42565) = {X(372),X(10576)}-harmonic conjugate of X(42563)

X(42566) = GIBERT (5*SQRT(3), 9, 24) POINT

Barycentrics    a^2*(5*S + 24*SA) + 18*SB*SC : :

X(42566) lies on the cubic K458 and these lines: {2, 6437}, {5, 6200}, {6, 3525}, {376, 8253}, {590, 5054}, {615, 10124}, {631, 6434}, {1587, 6440}, {1657, 42277}, {3068, 6442}, {3070, 3523}, {3071, 6468}, {3090, 6433}, {3146, 6411}, {3628, 6480}, {5418, 6199}, {6396, 12108}, {6436, 32787}, {6438, 10303}, {6445, 42270}, {6469, 13886}, {6476, 35255}, {6481, 14869}, {6486, 12812}, {6490, 42262}, {6560, 15718}, {9690, 15703}, {10576, 33923}, {12100, 18538}, {12103, 42273}, {13665, 15722}, {18762, 41963}, {21734, 42265}, {23267, 42418}, {31454, 32786}

X(42567) = GIBERT (-5*SQRT(3), 9, 24) POINT

Barycentrics    a^2*(5*S - 24*SA) - 18*SB*SC : :

X(42567) lies on the cubic K458 and these lines: {2, 6438}, {5, 6396}, {6, 3525}, {376, 8252}, {590, 10124}, {615, 5054}, {631, 6433}, {1588, 6439}, {1657, 42274}, {3069, 6441}, {3070, 6469}, {3071, 3523}, {3090, 6434}, {3146, 6412}, {3628, 6481}, {5420, 6395}, {6200, 12108}, {6435, 32788}, {6437, 10303}, {6446, 42273}, {6468, 13939}, {6477, 35256}, {6480, 14869}, {6487, 12812}, {6491, 42265}, {6561, 15718}, {10577, 33923}, {12100, 18762}, {12103, 42270}, {13785, 15722}, {15703, 41946}, {18538, 41964}, {21734, 42262}, {23273, 42417}

X(42568) = GIBERT (5*SQRT(3), 2, 12) POINT

Barycentrics    a^2*(5*S + 12*SA) + 4*SB*SC : :

X(42568) lies on the cubic K458 and these lines: {2, 6429}, {3, 35815}, {4, 6433}, {5, 1151}, {6, 3523}, {30, 12818}, {140, 6437}, {371, 5054}, {376, 3070}, {381, 6484}, {382, 6486}, {485, 12103}, {486, 10124}, {549, 6431}, {590, 3146}, {1152, 12100}, {1588, 3317}, {1656, 6480}, {1657, 6200}, {3068, 21734}, {3071, 6468}, {3090, 10141}, {3312, 15718}, {3526, 42557}, {3530, 6432}, {3592, 12108}, {3830, 6449}, {3839, 42258}, {3854, 32785}, {3860, 22615}, {5067, 10139}, {5079, 6482}, {6221, 10577}, {6407, 15703}, {6410, 7581}, {6411, 8981}, {6417, 15722}, {6430, 15717}, {6434, 10299}, {6438, 15712}, {6439, 32789}, {6445, 10576}, {6451, 8960}, {6453, 42262}, {6455, 35812}, {6459, 41955}, {6487, 15706}, {6488, 12102}, {6490, 18762}, {6496, 35822}, {6519, 6565}, {8972, 42414}, {9541, 10147}, {9615, 37712}, {9692, 42561}, {10195, 42225}, {15533, 33364}, {15693, 35770}, {15701, 35814}, {15705, 32787}, {23253, 41950}, {23275, 41945}, {26516, 31884}, {35404, 42269}, {42263, 42558}

X(42569) = GIBERT (-5*SQRT(3), 2, 12) POINT

Barycentrics    a^2*(5*S - 12*SA) - 4*SB*SC : :

X(42569) lies on the cubic K458 and these lines: {2, 6430}, {3, 35814}, {4, 6434}, {5, 1152}, {6, 3523}, {30, 12819}, {140, 6438}, {372, 5054}, {376, 3071}, {381, 6485}, {382, 6487}, {485, 10124}, {486, 12103}, {549, 6432}, {615, 3146}, {1151, 12100}, {1587, 3316}, {1656, 6481}, {1657, 6396}, {3069, 21734}, {3070, 6469}, {3090, 10142}, {3311, 15718}, {3526, 42558}, {3530, 6431}, {3594, 8981}, {3830, 6450}, {3839, 42259}, {3854, 32786}, {3860, 22644}, {5067, 10140}, {5079, 6483}, {6398, 10576}, {6408, 15703}, {6409, 7582}, {6412, 13966}, {6418, 15722}, {6429, 15717}, {6433, 10299}, {6437, 15712}, {6440, 32790}, {6446, 10577}, {6454, 42265}, {6456, 35813}, {6460, 17852}, {6486, 15706}, {6489, 12102}, {6491, 18538}, {6497, 35823}, {6522, 6564}, {10194, 42226}, {13941, 42413}, {15533, 33365}, {15693, 35771}, {15701, 35815}, {15705, 32788}, {23263, 41949}, {23269, 41946}, {26521, 31884}, {35404, 42268}, {42264, 42557}

X(42570) = GIBERT (10*SQRT(3), 11, 6) POINT

Barycentrics    a^2*(5*S + 3*SA) + 11*SB*SC : :

X(42570) lies on the cubic K458 and these lines: {2, 6430}, {5, 1587}, {6, 3854}, {376, 485}, {590, 21734}, {631, 42558}, {1131, 3068}, {1657, 6445}, {3070, 3523}, {3071, 3839}, {3311, 14893}, {3525, 6460}, {3830, 6459}, {3860, 19117}, {5420, 23267}, {6410, 41952}, {6472, 9541}, {6476, 8960}, {6564, 7582}, {7583, 23263}, {8972, 42414}, {8976, 33923}, {9540, 12103}, {12100, 42526}, {13886, 42260}, {13925, 19710}, {13935, 15703}, {15682, 35815}, {15705, 42259}, {19053, 41951}, {35771, 41099}, {35822, 41106}, {41954, 42265}, {41965, 42264}

X(42571) = GIBERT (-10*SQRT(3), 11, 6) POINT

Barycentrics    a^2*(5*S - 3*SA) - 11*SB*SC : :

X(42571) lies on the cubic K458 and these lines: {2, 6429}, {5, 1588}, {6, 3854}, {376, 486}, {615, 21734}, {631, 42557}, {1132, 3069}, {1657, 6446}, {3070, 3839}, {3071, 3523}, {3312, 14893}, {3525, 6459}, {3830, 6460}, {3860, 19116}, {5418, 23273}, {6409, 41951}, {6565, 7581}, {7584, 23253}, {9540, 15703}, {9541, 12108}, {9690, 18762}, {12100, 42527}, {12103, 13935}, {13939, 42261}, {13941, 42413}, {13951, 33923}, {13993, 19710}, {15682, 35814}, {15705, 42258}, {19054, 41952}, {31412, 35823}, {35770, 41099}, {41953, 42262}, {41966, 42263}

X(42572) = GIBERT (15*SQRT(3), 13, 8) POINT

Barycentrics    a^2*(15*S + 8*SA) + 26*SB*SC : :

X(42572) lies on the cubic K458 and these lines: {2, 6438}, {5, 6420}, {6, 14226}, {30, 35815}, {371, 35404}, {376, 3070}, {485, 5054}, {590, 12100}, {1327, 3830}, {1657, 6519}, {3068, 42538}, {3071, 3839}, {3146, 41945}, {3523, 31414}, {3525, 17852}, {3860, 6564}, {5215, 13701}, {6280, 13932}, {6437, 15640}, {6472, 42272}, {6481, 11540}, {7583, 14893}, {8960, 12103}, {8976, 15718}, {10138, 15694}, {11737, 35770}, {13663, 13678}, {15703, 41952}, {17851, 32789}, {19710, 42525}, {23046, 35771}, {23267, 42418}, {41961, 42276}, {42216, 42558}, {42265, 42523}

X(42573) = GIBERT (-15*SQRT(3), 13, 8) POINT

Barycentrics    a^2*(15*S - 8*SA) - 26*SB*SC : :

X(42573) lies on the cubic K458 and these lines: {2, 6437}, {5, 6419}, {6, 14226}, {30, 35814}, {372, 35404}, {376, 3071}, {486, 5054}, {615, 12100}, {1328, 3830}, {1657, 6522}, {3069, 42537}, {3070, 3839}, {3146, 41946}, {3860, 6565}, {5215, 13821}, {6279, 13850}, {6438, 15640}, {6473, 42271}, {6480, 11540}, {7584, 14893}, {10137, 15694}, {11737, 35771}, {13783, 13798}, {13951, 15718}, {15703, 41951}, {19710, 42524}, {23046, 35770}, {23273, 42417}, {41962, 42275}, {42215, 42557}, {42262, 42522}

X(42574) = GIBERT (26*SQRT(3), 9, -30) POINT

Barycentrics    a^2*(13*S - 15*SA) + 9*SB*SC : :

X(42574) lies on the cubic K458 and these lines: {2, 6440}, {5, 6398}, {20, 6442}, {3068, 6412}, {3071, 42414}, {3090, 6477}, {3528, 6476}, {3544, 6479}, {3590, 6434}, {6199, 15688}, {6200, 7581}, {6396, 13886}, {6436, 6459}, {6468, 19054}, {6481, 31412}, {6561, 11001}, {13941, 41947}, {15684, 23259}, {15701, 42216}, {15709, 23267}, {15723, 18538}, {18510, 42537}

X(42575) = GIBERT (-26*SQRT(3), 9, -30) POINT

Barycentrics    a^2*(13*S + 15*SA) - 9*SB*SC : :

X(42575) lies on the cubic K458 and these lines: {2, 6439}, {5, 6221}, {20, 6441}, {3069, 6411}, {3070, 42413}, {3090, 6476}, {3528, 6477}, {3544, 6478}, {3591, 6433}, {6200, 13939}, {6395, 9541}, {6396, 7582}, {6435, 6460}, {6469, 19053}, {6480, 42561}, {6560, 11001}, {8972, 41948}, {9542, 42417}, {9543, 32790}, {9681, 35814}, {15684, 23249}, {15701, 42215}, {15709, 23273}, {15723, 18762}, {18512, 42538}, {31414, 42275}

X(42576) = GIBERT (9*SQRT(3), 26, -20) POINT

Barycentrics    a^2*(9*S - 20*SA) + 52*SB*SC : :

X(42576) lies on the cubic K369 and these lines: {2, 42272}, {4, 10148}, {6, 15640}, {20, 41952}, {30, 3592}, {1152, 12101}, {3068, 41959}, {3071, 6471}, {3534, 23251}, {3594, 35404}, {3830, 6398}, {3845, 5420}, {3860, 42261}, {6407, 15685}, {6410, 41106}, {6433, 11001}, {6435, 42263}, {6483, 38335}, {8252, 41099}, {8253, 8703}, {12100, 22644}, {14269, 42524}, {15681, 35812}, {15695, 42265}, {15698, 42284}, {15711, 42269}, {19709, 42267}, {23261, 33699}, {32787, 42538}

X(42577) = GIBERT (-9*SQRT(3), 26, -20) POINT

Barycentrics    a^2*(9*S + 20*SA) - 52*SB*SC : :

X(42577) lies on the cubic K369 and these lines: {2, 42271}, {4, 10147}, {6, 15640}, {20, 41951}, {30, 3594}, {1151, 12101}, {3069, 41960}, {3070, 6470}, {3534, 23261}, {3592, 35404}, {3830, 6221}, {3845, 5418}, {3860, 42260}, {6408, 15685}, {6409, 41106}, {6434, 11001}, {6436, 42264}, {6482, 38335}, {8252, 8703}, {8253, 41099}, {12100, 22615}, {14269, 42525}, {15681, 35813}, {15695, 42262}, {15698, 42283}, {15711, 42268}, {19709, 42266}, {23251, 33699}, {32788, 42537}

X(42578) = GIBERT (11*SQRT(3), 10, 12) POINT

Barycentrics    a^2*(11*S + 12*SA) + 20*SB*SC : :

X(42578) lies on the cubic K369 and these lines: {2, 41948}, {6, 5056}, {30, 485}, {372, 15723}, {590, 15717}, {1132, 32787}, {1587, 3316}, {1656, 6436}, {3070, 21735}, {3071, 3855}, {3312, 5070}, {3529, 41954}, {3590, 32789}, {3592, 41991}, {5055, 6499}, {5072, 6419}, {6199, 8960}, {6396, 8976}, {6408, 35822}, {6409, 23269}, {6410, 15719}, {6429, 42413}, {6438, 10195}, {6440, 32785}, {6441, 18538}, {6447, 6564}, {6451, 42267}, {6459, 41952}, {6468, 23253}, {6480, 35405}, {6489, 42216}, {6497, 15718}, {6500, 42262}, {8972, 42414}, {10303, 41970}, {11541, 41961}, {42272, 42540}, {42273, 42522}

X(42579) = GIBERT (-11*SQRT(3), 10, 12) POINT

Barycentrics    a^2*(11*S - 12*SA) - 20*SB*SC : :

X(42579) lies on the cubic K369 and these lines: {2, 41947}, {6, 5056}, {30, 486}, {371, 15723}, {615, 15717}, {1131, 32788}, {1588, 3317}, {1656, 6435}, {3070, 3855}, {3071, 21735}, {3311, 5070}, {3529, 41953}, {3591, 32790}, {3594, 41991}, {5055, 6498}, {5072, 6420}, {6200, 13951}, {6395, 23251}, {6407, 35823}, {6409, 15719}, {6410, 23275}, {6430, 42414}, {6437, 10194}, {6439, 32786}, {6442, 18762}, {6448, 6565}, {6452, 42266}, {6460, 41951}, {6469, 23263}, {6481, 35405}, {6488, 42215}, {6496, 15718}, {6501, 42265}, {10303, 41969}, {11541, 41962}, {13941, 42413}, {17851, 42267}, {42270, 42523}, {42271, 42539}

X(42580) = GIBERT (-3, 6, 7) POINT

Barycentrics    a^2*(Sqrt[3]*S - 7*SA) - 12*SB*SC : :

X(42580) lies on these lines: {2, 5238}, {3, 16809}, {4, 5351}, {5, 13}, {6, 5079}, {14, 1656}, {15, 3628}, {16, 3091}, {17, 5055}, {61, 3090}, {140, 36967}, {202, 3614}, {303, 22845}, {381, 36843}, {382, 42528}, {396, 35018}, {398, 547}, {546, 5237}, {548, 42430}, {549, 12817}, {619, 20378}, {621, 630}, {623, 7944}, {629, 11304}, {631, 36970}, {632, 5321}, {636, 21359}, {1657, 10187}, {3146, 42089}, {3180, 33464}, {3200, 13434}, {3364, 42191}, {3365, 42193}, {3389, 42274}, {3390, 42277}, {3525, 10645}, {3526, 42157}, {3529, 42103}, {3530, 5349}, {3544, 11489}, {3545, 41100}, {3627, 10646}, {3830, 42491}, {3832, 42431}, {3843, 36968}, {3850, 16773}, {3851, 16645}, {3855, 42151}, {3857, 42121}, {5054, 42434}, {5056, 37832}, {5066, 41944}, {5067, 10654}, {5068, 10653}, {5070, 5339}, {5071, 16268}, {5072, 16808}, {5076, 42100}, {5318, 12811}, {5340, 16963}, {5350, 38071}, {5366, 42510}, {5418, 42235}, {5420, 42237}, {5460, 33414}, {5469, 8724}, {5611, 22849}, {6670, 11289}, {6777, 20416}, {7006, 7173}, {7486, 42152}, {9761, 22844}, {10095, 36979}, {10109, 16267}, {10303, 42085}, {10576, 35730}, {10612, 16529}, {10658, 15027}, {11267, 12010}, {11272, 32465}, {11305, 22490}, {11444, 36981}, {11543, 12812}, {12103, 42101}, {12108, 42087}, {14869, 42135}, {15022, 18582}, {15686, 42543}, {15699, 16772}, {15703, 41101}, {15720, 42529}, {16961, 42098}, {18874, 36978}, {22891, 33422}, {23515, 36209}, {31694, 36767}, {31706, 39555}, {33417, 36836}, {33561, 36770}, {33923, 42501}, {34755, 42110}, {35739, 42226}, {41120, 41943}, {41991, 42102}, {42086, 42473}, {42144, 42493}, {42156, 42475}

X(42580) = {X(6),X(5079)}-harmonic conjugate of X(42581)

X(42581) = GIBERT (3, 6, 7) POINT

Barycentrics    a^2*(Sqrt[3]*S + 7*SA) + 12*SB*SC : :

X(42581) lies on these lines: {2, 5237}, {3, 16808}, {4, 5352}, {5, 14}, {6, 5079}, {13, 1656}, {15, 3091}, {16, 3628}, {18, 5055}, {62, 3090}, {140, 36968}, {203, 3614}, {302, 22844}, {381, 36836}, {382, 42529}, {395, 35018}, {397, 547}, {546, 5238}, {548, 42429}, {549, 12816}, {618, 20377}, {622, 629}, {624, 7944}, {630, 11303}, {631, 36969}, {632, 5318}, {635, 21360}, {1657, 10188}, {3146, 42092}, {3181, 33465}, {3201, 13434}, {3364, 42274}, {3365, 42277}, {3389, 42192}, {3390, 42194}, {3525, 10646}, {3526, 42158}, {3529, 42106}, {3530, 5350}, {3544, 11488}, {3545, 41101}, {3627, 10645}, {3830, 42490}, {3832, 42432}, {3843, 36967}, {3850, 16772}, {3851, 16644}, {3855, 42150}, {3857, 42124}, {5054, 42433}, {5056, 37835}, {5066, 41943}, {5067, 10653}, {5068, 10654}, {5070, 5340}, {5071, 16267}, {5072, 16809}, {5076, 42099}, {5321, 12811}, {5339, 16962}, {5349, 38071}, {5365, 42511}, {5418, 42236}, {5420, 42238}, {5459, 33415}, {5470, 8724}, {5615, 22895}, {6565, 35730}, {6669, 11290}, {6778, 20415}, {7005, 7173}, {7486, 42149}, {9763, 22845}, {10095, 36981}, {10109, 16268}, {10303, 42086}, {10611, 16530}, {10657, 15027}, {11268, 12010}, {11272, 32466}, {11306, 22489}, {11444, 36979}, {11542, 12812}, {12103, 42102}, {12108, 42088}, {14869, 42138}, {15022, 18581}, {15686, 42544}, {15699, 16773}, {15703, 41100}, {15720, 42528}, {16001, 36766}, {16960, 42095}, {18874, 36980}, {22846, 33423}, {23515, 36208}, {31705, 39554}, {33416, 36843}, {33923, 42500}, {34754, 42107}, {41119, 41944}, {41991, 42101}, {42085, 42472}, {42145, 42492}, {42153, 42474}

X(42581) = {X(6),X(5079)}-harmonic conjugate of X(42580)

X(42582) = GIBERT (SQRT(3), 3, 4) POINT

Barycentrics    a^2*(S + 4*SA) + 6*SB*SC : :

X(42582) lies on these lines: {2, 490}, {3, 22644}, {4, 6409}, {5, 371}, {6, 3090}, {140, 6564}, {372, 3628}, {373, 12240}, {381, 5418}, {382, 6496}, {485, 615}, {486, 5055}, {491, 23311}, {546, 6200}, {547, 7583}, {549, 35820}, {550, 35786}, {631, 23251}, {632, 6396}, {640, 7867}, {1151, 3091}, {1327, 15694}, {1587, 5067}, {1588, 3316}, {2045, 42241}, {2046, 42239}, {2066, 7173}, {2067, 3614}, {3054, 12968}, {3068, 5056}, {3069, 7486}, {3146, 6411}, {3297, 10589}, {3298, 10588}, {3311, 5079}, {3317, 41950}, {3364, 42191}, {3365, 16966}, {3366, 18585}, {3389, 42192}, {3390, 16967}, {3391, 15765}, {3523, 42264}, {3524, 23253}, {3525, 6410}, {3526, 6456}, {3530, 42267}, {3544, 6425}, {3545, 6429}, {3583, 31499}, {3592, 8972}, {3594, 32786}, {3832, 42263}, {3843, 42260}, {3845, 42266}, {3850, 6484}, {3851, 6407}, {3855, 9541}, {3857, 42225}, {5054, 42261}, {5066, 35787}, {5068, 6459}, {5070, 5420}, {5072, 6221}, {5076, 6451}, {5901, 35788}, {6412, 10303}, {6419, 12812}, {6424, 31415}, {6426, 23267}, {6432, 13941}, {6453, 12811}, {6455, 42275}, {6478, 11737}, {6485, 41992}, {6486, 41991}, {6487, 16239}, {6501, 13951}, {6931, 31473}, {7516, 35776}, {7581, 13847}, {7584, 8960}, {7741, 9646}, {7852, 32490}, {7951, 9661}, {7969, 10175}, {7988, 13893}, {8227, 13911}, {8407, 13882}, {8854, 11548}, {9542, 41965}, {9605, 13711}, {9674, 18424}, {9975, 14561}, {10109, 35823}, {10146, 41970}, {10171, 13883}, {10283, 35842}, {10592, 35768}, {10593, 35808}, {11291, 32459}, {12222, 32812}, {12818, 15700}, {12964, 23332}, {13881, 31463}, {13966, 15699}, {14869, 42226}, {15325, 35800}, {15692, 42414}, {15703, 41952}, {18357, 35763}, {19709, 42417}, {23302, 42240}, {23303, 35740}, {32497, 37342}, {35610, 38034}, {35641, 38042}, {35732, 42095}, {35739, 42214}, {35765, 37942}, {35827, 40685}, {35878, 38229}, {41948, 41949}, {41953, 42522}, {41954, 41964}, {42098, 42282}, {42150, 42243}, {42151, 42245}

X(42582) = {X(6),X(3090)}-harmonic conjugate of X(42583)

X(42583) = GIBERT (-SQRT(3), 3, 4) POINT

Barycentrics    a^2*(S - 4*SA) - 6*SB*SC : :

X(42583) lies on these lines: {2, 489}, {3, 22615}, {4, 6410}, {5, 372}, {6, 3090}, {140, 6565}, {371, 3628}, {373, 12239}, {381, 5420}, {382, 6497}, {485, 5055}, {486, 590}, {492, 23312}, {546, 6396}, {547, 7584}, {549, 35821}, {550, 35787}, {631, 23261}, {632, 6200}, {639, 7867}, {1152, 3091}, {1328, 15694}, {1587, 3317}, {1588, 5067}, {2045, 42240}, {2046, 35740}, {3054, 12963}, {3068, 7486}, {3069, 5056}, {3146, 6412}, {3297, 10588}, {3298, 10589}, {3312, 5079}, {3316, 41949}, {3364, 16966}, {3365, 42193}, {3367, 15765}, {3389, 16967}, {3390, 42194}, {3392, 18585}, {3523, 42263}, {3524, 23263}, {3525, 6409}, {3526, 6455}, {3530, 42266}, {3533, 9541}, {3544, 6426}, {3545, 6430}, {3592, 32785}, {3594, 13941}, {3614, 6502}, {3832, 42264}, {3843, 42261}, {3845, 42267}, {3850, 6485}, {3851, 6408}, {3857, 42226}, {5054, 42260}, {5066, 35786}, {5068, 6460}, {5070, 5418}, {5072, 6398}, {5076, 6452}, {5414, 7173}, {5901, 35789}, {6411, 10303}, {6420, 12812}, {6423, 31415}, {6425, 23273}, {6431, 8972}, {6454, 12811}, {6456, 42276}, {6479, 11737}, {6484, 41992}, {6486, 16239}, {6487, 41991}, {6500, 8976}, {6933, 31473}, {7516, 35777}, {7582, 13846}, {7583, 35018}, {7852, 32491}, {7968, 10175}, {7988, 13947}, {8227, 13973}, {8400, 13934}, {8855, 11548}, {8960, 19116}, {8981, 15699}, {9605, 13834}, {9616, 19872}, {9974, 14561}, {10109, 35822}, {10145, 41969}, {10171, 13936}, {10283, 35843}, {10592, 35769}, {10593, 35809}, {11292, 32459}, {12221, 32813}, {12819, 15700}, {12970, 23332}, {13955, 31472}, {14869, 42225}, {15325, 35801}, {15692, 42413}, {15703, 41951}, {18357, 35762}, {19709, 42418}, {23302, 42239}, {23303, 42241}, {31414, 41954}, {32488, 32807}, {32494, 37343}, {35611, 38034}, {35642, 38042}, {35732, 42098}, {35739, 42281}, {35764, 37942}, {35826, 40685}, {35879, 38229}, {41947, 41950}, {41953, 41963}, {42095, 42282}, {42150, 42242}, {42151, 42244}

X(42583) = {X(6),X(3090)}-harmonic conjugate of X(42582)

X(42584) = GIBERT (2, 3, -5) POINT

Barycentrics    a^2*(2*Sqrt[3]*S - 15*SA) + 18*SB*SC : :

X(42584) lies on these lines: {3, 42134}, {5, 42091}, {6, 15704}, {13, 15690}, {14, 16}, {15, 12103}, {17, 41981}, {20, 11485}, {140, 19106}, {376, 42124}, {382, 42121}, {396, 15691}, {546, 10646}, {547, 42528}, {548, 5318}, {549, 42094}, {550, 5340}, {632, 42106}, {1657, 42117}, {3146, 42115}, {3522, 42128}, {3528, 42132}, {3529, 11486}, {3530, 16808}, {3534, 5335}, {3543, 42129}, {3627, 11481}, {3628, 42102}, {3845, 42089}, {3853, 23303}, {3861, 16967}, {5059, 42126}, {5066, 33416}, {5073, 11489}, {5237, 42101}, {5334, 17800}, {5350, 33417}, {5351, 12102}, {7667, 37776}, {8703, 18582}, {8972, 42213}, {10645, 42165}, {10653, 19710}, {11001, 42130}, {11488, 15696}, {12100, 16966}, {12101, 16242}, {12816, 42500}, {13941, 42211}, {14869, 42114}, {14892, 42501}, {15681, 42119}, {15686, 42090}, {15687, 42095}, {15694, 42472}, {15712, 42098}, {15759, 37832}, {16645, 35404}, {17538, 42116}, {22238, 42112}, {23302, 33923}, {33703, 42125}, {34200, 36969}, {34755, 42164}, {35738, 42193}, {36843, 42104}, {41991, 42493}, {42087, 42158}, {42096, 42151}, {42099, 42148}, {42415, 42420}, {42496, 42529}

X(42585) = GIBERT (-2, 3, -5) POINT

Barycentrics    a^2*(2*Sqrt[3]*S + 15*SA) - 18*SB*SC : :

X(42585) lies on these lines: {3, 42133}, {5, 42090}, {6, 15704}, {13, 15}, {14, 15690}, {16, 12103}, {18, 41981}, {20, 11486}, {140, 19107}, {376, 42121}, {382, 42124}, {395, 15691}, {546, 10645}, {547, 42529}, {548, 5321}, {549, 42093}, {550, 5339}, {632, 42103}, {1657, 42118}, {3146, 42116}, {3522, 42125}, {3528, 42129}, {3529, 11485}, {3530, 16809}, {3534, 5334}, {3543, 42132}, {3627, 11480}, {3628, 42101}, {3845, 42092}, {3853, 23302}, {3861, 16966}, {5059, 42127}, {5066, 33417}, {5073, 11488}, {5238, 42102}, {5335, 17800}, {5349, 33416}, {5352, 12102}, {7667, 37775}, {8703, 18581}, {8972, 42214}, {10646, 42164}, {10654, 19710}, {11001, 42131}, {11489, 15696}, {12100, 16967}, {12101, 16241}, {12817, 42501}, {13941, 42212}, {14869, 42111}, {14892, 42500}, {15681, 42120}, {15686, 42091}, {15687, 42098}, {15694, 42473}, {15712, 42095}, {15759, 37835}, {16644, 35404}, {17538, 42115}, {22236, 42113}, {23303, 33923}, {33703, 42128}, {34200, 36970}, {34754, 42165}, {35738, 42192}, {36836, 42105}, {41991, 42492}, {42088, 42157}, {42097, 42150}, {42100, 42147}, {42416, 42419}, {42497, 42528}

X(42586) = GIBERT (9, 14, -20) POINT

Barycentrics    a^2*(3*Sqrt[3]*S - 20*SA) + 28*SB*SC : :

X(42586) lies on these lines: {3, 10188}, {6, 15683}, {14, 35400}, {30, 5339}, {376, 5318}, {381, 10646}, {382, 41944}, {547, 42091}, {549, 42094}, {3534, 5238}, {3543, 16645}, {3843, 10187}, {3845, 42491}, {3851, 42546}, {5350, 15698}, {10124, 42474}, {11480, 15691}, {11481, 15687}, {11485, 15681}, {11737, 42105}, {12103, 41112}, {14093, 36969}, {14269, 42433}, {15682, 36843}, {15684, 36968}, {15685, 42158}, {15686, 42086}, {15688, 42431}, {15689, 42156}, {15690, 42161}, {15694, 19106}, {15700, 42098}, {15703, 42528}, {15714, 42137}, {15718, 16808}, {17800, 41100}, {19710, 22236}, {22235, 42165}, {34200, 42145}, {35403, 42095}, {35404, 42113}, {35408, 42497}, {41101, 42543}, {41943, 42127}, {42096, 42429}, {42109, 42473}, {42131, 42154}, {42419, 42509}

X(42587) = GIBERT (-9, 14, -20) POINT

Barycentrics    a^2*(3*Sqrt[3]*S + 20*SA) - 28*SB*SC : :

X(42587) lies on these lines: {3, 10187}, {6, 15683}, {13, 35400}, {30, 5340}, {376, 5321}, {381, 10645}, {382, 41943}, {547, 42090}, {549, 42093}, {3534, 5237}, {3543, 16644}, {3843, 10188}, {3845, 42490}, {3851, 42545}, {5349, 15698}, {10124, 42475}, {11480, 15687}, {11481, 15691}, {11486, 15681}, {11737, 42104}, {12103, 41113}, {14093, 36970}, {14269, 42434}, {15682, 36836}, {15684, 36967}, {15685, 42157}, {15686, 42085}, {15688, 42432}, {15689, 42153}, {15690, 42160}, {15694, 19107}, {15700, 42095}, {15703, 42529}, {15714, 42136}, {15718, 16809}, {17800, 41101}, {19710, 22238}, {22237, 42164}, {34200, 42144}, {35403, 42098}, {35404, 42112}, {35408, 42496}, {41100, 42544}, {41944, 42126}, {42097, 42430}, {42108, 42472}, {42130, 42155}, {42420, 42508}

X(42588) = GIBERT (18,13,-10) POINT

Barycentrics    a^2*(3*Sqrt[3]*S - 5*SA) + 13*SB*SC : :

X(42588) lies on these lines: {2, 5318}, {4, 3411}, {6, 15640}, {13, 19708}, {16, 41106}, {17, 15710}, {376, 5352}, {395, 42508}, {396, 15697}, {397, 15683}, {538, 5863}, {549, 5344}, {3524, 41121}, {3528, 33604}, {3534, 5335}, {3543, 5339}, {3545, 12816}, {3830, 37641}, {3839, 42148}, {3845, 42127}, {3855, 41944}, {5054, 42494}, {5055, 5366}, {5066, 42134}, {5071, 42151}, {5334, 33699}, {5340, 10304}, {6221, 36446}, {6398, 36465}, {8703, 11488}, {10653, 15682}, {11001, 34754}, {11486, 12101}, {11489, 36969}, {11542, 15695}, {11812, 42128}, {12817, 42105}, {14226, 36447}, {14241, 36464}, {15690, 42131}, {15698, 36968}, {15701, 42123}, {15702, 42162}, {15708, 42166}, {15715, 42433}, {15719, 18582}, {16242, 42472}, {16962, 17538}, {16963, 42495}, {19106, 41113}, {19711, 42132}, {22238, 42519}, {22513, 35749}, {23006, 36344}, {33603, 40694}, {33610, 37172}, {33703, 41974}, {35409, 42432}, {36445, 42233}, {36463, 42234}, {42087, 42516}

X(42589) = GIBERT (-18,13,-10) POINT

Barycentrics    a^2*(3*Sqrt[3]*S + 5*SA) - 13*SB*SC : :

X(42589) lies on these lines: {2, 5321}, {4, 3412}, {6, 15640}, {14, 19708}, {15, 41106}, {18, 15710}, {376, 5351}, {395, 15697}, {396, 42509}, {398, 15683}, {538, 5862}, {549, 5343}, {3524, 41122}, {3528, 33605}, {3534, 5334}, {3543, 5340}, {3545, 12817}, {3830, 37640}, {3839, 42147}, {3845, 42126}, {3855, 41943}, {5054, 42495}, {5055, 5365}, {5066, 42133}, {5071, 42150}, {5335, 33699}, {5339, 10304}, {6221, 36464}, {6398, 36447}, {8703, 11489}, {10654, 15682}, {11001, 34755}, {11485, 12101}, {11488, 36970}, {11543, 15695}, {11812, 42125}, {12816, 42104}, {14226, 36465}, {14241, 36446}, {15690, 42130}, {15698, 36967}, {15701, 42122}, {15702, 42159}, {15708, 42163}, {15715, 42434}, {15719, 18581}, {16241, 42473}, {16962, 42494}, {16963, 17538}, {19107, 41112}, {19711, 42129}, {22236, 42518}, {22512, 36327}, {23013, 36319}, {33602, 40693}, {33611, 37173}, {33703, 41973}, {35409, 42431}, {36445, 42232}, {36463, 42231}, {42088, 42517}

X(42590) = GIBERT (6,9,17) POINT

Barycentrics    a^2*(2*Sqrt[3]*S + 17*SA) + 18*SB*SC : :

X(42590) lies on these lines: {3, 42134}, {5, 36836}, {6, 42492}, {13, 140}, {15, 12812}, {17, 16239}, {61, 3628}, {395, 10187}, {397, 10124}, {546, 5352}, {547, 41108}, {549, 42162}, {630, 33477}, {632, 11542}, {3090, 42124}, {3091, 42122}, {3412, 42497}, {3525, 42132}, {3530, 37832}, {3544, 42116}, {3627, 42092}, {3845, 42490}, {3850, 16241}, {3857, 11480}, {3859, 36967}, {5067, 22237}, {5079, 42117}, {5238, 12811}, {5344, 15701}, {5349, 14892}, {10109, 42147}, {10303, 42118}, {10645, 12102}, {11539, 42156}, {11737, 42157}, {11812, 16965}, {12108, 33417}, {14869, 18582}, {14891, 42431}, {15022, 42135}, {15699, 42152}, {15704, 42098}, {15713, 42151}, {16772, 35018}, {16962, 42503}, {22236, 42143}, {33413, 35303}, {40694, 42519}, {41983, 42433}

X(42591) = GIBERT (-6,9,17) POINT

Barycentrics    a^2*(2*Sqrt[3]*S - 17*SA) - 18*SB*SC : :

X(42591) lies on these lines: {3, 42133}, {5, 36843}, {6, 42492}, {14, 140}, {16, 12812}, {18, 16239}, {62, 3628}, {396, 10188}, {398, 10124}, {546, 5351}, {547, 41107}, {549, 42159}, {629, 33476}, {632, 11543}, {3090, 42121}, {3091, 42123}, {3411, 42496}, {3525, 42129}, {3530, 37835}, {3544, 42115}, {3627, 42089}, {3845, 42491}, {3850, 16242}, {3857, 11481}, {3859, 36968}, {5067, 22235}, {5079, 42118}, {5237, 12811}, {5343, 15701}, {5350, 14892}, {10109, 42148}, {10303, 42117}, {10646, 12102}, {11539, 42153}, {11737, 42158}, {11812, 16964}, {12108, 33416}, {14869, 18581}, {14891, 42432}, {15022, 42138}, {15699, 42149}, {15704, 42095}, {15713, 42150}, {16773, 35018}, {16963, 42502}, {22238, 42146}, {33412, 35304}, {40693, 42518}, {41983, 42434}

X(42592) = GIBERT (9,12,25) POINT

Barycentrics    a^2*(3*Sqrt[3]*S + 25*SA) + 24*SB*SC : :

X(42592) lies on these lines: {2, 3412}, {3, 36969}, {4, 42515}, {5, 10188}, {13, 14869}, {15, 3090}, {17, 3525}, {61, 42129}, {62, 632}, {140, 41100}, {395, 41992}, {398, 3628}, {546, 5352}, {630, 7828}, {631, 41119}, {1656, 41108}, {3091, 16241}, {3146, 42092}, {3526, 16267}, {3544, 42157}, {3627, 42430}, {3857, 36967}, {5054, 41974}, {5067, 41122}, {5070, 41943}, {5072, 5238}, {5076, 10645}, {5237, 5335}, {5351, 42132}, {5365, 15022}, {7486, 41101}, {10646, 12108}, {12812, 16964}, {12816, 21735}, {15704, 42102}, {15720, 41121}, {16808, 17538}, {23046, 42504}, {41989, 42164}, {42152, 42516}, {42433, 42500}

X(42593) = GIBERT (-9,12,25) POINT

Barycentrics    a^2*(3*Sqrt[3]*S - 25*SA) - 24*SB*SC : :

X(42593) lies on these lines: {2, 3411}, {3, 36970}, {4, 42514}, {5, 10187}, {14, 14869}, {16, 3090}, {18, 3525}, {61, 632}, {62, 42132}, {140, 41101}, {396, 41992}, {397, 3628}, {546, 5351}, {629, 7828}, {631, 41120}, {1656, 41107}, {3091, 16242}, {3146, 42089}, {3526, 16268}, {3544, 42158}, {3627, 42429}, {3857, 36968}, {5054, 41973}, {5067, 41121}, {5070, 41944}, {5072, 5237}, {5076, 10646}, {5238, 5334}, {5352, 42129}, {5366, 15022}, {7486, 41100}, {10645, 12108}, {12812, 16965}, {12817, 21735}, {15704, 42101}, {15720, 41122}, {16809, 17538}, {23046, 42505}, {41989, 42165}, {42149, 42517}, {42434, 42501}

leftri

Gibert points on the cubic K1204: X(42594)-X(42609)

rightri

This preamble and points X(42594)-X(42609) are contributed by Peter Moses, April 13, 2021. See also the preambles just before X(42085), X(42413), and X(42429). See K1204.



X(42594) = GIBERT (3,23,52) POINT

Barycentrics    a^2*(Sqrt[3]*S + 52*SA) + 46*SB*SC : :

X(42594) lies on the cubic K1204 and these lines: {2, 5321}, {13, 10124}, {15, 41984}, {17, 632}, {18, 16239}, {140, 42528}, {549, 42429}, {631, 42474}, {3525, 5366}, {3526, 42151}, {3533, 42491}, {5054, 42106}, {5318, 11539}, {10109, 42430}, {14890, 19106}, {15694, 42086}, {15702, 42586}, {15703, 42101}, {15713, 42110}, {15721, 42102}, {15723, 23302}, {16967, 41971}, {23303, 41943}, {33416, 42496}, {33417, 42493}, {36967, 41985}, {41107, 42492}

X(42595) = GIBERT (-3,23,52) POINT

Barycentrics    a^2*(Sqrt[3]*S - 52*SA) - 46*SB*SC : :

X(42595) lies on the cubic K1204 and these lines: {2, 5318}, {14, 10124}, {16, 41984}, {17, 16239}, {18, 632}, {140, 42529}, {549, 42430}, {631, 42475}, {3525, 5365}, {3526, 42150}, {3533, 42490}, {5054, 42103}, {5321, 11539}, {10109, 42429}, {14890, 19107}, {15694, 42085}, {15702, 42587}, {15703, 42102}, {15713, 42107}, {15721, 42101}, {15723, 23303}, {16966, 41972}, {23302, 41944}, {33416, 42492}, {33417, 42497}, {36968, 41985}, {41108, 42493}

X(42596) = GIBERT (3,10,25) POINT

Barycentrics    a^2*(Sqrt[3]*S + 25*SA) + 20*SB*SC : :

X(42596) lies on the cubic K1204 and these lines: {2, 5238}, {3, 42429}, {5, 42099}, {6, 3411}, {13, 140}, {15, 16239}, {17, 15694}, {18, 632}, {61, 3533}, {62, 11539}, {398, 33606}, {549, 5350}, {630, 36770}, {631, 16966}, {1656, 42434}, {3525, 16242}, {3530, 19106}, {3545, 42515}, {3628, 5349}, {3850, 42430}, {5054, 42158}, {5055, 42587}, {5067, 10645}, {5070, 16809}, {5079, 42529}, {5344, 10303}, {5351, 15702}, {5352, 42500}, {10124, 16962}, {11300, 33414}, {11485, 42499}, {11540, 16267}, {12108, 36969}, {12815, 36782}, {15684, 42543}, {15699, 42432}, {15709, 41100}, {15713, 42166}, {15720, 42528}, {15721, 42161}, {15723, 22236}, {16241, 42153}, {16773, 16960}, {16967, 42490}, {35381, 42533}, {36843, 42505}, {42092, 42489}, {42124, 42435}

X(42596) = {X(6),X(3526)}-harmonic conjugate of X(42597)

X(42597) = GIBERT (-3,10,25) POINT

Barycentrics    a^2*(Sqrt[3]*S - 25*SA) - 20*SB*SC : :

X(42597) lies on the cubic K1204 and these lines: {2, 5237}, {3, 42430}, {5, 42100}, {6, 3411}, {14, 140}, {16, 16239}, {17, 632}, {18, 15694}, {61, 11539}, {62, 3533}, {397, 33607}, {549, 5349}, {631, 16967}, {1656, 42433}, {3525, 16241}, {3530, 19107}, {3545, 42514}, {3628, 5350}, {3850, 42429}, {5054, 42157}, {5055, 42586}, {5067, 10646}, {5070, 16808}, {5079, 42528}, {5343, 10303}, {5351, 42501}, {5352, 15702}, {10124, 16963}, {11299, 33415}, {11310, 36770}, {11486, 42498}, {11540, 16268}, {12108, 36970}, {15684, 42544}, {15699, 42431}, {15709, 41101}, {15713, 42163}, {15720, 42529}, {15721, 42160}, {15723, 22238}, {16242, 42156}, {16772, 16961}, {16966, 42491}, {35381, 42532}, {36836, 42504}, {42089, 42488}, {42121, 42436}

X(42597) = {X(6),X(3526)}-harmonic conjugate of X(42596)

X(42598) = GIBERT (3,3,4) POINT

Barycentrics    a^2*(Sqrt[3]*S + 4*SA) + 6*SB*SC : :

X(42598) lies on the cubic K1204 and these lines: {2, 397}, {3, 5318}, {4, 16644}, {5, 14}, {6, 3090}, {13, 140}, {15, 546}, {16, 632}, {18, 547}, {20, 5350}, {30, 5352}, {62, 3628}, {203, 10592}, {302, 22113}, {376, 42490}, {381, 5349}, {395, 1656}, {548, 36969}, {549, 16965}, {550, 16241}, {590, 42251}, {615, 42253}, {618, 6673}, {624, 7889}, {630, 2482}, {631, 5340}, {633, 33458}, {636, 6669}, {1151, 42218}, {1152, 42220}, {1216, 36978}, {2045, 42252}, {2046, 42250}, {2307, 3614}, {3091, 5321}, {3146, 11480}, {3364, 18762}, {3365, 18538}, {3367, 35730}, {3523, 42155}, {3524, 5344}, {3525, 5335}, {3526, 10653}, {3528, 5366}, {3529, 42094}, {3530, 42158}, {3533, 42491}, {3544, 5334}, {3545, 5339}, {3627, 5238}, {3832, 42154}, {3843, 42150}, {3845, 41943}, {3850, 16964}, {3851, 10654}, {3853, 36967}, {3857, 42117}, {3858, 36970}, {3861, 42432}, {5054, 41119}, {5055, 40694}, {5056, 37640}, {5066, 16962}, {5067, 16645}, {5070, 42149}, {5072, 11485}, {5076, 42106}, {5079, 18581}, {5351, 14869}, {5365, 41106}, {5478, 22892}, {6036, 6115}, {6694, 37351}, {6783, 20416}, {7005, 10593}, {7486, 37641}, {7789, 37178}, {8703, 42431}, {10109, 42503}, {10124, 41100}, {10170, 11624}, {10187, 42436}, {10303, 11481}, {10616, 20429}, {10645, 15704}, {10646, 12108}, {11303, 33413}, {11539, 41107}, {11543, 12812}, {11737, 41108}, {12100, 42433}, {12102, 42122}, {12103, 19106}, {12811, 16809}, {12816, 15686}, {13350, 31705}, {14136, 22847}, {14892, 42435}, {15022, 42095}, {15694, 41112}, {15699, 42489}, {15712, 36968}, {15765, 36469}, {16239, 16242}, {17538, 42134}, {18358, 36757}, {18585, 36453}, {21402, 33517}, {22114, 37786}, {33414, 40334}, {33425, 33447}, {33427, 33446}, {34754, 42135}, {35018, 37835}, {35256, 35738}, {35732, 42262}, {35786, 42280}, {35787, 42281}, {38071, 41101}, {41991, 42530}, {41997, 42001}, {42192, 42273}, {42194, 42270}, {42265, 42282}

X(42598) = {X(6),X(3090)}-harmonic conjugate of X(42599)

X(42599) = GIBERT (-3,3,4) POINT

Barycentrics    a^2*(Sqrt[3]*S - 4*SA) - 6*SB*SC : :

X(42599) lies on the cubic K1204 and these lines: {2, 398}, {3, 5321}, {4, 16645}, {5, 13}, {6, 3090}, {14, 140}, {15, 632}, {16, 546}, {17, 547}, {20, 5349}, {30, 5351}, {61, 3628}, {202, 10592}, {303, 22114}, {376, 42491}, {381, 5350}, {396, 1656}, {548, 36970}, {549, 16964}, {550, 16242}, {590, 42250}, {615, 42252}, {619, 6674}, {623, 7889}, {629, 2482}, {631, 5339}, {634, 33459}, {635, 6670}, {1151, 42217}, {1152, 42219}, {1216, 36980}, {2045, 42251}, {2046, 42253}, {3091, 5318}, {3146, 11481}, {3389, 18762}, {3390, 18538}, {3523, 42154}, {3524, 5343}, {3525, 5334}, {3526, 10654}, {3528, 5365}, {3529, 42093}, {3530, 42157}, {3533, 42490}, {3544, 5335}, {3545, 5340}, {3627, 5237}, {3832, 42155}, {3843, 42151}, {3845, 41944}, {3850, 16965}, {3851, 10653}, {3853, 36968}, {3857, 42118}, {3858, 36969}, {3861, 42431}, {5054, 41120}, {5055, 40693}, {5056, 37641}, {5066, 16963}, {5067, 16644}, {5070, 42152}, {5072, 11486}, {5076, 42103}, {5079, 18582}, {5352, 14869}, {5366, 41106}, {5479, 22848}, {6036, 6114}, {6695, 37352}, {6782, 20415}, {7006, 10593}, {7127, 7173}, {7486, 37640}, {7789, 37177}, {8703, 42432}, {10109, 42502}, {10124, 41101}, {10170, 11626}, {10188, 42435}, {10303, 11480}, {10617, 20428}, {10645, 12108}, {10646, 15704}, {11304, 33412}, {11539, 41108}, {11542, 12812}, {11737, 41107}, {12100, 42434}, {12102, 42123}, {12103, 19107}, {12811, 16808}, {12817, 15686}, {13349, 31706}, {14137, 22893}, {14892, 42436}, {15022, 42098}, {15694, 41113}, {15699, 42488}, {15712, 36967}, {15765, 36470}, {16239, 16241}, {17538, 42133}, {18358, 36758}, {18585, 36452}, {21401, 33518}, {22113, 37785}, {31694, 36769}, {33415, 40335}, {33424, 33444}, {33426, 33445}, {34755, 42138}, {35018, 37832}, {35255, 35738}, {35732, 42265}, {35786, 42281}, {35787, 42280}, {38071, 41100}, {41991, 42531}, {41998, 42002}, {42191, 42273}, {42193, 42270}, {42262, 42282}

X(42599) = {X(6),X(3090)}-harmonic conjugate of X(42598)

X(42600) = GIBERT (SQRT(3),7,17) POINT

Barycentrics    a^2*(S + 17*SA) + 14*SB*SC : :

X(42600) lies on the cubic K1204 and these lines: {2, 1328}, {6, 10124}, {140, 6410}, {485, 3525}, {486, 41949}, {547, 42275}, {549, 42276}, {590, 3312}, {631, 42267}, {632, 3592}, {1656, 42271}, {3069, 3533}, {3628, 42263}, {5054, 42277}, {5067, 22615}, {5070, 42260}, {6396, 15709}, {6411, 15699}, {6412, 15713}, {6429, 9680}, {6438, 8253}, {6440, 11540}, {6446, 13665}, {6487, 10576}, {6519, 41953}, {6564, 15702}, {9540, 10194}, {10147, 42262}, {10303, 42261}, {11812, 42264}, {15701, 42284}, {15720, 22644}, {15723, 18510}, {41950, 41960}

X(42601) = GIBERT (-SQRT(3),7,17) POINT

Barycentrics    a^2*(S - 17*SA) - 14*SB*SC : :

X(42601) lies on the cubic K1204 and these lines: {2, 1327}, {6, 10124}, {140, 6409}, {485, 41950}, {486, 3525}, {547, 42276}, {549, 42275}, {615, 3311}, {631, 42266}, {632, 3594}, {1656, 42272}, {3068, 3533}, {3628, 42264}, {5054, 42274}, {5067, 22644}, {5070, 42261}, {6200, 15709}, {6411, 15713}, {6412, 15699}, {6430, 16239}, {6437, 8252}, {6439, 11540}, {6445, 13785}, {6486, 9681}, {6522, 41954}, {6565, 15702}, {9542, 35823}, {10148, 42265}, {10195, 13935}, {10303, 42260}, {11812, 42263}, {13665, 17851}, {15701, 42283}, {15720, 22615}, {15723, 18512}, {41949, 41959}

X(42602) = GIBERT (3*SQRT(3),5,7) POINT

Barycentrics    a^2*(3*S + 7*SA) + 10*SB*SC : :

X(42602) lies on the cubic K1204 and these lines: {2, 372}, {3, 1327}, {4, 9680}, {5, 3592}, {6, 547}, {17, 36468}, {18, 36450}, {30, 5418}, {371, 1328}, {376, 6564}, {381, 590}, {486, 5055}, {546, 9681}, {549, 6412}, {615, 15703}, {639, 32811}, {1131, 15708}, {1151, 3845}, {1152, 11539}, {1504, 19099}, {1506, 19105}, {1656, 6428}, {3068, 5071}, {3070, 5054}, {3071, 19709}, {3090, 8960}, {3091, 35812}, {3241, 35788}, {3524, 31412}, {3526, 6522}, {3533, 6454}, {3534, 22644}, {3543, 6200}, {3582, 31472}, {3590, 7486}, {3828, 35774}, {3830, 42260}, {3832, 6453}, {3839, 9540}, {3843, 41963}, {3850, 6425}, {3851, 31454}, {5056, 6419}, {5062, 22541}, {5066, 8981}, {5067, 6420}, {5309, 13711}, {6281, 22616}, {6396, 15702}, {6398, 15723}, {6410, 11812}, {6411, 15686}, {6421, 19100}, {6426, 16239}, {6432, 42578}, {6446, 13665}, {6449, 38335}, {6450, 42418}, {6459, 41106}, {6460, 14241}, {6469, 10124}, {6486, 42413}, {6565, 8972}, {7583, 13847}, {8703, 23251}, {9646, 11238}, {9661, 11237}, {9974, 22165}, {10109, 13925}, {10304, 35820}, {10385, 35802}, {10577, 13886}, {11050, 35790}, {11737, 42215}, {13893, 38021}, {13902, 38074}, {13903, 42270}, {13951, 41948}, {13973, 38083}, {14269, 42258}, {14891, 42226}, {14893, 42263}, {15681, 42284}, {15682, 35786}, {15687, 35255}, {15689, 42272}, {15692, 23249}, {15693, 42259}, {15719, 23269}, {15765, 42151}, {16267, 36467}, {16268, 36449}, {18510, 41951}, {18512, 32790}, {18581, 36439}, {18582, 36457}, {18585, 42150}, {19708, 42267}, {21356, 35840}, {23261, 38071}, {31145, 35810}, {34200, 42264}, {34551, 42491}, {34552, 42490}, {34559, 42149}, {34562, 42152}, {34627, 35763}, {35382, 41953}, {35815, 42561}, {35821, 41099}, {35878, 41135}, {36436, 42142}, {36437, 36968}, {36438, 42132}, {36445, 42243}, {36446, 42230}, {36454, 42139}, {36455, 36967}, {36456, 42129}, {36463, 42245}, {36464, 42228}, {41950, 41968}

X(42602) = {X(6),X(547)}-harmonic conjugate of X(42603)

X(42603) = GIBERT (-3*SQRT(3),5,7) POINT

Barycentrics    a^2*(3*S - 7*SA) - 10*SB*SC : :

X(42603) lies on the cubic K1204 and these lines: {2, 371}, {3, 1328}, {5, 3594}, {6, 547}, {17, 36449}, {18, 36467}, {30, 5420}, {99, 32807}, {140, 9681}, {372, 1327}, {376, 6565}, {381, 615}, {485, 5055}, {546, 17852}, {549, 6411}, {590, 15703}, {632, 9680}, {640, 32810}, {1132, 15708}, {1151, 11539}, {1152, 3845}, {1505, 19100}, {1506, 19102}, {1656, 6427}, {3069, 5071}, {3070, 19709}, {3071, 5054}, {3090, 19053}, {3091, 35813}, {3241, 35789}, {3524, 42260}, {3526, 6519}, {3533, 6453}, {3534, 22615}, {3543, 6396}, {3591, 7486}, {3828, 35775}, {3830, 42261}, {3832, 6454}, {3839, 13935}, {3843, 41964}, {3850, 6426}, {5056, 6420}, {5058, 19101}, {5066, 13966}, {5067, 6419}, {5309, 13834}, {6200, 15702}, {6221, 15723}, {6278, 22645}, {6409, 11812}, {6412, 15686}, {6422, 19099}, {6425, 16239}, {6431, 42579}, {6445, 13785}, {6449, 42417}, {6450, 38335}, {6459, 14226}, {6460, 41106}, {6468, 10124}, {6487, 42414}, {6564, 13941}, {7584, 13846}, {8703, 23261}, {8976, 41947}, {9541, 15721}, {9975, 22165}, {10109, 13993}, {10304, 35821}, {10385, 35803}, {10576, 13939}, {11050, 35791}, {11737, 42216}, {13911, 38083}, {13947, 38021}, {13959, 38074}, {13961, 42273}, {14269, 42259}, {14891, 42225}, {14893, 42264}, {15681, 42283}, {15682, 35787}, {15687, 35256}, {15689, 42271}, {15692, 23259}, {15693, 42258}, {15719, 23275}, {15765, 42150}, {16267, 36450}, {16268, 36468}, {18510, 32789}, {18512, 41952}, {18581, 36457}, {18582, 36439}, {18585, 42151}, {19708, 42266}, {21356, 35841}, {23251, 38071}, {31145, 35811}, {31412, 35814}, {34200, 42263}, {34551, 42490}, {34552, 42491}, {34559, 42152}, {34562, 42149}, {34627, 35762}, {35382, 41954}, {35820, 41099}, {35879, 41135}, {36436, 42139}, {36437, 36967}, {36438, 42129}, {36445, 42244}, {36447, 42227}, {36454, 42142}, {36455, 36968}, {36456, 42132}, {36463, 42242}, {36465, 42229}, {41949, 41967}

X(42603) = {X(6),X(547)}-harmonic conjugate of X(42602)

X(42604) = GIBERT (16*SQRT(3),25,26) POINT

Barycentrics    a^2*(8*S + 13*SA) + 25*SB*SC : :

X(42604) lies on the cubic K1204 and these lines: {2, 6398}, {3, 42540}, {4, 9691}, {371, 3832}, {485, 15022}, {590, 3146}, {1131, 6410}, {3316, 5059}, {3522, 35820}, {3543, 6445}, {3590, 42273}, {3854, 42215}, {5056, 6418}, {5068, 7585}, {6199, 42539}, {6564, 15683}, {8972, 41945}, {10146, 16239}, {15705, 23249}, {15717, 31412}, {32786, 41952}, {35731, 42189}, {41970, 42570}

X(42605) = GIBERT (-16*SQRT(3),25,26) POINT

Barycentrics    a^2*(8*S - 13*SA) - 25*SB*SC : :

X(42605) lies on the cubic K1204 and these lines: {2, 6221}, {3, 42539}, {372, 3832}, {486, 15022}, {615, 3146}, {1132, 6409}, {3317, 5059}, {3522, 35821}, {3543, 6446}, {3591, 42270}, {3854, 42216}, {5056, 6417}, {5068, 7586}, {6395, 42540}, {6565, 15683}, {10145, 16239}, {13941, 41946}, {15705, 23259}, {15717, 42561}, {31414, 42579}, {32785, 41951}, {41969, 42571}

X(42606) = GIBERT (27*SQRT(3),35,52) POINT

Barycentrics    a^2*(27*S + 52*SA) + 70*SB*SC : :

X(42606) lies on the cubic K1204 and these lines: {2, 3590}, {371, 5066}, {590, 3830}, {3070, 15693}, {3316, 6409}, {3543, 6488}, {3845, 6453}, {3860, 35812}, {6396, 11812}, {6411, 15697}, {6437, 42417}, {6522, 10195}, {8703, 42267}, {8976, 41947}, {10148, 15702}, {12100, 41952}, {12101, 41963}, {13846, 23273}, {15709, 17852}, {31454, 41106}, {32785, 41950}, {35822, 41948}, {41099, 41945}, {41967, 42266}, {42572, 42574}

X(42607) = GIBERT (-27*SQRT(3),35,52) POINT

Barycentrics    a^2*(27*S - 52*SA) - 70*SB*SC : :

X(42607) lies on the cubic K1204 and these lines: {2, 3591}, {372, 5066}, {615, 3830}, {3071, 15693}, {3317, 6410}, {3543, 6489}, {3845, 6454}, {3860, 35813}, {6200, 11812}, {6412, 15697}, {6438, 42418}, {6519, 10194}, {8703, 42266}, {10147, 15702}, {12100, 41951}, {12101, 41964}, {13847, 23267}, {13951, 41948}, {32786, 41949}, {35823, 41947}, {41099, 41946}, {41968, 42267}, {42573, 42575}

X(42608) = GIBERT (27*SQRT(3),35,25) POINT

Barycentrics    a^2*(27*S + 25*SA) + 70*SB*SC : :

X(42608) lies on the cubic K1204 and these lines: {2, 6454}, {6, 5066}, {30, 10147}, {485, 3830}, {1132, 35771}, {1327, 6200}, {3534, 41952}, {3592, 3845}, {5418, 8703}, {6410, 11812}, {6446, 42418}, {6453, 15682}, {6489, 11539}, {6560, 15693}, {9681, 33699}, {10124, 10148}, {10195, 15719}, {13939, 35822}, {14241, 42277}, {15640, 23253}, {15698, 23269}, {23275, 31412}, {35255, 42576}, {42274, 42572}

X(42609) = GIBERT (-27*SQRT(3),35,25) POINT

Barycentrics    a^2*(27*S - 25*SA) - 70*SB*SC : :

X(42609) lies on the cubic K1204 and these lines: {2, 6453}, {6, 5066}, {30, 10148}, {486, 3830}, {1131, 35770}, {1328, 6396}, {3534, 41951}, {3594, 3845}, {5420, 8703}, {6409, 11812}, {6445, 42417}, {6454, 15682}, {6488, 11539}, {6561, 15693}, {9681, 11540}, {10124, 10147}, {10194, 15719}, {13886, 35823}, {14226, 42274}, {15640, 23263}, {15698, 23275}, {23269, 35786}, {35256, 42577}, {42277, 42573}

X(42610) = GIBERT (3,8,14) POINT

Barycentrics    a^2*(Sqrt[3]*S + 14*SA) + 16*SB*SC : :

X(42610) lies on the cubic K1205 and these lines: {2, 397}, {5, 11480}, {6, 5070}, {14, 1656}, {20, 42472}, {61, 15703}, {140, 42161}, {382, 33417}, {546, 42474}, {547, 5339}, {548, 42114}, {631, 42088}, {632, 5340}, {3090, 5343}, {3146, 42500}, {3412, 42129}, {3525, 42155}, {3526, 11481}, {3528, 42110}, {3530, 42094}, {3533, 42166}, {3628, 16644}, {3855, 42096}, {3856, 42090}, {5054, 42433}, {5055, 36836}, {5056, 42154}, {5067, 23302}, {5079, 16241}, {5352, 19709}, {6669, 11310}, {6673, 11312}, {7486, 16772}, {10109, 42160}, {10124, 42151}, {11539, 42162}, {12812, 42150}, {15699, 42152}, {15701, 42431}, {15702, 42165}, {15717, 42097}, {16239, 18582}, {21734, 42102}, {36843, 37832}, {41983, 42586}, {41984, 42510}, {42159, 42475}

X(42611) = GIBERT (-3,8,14) POINT

Barycentrics    a^2*(Sqrt[3]*S - 14*SA) - 16*SB*SC : :

X(42611) lies on the cubic K1205 and these lines: {2, 398}, {5, 11481}, {6, 5070}, {13, 1656}, {20, 42473}, {62, 15703}, {140, 42160}, {382, 33416}, {546, 42475}, {547, 5340}, {548, 42111}, {631, 42087}, {632, 5339}, {3090, 5344}, {3146, 42501}, {3411, 42132}, {3525, 42154}, {3526, 11480}, {3528, 42107}, {3530, 42093}, {3533, 42163}, {3628, 16645}, {3855, 42097}, {3856, 42091}, {5054, 42434}, {5055, 36843}, {5056, 42155}, {5067, 23303}, {5079, 16242}, {5351, 19709}, {6670, 11309}, {6674, 11311}, {7486, 16773}, {10109, 42161}, {10124, 42150}, {11539, 42159}, {12812, 42151}, {15699, 42149}, {15701, 42432}, {15702, 42164}, {15717, 42096}, {16239, 18581}, {16644, 42590}, {21734, 42101}, {33415, 36770}, {36836, 37835}, {41983, 42587}, {41984, 42511}, {42162, 42474}

X(42612) = GIBERT (45,12,-1) POINT

Barycentrics    a^2*(15*Sqrt[3]*S - SA) + 24*SB*SC : :

X(42612) lies on the cubic K1205 and these lines: {13, 3544}, {14, 397}, {16, 14869}, {61, 3529}, {62, 5079}, {382, 41107}, {3412, 34200}, {3526, 42518}, {3530, 41943}, {3851, 16268}, {5068, 42521}, {5238, 42123}, {5344, 12820}, {5350, 12821}, {10299, 41100}, {11542, 42499}, {12103, 34754}, {15681, 41974}, {15688, 42508}, {30472, 33465}, {35018, 41121}, {38071, 42503}

X(42613) = GIBERT (-45,12,-1) POINT

Barycentrics    a^2*(15*Sqrt[3]*S + SA) - 24*SB*SC : :

X(42613) lies on the cubic K1205 and these lines: {13, 398}, {14, 3544}, {15, 14869}, {61, 5079}, {62, 3529}, {382, 41108}, {3411, 34200}, {3526, 42519}, {3530, 41944}, {3851, 16267}, {5068, 42520}, {5237, 42122}, {5343, 12821}, {5349, 12820}, {10299, 41101}, {11543, 42498}, {12103, 34755}, {15681, 41973}, {15688, 42509}, {30471, 33464}, {35018, 41122}, {38071, 42502}

leftri

Central angle points: X(42614)-X(42621)

rightri

This preamble and points X(42614)-X(42621) are contributed by Clark Kimberling and Peter Moses, April 15, 2021.

Suppose the P is a point in the plane of a triangle ABC. Let A' = angle BPC, B' = angle CPA, C' = angle APB, and assume that A' = t*A + u*(B + C) for some real numbers t and u. Since B + C = π - A, the angle A' is given by

A' = A'(t) = t*(3A - π)/2 + π - A, and B' and C' are determined cyclically, and the corresponding point P = P(t) is given by

P(t)= 1/(cot(A) + cot(A - t*(3*A - π)/2)) : : ,

so that P(t) is a major center, here named the t-central angle point. Let L denote the locus of P(t) as t traverses the real number line, and note that P(2 - t) = isogonal conjugate of P(t), so that if a point X is on L, then the isogonal conjugate of X is also on L. The appearance of (t,i) in the following list means P = X(i) is the point for which A'(t) = angle BPC, B'(t) = angle CPA, C'(t) = angle APB. The list is presented in isogonal conjugate pairs:

(-2,5964); (4,5963)
(-1,41622); (3,42621)
(-2/3,42619; (8/3,42620)
(0,4); (2,3)
(1/3,42615); (5/3,42616)
(1/2,42618); (3/2,42614)
(2/3,13); (4/3,15)
(1,1); (1,1)



X(42614) = (3/2)-CENTRAL ANGLE POINT

Barycentrics    1/(Cot[A] + Cot[A - 3*(3*A - Pi)/4]) : :

X(42614) is the point P for which the central angles are given by
BPC = (5A+ π)/4, CPA = (5B + π)/4, APB = (5C + π)/4.

X(42614) lies on these lines: {3, 10231}, {36, 266}, {56, 1130}, {10215, 12523}

X(42614) = isogonal conjugate of X(42617)
X(42614) = circumcircle-inverse of X(10231)

X(42615) = (1/3)-CENTRAL ANGLE POINT

Barycentrics    1/(Cot[A] + Cot[A + (-3*A + Pi)/6]) : :

X(42615) is the point P for which the central angles are given by
BPC = (-3A+ π)/6, CPA = (-3B + π)/6, APB = (-3C + π)/6.

X(42615) lies on this line: {7951, 10651}

X(42615) = isogonal conjugate of X(42616)

X(42616) = (5/3)-CENTRAL ANGLE POINT

Barycentrics    1/(Cot[A] + Cot[A - 5*(3*A - Pi)/6]) : :

X(42616) is the point P for which the central angles are given by
BPC = 3A/2 + π/6, CPA = 3B/2 + π/6, APB = 3C/2 + π/6.

X(42616) lies on these lines: {3, 39151}, {35, 19551}, {36, 33655}, {993, 7026}, {1324, 19305}, {2153, 6104}, {2161, 32613}, {5010, 11752}, {6187, 39150}, {8715, 36931}

X(42616) = isogonal conjugate of X(42615)
X(42616) = circumcircle-inverse of X(39151)

X(42617) = (1/2)-CENTRAL ANGLE POINT

Barycentrics    1/(Cot[A] + Cot[A + (-3*A + Pi)/4]) : :

X(42617) is the point P for which the central angles are given by
BPC = -A/4 + 3π/4, CPA = -B/4 + 3π/4, APB = -C/4 + 3π/4.

X(42617) lies on these lines: {188, 3814}, {8133, 30370}

X(42617) = isogonal conjugate of X(42614)

X(42618) = (-2/3)-CENTRAL ANGLE POINT

Barycentrics    1/(Cot[A] + Cot[A + (3*A - Pi)/3]) : :

X(42618) is the point P for which the central angles are given by
BPC = -2A + 4π/3, CPA = -2B + 4π/3, APB = -2C + 4π/3.

X(42618) lies on this line: {20429, 36981}

X(42618) = isogonal conjugate of X(42619)

X(42619) = (8/3)-CENTRAL ANGLE POINT

Barycentrics    1/(Cot[A] + Cot[A - 4*(3*A - Pi)/3]) : :

X(42619) is the point P for which the central angles are given by
BPC = 3A - π/3, CPA = 3B - π/3, APB = 3C - π/3.

X(42619) lies on these lines: {3, 11601}, {13, 36249}, {18, 38943}, {2070, 11586}, {6104, 11082}, {7502, 40105}, {8173, 34008}

X(42619) = isogonal conjugate of X(42618)
X(42619) = circumcircle-inverse of X(11601)

X(42620) = (3)-CENTRAL ANGLE POINT

Barycentrics    1/(Cot[A] + Cot[A - 3*(3*A - Pi)/2]) : :

X(42620) is the point P for which the central angles are given by
BPC = (7A - π)/2, CPA = (7B - π)/2, APB = (7C - π)/2.

X(42620) lies on this line: {3, 33599}

X(42620) = isogonal conjugate of X(42621)
X(42620) = circumcircle-inverse of X(33599)

X(42621) = (-1)-CENTRAL ANGLE POINT

Barycentrics    1/(Cot[A] + Cot[A +(3*A - Pi)/2]) : :

X(42621) is the point P for which the central angles are given by
BPC = (-5A + 3π)/2, CPA = (-5B + 3π)/2, APB = (-5C - 3π)/2.

X(42621) lies on this line: (pending)

X(42621) = isogonal conjugate of X(42620)

X(42622) = DAO-LOZADA TANGENTIAL PERSPECTOR OF X(1)

Barycentrics    a*sin(A/2)*(1+sin(A/2)) : :

This introduction and centers X(46622)-X(42624) were contributed by César E. Lozada, April 16, 2021.

Let ABC be an acute triangle with circumcircle Ω and P a finite point not on Ω. Denote as {{a'}}, {{b'}}, {{c'}} the circles {{B, C, P}}, {{C, A, P}}, {{A, B, P}}, respectively. Also, denote {{a"}} the circle internally tangent to Ω and externally tangent to {{b'}} and {{c'}} and let A" be its center. Define {{b"}}, {{c"}}, B", C" cyclically. Let Ta, Tb, Tc be the touchpoints of Ω and {{a"}}, {{b"}} and {{c"}}, respectively. Then the lines ATa, BTb, CTc concur at a point Z'(P). (Dao Thanh Oai, April 10, 2021)

If P = u : v : w (exact trilinears), then Z'(P) = S*u*ρ(A)+a*R*(u^2-v*w*cos(A)+w*u*cos(B)+u*v*cos(C)) : : , where ρ(A) is the radius of {{a'}}. Z'(P) is named here the Dao-Lozada tangential perspector of P.

The appearance of (i,j) in the following list means that Z'(X(i))=X(j): (1, 42622), (3, 55), (4, 25), (13, 42623), (14, 42624), (15, 6)

Dao Thanh Oai also conjectured that triangles ABC and A"B"C" are perspective with perspector Z"(P). Although this conjecture has not been proved yet, the appearance of (i,j) in the following list means that Z"(X(i))=X(j): (1, 1130), (3, 35), (4, 4), (15, 61).

X(42622) lies on these lines: {1, 20183}, {3, 1130}, {55, 259}, {56, 266}, {57, 13444}, {188, 7587}, {999, 10231}

X(42622) = isogonal conjugate of X(7048)
X(42622) = anticomplement of the complementary conjugate of X(236)
X(42622) = X(266)-Ceva conjugate of-X(6)
X(42622) = barycentric product X(i)*X(j) for these {i, j}: {1, 173}, {6, 7057}, {55, 18886}, {236, 266}, {259, 2089}
X(42622) = barycentric quotient X(i)/X(j) for these (i, j): (31, 258), (56, 21456), (173, 75)
X(42622) = trilinear product X(i)*X(j) for these {i, j}: {6, 173}, {31, 7057}, {41, 18886}
X(42622) = trilinear quotient X(i)/X(j) for these (i, j): (6, 258), (57, 21456), (173, 2), (236, 556), (259, 7028), (266, 1488)
X(42622) = intersection, other than A,B,C, of conics {{A, B, C, X(6), X(259)}} and {{A, B, C, X(173), X(18888)}}
X(42622) = pole of the trilinear polar of X(266) with respect to circumcircle
X(42622) = crosssum of X(i) and X(j) for these (i, j): {1, 20183}, {188, 7028}
X(42622) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 258}, {9, 21456}, {174, 7028}, {188, 1488}
X(42622) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 258), (56, 21456), (173, 75)

X(42623) = DAO-LOZADA TANGENTIAL PERSPECTOR OF X(13)

Barycentrics    (SB+SC)*(SQRT(3)*SB+S)*(SQRT(3)*SC+S)*(SA-SQRT(3)*S-2*b*c) : :

X(42623) lies on these lines: {6, 2151}, {36, 3179}, {55, 199}, {56, 2306}, {396, 10648}, {999, 39153}, {2153, 11142}, {21310, 39151}

X(42623) = barycentric product X(i)*X(j) for these {i, j}: {1, 3179}, {13, 202}, {79, 5357}, {1251, 37773}
X(42623) = barycentric quotient X(202)/X(298)
X(42623) = trilinear product X(i)*X(j) for these {i, j}: {6, 3179}, {36, 11072}, {202, 2153}, {1251, 19373}
X(42623) = trilinear quotient X(i)/X(j) for these (i, j): (1251, 7026), (2151, 7006), (2153, 14358)
X(42623) = intersection, other than A,B,C, of conics {{A, B, C, X(6), X(5240)}} and {{A, B, C, X(36), X(56)}}
X(42623) = pole of the trilinear polar of X(2153) with respect to circumcircle
X(42623) = X(2153)-Ceva conjugate of-X(6)
X(42623) = X(i)-isoconjugate-of-X(j) for these {i, j}: {319, 11073}, {1082, 7026}
X(42623) = X(202)-reciprocal conjugate of-X(298)

X(42624) = DAO-LOZADA TANGENTIAL PERSPECTOR OF X(14)

Barycentrics    (SB+SC)*(SQRT(3)*SB-S)*(SQRT(3)*SC-S)*(SA+SQRT(3)*S+2*b*c) : :

X(42624) lies on these lines: {3, 39150}, {35, 7150}, {45, 55}, {56, 2306}, {559, 7202}, {759, 14359}, {958, 7043}, {2154, 11141}, {2174, 10638}, {3913, 36930}, {7005, 17104}

X(42624) = barycentric product X(i)*X(j) for these {i, j}: {1, 7150}, {14, 7005}, {16, 14359}, {80, 5357}, {559, 7126}
X(42624) = barycentric quotient X(31)/X(41225)
X(42624) = trilinear product X(i)*X(j) for these {i, j}: {6, 7150}, {35, 11072}, {2152, 14359}, {2154, 7005}, {2161, 5357}
X(42624) = trilinear quotient X(i)/X(j) for these (i, j): (6, 41225), (2152, 203), (2174, 5353)
X(42624) = intersection, other than A,B,C, of conics {{A, B, C, X(6), X(2154)}} and {{A, B, C, X(16), X(3285)}}
X(42624) = X(2152)-cross conjugate of-X(6)
X(42624) = X(i)-isoconjugate-of-X(j) for these {i, j}: {320, 11073}, {554, 5239}
X(42624) = X(31)-reciprocal conjugate of-X(41225)

leftri

Gibert points on the cubic K1191 (Evans 5th cubic): X(42625)-X(42648)

rightri

This preamble and points X(42625)-X(42648) are contributed by Peter Moses, April 16, 2021. See K1191 and the preambles just before X(42085), X(42413), and X(42429).



X(42625) = GIBERT (3,2,-8) POINT

Barycentrics    a^2*(Sqrt[3]*S - 8*SA) + 4*SB*SC : :

X(42625) lies on the cubic K1191 and these lines: {2, 42088}, {3, 13}, {4, 42491}, {6, 376}, {14, 15681}, {15, 15688}, {16, 3534}, {18, 17800}, {20, 395}, {30, 11481}, {62, 15696}, {381, 10646}, {382, 5351}, {396, 10304}, {397, 3528}, {398, 17538}, {547, 42145}, {548, 22236}, {549, 42086}, {550, 10654}, {599, 616}, {617, 40341}, {618, 11296}, {1657, 5237}, {3522, 36836}, {3523, 42165}, {3524, 5318}, {3525, 5350}, {3526, 42431}, {3529, 16773}, {3530, 42161}, {3543, 23303}, {3763, 11300}, {3830, 16242}, {3839, 42109}, {3845, 42089}, {3850, 42611}, {5054, 36969}, {5055, 19106}, {5059, 42163}, {5066, 42105}, {5071, 42102}, {5076, 42489}, {5321, 11001}, {5335, 19708}, {5859, 36326}, {6411, 36457}, {6412, 36439}, {8252, 36455}, {8253, 36437}, {8703, 10653}, {10124, 42114}, {10299, 42598}, {10645, 14093}, {11134, 37480}, {11485, 15695}, {11486, 15689}, {11489, 15683}, {11539, 42137}, {11543, 19710}, {11812, 42138}, {12100, 18582}, {12103, 40694}, {13961, 35739}, {14269, 16967}, {14869, 42610}, {14893, 42111}, {15640, 42139}, {15684, 16809}, {15685, 19107}, {15686, 42085}, {15687, 42113}, {15690, 42090}, {15691, 42117}, {15692, 23302}, {15693, 37832}, {15694, 16808}, {15697, 42119}, {15699, 42106}, {15700, 42128}, {15701, 16966}, {15702, 42134}, {15704, 42149}, {15706, 42132}, {15707, 33417}, {15708, 42142}, {15709, 42594}, {15711, 41119}, {15712, 42162}, {15716, 41121}, {15717, 42166}, {15759, 41112}, {16268, 42126}, {16772, 21735}, {16963, 42099}, {17504, 42092}, {19709, 33416}, {20791, 36978}, {33699, 42103}, {33703, 42599}, {33923, 40693}, {34200, 42118}, {35404, 42143}, {37641, 42087}, {41120, 42136}, {41944, 42125}, {42108, 42515}, {42144, 42497}, {42169, 42218}, {42170, 42220}

X(42625) = {X(6),X(376)}-harmonic conjugate of X(42626)

X(42626) = GIBERT (3,-2,8) POINT

Barycentrics    a^2*(Sqrt[3]*S + 8*SA) - 4*SB*SC : :

X(42626) lies on the cubic K1191 and these lines: {2, 42087}, {3, 14}, {4, 42490}, {6, 376}, {13, 15681}, {15, 3534}, {16, 15688}, {17, 17800}, {20, 396}, {30, 11480}, {61, 15696}, {381, 10645}, {382, 5352}, {395, 10304}, {397, 17538}, {398, 3528}, {547, 42144}, {548, 22238}, {549, 42085}, {550, 10653}, {599, 617}, {616, 40341}, {619, 11295}, {1657, 5238}, {3522, 36843}, {3523, 42164}, {3524, 5321}, {3525, 5349}, {3526, 42432}, {3529, 16772}, {3530, 42160}, {3543, 23302}, {3763, 11299}, {3830, 16241}, {3839, 42108}, {3845, 42092}, {3850, 42610}, {5054, 36970}, {5055, 19107}, {5059, 42166}, {5066, 42104}, {5071, 42101}, {5076, 42488}, {5318, 11001}, {5334, 19708}, {5858, 36324}, {6411, 36439}, {6412, 36457}, {8252, 36437}, {8253, 36455}, {8703, 10654}, {10124, 42111}, {10299, 42599}, {10646, 14093}, {11137, 37480}, {11485, 15689}, {11486, 15695}, {11488, 15683}, {11539, 42136}, {11542, 19710}, {11812, 42135}, {12100, 18581}, {12103, 40693}, {14269, 16966}, {14869, 42611}, {14893, 42114}, {15640, 42142}, {15684, 16808}, {15685, 19106}, {15686, 42086}, {15687, 42112}, {15690, 42091}, {15691, 42118}, {15692, 23303}, {15693, 37835}, {15694, 16809}, {15697, 42120}, {15699, 42103}, {15700, 42125}, {15701, 16967}, {15702, 42133}, {15704, 42152}, {15706, 42129}, {15707, 33416}, {15708, 42139}, {15709, 42595}, {15711, 41120}, {15712, 42159}, {15716, 41122}, {15717, 42163}, {15759, 41113}, {16267, 42127}, {16773, 21735}, {16962, 42100}, {17504, 42089}, {19709, 33417}, {20791, 36980}, {33699, 42106}, {33703, 42598}, {33923, 40694}, {34200, 42117}, {35404, 42146}, {37640, 42088}, {41119, 42137}, {41943, 42128}, {42109, 42514}, {42145, 42496}, {42167, 42217}, {42168, 42219}

X(42626) = {X(6),X(376)}-harmonic conjugate of X(42625)

X(42627) = GIBERT (4,3,5) POINT

Barycentrics    a^2*(4*Sqrt[3]*S + 15*SA) + 18*SB*SC : :

X(42627) lies on the cubic K1191 and these lines: {2, 42492}, {5, 5334}, {6, 3628}, {13, 12100}, {15, 546}, {16, 17}, {30, 11480}, {61, 12812}, {62, 42590}, {396, 547}, {548, 5318}, {549, 5335}, {550, 5366}, {590, 34562}, {615, 34559}, {632, 11486}, {3411, 16960}, {3530, 42092}, {3627, 42116}, {3845, 42119}, {3850, 42098}, {3853, 16772}, {3856, 42093}, {3857, 42133}, {3858, 42126}, {3859, 42147}, {3860, 42154}, {3861, 42085}, {5066, 5321}, {5238, 42102}, {5352, 42109}, {6676, 37776}, {8703, 42127}, {10109, 41120}, {10124, 42089}, {10641, 16198}, {10645, 12103}, {10653, 11812}, {10654, 11737}, {11481, 12108}, {12102, 36836}, {12811, 22236}, {14869, 42115}, {14891, 42155}, {14892, 16962}, {14893, 19107}, {15687, 42130}, {15690, 41121}, {15691, 36969}, {15699, 37640}, {15704, 42134}, {15712, 42120}, {15720, 22235}, {15759, 41119}, {16239, 40693}, {16241, 34200}, {16267, 33416}, {18538, 42193}, {18581, 35018}, {18762, 42191}, {33923, 42086}, {34754, 42107}, {35738, 42224}, {38071, 42415}, {41107, 42500}, {41113, 42474}, {41989, 42159}, {42091, 42490}, {42145, 42162}

X(42627) = {X(6),X(3628)}-harmonic conjugate of X(42628)

X(42628) = GIBERT (-4,3,5) POINT

Barycentrics    a^2*(4*Sqrt[3]*S - 15*SA) - 18*SB*SC : :

X(42628) lies on the cubic K1191 and these lines: {2, 42493}, {5, 5335}, {6, 3628}, {14, 12100}, {15, 18}, {16, 546}, {30, 11481}, {61, 42591}, {62, 12812}, {395, 547}, {548, 5321}, {549, 5334}, {550, 5365}, {590, 34559}, {615, 34562}, {632, 11485}, {3412, 16961}, {3530, 42089}, {3627, 42115}, {3845, 42120}, {3850, 42095}, {3853, 16773}, {3856, 42094}, {3857, 42134}, {3858, 42127}, {3859, 42148}, {3860, 42155}, {3861, 42086}, {5066, 5318}, {5237, 42101}, {5351, 42108}, {6676, 37775}, {8703, 42126}, {10109, 41119}, {10124, 42092}, {10642, 16198}, {10646, 12103}, {10653, 11737}, {10654, 11812}, {11480, 12108}, {12102, 36843}, {12811, 22238}, {14869, 42116}, {14891, 42154}, {14892, 16963}, {14893, 19106}, {15687, 42131}, {15690, 41122}, {15691, 36970}, {15699, 37641}, {15704, 42133}, {15712, 42119}, {15720, 22237}, {15759, 41120}, {16239, 40694}, {16242, 34200}, {16268, 33417}, {18538, 42194}, {18582, 35018}, {18762, 42192}, {33923, 42085}, {34755, 42110}, {35738, 42221}, {38071, 42416}, {41108, 42501}, {41112, 42475}, {41989, 42162}, {42090, 42491}, {42144, 42159}

X(42628) = {X(6),X(3628)}-harmonic conjugate of X(42627)

X(42629) = GIBERT (5,6,-3) POINT

Barycentrics    a^2*(5*Sqrt[3]*S - 9*SA) + 36*SB*SC : :

X(42629) lies on the cubic K1191 and these lines: {2, 10646}, {4, 16961}, {6, 382}, {13, 15681}, {14, 12821}, {15, 3529}, {16, 546}, {17, 550}, {30, 34754}, {61, 42109}, {62, 42105}, {376, 42512}, {381, 12820}, {1657, 16960}, {3364, 42185}, {3365, 42186}, {3412, 42087}, {3528, 18582}, {3530, 33417}, {3544, 5237}, {3830, 42521}, {3851, 16967}, {3855, 42111}, {5079, 11481}, {5334, 41974}, {5335, 42112}, {5340, 42099}, {5344, 42090}, {5350, 35018}, {5351, 42110}, {5366, 42092}, {10299, 42091}, {11488, 42529}, {11542, 42434}, {11543, 42416}, {14269, 16809}, {14869, 42138}, {15640, 42520}, {15688, 16241}, {15707, 42528}, {15720, 16966}, {16644, 42504}, {17504, 37832}, {19710, 33607}, {22844, 33959}, {23302, 34200}, {23303, 38071}, {36967, 42506}, {36992, 39874}, {37640, 42514}, {41100, 42125}, {41101, 42096}, {41107, 42117}, {42098, 42433}, {42108, 42612}, {42160, 42613}, {42166, 42584}, {42192, 42209}, {42194, 42210}, {42283, 42564}, {42284, 42565}, {42533, 42588}

X(42629) = {X(6),X(382)}-harmonic conjugate of X(42630)

X(42630) = GIBERT (5,-6,3) POINT

Barycentrics    a^2*(5*Sqrt[3]*S + 9*SA) - 36*SB*SC : :

X(42630) lies on the cubic K1191 and these lines: {2, 10645}, {4, 16960}, {6, 382}, {13, 12820}, {14, 15681}, {15, 546}, {16, 3529}, {18, 550}, {30, 34755}, {61, 42104}, {62, 42108}, {376, 42513}, {381, 12821}, {1657, 16961}, {3389, 42183}, {3390, 42184}, {3411, 42088}, {3528, 18581}, {3530, 33416}, {3544, 5238}, {3830, 42520}, {3851, 16966}, {3855, 42114}, {5079, 11480}, {5334, 42113}, {5335, 41973}, {5339, 42100}, {5343, 42091}, {5349, 35018}, {5352, 42107}, {5365, 42089}, {6200, 35733}, {10299, 42090}, {11489, 42528}, {11542, 42415}, {11543, 42433}, {14269, 16808}, {14869, 42135}, {15640, 42521}, {15688, 16242}, {15707, 42529}, {15720, 16967}, {16645, 42505}, {17504, 37835}, {19710, 33606}, {22845, 33960}, {23302, 38071}, {23303, 34200}, {35730, 42186}, {36968, 42507}, {36994, 39874}, {37641, 42515}, {41100, 42097}, {41101, 42128}, {41108, 42118}, {42095, 42434}, {42109, 42613}, {42161, 42612}, {42163, 42585}, {42191, 42207}, {42193, 42208}, {42283, 42562}, {42284, 42563}, {42532, 42589}

X(42630) = {X(6),X(382)}-harmonic conjugate of X(42629)

X(42631) = GIBERT (9,4,-19) POINT

Barycentrics    a^2*(3*Sqrt[3]*S - 19*SA) + 8*SB*SC : :

X(42631) lies on the cubic K1191 and these lines: {2, 10646}, {3, 16267}, {6, 15695}, {13, 12100}, {14, 11001}, {15, 8703}, {16, 3534}, {17, 15692}, {18, 30}, {20, 16963}, {61, 15688}, {62, 376}, {381, 5351}, {395, 19710}, {396, 15759}, {398, 15691}, {530, 30471}, {531, 33611}, {549, 42158}, {550, 42613}, {3411, 12103}, {3412, 21735}, {3522, 42520}, {3524, 16965}, {3830, 11481}, {3845, 16242}, {5055, 42431}, {5066, 19106}, {5238, 14093}, {5318, 11812}, {5340, 15700}, {5352, 10304}, {5862, 36329}, {6778, 35750}, {6779, 36383}, {7811, 35932}, {9885, 35752}, {10109, 33416}, {10653, 19708}, {10654, 15697}, {11539, 42165}, {11540, 42594}, {11543, 42430}, {12101, 23303}, {14269, 42489}, {14893, 42580}, {15640, 18581}, {15681, 16268}, {15682, 42100}, {15683, 42149}, {15685, 36970}, {15686, 16964}, {15689, 22238}, {15690, 34755}, {15693, 41121}, {15698, 16241}, {15701, 37832}, {15702, 42161}, {15706, 42156}, {15708, 42162}, {15709, 42581}, {15710, 42152}, {15711, 42118}, {15713, 16966}, {15714, 16772}, {15716, 16644}, {15719, 18582}, {15764, 42259}, {16809, 33699}, {16960, 42504}, {16962, 34200}, {16967, 41099}, {19107, 41120}, {19711, 23302}, {19780, 39593}, {25235, 36318}, {33603, 42544}, {35404, 42599}, {36994, 41027}, {38335, 42586}, {40694, 42589}, {41106, 42089}, {41983, 42598}, {42099, 42507}, {42137, 42501}, {42481, 42521}, {42490, 42518}, {42511, 42529}

X(42631) = {X(6),X(15695)}-harmonic conjugate of X(42632)

X(42632) = GIBERT (9,-4,19) POINT

Barycentrics    a^2*(3*Sqrt[3]*S + 19*SA) - 8*SB*SC : :

X(42632) lies on the cubic K1191 and these lines: {2, 10645}, {3, 16268}, {6, 15695}, {13, 11001}, {14, 12100}, {15, 3534}, {16, 8703}, {17, 30}, {18, 15692}, {20, 16962}, {61, 376}, {62, 15688}, {381, 5352}, {395, 15759}, {396, 19710}, {397, 15691}, {530, 33610}, {531, 30472}, {549, 42157}, {550, 42612}, {3411, 21735}, {3412, 12103}, {3522, 42521}, {3524, 16964}, {3830, 11480}, {3845, 16241}, {5055, 42432}, {5066, 19107}, {5237, 14093}, {5321, 11812}, {5339, 15700}, {5351, 10304}, {5863, 35751}, {6777, 36331}, {6780, 36382}, {7811, 35931}, {9886, 36330}, {10109, 33417}, {10653, 15697}, {10654, 19708}, {11539, 42164}, {11540, 42595}, {11542, 42429}, {12101, 23302}, {14269, 42488}, {14893, 42581}, {15640, 18582}, {15681, 16267}, {15682, 42099}, {15683, 42152}, {15685, 36969}, {15686, 16965}, {15689, 22236}, {15690, 34754}, {15693, 41122}, {15698, 16242}, {15701, 37835}, {15702, 42160}, {15706, 42153}, {15708, 42159}, {15709, 42580}, {15710, 42149}, {15711, 42117}, {15713, 16967}, {15714, 16773}, {15716, 16645}, {15719, 18581}, {15764, 42258}, {16808, 33699}, {16961, 42505}, {16963, 34200}, {16966, 41099}, {19106, 41119}, {19711, 23303}, {19781, 39593}, {25236, 36320}, {33602, 42543}, {35404, 42598}, {36992, 41026}, {38335, 42587}, {40693, 42588}, {41106, 42092}, {41983, 42599}, {42100, 42506}, {42136, 42500}, {42480, 42520}, {42491, 42519}, {42510, 42528}

X(42632) = {X(6),X(15695)}-harmonic conjugate of X(42631)

X(42633) = GIBERT (12,1,5) POINT

Barycentrics    a^2*(4*Sqrt[3]*S + 5*SA) + 2*SB*SC : :

X(42633) lies on the cubic K1191 and these lines: {2, 42493}, {5, 14}, {6, 549}, {13, 12820}, {15, 8703}, {16, 17504}, {18, 42592}, {30, 5335}, {62, 15712}, {140, 37641}, {193, 11301}, {381, 42496}, {395, 11539}, {397, 15704}, {546, 5365}, {547, 11488}, {550, 10653}, {597, 619}, {618, 3629}, {632, 16645}, {3180, 37340}, {3627, 40693}, {3830, 33602}, {3845, 10654}, {3856, 5343}, {3857, 5339}, {3858, 42156}, {3859, 42494}, {3860, 42142}, {5066, 5334}, {5318, 33699}, {5321, 16267}, {6199, 36455}, {6395, 36437}, {6670, 33475}, {6671, 33459}, {10109, 42132}, {10124, 11489}, {10645, 15714}, {11307, 40898}, {11481, 15711}, {11486, 12100}, {11543, 15699}, {11737, 42125}, {12101, 42126}, {12817, 42502}, {13084, 20583}, {14869, 16242}, {14891, 42115}, {14892, 42139}, {14893, 42128}, {15686, 34754}, {15690, 42120}, {15713, 16241}, {16960, 41108}, {18581, 42512}, {18582, 38071}, {19116, 34551}, {19117, 34552}, {19710, 42122}, {23303, 41943}, {33606, 37835}, {34200, 42116}, {35404, 42085}, {36969, 42147}, {36970, 42138}, {41107, 42087}, {41112, 42137}, {41113, 42098}, {41944, 42500}, {42129, 42492}, {42143, 42475}, {42148, 42529}

X(42633) = {X(6),X(549)}-harmonic conjugate of X(42634)

X(42634) = GIBERT (-12,1,5) POINT

Barycentrics    a^2*(4*Sqrt[3]*S - 5*SA) - 2*SB*SC : :

X(42634) lies on the cubic K1191 and these lines: {2, 42492}, {5, 13}, {6, 549}, {14, 12821}, {15, 17504}, {16, 8703}, {17, 42593}, {30, 5334}, {61, 15712}, {140, 37640}, {193, 11302}, {381, 42497}, {396, 11539}, {398, 15704}, {546, 5366}, {547, 11489}, {550, 10654}, {597, 618}, {619, 3629}, {632, 16644}, {3181, 37341}, {3627, 40694}, {3830, 33603}, {3845, 10653}, {3856, 5344}, {3857, 5340}, {3858, 42153}, {3859, 42495}, {3860, 42139}, {5066, 5335}, {5318, 16268}, {5321, 33699}, {6199, 36437}, {6395, 36455}, {6669, 33474}, {6672, 33458}, {10109, 42129}, {10124, 11488}, {10646, 15714}, {11308, 40899}, {11480, 15711}, {11485, 12100}, {11542, 15699}, {11737, 42128}, {12101, 42127}, {12816, 42503}, {13083, 20583}, {14869, 16241}, {14891, 42116}, {14892, 42142}, {14893, 42125}, {15686, 34755}, {15690, 42119}, {15713, 16242}, {16961, 41107}, {18581, 38071}, {18582, 42513}, {19116, 34552}, {19117, 34551}, {19710, 42123}, {23302, 41944}, {33607, 37832}, {34200, 42115}, {35404, 42086}, {36969, 42135}, {36970, 42148}, {41108, 42088}, {41112, 42095}, {41113, 42136}, {41943, 42501}, {42132, 42493}, {42146, 42474}, {42147, 42528}

X(42634) = {X(6),X(549)}-harmonic conjugate of X(42633)

X(42635) = GIBERT (45,4,23) POINT

Barycentrics    a^2*(15*Sqrt[3]*S + 23*SA) + 8*SB*SC : :

X(42635) lies on the cubic K1191 and these lines: {2, 18}, {6, 15707}, {13, 42140}, {15, 15688}, {16, 17504}, {17, 11737}, {30, 34754}, {62, 15700}, {381, 42518}, {396, 38071}, {546, 3412}, {549, 42520}, {550, 42612}, {3523, 42521}, {3524, 42517}, {3528, 41100}, {3529, 42511}, {3545, 42516}, {3839, 16960}, {3851, 41108}, {5067, 33606}, {5238, 34200}, {5318, 41971}, {5351, 15715}, {10645, 15710}, {11485, 14269}, {12821, 42496}, {13903, 36469}, {13961, 36453}, {14893, 33607}, {15681, 22236}, {15687, 41101}, {15706, 34755}, {16773, 41978}, {37640, 42090}, {37832, 42125}, {42147, 42506}

X(42636) = GIBERT (-45,4,23) POINT

Barycentrics    a^2*(15*Sqrt[3]*S - 23*SA) - 8*SB*SC : :

X(42636) lies on the cubic K1191 and these lines: {2, 17}, {6, 15707}, {14, 42141}, {15, 17504}, {16, 15688}, {18, 11737}, {30, 34755}, {61, 15700}, {381, 42519}, {395, 38071}, {546, 3411}, {549, 42521}, {550, 42613}, {3523, 42520}, {3524, 42516}, {3528, 41101}, {3529, 42510}, {3545, 42517}, {3839, 16961}, {3851, 41107}, {5067, 33607}, {5237, 34200}, {5321, 41972}, {5352, 15715}, {10646, 15710}, {11486, 14269}, {12820, 42497}, {13903, 36452}, {13961, 36470}, {14893, 33606}, {15681, 22238}, {15687, 41100}, {15706, 34754}, {16772, 41977}, {37641, 42091}, {37835, 42128}, {42148, 42507}

X(42637) = GIBERT (2 SQRT(3),1,-6) POINT

Barycentrics    a^2*(S - 3*SA) + SB*SC : :

X(42637) lies on the cubic K1191 and these lines: {2, 6410}, {3, 1587}, {4, 5420}, {5, 6456}, {6, 3522}, {14, 35739}, {20, 1152}, {30, 6450}, {140, 6452}, {165, 19066}, {371, 3528}, {372, 376}, {382, 35256}, {485, 3524}, {486, 3529}, {488, 35948}, {489, 5860}, {490, 5591}, {511, 26295}, {516, 13959}, {548, 3312}, {549, 6497}, {550, 1588}, {590, 15717}, {615, 3146}, {631, 6560}, {638, 2482}, {1131, 8253}, {1132, 13847}, {1151, 10304}, {1204, 18924}, {1327, 15709}, {1656, 23253}, {1657, 6446}, {2045, 42220}, {2046, 42219}, {3070, 3523}, {3090, 35820}, {3091, 42264}, {3093, 37460}, {3098, 39875}, {3311, 8703}, {3317, 15682}, {3525, 6564}, {3530, 13665}, {3533, 42277}, {3534, 6408}, {3543, 42262}, {3545, 22644}, {3832, 8252}, {3839, 42583}, {4297, 19065}, {4316, 13963}, {4324, 13962}, {5056, 42284}, {5059, 6434}, {5067, 42269}, {5068, 32790}, {5071, 35786}, {5073, 18762}, {5217, 31408}, {5418, 10299}, {5590, 11293}, {5894, 17820}, {6036, 12975}, {6200, 7581}, {6221, 33923}, {6225, 10534}, {6409, 7585}, {6418, 15688}, {6426, 7586}, {6430, 32788}, {6432, 41945}, {6438, 42523}, {6448, 19116}, {6454, 6561}, {6455, 19117}, {6481, 23273}, {6485, 11001}, {6487, 6565}, {6522, 12103}, {7389, 33364}, {7738, 12968}, {7822, 11291}, {7889, 11292}, {7967, 35611}, {7968, 9778}, {7987, 13902}, {8277, 12082}, {8976, 15712}, {9681, 35770}, {9733, 35944}, {9862, 9986}, {10303, 42265}, {10820, 12244}, {11418, 30552}, {11495, 19013}, {11836, 14654}, {12124, 36701}, {12172, 26376}, {12239, 20791}, {12257, 40275}, {12323, 26362}, {12512, 18992}, {12963, 26463}, {12969, 26457}, {13785, 15704}, {13846, 15705}, {13883, 16192}, {13925, 17504}, {13947, 28164}, {13961, 15681}, {13980, 17845}, {14813, 42127}, {14814, 42126}, {15515, 31411}, {15696, 42215}, {15698, 35822}, {15720, 18538}, {15815, 31403}, {17576, 31473}, {17578, 42270}, {19055, 38736}, {19059, 38726}, {19108, 38747}, {19110, 37853}, {19112, 38759}, {19145, 33750}, {22615, 35813}, {23275, 42275}, {42217, 42584}, {42218, 42585}

X(42637) = {X(6),X(3522)}-harmonic conjugate of X(42638)

X(42638) = GIBERT (2 SQRT(3),-1,6) POINT

Barycentrics    a^2*(S + 3*SA) - SB*SC : :

X(42638) lies on the cubic K1191 and these lines: {2, 6409}, {3, 1588}, {4, 5418}, {5, 6455}, {6, 3522}, {20, 1151}, {30, 6449}, {140, 6451}, {165, 19065}, {186, 9683}, {371, 376}, {372, 3528}, {382, 35255}, {485, 3529}, {486, 3524}, {487, 35949}, {489, 5590}, {490, 5861}, {511, 26294}, {515, 9582}, {516, 9615}, {548, 3311}, {549, 6496}, {550, 1587}, {590, 3146}, {615, 15717}, {631, 6561}, {637, 2482}, {1131, 13846}, {1132, 8252}, {1152, 10304}, {1204, 18923}, {1328, 15709}, {1656, 23263}, {1657, 6445}, {2045, 42217}, {2046, 42218}, {3071, 3523}, {3085, 9647}, {3086, 9660}, {3090, 35821}, {3091, 42263}, {3092, 37460}, {3098, 39876}, {3312, 8703}, {3316, 15682}, {3525, 6565}, {3530, 13785}, {3533, 42274}, {3534, 6407}, {3543, 42265}, {3545, 22615}, {3832, 8253}, {3839, 42582}, {4297, 9616}, {4316, 13905}, {4324, 13904}, {5056, 42283}, {5059, 6433}, {5067, 42268}, {5068, 32789}, {5071, 35787}, {5073, 18538}, {5420, 10299}, {5591, 11294}, {5894, 17819}, {6036, 12974}, {6225, 10533}, {6396, 7582}, {6398, 33923}, {6410, 7586}, {6417, 15688}, {6425, 7585}, {6429, 32787}, {6431, 41946}, {6437, 42522}, {6447, 19117}, {6453, 6560}, {6456, 19116}, {6480, 23267}, {6484, 11001}, {6486, 6564}, {6519, 12103}, {6781, 31411}, {7388, 33365}, {7737, 9674}, {7738, 12963}, {7822, 11292}, {7889, 11291}, {7967, 35610}, {7969, 9778}, {7987, 13959}, {8276, 12082}, {8960, 23269}, {8991, 17845}, {9583, 31730}, {9649, 18996}, {9662, 19038}, {9682, 12088}, {9690, 42226}, {9691, 18512}, {9694, 33524}, {9732, 35945}, {9862, 9987}, {10303, 42262}, {10590, 31499}, {10819, 12244}, {11417, 30552}, {11495, 19014}, {11835, 14654}, {12123, 36703}, {12171, 26375}, {12240, 20791}, {12256, 40274}, {12322, 26361}, {12512, 18991}, {12962, 26462}, {12968, 26456}, {13665, 15704}, {13847, 15705}, {13893, 28164}, {13897, 31500}, {13903, 15681}, {13936, 16192}, {13951, 15712}, {13993, 17504}, {14813, 42126}, {14814, 42127}, {15326, 31408}, {15696, 42216}, {15698, 35823}, {15720, 18762}, {17578, 42273}, {19056, 38736}, {19060, 38726}, {19109, 38747}, {19111, 37853}, {19113, 38759}, {19146, 33750}, {22644, 35812}, {31473, 37267}, {42219, 42584}, {42220, 42585}

X(42638) = {X(6),X(3522)}-harmonic conjugate of X(42637)

X(42639) = GIBERT (12 SQRT(3),13,17) POINT

Barycentrics    a^2*(12*S + 17*SA) + 26*SB*SC : :

X(42639) lies on the cubic K1191 and these lines: {2, 6395}, {3, 3590}, {5, 6419}, {6, 42518}, {30, 6449}, {140, 6522}, {371, 23046}, {372, 41948}, {381, 13925}, {485, 549}, {547, 13951}, {590, 8703}, {1131, 15688}, {1151, 35404}, {1327, 19710}, {1328, 38071}, {1587, 10124}, {1588, 14892}, {3068, 5066}, {3070, 17504}, {3311, 11737}, {3316, 5054}, {3543, 10137}, {3830, 8972}, {3839, 13903}, {3845, 6437}, {5055, 13886}, {6199, 41106}, {6221, 12101}, {6396, 42572}, {6398, 11540}, {6445, 15640}, {6473, 15694}, {6560, 15711}, {6564, 33699}, {7583, 13847}, {8981, 15687}, {10109, 19054}, {11539, 35822}, {11812, 32785}, {12100, 13665}, {12108, 31414}, {12811, 31487}, {13897, 15170}, {14093, 23269}, {14869, 41946}, {15686, 41952}, {15690, 23249}, {15701, 23267}, {15713, 42216}, {32789, 42606}, {41947, 42582}, {41950, 41955}, {42276, 42608}

X(42640) = GIBERT (-12 SQRT(3),13,17) POINT

Barycentrics    a^2*(12*S - 17*SA) - 26*SB*SC : :

X(42640) lies on the cubic K1191 and these lines: {2, 6199}, {3, 3591}, {5, 6420}, {6, 42518}, {30, 6450}, {140, 6519}, {371, 41947}, {372, 23046}, {381, 13993}, {486, 549}, {547, 8976}, {615, 8703}, {1132, 15688}, {1152, 35404}, {1327, 38071}, {1328, 19710}, {1587, 14892}, {1588, 10124}, {3069, 5066}, {3071, 17504}, {3312, 11737}, {3317, 5054}, {3543, 10138}, {3627, 17852}, {3830, 13941}, {3839, 13961}, {3845, 6438}, {5055, 13939}, {6200, 42573}, {6221, 11540}, {6395, 41106}, {6398, 12101}, {6446, 15640}, {6472, 15694}, {6561, 15711}, {6565, 33699}, {7584, 13846}, {10109, 19053}, {11539, 35823}, {11812, 32786}, {12100, 13785}, {13954, 15170}, {13966, 15687}, {14093, 23275}, {14869, 41945}, {15686, 41951}, {15690, 23259}, {15701, 23273}, {15713, 42215}, {32790, 42607}, {41948, 42583}, {41949, 41956}, {42275, 42609}

X(42641) = GIBERT (15 SQRT(3),26,-8) POINT

Barycentrics    a^2*(15*S - 8*SA) + 52*SB*SC : :

X(42641) lies on the cubic K1191 and these lines: {2, 6410}, {4, 42573}, {30, 6437}, {382, 6419}, {546, 13847}, {1151, 42576}, {1152, 11737}, {1327, 34200}, {3311, 42577}, {3529, 31454}, {3851, 6522}, {3855, 41946}, {6395, 6565}, {6429, 42572}, {6430, 41106}, {6431, 35404}, {6432, 12101}, {6438, 23046}, {6449, 13846}, {6460, 41947}, {6560, 38071}, {6564, 15707}, {8253, 17504}, {10137, 15685}, {15686, 42568}, {15687, 19116}, {15688, 42264}, {15700, 42265}, {19709, 42569}, {23249, 41954}, {41952, 42414}

X(42642) = GIBERT (15 SQRT(3),-26,8) POINT

Barycentrics    a^2*(15*S + 8*SA) - 52*SB*SC : :

X(42642) lies on the cubic K1191 and these lines: {2, 6409}, {4, 42572}, {30, 6438}, {382, 6420}, {546, 13846}, {1151, 11737}, {1152, 42577}, {1328, 34200}, {3312, 42576}, {3529, 17852}, {3851, 6519}, {3855, 41945}, {6199, 6564}, {6429, 41106}, {6430, 42573}, {6431, 12101}, {6432, 35404}, {6437, 23046}, {6450, 13847}, {6459, 41948}, {6561, 38071}, {6565, 15707}, {8252, 17504}, {10138, 15685}, {15686, 42569}, {15687, 19117}, {15688, 42263}, {15700, 42262}, {19709, 42568}, {23259, 41953}, {41951, 42413}

X(42643) = GIBERT (20 SQRT(3),3,21) POINT

Barycentrics    a^2*(20*S + 21*SA) + 6*SB*SC : :

X(42643) lies on the cubic K1191 and these lines: {2, 6199}, {6, 3530}, {30, 6437}, {140, 42567}, {371, 546}, {382, 1131}, {548, 6480}, {550, 1587}, {3068, 15687}, {3311, 14869}, {3528, 6445}, {3592, 13993}, {3851, 8972}, {3853, 35815}, {3855, 13903}, {3856, 12819}, {5079, 23273}, {6200, 34200}, {6395, 10299}, {6398, 17504}, {6425, 42226}, {6431, 12108}, {6433, 33923}, {6434, 14891}, {6435, 41963}, {6441, 13966}, {6447, 23249}, {6468, 42216}, {6476, 41958}, {7585, 9690}, {8981, 10195}, {9542, 15710}, {10300, 18457}, {11737, 42215}, {15681, 23267}, {18762, 31454}, {23259, 38071}

X(42644) = GIBERT (-20 SQRT(3),3,21) POINT

Barycentrics    a^2*(20*S - 21*SA) - 6*SB*SC : :

X(42644) lies on the cubic K1191 and these lines: {2, 6395}, {6, 3530}, {30, 6438}, {140, 42566}, {372, 546}, {382, 1132}, {548, 6481}, {550, 1588}, {3069, 15687}, {3312, 14869}, {3528, 6446}, {3594, 13925}, {3851, 13941}, {3853, 35814}, {3855, 13961}, {3856, 12818}, {5079, 23267}, {6199, 10299}, {6221, 17504}, {6396, 34200}, {6426, 42225}, {6432, 12108}, {6433, 14891}, {6434, 33923}, {6436, 41964}, {6442, 8981}, {6448, 23259}, {6469, 42215}, {6477, 41957}, {7586, 15688}, {10194, 13966}, {10300, 18459}, {11737, 42216}, {15681, 23273}, {23249, 38071}

X(42645) = GIBERT (SQRT(3/2),1,0) POINT

Barycentrics    Sqrt[2]*a^2*S + 4*SB*SC : :

X(42645) lies on the cubic K1191 and these lines: {3, 3373}, {4, 6}, {5, 41975}, {550, 41976}, {1151, 14785}, {1152, 14784}, {3371, 35821}, {3372, 6564}, {3385, 35820}, {3386, 6565}, {3627, 41979}, {14782, 42265}, {14783, 42262}

X(42646) = GIBERT (-SQRT(3/2),1,0) POINT

Barycentrics    Sqrt[2]*a^2*S - 4*SB*SC : :

X(42646) lies on the cubic K1191 and these lines: {3, 3374}, {4, 6}, {5, 41976}, {550, 41975}, {1151, 14784}, {1152, 14785}, {3371, 6564}, {3372, 35821}, {3385, 6565}, {3386, 35820}, {3627, 41980}, {14782, 42262}, {14783, 42265}

X(42647) = GIBERT (2 SQRT(6),3,3) POINT

Barycentrics    a^2*(2*Sqrt[2]*S + 3*SA) + 6*SB*SC : :

X(42647) lies on the cubic K1191 and these lines: {5, 6}, {549, 41980}, {550, 41976}, {3373, 6396}, {3387, 6200}, {3845, 41979}, {8972, 14785}, {13941, 14784}, {14782, 23267}, {14783, 23273}

X(42648) = GIBERT (-2 SQRT(6),3,3) POINT

Barycentrics    a^2*(2*Sqrt[2]*S - 3*SA) - 6*SB*SC : :

X(42648) lies on the cubic K1191 and these lines: {5, 6}, {549, 41979}, {550, 41975}, {3374, 6396}, {3388, 6200}, {3845, 41980}, {8972, 14784}, {13941, 14785}, {14782, 23273}, {14783, 23267}

X(42649) = X(187)X(237)∩X(654)X(4041)

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

X(42649) lies on these lines: {187, 237}, {654, 4041}, {2355, 18344}, {4063, 21132}

X(42649) = center of circle {{X(15), X(16), X(35), X(484), X(3483), X(14102)}}
X(42649) = X(664)-isoconjugate of X(3467)
X(42649) = crosspoint of X(109) and X(2160)
X(42649) = crosssum of X(522) and X(3219)
X(42649) = crossdifference of every pair of points on line {2, 24148}
X(42649) = barycentric product X(i)*X(j) for these {i,j}: {522, 21773}, {649, 27529}, {650, 3336}, {663, 17483}, {3064, 23070}, {3737, 21863}, {3738, 11069}
X(42649) = barycentric quotient X(i)/X(j) for these {i,j}: {3063, 3467}, {3336, 4554}, {11069, 35174}, {17483, 4572}, {21773, 664}, {27529, 1978}

X(42650) = X(187)X(237)∩X(3574)X(32478)

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

X(42650) lies on these lines: {187, 237}, {3574, 32478}

X(42650) = center of circle {{X(15), X(16), X(54), X(1157), X(3482), X(18335)}}
X(42650) = crosspoint of X(i) and X(j) for these (i,j): {51, 32737}, {53, 933}
X(42650) = crosssum of X(i) and X(j) for these (i,j): {95, 41298}, {97, 6368}
X(42650) = crossdifference of every pair of points on line {2, 34520}
X(42650) = barycentric product X(195)*X(12077)

X(42651) = X(110)X(933)∩X(184)X(2081)

Barycentrics    a^2*(b - c)*(b + c)*(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(42651) lies on these lines: {110, 933}, {184, 2081}, {187, 237}, {520, 14696}, {3124, 15450}, {6130, 32193}

X(42651) = center of circle {{X(15), X(16), X(125), X(184), X(2081), X(13558)}}
X(42651) = Parry-circle-inverse of X(15451)
X(42651) = barycentric product X(647)*X(41203)
X(42651) = barycentric quotient X(41203)/X(6331)
X(42651) = {X(5638),X(5639)}-harmonic conjugate of X(15451)

X(42652) = X(187)X(237)∩X(385)X(804)

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

X(42652) lies on these lines: {187, 237}, {385, 804}, {691, 9150}, {805, 881}, {2086, 2679}, {5970, 14898}, {22329, 25423}

X(42652) = center of circle {{X(15), X(16), X(385), X(805), X(5970), X(32531)}}
X(42652) =X(35146)-isoconjugate of X(37134)
X(42652) =crosspoint of X(805) and X(5970)
X(42652) =crosssum of X(804) and X(5969)
X(42652) =crossdifference of every pair of points on line {2, 18829}
X(42652) =barycentric product X(i)*X(j) for these {i,j}: {804, 5106}, {1691, 11182}, {2086, 14607}, {5027, 5969}
X(42652) =barycentric quotient X(i)/X(j) for these {i,j}: {5027, 35146}, {5106, 18829}, {11182, 18896}
X(42652) ={X(669),X(3231)}-harmonic conjugate of X(351)

X(42653) = X(187)X(237)∩X(520)X(34975)

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

X(42653) lies on these lines: {187, 237}, {520, 34975}, {523, 21179}, {650, 6367}, {690, 905}, {804, 21260}, {810, 3725}, {1962, 4041}, {3309, 11615}, {3709, 9279}, {3743, 14838}, {4155, 6586}, {4983, 21828}, {6370, 20517}, {8574, 21837}, {9147, 21301}, {9148, 31251}, {9402, 17990}, {11176, 31288}, {21192, 31947}, {24782, 25686}, {25084, 25473}

X(42653) = center of circle {{X(15), X(16), X(501), X(3743), X(5127), X(14838), X(14873), X(39149)}}
X(42653) = X(4705)-Ceva conjugate of X(512)
X(42653) = X(i)-isoconjugate of X(j) for these (i,j): {99, 267}, {190, 40143}, {662, 1029}, {799, 3444}, {4610, 21353}
X(42653) = crosspoint of X(37) and X(110)
X(42653) = crosssum of X(i) and X(j) for these (i,j): {81, 523}, {86, 4467}
X(42653) = crossdifference of every pair of points on line {2, 1029}
X(42653) = barycentric product X(i)*X(j) for these {i,j}: {37, 31947}, {42, 21192}, {191, 661}, {451, 647}, {501, 4024}, {512, 2895}, {513, 21873}, {523, 1030}, {649, 21081}, {798, 20932}, {2501, 22136}, {3700, 8614}, {3709, 41808}, {4556, 21723}, {4705, 40592}
X(42653) = barycentric quotient X(i)/X(j) for these {i,j}: {191, 799}, {451, 6331}, {501, 4610}, {512, 1029}, {667, 40143}, {669, 3444}, {798, 267}, {1030, 99}, {2895, 670}, {4079, 502}, {8614, 4573}, {20932, 4602}, {21081, 1978}, {21192, 310}, {21873, 668}, {22136, 4563}, {31947, 274}, {40592, 4623}

X(42654) = X(110)X(250)∩X(187)X(237)

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

X(42654) lies on these lines: {110, 250}, {187, 237}, {247, 3258}, {523, 15448}, {879, 35260}, {1503, 22264}, {2433, 26864}, {2485, 20998}, {9155, 13480}, {13394, 40550}, {14165, 16229}, {35259, 41167}

X(42654) = center of circle {{X(15), X(16), X(647), X(1495), X(14685), X(16319), X(35901)}}
X(42654) = Parry-circle-inverse of X(9409)
X(42654) = crossdifference of every pair of points on line {2, 30227}
X(42654) = {X(5638),X(5639)}-harmonic conjugate of X(9409)

X(42655) = X(110)X(898)∩X(187)X(237)

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

X(42655) lies on these lines: {110, 898}, {187, 237}, {238, 4367}, {875, 2176}, {1083, 24286}

X(42655) = center of circle {{X(15), X(16), X(667), X(1083), X(3230), X(11650), X(11651), X(11652)}}
X(42655) = Parry-circle-inverse of X(890)
X(42655) = crosspoint of X(11651) and X(11652)
X(42655) = crossdifference of every pair of points on line {2, 24289}
X(42655) = {X(5638),X(5639)}-harmonic conjugate of X(890)

X(42656) = X(187)X(237)∩X(526)X(14157)

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

X(42656) lies on these lines: {187, 237}, {526, 14157}

X(42656) = center of circle {{X(15), X(16), X(1138), X(2132), X(6794), X(12112), X(14354)}}
X(42656) = X(36034)-isoconjugate of X(40705)
X(42656) = crosspoint of X(i) and X(j) for these (i,j): {1304, 1990}, {1495, 14560}
X(42656) = crosssum of X(i) and X(j) for these (i,j): {1494, 3268}, {9033, 14919}
X(42656) = barycentric product X(i)*X(j) for these {i,j}: {399, 1637}, {1272, 14398}, {1495, 14566}, {19303, 36035}
X(42656) = barycentric quotient X(i)/X(j) for these {i,j}: {1637, 40705}, {14398, 1138}

X(42657) = X(40)X(30574)∩X(187)X(237)

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

X(42657) lies on these lines: {40, 30574}, {187, 237}, {652, 4814}, {654, 4895}, {692, 36072}, {2254, 2775}, {2774, 3746}, {4041, 9404}, {4088, 12514}, {5250, 14432}, {21132, 21385}

X(42657) = center of circle {{X(15), X(16), X(3065), X(3464), X(5540), X(6126)}}
X(42657) = X(34921)-Ceva conjugate of X(6)
X(42657) = X(i)-isoconjugate of X(j) for these (i,j): {75, 34921}, {109, 40716}, {651, 21739}, {664, 3065}, {4554, 19302}, {4585, 26743}, {14147, 17078}
X(42657) = crosspoint of X(i) and X(j) for these (i,j): {6, 34921}, {109, 2161}
X(42657) = crosssum of X(i) and X(j) for these (i,j): {57, 30572}, {514, 3582}, {522, 3218}, {4707, 11263}
X(42657) = crossdifference of every pair of points on line {2, 21739}
X(42657) = barycentric product X(i)*X(j) for these {i,j}: {37, 35055}, {484, 650}, {522, 19297}, {663, 17484}, {3063, 17791}, {3064, 23071}, {3737, 21864}, {11076, 35057}
X(42657) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 34921}, {484, 4554}, {650, 40716}, {663, 21739}, {3063, 3065}, {17484, 4572}, {19297, 664}, {35055, 274}

leftri

Points on the Lemoine axis: X(42658)-X(42671)

rightri

This preamble and points X(42658-X(42671) are contributed by Peter Moses, April 19, 2021.

Suppose that P' = p' : q' : r' is a point on a line p x + q y + r z = 0 and that u x + v y + w z = 0 is a line, L. Then the point P'' = (p/u)*p' : (q/v)*q' + (r/w)*r' (p/u)*p' : (q/v)*q' + (r/w)*r' lies on L For example, if P' is on the Euler line and L is the Lemoine axis, X(187)X(237), then P'' is on L. Points X(42658)-X(42671) are obtained in this manner, where, in the same order, P' = X(i) for i = 20, 23, 378, 429, 447, 460, 469, 858, 860, 1113, 1114, 1981, 2074, 2409.



X(42658) = CROSSSUM OF X(4) AND X(525)

Barycentrics    a^2*(b - c)*(b + c)*(a^2 - b^2 - c^2)*(3*a^4 - 2*a^2*b^2 - b^4 - 2*a^2*c^2 + 2*b^2*c^2 - c^4) : :
X(42658) = X[647] + 2 X[9409], 3 X[647] - 2 X[15451], 3 X[8644] - 4 X[34952], 3 X[9409] + X[15451], X[15451] - 3 X[39201]

X(42658) lies on these lines: {3, 2435}, {112, 32649}, {184, 2430}, {187, 237}, {520, 11589}, {523, 37931}, {878, 40319}, {2485, 2881}, {2524, 39469}, {3198, 14308}, {6130, 16229}, {7669, 34190}, {8057, 15427}, {9517, 39228}, {38608, 39071}

X(42658) = midpoint of X(9409) and X(39201)
X(42658) = reflection of X(i) in X(j) for these {i,j}: {647, 39201}, {16229, 6130}
X(42658) = isogonal conjugate of the anticomplement of X(39020)
X(42658) = isogonal conjugate of the isotomic conjugate of X(8057)
X(42658) = isogonal conjugate of the polar conjugate of X(6587)
X(42658) = anticomplement of complementary conjugate of X(39020)
X(42658) = pole wrt polar circle of line X(253)X(264)
X(42658) = X(20402)-complementary conjugate of X(34846)
X(42658) = X(i)-Ceva conjugate of X(j) for these (i,j): {20, 1562}, {112, 3172}, {520, 647}, {1301, 6}, {3532, 3269}, {22089, 2524}, {32713, 184}, {34285, 125}
X(42658) = X(i)-isoconjugate of X(j) for these (i,j): {64, 811}, {75, 1301}, {107, 19611}, {108, 5931}, {162, 253}, {459, 662}, {648, 2184}, {799, 41489}, {823, 1073}, {2155, 6331}, {4592, 6526}, {6528, 19614}, {8809, 36797}, {14208, 15384}, {15394, 36126}, {16096, 36092}, {23052, 35571}, {24019, 34403}, {32676, 41530}
X(42658) = crosspoint of X(i) and X(j) for these (i,j): {3, 112}, {6, 1301}, {110, 41894}, {6525, 32713}, {6587, 8057}
X(42658) = crosssum of X(i) and X(j) for these (i,j): {2, 8057}, {4, 525}, {25, 2451}, {27, 7253}, {523, 26958}, {3265, 15394}
X(42658) = crossdifference of every pair of points on line {2, 253}
X(42658) = barycentric product X(i)*X(j) for these {i,j}: {3, 6587}, {6, 8057}, {20, 647}, {25, 20580}, {48, 17898}, {71, 21172}, {73, 14331}, {74, 14345}, {110, 1562}, {112, 122}, {154, 525}, {204, 24018}, {222, 14308}, {512, 37669}, {520, 1249}, {521, 30456}, {523, 15905}, {610, 656}, {652, 5930}, {810, 18750}, {822, 1895}, {905, 3198}, {1301, 39020}, {1394, 8611}, {1459, 8804}, {1559, 2430}, {1636, 10152}, {2501, 35602}, {3049, 14615}, {3172, 3265}, {6368, 33629}, {9033, 15291}, {14249, 32320}, {15466, 39201}, {17434, 38808}, {20975, 36841}, {23286, 42459}
X(42658) = barycentric quotient X(i)/X(j) for these {i,j}: {20, 6331}, {32, 1301}, {122, 3267}, {154, 648}, {204, 823}, {512, 459}, {520, 34403}, {525, 41530}, {610, 811}, {647, 253}, {652, 5931}, {669, 41489}, {810, 2184}, {822, 19611}, {1249, 6528}, {1562, 850}, {2489, 6526}, {2972, 14638}, {3049, 64}, {3172, 107}, {3198, 6335}, {6525, 15352}, {6587, 264}, {8057, 76}, {14308, 7017}, {14345, 3260}, {15291, 16077}, {15451, 13157}, {15905, 99}, {17898, 1969}, {20580, 305}, {30456, 18026}, {32320, 15394}, {33629, 18831}, {35602, 4563}, {37669, 670}, {38808, 42405}, {39201, 1073}, {40933, 13149}, {42293, 8798}

X(42659) = CROSSSUM OF X(2) AND X(9517)

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

X(42659) lies on these lines: {2, 25644}, {3, 14417}, {22, 2799}, {23, 9979}, {25, 1637}, {184, 39469}, {187, 237}, {523, 37969}, {684, 22085}, {690, 3455}, {878, 14582}, {1576, 2491}, {3268, 6636}, {4108, 39214}, {7669, 10117}, {8428, 14273}, {9131, 11616}, {9517, 16165}, {9529, 12082}, {20975, 23216}

X(42659) = isogonal conjugate of the isotomic conjugate of X(9517)
X(42659) = isogonal conjugate of the polar conjugate of X(2492)
X(42659) = X(i)-Ceva conjugate of X(j) for these (i,j): {935, 6}, {9076, 125}, {10097, 3049}, {32729, 184}, {34437, 3269}
X(42659) = X(i)-isoconjugate of X(j) for these (i,j): {67, 811}, {75, 935}, {92, 17708}, {162, 18019}, {799, 8791}, {823, 34897}, {2157, 6331}, {37221, 41676}
X(42659) = crosspoint of X(i) and X(j) for these (i,j): {6, 935}, {112, 1177}, {1576, 14908}, {2492, 9517}, {4630, 9076}
X(42659) = crosssum of X(i) and X(j) for these (i,j): {2, 9517}, {525, 858}, {935, 17708}, {9019, 23285}
X(42659) = crossdifference of every pair of points on line {2, 339}
X(42659) = barycentric product X(i)*X(j) for these {i,j}: {3, 2492}, {6, 9517}, {23, 647}, {184, 9979}, {248, 33752}, {316, 3049}, {512, 22151}, {520, 8744}, {523, 10317}, {525, 18374}, {669, 37804}, {810, 16568}, {2200, 21205}, {2433, 16165}, {2435, 28343}, {3292, 10561}, {6593, 10097}, {10510, 30491}, {14908, 18311}, {37765, 39201}
X(42659) = barycentric quotient X(i)/X(j) for these {i,j}: {23, 6331}, {32, 935}, {184, 17708}, {647, 18019}, {669, 8791}, {2492, 264}, {3049, 67}, {8744, 6528}, {9517, 76}, {9979, 18022}, {10317, 99}, {18374, 648}, {22151, 670}, {30491, 10512}, {37804, 4609}, {39201, 34897}
X(42659) = {X(669),X(34952)}-harmonic conjugate of X(8644)

X(42660) = CROSSSUM OF X(2) AND X(8675)

Barycentrics    a^4*(b - c)*(b + c)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 4*b^2*c^2 + c^4) : :
X(42660) = 2 X[669] - 3 X[34952], X[669] - 3 X[39201], 4 X[14270] - 3 X[34952], 2 X[14270] - 3 X[39201], 3 X[17414] - 2 X[18117]

X(42660) lies on these lines: {3, 523}, {32, 3049}, {39, 2451}, {187, 237}, {826, 22089}, {3050, 3053}, {3566, 35463}, {3800, 39228}, {8029, 37457}, {8675, 10564}, {8722, 38354}, {9605, 39520}, {12054, 39513}, {12073, 39477}, {26316, 39495}, {32231, 34291}, {34347, 40799}

X(42660) = midpoint of X(3005) and X(9409)
X(42660) = reflection of X(i) in X(j) for these {i,j}: {669, 14270}, {21731, 647}, {34291, 32231}, {34952, 39201}
X(42660) = circumcircle-inverse of X(6795)
X(42660) = isogonal conjugate of the isotomic conjugate of X(8675)
X(42660) = X(1302)-Ceva conjugate of X(6)
X(42660) = X(i)-isoconjugate of X(j) for these (i,j): {75, 1302}, {76, 36149}, {561, 32738}, {662, 34289}, {799, 34288}, {811, 4846}, {3260, 36083}
X(42660) = crosspoint of X(i) and X(j) for these (i,j): {6, 1302}, {10419, 32681}
X(42660) = crosssum of X(i) and X(j) for these (i,j): {2, 8675}, {512, 5309}, {523, 37648}, {525, 15760}
X(42660) = crossdifference of every pair of points on line {2, 3003}
X(42660) = bicentric difference of trilinear product P(9)*P(86) and trilinear product U(9)*U(86)
X(42660) = barycentric product X(i)*X(j) for these {i,j}: {6, 8675}, {32, 30474}, {378, 647}, {512, 15066}, {523, 5063}, {669, 32833}, {2433, 10564}, {2623, 5891}, {3569, 11653}
X(42660) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 1302}, {378, 6331}, {512, 34289}, {560, 36149}, {669, 34288}, {1501, 32738}, {3049, 4846}, {5063, 99}, {8675, 76}, {15066, 670}, {30474, 1502}, {32833, 4609}
X(42660) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {669, 14270, 34952}, {669, 39201, 14270}

X(42661) = CROSSSUM OF X(110) AND X(4612)

Barycentrics    a^2*(b - c)*(b + c)^2*(a*b + b^2 + a*c + c^2) : :
X(42661) = 3 X[351] - 2 X[667], 3 X[9147] - X[31291], 3 X[9148] - 4 X[21260]

X(42661) lies on these lines: {37, 18002}, {187, 237}, {523, 4391}, {690, 2530}, {804, 21301}, {830, 3743}, {2512, 4843}, {3801, 6370}, {4024, 4705}, {4041, 4155}, {4079, 17411}, {4983, 8034}, {9147, 31291}, {9148, 21260}, {17994, 18344}

X(42661) = reflection of X(8639) in X(647)
X(42661) = X(i)-Ceva conjugate of X(j) for these (i,j): {37, 3124}, {1402, 20975}, {34434, 35506}
X(42661) = X(i)-isoconjugate of X(j) for these (i,j): {99, 2363}, {163, 40827}, {261, 36098}, {662, 14534}, {757, 8707}, {799, 1169}, {811, 1798}, {873, 32736}, {1509, 36147}, {2185, 6648}, {2298, 4610}, {4556, 30710}, {4581, 24041}, {4636, 31643}
X(42661) = crosspoint of X(i) and X(j) for these (i,j): {512, 4705}, {8687, 18772}
X(42661) = crosssum of X(i) and X(j) for these (i,j): {110, 4612}, {523, 6703}, {1798, 15420}, {3910, 4999}, {4581, 14534}
X(42661) = crossdifference of every pair of points on line {2, 261}
X(42661) = barycentric product X(i)*X(j) for these {i,j}: {42, 21124}, {181, 3910}, {429, 647}, {512, 1211}, {513, 21810}, {523, 2092}, {594, 6371}, {649, 20653}, {661, 2292}, {669, 1228}, {798, 18697}, {872, 4509}, {1193, 4024}, {1500, 3004}, {1577, 3725}, {2171, 17420}, {2300, 4036}, {2354, 4064}, {2501, 22076}, {2643, 3882}, {3005, 27067}, {3666, 4705}, {3704, 7180}, {3709, 41003}, {4017, 21033}, {4079, 4357}, {7178, 40966}, {14394, 38882}
X(42661) = barycentric quotient X(i)/X(j) for these {i,j}: {181, 6648}, {429, 6331}, {512, 14534}, {523, 40827}, {669, 1169}, {798, 2363}, {872, 36147}, {960, 4631}, {1193, 4610}, {1211, 670}, {1228, 4609}, {1500, 8707}, {2092, 99}, {2292, 799}, {3049, 1798}, {3124, 4581}, {3666, 4623}, {3725, 662}, {3882, 24037}, {3910, 18021}, {4024, 1240}, {4079, 1220}, {4705, 30710}, {6371, 1509}, {7109, 32736}, {18697, 4602}, {20653, 1978}, {20967, 4612}, {20975, 15420}, {21033, 7257}, {21124, 310}, {21810, 668}, {22076, 4563}, {27067, 689}, {40966, 645}

X(42662) = CROSSSUM OF X(1) AND X(4707)

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

X(42662) lies on these lines: {1, 2785}, {58, 2774}, {74, 106}, {101, 112}, {187, 237}, {214, 40613}, {248, 38865}, {976, 4088}, {1010, 24353}, {1015, 3269}, {1017, 9408}, {1459, 3960}, {2254, 8578}, {3430, 9527}, {3924, 30574}, {4040, 29118}, {4449, 29094}, {4724, 29029}, {6184, 9475}, {9412, 21781}, {9862, 41190}

X(42662) = isogonal conjugate of X(35169)
X(42662) = isogonal conjugate of the anticomplement of X(35122)
X(42662) = X(4242)-Ceva conjugate of X(2183)
X(42662) = X(i)-isoconjugate of X(j) for these (i,j): {1, 35169}, {100, 16099}, {162, 40715}
X(42662) = crosspoint of X(1897) and X(2161)
X(42662) = crosssum of X(i) and X(j) for these (i,j): {1, 4707}, {514, 30117}, {1459, 3218}
X(42662) = crossdifference of every pair of points on line {2, 1762}
X(42662) = barycentric product X(i)*X(j) for these {i,j}: {101, 867}, {447, 647}, {649, 16086}
X(42662) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 35169}, {447, 6331}, {647, 40715}, {649, 16099}, {867, 3261}, {16086, 1978}
X(42662) = {X(39665),X(39666)}-harmonic conjugate of X(649)

X(42663) = CROSSSUM OF X(99) AND X(2396)

Barycentrics    a^2*(b - c)*(b + c)*(2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4) : :
X(42663) = 3 X[351] - 2 X[3569], 3 X[351] - 4 X[5027], 9 X[351] - 8 X[5113], 5 X[351] - 4 X[9208], 3 X[3569] - 4 X[5113], X[3569] - 3 X[9135], 5 X[3569] - 6 X[9208], 3 X[5027] - 2 X[5113], 2 X[5027] - 3 X[9135], 5 X[5027] - 3 X[9208], 4 X[5113] - 9 X[9135], 10 X[5113] - 9 X[9208], 3 X[5652] - 2 X[24284], 2 X[6333] - 3 X[11123], 5 X[9135] - 2 X[9208], 3 X[9148] - 4 X[24284], 3 X[14398] - 2 X[22260]

X(42663) lies on these lines: {6, 2872}, {69, 6131}, {110, 3565}, {187, 237}, {399, 2780}, {523, 32220}, {542, 32121}, {690, 24981}, {804, 25046}, {1510, 21006}, {1976, 17994}, {2422, 14601}, {2444, 17993}, {2514, 3050}, {2971, 3124}, {3566, 6562}, {3800, 14316}, {5652, 6033}, {6088, 10765}, {6132, 35364}, {6333, 11123}, {9517, 11641}, {13306, 31299}, {14398, 22260}, {14610, 39905}, {18105, 20188}, {21905, 39689}

X(42663) = reflection of X(i) in X(j) for these {i,j}: {69, 6131}, {351, 9135}, {2514, 3050}, {3005, 3288}, {3569, 5027}, {9148, 5652}, {35364, 6132}, {39905, 14610}
X(42663) = Parry-circle-inverse of X(8651)
X(42663) = X(i)-Ceva conjugate of X(j) for these (i,j): {511, 2086}, {1976, 3124}, {10425, 6}, {39644, 20975}
X(42663) = X(i)-isoconjugate of X(j) for these (i,j): {69, 36105}, {75, 10425}, {99, 8773}, {304, 32697}, {662, 8781}, {670, 36051}, {799, 2987}, {4592, 35142}, {4602, 32654}, {24037, 35364}
X(42663) = crosspoint of X(i) and X(j) for these (i,j): {6, 10425}, {99, 6531}, {512, 2422}, {2207, 32696}
X(42663) = crosssum of X(i) and X(j) for these (i,j): {99, 2396}, {512, 36212}, {3926, 6333}
X(42663) = crossdifference of every pair of points on line {2, 2987}
X(42663) = barycentric product X(i)*X(j) for these {i,j}: {114, 2422}, {230, 512}, {460, 647}, {523, 1692}, {661, 8772}, {798, 1733}, {882, 12829}, {2489, 3564}, {2491, 14265}, {3124, 4226}, {5477, 9178}, {6041, 34174}, {6132, 14384}, {14398, 36875}, {32696, 41181}
X(42663) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 10425}, {230, 670}, {460, 6331}, {512, 8781}, {669, 2987}, {798, 8773}, {1084, 35364}, {1692, 99}, {1733, 4602}, {1924, 36051}, {1973, 36105}, {1974, 32697}, {2422, 40428}, {2489, 35142}, {4226, 34537}, {8772, 799}, {9426, 32654}, {12829, 880}, {14398, 36891}
X(42663) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3569, 5027, 351}, {3569, 9135, 5027}, {5191, 21731, 351}, {5638, 5639, 8651}

X(42664) = CROSSSUM OF X(2) AND X(23879)

Barycentrics    a^2*(b - c)*(b + c)*(a*b + b^2 + a*c + b*c + c^2) : :
X(42664) = 7 X[27138] - 5 X[31072], 4 X[30476] - 5 X[30835]

X(42664) lies on these lines: {187, 237}, {523, 661}, {525, 16892}, {650, 4132}, {850, 3835}, {1499, 38329}, {2611, 20974}, {2786, 27469}, {3050, 7252}, {4129, 24083}, {4139, 4893}, {4467, 4481}, {4502, 4526}, {4750, 28372}, {4785, 36900}, {4826, 21828}, {4979, 21123}, {14349, 23879}, {20295, 31296}, {21051, 21715}, {21196, 27647}, {21721, 31946}, {23878, 31147}, {27138, 31072}, {30476, 30835}

X(42664) = midpoint of X(i) and X(j) for these {i,j}: {3005, 8663}, {20295, 31296}
X(42664) = reflection of X(i) in X(j) for these {i,j}: {649, 647}, {850, 3835}, {3804, 8653}
X(42664) = isogonal conjugate of the isotomic conjugate of X(23879)
X(42664) = X(i)-Ceva conjugate of X(j) for these (i,j): {835, 20966}, {34819, 20982}, {39967, 3124}
X(42664) = X(i)-isoconjugate of X(j) for these (i,j): {58, 37218}, {81, 835}, {99, 2214}
X(42664) = crosspoint of X(i) and X(j) for these (i,j): {834, 14349}, {835, 40394}, {4033, 31359}
X(42664) = crosssum of X(i) and X(j) for these (i,j): {2, 23879}, {523, 17398}, {525, 7536}
X(42664) = crossdifference of every pair of points on line {2, 58}
X(42664) = barycentric product X(i)*X(j) for these {i,j}: {6, 23879}, {10, 834}, {37, 14349}, {58, 23282}, {313, 8637}, {386, 523}, {469, 647}, {512, 5224}, {661, 28606}, {798, 33935}, {3122, 33948}, {3709, 33949}, {3876, 4017}
X(42664) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 37218}, {42, 835}, {386, 99}, {469, 6331}, {798, 2214}, {834, 86}, {3876, 7257}, {5224, 670}, {8637, 58}, {14349, 274}, {23282, 313}, {23879, 76}, {28606, 799}, {33935, 4602}
X(42664) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 21834, 4024}, {21051, 21719, 21720}, {21051, 23948, 21726}

X(42665) = CROSSSUM OF X(4) AND X(9979)

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

X(42665) lies on these lines: {25, 2881}, {122, 125}, {184, 1636}, {187, 237}, {526, 15106}, {686, 39469}, {1184, 2508}, {1576, 2445}, {1637, 17994}, {3258, 38368}, {3292, 13303}, {5489, 14424}, {5505, 14380}, {9517, 14908}, {14416, 42442}

X(42665) = X(i)-Ceva conjugate of X(j) for these (i,j): {67, 3269}, {2373, 38356}, {10423, 6}, {14908, 20975}, {32709, 10602}, {40347, 3124}
X(42665) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36095}, {75, 10423}, {112, 37220}, {162, 2373}, {811, 1177}, {823, 18876}
X(42665) = crosspoint of X(i) and X(j) for these (i,j): {6, 10423}, {112, 895}, {523, 10097}
X(42665) = crosssum of X(i) and X(j) for these (i,j): {4, 9979}, {110, 4235}, {468, 525}, {1974, 14273}, {2393, 2485}
X(42665) = crossdifference of every pair of points on line {2, 112}
X(42665) = barycentric product X(i)*X(j) for these {i,j}: {71, 21109}, {520, 5523}, {523, 14961}, {525, 2393}, {647, 858}, {656, 18669}, {810, 20884}, {1236, 3049}, {1459, 21017}, {3265, 14580}, {5181, 10097}, {19510, 30491}, {34158, 35522}
X(42665) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36095}, {32, 10423}, {647, 2373}, {656, 37220}, {858, 6331}, {2393, 648}, {3049, 1177}, {5523, 6528}, {14580, 107}, {14961, 99}, {18669, 811}, {34158, 691}, {39201, 18876}, {39469, 36823}
X(42665) = {X(17414),X(39201)}-harmonic conjugate of X(647)

X(42666) = CROSSSUM OF X(2) AND X(6370)

Barycentrics    a^2*(b - c)*(b + c)^2*(a^2 - b^2 + b*c - c^2) : :
X(42666) = 3 X[351] - 2 X[1960], 3 X[1962] - X[4895], X[2650] - 3 X[14413]

X(42666) lies on these lines: {10, 18003}, {187, 237}, {291, 18009}, {523, 10015}, {526, 6126}, {690, 2254}, {758, 3960}, {804, 24462}, {1769, 6089}, {1962, 4895}, {2491, 40986}, {2492, 22108}, {2642, 2643}, {2650, 14413}, {3743, 3887}, {4041, 4838}, {4142, 4151}, {4707, 4736}, {21756, 23648}, {21784, 23861}

X(42666) = midpoint of X(2254) and X(2292)
X(42666) = isogonal conjugate of the isotomic conjugate of X(6370)
X(42666) = X(i)-Ceva conjugate of X(j) for these (i,j): {759, 20982}, {1464, 2088}, {2433, 3709}, {36069, 6}
X(42666) = X(i)-isoconjugate of X(j) for these (i,j): {2, 37140}, {60, 35174}, {75, 36069}, {76, 32671}, {99, 759}, {110, 14616}, {261, 2222}, {593, 36804}, {655, 2185}, {662, 24624}, {799, 34079}, {850, 9274}, {1414, 6740}, {1577, 9273}, {2006, 4612}, {2161, 4610}, {2341, 4573}, {2617, 39277}, {4556, 18359}, {4623, 6187}, {4636, 18815}, {14838, 39295}, {17104, 35139}, {32678, 34016}, {32680, 40214}, {36066, 36815}
X(42666) = crosspoint of X(6) and X(36069)
X(42666) = crosssum of X(i) and X(j) for these (i,j): {2, 6370}, {523, 35466}, {758, 14838}, {3738, 16579}
X(42666) = crossdifference of every pair of points on line {2, 662}
X(42666) = barycentric product X(i)*X(j) for these {i,j}: {1, 2610}, {6, 6370}, {10, 21828}, {12, 654}, {36, 4024}, {42, 4707}, {181, 3904}, {320, 4079}, {512, 3936}, {513, 4053}, {523, 2245}, {526, 8818}, {647, 860}, {661, 758}, {756, 3960}, {798, 35550}, {1089, 21758}, {1109, 1983}, {1464, 3700}, {1500, 4453}, {1577, 3724}, {1835, 8611}, {2088, 6742}, {2171, 3738}, {2433, 6739}, {2624, 6757}, {2643, 4585}, {3218, 4705}, {3708, 4242}, {3709, 41804}, {4036, 7113}, {4041, 18593}, {6358, 8648}
X(42666) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 37140}, {32, 36069}, {36, 4610}, {181, 655}, {512, 24624}, {526, 34016}, {560, 32671}, {654, 261}, {661, 14616}, {669, 34079}, {756, 36804}, {758, 799}, {798, 759}, {860, 6331}, {1464, 4573}, {1576, 9273}, {1983, 24041}, {2088, 4467}, {2171, 35174}, {2245, 99}, {2361, 4612}, {2610, 75}, {2623, 39277}, {3218, 4623}, {3709, 6740}, {3724, 662}, {3904, 18021}, {3936, 670}, {3960, 873}, {4024, 20566}, {4053, 668}, {4079, 80}, {4511, 4631}, {4585, 24037}, {4705, 18359}, {4707, 310}, {6370, 76}, {8648, 2185}, {8818, 35139}, {14270, 40214}, {18593, 4625}, {21758, 757}, {21828, 86}, {35550, 4602}
X(42666) = {X(3724),X(8648)}-harmonic conjugate of X(14270)

X(42667) = CROSSSUM OF X(2) AND X(2575)

Barycentrics    a^2*(b^2 - c^2)*SA*(a^2*(1 - J)*SA - 2*SB*SC) : :

X(42667) lies on these lines: {3, 2575}, {25, 8106}, {98, 1113}, {187, 237}, {228, 2579}, {1114, 35278}, {1344, 9756}, {1799, 22340}, {1995, 9174}, {15167, 20975}

X(42667) = reflection of X(42668) in X(14270)
X(42667) = isogonal conjugate of X(15165)
X(42667) = isogonal conjugate of the anticomplement of X(15167)
X(42667) = isogonal conjugate of the isotomic conjugate of X(2575)
X(42667) = isogonal conjugate of the polar conjugate of X(8106)
X(42667) = circumcircle-inverse of X(13414)
X(42667) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 15167}, {1114, 6}
X(42667) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15165}, {2, 2581}, {69, 2587}, {75, 1114}, {76, 2577}, {92, 8116}, {99, 2588}, {162, 22339}, {264, 1823}, {648, 2582}, {662, 2592}, {799, 8105}, {811, 2574}, {1577, 39299}, {2578, 6331}, {2584, 6528}, {24041, 39240}
X(42667) = crosspoint of X(i) and X(j) for these (i,j): {6, 1114}, {110, 41941}, {112, 15461}, {2575, 8106}
X(42667) = crosssum of X(i) and X(j) for these (i,j): {2, 2575}, {4, 2593}, {69, 22340}, {525, 1313}, {1114, 8116}, {2592, 39240}
X(42667) = crossdifference of every pair of points on line {2, 2592}
X(42667) = barycentric product X(i)*X(j) for these {i,j}: {1, 2579}, {3, 8106}, {6, 2575}, {19, 2585}, {31, 2583}, {32, 22340}, {48, 2589}, {184, 2593}, {512, 8115}, {647, 1113}, {656, 2576}, {661, 1822}, {810, 2580}, {822, 2586}, {1114, 15167}, {3049, 15164}, {20975, 39298}, {23110, 41942}, {32661, 39241}
X(42667) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 15165}, {31, 2581}, {32, 1114}, {184, 8116}, {512, 2592}, {560, 2577}, {647, 22339}, {669, 8105}, {798, 2588}, {810, 2582}, {1113, 6331}, {1576, 39299}, {1822, 799}, {1973, 2587}, {2575, 76}, {2576, 811}, {2579, 75}, {2583, 561}, {2585, 304}, {2589, 1969}, {2593, 18022}, {3049, 2574}, {3124, 39240}, {8106, 264}, {8115, 670}, {9247, 1823}, {15167, 22340}, {22340, 1502}
X(42667) = {X(237),X(5191)}-harmonic conjugate of X(42668)

X(42668) = CROSSSUM OF X(2) AND X(2574)

Barycentrics    a^2*(b^2 - c^2)*SA*(a^2*(1 + J)*SA - 2*SB*SC) : :

X(42668) lies on these lines: {3, 2574}, {25, 8105}, {98, 1114}, {187, 237}, {228, 2578}, {1113, 35278}, {1345, 9756}, {1799, 22339}, {1995, 9173}, {15166, 20975}

X(42668) = reflection of X(42667) in X(14270)
X(42668) = circumcircle-inverse of X(13415)
X(42668) = isogonal conjugate of X(15164)
X(42668) = isogonal conjugate of the anticomplement of X(15166)
X(42668) = isogonal conjugate of the isotomic conjugate of X(2574)
X(42668) = isogonal conjugate of the polar conjugate of X(8105)
X(42668) = circumcircle-inverse of X(13415)
X(42668) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 15166}, {1113, 6}
X(42668) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15164}, {2, 2580}, {69, 2586}, {75, 1113}, {76, 2576}, {92, 8115}, {99, 2589}, {162, 22340}, {264, 1822}, {648, 2583}, {662, 2593}, {799, 8106}, {811, 2575}, {1577, 39298}, {2579, 6331}, {2585, 6528}, {24041, 39241}
X(42668) = crosspoint of X(i) and X(j) for these (i,j): {6, 1113}, {110, 41942}, {112, 15460}, {2574, 8105}
X(42668) = crosssum of X(i) and X(j) for these (i,j): {2, 2574}, {4, 2592}, {69, 22339}, {525, 1312}, {1113, 8115}, {2593, 39241}
X(42668) = crossdifference of every pair of points on line {2, 2593}
X(42668) = {X(237),X(5191)}-harmonic conjugate of X(42667)
X(42668) = barycentric product X(i)*X(j) for these {i,j}: {1, 2578}, {3, 8105}, {6, 2574}, {19, 2584}, {31, 2582}, {32, 22339}, {48, 2588}, {184, 2592}, {512, 8116}, {647, 1114}, {656, 2577}, {661, 1823}, {810, 2581}, {822, 2587}, {1113, 15166}, {3049, 15165}, {20975, 39299}, {23109, 41941}, {32661, 39240}
X(42668) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 15164}, {31, 2580}, {32, 1113}, {184, 8115}, {512, 2593}, {560, 2576}, {647, 22340}, {669, 8106}, {798, 2589}, {810, 2583}, {1114, 6331}, {1576, 39298}, {1823, 799}, {1973, 2586}, {2574, 76}, {2577, 811}, {2578, 75}, {2582, 561}, {2584, 304}, {2588, 1969}, {2592, 18022}, {3049, 2575}, {3124, 39241}, {8105, 264}, {8116, 670}, {9247, 1822}, {15166, 22339}, {22339, 1502}

X(42669) = CROSSSUM OF X(2) AND X(8680)

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

X(42669) lies on these lines: {1, 19}, {10, 22061}, {41, 2650}, {56, 40978}, {65, 2200}, {73, 2333}, {101, 758}, {187, 237}, {213, 1042}, {572, 25081}, {604, 40977}, {607, 2658}, {859, 1755}, {993, 22099}, {1460, 3725}, {1464, 39690}, {1944, 5088}, {1945, 17963}, {1951, 26884}, {2176, 2178}, {2179, 23383}, {2292, 9310}, {2654, 40975}, {4020, 23361}, {4245, 24511}, {4390, 21020}, {4456, 20727}, {6603, 20718}, {8235, 12520}, {9247, 14529}, {12081, 17439}, {14963, 22098}, {18047, 35544}, {20963, 21748}

X(42669) = isogonal conjugate of X(35145)
X(42669) = isogonal conjugate of the anticomplement of X(35075)
X(42669) = isogonal conjugate of the isotomic conjugate of X(8680)
X(42669) = X(2249)-Ceva conjugate of X(6)
X(42669) = X(i)-isoconjugate of X(j) for these (i,j): {1, 35145}, {2, 37142}, {21, 1952}, {29, 40843}, {75, 2249}, {296, 31623}, {314, 1945}, {333, 1937}, {521, 41207}, {522, 41206}, {2713, 17899}
X(42669) = crosspoint of X(i) and X(j) for these (i,j): {6, 2249}, {1951, 2202}
X(42669) = crosssum of X(i) and X(j) for these (i,j): {2, 8680}, {333, 40882}, {1952, 40843}, {9391, 16573}
X(42669) = crossdifference of every pair of points on line {2, 656}
X(42669) = barycentric product X(i)*X(j) for these {i,j}: {1, 851}, {6, 8680}, {10, 26884}, {42, 5088}, {65, 1936}, {72, 1430}, {73, 243}, {162, 9391}, {226, 1951}, {647, 1981}, {656, 23353}, {798, 15418}, {1042, 7360}, {1214, 2202}, {1400, 1944}, {1409, 1948}, {1425, 15146}, {1880, 6518}, {2249, 35075}
X(42669) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 35145}, {31, 37142}, {32, 2249}, {851, 75}, {1400, 1952}, {1402, 1937}, {1409, 40843}, {1415, 41206}, {1430, 286}, {1936, 314}, {1944, 28660}, {1951, 333}, {1981, 6331}, {2202, 31623}, {5088, 310}, {8680, 76}, {9391, 14208}, {15418, 4602}, {23353, 811}, {26884, 86}, {32674, 41207}
X(42669) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {65, 2200, 23621}, {73, 2333, 23619}, {3724, 5202, 3747}

X(42670) = CROSSSUM OF X(2) AND X(8674)

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

X(42670) lies on these lines: {3, 2775}, {21, 2787}, {35, 9508}, {55, 4730}, {163, 692}, {187, 237}, {405, 14431}, {659, 21201}, {993, 4922}, {2530, 22160}, {3271, 20975}, {4010, 5248}, {4455, 7669}, {4705, 21789}, {6050, 11934}, {8674, 16164}, {16865, 30709}, {34858, 40352}

X(42670) = midpoint of X(21) and X(16158)
X(42670) = isogonal conjugate of X(35156)
X(42670) = isogonal conjugate of the anticomplement of X(35090)
X(42670) = isogonal conjugate of the isotomic conjugate of X(8674)
X(42670) = X(i)-Ceva conjugate of X(j) for these (i,j): {1290, 6}, {1983, 2251}
X(42670) = X(i)-isoconjugate of X(j) for these (i,j): {1, 35156}, {75, 1290}, {99, 5620}, {190, 21907}, {664, 11604}
X(42670) = crosspoint of X(i) and X(j) for these (i,j): {6, 1290}, {692, 6187}
X(42670) = crosssum of X(i) and X(j) for these (i,j): {2, 8674}, {320, 693}, {513, 33129}
X(42670) = crossdifference of every pair of points on line {2, 16732}
X(42670) = barycentric product X(i)*X(j) for these {i,j}: {6, 8674}, {512, 37783}, {513, 17796}, {523, 19622}, {647, 2074}, {650, 5172}, {661, 5127}, {667, 32849}, {1290, 35090}, {1946, 37799}, {2433, 16164}
X(42670) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 35156}, {32, 1290}, {667, 21907}, {798, 5620}, {2074, 6331}, {3063, 11604}, {5127, 799}, {5172, 4554}, {8674, 76}, {17796, 668}, {19622, 99}, {32849, 6386}, {37783, 670}
X(42670) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {667, 8641, 4775}, {1960, 8648, 667}, {8636, 8637, 667}, {8645, 8648, 1960}

X(42671) = CROSSSUM OF X(2) AND X(1508)

Barycentrics    a^2*(2*a^6 - a^4*b^2 - b^6 - a^4*c^2 + b^4*c^2 + b^2*c^4 - c^6) : :
X(42671) = X[401] - 3 X[35278], 2 X[441] - 3 X[35282]

X(42671) lies on the cubics K784 and I785 and these lines: {3, 64}, {6, 33582}, {22, 5188}, {23, 9157}, {25, 32}, {31, 8615}, {39, 184}, {50, 19596}, {51, 5007}, {69, 15594}, {98, 419}, {110, 2710}, {115, 460}, {157, 206}, {159, 577}, {160, 22052}, {161, 10316}, {187, 237}, {232, 248}, {297, 2794}, {394, 30270}, {401, 35278}, {418, 23208}, {420, 9862}, {441, 1503}, {468, 10991}, {511, 3506}, {571, 20987}, {574, 26864}, {800, 1974}, {1384, 41424}, {1576, 2393}, {1660, 22401}, {1661, 3053}, {1692, 1976}, {1843, 14575}, {1915, 13357}, {2080, 14673}, {2187, 37586}, {2409, 34156}, {2908, 42447}, {3003, 7669}, {3095, 34986}, {3292, 37916}, {3313, 33801}, {3398, 5943}, {3424, 11348}, {3455, 40352}, {3767, 6620}, {3785, 10565}, {3796, 37479}, {4224, 5337}, {4512, 8235}, {5008, 34417}, {5012, 37335}, {5041, 13366}, {5065, 19459}, {5117, 9873}, {5158, 19153}, {5595, 26953}, {5596, 6389}, {5938, 14961}, {6292, 7499}, {6688, 21513}, {6750, 6756}, {6800, 21163}, {7494, 7800}, {7712, 34099}, {7772, 11402}, {7795, 14826}, {7816, 35926}, {7889, 37439}, {8573, 33578}, {8721, 11206}, {8779, 9475}, {8854, 39648}, {8855, 39679}, {8968, 36709}, {9407, 20975}, {9605, 17809}, {9924, 15905}, {10547, 10551}, {11328, 13335}, {11430, 32444}, {11550, 14003}, {11672, 39072}, {14096, 22352}, {14913, 37893}, {15513, 41275}, {15585, 41008}, {16318, 23976}, {17810, 30435}, {18437, 34776}, {18475, 35934}, {19761, 37052}, {20897, 35007}, {21309, 31860}, {21458, 30737}, {21637, 23635}, {21639, 34569}, {23606, 34750}, {26881, 37184}, {26882, 37114}, {32621, 33871}, {34565, 34571}, {34774, 41005}, {35225, 41580}, {35259, 37344}, {35265, 35296}, {37457, 37512}

X(42671) = reflection of X(3284) in X(1576)
X(42671) = isogonal conjugate of X(35140)
X(42671) = isogonal conjugate of the anticomplement of X(23976)
X(42671) = isogonal conjugate of the isotomic conjugate of X(1503)
X(42671) = isogonal conjugate of the polar conjugate of X(16318)
X(42671) = polar conjugate of the isotomic conjugate of X(8779)
X(42671) = circumcircle-inverse of X(107)-of-1st-Brocard-triangle
X(42671) = X(34129)-complementary conjugate of X(20305)
X(42671) = X(i)-Ceva conjugate of X(j) for these (i,j): {232, 1692}, {248, 32}, {1297, 6}, {1503, 8779}, {21458, 1503}, {32696, 512}, {34156, 23976}
X(42671) = crosspoint of X(i) and X(j) for these (i,j): {6, 1297}, {25, 1976}, {248, 34156}, {685, 23590}, {1503, 16318}, {15384, 32687}, {34135, 41200}, {34136, 41201}
X(42671) = crosssum of X(i) and X(j) for these (i,j): {2, 1503}, {8, 857}, {69, 325}, {122, 39473}, {160, 3289}, {297, 39265}, {5002, 41199}, {5003, 41198}, {6330, 14944}
X(42671) = crossdifference of every pair of points on line {2, 2419}
X(42671) = X(i)-isoconjugate of X(j) for these (i,j): {1, 35140}, {63, 6330}, {69, 8767}, {75, 1297}, {162, 2419}, {336, 39265}, {799, 34212}, {811, 2435}, {1959, 9476}, {3265, 36092}, {3267, 36046}, {14944, 19611}, {15407, 40703}
X(42671) = barycentric product X(i)*X(j) for these {i,j}: {1, 2312}, {3, 16318}, {4, 8779}, {6, 1503}, {19, 8766}, {25, 441}, {32, 30737}, {39, 21458}, {67, 28343}, {74, 6793}, {98, 9475}, {111, 35282}, {132, 248}, {232, 34156}, {512, 34211}, {520, 23977}, {525, 2445}, {647, 2409}, {822, 24024}, {1297, 23976}, {1976, 15595}, {2435, 15639}, {3172, 16096}, {6103, 40080}, {32713, 39473}
X(42671) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 35140}, {25, 6330}, {32, 1297}, {441, 305}, {647, 2419}, {669, 34212}, {1503, 76}, {1973, 8767}, {1976, 9476}, {2211, 39265}, {2312, 75}, {2409, 6331}, {2445, 648}, {3049, 2435}, {3172, 14944}, {6793, 3260}, {8766, 304}, {8779, 69}, {9475, 325}, {14600, 15407}, {16318, 264}, {21458, 308}, {23976, 30737}, {23977, 6528}, {28343, 316}, {30737, 1502}, {34211, 670}, {35282, 3266}
X(42671) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {51, 34396, 5007}, {110, 37183, 36212}, {157, 206, 216}, {184, 3148, 39}, {1495, 5191, 187}, {1974, 40947, 800}, {7669, 18374, 3003}, {11206, 37188, 8721}, {36212, 37183, 18860}

X(42672) = X(16)X(627)∩X(17)X(76)

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

X(42672) lies on the Kiepert circumhyperbola of the Brocard triangle and these lines: {2, 5469}, {3, 623}, {5, 33383}, {16, 627}, {17, 76}, {141, 22737}, {182, 3642}, {302, 39554}, {532, 599}, {636, 16629}, {1352, 22687}, {3314, 22508}, {3618, 22683}, {3643, 24206}, {3734, 42673}, {5965, 22685}, {6673, 11311}, {9743, 16652}, {11300, 13084}, {11307, 16967}, {18582, 20377}, {22911, 37341}, {33225, 42489}, {34508, 36759}

X(42672) = midpoint of X(627) and X(22907)
X(42672) = reflection of X(22737) in X(141)
X(42672) = X(17)-of-Brocard-triangle
X(42672) = 1st-Brocard-isogonal conjugate of X(42674)
X(42672) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14144, 36782}, {3107, 11132, 35689}

X(42673) = X(15)X(628)∩X(18)X(76)

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

X(42673) lies on the Kiepert circumhyperbola of the Brocard triangle and these lines: {2, 5470}, {3, 624}, {5, 33382}, {15, 628}, {18, 76}, {141, 22736}, {182, 3643}, {303, 39555}, {533, 599}, {635, 16628}, {1352, 22689}, {3314, 22506}, {3618, 22685}, {3642, 24206}, {3734, 42672}, {5965, 22683}, {6674, 11312}, {9743, 16653}, {11299, 13083}, {11308, 16966}, {18581, 20378}, {22866, 37340}, {33225, 42488}, {34509, 36760}

X(42673) = midpoint of X(628) and X(22861)
X(42673) = reflection of X(22736) in X(141)
X(42673) = X(18)-of-Brocard-triangle
X(42673) = 1st-Brocard-isogonal conjugate of X(42675)
X(42673) = {X(3106),X(11133)}-harmonic conjugate of X(35688)

X(42674) = X(2)X(5470)∩X(4)X(623)

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

X(42674) lies on these lines: {2, 5470}, {3, 33421}, {4, 623}, {6, 22527}, {76, 36759}, {182, 2782}, {384, 36760}, {622, 636}, {629, 16967}, {1078, 30559}, {1352, 3642}, {3552, 30560}, {3643, 24206}, {3934, 13349}, {6295, 25157}, {7697, 33389}, {7816, 13350}, {10614, 31712}, {11185, 36252}, {18582, 37178}, {22683, 39561}, {22708, 24273}, {22737, 22907}

X(42674) = X(61)-of-Brocard-triangle
X(42674) = 1st-Brocard-isogonal conjugate of X(42672)
X(42674) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 3734, 42675}, {3734, 22687, 22689}, {25157, 35917, 6295}

X(42675) = X(2)X(5469)∩X(4)X(624)

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

X(42675) lies on these lines: {2, 5469}, {3, 33420}, {4, 624}, {6, 22526}, {76, 36760}, {182, 2782}, {384, 36759}, {621, 635}, {630, 16966}, {1078, 30560}, {1352, 3643}, {3552, 30559}, {3642, 24206}, {3934, 13350}, {6582, 25167}, {7697, 33388}, {7816, 13349}, {10613, 31711}, {11185, 36251}, {18581, 37177}, {22685, 39561}, {22707, 24273}, {22736, 22861}

X(42675) = X(62)-of-Brocard-triangle
X(42675) = 1st-Brocard-isogonal conjugate of X(42673)
X(42675) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 3734, 42674}, {3734, 22689, 22687}, {25167, 35918, 6582}

leftri

Centers on cubic K588: X(42676)-X(42681)

rightri

This preamble and centers X(42676)-X(42681) were contributed by César Eliud Lozada, April 19, 2021.

The three internal bisectors AI, BI, CI of ABC are rotated about each corresponding vertex of ABC of a same angle θ, all outwardly or all inwardly. The six rotated bisectors define a triangle NaNbNc which is perspective to ABC at a point P. The locus of P is K588. (Reference: Bernard Gibert, CTC K588)

For a given angle θ, the perspector P(θ), here denoted by K588(θ), has barycentrics coordinates:

  P(θ) = a*sin(A/2 - θ)/sin(A/2 + θ) : :

or, equivalently,

  P(t) = a*((a+b+c)*(-a+b+c)*t-S*(1-t^2))/((a+b+c)*(-a+b+c)*t+S*(1-t^2)) : :, where t = tan(θ/2)

Some perspectors K588(θ) are shown in the following table:

θ -π/2 = -90° -5π/12 = -75° -π/3 = -60° -π/4 = -45° -π/6 = -30° -π/12 = -15° 0 π/12 = 15° π/6 = 30° π/4 = 45° π/3 = 60° 5π/12 = 75° π/2 = 90°
K588(θ) X(1) X(42676) X(42677) X(6212) X(39150) X(42678) X(1) X(42679) X(39151) X(6213) X(42680) X(42681) X(1)

Note: P(θ) and P(-θ) are isogonal conjugates.

X(42676) = K588(-5 π/12 = -75°)

Barycentrics    a*(-2*S+(2+sqrt(3))*(a+b+c)*(a+b-c))*(-2*S+(2+sqrt(3))*(a+b+c)*(a-b+c))*(2*S+(2+sqrt(3))*(-a+b+c)*(a+b+c)) : :
Barycentrics    a*sin(A/2 - 5*Pi/12)/sin(A/2 + 5*Pi/12) : :

X(42676) lies on the cubic K588 and these lines: {1, 3389}, {10, 17}, {58, 7968}, {3302, 33655}

X(42676) = isogonal conjugate of X(42681)
X(42676) = trilinear product X(i)*X(j) for these {i, j}: {17, 3299}, {62, 3302}
X(42676) = trilinear quotient X(i)/X(j) for these (i, j): (17, 3300), (62, 3301), (303, 32792)
X(42676) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(3367)}} and {{A, B, C, X(10), X(42678)}}
X(42676) = X(i)-isoconjugate-of-X(j) for these {i, j}: {18, 3301}, {61, 3300}

X(42677) = K588(π/3 = -60°)

Barycentrics    a*(2*S+(-a+b+c)*(a+b+c)*sqrt(3))*(-2*S+(a+b+c)*(a-b+c)*sqrt(3))*(-2*S+(a+b+c)*(a+b-c)*sqrt(3)) : :
Barycentrics    a*sin(A/2 - Pi/3)/sin(A/2 + Pi/3) : :

X(42677) lies on the cubics K261a, K588, K1146 and these lines: {1, 15}, {3, 42623}, {10, 13}, {14, 79}, {16, 3647}, {35, 6104}, {37, 2160}, {58, 11072}, {62, 6191}, {100, 2381}, {202, 7059}, {532, 3578}, {553, 1081}, {559, 7005}, {846, 2952}, {3383, 19551}, {5237, 11789}, {5240, 5267}, {11142, 42616}, {37830, 40693}

X(42677) = isogonal conjugate of X(42680)
X(42677) = barycentric product X(i)*X(j) for these {i, j}: {299, 11072}, {2306, 40714}
X(42677) = barycentric quotient X(i)/X(j) for these (i, j): (2152, 5353), (2174, 7006), (2306, 554)
X(42677) = trilinear product X(i)*X(j) for these {i, j}: {13, 5357}, {79, 7005}, {559, 1251}, {1081, 10638}
X(42677) = trilinear quotient X(i)/X(j) for these (i, j): (16, 5353), (35, 7006), (559, 1082), (1081, 554), (1251, 33653), (2153, 11073)
X(42677) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(14)}} and {{A, B, C, X(10), X(39150)}}
X(42677) = X(i)-isoconjugate-of-X(j) for these {i, j}: {14, 5353}, {79, 7006}, {554, 1250}, {1082, 33653}
X(42677) = X(2152)-reciprocal conjugate of-X(5353)
X(42677) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 2306, 39153), (1, 3179, 2306), (37, 3579, 42680), (1251, 2306, 1), (1251, 3179, 39153)

X(42678) = K588(-π/12 = -15°)

Barycentrics    a*(2*S-(sqrt(3)-2)*(-a+b+c)*(a+b+c))*(2*S+(a+b+c)*(a-b+c)*(sqrt(3)-2))*(2*S+(a+b+c)*(a+b-c)*(sqrt(3)-2)) : :
Barycentrics    a*sin(A/2 - Pi/12)/sin(A/2 + Pi/12) : :

X(42678) lies on the cubic K588 and these lines: {1, 3364}, {10, 18}, {58, 7968}, {3302, 7052}

X(42678) = isogonal conjugate of X(42679)
X(42678) = trilinear product X(i)*X(j) for these {i, j}: {18, 3299}, {61, 3302}
X(42678) = trilinear quotient X(i)/X(j) for these (i, j): (18, 3300), (61, 3301), (302, 32792)
X(42678) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(3392)}} and {{A, B, C, X(10), X(42676)}}
X(42678) = X(i)-isoconjugate-of-X(j) for these {i, j}: {17, 3301}, {62, 3300}

X(42679) = K588(π/12 = 15°)

Barycentrics    a*(-2*S+(a+b+c)*(a+b-c)*(sqrt(3)-2))*(2*S+(sqrt(3)-2)*(-a+b+c)*(a+b+c))*(-2*S+(a+b+c)*(a-b+c)*(sqrt(3)-2)) : :
Barycentrics    a*sin(A/2+Pi/12)/sin(A/2-Pi/12) : :

X(42679) lies on the cubic K588 and these lines: {1, 3390}, {10, 17}, {58, 7969}, {3300, 33655}

X(42679) = isogonal conjugate of X(42678)
X(42679) = trilinear product X(i)*X(j) for these {i, j}: {17, 3301}, {62, 3300}
X(42679) = trilinear quotient X(i)/X(j) for these (i, j): (17, 3302), (62, 3299), (303, 32791)
X(42679) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(3366)}} and {{A, B, C, X(10), X(42681)}}
X(42679) = X(i)-isoconjugate-of-X(j) for these {i, j}: {18, 3299}, {61, 3302}

X(42680) = K588(π/3 = 60°)

Barycentrics    a*(2*S-sqrt(3)*(-a+b+c)*(a+b+c))*(2*S+sqrt(3)*(a+b+c)*(a-b+c))*(2*S+sqrt(3)*(a+b+c)*(a+b-c)) : :
Barycentrics    a*sin(A/2 + Pi/3)/sin(A/2 -Pi/3) : :

X(42680) lies on the cubics K261b, K588, K1146 and these lines: {1, 16}, {10, 14}, {13, 79}, {15, 3647}, {35, 6105}, {37, 2160}, {58, 11073}, {61, 6192}, {100, 2380}, {203, 7060}, {533, 3578}, {553, 554}, {846, 2953}, {1082, 7006}, {3376, 7126}, {5238, 11752}, {5239, 5267}, {21311, 42624}, {37833, 40694}

X(42680) = isogonal conjugate of X(42677)
X(42680) = barycentric product X(298)*X(11073)
X(42680) = barycentric quotient X(i)/X(j) for these (i, j): (2151, 5357), (2174, 7005), (2307, 559)
X(42680) = trilinear product X(i)*X(j) for these {i, j}: {14, 5353}, {79, 7006}, {554, 1250}, {1082, 33653}
X(42680) = trilinear quotient X(i)/X(j) for these (i, j): (15, 5357), (35, 7005), (554, 1081), (1082, 559), (1250, 10638), (2154, 11072)
X(42680) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(13)}} and {{A, B, C, X(10), X(39151)}}
X(42680) = X(i)-isoconjugate-of-X(j) for these {i, j}: {13, 5357}, {79, 7005}, {559, 1251}, {1081, 10638}
X(42680) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 33654, 39152), (1, 41225, 33654), (14, 2154, 39150), (37, 3579, 42677), (33653, 33654, 1), (33653, 41225, 39152)

X(42681) = K588(5 π/12 = 75°)

Barycentrics    a*(2*S+(2+sqrt(3))*(a+b+c)*(a+b-c))*(2*S+(2+sqrt(3))*(a+b+c)*(a-b+c))*(2*S-(2+sqrt(3))*(-a+b+c)*(a+b+c)) : :
Barycentrics    a*sin(A/2+5*Pi/12)/sin(A/2-5*Pi/12) : :

X(42681) lies on the cubic K588 and these lines: {1, 3365}, {10, 18}, {58, 7969}, {3300, 7052}

X(42681) = isogonal conjugate of X(42676)
X(42681) = trilinear product X(i)*X(j) for these {i, j}: {18, 3301}, {61, 3300}
X(42681) = trilinear quotient X(i)/X(j) for these (i, j): (18, 3302), (61, 3299), (302, 32791)
X(42681) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(3391)}} and {{A, B, C, X(10), X(42679)}}
X(42681) = X(i)-isoconjugate-of-X(j) for these {i, j}: {17, 3299}, {62, 3302}

leftri

Gibert (i,j,k) points on cubics K1206a and K1206b: X(42682)-X(42695)

rightri

This preamble and points X(42682)-X(42695) are contributed by Peter Moses, April 19, 2021

See
K1206

Gibert points are introduced in the preamble just before X(42085)



X(42682) = GIBERT (5,-7,2) POINT

Barycentrics    (5*a^2*S)/Sqrt[3] + 2*a^2*SA - 14*SB*SC : :

X(42682) lies on the cubic K1206a and these lines:{5, 42630}, {6, 17578}, {14, 16}, {15, 3858}, {398, 42104}, {631, 42087}, {632, 16809}, {1656, 5349}, {3091, 23302}, {3522, 23303}, {3534, 42513}, {3627, 42613}, {3843, 18582}, {3859, 16772}, {3860, 12821}, {3861, 34754}, {5071, 11480}, {5076, 5318}, {5238, 41989}, {5334, 42165}, {5339, 42109}, {5343, 42097}, {5365, 11481}, {10646, 42531}, {10654, 35403}, {11485, 41119}, {12101, 42520}, {12812, 42122}, {12817, 15713}, {14093, 42089}, {15692, 42139}, {15693, 42090}, {15694, 42130}, {15695, 42129}, {15696, 18581}, {15712, 33416}, {15714, 37835}, {16773, 42112}, {16960, 42117}, {16964, 42102}, {17538, 42096}, {19709, 42103}, {35407, 42131}, {35434, 42105}, {41099, 42110}, {42099, 42599}, {42146, 42530}, {42514, 42517}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 17578, 42683}, {5321, 19107, 42088}, {5321, 42108, 395}, {5349, 42085, 42107}, {19107, 42088, 42108}, {36970, 42136, 5321}, {42093, 42164, 23302}, {42101, 42126, 42147}

X(42683) = GIBERT (5,7,-2) POINT

Barycentrics    (5*a^2*S)/Sqrt[3] - 2*a^2*SA + 14*SB*SC : :

X(42683) lies on the cubic K1206b and these lines:{5, 42629}, {6, 17578}, {13, 15}, {16, 3858}, {397, 42105}, {631, 42088}, {632, 16808}, {1656, 5350}, {3091, 23303}, {3522, 23302}, {3534, 42512}, {3627, 42612}, {3843, 18581}, {3859, 16773}, {3860, 12820}, {3861, 34755}, {5071, 11481}, {5076, 5321}, {5237, 41989}, {5335, 42164}, {5340, 42108}, {5344, 42096}, {5366, 11480}, {10645, 42530}, {10653, 35403}, {11486, 41120}, {12101, 42521}, {12812, 42123}, {12816, 15713}, {14093, 42092}, {15692, 42142}, {15693, 42091}, {15694, 42131}, {15695, 42132}, {15696, 18582}, {15712, 33417}, {15714, 37832}, {16772, 42113}, {16961, 42118}, {16965, 42101}, {17538, 42097}, {19709, 42106}, {35407, 42130}, {35434, 42104}, {41099, 42107}, {42100, 42598}, {42143, 42531}, {42515, 42516}

X(42683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 17578, 42682}, {5318, 19106, 42087}, {5318, 42109, 396}, {5350, 42086, 42110}, {19106, 42087, 42109}, {36969, 42137, 5318}, {42094, 42165, 23303}, {42102, 42127, 42148}

X(42684) = GIBERT (5,-1,10) POINT

Barycentrics    (5*a^2*S)/Sqrt[3] + 10*a^2*SA - 2*SB*SC : :

X(42684) lies on the cubic K1206b and these lines:{4, 11480}, {6, 10304}, {14, 549}, {15, 548}, {395, 15698}, {396, 3534}, {485, 42168}, {486, 42167}, {547, 42630}, {3526, 5321}, {3628, 5352}, {3856, 16966}, {3857, 19107}, {5055, 42085}, {5066, 36967}, {5072, 42092}, {5238, 5318}, {5349, 33417}, {7486, 42107}, {8703, 34754}, {10303, 42119}, {10646, 15759}, {10654, 15706}, {11001, 42518}, {11488, 15683}, {11489, 15717}, {11540, 42143}, {12103, 16960}, {14890, 37835}, {15022, 42093}, {15640, 16644}, {15684, 42102}, {15709, 42154}, {16241, 23046}, {16772, 17800}, {16808, 33699}, {19710, 33607}, {34200, 34755}, {36836, 42088}, {37640, 42508}, {42099, 42598}, {42111, 42500}, {42118, 42529}, {42124, 42434}, {42140, 42490}

X(42684) = {X(6),X(10304)}-harmonic conjugate of X(42685)
X(42684) = {X(16772),X(42090)}-harmonic conjugate of X(42109)

X(42685) = GIBERT (5,1,-10) POINT

Barycentrics    (5*a^2*S)/Sqrt[3] - 10*a^2*SA + 2*SB*SC : :

X(42685) lies on the cubic K1206a and these lines:{4, 11481}, {6, 10304}, {13, 549}, {16, 548}, {395, 3534}, {396, 15698}, {485, 42170}, {486, 42169}, {547, 42629}, {3526, 5318}, {3628, 5351}, {3856, 16967}, {3857, 19106}, {5055, 42086}, {5066, 36968}, {5072, 42089}, {5237, 5321}, {5350, 33416}, {7486, 42110}, {8703, 34755}, {10303, 42120}, {10645, 15759}, {10653, 15706}, {11001, 42519}, {11488, 15717}, {11489, 15683}, {11540, 42146}, {12103, 16961}, {14890, 37832}, {15022, 42094}, {15640, 16645}, {15684, 42101}, {15709, 42155}, {16242, 23046}, {16773, 17800}, {16809, 33699}, {19710, 33606}, {34200, 34754}, {36843, 42087}, {37641, 42509}, {42100, 42599}, {42114, 42501}, {42117, 42528}, {42121, 42433}, {42141, 42491}

X(42685) = {X(16773),X(42091)}-harmonic conjugate of X(42108)

X(42686) = GIBERT (-5,1,10) POINT

Barycentrics    (-5*a^2*S)/Sqrt[3] + 10*a^2*SA + 2*SB*SC : :

X(42686) lies on the cubic K1206b and these lines:{4, 11481}, {5, 42629}, {6, 15717}, {13, 11540}, {16, 396}, {395, 10304}, {548, 10646}, {3526, 18582}, {3530, 34755}, {3534, 5321}, {3628, 5237}, {3856, 19106}, {3857, 16967}, {5054, 42512}, {5055, 42089}, {5066, 16242}, {5072, 42086}, {5335, 15709}, {5349, 42628}, {5351, 15704}, {6560, 42167}, {6561, 42168}, {7486, 42120}, {8703, 16961}, {10303, 23302}, {10653, 42502}, {11480, 15698}, {11485, 15706}, {11489, 42164}, {12100, 42521}, {12108, 16960}, {15022, 42165}, {15640, 42139}, {15683, 16645}, {15684, 42129}, {15685, 42513}, {15713, 33607}, {16966, 42501}, {17800, 18581}, {23046, 36968}, {33699, 42100}, {37832, 42505}, {37835, 42584}, {41100, 42627}, {41121, 42492}, {42091, 42599}, {42118, 42499}, {42136, 42528}, {42143, 42433}, {42145, 42489}, {42500, 42510}

X(42685) = {X(6),X(10304)}-harmonic conjugate of X(42684)
X(42686) = {X(10646),X(16773)}-harmonic conjugate of X(42087)

X(42687) = GIBERT (5,1,10) POINT

Barycentrics    (5*a^2*S)/Sqrt[3] + 10*a^2*SA + 2*SB*SC : :

X(42687) lies on the cubic K1206a and these lines:{4, 11480}, {5, 42630}, {6, 15717}, {14, 11540}, {15, 395}, {396, 10304}, {548, 10645}, {3526, 18581}, {3530, 34754}, {3534, 5318}, {3628, 5238}, {3856, 19107}, {3857, 16966}, {5054, 42513}, {5055, 42092}, {5066, 16241}, {5072, 42085}, {5334, 15709}, {5350, 42627}, {5352, 15704}, {6560, 42169}, {6561, 42170}, {7486, 42119}, {8703, 16960}, {10303, 23303}, {10654, 42503}, {11481, 15698}, {11486, 15706}, {11488, 42165}, {12100, 42520}, {12108, 16961}, {15022, 42164}, {15640, 42142}, {15683, 16644}, {15684, 42132}, {15685, 42512}, {15713, 33606}, {16967, 42500}, {17800, 18582}, {23046, 36967}, {33699, 42099}, {37832, 42585}, {37835, 42504}, {41101, 42628}, {41122, 42493}, {42090, 42598}, {42117, 42498}, {42137, 42529}, {42144, 42488}, {42146, 42434}, {42501, 42511}

X(42687) = {X(10645),X(16772)}-harmonic conjugate of X(42088)

X(42688) = GIBERT (10,-8,5) POINT

Barycentrics    (10*a^2*S)/Sqrt[3] + 5*a^2*SA - 16*SB*SC : :

X(42688) lies on the cubic K1206a and these lines:{4, 11408}, {6, 15684}, {381, 42512}, {395, 3534}, {548, 11489}, {549, 42125}, {3526, 5321}, {3628, 42119}, {3830, 42520}, {3857, 42132}, {5055, 16241}, {5066, 42133}, {5072, 23302}, {5334, 15704}, {7486, 42135}, {10303, 42122}, {11486, 16964}, {11488, 23046}, {14269, 34754}, {15640, 42118}, {15683, 42144}, {15685, 34755}, {15695, 33606}, {15706, 23303}, {15709, 42143}, {15717, 42129}, {42086, 42164}, {42095, 42498}

X(42689) = GIBERT (10,8,-5) POINT

Barycentrics    (10*a^2*S)/Sqrt[3] - 5*a^2*SA + 16*SB*SC : :

X(42689) lies on the cubic K1206b and these lines:{4, 11409}, {6, 15684}, {381, 42513}, {396, 3534}, {548, 11488}, {549, 42128}, {3526, 5318}, {3628, 42120}, {3830, 42521}, {3857, 42129}, {5055, 16242}, {5066, 42134}, {5072, 23303}, {5335, 15704}, {7486, 42138}, {10303, 42123}, {11485, 16965}, {11489, 23046}, {14269, 34755}, {15640, 42117}, {15683, 42145}, {15685, 34754}, {15695, 33607}, {15706, 23302}, {15709, 42146}, {15717, 42132}, {42085, 42165}, {42098, 42499}

X(42690) = GIBERT (-10,8,5) POINT

Barycentrics    (-10*a^2*S)/Sqrt[3] + 5*a^2*SA + 16*SB*SC : :

X(42690) lies on the cubic K1206a and these lines:{4, 11409}, {14, 5055}, {16, 15684}, {548, 42126}, {549, 42119}, {632, 42415}, {3526, 18581}, {3534, 5321}, {3628, 5334}, {3830, 12821}, {3857, 42128}, {5066, 42139}, {5072, 18582}, {5335, 23046}, {5339, 33416}, {5343, 42628}, {7486, 42143}, {10303, 42117}, {10304, 42130}, {11480, 41122}, {11489, 15704}, {15022, 42132}, {15640, 42123}, {15683, 42136}, {15706, 42089}, {17800, 19107}, {33602, 42138}, {42088, 42159}, {42141, 42497}

X(42691) = GIBERT (10,8,5) POINT

Barycentrics    (10*a^2*S)/Sqrt[3] + 5*a^2*SA + 16*SB*SC : :

X(42691) lies on the cubic K1206b and these lines:{4, 11408}, {13, 5055}, {15, 15684}, {548, 42127}, {549, 42120}, {632, 42416}, {3526, 18582}, {3534, 5318}, {3628, 5335}, {3830, 12820}, {3857, 42125}, {5066, 42142}, {5072, 18581}, {5334, 23046}, {5340, 33417}, {5344, 42627}, {7486, 42146}, {10303, 42118}, {10304, 42131}, {11481, 41121}, {11488, 15704}, {15022, 42129}, {15640, 42122}, {15683, 42137}, {15706, 42092}, {17800, 19106}, {33603, 42135}, {42087, 42162}, {42140, 42496}

X(42692) = GIBERT (-5,7,2) POINT

Barycentrics    (-5*a^2*S)/Sqrt[3] + 2*a^2*SA + 14*SB*SC : :

X(42692) lies on the cubic K1206a and these lines:{5, 15}, {6, 3839}, {14, 14893}, {376, 23303}, {395, 3830}, {396, 41106}, {398, 42103}, {549, 42630}, {1657, 5349}, {3146, 11489}, {3523, 42087}, {3525, 42095}, {3853, 16961}, {3854, 5339}, {3857, 16960}, {3860, 16808}, {5054, 42085}, {5066, 34754}, {5318, 42159}, {5334, 42166}, {5343, 42098}, {5365, 11480}, {10124, 10645}, {10646, 12817}, {11543, 12102}, {12100, 36970}, {12101, 42629}, {12103, 19107}, {12108, 16967}, {15687, 34755}, {15703, 42111}, {16773, 42104}, {21734, 42140}, {33923, 42136}, {35408, 42429}, {36836, 42473}, {37835, 42144}, {41973, 42627}, {41989, 42415}, {42109, 42153}, {42121, 42531}, {42489, 42585}, {42499, 42632}

X(42692) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5321, 16809, 23302}, {5321, 42107, 42147}, {5349, 18581, 42108}, {16809, 23302, 42107}, {42093, 42163, 42088}, {42101, 42125, 395}

X(42693) = GIBERT (5,7,2) POINT

Barycentrics    (5*a^2*S)/Sqrt[3] + 2*a^2*SA + 14*SB*SC : :

X(42693) lies on the cubic K1206b and these lines:{5, 16}, {6, 3839}, {13, 14893}, {376, 23302}, {395, 41106}, {396, 3830}, {397, 42106}, {549, 42629}, {1657, 5350}, {3146, 11488}, {3523, 42088}, {3525, 42098}, {3853, 16960}, {3854, 5340}, {3857, 16961}, {3860, 16809}, {5054, 42086}, {5066, 34755}, {5321, 42162}, {5335, 42163}, {5344, 42095}, {5366, 11481}, {10124, 10646}, {10645, 12816}, {11542, 12102}, {12100, 36969}, {12101, 42630}, {12103, 19106}, {12108, 16966}, {15687, 34754}, {15703, 42114}, {16772, 42105}, {21734, 42141}, {33923, 42137}, {35408, 42430}, {36843, 42472}, {37832, 42145}, {41974, 42628}, {41989, 42416}, {42108, 42156}, {42124, 42530}, {42488, 42584}, {42498, 42631}

X(42693) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5318, 16808, 23303}, {5318, 42110, 42148}, {5350, 18582, 42109}, {16808, 23303, 42110}, {42094, 42166, 42087}, {42102, 42128, 396}

X(42694) = GIBERT (-15,32,5) POINT

Barycentrics    -5*Sqrt[3]*a^2*S + 5*a^2*SA + 64*SB*SC : :

X(24694) lies on the cubic K1206a and these lines:{4, 14}, {5, 42630}, {18, 33699}, {548, 16809}, {3146, 12821}, {3526, 42093}, {3534, 42489}, {3628, 42432}, {3839, 42520}, {3856, 16964}, {3857, 42147}, {5055, 5352}, {5066, 5349}, {5072, 36970}, {5237, 15684}, {5365, 16267}, {10646, 17800}, {12817, 23046}, {15687, 33606}, {15704, 37835}, {15717, 19107}, {41988, 42521}, {42096, 42477}, {42103, 42488}, {42107, 42498}, {42121, 42433}, {42495, 42631}

X(42695) = GIBERT (15,32,5) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 5*a^2*SA + 64*SB*SC : :

X(42695) lies on the cubic K1206b and these lines:{4, 13}, {5, 42629}, {17, 33699}, {548, 16808}, {3146, 12820}, {3526, 42094}, {3534, 42488}, {3628, 42431}, {3839, 42521}, {3856, 16965}, {3857, 42148}, {5055, 5351}, {5066, 5350}, {5072, 36969}, {5238, 15684}, {5366, 16268}, {10645, 17800}, {12816, 23046}, {15687, 33607}, {15704, 37832}, {15717, 19106}, {41988, 42520}, {42097, 42476}, {42106, 42489}, {42110, 42499}, {42124, 42434}, {42494, 42632}

X(42696) = ISOTOMIC CONJUGATE OF X(3296)

Barycentrics    a^2 - b^2 - c^2 - 4*b*c : :
Barycentrics    (2 + Cos[A])*Csc[A] : :

X(42696) lies on these lines: {1, 4464}, {2, 594}, {4, 33941}, {6, 4399}, {7, 8}, {9, 4431}, {10, 3875}, {37, 27480}, {80, 4986}, {81, 19825}, {86, 145}, {141, 17119}, {142, 4060}, {144, 17346}, {183, 7172}, {190, 391}, {192, 966}, {193, 4363}, {239, 2345}, {264, 7046}, {269, 25719}, {280, 20477}, {307, 36889}, {313, 4441}, {314, 1000}, {321, 14555}, {326, 3872}, {329, 4886}, {332, 37728}, {344, 2321}, {345, 5271}, {346, 17277}, {347, 33298}, {350, 3974}, {491, 32793}, {492, 32794}, {497, 33931}, {519, 10436}, {524, 7231}, {536, 17257}, {599, 4478}, {894, 1992}, {956, 1444}, {1007, 3705}, {1058, 33939}, {1086, 3620}, {1211, 30699}, {1213, 17318}, {1219, 7268}, {1265, 3596}, {1266, 4668}, {1267, 32806}, {1278, 1654}, {1387, 4561}, {2324, 28827}, {2551, 33938}, {2968, 40680}, {3008, 4058}, {3161, 17335}, {3187, 19822}, {3226, 26076}, {3241, 17394}, {3247, 24603}, {3305, 42032}, {3434, 17163}, {3436, 21273}, {3578, 20078}, {3589, 4405}, {3598, 37671}, {3616, 4460}, {3617, 3672}, {3619, 3661}, {3621, 3945}, {3625, 3664}, {3626, 3663}, {3632, 3879}, {3644, 17256}, {3662, 21356}, {3679, 4357}, {3681, 21867}, {3686, 3729}, {3687, 5219}, {3706, 30758}, {3707, 25728}, {3739, 17299}, {3758, 7229}, {3759, 5749}, {3763, 4395}, {3790, 38057}, {3886, 30331}, {3911, 11679}, {3912, 4007}, {3943, 17259}, {3946, 17308}, {3996, 16992}, {4034, 4416}, {4043, 28809}, {4046, 37703}, {4072, 25072}, {4329, 5178}, {4346, 17273}, {4359, 18141}, {4373, 39710}, {4389, 4452}, {4393, 28604}, {4398, 17271}, {4402, 16706}, {4420, 7269}, {4440, 4821}, {4454, 17347}, {4470, 17379}, {4472, 16884}, {4643, 4686}, {4644, 11008}, {4648, 4699}, {4664, 5296}, {4669, 17274}, {4675, 4739}, {4688, 4851}, {4690, 4726}, {4727, 31238}, {4740, 6646}, {4748, 17247}, {4751, 5308}, {4764, 17258}, {4772, 17300}, {4798, 4910}, {4816, 4888}, {4852, 17303}, {4869, 17295}, {4873, 25101}, {4916, 17391}, {4980, 5905}, {5015, 32006}, {5082, 5195}, {5084, 33932}, {5222, 17289}, {5257, 17133}, {5295, 5722}, {5391, 32805}, {5554, 24547}, {5736, 20013}, {5739, 17484}, {5750, 16834}, {7081, 34229}, {7222, 17364}, {7228, 40341}, {8025, 20046}, {9780, 17322}, {10327, 26234}, {10444, 11362}, {10446, 12245}, {14213, 26872}, {14552, 32939}, {14828, 20015}, {15668, 17388}, {16685, 27640}, {16815, 17242}, {16816, 17280}, {16833, 17353}, {16969, 28252}, {17014, 17381}, {17135, 30962}, {17142, 25291}, {17184, 19819}, {17228, 37756}, {17229, 17278}, {17234, 29616}, {17239, 17301}, {17240, 29627}, {17245, 17309}, {17246, 17251}, {17262, 17330}, {17264, 18230}, {17268, 29628}, {17269, 17337}, {17281, 17348}, {17282, 29594}, {17296, 24199}, {17302, 29593}, {17310, 27147}, {17311, 34824}, {17319, 28635}, {17327, 17395}, {17332, 20073}, {17350, 37654}, {17352, 24599}, {17354, 37681}, {17358, 29590}, {17365, 20080}, {17373, 26806}, {17378, 31145}, {17383, 29591}, {17396, 29610}, {18228, 42034}, {18697, 33937}, {19789, 32782}, {19804, 34255}, {19826, 33146}, {20012, 37632}, {20050, 41847}, {20879, 26871}, {20947, 26105}, {21020, 33088}, {21085, 33144}, {21271, 21279}, {21868, 28358}, {23897, 27556}, {24048, 24058}, {24963, 31012}, {26038, 30963}, {26042, 26801}, {26048, 26107}, {26774, 27192}, {27484, 41325}, {28329, 28639}, {28641, 29580}, {29016, 36706}, {30828, 33077}, {31130, 33090}, {32791, 32813}, {32792, 32812}, {32797, 32811}, {32798, 32810}, {32800, 32807}, {35550, 36500}, {38000, 42049}

X(42696) = isotomic conjugate of X(3296)
X(42696) = anticomplement of the isogonal conjugate of X(25417)
X(42696) = isotomic conjugate of the isogonal conjugate of X(3295)
X(42696) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {58, 30562}, {8652, 514}, {25417, 8}, {28625, 1654}, {30590, 21291}, {30598, 69}, {32042, 20295}, {34819, 192}, {37211, 513}, {42030, 3436}
X(42696) = X(3697)-cross conjugate of X(3305)
X(42696) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3296}, {1973, 30679}
X(42696) = cevapoint of X(8) and X(41915)
X(42696) = crosspoint of X(4998) and X(32042)
X(42696) = crosssum of X(3271) and X(4834)
X(42696) = barycentric product X(i)*X(j) for these {i,j}: {7, 42032}, {75, 3305}, {76, 3295}, {274, 3697}, {312, 7190}, {4917, 40014}
X(42696) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3296}, {69, 30679}, {3295, 6}, {3305, 1}, {3697, 37}, {4917, 1743}, {7190, 57}, {42032, 8}
X(42696) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 8, 319}, {7, 319, 69}, {8, 75, 69}, {8, 31995, 32099}, {8, 32087, 75}, {10, 3875, 17321}, {69, 75, 42697}, {75, 319, 7}, {75, 320, 31995}, {75, 5564, 8}, {75, 17360, 7321}, {75, 20930, 20880}, {142, 4060, 17294}, {239, 2345, 3618}, {320, 32099, 69}, {391, 4461, 190}, {594, 4361, 2}, {594, 17366, 17293}, {894, 5839, 1992}, {894, 29617, 5839}, {1086, 4445, 3620}, {1278, 1654, 4419}, {2321, 4384, 344}, {2345, 4371, 239}, {3008, 4058, 17286}, {3616, 4460, 17393}, {3616, 5936, 28653}, {3617, 3672, 5224}, {3621, 3945, 17377}, {3626, 3663, 17270}, {3632, 25590, 3879}, {3661, 4000, 3619}, {3661, 17117, 4000}, {3679, 17151, 4357}, {3739, 17299, 17316}, {4034, 4659, 4416}, {4361, 17293, 17366}, {4363, 17362, 193}, {4389, 32025, 5232}, {4399, 4665, 6}, {4402, 29611, 16706}, {4452, 4678, 5232}, {4452, 5232, 4389}, {4460, 5936, 3616}, {4478, 7263, 599}, {4644, 17363, 11008}, {4678, 5232, 32025}, {4690, 4726, 17276}, {4699, 6542, 4648}, {4739, 17372, 4675}, {4751, 17315, 5308}, {4772, 20055, 17300}, {4821, 17343, 4440}, {4852, 17303, 26626}, {4886, 42029, 329}, {5224, 17160, 3672}, {5564, 32087, 69}, {7321, 17360, 21296}, {15668, 17388, 29585}, {16816, 17280, 37650}, {17116, 17363, 4644}, {17229, 17278, 29579}, {17245, 17309, 29583}, {17281, 17348, 26685}, {17293, 17366, 2}, {17360, 21296, 69}, {17393, 28653, 3616}, {31995, 32099, 320}, {34255, 41915, 19804}, {36928, 36929, 388}

X(42697) = ISOTOMIC CONJUGATE OF X(1000)

Barycentrics    a^2 - b^2 -c^2 + 4*b*c : :
Barycentrics    (2 - Cos[A])*Csc[A] : :

X(42697) lies on this lines: {1, 1266}, {2, 45}, {4, 33940}, {6, 4395}, {7, 8}, {9, 4480}, {10, 4887}, {38, 24445}, {63, 9816}, {79, 15434}, {81, 19789}, {86, 3445}, {141, 17118}, {142, 344}, {144, 17277}, {145, 17160}, {183, 3598}, {192, 4648}, {193, 4361}, {239, 1992}, {264, 1119}, {274, 957}, {307, 8797}, {312, 9776}, {314, 3296}, {321, 18141}, {326, 7190}, {329, 19804}, {332, 16137}, {333, 9965}, {341, 11024}, {345, 5249}, {346, 17234}, {347, 20477}, {348, 22464}, {350, 30947}, {374, 41772}, {376, 39552}, {391, 17347}, {443, 1265}, {491, 32794}, {492, 32793}, {497, 4459}, {519, 4896}, {524, 4405}, {527, 3707}, {536, 4675}, {537, 24693}, {553, 11679}, {573, 29382}, {594, 3620}, {599, 4665}, {870, 9432}, {894, 3618}, {940, 30699}, {948, 40862}, {966, 4699}, {982, 24463}, {988, 1125}, {1000, 20569}, {1001, 24280}, {1007, 7179}, {1043, 11036}, {1056, 20924}, {1213, 17255}, {1227, 17165}, {1267, 32805}, {1268, 36606}, {1278, 17300}, {1376, 21320}, {1443, 4861}, {1444, 37227}, {1447, 34229}, {1633, 26241}, {1654, 4772}, {1698, 4357}, {1958, 18162}, {1964, 25570}, {1996, 5231}, {1997, 5437}, {2321, 17298}, {2345, 3619}, {2481, 34919}, {2551, 33944}, {2796, 24331}, {3161, 17263}, {3187, 19819}, {3210, 5712}, {3241, 36588}, {3244, 3664}, {3306, 4054}, {3421, 33934}, {3434, 17140}, {3474, 3757}, {3475, 32932}, {3589, 7231}, {3616, 17320}, {3617, 17271}, {3623, 3945}, {3633, 3879}, {3644, 17317}, {3661, 21356}, {3685, 38053}, {3687, 4654}, {3717, 38052}, {3739, 17257}, {3753, 20925}, {3758, 5222}, {3759, 4402}, {3763, 7227}, {3826, 27549}, {3834, 17281}, {3872, 17079}, {3883, 4312}, {3886, 5542}, {3912, 4659}, {3943, 17313}, {3980, 33144}, {4009, 30758}, {4029, 28301}, {4307, 32922}, {4310, 5263}, {4359, 5905}, {4371, 17363}, {4399, 40341}, {4418, 29638}, {4429, 7613}, {4431, 17296}, {4441, 29824}, {4461, 4869}, {4488, 17336}, {4569, 6063}, {4618, 36944}, {4643, 4688}, {4664, 5308}, {4667, 4982}, {4670, 17301}, {4673, 11037}, {4676, 16020}, {4679, 30796}, {4686, 4727}, {4691, 17270}, {4726, 17299}, {4738, 32097}, {4739, 17275}, {4740, 6542}, {4741, 24699}, {4747, 17014}, {4748, 17254}, {4751, 5296}, {4764, 17315}, {4795, 16666}, {4798, 41311}, {4821, 17375}, {4859, 17353}, {4886, 41915}, {4899, 38200}, {4902, 4967}, {4911, 32006}, {4947, 24456}, {5057, 26234}, {5224, 32089}, {5232, 17273}, {5278, 20078}, {5391, 8243}, {5554, 17895}, {5695, 25557}, {5698, 16823}, {5739, 17483}, {5744, 30608}, {5749, 16706}, {5750, 17304}, {5839, 11008}, {5902, 20894}, {5936, 39707}, {5949, 27704}, {6172, 17335}, {6356, 40680}, {6666, 25728}, {6687, 17278}, {6745, 40719}, {7172, 37671}, {7229, 17289}, {7240, 18194}, {7359, 27509}, {7736, 33891}, {8817, 21436}, {8822, 37113}, {9780, 17250}, {10444, 31730}, {10446, 29309}, {10527, 41804}, {14213, 26871}, {14829, 21454}, {15668, 17246}, {16064, 24822}, {16670, 41140}, {16709, 17183}, {16815, 17333}, {16816, 20072}, {16825, 24695}, {17132, 29571}, {17133, 29605}, {17146, 21283}, {17164, 35550}, {17169, 30939}, {17170, 39731}, {17184, 19822}, {17227, 29611}, {17235, 17303}, {17236, 28604}, {17245, 17262}, {17249, 28653}, {17259, 17334}, {17261, 27147}, {17264, 29627}, {17265, 17340}, {17279, 31243}, {17282, 17355}, {17286, 21255}, {17297, 29616}, {17318, 17392}, {17322, 25581}, {17323, 17398}, {17344, 28634}, {17349, 31300}, {17350, 37650}, {17362, 20080}, {17377, 20014}, {17740, 27757}, {17776, 27186}, {17868, 18161}, {17889, 29861}, {17891, 18207}, {18135, 39995}, {19276, 39544}, {19785, 29833}, {19825, 32782}, {20054, 32093}, {20195, 25101}, {20533, 36494}, {20568, 21290}, {20879, 26872}, {20905, 20927}, {20917, 40875}, {21061, 29747}, {24165, 26098}, {24248, 24325}, {24334, 36538}, {24357, 41842}, {24589, 31018}, {24616, 35596}, {24715, 31178}, {24723, 39581}, {24789, 26065}, {24833, 36474}, {26040, 32937}, {26042, 26149}, {26229, 37762}, {26245, 37540}, {26842, 28605}, {28827, 40880}, {28968, 37800}, {29069, 36698}, {30035, 34830}, {30589, 37635}, {30598, 39709}, {30712, 39710}, {32025, 33800}, {32791, 32812}, {32792, 32813}, {32797, 32810}, {32798, 32811}, {32799, 32807}, {34255, 42029}, {35171, 35175}

X(42697) = isogonal conjugate of X(34446)
X(42697) = isotomic conjugate of X(1000)
X(42697) = isotomic conjugate of the anticomplement of X(40587)
X(42697) = isotomic conjugate of the isogonal conjugate of X(999)
X(42697) = complement of X(20073)
X(42697) = anticomplement of X(45)
X(42697) = anticomplement of the isogonal conjugate of X(89)
X(42697) = anticomplement of the isotomic conjugate of X(20569)
X(42697) = polar conjugate of the isogonal conjugate of X(22129)
X(42697) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2, 21291}, {6, 17488}, {58, 30564}, {89, 8}, {649, 39364}, {2163, 2}, {2320, 329}, {2364, 144}, {4588, 514}, {4597, 20295}, {4604, 513}, {5385, 3952}, {5549, 4468}, {20569, 6327}, {28607, 192}, {28658, 1654}, {30588, 1330}, {30608, 3436}, {34073, 17494}, {39428, 17310}, {39704, 69}, {40833, 21282}
X(42697) = X(i)-Ceva conjugate of X(j) for these (i,j): {20569, 2}, {20925, 28808}
X(42697) = X(i)-cross conjugate of X(j) for these (i,j): {3306, 17079}, {3753, 3306}, {3872, 28808}, {4054, 20925}, {40587, 2}
X(42697) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34446}, {31, 1000}, {604, 36916}, {1973, 30680}
X(42697) = cevapoint of X(i) and X(j) for these (i,j): {999, 22129}, {3241, 5744}, {3306, 3872}, {3753, 4054}
X(42697) = crosspoint of X(4597) and X(4998)
X(42697) = crosssum of X(3271) and X(4775)
X(42697) = crossdifference of every pair of points on line {1960, 3063}
X(42697) = barycentric product X(i)*X(j) for these {i,j}: {1, 20925}, {7, 28808}, {8, 17079}, {75, 3306}, {76, 999}, {85, 3872}, {86, 4054}, {190, 21183}, {264, 22129}, {274, 3753}, {1231, 17519}, {3261, 35281}, {20569, 40587}, {30608, 36595}, {36919, 40833}
X(42697) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 1000}, {6, 34446}, {8, 36916}, {69, 30680}, {999, 6}, {3306, 1}, {3672, 14556}, {3753, 37}, {3872, 9}, {4054, 10}, {4997, 36596}, {17079, 7}, {17519, 1172}, {20925, 75}, {21183, 514}, {22129, 3}, {28808, 8}, {35281, 101}, {36595, 5219}, {36914, 36920}, {36919, 4908}, {40587, 45}
X(42697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4346, 4389}, {2, 4440, 4419}, {2, 4454, 190}, {2, 20073, 45}, {7, 8, 320}, {7, 75, 69}, {7, 31598, 1122}, {7, 31995, 75}, {7, 32087, 21296}, {8, 320, 69}, {10, 4887, 17274}, {45, 31139, 34824}, {45, 31244, 31285}, {45, 34824, 2}, {69, 75, 42696}, {75, 85, 3262}, {75, 319, 32087}, {75, 320, 8}, {75, 7321, 7}, {75, 17361, 5564}, {75, 20930, 20895}, {86, 4398, 3672}, {142, 3729, 344}, {190, 29451, 29505}, {192, 26806, 4648}, {239, 4644, 1992}, {319, 21296, 69}, {391, 20059, 17347}, {594, 7232, 3620}, {894, 4000, 3618}, {903, 4389, 4346}, {1086, 4363, 2}, {1086, 17369, 17290}, {1278, 17300, 17314}, {2345, 3662, 3619}, {3306, 4054, 28808}, {3662, 17116, 2345}, {3663, 10436, 17321}, {3672, 4373, 4398}, {3739, 17276, 17257}, {3758, 37756, 5222}, {3834, 17281, 29579}, {3943, 17313, 29583}, {3945, 4452, 4360}, {4000, 7222, 894}, {4359, 5905, 14555}, {4361, 17365, 193}, {4363, 17290, 17369}, {4461, 4869, 17233}, {4472, 17325, 2}, {4488, 18230, 17336}, {4659, 6173, 3912}, {4665, 7238, 599}, {4670, 17301, 26626}, {4699, 6646, 966}, {4726, 17376, 17299}, {4739, 17345, 17275}, {4751, 17258, 5296}, {4862, 25590, 4357}, {4888, 17151, 3879}, {5222, 35578, 3758}, {5564, 17361, 32099}, {5839, 17364, 11008}, {7228, 7263, 6}, {7321, 31995, 69}, {16816, 20072, 37654}, {17117, 17364, 5839}, {17160, 17378, 145}, {17254, 29576, 4748}, {17278, 17351, 26685}, {17290, 17369, 2}, {17318, 17392, 29585}, {17320, 41847, 3616}, {17354, 27191, 2}, {17361, 32099, 69}, {17740, 31019, 30828}, {20331, 28363, 27638}, {20331, 30958, 2}, {21296, 32087, 319}, {24594, 30566, 2}, {24715, 31178, 36479}, {24894, 25659, 2}, {26039, 26104, 2}, {26769, 26817, 2}, {26976, 27107, 2}, {27037, 27160, 2}, {27266, 27316, 2}, {31244, 31285, 2}, {31285, 34824, 31244}

leftri

Points on the line X(2)X(37): X(42698)-X(42724)

rightri

This preamble and points X(42698-X(42724) are contributed by Peter Moses, April 21, 2021

Suppose that P' = p' : q' : r' is a point on a line p x + q y + r z = 0 and that u x + v y + w z = 0 is a line, L. Then the point P'' = (p/u)*p' : (q/v)*q' + (r/w)*r' (p/u)*p' : (q/v)*q' + (r/w)*r' lies on L For example, if P' is on the Euler line and L is the line X(2)X(37), then P'' is on L. Points X(42698)-X(42715) are obtained in this manner from the Euler line, where, in the same order, P' = X(i) for i = 5, 20, 24, 186, 237, 297, 378, 404, 405, 406, 407, 447, 451, 458, 461, 468, 469, 475. Points X(42716)-X(42724) are obtained from points P' on the line at infinity, with indices in this order: 30, 511, 515, 516, 518, 524, 528, 674, 1499.



X(42698) = X(2)X(37)∩X(68)X(72)

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

X(42698) lies on these lines: {2, 37}, {5, 14213}, {68, 72}, {306, 18588}, {343, 18695}, {7283, 17515}, {18027, 27801}, {18855, 41013}, {23120, 23130}

X(42698) = crosspoint of X(i) and X(j) for these (i,j): {18695, 28706}, {20336, 27801}
X(42698) = X(i)-isoconjugate of X(j) for these (i,j): {28, 2148}, {54, 1474}, {58, 8882}, {275, 2206}, {608, 35196}, {649, 933}, {1333, 2190}, {1919, 18831}, {2167, 2203}, {2169, 5317}, {6591, 36134}, {7649, 14586}, {8747, 14533}
X(42698) = barycentric product X(i)*X(j) for these {i,j}: {5, 20336}, {10, 18695}, {37, 28706}, {72, 311}, {216, 27801}, {304, 21011}, {305, 21807}, {306, 14213}, {321, 343}, {324, 3998}, {668, 6368}, {906, 15415}, {1332, 18314}, {1953, 40071}, {2618, 4561}, {6386, 15451}, {16697, 28654}
X(42698) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 28}, {10, 2190}, {37, 8882}, {51, 2203}, {53, 5317}, {71, 2148}, {72, 54}, {78, 35196}, {100, 933}, {216, 1333}, {306, 2167}, {311, 286}, {313, 40440}, {321, 275}, {343, 81}, {668, 18831}, {906, 14586}, {1331, 36134}, {1332, 18315}, {1953, 1474}, {2618, 7649}, {3682, 2169}, {3990, 14533}, {3998, 97}, {4064, 2616}, {5562, 1437}, {6332, 39177}, {6335, 16813}, {6368, 513}, {7069, 2299}, {12077, 6591}, {14213, 27}, {14391, 14399}, {15451, 667}, {16697, 593}, {17434, 22383}, {18314, 17924}, {18695, 86}, {20336, 95}, {21011, 19}, {21807, 25}, {27801, 276}, {28706, 274}, {30493, 1408}, {35307, 32674}, {35442, 18210}, {41013, 8884}
X(42698) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 20336, 3998}

X(42699) = X(2)X(37)∩X(20)X(3198)

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

X(42699) lies on these lines: {2, 37}, {20, 3198}, {72, 15740}, {100, 34168}, {306, 1231}, {440, 20235}, {1105, 4219}, {1259, 23661}, {4183, 7283}

X(42699) = X(i)-isoconjugate of X(j) for these (i,j): {27, 33581}, {28, 2155}, {58, 41489}, {64, 1474}, {459, 2206}, {649, 1301}, {2184, 2203}, {2204, 8809}, {5317, 19614}, {8747, 14642}
X(42699) = barycentric product X(i)*X(j) for these {i,j}: {20, 20336}, {72, 14615}, {304, 8804}, {305, 3198}, {306, 18750}, {321, 37669}, {610, 40071}, {668, 8057}, {1231, 27382}, {1562, 4601}, {3710, 33673}, {3718, 5930}, {3998, 15466}, {4561, 17898}, {6335, 20580}, {6386, 42658}, {15905, 27801}
X(42699) = barycentric quotient X(i)/X(j) for these {i,j}: {20, 28}, {37, 41489}, {71, 2155}, {72, 64}, {100, 1301}, {122, 18210}, {154, 2203}, {228, 33581}, {306, 2184}, {307, 8809}, {321, 459}, {610, 1474}, {1249, 5317}, {1562, 3125}, {1895, 8747}, {3198, 25}, {3682, 19614}, {3694, 30457}, {3718, 5931}, {3990, 14642}, {3998, 1073}, {5379, 15384}, {5930, 34}, {6587, 6591}, {7070, 2299}, {8057, 513}, {8804, 19}, {14308, 18344}, {14345, 14399}, {14615, 286}, {15905, 1333}, {17898, 7649}, {18623, 1396}, {18750, 27}, {20336, 253}, {20580, 905}, {27382, 1172}, {30456, 608}, {35602, 1437}, {36908, 1435}, {37669, 81}, {40933, 1398}, {41013, 6526}, {41086, 7151}, {42658, 667}
X(42699) = {X(321),X(3998)}-harmonic conjugate of X(20336)

X(42700) = X(2)X(37)∩X(54)X(72)

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

X(42700) lies on these lines: {2, 37}, {24, 1748}, {54, 72}, {63, 21078}, {100, 1824}, {190, 31631}, {228, 3425}, {254, 5552}, {306, 16577}, {908, 22001}, {1214, 3936}, {1708, 22021}, {1737, 2901}, {1812, 3219}, {1867, 11681}, {3187, 8609}, {3262, 17479}, {3694, 3969}, {4416, 16585}, {4552, 40149}, {4567, 18879}, {5016, 37528}, {5278, 40937}, {5294, 25078}, {6745, 22027}, {7283, 11103}, {11517, 26377}, {18607, 32859}, {20227, 26747}, {20305, 27725}, {20769, 21367}, {22000, 22003}, {22002, 22020}, {25083, 32933}, {25252, 27287}

X(42700) = crosspoint of X(4567) and X(6335)
X(42700) = crosssum of X(3125) and X(22383)
X(42700) = X(i)-isoconjugate of X(j) for these (i,j): {27, 2351}, {28, 1820}, {58, 2165}, {68, 1474}, {91, 1333}, {513, 36145}, {514, 32734}, {649, 925}, {1790, 14593}, {2168, 18180}, {2206, 5392}, {17167, 41271}, {21102, 32692}
X(42700) = barycentric product X(i)*X(j) for these {i,j}: {24, 20336}, {37, 7763}, {47, 313}, {72, 317}, {100, 6563}, {306, 1748}, {321, 1993}, {571, 27801}, {668, 924}, {3998, 11547}, {4570, 17881}, {6386, 34952}, {9723, 41013}, {18605, 28654}, {27808, 34948}
X(42700) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 91}, {24, 28}, {37, 2165}, {47, 58}, {52, 18180}, {71, 1820}, {72, 68}, {100, 925}, {101, 36145}, {228, 2351}, {313, 20571}, {317, 286}, {321, 5392}, {571, 1333}, {692, 32734}, {924, 513}, {1147, 1437}, {1748, 27}, {1824, 14593}, {1993, 81}, {6335, 30450}, {6563, 693}, {6753, 6591}, {7763, 274}, {8745, 5317}, {9723, 1444}, {14397, 14399}, {17881, 21207}, {18605, 593}, {20336, 20563}, {30451, 22383}, {34948, 3733}, {34952, 667}, {41013, 847}
X(42700) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 3998, 321}

X(42701) = X(2)X(37)∩X(100)X(842)

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

X(42701) lies on these lines: {2, 37}, {63, 24048}, {72, 3431}, {100, 842}, {249, 1931}, {908, 22003}, {1468, 22836}, {2174, 3219}, {3218, 4053}, {3578, 16585}, {3936, 18593}, {3969, 16577}, {4062, 16598}, {4467, 7265}, {7283, 13746}, {16553, 21376}, {25080, 41809}, {25083, 39767}

X(42701) = crosssum of X(3125) and X(14399)
X(42701) = trilinear pole of line {526, 32679}
X(42701) = crossdifference of every pair of points on line {667, 6186}
X(42701) = X(i)-isoconjugate of X(j) for these (i,j): {58, 1989}, {79, 34079}, {86, 11060}, {94, 2206}, {265, 1474}, {476, 649}, {513, 32678}, {514, 14560}, {667, 32680}, {759, 2160}, {1333, 2166}, {1790, 18384}, {1919, 35139}, {3122, 39295}, {4556, 15475}, {6186, 24624}, {6591, 36061}, {7649, 32662}, {11075, 14158}, {18653, 40355}, {22383, 36129}
X(42701) = barycentric product X(i)*X(j) for these {i,j}: {35, 35550}, {37, 7799}, {50, 27801}, {72, 340}, {100, 3268}, {186, 20336}, {190, 32679}, {313, 6149}, {319, 758}, {320, 3678}, {321, 323}, {526, 668}, {1978, 2624}, {2088, 4601}, {2245, 33939}, {3218, 3969}, {3219, 3936}, {3998, 14165}, {4036, 10411}, {4053, 34016}, {4420, 41804}, {4511, 40999}, {4585, 7265}, {6335, 8552}, {6386, 14270}, {16577, 32851}, {18593, 42033}
X(42701) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 2166}, {35, 759}, {37, 1989}, {50, 1333}, {72, 265}, {100, 476}, {101, 32678}, {186, 28}, {190, 32680}, {213, 11060}, {319, 14616}, {321, 94}, {323, 81}, {340, 286}, {526, 513}, {668, 35139}, {692, 14560}, {758, 79}, {906, 32662}, {1154, 18180}, {1331, 36061}, {1824, 18384}, {1897, 36129}, {2088, 3125}, {2174, 34079}, {2245, 2160}, {2594, 1411}, {2624, 649}, {3219, 24624}, {3268, 693}, {3678, 80}, {3724, 6186}, {3936, 30690}, {3969, 18359}, {4036, 10412}, {4053, 8818}, {4420, 6740}, {4511, 3615}, {4567, 39295}, {4705, 15475}, {6126, 14158}, {6149, 58}, {7206, 15065}, {7799, 274}, {8552, 905}, {9126, 30234}, {14270, 667}, {16186, 18210}, {16577, 2006}, {20336, 328}, {22115, 1437}, {27801, 20573}, {32679, 514}, {34397, 2203}, {34834, 18609}, {35550, 20565}, {39149, 30602}, {39495, 4164}, {40999, 18815}, {41013, 6344}

X(42702) = X(2)X(37)∩X(647)X(656)

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

X(42702) lies on these lines: {2, 37}, {48, 184}, {213, 40799}, {232, 240}, {237, 1755}, {647, 656}, {828, 22057}, {1101, 19622}, {2198, 41526}, {4053, 8607}

X(42702) = isotomic conjugate of the polar conjugate of X(5360)
X(42702) = crosspoint of X(295) and X(1214)
X(42702) = crosssum of X(i) and X(j) for these (i,j): {242, 1172}, {6531, 36120}
X(42702) = crossdifference of every pair of points on line {28, 667}
X(42702) = X(i)-isoconjugate of X(j) for these (i,j): {27, 98}, {28, 1821}, {58, 16081}, {81, 36120}, {86, 6531}, {286, 1910}, {287, 8747}, {290, 1474}, {336, 5317}, {514, 685}, {649, 22456}, {693, 36104}, {2966, 7649}, {3122, 41174}, {3261, 32696}, {4025, 20031}, {6591, 36036}, {17924, 36084}
X(42702) = barycentric product X(i)*X(j) for these {i,j}: {37, 36212}, {69, 5360}, {71, 1959}, {72, 511}, {100, 684}, {213, 6393}, {228, 325}, {232, 3998}, {237, 20336}, {240, 3682}, {297, 3990}, {306, 1755}, {321, 3289}, {668, 39469}, {692, 6333}, {906, 2799}, {1332, 3569}, {3949, 17209}, {4055, 40703}, {4064, 23997}, {4567, 41172}, {9417, 40071}
X(42702) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 16081}, {42, 36120}, {71, 1821}, {72, 290}, {100, 22456}, {213, 6531}, {228, 98}, {237, 28}, {511, 286}, {684, 693}, {692, 685}, {906, 2966}, {1331, 36036}, {1755, 27}, {2200, 1910}, {2211, 5317}, {2491, 6591}, {3289, 81}, {3569, 17924}, {3682, 336}, {3990, 287}, {4055, 293}, {4567, 41174}, {5360, 4}, {6333, 40495}, {6393, 6385}, {9417, 1474}, {9418, 2203}, {20336, 18024}, {32656, 36084}, {32739, 36104}, {36212, 274}, {39469, 513}, {41172, 16732}

X(42703) = X(2)X(37)∩X(100)X(2857)

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

X(42703) lies on these lines: {2, 37}, {100, 2857}, {297, 40703}, {327, 27801}, {422, 4601}, {668, 5641}, {850, 4036}, {1330, 21595}, {1824, 34405}, {2901, 3905}, {3454, 21421}, {4053, 35551}, {5360, 20022}, {13485, 20553}, {17864, 40071}, {18022, 40363}, {20932, 30660}

X(42703) = X(i)-isoconjugate of X(j) for these (i,j): {27, 14600}, {58, 1976}, {86, 14601}, {98, 2206}, {248, 1474}, {293, 2203}, {649, 2715}, {667, 36084}, {1333, 1910}, {1459, 32696}, {1919, 2966}, {1980, 36036}, {2422, 4556}, {15628, 16947}, {22383, 36104}
X(42703) = barycentric product X(i)*X(j) for these {i,j}: {240, 40071}, {297, 20336}, {306, 40703}, {313, 1959}, {321, 325}, {511, 27801}, {668, 2799}, {868, 4601}, {1502, 5360}, {2396, 4036}, {3569, 6386}, {6333, 6335}, {6393, 41013}
X(42703) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 1910}, {37, 1976}, {72, 248}, {100, 2715}, {190, 36084}, {213, 14601}, {228, 14600}, {232, 2203}, {240, 1474}, {297, 28}, {306, 293}, {313, 1821}, {321, 98}, {325, 81}, {511, 1333}, {668, 2966}, {684, 22383}, {868, 3125}, {1755, 2206}, {1783, 32696}, {1897, 36104}, {1959, 58}, {1978, 36036}, {2491, 1980}, {2799, 513}, {3569, 667}, {3701, 15628}, {3998, 17974}, {4036, 2395}, {4463, 11610}, {4705, 2422}, {5360, 32}, {6333, 905}, {6335, 685}, {6393, 1444}, {6530, 5317}, {15523, 3404}, {16230, 6591}, {16591, 1428}, {17209, 849}, {20336, 287}, {21833, 15630}, {27801, 290}, {36212, 1437}, {40071, 336}, {40703, 27}, {41013, 6531}

X(42704) = X(2)X(37)∩X(72)X(74)

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

X(42704) lies on these lines: {2, 37}, {72, 74}, {306, 18593}, {518, 11322}, {1150, 25083}, {1214, 3969}, {3306, 3970}, {3681, 37400}, {3694, 3936}, {3811, 5264}, {4527, 16598}, {5295, 33089}, {7283, 17584}, {24048, 24611}, {27801, 40832}

X(42704) = crossdifference of every pair of points on line {667, 14399}
X(42704) = X(i)-isoconjugate of X(j) for these (i,j): {58, 34288}, {513, 36149}, {514, 32738}, {649, 1302}, {1474, 4846}, {2206, 34289}, {11125, 32681}, {14399, 36083}
X(42704) = barycentric product X(i)*X(j) for these {i,j}: {37, 32833}, {100, 30474}, {321, 15066}, {378, 20336}, {668, 8675}, {5063, 27801}, {6386, 42660}
X(42704) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 34288}, {72, 4846}, {100, 1302}, {101, 36149}, {321, 34289}, {378, 28}, {692, 32738}, {5063, 1333}, {5891, 18180}, {8675, 513}, {15066, 81}, {30474, 693}, {32833, 274}, {42660, 667}

X(42705) = X(2)X(37)∩X(72)X(3784)

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

X(42705) lies on these lines: {2, 37}, {72, 3784}, {190, 1817}, {306, 4466}, {404, 32939}, {1265, 37180}, {1812, 4561}, {3264, 18662}, {4552, 30713}, {7283, 37168}, {18141, 22021}

X(42705) = barycentric product X(i)*X(j) for these {i,j}: {306, 32939}, {404, 20336}, {4563, 21721}
X(42705) = barycentric quotient X(i)/X(j) for these {i,j}: {404, 28}, {21721, 2501}, {32939, 27}
X(42705) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3998, 20336, 345}

X(42706) = X(2)X(37)∩X(72)X(306)

Barycentrics    (b + c)*(-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(42706) lies on these lines: {2, 37}, {27, 7283}, {72, 306}, {304, 18607}, {405, 5271}, {1104, 3187}, {1259, 11679}, {1999, 16050}, {2901, 40940}, {3151, 7270}, {3159, 20106}, {3198, 10327}, {3694, 40161}, {3933, 18651}, {4463, 32862}, {14021, 34255}, {21062, 22020}, {27801, 40447}

X(42706) = isotomic conjugate of the polar conjugate of X(5295)
X(42706) = X(i)-isoconjugate of X(j) for these (i,j): {28, 2215}, {649, 36077}
X(42706) = barycentric product X(i)*X(j) for these {i,j}: {69, 5295}, {306, 5271}, {405, 20336}, {1264, 1882}
X(42706) = barycentric quotient X(i)/X(j) for these {i,j}: {71, 2215}, {100, 36077}, {405, 28}, {1882, 1118}, {3694, 2335}, {4574, 36080}, {5271, 27}, {5295, 4}, {5320, 2203}, {23882, 17925}, {37543, 1396}, {39585, 8747}
X(42706) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 17776, 37}, {345, 20336, 3998}, {440, 3695, 306}

X(42707) = X(2)X(37)∩X(25)X(32929)

Barycentrics    b*c*(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(42707) lies on these lines: {2, 37}, {25, 32929}, {304, 5905}, {306, 21062}, {405, 3702}, {429, 3695}, {1230, 1441}, {1824, 10327}, {3685, 37325}, {4082, 22027}, {4239, 32932}, {7283, 16049}, {17016, 41813}, {17742, 22001}, {20932, 33066}, {26689, 27643}

X(42707) = barycentric product X(i)*X(j) for these {i,j}: {313, 12514}, {321, 5739}, {406, 20336}, {27174, 28654}, {27801, 36744}
X(42707) = barycentric quotient X(i)/X(j) for these {i,j}: {406, 28}, {5739, 81}, {12514, 58}, {27174, 593}, {36744, 1333}

X(42708) = X(2)X(37)∩X(10)X(41501)

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

X(42708) lies on these lines: {2, 37}, {10, 41501}, {72, 1478}, {92, 17275}, {125, 21692}, {226, 4053}, {329, 21873}, {338, 21690}, {407, 21677}, {594, 6354}, {1109, 8013}, {1211, 16732}, {1834, 4647}, {1848, 22007}, {2901, 30143}, {4036, 23930}, {4046, 17874}, {4415, 21810}, {4665, 20237}, {5743, 20236}, {5745, 22003}, {7211, 14973}, {17056, 18698}, {21020, 40967}, {21029, 39245}, {21096, 24044}, {24048, 28609}, {30690, 31143}

X(42708) = X(18698)-Ceva conjugate of X(21674)
X(42708) = crosspoint of X(321) and X(6358)
X(42708) = crosssum of X(1333) and X(2150)
X(42708) = X(i)-isoconjugate of X(j) for these (i,j): {1333, 40430}, {2150, 17097}, {2189, 40442}
X(42708) = barycentric product X(i)*X(j) for these {i,j}: {10, 18698}, {75, 21674}, {313, 2650}, {321, 17056}, {349, 21811}, {407, 20336}, {1089, 3664}, {1441, 21677}, {1577, 22003}, {2646, 34388}, {4033, 23755}, {4036, 17136}, {5745, 6358}
X(42708) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 40430}, {12, 17097}, {201, 40442}, {407, 28}, {2646, 60}, {2650, 58}, {3664, 757}, {5745, 2185}, {6737, 1098}, {17056, 81}, {18698, 86}, {21674, 1}, {21677, 21}, {21748, 2150}, {21811, 284}, {22003, 662}, {23755, 1019}, {30604, 4833}, {40950, 270}
X(42708) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 27569, 42034}

X(42709) = X(2)X(37)∩X(190)X(21368)

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

X(42709) lies on these lines: {2, 37}, {190, 21368}, {304, 40075}, {306, 2064}, {341, 5086}, {668, 14206}, {693, 15416}, {976, 4385}, {1008, 32931}, {1089, 5293}, {3145, 7283}, {3729, 36572}, {3936, 17789}, {3952, 14956}, {4033, 20920}, {4647, 36499}, {4673, 36500}, {7035, 31905}, {7081, 36559}, {11679, 36504}, {17788, 33077}, {18750, 21286}, {21600, 35516}, {27538, 37193}, {32932, 36497}, {33136, 36568}

X(42709) = X(i)-isoconjugate of X(j) for these (i,j): {32, 16099}, {1919, 35169}
X(42709) = barycentric product X(i)*X(j) for these {i,j}: {75, 16086}, {447, 20336}, {867, 7035}, {6386, 42662}
X(42709) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 16099}, {447, 28}, {668, 35169}, {867, 244}, {16086, 1}, {20336, 40715}, {42662, 667}
X(42709) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {306, 2064, 20929}, {321, 4358, 37759}, {321, 32779, 75}

X(42710) = X(2)X(37)∩X(304)X(32859)

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

X(42710) lies on these lines: {2, 37}, {304, 32859}, {1230, 35550}, {1325, 7283}, {2895, 20932}, {3695, 30447}, {3701, 6757}, {3702, 5259}, {3948, 20896}, {4053, 32858}, {4115, 17781}, {4601, 31614}, {14210, 42045}, {18697, 41809}, {20988, 32929}, {21810, 32782}

X(42710) = isotomic conjugate of X(40143)
X(42710) = isotomic conjugate of the isogonal conjugate of X(21873)
X(42710) = X(i)-Ceva conjugate of X(j) for these (i,j): {20932, 21081}, {28654, 321}
X(42710) = X(2895)-cross conjugate of X(321)
X(42710) = crosspoint of X(4601) and X(27808)
X(42710) = X(i)-isoconjugate of X(j) for these (i,j): {31, 40143}, {58, 3444}, {267, 1333}, {849, 21353}, {1029, 2206}
X(42710) = barycentric product X(i)*X(j) for these {i,j}: {10, 20932}, {75, 21081}, {76, 21873}, {191, 313}, {321, 2895}, {451, 20336}, {1030, 27801}, {3701, 41808}, {4033, 21192}, {6386, 42653}, {21723, 24037}, {27808, 31947}, {28654, 40592}
X(42710) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 40143}, {10, 267}, {37, 3444}, {191, 58}, {321, 1029}, {451, 28}, {501, 849}, {594, 21353}, {1030, 1333}, {1089, 502}, {2895, 81}, {6757, 30602}, {8614, 1408}, {20932, 86}, {21081, 1}, {21192, 1019}, {21723, 2643}, {21873, 6}, {22136, 1437}, {31947, 3733}, {40592, 593}, {41808, 1014}, {42653, 667}
X(42710) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 27705, 4359}

X(42711) = X(2)X(37)∩X(72)X(290)

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

X(42711) lies on these lines: {2, 37}, {65, 1237}, {72, 290}, {183, 3403}, {210, 35544}, {313, 3967}, {319, 30660}, {518, 4485}, {1212, 18050}, {1824, 40717}, {3914, 21238}, {16583, 21412}, {16605, 21435}, {20723, 22278}, {21403, 40071}

X(42711) = crosspoint of X(3403) and X(20023)
X(42711) = X(i)-isoconjugate of X(j) for these (i,j): {58, 263}, {81, 3402}, {262, 2206}, {649, 26714}, {1333, 2186}, {17187, 42288}
X(42711) = barycentric product X(i)*X(j) for these {i,j}: {10, 3403}, {37, 20023}, {182, 27801}, {183, 321}, {458, 20336}, {668, 23878}, {3288, 6386}
X(42711) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 2186}, {37, 263}, {42, 3402}, {100, 26714}, {182, 1333}, {183, 81}, {321, 262}, {458, 28}, {3288, 667}, {3403, 86}, {6784, 3121}, {10311, 2203}, {14994, 16696}, {18098, 42288}, {20023, 274}, {20336, 42313}, {23878, 513}, {27801, 327}, {33971, 5317}

X(42712) = X(2)X(37)∩X(9)X(3702)

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

X(42712) lies on these lines: {2, 37}, {9, 3702}, {198, 32929}, {306, 21068}, {391, 4673}, {1089, 3950}, {1108, 26770}, {1441, 4044}, {1449, 4742}, {1696, 5695}, {2171, 21071}, {2321, 3701}, {2324, 27410}, {3247, 4968}, {3294, 3692}, {3686, 3902}, {3986, 4647}, {3992, 4058}, {4007, 4723}, {4066, 4098}, {4072, 4125}, {4082, 21039}, {4696, 17314}, {5179, 21070}, {5279, 37422}, {7101, 41013}, {7283, 37402}, {17751, 21871}

X(42712) = X(4673)-Ceva conjugate of X(4061)
X(42712) = X(i)-isoconjugate of X(j) for these (i,j): {649, 5545}, {1408, 25430}, {1412, 2334}, {5936, 16947}, {7203, 34074}
X(42712) = barycentric product X(i)*X(j) for these {i,j}: {10, 4673}, {75, 4061}, {312, 5257}, {313, 4512}, {318, 4101}, {321, 391}, {341, 3671}, {461, 20336}, {646, 4841}, {668, 4843}, {1449, 30713}, {1577, 30728}, {2321, 19804}, {3596, 37593}, {3616, 3701}, {3699, 4815}, {3710, 5342}, {3952, 4811}, {4033, 4765}, {4047, 7017}, {4258, 27801}, {4801, 30730}, {6386, 8653}
X(42712) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 5545}, {210, 2334}, {391, 81}, {461, 28}, {644, 4627}, {646, 4633}, {1449, 1412}, {2321, 25430}, {3616, 1014}, {3671, 269}, {3699, 4614}, {3701, 5936}, {4033, 4624}, {4047, 222}, {4061, 1}, {4069, 8694}, {4082, 4866}, {4101, 77}, {4258, 1333}, {4512, 58}, {4515, 34820}, {4673, 86}, {4765, 1019}, {4771, 1429}, {4778, 7203}, {4801, 17096}, {4811, 7192}, {4815, 3676}, {4819, 1319}, {4827, 7252}, {4829, 1284}, {4841, 3669}, {4843, 513}, {5257, 57}, {8653, 667}, {14625, 1462}, {19804, 1434}, {30713, 40023}, {30728, 662}, {30730, 4606}, {37593, 56}
X(42712) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 22016, 22040}, {4043, 20336, 321}, {22016, 27569, 321}

X(42713) = X(2)X(37)∩X(72)X(5486)

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

X(42713) lies on these lines: {2, 37}, {69, 21873}, {72, 5486}, {100, 2770}, {141, 21810}, {213, 9516}, {228, 40102}, {304, 4643}, {468, 3712}, {523, 1577}, {524, 14210}, {527, 4115}, {668, 18823}, {740, 39688}, {744, 4368}, {908, 22007}, {1213, 18697}, {1279, 4742}, {1654, 20932}, {1930, 4364}, {2325, 22003}, {3230, 9022}, {3663, 24067}, {3701, 4377}, {3718, 4851}, {3834, 24076}, {3912, 4053}, {3936, 16581}, {3948, 16732}, {3954, 42286}, {3985, 8680}, {4026, 4714}, {4035, 18589}, {4039, 21254}, {4062, 16597}, {4078, 4125}, {4118, 22196}, {4363, 33942}, {4436, 20857}, {4553, 5360}, {4567, 4590}, {4647, 17514}, {4708, 20911}, {4971, 4986}, {5277, 24335}, {5695, 19309}, {6542, 26147}, {7267, 16702}, {7283, 11116}, {17251, 33936}, {17296, 24048}, {17318, 33937}, {17444, 30059}, {21076, 27559}, {22017, 24092}, {24058, 24199}, {27801, 40826}

X(42713) = isotomic conjugate of the isogonal conjugate of X(21839)
X(42713) = X(14210)-Ceva conjugate of X(4062)
X(42713) = crosspoint of X(3266) and X(14210)
X(42713) = crosssum of X(923) and X(32740)
X(42713) = crossdifference of every pair of points on line {667, 1333}
X(42713) = X(i)-isoconjugate of X(j) for these (i,j): {27, 14908}, {28, 36060}, {58, 111}, {81, 923}, {86, 32740}, {284, 7316}, {310, 19626}, {513, 36142}, {514, 32729}, {649, 691}, {667, 36085}, {671, 2206}, {892, 1919}, {895, 1474}, {897, 1333}, {1412, 5547}, {1437, 36128}, {1790, 8753}, {4556, 9178}, {4786, 32648}, {6629, 41936}, {30234, 36045}
X(42713) = barycentric product X(i)*X(j) for these {i,j}: {10, 14210}, {37, 3266}, {75, 4062}, {76, 21839}, {100, 35522}, {187, 27801}, {313, 896}, {321, 524}, {351, 6386}, {468, 20336}, {594, 16741}, {668, 690}, {1089, 6629}, {1441, 3712}, {1648, 4601}, {1978, 2642}, {3701, 7181}, {3998, 37778}, {4024, 24039}, {4033, 4750}, {4036, 5468}, {4647, 31013}, {6335, 14417}, {6390, 41013}, {14419, 27808}, {16702, 28654}
X(42713) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 897}, {37, 111}, {42, 923}, {65, 7316}, {71, 36060}, {72, 895}, {100, 691}, {101, 36142}, {126, 16756}, {187, 1333}, {190, 36085}, {210, 5547}, {213, 32740}, {228, 14908}, {321, 671}, {351, 667}, {468, 28}, {524, 81}, {668, 892}, {690, 513}, {692, 32729}, {896, 58}, {922, 2206}, {1648, 3125}, {1649, 14419}, {1824, 8753}, {1826, 36128}, {2205, 19626}, {2482, 16702}, {2642, 649}, {3266, 274}, {3292, 1437}, {3712, 21}, {3908, 32583}, {3952, 5380}, {4024, 23894}, {4036, 5466}, {4062, 1}, {4553, 36827}, {4705, 9178}, {4750, 1019}, {4933, 4653}, {4938, 4658}, {5380, 34574}, {6390, 1444}, {6629, 757}, {7181, 1014}, {7813, 16696}, {9125, 30234}, {11183, 4164}, {14210, 86}, {14273, 6591}, {14417, 905}, {14419, 3733}, {14424, 2530}, {14432, 3737}, {16597, 7292}, {16702, 593}, {16741, 1509}, {20336, 30786}, {21814, 41272}, {21839, 6}, {21906, 3121}, {22105, 18108}, {23106, 16733}, {23889, 4556}, {24038, 6629}, {24039, 4610}, {27801, 18023}, {30595, 4840}, {30605, 4833}, {31013, 40438}, {35522, 693}, {36792, 16741}, {41013, 17983}, {41586, 18180}
X(42713) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3948, 35550, 16732}, {27565, 27697, 37}, {27569, 27705, 75}, {27586, 27727, 192}

X(42714) = X(2)X(37)∩X(72)X(319)

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

X(42714) lies on these lines: {2, 37}, {69, 21594}, {72, 319}, {86, 33939}, {313, 1089}, {314, 33775}, {594, 26601}, {1269, 1930}, {1386, 3702}, {1909, 20932}, {1978, 37842}, {2321, 4150}, {2478, 42696}, {2901, 4360}, {3159, 4357}, {3759, 41249}, {3969, 27052}, {4066, 6541}, {5224, 33935}, {5295, 5564}, {5695, 23868}, {7148, 23498}, {17233, 22021}, {18133, 20911}, {20234, 20337}, {21070, 22012}, {22018, 24044}, {25354, 42031}

X(42714) = X(1333)-isoconjugate of X(2214)
X(42714) = barycentric product X(i)*X(j) for these {i,j}: {10, 33935}, {313, 28606}, {321, 5224}, {349, 3876}, {386, 27801}, {469, 20336}, {668, 23879}, {799, 23282}, {1577, 33948}, {3701, 33949}, {6386, 42664}, {14349, 27808}
X(42714) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 2214}, {386, 1333}, {469, 28}, {3876, 284}, {4033, 835}, {5224, 81}, {14349, 3733}, {23282, 661}, {23879, 513}, {27808, 37218}, {28606, 58}, {33935, 86}, {33948, 662}, {33949, 1014}, {42664, 667}
X(42714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 312, 18147}, {75, 20947, 28653}, {321, 20336, 75}, {321, 27569, 37}, {1089, 18697, 313}

X(42715) = X(2)X(37)∩X(72)X(10327)

Barycentrics    b*c*(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(42715) lies on these lines: {2, 37}, {72, 10327}, {305, 27801}, {306, 4006}, {427, 3006}, {442, 1230}, {614, 2901}, {1441, 28654}, {1759, 15487}, {2049, 4968}, {3187, 16502}, {3702, 37060}, {3718, 5905}, {4228, 7283}, {5256, 33937}, {5287, 33942}, {6735, 20238}, {30713, 35550}

X(42715) = barycentric product X(i)*X(j) for these {i,j}: {475, 20336}, {27801, 36743}
X(42715) = barycentric quotient X(i)/X(j) for these {i,j}: {475, 28}, {36743, 1333}

X(42716) = X(2)X(37)∩X(100)X(1302)

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

X(42716) lies on these lines: {2, 37}, {100, 1302}, {190, 15455}, {645, 648}, {2517, 3573}, {3260, 7359}, {4240, 24001}, {4391, 4585}, {4567, 30528}, {4601, 6035}, {6386, 9211}, {15413, 15418}, {18752, 39767}

X(42716) = X(14399)-cross conjugate of X(30)
X(42716) = cevapoint of X(30) and X(14399)
X(42716) = trilinear pole of line {30, 14206}
X(42716) = X(i)-isoconjugate of X(j) for these (i,j): {58, 2433}, {74, 649}, {513, 2159}, {514, 40352}, {667, 2349}, {1459, 8749}, {1474, 14380}, {1494, 1919}, {1980, 33805}, {2206, 2394}, {3120, 32640}, {3125, 36034}, {4025, 40354}, {4466, 32715}, {6591, 35200}, {7649, 18877}, {11125, 40353}, {18210, 36131}, {22383, 36119}
X(42716) = barycentric product X(i)*X(j) for these {i,j}: {30, 668}, {100, 3260}, {190, 14206}, {306, 24001}, {321, 2407}, {646, 6357}, {1495, 6386}, {1637, 4601}, {1784, 4561}, {1978, 2173}, {2420, 27801}, {4033, 18653}, {4240, 20336}, {4554, 7359}, {4567, 41079}, {4600, 36035}, {6335, 11064}, {7035, 11125}, {14399, 31625}
X(42716) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 513}, {37, 2433}, {72, 14380}, {100, 74}, {101, 2159}, {190, 2349}, {321, 2394}, {644, 15627}, {668, 1494}, {692, 40352}, {906, 18877}, {1099, 11125}, {1331, 35200}, {1332, 14919}, {1495, 667}, {1637, 3125}, {1783, 8749}, {1784, 7649}, {1897, 36119}, {1978, 33805}, {1990, 6591}, {2173, 649}, {2407, 81}, {2420, 1333}, {3163, 14399}, {3260, 693}, {3284, 22383}, {4036, 12079}, {4240, 28}, {4570, 36034}, {5379, 1304}, {5380, 9139}, {5642, 14419}, {6335, 16080}, {6357, 3669}, {7359, 650}, {9033, 18210}, {9406, 1919}, {9407, 1980}, {11064, 905}, {11125, 244}, {14206, 514}, {14395, 7117}, {14398, 3121}, {14399, 1015}, {14400, 2170}, {18653, 1019}, {20336, 34767}, {23347, 2203}, {24001, 27}, {35266, 30234}, {36035, 3120}, {41013, 18808}, {41079, 16732}
X(42716) = {X({}),X(1)}-harmonic conjugate of X({}[[1]][[3]])

X(42717) = X(2)X(37)∩X(100)X(110)

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

X(42717) lies on these lines: {2, 37}, {39, 36230}, {69, 24499}, {72, 9513}, {100, 110}, {190, 27805}, {650, 3570}, {4567, 5649}, {6331, 6335}, {7283, 37041}, {18047, 21859}, {18061, 34460}

X(42717) = crosspoint of X(4554) and X(4589)
X(42717) = crosssum of X(i) and X(j) for these (i,j): {513, 4164}, {3063, 4455}
X(42717) = trilinear pole of line {511, 1959}
X(42717) = crossdifference of every pair of points on line {667, 3125}
X(42717) = X(i)-isoconjugate of X(j) for these (i,j): {27, 878}, {58, 2395}, {86, 2422}, {98, 649}, {248, 7649}, {290, 1919}, {293, 6591}, {513, 1910}, {514, 1976}, {667, 1821}, {879, 1474}, {1459, 6531}, {2715, 3120}, {2966, 3122}, {3121, 36036}, {3125, 36084}, {3261, 14601}, {3404, 18108}, {4107, 34238}, {4466, 32696}, {4610, 15630}, {18210, 36104}, {22383, 36120}
X(42717) = barycentric product X(i)*X(j) for these {i,j}: {37, 2396}, {72, 877}, {100, 325}, {190, 1959}, {237, 6386}, {240, 4561}, {297, 1332}, {313, 23997}, {321, 2421}, {511, 668}, {670, 5360}, {1331, 40703}, {1755, 1978}, {1783, 6393}, {2799, 4567}, {3405, 4568}, {3569, 4601}, {4033, 17209}, {4230, 20336}, {4553, 20022}, {5379, 6333}, {6335, 36212}, {14966, 27801}
X(42717) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 2395}, {72, 879}, {100, 98}, {101, 1910}, {190, 1821}, {213, 2422}, {228, 878}, {232, 6591}, {237, 667}, {240, 7649}, {297, 17924}, {325, 693}, {511, 513}, {644, 15628}, {668, 290}, {684, 18210}, {692, 1976}, {877, 286}, {906, 248}, {1331, 293}, {1332, 287}, {1755, 649}, {1783, 6531}, {1897, 36120}, {1959, 514}, {2396, 274}, {2421, 81}, {2491, 3121}, {2799, 16732}, {3289, 22383}, {3405, 10566}, {3569, 3125}, {4230, 28}, {4553, 20021}, {4561, 336}, {4567, 2966}, {4570, 36084}, {4600, 36036}, {5360, 512}, {5379, 685}, {5380, 9154}, {5976, 14296}, {6335, 16081}, {6386, 18024}, {6393, 15413}, {9155, 14419}, {9417, 1919}, {9418, 1980}, {14966, 1333}, {16591, 7212}, {17209, 1019}, {23997, 58}, {36212, 905}, {36213, 4164}

X(42718) = X(2)X(37)∩X(190)X(653)

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

X(42718) lies on these lines: {2, 37}, {100, 9056}, {190, 653}, {646, 4561}, {651, 29000}, {1332, 4033}, {2398, 4397}, {4585, 13136}, {21362, 29733}

X(42718) = X(14304)-cross conjugate of X(35516)
X(42718) = X(i)-isoconjugate of X(j) for these (i,j): {11, 32643}, {56, 2432}, {102, 649}, {513, 32677}, {667, 36100}, {1397, 2399}, {1919, 34393}, {2170, 36040}, {6591, 36055}, {7004, 32667}, {7117, 36067}, {22383, 36121}
X(42718) = barycentric product X(i)*X(j) for these {i,j}: {100, 35516}, {312, 2406}, {345, 24035}, {515, 668}, {646, 34050}, {1978, 2182}, {2425, 28659}, {3718, 23987}, {4998, 14304}, {7452, 20336}
X(42718) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 2432}, {59, 36040}, {100, 102}, {101, 32677}, {190, 36100}, {312, 2399}, {515, 513}, {644, 15629}, {668, 34393}, {1331, 36055}, {1897, 36121}, {2149, 32643}, {2182, 649}, {2406, 57}, {2425, 604}, {4397, 15633}, {7012, 36067}, {7115, 32667}, {7452, 28}, {8755, 6591}, {14304, 11}, {23987, 34}, {24035, 278}, {34050, 3669}, {35516, 693}, {39471, 7004}

X(42719) = X(2)X(37)∩X(190)X(658)

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

X(42719) lies on these lines: {2, 37}, {100, 9057}, {190, 658}, {220, 18738}, {651, 28999}, {668, 30728}, {811, 7259}, {1023, 1577}, {1897, 3699}, {3730, 29477}, {3882, 29421}, {4562, 14727}, {4585, 31633}, {17742, 21579}, {35517, 40869}

X(42719) = cevapoint of X(676) and X(17747)
X(42719) = trilinear pole of line {516, 30807}
X(42719) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2424}, {32, 2400}, {103, 649}, {244, 36039}, {513, 911}, {667, 36101}, {677, 1015}, {1086, 32642}, {1919, 18025}, {2310, 32668}, {3937, 40116}, {6591, 36056}, {7649, 32657}, {14936, 24016}, {15634, 32739}, {20974, 35184}, {22084, 32701}, {22383, 36122}
X(42719) = barycentric product X(i)*X(j) for these {i,j}: {75, 2398}, {100, 35517}, {190, 30807}, {304, 41321}, {341, 23973}, {346, 24015}, {516, 668}, {561, 2426}, {676, 7035}, {799, 17747}, {910, 1978}, {4033, 14953}, {4241, 20336}, {4554, 40869}, {4572, 41339}, {6335, 26006}, {9502, 36803}
X(42719) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2424}, {75, 2400}, {100, 103}, {101, 911}, {190, 36101}, {516, 513}, {644, 2338}, {666, 9503}, {668, 18025}, {676, 244}, {693, 15634}, {765, 677}, {906, 32657}, {910, 649}, {1110, 32642}, {1252, 36039}, {1262, 32668}, {1331, 36056}, {1332, 1815}, {1886, 6591}, {1897, 36122}, {2398, 1}, {2426, 31}, {3234, 910}, {4241, 28}, {7045, 24016}, {9502, 665}, {14953, 1019}, {17747, 661}, {23973, 269}, {24014, 676}, {24015, 279}, {26006, 905}, {28345, 22108}, {28346, 9508}, {30807, 514}, {35517, 693}, {39470, 3942}, {40869, 650}, {41321, 19}, {41339, 663}

X(42720) = X(2)X(37)∩X(100)X(190)

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

X(42720) lies on these lines: {2, 37}, {8, 14947}, {39, 28598}, {100, 190}, {514, 4169}, {644, 4561}, {646, 1978}, {662, 10330}, {664, 6558}, {666, 39272}, {668, 30730}, {672, 27919}, {874, 4583}, {876, 4562}, {883, 1025}, {919, 35574}, {1016, 30731}, {1018, 4568}, {1023, 32094}, {1500, 25263}, {1644, 4937}, {1909, 25244}, {2321, 24318}, {3177, 25278}, {3252, 3930}, {3257, 5387}, {3616, 19895}, {3681, 36294}, {3695, 37165}, {3729, 9318}, {3938, 7032}, {4363, 31063}, {4518, 13576}, {4595, 21272}, {4606, 37215}, {4986, 24036}, {6376, 25237}, {6632, 31615}, {6634, 31628}, {7080, 32034}, {7283, 37009}, {9055, 20331}, {14439, 17755}, {16549, 17141}, {16705, 28594}, {16720, 26759}, {17136, 18047}, {17152, 33299}, {18055, 20244}, {20345, 39350}, {20955, 26757}, {21431, 27071}, {21604, 26794}, {22003, 22033}, {24330, 31052}, {24407, 27912}, {25268, 30610}, {26770, 33938}, {27025, 33944}, {27096, 33930}, {27109, 33937}, {28742, 33933}, {30790, 30857}

X(42720) = isogonal conjugate of X(43929)
X(42720) = anticomplement of X(27918)
X(42720) = isotomic conjugate of the isogonal conjugate of X(2284)
X(42720) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {660, 150}, {692, 39362}, {765, 20345}, {813, 149}, {1016, 20554}, {1110, 33888}, {1252, 17794}, {4562, 21293}, {5378, 69}, {23990, 30667}, {34067, 4440}, {36081, 25049}
X(42720) = X(i)-Ceva conjugate of X(j) for these (i,j): {874, 23354}, {1016, 4437}, {4583, 3952}, {35574, 100}, {36803, 668}
X(42720) = X(i)-cross conjugate of X(j) for these (i,j): {665, 518}, {918, 3912}, {1026, 883}, {2254, 30941}, {4437, 1016}, {4925, 9436}
X(42720) = cevapoint of X(i) and X(j) for these (i,j): {518, 665}, {812, 3008}, {918, 3912}, {2254, 3930}
X(42720) = crosspoint of X(i) and X(j) for these (i,j): {190, 4562}, {668, 36803}
X(42720) = crosssum of X(649) and X(8632)
X(42720) = trilinear pole of line {518, 3717}
X(42720) = crossdifference of every pair of points on line {667, 1015}
X(42720) = X(i)-isoconjugate of X(j) for these (i,j): {6, 1027}, {56, 1024}, {57, 884}, {105, 649}, {244, 919}, {513, 1438}, {604, 885}, {608, 23696}, {650, 1416}, {663, 1462}, {666, 3248}, {667, 673}, {875, 6654}, {985, 29956}, {1015, 36086}, {1086, 32666}, {1106, 28132}, {1459, 8751}, {1474, 10099}, {1919, 2481}, {1980, 18031}, {2170, 32735}, {2191, 2440}, {2195, 3669}, {2254, 41934}, {3271, 36146}, {3733, 18785}, {5377, 21143}, {6591, 36057}, {7649, 32658}, {22383, 36124}, {23349, 36816}
X(42720) = barycentric product X(i)*X(j) for these {i,j}: {8, 883}, {75, 1026}, {76, 2284}, {99, 3932}, {100, 3263}, {120, 35574}, {190, 3912}, {241, 646}, {312, 1025}, {341, 41353}, {344, 2414}, {518, 668}, {644, 40704}, {664, 3717}, {665, 31625}, {666, 4437}, {670, 20683}, {672, 1978}, {799, 3930}, {874, 22116}, {918, 1016}, {1018, 18157}, {1861, 4561}, {2223, 6386}, {2254, 7035}, {2283, 3596}, {2340, 4572}, {3252, 27853}, {3286, 27808}, {3570, 40217}, {3693, 4554}, {3699, 9436}, {3952, 30941}, {4033, 18206}, {4088, 4600}, {4238, 20336}, {4562, 17755}, {4583, 8299}, {4601, 24290}, {4602, 39258}, {4966, 6540}, {6184, 36803}, {6335, 25083}, {10029, 30720}, {30610, 40883}, {36801, 39775}
X(42720) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1027}, {8, 885}, {9, 1024}, {55, 884}, {59, 32735}, {72, 10099}, {78, 23696}, {100, 105}, {101, 1438}, {109, 1416}, {120, 23770}, {190, 673}, {218, 2440}, {241, 3669}, {344, 2402}, {346, 28132}, {518, 513}, {644, 294}, {646, 36796}, {651, 1462}, {665, 1015}, {666, 6185}, {668, 2481}, {672, 649}, {765, 36086}, {883, 7}, {906, 32658}, {918, 1086}, {919, 41934}, {926, 3271}, {1016, 666}, {1018, 18785}, {1025, 57}, {1026, 1}, {1110, 32666}, {1252, 919}, {1331, 36057}, {1332, 1814}, {1642, 1643}, {1783, 8751}, {1818, 1459}, {1861, 7649}, {1897, 36124}, {1978, 18031}, {2223, 667}, {2254, 244}, {2276, 29956}, {2283, 56}, {2284, 6}, {2340, 663}, {2414, 277}, {3126, 3675}, {3252, 3572}, {3263, 693}, {3286, 3733}, {3570, 6654}, {3675, 764}, {3693, 650}, {3699, 14942}, {3717, 522}, {3912, 514}, {3930, 661}, {3932, 523}, {3939, 2195}, {3952, 13576}, {4076, 36802}, {4088, 3120}, {4238, 28}, {4437, 918}, {4447, 4367}, {4554, 34018}, {4561, 31637}, {4564, 36146}, {4578, 28071}, {4684, 4778}, {4712, 2254}, {4899, 3667}, {4925, 3756}, {4966, 4977}, {4998, 927}, {5089, 6591}, {6184, 665}, {6558, 6559}, {8299, 659}, {9436, 3676}, {9454, 1919}, {9455, 1980}, {14439, 1635}, {15149, 17925}, {16593, 6084}, {17755, 812}, {18157, 7199}, {18206, 1019}, {20662, 8659}, {20683, 512}, {20752, 22383}, {20776, 23225}, {20778, 22384}, {22116, 876}, {23102, 3126}, {23225, 22096}, {23829, 17205}, {23891, 36816}, {24290, 3125}, {25083, 905}, {27919, 4375}, {30941, 7192}, {31625, 36803}, {34230, 23345}, {35293, 14413}, {36801, 33676}, {39258, 798}, {40217, 4444}, {40704, 24002}, {40730, 875}, {40883, 4885}, {41353, 269}, {42341, 4014}
X(42720) = trilinear product X(i)*X(j) for these {i,j}: {2, 1026}, {8, 1025}, {9, 883}, {75, 2284}, {99, 3930}, {100, 3912}, {101, 3263}, {190, 518}, {241, 3699}, {306, 4238}, {312, 2283}, {346, 41353}, {644, 9436}, {646, 1458}, {651, 3717}, {660, 17755}, {662, 3932}, {664, 3693}, {665, 7035}, {666, 4712}, {668, 672}, {670, 39258}, {765, 918}, {799, 20683}, {874, 3252}, {1016, 2254}, {1018, 30941}, {1332, 1861}, {1818, 6335}, {1897, 25083}, {1978, 2223}, {2340, 4554}, {2397, 36819}, {2414, 3870}, {3286, 4033}, {3570, 22116}, {3573, 40217}, {3675, 6632}, {3939, 40704}, {3952, 18206}, {4088, 4567}, {4437, 36086}, {4447, 27805}, {4555, 14439}, {4557, 18157}, {4561, 5089}, {4562, 8299}, {4571, 5236}, {4600, 24290}, {4606, 4684}, {4899, 27834}, {4925, 5382}, {4966, 37212}, {6386, 9454}, {6558, 34855}, {17464, 35574}, {24004, 34230}, {27853, 40730}, {34253, 36801}, {36803, 42079}
X(42720) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 192, 24403}, {190, 3807, 3952}, {3693, 40883, 3263}, {4595, 33946, 21272}, {21272, 25272, 33946}

X(42721) = X(2)X(37)∩X(99)X(100)

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

X(42721) lies on these lines: {2, 37}, {99, 100}, {190, 35181}, {693, 874}, {889, 35147}, {1290, 35574}, {3266, 3712}, {4062, 16741}, {4601, 9170}, {4933, 14210}, {5380, 39296}, {5468, 24039}, {7283, 37014}, {14608, 21839}, {16703, 33160}

X(42721) = X(i)-cross conjugate of X(j) for these (i,j): {4750, 16741}, {14419, 524}
X(42721) = cevapoint of X(i) and X(j) for these (i,j): {524, 14419}, {4062, 4750}
X(42721) = trilinear pole of line {524, 14210}
X(42721) = crossdifference of every pair of points on line {667, 3121}
X(42721) = X(i)-isoconjugate of X(j) for these (i,j): {58, 9178}, {111, 649}, {513, 923}, {514, 32740}, {663, 7316}, {667, 897}, {671, 1919}, {691, 3122}, {1333, 23894}, {1459, 8753}, {1474, 10097}, {2206, 5466}, {3120, 32729}, {3121, 36085}, {3125, 36142}, {3248, 5380}, {3261, 19626}, {4750, 41936}, {6591, 36060}, {7649, 14908}, {10566, 41272}, {22383, 36128}
X(42721) = barycentric product X(i)*X(j) for these {i,j}: {10, 24039}, {100, 3266}, {187, 6386}, {190, 14210}, {313, 23889}, {321, 5468}, {524, 668}, {646, 7181}, {670, 21839}, {690, 4601}, {799, 4062}, {896, 1978}, {3712, 4554}, {3952, 16741}, {4033, 6629}, {4235, 20336}, {4567, 35522}, {4583, 4760}, {4750, 7035}, {5380, 36792}, {5467, 27801}, {6335, 6390}, {14419, 31625}, {16702, 27808}
X(42721) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 23894}, {37, 9178}, {72, 10097}, {100, 111}, {101, 923}, {187, 667}, {190, 897}, {321, 5466}, {351, 3121}, {468, 6591}, {524, 513}, {644, 5547}, {651, 7316}, {668, 671}, {690, 3125}, {692, 32740}, {896, 649}, {906, 14908}, {922, 1919}, {1016, 5380}, {1331, 36060}, {1332, 895}, {1783, 8753}, {1897, 36128}, {2482, 14419}, {2642, 3122}, {3266, 693}, {3292, 22383}, {3712, 650}, {3793, 3803}, {3908, 42007}, {4062, 661}, {4235, 28}, {4567, 691}, {4570, 36142}, {4600, 36085}, {4601, 892}, {4750, 244}, {4760, 659}, {4831, 4790}, {4933, 4893}, {4938, 4813}, {5026, 4164}, {5380, 10630}, {5467, 1333}, {5468, 81}, {5642, 14399}, {6335, 17983}, {6386, 18023}, {6390, 905}, {6629, 1019}, {7181, 3669}, {7267, 4367}, {7813, 2530}, {14210, 514}, {14417, 18210}, {14419, 1015}, {14432, 2170}, {14567, 1980}, {16702, 3733}, {16741, 7192}, {20336, 14977}, {21839, 512}, {23889, 58}, {24038, 4750}, {24039, 86}, {27088, 30234}, {35522, 16732}

X(42722) = X(2)X(37)∩X(190)X(693)

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

X(42722) lies on these lines: {2, 37}, {190, 693}, {644, 666}, {646, 7035}, {1577, 32094}, {3699, 4397}, {3762, 6633}, {4462, 6631}, {4554, 4582}, {4801, 32028}, {4978, 32106}, {21362, 29738}

X(42722) = X(1643)-cross conjugate of X(528)
X(42722) = cevapoint of X(528) and X(1643)
X(42722) = X(i)-isoconjugate of X(j) for these (i,j): {649, 840}, {667, 37131}, {1919, 18821}
X(42722) = barycentric product X(i)*X(j) for these {i,j}: {528, 668}, {646, 5723}, {1642, 36803}, {1643, 31625}, {1978, 2246}
X(42722) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 840}, {190, 37131}, {528, 513}, {668, 18821}, {1642, 665}, {1643, 1015}, {2246, 649}, {5723, 3669}, {14190, 23345}, {17780, 14191}, {35113, 1643}
X(42722) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {350, 17264, 4358}

X(42723) = X(2)X(37)∩X(100)X(101)

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

X(42723) lies on these lines: {2, 37}, {100, 101}, {650, 17780}, {1150, 36258}, {3909, 7239}, {4427, 35310}, {7283, 37040}, {16975, 34362}, {21580, 27134}, {32933, 34361}

X(42723) = crossdifference of every pair of points on line {244, 667}
X(42723) = X(i)-isoconjugate of X(j) for these (i,j): {244, 36087}, {513, 2224}, {649, 675}, {667, 37130}, {1086, 32682}, {15397, 29240}
X(42723) = barycentric product X(i)*X(j) for these {i,j}: {100, 3006}, {668, 674}, {765, 23887}, {1978, 2225}, {4033, 14964}, {4249, 20336}, {6386, 8618}
X(42723) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 675}, {101, 2224}, {190, 37130}, {674, 513}, {1110, 32682}, {1252, 36087}, {2225, 649}, {3006, 693}, {4249, 28}, {8618, 667}, {14964, 1019}, {23887, 1111}

X(42724) = X(2)X(37)∩X(100)X(9084)

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

X(42724) lies on these lines: {2, 37}, {100, 9084}, {190, 1434}, {213, 1332}, {1001, 4742}, {3159, 24171}, {3262, 30830}, {3896, 39688}, {3986, 18697}, {3992, 4078}, {6335, 17983}, {9227, 22028}, {21078, 22047}

X(42724) = trilinear pole of line {1499, 14207}
X(42724) = X(i)-isoconjugate of X(j) for these (i,j): {58, 21448}, {86, 39238}, {649, 1296}, {667, 37216}, {1919, 35179}, {2206, 5485}, {4750, 32648}, {14419, 36045}
X(42724) = barycentric product X(i)*X(j) for these {i,j}: {37, 11059}, {190, 14207}, {313, 36277}, {321, 1992}, {668, 1499}, {1384, 27801}, {4033, 4786}, {4232, 20336}, {4601, 6791}, {6386, 8644}, {27808, 30234}
X(42724) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 21448}, {100, 1296}, {190, 37216}, {213, 39238}, {321, 5485}, {668, 35179}, {1384, 1333}, {1499, 513}, {1992, 81}, {4232, 28}, {4786, 1019}, {6791, 3125}, {8644, 667}, {9125, 14419}, {11059, 274}, {14207, 514}, {27088, 16702}, {30234, 3733}, {36277, 58}

leftri

Gibert points on cubic K1207: X(42725)-X(42730)

rightri

This preamble and points X(42725)-X(42730) are contributed by Peter Moses, April 21, 2021

See
K1207

Gibert points are introduced in the preamble just before X(42085)



X(42725) = GIBERT (6 SQRT(6),5,4) POINT

Barycentrics    3*Sqrt[2]*a^2*S + 2*a^2*SA + 5*SB*SC : :

X(42725) lies on the cubic K1207 and these lines: {2, 41975}, {6, 3545}, {5055, 42647}, {10304, 41980}, {14785, 31487}, {15682, 42645}, {15692, 41976}

X(42726) = GIBERT (-6 SQRT(6),5,4) POINT

Barycentrics    -3*Sqrt[2]*a^2*S + 2*a^2*SA + 5*SB*SC : :

X(42726) lies on the cubic K1207 and these lines: {2, 41976}, {6, 3545}, {5055, 42648}, {10304, 41979}, {14784, 31487}, {15682, 42646}, {15692, 41975}

X(42727) = GIBERT (3 SQRT(3/2),5,1) POINT

Barycentrics    (3*a^2*S)/Sqrt[2] + a^2*SA + 10*SB*SC : :

X(42727) lies on the cubic K1207 and these lines: {6, 1327}, {30, 41976}, {381, 42645}, {3830, 12822}, {5066, 41980}, {11737, 41975}, {12101, 41979}, {14269, 42646}, {33699, 42647}

X(42728) = GIBERT (-3 SQRT(3/2),5,1) POINT

Barycentrics    (-3*a^2*S)/Sqrt[2] + a^2*SA + 10*SB*SC : :

X(42728) lies on the cubic K1207 and these lines: {6, 1327}, {30, 41975}, {381, 42646}, {3830, 12823}, {5066, 41979}, {11737, 41976}, {12101, 41980}, {14269, 42645}, {33699, 42648}

X(42729) = GIBERT (2 SQRT(2/3),1,-2) POINT

Barycentrics    (Sqrt[2]*a^2*S)/3 - a^2*SA + SB*SC : :

X(42729) lies on the cubic K1207 and these lines: {3, 42647}, {4, 41975}, {6, 20}, {376, 41980}, {382, 42648}, {3523, 42645}, {11001, 41979}, {14784, 42226}, {14785, 42225}, {21735, 41976}

X(42730) = GIBERT (2 SQRT(2/3),-1,2) POINT

Barycentrics    (Sqrt[2]*a^2*S)/3 + a^2*SA - SB*SC : :

X(42730) lies on the cubic K1207 and these lines: {3, 42648}, {4, 41976}, {6, 20}, {376, 41979}, {382, 42647}, {3523, 42646}, {11001, 41980}, {14784, 42225}, {14785, 42226}, {21735, 41975}

leftri

Centers of circles that pass through X(13) and X(14): X(42731)-X(42738)

rightri

This preamble and points X(42731)-X(42738) are contributed by Clark Kimberling and Peter Moses, April 22, 2021

See X(13) for a list of circles that pass through X(13) and X(14), and see X(15) for circles through X(15) and X(16).



X(42731) = CENTER OF CIRCLE {{{13,14,112}}

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

X(42731) lies on these lines: {3, 24978}, {115, 125}, {140, 41078}, {186, 523}, {2797, 9979}, {2799, 38748}, {2848, 9409}, {5489, 6130}, {14656, 39857}

X(42731) = tripolar centroid of X(275)
X(42731) = crossdifference of every pair of points on line {110, 216}

X(42732) = CENTER OF CIRCLE {{{13,14,2079}}

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

X(42732) lies on these lines: {115, 125}, {523, 31667}, {6140, 10279}

X(42732) = tripolar centroid of X(13585)

X(42733) = CENTER OF CIRCLE {{{4,13,14}}

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

X(42733) lies on these lines: {3, 14566}, {4, 523}, {5, 5664}, {30, 18556}, {115, 125}, {378, 39201}, {381, 525}, {512, 32062}, {520, 15030}, {647, 33843}, {879, 1499}, {1316, 1649}, {1995, 30474}, {2777, 30497}, {2797, 3268}, {2799, 9880}, {3265, 32815}, {3906, 22682}, {5094, 9209}, {5478, 23870}, {5479, 23871}, {6249, 33752}, {6644, 22089}, {9007, 11180}, {14223, 14639}, {18809, 42426}

X(42733) = reflection of X(381) in X(39491)
X(42733) = pole wrt orthocentroidal circle of van Aubel line
X(42733) = tripolar centroid of X(16080)
X(42733) = X(16075)-isoconjugate of X(36034)
X(42733) = crossdifference of every pair of points on line {110, 3284}
X(42733) = barycentric product X(i)*X(j) for these {i,j}: {1637, 16076}, {1651, 2394}
X(42733) = barycentric quotient X(i)/X(j) for these {i,j}: {1637, 16075}, {1651, 2407}, {2433, 41433}
X(42733) = {X(868),X(1640)}-harmonic conjugate of X(8371)

X(42734) = CENTER OF CIRCLE {{{13,14,616}}

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

X(42734) lies on these lines: {115, 125}, {298, 523}, {618, 1649}, {5466, 11121}, {8029, 23870}, {9205, 11123}, {14082, 32553}, {14424, 23871}

X(42734) = reflection of X(42735) in X(9148)
X(42734) = tripolar centroid of X(40706)
X(42734) = {X(9200),X(11182)}-harmonic conjugate of X(8371)

X(42735) = CENTER OF CIRCLE {{{13,14,617}}

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

X(42735) lies on these lines: {115, 125}, {299, 523}, {619, 1649}, {5466, 11122}, {8029, 23871}, {9204, 11123}, {14081, 32552}, {14424, 23870}

X(42735) = reflection of X(42734) in X(9148)
X(42735) = tripolar centroid of X(40707)
X(42735) = {X(9201),X(11182)}-harmonic conjugate of X(8371)

X(42736) = CENTER OF CIRCLE {{{13,14,125}}

Barycentrics    (b^2 - c^2)*(-2*a^10 + 3*a^8*b^2 + 5*a^6*b^4 - 10*a^4*b^6 + 3*a^2*b^8 + b^10 + 3*a^8*c^2 - 16*a^6*b^2*c^2 + 11*a^4*b^4*c^2 + 8*a^2*b^6*c^2 - 6*b^8*c^2 + 5*a^6*c^4 + 11*a^4*b^2*c^4 - 22*a^2*b^4*c^4 + 5*b^6*c^4 - 10*a^4*c^6 + 8*a^2*b^2*c^6 + 5*b^4*c^6 + 3*a^2*c^8 - 6*b^2*c^8 + c^10) : :

Let A', B', C' be the orthic axis intercepts of lines BC, CA, AB, resp. Let LA, LB, LC be the reflections of the orthic axis in BC, CA, AB, resp. Let AB, AC be the orthogonal projections of A' on LB, LC, resp. Define BC, BA, CA, CB cyclically. The circumcircles of A'ABAC, B'BCBA, C'CACB are coaxial, and X(42736) is the centroid of their centers. (See Hyacinthos #21468, Antreas Hatzipolakis, Jan 30, 2013) (Randy Hutson, May 31, 2021)

X(42736) lies on these lines: {2, 9033}, {98, 9189}, {115, 125}, {523, 22264}, {526, 10189}, {1499, 37984}, {2848, 24930}, {3268, 15059}, {5466, 16080}, {6130, 9003}, {9140, 14697}, {12099, 39469}, {15475, 34310}, {16315, 33921}

X(42737) = CENTER OF CIRCLE {{{13,14,110}}

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

X(42737) lies on these lines: {115, 125}, {323, 523}, {526, 8029}, {804, 14698}, {1499, 7574}, {1649, 6132}, {5466, 13582}, {5642, 13290}

X(42737) = Hutson-Parry-circle-inverse of X(1116)
X(42737) = crossdifference of every pair of points on line {110, 15544}
X(42737) = {X(13636),X(13722)}-harmonic conjugate of X(1116)

X(42738) = CENTER OF CIRCLE {{{13,14,98}}

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

X(42738) lies on these lines: {98, 523}, {115, 125}, {525, 11632}, {2394, 14651}, {2782, 5664}, {2793, 16230}, {2799, 6055}, {5489, 11623}, {9180, 16080}, {12042, 18556}, {14566, 38224}

X(42738) = Dao-Moses-Telv-circle-inverse of X(1640)
X(42738) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {125, 1637, 8371}, {8371, 14420, 13291}

X(42739) = CENTER OF CIRCLE {{{13,14,74}}

Barycentrics    (b^2 - c^2)*(-2*a^14 + 4*a^12*b^2 + 9*a^10*b^4 - 35*a^8*b^6 + 40*a^6*b^8 - 18*a^4*b^10 + a^2*b^12 + b^14 + 4*a^12*c^2 - 30*a^10*b^2*c^2 + 39*a^8*b^4*c^2 + a^6*b^6*c^2 - 24*a^4*b^8*c^2 + 15*a^2*b^10*c^2 - 5*b^12*c^2 + 9*a^10*c^4 + 39*a^8*b^2*c^4 - 84*a^6*b^4*c^4 + 42*a^4*b^6*c^4 - 15*a^2*b^8*c^4 + 9*b^10*c^4 - 35*a^8*c^6 + a^6*b^2*c^6 + 42*a^4*b^4*c^6 - 2*a^2*b^6*c^6 - 5*b^8*c^6 + 40*a^6*c^8 - 24*a^4*b^2*c^8 - 15*a^2*b^4*c^8 - 5*b^6*c^8 - 18*a^4*c^10 + 15*a^2*b^2*c^10 + 9*b^4*c^10 + a^2*c^12 - 5*b^2*c^12 + c^14) : :

X(42739) lies on these lines: {115, 125}, {523, 1138}, {5664, 10264}

leftri

Dao-Lester and Dao-Parry circles: X(42740)-X(42747)

rightri

This preamble and centers X(42740)-X(42747) were contributed by César Eliud Lozada, April 22, 2021.

These constructions are based on two problems in the paper "Generalizations of some famous classical Euclidean geometry theorems", by Dao Thanh Oai & als., published in International Journal of Computer Discovered Mathematics, Vol. 1, No. 3, 2016, pp. 13-20.

Problem 1 (A generalization of the Lester circle associated with the Neuberg cubic). Let ABC be a triangle and P a point on the Neuberg cubic of ABC. Let Pa be the reflection of P in the line BC, and define Pb and Pc cyclically. It is known that lines APa, BPb, CPc concur at a point Q(P). Then P, Q(P) and the two Fermat points of ABC lie on a circle. (Remark: If P=X(3) then Q(P)=X(5) and the given circle is the Lester circle of ABC. See Lester circle in WolframMathworld).

The described circle is named here the Dao-Lester circle of P. Its center O(P) lies on the line X(115)X(125). For P = x : y : z (barycentrics) on the Neuberg cubic of ABC, O(P) has coordinates:

  O(P) = (2*(S^2-3*SA^2)*x^2+4*(S^2-3*SB*SC)*y*z-(S^2-3*SB^2)*y^2-(S^2-3*SC^2)*z^2-2*(S^2-3*SA*SB)*x*y-2*(S^2-3*SA*SC)*x*z)*(SB-SC) : :

The appearance of (i, j) in the following list means that O(X(i))=X(j):
(1, 42740), (3, 1116), (4, 42733), (15, 9201), (16, 9200), (30, 690), (74, 42739), (399, 690), (484, 30574), (616, 42734), (617, 42735), (1157, 42731), (2132, 42733), (3464, 30574), (5623, 9200), (5624, 9201), (5667, 42731), (5668, 14446), (5669, 14447), (5670, 42739), (5671, 1116), (5672, 4120), (5673, 4120), (5674, 42735), (5675, 42734), (5677, 42740), (8172, 14446), (8173, 14447)

Problem 2 (A generalization of the Parry circle associated with two isogonal conjugate points). Let ℍ be a rectangular circum-hyperbola of ABC and ℓ be the line isogonal conjugate of ℍ. The tangent line to the ℍ at X(4) meets ℓ at point K. The line through K and the center of ℍ meets ℍ at P1, P2. Let P1*, P2*, K* be the isogonal conjugates of P1, P2 and K, respectively. Let K' be the inverse point of K* with respect to the circumcircle of ABC. Then the five points P1*, P2*, K*, K' and X(110) lie on a circle. Furthermore K lie on the Jerabek hyperbola. (Remark: It can be proved that if ℍ is the Kiepert hyperbola of ABC, then the given circle is the Parry circle of ABC).

The last circle is named here the Dao-Parry circle of ℍ. Its center O(ℍ) lies on the line X(110)X(351). If P = x : y : z is any point on ℍ, other than A, B, C, X(4), then:

  O(ℍ) = (SB+SC)*(SA-SB)*(SA-SC)*(-(y-z)*SA*x-(x+z)*SB*y+(x+y)*SC*z)*(x*((y-z)*S^2-4*SA*(SB*y-SC*z))+(x+z)*SB^2*y-(x+y)*SC^2*z) : :

O(ℍ)=X(42741), X(351), X(526) for ℍ = Feuerbach, Kiepert, Jerabek circum-hyperbola, respectively. In general, since ℍ is a rectangular circum-hyperbola of ABC, its center ℍo lies on the nine-point-circle of ABC. The appearance of (i, j) in the following list means that if ℍo = X(i) then O(ℍ) = X(j):
(11, 42741), (113, 42742), (114, 42743), (115, 351), (116, 42744), (118, 42745), (119, 42746), (120, 42747), (125, 526), (3258, 526), (5099, 351), (5520, 42741), (16188, 42743), (25641, 42742), (42422, 42746)

X(42740) = CENTER OF THE DAO-LESTER CIRCLE OF X(1)

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

X(42740) lies on these lines: {115, 125}, {523, 3649}, {4926, 6129}, {11705, 35051}, {11706, 35052}

X(42741) = CENTER OF THE DAO-PARRY CIRCLE OF THE FEUERBACH CIRCUM-HYPERBOLA

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

X(42741) lies on these lines: {21, 900}, {28, 39534}, {36, 238}, {110, 351}, {404, 24920}, {665, 1333}, {759, 6089}, {1283, 9508}, {1635, 19302}, {2070, 39210}, {2605, 42653}, {4225, 28284}, {4228, 26275}, {5047, 24959}, {5260, 21714}, {7202, 18181}, {7419, 28396}, {8648, 34442}, {8674, 16164}, {11115, 26078}, {16047, 28779}, {17588, 26144}, {22586, 35053}

X(42741) = isogonal conjugate of the anticomplement of X(38982)
X(42741) = barycentric product X(i)*X(j) for these {i, j}: {81, 8674}, {274, 42670}, {513, 37783}, {514, 5127}, {693, 19622}, {905, 2074}
X(42741) = barycentric quotient X(i)/X(j) for these (i, j): (81, 35156), (649, 5620), (1333, 1290)
X(42741) = trilinear product X(i)*X(j) for these {i, j}: {58, 8674}, {86, 42670}, {513, 5127}, {514, 19622}, {649, 37783}, {1019, 17796}
X(42741) = trilinear quotient X(i)/X(j) for these (i, j): (58, 1290), (86, 35156), (513, 5620), (1019, 21907)
X(42741) = intersection, other than A,B,C, of conics {{A, B, C, X(36), X(759)}} and {{A, B, C, X(110), X(513)}}
X(42741) = pole of the trilinear polar of X(37140) with respect to circumcircle
X(42741) = crossdifference of every pair of points on line {X(37), X(115)}
X(42741) = crosspoint of X(i) and X(j) for these (i, j): {58, 36069}, {110, 759}
X(42741) = crosssum of X(i) and X(j) for these (i, j): {10, 6370}, {523, 758}
X(42741) = X(i)-isoconjugate-of-X(j) for these {i, j}: {10, 1290}, {42, 35156}, {100, 5620}, {1018, 21907}
X(42741) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (81, 35156), (649, 5620), (1333, 1290)
X(42741) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (110, 15329, 42746), (1634, 5467, 42747), (3733, 21789, 4833)

X(42742) = CENTER OF THE DAO-PARRY CIRCLE OF THE CIRCUM-HYPERBOLA WITH CENTER X(113)

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

X(42742) lies on these lines: {30, 113}, {110, 351}, {399, 14933}, {3134, 5972}, {5663, 39987}, {7471, 16171}

X(42742) = midpoint of X(i) and X(j) for these {i, j}: {110, 15329}, {399, 14933}
X(42742) = reflection of X(3134) in X(5972)
X(42742) = barycentric product X(1511)*X(2410)
X(42742) = barycentric quotient X(i)/X(j) for these (i, j): (1511, 2411), (1553, 41079)
X(42742) = trilinear product X(1553)*X(36034)
X(42742) = trilinear quotient X(i)/X(j) for these (i, j): (250, 36117), (1553, 36035)
X(42742) = intersection, other than A,B,C, of conics {{A, B, C, X(30), X(110)}} and {{A, B, C, X(113), X(2437)}}
X(42742) = crossdifference of every pair of points on line {X(115), X(2433)}
X(42742) = X(125)-isoconjugate-of-X(36117)
X(42742) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1511, 2411), (1553, 41079)
X(42742) = intersection of Simson line of X(110) and tangent to circumcircle at X(110)

X(42743) = CENTER OF THE DAO-PARRY CIRCLE OF THE CIRCUM-HYPERBOLA WITH CENTER X(114)

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

X(42743) lies on these lines: {110, 351}, {237, 511}, {325, 3233}, {542, 5191}, {804, 4226}, {3289, 39689}, {3569, 14966}, {4230, 17994}, {7468, 20403}, {14999, 36885}, {20976, 23584}

X(42743) = midpoint of X(1634) and X(5467)
X(42743) = barycentric product X(i)*X(j) for these {i, j}: {511, 14999}, {542, 2421}
X(42743) = barycentric quotient X(i)/X(j) for these (i, j): (237, 14998), (511, 14223)
X(42743) = trilinear product X(i)*X(j) for these {i, j}: {542, 23997}, {1755, 14999}
X(42743) = trilinear quotient X(i)/X(j) for these (i, j): (1755, 14998), (1959, 14223)
X(42743) = intersection, other than A,B,C, of conics {{A, B, C, X(110), X(511)}} and {{A, B, C, X(237), X(1576)}}
X(42743) = crossdifference of every pair of points on line {X(115), X(2395)}
X(42743) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (237, 14998), (511, 14223)
X(42743) = {X(110), X(15329)}-harmonic conjugate of X(351)

X(42744) = CENTER OF THE DAO-PARRY CIRCLE OF THE CIRCUM-HYPERBOLA WITH CENTER X(116)

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

X(42744) lies on these lines: {110, 351}, {239, 514}, {926, 4184}, {4466, 17198}

X(42744) = barycentric product X(i)*X(j) for these {i, j}: {86, 2774}, {2073, 4025}
X(42744) = barycentric quotient X(i)/X(j) for these (i, j): (58, 2690), (1459, 38535), (2073, 1897)
X(42744) = trilinear product X(i)*X(j) for these {i, j}: {81, 2774}, {905, 2073}
X(42744) = trilinear quotient X(i)/X(j) for these (i, j): (81, 2690), (905, 38535), (2073, 1783)
X(42744) = crossdifference of every pair of points on line {X(42), X(115)}
X(42744) = X(37)-isoconjugate-of-X(2690)
X(42744) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (58, 2690), (1459, 38535)
X(42744) = {X(110), X(15329)}-harmonic conjugate of X(42745)

X(42745) = CENTER OF THE DAO-PARRY CIRCLE OF THE CIRCUM-HYPERBOLA WITH CENTER X(118)

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

X(42745) lies on these lines: {110, 351}, {516, 14953}, {926, 4243}

X(42745) = {X(110), X(15329)}-harmonic conjugate of X(42744)

X(42746) = CENTER OF THE DAO-PARRY CIRCLE OF THE CIRCUM-HYPERBOLA WITH CENTER X(119)

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

X(42746) lies on these lines: {110, 351}, {517, 859}, {900, 3658}, {4246, 39534}

X(42746) = {X(110), X(15329)}-harmonic conjugate of X(42741)

X(42747) = CENTER OF THE DAO-PARRY CIRCLE OF THE CIRCUM-HYPERBOLA WITH CENTER X(120)

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

X(42747) lies on these lines: {110, 351}, {518, 2223}, {4236, 6084}

X(42747) = trilinear product X(1818)*X(7476)
X(42747) = {X(1634), X(5467)}-harmonic conjugate of X(42741)

X(42748) = ANTIPODE OF X(1) IN THE DAO-LESTER CIRCLE OF X(1)

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

Dao-Lester circles are defined in the preamble just before X(42740).

X(42748) lies on these lines: {1,42740}, {79, 523}, {690, 13178}, {4926, 15079}

X(42748) = reflection of X(1) in X(42740)

X(42749) = ANTIPODE OF X(79) IN THE DAO-LESTER CIRCLE OF X(1)

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

X(42749) lies on these lines: {1, 523}, {79,42740}, {1699, 28473}, {5692, 35057}

X(42749) = reflection of X(79) in X(42740)

leftri

Points on the Sherman line: X(42750)-X(42772)

rightri

This preamble and points X(42750-X(42772) are contributed by Peter Moses, April 23, 2021

Suppose that P' = p' : q' : r' is a point on a line p x + q y + r z = 0 and that u x + v y + w z = 0 is a line, L. Then the point P'' = (p/u)*p' : (q/v)*q' + (r/w)*r' (p/u)*p' : (q/v)*q' + (r/w)*r' lies on L For example, if P' is on the line at infinity and L is the Sherman line, X(3259)X(3326), then the point P'*X(10015) is on L. Points X(42750)-X(42772) are obtained in this manner from the line at infinity, where, in the same order, P' = X(i) for i = 30, 511, 512, 513, 514, 515, 516, 517, 518, 523, 524, 525, 527, 528, 536, 537, 726, 740, 758, 912, 918, 926, 971.



X(42750) = X(113)X(133)∩X(3259)X(3326)

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

X(42750) lies on these lines: {113, 133}, {513, 942}, {520, 24474}, {522, 18483}, {523, 946}, {1354, 11125}, {1845, 8677}, {2804, 12611}, {3259, 3326}, {6087, 11719}, {7978, 14224}

X(42750) = crossdifference of every pair of points on line {15627, 17796}
X(42750) = X(i)-isoconjugate of X(j) for these (i,j): {74, 36037}, {1309, 35200}, {2159, 13136}, {2349, 32641}, {15627, 37136}, {36034, 38955}
X(42750) = barycentric product X(i)*X(j) for these {i,j}: {30, 10015}, {859, 41079}, {908, 11125}, {1637, 17139}, {1769, 14206}, {2173, 36038}, {2804, 6357}, {3260, 3310}, {3262, 14399}, {11064, 39534}, {14400, 22464}
X(42750) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 13136}, {1495, 32641}, {1637, 38955}, {1769, 2349}, {1990, 1309}, {2173, 36037}, {3310, 74}, {8677, 14919}, {10015, 1494}, {11125, 34234}, {14395, 1809}, {14399, 104}, {14581, 14776}, {23220, 18877}, {36038, 33805}, {39534, 16080}

X(42751) = X(114)X(132)∩X(3259)X(3326)

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

X(42751) lies on these lines: {114, 132}, {512, 1064}, {513, 3666}, {3259, 3326}, {3310, 8677}, {15451, 39212}, {23224, 40956}

X(42751) = crossdifference of every pair of points on line {248, 5291}
X(42751) = X(i)-isoconjugate of X(j) for these (i,j): {98, 36037}, {293, 1309}, {336, 14776}, {1821, 32641}, {1910, 13136}, {2250, 2966}, {15628, 37136}, {36084, 38955}
X(42751) = barycentric product X(i)*X(j) for these {i,j}: {297, 8677}, {325, 3310}, {511, 10015}, {859, 2799}, {1755, 36038}, {1769, 1959}, {3569, 17139}, {36212, 39534}
X(42751) = barycentric quotient X(i)/X(j) for these {i,j}: {232, 1309}, {237, 32641}, {511, 13136}, {859, 2966}, {1755, 36037}, {1769, 1821}, {2211, 14776}, {3310, 98}, {3569, 38955}, {8677, 287}, {10015, 290}, {23220, 248}, {39534, 16081}

X(42752) = X(98)X(17981)∩X(3259)X(3326)

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

X(42752) lies on these lines: {98, 17981}, {115, 2971}, {1356, 3122}, {1402, 40934}, {3259, 3326}, {7983, 11609}

X(42752) = X(859)-Ceva conjugate of X(3310)
X(42752) = crosspoint of X(i) and X(j) for these (i,j): {859, 3310}, {1769, 21801}
X(42752) = crosssum of X(i) and X(j) for these (i,j): {110, 16704}, {13136, 38955}
X(42752) = crossdifference of every pair of points on line {645, 4558}
X(42752) = X(i)-isoconjugate of X(j) for these (i,j): {99, 36037}, {104, 4600}, {645, 37136}, {662, 13136}, {799, 32641}, {909, 4601}, {1309, 4592}, {1812, 39294}, {2250, 4590}, {2720, 7257}, {4567, 34234}, {4570, 18816}, {24041, 38955}
X(42752) = barycentric product X(i)*X(j) for these {i,j}: {115, 859}, {244, 21801}, {512, 10015}, {517, 3125}, {523, 3310}, {647, 39534}, {661, 1769}, {798, 36038}, {908, 3122}, {1015, 17757}, {1400, 35015}, {1457, 21044}, {1465, 4516}, {1880, 35014}, {2183, 3120}, {2397, 8034}, {2501, 8677}, {2680, 17946}, {2804, 7180}, {3121, 3262}, {3124, 17139}, {4079, 23788}, {14571, 18210}, {14618, 23220}
X(42752) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 13136}, {517, 4601}, {669, 32641}, {798, 36037}, {859, 4590}, {1457, 4620}, {1769, 799}, {2183, 4600}, {2489, 1309}, {2680, 17790}, {3121, 104}, {3122, 34234}, {3124, 38955}, {3125, 18816}, {3310, 99}, {4516, 36795}, {8034, 2401}, {8677, 4563}, {10015, 670}, {17139, 34537}, {17757, 31625}, {21801, 7035}, {23220, 4558}, {35015, 28660}, {36038, 4602}, {39534, 6331}

X(42753) = X(25)X(34)∩X(3259)X(3326)

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

X(42753) lies on the cubic K583 and these lines: {2, 19884}, {11, 2969}, {25, 34}, {43, 3987}, {63, 36280}, {104, 36125}, {244, 1357}, {517, 14260}, {661, 17435}, {764, 1647}, {1393, 42448}, {1421, 20999}, {1465, 23981}, {1482, 3870}, {1577, 3141}, {1772, 2841}, {3159, 22000}, {3259, 3326}, {3817, 21318}, {5400, 22321}, {5687, 12876}, {6127, 16110}, {7004, 38389}, {9955, 18115}, {11681, 29641}, {14008, 18175}, {14249, 37372}, {14455, 26098}, {15507, 16586}, {15635, 23345}, {15906, 34586}, {17605, 21807}, {20060, 29840}, {21339, 36197}, {24590, 36279}

X(42753) = X(i)-Ceva conjugate of X(j) for these (i,j): {517, 1769}, {1465, 3310}, {3262, 10015}, {23345, 764}, {36125, 513}
X(42753) = crosspoint of X(i) and X(j) for these (i,j): {88, 693}, {269, 1022}, {513, 1411}, {517, 1769}, {908, 23788}, {1875, 39534}, {3262, 10015}, {14260, 23345}
X(42753) = crosssum of X(i) and X(j) for these (i,j): {44, 692}, {100, 4511}, {104, 36037}, {200, 1023}, {17780, 36944}, {32641, 34858}
X(42753) = crossdifference of every pair of points on line {644, 906}
X(42753) = X(i)-isoconjugate of X(j) for these (i,j): {100, 36037}, {101, 13136}, {104, 765}, {190, 32641}, {219, 39294}, {644, 37136}, {646, 32669}, {909, 1016}, {1110, 18816}, {1252, 34234}, {1309, 1331}, {1795, 15742}, {1809, 7012}, {2149, 36795}, {2250, 4567}, {2342, 4998}, {2423, 6632}, {2720, 3699}, {4561, 14776}, {4570, 38955}, {4571, 36110}, {5377, 36819}, {7035, 34858}, {9268, 36944}
X(42753) = barycentric product X(i)*X(j) for these {i,j}: {11, 1465}, {57, 35015}, {88, 3259}, {244, 908}, {278, 35014}, {513, 10015}, {514, 1769}, {517, 1086}, {649, 36038}, {661, 23788}, {693, 3310}, {764, 2397}, {859, 16732}, {905, 39534}, {1015, 3262}, {1022, 23757}, {1111, 2183}, {1427, 14010}, {1457, 4858}, {1565, 14571}, {1785, 3942}, {1875, 26932}, {2170, 22464}, {2804, 3669}, {3125, 17139}, {3326, 34051}, {8677, 17924}, {15635, 26611}, {16082, 35012}, {16726, 17757}, {17205, 21801}, {21132, 24029}, {23981, 40166}
X(42753) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 36795}, {34, 39294}, {244, 34234}, {513, 13136}, {517, 1016}, {649, 36037}, {667, 32641}, {764, 2401}, {859, 4567}, {908, 7035}, {1015, 104}, {1086, 18816}, {1357, 34051}, {1457, 4564}, {1465, 4998}, {1769, 190}, {1977, 34858}, {2087, 36944}, {2183, 765}, {2804, 646}, {2969, 16082}, {3122, 2250}, {3125, 38955}, {3248, 909}, {3259, 4358}, {3262, 31625}, {3310, 100}, {6591, 1309}, {7117, 1809}, {8027, 2423}, {8677, 1332}, {10015, 668}, {14260, 5376}, {14571, 15742}, {17139, 4601}, {22096, 14578}, {23220, 906}, {23757, 24004}, {23788, 799}, {23981, 31615}, {35014, 345}, {35015, 312}, {36038, 1978}, {39534, 6335}

X(42754) = X(19)X(57)∩X(3259)X(3326)

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

X(42754) lies on these lines: {19, 57}, {116, 2973}, {192, 31053}, {344, 30852}, {903, 4638}, {908, 2397}, {1022, 2401}, {1086, 1358}, {2183, 22464}, {2265, 5723}, {2280, 17301}, {2405, 5236}, {2969, 7004}, {3254, 10695}, {3259, 3326}, {3675, 7336}, {4957, 21044}, {6336, 34234}, {6545, 23760}, {16200, 41570}, {16560, 37771}, {16732, 23773}, {30858, 36910}

X(42754) = X(34179)-anticomplementary conjugate of X(30578)
X(42754) = X(i)-Ceva conjugate of X(j) for these (i,j): {908, 10015}, {1022, 6545}, {4089, 1647}, {6336, 514}, {22464, 1769}
X(42754) = X(i)-isoconjugate of X(j) for these (i,j): {100, 32641}, {101, 36037}, {104, 1252}, {212, 39294}, {644, 2720}, {692, 13136}, {765, 909}, {906, 1309}, {1016, 34858}, {1110, 34234}, {1332, 14776}, {1809, 7115}, {2250, 4570}, {2342, 4564}, {3699, 32669}, {3939, 37136}, {4571, 32702}, {4587, 36110}, {6065, 34051}, {14578, 15742}, {18816, 23990}
X(42754) = crosspoint of X(i) and X(j) for these (i,j): {279, 6548}, {514, 2006}, {903, 3261}, {908, 10015}
X(42754) = crosssum of X(i) and X(j) for these (i,j): {101, 2323}, {220, 23344}, {902, 32739}, {909, 32641}
X(42754) = crossdifference of every pair of points on line {1110, 3939}
X(42754) = barycentric product X(i)*X(j) for these {i,j}: {7, 35015}, {11, 22464}, {244, 3262}, {273, 35014}, {513, 36038}, {514, 10015}, {517, 1111}, {523, 23788}, {693, 1769}, {859, 21207}, {903, 3259}, {908, 1086}, {1145, 6549}, {1358, 6735}, {1457, 34387}, {1465, 4858}, {1565, 1785}, {1875, 17880}, {2183, 23989}, {2397, 6545}, {2427, 23100}, {2804, 3676}, {2973, 22350}, {3120, 17139}, {3261, 3310}, {3668, 14010}, {4025, 39534}, {6548, 23757}, {16727, 21801}, {17205, 17757}, {24029, 40166}
X(42754) = barycentric quotient X(i)/X(j) for these {i,j}: {244, 104}, {278, 39294}, {513, 36037}, {514, 13136}, {517, 765}, {649, 32641}, {859, 4570}, {908, 1016}, {1015, 909}, {1086, 34234}, {1111, 18816}, {1457, 59}, {1465, 4564}, {1647, 36944}, {1769, 100}, {1785, 15742}, {1875, 7012}, {2183, 1252}, {2397, 6632}, {2804, 3699}, {2969, 36123}, {3120, 38955}, {3125, 2250}, {3248, 34858}, {3259, 519}, {3262, 7035}, {3271, 2342}, {3310, 101}, {3326, 6735}, {3669, 37136}, {3675, 36819}, {3937, 1795}, {4858, 36795}, {6545, 2401}, {6735, 4076}, {7004, 1809}, {7649, 1309}, {8677, 1331}, {10015, 190}, {14010, 1043}, {14260, 9268}, {17139, 4600}, {21143, 2423}, {22464, 4998}, {23220, 32656}, {23757, 17780}, {23788, 99}, {24029, 31615}, {35012, 22350}, {35014, 78}, {35015, 8}, {36038, 668}, {39534, 1897}

X(42755) = X(4)X(522)∩X(3259)X(3326)

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

X(42755) lies on these lines: {4, 522}, {19, 652}, {46, 21186}, {65, 513}, {117, 14304}, {208, 7649}, {407, 656}, {514, 3577}, {661, 1901}, {1359, 6087}, {1420, 21172}, {1537, 2804}, {1769, 1846}, {1845, 2849}, {3259, 3326}, {7982, 8058}, {8677, 14299}, {23726, 23760}, {37259, 39199}

X(42755) = orthic-isogonal conjugate of X(35015)
X(42755) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 35015}, {522, 1769}, {653, 8755}, {36127, 1457}
X(42755) = crosspoint of X(i) and X(j) for these (i,j): {4, 23987}, {522, 14304}, {653, 22464}
X(42755) = crosssum of X(i) and X(j) for these (i,j): {109, 36040}, {652, 2342}
X(42755) = crossdifference of every pair of points on line {2323, 15629}
X(42755) = X(i)-isoconjugate of X(j) for these (i,j): {102, 36037}, {1309, 36055}, {1809, 36067}, {6081, 15501}, {13136, 32677}, {15629, 37136}, {32641, 36100}, {32643, 36795}
X(42755) = barycentric product X(i)*X(j) for these {i,j}: {515, 10015}, {653, 10017}, {1465, 14304}, {2182, 36038}, {2406, 35015}, {2804, 34050}, {3310, 35516}, {24035, 35014}
X(42755) = barycentric quotient X(i)/X(j) for these {i,j}: {515, 13136}, {1455, 37136}, {1769, 36100}, {2182, 36037}, {3310, 102}, {8755, 1309}, {10015, 34393}, {10017, 6332}, {14304, 36795}, {23987, 39294}, {35015, 2399}

X(42756) = X(354)X(513)∩X(3259)X(3326)

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

X(42756) lies on these lines: {118, 20622}, {196, 7649}, {354, 513}, {514, 5603}, {522, 1699}, {523, 23615}, {676, 1360}, {1427, 6129}, {1459, 34036}, {2093, 14837}, {2849, 11125}, {3259, 3326}, {4064, 22000}, {8058, 25568}, {9521, 14414}, {20988, 39199}

X(42756) = crosssum of X(36819) and X(37628)
X(42756) = crossdifference of every pair of points on line {1795, 2338}
X(42756) = X(i)-isoconjugate of X(j) for these (i,j): {103, 36037}, {104, 677}, {911, 13136}, {1309, 36056}, {2338, 37136}, {18816, 32642}, {32641, 36101}, {34234, 36039}
X(42756) = barycentric product X(i)*X(j) for these {i,j}: {516, 10015}, {676, 908}, {910, 36038}, {1769, 30807}, {1785, 39470}, {3310, 35517}, {17747, 23788}, {26006, 39534}
X(42756) = barycentric quotient X(i)/X(j) for these {i,j}: {516, 13136}, {676, 34234}, {910, 36037}, {1456, 37136}, {1769, 36101}, {1886, 1309}, {2183, 677}, {3310, 103}, {8677, 1815}, {10015, 18025}, {23220, 32657}

X(42757) = X(1)X(513)∩X(3259)X(3326)

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

X(42757) lies on on the cubic K583 and these lines: {1, 513}, {56, 6129}, {119, 2804}, {517, 37629}, {521, 1482}, {522, 946}, {523, 42440}, {900, 1537}, {1361, 1769}, {1459, 23842}, {1486, 8641}, {2849, 11700}, {3259, 3326}, {3577, 3900}, {3738, 25485}, {4017, 39791}, {4077, 41003}, {4397, 11681}, {4777, 27471}, {5903, 21189}, {6073, 23101}, {6089, 21731}, {23706, 23981}, {38505, 38514}, {39200, 42670}

X(42757) = X(i)-Ceva conjugate of X(j) for these (i,j): {693, 10015}, {934, 1465}, {15632, 24028}, {21664, 3326}
X(42757) = X(35012)-cross conjugate of X(1361)
X(42757) = crosspoint of X(i) and X(j) for these (i,j): {693, 10015}, {934, 1465}, {15632, 24028}, {23981, 39173}
X(42757) = crosssum of X(i) and X(j) for these (i,j): {522, 10265}, {692, 32641}
X(42757) = crossdifference of every pair of points on line {44, 14578}
X(42757) = X(i)-isoconjugate of X(j) for these (i,j): {104, 36037}, {190, 41933}, {909, 13136}, {1309, 1795}, {1809, 36110}, {32641, 34234}, {32669, 36795}
X(42757) = barycentric product X(i)*X(j) for these {i,j}: {513, 26611}, {514, 24028}, {517, 10015}, {651, 3326}, {693, 23980}, {905, 21664}, {908, 1769}, {1086, 15632}, {1361, 4391}, {1465, 2804}, {2183, 36038}, {2401, 23101}, {3261, 42078}, {3262, 3310}, {6335, 35012}, {13149, 41215}, {15413, 42072}, {21801, 23788}, {24029, 35015}
X(42757) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 13136}, {667, 41933}, {1361, 651}, {1457, 37136}, {1769, 34234}, {2183, 36037}, {2804, 36795}, {3310, 104}, {3326, 4391}, {10015, 18816}, {14571, 1309}, {15632, 1016}, {21664, 6335}, {23101, 2397}, {23220, 14578}, {23706, 39294}, {23980, 100}, {24028, 190}, {26611, 668}, {35012, 905}, {39534, 16082}, {41220, 36054}, {42072, 1783}, {42078, 101}

X(42758) = X(55)X(513)∩X(3259)X(3326)

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

X(42758) lies on these lines: {12, 42455}, {43, 21189}, {55, 513}, {120, 20621}, {226, 522}, {514, 31397}, {521, 3870}, {523, 17874}, {614, 6129}, {650, 40131}, {656, 40952}, {693, 7179}, {764, 21105}, {900, 12831}, {905, 999}, {926, 1362}, {1056, 2401}, {1470, 22091}, {1491, 29639}, {1734, 5902}, {1769, 3310}, {1946, 8069}, {2099, 3900}, {2530, 4449}, {2804, 36038}, {3126, 3675}, {3259, 3326}, {3309, 18446}, {3667, 41561}, {3738, 41553}, {4397, 29641}, {4705, 21118}, {4885, 30742}, {15632, 23981}, {34230, 36819}

X(42758) = X(34230)-Ceva conjugate of X(3675)
X(42758) = crossdifference of every pair of points on line {104, 294}
X(42758) = X(i)-isoconjugate of X(j) for these (i,j): {104, 36086}, {105, 36037}, {294, 37136}, {666, 909}, {673, 32641}, {919, 34234}, {927, 2342}, {1309, 36057}, {1438, 13136}, {2720, 14942}, {14776, 31637}, {18816, 32666}, {32669, 36796}
X(42758) = barycentric product X(i)*X(j) for these {i,j}: {241, 2804}, {517, 918}, {518, 10015}, {665, 3262}, {672, 36038}, {908, 2254}, {1025, 35015}, {1769, 3912}, {2397, 3675}, {3263, 3310}, {3930, 23788}, {17139, 24290}, {21801, 23829}, {25083, 39534}
X(42758) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 666}, {518, 13136}, {665, 104}, {672, 36037}, {918, 18816}, {1457, 36146}, {1458, 37136}, {1465, 927}, {1769, 673}, {2183, 36086}, {2223, 32641}, {2254, 34234}, {2427, 5377}, {2804, 36796}, {3262, 36803}, {3310, 105}, {3675, 2401}, {5089, 1309}, {8677, 1814}, {10015, 2481}, {22464, 34085}, {23220, 32658}, {23225, 14578}, {24029, 39293}, {24290, 38955}, {36038, 18031}

X(42759) = X(65)X(225)∩X(3259)X(3326)

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

X(42759) lies on these lines: {65, 225}, {125, 136}, {522, 867}, {1365, 2611}, {1647, 7336}, {2969, 3270}, {3259, 3326}, {5563, 33147}, {7984, 11604}, {10222, 41571}

X(42759) = X(17139)-Ceva conjugate of X(10015)
X(42759) = crosspoint of X(i) and X(j) for these (i,j): {65, 3657}, {850, 4080}, {3668, 4049}, {10015, 17139}
X(42759) = crosssum of X(i) and X(j) for these (i,j): {21, 3658}, {1576, 3285}
X(42759) = crossdifference of every pair of points on line {5546, 23090}
X(42759) = barycentric product of Kiepert hyperbola intercepts of the Sherman line
X(42759) = X(i)-isoconjugate of X(j) for these (i,j): {104, 4570}, {110, 36037}, {163, 13136}, {249, 2250}, {643, 2720}, {645, 32669}, {662, 32641}, {909, 4567}, {1101, 38955}, {1309, 4575}, {1795, 5379}, {2193, 39294}, {4592, 14776}, {4600, 34858}, {5546, 37136}, {18315, 35321}
X(42759) = barycentric product X(i)*X(j) for these {i,j}: {115, 17139}, {226, 35015}, {338, 859}, {517, 16732}, {523, 10015}, {525, 39534}, {661, 36038}, {850, 3310}, {908, 3120}, {1086, 17757}, {1111, 21801}, {1577, 1769}, {1785, 4466}, {2183, 21207}, {2677, 21907}, {2804, 7178}, {3125, 3262}, {3259, 4080}, {4024, 23788}, {4049, 23757}, {6354, 14010}, {6549, 21942}, {8677, 14618}, {21044, 22464}, {35014, 40149}
X(42759) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 38955}, {225, 39294}, {512, 32641}, {517, 4567}, {523, 13136}, {661, 36037}, {859, 249}, {908, 4600}, {1769, 662}, {2183, 4570}, {2489, 14776}, {2501, 1309}, {2643, 2250}, {2677, 32849}, {2680, 5291}, {2804, 645}, {3120, 34234}, {3121, 34858}, {3122, 909}, {3125, 104}, {3259, 16704}, {3262, 4601}, {3310, 110}, {4017, 37136}, {7180, 2720}, {8034, 2423}, {8677, 4558}, {10015, 99}, {14010, 7058}, {14571, 5379}, {16732, 18816}, {17139, 4590}, {17757, 1016}, {21801, 765}, {22464, 4620}, {23220, 32661}, {23788, 4610}, {35014, 1812}, {35015, 333}, {36038, 799}, {39534, 648}
X(42759) = {X(2969),X(38357)}-harmonic conjugate of X(38389)

X(42760) = X(126)X(1560)∩X(3259)X(3326)

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

X(42760) lies on these lines: {126, 1560}, {523, 29639}, {1366, 4750}, {3259, 3326}, {3310, 10015}, {7658, 40940}, {17069, 37520}

X(42760) = crossdifference of every pair of points on line {5547, 14908}
X(42760) = X(i)-isoconjugate of X(j) for these (i,j): {111, 36037}, {691, 2250}, {897, 32641}, {909, 5380}, {923, 13136}, {1309, 36060}, {5547, 37136}, {36142, 38955}
X(42760) = barycentric product X(i)*X(j) for these {i,j}: {524, 10015}, {690, 17139}, {859, 35522}, {896, 36038}, {908, 4750}, {1769, 14210}, {2804, 7181}, {3262, 14419}, {3266, 3310}, {4062, 23788}, {6390, 39534}, {14432, 22464}
X(42760) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 32641}, {468, 1309}, {517, 5380}, {524, 13136}, {690, 38955}, {859, 691}, {896, 36037}, {1769, 897}, {2642, 2250}, {3310, 111}, {4750, 34234}, {8677, 895}, {10015, 671}, {14419, 104}, {17139, 892}, {23220, 14908}, {30605, 36921}, {39534, 17983}

X(42761) = X(37)X(226)∩X(3259)X(3326)

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

X(42761) lies on these lines: {3, 36735}, {37, 226}, {115, 127}, {1086, 16596}, {1367, 4466}, {3259, 3326}, {14919, 21907}, {16595, 40622}, {17073, 17276}, {20278, 21659}

X(42761) = X(i)-complementary conjugate of X(j) for these (i,j): {647, 31845}, {759, 30476}, {1807, 3835}, {2161, 20316}, {3049, 35069}, {22383, 214}, {24624, 21259}, {32671, 5972}, {34079, 8062}
X(42761) = X(i)-Ceva conjugate of X(j) for these (i,j): {4080, 525}, {17139, 8677}, {41804, 9033}
X(42761) = crosssum of X(14591) and X(41502)
X(42761) = crossdifference of every pair of points on line {1576, 14776}
X(42761) = X(i)-isoconjugate of X(j) for these (i,j): {112, 36037}, {162, 32641}, {163, 1309}, {250, 2250}, {643, 32702}, {662, 14776}, {909, 5379}, {933, 35321}, {2194, 39294}, {5546, 36110}, {13136, 32676}, {32669, 36797}
X(42761) = barycentric product X(i)*X(j) for these {i,j}: {125, 17139}, {307, 35015}, {339, 859}, {525, 10015}, {656, 36038}, {850, 8677}, {908, 4466}, {1441, 35014}, {1565, 17757}, {1769, 14208}, {1785, 17216}, {2804, 17094}, {3262, 18210}, {3265, 39534}, {3267, 3310}, {4064, 23788}, {6356, 14010}, {21207, 22350}
X(42761) = barycentric quotient X(i)/X(j) for these {i,j}: {125, 38955}, {226, 39294}, {512, 14776}, {517, 5379}, {523, 1309}, {525, 13136}, {647, 32641}, {656, 36037}, {859, 250}, {1769, 162}, {2804, 36797}, {3120, 36123}, {3259, 37168}, {3310, 112}, {3708, 2250}, {4017, 36110}, {4466, 34234}, {7180, 32702}, {8677, 110}, {10015, 648}, {16732, 16082}, {17139, 18020}, {17757, 15742}, {18210, 104}, {22350, 4570}, {23220, 1576}, {35012, 859}, {35014, 21}, {35015, 29}, {36038, 811}, {39534, 107}

X(42762) = X(57)X(652)∩X(3259)X(3326)

Barycentrics    (b - c)*(-2*a^2 + a*b + b^2 + a*c - 2*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(42762) lies on these lines: {57, 652}, {513, 17603}, {514, 5219}, {661, 6545}, {1638, 3321}, {3259, 3326}, {3835, 23726}, {4025, 31164}, {4120, 23737}, {4369, 23728}, {4885, 23727}, {6332, 30828}, {14475, 23730}, {17605, 23615}, {25259, 31053}, {33573, 40629}

X(42762) = crossdifference of every pair of points on line {2342, 4845}
X(42762) = X(i)-isoconjugate of X(j) for these (i,j): {1156, 32641}, {2291, 36037}, {2342, 37139}, {2720, 41798}, {4845, 37136}, {13136, 34068}, {32728, 36795}
X(42762) = barycentric product X(i)*X(j) for these {i,j}: {527, 10015}, {908, 1638}, {1155, 36038}, {1323, 2804}, {1769, 30806}, {3262, 14413}, {6366, 22464}, {17139, 30574}, {23757, 36887}
X(42762) = barycentric quotient X(i)/X(j) for these {i,j}: {527, 13136}, {1055, 32641}, {1155, 36037}, {1457, 14733}, {1465, 37139}, {1638, 34234}, {1769, 1156}, {3310, 2291}, {6139, 2342}, {6610, 37136}, {10015, 1121}, {14413, 104}, {14414, 1809}, {22464, 35157}, {23710, 1309}, {30573, 36944}, {30574, 38955}

X(42763) = X(513)X(11934)∩X(3259)X(3326)

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

X(42763) lies on these lines: {513, 11934}, {517, 10015}, {676, 1155}, {908, 2804}, {3259, 3326}, {3328, 23766}, {6550, 23745}

X(42763) = crossdifference of every pair of points on line {218, 32641}
X(42763) = X(i)-isoconjugate of X(j) for these (i,j): {840, 36037}, {32641, 37131}
X(42763) = barycentric product X(i)*X(j) for these {i,j}: {528, 10015}, {1643, 3262}, {2246, 36038}, {2804, 5723}
X(42763) = barycentric quotient X(i)/X(j) for these {i,j}: {528, 13136}, {1643, 104}, {1769, 37131}, {2246, 36037}, {3310, 840}, {10015, 18821}

X(42764) = X(3120)X(3126)∩X(3259)X(3326)

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

X(42764) lies on these lines: {693, 33151}, {3120, 3126}, {3259, 3326}, {4415, 40166}, {4526, 4728}, {4885, 17595}, {7658, 24177}, {10015, 26611}

X(42764) = crossdifference of every pair of points on line {32641, 32718}
X(42764) = X(i)-isoconjugate of X(j) for these (i,j): {104, 34075}, {739, 36037}, {898, 909}, {4607, 34858}, {32641, 37129}, {32669, 36798}, {32718, 34234}
X(42764) = barycentric product X(i)*X(j) for these {i,j}: {536, 10015}, {891, 3262}, {899, 36038}, {908, 4728}, {1769, 6381}, {3310, 35543}, {3994, 23788}, {14430, 22464}, {14431, 17139}
X(42764) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 898}, {536, 13136}, {890, 34858}, {891, 104}, {899, 36037}, {908, 4607}, {1646, 2423}, {1769, 37129}, {2183, 34075}, {2397, 5381}, {2804, 36798}, {3230, 32641}, {3262, 889}, {3310, 739}, {3768, 909}, {4728, 34234}, {10015, 3227}, {14431, 38955}, {23757, 36872}, {28603, 36921}, {30583, 36944}, {36038, 31002}

X(42765) = X(908)X(1769)∩X(3259)X(3326)

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

X(42765) lies on these lines: {908, 1769}, {2254, 32856}, {3259, 3326}, {3262, 36038}, {4768, 21241}, {10015, 17757}, {18201, 25380}

X(42765) = X(2382)-isoconjugate of X(36037)
X(42765) = barycentric product X(i)*X(j) for these {i,j}: {537, 10015}, {908, 36848}, {20331, 36038}
X(42765) = barycentric quotient X(i)/X(j) for these {i,j}: {537, 13136}, {3310, 2382}, {10015, 18822}, {20331, 36037}, {36848, 34234}

X(42766) = X(513)X(20359)∩X(3259)X(3326)

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

X(42766) lies on these lines: {513, 20359}, {522, 3944}, {1459, 33144}, {3259, 3326}, {3837, 20366}, {20316, 27538}

X(42766) = X(36814)-Ceva conjugate of X(21140)
X(42766) = X(i)-isoconjugate of X(j) for these (i,j): {727, 36037}, {2720, 8851}, {8709, 34858}, {13136, 34077}, {20332, 32641}, {32669, 36799}
X(42766) = barycentric product X(i)*X(j) for these {i,j}: {517, 20908}, {726, 10015}, {908, 3837}, {1575, 36038}, {2397, 21140}, {3310, 35538}, {17139, 21053}
X(42766) = barycentric quotient X(i)/X(j) for these {i,j}: {726, 13136}, {908, 8709}, {1463, 37136}, {1575, 36037}, {1769, 20332}, {2804, 36799}, {3009, 32641}, {3310, 727}, {3837, 34234}, {6373, 909}, {10015, 3226}, {20908, 18816}, {21053, 38955}, {21140, 2401}, {22092, 1795}, {36038, 32020}

X(42767) = X(513)X(21334)∩X(3259)X(3326)

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

X(42767) lies on these lines: {513, 21334}, {522, 24210}, {523, 4415}, {656, 3914}, {804, 3027}, {1577, 4424}, {1769, 23788}, {3259, 3326}, {3971, 4086}

X(42767) = crossdifference of every pair of points on line {2311, 32641}
X(42767) = X(i)-isoconjugate of X(j) for these (i,j): {741, 36037}, {909, 4584}, {1808, 36110}, {2311, 37136}, {4589, 34858}, {13136, 18268}, {32641, 37128}, {32669, 36800}
X(42767) = barycentric product X(i)*X(j) for these {i,j}: {740, 10015}, {812, 17757}, {908, 4010}, {1577, 15507}, {1769, 3948}, {1785, 24459}, {2238, 36038}, {2804, 16609}, {3262, 21832}, {3310, 35544}, {3766, 21801}, {4037, 23788}, {6735, 7212}
X(42767) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 4584}, {740, 13136}, {908, 4589}, {1284, 37136}, {1769, 37128}, {2238, 36037}, {2804, 36800}, {3262, 4639}, {3310, 741}, {3747, 32641}, {4010, 34234}, {4155, 2250}, {4455, 909}, {10015, 18827}, {15507, 662}, {17757, 4562}, {21801, 660}, {21832, 104}, {36038, 40017}

X(42768) = X(12)X(523)∩X(3259)X(3326)

Barycentrics    a*(b - c)*(b + c)*(a^2 - b^2 + 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(42768) lies on these lines: {1, 35050}, {12, 523}, {37, 661}, {65, 656}, {73, 3657}, {513, 2646}, {522, 12047}, {526, 3028}, {652, 2260}, {1104, 6129}, {1769, 14299}, {3259, 3326}, {3737, 37816}, {6003, 21740}, {11009, 35057}, {14310, 36035}

X(42768) = X(i)-Ceva conjugate of X(j) for these (i,j): {1020, 2245}, {1577, 2610}
X(42768) = crosspoint of X(i) and X(j) for these (i,j): {1, 4242}, {758, 4551}, {1577, 36038}
X(42768) = crosssum of X(759) and X(3737)
X(42768) = crossdifference of every pair of points on line {2250, 2341}
X(42768) = X(i)-isoconjugate of X(j) for these (i,j): {110, 40437}, {759, 36037}, {1793, 36110}, {2250, 37140}, {2341, 37136}, {2720, 6740}, {13136, 34079}, {24624, 32641}, {36069, 38955}
X(42768) = barycentric product X(i)*X(j) for these {i,j}: {517, 4707}, {523, 16586}, {525, 1845}, {758, 10015}, {1577, 34586}, {1769, 3936}, {2245, 36038}, {2610, 17139}, {2804, 18593}, {3262, 21828}, {3310, 35550}, {3960, 17757}, {4053, 23788}, {4453, 21801}
X(42768) = barycentric quotient X(i)/X(j) for these {i,j}: {661, 40437}, {758, 13136}, {859, 37140}, {1464, 37136}, {1769, 24624}, {1845, 648}, {2245, 36037}, {2610, 38955}, {3310, 759}, {3724, 32641}, {4707, 18816}, {10015, 14616}, {16586, 99}, {17757, 36804}, {21828, 104}, {34586, 662}, {42666, 2250}

X(42769) = X(3)X(513)∩X(3259)X(3326)

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

X(42769) lies on these lines: {3, 513}, {73, 1459}, {119, 34332}, {521, 37700}, {522, 12608}, {661, 18591}, {1643, 5158}, {1745, 23800}, {3259, 3326}, {3835, 18589}, {6261, 15313}, {17102, 24457}, {20315, 34823}, {21530, 31946}, {41172, 41179}

X(42769) = complement of X(43933)
X(42769) = X(i)-complementary conjugate of X(j) for these (i,j): {101, 26011}, {255, 35014}, {765, 8677}, {906, 3911}, {1331, 517}, {1795, 33646}, {2397, 20305}, {2427, 226}, {4575, 15325}, {22350, 11}, {23981, 1210}, {24029, 16608}, {32656, 8609}
X(42769) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 35014}, {513, 8677}, {13397, 517}
X(42769) = crosssum of X(i) and X(j) for these (i,j): {100, 6099}, {1783, 14776}
X(42769) = crossdifference of every pair of points on line {8609, 15500}
X(42769) = X(i)-isoconjugate of X(j) for these (i,j): {104, 36106}, {913, 13136}, {915, 36037}, {1309, 36052}, {1897, 15381}, {6099, 36123}, {32641, 37203}, {32698, 34234}
X(42769) = barycentric product X(i)*X(j) for these {i,j}: {119, 905}, {912, 10015}, {914, 1769}, {2252, 36038}
X(42769) = barycentric quotient X(i)/X(j) for these {i,j}: {119, 6335}, {912, 13136}, {1769, 37203}, {2183, 36106}, {2252, 36037}, {3310, 915}, {8609, 1309}, {8677, 2990}, {22383, 15381}, {23220, 32655}

X(42770) = X(650)X(1086)∩X(3259)X(3326)

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

X(42770) lies on these lines: {241, 5089}, {650, 1086}, {908, 1465}, {1566, 3323}, {3259, 3326}, {3328, 21105}, {4077, 4858}, {4468, 26932}, {5532, 21118}, {16732, 23749}

X(42770) = X(i)-isoconjugate of X(j) for these (i,j): {909, 5377}, {919, 36037}, {13136, 32666}, {32641, 36086}, {32669, 36802}
X(42770) = barycentric product X(i)*X(j) for these {i,j}: {918, 10015}, {2254, 36038}, {3262, 3675}, {4088, 23788}, {9436, 35015}
X(42770) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 5377}, {665, 32641}, {918, 13136}, {1769, 36086}, {2254, 36037}, {2804, 36802}, {3310, 919}, {3675, 104}, {5236, 39294}, {10015, 666}, {22464, 39293}, {35015, 14942}

X(42771) = X(11)X(1491)∩X(3259)X(3326)

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

X(42771) lies on these lines: {11, 1491}, {55, 24488}, {661, 2310}, {764, 3328}, {2183, 41215}, {2223, 2356}, {3022, 4775}, {3259, 3326}, {3271, 8641}, {4705, 5532}, {15615, 35505}

X(42771) = crossdifference of every pair of points on line {666, 2401}
X(42771) = X(i)-isoconjugate of X(j) for these (i,j): {104, 39293}, {666, 37136}, {927, 36037}, {1814, 39294}, {13136, 36146}, {32641, 34085}, {32669, 36803}
X(42771) = barycentric product X(i)*X(j) for these {i,j}: {517, 17435}, {665, 2804}, {672, 35015}, {926, 10015}, {5089, 35014}
X(42771) = barycentric quotient X(i)/X(j) for these {i,j}: {926, 13136}, {1769, 34085}, {2183, 39293}, {2356, 39294}, {2804, 36803}, {3310, 927}, {8638, 32641}, {17435, 18816}, {35015, 18031}

X(42772) = X(57)X(513)∩X(3259)X(3326)

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

X(42772) lies on these lines: {25, 23224}, {57, 513}, {514, 7682}, {521, 19541}, {3259, 3326}, {15762, 39212}

X(42772) = crossdifference of every pair of points on line {6603, 15501}
X(42772) = X(972)-isoconjugate of X(36037)
X(42772) = barycentric product X(i)*X(j) for these {i,j}: {971, 10015}, {2272, 36038}
X(42772) = barycentric quotient X(i)/X(j) for these {i,j}: {971, 13136}, {2272, 36037}, {3310, 972}

leftri

Gibert (i,j,k) points on the cubic K1208: X(42773)-X(42784)

rightri

This preamble and points X(42773)-X(424784) are contributed by Peter Moses, April 24, 2021.

Gibert points are introduced in the preamble just before X(42085). See K1208.



X(42773) = GIBERT (3,2,12) POINT

Barycentrics    Sqrt[3]*a^2*S + 12*a^2*SA + 4*SB*SC : :

X(42773) lies on the cubic K1208 and these lines: {2, 42164}, {3, 13}, {5, 42626}, {6, 3523}, {15, 15720}, {18, 42116}, {62, 15693}, {140, 5339}, {376, 5350}, {395, 42479}, {396, 15717}, {397, 10299}, {398, 631}, {546, 42474}, {549, 22236}, {550, 42092}, {1656, 10645}, {1657, 42098}, {3090, 42500}, {3522, 23302}, {3524, 16772}, {3525, 5343}, {3526, 5352}, {3528, 5366}, {3530, 22238}, {3533, 5321}, {3534, 42488}, {3545, 42587}, {3839, 42515}, {3843, 42529}, {3850, 42090}, {3851, 33417}, {3854, 42108}, {5054, 5238}, {5055, 42434}, {5056, 42087}, {5070, 36967}, {5073, 16966}, {5318, 21735}, {5351, 15700}, {8703, 42586}, {10303, 42147}, {10304, 42166}, {10654, 14869}, {11134, 13347}, {11481, 15712}, {11489, 42687}, {11539, 42159}, {12100, 40693}, {12108, 40694}, {15692, 42148}, {15694, 16964}, {15696, 37832}, {15701, 42507}, {15702, 42599}, {15703, 42596}, {15706, 41943}, {15713, 42509}, {15714, 41119}, {15716, 16267}, {15718, 16962}, {15722, 16963}, {16239, 42160}, {17800, 42581}, {18582, 33923}, {21734, 42165}, {22237, 23303}, {34200, 42161}, {41120, 42591}, {41973, 42129}, {41981, 42138}, {42095, 42157}, {42124, 42151}, {42132, 42431}, {42139, 42684}, {42436, 42532}

X(42773) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 16241, 42156}, {3, 42156, 42625}, {3, 42490, 16644}, {6, 3523, 42774}, {140, 11480, 5339}, {546, 42610, 42474}, {549, 22236, 42491}, {631, 36836, 16645}, {3524, 16772, 36843}, {3526, 5352, 42154}, {5054, 5238, 42153}, {5340, 42625, 42158}, {11539, 42159, 42611}, {15712, 42152, 11481}, {16241, 42625, 16644}, {42156, 42158, 5340}

X(42774) = GIBERT (-3,2,12) POINT

Barycentrics    Sqrt[3]*a^2*S - 12*a^2*SA - 4*SB*SC : :

X(42774) lies on the cubic K1208 and these lines: {2, 42165}, {3, 14}, {5, 42625}, {6, 3523}, {16, 15720}, {17, 42115}, {61, 15693}, {140, 5340}, {376, 5349}, {395, 15717}, {396, 42478}, {397, 631}, {398, 10299}, {546, 42475}, {549, 22238}, {550, 42089}, {1656, 10646}, {1657, 42095}, {3090, 42501}, {3522, 23303}, {3524, 16773}, {3525, 5344}, {3526, 5351}, {3528, 5365}, {3530, 22236}, {3533, 5318}, {3534, 42489}, {3545, 42586}, {3839, 42514}, {3843, 42528}, {3850, 42091}, {3851, 33416}, {3854, 42109}, {5054, 5237}, {5055, 42433}, {5056, 42088}, {5070, 36968}, {5073, 16967}, {5321, 21735}, {5352, 15700}, {8703, 42587}, {10303, 42148}, {10304, 42163}, {10653, 14869}, {11137, 13347}, {11480, 15712}, {11488, 42686}, {11539, 42162}, {12100, 40694}, {12108, 40693}, {15692, 42147}, {15694, 16965}, {15696, 37835}, {15701, 42506}, {15702, 42598}, {15703, 42597}, {15706, 41944}, {15713, 42508}, {15714, 41120}, {15716, 16268}, {15718, 16963}, {15722, 16962}, {16239, 42161}, {17800, 42580}, {18581, 33923}, {21734, 42164}, {22235, 23302}, {34200, 42160}, {41119, 42590}, {41974, 42132}, {41981, 42135}, {42098, 42158}, {42121, 42150}, {42129, 42432}, {42142, 42685}, {42435, 42533}

X(42774) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 16242, 42153}, {3, 42153, 42626}, {3, 42491, 16645}, {6, 3523, 42773}, {140, 11481, 5340}, {546, 42611, 42475}, {549, 22238, 42490}, {631, 36843, 16644}, {3524, 16773, 36836}, {3526, 5351, 42155}, {5054, 5237, 42156}, {5339, 42626, 42157}, {11539, 42162, 42610}, {15712, 42149, 11480}, {16242, 42626, 16645}, {42153, 42157, 5339}

X(42775) = GIBERT (6,11,6) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 11*SB*SC : :

X(42774) lies on the cubic K1208 and these lines: {2, 42165}, {4, 15}, {5, 5344}, {6, 3854}, {13, 3855}, {18, 3545}, {61, 41099}, {140, 42131}, {397, 3091}, {546, 5365}, {547, 42588}, {631, 42431}, {1656, 5366}, {1657, 42146}, {3090, 16242}, {3146, 42626}, {3522, 42094}, {3523, 5350}, {3524, 42581}, {3525, 36969}, {3528, 42546}, {3529, 12820}, {3533, 42086}, {3543, 42598}, {3544, 10653}, {3832, 5339}, {3839, 5349}, {3850, 42128}, {3851, 5335}, {3858, 5334}, {5056, 5318}, {5059, 23302}, {5067, 42161}, {5068, 5340}, {5071, 16965}, {5343, 11542}, {7486, 42155}, {10299, 16966}, {12816, 15702}, {15022, 42148}, {15683, 42490}, {15688, 42590}, {15708, 42610}, {15709, 42433}, {15720, 42137}, {16644, 17578}, {17538, 42488}, {19106, 21735}, {22237, 42107}, {35018, 42493}, {40694, 41106}, {41121, 42160}, {42114, 42158}, {42429, 42592}

X(42775) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 17, 42119}, {4, 42142, 42494}, {4, 42494, 11488}, {17, 42106, 4}, {397, 3091, 42495}, {397, 42495, 37641}, {1656, 5366, 42120}, {1656, 42138, 5366}, {3523, 5350, 42141}, {3832, 22235, 5339}, {3832, 42166, 37640}, {5068, 5340, 11489}, {5339, 22235, 37640}, {5339, 42166, 22235}, {5340, 42110, 5068}, {5350, 42098, 3523}, {18582, 42140, 11488}

X(42776) = GIBERT (-6,11,6) POINT

Barycentrics    -Sqrt[3]*a^2*S + 3*a^2*SA + 11*SB*SC : :

X(42776) lies on the cubic K1208 and these lines: {2, 42164}, {4, 16}, {5, 5343}, {6, 3854}, {14, 3855}, {17, 3545}, {62, 41099}, {140, 42130}, {398, 3091}, {546, 5366}, {547, 42589}, {631, 42432}, {1656, 5365}, {1657, 42143}, {3090, 16241}, {3146, 42625}, {3522, 42093}, {3523, 5349}, {3524, 42580}, {3525, 36970}, {3528, 42545}, {3529, 12821}, {3533, 42085}, {3543, 42599}, {3544, 10654}, {3832, 5340}, {3839, 5350}, {3850, 42125}, {3851, 5334}, {3858, 5335}, {5056, 5321}, {5059, 23303}, {5067, 42160}, {5068, 5339}, {5071, 16964}, {5344, 11543}, {7486, 42154}, {10299, 16967}, {12817, 15702}, {15022, 42147}, {15683, 42491}, {15688, 42591}, {15708, 42611}, {15709, 42434}, {15720, 42136}, {16645, 17578}, {17538, 42489}, {19107, 21735}, {22235, 42110}, {35018, 42492}, {40693, 41106}, {41122, 42161}, {42111, 42157}, {42430, 42593}

X(42776) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 18, 42120}, {4, 42139, 42495}, {4, 42495, 11489}, {18, 42103, 4}, {398, 3091, 42494}, {398, 42494, 37640}, {1656, 5365, 42119}, {1656, 42135, 5365}, {3523, 5349, 42140}, {3832, 22237, 5340}, {3832, 42163, 37641}, {5068, 5339, 11488}, {5339, 42107, 5068}, {5340, 22237, 37641}, {5340, 42163, 22237}, {5349, 42095, 3523}, {18581, 42141, 11489}

X(42777) = GIBERT (15,7,8) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 8*a^2*SA + 14*SB*SC : :

X(42777) lies on the cubic K1208 and these lines: {2, 42517}, {6, 5071}, {13, 15}, {16, 15713}, {17, 632}, {61, 3858}, {381, 42692}, {395, 1656}, {397, 631}, {398, 3091}, {546, 42694}, {3412, 42164}, {3522, 16772}, {3843, 5349}, {3845, 12821}, {5076, 42147}, {5321, 41099}, {5335, 19708}, {5340, 17538}, {5965, 22847}, {10124, 34755}, {10653, 15693}, {11480, 15697}, {11485, 41119}, {11488, 15692}, {11812, 42686}, {12812, 37835}, {15686, 42684}, {15687, 34754}, {15688, 42687}, {15694, 23302}, {15695, 41112}, {15696, 42152}, {15700, 42685}, {15711, 41107}, {15712, 16241}, {15714, 41943}, {16242, 42627}, {16808, 42633}, {16961, 37832}, {16966, 42521}, {17131, 37352}, {17578, 22235}, {18582, 19709}, {23303, 42634}, {31693, 35019}, {35403, 42128}, {35434, 42085}, {38335, 42691}, {41101, 42138}, {41121, 42110}, {41985, 42636}, {42095, 42503}, {42101, 42516}, {42108, 42511}

X(42777) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5071, 42778}, {13, 16267, 42496}, {13, 42496, 396}, {396, 42087, 16962}, {11542, 16267, 396}, {11542, 42496, 13}, {15694, 42512, 23302}

X(42778) = GIBERT (-15,7,8) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 8*a^2*SA - 14*SB*SC : :

X(42778) lies on the cubic K1208 and these lines: {2, 42516}, {6, 5071}, {14, 16}, {15, 15713}, {18, 632}, {62, 3858}, {381, 42693}, {396, 1656}, {397, 3091}, {398, 631}, {546, 42695}, {3411, 42165}, {3522, 16773}, {3843, 5350}, {3845, 12820}, {5076, 42148}, {5318, 41099}, {5334, 19708}, {5339, 17538}, {5965, 22893}, {10124, 34754}, {10654, 15693}, {11481, 15697}, {11486, 41120}, {11489, 15692}, {11812, 42687}, {12812, 37832}, {15686, 42685}, {15687, 34755}, {15688, 42686}, {15694, 23303}, {15695, 41113}, {15696, 42149}, {15700, 42684}, {15711, 41108}, {15712, 16242}, {15714, 41944}, {16241, 42628}, {16809, 42634}, {16960, 37835}, {16967, 42520}, {17131, 37351}, {17578, 22237}, {18581, 19709}, {23302, 42633}, {31694, 35020}, {35403, 42125}, {35434, 42086}, {38335, 42690}, {41100, 42135}, {41122, 42107}, {41985, 42635}, {42098, 42502}, {42102, 42517}, {42109, 42510}

X(42778) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5071, 42777}, {14, 16268, 42497}, {14, 42497, 395}, {395, 42088, 16963}, {11543, 16268, 395}, {11543, 42497, 14}, {15694, 42513, 23303}

X(42779) = GIBERT (15,4,3) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 3*a^2*SA + 8*SB*SC : :

X(42779) lies on the cubic K1208 and these lines: {2, 17}, {3, 42612}, {6, 3851}, {13, 398}, {14, 3855}, {15, 397}, {16, 15720}, {18, 11542}, {61, 382}, {140, 16960}, {396, 3530}, {1657, 34754}, {3107, 32450}, {3411, 42598}, {3412, 3528}, {3529, 16965}, {3543, 42520}, {3544, 40694}, {5056, 16961}, {5071, 33607}, {5079, 37835}, {5238, 15688}, {5318, 42630}, {5335, 42112}, {5343, 42162}, {5344, 19107}, {5350, 15687}, {5351, 15700}, {5366, 10654}, {10188, 42627}, {10299, 10646}, {11485, 42431}, {11737, 41122}, {14269, 41108}, {14869, 42500}, {14892, 33606}, {15681, 22236}, {15699, 42521}, {15707, 36843}, {16242, 41977}, {16772, 17504}, {16773, 42496}, {16962, 34200}, {18581, 22235}, {22114, 33560}, {22846, 33464}, {33923, 42416}, {35739, 42230}, {37641, 42581}, {38071, 42166}, {41101, 42161}, {41121, 42153}, {42137, 42415}, {42165, 42633}, {42593, 42610}

X(42779) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42636, 41944}, {6, 3851, 42780}, {15, 397, 41974}, {61, 5340, 42432}, {62, 16267, 42488}, {62, 40693, 16267}, {62, 42488, 41944}, {3412, 10653, 5352}, {5340, 42432, 36969}, {41107, 42635, 15681}

X(42780) = GIBERT (-15,4,3) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 3*a^2*SA - 8*SB*SC : :

X(42780) lies on the cubic K1208 and these lines: {2, 18}, {3, 42613}, {6, 3851}, {13, 3855}, {14, 397}, {15, 15720}, {16, 398}, {17, 11543}, {62, 382}, {140, 16961}, {395, 3530}, {1657, 34755}, {3106, 32450}, {3411, 3528}, {3412, 42599}, {3529, 16964}, {3543, 42521}, {3544, 40693}, {5056, 16960}, {5071, 33606}, {5079, 37832}, {5237, 15688}, {5321, 42629}, {5334, 42113}, {5343, 19106}, {5344, 42159}, {5349, 15687}, {5352, 15700}, {5365, 10653}, {10187, 42628}, {10299, 10645}, {11486, 42432}, {11737, 41121}, {14269, 41107}, {14869, 42501}, {14892, 33607}, {15681, 22238}, {15699, 42520}, {15707, 36836}, {16241, 41978}, {16772, 42497}, {16773, 17504}, {16963, 34200}, {18582, 22237}, {22113, 33561}, {22891, 33465}, {33923, 42415}, {37640, 42580}, {38071, 42163}, {41100, 42160}, {41122, 42156}, {42136, 42416}, {42164, 42634}, {42592, 42611}

X(42780) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42635, 41943}, {6, 3851, 42779},{16, 398, 41973}, {61, 16268, 42489}, {61, 40694, 16268}, {61, 42489, 41943}, {62, 5339, 42431}, {3411, 10654, 5351}, {5339, 42431, 36970}, {41108, 42636, 15681}

X(42781) = GIBERT (25,9,8) POINT

Barycentrics    25*a^2*S/Sqrt[3] + 8*a^2*SA + 18*SB*SC : :

X(42781) lies on the cubic K1208 and these lines: {2, 42517}, {6, 3544}, {14, 38071}, {16, 14869}, {18, 11542}, {382, 5318}, {396, 34200}, {397, 10299}, {550, 42684}, {3530, 16960}, {5335, 42626}, {5349, 42138}, {16267, 42501}, {16773, 42627}, {33602, 42094}, {42124, 42506}, {42691, 42692}

X(42782) = GIBERT (-25,9,8) POINT

Barycentrics    25*a^2*S/Sqrt[3] - 8*a^2*SA - 18*SB*SC : :

X(42782) lies on the cubic K1208 and these lines: {2, 42516}, {6, 3544}, {13, 38071}, {15, 14869}, {17, 11543}, {382, 5321}, {395, 34200}, {398, 10299}, {550, 42685}, {3530, 16961}, {5334, 42625}, {5350, 42135}, {16268, 42500}, {16772, 42628}, {33603, 42093}, {42121, 42507}, {42690, 42693}

X(42783) = GIBERT (SQRT(6),1,1) POINT

Barycentrics    Sqrt[2]*a^2*S + a^2*SA + 2*SB*SC : :

X(42783) lies on the cubic K1208 and these lines: {2, 41975}, {3, 41976}, {4, 41979}, {5, 6}, {30, 42645}, {371, 3387}, {372, 3373}, {546, 42646}, {590, 3372}, {615, 3386}, {1587, 14782}, {1588, 14783}, {3068, 14785}, {3069, 14784}, {3070, 3385}, {3071, 3371}, {3374, 6419}, {3388, 6420}

X(42783) = crosspoint of X(3373) and X(3387)
X(42783) = crosssum of X(3371) and X(3385)
X(42783) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11542, 11543, 42647}, {41976, 41980, 3}

X(42784) = GIBERT (-SQRT(6),1,1) POINT

Barycentrics    Sqrt[2]*a^2*S - a^2*SA - 2*SB*SC : :

X(42784) lies on the cubic K1208 and these lines: {2, 41976}, {3, 41975}, {4, 41980}, {5, 6}, {30, 42646}, {371, 3388}, {372, 3374}, {546, 42645}, {590, 3371}, {615, 3385}, {1587, 14783}, {1588, 14782}, {3068, 14784}, {3069, 14785}, {3070, 3386}, {3071, 3372}, {3373, 6419}, {3387, 6420}

X(42784) = crosspoint of X(3374) and X(3388)
X(42784) = crosssum of X(3372) and X(3386)
X(42784) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11542, 11543, 42648}, {41975, 41979, 3}

X(42785) = X(5)X(3631)∩X(6)X(13)

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

X(42785) lies on the cubic K1209 and these lines: {5, 3631}, {6, 13}, {20, 5092}, {140, 3098}, {141, 10109}, {182, 3627}, {193, 25561}, {262, 8782}, {511, 3090}, {546, 39561}, {576, 12811}, {597, 12101}, {3091, 5097}, {3524, 31670}, {3545, 7926}, {3589, 8703}, {3618, 15682}, {3620, 20423}, {3629, 5066}, {3630, 11178}, {3763, 25565}, {3845, 6329}, {3851, 5965}, {3858, 12007}, {3861, 18583}, {5068, 14853}, {5070, 33878}, {5072, 5102}, {5073, 12017}, {5640, 13417}, {5943, 12058}, {7706, 34584}, {7875, 14492}, {10168, 15689}, {11541, 20190}, {15699, 21850}, {15701, 19924}, {18376, 41593}, {18394, 39874}, {19709, 40341}, {22234, 39884}, {22819, 23259}, {22820, 23249}, {32455, 41990}, {34754, 37332}, {34755, 37333}

X(42785) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5476, 19130, 3818}

X(42786) = X(5)X(3098)∩X(6)X(17)

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

X(42786) lies on the cubic K1209 and these lines: {2, 1495}, {5, 3098}, {6, 17}, {141, 547}, {156, 182}, {511, 3090}, {542, 15703}, {575, 40330}, {576, 3631}, {632, 17508}, {1350, 5079}, {1352, 5067}, {1514, 7399}, {3054, 41412}, {3091, 14810}, {3523, 29323}, {3526, 29012}, {3589, 11178}, {3620, 7486}, {3630, 18583}, {3763, 5055}, {3850, 21167}, {3851, 29317}, {5070, 10516}, {5071, 31670}, {5072, 31884}, {5097, 20080}, {5169, 5888}, {5480, 35018}, {6644, 32600}, {6683, 32429}, {6688, 37643}, {6723, 32305}, {7388, 22819}, {7389, 22820}, {7405, 11438}, {7571, 15066}, {7822, 35002}, {9301, 15821}, {9873, 16896}, {9993, 16988}, {10168, 18440}, {10182, 34775}, {10564, 14787}, {11430, 14786}, {12055, 31455}, {12584, 23515}, {12900, 19140}, {15088, 32273}, {15720, 33751}, {16187, 37454}, {18376, 35228}, {18553, 39874}, {20582, 21850}, {21358, 25565}, {31415, 41413}, {32455, 38079}, {34417, 37990}, {37353, 41462}

X(42786) = crossdifference of every pair of points on line {1510, 9210}
X(42786) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 34573, 3098}, {1656, 24206, 38317}, {3763, 5055, 19130}, {10576, 10577, 7755}, {16966, 16967, 7746}, {24206, 38317, 34507}

X(42787) = X(3)X(147)∩X(5)X(3098)

Barycentrics    2*a^8 + 3*a^6*b^2 - 2*a^4*b^4 - 4*a^2*b^6 + b^8 + 3*a^6*c^2 - 4*a^4*b^2*c^2 - 11*a^2*b^4*c^2 - b^6*c^2 - 2*a^4*c^4 - 11*a^2*b^2*c^4 - 4*a^2*c^6 - b^2*c^6 + c^8 : :

X(42787) lies on the cubic K1209 and these lines: {3, 147}, {5, 3098}, {30, 3096}, {32, 549}, {140, 262}, {376, 18503}, {548, 9873}, {550, 9996}, {626, 22566}, {631, 9301}, {2023, 7749}, {2076, 2548}, {3094, 5305}, {3530, 26316}, {3627, 10356}, {3628, 9993}, {5054, 10583}, {5092, 7882}, {5901, 12497}, {6704, 14881}, {7789, 7865}, {7811, 7871}, {7905, 12054}, {9857, 34773}, {9983, 32516}, {9984, 10272}, {10877, 15325}, {22803, 24206}, {37450, 40252}

X(42788) = X(5)X(99)∩X(30)X(1506)

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

X(42788) lies on the cubic K1209 and these lines: {5, 99}, {30, 1506}, {83, 549}, {140, 143}, {547, 7789}, {550, 7608}, {3628, 7874}, {5038, 31406}, {5054, 10583}, {5055, 7891}, {5116, 31401}, {7777, 32151}, {9698, 12042}, {16239, 39784}, {17005, 37243}, {18501, 33274}, {25561, 32190}, {31489, 40279}, {33024, 38733}

X(42789) = 1ST MONTESDEOCA-EULER POINT

Barycentrics    a*(b*c*SB*SC + Sqrt[2]*a*SA*Sqrt[SA*SB*SC]) : :

The mapping x(3) + t x(4) 8 t SA SB SC X(3) + a^2 b^2 c^2 X(4) is an involution of the Euler line. The mapping includes {X(3), X(4)} and {X(1113), X(1114)} as involutory pairs. The fixed points of the mapping are

(a (b c SBSC + Sqrt[2] a SA Sqrt[SA SB SC]) : : and (a (b c SB SC - Sqrt[2] a SA Sqrt[SA SB SC]) : : ,

These points are real if and only if the reference triangle ABC is acute. (Angel Montesdeoca, April 26, 2021.) The points are here named the 1st Montesdeoca-Euler point and 2nd Montesdeoca-Euler point, respectively.

X(42789) lies on the curves K114 and Q023 and this line: {2, 3}

For a figure showing X(42789) and X(42790) on the curves K114 and Q023, see Euler line, points, and curves. (Angel Montesdeoca, April 27, 2021)j

X(42789) = reflection of X(42790) in X(186)
X(42789) = circumcircle-inverse of X(42790)
X(42789) = X(74)-Ceva conjugate of X(42790)
X(42789) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 378, X(42790)}, {3, 4, X(42790)}, {5, 3520, X(42790)}, {20, 24, X(42790)}, {21, 7414, X(42790)}, {22, 18533, X(42790)}, {23, 10295, X(42790)}, {25, 376, X(42790)}, {26, 35471, X(42790)}, {27, 7430, X(42790)}, {28, 3651, X(42790)}, {29, 7421, X(42790)}, {140, 14865, X(42790)}, {237, 35474, X(42790)}, {381, 35473, X(42790)}, {382, 21844, X(42790)}, {384, 35476, X(42790)}, {403, 2071, X(42790)}, {411, 37117, X(42790)}, {412, 37115, X(42790)}, {427, 35921, X(42790)}, {468, 7464, X(42790)}, {470, 35469, X(42790)}, {471, 35470, X(42790)}, {548, 34484, X(42790)}, {549, 13596, X(42790)}, {550, 3518, X(42790)}, {631, 1593, X(42790)}, {1006, 4219, X(42790)}, {1012, 37441, X(42790)}, {1113, 1114, X(42790)}, {1325, 37979, X(42790)}, {1594, 14118, X(42790)}, {1597, 3524, X(42790)}, {1598, 3528, X(42790)}, {1656, 35475, X(42790)}, {1658, 34797, X(42790)}, {1995, 35485, X(42790)}, {2070, 13619, X(42790)}, {2073, 36026, X(42790)}, {2074, 36001, X(42790)}, {3088, 7509, X(42790)}, {3090, 3516, X(42790)}, {3091, 35477, X(42790)}, {3146, 32534, X(42790)}, {3147, 12085, X(42790)}, {3153, 37970, X(42790)}, {3515, 3529, X(42790)}, {3517, 17538, X(42790)}, {3522, 10594, X(42790)}, {3523, 35502, X(42790)}, {3541, 7503, X(42790)}, {3542, 11413, X(42790)}, {3543, 35472, X(42790)}, {3545, 11410, X(42790)}, {3575, 7512, X(42790)}, {3627, 17506, X(42790)}, {3628, 35478, X(42790)}, {3843, 23040, X(42790)}, {4185, 6876, X(42790)}, {4220, 4227, X(42790)}, {4221, 4231, X(42790)}, {4222, 37403, X(42790)}, {4230, 7422, X(42790)}, {4235, 7418, X(42790)}, {4238, 7425, X(42790)}, {4241, 7440, X(42790)}, {4242, 14127, X(42790)}, {4246, 7429, X(42790)}, {4249, 7433, X(42790)}, {4250, 7442, X(42790)}, {5000, 40894, X(42790)}, {5001, 40895, X(42790)}, {5059, 35479, X(42790)}, {5198, 21735, X(42790)}, {5899, 35489, X(42790)}, {6143, 14130, X(42790)}, {6240, 7488, X(42790)}, {6353, 21312, X(42790)}, {6636, 7576, X(42790)}, {6644, 35481, X(42790)}, {6875, 37194, X(42790)}, {6905, 37305, X(42790)}, {6906, 7412, X(42790)}, {6998, 7431, X(42790)}, {7411, 36009, X(42790)}, {7413, 7436, X(42790)}, {7441, 7463, X(42790)}, {7452, 7454, X(42790)}, {7456, 7461, X(42790)}, {7470, 27369, X(42790)}, {7480, 36164, X(42790)}, {7482, 36166, X(42790)}, {7487, 10323, X(42790)}, {7496, 35484, X(42790)}, {7501, 7580, X(42790)}, {7502, 18559, X(42790)}, {7505, 12084, X(42790)}, {7513, 37120, X(42790)}, {7517, 35503, X(42790)}, {7526, 37119, X(42790)}, {7527, 37118, X(42790)}, {7531, 37195, X(42790)}, {7556, 37196, X(42790)}, {7577, 18570, X(42790)}, {10018, 12086, X(42790)}, {10151, 37948, X(42790)}, {10298, 35480, X(42790)}, {10299, 11403, X(42790)}, {11250, 16868, X(42790)}, {11284, 35483, X(42790)}, {12082, 37460, X(42790)}, {14709, 14710, X(42790)}, {15559, 37126, X(42790)}, {15702, 35501, X(42790)}, {15750, 33703, X(42790)}, {16042, 35492, X(42790)}, {16049, 31384, X(42790)}, {16386, 37951, X(42790)}, {17562, 37426, X(42790)}, {18535, 19708, X(42790)}, {18560, 22467, X(42790)}, {18859, 37943, X(42790)}, {21669, 37289, X(42790)}, {26863, 33923, X(42790)}, {30267, 30733, X(42790)}, {34864, 35482, X(42790)}, {37114, 37200, X(42790)}, {37925, 37931, X(42790)}, {37934, 37946, X(42790)}, {37959, 37961, X(42790)}

X(42790) = 2ND MONTESDEOCA-EULER POINT

Barycentrics    a*(b*c*SB*SC - Sqrt[2]*a*SA*Sqrt[SA*SB*SC]) : :

X(42790) lies on the curves K114 and Q023 and this line: {2, 3}

X(42790) = reflection of X(42789) in X(186)
X(42790) = circumcircle-inverse of X(42789)
X(42790) = X(74)-Ceva conjugate of X(42789)
X(42790) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 378, X(42789)}, {3, 4, X(42789)}, {5, 3520, X(42789)}, {20, 24, X(42789)}, {21, 7414, X(42789)}, {22, 18533, X(42789)}, {23, 10295, X(42789)}, {25, 376, X(42789)}, {26, 35471, X(42789)}, {27, 7430, X(42789)}, {28, 3651, X(42789)}, {29, 7421, X(42789)}, {140, 14865, X(42789)}, {237, 35474, X(42789)}, {381, 35473, X(42789)}, {382, 21844, X(42789)}, {384, 35476, X(42789)}, {403, 2071, X(42789)}, {411, 37117, X(42789)}, {412, 37115, X(42789)}, {427, 35921, X(42789)}, {468, 7464, X(42789)}, {470, 35469, X(42789)}, {471, 35470, X(42789)}, {548, 34484, X(42789)}, {549, 13596, X(42789)}, {550, 3518, X(42789)}, {631, 1593, X(42789)}, {1006, 4219, X(42789)}, {1012, 37441, X(42789)}, {1113, 1114, X(42789)}, {1325, 37979, X(42789)}, {1594, 14118, X(42789)}, {1597, 3524, X(42789)}, {1598, 3528, X(42789)}, {1656, 35475, X(42789)}, {1658, 34797, X(42789)}, {1995, 35485, X(42789)}, {2070, 13619, X(42789)}, {2073, 36026, X(42789)}, {2074, 36001, X(42789)}, {3088, 7509, X(42789)}, {3090, 3516, X(42789)}, {3091, 35477, X(42789)}, {3146, 32534, X(42789)}, {3147, 12085, X(42789)}, {3153, 37970, X(42789)}, {3515, 3529, X(42789)}, {3517, 17538, X(42789)}, {3522, 10594, X(42789)}, {3523, 35502, X(42789)}, {3541, 7503, X(42789)}, {3542, 11413, X(42789)}, {3543, 35472, X(42789)}, {3545, 11410, X(42789)}, {3575, 7512, X(42789)}, {3627, 17506, X(42789)}, {3628, 35478, X(42789)}, {3843, 23040, X(42789)}, {4185, 6876, X(42789)}, {4220, 4227, X(42789)}, {4221, 4231, X(42789)}, {4222, 37403, X(42789)}, {4230, 7422, X(42789)}, {4235, 7418, X(42789)}, {4238, 7425, X(42789)}, {4241, 7440, X(42789)}, {4242, 14127, X(42789)}, {4246, 7429, X(42789)}, {4249, 7433, X(42789)}, {4250, 7442, X(42789)}, {5000, 40894, X(42789)}, {5001, 40895, X(42789)}, {5059, 35479, X(42789)}, {5198, 21735, X(42789)}, {5899, 35489, X(42789)}, {6143, 14130, X(42789)}, {6240, 7488, X(42789)}, {6353, 21312, X(42789)}, {6636, 7576, X(42789)}, {6644, 35481, X(42789)}, {6875, 37194, X(42789)}, {6905, 37305, X(42789)}, {6906, 7412, X(42789)}, {6998, 7431, X(42789)}, {7411, 36009, X(42789)}, {7413, 7436, X(42789)}, {7441, 7463, X(42789)}, {7452, 7454, X(42789)}, {7456, 7461, X(42789)}, {7470, 27369, X(42789)}, {7480, 36164, X(42789)}, {7482, 36166, X(42789)}, {7487, 10323, X(42789)}, {7496, 35484, X(42789)}, {7501, 7580, X(42789)}, {7502, 18559, X(42789)}, {7505, 12084, X(42789)}, {7513, 37120, X(42789)}, {7517, 35503, X(42789)}, {7526, 37119, X(42789)}, {7527, 37118, X(42789)}, {7531, 37195, X(42789)}, {7556, 37196, X(42789)}, {7577, 18570, X(42789)}, {10018, 12086, X(42789)}, {10151, 37948, X(42789)}, {10298, 35480, X(42789)}, {10299, 11403, X(42789)}, {11250, 16868, X(42789)}, {11284, 35483, X(42789)}, {12082, 37460, X(42789)}, {14709, 14710, X(42789)}, {15559, 37126, X(42789)}, {15702, 35501, X(42789)}, {15750, 33703, X(42789)}, {16042, 35492, X(42789)}, {16049, 31384, X(42789)}, {16386, 37951, X(42789)}, {17562, 37426, X(42789)}, {18535, 19708, X(42789)}, {18560, 22467, X(42789)}, {18859, 37943, X(42789)}, {21669, 37289, X(42789)}, {26863, 33923, X(42789)}, {30267, 30733, X(42789)}, {34864, 35482, X(42789)}, {37114, 37200, X(42789)}, {37925, 37931, X(42789)}, {37934, 37946, X(42789)}, {37959, 37961, X(42789)}

X(42791) = GIBERT (9,-1,16) POINT

Barycentrics    3*Sqrt[3]*a^2*S + 16*a^2*SA - 2*SB*SC : :

X(42791) lies on these lines: {2, 5321}, {3, 42511}, {6, 19708}, {13, 19710}, {14, 11812}, {15, 8703}, {16, 15759}, {17, 30}, {18, 549}, {61, 34200}, {376, 397}, {395, 10645}, {396, 3534}, {398, 3524}, {524, 33622}, {547, 42157}, {550, 16962}, {3525, 33603}, {3530, 16268}, {3543, 42598}, {3830, 42087}, {3845, 23302}, {3860, 19107}, {5054, 41120}, {5055, 42164}, {5066, 16241}, {5071, 5349}, {5237, 15714}, {5318, 11001}, {5334, 33605}, {5339, 15702}, {5344, 33604}, {6411, 36467}, {6412, 36450}, {7801, 35304}, {10109, 36970}, {10304, 22236}, {10653, 15695}, {10654, 15693}, {11485, 42510}, {11539, 16964}, {12101, 37832}, {12108, 41973}, {12817, 42107}, {12820, 42099}, {14891, 16963}, {15681, 42152}, {15682, 16644}, {15683, 42156}, {15685, 41119}, {15686, 16267}, {15688, 42148}, {15689, 40693}, {15690, 41107}, {15691, 16965}, {15692, 16773}, {15694, 42163}, {15697, 42155}, {15700, 40694}, {15701, 23303}, {15703, 42160}, {15706, 42149}, {15708, 42153}, {15709, 42773}, {15710, 36843}, {15712, 41944}, {15713, 41122}, {15719, 16645}, {15722, 42089}, {15764, 35823}, {16242, 19711}, {16961, 41971}, {16967, 42595}, {17578, 42515}, {19709, 42085}, {23046, 42488}, {33458, 35931}, {33459, 33627}, {33607, 42429}, {33699, 42124}, {36448, 42198}, {36466, 42196}, {37835, 42493}, {38071, 42432}, {41106, 42101}, {42100, 42496}, {42121, 42507}, {42138, 42430}

X(42791) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 19708, 42792}, {15, 42528, 42633}, {15, 42631, 42532}, {10645, 41101, 12100}, {12100, 41101, 395}, {15686, 16267, 42165}, {15690, 41107, 42088}, {15701, 41113, 23303}, {15713, 42117, 41122}, {41107, 42529, 15690}, {41119, 42090, 15685}

X(42792) = GIBERT (9,1,-16) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 16*a^2*SA + 2*SB*SC : :

X(42792) lies on these lines: {2, 5318}, {3, 42510}, {6, 19708}, {13, 11812}, {14, 19710}, {15, 15759}, {16, 8703}, {17, 549}, {18, 30}, {62, 34200}, {376, 398}, {395, 3534}, {396, 10646}, {397, 3524}, {524, 33624}, {547, 42158}, {550, 16963}, {3525, 33602}, {3530, 16267}, {3543, 42599}, {3830, 42088}, {3845, 23303}, {3860, 19106}, {5054, 41119}, {5055, 42165}, {5066, 16242}, {5071, 5350}, {5238, 15714}, {5321, 11001}, {5335, 33604}, {5340, 15702}, {5343, 33605}, {6411, 36449}, {6412, 36468}, {7801, 35303}, {10109, 36969}, {10304, 22238}, {10653, 15693}, {10654, 15695}, {11486, 42511}, {11539, 16965}, {12101, 37835}, {12108, 41974}, {12816, 42110}, {12821, 42100}, {14891, 16962}, {15681, 42149}, {15682, 16645}, {15683, 42153}, {15685, 41120}, {15686, 16268}, {15688, 42147}, {15689, 40694}, {15690, 41108}, {15691, 16964}, {15692, 16772}, {15694, 42166}, {15697, 42154}, {15700, 40693}, {15701, 23302}, {15703, 42161}, {15706, 42152}, {15708, 42156}, {15709, 42774}, {15710, 36836}, {15712, 41943}, {15713, 41121}, {15719, 16644}, {15722, 42092}, {15764, 35822}, {16241, 19711}, {16960, 41972}, {16966, 42594}, {17578, 42514}, {19709, 42086}, {22513, 36767}, {23046, 42489}, {33458, 33626}, {33459, 35932}, {33606, 42430}, {33699, 42121}, {36448, 42195}, {36466, 42197}, {37832, 42492}, {38071, 42431}, {41106, 42102}, {42099, 42497}, {42124, 42506}, {42135, 42429}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 19708, 42791}, {16, 42529, 42634}, {16, 42632, 42533}, {10646, 41100, 12100}, {12100, 41100, 396}, {15686, 16268, 42164}, {15690, 41108, 42087}, {15701, 41112, 23302}, {15713, 42118, 41121}, {41108, 42528, 15690}, {41120, 42091, 15685}

X(42793) = GIBERT (-9,1,18) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 18*a^2*SA - 2*SB*SC : :

X(42793) lies on these lines: {3, 42511}, {4, 11481}, {13, 140}, {14, 550}, {16, 15712}, {18, 42136}, {395, 3522}, {396, 3523}, {397, 15720}, {398, 10646}, {549, 42506}, {631, 42518}, {1656, 42161}, {1657, 42163}, {3411, 34200}, {3533, 42166}, {3850, 16242}, {3853, 42631}, {3858, 36968}, {5054, 42502}, {5056, 42165}, {5059, 16645}, {5073, 42599}, {5340, 42476}, {5349, 42121}, {5350, 42089}, {8703, 41973}, {10187, 42431}, {10299, 22238}, {10304, 42509}, {12103, 41944}, {12108, 41100}, {15691, 42503}, {15699, 42505}, {16964, 41981}, {16965, 42501}, {17538, 42519}, {21735, 42147}, {22235, 23302}, {33416, 42693}, {35018, 42110}, {36768, 37341}, {38071, 42593}, {42087, 42149}, {42128, 42151}

X(42793) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 41974, 42598}, {11481, 42686, 23303}

X(42794) = GIBERT (9,1,18) POINT

Barycentrics    3*Sqrt[3]*a^2*S + 18*a^2*SA + 2*SB*SC : :

X(42794) lies on these lines: {3, 42510}, {4, 11480}, {13, 550}, {14, 140}, {15, 15712}, {17, 42137}, {395, 3523}, {396, 3522}, {397, 10645}, {398, 15720}, {549, 42507}, {631, 42519}, {1656, 42160}, {1657, 42166}, {3412, 34200}, {3533, 42163}, {3850, 16241}, {3853, 42632}, {3858, 36967}, {5054, 42503}, {5056, 42164}, {5059, 16644}, {5073, 42598}, {5339, 42477}, {5349, 42092}, {5350, 42124}, {8703, 41974}, {10188, 42432}, {10299, 22236}, {10304, 42508}, {12103, 41943}, {12108, 41101}, {15691, 42502}, {15699, 42504}, {16964, 42500}, {16965, 41981}, {17538, 42518}, {21735, 42148}, {22237, 23303}, {33417, 42692}, {35018, 42107}, {38071, 42592}, {42088, 42152}, {42125, 42150}

X(42794) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 41973, 42599}, {11480, 42687, 23302}

X(42795) = GIBERT (15,-2,35) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 35*a^2*SA - 4*SB*SC : :

X(42795) lies on these lines: {4, 5352}, {5, 12821}, {13, 3534}, {14, 549}, {15, 10304}, {16, 15759}, {17, 15704}, {30, 42687}, {395, 41971}, {397, 548}, {550, 42777}, {618, 36329}, {3090, 42694}, {3523, 42513}, {3526, 42157}, {3628, 36970}, {5055, 33417}, {5066, 19107}, {5072, 42610}, {5321, 11540}, {5343, 10303}, {5474, 38224}, {7850, 30471}, {10187, 16964}, {10654, 15717}, {12100, 16961}, {12816, 42124}, {12820, 35400}, {15022, 42432}, {15640, 42090}, {15683, 42134}, {15684, 16808}, {15686, 42629}, {15689, 16960}, {15693, 33606}, {15694, 42688}, {15698, 41101}, {15701, 42690}, {15703, 42630}, {15709, 16967}, {15710, 42517}, {15764, 42573}, {16644, 17800}, {23046, 42087}, {33699, 37832}, {34200, 34754}, {36836, 42528}, {41943, 42429}, {41982, 42635}, {42088, 42506}, {42116, 42625}, {42164, 42594}, {42598, 42695}

X(42796) = GIBERT (15,2,-35) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 35*a^2*SA + 4*SB*SC : :

X(42796) lies on these lines: {4, 5351}, {5, 12820}, {13, 549}, {14, 3534}, {15, 15759}, {16, 10304}, {18, 15704}, {30, 42686}, {396, 41972}, {398, 548}, {550, 42778}, {619, 35751}, {3090, 42695}, {3523, 42512}, {3526, 42158}, {3628, 36969}, {5055, 33416}, {5066, 19106}, {5072, 42611}, {5318, 11540}, {5344, 10303}, {5473, 38224}, {7850, 30472}, {10188, 16965}, {10653, 15717}, {12100, 16960}, {12817, 42121}, {12821, 35400}, {15022, 42431}, {15640, 42091}, {15683, 42133}, {15684, 16809}, {15686, 42630}, {15689, 16961}, {15693, 33607}, {15694, 42689}, {15698, 41100}, {15701, 42691}, {15703, 42629}, {15709, 16966}, {15710, 42516}, {15764, 42572}, {16645, 17800}, {23046, 42088}, {33699, 37835}, {34200, 34755}, {36843, 42529}, {41944, 42430}, {41982, 42636}, {42087, 42507}, {42115, 42626}, {42165, 42595}, {42599, 42694}

X(42797) = GIBERT (-15,2,39) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 39*a^2*SA - 4*SB*SC : :

X(42797) lies on these lines: {2, 5351}, {5, 12820}, {13, 14869}, {16, 10299}, {17, 11481}, {18, 550}, {62, 17504}, {382, 16242}, {396, 3530}, {398, 34200}, {546, 42433}, {1656, 42629}, {3523, 16960}, {3528, 36967}, {3529, 42528}, {3851, 19106}, {5079, 36968}, {5238, 15715}, {10187, 42097}, {10188, 42118}, {11737, 42631}, {12817, 15681}, {14269, 42491}, {15687, 42580}, {15688, 16964}, {15692, 42635}, {15700, 16962}, {15705, 42521}, {15707, 41100}, {16966, 42774}, {33416, 35018}, {33923, 42686}, {35733, 42265}, {42115, 42773}, {42120, 42498}, {42150, 42780}, {42434, 42507}

X(42797) = {X(18),X(550)}-harmonic conjugate of X(42630)

X(42798) = GIBERT (15,2,39) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 39*a^2*SA + 4*SB*SC : :

X(42798) lies on these lines: {2, 5352}, {5, 12821}, {14, 14869}, {15, 10299}, {17, 550}, {18, 11480}, {61, 17504}, {382, 16241}, {395, 3530}, {397, 34200}, {546, 42434}, {1656, 42630}, {3523, 16961}, {3528, 36968}, {3529, 42529}, {3851, 19107}, {5079, 36967}, {5237, 15715}, {10187, 42117}, {10188, 42096}, {11737, 42632}, {12816, 15681}, {14269, 42490}, {15687, 42581}, {15688, 16965}, {15692, 42636}, {15700, 16963}, {15705, 42520}, {15707, 41101}, {16967, 42773}, {33417, 35018}, {33923, 42687}, {42116, 42774}, {42119, 42499}, {42151, 42779}, {42433, 42506}

X(42798) = {X(17),X(550)}-harmonic conjugate of X(42629)

X(42799) = GIBERT (21,-4,7) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 7*a^2*SA - 8*SB*SC : :

X(42799) lies on these lines: {4, 13}, {6, 15681}, {14, 547}, {15, 5054}, {16, 8703}, {17, 12811}, {62, 15696}, {395, 3530}, {396, 38071}, {398, 632}, {618, 22496}, {3091, 42435}, {3412, 3859}, {3860, 5321}, {5070, 22236}, {5079, 16644}, {5334, 16962}, {5351, 21734}, {10645, 15692}, {10653, 42430}, {11485, 19709}, {11540, 11543}, {11542, 41987}, {12103, 36968}, {12816, 42136}, {15710, 37641}, {15719, 16242}, {16808, 42633}, {16965, 42612}, {16966, 41113}, {18582, 42532}, {33416, 42513}, {33417, 41984}, {33923, 42436}, {34755, 42626}, {35404, 42117}, {36967, 42091}, {41100, 42119}, {41107, 42127}, {41944, 42116}, {41981, 42434}, {42089, 42507}, {42100, 42419}, {42105, 42589}, {42125, 42474}, {42130, 42509}, {42150, 42528}, {42490, 42593}

X(42799) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 34754, 41943}, {61, 10654, 36970}, {10654, 36970, 41973}, {10654, 37640, 16964}, {11485, 41108, 37832}

X(42800) = GIBERT (21,4,-7) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 7*a^2*SA + 8*SB*SC : :

X(42800) lies on these lines: {4, 14}, {6, 15681}, {13, 547}, {15, 8703}, {16, 5054}, {18, 12811}, {61, 15696}, {395, 38071}, {396, 3530}, {397, 632}, {619, 22495}, {3091, 42436}, {3411, 3859}, {3860, 5318}, {5070, 22238}, {5079, 16645}, {5335, 16963}, {5352, 21734}, {10646, 15692}, {10654, 42429}, {11486, 19709}, {11540, 11542}, {11543, 41987}, {12103, 36967}, {12817, 42137}, {15710, 37640}, {15719, 16241}, {16809, 42634}, {16964, 42613}, {16967, 41112}, {18581, 42533}, {33416, 41984}, {33417, 42512}, {33923, 42435}, {34754, 42625}, {35404, 42118}, {36968, 42090}, {41101, 42120}, {41108, 42126}, {41943, 42115}, {41981, 42433}, {42092, 42506}, {42099, 42420}, {42104, 42588}, {42128, 42475}, {42131, 42508}, {42151, 42529}, {42491, 42592}

X(42800) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 34755, 41944}, {62, 10653, 36969}, {10653, 36969, 41974}, {10653, 37641, 16965}, {11486, 41107, 37835}

X(42801) = GIBERT (-21,4,15) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 15*a^2*SA - 8*SB*SC : :

X(42801) lies on these lines: {2, 17}, {13, 12812}, {14, 33703}, {15, 15712}, {16, 1657}, {18, 3850}, {61, 42773}, {395, 3627}, {398, 548}, {3843, 22238}, {5072, 5340}, {5238, 15706}, {5343, 36968}, {5350, 23046}, {5351, 14093}, {5352, 37641}, {6144, 36758}, {10646, 21735}, {11481, 42780}, {12108, 16773}, {14892, 42580}, {14893, 41122}, {15684, 16268}, {15686, 16964}, {15689, 36843}, {15718, 22236}, {16961, 22237}, {16967, 42494}, {17538, 40694}, {34754, 42774}, {38335, 42153}, {41972, 42165}, {41973, 42115}, {42147, 42613}, {42164, 42507}, {42588, 42776}

X(42801) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42436, 62}, {18, 34755, 41974}, {62, 41944, 42488}, {40693, 42533, 62}, {42488, 42636, 62}

X(42802) = GIBERT (21,4,15) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 15*a^2*SA + 8*SB*SC : :

X(42802) lies on these lines: {2, 18}, {13, 33703}, {14, 12812}, {15, 1657}, {16, 15712}, {17, 3850}, {62, 42774}, {396, 3627}, {397, 548}, {3843, 22236}, {5072, 5339}, {5237, 15706}, {5344, 36967}, {5349, 23046}, {5351, 37640}, {5352, 14093}, {6144, 36757}, {10645, 21735}, {11480, 42779}, {12108, 16772}, {14892, 42581}, {14893, 41121}, {15684, 16267}, {15686, 16965}, {15689, 36836}, {15718, 22238}, {16960, 22235}, {16966, 42495}, {17538, 40693}, {34755, 42773}, {38335, 42156}, {41971, 42164}, {41974, 42116}, {42148, 42612}, {42165, 42506}, {42589, 42775}

X(42802) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42435, 61}, {17, 34754, 41973}, {61, 41943, 42489}, {40694, 42532, 61}, {42489, 42635, 61}

X(42803) = GIBERT (48,-7,22) POINT

Barycentrics    8*Sqrt[3]*a^2*S + 11*a^2*SA - 7*SB*SC : :

X(42803) lies on these lines: {2, 33605}, {6, 15697}, {15, 15721}, {16, 10304}, {17, 3091}, {193, 36352}, {395, 3523}, {3543, 5318}, {3839, 11485}, {5334, 41943}, {7486, 22236}, {15640, 42144}, {16644, 42139}, {16773, 42479}, {21734, 42634}, {36970, 41119}, {41101, 42086}, {41972, 42090}, {42112, 42520}, {42115, 42419}, {42153, 42594}, {42516, 42682}

X(42804) = GIBERT (48,7,-22) POINT

Barycentrics    8*Sqrt[3]*a^2*S - 11*a^2*SA + 7*SB*SC : :

X(42804) lies on these lines: {2, 33604}, {6, 15697}, {15, 10304}, {16, 15721}, {18, 3091}, {193, 36346}, {396, 3523}, {3543, 5321}, {3839, 11486}, {5335, 41944}, {7486, 22238}, {15640, 42145}, {16645, 42142}, {16772, 42478}, {21734, 42633}, {36969, 41120}, {41100, 42085}, {41971, 42091}, {42113, 42521}, {42116, 42420}, {42156, 42595}, {42517, 42683}

X(42805) = GIBERT (-48,7,36) POINT

Barycentrics    -8*Sqrt[3]*a^2*S + 18*a^2*SA + 7*SB*SC : :

X(42805) lies on these lines: {13, 3090}, {14, 33703}, {15, 10299}, {62, 15709}, {376, 398}, {3533, 23302}, {3855, 5366}, {5343, 42088}, {11486, 22235}, {11489, 41974}, {15682, 22237}, {15719, 42532}, {16963, 41099}, {34755, 42472}, {41120, 42158}, {41977, 42436}

X(42806) = GIBERT (48,7,36) POINT

Barycentrics    8*Sqrt[3]*a^2*S + 18*a^2*SA + 7*SB*SC : :

X(42806) lies on these lines: {13, 33703}, {14, 3090}, {16, 10299}, {61, 15709}, {376, 397}, {3533, 23303}, {3855, 5365}, {5344, 42087}, {11485, 22237}, {11488, 41973}, {15682, 22235}, {15719, 42533}, {16962, 41099}, {34754, 42473}, {41119, 42157}, {41978, 42435}

X(42807) = GIBERT (0,3-SQRT(6),3) POINT

Barycentrics    3*a^2*SA + 2*(3 - Sqrt[6])*SB*SC : :

X(42807) lies on these lines: {2, 3}, {15, 41975}, {16, 41976}, {17, 41980}, {18, 41979}, {3373, 42234}, {3374, 42232}, {3387, 42233}, {3388, 42231}, {5334, 42648}, {5335, 42647}, {18581, 42646}, {18582, 42645}

X(42808) = GIBERT (0,3+SQRT(6),3) POINT

Barycentrics    3*a^2*SA + 2*(3 + Sqrt[6])*SB*SC : :

X(42808) lies on these lines: {2, 3}, {15, 41976}, {16, 41975}, {17, 41979}, {18, 41980}, {3373, 42232}, {3374, 42234}, {3387, 42231}, {3388, 42233}, {5334, 42647}, {5335, 42648}, {18581, 42645}, {18582, 42646}

X(42809) = ANTIGONAL IMAGE OF X(5000)

Barycentrics    S*SB*SC*(2*SA^2 + SB^2 + SC^2 - 2*SB*SC - SC*SA - SA*SB) - SA*(SA*SB + SC*SA - SB^2 - SC^2)*Sqrt[SA*SB*SC*SW] : :

X(42809) lies on the cubics K025 and K337 and these lines: {114, 5000}, {230, 5001}, {2987, 3564}, {34174, 34240}, {34175, 34239}

X(42809) = antigonal image of X(5000)
X(42809) = X(511)-cross conjugate of X(5000)
X(42809) = antigonal image of X(5000)
X(42809) = crosspoint of X(35142) and X(41195)

X(42810) = ANTIGONAL IMAGE OF X(5001)

Barycentrics    S*SB*SC*(2*SA^2 + SB^2 + SC^2 - 2*SB*SC - SC*SA - SA*SB) + SA*(SA*SB + SC*SA - SB^2 - SC^2)*Sqrt[SA*SB*SC*SW] : :

X(42810) lies on the cubics K025 and K337 and these lines: {114, 5001}, {230, 5000}, {2987, 3564}, {34174, 34239}, {34175, 34240}

X(42810) = antigonal image of X(5001)
X(42810) = X(511)-cross conjugate of X(5001)
X(42810) = crosspoint of X(35142) and X(41194)

X(42811) = ISOTOMIC CONJUGATE OF X(5000)

Barycentrics    1/(a^2*(S*SB*SC + SA*Sqrt[SA*SB*SC*SW])) : :

X(42811) lies on these lines: {2, 41194}, {3, 76}, {69, 32618}, {264, 5001}, {287, 41198}, {385, 41196}, {5002, 30737}, {41199, 42313}

X(42811) = isotomic conjugate of X(5000)
X(42811) = isotomic conjugate of the complement of X(5002)
X(42811) = isotomic conjugate of the isogonal conjugate of X(32618)
X(42811) = isotomic conjugate of the polar conjugate of X(41194)
X(42811) = X(i)-cross conjugate of X(j) for these (i,j): {32618, 41194}, {41198, 76}
X(42811) = cevapoint of X(i) and X(j) for these (i,j): {2, 5002}, {3, 41198}
X(42811) = trilinear pole of line {525, 41199}
X(42811) = X(i)-isoconjugate of X(j) for these (i,j): {19, 41196}, {31, 5000}, {1755, 41201}, {1973, 41198}, {9417, 41195}
X(42811) = barycentric product X(i)*X(j) for these {i,j}: {69, 41194}, {76, 32618}, {290, 41199}, {305, 41200}, {18024, 41197}
X(42811) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 5000}, {3, 41196}, {69, 41198}, {98, 41201}, {287, 32619}, {290, 41195}, {5001, 232}, {32618, 6}, {41194, 4}, {41197, 237}, {41199, 511}, {41200, 25}

X(42812) = ISOTOMIC CONJUGATE OF X(5001)

Barycentrics    1/(a^2*(S*SB*SC - SA*Sqrt[SA*SB*SC*SW])) : :

X(42812) lies on these lines: {2, 41195}, {3, 76}, {69, 32619}, {264, 5000}, {287, 41199}, {385, 41197}, {5003, 30737}, {41198, 42313}

X(42812) = isotomic conjugate of X(5001)
X(42812) = isotomic conjugate of the complement of X(5003)
X(42812) = isotomic conjugate of the isogonal conjugate of X(32619)
X(42812) = isotomic conjugate of the polar conjugate of X(41195)
X(42812) = X(i)-cross conjugate of X(j) for these (i,j): {32619, 41195}, {41199, 76}
X(42812) = cevapoint of X(i) and X(j) for these (i,j): {2, 5003}, {3, 41199}
X(42812) = trilinear pole of line {525, 41198}
X(42812) = X(i)-isoconjugate of X(j) for these (i,j): {19, 41197}, {31, 5001}, {1755, 41200}, {1973, 41199}, {9417, 41194}
X(42812) = barycentric product X(i)*X(j) for these {i,j}: {69, 41195}, {76, 32619}, {290, 41198}, {305, 41201}, {18024, 41196}
X(42812) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 5001}, {3, 41197}, {69, 41199}, {98, 41200}, {287, 32618}, {290, 41194}, {5000, 232}, {32619, 6}, {41195, 4}, {41196, 237}, {41198, 511}, {41201, 25}

X(42813) = GIBERT (3,4,1) POINT

Barycentrics    Sqrt[3]*a^2*S + a^2*SA + 8*SB*SC : :

X(42813) lies on the cubic K1213b and these lines: {2, 5351}, {3, 36969}, {4, 13}, {5, 16}, {6, 3843}, {14, 397}, {15, 382}, {17, 30}, {18, 3091}, {20, 10645}, {62, 381}, {140, 36968}, {202, 10896}, {203, 3585}, {376, 42494}, {395, 3850}, {396, 3627}, {398, 3845}, {485, 42184}, {486, 42183}, {511, 16629}, {530, 627}, {531, 33465}, {533, 22113}, {542, 22795}, {548, 23302}, {550, 16241}, {576, 16628}, {578, 3206}, {622, 635}, {631, 16966}, {636, 11303}, {1352, 31703}, {1656, 5237}, {1657, 5352}, {2041, 42245}, {2042, 42244}, {2043, 42602}, {2044, 42603}, {2307, 18513}, {3090, 16242}, {3105, 6248}, {3146, 36967}, {3200, 10539}, {3201, 37472}, {3205, 10540}, {3364, 23261}, {3365, 23251}, {3389, 6564}, {3390, 6565}, {3411, 3855}, {3412, 3853}, {3523, 42528}, {3526, 10646}, {3528, 42092}, {3530, 33417}, {3543, 16962}, {3545, 41100}, {3564, 22900}, {3583, 7005}, {3830, 16267}, {3832, 5335}, {3839, 41112}, {3851, 22238}, {3856, 11543}, {3858, 42163}, {3859, 16961}, {3861, 5321}, {5055, 36843}, {5066, 16963}, {5067, 33416}, {5070, 11481}, {5072, 16645}, {5073, 36836}, {5076, 42154}, {5079, 42593}, {5343, 12817}, {5446, 36981}, {5873, 20428}, {5876, 36978}, {6669, 33413}, {7006, 10895}, {7486, 42089}, {7684, 36994}, {7747, 41407}, {8739, 35488}, {10113, 36208}, {10188, 10299}, {11243, 34786}, {11308, 40335}, {11480, 17800}, {11488, 33703}, {12101, 42506}, {12103, 42429}, {12155, 33006}, {12820, 22235}, {13881, 41406}, {14269, 41108}, {14814, 35731}, {15687, 41101}, {15688, 42773}, {15694, 42631}, {15696, 42097}, {15704, 42529}, {15717, 42091}, {15720, 42625}, {16239, 42123}, {16631, 36759}, {16960, 17578}, {18436, 36979}, {18502, 36760}, {18586, 42233}, {18587, 42234}, {19130, 22794}, {19709, 41944}, {22237, 42507}, {22489, 37172}, {22510, 36962}, {22832, 22891}, {29012, 31704}, {31857, 37776}, {33386, 37173}, {33602, 41113}, {33654, 37718}, {34755, 42095}, {35730, 42282}, {36757, 36990}, {41120, 42776}, {41971, 42777}, {41972, 42475}, {41977, 42508}, {42104, 42435}, {42109, 42124}, {42145, 42683}, {42236, 42271}, {42238, 42272}, {42499, 42685}, {42500, 42590}, {42530, 42687}, {42794, 42795}

X(42813) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5366, 42161}, {2, 42158, 5351}, {2, 42161, 42158}, {3, 36969, 42431}, {4, 13, 61}, {4, 61, 36970}, {4, 37640, 42160}, {4, 40693, 16964}, {4, 42162, 13}, {5, 16, 42489}, {5, 5318, 16965}, {5, 16773, 16967}, {5, 16965, 16}, {5, 42118, 16773}, {6, 3843, 42814}, {13, 16964, 40693}, {17, 5238, 41943}, {17, 42166, 41121}, {17, 42434, 16772}, {61, 36970, 41973}, {61, 41973, 42799}, {62, 5340, 41107}, {140, 42165, 36968}, {381, 5340, 62}, {381, 41107, 16268}, {382, 42128, 42156}, {382, 42156, 15}, {396, 3627, 42157}, {397, 546, 14}, {550, 42598, 16241}, {631, 42086, 42433}, {1656, 42155, 5237}, {1657, 16644, 5352}, {3090, 42151, 16242}, {3091, 5344, 10653}, {3091, 10653, 18}, {3146, 42152, 36967}, {3391, 3392, 5318}, {3412, 19107, 42147}, {3412, 42147, 34754}, {3543, 41119, 16962}, {3545, 42149, 42580}, {3830, 22236, 42432}, {3832, 5335, 40694}, {3832, 40694, 16809}, {3851, 22238, 37835}, {3853, 11542, 42147}, {3853, 42147, 19107}, {5238, 41121, 17}, {5318, 16808, 16}, {5318, 42110, 42118}, {5318, 42138, 16808}, {5318, 42693, 42138}, {5335, 42106, 16809}, {11488, 42105, 42099}, {11542, 19107, 34754}, {11542, 42102, 19107}, {11542, 42147, 3412}, {15696, 42132, 42490}, {16267, 42432, 22236}, {16772, 42434, 5238}, {16773, 42110, 5}, {16808, 16965, 5}, {16808, 16967, 42110}, {16964, 40693, 61}, {16966, 42433, 631}, {16967, 42118, 16}, {18582, 19106, 10645}, {18582, 42134, 19106}, {23302, 42137, 42100}, {33417, 42629, 42088}, {36968, 42581, 140}, {37832, 42431, 3}, {37835, 41974, 22238}, {40694, 42106, 3832}, {41100, 42580, 42149}, {42086, 42142, 16966}, {42088, 42146, 33417}, {42094, 42128, 15}, {42094, 42156, 382}, {42097, 42490, 15696}, {42098, 42127, 10646}, {42102, 42147, 3853}, {42110, 42118, 16967}, {42114, 42120, 33416}

X(42814) = GIBERT (-3,4,1) POINT

Barycentrics    Sqrt[3]*a^2*S - a^2*SA - 8*SB*SC : :

X(42814) lies on the cubic K1213a and these lines: {2, 5352}, {3, 36970}, {4, 14}, {5, 15}, {6, 3843}, {13, 398}, {16, 382}, {17, 3091}, {18, 30}, {20, 10646}, {61, 381}, {140, 36967}, {202, 3585}, {203, 10896}, {376, 42495}, {395, 3627}, {396, 3850}, {397, 3845}, {485, 42186}, {486, 42185}, {511, 16628}, {530, 33464}, {531, 628}, {532, 22114}, {542, 22794}, {548, 23303}, {550, 16242}, {576, 16629}, {578, 3205}, {621, 636}, {631, 16967}, {635, 11304}, {1352, 31704}, {1656, 5238}, {1657, 5351}, {2041, 35739}, {2042, 42243}, {2043, 42603}, {2044, 42602}, {2306, 37718}, {3090, 16241}, {3104, 6248}, {3146, 36968}, {3200, 37472}, {3201, 10539}, {3206, 10540}, {3364, 6564}, {3365, 6565}, {3389, 23261}, {3390, 23251}, {3411, 3853}, {3412, 3855}, {3523, 42529}, {3526, 10645}, {3528, 42089}, {3530, 33416}, {3543, 16963}, {3545, 41101}, {3564, 22856}, {3583, 7006}, {3830, 16268}, {3832, 5334}, {3839, 41113}, {3851, 22236}, {3856, 11542}, {3858, 42166}, {3859, 16960}, {3861, 5318}, {5055, 36836}, {5066, 16962}, {5067, 33417}, {5070, 11480}, {5072, 16644}, {5073, 36843}, {5076, 42155}, {5079, 42592}, {5344, 12816}, {5446, 36979}, {5872, 20429}, {5876, 36980}, {6670, 33412}, {7005, 10895}, {7127, 18514}, {7486, 42092}, {7685, 36992}, {7747, 41406}, {8740, 35488}, {10113, 36209}, {10187, 10299}, {11244, 34786}, {11307, 40334}, {11481, 17800}, {11489, 33703}, {12101, 42507}, {12103, 42430}, {12154, 33006}, {12821, 22237}, {13881, 41407}, {14269, 41107}, {15687, 41100}, {15688, 42774}, {15694, 42632}, {15696, 42096}, {15704, 42528}, {15717, 42090}, {15720, 42626}, {16239, 42122}, {16630, 36760}, {16961, 17578}, {18436, 36981}, {18502, 36759}, {18586, 42232}, {18587, 42231}, {19130, 22795}, {19709, 41943}, {22235, 42506}, {22490, 37173}, {22511, 36961}, {22831, 22846}, {29012, 31703}, {31857, 37775}, {33387, 37172}, {33603, 41112}, {34754, 42098}, {35731, 42228}, {36758, 36990}, {41119, 42775}, {41971, 42474}, {41972, 42778}, {41978, 42509}, {42105, 42436}, {42108, 42121}, {42144, 42682}, {42235, 42271}, {42237, 42272}, {42498, 42684}, {42501, 42591}, {42531, 42686}, {42793, 42796}

X(42814) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5365, 42160}, {2, 42157, 5352}, {2, 42160, 42157}, {3, 36970, 42432}, {4, 14, 62}, {4, 62, 36969}, {4, 37641, 42161}, {4, 40694, 16965}, {4, 42159, 14}, {5, 15, 42488}, {5, 5321, 16964}, {5, 16772, 16966}, {5, 16964, 15}, {5, 42117, 16772}, {6, 3843, 42813}, {14, 16965, 40694}, {18, 5237, 41944}, {18, 42163, 41122}, {18, 42433, 16773}, {61, 5339, 41108}, {62, 36969, 41974}, {62, 41974, 42800}, {140, 42164, 36967}, {381, 5339, 61}, {381, 41108, 16267}, {382, 42125, 42153}, {382, 42153, 16}, {395, 3627, 42158}, {398, 546, 13}, {550, 42599, 16242}, {631, 42085, 42434}, {1656, 42154, 5238}, {1657, 16645, 5351}, {3090, 42150, 16241}, {3091, 5343, 10654}, {3091, 10654, 17}, {3146, 42149, 36968}, {3366, 3367, 5321}, {3411, 19106, 42148}, {3411, 42148, 34755}, {3543, 41120, 16963}, {3545, 42152, 42581}, {3830, 22238, 42431}, {3832, 5334, 40693}, {3832, 40693, 16808}, {3851, 22236, 37832}, {3853, 11543, 42148}, {3853, 42148, 19106}, {5237, 41122, 18}, {5321, 16809, 15}, {5321, 42107, 42117}, {5321, 42135, 16809}, {5321, 42692, 42135}, {5334, 42103, 16808}, {11489, 42104, 42100}, {11543, 19106, 34755}, {11543, 42101, 19106}, {11543, 42148, 3411}, {15696, 42129, 42491}, {16268, 42431, 22238}, {16772, 42107, 5}, {16773, 42433, 5237}, {16809, 16964, 5}, {16809, 16966, 42107}, {16965, 40694, 62}, {16966, 42117, 15}, {16967, 42434, 631}, {18581, 19107, 10646}, {18581, 42133, 19107}, {23303, 42136, 42099}, {33416, 42630, 42087}, {36967, 42580, 140}, {37832, 41973, 22236}, {37835, 42432, 3}, {40693, 42103, 3832}, {41101, 42581, 42152}, {42085, 42139, 16967}, {42087, 42143, 33416}, {42093, 42125, 16}, {42093, 42153, 382}, {42095, 42126, 10645}, {42096, 42491, 15696}, {42101, 42148, 3853}, {42107, 42117, 16966}, {42111, 42119, 33417}

X(42815) = GIBERT (4,2,1) POINT

Barycentrics    4*a^2*S/Sqrt[3] + a^2*SA + 4*SB*SC : :

X(42815) lies on the cubic K1213b and these lines: {2, 33604}, {3, 5335}, {6, 13}, {15, 1657}, {16, 3526}, {17, 11481}, {61, 5076}, {62, 5079}, {140, 22235}, {193, 31693}, {376, 42496}, {382, 5318}, {395, 41119}, {396, 3534}, {397, 1656}, {398, 42106}, {631, 42627}, {3311, 42247}, {3312, 42249}, {3412, 42099}, {3543, 42633}, {3589, 22492}, {3620, 37352}, {3830, 37640}, {3843, 5334}, {3851, 11543}, {5054, 10653}, {5055, 11489}, {5056, 42628}, {5070, 42121}, {5071, 42634}, {5072, 18581}, {5073, 5344}, {5321, 42162}, {5339, 42779}, {5350, 42104}, {5353, 9654}, {5357, 9669}, {5362, 17528}, {5366, 42140}, {5858, 33560}, {6199, 18587}, {6221, 42196}, {6395, 18586}, {6398, 42198}, {6410, 35730}, {6412, 35731}, {7583, 42212}, {7584, 42214}, {8972, 36457}, {9763, 35692}, {10645, 15688}, {10646, 15693}, {10654, 38335}, {11298, 34541}, {11303, 40901}, {11305, 34540}, {11408, 18494}, {11480, 15696}, {12101, 33602}, {13903, 42205}, {13941, 36439}, {13961, 42206}, {14093, 42777}, {14269, 42133}, {15681, 42145}, {15684, 42144}, {15706, 16241}, {15765, 23267}, {16242, 42499}, {16645, 41121}, {16772, 42091}, {16966, 22238}, {16967, 42436}, {17800, 42122}, {18585, 23273}, {19106, 22236}, {19709, 37641}, {20080, 37170}, {20425, 33878}, {21309, 37333}, {22491, 32455}, {22495, 40341}, {32785, 36438}, {32786, 36456}, {33417, 36843}, {34754, 36969}, {34755, 37832}, {36331, 37786}, {36836, 42100}, {36967, 42506}, {39874, 41016}, {40694, 42110}, {41113, 42692}, {41943, 42625}, {42087, 42161}, {42088, 42152}, {42089, 42598}, {42090, 42165}, {42092, 42148}, {42109, 42150}, {42151, 42685}, {42500, 42512}, {42502, 42510}

X(42815) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 13, 42128}, {6, 16808, 42125}, {6, 42128, 381}, {15, 5340, 42127}, {15, 42127, 1657}, {16, 42132, 3526}, {16, 42156, 42132}, {61, 42094, 42126}, {62, 42098, 42129}, {396, 42086, 42116}, {397, 18582, 11486}, {5318, 11485, 382}, {5318, 40693, 11485}, {5318, 42147, 42105}, {5334, 42138, 3843}, {5335, 11488, 42118}, {5335, 11542, 3}, {5344, 42119, 42137}, {10653, 23302, 42115}, {11480, 16965, 42131}, {11480, 42131, 15696}, {11486, 18582, 1656}, {11488, 42118, 3}, {11489, 42146, 5055}, {11542, 42118, 11488}, {11543, 42142, 3851}, {13665, 13785, 13}, {16808, 42125, 381}, {16960, 16965, 11480}, {19106, 22236, 42130}, {23302, 42115, 5054}, {34754, 36969, 42096}, {37640, 42134, 42117}, {42086, 42116, 3534}, {42094, 42126, 5076}, {42098, 42129, 5079}, {42117, 42134, 3830}, {42119, 42137, 5073}, {42120, 42124, 3}, {42122, 42141, 17800}, {42125, 42128, 16808}

X(42816) = GIBERT (-4,2,1) POINT

Barycentrics    4*a^2*S/Sqrt[3] - a^2*SA - 4*SB*SC : :

X(42816) lies on the cubic K1213a and these lines: {2, 33605}, {3, 5334}, {6, 13}, {15, 3526}, {16, 1657}, {18, 11480}, {61, 5079}, {62, 5076}, {140, 22237}, {193, 31694}, {376, 42497}, {382, 5321}, {395, 3534}, {396, 41120}, {397, 42103}, {398, 1656}, {631, 42628}, {3311, 42246}, {3312, 42248}, {3411, 42100}, {3543, 42634}, {3589, 22491}, {3620, 37351}, {3830, 37641}, {3843, 5335}, {3851, 11542}, {5054, 10654}, {5055, 11488}, {5056, 42627}, {5070, 42124}, {5071, 42633}, {5072, 18582}, {5073, 5343}, {5318, 42159}, {5340, 42780}, {5349, 42105}, {5353, 9669}, {5357, 9654}, {5365, 42141}, {5367, 17528}, {5859, 33561}, {6199, 18586}, {6221, 42195}, {6395, 18587}, {6398, 42197}, {6470, 35730}, {7583, 42211}, {7584, 42213}, {8972, 36439}, {9761, 35696}, {10645, 15693}, {10646, 15688}, {10653, 38335}, {11297, 34540}, {11304, 40900}, {11306, 34541}, {11409, 18494}, {11481, 15696}, {12101, 33603}, {13903, 42203}, {13941, 36457}, {13961, 42204}, {14093, 42778}, {14269, 42134}, {15681, 42144}, {15684, 42145}, {15706, 16242}, {15765, 23273}, {16241, 42498}, {16644, 41122}, {16773, 42090}, {16966, 42435}, {16967, 22236}, {17800, 42123}, {18585, 23267}, {19107, 22238}, {19709, 37640}, {20080, 37171}, {20426, 33878}, {21309, 37332}, {22492, 32455}, {22496, 40341}, {32785, 36456}, {32786, 36438}, {33416, 36836}, {34754, 37835}, {34755, 36970}, {35750, 37785}, {36843, 42099}, {36968, 42507}, {39874, 41017}, {40693, 42107}, {41112, 42693}, {41944, 42626}, {42087, 42149}, {42088, 42160}, {42089, 42147}, {42091, 42164}, {42092, 42599}, {42108, 42151}, {42150, 42684}, {42501, 42513}, {42503, 42511}

X(42816) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14, 42125}, {6, 16809, 42128}, {6, 42125, 381}, {15, 42129, 3526}, {15, 42153, 42129}, {16, 5339, 42126}, {16, 42126, 1657}, {61, 42095, 42132}, {62, 42093, 42127}, {395, 42085, 42115}, {398, 18581, 11485}, {5321, 11486, 382}, {5321, 40694, 11486}, {5321, 42148, 42104}, {5334, 11489, 42117}, {5334, 11543, 3}, {5335, 42135, 3843}, {5343, 42120, 42136}, {10654, 23303, 42116}, {11481, 16964, 42130}, {11481, 42130, 15696}, {11485, 18581, 1656}, {11488, 42143, 5055}, {11489, 42117, 3}, {11542, 42139, 3851}, {11543, 42117, 11489}, {13665, 13785, 14}, {16809, 42128, 381}, {16961, 16964, 11481}, {19107, 22238, 42131}, {23303, 42116, 5054}, {34755, 36970, 42097}, {37641, 42133, 42118}, {42085, 42115, 3534}, {42093, 42127, 5076}, {42095, 42132, 5079}, {42118, 42133, 3830}, {42119, 42121, 3}, {42120, 42136, 5073}, {42123, 42140, 17800}, {42125, 42128, 16809}

X(42817) = GIBERT (4,2,3) POINT

Barycentrics    4*a^2*S/Sqrt[3] + 3*a^2*SA + 4*SB*SC : :

X(42817) lies on the cubic K1213b and these lines: {2, 42492}, {3, 5335}, {4, 42806}, {6, 17}, {13, 3534}, {15, 382}, {16, 5054}, {61, 5072}, {381, 396}, {397, 15720}, {398, 42114}, {485, 42193}, {486, 42191}, {550, 22235}, {1657, 5318}, {3411, 42610}, {3412, 16809}, {3526, 11486}, {3545, 42633}, {3830, 42119}, {3843, 42117}, {3851, 5334}, {5055, 11543}, {5066, 33603}, {5067, 42628}, {5070, 11489}, {5073, 42122}, {5076, 42085}, {5079, 18581}, {5238, 42097}, {5340, 10645}, {5344, 42145}, {5350, 42112}, {5353, 31479}, {5472, 36763}, {5859, 6669}, {6221, 42255}, {6398, 42257}, {8972, 14814}, {8981, 42222}, {10632, 18494}, {10634, 18536}, {10653, 15693}, {11268, 37776}, {11309, 22113}, {11311, 34541}, {12821, 41101}, {13941, 14813}, {13966, 42224}, {14093, 41943}, {14269, 42136}, {15681, 42141}, {15688, 42088}, {15689, 42584}, {15696, 16772}, {15697, 33604}, {15700, 16241}, {15703, 37641}, {15716, 41107}, {15723, 33416}, {16242, 42506}, {16645, 42477}, {16808, 22236}, {16962, 19107}, {17800, 42137}, {19106, 36836}, {19709, 42139}, {22238, 33417}, {22615, 42251}, {22644, 42253}, {22892, 23006}, {34754, 42093}, {36366, 36770}, {37832, 41122}, {40334, 40341}, {41119, 42105}, {41121, 41971}, {41974, 42773}, {42087, 42162}, {42102, 42150}, {42106, 42147}, {42133, 42494}, {42500, 42510}, {42512, 42595}, {42687, 42689}

X(42817) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 17, 42132}, {6, 1656, 42818}, {6, 16966, 42129}, {6, 42132, 1656}, {13, 11480, 42127}, {15, 42094, 42130}, {15, 42128, 382}, {15, 42156, 42128}, {17, 16960, 6}, {61, 42098, 42125}, {396, 18582, 11485}, {397, 42092, 42115}, {5318, 42116, 1657}, {5318, 42152, 42116}, {5334, 42146, 3851}, {5335, 11488, 42124}, {5335, 42124, 3}, {5340, 10645, 42131}, {8976, 13951, 17}, {10654, 18582, 42110}, {11480, 42127, 3534}, {11485, 18582, 381}, {11486, 23302, 3526}, {11488, 11542, 3}, {11542, 42124, 5335}, {16808, 22236, 42126}, {16966, 42129, 1656}, {23302, 40693, 11486}, {33607, 42529, 13}, {37832, 41122, 42474}, {42092, 42115, 15720}, {42094, 42130, 382}, {42098, 42125, 5072}, {42117, 42142, 3843}, {42119, 42138, 3830}, {42122, 42134, 5073}, {42128, 42130, 42094}, {42129, 42132, 16966}, {42201, 42202, 11488}

X(42818) = GIBERT (-4,2,3) POINT

Barycentrics    4*a^2*S/Sqrt[3] - 3*a^2*SA - 4*SB*SC : :

X(42818) lies on the cubic K1213a and these lines: {2, 42493}, {3, 5334}, {4, 42805}, {6, 17}, {14, 3534}, {15, 5054}, {16, 382}, {62, 5072}, {381, 395}, {397, 42111}, {398, 15720}, {485, 42194}, {486, 42192}, {550, 22237}, {1657, 5321}, {3411, 16808}, {3412, 42611}, {3526, 11485}, {3545, 42634}, {3830, 42120}, {3843, 42118}, {3851, 5335}, {5055, 11542}, {5066, 33602}, {5067, 42627}, {5070, 11488}, {5073, 42123}, {5076, 42086}, {5079, 18582}, {5237, 42096}, {5339, 10646}, {5343, 42144}, {5349, 42113}, {5357, 31479}, {5858, 6670}, {6221, 42254}, {6398, 42256}, {8972, 14813}, {8981, 42221}, {10633, 18494}, {10635, 18536}, {10654, 15693}, {11267, 37775}, {11310, 22114}, {11312, 34540}, {12820, 41100}, {13941, 14814}, {13966, 42223}, {14093, 41944}, {14269, 42137}, {15681, 42140}, {15688, 42087}, {15689, 42585}, {15696, 16773}, {15697, 33605}, {15700, 16242}, {15703, 37640}, {15716, 41108}, {15723, 33417}, {16241, 42507}, {16644, 42476}, {16809, 22238}, {16963, 19106}, {17800, 42136}, {19107, 36843}, {19709, 42142}, {22236, 33416}, {22615, 42250}, {22644, 42252}, {22848, 23013}, {34755, 42094}, {37835, 41121}, {40335, 40341}, {41120, 42104}, {41122, 41972}, {41973, 42774}, {42088, 42159}, {42101, 42151}, {42103, 42148}, {42134, 42495}, {42501, 42511}, {42513, 42594}, {42686, 42688}

X(42818) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 18, 42129}, {6, 1656, 42817}, {6, 16967, 42132}, {6, 42129, 1656}, {14, 11481, 42126}, {16, 42093, 42131}, {16, 42125, 382}, {16, 42153, 42125}, {18, 16961, 6}, {62, 42095, 42128}, {395, 18581, 11486}, {398, 42089, 42116}, {5321, 42115, 1657}, {5321, 42149, 42115}, {5334, 11489, 42121}, {5334, 42121, 3}, {5335, 42143, 3851}, {5339, 10646, 42130}, {8976, 13951, 18}, {10653, 18581, 42107}, {11481, 42126, 3534}, {11485, 23303, 3526}, {11486, 18581, 381}, {11489, 11543, 3}, {11543, 42121, 5334}, {16809, 22238, 42127}, {16967, 42132, 1656}, {23303, 40694, 11485}, {33606, 42528, 14}, {37835, 41121, 42475}, {42089, 42116, 15720}, {42093, 42131, 382}, {42095, 42128, 5072}, {42118, 42139, 3843}, {42120, 42135, 3830}, {42123, 42133, 5073}, {42125, 42131, 42093}, {42129, 42132, 16967}, {42199, 42200, 11489}

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Parallels-perspeconics: X(42819)-X(42887)

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This preamble and centers X(42819)-X(42887) were contributed by César Eliud Lozada, April 27, 2021.

Let A'B'C' be a triangle perspective to ABC with perspector P. Let Ab and Ac be the points at which the parallel line to B'C' through P cuts AC and AB, respectively, and build Bc, Ba, Ca, Cb cyclically. Then these six points lie on a conic q. Swapping the triangles, the six points A'b, A'c, B'c, B'a, C'a C'b, constructed similarly, also lie on another conic q'.

Conics q and q' are introduced here as the parallels-perspeconic of ABC to A'B'C' and the parallels-perspeconic of A'B'C to ABC, respectively.

Assume ABC is reference triangle, the perspector P = x : y : z (barycentrics) and Q, Q' are the centers of q and q', respectively.

  1. If A'B'C' is the cevian triangle of P then Q' = P and Q = (y + z)*x : :, i.e., Q is the crosspoint of X(2) and P.
  2. If A'B'C' is the anticevian triangle of P then Q = P and Q' = x*(y + z-x): :, i.e., Q' is the X(2)-CevaConjugate-of-P.
  3. If A'B'C' is the circumcevian triangle of P then:
      Q = 2*(y + z)*b^2*c^2*x^3 + ((3*a^2 + b^2 - c^2)*c^2*y^2 + 4*S^2*y*z + (3*a^2 - b^2 + c^2)*b^2*z^2)*x^2 + 2*((2*y + z)*z^2*b^2 + (y + 2*z)*y^2*c^2)*a^2*x + 2*a^4*y^2*z^2 : :

      Q' = 4*(y + z)*b^2*c^2*x^3 + x^2*(c^2*y^2 + b^2*z^2)*(3*a^2 + b^2 + c^2)-x*y*z*((a^2*(a^2-b^2-c^2)-4*b^2*c^2)*x + a^2*(a^2-b^2-3*c^2)*y + a^2*(a^2-3*b^2-c^2)*z)-2*a^4*y^2*z^2 : :

More generally: If A'B'C' is a central triangle perspective at P to ABC then there exists an homogeneous degree-0 function ƒ(a,b,c) such that PA'=ƒ(a,b,c)*PA, PB'=ƒ(b,c,a)*PB and PC'=ƒ(c,a,b)*PC. Shortening the notation to ƒ(a,b,c)=ƒa, ƒ(b,c,a)=ƒb, ƒ(c,a,b)=ƒc, the centers of the conics are:

  Q = ƒb*ƒc*((2*((ƒb + ƒc)*x + (y + z)*ƒa))*y*z*ƒa + (-x^2*ƒb*ƒc + y^2*ƒa*ƒc + z^2*ƒa*ƒb)*x)*x : :

  Q' = x*(ƒb*ƒc*((x + (y + z)*ƒa)*x^3*ƒb*ƒc - y*z*((y + 2*z)*z*ƒb + (2*y + z)*y*ƒc + 2*y*z)*ƒa^2) + x*ƒa*ƒb*ƒc*(((y^2 + 4*y*z + z^2)*ƒb*ƒc - 2*(2*y + z)*z*ƒb - 2*(y + 2*z)*y*ƒc)*x
   - ƒa*(y^3*ƒc + z^3*ƒb) - ((ƒc + 4)*ƒa - 2*(ƒb - 2)*ƒc)*y^2*z - ((ƒb + 4)*ƒa - 2*(ƒc - 2)*ƒb)*y*z^2) - ((ƒb - 1)*y^4*ƒc^2 + (ƒc - 1)*z^4*ƒb^2)*ƒa^2) : :

The appearance of (T, i, j) in the following partial list means that the centers of the parallels-perspeconics of triangles ABC-to-T and T-to-ABC are X(i) and X(j) (-- indicates a not calculated center):

(ABC-X3 reflections, 182, 3098), (anti-Aquila, 1001, 42819), (anti-Ara, 42820, 42821), (anti-Atik, 41385, --), (1st anti-Brocard, 42822, 42823), (4th anti-Brocard, 42824, 42825), (5th anti-Brocard, 42826, 42827), (2nd anti-circumperp-tangential, 42828, 42829), (anti-Conway, 6, 578), (2nd anti-Conway, 6, 389), (anti-Ehrmann-mid, 42830, 42831), (anti-Euler, 10002, 1249), (anti-excenters-reflections, 6, 4), (2nd anti-extouch, 37864, --), (anti-inner-Grebe, 182, 42832), (anti-outer-Grebe, 182, 42833), (anti-Honsberger, 6, 182), (anti-Hutson intouch, 33584, --), (anti-inverse-in-incircle, 6, 4), (anti-1st Kenmotu-free-vertices, 42864, --), (anti-2nd Kenmotu-free-vertices, 42866, --), (anti-Mandart-incircle, 42834, 42835), (6th anti-mixtilinear, 41385, 42836), (anti-2nd Parry, 39461, --), (anti-tangential-midarc, 41381, 42837), (anti-3rd tri-squares-central, 42838, 42839), (anti-4th tri-squares-central, 42840, 42841), (anti-X3-ABC reflections, 182, 5092), (anti-inner-Yff, 1001, 42842), (anti-outer-Yff, 1001, 42843), (anticomplementary, 2, 2), (Aquila, 1001, 9), (Ara, 42820, --), (Atik, 42872, --), (Bevan antipodal, 57, 223), (1st Brocard, 42844, 42845), (5th Brocard, 42826, 42846), (8th Brocard, 42847, 42848), (circummedial, 42849, 42850), (circumorthic, 6, 4), (2nd circumperp tangential, 42828, 42851), (2nd circumperp, 1, 1001), (circumsymmedial, 42852, 42852), (Conway, 1, 7), (2nd Conway, 1, 7), (Ehrmann-mid, 42830, 42853), (Ehrmann-vertex, 6, 4), (2nd Ehrmann, 6, 576), (Euler, 10002, 42854), (2nd Euler, 41384, --), (5th Euler, 42849, 42849), (excenters-reflections, 1, 3243), (excentral, 1, 9), (1st excosine, 33584, --), (extangents, 41381, 42855), (extouch, 9, 8), (2nd extouch, 42856, 42857), (outer-Garcia, 3842, 4732), (inner-Grebe, 182, 42858), (outer-Grebe, 182, 42859), (2nd Hatzipolakis, 17054, 1119), (Honsberger, 1, 7), (Hutson intouch, 42860, 42861), (incentral, 37, 1), (intouch, 1, 7), (inverse-in-Conway, 1, 35892), (inverse-in-incircle, 1, 5572), (Johnson, 10003, 42862), (inner-Johnson, 10006, 42863), (2nd Johnson-Yff, 10006, --), (1st Kenmotu-free-vertices, 42864, 42865), (2nd Kenmotu-free-vertices, 42866, 42867), (1st Kenmotu diagonals, 6, 371), (2nd Kenmotu diagonals, 6, 372), (Kosnita, 41380, --), (Lemoine, 597, 598), (1st Lemoine-Dao, 36310, --), (2nd Lemoine-Dao, 36307, --), (Macbeath, 5, 264), (Mandart-incircle, 42834, 42868), (medial, 2, 2), (4th mixtilinear, 42869, 42870), (5th mixtilinear, 1001, 42871), (6th mixtilinear, 42872, --), (Moses-Steiner osculatory, 17983, --), (orthic, 6, 4), (orthic axes, 42873, 42874), (orthocentroidal, 42875, 42876), (2nd Parry, 39465, --), (Pelletier, 650, 11), (reflection, 42877, 42878), (Schroeter, --, 523), (1st Sharygin, 42879, 42880), (2nd Sharygin, 4562, 42881), (Soddy, 7, 3160), (inner-squares, 485, 8966), (outer-squares, 486, 13960), (Steiner, 523, --), (symmedial, 39, 6), (tangential, 6, 3), (inner tri-equilateral, 6, 15), (outer tri-equilateral, 6, 16), (3rd tri-squares-central, 42838, 42882), (4th tri-squares-central, 42840, 42883), (Trinh, 40355, --), (Vu-Dao-X(15)-isodynamic, 36311, --), (Vu-Dao-X(16)-isodynamic, 36308, --), (X-parabola-tangential, --, 523), (X3-ABC reflections, 182, 6), (Yff contact, 514, --), (inner-Yff, 1001, 954), (outer-Yff, 1001, 42884), (inner-Yff tangents, 1001, 42885), (outer-Yff tangents, 1001, 42886), (2nd Zaniah, 42860, 42887)

X(42819) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-AQUILA TO ABC

Barycentrics    a*(2*a^2-3*(b+c)*a+b^2-4*b*c+c^2) : :
X(42819) = 3*X(1)+X(9) = 5*X(1)-X(3243) = 5*X(1)+X(5220) = 7*X(1)+X(5223) = 2*X(1)+X(15254) = 4*X(1)+X(15481) = X(1)+3*X(38316) = 3*X(1)-X(42871) = X(9)-3*X(1001) = 5*X(9)+3*X(3243) = 5*X(9)-3*X(5220) = 7*X(9)-3*X(5223) = 2*X(9)-3*X(15254) = 4*X(9)-3*X(15481) = 2*X(9)+3*X(15570) = X(9)-9*X(38316) = 3*X(392)+X(15185) = 5*X(1001)+X(3243) = 5*X(1001)-X(5220) = 7*X(1001)-X(5223) = 4*X(1001)-X(15481) = 2*X(1001)+X(15570) = X(1001)-3*X(38316) = 3*X(1001)+X(42871)

The center of the reciprocal parallels-perspeconic of these triangles is X(1001)

X(42819) lies on these lines: {1, 6}, {2, 3689}, {7, 1319}, {8, 17240}, {21, 17609}, {31, 4883}, {55, 3306}, {57, 4428}, {65, 7677}, {75, 4702}, {142, 214}, {145, 38057}, {200, 8167}, {210, 3957}, {239, 31342}, {244, 4689}, {354, 1621}, {390, 2646}, {480, 3872}, {497, 3838}, {515, 42356}, {516, 550}, {519, 6666}, {673, 16826}, {752, 17376}, {846, 21342}, {902, 17450}, {908, 37703}, {944, 38037}, {968, 17597}, {971, 15178}, {993, 5049}, {999, 3941}, {1058, 28628}, {1125, 3813}, {1149, 1964}, {1317, 38060}, {1320, 2346}, {1376, 3848}, {1420, 12560}, {1445, 2099}, {1482, 38031}, {1483, 38043}, {1484, 11230}, {1697, 10107}, {1837, 10587}, {1890, 11363}, {1960, 6009}, {1962, 29818}, {2177, 16610}, {2550, 3616}, {2801, 19907}, {2951, 30392}, {3036, 31397}, {3058, 5249}, {3059, 4511}, {3175, 32923}, {3241, 3759}, {3244, 4974}, {3254, 5424}, {3286, 17207}, {3295, 3812}, {3303, 3895}, {3305, 41711}, {3315, 4003}, {3475, 24703}, {3476, 8232}, {3576, 11495}, {3623, 5686}, {3624, 38200}, {3655, 31672}, {3656, 13151}, {3666, 4906}, {3679, 17267}, {3683, 3873}, {3696, 16823}, {3697, 25542}, {3711, 3740}, {3720, 3744}, {3722, 30950}, {3739, 24331}, {3745, 29814}, {3746, 5439}, {3749, 37674}, {3750, 3752}, {3753, 5541}, {3816, 13405}, {3822, 18527}, {3834, 4660}, {3877, 11025}, {3880, 6600}, {3881, 31445}, {3883, 4966}, {3884, 20116}, {3893, 32634}, {3898, 30329}, {3911, 17051}, {3928, 30350}, {3950, 28503}, {3979, 4849}, {3983, 17536}, {3999, 4414}, {4004, 37563}, {4078, 9053}, {4312, 21842}, {4326, 13384}, {4335, 24661}, {4362, 4891}, {4395, 4780}, {4421, 5437}, {4432, 17351}, {4533, 5506}, {4653, 16696}, {4662, 11108}, {4686, 4693}, {4687, 36534}, {4698, 36480}, {4851, 28538}, {4860, 35258}, {4914, 32858}, {5045, 5248}, {5048, 15837}, {5087, 17718}, {5123, 10056}, {5328, 10578}, {5426, 37602}, {5434, 41857}, {5440, 20195}, {5542, 5625}, {5698, 11038}, {5805, 24299}, {5851, 11715}, {5901, 37837}, {6173, 37525}, {6690, 11019}, {6763, 36946}, {7171, 11496}, {7191, 37593}, {7263, 28580}, {7672, 11011}, {7673, 37568}, {7675, 34471}, {7676, 37600}, {7686, 16202}, {7982, 21153}, {8299, 28600}, {8543, 8581}, {9624, 33597}, {9776, 10385}, {9780, 12630}, {9957, 30143}, {10202, 12515}, {10222, 31658}, {10246, 15726}, {10267, 13374}, {11235, 25525}, {11238, 31266}, {11281, 12053}, {11526, 41712}, {12573, 16888}, {12609, 15172}, {12730, 41541}, {12740, 14100}, {14151, 29007}, {15808, 38204}, {15950, 21617}, {16593, 17023}, {16825, 28581}, {17231, 33076}, {17261, 24841}, {17279, 36479}, {17357, 29659}, {17384, 29660}, {17469, 37595}, {17614, 38052}, {17715, 26102}, {18450, 31391}, {19765, 28011}, {20533, 29586}, {21870, 37680}, {24217, 29675}, {24542, 29835}, {24927, 38030}, {26626, 38186}, {27186, 34611}, {27475, 29570}, {28082, 37548}, {29626, 32096}, {30147, 31792}, {30282, 40726}, {31993, 32943}, {32920, 35652}, {33165, 41310}, {33595, 38093}, {33596, 38122}, {34747, 38097}, {37727, 38108}, {37734, 38061}

X(42819) = midpoint of X(i) and X(j) for these {i, j}: {1, 1001}, {9, 42871}, {142, 30331}, {390, 5880}, {3243, 5220}, {3244, 24393}, {3884, 20116}, {10222, 31658}, {15254, 15570}
X(42819) = reflection of X(i) in X(j) for these (i, j): (3826, 1125), (15254, 1001), (15481, 15254), (15570, 1)
X(42819) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(42871)}} and {{A, B, C, X(7), X(45)}}
X(42819) = (anti-Aquila)-complement-of-X(142)
X(42819) = (2nd circumperp)-complement-of-X(11495)
X(42819) = (hexyl)-complement-of-X(11495)
X(42819) = X(1001)-of-anti-Aquila triangle
X(42819) = X(5480)-of-2nd circumperp triangle
X(42819) = X(15570)-of-5th mixtilinear triangle
X(42819) = X(15577)-of-incircle-circles triangle
X(42819) = X(15578)-of-Hutson intouch triangle
X(42819) = X(18382)-of-inverse-in-incircle triangle
X(42819) = X(35228)-of-intouch triangle
X(42819) = center of circle {{116, 3022, 3323}}
X(42819) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 9, 42871), (1, 405, 34791), (1, 984, 4864), (1, 1279, 1386), (1, 5259, 3555), (1, 5436, 12513), (1, 16484, 37), (1, 16487, 1449), (1, 16491, 16884), (1, 38316, 1001), (1, 42884, 5572), (55, 4666, 3742), (354, 1621, 4640), (1001, 15570, 15481), (1001, 42871, 9), (1621, 29817, 354), (3555, 5259, 5302), (3616, 8236, 2550), (3957, 5284, 210), (5239, 5240, 1212), (10389, 10582, 1376), (16484, 16503, 1001), (24331, 32941, 3739)

X(42820) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO ANTI-ARA

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42821)

X(42820) lies on these lines: {2, 32713}, {25, 32}, {13567, 19136}, {13575, 40413}

X(42820) = midpoint of X(25) and X(3162)
X(42820) = X(42821)-of-Ara triangle

X(42821) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-ARA TO ABC

Barycentrics    (SB+SC)*((48*R^6-8*R^2*SW^2+SW^3)*S^2+(4*R^2-SW)*((6*SA^2-6*SA*SW-8*SW^2)*R^2-(SA^2-SA*SW-SW^2)*SW)*SW)*SB*SC : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42820)

X(42821) lies on this line: {25, 32}

X(42821) = X(42820)-of-anti-Ara triangle

X(42822) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 1st ANTI-BROCARD

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42823)

X(42822) lies on these lines: {76, 18872}, {290, 325}, {524, 42844}, {9468, 40858}

X(42822) = X(42845)-of-1st anti-Brocard triangle
X(42822) = {X(3978), X(18829)}-harmonic conjugate of X(18896)

X(42823) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 1st ANTI-BROCARD TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42822)

X(42823) lies on this line: {115, 3978}

X(42823) = X(42844)-of-1st anti-Brocard triangle

X(42824) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 4th ANTI-BROCARD

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42825)

X(42824) lies on these lines: {23, 111}, {5913, 42008}

X(42825) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 4th ANTI-BROCARD TO ABC

Barycentrics    a^2*(a^16+20*(b^2+c^2)*a^14-(32*b^4+235*b^2*c^2+32*c^4)*a^12-2*(b^2+c^2)*(53*b^4-317*b^2*c^2+53*c^4)*a^10+(40*b^8+40*c^8+b^2*c^2*(529*b^4-2343*b^2*c^2+529*c^4))*a^8+2*(b^2+c^2)*(76*b^8+76*c^8-b^2*c^2*(659*b^4-1392*b^2*c^2+659*c^4))*a^6+(28*b^12+28*c^12-(525*b^8+525*c^8-b^2*c^2*(3075*b^4-5461*b^2*c^2+3075*c^4))*b^2*c^2)*a^4-2*(b^2+c^2)*(17*b^12+17*c^12-(204*b^8+204*c^8-b^2*c^2*(813*b^4-1253*b^2*c^2+813*c^4))*b^2*c^2)*a^2-(5*b^12+5*c^12+(3*b^8+3*c^8-b^2*c^2*(87*b^4-154*b^2*c^2+87*c^4))*b^2*c^2)*(b^2+c^2)^2) : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42824)

X(42825) lies on this line: {23, 111}

X(42826) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 5th ANTI-BROCARD

Barycentrics    a^4*(a^8-(b^4+c^4)*a^4-2*b^4*c^4) : :
X(42826) = X(315)-5*X(31267) = X(5017)+3*X(19153) = 3*X(9753)+X(36989)

The center of the reciprocal parallels-perspeconic of these triangles is X(42827)

X(42826) lies on these lines: {2, 4630}, {32, 206}, {66, 40416}, {182, 14574}, {315, 31267}, {511, 1658}, {1503, 20576}, {1691, 40373}, {5017, 19153}, {5116, 19575}, {6680, 6697}, {9753, 36989}, {13335, 34146}, {15577, 35431}, {34117, 35424}

X(42826) = midpoint of X(i) and X(j) for these {i, j}: {32, 206}, {15577, 35431}, {34117, 35424}
X(42826) = reflection of X(6697) in X(6680)
X(42826) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(3852)}} and {{A, B, C, X(66), X(8265)}}
X(42826) = X(42827)-of-5th Brocard triangle
X(42826) = X(42846)-of-5th anti-Brocard triangle

X(42827) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 5th ANTI-BROCARD TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42826)

X(42827) lies on these lines: {32, 206}, {2781, 39750}

X(42827) = X(42826)-of-5th anti-Brocard triangle

X(42828) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 2nd ANTI-CIRCUMPERP-TANGENTIAL

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42829)

X(42828) lies on this line: {56, 478}

X(42828) = midpoint of X(56) and X(478)
X(42828) = X(42851)-of-2nd anti-circumperp-tangential triangle

X(42829) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 2nd ANTI-CIRCUMPERP-TANGENTIAL TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42828)

X(42829) lies on this line: {56, 478}

X(42829) = X(42828)-of-2nd anti-circumperp-tangential triangle

X(42830) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO ANTI-EHRMANN-MID

Barycentrics    (a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*(a^8-7*(b^2+c^2)*a^6+(9*b^4+4*b^2*c^2+9*c^4)*a^4-(b^4-c^4)*(b^2-c^2)*a^2-2*(b^6-c^6)*(b^2-c^2)) : :
X(42830) = 3*X(381)-X(42831) = 3*X(381)-2*X(42853) = 5*X(5071)-X(36889) = 6*X(18552)-X(42831) = 3*X(18552)-X(42853)

The center of the reciprocal parallels-perspeconic of these triangles is X(42831)

X(42830) lies on these lines: {30, 182}, {381, 5158}, {5055, 30258}, {5071, 36889}, {14836, 18390}, {18388, 34288}

X(42830) = reflection of X(i) in X(j) for these (i, j): (381, 18552), (42831, 42853)
X(42830) = anticomplement of X(42853) w/r to these triangles: Euler, Johnson, X3-ABC reflections
X(42830) = X(42831)-of-Ehrmann-mid triangle
X(42830) = X(42853)-of-anti-Ehrmann-mid triangle
X(42830) = {X(381), X(42831)}-harmonic conjugate of X(42853)

X(42831) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-EHRMANN-MID TO ABC

Barycentrics    (a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*(11*a^8-14*(b^2+c^2)*a^6+8*b^2*c^2*a^4-2*(b^4-c^4)*(b^2-c^2)*a^2+(5*b^4+14*b^2*c^2+5*c^4)*(b^2-c^2)^2) : :
X(42831) = 5*X(381)-4*X(18552) = 3*X(381)-2*X(42830) = 3*X(381)-4*X(42853) = 6*X(18552)-5*X(42830) = 3*X(18552)-5*X(42853)

The center of the reciprocal parallels-perspeconic of these triangles is X(42830)

X(42831) lies on these lines: {30, 599}, {381, 5158}, {3543, 36889}, {3545, 33971}, {14269, 42350}

X(42831) = midpoint of X(3543) and X(36889)
X(42831) = reflection of X(42830) in X(42853)
X(42831) = anticomplement of X(42830) w/r to these triangles: Euler, Johnson, X3-ABC reflections
X(42831) = X(42830)-of-anti-Ehrmann-mid triangle
X(42831) = {X(42830), X(42853)}-harmonic conjugate of X(381)

X(42832) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-INNER-GREBE TO ABC

Barycentrics    a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2+4*S*(a^2+b^2+c^2)) : :
X(42832) = 3*X(5050)+X(11917) = 3*X(19053)+X(39875)

The center of the reciprocal parallels-perspeconic of these triangles is X(182)

X(42832) lies on these lines: {3, 6}, {542, 19053}, {1352, 7586}, {1503, 19116}, {1587, 19130}, {1588, 19091}, {3069, 24206}, {3589, 19117}, {3763, 13961}, {3818, 7584}, {5476, 36723}, {5965, 19095}, {6460, 29317}, {7581, 14561}, {7583, 13972}, {9541, 33751}, {10168, 19054}, {10519, 42523}, {11178, 32788}, {18510, 36990}, {19004, 38029}, {19052, 20301}

X(42832) = midpoint of X(6) and X(3312)
X(42832) = (anti-inner-Grebe)-isogonal conjugate-of- X(19063)
X(42832) = X(182)-of-anti-inner-Grebe triangle
X(42832) = X(42832)-of-circumsymmedial triangle
X(42832) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 182, 42833), (6, 5062, 5039), (6, 5085, 6417), (182, 576, 42858), (3311, 3312, 40243), (5039, 35426, 42833), (5050, 6501, 6), (7583, 13972, 38317)

X(42833) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-OUTER-GREBE TO ABC

Barycentrics    a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2-4*S*(a^2+b^2+c^2)) : :
X(42833) = 3*X(5050)+X(11916) = 3*X(19054)+X(39876)

The center of the reciprocal parallels-perspeconic of these triangles is X(182)

X(42833) lies on these lines: {3, 6}, {542, 19054}, {1352, 7585}, {1503, 19117}, {1587, 19092}, {1588, 19130}, {3068, 24206}, {3589, 19116}, {3763, 13903}, {3818, 7583}, {5476, 36726}, {5965, 19096}, {6459, 29317}, {7582, 14561}, {7584, 13910}, {10168, 19053}, {10519, 42522}, {11178, 32787}, {18512, 36990}, {19003, 38029}, {19051, 20301}

X(42833) = midpoint of X(6) and X(3311)
X(42833) = (anti-outer-Grebe)-isogonal conjugate-of- X(19064)
X(42833) = X(182)-of-anti-outer-Grebe triangle
X(42833) = X(42833)-of-circumsymmedial triangle
X(42833) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 182, 42832), (6, 5058, 5039), (6, 5085, 6418), (182, 576, 42859), (3311, 3312, 40244), (5039, 35426, 42832), (5050, 6500, 6), (7584, 13910, 38317)

X(42834) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO ANTI-MANDART-INCIRCLE

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42835)

X(42834) lies on these lines: {55, 2195}, {6690, 18214}, {13577, 40419}

X(42834) = midpoint of X(55) and X(5452)
X(42834) = reflection of X(18214) in X(6690)
X(42834) = X(42835)-of-Mandart-incircle triangle
X(42834) = X(42868)-of-anti-Mandart-incircle triangle

X(42835) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42834)

X(42835) lies on this line: {55, 2195}

X(42835) = X(42834)-of-anti-Mandart-incircle triangle

X(42836) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 6th ANTI-MIXTILINEAR TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(41385)

X(42836) lies on these lines: {3, 5139}, {68, 69}, {1368, 15261}, {7386, 15591}

X(42837) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-TANGENTIAL-MIDARC TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(41381)

X(42837) lies on these lines: {65, 42855}, {73, 3649}, {3664, 10106}, {5717, 14749}

X(42838) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO ANTI-3rd TRI-SQUARES-CENTRAL

Barycentrics    (S+a^2)*(-12*(b^2+c^2)*S+7*a^4-10*(b^2+c^2)*a^2+3*b^4-14*b^2*c^2+3*c^4) : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42839)

X(42838) lies on these lines: {2, 6568}, {488, 3068}, {1270, 32825}, {10007, 42840}

X(42838) = midpoint of X(3068) and X(33364)
X(42838) = X(42839)-of-3rd tri-squares-central triangle
X(42838) = X(42882)-of-anti-3rd tri-squares-central triangle

X(42839) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-3rd TRI-SQUARES-CENTRAL TO ABC

Barycentrics    (S+a^2)*(-(15*a^4+6*(b^2+c^2)*a^2-22*b^2*c^2-13*c^4-13*b^4)*S+6*a^6-22*(b^2+c^2)*a^4+2*(3*b^2+4*b*c+3*c^2)*(3*b^2-4*b*c+3*c^2)*a^2+2*(4*b^2*c^2-(b^2-c^2)^2)*(b^2+c^2)) : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42838)

X(42839) lies on this line: {488, 3068}

X(42839) = X(42838)-of-anti-3rd tri-squares-central triangle

X(42840) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO ANTI-4th TRI-SQUARES-CENTRAL

Barycentrics    (S-a^2)*(12*(b^2+c^2)*S+7*a^4-10*(b^2+c^2)*a^2+3*b^4-14*b^2*c^2+3*c^4) : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42841)

X(42840) lies on these lines: {2, 6569}, {487, 3069}, {1271, 32825}, {10007, 42838}

X(42840) = midpoint of X(3069) and X(33365)
X(42840) = X(42841)-of-4th tri-squares-central triangle

X(42841) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-4th TRI-SQUARES-CENTRAL TO ABC

Barycentrics    (S-a^2)*((15*a^4+6*(b^2+c^2)*a^2-13*b^4-13*c^4-22*b^2*c^2)*S+6*a^6-22*(b^2+c^2)*a^4+2*(3*b^2+4*b*c+3*c^2)*(3*b^2-4*b*c+3*c^2)*a^2+2*(4*b^2*c^2-(b^2-c^2)^2)*(b^2+c^2)) : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42840)

X(42841) lies on this line: {487, 3069}

X(42842) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-INNER-YFF TO ABC

Barycentrics    a*(a^5-2*(b+c)*a^4+2*b*c*a^3+2*(b^2-c^2)*(b-c)*a^2-(b^2+c^2)*(b^2-4*b*c+c^2)*a-2*(b^2-c^2)*(b-c)*b*c) : :
X(42842) = 3*X(1001)+X(12513) = X(6600)-3*X(38031) = X(11523)-9*X(38316) = 2*X(12513)+3*X(42843)

The center of the reciprocal parallels-perspeconic of these triangles is X(1001)

X(42842) lies on these lines: {1, 6}, {2, 33925}, {3, 528}, {7, 26437}, {21, 11240}, {55, 26015}, {56, 5880}, {63, 18839}, {105, 26258}, {390, 4189}, {404, 2550}, {497, 1005}, {516, 5450}, {519, 6883}, {527, 3560}, {529, 6913}, {999, 25557}, {1004, 31140}, {1006, 34625}, {1012, 5735}, {1319, 5784}, {1376, 2078}, {1385, 15733}, {1388, 42014}, {1617, 2886}, {1621, 24477}, {1890, 26377}, {2801, 40257}, {2975, 5698}, {3058, 20835}, {3254, 15446}, {3304, 37228}, {3434, 36003}, {3651, 12116}, {3740, 25893}, {3826, 6691}, {3829, 19541}, {3897, 7671}, {3913, 34486}, {4428, 31146}, {4861, 37787}, {5047, 38025}, {5248, 40270}, {5284, 25568}, {5428, 32214}, {5445, 5687}, {5563, 6173}, {5695, 20881}, {5696, 21842}, {5852, 12001}, {5853, 6684}, {5855, 6767}, {5857, 20330}, {6067, 10949}, {6600, 16202}, {6601, 10806}, {6734, 11510}, {6912, 34610}, {6933, 26481}, {6985, 24387}, {7580, 11235}, {7742, 24390}, {8071, 41555}, {8167, 20196}, {8545, 22759}, {9708, 38455}, {9710, 16410}, {10074, 25558}, {10198, 16853}, {10532, 38037}, {10587, 17570}, {10680, 13743}, {11012, 11495}, {11108, 12607}, {11269, 30979}, {11344, 37722}, {12114, 15726}, {13279, 30332}, {15621, 16434}, {15931, 24392}, {17572, 38092}, {18613, 25514}, {19537, 36152}, {22769, 31394}, {22770, 38454}, {26332, 42356}, {29676, 36528}, {34606, 38060}, {34612, 37309}

X(42842) = midpoint of X(11260) and X(15254)
X(42842) = reflection of X(42843) in X(1001)
X(42842) = X(5880)-of-2nd circumperp tangential triangle
X(42842) = X(34117)-of-2nd circumperp triangle
X(42842) = X(42843)-of-outer-Yff tangents triangle
X(42842) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (958, 1001, 15254), (1001, 42871, 954), (1001, 42886, 1), (2078, 5231, 1376), (31140, 41341, 1004)

X(42843) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ANTI-OUTER-YFF TO ABC

Barycentrics    a*(a^5-2*(b+c)*a^4+2*b*c*a^3+2*(b+c)*(b^2+c^2)*a^2-(b^2+c^2)^2*a-2*(b^2-c^2)*(b-c)*b*c) : :
X(42843) = 5*X(1001)-X(12513) = 2*X(12513)-5*X(42842)

The center of the reciprocal parallels-perspeconic of these triangles is X(1001)

X(42843) lies on these lines: {1, 6}, {3, 17768}, {7, 1470}, {55, 908}, {56, 41572}, {119, 381}, {390, 5046}, {404, 16133}, {474, 37701}, {480, 6735}, {516, 6796}, {527, 10269}, {758, 6883}, {1012, 6326}, {1259, 5832}, {1260, 2886}, {1284, 36741}, {1376, 3256}, {1445, 18838}, {1486, 15507}, {1621, 25568}, {1890, 26378}, {2077, 11495}, {2318, 25885}, {2346, 11239}, {2476, 2550}, {3035, 37541}, {3255, 15175}, {3295, 12607}, {3303, 32049}, {3428, 34647}, {3560, 20117}, {3649, 37282}, {3685, 20927}, {3742, 25893}, {3826, 6668}, {3871, 5225}, {3913, 5587}, {4428, 31142}, {4511, 29007}, {4571, 30741}, {5263, 27254}, {5284, 24477}, {5440, 17668}, {5554, 38057}, {5660, 13205}, {5687, 7951}, {5695, 20236}, {5698, 20846}, {5720, 11496}, {5727, 32537}, {5852, 16203}, {5853, 10915}, {5855, 9708}, {5856, 11729}, {5880, 11509}, {5905, 37578}, {6601, 10596}, {6767, 38455}, {6990, 10531}, {7082, 16465}, {7677, 41563}, {8069, 41548}, {8167, 31249}, {8715, 18483}, {10267, 21077}, {11246, 37309}, {11281, 37244}, {11415, 37601}, {11502, 30852}, {11517, 12047}, {12329, 31394}, {12531, 12648}, {15931, 28609}, {16143, 37022}, {16371, 35204}, {31658, 34339}

X(42843) = reflection of X(42842) in X(1001)
X(42843) = X(42842)-of-inner-Yff tangents triangle
X(42843) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1001, 42871, 42884), (1001, 42885, 1)

X(42844) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 1st BROCARD

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42845)

X(42844) lies on these lines: {141, 308}, {524, 42822}, {5104, 41073}, {9468, 25054}

X(42844) = X(42823)-of-1st Brocard triangle
X(42844) = {X(670), X(694)}-harmonic conjugate of X(18896)

X(42845) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 1st BROCARD TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42844)

X(42845) lies on this line: {115, 694}

X(42845) = X(42822)-of-1st Brocard triangle

X(42846) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 5th BROCARD TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42826)

X(42846) lies on this line: {32, 206}

X(42846) = X(42826)-of-5th Brocard triangle

X(42847) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 8th BROCARD

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42848)

X(42847) lies on these lines: {3, 512}, {184, 216}

X(42847) = X(3)-Daleth conjugate of-X(512)

X(42848) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 8th BROCARD TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42847)

X(42848) lies on this line: {187, 237}

X(42849) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO CIRCUMMEDIAL

Barycentrics    a^4+11*(b^2+c^2)*a^2-2*b^4+8*b^2*c^2-2*c^4 : :
X(42849) = 5*X(2)-X(15589) = 7*X(2)-2*X(15598) = 2*X(7736)+X(15271) = X(7736)+2*X(15491) = 5*X(7736)+X(15589) = 7*X(7736)+2*X(15598) = 3*X(7736)+X(42850) = X(15271)-4*X(15491) = 5*X(15271)-2*X(15589) = 7*X(15271)-4*X(15598) = 3*X(15271)-2*X(42850) = 2*X(15482)+X(15484) = 10*X(15491)-X(15589) = 7*X(15491)-X(15598) = 6*X(15491)-X(42850) = 7*X(15589)-10*X(15598) = 3*X(15589)-5*X(42850) = 6*X(15598)-7*X(42850)

The center of the reciprocal parallels-perspeconic of these triangles is X(42850)

X(42849) lies on these lines: {2, 6}, {39, 34505}, {98, 8787}, {114, 5055}, {126, 6094}, {381, 11171}, {384, 31492}, {543, 5024}, {549, 37809}, {574, 11159}, {598, 11155}, {620, 14535}, {671, 2023}, {1384, 5569}, {1506, 11318}, {1513, 38072}, {1634, 9172}, {1656, 7817}, {2021, 11287}, {2080, 5054}, {2482, 11286}, {2548, 8359}, {2549, 3363}, {3524, 14494}, {3734, 11165}, {3849, 15482}, {4045, 8176}, {5013, 8370}, {5050, 6055}, {5070, 7829}, {5077, 5475}, {5079, 7902}, {5094, 10162}, {5476, 40248}, {6054, 10516}, {6683, 7775}, {7615, 15048}, {7622, 7804}, {7745, 33215}, {7769, 8366}, {7786, 7841}, {7790, 18584}, {7801, 9698}, {7808, 31467}, {7812, 11285}, {7827, 13881}, {8182, 18907}, {8357, 31417}, {8367, 31406}, {8369, 31401}, {9606, 32968}, {9607, 32987}, {9756, 11179}, {10011, 38079}, {10153, 11669}, {10717, 15302}, {13191, 34226}, {15815, 33007}, {16924, 22332}, {19661, 21843}, {19662, 25486}, {20423, 37451}, {22331, 33001}, {24239, 41313}, {30435, 34506}, {31404, 33190}, {31407, 32960}, {31415, 37350}

X(42849) = midpoint of X(2) and X(7736)
X(42849) = reflection of X(i) in X(j) for these (i, j): (2, 15491), (15271, 2)
X(42849) = complement of X(42850)
X(42849) = intersection, other than A,B,C, of conics {{A, B, C, X(69), X(13377)}} and {{A, B, C, X(83), X(7610)}}
X(42849) = complement of X(42850) w/r to these triangles: anti-Artzt, 1st anti-Brocard, anti-McCay, anticomplementary, Artzt, 1st Brocard-reflected, 1st Brocard, inner-Fermat, outer-Fermat, 1st half-diamonds, 2nd half-diamonds, 1st half-squares, 2nd half-squares, inverse-in-excircles, McCay, medial, 1st Neuberg, 2nd Neuberg, inner-Vecten, outer-Vecten
X(42849) = center of circle {{2, 7736, 34235}}
X(42849) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6, 7610), (2, 325, 21358), (2, 1992, 11168), (2, 3815, 11184), (2, 5032, 34229), (2, 7735, 15597), (2, 9300, 8667), (2, 9770, 141), (2, 11163, 599), (2, 11184, 7778), (2, 41136, 16986), (2, 41624, 8556), (599, 11163, 9766), (1992, 11168, 8667), (3589, 9771, 2), (7736, 15491, 15271), (8367, 31406, 34511), (9300, 11168, 1992)

X(42850) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: CIRCUMMEDIAL TO ABC

Barycentrics    5*a^4-8*(b^2+c^2)*a^2-b^4-c^4-14*b^2*c^2 : :
X(42850) = 5*X(2)-4*X(15491) = X(2)+4*X(15598) = X(7736)-4*X(15271) = 5*X(7736)-8*X(15491) = X(7736)+2*X(15589) = X(7736)+8*X(15598) = 3*X(7736)-4*X(42849) = 5*X(15271)-2*X(15491) = 2*X(15271)+X(15589) = X(15271)+2*X(15598) = 3*X(15271)-X(42849) = 4*X(15491)+5*X(15589) = X(15491)+5*X(15598) = 6*X(15491)-5*X(42849) = X(15589)-4*X(15598) = 3*X(15589)+2*X(42849) = 6*X(15598)+X(42849)

The center of the reciprocal parallels-perspeconic of these triangles is X(42849)

X(42850) lies on these lines: {2, 6}, {4, 7810}, {76, 11172}, {98, 2482}, {376, 9466}, {574, 9741}, {631, 7801}, {671, 32986}, {1078, 32985}, {2549, 5485}, {2896, 33006}, {3090, 7854}, {3363, 23334}, {3525, 7794}, {3528, 17130}, {3545, 31173}, {3734, 8182}, {3767, 33230}, {3785, 8370}, {3855, 7873}, {5071, 7818}, {5077, 7620}, {5461, 7865}, {5642, 9769}, {5976, 8591}, {5984, 10488}, {7493, 9829}, {7615, 7761}, {7618, 32817}, {7619, 7908}, {7710, 11180}, {7738, 8359}, {7751, 32960}, {7768, 32975}, {7780, 16045}, {7795, 34506}, {7800, 7861}, {7811, 32983}, {7812, 32968}, {7815, 34511}, {7817, 32956}, {7835, 10302}, {7841, 32828}, {7848, 8176}, {7849, 32955}, {7869, 32959}, {7879, 32838}, {7883, 32832}, {7904, 33192}, {7922, 32976}, {8716, 32869}, {9772, 11177}, {9774, 39874}, {9939, 16924}, {9993, 41106}, {10033, 15682}, {10717, 25051}, {11179, 15819}, {11284, 33977}, {14023, 32957}, {14033, 39266}, {14039, 37809}, {17128, 33208}, {17968, 37863}, {18840, 33197}, {30532, 41916}, {31168, 33223}, {31276, 33007}, {32006, 33013}, {32815, 35955}, {32822, 34504}, {32834, 34505}, {32885, 33228}, {32893, 33210}

X(42850) = midpoint of X(2) and X(15589)
X(42850) = reflection of X(i) in X(j) for these (i, j): (2, 15271), (7736, 2)
X(42850) = anticomplement of X(42849)
X(42850) = intersection, other than A,B,C, of conics {{A, B, C, X(6), X(11172)}} and {{A, B, C, X(76), X(9770)}}
X(42850) = anticomplement of X(42849) w/r to these triangles: anti-Artzt, 1st anti-Brocard, anti-McCay, anticomplementary, Artzt, 1st Brocard-reflected, 1st Brocard, inner-Fermat, outer-Fermat, 1st half-diamonds, 2nd half-diamonds, 1st half-squares, 2nd half-squares, inverse-in-excircles, McCay, medial, 1st Neuberg, 2nd Neuberg, inner-Vecten, outer-Vecten
X(42850) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 69, 9770), (2, 5032, 11174), (2, 9740, 6), (2, 11160, 11163), (2, 16990, 21356), (2, 37668, 11184), (141, 7610, 2), (230, 21358, 2), (599, 8556, 11168), (599, 11168, 2), (3620, 37688, 37690), (7778, 15597, 2), (7883, 32832, 32984), (8859, 16986, 2), (11163, 37671, 11160), (11184, 22165, 37668), (15271, 15589, 7736), (15271, 15598, 15589), (21356, 34229, 2)

X(42851) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 2nd CIRCUMPERP TANGENTIAL TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42828)

X(42851) lies on these lines: {56, 478}, {3827, 24928}

X(42851) = X(42828)-of-2nd circumperp tangential triangle

X(42852) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO CIRCUMSYMMEDIAL

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42852)

X(42852) lies on these lines: {3, 6}, {99, 14482}, {111, 11175}, {352, 15302}, {524, 15482}, {542, 7736}, {597, 3734}, {1383, 35268}, {3506, 39689}, {3619, 7909}, {3815, 11178}, {5182, 14931}, {5286, 25555}, {5304, 38064}, {5476, 15048}, {7735, 10168}, {8541, 30534}, {8744, 19124}, {9465, 22111}, {11166, 39389}, {11179, 37665}, {11580, 22112}, {11645, 15484}, {20481, 40130}, {31400, 40107}, {31406, 34507}, {34986, 39951}

X(42852) = midpoint of X(6) and X(5024)
X(42852) = intersection, other than A,B,C, of conics {{A, B, C, X(111), X(5039)}} and {{A, B, C, X(187), X(11175)}}
X(42852) = X(42852)-of-circumsymmedial triangle
X(42852) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 187, 5039), (6, 5013, 11173), (6, 5085, 21309), (5050, 22246, 6), (5085, 21309, 38010), (38011, 38012, 182)

X(42853) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: EHRMANN-MID TO ABC

Barycentrics    (a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*(10*a^8-7*(b^2+c^2)*a^6-(9*b^4-4*b^2*c^2+9*c^4)*a^4-(b^4-c^4)*(b^2-c^2)*a^2+(7*b^4+16*b^2*c^2+7*c^4)*(b^2-c^2)^2) : :
X(42853) = 3*X(381)-X(42830) = 3*X(381)+X(42831) = 3*X(18552)-2*X(42830) = 3*X(18552)+2*X(42831)

The center of the reciprocal parallels-perspeconic of these triangles is X(42830)

X(42853) lies on these lines: {30, 14810}, {381, 5158}, {3839, 39530}

X(42853) = midpoint of X(42830) and X(42831)
X(42853) = reflection of X(18552) in X(381)
X(42853) = complement of X(42830) w/r to these triangles: Euler, Johnson, X3-ABC reflections
X(42853) = X(42830)-of-Ehrmann-mid triangle
X(42853) = {X(381), X(42831)}-harmonic conjugate of X(42830)

X(42854) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: EULER TO ABC

Barycentrics    (3*a^8-(b^2+c^2)*a^6-(3*b^4-2*b^2*c^2+3*c^4)*a^4-3*(b^4-c^4)*(b^2-c^2)*a^2+4*(b^6-c^6)*(b^2-c^2))*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
X(42854) = 3*X(4)+X(1249) = 5*X(4)+X(15258) = 2*X(4)+X(15274) = 4*X(4)+X(15576) = 7*X(4)+X(41374) = X(253)-9*X(3839) = 3*X(381)-X(20208) = X(1249)-3*X(10002) = 5*X(1249)-3*X(15258) = 2*X(1249)-3*X(15274) = 4*X(1249)-3*X(15576) = 7*X(1249)-3*X(41374) = 5*X(10002)-X(15258) = 4*X(10002)-X(15576) = 7*X(10002)-X(41374) = 2*X(15258)-5*X(15274) = 4*X(15258)-5*X(15576) = 7*X(15258)-5*X(41374) = 7*X(15274)-2*X(41374) = 7*X(15576)-4*X(41374)

The center of the reciprocal parallels-perspeconic of these triangles is X(10002)

X(42854) lies on these lines: {4, 6}, {30, 20204}, {127, 133}, {132, 9756}, {253, 3839}, {382, 39569}, {458, 6330}, {546, 15312}, {1596, 15594}, {3545, 20200}, {3830, 23347}, {3843, 39530}, {5667, 10606}, {6525, 23332}, {10151, 16312}, {13481, 35908}, {14165, 41424}, {14918, 33586}, {20299, 42457}, {23324, 36876}, {33924, 34186}, {36794, 38072}

X(42854) = midpoint of X(4) and X(10002)
X(42854) = reflection of X(i) in X(j) for these (i, j): (15274, 10002), (15576, 15274)
X(42854) = complement of X(20208) w/r to these triangles: Euler, Johnson, X3-ABC reflections
X(42854) = X(10002)-of-Euler triangle
X(42854) = X(20208)-of-Ehrmann-mid triangle
X(42854) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 6530, 36990), (4, 41372, 18405), (4, 41375, 34775), (53, 42874, 4)

X(42855) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: EXTANGENTS TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(41381)

X(42855) lies on these lines: {65, 42837}, {71, 594}

X(42856) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 2nd EXTOUCH

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42857)

X(42856) lies on these lines: {1, 8750}, {4, 4644}, {6, 19}, {33, 1430}, {57, 3192}, {58, 30733}, {208, 30493}, {320, 17555}, {354, 3195}, {518, 23050}, {942, 36103}, {969, 5738}, {1712, 5728}, {1861, 3751}, {1892, 17365}, {3758, 11109}, {7079, 17750}, {11393, 41011}, {24989, 32859}

X(42857) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 2nd EXTOUCH TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42856)

X(42857) lies on these lines: {4, 3827}, {222, 226}

X(42857) = X(37864)-of-2nd extouch triangle

X(42858) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: INNER-GREBE TO ABC

Barycentrics    a^2*((a^4-(b^2+c^2)*a^2-2*b^2*c^2)*S-(a^2+b^2+c^2)*((b^2+c^2)*a^2-b^4-c^4)) : :
X(42858) = X(1160)-3*X(5085) = 3*X(5861)+X(39887) = 2*X(9739)-3*X(17508)

The center of the reciprocal parallels-perspeconic of these triangles is X(182)

X(42858) lies on these lines: {3, 6}, {542, 5861}, {1271, 1352}, {1503, 5875}, {3818, 6215}, {5591, 24206}, {5871, 6275}, {5965, 6277}, {6202, 19130}, {7375, 14561}, {11645, 36734}, {20423, 26620}, {26336, 36990}

X(42858) = midpoint of X(6) and X(1161)
X(42858) = reflection of X(i) in X(j) for these (i, j): (3098, 9738), (9733, 5092), (42859, 182)
X(42858) = (inner-Grebe)-isogonal conjugate-of- X(22699)
X(42858) = X(182)-of-inner-Grebe triangle
X(42858) = X(42858)-of-circumsymmedial triangle
X(42858) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (182, 576, 42832), (1161, 26341, 40268), (5171, 9738, 12974), (26341, 40268, 9733)

X(42859) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: OUTER-GREBE TO ABC

Barycentrics    a^2*((a^4-(b^2+c^2)*a^2-2*b^2*c^2)*S+(a^2+b^2+c^2)*((b^2+c^2)*a^2-b^4-c^4)) : :
X(42859) = X(1161)-3*X(5085) = 3*X(5860)+X(39888) = 2*X(9738)-3*X(17508)

The center of the reciprocal parallels-perspeconic of these triangles is X(182)

X(42859) lies on these lines: {3, 6}, {542, 5860}, {1270, 1352}, {1503, 5874}, {3818, 6214}, {5590, 24206}, {5870, 6274}, {5965, 6276}, {6201, 19130}, {7376, 14561}, {11645, 36718}, {20423, 26619}, {26346, 36990}

X(42859) = midpoint of X(6) and X(1160)
X(42859) = reflection of X(i) in X(j) for these (i, j): (3098, 9739), (9732, 5092), (42858, 182)
X(42859) = (outer-Grebe)-isogonal conjugate-of- X(22700)
X(42859) = X(182)-of-outer-Grebe triangle
X(42859) = X(42859)-of-circumsymmedial triangle
X(42859) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (182, 576, 42833), (1160, 26348, 40268), (5171, 9739, 12975), (26348, 40268, 9732)

X(42860) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO HUTSON INTOUCH

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42861)

X(42860) lies on these lines: {9, 3057}, {3306, 31343}, {12053, 42861}, {14923, 27834}

X(42861) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: HUTSON INTOUCH TO ABC

Barycentrics    (-a+b+c)*(a^8+2*(b+c)*a^7-8*(2*b^2+3*b*c+2*c^2)*a^6-2*(b+c)*(b^2-42*b*c+c^2)*a^5+2*(15*b^4+15*c^4-2*b*c*(9*b^2+41*b*c+9*c^2))*a^4-2*(b+c)*(b^4+c^4+2*b*c*(5*b-2*c)*(2*b-5*c))*a^3-16*(b^2-3*b*c+c^2)*(b^2-b*c+c^2)*(b-c)^2*a^2+2*(b^2-c^2)*(b-c)^5*a+(b^2-c^2)^2*(b-c)^4) : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42860)

X(42861) lies on these lines: {8, 1229}, {12053, 42860}

X(42861) = reflection of X(8) in X(42887)
X(42861) = X(33584)-of-Hutson intouch triangle

X(42862) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: JOHNSON TO ABC

Barycentrics    ((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^8-(3*b^4+b^2*c^2+3*c^4)*a^4+2*(b^4-c^4)*(b^2-c^2)*a^2+3*(b^2-c^2)^2*b^2*c^2) : :
X(42862) = 3*X(5)-X(216) = X(20)-5*X(40329) = 2*X(216)-3*X(10003) = X(216)+3*X(39530) = X(264)+3*X(381) = 5*X(1656)-X(42329) = 5*X(3091)-X(30258) = 15*X(3091)+X(40896) = X(3164)-9*X(3545) = X(10003)+2*X(39530) = 3*X(30258)+X(40896)

The center of the reciprocal parallels-perspeconic of these triangles is X(10003)

X(42862) lies on these lines: {5, 53}, {20, 40329}, {30, 14767}, {264, 339}, {418, 10184}, {511, 546}, {1656, 42329}, {2790, 34845}, {3091, 30258}, {3164, 3545}, {9996, 11818}, {11197, 30506}, {13391, 42487}

X(42862) = midpoint of X(5) and X(39530)
X(42862) = reflection of X(10003) in X(5)
X(42862) = X(10003)-of-Johnson triangle

X(42863) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: INNER-JOHNSON TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(10006)

X(42863) lies on these lines: {11, 1566}, {10584, 11124}

X(42863) = X(10006)-of-inner-Johnson triangle

X(42864) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 1st KENMOTU-FREE-VERTICES

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42865)

X(42864) lies on these lines: {32, 6402}, {372, 1147}, {10003, 42866}

X(42864) = midpoint of X(372) and X(10960)
X(42864) = X(42865)-of-anti-1st Kenmotu-free-vertices triangle

X(42865) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 1st KENMOTU-FREE-VERTICES TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42864)

X(42865) lies on this line: {372, 1147}

X(42865) = X(42864)-of-1st Kenmotu-free-vertices triangle

X(42866) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 2nd KENMOTU-FREE-VERTICES

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42867)

X(42866) lies on these lines: {32, 6401}, {371, 1147}, {10003, 42864}

X(42866) = midpoint of X(371) and X(10962)

X(42867) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 2nd KENMOTU-FREE-VERTICES TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42866)

X(42867) lies on this line: {371, 1147}

X(42867) = X(42866)-of-2nd Kenmotu-free-vertices triangle

X(42868) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: MANDART-INCIRCLE TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42834)

X(42868) lies on this line: {55, 2195}

X(42868) = X(42834)-of-Mandart-incircle triangle

X(42869) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 4th MIXTILINEAR

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42870)

X(42869) lies on these lines: {6, 13404}, {4845, 6767}, {4907, 10389}

X(42870) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 4th MIXTILINEAR TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42869)

X(42870) lies on these lines: {573, 6244}, {4640, 15733}

X(42871) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 5th MIXTILINEAR TO ABC

Barycentrics    a*(a^2-3*(b+c)*a+2*c^2-2*b*c+2*b^2) : :
X(42871) = 3*X(1)-X(9) = 4*X(1)-X(5220) = 5*X(1)-X(5223) = 5*X(1)-2*X(15254) = 7*X(1)-2*X(15481) = 5*X(1)-3*X(38316) = 3*X(1)-2*X(42819) = 2*X(9)-3*X(1001) = X(9)+3*X(3243) = 4*X(9)-3*X(5220) = 5*X(9)-3*X(5223) = 5*X(9)-6*X(15254) = 7*X(9)-6*X(15481) = X(9)-6*X(15570) = 5*X(9)-9*X(38316) = X(1001)+2*X(3243) = 5*X(1001)-2*X(5223) = 5*X(1001)-4*X(15254) = 7*X(1001)-4*X(15481) = X(1001)-4*X(15570) = 5*X(1001)-6*X(38316) = 3*X(1001)-4*X(42819)

The center of the reciprocal parallels-perspeconic of these triangles is X(1001)

X(42871) lies on these lines: {1, 6}, {2, 3711}, {3, 3881}, {7, 528}, {8, 3826}, {10, 17265}, {42, 17597}, {55, 3218}, {56, 3889}, {57, 4421}, {63, 3748}, {65, 3895}, {78, 17609}, {86, 36534}, {100, 4860}, {141, 36479}, {142, 519}, {145, 2550}, {192, 24841}, {200, 3742}, {210, 4666}, {214, 999}, {226, 11235}, {239, 27475}, {335, 20162}, {354, 1376}, {390, 2098}, {480, 4511}, {516, 1482}, {517, 11495}, {527, 30331}, {529, 3488}, {537, 17262}, {551, 3940}, {599, 33076}, {612, 4883}, {673, 4393}, {758, 4068}, {938, 5828}, {940, 3938}, {942, 3913}, {952, 20330}, {971, 10222}, {982, 3979}, {997, 5049}, {1002, 1280}, {1056, 6601}, {1125, 24393}, {1150, 17145}, {1159, 2802}, {1319, 1445}, {1388, 7677}, {1478, 12690}, {1621, 4430}, {1890, 11396}, {1953, 5781}, {2136, 10107}, {2177, 17449}, {2320, 2346}, {2334, 5262}, {2650, 37542}, {2801, 10247}, {2886, 3475}, {2951, 11224}, {2999, 4906}, {3036, 18391}, {3052, 17715}, {3057, 7675}, {3058, 5905}, {3059, 3872}, {3158, 10980}, {3174, 3880}, {3189, 11037}, {3240, 3315}, {3244, 4780}, {3254, 7972}, {3295, 3874}, {3303, 3868}, {3304, 34772}, {3340, 4321}, {3416, 4684}, {3487, 3813}, {3586, 34739}, {3616, 17352}, {3621, 40333}, {3622, 5686}, {3624, 36946}, {3625, 38204}, {3632, 38200}, {3633, 4716}, {3656, 31672}, {3679, 17231}, {3681, 4423}, {3699, 30947}, {3715, 4661}, {3722, 37540}, {3729, 4702}, {3740, 10582}, {3753, 8168}, {3763, 29659}, {3781, 9049}, {3811, 5045}, {3812, 6765}, {3816, 5328}, {3829, 5226}, {3838, 24392}, {3848, 8580}, {3871, 5221}, {3877, 8162}, {3912, 38186}, {3935, 4413}, {3961, 37674}, {3976, 4255}, {4015, 16853}, {4085, 17290}, {4304, 34620}, {4312, 11009}, {4326, 7962}, {4342, 15006}, {4363, 32941}, {4387, 4942}, {4585, 42014}, {4640, 10389}, {4650, 21000}, {4660, 7232}, {4677, 38093}, {4775, 28910}, {4849, 5272}, {4861, 28965}, {4863, 5249}, {4880, 16558}, {4900, 10390}, {4941, 24397}, {5048, 14100}, {5083, 13205}, {5119, 24473}, {5208, 18185}, {5219, 31146}, {5252, 21617}, {5425, 6173}, {5437, 30350}, {5440, 40726}, {5528, 12653}, {5534, 13374}, {5541, 5902}, {5603, 42356}, {5687, 18398}, {5695, 24349}, {5698, 5852}, {5708, 8715}, {5722, 11236}, {5732, 7982}, {5734, 36991}, {5737, 29651}, {5784, 36846}, {5805, 37727}, {5836, 11518}, {5851, 10698}, {5854, 11041}, {5856, 12735}, {5881, 38150}, {6006, 23345}, {6009, 21343}, {6690, 10578}, {6738, 32049}, {6764, 28629}, {7171, 12675}, {7373, 20116}, {7967, 38454}, {7994, 10178}, {8227, 38154}, {8581, 11011}, {9041, 17243}, {9957, 12559}, {9965, 10385}, {10072, 38211}, {10246, 23344}, {10306, 12005}, {10427, 25416}, {10587, 21677}, {10595, 38037}, {10679, 12515}, {11194, 24929}, {11238, 31053}, {11239, 40663}, {11240, 15950}, {11246, 20075}, {11269, 17724}, {11552, 34719}, {12001, 37733}, {12437, 12577}, {12563, 21627}, {12647, 41555}, {12649, 15888}, {15178, 31658}, {15668, 36480}, {15726, 16200}, {16593, 17316}, {17018, 17599}, {17118, 31178}, {17135, 31006}, {17259, 24331}, {17267, 33165}, {17311, 32847}, {17314, 28503}, {17463, 31395}, {17483, 34611}, {17594, 21342}, {17598, 42042}, {17718, 26015}, {17783, 29662}, {18230, 38314}, {18482, 28204}, {18613, 20760}, {19862, 38210}, {20015, 26040}, {20049, 38092}, {20533, 29588}, {20872, 22769}, {21454, 34607}, {24475, 37622}, {25439, 36279}, {25716, 42309}, {27484, 29570}, {29675, 31187}, {29820, 37679}, {29835, 33122}, {29843, 33126}, {30628, 38460}, {30811, 33120}, {30825, 31038}, {31019, 31140}, {31397, 41573}, {32920, 42057}, {34747, 38024}, {37624, 38031}, {38055, 41548}

X(42871) = midpoint of X(i) and X(j) for these {i, j}: {1, 3243}, {145, 2550}, {3244, 5542}, {3254, 7972}, {5528, 12653}, {5732, 7982}, {5805, 37727}, {10427, 25416}
X(42871) = reflection of X(i) in X(j) for these (i, j): (1, 15570), (8, 3826), (9, 42819), (1001, 1), (2550, 25557), (5220, 1001), (5223, 15254), (5880, 5542), (24393, 1125), (31658, 15178)
X(42871) = barycentric product X(72)*X(31923)
X(42871) = trilinear product X(71)*X(31923)
X(42871) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(32015)}} and {{A, B, C, X(2), X(42819)}}
X(42871) = (anti-Aquila)-anticomplement-of-X(6666)
X(42871) = X(1001)-of-5th mixtilinear triangle
X(42871) = X(3243)-of-anti-Aquila triangle
X(42871) = X(5480)-of-excenters-reflections triangle
X(42871) = X(7672)-of-2nd circumperp tangential triangle
X(42871) = X(15570)-of-Aquila triangle
X(42871) = X(36990)-of-2nd circumperp triangle
X(42871) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 9, 42819), (1, 1743, 35227), (1, 3555, 958), (1, 3751, 1279), (1, 4649, 38315), (1, 5223, 38316), (1, 7174, 15569), (1, 16496, 37), (1, 18412, 42884), (1, 34791, 12513), (1, 41863, 960), (9, 42819, 1001), (954, 42842, 1001), (1743, 35227, 3246), (3243, 15570, 1001), (3475, 36845, 2886), (3873, 3957, 55), (4661, 5284, 3715), (5223, 38316, 15254), (5239, 5240, 220), (10578, 24477, 6690), (10580, 25568, 3816), (15254, 38316, 1001), (17715, 32913, 3052), (42843, 42884, 1001), (42885, 42886, 1001)

X(42872) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 6th MIXTILINEAR

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

X(42872) lies on these lines: {1, 972}, {4, 3062}, {57, 7955}, {189, 10405}, {942, 3345}, {1214, 40069}, {2184, 19605}, {3306, 36100}

X(42872) = barycentric product X(i)*X(j) for these {i, j}: {40, 36620}, {223, 10405}, {347, 3062}
X(42872) = barycentric quotient X(i)/X(j) for these (i, j): (221, 165), (223, 144), (227, 21060), (347, 16284)
X(42872) = trilinear product X(i)*X(j) for these {i, j}: {198, 36620}, {221, 10405}, {223, 3062}, {347, 11051}
X(42872) = trilinear quotient X(i)/X(j) for these (i, j): (221, 3207), (223, 165), (227, 21872), (347, 144)
X(42872) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(14837)}} and {{A, B, C, X(4), X(40)}}
X(42872) = X(i)-isoconjugate-of-X(j) for these {i, j}: {144, 2192}, {165, 282}, {280, 3207}, {285, 21872}
X(42872) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (221, 165), (223, 144), (227, 21060), (347, 16284)
X(42872) = X(42836)-of-6th mixtilinear triangle

X(42873) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO ORTHIC AXES

Barycentrics    (2*a^8-7*(b^2+c^2)*a^6+(7*b^4+4*b^2*c^2+7*c^4)*a^4-(b^4-c^4)*(b^2-c^2)*a^2-(b^4+c^4)*(b^2-c^2)^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
X(42873) = 5*X(4)-6*X(42874)

The center of the reciprocal parallels-perspeconic of these triangles is X(42874)

X(42873) lies on these lines: {4, 6}, {5, 648}, {54, 32713}, {140, 30258}, {262, 16318}, {264, 18583}, {275, 14569}, {297, 576}, {317, 5093}, {597, 37124}, {1351, 17907}, {1656, 40995}, {2967, 7792}, {3168, 23292}, {5097, 27377}, {6747, 34565}, {7608, 16080}, {7762, 39604}, {9308, 14561}, {9777, 11547}, {12242, 14363}, {14389, 35360}, {16989, 40801}, {19189, 40981}, {20423, 37200}

X(42873) = polar conjugate of the isotomic conjugate of X(35937)
X(42873) = barycentric product X(4)*X(35937)
X(42873) = trilinear product X(19)*X(35937)
X(42873) = intersection, other than A,B,C, of conics {{A, B, C, X(54), X(13509)}} and {{A, B, C, X(262), X(15274)}}
X(42873) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 15274, 6530), (4, 41371, 15274), (6, 15274, 4), (6, 41371, 6530), (5097, 39569, 27377), (5480, 41204, 16264)

X(42874) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ORTHIC AXES TO ABC

Barycentrics  &nbsnbsp; (6*a^8-(b^2+c^2)*a^6-(9*b^4-2*b^2*c^2+9*c^4)*a^4-3*(b^4-c^4)*(b^2-c^2)*a^2+(7*b^4+10*b^2*c^2+7*c^4)*(b^2-c^2)^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
X(42874) = 5*X(4)+X(42873)

The center of the reciprocal parallels-perspeconic of these triangles is X(42873)

X(42874) lies on these lines: {4, 6}, {3853, 39569}, {3861, 39530}, {10151, 16321}

X(42874) = {X(4), X(42854)}-harmonic conjugate of X(53)

X(42875) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO ORTHOCENTROIDAL

Barycentrics    (S^2-3*SA*SB)*(S^2-3*SA*SC)*((9*R^2+SA-2*SW)*S^2-(6*R^2-SW)*SA*SW)*(SB+SC)*SB*SC : :
X(42875) = X(74)-3*X(15291) = 4*X(7687)-3*X(42876)

The center of the reciprocal parallels-perspeconic of these triangles is X(42876)

X(42875) lies on these lines: {6, 74}, {146, 648}, {323, 1304}, {511, 32715}, {7687, 42876}, {19504, 40352}

X(42876) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ORTHOCENTROIDAL TO ABC

Barycentrics    3*a^24-10*(b^2+c^2)*a^22+2*(b^4+27*b^2*c^2+c^4)*a^20+2*(b^2+c^2)*(15*b^4-53*b^2*c^2+15*c^4)*a^18-(45*b^8+45*c^8+b^2*c^2*(32*b^4-237*b^2*c^2+32*c^4))*a^16+2*(b^2+c^2)*(12*b^8+12*c^8+b^2*c^2*(57*b^4-148*b^2*c^2+57*c^4))*a^14-(76*b^8+76*c^8+b^2*c^2*(127*b^4-414*b^2*c^2+127*c^4))*b^2*c^2*a^12-2*(b^4-c^4)*(b^2-c^2)*(12*b^8+12*c^8-b^2*c^2*(5*b^4+71*b^2*c^2+5*c^4))*a^10+(45*b^12+45*c^12+2*(3*b^8+3*c^8-b^2*c^2*(4*b^4+67*b^2*c^2+4*c^4))*b^2*c^2)*(b^2-c^2)^2*a^8-2*(b^4-c^4)*(b^2-c^2)^3*(15*b^8+15*c^8+b^2*c^2*(29*b^4+20*b^2*c^2+29*c^4))*a^6-(b^2-c^2)^4*(2*b^12+2*c^12-(54*b^8+54*c^8+b^2*c^2*(33*b^4-2*b^2*c^2+33*c^4))*b^2*c^2)*a^4+2*(b^2-c^2)^6*(b^2+c^2)*(5*b^8+5*c^8-b^2*c^2*(2*b^4+9*b^2*c^2+2*c^4))*a^2-3*(b^2+c^2)^4*(b^2-c^2)^8 : :
X(42876) = 4*X(7687)-X(42875) = 3*X(14644)-X(15291)

The center of the reciprocal parallels-perspeconic of these triangles is X(42875)

X(42876) lies on these lines: {4, 67}, {6128, 14644}, {7687, 42875}

X(42877) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO REFLECTION

Barycentrics    (S^2+SA*SB)*(S^2+SA*SC)*((9*R^2-SA-2*SW)*S^2+(2*R^2-SW)*SA*SW)*(SB+SC)*SB*SC : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42878)

X(42877) lies on these lines: {6, 24}, {933, 15018}, {13403, 42878}

X(42878) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: REFLECTION TO ABC

Barycentrics    a^24-2*(b^2+c^2)*a^22-2*(b^4-5*b^2*c^2+c^4)*a^20-2*(b^2+c^2)*(b^4+19*b^2*c^2+c^4)*a^18+(33*b^8+33*c^8+(88*b^4+151*b^2*c^2+88*c^4)*b^2*c^2)*a^16-6*(b^2+c^2)*(8*b^8+8*c^8+(5*b^4+22*b^2*c^2+5*c^4)*b^2*c^2)*a^14+3*(4*b^8+4*c^8+(17*b^4+30*b^2*c^2+17*c^4)*b^2*c^2)*b^2*c^2*a^12+2*(b^4-c^4)*(b^2-c^2)*(24*b^8+24*c^8+(17*b^4+31*b^2*c^2+17*c^4)*b^2*c^2)*a^10-(b^2-c^2)^2*(33*b^12+33*c^12+2*(3*b^8+b^4*c^4+3*c^8)*b^2*c^2)*a^8+2*(b^4-c^4)*(b^2-c^2)^3*(b^8+c^8-(21*b^4+2*b^2*c^2+21*c^4)*b^2*c^2)*a^6+(2*b^12+2*c^12+(26*b^8+26*c^8-(21*b^4+22*b^2*c^2+21*c^4)*b^2*c^2)*b^2*c^2)*(b^2-c^2)^4*a^4+2*(b^2-c^2)^6*(b^2+c^2)*(b^8+7*b^4*c^4+c^8)*a^2-(b^2+c^2)^4*(b^2-c^2)^8 : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42877)

X(42878) lies on these lines: {4, 9973}, {13403, 42877}

X(42879) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: ABC TO 1st SHARYGIN

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42880)

X(42879) lies on these lines: {239, 257}, {256, 17770}, {1916, 6625}

X(42879) = intersection, other than A,B,C, of conics {{A, B, C, X(239), X(6625)}} and {{A, B, C, X(330), X(14949)}}

X(42880) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 1st SHARYGIN TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42879)

X(42880) lies on these lines: {1, 6646}, {846, 30660}

X(42881) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 2nd SHARYGIN TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(4562)

X(42881) lies on these lines: {1, 2}, {726, 39362}

X(42881) = reflection of X(3783) in X(239)

X(42882) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 3rd TRI-SQUARES-CENTRAL TO ABC

Barycentrics    (a^2+S)*(5*a^4-17*(b^2+c^2)*a^2+4*b^4-18*b^2*c^2+4*c^4-S*(13*a^2+16*b^2+16*c^2)) : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42838)

X(42882) lies on this line: {488, 3068}

X(42882) = X(42838)-of-3rd tri-squares-central triangle

X(42883) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 4th TRI-SQUARES-CENTRAL TO ABC

Barycentrics    (a^2-S)*(5*a^4-17*(b^2+c^2)*a^2+4*b^4-18*b^2*c^2+4*c^4+S*(13*a^2+16*b^2+16*c^2)) : :

The center of the reciprocal parallels-perspeconic of these triangles is X(42840)

X(42883) lies on this line: {487, 3069}

X(42883) = X(42840)-of-4th tri-squares-central triangle

X(42884) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: OUTER-YFF TO ABC

Barycentrics    a*(a^5-2*(b+c)*a^4+4*b*c*a^3+2*(b+c)*(b^2-3*b*c+c^2)*a^2-(b-c)^4*a-2*(b^2-c^2)*(b-c)*b*c) : :
X(42884) = 2*X(1)+X(5729) = X(5730)-6*X(38316) = 3*X(17728)+2*X(30331)

The center of the reciprocal parallels-perspeconic of these triangles is X(1001).

X(42884) lies on these lines: {1, 6}, {3, 390}, {7, 104}, {11, 33925}, {21, 26818}, {36, 11495}, {55, 3911}, {56, 516}, {57, 17613}, {63, 12915}, {100, 33994}, {105, 40127}, {142, 20270}, {145, 25875}, {149, 1004}, {200, 25893}, {381, 7678}, {388, 38037}, {474, 2550}, {480, 519}, {496, 3149}, {497, 1617}, {498, 16854}, {499, 3826}, {517, 1445}, {528, 2932}, {673, 37272}, {938, 3295}, {944, 5809}, {946, 12573}, {971, 24928}, {997, 3059}, {1000, 2346}, {1033, 37393}, {1056, 6913}, {1125, 19521}, {1145, 6600}, {1156, 12773}, {1210, 5687}, {1260, 36845}, {1319, 14100}, {1376, 24392}, {1385, 7675}, {1420, 5732}, {1476, 10307}, {1478, 42356}, {1482, 7672}, {1484, 6911}, {1497, 41344}, {1512, 5722}, {1621, 5744}, {1656, 7679}, {1697, 21153}, {1708, 17642}, {1890, 11399}, {2098, 41712}, {2099, 15558}, {2801, 12740}, {2951, 13462}, {3058, 37578}, {3085, 16842}, {3174, 5440}, {3303, 6738}, {3304, 5542}, {3333, 11496}, {3358, 12672}, {3419, 24389}, {3434, 37270}, {3560, 5843}, {3576, 4326}, {3616, 19520}, {3622, 37228}, {3673, 14189}, {3940, 34784}, {4000, 15287}, {4304, 15006}, {4308, 36991}, {4312, 5563}, {4314, 8273}, {4321, 11372}, {4335, 37617}, {4423, 5316}, {4511, 30628}, {4666, 11018}, {4860, 18240}, {5082, 16410}, {5120, 41325}, {5248, 21625}, {5274, 8166}, {5284, 10578}, {5435, 6244}, {5584, 12575}, {5704, 9709}, {5759, 22770}, {5762, 10680}, {5805, 11373}, {5851, 10074}, {5880, 10094}, {5886, 21617}, {5919, 15837}, {6601, 37249}, {6666, 31397}, {6918, 38149}, {7191, 25907}, {7671, 10246}, {7673, 12702}, {7743, 18482}, {8071, 19535}, {8168, 30286}, {8545, 22758}, {8581, 20323}, {9708, 18230}, {9848, 12520}, {9957, 31658}, {10056, 19536}, {10222, 11526}, {10269, 30379}, {10394, 21740}, {10475, 39553}, {10529, 37248}, {10889, 37620}, {10934, 16370}, {11020, 29817}, {11025, 14988}, {11329, 41845}, {12331, 12730}, {12433, 16202}, {13743, 16133}, {14151, 19907}, {14793, 19704}, {15008, 15178}, {15171, 37426}, {15251, 37800}, {15252, 26228}, {16203, 31657}, {16408, 40333}, {16435, 23853}, {16678, 37078}, {17127, 22117}, {17542, 38025}, {17625, 30223}, {19525, 41555}, {20075, 37309}, {20533, 21477}, {20789, 36846}, {22753, 37704}, {24552, 37059}, {25416, 34894}, {25524, 38052}, {26667, 26981}, {30312, 38121}, {34753, 35448}, {37579, 37722}, {37709, 38154}

X(42884) = midpoint of X(i) and X(j) for these {i, j}: {1, 15299}, {1001, 42886}, {2098, 41712}
X(42884) = reflection of X(5729) in X(15299)
X(42884) = X(954)-of-outer-Yff tangents triangle
X(42884) = X(1001)-of-outer-Yff triangle
X(42884) = X(15299)-of-anti-Aquila triangle
X(42884) = X(42886)-of-inner-Yff triangle
X(42884) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 1001, 954), (1, 1736, 3242), (1, 10396, 3555), (1, 10398, 3243), (1, 15485, 9440), (1, 18412, 42871), (390, 7677, 3), (390, 8732, 35514), (497, 1617, 7580), (1001, 42871, 42843), (1420, 10384, 5732), (5572, 42819, 1), (15299, 15518, 15297), (18216, 35227, 1)

X(42885) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: INNER-YFF TANGENTS TO ABC

Barycentrics    a*(a^5-2*(b+c)*a^4+2*(b+c)^3*a^2-(b^4+c^4+2*b*c*(b^2-b*c+c^2))*a-2*(b^2-c^2)*(b-c)*b*c) : :
X(42885) = 5*X(954)-X(956) = 2*X(956)-5*X(1001) = X(5832)-3*X(17718)

The center of the reciprocal parallels-perspeconic of these triangles is X(1001)

X(42885) lies on these lines: {1, 6}, {7, 11509}, {8, 28980}, {55, 5905}, {390, 10965}, {480, 3826}, {495, 3913}, {516, 10679}, {528, 10956}, {1376, 5249}, {1890, 11400}, {2346, 5698}, {2550, 10528}, {3256, 4421}, {3627, 6256}, {3871, 16133}, {4428, 17781}, {5303, 22768}, {5719, 25524}, {5762, 11248}, {5851, 12775}, {5880, 6600}, {10531, 42356}, {10596, 38037}, {11496, 16112}, {11507, 41548}, {12000, 18525}, {13373, 31658}, {20872, 24328}, {22760, 40269}, {37579, 41572}

X(42885) = reflection of X(i) in X(j) for these (i, j): (1001, 954), (5220, 15296)
X(42885) = X(1001)-of-inner-Yff tangents triangle
X(42885) = X(42843)-of-inner-Yff triangle
X(42885) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 42843, 1001), (1001, 42871, 42886)

X(42886) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: OUTER-YFF TANGENTS TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(1001)

X(42886) lies on these lines: {1, 6}, {7, 18967}, {56, 528}, {390, 10966}, {516, 10680}, {548, 11249}, {999, 5880}, {1376, 4863}, {1482, 17463}, {1776, 3873}, {1788, 3871}, {1890, 11401}, {2078, 4421}, {2550, 5253}, {3304, 25557}, {3826, 10527}, {5260, 38025}, {5267, 30331}, {5784, 20323}, {5851, 12776}, {5853, 25440}, {8256, 12649}, {8543, 22759}, {9709, 10916}, {10532, 42356}, {10597, 38037}, {11194, 15170}, {11362, 16202}, {12001, 26321}, {12114, 22791}, {15733, 24928}, {22753, 37726}, {22766, 41555}, {25524, 31419}, {34749, 38060}

X(42886) = reflection of X(i) in X(j) for these (i, j): (1001, 42884), (5220, 15297)
X(42886) = X(1001)-of-outer-Yff tangents triangle
X(42886) = X(42842)-of-outer-Yff triangle
X(42886) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 42842, 1001), (1001, 12513, 5220), (1001, 42871, 42885), (26015, 33925, 1376)

X(42887) = CENTER OF THE PARALLELS-PERSPECONIC OF THESE TRIANGLES: 2nd ZANIAH TO ABC

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

The center of the reciprocal parallels-perspeconic of these triangles is X(42860)

X(42887) lies on these lines: {8, 1229}, {9, 40617}, {8051, 18228}

X(42887) = midpoint of X(8) and X(42861)
X(42887) = X(33584)-of-2nd Zaniah triangle

X(42888) = GIBERT (4,-7,3) POINT

Barycentrics    4*a^2*S/Sqrt[3] + 3*a^2*SA - 14*SB*SC : :

X(42888) lies on the cubic K1210a and these lines: {4, 42806}, {5, 42130}, {14, 16}, {15, 3861}, {20, 42628}, {62, 42416}, {140, 42090}, {546, 36836}, {547, 42103}, {548, 42089}, {550, 42129}, {3530, 16809}, {3627, 5335}, {3628, 42087}, {3845, 42119}, {3850, 16966}, {3853, 40693}, {3856, 23302}, {3858, 42116}, {5059, 42818}, {5066, 11480}, {5318, 42630}, {5339, 42145}, {5343, 42131}, {5349, 33923}, {5352, 41989}, {5365, 42115}, {8703, 42139}, {10645, 35018}, {11485, 15687}, {11540, 42529}, {11542, 12102}, {11737, 36967}, {12100, 42095}, {12101, 41119}, {12103, 18581}, {12821, 42632}, {14891, 33416}, {14893, 18582}, {15704, 42125}, {15717, 42493}, {16239, 42107}, {16644, 41987}, {16964, 42137}, {19709, 42492}, {33699, 42127}, {33703, 42816}, {35404, 42141}, {41122, 42686}, {42112, 42121}, {42118, 42160}, {42146, 42157}, {42436, 42782}, {42590, 42687}, {42633, 42803}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3845, 42119, 42627}, {5321, 42100, 11543}, {5321, 42108, 42100}, {5349, 42099, 42143}, {11543, 42136, 36970}, {12101, 42154, 42496}, {16809, 42585, 3530}, {19107, 36970, 42108}, {36970, 42100, 5321}, {36970, 42108, 11543}, {42088, 42778, 16}, {42093, 42144, 140}, {42096, 42135, 548}, {42099, 42143, 33923}, {42101, 42122, 3850}, {42101, 42432, 42122}, {42104, 42117, 3853}

X(42889) = GIBERT (4,7,-3) POINT

Barycentrics    4*a^2*S/Sqrt[3] - 3*a^2*SA + 14*SB*SC : :

X(42889) lies on the cubic K1210b and these lines: {4, 42805}, {5, 42131}, {13, 15}, {16, 3861}, {20, 42627}, {61, 42415}, {140, 42091}, {546, 36843}, {547, 42106}, {548, 42092}, {550, 42132}, {3530, 16808}, {3627, 5334}, {3628, 42088}, {3845, 42120}, {3850, 16967}, {3853, 40694}, {3856, 23303}, {3858, 42115}, {5059, 42817}, {5066, 11481}, {5321, 42629}, {5340, 42144}, {5344, 42130}, {5350, 33923}, {5351, 41989}, {5366, 42116}, {8703, 42142}, {10646, 35018}, {11486, 15687}, {11540, 42528}, {11543, 12102}, {11737, 36968}, {12100, 42098}, {12101, 41120}, {12103, 18582}, {12820, 42631}, {14891, 33417}, {14893, 18581}, {15704, 42128}, {15717, 42492}, {16239, 42110}, {16645, 41987}, {16965, 42136}, {19709, 42493}, {33699, 42126}, {33703, 42815}, {35404, 42140}, {41121, 42687}, {42113, 42124}, {42117, 42161}, {42143, 42158}, {42435, 42781}, {42591, 42686}, {42634, 42804}

X(42889) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3845, 42120, 42628}, {5318, 42099, 11542}, {5318, 42109, 42099}, {5350, 42100, 42146}, {11542, 42137, 36969}, {12101, 42155, 42497}, {16808, 42584, 3530}, {19106, 36969, 42109}, {36969, 42099, 5318}, {36969, 42109, 11542}, {42087, 42777, 15}, {42094, 42145, 140}, {42097, 42138, 548}, {42100, 42146, 33923}, {42102, 42123, 3850}, {42102, 42431, 42123}, {42105, 42118, 3853}

X(42890) = GIBERT (15,-10,17) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 17*a^2*SA - 20*SB*SC : :

X(42890) lies on the cubic K1210a and these lines: {3, 14}, {5, 42630}, {15, 3853}, {17, 38335}, {30, 42779}, {61, 5059}, {62, 15686}, {382, 16960}, {398, 15690}, {547, 12817}, {3411, 42117}, {3412, 42096}, {3533, 42160}, {3543, 16962}, {3545, 5238}, {3627, 12820}, {3832, 42085}, {3845, 16772}, {3850, 42488}, {5056, 36970}, {5067, 16809}, {5237, 41981}, {5321, 42493}, {5340, 35400}, {5351, 42507}, {5352, 42500}, {8703, 42797}, {11001, 42158}, {11539, 42580}, {15708, 42159}, {16239, 42122}, {16965, 42130}, {17578, 42695}, {19106, 33703}, {19711, 42599}, {22236, 42506}, {34755, 42087}, {41973, 42528}, {42099, 42118}, {42161, 42532}, {42222, 42259}, {42224, 42258}

X(42890) = {X(5),X(42682)}-harmonic conjugate of X(42694)

X(42891) = GIBERT (15,10,-17) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 17*a^2*SA + 20*SB*SC : :

X(42891) lies on the cubic K1210b and these lines: {3, 13}, {5, 42629}, {16, 3853}, {18, 38335}, {30, 42780}, {61, 15686}, {62, 5059}, {382, 16961}, {397, 15690}, {547, 12816}, {3411, 42097}, {3412, 42118}, {3533, 42161}, {3543, 16963}, {3545, 5237}, {3627, 12821}, {3832, 42086}, {3845, 16773}, {3850, 42489}, {5056, 36969}, {5067, 16808}, {5238, 41981}, {5318, 42492}, {5339, 35400}, {5351, 42501}, {5352, 42506}, {8703, 42798}, {11001, 42157}, {11539, 42581}, {15708, 42162}, {16239, 42123}, {16964, 42131}, {17578, 42694}, {19107, 33703}, {19711, 42598}, {22238, 42507}, {34754, 42088}, {41974, 42529}, {42100, 42117}, {42160, 42533}, {42221, 42259}, {42223, 42258}

X(42891) = {X(5),X(42683)}-harmonic conjugate of X(42695)

X(42892) = GIBERT (33,8,31) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 31*a^2*SA + 16*SB*SC : :

X(42892) lies on the cubic K1210a and these lines: {3, 41972}, {13, 15683}, {14, 547}, {15, 3830}, {16, 3524}, {17, 3861}, {61, 3526}, {381, 41971}, {395, 42635}, {396, 550}, {3091, 5365}, {10645, 14093}, {10653, 21734}, {10654, 33603}, {11488, 42630}, {11542, 42429}, {12108, 16772}, {15698, 42478}, {15713, 16241}, {15759, 42687}, {16267, 42127}, {16268, 42124}, {16967, 42503}, {19106, 42514}, {23046, 36970}, {33417, 42497}, {33607, 42137}, {33703, 36967}, {41101, 42135}, {41107, 42091}, {42092, 42532}, {42475, 42488}, {42489, 42778}, {42498, 42513}, {42502, 42585}

X(42892) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16241, 42520, 42121}, {41943, 42799, 23302}

X(42893) = GIBERT (-33,8,31) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 31*a^2*SA - 16*SB*SC : :

X(42893) lies on the cubic K1210b and these lines: {3, 41971}, {13, 547}, {14, 15683}, {15, 3524}, {16, 3830}, {18, 3861}, {62, 3526}, {381, 41972}, {395, 550}, {396, 42636}, {3091, 5366}, {10646, 14093}, {10653, 33602}, {10654, 21734}, {11489, 42629}, {11543, 42430}, {12108, 16773}, {15698, 42479}, {15713, 16242}, {15759, 42686}, {16267, 42121}, {16268, 42126}, {16966, 42502}, {19107, 42515}, {23046, 36969}, {33416, 42496}, {33606, 42136}, {33703, 36968}, {41100, 42138}, {41108, 42090}, {42089, 42533}, {42474, 42489}, {42488, 42777}, {42499, 42512}, {42503, 42584}

X(42893) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16242, 42521, 42124}, {41944, 42800, 23303}

X(42894) = GIBERT (-11,6,3) POINT

Barycentrics    11*a^2*S/Sqrt[3] - 3*a^2*SA - 12*SB*SC : :

X(42894) lies on the cubic K1210a and these lines: {6, 13}, {15, 632}, {16, 3529}, {18, 3523}, {61, 15022}, {62, 12102}, {395, 19710}, {398, 16966}, {548, 10646}, {550, 41977}, {3411, 19107}, {3620, 22493}, {5067, 18581}, {5321, 34755}, {5335, 42780}, {5339, 16961}, {5352, 42628}, {10187, 42129}, {10654, 15709}, {11485, 42580}, {11488, 41120}, {11489, 19708}, {11812, 23303}, {12817, 33603}, {15640, 36970}, {15702, 41971}, {16242, 17504}, {16268, 42085}, {16645, 33606}, {16960, 42114}, {16963, 42096}, {17578, 19106}, {20080, 22496}, {23302, 41122}, {33416, 42116}, {33417, 42611}, {33561, 40901}, {35404, 41972}, {36368, 40900}, {36969, 42521}, {39874, 41037}, {42093, 42629}, {42098, 42690}, {42102, 42814}, {42126, 42433}, {42134, 42159}, {42146, 42163}, {42157, 42818}, {42165, 42782}, {42688, 42796}

X(42894) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 381, 42895}, {13, 42125, 16809}, {5334, 22237, 42089}, {5334, 42089, 41973}, {5339, 16961, 42099}, {22237, 41973, 18}

X(42895) = GIBERT (11,6,3) POINT

Barycentrics    11*a^2*S/Sqrt[3] + 3*a^2*SA + 12*SB*SC : :

X(42895) lies on the cubic K1210b and these lines: {6, 13}, {15, 3529}, {16, 632}, {17, 3523}, {61, 12102}, {62, 15022}, {396, 19710}, {397, 16967}, {548, 10645}, {550, 41978}, {3412, 19106}, {3620, 22494}, {5067, 18582}, {5318, 34754}, {5334, 42779}, {5340, 16960}, {5351, 42627}, {6412, 35730}, {10188, 42132}, {10653, 15709}, {11486, 42581}, {11488, 19708}, {11489, 41119}, {11812, 23302}, {12816, 33602}, {15640, 36969}, {15702, 41972}, {16241, 17504}, {16267, 42086}, {16644, 33607}, {16961, 42111}, {16962, 42097}, {17578, 19107}, {20080, 22495}, {23303, 41121}, {33416, 42610}, {33417, 42115}, {33560, 40900}, {35404, 41971}, {36366, 40901}, {36970, 42520}, {39874, 41036}, {42094, 42630}, {42095, 42691}, {42101, 42813}, {42127, 42434}, {42133, 42162}, {42143, 42166}, {42158, 42817}, {42164, 42781}, {42689, 42795}

X(42895) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 381, 42894}, {14, 42128, 16808}, {5335, 22235, 42092}, {5335, 42092, 41974}, {5340, 16960, 42100}, {22235, 41974, 17}

X(42896) = GIBERT (13,2,3) POINT

Barycentrics    13*a^2*S/Sqrt[3] + 3*a^2*SA + 4*SB*SC : :

X(42896) lies on the cubic K1210a and these lines: {6, 17}, {13, 3845}, {15, 548}, {16, 3524}, {61, 3146}, {62, 14869}, {396, 10124}, {397, 42099}, {3411, 23302}, {3412, 11486}, {3643, 33626}, {3855, 16809}, {5318, 42630}, {10653, 15697}, {11480, 41100}, {11485, 15681}, {11542, 12811}, {11543, 16267}, {12820, 36970}, {15693, 42480}, {16242, 42533}, {16808, 42691}, {16964, 42094}, {16965, 42130}, {19709, 42481}, {23303, 42590}, {32455, 40334}, {33604, 41113}, {33607, 42690}, {34754, 42090}, {35730, 42171}, {35733, 42202}, {37832, 42507}, {41101, 42127}, {41107, 41971}, {41112, 42799}, {41121, 42139}, {41122, 42777}, {41973, 42134}, {41974, 42122}, {42088, 42633}, {42092, 42805}, {42111, 42780}, {42154, 42520}, {42501, 42636}

X(42896) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 1656, 42897}, {6, 16960, 18}, {6, 42817, 16961}, {17, 42129, 16966}, {16961, 42817, 16966}

X(42897) = GIBERT (-13,2,3) POINT

Barycentrics    13*a^2*S/Sqrt[3] - 3*a^2*SA - 4*SB*SC : :

X(42897) lies on the cubic K1210b and these lines: {6, 17}, {14, 3845}, {15, 3524}, {16, 548}, {61, 14869}, {62, 3146}, {395, 10124}, {398, 42100}, {3411, 11485}, {3412, 23303}, {3642, 33627}, {3855, 16808}, {5321, 42629}, {10654, 15697}, {11481, 41101}, {11486, 15681}, {11542, 16268}, {11543, 12811}, {12821, 36969}, {15693, 42481}, {16241, 42532}, {16809, 42690}, {16964, 42131}, {16965, 42093}, {19709, 42480}, {23302, 42591}, {32455, 40335}, {33605, 41112}, {33606, 42691}, {34755, 42091}, {37835, 42506}, {41100, 42126}, {41108, 41972}, {41113, 42800}, {41121, 42778}, {41122, 42142}, {41973, 42123}, {41974, 42133}, {42087, 42634}, {42089, 42806}, {42114, 42779}, {42155, 42521}, {42500, 42635}

X(42897) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 1656, 42896}, {6, 16961, 17}, {6, 42818, 16960}, {18, 42132, 16967}, {16960, 42818, 16967}

X(42898) = GIBERT (27,7,8) POINT

Barycentrics    9*Sqrt[3]*a^2*S + 8*a^2*SA + 14*SB*SC : :

X(42898) lies on the cubic K1210a and these lines: {5, 42503}, {6, 5071}, {13, 14893}, {15, 15691}, {16, 396}, {18, 547}, {30, 42532}, {61, 12816}, {62, 10124}, {376, 397}, {381, 398}, {395, 15703}, {632, 42533}, {3412, 8703}, {3528, 42508}, {3543, 5318}, {3545, 42502}, {3861, 42419}, {5321, 42781}, {10653, 14093}, {10654, 35403}, {11488, 42501}, {11542, 11737}, {14136, 32907}, {14891, 41100}, {15681, 42086}, {15683, 22236}, {15684, 41112}, {15686, 41107}, {15690, 41974}, {15692, 16772}, {15694, 16773}, {15700, 42152}, {15702, 42491}, {15718, 42510}, {15721, 22238}, {15723, 23302}, {16960, 41944}, {16962, 34200}, {23303, 42496}, {35400, 42161}, {35404, 41101}, {37352, 41748}, {41108, 42694}, {41121, 42163}, {41983, 42793}, {42096, 42516}, {42144, 42633}, {42156, 42495}, {42165, 42511}, {42520, 42813}, {42688, 42815}

X(42899) = GIBERT (-27,7,8) POINT

Barycentrics    9*Sqrt[3]*a^2*S - 8*a^2*SA - 14*SB*SC : :

X(42899) lies on the cubic K1210b and these lines: {5, 42502}, {6, 5071}, {14, 14893}, {15, 395}, {16, 15691}, {17, 547}, {30, 42533}, {61, 10124}, {62, 12817}, {376, 398}, {381, 397}, {396, 15703}, {632, 42532}, {3411, 8703}, {3528, 42509}, {3543, 5321}, {3545, 42503}, {3861, 42420}, {5318, 42782}, {10653, 35403}, {10654, 14093}, {11489, 42500}, {11543, 11737}, {14137, 32909}, {14891, 41101}, {15681, 42085}, {15683, 22238}, {15684, 41113}, {15686, 41108}, {15690, 41973}, {15692, 16773}, {15694, 16772}, {15700, 42149}, {15702, 42490}, {15718, 42511}, {15721, 22236}, {15723, 23303}, {16961, 41943}, {16963, 34200}, {23302, 42497}, {35400, 42160}, {35404, 41100}, {37351, 41748}, {41107, 42695}, {41122, 42166}, {41983, 42794}, {42097, 42517}, {42145, 42634}, {42153, 42494}, {42164, 42510}, {42521, 42814}, {42689, 42816}

X(42900) = GIBERT (11,12,-3) POINT

Barycentrics    11*a^2*S/Sqrt[3] - 3*a^2*SA + 24*SB*SC : :

X(42900) lies on the cubic K1210a and these lines: {6, 3830}, {13, 15683}, {16, 3091}, {17, 550}, {61, 42108}, {381, 41972}, {547, 16808}, {3524, 37832}, {3526, 10646}, {3861, 11543}, {5238, 42141}, {5344, 42099}, {5350, 42143}, {5351, 42138}, {5366, 16966}, {11488, 33602}, {12108, 42146}, {12816, 23303}, {12820, 16809}, {14093, 42128}, {15713, 36968}, {15759, 23302}, {16963, 23046}, {18582, 21734}, {19106, 33703}, {19107, 42683}, {20080, 35752}, {34755, 42094}, {42105, 42630}, {42110, 42493}, {42114, 42158}, {42144, 42633}

X(42900) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5318, 42629, 10645}, {10645, 42629, 42431}

X(42901) = GIBERT (11,-12,3) POINT

Barycentrics    11*a^2*S/Sqrt[3] + 3*a^2*SA - 24*SB*SC : :

X(42901) lies on the cubic K1210b and these lines: {6, 3830}, {14, 15683}, {15, 3091}, {18, 550}, {62, 42109}, {381, 41971}, {547, 16809}, {3524, 37835}, {3526, 10645}, {3861, 11542}, {5237, 42140}, {5343, 42100}, {5349, 42146}, {5352, 42135}, {5365, 16967}, {11489, 33603}, {12108, 42143}, {12817, 23302}, {12821, 16808}, {14093, 42125}, {15713, 36967}, {15759, 23303}, {16962, 23046}, {18581, 21734}, {19106, 42682}, {19107, 33703}, {20080, 36330}, {34754, 42093}, {35739, 42208}, {42104, 42629}, {42107, 42492}, {42111, 42157}, {42145, 42634}

X(42901) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5321, 42630, 10646}, {10646, 42630, 42432}

X(42902) = GIBERT (-13,12,5) POINT

Barycentrics    13*a^2*S/Sqrt[3] - 5*a^2*SA - 24*SB*SC : :

X(42902) lies on the cubic K1210a and these lines: {14, 3845}, {15, 1656}, {16, 3146}, {18, 42140}, {61, 12811}, {548, 5321}, {3524, 18581}, {3855, 16809}, {5334, 37832}, {5343, 33416}, {10124, 16967}, {10645, 14869}, {11481, 15681}, {11486, 42814}, {11543, 42431}, {12817, 42120}, {15697, 42099}, {15714, 42087}, {16268, 42093}, {16960, 41113}, {16961, 42109}, {16962, 42473}, {16965, 42692}, {34754, 42139}, {41120, 42515}, {41122, 42126}, {42132, 42799}, {42597, 42684}, {42813, 42816}

X(42903) = GIBERT (13,12,5) POINT

Barycentrics    13*a^2*S/Sqrt[3] + 5*a^2*SA + 24*SB*SC : :

X(42903) lies on the cubic K1210b and these lines: {13, 3845}, {15, 3146}, {16, 1656}, {17, 42141}, {62, 12811}, {548, 5318}, {3524, 18582}, {3855, 16808}, {5335, 37835}, {5344, 33417}, {10124, 16966}, {10646, 14869}, {11480, 15681}, {11485, 42813}, {11542, 42432}, {12816, 42119}, {15697, 42100}, {15714, 42088}, {16267, 42094}, {16960, 42108}, {16961, 41112}, {16963, 42472}, {16964, 42693}, {34755, 42142}, {41119, 42514}, {41121, 42127}, {42129, 42800}, {42596, 42685}, {42814, 42815}

X(42904) = GIBERT (-11,14,3) POINT

Barycentrics    11*a^2*S/Sqrt[3] - 3*a^2*SA - 28*SB*SC : :

X(42904) lies on the cubic K1210a and these lines: {5, 15}, {14, 38335}, {16, 12817}, {18, 5059}, {62, 42683}, {5349, 42123}, {5365, 10645}, {10299, 42090}, {10304, 36970}, {14891, 37835}, {15681, 16645}, {15690, 16242}, {15693, 33416}, {15702, 36967}, {16960, 42494}, {16961, 42093}, {16963, 42690}, {16967, 42477}, {17538, 18581}, {18582, 42532}, {19106, 42159}, {22236, 42530}, {34754, 42472}, {36843, 42100}, {37640, 42103}, {41108, 42777}, {41113, 42479}, {41122, 42108}, {42099, 42129}, {42126, 42580}

X(42904) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15, 42814, 42692}, {16964, 42135, 16809}

X(42905) = GIBERT (11,14,3) POINT

Barycentrics    11*a^2*S/Sqrt[3] + 3*a^2*SA + 28*SB*SC : :

X(42905) lies on the cubic K1210b and these lines: {5, 16}, {13, 38335}, {15, 12816}, {17, 5059}, {61, 42682}, {5350, 42122}, {5366, 10646}, {10299, 42091}, {10304, 36969}, {14891, 37832}, {15681, 16644}, {15690, 16241}, {15693, 33417}, {15702, 36968}, {16960, 42094}, {16961, 42495}, {16962, 42691}, {16966, 42476}, {17538, 18582}, {18581, 42533}, {19107, 42162}, {22238, 42531}, {34755, 42473}, {36836, 42099}, {37641, 42106}, {41107, 42778}, {41112, 42478}, {41121, 42109}, {42100, 42132}, {42127, 42581}

X(42905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16, 42813, 42693}, {16965, 42138, 16808}

X(42906) = GIBERT (-10,15,1) POINT

Barycentrics    10*a^2*S/Sqrt[3] - a^2*SA - 30*SB*SC : :

X(42906) lies on the cubic K1210a and these lines: {3, 42133}, {13, 3845}, {16, 5349}, {547, 11480}, {549, 42682}, {550, 42692}, {632, 42630}, {3543, 11543}, {3545, 42124}, {3627, 34755}, {3830, 42517}, {3832, 11485}, {3850, 42098}, {3853, 40694}, {3860, 42518}, {5056, 42126}, {5067, 42122}, {5068, 42688}, {5365, 11542}, {10645, 41992}, {11539, 36970}, {11812, 42095}, {15682, 42690}, {15686, 19107}, {15702, 42130}, {16239, 42085}, {16960, 42694}, {16961, 33699}, {23046, 42635}, {33703, 42125}, {34754, 41991}, {35401, 37641}, {41981, 42096}, {41983, 42090}, {42108, 42121}, {42145, 42159}

X(42907) = GIBERT (10,15,1) POINT

Barycentrics    10*a^2*S/Sqrt[3] + a^2*SA + 30*SB*SC : :

X(42907) lies on the cubic K1210b and these lines: {3, 42134}, {14, 3845}, {15, 5350}, {547, 11481}, {549, 42683}, {550, 42693}, {632, 42629}, {3543, 11542}, {3545, 42121}, {3627, 34754}, {3830, 42516}, {3832, 11486}, {3850, 42095}, {3853, 40693}, {3860, 42519}, {5056, 42127}, {5067, 42123}, {5068, 42689}, {5366, 11543}, {10646, 41992}, {11539, 36969}, {11812, 42098}, {15682, 42691}, {15686, 19106}, {15702, 42131}, {16239, 42086}, {16960, 33699}, {16961, 42695}, {23046, 42636}, {33703, 42128}, {34755, 41991}, {35401, 37640}, {41981, 42097}, {41983, 42091}, {42109, 42124}, {42144, 42162}

X(42908) = GIBERT (9,-16,3) POINT

Barycentrics    3*Sqrt[3]*a^2*S + 3*a^2*SA - 32*SB*SC : :

X(42908) lies on the cubic K1210a and these lines: {4, 13}, {16, 5073}, {17, 42101}, {18, 5059}, {20, 12817}, {140, 42529}, {382, 42636}, {398, 42683}, {550, 5349}, {1656, 10645}, {1657, 5351}, {3090, 42632}, {3146, 16268}, {3411, 15682}, {3522, 42489}, {3523, 16809}, {3529, 42515}, {3533, 42140}, {3545, 10188}, {3832, 41943}, {3850, 23302}, {3851, 5238}, {3853, 41107}, {3858, 37832}, {3861, 41101}, {5056, 36967}, {5068, 42085}, {5076, 41108}, {5321, 42431}, {5339, 41974}, {5343, 19106}, {5365, 42104}, {8703, 42593}, {10299, 42580}, {11541, 41120}, {12821, 42581}, {16808, 42682}, {17800, 41122}, {21735, 42099}, {22237, 42113}, {33416, 42776}, {41963, 42200}, {41964, 42199}, {41978, 42132}, {42110, 42530}, {42112, 42495}, {42131, 42801}, {42150, 42630}, {42434, 42594}

X(42908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61, 42695, 13}, {5343, 19106, 42780}, {5365, 42104, 42158}, {16964, 42162, 42799}, {36970, 42813, 42160}, {37640, 42160, 16964}

X(42909) = GIBERT (9,16,-3) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 3*a^2*SA + 32*SB*SC : :

X(42909) lies on the cubic K1210b and these lines: {4, 14}, {15, 5073}, {17, 5059}, {18, 42102}, {20, 12816}, {140, 42528}, {382, 42635}, {397, 42682}, {550, 5350}, {1656, 10646}, {1657, 5352}, {3090, 42631}, {3146, 16267}, {3412, 15682}, {3522, 42488}, {3523, 16808}, {3529, 42514}, {3533, 42141}, {3545, 10187}, {3832, 41944}, {3850, 23303}, {3851, 5237}, {3853, 41108}, {3858, 37835}, {3861, 41100}, {5056, 36968}, {5068, 42086}, {5076, 41107}, {5318, 42432}, {5340, 41973}, {5344, 19107}, {5366, 42105}, {8703, 42592}, {10299, 42581}, {11541, 41119}, {12820, 42580}, {16809, 42683}, {17800, 41121}, {21735, 42100}, {22235, 42112}, {33417, 42775}, {41963, 42202}, {41964, 42201}, {41977, 42129}, {42107, 42531}, {42113, 42494}, {42130, 42802}, {42151, 42629}, {42433, 42595}

X(42909) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {62, 42694, 14}, {5344, 19107, 42779}, {5366, 42105, 42157}, {16965, 42159, 42800}, {36969, 42814, 42161}, {37641, 42161, 16965}

X(42910) = GIBERT (-3,5,7) POINT

Barycentrics    Sqrt[3]*a^2*S - 7*a^2*SA - 10*SB*SC : :

X(42910) lies on the cubic K1211a and these lines: {2, 14}, {3, 5349}, {4, 5351}, {5, 5340}, {6, 547}, {13, 5071}, {16, 3545}, {17, 7486}, {18, 3090}, {30, 42089}, {61, 5067}, {62, 5056}, {140, 42154}, {298, 32832}, {376, 16809}, {381, 23303}, {395, 5055}, {396, 1656}, {397, 5079}, {398, 5070}, {549, 42085}, {550, 42591}, {618, 37171}, {631, 36967}, {632, 5339}, {2043, 35787}, {2044, 35786}, {3091, 36969}, {3522, 10187}, {3523, 42529}, {3524, 33416}, {3525, 16964}, {3526, 42150}, {3528, 42545}, {3529, 42593}, {3533, 5238}, {3534, 42104}, {3543, 10646}, {3544, 42813}, {3618, 6669}, {3627, 42491}, {3628, 42152}, {3830, 42091}, {3832, 5237}, {3839, 36968}, {3845, 11481}, {3850, 36843}, {3851, 16773}, {3855, 12820}, {5054, 5321}, {5066, 42106}, {5068, 16965}, {5072, 42148}, {5318, 19709}, {5335, 16963}, {5343, 5352}, {5365, 42434}, {5418, 34559}, {5420, 34562}, {5617, 36519}, {6108, 36765}, {6782, 22489}, {8703, 42093}, {10109, 41119}, {10124, 42117}, {10303, 42157}, {10304, 19107}, {10645, 15702}, {11185, 30472}, {11480, 11539}, {11486, 41112}, {11543, 15699}, {11737, 42118}, {12100, 42135}, {12817, 15698}, {14269, 42088}, {14891, 42144}, {14892, 42138}, {14893, 42097}, {15681, 42101}, {15682, 42528}, {15687, 42113}, {15689, 42108}, {15692, 42133}, {15693, 42087}, {15694, 42125}, {15701, 42126}, {15703, 23302}, {15704, 42774}, {15707, 42130}, {15709, 42119}, {15711, 42585}, {15713, 42122}, {15717, 42432}, {15718, 42692}, {15720, 42164}, {15723, 42116}, {15765, 42260}, {16239, 36836}, {16267, 16961}, {16268, 16966}, {16634, 22848}, {16808, 41944}, {16962, 42516}, {17504, 42136}, {18585, 42261}, {18586, 42582}, {18587, 42583}, {19106, 41099}, {19708, 42099}, {21359, 40335}, {22861, 37170}, {23046, 42123}, {34200, 42096}, {35018, 42156}, {36437, 42195}, {36439, 42277}, {36445, 42189}, {36455, 42197}, {36457, 42274}, {36463, 42187}, {38071, 42094}, {41106, 42120}, {41107, 42142}, {42131, 42792}, {42146, 42474}

X(42910) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5334, 16241}, {2, 10654, 42092}, {2, 18581, 10654}, {2, 37835, 18581}, {2, 41122, 42511}, {5, 16645, 10653}, {5, 42149, 42162}, {6, 547, 42911}, {13, 5071, 42114}, {15, 41113, 10654}, {18, 3090, 40693}, {18, 37832, 37641}, {395, 5055, 18582}, {1656, 42599, 40694}, {1656, 42778, 42512}, {3090, 37641, 37832}, {3524, 36970, 42090}, {3524, 42139, 36970}, {3525, 42495, 16964}, {3526, 42163, 42150}, {3628, 42153, 42152}, {3839, 36968, 42105}, {3851, 16773, 42161}, {5055, 42129, 395}, {5066, 42121, 42155}, {5066, 42155, 42106}, {5071, 11489, 13}, {5334, 16241, 42511}, {5334, 42511, 10654}, {5339, 42611, 632}, {10653, 16645, 42149}, {10654, 18581, 41120}, {11543, 15699, 16644}, {15687, 42625, 42113}, {15723, 42116, 42500}, {16241, 41122, 5334}, {16268, 16966, 37640}, {16967, 37835, 2}, {23303, 42111, 42086}, {33416, 36970, 3524}, {33416, 42139, 42090}, {37641, 37832, 40693}, {41120, 42092, 10654}, {42089, 42095, 42103}, {42489, 42580, 4}

X(42911) = GIBERT (3,5,7) POINT

Barycentrics    Sqrt[3]*a^2*S + 7*a^2*SA + 10*SB*SC : :

X(42911) lies on the cubic K1211b and these lines: {2, 13}, {3, 5350}, {4, 5352}, {5, 5339}, {6, 547}, {14, 5071}, {15, 3545}, {17, 3090}, {18, 7486}, {30, 42092}, {61, 5056}, {62, 5067}, {140, 42155}, {299, 32832}, {376, 16808}, {381, 23302}, {395, 1656}, {396, 5055}, {397, 5070}, {398, 5079}, {549, 42086}, {550, 42590}, {619, 37170}, {631, 36968}, {632, 5340}, {2043, 35786}, {2044, 35787}, {3091, 36970}, {3522, 10188}, {3523, 42528}, {3524, 33417}, {3525, 16965}, {3526, 42151}, {3528, 42546}, {3529, 42592}, {3533, 5237}, {3534, 42105}, {3543, 10645}, {3544, 42814}, {3618, 6670}, {3627, 42490}, {3628, 42149}, {3830, 42090}, {3832, 5238}, {3839, 36967}, {3845, 11480}, {3850, 36836}, {3851, 16772}, {3855, 12821}, {5054, 5318}, {5066, 42103}, {5068, 16964}, {5072, 42147}, {5321, 19709}, {5334, 16962}, {5344, 5351}, {5366, 42433}, {5418, 34562}, {5420, 34559}, {5613, 36519}, {6783, 22490}, {8703, 42094}, {10109, 41120}, {10124, 42118}, {10303, 42158}, {10304, 19106}, {10646, 15702}, {11185, 30471}, {11481, 11539}, {11485, 41113}, {11542, 15699}, {11737, 42117}, {12100, 42138}, {12816, 15698}, {14269, 42087}, {14891, 42145}, {14892, 42135}, {14893, 42096}, {15681, 42102}, {15682, 42529}, {15687, 42112}, {15689, 42109}, {15692, 42134}, {15693, 42088}, {15694, 42128}, {15701, 42127}, {15703, 23303}, {15704, 42773}, {15707, 42131}, {15709, 42120}, {15711, 42584}, {15713, 42123}, {15717, 42431}, {15718, 42693}, {15720, 42165}, {15723, 42115}, {15765, 42261}, {16239, 36843}, {16267, 16967}, {16268, 16960}, {16635, 22892}, {16809, 41943}, {16963, 42517}, {17504, 42137}, {18585, 42260}, {18586, 42583}, {18587, 42582}, {19107, 41099}, {19708, 42100}, {21360, 40334}, {22907, 37171}, {23046, 42122}, {31710, 36764}, {34200, 42097}, {35018, 42153}, {36437, 42198}, {36439, 42274}, {36445, 42188}, {36455, 42196}, {36457, 42277}, {36463, 42190}, {38071, 42093}, {41106, 42119}, {41108, 42139}, {42130, 42791}, {42143, 42475}

X(42911) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5335, 16242}, {2, 10653, 42089}, {2, 18582, 10653}, {2, 37832, 18582}, {2, 41121, 42510}, {5, 16644, 10654}, {5, 42152, 42159}, {6, 547, 42910}, {14, 5071, 42111}, {16, 41112, 10653}, {17, 3090, 40694}, {17, 37835, 37640}, {396, 5055, 18581}, {1656, 42598, 40693}, {1656, 42777, 42513}, {3090, 37640, 37835}, {3524, 36969, 42091}, {3524, 42142, 36969}, {3525, 42494, 16965}, {3526, 42166, 42151}, {3628, 42156, 42149}, {3839, 36967, 42104}, {3851, 16772, 42160}, {5055, 42132, 396}, {5066, 42124, 42154}, {5066, 42154, 42103}, {5071, 11488, 14}, {5335, 16242, 42510}, {5335, 42510, 10653}, {5340, 42610, 632}, {10653, 18582, 41119}, {10654, 16644, 42152}, {11542, 15699, 16645}, {15687, 42626, 42112}, {15723, 42115, 42501}, {16242, 41121, 5335}, {16267, 16967, 37641}, {16966, 37832, 2}, {23302, 42114, 42085}, {33417, 36969, 3524}, {33417, 42142, 42091}, {37640, 37835, 40694}, {41119, 42089, 10653}, {42092, 42098, 42106}, {42488, 42581, 4}

X(42912) = GIBERT (6,1,5) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 5*a^2*SA + 2*SB*SC : :
X(42912) = X(13) + 3 X(15)

X(42912) lies on the cubic K1211a and these lines: {2, 11485}, {3, 37640}, {5, 5339}, {6, 549}, {13, 15}, {14, 547}, {16, 12100}, {17, 546}, {18, 16239}, {61, 140}, {62, 3530}, {69, 11301}, {114, 6109}, {299, 7767}, {303, 37351}, {376, 42116}, {381, 11488}, {397, 548}, {398, 3628}, {428, 10632}, {524, 618}, {531, 5461}, {533, 6671}, {550, 36836}, {590, 36469}, {597, 13083}, {615, 36453}, {616, 35304}, {617, 37352}, {619, 3589}, {631, 42806}, {632, 40694}, {1656, 42590}, {2306, 16137}, {3055, 5471}, {3106, 22686}, {3524, 11486}, {3534, 5335}, {3543, 42128}, {3545, 42132}, {3618, 11302}, {3627, 42150}, {3642, 7834}, {3643, 33458}, {3830, 42119}, {3839, 42126}, {3845, 18582}, {3850, 16964}, {3853, 42157}, {3856, 5349}, {3858, 42160}, {3860, 42110}, {3861, 42164}, {4995, 5353}, {5054, 37641}, {5055, 5334}, {5056, 42803}, {5066, 5321}, {5071, 42125}, {5072, 5343}, {5298, 5357}, {5340, 15704}, {5344, 17800}, {5352, 33923}, {5362, 15670}, {5617, 36764}, {6221, 36455}, {6390, 30471}, {6398, 36437}, {6770, 41035}, {6774, 41621}, {6780, 22510}, {7583, 34552}, {7584, 34551}, {8176, 33475}, {8584, 13084}, {8703, 10653}, {8739, 37935}, {8981, 18585}, {10109, 16966}, {10124, 23303}, {10634, 10691}, {10638, 15170}, {10645, 34200}, {10646, 14891}, {11001, 42127}, {11092, 18883}, {11137, 40111}, {11481, 17504}, {11489, 15694}, {11539, 16645}, {11540, 33416}, {11737, 16809}, {11812, 16242}, {12101, 19107}, {12102, 42432}, {12103, 16965}, {12108, 16773}, {12811, 42814}, {12816, 42502}, {12817, 42415}, {13392, 36209}, {13966, 15765}, {14269, 42142}, {14869, 42149}, {14892, 42107}, {14893, 16808}, {15681, 42145}, {15682, 42130}, {15684, 42134}, {15685, 42141}, {15686, 42086}, {15687, 42085}, {15688, 42120}, {15690, 41107}, {15692, 42115}, {15693, 42517}, {15699, 18581}, {15703, 42816}, {15711, 42420}, {15712, 22238}, {15713, 42089}, {15759, 41100}, {15764, 36449}, {15768, 21466}, {16021, 30459}, {16268, 33417}, {16963, 42635}, {18586, 42561}, {18587, 31412}, {19710, 41112}, {20252, 31710}, {22235, 33703}, {22998, 36782}, {23046, 42093}, {30463, 31945}, {33699, 41119}, {34380, 36757}, {35018, 42163}, {35404, 42096}, {35734, 36465}, {36436, 42222}, {36439, 42215}, {36454, 42224}, {36457, 42216}, {37776, 37904}, {38071, 42098}, {38335, 42140}, {41113, 42095}, {41944, 42501}, {41973, 42581}, {41974, 41981}, {42100, 42506}, {42114, 42512}, {42165, 42434}, {42433, 42779}, {42479, 42818}, {42504, 42686}

X(42912) = midpoint of X(15) and X(396)
X(42912) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 549, 42913}, {13, 396, 42496}, {13, 42430, 36969}, {13, 42496, 11542}, {14, 547, 42143}, {14, 23302, 547}, {14, 41943, 23302}, {15, 11542, 42122}, {15, 16267, 36967}, {15, 16960, 42087}, {15, 16962, 396}, {17, 42147, 546}, {18, 16239, 42591}, {61, 16241, 395}, {61, 16772, 140}, {395, 16241, 140}, {395, 16772, 16241}, {396, 5318, 16267}, {397, 5238, 548}, {549, 42633, 6}, {3412, 5238, 397}, {3845, 42154, 42136}, {5054, 37641, 42121}, {5066, 42627, 37832}, {5238, 42802, 3412}, {5321, 37832, 5066}, {5352, 42148, 33923}, {8703, 10653, 42123}, {10124, 42497, 23303}, {10653, 11480, 8703}, {10654, 16644, 5}, {10654, 42152, 16644}, {11485, 42124, 11543}, {11488, 42117, 42146}, {11542, 42122, 42137}, {11542, 42585, 5318}, {16267, 36967, 5318}, {16644, 22236, 10654}, {16645, 42092, 11539}, {16960, 42430, 13}, {16964, 42598, 3850}, {18582, 42154, 3845}, {18582, 42511, 42154}, {22236, 42152, 5}, {34754, 41943, 14}, {36836, 40693, 550}, {37832, 41101, 5321}, {41107, 42529, 42088}, {41107, 42791, 15690}, {42086, 42626, 15686}, {42088, 42529, 15690}, {42088, 42791, 42529}, {42119, 42817, 42138}, {42149, 42490, 14869}, {42150, 42156, 3627}, {42157, 42166, 3853}, {42163, 42488, 35018}

X(42913) = GIBERT (-6,1,5) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 5*a^2*SA - 2*SB*SC : :
X(42913) = X(14) + 3 X(16)

X(42913) lies on the cubic K1211b and these lines: {2, 11486}, {3, 37641}, {5, 5340}, {6, 549}, {13, 547}, {14, 16}, {15, 12100}, {17, 16239}, {18, 546}, {61, 3530}, {62, 140}, {69, 11302}, {114, 6108}, {298, 7767}, {302, 37352}, {376, 42115}, {381, 11489}, {397, 3628}, {398, 548}, {428, 10633}, {524, 619}, {530, 5461}, {532, 6672}, {550, 36843}, {590, 36452}, {597, 13084}, {615, 36470}, {616, 37351}, {617, 35303}, {618, 3589}, {631, 42805}, {632, 40693}, {1250, 15170}, {1656, 42591}, {3055, 5472}, {3107, 22684}, {3524, 11485}, {3534, 5334}, {3543, 42125}, {3545, 42129}, {3618, 11301}, {3627, 42151}, {3642, 33459}, {3643, 7834}, {3830, 42120}, {3839, 42127}, {3845, 18581}, {3850, 16965}, {3853, 42158}, {3856, 5350}, {3858, 42161}, {3860, 42107}, {3861, 42165}, {4995, 5357}, {5054, 37640}, {5055, 5335}, {5056, 42804}, {5066, 5318}, {5071, 42128}, {5072, 5344}, {5298, 5353}, {5339, 15704}, {5343, 17800}, {5351, 33923}, {5367, 15670}, {6221, 36437}, {6390, 30472}, {6398, 36455}, {6771, 41620}, {6773, 41034}, {6779, 22511}, {7127, 15325}, {7583, 34551}, {7584, 34552}, {8176, 33474}, {8584, 13083}, {8703, 10654}, {8740, 37935}, {8981, 15765}, {10109, 16967}, {10124, 23302}, {10635, 10691}, {10645, 14891}, {10646, 34200}, {11001, 42126}, {11078, 18883}, {11134, 40111}, {11480, 17504}, {11488, 15694}, {11539, 16644}, {11540, 33417}, {11737, 16808}, {11812, 16241}, {12101, 19106}, {12102, 42431}, {12103, 16964}, {12108, 16772}, {12811, 42813}, {12816, 42416}, {12817, 42503}, {13392, 36208}, {13966, 18585}, {14269, 42139}, {14869, 42152}, {14892, 42110}, {14893, 16809}, {15681, 42144}, {15682, 42131}, {15684, 42133}, {15685, 42140}, {15686, 42085}, {15687, 42086}, {15688, 42119}, {15690, 41108}, {15692, 42116}, {15693, 42516}, {15699, 18582}, {15703, 42815}, {15711, 42419}, {15712, 22236}, {15713, 42092}, {15759, 41101}, {15764, 36450}, {15769, 21467}, {16022, 30462}, {16137, 33654}, {16267, 33416}, {16962, 42636}, {18586, 31412}, {18587, 42561}, {19710, 41113}, {20253, 31709}, {22237, 33703}, {23046, 42094}, {30460, 31945}, {33699, 41120}, {34380, 36758}, {35018, 42166}, {35404, 42097}, {35733, 42565}, {35734, 36464}, {36436, 42223}, {36439, 42216}, {36454, 42221}, {36457, 42215}, {37775, 37904}, {38071, 42095}, {38335, 42141}, {41112, 42098}, {41943, 42500}, {41973, 41981}, {41974, 42580}, {42099, 42507}, {42111, 42513}, {42164, 42433}, {42434, 42780}, {42478, 42817}, {42505, 42687}

X(42913) = midpoint of X(16) and X(395)
X(42913) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 549, 42912}, {13, 547, 42146}, {13, 23303, 547}, {13, 41944, 23303}, {14, 395, 42497}, {14, 42429, 36970}, {14, 42497, 11543}, {16, 11543, 42123}, {16, 16268, 36968}, {16, 16961, 42088}, {16, 16963, 395}, {17, 16239, 42590}, {18, 42148, 546}, {62, 16242, 396}, {62, 16773, 140}, {395, 5321, 16268}, {396, 16242, 140}, {396, 16773, 16242}, {398, 5237, 548}, {549, 42634, 6}, {3411, 5237, 398}, {3845, 42155, 42137}, {5054, 37640, 42124}, {5066, 42628, 37835}, {5237, 42801, 3411}, {5318, 37835, 5066}, {5351, 42147, 33923}, {8703, 10654, 42122}, {10124, 42496, 23302}, {10653, 16645, 5}, {10653, 42149, 16645}, {10654, 11481, 8703}, {11486, 42121, 11542}, {11489, 42118, 42143}, {11543, 42123, 42136}, {11543, 42584, 5321}, {16268, 36968, 5321}, {16644, 42089, 11539}, {16645, 22238, 10653}, {16961, 42429, 14}, {16965, 42599, 3850}, {18581, 42155, 3845}, {18581, 42510, 42155}, {22238, 42149, 5}, {34755, 41944, 13}, {36843, 40694, 550}, {37835, 41100, 5318}, {41108, 42528, 42087}, {41108, 42792, 15690}, {42085, 42625, 15686}, {42087, 42528, 15690}, {42087, 42792, 42528}, {42120, 42818, 42135}, {42151, 42153, 3627}, {42152, 42491, 14869}, {42158, 42163, 3853}, {42166, 42489, 35018}

X(42914) = GIBERT (-1,4,5) POINT

Barycentrics    a^2*S/Sqrt[3] - 5*a^2*SA - 8*SB*SC : :

X(42914) lies on the cubic K1211a and these lines: {2, 10645}, {4, 33416}, {5, 16}, {6, 5055}, {13, 5071}, {14, 547}, {15, 1656}, {17, 11543}, {18, 5056}, {61, 3090}, {62, 5079}, {140, 19107}, {381, 10646}, {395, 10109}, {396, 42503}, {397, 42628}, {398, 42802}, {546, 42100}, {548, 42597}, {549, 42101}, {623, 40335}, {624, 34540}, {631, 42099}, {632, 42087}, {2072, 11516}, {3091, 5351}, {3412, 42627}, {3523, 42104}, {3524, 42112}, {3525, 42090}, {3526, 42093}, {3530, 42108}, {3533, 42140}, {3544, 42120}, {3545, 16242}, {3589, 22490}, {3618, 22489}, {3620, 21359}, {3628, 5238}, {3631, 21360}, {3832, 42091}, {3839, 42113}, {3843, 42611}, {3850, 42088}, {3851, 11481}, {3855, 42105}, {3856, 42584}, {3858, 42109}, {5054, 42096}, {5066, 36968}, {5067, 16964}, {5068, 42106}, {5070, 11480}, {5072, 5237}, {5243, 11791}, {5334, 7486}, {5335, 15022}, {5352, 42126}, {5475, 41408}, {6114, 22891}, {6669, 6777}, {7570, 37775}, {7577, 10642}, {10170, 36981}, {10187, 42137}, {10255, 10635}, {10658, 20304}, {10676, 32767}, {10678, 13565}, {11306, 40334}, {11476, 16868}, {11485, 42488}, {11486, 42801}, {11539, 42144}, {11542, 12812}, {11737, 42629}, {12811, 42123}, {12821, 42595}, {14893, 42429}, {15687, 42501}, {15692, 42430}, {15698, 42515}, {15699, 16241}, {15703, 42116}, {15723, 42626}, {16239, 42136}, {16644, 41122}, {16645, 34755}, {16960, 40694}, {18584, 41406}, {19709, 36969}, {20252, 25235}, {23325, 30403}, {34508, 40901}, {36770, 37171}, {37463, 41037}, {37637, 41409}, {38071, 42145}, {42124, 42163}, {42131, 42491}, {42132, 42153}, {42135, 42157}, {42142, 42149}, {42156, 42818}, {42162, 42472}, {42165, 42591}, {42191, 42564}, {42193, 42565}, {42494, 42531}, {42496, 42778}, {42504, 42589}

X(42914) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16809, 10645}, {2, 42111, 16809}, {5, 16967, 16}, {5, 23303, 16808}, {5, 42121, 42110}, {5, 42489, 42813}, {6, 5055, 42915}, {14, 23302, 34754}, {14, 41943, 42799}, {16, 16967, 42489}, {140, 42107, 19107}, {547, 42143, 23302}, {631, 42103, 42099}, {631, 42473, 42103}, {1656, 42095, 15}, {3090, 18581, 16966}, {3090, 42580, 61}, {3091, 42089, 19106}, {3391, 3392, 16773}, {3628, 5321, 33417}, {5055, 37835, 37832}, {5067, 42139, 42092}, {5071, 11489, 42114}, {5079, 42129, 42098}, {5321, 33417, 5238}, {10645, 16809, 36970}, {11489, 42114, 13}, {11542, 42599, 16961}, {12812, 42599, 42581}, {16645, 42128, 34755}, {16808, 16967, 23303}, {16808, 23303, 16}, {16809, 36967, 42133}, {16961, 42581, 11542}, {16965, 42121, 16}, {16966, 18581, 61}, {16966, 42580, 18581}, {19106, 42089, 5351}, {23302, 34754, 41943}, {23302, 42143, 14}, {34755, 42128, 41107}, {37832, 37835, 16268}, {42092, 42139, 16964}, {42098, 42129, 62}, {42110, 42121, 16965}

X(42915) = GIBERT (1,4,5) POINT

Barycentrics    a^2*S/Sqrt[3] + 5*a^2*SA + 8*SB*SC : :

X(42915) lies on the cubic K1211b and these lines: {2, 10646}, {4, 33417}, {5, 15}, {6, 5055}, {13, 547}, {14, 5071}, {16, 1656}, {17, 5056}, {18, 11542}, {61, 5079}, {62, 3090}, {140, 19106}, {381, 10645}, {395, 42502}, {396, 10109}, {397, 42801}, {398, 42627}, {546, 42099}, {548, 42596}, {549, 42102}, {623, 34541}, {624, 40334}, {631, 42100}, {632, 42088}, {2072, 11515}, {3091, 5352}, {3411, 42628}, {3523, 42105}, {3524, 42113}, {3525, 42091}, {3526, 42094}, {3530, 42109}, {3533, 42141}, {3544, 42119}, {3545, 16241}, {3589, 22489}, {3618, 22490}, {3620, 21360}, {3628, 5237}, {3631, 21359}, {3832, 42090}, {3839, 42112}, {3843, 42610}, {3850, 42087}, {3851, 11480}, {3855, 42104}, {3856, 42585}, {3858, 42108}, {5054, 42097}, {5066, 36967}, {5067, 16965}, {5068, 42103}, {5070, 11481}, {5072, 5238}, {5242, 11790}, {5334, 15022}, {5335, 7486}, {5351, 42127}, {5475, 41409}, {6115, 22846}, {6670, 6778}, {7570, 37776}, {7577, 10641}, {10170, 36979}, {10188, 42136}, {10255, 10634}, {10657, 20304}, {10675, 32767}, {10677, 13565}, {11305, 40335}, {11475, 16868}, {11485, 42802}, {11486, 42489}, {11539, 42145}, {11543, 12812}, {11737, 42630}, {12811, 42122}, {12820, 42594}, {14893, 42430}, {15687, 42500}, {15692, 42429}, {15698, 42514}, {15699, 16242}, {15703, 42115}, {15723, 42625}, {16239, 42137}, {16644, 34754}, {16645, 41121}, {16961, 40693}, {18358, 36765}, {18584, 41407}, {19709, 36970}, {20253, 25236}, {22511, 36771}, {23325, 30402}, {34509, 40900}, {37464, 41036}, {37637, 41408}, {38071, 42144}, {42121, 42166}, {42129, 42156}, {42130, 42490}, {42138, 42158}, {42139, 42152}, {42153, 42817}, {42159, 42473}, {42164, 42590}, {42192, 42562}, {42194, 42563}, {42495, 42530}, {42497, 42777}, {42505, 42588}

X(42915) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16808, 10646}, {2, 42114, 16808}, {5, 16966, 15}, {5, 23302, 16809}, {5, 42124, 42107}, {5, 42488, 42814}, {6, 5055, 42914}, {13, 23303, 34755}, {13, 41944, 42800}, {15, 16966, 42488}, {140, 42110, 19106}, {547, 42146, 23303}, {631, 42106, 42100}, {631, 42472, 42106}, {1656, 42098, 16}, {3090, 18582, 16967}, {3090, 42581, 62}, {3091, 42092, 19107}, {3366, 3367, 16772}, {3628, 5318, 33416}, {5055, 37832, 37835}, {5067, 42142, 42089}, {5071, 11488, 42111}, {5079, 42132, 42095}, {5318, 33416, 5237}, {10646, 16808, 36969}, {11488, 42111, 14}, {11543, 42598, 16960}, {12812, 42598, 42580}, {16644, 42125, 34754}, {16808, 36968, 42134}, {16809, 16966, 23302}, {16809, 23302, 15}, {16960, 42580, 11543}, {16964, 42124, 15}, {16967, 18582, 62}, {16967, 42581, 18582}, {19107, 42092, 5352}, {23303, 34755, 41944}, {23303, 42146, 13}, {34754, 42125, 41108}, {37832, 37835, 16267}, {42089, 42142, 16965}, {42095, 42132, 61}, {42107, 42124, 16964}

X(42916) = GIBERT (8,3,7) POINT

Barycentrics    8*a^2*S/Sqrt[3] + 7*a^2*SA + 6*SB*SC : :

X(42916) lies on the cubic K1211a and these lines: {5, 5334}, {6, 632}, {13, 19710}, {15, 3627}, {16, 396}, {17, 3858}, {18, 10188}, {30, 42817}, {548, 42815}, {550, 5340}, {3412, 23303}, {3545, 42803}, {3845, 18582}, {3854, 42806}, {3857, 22236}, {5238, 42145}, {5318, 42434}, {5321, 16962}, {5335, 8703}, {10154, 37776}, {10653, 15711}, {11309, 20080}, {11486, 14869}, {11539, 37640}, {11543, 15699}, {13941, 35738}, {15686, 42127}, {15687, 42119}, {15704, 42116}, {15713, 42517}, {16267, 42088}, {16772, 16960}, {16966, 41122}, {33699, 42130}, {34754, 42135}, {35018, 42816}, {35404, 42094}, {36836, 42137}, {41991, 42133}, {42089, 42634}, {42092, 42491}, {42105, 42122}, {42148, 42781}, {42158, 42687}, {42162, 42585}, {42431, 42684}

X(42916) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 632, 42917}, {15, 42166, 42144}, {11485, 11488, 42627}, {11485, 42132, 42139}, {11485, 42627, 5}, {16644, 42633, 15699}, {16772, 16960, 42118}, {34754, 42598, 42135}

X(42917) = GIBERT (-8,3,7) POINT

Barycentrics    8*a^2*S/Sqrt[3] - 7*a^2*SA - 6*SB*SC : :

X(42917) lies on the cubic K1211b and these lines: {5, 5335}, {6, 632}, {14, 19710}, {15, 395}, {16, 3627}, {17, 10187}, {18, 3858}, {30, 42818}, {548, 42816}, {550, 5339}, {3411, 23302}, {3545, 42804}, {3845, 18581}, {3854, 42805}, {3857, 22238}, {5237, 42144}, {5318, 16963}, {5321, 42433}, {5334, 8703}, {8972, 35738}, {10154, 37775}, {10654, 15711}, {11310, 20080}, {11485, 14869}, {11539, 37641}, {11542, 15699}, {15686, 42126}, {15687, 42120}, {15704, 42115}, {15713, 42516}, {16268, 42087}, {16773, 16961}, {16967, 41121}, {33699, 42131}, {34755, 42138}, {35018, 42815}, {35404, 42093}, {36843, 42136}, {41991, 42134}, {42089, 42490}, {42092, 42633}, {42104, 42123}, {42147, 42782}, {42157, 42686}, {42159, 42584}, {42432, 42685}

X(42917) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 632, 42916}, {16, 42163, 42145}, {11486, 11489, 42628}, {11486, 42129, 42142}, {11486, 42628, 5}, {16645, 42634, 15699}, {16773, 16961, 42117}, {34755, 42599, 42138}

X(42918) = GIBERT (-1,4,3) POINT

Barycentrics    a^2*S/Sqrt[3] - 3*a^2*SA - 8*SB*SC : :

X(42918) lies on the cubic K1211a and these lines: {2, 12821}, {4, 10187}, {5, 15}, {6, 3851}, {13, 5066}, {14, 3545}, {16, 381}, {17, 5068}, {18, 3850}, {30, 33416}, {61, 5072}, {62, 3091}, {140, 42099}, {395, 38071}, {396, 11737}, {398, 16960}, {546, 5237}, {547, 36967}, {549, 42108}, {631, 42104}, {1656, 10645}, {2045, 42184}, {2046, 42183}, {3090, 5352}, {3364, 42178}, {3365, 42177}, {3389, 42204}, {3390, 42203}, {3523, 42112}, {3526, 42096}, {3528, 42597}, {3544, 11488}, {3628, 42087}, {3832, 42086}, {3839, 36968}, {3843, 11481}, {3845, 16242}, {3854, 42134}, {3855, 11489}, {3856, 16773}, {3857, 42118}, {3858, 42102}, {3859, 42148}, {3861, 42109}, {5054, 42475}, {5055, 11480}, {5056, 42092}, {5067, 42140}, {5071, 16241}, {5079, 5238}, {5339, 34754}, {5340, 42818}, {5349, 35018}, {5351, 42097}, {6777, 20253}, {7486, 42694}, {7547, 10642}, {7577, 11475}, {7684, 22850}, {7685, 41036}, {7746, 41409}, {10024, 11515}, {10109, 12817}, {10254, 10634}, {10303, 42499}, {10641, 16868}, {10653, 41106}, {10658, 14644}, {10676, 23325}, {11304, 40334}, {11476, 35488}, {11485, 19709}, {11486, 42813}, {11542, 12811}, {12100, 42430}, {12812, 42164}, {14892, 16962}, {14893, 42584}, {15022, 42160}, {15687, 42528}, {15765, 42179}, {16239, 42585}, {17800, 42611}, {18383, 30403}, {18585, 42181}, {19780, 39590}, {22615, 42172}, {22644, 35739}, {22846, 31706}, {23005, 36765}, {35738, 42168}, {36836, 42592}, {36992, 37464}, {40694, 42142}, {41037, 41040}, {41099, 42141}, {41990, 42634}, {41991, 42165}, {42115, 42431}, {42128, 42153}, {42151, 42629}, {42152, 42776}, {42156, 42816}, {42209, 42237}, {42210, 42235}, {42229, 42274}, {42230, 42277}

X(42918) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42103, 19107}, {4, 16967, 10646}, {4, 42089, 42100}, {4, 42111, 16967}, {4, 42473, 42111}, {5, 5321, 16966}, {5, 16809, 15}, {5, 42107, 16809}, {5, 42135, 23302}, {5, 42814, 42488}, {6, 3851, 42919}, {15, 16809, 42814}, {16, 42095, 37835}, {18, 5318, 34755}, {18, 41974, 42801}, {140, 42101, 42099}, {381, 37835, 36969}, {381, 42095, 16}, {381, 42129, 42094}, {395, 42800, 42636}, {398, 42146, 16960}, {546, 23303, 19106}, {546, 42580, 5237}, {1656, 42093, 10645}, {3090, 42085, 33417}, {3091, 18581, 16808}, {3366, 3367, 42147}, {3544, 42159, 42581}, {3545, 42139, 18582}, {3850, 42143, 5318}, {3855, 11489, 42106}, {3858, 42121, 42102}, {5056, 42133, 42092}, {5066, 11543, 42110}, {5068, 5334, 42114}, {5072, 42125, 42098}, {5318, 34755, 41974}, {5318, 42143, 18}, {5321, 16966, 15}, {5334, 42114, 17}, {5335, 16961, 62}, {5335, 18581, 16961}, {5339, 42132, 34754}, {5349, 42122, 42630}, {10645, 42093, 42432}, {11489, 42106, 16965}, {11543, 42110, 13}, {16645, 42127, 16}, {16808, 16961, 5335}, {16808, 18581, 62}, {16809, 16964, 42135}, {16809, 16966, 5321}, {16964, 23302, 15}, {16967, 42100, 42089}, {18582, 42139, 14}, {19106, 23303, 5237}, {19106, 42580, 23303}, {23302, 42135, 16964}, {33417, 42085, 5352}, {36969, 37835, 41944}, {42089, 42100, 10646}, {42092, 42133, 42157}, {42094, 42095, 42129}, {42094, 42129, 16}, {42098, 42125, 61}, {42102, 42121, 42158}

X(42919) = GIBERT (1,4,3) POINT

Barycentrics    a^2*S/Sqrt[3] + 3*a^2*SA + 8*SB*SC : :

X(42919) lies on the cubic K1211b and these lines: {2, 12820}, {4, 10188}, {5, 16}, {6, 3851}, {13, 3545}, {14, 5066}, {15, 381}, {17, 3850}, {18, 5068}, {30, 33417}, {61, 3091}, {62, 5072}, {140, 42100}, {395, 11737}, {396, 38071}, {397, 16961}, {546, 5238}, {547, 36968}, {549, 42109}, {631, 42105}, {1656, 10646}, {2045, 42185}, {2046, 42186}, {3090, 5351}, {3364, 42206}, {3365, 42205}, {3389, 42176}, {3390, 42175}, {3523, 42113}, {3526, 42097}, {3528, 42596}, {3544, 11489}, {3628, 42088}, {3832, 42085}, {3839, 36967}, {3843, 11480}, {3845, 16241}, {3854, 42133}, {3855, 11488}, {3856, 16772}, {3857, 42117}, {3858, 42101}, {3859, 42147}, {3861, 42108}, {5054, 42474}, {5055, 11481}, {5056, 42089}, {5067, 42141}, {5071, 16242}, {5079, 5237}, {5339, 42817}, {5340, 34755}, {5350, 35018}, {5352, 42096}, {5478, 36766}, {6778, 20252}, {7486, 42695}, {7547, 10641}, {7577, 11476}, {7684, 41037}, {7685, 22894}, {7746, 41408}, {10024, 11516}, {10109, 12816}, {10254, 10635}, {10303, 42498}, {10642, 16868}, {10654, 41106}, {10657, 14644}, {10675, 23325}, {11303, 40335}, {11475, 35488}, {11485, 42814}, {11486, 19709}, {11543, 12811}, {12100, 42429}, {12812, 42165}, {14892, 16963}, {14893, 42585}, {15022, 42161}, {15687, 42529}, {15765, 42182}, {16239, 42584}, {17800, 42610}, {18383, 30402}, {18585, 42180}, {19781, 39590}, {22615, 42174}, {22644, 42173}, {22891, 31705}, {35738, 42169}, {36843, 42593}, {36994, 37463}, {40693, 42139}, {41036, 41041}, {41099, 42140}, {41990, 42633}, {41991, 42164}, {42116, 42432}, {42125, 42156}, {42149, 42775}, {42150, 42630}, {42153, 42815}, {42207, 42238}, {42208, 42236}, {42227, 42274}, {42228, 42277}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42106, 19106}, {4, 16966, 10645}, {4, 42092, 42099}, {4, 42114, 16966}, {4, 42472, 42114}, {5, 5318, 16967}, {5, 16808, 16}, {5, 42110, 16808}, {5, 42138, 23303}, {5, 42813, 42489}, {6, 3851, 42918}, {15, 42098, 37832}, {16, 16808, 42813}, {17, 5321, 34754}, {17, 41973, 42802}, {140, 42102, 42100}, {381, 37832, 36970}, {381, 42098, 15}, {381, 42132, 42093}, {396, 42799, 42635}, {397, 42143, 16961}, {546, 23302, 19107}, {546, 42581, 5238}, {1656, 42094, 10646}, {3090, 42086, 33416}, {3091, 18582, 16809}, {3391, 3392, 42148}, {3544, 42162, 42580}, {3545, 42142, 18581}, {3850, 42146, 5321}, {3855, 11488, 42103}, {3858, 42124, 42101}, {5056, 42134, 42089}, {5066, 11542, 42107}, {5068, 5335, 42111}, {5072, 42128, 42095}, {5318, 16967, 16}, {5321, 34754, 41973}, {5321, 42146, 17}, {5334, 16960, 61}, {5334, 18582, 16960}, {5335, 42111, 18}, {5340, 42129, 34755}, {5350, 42123, 42629}, {10646, 42094, 42431}, {11488, 42103, 16964}, {11542, 42107, 14}, {16644, 42126, 15}, {16808, 16965, 42138}, {16808, 16967, 5318}, {16809, 16960, 5334}, {16809, 18582, 61}, {16965, 23303, 16}, {16966, 42099, 42092}, {18581, 42142, 13}, {19107, 23302, 5238}, {19107, 42581, 23302}, {23303, 42138, 16965}, {33416, 42086, 5351}, {36970, 37832, 41943}, {42089, 42134, 42158}, {42092, 42099, 10645}, {42093, 42098, 42132}, {42093, 42132, 15}, {42095, 42128, 62}, {42101, 42124, 42157}

X(42920) = GIBERT (-3,5,3) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA - 10*SB*SC : :

X(42920) lies on the cubic K1211a and these lines: {2, 5352}, {3, 5349}, {4, 16}, {5, 5339}, {6, 3850}, {13, 3855}, {14, 3091}, {15, 5056}, {17, 5068}, {20, 37835}, {61, 3545}, {62, 3832}, {140, 42085}, {376, 42489}, {381, 397}, {382, 42599}, {395, 3843}, {396, 5072}, {398, 3851}, {546, 10653}, {547, 36836}, {550, 42089}, {631, 36970}, {633, 22491}, {635, 37171}, {1656, 5321}, {1657, 23303}, {3090, 16964}, {3146, 42429}, {3522, 19107}, {3523, 16967}, {3524, 12817}, {3525, 36967}, {3526, 42164}, {3529, 16242}, {3533, 10645}, {3543, 5237}, {3544, 37832}, {3627, 16645}, {3628, 42154}, {3830, 16773}, {3839, 16965}, {3845, 22238}, {3853, 36843}, {3854, 16808}, {3858, 5340}, {3861, 42155}, {5055, 42147}, {5059, 10646}, {5066, 42156}, {5067, 5238}, {5071, 41978}, {5073, 42091}, {5079, 16772}, {5335, 22237}, {5350, 11486}, {5351, 33703}, {5869, 7694}, {7486, 16241}, {10299, 33416}, {10303, 42434}, {11488, 42802}, {14269, 42165}, {14869, 42611}, {15022, 42488}, {15682, 42433}, {15683, 42694}, {15699, 42490}, {15704, 42491}, {15708, 42597}, {15711, 42587}, {15712, 42136}, {15720, 42087}, {16268, 41099}, {16960, 42472}, {16961, 41974}, {16966, 41973}, {17578, 36968}, {19709, 42598}, {21735, 42099}, {33603, 42806}, {33923, 42096}, {35018, 42117}, {37641, 42813}, {38071, 41119}, {41108, 42581}, {42097, 42628}, {42102, 42818}, {42110, 42816}, {42113, 42121}, {42122, 42773}, {42126, 42692}, {42188, 42565}, {42190, 42564}, {42207, 42277}, {42208, 42274}, {42242, 42273}, {42243, 42270}, {42690, 42815}

X(42920) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5365, 42157}, {2, 42814, 42160}, {4, 18, 42151}, {4, 11489, 42158}, {4, 18581, 42149}, {4, 42149, 42086}, {4, 42158, 42105}, {4, 42495, 18}, {4, 42776, 16809}, {5, 5339, 42152}, {5, 42159, 10654}, {6, 3850, 42921}, {14, 3091, 40693}, {17, 5068, 42114}, {18, 42151, 42149}, {18, 42495, 18581}, {381, 40694, 42162}, {381, 42163, 40694}, {395, 3843, 42161}, {398, 3851, 18582}, {398, 42107, 3851}, {546, 42153, 10653}, {1656, 5321, 42150}, {1656, 42150, 42092}, {3523, 42133, 42432}, {3523, 42432, 42090}, {3851, 42125, 398}, {3858, 5340, 42106}, {3858, 11543, 5340}, {5056, 5343, 15}, {5068, 5334, 17}, {5321, 42111, 42092}, {5339, 42152, 10654}, {5365, 42157, 42160}, {16809, 18581, 42103}, {16809, 42139, 18581}, {16967, 42133, 42090}, {16967, 42432, 3523}, {18581, 42103, 42086}, {18581, 42105, 11489}, {18581, 42151, 18}, {36970, 42580, 631}, {40694, 42163, 41120}, {41120, 42162, 40694}, {42089, 42093, 42112}, {42093, 42143, 42089}, {42095, 42135, 42085}, {42101, 42129, 42091}, {42103, 42149, 4}, {42107, 42125, 18582}, {42111, 42150, 1656}, {42139, 42776, 4}, {42152, 42159, 5339}, {42157, 42814, 5365}, {42611, 42626, 14869}

X(42921) = GIBERT (3,5,3) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA + 10*SB*SC : :

X(42921) lies on the cubic K1211b and these lines: {2, 5351}, {3, 5350}, {4, 15}, {5, 5340}, {6, 3850}, {13, 3091}, {14, 3855}, {16, 5056}, {18, 5068}, {20, 37832}, {61, 3832}, {62, 3545}, {140, 42086}, {376, 42488}, {381, 398}, {382, 42598}, {395, 5072}, {396, 3843}, {397, 3851}, {546, 10654}, {547, 36843}, {550, 42092}, {631, 36969}, {634, 22492}, {636, 37170}, {1656, 5318}, {1657, 23302}, {3090, 16965}, {3146, 42430}, {3522, 19106}, {3523, 16966}, {3524, 12816}, {3525, 36968}, {3526, 42165}, {3529, 16241}, {3533, 10646}, {3543, 5238}, {3544, 37835}, {3627, 16644}, {3628, 42155}, {3830, 16772}, {3839, 16964}, {3845, 22236}, {3853, 36836}, {3854, 16809}, {3858, 5339}, {3861, 42154}, {5055, 42148}, {5059, 10645}, {5066, 42153}, {5067, 5237}, {5071, 41977}, {5073, 42090}, {5079, 16773}, {5334, 22235}, {5349, 11485}, {5352, 33703}, {5868, 7694}, {7486, 16242}, {10299, 33417}, {10303, 42433}, {11489, 42801}, {14269, 42164}, {14869, 42610}, {15022, 42489}, {15682, 42434}, {15683, 42695}, {15699, 42491}, {15704, 42490}, {15708, 42596}, {15711, 42586}, {15712, 42137}, {15720, 42088}, {16267, 41099}, {16960, 41973}, {16961, 42473}, {16967, 41974}, {17578, 36967}, {19709, 42599}, {21735, 42100}, {33602, 42805}, {33923, 42097}, {35018, 42118}, {37640, 42814}, {38071, 41120}, {41107, 42580}, {42096, 42627}, {42101, 42817}, {42107, 42815}, {42112, 42124}, {42123, 42774}, {42127, 42693}, {42187, 42563}, {42189, 42562}, {42209, 42277}, {42210, 42274}, {42244, 42273}, {42245, 42270}, {42691, 42816}

X(42921) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5366, 42158}, {2, 42813, 42161}, {4, 17, 42150}, {4, 11488, 42157}, {4, 18582, 42152}, {4, 42152, 42085}, {4, 42157, 42104}, {4, 42494, 17}, {4, 42775, 16808}, {5, 5340, 42149}, {5, 42162, 10653}, {6, 3850, 42920}, {13, 3091, 40694}, {17, 42150, 42152}, {17, 42494, 18582}, {18, 5068, 42111}, {381, 40693, 42159}, {381, 42166, 40693}, {396, 3843, 42160}, {397, 3851, 18581}, {397, 42110, 3851}, {546, 42156, 10654}, {1656, 5318, 42151}, {1656, 42151, 42089}, {3523, 42134, 42431}, {3523, 42431, 42091}, {3851, 42128, 397}, {3858, 5339, 42103}, {3858, 11542, 5339}, {5056, 5344, 16}, {5068, 5335, 18}, {5318, 42114, 42089}, {5340, 42149, 10653}, {5366, 42158, 42161}, {16808, 18582, 42106}, {16808, 42142, 18582}, {16966, 42134, 42091}, {16966, 42431, 3523}, {18582, 42104, 11488}, {18582, 42106, 42085}, {18582, 42150, 17}, {36969, 42581, 631}, {40693, 42166, 41119}, {41119, 42159, 40693}, {42092, 42094, 42113}, {42094, 42146, 42092}, {42098, 42138, 42086}, {42102, 42132, 42090}, {42106, 42152, 4}, {42110, 42128, 18581}, {42114, 42151, 1656}, {42142, 42775, 4}, {42149, 42162, 5340}, {42158, 42813, 5366}, {42610, 42625, 14869}

X(42922) = GIBERT (8,3,-1) POINT

Barycentrics    8*a^2*S/Sqrt[3] - a^2*SA + 6*SB*SC : :

X(42922) lies on the cubic K1211a and these lines: {5, 5335}, {6, 3627}, {13, 15699}, {14, 3845}, {15, 397}, {16, 632}, {17, 42793}, {61, 42145}, {62, 3857}, {140, 22235}, {549, 10653}, {3530, 42817}, {3858, 5340}, {3861, 42816}, {5056, 42805}, {5066, 33602}, {5334, 15687}, {5344, 42125}, {8703, 42120}, {11485, 15704}, {11488, 15712}, {11539, 42132}, {14869, 42115}, {15686, 37640}, {15711, 16960}, {16965, 42109}, {17504, 42416}, {18581, 38071}, {19106, 35404}, {19710, 42122}, {22236, 42584}, {22238, 42146}, {23046, 37641}, {23267, 35738}, {33699, 42126}, {34755, 42166}, {36970, 42683}, {40693, 42123}, {41100, 42502}, {41112, 42098}, {41991, 42139}, {42086, 42585}, {42089, 42610}, {42124, 42148}, {42127, 42140}, {42143, 42162}, {42144, 42165}, {42164, 42629}, {42528, 42687}

X(42922) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3627, 42923}, {6, 42161, 42136}, {11486, 42142, 42628}, {41974, 42088, 42118}, {42115, 42627, 14869}, {42142, 42628, 5}, {42155, 42633, 19710}

X(42923) = GIBERT (8,-3,1) POINT

Barycentrics    8*a^2*S/Sqrt[3] + a^2*SA - 6*SB*SC : :

X(42923) lies on the cubic K1211b and these lines: {5, 5334}, {6, 3627}, {13, 3845}, {14, 15699}, {15, 632}, {16, 398}, {18, 42794}, {61, 3857}, {62, 42144}, {140, 22237}, {549, 10654}, {3530, 42818}, {3858, 5339}, {3861, 42815}, {5056, 42806}, {5066, 33603}, {5335, 15687}, {5343, 42128}, {8703, 42119}, {11486, 15704}, {11489, 15712}, {11539, 42129}, {14869, 42116}, {15686, 37641}, {15711, 16961}, {16964, 42108}, {17504, 42415}, {18582, 38071}, {19107, 35404}, {19710, 42123}, {22236, 42143}, {22238, 42585}, {23046, 37640}, {23273, 35738}, {33699, 42127}, {34754, 42163}, {36969, 42682}, {40694, 42122}, {41101, 42503}, {41113, 42095}, {41991, 42142}, {42085, 42584}, {42092, 42611}, {42121, 42147}, {42126, 42141}, {42145, 42164}, {42146, 42159}, {42165, 42630}, {42529, 42686}

X(42923) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3627, 42922}, {6, 42160, 42137}, {11485, 42139, 42627}, {41973, 42087, 42117}, {42116, 42628, 14869}, {42139, 42627, 5}, {42154, 42634, 19710}

X(42924) = GIBERT (6,1,-3) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*a^2*SA + 2*SB*SC : :

X(42924) lies on the cubic K1211a and these lines: {3, 37640}, {4, 11409}, {5, 5340}, {6, 550}, {13, 3628}, {14, 3853}, {15, 33923}, {16, 17}, {18, 3850}, {20, 42804}, {30, 62}, {61, 548}, {202, 15172}, {381, 5366}, {382, 5343}, {395, 546}, {396, 3530}, {530, 6695}, {547, 41107}, {549, 36843}, {627, 37352}, {632, 42156}, {634, 37341}, {1587, 42202}, {1588, 42201}, {1656, 5335}, {1657, 42117}, {3070, 42178}, {3071, 42177}, {3411, 3861}, {3522, 11485}, {3523, 42115}, {3526, 42590}, {3533, 22235}, {3534, 42419}, {3545, 42805}, {3627, 40694}, {3843, 42776}, {3845, 42153}, {3851, 5344}, {3858, 18581}, {5056, 42128}, {5059, 42131}, {5066, 16963}, {5068, 42129}, {5073, 5334}, {5076, 42517}, {5238, 34200}, {5321, 42431}, {5339, 42086}, {5349, 19106}, {5351, 12100}, {5365, 42141}, {5873, 40921}, {6111, 6750}, {7127, 18990}, {7583, 42230}, {7584, 42229}, {8367, 12155}, {8703, 22236}, {8739, 13488}, {10109, 41944}, {10124, 42488}, {10654, 15704}, {11481, 15712}, {11488, 15720}, {11539, 42491}, {11737, 42580}, {11812, 16267}, {12101, 42533}, {12102, 42814}, {12103, 36968}, {12108, 42496}, {12811, 37835}, {12812, 42489}, {14813, 42216}, {14814, 42215}, {14869, 16644}, {14891, 16962}, {14893, 16268}, {15687, 42159}, {15690, 42434}, {15691, 41101}, {15699, 41112}, {16239, 16242}, {16808, 42628}, {16881, 36978}, {16961, 42102}, {18470, 34002}, {19107, 42780}, {21735, 42116}, {22531, 41035}, {23303, 35018}, {33699, 42508}, {35404, 41113}, {35738, 42234}, {36836, 42633}, {36967, 41972}, {38335, 42588}, {41943, 41983}, {41973, 42100}, {41982, 42791}, {41992, 42610}, {42088, 42157}, {42092, 42774}, {42134, 42495}, {42685, 42794}

X(42924) = crosssum of X(61) and X(5237)
X(42924) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 550, 42925}, {6, 42123, 42122}, {6, 42151, 550}, {13, 16773, 3628}, {14, 42165, 3853}, {16, 397, 140}, {18, 3850, 42143}, {18, 5318, 3850}, {18, 41974, 5318}, {62, 41100, 42148}, {62, 42158, 398}, {140, 397, 11542}, {395, 16965, 546}, {396, 5237, 3530}, {398, 42148, 42158}, {550, 42151, 42123}, {3411, 36969, 42163}, {3411, 42163, 42497}, {3533, 22235, 42132}, {3627, 42634, 40694}, {3851, 5344, 42138}, {3861, 42497, 42163}, {5335, 42121, 42146}, {5340, 22238, 42149}, {5340, 42149, 5}, {5344, 11489, 3851}, {5351, 16772, 12100}, {10653, 22238, 5}, {10653, 42149, 5340}, {11481, 42152, 15712}, {11486, 42118, 11543}, {11543, 42118, 42137}, {16242, 42598, 16239}, {16645, 42162, 5}, {16962, 42792, 14891}, {16963, 42813, 42599}, {34755, 41974, 18}, {36843, 40693, 549}, {36968, 42147, 12103}, {36969, 42163, 3861}, {40693, 42510, 36843}, {40694, 42155, 3627}, {42117, 42120, 42584}, {42118, 42135, 42127}, {42153, 42161, 3845}, {42599, 42813, 5066}

X(42925) = GIBERT (6,-1,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*a^2*SA - 2*SB*SC : :

X(42925) lies on the cubic K1211b and these lines: {3, 37641}, {4, 11408}, {5, 5339}, {6, 550}, {13, 3853}, {14, 3628}, {15, 18}, {16, 33923}, {17, 3850}, {20, 42803}, {30, 61}, {62, 548}, {203, 15172}, {381, 5365}, {382, 5344}, {395, 3530}, {396, 546}, {531, 6694}, {547, 41108}, {549, 36836}, {628, 37351}, {632, 42153}, {633, 37340}, {1587, 42200}, {1588, 42199}, {1656, 5334}, {1657, 42118}, {2307, 15171}, {3070, 42176}, {3071, 42175}, {3412, 3861}, {3522, 11486}, {3523, 42116}, {3526, 42591}, {3533, 22237}, {3534, 42420}, {3545, 42806}, {3627, 40693}, {3843, 42775}, {3845, 42156}, {3851, 5343}, {3858, 18582}, {5056, 42125}, {5059, 42130}, {5066, 16962}, {5068, 42132}, {5073, 5335}, {5076, 42516}, {5237, 34200}, {5318, 42432}, {5340, 42085}, {5350, 19107}, {5352, 12100}, {5366, 42140}, {5872, 40922}, {6110, 6750}, {7583, 42228}, {7584, 42227}, {8367, 12154}, {8703, 22238}, {8740, 13488}, {10109, 41943}, {10124, 42489}, {10653, 15704}, {11480, 15712}, {11489, 15720}, {11539, 42490}, {11737, 42581}, {11812, 16268}, {12101, 42532}, {12102, 42813}, {12103, 36967}, {12108, 42497}, {12811, 37832}, {12812, 42488}, {14813, 42215}, {14814, 42216}, {14869, 16645}, {14891, 16963}, {14893, 16267}, {15687, 42162}, {15690, 42433}, {15691, 41100}, {15699, 41113}, {16239, 16241}, {16809, 42627}, {16881, 36980}, {16960, 42101}, {18468, 34002}, {19106, 42779}, {21735, 42115}, {22532, 41034}, {23302, 35018}, {33699, 42509}, {35404, 41112}, {35738, 42231}, {36843, 42634}, {36968, 41971}, {38335, 42589}, {41944, 41983}, {41974, 42099}, {41982, 42792}, {41992, 42611}, {42087, 42158}, {42089, 42773}, {42133, 42494}, {42684, 42793}

X(42925) = crosssum of X(62) and X(5238)
X(42925) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 550, 42924}, {6, 42122, 42123}, {6, 42150, 550}, {13, 42164, 3853}, {14, 16772, 3628}, {15, 398, 140}, {17, 3850, 42146}, {17, 5321, 3850}, {17, 41973, 5321}, {61, 41101, 42147}, {61, 42157, 397}, {140, 398, 11543}, {395, 5238, 3530}, {396, 16964, 546}, {397, 42147, 42157}, {550, 42150, 42122}, {3412, 36970, 42166}, {3412, 42166, 42496}, {3533, 22237, 42129}, {3627, 42633, 40693}, {3851, 5343, 42135}, {3861, 42496, 42166}, {5334, 42124, 42143}, {5339, 22236, 42152}, {5339, 42152, 5}, {5343, 11488, 3851}, {5352, 16773, 12100}, {10654, 22236, 5}, {10654, 42152, 5339}, {11480, 42149, 15712}, {11485, 42117, 11542}, {11542, 42117, 42136}, {16241, 42599, 16239}, {16644, 42159, 5}, {16962, 42814, 42598}, {16963, 42791, 14891}, {34754, 41973, 17}, {36836, 40694, 549}, {36967, 42148, 12103}, {36970, 42166, 3861}, {40693, 42154, 3627}, {40694, 42511, 36836}, {42117, 42138, 42126}, {42118, 42119, 42585}, {42156, 42160, 3845}, {42598, 42814, 5066}

X(42926) = GIBERT (24,5,-36) POINT

Barycentrics    4*Sqrt[3]*a^2*S - 18*a^2*SA + 5*SB*SC : :

X(42926) lies on the cubic K1212a and these lines: {4, 42115}, {13, 631}, {14, 3529}, {15, 21735}, {18, 15682}, {376, 22238}, {397, 10299}, {549, 33604}, {3090, 42491}, {3523, 42815}, {3533, 5344}, {3545, 5237}, {5334, 42805}, {5349, 33703}, {5365, 42108}, {5366, 42793}, {11489, 41977}, {15698, 42152}, {15709, 42774}, {15717, 42496}, {15719, 42508}, {16242, 42695}, {19708, 42420}, {35409, 42814}, {36968, 42495}, {41113, 42433}, {42794, 42806}

X(42927) = GIBERT (24,-5,36) POINT

Barycentrics    4*Sqrt[3]*a^2*S + 18*a^2*SA - 5*SB*SC : :

X(42927) lies on the cubic K1212b and these lines: {4, 42116}, {13, 3529}, {14, 631}, {16, 21735}, {17, 15682}, {376, 22236}, {398, 10299}, {549, 33605}, {3090, 42490}, {3523, 42816}, {3533, 5343}, {3545, 5238}, {5335, 42806}, {5350, 33703}, {5365, 42794}, {5366, 42109}, {11488, 41978}, {15698, 42149}, {15709, 42773}, {15717, 42497}, {15719, 42509}, {16241, 42694}, {19708, 42419}, {35409, 42813}, {36967, 42494}, {41112, 42434}, {42793, 42805}

X(42928) = GIBERT (7,2,-17) POINT

Barycentrics    7*a^2*S/Sqrt[3] - 17*a^2*SA + 4*SB*SC : :

X(42928) lies on the cubic K1210a and these lines: {2, 10646}, {6, 14093}, {13, 15718}, {14, 15686}, {15, 21735}, {16, 548}, {17, 15712}, {18, 1657}, {3627, 5351}, {3843, 16967}, {3850, 42088}, {5072, 19106}, {5237, 16961}, {5318, 42492}, {11480, 42435}, {12108, 33417}, {14890, 42146}, {14891, 41943}, {14892, 42102}, {15684, 16809}, {15689, 16963}, {15706, 16241}, {16242, 38335}, {16965, 42132}, {23302, 41983}, {33703, 42091}, {34754, 42791}, {34755, 42529}, {41944, 42112}, {42096, 42519}, {42110, 42597}, {42116, 42532}, {42117, 42792}, {42135, 42793}, {42148, 42781}, {42157, 42801}, {42158, 42689}, {42489, 42584}, {42798, 42802}

X(42928) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10646, 42631, 42086}, {12816, 42086, 42629}

X(42929) = GIBERT (7,-2,17) POINT

Barycentrics    7*a^2*S/Sqrt[3] + 17*a^2*SA - 4*SB*SC : :

X(42929) lies on the cubic K1212b and these lines: {2, 10645}, {6, 14093}, {13, 15686}, {14, 15718}, {15, 548}, {16, 21735}, {17, 1657}, {18, 15712}, {3627, 5352}, {3843, 16966}, {3850, 42087}, {5072, 19107}, {5238, 16960}, {5321, 42493}, {11481, 42436}, {12108, 33416}, {14890, 42143}, {14891, 41944}, {14892, 42101}, {15684, 16808}, {15689, 16962}, {15706, 16242}, {16241, 38335}, {16964, 42129}, {23303, 41983}, {33703, 42090}, {34754, 42528}, {34755, 42792}, {41943, 42113}, {42097, 42518}, {42107, 42596}, {42115, 42533}, {42118, 42791}, {42138, 42794}, {42147, 42782}, {42157, 42688}, {42158, 42802}, {42488, 42585}, {42797, 42801}

X(42929) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10645, 42632, 42085}, {12817, 42085, 42630}

X(42930) = GIBERT (7,2,21) POINT

Barycentrics    7*a^2*S/Sqrt[3] + 21*a^2*SA + 4*SB*SC : :

X(42930) lies on the cubic K1212a and these lines: {4, 10188}, {13, 8703}, {14, 5054}, {15, 3411}, {16, 15692}, {62, 42687}, {547, 36967}, {632, 5321}, {5070, 16809}, {5079, 33417}, {5238, 42089}, {5318, 41981}, {5335, 21734}, {12103, 19106}, {12811, 42087}, {12817, 42500}, {15681, 16241}, {15696, 42100}, {15719, 16242}, {16960, 41974}, {16961, 42116}, {16962, 42796}, {16967, 42773}, {19107, 19709}, {21156, 38730}, {22235, 42091}, {33606, 42531}, {34755, 42793}, {37832, 42543}, {38071, 42492}, {42103, 42632}, {42110, 42430}, {42121, 42794}, {42158, 42817}, {42434, 42610}, {42498, 42684}

X(42930) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15719, 42799, 16242}, {42090, 42092, 42472}

X(42931) = GIBERT (-7,2,21) POINT

Barycentrics    7*a^2*S/Sqrt[3] - 21*a^2*SA - 4*SB*SC : :

X(42931) lies on the cubic K1212b and these lines: {4, 10187}, {13, 5054}, {14, 8703}, {15, 15692}, {16, 3412}, {61, 42686}, {547, 36968}, {632, 5318}, {5070, 16808}, {5079, 33416}, {5237, 42092}, {5321, 41981}, {5334, 21734}, {12103, 19107}, {12811, 42088}, {12816, 42501}, {15681, 16242}, {15696, 42099}, {15719, 16241}, {16960, 42115}, {16961, 41973}, {16963, 42795}, {16966, 42774}, {19106, 19709}, {21157, 38730}, {22237, 42090}, {33607, 42530}, {34754, 42794}, {37835, 42544}, {38071, 42493}, {42106, 42631}, {42107, 42429}, {42124, 42793}, {42157, 42818}, {42433, 42611}, {42499, 42685}

X(42931) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15719, 42800, 16241}, {42089, 42091, 42473}

X(42932) = GIBERT (24,5,46) POINT

Barycentrics    4*Sqrt[3]*a^2*S + 23*a^2*SA + 5*SB*SC : :

X(42932) lies on the cubic K1212a and these lines: {2, 33603}, {15, 15708}, {16, 15692}, {17, 20}, {18, 10303}, {376, 42817}, {396, 10304}, {631, 42497}, {3523, 16773}, {3524, 42634}, {3543, 11480}, {3839, 36967}, {5056, 5238}, {5071, 42492}, {5334, 41971}, {7486, 42154}, {10299, 42633}, {10645, 41112}, {11488, 15697}, {11489, 42803}, {15683, 42124}, {15721, 16645}, {16241, 42103}, {16644, 42693}, {33607, 42086}, {37640, 42792}, {42626, 42794}

X(42933) = GIBERT (-24,5,46) POINT

Barycentrics    4*Sqrt[3]*a^2*S - 23*a^2*SA - 5*SB*SC : :

X(42933) lies on the cubic K1212b and these lines: {2, 33602}, {15, 15692}, {16, 15708}, {17, 10303}, {18, 20}, {376, 42818}, {395, 10304}, {631, 42496}, {3523, 16772}, {3524, 42633}, {3543, 11481}, {3839, 36968}, {5056, 5237}, {5071, 42493}, {5335, 41972}, {7486, 42155}, {10299, 42634}, {10646, 41113}, {11488, 42804}, {11489, 15697}, {15683, 42121}, {15721, 16644}, {16242, 42106}, {16645, 42692}, {33606, 42085}, {37641, 42791}, {42625, 42793}

X(42934) = GIBERT (15,-4,5) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 5*a^2*SA - 8*SB*SC : :

X(42934) lies on the cubic K1212a and these lines: {3, 42613}, {4, 13}, {5, 34754}, {6, 17800}, {14, 3628}, {15, 3526}, {16, 548}, {17, 5066}, {18, 10303}, {62, 3534}, {381, 42518}, {395, 41971}, {396, 3857}, {398, 549}, {627, 22496}, {3146, 42612}, {3412, 3856}, {3530, 16961}, {3830, 42779}, {3832, 16960}, {5054, 42519}, {5055, 22236}, {5072, 5339}, {5334, 7486}, {5349, 42633}, {5351, 10304}, {5352, 42491}, {10187, 42500}, {10645, 15717}, {11485, 42814}, {11543, 42687}, {12108, 42778}, {15022, 42152}, {15683, 42158}, {15684, 41107}, {15687, 42520}, {15695, 42636}, {15696, 34755}, {15698, 42149}, {15704, 42148}, {15709, 33606}, {15759, 16963}, {16241, 42594}, {16773, 42684}, {16962, 42159}, {16965, 42109}, {17578, 42630}, {18582, 42435}, {23046, 41121}, {33607, 42166}, {33699, 42164}, {37641, 42796}, {41113, 42580}, {42119, 42433}, {42154, 42431}, {42156, 42694}, {42215, 42239}, {42216, 42240}

X(42934) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 17800, 42935}, {61, 10654, 41973}, {61, 16964, 42813}, {61, 41973, 36970}, {398, 5238, 16268}, {398, 41101, 5238}, {5351, 42150, 42632}, {10654, 42799, 36970}, {16964, 42813, 36970}, {41973, 42799, 61}, {41973, 42813, 16964}

X(42935) = GIBERT (15,4,-5) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 5*a^2*SA + 8*SB*SC : :

X(42935) lies on the cubic K1212b and these lines: {3, 42612}, {4, 14}, {5, 34755}, {6, 17800}, {13, 3628}, {15, 548}, {16, 3526}, {17, 10303}, {18, 5066}, {61, 3534}, {381, 42519}, {395, 3857}, {396, 41972}, {397, 549}, {628, 22495}, {3146, 42613}, {3411, 3856}, {3530, 16960}, {3830, 42780}, {3832, 16961}, {5054, 42518}, {5055, 22238}, {5072, 5340}, {5335, 7486}, {5350, 42634}, {5351, 42490}, {5352, 10304}, {10188, 42501}, {10646, 15717}, {11486, 42813}, {11542, 42686}, {12108, 42777}, {15022, 42149}, {15683, 42157}, {15684, 41108}, {15687, 42521}, {15695, 42635}, {15696, 34754}, {15698, 42152}, {15704, 42147}, {15709, 33607}, {15759, 16962}, {16242, 42595}, {16772, 42685}, {16963, 42162}, {16964, 42108}, {17578, 42629}, {18581, 42436}, {23046, 41122}, {33606, 42163}, {33699, 42165}, {35740, 42216}, {37640, 42795}, {41112, 42581}, {42120, 42434}, {42153, 42695}, {42155, 42432}, {42215, 42241}

X(42935) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 17800, 42934}, {62, 10653, 41974}, {62, 16965, 42814}, {62, 41974, 36969}, {397, 5237, 16267}, {397, 41100, 5237}, {5352, 42151, 42631}, {10653, 42800, 36969}, {16965, 42814, 36969}, {41974, 42800, 62}, {41974, 42814, 16965}

X(42936) = GIBERT (3,4,9) POINT

Barycentrics    Sqrt[3]*a^2*S + 9*a^2*SA + 8*SB*SC : :

X(42936) lies on the cubic K1212a and these lines: {2, 18}, {3, 36969}, {4, 10188}, {5, 5238}, {6, 11614}, {13, 631}, {14, 3628}, {15, 1656}, {16, 17}, {30, 42581}, {62, 3526}, {182, 3206}, {299, 629}, {316, 6671}, {376, 42775}, {381, 5352}, {395, 3412}, {396, 632}, {398, 16967}, {546, 42434}, {547, 42147}, {549, 16965}, {550, 16808}, {619, 6673}, {624, 30559}, {1506, 41407}, {1657, 42098}, {2045, 3366}, {2046, 3367}, {3090, 16964}, {3091, 36967}, {3104, 33479}, {3105, 15819}, {3106, 6683}, {3201, 13353}, {3364, 8252}, {3365, 8253}, {3411, 37640}, {3522, 19106}, {3523, 5344}, {3524, 42162}, {3525, 16242}, {3530, 36968}, {3533, 11488}, {3627, 42529}, {3763, 36757}, {3850, 19107}, {3851, 11480}, {3856, 42795}, {3858, 42087}, {5054, 5237}, {5055, 36836}, {5056, 5365}, {5059, 42106}, {5067, 10654}, {5068, 42085}, {5070, 22236}, {5071, 42160}, {5079, 42154}, {5318, 15712}, {5321, 35018}, {5340, 10646}, {5343, 42111}, {5350, 33923}, {5366, 42091}, {5462, 36981}, {6143, 8740}, {6669, 36782}, {7486, 42159}, {7790, 11289}, {7815, 36759}, {9993, 37464}, {10124, 16963}, {10187, 16961}, {10299, 42086}, {10303, 10653}, {11298, 16631}, {11306, 35229}, {11481, 41974}, {11486, 42779}, {11539, 16773}, {11540, 42420}, {11737, 42791}, {12100, 42165}, {12816, 34200}, {14813, 42583}, {14814, 42582}, {14864, 30402}, {14869, 42148}, {14890, 33607}, {15694, 16267}, {15699, 41101}, {15702, 41100}, {15703, 41108}, {15707, 42631}, {15708, 41119}, {15717, 42161}, {15721, 41112}, {16530, 33405}, {16645, 42593}, {16960, 42089}, {17578, 42430}, {21360, 33387}, {21735, 42142}, {22489, 37173}, {22511, 22892}, {31276, 32465}, {32205, 36980}, {32789, 42200}, {32790, 42199}, {33386, 37178}, {34128, 36208}, {34755, 42817}, {41106, 42504}, {41992, 42633}, {42117, 42492}, {42122, 42794}, {42136, 42687}, {42491, 42612}

X(42936) = crosspoint of X(17) and X(10187)
X(42936) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61, 42489}, {2, 41943, 16268}, {2, 42152, 18}, {3, 37832, 42813}, {3, 42488, 37832}, {5, 5238, 36970}, {5, 16241, 5238}, {13, 631, 5351}, {17, 140, 16}, {17, 33417, 140}, {18, 61, 42780}, {18, 42152, 61}, {18, 42780, 16268}, {61, 42152, 42802}, {61, 42489, 16268}, {140, 23302, 17}, {381, 42490, 5352}, {549, 42598, 16965}, {3523, 18582, 42158}, {3524, 42162, 42433}, {3525, 40693, 16242}, {3526, 16644, 62}, {3530, 42166, 36968}, {3533, 11488, 42149}, {3533, 42149, 33416}, {3628, 16772, 14}, {3851, 11480, 42432}, {5054, 42156, 5237}, {5055, 36836, 42814}, {5056, 42150, 16809}, {5067, 10654, 42580}, {5070, 22236, 37835}, {5237, 42156, 41107}, {5340, 15720, 10646}, {5350, 33923, 42100}, {10299, 42494, 42086}, {15717, 42161, 42528}, {15720, 42132, 5340}, {16242, 42596, 3525}, {16962, 40694, 61}, {16965, 42598, 41121}, {16966, 42092, 10645}, {16966, 42099, 42114}, {16967, 42124, 34754}, {23302, 33417, 16}, {33923, 42146, 5350}, {36836, 42610, 5055}, {41943, 42489, 61}, {41943, 42780, 42802}, {41943, 42802, 42152}, {42098, 42773, 1657}, {42166, 42500, 3530}, {42489, 42780, 18}, {42489, 42802, 42780}, {42562, 42563, 33417}, {42780, 42802, 61}

X(42937) = GIBERT (-3,4,9) POINT

Barycentrics    Sqrt[3]*a^2*S - 9*a^2*SA - 8*SB*SC : :

X(42937) lies on the cubic K1212b and these lines: {2, 17}, {3, 36970}, {4, 10187}, {5, 5237}, {6, 11614}, {13, 3628}, {14, 631}, {15, 18}, {16, 1656}, {30, 42580}, {61, 3526}, {182, 3205}, {298, 630}, {316, 6672}, {376, 42776}, {381, 5351}, {395, 632}, {396, 3411}, {397, 16966}, {546, 42433}, {547, 42148}, {549, 16964}, {550, 16809}, {618, 6674}, {623, 30560}, {1506, 41406}, {1657, 42095}, {2045, 3392}, {2046, 3391}, {3090, 16965}, {3091, 36968}, {3104, 15819}, {3105, 33478}, {3107, 6683}, {3200, 13353}, {3389, 8252}, {3390, 8253}, {3412, 37641}, {3522, 19107}, {3523, 5343}, {3524, 42159}, {3525, 16241}, {3530, 36967}, {3533, 11489}, {3627, 42528}, {3763, 36758}, {3850, 19106}, {3851, 11481}, {3856, 42796}, {3858, 42088}, {5054, 5238}, {5055, 36843}, {5056, 5366}, {5059, 42103}, {5067, 10653}, {5068, 42086}, {5070, 22238}, {5071, 42161}, {5079, 42155}, {5318, 35018}, {5321, 15712}, {5339, 10645}, {5344, 42114}, {5349, 33923}, {5365, 42090}, {5462, 36979}, {6143, 8739}, {7486, 42162}, {7790, 11290}, {7815, 36760}, {9993, 37463}, {10124, 16962}, {10188, 16960}, {10299, 42085}, {10303, 10654}, {11297, 16630}, {11305, 35230}, {11480, 41973}, {11485, 42780}, {11539, 16772}, {11540, 42419}, {11737, 42792}, {12100, 42164}, {12817, 34200}, {14813, 42582}, {14814, 42583}, {14864, 30403}, {14869, 42147}, {14890, 33606}, {15694, 16268}, {15699, 41100}, {15702, 41101}, {15703, 41107}, {15707, 42632}, {15708, 41120}, {15717, 42160}, {15721, 41113}, {16529, 33404}, {16644, 42592}, {16961, 42092}, {17578, 42429}, {21359, 33386}, {21735, 42139}, {22490, 37172}, {22510, 22848}, {22511, 36770}, {31276, 32466}, {32205, 36978}, {32789, 42202}, {32790, 42201}, {33387, 37177}, {34128, 36209}, {34754, 42818}, {41106, 42505}, {41992, 42634}, {42118, 42493}, {42123, 42793}, {42137, 42686}, {42490, 42613}

X(42937) = crosspoint of X(18) and X(10188)
X(42937) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 62, 42488}, {2, 41944, 16267}, {2, 42149, 17}, {3, 37835, 42814}, {3, 42489, 37835}, {5, 5237, 36969}, {5, 16242, 5237}, {14, 631, 5352}, {17, 62, 42779}, {17, 42149, 62}, {17, 42779, 16267}, {18, 140, 15}, {18, 33416, 140}, {62, 42149, 42801}, {62, 42488, 16267}, {140, 23303, 18}, {381, 42491, 5351}, {549, 42599, 16964}, {3523, 18581, 42157}, {3524, 42159, 42434}, {3525, 40694, 16241}, {3526, 16645, 61}, {3530, 42163, 36967}, {3533, 11489, 42152}, {3533, 42152, 33417}, {3628, 16773, 13}, {3851, 11481, 42431}, {5054, 42153, 5238}, {5055, 36843, 42813}, {5056, 42151, 16808}, {5067, 10653, 42581}, {5070, 22238, 37832}, {5238, 42153, 41108}, {5339, 15720, 10645}, {5349, 33923, 42099}, {10299, 42495, 42085}, {15717, 42160, 42529}, {15720, 42129, 5339}, {16241, 42597, 3525}, {16963, 40693, 62}, {16964, 42599, 41122}, {16966, 42121, 34755}, {16967, 42089, 10646}, {16967, 42100, 42111}, {23303, 33416, 15}, {33923, 42143, 5349}, {36843, 42611, 5055}, {41944, 42488, 62}, {41944, 42779, 42801}, {41944, 42801, 42149}, {42095, 42774, 1657}, {42163, 42501, 3530}, {42488, 42779, 17}, {42488, 42801, 42779}, {42564, 42565, 33416}, {42779, 42801, 62}

X(42938) = GIBERT (-15,4,13) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 13*a^2*SA - 8*SB*SC : :

X(42938) lies on the cubic K1212a and these lines: {2, 17}, {3, 42613}, {5, 34755}, {6, 42939}, {13, 35018}, {14, 3529}, {15, 3411}, {16, 382}, {18, 546}, {20, 16961}, {30, 33606}, {61, 15720}, {381, 42695}, {395, 550}, {396, 42596}, {398, 34200}, {524, 33386}, {3412, 42089}, {3528, 10646}, {3544, 10653}, {3618, 33387}, {3851, 22238}, {3855, 11489}, {5068, 42513}, {5079, 16645}, {5238, 15700}, {5351, 15688}, {5352, 10299}, {5365, 42429}, {8739, 35482}, {10188, 42496}, {11486, 42489}, {11488, 42597}, {11539, 42521}, {11543, 42433}, {11737, 42580}, {14139, 33464}, {14869, 16242}, {15681, 16268}, {15687, 41122}, {15704, 42778}, {15707, 22236}, {15710, 42150}, {15715, 41101}, {15721, 42520}, {16239, 16960}, {16628, 21402}, {16966, 42493}, {17504, 42791}, {17578, 42694}, {18581, 42629}, {33602, 42805}, {36758, 40341}, {37832, 42611}, {38071, 41100}, {42117, 42782}, {42143, 42416}, {42415, 42686}

X(42938) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 62, 42779}, {62, 16963, 42801}, {62, 42149, 41944}, {3411, 16773, 15}, {16268, 36843, 42432}, {16963, 42149, 62}, {22238, 37835, 41974}, {36843, 42432, 42631}, {40693, 42436, 62}, {41944, 42636, 2}, {41944, 42801, 62}, {42636, 42779, 62}

X(42939) = GIBERT (15,4,13) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 13*a^2*SA + 8*SB*SC : :

X(42939) lies on the cubic K1212b and these lines: {2, 18}, {3, 42612}, {5, 34754}, {6, 42938}, {13, 3529}, {14, 35018}, {15, 382}, {16, 3412}, {17, 546}, {20, 16960}, {30, 33607}, {62, 15720}, {381, 42694}, {395, 42597}, {396, 550}, {397, 34200}, {524, 33387}, {3411, 42092}, {3528, 10645}, {3544, 10654}, {3618, 33386}, {3851, 22236}, {3855, 11488}, {5068, 42512}, {5079, 16644}, {5237, 15700}, {5351, 10299}, {5352, 15688}, {5366, 42430}, {8740, 35482}, {10187, 42497}, {11485, 42488}, {11489, 42596}, {11539, 42520}, {11542, 42434}, {11737, 42581}, {14138, 33465}, {14869, 16241}, {15681, 16267}, {15687, 41121}, {15704, 42777}, {15707, 22238}, {15710, 42151}, {15715, 41100}, {15721, 42521}, {16239, 16961}, {16629, 21401}, {16967, 42492}, {17504, 42792}, {17578, 42695}, {18582, 42630}, {33603, 42806}, {36757, 40341}, {37835, 42610}, {38071, 41101}, {42118, 42781}, {42146, 42415}, {42416, 42687}

X(42939) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 61, 42780}, {61, 16962, 42802}, {61, 42152, 41943}, {3412, 16772, 16}, {16267, 36836, 42431}, {16962, 42152, 61}, {22236, 37832, 41973}, {36836, 42431, 42632}, {40694, 42435, 61}, {41943, 42635, 2}, {41943, 42802, 61}, {42635, 42780, 61}

leftri

Gibert points on the KHO cubics K1215-K1217): X(42940)-X(43033)

rightri

This preamble and points X(42940)-X(43033) are contributed by Peter Moses, May 2, 2021. See also the preambles just before X(42085), X(42413), and X(42429).

See KHO curves and Catalog, with access to cubics K1215-K1217



X(42940) = GIBERT (3,-5,2) POINT

Barycentrics    Sqrt[3]*a^2*S + 2*a^2*SA - 10*SB*SC : :
X(42940) = 5 X[14] - 3 X[16], 4 X[14] - 3 X[395], 2 X[14] - 3 X[5321], 7 X[14] - 6 X[11543], 11 X[14] - 9 X[16268], 19 X[14] - 15 X[16961], 13 X[14] - 9 X[16963], X[14] + 3 X[19107], 7 X[14] - 3 X[36968], X[14] - 3 X[36970], 8 X[14] - 3 X[42088], 11 X[14] - 3 X[42100], 4 X[14] + 3 X[42108], 13 X[14] - 6 X[42123], X[14] - 6 X[42136], 5 X[14] - X[42429], 5 X[14] - 4 X[42497], 19 X[14] - 6 X[42584], 4 X[14] - 15 X[42682], 6 X[14] - 5 X[42778], X[14] + 12 X[42888], 3 X[14] - 2 X[42913], 4 X[16] - 5 X[395], 2 X[16] - 5 X[5321], 7 X[16] - 10 X[11543], 11 X[16] - 15 X[16268], 19 X[16] - 25 X[16961], 13 X[16] - 15 X[16963], X[16] + 5 X[19107], 7 X[16] - 5 X[36968], X[16] - 5 X[36970], 8 X[16] - 5 X[42088], 11 X[16] - 5 X[42100], 4 X[16] + 5 X[42108], 13 X[16] - 10 X[42123], X[16] - 10 X[42136], 3 X[16] - X[42429], 3 X[16] - 4 X[42497], 19 X[16] - 10 X[42584], 4 X[16] - 25 X[42682], 18 X[16] - 25 X[42778], X[16] + 20 X[42888], 9 X[16] - 10 X[42913], 7 X[395] - 8 X[11543], 11 X[395] - 12 X[16268], 19 X[395] - 20 X[16961], 13 X[395] - 12 X[16963], X[395] + 4 X[19107], 7 X[395] - 4 X[36968], X[395] - 4 X[36970], 11 X[395] - 4 X[42100], 13 X[395] - 8 X[42123], X[395] - 8 X[42136], 15 X[395] - 4 X[42429], 15 X[395] - 16 X[42497], 19 X[395] - 8 X[42584], X[395] - 5 X[42682], 9 X[395] - 10 X[42778], X[395] + 16 X[42888], 9 X[395] - 8 X[42913], 2 X[619] - 3 X[31694]

X(42940) lies on the cubic K1216a and these lines: {2, 42087}, {3, 5349}, {4, 396}, {5, 5352}, {6, 3543}, {13, 12820}, {14, 16}, {15, 3845}, {17, 3861}, {18, 15704}, {20, 16645}, {61, 3853}, {140, 42529}, {298, 32819}, {376, 23303}, {381, 23302}, {382, 398}, {397, 3627}, {546, 16772}, {547, 10645}, {549, 16809}, {550, 16242}, {619, 31694}, {621, 33625}, {1657, 16773}, {2043, 42239}, {2044, 42240}, {3091, 42932}, {3146, 5339}, {3524, 42095}, {3529, 5365}, {3534, 18581}, {3545, 11480}, {3628, 42434}, {3830, 5318}, {3832, 36836}, {3839, 16644}, {3843, 42150}, {3850, 5238}, {3851, 42794}, {3855, 42927}, {3856, 42581}, {3857, 42488}, {3860, 42919}, {5054, 42090}, {5055, 42103}, {5059, 36843}, {5066, 16241}, {5068, 42490}, {5073, 40694}, {5076, 40693}, {5334, 15682}, {5340, 17578}, {5343, 22238}, {5479, 41034}, {6000, 36980}, {6108, 35021}, {6670, 35303}, {6772, 36961}, {7486, 42773}, {8703, 12817}, {8740, 13473}, {10109, 33417}, {10124, 42914}, {10304, 42139}, {10646, 15686}, {11001, 11481}, {11485, 38335}, {11486, 41113}, {11489, 15683}, {11542, 12101}, {11737, 12821}, {12100, 16967}, {12102, 42813}, {12811, 42936}, {14269, 18582}, {14893, 16808}, {15640, 42120}, {15681, 42112}, {15684, 42086}, {15685, 41120}, {15688, 42089}, {15689, 42129}, {15692, 42587}, {15694, 42111}, {15699, 42918}, {15712, 42580}, {15717, 42776}, {15764, 42175}, {16267, 42138}, {16960, 42502}, {16966, 38071}, {17504, 33416}, {17800, 42149}, {18586, 22615}, {18587, 22644}, {19106, 33699}, {19709, 42092}, {19710, 41122}, {22893, 41017}, {23046, 42124}, {33923, 42489}, {34200, 42143}, {34754, 42496}, {35403, 42128}, {35404, 42118}, {36436, 42264}, {36437, 42283}, {36439, 42208}, {36445, 42194}, {36454, 42263}, {36455, 42284}, {36457, 42207}, {36463, 42192}, {36962, 41746}, {37640, 42094}, {39838, 41022}, {41099, 42098}, {41107, 42137}, {41943, 42146}, {41971, 41988}, {41972, 42158}, {41987, 42627}, {41991, 42890}, {42106, 42511}, {42113, 42816}, {42131, 42510}, {42145, 42634}, {42415, 42635}, {42491, 42495}, {42503, 42818}, {42516, 42589}, {42545, 42797}, {42688, 42815}

X(42940) = midpoint of X(i) and X(j) for these {i,j}: {395, 42108}, {19107, 36970}
X(42940) = reflection of X(i) in X(j) for these {i,j}: {395, 5321}, {5321, 36970}, {36968, 11543}, {36970, 42136}, {41034, 5479}, {42088, 395}
X(42940) = crosssum of X(16) and X(11480)
X(42940) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 42910, 42501}, {4, 42147, 42166}, {4, 42154, 396}, {4, 42164, 42147}, {6, 3543, 42941}, {13, 15687, 42102}, {14, 16, 42497}, {14, 42429, 16}, {14, 42913, 42778}, {61, 3853, 5350}, {381, 42116, 42911}, {382, 398, 42165}, {382, 42160, 398}, {396, 42154, 42147}, {396, 42164, 42154}, {546, 42157, 16772}, {547, 10645, 42500}, {550, 42814, 42599}, {1657, 42159, 16773}, {3146, 5339, 42148}, {3529, 5365, 42153}, {3627, 16964, 397}, {3830, 10654, 5318}, {3830, 42126, 10654}, {3839, 16644, 42110}, {3839, 42119, 16644}, {3843, 42150, 42598}, {5066, 42122, 16241}, {5321, 19107, 42108}, {5321, 42108, 42088}, {5321, 42136, 42682}, {5334, 15682, 42155}, {5343, 33703, 22238}, {8703, 42135, 37835}, {10646, 42430, 15686}, {10654, 42104, 3830}, {11489, 15683, 42625}, {12102, 42925, 42813}, {12817, 37835, 42135}, {12817, 42099, 37835}, {14893, 42912, 16808}, {15682, 42155, 42109}, {15685, 41120, 42792}, {15687, 42117, 13}, {16241, 42122, 42791}, {16241, 42791, 42687}, {19107, 42136, 5321}, {19107, 42682, 42088}, {19710, 42121, 42528}, {23303, 42133, 42692}, {37835, 42099, 8703}, {41122, 42528, 42121}, {42085, 42101, 23302}, {42087, 42093, 42107}, {42093, 42140, 42087}, {42096, 42133, 23303}, {42104, 42126, 5318}, {42108, 42682, 5321}, {42136, 42888, 19107}, {42778, 42913, 395}

X(42941) = GIBERT (3,5,-2) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*a^2*SA + 10*SB*SC : :
X(42941) = 5 X[13] - 3 X[15], 4 X[13] - 3 X[396], 2 X[13] - 3 X[5318], 7 X[13] - 6 X[11542], 11 X[13] - 9 X[16267], 19 X[13] - 15 X[16960], 13 X[13] - 9 X[16962], X[13] + 3 X[19106], 7 X[13] - 3 X[36967], X[13] - 3 X[36969], 8 X[13] - 3 X[42087], 11 X[13] - 3 X[42099], 4 X[13] + 3 X[42109], 13 X[13] - 6 X[42122], X[13] - 6 X[42137], 5 X[13] - X[42430], 5 X[13] - 4 X[42496], 19 X[13] - 6 X[42585], 4 X[13] - 15 X[42683], 6 X[13] - 5 X[42777], X[13] + 12 X[42889], 3 X[13] - 2 X[42912], 4 X[15] - 5 X[396], 2 X[15] - 5 X[5318], 7 X[15] - 10 X[11542], 11 X[15] - 15 X[16267], 19 X[15] - 25 X[16960], 13 X[15] - 15 X[16962], X[15] + 5 X[19106], 7 X[15] - 5 X[36967], X[15] - 5 X[36969], 8 X[15] - 5 X[42087], 11 X[15] - 5 X[42099], 4 X[15] + 5 X[42109], 13 X[15] - 10 X[42122], X[15] - 10 X[42137], 3 X[15] - X[42430], 3 X[15] - 4 X[42496], 19 X[15] - 10 X[42585], 4 X[15] - 25 X[42683], 18 X[15] - 25 X[42777], X[15] + 20 X[42889], 9 X[15] - 10 X[42912], 7 X[396] - 8 X[11542], 11 X[396] - 12 X[16267], 19 X[396] - 20 X[16960], 13 X[396] - 12 X[16962], X[396] + 4 X[19106], 7 X[396] - 4 X[36967], X[396] - 4 X[36969], 11 X[396] - 4 X[42099], 13 X[396] - 8 X[42122], X[396] - 8 X[42137], 15 X[396] - 4 X[42430], 15 X[396] - 16 X[42496]

X(42941) lies on the cubic K1216b and these lines: {2, 42088}, {3, 5350}, {4, 395}, {5, 5351}, {6, 3543}, {13, 15}, {14, 12821}, {16, 3845}, {17, 15704}, {18, 3861}, {20, 16644}, {62, 3853}, {140, 42528}, {299, 32819}, {376, 23302}, {381, 23303}, {382, 397}, {398, 3627}, {546, 16773}, {547, 10646}, {549, 16808}, {550, 16241}, {618, 31693}, {622, 33623}, {1657, 16772}, {2043, 35740}, {2044, 42241}, {3091, 42933}, {3146, 5340}, {3524, 42098}, {3529, 5366}, {3534, 18582}, {3545, 11481}, {3628, 42433}, {3830, 5321}, {3832, 36843}, {3839, 16645}, {3843, 42151}, {3850, 5237}, {3851, 42793}, {3855, 42926}, {3856, 42580}, {3857, 42489}, {3860, 42918}, {5054, 42091}, {5055, 42106}, {5059, 36836}, {5066, 16242}, {5068, 42491}, {5073, 40693}, {5076, 40694}, {5335, 15682}, {5339, 17578}, {5344, 22236}, {5478, 41035}, {6000, 36978}, {6109, 35021}, {6669, 35304}, {6775, 36962}, {7486, 42774}, {8703, 12816}, {8739, 13473}, {10109, 33416}, {10124, 42915}, {10304, 42142}, {10645, 15686}, {11001, 11480}, {11485, 41112}, {11486, 38335}, {11488, 15683}, {11543, 12101}, {11737, 12820}, {12100, 16966}, {12102, 42814}, {12811, 42937}, {14269, 18581}, {14893, 16809}, {15640, 42119}, {15681, 42113}, {15684, 42085}, {15685, 41119}, {15688, 42092}, {15689, 42132}, {15692, 42586}, {15694, 42114}, {15699, 42919}, {15712, 42581}, {15717, 42775}, {15764, 42178}, {16268, 42135}, {16961, 42503}, {16967, 38071}, {17504, 33417}, {17800, 42152}, {18586, 22644}, {18587, 22615}, {19107, 33699}, {19709, 42089}, {19710, 41121}, {22847, 41016}, {23046, 42121}, {33923, 42488}, {34200, 42146}, {34755, 42497}, {35403, 42125}, {35404, 42117}, {36436, 42263}, {36437, 42284}, {36439, 42209}, {36445, 42191}, {36454, 42264}, {36455, 42283}, {36457, 42210}, {36463, 42193}, {36961, 41745}, {37641, 42093}, {39838, 41023}, {41099, 42095}, {41108, 42136}, {41944, 42143}, {41971, 42157}, {41972, 41988}, {41987, 42628}, {41991, 42891}, {42103, 42510}, {42112, 42815}, {42130, 42511}, {42144, 42633}, {42416, 42636}, {42490, 42494}, {42502, 42817}, {42517, 42588}, {42546, 42798}, {42689, 42816}

X(42941) = midpoint of X(i) and X(j) for these {i,j}: {396, 42109}, {19106, 36969}
X(42941) = reflection of X(i) in X(j) for these {i,j}: {396, 5318}, {5318, 36969}, {36967, 11542}, {36969, 42137}, {41035, 5478}, {42087, 396}
X(42941) = crosssum of X(15) and X(11481)
X(42941) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 42911, 42500}, {4, 42148, 42163}, {4, 42155, 395}, {4, 42165, 42148}, {6, 3543, 42940}, {13, 15, 42496}, {13, 42430, 15}, {13, 42912, 42777}, {14, 15687, 42101}, {62, 3853, 5349}, {381, 42115, 42910}, {382, 397, 42164}, {382, 42161, 397}, {395, 42155, 42148}, {395, 42165, 42155}, {546, 42158, 16773}, {547, 10646, 42501}, {550, 42813, 42598}, {1657, 42162, 16772}, {3146, 5340, 42147}, {3529, 5366, 42156}, {3627, 16965, 398}, {3830, 10653, 5321}, {3830, 42127, 10653}, {3839, 16645, 42107}, {3839, 42120, 16645}, {3843, 42151, 42599}, {5066, 42123, 16242}, {5318, 19106, 42109}, {5318, 42109, 42087}, {5318, 42137, 42683}, {5335, 15682, 42154}, {5344, 33703, 22236}, {8703, 42138, 37832}, {10645, 42429, 15686}, {10653, 42105, 3830}, {11488, 15683, 42626}, {12102, 42924, 42814}, {12816, 37832, 42138}, {12816, 42100, 37832}, {14893, 42913, 16809}, {15682, 42154, 42108}, {15685, 41119, 42791}, {15687, 42118, 14}, {16242, 42123, 42792}, {16242, 42792, 42686}, {19106, 42137, 5318}, {19106, 42683, 42087}, {19710, 42124, 42529}, {23302, 42134, 42693}, {37832, 42100, 8703}, {41121, 42529, 42124}, {42086, 42102, 23303}, {42088, 42094, 42110}, {42094, 42141, 42088}, {42097, 42134, 23302}, {42105, 42127, 5321}, {42109, 42683, 5318}, {42137, 42889, 19106}, {42777, 42912, 396}

X(42942) = GIBERT (3,-1,4) POINT

Barycentrics    Sqrt[3]*a^2*S + 4*a^2*SA - 2*SB*SC : :
X(42942) = X[13] - 3 X[15], 2 X[13] - 3 X[396], 4 X[13] - 3 X[5318], 5 X[13] - 6 X[11542], 7 X[13] - 9 X[16267], 11 X[13] - 15 X[16960], 5 X[13] - 9 X[16962], 7 X[13] - 3 X[19106], X[13] + 3 X[36967], 5 X[13] - 3 X[36969], 2 X[13] + 3 X[42087], 5 X[13] + 3 X[42099], 10 X[13] - 3 X[42109], X[13] + 6 X[42122], 11 X[13] - 6 X[42137], 3 X[13] + X[42430], 3 X[13] - 4 X[42496], 7 X[13] + 6 X[42585], 26 X[13] - 15 X[42683], 4 X[13] - 5 X[42777], 25 X[13] - 12 X[42889], 4 X[15] - X[5318], 5 X[15] - 2 X[11542], 7 X[15] - 3 X[16267], 11 X[15] - 5 X[16960], 5 X[15] - 3 X[16962], 7 X[15] - X[19106], 5 X[15] - X[36969], 2 X[15] + X[42087], 5 X[15] + X[42099], 10 X[15] - X[42109], X[15] + 2 X[42122], 11 X[15] - 2 X[42137], 9 X[15] + X[42430], 9 X[15] - 4 X[42496], 7 X[15] + 2 X[42585], 26 X[15] - 5 X[42683], 12 X[15] - 5 X[42777], 25 X[15] - 4 X[42889], 3 X[15] - 2 X[42912], 5 X[396] - 4 X[11542], 7 X[396] - 6 X[16267], 11 X[396] - 10 X[16960], 5 X[396] - 6 X[16962], 7 X[396] - 2 X[19106], X[396] + 2 X[36967], 5 X[396] - 2 X[36969], 5 X[396] + 2 X[42099], 5 X[396] - X[42109], X[396] + 4 X[42122], 11 X[396] - 4 X[42137], 9 X[396] + 2 X[42430], 9 X[396] - 8 X[42496], 7 X[396] + 4 X[42585], 13 X[396] - 5 X[42683], 6 X[396] - 5 X[42777]

X(42942) lies on the cubic K1216a and these lines: {2, 5321}, {3, 395}, {4, 16644}, {5, 5238}, {6, 376}, {13, 15}, {14, 549}, {16, 8703}, {17, 3627}, {18, 3530}, {20, 397}, {61, 550}, {62, 548}, {140, 5352}, {141, 617}, {299, 7750}, {325, 30471}, {381, 23302}, {382, 42152}, {428, 11475}, {511, 25174}, {524, 616}, {531, 618}, {546, 42432}, {547, 16809}, {590, 36455}, {597, 35932}, {615, 36437}, {619, 7853}, {622, 33458}, {631, 5339}, {1080, 36993}, {1656, 42160}, {1657, 40693}, {2041, 42253}, {2042, 42251}, {2043, 42259}, {2044, 42258}, {2306, 10543}, {2307, 15338}, {3058, 7051}, {3090, 42490}, {3104, 32516}, {3146, 5350}, {3181, 7783}, {3366, 34562}, {3367, 34559}, {3389, 34551}, {3390, 34552}, {3412, 42431}, {3522, 22238}, {3523, 42153}, {3524, 5334}, {3525, 5343}, {3526, 42159}, {3528, 36843}, {3529, 5340}, {3534, 10653}, {3543, 11488}, {3545, 42093}, {3589, 11300}, {3628, 42814}, {3642, 7822}, {3830, 18582}, {3839, 42098}, {3845, 19107}, {3850, 42488}, {3858, 42581}, {3860, 42888}, {5054, 18581}, {5055, 42092}, {5066, 16966}, {5067, 5365}, {5070, 42920}, {5071, 42133}, {5073, 42162}, {5076, 42921}, {5237, 33923}, {5306, 19781}, {5335, 11001}, {5362, 15677}, {5366, 11541}, {5434, 10638}, {5464, 22512}, {5471, 8589}, {5473, 41745}, {5474, 6775}, {6036, 6109}, {6200, 36439}, {6393, 11129}, {6396, 36457}, {6560, 42197}, {6561, 42195}, {6669, 31693}, {6771, 21401}, {6780, 22507}, {7789, 37172}, {7889, 37341}, {7913, 37352}, {8594, 11161}, {8739, 37931}, {9117, 41023}, {9730, 36980}, {10109, 12817}, {10124, 42143}, {10299, 42491}, {10304, 11481}, {10576, 18585}, {10577, 15765}, {10636, 34618}, {10646, 34200}, {11243, 15311}, {11486, 15688}, {11489, 15692}, {11539, 16967}, {11540, 42930}, {11543, 12100}, {11737, 42630}, {11749, 15743}, {11812, 33416}, {12101, 42627}, {12103, 42158}, {12108, 42937}, {12816, 42916}, {12821, 38071}, {13083, 31694}, {14093, 42115}, {14269, 42104}, {14634, 35469}, {14677, 36208}, {14869, 42489}, {14891, 41944}, {14893, 42146}, {15022, 42610}, {15048, 41407}, {15640, 42502}, {15681, 42086}, {15682, 42094}, {15683, 42097}, {15684, 42112}, {15685, 41112}, {15686, 34754}, {15687, 16808}, {15689, 42091}, {15690, 41100}, {15693, 41113}, {15694, 42125}, {15695, 42510}, {15696, 42151}, {15698, 42509}, {15699, 33417}, {15700, 42816}, {15701, 41120}, {15703, 42111}, {15704, 16965}, {15706, 42818}, {15711, 16961}, {15712, 41973}, {15759, 42686}, {15764, 42167}, {16239, 42580}, {16268, 17504}, {17800, 42161}, {18586, 42255}, {18587, 42257}, {19709, 42103}, {19710, 41107}, {22892, 41016}, {22893, 22906}, {23046, 42919}, {23721, 36299}, {30459, 41997}, {33699, 41121}, {35403, 42512}, {35404, 42693}, {36436, 42284}, {36453, 42222}, {36454, 42283}, {36469, 42224}, {36764, 36961}, {38335, 42106}, {41022, 41035}, {41119, 42105}, {41983, 42628}, {42113, 42815}, {42134, 42587}, {42145, 42429}, {42415, 42507}, {42433, 42924}, {42435, 42779}, {42493, 42902}, {42532, 42584}, {42613, 42797}, {42793, 42934}

X(42942) = midpoint of X(i) and X(j) for these {i,j}: {15, 36967}, {396, 42087}, {1080, 36993}, {36969, 42099}
X(42942) = reflection of X(i) in X(j) for these {i,j}: {13, 42912}, {396, 15}, {5318, 396}, {6771, 21401}, {36967, 42122}, {36969, 11542}, {42087, 36967}, {42109, 36969}
X(42942) = crosssum of X(15) and X(11486)
X(42942) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42119, 42154}, {2, 42154, 5321}, {3, 398, 16773}, {3, 10654, 395}, {3, 42147, 398}, {3, 42150, 42147}, {4, 16772, 42598}, {4, 36836, 16772}, {5, 42157, 42164}, {5, 42164, 5349}, {6, 376, 42943}, {6, 42626, 376}, {13, 15, 42912}, {13, 396, 42777}, {13, 42912, 396}, {14, 549, 23303}, {14, 10645, 549}, {15, 36969, 16962}, {15, 42087, 5318}, {15, 42099, 11542}, {15, 42122, 42087}, {15, 42430, 42496}, {16, 41971, 42799}, {16, 42529, 8703}, {16, 42632, 42529}, {20, 22236, 397}, {20, 37640, 42155}, {61, 550, 42148}, {61, 42434, 550}, {140, 16964, 42163}, {382, 42152, 42166}, {395, 10654, 398}, {395, 42147, 10654}, {548, 42925, 62}, {549, 23303, 42501}, {549, 42117, 14}, {617, 11299, 141}, {631, 5339, 42599}, {1657, 40693, 42165}, {3146, 42156, 5350}, {3524, 5334, 16645}, {3534, 10653, 42088}, {3534, 11485, 10653}, {3845, 37832, 42110}, {3845, 42124, 37832}, {5238, 36970, 16241}, {5238, 42157, 5}, {5318, 42777, 13}, {5352, 16964, 140}, {10304, 37641, 11481}, {10645, 42117, 23303}, {10653, 42090, 3534}, {10653, 42511, 11485}, {11480, 42119, 5321}, {11480, 42154, 2}, {11485, 42090, 42088}, {11488, 42096, 42102}, {11542, 16962, 396}, {11542, 42099, 42109}, {11542, 42109, 5318}, {11543, 12100, 16242}, {15686, 42633, 42118}, {15694, 42125, 42910}, {16241, 36970, 5}, {16241, 42157, 36970}, {16242, 41108, 11543}, {16267, 36967, 42585}, {16962, 36967, 42099}, {16962, 36969, 11542}, {16962, 42099, 36969}, {18582, 42130, 42108}, {19107, 37832, 3845}, {19107, 42124, 42110}, {22236, 42155, 37640}, {23302, 42085, 42101}, {23303, 42684, 10645}, {34200, 42913, 10646}, {37640, 42155, 397}, {41101, 42529, 16}, {41101, 42632, 8703}, {41971, 42529, 42634}, {41971, 42799, 41101}, {42085, 42116, 23302}, {42087, 42109, 42099}, {42090, 42511, 10653}, {42092, 42126, 42107}, {42107, 42687, 42092}

X(42943) = GIBERT (3,1,-4) POINT

Barycentrics    Sqrt[3]*a^2*S - 4*a^2*SA + 2*SB*SC : :
X(42943) = X[14] - 3 X[16], 2 X[14] - 3 X[395], 4 X[14] - 3 X[5321], 5 X[14] - 6 X[11543], 7 X[14] - 9 X[16268], 11 X[14] - 15 X[16961], 5 X[14] - 9 X[16963], 7 X[14] - 3 X[19107], X[14] + 3 X[36968], 5 X[14] - 3 X[36970], 2 X[14] + 3 X[42088], 5 X[14] + 3 X[42100], 10 X[14] - 3 X[42108], X[14] + 6 X[42123], 11 X[14] - 6 X[42136], 3 X[14] + X[42429], 3 X[14] - 4 X[42497], 7 X[14] + 6 X[42584], 26 X[14] - 15 X[42682], 4 X[14] - 5 X[42778], 25 X[14] - 12 X[42888], 4 X[16] - X[5321], 5 X[16] - 2 X[11543], 7 X[16] - 3 X[16268], 11 X[16] - 5 X[16961], 5 X[16] - 3 X[16963], 7 X[16] - X[19107], 5 X[16] - X[36970], 2 X[16] + X[42088], 5 X[16] + X[42100], 10 X[16] - X[42108], X[16] + 2 X[42123], 11 X[16] - 2 X[42136], 9 X[16] + X[42429], 9 X[16] - 4 X[42497], 7 X[16] + 2 X[42584], 26 X[16] - 5 X[42682], 12 X[16] - 5 X[42778], 25 X[16] - 4 X[42888], 3 X[16] - 2 X[42913], 5 X[395] - 4 X[11543], 7 X[395] - 6 X[16268], 11 X[395] - 10 X[16961], 5 X[395] - 6 X[16963], 7 X[395] - 2 X[19107], X[395] + 2 X[36968], 5 X[395] - 2 X[36970], 5 X[395] + 2 X[42100], 5 X[395] - X[42108], X[395] + 4 X[42123], 11 X[395] - 4 X[42136], 9 X[395] + 2 X[42429], 9 X[395] - 8 X[42497], 7 X[395] + 4 X[42584], 13 X[395] - 5 X[42682], 6 X[395] - 5 X[42778]

X(42943) lies on the cubic K1216b and these lines: {2, 5318}, {3, 396}, {4, 16645}, {5, 5237}, {6, 376}, {13, 549}, {14, 16}, {15, 8703}, {17, 3530}, {18, 3627}, {20, 398}, {61, 548}, {62, 550}, {140, 5351}, {141, 616}, {298, 7750}, {325, 30472}, {381, 23303}, {382, 42149}, {383, 36995}, {428, 11476}, {511, 25179}, {524, 617}, {530, 619}, {546, 42431}, {547, 16808}, {590, 36437}, {597, 35931}, {615, 36455}, {618, 7853}, {621, 33459}, {631, 5340}, {1250, 5434}, {1656, 42161}, {1657, 40694}, {2041, 42250}, {2042, 42252}, {2043, 42258}, {2044, 42259}, {3058, 19373}, {3090, 42491}, {3105, 32516}, {3146, 5349}, {3180, 7783}, {3364, 34552}, {3365, 34551}, {3391, 34559}, {3392, 34562}, {3411, 42432}, {3522, 22236}, {3523, 42156}, {3524, 5335}, {3525, 5344}, {3526, 42162}, {3528, 36836}, {3529, 5339}, {3534, 10654}, {3543, 11489}, {3545, 42094}, {3589, 11299}, {3628, 42813}, {3643, 7822}, {3830, 18581}, {3839, 42095}, {3845, 19106}, {3850, 42489}, {3858, 42580}, {3860, 42889}, {5054, 18582}, {5055, 42089}, {5066, 16967}, {5067, 5366}, {5070, 42921}, {5071, 42134}, {5073, 42159}, {5076, 42920}, {5238, 33923}, {5306, 19780}, {5334, 11001}, {5365, 11541}, {5367, 15677}, {5463, 22513}, {5472, 8589}, {5473, 6772}, {5474, 41746}, {6036, 6108}, {6200, 36457}, {6393, 11128}, {6396, 36439}, {6560, 42198}, {6561, 42196}, {6670, 31694}, {6774, 21402}, {6779, 22509}, {7127, 15326}, {7789, 37173}, {7889, 37340}, {7913, 37351}, {8595, 11161}, {8740, 37931}, {9115, 41022}, {9730, 36978}, {10109, 12816}, {10124, 42146}, {10299, 42490}, {10304, 11480}, {10543, 33654}, {10576, 15765}, {10577, 18585}, {10637, 34618}, {10645, 34200}, {11244, 15311}, {11485, 15688}, {11488, 15692}, {11539, 16966}, {11540, 42931}, {11542, 12100}, {11586, 11749}, {11737, 42629}, {11812, 33417}, {12101, 42628}, {12103, 42157}, {12108, 42936}, {12817, 42917}, {12820, 38071}, {13084, 31693}, {14093, 42116}, {14269, 42105}, {14634, 35470}, {14677, 36209}, {14869, 42488}, {14891, 41943}, {14893, 42143}, {15022, 42611}, {15048, 41406}, {15640, 42503}, {15681, 42085}, {15682, 42093}, {15683, 42096}, {15684, 42113}, {15685, 41113}, {15686, 34755}, {15687, 16809}, {15689, 42090}, {15690, 41101}, {15693, 41112}, {15694, 42128}, {15695, 42511}, {15696, 42150}, {15698, 42508}, {15699, 33416}, {15700, 42815}, {15701, 41119}, {15703, 42114}, {15704, 16964}, {15706, 42817}, {15711, 16960}, {15712, 41974}, {15759, 42687}, {15764, 42170}, {16239, 42581}, {16267, 17504}, {17800, 42160}, {18586, 42256}, {18587, 42254}, {19709, 42106}, {19710, 41108}, {22847, 22862}, {22848, 41017}, {23046, 42918}, {23722, 36298}, {30462, 41998}, {33699, 41122}, {35403, 42513}, {35404, 42692}, {36436, 42283}, {36452, 42223}, {36454, 42284}, {36470, 42221}, {38335, 42103}, {41023, 41034}, {41120, 42104}, {41983, 42627}, {42112, 42816}, {42133, 42586}, {42144, 42430}, {42416, 42506}, {42434, 42925}, {42436, 42780}, {42492, 42903}, {42533, 42585}, {42612, 42798}, {42794, 42935}

X(42943) = midpoint of X(i) and X(j) for these {i,j}: {16, 36968}, {383, 36995}, {395, 42088}, {36970, 42100}
X(42943) = reflection of X(i) in X(j) for these {i,j}: {14, 42913}, {395, 16}, {5321, 395}, {6774, 21402}, {36968, 42123}, {36970, 11543}, {42088, 36968}, {42108, 36970}
X(42943) = crosssum of X(16) and X(11485)
X(42943) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42120, 42155}, {2, 42155, 5318}, {3, 397, 16772}, {3, 10653, 396}, {3, 42148, 397}, {3, 42151, 42148}, {4, 16773, 42599}, {4, 36843, 16773}, {5, 42158, 42165}, {5, 42165, 5350}, {6, 376, 42942}, {6, 42625, 376}, {13, 549, 23302}, {13, 10646, 549}, {14, 16, 42913}, {14, 395, 42778}, {14, 42913, 395}, {15, 41972, 42800}, {15, 42528, 8703}, {15, 42631, 42528}, {16, 36970, 16963}, {16, 42088, 5321}, {16, 42100, 11543}, {16, 42123, 42088}, {16, 42429, 42497}, {20, 22238, 398}, {20, 37641, 42154}, {62, 550, 42147}, {62, 42433, 550}, {140, 16965, 42166}, {382, 42149, 42163}, {396, 10653, 397}, {396, 42148, 10653}, {548, 42924, 61}, {549, 23302, 42500}, {549, 42118, 13}, {616, 11300, 141}, {631, 5340, 42598}, {1657, 40694, 42164}, {3146, 42153, 5349}, {3524, 5335, 16644}, {3534, 10654, 42087}, {3534, 11486, 10654}, {3845, 37835, 42107}, {3845, 42121, 37835}, {5237, 36969, 16242}, {5237, 42158, 5}, {5321, 42778, 14}, {5351, 16965, 140}, {10304, 37640, 11480}, {10646, 42118, 23302}, {10654, 42091, 3534}, {10654, 42510, 11486}, {11481, 42120, 5318}, {11481, 42155, 2}, {11486, 42091, 42087}, {11489, 42097, 42101}, {11542, 12100, 16241}, {11543, 16963, 395}, {11543, 42100, 42108}, {11543, 42108, 5321}, {15686, 42634, 42117}, {15694, 42128, 42911}, {16241, 41107, 11542}, {16242, 36969, 5}, {16242, 42158, 36969}, {16268, 36968, 42584}, {16963, 36968, 42100}, {16963, 36970, 11543}, {16963, 42100, 36970}, {18581, 42131, 42109}, {19106, 37835, 3845}, {19106, 42121, 42107}, {22238, 42154, 37641}, {23302, 42685, 10646}, {23303, 42086, 42102}, {34200, 42912, 10645}, {37641, 42154, 398}, {41100, 42528, 15}, {41100, 42631, 8703}, {41972, 42528, 42633}, {41972, 42800, 41100}, {42086, 42115, 23303}, {42088, 42108, 42100}, {42089, 42127, 42110}, {42091, 42510, 10654}, {42110, 42686, 42089}

X(42944) = GIBERT (-3,1,6) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*a^2*SA - 2*SB*SC : :
X(42944) = 2 X[5351] + X[42599]

X(42944) lies on the cubic K1216a and these lines: {2, 5340}, {3, 395}, {4, 11481}, {5, 5237}, {6, 3523}, {13, 632}, {14, 548}, {15, 15712}, {16, 17}, {18, 550}, {20, 16645}, {30, 5351}, {61, 3530}, {62, 549}, {376, 5343}, {381, 42792}, {396, 631}, {546, 36968}, {547, 42813}, {629, 37352}, {1656, 5318}, {1657, 5349}, {3070, 42167}, {3071, 42168}, {3090, 5366}, {3091, 42933}, {3146, 42625}, {3389, 35256}, {3390, 35255}, {3411, 5352}, {3522, 5339}, {3524, 22236}, {3525, 42156}, {3526, 10653}, {3528, 42154}, {3533, 5335}, {3534, 42159}, {3627, 37835}, {3628, 16965}, {3843, 42910}, {3845, 42580}, {3850, 16967}, {3851, 42086}, {3854, 42141}, {3858, 19106}, {5054, 40693}, {5055, 42161}, {5056, 42110}, {5059, 42093}, {5066, 42591}, {5068, 42094}, {5070, 42162}, {5071, 42611}, {5073, 42091}, {5238, 12100}, {5334, 21735}, {5344, 42098}, {5365, 42096}, {5418, 42170}, {5420, 42169}, {5473, 22847}, {6564, 14813}, {6565, 14814}, {6695, 37340}, {6696, 11244}, {8260, 14541}, {8703, 16964}, {10124, 41107}, {10187, 42137}, {10188, 42922}, {10299, 11480}, {10303, 16644}, {10614, 10616}, {10617, 14538}, {10645, 42925}, {11485, 42687}, {11486, 15720}, {11539, 41100}, {11540, 42502}, {11543, 33923}, {11812, 42420}, {12103, 36970}, {12108, 16241}, {12811, 42593}, {13084, 37341}, {14093, 41113}, {14139, 36756}, {14869, 42500}, {14891, 41101}, {15644, 36980}, {15686, 41122}, {15687, 42631}, {15689, 41120}, {15694, 42510}, {15695, 42503}, {15696, 42160}, {15704, 42528}, {15706, 42511}, {15713, 16267}, {15717, 36836}, {15723, 41119}, {16239, 37832}, {16268, 34200}, {16808, 35018}, {16961, 41973}, {16966, 41974}, {17504, 42791}, {19107, 42628}, {21734, 42626}, {22531, 37464}, {31406, 41406}, {33416, 42118}, {34755, 42124}, {36967, 42778}, {37640, 42490}, {41983, 42436}, {42090, 42818}, {42100, 42143}, {42111, 42131}, {42125, 42682}, {42145, 42918}, {42492, 42498}, {42497, 42529}, {42532, 42636}, {42683, 42926}, {42693, 42775}, {42798, 42897}

X(42944) = crosspoint of X(17) and X(22237)
X(42944) = crosssum of X(61) and X(22238)
X(42944) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36843, 42148}, {2, 42148, 42166}, {3, 395, 42147}, {3, 16773, 395}, {3, 42149, 398}, {5, 42158, 5350}, {6, 3523, 42945}, {6, 42774, 3523}, {15, 41977, 42801}, {16, 17, 42924}, {16, 140, 397}, {17, 42924, 397}, {18, 550, 5321}, {18, 10646, 550}, {20, 16645, 42163}, {62, 549, 16772}, {140, 397, 23302}, {140, 11542, 42936}, {140, 42924, 17}, {376, 42153, 42164}, {398, 16773, 42149}, {398, 42149, 395}, {550, 42121, 18}, {631, 22238, 396}, {1656, 42115, 42151}, {1656, 42151, 5318}, {1657, 5349, 42108}, {1657, 18581, 5349}, {3522, 5339, 42087}, {3522, 11489, 5339}, {3526, 10653, 42598}, {3530, 42913, 61}, {3850, 42123, 42431}, {3850, 42431, 42102}, {5059, 42495, 42093}, {5073, 42129, 42920}, {5073, 42920, 42101}, {5237, 16242, 5}, {5237, 42937, 42158}, {5350, 42158, 42165}, {10646, 42121, 5321}, {11481, 23303, 42088}, {11481, 42088, 42685}, {11486, 15720, 42152}, {11543, 33923, 42157}, {15717, 37641, 36836}, {16242, 42158, 42937}, {16967, 42123, 42102}, {16967, 42431, 3850}, {18581, 42108, 42692}, {23303, 42088, 42107}, {23303, 42109, 42095}, {23303, 42686, 11481}, {36843, 42491, 2}, {36968, 42489, 546}, {37835, 42433, 3627}, {42089, 42115, 5318}, {42089, 42151, 1656}, {42091, 42129, 42101}, {42091, 42920, 5073}, {42107, 42685, 42088}, {42158, 42937, 5}, {42501, 42598, 3526}, {42528, 42814, 15704}, {42562, 42563, 42627}

X(42945) = GIBERT (3,1,6) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*a^2*SA + 2*SB*SC : :
X(42945) = 2 X[5352] + X[42598]

X(42945) lies on the cubic K1216b and these lines: {2, 5339}, {3, 396}, {4, 11480}, {5, 5238}, {6, 3523}, {13, 548}, {14, 632}, {15, 18}, {16, 15712}, {17, 550}, {20, 16644}, {30, 5352}, {61, 549}, {62, 3530}, {376, 5344}, {381, 42791}, {395, 631}, {546, 36967}, {547, 42814}, {630, 37351}, {1656, 5321}, {1657, 5350}, {3070, 42169}, {3071, 42170}, {3090, 5365}, {3091, 42932}, {3146, 42626}, {3364, 35256}, {3365, 35255}, {3412, 5351}, {3522, 5340}, {3524, 22238}, {3525, 42153}, {3526, 10654}, {3528, 42155}, {3533, 5334}, {3534, 42162}, {3627, 37832}, {3628, 16964}, {3843, 42911}, {3845, 42581}, {3850, 16966}, {3851, 42085}, {3854, 42140}, {3858, 19107}, {5054, 40694}, {5055, 42160}, {5056, 42107}, {5059, 42094}, {5066, 42590}, {5068, 42093}, {5070, 42159}, {5071, 42610}, {5073, 42090}, {5237, 12100}, {5335, 21735}, {5343, 42095}, {5366, 42097}, {5418, 42168}, {5420, 42167}, {5474, 22893}, {6564, 14814}, {6565, 14813}, {6694, 37341}, {6696, 11243}, {8259, 14540}, {8703, 16965}, {10124, 41108}, {10187, 42923}, {10188, 42136}, {10299, 11481}, {10303, 16645}, {10613, 10617}, {10616, 14539}, {10646, 42924}, {11485, 15720}, {11486, 42686}, {11539, 41101}, {11540, 42503}, {11542, 33923}, {11812, 42419}, {12103, 36969}, {12108, 16242}, {12811, 42592}, {13083, 37340}, {14093, 41112}, {14138, 36755}, {14869, 42501}, {14891, 41100}, {15644, 36978}, {15686, 41121}, {15687, 42632}, {15689, 41119}, {15694, 42511}, {15695, 42502}, {15696, 42161}, {15704, 42529}, {15706, 42510}, {15713, 16268}, {15717, 36843}, {15723, 41120}, {16239, 37835}, {16267, 34200}, {16809, 35018}, {16960, 41974}, {16967, 41973}, {17504, 42792}, {19106, 42627}, {21734, 42625}, {22532, 37463}, {31406, 41407}, {33417, 42117}, {34754, 42121}, {36968, 42777}, {37641, 42491}, {41983, 42435}, {42091, 42817}, {42099, 42146}, {42114, 42130}, {42128, 42683}, {42144, 42919}, {42493, 42499}, {42496, 42528}, {42533, 42635}, {42682, 42927}, {42692, 42776}, {42797, 42896}

X(42945) = crosspoint of X(18) and X(22235)
X(42945) = crosssum of X(62) and X(22236)
X(42945) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36836, 42147}, {2, 42147, 42163}, {3, 396, 42148}, {3, 16772, 396}, {3, 42152, 397}, {5, 42157, 5349}, {6, 3523, 42944}, {6, 42773, 3523}, {15, 18, 42925}, {15, 140, 398}, {16, 41978, 42802}, {17, 550, 5318}, {17, 10645, 550}, {18, 42925, 398}, {20, 16644, 42166}, {61, 549, 16773}, {140, 398, 23303}, {140, 11543, 42937}, {140, 42925, 18}, {376, 42156, 42165}, {397, 16772, 42152}, {397, 42152, 396}, {550, 42124, 17}, {631, 22236, 395}, {1656, 42116, 42150}, {1656, 42150, 5321}, {1657, 5350, 42109}, {1657, 18582, 5350}, {3522, 5340, 42088}, {3522, 11488, 5340}, {3526, 10654, 42599}, {3530, 42912, 62}, {3850, 42122, 42432}, {3850, 42432, 42101}, {5059, 42494, 42094}, {5073, 42132, 42921}, {5073, 42921, 42102}, {5238, 16241, 5}, {5238, 42936, 42157}, {5349, 42157, 42164}, {10645, 42124, 5318}, {11480, 23302, 42087}, {11480, 42087, 42684}, {11485, 15720, 42149}, {11542, 33923, 42158}, {15717, 37640, 36843}, {16241, 42157, 42936}, {16966, 42122, 42101}, {16966, 42432, 3850}, {18582, 42109, 42693}, {23302, 42087, 42110}, {23302, 42108, 42098}, {23302, 42687, 11480}, {36836, 42490, 2}, {36967, 42488, 546}, {37832, 42434, 3627}, {42090, 42132, 42102}, {42090, 42921, 5073}, {42092, 42116, 5321}, {42092, 42150, 1656}, {42110, 42684, 42087}, {42157, 42936, 5}, {42500, 42599, 3526}, {42529, 42813, 15704}, {42564, 42565, 42628}

X(42946) = GIBERT (-15,12,29) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 29*a^2*SA - 24*SB*SC : :

X(42946) lies on the cubic K1216a and these lines: {2, 17}, {3, 42688}, {14, 10299}, {15, 14869}, {16, 5079}, {18, 3530}, {30, 42797}, {382, 5351}, {546, 5237}, {550, 16242}, {1656, 42935}, {3091, 42629}, {3528, 42159}, {3529, 10646}, {3544, 16967}, {3628, 34755}, {3850, 12820}, {3851, 36843}, {3854, 42891}, {5059, 42694}, {5238, 15720}, {5352, 42089}, {10187, 10653}, {10303, 16961}, {10654, 42798}, {11486, 42612}, {12102, 42686}, {12821, 42920}, {14891, 42890}, {15687, 42631}, {15688, 42432}, {15694, 42635}, {15700, 42153}, {15701, 42934}, {15707, 41108}, {15710, 33603}, {15715, 42434}, {15717, 42513}, {16773, 35018}, {16964, 17504}, {22236, 42780}, {22238, 42593}, {33606, 41983}, {34200, 41122}, {37641, 42597}, {38071, 42158}, {41100, 41977}, {41107, 42611}, {42121, 42166}, {42122, 42531}, {42163, 42585}

X(42946) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 41944, 42636}, {2, 42779, 42488}, {2, 42938, 42779}, {41944, 42488, 42801}, {41944, 42779, 42938}, {41944, 42937, 42488}, {42488, 42636, 42779}, {42636, 42938, 42801}, {42779, 42938, 42636}, {42937, 42938, 2}

X(42947) = GIBERT (15,12,29) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 29*a^2*SA + 24*SB*SC : :

X(42947) lies on the cubic K1216b and these lines: {2, 18}, {3, 42689}, {13, 10299}, {15, 5079}, {16, 14869}, {17, 3530}, {30, 42798}, {382, 5352}, {546, 5238}, {550, 16241}, {1656, 42934}, {3091, 42630}, {3528, 42162}, {3529, 10645}, {3544, 16966}, {3628, 34754}, {3850, 12821}, {3851, 36836}, {3854, 42890}, {5059, 42695}, {5237, 15720}, {5351, 42092}, {10188, 10654}, {10303, 16960}, {10653, 42797}, {11485, 42613}, {12102, 42687}, {12820, 42921}, {14891, 42891}, {15687, 42632}, {15688, 42431}, {15694, 42636}, {15700, 42156}, {15701, 42935}, {15707, 41107}, {15710, 33602}, {15715, 42433}, {15717, 42512}, {16772, 35018}, {16965, 17504}, {22236, 42592}, {22238, 42779}, {33607, 41983}, {34200, 41121}, {35019, 36782}, {37640, 42596}, {38071, 42157}, {41101, 41978}, {41108, 42610}, {42123, 42530}, {42124, 42163}, {42166, 42584}

X(42947) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 41943, 42635}, {2, 42780, 42489}, {2, 42939, 42780}, {41943, 42489, 42802}, {41943, 42780, 42939}, {41943, 42936, 42489}, {42489, 42635, 42780}, {42635, 42939, 42802}, {42780, 42939, 42635}, {42936, 42939, 2}

X(42948) = GIBERT (-3,5,12) POINT

Barycentrics    Sqrt[3]*a^2*S - 12*a^2*SA - 10*SB*SC : :

X(42948) lies on the cubic K1216a and these lines: {2, 397}, {3, 5349}, {4, 42774}, {5, 5351}, {6, 3533}, {14, 14869}, {15, 18}, {17, 42121}, {61, 11539}, {62, 16239}, {395, 3526}, {396, 632}, {547, 5237}, {548, 42430}, {549, 42157}, {550, 16967}, {631, 5339}, {633, 33474}, {1656, 5318}, {1657, 42107}, {2045, 42258}, {2046, 42259}, {3090, 42491}, {3091, 42611}, {3522, 42095}, {3523, 5321}, {3524, 5365}, {3525, 16645}, {3530, 37835}, {3628, 16242}, {3850, 10646}, {3851, 42088}, {3854, 42097}, {3855, 42625}, {3858, 42109}, {3861, 42528}, {5054, 41113}, {5055, 42165}, {5056, 5350}, {5066, 42433}, {5067, 5344}, {5068, 42102}, {5070, 42166}, {5073, 42111}, {5334, 42773}, {5352, 11812}, {6672, 31275}, {6674, 37351}, {7486, 42155}, {9681, 42246}, {10187, 15712}, {10188, 42627}, {10303, 42153}, {12100, 42814}, {12108, 16964}, {12812, 36969}, {14892, 42631}, {15693, 42160}, {15694, 40694}, {15699, 16965}, {15702, 36836}, {15703, 42162}, {15709, 42490}, {15713, 42503}, {15720, 18581}, {15721, 42791}, {16241, 41978}, {16267, 42590}, {16644, 42594}, {16808, 42686}, {16809, 33923}, {16960, 42801}, {16963, 42898}, {16966, 42924}, {21735, 42093}, {22236, 42500}, {23302, 42149}, {35018, 42110}, {41974, 42146}, {42096, 42776}, {42106, 42685}, {42124, 42802}, {42129, 42150}, {42143, 42432}, {42167, 42267}, {42168, 42266}, {42488, 42913}, {42505, 42891}, {42687, 42816}

X(42948) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16773, 42598}, {6, 3533, 42949}, {61, 42597, 11539}, {140, 23303, 398}, {140, 42937, 23303}, {549, 42489, 42163}, {1656, 42115, 42921}, {3525, 16645, 16772}, {3530, 37835, 42164}, {3530, 42591, 37835}, {3628, 16242, 42148}, {5056, 11481, 5350}, {10188, 42779, 42627}, {33416, 42937, 140}, {35018, 42158, 42110}, {42110, 42793, 42158}

X(42949) = GIBERT (3,5,12) POINT

Barycentrics    Sqrt[3]*a^2*S + 12*a^2*SA + 10*SB*SC : :

X(42949) lies on the cubic K1216b and these lines: {2, 398}, {3, 5350}, {4, 42773}, {5, 5352}, {6, 3533}, {13, 14869}, {16, 17}, {18, 42124}, {61, 16239}, {62, 11539}, {395, 632}, {396, 3526}, {547, 5238}, {548, 42429}, {549, 42158}, {550, 16966}, {631, 5340}, {634, 33475}, {1656, 5321}, {1657, 42110}, {2045, 42259}, {2046, 42258}, {3090, 42490}, {3091, 42610}, {3522, 42098}, {3523, 5318}, {3524, 5366}, {3525, 16644}, {3530, 37832}, {3628, 16241}, {3850, 10645}, {3851, 42087}, {3854, 42096}, {3855, 42626}, {3858, 42108}, {3861, 42529}, {5054, 41112}, {5055, 42164}, {5056, 5349}, {5066, 42434}, {5067, 5343}, {5068, 42101}, {5070, 42163}, {5073, 42114}, {5335, 42774}, {5351, 11812}, {6671, 31275}, {6673, 37352}, {7486, 42154}, {9681, 42247}, {10187, 42628}, {10188, 15712}, {10303, 42156}, {12100, 42813}, {12108, 16965}, {12812, 36970}, {14892, 42632}, {15693, 42161}, {15694, 40693}, {15699, 16964}, {15702, 36843}, {15703, 42159}, {15709, 42491}, {15713, 42502}, {15720, 18582}, {15721, 42792}, {16242, 41977}, {16268, 42591}, {16645, 42595}, {16808, 33923}, {16809, 42687}, {16961, 42802}, {16962, 42899}, {16967, 42925}, {21735, 42094}, {22238, 42501}, {23303, 42152}, {35018, 42107}, {41973, 42143}, {42097, 42775}, {42103, 42684}, {42121, 42801}, {42132, 42151}, {42146, 42431}, {42169, 42267}, {42170, 42266}, {42489, 42912}, {42504, 42890}, {42686, 42815}

X(42949) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16772, 42599}, {6, 3533, 42948}, {62, 42596, 11539}, {140, 23302, 397}, {140, 42936, 23302}, {549, 42488, 42166}, {1656, 42116, 42920}, {3525, 16644, 16773}, {3530, 37832, 42165}, {3530, 42590, 37832}, {3628, 16241, 42147}, {5056, 11480, 5349}, {10187, 42780, 42628}, {33417, 42936, 140}, {35018, 42157, 42107}, {42107, 42794, 42157}

X(42950) = GIBERT (4,6,9) POINT

Barycentrics    4*a^2*S/Sqrt[3] + 9*a^2*SA + 12*SB*SC : :

X(42950) lies on the cubic K1216a and these lines: {2, 33604}, {3, 42134}, {6, 17}, {13, 15723}, {15, 5072}, {381, 23302}, {382, 10645}, {1657, 42092}, {3090, 42627}, {3525, 42492}, {3526, 18582}, {3534, 16808}, {3628, 42917}, {3843, 42144}, {3851, 42124}, {5054, 10646}, {5055, 11488}, {5070, 11542}, {5076, 42110}, {5079, 11485}, {5318, 15720}, {6221, 42247}, {6398, 42249}, {6451, 42196}, {6452, 42198}, {11480, 42581}, {11486, 42598}, {11489, 15703}, {12812, 42916}, {14093, 42097}, {15693, 42086}, {15694, 42118}, {15696, 42113}, {15700, 42629}, {15716, 36969}, {16241, 38335}, {16644, 34754}, {19709, 42117}, {21735, 42889}, {33416, 42610}, {33417, 42127}, {34755, 42156}, {36836, 42630}, {41100, 42499}, {41943, 42474}, {41974, 42476}, {42094, 42936}, {42096, 42632}, {42122, 42472}, {42123, 42494}, {42130, 42919}, {42473, 42925}, {42500, 42693}, {42511, 42692}, {42513, 42898}, {42899, 42910}

X(42950) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17, 16967, 42896}, {1656, 42132, 42817}, {1656, 42817, 42818}, {5055, 11488, 42816}, {16644, 42915, 42125}, {16966, 42132, 1656}, {18582, 42148, 42691}, {23302, 42114, 42116}, {42114, 42116, 381}, {42129, 42132, 17}, {42145, 42146, 42142}

X(42951) = GIBERT (-4,6,9) POINT

Barycentrics    4*a^2*S/Sqrt[3] - 9*a^2*SA - 12*SB*SC : :

X(42951) lies on the cubic K1216b and these lines: {2, 33605}, {3, 42133}, {6, 17}, {14, 15723}, {16, 5072}, {381, 23303}, {382, 10646}, {1657, 42089}, {3090, 42628}, {3525, 42493}, {3526, 18581}, {3534, 16809}, {3628, 42916}, {3843, 42145}, {3851, 42121}, {5054, 10645}, {5055, 11489}, {5070, 11543}, {5076, 42107}, {5079, 11486}, {5321, 15720}, {6221, 42246}, {6398, 42248}, {6451, 42195}, {6452, 42197}, {11481, 42580}, {11485, 42599}, {11488, 15703}, {12812, 42917}, {14093, 42096}, {15693, 42085}, {15694, 42117}, {15696, 42112}, {15700, 42630}, {15716, 36970}, {16242, 38335}, {16645, 34755}, {19709, 42118}, {21735, 42888}, {33416, 42126}, {33417, 42611}, {34754, 42153}, {36843, 42629}, {41101, 42498}, {41944, 42475}, {41973, 42477}, {42093, 42937}, {42097, 42631}, {42122, 42495}, {42123, 42473}, {42131, 42918}, {42472, 42924}, {42501, 42692}, {42510, 42693}, {42512, 42899}, {42898, 42911}

X(42951) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {18, 16966, 42897}, {1656, 42129, 42818}, {1656, 42818, 42817}, {5055, 11489, 42815}, {16645, 42914, 42128}, {16967, 42129, 1656}, {18581, 42147, 42690}, {23303, 42111, 42115}, {42111, 42115, 381}, {42129, 42132, 18}, {42143, 42144, 42139}

X(42952) = GIBERT (45,40,53) POINT

Barycentrics    15*Sqrt[3]*a^2*S + 53*a^2*SA + 80*SB*SC : :

X(42952) lies on the cubic K1216a and these lines: {2, 33607}, {3, 41121}, {5, 42613}, {13, 11812}, {15, 3845}, {17, 3545}, {18, 547}, {381, 42694}, {396, 42419}, {3832, 42511}, {3850, 16962}, {5072, 42635}, {5237, 15702}, {5459, 30471}, {10109, 16960}, {10124, 42935}, {11001, 12816}, {11488, 42901}, {11539, 41100}, {12817, 42146}, {12821, 41099}, {15682, 42512}, {15690, 36969}, {15699, 42521}, {15719, 41119}, {15723, 42156}, {16242, 42492}, {16644, 42632}, {16966, 42634}, {19711, 23302}, {33604, 42510}, {35401, 36836}, {37832, 41122}, {38335, 41943}, {40693, 42480}, {41101, 42103}, {41107, 41972}, {41120, 42581}, {41985, 42937}, {42496, 42507}, {42506, 42911}, {42532, 42918}, {42588, 42891}, {42595, 42800}

X(42953) = GIBERT (-45,40,53) POINT

Barycentrics    15*Sqrt[3]*a^2*S - 53*a^2*SA - 80*SB*SC : :

X(42953) lies on the cubic K1216b and these lines: {2, 33606}, {3, 41122}, {5, 42612}, {14, 11812}, {16, 3845}, {17, 547}, {18, 3545}, {381, 42695}, {395, 42420}, {3832, 42510}, {3850, 16963}, {5072, 42636}, {5238, 15702}, {5460, 30472}, {10109, 16961}, {10124, 42934}, {11001, 12817}, {11489, 42900}, {11539, 41101}, {12816, 42143}, {12820, 41099}, {15682, 42513}, {15690, 36970}, {15699, 42520}, {15719, 41120}, {15723, 42153}, {16241, 42493}, {16645, 42631}, {16967, 42633}, {19711, 23303}, {33605, 42511}, {35401, 36843}, {37835, 41121}, {38335, 41944}, {40694, 42481}, {41100, 42106}, {41108, 41971}, {41119, 42580}, {41985, 42936}, {42497, 42506}, {42507, 42910}, {42533, 42919} , {42589, 42890}, {42594, 42799}

X(42954) = GIBERT (-5,6,15) POINT

Barycentrics    5*a^2*S/Sqrt[3] - 15*a^2*SA - 12*SB*SC : :

X(42954) lies on the cubic K1216a and these lines: {2, 33607}, {3, 42630}, {4, 10187}, {5, 42629}, {6, 3411}, {14, 549}, {15, 10303}, {16, 3628}, {17, 42121}, {18, 42116}, {140, 16961}, {381, 42796}, {395, 11540}, {548, 19107}, {3534, 16809}, {3856, 42088}, {3857, 5351}, {5055, 16242}, {5066, 36968}, {5070, 42691}, {5072, 11481}, {5237, 15022}, {5238, 42628}, {7486, 16965}, {10304, 37835}, {11480, 42894}, {11488, 41944}, {11489, 15709}, {11543, 42687}, {12821, 15686}, {14890, 16268}, {15683, 42910}, {15698, 42085}, {15704, 42101}, {15706, 42125}, {15717, 18581}, {15721, 42513}, {15759, 36970}, {16644, 42498}, {16645, 42507}, {16963, 23302}, {16964, 42690}, {16966, 42895}, {17800, 42095}, {18582, 42935}, {19106, 42491}, {23046, 42928}, {33606, 42816}, {34200, 42692}, {36967, 42688}, {40693, 42530}, {42090, 42901}, {42107, 42591}, {42110, 42493}, {42124, 42897}, {42127, 42611}, {42129, 42157}, {42496, 42595}

X(42954) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 549, 42795}, {10187, 42089, 42931}, {10187, 42100, 16967}, {10646, 42918, 42113}, {11543, 42687, 42934}, {16963, 42499, 23302}, {23303, 42501, 42117}, {33416, 33417, 42597}, {42089, 42937, 16967}

X(42955) = GIBERT (5,6,15) POINT

Barycentrics    5*a^2*S/Sqrt[3] + 15*a^2*SA + 12*SB*SC : :

X(42955) lies on the cubic K1216b and these lines: {2, 33606}, {3, 42629}, {4, 10188}, {5, 42630}, {6, 3411}, {13, 549}, {15, 3628}, {16, 10303}, {17, 42115}, {18, 42124}, {140, 16960}, {381, 42795}, {396, 11540}, {548, 19106}, {3534, 16808}, {3856, 42087}, {3857, 5352}, {5055, 16241}, {5066, 36967}, {5070, 42690}, {5072, 11480}, {5237, 42627}, {5238, 15022}, {7486, 16964}, {10304, 37832}, {11481, 42895}, {11488, 15709}, {11489, 41943}, {11542, 42686}, {12820, 15686}, {14890, 16267}, {15683, 42911}, {15698, 42086}, {15704, 42102}, {15706, 42128}, {15717, 18582}, {15721, 42512}, {15759, 36969}, {16644, 42506}, {16645, 42499}, {16962, 23303}, {16965, 42691}, {16967, 42894}, {17800, 42098}, {18581, 42934}, {19107, 42490}, {23046, 42929}, {33475, 36767}, {33607, 42815}, {34200, 42693}, {34541, 36770}, {36968, 42689}, {40694, 42531}, {42091, 42900}, {42107, 42492}, {42110, 42590}, {42121, 42896}, {42126, 42610}, {42132, 42158}, {42497, 42594}

X(42955) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 549, 42796}, {10188, 42092, 42930}, {10188, 42099, 16966}, {10645, 42919, 42112}, {11542, 42686, 42935}, {16962, 42498, 23303}, {23302, 42500, 42118}, {33416, 33417, 42596}, {42092, 42936, 16966}

X(42956) = GIBERT (-11,9,22) POINT

Barycentrics    11*a^2*S/Sqrt[3] - 22*a^2*SA - 18*SB*SC : :

X(42956) lies on the cubic K1216a and these lines: {2, 42476}, {4, 11481}, {13, 15699}, {14, 12100}, {15, 14869}, {16, 12812}, {62, 42492}, {140, 41978}, {395, 15694}, {3628, 42895}, {11486, 42598}, {11489, 42490}, {11737, 16967}, {15685, 42104}, {15686, 16242}, {15688, 18581}, {15708, 16645}, {16239, 23302}, {16773, 42128}, {31695, 36768}, {33416, 42917}, {41989, 42900}, {42089, 42147}, {42129, 42692}, {42136, 42599}, {42137, 42489}, {42140, 42491}, {42146, 42593}, {42148, 42472}, {42501, 42511}, {42502, 42913}

X(42956) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42088, 42793, 42685}, {42107, 42685, 42109}, {42501, 42818, 42687}

X(42957) = GIBERT (11,9,22) POINT

Barycentrics    11*a^2*S/Sqrt[3] + 22*a^2*SA + 18*SB*SC : :

X(42957) lies on the cubic K1216b and these lines: {2, 42477}, {4, 11480}, {13, 12100}, {14, 15699}, {15, 12812}, {16, 14869}, {61, 42493}, {140, 41977}, {396, 15694}, {3628, 42894}, {11485, 42599}, {11488, 42491}, {11737, 16966}, {15685, 42105}, {15686, 16241}, {15688, 18582}, {15708, 16644}, {16239, 23303}, {16772, 42125}, {33417, 42916}, {41989, 42901}, {42092, 42148}, {42132, 42693}, {42136, 42488}, {42137, 42598}, {42141, 42490}, {42143, 42592}, {42147, 42473}, {42500, 42510}, {42503, 42912}

X(42957) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42087, 42794, 42684}, {42110, 42684, 42108}, {42500, 42817, 42686}

X(42958) = GIBERT (-9,4,27) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 27*a^2*SA - 8*SB*SC : :

X(42958) lies on the cubic K1216a and these lines: {3, 16268}, {4, 10187}, {5, 42631}, {13, 140}, {14, 21735}, {15, 15712}, {16, 15720}, {18, 33923}, {62, 3523}, {548, 41122}, {550, 16242}, {631, 16267}, {1656, 5351}, {1657, 37835}, {3411, 12100}, {3412, 42480}, {3522, 42160}, {3524, 42505}, {3530, 42636}, {3533, 16965}, {3534, 42908}, {3830, 42593}, {3850, 42433}, {3851, 42611}, {5056, 36968}, {5073, 42489}, {5352, 10299}, {14869, 41100}, {15717, 16963}, {16239, 42792}, {17504, 42613}, {22237, 42157}, {33416, 35018}, {34200, 42503}, {34755, 42896}, {36843, 42935}, {41107, 42592}, {41981, 42163}, {42088, 42493}, {42115, 42936}, {42121, 42894}, {42125, 42432}, {42138, 42158}, {42161, 42597}, {42686, 42924}

X(42958) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 42089, 10187}, {140, 5237, 41974}, {140, 41974, 42488}, {5056, 36968, 42909}, {42089, 42931, 10646}, {42148, 42590, 13}

X(42959) = GIBERT (9,4,27) POINT

Barycentrics    3*Sqrt[3]*a^2*S + 27*a^2*SA + 8*SB*SC : :

X(42959) lies on the cubic K1216b and these lines: {3, 16267}, {4, 10188}, {5, 42632}, {13, 21735}, {14, 140}, {15, 15720}, {16, 15712}, {17, 33923}, {61, 3523}, {548, 41121}, {550, 16241}, {631, 16268}, {1656, 5352}, {1657, 37832}, {3411, 42481}, {3412, 12100}, {3522, 42161}, {3524, 42504}, {3530, 42635}, {3533, 16964}, {3534, 42909}, {3830, 42592}, {3850, 42434}, {3851, 42610}, {5056, 36967}, {5073, 42488}, {5351, 10299}, {14869, 41101}, {15717, 16962}, {16239, 42791}, {17504, 42612}, {22235, 42158}, {33417, 35018}, {34200, 42502}, {34754, 42897}, {36836, 42934}, {41108, 42593}, {41981, 42166}, {42087, 42492}, {42116, 42937}, {42124, 42895}, {42128, 42431}, {42135, 42157}, {42160, 42596}, {42687, 42925}

X(42959) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 42092, 10188}, {140, 5238, 41973}, {140, 41973, 42489}, {5056, 36967, 42908}, {42092, 42930, 10645}, {42147, 42591, 14}

X(42960) = GIBERT (45,40,27) POINT

Barycentrics    15*Sqrt[3]*a^2*S + 27*a^2*SA + 80*SB*SC : :

X(42960) lies on the cubic K1216a and these lines: {3, 41121}, {4, 16960}, {5, 42612}, {13, 5056}, {14, 3850}, {17, 42137}, {381, 42613}, {382, 42518}, {1656, 42935}, {3533, 37832}, {3545, 42507}, {3832, 41119}, {3845, 41973}, {3861, 33607}, {5059, 5238}, {5067, 41107}, {10187, 42146}, {10188, 18582}, {11539, 42793}, {15723, 42508}, {16267, 42908}, {41974, 42491}, {41978, 42128}, {42095, 42815}, {42123, 42936}, {42138, 42802}

X(42961) = GIBERT (-45,40,27) POINT

Barycentrics    15*Sqrt[3]*a^2*S - 27*a^2*SA - 80*SB*SC : :

X(42961) lies on the cubic K1216b and these lines: {3, 41122}, {4, 16961}, {5, 42613}, {13, 3850}, {14, 5056}, {18, 42136}, {381, 42612}, {382, 42519}, {1656, 42934}, {3533, 37835}, {3545, 42506}, {3832, 41120}, {3845, 41974}, {3861, 33606}, {5059, 5237}, {5067, 41108}, {10187, 18581}, {10188, 42143}, {11539, 42794}, {15723, 42509}, {16268, 42909}, {41973, 42490}, {41977, 42125}, {42098, 42816}, {42122, 42937}, {42135, 42801}

X(42962) = GIBERT (4,6,3) POINT

Barycentrics    4*a^2*S/Sqrt[3] + 3*a^2*SA + 12*SB*SC : :

X(42962) lies on the cubic K1216a and these lines: {3, 42134}, {4, 42806}, {6, 13}, {15, 5076}, {16, 5079}, {17, 42130}, {302, 35749}, {382, 16772}, {546, 42923}, {1656, 5318}, {1657, 10645}, {3090, 42493}, {3146, 42627}, {3522, 42889}, {3526, 10646}, {3534, 23302}, {3544, 42628}, {3620, 31693}, {3631, 22492}, {3830, 11488}, {3843, 11542}, {3850, 22237}, {3851, 5335}, {3860, 33603}, {5054, 42086}, {5055, 42118}, {5070, 42120}, {5072, 11486}, {5073, 42124}, {5340, 34755}, {5344, 42121}, {5350, 42092}, {5366, 42123}, {6221, 42188}, {6398, 42190}, {6433, 35730}, {6445, 18587}, {6446, 18586}, {11485, 42101}, {11489, 19709}, {12102, 42916}, {12811, 42922}, {14269, 42117}, {15688, 37832}, {15693, 36969}, {15696, 19106}, {15700, 42911}, {15720, 16966}, {16267, 42901}, {16644, 42632}, {16965, 42611}, {22236, 42630}, {23303, 42510}, {34754, 42126}, {35403, 42912}, {37640, 42419}, {38335, 42085}, {40693, 42691}, {41973, 42093}, {42090, 42794}, {42105, 42598}, {42155, 42915}, {42158, 42905}, {42477, 42937}, {42498, 42928}, {42773, 42909}

X(42962) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 42128, 42815}, {381, 42815, 42816}, {3851, 5335, 42818}, {5318, 42114, 42115}, {5340, 42919, 42129}, {5344, 42472, 42121}, {11486, 42110, 5072}, {16808, 42128, 381}, {16809, 42895, 6}, {16966, 42131, 15720}, {18582, 42102, 42116}, {42094, 42132, 1657}, {42098, 42127, 3526}, {42098, 42813, 42127}, {42102, 42116, 382}, {42106, 42166, 11485}, {42110, 42162, 11486}, {42114, 42115, 1656}, {42125, 42128, 13}, {42134, 42142, 42146}, {42134, 42146, 3}, {42138, 42142, 3}, {42138, 42146, 42134}, {42209, 42210, 42142}

X(42963) = GIBERT (-4,6,3) POINT

Barycentrics    4*a^2*S/Sqrt[3] - 3*a^2*SA - 12*SB*SC : :

X(42963) lies on the cubic K1216b and these lines: {3, 42133}, {4, 42805}, {6, 13}, {15, 5079}, {16, 5076}, {18, 42131}, {303, 36327}, {382, 16773}, {546, 42922}, {1656, 5321}, {1657, 10646}, {3090, 42492}, {3146, 42628}, {3522, 42888}, {3526, 10645}, {3534, 23303}, {3544, 42627}, {3620, 31694}, {3631, 22491}, {3830, 11489}, {3843, 11543}, {3850, 22235}, {3851, 5334}, {3860, 33602}, {5054, 42085}, {5055, 42117}, {5070, 42119}, {5072, 11485}, {5073, 42121}, {5339, 34754}, {5343, 42124}, {5349, 42089}, {5365, 42122}, {6221, 42187}, {6398, 42189}, {6445, 18586}, {6446, 18587}, {11486, 42102}, {11488, 19709}, {12102, 42917}, {12811, 42923}, {14269, 42118}, {15688, 37835}, {15693, 36970}, {15696, 19107}, {15700, 42910}, {15720, 16967}, {16268, 42900}, {16645, 42631}, {16964, 42610}, {22238, 42629}, {23302, 42511}, {34755, 42127}, {35403, 42913}, {37641, 42420}, {38335, 42086}, {40694, 42690}, {41974, 42094}, {42091, 42793}, {42104, 42599}, {42154, 42914}, {42157, 42904}, {42476, 42936}, {42499, 42929}, {42774, 42908}

X(42963) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 42125, 42816}, {381, 42816, 42815}, {3851, 5334, 42817}, {5321, 42111, 42116}, {5339, 42918, 42132}, {5343, 42473, 42124}, {11485, 42107, 5072}, {16808, 42894, 6}, {16809, 42125, 381}, {16967, 42130, 15720}, {18581, 42101, 42115}, {42093, 42129, 1657}, {42095, 42126, 3526}, {42095, 42814, 42126}, {42101, 42115, 382}, {42103, 42163, 11486}, {42107, 42159, 11485}, {42111, 42116, 1656}, {42125, 42128, 14}, {42133, 42139, 42143}, {42133, 42143, 3}, {42135, 42139, 3}, {42135, 42143, 42133}, {42207, 42208, 42139}

X(42964) = GIBERT (15,-12,5) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 5*a^2*SA - 24*SB*SC : :
X(42964) = 11 X[42780] - 4 X[42891]

X(42964) lies on the cubic K1216a and these lines: {3, 42688}, {4, 13}, {14, 548}, {6, 42965}, {15, 5072}, {16, 15704}, {17, 3856}, {18, 10304}, {30, 42780}, {62, 42097}, {140, 42795}, {376, 33606}, {381, 42694}, {546, 34754}, {549, 42157}, {3146, 42630}, {3523, 42890}, {3526, 5352}, {3534, 5237}, {3627, 42612}, {3628, 5238}, {3845, 42635}, {3857, 42117}, {5055, 36836}, {5066, 41943}, {5343, 15717}, {5349, 23046}, {5351, 42085}, {7486, 42150}, {10124, 42798}, {10303, 10645}, {11485, 42901}, {12102, 42682}, {12103, 16961}, {12812, 42692}, {12817, 42152}, {15022, 16809}, {15683, 40694}, {15684, 41108}, {15706, 41122}, {15709, 42589}, {16002, 38738}, {16965, 33699}, {16967, 42684}, {17800, 22238}, {19107, 42165}, {41100, 42515}, {41113, 42433}, {41121, 42925}, {42119, 42580}, {42149, 42796}, {42593, 42902}

X(42964) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 13, 42695}, {61, 42160, 36970}, {15684, 42935, 42431}, {16964, 36970, 41973}, {16964, 42160, 61}, {36970, 41973, 42813}, {36970, 42934, 4}, {41973, 42813, 42799}, {42157, 42489, 42632}

X(42965) = GIBERT (15,12,-5) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 5*a^2*SA + 24*SB*SC : :
X(42965) = 11 X[42779] - 4 X[42890]

X(42965) lies on the cubic K1216b and these lines: {3, 42689}, {4, 14}, {6, 42964}, {13, 548}, {15, 15704}, {16, 5072}, {17, 10304}, {18, 3856}, {30, 42779}, {61, 42096}, {140, 42796}, {376, 33607}, {381, 42695}, {546, 34755}, {549, 42158}, {3146, 42629}, {3523, 42891}, {3526, 5351}, {3534, 5238}, {3627, 42613}, {3628, 5237}, {3845, 42636}, {3857, 42118}, {5055, 36843}, {5066, 41944}, {5344, 15717}, {5350, 23046}, {5352, 42086}, {7486, 42151}, {10124, 42797}, {10303, 10646}, {11486, 42900}, {12102, 42683}, {12103, 16960}, {12812, 42693}, {12816, 42149}, {15022, 16808}, {15683, 40693}, {15684, 41107}, {15706, 41121}, {15709, 42588}, {16001, 38738}, {16964, 33699}, {16966, 42685}, {17800, 22236}, {19106, 42164}, {41101, 42514}, {41112, 42434}, {41122, 42924}, {42120, 42581}, {42152, 42795}, {42592, 42903}

X(42965) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 14, 42694}, {62, 42161, 36969}, {15684, 42934, 42432}, {16965, 36969, 41974}, {16965, 42161, 62}, {36969, 41974, 42814}, {36969, 42935, 4}, {41974, 42814, 42800}, {42158, 42488, 42631}

X(42966) = GIBERT (39,12,-13) POINT

Barycentrics    13*Sqrt[3]*a^2*S - 13*a^2*SA + 24*SB*SC : :

X(42966) lies on the cubic K1216a and these lines: {4, 14}, {17, 15721}, {398, 42420}, {5079, 42903}, {5237, 11542}, {5238, 42625}, {5340, 42938}, {5351, 15693}, {5366, 42533}, {10109, 41944}, {11480, 42612}, {11539, 41100}, {15689, 22236}, {15703, 41107}, {15705, 40693}, {16962, 34200}, {19710, 42158}, {22238, 42914}, {34755, 42110}, {36843, 42936}, {42109, 42613}, {42121, 42166}, {42498, 42598}, {42592, 42815}, {42599, 42801}

X(42966) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10653, 42935, 41974}, {41974, 42800, 42814}, {41974, 42935, 42800}, {42148, 42779, 42631}

X(42967) = GIBERT (39,-12,13) POINT

Barycentrics    13*Sqrt[3]*a^2*S + 13*a^2*SA - 24*SB*SC : :

X(42967) lies on the cubic K1216b and these lines: {4, 13}, {18, 15721}, {397, 42419}, {5079, 42902}, {5237, 42626}, {5238, 11543}, {5339, 42939}, {5352, 15693}, {5365, 42532}, {10109, 41943}, {11481, 42613}, {11539, 41101}, {15689, 22238}, {15703, 41108}, {15705, 40694}, {16963, 34200}, {19710, 42157}, {22236, 42915}, {34754, 42107}, {36836, 42937}, {42108, 42612}, {42124, 42163}, {42499, 42599}, {42593, 42816}, {42598, 42802}

X(42967) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10654, 42934, 41973}, {41973, 42799, 42813}, {41973, 42934, 42799}, {42147, 42780, 42632}

X(42968) = GIBERT (60,26,-5) POINT

Barycentrics    20*Sqrt[3]*a^2*S - 5*a^2*SA + 52*SB*SC : :

X(42968) lies on the cubic K1216a and these lines: {15, 3534}, {18, 5072}, {381, 42693}, {549, 42815}, {1656, 42935}, {3526, 10653}, {5055, 5335}, {5066, 33602}, {11481, 33607}, {15683, 42633}, {15684, 42117}, {15685, 42516}, {15688, 42781}, {15706, 42817}, {15709, 42933}, {15719, 42416}, {15720, 42512}, {41112, 42691}, {41972, 42156}, {42113, 42689}, {42128, 42475}

X(42969) = GIBERT (60,-26,5) POINT

Barycentrics    20*Sqrt[3]*a^2*S + 5*a^2*SA - 52*SB*SC : :

X(42969) lies on the cubic K1216b and these lines: {16, 3534}, {17, 5072}, {381, 42692}, {549, 42816}, {1656, 42934}, {3526, 10654}, {5055, 5334}, {5066, 33603}, {11480, 33606}, {15683, 42634}, {15684, 42118}, {15685, 42517}, {15688, 42782}, {15706, 42818}, {15709, 42932}, {15719, 42415}, {15720, 42513}, {41113, 42690}, {41971, 42153}, {42112, 42688}, {42125, 42474}

X(42970) = GIBERT (11,-9,4) POINT

Barycentrics    11*a^2*S/Sqrt[3] + 4*a^2*SA - 18*SB*SC : :

X(42970) lies on the cubic K1216a and these lines: {2, 5321}, {15, 12811}, {16, 15704}, {17, 3858}, {18, 33923}, {30, 41972}, {61, 42781}, {398, 5073}, {546, 42901}, {547, 42904}, {3627, 42900}, {3853, 5318}, {10645, 42493}, {10654, 35403}, {11485, 42101}, {11543, 15691}, {12103, 42894}, {15696, 16773}, {16961, 42792}, {16962, 42415}, {18581, 42688}, {19107, 35404}, {23303, 42434}, {33606, 42686}, {35414, 42899}, {36970, 42138}, {41943, 42906}, {42099, 42938}, {42103, 42132}, {42109, 42613}, {42133, 42598}, {42135, 42492}, {42148, 42897}, {42150, 42692}, {42432, 42584}, {42532, 42777}, {42687, 42920}

X(42971) = GIBERT (11,9,-4) POINT

Barycentrics    11*a^2*S/Sqrt[3] - 4*a^2*SA + 18*SB*SC : :

X(42971) lies on the cubic K1216b and these lines: {2, 5318}, {15, 15704}, {16, 12811}, {17, 33923}, {18, 3858}, {30, 41971}, {62, 42782}, {397, 5073}, {546, 42900}, {547, 42905}, {3627, 42901}, {3853, 5321}, {10646, 42492}, {10653, 35403}, {11486, 42102}, {11542, 15691}, {12103, 42895}, {15696, 16772}, {16960, 42791}, {16963, 42416}, {18582, 42689}, {19106, 35404}, {23302, 42433}, {33607, 42687}, {35414, 42898}, {36969, 42135}, {41944, 42907}, {42100, 42939}, {42106, 42129}, {42108, 42612}, {42134, 42599}, {42138, 42493}, {42147, 42896}, {42151, 42693}, {42431, 42585}, {42533, 42778}, {42686, 42921}

X(42972) = GIBERT (-9,8,1) POINT

Barycentrics    3*Sqrt[3]*a^2*S - a^2*SA - 16*SB*SC : :
X(42972) = 4 X[14] - X[16], 5 X[14] - 2 X[395], X[14] + 2 X[5321], 7 X[14] - 4 X[11543], 11 X[14] - 5 X[16961], 3 X[14] - X[16963], 5 X[14] + X[19107], 7 X[14] - X[36968], 2 X[14] + X[36970], 17 X[14] - 2 X[42088], 13 X[14] - X[42100], 19 X[14] + 2 X[42108], 25 X[14] - 4 X[42123], 11 X[14] + 4 X[42136], 19 X[14] - X[42429], 17 X[14] - 8 X[42497], 43 X[14] - 4 X[42584], 23 X[14] + 10 X[42682], 19 X[14] - 10 X[42778], 31 X[14] + 8 X[42888], 13 X[14] - 4 X[42913], 5 X[16] - 8 X[395], X[16] + 8 X[5321], 7 X[16] - 16 X[11543], 11 X[16] - 20 X[16961], 3 X[16] - 4 X[16963], 5 X[16] + 4 X[19107], 7 X[16] - 4 X[36968], X[16] + 2 X[36970], 17 X[16] - 8 X[42088], 13 X[16] - 4 X[42100], 19 X[16] + 8 X[42108], 25 X[16] - 16 X[42123], 11 X[16] + 16 X[42136], 19 X[16] - 4 X[42429], 17 X[16] - 32 X[42497], 43 X[16] - 16 X[42584], 23 X[16] + 40 X[42682], 19 X[16] - 40 X[42778], 31 X[16] + 32 X[42888], 13 X[16] - 16 X[42913], X[395] + 5 X[5321], 7 X[395] - 10 X[11543], 4 X[395] - 5 X[16268], 22 X[395] - 25 X[16961], 6 X[395] - 5 X[16963], 2 X[395] + X[19107], 14 X[395] - 5 X[36968], 4 X[395] + 5 X[36970], 17 X[395] - 5 X[42088], 26 X[395] - 5 X[42100], 19 X[395] + 5 X[42108], 5 X[395] - 2 X[42123], 11 X[395] + 10 X[42136], 38 X[395] - 5 X[42429]

X(42972) lies on the cubic K1215a and these lines: {2, 5238}, {3, 41122}, {4, 12817}, {5, 41101}, {6, 14269}, {13, 3839}, {14, 16}, {15, 5055}, {17, 5066}, {18, 376}, {61, 381}, {62, 3830}, {382, 42636}, {396, 38071}, {397, 12816}, {398, 3845}, {532, 11054}, {547, 42147}, {549, 42157}, {617, 33561}, {631, 42589}, {1327, 3367}, {1328, 3366}, {1657, 42631}, {3146, 3411}, {3412, 3850}, {3523, 42593}, {3524, 18581}, {3534, 5351}, {3543, 5365}, {3545, 10654}, {3832, 41119}, {3856, 33607}, {3858, 42520}, {3860, 42166}, {5054, 10645}, {5071, 41978}, {5076, 41974}, {5237, 15681}, {5349, 15687}, {5352, 15694}, {5469, 14651}, {5859, 7843}, {5868, 41029}, {6000, 30440}, {6773, 36994}, {6777, 12243}, {8703, 42164}, {10109, 16772}, {10124, 42791}, {10187, 12108}, {10304, 16242}, {10646, 15689}, {10653, 42133}, {11001, 42149}, {11489, 42528}, {11539, 16967}, {11645, 36758}, {11737, 42581}, {12100, 42434}, {12154, 33228}, {13102, 14539}, {14540, 16628}, {14890, 42795}, {14892, 42107}, {15682, 42158}, {15683, 33606}, {15684, 22238}, {15685, 36843}, {15686, 16773}, {15688, 16645}, {15693, 42937}, {15696, 42587}, {15699, 16241}, {15702, 42495}, {15703, 36836}, {15704, 42792}, {15705, 42089}, {15706, 42129}, {15708, 33416}, {15709, 42119}, {15710, 42090}, {15719, 42890}, {16644, 42892}, {16808, 23046}, {17504, 23303}, {19106, 37641}, {19709, 22236}, {19710, 42503}, {21359, 22491}, {21360, 31694}, {31412, 36445}, {33699, 42148}, {36449, 42269}, {36463, 42561}, {36468, 42268}, {36757, 38072}, {36969, 38335}, {37640, 42103}, {40693, 41099}, {41106, 42532}, {41982, 42628}, {41984, 42500}, {42086, 42894}, {42096, 42901}, {42110, 42633}, {42127, 42800}, {42137, 42897}, {42140, 42430}, {42155, 42816}, {42165, 42899}, {42419, 42502}, {42586, 42801}, {42598, 42802}, {42625, 42818}

X(42972) = midpoint of X(i) and X(j) for these {i,j}: {16268, 36970}, {21360, 36330}
X(42972) = reflection of X(i) in X(j) for these {i,j}: {16, 16268}, {16268, 14}, {21360, 31694}
X(42972) = crosspoint of X(14) and X(12821)
X(42972) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 41101, 41943}, {6, 14269, 42973}, {14, 5321, 36970}, {14, 19107, 395}, {14, 36968, 11543}, {14, 36970, 16}, {14, 42429, 42778}, {61, 381, 41121}, {376, 41120, 18}, {381, 5339, 41108}, {381, 41108, 61}, {397, 14893, 12816}, {549, 42157, 42632}, {617, 33561, 40335}, {3534, 41944, 5351}, {3534, 42153, 41944}, {3543, 40694, 41100}, {3543, 41100, 42431}, {3545, 10654, 16962}, {3545, 16962, 37832}, {5339, 42814, 61}, {5343, 42159, 16964}, {10654, 16809, 37832}, {10654, 37832, 34754}, {12817, 41113, 41107}, {16809, 16962, 3545}, {16964, 42580, 42150}, {37835, 42154, 10645}, {41108, 42814, 381}, {41120, 42160, 376}, {41943, 41973, 41101}, {41944, 42432, 3534}, {42125, 42154, 37835}, {42153, 42432, 5351}, {42157, 42163, 42489}, {42489, 42632, 549}, {42511, 42920, 5071}, {42581, 42925, 42939}, {42799, 42919, 396}

X(42973) = GIBERT (9,8,1) POINT

Barycentrics    3*Sqrt[3]*a^2*S + a^2*SA + 16*SB*SC : :
X(42973) = 4 X[13] - X[15], 5 X[13] - 2 X[396], X[13] + 2 X[5318], 7 X[13] - 4 X[11542], 11 X[13] - 5 X[16960], 3 X[13] - X[16962], 5 X[13] + X[19106], 7 X[13] - X[36967], 2 X[13] + X[36969], 17 X[13] - 2 X[42087], 13 X[13] - X[42099], 19 X[13] + 2 X[42109], 25 X[13] - 4 X[42122], 11 X[13] + 4 X[42137], 19 X[13] - X[42430], 17 X[13] - 8 X[42496], 43 X[13] - 4 X[42585], 23 X[13] + 10 X[42683], 19 X[13] - 10 X[42777], 31 X[13] + 8 X[42889], 13 X[13] - 4 X[42912], 5 X[15] - 8 X[396], X[15] + 8 X[5318], 7 X[15] - 16 X[11542], 11 X[15] - 20 X[16960], 3 X[15] - 4 X[16962], 5 X[15] + 4 X[19106], 7 X[15] - 4 X[36967], X[15] + 2 X[36969], 17 X[15] - 8 X[42087], 13 X[15] - 4 X[42099], 19 X[15] + 8 X[42109], 25 X[15] - 16 X[42122], 11 X[15] + 16 X[42137], 19 X[15] - 4 X[42430], 17 X[15] - 32 X[42496], 43 X[15] - 16 X[42585], 23 X[15] + 40 X[42683], 19 X[15] - 40 X[42777], 31 X[15] + 32 X[42889], 13 X[15] - 16 X[42912], X[396] + 5 X[5318], 7 X[396] - 10 X[11542], 4 X[396] - 5 X[16267], 22 X[396] - 25 X[16960], 6 X[396] - 5 X[16962], 2 X[396] + X[19106], 14 X[396] - 5 X[36967], 4 X[396] + 5 X[36969], 17 X[396] - 5 X[42087], 26 X[396] - 5 X[42099], 19 X[396] + 5 X[42109], 5 X[396] - 2 X[42122], 11 X[396] + 10 X[42137]

X(42973) lies on the cubic K1215b and these lines: {2, 5237}, {3, 41121}, {4, 12816}, {5, 41100}, {6, 14269}, {13, 15}, {14, 3839}, {16, 5055}, {17, 376}, {18, 5066}, {61, 3830}, {62, 381}, {382, 42635}, {395, 38071}, {397, 3845}, {398, 12817}, {533, 11054}, {547, 42148}, {549, 42158}, {616, 33560}, {631, 42588}, {1327, 3392}, {1328, 3391}, {1657, 42632}, {3146, 3412}, {3411, 3850}, {3523, 42592}, {3524, 18582}, {3534, 5352}, {3543, 5366}, {3545, 10653}, {3832, 41120}, {3856, 33606}, {3858, 42521}, {3860, 42163}, {5054, 10646}, {5071, 41977}, {5076, 41973}, {5238, 15681}, {5350, 15687}, {5351, 15694}, {5470, 14651}, {5858, 7843}, {5869, 41028}, {6000, 30439}, {6770, 36992}, {6778, 12243}, {8703, 42165}, {10109, 16773}, {10124, 42792}, {10188, 12108}, {10304, 16241}, {10645, 15689}, {10654, 42134}, {11001, 42152}, {11488, 42529}, {11539, 16966}, {11645, 36757}, {11737, 42580}, {12100, 42433}, {12155, 33228}, {13103, 14538}, {14541, 16629}, {14890, 42796}, {14892, 42110}, {15682, 42157}, {15683, 33607}, {15684, 22236}, {15685, 36836}, {15686, 16772}, {15688, 16644}, {15693, 42936}, {15696, 42586}, {15699, 16242}, {15702, 42494}, {15703, 36843}, {15704, 42791}, {15705, 42092}, {15706, 42132}, {15708, 33417}, {15709, 42120}, {15710, 42091}, {15719, 42891}, {16645, 42893}, {16809, 23046}, {17504, 23302}, {19107, 37640}, {19709, 22238}, {19710, 42502}, {21359, 31693}, {21360, 22492}, {31412, 36463}, {33699, 42147}, {34552, 35730}, {35731, 42244}, {36445, 42561}, {36450, 42268}, {36467, 42269}, {36758, 38072}, {36970, 38335}, {37641, 42106}, {40694, 41099}, {41106, 42533}, {41982, 42627}, {41984, 42501}, {42085, 42895}, {42097, 42900}, {42107, 42634}, {42126, 42799}, {42136, 42896}, {42141, 42429}, {42154, 42815}, {42164, 42898}, {42420, 42503}, {42587, 42802}, {42599, 42801}, {42626, 42817}

X(42973) = midpoint of X(i) and X(j) for these {i,j}: {16267, 36969}, {21359, 35752}
X(42973) = reflection of X(i) in X(j) for these {i,j}: {15, 16267}, {16267, 13}, {21359, 31693}
X(42973) = crosspoint of X(13) and X(12820)
X(42973) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 41100, 41944}, {6, 14269, 42972}, {13, 5318, 36969}, {13, 19106, 396}, {13, 36967, 11542}, {13, 36969, 15}, {13, 42430, 42777}, {62, 381, 41122}, {376, 41119, 17}, {381, 5340, 41107}, {381, 41107, 62}, {398, 14893, 12817}, {549, 42158, 42631}, {616, 33560, 40334}, {3534, 41943, 5352}, {3534, 42156, 41943}, {3543, 40693, 41101}, {3543, 41101, 42432}, {3545, 10653, 16963}, {3545, 16963, 37835}, {5340, 42813, 62}, {5344, 42162, 16965}, {10653, 16808, 37835}, {10653, 37835, 34755}, {12816, 41112, 41108}, {16808, 16963, 3545}, {16965, 42581, 42151}, {37832, 42155, 10646}, {41107, 42813, 381}, {41119, 42161, 376}, {41943, 42431, 3534}, {41944, 41974, 41100}, {42128, 42155, 37832}, {42156, 42431, 5352}, {42158, 42166, 42488}, {42488, 42631, 549}, {42510, 42921, 5071}, {42580, 42924, 42938}, {42800, 42918, 395}

X(42974) = GIBERT (6,2,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S + a^2*SA + 4*SB*SC : :
X(42974) = 2 X[5335] + X[11485], 5 X[5335] + X[42119], 4 X[5335] - X[42127], 8 X[5335] + X[42130], 7 X[5335] - X[42141], 9 X[5335] + 5 X[42516], 3 X[5335] + 2 X[42633], 5 X[11485] - 2 X[42119], 2 X[11485] + X[42127], 4 X[11485] - X[42130], 7 X[11485] + 2 X[42141], 9 X[11485] - 10 X[42516], 3 X[11485] - 4 X[42633], 5 X[37640] - X[42119], 4 X[37640] + X[42127], 8 X[37640] - X[42130], 7 X[37640] + X[42141], 9 X[37640] - 5 X[42516], 3 X[37640] - 2 X[42633], 4 X[42119] + 5 X[42127], 8 X[42119] - 5 X[42130], 7 X[42119] + 5 X[42141], 9 X[42119] - 25 X[42516], 3 X[42119] - 10 X[42633], 2 X[42127] + X[42130], 7 X[42127] - 4 X[42141], 9 X[42127] + 20 X[42516], 3 X[42127] + 8 X[42633], 7 X[42130] + 8 X[42141], 9 X[42130] - 40 X[42516], 3 X[42130] - 16 X[42633], 9 X[42141] + 35 X[42516], 3 X[42141] + 14 X[42633], 5 X[42516] - 6 X[42633]

X(42974) lies on the cubic K1215a and these lines: {2, 11486}, {3, 396}, {5, 37641}, {6, 13}, {15, 3534}, {16, 5054}, {17, 3526}, {18, 5079}, {30, 5335}, {61, 382}, {62, 1656}, {69, 37352}, {193, 37170}, {298, 7776}, {299, 11298}, {303, 11302}, {376, 42116}, {395, 5055}, {398, 3843}, {473, 36302}, {547, 11489}, {549, 11488}, {590, 36438}, {597, 22492}, {599, 22495}, {615, 36456}, {616, 11301}, {617, 11296}, {619, 9763}, {622, 11297}, {623, 5858}, {631, 42924}, {634, 11311}, {1080, 9755}, {1152, 35731}, {1587, 15765}, {1588, 18585}, {1657, 16965}, {1992, 31693}, {2043, 7583}, {2044, 7584}, {2307, 9655}, {2452, 16179}, {3068, 36457}, {3069, 36439}, {3090, 22235}, {3107, 32519}, {3130, 21310}, {3146, 42925}, {3180, 7754}, {3201, 11935}, {3311, 18587}, {3312, 18586}, {3411, 42581}, {3412, 15696}, {3524, 42124}, {3543, 42117}, {3545, 11543}, {3618, 37351}, {3627, 5344}, {3642, 5859}, {3830, 5318}, {3839, 42138}, {3845, 5334}, {3851, 40694}, {3853, 5366}, {3857, 42775}, {3859, 42776}, {3861, 5343}, {3926, 37341}, {5066, 42142}, {5070, 42149}, {5071, 42146}, {5072, 42153}, {5073, 42147}, {5076, 16964}, {5093, 20426}, {5238, 41974}, {5321, 14269}, {5339, 42813}, {5350, 42160}, {5351, 42490}, {5353, 11237}, {5357, 11238}, {5459, 9761}, {5478, 41038}, {5615, 6108}, {5617, 41620}, {6115, 41745}, {6426, 35730}, {6772, 13103}, {6773, 41040}, {6775, 6783}, {6776, 41016}, {7127, 31479}, {7576, 11408}, {7585, 36436}, {7586, 36454}, {8014, 10217}, {8584, 22491}, {8703, 42120}, {8740, 18494}, {8919, 11555}, {8976, 42562}, {9605, 37332}, {10188, 42597}, {10303, 42804}, {10304, 42123}, {10645, 14093}, {10646, 15700}, {11001, 42122}, {11289, 22113}, {11300, 31859}, {11480, 15688}, {11481, 15693}, {11539, 42627}, {12154, 31695}, {12811, 42495}, {12816, 12820}, {13102, 31709}, {13951, 42563}, {14853, 41017}, {14892, 42472}, {14893, 42133}, {15681, 42086}, {15682, 42137}, {15683, 42145}, {15684, 42085}, {15685, 42087}, {15687, 42134}, {15689, 42088}, {15694, 23302}, {15695, 42091}, {15701, 42092}, {15703, 23303}, {15706, 42796}, {15707, 42781}, {15720, 36843}, {15723, 34755}, {16268, 42095}, {16963, 16966}, {17504, 42916}, {17800, 42150}, {18581, 19709}, {19106, 41101}, {19107, 42896}, {19710, 42588}, {21358, 22494}, {21734, 42932}, {22580, 40671}, {25164, 41621}, {30435, 37333}, {31487, 42233}, {32787, 42193}, {32788, 42191}, {33560, 34508}, {33607, 42533}, {33699, 42140}, {34754, 42097}, {35381, 42530}, {35400, 42112}, {35403, 42102}, {35434, 42799}, {35735, 42174}, {36437, 42216}, {36455, 42215}, {36970, 38335}, {37835, 41121}, {38071, 42139}, {41099, 42135}, {41108, 42093}, {41113, 42106}, {41120, 42107}, {41122, 42919}, {41984, 42492}, {42099, 42532}, {42163, 42921}, {42436, 42611}, {42474, 42914}, {42491, 42612}, {42507, 42897}, {42508, 42631}

X(42974) = midpoint of X(i) and X(j) for these {i,j}: {13, 9112}, {5335, 37640}
X(42974) = reflection of X(11485) in X(37640)
X(42974) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 13, 381}, {6, 381, 42975}, {6, 16808, 42816}, {6, 42128, 42125}, {6, 42815, 42128}, {13, 381, 42128}, {15, 41107, 42155}, {15, 42155, 3534}, {16, 16267, 16644}, {16, 16644, 5054}, {17, 22238, 3526}, {61, 5340, 382}, {61, 36969, 42154}, {62, 37832, 16645}, {62, 42156, 1656}, {376, 42912, 42116}, {381, 42815, 13}, {395, 5055, 42129}, {395, 18582, 5055}, {396, 397, 10653}, {396, 10653, 3}, {397, 40693, 3}, {398, 42162, 3843}, {547, 42634, 11489}, {549, 42496, 11488}, {3412, 42158, 36836}, {3534, 42155, 42131}, {3830, 10654, 42126}, {5054, 42817, 16644}, {5318, 10654, 3830}, {5335, 11485, 42127}, {5340, 42154, 36969}, {10645, 42625, 14093}, {10653, 40693, 396}, {10654, 41112, 5318}, {11480, 36968, 15688}, {11481, 16241, 15693}, {11485, 42127, 42130}, {11486, 11542, 42132}, {13665, 13785, 42128}, {16241, 41100, 11481}, {16241, 42506, 16960}, {16267, 16644, 42817}, {16645, 37832, 1656}, {16645, 42156, 37832}, {16772, 42151, 3}, {16960, 41100, 16241}, {16962, 36968, 11480}, {16965, 22236, 1657}, {23303, 42911, 15703}, {31709, 41746, 13102}, {36836, 42158, 15696}, {36969, 42154, 382}, {36970, 42094, 38335}, {37835, 41121, 42098}, {38072, 41043, 381}, {40694, 42166, 3851}, {42118, 42912, 376}, {42147, 42161, 5073}, {42148, 42152, 3}, {42149, 42598, 5070}, {42150, 42165, 17800}

X(42975) = GIBERT (-6,2,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S - a^2*SA - 4*SB*SC : :
X(42975) = 2 X[5334] + X[11486], 5 X[5334] + X[42120], 4 X[5334] - X[42126], 8 X[5334] + X[42131], 7 X[5334] - X[42140], 9 X[5334] + 5 X[42517], 3 X[5334] + 2 X[42634], 5 X[11486] - 2 X[42120], 2 X[11486] + X[42126], 4 X[11486] - X[42131], 7 X[11486] + 2 X[42140], 9 X[11486] - 10 X[42517], 3 X[11486] - 4 X[42634], 5 X[37641] - X[42120], 4 X[37641] + X[42126], 8 X[37641] - X[42131], 7 X[37641] + X[42140], 9 X[37641] - 5 X[42517], 3 X[37641] - 2 X[42634], 4 X[42120] + 5 X[42126], 8 X[42120] - 5 X[42131], 7 X[42120] + 5 X[42140], 9 X[42120] - 25 X[42517], 3 X[42120] - 10 X[42634], 2 X[42126] + X[42131], 7 X[42126] - 4 X[42140], 9 X[42126] + 20 X[42517], 3 X[42126] + 8 X[42634], 7 X[42131] + 8 X[42140], 9 X[42131] - 40 X[42517], 3 X[42131] - 16 X[42634], 9 X[42140] + 35 X[42517], 3 X[42140] + 14 X[42634], 5 X[42517] - 6 X[42634]

X(42975) lies on the cubic K1215b and these lines: {2, 11485}, {3, 395}, {5, 37640}, {6, 13}, {15, 5054}, {16, 3534}, {17, 5079}, {18, 3526}, {30, 5334}, {61, 1656}, {62, 382}, {69, 37351}, {193, 37171}, {298, 11297}, {299, 7776}, {302, 11301}, {376, 42115}, {383, 9755}, {396, 5055}, {397, 3843}, {472, 36303}, {547, 11488}, {549, 11489}, {590, 36456}, {597, 22491}, {599, 22496}, {615, 36438}, {616, 11295}, {617, 11302}, {618, 9761}, {621, 11298}, {624, 5859}, {631, 42925}, {633, 11312}, {1587, 18585}, {1588, 15765}, {1657, 16964}, {1992, 31694}, {2043, 7584}, {2044, 7583}, {2452, 16180}, {3068, 36439}, {3069, 36457}, {3090, 22237}, {3106, 32519}, {3129, 21311}, {3146, 42924}, {3181, 7754}, {3200, 11935}, {3311, 18586}, {3312, 18587}, {3411, 15696}, {3412, 42580}, {3524, 42121}, {3543, 42118}, {3545, 11542}, {3592, 35731}, {3618, 37352}, {3627, 5343}, {3643, 5858}, {3830, 5321}, {3839, 42135}, {3845, 5335}, {3851, 40693}, {3853, 5365}, {3857, 42776}, {3859, 42775}, {3861, 5344}, {3926, 37340}, {5066, 42139}, {5070, 42152}, {5071, 42143}, {5072, 42156}, {5073, 42148}, {5076, 16965}, {5093, 20425}, {5237, 41973}, {5318, 14269}, {5340, 42814}, {5349, 42161}, {5352, 42491}, {5353, 11238}, {5357, 11237}, {5460, 9763}, {5479, 41039}, {5611, 6109}, {5613, 41621}, {6114, 41746}, {6770, 41041}, {6772, 6782}, {6775, 13102}, {6776, 41017}, {7127, 9668}, {7576, 11409}, {7585, 36454}, {7586, 36436}, {8015, 10218}, {8584, 22492}, {8703, 42119}, {8739, 18494}, {8918, 11556}, {8976, 42564}, {9605, 37333}, {10187, 42596}, {10303, 42803}, {10304, 42122}, {10645, 15700}, {10646, 14093}, {11001, 42123}, {11290, 22114}, {11299, 31859}, {11480, 15693}, {11481, 15688}, {11539, 42628}, {12155, 31696}, {12811, 42494}, {12817, 12821}, {13103, 31710}, {13951, 42565}, {14853, 41016}, {14892, 42473}, {14893, 42134}, {15681, 42085}, {15682, 42136}, {15683, 42144}, {15684, 42086}, {15685, 42088}, {15687, 42133}, {15689, 42087}, {15694, 23303}, {15695, 42090}, {15701, 42089}, {15703, 23302}, {15706, 42795}, {15707, 42782}, {15720, 36836}, {15723, 34754}, {16267, 42098}, {16962, 16967}, {17504, 42917}, {17800, 42151}, {18582, 19709}, {19106, 42897}, {19107, 41100}, {19710, 42589}, {21358, 22493}, {21734, 42933}, {22579, 40672}, {25154, 41620}, {30435, 37332}, {31487, 42231}, {32787, 42194}, {32788, 42192}, {33561, 34509}, {33606, 42532}, {33699, 42141}, {34755, 42096}, {35381, 42531}, {35400, 42113}, {35403, 42101}, {35434, 42800}, {35735, 42171}, {36437, 42215}, {36455, 42216}, {36969, 38335}, {37832, 41122}, {38071, 42142}, {41099, 42138}, {41107, 42094}, {41112, 42103}, {41119, 42110}, {41121, 42918}, {41984, 42493}, {42100, 42533}, {42166, 42920}, {42435, 42610}, {42475, 42915}, {42490, 42613}, {42506, 42896}, {42509, 42632}

X(42975) = midpoint of X(i) and X(j) for these {i,j}: {14, 9113}, {5334, 37641}
X(42975) = reflection of X(11486) in X(37641)
X(42975) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14, 381}, {6, 381, 42974}, {6, 16809, 42815}, {6, 42125, 42128}, {6, 42816, 42125}, {14, 381, 42125}, {15, 16268, 16645}, {15, 16645, 5054}, {16, 41108, 42154}, {16, 42154, 3534}, {18, 22236, 3526}, {61, 37835, 16644}, {61, 42153, 1656}, {62, 5339, 382}, {62, 36970, 42155}, {376, 42913, 42115}, {381, 42816, 14}, {395, 398, 10654}, {395, 10654, 3}, {396, 5055, 42132}, {396, 18581, 5055}, {397, 42159, 3843}, {398, 40694, 3}, {547, 42633, 11488}, {549, 42497, 11489}, {3411, 42157, 36843}, {3534, 42154, 42130}, {3830, 10653, 42127}, {5054, 42818, 16645}, {5321, 10653, 3830}, {5334, 11486, 42126}, {5339, 42155, 36970}, {10646, 42626, 14093}, {10653, 41113, 5321}, {10654, 40694, 395}, {11480, 16242, 15693}, {11481, 36967, 15688}, {11485, 11543, 42129}, {11486, 42126, 42131}, {13665, 13785, 42125}, {16242, 41101, 11480}, {16242, 42507, 16961}, {16268, 16645, 42818}, {16644, 37835, 1656}, {16644, 42153, 37835}, {16773, 42150, 3}, {16961, 41101, 16242}, {16963, 36967, 11481}, {16964, 22238, 1657}, {23302, 42910, 15703}, {31710, 41745, 13103}, {36843, 42157, 15696}, {36969, 42093, 38335}, {36970, 42155, 382}, {37832, 41122, 42095}, {38072, 41042, 381}, {40693, 42163, 3851}, {42117, 42913, 376}, {42147, 42149, 3}, {42148, 42160, 5073}, {42151, 42164, 17800}, {42152, 42599, 5070}

X(42976) = GIBERT (27,4,17) POINT

Barycentrics    9*Sqrt[3]*a^2*S + 17*a^2*SA + 8*SB*SC : :
X(42976) = 3 X[3412] - X[42506]

X(42976) lies on the cubic K1215a and these lines: {2, 18}, {6, 15701}, {13, 15682}, {14, 10109}, {15, 3534}, {16, 12100}, {17, 5066}, {30, 3412}, {62, 15693}, {381, 41973}, {395, 11540}, {396, 3845}, {397, 15690}, {547, 42419}, {549, 42533}, {550, 42898}, {3411, 15702}, {3524, 42504}, {3830, 16267}, {3860, 42925}, {5237, 15716}, {5238, 8703}, {5351, 15698}, {5366, 42890}, {5469, 36327}, {10187, 41984}, {10645, 19708}, {10654, 41106}, {11001, 40693}, {11480, 42631}, {11485, 19709}, {11488, 41113}, {11542, 12816}, {11812, 16772}, {12101, 42147}, {12817, 18582}, {15534, 36757}, {15640, 42150}, {15685, 42431}, {15688, 42508}, {15689, 41974}, {15695, 36836}, {15697, 42158}, {15699, 42503}, {15713, 16241}, {15723, 42593}, {16529, 36362}, {16644, 41122}, {16960, 41119}, {16964, 41099}, {16965, 19710}, {16966, 41120}, {18581, 42516}, {19107, 33607}, {22510, 36330}, {33606, 42910}, {33622, 36768}, {33699, 42157}, {36967, 41112}, {36968, 42791}, {41978, 42505}, {42090, 42588}, {42093, 42518}, {42123, 42795}, {42156, 42509}

X(42976) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42532, 61}, {15, 41107, 42632}, {61, 16962, 41943}, {61, 41943, 16268}, {61, 42152, 42489}, {61, 42802, 42939}, {61, 42939, 42936}, {396, 34754, 36970}, {396, 41101, 41121}, {11485, 37832, 42799}, {16268, 41943, 42936}, {16268, 42939, 41943}, {16962, 41943, 42939}, {16962, 42532, 2}, {16962, 42635, 16268}, {34754, 41121, 41101}, {41101, 41121, 36970}, {41943, 42635, 61}, {41943, 42802, 16962}, {42147, 42502, 12101}, {42152, 42435, 61}, {42635, 42802, 41943}

X(42977) = GIBERT (-27,4,17) POINT

Barycentrics    9*Sqrt[3]*a^2*S - 17*a^2*SA - 8*SB*SC : :
X(42977) = 3 X[3411] - X[42507]

X(42977) lies on the cubic K1215b and these lines: {2, 17}, {6, 15701}, {13, 10109}, {14, 15682}, {15, 12100}, {16, 3534}, {18, 5066}, {30, 3411}, {61, 15693}, {381, 41974}, {395, 3845}, {396, 11540}, {398, 15690}, {547, 42420}, {549, 42532}, {550, 42899}, {3412, 15702}, {3524, 42505}, {3830, 16268}, {3860, 42924}, {5237, 8703}, {5238, 15716}, {5352, 15698}, {5365, 42891}, {5470, 35749}, {10188, 41984}, {10646, 19708}, {10653, 41106}, {11001, 40694}, {11481, 42632}, {11486, 19709}, {11489, 41112}, {11543, 12817}, {11812, 16773}, {12101, 42148}, {12816, 18581}, {15534, 36758}, {15640, 42151}, {15685, 42432}, {15688, 42509}, {15689, 41973}, {15695, 36843}, {15697, 42157}, {15699, 42502}, {15713, 16242}, {15723, 42592}, {16530, 36363}, {16645, 41121}, {16961, 41120}, {16964, 19710}, {16965, 41099}, {16967, 41119}, {18582, 42517}, {19106, 33606}, {22511, 35752}, {33607, 42911}, {33699, 42158}, {36967, 42792}, {36968, 41113}, {41977, 42504}, {42091, 42589}, {42094, 42519}, {42122, 42796}, {42153, 42508}

X(42977) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42533, 62}, {16, 41108, 42631}, {62, 16963, 41944}, {62, 41944, 16267}, {62, 42149, 42488}, {62, 42801, 42938}, {62, 42938, 42937}, {395, 34755, 36969}, {395, 41100, 41122}, {11486, 37835, 42800}, {16267, 41944, 42937}, {16267, 42938, 41944}, {16963, 41944, 42938}, {16963, 42533, 2}, {16963, 42636, 16267}, {34755, 41122, 41100}, {41100, 41122, 36969}, {41944, 42636, 62}, {41944, 42801, 16963}, {42148, 42503, 12101}, {42149, 42436, 62}, {42636, 42801, 41944}

X(42978) = GIBERT (-9,8,15) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 15*a^2*SA - 16*SB*SC : :

X(42978) lies on the cubic K1215a and these lines: {2, 3412}, {3, 41122}, {4, 5237}, {5, 41100}, {13, 35018}, {14, 3523}, {15, 18}, {16, 3851}, {17, 11489}, {62, 1656}, {298, 6674}, {381, 42909}, {395, 42488}, {396, 10188}, {397, 42801}, {547, 42420}, {550, 16242}, {631, 41108}, {1657, 10646}, {3090, 16963}, {3391, 10194}, {3392, 10195}, {3411, 3628}, {3522, 5365}, {3526, 16268}, {3533, 40694}, {3544, 42510}, {3627, 42631}, {3850, 16773}, {3854, 42151}, {3858, 42102}, {5056, 5335}, {5068, 16965}, {5073, 5351}, {5079, 41107}, {5340, 42914}, {5352, 15720}, {6695, 40334}, {10124, 42507}, {10299, 42089}, {10303, 41101}, {11695, 30439}, {12102, 42792}, {12103, 12817}, {12154, 33206}, {14869, 42794}, {14890, 42504}, {15683, 42505}, {15712, 16964}, {15717, 41120}, {16239, 16962}, {16241, 42513}, {16961, 42152}, {16966, 42779}, {19107, 42495}, {21735, 42159}, {22238, 42893}, {33923, 42163}, {36452, 42279}, {36470, 42278}, {36970, 42491}, {41981, 42099}, {42091, 42776}, {42095, 42431}, {42112, 42931}, {42125, 42774}, {42166, 42800}, {42433, 42793}, {42473, 42629}, {42596, 42912}, {42773, 42816}, {42780, 42818}, {42913, 42935}

X(42978) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3412, 42592}, {18, 23303, 42937}, {18, 33416, 398}, {18, 42937, 15}, {398, 42628, 18}, {3411, 3628, 16267}, {15720, 41973, 5352}, {15720, 42153, 41973}, {16242, 42599, 42814}, {16268, 42593, 3526}, {16645, 42489, 62}, {16773, 42580, 36969}, {23303, 42628, 33416}, {42801, 42915, 397}

X(42979) = GIBERT (9,8,15) POINT

Barycentrics    3*Sqrt[3]*a^2*S + 15*a^2*SA + 16*SB*SC : :

X(42979) lies on the cubic K1215b and these lines: {2, 3411}, {3, 41121}, {4, 5238}, {5, 41101}, {13, 3523}, {14, 35018}, {15, 3851}, {16, 17}, {18, 11488}, {61, 1656}, {299, 6673}, {381, 42908}, {395, 10187}, {396, 42489}, {398, 42802}, {547, 42419}, {550, 16241}, {631, 41107}, {1657, 10645}, {3090, 16962}, {3366, 10194}, {3367, 10195}, {3412, 3628}, {3522, 5366}, {3526, 16267}, {3533, 40693}, {3544, 42511}, {3627, 42632}, {3850, 16772}, {3854, 42150}, {3858, 42101}, {5056, 5334}, {5068, 16964}, {5073, 5352}, {5079, 41108}, {5339, 42915}, {5351, 15720}, {6694, 40335}, {10124, 42506}, {10299, 42092}, {10303, 41100}, {11695, 30440}, {12102, 42791}, {12103, 12816}, {12155, 33206}, {14869, 42793}, {14890, 42505}, {15683, 42504}, {15712, 16965}, {15717, 41119}, {16239, 16963}, {16242, 42512}, {16960, 42149}, {16967, 42780}, {19106, 42494}, {21735, 42162}, {22236, 42892}, {33923, 42166}, {36453, 42279}, {36469, 42278}, {36969, 42490}, {41981, 42100}, {42090, 42775}, {42098, 42432}, {42113, 42930}, {42128, 42773}, {42163, 42799}, {42434, 42794}, {42472, 42630}, {42597, 42913}, {42774, 42815}, {42779, 42817}, {42912, 42934}

X(42979) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3411, 42593}, {17, 23302, 42936}, {17, 33417, 397}, {17, 42936, 16}, {397, 42627, 17}, {3412, 3628, 16268}, {15720, 41974, 5351}, {15720, 42156, 41974}, {16241, 42598, 42813}, {16267, 42592, 3526}, {16644, 42488, 61}, {16772, 42581, 36970}, {23302, 42627, 33417}, {42802, 42914, 398}

X(42980) = GIBERT (33,-2,51) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 51*a^2*SA - 4*SB*SC : :

X(42980) lies on the cubic K1215a and these lines: {2, 5238}, {13, 15704}, {15, 33923}, {17, 5073}, {18, 42930}, {20, 42892}, {61, 42796}, {62, 15714}, {397, 42929}, {1656, 42904}, {3411, 5352}, {3412, 15696}, {3853, 36967}, {3858, 23302}, {5059, 41978}, {10188, 42157}, {15691, 16962}, {16772, 35404}, {16966, 42908}, {33416, 42773}, {35414, 41119}, {37640, 42433}, {42149, 42799}, {42493, 42794}

X(42981) = GIBERT (33,2,-51) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 51*a^2*SA + 4*SB*SC : :

X(42981) lies on the cubic K1215b and these lines: {2, 5237}, {14, 15704}, {16, 33923}, {17, 42931}, {18, 5073}, {20, 42893}, {61, 15714}, {62, 42795}, {398, 42928}, {1656, 42905}, {3411, 15696}, {3412, 5351}, {3853, 36968}, {3858, 23303}, {5059, 41977}, {10187, 42158}, {15691, 16963}, {16773, 35404}, {16967, 42909}, {33417, 42774}, {35414, 41120}, {37641, 42434}, {42152, 42800}, {42492, 42793}

X(42982) = GIBERT (8,3,2) POINT

Barycentrics    4*a^2*S/Sqrt[3] + a^2*SA + 3*SB*SC : :

X(42982) lies on the cubic K1215a and these lines: {2, 11486}, {3, 42916}, {4, 42815}, {6, 3091}, {13, 3839}, {15, 20}, {16, 10303}, {18, 5056}, {61, 42104}, {396, 10304}, {397, 3523}, {631, 42817}, {1587, 42562}, {1588, 42563}, {1656, 42917}, {3090, 42628}, {3146, 11485}, {3522, 42118}, {3524, 42496}, {3525, 42627}, {3543, 5318}, {3620, 22113}, {3832, 42128}, {3854, 42125}, {3855, 42816}, {4208, 5362}, {5059, 42127}, {5066, 33605}, {5068, 11543}, {5071, 42818}, {5261, 5353}, {5274, 5357}, {5304, 5472}, {5340, 42109}, {5344, 42085}, {5366, 19107}, {7398, 37775}, {7486, 11489}, {7583, 42204}, {7584, 42203}, {10653, 15692}, {10654, 12816}, {11480, 42781}, {15022, 42146}, {15640, 19106}, {15682, 42633}, {15683, 42122}, {15697, 42155}, {15708, 16267}, {15715, 42416}, {15717, 42124}, {15721, 16644}, {16241, 41972}, {16808, 42779}, {16967, 42513}, {17578, 42117}, {18581, 42897}, {19709, 33604}, {21734, 42123}, {22236, 42141}, {23302, 42491}, {34754, 42161}, {37641, 42098}, {41107, 42091}, {41119, 42919}, {42089, 42498}, {42095, 42494}, {42131, 42912}, {42133, 42162}, {42136, 42907}, {42151, 42928}, {42153, 42472}, {42218, 42522}, {42220, 42523}, {42473, 42503}, {42506, 42631}, {42515, 42516}, {42588, 42626}, {42685, 42773}, {42777, 42804}, {42813, 42896}

X(42982) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 42166, 42139}, {3543, 42803, 42154}, {42154, 42898, 37640}

X(42983) = GIBERT (-8,3,2) POINT

Barycentrics    4*a^2*S/Sqrt[3] - a^2*SA - 3*SB*SC : :

X(42983) lies on the cubic K1215b and these lines: {2, 11485}, {3, 42917}, {4, 42816}, {6, 3091}, {14, 3839}, {15, 10303}, {16, 20}, {17, 5056}, {62, 42105}, {395, 10304}, {398, 3523}, {631, 42818}, {1587, 42564}, {1588, 42565}, {1656, 42916}, {3090, 42627}, {3146, 11486}, {3522, 42117}, {3524, 42497}, {3525, 42628}, {3543, 5321}, {3620, 22114}, {3832, 42125}, {3854, 42128}, {3855, 42815}, {4208, 5367}, {5059, 42126}, {5066, 33604}, {5068, 11542}, {5071, 42817}, {5261, 5357}, {5274, 5353}, {5304, 5471}, {5339, 42108}, {5343, 42086}, {5365, 19106}, {7398, 37776}, {7486, 11488}, {7583, 42206}, {7584, 42205}, {10653, 12817}, {10654, 15692}, {11481, 42782}, {15022, 42143}, {15640, 19107}, {15682, 42634}, {15683, 42123}, {15697, 42154}, {15708, 16268}, {15715, 42415}, {15717, 42121}, {15721, 16645}, {16242, 41971}, {16809, 42780}, {16966, 42512}, {17578, 42118}, {18582, 42896}, {19709, 33605}, {21734, 42122}, {22238, 42140}, {23303, 42490}, {34755, 42160}, {37640, 42095}, {41108, 42090}, {41120, 42918}, {42092, 42499}, {42098, 42495}, {42130, 42913}, {42134, 42159}, {42137, 42906}, {42150, 42929}, {42156, 42473}, {42217, 42522}, {42219, 42523}, {42472, 42502}, {42507, 42632}, {42514, 42517}, {42589, 42625}, {42684, 42774}, {42778, 42803}, {42814, 42897}

X(42983) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 42163, 42142}, {3543, 42804, 42155}, {42155, 42899, 37641}

X(42984) = GIBERT (12,20,37) POINT

Barycentrics    4*Sqrt[3]*a^2*S + 37*a^2*SA + 40*SB*SC : :

X(42984) lies on the cubic K1215a and these lines: {2, 42492}, {3, 5350}, {13, 15694}, {15, 5055}, {18, 3412}, {381, 42144}, {396, 42513}, {1656, 42590}, {3525, 42933}, {3545, 42932}, {3830, 16966}, {3843, 42936}, {3851, 10188}, {5054, 42120}, {5079, 42776}, {6669, 9885}, {10124, 42815}, {14269, 42092}, {15689, 42098}, {15700, 42146}, {15701, 37832}, {15703, 23302}, {15706, 42142}, {15707, 33417}, {15716, 42138}, {15722, 42127}, {16242, 33607}, {18582, 42792}, {19709, 42103}, {22238, 42488}, {35403, 42114}, {36970, 42592}, {37835, 42610}, {42132, 42594}, {42490, 42795}

X(42985) = GIBERT (-12,20,37) POINT

Barycentrics    4*Sqrt[3]*a^2*S - 37*a^2*SA - 40*SB*SC : :

X(42985) lies on the cubic K1215b and these lines: {2, 42493}, {3, 5349}, {14, 15694}, {16, 5055}, {17, 3411}, {381, 42145}, {395, 42512}, {1656, 42591}, {3525, 42932}, {3545, 42933}, {3830, 16967}, {3843, 42937}, {3851, 10187}, {5054, 42119}, {5079, 42775}, {6670, 9886}, {10124, 42816}, {14269, 42089}, {15689, 42095}, {15700, 42143}, {15701, 37835}, {15703, 23303}, {15706, 42139}, {15707, 33416}, {15716, 42135}, {15722, 42126}, {16241, 33606}, {18581, 42791}, {19709, 42106}, {22236, 42489}, {35403, 42111}, {36969, 42593}, {37832, 42611}, {42129, 42595}, {42491, 42796}

X(42986) = GIBERT (8,3,4) POINT

Barycentrics    4*a^2*S/Sqrt[3] + 2*a^2*SA + 3*SB*SC : :

X(42986) lies on the cubic K1215a and these lines: {2, 42492}, {3, 42916}, {4, 11408}, {6, 3090}, {13, 15682}, {14, 3545}, {15, 3529}, {16, 631}, {17, 11489}, {20, 42815}, {61, 42103}, {376, 396}, {381, 42923}, {397, 10299}, {3068, 42172}, {3069, 42171}, {3412, 42085}, {3524, 42124}, {3525, 11486}, {3528, 42118}, {3533, 23302}, {3544, 42146}, {3830, 33604}, {3839, 42633}, {3855, 5334}, {5067, 42132}, {5068, 42816}, {5071, 11543}, {5318, 33703}, {5321, 41099}, {5340, 42927}, {5344, 42087}, {5353, 8164}, {5366, 42096}, {5862, 6669}, {6353, 37776}, {7486, 42818}, {7581, 42565}, {7582, 42564}, {10188, 42149}, {10653, 15698}, {11001, 42127}, {11466, 39874}, {11541, 42137}, {14093, 42932}, {15709, 16644}, {15710, 42930}, {16645, 42898}, {16809, 42494}, {16961, 42911}, {16962, 42090}, {16963, 42512}, {16966, 37641}, {17538, 42116}, {18581, 42780}, {19107, 42903}, {19708, 42123}, {21735, 41974}, {22236, 42108}, {23303, 42610}, {31683, 36772}, {31696, 36327}, {33417, 42779}, {34754, 42140}, {35255, 42201}, {35256, 42202}, {36970, 42516}, {37832, 42507}, {41112, 42100}, {41978, 42158}, {42091, 42891}, {42133, 42166}, {42229, 42637}, {42529, 42588}
X(42986) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3090, 42987}, {14, 18582, 42472}, {15, 42895, 42161}, {11485, 42128, 42136}, {11542, 42128, 22235}, {16960, 40693, 11488}, {33602, 42511, 15682}, {34754, 42162, 42140}

X(42987) = GIBERT (-8,3,4) POINT

Barycentrics    4*a^2*S/Sqrt[3] - 2*a^2*SA - 3*SB*SC : :

X(42987) lies on the cubic K1215b and these lines: {2, 42493}, {3, 42917}, {4, 11409}, {6, 3090}, {13, 3545}, {14, 15682}, {15, 631}, {16, 3529}, {18, 11488}, {20, 42816}, {62, 42106}, {376, 395}, {381, 42922}, {398, 10299}, {3068, 42174}, {3069, 42173}, {3411, 42086}, {3524, 42121}, {3525, 11485}, {3528, 42117}, {3533, 23303}, {3544, 42143}, {3830, 33605}, {3839, 42634}, {3855, 5335}, {5067, 42129}, {5068, 42815}, {5071, 11542}, {5318, 41099}, {5321, 33703}, {5339, 42926}, {5343, 42088}, {5357, 8164}, {5365, 42097}, {5863, 6670}, {6353, 37775}, {7486, 42817}, {7581, 42563}, {7582, 42562}, {10187, 42152}, {10654, 15698}, {11001, 42126}, {11467, 39874}, {11541, 42136}, {14093, 42933}, {15709, 16645}, {15710, 42931}, {16644, 42899}, {16808, 42495}, {16960, 42910}, {16962, 42513}, {16963, 42091}, {16967, 37640}, {17538, 42115}, {18582, 42779}, {19106, 42902}, {19708, 42122}, {21735, 41973}, {22238, 42109}, {23302, 42611}, {31695, 35749}, {33416, 42780}, {34755, 42141}, {35255, 42199}, {35256, 42200}, {36969, 42517}, {37835, 42506}, {41113, 42099}, {41977, 42157}, {42090, 42890}, {42134, 42163}, {42227, 42637}, {42528, 42589}

X(42987) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3090, 42986}, {13, 18581, 42473}, {16, 42894, 42160}, {11486, 42125, 42137}, {11543, 42125, 22237}, {16961, 40694, 11489}, {33603, 42510, 15682}, {34755, 42159, 42141}

X(42988) = GIBERT (6,2,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 3*a^2*SA + 4*SB*SC : :
X(42988) = 59 X[5344] - 9 X[42514]

X(42988) lies on the cubic K1215a and these lines: {2, 42590}, {3, 396}, {4, 11408}, {5, 37640}, {6, 17}, {13, 382}, {14, 5072}, {15, 1657}, {16, 15720}, {20, 42912}, {30, 5344}, {61, 381}, {62, 3526}, {140, 11486}, {299, 11311}, {395, 5070}, {398, 3851}, {546, 5365}, {550, 5335}, {627, 11309}, {628, 11298}, {633, 11305}, {635, 5859}, {2045, 7583}, {2046, 7584}, {2307, 9654}, {3053, 5472}, {3068, 14814}, {3069, 14813}, {3070, 42205}, {3071, 42206}, {3107, 32520}, {3364, 18510}, {3365, 18512}, {3389, 13903}, {3390, 13961}, {3522, 42118}, {3523, 42115}, {3525, 42913}, {3529, 42806}, {3533, 42121}, {3534, 16962}, {3628, 37641}, {3643, 33465}, {3830, 42147}, {3843, 5349}, {3850, 5334}, {3854, 42135}, {3858, 5343}, {5054, 22238}, {5055, 40694}, {5056, 11543}, {5059, 42122}, {5068, 42146}, {5073, 5318}, {5076, 42154}, {5079, 37832}, {5237, 15693}, {5238, 15696}, {5321, 42921}, {5350, 42085}, {5352, 15688}, {5366, 42119}, {5864, 6771}, {5868, 7684}, {6144, 40334}, {6694, 34509}, {7754, 11289}, {8981, 42201}, {9755, 37463}, {10645, 41974}, {10646, 42773}, {11307, 22113}, {11480, 42158}, {11489, 42627}, {11555, 40578}, {12816, 35434}, {13665, 42278}, {13785, 42279}, {13966, 42202}, {14093, 42433}, {14269, 41119}, {15681, 41112}, {15684, 42511}, {15691, 42588}, {15694, 16773}, {15700, 41100}, {15706, 42935}, {15707, 42510}, {15712, 42916}, {15723, 16963}, {16239, 42634}, {16241, 36843}, {16645, 42488}, {17800, 42161}, {18586, 36449}, {18587, 36468}, {19709, 42163}, {21735, 42123}, {22237, 42143}, {22844, 36770}, {23302, 42149}, {33923, 42120}, {34559, 36465}, {34562, 36446}, {34754, 42094}, {36757, 39899}, {38335, 41101}, {41122, 42518}, {41973, 42093}, {42098, 42816}, {42099, 42895}, {42533, 42597}, {42592, 42938}, {42599, 42911}, {42781, 42794}

X(42988) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 17, 1656}, {6, 1656, 42989}, {6, 16960, 42817}, {6, 16966, 42818}, {6, 42132, 42129}, {6, 42817, 42132}, {13, 3412, 22236}, {13, 22236, 382}, {15, 5340, 1657}, {15, 42815, 42127}, {17, 1656, 42132}, {61, 16267, 42156}, {61, 41121, 42814}, {61, 42156, 381}, {62, 16644, 3526}, {396, 397, 42152}, {396, 40693, 3}, {397, 42152, 3}, {398, 3851, 42125}, {398, 18582, 3851}, {1656, 42817, 17}, {1657, 5340, 42127}, {1657, 42815, 5340}, {3523, 42924, 42115}, {5073, 42150, 42130}, {5237, 41943, 42490}, {5237, 42490, 15693}, {5238, 42155, 15696}, {5318, 42150, 5073}, {5334, 42494, 3850}, {5335, 42116, 42131}, {5343, 42142, 3858}, {5365, 42775, 546}, {8976, 13951, 42132}, {10653, 16772, 3}, {10654, 42166, 3843}, {11485, 11542, 42128}, {11485, 42128, 42126}, {16962, 16965, 36836}, {16965, 36836, 3534}, {16967, 42896, 6}, {37832, 42153, 5079}, {40693, 42152, 397}, {40694, 42598, 5055}, {41107, 42939, 5352}, {42124, 42924, 3523}, {42138, 42691, 42128}, {42147, 42162, 3830}, {42154, 42813, 5076}, {42229, 42230, 396}, {42431, 42802, 15}

X(42989) = GIBERT (-6,2,3) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 3*a^2*SA - 4*SB*SC : :
X(42989) = 59 X[5343] - 9 X[42515]

X(42989) lies on the cubic K1215b and these lines: {2, 42591}, {3, 395}, {4, 11409}, {5, 37641}, {6, 17}, {13, 5072}, {14, 382}, {15, 15720}, {16, 1657}, {20, 42913}, {30, 5343}, {61, 3526}, {62, 381}, {140, 11485}, {298, 11312}, {396, 5070}, {397, 3851}, {546, 5366}, {550, 5334}, {627, 11297}, {628, 11310}, {634, 11306}, {636, 5858}, {2045, 7584}, {2046, 7583}, {3053, 5471}, {3068, 14813}, {3069, 14814}, {3070, 42203}, {3071, 42204}, {3106, 32520}, {3364, 13903}, {3365, 13961}, {3389, 18510}, {3390, 18512}, {3522, 42117}, {3523, 42116}, {3525, 42912}, {3529, 42805}, {3533, 42124}, {3534, 16963}, {3628, 37640}, {3642, 33464}, {3830, 42148}, {3843, 5350}, {3850, 5335}, {3854, 42138}, {3858, 5344}, {5054, 22236}, {5055, 40693}, {5056, 11542}, {5059, 42123}, {5068, 42143}, {5073, 5321}, {5076, 42155}, {5079, 37835}, {5237, 15696}, {5238, 15693}, {5318, 42920}, {5349, 42086}, {5351, 15688}, {5365, 42120}, {5865, 6774}, {5869, 7685}, {6144, 40335}, {6695, 34508}, {7127, 9669}, {7754, 11290}, {8981, 42199}, {9755, 37464}, {10645, 42774}, {10646, 41973}, {11308, 22114}, {11481, 42157}, {11488, 42628}, {11556, 40579}, {12817, 35434}, {13665, 42279}, {13785, 42278}, {13966, 42200}, {14093, 42434}, {14269, 41120}, {15681, 41113}, {15684, 42510}, {15691, 42589}, {15694, 16772}, {15700, 41101}, {15706, 42934}, {15707, 42511}, {15712, 42917}, {15723, 16962}, {16239, 42633}, {16242, 36836}, {16644, 42489}, {17800, 42160}, {18586, 36450}, {18587, 36467}, {19709, 42166}, {21735, 42122}, {22235, 42146}, {23303, 42152}, {33923, 42119}, {34559, 36464}, {34562, 36447}, {34755, 42093}, {36758, 39899}, {38335, 41100}, {41121, 42519}, {41974, 42094}, {42095, 42815}, {42100, 42894}, {42532, 42596}, {42593, 42939}, {42598, 42910}, {42782, 42793}

X(42989) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 18, 1656}, {6, 1656, 42988}, {6, 16961, 42818}, {6, 16967, 42817}, {6, 42129, 42132}, {6, 42818, 42129}, {14, 3411, 22238}, {14, 22238, 382}, {16, 5339, 1657}, {16, 42816, 42126}, {18, 1656, 42129}, {61, 16645, 3526}, {62, 16268, 42153}, {62, 41122, 42813}, {62, 42153, 381}, {395, 398, 42149}, {395, 40694, 3}, {397, 3851, 42128}, {397, 18581, 3851}, {398, 42149, 3}, {1656, 42818, 18}, {1657, 5339, 42126}, {1657, 42816, 5339}, {3523, 42925, 42116}, {5073, 42151, 42131}, {5237, 42154, 15696}, {5238, 41944, 42491}, {5238, 42491, 15693}, {5321, 42151, 5073}, {5334, 42115, 42130}, {5335, 42495, 3850}, {5344, 42139, 3858}, {5366, 42776, 546}, {8976, 13951, 42129}, {10653, 42163, 3843}, {10654, 16773, 3}, {11486, 11543, 42125}, {11486, 42125, 42127}, {16963, 16964, 36843}, {16964, 36843, 3534}, {16966, 42897, 6}, {37835, 42156, 5079}, {40693, 42599, 5055}, {40694, 42149, 398}, {41108, 42938, 5351}, {42121, 42925, 3523}, {42135, 42690, 42125}, {42148, 42159, 3830}, {42155, 42814, 5076}, {42227, 42228, 395}, {42432, 42801, 16}

X(42990) = GIBERT (9,2,-1) POINT

Barycentrics    3*Sqrt[3]*a^2*S - a^2*SA + 4*SB*SC : :
X(42990) = 19 X[41974] + 12 X[42419]

X(42990) lies on the cubic K1215a and these lines: {2, 42612}, {3, 3412}, {4, 12817}, {5, 13}, {6, 382}, {14, 3843}, {15, 548}, {16, 631}, {17, 3526}, {20, 61}, {30, 41974}, {39, 9112}, {54, 8919}, {140, 16267}, {202, 37722}, {203, 4317}, {303, 33386}, {372, 35733}, {376, 42532}, {381, 42507}, {384, 12155}, {396, 3530}, {398, 3853}, {532, 11289}, {547, 42420}, {616, 6694}, {632, 10188}, {1656, 16963}, {1657, 41101}, {2042, 35730}, {2307, 4325}, {3090, 41121}, {3091, 16268}, {3146, 41973}, {3180, 22845}, {3200, 9705}, {3206, 9706}, {3523, 41943}, {3528, 5238}, {3567, 30440}, {3627, 41108}, {3628, 41944}, {3832, 5335}, {3850, 41122}, {3855, 37641}, {3856, 42163}, {3857, 33606}, {3859, 11543}, {3861, 5318}, {4309, 7005}, {5054, 42506}, {5055, 42533}, {5056, 41119}, {5067, 37832}, {5070, 11486}, {5321, 42922}, {5344, 42159}, {5350, 12820}, {5351, 15717}, {5463, 11307}, {5470, 20416}, {5472, 9698}, {5611, 22843}, {6777, 36252}, {7006, 15888}, {7127, 37719}, {7486, 18582}, {7870, 11308}, {10187, 15703}, {10645, 21734}, {10646, 16772}, {10654, 33703}, {11300, 36388}, {11302, 36366}, {11303, 22493}, {11304, 35752}, {11485, 42434}, {11539, 42592}, {11541, 42588}, {11542, 16239}, {11624, 12006}, {12007, 36992}, {12100, 42898}, {13630, 30439}, {15063, 36209}, {15687, 42909}, {15689, 42508}, {15696, 22236}, {16241, 36843}, {16645, 42581}, {16808, 42153}, {16961, 42128}, {16967, 42436}, {17504, 42504}, {17538, 42511}, {17578, 36970}, {17800, 42155}, {22235, 42911}, {22495, 37341}, {23046, 42899}, {23236, 36208}, {23302, 42596}, {23303, 42938}, {32467, 41020}, {33404, 33414}, {33417, 42491}, {33923, 42631}, {34754, 42120}, {35018, 42636}, {35751, 37340}, {41977, 42590}, {42085, 42934}, {42089, 42498}, {42098, 42895}, {42099, 42118}, {42115, 42490}, {42125, 42897}, {42165, 42432}, {42494, 42910}, {42598, 42913}

X(42990) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 62, 3411}, {5, 3411, 18}, {6, 382, 42991}, {6, 16965, 16964}, {13, 62, 18}, {13, 3411, 5}, {15, 42148, 42433}, {15, 42935, 42148}, {17, 22238, 16242}, {61, 10653, 42158}, {61, 42158, 36967}, {62, 397, 13}, {395, 42580, 18}, {396, 42924, 5237}, {5237, 42779, 396}, {5237, 42800, 42924}, {5238, 42151, 42528}, {5335, 40694, 42813}, {11542, 16773, 42488}, {11542, 34755, 33416}, {16773, 42488, 33416}, {16964, 16965, 19106}, {34755, 42488, 16773}, {37640, 42151, 5238}, {40694, 42813, 16809}, {42099, 42147, 42890}, {42598, 42913, 42937}, {42779, 42800, 5237}

X(42991) = GIBERT (9,-2,1) POINT

Barycentrics    3*Sqrt[3]*a^2*S + a^2*SA - 4*SB*SC : :
X(42991) = 19 X[41973] + 12 X[42420]

X(42991) lies on the cubic K1215b and these lines: {2, 42613}, {3, 3411}, {4, 12816}, {5, 14}, {6, 382}, {13, 3843}, {15, 631}, {16, 548}, {18, 3526}, {20, 62}, {30, 41973}, {39, 9113}, {54, 8918}, {140, 16268}, {202, 4317}, {203, 37722}, {302, 33387}, {376, 42533}, {381, 42506}, {384, 12154}, {395, 3530}, {397, 3853}, {533, 11290}, {547, 42419}, {617, 6695}, {632, 10187}, {1656, 16962}, {1657, 41100}, {2307, 37720}, {3090, 41122}, {3091, 16267}, {3146, 41974}, {3181, 22844}, {3201, 9705}, {3205, 9706}, {3523, 41944}, {3528, 5237}, {3567, 30439}, {3627, 41107}, {3628, 41943}, {3832, 5334}, {3850, 41121}, {3855, 37640}, {3856, 42166}, {3857, 33607}, {3859, 11542}, {3861, 5321}, {4309, 7006}, {4330, 7127}, {5054, 42507}, {5055, 42532}, {5056, 41120}, {5067, 37835}, {5070, 11485}, {5318, 42923}, {5343, 42162}, {5349, 12821}, {5352, 15717}, {5464, 11308}, {5469, 20415}, {5471, 9698}, {5615, 22890}, {6778, 36251}, {7005, 15888}, {7486, 18581}, {7870, 11307}, {10188, 15703}, {10645, 16773}, {10646, 21734}, {10653, 33703}, {11299, 36386}, {11301, 36368}, {11303, 36330}, {11304, 22494}, {11486, 42433}, {11539, 42593}, {11541, 42589}, {11543, 16239}, {11626, 12006}, {12007, 36994}, {12100, 42899}, {13630, 30440}, {15063, 36208}, {15687, 42908}, {15689, 42509}, {15696, 22238}, {16242, 36836}, {16644, 42580}, {16809, 42156}, {16960, 42125}, {16966, 42435}, {17504, 42505}, {17538, 42510}, {17578, 36969}, {17800, 42154}, {22237, 42910}, {22496, 37340}, {23046, 42898}, {23236, 36209}, {23302, 42939}, {23303, 42597}, {32467, 41021}, {33405, 33415}, {33416, 42490}, {33923, 42632}, {34755, 42119}, {35018, 42635}, {35731, 42231}, {36329, 37341}, {41978, 42591}, {42086, 42935}, {42092, 42499}, {42095, 42894}, {42100, 42117}, {42116, 42491}, {42128, 42896}, {42164, 42431}, {42495, 42911}, {42599, 42912}

X(42991) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 61, 3412}, {5, 3412, 17}, {6, 382, 42990}, {6, 16964, 16965}, {14, 61, 17}, {14, 3412, 5}, {16, 42147, 42434}, {16, 42934, 42147}, {18, 22236, 16241}, {61, 398, 14}, {62, 10654, 42157}, {62, 42157, 36968}, {395, 42925, 5238}, {396, 42581, 17}, {5237, 42150, 42529}, {5238, 42780, 395}, {5238, 42799, 42925}, {5334, 40693, 42814}, {11543, 16772, 42489}, {11543, 34754, 33417}, {16772, 42489, 33417}, {16964, 16965, 19107}, {34754, 42489, 16772}, {37641, 42150, 5237}, {40693, 42814, 16808}, {42100, 42148, 42891}, {42599, 42912, 42936}, {42780, 42799, 5238}

X(42992) = GIBERT (9,4,3) POINT

Barycentrics    3*Sqrt[3]*a^2*S + 3*a^2*SA + 8*SB*SC : :
X(42992) = X[3412] - 3 X[42506]

X(42992) lies on the cubic K1215a and these lines: {2, 42612}, {3, 16267}, {4, 13}, {5, 16268}, {6, 3851}, {14, 3850}, {15, 1657}, {16, 17}, {18, 5056}, {20, 16962}, {30, 3412}, {62, 1656}, {203, 5270}, {299, 33465}, {382, 42635}, {395, 35018}, {396, 550}, {398, 3858}, {547, 42502}, {548, 42794}, {622, 6694}, {627, 6669}, {631, 41100}, {635, 22113}, {3090, 3411}, {3091, 41119}, {3104, 22688}, {3181, 33413}, {3389, 8960}, {3390, 42234}, {3522, 5335}, {3523, 5351}, {3533, 10188}, {3543, 42532}, {3627, 41101}, {3628, 10187}, {3767, 9112}, {3843, 41108}, {3845, 42898}, {3853, 12816}, {3854, 16809}, {4857, 7005}, {5059, 36967}, {5068, 40694}, {5070, 41944}, {5072, 41122}, {5073, 22236}, {5237, 15720}, {5318, 34754}, {5334, 42896}, {5339, 42128}, {5343, 42106}, {5344, 19106}, {5349, 42138}, {5350, 19107}, {5352, 42155}, {5366, 42085}, {5462, 30440}, {5472, 7755}, {5868, 41036}, {6102, 11624}, {6695, 40335}, {7781, 9763}, {10299, 11488}, {10303, 42510}, {10611, 22511}, {10646, 42817}, {11054, 11303}, {11289, 34509}, {11305, 22495}, {11485, 42432}, {11486, 42937}, {11555, 36211}, {11626, 18874}, {12155, 16925}, {14540, 20425}, {14814, 31454}, {14892, 42899}, {15694, 42592}, {15699, 42533}, {15706, 42508}, {15710, 42504}, {15712, 16241}, {16626, 20252}, {16772, 33923}, {16961, 42146}, {16966, 42149}, {18581, 42494}, {21735, 42433}, {22238, 42488}, {22510, 41021}, {25555, 36758}, {30439, 34783}, {32907, 37333}, {33604, 41120}, {33703, 42511}, {34755, 42132}, {35434, 42509}, {35752, 37172}, {36304, 41724}, {36366, 37352}, {36843, 42935}, {37641, 42580}, {41978, 41981}, {42122, 42629}, {42142, 42920}, {42143, 42897}, {42164, 42633}, {42165, 42434}

X(42992) = crosssum of X(61) and X(5238)
X(42992) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 61, 41973}, {4, 16964, 42908}, {4, 41973, 36970}, {6, 3851, 42993}, {13, 61, 42813}, {13, 16964, 42162}, {13, 40693, 61}, {15, 5340, 42431}, {16, 17, 42936}, {17, 397, 16}, {61, 16964, 42799}, {61, 36970, 42934}, {61, 42813, 36970}, {62, 37832, 42489}, {62, 42156, 37832}, {396, 5238, 42939}, {396, 16965, 5238}, {396, 42529, 42892}, {397, 11542, 17}, {397, 23302, 42924}, {5070, 41944, 42593}, {5335, 16960, 10645}, {5335, 42152, 42158}, {5344, 42150, 19106}, {5350, 42925, 19107}, {10188, 16242, 3533}, {16267, 41107, 41943}, {16960, 42158, 42152}, {16964, 37640, 61}, {37640, 42162, 16964}, {40693, 42162, 37640}, {41973, 42813, 4}, {42152, 42158, 10645}, {42165, 42912, 42434}

X(42993) = GIBERT (-9,4,3) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 3*a^2*SA - 8*SB*SC : :
X[3411] - 3 X[42507]

X(42993) lies on the cubic K1215b and these lines: {2, 42613}, {3, 16268}, {4, 14}, {5, 16267}, {6, 3851}, {13, 3850}, {15, 18}, {16, 1657}, {17, 5056}, {20, 16963}, {30, 3411}, {61, 1656}, {202, 5270}, {298, 33464}, {382, 42636}, {395, 550}, {396, 35018}, {397, 3858}, {547, 42503}, {548, 42793}, {621, 6695}, {628, 6670}, {631, 41101}, {636, 22114}, {3090, 3412}, {3091, 41120}, {3105, 22690}, {3180, 33412}, {3364, 8960}, {3365, 42232}, {3522, 5334}, {3523, 5352}, {3533, 10187}, {3543, 42533}, {3627, 41100}, {3628, 10188}, {3767, 9113}, {3843, 41107}, {3845, 42899}, {3853, 12817}, {3854, 16808}, {4857, 7006}, {5059, 36968}, {5068, 40693}, {5070, 41943}, {5072, 41121}, {5073, 22238}, {5238, 15720}, {5321, 34755}, {5335, 42897}, {5340, 42125}, {5343, 19107}, {5344, 42103}, {5349, 19106}, {5350, 42135}, {5351, 42154}, {5365, 42086}, {5462, 30439}, {5471, 7755}, {5869, 41037}, {6102, 11626}, {6694, 40334}, {7781, 9761}, {10299, 11489}, {10303, 42511}, {10612, 22510}, {10645, 42818}, {11054, 11304}, {11290, 34508}, {11306, 22496}, {11485, 42936}, {11486, 42431}, {11556, 36210}, {11624, 18874}, {12154, 16925}, {14541, 20426}, {14813, 31454}, {14892, 42898}, {15694, 42593}, {15699, 42532}, {15706, 42509}, {15710, 42505}, {15712, 16242}, {16627, 20253}, {16773, 33923}, {16960, 42143}, {16967, 42152}, {18582, 42495}, {21735, 42434}, {22236, 42489}, {22511, 41020}, {25555, 36757}, {30440, 34783}, {32909, 37332}, {33605, 41119}, {33703, 42510}, {34754, 42129}, {35434, 42508}, {35739, 42227}, {36305, 41724}, {36330, 37173}, {36368, 37351}, {36836, 42934}, {37640, 42581}, {41977, 41981}, {42123, 42630}, {42139, 42921}, {42146, 42896}, {42164, 42433}, {42165, 42634}

X(42993) = crosssum of X(62) and X(5237)
X(42993) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 62, 41974}, {4, 16965, 42909}, {4, 41974, 36969}, {6, 3851, 42992}, {14, 62, 42814}, {14, 16965, 42159}, {14, 40694, 62}, {15, 18, 42937}, {16, 5339, 42432}, {18, 398, 15}, {61, 37835, 42488}, {61, 42153, 37835}, {62, 16965, 42800}, {62, 36969, 42935}, {62, 42814, 36969}, {395, 5237, 42938}, {395, 16964, 5237}, {395, 42528, 42893}, {398, 11543, 18}, {398, 23303, 42925}, {5070, 41943, 42592}, {5334, 16961, 10646}, {5334, 42149, 42157}, {5343, 42151, 19107}, {5349, 42924, 19106}, {10187, 16241, 3533}, {16268, 41108, 41944}, {16961, 42157, 42149}, {16965, 37641, 62}, {37641, 42159, 16965}, {40694, 42159, 37641}, {41974, 42814, 4}, {42149, 42157, 10646}, {42164, 42913, 42433}

X(42994) = GIBERT (27,4,-9) POINT

Barycentrics    9*Sqrt[3]*a^2*S - 9*a^2*SA + 8*SB*SC : :

X(42994) lies on the cubic K1215a and these lines: {4, 14}, {13, 35018}, {15, 33923}, {16, 15720}, {18, 42110}, {61, 42625}, {140, 16267}, {397, 16966}, {398, 42630}, {546, 42503}, {548, 42420}, {550, 41100}, {631, 42505}, {1656, 41121}, {1657, 42587}, {3091, 42533}, {3411, 3850}, {3412, 10299}, {3522, 42520}, {3851, 41107}, {3858, 41122}, {3861, 42507}, {5056, 16963}, {5073, 41108}, {5237, 15712}, {5340, 42818}, {5343, 42897}, {5344, 16961}, {5351, 42892}, {5365, 42629}, {10187, 18582}, {10188, 11542}, {10303, 42506}, {11486, 42801}, {21735, 42480}, {22238, 42488}, {33416, 41977}, {41972, 42433}, {42097, 42432}, {42117, 42158}, {42118, 42682}, {42148, 42890}, {42149, 42915}, {42162, 42436}, {42592, 42612}, {42596, 42777}

X(42994) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {62, 10653, 42814}, {62, 42800, 42935}, {62, 42935, 36969}, {397, 34755, 42937}

X(42995) = GIBERT (27,-4,9) POINT

Barycentrics    9*Sqrt[3]*a^2*S + 9*a^2*SA - 8*SB*SC : :

X(42995) lies on the cubic K1215b and these lines: {4, 13}, {14, 35018}, {15, 15720}, {16, 33923}, {17, 42107}, {62, 42626}, {140, 16268}, {397, 42629}, {398, 16967}, {546, 42502}, {548, 42419}, {550, 41101}, {631, 42504}, {1656, 41122}, {1657, 42586}, {3091, 42532}, {3411, 10299}, {3412, 3850}, {3522, 42521}, {3851, 41108}, {3858, 41121}, {3861, 42506}, {5056, 16962}, {5073, 41107}, {5238, 15712}, {5339, 42817}, {5343, 16960}, {5344, 42896}, {5352, 42893}, {5366, 42630}, {10187, 11543}, {10188, 18581}, {10303, 42507}, {11485, 42802}, {21735, 42481}, {22236, 42489}, {33417, 41978}, {41971, 42434}, {42096, 42431}, {42117, 42683}, {42118, 42157}, {42147, 42891}, {42152, 42914}, {42159, 42435}, {42593, 42613}, {42597, 42778}

X(42995) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61, 10654, 42813}, {61, 42799, 42934}, {61, 42934, 36970}, {398, 34754, 42936}

X(42996) = GIBERT (-33,2,55) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 55*a^2*SA - 4*SB*SC : :

X(42996) lies on the cubic K1215a and these lines: {4, 5237}, {13, 15694}, {14, 15686}, {15, 42517}, {16, 12100}, {17, 14869}, {62, 42798}, {376, 42893}, {396, 42931}, {5318, 15699}, {5339, 42528}, {10654, 42801}, {11481, 15688}, {11737, 42629}, {12816, 16242}, {12821, 42100}, {14890, 33417}, {15685, 19107}, {15697, 16961}, {15702, 41972}, {15708, 16267}, {16239, 42166}, {16241, 36843}, {16268, 42585}, {16809, 42586}, {17538, 41977}, {21735, 42479}, {34200, 41971}, {37832, 42505}, {41944, 42133}, {42089, 42588}, {42151, 42933}, {42634, 42795}, {42799, 42897}

X(42996) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15702, 41972, 42895}, {37832, 42686, 42505}

X(42997) = GIBERT (33,2,55) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 55*a^2*SA + 4*SB*SC : :

X(42997) lies on the cubic K1215b and these lines: {4, 5238}, {13, 15686}, {14, 15694}, {15, 12100}, {16, 42516}, {18, 14869}, {61, 42797}, {376, 42892}, {395, 42930}, {5321, 15699}, {5340, 42529}, {10653, 42802}, {11480, 15688}, {11737, 42630}, {12817, 16241}, {12820, 42099}, {14890, 33416}, {15685, 19106}, {15697, 16960}, {15702, 41971}, {15708, 16268}, {16239, 42163}, {16242, 36836}, {16267, 42584}, {16808, 42587}, {17538, 41978}, {21735, 42478}, {34200, 41972}, {37835, 42504}, {41943, 42134}, {42092, 42589}, {42150, 42932}, {42633, 42796}, {42800, 42896}

X(42997) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15702, 41971, 42894}, {37835, 42687, 42504}

X(42998) = GIBERT (6,1,0) POINT

Barycentrics    Sqrt[3]*a^2*S + SB*SC : :

X(42998) lies on the cubic K1217a and these lines: {2, 17}, {3, 37640}, {4, 6}, {5, 37641}, {13, 3091}, {14, 3832}, {15, 3522}, {16, 3523}, {18, 5056}, {20, 61}, {30, 42588}, {32, 16941}, {69, 11289}, {140, 11486}, {193, 633}, {202, 14986}, {203, 3600}, {299, 37178}, {303, 32829}, {371, 42229}, {372, 42230}, {376, 22236}, {381, 42776}, {390, 7005}, {395, 3090}, {396, 631}, {462, 9777}, {463, 11402}, {470, 11433}, {471, 11427}, {548, 42633}, {550, 11485}, {616, 14136}, {622, 36758}, {628, 40921}, {632, 42496}, {966, 37146}, {1656, 11489}, {1657, 42118}, {1992, 11303}, {2043, 19054}, {2044, 19053}, {2045, 3068}, {2046, 3069}, {2307, 4293}, {2548, 5472}, {3085, 7127}, {3089, 8739}, {3146, 10654}, {3311, 14814}, {3312, 14813}, {3389, 7585}, {3390, 7586}, {3411, 7486}, {3412, 5237}, {3524, 16772}, {3525, 16644}, {3526, 42913}, {3528, 36836}, {3529, 42147}, {3533, 23302}, {3543, 16964}, {3545, 42153}, {3618, 11290}, {3628, 42634}, {3839, 41112}, {3850, 42128}, {3851, 11543}, {3854, 16808}, {3855, 42163}, {3858, 42125}, {5059, 41974}, {5067, 16645}, {5068, 18581}, {5071, 42599}, {5073, 42117}, {5238, 10304}, {5305, 41040}, {5319, 6773}, {5351, 15692}, {5352, 21734}, {5362, 37462}, {5862, 37352}, {5863, 11298}, {6191, 37830}, {6199, 42201}, {6395, 42202}, {6417, 42278}, {6418, 42279}, {6419, 42228}, {6420, 35732}, {6427, 42280}, {6428, 42281}, {6431, 42241}, {6432, 35740}, {6435, 42177}, {6436, 42178}, {6437, 42169}, {6438, 42170}, {6770, 7772}, {7487, 8740}, {7735, 37463}, {7736, 37464}, {8014, 8919}, {8960, 42562}, {9112, 9749}, {9605, 41034}, {9742, 33378}, {10299, 11481}, {10645, 42896}, {11001, 42586}, {11139, 13472}, {11480, 21735}, {14561, 37825}, {14683, 36208}, {15022, 37835}, {15640, 42934}, {15682, 42164}, {15683, 41101}, {15684, 42589}, {15693, 42420}, {15696, 42516}, {15702, 42491}, {15708, 41943}, {15712, 42115}, {15715, 42792}, {15720, 42124}, {16001, 22234}, {16268, 41119}, {16809, 42780}, {16960, 42089}, {16961, 42114}, {17578, 36969}, {19106, 41973}, {30435, 41035}, {33703, 42154}, {33923, 42116}, {34754, 42091}, {34755, 42092}, {35018, 42129}, {35770, 42231}, {35771, 42232}, {36968, 42935}, {36970, 42612}, {37144, 37654}, {37173, 37786}, {41108, 42480}, {41121, 42580}, {42085, 42431}, {42106, 42902}, {42121, 42817}, {42127, 42140}, {42138, 42816}, {42143, 42472}, {42146, 42818}, {42434, 42511}, {42435, 42528}, {42489, 42911}, {42581, 42910}, {42592, 42597}, {42794, 42806}, {42797, 42939}, {42895, 42897}

X(42998) = polar conjugate of the isogonal conjugate of X(19363)
X(42998) = barycentric product X(264)*X(19363)
X(42998) = barycentric quotient X(19363)/X(3)
X(42998) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 6, 42999}, {4, 397, 5335}, {4, 398, 5343}, {4, 5334, 5365}, {4, 5335, 5344}, {4, 5339, 42133}, {4, 5340, 5366}, {4, 5344, 42134}, {6, 397, 4}, {6, 5335, 5334}, {6, 5340, 398}, {13, 40694, 3091}, {14, 42162, 3832}, {15, 42151, 3522}, {16, 42152, 3523}, {17, 62, 42149}, {17, 42149, 2}, {17, 42779, 40693}, {18, 18582, 5056}, {61, 10653, 20}, {61, 42158, 42150}, {62, 40693, 2}, {62, 41944, 42436}, {62, 42488, 16963}, {62, 42779, 17}, {62, 42938, 42533}, {395, 42156, 3090}, {396, 22238, 631}, {397, 398, 5340}, {398, 5340, 4}, {398, 5343, 5334}, {1587, 1588, 5335}, {1657, 42925, 42119}, {3070, 3071, 42094}, {3850, 42128, 42775}, {3851, 11543, 42495}, {5056, 22235, 18582}, {5318, 5339, 4}, {5334, 5335, 42134}, {5334, 5344, 4}, {5335, 5343, 5366}, {5335, 5366, 5340}, {5335, 42133, 5318}, {5340, 5366, 5344}, {5343, 5366, 4}, {5349, 42094, 4}, {5365, 42134, 4}, {5480, 5869, 4}, {6419, 42233, 42228}, {6420, 42234, 42227}, {10653, 42150, 42158}, {10654, 16965, 3146}, {11543, 42815, 42142}, {16644, 16773, 3525}, {16645, 42598, 5067}, {16772, 36843, 3524}, {16808, 42920, 3854}, {16962, 42510, 15692}, {16964, 41107, 42161}, {16964, 42161, 3543}, {22236, 42148, 376}, {36969, 42160, 17578}, {40693, 42149, 17}, {41112, 42159, 42813}, {41974, 42157, 42086}, {42086, 42157, 5059}, {42118, 42925, 1657}, {42139, 42775, 3850}, {42142, 42495, 3851}, {42147, 42155, 3529}, {42150, 42158, 20}, {42153, 42166, 3545}, {42154, 42165, 33703}, {42159, 42813, 3839}, {42227, 42234, 35732}, {42228, 42233, 42282}, {42779, 42801, 16267}, {42895, 42897, 42918}

X(42999) = GIBERT (-6,1,0) POINT

Barycentrics    Sqrt[3]*a^2*S - SB*SC : :

X(42999) lies on the cubic K1217b and these lines: {2, 18}, {3, 37641}, {4, 6}, {5, 37640}, {13, 3832}, {14, 3091}, {15, 3523}, {16, 3522}, {17, 5056}, {20, 62}, {30, 42589}, {32, 16940}, {69, 11290}, {140, 11485}, {193, 634}, {202, 3600}, {203, 14986}, {298, 37177}, {302, 32829}, {371, 42227}, {372, 42228}, {376, 22238}, {381, 42775}, {390, 7006}, {395, 631}, {396, 3090}, {462, 11402}, {463, 9777}, {470, 11427}, {471, 11433}, {548, 42634}, {550, 11486}, {617, 14137}, {621, 36757}, {627, 40922}, {632, 42497}, {966, 37147}, {1656, 11488}, {1657, 42117}, {1992, 11304}, {2043, 19053}, {2044, 19054}, {2045, 3069}, {2046, 3068}, {2307, 3086}, {2548, 5471}, {3089, 8740}, {3146, 10653}, {3311, 14813}, {3312, 14814}, {3364, 7585}, {3365, 7586}, {3411, 5238}, {3412, 7486}, {3524, 16773}, {3525, 16645}, {3526, 42912}, {3528, 36843}, {3529, 42148}, {3533, 23303}, {3543, 16965}, {3545, 42156}, {3618, 11289}, {3628, 42633}, {3839, 41113}, {3850, 42125}, {3851, 11542}, {3854, 16809}, {3855, 42166}, {3858, 42128}, {4294, 7127}, {5059, 41973}, {5067, 16644}, {5068, 18582}, {5071, 42598}, {5073, 42118}, {5237, 10304}, {5305, 41041}, {5319, 6770}, {5351, 21734}, {5352, 15692}, {5367, 37462}, {5862, 11297}, {5863, 37351}, {6192, 37833}, {6199, 42199}, {6395, 42200}, {6417, 42279}, {6418, 42278}, {6419, 35732}, {6420, 42229}, {6427, 42281}, {6428, 42280}, {6431, 42239}, {6432, 42240}, {6435, 42175}, {6436, 42176}, {6437, 42167}, {6438, 42168}, {6773, 7772}, {7487, 8739}, {7735, 37464}, {7736, 37463}, {8015, 8918}, {8960, 42564}, {9113, 9750}, {9605, 41035}, {9742, 33379}, {10299, 11480}, {10646, 42897}, {11001, 42587}, {11138, 13472}, {11481, 21735}, {14561, 37824}, {14683, 36209}, {15022, 37832}, {15640, 42935}, {15682, 42165}, {15683, 41100}, {15684, 42588}, {15693, 42419}, {15696, 42517}, {15702, 42490}, {15708, 41944}, {15712, 42116}, {15715, 42791}, {15720, 42121}, {16002, 22234}, {16267, 41120}, {16808, 42779}, {16960, 42111}, {16961, 42092}, {17578, 36970}, {19107, 41974}, {30435, 41034}, {33703, 42155}, {33923, 42115}, {34754, 42089}, {34755, 42090}, {35018, 42132}, {35770, 42233}, {35771, 42234}, {36967, 42934}, {36969, 42613}, {37145, 37654}, {37172, 37785}, {41107, 42481}, {41122, 42581}, {42086, 42432}, {42103, 42903}, {42124, 42818}, {42126, 42141}, {42135, 42815}, {42143, 42817}, {42146, 42473}, {42433, 42510}, {42436, 42529}, {42488, 42910}, {42580, 42911}, {42593, 42596}, {42793, 42805}, {42798, 42938}, {42894, 42896}

X(42999) = polar conjugate of the isogonal conjugate of X(19364)
X(42999) = barycentric product X(264)*X(19364)
X(42999) = barycentric quotient X(19364)/X(3)
X(42999) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 6, 42998}, {4, 397, 5344}, {4, 398, 5334}, {4, 5334, 5343}, {4, 5335, 5366}, {4, 5339, 5365}, {4, 5340, 42134}, {4, 5343, 42133}, {6, 398, 4}, {6, 5334, 5335}, {6, 5339, 397}, {13, 42159, 3832}, {14, 40693, 3091}, {15, 42149, 3523}, {16, 42150, 3522}, {17, 18581, 5056}, {18, 61, 42152}, {18, 42152, 2}, {18, 42780, 40694}, {61, 40694, 2}, {61, 41943, 42435}, {61, 42489, 16962}, {61, 42780, 18}, {61, 42939, 42532}, {62, 10654, 20}, {62, 42157, 42151}, {395, 22236, 631}, {396, 42153, 3090}, {397, 398, 5339}, {397, 5339, 4}, {397, 5344, 5335}, {1587, 1588, 5334}, {1657, 42924, 42120}, {3070, 3071, 42093}, {3850, 42125, 42776}, {3851, 11542, 42494}, {5056, 22237, 18581}, {5321, 5340, 4}, {5334, 5335, 42133}, {5334, 5344, 5365}, {5334, 5365, 5339}, {5334, 42134, 5321}, {5335, 5343, 4}, {5339, 5365, 5343}, {5344, 5365, 4}, {5350, 42093, 4}, {5366, 42133, 4}, {5480, 5868, 4}, {6419, 42231, 42230}, {6420, 42232, 42229}, {10653, 16964, 3146}, {10654, 42151, 42157}, {11542, 42816, 42139}, {16644, 42599, 5067}, {16645, 16772, 3525}, {16773, 36836, 3524}, {16809, 42921, 3854}, {16963, 42511, 15692}, {16965, 41108, 42160}, {16965, 42160, 3543}, {22238, 42147, 376}, {36970, 42161, 17578}, {40694, 42152, 18}, {41113, 42162, 42814}, {41973, 42158, 42085}, {42085, 42158, 5059}, {42117, 42924, 1657}, {42139, 42494, 3851}, {42142, 42776, 3850}, {42148, 42154, 3529}, {42151, 42157, 20}, {42155, 42164, 33703}, {42156, 42163, 3545}, {42162, 42814, 3839}, {42229, 42232, 42282}, {42230, 42231, 35732}, {42780, 42802, 16268}, {42894, 42896, 42919}

X(43000) = GIBERT (105,56,55) POINT

Barycentrics    35*Sqrt[3]*a^2*S + 55*a^2*SA + 112*SB*SC : :

X(43000) lies on the cubic K1217a and these lines: {4, 42435}, {13, 15683}, {14, 5066}, {16, 15709}, {3411, 7486}, {3526, 42800}, {3628, 42436}, {5349, 42633}, {10304, 42930}, {15682, 16960}, {15687, 34754}, {15691, 42795}, {15721, 42512}, {16267, 42094}, {41107, 42796}, {41989, 42780}, {42154, 42695}

X(43001) = GIBERT (-105,56,55) POINT

Barycentrics    35*Sqrt[3]*a^2*S - 55*a^2*SA - 112*SB*SC : :

X(423001) lies on the cubic K1217b and these lines: {4, 42436}, {13, 5066}, {14, 15683}, {15, 15709}, {3412, 7486}, {3526, 42799}, {3628, 42435}, {5350, 42634}, {10304, 42931}, {15682, 16961}, {15687, 34755}, {15691, 42796}, {15721, 42513}, {16268, 42093}, {41108, 42795}, {41989, 42779}, {42155, 42694}

X(43002) = GIBERT (18,-1,70) POINT

Barycentrics    3*Sqrt[3]*a^2*S + 35*a^2*SA - SB*SC : :

X(43002) lies on the cubic K1217a and these lines: {2, 42087}, {6, 41959}, {17, 376}, {18, 3524}, {397, 10304}, {398, 15692}, {549, 5343}, {3412, 21735}, {3525, 12817}, {3528, 41107}, {3534, 42134}, {3830, 42472}, {3839, 42610}, {5054, 5365}, {5335, 8703}, {5352, 15710}, {5863, 36352}, {10645, 19708}, {11001, 37832}, {11480, 42792}, {11489, 12100}, {11540, 42133}, {15022, 42587}, {15693, 42119}, {15694, 42776}, {15697, 42141}, {15698, 41101}, {15702, 42580}, {15708, 42495}, {15719, 41122}, {15722, 42122}, {15759, 42633}, {19710, 42142}, {19711, 42628}, {22235, 35418}, {33416, 42632}, {33703, 42592}, {35409, 42581}, {37641, 42791}, {41099, 42529}

X(43003) = GIBERT (18,1,-70) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 35*a^2*SA + SB*SC : :

X(43003) lies on the cubic K1217b and these lines: {2, 42088}, {6, 41959}, {17, 3524}, {18, 376}, {397, 15692}, {398, 10304}, {549, 5344}, {3411, 21735}, {3525, 12816}, {3528, 41108}, {3534, 42133}, {3830, 42473}, {3839, 42611}, {5054, 5366}, {5334, 8703}, {5351, 15710}, {5862, 36346}, {10646, 19708}, {11001, 37835}, {11481, 42791}, {11488, 12100}, {11540, 42134}, {15022, 42586}, {15693, 42120}, {15694, 42775}, {15697, 42140}, {15698, 41100}, {15702, 42581}, {15708, 42494}, {15719, 41121}, {15722, 42123}, {15759, 42634}, {19710, 42139}, {19711, 42627}, {22237, 35418}, {33417, 42631}, {33703, 42593}, {35409, 42580}, {37640, 42792}, {41099, 42528}

X(43004) = GIBERT (11,6,7) POINT

Barycentrics    11*a^2*S/Sqrt[3] + 7*a^2*SA + 12*SB*SC : :

X(43004) lies on the cubic K1217a and these lines: {2, 42893}, {3, 42895}, {6, 5079}, {13, 3534}, {14, 3545}, {15, 3146}, {16, 17}, {30, 42892}, {61, 3857}, {381, 42904}, {382, 42905}, {396, 15687}, {3412, 3843}, {3528, 11488}, {3860, 5321}, {5072, 42894}, {5238, 42629}, {5318, 42434}, {5335, 15692}, {5343, 42103}, {6669, 36366}, {7486, 16967}, {11489, 42779}, {12101, 41971}, {12816, 42502}, {15703, 16645}, {15704, 42900}, {15707, 16644}, {15708, 41972}, {16772, 42584}, {16773, 42499}, {16961, 37832}, {16962, 42094}, {19711, 41107}, {22235, 42086}, {23303, 42781}, {33465, 34540}, {34754, 42136}, {35400, 36967}, {36968, 42124}, {41100, 42518}, {41119, 42119}, {41943, 42088}, {41989, 42146}, {42095, 42896}, {42096, 42691}, {42108, 42813}, {42117, 42908}, {42122, 42939}, {42128, 42157}, {42132, 42610}, {42141, 42152}, {42474, 42507}, {42897, 42914}

X(43004) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15, 42903, 42105}, {17, 23302, 42530}, {16808, 16960, 3412}, {16960, 42156, 16808}, {18582, 37640, 42918}, {37832, 42777, 42506}, {42127, 42529, 42100}

X(43005) = GIBERT (-11,6,7) POINT

Barycentrics    11*a^2*S/Sqrt[3] - 7*a^2*SA - 12*SB*SC : :

X(43005) lies on the cubic K1217b and these lines: {2, 42892}, {3, 42894}, {6, 5079}, {13, 3545}, {14, 3534}, {15, 18}, {16, 3146}, {30, 42893}, {62, 3857}, {381, 42905}, {382, 42904}, {395, 15687}, {3411, 3843}, {3528, 11489}, {3860, 5318}, {5072, 42895}, {5237, 42630}, {5321, 42433}, {5334, 15692}, {5344, 42106}, {6670, 36368}, {7486, 16966}, {11488, 42780}, {12101, 41972}, {12817, 42503}, {15703, 16644}, {15704, 42901}, {15707, 16645}, {15708, 41971}, {16772, 42498}, {16773, 42585}, {16960, 37835}, {16963, 42093}, {19711, 41108}, {22237, 42085}, {23302, 42782}, {33464, 34541}, {34755, 42137}, {35400, 36968}, {36967, 42121}, {41101, 42519}, {41120, 42120}, {41944, 42087}, {41989, 42143}, {42097, 42690}, {42098, 42897}, {42109, 42814}, {42118, 42909}, {42123, 42938}, {42125, 42158}, {42129, 42611}, {42140, 42149}, {42475, 42506}, {42896, 42915}

X(43005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16, 42902, 42104}, {18, 23303, 42531}, {16809, 16961, 3411}, {16961, 42153, 16809}, {18581, 37641, 42919}, {37835, 42778, 42507}, {42126, 42528, 42099}

X(43006) = GIBERT (33,4,-7) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 7*a^2*SA + 8*SB*SC : :

X(43006) lies on the cubic K1217a and these lines: {2, 42893}, {5, 13}, {6, 15681}, {14, 42134}, {15, 10304}, {16, 15693}, {61, 42625}, {376, 41972}, {3525, 41977}, {3534, 41971}, {3543, 42901}, {5059, 10654}, {5071, 42895}, {5237, 10299}, {5318, 41987}, {5335, 41122}, {5343, 16965}, {10646, 14891}, {10653, 15682}, {11485, 42631}, {11486, 16267}, {11488, 15702}, {11540, 16242}, {11542, 41985}, {11543, 42521}, {14893, 42894}, {15690, 41100}, {15700, 42892}, {16644, 42779}, {16645, 42636}, {16773, 42592}, {16961, 41112}, {16963, 42517}, {17538, 36968}, {18582, 33604}, {35403, 42900}, {36969, 38335}, {36970, 41974}, {37641, 42106}, {41107, 42690}, {42089, 42506}, {42130, 42508}, {42155, 42432}, {42156, 42801}, {42474, 42815}, {42528, 42924}, {42594, 42627}, {42610, 42937}, {42777, 42913}

X(43006) = {X(42517),X(42911)}-harmonic conjugate of X(16963)

X(43007) = GIBERT (33,-4,7) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 7*a^2*SA - 8*SB*SC : :

X(43007) lies on the cubic K1217b and these lines: {2, 42892}, {5, 14}, {6, 15681}, {13, 42133}, {15, 15693}, {16, 10304}, {62, 42626}, {376, 41971}, {3525, 41978}, {3534, 41972}, {3543, 42900}, {5059, 10653}, {5071, 42894}, {5238, 10299}, {5321, 41987}, {5334, 41121}, {5344, 16964}, {10645, 14891}, {10654, 15682}, {11485, 16268}, {11486, 42632}, {11489, 15702}, {11540, 16241}, {11542, 42520}, {11543, 41985}, {14893, 42895}, {15690, 41101}, {15700, 42893}, {16644, 42635}, {16645, 42780}, {16772, 42593}, {16960, 41113}, {16962, 42516}, {17538, 36967}, {18581, 33605}, {35403, 42901}, {36969, 41973}, {36970, 38335}, {37640, 42103}, {41108, 42691}, {42092, 42507}, {42131, 42509}, {42153, 42802}, {42154, 42431}, {42475, 42816}, {42529, 42925}, {42595, 42628}, {42611, 42936}, {42778, 42912}

X(43007) = {X(42516),X(42910)}-harmonic conjugate of X(16962)

X(43008) = GIBERT (21,2,-7) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 7*a^2*SA + 4*SB*SC : :

X(43008) lies on the cubic K1217a and these lines: {3, 42435}, {4, 14}, {5, 42436}, {6, 15696}, {13, 5079}, {15, 21734}, {16, 3412}, {17, 632}, {18, 19709}, {61, 8703}, {395, 12811}, {397, 547}, {575, 22890}, {630, 36366}, {3090, 42801}, {3411, 16808}, {3859, 16961}, {3860, 16268}, {5054, 22238}, {5070, 11486}, {5093, 22843}, {5237, 15692}, {5344, 41122}, {5352, 15710}, {10187, 37832}, {11481, 42930}, {11540, 42420}, {12100, 42802}, {12103, 36968}, {12816, 42163}, {15681, 41100}, {15719, 42152}, {16960, 42491}, {16964, 42097}, {18582, 42938}, {33417, 34755}, {33607, 42598}, {35404, 42431}, {35434, 42521}, {38071, 41107}, {41101, 42151}, {41112, 42636}, {41943, 42505}, {41972, 42804}, {41973, 42429}, {41977, 42592}, {41991, 42634}, {42088, 42934}, {42100, 42117}, {42118, 42897}, {42165, 42780}, {42596, 42817}

X(43008) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 15696, 43009}, {17, 16773, 42597}, {62, 41974, 37641}, {62, 42800, 4}, {62, 42935, 40694}, {397, 16963, 42581}, {10653, 42814, 16965}, {40694, 42935, 16965}

X(43009) = GIBERT (21,-2,7) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 7*a^2*SA - 4*SB*SC : :

X(43009) lies on the cubic K1217b and these lines: {3, 42436}, {4, 13}, {5, 42435}, {6, 15696}, {14, 5079}, {15, 3411}, {16, 21734}, {17, 19709}, {18, 632}, {62, 8703}, {396, 12811}, {398, 547}, {575, 22843}, {627, 36767}, {629, 36368}, {3090, 42802}, {3412, 16809}, {3859, 16960}, {3860, 16267}, {5054, 22236}, {5070, 11485}, {5093, 22890}, {5238, 15692}, {5343, 41121}, {5351, 15710}, {10188, 37835}, {11480, 42931}, {11540, 42419}, {12100, 42801}, {12103, 36967}, {12817, 42166}, {15681, 41101}, {15719, 42149}, {16961, 42490}, {16965, 42096}, {18581, 42939}, {22114, 36770}, {33416, 34754}, {33606, 42599}, {35404, 42432}, {35434, 42520}, {38071, 41108}, {41100, 42150}, {41113, 42635}, {41944, 42504}, {41971, 42803}, {41974, 42430}, {41978, 42593}, {41991, 42633}, {42087, 42935}, {42099, 42118}, {42117, 42896}, {42164, 42779}, {42597, 42818}

X(43009) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 15696, 43008}, {18, 16772, 42596}, {61, 41973, 37640}, {61, 42799, 4}, {61, 42934, 40693}, {398, 16962, 42580}, {10654, 42813, 16964}, {40693, 42934, 16964}

X(43010) = GIBERT (11,6,5) POINT

Barycentrics    11*a^2*S/Sqrt[3] + 5*a^2*SA + 12*SB*SC : :
X(43010) = 9 X[13] + 2 X[15], 7 X[13] + 4 X[396], 15 X[13] - 4 X[5318], 3 X[13] + 8 X[11542], 5 X[13] + 6 X[16267], 6 X[13] + 5 X[16960], 8 X[13] + 3 X[16962], 12 X[13] - X[19106], 10 X[13] + X[36967], 13 X[13] - 2 X[36969], 51 X[13] + 4 X[42087], 21 X[13] + X[42099], 81 X[13] - 4 X[42109], 69 X[13] + 8 X[42122], 63 X[13] - 8 X[42137], 32 X[13] + X[42430], 17 X[13] + 16 X[42496], 135 X[13] + 8 X[42585], 141 X[13] - 20 X[42683], 13 X[13] + 20 X[42777], 159 X[13] - 16 X[42889], 25 X[13] + 8 X[42912], 7 X[15] - 18 X[396], 5 X[15] + 6 X[5318], X[15] - 12 X[11542], 5 X[15] - 27 X[16267], 4 X[15] - 15 X[16960], 16 X[15] - 27 X[16962], 8 X[15] + 3 X[19106], 20 X[15] - 9 X[36967], 13 X[15] + 9 X[36969], 17 X[15] - 6 X[42087], 14 X[15] - 3 X[42099], 9 X[15] + 2 X[42109], 23 X[15] - 12 X[42122], 7 X[15] + 4 X[42137], 64 X[15] - 9 X[42430], 17 X[15] - 72 X[42496], 15 X[15] - 4 X[42585], 47 X[15] + 30 X[42683], 13 X[15] - 90 X[42777], 53 X[15] + 24 X[42889], 25 X[15] - 36 X[42912], 15 X[396] + 7 X[5318], 3 X[396] - 14 X[11542], 10 X[396] - 21 X[16267], 24 X[396] - 35 X[16960], 32 X[396] - 21 X[16962], 48 X[396] + 7 X[19106], 40 X[396] - 7 X[36967], 26 X[396] + 7 X[36969], 51 X[396] - 7 X[42087], 12 X[396] - X[42099], 81 X[396] + 7 X[42109]

X(43010) lies on the cubic K1217a and these lines: {3, 42895}, {6, 5072}, {13, 15}, {16, 3525}, {17, 11481}, {18, 5056}, {61, 42106}, {62, 42917}, {397, 33416}, {3091, 42894}, {3411, 42628}, {3412, 42094}, {3529, 42900}, {3830, 42905}, {3832, 42904}, {3855, 16809}, {5070, 11486}, {5237, 42627}, {5321, 42694}, {5334, 41119}, {5335, 15717}, {5339, 16808}, {5340, 42689}, {5366, 42802}, {6671, 35752}, {10188, 42924}, {10611, 22894}, {10653, 15721}, {11001, 42892}, {11485, 42630}, {11488, 21735}, {11543, 42779}, {11812, 41972}, {12817, 42506}, {12820, 33604}, {15715, 42120}, {15716, 16241}, {15718, 16644}, {15719, 41107}, {15723, 16242}, {16964, 42128}, {16965, 42817}, {18581, 41121}, {23302, 42922}, {23303, 42801}, {33417, 33607}, {34754, 42140}, {34755, 42598}, {35401, 42154}, {36836, 42629}, {41112, 42528}, {41943, 42091}, {41991, 42135}, {42093, 42691}, {42100, 42929}, {42102, 42903}, {42104, 42435}, {42124, 42433}, {42146, 42580}, {42163, 42781}, {42165, 42916}, {42233, 42578}, {42234, 42579}, {42416, 42792}, {42488, 42498}, {42521, 42910}, {42529, 42586}, {42596, 42935}, {42693, 42925}
X(43010) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5072, 43011}, {13, 11542, 16960}, {13, 16267, 36967}, {13, 16960, 19106}, {15, 42137, 42099}, {396, 42137, 15}, {5318, 11542, 16267}, {5318, 36967, 19106}, {16809, 40693, 42896}, {16960, 19106, 16962}

X(43011) = GIBERT (-11,6,5) POINT

Barycentrics    11*a^2*S/Sqrt[3] - 5*a^2*SA - 12*SB*SC : :
X(43011) = 9 X[14] + 2 X[16], 7 X[14] + 4 X[395], 15 X[14] - 4 X[5321], 3 X[14] + 8 X[11543], 5 X[14] + 6 X[16268], 6 X[14] + 5 X[16961], 8 X[14] + 3 X[16963], 12 X[14] - X[19107], 10 X[14] + X[36968], 13 X[14] - 2 X[36970], 51 X[14] + 4 X[42088], 21 X[14] + X[42100], 81 X[14] - 4 X[42108], 69 X[14] + 8 X[42123], 63 X[14] - 8 X[42136], 32 X[14] + X[42429], 17 X[14] + 16 X[42497], 135 X[14] + 8 X[42584], 141 X[14] - 20 X[42682], 13 X[14] + 20 X[42778], 159 X[14] - 16 X[42888], 25 X[14] + 8 X[42913], 7 X[16] - 18 X[395], 5 X[16] + 6 X[5321], X[16] - 12 X[11543], 5 X[16] - 27 X[16268], 4 X[16] - 15 X[16961], 16 X[16] - 27 X[16963], 8 X[16] + 3 X[19107], 20 X[16] - 9 X[36968], 13 X[16] + 9 X[36970], 17 X[16] - 6 X[42088], 14 X[16] - 3 X[42100], 9 X[16] + 2 X[42108], 23 X[16] - 12 X[42123], 7 X[16] + 4 X[42136], 64 X[16] - 9 X[42429], 17 X[16] - 72 X[42497], 15 X[16] - 4 X[42584], 47 X[16] + 30 X[42682], 13 X[16] - 90 X[42778], 53 X[16] + 24 X[42888], 25 X[16] - 36 X[42913], 15 X[395] + 7 X[5321], 3 X[395] - 14 X[11543], 10 X[395] - 21 X[16268], 24 X[395] - 35 X[16961], 32 X[395] - 21 X[16963], 48 X[395] + 7 X[19107], 40 X[395] - 7 X[36968], 26 X[395] + 7 X[36970], 51 X[395] - 7 X[42088], 12 X[395] - X[42100]

X(43011) lies on the cubic K1217b and these lines: {3, 42894}, {6, 5072}, {14, 16}, {15, 3525}, {17, 5056}, {18, 11480}, {61, 42916}, {62, 42103}, {398, 33417}, {3091, 42895}, {3411, 42093}, {3412, 42627}, {3529, 42901}, {3830, 42904}, {3832, 42905}, {3855, 16808}, {5070, 11485}, {5238, 42628}, {5318, 42695}, {5334, 15717}, {5335, 41120}, {5339, 42688}, {5340, 16809}, {5365, 42801}, {6672, 36330}, {10187, 42925}, {10612, 22850}, {10654, 15721}, {11001, 42893}, {11486, 42629}, {11489, 21735}, {11542, 42780}, {11812, 41971}, {12816, 42507}, {12821, 33605}, {15715, 42119}, {15716, 16242}, {15718, 16645}, {15719, 41108}, {15723, 16241}, {16964, 42818}, {16965, 42125}, {18582, 41122}, {23302, 42802}, {23303, 42923}, {33416, 33606}, {34754, 42599}, {34755, 42141}, {35401, 42155}, {36843, 42630}, {41113, 42529}, {41944, 42090}, {41991, 42138}, {42094, 42690}, {42099, 42928}, {42101, 42902}, {42105, 42436}, {42121, 42434}, {42143, 42581}, {42164, 42917}, {42166, 42782}, {42231, 42578}, {42232, 42579}, {42415, 42791}, {42489, 42499}, {42520, 42911}, {42528, 42587}, {42597, 42934}, {42692, 42924}

X(43011) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5072, 43010}, {14, 11543, 16961}, {14, 16268, 36968}, {14, 16961, 19107}, {16, 42136, 42100}, {395, 42136, 16}, {5321, 11543, 16268}, {5321, 36968, 19107}, {16808, 40694, 42897}, {16961, 19107, 16963}

X(43012) = GIBERT (-33,20,23) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 23*a^2*SA - 40*SB*SC : :

X(43012) lies on the cubic K1217a and these lines: {4, 41972}, {6, 43013}, {14, 3522}, {15, 42597}, {16, 382}, {17, 3090}, {18, 549}, {20, 42901}, {62, 3850}, {3146, 42893}, {3529, 41977}, {3530, 42894}, {3839, 16965}, {3843, 42900}, {5237, 11001}, {5343, 42933}, {12101, 42163}, {12103, 16773}, {15689, 41944}, {15710, 42157}, {16268, 19709}, {16772, 42493}, {16961, 42106}, {22236, 42489}, {41112, 42775}, {42139, 42436}, {42158, 42694}, {42159, 42429}, {42580, 42778}, {42592, 42939}, {42599, 42633}

X(43013) = GIBERT (33,20,23) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 23*a^2*SA + 40*SB*SC : :

X(43013) lies on the cubic K1217b and these lines: {4, 41971}, {6, 43012}, {13, 3522}, {15, 382}, {16, 42596}, {17, 549}, {18, 3090}, {20, 42900}, {61, 3850}, {3146, 42892}, {3529, 41978}, {3530, 42895}, {3839, 16964}, {3843, 42901}, {5238, 11001}, {5344, 42932}, {12101, 42166}, {12103, 16772}, {15689, 41943}, {15710, 42158}, {16267, 19709}, {16773, 42492}, {16960, 42103}, {22238, 42488}, {41113, 42776}, {42142, 42435}, {42157, 42695}, {42162, 42430}, {42581, 42777}, {42593, 42938}, {42598, 42634}

X(43014) = GIBERT (11,2,3) POINT

Barycentrics    11*a^2*S/Sqrt[3] + 3*a^2*SA + 4*SB*SC : :

X(43014) lies on the cubic K1217a and these lines: {4, 42895}, {6, 17}, {13, 12821}, {14, 5066}, {15, 376}, {16, 3412}, {30, 41971}, {61, 3627}, {62, 10303}, {396, 11539}, {397, 34754}, {1992, 40334}, {3544, 18582}, {3545, 42479}, {3642, 33624}, {3832, 5334}, {3851, 42894}, {5335, 42112}, {6329, 40335}, {6778, 14136}, {8259, 22895}, {10654, 12816}, {11481, 15706}, {11485, 16965}, {11486, 15701}, {11488, 42499}, {11543, 42581}, {12100, 42892}, {15709, 42893}, {15711, 42792}, {16267, 18581}, {16268, 42496}, {16773, 42916}, {16964, 42815}, {19106, 41101}, {19708, 41972}, {22236, 42131}, {23303, 42492}, {33603, 41119}, {34755, 42152}, {35407, 42096}, {41107, 42087}, {41108, 42106}, {41112, 42140}, {41973, 42102}, {41974, 42090}, {42118, 42434}, {42136, 42934}, {42143, 42780}, {42155, 42532}, {42435, 42891}, {42489, 42627}, {42781, 42923}, {42802, 42924}, {42889, 42925}

X(43014) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 17, 16961}, {6, 1656, 43015}, {6, 16960, 16967}, {6, 16967, 42897}, {6, 42817, 18}, {15, 42120, 42529}, {17, 42897, 16967}, {397, 34754, 42100}, {5335, 42157, 42629}, {11542, 42107, 41121}, {16960, 16967, 17}, {16966, 42818, 16967}, {16967, 42897, 16961}

X(43015) = GIBERT (-11,2,3) POINT

Barycentrics    11*a^2*S/Sqrt[3] - 3*a^2*SA - 4*SB*SC : :

X(43015) lies on the cubic K1217b and these lines: {4, 42894}, {6, 17}, {13, 5066}, {14, 12820}, {15, 3411}, {16, 376}, {30, 41972}, {61, 10303}, {62, 3627}, {395, 11539}, {398, 34755}, {1992, 40335}, {3544, 18581}, {3545, 42478}, {3643, 33622}, {3832, 5335}, {3851, 42895}, {5334, 42113}, {6329, 40334}, {6777, 14137}, {8260, 22849}, {10653, 12817}, {11480, 15706}, {11485, 15701}, {11486, 16964}, {11489, 42498}, {11542, 42580}, {12100, 42893}, {15709, 42892}, {15711, 42791}, {16267, 42497}, {16268, 18582}, {16772, 42917}, {16965, 42816}, {19107, 41100}, {19708, 41971}, {22238, 42130}, {23302, 42493}, {33602, 41120}, {34754, 42149}, {35407, 42097}, {35733, 42171}, {41107, 42103}, {41108, 42088}, {41113, 42141}, {41973, 42091}, {41974, 42101}, {42117, 42433}, {42137, 42935}, {42146, 42779}, {42154, 42533}, {42436, 42890}, {42488, 42628}, {42782, 42922}, {42801, 42925}, {42888, 42924}

X(43015) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 18, 16960}, {6, 1656, 43014}, {6, 16961, 16966}, {6, 16966, 42896}, {6, 42818, 17}, {16, 42119, 42528}, {18, 42896, 16966}, {398, 34755, 42099}, {5334, 42158, 42630}, {11543, 42110, 41122}, {16961, 16966, 18}, {16966, 42896, 16960}, {16967, 42817, 16966}

X(43016) = GIBERT (33,28,9) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 9*a^2*SA + 56*SB*SC : :

X(43016) lies on the cubic K1217a and these lines: {4, 42895}, {13, 3627}, {14, 3832}, {15, 5366}, {16, 1656}, {17, 376}, {18, 42922}, {62, 5066}, {398, 42693}, {1657, 41978}, {3090, 41977}, {3530, 42158}, {3544, 37835}, {5067, 41972}, {5237, 42494}, {5344, 42092}, {10188, 10646}, {10303, 16965}, {11539, 42166}, {11542, 42909}, {14269, 41108}, {15022, 42893}, {15701, 42488}, {15706, 41121}, {16808, 42495}, {16964, 42898}, {16966, 42793}, {17800, 36836}, {18582, 42928}, {34755, 42472}, {41100, 42591}, {41107, 42801}, {42086, 42530}, {42136, 42781}, {42155, 42592}

X(43017) = GIBERT (-33,28,9) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 9*a^2*SA - 56*SB*SC : :

X(43017) lies on the cubic K1217b and these lines: {4, 42894}, {13, 3832}, {14, 3627}, {15, 1656}, {16, 5365}, {17, 42923}, {18, 376}, {61, 5066}, {397, 42692}, {1657, 41977}, {3090, 41978}, {3530, 42157}, {3544, 37832}, {5067, 41971}, {5238, 42495}, {5343, 42089}, {10187, 10645}, {10303, 16964}, {11539, 42163}, {11543, 42908}, {14269, 41107}, {15022, 42892}, {15701, 42489}, {15706, 41122}, {16809, 42494}, {16965, 42899}, {16967, 42794}, {17800, 36843}, {18581, 42929}, {34754, 42473}, {41101, 42590}, {41108, 42802}, {42085, 42531}, {42137, 42782}, {42154, 42593}

X(43018) = GIBERT (33,4,15) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 15*a^2*SA + 8*SB*SC : :

X(43018) lies on the cubic K1217a and these lines: {5, 14}, {6, 42801}, {16, 10299}, {62, 15693}, {397, 42584}, {631, 42892}, {3146, 41971}, {3523, 41978}, {5059, 5335}, {5073, 42900}, {5238, 10304}, {5350, 41101}, {5351, 14891}, {5365, 42921}, {10645, 42924}, {11485, 42432}, {15681, 22236}, {15682, 40693}, {15702, 16962}, {15720, 41977}, {16267, 42934}, {16960, 42494}, {16964, 41119}, {16966, 22237}, {17538, 37640}, {19107, 42907}, {33416, 42152}, {38335, 42813}, {41943, 42937}, {41973, 42093}, {41987, 42166}, {42102, 42888}, {42129, 42476}, {42137, 42157}, {42151, 42896}, {42156, 42799}, {42162, 42516}, {42164, 42506}, {42477, 42818}, {42489, 42592}

X(43018) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {61, 3412, 37832}, {3412, 42633, 61}

X(43019) = GIBERT (-33,4,15) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 15*a^2*SA - 8*SB*SC : :

X(43019) lies on the cubic K1217b and these lines: {5, 13}, {6, 42801}, {15, 10299}, {61, 15693}, {398, 42585}, {631, 42893}, {3146, 41972}, {3523, 41977}, {5059, 5334}, {5073, 42901}, {5237, 10304}, {5349, 41100}, {5352, 14891}, {5366, 42920}, {10646, 42925}, {11486, 42431}, {15681, 22238}, {15682, 40694}, {15702, 16963}, {15720, 41978}, {16268, 42935}, {16961, 42495}, {16965, 41120}, {16967, 22235}, {17538, 37641}, {19106, 42906}, {33417, 42149}, {38335, 42814}, {41944, 42936}, {41974, 42094}, {41987, 42163}, {42101, 42889}, {42132, 42477}, {42136, 42158}, {42150, 42897}, {42153, 42800}, {42159, 42517}, {42165, 42507}, {42476, 42817}, {42488, 42593}

X(43019) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {62, 3411, 37835}, {3411, 42634, 62}

X(43020) = GIBERT (33,2,-17) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 17*a^2*SA + 4*SB*SC : :

X(43020) lies on the cubic K1217a and these lines: {6, 14093}, {13, 547}, {14, 3830}, {15, 15759}, {16, 3524}, {17, 3526}, {18, 3091}, {30, 41972}, {61, 21734}, {62, 550}, {376, 41971}, {395, 23046}, {396, 12108}, {631, 42478}, {3411, 3861}, {3543, 42894}, {5238, 42516}, {5351, 42435}, {6670, 35752}, {6779, 10614}, {10646, 42633}, {10654, 42521}, {11543, 42636}, {12816, 42818}, {12820, 16809}, {15683, 42085}, {15703, 42895}, {15713, 16960}, {16239, 41977}, {16267, 42501}, {16963, 42129}, {16964, 42429}, {33416, 42492}, {33703, 37641}, {36968, 42130}, {37835, 42917}, {40694, 42908}, {41107, 42142}, {42086, 42517}, {42118, 42778}, {42145, 42634}, {42510, 42528}, {42580, 42935}

X(43020) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14093, 43021}, {11486, 42155, 42533}, {12817, 42155, 19106}, {34755, 42800, 42913}, {41100, 42533, 12817}, {42145, 42634, 42899}, {42800, 42913, 13}

X(43021) = GIBERT (33,-2,17) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 17*a^2*SA - 4*SB*SC : :

X(43021) lies on the cubic K1217b and these lines: {6, 14093}, {13, 3830}, {14, 547}, {15, 3524}, {16, 15759}, {17, 3091}, {18, 3526}, {30, 41971}, {61, 550}, {62, 21734}, {376, 41972}, {395, 12108}, {396, 23046}, {631, 42479}, {3412, 3861}, {3543, 42895}, {5237, 42517}, {5352, 42436}, {6669, 36330}, {6780, 10613}, {10645, 42634}, {10653, 42520}, {11542, 42635}, {12817, 42817}, {12821, 16808}, {15683, 42086}, {15703, 42894}, {15713, 16961}, {16239, 41978}, {16268, 42500}, {16962, 42132}, {16965, 42430}, {33417, 42493}, {33703, 37640}, {36967, 42131}, {37832, 42916}, {40693, 42909}, {41108, 42139}, {42085, 42516}, {42117, 42777}, {42144, 42633}, {42511, 42529}, {42581, 42934}

X(43021) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14093, 43020}, {11485, 42154, 42532}, {12816, 42154, 19107}, {34754, 42799, 42912}, {41101, 42532, 12816}, {42144, 42633, 42898}, {42799, 42912, 14}

X(43022) = GIBERT (33,2,21) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 21*a^2*SA + 4*SB*SC : :

X(43022) lies on the cubic K1217a and these lines: {6, 42930}, {13, 382}, {14, 3090}, {15, 3522}, {16, 42794}, {17, 3850}, {18, 10187}, {61, 549}, {140, 41978}, {397, 12103}, {1656, 42894}, {3523, 41977}, {3628, 42892}, {3839, 41101}, {3853, 41971}, {5073, 42895}, {5339, 16962}, {5344, 42511}, {5352, 15710}, {10188, 42816}, {11001, 16965}, {12101, 42147}, {15689, 42435}, {16772, 42497}, {16967, 22237}, {19107, 42693}, {22235, 42432}, {22238, 42520}, {36836, 42532}, {41943, 42590}, {41984, 42489}, {42087, 42431}, {42599, 42912}, {42632, 42891}

X(43022) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {34754, 42802, 42925}, {42802, 42925, 17}

X(43023) = GIBERT (-33,2,21) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 21*a^2*SA - 4*SB*SC : :

X(43023) lies on the cubic K1217b and these lines: {6, 42930}, {13, 3090}, {14, 382}, {15, 42793}, {16, 3522}, {17, 10188}, {18, 3850}, {62, 549}, {140, 41977}, {398, 12103}, {1656, 42895}, {3523, 41978}, {3628, 42893}, {3839, 41100}, {3853, 41972}, {5073, 42894}, {5340, 16963}, {5343, 42510}, {5351, 15710}, {10187, 42815}, {11001, 16964}, {12101, 42148}, {15689, 42436}, {16773, 42496}, {16966, 22235}, {19106, 42692}, {22236, 42521}, {22237, 42431}, {36843, 42533}, {41944, 42591}, {41984, 42488}, {42088, 42432}, {42598, 42913}, {42631, 42890}

X(43023) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {34755, 42801, 42924}, {42801, 42924, 18}

X(43024) = GIBERT (33,28,47) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 47*a^2*SA + 56*SB*SC : :

X(43024) lies on the cubic K1217a and these lines: {13, 3523}, {14, 42916}, {15, 381}, {16, 15709}, {17, 632}, {18, 5067}, {61, 35018}, {395, 42627}, {548, 16241}, {3091, 41971}, {3529, 42494}, {3545, 42892}, {3832, 41978}, {5054, 41972}, {5238, 17578}, {8703, 42900}, {10645, 12816}, {11488, 41120}, {11812, 23302}, {15022, 42911}, {15640, 42932}, {15691, 42905}, {16808, 42791}, {16962, 42139}, {16966, 42512}, {16967, 42899}, {17504, 36968}, {18582, 42930}, {19708, 41121}, {34754, 42803}, {36843, 42936}, {41100, 42933}, {41101, 42692}, {42095, 42635}, {42113, 42504}, {42434, 42598}, {42530, 42898}

X(43024) = {X(41943),X(42132)}-harmonic conjugate of X(37832)

X(43025) = GIBERT (-33,28,47) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 47*a^2*SA - 56*SB*SC : :

X(43025) lies on the cubic K1217b and these lines: {13, 42917}, {14, 3523}, {15, 15709}, {16, 381}, {17, 5067}, {18, 632}, {62, 35018}, {396, 42628}, {548, 16242}, {3091, 41972}, {3529, 42495}, {3545, 42893}, {3832, 41977}, {5054, 41971}, {5237, 17578}, {8703, 42901}, {10646, 12817}, {11489, 41119}, {11812, 23303}, {15022, 42910}, {15640, 42933}, {15691, 42904}, {16809, 42792}, {16963, 42142}, {16966, 42898}, {16967, 42513}, {17504, 36967}, {18581, 42931}, {19708, 41122}, {34755, 42804}, {36836, 42937}, {41100, 42693}, {41101, 42932}, {42098, 42636}, {42112, 42505}, {42433, 42599}, {42531, 42899}

X(43025) = {X(41944),X(42129)}-harmonic conjugate of X(37835)

X(43026) = GIBERT (-33,26,45) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 45*a^2*SA - 52*SB*SC : :

X(43026) lies on the cubic K1217a and these lines: {13, 5079}, {15, 18}, {17, 15703}, {546, 41977}, {3146, 42433}, {3411, 7486}, {3528, 16242}, {3534, 42505}, {3545, 41100}, {3843, 16645}, {3857, 5350}, {3860, 41944}, {5238, 33606}, {5365, 42099}, {10187, 42818}, {12811, 42893}, {15687, 42599}, {15692, 16964}, {15707, 42153}, {15720, 42894}, {16268, 42596}, {18581, 42908}, {37640, 42489}, {41973, 42927}, {41989, 42924}, {42504, 42934}, {42797, 42814}

X(43027) = GIBERT (33,26,45) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 45*a^2*SA + 52*SB*SC : :

X(43027) lies on the cubic K1217b and these lines: {14, 5079}, {16, 17}, {18, 15703}, {546, 41978}, {3146, 42434}, {3412, 7486}, {3528, 16241}, {3534, 42504}, {3545, 41101}, {3843, 16644}, {3857, 5349}, {3860, 41943}, {5237, 33607}, {5366, 42100}, {10188, 42817}, {12811, 42892}, {15687, 42598}, {15692, 16965}, {15707, 42156}, {15720, 42895}, {16267, 42597}, {18582, 42909}, {37641, 42488}, {41974, 42926}, {41989, 42925}, {42505, 42935}, {42798, 42813}

X(43028) = GIBERT (-1,2,4) POINT

Barycentrics    a^2*S/Sqrt[3] - 4*a^2*SA - 4*SB*SC : :

X(43028) lies on the cubic K1217a and these lines: {2, 6}, {3, 16809}, {4, 42774}, {5, 11481}, {13, 15703}, {14, 15694}, {15, 3526}, {16, 1656}, {18, 10187}, {20, 42107}, {30, 42111}, {45, 5242}, {61, 42818}, {62, 42132}, {115, 36770}, {125, 19364}, {140, 5339}, {187, 40334}, {376, 42101}, {381, 10646}, {382, 42918}, {398, 3533}, {546, 42091}, {547, 42114}, {548, 42104}, {549, 42085}, {550, 42103}, {631, 5321}, {632, 11543}, {1030, 21480}, {1151, 42246}, {1152, 42248}, {1853, 30403}, {2045, 23261}, {2046, 23251}, {3090, 5318}, {3091, 42088}, {3146, 42473}, {3522, 42108}, {3523, 42087}, {3524, 42133}, {3525, 5334}, {3530, 42090}, {3545, 42102}, {3628, 18582}, {3832, 42109}, {3843, 42100}, {3845, 42113}, {3850, 42105}, {3851, 19106}, {3858, 42584}, {5023, 37178}, {5054, 10645}, {5055, 16242}, {5056, 42110}, {5066, 42145}, {5067, 5335}, {5068, 42141}, {5070, 11486}, {5071, 42134}, {5072, 5351}, {5079, 5237}, {5094, 10642}, {5124, 21481}, {5210, 37341}, {5243, 16885}, {5349, 10299}, {5585, 37173}, {6411, 15765}, {6412, 18585}, {6564, 36456}, {6565, 36438}, {6670, 11301}, {6672, 11305}, {6674, 11312}, {6774, 12017}, {7486, 42142}, {7748, 33387}, {8703, 42112}, {10303, 42119}, {10641, 37453}, {10653, 15699}, {10654, 11539}, {10676, 40686}, {11268, 31283}, {11311, 19780}, {11421, 30744}, {11516, 30771}, {11540, 41113}, {11542, 42149}, {12100, 42144}, {12108, 42160}, {12812, 42161}, {13665, 36452}, {13785, 36470}, {14269, 42528}, {14869, 42122}, {15022, 42165}, {15484, 41408}, {15692, 42587}, {15693, 36970}, {15701, 36967}, {15707, 42529}, {15712, 42136}, {15717, 42140}, {15720, 42126}, {15723, 34754}, {15815, 37177}, {16239, 40694}, {16241, 42499}, {16960, 42476}, {16964, 42597}, {18510, 36453}, {18512, 36469}, {19709, 36968}, {34755, 37832}, {35018, 42138}, {35403, 42429}, {36990, 37464}, {40693, 42610}, {41101, 42894}, {41120, 42509}, {42130, 42814}, {42157, 42688}, {42167, 42193}, {42168, 42191}, {42488, 42817}, {42497, 42513}, {42683, 42793}, {42911, 42913}

X(43028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 43029}, {2, 11489, 23302}, {2, 16645, 16644}, {2, 23303, 6}, {3, 16809, 42096}, {3, 16967, 42095}, {3, 42095, 42093}, {5, 11481, 42094}, {5, 42089, 11481}, {5, 42123, 42106}, {6, 23303, 16645}, {15, 42129, 42153}, {15, 42489, 42129}, {16, 1656, 42098}, {16, 42098, 5340}, {16, 42915, 42128}, {18, 33417, 11485}, {140, 5339, 42773}, {140, 18581, 11480}, {303, 9761, 40341}, {381, 10646, 42097}, {395, 11488, 6}, {547, 42118, 42114}, {549, 42143, 42085}, {590, 615, 37641}, {632, 11543, 42092}, {1656, 42128, 42915}, {3523, 42139, 42087}, {3525, 42599, 36836}, {3526, 42129, 15}, {3526, 42153, 42490}, {3526, 42489, 42153}, {3530, 42135, 42090}, {3628, 42121, 18582}, {5054, 37835, 42154}, {5054, 42125, 10645}, {5055, 16242, 42155}, {5055, 42115, 16808}, {5056, 42120, 42110}, {5070, 11486, 16966}, {5079, 42127, 42919}, {5237, 42919, 42127}, {8252, 8253, 16645}, {10645, 37835, 42125}, {10645, 42125, 42154}, {10646, 42097, 42625}, {10646, 42914, 381}, {11480, 18581, 5339}, {11481, 42089, 42491}, {11486, 16966, 42156}, {11489, 23302, 6}, {11543, 42092, 22236}, {16239, 42628, 42124}, {16242, 16808, 42115}, {16808, 42115, 42155}, {16809, 42096, 42093}, {16967, 19107, 42580}, {16967, 33416, 3}, {18582, 42121, 22238}, {23302, 23303, 11489}, {34755, 37832, 42815}, {42085, 42910, 42143}, {42089, 42493, 42611}, {42094, 42491, 11481}, {42095, 42096, 16809}, {42124, 42628, 40694}, {42128, 42915, 42098}, {42475, 42625, 381}, {42493, 42611, 42477}

X(43029) = GIBERT (1,2,4) POINT

Barycentrics    a^2*S/Sqrt[3] + 4*a^2*SA + 4*SB*SC : :

X(43029) lies on the cubic K1217b and these lines: {2, 6}, {3, 16808}, {4, 42773}, {5, 11480}, {13, 15694}, {14, 15703}, {15, 1656}, {16, 3526}, {17, 10188}, {20, 42110}, {30, 42114}, {45, 5243}, {61, 42129}, {62, 42817}, {125, 19363}, {140, 5340}, {187, 40335}, {376, 42102}, {381, 10645}, {382, 42919}, {397, 3533}, {546, 42090}, {547, 42111}, {548, 42105}, {549, 42086}, {550, 42106}, {631, 5318}, {632, 11542}, {1030, 21481}, {1151, 42247}, {1152, 42249}, {1853, 30402}, {2045, 23251}, {2046, 23261}, {3090, 5321}, {3091, 42087}, {3146, 42472}, {3522, 42109}, {3523, 42088}, {3524, 42134}, {3525, 5335}, {3530, 42091}, {3545, 42101}, {3628, 18581}, {3832, 42108}, {3843, 42099}, {3845, 42112}, {3850, 42104}, {3851, 19107}, {3858, 42585}, {5023, 37177}, {5054, 10646}, {5055, 16241}, {5056, 42107}, {5066, 42144}, {5067, 5334}, {5068, 42140}, {5070, 11485}, {5071, 42133}, {5072, 5352}, {5079, 5238}, {5094, 10641}, {5124, 21480}, {5210, 37340}, {5242, 16885}, {5350, 10299}, {5472, 36770}, {5585, 37172}, {6411, 18585}, {6412, 15765}, {6564, 36438}, {6565, 36456}, {6669, 11302}, {6671, 11306}, {6673, 11311}, {6771, 12017}, {7486, 42139}, {7748, 33386}, {8703, 42113}, {10303, 42120}, {10642, 37453}, {10653, 11539}, {10654, 15699}, {10675, 40686}, {11267, 31283}, {11312, 19781}, {11420, 30744}, {11515, 30771}, {11540, 41112}, {11543, 42152}, {12100, 42145}, {12108, 42161}, {12812, 42160}, {13665, 36469}, {13785, 36453}, {14269, 42529}, {14869, 42123}, {15022, 42164}, {15484, 41409}, {15692, 42586}, {15693, 36969}, {15701, 36968}, {15707, 42528}, {15712, 42137}, {15717, 42141}, {15720, 42127}, {15723, 34755}, {15815, 37178}, {16239, 40693}, {16242, 42498}, {16961, 42477}, {16965, 42596}, {18510, 36470}, {18512, 36452}, {19709, 36967}, {34754, 37835}, {35018, 42135}, {35403, 42430}, {36990, 37463}, {40694, 42611}, {41100, 42895}, {41119, 42508}, {42131, 42813}, {42158, 42689}, {42169, 42194}, {42170, 42192}, {42489, 42818}, {42496, 42512}, {42682, 42794}, {42910, 42912}

X(43029) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 43028}, {2, 11488, 23303}, {2, 16644, 16645}, {2, 23302, 6}, {3, 16808, 42097}, {3, 16966, 42098}, {3, 42098, 42094}, {5, 11480, 42093}, {5, 42092, 11480}, {5, 42122, 42103}, {6, 23302, 16644}, {15, 1656, 42095}, {15, 42095, 5339}, {15, 42914, 42125}, {16, 42132, 42156}, {16, 42488, 42132}, {17, 33416, 11486}, {140, 5340, 42774}, {140, 18582, 11481}, {302, 9763, 40341}, {381, 10645, 42096}, {396, 11489, 6}, {547, 42117, 42111}, {549, 42146, 42086}, {590, 615, 37640}, {632, 11542, 42089}, {1656, 42125, 42914}, {3523, 42142, 42088}, {3525, 42598, 36843}, {3526, 42132, 16}, {3526, 42156, 42491}, {3526, 42488, 42156}, {3530, 42138, 42091}, {3628, 42124, 18581}, {5054, 37832, 42155}, {5054, 42128, 10646}, {5055, 16241, 42154}, {5055, 42116, 16809}, {5056, 42119, 42107}, {5070, 11485, 16967}, {5079, 42126, 42918}, {5238, 42918, 42126}, {8252, 8253, 16644}, {10645, 42096, 42626}, {10645, 42915, 381}, {10646, 37832, 42128}, {10646, 42128, 42155}, {11480, 42092, 42490}, {11481, 18582, 5340}, {11485, 16967, 42153}, {11488, 23303, 6}, {11542, 42089, 22238}, {16239, 42627, 42121}, {16241, 16809, 42116}, {16808, 42097, 42094}, {16809, 42116, 42154}, {16966, 19106, 42581}, {16966, 33417, 3}, {18581, 42124, 22236}, {23302, 23303, 11488}, {34754, 37835, 42816}, {42086, 42911, 42146}, {42092, 42492, 42610}, {42093, 42490, 11480}, {42097, 42098, 16808}, {42121, 42627, 40693}, {42125, 42914, 42095}, {42474, 42626, 381}, {42492, 42610, 42476}

X(43030) = GIBERT (11,2,1) POINT

Barycentrics    11*a^2*S/Sqrt[3] + a^2*SA + 4*SB*SC : :

X(43030) lies on the cubic K1217a and these lines: {6, 13}, {15, 548}, {16, 3523}, {18, 11542}, {61, 3529}, {62, 632}, {140, 41977}, {376, 42478}, {396, 11812}, {397, 19106}, {3312, 35730}, {3411, 5067}, {3412, 11481}, {3543, 42900}, {3589, 22495}, {3629, 22493}, {3843, 42904}, {5070, 42477}, {5318, 12102}, {5335, 16964}, {5350, 42923}, {6395, 35731}, {6435, 18587}, {6436, 18586}, {8550, 41024}, {10124, 42893}, {10188, 42149}, {10645, 19708}, {10646, 16962}, {10653, 34754}, {11485, 42158}, {11486, 42491}, {11488, 15709}, {12007, 41036}, {14075, 37333}, {15022, 18582}, {15640, 41107}, {15683, 41971}, {15687, 42901}, {15692, 42892}, {16267, 23303}, {16268, 42114}, {16645, 42506}, {16961, 42156}, {16965, 42096}, {16967, 42531}, {18581, 42494}, {19107, 42688}, {19710, 36967}, {33560, 36368}, {33604, 33606}, {34200, 41972}, {36968, 42508}, {36969, 42630}, {37641, 42914}, {41101, 42097}, {41108, 42102}, {41112, 42133}, {41121, 42111}, {41944, 42496}, {41973, 42105}, {41974, 42087}, {42089, 42596}, {42095, 42897}, {42116, 42528}, {42138, 42692}, {42139, 42780}, {42140, 42934}, {42145, 42430}, {42147, 42922}, {42154, 42629}, {42504, 42510}, {42581, 42818}, {42627, 42937}, {42800, 42912}, {42898, 42913}

X(43030) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 381, 43031}, {6, 42815, 14}, {6, 42895, 42894}, {15, 42935, 42123}, {62, 16960, 33416}, {16808, 42816, 16809}

X(43031) = GIBERT (-11,2,1) POINT

Barycentrics    11*a^2*S/Sqrt[3] - a^2*SA - 4*SB*SC : :

X(43031) lies on the cubic K1217b and these lines: {6, 13}, {15, 3523}, {16, 548}, {17, 11543}, {61, 632}, {62, 3529}, {140, 41978}, {376, 42479}, {395, 11812}, {398, 19107}, {3411, 11480}, {3412, 5067}, {3543, 42901}, {3589, 22496}, {3629, 22494}, {3843, 42905}, {5070, 42476}, {5321, 12102}, {5334, 16965}, {5349, 42922}, {6435, 18586}, {6436, 18587}, {8550, 41025}, {10124, 42892}, {10187, 42152}, {10645, 16963}, {10646, 19708}, {10654, 34755}, {11485, 42490}, {11486, 42157}, {11489, 15709}, {12007, 41037}, {14075, 37332}, {15022, 18581}, {15640, 41108}, {15683, 41972}, {15687, 42900}, {15692, 42893}, {16267, 42111}, {16268, 23302}, {16644, 42507}, {16960, 42153}, {16964, 42097}, {16966, 42530}, {18582, 42495}, {19106, 42689}, {19710, 36968}, {33561, 36366}, {33605, 33607}, {34200, 41971}, {36768, 37785}, {36967, 42509}, {36970, 42629}, {37640, 42915}, {41100, 42096}, {41107, 42101}, {41113, 42134}, {41122, 42114}, {41943, 42497}, {41973, 42088}, {41974, 42104}, {42092, 42597}, {42098, 42896}, {42115, 42529}, {42135, 42693}, {42141, 42935}, {42142, 42779}, {42144, 42429}, {42148, 42923}, {42155, 42630}, {42505, 42511}, {42580, 42817}, {42628, 42936}, {42799, 42913}, {42899, 42912}

X(43031) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 381, 43030}, {6, 42816, 13}, {6, 42894, 42895}, {16, 42934, 42122}, {61, 16961, 33417}, {16809, 42815, 16808}

X(43032) = GIBERT (-33,26,7) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 7*a^2*SA - 52*SB*SC : :
X(43032) = 13 X[14] - 2 X[16], 15 X[14] - 4 X[395], 7 X[14] + 4 X[5321], 19 X[14] - 8 X[11543], 17 X[14] - 6 X[16268], 16 X[14] - 5 X[16961], 14 X[14] - 3 X[16963], 10 X[14] + X[19107], 12 X[14] - X[36968], 9 X[14] + 2 X[36970], 59 X[14] - 4 X[42088], 23 X[14] - X[42100], 73 X[14] + 4 X[42108], 85 X[14] - 8 X[42123], 47 X[14] + 8 X[42136], 34 X[14] - X[42429], 49 X[14] - 16 X[42497], 151 X[14] - 8 X[42584], 101 X[14] + 20 X[42682], 53 X[14] - 20 X[42778], 127 X[14] + 16 X[42888], 41 X[14] - 8 X[42913], 15 X[16] - 26 X[395], 7 X[16] + 26 X[5321], 19 X[16] - 52 X[11543], 17 X[16] - 39 X[16268], 32 X[16] - 65 X[16961], 28 X[16] - 39 X[16963], 20 X[16] + 13 X[19107], 24 X[16] - 13 X[36968], 9 X[16] + 13 X[36970], 59 X[16] - 26 X[42088], 46 X[16] - 13 X[42100], 73 X[16] + 26 X[42108], 85 X[16] - 52 X[42123], 47 X[16] + 52 X[42136], 68 X[16] - 13 X[42429], 49 X[16] - 104 X[42497], 151 X[16] - 52 X[42584], 101 X[16] + 130 X[42682], 53 X[16] - 130 X[42778], 127 X[16] + 104 X[42888], 41 X[16] - 52 X[42913], 7 X[395] + 15 X[5321], 19 X[395] - 30 X[11543], 34 X[395] - 45 X[16268], 64 X[395] - 75 X[16961], 56 X[395] - 45 X[16963], 8 X[395] + 3 X[19107], 16 X[395] - 5 X[36968], 6 X[395] + 5 X[36970], 59 X[395] - 15 X[42088], 92 X[395] - 15 X[42100]

X(43032) lies on the cubic K1217a and these lines: {14, 16}, {17, 5072}, {398, 41991}, {3525, 37835}, {3529, 42893}, {3628, 41971}, {3830, 42894}, {3855, 37640}, {5056, 10654}, {5070, 5339}, {11001, 42901}, {11488, 41108}, {12816, 33603}, {12817, 42816}, {12821, 16965}, {14269, 42904}, {15715, 42529}, {15716, 36967}, {15717, 42157}, {15718, 42154}, {15719, 41122}, {15720, 16964}, {15721, 18581}, {15723, 16967}, {16808, 41113}, {33561, 36330}, {33606, 42115}, {35401, 42093}, {37641, 42629}, {41099, 42895}, {41101, 42125}, {41944, 42933}, {42117, 42499}, {42144, 42503}, {42489, 42795}, {42581, 42799}, {42626, 42690}

X(43032) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 5321, 16963}, {395, 19107, 36968}

X(43033) = GIBERT (33,26,7) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 7*a^2*SA + 52*SB*SC : :
X(43033 = 13 X[13] - 2 X[15], 15 X[13] - 4 X[396], 7 X[13] + 4 X[5318], 19 X[13] - 8 X[11542], 17 X[13] - 6 X[16267], 16 X[13] - 5 X[16960], 14 X[13] - 3 X[16962], 10 X[13] + X[19106], 12 X[13] - X[36967], 9 X[13] + 2 X[36969], 59 X[13] - 4 X[42087], 23 X[13] - X[42099], 73 X[13] + 4 X[42109], 85 X[13] - 8 X[42122], 47 X[13] + 8 X[42137], 34 X[13] - X[42430], 49 X[13] - 16 X[42496], 151 X[13] - 8 X[42585], 101 X[13] + 20 X[42683], 53 X[13] - 20 X[42777], 127 X[13] + 16 X[42889], 41 X[13] - 8 X[42912], 15 X[15] - 26 X[396], 7 X[15] + 26 X[5318], 19 X[15] - 52 X[11542], 17 X[15] - 39 X[16267], 32 X[15] - 65 X[16960], 28 X[15] - 39 X[16962], 20 X[15] + 13 X[19106], 24 X[15] - 13 X[36967], 9 X[15] + 13 X[36969], 59 X[15] - 26 X[42087], 46 X[15] - 13 X[42099], 73 X[15] + 26 X[42109], 85 X[15] - 52 X[42122], 47 X[15] + 52 X[42137], 68 X[15] - 13 X[42430], 49 X[15] - 104 X[42496], 151 X[15] - 52 X[42585], 101 X[15] + 130 X[42683], 53 X[15] - 130 X[42777], 127 X[15] + 104 X[42889], 41 X[15] - 52 X[42912], 7 X[396] + 15 X[5318], 19 X[396] - 30 X[11542], 34 X[396] - 45 X[16267], 64 X[396] - 75 X[16960], 56 X[396] - 45 X[16962], 8 X[396] + 3 X[19106], 16 X[396] - 5 X[36967], 6 X[396] + 5 X[36969], 59 X[396] - 15 X[42087]

X(43033) lies on the cubic K1217b and these lines: {13, 15}, {18, 5072}, {397, 41991}, {3525, 37832}, {3529, 42892}, {3628, 41972}, {3830, 42895}, {3855, 37641}, {5056, 10653}, {5070, 5340}, {11001, 42900}, {11489, 41107}, {12816, 42815}, {12817, 33602}, {12820, 16964}, {14269, 42905}, {15715, 42528}, {15716, 36968}, {15717, 42158}, {15718, 42155}, {15719, 41121}, {15720, 16965}, {15721, 18582}, {15723, 16966}, {16809, 41112}, {33560, 35752}, {33607, 42116}, {35401, 42094}, {37640, 42630}, {41099, 42894}, {41100, 42128}, {41943, 42932}, {42118, 42498}, {42145, 42502}, {42488, 42796}, {42580, 42800}, {42625, 42691}
X(43033) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 5318, 16962}, {396, 19106, 36967}

leftri

Points on the Gergonne line: X(43034)-X(43068)

rightri

This preamble is contributed by Peter Moses, May 3, 2021.

The Gergonne line of a triangle ABC is the line X(241)X(514). If X is a point on the line at infinity, then the barycentric product X(7)*X is on the Gergonne line. Let g(X) denote the isogonal conjugate of X. Then the X(9)-isoconjugate of g(X) lies on the circumcircle.

More generally, if P = p:q:r, then the P-isoconjugate of the isogonal of the line at infinity is the line b*c*p + c*a*q + a*b*r = 0, and the P-isoconjugate of the line at infinity is the circumconic a^3*q*r*y*z + b^3*r*p*x*z + c^3*p*q*x*y = 0.



X(43034) = X(9)-ISOCONJUGATE OF X(98)

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

X(43034) lies on these lines: {2, 34061}, {39, 7146}, {56, 58}, {57, 893}, {65, 15953}, {73, 37609}, {109, 2700}, {172, 2003}, {216, 18161}, {223, 34497}, {226, 24215}, {241, 514}, {274, 278}, {292, 24479}, {347, 27334}, {441, 1214}, {608, 1804}, {856, 1038}, {1015, 1429}, {1423, 17053}, {1442, 2197}, {1848, 18608}, {1959, 36212}, {2183, 23585}, {3003, 7202}, {3212, 24598}, {3665, 7217}, {3778, 41350}, {3978, 4554}, {4447, 4551}, {6358, 16720}, {7117, 7291}, {8607, 34371}, {16696, 41003}, {17081, 17082}, {17084, 40773}, {17086, 27349}, {17091, 18624}, {17946, 34051}, {20744, 34586}, {22070, 24635}, {27305, 37800}

X(43034) = isogonal conjugate of X(15628)
X(43034) = X(29056)-complementary conjugate of X(141)
X(43034) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 1355}, {37128, 57}
X(43034) = X(i)-cross conjugate of X(j) for these (i,j): {1355, 7}, {1755, 511}
X(43034) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15628}, {8, 1910}, {9, 98}, {33, 287}, {41, 290}, {55, 1821}, {78, 6531}, {212, 16081}, {219, 36120}, {248, 318}, {281, 293}, {312, 1976}, {336, 607}, {643, 2395}, {685, 8611}, {2422, 7257}, {2715, 4086}, {2966, 4041}, {3700, 36084}, {3709, 36036}, {4529, 36065}, {9447, 18024}, {14601, 28659}
X(43034) = crosssum of X(i) and X(j) for these (i,j): {220, 4433}, {1146, 4435}
X(43034) = trilinear pole of line {1355, 42751}
X(43034) = crossdifference of every pair of points on line {55, 3700}
X(43034) = barycentric product X(i)*X(j) for these {i,j}: {7, 511}, {56, 325}, {57, 1959}, {77, 240}, {85, 1755}, {222, 297}, {226, 17209}, {232, 348}, {237, 6063}, {278, 36212}, {290, 1355}, {331, 3289}, {603, 40703}, {608, 6393}, {1401, 20022}, {1408, 42703}, {1804, 6530}, {2396, 7180}, {2421, 7178}, {2799, 4565}, {3569, 4573}, {3669, 42717}, {4077, 23997}, {4230, 17094}, {5968, 7181}, {6357, 35910}, {7055, 34854}, {9417, 20567}, {9418, 41283}, {16591, 37128}
X(43034) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 15628}, {7, 290}, {34, 36120}, {56, 98}, {57, 1821}, {77, 336}, {222, 287}, {232, 281}, {237, 55}, {240, 318}, {278, 16081}, {297, 7017}, {325, 3596}, {511, 8}, {603, 293}, {604, 1910}, {608, 6531}, {1355, 511}, {1356, 15630}, {1397, 1976}, {1401, 20021}, {1414, 36036}, {1755, 9}, {1804, 6394}, {1959, 312}, {2211, 607}, {2421, 645}, {2491, 3709}, {3289, 219}, {3569, 3700}, {4230, 36797}, {4565, 2966}, {5360, 210}, {6063, 18024}, {7180, 2395}, {7251, 11610}, {7316, 9154}, {7335, 17974}, {9155, 3712}, {9417, 41}, {9418, 2175}, {14966, 5546}, {16591, 3948}, {17209, 333}, {23611, 7062}, {23997, 643}, {34854, 1857}, {36212, 345}, {41280, 14601}, {42702, 3694}, {42717, 646}, {42751, 2804}
{X(28391),X(37596)}-harmonic conjugate of X(226)

X(43035) = X(9)-ISOCONJUGATE OF X(103)

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

X(43035) lies on these lines: {1, 4}, {2, 3160}, {6, 3668}, {7, 1419}, {9, 347}, {57, 279}, {77, 142}, {85, 17023}, {109, 2724}, {144, 36640}, {196, 7156}, {218, 10402}, {220, 34048}, {222, 553}, {239, 9436}, {241, 514}, {269, 4000}, {273, 40942}, {277, 1422}, {307, 3686}, {348, 4384}, {475, 39130}, {516, 1456}, {527, 651}, {610, 1119}, {664, 3912}, {673, 9503}, {908, 37798}, {910, 23972}, {934, 11349}, {1020, 2183}, {1086, 6610}, {1155, 15725}, {1211, 12447}, {1212, 1214}, {1266, 40862}, {1362, 20358}, {1386, 12573}, {1407, 24177}, {1418, 17366}, {1427, 23653}, {1429, 1438}, {1435, 1763}, {1439, 2262}, {1441, 5750}, {1442, 21617}, {1443, 17067}, {1471, 4989}, {1604, 34813}, {1708, 16572}, {1738, 5018}, {2003, 34035}, {2006, 34056}, {2114, 14189}, {2202, 7128}, {2263, 3755}, {2264, 6046}, {2310, 3012}, {2321, 28739}, {2325, 4552}, {2338, 26003}, {2340, 4551}, {2801, 22465}, {2999, 7365}, {3247, 8232}, {3452, 25930}, {3474, 34033}, {3554, 4341}, {3661, 25719}, {3663, 6180}, {3674, 41245}, {3975, 4554}, {3982, 14756}, {4031, 21314}, {4298, 5244}, {4318, 5853}, {4353, 8581}, {4357, 17086}, {4700, 41804}, {5219, 5308}, {5226, 29624}, {5435, 32079}, {5745, 17080}, {5932, 18634}, {6542, 25726}, {6604, 16834}, {6611, 11347}, {6743, 26942}, {7269, 41857}, {7955, 23511}, {8270, 28043}, {9502, 26006}, {9578, 39587}, {12848, 16670}, {13737, 37818}, {16577, 16601}, {16826, 25723}, {17044, 34852}, {17073, 20262}, {17078, 41140}, {17093, 24600}, {17095, 24603}, {17316, 25716}, {17923, 39053}, {20258, 34062}, {20270, 24213}, {24181, 34052}, {25718, 29616}, {26626, 40719}, {27304, 27325}, {28301, 41803}, {29571, 30808}, {31183, 31185}, {34051, 34578}, {34522, 37695}, {34529, 38459}, {40407, 40573}

X(43035) = midpoint of X(651) and X(22464)
X(43035) = isogonal conjugate of X(2338)
X(43035) = X(972)-complementary conjugate of X(141)
X(43035) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 1360}, {673, 57}, {23973, 676}
X(43035) = X(i)-cross conjugate of X(j) for these (i,j): {676, 23973}, {910, 516}, {1360, 7}
X(43035) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2338}, {8, 911}, {9, 103}, {33, 1815}, {41, 18025}, {55, 36101}, {219, 36122}, {281, 36056}, {318, 32657}, {521, 40116}, {522, 36039}, {644, 2424}, {650, 677}, {2340, 9503}, {4130, 24016}, {4163, 32668}, {4391, 32642}
X(43035) = cevapoint of X(i) and X(j) for these (i,j): {910, 1456}, {1458, 2272}
X(43035) = crosspoint of X(7128) and X(36146)
X(43035) = crosssum of X(i) and X(j) for these (i,j): {6, 2272}, {220, 2340}
X(43035) = trilinear pole of line {676, 1360}
X(43035) = crossdifference of every pair of points on line {55, 652}
X(43035) = barycentric product X(i)*X(j) for these {i,j}: {7, 516}, {56, 35517}, {57, 30807}, {75, 1456}, {85, 910}, {226, 14953}, {278, 26006}, {279, 40869}, {348, 1886}, {522, 23973}, {650, 24015}, {653, 39470}, {664, 676}, {673, 39063}, {1088, 41339}, {1360, 18025}, {1434, 17747}, {2398, 3676}, {3669, 42719}, {4241, 17094}, {9502, 34018}
X(43035) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 2338}, {7, 18025}, {34, 36122}, {56, 103}, {57, 36101}, {109, 677}, {222, 1815}, {516, 8}, {603, 36056}, {604, 911}, {676, 522}, {910, 9}, {1358, 15634}, {1360, 516}, {1415, 36039}, {1456, 1}, {1462, 9503}, {1886, 281}, {2398, 3699}, {2426, 3939}, {3676, 2400}, {4241, 36797}, {6614, 24016}, {9502, 3693}, {14953, 333}, {17747, 2321}, {23972, 40869}, {23973, 664}, {24015, 4554}, {26006, 345}, {30807, 312}, {32674, 40116}, {35517, 3596}, {39063, 3912}, {39470, 6332}, {40869, 346}, {41339, 200}, {42077, 41339}, {42719, 646}, {42756, 2804}
X(43035) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 948, 226}, {34, 5930, 950}, {77, 37800, 142}, {223, 278, 226}, {241, 3008, 3911}, {241, 5723, 3008}, {279, 5222, 57}, {1323, 3008, 241}, {1323, 5723, 3911}, {1443, 37771, 30379}, {1465, 6357, 34050}, {1465, 34050, 3911}, {1659, 13390, 1699}, {2635, 23710, 16870}, {5228, 10481, 553}, {7177, 24590, 57}, {14256, 24604, 57}, {16662, 16663, 9533}, {26006, 30807, 40869}, {30379, 37771, 17067}

X(43036) = X(9)-ISOCONJUGATE OF X(38882)

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

X(43036) lies on these lines: {7, 940}, {11, 5018}, {77, 5718}, {223, 37663}, {241, 514}, {269, 17720}, {278, 40688}, {347, 17595}, {348, 37660}, {908, 6610}, {1038, 5252}, {1086, 37798}, {1427, 37634}, {1443, 37691}, {1458, 17724}, {3668, 37520}, {4315, 37539}, {4334, 17602}, {4383, 18623}, {15950, 37523}, {17366, 37642}, {17484, 26611}, {17811, 31018}, {26228, 42314}

X(43036) = X(9)-isoconjugate of X(38882)
X(43036) = barycentric product X(7)*X(529)
X(43036) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 38882}, {529, 8}
X(43036) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {241, 34050, 35466}, {3911, 6357, 5723}

X(43037) = X(9)-ISOCONJUGATE OF X(739)

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

X(43037) lies on these lines: {7, 8}, {10, 3665}, {12, 3674}, {56, 9312}, {57, 7223}, {226, 29594}, {241, 514}, {257, 17291}, {279, 1788}, {348, 24914}, {517, 1111}, {664, 1319}, {672, 21139}, {910, 9317}, {960, 26563}, {1155, 5088}, {1266, 13996}, {1317, 39775}, {1358, 9436}, {1388, 25716}, {1565, 1737}, {1837, 17170}, {2099, 40719}, {2348, 3732}, {3057, 3673}, {3160, 7288}, {3230, 36816}, {3290, 21138}, {3476, 3598}, {3664, 5724}, {3693, 21232}, {3706, 33936}, {3761, 7243}, {3880, 21272}, {4009, 6381}, {4021, 37548}, {4056, 18480}, {4361, 28017}, {4566, 34855}, {4848, 10481}, {4851, 28081}, {4852, 7225}, {5045, 7278}, {5048, 24203}, {5123, 33864}, {5219, 7146}, {5839, 28079}, {6603, 9318}, {6706, 17451}, {7176, 32636}, {7185, 24798}, {7198, 10106}, {7233, 40093}, {7264, 9957}, {10027, 41794}, {10944, 25719}, {11011, 24805}, {16749, 18178}, {17078, 17089}, {17181, 17606}, {17314, 28015}, {17366, 41015}, {19582, 33780}, {20247, 34791}, {20925, 24282}, {24599, 24620}, {26653, 30618}, {30946, 31165}, {31188, 31189}, {41712, 42309}

X(43037) = midpoint of X(672) and X(21139)
X(43037) = reflection of X(3693) in X(21232)
X(43037) = isotomic conjugate of X(36798)
X(43037) = X(29352)-complementary conjugate of X(141)
X(43037) = X(899)-cross conjugate of X(536)
X(43037) = X(i)-isoconjugate of X(j) for these (i,j): {9, 739}, {31, 36798}, {41, 3227}, {55, 37129}, {522, 32718}, {644, 23892}, {650, 34075}, {663, 898}, {2175, 31002}, {2194, 41683}, {3063, 4607}, {3699, 23349}
X(43037) = trilinear pole of line {4526, 4728}
X(43037) = crossdifference of every pair of points on line {55, 3063}
X(43037) = {P,U}-harmonic conjugate of X(7), where P and U are the incircle intercepts of line X(7)X(8)
X(43037) = barycentric product X(i)*X(j) for these {i,j}: {7, 536}, {56, 35543}, {57, 6381}, {85, 899}, {279, 4009}, {658, 14430}, {664, 4728}, {891, 4554}, {1434, 3994}, {3230, 6063}, {3669, 41314}, {3676, 23891}, {3768, 4572}, {4465, 7233}, {4526, 4569}, {4573, 14431}, {9436, 36816}, {23343, 24002}
X(43037) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 36798}, {7, 3227}, {56, 739}, {57, 37129}, {85, 31002}, {109, 34075}, {226, 41683}, {536, 8}, {651, 898}, {664, 4607}, {890, 3063}, {891, 650}, {899, 9}, {1415, 32718}, {1646, 3271}, {3230, 55}, {3768, 663}, {3911, 36872}, {3994, 2321}, {4009, 346}, {4465, 3685}, {4526, 3900}, {4554, 889}, {4706, 391}, {4728, 522}, {4937, 4873}, {4998, 5381}, {6381, 312}, {7178, 35353}, {13466, 4009}, {14404, 3709}, {14430, 3239}, {14431, 3700}, {14433, 3716}, {14434, 4526}, {14437, 4895}, {19945, 2170}, {23343, 644}, {23891, 3699}, {28603, 4944}, {30583, 1639}, {30592, 4976}, {35543, 3596}, {36816, 14942}, {41314, 646}, {42764, 2804}
X(43037) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 7195, 30617}, {65, 85, 4059}, {65, 4059, 4955}, {85, 3212, 65}, {664, 1447, 1319}, {1323, 3911, 7181}, {1358, 40663, 9436}, {3212, 17090, 85}, {7185, 33298, 24798}, {10106, 10521, 7198}, {24796, 41687, 6604}, {36928, 36929, 32850}

X(43038) = X(9)-ISOCONJUGATE OF X(2384)

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

X(43038) lies on these lines: {7, 528}, {11, 38941}, {77, 1411}, {80, 1565}, {85, 15950}, {241, 514}, {952, 4089}, {1111, 1387}, {1120, 4452}, {1443, 26749}, {2246, 23766}, {3665, 5252}, {4315, 7198}, {5433, 17090}, {7185, 10944}, {7294, 41807}, {9318, 35110}, {9436, 36920}, {16236, 21314}, {17044, 21139}, {17078, 40663}, {24796, 25716}, {24797, 25718}, {24798, 25719}, {24800, 25720}, {24801, 25721}, {24803, 25726}, {24805, 25723}, {39775, 39782}

X(43038) = midpoint of X(2246) and X(23766)
X(43038) = X(i)-isoconjugate of X(j) for these (i,j): {9, 2384}, {41, 35168}
X(43038) = barycentric product X(i)*X(j) for these {i,j}: {7, 545}, {664, 14475}, {3676, 6633}, {4554, 14421}, {6063, 8649}, {7233, 27921}, {30725, 34762}
X(43038) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 35168}, {56, 2384}, {545, 8}, {1644, 2325}, {6633, 3699}, {8649, 55}, {14421, 650}, {14475, 522}, {27921, 3685}, {30725, 34764}, {33920, 1639}, {34762, 4582}
X(43038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 664, 1317}, {664, 17089, 1358}, {1317, 1358, 7}

X(43039) = X(9)-ISOCONJUGATE OF X(675)

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

X(43039) lies on these lines: {6, 41}, {12, 1107}, {36, 1415}, {37, 15950}, {39, 65}, {109, 5030}, {201, 39244}, {216, 2262}, {221, 5022}, {227, 40133}, {232, 1875}, {241, 514}, {292, 1411}, {348, 17075}, {478, 5120}, {515, 11998}, {517, 13006}, {519, 21859}, {583, 1409}, {608, 36743}, {664, 37686}, {672, 1457}, {910, 7117}, {1015, 1319}, {1042, 23649}, {1100, 2197}, {1212, 22070}, {1393, 17451}, {1399, 33863}, {1500, 11011}, {1575, 40663}, {1735, 38345}, {1737, 34460}, {1880, 8756}, {1909, 28771}, {1914, 5172}, {1950, 5124}, {2078, 16784}, {2099, 2276}, {2170, 8608}, {2285, 5069}, {2361, 17798}, {2594, 20963}, {3061, 37591}, {3665, 16888}, {4253, 10571}, {5013, 11509}, {5024, 37541}, {5252, 16975}, {5283, 11375}, {5299, 37583}, {5396, 37609}, {5433, 16604}, {5701, 22464}, {5718, 37596}, {5750, 40937}, {7198, 14758}, {9575, 37550}, {9596, 18962}, {9597, 18961}, {10944, 17448}, {11434, 36751}, {11510, 16781}, {16502, 37579}, {17754, 24806}, {20616, 25092}, {21384, 37694}, {26481, 31466}, {27109, 28777}, {31187, 31230}, {34036, 40606}

X(43039) = X(29068)-complementary conjugate of X(141)
X(43039) = X(2225)-cross conjugate of X(674)
X(43039) = X(i)-isoconjugate of X(j) for these (i,j): {8, 2224}, {9, 675}, {55, 37130}, {522, 36087}, {4391, 32682}
X(43039) = crossdifference of every pair of points on line {55, 522}
X(43039) = barycentric product X(i)*X(j) for these {i,j}: {7, 674}, {56, 3006}, {85, 2225}, {109, 23887}, {226, 14964}, {3669, 42723}, {4249, 17094}, {6063, 8618}
X(43039) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 675}, {57, 37130}, {604, 2224}, {674, 8}, {1415, 36087}, {2225, 9}, {3006, 3596}, {4249, 36797}, {8618, 55}, {14964, 333}, {23887, 35519}, {42723, 646}
X(43039) = {X(672),X(1457)}-harmonic conjugate of X(4559)

X(43040) = X(9)-ISOCONJUGATE OF X(727)

Barycentrics    (a + b - c)*(a - b + c)*(a*b^2 - b^2*c + a*c^2 - b*c^2) : :
X(43040) = 3 X[1463] - X[24816]

X(43040) lies on these lines: {1, 20731}, {2, 17090}, {7, 1278}, {10, 36493}, {57, 239}, {65, 519}, {75, 41777}, {76, 85}, {141, 16888}, {241, 514}, {388, 32847}, {664, 1429}, {726, 1463}, {742, 4032}, {942, 29331}, {1441, 20892}, {1565, 26012}, {1959, 20335}, {3009, 21140}, {3661, 7185}, {3665, 16603}, {3687, 20955}, {3784, 24218}, {3959, 24177}, {3982, 4059}, {4475, 23682}, {4654, 17310}, {4741, 27492}, {5219, 17266}, {5435, 29590}, {5575, 17151}, {6358, 20432}, {7233, 9436}, {7248, 24165}, {7291, 9317}, {7308, 27288}, {10030, 40844}, {11246, 28909}, {19804, 41773}, {20016, 21454}, {21139, 30807}, {21232, 25083}, {24209, 24237}, {24225, 29353}, {24318, 25007}, {24692, 24836}, {25080, 25132}, {27321, 27339}, {29607, 31231}, {30117, 37523}, {31225, 31234}, {39775, 41794}

X(43040) = isotomic conjugate of X(36799)
X(43040) = X(15323)-complementary conjugate of X(141)
X(43040) = X(10030)-Ceva conjugate of X(9436)
X(43040) = X(1575)-cross conjugate of X(726)
X(43040) = X(i)-isoconjugate of X(j) for these (i,j): {6, 8851}, {8, 34077}, {9, 727}, {31, 36799}, {41, 3226}, {55, 20332}, {284, 18793}, {644, 23355}, {2175, 32020}, {2194, 27809}, {3063, 8709}
X(43040) = cevapoint of X(1463) and X(1575)
X(43040) = crosspoint of X(85) and X(7233)
X(43040) = trilinear pole of line {3837, 20366}
X(43040) = barycentric product X(i)*X(j) for these {i,j}: {7, 726}, {56, 35538}, {75, 1463}, {85, 1575}, {331, 20785}, {334, 8850}, {651, 20908}, {664, 3837}, {903, 24816}, {1441, 18792}, {3009, 6063}, {3676, 23354}, {4572, 6373}, {4573, 21053}, {4998, 21140}, {7233, 17793}, {18033, 40155}, {20567, 21760}, {30545, 40881}
X(43040) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8851}, {2, 36799}, {7, 3226}, {56, 727}, {57, 20332}, {65, 18793}, {85, 32020}, {226, 27809}, {604, 34077}, {664, 8709}, {726, 8}, {1447, 3253}, {1463, 1}, {1575, 9}, {3009, 55}, {3837, 522}, {6373, 663}, {8850, 238}, {17475, 3684}, {17793, 3685}, {18792, 21}, {20681, 4433}, {20777, 212}, {20785, 219}, {20908, 4391}, {21053, 3700}, {21140, 11}, {21760, 41}, {21830, 1334}, {22092, 652}, {23354, 3699}, {24816, 519}, {30545, 40844}, {35538, 3596}, {36814, 1320}, {40155, 7077}, {40881, 2319}, {42766, 2804}
X(43040) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {85, 7146, 226}, {241, 16609, 3911}, {3661, 7185, 36482}

X(43041) = X(9)-ISOCONJUGATE OF X(813)

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

X(43041) lies on these lines: {241, 514}, {663, 30804}, {664, 668}, {693, 3907}, {812, 4107}, {1357, 1358}, {1423, 3768}, {1429, 8632}, {2789, 4927}, {2827, 3663}, {3716, 3766}, {3810, 4025}, {4077, 29051}, {4106, 4162}, {4408, 8062}, {4453, 24126}, {4897, 28487}, {7192, 23738}, {15253, 29240}, {16603, 21261}, {21297, 23057}, {23819, 42312}, {25356, 27691}

X(43041) = isotomic conjugate of X(36801)
X(43041) = X(i)-Ceva conjugate of X(j) for these (i,j): {664, 39775}, {34085, 57}
X(43041) = X(i)-cross conjugate of X(j) for these (i,j): {659, 812}, {27846, 1429}
X(43041) = X(i)-isoconjugate of X(j) for these (i,j): {8, 34067}, {9, 813}, {31, 36801}, {41, 4562}, {55, 660}, {100, 7077}, {101, 4876}, {291, 3939}, {292, 644}, {646, 1922}, {663, 5378}, {668, 18265}, {692, 4518}, {741, 4069}, {875, 4076}, {876, 6065}, {1018, 2311}, {1334, 4584}, {1911, 3699}, {2175, 4583}, {3056, 8684}, {3688, 36081}, {4517, 30664}, {7064, 36066}, {7109, 36806}, {18268, 30730}, {36802, 40730}
X(43041) = crosssum of X(663) and X(2340)
X(43041) = crossdifference of every pair of points on line {55, 7077}
X(43041) = barycentric product X(i)*X(j) for these {i,j}: {7, 812}, {57, 3766}, {85, 659}, {86, 7212}, {238, 24002}, {239, 3676}, {279, 3716}, {331, 22384}, {350, 3669}, {479, 4148}, {513, 10030}, {514, 1447}, {649, 18033}, {658, 4124}, {664, 27918}, {693, 1429}, {740, 17096}, {1088, 4435}, {1284, 7199}, {1357, 27853}, {1358, 3570}, {1428, 3261}, {1432, 14296}, {1434, 4010}, {1874, 15419}, {3948, 7203}, {4017, 30940}, {4107, 7249}, {4375, 7233}, {4554, 27846}, {4625, 39786}, {6063, 8632}, {7178, 33295}, {7179, 23597}, {7192, 16609}, {17094, 31905}, {27922, 30725}, {34085, 38989}
X(43041) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 36801}, {7, 4562}, {56, 813}, {57, 660}, {85, 4583}, {238, 644}, {239, 3699}, {350, 646}, {513, 4876}, {514, 4518}, {604, 34067}, {649, 7077}, {651, 5378}, {659, 9}, {740, 30730}, {804, 4095}, {812, 8}, {873, 36806}, {1014, 4584}, {1284, 1018}, {1357, 3572}, {1358, 4444}, {1428, 101}, {1429, 100}, {1434, 4589}, {1447, 190}, {1914, 3939}, {1919, 18265}, {2238, 4069}, {3570, 4076}, {3669, 291}, {3676, 335}, {3684, 4578}, {3685, 6558}, {3716, 346}, {3733, 2311}, {3766, 312}, {3808, 3061}, {4010, 2321}, {4107, 7081}, {4124, 3239}, {4148, 5423}, {4164, 2329}, {4375, 3685}, {4432, 30731}, {4435, 200}, {4448, 2325}, {4455, 1334}, {4486, 3790}, {4800, 4873}, {4810, 4007}, {4830, 391}, {4839, 4061}, {4974, 30729}, {5009, 5546}, {6654, 36802}, {7132, 8684}, {7192, 36800}, {7193, 4587}, {7203, 37128}, {7212, 10}, {7235, 4103}, {7254, 1808}, {8632, 55}, {10030, 668}, {14296, 17787}, {14433, 4009}, {16609, 3952}, {17096, 18827}, {18033, 1978}, {20769, 4571}, {21832, 210}, {22384, 219}, {24002, 334}, {24459, 3710}, {27846, 650}, {27855, 3975}, {27918, 522}, {27922, 4582}, {30940, 7257}, {31905, 36797}, {33295, 645}, {34253, 1026}, {35119, 3716}, {39775, 42720}, {39786, 4041}

X(43042) = X(9)-ISOCONJUGATE OF X(919)

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

X(43042) lies on these lines: {7, 900}, {11, 1111}, {85, 3766}, {100, 658}, {104, 15728}, {241, 514}, {273, 39534}, {513, 31605}, {523, 24002}, {673, 2402}, {676, 885}, {693, 6362}, {876, 7233}, {918, 16593}, {1317, 3321}, {1445, 22108}, {1447, 26275}, {2223, 28473}, {3309, 4897}, {3777, 30804}, {3887, 5083}, {3900, 4025}, {3910, 7216}, {4077, 23599}, {4357, 25923}, {4367, 8638}, {4435, 5228}, {4777, 30181}, {7192, 21789}, {7250, 23785}, {10436, 25996}, {17090, 24093}, {17091, 24108}, {21127, 23748}, {23829, 39775}

X(43042) = midpoint of X(21127) and X(23748)
X(43042) = reflection of X(i) in X(j) for these {i,j}: {885, 676}, {14330, 7658}
X(43042) = isotomic conjugate of X(36802)
X(43042) = X(1477)-anticomplementary conjugate of X(37781)
X(43042) = X(2736)-complementary conjugate of X(141)
X(43042) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 3323}, {658, 39063}, {883, 9436}, {927, 7}, {4573, 34253}, {7233, 1358}, {34018, 1086}
X(43042) = X(i)-cross conjugate of X(j) for these (i,j): {2254, 918}, {3323, 7}, {3675, 241}
X(43042) = X(i)-isoconjugate of X(j) for these (i,j): {8, 32666}, {9, 919}, {31, 36802}, {41, 666}, {55, 36086}, {100, 2195}, {101, 294}, {105, 3939}, {109, 28071}, {200, 32735}, {220, 36146}, {644, 1438}, {663, 5377}, {692, 14942}, {765, 884}, {885, 1110}, {927, 1253}, {1024, 1252}, {1027, 6065}, {1415, 6559}, {1416, 4578}, {2149, 28132}, {3886, 32724}, {4587, 8751}, {5546, 18785}, {6600, 36041}, {8641, 39293}, {8647, 39272}, {9447, 36803}, {14827, 34085}, {32739, 36796}, {36138, 37658}
X(43042) = cevapoint of X(i) and X(j) for these (i,j): {676, 6084}, {918, 4925}
X(43042) = crosspoint of X(i) and X(j) for these (i,j): {7, 927}, {664, 35160}, {693, 2400}, {883, 9436}, {2414, 3912}, {3449, 35185}, {4569, 34018}
X(43042) = crosssum of X(i) and X(j) for these (i,j): {55, 926}, {663, 8647}, {692, 2426}, {884, 2195}, {918, 18214}, {1438, 2440}, {8659, 16502}
X(43042) = trilinear pole of line {1566, 3323}
X(43042) = crossdifference of every pair of points on line {55, 2195}
X(43042) = barycentric product X(i)*X(j) for these {i,j}: {7, 918}, {85, 2254}, {226, 23829}, {241, 693}, {513, 40704}, {514, 9436}, {518, 24002}, {665, 6063}, {666, 3323}, {883, 1086}, {927, 35094}, {1025, 1111}, {1358, 42720}, {1434, 4088}, {1458, 3261}, {1876, 15413}, {2283, 23989}, {2400, 39063}, {2414, 40615}, {3126, 34018}, {3263, 3669}, {3667, 10029}, {3675, 4554}, {3676, 3912}, {3932, 17096}, {4017, 18157}, {4025, 5236}, {4077, 18206}, {4391, 34855}, {4444, 39775}, {4569, 17435}, {4858, 41353}, {4925, 27818}, {7178, 30941}, {15149, 17094}
X(43042) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 36802}, {7, 666}, {11, 28132}, {56, 919}, {57, 36086}, {241, 100}, {244, 1024}, {269, 36146}, {279, 927}, {513, 294}, {514, 14942}, {518, 644}, {522, 6559}, {604, 32666}, {649, 2195}, {650, 28071}, {651, 5377}, {658, 39293}, {665, 55}, {672, 3939}, {693, 36796}, {883, 1016}, {918, 8}, {926, 220}, {1015, 884}, {1025, 765}, {1086, 885}, {1088, 34085}, {1362, 2284}, {1407, 32735}, {1458, 101}, {1818, 4587}, {1876, 1783}, {2254, 9}, {2283, 1252}, {2284, 6065}, {3126, 3693}, {3263, 646}, {3286, 5546}, {3323, 918}, {3669, 105}, {3675, 650}, {3676, 673}, {3693, 4578}, {3717, 6558}, {3912, 3699}, {3930, 4069}, {3932, 30730}, {3942, 23696}, {4017, 18785}, {4088, 2321}, {4444, 33676}, {4684, 30728}, {4899, 30720}, {4925, 3161}, {4966, 30729}, {5236, 1897}, {6063, 36803}, {7178, 13576}, {8638, 14827}, {9436, 190}, {15149, 36797}, {17107, 36041}, {17435, 3900}, {18157, 7257}, {18206, 643}, {23773, 4147}, {23829, 333}, {24002, 2481}, {24290, 210}, {25083, 4571}, {30941, 645}, {31605, 31638}, {34230, 5548}, {34253, 3573}, {34855, 651}, {35505, 926}, {38989, 4435}, {39063, 2398}, {39775, 3570}, {40217, 36801}, {40615, 2402}, {40704, 668}, {41353, 4564}, {42341, 4513}, {42720, 4076}, {42770, 2804}
X(43042) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1638, 30725, 5723}, {3676, 17094, 3004}

X(43043) = X(9)-ISOCONJUGATE OF X(953)

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

X(43043) lies on these lines: {1, 11219}, {2, 222}, {5, 603}, {11, 109}, {56, 34030}, {57, 1020}, {63, 26611}, {73, 140}, {88, 278}, {212, 37364}, {221, 499}, {223, 31231}, {225, 37582}, {226, 4896}, {241, 514}, {244, 15253}, {255, 6922}, {498, 34046}, {528, 23703}, {952, 39758}, {1076, 37623}, {1214, 16586}, {1262, 23592}, {1317, 24864}, {1364, 34462}, {1393, 34753}, {1411, 12832}, {1419, 17337}, {1421, 3756}, {1422, 23511}, {1455, 1737}, {1457, 15325}, {1466, 5292}, {1714, 41402}, {1768, 38357}, {1777, 7681}, {1846, 36058}, {1935, 4187}, {1936, 37374}, {1952, 30608}, {2003, 37662}, {3011, 3660}, {3035, 4551}, {3075, 6831}, {3086, 34040}, {3120, 24465}, {3157, 6958}, {3215, 37356}, {3306, 37695}, {3562, 6972}, {4565, 24624}, {4675, 5219}, {4999, 37558}, {5083, 17724}, {5121, 34049}, {5222, 34056}, {5433, 10571}, {5745, 16578}, {6610, 31201}, {6713, 34586}, {6718, 25968}, {6833, 41344}, {6862, 19349}, {6891, 7078}, {6959, 8757}, {7004, 13226}, {7483, 37523}, {9316, 29662}, {9364, 33140}, {9370, 26364}, {10265, 11700}, {11269, 37541}, {13747, 37694}, {14829, 26942}, {15326, 38945}, {15730, 29571}, {15844, 37522}, {17366, 26742}, {17728, 34036}, {21147, 24914}, {22464, 30684}, {23706, 23711}, {24145, 37798}, {31187, 34042}, {32851, 40863}, {33129, 37789}, {40420, 41806}

X(43043) = X(2716)-complementary conjugate of X(141)
X(43043) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 3319}, {37222, 57}
X(43043) = X(i)-cross conjugate of X(j) for these (i,j): {2265, 952}, {3319, 7}
X(43043) = X(i)-isoconjugate of X(j) for these (i,j): {9, 953}, {32641, 37629}
X(43043) = trilinear pole of line {3319, 35013}
X(43043) = barycentric product X(i)*X(j) for these {i,j}: {7, 952}, {85, 2265}, {4998, 6075}
X(43043) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 953}, {952, 8}, {1769, 37629}, {2265, 9}, {2720, 35011}, {3319, 952}, {6075, 11}, {35013, 2804}
X(43043) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 34234, 26932}, {57, 2006, 1086}, {651, 34051, 222}, {1465, 34050, 6357}, {3911, 34050, 1465}, {5435, 37771, 88}, {6718, 34589, 25968}, {13226, 15252, 7004}

X(43044) = X(9)-ISOCONJUGATE OF X(972)

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

X(43044) lies on these lines: {1, 84}, {6, 34492}, {9, 34488}, {19, 7053}, {37, 1419}, {55, 34041}, {57, 7955}, {77, 40937}, {109, 41339}, {223, 1212}, {227, 9588}, {241, 514}, {269, 1108}, {278, 279}, {281, 1440}, {651, 6510}, {664, 25083}, {934, 7291}, {1020, 34371}, {1214, 3160}, {1412, 40980}, {1439, 18161}, {1442, 34028}, {1461, 2182}, {1565, 5236}, {6610, 8609}, {6611, 21370}, {7146, 34497}, {16601, 34032}, {17073, 31600}, {25930, 34048}, {31793, 40152}, {34042, 34522}, {34051, 34056}

X(43044) = X(36101)-Ceva conjugate of X(57)
X(43044) = X(2272)-cross conjugate of X(971)
X(43044) = X(9)-isoconjugate of X(972)
X(43044) = crosssum of X(220) and X(41339)
X(43044) = crossdifference of every pair of points on line {55, 14298}
X(43044) = barycentric product X(i)*X(j) for these {i,j}: {7, 971}, {85, 2272}, {1156, 28344}
X(43044) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 972}, {971, 8}, {2272, 9}, {28344, 30806}, {42772, 2804}
X(43044) = {X(3160),X(24635)}-harmonic conjugate of X(1214)

X(43045) = X(9)-ISOCONJUGATE OF X(1297)

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

X(43045) lies on these lines: {28, 56}, {77, 26543}, {109, 2741}, {172, 6354}, {222, 3665}, {223, 936}, {226, 3429}, {241, 514}, {333, 348}, {347, 11683}, {940, 40765}, {948, 1035}, {1436, 4000}, {1455, 5236}, {1503, 8766}, {1804, 18629}, {1817, 18632}, {2303, 41003}, {6611, 7365}, {7198, 7251}, {17081, 18624}, {24882, 40669}, {27319, 27330}, {31216, 31230}

X(43045) = X(37202)-Ceva conjugate of X(57)
X(43045) = X(2312)-cross conjugate of X(1503)
X(43045) = X(i)-isoconjugate of X(j) for these (i,j): {9, 1297}, {41, 35140}, {212, 6330}, {219, 8767}, {643, 34212}
X(43045) = barycentric product X(i)*X(j) for these {i,j}: {7, 1503}, {56, 30737}, {85, 2312}, {273, 8766}, {278, 441}, {331, 8779}, {348, 16318}, {2409, 17094}, {3665, 21458}, {6063, 42671}, {7178, 34211}
X(43045) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 35140}, {34, 8767}, {56, 1297}, {278, 6330}, {441, 345}, {1503, 8}, {2312, 9}, {2409, 36797}, {6793, 7359}, {7180, 34212}, {8766, 78}, {8779, 219}, {16318, 281}, {17094, 2419}, {30737, 3596}, {34211, 645}, {35282, 3712}, {42671, 55}

X(43046) = X(9)-ISOCONJUGATE OF X(2369)

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

X(43046) lies on these lines: {6, 31}, {37, 37703}, {241, 514}, {354, 16588}, {516, 38347}, {518, 23988}, {908, 5701}, {1155, 14936}, {1200, 22053}, {1458, 35326}, {1617, 5452}, {1723, 40590}, {1736, 38358}, {2225, 8679}, {3058, 21856}, {3689, 6184}, {3748, 21795}, {3870, 40599}, {5853, 35310}, {17093, 37800}, {22070, 40133}, {30706, 37578}, {31187, 31195}, {40869, 40937}

X(43046) = midpoint of X(2225) and X(20974)
X(43046) = X(i)-isoconjugate of X(j) for these (i,j): {7, 26722}, {9, 2369}
X(43046) = crossdifference of every pair of points on line {55, 514}
X(43046) = barycentric product X(7)*X(2389)
X(43046) = barycentric quotient X(i)/X(j) for these {i,j}: {41, 26722}, {56, 2369}, {2389, 8}
X(43046) = {X(16588),X(23653)}-harmonic conjugate of X(354)

X(43047) = X(9)-ISOCONJUGATE OF X(2717)

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

X(43047) lies on these lines: {1, 104}, {9, 77}, {55, 11714}, {57, 934}, {222, 4559}, {226, 1565}, {241, 514}, {278, 34578}, {279, 2006}, {1020, 3942}, {1086, 1108}, {1212, 5316}, {1214, 35072}, {1422, 1708}, {1445, 34492}, {1461, 16560}, {1726, 7099}, {2003, 21742}, {2283, 2809}, {2801, 39759}, {3160, 5744}, {3451, 3512}, {4551, 35293}, {5222, 26742}, {7291, 32625}, {8732, 37771}, {14936, 40133}, {16579, 17074}, {17613, 41339}, {30684, 37798}

X(43047) = X(37131)-Ceva conjugate of X(57)
X(43047) = X(i)-isoconjugate of X(j) for these (i,j): {9, 2717}, {41, 35164}
X(43047) = crossdifference of every pair of points on line {55, 14392}
X(43047) = barycentric product X(7)*X(2801)
X(43047) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 35164}, {56, 2717}, {2801, 8}
X(43047) = {X(241),X(1323)}-harmonic conjugate of X(18593)

X(43048) = X(9)-ISOCONJUGATE OF X(2718)

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

X(43048) lies on these lines: {1, 6946}, {2, 2006}, {7, 26742}, {11, 24025}, {35, 7550}, {56, 16427}, {57, 88}, {100, 1421}, {106, 41554}, {109, 1054}, {214, 1411}, {223, 8056}, {226, 1086}, {241, 514}, {244, 4551}, {278, 17906}, {948, 34578}, {1214, 16602}, {1393, 3216}, {1427, 39981}, {1457, 1739}, {1708, 23511}, {1718, 10090}, {1772, 2800}, {1943, 27002}, {2003, 27003}, {2078, 7292}, {2802, 39753}, {2835, 42753}, {3035, 15253}, {3315, 37736}, {3452, 26611}, {3666, 24224}, {4850, 5219}, {4868, 15950}, {5228, 15730}, {5316, 25939}, {5400, 7004}, {6127, 11570}, {6667, 34977}, {6915, 33178}, {9519, 23832}, {9946, 34465}, {10571, 24174}, {11501, 30148}, {11512, 21147}, {11717, 20586}, {12736, 34586}, {15558, 24028}, {16594, 25097}, {17080, 31231}, {17749, 37591}, {18838, 24168}, {24046, 37694}, {27339, 27342}, {34056, 39963}

X(43048) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 31841}, {953, 141}
X(43048) = X(7)-Ceva conjugate of X(13756)
X(43048) = X(13756)-cross conjugate of X(7)
X(43048) = X(i)-isoconjugate of X(j) for these (i,j): {9, 2718}, {41, 35175}, {55, 37222}
X(43048) = crosssum of X(6) and X(2265)
X(43048) = trilinear pole of line {13756, 24457}
X(43048) = crossdifference of every pair of points on line {55, 4895}
X(43048) = barycentric product X(i)*X(j) for these {i,j}: {7, 2802}, {57, 30566}, {664, 24457}, {4453, 37630}, {13756, 35175}
X(43048) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 35175}, {56, 2718}, {57, 37222}, {2802, 8}, {13756, 2802}, {24457, 522}, {30566, 312}
X(43048) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16586, 16578}, {2, 37771, 2006}, {88, 651, 57}, {226, 3752, 26740}, {244, 4551, 5083}, {1393, 3216, 15556}, {1465, 3911, 18593}, {1465, 16610, 3911}, {1718, 10090, 11700}, {24028, 32486, 15558}

X(43049) = X(9)-ISOCONJUGATE OF X(1292)

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

X(43049) lies on these lines: {1, 30199}, {7, 4380}, {56, 30234}, {57, 4394}, {109, 2736}, {223, 20314}, {226, 4106}, {241, 514}, {278, 6591}, {388, 28475}, {513, 2078}, {521, 2254}, {651, 1252}, {918, 28984}, {1021, 7203}, {1617, 8642}, {2402, 17093}, {4017, 4724}, {4077, 4762}, {4449, 6608}, {4468, 24562}, {4498, 7216}, {4521, 25925}, {5083, 42322}, {6003, 42319}, {16751, 17096}, {17494, 24002}, {26641, 31603}, {30235, 38324}

X(43049) = X(32739)-complementary conjugate of X(24771)
X(43049) = X(i)-Ceva conjugate of X(j) for these (i,j): {100, 57}, {651, 218}, {664, 15185}, {1440, 38386}, {3732, 14524}, {17093, 40615}, {31605, 3309}
X(43049) = X(i)-isoconjugate of X(j) for these (i,j): {9, 1292}, {55, 37206}, {101, 6601}, {277, 3939}, {644, 2191}, {2195, 2414}, {2428, 14942}, {3693, 36041}, {3717, 32644}, {4578, 17107}
X(43049) = crosspoint of X(i) and X(j) for these (i,j): {100, 3870}, {279, 651}, {664, 10509}
X(43049) = crosssum of X(i) and X(j) for these (i,j): {220, 650}, {513, 2191}, {663, 8012}, {3900, 28070}
X(43049) = crossdifference of every pair of points on line {55, 1212}
X(43049) = barycentric product X(i)*X(j) for these {i,j}: {1, 31605}, {7, 3309}, {57, 4468}, {100, 40615}, {218, 24002}, {241, 2402}, {278, 24562}, {344, 3669}, {513, 6604}, {514, 1445}, {522, 4350}, {649, 21609}, {650, 17093}, {651, 4904}, {658, 38375}, {693, 1617}, {1414, 21945}, {2440, 40704}, {3676, 3870}, {3991, 17096}, {4233, 17094}, {4564, 23760}, {6063, 8642}, {7178, 41610}, {7192, 41539}, {17924, 23144}, {27819, 30719}
X(43049) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 1292}, {57, 37206}, {218, 644}, {241, 2414}, {344, 646}, {513, 6601}, {1416, 36041}, {1445, 190}, {1617, 100}, {2402, 36796}, {2440, 294}, {3309, 8}, {3669, 277}, {3870, 3699}, {3991, 30730}, {4233, 36797}, {4350, 664}, {4468, 312}, {4878, 4069}, {4904, 4391}, {6600, 4578}, {6604, 668}, {8642, 55}, {17093, 4554}, {21059, 3939}, {21609, 1978}, {21945, 4086}, {23144, 1332}, {23760, 4858}, {24562, 345}, {31605, 75}, {38375, 3239}, {40615, 693}, {41539, 3952}, {41610, 645}
X(43049) = {X(650),X(3669)}-harmonic conjugate of X(3676)

X(43050) = X(9)-ISOCONJUGATE OF X(1308)

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

X(43050) lies on these lines: {1, 38324}, {46, 38327}, {55, 2820}, {57, 1635}, {88, 37626}, {100, 109}, {222, 21786}, {226, 812}, {241, 514}, {513, 6139}, {676, 15253}, {1086, 14936}, {1697, 38329}, {2003, 21758}, {2078, 8645}, {2222, 36146}, {2291, 15728}, {2827, 41166}, {3239, 28984}, {3887, 15730}, {4077, 17494}, {4468, 26641}, {4521, 24562}, {4724, 5075}, {4728, 5219}, {5119, 38328}, {5226, 21297}, {7203, 16751}, {9511, 11124}, {14413, 34056}, {16578, 23988}, {17420, 34496}, {17992, 30665}, {18006, 29102}, {21141, 21828}, {24002, 31150}, {37736, 38325}

X(43050) = X(2742)-complementary conjugate of X(141)
X(43050) = X(i)-Ceva conjugate of X(j) for these (i,j): {651, 15730}, {37139, 57}
X(43050) = X(22108)-cross conjugate of X(3887)
X(43050) = X(i)-isoconjugate of X(j) for these (i,j): {9, 1308}, {41, 35171}, {55, 37143}, {101, 3254}, {651, 42064}, {3939, 34578}
X(43050) = crosspoint of X(651) and X(34056)
X(43050) = crosssum of X(i) and X(j) for these (i,j): {220, 14392}, {650, 6603}
X(43050) = crossdifference of every pair of points on line {55, 2170}
X(43050) = barycentric product X(i)*X(j) for these {i,j}: {7, 3887}, {57, 30565}, {85, 22108}, {514, 37787}, {522, 38459}, {650, 37757}, {693, 2078}, {3669, 17264}, {3676, 3935}, {5526, 24002}, {6063, 8645}, {6548, 41553}, {37139, 40629}
X(43050) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 35171}, {56, 1308}, {57, 37143}, {513, 3254}, {663, 42064}, {2078, 100}, {3669, 34578}, {3887, 8}, {3935, 3699}, {5526, 644}, {8645, 55}, {17264, 646}, {19624, 3939}, {22108, 9}, {30565, 312}, {37757, 4554}, {37787, 190}, {38459, 664}, {41553, 17780}

X(43051) = X(9)-ISOCONJUGATE OF X(932)

Barycentrics    a*(b - c)*(a + b - c)*(a - b + c)*(a*b + a*c - b*c) : :
X(43051) = 3 X[1638] - X[20508], 3 X[1638] - 2 X[20521]

X(430) lies on these lines: {56, 21005}, {241, 514}, {614, 8642}, {664, 9362}, {693, 7212}, {1403, 8640}, {1427, 3572}, {1428, 1980}, {1469, 20983}, {1491, 4017}, {3261, 4885}, {3666, 4106}, {3752, 4394}, {3777, 28024}, {3835, 25098}, {4083, 22090}, {4380, 4850}, {4449, 4477}, {6129, 28042}, {18197, 23092}, {20906, 27346}, {23803, 30097}, {28475, 37592}

X(43051) = reflection of X(i) in X(j) for these {i,j}: {650, 24782}, {20508, 20521}
X(43051) = X(28469)-complementary conjugate of X(141)
X(43051) = X(i)-Ceva conjugate of X(j) for these (i,j): {4554, 30545}, {4572, 65}
X(43051) = X(i)-cross conjugate of X(j) for these (i,j): {6377, 1403}, {20979, 4083}
X(43051) = X(i)-isoconjugate of X(j) for these (i,j): {8, 34071}, {9, 932}, {41, 18830}, {55, 4598}, {87, 644}, {100, 2319}, {101, 7155}, {190, 2053}, {330, 3939}, {643, 16606}, {645, 23493}, {646, 7121}, {663, 5383}, {692, 27424}, {2162, 3699}, {4578, 7153}, {4612, 7148}, {5546, 42027}, {7257, 21759}
X(43051) = crosspoint of X(i) and X(j) for these (i,j): {57, 4554}, {651, 7132}, {17921, 18197}
X(43051) = crosssum of X(i) and X(j) for these (i,j): {9, 3063}, {650, 3061}
X(43051) = crossdifference of every pair of points on line {55, 2053}
X(43051) = barycentric product X(i)*X(j) for these {i,j}: {7, 4083}, {43, 3676}, {56, 20906}, {57, 3835}, {65, 17217}, {85, 20979}, {192, 3669}, {226, 18197}, {269, 4147}, {273, 22090}, {278, 25098}, {513, 3212}, {514, 1423}, {649, 30545}, {651, 21138}, {664, 3123}, {693, 1403}, {1014, 21051}, {1214, 17921}, {1357, 36863}, {1427, 27527}, {1434, 21834}, {1441, 16695}, {2176, 24002}, {3261, 41526}, {3971, 7203}, {4017, 33296}, {4077, 38832}, {4551, 23824}, {4552, 16742}, {4554, 6377}, {4572, 38986}, {6063, 8640}, {7153, 23886}, {7178, 27644}, {7180, 31008}, {7249, 24533}, {17096, 20691}, {23092, 40149}, {23773, 36146}
X(43051) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 18830}, {43, 3699}, {56, 932}, {57, 4598}, {192, 646}, {513, 7155}, {514, 27424}, {604, 34071}, {649, 2319}, {651, 5383}, {667, 2053}, {1403, 100}, {1423, 190}, {2176, 644}, {2209, 3939}, {3123, 522}, {3208, 6558}, {3212, 668}, {3669, 330}, {3676, 6384}, {3835, 312}, {4017, 42027}, {4083, 8}, {4147, 341}, {4992, 3702}, {6377, 650}, {7153, 32039}, {7180, 16606}, {7304, 4631}, {8640, 55}, {14408, 2325}, {14426, 4009}, {16695, 21}, {16742, 4560}, {17217, 314}, {17921, 31623}, {18197, 333}, {20691, 30730}, {20760, 4571}, {20906, 3596}, {20979, 9}, {21051, 3701}, {21138, 4391}, {21762, 3063}, {21834, 2321}, {21835, 3709}, {22090, 78}, {22386, 1946}, {23092, 1812}, {23824, 18155}, {23886, 4110}, {24002, 6383}, {24533, 7081}, {25098, 345}, {25142, 27538}, {27644, 645}, {30545, 1978}, {30719, 27496}, {33296, 7257}, {38832, 643}, {38986, 663}, {41526, 101}, {41531, 36801}
X(43051) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1638, 20508, 20521}, {3676, 7180, 3669}

X(43052) = X(9)-ISOCONJUGATE OF X(4588)

Barycentrics    (a - 2*b - 2*c)*(b - c)*(a + b - c)*(a - b + c) : :
X(43052) = 3 X[3669] - 4 X[3676], 5 X[3669] - 4 X[30719], 9 X[3669] - 10 X[30722], 7 X[3669] - 8 X[30723], 5 X[3669] - 6 X[30724], 3 X[3669] - 2 X[30725], 7 X[3669] - 6 X[30726], 2 X[3676] - 3 X[7178], 5 X[3676] - 3 X[30719], 6 X[3676] - 5 X[30722], 7 X[3676] - 6 X[30723], 10 X[3676] - 9 X[30724], 14 X[3676] - 9 X[30726], 4 X[4791] - 3 X[4944], 5 X[7178] - 2 X[30719], 9 X[7178] - 5 X[30722], 7 X[7178] - 4 X[30723], 5 X[7178] - 3 X[30724], 3 X[7178] - X[30725], 7 X[7178] - 3 X[30726], 18 X[30719] - 25 X[30722], 7 X[30719] - 10 X[30723], 2 X[30719] - 3 X[30724], 6 X[30719] - 5 X[30725], 14 X[30719] - 15 X[30726], 35 X[30722] - 36 X[30723], 25 X[30722] - 27 X[30724], 5 X[30722] - 3 X[30725], 35 X[30722] - 27 X[30726], 20 X[30723] - 21 X[30724], 12 X[30723] - 7 X[30725], 4 X[30723] - 3 X[30726], 9 X[30724] - 5 X[30725], 7 X[30724] - 5 X[30726], 7 X[30725] - 9 X[30726]

X(43052) lies on these lines: {1, 28537}, {7, 28910}, {56, 4378}, {65, 513}, {85, 20949}, {241, 514}, {918, 30181}, {1146, 42770}, {2099, 4775}, {3762, 4077}, {3900, 21118}, {3904, 4885}, {4017, 4802}, {4059, 28851}, {4106, 28468}, {4162, 21185}, {4170, 28573}, {4391, 18074}, {4462, 26546}, {4467, 23880}, {4504, 28553}, {4707, 23749}, {4774, 4777}, {4790, 29126}, {4791, 4944}, {4820, 23876}, {4955, 28855}, {5219, 23598}, {7212, 28894}, {15313, 21111}, {28151, 30572}

X(43052) = reflection of X(i) in X(j) for these {i,j}: {650, 10015}, {3669, 7178}, {3904, 4885}, {4162, 21185}, {30725, 3676}
X(43052) = isogonal conjugate of X(5549)
X(43052) = X(664)-Ceva conjugate of X(39782)
X(43052) = X(4893)-cross conjugate of X(4777)
X(43052) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5549}, {8, 34073}, {9, 4588}, {41, 4597}, {55, 4604}, {89, 3939}, {100, 2364}, {101, 2320}, {643, 28658}, {644, 2163}, {663, 5385}, {692, 30608}, {3699, 28607}
X(43052) = crossdifference of every pair of points on line {55, 2323}
X(43052) = barycentric product X(i)*X(j) for these {i,j}: {7, 4777}, {45, 24002}, {57, 4791}, {85, 4893}, {279, 4944}, {514, 5219}, {651, 4957}, {693, 2099}, {1088, 4814}, {1358, 4767}, {1405, 3261}, {1434, 4931}, {1441, 4833}, {2006, 23884}, {3669, 4671}, {3676, 3679}, {3911, 23598}, {4077, 4653}, {4125, 7203}, {4608, 4870}, {4774, 7249}, {4775, 6063}, {4800, 7233}, {4945, 30725}, {5235, 7178}, {6548, 36920}, {36594, 39771}
X(43052) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5549}, {7, 4597}, {45, 644}, {56, 4588}, {57, 4604}, {513, 2320}, {514, 30608}, {604, 34073}, {649, 2364}, {651, 5385}, {1405, 101}, {2099, 100}, {2177, 3939}, {3669, 89}, {3676, 39704}, {3679, 3699}, {3711, 4578}, {3940, 4571}, {4273, 5546}, {4653, 643}, {4671, 646}, {4720, 7256}, {4767, 4076}, {4770, 210}, {4774, 7081}, {4775, 55}, {4777, 8}, {4787, 40499}, {4791, 312}, {4800, 3685}, {4814, 200}, {4825, 3711}, {4833, 21}, {4870, 4427}, {4873, 6558}, {4893, 9}, {4908, 30731}, {4931, 2321}, {4944, 346}, {4945, 4582}, {4951, 3790}, {4957, 4391}, {5219, 190}, {5235, 645}, {7178, 30588}, {7180, 28658}, {16590, 30727}, {21130, 5233}, {23352, 1320}, {23598, 4997}, {23884, 32851}, {24002, 20569}, {28603, 4009}, {30604, 21677}, {30605, 3712}, {36920, 17780}, {39782, 4781}
X(43052) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3676, 30725, 3669}, {7178, 30725, 3676}, {30719, 30724, 3669}, {30723, 30726, 3669}

X(43053) = X(9)-ISOCONJUGATE OF X(28479)

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

X(43053) lies on these lines: {2, 12}, {7, 17305}, {11, 6996}, {57, 1759}, {65, 17023}, {140, 37609}, {141, 604}, {172, 37662}, {193, 38296}, {226, 7198}, {239, 40663}, {241, 514}, {348, 5435}, {524, 1404}, {597, 1405}, {1038, 2999}, {1284, 26986}, {1317, 6542}, {1319, 3912}, {1388, 17316}, {1400, 3589}, {1408, 24632}, {1420, 17284}, {1445, 38186}, {1466, 24609}, {1470, 11343}, {1617, 21526}, {1766, 20270}, {1788, 5222}, {2099, 26626}, {2171, 17045}, {2275, 37646}, {2285, 4657}, {3035, 4447}, {3086, 7397}, {3476, 29611}, {3649, 29614}, {3661, 10944}, {4293, 7402}, {4299, 36731}, {4384, 24914}, {5053, 26932}, {5172, 21495}, {5204, 36698}, {5252, 17308}, {5432, 21010}, {6284, 37416}, {6999, 15326}, {7173, 7384}, {7354, 7377}, {7406, 10896}, {7499, 40956}, {7677, 16593}, {7741, 36728}, {10106, 29604}, {10401, 17306}, {11375, 29603}, {12513, 28795}, {12607, 28789}, {12635, 28922}, {15325, 19512}, {15950, 17397}, {16832, 31231}, {16834, 41687}, {17081, 31994}, {17294, 37738}, {18097, 27005}, {21477, 37579}, {23292, 28274}, {24266, 40997}, {27633, 40590}, {37326, 37583}, {37596, 37634}

X(43053) = X(9)-isoconjugate of X(28479)
X(43053) = barycentric product X(7)*X(5846)
X(43053) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 28479}, {5846, 8}
X(43053) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2975, 30847}, {2, 3436, 30826}, {2, 24583, 4999}, {2, 24612, 1329}, {2, 41245, 12}, {12, 31221, 2}, {56, 31230, 2}, {56, 36493, 5434}, {1375, 3008, 26007}

X(43054) = X(9)-ISOCONJUGATE OF X(28476)

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

X(43054) lies on these lines: {2, 7176}, {7, 17324}, {39, 1214}, {41, 35290}, {56, 226}, {57, 348}, {223, 978}, {241, 514}, {307, 604}, {386, 1038}, {515, 26012}, {516, 17798}, {553, 3665}, {672, 26006}, {948, 7288}, {1210, 24268}, {1412, 16887}, {1427, 16604}, {1429, 9436}, {1708, 4253}, {2082, 24580}, {2275, 40940}, {3361, 29646}, {3436, 30757}, {3982, 7198}, {4032, 5750}, {4357, 7175}, {4447, 6745}, {5120, 17073}, {5226, 29612}, {5244, 32636}, {5435, 17367}, {7113, 9028}, {10106, 16603}, {10481, 36538}, {13405, 21010}, {13411, 37609}, {13462, 29660}, {15953, 24806}, {16577, 25092}, {17030, 27332}, {17080, 24598}, {17095, 41245}, {18589, 36743}, {18652, 28274}, {31211, 31230}, {37596, 39595}

X(43054) = X(9)-isoconjugate of X(28476)
X(43054) = barycentric product X(7)*X(5847)
X(43054) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 28476}, {5847, 8}

X(43055) = BARYCENTRIC PRODUCT X(7)*X(5854)

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

X(43055) lies on these lines: {1, 6174}, {2, 45}, {11, 1054}, {57, 21362}, {100, 3756}, {106, 1145}, {241, 514}, {244, 3035}, {524, 24593}, {528, 1647}, {651, 1407}, {750, 17726}, {952, 41343}, {1155, 5121}, {1317, 26727}, {1320, 24869}, {1387, 4674}, {1739, 15325}, {2006, 8056}, {2177, 17051}, {2802, 14028}, {3120, 6667}, {3216, 34753}, {3271, 34583}, {3306, 4675}, {3666, 6692}, {3689, 24216}, {3712, 4871}, {3722, 35023}, {3752, 16586}, {3772, 31224}, {3999, 6745}, {4432, 25377}, {4667, 24685}, {4741, 5233}, {4767, 12035}, {4850, 17395}, {4995, 29820}, {5222, 35110}, {5241, 17256}, {5326, 33130}, {5400, 13226}, {5432, 17063}, {5433, 24174}, {5554, 8572}, {6681, 24168}, {6691, 24443}, {6715, 34587}, {6788, 10609}, {6921, 17054}, {7294, 24161}, {8256, 32577}, {9041, 17780}, {11512, 24914}, {13747, 24046}, {14554, 24237}, {14757, 17476}, {14985, 16575}, {17020, 40612}, {17023, 32043}, {17266, 32851}, {17269, 17740}, {17365, 37651}, {17397, 26629}, {17567, 37549}, {17719, 31235}, {17720, 31190}, {18253, 28257}, {19515, 29243}, {21907, 31204}, {23845, 28393}, {25430, 31326}, {26062, 37542}, {26746, 37646}, {27003, 37662}, {29628, 30608}, {30684, 31201}, {31183, 34578}

X(43055) = complement of X(30566)
X(43055) = complement of the isotomic conjugate of X(37222)
X(43055) = X(i)-complementary conjugate of X(j) for these (i,j): {32, 35129}, {2718, 141}, {21758, 35587}, {35175, 626}, {37222, 2887}
X(43055) = crosspoint of X(2) and X(37222)
X(43055) = crossdifference of every pair of points on line {55, 1960}
X(43055) = barycentric product X(7)*X(5854)
X(43055) = barycentric quotient X(5854)/X(8)
X(43055) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 88, 1086}, {2, 190, 16594}, {2, 1086, 37691}, {2, 4440, 4997}, {2, 24183, 40480}, {2, 24594, 34824}, {2, 30577, 190}, {2, 30578, 30855}, {2, 42697, 30824}, {45, 31202, 2}, {190, 31227, 2}, {244, 3035, 17724}, {1086, 26611, 3782}, {1638, 26007, 5723}, {3911, 16610, 35466}, {8056, 31231, 24789}, {30577, 31227, 16594}

X(43056) = BARYCENTRIC PRODUCT X(7)*X(5855)

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

X(43056) lies on these lines: {2, 6354}, {6, 5435}, {11, 1758}, {56, 5724}, {57, 4888}, {65, 15489}, {241, 514}, {1086, 37797}, {1214, 37634}, {1254, 4999}, {1319, 24216}, {1411, 5298}, {1708, 37663}, {2361, 9364}, {3361, 5725}, {3756, 7677}, {4383, 34042}, {5396, 34753}, {5744, 6180}, {6692, 40937}, {17080, 37646}, {31187, 37800}, {31231, 37695}

X(43056) = barycentric product X(7)*X(5855)
X(43056) = barycentric quotient X(5855)/X(8)
X(43056) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1465, 3911, 35466}, {1465, 35466, 5723}

X(43057) = BARYCENTRIC PRODUCT X(7)*X(5856)

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

X(43057) lies on these lines: {1, 528}, {88, 5222}, {101, 1358}, {218, 279}, {241, 514}, {277, 3160}, {664, 4904}, {673, 38941}, {1111, 17044}, {1565, 9317}, {3732, 17089}, {4089, 5845}, {5308, 37445}, {9312, 20269}, {10481, 15730}, {11200, 36489}, {14996, 17014}, {15725, 15803}, {16578, 16601}, {16586, 37597}, {25930, 26611}, {27304, 27342}, {29571, 37691}

X(43057) = crossdifference of every pair of points on line {55, 22108}
X(43057) = barycentric product X(7)*X(5856)
X(43057) = barycentric quotient X(5856)/X(8)
X(43057) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 34578, 1086}, {1086, 35110, 1}, {3160, 37771, 34056}

X(43058) = BARYCENTRIC PRODUCT X(7)*X(6001)

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

X(43058) lies on these lines: {1, 1035}, {2, 31600}, {9, 223}, {34, 1712}, {56, 3420}, {57, 1422}, {73, 37528}, {77, 34042}, {104, 1455}, {109, 2739}, {208, 37818}, {222, 3666}, {226, 41007}, {227, 5657}, {241, 514}, {278, 393}, {392, 10571}, {956, 21147}, {1158, 2122}, {1394, 17102}, {1396, 18603}, {1410, 1829}, {1456, 8758}, {1604, 1763}, {1804, 24611}, {1876, 18210}, {5744, 17080}, {7114, 40660}, {26011, 37790}, {34036, 42884}, {34051, 41933}, {34491, 37565}

X(43058) = X(36100)-Ceva conjugate of X(57)
X(43058) = X(i)-isoconjugate of X(j) for these (i,j): {9, 1295}, {1897, 2431}, {2417, 8750}
X(43058) = crosspoint of X(i) and X(j) for these (i,j): {189, 16082}, {278, 34051}
X(43058) = barycentric product X(i)*X(j) for these {i,j}: {7, 6001}, {905, 2405}, {934, 14312}, {2443, 15413}, {7435, 17094}
X(43058) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 1295}, {905, 2417}, {2405, 6335}, {2443, 1783}, {6001, 8}, {7435, 36797}, {14312, 4397}, {22383, 2431}, {39175, 1809}
X(43058) = {X(1214),X(34048)}-harmonic conjugate of X(25091)

X(43059) = BARYCENTRIC PRODUCT X(7)*X(6007)

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

X(43059) lies on these lines: {1, 256}, {7, 16975}, {10, 28391}, {39, 3212}, {58, 40765}, {85, 17030}, {220, 29497}, {241, 514}, {274, 279}, {348, 27299}, {651, 5291}, {664, 40859}, {956, 6180}, {1015, 1447}, {1107, 3674}, {1212, 17353}, {1424, 17114}, {1573, 7179}, {3160, 31604}, {5228, 14964}, {6184, 39940}, {16589, 17084}, {17095, 27324}, {17946, 34056}, {24915, 41807}, {28278, 41006}

X(43059) = X(9)-isoconjugate of X(6015)
X(43059) = crossdifference of every pair of points on line {55, 3287}
X(43059) = barycentric product X(7)*X(6007)
X(43059) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 6015}, {6007, 8}

X(43060) = BARYCENTRIC PRODUCT X(7)*X(8676)

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

X(43060) lies on these lines: {109, 35182}, {241, 514}, {513, 647}, {649, 834}, {654, 36054}, {659, 23768}, {661, 6586}, {669, 9313}, {918, 3265}, {2254, 8611}, {2512, 8678}, {3239, 21894}, {3310, 4394}, {3666, 3798}, {3700, 21348}, {3766, 25511}, {4897, 25098}, {6591, 23770}, {9404, 20980}, {17072, 21721}, {20979, 23751}, {27345, 35519}

X(43060) = X(29014)-complementary conjugate of X(141)
X(43060) = X(i)-Ceva conjugate of X(j) for these (i,j): {1813, 56}, {17925, 513}, {23800, 8676}
X(43060) = X(i)-isoconjugate of X(j) for these (i,j): {9, 1305}, {100, 1751}, {101, 2997}, {162, 40161}, {190, 2218}, {272, 1018}, {662, 41506}, {692, 40011}, {4564, 23289}
X(43060) = crosspoint of X(i) and X(j) for these (i,j): {28, 651}, {81, 13397}, {109, 278}
X(43060) = crosssum of X(i) and X(j) for these (i,j): {37, 15313}, {72, 650}, {219, 522}, {514, 24789}
X(43060) = crossdifference of every pair of points on line {10, 55}
X(43060) = barycentric product X(i)*X(j) for these {i,j}: {1, 23800}, {7, 8676}, {56, 20294}, {209, 7192}, {513, 3868}, {514, 579}, {522, 4306}, {649, 18134}, {693, 2352}, {1019, 22021}, {1415, 17878}, {1459, 5125}, {1813, 5190}, {2198, 7199}, {3190, 3676}, {3669, 27396}
X(43060) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 1305}, {209, 3952}, {512, 41506}, {513, 2997}, {514, 40011}, {579, 190}, {647, 40161}, {649, 1751}, {667, 2218}, {2198, 1018}, {2352, 100}, {3190, 3699}, {3271, 23289}, {3676, 15467}, {3733, 272}, {3868, 668}, {4306, 664}, {8676, 8}, {18134, 1978}, {20294, 3596}, {22021, 4033}, {23800, 75}, {27396, 646}
X(43060) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 1459, 7252}, {649, 21828, 6589}, {665, 7180, 650}

X(43061) = BARYCENTRIC PRODUCT X(7)*X(8710)

Barycentrics    (b - c)*(5*a^2 - 2*a*b + b^2 - 2*a*c + 2*b*c + c^2) : :
X(43061) = 5 X[649] + 3 X[4120], 5 X[650] - X[4841], 3 X[1635] - X[4765], 15 X[1635] + X[4838], 3 X[1635] + X[6590], 3 X[1639] + X[4790], 3 X[1639] - 2 X[14350], 2 X[2527] + X[4521], 5 X[3239] - 3 X[4120], X[3700] + 2 X[14351], X[4025] - 5 X[27013], 5 X[4765] + X[4838], 3 X[4773] + X[4820], 3 X[4786] + X[25259], X[4790] + 2 X[14350], X[4813] - 9 X[6544], X[4838] - 5 X[6590], X[4841] - 10 X[31182], X[4932] + 3 X[10196], 3 X[7658] - 2 X[21212], X[21212] - 3 X[31286], X[23729] - 5 X[31250]

X(43061) lies on these lines: {241, 514}, {513, 2490}, {522, 4394}, {523, 2516}, {649, 3239}, {661, 28225}, {667, 4477}, {784, 2500}, {1635, 4765}, {1639, 4790}, {2487, 30520}, {2529, 4977}, {3700, 4962}, {4025, 27013}, {4773, 4820}, {4778, 14425}, {4786, 25259}, {4807, 8611}, {4813, 6544}, {4932, 10196}, {5592, 18231}, {6006, 14321}, {14825, 31359}, {23729, 31250}

X(43061) = midpoint of X(i) and X(j) for these {i,j}: {649, 3239}, {2490, 2527}, {4369, 11068}, {4765, 6590}
X(43061) = reflection of X(i) in X(j) for these {i,j}: {650, 31182}, {4521, 2490}, {7658, 31286}
X(43061) = X(i)-complementary conjugate of X(j) for these (i,j): {1219, 21252}, {2297, 116}, {6574, 141}, {7050, 11}, {7091, 17059}
X(43061) = X(9)-isoconjugate of X(6571)
X(43061) = crosspoint of X(190) and X(7320)
X(43061) = crosssum of X(i) and X(j) for these (i,j): {649, 3304}, {652, 33587}, {657, 10387}, {3057, 40137}
X(43061) = crossdifference of every pair of points on line {55, 1201}
X(43061) = barycentric product X(i)*X(j) for these {i,j}: {7, 8710}, {522, 4308}
X(43061) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 6571}, {4308, 664}, {8710, 8}
X(43061) = {X(1635),X(6590)}-harmonic conjugate of X(4765)

X(43062) = BARYCENTRIC PRODUCT X(7)*X(9025)

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

X(43062) lies on these lines: {56, 87}, {77, 27633}, {85, 16604}, {241, 514}, {348, 2275}, {664, 1575}, {934, 33854}, {978, 34497}, {1015, 9436}, {1025, 3230}, {1042, 28367}, {1107, 17095}, {1149, 6168}, {1434, 16744}, {1500, 25723}, {1574, 25719}, {1914, 6516}, {3177, 9367}, {7183, 39248}, {17353, 25067}, {17448, 33298}, {17720, 37596}, {26134, 31997}, {26986, 40704}, {27918, 38468}, {31210, 31230}

X(43062) = X(9)-isoconjugate of X(9082)
X(43062) = barycentric product X(7)*X(9025)
X(43062) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 9082}, {9025, 8}

X(43063) = BARYCENTRIC PRODUCT X(7)*X(14839)

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

X(43063) lies on these lines: {2, 4554}, {7, 17756}, {39, 85}, {43, 57}, {100, 1462}, {241, 514}, {349, 3934}, {664, 1015}, {673, 14936}, {1020, 28283}, {1025, 20331}, {1111, 13006}, {1214, 6676}, {1365, 16591}, {1416, 8301}, {1427, 39979}, {1565, 34460}, {1574, 33298}, {1575, 9436}, {2092, 41246}, {2275, 9312}, {2276, 40719}, {3666, 4353}, {3668, 27633}, {3752, 23587}, {3795, 39792}, {4552, 24403}, {4564, 8649}, {4573, 37128}, {4998, 40098}, {5219, 40784}, {5435, 17082}, {7117, 9317}, {7786, 26134}, {16578, 25342}, {17448, 25719}, {31198, 31225}, {31200, 31231}, {32462, 39789}

X(43063) = X(12032)-complementary conjugate of X(141)
X(43063) = X(9)-isoconjugate of X(14665)
X(43063) = crossdifference of every pair of points on line {55, 4435}
X(43063) = barycentric product X(7)*X(14839)
X(43063) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 14665}, {14839, 8}
X(43063) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 4551, 34253}, {673, 24499, 14936}

X(43064) = BARYCENTRIC PRODUCT X(7)*X(15726)

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

X(43064) lies on these lines: {1, 971}, {65, 34497}, {77, 34522}, {241, 514}, {278, 38461}, {279, 1418}, {347, 42050}, {348, 4875}, {651, 6603}, {664, 3693}, {910, 934}, {948, 17720}, {1100, 34028}, {1212, 3160}, {1427, 18624}, {1455, 18461}, {2170, 34855}, {3666, 18623}, {3880, 6168}, {4515, 25718}, {5527, 41339}, {6554, 34060}, {6610, 34056}, {7955, 16572}, {24635, 25939}

X(43064) = X(1156)-Ceva conjugate of X(57)
X(43064) = X(9)-isoconjugate of X(15731)
X(43064) = crosspoint of X(279) and X(34056)
X(43064) = crosssum of X(220) and X(6603)
X(43064) = barycentric product X(7)*X(15726)
X(43064) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 15731}, {15726, 8}
X(43064) = {X(241),X(5723)}-harmonic conjugate of X(16610)

X(43065) = BARYCENTRIC PRODUCT X(7)*X(15733)

Barycentrics    a*(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(43065) = 5 X[4699] - 3 X[20435], 7 X[4751] - 3 X[20448]

X(43065) lies on these lines: {1, 6}, {2, 30806}, {3, 2082}, {7, 7960}, {8, 25066}, {10, 4875}, {11, 5179}, {19, 5120}, {31, 28125}, {35, 34867}, {36, 910}, {39, 41015}, {41, 1385}, {42, 25074}, {43, 25075}, {46, 5022}, {55, 39393}, {56, 169}, {58, 16699}, {65, 4253}, {85, 24774}, {101, 1319}, {104, 294}, {145, 3991}, {210, 41276}, {239, 25083}, {241, 514}, {277, 279}, {348, 20269}, {517, 672}, {519, 3693}, {572, 2264}, {579, 2262}, {644, 38460}, {651, 38459}, {673, 5088}, {728, 12629}, {899, 35293}, {906, 1914}, {942, 1475}, {948, 37695}, {997, 37658}, {999, 40131}, {1000, 40779}, {1015, 3290}, {1018, 3880}, {1053, 2958}, {1055, 2246}, {1125, 25086}, {1145, 6184}, {1146, 1737}, {1155, 1308}, {1200, 11227}, {1202, 11018}, {1210, 41006}, {1278, 25242}, {1334, 9957}, {1418, 4859}, {1436, 39943}, {1447, 3732}, {1731, 2182}, {1783, 1870}, {1880, 39956}, {2140, 4059}, {2275, 16583}, {2280, 24929}, {2287, 18465}, {2340, 21805}, {2361, 41339}, {2401, 28132}, {2646, 4251}, {2975, 33950}, {3057, 3730}, {3086, 6554}, {3177, 3673}, {3207, 37618}, {3419, 24247}, {3496, 3916}, {3501, 4051}, {3612, 4258}, {3632, 4515}, {3644, 17158}, {3684, 5440}, {3691, 5044}, {3694, 5839}, {3702, 26770}, {3753, 17754}, {3813, 21073}, {3884, 4520}, {3914, 15048}, {3941, 21867}, {3965, 25078}, {4000, 42050}, {4262, 37600}, {4292, 5829}, {4293, 5819}, {4456, 40964}, {4487, 30730}, {4534, 40663}, {4699, 20435}, {4751, 20448}, {4850, 5222}, {4904, 9436}, {4986, 40883}, {5045, 17474}, {5119, 42316}, {5124, 7300}, {5176, 26074}, {5285, 40970}, {5316, 5718}, {5657, 11200}, {5697, 21872}, {5731, 5838}, {5755, 31793}, {5836, 16549}, {7176, 17682}, {7292, 37763}, {7347, 16432}, {7348, 16433}, {8012, 12915}, {8071, 32561}, {8558, 36049}, {8608, 13006}, {8776, 9502}, {9310, 24928}, {10025, 24203}, {10481, 24181}, {10916, 40997}, {11998, 34930}, {12701, 17732}, {12723, 36635}, {14557, 27659}, {14964, 18191}, {16020, 40127}, {16756, 37128}, {17095, 24784}, {17112, 34591}, {17272, 25887}, {17439, 25405}, {17449, 20590}, {17747, 30384}, {18607, 26723}, {19624, 42064}, {20270, 27509}, {20335, 35102}, {20992, 40965}, {21332, 24512}, {21856, 33141}, {23649, 24443}, {23972, 35128}, {24047, 37568}, {25092, 37548}, {25261, 26805}, {25918, 27299}, {25994, 26959}, {26685, 35274}, {27132, 28734}, {27348, 33891}, {30305, 41325}, {31183, 31187}, {33299, 34790}, {34056, 37787}, {35066, 35090}, {35110, 35125}, {38347, 41166}

X(43065) = midpoint of X(672) and X(2170)
X(43065) = reflection of X(3693) in X(24036)
X(43065) = complement of X(30806)
X(43065) = complement of the isogonal conjugate of X(34068)
X(43065) = complement of the isotomic conjugate of X(1156)
X(43065) = isogonal conjugate of the isotomic conjugate of X(37788)
X(43065) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 31844}, {31, 10427}, {32, 35110}, {1121, 626}, {1156, 2887}, {2291, 141}, {4845, 1329}, {14733, 17072}, {18889, 3452}, {23351, 124}, {32728, 522}, {34056, 17046}, {34068, 10}, {35348, 21252}, {36141, 4885}, {41798, 21244}
X(43065) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 10427}, {7, 5580}, {26015, 15733}, {30379, 3660}, {34056, 1}, {37143, 513}, {37780, 15726}, {37787, 1155}
X(43065) = X(5580)-cross conjugate of X(7)
X(43065) = X(i)-isoconjugate of X(j) for these (i,j): {9, 15728}, {57, 34894}, {514, 2742}, {527, 10426}
X(43065) = crosspoint of X(i) and X(j) for these (i,j): {1, 34578}, {2, 1156}, {765, 37139}, {26015, 30379}
X(43065) = crosssum of X(i) and X(j) for these (i,j): {1, 5526}, {6, 1155}
X(43065) = crossdifference of every pair of points on line {55, 513}
X(43065) = perspector of 2nd mixtilinear triangle and unary cofactor triangle of 1st mixtilinear triangle
X(43065) = barycentric product X(i)*X(j) for these {i,j}: {1, 26015}, {6, 37788}, {7, 15733}, {8, 3660}, {9, 30379}, {55, 38468}, {100, 2826}, {1156, 10427}, {1320, 41556}, {2346, 41555}
X(43065) = barycentric quotient X(i)/X(j) for these {i,j}: {55, 34894}, {56, 15728}, {692, 2742}, {2826, 693}, {3660, 7}, {5580, 15733}, {10427, 30806}, {15733, 8}, {26015, 75}, {30379, 85}, {34068, 10426}, {37788, 76}, {38468, 6063}, {41555, 20880}
X(43065) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1212, 16601}, {1, 5526, 6603}, {1, 16572, 218}, {6, 34522, 1}, {8, 26690, 25066}, {36, 5540, 910}, {44, 6603, 5526}, {145, 25082, 3991}, {241, 5723, 1465}, {348, 41785, 20269}, {1212, 34522, 40937}, {1212, 40133, 1}, {1319, 2348, 101}, {1475, 17451, 942}, {1642, 2087, 1}, {1731, 5053, 2182}, {3061, 21384, 72}, {3501, 4051, 10914}, {3554, 34526, 1}, {3691, 39244, 5044}, {5011, 5030, 1155}, {5222, 24635, 37597}, {5723, 35466, 3008}, {17474, 21808, 5045}

X(43066) = BARYCENTRIC PRODUCT X(7)*X(17768)

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

X(43066) lies on these lines: {1, 30}, {2, 41807}, {7, 16884}, {77, 4675}, {81, 279}, {85, 17397}, {141, 17075}, {239, 17078}, {241, 514}, {307, 4690}, {347, 2256}, {524, 41804}, {651, 17796}, {664, 6542}, {857, 948}, {1086, 1443}, {1212, 16585}, {1213, 41808}, {1358, 1429}, {1441, 4472}, {3012, 15726}, {3668, 4667}, {3723, 41857}, {4114, 10481}, {4862, 33633}, {5018, 24715}, {5244, 7176}, {6610, 22464}, {6996, 38941}, {7238, 41801}, {9312, 17308}, {10944, 36482}, {11064, 18668}, {14189, 39063}, {17044, 30807}, {17079, 26626}, {17086, 17305}, {17092, 17366}, {17160, 40892}, {17269, 28739}, {21907, 34056}, {26611, 35110}, {29584, 32007}, {36493, 37165}

X(43066) = X(i)-isoconjugate of X(j) for these (i,j): {9, 28471}, {41, 35141}, {5546, 35347}
X(43066) = crossdifference of every pair of points on line {55, 4524}
X(43066) = barycentric product X(7)*X(17768)
X(43066) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 35141}, {56, 28471}, {4017, 35347}, {17768, 8}
X(43066) = {X(6357),X(18593)}-harmonic conjugate of X(35466)

X(43067) = BARYCENTRIC PRODUCT X(7)*X(23880)

Barycentrics    (b - c)*(a^2 + a*b + a*c + 2*b*c) : :
Barycentrics    (B-power of A-Odehnal tritangent circle) - (C-power of A-Odehnal tritangent circle) : :
X(43067) = X[649] - 3 X[31148], 5 X[650] - 6 X[4763], 3 X[650] - 4 X[31286], X[661] - 3 X[4379], 3 X[661] - 5 X[30835], 3 X[693] - X[20295], 5 X[693] - 3 X[21297], 3 X[693] - 2 X[23813], 3 X[1638] - X[4841], 4 X[2516] - 5 X[27013], 4 X[2516] - 3 X[31150], X[4106] + 2 X[7192], 3 X[4106] - 2 X[20295], 5 X[4106] - 6 X[21297], 3 X[4106] - 4 X[23813], 5 X[4369] - 3 X[4763], 3 X[4369] - 2 X[31286], 3 X[4379] - 2 X[4885], 9 X[4379] - 5 X[30835], 3 X[4728] - X[4813], 3 X[4728] - 2 X[4940], 9 X[4763] - 10 X[31286], 3 X[4776] - 5 X[26985], 3 X[4776] - X[31290], 3 X[4789] - X[25259], 6 X[4885] - 5 X[30835], 3 X[4893] - 5 X[24924], 3 X[4893] - 4 X[31287], X[4963] - 5 X[30795], 3 X[7192] + X[20295], 5 X[7192] + 3 X[21297], 3 X[7192] + 2 X[23813], 4 X[7653] - X[17494], 5 X[20295] - 9 X[21297], 9 X[21297] - 10 X[23813], 5 X[24924] - 4 X[31287], 4 X[25666] - 5 X[31250], 5 X[26985] - X[31290], 5 X[27013] - 3 X[31150]

X(43067) lies on these lines: {241, 514}, {320, 350}, {522, 4897}, {523, 4025}, {649, 4762}, {661, 4379}, {784, 23829}, {812, 4790}, {850, 4411}, {891, 4507}, {918, 6590}, {1019, 23882}, {2516, 27013}, {2526, 24720}, {2533, 22318}, {2786, 4500}, {3239, 28878}, {3700, 28846}, {3716, 4778}, {3766, 29198}, {3768, 28398}, {3798, 4976}, {3803, 29186}, {3835, 28840}, {3900, 17166}, {4024, 28898}, {4374, 35519}, {4378, 7234}, {4380, 26824}, {4382, 4979}, {4391, 18154}, {4394, 7653}, {4453, 4802}, {4462, 30024}, {4467, 4777}, {4581, 24002}, {4608, 28151}, {4724, 24666}, {4728, 4813}, {4761, 14077}, {4776, 26985}, {4789, 25259}, {4801, 8712}, {4823, 15309}, {4874, 4977}, {4893, 24924}, {4913, 28147}, {4944, 28855}, {4960, 14349}, {4963, 30795}, {6545, 41850}, {6548, 30598}, {7203, 21173}, {13401, 40166}, {14321, 28902}, {16759, 21137}, {16892, 28894}, {17161, 28165}, {18199, 22383}, {21204, 27929}, {24192, 34590}, {25511, 27527}, {25666, 31250}, {25925, 26017}, {25981, 26640}, {26248, 28195}, {27417, 40137}, {27855, 38238}

X(43067) = midpoint of X(i) and X(j) for these {i,j}: {693, 7192}, {4380, 26824}, {4382, 4979}, {4960, 14349}
X(43067) = reflection of X(i) in X(j) for these {i,j}: {650, 4369}, {661, 4885}, {2526, 24720}, {3004, 3676}, {4106, 693}, {4394, 7653}, {4790, 4932}, {4813, 4940}, {4820, 4500}, {4976, 3798}, {17494, 4394}, {20295, 23813}
X(43067) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {109, 41913}, {28162, 2}, {30712, 150}, {31503, 21221}, {39980, 149}
X(43067) = X(i)-complementary conjugate of X(j) for these (i,j): {6013, 141}, {10013, 116}
X(43067) = X(7)-Ceva conjugate of X(3026)
X(43067) = X(i)-cross conjugate of X(j) for these (i,j): {3026, 7}, {17418, 23880}
X(43067) = X(i)-isoconjugate of X(j) for these (i,j): {9, 32693}, {41, 32038}, {42, 931}, {100, 2258}, {101, 941}, {692, 31359}, {959, 3939}, {4557, 5331}, {8750, 34259}, {32739, 34258}
X(43067) = crosspoint of X(668) and X(5936)
X(43067) = crosssum of X(650) and X(5283)
X(43067) = crossdifference of every pair of points on line {55, 213}
X(43067) = barycentric product X(i)*X(j) for these {i,j}: {7, 23880}, {85, 17418}, {274, 8672}, {513, 34284}, {514, 10436}, {693, 940}, {958, 24002}, {1468, 3261}, {1867, 15419}, {3026, 32038}, {3676, 11679}, {3714, 17096}, {4025, 5307}, {4185, 15413}, {5019, 40495}, {6385, 8639}, {7192, 31993}
X(43067) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 32038}, {56, 32693}, {81, 931}, {513, 941}, {514, 31359}, {649, 2258}, {693, 34258}, {905, 34259}, {940, 100}, {958, 644}, {1019, 5331}, {1468, 101}, {2268, 3939}, {3026, 23880}, {3669, 959}, {3713, 4578}, {3714, 30730}, {4185, 1783}, {5019, 692}, {5307, 1897}, {7192, 37870}, {8639, 213}, {8672, 37}, {10436, 190}, {11679, 3699}, {17110, 6013}, {17418, 9}, {23880, 8}, {31993, 3952}, {34284, 668}, {40495, 40828}
X(43067) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4379, 4885}, {693, 20295, 23813}, {4728, 4813, 4940}, {4893, 24924, 31287}, {20295, 23813, 4106}, {26985, 31290, 4776}, {27013, 31150, 2516}

X(43068) = BARYCENTRIC PRODUCT X(7)*X(28234)

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

X(43068) lies on these lines: {2, 20223}, {57, 2183}, {88, 30379}, {223, 1443}, {226, 4887}, {241, 514}, {278, 8756}, {676, 35013}, {1214, 6692}, {1393, 13411}, {1512, 15737}, {1758, 5121}, {3752, 8607}, {4419, 5219}, {5265, 34039}, {6700, 37591}, {10164, 34036}, {17078, 41802}, {28301, 36914}, {30577, 40862}, {36913, 41141}, {37651, 41572}

X(43068) = X(9)-isoconjugate of X(28233)
X(43068) = barycentric product X(7)*X(28234)
X(43068) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 28233}, {28234, 8}
X(43068) = {X(1465),X(3911)}-harmonic conjugate of X(34050)

X(43069) = ISOTOMIC CONJUGATE OF X(41299)

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

X(43069) lies on the circumconic with center X(9) and these lines: {190, 21859}, {662, 4559}, {799, 4552}, {32675, 37140}, {34234, 38000}

X(43069) = isotomic conjugate of X(41299)
X(43069) = X(2092)-cross conjugate of X(59)
X(43069) = X(i)-isoconjugate of X(j) for these (i,j): {31, 41299}, {650, 37607}
X(43069) = cevapoint of X(650) and X(37548)
X(43069) = trilinear pole of line {1, 181}
X(43069) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 41299}, {109, 37607}

X(43070) = X(1)X(181)∩X(65)X(86)

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

X(43070) lies on the circumconic {{A,B,C,X(1),X(6)}} and these lines: {1, 181}, {6, 23623}, {58, 1402}, {65, 86}, {106, 10475}, {269, 7143}, {388, 870}, {960, 1220}, {996, 3678}, {9277, 39780}

X(43070) = isogonal conjugate of the anticomplement of X(5530)
X(43070) = X(i)-isoconjugate of X(j) for these (i,j): {8, 37607}, {101, 41299}
X(43070) = cevapoint of X(i) and X(j) for these (i,j): {1402, 2300}, {5247, 5255}
X(43070) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 41299}, {604, 37607}

X(43071) = X(1)X(181)∩X(2)X(2171)

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

X(43071) lies on the circumconic {{A,B,C,X(1),X(2)}} and these lines: {1, 181}, {2, 2171}, {57, 2277}, {81, 1400}, {226, 274}, {279, 7147}, {961, 1193}, {985, 1460}, {3687, 30710}

X(43071) = X(i)-isoconjugate of X(j) for these (i,j): {9, 37607}, {692, 41299}
X(43071) = cevapoint of X(i) and X(j) for these (i,j): {1193, 1400}, {1999, 27064}
X(43071) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 37607}, {514, 41299}

X(43072) = X(1)X(181)∩X(3)X(22400)

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

X(43072) lies on the circumconic {{A,B,C,X(1),X(3)}} and these lines: {1, 181}, {3, 22400}, {29, 1824}, {72, 332}, {77, 1425}, {78, 3690}, {213, 284}, {228, 283}, {869, 1036}, {2359, 22074}, {5293, 40966}, {31637, 37613}

X(43072) = X(i)-isoconjugate of X(j) for these (i,j): {4, 37607}, {32674, 41299}
X(43072) = cevapoint of X(228) and X(22074)
X(43072) = barycentric quotient X(i)/X(j) for these {i,j}: {48, 37607}, {521, 41299}

X(43073) = X(1)X(181)∩X(4)X(18677)

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

X(43073) lies on the Feuerbach circumhyperbola and these lines: {1, 181}, {4, 18677}, {7, 986}, {8, 756}, {9, 1500}, {10, 314}, {21, 42}, {55, 987}, {79, 4424}, {84, 17594}, {256, 3931}, {943, 3750}, {982, 3296}, {983, 3295}, {984, 30479}, {988, 7091}, {989, 1697}, {1172, 2333}, {1320, 10459}, {1476, 4322}, {2269, 2298}, {2320, 19767}, {2481, 13161}, {2997, 37716}, {3670, 5557}, {3743, 11609}, {3976, 5558}, {4642, 26051}, {7148, 7155}, {10435, 10825}, {17719, 39768}, {24440, 37153}, {26065, 38251}

X(43073) = reflection of X(35616) in X(10)
X(43073) = isogonal conjugate of X(37607)
X(43073) = X(i)-cross conjugate of X(j) for these (i,j): {37548, 1}, {38469, 100}
X(43073) = X(i)-isoconjugate of X(j) for these (i,j): {1, 37607}, {1415, 41299}, {7587, 7588}
X(43073) = cevapoint of X(42) and X(2269)
X(43073) = trilinear pole of line {650, 4079}
X(43073) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 37607}, {522, 41299}

X(43074) = X(1)X(181)∩X(12)X(75)

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

X(43074) lies on these lines: {1, 181}, {10, 22022}, {12, 75}, {596, 10408}, {2190, 11398}, {2214, 4271}, {2363, 4267}

X(43074) = X(42661)-cross conjugate of X(4559)
X(43074) = X(i)-isoconjugate of X(j) for these (i,j): {21, 37607}, {163, 41299}
X(43074) = cevapoint of X(181) and X(2092)
X(43074) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 41299}, {1400, 37607}

X(43075) = X(1)X(181)∩X(57)X(1509)

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

X(43075) lies on these lines: {1, 181}, {57, 1509}, {83, 18701}, {1019, 7180}, {2285, 14621}, {3305, 17743}, {5256, 40432}, {16609, 30940}

X(43075) = X(i)-isoconjugate of X(j) for these (i,j): {4876, 37607}, {34067, 41299}
X(43075) = barycentric quotient X(i)/X(j) for these {i,j}: {812, 41299}, {1428, 37607}

X(43076) = ISOGONAL CONJUGATE OF X(4151)

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

X(43076) lies on the circumcircle and these lines: {58, 105}, {98, 17758}, {101, 1634}, {104, 4653}, {111, 2350}, {163, 919}, {595, 741}, {662, 8708}, {675, 39734}, {692, 6577}, {739, 38832}, {759, 13476}, {767, 40004}, {827, 4556}, {927, 1414}, {1326, 2711}, {3573, 34594}, {4584, 36081}

X(43076) = isogonal conjugate of X(4151)
X(43076) = X(i)-cross conjugate of X(j) for these (i,j): {1019, 58}, {16064, 250}, {33863, 249}
X(43076) = X(i)-isoconjugate of X(j) for these (i,j): {1, 4151}, {10, 4040}, {37, 17494}, {42, 20954}, {86, 21727}, {100, 2486}, {321, 21007}, {512, 17143}, {513, 4651}, {514, 3294}, {523, 1621}, {649, 4043}, {656, 14004}, {661, 17277}, {669, 40088}, {798, 18152}, {1018, 17761}, {1577, 4251}, {3996, 4017}, {4033, 38346}, {4171, 33765}, {4455, 40094}, {4552, 38347}, {4557, 40619}, {4560, 20616}, {7192, 40607}, {22160, 41013}
X(43076) = cevapoint of X(i) and X(j) for these (i,j): {31, 3733}, {1019, 39950}
X(43076) = trilinear pole of line {6, 2350}
X(43076) = barycentric product X(i)*X(j) for these {i,j}: {99, 2350}, {100, 39950}, {101, 39734}, {110, 17758}, {163, 40216}, {662, 13476}, {692, 40004}
X(43076) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 4151}, {58, 17494}, {81, 20954}, {99, 18152}, {100, 4043}, {101, 4651}, {110, 17277}, {112, 14004}, {163, 1621}, {213, 21727}, {649, 2486}, {662, 17143}, {692, 3294}, {799, 40088}, {1019, 40619}, {1333, 4040}, {1576, 4251}, {2206, 21007}, {2350, 523}, {3733, 17761}, {4584, 40094}, {5546, 3996}, {13476, 1577}, {17758, 850}, {39734, 3261}, {39950, 693}, {40004, 40495}, {40216, 20948}

X(43077) = ISOGONAL CONJUGATE OF X(4785)

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

X(43077) lies on the circumcircle and these lines: {6, 727}, {98, 34475}, {99, 4482}, {101, 8671}, {103, 3098}, {105, 2108}, {106, 574}, {190, 8709}, {644, 29227}, {675, 27494}, {731, 4256}, {739, 2177}, {898, 4752}, {902, 9111}, {932, 1018}, {1331, 29079}, {2700, 35002}, {2702, 3939}, {2712, 5104}, {4598, 35572}, {5030, 14665}, {9082, 40780}, {16785, 35105}, {23597, 32041}, {29199, 35342}

X(43077) = isogonal conjugate of X(4785)
X(43077) = X(i)-isoconjugate of X(j) for these (i,j): {1, 4785}, {2, 4782}, {81, 4806}, {513, 4393}, {514, 16468}, {649, 30963}, {656, 31912}, {667, 10009}, {693, 21793}, {1019, 3993}, {1022, 4759}, {1577, 34476}, {3795, 4817}, {3835, 40753}, {4083, 40720}, {7192, 21904}, {17924, 23095}
X(43077) = cevapoint of X(649) and X(2276)
X(43077) = trilinear pole of line {6, 3009}
X(43077) = barycentric product X(i)*X(j) for these {i,j}: {101, 27494}, {110, 34475}, {668, 40735}, {932, 40780}
X(43077) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 4785}, {31, 4782}, {42, 4806}, {100, 30963}, {101, 4393}, {112, 31912}, {190, 10009}, {692, 16468}, {1576, 34476}, {4557, 3993}, {23344, 4759}, {27494, 3261}, {32656, 23095}, {32739, 21793}, {34071, 40720}, {34475, 850}, {35327, 4991}, {40735, 513}, {40780, 20906}

X(43078) = ISOGONAL CONJUGATE OF X(5840)

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

X(43078) lies on the circumcircle and these lines: {3, 6099}, {4, 15608}, {36, 36082}, {46, 2222}, {100, 912}, {101, 2252}, {104, 15313}, {108, 18838}, {109, 32760}, {513, 915}, {517, 13397}, {901, 11248}, {1290, 24474}, {1308, 37569}, {1309, 14266}, {2720, 37579}

X(43078) = reflection of X(i) in X(j) for these {i,j}: {4, 15608}, {6099, 3}
X(43078) = reflection of X(915) in the line X(1)X(3)
X(43078) = isogonal conjugate of X(5840)
X(43078) = ΛX(4), X(100))
X(43078) = Collings transform of X(i) for these i: {15608, 39002}

X(43079) = ISOGONAL CONJUGATE OF X(5845)

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

X(43079) lies on the circumcircle and these lines: {2, 927}, {25, 40116}, {55, 919}, {99, 14953}, {100, 910}, {101, 2340}, {103, 649}, {105, 650}, {108, 5089}, {109, 672}, {112, 37908}, {165, 2736}, {241, 934}, {901, 42316}, {902, 26716}, {935, 14119}, {1407, 24016}, {2222, 40131}, {2702, 35270}, {3218, 6183}, {6078, 38876}, {14936, 41934}, {24808, 36028}, {35185, 40141}

X(43079) = isogonal conjugate of X(5845)
X(43079) = isogonal conjugate of the isotomic conjugate of X(35158)
X(43079) = Stevanovic-circle-inverse of X(105)
X(43079) = orthoptic-circle-of-Steiner-inellipe-inverse of X(1566)
X(43079) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(14732)
X(43079) = Collings transform of X(39014)
X(43079) = trilinear pole of line {6, 926}
X(43079) = ΛX(6), X(7))
X(43079) = ΨX(6), X(926))
X(43079) = barycentric product X(6)*X(35158)
X(43079) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5845}, {35158, 76}

X(43080) = ISOGONAL CONJUGATE OF X(5851)

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

X(43080) lies on the circumcircle and these lines: {55, 14733}, {100, 15726}, {101, 5537}, {104, 14077}, {165, 1308}, {479, 3328}, {513, 15731}, {517, 14074}, {657, 2291}, {934, 1155}, {2077, 28291}, {2222, 35445}, {2720, 37541}, {2742, 6244}, {13528, 30237}, {20219, 35000}

X(43080) = reflection of X(15731) in the OI line
X(43080) = isogonal conjugate of X(5851)

X(43081) = ISOGONAL CONJUGATE OF X(5854)

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

X(43081) lies on the circumcircle and these lines: {1, 2743}, {8, 6079}, {36, 1293}, {56, 901}, {59, 6551}, {100, 1319}, {101, 1404}, {104, 30198}, {108, 1878}, {109, 1149}, {513, 8686}, {517, 30236}, {997, 2748}, {999, 2742}, {1292, 5126}, {1308, 13462}, {1318, 1357}, {1420, 2222}, {2078, 6014}, {2716, 41343}, {2720, 41426}, {2731, 3086}, {5172, 28218}, {7292, 9058}, {9059, 37762}

X(43081) = reflection of X(8686) in the OI line
X(43081) = isogonal conjugate of X(5854)
X(43081) = X(17100)-cross conjugate of X(3450)
X(43081) = X(1)-isoconjugate of X(5854)

X(43082) = BARYCENTRIC PRODUCT X(94)X(513)

Barycentrics    b*c*(b - 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) : :

X(43082) lies on these lines: {5, 523}, {79, 513}, {94, 35353}, {265, 3657}, {476, 1290}, {661, 1953}, {693, 20565}, {1141, 26707}, {1393, 4017}, {32680, 37135}, {35139, 35147}

X(43082) = X(14399)-cross conjugate of X(17924)
X(43082) = X(i)-isoconjugate of X(j) for these (i,j): {42, 10411}, {50, 190}, {71, 14590}, {100, 6149}, {101, 323}, {163, 42701}, {186, 1331}, {306, 14591}, {340, 32656}, {526, 4570}, {1897, 22115}, {1978, 19627}, {1983, 3219}, {2174, 4585}, {2624, 4567}, {4561, 34397}, {4600, 14270}, {7799, 32739}
X(43082) = crossdifference of every pair of points on line {50, 6149}
X(43082) = barycentric product X(i)*X(j) for these {i,j}: {28, 14592}, {81, 10412}, {94, 513}, {265, 17924}, {274, 15475}, {286, 14582}, {328, 6591}, {476, 16732}, {514, 2166}, {667, 20573}, {693, 1989}, {905, 6344}, {3120, 32680}, {3125, 35139}, {4466, 36129}, {11060, 40495}, {15413, 18384}, {18817, 22383}, {21207, 32678}
X(43082) = barycentric quotient X(i)/X(j) for these {i,j}: {28, 14590}, {79, 4585}, {81, 10411}, {94, 668}, {265, 1332}, {476, 4567}, {513, 323}, {523, 42701}, {649, 6149}, {667, 50}, {693, 7799}, {1980, 19627}, {1989, 100}, {2166, 190}, {2203, 14591}, {3120, 32679}, {3121, 14270}, {3122, 2624}, {3125, 526}, {6186, 1983}, {6344, 6335}, {6591, 186}, {10412, 321}, {11060, 692}, {14254, 42716}, {14356, 42717}, {14399, 1511}, {14582, 72}, {14592, 20336}, {15475, 37}, {16732, 3268}, {17924, 340}, {18210, 8552}, {18384, 1783}, {20573, 6386}, {22383, 22115}, {32678, 4570}, {32680, 4600}, {35139, 4601}

X(43083) = BARYCENTRIC PRODUCT X(94)X(520)

Barycentrics    (b^2 - c^2)*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(-a^2 + b^2 - a*c - c^2)*(-a^2 + b^2 + a*c - c^2)*(-a^2 + b^2 + c^2)^2 : :
X(43083) = 4 X[10412] - 3 X[15475]

X(43083) lies on these lines: {3, 6368}, {5, 523}, {216, 647}, {264, 41298}, {265, 6334}, {476, 1304}, {520, 5489}, {525, 35254}, {526, 30511}, {1141, 18401}, {1989, 34212}, {2394, 34298}, {5961, 13289}, {11911, 14993}, {12026, 14225}, {12028, 15328}, {14966, 23968}, {16230, 18883}, {23306, 34900}

X(43083) = reflection of X(i) in X(j) for these {i,j}: {14225, 12026}, {14314, 6334}
X(43083) = isotomic conjugate of the polar conjugate of X(14582)
X(43083) = isogonal conjugate of the polar conjugate of X(14592)
X(43083) = X(i)-Ceva conjugate of X(j) for these (i,j): {476, 265}, {12028, 125}, {14592, 14582}
X(43083) = X(1636)-cross conjugate of X(525)
X(43083) = X(i)-isoconjugate of X(j) for these (i,j): {19, 14590}, {50, 823}, {92, 14591}, {107, 6149}, {162, 186}, {163, 14165}, {323, 24019}, {340, 32676}, {526, 24000}, {811, 34397}, {1096, 10411}, {1304, 35201}, {1986, 36114}, {2290, 16813}, {2624, 23582}, {3043, 36129}, {14270, 23999}, {14920, 36131}, {22115, 36126}, {23964, 32679}, {32680, 36423}
X(43083) = cevapoint of X(i) and X(j) for these (i,j): {1650, 5489}, {6368, 9033}
X(43083) = crosspoint of X(i) and X(j) for these (i,j): {265, 476}, {15421, 34767}
X(43083) = crosssum of X(186) and X(526)
X(43083) = trilinear pole of line {3269, 17434}
X(43083) = crossdifference of every pair of points on line {50, 186}
X(43083) = barycentric product X(i)*X(j) for these {i,j}: {3, 14592}, {69, 14582}, {74, 18557}, {94, 520}, {265, 525}, {328, 647}, {339, 32662}, {394, 10412}, {476, 15526}, {1494, 18558}, {1650, 39290}, {1989, 3265}, {2166, 24018}, {2632, 32680}, {3269, 35139}, {3926, 15475}, {4143, 18384}, {5489, 39295}, {5627, 41077}, {6334, 12028}, {14560, 36793}, {15421, 39170}, {17879, 32678}, {18817, 32320}, {20573, 39201}, {20902, 36061}, {23895, 41998}, {23896, 41997}
X(43083) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 14590}, {94, 6528}, {184, 14591}, {265, 648}, {328, 6331}, {394, 10411}, {476, 23582}, {520, 323}, {523, 14165}, {525, 340}, {647, 186}, {686, 1986}, {822, 6149}, {1141, 16813}, {1636, 1511}, {1650, 5664}, {1989, 107}, {2166, 823}, {2631, 35201}, {2632, 32679}, {2972, 8552}, {3049, 34397}, {3265, 7799}, {3269, 526}, {5627, 15459}, {5961, 41679}, {6344, 15352}, {6368, 14918}, {9033, 14920}, {9409, 39176}, {10412, 2052}, {11060, 32713}, {11077, 933}, {11079, 1304}, {12028, 687}, {14270, 36423}, {14560, 23964}, {14582, 4}, {14592, 264}, {15451, 11062}, {15475, 393}, {15526, 3268}, {17434, 1154}, {18384, 6529}, {18557, 3260}, {18558, 30}, {32320, 22115}, {32662, 250}, {32678, 24000}, {32680, 23999}, {35442, 41078}, {39170, 16237}, {39201, 50}, {39290, 42308}, {40355, 32695}, {41077, 6148}, {41997, 23871}, {41998, 23870}

X(43084) = BARYCENTRIC PRODUCT X(94)X(524)

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

X(43084) lies on the cubic K527 and these lines: {2, 94}, {5, 523}, {76, 4590}, {264, 34370}, {265, 1352}, {339, 41392}, {468, 9176}, {476, 1995}, {2782, 13233}, {3260, 34827}, {5961, 14655}, {5967, 6593}, {5968, 10415}, {7785, 35511}, {7789, 36953}, {9516, 11060}, {9818, 12028}, {11062, 16237}, {11079, 39290}, {16310, 24975}, {18823, 35139}, {20573, 40822}, {32662, 40856}, {41512, 41670}

X(43084) = isotomic conjugate of the anticomplement of X(13162)
X(43084) = X(13162)-cross conjugate of X(2)
X(43084) = X(i)-isoconjugate of X(j) for these (i,j): {50, 897}, {111, 6149}, {163, 9213}, {186, 36060}, {323, 923}, {526, 36142}, {691, 2624}, {9126, 36045}, {14270, 36085}, {22115, 36128}, {32679, 32729}
X(43084) = trilinear pole of line {690, 41586}
X(43084) = crossdifference of every pair of points on line {50, 14270}
X(43084) = barycentric product X(i)*X(j) for these {i,j}: {94, 524}, {187, 20573}, {328, 468}, {476, 35522}, {690, 35139}, {850, 14559}, {1989, 3266}, {2166, 14210}, {3292, 18817}, {4235, 14592}, {5468, 10412}, {6344, 6390}, {14254, 36890}
X(43084) = barycentric quotient X(i)/X(j) for these {i,j}: {94, 671}, {187, 50}, {265, 895}, {328, 30786}, {351, 14270}, {468, 186}, {476, 691}, {523, 9213}, {524, 323}, {690, 526}, {896, 6149}, {1648, 2088}, {1989, 111}, {2166, 897}, {2642, 2624}, {3266, 7799}, {3292, 22115}, {4235, 14590}, {5468, 10411}, {5627, 9139}, {5642, 1511}, {5967, 14355}, {6344, 17983}, {9115, 19294}, {9117, 19295}, {9125, 9126}, {9717, 14385}, {10412, 5466}, {11060, 32740}, {11183, 39495}, {12828, 1986}, {14254, 9214}, {14356, 5968}, {14417, 8552}, {14559, 110}, {14560, 32729}, {14567, 19627}, {14582, 10097}, {14592, 14977}, {15475, 9178}, {18384, 8753}, {20573, 18023}, {32225, 3581}, {32678, 36142}, {32680, 36085}, {35139, 892}, {35522, 3268}, {37778, 14165}, {41586, 1154}, {42713, 42701}

X(43085) = BARYCENTRIC PRODUCT X(94)X(532)

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

X(43085) lies on the cubic K342b and these lines: {2, 36211}, {5, 523}, {13, 76}, {17, 94}, {61, 23895}, {265, 37824}, {301, 11119}, {338, 5459}, {532, 8014}, {622, 11581}, {623, 3260}, {634, 16770}, {689, 2381}, {3643, 11080}, {6671, 23714}, {11537, 37340}

X(43085) = isotomic conjugate of X(38403)
X(43085) = isotomic conjugate of the anticomplement of X(16536)
X(43085) = isotomic conjugate of the isogonal conjugate of X(8014)
X(43085) = X(300)-Ceva conjugate of X(41000)
X(43085) = X(16536)-cross conjugate of X(2)
X(43085) = X(i)-isoconjugate of X(j) for these (i,j): {31, 38403}, {1094, 16459}, {2151, 2981}, {2380, 6149}
X(43085) = barycentric product X(i)*X(j) for these {i,j}: {13, 41000}, {76, 8014}, {94, 532}, {300, 396}, {328, 23714}, {14446, 35139}
X(43085) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 38403}, {13, 2981}, {94, 11117}, {300, 40707}, {396, 15}, {463, 8739}, {532, 323}, {618, 11131}, {1989, 2380}, {6671, 11146}, {8014, 6}, {11080, 16459}, {11139, 34321}, {14446, 526}, {23714, 186}, {23895, 10409}, {30462, 19294}, {35314, 17402}, {36304, 8603}, {38931, 40156}, {41000, 298}

X(43086) = BARYCENTRIC PRODUCT X(94)X(533)

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

X(43086) lies on the cubic K342a and these lines: {2, 36210}, {5, 523}, {14, 76}, {18, 94}, {62, 23896}, {265, 37825}, {300, 11120}, {338, 5460}, {533, 8015}, {621, 11582}, {624, 3260}, {633, 16771}, {689, 2380}, {3642, 11085}, {6672, 23715}, {11549, 37341}

X(43086) = isotomic conjugate of X(38404)
X(43086) = isotomic conjugate of the anticomplement of X(16537)
X(43086) = isotomic conjugate of the isogonal conjugate of X(8015)
X(43086) = X(301)-Ceva conjugate of X(41001)
X(43086) = X(16537)-cross conjugate of X(2)
X(43086) = X(i)-isoconjugate of X(j) for these (i,j): {31, 38404}, {1095, 16460}, {2152, 6151}, {2381, 6149}
X(43086) = barycentric product X(i)*X(j) for these {i,j}: {14, 41001}, {76, 8015}, {94, 533}, {301, 395}, {328, 23715}, {14447, 35139}
X(43086) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 38404}, {14, 6151}, {94, 11118}, {301, 40706}, {395, 16}, {462, 8740}, {533, 323}, {619, 11130}, {1989, 2381}, {6672, 11145}, {8015, 6}, {11085, 16460}, {11138, 34322}, {14447, 526}, {23715, 186}, {23896, 10410}, {30459, 19295}, {35315, 17403}, {36305, 8604}, {38932, 40157}, {41001, 299}

X(43087) = BARYCENTRIC PRODUCT X(94)X(542)

Barycentrics    b^2*c^2*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(-a^2 + b^2 - a*c - c^2)*(-a^2 + b^2 + a*c - c^2)*(-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(43087) lies on the cubics K433 and K504 and on these lines: {5, 523}, {23, 94}, {67, 265}, {328, 1494}, {1141, 1287}, {1989, 3003}, {6103, 38552}, {6344, 17983}, {22104, 36789}, {23097, 34150}, {23968, 34369}

X(43087) = X(i)-isoconjugate of X(j) for these (i,j): {842, 6149}, {2624, 5649}
X(43087) = barycentric product X(i)*X(j) for these {i,j}: {94, 542}, {328, 6103}, {476, 18312}, {850, 23968}, {1640, 35139}, {5191, 20573}, {7473, 14592}, {10412, 14999}
X(43087) = barycentric quotient X(i)/X(j) for these {i,j}: {94, 5641}, {476, 5649}, {542, 323}, {1640, 526}, {1989, 842}, {2247, 6149}, {5191, 50}, {6041, 14270}, {6103, 186}, {7473, 14590}, {10412, 14223}, {14582, 35909}, {14999, 10411}, {15475, 14998}, {18312, 3268}, {23968, 110}, {34369, 14355}, {35139, 6035}

X(43088) = BARYCENTRIC PRODUCT X(94)X(924)

Barycentrics    (b^2 - c^2)*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(-a^2 + b^2 - a*c - c^2)*(-a^2 + b^2 + a*c - c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4) : :
X(43088) = 2 X[10412] - 3 X[15475]

X(43088) lies on these lines: {5, 523}, {6, 2623}, {52, 924}, {265, 13556}, {382, 20184}, {476, 2407}, {1141, 2383}, {1166, 2413}, {1510, 6102}, {1989, 14273}, {3432, 16035}, {5627, 18808}, {6368, 9927}, {6563, 39113}, {6753, 14576}

X(43088) = reflection of X(30511) in X(15328)
X(43088) = X(476)-Ceva conjugate of X(5961)
X(43088) = X(i)-isoconjugate of X(j) for these (i,j): {163, 37802}, {323, 36145}, {925, 6149}, {1820, 14590}, {4575, 5962}
X(43088) = cevapoint of X(539) and X(34844)
X(43088) = crosspoint of X(476) and X(6344)
X(43088) = crosssum of X(i) and X(j) for these (i,j): {523, 15367}, {526, 22115}
X(43088) = crossdifference of every pair of points on line {50, 1154}
X(43088) = barycentric product X(i)*X(j) for these {i,j}: {24, 14592}, {94, 924}, {317, 14582}, {328, 6753}, {523, 18883}, {1989, 6563}, {1993, 10412}, {5961, 14618}, {7763, 15475}, {17881, 32678}, {18817, 30451}, {20573, 34952}
X(43088) = barycentric quotient X(i)/X(j) for these {i,j}: {24, 14590}, {523, 37802}, {924, 323}, {1989, 925}, {1993, 10411}, {2501, 5962}, {5961, 4558}, {6344, 30450}, {6563, 7799}, {6753, 186}, {10412, 5392}, {11060, 32734}, {14397, 1511}, {14582, 68}, {14592, 20563}, {15475, 2165}, {18883, 99}, {30451, 22115}, {34952, 50}

X(43089) = BARYCENTRIC PRODUCT X(94)X(1503)

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

X(43089 lies on these lines: {5, 523}, {22, 476}, {66, 265}, {94, 3424}, {253, 328}, {393, 1989}, {428, 14583}, {2790, 2980}, {5627, 35908}, {7517, 10688}, {13573, 37444}

X(43089) = X(i)-isoconjugate of X(j) for these (i,j): {1297, 6149}, {8552, 36046}, {8767, 22115}
X(43089) = barycentric product X(i)*X(j) for these {i,j}: {94, 1503}, {328, 16318}, {441, 6344}, {1989, 30737}, {2409, 14592}, {8779, 18817}, {10412, 34211}, {20573, 42671}
X(43089) = barycentric quotient X(i)/X(j) for these {i,j}: {94, 35140}, {1503, 323}, {1989, 1297}, {2312, 6149}, {2409, 14590}, {2445, 14591}, {6344, 6330}, {6793, 1511}, {8779, 22115}, {14582, 2435}, {14592, 2419}, {15475, 34212}, {16318, 186}, {30737, 7799}, {34211, 10411}, {42671, 50}

X(43090) = BARYCENTRIC PRODUCT X(94)X(2781)

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

X(43090) lies on these lines: {5, 523}, {30, 14634}, {265, 1177}, {403, 1989}, {427, 14583}, {476, 858}, {1552, 34298}, {2072, 14993}, {6344, 6530}, {18384, 37981}, {23969, 34366}, {34310, 40355}

X(43090) = midpoint of X(265) and X(14560)
X(43090) = nine-point-circle-inverse of X(14566)
X(43090) = X(2697)-isoconjugate of X(6149)
X(43090) = barycentric product X(i)*X(j) for these {i,j}: {94, 2781}, {14592, 37937}
X(43090) = barycentric quotient X(i)/X(j) for these {i,j}: {1989, 2697}, {2781, 323}, {37937, 14590}

X(43091) = ISOTOMIC CONJUGATE OF X(530)

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

X(43091) lies on the Steiner circumellipse and these lines: {2, 18777}, {99, 298}, {299, 892}, {301, 35139}, {470, 648}, {523, 9140}, {524, 11092}, {671, 23871}, {2966, 37785}, {5459, 11119}, {9761, 40854}, {11612, 34315}, {19778, 32037}, {30468, 36307}

X(43091) = reflection of X(23895) in X(2)
X(43091) = isotomic conjugate of X(530)
X(43091) = polar conjugate of X(23712)
X(43091) = isotomic conjugate of the isogonal conjugate of X(2378)
X(43091) = X(i)-cross conjugate of X(j) for these (i,j): {530, 2}, {16256, 36316}
X(43091) = X(i)-isoconjugate of X(j) for these (i,j): {31, 530}, {48, 23712}, {163, 9200}, {2151, 11537}, {2152, 18776}
X(43091) = cevapoint of X(2) and X(530)
X(43091) = trilinear pole of line {2, 9201}
X(43091) = barycentric product X(i)*X(j) for these {i,j}: {76, 2378}, {298, 36316}, {16256, 40707}
X(43091) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 530}, {4, 23712}, {13, 11537}, {14, 18776}, {523, 9200}, {2378, 6}, {11537, 42001}, {16256, 396}, {18776, 30469}, {36316, 13}

X(43092) = ISOTOMIC CONJUGATE OF X(531)

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

X(43092) lies on the Steiner circumellipse and these lines: {2, 18776}, {99, 299}, {298, 892}, {300, 35139}, {471, 648}, {523, 9140}, {524, 11078}, {671, 23870}, {2966, 37786}, {5460, 11120}, {9763, 40855}, {11613, 34316}, {19779, 32036}, {30465, 36310}

X(43092) = reflection of X(23896) in X(2)
X(43092) = isotomic conjugate of X(531)
X(43092) = polar conjugate of X(23713)
X(43092) = isotomic conjugate of the isogonal conjugate of X(2379)
X(43092) = X(i)-cross conjugate of X(j) for these (i,j): {531, 2}, {16255, 36317}
X(43092) = X(i)-isoconjugate of X(j) for these (i,j): {31, 531}, {48, 23713}, {163, 9201}, {2151, 18777}, {2152, 11549}
X(43092) = cevapoint of X(2) and X(531)
X(43092) = trilinear pole of line {2, 9200}
X(43092) = barycentric product X(i)*X(j) for these {i,j}: {76, 2379}, {299, 36317}, {16255, 40706}
X(43092) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 531}, {4, 23713}, {13, 18777}, {14, 11549}, {523, 9201}, {2379, 6}, {11549, 42002}, {16255, 395}, {18777, 30466}, {36317, 14}

X(43093) = ISOTOMIC CONJUGATE OF X(674)

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

X(43092) lies on the Steiner circumellipse and these lines: {76, 190}, {99, 310}, {116, 31624}, {316, 39993}, {561, 668}, {664, 6063}, {666, 18031}, {670, 33297}, {2224, 4586}, {3261, 10708}, {4562, 18895}, {18033, 35174}, {23989, 24281}

X(43093) = isogonal conjugate of X(8618)
X(43093) = isotomic conjugate of X(674)
X(43093) = isotomic conjugate of the isogonal conjugate of X(675)
X(43093) = X(i)-cross conjugate of X(j) for these (i,j): {674, 2}, {20045, 308}, {23887, 31624}
X(43093) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8618}, {6, 2225}, {31, 674}, {41, 43039}, {213, 14964}, {560, 3006}, {810, 4249}, {1919, 42723}
X(43093) = cevapoint of X(i) and X(j) for these (i,j): {2, 674}, {116, 23887}
X(43093) = trilinear pole of line {2, 2412}
X(43093) = barycentric product X(i)*X(j) for these {i,j}: {75, 37130}, {76, 675}, {561, 2224}, {36087, 40495}
X(43093) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2225}, {2, 674}, {6, 8618}, {7, 43039}, {76, 3006}, {86, 14964}, {648, 4249}, {668, 42723}, {675, 6}, {2224, 31}, {3261, 23887}, {32682, 32739}, {36087, 692}, {37130, 1}

X(43094) = ISOTOMIC CONJUGATE OF X(702)

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

X(43094) lies on the Steiner circumellipse and these lines: {2, 42371}, {32, 4577}, {39, 670}, {99, 703}, {190, 41267}, {648, 27369}, {668, 21814}, {754, 14946}, {881, 14970}, {886, 40858}, {892, 41272}

X(43094) = reflection of X(42371) in X(2)
X(43094) = isotomic conjugate of X(702)
X(43094) = isotomic conjugate of the isogonal conjugate of X(703)
X(43094) = X(702)-cross conjugate of X(2)
X(43094) = X(i)-isoconjugate of X(j) for these (i,j): {31, 702}, {560, 35526}
X(43094) = cevapoint of X(2) and X(702)
X(43094) = trilinear pole of line {2, 688}
X(43094) = barycentric product X(76)*X(703)
X(43094) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 702}, {76, 35526}, {703, 6}

X(43095) = ISOTOMIC CONJUGATE OF X(716)

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

X(43095) lies on the Steiner circumellipse and these lines: {2, 39347}, {31, 4586}, {99, 717}, {190, 869}, {292, 41072}, {668, 2276}, {670, 40773}, {752, 14945}, {2481, 29956}, {30650, 30667}, {38276, 40382}

X(43095) = midpoint of X(2) and X(39347)
X(43095) = isogonal conjugate of X(8621)
X(43095) = isotomic conjugate of X(716)
X(43095) = isotomic conjugate of the isogonal conjugate of X(717)
X(43095) = X(716)-cross conjugate of X(2)
X(43095) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8621}, {6, 2230}, {31, 716}, {560, 35533}, {1501, 30875}
X(43095) = cevapoint of X(2) and X(716)
X(43095) = trilinear pole of line {2, 788}
X(43095) = barycentric product X(76)*X(717)
X(43095) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2230}, {2, 716}, {6, 8621}, {76, 35533}, {561, 30875}, {717, 6}, {3805, 30641}, {30665, 30640}

X(43096) = ISOTOMIC CONJUGATE OF X(730)

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

X(43096) lies on the Steiner circumellipse and these lines: {6, 4586}, {99, 731}, {190, 2276}, {291, 41072}, {664, 1469}, {668, 984}, {670, 30966}, {742, 3862}, {4569, 7204}, {33514, 38813}, {37133, 38995}

X(43096) = isogonal conjugate of X(8622)
X(43096) = isotomic conjugate of X(730)
X(43096) = isotomic conjugate of the isogonal conjugate of X(731)
X(43096) = X(730)-cross conjugate of X(2)
X(43096) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8622}, {6, 2235}, {31, 730}, {560, 35539}
X(43096) = cevapoint of X(2) and X(730)
X(43096) = trilinear pole of line {2, 3250}
X(43096) = barycentric product X(76)*X(731)
X(43096) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2235}, {2, 730}, {6, 8622}, {76, 35539}, {731, 6}

X(43097) = ISOTOMIC CONJUGATE OF X(752)

Barycentrics    (a^3 + b^3 - 2*c^3)*(a^3 - 2*b^3 + c^3) : :
X(43097) = X[4586] + 2 X[39345]

X(43097) lies on the Steiner circumellipse and these lines: {2, 4586}, {99, 753}, {190, 3661}, {334, 4495}, {561, 31134}, {648, 31909}, {664, 5252}, {666, 5386}, {668, 33931}, {3227, 10708}, {3228, 31175}, {4555, 32847}, {4597, 36480}, {7357, 33767}, {10707, 18822}, {20345, 30635}, {33514, 40415}

X(43097) = midpoint of X(2) and X(39345)
X(43097) = reflection of X(4586) in X(2)
X(43097) = isogonal conjugate of X(8626)
X(43097) = isotomic conjugate of X(752)
X(43097) = isotomic conjugate of the isogonal conjugate of X(753)
X(43097) = X(i)-cross conjugate of X(j) for these (i,j): {752, 2}, {33904, 4586}
X(43097) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8626}, {6, 2243}, {31, 752}, {101, 14438}, {560, 35548}, {604, 4070}, {692, 4809}, {1333, 4144}, {1501, 30874}, {4586, 14402}, {33904, 34069}
X(43097) = cevapoint of X(2) and X(752)
X(43097) = trilinear pole of line {2, 824}
X(43097) = barycentric product X(i)*X(j) for these {i,j}: {76, 753}, {693, 5386}
X(43097) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2243}, {2, 752}, {6, 8626}, {8, 4070}, {10, 4144}, {76, 35548}, {513, 14438}, {514, 4809}, {561, 30874}, {753, 6}, {788, 14402}, {824, 33904}, {3805, 30656}, {5386, 100}, {30665, 30655}, {33904, 33568}

X(43098) = ISOTOMIC CONJUGATE OF X(754)

Barycentrics    (a^4 + b^4 - 2*c^4)*(a^4 - 2*b^4 + c^4) : :
X(43098) = X[4577] - 4 X[15449], X[4577] + 2 X[39346], 2 X[15449] + X[39346], X[15588] - 3 X[21358]

X(43091) lies on the Steiner circumellipse and these lines: {2, 4577}, {30, 14718}, {66, 33768}, {99, 141}, {190, 4683}, {427, 648}, {524, 17949}, {666, 5389}, {670, 8024}, {671, 9479}, {702, 18828}, {892, 7779}, {1502, 7818}, {2966, 20021}, {3228, 9140}, {3329, 23297}, {14617, 33514}, {15588, 21358}, {16077, 40889}, {18822, 31175}, {33515, 40416}

X(43098) = midpoint of X(2) and X(39346)
X(43098) = reflection of X(i) in X(j) for these {i,j}: {2, 15449}, {4577, 2}
X(43098) = isogonal conjugate of X(8627)
X(43098) = isotomic conjugate of X(754)
X(43098) = isotomic conjugate of the isogonal conjugate of X(755)
X(43098) = X(i)-cross conjugate of X(j) for these (i,j): {754, 2}, {33907, 4577}
X(43098) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8627}, {6, 2244}, {31, 754}, {41, 7214}, {163, 14420}, {560, 35549}, {604, 4157}, {662, 14428}, {1333, 4156}, {4593, 14403}, {33907, 34072}
X(43098) = cevapoint of X(i) and X(j) for these (i,j): {2, 754}, {15449, 33907}
X(43098) = trilinear pole of line {2, 826}
X(43098) = barycentric product X(i)*X(j) for these {i,j}: {76, 755}, {693, 5389}
X(43098) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2244}, {2, 754}, {6, 8627}, {7, 7214}, {8, 4157}, {10, 4156}, {76, 35549}, {512, 14428}, {523, 14420}, {688, 14403}, {755, 6}, {826, 33907}, {5389, 100}
X(43098) = {X(15449),X(39346)}-harmonic conjugate of X(4577)

X(43099) = ISOTOMIC CONJUGATE OF X(760)

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

X(43099) lies on the Steiner circumellipse and these lines: {75, 4586}, {99, 761}, {190, 5282}, {664, 5263}, {666, 742}, {668, 3416}, {1892, 18026}, {17281, 32041}, {18895, 41072}, {33514, 38810}

X(43099) = isogonal conjugate of X(8628)
X(43099) = isotomic conjugate of X(760)
X(43099) = isotomic conjugate of the isogonal conjugate of X(761)
X(43099) = X(760)-cross conjugate of X(2)
X(43099) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8628}, {31, 760}, {32, 4766}, {560, 35551}
X(43099) = cevapoint of X(2) and X(760)
X(43099) = barycentric product X(i)*X(j) for these {i,j}: {75, 37208}, {76, 761}
X(43099) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 760}, {6, 8628}, {75, 4766}, {76, 35551}, {761, 6}, {37208, 1}

X(43100) = GIBERT (-9,7,20) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 20*a^2*SA - 14*SB*SC : :
X(43100) = X[10646] - 7 X[16242], 11 X[10646] + 7 X[16809], 2 X[10646] + 7 X[23303], 5 X[10646] + 7 X[37835], 20 X[10646] + 7 X[42101], 13 X[10646] + 14 X[42143], 13 X[10646] - 7 X[42528], 11 X[16242] + X[16809], 2 X[16242] + X[23303], 5 X[16242] + X[37835], 20 X[16242] + X[42101], 13 X[16242] + 2 X[42143], 13 X[16242] - X[42528], 2 X[16809] - 11 X[23303], 5 X[16809] - 11 X[37835], 20 X[16809] - 11 X[42101], 13 X[16809] - 22 X[42143], 13 X[16809] + 11 X[42528], 5 X[23303] - 2 X[37835], 10 X[23303] - X[42101], 13 X[23303] - 4 X[42143], 13 X[23303] + 2 X[42528], 4 X[37835] - X[42101], 13 X[37835] - 10 X[42143], 13 X[37835] + 5 X[42528], 13 X[42101] - 40 X[42143], 13 X[42101] + 20 X[42528], 2 X[42143] + X[42528]

X(43100) lies on the cubic K1218 and these lines: {2, 397}, {3, 41120}, {4, 42586}, {5, 10187}, {6, 15709}, {14, 17504}, {16, 15699}, {18, 12100}, {20, 43003}, {30, 10646}, {61, 15713}, {62, 10124}, {140, 3411}, {376, 42491}, {381, 42792}, {395, 5054}, {396, 11539}, {398, 549}, {546, 42793}, {547, 42148}, {548, 42978}, {632, 42979}, {3523, 42791}, {3524, 5334}, {3530, 41108}, {3534, 5349}, {3545, 42094}, {3628, 41100}, {3839, 11481}, {3845, 42489}, {5055, 5318}, {5066, 5237}, {5070, 41112}, {5071, 5366}, {5321, 10304}, {5339, 15698}, {5351, 15687}, {5365, 42587}, {8703, 42163}, {10654, 15707}, {11480, 42778}, {11486, 42777}, {11489, 15708}, {11540, 43019}, {11542, 41984}, {11543, 41983}, {11737, 42158}, {11812, 42419}, {12101, 42433}, {12103, 42958}, {12817, 15691}, {14093, 42159}, {14269, 42088}, {14890, 42912}, {14891, 16964}, {14892, 36969}, {14893, 42580}, {15022, 42588}, {15685, 42920}, {15688, 18581}, {15689, 42129}, {15690, 42814}, {15692, 42153}, {15693, 42147}, {15694, 42149}, {15697, 42495}, {15700, 41113}, {15701, 40694}, {15702, 16772}, {15703, 42166}, {15705, 42154}, {15711, 42157}, {15718, 42150}, {15720, 42511}, {15721, 22236}, {15723, 40693}, {16241, 42635}, {16267, 33416}, {16960, 42893}, {16966, 41985}, {16967, 38071}, {19708, 42774}, {19709, 42165}, {23046, 36968}, {33699, 42505}, {34200, 41122}, {36967, 42628}, {37641, 42500}, {37832, 42954}, {38335, 42107}, {41987, 42918}, {42087, 42972}, {42127, 42985}, {42141, 42933}, {42506, 43027}, {42507, 42925}, {42533, 42936}, {42584, 42796}, {42596, 42801}, {42952, 42994} on K1218

X(43100) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 42944, 42792}, {395, 42089, 42501}, {11539, 16963, 396}, {11539, 42121, 16963}, {15703, 42510, 42166}, {16773, 42948, 42598}, {33417, 42634, 396}, {34200, 41122, 42164}, {42580, 42631, 14893}

X(43101) = GIBERT (-3,7,8) POINT

Barycentrics    Sqrt[3]*a^2*S - 8*a^2*SA - 14*SB*SC : :
X(43101) = 2 X[16967] + X[42107]

X(43101) lies on the cubic K1218 and these lines: {2, 5321}, {4, 42491}, {5, 13}, {6, 5071}, {14, 547}, {15, 15699}, {16, 5066}, {17, 12812}, {20, 42948}, {30, 16967}, {61, 35018}, {140, 36970}, {376, 42101}, {381, 23303}, {396, 5055}, {398, 3090}, {546, 36968}, {549, 16809}, {616, 33474}, {618, 31694}, {631, 5349}, {632, 42814}, {1656, 10654}, {3091, 5350}, {3523, 42611}, {3524, 42093}, {3526, 42164}, {3534, 42103}, {3544, 5340}, {3545, 5318}, {3627, 42528}, {3628, 16241}, {3830, 42089}, {3839, 11481}, {3845, 16242}, {3850, 42165}, {3851, 42148}, {3853, 42591}, {3855, 36843}, {3856, 42431}, {3857, 42158}, {3858, 5237}, {3860, 42123}, {3861, 5351}, {5054, 42087}, {5056, 37640}, {5067, 5339}, {5068, 22238}, {5070, 42159}, {5072, 42149}, {5079, 40694}, {5343, 42490}, {5460, 6669}, {6670, 37352}, {7486, 22236}, {8703, 33416}, {10109, 11543}, {10124, 10645}, {10170, 36980}, {10303, 42776}, {10612, 41621}, {10616, 31706}, {10646, 15687}, {10653, 19709}, {11485, 41120}, {11539, 36967}, {11542, 16268}, {11737, 16808}, {11812, 42136}, {12100, 19107}, {12101, 42100}, {12102, 42593}, {12811, 16965}, {12817, 15713}, {12821, 34200}, {14093, 42112}, {14269, 42109}, {14845, 36978}, {14869, 42432}, {14892, 16963}, {14893, 42928}, {15022, 42156}, {15684, 42985}, {15688, 42104}, {15692, 42096}, {15694, 42085}, {15701, 42090}, {15702, 42133}, {15703, 42125}, {15708, 42140}, {15723, 42963}, {15765, 42266}, {16239, 42157}, {16961, 41121}, {16966, 41122}, {17504, 42099}, {18582, 42502}, {18585, 42267}, {19106, 23046}, {30471, 37647}, {33417, 42972}, {33458, 33627}, {33561, 37340}, {33603, 42509}, {33703, 42774}, {35403, 42113}, {36969, 38071}, {37641, 42098}, {38335, 42091}, {41099, 42792}, {41100, 42138}, {41106, 42094}, {41108, 42124}, {41113, 42984}, {41944, 41972}, {41973, 43032}, {41983, 42585}, {42105, 42686}, {42114, 42974}, {42122, 42795}, {42142, 42517}, {42146, 42497}, {42429, 42954}, {42479, 42983}, {42512, 42950}, {42956, 42996}

X(43101) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42139, 42154}, {2, 42942, 42500}, {5, 18, 42166}, {5, 37835, 395}, {5, 42599, 397}, {6, 42475, 5071}, {6, 42778, 42899}, {14, 547, 23302}, {14, 42914, 547}, {376, 43028, 42501}, {381, 23303, 42943}, {381, 42910, 23303}, {381, 42943, 42102}, {395, 37835, 42599}, {546, 42489, 42944}, {547, 42143, 14}, {549, 16809, 42940}, {1656, 42163, 16772}, {3091, 16773, 5350}, {3526, 42920, 42164}, {3545, 16645, 5318}, {3628, 42147, 42949}, {3845, 16242, 42088}, {5055, 18581, 396}, {5055, 42975, 42911}, {5056, 42153, 42598}, {5070, 42159, 42945}, {5321, 42500, 42942}, {5321, 42791, 42154}, {7486, 42495, 22236}, {10109, 11543, 37832}, {10653, 19709, 42110}, {11539, 42135, 36967}, {11737, 42913, 16808}, {11812, 42136, 42529}, {15702, 42133, 42626}, {16242, 42918, 3845}, {18581, 42911, 42975}, {19709, 42129, 10653}, {38071, 42121, 36969}, {41943, 43021, 42912}, {42086, 42951, 23303}, {42101, 42501, 376}, {42111, 42910, 381}, {42143, 42914, 23302}, {42911, 42975, 396}

X(43102) = GIBERT (-2,3,7) POINT

Barycentrics    2*a^2*S/Sqrt[3] - 7*a^2*SA - 6*SB*SC : :
X(43102) = 3 X[16967] - X[42107]

X(43102) lies on the cubic K1218 and these lines: {2, 11486}, {3, 42133}, {5, 11481}, {6, 632}, {14, 11812}, {15, 18}, {16, 3628}, {30, 16967}, {62, 42590}, {395, 10124}, {396, 42594}, {546, 10646}, {547, 5318}, {548, 16809}, {549, 18581}, {550, 42095}, {625, 6672}, {629, 34573}, {630, 3631}, {631, 42117}, {1656, 5344}, {2045, 42211}, {2046, 42213}, {3090, 42115}, {3091, 42145}, {3411, 42498}, {3523, 42125}, {3524, 42126}, {3525, 11485}, {3526, 11489}, {3530, 5321}, {3534, 42985}, {3545, 42131}, {3619, 11310}, {3627, 42111}, {3830, 42473}, {3845, 42091}, {3850, 42088}, {3853, 42918}, {3857, 42105}, {3858, 42097}, {3859, 42433}, {3860, 42931}, {3861, 42100}, {5054, 5334}, {5055, 42120}, {5056, 42127}, {5066, 19106}, {5067, 42128}, {5070, 5335}, {5072, 42141}, {5079, 42134}, {5159, 10635}, {5237, 12812}, {5326, 5357}, {5351, 12811}, {5353, 7294}, {7499, 37775}, {8703, 42093}, {10109, 12816}, {10187, 19107}, {10188, 42801}, {10303, 42116}, {10645, 12108}, {10654, 15713}, {11268, 32144}, {11476, 37942}, {11480, 14869}, {11539, 16645}, {11540, 16241}, {11737, 36968}, {12100, 37835}, {12101, 42528}, {12103, 42101}, {14890, 42687}, {14891, 36970}, {14892, 42941}, {15694, 42818}, {15699, 42098}, {15704, 42103}, {15709, 42975}, {15712, 42085}, {15717, 42130}, {15720, 42119}, {15723, 37640}, {15759, 42940}, {16239, 23302}, {16268, 42500}, {16772, 16961}, {16773, 16966}, {16808, 35018}, {16960, 41944}, {16963, 41984}, {18538, 42249}, {18582, 42922}, {18762, 42247}, {19711, 42626}, {23046, 42625}, {32789, 35738}, {34200, 42099}, {34755, 42598}, {35381, 42516}, {36836, 42923}, {36843, 42114}, {36967, 41983}, {41992, 42492}, {42148, 42915}, {42149, 43029}, {42157, 42902}, {42158, 42686}, {42163, 42970}, {42431, 42685}, {42481, 42532}, {42499, 42936}, {42595, 43014}, {42596, 43015}, {42683, 42792}, {42813, 42971}, {42938, 43030}

X(43102) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42121, 11542}, {3, 42135, 42585}, {3, 42139, 42144}, {3, 42143, 42136}, {3, 42951, 42139}, {5, 11481, 42137}, {15, 23303, 42628}, {15, 42628, 11543}, {15, 43005, 398}, {16, 3628, 42146}, {140, 23303, 11543}, {140, 42628, 15}, {546, 10646, 42584}, {549, 18581, 42122}, {631, 42129, 42117}, {3090, 42115, 42138}, {3526, 11489, 42124}, {11481, 42137, 42123}, {11486, 42132, 42982}, {11539, 16645, 42912}, {11540, 42497, 16241}, {11542, 42121, 42913}, {23303, 33416, 140}, {23303, 42948, 33416}, {33416, 42937, 23303}, {33417, 42897, 41943}, {37835, 42501, 12100}, {42086, 42089, 42491}, {42088, 42914, 3850}, {42089, 42493, 42137}, {42089, 43028, 5}, {42094, 43028, 42611}, {42135, 42585, 42136}, {42143, 42585, 42135}, {42144, 42951, 42143}, {42564, 42565, 42948}, {42937, 42948, 140}

X(43103) = GIBERT (2,3,7) POINT

Barycentrics    2*a^2*S/Sqrt[3] + 7*a^2*SA + 6*SB*SC : :

X(43103) = 3 X[16966] - X[42110]

X(43103) lies on the cubic K1218 and these lines: {2, 11485}, {3, 42134}, {5, 11480}, {6, 632}, {13, 11812}, {15, 3628}, {16, 17}, {30, 16966}, {61, 42591}, {395, 42595}, {396, 10124}, {546, 10645}, {547, 5321}, {548, 16808}, {549, 18582}, {550, 42098}, {625, 6671}, {629, 3631}, {630, 34573}, {631, 42118}, {1656, 5343}, {2045, 42214}, {2046, 42212}, {3090, 42116}, {3091, 42144}, {3412, 42499}, {3523, 42128}, {3524, 42127}, {3525, 11486}, {3526, 11488}, {3530, 5318}, {3534, 42984}, {3545, 42130}, {3619, 11309}, {3627, 42114}, {3830, 42472}, {3845, 42090}, {3850, 42087}, {3853, 42919}, {3857, 42104}, {3858, 42096}, {3859, 42434}, {3860, 42930}, {3861, 42099}, {5054, 5335}, {5055, 42119}, {5056, 42126}, {5066, 19107}, {5067, 42125}, {5070, 5334}, {5072, 42140}, {5079, 42133}, {5159, 10634}, {5238, 12812}, {5326, 5353}, {5352, 12811}, {5357, 7294}, {7499, 37776}, {8703, 42094}, {10109, 12817}, {10187, 42802}, {10188, 19106}, {10303, 42115}, {10646, 12108}, {10653, 15713}, {11267, 32144}, {11475, 37942}, {11481, 14869}, {11539, 16644}, {11540, 16242}, {11737, 36967}, {12100, 37832}, {12101, 42529}, {12103, 42102}, {14890, 42686}, {14891, 36969}, {14892, 42940}, {15694, 42817}, {15699, 42095}, {15704, 42106}, {15709, 42974}, {15712, 42086}, {15717, 42131}, {15720, 42120}, {15723, 37641}, {15759, 42941}, {16239, 23303}, {16267, 42501}, {16772, 16967}, {16773, 16960}, {16809, 35018}, {16961, 41943}, {16962, 41984}, {18538, 42248}, {18581, 42923}, {18762, 42246}, {19711, 42625}, {23046, 42626}, {32790, 35738}, {34200, 42100}, {34754, 42599}, {35381, 42517}, {36836, 42111}, {36843, 42922}, {36968, 41983}, {41992, 42493}, {42147, 42914}, {42152, 43028}, {42157, 42687}, {42158, 42903}, {42166, 42971}, {42432, 42684}, {42480, 42533}, {42498, 42937}, {42594, 43015}, {42597, 43014}, {42682, 42791}, {42814, 42970}, {42939, 43031}

X(43103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42124, 11543}, {3, 42138, 42584}, {3, 42142, 42145}, {3, 42146, 42137}, {3, 42950, 42142}, {5, 11480, 42136}, {15, 3628, 42143}, {16, 23302, 42627}, {16, 42627, 11542}, {16, 43004, 397}, {140, 23302, 11542}, {140, 42627, 16}, {546, 10645, 42585}, {549, 18582, 42123}, {631, 42132, 42118}, {3090, 42116, 42135}, {3526, 11488, 42121}, {11480, 42136, 42122}, {11485, 42129, 42983}, {11539, 16644, 42913}, {11540, 42496, 16242}, {11543, 42124, 42912}, {23302, 33417, 140}, {23302, 42949, 33417}, {33416, 42896, 41944}, {33417, 42936, 23302}, {37832, 42500, 12100}, {42085, 42092, 42490}, {42087, 42915, 3850}, {42092, 42492, 42136}, {42092, 43029, 5}, {42093, 43029, 42610}, {42138, 42584, 42137}, {42145, 42950, 42146}, {42146, 42584, 42138}, {42562, 42563, 42949}, {42936, 42949, 140}

X(43104) = GIBERT (3,7,8) POINT

Barycentrics    Sqrt[3]*a^2*S + 8*a^2*SA + 14*SB*SC : :
X(43104) = 2 X[16966] + X[42110]

X(43104) lies on the cubic K1218 and these lines: {2, 5318}, {4, 42490}, {5, 14}, {6, 5071}, {13, 547}, {15, 5066}, {16, 15699}, {18, 12812}, {20, 42949}, {30, 16966}, {62, 35018}, {140, 36969}, {376, 42102}, {381, 23302}, {395, 5055}, {397, 3090}, {546, 36967}, {549, 16808}, {617, 33475}, {619, 31693}, {631, 5350}, {632, 42813}, {1656, 10653}, {3091, 5349}, {3523, 42610}, {3524, 42094}, {3526, 42165}, {3534, 42106}, {3544, 5339}, {3545, 5321}, {3627, 42529}, {3628, 16242}, {3830, 42092}, {3839, 11480}, {3845, 16241}, {3850, 42164}, {3851, 42147}, {3853, 42590}, {3855, 36836}, {3856, 42432}, {3857, 42157}, {3858, 5238}, {3860, 42122}, {3861, 5352}, {5054, 42088}, {5056, 37641}, {5067, 5340}, {5068, 22236}, {5070, 42162}, {5072, 42152}, {5079, 40693}, {5344, 42491}, {5459, 6670}, {6669, 37351}, {7486, 22238}, {8703, 33417}, {10109, 11542}, {10124, 10646}, {10170, 36978}, {10303, 42775}, {10611, 41620}, {10617, 31705}, {10645, 15687}, {10654, 19709}, {11486, 41119}, {11539, 36968}, {11543, 16267}, {11737, 16809}, {11812, 42137}, {12100, 19106}, {12101, 42099}, {12102, 42592}, {12811, 16964}, {12816, 15713}, {12820, 34200}, {14093, 42113}, {14269, 42108}, {14845, 36980}, {14869, 42431}, {14892, 16962}, {14893, 42929}, {15022, 42153}, {15684, 42984}, {15688, 42105}, {15692, 42097}, {15694, 42086}, {15701, 42091}, {15702, 42134}, {15703, 42128}, {15708, 42141}, {15723, 42962}, {15765, 42267}, {16239, 42158}, {16960, 41122}, {16967, 41121}, {17504, 42100}, {18581, 42503}, {18585, 42266}, {19107, 23046}, {30472, 37647}, {33416, 42973}, {33459, 33626}, {33560, 37341}, {33602, 42508}, {33703, 42773}, {35403, 42112}, {36970, 38071}, {37640, 42095}, {38335, 42090}, {41099, 42791}, {41101, 42135}, {41106, 42093}, {41107, 42121}, {41112, 42985}, {41943, 41971}, {41974, 43033}, {41983, 42584}, {42104, 42687}, {42111, 42975}, {42123, 42796}, {42139, 42516}, {42143, 42496}, {42430, 42955}, {42478, 42982}, {42513, 42951}, {42957, 42997}

X(43104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42142, 42155}, {2, 42943, 42501}, {5, 17, 42163}, {5, 37832, 396}, {5, 42598, 398}, {6, 42474, 5071}, {6, 42777, 42898}, {13, 547, 23303}, {13, 42915, 547}, {376, 43029, 42500}, {381, 23302, 42942}, {381, 42911, 23302}, {381, 42942, 42101}, {396, 37832, 42598}, {546, 42488, 42945}, {547, 42146, 13}, {549, 16808, 42941}, {1656, 42166, 16773}, {3091, 16772, 5349}, {3526, 42921, 42165}, {3545, 16644, 5321}, {3628, 42148, 42948}, {3845, 16241, 42087}, {5055, 18582, 395}, {5055, 42974, 42910}, {5056, 42156, 42599}, {5070, 42162, 42944}, {5318, 42501, 42943}, {5318, 42792, 42155}, {7486, 42494, 22238}, {10109, 11542, 37835}, {10654, 19709, 42107}, {11539, 42138, 36968}, {11737, 42912, 16809}, {11812, 42137, 42528}, {15702, 42134, 42625}, {16241, 42919, 3845}, {18582, 42910, 42974}, {19709, 42132, 10654}, {38071, 42124, 36970}, {41944, 43020, 42913}, {42085, 42950, 23302}, {42102, 42500, 376}, {42114, 42911, 381}, {42146, 42915, 23303}, {42910, 42974, 395}

X(43105) = GIBERT (5,-3,4) POINT

Barycentrics    5*a^2*S/Sqrt[3] + 4*a^2*SA - 6*SB*SC : :

X(43105) lies on the cubic K1218 and these lines: {2, 5321}, {5, 42906}, {6, 3529}, {14, 17504}, {15, 546}, {16, 398}, {30, 42415}, {61, 42109}, {62, 42585}, {140, 42684}, {381, 42682}, {382, 5318}, {395, 15688}, {396, 15687}, {397, 42096}, {548, 42890}, {632, 42964}, {1656, 42687}, {3528, 5334}, {3530, 16964}, {3544, 36836}, {3627, 34754}, {3830, 42777}, {3851, 5349}, {3853, 16960}, {3855, 16772}, {5079, 42107}, {5238, 42135}, {5339, 10299}, {5343, 43028}, {5352, 42143}, {5365, 42949}, {8703, 16961}, {10304, 42778}, {10645, 14869}, {10654, 15681}, {11481, 42782}, {11542, 42432}, {11543, 34200}, {11737, 16966}, {12103, 34755}, {12812, 42955}, {12820, 16267}, {12821, 37832}, {14269, 18582}, {15693, 42690}, {15696, 42685}, {15700, 42089}, {15707, 42129}, {15710, 42626}, {15713, 42795}, {15715, 16645}, {15716, 42513}, {15720, 18581}, {16241, 42492}, {16242, 42503}, {16808, 42916}, {16809, 35018}, {19106, 42779}, {22236, 42102}, {36969, 42898}, {36970, 38071}, {41101, 42941}, {42094, 42986}, {42099, 42148}, {42104, 42166}, {42112, 42165}, {42121, 42434}, {42158, 42416}, {42211, 42239}, {42213, 42240}, {42511, 42817}, {42612, 42922}, {42628, 42946}, {42636, 43015}, {42792, 42975}, {42794, 42920}, {42797, 42993}, {42816, 42944}, {42888, 42912}, {42929, 42937}

X(43105) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15, 42101, 42598}, {15, 42136, 42110}, {15, 42164, 42101}, {15, 42630, 546}, {61, 42144, 42109}, {3853, 16960, 42693}, {5321, 42119, 42942}, {8703, 16961, 42686}, {10654, 42130, 42088}, {11485, 42085, 42108}, {11485, 42108, 5318}, {16964, 42122, 23303}, {22236, 42140, 42102}, {23302, 42126, 5349}, {42085, 42147, 5318}, {42087, 42117, 398}, {42108, 42147, 11485}, {42110, 42136, 42101}, {42110, 42164, 42136}, {42116, 42160, 42107}, {42117, 42157, 42087}, {42119, 42154, 5321}, {42126, 42150, 23302}, {42687, 42692, 1656}

X(43106) = GIBERT (5,3,-4) POINT

Barycentrics    5*a^2*S/Sqrt[3] - 4*a^2*SA + 6*SB*SC : :

X(43106) lies on the cubic K1218 and these lines: {2, 5318}, {5, 42907}, {6, 3529}, {13, 17504}, {15, 397}, {16, 546}, {30, 42416}, {61, 42584}, {62, 42108}, {140, 42685}, {381, 42683}, {382, 5321}, {395, 15687}, {396, 15688}, {398, 42097}, {548, 42891}, {632, 42965}, {1656, 42686}, {3528, 5335}, {3530, 16965}, {3544, 36843}, {3627, 34755}, {3830, 42778}, {3851, 5350}, {3853, 16961}, {3855, 16773}, {5079, 42110}, {5237, 42138}, {5340, 10299}, {5344, 43029}, {5351, 42146}, {5366, 42948}, {8703, 16960}, {10304, 42777}, {10646, 14869}, {10653, 15681}, {11480, 42781}, {11542, 34200}, {11543, 42431}, {11737, 16967}, {12103, 34754}, {12812, 42954}, {12820, 37835}, {12821, 16268}, {14269, 18581}, {15693, 42691}, {15696, 42684}, {15700, 42092}, {15707, 42132}, {15710, 42625}, {15713, 42796}, {15715, 16644}, {15716, 42512}, {15720, 18582}, {16241, 42502}, {16242, 42493}, {16808, 35018}, {16809, 42917}, {19107, 42780}, {22238, 42101}, {35740, 42214}, {36969, 38071}, {36970, 42899}, {41100, 42940}, {42093, 42987}, {42100, 42147}, {42105, 42163}, {42113, 42164}, {42124, 42433}, {42157, 42415}, {42212, 42241}, {42510, 42818}, {42613, 42923}, {42627, 42947}, {42635, 43014}, {42791, 42974}, {42793, 42921}, {42798, 42992}, {42815, 42945}, {42889, 42913}, {42928, 42936}

X(43106) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16, 42102, 42599}, {16, 42137, 42107}, {16, 42165, 42102}, {16, 42629, 546}, {62, 42145, 42108}, {3853, 16961, 42692}, {5318, 42120, 42943}, {8703, 16960, 42687}, {10653, 42131, 42087}, {11486, 42086, 42109}, {11486, 42109, 5321}, {16965, 42123, 23302}, {22238, 42141, 42101}, {23303, 42127, 5350}, {42086, 42148, 5321}, {42088, 42118, 397}, {42107, 42137, 42102}, {42107, 42165, 42137}, {42109, 42148, 11486}, {42115, 42161, 42110}, {42118, 42158, 42088}, {42120, 42155, 5318}, {42127, 42151, 23303}, {42686, 42693, 1656}

X(43107) = GIBERT (9,7,20) POINT

Barycentrics    3*Sqrt[3]*a^2*S + 20*a^2*SA + 14*SB*SC : :
X(43107) = X[10645] - 7 X[16241], 11 X[10645] + 7 X[16808], 2 X[10645] + 7 X[23302], 5 X[10645] + 7 X[37832], 20 X[10645] + 7 X[42102], 13 X[10645] + 14 X[42146], 13 X[10645] - 7 X[42529], 11 X[16241] + X[16808], 2 X[16241] + X[23302], 5 X[16241] + X[37832], 20 X[16241] + X[42102], 13 X[16241] + 2 X[42146], 13 X[16241] - X[42529], 2 X[16808] - 11 X[23302], 5 X[16808] - 11 X[37832], 20 X[16808] - 11 X[42102], 13 X[16808] - 22 X[42146], 13 X[16808] + 11 X[42529], 5 X[23302] - 2 X[37832], 10 X[23302] - X[42102], 13 X[23302] - 4 X[42146], 13 X[23302] + 2 X[42529], 4 X[37832] - X[42102], 13 X[37832] - 10 X[42146], 13 X[37832] + 5 X[42529], 13 X[42102] - 40 X[42146], 13 X[42102] + 20 X[42529], 2 X[42146] + X[42529]

X(43107) lies on the cubic K1218 and these lines: {2, 398}, {3, 41119}, {4, 42587}, {5, 10188}, {6, 15709}, {13, 17504}, {15, 15699}, {17, 12100}, {20, 43002}, {30, 10645}, {61, 10124}, {62, 15713}, {140, 3412}, {376, 42490}, {381, 42791}, {395, 11539}, {396, 5054}, {397, 549}, {546, 42794}, {547, 42147}, {548, 42979}, {632, 42978}, {3523, 42792}, {3524, 5335}, {3530, 41107}, {3534, 5350}, {3545, 42093}, {3628, 41101}, {3839, 11480}, {3845, 42488}, {5055, 5321}, {5066, 5238}, {5070, 41113}, {5071, 5365}, {5318, 10304}, {5340, 15698}, {5352, 15687}, {5366, 42586}, {8703, 42166}, {10653, 15707}, {11481, 42777}, {11485, 42778}, {11488, 15708}, {11540, 43018}, {11542, 41983}, {11543, 41984}, {11737, 42157}, {11812, 42420}, {12101, 42434}, {12103, 42959}, {12816, 15691}, {14093, 42162}, {14269, 42087}, {14890, 42913}, {14891, 16965}, {14892, 36970}, {14893, 42581}, {15022, 42589}, {15685, 42921}, {15688, 18582}, {15689, 42132}, {15690, 42813}, {15692, 42156}, {15693, 42148}, {15694, 42152}, {15697, 42494}, {15700, 41112}, {15701, 40693}, {15702, 16773}, {15703, 42163}, {15705, 42155}, {15711, 42158}, {15718, 42151}, {15720, 42510}, {15721, 22238}, {15723, 40694}, {16242, 42636}, {16268, 33417}, {16961, 42892}, {16966, 38071}, {16967, 41985}, {19708, 42773}, {19709, 42164}, {23046, 36967}, {33699, 42504}, {34200, 41121}, {36968, 42627}, {37640, 42501}, {37835, 42955}, {38335, 42110}, {41987, 42919}, {42088, 42973}, {42126, 42984}, {42140, 42932}, {42506, 42924}, {42507, 43026}, {42532, 42937}, {42585, 42795}, {42597, 42802}, {42953, 42995}

X(43107) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 42945, 42791}, {396, 42092, 42500}, {11539, 16962, 395}, {11539, 42124, 16962}, {15703, 42511, 42163}, {16772, 42949, 42599}, {33416, 42633, 395}, {34200, 41121, 42165}, {42581, 42632, 14893}

X(43108) = GIBERT (18,-7,13) POINT

Barycentrics    6*Sqrt[3]*a^2*S + 13*a^2*SA - 14*SB*SC : :
X(43108) = 13 X[61] - 7 X[397], 19 X[61] - 7 X[16965], 3 X[61] - 7 X[41101], 15 X[61] - 7 X[41107], X[61] - 7 X[42147], 5 X[61] + 7 X[42157], 25 X[61] - 7 X[42165], 31 X[61] - 7 X[42431], 39 X[61] - 35 X[42520], 4 X[61] - 7 X[42925], 19 X[397] - 13 X[16965], 3 X[397] - 13 X[41101], 15 X[397] - 13 X[41107], X[397] - 13 X[42147], 5 X[397] + 13 X[42157], 25 X[397] - 13 X[42165], 31 X[397] - 13 X[42431], 3 X[397] - 5 X[42520], 4 X[397] - 13 X[42925], 3 X[16965] - 19 X[41101], 15 X[16965] - 19 X[41107], X[16965] - 19 X[42147], 5 X[16965] + 19 X[42157], 25 X[16965] - 19 X[42165], 31 X[16965] - 19 X[42431], 39 X[16965] - 95 X[42520], 4 X[16965] - 19 X[42925], 5 X[41101] - X[41107], X[41101] - 3 X[42147], 5 X[41101] + 3 X[42157], 25 X[41101] - 3 X[42165], 31 X[41101] - 3 X[42431], 13 X[41101] - 5 X[42520], 4 X[41101] - 3 X[42925], X[41107] - 15 X[42147], X[41107] + 3 X[42157], 5 X[41107] - 3 X[42165], 31 X[41107] - 15 X[42431], 13 X[41107] - 25 X[42520], 4 X[41107] - 15 X[42925], 5 X[42147] + X[42157], 25 X[42147] - X[42165], 31 X[42147] - X[42431], 39 X[42147] - 5 X[42520], 4 X[42147] - X[42925], 5 X[42157] + X[42165], 31 X[42157] + 5 X[42431], 39 X[42157] + 25 X[42520], 4 X[42157] + 5 X[42925], 31 X[42165] - 25 X[42431], 39 X[42165] - 125 X[42520], 4 X[42165] - 25 X[42925], 39 X[42431] - 155 X[42520], 4 X[42431] - 31 X[42925], 20 X[42520] - 39 X[42925]

X(43108) lies on the cubic K1218 and these lines: {2, 33603}, {6, 19710}, {14, 11812}, {15, 5066}, {16, 42415}, {18, 41983}, {30, 61}, {62, 15691}, {140, 41122}, {381, 42589}, {395, 15759}, {396, 12101}, {398, 34200}, {547, 16964}, {548, 42792}, {549, 41113}, {550, 42510}, {3530, 41973}, {3534, 42119}, {3543, 33602}, {3628, 42972}, {3830, 11542}, {3845, 18582}, {3850, 41943}, {3853, 16267}, {3860, 36970}, {5238, 10124}, {5318, 42532}, {5321, 10109}, {5334, 15693}, {5339, 11539}, {5343, 15703}, {5351, 42899}, {8358, 12154}, {8703, 10654}, {11001, 42131}, {11480, 15713}, {11485, 15682}, {11486, 15697}, {11489, 15716}, {11543, 12100}, {11737, 16772}, {12816, 34754}, {14269, 42775}, {14890, 42489}, {14891, 16268}, {14893, 16962}, {15640, 42974}, {15685, 42118}, {15686, 42924}, {15687, 22236}, {15689, 42999}, {15690, 34755}, {15695, 37641}, {15698, 42121}, {15699, 36836}, {15700, 43002}, {15702, 42591}, {15714, 42149}, {15719, 33605}, {16645, 19711}, {16963, 33923}, {17504, 42774}, {19107, 33607}, {19708, 42975}, {19709, 42124}, {23046, 42152}, {33606, 42684}, {33699, 42085}, {35404, 40693}, {36363, 36772}, {36449, 42226}, {36468, 42225}, {37640, 42144}, {38071, 42160}, {41099, 42126}, {41100, 42087}, {41112, 42137}, {41121, 42940}, {41990, 42103}, {42088, 42799}, {42090, 42634}, {42503, 42628}, {42590, 42814}, {42782, 42931}

X(43108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 42791, 11812}, {395, 42632, 15759}, {3845, 42511, 42912}, {10654, 42122, 42913}, {11480, 41120, 15713}, {12100, 41108, 11543}, {16962, 42164, 14893}, {19710, 42419, 42420}, {41101, 42157, 41107}, {41108, 42942, 12100}, {42154, 42511, 3845}, {42154, 42912, 42136}

X(43109) = GIBERT (18,7,-13) POINT

Barycentrics    6*Sqrt[3]*a^2*S - 13*a^2*SA + 14*SB*SC : :
X(43109) = 13 X[62] - 7 X[398], 19 X[62] - 7 X[16964], 3 X[62] - 7 X[41100], 15 X[62] - 7 X[41108], X[62] - 7 X[42148], 5 X[62] + 7 X[42158], 25 X[62] - 7 X[42164], 31 X[62] - 7 X[42432], 39 X[62] - 35 X[42521], 4 X[62] - 7 X[42924], 19 X[398] - 13 X[16964], 3 X[398] - 13 X[41100], 15 X[398] - 13 X[41108], X[398] - 13 X[42148], 5 X[398] + 13 X[42158], 25 X[398] - 13 X[42164], 31 X[398] - 13 X[42432], 3 X[398] - 5 X[42521], 4 X[398] - 13 X[42924], 3 X[16964] - 19 X[41100], 15 X[16964] - 19 X[41108], X[16964] - 19 X[42148], 5 X[16964] + 19 X[42158], 25 X[16964] - 19 X[42164], 31 X[16964] - 19 X[42432], 39 X[16964] - 95 X[42521], 4 X[16964] - 19 X[42924], 5 X[41100] - X[41108], X[41100] - 3 X[42148], 5 X[41100] + 3 X[42158], 25 X[41100] - 3 X[42164], 31 X[41100] - 3 X[42432], 13 X[41100] - 5 X[42521], 4 X[41100] - 3 X[42924], X[41108] - 15 X[42148], X[41108] + 3 X[42158], 5 X[41108] - 3 X[42164], 31 X[41108] - 15 X[42432], 13 X[41108] - 25 X[42521], 4 X[41108] - 15 X[42924], 5 X[42148] + X[42158], 25 X[42148] - X[42164], 31 X[42148] - X[42432], 39 X[42148] - 5 X[42521], 4 X[42148] - X[42924], 5 X[42158] + X[42164], 31 X[42158] + 5 X[42432], 39 X[42158] + 25 X[42521], 4 X[42158] + 5 X[42924], 31 X[42164] - 25 X[42432], 39 X[42164] - 125 X[42521], 4 X[42164] - 25 X[42924], 39 X[42432] - 155 X[42521], 4 X[42432] - 31 X[42924], 20 X[42521] - 39 X[42924]

X(43109) lies on the cubic K1218 and these lines: {2, 33602}, {6, 19710}, {13, 11812}, {15, 42416}, {16, 5066}, {17, 41983}, {30, 62}, {61, 15691}, {140, 41121}, {381, 42588}, {395, 12101}, {396, 15759}, {397, 34200}, {547, 16965}, {548, 42791}, {549, 41112}, {550, 42511}, {3530, 41974}, {3534, 42120}, {3543, 33603}, {3628, 42973}, {3830, 11543}, {3845, 18581}, {3850, 41944}, {3853, 16268}, {3860, 36969}, {5237, 10124}, {5318, 10109}, {5321, 42533}, {5335, 15693}, {5340, 11539}, {5344, 15703}, {5352, 42898}, {8358, 12155}, {8703, 10653}, {11001, 42130}, {11481, 15713}, {11485, 15697}, {11486, 15682}, {11488, 15716}, {11542, 12100}, {11737, 16773}, {12817, 34755}, {14269, 42776}, {14890, 42488}, {14891, 16267}, {14893, 16963}, {15640, 42975}, {15685, 42117}, {15686, 42925}, {15687, 22238}, {15689, 42998}, {15690, 34754}, {15695, 37640}, {15698, 42124}, {15699, 36843}, {15700, 43003}, {15702, 42590}, {15714, 42152}, {15719, 33604}, {16644, 19711}, {16962, 33923}, {17504, 42773}, {19106, 33606}, {19708, 42974}, {19709, 42121}, {23046, 42149}, {33607, 42685}, {33699, 42086}, {35404, 40694}, {36450, 42225}, {36467, 42226}, {37641, 42145}, {38071, 42161}, {41099, 42127}, {41101, 42088}, {41113, 42136}, {41122, 42941}, {41990, 42106}, {42087, 42800}, {42091, 42633}, {42502, 42627}, {42591, 42813}, {42781, 42930}

X(43109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 42792, 11812}, {396, 42631, 15759}, {3845, 42510, 42913}, {10653, 42123, 42912}, {11481, 41119, 15713}, {12100, 41107, 11542}, {16963, 42165, 14893}, {19710, 42420, 42419}, {41100, 42158, 41108}, {41107, 42943, 12100}, {42155, 42510, 3845}, {42155, 42913, 42137}

X(43110) = GIBERT (30,-7,1) POINT

Barycentrics    10*Sqrt[3]*a^2*S + a^2*SA - 14*SB*SC : :

X(43110) lies on the cubic K1218 and these lines: {2, 11485}, {6, 15687}, {13, 398}, {14, 11737}, {16, 42415}, {30, 42416}, {61, 35018}, {382, 42999}, {395, 3530}, {550, 10654}, {3529, 42924}, {3534, 42517}, {3628, 42939}, {3830, 42969}, {3851, 37640}, {3855, 22235}, {5066, 42777}, {5321, 12816}, {5334, 14269}, {10124, 34754}, {10187, 16772}, {10645, 42899}, {10646, 34200}, {10653, 42923}, {11539, 42513}, {11542, 38071}, {11812, 16961}, {12102, 42612}, {12820, 42101}, {14869, 40694}, {14891, 42795}, {14892, 16960}, {15681, 42117}, {15688, 37641}, {15691, 34755}, {15703, 42516}, {15707, 42121}, {16241, 42593}, {16268, 42500}, {16963, 41971}, {16964, 43006}, {23302, 43007}, {33923, 42934}, {35401, 42968}, {36967, 42636}, {41108, 42136}, {41120, 42474}, {41122, 42627}, {42085, 42586}, {42143, 42475}, {42153, 42590}, {42154, 42584}, {42436, 42967}, {42629, 42940}, {42632, 42996}, {42943, 43031}, {42945, 42946}, {42976, 43011}, {42992, 43032}

X(43110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16268, 43021, 42500}, {34754, 42778, 10124}, {42912, 42975, 11543}

X(43111) = GIBERT (30,7,-1) POINT

Barycentrics    10*Sqrt[3]*a^2*S - a^2*SA + 14*SB*SC : :

X(43111) lies on the cubic K1218 and these lines: {2, 11486}, {6, 15687}, {13, 11737}, {14, 397}, {15, 42416}, {30, 42415}, {62, 35018}, {382, 42998}, {396, 3530}, {550, 10653}, {3529, 42925}, {3534, 42516}, {3628, 42938}, {3830, 42968}, {3851, 37641}, {3855, 22237}, {5066, 42778}, {5318, 12817}, {5335, 14269}, {10124, 34755}, {10188, 16773}, {10645, 34200}, {10646, 42898}, {10654, 42922}, {11539, 42512}, {11543, 38071}, {11812, 16960}, {12102, 42613}, {12821, 42102}, {14869, 40693}, {14891, 42796}, {14892, 16961}, {15681, 42118}, {15688, 37640}, {15691, 34754}, {15703, 42517}, {15707, 42124}, {16242, 42592}, {16267, 42501}, {16962, 41972}, {16965, 43007}, {23303, 43006}, {33923, 42935}, {35401, 42969}, {36968, 42635}, {41107, 42137}, {41119, 42475}, {41121, 42628}, {42086, 42587}, {42146, 42474}, {42155, 42585}, {42156, 42591}, {42435, 42966}, {42630, 42941}, {42631, 42997}, {42942, 43030}, {42944, 42947}, {42977, 43010}, {42993, 43033}

X(43111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16267, 43020, 42501}, {34755, 42777, 10124}, {42913, 42974, 11542}

X(43112) = X(237)X(3049)∩X(297)X(523)

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

X(43112) lies on the cubic K214 and these lines: {237, 3049}, {297, 523}, {526, 9513}, {684, 36790}, {3569, 20975}, {11672, 39469}

X(43112) = X(i)-isoconjugate of X(j) for these (i,j): {1316, 36036}, {1821, 40866}
X(43112) = barycentric product X(3569)*X(9513)
X(43112) = barycentric quotient X(i)/X(j) for these {i,j}: {237, 40866}, {2491, 1316}

X(43113) = X(98)X(230)∩X(250)X(523)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(a^4 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 - a^2*b^2 - b^2*c^2 + c^4)*(a^8 - a^6*b^2 - a^6*c^2 + a^4*b^2*c^2 + b^6*c^2 - 2*b^4*c^4 + b^2*c^6) : :
X(43113) = 3 X[685] - X[39462], 3 X[2966] + X[39462]

X(43113) lies on the cubics K214 and K1072 and these lines: {98, 230}, {250, 523}, {21445, 32640}, {35088, 40542}

X(43113) = midpoint of X(685) and X(2966)
X(43113) = reflection of X(35088) in X(40542)
X(43113) = X(31953)-cross conjugate of X(1316)
X(43113) = cevapoint of X(1316) and X(31953)
X(43113) = crossdifference of every pair of points on line {41167, 41172}
X(43113) = barycentric product X(i)*X(j) for these {i,j}: {98, 40866}, {1316, 2966}
X(43113) = barycentric quotient X(i)/X(j) for these {i,j}: {1316, 2799}, {2715, 9513}, {31953, 35088}, {40866, 325}

X(43114) = X(2)X(87)∩X(43)X(4598)

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

X(43114) lies on the cubic K101 and these lines: {1, 43115}, {2, 87}, {43, 4598}, {171, 17105}, {932, 3550}, {940, 40753}, {982, 2319}, {2162, 23417}, {7121, 37604}, {8026, 18830}, {25502, 40720}

X(43114) = X(1)-Ceva conjugate of X(87)
X(43114) = X(6)-isoconjugate of X(43115)
X(43114) = barycentric product X(i)*X(j) for these {i,j}: {87, 21219}, {6384, 21780}
X(43114) = barycentric quotient X(i)/X(j) for these {i,j}: {1, P2}, {21219, 6376}, {21780, 43}, {21884, 3971}, {23080, 22370}

X(43115) = X(2)-CROSS CONJUGATE OF X(192)

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

X(43115) lies on the cubic K101 and these lines: {1, 43114}, {192, 21219}

X(43115) = X(2)-cross conjugate of X(192)
X(43115) = X(i)-isoconjugate of X(j) for these (i,j): {6, 43114}, {87, 21780}, {7121, 21219}
X(43115) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 43114}, {192, 21219}, {2176, 21780}, {20691, 21884}, {20760, 23080}

X(43116) = X(1)X(31641)∩X(42)X(192)

Barycentrics    a*(b*c*(a*b + a*c - b*c)*(a*b + a*c + b*c) + a*(b + c)*Sqrt[(a*b + a*c - b*c)*(a*b - a*c + b*c)*(-(a*b) + a*c + b*c)*(a*b + a*c + b*c)]) : :

X(43116) lies on the cubic K101 and these lines: {1, 31641}, {42, 192}

X(43116) = X(2)-cross conjugate of X(43117)
X(43116) = X(6)-isoconjugate of X(31641)
X(43116) = barycentric quotient X(1)/X(31641)
X(43116) = {X(42),X(192)}-harmonic conjugate of X(43117)

X(43117) = X(2)-CROSS CONJUGATE OF X(43116)

Barycentrics    a*(b*c*(a*b + a*c - b*c)*(a*b + a*c + b*c) - a*(b + c)*Sqrt[(a*b + a*c - b*c)*(a*b - a*c + b*c)*(-(a*b) + a*c + b*c)*(a*b + a*c + b*c)]) : :

X(43117) lies on the cubic K101 and these lines: {1, 31642}, {42, 192}

X(43117) = X(2)-cross conjugate of 43116
X(43117) = X(6)-isoconjugate of X(31642)
X(43117) = barycentric quotient X(1)/X(31642)
X(43117) = {X(42),X(192)}-harmonic conjugate of X(43116)

leftri

Points associated witrh co-Brocard circles: X(43118)-X(43192)

rightri

This preamble and centers X(43118)-X(43192) were contributed by César Eliud Lozada, May 6, 2021.

If two non-equilateral triangles T' and T" share the same Brocard axis then their Brocard points, which are symmetrical with respect to this axis, lie on a circle. This circle is named here the co-Brocard circle of T' and T" and its center lies on the common Brocard axis. (Note: the given condition is sufficient for the circularity of Brocard points, but not necessary).

The reference triangle ABC shares its Brocard axis with these triangles: ABC-X3 reflections, 5th anti-Brocard, anti-inner-Grebe, anti-outer-Grebe, anti-1st Kenmotu-free-vertices, anti-2nd Kenmotu-free-vertices, anti-X3-ABC reflections, Apollonius, 2nd Brocard, 5th Brocard, circumsymmedial, inner-Grebe, outer-Grebe, 1st Kenmotu-free-vertices, 2nd Kenmotu-free-vertices, Lucas inner, Lucas(-1) inner, Lucas tangents, Lucas(-1) tangents, X3-ABC reflections. Other groups of triangles having common Brocard axes are showed in the following table:

Brocard axis Triangles
tripolar of X(6)
X(187)X(237)		 1st Parry, 2nd Parry, 3rd Parry
tripolar of X(476)
X(6)X(13)		 anti-orthocentroidal, 4th Brocard, orthocentroidal
tripolar of X(658)
X(1)X(7)		 Conway, 2nd Conway, 3rd Conway, hexyl, Honsberger, Hutson intouch, incircle-circles, intouch, 6th mixtilinear, inner-Soddy, outer-Soddy
tripolar of X(1897)
X(4)X(9)		 excentral, 2nd extouch, 2nd Zaniah
tripolar of X(6331)
X(4)X(69)		 anti-Ara, anticomplementary, Ehrmann-mid, Johnson
tripolar of X(11794)
X(5)X(141)		 Euler, medial
tripolar of X(35360)
X(5)X(53)		 2nd Euler, orthic
tripolar of X(37137)
X(1)X(256)		 2nd anti-circumperp-tangential, Mandart-incircle
tripolar of X(42405)
X(3)X(95)		 anti-Ascella, 1st anti-circumperp, circumorthic
tripolar of X(43187)
X(3)X(76)		 1st anti-Brocard, 6th Brocard, circummedial
X(182)X(2782) 6th anti-Brocard, 1st Brocard
tripolar of X(43188)
X(20)X(185)		 anti-Euler, anti-3rd-tri-squares-central, anti-4th-tri-squares-central
tripolar of X(43189)
X(3)X(2783)		 anti-inner-Garcia, inner-Garcia
X(511)X(11248) anti-Mandart-incircle, anti-outer-Yff
X(511)X(11249) anti-inner-Yff, 2nd circumperp tangential
tripolar of X(43190)
X(3)X(142)		 Ascella, 1st circumperp, 2nd circumperp, 2nd Pamfilos-Zhou, Wasat
tripolar of X(43191)
X(5)X(516)		 3rd Euler, 4th Euler
tripolar of X(43192) midarc, 2nd midarc

In this section, a set of new anti-triangles is introduced: {anti-1st Auriga, anti-2nd Auriga, anti-Ehrmann-mid, anti-inner-Garcia, anti-1st Kenmotu-free-vertices, anti-2nd Kenmotu-free-vertices, anti-1st Parry, anti-2nd Parry, anti-3rd tri-squares-central, anti-4th tri-squares-central, anti-X3-ABC reflections, anti-inner-Yff, anti-outer-Yff}. The anti-triangle of a triangle T (denoted anti-T) is defined as the triangle A'B'C' such that T-of-A'B'C' is the reference triangle ABC. For coordinates of all triangles cited here, see the Index of triangles referenced in ETC.

X(43118) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC AND ANTI-INNER-GREBE

Barycentrics    a^2*((-a^2+b^2+c^2)*(a^2-S)+2*b^2*c^2) : :
Trilinears    sin A - (1 - cot ω) cos A : :
X(43118) = 3*X(3)+X(11917) = 3*X(3312)-X(11917) = X(10784)+3*X(26620)

X(43118) lies on these lines: {2, 6290}, {3, 6}, {5, 13749}, {184, 1584}, {487, 14912}, {488, 491}, {494, 12972}, {549, 1991}, {641, 7778}, {1503, 37342}, {1587, 13638}, {1600, 5012}, {3060, 13616}, {3069, 21737}, {3155, 10601}, {3156, 3796}, {3524, 26516}, {3589, 37343}, {3618, 21736}, {5408, 7484}, {5409, 11402}, {5875, 15834}, {6036, 10576}, {6289, 7389}, {6459, 35944}, {6463, 33748}, {6466, 17928}, {6776, 11291}, {6811, 7792}, {7388, 8982}, {7499, 11090}, {8963, 19355}, {9766, 41490}, {10784, 26620}, {11091, 11245}, {12601, 35823}, {13050, 26293}, {14561, 36709}, {16432, 37527}, {19130, 36711}, {19440, 19442}, {19441, 26507}, {26441, 35948}, {29012, 36712}, {35945, 42637}

X(43118) = midpoint of X(i) and X(j) for these {i, j}: {3, 3312}, {43137, 43138}
X(43118) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(9732)}} and {{A, B, C, X(4), X(6421)}}
X(43118) = Brocard circle-inverse of-X(9732)
X(43118) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 9732), (3, 182, 43119), (3, 1160, 3098), (3, 5050, 371), (3, 6395, 1160), (3, 6418, 1161), (3, 26341, 182), (6, 8406, 372), (6, 12305, 3095), (182, 43121, 3), (371, 372, 6421), (575, 9738, 3311), (1152, 5085, 3), (1161, 6418, 576), (5092, 9739, 3), (6420, 11824, 1351), (6428, 11916, 5097), (12975, 43120, 3), (13334, 43121, 6396), (15884, 19145, 39), (22234, 43143, 6500)

X(43119) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC AND ANTI-OUTER-GREBE

Barycentrics    a^2*((-a^2+b^2+c^2)*(a^2+S)+2*b^2*c^2) : :
Trilinears    sin A + (1 + cot ω) cos A : :
X(43119) = 3*X(3)+X(11916) = 3*X(3311)-X(11916) = X(10783)+3*X(26619)

X(43119) lies on these lines: {2, 6222}, {3, 6}, {5, 13748}, {184, 1583}, {487, 492}, {488, 14912}, {493, 12973}, {549, 591}, {642, 7778}, {1503, 37343}, {1588, 13758}, {1599, 5012}, {3060, 13617}, {3155, 3796}, {3156, 10601}, {3524, 26521}, {3589, 37342}, {5408, 11402}, {5409, 7484}, {5874, 15835}, {6036, 10577}, {6290, 7388}, {6459, 21737}, {6460, 35945}, {6462, 33748}, {6465, 17928}, {6776, 11292}, {6813, 7792}, {7389, 26441}, {7499, 11091}, {8982, 35949}, {9681, 12123}, {9766, 41491}, {10783, 26619}, {11090, 11245}, {12602, 35822}, {13049, 26292}, {14561, 36714}, {16433, 37527}, {19130, 36712}, {19440, 26498}, {19441, 19443}, {21736, 25406}, {29012, 36711}, {35944, 42638}

X(43119) = midpoint of X(i) and X(j) for these {i, j}: {3, 3311}, {6459, 21737}, {43139, 43140}
X(43119) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(9733)}} and {{A, B, C, X(4), X(6422)}}
X(43119) = Brocard circle-inverse of-X(9733)
X(43119) = Schoute circle-inverse of-X(9600)
X(43119) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 9733), (3, 182, 43118), (3, 371, 9732), (3, 1161, 3098), (3, 5050, 372), (3, 6199, 1161), (3, 6417, 1160), (6, 8414, 371), (6, 12306, 3095), (15, 16, 9600), (182, 43120, 3), (371, 372, 6422), (575, 9739, 3312), (1151, 5085, 3), (1160, 6417, 576), (5092, 9738, 3), (6419, 11825, 1351), (6427, 11917, 5097), (12974, 43121, 3), (13334, 43120, 6200), (15883, 19146, 39), (22234, 43145, 6501)

X(43120) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC AND ANTI-1st KENMOTU-FREE-VERTICES

Barycentrics    a^2*((-a^2+b^2+c^2)*(a^2+2*S)+2*b^2*c^2) : :
X(43120) = 3*X(2)+X(26441) = 3*X(3)-X(11825) = 3*X(371)+X(11825) = 5*X(631)-X(637) = 7*X(3523)+X(43134) = 3*X(5050)-X(35840) = X(12306)+3*X(12963)

X(43120) lies on these lines: {2, 14234}, {3, 6}, {5, 6118}, {98, 8316}, {140, 639}, {184, 1599}, {549, 32419}, {620, 641}, {626, 642}, {631, 637}, {754, 41491}, {1352, 11292}, {1583, 9306}, {1587, 35945}, {3071, 6036}, {3156, 5943}, {3523, 43134}, {3818, 37343}, {3819, 5409}, {5406, 11402}, {5407, 7484}, {5408, 34986}, {5461, 6251}, {6289, 11315}, {6306, 6771}, {6307, 6774}, {8908, 10962}, {8962, 32568}, {9541, 21737}, {10851, 15819}, {11179, 12256}, {11198, 19440}, {11294, 36998}, {12973, 40067}, {15717, 26521}, {16441, 37527}, {19054, 26294}, {19130, 36714}, {19430, 19588}, {21445, 22726}, {21640, 26912}, {29012, 36709}, {37342, 38317}

X(43120) = midpoint of X(3) and X(371)
X(43120) = reflection of X(i) in X(j) for these (i, j): (639, 140), (43121, 13335)
X(43120) = complement of the complement of X(26441)
X(43120) = isogonal conjugate of X(14245)
X(43120) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(9739)}} and {{A, B, C, X(4), X(1504)}}
X(43120) = Brocard circle-inverse of-X(9739)
X(43120) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 182, 43121), (3, 5050, 1152), (3, 6199, 1160), (3, 6221, 9732), (3, 9732, 3098), (3, 9733, 7690), (3, 12313, 1350), (3, 39648, 5171), (3, 43119, 182), (182, 12974, 3), (371, 372, 1504), (575, 43141, 372), (575, 43144, 574), (1151, 12963, 371), (3311, 9733, 576), (3592, 12305, 1351), (5085, 6409, 3), (5092, 43144, 3), (7692, 17508, 3), (9732, 21309, 576), (11292, 12257, 1352), (26348, 43118, 182)

X(43121) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC AND ANTI-2nd KENMOTU-FREE-VERTICES

Barycentrics    a^2*((-a^2+b^2+c^2)*(a^2-2*S)+2*b^2*c^2) : :
X(43121) = 3*X(2)+X(8982) = 3*X(3)-X(11824) = 3*X(372)+X(11824) = 5*X(631)-X(638) = 7*X(3523)+X(43133) = 3*X(5050)-X(35841) = X(12305)+3*X(12968)

X(43121) lies on these lines: {2, 8982}, {3, 6}, {5, 6119}, {98, 8317}, {140, 640}, {184, 1600}, {549, 32421}, {620, 642}, {626, 641}, {631, 638}, {754, 41490}, {1352, 11291}, {1584, 9306}, {1588, 35944}, {3070, 6036}, {3155, 5943}, {3523, 43133}, {3818, 37342}, {3819, 5408}, {5406, 7484}, {5407, 11402}, {5409, 34986}, {5461, 6250}, {6290, 11316}, {6302, 6771}, {6303, 6774}, {6642, 8996}, {6644, 8989}, {8963, 26920}, {8964, 13567}, {10852, 15819}, {11179, 12257}, {11293, 36998}, {12972, 40068}, {13935, 21737}, {14561, 21736}, {15717, 26516}, {16440, 37527}, {19053, 26295}, {19130, 36709}, {19431, 19588}, {19441, 32077}, {21445, 22727}, {29012, 36714}, {37343, 38317}

X(43121) = midpoint of X(3) and X(372)
X(43121) = reflection of X(i) in X(j) for these (i, j): (640, 140), (43120, 13335)
X(43121) = complement of the complement of X(8982)
X(43121) = isogonal conjugate of X(14231)
X(43121) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(9738)}} and {{A, B, C, X(4), X(1505)}}
X(43121) = Brocard circle-inverse of-X(9738)
X(43121) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 182, 43120), (3, 3312, 9732), (3, 5050, 1151), (3, 6395, 1161), (3, 9732, 7692), (3, 9733, 3098), (3, 12314, 1350), (3, 39679, 5171), (3, 43118, 182), (182, 12975, 3), (371, 372, 1505), (575, 43141, 574), (575, 43144, 371), (1152, 12968, 372), (3312, 9732, 576), (3594, 12306, 1351), (5085, 6410, 3), (5092, 43141, 3), (7690, 17508, 3), (9733, 21309, 576), (11291, 12256, 1352), (26341, 43119, 182)

X(43122) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC AND LUCAS INNER

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

X(43122) lies on this line: {3, 6}

X(43122) = intersection, other than A,B,C, of conics {{A, B, C, X(83), X(6471)}} and {{A, B, C, X(98), X(6407)}}
X(43122) = X(43122)-of-circumsymmedial triangle
X(43122) = X(43186)-of-Lucas central triangle
X(43122) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (32, 182, 43123), (1342, 1343, 6471), (1687, 1688, 6407)

X(43123) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC AND LUCAS(-1) INNER

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

X(43123) lies on this line: {3, 6}

X(43123) = intersection, other than A,B,C, of conics {{A, B, C, X(83), X(6470)}} and {{A, B, C, X(98), X(6408)}}
X(43123) = X(43123)-of-circumsymmedial triangle
X(43123) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (32, 182, 43122), (1342, 1343, 6470), (1687, 1688, 6408)

X(43124) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC AND LUCAS TANGENTS

Barycentrics    a^2*(a^2*(-a^2+b^2+c^2)+2*b^2*c^2+4*S*a^2) : :
Trilinears    cos(A - ω) + 2 sin(A - ω) : :

X(43124) lies on these lines: {3, 6}, {83, 3317}, {98, 1131}, {641, 7759}, {1078, 32806}, {6250, 14230}, {6289, 13644}, {12150, 26620}, {19053, 26430}, {26429, 42413}, {26521, 37665}

X(43124) = midpoint of X(6423) and X(39648)
X(43124) = intersection, other than A,B,C, of conics {{A, B, C, X(39), X(3317)}} and {{A, B, C, X(83), X(3312)}}
X(43124) = circle-{{X(1687),X(1688),PU(1),PU(2)}}-inverse of X(1151)
X(43124) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (32, 182, 43125), (32, 18993, 5039), (187, 371, 12974), (371, 5062, 576), (371, 12968, 9739), (372, 5007, 42832), (1342, 1343, 3312), (1687, 1688, 1151), (3053, 19145, 43120), (5007, 10793, 5039), (5171, 41412, 43125), (12975, 42833, 39)

X(43125) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC AND LUCAS(-1) TANGENTS

Barycentrics    a^2*(a^2*(-a^2+b^2+c^2)+2*b^2*c^2-4*S*a^2) : :
Trilinears    cos(A - ω) - 2 sin(A - ω) : :

X(43125) lies on these lines: {3, 6}, {83, 3316}, {98, 1132}, {642, 7759}, {1078, 32805}, {6251, 14233}, {6290, 13763}, {12150, 26619}, {19054, 26429}, {26430, 42414}, {26516, 37665}

X(43125) = midpoint of X(6424) and X(39679)
X(43125) = intersection, other than A,B,C, of conics {{A, B, C, X(39), X(3316)}} and {{A, B, C, X(83), X(3311)}}
X(43125) = circle-{{X(1687),X(1688),PU(1),PU(2)}}-inverse of X(1152)
X(43125) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (32, 182, 43124), (32, 18994, 5039), (187, 372, 12975), (371, 5007, 42833), (372, 5058, 576), (1342, 1343, 3311), (1687, 1688, 1152), (3053, 19146, 43121), (5007, 10792, 5039), (5171, 41412, 43124), (12974, 42832, 39)

X(43126) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND ANTI-1st KENMOTU-FREE-VERTICES

Barycentrics    a^2*(2*(-a^2+b^2+c^2)*S+3*a^4+(b^2+c^2)*a^2-4*b^4-6*b^2*c^2-4*c^4) : :
X(43126) = 7*X(3)-X(6420) = 8*X(3)-X(43145) = 8*X(6420)-7*X(43145)

X(43126) lies on these lines: {3, 6}, {8703, 35758}

X(43126) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 3098, 43121), (3, 9732, 17508), (3, 11824, 5092), (3, 31884, 9739), (3, 35246, 43119), (182, 1161, 43143)

X(43127) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND ANTI-2nd KENMOTU-FREE-VERTICES

Barycentrics    a^2*(-2*(-a^2+b^2+c^2)*S+3*a^4+(b^2+c^2)*a^2-4*b^4-6*b^2*c^2-4*c^4) : :
X(43127) = 7*X(3)-X(6419) = 8*X(3)-X(43143) = 8*X(6419)-7*X(43143)

X(43127) lies on this line: {3, 6}

X(43127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 3098, 43120), (3, 9733, 17508), (3, 11825, 5092), (3, 31884, 9738), (3, 35247, 43118), (182, 1160, 43145)

X(43128) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ABC-X3 REFLECTIONS AND 2nd BROCARD

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

X(43128) lies on these lines: {3, 6}, {8719, 18440}

X(43128) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 1350, 35429), (3098, 8589, 33878)

X(43129) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-ARA AND EHRMANN-MID

Barycentrics    a^2*((b^2+c^2)*a^8-2*(b^4+3*b^2*c^2+c^4)*a^6+2*(b^8-4*b^4*c^4+c^8)*a^2-(b^4-c^4)*(b^2-c^2)*(b^4-4*b^2*c^2+c^4)) : :
X(43129) = 3*X(5)-X(17710) = 3*X(381)+X(9973) = 5*X(1352)-X(11412) = 5*X(1843)+3*X(15030) = X(3098)-3*X(29959) = X(3313)-3*X(11178) = 5*X(3818)-3*X(15030) = 3*X(5476)-X(6467) = 2*X(6329)-3*X(13364) = 3*X(9971)+X(18440) = 3*X(11188)+X(31670) = X(12272)+3*X(20423) = 3*X(13598)+5*X(14913) = X(13598)+5*X(43130) = X(14913)-3*X(43130)

X(43129) lies on these lines: {4, 69}, {5, 17710}, {6, 10540}, {30, 41579}, {182, 7506}, {206, 575}, {381, 9973}, {542, 9969}, {1495, 5012}, {1503, 13630}, {2071, 32600}, {2072, 11574}, {2393, 19130}, {3098, 29959}, {3313, 11178}, {3631, 13391}, {3819, 31074}, {5092, 6644}, {5097, 10110}, {5446, 5965}, {5476, 6467}, {6329, 13364}, {9019, 18358}, {9971, 18440}, {9972, 26863}, {10095, 12007}, {11645, 38321}, {11649, 23323}, {12084, 14810}, {12272, 20423}, {13371, 24206}, {14641, 29012}, {15082, 30745}, {15516, 21637}, {15580, 32046}, {34417, 40914}

X(43129) = midpoint of X(i) and X(j) for these {i, j}: {4, 41714}, {1843, 3818}
X(43129) = reflection of X(i) in X(j) for these (i, j): (5092, 9822), (5097, 10110), (12007, 10095)

X(43130) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-ARA AND JOHNSON

Barycentrics    a^2*((b^2+c^2)*a^8-2*(b^4+3*b^2*c^2+c^4)*a^6+2*(b^2+c^2)*b^2*c^2*a^4+2*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)*(b^4-4*b^2*c^2+c^4)) : :
X(43130) = X(3)-3*X(29959) = X(4)+3*X(11188) = 3*X(5)-X(15074) = X(52)-3*X(9971) = 3*X(141)-2*X(5447) = 2*X(143)-3*X(9969) = 3*X(182)-4*X(11695) = 2*X(575)-3*X(5943) = 3*X(599)-X(10625) = 3*X(1352)-X(5562) = 3*X(1843)+X(5562) = 3*X(1992)-7*X(9781) = 5*X(3091)-X(15073) = 3*X(6403)+5*X(15058) = 3*X(9822)-2*X(11695) = 3*X(9971)+X(15069) = X(13598)+3*X(14913) = X(13598)-6*X(43129) = X(14913)+2*X(43129) = X(40647)-6*X(41579)

X(43130) lies on these lines: {3, 29959}, {4, 69}, {5, 2393}, {6, 7529}, {52, 9971}, {141, 5447}, {143, 3564}, {155, 576}, {159, 182}, {184, 575}, {389, 542}, {524, 5446}, {546, 14984}, {599, 10625}, {858, 3819}, {895, 1173}, {1216, 9019}, {1503, 31833}, {1595, 8263}, {1992, 9781}, {2353, 13335}, {2386, 35930}, {2854, 16534}, {3091, 15073}, {3098, 12085}, {3618, 12283}, {3917, 31099}, {5092, 17928}, {5448, 5480}, {5462, 8550}, {5889, 11180}, {5965, 11808}, {6467, 14561}, {6688, 34750}, {6759, 9813}, {6776, 15043}, {7394, 27365}, {7530, 8542}, {7716, 37488}, {8548, 13861}, {8705, 10170}, {9729, 9833}, {9818, 34787}, {9925, 39522}, {9926, 19139}, {9967, 9973}, {9970, 32260}, {9977, 32379}, {10297, 11649}, {10594, 41614}, {11178, 11793}, {11413, 14810}, {11574, 11585}, {11645, 38323}, {12106, 35370}, {12162, 37473}, {12220, 40330}, {12272, 14853}, {12367, 37513}, {13334, 23208}, {13570, 18418}, {14128, 18358}, {15582, 18475}, {15644, 16789}, {18369, 39562}, {18440, 19161}, {18583, 18874}, {19131, 20987}, {21849, 41628}, {24981, 41671}, {32275, 40949}, {34146, 39884}, {36990, 37511}

X(43130) = midpoint of X(i) and X(j) for these {i, j}: {52, 15069}, {1352, 1843}, {3818, 41714}, {9967, 9973}, {9970, 32260}, {12162, 37473}, {18440, 19161}, {32275, 40949}, {36990, 37511}
X(43130) = reflection of X(i) in X(j) for these (i, j): (182, 9822), (576, 10110), (5907, 18553), (8550, 5462), (11574, 24206), (15644, 40107), (32366, 18583)
X(43130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6642, 8549, 182), (8548, 13861, 19136), (8550, 16776, 5462), (9973, 10516, 9967)

X(43131) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-ASCELLA AND 1st ANTI-CIRCUMPERP

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

X(43131) lies on these lines: {3, 95}, {53, 6676}, {157, 15818}, {1368, 23333}, {3186, 35952}, {6751, 9967}, {12362, 42353}, {31829, 36988}

X(43132) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-ASCELLA AND CIRCUMORTHIC

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

X(43132) lies on these lines: {3, 95}, {4, 34396}, {32, 53}, {578, 1503}, {1970, 9833}, {7404, 18437}, {8887, 42671}, {10316, 13322}

X(43132) = intersection, other than A,B,C, of conics {{A, B, C, X(32), X(19185)}} and {{A, B, C, X(276), X(34449)}}

X(43133) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-EULER AND ANTI-3rd TRI-SQUARES-CENTRAL

Barycentrics    3*a^4-2*(b^2+c^2)*a^2+(6*a^2-2*b^2-2*c^2)*S-(b^2-c^2)^2 : :
X(43133) = 3*X(2)-4*X(372) = 9*X(2)-8*X(640) = 3*X(372)-2*X(640) = 3*X(638)-4*X(640) = 5*X(3522)-4*X(11824) = 7*X(3523)-8*X(43121)

X(43133) lies on these lines: {2, 372}, {6, 490}, {20, 185}, {23, 8996}, {32, 7585}, {69, 6460}, {147, 6463}, {148, 33430}, {176, 17950}, {239, 31549}, {315, 1270}, {384, 39875}, {385, 12256}, {487, 40275}, {489, 524}, {491, 1152}, {492, 3070}, {591, 23251}, {637, 6560}, {642, 6454}, {671, 1132}, {1131, 3593}, {1160, 7762}, {1161, 35946}, {1271, 3926}, {1505, 5286}, {1991, 6410}, {1992, 6459}, {2459, 32964}, {2996, 14234}, {3068, 12968}, {3069, 12323}, {3103, 32965}, {3146, 5870}, {3311, 35949}, {3312, 7388}, {3522, 11824}, {3523, 43121}, {3629, 42258}, {5860, 12322}, {5861, 42637}, {6231, 14639}, {6318, 14023}, {6395, 11314}, {6398, 39388}, {6566, 7763}, {6656, 8416}, {6813, 12314}, {7389, 7879}, {7581, 11292}, {7583, 39387}, {7774, 9733}, {7783, 12257}, {7797, 42523}, {7839, 39876}, {11315, 18512}, {12510, 14912}, {13757, 42262}, {17364, 31550}, {26339, 42638}, {26361, 31414}, {31412, 32805}, {31859, 35947}, {32419, 42267}, {32432, 33277}, {32807, 42265}, {32809, 41946}, {32811, 33365}, {33350, 42248}, {33352, 42249}

X(43133) = reflection of X(i) in X(j) for these (i, j): (20, 8982), (489, 42259), (638, 372), (12323, 12969), (32809, 41946), (43134, 20065)
X(43133) = anticomplement of X(638)
X(43133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 490, 11294), (20, 193, 43134), (69, 6460, 11293), (194, 6776, 43134), (372, 638, 2), (488, 1587, 2), (492, 3070, 32489), (1587, 26288, 488), (3069, 12323, 32488)

X(43134) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-EULER AND ANTI-4th TRI-SQUARES-CENTRAL

Barycentrics    3*a^4-2*(b^2+c^2)*a^2-(6*a^2-2*b^2-2*c^2)*S-(b^2-c^2)^2 : :
X(43134) = 3*X(2)-4*X(371) = 9*X(2)-8*X(639) = 3*X(371)-2*X(639) = 3*X(637)-4*X(639) = 5*X(3522)-4*X(11825) = 7*X(3523)-8*X(43120)

X(43134) lies on these lines: {2, 371}, {6, 489}, {20, 185}, {32, 7586}, {69, 6459}, {147, 6462}, {148, 33431}, {175, 17950}, {239, 31550}, {315, 1271}, {384, 39876}, {385, 12257}, {488, 9541}, {490, 524}, {491, 3071}, {492, 1151}, {591, 6409}, {638, 6561}, {641, 6453}, {671, 1131}, {1132, 3595}, {1160, 35947}, {1161, 7762}, {1270, 3926}, {1504, 5286}, {1991, 23261}, {1992, 6460}, {2460, 32964}, {2996, 14238}, {3068, 12322}, {3069, 12963}, {3102, 32965}, {3146, 5871}, {3311, 7389}, {3312, 35948}, {3522, 11825}, {3523, 43120}, {3629, 42259}, {5860, 42638}, {5861, 12323}, {6199, 11313}, {6221, 39387}, {6230, 14639}, {6314, 14023}, {6567, 7763}, {6656, 8396}, {6811, 12313}, {7388, 7879}, {7582, 11291}, {7584, 39388}, {7774, 9732}, {7783, 12256}, {7797, 42522}, {7839, 39875}, {9543, 42009}, {9675, 13941}, {11316, 18510}, {12509, 14912}, {13637, 42265}, {17364, 31549}, {23311, 31454}, {26340, 42637}, {31859, 35946}, {32421, 42266}, {32435, 33277}, {32806, 42561}, {32808, 41945}, {32810, 33364}, {33351, 42247}, {33353, 42246}

X(43134) = reflection of X(i) in X(j) for these (i, j): (20, 26441), (490, 42258), (637, 371), (12322, 12962), (32808, 41945), (43133, 20065)
X(43134) = anticomplement of X(637)
X(43134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 489, 11293), (20, 193, 43133), (69, 6459, 11294), (194, 6776, 43133), (371, 637, 2), (487, 1588, 2), (491, 3071, 32488), (1588, 26289, 487), (3068, 12322, 32489)

X(43135) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-INNER-GARCIA AND INNER-GARCIA

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

X(43135) lies on these lines: {3, 2783}, {9, 80}, {100, 312}, {536, 1319}, {740, 5150}, {2791, 38531}, {3035, 17594}, {3685, 17790}, {3923, 37516}, {4387, 37366}, {4553, 24410}

X(43136) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-INNER-GREBE AND ANTI-OUTER-GREBE

Barycentrics    a^2*(5*a^2+3*b^2+3*c^2) : :
Trilinears    4 sin A - cos A tan ω : :
Trilinears    cos A - 4 sin A cot ω : :
Trilinears    2 a + R cos A tan ω : :

The perspeconic of the anti-inner Grebe and anti-outer Grebe triangles is a circle, here named the anti-Grebe circle, with center X(43136). (Randy Hutson, May 31, 2021)

X(43136) lies on these lines: {3, 6}, {5, 5304}, {25, 34482}, {81, 21514}, {83, 14614}, {140, 37665}, {183, 7878}, {193, 7819}, {206, 33580}, {218, 21764}, {230, 5070}, {251, 9909}, {381, 5305}, {382, 5286}, {384, 20105}, {391, 17698}, {550, 1285}, {597, 7800}, {599, 7889}, {631, 14930}, {940, 21529}, {999, 5299}, {1003, 7839}, {1194, 20850}, {1249, 6756}, {1506, 15703}, {1572, 8148}, {1587, 36711}, {1588, 36712}, {1595, 40065}, {1597, 3172}, {1598, 8743}, {1627, 34572}, {1656, 7735}, {1657, 15048}, {1743, 5266}, {1975, 7894}, {1992, 3933}, {1994, 37344}, {2207, 18535}, {2221, 23089}, {2300, 22147}, {2548, 5055}, {2549, 17800}, {3295, 5280}, {3517, 10312}, {3522, 14482}, {3526, 7736}, {3534, 7738}, {3589, 14023}, {3618, 7767}, {3628, 37689}, {3629, 7795}, {3763, 7826}, {3767, 3851}, {3793, 16043}, {3830, 5254}, {3843, 5319}, {3917, 31885}, {3926, 33242}, {3934, 14535}, {4383, 21542}, {5020, 5359}, {5032, 8369}, {5054, 31406}, {5073, 7737}, {5077, 7864}, {5198, 8744}, {5275, 16853}, {5276, 11108}, {5283, 16866}, {5309, 14269}, {5332, 6767}, {5346, 7753}, {5354, 11284}, {5368, 5475}, {5644, 42295}, {5702, 37458}, {6144, 7794}, {6179, 11174}, {6680, 9766}, {6803, 36413}, {6918, 40129}, {7296, 7373}, {7581, 36709}, {7582, 36714}, {7739, 15681}, {7748, 15684}, {7754, 7787}, {7758, 32455}, {7762, 7866}, {7766, 7770}, {7773, 7856}, {7774, 32954}, {7776, 7792}, {7778, 7838}, {7779, 33217}, {7784, 7829}, {7785, 11318}, {7788, 7846}, {7789, 8584}, {7808, 8667}, {7812, 7851}, {7822, 40341}, {7837, 7881}, {7841, 7920}, {7855, 15534}, {7857, 11163}, {7867, 41750}, {7868, 7877}, {7875, 7879}, {7887, 7921}, {7900, 33219}, {7906, 33220}, {7941, 33218}, {7947, 8366}, {8368, 32818}, {8721, 12007}, {8779, 19347}, {9300, 15694}, {9575, 10246}, {9606, 21843}, {9777, 34396}, {11147, 19661}, {11287, 20065}, {11343, 37685}, {11402, 41266}, {13903, 31403}, {14537, 35403}, {14567, 20854}, {14929, 32956}, {14996, 21496}, {14997, 21519}, {15257, 34777}, {15720, 31400}, {15934, 16780}, {16060, 37677}, {16308, 37923}, {16408, 33854}, {16667, 37592}, {16670, 25066}, {16855, 37675}, {18494, 41361}, {19101, 19102}, {19105, 22541}, {19116, 37342}, {19117, 37343}, {19125, 34416}, {19697, 32830}, {20583, 34511}, {20968, 33582}, {21526, 32911}, {23133, 26206}, {32467, 39656}, {32816, 33240}, {32823, 33186}, {33185, 37668}

X(43136) = midpoint of X(3311) and X(3312)
X(43136) = isogonal conjugate of the polar conjugate of X(7408)
X(43136) = barycentric product X(3)*X(7408)
X(43136) = trilinear product X(48)*X(7408)
X(43136) = center of circle-{X(371),X(372),PU(1),PU(39)}-inverse-of-circle-O(1151,1152)
X(43136) = radical center of Lucas(-8 cot ω) circles
X(43136) = intersection, other than A,B,C, of conics {{A, B, C, X(3), X(7408)}} and {{A, B, C, X(4), X(31884)}}
X(43136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 22246, 39), (6, 5039, 1351), (6, 30435, 3), (32, 5023, 1384), (32, 9605, 3), (32, 37512, 3053), (39, 1384, 3), (371, 372, 31884), (1351, 3398, 3), (3053, 5024, 3), (5008, 7772, 3053), (5008, 37512, 32), (5286, 18907, 382), (7772, 8588, 39), (7772, 34571, 6), (7894, 12150, 1975), (7920, 20088, 7841), (9605, 30435, 32), (9821, 12017, 3), (11485, 11486, 3098), (12962, 12969, 3094), (15655, 15815, 3), (43118, 43137, 3), (43119, 43140, 3)

X(43137) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-INNER-GREBE AND INNER-GREBE

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

X(43137) lies on these lines: {3, 6}, {5409, 41266}, {6811, 7776}, {7767, 21736}

X(43137) = midpoint of X(1161) and X(3312)
X(43137) = reflection of X(43138) in X(43118)
X(43137) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 43136, 43118), (32, 12306, 3), (1151, 5188, 3), (9732, 42858, 43139), (11824, 39648, 3)

X(43138) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-INNER-GREBE AND OUTER-GREBE

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

X(43138) lies on these lines: {3, 6}, {6813, 37668}

X(43138) = midpoint of X(1160) and X(3312)
X(43138) = reflection of X(43137) in X(43118)
X(43138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 1351, 8396), (6424, 12305, 3), (9733, 42859, 43140), (11825, 19146, 3)

X(43139) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-OUTER-GREBE AND INNER-GREBE

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

X(43139) lies on these lines: {3, 6}, {6811, 37668}

X(43139) = midpoint of X(1161) and X(3311)
X(43139) = reflection of X(43140) in X(43119)
X(43139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 1351, 8416), (6423, 12306, 3), (9732, 42858, 43137), (11824, 19145, 3)

X(43140) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-OUTER-GREBE AND OUTER-GREBE

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

X(43140) lies on these lines: {3, 6}, {5408, 41266}, {6813, 7776}

X(43140) = midpoint of X(1160) and X(3311)
X(43140) = reflection of X(43139) in X(43119)
X(43140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 43136, 43119), (32, 12305, 3), (1152, 5188, 3), (9733, 42859, 43138), (11825, 39679, 3)

X(43141) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-1st KENMOTU-FREE-VERTICES AND ANTI-X3-ABC REFLECTIONS

Barycentrics    a^2*(-b^4-c^4+(b^2+c^2)*a^2+4*(a^2-b^2-c^2)*S) : :
X(43141) = 7*X(3)+X(1160) = 9*X(3)-X(1161) = 5*X(3)-X(9732) = 3*X(3)+X(9733) = 3*X(3)-X(9738) = 9*X(1160)+7*X(1161) = 5*X(1160)+7*X(9732) = 3*X(1160)-7*X(9733) = 3*X(1160)+7*X(9738) = X(1160)-7*X(9739) = 2*X(1160)+7*X(43144) = 5*X(1161)-9*X(9732) = X(1161)+3*X(9733) = X(1161)-3*X(9738) = X(1161)+9*X(9739) = 2*X(1161)-9*X(43144) = 3*X(9732)+5*X(9733) = 3*X(9732)-5*X(9738) = X(9732)+5*X(9739) = 2*X(9732)-5*X(43144)

X(43141) lies on these lines: {2, 14240}, {3, 6}, {4, 32812}, {30, 14239}, {140, 6118}, {488, 34507}, {542, 35686}, {620, 640}, {639, 7830}, {1583, 6688}, {1599, 5943}, {1600, 3819}, {5406, 9306}, {7842, 32435}, {8253, 12602}, {10282, 30428}, {10514, 13712}, {11257, 33370}, {11292, 38317}, {12510, 32806}, {13030, 13049}, {13935, 35945}, {14160, 42267}, {14162, 22644}, {16001, 35740}, {16002, 42240}, {21567, 37521}

X(43141) = midpoint of X(i) and X(j) for these {i, j}: {3, 9739}, {9733, 9738}
X(43141) = reflection of X(43144) in X(3)
X(43141) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(12974)}} and {{A, B, C, X(6), X(14240)}}
X(43141) = Brocard circle-inverse of-X(12974)
X(43141) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 12974), (3, 1152, 182), (3, 1350, 7692), (3, 1351, 6409), (3, 3365, 13349), (3, 6410, 12975), (3, 9733, 9738), (3, 11916, 6451), (3, 11917, 6455), (3, 12305, 3098), (3, 12313, 6411), (3, 12314, 1151), (3, 43121, 5092), (372, 43120, 575), (574, 43121, 575), (1151, 12314, 576), (6412, 12305, 3), (6566, 37512, 3103), (7690, 12975, 3), (9738, 9739, 9733)

X(43142) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-1st KENMOTU-FREE-VERTICES AND 1st KENMOTU-FREE-VERTICES

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

X(43142) lies on these lines: {3, 6}, {34506, 41491}

X(43142) = {X(182), X(371)}-harmonic conjugate of X(43120)

X(43143) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-1st KENMOTU-FREE-VERTICES AND X3-ABC REFLECTIONS

Barycentrics    a^2*(3*a^4+4*b^4-6*b^2*c^2+4*c^4-7*(b^2+c^2)*a^2-2*(-a^2+b^2+c^2)*S) : :
X(43143) = X(3)-7*X(6419) = 8*X(3)-7*X(43127) = 8*X(6419)-X(43127)

X(43143) lies on these lines: {3, 6}, {3858, 22625}, {5068, 26468}, {14230, 15687}

X(43143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 15520, 43145), (182, 1161, 43126), (576, 3311, 43120), (576, 7690, 11917), (3592, 5093, 9739), (6427, 9732, 39561), (6500, 43118, 22234)

X(43144) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-2nd KENMOTU-FREE-VERTICES AND ANTI-X3-ABC REFLECTIONS

Barycentrics    a^2*(-b^4-c^4+(b^2+c^2)*a^2+4*(-a^2+b^2+c^2)*S) : :
X(43144) = 9*X(3)-X(1160) = 7*X(3)+X(1161) = 3*X(3)+X(9732) = 5*X(3)-X(9733) = 3*X(3)-X(9739) = 7*X(1160)+9*X(1161) = X(1160)+3*X(9732) = 5*X(1160)-9*X(9733) = X(1160)+9*X(9738) = X(1160)-3*X(9739) = 2*X(1160)-9*X(43141) = 3*X(1161)-7*X(9732) = 5*X(1161)+7*X(9733) = X(1161)-7*X(9738) = 3*X(1161)+7*X(9739) = 2*X(1161)+7*X(43141) = 5*X(9732)+3*X(9733) = X(9732)-3*X(9738) = 2*X(9732)+3*X(43141) = X(9733)+5*X(9738) = 3*X(9733)-5*X(9739) = 2*X(9733)-5*X(43141)

X(43144) lies on these lines: {2, 14236}, {3, 6}, {4, 32813}, {30, 14235}, {140, 6119}, {487, 34507}, {620, 639}, {640, 7830}, {1584, 6688}, {1599, 3819}, {1600, 5943}, {3818, 21736}, {5407, 9306}, {7842, 32432}, {8252, 12601}, {9540, 35944}, {10282, 30427}, {10515, 13835}, {11257, 33371}, {11291, 38317}, {12509, 32805}, {13032, 13050}, {14160, 42266}, {14162, 22615}, {16001, 42241}, {16002, 42239}, {21566, 37521}, {29012, 35756}

X(43144) = midpoint of X(i) and X(j) for these {i, j}: {3, 9738}, {9732, 9739}
X(43144) = reflection of X(43141) in X(3)
X(43144) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(12975)}} and {{A, B, C, X(6), X(14236)}}
X(43144) = Brocard circle-inverse of-X(12975)
X(43144) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 12975), (3, 1151, 182), (3, 1350, 7690), (3, 1351, 6410), (3, 3364, 13349), (3, 6409, 12974), (3, 9732, 9739), (3, 11916, 6456), (3, 11917, 6452), (3, 12306, 3098), (3, 12313, 1152), (3, 12314, 6412), (3, 43120, 5092), (371, 43121, 575), (574, 43120, 575), (1152, 12313, 576), (6411, 12306, 3), (6567, 37512, 3102), (7692, 12974, 3), (9738, 9739, 9732)

X(43145) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-2nd KENMOTU-FREE-VERTICES AND X3-ABC REFLECTIONS

Barycentrics    a^2*(2*(-a^2+b^2+c^2)*S+3*a^4-7*(b^2+c^2)*a^2+4*b^4-6*b^2*c^2+4*c^4) : :
X(43145) = X(3)-7*X(6420) = 8*X(3)-7*X(43126) = 8*X(6420)-X(43126)

X(43145) lies on these lines: {3, 6}, {3858, 22596}, {5068, 26469}, {14233, 15687}

X(43145) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 15520, 43143), (182, 1160, 43127), (576, 3312, 43121), (576, 7692, 11916), (3594, 5093, 9738), (6428, 9733, 39561), (6501, 43119, 22234)

X(43146) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE AND ANTI-OUTER-YFF

Barycentrics    a^2*(a^4-(b^2+c^2)*a^2+2*(b+c)*b*c*a-2*(b^2+b*c+c^2)*b*c) : :
X(43146) = X(37517)+2*X(41454)

X(43146) lies on these lines: {3, 2810}, {6, 595}, {8, 4579}, {182, 518}, {184, 3681}, {200, 3955}, {210, 9306}, {511, 11248}, {542, 12587}, {576, 674}, {611, 4260}, {692, 5220}, {1386, 31792}, {1397, 3961}, {1428, 16496}, {1757, 2175}, {2330, 3601}, {3098, 8679}, {3579, 34371}, {3811, 13323}, {3870, 26890}, {4661, 5012}, {4662, 14529}, {5053, 37590}, {5092, 22769}, {5135, 37606}, {5197, 5524}, {5223, 7193}, {5848, 34507}, {6600, 37474}, {8193, 29958}, {8715, 9025}, {9026, 17508}, {9047, 37517}, {9049, 39561}, {10756, 24047}, {12586, 18059}, {12594, 36741}, {12675, 13347}, {16475, 37556}, {23693, 31394}, {23841, 37547}, {24264, 32935}, {24265, 32941}, {25568, 37527}, {31787, 34381}

X(43146) = reflection of X(i) in X(j) for these (i, j): (22769, 5092), (43149, 182)
X(43146) = {X(2330), X(3751)}-harmonic conjugate of X(5138)

X(43147) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS AND 2nd BROCARD

Barycentrics    a^2*((3*b^4+4*b^2*c^2+3*c^4)*a^4-(b^2+c^2)*(5*b^4+3*b^2*c^2+5*c^4)*a^2+2*c^8-3*(b^4+c^4)*b^2*c^2+2*b^8) : :
X(43147) = 5*X(3094)-X(3095) = 3*X(5092)-2*X(13354) = 5*X(5092)-6*X(21163) = 3*X(13331)-2*X(22330) = 5*X(13354)-9*X(21163) = 3*X(32447)-X(37517) = 3*X(32519)+X(40341)

X(43147) lies on these lines: {3, 6}, {698, 40107}, {1916, 15819}, {2782, 43150}, {5965, 7830}, {7935, 13108}, {32519, 40341}

X(43147) = reflection of X(i) in X(j) for these (i, j): (5097, 39), (13330, 15516)
X(43147) = {X(3102), X(3103)}-harmonic conjugate of X(37512)

X(43148) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS AND 5th BROCARD

Barycentrics    a^2*(4*a^8-6*(b^2+c^2)*a^6-(3*b^4+20*b^2*c^2+3*c^4)*a^4+9*(b^4+b^2*c^2+c^4)*(b^2+c^2)*a^2-4*b^8+(b^4+4*b^2*c^2+c^4)*b^2*c^2-4*c^8) : :
X(43148) = X(576)-3*X(39560)

X(43148) lies on these lines: {3, 6}, {33014, 34507}

X(43148) = {X(3), X(2076)}-harmonic conjugate of X(43157)

X(43149) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTI-INNER-YFF AND 2nd CIRCUMPERP TANGENTIAL

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

X(43149) lies on these lines: {1, 2175}, {3, 9052}, {6, 101}, {36, 3779}, {56, 4260}, {182, 518}, {184, 3873}, {354, 9306}, {511, 11249}, {542, 12586}, {576, 8679}, {674, 3098}, {692, 42871}, {1386, 5045}, {1397, 32913}, {1420, 1428}, {1468, 7032}, {2194, 17597}, {2330, 13384}, {2975, 10477}, {3242, 5135}, {3827, 6759}, {3870, 26889}, {4430, 5012}, {4658, 38315}, {4666, 26885}, {5092, 12329}, {5320, 7191}, {5845, 20330}, {5849, 34507}, {8539, 37587}, {9026, 39561}, {9037, 37517}, {9049, 17508}, {9798, 12109}, {12587, 24206}, {12595, 36740}, {12675, 13346}, {16560, 31395}, {18162, 31394}, {24264, 32941}, {24265, 32935}, {24477, 37527}

X(43149) = reflection of X(i) in X(j) for these (i, j): (12329, 5092), (12587, 24206), (43146, 182)
X(43149) = circumtangential-isogonal conjugate of the anticomplement of X(29641)

X(43150) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ANTICOMPLEMENTARY AND EHRMANN-MID

Barycentrics    2*a^6-3*(b^2+c^2)*a^4+(3*b^4+4*b^2*c^2+3*c^4)*a^2-2*(b^4-c^4)*(b^2-c^2) : :
X(43150) = 3*X(4)+5*X(69) = X(4)-5*X(1352) = 3*X(4)-5*X(3818) = 2*X(4)-5*X(18553) = 9*X(4)-5*X(31670) = X(4)+5*X(34507) = 3*X(5)-X(3629) = X(69)+3*X(1352) = 2*X(69)+3*X(18553) = 3*X(69)+X(31670) = X(69)-3*X(34507) = 3*X(1352)-X(3818) = 9*X(1352)-X(31670) = 2*X(3629)-3*X(5097) = 2*X(3818)-3*X(18553) = 3*X(3818)-X(31670) = X(3818)+3*X(34507) = 9*X(18553)-2*X(31670) = X(18553)+2*X(34507) = X(31670)+9*X(34507)

X(43150) lies on these lines: {4, 69}, {5, 3629}, {6, 5055}, {30, 3631}, {49, 182}, {51, 7693}, {67, 13623}, {98, 7931}, {114, 37688}, {141, 542}, {147, 15819}, {193, 5476}, {265, 5891}, {302, 5613}, {303, 5617}, {343, 32223}, {373, 41724}, {381, 7845}, {524, 5066}, {538, 9996}, {547, 6329}, {548, 1503}, {575, 3564}, {576, 5072}, {599, 3098}, {1154, 41579}, {1216, 34514}, {1350, 17800}, {1353, 25555}, {1656, 39561}, {2782, 43147}, {2914, 34155}, {3410, 3917}, {3448, 5650}, {3545, 7926}, {3618, 42786}, {3619, 11179}, {3620, 10304}, {3630, 21850}, {3819, 11442}, {3851, 5102}, {3856, 34380}, {3857, 5480}, {3972, 34623}, {5111, 39565}, {5447, 14864}, {5921, 15717}, {5943, 37644}, {6033, 9466}, {6053, 15760}, {6776, 7945}, {7470, 32027}, {7486, 15516}, {7495, 24981}, {7525, 15580}, {7703, 13857}, {7754, 10356}, {7813, 37345}, {7816, 32151}, {7820, 13335}, {7849, 14880}, {7853, 12188}, {7882, 14881}, {8584, 25565}, {8589, 8724}, {8675, 10412}, {9306, 34397}, {9729, 18917}, {9927, 40247}, {9973, 23039}, {10109, 20583}, {10168, 34573}, {10170, 32366}, {10272, 41593}, {10519, 41482}, {10546, 32225}, {11064, 21243}, {11225, 37439}, {11411, 15012}, {11540, 20582}, {11591, 18383}, {12017, 21358}, {12584, 32600}, {13562, 37942}, {13851, 18387}, {14389, 34986}, {14561, 15022}, {14643, 41731}, {14982, 22584}, {15067, 17710}, {15082, 18911}, {15321, 34483}, {15605, 41587}, {15684, 33878}, {15698, 21356}, {15704, 29012}, {15993, 41413}, {16187, 26869}, {17006, 23234}, {18400, 35254}, {19924, 22165}, {20080, 20423}, {22110, 32414}, {23325, 34777}, {29317, 39884}, {33749, 38110}

X(43150) = midpoint of X(i) and X(j) for these {i, j}: {69, 3818}, {182, 15069}, {576, 11898}, {1352, 34507}, {3098, 18440}, {3630, 21850}, {5562, 41714}, {37517, 40341}
X(43150) = reflection of X(i) in X(j) for these (i, j): (575, 24206), (1353, 25555), (5092, 141), (5097, 5), (6776, 20190), (8584, 25565), (12007, 3628), (14810, 40107), (18553, 1352), (19130, 18358), (20583, 10109)
X(43150) = intersection, other than A,B,C, of conics {{A, B, C, X(3), X(7860)}} and {{A, B, C, X(4), X(14479)}}
X(43150) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (69, 1352, 3818), (381, 40341, 37517), (599, 18440, 3098), (3763, 15069, 39899), (3763, 39899, 182), (3818, 34507, 69), (10516, 11898, 576), (18358, 19130, 25561)

X(43151) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: ASCELLA AND 1st CIRCUMPERP

Barycentrics    2*a^5-7*(b+c)*a^4+8*(b^2+c^2)*a^3-2*(b^2-c^2)*(b-c)*a^2-2*(b-c)^4*a+(b^2-c^2)*(b-c)^3 : :
X(43151) = 3*X(2)+X(2951) = X(4)-3*X(38204) = X(7)+3*X(165) = X(9)-3*X(10164) = 5*X(10)-3*X(38154) = X(20)+3*X(38052) = X(40)+3*X(21151) = X(390)-5*X(7987) = 3*X(551)-X(43166) = 5*X(631)-X(11372) = 5*X(631)-3*X(38059) = X(946)-3*X(38122) = 5*X(1698)-X(36991) = 5*X(1698)-3*X(38158) = X(5542)-3*X(21151) = 5*X(5732)+3*X(38154) = X(5805)-3*X(38123) = 2*X(6684)+X(43181) = 3*X(10164)+X(43182) = X(11372)-3*X(38059) = X(31730)+3*X(38123)

Let A"B"C" be as at X(43174). Then X(43151) = X(38204)-of-A"B"C". See also X(5882). (Randy Hutson, May 31, 2021)

X(43151) lies on these lines: {1, 15841}, {2, 2951}, {3, 142}, {4, 38204}, {7, 165}, {9, 5658}, {10, 5732}, {20, 38052}, {40, 5542}, {144, 6745}, {344, 9950}, {390, 7987}, {518, 31787}, {519, 3174}, {551, 43166}, {553, 7964}, {631, 11372}, {971, 6684}, {1323, 23062}, {1385, 43179}, {1698, 36991}, {1721, 29571}, {1742, 3008}, {2346, 5537}, {2550, 4297}, {2801, 40659}, {3059, 10167}, {3062, 18230}, {3160, 17113}, {3576, 30331}, {3579, 31657}, {3634, 6908}, {3664, 9441}, {3671, 37551}, {3817, 20195}, {3826, 19925}, {3911, 14100}, {4298, 5584}, {4301, 38053}, {4312, 13411}, {4326, 8732}, {4335, 39595}, {5393, 30355}, {5405, 30354}, {5432, 31391}, {5435, 30330}, {5493, 38054}, {5572, 11227}, {5686, 9588}, {5691, 40333}, {5745, 10178}, {5759, 30424}, {5762, 31663}, {5779, 38130}, {5817, 31423}, {5850, 37560}, {5853, 11260}, {6361, 38036}, {6601, 43175}, {6666, 15726}, {6685, 10443}, {6700, 21153}, {6738, 7675}, {6743, 10884}, {6744, 8726}, {6825, 31253}, {6865, 12571}, {6916, 28164}, {6926, 19878}, {6987, 28158}, {7288, 10384}, {7676, 15931}, {7982, 10390}, {7991, 11038}, {8232, 30353}, {8236, 30389}, {8273, 12575}, {9940, 20116}, {9943, 18249}, {10171, 37364}, {10175, 31672}, {10392, 24914}, {10624, 35202}, {12447, 12520}, {12563, 31793}, {12702, 38030}, {15008, 34753}, {18243, 31658}, {18481, 38121}, {18482, 28150}, {19862, 38037}, {20330, 28194}, {21617, 30295}, {21628, 37407}, {21734, 24541}, {22793, 38171}, {34628, 38092}, {34632, 38024}, {34638, 38094}, {37423, 38150}

X(43151) = midpoint of X(i) and X(j) for these {i, j}: {9, 43182}, {10, 5732}, {40, 5542}, {142, 11495}, {2550, 4297}, {3579, 31657}, {5759, 30424}, {5805, 31730}, {10443, 43173}, {30331, 35514}, {43174, 43176}
X(43151) = reflection of X(i) in X(j) for these (i, j): (19925, 3826), (20116, 9940), (43179, 1385), (43180, 31657)
X(43151) = complement of the complement of X(2951)
X(43151) = centroid of {{IA,IB,IC,X(7)}}, where IA, IB, IC are the excenters
X(43151) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (40, 21151, 5542), (631, 11372, 38059), (1698, 36991, 38158), (3576, 35514, 30331), (4326, 8732, 11019), (10164, 43182, 9), (31730, 38123, 5805)

X(43152) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 2nd BROCARD AND 5th BROCARD

Barycentrics    (a^8-2*(b^2+c^2)*a^6-(b^4+6*b^2*c^2+c^4)*a^4+3*(b^4+b^2*c^2+c^4)*(b^2+c^2)*a^2-b^8+(b^2+c^2)^2*b^2*c^2-c^8)*a^2 : :
Trilinears    cos A (cot ω + 4 sin 2ω) - sin A : :

X(43152) lies on these lines: {3, 6}, {352, 40251}, {1352, 34885}, {3619, 35951}, {3818, 11676}, {4048, 40107}, {5476, 33273}, {5999, 17006}, {6310, 10323}, {7606, 19924}, {7824, 38317}, {7830, 24206}, {10519, 33014}, {10997, 22712}, {14561, 33004}, {14853, 33022}

X(43152) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 2076, 182), (3, 35424, 5092), (3098, 8588, 5092), (9738, 9739, 9821)

X(43153) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 2nd BROCARD AND LUCAS TANGENTS

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

X(43153) lies on these lines: {3, 6}, {3552, 8981}, {7582, 33022}, {7584, 33004}, {7824, 13951}, {8972, 35951}, {11676, 13665}, {35255, 35925}

X(43153) = Brocard circle-inverse of-X(43154)
X(43153) = {X(3), X(6)}-harmonic conjugate of X(43154)

X(43154) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 2nd BROCARD AND LUCAS(-1) TANGENTS

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

X(43154) lies on these lines: {3, 6}, {3552, 13966}, {7581, 33022}, {7583, 33004}, {7824, 8976}, {11676, 13785}, {13941, 35951}, {35256, 35925}

X(43154) = Brocard circle-inverse of-X(43153)
X(43154) = {X(3), X(6)}-harmonic conjugate of X(43153)

X(43155) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 5th BROCARD AND INNER-GREBE

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

X(43155) lies on these lines: {3, 6}, {487, 37334}, {5999, 12257}, {12215, 21736}

X(43155) = {X(5116), X(12306)}-harmonic conjugate of X(3)

X(43156) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 5th BROCARD AND OUTER-GREBE

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

X(43156) lies on these lines: {3, 6}, {488, 37334}, {5999, 12256}

X(43156) = {X(5116), X(12305)}-harmonic conjugate of X(3)

X(43157) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 5th BROCARD AND X3-ABC REFLECTIONS

Barycentrics    a^2*(a^8-3*(b^2+c^2)*a^6+(3*b^4+b^2*c^2+3*c^4)*a^4+9*(b^2+c^2)*b^2*c^2*a^2-c^8-b^8-2*(b^2-c^2)^2*b^2*c^2) : :
X(43157) = X(3)-3*X(5116) = 2*X(575)-3*X(5038)

X(43157) lies on these lines: {3, 6}, {114, 17005}, {384, 10992}, {542, 37334}, {4048, 38317}, {5026, 11272}, {5152, 32135}, {5476, 34504}, {7769, 12215}, {7824, 40107}, {7827, 10168}, {9878, 37336}, {10998, 32467}, {14060, 30534}, {36213, 37335}

X(43157) = {X(3), X(2076)}-harmonic conjugate of X(43148)

X(43158) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 1st CIRCUMPERP AND WASAT

Barycentrics    2*(b+c)*a^6-(7*b^2+4*b*c+7*c^2)*a^5+(b+c)*(8*b^2-7*b*c+8*c^2)*a^4-2*(b^2-c^2)^2*a^3-2*(b^3+c^3)*(b-c)^2*a^2+(b^2+c^2)*(b-c)^4*a+(b^2-c^2)*(b-c)^3*b*c : :
X(43158) = 3*X(2)+X(170) = 3*X(165)+X(17753) = X(3730)-3*X(10164) = 3*X(10164)+X(43168)

X(43158) lies on these lines: {2, 170}, {3, 142}, {165, 17753}, {2808, 6684}, {3008, 32462}, {3730, 10164}, {3911, 39789}, {9441, 10482}, {30503, 36480}

X(43158) = midpoint of X(i) and X(j) for these {i, j}: {170, 34848}, {3730, 43168}
X(43158) = complement of X(34848)
X(43158) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 170, 34848), (10164, 43168, 3730)

X(43159) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: CONWAY AND 3rd CONWAY

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

X(43159) lies on these lines: {1, 7}, {758, 10441}, {1695, 16817}, {2650, 19645}, {3741, 12617}, {3757, 7991}, {4362, 12435}, {5208, 15071}, {5248, 37620}, {6001, 15486}, {10454, 16124}, {10476, 12514}, {10477, 31803}, {10888, 19925}, {12526, 35621}, {12564, 35620}, {12709, 21334}, {21621, 39598}, {35633, 35635}

X(43159) = midpoint of X(1) and X(12544)
X(43159) = reflection of X(35632) in X(35631)
X(43159) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 10444, 4297), (1, 39553, 43164)

X(43160) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: CONWAY AND HEXYL

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

X(43160) lies on these lines: {1, 7}, {3, 8680}, {4, 2822}, {5, 18644}, {19, 1075}, {57, 243}, {4652, 21160}, {5884, 24257}, {6245, 6523}, {18634, 39531}, {24467, 34176}

X(43160) = midpoint of X(18655) and X(30265)

X(43161) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: CONWAY AND HONSBERGER

Barycentrics    3*a^6-6*(b+c)*a^5+(b+c)^2*a^4+4*(b^3+c^3)*a^3-(3*b^2+2*b*c+3*c^2)*(b-c)^2*a^2+2*(b^4-c^4)*(b-c)*a-(b^2-c^2)^2*(b-c)^2 : :
X(43161) = 5*X(3)-3*X(38121) = 2*X(4)-3*X(38037) = 3*X(4)-4*X(42356) = 2*X(5)-3*X(38031) = X(7)-3*X(5731) = 2*X(10)-3*X(21153) = 3*X(376)-2*X(11495) = 3*X(376)-X(35514) = X(962)-3*X(8236) = 4*X(1001)-3*X(38037) = 3*X(1001)-2*X(42356) = 5*X(2550)-6*X(38121) = 5*X(4297)-2*X(43181) = 3*X(4297)-X(43182) = 5*X(5732)-4*X(43181) = 3*X(5732)-2*X(43182) = 2*X(6601)-3*X(34625) = X(30332)+2*X(43178) = 9*X(38037)-8*X(42356) = 6*X(43181)-5*X(43182)

X(43161) lies on these lines: {1, 7}, {2, 15931}, {3, 1602}, {4, 1001}, {5, 38031}, {9, 515}, {10, 21153}, {36, 8732}, {40, 5768}, {104, 376}, {119, 6827}, {142, 3576}, {144, 2801}, {145, 25241}, {149, 35986}, {165, 4847}, {219, 41325}, {355, 31658}, {381, 38025}, {387, 5156}, {388, 954}, {411, 3086}, {443, 6253}, {452, 5691}, {480, 3421}, {497, 1617}, {517, 15185}, {518, 944}, {519, 7674}, {546, 38043}, {550, 22770}, {631, 3826}, {673, 36698}, {919, 2723}, {946, 38316}, {971, 5698}, {1125, 38150}, {1385, 5805}, {1444, 4229}, {1445, 18391}, {1478, 8232}, {1479, 37421}, {1621, 10431}, {1622, 9122}, {1709, 10430}, {1723, 5838}, {1750, 40998}, {1890, 7487}, {2320, 15909}, {2947, 25941}, {3062, 34628}, {3085, 6836}, {3174, 6282}, {3189, 31793}, {3218, 9778}, {3243, 5882}, {3254, 11715}, {3434, 7411}, {3474, 5173}, {3486, 5728}, {3488, 5572}, {3523, 19854}, {3579, 5770}, {3651, 12116}, {3869, 12669}, {4863, 7964}, {5082, 5584}, {5129, 19925}, {5218, 37374}, {5220, 21168}, {5223, 6737}, {5248, 37434}, {5252, 15837}, {5263, 36706}, {5274, 37797}, {5480, 38048}, {5541, 9803}, {5587, 6666}, {5603, 42819}, {5658, 24703}, {5762, 34773}, {5766, 15298}, {5775, 43174}, {5809, 10572}, {5817, 6936}, {5819, 40937}, {5842, 6916}, {5851, 12248}, {5880, 6934}, {5881, 24393}, {5886, 18482}, {5918, 17642}, {6244, 34607}, {6245, 10268}, {6361, 9943}, {6594, 12751}, {6600, 34619}, {6684, 38200}, {6796, 6926}, {6838, 10591}, {6840, 10590}, {6847, 10902}, {6851, 10267}, {6865, 11500}, {6872, 36991}, {6876, 10785}, {6885, 13624}, {6899, 11491}, {6903, 10786}, {6904, 7987}, {6908, 31418}, {6909, 7676}, {6925, 10724}, {6930, 28160}, {6932, 7678}, {6938, 15726}, {6943, 7679}, {6986, 19855}, {6989, 18517}, {6992, 18230}, {7397, 16593}, {7967, 38454}, {9799, 12514}, {9812, 31019}, {9841, 31730}, {10165, 20195}, {10246, 20330}, {10805, 42885}, {10806, 42886}, {10950, 41712}, {12115, 42843}, {12667, 31789}, {12848, 18412}, {15104, 20015}, {15692, 38092}, {15712, 38170}, {17580, 38204}, {17768, 36996}, {18357, 38113}, {18480, 38108}, {18610, 19262}, {19541, 26105}, {20059, 20067}, {20119, 38693}, {20533, 37416}, {30275, 37525}, {30283, 34610}, {31666, 38172}, {34648, 38075}, {37028, 38860}, {37254, 39475}, {40269, 41563}

X(43161) = midpoint of X(i) and X(j) for these {i, j}: {20, 390}, {944, 5759}, {3869, 12669}
X(43161) = reflection of X(i) in X(j) for these (i, j): (1, 43175), (4, 1001), (355, 31658), (2550, 3), (3243, 5882), (3254, 11715), (4301, 43179), (4312, 43177), (5732, 4297), (5735, 5542), (5805, 1385), (5881, 24393), (12751, 6594), (30424, 43176), (31671, 20330), (35514, 11495), (43166, 30331)
X(43161) = intersection, other than A,B,C, of conics {{A, B, C, X(104), X(4350)}} and {{A, B, C, X(279), X(3427)}}
X(43161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 1001, 38037), (20, 5731, 4293), (355, 31658, 38057), (631, 38149, 3826), (962, 5731, 18444), (1385, 5805, 38053), (6253, 8273, 443), (9778, 36845, 41338), (10246, 31671, 20330), (10572, 15299, 5809)

X(43162) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: CONWAY AND HUTSON INTOUCH

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

X(43162) lies on these lines: {1, 7}, {10, 19512}, {1279, 10443}, {7991, 39567}

X(43162) = {X(1), X(43170)}-harmonic conjugate of X(4301)

X(43163) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: CONWAY AND 6th MIXTILINEAR

Barycentrics    a^7-2*(b+c)*a^6+2*(b+c)^2*a^5-(b+c)*(4*b^2-5*b*c+4*c^2)*a^4+(5*b^2+4*b*c+5*c^2)*(b-c)^2*a^3-2*(b^4-c^4)*(b-c)*a^2+2*(b-c)^4*b*c*a-(b^2-c^2)*(b-c)^3*b*c : :
X(43163) = 3*X(165)-X(30625)

X(43163) lies on these lines: {1, 7}, {165, 28058}

X(43163) = midpoint of X(2951) and X(42309)

X(43164) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 2nd CONWAY AND 3rd CONWAY

Barycentrics    2*(b+c)*a^6+3*(b^2+c^2)*a^5+5*(b+c)*b*c*a^4-2*(b^4+c^4-(b^2-4*b*c+c^2)*b*c)*a^3-2*(b+c)*(b^4+c^4+2*(b-c)^2*b*c)*a^2-(b^2-c^2)^2*(b+c)^2*a-(b^2-c^2)^2*(b+c)*b*c : :
X(43164) = X(10454)-3*X(42057)

X(43164) lies on these lines: {1, 7}, {8, 35621}, {10, 10476}, {515, 15488}, {519, 10441}, {740, 31779}, {752, 31774}, {1125, 2051}, {1764, 43174}, {3741, 19925}, {5691, 10453}, {6737, 35614}, {6738, 10473}, {6744, 35620}, {9535, 21214}, {10106, 21334}, {10171, 19863}, {10439, 28236}, {10454, 42057}, {11531, 20037}, {12447, 35628}, {28164, 39550}

X(43164) = midpoint of X(1) and X(12545)
X(43164) = reflection of X(35633) in X(35631)
X(43164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 10446, 4301), (1, 10465, 4297), (1, 39553, 43159)

X(43165) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 2nd CONWAY AND HEXYL

Barycentrics    3*(b^2+c^2)*a^7-(b+c)*(2*b^2-3*b*c+2*c^2)*a^6-(7*b^4+2*b^2*c^2+7*c^4)*a^5+(b^2-c^2)*(b-c)*(4*b^2+b*c+4*c^2)*a^4+5*(b^4-c^4)*(b^2-c^2)*a^3-(b^2-c^2)*(b-c)*(2*b^4+2*c^4-(b-c)^2*b*c)*a^2-(b^2-c^2)^4*a-(b^2-c^2)^3*(b-c)*b*c : :
X(43165) = 2*X(5)-3*X(34830) = X(20)+3*X(17220) = 3*X(71)-5*X(631) = 7*X(9624)-3*X(33536)

X(43165) lies on these lines: {1, 7}, {5, 916}, {71, 631}, {226, 11436}, {2772, 15063}, {4184, 17168}, {6994, 41561}, {9624, 33536}, {26013, 38397}

X(43166) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 2nd CONWAY AND HONSBERGER

Barycentrics    a*(a^5-3*(b+c)*a^4+2*(b^2+6*b*c+c^2)*a^3+2*(b+c)*(b^2-4*b*c+c^2)*a^2-(3*b^2+2*b*c+3*c^2)*(b-c)^2*a+(b^2-c^2)*(b-c)*(b^2-6*b*c+c^2)) : :
X(43166) = 3*X(1)-X(2951) = 5*X(1)-2*X(43178) = 2*X(3)-3*X(38316) = 4*X(5)-3*X(38200) = 2*X(8)-3*X(38154) = 2*X(10)-3*X(38037) = X(20)-3*X(8236) = 2*X(40)-3*X(21153) = 2*X(142)-3*X(5603) = 4*X(1001)-3*X(21153) = 2*X(2951)-3*X(5732) = 5*X(2951)-6*X(43178) = 4*X(4301)-X(5735) = 3*X(5603)-X(35514) = 5*X(5732)-4*X(43178) = 5*X(5734)-3*X(11038) = 5*X(5734)-2*X(43177) = 3*X(7982)+2*X(16112) = 3*X(8236)-2*X(43175) = 3*X(11038)-2*X(43177)

X(43166) lies on these lines: {1, 7}, {2, 7994}, {3, 23397}, {4, 5853}, {5, 38200}, {8, 38154}, {9, 374}, {10, 38037}, {40, 1001}, {57, 17613}, {142, 5603}, {144, 3872}, {145, 36991}, {149, 1998}, {165, 1621}, {200, 908}, {226, 10388}, {322, 3886}, {354, 10860}, {518, 5693}, {528, 1537}, {551, 43151}, {936, 946}, {952, 31672}, {954, 1697}, {958, 6766}, {971, 1482}, {1320, 2801}, {1445, 2093}, {1490, 12699}, {1706, 5806}, {1750, 3870}, {2098, 8581}, {2099, 14100}, {2324, 5819}, {2835, 18725}, {3036, 38159}, {3158, 19541}, {3340, 5728}, {3358, 24474}, {3488, 15006}, {3576, 11495}, {3579, 38031}, {3626, 38158}, {3656, 6173}, {3679, 38075}, {3681, 30326}, {3817, 5328}, {3826, 8227}, {3868, 7995}, {3869, 4853}, {3873, 30304}, {3874, 7992}, {4512, 41338}, {4666, 9778}, {4863, 7965}, {4882, 19925}, {4915, 18222}, {5045, 9841}, {5047, 5250}, {5048, 31391}, {5049, 10390}, {5178, 37714}, {5289, 15587}, {5330, 10861}, {5437, 6244}, {5528, 6265}, {5534, 22793}, {5572, 11529}, {5587, 42356}, {5657, 6666}, {5690, 38108}, {5697, 15298}, {5720, 18482}, {5779, 8148}, {5805, 12700}, {5817, 12245}, {5851, 6264}, {5852, 41705}, {5880, 38036}, {5886, 20195}, {5901, 38122}, {5903, 15299}, {6001, 15185}, {6361, 8726}, {6601, 30500}, {6925, 41857}, {7091, 16215}, {7580, 10389}, {7672, 10398}, {7673, 8543}, {7676, 30282}, {7677, 15803}, {7956, 30827}, {7957, 31435}, {7988, 33108}, {8232, 31397}, {8583, 11522}, {8727, 24392}, {9580, 10382}, {9856, 11523}, {10394, 11526}, {10443, 30116}, {10595, 21151}, {10724, 12730}, {10864, 34791}, {11362, 38057}, {11496, 31424}, {11520, 12669}, {11682, 41228}, {12688, 41863}, {12702, 31658}, {12703, 42843}, {12704, 42842}, {12705, 18219}, {13374, 37560}, {13464, 38053}, {15726, 16200}, {16189, 34195}, {18412, 25415}, {18421, 30329}, {18443, 28174}, {18493, 38121}, {20059, 38460}, {21629, 36479}, {28194, 30503}, {31164, 34611}, {31393, 39779}, {31671, 37533}, {34718, 38097}, {35258, 38399}, {38059, 43174}

X(43166) = midpoint of X(i) and X(j) for these {i, j}: {145, 36991}, {390, 962}, {5223, 11531}, {5779, 8148}, {7982, 11372}, {10724, 12730}, {12560, 12651}
X(43166) = reflection of X(i) in X(j) for these (i, j): (20, 43175), (40, 1001), (2550, 946), (3243, 1482), (4297, 43179), (5528, 6265), (5732, 1), (5805, 22791), (6173, 3656), (11495, 42819), (12245, 24393), (12702, 31658), (35514, 142), (43161, 30331)
X(43166) = intersection, other than A,B,C, of conics {{A, B, C, X(77), X(42470)}} and {{A, B, C, X(279), X(3577)}}
X(43166) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 4312, 4321), (1, 9589, 12565), (20, 8236, 43175), (40, 1001, 21153), (946, 2550, 38150), (946, 6769, 936), (3340, 10384, 5728), (3870, 9812, 1750), (4666, 9778, 10857), (5603, 35514, 142), (5817, 12245, 24393), (11495, 42819, 3576), (11531, 24644, 5223), (18421, 30330, 30329)

X(43167) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 2nd CONWAY AND HUTSON INTOUCH

Barycentrics    4*a^6-9*(b+c)*a^5+(15*b^2+22*b*c+15*c^2)*a^4+2*(b+c)*(5*b^2-8*b*c+5*c^2)*a^3-2*(9*b^4+9*c^4-2*(3*b^2-b*c+3*c^2)*b*c)*a^2-(b^2-c^2)*(b-c)*(b^2+18*b*c+c^2)*a-(b^2-c^2)^2*(b+c)^2 : :

X(43167) lies on these lines: {1, 7}, {11224, 39567}

X(43167) = {X(1), X(43170)}-harmonic conjugate of X(4297)

X(43168) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 2nd CONWAY AND 6th MIXTILINEAR

Barycentrics    (3*b^2-2*b*c+3*c^2)*a^5-(b+c)*(8*b^2-13*b*c+8*c^2)*a^4+2*(3*b^2+5*b*c+3*c^2)*(b-c)^2*a^3-4*(b^2-c^2)*(b-c)*b*c*a^2-(b^2+c^2)*(b-c)^4*a-(b^2-c^2)*(b-c)^3*b*c : :
X(43168) = 4*X(2140)-3*X(3817) = 2*X(3730)-3*X(10164) = 3*X(3817)-2*X(34848) = 3*X(10164)-4*X(43158)

X(43168) lies on these lines: {1, 7}, {2, 41680}, {10, 2808}, {2140, 3817}, {3730, 10164}, {11019, 39789}, {21060, 28058}

X(43168) = midpoint of X(170) and X(17753)
X(43168) = reflection of X(i) in X(j) for these (i, j): (3730, 43158), (34848, 2140)
X(43168) = complement of X(41680)
X(43168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2140, 34848, 3817), (3730, 43158, 10164)

X(43169) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 3rd CONWAY AND HEXYL

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

X(43169) lies on these lines: {1, 7}, {3, 4670}, {518, 31778}, {971, 37536}, {1699, 17184}, {5805, 29181}

X(43169) = midpoint of X(i) and X(j) for these {i, j}: {5732, 10442}, {39553, 43173}

X(43170) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 3rd CONWAY AND HUTSON INTOUCH

Barycentrics    4*a^6-(b+c)*a^5+7*(b+c)^2*a^4+2*(b+c)*(b^2-4*b*c+c^2)*a^3-2*(5*b^4+5*c^4-2*(b^2-b*c+c^2)*b*c)*a^2-(b^2-c^2)*(b-c)*(b^2+10*b*c+c^2)*a-(b^2-c^2)^2*(b+c)^2 : :
X(43170) = 3*X(39553)-2*X(43171) = 4*X(43171)-3*X(43172)

X(43170) lies on these lines: {1, 7}, {518, 31779}, {1001, 10443}, {3817, 19868}, {5819, 15829}, {37035, 38059}, {39581, 43174}

X(43170) = midpoint of X(390) and X(10442)
X(43170) = reflection of X(i) in X(j) for these (i, j): (10443, 1001), (43172, 39553)
X(43170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4297, 43167, 1), (4301, 43162, 1)

X(43171) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 3rd CONWAY AND INCIRCLE-CIRCLES

Barycentrics    2*a^6+7*(b+c)*a^5+(17*b^2+10*b*c+17*c^2)*a^4-2*(b+c)^3*a^3-4*(5*b^4+5*c^4-2*(b^2-b*c+c^2)*b*c)*a^2-(b^2-c^2)*(b-c)*(5*b^2+14*b*c+5*c^2)*a+(b^2-10*b*c+c^2)*(b^2-c^2)^2 : :
X(43171) = 3*X(39553)-X(43170) = X(43170)+3*X(43172)

X(43171) lies on these lines: {1, 7}, {518, 31780}

X(43171) = midpoint of X(i) and X(j) for these {i, j}: {5542, 10442}, {39553, 43172}

X(43172) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 3rd CONWAY AND INTOUCH

Barycentrics    5*(b+c)*a^4+4*(b-c)^2*a^3-2*(b+c)*(3*b^2-4*b*c+3*c^2)*a^2-4*(b^2+c^2)*(b-c)^2*a+(b^2-c^2)*(b-c)*(b^2-6*b*c+c^2) : :
X(43172) = X(43170)-4*X(43171)

X(43172) lies on these lines: {1, 7}, {142, 2051}, {518, 31781}, {527, 4052}, {971, 15488}, {3741, 10435}, {3817, 4357}, {3950, 29069}, {3986, 24220}, {4452, 11531}, {5691, 21296}, {7991, 31995}, {9535, 24175}, {10164, 10436}, {10445, 21255}, {17272, 19925}, {20245, 21060}, {25590, 43174}

X(43172) = midpoint of X(7) and X(10442)
X(43172) = reflection of X(i) in X(j) for these (i, j): (10443, 142), (39553, 43171), (43170, 39553)
X(43172) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3663, 10446, 4301), (3664, 10444, 4297)

X(43173) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 3rd CONWAY AND 6th MIXTILINEAR

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

X(43173) lies on these lines: {1, 7}, {9, 7413}, {144, 7081}, {165, 894}, {200, 20348}, {518, 31785}, {1699, 3662}, {3062, 7155}, {3729, 18788}, {4645, 5691}, {5749, 10164}, {5880, 29181}, {6685, 10443}, {7988, 17291}, {7991, 24349}, {8245, 16831}, {9746, 10436}, {11495, 37619}, {15726, 37521}, {17364, 39878}, {20359, 31391}, {26051, 38052}

X(43173) = midpoint of X(2951) and X(10442)
X(43173) = reflection of X(i) in X(j) for these (i, j): (10443, 43151), (39553, 43169)

X(43174) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: EXCENTRAL AND 2nd ZANIAH

Barycentrics    2*a^4+3*(b+c)*a^3-3*(b+c)^2*a^2-3*(b^2-c^2)*(b-c)*a+(b^2-c^2)^2 : :
X(43174) = 3*X(1)-7*X(3523) = X(1)-3*X(10164) = 3*X(2)+X(7991) = 3*X(2)-7*X(9588) = 9*X(2)-5*X(11522) = X(3)+3*X(3654) = 7*X(3)-3*X(3655) = 3*X(3)-X(5882) = 5*X(3)+3*X(34718) = 19*X(3)-3*X(34748) = 5*X(3)-X(37727) = X(4) - 3*X(10) = X(8) + 3*X(165) = 7*X(3523)-9*X(10164) = 7*X(3654)+X(3655) = 9*X(3654)+X(5882) = 3*X(3654)-X(11362) = 5*X(3654)-X(34718) = 19*X(3654)+X(34748) = 15*X(3654)+X(37727) = X(4301)-7*X(9588) = 3*X(4301)-5*X(11522) = X(7991)+7*X(9588) = 3*X(7991)+5*X(11522)

Let A'B'C' be the Euler triangle. Let LA be the reflection of line B'C' in line BC, and define LB and LC cyclically. Let A" = LB∩LC, and define B" and C" cyclically. Triangle A"B"C" is homothetic to ABC at X(4), and X(43174) = X(10)-of-A"B"C". See also X(5882), X(43151). (Randy Hutson, May 31, 2021)

X(43174) lies on these lines: {1, 3523}, {2, 4301}, {3, 519}, {4, 9}, {5, 3828}, {8, 165}, {12, 5183}, {20, 3679}, {21, 5537}, {30, 4745}, {35, 17010}, {36, 1476}, {39, 4646}, {46, 4298}, {55, 4848}, {57, 12577}, {63, 6736}, {65, 12563}, {100, 6737}, {140, 517}, {145, 7987}, {200, 12520}, {210, 31803}, {226, 37567}, {355, 1657}, {376, 4669}, {381, 31399}, {382, 38066}, {388, 5128}, {484, 4292}, {515, 550}, {518, 31787}, {527, 12607}, {535, 31775}, {546, 28198}, {548, 28204}, {549, 10222}, {551, 631}, {553, 15888}, {572, 4856}, {758, 31788}, {938, 21153}, {944, 3625}, {946, 1656}, {950, 37568}, {952, 4701}, {958, 6244}, {960, 20103}, {962, 1698}, {971, 4662}, {986, 4353}, {993, 10310}, {1145, 3916}, {1210, 5119}, {1323, 36638}, {1376, 5837}, {1385, 3635}, {1482, 3636}, {1483, 17502}, {1572, 31396}, {1697, 1788}, {1699, 5068}, {1737, 4857}, {1750, 9949}, {1764, 43164}, {2077, 5267}, {2093, 3085}, {2136, 24477}, {2321, 37499}, {2328, 4248}, {2784, 3704}, {2800, 31837}, {2801, 9943}, {2802, 20418}, {2807, 31752}, {2951, 5686}, {3008, 24440}, {3057, 3911}, {3086, 4342}, {3090, 31162}, {3091, 9589}, {3146, 34648}, {3241, 15717}, {3244, 3576}, {3245, 12047}, {3293, 4300}, {3295, 6744}, {3339, 5542}, {3340, 5218}, {3359, 10915}, {3428, 25440}, {3452, 37828}, {3474, 9578}, {3486, 35445}, {3515, 8193}, {3524, 31425}, {3525, 9624}, {3526, 3656}, {3528, 34641}, {3529, 34638}, {3530, 15178}, {3533, 5603}, {3587, 6245}, {3616, 11531}, {3617, 5059}, {3622, 11224}, {3623, 30392}, {3632, 5731}, {3678, 6001}, {3680, 34711}, {3681, 15071}, {3697, 12688}, {3740, 9856}, {3746, 6986}, {3753, 7957}, {3811, 30503}, {3813, 37364}, {3814, 15908}, {3832, 38076}, {3841, 7680}, {3850, 9956}, {3851, 10175}, {3853, 28202}, {3854, 7989}, {3858, 22793}, {3868, 15104}, {3869, 6745}, {3871, 15931}, {3878, 6700}, {3881, 9940}, {3918, 7686}, {3919, 37625}, {3947, 4295}, {3951, 41561}, {3956, 31871}, {3983, 5927}, {4015, 5777}, {4134, 5693}, {4192, 9568}, {4208, 5735}, {4304, 10573}, {4309, 6992}, {4311, 12647}, {4312, 5261}, {4313, 31508}, {4314, 18391}, {4315, 15803}, {4640, 5795}, {4642, 40940}, {4677, 10304}, {4678, 37712}, {4685, 37400}, {4709, 30273}, {4746, 18481}, {4853, 5744}, {4868, 37528}, {4882, 5732}, {5044, 31797}, {5067, 38021}, {5073, 5790}, {5217, 41687}, {5223, 43182}, {5248, 10306}, {5250, 8582}, {5255, 13329}, {5258, 6909}, {5290, 30424}, {5437, 6766}, {5445, 30384}, {5450, 35238}, {5554, 35258}, {5558, 10980}, {5584, 5687}, {5703, 18421}, {5709, 12436}, {5734, 10303}, {5745, 5836}, {5771, 6705}, {5775, 43161}, {5806, 6666}, {5844, 13607}, {5847, 8550}, {5886, 19878}, {5903, 13411}, {6246, 38128}, {6685, 31785}, {6735, 12527}, {6796, 35239}, {6889, 10197}, {6922, 24387}, {6935, 31458}, {6967, 10199}, {7080, 12526}, {7288, 7962}, {7486, 19876}, {7688, 11491}, {7964, 21677}, {7968, 41964}, {7969, 41963}, {7988, 19877}, {8158, 25524}, {8583, 26062}, {8727, 9710}, {8960, 35611}, {9616, 19065}, {9819, 14986}, {9881, 38664}, {9947, 15726}, {9948, 11495}, {9950, 27549}, {9955, 10172}, {10056, 37112}, {10176, 12672}, {10385, 37723}, {10595, 15808}, {11024, 38204}, {11227, 34791}, {11231, 22791}, {11257, 22697}, {11278, 38028}, {11500, 12511}, {11523, 34744}, {12005, 40296}, {12053, 24914}, {12103, 28208}, {12258, 38740}, {12616, 12620}, {12625, 34607}, {12648, 16209}, {12649, 16208}, {12780, 41021}, {12781, 41020}, {13912, 35774}, {13975, 35775}, {15022, 30308}, {15177, 32534}, {15701, 41150}, {15863, 24466}, {16189, 38314}, {16201, 20116}, {17538, 34627}, {17928, 37546}, {18220, 31188}, {18258, 31800}, {18357, 28146}, {18480, 28150}, {19054, 31440}, {21620, 36279}, {21625, 31393}, {21734, 31145}, {21872, 40869}, {22361, 23703}, {22754, 22770}, {22837, 37611}, {24474, 33815}, {24982, 37162}, {25485, 38760}, {25590, 43172}, {26921, 40256}, {28172, 38176}, {28224, 41981}, {29594, 36698}, {30143, 37569}, {30147, 37531}, {31446, 37434}, {31792, 33575}, {31806, 37562}, {33337, 34474}, {33697, 38138}, {33703, 38074}, {33709, 38133}, {34606, 37829}, {34619, 37108}, {34639, 37423}, {37462, 41338}, {37598, 39595}, {38059, 43166}, {38151, 40333}, {39581, 43170}, {41006, 42316}

X(43174) = midpoint of X(i) and X(j) for these {i, j}: {3, 11362}, {4, 5493}, {8, 4297}, {10, 40}, {355, 31730}, {376, 4669}, {944, 3625}, {946, 12702}, {960, 31798}, {3244, 12245}, {3579, 5690}, {3626, 12512}, {3913, 24391}, {4301, 7991}, {4709, 30273}, {5044, 31797}, {5223, 43182}, {5836, 31793}, {9778, 38155}, {9943, 34790}, {11495, 24393}, {12513, 12640}, {15863, 24466}, {18258, 31800}, {31806, 37562}
X(43174) = reflection of X(i) in X(j) for these (i, j): (355, 4691), (946, 3634), (1125, 6684), (1482, 3636), (3626, 5690), (3635, 1385), (3881, 9940), (5777, 4015), (7686, 3918), (10171, 26446), (12005, 40296), (12512, 3579), (12699, 12571), (13464, 140), (13607, 13624), (15178, 3530), (18483, 9956), (19925, 10), (24474, 33815), (43176, 43151)
X(43174) = complement of X(4301)
X(43174) = X(8)-Beth conjugate of-X(19925)
X(43174) = centroid of {{IA,IB,IC,X(8)}}, where IA, IB, IC are the excenters
X(43174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 7991, 4301), (3, 3654, 11362), (3, 34718, 37727), (4, 40, 5493), (8, 165, 4297), (10, 5493, 4), (10, 12514, 18250), (40, 5587, 6361), (40, 5657, 10), (46, 31397, 4298), (55, 4848, 6738), (65, 13405, 12563), (140, 13464, 1125), (355, 38127, 4691), (484, 10039, 4292), (631, 7982, 551), (3576, 12245, 3244), (4295, 31434, 3947), (6684, 13464, 140), (7991, 9588, 2), (9578, 41348, 3474), (9589, 19875, 3091), (9780, 20070, 1699), (10222, 31447, 549), (12702, 26446, 946), (31730, 38127, 355), (37568, 40663, 950)

X(43175) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: HEXYL AND HUTSON INTOUCH

Barycentrics    4*a^6-9*(b+c)*a^5+3*(b+c)^2*a^4+2*(b+c)*(3*b^2-4*b*c+3*c^2)*a^3-2*(3*b^2+2*b*c+3*c^2)*(b-c)^2*a^2+(b^2-c^2)*(b-c)*(3*b^2-2*b*c+3*c^2)*a-(b^2-c^2)^2*(b-c)^2 : :
X(43175) = X(4)-3*X(38316) = X(8)-3*X(21153) = X(20)+3*X(8236) = 7*X(142)-6*X(38172) = X(355)-3*X(38031) = X(390)+3*X(5731) = 5*X(631)-3*X(38200) = 7*X(1385)-3*X(38172) = X(2550)-3*X(3576) = X(3243)-3*X(7967) = 5*X(3616)-3*X(38150) = 2*X(3826)-3*X(10165) = 3*X(3877)+X(12669) = X(5691)-3*X(38037) = 3*X(5731)-X(5732) = X(5735)-3*X(11038) = X(5759)+3*X(7967) = 2*X(6666)-3*X(38031) = 3*X(8236)-X(43166) = 4*X(43176)-3*X(43177)

X(43175) lies on these lines: {1, 7}, {3, 5853}, {4, 38316}, {8, 21153}, {9, 944}, {100, 4847}, {142, 1385}, {165, 36845}, {355, 6666}, {515, 1001}, {518, 5882}, {519, 7966}, {527, 3655}, {528, 11715}, {631, 38200}, {946, 42819}, {950, 42884}, {952, 6594}, {954, 10106}, {971, 34773}, {1125, 6864}, {1210, 7677}, {1617, 11019}, {2550, 3576}, {2801, 33337}, {3243, 5759}, {3244, 14110}, {3616, 38150}, {3817, 31266}, {3826, 10165}, {3877, 12669}, {5047, 38059}, {5083, 10167}, {5223, 18452}, {5691, 38037}, {5698, 41705}, {5805, 10246}, {5881, 38057}, {5901, 18482}, {6245, 10267}, {6601, 43151}, {6765, 37423}, {7674, 12629}, {8232, 9613}, {9809, 41561}, {9843, 11500}, {10385, 10860}, {10386, 31805}, {10445, 16503}, {10857, 17784}, {10944, 15837}, {11012, 41573}, {11495, 22770}, {12645, 38126}, {12730, 38693}, {13607, 42871}, {15178, 20330}, {15570, 38454}, {18230, 38154}, {18357, 38318}, {18525, 38108}, {20195, 38149}, {24389, 42842}, {30389, 38052}, {31671, 37624}, {31673, 42356}, {35262, 37462}, {37705, 38113}, {37740, 41712}

X(43175) = midpoint of X(i) and X(j) for these {i, j}: {1, 43161}, {9, 944}, {20, 43166}, {390, 5732}, {3243, 5759}, {4297, 30331}, {7674, 12629}, {14110, 15185}
X(43175) = reflection of X(i) in X(j) for these (i, j): (142, 1385), (355, 6666), (946, 42819), (18482, 5901), (20330, 15178), (24389, 42842), (24393, 31658), (31673, 42356), (42871, 13607)
X(43175) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 12573, 5542), (20, 8236, 43166), (355, 38031, 6666), (390, 5731, 5732), (4304, 5731, 4297), (4847, 15931, 10164), (5759, 7967, 3243)

X(43176) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: HEXYL AND INCIRCLE-CIRCLES

Barycentrics    2*a^6-9*(b+c)*a^5+3*(3*b^2-2*b*c+3*c^2)*a^4+2*(b+c)*(3*b^2-2*b*c+3*c^2)*a^3-4*(3*b^2+2*b*c+3*c^2)*(b-c)^2*a^2+(b^2-c^2)*(b-c)*(3*b^2+2*b*c+3*c^2)*a+(b^2-c^2)^2*(b-c)^2 : :
X(43176) = X(4)-3*X(38054) = X(10)-3*X(21151) = X(144)-5*X(7987) = X(355)-3*X(38123) = 3*X(551)-X(11372) = X(946)-3*X(38030) = X(2951)+3*X(11038) = X(3062)-5*X(3616) = 3*X(3576)+X(36996) = 9*X(3576)-X(41705) = 7*X(3622)-3*X(24644) = 2*X(3634)-3*X(38122) = 3*X(3817)-X(36991) = X(4301)-3*X(11038) = X(4312)+3*X(5731) = X(5223)-3*X(10164) = X(5691)-3*X(38151) = X(5779)-3*X(10165) = 3*X(36996)+X(41705) = X(43175)+3*X(43177)

X(43176) lies on these lines: {1, 7}, {2, 30291}, {3, 5850}, {4, 38054}, {9, 22088}, {10, 21151}, {142, 5787}, {144, 7987}, {355, 38123}, {515, 31657}, {518, 31787}, {551, 11372}, {946, 38030}, {971, 1125}, {1071, 18249}, {2550, 28236}, {2801, 3035}, {3062, 3616}, {3244, 35514}, {3576, 36996}, {3622, 24644}, {3634, 5789}, {3817, 36991}, {5223, 10164}, {5658, 10171}, {5691, 38151}, {5779, 10165}, {5805, 28164}, {5817, 19862}, {5843, 13624}, {5881, 38201}, {6246, 38124}, {8581, 10167}, {8726, 18250}, {9809, 40998}, {10857, 21060}, {12571, 31672}, {18480, 38111}, {19878, 38108}, {20195, 38158}, {22793, 38041}, {31673, 38107}, {33697, 38137}, {38155, 40333}

X(43176) = midpoint of X(i) and X(j) for these {i, j}: {1, 43182}, {7, 4297}, {2951, 4301}, {3244, 35514}, {5542, 5732}, {30424, 43161}
X(43176) = reflection of X(i) in X(j) for these (i, j): (19925, 142), (31672, 12571), (43174, 43151)
X(43176) = {X(2951), X(11038)}-harmonic conjugate of X(4301)

X(43177) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: HEXYL AND INTOUCH

Barycentrics    3*(b+c)*a^5-(5*b^2-6*b*c+5*c^2)*a^4-2*(b+c)*(b^2+c^2)*a^3+2*(3*b^2+2*b*c+3*c^2)*(b-c)^2*a^2-(b^2-c^2)^2*(b+c)*a-(b^2-c^2)^2*(b-c)^2 : :
X(43177) = X(4)-3*X(6173) = 5*X(4)-9*X(38073) = 2*X(5)-3*X(142) = X(5)-3*X(31657) = 5*X(5)-9*X(38111) = 11*X(5)-9*X(38139) = 7*X(5)-9*X(38171) = 3*X(7)+X(20) = 3*X(7)-X(5735) = X(20)-3*X(5732) = X(962)-5*X(30340) = 3*X(2951)+X(9589) = X(4301)-3*X(5542) = X(4301)+3*X(43182) = 3*X(5732)+X(5735) = 5*X(5734)-9*X(11038) = 5*X(5734)-3*X(43166) = 5*X(6173)-3*X(38073) = 3*X(11038)-X(43166) = X(43175)-4*X(43176) = X(43178)+2*X(43180)

X(43177) lies on these lines: {1, 7}, {2, 11407}, {3, 527}, {4, 6173}, {5, 142}, {9, 631}, {10, 1071}, {21, 18645}, {40, 41570}, {63, 6745}, {84, 1125}, {144, 4652}, {165, 9965}, {226, 10167}, {329, 10857}, {382, 5805}, {515, 5880}, {518, 5884}, {519, 6916}, {528, 5882}, {548, 5762}, {551, 1012}, {553, 7580}, {946, 15726}, {1001, 5450}, {1210, 6932}, {1445, 6962}, {1490, 12436}, {1656, 38065}, {1699, 10430}, {1750, 9776}, {1765, 3986}, {2096, 3576}, {2550, 5881}, {2800, 25558}, {3062, 38037}, {3090, 38093}, {3243, 35514}, {3358, 6892}, {3452, 11227}, {3475, 10860}, {3487, 9841}, {3523, 6172}, {3526, 5779}, {3528, 5759}, {3530, 5843}, {3660, 10391}, {3817, 5249}, {3826, 31399}, {3832, 36991}, {3843, 31672}, {3853, 18482}, {3858, 38080}, {3911, 5729}, {4197, 7705}, {4423, 41706}, {4847, 5696}, {5056, 38075}, {5067, 5817}, {5070, 38108}, {5220, 6684}, {5223, 7080}, {5316, 13257}, {5436, 12246}, {5437, 5658}, {5493, 37426}, {5537, 7411}, {5660, 13243}, {5728, 37566}, {5766, 30282}, {5785, 31446}, {5850, 37560}, {5851, 10165}, {5853, 37727}, {6147, 31805}, {6736, 41228}, {6839, 34648}, {6930, 18443}, {6943, 21617}, {6955, 18446}, {6966, 8545}, {6970, 8257}, {6993, 38076}, {7682, 10202}, {7702, 9670}, {8255, 9943}, {8581, 15888}, {8726, 12572}, {8732, 10398}, {9569, 10443}, {9612, 30275}, {9624, 11372}, {9710, 15587}, {9799, 19925}, {9948, 25466}, {9960, 12617}, {10177, 11263}, {10306, 11495}, {10864, 28629}, {11522, 38024}, {12053, 38055}, {12609, 12671}, {12618, 21255}, {12675, 15733}, {12848, 15803}, {14100, 37722}, {15298, 31452}, {15481, 38130}, {15720, 38067}, {15841, 20116}, {15908, 41555}, {17274, 36706}, {17576, 30389}, {17800, 31671}, {20059, 21734}, {24391, 37424}, {31730, 38454}, {34619, 37108}, {34937, 37501}, {37714, 38052}, {38154, 40333}

X(43177) = midpoint of X(i) and X(j) for these {i, j}: {7, 5732}, {9, 36996}, {20, 5735}, {1071, 5784}, {3243, 35514}, {4297, 30424}, {4312, 43161}, {5542, 43182}, {43180, 43181}
X(43177) = reflection of X(i) in X(j) for these (i, j): (142, 31657), (946, 25557), (5220, 6684), (5779, 6666), (43178, 43181)
X(43177) = intersection, other than A,B,C, of conics {{A, B, C, X(279), X(10305)}} and {{A, B, C, X(347), X(34919)}}
X(43177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (7, 20, 5735), (7, 4292, 30424), (7, 8544, 4292), (4292, 10884, 4297), (5542, 30424, 3671), (5732, 5735, 20), (5779, 38122, 6666), (6260, 9940, 9843), (8544, 10884, 5732), (10394, 30379, 1210), (21151, 36996, 9)

X(43178) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: HEXYL AND 6th MIXTILINEAR

Barycentrics    a*(a^5-3*(b+c)*a^4+2*(b^2-4*b*c+c^2)*a^3+2*(b+c)*(b^2+b*c+c^2)*a^2-(3*b^2+2*b*c+3*c^2)*(b-c)^2*a+(b^2-c^2)*(b-c)*(b^2+4*b*c+c^2)) : :
X(43178) = X(1)+3*X(2951) = X(1)-3*X(5732) = 5*X(1)-3*X(43166) = 3*X(3)-2*X(15254) = 3*X(9)-5*X(35242) = 3*X(142)-2*X(18483) = 3*X(376)-X(5698) = 3*X(1001)-4*X(13624) = 5*X(2951)+X(43166) = X(3062)-3*X(21153) = 2*X(3579)-3*X(11495) = 2*X(3634)-3*X(43151) = X(5220)-3*X(11495) = 11*X(5550)-9*X(38037) = 5*X(5732)-X(43166) = 3*X(6173)-X(41869) = X(30332)-3*X(43161) = X(30424)-3*X(43182) = 3*X(43177)-2*X(43180) = X(43180)-3*X(43181)

X(43178) lies on these lines: {1, 7}, {2, 41860}, {3, 15254}, {9, 2173}, {10, 37427}, {30, 5880}, {35, 8545}, {40, 2801}, {46, 10394}, {63, 5696}, {78, 3648}, {84, 12511}, {90, 411}, {142, 6851}, {144, 4420}, {165, 3219}, {376, 997}, {518, 12702}, {527, 3811}, {528, 18481}, {550, 6261}, {954, 31391}, {971, 1158}, {1001, 13624}, {1445, 37524}, {1479, 30379}, {1490, 12512}, {1699, 27186}, {1708, 1864}, {1709, 7411}, {1750, 10164}, {2475, 38052}, {3062, 21153}, {3174, 5850}, {3338, 7671}, {3534, 28534}, {3612, 8543}, {3634, 6908}, {3817, 10857}, {3826, 31672}, {3828, 18529}, {3872, 34628}, {3916, 42014}, {3935, 9778}, {4860, 10167}, {5177, 38204}, {5221, 5728}, {5302, 15587}, {5550, 38037}, {5697, 30318}, {5784, 12514}, {5851, 12738}, {6173, 41869}, {6594, 6796}, {6765, 34639}, {6845, 20195}, {6847, 19862}, {6850, 31673}, {6895, 38150}, {6899, 41540}, {6906, 11372}, {6985, 8257}, {7676, 15298}, {9780, 36991}, {9943, 36279}, {10178, 19541}, {10427, 37428}, {10826, 30312}, {10860, 35445}, {11220, 41338}, {11278, 42871}, {11684, 41228}, {12617, 37108}, {12699, 25557}, {12701, 38055}, {14100, 32636}, {14151, 30323}, {16112, 31658}, {18443, 28150}, {19861, 37299}, {28164, 30503}, {30311, 37692}, {31803, 37551}, {37022, 37600}, {37572, 41700}, {38122, 42356}

X(43178) = midpoint of X(2951) and X(5732)
X(43178) = reflection of X(i) in X(j) for these (i, j): (5220, 3579), (12699, 25557), (16112, 31658), (31672, 3826), (43177, 43181)
X(43178) = intersection, other than A,B,C, of conics {{A, B, C, X(90), X(1323)}} and {{A, B, C, X(279), X(10308)}}
X(43178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 30353, 30424), (5220, 11495, 3579), (5732, 5735, 10884), (10394, 30295, 46), (18450, 30332, 1), (31730, 41854, 3811)

X(43179) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: HUTSON INTOUCH AND INCIRCLE-CIRCLES

Barycentrics    6*a^3-9*(b+c)*a^2+4*(b-c)^2*a-(b^2-c^2)*(b-c) : :
X(43179) = 5*X(1)-X(7) = 3*X(1)+X(390) = 9*X(1)-X(4312) = 3*X(1)-X(5542) = X(1)+3*X(8236) = 7*X(1)-3*X(11038) = 11*X(1)+X(30332) = 17*X(1)-5*X(30340) = 7*X(1)-X(30424) = 4*X(1)-X(43180) = 3*X(7)+5*X(390) = 9*X(7)-5*X(4312) = 3*X(7)-5*X(5542) = X(7)+15*X(8236) = 7*X(7)-15*X(11038) = X(7)+5*X(30331) = 11*X(7)+5*X(30332) = 7*X(7)-5*X(30424) = 4*X(7)-5*X(43180) = 3*X(390)+X(4312) = X(390)-9*X(8236) = 7*X(390)+9*X(11038) = X(390)-3*X(30331) = 11*X(390)-3*X(30332) = 17*X(390)+15*X(30340) = 7*X(390)+3*X(30424) = 4*X(390)+3*X(43180)

X(43179) lies on these lines: {1, 7}, {8, 38059}, {9, 3244}, {10, 38316}, {11, 3748}, {142, 3636}, {144, 20057}, {495, 19925}, {517, 20116}, {518, 3635}, {519, 1001}, {527, 15570}, {551, 2550}, {954, 10392}, {971, 13607}, {1125, 3813}, {1279, 4989}, {1385, 43151}, {2346, 5559}, {2801, 12735}, {3057, 30329}, {3241, 5223}, {3295, 6744}, {3303, 6738}, {3488, 28236}, {3522, 30343}, {3616, 38204}, {3622, 38052}, {3625, 38057}, {3626, 6666}, {3632, 18230}, {3633, 5686}, {3679, 12630}, {3746, 7677}, {3817, 10578}, {3878, 15185}, {3883, 17360}, {3957, 26792}, {4419, 15600}, {4669, 38025}, {4677, 38101}, {5045, 12512}, {5218, 10389}, {5563, 7676}, {5572, 9957}, {5728, 5919}, {5759, 16200}, {5762, 33179}, {5838, 16673}, {5850, 42871}, {5881, 38158}, {5902, 7673}, {5903, 11025}, {6692, 35023}, {7373, 11495}, {7678, 37719}, {7679, 37720}, {7967, 11372}, {9624, 38149}, {9668, 21620}, {9778, 30350}, {9819, 15933}, {10164, 10580}, {10175, 18530}, {10572, 30311}, {11034, 21454}, {11041, 31393}, {11362, 38031}, {12730, 16173}, {14100, 17622}, {15808, 20195}, {15837, 39777}, {15863, 38060}, {15934, 28228}, {15935, 28234}, {16503, 17355}, {17715, 39595}, {19862, 38200}, {20095, 29817}, {25055, 40333}, {29580, 41845}

X(43179) = midpoint of X(i) and X(j) for these {i, j}: {1, 30331}, {9, 3244}, {390, 5542}, {3057, 30329}, {3878, 15185}, {4297, 43166}, {4301, 43161}, {5572, 9957}
X(43179) = reflection of X(i) in X(j) for these (i, j): (142, 3636), (1125, 42819), (3626, 6666), (43151, 1385)
X(43179) = intersection, other than A,B,C, of conics {{A, B, C, X(269), X(9343)}} and {{A, B, C, X(279), X(9328)}}
X(43179) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 390, 5542), (1, 4314, 12577), (1, 8236, 30331), (1, 12575, 12563), (1, 31567, 31570), (1, 31568, 31569), (3295, 6744, 43174), (3632, 18230, 38210), (5542, 30331, 390), (15808, 38201, 20195)

X(43180) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: INCIRCLE-CIRCLES AND INTOUCH

Barycentrics    2*a^3+5*(b+c)*a^2-4*(b-c)^2*a-3*(b^2-c^2)*(b-c) : :
X(43180) = X(1)+3*X(7) = 7*X(1)-3*X(390) = 5*X(1)+3*X(4312) = X(1)-3*X(5542) = 13*X(1)-9*X(8236) = 5*X(1)-9*X(11038) = 5*X(1)-3*X(30331) = 5*X(1)-X(30332) = X(1)-5*X(30340) = 4*X(1)-3*X(43179) = 7*X(7)+X(390) = 5*X(7)-X(4312) = 13*X(7)+3*X(8236) = 5*X(7)+3*X(11038) = 5*X(7)+X(30331) = 15*X(7)+X(30332) = 3*X(7)+5*X(30340) = 3*X(7)-X(30424) = 4*X(7)+X(43179) = 5*X(390)+7*X(4312) = X(390)-7*X(5542) = 5*X(390)-7*X(30331) = 15*X(390)-7*X(30332) = 3*X(390)+7*X(30424) = 4*X(390)-7*X(43179)

X(43180) lies on these lines: {1, 7}, {9, 5551}, {10, 6173}, {55, 4114}, {142, 3634}, {144, 5550}, {226, 4860}, {354, 3982}, {518, 3626}, {519, 1159}, {527, 1125}, {528, 3635}, {551, 5698}, {553, 4995}, {942, 2801}, {946, 12684}, {954, 5204}, {971, 12005}, {1156, 5557}, {2550, 3625}, {3296, 21625}, {3337, 37787}, {3338, 8545}, {3475, 35445}, {3579, 31657}, {3616, 38024}, {3617, 17288}, {3624, 6172}, {3649, 4934}, {3746, 30295}, {3817, 10980}, {3873, 5696}, {3874, 5784}, {3881, 15733}, {3935, 26842}, {3947, 30275}, {4031, 17718}, {4654, 11019}, {4663, 17067}, {4668, 38092}, {4684, 7321}, {4989, 7277}, {5045, 15726}, {5223, 9780}, {5445, 13407}, {5563, 8543}, {5572, 11544}, {5714, 15841}, {5762, 13624}, {5805, 31673}, {5852, 6666}, {6738, 10404}, {8581, 30329}, {9776, 21060}, {9812, 30350}, {10164, 21454}, {10394, 18398}, {11529, 28236}, {12512, 24470}, {12609, 12864}, {15808, 38053}, {15934, 28164}, {15935, 28172}, {17483, 40998}, {18492, 38073}, {18541, 28158}, {21151, 35242}, {21617, 41700}, {21620, 36279}, {25639, 41555}, {30311, 37720}, {30312, 37719}, {30404, 30420}, {30405, 30408}, {31253, 34753}, {33103, 39595}, {34502, 37568}, {36996, 38036}, {38210, 40333}

X(43180) = midpoint of X(i) and X(j) for these {i, j}: {1, 30424}, {7, 5542}, {3874, 5784}, {4297, 5735}, {4312, 30331}, {8581, 30329}
X(43180) = reflection of X(i) in X(j) for these (i, j): (1125, 25557), (5220, 3634), (43151, 31657), (43181, 43177)
X(43180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 7, 30424), (1, 4312, 30332), (1, 30332, 30331), (1, 30340, 5542), (7, 11036, 5735), (7, 11038, 4312), (7, 30340, 1), (142, 5220, 3634), (3664, 24231, 4353), (4310, 4888, 4349), (4312, 11038, 30331), (4355, 11036, 4297), (5542, 30331, 11038), (5542, 30424, 1), (11038, 30332, 1)

X(43181) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: INCIRCLE-CIRCLES AND 6th MIXTILINEAR

Barycentrics    2*a^6-9*(b+c)*a^5+(9*b^2-22*b*c+9*c^2)*a^4+2*(b+c)*(3*b^2+2*b*c+3*c^2)*a^3-4*(3*b^2+2*b*c+3*c^2)*(b-c)^2*a^2+(b^2-c^2)*(b-c)*(3*b+c)*(b+3*c)*a+(b^2-c^2)^2*(b-c)^2 : :
X(43181) = 3*X(142)-2*X(12571) = 5*X(355)-9*X(38121) = X(962)+3*X(2951) = X(962)-3*X(5542) = X(3062)-3*X(38059) = X(4297)-3*X(5732) = 5*X(4297)-3*X(43161) = X(4297)+3*X(43182) = X(5696)+3*X(11220) = 5*X(5732)-X(43161) = 3*X(6172)-7*X(16192) = 2*X(6684)-3*X(43151) = 7*X(7989)-3*X(36991) = 7*X(7989)-9*X(38204) = 5*X(8227)-9*X(21151) = X(9589)-5*X(30340) = X(22793)-3*X(31657) = X(36991)-3*X(38204) = X(43161)+5*X(43182) = 2*X(43178)+X(43180)

X(43181) lies on these lines: {1, 7}, {142, 12571}, {355, 38121}, {518, 31797}, {527, 12512}, {971, 6684}, {1125, 15726}, {2801, 9943}, {3062, 38059}, {3616, 11379}, {3646, 9841}, {5696, 11220}, {5703, 9814}, {5784, 18249}, {5850, 8715}, {5880, 28164}, {5918, 13405}, {6172, 16192}, {7989, 36991}, {8227, 21151}, {10164, 30393}, {10171, 41867}, {10178, 20103}, {17528, 19925}, {22793, 31657}, {31672, 38123}

X(43181) = midpoint of X(i) and X(j) for these {i, j}: {20, 30424}, {2951, 5542}, {5732, 43182}, {43177, 43178}
X(43181) = reflection of X(43180) in X(43177)

X(43182) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: INTOUCH AND 6th MIXTILINEAR

Barycentrics    (3*a^2-2*(b+c)*a-(b-c)^2)*((b+c)*a^2-2*(b-c)^2*a+(b^2-c^2)*(b-c)) : :
X(43182) = 2*X(4)-3*X(38151) = 2*X(5)-3*X(38123) = 2*X(9)-3*X(10164) = 4*X(142)-3*X(3817) = 3*X(142)-2*X(42356) = X(144)-3*X(165) = 2*X(355)-3*X(38201) = 2*X(381)-3*X(38094) = 2*X(546)-3*X(38172) = 2*X(946)-3*X(38054) = 9*X(3817)-8*X(42356) = 3*X(4297)-2*X(43161) = X(4297)-4*X(43181) = X(4301)-4*X(43177) = 3*X(5658)+X(10307) = 3*X(5732)-X(43161) = 3*X(5918)+X(31391) = 3*X(10164)-4*X(43151) = X(30424)+2*X(43178) = X(43161)-6*X(43181)

X(43182) lies on these lines: {1, 7}, {2, 3062}, {4, 38151}, {5, 38123}, {9, 5658}, {10, 971}, {40, 5850}, {142, 1538}, {144, 165}, {214, 38759}, {226, 5918}, {355, 38201}, {381, 38094}, {442, 38204}, {515, 40587}, {518, 12640}, {519, 35514}, {527, 4421}, {546, 38172}, {946, 31657}, {1001, 22754}, {1125, 9841}, {1145, 2801}, {1210, 30287}, {2092, 10443}, {2550, 11530}, {3126, 3667}, {3428, 34646}, {3452, 10178}, {3579, 5843}, {3616, 24644}, {3634, 5817}, {3647, 31658}, {3826, 38158}, {3912, 9950}, {4847, 11220}, {5223, 43174}, {5480, 38187}, {5493, 12631}, {5572, 15841}, {5696, 12669}, {5759, 12512}, {5762, 31730}, {5779, 6684}, {5785, 7992}, {5833, 9799}, {5851, 6594}, {5853, 15347}, {6223, 18250}, {6666, 15346}, {6828, 41862}, {6857, 38059}, {9778, 20059}, {9801, 17298}, {9949, 9961}, {9955, 38111}, {10167, 11019}, {10398, 37421}, {10427, 21635}, {10860, 13405}, {10865, 31397}, {13464, 38030}, {15071, 41228}, {15837, 17613}, {15876, 17355}, {15909, 20292}, {16174, 38124}, {17060, 21255}, {18483, 38107}, {19862, 38122}, {19925, 36991}, {21168, 35242}, {24009, 28344}, {28150, 31671}, {30295, 41572}

X(43182) = midpoint of X(i) and X(j) for these {i, j}: {7, 2951}, {20, 4312}, {40, 36996}, {5696, 12669}, {15071, 41228}
X(43182) = reflection of X(i) in X(j) for these (i, j): (1, 43176), (9, 43151), (946, 31657), (4297, 5732), (4301, 5542), (5223, 43174), (5542, 43177), (5732, 43181), (5759, 12512), (5779, 6684), (11372, 1125), (16112, 6666), (21635, 10427), (36991, 19925)
X(43182) = complement of X(3062)
X(43182) = complementary conjugate of X(3817)
X(43182) = barycentric product X(i)*X(j) for these {i, j}: {144, 11019}, {165, 20905}
X(43182) = trilinear product X(i)*X(j) for these {i, j}: {144, 40133}, {165, 11019}, {1200, 31627}, {1419, 41006}
X(43182) = intersection, other than A,B,C, of conics {{A, B, C, X(1), X(14100)}} and {{A, B, C, X(7), X(11019)}}
X(43182) = crosspoint of X(2) and X(16284)
X(43182) = X(2)-Ceva conjugate of-X(40133)
X(43182) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 3817), (6, 7), (31, 40133), (55, 23058)
X(43182) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (9, 43151, 10164), (165, 41561, 21060), (946, 31657, 38054), (7992, 37108, 18249), (9948, 37424, 10), (11372, 21151, 1125), (35242, 41705, 21168), (36991, 38052, 19925)

X(43183) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 1st KENMOTU-FREE-VERTICES AND 2nd KENMOTU-FREE-VERTICES

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

X(43183) lies on these lines: {3, 6}, {22, 14602}, {76, 10350}, {183, 626}, {194, 39097}, {315, 385}, {394, 3229}, {736, 7754}, {754, 5309}, {1916, 38907}, {1993, 3117}, {2023, 10104}, {2548, 9753}, {2549, 36998}, {2794, 7748}, {3329, 7907}, {3788, 32458}, {3815, 20576}, {5077, 39593}, {5286, 6655}, {5976, 10349}, {6680, 11174}, {7739, 7833}, {7745, 40279}, {7758, 39099}, {7763, 39101}, {7767, 8177}, {7770, 18806}, {7793, 39089}, {7801, 14645}, {7818, 8667}, {7867, 15271}, {8290, 10351}, {8623, 42295}, {9755, 23718}, {11610, 38525}, {12829, 14880}, {14881, 42535}, {20859, 34396}, {31400, 33259}

X(43183) = midpoint of X(1504) and X(1505)
X(43183) = harmonic center of Moses circle and 2nd Lemoine circle
X(43183) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 35429, 39764), (32, 574, 13335), (32, 5028, 39), (32, 5162, 3053), (32, 7772, 13357), (32, 30270, 187), (32, 32452, 3), (371, 372, 35424), (2031, 13335, 32), (2560, 2561, 182), (5017, 30435, 32), (5028, 35388, 6), (5111, 34870, 3095), (10350, 36849, 76)

X(43184) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 1st KENMOTU-FREE-VERTICES AND X3-ABC REFLECTIONS

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

X(43184) lies on these lines: {3, 6}, {7766, 26441}, {33371, 39089}

X(43185) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: 2nd KENMOTU-FREE-VERTICES AND X3-ABC REFLECTIONS

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

X(43185) lies on these lines: {3, 6}, {7766, 8982}, {33370, 39089}

X(43186) = CENTER OF THE CO-BROCARD CIRCLE OF THESE TRIANGLES: INNER-SODDY AND OUTER-SODDY

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

X(43186) lies on these lines: {1, 7}, {85, 19883}, {348, 3828}, {4669, 17078}, {4691, 9312}

X(43186) = {X(279), X(5543)}-harmonic conjugate of X(21314)

X(43187) = ISOGONAL CONJUGATE OF X(2491)

Barycentrics    b^2*c^2*(a^4-b^2*a^2-(b^2-c^2)*c^2)*(a^2-c^2)*(a^4-c^2*a^2+(b^2-c^2)*b^2)*(a^2-b^2) : :
Barycentrics    csc A sec(A + ω)/(b^2 - c^2) : :

X(43187) lies on the MacBeath circumconic and these lines: {76, 6035}, {98, 9150}, {99, 6037}, {110, 685}, {287, 3978}, {290, 892}, {648, 2451}, {670, 2966}, {689, 2715}, {804, 17938}, {880, 2395}, {1331, 1978}, {1332, 4601}, {1797, 4615}, {1813, 4572}, {2987, 16081}, {3266, 14919}, {4563, 4609}, {5207, 20021}, {5967, 14382}, {6528, 41074}, {6531, 41909}, {9170, 11059}, {12215, 39058}, {17941, 41173}, {30736, 34369}, {36084, 37133}

X(43187) = isogonal conjugate of X(2491)
X(43187) = isotomic conjugate of X(3569)
X(43187) = polar conjugate of X(17994)
X(43187) = barycentric product X(i)*X(j) for these {i, j}: {69, 22456}, {75, 36036}, {76, 2966}, {98, 670}, {99, 290}, {110, 18024}
X(43187) = barycentric quotient X(i)/X(j) for these (i, j): (3, 39469), (4, 17994), (69, 684), (76, 2799), (98, 512), (99, 511)
X(43187) = trilinear product X(i)*X(j) for these {i, j}: {2, 36036}, {63, 22456}, {75, 2966}, {76, 36084}, {92, 17932}, {98, 799}
X(43187) = trilinear quotient X(i)/X(j) for these (i, j): (63, 39469), (92, 17994), (98, 798), (99, 1755), (110, 9417), (162, 2211)
X(43187) = 1st Saragossa point of X(17938)
X(43187) = orthocorrespondent of X(2679)
X(43187) = trilinear pole of the line {3, 76}, which is the Brocard axis of these triangles: 1st anti-Brocard, 6th Brocard, circummedial
X(43187) = intersection, other than A,B,C, of conics {{A, B, C, X(6), X(17938)}} and {{A, B, C, X(76), X(35139)}}
X(43187) = Cevapoint of X(i) and X(j) for these (i, j): {6, 804}, {98, 2422}, {99, 2421}, {325, 525}
X(43187) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 39469}, {48, 17994}, {232, 810}, {237, 661}
X(43187) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 39469), (4, 17994), (69, 684), (76, 2799)

X(43188) = ISOGONAL CONJUGATE OF X(2451)

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

X(43188) lies on these lines: {110, 22264}, {647, 6331}, {1624, 4230}, {2421, 36841}, {2491, 41678}, {5968, 9307}, {5972, 9513}, {9289, 35910}

X(43188) = isogonal conjugate of X(2451)
X(43188) = isotomic conjugate of X(30476)
X(43188) = polar conjugate of X(16229)
X(43188) = barycentric product X(i)*X(j) for these {i, j}: {99, 9307}, {648, 9289}, {670, 9292}, {799, 9258}, {811, 9255}
X(43188) = barycentric quotient X(i)/X(j) for these (i, j): (1, 17478), (3, 22089), (4, 16229), (10, 21050), (75, 17893), (86, 17215)
X(43188) = trilinear product X(i)*X(j) for these {i, j}: {99, 9258}, {162, 9289}, {648, 9255}, {662, 9307}, {799, 9292}
X(43188) = trilinear quotient X(i)/X(j) for these (i, j): (2, 17478), (63, 22089), (76, 17893), (92, 16229), (99, 1958), (162, 1968)
X(43188) = trilinear pole of the line {20, 185}, which is the Brocard axis of these triangles: anti-Euler, anti-3rd-tri-squares-central, anti-4th-tri-squares-central
X(43188) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(110)}} and {{A, B, C, X(99), X(30610)}}
X(43188) = Cevapoint of X(2) and X(647)
X(43188) = X(877)-cross conjugate of-X(2966)
X(43188) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 17478}, {19, 22089}, {32, 17893}, {48, 16229}
X(43188) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 17478), (3, 22089), (4, 16229), (10, 21050)
X(43188) = X(25)-vertex conjugate of-X(6331)

X(43189) = TRILINEAR POLE OF THE LINE X(3)X(2783)

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

X(43189) lies on the MacBeath circumconic and these lines: {110, 4391}, {651, 850}, {1813, 14208}, {4558, 35518}, {24602, 24619}

X(43189) = trilinear pole of the line {3, 2783}, which is the Brocard axis of these triangles: anti-inner-Garcia, inner-Garcia
X(43189) = Cevapoint of X(6) and X(2787)

X(43190) = ISOGONAL CONJUGATE OF X(6586)

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

X(43190) lies on the MacBeath circumconic and these lines: {2, 1815}, {6, 23989}, {109, 17494}, {110, 3732}, {514, 15378}, {675, 20974}, {677, 1897}, {895, 15320}, {1331, 2398}, {1332, 42719}, {1783, 26693}, {1797, 5773}, {1813, 35312}, {1993, 2989}, {2991, 3187}, {4563, 31624}, {9057, 35184}, {10756, 25049}

X(43190) = anticomplement of X(40618)
X(43190) = isogonal conjugate of X(6586)
X(43190) = isotomic conjugate of X(25259)
X(43190) = barycentric product X(i)*X(j) for these {i, j}: {6, 31624}, {69, 26705}, {99, 15320}, {190, 14377}
X(43190) = barycentric quotient X(i)/X(j) for these (i, j): (1, 1734), (81, 16751), (99, 33297), (100, 3681), (101, 3730), (110, 4184)
X(43190) = trilinear product X(i)*X(j) for these {i, j}: {31, 31624}, {63, 26705}, {100, 14377}, {662, 15320}, {693, 15378}, {1111, 31616}
X(43190) = trilinear quotient X(i)/X(j) for these (i, j): (2, 1734), (42, 21837), (48, 22388), (86, 16751), (100, 3730), (101, 15624)
X(43190) = 1st Saragossa point of X(32739)
X(43190) = orthocorrespondent of X(116)
X(43190) = trilinear pole of the line {3, 142}, which is the Brocard axis of these triangles: Ascella, 1st circumperp, 2nd circumperp, 2nd Pamfilos-Zhou, Wasat
X(43190) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(658)}} and {{A, B, C, X(6), X(2438)}}
X(43190) = Cevapoint of X(i) and X(j) for these (i, j): {6, 514}, {513, 16583}, {521, 1212}, {525, 1213}
X(43190) = X(6)-cross conjugate of-X(15378)
X(43190) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 1734}, {42, 16751}, {86, 21837}, {92, 22388}
X(43190) = X(675)-line conjugate of-X(20974)
X(43190) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 1734), (81, 16751), (99, 33297), (100, 3681)

X(43191) = TRILINEAR POLE OF THE LINE X(5)X(516)

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

X(43191) lies on these lines: {4241, 35360}, {17753, 25049}

X(43191) = isotomic conjugate of the anticomplement of X(25259)
X(43191) = barycentric quotient X(i)/X(j) for these (i, j): (101, 24047), (190, 17295)
X(43191) = trilinear quotient X(i)/X(j) for these (i, j): (100, 24047), (668, 17295)
X(43191) = trilinear pole of the line {5, 516}, which is the Brocard axis of these triangles: 3rd Euler, 4th Euler
X(43191) = intersection, other than A,B,C, of conics {{A, B, C, X(2), X(658)}} and {{A, B, C, X(94), X(648)}}
X(43191) = Cevapoint of X(i) and X(j) for these (i, j): {514, 17366}, {523, 20970}
X(43191) = X(i)-isoconjugate-of-X(j) for these {i, j}: {513, 24047}, {667, 17295}
X(43191) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (101, 24047), (190, 17295)

X(43192) = ISOGONAL CONJUGATE OF X(10495)

Barycentrics    a*((a-b+c)*sin(B/2)+(a+b-c)*sin(C/2))*(a-b)*(a-b+c)*(a-c)*(a+b-c) : :

X(43192) lies on these lines: {1, 8099}, {55, 503}, {57, 12809}, {88, 10490}, {109, 10496}, {164, 13443}, {174, 6732}, {177, 1130}, {178, 34234}, {234, 673}, {266, 2089}, {651, 6733}, {1156, 7707}, {3659, 13444}, {7589, 10498}, {8140, 11372}, {10231, 13385}, {12771, 18454}

X(43192) = isogonal conjugate of X(10495)
X(43192) = trilinear pole of line X(1)X(168)
X(43192) = trilinear pole of the common Brocard axis of midarc and 2nd midarc triangles
X(43192) = barycentric product X(i)*X(j) for these {i, j}: {100, 234}, {178, 651}, {190, 10490}, {556, 13444}, {664, 7707}
X(43192) = barycentric quotient X(i)/X(j) for these (i, j): (178, 4391), (234, 693)
X(43192) = trilinear product X(i)*X(j) for these {i, j}: {100, 10490}, {101, 234}, {109, 178}, {177, 6733}, {188, 13444}, {651, 7707}
X(43192) = trilinear quotient X(i)/X(j) for these (i, j): (177, 6728), (178, 522), (234, 514)
X(43192) = Cevapoint of X(1) and X(10495)
X(43192) = X(177)-Aleph conjugate of-X(2957)
X(43192) = X(260)-isoconjugate-of-X(6728)
X(43192) = X(1)-line conjugate of-X(10501)
X(43192) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (178, 4391), (234, 693)
X(43192) = X(259)-Zayin conjugate of-X(650)

leftri

Gibert points on the cubic K1220: X(43193)-X(43212)

rightri

This preamble and points X(43193)-X(43212) are contributed by Peter Moses, May 8, 2021. See also the preambles just before X(42085), X(42413), and X(42429) and others.

See K1220.



X(43193) = GIBERT (3,2,-4) POINT

Barycentrics    Sqrt[3]*a^2*S - 4*a^2*SA + 4*SB*SC : :
X(43193) = 3 X[5339] - 4 X[40694], 11 X[5339] - 12 X[41113], X[5339] - 4 X[42151], 5 X[5339] - 4 X[42160], 5 X[5339] - 12 X[42510], 2 X[5339] + 3 X[42586], 3 X[22238] - 2 X[40694], 11 X[22238] - 6 X[41113], 5 X[22238] - 2 X[42160], 5 X[22238] - 6 X[42510], 4 X[22238] + 3 X[42586], 11 X[40694] - 9 X[41113], X[40694] - 3 X[42151], 5 X[40694] - 3 X[42160], 5 X[40694] - 9 X[42510], 8 X[40694] + 9 X[42586], 3 X[41113] - 11 X[42151], 15 X[41113] - 11 X[42160], 5 X[41113] - 11 X[42510], 8 X[41113] + 11 X[42586], 5 X[42151] - X[42160], 5 X[42151] - 3 X[42510], 8 X[42151] + 3 X[42586], X[42160] - 3 X[42510], 8 X[42160] + 15 X[42586], 8 X[42510] + 5 X[42586]

X(43193) lies on the cubic K1220 and these lines: {2, 42165}, {3, 13}, {4, 16645}, {5, 11481}, {6, 20}, {14, 5073}, {15, 15696}, {16, 382}, {18, 3830}, {30, 5339}, {61, 3534}, {62, 1657}, {140, 42161}, {376, 397}, {381, 5237}, {395, 3146}, {396, 3522}, {398, 3529}, {548, 11480}, {549, 42162}, {550, 10653}, {628, 35749}, {631, 5318}, {632, 42921}, {633, 33622}, {635, 11296}, {1151, 42256}, {1152, 42254}, {1250, 9657}, {1656, 5351}, {2041, 23261}, {2042, 23251}, {3090, 5350}, {3091, 42933}, {3411, 19107}, {3412, 42116}, {3523, 42166}, {3524, 5344}, {3525, 5366}, {3526, 10646}, {3528, 5335}, {3530, 18582}, {3533, 43104}, {3543, 42163}, {3545, 42792}, {3627, 42149}, {3628, 42474}, {3832, 23303}, {3843, 19106}, {3851, 10187}, {3853, 18581}, {3855, 42102}, {3856, 42111}, {3858, 42910}, {3859, 42889}, {3861, 42105}, {5054, 42631}, {5059, 37641}, {5067, 42134}, {5068, 42793}, {5070, 16808}, {5071, 42948}, {5072, 42937}, {5076, 41977}, {5238, 41974}, {5321, 33703}, {5334, 42970}, {5343, 11541}, {5349, 15682}, {5352, 15688}, {5365, 33603}, {5895, 11244}, {7486, 42110}, {8252, 42241}, {8253, 35740}, {8703, 42152}, {9670, 19373}, {10304, 42945}, {10574, 36978}, {10654, 15704}, {11001, 42587}, {11134, 13346}, {11485, 42434}, {11486, 16964}, {11488, 21734}, {11489, 17578}, {11543, 42113}, {12103, 42150}, {12816, 15703}, {13846, 42252}, {13847, 42250}, {14093, 16267}, {14869, 42911}, {15681, 41100}, {15684, 16963}, {15686, 42925}, {15687, 42920}, {15689, 42435}, {15691, 42511}, {15692, 42588}, {15693, 42936}, {15694, 42581}, {15695, 16962}, {15700, 41121}, {15715, 43107}, {15717, 23302}, {15720, 37832}, {16239, 42138}, {16268, 43017}, {17504, 41119}, {17538, 42942}, {19710, 42509}, {19773, 26958}, {33416, 42629}, {34200, 41112}, {34755, 42126}, {35404, 41120}, {36970, 42989}, {36990, 36995}, {38335, 41944}, {41099, 42926}, {41106, 43100}, {41122, 42694}, {42085, 42584}, {42099, 42991}, {42128, 42488}, {42159, 42913}, {42173, 42212}, {42174, 42214}, {42183, 42221}, {42184, 42223}, {42432, 42975}, {42612, 43018}, {42892, 42968}

X(43193) = reflection of X(i) in X(j) for these {i,j}: {5339, 22238}, {22238, 42151}
X(43193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5340, 16644}, {3, 16644, 42773}, {3, 16965, 42156}, {3, 42155, 5340}, {3, 42156, 42490}, {3, 42158, 42155}, {4, 36843, 16645}, {4, 42943, 36843}, {5, 11481, 42491}, {5, 42089, 42611}, {5, 42491, 43028}, {6, 20, 43194}, {16, 382, 42153}, {16, 42097, 42093}, {16, 42131, 42097}, {17, 42528, 3}, {20, 42120, 42148}, {20, 42148, 6}, {62, 1657, 42154}, {376, 397, 36836}, {382, 42153, 42093}, {548, 40693, 11480}, {548, 42118, 40693}, {550, 10653, 22236}, {550, 22236, 42626}, {3524, 5344, 42598}, {3526, 42127, 42813}, {3526, 42813, 42098}, {3528, 5335, 16772}, {5059, 37641, 42164}, {5237, 42431, 381}, {5238, 41974, 42974}, {5340, 42490, 42156}, {5340, 42625, 3}, {5351, 36969, 1656}, {5352, 41107, 42988}, {10646, 42127, 42098}, {10646, 42813, 3526}, {11481, 42086, 42094}, {11481, 42094, 43028}, {11486, 17800, 16964}, {11486, 42100, 42096}, {15688, 42988, 5352}, {15704, 42924, 10654}, {16964, 17800, 42096}, {16964, 42100, 17800}, {16965, 36968, 42433}, {16965, 42156, 5340}, {16965, 42433, 3}, {16965, 42891, 42158}, {17538, 42998, 42942}, {19106, 42115, 42095}, {36968, 42155, 42625}, {36968, 42158, 3}, {36968, 42891, 16965}, {40693, 42091, 548}, {42086, 42089, 42137}, {42086, 42123, 11481}, {42088, 42120, 6}, {42088, 42148, 20}, {42091, 42118, 11480}, {42094, 42491, 5}, {42097, 42153, 382}, {42137, 42493, 42106}, {42151, 42160, 42510}, {42155, 42156, 16965}, {42155, 42433, 42490}, {42155, 42625, 16644}, {42156, 42490, 16644}, {42158, 42433, 16965}, {42258, 42259, 42120}, {42434, 42990, 11485}, {42814, 42938, 43012}, {42941, 42944, 3091}

X(43194) = GIBERT (3,-2,4) POINT

Barycentrics    Sqrt[3]*a^2*S + 4*a^2*SA - 4*SB*SC : :
X(43195) = 3 X[5340] - 4 X[40693], 11 X[5340] - 12 X[41112], X[5340] - 4 X[42150], 5 X[5340] - 4 X[42161], 5 X[5340] - 12 X[42511], 2 X[5340] + 3 X[42587], 3 X[22236] - 2 X[40693], 11 X[22236] - 6 X[41112], 5 X[22236] - 2 X[42161], 5 X[22236] - 6 X[42511], 4 X[22236] + 3 X[42587], 11 X[40693] - 9 X[41112], X[40693] - 3 X[42150], 5 X[40693] - 3 X[42161], 5 X[40693] - 9 X[42511], 8 X[40693] + 9 X[42587], 3 X[41112] - 11 X[42150], 15 X[41112] - 11 X[42161], 5 X[41112] - 11 X[42511], 8 X[41112] + 11 X[42587], 5 X[42150] - X[42161], 5 X[42150] - 3 X[42511], 8 X[42150] + 3 X[42587], X[42161] - 3 X[42511], 8 X[42161] + 15 X[42587], 8 X[42511] + 5 X[42587]

X(43195) lies on the cubic K1220 and these lines: {2, 42164}, {3, 14}, {4, 16644}, {5, 11480}, {6, 20}, {13, 5073}, {15, 382}, {16, 15696}, {17, 3830}, {30, 5340}, {61, 1657}, {62, 3534}, {140, 42160}, {376, 398}, {381, 5238}, {395, 3522}, {396, 3146}, {397, 3529}, {548, 11481}, {549, 42159}, {550, 10654}, {627, 35931}, {631, 5321}, {632, 42920}, {634, 33624}, {636, 11295}, {1151, 42257}, {1152, 42255}, {1656, 5352}, {2041, 23251}, {2042, 23261}, {3090, 5349}, {3091, 42932}, {3411, 42115}, {3412, 19106}, {3523, 42163}, {3524, 5343}, {3525, 5365}, {3526, 10645}, {3528, 5334}, {3530, 18581}, {3533, 43101}, {3543, 42166}, {3545, 42791}, {3627, 42152}, {3628, 42475}, {3832, 23302}, {3843, 19107}, {3851, 10188}, {3853, 18582}, {3855, 42101}, {3856, 42114}, {3858, 42911}, {3859, 42888}, {3861, 42104}, {5054, 42632}, {5059, 37640}, {5067, 42133}, {5068, 42794}, {5070, 16809}, {5071, 42949}, {5072, 42936}, {5076, 41978}, {5237, 41973}, {5318, 33703}, {5335, 42971}, {5344, 11541}, {5350, 15682}, {5351, 15688}, {5366, 33602}, {5895, 11243}, {7051, 9670}, {7486, 42107}, {8252, 42239}, {8253, 42240}, {8703, 42149}, {9657, 10638}, {10304, 42944}, {10574, 36980}, {10653, 15704}, {11001, 42586}, {11137, 13346}, {11485, 16965}, {11486, 42433}, {11488, 17578}, {11489, 21734}, {11542, 42112}, {12103, 42151}, {12817, 15703}, {13846, 42253}, {13847, 42251}, {14093, 16268}, {14869, 42910}, {15681, 41101}, {15684, 16962}, {15686, 42924}, {15687, 42921}, {15689, 42436}, {15691, 42510}, {15692, 42589}, {15693, 42937}, {15694, 42580}, {15695, 16963}, {15700, 41122}, {15715, 43100}, {15717, 23303}, {15720, 37835}, {16239, 42135}, {16267, 43016}, {17504, 41120}, {17538, 42943}, {19710, 42508}, {19772, 26958}, {33417, 42630}, {34200, 41113}, {34754, 42127}, {35404, 41119}, {36969, 42988}, {36990, 36993}, {38335, 41943}, {41099, 42927}, {41106, 43107}, {41121, 42695}, {42086, 42585}, {42100, 42990}, {42125, 42489}, {42162, 42912}, {42171, 42211}, {42172, 42213}, {42185, 42222}, {42186, 42224}, {42431, 42974}, {42613, 43019}, {42893, 42969}

X(43194) = reflection of X(i) in X(j) for these {i,j}: {5340, 22236}, {22236, 42150}
X(43194) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5339, 16645}, {3, 16645, 42774}, {3, 16964, 42153}, {3, 42153, 42491}, {3, 42154, 5339}, {3, 42157, 42154}, {4, 36836, 16644}, {4, 42942, 36836}, {5, 11480, 42490}, {5, 42092, 42610}, {5, 42490, 43029}, {6, 20, 43193}, {15, 382, 42156}, {15, 42096, 42094}, {15, 42130, 42096}, {18, 42529, 3}, {20, 42119, 42147}, {20, 42147, 6}, {61, 1657, 42155}, {376, 398, 36843}, {382, 42156, 42094}, {548, 40694, 11481}, {548, 42117, 40694}, {550, 10654, 22238}, {550, 22238, 42625}, {3524, 5343, 42599}, {3526, 42126, 42814}, {3526, 42814, 42095}, {3528, 5334, 16773}, {5059, 37640, 42165}, {5237, 41973, 42975}, {5238, 42432, 381}, {5339, 42491, 42153}, {5339, 42626, 3}, {5351, 41108, 42989}, {5352, 36970, 1656}, {10645, 42126, 42095}, {10645, 42814, 3526}, {11480, 42085, 42093}, {11480, 42093, 43029}, {11485, 17800, 16965}, {11485, 42099, 42097}, {15688, 42989, 5351}, {15704, 42925, 10653}, {16964, 36967, 42434}, {16964, 42153, 5339}, {16964, 42434, 3}, {16964, 42890, 42157}, {16965, 17800, 42097}, {16965, 42099, 17800}, {17538, 42999, 42943}, {19107, 42116, 42098}, {36967, 42154, 42626}, {36967, 42157, 3}, {36967, 42890, 16964}, {40694, 42090, 548}, {42085, 42092, 42136}, {42085, 42122, 11480}, {42087, 42119, 6}, {42087, 42147, 20}, {42090, 42117, 11481}, {42093, 42490, 5}, {42096, 42156, 382}, {42136, 42492, 42103}, {42150, 42161, 42511}, {42153, 42154, 16964}, {42153, 42491, 16645}, {42154, 42434, 42491}, {42154, 42626, 16645}, {42157, 42434, 16964}, {42258, 42259, 42119}, {42433, 42991, 11486}, {42813, 42939, 43013}, {42940, 42945, 3091}

X(43195) = GIBERT (5,12,-1) POINT

Barycentrics    5*a^2*S/Sqrt[3] - a^2*SA + 24*SB*SC : :
X(43195) = 38 X[42687] - 33 X[42795]

X(43195) lies on the cubic K1220 and these lines: {2, 12820}, {4, 42780}, {6, 42612}, {13, 42140}, {14, 42782}, {15, 382}, {16, 546}, {17, 42585}, {20, 42695}, {30, 42687}, {61, 42104}, {62, 42900}, {395, 42416}, {396, 42905}, {550, 16808}, {3528, 16966}, {3529, 10645}, {3530, 42100}, {3543, 16960}, {3544, 5351}, {3627, 34754}, {3843, 42938}, {3845, 42683}, {3851, 11481}, {3853, 42934}, {3855, 42086}, {3859, 42891}, {3861, 16961}, {5076, 42964}, {5079, 10646}, {5238, 42138}, {5318, 15687}, {5344, 42908}, {5350, 19107}, {5352, 42962}, {11486, 14269}, {11542, 12816}, {11543, 42971}, {11737, 36968}, {12101, 43111}, {12811, 42954}, {12821, 42972}, {14869, 42110}, {15681, 37832}, {15688, 42098}, {15720, 42097}, {16965, 42135}, {16967, 38071}, {17538, 42955}, {33417, 34200}, {35018, 42088}, {35730, 42181}, {36994, 38227}, {38335, 42969}, {41107, 42093}, {41121, 42087}, {41943, 42099}, {41973, 42779}, {42085, 43010}, {42101, 42922}, {42103, 43005}, {42115, 42946}, {42119, 42802}, {42126, 42799}, {42127, 42909}, {42164, 42781}, {42798, 42979}, {42921, 42959}, {42940, 43014}

X(43195) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {382, 42813, 42939}, {546, 42137, 43106}, {546, 42629, 16}, {42137, 42628, 42165}, {42137, 43106, 42629}

X(43196) = GIBERT (5,-12,1) POINT

Barycentrics    5*a^2*S/Sqrt[3] + a^2*SA - 24*SB*SC : :
X(43196) = 38 X[42686] - 33 X[42796]

X(43196) lies on the cubic K1220 and these lines: {2, 12821}, {4, 42779}, {6, 42612}, {13, 42781}, {14, 42141}, {15, 546}, {16, 382}, {18, 42584}, {20, 42694}, {30, 42686}, {61, 42901}, {62, 42105}, {395, 42904}, {396, 42415}, {550, 16809}, {3528, 16967}, {3529, 10646}, {3530, 42099}, {3543, 16961}, {3544, 5352}, {3627, 34755}, {3843, 42939}, {3845, 42682}, {3851, 11480}, {3853, 42935}, {3855, 42085}, {3859, 42890}, {3861, 16960}, {5076, 42965}, {5079, 10645}, {5237, 42135}, {5321, 15687}, {5343, 42909}, {5349, 19106}, {5351, 42963}, {11485, 14269}, {11542, 42970}, {11543, 12817}, {11737, 36967}, {12101, 43110}, {12811, 42955}, {12820, 42973}, {14869, 42107}, {15681, 37835}, {15688, 42095}, {15720, 42096}, {16964, 42138}, {16966, 38071}, {17538, 42954}, {33416, 34200}, {35018, 42087}, {36992, 38227}, {38335, 42968}, {41108, 42094}, {41122, 42088}, {41944, 42100}, {41974, 42780}, {42086, 43011}, {42102, 42923}, {42106, 43004}, {42116, 42947}, {42120, 42801}, {42126, 42908}, {42127, 42800}, {42165, 42782}, {42797, 42978}, {42920, 42958}, {42941, 43015}

X(43196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {382, 42814, 42938}, {546, 42136, 43105}, {546, 42630, 15}, {42136, 42627, 42164}, {42136, 43105, 42630}

X(43197) = GIBERT (8,3,9) POINT

Barycentrics    8*a^2*S/Sqrt[3] + 9*a^2*SA + 6*SB*SC : :
X(43197) = 3 X[11488] + X[42116], 5 X[11488] - X[42128], 9 X[11488] - X[42134], 5 X[42116] + 3 X[42128], 3 X[42116] + X[42134], 9 X[42128] - 5 X[42134]

X(43197) lies on the cubic K1220 and these lines: {3, 42916}, {5, 42950}, {6, 140}, {13, 15691}, {14, 547}, {15, 546}, {17, 41978}, {30, 11488}, {61, 42591}, {395, 42520}, {396, 10646}, {397, 42959}, {398, 10188}, {548, 10645}, {550, 22235}, {3090, 42923}, {3525, 42917}, {3530, 42115}, {3627, 42962}, {3628, 11485}, {3631, 6671}, {3850, 42132}, {3853, 18582}, {3856, 42126}, {3859, 42098}, {3861, 42119}, {5066, 16644}, {5238, 42137}, {5318, 43016}, {5334, 35018}, {5335, 33923}, {5352, 42584}, {8703, 42815}, {8972, 34552}, {10109, 42125}, {10124, 11489}, {10632, 16198}, {11480, 12103}, {11486, 12108}, {11540, 37641}, {11543, 43012}, {11812, 37640}, {12101, 16808}, {12102, 42142}, {12812, 22236}, {13941, 34551}, {14891, 42974}, {14892, 16809}, {14893, 42085}, {15690, 42086}, {15695, 42932}, {15699, 42816}, {16267, 41982}, {16960, 41974}, {16961, 42802}, {16962, 23303}, {16966, 42925}, {18581, 42610}, {19710, 33602}, {33417, 42939}, {34200, 42118}, {36836, 42112}, {36969, 42684}, {41981, 42131}, {42090, 42889}, {42113, 42156}, {42150, 42888}, {42165, 43004}, {42166, 42585}, {42497, 42513}, {42502, 42629}, {42590, 42894}, {42694, 42901}, {42793, 42994}, {42896, 43023}, {42929, 42973}, {42944, 43014}, {42948, 43015}, {42954, 42956}, {42976, 43031}

X(43197) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 42986, 42922}, {15, 42598, 42136}, {15, 42627, 546}, {61, 43103, 42628}, {10645, 42895, 42088}, {16960, 42930, 41974}, {16960, 42945, 42123}, {23302, 34754, 42143}, {42143, 42912, 34754}

X(43198) = GIBERT (-8,3,9) POINT

Barycentrics    8*a^2*S/Sqrt[3] - 9*a^2*SA - 6*SB*SC : :
X(43198) = 3 X[11489] + X[42115], 5 X[11489] - X[42125], 9 X[11489] - X[42133], 5 X[42115] + 3 X[42125], 3 X[42115] + X[42133], 9 X[42125] - 5 X[42133]

X(43198) lies on the cubic K1220 and these lines: {3, 42917}, {5, 42951}, {6, 140}, {13, 547}, {14, 15691}, {16, 546}, {18, 41977}, {30, 11489}, {62, 42590}, {395, 10645}, {396, 42521}, {397, 10187}, {398, 42958}, {548, 10646}, {550, 22237}, {3090, 42922}, {3525, 42916}, {3530, 42116}, {3627, 42963}, {3628, 11486}, {3631, 6672}, {3850, 42129}, {3853, 18581}, {3856, 42127}, {3859, 42095}, {3861, 42120}, {5066, 16645}, {5237, 42136}, {5321, 43017}, {5334, 33923}, {5335, 35018}, {5351, 42585}, {8703, 42816}, {8972, 34551}, {10109, 42128}, {10124, 11488}, {10633, 16198}, {11481, 12103}, {11485, 12108}, {11540, 37640}, {11542, 43013}, {11812, 37641}, {12101, 16809}, {12102, 42139}, {12812, 22238}, {13941, 34552}, {14891, 42975}, {14892, 16808}, {14893, 42086}, {15690, 42085}, {15695, 42933}, {15699, 42815}, {16268, 41982}, {16960, 42801}, {16961, 41973}, {16963, 23302}, {16967, 42924}, {18582, 42611}, {19710, 33603}, {33416, 42938}, {34200, 42117}, {36843, 42113}, {36970, 42685}, {41981, 42130}, {42091, 42888}, {42112, 42153}, {42151, 42889}, {42163, 42584}, {42164, 43005}, {42496, 42512}, {42503, 42630}, {42591, 42895}, {42695, 42900}, {42794, 42995}, {42897, 43022}, {42928, 42972}, {42945, 43015}, {42949, 43014}, {42955, 42957}, {42977, 43030}

X(43198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 42987, 42923}, {16, 42599, 42137}, {16, 42628, 546}, {62, 43102, 42627}, {10646, 42894, 42087}, {16961, 42931, 41973}, {16961, 42944, 42122}, {23303, 34755, 42146}, {42146, 42913, 34755}

X(43199) = GIBERT (15,10,23) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 23*a^2*SA + 20*SB*SC : :
X(43199) = 12 X[42687] - 7 X[42795]

X(43) lies on the cubic K1220 and these lines: {2, 16961}, {3, 13}, {6, 15723}, {14, 547}, {15, 3545}, {16, 11812}, {20, 42798}, {30, 42687}, {140, 42947}, {376, 42512}, {381, 12821}, {395, 3412}, {396, 11539}, {549, 42777}, {618, 22494}, {629, 40899}, {3091, 42694}, {3533, 37640}, {3543, 16808}, {3628, 42939}, {3832, 42157}, {3845, 19107}, {3850, 16772}, {3853, 5238}, {5054, 16960}, {5056, 10654}, {5059, 5352}, {5067, 37835}, {5318, 42530}, {5321, 41971}, {5464, 6669}, {6671, 21360}, {9763, 36770}, {10124, 42954}, {10188, 42153}, {10303, 42779}, {10645, 15686}, {10653, 15719}, {11001, 12816}, {11480, 42430}, {11485, 42984}, {11488, 15702}, {11542, 41983}, {11543, 42953}, {12100, 33607}, {15690, 41121}, {15694, 42955}, {15708, 16267}, {15709, 42517}, {15718, 42796}, {16268, 41985}, {16645, 42897}, {16809, 42474}, {16962, 16967}, {16966, 41101}, {19711, 41107}, {21734, 42965}, {35018, 42934}, {35019, 35932}, {35400, 42626}, {35401, 42096}, {35402, 42997}, {35404, 42684}, {36836, 42890}, {36967, 38335}, {40693, 42994}, {40694, 42592}, {41100, 42817}, {41981, 42960}, {42089, 42533}, {42165, 42959}, {42434, 42598}, {42503, 43011}, {42511, 42918}, {42594, 42916}, {42597, 42949}, {42599, 42802}, {42633, 43031}, {42685, 43000}, {42895, 42928}, {42929, 42962}, {42945, 43027}, {42987, 43025}
on K1220
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 42625, 16965}, {14, 42912, 43021}, {17, 16241, 36968}, {396, 16963, 43014}, {396, 33417, 16963}, {547, 34754, 14}, {16241, 16644, 17}, {16772, 42979, 42581}, {18582, 42529, 12816}, {23302, 41943, 14}, {41943, 42914, 42892}, {42496, 42500, 16}, {42799, 43101, 14}, {42912, 43101, 42799}

X(43200) = GIBERT (-15,10,23) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 23*a^2*SA - 20*SB*SC : :
X(43200) = 12 X[42686] - 7 X[42796]

X(43200) lies on the cubic K1220 and these lines: {2, 16960}, {3, 14}, {6, 15723}, {13, 547}, {15, 11812}, {16, 3545}, {20, 42797}, {30, 42686}, {140, 42946}, {376, 42513}, {381, 12820}, {395, 11539}, {396, 3411}, {549, 42778}, {619, 22493}, {630, 40898}, {3091, 42695}, {3533, 37641}, {3543, 16809}, {3628, 42938}, {3832, 42158}, {3845, 19106}, {3850, 16773}, {3853, 5237}, {5054, 16961}, {5056, 10653}, {5059, 5351}, {5067, 37832}, {5318, 41972}, {5321, 42531}, {5463, 6670}, {6672, 21359}, {10124, 42955}, {10187, 42156}, {10303, 42780}, {10646, 15686}, {10654, 15719}, {11001, 12817}, {11481, 42429}, {11486, 42985}, {11489, 15702}, {11542, 42952}, {11543, 41983}, {12100, 33606}, {15690, 41122}, {15694, 42954}, {15708, 16268}, {15709, 42516}, {15718, 42795}, {16267, 41985}, {16644, 42896}, {16808, 42475}, {16963, 16966}, {16967, 41100}, {19711, 41108}, {21734, 42964}, {35018, 42935}, {35020, 35931}, {35400, 42625}, {35401, 42097}, {35402, 42996}, {35404, 42685}, {36843, 42891}, {36968, 38335}, {40693, 42593}, {40694, 42995}, {41101, 42818}, {41981, 42961}, {42092, 42532}, {42164, 42958}, {42433, 42599}, {42502, 43010}, {42510, 42919}, {42595, 42917}, {42596, 42948}, {42598, 42801}, {42634, 43030}, {42684, 43001}, {42894, 42929}, {42928, 42963}, {42944, 43026}, {42986, 43024}

X(43200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 42913, 43020}, {14, 42626, 16964}, {18, 16242, 36967}, {395, 16962, 43015}, {395, 33416, 16962}, {547, 34755, 13}, {16242, 16645, 18}, {16773, 42978, 42580}, {18581, 42528, 12817}, {23303, 41944, 13}, {41944, 42915, 42893}, {42497, 42501, 15}, {42800, 43104, 13}, {42913, 43104, 42800}

X(43201) = GIBERT (18,25,2) POINT

Barycentrics    3*Sqrt[3]*a^2*S + a^2*SA + 25*SB*SC : :
X(43201) = 25 X[11488] - 16 X[42116], 7 X[11488] - 16 X[42128], X[11488] + 8 X[42134], 7 X[42116] - 25 X[42128], 2 X[42116] + 25 X[42134], 2 X[42128] + 7 X[42134]

X(43201) lies on the cubic K1220 and these lines: {2, 42165}, {4, 12816}, {5, 42588}, {6, 42539}, {13, 42140}, {16, 3545}, {30, 11488}, {140, 43003}, {376, 42494}, {381, 5366}, {3524, 33417}, {3529, 41121}, {3543, 5350}, {3830, 42925}, {3839, 5318}, {3845, 5344}, {3855, 41100}, {5054, 42138}, {5055, 42120}, {5071, 42161}, {5072, 43109}, {5335, 14269}, {5352, 11001}, {6459, 36446}, {6460, 36465}, {10304, 42141}, {10653, 42636}, {14893, 42998}, {15640, 42156}, {15682, 16962}, {15683, 42166}, {15688, 42137}, {15692, 42949}, {15697, 42598}, {15698, 42431}, {15699, 42127}, {15702, 42921}, {15705, 42693}, {15706, 42146}, {15707, 42962}, {15709, 42086}, {15710, 37832}, {16267, 42119}, {16268, 41099}, {16963, 42106}, {16965, 41106}, {18582, 42429}, {19107, 42516}, {21734, 42586}, {23046, 42139}, {33602, 40693}, {35409, 36967}, {36436, 42234}, {36454, 42233}, {37640, 42094}, {38071, 42416}, {38335, 42907}, {42097, 43107}, {42155, 43100}, {42472, 42943}, {42533, 43012}

X(43202) = GIBERT (-18,25,2) POINT

Barycentrics    3*Sqrt[3]*a^2*S - a^2*SA - 25*SB*SC : :
X(43202) = 25 X[11489] - 16 X[42115], 7 X[11489] - 16 X[42125], X[11489] + 8 X[42133], 7 X[42115] - 25 X[42125], 2 X[42115] + 25 X[42133], 2 X[42125] + 7 X[42133]

X(43202) lies on the cubic K1220 and these lines: {2, 42164}, {4, 12817}, {5, 42589}, {6, 42539}, {14, 42141}, {15, 3545}, {30, 11489}, {140, 43002}, {376, 42495}, {381, 5365}, {3524, 33416}, {3529, 41122}, {3543, 5349}, {3830, 42924}, {3839, 5321}, {3845, 5343}, {3855, 41101}, {5054, 42135}, {5055, 42119}, {5071, 42160}, {5072, 43108}, {5334, 14269}, {5351, 11001}, {6459, 36464}, {6460, 36447}, {10304, 42140}, {10654, 42635}, {14893, 42999}, {15640, 42153}, {15682, 16963}, {15683, 42163}, {15688, 42136}, {15692, 42948}, {15697, 42599}, {15698, 42432}, {15699, 42126}, {15702, 42920}, {15705, 42692}, {15706, 42143}, {15707, 42963}, {15709, 42085}, {15710, 37835}, {16267, 41099}, {16268, 42120}, {16962, 42103}, {16964, 41106}, {18581, 42430}, {19106, 42517}, {21734, 42587}, {23046, 42142}, {33603, 40694}, {35409, 36968}, {36436, 42231}, {36454, 42232}, {37641, 42093}, {38071, 42415}, {38335, 42906}, {42096, 43100}, {42154, 43107}, {42473, 42942}, {42532, 43013}

X(43203) = GIBERT (33,50,-65) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 65*a^2*SA + 100*SB*SC : :
X(43203) = 11 X[41972] - 6 X[42970], 4 X[41972] - 3 X[43015], 8 X[41972] - 7 X[43020], 8 X[42970] - 11 X[43015], 48 X[42970] - 77 X[43020], 6 X[43015] - 7 X[43020]

X(43203) lies on the cubic K1220 and these lines: {2, 12820}, {6, 42429}, {13, 15691}, {14, 5073}, {17, 15696}, {30, 41972}, {376, 42900}, {396, 42980}, {397, 15704}, {550, 43033}, {3529, 43007}, {3534, 42997}, {3853, 5237}, {3858, 42433}, {5318, 42504}, {5349, 42938}, {10653, 42995}, {12817, 42818}, {15714, 42145}, {16645, 42981}, {16960, 42791}, {16962, 42100}, {18581, 42514}, {33606, 42913}, {33923, 36969}, {35403, 42097}, {35404, 42692}, {35414, 42085}, {41971, 42478}, {42099, 43108}, {42155, 42520}, {42507, 42940}, {42596, 43104}

X(43203) = {X(41972),X(43015)}-harmonic conjugate of X(43020)

X(43204) = GIBERT (33,-50,65) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 65*a^2*SA - 100*SB*SC : :
X(43204) = 11 X[41971] - 6 X[42971], 4 X[41971] - 3 X[43014], 8 X[41971] - 7 X[43021], 8 X[42971] - 11 X[43014], 48 X[42971] - 77 X[43021], 6 X[43014] - 7 X[43021]

X(43204) lies on the cubic K1220 and these lines: {2, 12821}, {6, 42429}, {13, 5073}, {14, 15691}, {18, 15696}, {30, 41971}, {376, 42901}, {395, 42981}, {398, 15704}, {550, 43032}, {3529, 43006}, {3534, 42996}, {3853, 5238}, {3858, 42434}, {5321, 42505}, {5350, 42939}, {10654, 42994}, {12816, 42817}, {15714, 42144}, {16644, 42980}, {16961, 42792}, {16963, 42099}, {18582, 42515}, {33607, 42912}, {33923, 36970}, {35403, 42096}, {35404, 42693}, {35414, 42086}, {41972, 42479}, {42100, 43109}, {42154, 42521}, {42506, 42941}, {42597, 43101}

X(43204) = {X(41971),X(43014)}-harmonic conjugate of X(43021)

X(43205) = GIBERT (55,12,13) POINT

Barycentrics    55*a^2*S/Sqrt[3] + 13*a^2*SA + 24*SB*SC : :
X(43205) = 99 X[41971] + 76 X[42971], 3 X[41971] - 38 X[43014], 23 X[41971] - 38 X[43021], 2 X[42971] + 33 X[43014], 46 X[42971] + 99 X[43021], 23 X[43014] - 3 X[43021]

X(43205) lies on the cubic K1220 and these lines: {2, 16960}, {15, 15696}, {30, 41971}, {61, 42105}, {398, 3858}, {631, 43030}, {3091, 42894}, {3853, 42934}, {5071, 43005}, {5073, 42779}, {5318, 42520}, {11488, 42805}, {12812, 43004}, {15691, 43106}, {15704, 34754}, {15711, 42892}, {16268, 42777}, {16967, 42898}, {35403, 36970}, {35404, 42683}, {40693, 42472}, {41989, 43011}, {42099, 42516}, {42104, 42799}, {42134, 42967}, {42416, 42795}, {42506, 42778}, {42509, 42974}, {42813, 42896}, {42914, 42987}, {42919, 42975}, {42976, 43109}

X(43206) = GIBERT (-55,12,13) POINT

Barycentrics    55*a^2*S/Sqrt[3] - 13*a^2*SA - 24*SB*SC : :
X(43206) = 99 X[41972] + 76 X[42970], 3 X[41972] - 38 X[43015], 23 X[41972] - 38 X[43020], 2 X[42970] + 33 X[43015], 46 X[42970] + 99 X[43020], 23 X[43015] - 3 X[43020]

X(43206) lies on the cubic K1220 and these lines: {2, 16961}, {16, 15696}, {30, 41972}, {62, 42104}, {397, 3858}, {631, 43031}, {3091, 42895}, {3853, 42935}, {5071, 43004}, {5073, 42780}, {5321, 42521}, {11489, 42806}, {12812, 43005}, {15691, 43105}, {15704, 34755}, {15711, 42893}, {16267, 42778}, {16966, 42899}, {35403, 36969}, {35404, 42682}, {40694, 42473}, {41989, 43010}, {42100, 42517}, {42105, 42800}, {42133, 42966}, {42415, 42796}, {42507, 42777}, {42508, 42975}, {42814, 42897}, {42915, 42986}, {42918, 42974}, {42977, 43108}

X(43207) = GIBERT (72,25,23) POINT

Barycentrics    24*Sqrt[3]*a^2*S + 23*a^2*SA + 50*SB*SC : :
X(43207) = 25 X[5340] + 23 X[22236], X[5340] + 23 X[40693], 15 X[5340] - 23 X[41112], 49 X[5340] + 23 X[42150], 47 X[5340] - 23 X[42161], 33 X[5340] + 23 X[42511], 137 X[5340] + 23 X[42587], X[22236] - 25 X[40693], 3 X[22236] + 5 X[41112], 49 X[22236] - 25 X[42150], 47 X[22236] + 25 X[42161], 33 X[22236] - 25 X[42511], 137 X[22236] - 25 X[42587], 15 X[40693] + X[41112], 49 X[40693] - X[42150], 47 X[40693] + X[42161], 33 X[40693] - X[42511], 137 X[40693] - X[42587], 49 X[41112] + 15 X[42150], 47 X[41112] - 15 X[42161], 11 X[41112] + 5 X[42511], 137 X[41112] + 15 X[42587], 47 X[42150] + 49 X[42161], 33 X[42150] - 49 X[42511], 137 X[42150] - 49 X[42587], 33 X[42161] + 47 X[42511], 137 X[42161] + 47 X[42587], 137 X[42511] - 33 X[42587]

X(43207) lies on the cubic K1220 and these lines: {13, 42781}, {16, 11812}, {17, 41984}, {30, 5340}, {62, 41985}, {381, 33604}, {396, 15759}, {397, 14891}, {3530, 41100}, {3534, 42982}, {3860, 16808}, {3861, 42992}, {5066, 42139}, {10109, 11542}, {10124, 16267}, {11543, 42502}, {11737, 41121}, {12100, 42974}, {12101, 37640}, {12103, 42588}, {12811, 41120}, {12816, 42940}, {15690, 42116}, {15693, 42986}, {15698, 42916}, {19708, 42922}, {23302, 42420}, {33607, 42146}, {33699, 42815}, {34200, 42988}, {37832, 42480}, {41107, 43106}, {41108, 42694}, {41988, 42162}, {42140, 42633}, {42429, 42976}, {42492, 42517}, {42521, 42598}, {42779, 43026}, {42897, 43000}

X(43208) = GIBERT (-72,25,23) POINT

Barycentrics    24*Sqrt[3]*a^2*S - 23*a^2*SA - 50*SB*SC : :
X(43208) = 25 X[5339] + 23 X[22238], X[5339] + 23 X[40694], 15 X[5339] - 23 X[41113], 49 X[5339] + 23 X[42151], 47 X[5339] - 23 X[42160], 33 X[5339] + 23 X[42510], 137 X[5339] + 23 X[42586], X[22238] - 25 X[40694], 3 X[22238] + 5 X[41113], 49 X[22238] - 25 X[42151], 47 X[22238] + 25 X[42160], 33 X[22238] - 25 X[42510], 137 X[22238] - 25 X[42586], 15 X[40694] + X[41113], 49 X[40694] - X[42151], 47 X[40694] + X[42160], 33 X[40694] - X[42510], 137 X[40694] - X[42586], 49 X[41113] + 15 X[42151], 47 X[41113] - 15 X[42160], 11 X[41113] + 5 X[42510], 137 X[41113] + 15 X[42586], 47 X[42151] + 49 X[42160], 33 X[42151] - 49 X[42510], 137 X[42151] - 49 X[42586], 33 X[42160] + 47 X[42510], 137 X[42160] + 47 X[42586], 137 X[42510] - 33 X[42586]

X(43208) lies on the cubic K1220 and these lines: {14, 42782}, {15, 11812}, {18, 41984}, {30, 5339}, {61, 41985}, {381, 33605}, {395, 15759}, {398, 14891}, {3530, 41101}, {3534, 42983}, {3860, 16809}, {3861, 42993}, {5066, 42142}, {10109, 11543}, {10124, 16268}, {11542, 42503}, {11737, 41122}, {12100, 42975}, {12101, 37641}, {12103, 42589}, {12811, 41119}, {12817, 42941}, {15690, 42115}, {15693, 42987}, {15698, 42917}, {19708, 42923}, {23303, 42419}, {33606, 42143}, {33699, 42816}, {34200, 42989}, {37835, 42481}, {41107, 42695}, {41108, 43105}, {41988, 42159}, {42141, 42634}, {42430, 42977}, {42493, 42516}, {42520, 42599}, {42780, 43027}, {42896, 43001}

X(43209) = GIBERT (3 SQRT(3),5,-8) POINT

Barycentrics    3*a^2*S - 8*a^2*SA + 10*SB*SC : :
X(43209) = 8 X[372] - 5 X[3071], 13 X[372] - 10 X[7584], 6 X[372] - 5 X[32788], 11 X[372] - 5 X[35821], 7 X[372] - 5 X[35823], 4 X[372] - 5 X[41946], 2 X[372] - 5 X[42259], X[372] + 5 X[42267], 14 X[372] - 5 X[42271], 13 X[3071] - 16 X[7584], 3 X[3071] - 4 X[32788], 11 X[3071] - 8 X[35821], 7 X[3071] - 8 X[35823], X[3071] - 4 X[42259], X[3071] + 8 X[42267], 7 X[3071] - 4 X[42271], 12 X[7584] - 13 X[32788], 22 X[7584] - 13 X[35821], 14 X[7584] - 13 X[35823], 8 X[7584] - 13 X[41946], 4 X[7584] - 13 X[42259], 2 X[7584] + 13 X[42267], 28 X[7584] - 13 X[42271], 11 X[32788] - 6 X[35821], 7 X[32788] - 6 X[35823], 2 X[32788] - 3 X[41946], X[32788] - 3 X[42259], X[32788] + 6 X[42267], 7 X[32788] - 3 X[42271], 7 X[35821] - 11 X[35823], 4 X[35821] - 11 X[41946], 2 X[35821] - 11 X[42259], X[35821] + 11 X[42267], 14 X[35821] - 11 X[42271], 4 X[35823] - 7 X[41946], 2 X[35823] - 7 X[42259], X[35823] + 7 X[42267], X[41946] + 4 X[42267], 7 X[41946] - 2 X[42271], X[42259] + 2 X[42267], 7 X[42259] - X[42271], 14 X[42267] + X[42271]

X(43209) lies on the cubic K1220 and these lines: {2, 6412}, {3, 1327}, {6, 11001}, {20, 3592}, {30, 372}, {371, 15686}, {376, 3070}, {381, 6456}, {382, 6522}, {485, 15688}, {486, 15684}, {549, 35820}, {550, 31454}, {590, 8703}, {615, 3830}, {1152, 3543}, {1161, 13786}, {1328, 6398}, {1657, 6428}, {1975, 32809}, {3068, 15697}, {3069, 15640}, {3524, 23251}, {3534, 6221}, {3545, 6410}, {3594, 5059}, {3627, 41964}, {3839, 42583}, {3845, 6396}, {5054, 42273}, {5055, 22644}, {5066, 32790}, {5418, 14093}, {5420, 14269}, {6200, 15690}, {6417, 15681}, {6426, 33703}, {6430, 23263}, {6432, 42413}, {6450, 38335}, {6460, 15683}, {6469, 13847}, {6561, 15685}, {6564, 12100}, {6565, 33699}, {7583, 15691}, {8252, 41099}, {8253, 15698}, {10576, 17504}, {10577, 14893}, {12101, 35256}, {13665, 15695}, {13941, 41962}, {13961, 41970}, {13966, 35404}, {14226, 23261}, {15687, 42270}, {15692, 42265}, {15693, 32789}, {15694, 42269}, {15696, 41963}, {15699, 35786}, {15701, 42277}, {15702, 23253}, {15715, 42641}, {15759, 18538}, {15764, 42528}, {15765, 42581}, {17851, 42609}, {18585, 42580}, {19053, 42263}, {19708, 23249}, {19710, 42216}, {23259, 42573}, {36437, 42241}, {36445, 43100}, {36450, 42154}, {36455, 42239}, {36463, 43107}, {36468, 42155}, {41106, 42567}, {41121, 42224}, {41122, 42223}

X(43209) = reflection of X(i) in X(j) for these {i,j}: {3071, 41946}, {41946, 42259}, {42271, 35823}
X(43209) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3070, 13846, 42572}, {3534, 6560, 32787}, {6450, 38335, 42603}, {11001, 42418, 42417}, {13847, 15682, 42283}

X(43210) = GIBERT (3 SQRT(3),-5,8) POINT

Barycentrics    3*a^2*S + 8*a^2*SA - 10*SB*SC : :
X(43210) = 8 X[371] - 5 X[3070], 13 X[371] - 10 X[7583], 6 X[371] - 5 X[32787], 11 X[371] - 5 X[35820], 7 X[371] - 5 X[35822], 4 X[371] - 5 X[41945], 2 X[371] - 5 X[42258], X[371] + 5 X[42266], 14 X[371] - 5 X[42272], 13 X[3070] - 16 X[7583], 3 X[3070] - 4 X[32787], 11 X[3070] - 8 X[35820], 7 X[3070] - 8 X[35822], X[3070] - 4 X[42258], X[3070] + 8 X[42266], 7 X[3070] - 4 X[42272], 12 X[7583] - 13 X[32787], 22 X[7583] - 13 X[35820], 14 X[7583] - 13 X[35822], 8 X[7583] - 13 X[41945], 4 X[7583] - 13 X[42258], 2 X[7583] + 13 X[42266], 28 X[7583] - 13 X[42272], 11 X[32787] - 6 X[35820], 7 X[32787] - 6 X[35822], 2 X[32787] - 3 X[41945], X[32787] - 3 X[42258], X[32787] + 6 X[42266], 7 X[32787] - 3 X[42272], 7 X[35820] - 11 X[35822], 4 X[35820] - 11 X[41945], 2 X[35820] - 11 X[42258], X[35820] + 11 X[42266], 14 X[35820] - 11 X[42272], 4 X[35822] - 7 X[41945], 2 X[35822] - 7 X[42258], X[35822] + 7 X[42266], X[41945] + 4 X[42266], 7 X[41945] - 2 X[42272], X[42258] + 2 X[42266], 7 X[42258] - X[42272], 14 X[42266] + X[42272]

X(43210) lies on the cubic K1220 and these lines: {2, 6411}, {3, 1328}, {6, 11001}, {20, 3594}, {30, 371}, {372, 15686}, {376, 3071}, {381, 6455}, {382, 6519}, {485, 9691}, {486, 15688}, {549, 35821}, {550, 35823}, {590, 3830}, {615, 8703}, {1151, 3543}, {1160, 13666}, {1327, 6221}, {1657, 6427}, {1975, 32808}, {3068, 15640}, {3069, 15697}, {3146, 31454}, {3524, 23261}, {3534, 6398}, {3545, 6409}, {3592, 5059}, {3627, 41963}, {3839, 42582}, {3845, 6200}, {5054, 42270}, {5055, 22615}, {5066, 32789}, {5073, 9681}, {5076, 9680}, {5418, 14269}, {5420, 14093}, {6396, 15690}, {6418, 15681}, {6425, 33703}, {6429, 23253}, {6431, 42414}, {6449, 38335}, {6459, 15683}, {6468, 9541}, {6560, 15685}, {6564, 33699}, {6565, 12100}, {7584, 15691}, {8252, 15698}, {8253, 41099}, {8972, 41961}, {8981, 35404}, {10576, 14893}, {10577, 17504}, {12101, 35255}, {13785, 15695}, {13903, 41969}, {14241, 23251}, {15687, 42273}, {15692, 42262}, {15693, 32790}, {15694, 42268}, {15696, 41964}, {15699, 35787}, {15701, 42274}, {15702, 23263}, {15715, 42642}, {15759, 18762}, {15764, 42529}, {15765, 42580}, {17538, 17852}, {18585, 42581}, {19054, 42264}, {19708, 23259}, {19710, 42215}, {23249, 42572}, {35740, 36455}, {36437, 42240}, {36445, 43107}, {36449, 42155}, {36463, 43100}, {36467, 42154}, {41106, 42566}, {41121, 42222}, {41122, 42221}

X(43210) = reflection of X(i) in X(j) for these {i,j}: {3070, 41945}, {41945, 42258}, {42272, 35822}
X(43210) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3071, 13847, 42573}, {3534, 6561, 32788}, {6449, 38335, 42602}, {9541, 15682, 13846}, {11001, 42417, 42418}, {13846, 15682, 42284}

X(43211) = GIBERT (6 SQRT(3),5,13) POINT

Barycentrics    6*a^2*S + 13*a^2*SA + 10*SB*SC : :
X(43211) = 5 X[590] + X[6200], 7 X[590] - X[6564], 4 X[590] - X[18538], 2 X[590] + X[35255], 13 X[590] - X[42284], 7 X[6200] + 5 X[6564], 4 X[6200] + 5 X[18538], 2 X[6200] - 5 X[35255], 13 X[6200] + 5 X[42284], 4 X[6564] - 7 X[18538], 2 X[6564] + 7 X[35255], 13 X[6564] - 7 X[42284], X[18538] + 2 X[35255], 13 X[18538] - 4 X[42284], 13 X[35255] + 2 X[42284]

X(43211) lies on the cubic K1220 and these lines: {2, 3311}, {3, 31414}, {5, 1328}, {6, 11539}, {30, 590}, {140, 6420}, {371, 547}, {372, 11812}, {376, 1131}, {381, 6407}, {485, 8703}, {546, 41963}, {549, 1152}, {550, 42639}, {615, 6435}, {631, 6448}, {632, 13847}, {1151, 3845}, {1327, 6409}, {1587, 15693}, {1588, 15703}, {3068, 5054}, {3070, 34200}, {3071, 10109}, {3312, 15702}, {3316, 3543}, {3522, 14241}, {3524, 6452}, {3525, 31487}, {3526, 19053}, {3530, 8960}, {3533, 6427}, {3545, 6221}, {3582, 13901}, {3584, 18965}, {3590, 17538}, {3592, 42603}, {3627, 6488}, {3628, 31454}, {3655, 13893}, {3830, 42413}, {3832, 6519}, {3839, 42225}, {3850, 6453}, {3854, 9693}, {3858, 9681}, {3860, 35821}, {5055, 32785}, {5056, 6447}, {5066, 10576}, {5875, 13692}, {6396, 41983}, {6398, 15708}, {6410, 19711}, {6417, 15723}, {6419, 16239}, {6439, 23046}, {6445, 38335}, {6450, 15719}, {6451, 42540}, {6455, 11001}, {6459, 6474}, {6460, 15700}, {6471, 15713}, {6478, 11737}, {6486, 42606}, {6501, 13903}, {6561, 38071}, {7581, 15721}, {7585, 15709}, {8253, 15699}, {9541, 14269}, {9661, 15170}, {9691, 23263}, {10124, 32788}, {10194, 41992}, {10304, 13665}, {11315, 32811}, {11540, 35815}, {12100, 13925}, {12101, 42273}, {13886, 15692}, {13902, 34718}, {13908, 33813}, {14893, 42258}, {15681, 31412}, {15682, 42526}, {15687, 42265}, {15688, 42226}, {15689, 23249}, {15691, 35820}, {15705, 23267}, {15707, 18512}, {15714, 42261}, {15716, 42637}, {15759, 42259}, {18586, 42495}, {18587, 42494}, {19058, 38750}, {19710, 23251}, {32790, 41984}, {33699, 42260}, {34559, 36470}, {34562, 36453}, {35404, 42269}, {35775, 38022}, {35786, 42525}, {36445, 42200}, {36463, 42202}, {41965, 41987}, {42283, 42558}, {42579, 42640}

X(43211) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {549, 13846, 7583}, {590, 35255, 18538}, {1151, 42602, 3845}, {1327, 6409, 15686}, {5418, 13846, 549}, {6425, 10195, 5}, {6496, 8976, 1131}, {10576, 41945, 5066}, {12100, 13925, 35822}, {13903, 15694, 19054}, {15694, 19054, 13966}

X(43212) = GIBERT (-6 SQRT(3),5,13) POINT

Barycentrics    6*a^2*S - 13*a^2*SA - 10*SB*SC : :
X(43212) = 5 X[615] + X[6396], 7 X[615] - X[6565], 4 X[615] - X[18762], 2 X[615] + X[35256], 13 X[615] - X[42283], 7 X[6396] + 5 X[6565], 4 X[6396] + 5 X[18762], 2 X[6396] - 5 X[35256], 13 X[6396] + 5 X[42283], 4 X[6565] - 7 X[18762], 2 X[6565] + 7 X[35256], 13 X[6565] - 7 X[42283], X[18762] + 2 X[35256], 13 X[18762] - 4 X[42283], 13 X[35256] + 2 X[42283]

X(43212) lies on the cubic K1220 and these lines: {2, 3312}, {5, 1327}, {6, 11539}, {30, 615}, {140, 6419}, {371, 11812}, {372, 547}, {376, 1132}, {381, 6408}, {486, 8703}, {546, 41964}, {549, 1151}, {550, 42640}, {590, 6436}, {631, 6447}, {632, 13846}, {1152, 3845}, {1328, 6410}, {1587, 15703}, {1588, 15693}, {1656, 31414}, {3069, 5054}, {3070, 10109}, {3071, 34200}, {3311, 15702}, {3317, 3543}, {3522, 14226}, {3524, 6451}, {3526, 19054}, {3530, 41945}, {3533, 6428}, {3545, 6398}, {3582, 13958}, {3584, 18966}, {3591, 17538}, {3594, 42602}, {3627, 6489}, {3628, 35822}, {3655, 13947}, {3830, 42414}, {3832, 6522}, {3839, 42226}, {3850, 6454}, {3860, 35820}, {5055, 32786}, {5056, 6448}, {5066, 10577}, {5874, 13812}, {6200, 41983}, {6221, 15708}, {6409, 19711}, {6418, 15723}, {6420, 16239}, {6440, 23046}, {6446, 38335}, {6449, 15719}, {6452, 42539}, {6456, 11001}, {6459, 15700}, {6460, 6475}, {6470, 15713}, {6479, 11737}, {6487, 42607}, {6500, 8981}, {6560, 38071}, {7582, 15721}, {7586, 15709}, {8252, 15699}, {9541, 15706}, {10124, 32787}, {10195, 41992}, {10304, 13785}, {11316, 32810}, {11540, 35814}, {12100, 13993}, {12101, 42270}, {13939, 15692}, {13959, 34718}, {13968, 33813}, {14893, 42259}, {15681, 42537}, {15682, 42527}, {15684, 42637}, {15687, 42262}, {15688, 42225}, {15689, 23259}, {15691, 35821}, {15705, 23273}, {15707, 18510}, {15714, 42260}, {15759, 42258}, {17852, 41991}, {18586, 42494}, {18587, 42495}, {19057, 38750}, {19710, 23261}, {32789, 41984}, {33699, 42261}, {34559, 36469}, {34562, 36452}, {35404, 42268}, {35774, 38022}, {35787, 42524}, {36445, 42201}, {36463, 42199}, {41966, 41987}, {42284, 42557}, {42578, 42639}

X(43212) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {549, 13847, 7584}, {615, 35256, 18762}, {1152, 42603, 3845}, {1328, 6410, 15686}, {5420, 13847, 549}, {6426, 10194, 5}, {6497, 13951, 1132}, {10577, 41946, 5066}, {12100, 13993, 35823}, {13961, 15694, 19053}, {15694, 19053, 8981}

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Perspectors involving ther inverses of triangles Gemini 15 and 16: X(43213)-X(43225)

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This preamble and points X(43213)-X(43212) are contributed by Clark Kimberling and Peter Moses, May 9, 2021.

The vertices of the inverse of Gemini 15 are shown here:

a (b + c) (a + b + c) : -b (a + b - c) (a + c) : -c (a + b) (a - b + c)
-a (a + b - c) (b + c) : b (a + c) (a + b + c) : c (a + b) (a - b - c)
-a (a - b + c) (b + c) : -b (a + c) (-a + b + c) : c (a + b) (a + b + c)

The vertices of the inverse of Gemini 16 are shown here:

(b + c) (a b + a c + b c) : -(a + c) (-a b + a c + b c) : -(a + b) (a b - a c + b c)
-(b + c) (-a b + a c + b c) : (a + c) (a b + a c + b c) : -(a + b) (a b + a c - b c)}
-(b + c) (a b - a c + b c) : -(a + c) (a b + a c - b c) : (a + b) (a b + a c + b c)}

The appearance of (T,i) in the following list means that the triangle T is perspective to the inverse of Gemini triangle 15 and that the perspector is X(i):

(ABC, 65), (orthic, 1824), (incentral, 37), (extouch, 72), (extangents, 65), (2nd extouch, 72), (3rd extouch, 43213), (Ayme, 43214), (orthic of intouch, 43125), (inner Conway, 43216), (2nd anti-circumperp-tangential, 43217), (anti-Wasat, 43218), (Gemini 11, 25917), (Gemini 13, 43219), (Gemini 15, 43220), (Gemini 16, 31993), (Gemini 18, 321), (Gemini 63, 43221) The appearance of (T,i) in the following list means that the triangle T is perspective to the inverse of Gemini triangle 15 and that the perspector is X(i):

The appearance of (T,i) in the next list means that the triangle T is perspective to the inverse of Gemini triangle 16 and that the perspector is X(i):

(ABC, 42027), (outer Garcia, 43222), (Gemini 13, 10), (Gemini 15, 43223), (Gemini 16, 43224), (Gemini 17,42), (Gemini 114, 43225)

The locus of a point X such that the cevian triangle of X is perspective to the inverse of triangle Gemini 15 is the cubic K033 = pK(X(37),X(8)), which passes through X(i) for i = 1,4,8,10,40,65,72,3176,5930,39130,39131l.

The locus of a point X such that the anticevian triangle of X is perspective to the inverse of triangle Gemini 15 is the cubic pK(X(1500),X(10)), which passes through X(i) for i = 10,37,42,65,71,210,227,1826.

The locus of a point X such that the cevian triangle of X is perspective to the inverse of triangle Gemini 16 is the cubic pK (X(10),X(192)), which passes through X(i) for i = 37,75,192,2998,21080,39467,42027.

The locus of a point X such that the anticevian triangle of X is perspective to the inverse of triangle Gemini 16 is the cubic pK(X(594),X(37)), which passes through X(i) for i = 10,37,321,3971,22028,42027.



X(43213) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 15 AND 3RD EXTOUCH

Barycentrics    a*(b + c)*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 3*a^4*c - 2*a^3*b*c + 2*a*b^3*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 + 2*a*b*c^3 + 4*b^2*c^3 - 3*a*c^4 - 3*b*c^4 - c^5) : :
X(43213) = 3 X[392] - 4 X[9895], 3 X[3753] - 2 X[41340]

X(43213) lies on these lines: {1, 3198}, {4, 8}, {37, 1697}, {40, 37046}, {51, 9844}, {65, 1439}, {223, 3340}, {228, 3295}, {388, 10400}, {392, 7532}, {916, 16980}, {950, 2262}, {956, 37066}, {2093, 3182}, {2136, 22021}, {3057, 40960}, {3753, 18641}, {3868, 4452}, {4848, 8808}, {5252, 10368}, {5691, 5895}, {5837, 20262}, {5903, 8274}, {7070, 37052}, {8807, 15556}, {9579, 34371}, {10267, 37310}, {10362, 10369}, {10364, 10371}, {10366, 41687}, {10573, 11212}, {10904, 31533}, {10905, 31532}, {11406, 37547}, {16465, 41723}, {21370, 37537}, {21867, 22299}, {22300, 41539}

X(43213) = reflection of X(i) in X(j) for these {i,j}: {10373, 4}, {12672, 1871}
X(43213) = Fuhrmann circle inverse of X(10367)
X(43213) = barycentric product X(321)*X(37260)
X(43213) = barycentric quotient X(37260)/X(81)
X(43213) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 8, 10367}, {65, 5930, 1439}

X(43214) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 15 AND AYME

Barycentrics    a*(b + c)*(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(43214) lies on these lines: {1, 7535}, {2, 4463}, {10, 12}, {19, 25}, {40, 7322}, {42, 2294}, {71, 756}, {171, 1762}, {200, 22021}, {213, 5452}, {321, 2550}, {354, 40940}, {518, 4042}, {750, 26934}, {942, 1714}, {960, 27413}, {984, 24310}, {1118, 41013}, {1376, 3998}, {1400, 40967}, {1402, 21804}, {1751, 5728}, {1760, 37090}, {1781, 5285}, {1868, 1888}, {1871, 37528}, {2171, 2318}, {2218, 5266}, {2264, 3745}, {2330, 10536}, {2352, 40937}, {3057, 40960}, {3101, 5297}, {3175, 28580}, {3579, 11259}, {3610, 6057}, {3683, 12723}, {3690, 21853}, {3920, 41230}, {3932, 42706}, {3995, 17784}, {4123, 19310}, {4640, 21376}, {5249, 24476}, {5268, 10319}, {5439, 20083}, {5716, 40964}, {5880, 14455}, {9958, 40263}, {11237, 15940}, {11435, 26063}, {14547, 17451}, {16465, 18165}, {17056, 17441}, {19791, 32926}, {26098, 41581}, {30142, 37080}, {33112, 41717}, {37539, 40980}, {37593, 40965}

X(43214) = crossdifference of every pair of points on line {905, 7252}
X(43214) = X(3737)-isoconjugate of X(13395)
X(43214) = barycentric product X(i)*X(j) for these {i,j}: {37, 377}, {321, 37538}, {1448, 2321}
X(43214) = barycentric quotient X(i)/X(j) for these {i,j}: {377, 274}, {1448, 1434}, {4559, 13395}, {37538, 81}
X(43214) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {19, 612, 55}, {37, 3198, 55}, {65, 210, 209}

X(43215) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 15 AND ORTHIC OF INTOUCH

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

X(43215) lies on these lines: {37, 57}, {65, 4356}, {72, 4298}, {4032, 41539}

X(43215) = barycentric product X(1441)*X(41422)
X(43215) = barycentric quotient X(41422)/X(21)

X(43216) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 15 AND INNER CONWAY

Barycentrics    a*(a^3*b + a^2*b^2 - a*b^3 - b^4 + a^3*c - 2*a^2*b*c + a*b^2*c + a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 - c^4) : :
X(43216) = 3 X[210] - 2 X[17792], 3 X[3681] - X[25304]

X(43216) lies on these lines: {2, 24471}, {6, 63}, {9, 7146}, {37, 1959}, {65, 257}, {69, 189}, {72, 511}, {75, 2262}, {78, 1350}, {141, 908}, {144, 145}, {182, 3916}, {190, 21871}, {198, 326}, {210, 1654}, {226, 26543}, {241, 21371}, {321, 15983}, {354, 17379}, {374, 17277}, {385, 20359}, {513, 20713}, {517, 3729}, {524, 3175}, {573, 25083}, {611, 12514}, {651, 5279}, {760, 12723}, {910, 1958}, {960, 1469}, {1122, 3662}, {1212, 28287}, {1351, 3927}, {1386, 2975}, {1423, 3061}, {1760, 2182}, {2330, 4640}, {3098, 5440}, {3219, 15988}, {3242, 11682}, {3290, 28365}, {3416, 3436}, {3419, 31670}, {3509, 7175}, {3618, 5744}, {3619, 5748}, {3681, 25304}, {3687, 14557}, {3693, 22370}, {3694, 3882}, {3698, 28604}, {3706, 20557}, {3739, 30035}, {3751, 12526}, {3763, 30852}, {3844, 11681}, {3870, 10387}, {3940, 33878}, {3951, 11477}, {4431, 10914}, {4461, 14923}, {4468, 9002}, {4652, 5085}, {4663, 11684}, {4855, 31884}, {5480, 6734}, {5847, 12527}, {5919, 17319}, {6007, 40965}, {7957, 25242}, {9436, 14524}, {10025, 35614}, {10477, 30625}, {10527, 38035}, {11688, 37593}, {12530, 15726}, {12589, 24703}, {14110, 25252}, {15985, 30076}, {16609, 20258}, {17248, 25917}, {17333, 31165}, {17351, 21853}, {17787, 20719}, {20245, 20248}, {21078, 21362}, {24540, 26267}, {24553, 26258}, {25000, 33864}, {25887, 28402}, {26690, 27624}, {29965, 34852}, {30854, 41828}, {37142, 37206}

X(43216) = reflection of X(i) in X(j) for these {i,j}: {1469, 960}, {21853, 17351}
X(43216) = isotomic conjugate of X(26735)
X(43216) = anticomplement of X(24471)
X(43216) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {55, 5484}, {961, 36845}, {1169, 3875}, {1220, 3434}, {1240, 21280}, {2298, 7}, {2359, 347}, {2363, 3873}, {8687, 4025}, {8707, 21302}, {14534, 20244}, {14624, 2893}, {30710, 21285}, {32736, 522}, {36098, 3900}, {36147, 693}
X(43216) = crossdifference of every pair of points on line {8678, 20980}
X(43216) = X(31)-isoconjugate of X(26735)
X(43216) = barycentric quotient X(2)/X(26735)
X(43216) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 7146, 25099}, {144, 20110, 30616}, {144, 20535, 192}, {20245, 20248, 30807}

X(43217) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 15 AND 2ND ANTI-CIRCUMPERP-TANGENTIAL

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

X(43217) lies on these lines: {37, 56}, {65, 4854}, {72, 10106}, {208, 1824}

X(43218) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 15 AND ANTI-WASAT

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

X(43218) lies on these lines: {31, 184}, {51, 65}, {125, 2887}, {209, 3198}, {674, 6467}, {758, 2901}, {1204, 30269}, {1214, 3937}, {1899, 6327}, {2877, 3270}, {3690, 4047}, {6776, 20064}, {23154, 41340}

X(43218) = X(3952)-Ceva conjugate of X(647)
X(43218) = crosssum of X(3) and X(3187)
X(43218) = barycentric product X(i)*X(j) for these {i,j}: {71, 24046}, {228, 33146}, {1409, 4193}

X(43219) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 15 AND GEMINI 13

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

X(43219) lies on these lines: {37, 17868}, {908, 5743}

X(43220) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 15 AND GEMINI 15

Barycentrics    a*(b + c)*(a^4*b + a^3*b^2 - a^2*b^3 - a*b^4 + a^4*c + 5*a^3*b*c + 6*a^2*b^2*c + a*b^3*c - b^4*c + a^3*c^2 + 6*a^2*b*c^2 + 6*a*b^2*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(43220) lies on these lines: {1, 228}, {10, 4111}, {37, 579}, {65, 3743}, {72, 354}, {101, 4658}, {226, 39791}, {940, 27802}, {975, 35612}, {995, 5045}, {1071, 24220}, {1486, 5711}, {1824, 1844}, {2901, 5883}, {3191, 11518}, {3812, 5295}, {5439, 31993}, {5902, 31320}, {6005, 35672}, {6176, 24474}, {9843, 22020}, {10395, 37993}, {11028, 12564}, {11573, 17392}, {16607, 18635}, {18165, 37594}, {18180, 37595}, {18398, 26102}

X(43221) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 15 AND GEMINI 63

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

X(43221) lies on these lines: {2, 210}, {65, 27483}, {72, 27478}, {335, 4005}, {960, 27480}, {25917, 31319}

X(43222) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 15 AND OUTER GARCIA

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

X(43222) lies on these lines: {8, 4365}, {72, 3971}, {984, 7275}, {3696, 21080}, {4385, 31327}, {7226, 31339}

X(43222) = barycentric product X(10)*X(41835)
X(43222) = barycentric quotient X(41835)/X(86)

X(43223) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 16 AND GEMINI 15

Barycentrics    (b + c)*(2*a^2 + a*b + a*c + b*c) : :
X(43223) = 3 X[2] + X[17018]

X(43223) lies on these lines: {1, 2}, {3, 12545}, {31, 19684}, {35, 13588}, {37, 714}, {55, 11358}, {71, 17754}, {75, 4970}, {81, 32917}, {86, 171}, {87, 20146}, {100, 5333}, {140, 35631}, {142, 16056}, {165, 10446}, {209, 6679}, {210, 3842}, {226, 1284}, {291, 35623}, {313, 17725}, {321, 1962}, {333, 4649}, {354, 6682}, {516, 10434}, {631, 10476}, {726, 28606}, {740, 31993}, {756, 4090}, {846, 894}, {851, 12609}, {902, 19740}, {940, 32916}, {946, 4192}, {958, 16345}, {968, 3923}, {1001, 16058}, {1008, 13161}, {1010, 37573}, {1011, 5248}, {1051, 17121}, {1100, 3791}, {1107, 22199}, {1213, 21904}, {1376, 15668}, {1385, 37365}, {1403, 30097}, {1468, 16342}, {1478, 37193}, {1500, 21877}, {1575, 17398}, {1621, 4203}, {1764, 10164}, {1826, 4213}, {1869, 4212}, {1909, 31008}, {2200, 41239}, {2238, 4104}, {2276, 5750}, {2300, 24512}, {2308, 19717}, {2333, 6353}, {2887, 4026}, {3035, 38484}, {3136, 3822}, {3510, 26110}, {3589, 9054}, {3663, 24259}, {3666, 24165}, {3683, 4672}, {3696, 27798}, {3739, 22316}, {3740, 4698}, {3742, 22325}, {3745, 37869}, {3750, 5263}, {3758, 7262}, {3769, 17394}, {3812, 22300}, {3816, 37355}, {3821, 5249}, {3825, 39583}, {3835, 7234}, {3846, 5718}, {3848, 22278}, {3879, 30966}, {3896, 4709}, {3911, 10473}, {3925, 4085}, {3980, 10436}, {3986, 21060}, {3989, 17165}, {3995, 4135}, {3997, 7109}, {4003, 42053}, {4021, 4441}, {4038, 14829}, {4049, 17998}, {4065, 42031}, {4204, 21077}, {4292, 37175}, {4297, 10470}, {4357, 33064}, {4358, 31264}, {4363, 32934}, {4365, 27804}, {4368, 4656}, {4389, 33103}, {4416, 40721}, {4428, 16396}, {4434, 4682}, {4640, 4670}, {4645, 26109}, {4657, 20335}, {4667, 24690}, {4699, 4734}, {4713, 41312}, {4755, 42056}, {4848, 10474}, {5224, 33084}, {5235, 32864}, {5247, 11110}, {5266, 37148}, {5284, 32944}, {5432, 21334}, {5625, 37595}, {5711, 19715}, {5712, 32946}, {5737, 32853}, {5745, 35612}, {5886, 19540}, {6536, 26580}, {6666, 22312}, {6684, 10441}, {6690, 6703}, {6692, 35645}, {6822, 26105}, {7074, 19727}, {7987, 10465}, {8640, 23803}, {9791, 33099}, {10165, 37620}, {10171, 10886}, {10442, 43151}, {10454, 10887}, {10572, 14009}, {10856, 39553}, {10882, 43164}, {11176, 17990}, {11688, 30076}, {11813, 40109}, {12435, 43174}, {12436, 37262}, {16059, 25524}, {16484, 32942}, {16705, 24215}, {16777, 39967}, {16850, 21620}, {17045, 17061}, {17175, 25599}, {17234, 33174}, {17289, 33158}, {17300, 33085}, {17302, 33147}, {17321, 33144}, {17322, 33126}, {17381, 21035}, {17600, 32922}, {17601, 41847}, {17724, 17793}, {17766, 30969}, {17778, 33082}, {17798, 37327}, {17989, 22043}, {18134, 32784}, {18139, 32781}, {18235, 20258}, {19270, 37607}, {19278, 37608}, {19340, 39578}, {19741, 21747}, {19786, 33130}, {19804, 40328}, {19808, 33160}, {20131, 24586}, {20182, 32921}, {20788, 29311}, {21084, 25081}, {21241, 32773}, {21257, 27042}, {21727, 31209}, {21808, 22230}, {21921, 22173}, {22307, 42285}, {23791, 26114}, {24210, 25385}, {24342, 32932}, {24631, 31306}, {24692, 32950}, {24697, 33066}, {24723, 33097}, {27186, 33125}, {27268, 27538}, {27269, 41840}, {28346, 38479}, {28522, 28605}, {28619, 37559}, {30571, 30710}, {30986, 37737}, {31019, 32776}, {31997, 41849}, {32014, 38836}, {32780, 33116}, {32913, 38000}, {32918, 37633}, {32938, 33761}, {32947, 33112}, {32949, 33083}, {33073, 33076}, {37090, 37576}, {40533, 41850}

X(43223) = midpoint of X(i) and X(j) for these {i,j}: {10434, 10478}, {17018, 31330}, {28606, 32771}, {31993, 37593}
X(43223) = complement of X(31330)
X(43223) = complement of the isotomic conjugate of X(2296)
X(43223) = X(i)-complementary conjugate of X(j) for these (i,j): {785, 513}, {1218, 626}, {2296, 2887}
X(43223) = X(39738)-Ceva conjugate of X(37)
X(43223) = cevapoint of X(17379) and X(17689)
X(43223) = crosspoint of X(i) and X(j) for these (i,j): {2, 2296}, {835, 4600}, {17379, 31997}
X(43223) = crosssum of X(834) and X(3122)
X(43223) = crossdifference of every pair of points on line {649, 16695}
X(43223) = X(i)-isoconjugate of X(j) for these (i,j): {58, 17038}, {81, 39967}
X(43223) = barycentric product X(i)*X(j) for these {i,j}: {10, 17379}, {37, 31997}, {3952, 4932}
X(43223) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 17038}, {42, 39967}, {4932, 7192}, {17379, 86}, {17689, 6626}, {28622, 386}, {31997, 274}
X(43223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 3741}, {1, 1698, 10449}, {1, 3741, 42057}, {1, 10479, 35633}, {1, 18229, 39594}, {2, 42, 10}, {2, 1125, 25501}, {2, 3240, 26037}, {2, 3616, 26102}, {2, 3720, 3840}, {2, 5308, 30822}, {2, 17018, 31330}, {2, 17032, 3912}, {2, 17135, 30970}, {2, 26037, 3634}, {2, 26102, 4871}, {2, 26103, 31242}, {2, 26626, 17026}, {2, 29570, 31028}, {2, 29814, 30942}, {2, 29822, 42}, {2, 29824, 31241}, {2, 29829, 24892}, {2, 29830, 24943}, {2, 29831, 26238}, {2, 29837, 33140}, {2, 29839, 32783}, {2, 38314, 31137}, {10, 42, 4685}, {10, 4028, 21085}, {31, 19684, 33682}, {37, 1215, 3971}, {37, 16606, 21838}, {37, 25124, 42027}, {42, 4685, 4946}, {42, 28248, 43}, {75, 17592, 4970}, {321, 1962, 3993}, {551, 3840, 3720}, {1125, 6685, 2}, {1125, 20108, 19862}, {1149, 3616, 551}, {1215, 10180, 37}, {3214, 19874, 10}, {3293, 3624, 16828}, {3293, 16828, 10}, {3616, 5550, 26111}, {3616, 29825, 4871}, {3624, 16569, 2}, {3634, 35633, 10479}, {3666, 24325, 24165}, {3896, 21020, 4709}, {3971, 42027, 22024}, {4026, 17056, 2887}, {4640, 4670, 4697}, {4666, 29826, 29668}, {5287, 29828, 29649}, {7081, 16826, 1961}, {8640, 24674, 23803}, {10436, 17594, 3980}, {10454, 10887, 19925}, {19870, 31855, 10}, {20037, 38314, 1}, {21020, 21806, 3896}, {24331, 29650, 614}, {26093, 26115, 16828}, {26102, 29825, 2}, {26102, 31242, 26103}, {26103, 31242, 4871}, {27804, 31025, 4365}, {29644, 29651, 1}, {29647, 29661, 2}, {29666, 29853, 1125}, {29682, 29685, 3006}, {32773, 33111, 21241}, {33083, 37635, 32949}

X(43224) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 16 AND GEMINI 16

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

X(43224) lies on these lines: {10, 4446}, {3739, 21080}, {5836, 22316}

X(43225) = PERSPECTOR OF THESE TRIANGLES: INVERSE OF GEMINI 16 AND GEMINI 114

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

X(43225) = 3 X[3971] - 2 X[17760]

X(43225) lies on these lines: {1, 36858}, {8, 726}, {10, 2227}, {43, 194}, {76, 3741}, {256, 1221}, {538, 4685}, {698, 17792}, {1193, 36857}, {1478, 20350}, {1655, 3971}, {3840, 23473}, {5145, 27663}, {20340, 30092}, {20537, 32946}, {21443, 34086}, {24165, 34284}, {27424, 41886}, {29827, 31276}

X(43225) = X(1258)-anticomplementary conjugate of X(21281)

X(43226) = GIBERT (1,6,1) POINT

Barycentrics    a^2*S/Sqrt[3] + a^2*SA + 12*SB*SC : :
X(43226) = 13 X[33417] - 12 X[42500], 6 X[42500] - 13 X[42919]

X(43226) lies on the cubic K1221b and these lines: {2, 42429}, {4, 15}, {5, 42100}, {6, 17505}, {13, 12821}, {14, 3845}, {16, 546}, {18, 42127}, {20, 42915}, {30, 33417}, {61, 42101}, {62, 42103}, {381, 11481}, {382, 16966}, {395, 42971}, {397, 43031}, {621, 22494}, {1656, 42499}, {3090, 42113}, {3091, 10646}, {3146, 42114}, {3411, 3843}, {3412, 42117}, {3543, 42092}, {3545, 42091}, {3627, 10645}, {3830, 16241}, {3832, 42086}, {3839, 16963}, {3850, 42088}, {3851, 33416}, {3853, 23302}, {3854, 42937}, {3855, 42089}, {3856, 42123}, {3857, 5351}, {3858, 23303}, {3860, 42889}, {3861, 5321}, {5073, 43029}, {5076, 11480}, {5237, 42111}, {5238, 12102}, {5334, 42905}, {5335, 42814}, {5349, 42693}, {5350, 11543}, {5352, 42112}, {5365, 42779}, {5366, 42993}, {5478, 6778}, {10653, 42987}, {10654, 42506}, {10675, 18376}, {11267, 18566}, {11542, 14893}, {12101, 42122}, {12811, 42584}, {12817, 42974}, {12820, 41100}, {15687, 37832}, {15689, 42474}, {16261, 36979}, {16267, 43021}, {16268, 41987}, {16644, 35403}, {16960, 41101}, {16964, 42128}, {17578, 42090}, {18424, 19780}, {19709, 42528}, {22236, 42630}, {22237, 42994}, {22682, 32466}, {22794, 22850}, {22795, 22901}, {22796, 25235}, {23046, 42121}, {32789, 42280}, {32790, 42281}, {33699, 43104}, {33703, 42472}, {34754, 42136}, {34755, 42139}, {35731, 42176}, {36967, 38335}, {37349, 37775}, {37835, 41099}, {38071, 42493}, {41120, 42800}, {41121, 42940}, {41943, 42530}, {41972, 42588}, {42095, 42158}, {42115, 42580}, {42133, 42162}, {42144, 42598}, {42148, 42917}, {42149, 42909}, {42160, 43196}, {42433, 43028}, {42632, 42687}, {42682, 42925}, {42816, 42990}, {42956, 42996}

X(43226) = reflection of X(33417) in X(42919)
X(43226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 16808, 19107}, {4, 42106, 15}, {4, 42142, 42104}, {15, 42106, 16808}, {15, 42140, 42157}, {16, 43195, 42137}, {381, 19106, 16967}, {546, 42102, 16}, {546, 42137, 42107}, {3091, 42105, 10646}, {3627, 42110, 10645}, {3830, 42098, 42099}, {3832, 42086, 42918}, {3843, 42094, 16809}, {3850, 42088, 42914}, {3851, 42097, 33416}, {10645, 42110, 42581}, {12102, 42146, 42108}, {16242, 19106, 42131}, {16808, 19107, 17}, {16808, 42157, 18582}, {16809, 16965, 16961}, {16809, 42094, 16965}, {16960, 42126, 41101}, {16967, 19106, 36968}, {18582, 42140, 15}, {34754, 42166, 43004}, {42098, 42099, 16241}, {42101, 42138, 61}, {42102, 42107, 42137}, {42102, 42137, 43195}, {42103, 42134, 62}, {42104, 42106, 42142}, {42104, 42142, 15}, {42107, 42137, 16}, {42107, 43106, 42628}, {42108, 42146, 5238}, {42111, 42141, 5237}, {42135, 42907, 42922}, {42136, 42166, 34754}, {42137, 42628, 43106}, {42139, 42161, 34755}, {42143, 42165, 16}, {42180, 42182, 16808}, {42188, 42190, 11488}, {42628, 43106, 16}, {42907, 42922, 5318}

X(43227) = GIBERT (-1,6,1) POINT

Barycentrics    a^2*S/Sqrt[3] - a^2*SA - 12*SB*SC : :
X(43227) = 13 X[33416] - 12 X[42501], 6 X[42501] - 13 X[42918]

X(43227) lies on the cubic K1221a and these lines: {2, 42430}, {4, 16}, {5, 42099}, {6, 17505}, {13, 3845}, {14, 12820}, {15, 546}, {17, 42126}, {20, 42914}, {30, 33416}, {61, 42106}, {62, 42102}, {381, 11480}, {382, 16967}, {396, 42970}, {398, 43030}, {622, 22493}, {1656, 42498}, {3090, 42112}, {3091, 10645}, {3146, 42111}, {3411, 42118}, {3412, 3843}, {3543, 42089}, {3545, 42090}, {3627, 10646}, {3830, 16242}, {3832, 42085}, {3839, 16962}, {3850, 42087}, {3851, 33417}, {3853, 23303}, {3854, 42936}, {3855, 42092}, {3856, 42122}, {3857, 5352}, {3858, 23302}, {3860, 42888}, {3861, 5318}, {5073, 43028}, {5076, 11481}, {5237, 12102}, {5238, 42114}, {5334, 42813}, {5335, 42904}, {5349, 11542}, {5350, 42692}, {5351, 42113}, {5365, 42992}, {5366, 42780}, {5479, 6777}, {10653, 42507}, {10654, 42986}, {10676, 18376}, {11268, 18566}, {11543, 14893}, {12101, 42123}, {12811, 42585}, {12816, 42975}, {12821, 41101}, {15687, 37835}, {15689, 42475}, {16261, 36981}, {16267, 41987}, {16268, 43020}, {16645, 35403}, {16961, 41100}, {16965, 42125}, {17578, 42091}, {18424, 19781}, {19709, 42529}, {22235, 42995}, {22238, 42629}, {22682, 32465}, {22794, 22855}, {22795, 22894}, {22797, 25236}, {23046, 42124}, {32789, 35733}, {32790, 42280}, {33699, 43101}, {33703, 42473}, {34754, 42142}, {34755, 42137}, {35730, 42243}, {35731, 42204}, {36968, 38335}, {37349, 37776}, {37832, 41099}, {38071, 42492}, {41119, 42799}, {41122, 42941}, {41944, 42531}, {41971, 42589}, {42098, 42157}, {42116, 42581}, {42134, 42159}, {42145, 42599}, {42147, 42916}, {42152, 42908}, {42161, 43195}, {42434, 43029}, {42631, 42686}, {42683, 42924}, {42815, 42991}, {42957, 42997}

X(43227) = reflection of X(33416) in X(42918)
X(43227) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 16809, 19106}, {4, 42103, 16}, {4, 42139, 42105}, {15, 43196, 42136}, {16, 42103, 16809}, {16, 42141, 42158}, {381, 19107, 16966}, {546, 42101, 15}, {546, 42136, 42110}, {3091, 42104, 10645}, {3627, 42107, 10646}, {3830, 42095, 42100}, {3832, 42085, 42919}, {3843, 42093, 16808}, {3850, 42087, 42915}, {3851, 42096, 33417}, {10646, 42107, 42580}, {12102, 42143, 42109}, {16241, 19107, 42130}, {16808, 16964, 16960}, {16808, 42093, 16964}, {16809, 19106, 18}, {16809, 42158, 18581}, {16961, 42127, 41100}, {16966, 19107, 36967}, {18581, 42141, 16}, {34755, 42163, 43005}, {42095, 42100, 16242}, {42101, 42110, 42136}, {42101, 42136, 43196}, {42102, 42135, 62}, {42103, 42105, 42139}, {42105, 42139, 16}, {42106, 42133, 61}, {42109, 42143, 5237}, {42110, 42136, 15}, {42110, 43105, 42627}, {42114, 42140, 5238}, {42136, 42627, 43105}, {42137, 42163, 34755}, {42138, 42906, 42923}, {42142, 42160, 34754}, {42146, 42164, 15}, {42179, 42181, 16809}, {42187, 42189, 11489}, {42627, 43105, 15}, {42906, 42923, 5321}

X(43228) = GIBERT (9,1,2) POINT

Barycentrics    3*Sqrt[3]*a^2*S + 2*a^2*SA + 2*SB*SC : :
X(43228) = 2 X[61] + X[397], 5 X[61] + X[16965], 3 X[61] - X[41101], 3 X[61] + X[41107], 4 X[61] - X[42147], 7 X[61] - X[42157], 8 X[61] + X[42165], 11 X[61] + X[42431], 3 X[61] - 5 X[42520], 5 X[61] - 2 X[42925], 9 X[61] - 2 X[43108], 5 X[397] - 2 X[16965], 3 X[397] + 2 X[41101], 3 X[397] - 2 X[41107], 2 X[397] + X[42147], 7 X[397] + 2 X[42157], 4 X[397] - X[42165], 11 X[397] - 2 X[42431], 3 X[397] + 10 X[42520], 5 X[397] + 4 X[42925], 9 X[397] + 4 X[43108], 3 X[16965] + 5 X[41101], 3 X[16965] - 5 X[41107], 4 X[16965] + 5 X[42147], 7 X[16965] + 5 X[42157], 8 X[16965] - 5 X[42165], 11 X[16965] - 5 X[42431], 3 X[16965] + 25 X[42520], X[16965] + 2 X[42925], 9 X[16965] + 10 X[43108], 4 X[41101] - 3 X[42147], 7 X[41101] - 3 X[42157], 8 X[41101] + 3 X[42165], 11 X[41101] + 3 X[42431], X[41101] - 5 X[42520], 5 X[41101] - 6 X[42925], 3 X[41101] - 2 X[43108], 4 X[41107] + 3 X[42147], 7 X[41107] + 3 X[42157], 8 X[41107] - 3 X[42165], 11 X[41107] - 3 X[42431], X[41107] + 5 X[42520], 5 X[41107] + 6 X[42925], 3 X[41107] + 2 X[43108], 7 X[42147] - 4 X[42157], 2 X[42147] + X[42165], 11 X[42147] + 4 X[42431], 3 X[42147] - 20 X[42520], 5 X[42147] - 8 X[42925], 9 X[42147] - 8 X[43108], 8 X[42157] + 7 X[42165], 11 X[42157] + 7 X[42431], 3 X[42157] - 35 X[42520], 5 X[42157] - 14 X[42925], 9 X[42157] - 14 X[43108], 11 X[42165] - 8 X[42431], 3 X[42165] + 40 X[42520], 5 X[42165] + 16 X[42925], 9 X[42165] + 16 X[43108], 3 X[42431] + 55 X[42520], 5 X[42431] + 22 X[42925], 9 X[42431] + 22 X[43108], 25 X[42520] - 6 X[42925], 15 X[42520] - 2 X[43108], 9 X[42925] - 5 X[43108]

X(43228) lies on the cubic K1221a and these lines: {2, 6}, {3, 42510}, {4, 33602}, {5, 16267}, {13, 3845}, {14, 5066}, {15, 8703}, {16, 12100}, {17, 547}, {18, 15699}, {30, 61}, {32, 35304}, {39, 35303}, {51, 11624}, {62, 549}, {115, 41621}, {140, 3412}, {372, 15764}, {376, 22236}, {381, 398}, {428, 8740}, {465, 3284}, {466, 5158}, {472, 6749}, {473, 1990}, {531, 39593}, {532, 5007}, {533, 37352}, {542, 14136}, {546, 42972}, {550, 42990}, {632, 3411}, {1080, 8550}, {1353, 5617}, {2307, 5434}, {3106, 36385}, {3107, 36364}, {3524, 22238}, {3534, 10653}, {3543, 5340}, {3545, 42156}, {3627, 42909}, {3830, 5318}, {3839, 5339}, {3853, 41973}, {3860, 16808}, {4969, 40714}, {4995, 7127}, {5008, 36769}, {5054, 16773}, {5055, 40694}, {5059, 42587}, {5071, 42153}, {5097, 6771}, {5237, 17504}, {5238, 34200}, {5305, 22496}, {5309, 31693}, {5319, 11305}, {5334, 41099}, {5335, 15682}, {5349, 14269}, {5350, 15687}, {5351, 14891}, {5352, 42435}, {5460, 22893}, {5469, 20252}, {5472, 14537}, {5480, 6770}, {5613, 18583}, {5943, 11626}, {6034, 41754}, {6419, 18585}, {6420, 15765}, {6772, 9112}, {6773, 12007}, {6774, 15516}, {6775, 36329}, {7005, 15170}, {7739, 11296}, {7753, 31694}, {7757, 35943}, {7772, 37341}, {8014, 11537}, {8015, 18776}, {9115, 36768}, {9885, 19661}, {10109, 11543}, {10124, 42949}, {10304, 36836}, {10645, 15759}, {10646, 15711}, {11001, 42087}, {11480, 19708}, {11481, 15698}, {11486, 15693}, {11539, 41944}, {11812, 16241}, {12101, 12816}, {12150, 35942}, {12154, 35693}, {12155, 35696}, {14869, 42636}, {14893, 42813}, {15640, 42109}, {15681, 42150}, {15683, 43194}, {15684, 42161}, {15685, 42086}, {15686, 42158}, {15688, 42151}, {15690, 34754}, {15691, 42434}, {15692, 36843}, {15694, 42149}, {15697, 42120}, {15703, 42989}, {15704, 41974}, {15708, 42490}, {15713, 16242}, {15716, 42115}, {15717, 42793}, {15721, 42491}, {16646, 22488}, {16960, 37835}, {16961, 42627}, {16967, 42497}, {17369, 40713}, {18581, 42503}, {18582, 19709}, {19107, 42799}, {19710, 36967}, {19711, 34755}, {21476, 37503}, {21849, 36980}, {21969, 36978}, {22489, 22847}, {23046, 42814}, {32907, 36251}, {33416, 42916}, {33603, 33604}, {33605, 42098}, {33699, 36969}, {34325, 36299}, {34509, 37351}, {35404, 42432}, {35751, 41745}, {36330, 41746}, {36436, 42251}, {36448, 42187}, {36454, 42253}, {36466, 42189}, {38335, 42160}, {41106, 42110}, {41982, 43022}, {41983, 42802}, {41985, 42590}, {42092, 42501}, {42093, 42982}, {42094, 42682}, {42095, 42986}, {42099, 42922}, {42100, 43021}, {42101, 42815}, {42103, 42781}, {42119, 42588}, {42122, 43106}, {42123, 42529}, {42127, 43105}, {42132, 42910}, {42133, 42693}, {42140, 42683}, {42143, 43031}, {42429, 42585}, {42472, 42479}, {42505, 42892}, {42531, 43015}, {42581, 42780}, {42595, 42917}, {42597, 42947}, {42628, 42897}, {42817, 42911}, {42905, 43007}, {42915, 42952}, {42981, 43008}, {43103, 43199}

X(43228) = midpoint of X(41101) and X(41107)
X(43228) = complement of the isotomic conjugate of X(12816)
X(43228) = X(12816)-complementary conjugate of X(2887)
X(43228) = crosspoint of X(2) and X(12816)
X(43228) = crosssum of X(6) and X(10645)
X(43228) = centroid of pedal triangle of X(61)
X(43228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 43229}, {2, 1992, 5858}, {2, 5863, 599}, {2, 37786, 33458}, {3, 42510, 42792}, {6, 396, 395}, {6, 13846, 36467}, {6, 13847, 36450}, {6, 16644, 37641}, {6, 37640, 396}, {13, 41108, 3845}, {14, 41121, 5066}, {14, 42506, 41121}, {15, 8703, 42791}, {15, 41100, 8703}, {15, 42800, 42528}, {17, 16268, 547}, {61, 397, 42147}, {61, 16965, 42925}, {61, 41107, 41101}, {62, 16772, 42944}, {62, 16962, 549}, {140, 41943, 43107}, {395, 396, 23302}, {396, 23303, 16644}, {397, 42147, 42165}, {398, 40693, 42166}, {547, 16268, 42599}, {549, 16962, 16772}, {597, 33458, 2}, {3412, 16963, 41943}, {3534, 11485, 42511}, {3534, 42511, 42942}, {3830, 41112, 5318}, {3830, 42974, 41112}, {3845, 41108, 5321}, {5066, 11542, 41121}, {5066, 42506, 42502}, {5318, 10654, 42940}, {5335, 42154, 42941}, {7585, 36450, 32787}, {7586, 36467, 32788}, {8584, 33458, 41624}, {8703, 41100, 42943}, {10645, 42480, 42420}, {10653, 11485, 42942}, {10653, 42511, 3534}, {10653, 42942, 42088}, {10654, 41112, 3830}, {10654, 42974, 5318}, {11542, 41121, 42502}, {11543, 37832, 43101}, {11543, 42496, 37832}, {12101, 12816, 42102}, {12816, 36970, 12101}, {15687, 42973, 5350}, {15690, 43109, 36968}, {15694, 42149, 43100}, {16242, 42124, 42500}, {16242, 42521, 42977}, {16644, 37641, 23303}, {16963, 41943, 140}, {16964, 42973, 15687}, {18582, 41120, 19709}, {19053, 37640, 36468}, {19054, 37640, 36449}, {19709, 42975, 41120}, {22236, 42998, 42148}, {23303, 37641, 395}, {32787, 32788, 396}, {36449, 36468, 6}, {36449, 37640, 32788}, {36468, 37640, 32787}, {36968, 42632, 15690}, {40693, 41113, 41119}, {40694, 42988, 42598}, {41100, 42532, 15}, {41101, 42520, 61}, {41113, 41119, 381}, {41121, 42506, 11542}, {42124, 42634, 16242}, {42154, 42941, 42108}, {42156, 42999, 42163}, {42521, 42977, 42634}, {42599, 42899, 16268}, {42791, 42943, 8703}, {42991, 42992, 546}

X(43229) = GIBERT (-9,1,2) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 2*a^2*SA - 2*SB*SC : :
X(43229) = 2 X[62] + X[398], 5 X[62] + X[16964], 3 X[62] - X[41100], 3 X[62] + X[41108], 4 X[62] - X[42148], 7 X[62] - X[42158], 8 X[62] + X[42164], 11 X[62] + X[42432], 3 X[62] - 5 X[42521], 5 X[62] - 2 X[42924], 9 X[62] - 2 X[43109], 5 X[398] - 2 X[16964], 3 X[398] + 2 X[41100], 3 X[398] - 2 X[41108], 2 X[398] + X[42148], 7 X[398] + 2 X[42158], 4 X[398] - X[42164], 11 X[398] - 2 X[42432], 3 X[398] + 10 X[42521], 5 X[398] + 4 X[42924], 9 X[398] + 4 X[43109], 3 X[16964] + 5 X[41100], 3 X[16964] - 5 X[41108], 4 X[16964] + 5 X[42148], 7 X[16964] + 5 X[42158], 8 X[16964] - 5 X[42164], 11 X[16964] - 5 X[42432], 3 X[16964] + 25 X[42521], X[16964] + 2 X[42924], 9 X[16964] + 10 X[43109], 4 X[41100] - 3 X[42148], 7 X[41100] - 3 X[42158], 8 X[41100] + 3 X[42164], 11 X[41100] + 3 X[42432], X[41100] - 5 X[42521], 5 X[41100] - 6 X[42924], 3 X[41100] - 2 X[43109], 4 X[41108] + 3 X[42148], 7 X[41108] + 3 X[42158], 8 X[41108] - 3 X[42164], 11 X[41108] - 3 X[42432], X[41108] + 5 X[42521], 5 X[41108] + 6 X[42924], 3 X[41108] + 2 X[43109], 7 X[42148] - 4 X[42158], 2 X[42148] + X[42164], 11 X[42148] + 4 X[42432], 3 X[42148] - 20 X[42521], 5 X[42148] - 8 X[42924], 9 X[42148] - 8 X[43109], 8 X[42158] + 7 X[42164], 11 X[42158] + 7 X[42432], 3 X[42158] - 35 X[42521], 5 X[42158] - 14 X[42924], 9 X[42158] - 14 X[43109], 11 X[42164] - 8 X[42432], 3 X[42164] + 40 X[42521], 5 X[42164] + 16 X[42924], 9 X[42164] + 16 X[43109], 3 X[42432] + 55 X[42521], 5 X[42432] + 22 X[42924], 9 X[42432] + 22 X[43109], 25 X[42521] - 6 X[42924], 15 X[42521] - 2 X[43109], 9 X[42924] - 5 X[43109]

X(43229) lies on the cubic K1221b and these lines: {2, 6}, {3, 42511}, {4, 33603}, {5, 16268}, {13, 5066}, {14, 3845}, {15, 12100}, {16, 8703}, {17, 15699}, {18, 547}, {30, 62}, {32, 35303}, {39, 35304}, {51, 11626}, {61, 549}, {115, 41620}, {140, 3411}, {371, 15764}, {376, 22238}, {381, 397}, {383, 8550}, {428, 8739}, {465, 5158}, {466, 3284}, {472, 1990}, {473, 6749}, {530, 39593}, {532, 37351}, {533, 5007}, {542, 14137}, {546, 42973}, {550, 42991}, {632, 3412}, {1353, 5613}, {2307, 5298}, {3058, 7127}, {3106, 36365}, {3107, 36384}, {3524, 22236}, {3534, 10654}, {3543, 5339}, {3545, 42153}, {3627, 42908}, {3830, 5321}, {3839, 5340}, {3853, 41974}, {3860, 16809}, {4969, 40713}, {5008, 41621}, {5054, 16772}, {5055, 40693}, {5059, 42586}, {5071, 42156}, {5097, 6774}, {5237, 34200}, {5238, 17504}, {5305, 22495}, {5309, 31694}, {5319, 11306}, {5334, 15682}, {5335, 41099}, {5349, 15687}, {5350, 14269}, {5351, 42436}, {5352, 14891}, {5459, 22847}, {5470, 20253}, {5471, 14537}, {5480, 6773}, {5617, 18583}, {5943, 11624}, {6034, 41752}, {6419, 15765}, {6420, 18585}, {6770, 12007}, {6771, 15516}, {6772, 35751}, {6775, 9113}, {7006, 15170}, {7739, 11295}, {7753, 31693}, {7757, 35942}, {7772, 37340}, {8014, 18777}, {8015, 11549}, {9115, 36769}, {9886, 19661}, {10109, 11542}, {10124, 42948}, {10304, 36843}, {10645, 15711}, {10646, 15759}, {11001, 42088}, {11083, 41889}, {11480, 15698}, {11481, 19708}, {11485, 15693}, {11539, 41943}, {11812, 16242}, {12101, 12817}, {12150, 35943}, {12154, 35692}, {12155, 35697}, {14869, 42635}, {14893, 42814}, {15640, 42108}, {15681, 42151}, {15683, 43193}, {15684, 42160}, {15685, 42085}, {15686, 42157}, {15688, 42150}, {15690, 34755}, {15691, 42433}, {15692, 36836}, {15694, 42152}, {15697, 42119}, {15703, 42988}, {15704, 41973}, {15708, 42491}, {15713, 16241}, {15716, 42116}, {15717, 42794}, {15721, 42490}, {16647, 22487}, {16960, 42628}, {16961, 37832}, {16966, 42496}, {17369, 40714}, {18581, 19709}, {18582, 42502}, {19106, 42800}, {19710, 36968}, {19711, 34754}, {21475, 37503}, {21849, 36978}, {21969, 36980}, {22490, 22893}, {23046, 42813}, {32909, 36252}, {33417, 42917}, {33602, 33605}, {33604, 42095}, {33699, 36970}, {34326, 36298}, {34508, 37352}, {35404, 42431}, {35752, 41745}, {36329, 41746}, {36436, 42252}, {36448, 42190}, {36454, 42250}, {36466, 42188}, {38335, 42161}, {41106, 42107}, {41982, 43023}, {41983, 42801}, {41985, 42591}, {42089, 42500}, {42093, 42683}, {42094, 42983}, {42098, 42987}, {42099, 43020}, {42100, 42923}, {42102, 42816}, {42106, 42782}, {42120, 42589}, {42122, 42528}, {42123, 43105}, {42126, 43106}, {42129, 42911}, {42134, 42692}, {42141, 42682}, {42146, 43030}, {42430, 42584}, {42473, 42478}, {42504, 42893}, {42530, 43014}, {42580, 42779}, {42594, 42916}, {42596, 42946}, {42627, 42896}, {42818, 42910}, {42904, 43006}, {42914, 42953}, {42980, 43009}, {43102, 43200}

X(43229) = midpoint of X(41100) and X(41108)
X(43229) = complement of the isotomic conjugate of X(12817)
X(43229) = centroid of pedal triangle of X(62)
X(43229) = X(12817)-complementary conjugate of X(2887)
X(43229) = crosspoint of X(2) and X(12817)
X(43229) = crosssum of X(6) and X(10646)
X(43229) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 43228}, {2, 1992, 5859}, {2, 5862, 599}, {2, 37785, 33459}, {3, 42511, 42791}, {6, 395, 396}, {6, 13846, 36449}, {6, 13847, 36468}, {6, 16645, 37640}, {6, 37641, 395}, {13, 41122, 5066}, {13, 42507, 41122}, {14, 41107, 3845}, {16, 8703, 42792}, {16, 41101, 8703}, {16, 42799, 42529}, {18, 16267, 547}, {61, 16773, 42945}, {61, 16963, 549}, {62, 398, 42148}, {62, 16964, 42924}, {62, 41108, 41100}, {140, 41944, 43100}, {395, 396, 23303}, {395, 23302, 16645}, {397, 40694, 42163}, {398, 42148, 42164}, {547, 16267, 42598}, {549, 16963, 16773}, {597, 33459, 2}, {3411, 16962, 41944}, {3534, 11486, 42510}, {3534, 42510, 42943}, {3830, 41113, 5321}, {3830, 42975, 41113}, {3845, 41107, 5318}, {5066, 11543, 41122}, {5066, 42507, 42503}, {5321, 10653, 42941}, {5334, 42155, 42940}, {7585, 36468, 32787}, {7586, 36449, 32788}, {8584, 33459, 41624}, {8703, 41101, 42942}, {10646, 42481, 42419}, {10653, 41113, 3830}, {10653, 42975, 5321}, {10654, 11486, 42943}, {10654, 42510, 3534}, {10654, 42943, 42087}, {11542, 37835, 43104}, {11542, 42497, 37835}, {11543, 41122, 42503}, {12101, 12817, 42101}, {12817, 36969, 12101}, {15687, 42972, 5349}, {15690, 43108, 36967}, {15694, 42152, 43107}, {16241, 42121, 42501}, {16241, 42520, 42976}, {16645, 37640, 23302}, {16962, 41944, 140}, {16965, 42972, 15687}, {18581, 41119, 19709}, {19053, 37641, 36450}, {19054, 37641, 36467}, {19709, 42974, 41119}, {22238, 42999, 42147}, {23302, 37640, 396}, {32787, 32788, 395}, {36450, 36467, 6}, {36450, 37641, 32787}, {36467, 37641, 32788}, {36967, 42631, 15690}, {40693, 42989, 42599}, {40694, 41112, 41120}, {41100, 42521, 62}, {41101, 42533, 16}, {41112, 41120, 381}, {41122, 42507, 11543}, {42121, 42633, 16241}, {42153, 42998, 42166}, {42155, 42940, 42109}, {42520, 42976, 42633}, {42598, 42898, 16267}, {42792, 42942, 8703}, {42990, 42993, 546}

X(43230) = GIBERT (15,44,-77) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 77*a^2*SA + 88*SB*SC : :
X(43230) = 42 X[42686] - 47 X[42796], 80 X[42686] - 47 X[43196], 54 X[42686] - 47 X[43200], 40 X[42796] - 21 X[43196], 9 X[42796] - 7 X[43200], 27 X[43196] - 40 X[43200]

X(43230) lies on the cubic K1221b and these lines: {2, 42429}, {6, 15681}, {14, 3529}, {20, 42779}, {30, 42686}, {382, 42937}, {396, 42980}, {550, 36969}, {3528, 42581}, {3534, 42518}, {5344, 42529}, {12820, 34200}, {15688, 42094}, {15700, 42915}, {15715, 42113}, {16267, 42100}, {16967, 43003}, {19710, 43106}, {36967, 43111}, {36968, 42636}, {41944, 42133}, {41972, 42099}, {42154, 42613}, {42626, 42988}, {42630, 42913}, {42683, 42952}, {42782, 42943}, {42939, 42965}

X(43231) = GIBERT (15,-44,77) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 77*a^2*SA - 88*SB*SC : :
X(43231) = 42 X[42687] - 47 X[42795], 80 X[42687] - 47 X[43195], 54 X[42687] - 47 X[43199], 40 X[42795] - 21 X[43195], 9 X[42795] - 7 X[43199], 27 X[43195] - 40 X[43199]

X(43231) lies on the cubic K1221a and these lines: {2, 42430}, {6, 15681}, {13, 3529}, {20, 42780}, {30, 42687}, {382, 42936}, {395, 42981}, {550, 36970}, {3528, 42580}, {3534, 42519}, {5343, 42528}, {12821, 34200}, {15688, 42093}, {15700, 42914}, {15715, 42112}, {16268, 42099}, {16966, 43002}, {19710, 43105}, {36967, 42635}, {36968, 43110}, {41943, 42134}, {41971, 42100}, {42155, 42612}, {42625, 42989}, {42629, 42912}, {42682, 42953}, {42781, 42942}, {42938, 42964}

X(43232) = GIBERT (33,4,11) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 11*a^2*SA + 8*SB*SC : :
X(43232) = 23 X[41971] + 12 X[42971], X[41971] + 6 X[43014], 9 X[41971] - 2 X[43204], 4 X[41971] + 15 X[43205], 2 X[42971] - 23 X[43014], 6 X[42971] + 23 X[43021], 54 X[42971] + 23 X[43204], 16 X[42971] - 115 X[43205], 3 X[43014] + X[43021], 27 X[43014] + X[43204], 8 X[43014] - 5 X[43205], 9 X[43021] - X[43204], 8 X[43021] + 15 X[43205], 8 X[43204] + 135 X[43205]

X(43232) lies on the cubic K1221a and these lines: {2, 43015}, {3, 43006}, {4, 13}, {6, 15694}, {14, 11737}, {15, 15688}, {16, 12100}, {17, 12812}, {30, 41971}, {62, 42774}, {376, 42478}, {381, 43007}, {395, 3412}, {396, 15699}, {547, 43031}, {548, 43022}, {549, 42892}, {1656, 43024}, {1992, 36770}, {3530, 41978}, {3839, 43010}, {3850, 43032}, {3851, 43013}, {5054, 42893}, {5066, 43004}, {5071, 42479}, {5321, 42506}, {5344, 42803}, {6435, 36456}, {6436, 36438}, {6669, 22496}, {6694, 40899}, {10109, 43011}, {10645, 42997}, {10653, 15697}, {11485, 15685}, {11542, 42972}, {14093, 41972}, {14869, 16241}, {14890, 16963}, {15684, 42900}, {15686, 34754}, {15687, 42895}, {15692, 43020}, {15708, 16962}, {16267, 42902}, {16644, 42489}, {16966, 42481}, {22238, 42959}, {22891, 41621}, {33417, 42956}, {35402, 42815}, {37832, 41122}, {37835, 42780}, {41101, 42941}, {41113, 42986}, {41121, 42110}, {42086, 42516}, {42096, 42974}, {42113, 42430}, {42116, 42800}, {42117, 42898}, {42158, 42612}, {42435, 42528}, {42480, 42792}, {42795, 42943}, {42911, 42914}

X(43232) = reflection of X(41971) in X(43021)
X(43232) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 61, 42799}, {13, 42799, 36970}, {61, 40693, 41973}, {61, 42813, 42995}, {61, 42992, 42934}, {10654, 42813, 36970}, {36970, 42995, 10654}, {41122, 42817, 37832}, {42474, 42975, 41122}, {42532, 42896, 10653}, {42817, 42975, 42474}

X(43233) = GIBERT (-33,4,11) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 11*a^2*SA - 8*SB*SC : :
X(43233) = 23 X[41972] + 12 X[42970], X[41972] + 6 X[43015], 9 X[41972] - 2 X[43203], 4 X[41972] + 15 X[43206], 2 X[42970] - 23 X[43015], 6 X[42970] + 23 X[43020], 54 X[42970] + 23 X[43203], 16 X[42970] - 115 X[43206], 3 X[43015] + X[43020], 27 X[43015] + X[43203], 8 X[43015] - 5 X[43206], 9 X[43020] - X[43203], 8 X[43020] + 15 X[43206], 8 X[43203] + 135 X[43206]

X(43233) lies on the cubic K1221b and these lines: {2, 43014}, {3, 43007}, {4, 14}, {6, 15694}, {13, 11737}, {15, 12100}, {16, 15688}, {18, 12812}, {30, 41972}, {61, 42773}, {376, 42479}, {381, 43006}, {395, 15699}, {396, 3411}, {547, 43030}, {548, 43023}, {549, 42893}, {1656, 43025}, {3530, 41977}, {3839, 43011}, {3850, 43033}, {3851, 43012}, {5054, 42892}, {5066, 43005}, {5071, 42478}, {5318, 42507}, {5343, 42804}, {6329, 36770}, {6435, 36438}, {6436, 36456}, {6670, 22495}, {6695, 40898}, {10109, 43010}, {10646, 42996}, {10654, 15697}, {11486, 15685}, {11543, 42973}, {14093, 41971}, {14869, 16242}, {14890, 16962}, {15684, 42901}, {15686, 34755}, {15687, 42894}, {15692, 43021}, {15708, 16963}, {16268, 42903}, {16645, 42488}, {16967, 42480}, {22236, 42958}, {22846, 41620}, {33416, 42957}, {35402, 42816}, {37832, 42779}, {37835, 41121}, {41100, 42940}, {41112, 42987}, {41122, 42107}, {42085, 42517}, {42097, 42975}, {42112, 42429}, {42115, 42799}, {42118, 42899}, {42157, 42613}, {42436, 42529}, {42481, 42791}, {42796, 42942}, {42910, 42915}

X(43233) = reflection of X(41972) in X(43020)
X(43233) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 62, 42800}, {14, 42800, 36969}, {62, 40694, 41974}, {62, 42814, 42994}, {62, 42993, 42935}, {10653, 42814, 36969}, {36969, 42994, 10653}, {41121, 42818, 37835}, {42475, 42974, 41121}, {42533, 42897, 10654}, {42818, 42974, 42475}

X(43234) = GIBERT (77,6,5) POINT

Barycentrics    77*a^2*S/Sqrt[3] + 5*a^2*SA + 12*SB*SC : :

X(43234) lies on the cubic K1221b and these lines: {2, 43014}, {6, 5072}, {15, 21735}, {17, 42628}, {30, 42799}, {3412, 16773}, {3627, 42900}, {3843, 42904}, {3850, 43031}, {5335, 42991}, {11481, 42435}, {11486, 15718}, {12812, 43004}, {12816, 42093}, {15689, 43021}, {15706, 42996}, {15712, 43018}, {37832, 42897}, {41121, 42782}, {42106, 43032}, {42140, 42629}, {42429, 42480}

X(43235) = GIBERT (-77,6,5) POINT

Barycentrics    77*a^2*S/Sqrt[3] - 5*a^2*SA - 12*SB*SC : :

X(43235) lies on the cubic K1221a and these lines: {2, 43015}, {6, 5072}, {16, 21735}, {18, 42627}, {30, 42800}, {3411, 16772}, {3627, 42901}, {3843, 42905}, {3850, 43030}, {5334, 42990}, {11480, 42436}, {11485, 15718}, {12812, 43005}, {12817, 42094}, {15689, 43020}, {15706, 42997}, {15712, 43019}, {37835, 42896}, {41122, 42781}, {42103, 43033}, {42141, 42630}, {42430, 42481}

X(43236) = GIBERT (207,77,46) POINT

Barycentrics    69*Sqrt[3]*a^2*S + 46*a^2*SA + 154*SB*SC : :

X(43236) lies on the cubic K1221b and these lines: {4, 33602}, {16, 15713}, {397, 15707}, {12817, 42693}, {14891, 42148}, {16267, 42793}, {23303, 33607}, {41107, 42891}, {41112, 42683}, {41119, 42899}, {41120, 42110}, {41944, 42598}, {42127, 42511}, {42502, 42974}, {42506, 42922}, {42631, 42930}, {42898, 43108}

X(43237) = GIBERT (-207,77,46) POINT

Barycentrics    69*Sqrt[3]*a^2*S - 46*a^2*SA - 154*SB*SC : :

X(43237) lies on the cubic K1221a and these lines: {4, 33603}, {15, 15713}, {398, 15707}, {12816, 42692}, {14891, 42147}, {16268, 42794}, {23302, 33606}, {41108, 42890}, {41113, 42682}, {41119, 42107}, {41120, 42898}, {41943, 42599}, {42126, 42510}, {42503, 42975}, {42507, 42923}, {42632, 42931}, {42899, 43109}

X(43238) = GIBERT (3,2,6) POINT

Barycentrics    Sqrt[3]*a^2*S + 6*a^2*SA + 4*SB*SC : :

X(43238) lies on the cubic K1222 and these lines: {2, 398}, {3, 13}, {4, 11480}, {5, 36836}, {6, 140}, {14, 5070}, {15, 1656}, {16, 15720}, {18, 10187}, {20, 5350}, {30, 42921}, {61, 3526}, {62, 5054}, {376, 5366}, {381, 5238}, {382, 5352}, {395, 3525}, {396, 631}, {397, 3523}, {546, 42911}, {547, 42159}, {548, 42162}, {549, 36843}, {550, 18582}, {619, 11311}, {627, 5859}, {630, 11312}, {632, 40694}, {634, 9763}, {635, 11309}, {636, 11301}, {1151, 2046}, {1152, 2045}, {1657, 10645}, {3090, 5343}, {3091, 42942}, {3104, 33462}, {3412, 16242}, {3522, 5318}, {3524, 42148}, {3528, 42165}, {3530, 10653}, {3533, 23303}, {3534, 42813}, {3545, 42164}, {3628, 10654}, {3763, 6671}, {3830, 42434}, {3832, 43104}, {3839, 42791}, {3843, 36967}, {3850, 42085}, {3851, 16966}, {3854, 42101}, {3855, 42927}, {3858, 42114}, {5055, 16964}, {5056, 5321}, {5059, 42142}, {5067, 42163}, {5068, 5349}, {5072, 36970}, {5073, 16808}, {5079, 42592}, {5237, 42974}, {5335, 10299}, {5344, 21735}, {5351, 15693}, {5365, 42107}, {5868, 37463}, {7784, 11290}, {8703, 42161}, {10188, 16809}, {10303, 16773}, {10646, 42817}, {11134, 13336}, {11243, 40686}, {11305, 13083}, {11489, 42948}, {11542, 15712}, {11543, 42493}, {14093, 42973}, {14813, 42262}, {14814, 42265}, {15024, 36980}, {15685, 42504}, {15688, 41121}, {15692, 42518}, {15694, 16962}, {15695, 42586}, {15696, 36969}, {15699, 42511}, {15700, 41107}, {15701, 42505}, {15703, 41101}, {15707, 41100}, {15717, 42943}, {15722, 42506}, {15723, 16268}, {15815, 40922}, {16960, 42115}, {16967, 42894}, {17504, 41112}, {17538, 42941}, {17800, 42529}, {18581, 42923}, {22235, 42120}, {22332, 40921}, {22532, 41038}, {33475, 37172}, {33923, 42086}, {34200, 41119}, {34509, 36769}, {34754, 42129}, {35018, 42117}, {35786, 42278}, {35787, 42279}, {38335, 42587}, {41122, 42934}, {41974, 42815}, {41978, 42816}, {41981, 42145}, {42090, 42146}, {42102, 42775}, {42126, 42915}, {42128, 42431}, {42130, 42919}, {42435, 42597}, {42489, 42975}, {42509, 42972}, {42530, 42691}, {42613, 43012}, {42780, 42818}, {42793, 42986}, {42903, 42960}, {42939, 43018}, {42954, 43015}, {43002, 43201}

X(43238) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16772, 22236}, {2, 22236, 42153}, {2, 42599, 42611}, {3, 13, 43193}, {3, 17, 5340}, {3, 16241, 42490}, {3, 16644, 42156}, {3, 16965, 42625}, {3, 42156, 42155}, {4, 42945, 11480}, {5, 36836, 42154}, {6,140,43239}, {15, 1656, 5339}, {15, 42936, 1656}, {15, 43029, 42095}, {16, 15720, 42774}, {17, 5340, 42156}, {20, 42494, 5350}, {61, 3526, 16645}, {61, 42937, 42989}, {62, 5054, 42491}, {140, 42124, 42152}, {140, 42152, 6}, {381, 5238, 43194}, {382, 5352, 42626}, {396, 631, 22238}, {396, 42944, 42998}, {397, 3523, 11481}, {398, 42599, 22237}, {398, 42949, 2}, {549, 40693, 36843}, {631, 42998, 42944}, {632, 42912, 40694}, {1656, 5339, 42095}, {1656, 42936, 43029}, {3523, 11488, 397}, {3526, 42989, 42937}, {3533, 42806, 42987}, {3533, 42999, 23303}, {3851, 42116, 42157}, {3851, 42157, 42093}, {5068, 42119, 5349}, {5238, 42488, 381}, {5339, 43029, 1656}, {5340, 16644, 17}, {5340, 42490, 42773}, {5340, 42773, 3}, {5344, 21735, 42088}, {5350, 42598, 42494}, {5352, 37832, 382}, {5418, 5420, 42124}, {10303, 37640, 16773}, {10645, 42132, 42094}, {11480, 23302, 42098}, {11480, 42098, 42096}, {11485, 33417, 43028}, {11542, 15712, 42151}, {15720, 42988, 16}, {16644, 42490, 3}, {16644, 42773, 5340}, {16772, 42949, 398}, {16773, 42500, 10303}, {16966, 42116, 42093}, {16966, 42157, 3851}, {23302, 42687, 42110}, {23302, 42945, 4}, {33417, 43022, 10187}, {35018, 42117, 42920}, {36967, 42581, 3843}, {38335, 42632, 42587}, {41973, 42125, 5339}, {42087, 42945, 42794}, {42087, 42957, 23302}, {42092, 42124, 6}, {42092, 42152, 140}, {42121, 42124, 43197}, {42130, 42950, 42919}, {42780, 42978, 42818}, {42937, 42989, 16645}, {42944, 42998, 22238}

X(43239) = GIBERT (-3,2,6) POINT

Barycentrics    Sqrt[3]*a^2*S - 6*a^2*SA - 4*SB*SC : :

X(43239) lies on the cubic K1222 and these lines: {2, 397}, {3, 14}, {4, 11481}, {5, 36843}, {6, 140}, {13, 5070}, {15, 15720}, {16, 1656}, {17, 10188}, {20, 5349}, {30, 42920}, {61, 5054}, {62, 3526}, {376, 5365}, {381, 5237}, {382, 5351}, {395, 631}, {396, 3525}, {398, 3523}, {546, 42910}, {547, 42162}, {548, 42159}, {549, 36836}, {550, 18581}, {618, 11312}, {628, 5858}, {629, 11311}, {632, 40693}, {633, 9761}, {635, 11302}, {636, 11310}, {1151, 2045}, {1152, 2046}, {1657, 10646}, {3090, 5344}, {3091, 42943}, {3105, 33463}, {3411, 16241}, {3522, 5321}, {3524, 42147}, {3528, 42164}, {3530, 10654}, {3533, 23302}, {3534, 42814}, {3545, 42165}, {3628, 10653}, {3763, 6672}, {3830, 42433}, {3832, 43101}, {3839, 42792}, {3843, 36968}, {3850, 42086}, {3851, 16967}, {3854, 42102}, {3855, 42926}, {3858, 42111}, {5055, 16965}, {5056, 5318}, {5059, 42139}, {5067, 42166}, {5068, 5350}, {5072, 36969}, {5073, 16809}, {5079, 42593}, {5238, 42975}, {5334, 10299}, {5343, 21735}, {5352, 15693}, {5366, 42110}, {5869, 37464}, {7784, 11289}, {8703, 42160}, {10187, 16808}, {10303, 16772}, {10645, 42818}, {11137, 13336}, {11244, 40686}, {11306, 13084}, {11488, 42949}, {11542, 42492}, {11543, 15712}, {14093, 42972}, {14813, 42265}, {14814, 42262}, {15024, 36978}, {15685, 42505}, {15688, 41122}, {15692, 42519}, {15694, 16963}, {15695, 42587}, {15696, 36970}, {15699, 42510}, {15700, 41108}, {15701, 42504}, {15703, 41100}, {15707, 41101}, {15717, 42942}, {15722, 42507}, {15723, 16267}, {15815, 40921}, {16961, 42116}, {16966, 42895}, {17504, 41113}, {17538, 42940}, {17800, 42528}, {18582, 42922}, {22237, 42119}, {22332, 40922}, {22531, 41039}, {33474, 37173}, {33923, 42085}, {34200, 41120}, {34755, 42132}, {35018, 42118}, {35786, 42279}, {35787, 42278}, {38335, 42586}, {41121, 42935}, {41973, 42816}, {41977, 42815}, {41981, 42144}, {42091, 42143}, {42101, 42776}, {42125, 42432}, {42127, 42914}, {42131, 42918}, {42436, 42596}, {42488, 42974}, {42508, 42973}, {42531, 42690}, {42612, 43013}, {42779, 42817}, {42794, 42987}, {42902, 42961}, {42938, 43019}, {42955, 43014}, {43003, 43202}

X(43239) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16773, 22238}, {2, 22238, 42156}, {2, 42598, 42610}, {3, 14, 43194}, {3, 18, 5339}, {3, 16242, 42491}, {3, 16645, 42153}, {3, 16964, 42626}, {3, 42153, 42154}, {4, 42944, 11481}, {5, 36843, 42155}, {6,140,43238}, {15, 15720, 42773}, {16, 1656, 5340}, {16, 42937, 1656}, {16, 43028, 42098}, {18, 5339, 42153}, {20, 42495, 5349}, {61, 5054, 42490}, {62, 3526, 16644}, {62, 42936, 42988}, {140, 42121, 42149}, {140, 42149, 6}, {381, 5237, 43193}, {382, 5351, 42625}, {395, 631, 22236}, {395, 42945, 42999}, {397, 42598, 22235}, {397, 42948, 2}, {398, 3523, 11480}, {549, 40694, 36836}, {631, 42999, 42945}, {632, 42913, 40693}, {1656, 5340, 42098}, {1656, 42937, 43028}, {3523, 11489, 398}, {3526, 42988, 42936}, {3533, 42805, 42986}, {3533, 42998, 23302}, {3851, 42115, 42158}, {3851, 42158, 42094}, {5068, 42120, 5350}, {5237, 42489, 381}, {5339, 16645, 18}, {5339, 42491, 42774}, {5339, 42774, 3}, {5340, 43028, 1656}, {5343, 21735, 42087}, {5349, 42599, 42495}, {5351, 37835, 382}, {5418, 5420, 42121}, {10303, 37641, 16772}, {10646, 42129, 42093}, {11481, 23303, 42095}, {11481, 42095, 42097}, {11486, 33416, 43029}, {11543, 15712, 42150}, {15720, 42989, 15}, {16645, 42491, 3}, {16645, 42774, 5339}, {16772, 42501, 10303}, {16773, 42948, 397}, {16967, 42115, 42094}, {16967, 42158, 3851}, {23303, 42686, 42107}, {23303, 42944, 4}, {33416, 43023, 10188}, {35018, 42118, 42921}, {36968, 42580, 3843}, {38335, 42631, 42586}, {41974, 42128, 5340}, {42088, 42944, 42793}, {42088, 42956, 23303}, {42089, 42121, 6}, {42089, 42149, 140}, {42121, 42124, 43198}, {42131, 42951, 42918}, {42779, 42979, 42817}, {42936, 42988, 16644}, {42945, 42999, 22236}

X(43240) = GIBERT (5,12,13) POINT

Barycentrics    5*a^2*S/Sqrt[3] + 13*a^2*SA + 24*SB*SC : :
X(43240) = 3 X[16966] + 2 X[42110], 9 X[16966] - 4 X[43103], X[16966] - 6 X[43104], 3 X[42110] + 2 X[43103], X[42110] + 9 X[43104], 2 X[43103] - 27 X[43104]

X(43240) lies on the cubic K1222 and these lines: {3, 43195}, {4, 42798}, {5, 16960}, {6, 43205}, {15, 3091}, {16, 1656}, {17, 42139}, {30, 16966}, {62, 12812}, {140, 42683}, {381, 43196}, {631, 16808}, {632, 10646}, {3090, 34755}, {3522, 33417}, {3525, 42629}, {3545, 42512}, {3627, 42955}, {3843, 11480}, {3850, 43105}, {3857, 42630}, {3858, 23302}, {3859, 42136}, {5055, 42636}, {5071, 16961}, {5072, 34754}, {5076, 10645}, {5237, 42142}, {5238, 42950}, {5351, 42962}, {5352, 42108}, {10109, 42521}, {11485, 19709}, {11543, 42777}, {15692, 42100}, {15693, 42094}, {15694, 36969}, {15696, 43029}, {15712, 19106}, {15713, 42088}, {16239, 42693}, {16267, 42095}, {16809, 42627}, {16967, 43008}, {17538, 42106}, {17578, 42092}, {18581, 43004}, {19107, 41099}, {36968, 43201}, {40693, 43012}, {41106, 43199}, {41119, 42517}, {41121, 42129}, {41122, 42983}, {41989, 42598}, {42089, 42973}, {42107, 42916}, {42111, 42986}, {42122, 42957}, {42124, 42682}, {42126, 42979}, {42132, 42814}, {42473, 42991}, {42494, 42978}, {42499, 42905}, {42513, 43006}, {42518, 42975}, {42531, 42634}, {42599, 43010}, {43015, 43101}

X(43240) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5071, 18582, 16961}, {42111, 42986, 43011}, {42114, 42581, 15}, {42472, 42911, 19107}

X(43241) = GIBERT (-5,12,13) POINT

Barycentrics    5*a^2*S/Sqrt[3] - 13*a^2*SA - 24*SB*SC : :
X(43241) = 3 X[16967] + 2 X[42107], X[16967] - 6 X[43101], 9 X[16967] - 4 X[43102], X[42107] + 9 X[43101], 3 X[42107] + 2 X[43102], 27 X[43101] - 2 X[43102]

X(43241) lies on the cubic K1222 and these lines: {3, 43196}, {4, 42797}, {5, 16961}, {6, 43205}, {15, 1656}, {16, 3091}, {18, 42142}, {30, 16967}, {61, 12812}, {140, 42682}, {381, 43195}, {631, 16809}, {632, 10645}, {3090, 34754}, {3522, 33416}, {3525, 42630}, {3545, 42513}, {3627, 42954}, {3843, 11481}, {3850, 43106}, {3857, 42629}, {3858, 23303}, {3859, 42137}, {5055, 42635}, {5071, 16960}, {5072, 34755}, {5076, 10646}, {5237, 42951}, {5238, 42139}, {5351, 42109}, {5352, 42963}, {10109, 42520}, {11486, 19709}, {11542, 42778}, {15692, 42099}, {15693, 42093}, {15694, 36970}, {15696, 43028}, {15712, 19107}, {15713, 42087}, {16239, 42692}, {16268, 42098}, {16808, 42628}, {16966, 43009}, {17538, 42103}, {17578, 42089}, {18582, 43005}, {19106, 41099}, {36967, 43202}, {40694, 43013}, {41106, 43200}, {41120, 42516}, {41121, 42982}, {41122, 42132}, {41989, 42599}, {42092, 42972}, {42110, 42917}, {42114, 42987}, {42121, 42683}, {42123, 42956}, {42127, 42978}, {42129, 42813}, {42472, 42990}, {42495, 42979}, {42498, 42904}, {42512, 43007}, {42519, 42974}, {42530, 42633}, {42598, 43011}, {43014, 43104}

X(43241) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5071, 18581, 16960}, {42111, 42580, 16}, {42114, 42987, 43010}, {42473, 42910, 19106}

X(43242) = GIBERT (8,3,-6) POINT

Barycentrics    4*a^2*S/Sqrt[3] - 3*a^2*SA + 3*SB*SC : :

X(43242) lies on the cubic K1222 and these lines: {2, 33602}, {3, 42916}, {4, 42805}, {6, 20}, {13, 15721}, {14, 3543}, {16, 3091}, {17, 3523}, {62, 42112}, {376, 42633}, {381, 43198}, {396, 42508}, {3090, 42493}, {3146, 11486}, {3522, 42116}, {3524, 42815}, {3525, 42492}, {3528, 42416}, {3545, 42951}, {3627, 42987}, {3832, 42127}, {3839, 11489}, {3854, 42129}, {5056, 5318}, {5059, 42131}, {5068, 42121}, {5071, 42985}, {5334, 42113}, {5340, 42476}, {5344, 42089}, {5350, 42473}, {5366, 16967}, {7486, 16965}, {10299, 42817}, {10303, 11481}, {10304, 10645}, {11488, 15692}, {11542, 15717}, {11543, 17578}, {15022, 42138}, {15640, 37641}, {15682, 42816}, {15683, 42117}, {15697, 36968}, {15708, 23302}, {15715, 42496}, {15720, 42926}, {15722, 33604}, {16267, 42928}, {16644, 42685}, {16645, 42588}, {16809, 42510}, {16960, 42959}, {18581, 42629}, {19708, 42932}, {22237, 42431}, {22238, 42101}, {23249, 42178}, {23259, 42177}, {23267, 42202}, {23273, 42201}, {23303, 42475}, {34754, 42091}, {36843, 42142}, {36967, 42803}, {37640, 42791}, {41100, 42085}, {42100, 42999}, {42104, 42894}, {42110, 42956}, {42139, 42165}, {42140, 42970}, {42152, 42930}, {42517, 42940}

X(43242) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 42922, 42986}, {3146, 11486, 42983}, {5335, 42092, 22235}, {10646, 41974, 42895}, {10646, 42895, 42092}, {22238, 43106, 42141}, {34755, 42086, 42133}, {41974, 42092, 5335}, {42106, 42900, 42134}, {42119, 42120, 43193}, {42729, 42730, 42088}

X(43243) = GIBERT (8,-3,6) POINT

Barycentrics    4*a^2*S/Sqrt[3] + 3*a^2*SA - 3*SB*SC : :

X(43243) lies on the cubic K1222 and these lines: {2, 33603}, {3, 42917}, {4, 42806}, {6, 20}, {13, 3543}, {14, 15721}, {15, 3091}, {18, 3523}, {61, 42113}, {376, 42634}, {381, 43197}, {395, 42509}, {3090, 42492}, {3146, 11485}, {3522, 42115}, {3524, 42816}, {3525, 42493}, {3528, 42415}, {3545, 42950}, {3627, 42986}, {3832, 42126}, {3839, 11488}, {3854, 42132}, {5056, 5321}, {5059, 42130}, {5068, 42124}, {5071, 42984}, {5335, 42112}, {5339, 42477}, {5343, 42092}, {5349, 42472}, {5365, 16966}, {7486, 16964}, {10299, 42818}, {10303, 11480}, {10304, 10646}, {11489, 15692}, {11542, 17578}, {11543, 15717}, {15022, 42135}, {15640, 37640}, {15682, 42815}, {15683, 42118}, {15697, 36967}, {15708, 23303}, {15715, 42497}, {15720, 42927}, {15722, 33605}, {16268, 42929}, {16644, 42589}, {16645, 42684}, {16808, 42511}, {16961, 42958}, {18582, 42630}, {19708, 42933}, {22235, 42432}, {22236, 42102}, {23249, 42176}, {23259, 42175}, {23267, 42200}, {23273, 42199}, {23302, 42474}, {34755, 42090}, {36836, 42139}, {36968, 42804}, {37641, 42792}, {41101, 42086}, {42099, 42998}, {42105, 42895}, {42107, 42957}, {42141, 42971}, {42142, 42164}, {42149, 42931}, {42516, 42941}

X(43243) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 42923, 42987}, {3146, 11485, 42982}, {5334, 42089, 22237}, {10645, 41973, 42894}, {10645, 42894, 42089}, {22236, 43105, 42140}, {34754, 42085, 42134}, {41973, 42089, 5334}, {42103, 42901, 42133}, {42119, 42120, 43194}, {42729, 42730, 42087}

X(43244) = GIBERT (15,10,-13) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 13*a^2*SA + 20*SB*SC : :
X(43244) = 4 X[42416] - 19 X[43106], 54 X[42416] - 19 X[43110], 27 X[43106] - 2 X[43110]

X(43244) lies on the cubic K1222 and these lines: {3, 13}, {4, 42938}, {6, 42429}, {14, 3543}, {16, 3845}, {30, 42416}, {62, 33703}, {376, 42795}, {381, 12820}, {395, 3853}, {547, 16808}, {631, 42965}, {1657, 42890}, {3529, 42935}, {3533, 42581}, {3545, 16967}, {3830, 12821}, {3832, 37835}, {3839, 42513}, {3850, 42165}, {5056, 5237}, {5059, 10654}, {5067, 42161}, {5071, 42954}, {5318, 11539}, {5321, 42533}, {5351, 16239}, {8703, 42777}, {10124, 42685}, {10645, 42496}, {10646, 15702}, {10653, 11001}, {11480, 42506}, {11542, 41982}, {11812, 37832}, {12816, 16242}, {12817, 43011}, {15682, 42517}, {15686, 34754}, {15688, 16960}, {15690, 41107}, {15694, 42689}, {15708, 33417}, {15715, 42512}, {15718, 42955}, {15719, 18582}, {16267, 42091}, {16773, 41991}, {16963, 19106}, {17538, 42779}, {17578, 43001}, {18581, 42893}, {19107, 41100}, {19708, 33607}, {19710, 42520}, {19711, 41121}, {23046, 43195}, {33416, 42474}, {35400, 42097}, {35402, 42125}, {36967, 42131}, {36970, 42148}, {37640, 41974}, {38071, 42683}, {41122, 42105}, {41943, 42895}, {41971, 42087}, {41983, 42500}, {41985, 42905}, {42085, 42800}, {42109, 42972}, {42113, 43031}, {42115, 42985}, {42128, 42928}, {42138, 42792}, {42141, 42510}, {42142, 42931}, {42157, 42799}, {42432, 43008}, {42436, 43032}, {42493, 42907}, {42597, 42921}, {42598, 42960}

X(43244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 13, 43199}, {3, 42158, 42891}, {17, 36968, 42528}, {3543, 34755, 14}, {10653, 42100, 41101}, {16242, 42127, 12816}, {16965, 36968, 16241}, {36968, 42155, 16965}, {41107, 42088, 42529}, {42155, 42158, 36968}, {42528, 43193, 36968}

X(43245) = GIBERT (15,-10,13) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 13*a^2*SA - 20*SB*SC : :
X(43245) = 4 X[42415] - 19 X[43105], 54 X[42415] - 19 X[43111], 27 X[43105] - 2 X[43111]

X(43245) lies on the cubic K1222 and these lines: {3, 14}, {4, 42939}, {6, 42429}, {13, 3543}, {15, 3845}, {30, 42415}, {61, 33703}, {376, 42796}, {381, 12821}, {396, 3853}, {547, 16809}, {631, 42964}, {1657, 42891}, {3529, 42934}, {3533, 42580}, {3545, 16966}, {3830, 12820}, {3832, 37832}, {3839, 42512}, {3850, 42164}, {5056, 5238}, {5059, 10653}, {5067, 42160}, {5071, 42955}, {5318, 42532}, {5321, 11539}, {5352, 16239}, {8703, 42778}, {10124, 42684}, {10645, 15702}, {10646, 42497}, {10654, 11001}, {11481, 42507}, {11543, 41982}, {11812, 37835}, {12816, 43010}, {12817, 16241}, {15682, 42516}, {15686, 34755}, {15688, 16961}, {15690, 41108}, {15694, 42688}, {15708, 33416}, {15715, 42513}, {15718, 42954}, {15719, 18581}, {16268, 42090}, {16772, 41991}, {16962, 19107}, {17538, 42780}, {17578, 43000}, {18582, 42892}, {19106, 41101}, {19708, 33606}, {19710, 42521}, {19711, 41122}, {23046, 43196}, {33417, 42475}, {35400, 42096}, {35402, 42128}, {36968, 42130}, {36969, 42147}, {37641, 41973}, {38071, 42682}, {41121, 42104}, {41944, 42894}, {41972, 42088}, {41983, 42501}, {41985, 42904}, {42086, 42799}, {42108, 42973}, {42112, 43030}, {42116, 42984}, {42125, 42929}, {42135, 42791}, {42139, 42930}, {42140, 42511}, {42158, 42800}, {42431, 43009}, {42435, 43033}, {42492, 42906}, {42596, 42920}, {42599, 42961}

X(43245) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14, 43200}, {3, 42157, 42890}, {18, 36967, 42529}, {3543, 34754, 13}, {10654, 42099, 41100}, {16241, 42126, 12817}, {16964, 36967, 16242}, {36967, 42154, 16964}, {41108, 42087, 42528}, {42154, 42157, 36967}, {42529, 43194, 36967}

X(43246) = GIBERT (18,25,23) POINT

Barycentrics    6*Sqrt[3]*a^2*S + 23*a^2*SA + 50*SB*SC : :

X(43246) lies on the cubic K1222 and these lines: {2, 33602}, {3, 43201}, {5, 16268}, {6, 43207}, {15, 3845}, {17, 23046}, {30, 42921}, {381, 5365}, {397, 42636}, {398, 43013}, {546, 42511}, {547, 22238}, {549, 42165}, {632, 42958}, {3091, 33603}, {3534, 42142}, {3627, 42791}, {3830, 42124}, {3858, 16962}, {3860, 42117}, {5055, 42494}, {5066, 18582}, {5318, 15713}, {5344, 15723}, {5351, 11539}, {5366, 15707}, {8703, 12816}, {10109, 41119}, {10124, 42162}, {11488, 43108}, {11489, 42420}, {11540, 42155}, {11542, 19709}, {11737, 41120}, {11812, 42911}, {12100, 42091}, {12101, 16644}, {14892, 40693}, {15682, 42132}, {15684, 42775}, {15687, 42598}, {15692, 42590}, {15693, 42984}, {15694, 42588}, {15695, 42962}, {15698, 43103}, {15699, 41100}, {15711, 36969}, {15714, 42936}, {15759, 42145}, {16241, 43195}, {16808, 33699}, {17504, 42813}, {19708, 42137}, {19710, 23302}, {33604, 42974}, {36843, 41985}, {38071, 41108}, {41099, 42912}, {41101, 42110}, {41106, 42135}, {41107, 42121}, {41122, 42502}, {41990, 42633}, {42521, 42599}, {42581, 42948}, {42778, 43010}, {42796, 42971}, {42986, 43110}

X(43246) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5066, 42496, 41113}, {41119, 42098, 10109}

X(43247) = GIBERT (-18,25,23) POINT

Barycentrics    6*Sqrt[3]*a^2*S - 23*a^2*SA - 50*SB*SC : :

X(43247) lies on the cubic K1222 and these lines: {2, 33603}, {3, 43202}, {5, 16267}, {6, 43207}, {16, 3845}, {18, 23046}, {30, 42920}, {381, 5366}, {397, 43012}, {398, 42635}, {546, 42510}, {547, 22236}, {549, 42164}, {632, 42959}, {3091, 33602}, {3534, 42139}, {3627, 42792}, {3830, 42121}, {3858, 16963}, {3860, 42118}, {5055, 42495}, {5066, 18581}, {5321, 15713}, {5343, 15723}, {5352, 11539}, {5365, 15707}, {8703, 12817}, {10109, 41120}, {10124, 42159}, {11488, 42419}, {11489, 43109}, {11540, 42154}, {11543, 19709}, {11737, 41119}, {11812, 42910}, {12100, 42090}, {12101, 16645}, {14892, 40694}, {15682, 42129}, {15684, 42776}, {15687, 42599}, {15692, 42591}, {15693, 42985}, {15694, 42589}, {15695, 42963}, {15698, 43102}, {15699, 41101}, {15711, 36970}, {15714, 42937}, {15759, 42144}, {16242, 43196}, {16809, 33699}, {17504, 42814}, {19708, 42136}, {19710, 23303}, {33605, 42975}, {36836, 41985}, {38071, 41107}, {41099, 42913}, {41100, 42107}, {41106, 42138}, {41108, 42124}, {41121, 42503}, {41990, 42634}, {42520, 42598}, {42580, 42949}, {42777, 43011}, {42795, 42970}, {42987, 43111}

X(43247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5066, 42497, 41112}, {41120, 42095, 10109}

X(43248) = GIBERT (33,50,115) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 115*a^2*SA + 100*SB*SC : :
X(43248) = 49 X[16966] - 16 X[42110], X[16966] + 32 X[43103], 27 X[16966] - 16 X[43104], X[42110] + 98 X[43103], 27 X[42110] - 49 X[43104], 54 X[43103] + X[43104]

X(43248) lies on the cubic K1222 and these lines: {2, 42892}, {3, 43203}, {6, 15723}, {13, 15721}, {14, 5070}, {30, 16966}, {381, 43204}, {3525, 16242}, {5055, 42997}, {5056, 5238}, {5072, 36967}, {5237, 42949}, {5366, 15717}, {10188, 21735}, {15694, 43020}, {15713, 41972}, {15718, 42625}, {15720, 16965}, {16960, 35381}, {23302, 42800}, {33417, 33607}, {35401, 42430}, {41943, 42513}, {41984, 42957}, {42092, 42504}, {42099, 42515}, {42121, 42977}, {42474, 42929}, {42507, 42985}, {42512, 42982}, {42531, 42635}, {42630, 43029}, {42633, 42978}, {42914, 42955}

X(43249) = GIBERT (-33,50,115) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 115*a^2*SA - 100*SB*SC : :
X(43249) = 49 X[16967] - 16 X[42107], 27 X[16967] - 16 X[43101], X[16967] + 32 X[43102], 27 X[42107] - 49 X[43101], X[42107] + 98 X[43102], X[43101] + 54 X[43102]

X(43249) lies on the cubic K1222 and these lines: {2, 42893}, {3, 43204}, {6, 15723}, {13, 5070}, {14, 15721}, {30, 16967}, {381, 43203}, {3525, 16241}, {5055, 42996}, {5056, 5237}, {5072, 36968}, {5238, 42948}, {5365, 15717}, {10187, 21735}, {15694, 43021}, {15713, 41971}, {15718, 42626}, {15720, 16964}, {16961, 35381}, {23303, 42799}, {33416, 33606}, {35401, 42429}, {41944, 42512}, {41984, 42956}, {42089, 42505}, {42100, 42514}, {42124, 42976}, {42475, 42928}, {42506, 42984}, {42513, 42983}, {42530, 42636}, {42629, 43028}, {42634, 42979}, {42915, 42954}

X(43250) = GIBERT (55,12,-1) POINT

Barycentrics    55*a^2*S/Sqrt[3] - a^2*SA + 24*SB*SC : :
X(43250) = 36 X[42415] - 25 X[43105], 2 X[42415] + 75 X[43111], X[43105] + 54 X[43111]

X(43250) lies on the cubic K1222 and these lines: {2, 42893}, {3, 43205}, {6, 42612}, {16, 15720}, {30, 42415}, {62, 42917}, {381, 43206}, {546, 42894}, {550, 43030}, {3525, 34755}, {3528, 43014}, {3544, 42895}, {3855, 16808}, {5070, 42938}, {11480, 42631}, {15710, 41972}, {16242, 43207}, {16773, 42627}, {35018, 43019}, {38071, 43015}, {42105, 42998}, {42138, 43033}, {42140, 42629}, {42517, 42952}, {42636, 42974}, {42973, 43032}

X(43250) = {X(6),X(43195)}-harmonic conjugate of X(42613)

X(43251) = GIBERT (55,-12,1) POINT

Barycentrics    55*a^2*S/Sqrt[3] + a^2*SA - 24*SB*SC : :
X(43251) = 36 X[42416] - 25 X[43106], 2 X[42416] + 75 X[43110], X[43106] + 54 X[43110]

X(43251) lies on the cubic K1222 and these lines: {2, 42892}, {3, 43206}, {6, 42612}, {15, 15720}, {30, 42416}, {61, 42916}, {381, 43205}, {546, 42895}, {550, 43031}, {3525, 34754}, {3528, 43015}, {3544, 42894}, {3855, 16809}, {5070, 42939}, {11481, 42632}, {15710, 41971}, {16241, 43208}, {16772, 42628}, {35018, 43018}, {38071, 43014}, {42104, 42999}, {42135, 43032}, {42141, 42630}, {42516, 42953}, {42635, 42975}, {42972, 43033}

X(43251) = {X(6),X(43196)}-harmonic conjugate of X(42612)

X(43252) = GIBERT (72,25,2) POINT

Barycentrics    12*Sqrt[3]*a^2*S + a^2*SA + 25*SB*SC : :

X(43252) lies on the cubic K1222 and these lines: {2, 397}, {3, 43207}, {6, 42539}, {381, 33605}, {3522, 16962}, {3524, 42496}, {3545, 42497}, {3628, 33604}, {3832, 41112}, {3839, 42135}, {5054, 42933}, {5055, 42917}, {5334, 12821}, {5335, 36970}, {10304, 42123}, {10653, 15705}, {12100, 42926}, {15022, 42990}, {15683, 41107}, {15688, 42922}, {15708, 42115}, {16268, 42921}, {17504, 42986}, {23046, 42983}, {35418, 36968}, {36967, 43205}, {40693, 42631}, {41113, 42973}, {41119, 43026}, {42094, 42478}, {42140, 42941}, {42511, 42544}, {42636, 42895}

X(43253) = GIBERT (-72,25,2) POINT

Barycentrics    12*Sqrt[3]*a^2*S - a^2*SA - 25*SB*SC : :

X(43253) lies on the cubic K1222 and these lines: {2, 398}, {3, 43208}, {6, 42539}, {381, 33604}, {3522, 16963}, {3524, 42497}, {3545, 42496}, {3628, 33605}, {3832, 41113}, {3839, 42138}, {5054, 42932}, {5055, 42916}, {5334, 36969}, {5335, 12820}, {10304, 42122}, {10654, 15705}, {12100, 42927}, {15022, 42991}, {15683, 41108}, {15688, 42923}, {15708, 42116}, {16267, 42920}, {17504, 42987}, {23046, 42982}, {35418, 36967}, {36968, 43206}, {40694, 42632}, {41112, 42972}, {41120, 43027}, {42093, 42479}, {42141, 42940}, {42510, 42543}, {42635, 42894}

X(43254) = GIBERT (3 SQRT(3),5,13) POINT

Barycentrics    3*a^2*S + 13*a^2*SA + 10*SB*SC : :
X(43254) = X[6411] + 5 X[8253], 4 X[6411] + 5 X[42277], 4 X[8253] - X[42277]

X(43254) lies on the cubic K1222 and these lines: {2, 371}, {3, 1327}, {6, 11539}, {30, 6411}, {140, 3594}, {372, 15702}, {376, 10576}, {381, 6455}, {485, 549}, {547, 1151}, {590, 5054}, {615, 42600}, {631, 35822}, {641, 32811}, {1131, 42608}, {1152, 11812}, {1587, 15721}, {1656, 6519}, {2045, 35730}, {3068, 15709}, {3069, 42601}, {3070, 15693}, {3071, 9691}, {3090, 9681}, {3311, 15723}, {3316, 15719}, {3524, 6560}, {3525, 19054}, {3526, 6427}, {3533, 6419}, {3534, 42269}, {3545, 6200}, {3592, 10194}, {3830, 42582}, {3839, 42275}, {3845, 6409}, {5055, 6445}, {5066, 22615}, {5067, 6453}, {5070, 41963}, {5071, 42268}, {5420, 6418}, {6118, 13821}, {6281, 13692}, {6396, 15708}, {6407, 42417}, {6412, 41983}, {6437, 41985}, {6451, 38335}, {6456, 42418}, {6468, 15699}, {6486, 23263}, {6564, 10304}, {7583, 15713}, {8703, 42265}, {8960, 10303}, {8976, 15701}, {8980, 22247}, {8981, 10124}, {9466, 32470}, {10109, 23261}, {10515, 13812}, {11238, 31499}, {11540, 13966}, {12100, 42261}, {13665, 15707}, {13786, 43144}, {14241, 42637}, {14869, 17852}, {14892, 42225}, {15681, 42273}, {15683, 35786}, {15688, 42276}, {15689, 42284}, {15695, 42272}, {15698, 31412}, {15700, 42259}, {15705, 23249}, {15718, 41952}, {15722, 42526}, {17504, 18538}, {19145, 20582}, {19708, 35820}, {19709, 42258}, {19883, 35775}, {23251, 34200}, {35774, 38068}, {35787, 42525}, {36445, 42172}, {36449, 41944}, {36463, 42174}, {36467, 41943}, {38071, 42263}, {41099, 42266}

X(43254) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 371, 42603}, {2, 9540, 35823}, {3, 42602, 1327}, {381, 6455, 43210}, {547, 1151, 1328}, {1327, 10195, 42602}, {3592, 16239, 10194}, {8976, 15701, 41946}, {8981, 10124, 13847}, {11539, 43211, 6}, {15694, 32787, 5420}

X(43255) = GIBERT (-3 SQRT(3),5,13) POINT

Barycentrics    3*a^2*S - 13*a^2*SA - 10*SB*SC : :
X(43255) = X[6412] + 5 X[8252], 4 X[6412] + 5 X[42274], 4 X[8252] - X[42274]

X(43255) lies on the cubic K1222 and these lines: {2, 372}, {3, 1328}, {6, 11539}, {30, 6412}, {140, 3592}, {371, 15702}, {376, 10577}, {381, 6456}, {486, 549}, {547, 1152}, {590, 42601}, {615, 5054}, {631, 35823}, {642, 32810}, {1132, 42609}, {1151, 11812}, {1588, 15721}, {1656, 6522}, {3068, 42600}, {3069, 15709}, {3070, 15703}, {3071, 15693}, {3312, 15723}, {3317, 15719}, {3524, 6561}, {3525, 19053}, {3526, 6428}, {3533, 6420}, {3534, 42268}, {3545, 6396}, {3594, 10195}, {3830, 42583}, {3839, 42276}, {3845, 6410}, {5055, 6446}, {5066, 22644}, {5067, 6454}, {5070, 41964}, {5071, 42269}, {5418, 6417}, {6119, 13701}, {6200, 15708}, {6278, 13812}, {6408, 42418}, {6411, 41983}, {6438, 41985}, {6452, 38335}, {6455, 42417}, {6469, 15699}, {6487, 23253}, {6565, 10304}, {7584, 15713}, {7771, 32807}, {8703, 42262}, {8981, 11540}, {9466, 32471}, {9680, 10303}, {9681, 15720}, {10109, 23251}, {10124, 13846}, {10514, 13692}, {12100, 42260}, {13666, 43141}, {13785, 15707}, {13951, 15701}, {13967, 22247}, {14892, 42226}, {15681, 42270}, {15683, 35787}, {15688, 42275}, {15689, 42283}, {15695, 42271}, {15698, 42561}, {15700, 42258}, {15705, 23259}, {15718, 41951}, {15722, 42527}, {17504, 18762}, {19146, 20582}, {19708, 35821}, {19709, 42259}, {19883, 35774}, {23261, 34200}, {35775, 38068}, {35786, 42524}, {36445, 42173}, {36450, 41943}, {36463, 42171}, {36468, 41944}, {38071, 42264}, {41099, 42267}, {41106, 42637}

X(43255) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 372, 42602}, {2, 13935, 35822}, {3, 42603, 1328}, {381, 6456, 43209}, {547, 1152, 1327}, {1328, 10194, 42603}, {3594, 16239, 10195}, {10124, 13966, 13846}, {11539, 43212, 6}, {13951, 15701, 41945}, {15694, 32788, 5418}

X(43256) = GIBERT (6 SQRT(3),5,-8) POINT

Barycentrics    3*a^2*S - 4*a^2*SA + 5*SB*SC : :
X(43256) = 5 X[1588] - 8 X[3312], X[1588] - 4 X[6460], 3 X[1588] - 4 X[19053], 13 X[1588] - 16 X[19116], 5 X[1588] + 4 X[42414], 15 X[1588] - 4 X[42537], 2 X[3312] - 5 X[6460], 6 X[3312] - 5 X[19053], 13 X[3312] - 10 X[19116], 2 X[3312] + X[42414], 6 X[3312] - X[42537], 3 X[6460] - X[19053], 13 X[6460] - 4 X[19116], 5 X[6460] + X[42414], 15 X[6460] - X[42537], 13 X[19053] - 12 X[19116], 5 X[19053] + 3 X[42414], 5 X[19053] - X[42537], 20 X[19116] + 13 X[42414], 60 X[19116] - 13 X[42537], 3 X[42414] + X[42537]

X(43256) lies on the cubic K1222 and these lines: {2, 1327}, {3, 31414}, {4, 6426}, {6, 11001}, {20, 6419}, {30, 1588}, {194, 13798}, {372, 1132}, {376, 1151}, {381, 6408}, {485, 15692}, {547, 6450}, {549, 6497}, {550, 6447}, {590, 15698}, {615, 41099}, {1131, 15708}, {1152, 3545}, {1702, 34638}, {1991, 26616}, {3068, 6451}, {3069, 3830}, {3070, 3316}, {3071, 42642}, {3090, 6489}, {3091, 10194}, {3146, 35823}, {3311, 15686}, {3317, 6430}, {3534, 6199}, {3544, 42641}, {3594, 33703}, {3832, 6454}, {3839, 35820}, {3845, 6398}, {3850, 6522}, {3853, 6448}, {3855, 41964}, {5054, 31412}, {5059, 6420}, {5066, 32786}, {5071, 23251}, {5418, 15705}, {6200, 42542}, {6221, 15690}, {6395, 42538}, {6410, 15702}, {6412, 15719}, {6418, 42413}, {6436, 6561}, {6440, 41106}, {6452, 11812}, {6456, 11539}, {6459, 6500}, {6470, 7581}, {6475, 13966}, {6479, 22644}, {6496, 41982}, {7583, 15688}, {7584, 15684}, {7585, 15697}, {7586, 15640}, {8596, 35825}, {8960, 21734}, {8976, 17504}, {8981, 14093}, {9540, 10304}, {10576, 15721}, {11481, 35737}, {12100, 13665}, {12222, 22645}, {13785, 33699}, {13846, 19708}, {13886, 15710}, {13925, 15714}, {13951, 14893}, {13961, 35403}, {14226, 42283}, {15682, 23259}, {15683, 42267}, {15685, 42215}, {15687, 42561}, {15691, 19117}, {15693, 32785}, {15695, 18512}, {15701, 18538}, {15709, 42265}, {15715, 42578}, {15718, 42570}, {19058, 38749}, {19065, 28208}, {19100, 41410}, {19709, 35256}, {22615, 42523}, {23261, 42573}, {26288, 32808}, {31145, 35611}, {32811, 35948}, {42154, 42192}, {42155, 42191}, {42199, 42913}, {42201, 42912}

X(43256) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 43209, 11001}, {381, 6408, 43212}, {1131, 15708, 42602}, {1327, 6396, 2}, {3534, 19054, 9541}, {3534, 42216, 19054}, {6460, 42414, 3312}, {10304, 35822, 9540}, {15682, 32788, 23259}, {19053, 42414, 42537}, {19708, 23267, 13846}, {32788, 42264, 15682}, {35822, 42261, 10304}, {42418, 43209, 6}

X(43257) = GIBERT (6 SQRT(3),-5,8) POINT

Barycentrics    3*a^2*S + 4*a^2*SA - 5*SB*SC : :
X(43257) = 5 X[1587] - 8 X[3311], X[1587] - 4 X[6459], 3 X[1587] - 4 X[19054], 13 X[1587] - 16 X[19117], 5 X[1587] + 4 X[42413], 15 X[1587] - 4 X[42538], 2 X[3311] - 5 X[6459], 6 X[3311] - 5 X[19054], 13 X[3311] - 10 X[19117], 2 X[3311] + X[42413], 6 X[3311] - X[42538], 3 X[6459] - X[19054], 13 X[6459] - 4 X[19117], 5 X[6459] + X[42413], 15 X[6459] - X[42538], 13 X[19054] - 12 X[19117], 5 X[19054] + 3 X[42413], 5 X[19054] - X[42538], 20 X[19117] + 13 X[42413], 60 X[19117] - 13 X[42538], 3 X[42413] + X[42538]

X(43257) lies on the cubic K1222 and these lines: {2, 1328}, {3, 43212}, {4, 6425}, {6, 11001}, {20, 6420}, {30, 1587}, {194, 13678}, {371, 1131}, {376, 1152}, {381, 6407}, {486, 15692}, {547, 6449}, {549, 6496}, {550, 6448}, {590, 41099}, {591, 26615}, {615, 15698}, {1132, 15708}, {1151, 3545}, {1703, 34638}, {3068, 3830}, {3069, 6452}, {3070, 42641}, {3071, 3317}, {3090, 6488}, {3091, 9681}, {3146, 35822}, {3312, 15686}, {3316, 6429}, {3534, 6395}, {3544, 42642}, {3592, 33703}, {3828, 9582}, {3832, 6453}, {3839, 35821}, {3845, 6221}, {3850, 6519}, {3853, 6447}, {3854, 9692}, {3855, 41963}, {5054, 42561}, {5059, 6419}, {5066, 32785}, {5068, 9680}, {5071, 23261}, {5420, 15705}, {6199, 42537}, {6396, 42541}, {6398, 15690}, {6409, 15702}, {6411, 15719}, {6417, 42414}, {6435, 6560}, {6439, 41106}, {6451, 11812}, {6455, 11539}, {6460, 6501}, {6471, 7582}, {6474, 8981}, {6478, 22615}, {6497, 41982}, {7583, 15684}, {7584, 15688}, {7585, 15640}, {7586, 15697}, {8596, 35824}, {8976, 14893}, {9542, 42277}, {9543, 10576}, {9660, 10385}, {10304, 13935}, {10577, 15721}, {11480, 35737}, {12100, 13785}, {12221, 22616}, {13665, 33699}, {13847, 19708}, {13903, 35403}, {13939, 15710}, {13951, 17504}, {13966, 14093}, {13993, 15714}, {14241, 42284}, {14537, 31403}, {15682, 23249}, {15683, 42266}, {15685, 42216}, {15687, 31412}, {15689, 42637}, {15691, 19116}, {15693, 32786}, {15695, 18510}, {15701, 18762}, {15709, 42262}, {15715, 42579}, {15718, 42571}, {19057, 38749}, {19066, 28208}, {19099, 41411}, {19709, 35255}, {22644, 42522}, {23251, 42572}, {26289, 32809}, {31145, 35610}, {32810, 35949}, {42154, 42194}, {42155, 42193}, {42200, 42913}, {42202, 42912}

X(43257) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 43210, 11001}, {381, 6407, 43211}, {1132, 15708, 42603}, {1328, 6200, 2}, {3534, 42215, 19053}, {6459, 42413, 3311}, {6561, 9541, 23259}, {10304, 35823, 13935}, {15682, 32787, 23249}, {19054, 42413, 42538}, {19708, 23273, 13847}, {32787, 42263, 15682}, {35823, 42260, 10304}, {42417, 43210, 6}

X(43258) = GIBERT (39 SQRT(3),2,70) POINT

Barycentrics    39*a^2*S + 70*a^2*SA + 4*SB*SC : :

X(43258) lies on the cubic K1222 and these lines: {30, 6439}, {371, 15716}, {376, 1151}, {546, 9681}, {3526, 6453}, {3590, 17578}, {5054, 6476}, {5056, 9692}, {5073, 6519}, {6221, 15707}, {6407, 19709}, {6425, 15712}, {6429, 11812}, {6441, 15705}, {6468, 15699}, {6478, 15693}, {6480, 38335}, {6488, 19054}, {9542, 42284}, {10304, 42574}, {23259, 41959}, {41961, 41965}, {42265, 42606}

X(43259) = GIBERT (-39 SQRT(3),2,70) POINT

Barycentrics    39*a^2*S - 70*a^2*SA - 4*SB*SC : :

X(43259) lies on the cubic K1222 and these lines: {30, 6440}, {372, 15716}, {376, 1152}, {546, 17852}, {3526, 6454}, {3591, 17578}, {5054, 6477}, {5056, 41946}, {5073, 6522}, {6398, 15707}, {6408, 19709}, {6426, 15712}, {6430, 11812}, {6442, 15705}, {6469, 15699}, {6479, 15693}, {6481, 38335}, {6489, 19053}, {10304, 42575}, {23249, 41960}, {41962, 41966}, {42262, 42607}

leftri

Perpsectors of triangles ABC and inverse Gemini triangles: X(43260)-X(43272)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, May 10, 2021.

For an introduction to inverse triangles, see the preamble just before X(42005).

The appearance of (i,j) in the following list means that the triangles ABC and the inverse of Gemini triangle are perspective, and the perspector is X(j).

(1,4654), (2,3679), (3,4835), (4,27483), (9,4945), (10,4921), (11,42025), (12,43260), (13,553), (14,42026), (15,65), (16,42027), (19,6650), (20,39704), (21,42028), (22,4102), (23,42029), (24,42031), (25,43261), (26,52031), (27,41629), (28,39704), (31,43262), (32,43263), (33,7245), (34,4496), (35,42032), (36,17079), (37,42033), (38,17078), (39,42029), (40,42034), (41,428), (42,42037), (43,5064), (44,599), (45,3058), (46,5434), (47,11237), (48,11238), (50,42038), (51,42039), (53,42040), (54,42041), (55,43264), (56,453264), (57,43265), (58,43266), (59,42042), (60,42043), (65,3928), (66,3578), (67,43267), (68,42044), (69,42045), (70,26738), (72,42046), (73,43269), (74,43270), (75,43271), (76,42047), (77,42048), (78,42049), (79,42050), (80,42051), (81,3175), (82,9909), (83,42052), (84,34609), (85,4421), (86,1194), (87,11236), (88,11235), (90,4096), (91,42054), (92,42055), (93,42055), (94,42056), (96,43272), (99,42057), (100,4685), (101,1992), (102,3241), (103,42058), (104,l4664), (105,551), (106,597), (107,2) (108,31145), (109,2), (110,2), (111,2)



X(43260) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-12

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

X(43269) lies on these lines: {2, 594}, {10, 79}, {1126, 3679}, {1171, 4921}, {2214, 42030}, {3578, 28604}, {3828, 6538}, {3995, 32089}, {4980, 18145}, {5936, 33172}, {8701, 9103}, {19875, 39708}, {29615, 32014}, {40438, 42025}

X(43260) = X(4838)-cross conjugate of X(4756)
X(43260) = X(i)-isoconjugate of X(j) for these (i,j): {1125, 34819}, {2308, 25417}, {4979, 8652}
X(43260) = barycentric product X(i)*X(j) for these {i,j}: {1126, 30596}, {1255, 28605}, {1268, 1698}, {4066, 40438}, {4102, 4654}, {4608, 4756}, {4632, 4838}, {4802, 6540}, {4823, 37212}, {5333, 6539}, {16777, 32018}
X(43260) = barycentric quotient X(i)/X(j) for these {i,j}: {1255, 25417}, {1268, 30598}, {1698, 1125}, {3715, 3683}, {3927, 3916}, {4007, 3686}, {4066, 4647}, {4102, 42030}, {4654, 553}, {4716, 4974}, {4727, 4969}, {4756, 4427}, {4802, 4977}, {4813, 4979}, {4820, 4976}, {4823, 4978}, {4838, 4988}, {4880, 4973}, {4898, 4856}, {4958, 4984}, {5221, 32636}, {5333, 8025}, {6540, 32042}, {8701, 8652}, {16777, 1100}, {28605, 4359}, {28615, 34819}, {30596, 1269}, {31902, 31900}, {36074, 36075}, {37212, 37211}
X(43260) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4102, 1255}, {2, 6539, 4102}, {1268, 4102, 2}, {1268, 6539, 1255}

X(43261) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-25

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

X(43261) lies on these lines: {9, 46}, {86, 17190}, {2293, 7073}, {3723, 28202}

X(43261) = X(i)-isoconjugate of X(j) for these (i,j): {35, 27789}, {2174, 28650}, {14838, 28196}
X(43261) = barycentric product X(i)*X(j) for these {i,j}: {79, 3624}, {6742, 28195}, {8818, 42025}, {16884, 30690}
X(43261) = barycentric quotient X(i)/X(j) for these {i,j}: {79, 28650}, {2160, 27789}, {3624, 319}, {4034, 42033}, {16884, 3219}, {28195, 4467}, {42025, 34016}
X(43261) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {}

X(43262) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-31

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

X(43262) lies on these lines: {2, 292}, {171, 4586}, {190, 24722}, {291, 519}, {335, 545}, {524, 3862}, {752, 30663}, {1992, 7077}, {3252, 17378}, {3758, 3809}, {3864, 7757}, {4876, 18827}, {29617, 40848}, {31061, 42720}

X(43262) = X(i)-isoconjugate of X(j) for these (i,j): {1914, 4492}, {14599, 30635}
X(43262) = barycentric product X(i)*X(j) for these {i,j}: {334, 17126}, {335, 3758}, {609, 18895}, {660, 4406}, {3997, 40017}, {4589, 4761}
X(43262) = barycentric quotient X(i)/X(j) for these {i,j}: {291, 4492}, {334, 30635}, {609, 1914}, {3758, 239}, {3809, 3783}, {3997, 2238}, {4406, 3766}, {4761, 4010}, {4844, 4800}, {7208, 27918}, {7276, 7235}, {17126, 238}
X(43262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7245, 334}, {2, 30669, 7245}, {292, 7245, 2}, {292, 30669, 334}

X(43263) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-32

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

X(43263) lies on these lines: {2, 893}, {256, 4685}, {257, 29617}, {524, 3863}, {553, 1432}, {1431, 1992}, {3865, 7757}, {4451, 4664}, {4603, 41629}, {7303, 42028}

X(43263) = X(172)-isoconjugate of X(7241)
X(43263) = barycentric product X(i)*X(j) for these {i,j}: {257, 3759}, {3896, 32010}, {4170, 4594}, {4380, 27805}, {7018, 17127}
X(43263) = barycentric quotient X(i)/X(j) for these {i,j}: {256, 7241}, {3759, 894}, {3896, 1215}, {4099, 21021}, {4170, 2533}, {4380, 4369}, {4401, 4367}, {4965, 4459}, {7018, 30636}, {7031, 172}, {7189, 7184}, {17127, 171}
X(43263) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4496, 7018}, {2, 17493, 4496}, {893, 4496, 2}, {893, 17493, 7018}

X(43264) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-56

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

X(43264) lies on these lines: {2, 1908}, {31172, 33908}

X(43264) = barycentric product X(30638)*X(30650)
X(43264) = barycentric quotient X(i)/X(j) for these {i,j}: {17119, 4363}, {17125, 750}

X(43265) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-57

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

X(43265) lies on these lines: {2, 7033}, {2220, 17281}, {2238, 2321}, {3175, 3948}, {4102, 17743}, {6358, 21021}

X(43265) = X(i)-isoconjugate of X(j) for these (i,j): {60, 41777}, {552, 20665}, {593, 982}, {757, 2275}, {763, 3778}, {849, 3662}, {1333, 33947}, {1412, 3794}, {1437, 31917}, {1509, 7032}, {2150, 7185}, {2185, 7248}, {3061, 7341}, {3777, 4556}, {6628, 16584}
X(43265) = barycentric product X(i)*X(j) for these {i,j}: {594, 17743}, {756, 7033}, {762, 38810}, {872, 7034}, {983, 1089}, {4024, 4621}, {6535, 40415}
X(43265) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 33947}, {12, 7185}, {181, 7248}, {210, 3794}, {594, 3662}, {756, 982}, {762, 3721}, {872, 7032}, {983, 757}, {1089, 33930}, {1500, 2275}, {1826, 31917}, {2171, 41777}, {3690, 3784}, {4024, 3776}, {4037, 33891}, {4103, 33946}, {4155, 3808}, {4621, 4610}, {4705, 3777}, {6057, 3705}, {6535, 2887}, {7033, 873}, {7064, 3056}, {8684, 36066}, {17743, 1509}, {21021, 7187}, {21700, 23473}, {21803, 7184}, {40415, 6628}, {40521, 3888}

X(43266) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-58

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

X(43266) lies on these lines: {2, 292}, {244, 31148}, {551, 40718}, {903, 4586}, {985, 34578}, {1015, 1111}, {1086, 3248}, {2276, 32041}, {4688, 39981}, {4817, 6549}, {17205, 23597}, {17320, 20141}

X(43266) = X(14621)-Ceva conjugate of X(4817)
X(43266) = crosspoint of X(4817) and X(14621)
X(43266) = trilinear pole of line {6545, 8027}
X(43266) = X(i)-isoconjugate of X(j) for these (i,j): {101, 3799}, {692, 3807}, {765, 2276}, {788, 6632}, {869, 1016}, {984, 1252}, {1110, 3661}, {2149, 3790}, {3774, 4600}, {4505, 32739}, {4517, 4564}, {5378, 16514}, {6065, 7146}, {6635, 14436}, {7035, 40728}, {18900, 31625}, {23990, 33931}
X(43266) = barycentric product X(i)*X(j) for these {i,j}: {244, 870}, {514, 4817}, {764, 789}, {825, 23100}, {871, 3248}, {985, 1111}, {1086, 14621}, {4444, 23597}, {4586, 6545}, {7200, 40738}, {16727, 40747}, {17205, 40718}, {21143, 37133}, {23989, 40746}
X(43266) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 3790}, {244, 984}, {513, 3799}, {514, 3807}, {693, 4505}, {764, 1491}, {870, 7035}, {985, 765}, {1015, 2276}, {1086, 3661}, {1111, 33931}, {1357, 1469}, {1358, 7179}, {1647, 4439}, {1977, 40728}, {3120, 3773}, {3121, 3774}, {3248, 869}, {3271, 4517}, {3937, 3781}, {4586, 6632}, {4817, 190}, {6545, 824}, {8027, 788}, {8042, 4481}, {14621, 1016}, {16726, 40773}, {17205, 30966}, {18191, 3786}, {21132, 4522}, {21143, 3250}, {23597, 3570}, {27846, 3783}, {27918, 3797}, {40746, 1252}

X(43267) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-62

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

X(43267) lies on these lines: {6, 194}, {314, 3551}, {27447, 32010}

X(43268) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-67

Barycentrics    4*a^3 + 11*a^2*b + 8*a*b^2 + b^3 + 11*a^2*c + 16*a*b*c + 2*b^2*c + 8*a*c^2 + 2*b*c^2 + c^3 : :

X(43268) lies on these lines: {2, 594}, {405, 19738}, {551, 3159}, {3723, 41809}, {5224, 27789}, {17319, 41818}, {25056, 42044}, {29580, 42045}, {31332, 42028}

X(43268) = reflection of X(27790) in X(2)

X(43269) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-73

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

X(43269) lies on these lines: {2, 893}, {1045, 42043}, {3928, 9311}, {19580, 42046}

X(43269) = {X(893),X(30661)}-harmonic conjugate of X(1966)

X(43270) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-74

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

X(43270) lies on these lines: {2, 292}, {75, 537}, {291, 19973}, {350, 17310}, {561, 31134}, {752, 1966}, {1921, 31151}, {2481, 4479}, {3762, 28840}, {17321, 27295}, {30866, 30963}

X(43270) = reflection of X(42046) in X(2)
X(43270) = barycentric product X(334)*X(27931)
X(43270) = barycentric quotient X(27931)/X(238)
X(43270) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {334, 20345, 39044}, {668, 20568, 3761}

X(43271) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-75

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

X(43271) lies on these lines: {2, 893}, {314, 3551}, {16284, 17294}

X(43271) = {X(7018),X(30660)}-harmonic conjugate of X(1966)

X(43272) = PERSPECTOR OF THESE TRIANGLES: ABC AND INVERSE-OF-GEMINI-96

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

X(43272) lies on these lines: {2, 1908}, {668, 4671}

X(43272) = anticomplement of X(30644)

X(43273) = X(2)X(154)∩X(3)X(67)

Barycentrics    7*a^6 - 4*a^4*b^2 - a^2*b^4 - 2*b^6 - 4*a^4*c^2 - 6*a^2*b^2*c^2 + 2*b^4*c^2 - a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(43273) = 2 X[2] - 3 X[5085], 4 X[2] - 3 X[10516], X[2] - 3 X[25406], 4 X[3] - X[15069], 5 X[3] - 2 X[34507], 7 X[3] - 4 X[40107], 2 X[4] - 3 X[38072], 4 X[5] - 7 X[10541], 2 X[5] - 3 X[38064], 3 X[6] - 2 X[20423], 7 X[6] - 4 X[21850], 5 X[6] - 2 X[31670], X[20] + 2 X[8550], 2 X[20] + X[11477], X[69] - 3 X[10304], 2 X[141] - 3 X[3524], 2 X[141] + X[39874], 4 X[182] - X[36990], 2 X[355] - 3 X[38087], X[382] - 4 X[575], X[382] - 3 X[14848], 2 X[546] - 3 X[38079], 4 X[549] - 3 X[21358], 4 X[575] - 3 X[14848], 2 X[576] + X[1657], 4 X[597] - 3 X[38072], 5 X[599] - 4 X[34507], 7 X[599] - 8 X[40107], 5 X[631] - 4 X[20582], 2 X[946] - 3 X[38023], X[1350] + 2 X[6776], 2 X[1352] - 3 X[21358], 5 X[1656] - 8 X[20190], 5 X[1656] - 4 X[25561], 2 X[3098] - 3 X[15688], 2 X[3098] + X[39899], 4 X[3098] - X[40341], 5 X[3522] - X[11160], 3 X[3524] - X[11180], 3 X[3524] + X[39874], 7 X[3526] - 4 X[18553], X[3529] + 4 X[20583], 2 X[3534] + X[15534], 3 X[3545] - 4 X[3589], 5 X[3618] - 3 X[3839], 7 X[3619] - 9 X[15708], 5 X[3620] - 9 X[15705], 4 X[3631] - 9 X[15710], 2 X[3656] - 3 X[38315], 5 X[3763] - 6 X[5054], 5 X[3763] - 8 X[5092], 5 X[3763] - 4 X[11178], 5 X[3763] - 2 X[18440],

X(43273) lies on the cubic K1223 and these lines: {2, 154}, {3, 67}, {4, 597}, {5, 10541}, {6, 30}, {20, 1992}, {22, 15360}, {40, 28538}, {69, 10304}, {74, 6236}, {98, 6233}, {141, 3524}, {182, 381}, {183, 11177}, {184, 13857}, {186, 35707}, {206, 16072}, {353, 9745}, {355, 38087}, {376, 524}, {378, 10870}, {382, 575}, {389, 34726}, {511, 3534}, {541, 34319}, {546, 38079}, {547, 39884}, {549, 1352}, {576, 1657}, {598, 14485}, {631, 20582}, {732, 33706}, {944, 9041}, {946, 38023}, {1003, 34624}, {1176, 18434}, {1351, 15681}, {1353, 15686}, {1370, 17809}, {1386, 31162}, {1428, 11238}, {1498, 31166}, {1499, 18311}, {1656, 20190}, {1692, 11648}, {2080, 33683}, {2330, 11237}, {2777, 15303}, {2781, 15072}, {2794, 5077}, {3098, 15688}, {3242, 3655}, {3522, 11160}, {3526, 18553}, {3529, 20583}, {3543, 5480}, {3545, 3589}, {3564, 8703}, {3618, 3839}, {3619, 15708}, {3620, 15705}, {3631, 15710}, {3656, 38315}, {3751, 34628}, {3763, 5054}, {3818, 5055}, {3830, 5050}, {3843, 25555}, {3845, 14561}, {3851, 25565}, {4995, 12588}, {5012, 31133}, {5026, 6054}, {5032, 12007}, {5034, 14537}, {5064, 19124}, {5066, 38110}, {5093, 15685}, {5102, 8584}, {5182, 7841}, {5210, 15993}, {5298, 12589}, {5304, 20194}, {5309, 40825}, {5339, 25164}, {5340, 25154}, {5459, 41040}, {5460, 41041}, {5622, 18396}, {5642, 14982}, {5805, 38086}, {5868, 11303}, {5869, 11304}, {5890, 9019}, {5895, 34117}, {5921, 15692}, {5965, 15695}, {5967, 36194}, {5969, 11257}, {5999, 11163}, {6034, 9880}, {6055, 11646}, {6114, 16645}, {6115, 16644}, {6144, 15689}, {6593, 10706}, {6644, 19596}, {6770, 9763}, {6773, 9761}, {6781, 11173}, {6811, 13663}, {6813, 13783}, {7417, 9169}, {7426, 18911}, {7464, 8546}, {7540, 36752}, {7667, 37672}, {7694, 37350}, {7712, 37907}, {7788, 12215}, {7924, 39141}, {8369, 8721}, {8541, 37196}, {8549, 17845}, {8586, 11742}, {8593, 35955}, {8598, 8719}, {8787, 10753}, {9140, 15080}, {9143, 15066}, {9730, 9971}, {9744, 11184}, {9969, 16226}, {9974, 42267}, {9975, 42266}, {10387, 39901}, {10519, 19708}, {10620, 25336}, {10717, 14688}, {10982, 34613}, {10989, 11003}, {11161, 34473}, {11165, 18860}, {11188, 20791}, {11286, 35423}, {11295, 41023}, {11296, 41022}, {11482, 17800}, {11539, 18358}, {11898, 14093}, {12042, 19905}, {12101, 38136}, {12151, 13355}, {12241, 34621}, {12243, 12252}, {12244, 25329}, {12367, 37470}, {13169, 15055}, {13634, 17251}, {13635, 17313}, {13860, 42849}, {13881, 14880}, {14118, 15579}, {14269, 19130}, {14389, 31105}, {14458, 42534}, {14645, 34504}, {14683, 21766}, {14853, 15682}, {15045, 16776}, {15078, 15577}, {15311, 41719}, {15561, 25562}, {15581, 17928}, {15582, 22467}, {15640, 33748}, {15687, 18583}, {15690, 34380}, {15693, 17508}, {15694, 24206}, {15698, 21167}, {15702, 40330}, {15706, 43150}, {15709, 34573}, {15805, 23410}, {16063, 40112}, {16836, 29959}, {17825, 31383}, {18405, 23327}, {18559, 39588}, {19132, 41256}, {19145, 35822}, {19146, 35823}, {19153, 36201}, {19662, 38737}, {19709, 38317}, {19925, 38089}, {20192, 31860}, {21312, 32621}, {22329, 37182}, {24728, 28558}, {25556, 38790}, {25566, 38789}, {26255, 37648}, {26619, 39888}, {26620, 39887}, {26869, 32225}, {28194, 39870}, {29323, 39561}, {32135, 38744}, {33537, 34781}, {33987, 40879}, {34369, 35912}, {35228, 37941}, {36757, 41107}, {36758, 41108}, {36836, 40922}, {36843, 40921}, {37460, 41585}, {37473, 40647}, {37827, 37946}

X(43273) = midpoint of X(i) and X(j) for these {i,j}: {20, 1992}, {376, 6776}, {1351, 15681}, {1353, 15686}, {3543, 14927}, {3751, 34628}, {11180, 39874}
X(43273) = reflection of X(i) in X(j) for these {i,j}: {4, 597}, {6, 11179}, {381, 182}, {599, 3}, {1350, 376}, {1352, 549}, {1498, 31166}, {1853, 10249}, {1992, 8550}, {3242, 3655}, {3543, 5480}, {3818, 10168}, {3830, 5476}, {5085, 25406}, {5102, 14912}, {6054, 5026}, {9971, 9730}, {10516, 5085}, {10706, 6593}, {10717, 14688}, {10753, 8787}, {11178, 5092}, {11180, 141}, {11477, 1992}, {11646, 6055}, {14982, 5642}, {15069, 599}, {15687, 18583}, {18405, 23327}, {18440, 11178}, {19905, 12042}, {25561, 20190}, {29959, 16836}, {31162, 1386}, {36990, 381}, {39884, 547}
X(43273) = crossdifference of every pair of points on line {2492, 8675}
X(43273) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 597, 38072}, {20, 8550, 11477}, {549, 1352, 21358}, {3098, 39899, 40341}, {3524, 11180, 141}, {3524, 39874, 11180}, {3796, 10249, 5085}, {3818, 10168, 5055}, {3830, 5050, 5476}, {5054, 11178, 3763}, {5054, 18440, 11178}, {5055, 12017, 10168}, {5092, 11178, 5054}, {5092, 18440, 3763}, {5921, 15692, 21356}, {6055, 40248, 37637}, {10653, 10654, 15048}, {26864, 32216, 5642}

X(43274) = X(4)X(13)∩X(16)X(524)

Barycentrics    11*a^6 - 14*a^4*b^2 + 7*a^2*b^4 - 4*b^6 - 14*a^4*c^2 - 6*a^2*b^2*c^2 + 4*b^4*c^2 + 7*a^2*c^4 + 4*b^2*c^4 - 4*c^6 + 2*Sqrt[3]*a^2*(5*a^2 - b^2 - c^2)*S : :
X(43274) = X[36970] - 4 X[37640]

X(43274) lies on the cubic K1223 and these lines: {4, 13}, {16, 524}, {383, 41621}, {542, 41407}, {3105, 32450}, {6108, 22496}, {6114, 16268}, {9117, 14539}, {11485, 11645}, {14541, 42625}, {14981, 22998}, {39899, 41409}

X(43275) = X(4)X(14)∩X(15)X(524)

Barycentrics    11*a^6 - 14*a^4*b^2 + 7*a^2*b^4 - 4*b^6 - 14*a^4*c^2 - 6*a^2*b^2*c^2 + 4*b^4*c^2 + 7*a^2*c^4 + 4*b^2*c^4 - 4*c^6 - 2*Sqrt[3]*a^2*(5*a^2 - b^2 - c^2)*S : :
X(43275) = X[36969] - 4 X[37641]

X(43275) lies on the cubic K1223 and these lines: {4, 14}, {15, 524}, {542, 41406}, {1080, 41620}, {3104, 32450}, {6109, 22495}, {6115, 16267}, {9115, 14538}, {11486, 11645}, {14540, 42626}, {14981, 22997}, {39899, 41408}

X(43276) = X(4)X(15)∩X(14)X(524)

Barycentrics    3*a^2*(a^4 + 2*a^2*b^2 - 3*b^4 + 2*a^2*c^2 - 2*b^2*c^2 - 3*c^4) + 2*Sqrt[3]*(a^4 + a^2*b^2 - 6*b^4 + a^2*c^2 + 12*b^2*c^2 - 6*c^4)*S : :
X(43276) = 4 X[11488] + X[19107]

X(43276) lies on the cubic K1223 and these lines: {4, 15}, {14, 524}, {5334, 34509}, {5464, 31710}, {5470, 6108}, {5473, 37637}, {7746, 11481}, {7749, 22890}, {9116, 9877}, {10516, 16809}, {11296, 16241}, {11306, 16967}, {16644, 36772}, {25156, 31695}, {29012, 42128}, {33417, 37341}, {33517, 41021}, {34507, 42125}, {37824, 42135}

X(43276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16808, 19107, 41025}, {18582, 41036, 16808}

X(43277) = X(4)X(16)∩X(13)X(524)

Barycentrics    3*a^2*(a^4 + 2*a^2*b^2 - 3*b^4 + 2*a^2*c^2 - 2*b^2*c^2 - 3*c^4) - 2*Sqrt[3]*(a^4 + a^2*b^2 - 6*b^4 + a^2*c^2 + 12*b^2*c^2 - 6*c^4)*S : :
X(43277) = 4 X[11489] + X[19106]

X(43277) lies on the cubic K1223 and these lines: {4, 16}, {13, 524}, {5335, 34508}, {5463, 31709}, {5469, 6109}, {5474, 37637}, {7746, 11480}, {7749, 22843}, {9114, 9877}, {10516, 16808}, {11295, 16242}, {11305, 16966}, {25166, 31696}, {29012, 42125}, {33416, 37340}, {33518, 41020}, {34507, 42128}, {37825, 42138}

X(43277) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16809, 19106, 41024}, {18581, 41037, 16809}

X(43278) = X(4)X(6)∩X(5)X(525)

Barycentrics    (a^2 - b^2)^2*(a^2 + b^2 - c^2)^3*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4) - (a^2 - c^2)*(-a^2 + c^2)*(a^2 - b^2 + c^2)^3*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4) + (b^2 - c^2)^2*(-a^2 + b^2 + c^2)*(2*a^8 - 5*a^6*b^2 + 3*a^4*b^4 + a^2*b^6 - b^8 - 5*a^6*c^2 + 4*a^4*b^2*c^2 - a^2*b^4*c^2 + 2*b^6*c^2 + 3*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(43278) = X[4] + 3 X[6794], 5 X[3091] - X[18337], 3 X[6793] - X[14900], 3 X[6794] - X[18338], 3 X[14853] + X[35902]

X(43278) lies on these lines: {4, 6}, {5, 525}, {39, 38974}, {132, 1562}, {247, 11746}, {868, 13567}, {1316, 23292}, {1970, 2715}, {2409, 10192}, {2710, 7828}, {3091, 18337}, {6793, 14900}, {9730, 38971}, {32545, 41175}

X(43278) = midpoint of X(i) and X(j) for these {i,j}: {4, 18338}, {132, 1562}
X(43278) = reflection of X(43280) in X(4)
X(43278) = polar-circle-inverse of X(41204)
X(43278) = crossdifference of every pair of points on line {520, 1971}
X(43278) = {X(4),X(6794)}-harmonic conjugate of X(18338)

X(43279) = X(4)X(6)∩X(382)X(525)

Barycentrics    3*a^14 - 4*a^12*b^2 - 2*a^8*b^6 + 3*a^6*b^8 + 2*a^2*b^12 - 2*b^14 - 4*a^12*c^2 + 7*a^10*b^2*c^2 + a^8*b^4*c^2 - 2*a^6*b^6*c^2 - 2*a^4*b^8*c^2 - 5*a^2*b^10*c^2 + 5*b^12*c^2 + a^8*b^2*c^4 - 2*a^6*b^4*c^4 + 2*a^4*b^6*c^4 + 2*a^2*b^8*c^4 - 3*b^10*c^4 - 2*a^8*c^6 - 2*a^6*b^2*c^6 + 2*a^4*b^4*c^6 + 2*a^2*b^6*c^6 + 3*a^6*c^8 - 2*a^4*b^2*c^8 + 2*a^2*b^4*c^8 - 5*a^2*b^2*c^10 - 3*b^4*c^10 + 2*a^2*c^12 + 5*b^2*c^12 - 2*c^14 : :
X(43279) = 5 X[4] - 3 X[6794], 6 X[6794] - 5 X[18338]

X(43279) lies on these lines: {4, 6}, {382, 525}, {868, 31383}, {1316, 11550}, {1853, 2409}, {3146, 18337}

X(43279) = midpoint of X(3146) and X(18337)
X(43279) = reflection of X(18338) in X(4)

X(43280) = REFLECTION OF X(43278) IN X(4)

Barycentrics    4*a^14 - 5*a^12*b^2 - a^10*b^4 - a^8*b^6 + 2*a^6*b^8 + a^4*b^10 + 3*a^2*b^12 - 3*b^14 - 5*a^12*c^2 + 10*a^10*b^2*c^2 - 2*a^6*b^6*c^2 - 3*a^4*b^8*c^2 - 8*a^2*b^10*c^2 + 8*b^12*c^2 - a^10*c^4 + 2*a^4*b^6*c^4 + 5*a^2*b^8*c^4 - 6*b^10*c^4 - a^8*c^6 - 2*a^6*b^2*c^6 + 2*a^4*b^4*c^6 + b^8*c^6 + 2*a^6*c^8 - 3*a^4*b^2*c^8 + 5*a^2*b^4*c^8 + b^6*c^8 + a^4*c^10 - 8*a^2*b^2*c^10 - 6*b^4*c^10 + 3*a^2*c^12 + 8*b^2*c^12 - 3*c^14 : :
X(43280) = 7 X[4] - 3 X[6794], 3 X[4] - X[18338], 3 X[3543] + X[18337], 9 X[6794] - 7 X[18338]

X(43280) lies on these lines: {4, 6}, {525, 3627}, {2409, 23332}, {3543, 18337}, {18305, 18563}

leftri

Perpsectors of Gemini triangles and their inverses: X(43281)-X(43290)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, May 12, 2021.

For an introduction to inverse triangles, see the preamble just before X(42005). If T = A'B'C' is a central triangle of type 1 with A' = u : q : r, then the inverse of T is a central of type 1 with A-vertex given by

(v w - q r)(u + q + r) : q (r - w) (v + r + p) : r (q - v)( w + p + q).

(To see that this inverse is central of type 1, divide the coordinates by (r - w) (q - v).)

The appearance of (T,j) in the following list means that the triangle T is perspective to its inverse and that the perspector is X(j):

(medial,2), (anticomplementary,2), (orthic,155), (tangential,159), (incentral, 3159), (excentral, 40), (intouch,3174), (extouch,40), (Euler,4), (reflections of X(3) in ABC, 3), (extangents,40), (Pelletier,11934), (circum-medial, 110), (circum-orthic,110), (2nd circumperp,100), (tangential of 1st circumperp,55), (tangential of 2nd circumperp,56), (outer Napoleon,14144), (inner Napoleon,14145), (Yff central,12646), (half-altitude,17822), (reflection of ABC in sidelines of ABC, 17824), (2nd Sharygin,100), (Honsberger,100), (orthocentroidal, 6), (anti-1st-Brocard,2), (Aquilla,1), (Ara,25), (1st Auriga,5597), (2nd Auriga,5598), (inner Grebe,6), (outer Grebe,6), (Schroeter,523), (circumsymmedial,99), (inner Garcia,3), (3rd extouch,8282), (3rd mixtilinear,100), (4th mixtilinear,100), (6th mixtilinear,18222), (7th mixtilinear,15913), (1st Parry, 110), (2nd Parry, 111), (Mandart-incircle,55), (5th Brocard,32), 6th Brocard,10131), (inverse of ABC in incircle,11024), (1st orthosymmedial,251), (orthic-of-intouch,57), (intouch-of-orthic,25), (tangential-of-excentral,57), (Artzt,9772), (inner Yff,1), (outer Yff,1), (anti-Aquila,1), (anti-1st-Euler,4), (reflection of X(1) in ABC,34600), (inverse of ABC in Conway circle, 35616), (inner Johnson,11), (outer Johnson,12), (1st Johnson-Yff,12), (2nd Johnson-Yff,11), (inner Yff tangents, 1), (outer Yff tangents,1), (medial-of-orthic,15435), (5th-mixtilinear-of-orthic,11472), (tangential-of-anticomplementary,11487), (anti-5th-Brocard,32), (anti-6th-Brocard,10131), (X-parabola-tangential,12076), (Lucas homotheticT,493), (Lucas (-1) homtheticT,494), (3rd tri-squares central,3068), (4th tri-squares central,3069), (1st excosine,17822), (2nd excosine,3183), (1st Zaniah,18222), (1st isodynamic-Dao equilateral,5464), (2nd isodynamic-Dao equilateral,5463), (Ehrmann mid-triangle,381), (Ehrmann vertex-triangle,6288), (anti-inner-Grebe,6), (anti-outer-Grebe,6), ((2nd anti-circumperp-tangential,56), (1st anti-orthosymmedial,251), (Soddy,15913), (1st Kenmotu free vertices triangle,372), (2nd Kenmotu free vertices triangle,371), (1st Vijay-Paasche-Hutson,1123), (3rd Vijay-Paasche-Hutson,3083), (4th Vijay-Paasche-Hutson,1123), (6th Vijay-Paasche-Hutson,38488), (8th Vijay-Paasche-Hutson,1123), (9th Brocard,648)

The appearance of (i,j) in the following list means that the triangle Gemini i is perspective to its inverse and that the perspector is X(j):

(1,43281), (2,100), (4,31310), (9,43282), (13,43283), (14,43284), (15,43220), (16,43224), (22,27285), (24,43286), (28,43287), (36,43288), (44,110), (63,31310), (101,4563), (102,3699), (103,43289), (108,43290), (104,1978), (105,3952), (106,4576)), (109,2), (110,2), (111,2)

Let P = p : q : r be a triangle center. The inverse of the cevian triangle of P is the anticevian triangle of q + r : r + p : p + q, and the perspector is the P'-Ceva conjugate of P'', where P' = complement of P, and P'' = anticomplement of P. The perspector is given by

(q + r)(q^2 r + q r^2 - r^2 p - r p^2 - p^2 q - p q^2) :
(r + p)(r^2 p + r P^2 - p^2 q - p q^2 - q^2 r - q r^2) :
(p + q)(p^2 q + p q^2 - q^2 r - q r^2 - r^2 p - r p^2).

The inverse of the anticevian triangle of P is the cevian triangle of - p + q + r : p - q + r : p + q - r, and the perspector is the P'-Ceva conjugate of P'', where P' = anticomplement of P, and P'' = complement of P. The perspector is given by

p (p^3 - q^3 - r^3 + q^2 r + q r^2 - r^2 p - r p^2 - p^2 q - p q^2 - 2 p q r) :
q (q^3 - r^3 - p^3 + r^2 p + r p^2 - p^2 q - p q^2 - q^2 r - q r^2 - 2 p q r) :
r (r^3 - p^3 - q^3 + p^2 q + p q^2 - q^2 r - q r^2 - r^2 p - r p^2 - 2 p q r).

For circumcevian triangles and their inverses, see the preamble just before X(43344).



X(43281) = PERSPECTOR OF GEMINI 1 TRIANGLE AND ITS INVERSE

Barycentrics    a*(9*a^5 + 18*a^4*b - 18*a^2*b^3 - 9*a*b^4 + 18*a^4*c + 9*a^3*b*c - 51*a^2*b^2*c - 57*a*b^3*c - 15*b^4*c - 51*a^2*b*c^2 - 88*a*b^2*c^2 - 33*b^3*c^2 - 18*a^2*c^3 - 57*a*b*c^3 - 33*b^2*c^3 - 9*a*c^4 - 15*b*c^4) : :

X(43281) lies on these lines: {1449, 3929}, {3616, 6147}, {4654, 25056}

X(43282) = PERSPECTOR OF GEMINI 9 TRIANGLE AND ITS INVERSE

Barycentrics    5*a^4 - a^3*b - 15*a^2*b^2 + 11*a*b^3 + 2*b^4 - a^3*c + 15*a^2*b*c - 3*a*b^2*c - 10*b^3*c - 15*a^2*c^2 - 3*a*b*c^2 + 12*b^2*c^2 + 11*a*c^3 - 10*b*c^3 + 2*c^4 : :

X(43282) lies on these lines: {1, 545}, {551, 24408}, {918, 36911}, {4510, 4945}, {4715, 4867}, {4850, 24625}, {5219, 43038}

X(43283) = PERSPECTOR OF GEMINI 13 TRIANGLE AND ITS INVERSE

Barycentrics    2*a^6 + 5*a^5*b + 4*a^4*b^2 - a^3*b^3 - 5*a^2*b^4 - 4*a*b^5 - b^6 + 5*a^5*c + 14*a^4*b*c + 20*a^3*b^2*c + 17*a^2*b^3*c + 5*a*b^4*c - b^5*c + 4*a^4*c^2 + 20*a^3*b*c^2 + 44*a^2*b^2*c^2 + 29*a*b^3*c^2 + b^4*c^2 - a^3*c^3 + 17*a^2*b*c^3 + 29*a*b^2*c^3 + 2*b^3*c^3 - 5*a^2*c^4 + 5*a*b*c^4 + b^2*c^4 - 4*a*c^5 - b*c^5 - c^6 : :

X(43283) lies on these lines: {10, 4880}, {553, 27790}, {3187, 24184}, {24175, 37633}

X(43284) = PERSPECTOR OF GEMINI 14 TRIANGLE AND ITS INVERSE

Barycentrics    4*a^4 - 8*a^3*b - 3*a^2*b^2 - 11*a*b^3 - 2*b^4 - 8*a^3*c - 6*a^2*b*c + 39*a*b^2*c + b^3*c - 3*a^2*c^2 + 39*a*b*c^2 - 30*b^2*c^2 - 11*a*c^3 + b*c^3 - 2*c^4 : :

X(43284) lies on these lines: {10, 545}, {812, 16590}, {3679, 24408}, {27081, 27776}, {27791, 42026}

X(43285) = PERSPECTOR OF GEMINI 22 TRIANGLE AND ITS INVERSE

Barycentrics    b*c*(-9*a^4 - 9*a^3*b + 24*a^2*b^2 + 33*a*b^3 + 9*b^4 - 9*a^3*c + 43*a^2*b*c + 81*a*b^2*c + 27*b^3*c + 24*a^2*c^2 + 81*a*b*c^2 + 36*b^2*c^2 + 33*a*c^3 + 27*b*c^3 + 9*c^4) : :

X(43285) lies on these lines: {1, 41823}, {4102, 28609}, {17299, 17778}

X(43286) = PERSPECTOR OF GEMINI 24 TRIANGLE AND ITS INVERSE

Barycentrics    8*a^6 + 17*a^5*b + 7*a^4*b^2 - 7*a^3*b^3 - 11*a^2*b^4 - 10*a*b^5 - 4*b^6 + 17*a^5*c + 23*a^4*b*c - 7*a^3*b^2*c - 37*a^2*b^3*c - 40*a*b^4*c - 16*b^5*c + 7*a^4*c^2 - 7*a^3*b*c^2 - 43*a^2*b^2*c^2 - 52*a*b^3*c^2 - 23*b^4*c^2 - 7*a^3*c^3 - 37*a^2*b*c^3 - 52*a*b^2*c^3 - 22*b^3*c^3 - 11*a^2*c^4 - 40*a*b*c^4 - 23*b^2*c^4 - 10*a*c^5 - 16*b*c^5 - 4*c^6 : :

X(43286) lies on these lines: {3210, 17362}, {3928, 42030}, {4725, 41823}

X(43287) = PERSPECTOR OF GEMINI 28 TRIANGLE AND ITS INVERSE

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

X(43287) lies on these lines: {1, 903}, {9, 17228}, {86, 17382}, {190, 4715}, {192, 545}, {524, 31310}, {4370, 17230}, {4800, 21297}, {16590, 17292}, {17357, 31311}, {17370, 31312}, {27191, 36834}

X(43287) = reflection of X(i) in X(j) for these {i,j}: {903, 39704}, {17488, 4370}

X(43288) = PERSPECTOR OF GEMINI 36 TRIANGLE AND ITS INVERSE

Barycentrics    a^10 - 3*a^9*b + a^8*b^2 + 4*a^7*b^3 - 2*a^6*b^4 - 2*a^5*b^5 - 2*a^4*b^6 + 4*a^3*b^7 + a^2*b^8 - 3*a*b^9 + b^10 - 3*a^9*c + 19*a^8*b*c - 26*a^7*b^2*c - 3*a^6*b^3*c + 22*a^5*b^4*c - 5*a^4*b^5*c - 6*a^3*b^6*c - 5*a^2*b^7*c + 13*a*b^8*c - 6*b^9*c + a^8*c^2 - 26*a^7*b*c^2 + 34*a^6*b^2*c^2 - 8*a^5*b^3*c^2 + 22*a^4*b^4*c^2 - 26*a^3*b^5*c^2 + 10*a^2*b^6*c^2 - 20*a*b^7*c^2 + 13*b^8*c^2 + 4*a^7*c^3 - 3*a^6*b*c^3 - 8*a^5*b^2*c^3 - 50*a^4*b^3*c^3 + 28*a^3*b^4*c^3 + 25*a^2*b^5*c^3 + 12*a*b^6*c^3 - 8*b^7*c^3 - 2*a^6*c^4 + 22*a^5*b*c^4 + 22*a^4*b^2*c^4 + 28*a^3*b^3*c^4 - 62*a^2*b^4*c^4 - 2*a*b^5*c^4 - 14*b^6*c^4 - 2*a^5*c^5 - 5*a^4*b*c^5 - 26*a^3*b^2*c^5 + 25*a^2*b^3*c^5 - 2*a*b^4*c^5 + 28*b^5*c^5 - 2*a^4*c^6 - 6*a^3*b*c^6 + 10*a^2*b^2*c^6 + 12*a*b^3*c^6 - 14*b^4*c^6 + 4*a^3*c^7 - 5*a^2*b*c^7 - 20*a*b^2*c^7 - 8*b^3*c^7 + a^2*c^8 + 13*a*b*c^8 + 13*b^2*c^8 - 3*a*c^9 - 6*b*c^9 + c^10 : :

X(43288) lies on these lines: {528, 1836}, {3306, 5723}, {17079, 30673}

X(43289) = PERSPECTOR OF GEMINI 103 TRIANGLE AND ITS INVERSE

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

X(43289) lies on these lines: {789, 29063}, {4586, 33904}

X(43289) = X(i)-isoconjugate of X(j) for these (i,j): {788, 7357}, {824, 40145}, {1491, 7087}, {3250, 7096}
X(43289) = trilinear pole of line {6327, 32664}
X(43289) = barycentric product X(i)*X(j) for these {i,j}: {789, 1759}, {825, 40365}, {1492, 20444}, {1631, 37133}, {4586, 6327}
X(43289) = barycentric quotient X(i)/X(j) for these {i,j}: {825, 7087}, {1492, 7096}, {1631, 3250}, {1759, 1491}, {4153, 4122}, {4586, 7357}, {6327, 824}, {32664, 788}, {34069, 40145}, {40371, 8630}

X(43290) = PERSPECTOR OF GEMINI 108 TRIANGLE AND ITS INVERSE

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

X(43290) lies on these lines: {1, 31233}, {2, 17774}, {8, 1317}, {10, 31205}, {99, 28226}, {100, 190}, {101, 4169}, {109, 765}, {145, 3756}, {149, 4997}, {200, 14829}, {306, 31215}, {658, 4998}, {662, 7256}, {664, 31343}, {835, 28210}, {1018, 30728}, {1026, 4595}, {1054, 24841}, {1145, 6790}, {1376, 8850}, {1897, 7649}, {3030, 25048}, {3158, 4939}, {3189, 28019}, {3689, 5205}, {3696, 7081}, {3722, 9458}, {3913, 28083}, {4421, 27538}, {4434, 5524}, {4468, 25736}, {4487, 4881}, {4551, 23705}, {4562, 32040}, {4598, 37138}, {4738, 15015}, {4849, 18211}, {5435, 15519}, {5853, 37758}, {6154, 17777}, {6745, 32850}, {8694, 8707}, {8701, 9059}, {10327, 26231}, {10609, 21290}, {14425, 30720}, {17336, 35445}, {17724, 26073}, {20095, 30566}, {26007, 36807}, {29670, 40328}, {40533, 42043}

X(43290) = X(8699)-anticomplementary conjugate of X(149)
X(43290) = X(i)-Ceva conjugate of X(j) for these (i,j): {664, 190}, {4998, 5435}
X(43290) = X(i)-cross conjugate of X(j) for these (i,j): {1420, 765}, {3667, 145}, {4394, 41629}, {4521, 18743}, {4546, 3161}, {8643, 1743}, {14425, 31227}, {30720, 190}, {31182, 5435}
X(43290) = X(i)-isoconjugate of X(j) for these (i,j): {244, 1293}, {513, 3445}, {514, 38266}, {522, 16945}, {649, 8056}, {650, 40151}, {663, 19604}, {667, 4373}, {1015, 27834}, {1086, 34080}, {1357, 31343}, {1647, 36042}, {1919, 40014}, {2170, 38828}, {3063, 27818}, {4162, 16079}, {5382, 21143}, {9315, 27837}
X(43290) = cevapoint of X(i) and X(j) for these (i,j): {8, 4962}, {145, 3667}, {1743, 8643}, {3158, 4521}, {3161, 4546}, {4394, 4849}, {15519, 31182}
X(43290) = crosspoint of X(4998) and X(6632)
X(43290) = crosssum of X(3271) and X(21143)
X(43290) = trilinear pole of line {145, 1743}
X(43290) = barycentric product X(i)*X(j) for these {i,j}: {7, 30720}, {99, 3950}, {100, 18743}, {145, 190}, {644, 39126}, {645, 4848}, {646, 1420}, {658, 6555}, {664, 3161}, {666, 4899}, {668, 1743}, {765, 4462}, {799, 4849}, {1016, 3667}, {1275, 4546}, {1978, 3052}, {3158, 4554}, {3257, 4487}, {3699, 5435}, {3756, 6632}, {3952, 41629}, {4033, 16948}, {4076, 30719}, {4394, 7035}, {4404, 4567}, {4521, 4998}, {4569, 4936}, {4600, 14321}, {4601, 4729}, {4855, 6335}, {4856, 6540}, {4881, 36804}, {4898, 32042}, {4939, 31615}, {8643, 31625}, {17780, 31227}, {27808, 33628}
X(43290) = barycentric quotient X(i)/X(j) for these {i,j}: {59, 38828}, {100, 8056}, {101, 3445}, {109, 40151}, {145, 514}, {190, 4373}, {320, 27836}, {644, 3680}, {651, 19604}, {664, 27818}, {668, 40014}, {692, 38266}, {765, 27834}, {883, 10029}, {1110, 34080}, {1252, 1293}, {1376, 27837}, {1415, 16945}, {1420, 3669}, {1743, 513}, {2403, 6549}, {3052, 649}, {3158, 650}, {3161, 522}, {3667, 1086}, {3699, 6557}, {3756, 6545}, {3950, 523}, {3952, 4052}, {4162, 2170}, {4248, 17925}, {4394, 244}, {4404, 16732}, {4462, 1111}, {4487, 3762}, {4504, 7200}, {4521, 11}, {4534, 21132}, {4546, 1146}, {4729, 3125}, {4848, 7178}, {4849, 661}, {4855, 905}, {4856, 4977}, {4881, 3960}, {4884, 16892}, {4898, 4802}, {4899, 918}, {4918, 21124}, {4929, 30520}, {4936, 3900}, {4939, 40166}, {4943, 4534}, {4953, 42462}, {5435, 3676}, {6049, 30719}, {6516, 27832}, {6555, 3239}, {6558, 6556}, {7081, 27831}, {8643, 1015}, {12640, 21120}, {14321, 3120}, {14425, 1647}, {15519, 4521}, {16948, 1019}, {18211, 8042}, {18743, 693}, {20818, 1459}, {25737, 4862}, {30719, 1358}, {30720, 8}, {31182, 3756}, {31227, 6548}, {33628, 3733}, {38828, 16079}, {39126, 24002}, {40621, 23764}, {41629, 7192}
X(43290) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 3699, 190}, {100, 4756, 4781}, {100, 4767, 4427}, {100, 17780, 3699}, {3722, 9458, 25531}, {17724, 26073, 27191}

X(43291) = MIDPOINT OF X(115) AND X(230)

Barycentrics    2*a^4 - a^2*b^2 + 3*b^4 - a^2*c^2 - 6*b^2*c^2 + 3*c^4 : :
X(43291) = X[98] + 3 X[39663], 3 X[115] + X[187], 7 X[115] + X[6781], 7 X[115] - 3 X[39563], X[148] + 3 X[35297], X[187] - 3 X[230], 7 X[187] - 3 X[6781], 7 X[187] + 9 X[39563], 7 X[230] - X[6781], 7 X[230] + 3 X[39563], X[316] - 9 X[9166], X[316] + 3 X[22329], X[316] - 3 X[37350], X[325] - 5 X[14061], X[325] + 3 X[14568], X[385] + 3 X[33228], 3 X[620] - X[15301], X[625] - 3 X[5461], 2 X[625] - 3 X[8355], X[1513] + 3 X[14651], X[2482] - 3 X[41139], 7 X[3619] - 3 X[6393], X[3793] + 9 X[9166], X[3793] - 3 X[22329], X[3793] + 3 X[37350], X[5167] + 3 X[6784], X[5523] + 3 X[34366], 9 X[6034] - X[8586], 3 X[6034] + X[15993], X[6781] + 3 X[39563], X[7813] - 9 X[14971], X[7813] - 3 X[22110], X[7813] - 5 X[31275], 5 X[7925] + 3 X[19570], X[8352] + 3 X[8859], 3 X[8352] + X[14712], X[8586] + 3 X[15993], X[8598] + 3 X[41135], 9 X[8859] - X[14712], 3 X[9166] + X[22329], 3 X[9166] - X[37350], X[9301] + 3 X[15980], X[11054] + 3 X[41133], 5 X[14061] + 3 X[14568], 3 X[14971] - X[22110], 9 X[14971] - 5 X[31275], X[15301] + 3 X[32457], X[18860] - 5 X[38740], 3 X[22110] - 5 X[31275], X[35002] - 9 X[38224]
X(43291) = 3 X[13] + 3 X[14] + X[15] + X[16]

X(43291) lies on the cubic K1223 and these lines: {2, 2418}, {4, 1384}, {5, 6}, {11, 16784}, {12, 16785}, {20, 15655}, {30, 115}, {32, 546}, {39, 3055}, {69, 11318}, {76, 8361}, {98, 39663}, {111, 468}, {112, 10151}, {125, 15341}, {140, 574}, {141, 7844}, {148, 35297}, {183, 33184}, {193, 32984}, {194, 33249}, {232, 37942}, {316, 3793}, {325, 14061}, {381, 7735}, {385, 33228}, {395, 22490}, {396, 22489}, {403, 8744}, {441, 41254}, {442, 37675}, {460, 5191}, {511, 20398}, {524, 625}, {525, 3239}, {538, 6722}, {543, 32459}, {547, 3815}, {548, 7748}, {549, 2549}, {550, 5210}, {597, 7617}, {620, 15301}, {626, 3631}, {632, 5013}, {671, 10153}, {698, 3934}, {858, 11580}, {1007, 22253}, {1078, 8357}, {1194, 11548}, {1285, 3839}, {1503, 2030}, {1504, 13925}, {1505, 13993}, {1506, 35018}, {1513, 14651}, {1572, 38034}, {1609, 7530}, {1656, 5286}, {1989, 16303}, {1990, 12003}, {2023, 32515}, {2072, 22121}, {2079, 15646}, {2450, 13509}, {2482, 41139}, {2782, 10011}, {2996, 32970}, {3053, 3627}, {3090, 9605}, {3091, 30435}, {3143, 14898}, {3231, 21531}, {3291, 5159}, {3526, 7738}, {3530, 7749}, {3534, 15603}, {3545, 5304}, {3575, 10986}, {3589, 7817}, {3614, 5280}, {3619, 6393}, {3620, 14064}, {3629, 7775}, {3630, 7751}, {3734, 8368}, {3845, 7737}, {3850, 5008}, {3856, 39590}, {3860, 14537}, {3861, 7747}, {3933, 7887}, {5007, 12811}, {5023, 15704}, {5025, 7767}, {5030, 19512}, {5033, 14880}, {5055, 7736}, {5066, 5306}, {5067, 31467}, {5070, 31400}, {5071, 37665}, {5072, 43136}, {5077, 23055}, {5079, 31404}, {5107, 34380}, {5133, 5354}, {5167, 6784}, {5206, 12103}, {5276, 17530}, {5299, 7173}, {5318, 41036}, {5321, 41037}, {5334, 41041}, {5335, 41040}, {5346, 14075}, {5355, 7603}, {5477, 22566}, {5480, 40927}, {5512, 16183}, {5585, 8703}, {5912, 14120}, {6034, 8586}, {6103, 37984}, {6392, 32969}, {6443, 8252}, {6444, 8253}, {6622, 33630}, {6661, 16984}, {6668, 25092}, {6680, 19697}, {6756, 10985}, {7739, 15699}, {7753, 11737}, {7754, 32961}, {7756, 33923}, {7757, 37647}, {7761, 13468}, {7762, 32966}, {7765, 16239}, {7771, 8354}, {7772, 12812}, {7776, 20080}, {7789, 7886}, {7790, 8359}, {7793, 33229}, {7795, 33186}, {7797, 32992}, {7806, 8370}, {7808, 13196}, {7813, 14971}, {7819, 7828}, {7820, 8365}, {7841, 17008}, {7845, 15480}, {7851, 8362}, {7857, 32819}, {7865, 15598}, {7879, 33283}, {7881, 33248}, {7920, 33002}, {7921, 33011}, {7925, 19570}, {7934, 37671}, {7940, 32820}, {8176, 8584}, {8352, 8859}, {8356, 17004}, {8363, 31276}, {8369, 11185}, {8375, 42215}, {8376, 42216}, {8598, 41135}, {8667, 14929}, {9301, 15980}, {9463, 37988}, {9465, 37454}, {9466, 33213}, {9607, 31455}, {9620, 38042}, {9818, 34809}, {10124, 11614}, {10297, 10317}, {10312, 23047}, {10593, 16502}, {10630, 16092}, {10979, 16197}, {10987, 15171}, {11008, 32816}, {11054, 41133}, {11063, 37967}, {11173, 21850}, {11287, 34229}, {11288, 32815}, {11305, 11488}, {11306, 11489}, {11313, 32785}, {11314, 32786}, {11317, 19661}, {11648, 12100}, {11812, 15602}, {12102, 35007}, {12108, 37512}, {12188, 39095}, {12605, 18472}, {13491, 15575}, {14162, 22330}, {14869, 15815}, {15589, 33285}, {16041, 37667}, {16052, 26244}, {16611, 17070}, {16976, 35903}, {16990, 33219}, {17533, 33854}, {17734, 17747}, {17737, 17757}, {18840, 32872}, {18860, 38740}, {19780, 42137}, {19781, 42136}, {20481, 30739}, {21049, 24160}, {21841, 27376}, {22111, 37648}, {22242, 31863}, {22243, 31862}, {23249, 26330}, {23259, 26331}, {24880, 38930}, {29012, 38010}, {31133, 41394}, {32822, 33203}, {32830, 32955}, {32831, 32958}, {32834, 32951}, {32870, 32960}, {34152, 34866}, {34169, 41404}, {35002, 38224}, {36657, 41410}, {36658, 41411}, {38317, 42852}, {39884, 40825}, {41408, 42102}, {41409, 42101}

X(43291) = complement of X(6390)
X(43291) = midpoint of X(i) and X(j) for these {i,j}: {115, 230}, {316, 3793}, {620, 32457}, {671, 27088}, {7845, 15480}, {11542, 11543}, {14120, 16315}, {22329, 37350}
X(43291) = reflection of X(8355) in X(5461)
X(43291) = complement of the isogonal conjugate of X(8753)
X(43291) = complement of the isotomic conjugate of X(17983)
X(43291) = X(i)-complementary conjugate of X(j) for these (i,j): {19, 126}, {25, 16597}, {111, 18589}, {158, 34517}, {897, 1368}, {923, 3}, {1096, 5181}, {1973, 2482}, {5547, 34823}, {7316, 34822}, {8753, 10}, {9178, 34846}, {17983, 2887}, {23894, 127}, {32676, 1649}, {32740, 1214}, {36060, 6389}, {36128, 141}
X(43291) = X(17708)-Ceva conjugate of X(523)
X(43291) = crosspoint of X(2) and X(17983)
X(43291) = crosssum of X(i) and X(j) for these (i,j): {6, 3292}, {1147, 10317}
X(43291) = crossdifference of every pair of points on line {154, 924}
X(43291) = barycentric product X(1)*X(17897)
X(43291) = barycentric quotient X(17897)/X(75)
X(43291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 37689, 1384}, {5, 3767, 5305}, {6, 18584, 2548}, {115, 6781, 39563}, {141, 7844, 8360}, {316, 22329, 3793}, {381, 7735, 18907}, {485, 486, 15069}, {574, 3054, 140}, {574, 7746, 3054}, {1656, 5286, 31406}, {2549, 37637, 549}, {3054, 5254, 574}, {3545, 5304, 15484}, {3767, 13881, 5}, {3793, 37350, 316}, {5254, 7746, 140}, {5306, 18362, 5066}, {5355, 7603, 9300}, {7745, 39565, 3850}, {7755, 39565, 7745}, {7790, 37688, 8359}, {7813, 14971, 31275}, {7813, 31275, 22110}, {7851, 32832, 8362}, {9166, 22329, 37350}, {13711, 13834, 6}, {14061, 14568, 325}, {18538, 18762, 18358}, {18581, 18582, 10516}, {32872, 33182, 18840}

leftri

Gibert points on the cubic K1224: X(43292)-X(43323)

rightri

This preamble and points X(43292)-X(43323) are contributed by Peter Moses, May 12, 2021. See also the preambles just before X(42085), X(42413), and X(42429) and others.

See K1224.



X(43292) = GIBERT (7,30,3) POINT

Barycentrics    7*a^2*S/Sqrt[3] + 3*a^2*SA + 60*SB*SC : :

X(43292 lies on the cubic K1224 and these lines: {14, 42134}, {16, 546}, {20, 33417}, {549, 42429}, {1656, 42100}, {3412, 42630}, {3525, 42113}, {3545, 10646}, {3830, 16644}, {3851, 42931}, {3854, 16967}, {5066, 42928}, {5352, 42106}, {10187, 42131}, {12816, 43031}, {15022, 42105}, {16961, 42900}, {19106, 42491}, {19708, 42915}, {22236, 43004}, {33923, 42919}, {34754, 42496}, {34755, 42920}, {41988, 42799}, {42146, 42434}, {42157, 42962}, {42162, 42901}, {42529, 42950}, {42581, 42955}

X(43293) = GIBERT (-7,30,3) POINT

Barycentrics    7*a^2*S/Sqrt[3] - 3*a^2*SA - 60*SB*SC : :

X(43293) lies on the cubic K1224 and these lines: {13, 42133}, {15, 546}, {20, 33416}, {549, 42430}, {1656, 42099}, {3411, 42629}, {3525, 42112}, {3545, 10645}, {3830, 16645}, {3851, 42930}, {3854, 16966}, {5066, 42929}, {5351, 42103}, {10188, 42130}, {12817, 43030}, {15022, 42104}, {16960, 42901}, {19107, 42490}, {19708, 42914}, {22238, 43005}, {33923, 42918}, {34754, 42921}, {34755, 42497}, {41988, 42800}, {42143, 42433}, {42158, 42963}, {42159, 42900}, {42528, 42951}, {42580, 42954}

X(43294) = GIBERT (11,6,33) POINT

Barycentrics    11*a^2*S/Sqrt[3] + 33*a^2*SA + 12*SB*SC : :

X(43294) lies on the cubic K1224 and these lines: {3, 42895}, {4, 10188}, {6, 31457}, {14, 15694}, {15, 14869}, {140, 42894}, {381, 43204}, {396, 10646}, {549, 42893}, {3522, 42900}, {3523, 41978}, {3524, 43030}, {3533, 42980}, {3628, 42901}, {3851, 42476}, {5238, 43243}, {5352, 12812}, {10303, 43005}, {11480, 42963}, {11737, 42101}, {14890, 23303}, {15685, 16808}, {15686, 23302}, {15688, 16241}, {15697, 42134}, {15699, 16809}, {15701, 43031}, {15708, 16242}, {15718, 43020}, {15720, 43015}, {16239, 16964}, {16644, 42689}, {19106, 42490}, {19107, 42610}, {33417, 42630}, {33602, 42086}, {33923, 43016}, {41974, 42124}, {42115, 42773}, {42119, 42596}, {42130, 42798}, {42137, 42598}, {42141, 42947}, {42144, 42492}, {42504, 42511}, {42531, 42934}, {42914, 43245}, {42929, 43029} X(43294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3523, 41978, 43023}, {10645, 42936, 42112}, {42092, 42472, 42936}, {42092, 42959, 42930}

X(43295) = GIBERT (-11,6,33) POINT

Barycentrics    11*a^2*S/Sqrt[3] - 33*a^2*SA - 12*SB*SC : :

X(43295) lies on the cubic K1224 and these lines: {3, 42894}, {4, 10187}, {6, 31457}, {13, 15694}, {16, 14869}, {140, 42895}, {381, 43203}, {395, 10645}, {549, 42892}, {3522, 42901}, {3523, 41977}, {3524, 43031}, {3533, 42981}, {3628, 42900}, {3851, 42477}, {5237, 43242}, {5351, 12812}, {10303, 43004}, {11481, 42962}, {11737, 42102}, {14890, 23302}, {15685, 16809}, {15686, 23303}, {15688, 16242}, {15697, 42133}, {15699, 16808}, {15701, 43030}, {15708, 16241}, {15718, 43021}, {15720, 43014}, {16239, 16965}, {16645, 42688}, {19106, 42611}, {19107, 42491}, {33416, 42629}, {33603, 42085}, {33923, 43017}, {41973, 42121}, {42116, 42774}, {42120, 42597}, {42131, 42797}, {42136, 42599}, {42140, 42946}, {42145, 42493}, {42505, 42510}, {42530, 42935}, {42915, 43244}, {42928, 43028}

X(43295) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3523, 41977, 43022}, {10646, 42937, 42113}, {42089, 42473, 42937}, {42089, 42958, 42931}

X(43296) = GIBERT (19,6,38) POINT

Barycentrics    19*a^2*S/Sqrt[3] + 38*a^2*SA + 12*SB*SC : :

X(43296) lies on the cubic K1224 and these lines: {4, 11480}, {13, 15695}, {14, 42477}, {16, 15700}, {3411, 11485}, {5352, 42962}, {11812, 42089}, {15691, 42124}, {16772, 42781}, {41977, 42773}, {41989, 42103}, {42123, 42916}, {42125, 42490}, {42153, 42923}, {42156, 42584}, {42160, 43103}, {42473, 43105}, {42815, 43193}, {42817, 43000}

X(43297) = GIBERT (-19,6,38) POINT

Barycentrics    19*a^2*S/Sqrt[3] - 38*a^2*SA - 12*SB*SC : :

X(43297) lies on the cubic K1224 and these lines: {4, 11481}, {13, 42476}, {14, 15695}, {15, 15700}, {3412, 11486}, {5351, 42963}, {11812, 42092}, {15691, 42121}, {16773, 42782}, {41978, 42774}, {41989, 42106}, {42122, 42917}, {42128, 42491}, {42153, 42585}, {42156, 42922}, {42161, 43102}, {42472, 43106}, {42816, 43194}, {42818, 43001}

X(43298) = GIBERT (25,42,10) POINT

Barycentrics    25*a^2*S/Sqrt[3] + 10*a^2*SA + 84*SB*SC : :

X(43298) lies on the cubic K1224 and these lines: {4, 42682}, {14, 42905}, {16, 5072}, {549, 42091}, {3628, 42907}, {3856, 42106}, {5055, 43244}, {5066, 42416}, {7486, 11481}, {15022, 43106}, {15640, 42791}, {15709, 42683}, {16808, 42774}, {17800, 42094}, {33417, 43203}, {36836, 42112}, {42097, 42909}, {42128, 42695}, {42154, 42691}, {42689, 43239}, {42694, 42813}

X(43299) = GIBERT (-25,42,10) POINT

Barycentrics    25*a^2*S/Sqrt[3] - 10*a^2*SA - 84*SB*SC : :

X(43299) lies on the cubic K1224 and these lines: {4, 42683}, {13, 42904}, {15, 5072}, {549, 42090}, {3628, 42906}, {3856, 42103}, {5055, 43245}, {5066, 42415}, {7486, 11480}, {15022, 43105}, {15640, 42792}, {15709, 42682}, {16809, 42773}, {17800, 42093}, {33416, 43204}, {36843, 42113}, {42096, 42908}, {42125, 42694}, {42155, 42690}, {42688, 43238}, {42695, 42814}

X(43300) = GIBERT (25,12,-15) POINT

Barycentrics    25*a^2*S/Sqrt[3] - 15*a^2*SA + 24*SB*SC : :

X(43300) lies on the cubic K1224 and these lines: {4, 16961}, {6, 17800}, {13, 549}, {16, 5072}, {62, 42109}, {3534, 34754}, {3627, 42782}, {3628, 43240}, {3856, 42143}, {5237, 42903}, {7486, 16965}, {10645, 41974}, {11489, 41972}, {11543, 42694}, {15640, 41108}, {15683, 43244}, {15704, 43106}, {16966, 42793}, {36969, 42689}, {37835, 42134}, {41100, 42101}, {41112, 42928}, {42085, 43006}, {42093, 43019}, {42095, 42695}, {42097, 42800}, {42100, 43243}, {42122, 42158}, {42125, 42508}, {42138, 42956}, {42145, 42432}, {42146, 42686}, {42155, 42816}, {42433, 42687}, {42477, 42937}, {42488, 42691}, {42528, 43197}, {42580, 42971}, {42625, 42968}, {42631, 42815}, {42894, 42924}, {42900, 42918}

X(43301) = GIBERT (-25,12,-15) POINT

Barycentrics    25*a^2*S/Sqrt[3] + 15*a^2*SA - 24*SB*SC : :

X(43301) lies on the cubic K1224 and these lines: {4, 16960}, {6, 17800}, {14, 549}, {15, 5072}, {61, 42108}, {3534, 34755}, {3627, 42781}, {3628, 43241}, {3856, 42146}, {5238, 42902}, {7486, 16964}, {10646, 41973}, {11488, 41971}, {11542, 42695}, {15640, 41107}, {15683, 43245}, {15704, 43105}, {16967, 42794}, {36970, 42688}, {37832, 42133}, {41101, 42102}, {41113, 42929}, {42086, 43007}, {42094, 43018}, {42096, 42799}, {42098, 42694}, {42099, 43242}, {42123, 42157}, {42128, 42509}, {42135, 42957}, {42143, 42687}, {42144, 42431}, {42154, 42815}, {42434, 42686}, {42476, 42936}, {42489, 42690}, {42529, 43198}, {42581, 42970}, {42626, 42969}, {42632, 42816}, {42895, 42925}, {42901, 42919}

X(43302) = GIBERT (25,6,5) POINT

Barycentrics    25*a^2*S/Sqrt[3] + 5*a^2*SA + 12*SB*SC : :

X(43302) lies on the cubic K1224 and these lines: {4, 42779}, {5, 42781}, {6, 5072}, {13, 42904}, {16, 396}, {17, 43028}, {61, 42108}, {62, 42954}, {397, 42584}, {3412, 42935}, {3526, 16960}, {3534, 43244}, {3856, 16808}, {5055, 16961}, {5318, 42934}, {5334, 42903}, {5335, 15640}, {7486, 16967}, {10303, 34755}, {10653, 42795}, {11485, 16965}, {11486, 42955}, {12817, 42969}, {15022, 43240}, {15704, 34754}, {15717, 43250}, {16268, 43000}, {16809, 42691}, {16963, 42817}, {16966, 42480}, {18582, 33607}, {19107, 42896}, {33417, 42998}, {33699, 42520}, {37640, 42100}, {42092, 43008}, {42103, 42982}, {42110, 42992}, {42130, 43021}, {42131, 42435}, {42136, 43228}, {42138, 42895}, {42139, 43031}, {42141, 42965}, {42156, 42897}, {42429, 42968}, {42436, 43029}, {42496, 42533}, {42512, 42636}, {42513, 42952}, {42530, 42937}, {42693, 42906}, {42695, 42905}, {42801, 43027}, {42813, 42923}, {42815, 42991}, {43101, 43207}

X(43302) = {X(42896),X(42974)}-harmonic conjugate of X(19107).

X(43303) = GIBERT (-25,6,5) POINT

Barycentrics    25*a^2*S/Sqrt[3] - 5*a^2*SA - 12*SB*SC : :

X(43303) lies on the cubic K1224 and these lines: {4, 42780}, {5, 42782}, {6, 5072}, {14, 42905}, {15, 395}, {18, 43029}, {61, 42955}, {62, 42109}, {398, 42585}, {3411, 42934}, {3526, 16961}, {3534, 43245}, {3856, 16809}, {5055, 16960}, {5321, 42935}, {5334, 15640}, {5335, 42902}, {7486, 16966}, {10303, 34754}, {10654, 42796}, {11485, 42954}, {11486, 16964}, {12816, 42968}, {15022, 43241}, {15704, 34755}, {15717, 43251}, {16267, 43001}, {16808, 42690}, {16962, 42818}, {16967, 42481}, {18581, 33606}, {19106, 42897}, {33416, 42999}, {33699, 42521}, {37641, 42099}, {42089, 43009}, {42106, 42983}, {42107, 42993}, {42130, 42436}, {42131, 43020}, {42135, 42894}, {42137, 43229}, {42140, 42964}, {42142, 43030}, {42153, 42896}, {42430, 42969}, {42435, 43028}, {42497, 42532}, {42512, 42953}, {42513, 42635}, {42531, 42936}, {42692, 42907}, {42694, 42904}, {42802, 43026}, {42814, 42922}, {42816, 42990}, {43104, 43208}

X(43303) = {X(42897),X(42975)}-harmonic conjugate of X(19106).

X(43304) = GIBERT (33,10,-22) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 22*a^2*SA + 20*SB*SC : :

X(43304) lies on the cubic K1224 and these lines: {4, 395}, {6, 15686}, {13, 15694}, {15, 15688}, {16, 42508}, {381, 41972}, {382, 43019}, {3411, 12821}, {3534, 41971}, {3830, 42904}, {5351, 16644}, {10653, 12100}, {11481, 15708}, {11486, 43244}, {11737, 42118}, {12812, 42921}, {14869, 42156}, {15684, 43020}, {15685, 41100}, {15689, 43021}, {15697, 42942}, {15699, 42098}, {15720, 43013}, {15722, 43004}, {16239, 36843}, {34755, 35402}, {41113, 42136}, {42089, 43246}, {42095, 42510}, {42096, 43242}, {42097, 42975}, {42103, 42519}, {42151, 42912}, {42432, 42969}, {42474, 43239}, {42518, 42957}, {42594, 42933}, {42777, 43238}, {42795, 42990}, {42898, 42943}

X(43304) = {X(13),X(42996)}-harmonic conjugate of X(15694).

X(43305) = GIBERT (33,-10,22) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 22*a^2*SA - 20*SB*SC : :

X(43305) lies on the cubic K1224 and these lines: {4, 396}, {6, 15686}, {14, 15694}, {15, 42509}, {16, 15688}, {381, 41971}, {382, 43018}, {3412, 12820}, {3534, 41972}, {3830, 42905}, {5352, 16645}, {10654, 12100}, {11480, 15708}, {11485, 43245}, {11737, 42117}, {12812, 42920}, {14869, 42153}, {15684, 43021}, {15685, 41101}, {15689, 43020}, {15697, 42943}, {15699, 42095}, {15720, 43012}, {15722, 43005}, {16239, 36836}, {34754, 35402}, {41112, 42137}, {42092, 43247}, {42096, 42974}, {42097, 43243}, {42098, 42511}, {42106, 42518}, {42150, 42913}, {42431, 42968}, {42475, 43238}, {42519, 42956}, {42595, 42932}, {42778, 43239}, {42796, 42991}, {42899, 42942}

X(43305) = {X(14),X(42997)}-harmonic conjugate of X(15694).

X(43306) = GIBERT (44,15,11) POINT

Barycentrics    44*a^2*S/Sqrt[3] + 11*a^2*SA + 30*SB*SC : :

X(43306) lies on the cubic K1224 and these lines: {4, 42815}, {5, 43005}, {15, 15686}, {16, 14869}, {5318, 43232}, {8703, 42892}, {11486, 16239}, {11542, 15699}, {11737, 42473}, {12100, 42974}, {15687, 43014}, {15708, 42496}, {22236, 42113}, {40693, 42123}, {41112, 42137}, {42107, 42779}, {42124, 42935}, {42518, 42913}, {42895, 43205}, {42937, 42956}

X(43307) = GIBERT (-44,15,11) POINT

Barycentrics    44*a^2*S/Sqrt[3] - 11*a^2*SA - 30*SB*SC : :

X(43307) lies on the cubic K1224 and these lines: {4, 42816}, {5, 43004}, {15, 14869}, {16, 15686}, {5321, 43233}, {8703, 42893}, {11485, 16239}, {11543, 15699}, {11737, 42472}, {12100, 42975}, {15687, 43015}, {15708, 42497}, {22238, 42112}, {40694, 42122}, {41113, 42136}, {42110, 42780}, {42121, 42934}, {42519, 42912}, {42894, 43206}, {42936, 42957}

X(43308) = GIBERT (77,12,11) POINT

Barycentrics    77*a^2*S/Sqrt[3] + 11*a^2*SA + 24*SB*SC : :

X(43308) lies on the cubic K1224 and these lines: {5, 43234}, {15, 15688}, {20, 43030}, {61, 42145}, {397, 42415}, {546, 42895}, {549, 43014}, {1656, 43205}, {3544, 43235}, {3545, 43010}, {3830, 43007}, {10299, 41978}, {15022, 43005}, {16239, 23302}, {19708, 42997}, {33923, 43018}, {40693, 43241}, {41107, 43245}, {42492, 42593}, {42902, 42982}, {42906, 43226}, {43013, 43015}

X(43309) = GIBERT (-77,12,11) POINT

Barycentrics    77*a^2*S/Sqrt[3] - 11*a^2*SA - 24*SB*SC : :

X(43309) lies on the cubic K1224 and these lines: {5, 43235}, {16, 15688}, {20, 43031}, {62, 42144}, {398, 42416}, {546, 42894}, {549, 43015}, {1656, 43206}, {3544, 43234}, {3545, 43011}, {3830, 43006}, {10299, 41977}, {15022, 43004}, {16239, 23303}, {19708, 42996}, {33923, 43019}, {40694, 43240}, {41108, 43244}, {42493, 42592}, {42903, 42983}, {42907, 43227}, {43012, 43014}

X(43310) = GIBERT (99,70,-55) POINT

Barycentrics    33*Sqrt[3]*a^2*S - 55*a^2*SA + 140*SB*SC : :

X(43310) lies on the cubic K1224 and these lines: {4, 3411}, {15, 15686}, {549, 43248}, {5237, 15699}, {5238, 15697}, {5344, 15708}, {5350, 41944}, {11737, 23303}, {12100, 42158}, {14869, 42973}, {14891, 42957}, {15681, 43203}, {15684, 43235}, {15685, 43194}, {15687, 42904}, {15688, 16965}, {15692, 43024}, {15694, 16966}, {15700, 43033}, {35403, 43020}, {35434, 43015}, {41973, 42515}, {41977, 41990}, {42086, 42516}, {42118, 42899}, {42494, 42596}, {42795, 42997}

X(43311) = GIBERT (99,-70,55) POINT

Barycentrics    33*Sqrt[3]*a^2*S + 55*a^2*SA - 140*SB*SC : :

X(43311) lies on the cubic K1224 and these lines: {4, 3412}, {16, 15686}, {549, 43249}, {5237, 15697}, {5238, 15699}, {5343, 15708}, {5349, 41943}, {11737, 23302}, {12100, 42157}, {14869, 42972}, {14891, 42956}, {15681, 43204}, {15684, 43234}, {15685, 43193}, {15687, 42905}, {15688, 16964}, {15692, 43025}, {15694, 16967}, {15700, 43032}, {35403, 43021}, {35434, 43014}, {41974, 42514}, {41978, 41990}, {42085, 42517}, {42117, 42898}, {42495, 42597}, {42796, 42996}

X(43312) = GIBERT (4 SQRT(3),39,3) POINT

Barycentrics    4*a^2*S + 3*a^2*SA + 78*SB*SC : :

X(43312) lies on the cubic K1224 and these lines: {4, 6199}, {6, 12818}, {546, 6450}, {590, 15687}, {3317, 3843}, {3627, 6409}, {3832, 34091}, {3845, 6438}, {3857, 42276}, {3858, 42261}, {3859, 6452}, {6221, 12101}, {6396, 23046}, {6411, 35404}, {6420, 42284}, {6472, 8972}, {6519, 12102}, {6565, 41956}, {7586, 14269}, {9681, 18538}, {14893, 23249}, {17852, 22644}, {41953, 42216}, {41964, 42226}, {42215, 42572}, {42275, 42568}

X(43313) = GIBERT (-4 SQRT(3),39,3) POINT

Barycentrics    4*a^2*S - 3*a^2*SA - 78*SB*SC : :

X(43313) lies on the cubic K1224 and these lines: {4, 6395}, {6, 12818}, {546, 6449}, {615, 15687}, {3316, 3843}, {3627, 6410}, {3832, 34089}, {3845, 6437}, {3857, 42275}, {3858, 42260}, {3859, 6451}, {6200, 23046}, {6398, 12101}, {6412, 35404}, {6419, 42283}, {6473, 13941}, {6522, 12102}, {6564, 41955}, {7585, 14269}, {14893, 23259}, {41954, 42215}, {41963, 42225}, {42216, 42573}, {42276, 42569}

X(43314) = GIBERT (7 SQRT(3),3,21) POINT

Barycentrics    7*a^2*S + 21*a^2*SA + 6*SB*SC : :

X(43314) lies on the cubic K1224 and these lines: {4, 5418}, {6, 3530}, {140, 6468}, {485, 6451}, {486, 6480}, {547, 6433}, {590, 15681}, {615, 5054}, {632, 1151}, {1588, 6476}, {3068, 15710}, {3860, 42263}, {5070, 6445}, {5079, 6449}, {5420, 6437}, {6396, 7585}, {6398, 41963}, {6409, 12103}, {6411, 6560}, {6412, 42568}, {6439, 11540}, {6441, 35256}, {6452, 31454}, {6453, 32786}, {6455, 42284}, {6469, 12100}, {8253, 38071}, {8588, 13651}, {9540, 21734}, {9541, 43254}, {9690, 32790}, {12811, 42225}, {15719, 19053}, {19709, 42283}, {23273, 42603}, {35404, 42602}, {41981, 42226}, {41984, 42600}, {42164, 42198}, {42165, 42197}

X(43314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5418, 6200, 42275}, {6200, 32785, 42260}, {6445, 42274, 9681}

X(43315) = GIBERT (-7 SQRT(3),3,21) POINT

Barycentrics    7*a^2*S - 21*a^2*SA - 6*SB*SC : :

X(43315) lies on the cubic K1224 and these lines: {4, 5420}, {6, 3530}, {140, 6469}, {485, 6481}, {486, 6452}, {547, 6434}, {590, 5054}, {615, 15681}, {632, 1152}, {1587, 6477}, {3069, 15710}, {3860, 42264}, {5070, 6446}, {5079, 6450}, {5418, 6438}, {6200, 7586}, {6221, 41964}, {6410, 12103}, {6411, 42569}, {6412, 6561}, {6440, 11540}, {6442, 35255}, {6454, 32785}, {6456, 42283}, {6468, 12100}, {8252, 38071}, {8588, 13770}, {12811, 42226}, {13935, 21734}, {15719, 19054}, {19709, 42284}, {23267, 42602}, {32789, 41970}, {35404, 42603}, {41981, 42225}, {41984, 42601}, {42164, 42196}, {42165, 42195}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5420, 6396, 42276}, {6396, 32786, 42261}

X(43316) = GIBERT (14 SQRT(3),11,7) POINT

Barycentrics    14*a^2*S + 7*a^2*SA + 22*SB*SC : :

X(43316) lies on the cubic K1224 and these lines: {4, 1131}, {6, 38071}, {372, 41966}, {485, 632}, {547, 615}, {590, 3530}, {1587, 5070}, {3068, 9690}, {3069, 5079}, {3070, 12103}, {3859, 6565}, {3860, 6564}, {5054, 6446}, {6199, 35434}, {6411, 6560}, {6417, 42570}, {6429, 42260}, {6477, 11540}, {7584, 12811}, {8960, 41981}, {8972, 15710}, {8981, 15696}, {13785, 14241}, {13886, 21734}, {15692, 23267}, {18510, 42571}, {18512, 18762}, {19117, 41991}, {35404, 42263}, {35815, 41969}, {35823, 41954}, {41957, 42284}

X(43317) = GIBERT (-14 SQRT(3),11,7) POINT

Barycentrics    14*a^2*S - 7*a^2*SA - 22*SB*SC : :

X(43317) lies on the cubic K1224 and these lines: {4, 1132}, {6, 38071}, {371, 41965}, {486, 632}, {547, 590}, {615, 3530}, {1588, 5070}, {3068, 5079}, {3069, 15681}, {3071, 12103}, {3859, 6564}, {3860, 6565}, {5054, 6445}, {6395, 35434}, {6412, 6561}, {6418, 42571}, {6430, 42261}, {6476, 11540}, {7583, 12811}, {9681, 42579}, {13665, 14226}, {13939, 21734}, {13941, 15710}, {13966, 15696}, {15692, 23273}, {18510, 18538}, {18512, 42570}, {19116, 41991}, {35404, 42264}, {35814, 41970}, {35822, 41953}, {41958, 42283}

X(43318) = GIBERT (17 SQRT(3),2,34) POINT

Barycentrics    17*a^2*S + 34*a^2*SA + 4*SB*SC : :

X(43318) lies on the cubic K1224 and these lines: {4, 590}, {6, 17504}, {371, 42569}, {376, 41956}, {615, 6490}, {1328, 6439}, {3069, 9692}, {3592, 42523}, {5067, 41955}, {5418, 10141}, {6200, 14093}, {6221, 13847}, {6411, 9542}, {6425, 13966}, {6433, 6560}, {6437, 7586}, {6445, 42264}, {6453, 8252}, {6468, 10124}, {6484, 13665}, {6488, 42542}, {6519, 6565}, {6561, 14892}, {8253, 9690}, {32786, 43258}

X(43319) = GIBERT (-17 SQRT(3),2,34) POINT

Barycentrics    17*a^2*S - 34*a^2*SA - 4*SB*SC : :

X(43319) lies on the cubic K1224 and these lines: {4, 615}, {6, 17504}, {372, 42568}, {376, 41955}, {590, 6491}, {1327, 6440}, {3594, 42522}, {5067, 41956}, {5420, 10142}, {6396, 14093}, {6398, 13846}, {6410, 9681}, {6412, 19053}, {6426, 8981}, {6434, 6561}, {6438, 7585}, {6446, 42263}, {6454, 8253}, {6469, 10124}, {6485, 13785}, {6489, 42541}, {6522, 6564}, {6560, 14892}, {17852, 42265}, {32785, 43259}

X(43320) = GIBERT (22 SQRT(3),3,-33) POINT

Barycentrics    22*a^2*S - 33*a^2*SA + 6*SB*SC : :

X(43320) lies on the cubic K1224 and these lines: {4, 3591}, {140, 41948}, {547, 41962}, {1152, 14869}, {6395, 9541}, {6396, 12100}, {6408, 31412}, {6435, 34200}, {6436, 33923}, {6438, 6561}, {6446, 7583}, {6454, 12812}, {6460, 17851}, {6469, 15699}, {6477, 11737}, {6479, 13993}, {6481, 16239}, {6491, 6560}, {6522, 23267}, {7584, 42644}, {15694, 42216}, {15697, 42215}, {41954, 41984}

X(43321) = GIBERT (22 SQRT(3),-3,33) POINT

Barycentrics    22*a^2*S + 33*a^2*SA - 6*SB*SC : :

X(43321) lies on the cubic K1224 and these lines: {4, 3590}, {140, 41947}, {547, 41961}, {1151, 14869}, {3317, 9693}, {6199, 15688}, {6200, 12100}, {6407, 42561}, {6435, 33923}, {6436, 34200}, {6437, 6560}, {6445, 7584}, {6451, 9543}, {6453, 12812}, {6468, 15699}, {6476, 11737}, {6478, 13925}, {6480, 16239}, {6490, 6561}, {6519, 23273}, {7583, 42643}, {9541, 15685}, {9690, 15694}, {9691, 32785}, {15697, 42216}, {41953, 41984}

X(43322) = GIBERT (33 SQRT(3),13,11) POINT

Barycentrics    33*a^2*S + 11*a^2*SA + 26*SB*SC : :

X(43322) lies on the cubic K1224 and these lines: {4, 1327}, {6, 11737}, {381, 41954}, {590, 6395}, {1587, 15697}, {3590, 6420}, {5055, 41947}, {5418, 15708}, {6410, 8981}, {6427, 42572}, {6437, 6560}, {6449, 15688}, {7583, 13847}, {7586, 42603}, {10137, 42259}, {13846, 14869}, {15685, 41945}, {15693, 41970}, {18512, 42275}, {35402, 41955}, {42270, 42573}

X(43323) = GIBERT (-33 SQRT(3),13,11) POINT

Barycentrics    33*a^2*S - 11*a^2*SA - 26*SB*SC : :

X(43323) lies on the cubic K1224 and these lines: {4, 1328}, {6, 11737}, {381, 41953}, {615, 6199}, {1588, 15697}, {3591, 6419}, {5055, 41948}, {5420, 15708}, {6409, 12100}, {6428, 42573}, {6438, 6561}, {6450, 15688}, {7584, 13846}, {7585, 42602}, {9680, 13847}, {10138, 42258}, {15685, 41946}, {15693, 41969}, {18510, 42276}, {35402, 41956}, {42273, 42572}

leftri

Gibert points on the cubic K1225: X(43324)-X(43343)

rightri

This preamble and points X(43324)-X(43343) are contributed by Peter Moses, May 13, 2021. See also the preambles just before X(42085), X(42413), and X(42429) and others.

See K1225.



X(43324) = GIBERT (7,18,-21) POINT

Barycentrics    7*a^2*S/Sqrt[3] - 21*a^2*SA + 36*SB*SC : :

X(43324) lies on the cubic K1225 and these lines: {4, 10187}, {13, 15681}, {547, 42595}, {632, 42109}, {3411, 19107}, {3530, 42102}, {3830, 42928}, {5054, 42498}, {5079, 43226}, {5335, 43022}, {8703, 16808}, {10645, 12103}, {12817, 36968}, {15692, 42114}, {15696, 19106}, {15719, 42915}, {16241, 42134}, {16965, 34754}, {17800, 43009}, {21734, 33417}, {34755, 42160}, {35401, 42625}, {35404, 42101}, {41101, 42086}, {41973, 42144}, {41981, 42146}, {42085, 42800}, {42088, 43198}, {42096, 42508}, {42112, 43008}, {42118, 42799}, {42126, 42891}, {42131, 42630}, {42151, 42901}, {42431, 42895}, {42432, 43242}, {42584, 42599}, {42911, 43230}, {42930, 43238}, {42975, 43203}

X(43325) = GIBERT (7,-18,21) POINT

Barycentrics    7*a^2*S/Sqrt[3] + 21*a^2*SA - 36*SB*SC : :

X(43325) lies on the cubic K1225 and these lines: {4, 10188}, {14, 15681}, {547, 42594}, {632, 42108}, {3412, 19106}, {3530, 42101}, {3830, 42929}, {5054, 42499}, {5079, 43227}, {5334, 43023}, {8703, 16809}, {10646, 12103}, {12816, 36967}, {15692, 42111}, {15696, 19107}, {15719, 42914}, {16242, 42133}, {16964, 34755}, {17800, 43008}, {21734, 33416}, {34754, 42161}, {35401, 42626}, {35404, 42102}, {41100, 42085}, {41974, 42145}, {41981, 42143}, {42086, 42799}, {42087, 43197}, {42097, 42509}, {42113, 43009}, {42117, 42800}, {42127, 42890}, {42130, 42629}, {42150, 42900}, {42431, 43243}, {42432, 42894}, {42585, 42598}, {42910, 43231}, {42931, 43239}, {42974, 43204}

X(43326) = GIBERT (13,18,-26) POINT

Barycentrics    13*a^2*S/Sqrt[3] - 26*a^2*SA + 36*SB*SC : :

X(43326) lies on the cubic K1225 and these lines: {4, 11481}, {13, 15689}, {5340, 41978}, {11480, 42971}, {11539, 42091}, {12108, 42145}, {15693, 42098}, {15703, 19106}, {15705, 42142}, {19710, 42122}, {22238, 42782}, {34200, 42092}, {42099, 42509}, {42100, 42990}, {42105, 42493}, {42128, 42490}, {42131, 42154}, {42153, 42904}, {42161, 42584}, {42429, 42521}, {42505, 43203}, {42519, 42943}, {42816, 43193}

X(43326) = {X(42088),X(42097)}-harmonic conjugate of X(43239)

X(43327) = GIBERT (13,-18,26) POINT

Barycentrics    13*a^2*S/Sqrt[3] + 26*a^2*SA - 36*SB*SC : :

X(43327) lies on the cubic K1225 and these lines: {4, 11480}, {14, 15689}, {5339, 41977}, {11481, 42970}, {11539, 42090}, {12108, 42144}, {15693, 42095}, {15703, 19107}, {15705, 42139}, {19710, 42123}, {22236, 42781}, {34200, 42089}, {42099, 42991}, {42100, 42508}, {42104, 42492}, {42125, 42491}, {42130, 42155}, {42156, 42905}, {42160, 42585}, {42430, 42520}, {42504, 43204}, {42518, 42942}, {42815, 43194}

X(43327) = {X(42087),X(42096)}-harmonic conjugate of X(43238)

X(43328) = GIBERT (14,9,7) POINT

Barycentrics    14*a^2*S/Sqrt[3] + 7*a^2*SA + 18*SB*SC : :

X(43328) lies on the cubic K1225 and these lines: {4, 11408}, {6, 12811}, {13, 8703}, {14, 38071}, {16, 632}, {395, 43240}, {396, 35404}, {397, 43023}, {547, 16645}, {3411, 43250}, {3412, 42693}, {3530, 42092}, {3845, 42799}, {3859, 40693}, {3860, 41119}, {5054, 5335}, {5070, 42121}, {5079, 42146}, {5318, 42434}, {10653, 11540}, {11480, 12103}, {11486, 42591}, {11488, 15696}, {11543, 19709}, {15681, 42141}, {15692, 42123}, {16267, 43245}, {16808, 42923}, {16960, 42108}, {16966, 42800}, {19106, 43016}, {19107, 42777}, {23302, 41974}, {23303, 43008}, {33417, 42793}, {33604, 42129}, {33607, 42942}, {34755, 42956}, {41107, 42996}, {41981, 42086}, {41984, 42089}, {41991, 42135}, {42094, 42496}, {42105, 43194}, {42142, 42963}, {42143, 42982}, {42144, 42162}, {42148, 42931}, {42581, 42917}, {42813, 43105}, {42970, 43226}, {43009, 43227}

X(43328) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16, 42598, 42492}, {5318, 43004, 42916}, {11542, 42136, 42986}, {16960, 42903, 42108}, {22235, 42128, 11542}, {42088, 42930, 8703}, {42128, 42136, 42138}, {42128, 42986, 42136}, {42144, 42162, 42907}, {42492, 42922, 16}, {42598, 42895, 42922}

X(43329) = GIBERT (-14,9,7) POINT

Barycentrics    14*a^2*S/Sqrt[3] - 7*a^2*SA - 18*SB*SC : :

X(43329) lies on the cubic K1225 and these lines: {4, 11409}, {6, 12811}, {13, 38071}, {14, 8703}, {15, 632}, {395, 35404}, {396, 43241}, {398, 43022}, {547, 16644}, {3411, 42692}, {3412, 43251}, {3530, 42089}, {3845, 42800}, {3859, 40694}, {3860, 41120}, {5054, 5334}, {5070, 42124}, {5079, 42143}, {5321, 42433}, {10654, 11540}, {11481, 12103}, {11485, 42590}, {11489, 15696}, {11542, 19709}, {15681, 42140}, {15692, 42122}, {16268, 43244}, {16809, 42922}, {16961, 42109}, {16967, 42799}, {19106, 42778}, {19107, 43017}, {23302, 43009}, {23303, 41973}, {33416, 42794}, {33605, 42132}, {33606, 42943}, {34754, 42957}, {41108, 42997}, {41981, 42085}, {41984, 42092}, {41991, 42138}, {42093, 42497}, {42104, 43193}, {42139, 42962}, {42145, 42159}, {42146, 42983}, {42147, 42930}, {42580, 42916}, {42814, 43106}, {42971, 43227}, {43008, 43226}

X(43329) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15, 42599, 42493}, {5321, 43005, 42917}, {11543, 42137, 42987}, {16961, 42902, 42109}, {22237, 42125, 11543}, {42087, 42931, 8703}, {42125, 42137, 42135}, {42125, 42987, 42137}, {42145, 42159, 42906}, {42493, 42923, 15}, {42599, 42894, 42923}

X(43330) = GIBERT (21,20,-35) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 35*a^2*SA + 40*SB*SC : :

X(43330) lies on the cubic K1225 and these lines: {4, 5237}, {6, 15681}, {13, 8703}, {15, 43244}, {62, 42430}, {547, 10646}, {632, 5350}, {3530, 42528}, {3860, 16242}, {5054, 36969}, {5070, 42431}, {5071, 42928}, {5238, 15696}, {5335, 42795}, {5344, 16241}, {5352, 41981}, {10653, 42520}, {10654, 43008}, {11489, 12821}, {12103, 42158}, {12816, 43240}, {15640, 43001}, {15692, 42086}, {15710, 42091}, {15719, 42911}, {16961, 33605}, {16963, 35409}, {19106, 38071}, {19709, 42631}, {34755, 42429}, {35401, 42115}, {35404, 42692}, {35414, 42112}, {35434, 41944}, {41100, 42584}, {41108, 42100}, {41972, 42085}, {41984, 42137}, {42096, 43233}, {42102, 42796}, {42120, 43204}, {42126, 42636}, {42144, 43020}, {42145, 43101}, {42432, 42975}, {42594, 42683}, {42684, 42912}, {43228, 43250}

X(43331) = GIBERT (21,-20,35) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 35*a^2*SA - 40*SB*SC : :

X(43331) lies on the cubic K1225 and these lines: {4, 5238}, {6, 15681}, {14, 8703}, {16, 43245}, {61, 42429}, {547, 10645}, {632, 5349}, {3530, 42529}, {3860, 16241}, {5054, 36970}, {5070, 42432}, {5071, 42929}, {5237, 15696}, {5334, 42796}, {5343, 16242}, {5351, 41981}, {10653, 43009}, {10654, 42521}, {11488, 12820}, {12103, 42157}, {12817, 43241}, {15640, 43000}, {15692, 42085}, {15710, 42090}, {15719, 42910}, {16960, 33604}, {16962, 35409}, {19107, 38071}, {19709, 42632}, {34754, 42430}, {35401, 42116}, {35404, 42693}, {35414, 42113}, {35434, 41943}, {41101, 42585}, {41107, 42099}, {41971, 42086}, {41984, 42136}, {42097, 43232}, {42101, 42795}, {42119, 43203}, {42127, 42635}, {42144, 43104}, {42145, 43021}, {42431, 42974}, {42595, 42682}, {42685, 42913}, {43229, 43251}

X(43332) = GIBERT (21,10,14) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 14*a^2*SA + 20*SB*SC : :

X(43332) lies on the cubic K1225 and these lines: {4, 396}, {6, 547}, {13, 15681}, {14, 16960}, {16, 5054}, {17, 3411}, {381, 42799}, {395, 42986}, {632, 40693}, {3530, 10653}, {3534, 43000}, {3860, 10654}, {5076, 42802}, {5079, 37832}, {5321, 42516}, {5335, 15710}, {5339, 43009}, {5340, 5352}, {6669, 40341}, {8703, 11542}, {11481, 15719}, {11486, 42506}, {11488, 15692}, {11489, 42898}, {11540, 43207}, {12103, 42152}, {12811, 42920}, {12816, 42691}, {12820, 42157}, {16241, 42796}, {16242, 43008}, {16772, 42932}, {16962, 42094}, {18582, 38071}, {19106, 33607}, {22238, 42501}, {33417, 43020}, {33602, 42683}, {35401, 43245}, {35404, 42096}, {35434, 42128}, {36968, 42930}, {36969, 42892}, {37640, 42095}, {41100, 42931}, {41121, 42093}, {41943, 42625}, {41984, 42627}, {42100, 42997}, {42115, 43199}, {42126, 42976}, {42434, 43033}, {42490, 42992}, {42530, 42533}, {42598, 42778}, {42773, 42968}, {42816, 43232}, {42954, 43029}

X(43332) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {396, 42156, 42154}, {5054, 42974, 42800}, {16267, 42817, 16644}, {40693, 42512, 42913}, {41943, 42815, 42625}, {42116, 42429, 42626}

X(43333) = GIBERT (-21,10,14) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 14*a^2*SA - 20*SB*SC : :

X(43333) lies on the cubic K1225 and these lines: {4, 395}, {6, 547}, {13, 16961}, {14, 15681}, {15, 5054}, {18, 3412}, {381, 42800}, {396, 42987}, {632, 40694}, {3530, 10654}, {3534, 43001}, {3860, 10653}, {5076, 42801}, {5079, 37835}, {5318, 42517}, {5334, 15710}, {5339, 5351}, {5340, 43008}, {6670, 40341}, {8703, 11543}, {11480, 15719}, {11485, 42507}, {11488, 42899}, {11489, 15692}, {11540, 43208}, {12103, 42149}, {12811, 42921}, {12817, 42690}, {12821, 42158}, {16241, 43009}, {16242, 42795}, {16773, 42933}, {16963, 42093}, {18581, 38071}, {19107, 33606}, {22236, 42500}, {33416, 43021}, {33603, 42682}, {35401, 43244}, {35404, 42097}, {35434, 42125}, {36967, 42931}, {36970, 42893}, {37641, 42098}, {41101, 42930}, {41122, 42094}, {41944, 42626}, {41984, 42628}, {42099, 42996}, {42116, 43200}, {42127, 42977}, {42142, 43252}, {42433, 43032}, {42491, 42993}, {42531, 42532}, {42599, 42777}, {42774, 42969}, {42815, 43233}, {42955, 43028}

X(43333) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {395, 42153, 42155}, {5054, 42975, 42799}, {16268, 42818, 16645}, {40694, 42513, 42912}, {41944, 42816, 42626}, {42115, 42430, 42625}

X(43334) = GIBERT (35,18,7) POINT

Barycentrics    35*a^2*S/Sqrt[3] + 7*a^2*SA + 36*SB*SC : :

X(43334) lies on the cubic K1225 and these lines: {4, 42779}, {13, 16961}, {14, 42903}, {16, 632}, {631, 42931}, {3412, 42141}, {3530, 42685}, {3859, 16808}, {5054, 42968}, {5335, 15692}, {8703, 42777}, {10653, 33604}, {11480, 15696}, {12816, 42896}, {15719, 33607}, {16967, 43008}, {17504, 43000}, {18582, 42800}, {19107, 35434}, {34754, 42781}, {35381, 41100}, {35404, 43105}, {36968, 42930}, {41101, 42105}, {41107, 42500}, {41112, 42100}, {42127, 42506}, {42128, 43011}, {42139, 43206}, {42157, 42683}, {42166, 43241}, {42518, 43199}, {42520, 42799}, {42907, 42964}, {42970, 43205}, {42974, 43227}, {43009, 43014}

X(43334) = {X(42095),X(42521)}-harmonic conjugate of X(16961)

X(43335) = GIBERT (-35,18,7) POINT

Barycentrics    35*a^2*S/Sqrt[3] - 7*a^2*SA - 36*SB*SC : :

X(43335) lies on the cubic K1225 and these lines: {4, 42780}, {13, 42902}, {14, 16960}, {15, 632}, {631, 42930}, {3411, 42140}, {3530, 42684}, {3859, 16809}, {5054, 42969}, {5334, 15692}, {8703, 42778}, {10654, 33605}, {11481, 15696}, {12817, 42897}, {15719, 33606}, {16966, 43009}, {17504, 43001}, {18581, 42799}, {19106, 35434}, {34755, 42782}, {35381, 41101}, {35404, 43106}, {36967, 42931}, {41100, 42104}, {41108, 42501}, {41113, 42099}, {42125, 43010}, {42126, 42507}, {42142, 43205}, {42158, 42682}, {42163, 43240}, {42519, 43200}, {42521, 42800}, {42906, 42965}, {42971, 43206}, {42975, 43226}, {43008, 43015}

X(43335) = {X(42098),X(42520)}-harmonic conjugate of X(16960)

X(43336) = GIBERT (5 SQRT(3),9,-15) POINT

Barycentrics    5*a^2*S - 15*a^2*SA + 18*SB*SC : :
X(43336) = 53 X[6438] - 27 X[42642], 13 X[6438] - 12 X[42644], 117 X[42642] - 212 X[42644]

X(43336) lies on the cubic K1225 and these lines: {3, 42566}, {4, 5420}, {6, 15704}, {30, 6438}, {381, 42567}, {485, 548}, {486, 6469}, {549, 42264}, {550, 6433}, {631, 12818}, {1327, 15759}, {1328, 6477}, {3146, 6481}, {3526, 42284}, {3534, 6221}, {3627, 6434}, {3628, 6412}, {3857, 6410}, {5066, 42576}, {5072, 6452}, {5418, 41948}, {6395, 17800}, {6398, 22615}, {6437, 12103}, {6439, 7583}, {6441, 42216}, {6446, 42268}, {6480, 17538}, {6491, 23261}, {6561, 15683}, {6564, 15698}, {7581, 42575}, {10303, 42269}, {10304, 23249}, {15684, 41951}, {15710, 42558}, {15717, 35820}, {18762, 33699}, {23046, 43255}, {23259, 35814}, {23267, 35815}, {42085, 42223}, {42086, 42224}, {42087, 42197}, {42088, 42198}, {42112, 42212}, {42113, 42211}, {42130, 42256}, {42131, 42257}, {42193, 42963}, {42194, 42962}, {42524, 42538}

X(43336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10194, 42261, 42637}, {42261, 42276, 42274}

X(43337) = GIBERT (5 SQRT(3),-9,15) POINT

Barycentrics    5*a^2*S + 15*a^2*SA - 18*SB*SC : :
X(43337) = 53 X[6437] - 27 X[42641], 13 X[6437] - 12 X[42643], 117 X[42641] - 212 X[42643]

X(43337) lies on the cubic K1225 and these lines: {3, 42567}, {4, 5418}, {6, 15704}, {30, 6437}, {381, 42566}, {485, 6468}, {486, 548}, {549, 42263}, {550, 6434}, {631, 12819}, {1327, 6476}, {1328, 15759}, {3146, 6480}, {3526, 42283}, {3534, 6398}, {3627, 6433}, {3628, 6411}, {3857, 6409}, {5066, 42577}, {5072, 6451}, {5420, 41947}, {6199, 17800}, {6221, 22644}, {6438, 12103}, {6440, 7584}, {6442, 42215}, {6445, 42269}, {6481, 17538}, {6490, 23251}, {6560, 15683}, {6565, 15698}, {7582, 42574}, {9681, 23249}, {9690, 15684}, {10303, 42268}, {10304, 23259}, {15710, 42557}, {15717, 35821}, {18538, 33699}, {23046, 43254}, {23273, 35814}, {42085, 42221}, {42086, 42222}, {42087, 42195}, {42088, 42196}, {42112, 42214}, {42113, 42213}, {42130, 42254}, {42131, 42255}, {42191, 42963}, {42192, 42962}, {42525, 42537}

X(43337) = {X(42260),X(42275)}-harmonic conjugate of X(42277)

X(43338) = GIBERT (5 SQRT(3),2,-10) POINT

Barycentrics    5*a^2*S - 10*a^2*SA + 4*SB*SC : :

X(43338) lies on the cubic K1225 and these lines: {3, 35815}, {4, 615}, {5, 6434}, {6, 548}, {20, 6438}, {30, 6430}, {372, 3534}, {376, 6432}, {381, 6485}, {382, 6481}, {485, 549}, {486, 6469}, {1151, 10304}, {1587, 15698}, {1588, 41955}, {1656, 6487}, {3070, 10303}, {3071, 15683}, {3522, 6431}, {3526, 6396}, {3528, 6437}, {3594, 6459}, {3627, 10142}, {3628, 6560}, {3856, 42226}, {3857, 10148}, {5055, 6450}, {5066, 5420}, {5072, 8252}, {5076, 6483}, {6398, 17800}, {6408, 13847}, {6409, 19117}, {6412, 6460}, {6426, 7584}, {6429, 33923}, {6440, 42276}, {6446, 35820}, {6448, 42266}, {6454, 13961}, {6456, 8253}, {6471, 42260}, {6489, 15022}, {6491, 23259}, {6497, 35822}, {6522, 6565}, {10140, 12819}, {10576, 42524}, {13846, 15706}, {13966, 17852}, {15688, 35771}, {15721, 42570}, {22644, 23046}, {33699, 43259}, {41970, 42271}, {42153, 42223}, {42156, 42224}, {42273, 43256}, {42561, 43209}

X(43338) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 6485, 42569}, {1152, 42259, 42262}, {6398, 17800, 35814}, {6408, 42267, 13847}, {6426, 42261, 42263}, {41946, 42637, 1151}, {42259, 42262, 42264}

X(43339) = GIBERT (5 SQRT(3),-2,10) POINT

Barycentrics    5*a^2*S + 10*a^2*SA - 4*SB*SC : :

X(43339) lies on the cubic K1225 and these lines: {3, 35814}, {4, 590}, {5, 6433}, {6, 548}, {20, 6437}, {30, 6429}, {371, 3534}, {376, 6431}, {381, 6484}, {382, 6480}, {485, 6468}, {486, 549}, {1131, 9543}, {1152, 10304}, {1587, 41956}, {1588, 15698}, {1656, 6486}, {3070, 15683}, {3071, 10303}, {3522, 6432}, {3526, 6200}, {3528, 6438}, {3592, 6460}, {3627, 10141}, {3628, 6561}, {3856, 9680}, {3857, 10147}, {5055, 6449}, {5066, 5418}, {5072, 8253}, {5076, 6482}, {6221, 17800}, {6407, 13846}, {6410, 19116}, {6411, 6459}, {6425, 7583}, {6430, 33923}, {6439, 42275}, {6445, 35821}, {6447, 42267}, {6453, 13903}, {6455, 8252}, {6470, 42261}, {6488, 15022}, {6490, 9693}, {6496, 35823}, {6519, 6564}, {8960, 9691}, {9542, 42413}, {9690, 35812}, {10139, 12818}, {10577, 42525}, {13847, 15706}, {15688, 35770}, {15721, 42571}, {22615, 23046}, {31412, 43210}, {33699, 43258}, {41969, 42272}, {42153, 42221}, {42156, 42222}, {42270, 43257}

X(43339) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 6484, 42568}, {1151, 42258, 42265}, {6221, 17800, 35815}, {6407, 42266, 13846}, {6425, 42260, 42264}, {42258, 42265, 42263}

X(43340) = GIBERT (10 SQRT(3),11,5) POINT

Barycentrics    10*a^2*S + 5*a^2*SA + 22*SB*SC : :

X(43340) lies on the cubic K1225 and these lines: {3, 42570}, {4, 1131}, {5, 35814}, {6, 3856}, {30, 6429}, {371, 33699}, {381, 42571}, {485, 548}, {486, 5066}, {549, 3070}, {1587, 5072}, {3316, 15717}, {3526, 6446}, {3534, 9540}, {3628, 5420}, {3853, 12818}, {3857, 6564}, {5055, 13966}, {5418, 15759}, {6431, 14893}, {6473, 35256}, {6492, 22644}, {7486, 23267}, {7584, 31414}, {8976, 10304}, {8981, 15704}, {9690, 13903}, {10576, 41954}, {13886, 15683}, {14890, 42602}, {15687, 42572}, {15691, 42568}, {19117, 35787}, {23046, 35822}, {23269, 35255}, {35770, 38071}, {35815, 42258}, {42213, 42817}, {42214, 42818}

X(43340) ={X(1131),X(13665)}-harmonic conjugate of X(7583)

X(43341) = GIBERT (-10 SQRT(3),11,5) POINT

Barycentrics    10*a^2*S - 5*a^2*SA - 22*SB*SC : :

X(43341) lies on the cubic K1225 and these lines: {3, 42571}, {4, 1132}, {5, 35815}, {6, 3856}, {30, 6430}, {372, 33699}, {381, 42570}, {485, 5066}, {486, 548}, {549, 3071}, {1588, 5072}, {3317, 15717}, {3526, 6445}, {3534, 13935}, {3628, 5418}, {3853, 12819}, {3857, 6565}, {5055, 8981}, {5420, 15759}, {6432, 14893}, {6472, 35255}, {6493, 22615}, {7486, 23273}, {10304, 13951}, {10577, 41953}, {13939, 15683}, {13961, 17800}, {13966, 15704}, {14890, 42603}, {15687, 42573}, {15691, 42569}, {19116, 35786}, {23046, 35823}, {23275, 35256}, {35771, 38071}, {35814, 42259}, {42211, 42817}, {42212, 42818}

X(43341) ={X(1132),X(13785)}-harmonic conjugate of X(7584)

X(43342) = GIBERT (15 SQRT(3),13,5) POINT

Barycentrics    15*a^2*S + 5*a^2*SA + 26*SB*SC : :
X(43342) = 43 X[6437] - 52 X[42643], 43 X[42641] + 52 X[42643]

X(43342) lies on the cubic K1225 and these lines: {3, 42572}, {4, 1327}, {6, 23046}, {30, 6437}, {371, 15640}, {372, 14241}, {381, 42573}, {485, 549}, {486, 5066}, {548, 13846}, {590, 15706}, {615, 5055}, {1131, 35823}, {1152, 11540}, {3070, 3534}, {3312, 41947}, {3365, 33607}, {3390, 33606}, {3526, 6522}, {5071, 42570}, {5072, 32788}, {5418, 15698}, {6431, 12101}, {6432, 11737}, {6473, 41952}, {6560, 8972}, {7583, 33699}, {8253, 14890}, {9543, 15683}, {9680, 43209}, {10137, 15681}, {10195, 10303}, {12819, 35771}, {15684, 22644}, {15709, 23267}, {15759, 42261}, {16772, 42248}, {16773, 42249}, {18538, 43255}, {31412, 35814}, {35770, 41106}, {41955, 42284}, {42265, 43212}, {42414, 42525}

X(43342) = midpoint of X(6437) and X(42641)
X(43342) = {X(6395),X(13665)}-harmonic conjugate of X(41954)

X(43343) = GIBERT (-15 SQRT(3),13,5) POINT

Barycentrics    15*a^2*S - 5*a^2*SA - 26*SB*SC : :
X(43343) = 43 X[6438] - 52 X[42644], 43 X[42642] + 52 X[42644]

X(43343) lies on the cubic K1225 and these lines: {3, 42573}, {4, 1328}, {6, 23046}, {30, 6438}, {371, 14226}, {372, 15640}, {381, 42572}, {485, 5066}, {486, 549}, {548, 13847}, {590, 5055}, {615, 15706}, {1132, 35822}, {1151, 11540}, {3071, 3534}, {3311, 41948}, {3364, 33607}, {3389, 33606}, {3526, 6519}, {5071, 42571}, {5072, 32787}, {5420, 15698}, {6431, 11737}, {6432, 12101}, {6472, 41951}, {6561, 10304}, {7584, 33699}, {8252, 14890}, {10138, 15681}, {10194, 10303}, {12818, 35770}, {15683, 35814}, {15684, 22615}, {15704, 17852}, {15709, 23273}, {15759, 42260}, {16772, 42246}, {16773, 42247}, {17851, 42275}, {18762, 43254}, {35771, 41106}, {35815, 42561}, {41956, 42283}, {42262, 43211}, {42413, 42524}

X(43343) = midpoint of X(6438) and X(42642)
X(43343) = {X(6199),X(13785)}-harmonic conjugate of X(41953)

leftri

Perpsectors of circumcevian triangles and their inverses X(43344)-X(43363)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, May 13, 2021.

For an introduction to inverse triangles, see the preambles just before X(42005) and X43280).

The perspector of the circumcevian triangle T of a point P = p : q : r and the inverse of T lies on the circumcircle. The A-vertex of T is -a^2 q r : (b^2 r + c^2 q) q : (b^2 r + c^2 q) r. The inverse of T is given by the following A-vertex:

a^2 q r ((a^2-b^2-c^2) q r - b^2 r^2 - c^2 q^2) :
q (b^2 r + c^2 q)((a^2 - b^2 + c^2) p r + a^2 r^2 + c^2 p^2) :
r (c^2 p + a^2 r)((a^2 + b^2 - c^2) p q + a^2 r^2 + b^2 p^2).

The two triangles are perspective, and their perspector, f(P), is given by

a^2/(a^2 (q - r) + (b^2 - c^2) p) : b^2 (b^2 (r - p) + (c^2 - a^2) q) : c^2 (c^2 (p - q) + (a^2 - b^2) r).

Let L(P) denote the line of P and X(3). If U lies on L(P), then f(U) = a^2/(a^2(v - w) + (b^2-c^2)u) : :

In particular, f(Euler line) = X(110).

The appearance of (i,j) in the following list means that f(X(i)X(3)) = X(j):

(1,100), (2,110), (6,99), (7,43344), (8,901), (9,934), (10,109), (11,6099), (12,43345), (13,10409), (14,10410), (19,13395), (33,43346), (34,43377), (37,1310), (38,43348), (41,43349), (43,43350), (45,13396), (48,1305), (51,43351), (53,43352), (54,930), (59,43353), (60,43354), (63,13397), (64,107), (66,112), (67,691), (68,13398), (69,3565), (71,1305), (72,13397), (73,41906), (74,476), (75,815), (76,805), (80,43355), (81,43356), (83,43357), (85,43358), (86,43359), (87,43360), (88,43361), (90,30240), (95,1303), (97,930), (101,927), (102,1309), (105,6078), (106,6079), (107,6080), (108,6081), (111,6082), (112,2867), (113,1304), (114,2715), (115,10425), (116,34182), (117,35183), (118,35184),(119,2720), (120,35185), (121,35186), (124,35187), (125,10420), (126,35188), (143,20189), (145,28218), (146,16166), (154,107), (161,933), (169,6183), (190,43362), (191,1290), (1945,25424), (206,1289), (214,2222), (650,43363)



X(43344) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(7) AND ITS INVERSE

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

Let LA be the reflection of line X(3)X(7) in BC. Define LB and LC cyclically. Let A' = LB∩LC, and define B' and C' cyclically. The lines AA', BB', CC' concur in X(43344). (Randy Hutson, June 30, 2021)

X(43344) lies on the circumcircle and these lines: {2, 15607}, {105, 2646}, {106, 13404}, {927, 17136}, {972, 31793}, {2717, 5538}, {5173, 15728}, {7964, 15731}

X(43344) = anticomplement of X(15607)
X(43344) = isotomic conjugate of the anticomplement of X(33525)
X(43344) = Thomson-isogonal conjugate of X(5762)
X(43344) = Collings transform of X(i) for these i: {2886, 5044, 11018}
X(43344) = X(i)-cross conjugate of X(j) for these (i,j): {2293, 1252}, {15931, 59}, {33525, 2}
X(43344) = X(i)-isoconjugate of X(j) for these (i,j): {513, 13405}, {649, 25001}, {3676, 15837}, {15607, 36048}
X(43344) = cevapoint of X(i) and X(j) for these (i,j): {513, 11018}, {3900, 5044}
X(43344) = trilinear pole of line {6, 13404}
X(43344) = Λ(polar of X(7) wrt circumcircle)
X(43344) = intersection of antipedal lines of circumcircle intercepts of line X(3)X(7)
X(43344) = trilinear pole, wrt circumtangential triangle, of line X(3)X(7)
X(43344) = barycentric product X(190)*X(13404)
X(43344) = barycentric quotient X(i)/X(j) for these {i,j}: {100, 25001}, {101, 13405}, {13404, 514}, {33525, 15607}

X(43345) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(12) AND ITS INVERSE

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

X(43345) lies on the circumcircle and these lines: {104, 13369}, {915, 1829}

X(43345) = Thomson-isogonal conjugate of X(5841)
X(43345) = Collings transform of X(i) for these i: {13750, 34829}
X(43345) = X(1385)-cross conjugate of X(59)
X(43345) = X(i)-isoconjugate of X(j) for these (i,j): {513, 10039}, {7649, 31837}
X(43345) = cevapoint of X(513) and X(13750)
X(43345) = trilinear pole of line {6, 8071}
X(43345) = barycentric quotient X(i)/X(j) for these {i,j}: {101, 10039}, {906, 31837}

X(43346) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(33) AND ITS INVERSE

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

X(43346) lies on the circumcircle and these lines: {108, 14544}, {1633, 41906}

X(43346) = Collings transform of X(i) for these i: {12514, 20262, 41344}
X(43346) = cevapoint of X(i) and X(j) for these (i,j): {513, 41344}, {521, 12514}
X(43346) = trilinear pole of line {6, 1741}

X(43347) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(34) AND ITS INVERSE

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

X(43347) lies on the circumcircle and these lines: {2, 38957}, {63, 102}, {108, 2406}, {651, 36067}

X(43347) = anticomplement of X(38957)
X(43347) = Collings transform of X(i) for these i: {997, 1210}
X(43347) = cevapoint of X(521) and X(997)

X(43348) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(38) AND ITS INVERSE

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

X(43348) lies on the circumcircle and these lines: {2, 38958}, {104, 37328}, {759, 11115}, {3573, 29099}, {8707, 13589}

X(43348) = anticomplement of X(38958)
X(43348) = Collings transform of X(i) for these i: {5266, 21249}
X(43348) = X(649)-isoconjugate of X(33157)
X(43348) = cevapoint of X(513) and X(5266)
X(43348) = trilinear pole of line {6, 3874}
X(43348) = barycentric quotient X(100)/X(33157)

X(43349) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(41) AND ITS INVERSE

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

X(43349) lies on the circumcircle and these lines: {2, 38959}, {7, 1477}, {101, 17136}, {103, 43161}, {109, 35312}, {190, 6078}, {2291, 5744}, {2725, 5088}, {12032, 18461}, {17134, 26703}

X(43349) = anticomplement of X(38959)
X(43349) = Collings transform of X(i) for these i: {1001, 1212, 16593, 37597}
X(43349) = X(663)-isoconjugate of X(7672)
X(43349) = cevapoint of X(i) and X(j) for these (i,j): {513, 37597}, {514, 1001}, {1212, 6182}
X(43349) = trilinear pole of line {6, 142}
X(43349) = Λ(trilinear polar of X(1174))
X(43349) = circumcircle intercept, other than A, B, C, of the circumconic centered at X(1212)
X(43349) = barycentric quotient X(651)/X(7672)

X(43350) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(43) AND ITS INVERSE

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

X(43350) lies on the circumcircle and these lines: {2, 38961}, {100, 23363}, {106, 5248}, {932, 4427}, {1633, 38470}, {18830, 35572}

X(43350) = anticomplement of X(38961)
X(43350) = Collings transform of X(i) for these i: {986, 34832}
X(43350) = X(649)-isoconjugate of X(41839)
X(43350) = cevapoint of X(i) and X(j) for these (i,j): {513, 986}, {667, 1449}
X(43350) = trilinear pole of line {6, 978}
X(43350) = barycentric quotient X(100)/X(41839)

X(43351) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(51) AND ITS INVERSE

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

X(43351) lies on the circumcircle and these lines: {2, 5522}, {74, 3522}, {98, 7485}, {112, 35311}, {477, 37944}, {842, 37900}, {907, 4226}, {925, 1634}, {930, 1632}, {1141, 19179}, {1300, 1593}, {1302, 23181}, {3563, 6995}, {7953, 35278}, {10330, 35575}, {32710, 37931}, {37977, 40118}

X(43351) = anticomplement of X(5522)
X(43351) = Collings transform of X(i) for these i: {233, 1656}
X(43351) = X(2548)-cross conjugate of X(4590)
X(43351) = X(i)-isoconjugate of X(j) for these (i,j): {656, 10594}, {661, 5422}, {798, 32832}, {1577, 13345}
X(43351) = cevapoint of X(523) and X(1656)
X(43351) = trilinear pole of line {6, 140}
X(43351) = barycentric product X(648)*X(42021)
X(43351) = barycentric quotient X(i)/X(j) for these {i,j}: {99, 32832}, {110, 5422}, {112, 10594}, {1576, 13345}, {42021, 525}

X(43352) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(53) AND ITS INVERSE

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

X(43351) lies on the circumcircle and these lines: {2, 38965}, {98, 18909}

X(43352) = anticomplement of X(38965)
X(43352) = Collings transform of X(34836)
X(43352) = X(9786)-cross conjugate of X(249)

X(43353) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(59) AND ITS INVERSE

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

X(43353) lies on the circumcircle and these lines: {109, 21105}, {953, 1537}, {2723, 4996}, {2745, 24466}

X(43353) = Collings transform of X(i) for these i: {3035, 34345}
X(43353) = cevapoint of X(i) and X(j) for these (i,j): {513, 34345}, {2804, 3035}
X(43353) = trilinear pole of line {6, 34530}

X(43354) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(60) AND ITS INVERSE

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

X(43354) lies on the circumcircle and these lines: {3563, 37362}, {4427, 6083}

X(43354) = Collings transform of X(i) for these i: {4999, 6675}
X(43354) = X(4017)-isoconjugate of X(31660)
X(43354) = cevapoint of X(523) and X(6675)
X(43354) = trilinear pole of line {6, 24880}
X(43354) = barycentric quotient X(5546)/X(31660)

X(43355) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(80) AND ITS INVERSE

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

X(43355) lies on the circumcircle and these lines: {2, 13141}, {104, 14988}, {513, 33637}, {517, 14987}, {643, 930}, {953, 26286}, {2718, 21842}, {3814, 33599}

X(43355) = reflection of X(33599) in X(3814)
X(43355) = reflection of X(33637) in the OI line
X(43355) = anticomplement of X(13141)
X(43355) = Collings transform of X(i) for these i: {3814, 3878, 6149}
X(43355) = X(22765)-cross conjugate of X(59)
X(43355) = X(513)-isoconjugate of X(41684)
X(43355) = cevapoint of X(3738) and X(3878)
X(43355) = trilinear pole of line {6, 34544}
X(43355) = barycentric quotient X(101)/X(41684)

X(43356) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(81) AND ITS INVERSE

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

X(43356) lies on the circumcircle and these lines: {2, 38967}, {74, 37426}, {104, 37402}, {110, 4436}, {111, 39982}, {643, 4588}, {662, 8652}, {759, 37032}, {931, 4427}, {2718, 38476}, {3952, 8708}, {5546, 29041}, {5867, 28484}

X(43356) = anticomplement of X(38967)
X(43356) = Collings transform of X(i) for these i: {3739, 4261, 8728}
X(43356) = X(39578)-cross conjugate of X(59)
X(43356) = cevapoint of X(i) and X(j) for these (i,j): {512, 4261}, {523, 8728}, {3739, 23882}
X(43356) = trilinear pole of line {6, 4658}
X(43356) = X(i)-isoconjugate of X(j) for these (i,j): {512, 17394}, {656, 17562}, {661, 37685}
X(43356) = barycentric product X(i)*X(j) for these {i,j}: {99, 39982}, {662, 39708}
X(43356) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 37685}, {112, 17562}, {662, 17394}, {39708, 1577}, {39982, 523}

X(43357) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(83) AND ITS INVERSE

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

X(43357) lies on the circumcircle and these lines: {6, 733}, {98, 5092}, {574, 755}, {662, 8684}, {689, 880}, {691, 14509}, {703, 9463}, {729, 5008}, {805, 1634}, {1297, 41464}, {2698, 9301}, {3098, 29011}, {4579, 36081}, {5118, 12074}, {5467, 31951}, {9076, 15080}, {9150, 35356}

X(43357) = Collings transform of X(i) for these i: {3117, 3934, 24206, 36213}
X(43357) = X(i)-cross conjugate of X(j) for these (i,j): {5116, 249}, {14318, 6}, {21512, 250}
X(43357) = X(i)-isoconjugate of X(j) for these (i,j): {75, 14318}, {661, 3329}, {1577, 12212}
X(43357) = cevapoint of X(i) and X(j) for these (i,j): {6, 14318}, {688, 3117}, {826, 24206}, {3733, 40731}, {3934, 23878}
X(43357) = trilinear pole of line {6, 8623}
X(43357) = barycentric product X(i)*X(j) for these {i,j}: {110, 42006}, {39684, 43187}
X(43357) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 14318}, {110, 3329}, {1576, 12212}, {1634, 10007}, {2966, 39685}, {4630, 41295}, {39684, 3569}, {42006, 850}

X(43358) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(85) AND ITS INVERSE

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

X(43358) lies on the circumcircle and these lines: {1981, 26705}, {2249, 4184}

X(43358) = Collings transform of X(17046)
X(43358) = trilinear pole of line {6, 20793}

X(43359) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(86) AND ITS INVERSE

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

X(43359) lies on the circumcircle and these lines: {2, 38968}, {58, 28523}, {111, 39967}, {662, 932}, {739, 39673}, {741, 1468}, {759, 17038}, {789, 7257}, {825, 5546}, {931, 3573}, {1010, 28621}

X(43359) = anticomplement of X(38968)
X(43359) = Collings transform of X(i) for these i: {386, 3741}
X(43359) = cevapoint of X(i) and X(j) for these (i,j): {386, 512}, {3741, 28623}
X(43359) = trilinear pole of line {6, 16058}
X(43359) = X(i)-isoconjugate of X(j) for these (i,j): {37, 4932}, {512, 31997}, {513, 43223}, {661, 17379}
X(43359) = barycentric product X(i)*X(j) for these {i,j}: {99, 39967}, {662, 17038}
X(43359) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 4932}, {101, 43223}, {110, 17379}, {662, 31997}, {17038, 1577}, {39967, 523}

X(43360) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(86) AND ITS INVERSE

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

X(43360) lies on the circumcircle and these lines: {100, 25312}, {106, 36646}

X(43360) = Collings transform of X(i) for these i: {978, 3840}
X(43360) = cevapoint of X(978) and X(4083)
X(43360) = trilinear pole of line {6, 22140}

X(43361) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(88) AND ITS INVERSE

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

X(43361) lies on the circumcircle and these lines: {106, 4867}, {649, 29179}, {1252, 29044}

X(43361) = Collings transform of X(3834)
X(43361) = trilinear pole of line {6, 22141}

X(43362) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(190) AND ITS INVERSE

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

X(43362) lies on the circumcircle and these lines: {36, 727}, {59, 8685}, {99, 17217}, {100, 4083}, {101, 20979}, {104, 15310}, {110, 16695}, {513, 932}, {517, 15323}, {759, 18792}, {840, 38568}, {5378, 8684}, {9059, 14513}

X(43362) = reflection of X(932) in the OI line
X(43362) = Collings transform of X(i) for these i: {3835, 14963}
X(43362) = cevapoint of X(512) and X(14963)
X(43362) = trilinear pole of line {6, 6377}

X(43363) = PERSPECTOR OF THE CIRCUMCEVIAN TRIANGLE OF X(650) AND ITS INVERSE

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

X(43363) lies on the circumcircle and these lines: {2, 20623}, {7, 108}, {63, 101}, {69, 100}, {77, 109}, {81, 112}, {105, 4453}, {107, 286}, {110, 1444}, {189, 37378}, {693, 2723}, {759, 23829}, {919, 1814}, {929, 5088}, {934, 1621}, {1292, 9778}, {1309, 18816}, {2106, 9091}, {2222, 9436}, {2328, 43076}, {2995, 20901}, {3580, 9090}, {4329, 13397}, {6135, 13387}, {6136, 13386}, {8048, 40097}, {8693, 15066}, {13577, 26706}, {17134, 41906}, {24611, 28847}, {26705, 36010}, {36101, 40116}

X(43363) = anticomplement of X(20623)
X(43363) = isotomic conjugate of the anticomplement of X(8758)
X(43363) = Thomson isogonal conjugate of X(8760)
X(43363) = Collings transform of X(26932)
X(43363) = X(i)-cross conjugate of X(j) for these (i,j): {928, 651}, {8758, 2}, {26884, 81}
X(43363) = X(i)-isoconjugate of X(j) for these (i,j): {6, 5179}, {42, 14956}
X(43363) = trilinear pole of line {6, 905}
X(43363) = circumcircle-X(63)-antipode of X(101)
X(43363) = barycentric product X(1)*X(37214)
X(43363) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 5179}, {81, 14956}, {8758, 20623}, {37214, 75}

leftri

Gibert points on the cubic K1226: X(43364)-X(43387)

rightri

This preamble and points X(43364)-X(43387) are contributed by Peter Moses, May 13, 2021. See also the preambles just before X(42085), X(42413), and X(42429) and others

See K1226



X(43364) = GIBERT (4,9,2) POINT

Barycentrics    2*a^2*S/Sqrt[3] + a^2*SA + 9*SB*SC::

X(43364) lies on the cubic K1226 and these lines: {2, 42088}, {3, 42492}, {4, 11408}, {6, 18296}, {14, 3839}, {16, 3091}, {20, 16808}, {376, 43103}, {382, 42627}, {395, 43201}, {546, 42922}, {631, 42584}, {3090, 42137}, {3146, 11480}, {3522, 42098}, {3523, 19106}, {3525, 42145}, {3526, 42889}, {3529, 42146}, {3543, 18582}, {3544, 42115}, {3545, 42127}, {3627, 42962}, {3832, 5318}, {3845, 33602}, {3853, 42916}, {3854, 11489}, {3855, 42118}, {3856, 42818}, {3861, 42815}, {5056, 42086}, {5059, 23302}, {5067, 42131}, {5068, 5350}, {5071, 42123}, {5334, 42813}, {5343, 43016}, {5344, 16809}, {5366, 18581}, {7378, 37776}, {7486, 42695}, {8972, 42240}, {10303, 42114}, {10304, 16966}, {10654, 43196}, {11481, 15022}, {11488, 17578}, {11543, 41099}, {12103, 42950}, {12816, 42918}, {13941, 42239}, {15640, 42090}, {15682, 42124}, {15687, 42817}, {15692, 42100}, {15697, 42911}, {15705, 43104}, {15717, 42097}, {19107, 42511}, {21734, 43029}, {33703, 42132}, {35403, 42888}, {36843, 42956}, {37832, 42543}, {40693, 42903}, {41106, 42129}, {42087, 42494}, {42093, 42693}, {42101, 42781}, {42104, 43243}, {42113, 43195}, {42133, 42162}, {42140, 42166}, {42143, 42907}, {42148, 42473}, {42154, 42502}, {42156, 43105}, {42588, 43101}, {42589, 42777}, {42683, 42793}, {42814, 42905}, {42921, 42979}

X(43364) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 42986, 42136}, {546, 42922, 42963}, {3839, 42983, 42103}, {5335, 42103, 42983}, {42088, 42472, 2}, {42094, 42110, 42141}, {42102, 42142, 3146}, {42106, 42134, 3091}, {42110, 42141, 2}, {42128, 42136, 42986}, {42133, 42162, 42982}, {42136, 42138, 42128}, {42162, 43226, 42133}, {42212, 42214, 42988}

X(43365) = GIBERT (-4,9,2) POINT

Barycentrics    2*a^2*S/Sqrt[3] - a^2*SA - 9*SB*SC::

X(43365) lies on the cubic K1226 and these lines: {2, 42087}, {3, 42493}, {4, 11409}, {6, 18296}, {13, 3839}, {15, 3091}, {20, 16809}, {376, 43102}, {382, 42628}, {396, 43202}, {546, 42923}, {631, 42585}, {3090, 42136}, {3146, 11481}, {3522, 42095}, {3523, 19107}, {3525, 42144}, {3526, 42888}, {3529, 42143}, {3543, 18581}, {3544, 42116}, {3545, 42126}, {3627, 42963}, {3832, 5321}, {3845, 33603}, {3853, 42917}, {3854, 11488}, {3855, 42117}, {3856, 42817}, {3861, 42816}, {5056, 42085}, {5059, 23303}, {5067, 42130}, {5068, 5349}, {5071, 42122}, {5335, 42814}, {5343, 16808}, {5344, 43017}, {5365, 18582}, {7378, 37775}, {7486, 42694}, {8972, 35740}, {10303, 42111}, {10304, 16967}, {10653, 43195}, {11480, 15022}, {11489, 17578}, {11542, 41099}, {12103, 42951}, {12817, 42919}, {13941, 42241}, {15640, 42091}, {15682, 42121}, {15687, 42818}, {15692, 42099}, {15697, 42910}, {15705, 43101}, {15717, 42096}, {19106, 42510}, {21734, 43028}, {33703, 42129}, {35403, 42889}, {36836, 42957}, {37835, 42544}, {40694, 42902}, {41106, 42132}, {42088, 42495}, {42094, 42692}, {42102, 42782}, {42105, 43242}, {42112, 43196}, {42134, 42159}, {42141, 42163}, {42146, 42906}, {42147, 42472}, {42153, 43106}, {42155, 42503}, {42588, 42778}, {42589, 43104}, {42682, 42794}, {42813, 42904}, {42920, 42978}

X(43365) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 42987, 42137}, {546, 42923, 42962}, {3839, 42982, 42106}, {5334, 42106, 42982}, {42087, 42473, 2}, {42093, 42107, 42140}, {42101, 42139, 3146}, {42103, 42133, 3091}, {42107, 42140, 2}, {42125, 42137, 42987}, {42134, 42159, 42983}, {42135, 42137, 42125}, {42159, 43227, 42134}, {42211, 42213, 42989}

X(43366) = GIBERT (5,36,-3) POINT

Barycentrics    5*a^2*S/Sqrt[3] - 3*a^2*SA + 72*SB*SC::

X(43366) lies on the cubic K1226 and these lines: {4, 16961}, {6, 42612}, {13, 12820}, {62, 42782}, {382, 10645}, {546, 10646}, {3146, 43240}, {3529, 43226}, {3543, 42795}, {3839, 42954}, {3845, 42685}, {3855, 42113}, {5076, 34754}, {5352, 42957}, {12821, 43006}, {14269, 37835}, {15681, 42915}, {19106, 42531}, {36969, 42816}, {41122, 43242}, {41978, 42130}, {42094, 42779}, {42104, 42903}, {42112, 43292}, {42118, 43293}, {42125, 42636}, {42133, 43031}, {42134, 42901}, {42432, 42802}, {42635, 43301}, {42780, 42900}, {43106, 43227}

X(43366) = {X(15687),X(42102)}-harmonic conjugate of X(42630)

X(43367) = GIBERT (5,-36,3) POINT

Barycentrics    5*a^2*S/Sqrt[3] + 3*a^2*SA - 72*SB*SC::

X(43367) lies on the cubic K1226 and these lines: {4, 16960}, {6, 42612}, {14, 12821}, {61, 42781}, {382, 10646}, {546, 10645}, {3146, 43241}, {3529, 43227}, {3543, 42796}, {3839, 42955}, {3845, 42684}, {3855, 42112}, {5076, 34755}, {5351, 42956}, {12820, 43007}, {14269, 37832}, {15681, 42914}, {19107, 42530}, {36970, 42815}, {41121, 43243}, {41977, 42131}, {42093, 42780}, {42105, 42902}, {42113, 43293}, {42117, 43292}, {42128, 42635}, {42133, 42900}, {42134, 43030}, {42431, 42801}, {42636, 43300}, {42779, 42901}, {43105, 43226}

X(43367) = {X(15687),X(42101)}-harmonic conjugate of X(42629)

X(43368) = GIBERT (9,70,5) POINT

Barycentrics    3*Sqrt[3]*a^2*S + 5*a^2*SA + 140*SB*SC::

X(43368) lies on the cubic K1226 and these lines: {4, 3412}, {6, 12816}, {16, 3845}, {17, 35403}, {381, 42611}, {3545, 42514}, {3627, 42959}, {3830, 16241}, {3839, 5237}, {5238, 15687}, {5343, 42973}, {5344, 41113}, {5350, 14893}, {10653, 33605}, {12101, 16808}, {14269, 16965}, {15640, 33417}, {15681, 42596}, {15682, 42472}, {16967, 41099}, {22238, 43310}, {36836, 38335}, {36970, 42693}, {41106, 42100}, {41120, 43001}, {41987, 42431}, {42086, 43025}, {42106, 42530}, {42420, 42692}, {42495, 42510}, {42520, 42813}, {42533, 42778}, {42612, 42972}, {42888, 43108}, {42905, 43007}

X(43368) = {X(3412),X(42589)}-harmonic conjugate of X(41101)

X(43369) = GIBERT (-9,70,5) POINT

Barycentrics    3*Sqrt[3]*a^2*S - 5*a^2*SA - 140*SB*SC::

X(43369) lies on the cubic K1226 and these lines: {4, 3411}, {6, 12816}, {15, 3845}, {18, 35403}, {381, 42610}, {3545, 42515}, {3627, 42958}, {3830, 16242}, {3839, 5238}, {5237, 15687}, {5343, 41112}, {5344, 42972}, {5349, 14893}, {10654, 33604}, {12101, 16809}, {14269, 16964}, {15640, 33416}, {15681, 42597}, {15682, 42473}, {16966, 41099}, {22236, 43311}, {36843, 38335}, {36969, 42692}, {41106, 42099}, {41119, 43000}, {41987, 42432}, {42085, 43024}, {42103, 42531}, {42419, 42693}, {42494, 42511}, {42521, 42814}, {42532, 42777}, {42613, 42973}, {42889, 43109}, {42904, 43006}

X(43369) = {X(3411),X(42588)}-harmonic conjugate of X(41100)

X(43370) = GIBERT (13,18,39) POINT

Barycentrics    13*a^2*S/Sqrt[3] + 39*a^2*SA + 36*SB*SC::

X(43370) lies on the cubic K1226 and these lines: {2, 42481}, {4, 10188}, {13, 15721}, {14, 15703}, {15, 42492}, {5334, 41978}, {10109, 16809}, {10646, 12108}, {11539, 16242}, {11543, 43012}, {15689, 16808}, {15693, 36968}, {15705, 37832}, {16241, 42630}, {16644, 42498}, {16960, 43239}, {16964, 42610}, {19106, 42950}, {19710, 42102}, {33417, 42115}, {34200, 42146}, {41974, 42949}, {42088, 42488}, {42089, 43023}, {42096, 42984}, {42111, 42972}, {42123, 43016}, {42124, 42894}, {42133, 43245}, {42476, 43238}, {42491, 42530}, {42511, 42914}, {42580, 42967}, {42815, 43295}, {42915, 42940}, {42922, 42966}, {42948, 43019}

X(43370) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10188, 42092, 16966}, {42092, 42472, 42959}, {42472, 42959, 42099}

X(43371) = GIBERT (-13,18,39) POINT

Barycentrics    13*a^2*S/Sqrt[3] - 39*a^2*SA - 36*SB*SC::

X(43371) lies on the cubic K1226 and these lines: {2, 42480}, {4, 10187}, {13, 15703}, {14, 15721}, {16, 42493}, {5335, 41977}, {10109, 16808}, {10645, 12108}, {11539, 16241}, {11542, 43013}, {15689, 16809}, {15693, 36967}, {15705, 37835}, {16242, 42629}, {16645, 42499}, {16961, 43238}, {16965, 42611}, {19107, 42951}, {19710, 42101}, {33416, 42116}, {34200, 42143}, {41973, 42948}, {42087, 42489}, {42092, 43022}, {42097, 42985}, {42114, 42973}, {42121, 42895}, {42122, 43017}, {42134, 43244}, {42477, 43239}, {42490, 42531}, {42510, 42915}, {42581, 42966}, {42816, 43294}, {42914, 42941}, {42923, 42967}, {42949, 43018}

X(43371) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10187, 42089, 16967}, {42089, 42473, 42958}, {42473, 42958, 42100}

X(43372) = GIBERT (33,20,55) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 55*a^2*SA + 40*SB*SC::

X(43372) lies on the cubic K1226 and these lines: {2, 42892}, {3, 43013}, {4, 5238}, {6, 15694}, {13, 43294}, {14, 15699}, {15, 42509}, {16, 15708}, {18, 42516}, {30, 43024}, {61, 16239}, {376, 42900}, {396, 14869}, {549, 42996}, {631, 42478}, {3090, 41978}, {3526, 43018}, {3528, 43033}, {5071, 41971}, {5237, 42974}, {5335, 43000}, {5350, 42529}, {10124, 43249}, {10645, 15686}, {10646, 43304}, {10654, 43241}, {11542, 12100}, {11737, 23302}, {12812, 16772}, {12820, 42090}, {14890, 42913}, {14891, 42895}, {15687, 43204}, {15688, 16644}, {15693, 41972}, {15697, 41121}, {15698, 43010}, {15704, 43027}, {15713, 43014}, {15721, 43030}, {16645, 42939}, {17504, 43004}, {33417, 42633}, {34754, 42910}, {41101, 42902}, {42092, 43308}, {42132, 42632}, {42152, 42596}, {42153, 42936}, {42506, 43306}, {42520, 43102}, {42592, 42934}, {42593, 42802}, {42778, 43103}, {42799, 43029}, {42911, 43245}, {42915, 43301}, {42921, 42932}

X(43372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42892, 43007}, {36967, 42979, 37832}

X(43373) = GIBERT (-33,20,55) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 55*a^2*SA - 40*SB*SC::

X(43373) lies on the cubic K1226 and these lines: {2, 42893}, {3, 43012}, {4, 5237}, {6, 15694}, {13, 15699}, {14, 43295}, {15, 15708}, {16, 42508}, {17, 42517}, {30, 43025}, {62, 16239}, {376, 42901}, {395, 14869}, {549, 42997}, {631, 42479}, {3090, 41977}, {3526, 43019}, {3528, 43032}, {5071, 41972}, {5238, 42975}, {5334, 43001}, {5349, 42528}, {10124, 43248}, {10645, 43305}, {10646, 15686}, {10653, 43240}, {11543, 12100}, {11737, 23303}, {12812, 16773}, {12821, 42091}, {14890, 42912}, {14891, 42894}, {15687, 43203}, {15688, 16645}, {15693, 41971}, {15697, 41122}, {15698, 43011}, {15704, 43026}, {15713, 43015}, {15721, 43031}, {16644, 42938}, {17504, 43005}, {22580, 36770}, {33416, 42634}, {34755, 42911}, {41100, 42903}, {42089, 43309}, {42129, 42631}, {42149, 42597}, {42156, 42937}, {42507, 43307}, {42521, 43103}, {42592, 42801}, {42593, 42935}, {42777, 43102}, {42800, 43028}, {42910, 43244}, {42914, 43300}, {42920, 42933}

X(43373) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 42893, 43006}, {36968, 42978, 37835}

X(43374) = GIBERT (8 SQRT(3),9,24) POINT

Barycentrics    4*a^2*S + 12*a^2*SA + 9*SB*SC::

X(43374) lies on the cubic K1226 and these lines: {2, 6199}, {4, 5418}, {5, 9543}, {6, 3525}, {140, 42523}, {376, 18538}, {590, 3524}, {631, 6398}, {1151, 3544}, {1587, 6434}, {3068, 15702}, {3069, 42601}, {3090, 6221}, {3091, 6445}, {3316, 3528}, {3317, 31454}, {3529, 6451}, {3533, 8981}, {3545, 35255}, {3855, 42225}, {5055, 9542}, {5067, 6437}, {5071, 6468}, {6395, 10303}, {6396, 13886}, {6407, 15022}, {6409, 11541}, {6411, 17538}, {6433, 42582}, {6436, 35812}, {6442, 13935}, {6446, 13925}, {6459, 6476}, {6490, 23275}, {6560, 15715}, {7581, 41964}, {7582, 32790}, {7584, 34091}, {7585, 15709}, {8976, 10299}, {9541, 41106}, {9691, 12812}, {11001, 42284}, {13665, 15698}, {15697, 42604}, {15708, 18512}, {15719, 42216}, {21735, 42226}, {23263, 42568}, {23269, 41948}, {35732, 42963}, {42282, 42962}

X(43374) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9540, 32789, 23273}, {23273, 32789, 5067}

X(43375) = GIBERT (-8 SQRT(3),9,24) POINT

Barycentrics    4*a^2*S - 12*a^2*SA - 9*SB*SC::

X(43375) lies on the cubic K1226 and these lines: {2, 6395}, {4, 5420}, {5, 34091}, {6, 3525}, {140, 42522}, {376, 18762}, {615, 3524}, {631, 6221}, {1152, 3544}, {1588, 6433}, {3068, 42600}, {3069, 15702}, {3090, 6398}, {3091, 6446}, {3317, 3528}, {3529, 6452}, {3533, 8972}, {3545, 35256}, {3855, 42226}, {5067, 6438}, {5071, 6469}, {5079, 17851}, {6199, 10303}, {6200, 13939}, {6408, 15022}, {6410, 11541}, {6412, 17538}, {6434, 42583}, {6435, 35813}, {6441, 9540}, {6445, 13993}, {6460, 6477}, {6491, 23269}, {6561, 15715}, {7581, 32789}, {7582, 41963}, {7583, 34089}, {7586, 15709}, {9542, 11812}, {9690, 12108}, {10299, 13951}, {11001, 42283}, {13785, 15698}, {15697, 42605}, {15708, 18510}, {15719, 42215}, {21735, 42225}, {23253, 42569}, {23275, 41947}, {35732, 42962}, {42282, 42963}

X(43375) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13935, 32790, 23267}, {23267, 32790, 5067}

X(43376) = GIBERT (12 SQRT(3),11,6) POINT

Barycentrics    6*a^2*S + 3*a^2*SA + 11*SB*SC::

X(43376) lies on the cubic K1226 and these lines: {2, 6426}, {4, 1131}, {5, 3591}, {6, 3854}, {20, 8960}, {140, 6446}, {485, 3523}, {550, 13886}, {1132, 6564}, {1587, 5056}, {1657, 9690}, {3068, 5059}, {3070, 3522}, {3091, 35822}, {3146, 41945}, {3316, 15720}, {3533, 42216}, {3850, 18512}, {3851, 7581}, {3858, 7582}, {5068, 7586}, {5071, 42527}, {6410, 41958}, {6427, 41099}, {6477, 10576}, {8976, 10299}, {9680, 15697}, {9692, 11001}, {10195, 10303}, {15682, 31487}, {15683, 31454}, {15708, 42524}, {17578, 32787}, {23249, 42266}, {23253, 42522}, {32785, 41948}, {41966, 42604}

X(43376) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {485, 3523, 3590}, {1587, 42277, 42523}, {3068, 42272, 9543}, {41954, 42262, 31412}

X(43377) = GIBERT (-12 SQRT(3),11,6) POINT

Barycentrics    6*a^2*S - 3*a^2*SA - 11*SB*SC::

X(43377) lies on the cubic K1226 and these lines: {2, 6425}, {4, 1132}, {5, 3590}, {6, 3854}, {140, 6445}, {486, 3523}, {550, 13939}, {632, 9692}, {1131, 6565}, {1588, 5056}, {1657, 23275}, {3069, 5059}, {3071, 3522}, {3091, 35823}, {3146, 41946}, {3317, 15720}, {3533, 42215}, {3850, 18510}, {3851, 7582}, {3858, 7581}, {5068, 7585}, {5071, 42526}, {6409, 41957}, {6428, 41099}, {6476, 10577}, {9681, 15721}, {9693, 11539}, {10194, 10303}, {10299, 13951}, {15708, 42525}, {17578, 32788}, {23259, 42267}, {23263, 42523}, {32786, 41947}, {41965, 42605}

X(43377) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {486, 3523, 3591}, {1588, 42274, 42522}, {41953, 42265, 42561}

X(43378) = GIBERT (15 SQRT(3),26,60) POINT

Barycentrics    15*a^2*S + 60*a^2*SA + 52*SB*SC::

X(43378) lies on the cubic K1226 and these lines: {3, 42641}, {4, 6409}, {5, 42642}, {140, 6438}, {548, 43254}, {631, 42572}, {3526, 6420}, {3592, 42640}, {3594, 11540}, {5055, 6519}, {5056, 42568}, {6199, 10577}, {7486, 41963}, {8252, 19116}, {9540, 41953}, {10299, 42566}, {10303, 17852}, {23046, 42577}, {32785, 41948}, {43211, 43323}

X(43379) = GIBERT (-15 SQRT(3),26,60) POINT

Barycentrics    15*a^2*S - 60*a^2*SA - 52*SB*SC::

X(43379) lies on the cubic K1226 and these lines: {3, 42642}, {4, 6410}, {5, 42641}, {140, 6437}, {548, 43255}, {631, 42573}, {3526, 6419}, {3592, 11540}, {3594, 42639}, {5055, 6522}, {5056, 42569}, {6395, 10576}, {7486, 41964}, {8253, 19117}, {10299, 42567}, {13935, 41954}, {23046, 42576}, {32786, 41947}, {43212, 43322}

X(43380) = GIBERT (15 SQRT(3),26,60) POINT

Barycentrics    15*a^2*S + 10*a^2*SA + 46*SB*SC::

X(43380) lies on the cubic K1226 and these lines: {2, 6434}, {4, 3592}, {30, 6484}, {381, 42573}, {485, 9691}, {549, 10576}, {590, 1327}, {1131, 19053}, {1328, 13665}, {1587, 41951}, {3070, 5055}, {3522, 42641}, {3628, 41946}, {3845, 42572}, {3856, 35823}, {5066, 6564}, {6439, 9542}, {6487, 41984}, {7486, 41964}, {10304, 31412}, {13847, 42273}, {15683, 23251}, {15698, 23249}, {15704, 42639}, {15706, 42602}, {15709, 42265}, {15711, 42558}, {15716, 42566}, {15759, 18538}, {23046, 35822}, {33699, 42284}, {35815, 42271}, {42258, 42537}, {42277, 42418}

X(43380) = {X(6451),X(41950)}-harmonic conjugate of X(590)

X(43381) = GIBERT (-15 SQRT(3),23,10) POINT

Barycentrics    15*a^2*S - 10*a^2*SA - 46*SB*SC::

X(43381) lies on the cubic K1226 and these lines: {2, 6433}, {4, 3594}, {30, 6485}, {381, 42572}, {486, 15684}, {549, 10577}, {615, 1328}, {1132, 19054}, {1327, 13785}, {1588, 41952}, {3071, 5055}, {3522, 42642}, {3628, 41945}, {3845, 42573}, {3856, 35822}, {5066, 6565}, {6440, 13847}, {6486, 41984}, {7486, 41963}, {10304, 42561}, {13846, 42270}, {15683, 23261}, {15698, 23259}, {15704, 42640}, {15706, 42603}, {15709, 42262}, {15711, 42557}, {15716, 42567}, {15759, 18762}, {23046, 35823}, {33699, 42283}, {35814, 42272}, {42259, 42538}, {42274, 42417}

X(43381) = {X(6452),X(41949)}-harmonic conjugate of X(615)

X(43382) = GIBERT (20 SQRT(3),9,-30) POINT

Barycentrics    10*a^2*S - 15*a^2*SA + 9*SB*SC::

X(43382) lies on the cubic K1226 and these lines: {2, 6434}, {4, 3591}, {6, 42574}, {548, 6199}, {549, 23267}, {1131, 3526}, {1132, 35814}, {1152, 15022}, {3091, 6481}, {3146, 6438}, {3522, 6437}, {3628, 6446}, {3857, 6408}, {5073, 42644}, {6200, 7585}, {6395, 15704}, {6396, 10303}, {6412, 6460}, {6436, 42261}, {6440, 32786}, {6476, 42522}, {7486, 23249}, {7581, 9690}, {7586, 15683}, {10138, 12811}, {14093, 42643}, {15640, 23259}, {15698, 42216}, {15709, 18538}, {17800, 23273}, {32785, 41948}, {41962, 41966}, {41963, 42637}, {42274, 43256}, {42275, 42523}

X(43383) = GIBERT (20 SQRT(3),-9,30) POINT

Barycentrics    10*a^2*S + 15*a^2*SA - 9*SB*SC::

X(43383) lies on the cubic K1226 and these lines: {2, 6433}, {4, 3590}, {6, 42574}, {548, 6395}, {549, 23273}, {1131, 35815}, {1132, 3526}, {1151, 15022}, {3091, 6480}, {3146, 6437}, {3522, 6438}, {3628, 6445}, {3856, 9693}, {3857, 6407}, {5072, 9690}, {5073, 42643}, {6199, 15704}, {6200, 10303}, {6396, 7586}, {6411, 6459}, {6435, 42260}, {6439, 9543}, {6477, 42523}, {7486, 9681}, {7585, 15683}, {9542, 42277}, {10137, 12811}, {14093, 42644}, {15640, 23249}, {15698, 42215}, {15709, 18762}, {17800, 23267}, {31414, 42258}, {32786, 41947}, {41961, 41965}, {42276, 42522}

X(43384) = GIBERT (21 SQRT(3),22,-28) POINT

Barycentrics    21*a^2*S - 28*a^2*SA + 44*SB*SC::

X(43384) lies on the cubic K1226 and these lines: {4, 6426}, {6, 41957}, {372, 35434}, {547, 23251}, {1152, 38071}, {1327, 11540}, {1328, 42226}, {3070, 15710}, {3311, 15681}, {3530, 10195}, {3860, 42274}, {5054, 42265}, {5079, 42641}, {6411, 6560}, {6429, 32787}, {6446, 8252}, {6469, 41099}, {6473, 42262}, {6477, 42527}, {7584, 35404}, {8253, 15719}, {9541, 43209}, {9690, 42525}, {15692, 41952}, {18510, 42264}, {19053, 42271}, {32788, 42576}, {33699, 43317}, {42272, 42571}, {42418, 42577}

X(43385) = GIBERT (21 SQRT(3),-22,28) POINT

Barycentrics    21*a^2*S + 28*a^2*SA - 44*SB*SC::

X(43385) lies on the cubic K1226 and these lines: {4, 6425}, {6, 41957}, {371, 35434}, {547, 23261}, {1151, 38071}, {1327, 42225}, {1328, 11540}, {3071, 15710}, {3312, 15681}, {3530, 10194}, {3860, 42277}, {5054, 42262}, {5079, 42642}, {6412, 6561}, {6430, 32788}, {6445, 8253}, {6468, 41099}, {6472, 42265}, {6476, 42526}, {7583, 35404}, {8252, 15719}, {9541, 42566}, {9543, 41967}, {9681, 41991}, {15692, 41951}, {18512, 42263}, {19054, 42272}, {32787, 42577}, {33699, 43316}, {42271, 42570}, {42417, 42576}

X(43386) = GIBERT (24 SQRT(3),13,8) POINT

Barycentrics    12*a^2*S + 4*a^2*SA + 13*SB*SC::

X(43386) lies on the cubic K1226 and these lines: {2, 6395}, {4, 1327}, {6, 14226}, {15, 36446}, {16, 36464}, {30, 42522}, {376, 6449}, {631, 6522}, {1587, 3524}, {3068, 19708}, {3070, 42641}, {3525, 41964}, {3528, 41963}, {3545, 7584}, {3839, 19117}, {5054, 6473}, {5071, 7581}, {6199, 15640}, {6418, 42640}, {6437, 9541}, {6460, 15715}, {6500, 23046}, {6501, 11737}, {6560, 42525}, {7585, 15682}, {8252, 41950}, {8972, 15719}, {8981, 15710}, {9542, 15690}, {13665, 41099}, {13886, 15702}, {13925, 15708}, {15698, 42216}, {15703, 34091}, {17538, 43209}, {19053, 42274}, {23269, 42271}, {42213, 42974}, {42214, 42975}

X(43386) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14241, 41106}, {6395, 42639, 2}, {23267, 32787, 11001}

X(43387) = GIBERT (-24 SQRT(3),13,8) POINT

Barycentrics    12*a^2*S - 4*a^2*SA - 13*SB*SC::

X(43387) lies on the cubic K1226 and these lines: {2, 6199}, {4, 1328}, {6, 14226}, {15, 36465}, {16, 36447}, {30, 42523}, {376, 6450}, {549, 9543}, {631, 6519}, {1588, 3524}, {3069, 19708}, {3071, 42642}, {3090, 31487}, {3525, 41963}, {3528, 41964}, {3534, 17851}, {3545, 7583}, {3839, 19116}, {5054, 6472}, {5071, 7582}, {6395, 15640}, {6417, 42639}, {6438, 11001}, {6459, 15715}, {6500, 11737}, {6501, 23046}, {6561, 42524}, {7586, 15682}, {8253, 41949}, {13785, 41099}, {13939, 15702}, {13941, 15719}, {13966, 15710}, {13993, 15708}, {15698, 42215}, {15703, 34089}, {17538, 17852}, {19054, 42277}, {23275, 42272}, {42211, 42974}, {42212, 42975}

X(43387) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14226, 41106}, {6199, 42640, 2}, {23273, 32788, 11001}

X(43388) = CENTER OF CIRCUMCIRCLE OF SYMMETRIC TRAPEZIUM UOH'U'

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

See Sándor Nagydobai Kiss and Bálint Bíró, "Two Remarkable Triangles of a Triangle and Their Circumcircles" , Elemente der Mathematik, 2021; page 7 (Figure 10).

X(43388) lies on these lines: {2, 685}, {5, 182}, {98, 34235}, {1576, 2794}, {1968, 6530, {37334, 39575}

X(43389) = REFLECTION OF X(3) IN THE LINE X(5)X(525)

Barycentrics    a^14 - a^12*b^2 - 3*a^8*b^6 + 5*a^6*b^8 - 3*a^4*b^10 + 2*a^2*b^12 - b^14 - a^12*c^2 + a^10*b^2*c^2 + 3*a^8*b^4*c^2 - 3*a^6*b^6*c^2 - 2*a^2*b^10*c^2 + 2*b^12*c^2 + 3*a^8*b^2*c^4 - 4*a^6*b^4*c^4 + 3*a^4*b^6*c^4 - 2*a^2*b^8*c^4 - 3*a^8*c^6 - 3*a^6*b^2*c^6 + 3*a^4*b^4*c^6 + 4*a^2*b^6*c^6 - b^8*c^6 + 5*a^6*c^8 - 2*a^2*b^4*c^8 - b^6*c^8 - 3*a^4*c^10 - 2*a^2*b^2*c^10 + 2*a^2*c^12 + 2*b^2*c^12 - c^14 :
X(43389) = 3 X[381] - 2 X[43278], 5 X[3091] - 3 X[6794]

X(43389) lies on these lines: {3, 66}, {4, 525}, {5, 18338}, {30, 43279}, {113, 31854}, {147, 1625}, {343, 37921}, {381, 43278}, {382, 43280}, {2420, 5921}, {2710, 9873}, {3091, 6794}, {3410, 37918}, {4230, 11442}, {5877, 31850}, {12162, 31848}, {13509, 15052}, {23325, 38971}, {32345, 34190}, {37466, 41175}

X(43389 = midpoint of X(4) and X(18337)
X(43389) = reflection of X(i) in X(j) for these {i,j}: {{382, 43280}, {18338, 5}
X(43389) = crossdifference of every pair of points on line {2485, 8779}

leftri

Points associated with the Kiss-Moses mapping: X(43390)-X(43396)

rightri

This preamble and points X(43390)-X(43396) are contributed by Peter Moses, May 15, 2021.

In the plane of a triangle ABC, with circumcenter O and orthocenter H, let

D = AH∩BO, E = BH∩CO, F = CH∩AO
D' = AH∩CO, E' = BH∩AO, F' = CH∩BO
D" = midpoint(D,D'), E" = midpoint(E,E'), F" = midpoint(F,F')

The points D and D' and associated triangles, circles, and quadrangles comprise the Kiss-Biró configuration, introduced in "Two Remarkable Triangles of a Triangle and Their Circumcircles", by Sándor Nagydonbai Kiss and Bálint Biró. Elemente der Mathematik (April 2020).

Peter Moses noted that for many choices of i, the point X(i)-of-D"E"F" = X(j)-of-ABC for some j. If P = p : q : r is a point and P-of-D"E"F" = U = u : v : w, then the mapping P → U is here named the Kiss-Moses mapping, and the image of P is denoted by KM(P). Moses established that this mapping is one-to-one and gave formulas for the mapping and its inverse, denoted by MK(U):

KM(P) = a^2*(2*a^2*b^2*c^2*(a^2 - b^2 - c^2)*p + c^2*(a^2 + b^2 - c^2)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)*q + b^2*(a^2 - b^2 + c^2)*(a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*r) : :

MK(U) = a^2*((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - 3*a^6*c^2 + 7*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 - a^2*c^6 - b^2*c^6)*u + (a^4 - 2*a^2*b^2 + b^4 + a^2*c^2 + b^2*c^2 - 2*c^4)*(a^4 - a^2*b^2 - 2*a^2*c^2 - b^2*c^2 + c^4)*v + (a^4 - 2*a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2)*(a^4 + a^2*b^2 - 2*b^4 - 2*a^2*c^2 + b^2*c^2 + c^4)*w) : :

The fixed point of the two mappings is X(54).

The appearance of i → j in the following list means that KM(X(i)) = X(j):

15035 → 2→ 9730
110 → 3 → 5 → 13630
43390 → 43391 → 14157 → 74 → 4→ 185 → 13403→ 43392 → 43393
19128 → 5622 → 6 → 8550
14094 → 20 → 12162
23 → 16003 → 5446
34148 → 49 → 43394 → 15806
3448 → 52 → 10116
54 → 54 → 54 → 54 → 54 → 54 → 54 → 54 → 54 → 54 → 54
2071 → 113 → 40647
186 → 125 → 389
22115 → 1511 → 140 → 12006
2070 → 10264 → 143
15462 → 182 → 575→ 33749
15463 → 184 → 11430
323 → 30714 → 1216
403 → 974 → 12241
10540 → 12041 → 546
37477 → 5609 → 548
32609 → 549 → 13363
1113 → 43395 → 14374
1114 → 43396 → 14375
5504 → 1147 → 12038
1495 → 20417 → 10110
15132 → 1658 → 13561
25739 → 1986 → 6146
8718 → 15062 → 3521
14644 → 5890 → 12022
23061 → 23236 → 6101
10721 → 6241 → 18560
7575 → 20379 → 16881
21663 → 7687 → 13382
13445 → 7728 → 13491
11597 → 10610 → 8254
10295 → 15738 → 13568
12112 → 10990 → 13474
27866 → 13353 → 36153

If P is on the line at infinity, then KM(P) is also on the line at infinity, and KM(KM(P)) = P. The appearance of (i,j) in the following list means that X(i) is on the line at infinity and KM(X(i)) = X(j):

(30,5663), (511,542), (512,690), (513,8674), (514,2774), (515,2779), (516,2772), (517,2771), (518,2836), (519,2842), (520,9033), (521,2850), (522,2773), (523,526), (524,2854), (525,9517)

If P is on the line at infinity, then the self-inversive restriction of the mapping KM (to the line at infinity), here denoted by IKM, is given by

IKM(P) = a^2*(c^2*(a^2 - c^2)*q + b^2*(a^2 - b^2)*r)^2*((a^2 - b^2)*(a^2 + b^2 - c^2)*q - b^2*(b^2 - c^2)*r)*(c^2*(b^2 - c^2)*q + (a^2 - c^2)*(a^2 - b^2 + c^2)*r)*(-(c^2*q^2) + (a^2 - b^2 - c^2)*q*r - b^2*r^2) : :



X(43390) = X(4)X(54)∩X(399)X(35452)

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

X(43390) lies on these lines: {4, 54}, {399, 35452}, {1495, 10821}, {5012, 21308}, {5876, 13445}

X(43390) = crosspoint of X(13863) and X(32230)

X(43391) = X(54)X(74)∩X(110)X(550)

Barycentrics    a^2*(a^14 - 4*a^12*b^2 + 5*a^10*b^4 - 5*a^6*b^8 + 4*a^4*b^10 - a^2*b^12 - 4*a^12*c^2 + 16*a^10*b^2*c^2 - 16*a^8*b^4*c^2 - 7*a^6*b^6*c^2 + 17*a^4*b^8*c^2 - 5*a^2*b^10*c^2 - b^12*c^2 + 5*a^10*c^4 - 16*a^8*b^2*c^4 + 37*a^6*b^4*c^4 - 21*a^4*b^6*c^4 - 8*a^2*b^8*c^4 + 3*b^10*c^4 - 7*a^6*b^2*c^6 - 21*a^4*b^4*c^6 + 28*a^2*b^6*c^6 - 2*b^8*c^6 - 5*a^6*c^8 + 17*a^4*b^2*c^8 - 8*a^2*b^4*c^8 - 2*b^6*c^8 + 4*a^4*c^10 - 5*a^2*b^2*c^10 + 3*b^4*c^10 - a^2*c^12 - b^2*c^12) : :

X(43391) lies on these lines: {54, 74}, {110, 550}, {125, 35482}, {427, 14644}, {1291, 16169}, {1614, 12244}, {2777, 13619}, {2781, 19128}, {2935, 12281}, {3043, 10990}, {5012, 15041}, {5189, 17702}, {5663, 13445}, {6240, 10721}, {6241, 17847}, {6636, 15035}, {9919, 26882}, {10620, 34148}, {11413, 15102}, {11468, 17835}, {11807, 38848}, {12041, 18364}, {12084, 15100}, {12228, 15021}, {12317, 13346}, {13482, 20126}, {20417, 34564}

X(43391) = {X(110),X(20127)}-harmonic conjugate of X(8718)

X(43392) = X(5)X(11806)∩X(54)X(74)

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 - 2*a^10*b^2*c^2 + 6*a^8*b^4*c^2 - 17*a^6*b^6*c^2 + 20*a^4*b^8*c^2 - 9*a^2*b^10*c^2 + b^12*c^2 - 4*a^10*c^4 + 6*a^8*b^2*c^4 + 12*a^6*b^4*c^4 - 15*a^4*b^6*c^4 - 2*a^2*b^8*c^4 + 3*b^10*c^4 + 5*a^8*c^6 - 17*a^6*b^2*c^6 - 15*a^4*b^4*c^6 + 14*a^2*b^6*c^6 - 3*b^8*c^6 + 20*a^4*b^2*c^8 - 2*a^2*b^4*c^8 - 3*b^6*c^8 - 5*a^4*c^10 - 9*a^2*b^2*c^10 + 3*b^4*c^10 + 4*a^2*c^12 + b^2*c^12 - c^14) : :

X)43392) lies on these lines: {5, 11806}, {52, 3521}, {54, 74}, {140, 9729}, {143, 11558}, {389, 403}, {569, 34783}, {1885, 6000}, {5890, 14940}, {12006, 12900}, {12300, 13399}, {12897, 32375}, {13418, 32339}, {13619, 21660}, {18436, 37470}, {21649, 34007}, {34152, 40647}

X(43392) = {X(185),X(3520)}-harmonic conjugate of X(17855)

X(43393) = X(4)X(54)∩X(12006)X(17702)

Barycentrics    2*a^16 - 6*a^14*b^2 + 3*a^12*b^4 + 6*a^10*b^6 - 5*a^8*b^8 - 2*a^6*b^10 + a^4*b^12 + 2*a^2*b^14 - b^16 - 6*a^14*c^2 + 26*a^12*b^2*c^2 - 32*a^10*b^4*c^2 + a^8*b^6*c^2 + 15*a^6*b^8*c^2 + 5*a^4*b^10*c^2 - 13*a^2*b^12*c^2 + 4*b^14*c^2 + 3*a^12*c^4 - 32*a^10*b^2*c^4 + 54*a^8*b^4*c^4 - 13*a^6*b^6*c^4 - 35*a^4*b^8*c^4 + 27*a^2*b^10*c^4 - 4*b^12*c^4 + 6*a^10*c^6 + a^8*b^2*c^6 - 13*a^6*b^4*c^6 + 58*a^4*b^6*c^6 - 16*a^2*b^8*c^6 - 4*b^10*c^6 - 5*a^8*c^8 + 15*a^6*b^2*c^8 - 35*a^4*b^4*c^8 - 16*a^2*b^6*c^8 + 10*b^8*c^8 - 2*a^6*c^10 + 5*a^4*b^2*c^10 + 27*a^2*b^4*c^10 - 4*b^6*c^10 + a^4*c^12 - 13*a^2*b^2*c^12 - 4*b^4*c^12 + 2*a^2*c^14 + 4*b^2*c^14 - c^16 : :

X(43393) lies on these lines: {4, 54}, {12006, 17702}, {13163, 30522}, {13630, 31985}, {19457, 25563}

X(43394) = X(3)X(54)∩X(4)X(16665)

Barycentrics    a^2*(2*a^8 - 5*a^6*b^2 + 3*a^4*b^4 + a^2*b^6 - b^8 - 5*a^6*c^2 + 8*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - b^6*c^2 + 3*a^4*c^4 - 2*a^2*b^2*c^4 + 4*b^4*c^4 + a^2*c^6 - b^2*c^6 - c^8) : :
X(43394) = J^2*X[3] + (J^2 - 4)*X[54]

X(43394) lies on these lines: {3, 54}, {4, 16665}, {5, 1511}, {20, 3431}, {30, 5944}, {49, 3043}, {52, 15331}, {68, 18580}, {74, 9706}, {110, 14130}, {125, 5498}, {140, 12370}, {143, 186}, {156, 378}, {182, 22962}, {184, 11250}, {185, 10226}, {265, 6143}, {381, 11449}, {382, 11464}, {389, 15646}, {399, 9705}, {548, 10564}, {550, 18475}, {567, 12006}, {568, 21844}, {575, 40929}, {578, 5946}, {631, 14805}, {858, 13470}, {1092, 15067}, {1147, 5876}, {1199, 37941}, {1353, 5092}, {1495, 3853}, {1539, 18560}, {1594, 30522}, {1658, 10263}, {1994, 17506}, {3090, 38942}, {3292, 31834}, {3515, 39522}, {3516, 32139}, {3524, 18951}, {3530, 13292}, {3541, 34514}, {3581, 38448}, {3627, 10282}, {3830, 26882}, {5073, 26881}, {5446, 7575}, {5609, 12162}, {5907, 40111}, {6146, 23336}, {6241, 9704}, {6243, 10298}, {6288, 12383}, {6643, 18466}, {6644, 11425}, {7488, 13391}, {7502, 13346}, {7512, 37477}, {7514, 35602}, {7526, 15060}, {7527, 18350}, {7530, 17821}, {7577, 18379}, {8718, 35452}, {9544, 18439}, {9545, 32210}, {9703, 12111}, {9730, 36153}, {10095, 15033}, {10112, 20191}, {10116, 10264}, {10212, 32165}, {10224, 21659}, {10540, 14865}, {11202, 37440}, {11424, 12106}, {11454, 11935}, {11468, 35496}, {11562, 11702}, {11563, 12897}, {11591, 14118}, {11801, 17701}, {12022, 34128}, {12084, 19357}, {12121, 34007}, {13363, 13434}, {13366, 37968}, {13482, 37922}, {13561, 37118}, {13598, 37936}, {14374, 35231}, {14375, 35232}, {14627, 37955}, {14934, 36161}, {15032, 35497}, {15037, 15051}, {15039, 33539}, {15078, 36753}, {15080, 15696}, {15101, 32401}, {15463, 38898}, {16168, 36159}, {16227, 16881}, {18281, 19467}, {18324, 36747}, {18396, 31283}, {18445, 32138}, {20190, 32284}, {22352, 33923}, {22462, 38638}, {22804, 39504}, {23358, 32196}, {32142, 35921}, {32534, 36749}, {34152, 40647}, {34477, 41587}, {34513, 37497}, {35472, 37490}, {36179, 38610}, {40928, 40932}

X(43394) = midpoint of X(i) and X(j) for these {i,j}: {3, 34148}, {49, 3520}, {7488, 37495}
X(43394) = reflection of X(5944) in X(13367)
X(43394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 54, 13630}, {5, 12038, 1511}, {184, 11250, 13491}, {185, 10226, 12041}, {186, 37472, 143}, {567, 22467, 12006}, {578, 37814, 5946}, {1147, 18570, 5876}, {1658, 13352, 10263}, {9544, 35475, 18439}, {9545, 35473, 34783}, {9705, 15062, 399}, {10116, 25563, 10264}, {10264, 36966, 10116}, {10540, 14865, 32137}, {11430, 12038, 5}, {14118, 22115, 11591}, {18445, 35477, 32138}, {34783, 35473, 32210}

X(43395) = MIDPOINT OF X(4) AND X(32616)

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

X(43395) lies on the cubic K591 and these lines: {2, 32617}, {3, 2574}, {4, 2575}, {5, 113}, {74, 14374}, {110, 14709}, {265, 14375}, {511, 20408}, {1113, 14157}, {1181, 13414}, {1204, 20479}, {1312, 6000}, {1313, 13754}, {1344, 18451}, {1345, 10605}, {1346, 15305}, {1347, 5890}, {5562, 14499}, {10287, 14264}, {10539, 20478}, {11381, 14500}, {14915, 20409}, {18913, 31954}, {21663, 35232}

X(43395) = midpoint of X(4) and X(32616)
X(43395) = reflection of X(1313) in X(32550)
X(43395) = complement of X(32617)

X(43396) = MIDPOINT OF X(4) AND X(32617)

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

X(43396) lies on the cubic K591 and these lines: {2, 32616}, {3, 2575}, {4, 2574}, {5, 113}, {74, 14375}, {110, 14710}, {265, 14374}, {511, 20409}, {1114, 14157}, {1181, 13415}, {1204, 20478}, {1312, 13754}, {1313, 6000}, {1344, 10605}, {1345, 18451}, {1346, 5890}, {1347, 15305}, {5562, 14500}, {10288, 14264}, {10539, 20479}, {11381, 14499}, {14915, 20408}, {18913, 31955}, {21663, 35231}

X(43396) = midpoint of X(4) and X(32617)
X(43396) = reflection of X(1312) in X(32549)
X(43396) = complement of X(32616)

leftri

Gibert points on the cubic K1228: X(43397)-X(43415)

rightri

This preamble and points X(43397)-X(43415) are contributed by Peter Moses, May 16, 2021. See also the preambles just before X(42085), X(42413), and X(42429) and others

See K1228



X(43397) = GIBERT (2,27,-4) POINT

Barycentrics    a^2*S/Sqrt[3] - 2*a^2*SA + 27*SB*SC : :

X(43397) lies on the cubic K1228 and these lines: {4, 11481}, {13, 42104}, {15, 43364}, {382, 42472}, {3543, 42092}, {3830, 42122}, {3853, 42128}, {3861, 42493}, {5076, 42134}, {5334, 15687}, {5335, 42991}, {5343, 43031}, {5366, 43195}, {11486, 12102}, {12101, 42120}, {15682, 42476}, {17578, 42106}, {18582, 41978}, {19107, 22235}, {33602, 42940}, {35401, 37640}, {38335, 42135}, {42093, 42971}, {42101, 42782}, {42102, 42986}, {42105, 43242}, {42133, 42161}, {42137, 42816}, {42141, 42963}

X(43397) = {X(42109),X(42956)}-harmonic conjugate of X(43326)

X(43398) = GIBERT (2,-27,4) POINT

Barycentrics    a^2*S/Sqrt[3] + 2*a^2*SA - 27*SB*SC : :

X(43398) lies on the cubic K1228 and these lines: {4, 11480}, {14, 42105}, {16, 43365}, {382, 42473}, {3543, 42089}, {3830, 42123}, {3853, 42125}, {3861, 42492}, {5076, 42133}, {5334, 42990}, {5335, 15687}, {5344, 43030}, {5365, 43196}, {11485, 12102}, {12101, 42119}, {15682, 42477}, {17578, 42103}, {18581, 41977}, {19106, 22237}, {33603, 42941}, {35401, 37641}, {38335, 42138}, {42094, 42970}, {42101, 42987}, {42102, 42781}, {42104, 43243}, {42134, 42160}, {42136, 42815}, {42140, 42962}

X(43398) = {X(42108),X(42957)}-harmonic conjugate of X(43327)

X(43399) = GIBERT (3,20,-5) POINT

Barycentrics    Sqrt[3]*a^2*S - 5*a^2*SA + 40*SB*SC : :
X(43399) = 11 X[16966] - 14 X[42110], 31 X[16966] - 28 X[43103], 13 X[16966] - 14 X[43104], 32 X[16966] - 35 X[43240], 85 X[16966] - 77 X[43248], 31 X[42110] - 22 X[43103], 13 X[42110] - 11 X[43104], 64 X[42110] - 55 X[43240], 170 X[42110] - 121 X[43248], 26 X[43103] - 31 X[43104], 128 X[43103] - 155 X[43240], 340 X[43103] - 341 X[43248], 64 X[43104] - 65 X[43240], 170 X[43104] - 143 X[43248], 425 X[43240] - 352 X[43248]
X(43399) lies on the cubic K1228 and these lines: {2, 43366}, {4, 5237}, {6, 3830}, {13, 3627}, {14, 42105}, {15, 3543}, {16, 38335}, {17, 43204}, {30, 16966}, {62, 3853}, {376, 43226}, {382, 5238}, {395, 15687}, {546, 42528}, {550, 42596}, {3091, 42597}, {3146, 16241}, {3534, 42915}, {3545, 42429}, {3839, 42100}, {3845, 10646}, {3861, 42591}, {5073, 42488}, {5076, 42155}, {5339, 42965}, {5343, 16965}, {5344, 10654}, {5352, 42430}, {10653, 42897}, {11480, 43372}, {11486, 35401}, {11488, 42515}, {12101, 16809}, {12102, 42158}, {12816, 33604}, {12817, 42118}, {12820, 42138}, {12821, 42159}, {14269, 42918}, {14893, 16242}, {15681, 42919}, {15682, 16808}, {15683, 33417}, {15684, 37832}, {15696, 42474}, {16267, 42094}, {16268, 42690}, {16961, 41972}, {16962, 42108}, {16963, 42141}, {16964, 42909}, {19107, 37640}, {19711, 42498}, {23046, 33416}, {23302, 42504}, {32062, 36979}, {33699, 36967}, {33703, 42911}, {35403, 41944}, {35404, 42099}, {35434, 42154}, {37641, 42629}, {41099, 42113}, {41100, 42101}, {41101, 42134}, {41121, 42096}, {41122, 42086}, {41971, 42988}, {41974, 42975}, {42088, 43203}, {42097, 42631}, {42106, 42529}, {42125, 42977}, {42127, 42800}, {42145, 43025}, {42151, 42893}, {42433, 43101}, {42625, 42937}, {42630, 43228}, {42632, 43024}, {42779, 42799}, {42889, 43310}, {42921, 43199}, {42943, 43227}, {43012, 43244}
on K1228
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5237, 37835, 43373}, {14893, 42109, 16242}, {33699, 42102, 36967}, {37835, 43330, 5237}, {42127, 42972, 42800}, {42800, 43196, 42972}

X(43400) = GIBERT (3,-20,5) POINT

Barycentrics    Sqrt[3]*a^2*S + 5*a^2*SA - 40*SB*SC : :
X(43400) = 11 X[16967] - 14 X[42107], 13 X[16967] - 14 X[43101], 31 X[16967] - 28 X[43102], 32 X[16967] - 35 X[43241], 85 X[16967] - 77 X[43249], 13 X[42107] - 11 X[43101], 31 X[42107] - 22 X[43102], 64 X[42107] - 55 X[43241], 170 X[42107] - 121 X[43249], 31 X[43101] - 26 X[43102], 64 X[43101] - 65 X[43241], 170 X[43101] - 143 X[43249], 128 X[43102] - 155 X[43241], 340 X[43102] - 341 X[43249], 425 X[43241] - 352 X[43249]


X(43400) lies on the cubic K1228 and these lines: {2, 43367}, {4, 5238}, {6, 3830}, {13, 42104}, {14, 3627}, {15, 38335}, {16, 3543}, {18, 43203}, {30, 16967}, {61, 3853}, {376, 43227}, {382, 5237}, {396, 15687}, {546, 42529}, {550, 42597}, {3091, 42596}, {3146, 16242}, {3534, 42914}, {3545, 42430}, {3839, 42099}, {3845, 10645}, {3861, 42590}, {5073, 42489}, {5076, 42154}, {5340, 42964}, {5343, 10653}, {5344, 16964}, {5351, 42429}, {10654, 42896}, {11481, 43373}, {11485, 35401}, {11489, 42514}, {12101, 16808}, {12102, 42157}, {12816, 42117}, {12817, 33605}, {12820, 42162}, {12821, 42135}, {14269, 42919}, {14893, 16241}, {15681, 42918}, {15682, 16809}, {15683, 33416}, {15684, 37835}, {15696, 42475}, {16267, 42691}, {16268, 42093}, {16960, 41971}, {16962, 42140}, {16963, 42109}, {16965, 42908}, {19106, 37641}, {19711, 42499}, {23046, 33417}, {23303, 42505}, {32062, 36981}, {33699, 36968}, {33703, 42910}, {35403, 41943}, {35404, 42100}, {35434, 42155}, {37640, 42630}, {41099, 42112}, {41100, 42133}, {41101, 42102}, {41121, 42085}, {41122, 42097}, {41972, 42989}, {41973, 42974}, {42087, 43204}, {42096, 42632}, {42103, 42528}, {42126, 42799}, {42128, 42976}, {42144, 43024}, {42150, 42892}, {42434, 43104}, {42626, 42936}, {42629, 43229}, {42631, 43025}, {42780, 42800}, {42888, 43311}, {42920, 43200}, {42942, 43226}, {43013, 43245}

X(43400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5238, 37832, 43372}, {14893, 42108, 16241}, {33699, 42101, 36968}, {37832, 43331, 5238}, {42126, 42973, 42799}, {42799, 43195, 42973}

X(43401) = GIBERT (3,7,-4) POINT

Barycentrics    Sqrt[3]*a^2*S - 4*a^2*SA + 14*SB*SC : :
X(43401) = 7 X[13] - 5 X[15], 6 X[13] - 5 X[396], 4 X[13] - 5 X[5318], 11 X[13] - 10 X[11542], 17 X[13] - 15 X[16267], 29 X[13] - 25 X[16960], 19 X[13] - 15 X[16962], X[13] - 5 X[19106], 9 X[13] - 5 X[36967], 3 X[13] - 5 X[36969], 13 X[13] - 5 X[42099], 2 X[13] + 5 X[42109], 17 X[13] - 10 X[42122], 17 X[13] - 5 X[42430], 23 X[13] - 20 X[42496], 23 X[13] - 10 X[42585], 14 X[13] - 25 X[42683], 28 X[13] - 25 X[42777], 7 X[13] - 20 X[42889], 13 X[13] - 10 X[42912], 2 X[13] - 5 X[42941], 8 X[13] - 5 X[42942], 13 X[13] - 15 X[42973], 59 X[13] - 55 X[43010], 51 X[13] - 55 X[43033], 6 X[15] - 7 X[396], 4 X[15] - 7 X[5318], 11 X[15] - 14 X[11542], 17 X[15] - 21 X[16267], 29 X[15] - 35 X[16960], 19 X[15] - 21 X[16962], X[15] - 7 X[19106], 9 X[15] - 7 X[36967], 3 X[15] - 7 X[36969], 10 X[15] - 7 X[42087], 13 X[15] - 7 X[42099], 2 X[15] + 7 X[42109], 17 X[15] - 14 X[42122], 5 X[15] - 14 X[42137], 17 X[15] - 7 X[42430], 23 X[15] - 28 X[42496], 23 X[15] - 14 X[42585], 2 X[15] - 5 X[42683], 4 X[15] - 5 X[42777], X[15] - 4 X[42889], 13 X[15] - 14 X[42912], 2 X[15] - 7 X[42941], 8 X[15] - 7 X[42942], 13 X[15] - 21 X[42973], 59 X[15] - 77 X[43010], 51 X[15] - 77 X[43033], 2 X[396] - 3 X[5318], 11 X[396] - 12 X[11542]

X(43401) lies on the cubic K1228 and these lines: {2, 42097}, {3, 43104}, {4, 16645}, {5, 42501}, {6, 15682}, {13, 15}, {14, 3627}, {16, 15687}, {18, 12102}, {20, 5350}, {376, 42094}, {381, 42088}, {382, 398}, {395, 3830}, {397, 3146}, {524, 35690}, {546, 16242}, {547, 42528}, {548, 42590}, {549, 42100}, {550, 37832}, {1657, 42166}, {3091, 42611}, {3411, 41972}, {3528, 42949}, {3529, 16772}, {3530, 12820}, {3534, 23302}, {3543, 5321}, {3544, 42774}, {3545, 42625}, {3839, 11481}, {3843, 42910}, {3845, 23303}, {3850, 42433}, {3853, 42158}, {3855, 42475}, {3856, 42796}, {3858, 5351}, {3860, 42631}, {3861, 5237}, {5054, 42106}, {5055, 42091}, {5059, 42156}, {5066, 10646}, {5067, 42595}, {5071, 42586}, {5073, 42147}, {5076, 42151}, {5335, 43105}, {5340, 33703}, {5344, 11541}, {5366, 36836}, {8703, 16808}, {10304, 42098}, {10645, 12816}, {10654, 15684}, {11001, 16644}, {11480, 15683}, {11485, 42898}, {11488, 42791}, {11539, 42919}, {11543, 42904}, {11737, 33416}, {11812, 42915}, {12101, 16809}, {12811, 43203}, {12817, 34755}, {14269, 42107}, {14893, 37835}, {14915, 36978}, {15640, 37640}, {15681, 18582}, {15685, 42128}, {15686, 16241}, {15688, 42911}, {15689, 42092}, {15690, 42146}, {15693, 42114}, {15696, 42921}, {15704, 42529}, {15709, 42474}, {15721, 42472}, {16268, 43244}, {16963, 42135}, {16965, 41973}, {16966, 34200}, {16967, 23046}, {17504, 43195}, {17578, 22237}, {17800, 42162}, {18581, 38335}, {19107, 35404}, {19708, 43029}, {33458, 33623}, {33560, 35304}, {33603, 42133}, {33699, 36970}, {35400, 42130}, {35403, 42103}, {36439, 42177}, {36448, 42276}, {36457, 42178}, {36466, 42275}, {38071, 42493}, {41100, 42894}, {41101, 42144}, {41106, 43028}, {41107, 42117}, {41112, 42112}, {41119, 42116}, {41944, 42531}, {41987, 43330}, {42085, 43228}, {42093, 42987}, {42104, 42975}, {42111, 42685}, {42120, 43365}, {42136, 43309}, {42157, 42633}, {42489, 42793}, {42497, 42814}, {42502, 42514}, {42511, 42815}, {42634, 42972}, {42686, 42918}, {42895, 42976}, {42907, 43199}, {42914, 43295}, {42925, 43245}, {42932, 43201}, {42993, 43020}, {43202, 43304}

X(43401) = midpoint of X(42109) and X(42941)
X(43401) = reflection of X(i) in X(j) for these {i,j}: {13, 42137}, {396, 36969}, {5318, 42941}, {42087, 13}, {42099, 42912}, {42430, 42122}, {42585, 42496}, {42777, 42683}, {42941, 19106}, {42942, 5318}
X(43401) = crosspoint of X(13) and X(33603)
X(43401) = crosssum of X(15) and X(42115)
X(43401) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 43193, 42599}, {6, 15682, 43402}, {15, 19106, 42889}, {15, 42683, 5318}, {15, 42889, 42683}, {20, 5350, 42598}, {382, 10653, 42940}, {382, 42165, 398}, {395, 3830, 42101}, {395, 42125, 42503}, {395, 42692, 41120}, {396, 36969, 5318}, {396, 42941, 36969}, {547, 42584, 42528}, {3543, 42141, 42155}, {3543, 42155, 5321}, {3627, 42148, 5349}, {3627, 42431, 42148}, {3830, 42086, 395}, {3839, 11481, 43101}, {3845, 36968, 23303}, {3845, 42145, 36968}, {3853, 42158, 42163}, {5073, 42161, 42147}, {5344, 11541, 43194}, {10304, 42098, 42500}, {10653, 42940, 398}, {10654, 15684, 42108}, {11001, 42134, 16644}, {11481, 43101, 43100}, {14893, 42123, 37835}, {15640, 37640, 42096}, {15684, 42127, 10654}, {15686, 42138, 16241}, {15704, 42813, 42945}, {16267, 42430, 42122}, {19106, 42109, 5318}, {23303, 36968, 42792}, {33699, 42118, 36970}, {36970, 42118, 43229}, {37832, 42429, 550}, {42087, 42137, 5318}, {42099, 42973, 42912}, {42122, 43033, 396}, {42125, 42510, 395}, {42165, 42940, 10653}

X(43402) = GIBERT (3,-7,4) POINT

Barycentrics    Sqrt[3]*a^2*S + 4*a^2*SA - 14*SB*SC : :
X(43402) = 7 X[14] - 5 X[16], 6 X[14] - 5 X[395], 4 X[14] - 5 X[5321], 11 X[14] - 10 X[11543], 17 X[14] - 15 X[16268], 29 X[14] - 25 X[16961], 19 X[14] - 15 X[16963], X[14] - 5 X[19107], 9 X[14] - 5 X[36968], 3 X[14] - 5 X[36970], 13 X[14] - 5 X[42100], 2 X[14] + 5 X[42108], 17 X[14] - 10 X[42123], 17 X[14] - 5 X[42429], 23 X[14] - 20 X[42497], 23 X[14] - 10 X[42584], 14 X[14] - 25 X[42682], 28 X[14] - 25 X[42778], 7 X[14] - 20 X[42888], 13 X[14] - 10 X[42913], 2 X[14] - 5 X[42940], 8 X[14] - 5 X[42943], 13 X[14] - 15 X[42972], 59 X[14] - 55 X[43011], 51 X[14] - 55 X[43032], 6 X[16] - 7 X[395], 4 X[16] - 7 X[5321], 11 X[16] - 14 X[11543], 17 X[16] - 21 X[16268], 29 X[16] - 35 X[16961], 19 X[16] - 21 X[16963], X[16] - 7 X[19107], 9 X[16] - 7 X[36968], 3 X[16] - 7 X[36970], 10 X[16] - 7 X[42088], 13 X[16] - 7 X[42100], 2 X[16] + 7 X[42108], 17 X[16] - 14 X[42123], 5 X[16] - 14 X[42136], 17 X[16] - 7 X[42429], 23 X[16] - 28 X[42497], 23 X[16] - 14 X[42584], 2 X[16] - 5 X[42682], 4 X[16] - 5 X[42778], X[16] - 4 X[42888], 13 X[16] - 14 X[42913], 2 X[16] - 7 X[42940], 8 X[16] - 7 X[42943], 13 X[16] - 21 X[42972], 59 X[16] - 77 X[43011], 51 X[16] - 77 X[43032], 2 X[395] - 3 X[5321], 11 X[395] - 12 X[11543]

X(43402) lies on the cubic K1228 and these lines: {2, 42096}, {3, 43101}, {4, 16644}, {5, 42500}, {6, 15682}, {13, 3627}, {14, 16}, {15, 15687}, {17, 12102}, {20, 5349}, {376, 42093}, {381, 42087}, {382, 397}, {396, 3830}, {398, 3146}, {524, 35694}, {546, 16241}, {547, 42529}, {548, 42591}, {549, 42099}, {550, 37835}, {1657, 42163}, {3091, 42610}, {3412, 41971}, {3528, 42948}, {3529, 16773}, {3530, 12821}, {3534, 23303}, {3543, 5318}, {3544, 42773}, {3545, 42626}, {3839, 11480}, {3843, 42911}, {3845, 23302}, {3850, 42434}, {3853, 42157}, {3855, 42474}, {3856, 42795}, {3858, 5352}, {3860, 42632}, {3861, 5238}, {5054, 42103}, {5055, 42090}, {5059, 42153}, {5066, 10645}, {5067, 42594}, {5071, 42587}, {5073, 42148}, {5076, 42150}, {5334, 43106}, {5339, 33703}, {5343, 11541}, {5365, 36843}, {8703, 16809}, {10304, 42095}, {10646, 12817}, {10653, 15684}, {11001, 16645}, {11481, 15683}, {11486, 42899}, {11489, 42792}, {11539, 42918}, {11542, 42905}, {11737, 33417}, {11812, 42914}, {12101, 16808}, {12811, 43204}, {12816, 34754}, {14269, 42110}, {14893, 37832}, {14915, 36980}, {15640, 37641}, {15681, 18581}, {15685, 42125}, {15686, 16242}, {15688, 42910}, {15689, 42089}, {15690, 42143}, {15693, 42111}, {15696, 42920}, {15704, 42528}, {15709, 42475}, {15721, 42473}, {16267, 43245}, {16962, 42138}, {16964, 41974}, {16966, 23046}, {16967, 34200}, {17504, 43196}, {17578, 22235}, {17800, 42159}, {18582, 38335}, {19106, 35404}, {19708, 43028}, {33459, 33625}, {33561, 35303}, {33602, 42134}, {33699, 36969}, {35400, 42131}, {35403, 42106}, {36439, 42176}, {36448, 42275}, {36457, 42175}, {36466, 42276}, {38071, 42492}, {41100, 42145}, {41101, 42895}, {41106, 43029}, {41108, 42118}, {41113, 42113}, {41120, 42115}, {41943, 42530}, {41987, 43331}, {42086, 43229}, {42094, 42986}, {42105, 42974}, {42114, 42684}, {42119, 43364}, {42137, 43308}, {42158, 42634}, {42488, 42794}, {42496, 42813}, {42503, 42515}, {42510, 42816}, {42633, 42973}, {42687, 42919}, {42894, 42977}, {42906, 43200}, {42915, 43294}, {42924, 43244}, {42933, 43202}, {42992, 43021}, {43201, 43305}

X(43402) = midpoint of X(42108) and X(42940)
X(43402) = reflection of X(i) in X(j) for these {i,j}: {14, 42136}, {395, 36970}, {5321, 42940}, {42088, 14}, {42100, 42913}, {42429, 42123}, {42584, 42497}, {42778, 42682}, {42940, 19107}, {42943, 5321}
X(43402) = crosspoint of X(14) and X(33602)
X(43402) = crosssum of X(16) and X(42116)
X(43402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 43194, 42598}, {6, 15682, 43401}, {16, 19107, 42888}, {16, 42682, 5321}, {16, 42888, 42682}, {20, 5349, 42599}, {382, 10654, 42941}, {382, 42164, 397}, {395, 36970, 5321}, {395, 42940, 36970}, {396, 3830, 42102}, {396, 42128, 42502}, {396, 42693, 41119}, {547, 42585, 42529}, {3543, 42140, 42154}, {3543, 42154, 5318}, {3627, 42147, 5350}, {3627, 42432, 42147}, {3830, 42085, 396}, {3839, 11480, 43104}, {3845, 36967, 23302}, {3845, 42144, 36967}, {3853, 42157, 42166}, {5073, 42160, 42148}, {5343, 11541, 43193}, {10304, 42095, 42501}, {10653, 15684, 42109}, {10654, 42941, 397}, {11001, 42133, 16645}, {11480, 43104, 43107}, {14893, 42122, 37832}, {15640, 37641, 42097}, {15684, 42126, 10653}, {15686, 42135, 16242}, {15704, 42814, 42944}, {16268, 42429, 42123}, {19107, 42108, 5321}, {23302, 36967, 42791}, {33699, 42117, 36969}, {36969, 42117, 43228}, {37835, 42430, 550}, {42088, 42136, 5321}, {42100, 42972, 42913}, {42123, 43032, 395}, {42128, 42511, 396}, {42164, 42941, 10654}

X(43403) = GIBERT (6,5,4) POINT

Barycentrics    Sqrt[3]*a^2*S + 2*a^2*SA + 5*SB*SC : :
X(43403) = 5 X[11488] - 2 X[42116], X[11488] + 2 X[42128], 2 X[11488] + X[42134], 11 X[11488] - 8 X[43197], 5 X[11488] + 3 X[43201], X[42116] + 5 X[42128], 4 X[42116] + 5 X[42134], 11 X[42116] - 20 X[43197], 2 X[42116] + 3 X[43201], 4 X[42128] - X[42134], 11 X[42128] + 4 X[43197], 10 X[42128] - 3 X[43201], 11 X[42134] + 16 X[43197], 5 X[42134] - 6 X[43201], 40 X[43197] + 33 X[43201]

X(43403) lies on the cubic K1228 and these lines: {2, 13}, {3, 5344}, {4, 396}, {5, 37641}, {6, 3545}, {14, 3091}, {15, 3543}, {17, 20}, {18, 15022}, {30, 11488}, {61, 3832}, {62, 5056}, {298, 32816}, {299, 37170}, {303, 32815}, {376, 5318}, {381, 5334}, {395, 5071}, {397, 3090}, {398, 3855}, {546, 5365}, {547, 11486}, {549, 42120}, {617, 31709}, {621, 16634}, {631, 5340}, {634, 33411}, {1131, 3365}, {1132, 3364}, {1656, 42591}, {2043, 31412}, {2044, 42561}, {3146, 36967}, {3412, 42160}, {3522, 42161}, {3523, 16965}, {3524, 23302}, {3525, 42148}, {3528, 42165}, {3529, 16772}, {3533, 36843}, {3534, 42124}, {3544, 42153}, {3830, 42119}, {3839, 10654}, {3843, 42516}, {3845, 11485}, {3854, 42159}, {3856, 43253}, {5054, 42118}, {5055, 11489}, {5059, 5238}, {5066, 42139}, {5067, 22238}, {5068, 40694}, {5070, 42924}, {5072, 42495}, {5079, 43111}, {5321, 41099}, {5350, 33703}, {6564, 42184}, {6565, 42183}, {6770, 7694}, {6773, 11623}, {7486, 42149}, {7620, 9763}, {8703, 42127}, {8981, 18587}, {10109, 42129}, {10299, 43193}, {10303, 42151}, {10304, 16241}, {10646, 15708}, {11001, 11480}, {11481, 15702}, {11539, 42115}, {11543, 19709}, {11737, 42473}, {12100, 42588}, {12816, 15640}, {12817, 42799}, {12820, 42939}, {13966, 18586}, {14269, 42117}, {14893, 42126}, {15681, 42137}, {15682, 42094}, {15683, 19106}, {15684, 42122}, {15687, 42140}, {15689, 42145}, {15692, 36968}, {15693, 42123}, {15695, 42584}, {15697, 42100}, {15698, 42625}, {15701, 43103}, {15703, 42121}, {15705, 42528}, {15709, 43029}, {15710, 43107}, {15717, 42158}, {15719, 42500}, {15721, 33417}, {16268, 42111}, {16960, 36970}, {16962, 42085}, {16963, 42895}, {17538, 42945}, {17578, 42150}, {18581, 42897}, {19107, 42511}, {19708, 33602}, {21735, 42490}, {22113, 40898}, {22237, 42779}, {23249, 36463}, {23259, 36445}, {30472, 32829}, {31693, 40727}, {33560, 34509}, {33604, 42095}, {33607, 41108}, {33699, 42130}, {34200, 42131}, {35400, 42907}, {36437, 42220}, {36439, 42206}, {36455, 42218}, {36457, 42205}, {36765, 41620}, {37835, 42114}, {38071, 42125}, {41101, 43004}, {41106, 42110}, {41113, 42506}, {41120, 42918}, {42096, 42693}, {42108, 42518}, {42136, 42589}, {42244, 42267}, {42245, 42266}, {42433, 42979}, {42475, 42599}, {42513, 43006}, {42532, 43227}, {42798, 43230}, {42919, 43010}, {42952, 43244}, {42978, 43008}, {43000, 43007}, {43013, 43245}, {43243, 43292}

X(43403) = midpoint of X(13) and X(36771)
X(43403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13, 5335}, {5, 42974, 37641}, {6, 3545, 43404}, {13, 16, 41112}, {13, 16966, 41107}, {13, 18582, 2}, {13, 37832, 10653}, {13, 41121, 18582}, {16, 42911, 2}, {17, 42162, 20}, {20, 42162, 5366}, {61, 3832, 5343}, {61, 42921, 3832}, {381, 11542, 37640}, {381, 37640, 5334}, {395, 42098, 5071}, {396, 42940, 22236}, {397, 43104, 16645}, {3091, 22235, 40693}, {3091, 40693, 42999}, {3830, 42817, 42912}, {3830, 42912, 42119}, {3839, 10654, 42133}, {3845, 42496, 11485}, {5066, 42975, 42139}, {5318, 16644, 376}, {5321, 42502, 42777}, {5340, 42598, 631}, {5350, 36836, 33703}, {5352, 36969, 42429}, {5459, 22492, 2}, {10109, 42634, 42129}, {10653, 18582, 37832}, {10653, 37832, 2}, {10654, 16808, 3839}, {11480, 42941, 11001}, {11488, 42128, 42134}, {11542, 42142, 5334}, {16241, 42086, 10304}, {16241, 42973, 42086}, {16267, 16808, 10654}, {16645, 43104, 3090}, {18582, 41112, 42911}, {18582, 41119, 13}, {22236, 43332, 396}, {23302, 42155, 3524}, {36968, 42092, 15692}, {37640, 42142, 381}, {37641, 42974, 42998}, {41112, 42911, 16}, {41119, 41121, 2}, {42094, 42942, 15682}, {42138, 42817, 42119}, {42138, 42912, 3830}, {42146, 42815, 11489}, {42149, 42581, 7486}, {42151, 42488, 10303}, {42152, 42813, 3146}, {42156, 42166, 4}, {42165, 43238, 3528}, {42775, 42988, 5365}

X(43404) = GIBERT (-6,5,4) POINT

Barycentrics    Sqrt[3]*a^2*S - 2*a^2*SA - 5*SB*SC : :
X(43404) = 5 X[11489] - 2 X[42115], X[11489] + 2 X[42125], 2 X[11489] + X[42133], 11 X[11489] - 8 X[43198], 5 X[11489] + 3 X[43202], X[42115] + 5 X[42125], 4 X[42115] + 5 X[42133], 11 X[42115] - 20 X[43198], 2 X[42115] + 3 X[43202], 4 X[42125] - X[42133], 11 X[42125] + 4 X[43198], 10 X[42125] - 3 X[43202], 11 X[42133] + 16 X[43198], 5 X[42133] - 6 X[43202], 40 X[43198] + 33 X[43202]

X(43404) lies on the cubic K1228 and these lines: {2, 14}, {3, 5343}, {4, 395}, {5, 37640}, {6, 3545}, {13, 3091}, {16, 3543}, {17, 15022}, {18, 20}, {30, 11489}, {61, 5056}, {62, 3832}, {298, 37171}, {299, 32816}, {302, 32815}, {376, 5321}, {381, 5335}, {396, 5071}, {397, 3855}, {398, 3090}, {546, 5366}, {547, 11485}, {549, 42119}, {616, 31710}, {622, 16635}, {631, 5339}, {633, 33410}, {1131, 3390}, {1132, 3389}, {1656, 42590}, {2043, 42561}, {2044, 31412}, {3146, 36968}, {3411, 42161}, {3522, 42160}, {3523, 16964}, {3524, 23303}, {3525, 42147}, {3528, 42164}, {3529, 16773}, {3533, 36836}, {3534, 42121}, {3544, 42156}, {3830, 42120}, {3839, 10653}, {3843, 42517}, {3845, 11486}, {3854, 42162}, {5054, 42117}, {5055, 11488}, {5059, 5237}, {5066, 42142}, {5067, 22236}, {5068, 40693}, {5070, 42925}, {5072, 42494}, {5079, 43110}, {5318, 41099}, {5349, 33703}, {6564, 42186}, {6565, 42185}, {6770, 11623}, {6773, 7694}, {7486, 42152}, {7620, 9761}, {8703, 42126}, {8981, 18586}, {10109, 42132}, {10299, 43194}, {10303, 42150}, {10304, 16242}, {10645, 15708}, {11001, 11481}, {11480, 15702}, {11539, 42116}, {11542, 19709}, {11737, 42472}, {12100, 42589}, {12816, 42800}, {12817, 15640}, {12821, 42938}, {13966, 18587}, {14269, 42118}, {14893, 42127}, {15681, 42136}, {15682, 42093}, {15683, 19107}, {15684, 42123}, {15687, 42141}, {15689, 42144}, {15692, 36967}, {15693, 42122}, {15695, 42585}, {15697, 42099}, {15698, 42626}, {15701, 43102}, {15703, 42124}, {15705, 42529}, {15709, 43028}, {15710, 43100}, {15717, 42157}, {15719, 42501}, {15721, 33416}, {16267, 42114}, {16808, 43252}, {16961, 36969}, {16962, 42894}, {16963, 42086}, {17538, 42944}, {17578, 42151}, {18582, 42896}, {19106, 42510}, {19708, 33603}, {21735, 42491}, {22114, 40899}, {22235, 42780}, {23249, 36445}, {23259, 36463}, {30471, 32829}, {31694, 40727}, {33561, 34508}, {33605, 42098}, {33606, 41107}, {33699, 42131}, {34200, 42130}, {35400, 42906}, {36437, 42217}, {36439, 42203}, {36455, 42219}, {36457, 42204}, {37832, 42111}, {38071, 42128}, {41100, 43005}, {41106, 42107}, {41112, 42507}, {41119, 42919}, {42097, 42692}, {42109, 42519}, {42137, 42588}, {42242, 42267}, {42243, 42266}, {42434, 42978}, {42474, 42598}, {42512, 43007}, {42533, 43226}, {42797, 43231}, {42918, 43011}, {42953, 43245}, {42979, 43009}, {43001, 43006}, {43012, 43244}, {43242, 43293}

X(43404) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14, 5334}, {5, 42975, 37640}, {6, 3545, 43403}, {14, 15, 41113}, {14, 16967, 41108}, {14, 18581, 2}, {14, 37835, 10654}, {14, 41122, 18581}, {15, 42910, 2}, {18, 42159, 20}, {20, 42159, 5365}, {62, 3832, 5344}, {62, 42920, 3832}, {381, 11543, 37641}, {381, 37641, 5335}, {395, 42941, 22238}, {396, 42095, 5071}, {398, 43101, 16644}, {3091, 22237, 40694}, {3091, 40694, 42998}, {3830, 42818, 42913}, {3830, 42913, 42120}, {3839, 10653, 42134}, {3845, 42497, 11486}, {5066, 42974, 42142}, {5318, 42503, 42778}, {5321, 16645, 376}, {5339, 42599, 631}, {5349, 36843, 33703}, {5351, 36970, 42430}, {5460, 22491, 2}, {10109, 42633, 42132}, {10653, 16809, 3839}, {10654, 18581, 37835}, {10654, 37835, 2}, {11481, 42940, 11001}, {11489, 42125, 42133}, {11543, 42139, 5335}, {16242, 42085, 10304}, {16242, 42972, 42085}, {16268, 16809, 10653}, {16644, 43101, 3090}, {18581, 41113, 42910}, {18581, 41120, 14}, {22238, 43333, 395}, {23303, 42154, 3524}, {36967, 42089, 15692}, {37640, 42975, 42999}, {37641, 42139, 381}, {41113, 42910, 15}, {41120, 41122, 2}, {42093, 42943, 15682}, {42135, 42818, 42120}, {42135, 42913, 3830}, {42143, 42816, 11488}, {42149, 42814, 3146}, {42150, 42489, 10303}, {42152, 42580, 7486}, {42153, 42163, 4}, {42164, 43239, 3528}, {42776, 42989, 5366}

X(43405) = GIBERT (2 SQRT(3),27,-6) POINT

Barycentrics    a^2*S - 3*a^2*SA + 27*SB*SC : :

X(43405) lies on the cubic K1228 and these lines: {4, 5420}, {30, 43312}, {382, 32785}, {590, 3543}, {1131, 6459}, {3069, 15687}, {3146, 6411}, {3627, 6221}, {3830, 18512}, {3853, 19116}, {5076, 6395}, {6398, 12102}, {6435, 22615}, {6438, 42561}, {6469, 42272}, {6491, 13941}, {6560, 14226}, {7586, 42283}, {12819, 35820}, {13939, 42574}, {13961, 42226}, {15682, 42277}, {18538, 42413}, {18762, 38335}, {35401, 43317}, {35812, 42275}, {41962, 42264}, {42219, 42963}, {42220, 42962}, {42225, 42575}, {42263, 43383}, {43210, 43318}

X(43405) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32786, 42637, 43315}, {42183, 42185, 42267}, {43336, 43375, 42637}

X(43406) = GIBERT (2 SQRT(3),-27,6) POINT

Barycentrics    a^2*S + 3*a^2*SA - 27*SB*SC : :

X(43406) lies on the cubic K1228 and these lines: {4, 5418}, {30, 43313}, {382, 32786}, {615, 3543}, {1132, 6460}, {3068, 15687}, {3146, 6412}, {3627, 6398}, {3830, 18510}, {3853, 19117}, {5076, 6199}, {6221, 12102}, {6436, 22644}, {6437, 31412}, {6468, 42271}, {6490, 8972}, {6561, 14241}, {7585, 42284}, {9541, 12101}, {12818, 35821}, {13886, 42575}, {13903, 42225}, {15682, 42274}, {18538, 38335}, {18762, 42414}, {35401, 43316}, {35813, 42276}, {41961, 42263}, {42217, 42963}, {42218, 42962}, {42226, 42574}, {42264, 43382}, {43209, 43319}

X(43406) = {X(42184),X(42186)}-harmonic conjugate of X(42266)

X(43407) = GIBERT (2 SQRT(3),3,-4) POINT

Barycentrics    a^2*S - 2*a^2*SA + 3*SB*SC : :
X(43407) = 3 X[1588] - 4 X[3312], 5 X[1588] - 6 X[19053], 7 X[1588] - 8 X[19116], X[1588] + 2 X[42414], 17 X[1588] - 6 X[42537], X[1588] - 3 X[43256], 2 X[3312] - 3 X[6460], 10 X[3312] - 9 X[19053], 7 X[3312] - 6 X[19116], 2 X[3312] + 3 X[42414], 34 X[3312] - 9 X[42537], 4 X[3312] - 9 X[43256], 5 X[6460] - 3 X[19053], 7 X[6460] - 4 X[19116], 17 X[6460] - 3 X[42537], 2 X[6460] - 3 X[43256], 21 X[19053] - 20 X[19116], 3 X[19053] + 5 X[42414], 17 X[19053] - 5 X[42537], 2 X[19053] - 5 X[43256], 4 X[19116] + 7 X[42414], 68 X[19116] - 21 X[42537], 8 X[19116] - 21 X[43256], 17 X[42414] + 3 X[42537], 2 X[42414] + 3 X[43256], 2 X[42537] - 17 X[43256]

X(43407) lies on the cubic K1228 and these lines: {2, 12818}, {3, 18538}, {4, 615}, {5, 6456}, {6, 3529}, {13, 42257}, {14, 42256}, {20, 371}, {30, 1588}, {372, 3146}, {376, 3070}, {382, 3069}, {485, 3522}, {486, 3543}, {487, 8591}, {546, 6450}, {548, 6496}, {550, 3068}, {590, 3528}, {631, 23251}, {632, 6497}, {637, 26288}, {1131, 5418}, {1132, 42541}, {1151, 17538}, {1327, 15692}, {1328, 35814}, {1657, 6417}, {1703, 28164}, {2794, 5870}, {3071, 33703}, {3090, 6410}, {3091, 6396}, {3311, 15704}, {3316, 19708}, {3365, 35732}, {3371, 42730}, {3372, 42729}, {3390, 42085}, {3523, 6564}, {3524, 42265}, {3525, 6412}, {3534, 6407}, {3544, 32790}, {3594, 11541}, {3627, 6398}, {3628, 6452}, {3830, 13966}, {3832, 5420}, {3839, 10577}, {3843, 35256}, {3853, 13951}, {3855, 8252}, {4302, 31408}, {5056, 35786}, {5059, 6561}, {5073, 7584}, {5076, 6408}, {5265, 35802}, {5281, 35800}, {6200, 43336}, {6221, 12103}, {6418, 42225}, {6420, 42275}, {6426, 13939}, {6431, 7581}, {6435, 43337}, {6451, 13925}, {6454, 13941}, {6475, 13961}, {6478, 9543}, {6484, 35822}, {6501, 17800}, {6522, 12102}, {6565, 17578}, {7582, 41955}, {7586, 35821}, {7692, 35944}, {8253, 10299}, {8703, 8976}, {8972, 43314}, {8981, 15696}, {9542, 35815}, {10138, 38335}, {10140, 42576}, {10303, 42277}, {10576, 15717}, {12297, 13873}, {12323, 35948}, {13903, 15689}, {13959, 22793}, {13980, 18405}, {15640, 35823}, {15681, 19054}, {15682, 23261}, {15683, 42266}, {15684, 42538}, {15705, 42602}, {18992, 28150}, {19065, 28160}, {21735, 41950}, {22467, 35776}, {23275, 32788}, {29181, 39875}, {32787, 41969}, {35404, 42571}, {35738, 42205}, {35739, 42189}, {35777, 37945}, {41982, 42639}, {42087, 42252}, {42088, 42253}, {42164, 42193}, {42165, 42194}, {42237, 42489}, {42238, 42488}, {42254, 42891}, {42255, 42890}, {43210, 43384}, {43211, 43340}

X(43407) = midpoint of X(6460) and X(42414)
X(43407) = reflection of X(1588) in X(6460)
X(43407) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 35820, 23253}, {6, 3529, 43408}, {20, 1587, 9541}, {20, 6560, 1587}, {20, 7585, 42260}, {372, 3146, 23259}, {372, 42276, 3146}, {376, 3070, 9540}, {376, 13886, 6409}, {382, 3069, 23263}, {546, 6450, 32786}, {1131, 10304, 5418}, {1152, 42264, 42272}, {1152, 42272, 4}, {1588, 43256, 6460}, {1657, 42216, 6459}, {3070, 6409, 13886}, {3528, 23269, 590}, {3594, 42271, 23273}, {3627, 6398, 42561}, {5076, 6408, 18762}, {6396, 22644, 3091}, {6409, 13886, 9540}, {6410, 42284, 3090}, {6412, 42273, 3525}, {6426, 42283, 13939}, {6454, 42268, 13941}, {6560, 42267, 20}, {7581, 11001, 42258}, {11541, 23273, 42271}, {17538, 23267, 1151}, {17800, 42215, 42413}, {35820, 42261, 2}, {42219, 42220, 42226}, {42239, 42241, 42264}, {42259, 42264, 4}, {42259, 42272, 1152}

X(43408) = GIBERT (2 SQRT(3),-3,4) POINT

Barycentrics    a^2*S + 2*a^2*SA - 3*SB*SC : :
X(43408) = 3 X[1587] - 4 X[3311], 5 X[1587] - 6 X[19054], 7 X[1587] - 8 X[19117], X[1587] + 2 X[42413], 17 X[1587] - 6 X[42538], X[1587] - 3 X[43257], 2 X[3311] - 3 X[6459], 10 X[3311] - 9 X[19054], 7 X[3311] - 6 X[19117], 2 X[3311] + 3 X[42413], 34 X[3311] - 9 X[42538], 4 X[3311] - 9 X[43257], 5 X[6459] - 3 X[19054], 7 X[6459] - 4 X[19117], 17 X[6459] - 3 X[42538], 2 X[6459] - 3 X[43257], 21 X[19054] - 20 X[19117], 3 X[19054] + 5 X[42413], 17 X[19054] - 5 X[42538], 2 X[19054] - 5 X[43257], 4 X[19117] + 7 X[42413], 68 X[19117] - 21 X[42538], 8 X[19117] - 21 X[43257], 17 X[42413] + 3 X[42538], 2 X[42413] + 3 X[43257], 2 X[42538] - 17 X[43257]

X(43408) lies on the cubic K1228 and these lines: {2, 12819}, {3, 18762}, {4, 590}, {5, 6455}, {6, 3529}, {13, 42255}, {14, 42254}, {20, 372}, {30, 1587}, {371, 3146}, {376, 3071}, {382, 3068}, {388, 9660}, {485, 3543}, {486, 3522}, {488, 8591}, {497, 9647}, {546, 6449}, {548, 6497}, {550, 3069}, {615, 3528}, {631, 23261}, {632, 6496}, {638, 26289}, {1131, 42542}, {1132, 5420}, {1152, 17538}, {1327, 35815}, {1328, 15692}, {1657, 6418}, {1702, 28164}, {2794, 5871}, {3070, 33703}, {3090, 6409}, {3091, 6200}, {3312, 15704}, {3317, 19708}, {3364, 42086}, {3385, 42730}, {3386, 42729}, {3389, 35732}, {3523, 6565}, {3524, 42262}, {3525, 6411}, {3534, 6408}, {3544, 32789}, {3592, 11541}, {3627, 6221}, {3628, 6451}, {3830, 8981}, {3832, 5418}, {3839, 10576}, {3843, 35255}, {3853, 8976}, {3855, 8253}, {5056, 35787}, {5059, 6560}, {5073, 7583}, {5076, 6407}, {5265, 35803}, {5281, 35801}, {6396, 43337}, {6398, 12103}, {6417, 42226}, {6419, 42276}, {6425, 13886}, {6432, 7582}, {6436, 43336}, {6452, 13993}, {6453, 8972}, {6474, 13903}, {6485, 35823}, {6500, 17800}, {6519, 12102}, {6564, 9681}, {7581, 41956}, {7585, 35820}, {7690, 35945}, {7747, 31403}, {8252, 10299}, {8703, 13951}, {8991, 18405}, {9542, 35812}, {9543, 35786}, {9582, 19925}, {9615, 18483}, {9616, 31673}, {9649, 13898}, {9662, 13897}, {9683, 14118}, {10137, 38335}, {10139, 42577}, {10303, 42274}, {10483, 31408}, {10577, 15717}, {12296, 13926}, {12322, 35949}, {13902, 22793}, {13941, 43315}, {13961, 15689}, {13966, 15696}, {15640, 35822}, {15681, 19053}, {15682, 23251}, {15683, 42267}, {15684, 42537}, {15705, 42603}, {18991, 28150}, {19066, 28160}, {21735, 41949}, {22467, 35777}, {23269, 32787}, {29181, 39876}, {32788, 41970}, {35404, 42570}, {35738, 42204}, {35739, 42247}, {35776, 37945}, {41982, 42640}, {42087, 42250}, {42088, 42251}, {42164, 42191}, {42165, 42192}, {42235, 42489}, {42236, 42488}, {42256, 42891}, {42257, 42890}, {43209, 43385}, {43212, 43341}

X(43408) = midpoint of X(6459) and X(42413)
X(43408) = reflection of X(1587) in X(6459)
X(43408) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 35821, 23263}, {4, 9541, 9540}, {4, 42258, 9541}, {6, 3529, 43407}, {20, 6561, 1588}, {20, 7586, 42261}, {371, 3146, 23249}, {371, 42275, 3146}, {376, 3071, 13935}, {376, 13939, 6410}, {382, 3068, 23253}, {546, 6449, 32785}, {1132, 10304, 5420}, {1151, 42263, 42271}, {1151, 42271, 4}, {1587, 43257, 6459}, {1657, 42215, 6460}, {3071, 6410, 13939}, {3528, 23275, 615}, {3534, 7584, 42637}, {3592, 42272, 23267}, {3627, 6221, 31412}, {5076, 6407, 18538}, {6200, 22615, 3091}, {6409, 42283, 3090}, {6410, 13939, 13935}, {6411, 42270, 3525}, {6425, 42284, 13886}, {6453, 42269, 8972}, {6561, 42266, 20}, {7582, 11001, 42259}, {11541, 23267, 42272}, {17538, 23273, 1152}, {17800, 42216, 42414}, {35740, 42240, 42263}, {35821, 42260, 2}, {42217, 42218, 42225}, {42258, 42263, 4}, {42258, 42271, 1151}

X(43409) = GIBERT (9 SQRT(3),11,12) POINT

Barycentrics    9*a^2*S + 12*a^2*SA + 22*SB*SC : :

X(43409) lies on the Evans conic, the cubic K1228, and these lines: {3, 41952}, {4, 6425}, {5, 41951}, {13, 42252}, {14, 42253}, {140, 41946}, {371, 41957}, {372, 41966}, {485, 615}, {550, 590}, {1152, 43376}, {1587, 43375}, {1588, 42578}, {1657, 41967}, {3070, 3523}, {3071, 3850}, {3524, 42606}, {3533, 6430}, {3590, 5059}, {3592, 3854}, {3843, 42417}, {3851, 32787}, {5056, 19053}, {5068, 7585}, {5073, 6445}, {5418, 41948}, {6472, 42269}, {6476, 8981}, {6564, 41961}, {7583, 41949}, {10195, 13665}, {10303, 42418}, {10576, 41964}, {14813, 41944}, {14814, 41943}, {15688, 42608}, {21735, 41950}, {32788, 35018}, {32789, 41970}, {32790, 42644}, {33923, 43209}, {35812, 42639}, {35822, 41968}, {41954, 42259}, {41955, 42273}, {41959, 42258}, {41960, 42216}, {42270, 43341}, {42572, 42602}, {43211, 43380}

X(43409) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3070, 42566, 42637}, {6412, 42570, 3070}, {42561, 42604, 42265}

X(43410) = GIBERT (-9 SQRT(3),11,12) POINT

Barycentrics    9*a^2*S - 12*a^2*SA - 22*SB*SC : :

X(43410) lies on the Evans conic, the cubic K1228, and these lines: {3, 41951}, {4, 6426}, {5, 41952}, {13, 42250}, {14, 42251}, {140, 41945}, {371, 41965}, {372, 41958}, {486, 590}, {550, 615}, {1151, 43377}, {1587, 42579}, {1588, 43374}, {1657, 41968}, {3070, 3850}, {3071, 3523}, {3524, 42607}, {3533, 6429}, {3591, 5059}, {3594, 3854}, {3843, 42418}, {3851, 32788}, {5056, 19054}, {5068, 7586}, {5073, 6446}, {5420, 41947}, {6473, 42268}, {6477, 13966}, {6565, 41962}, {7584, 41950}, {8960, 41948}, {9690, 32790}, {10194, 13785}, {10303, 42417}, {10577, 41963}, {14813, 41943}, {14814, 41944}, {15688, 42609}, {21735, 41949}, {32787, 35018}, {32789, 42643}, {33923, 43210}, {35813, 42640}, {35823, 41967}, {41953, 42258}, {41956, 42270}, {41959, 42215}, {41960, 42259}, {42273, 43340}, {42573, 42603}, {43212, 43381}


X(43410) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6411, 42571, 3071}, {31412, 42605, 42262}

X(43411) = GIBERT (18 SQRT(3),13,6) POINT

Barycentrics    9*a^2*S + 3*a^2*SA + 13*SB*SC : :

X(43411) lies on the cubic K1228 and these lines: {4, 1327}, {140, 6522}, {485, 3533}, {550, 3068}, {590, 3523}, {1152, 3590}, {1587, 1656}, {3070, 5059}, {3591, 6432}, {3594, 42572}, {3850, 13665}, {3851, 19053}, {3854, 42573}, {5056, 13847}, {5068, 7586}, {5073, 7583}, {6420, 14241}, {6469, 41948}, {6473, 43316}, {7581, 42570}, {8960, 21735}, {23263, 43313}, {32787, 42641}

X(43411) = {X(35822),X(43342)}-harmonic conjugate of X(43386)

X(43412) = GIBERT (-18 SQRT(3),13,6) POINT

Barycentrics    9*a^2*S - 3*a^2*SA - 13*SB*SC : :

X(43412) lies on the cubic K1228 and these lines: {4, 1328}, {20, 17852}, {140, 6519}, {486, 3533}, {550, 3069}, {615, 3523}, {1151, 3591}, {1588, 1656}, {3071, 5059}, {3590, 6431}, {3592, 42573}, {3850, 13785}, {3851, 19054}, {3854, 42572}, {3858, 31414}, {5056, 13846}, {5068, 7585}, {5073, 7584}, {6419, 14226}, {6468, 41947}, {6472, 43317}, {7582, 42571}, {17851, 42413}, {21735, 23273}, {23253, 43312}, {32788, 42642}

X(43412) = {X(35823),X(43343)}-harmonic conjugate of X(43387)

X(43413) = GIBERT (18 SQRT(3),5,30) POINT

Barycentrics    9*a^2*S + 15*a^2*SA + 5*SB*SC : :

X(43413) lies on the cubic K1228 and these lines: {4, 6453}, {6, 3523}, {20, 10147}, {371, 3317}, {550, 3068}, {1131, 1151}, {1327, 6482}, {1656, 9540}, {3522, 31454}, {3590, 9543}, {3850, 6221}, {3854, 41945}, {5056, 6425}, {5068, 6459}, {5073, 8981}, {6445, 42414}, {6454, 9680}, {6460, 21735}, {6470, 42541}, {6480, 42413}, {8960, 23269}, {9542, 31412}, {9692, 13846}, {10148, 15692}, {13961, 35255}, {15720, 19053}, {23275, 32785}

X(43413) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8981, 9690, 23253}, {41963, 41964, 42568}

X(43414) = GIBERT (-18 SQRT(3),5,30) POINT

Barycentrics    9*a^2*S - 15*a^2*SA - 5*SB*SC : :

X(43414) lies on the cubic K1228 and these lines: {4, 6454}, {6, 3523}, {20, 10148}, {372, 3316}, {550, 3069}, {1132, 1152}, {1328, 6483}, {1656, 13935}, {3543, 17852}, {3591, 41949}, {3850, 6398}, {3854, 41946}, {5056, 6426}, {5068, 6460}, {5073, 13966}, {6446, 42413}, {6448, 31414}, {6453, 10299}, {6459, 21735}, {6471, 42542}, {6481, 42414}, {10147, 15692}, {13903, 35256}, {15720, 19054}, {23269, 32786}, {23275, 42275}

X(43414) = {X(41963),X(41964)}-harmonic conjugate of X(42569)

X(43415) = GIBERT (-8 SQRT(3),0,15) POINT

Barycentrics    8*a^2*S - 15*a^2*SA : :

X(43415) lies on these lines: {3, 6}, {5, 34091}, {382, 13941}, {399, 10818}, {615, 14269}, {1656, 23269}, {1657, 23275}, {3068, 15707}, {3069, 15681}, {3526, 23267}, {3534, 23273}, {3830, 18762}, {3843, 13935}, {3851, 23253}, {5055, 23249}, {5070, 6460}, {5072, 43382}, {5073, 13966}, {5343, 42208}, {5344, 42210}, {5349, 42173}, {5350, 42171}, {6560, 19709}, {7582, 43383}, {7585, 15700}, {7586, 15688}, {8252, 43319}, {8972, 15720}, {9542, 15711}, {11834, 38593}, {12108, 43374}, {13785, 15685}, {13943, 37949}, {13951, 42276}, {13961, 17800}, {14996, 21575}, {14997, 21572}, {15684, 41951}, {15689, 18510}, {15694, 42216}, {15695, 42215}, {15701, 18512}, {15703, 41946}, {18538, 42570}, {21557, 37687}, {21570, 37680}, {21577, 37633}, {32789, 41970}, {33923, 42523}, {35403, 42264}, {35813, 43338}, {41960, 41965}, {41964, 42274}, {42183, 42205}, {42185, 42203}, {42225, 42637}, {42524, 43385}, {42601, 42608}

X(43415) = Brocard-circle-inverse of X(9690)
X(43415) = Schoute-circle-inverse of X(6430)
X(43415) = Lucas(-1)-secondary-radical-circle-inverse of X(6567)
X(43415) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 9690}, {3, 372, 6501}, {3, 6475, 372}, {3, 6501, 9691}, {3, 10145, 6496}, {3, 10146, 6408}, {3, 17851, 6398}, {6, 6449, 6199}, {6, 6454, 6398}, {6, 6469, 6491}, {15, 16, 6430}, {372, 6396, 6411}, {372, 6425, 3312}, {372, 6434, 6452}, {372, 6452, 6199}, {372, 6480, 6442}, {372, 6483, 1152}, {1152, 6398, 6446}, {1152, 6408, 3}, {1152, 6426, 6485}, {1152, 6440, 6481}, {1152, 6454, 6450}, {1152, 6469, 6396}, {1152, 6481, 6398}, {1152, 6522, 6408}, {1152, 10138, 10146}, {1152, 10140, 371}, {1152, 17852, 372}, {3312, 6412, 6445}, {3594, 6487, 6497}, {3594, 6497, 6407}, {6199, 6445, 6425}, {6199, 6452, 3}, {6199, 17852, 17851}, {6221, 6398, 6438}, {6221, 6435, 6199}, {6221, 6438, 6395}, {6395, 6396, 3}, {6395, 6446, 6396}, {6396, 6398, 6395}, {6396, 6411, 6452}, {6396, 6438, 6221}, {6396, 6469, 6398}, {6396, 6477, 6438}, {6396, 6481, 6469}, {6398, 6408, 17851}, {6398, 6434, 6199}, {6398, 6446, 3}, {6398, 6450, 6}, {6398, 6451, 6448}, {6398, 6452, 372}, {6398, 6481, 6408}, {6398, 6522, 6481}, {6407, 6497, 3}, {6408, 6446, 6398}, {6408, 6450, 6473}, {6408, 6522, 10146}, {6408, 10138, 6522}, {6410, 6417, 3}, {6410, 6448, 6417}, {6411, 6434, 6396}, {6411, 6435, 6221}, {6412, 6445, 3}, {6418, 6456, 3}, {6425, 6430, 6493}, {6425, 6493, 372}, {6426, 6431, 372}, {6426, 6456, 6418}, {6426, 6485, 6456}, {6427, 6480, 6199}, {6438, 6469, 6477}, {6438, 6477, 6398}, {6440, 6446, 10146}, {6440, 6481, 6522}, {6442, 6480, 6427}, {6445, 6472, 9690}, {6446, 6473, 9690}, {6446, 6481, 17851}, {6450, 6491, 6395}, {6469, 6491, 6454}, {6481, 6483, 6434}, {11485, 11486, 6432}

leftri

Gibert points on the cubic K1229: X(43416)-X(43439)

rightri

This preamble and points X(43416)-X(43439) are contributed by Peter Moses, May 17, 2021. See also the preambles just before X(42085), X(42413), and X(42429) and others

See K1229



X(43416) = GIBERT (6,5,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S + a^2*SA + 10*SB*SC : :
X(43416) = 5 X[13] - X[15], 3 X[13] - X[396], 7 X[13] - 3 X[16267], 13 X[13] - 5 X[16960], 11 X[13] - 3 X[16962], 7 X[13] + X[19106], 9 X[13] - X[36967], 3 X[13] + X[36969], 11 X[13] - X[42087], 17 X[13] - X[42099], 13 X[13] + X[42109], 8 X[13] - X[42122], 4 X[13] + X[42137], 25 X[13] - X[42430], 5 X[13] - 2 X[42496], 14 X[13] - X[42585], 17 X[13] + 5 X[42683], 11 X[13] - 5 X[42777], 11 X[13] + 2 X[42889], 4 X[13] - X[42912], 5 X[13] + X[42941], 7 X[13] - X[42942], X[13] + 3 X[42973], 19 X[13] - 11 X[43010], 3 X[13] - 11 X[43033], 9 X[13] + X[43401], 3 X[15] - 5 X[396], X[15] + 5 X[5318], 2 X[15] - 5 X[11542], 7 X[15] - 15 X[16267], 13 X[15] - 25 X[16960], 11 X[15] - 15 X[16962], 7 X[15] + 5 X[19106], 9 X[15] - 5 X[36967], 3 X[15] + 5 X[36969], 11 X[15] - 5 X[42087], 17 X[15] - 5 X[42099], 13 X[15] + 5 X[42109], 8 X[15] - 5 X[42122], 4 X[15] + 5 X[42137], 5 X[15] - X[42430], 14 X[15] - 5 X[42585], 17 X[15] + 25 X[42683], 11 X[15] - 25 X[42777], 11 X[15] + 10 X[42889], 4 X[15] - 5 X[42912], 7 X[15] - 5 X[42942], X[15] + 15 X[42973], 19 X[15] - 55 X[43010], 3 X[15] - 55 X[43033], 9 X[15] + 5 X[43401], X[298] - 3 X[31693], X[396] + 3 X[5318], 2 X[396] - 3 X[11542], 7 X[396] - 9 X[16267]

X(43416) lies on the cubic K1229 and these lines: {2, 33602}, {3, 5344}, {4, 42974}, {5, 5340}, {6, 1327}, {13, 15}, {14, 397}, {16, 547}, {17, 548}, {18, 12811}, {61, 3853}, {62, 3850}, {140, 5351}, {298, 31683}, {376, 42124}, {381, 5335}, {382, 5366}, {395, 5066}, {398, 3861}, {530, 625}, {549, 18582}, {550, 42156}, {622, 37352}, {631, 42590}, {632, 42151}, {1503, 5478}, {2043, 8976}, {2044, 13951}, {3068, 36466}, {3069, 36448}, {3146, 42988}, {3524, 42132}, {3525, 42926}, {3526, 42494}, {3529, 22235}, {3530, 42158}, {3534, 11488}, {3543, 11485}, {3545, 11486}, {3627, 40693}, {3628, 16242}, {3643, 7914}, {3830, 37640}, {3839, 42135}, {3843, 42998}, {3855, 42989}, {3856, 42163}, {3857, 42153}, {3858, 40694}, {3859, 42778}, {3860, 16809}, {5054, 42120}, {5055, 42121}, {5072, 42775}, {5237, 16239}, {5238, 42429}, {5321, 14893}, {5334, 14269}, {6108, 20252}, {6459, 18587}, {6460, 18586}, {6671, 35019}, {7583, 42243}, {7584, 42242}, {8355, 12155}, {8703, 16644}, {8739, 37984}, {10109, 23303}, {10124, 16966}, {10304, 42131}, {10645, 15690}, {10646, 11812}, {10654, 15687}, {11001, 42116}, {11296, 32815}, {11480, 15686}, {11481, 11539}, {11489, 19709}, {11540, 42792}, {11623, 41023}, {11737, 37835}, {12100, 23302}, {12101, 12816}, {12102, 16964}, {12103, 16772}, {12108, 42488}, {12817, 43030}, {12820, 42779}, {14891, 42528}, {14892, 16963}, {15681, 42141}, {15682, 42144}, {15684, 42119}, {15691, 41943}, {15693, 42588}, {15698, 42689}, {15699, 42098}, {15704, 42152}, {15712, 43193}, {15713, 43029}, {16241, 34200}, {16268, 42107}, {16773, 35018}, {17504, 42092}, {18581, 38071}, {19710, 42097}, {21310, 35469}, {22796, 41620}, {23046, 42106}, {33417, 43106}, {33607, 42632}, {33699, 42085}, {34551, 42245}, {34552, 42244}, {34754, 42506}, {35404, 42105}, {35731, 42241}, {36437, 42214}, {36445, 42211}, {36455, 42212}, {36463, 42213}, {36836, 43332}, {38335, 42907}, {41099, 42125}, {41101, 42895}, {41108, 42101}, {41972, 42937}, {41982, 43199}, {41983, 42500}, {41986, 42893}, {41987, 42905}, {41991, 42920}, {42090, 42916}, {42096, 42511}, {42114, 42510}, {42126, 42982}, {42129, 42804}, {42130, 42986}, {42147, 42992}, {42415, 42781}, {42416, 43100}, {42433, 42965}, {42473, 42517}, {42499, 42505}, {42502, 42629}, {42503, 42521}, {42512, 43238}, {42580, 42935}, {42581, 42944}, {42682, 43334}, {42692, 43031}, {42791, 42900}, {42799, 43014}, {42888, 42898}, {42891, 42960}, {42914, 43198}, {42972, 43226}, {43195, 43232}, {43207, 43399}, {43236, 43366}

X(43416) = midpoint of X(i) and X(j) for these {i,j}: {13, 5318}, {15, 42941}, {396, 36969}, {19106, 42942}, {36967, 43401}, {42137, 42912}
X(43416) = reflection of X(i) in X(j) for these {i,j}: {15, 42496}, {6671, 35019}, {11542, 13}, {42122, 42912}, {42585, 42942}, {42912, 11542}
X(43416) = crosspoint of X(13) and X(12816)
X(43416) = crosssum of X(15) and X(10645)
X(43416) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 10653, 42913}, {6, 3845, 43417}, {13, 19106, 16267}, {13, 36969, 396}, {13, 42941, 42496}, {13, 42973, 5318}, {17, 42165, 548}, {61, 5350, 3853}, {395, 5066, 42143}, {395, 16808, 5066}, {396, 5318, 36969}, {396, 43401, 36967}, {397, 42813, 546}, {549, 42155, 42123}, {3627, 40693, 42925}, {3627, 42633, 42154}, {3830, 37640, 42117}, {3830, 42815, 37640}, {3839, 42975, 42135}, {5318, 11542, 42137}, {5335, 42138, 11543}, {5340, 42162, 5}, {10653, 42910, 22238}, {10653, 42913, 42924}, {10653, 42921, 42910}, {10654, 15687, 42136}, {10654, 42094, 15687}, {11481, 42911, 11539}, {11542, 42137, 42122}, {12816, 36970, 42102}, {12816, 43228, 12101}, {14892, 42628, 43101}, {16241, 42088, 34200}, {16242, 43104, 3628}, {16267, 19106, 42942}, {16267, 42585, 42912}, {16644, 42086, 8703}, {16772, 42431, 12103}, {16773, 35018, 42591}, {16808, 41107, 395}, {16963, 42919, 43101}, {16963, 43101, 42628}, {16965, 37832, 42943}, {16965, 42166, 140}, {18582, 42123, 43103}, {18582, 42155, 549}, {22238, 42921, 5}, {23302, 36968, 12100}, {34200, 42627, 16241}, {36967, 36969, 43401}, {36968, 41121, 23302}, {36970, 42102, 12101}, {37640, 42134, 3830}, {37832, 42943, 140}, {37835, 42110, 11737}, {38071, 42634, 18581}, {38071, 42922, 42634}, {40693, 42154, 42633}, {41119, 42086, 16644}, {42087, 42777, 16962}, {42092, 42625, 17504}, {42102, 43228, 36970}, {42118, 42128, 42146}, {42124, 42127, 42584}, {42134, 42815, 42117}, {42148, 43104, 16242}, {42154, 42633, 42925}, {42156, 42161, 550}, {42158, 42598, 3530}, {42166, 42943, 37832}, {42919, 43101, 14892}, {42973, 43033, 396}

X(43417) = GIBERT (-6,5,1) POINT

Barycentrics    2*Sqrt[3]*a^2*S - a^2*SA - 10*SB*SC : :
X(43417) = 5 X[14] - X[16], 3 X[14] - X[395], 7 X[14] - 3 X[16268], 13 X[14] - 5 X[16961], 11 X[14] - 3 X[16963], 7 X[14] + X[19107], 9 X[14] - X[36968], 3 X[14] + X[36970], 11 X[14] - X[42088], 17 X[14] - X[42100], 13 X[14] + X[42108], 8 X[14] - X[42123], 4 X[14] + X[42136], 25 X[14] - X[42429], 5 X[14] - 2 X[42497], 14 X[14] - X[42584], 17 X[14] + 5 X[42682], 11 X[14] - 5 X[42778], 11 X[14] + 2 X[42888], 4 X[14] - X[42913], 5 X[14] + X[42940], 7 X[14] - X[42943], X[14] + 3 X[42972], 19 X[14] - 11 X[43011], 3 X[14] - 11 X[43032], 9 X[14] + X[43402], 3 X[16] - 5 X[395], X[16] + 5 X[5321], 2 X[16] - 5 X[11543], 7 X[16] - 15 X[16268], 13 X[16] - 25 X[16961], 11 X[16] - 15 X[16963], 7 X[16] + 5 X[19107], 9 X[16] - 5 X[36968], 3 X[16] + 5 X[36970], 11 X[16] - 5 X[42088], 17 X[16] - 5 X[42100], 13 X[16] + 5 X[42108], 8 X[16] - 5 X[42123], 4 X[16] + 5 X[42136], 5 X[16] - X[42429], 14 X[16] - 5 X[42584], 17 X[16] + 25 X[42682], 11 X[16] - 25 X[42778], 11 X[16] + 10 X[42888], 4 X[16] - 5 X[42913], 7 X[16] - 5 X[42943], X[16] + 15 X[42972], 19 X[16] - 55 X[43011], 3 X[16] - 55 X[43032], 9 X[16] + 5 X[43402], X[299] - 3 X[31694], X[395] + 3 X[5321], 2 X[395] - 3 X[11543], 7 X[395] - 9 X[16268], 13 X[395] - 15 X[16961], 11 X[395] - 9 X[16963], 7 X[395] + 3 X[19107], 3 X[395] - X[36968], 11 X[395] - 3 X[42088], 17 X[395] - 3 X[42100], 13 X[395] + 3 X[42108], 8 X[395] - 3 X[42123], 4 X[395] + 3 X[42136], 25 X[395] - 3 X[42429], 5 X[395] - 6 X[42497], 14

X(43417) lies on the cubic K1229 and these lines: {2, 33603}, {3, 5343}, {4, 42975}, {5, 5339}, {6, 1327}, {13, 398}, {14, 16}, {15, 547}, {17, 12811}, {18, 548}, {61, 3850}, {62, 3853}, {140, 5352}, {299, 31684}, {376, 42121}, {381, 5334}, {382, 5365}, {396, 5066}, {397, 3861}, {531, 625}, {549, 18581}, {550, 42153}, {621, 37351}, {631, 42591}, {632, 42150}, {1503, 5479}, {2043, 13951}, {2044, 8976}, {3068, 36448}, {3069, 36466}, {3146, 42989}, {3524, 42129}, {3525, 42927}, {3526, 42495}, {3529, 22237}, {3530, 42157}, {3534, 11489}, {3543, 11486}, {3545, 11485}, {3627, 40694}, {3628, 16241}, {3642, 7914}, {3830, 37641}, {3839, 42138}, {3843, 42999}, {3855, 42988}, {3856, 42166}, {3857, 42156}, {3858, 40693}, {3859, 42777}, {3860, 16808}, {5054, 42119}, {5055, 42124}, {5072, 42776}, {5237, 42430}, {5238, 16239}, {5318, 14893}, {5335, 14269}, {6109, 20253}, {6459, 18586}, {6460, 18587}, {6672, 35020}, {7583, 42245}, {7584, 42244}, {8355, 12154}, {8703, 16645}, {8740, 37984}, {10109, 23302}, {10124, 16967}, {10304, 42130}, {10645, 11812}, {10646, 15690}, {10653, 15687}, {11001, 42115}, {11295, 32815}, {11480, 11539}, {11481, 15686}, {11488, 19709}, {11540, 42791}, {11623, 41022}, {11737, 37832}, {12100, 23303}, {12101, 12817}, {12102, 16965}, {12103, 16773}, {12108, 42489}, {12816, 43031}, {12821, 42780}, {14891, 42529}, {14892, 16962}, {15681, 42140}, {15682, 42145}, {15684, 42120}, {15691, 41944}, {15693, 42589}, {15698, 42688}, {15699, 42095}, {15704, 42149}, {15712, 43194}, {15713, 43028}, {16242, 34200}, {16267, 42110}, {16772, 35018}, {17504, 42089}, {18582, 38071}, {19710, 42096}, {21311, 35470}, {22797, 41621}, {23046, 42103}, {33416, 43105}, {33606, 42631}, {33699, 42086}, {34551, 42242}, {34552, 42243}, {34755, 42507}, {35404, 42104}, {36437, 42211}, {36445, 42214}, {36455, 42213}, {36463, 42212}, {36843, 43333}, {38335, 42906}, {41099, 42128}, {41100, 42894}, {41107, 42102}, {41971, 42936}, {41982, 43200}, {41983, 42501}, {41986, 42892}, {41987, 42904}, {41991, 42921}, {42091, 42917}, {42097, 42510}, {42111, 42511}, {42127, 42983}, {42131, 42987}, {42132, 42803}, {42148, 42993}, {42415, 43107}, {42416, 42782}, {42434, 42964}, {42472, 42516}, {42498, 42504}, {42502, 42520}, {42503, 42630}, {42513, 43239}, {42580, 42945}, {42581, 42934}, {42683, 43335}, {42693, 43030}, {42792, 42901}, {42800, 43015}, {42889, 42899}, {42890, 42961}, {42915, 43197}, {42973, 43227}, {43196, 43233}, {43208, 43400}, {43237, 43367}

X(43417) = midpoint of X(i) and X(j) for these {i,j}: {14, 5321}, {16, 42940}, {395, 36970}, {19107, 42943}, {36968, 43402}, {42136, 42913}
X(43417) = reflection of X(i) in X(j) for these {i,j}: {16, 42497}, {6672, 35020}, {11543, 14}, {42123, 42913}, {42584, 42943}, {42913, 11543}
X(43417) = crosspoint of X(14) and X(12817)
X(43417) = crosssum of X(16) and X(10646)
X(43417) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 10654, 42912}, {6, 3845, 43416}, {14, 19107, 16268}, {14, 36970, 395}, {14, 42940, 42497}, {14, 42972, 5321}, {18, 42164, 548}, {62, 5349, 3853}, {395, 5321, 36970}, {395, 43402, 36968}, {396, 5066, 42146}, {396, 16809, 5066}, {398, 42814, 546}, {549, 42154, 42122}, {3627, 40694, 42924}, {3627, 42634, 42155}, {3830, 37641, 42118}, {3830, 42816, 37641}, {3839, 42974, 42138}, {5321, 11543, 42136}, {5334, 42135, 11542}, {5339, 42159, 5}, {10653, 15687, 42137}, {10653, 42093, 15687}, {10654, 42911, 22236}, {10654, 42912, 42925}, {10654, 42920, 42911}, {11480, 42910, 11539}, {11543, 42136, 42123}, {12817, 36969, 42101}, {12817, 43229, 12101}, {14892, 42627, 43104}, {16241, 43101, 3628}, {16242, 42087, 34200}, {16268, 19107, 42943}, {16268, 42584, 42913}, {16645, 42085, 8703}, {16772, 35018, 42590}, {16773, 42432, 12103}, {16809, 41108, 396}, {16962, 42918, 43104}, {16962, 43104, 42627}, {16964, 37835, 42942}, {16964, 42163, 140}, {18581, 42122, 43102}, {18581, 42154, 549}, {22236, 42920, 5}, {23303, 36967, 12100}, {34200, 42628, 16242}, {36967, 41122, 23303}, {36968, 36970, 43402}, {36969, 42101, 12101}, {37641, 42133, 3830}, {37832, 42107, 11737}, {37835, 42942, 140}, {38071, 42633, 18582}, {38071, 42923, 42633}, {40694, 42155, 42634}, {41120, 42085, 16645}, {42088, 42778, 16963}, {42089, 42626, 17504}, {42101, 43229, 36969}, {42117, 42125, 42143}, {42121, 42126, 42585}, {42133, 42816, 42118}, {42147, 43101, 16241}, {42153, 42160, 550}, {42155, 42634, 42924}, {42157, 42599, 3530}, {42163, 42942, 37835}, {42918, 43104, 14892}, {42972, 43032, 395}

X(43418) = GIBERT (15,8,1) POINT

Barycentrics    5*Sqrt[3]*a^2*S + a^2*SA + 16*SB*SC : :
X(43418) = 5 X[34754] + 4 X[42629], 5 X[34754] - 6 X[42635], 2 X[42629] + 3 X[42635]

X(43418) lies on the cubic K1229 and these lines: {2, 13}, {3, 43000}, {4, 12820}, {6, 14269}, {14, 397}, {15, 15681}, {17, 3530}, {18, 3544}, {30, 34754}, {61, 382}, {62, 3851}, {376, 16960}, {395, 11737}, {396, 550}, {398, 43253}, {631, 42797}, {1656, 42935}, {1657, 42965}, {3090, 43200}, {3146, 43245}, {3411, 42921}, {3412, 42165}, {3523, 42512}, {3528, 42158}, {3529, 36967}, {3627, 42934}, {3850, 42778}, {3853, 42964}, {3855, 37641}, {5055, 34755}, {5066, 16961}, {5079, 16645}, {5318, 15687}, {5321, 12816}, {5334, 43251}, {5339, 42613}, {5344, 16964}, {5350, 42991}, {5351, 15720}, {8703, 42777}, {10645, 15688}, {10646, 15707}, {10654, 42630}, {11485, 41971}, {11488, 15710}, {11541, 42890}, {11542, 34200}, {12100, 33607}, {14869, 42148}, {15690, 42795}, {15700, 16644}, {15703, 42691}, {15706, 43300}, {15708, 42955}, {15715, 42120}, {15716, 42518}, {16241, 17504}, {16268, 16808}, {16772, 42798}, {16962, 42086}, {16963, 42914}, {16967, 42922}, {19106, 37640}, {19107, 42799}, {19709, 42953}, {22235, 43013}, {23046, 42693}, {33417, 42416}, {33602, 41120}, {33699, 42520}, {33703, 42516}, {33923, 42891}, {35018, 42166}, {35404, 42683}, {36843, 41972}, {37835, 42128}, {38335, 43366}, {41101, 42941}, {41106, 42521}, {41108, 42094}, {41113, 43227}, {41944, 42098}, {41973, 42940}, {41983, 42685}, {41987, 42692}, {42085, 42900}, {42088, 42496}, {42095, 42903}, {42099, 42982}, {42100, 42506}, {42105, 42896}, {42108, 42415}, {42109, 42898}, {42110, 42634}, {42119, 42532}, {42123, 43004}, {42126, 43399}, {42129, 42977}, {42134, 43030}, {42135, 42905}, {42137, 43014}, {42138, 43229}, {42139, 42507}, {42141, 42430}, {42149, 43020}, {42150, 43331}, {42153, 43233}, {42157, 42633}, {42164, 42995}, {42434, 42802}, {42475, 42994}, {42502, 42627}, {42581, 42924}, {42584, 42791}, {42592, 42774}, {42599, 43008}, {42625, 42817}, {42626, 42988}, {42781, 42942}, {42782, 42897}, {42801, 43025}, {42918, 43006}, {42975, 43250}, {42989, 43016}, {43193, 43332}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14269, 43419}, {13, 16, 41121}, {13, 5335, 41107}, {13, 10653, 37832}, {13, 16242, 43403}, {13, 16966, 41119}, {13, 41100, 18582}, {13, 41107, 16}, {17, 3530, 42947}, {382, 42779, 61}, {396, 5238, 42892}, {550, 42939, 5238}, {5335, 41112, 13}, {5340, 42974, 36969}, {5351, 42156, 42979}, {10653, 37832, 16}, {10653, 43403, 16242}, {11542, 36968, 41943}, {16242, 43403, 37832}, {16267, 42155, 10645}, {16965, 42992, 5238}, {19107, 43228, 42799}, {34200, 43106, 36968}, {36969, 42974, 61}, {36970, 43195, 15687}, {37832, 41107, 10653}, {41974, 42156, 5351}, {42100, 42506, 42912}, {42100, 42912, 42632}, {42141, 42511, 42430}, {42155, 42815, 16267}, {42612, 42813, 42780}, {42633, 43401, 42157}, {42780, 42813, 546}, {43007, 43400, 16964}

X(43419) = GIBERT (-15,8,1) POINT

Barycentrics    5*Sqrt[3]*a^2*S - a^2*SA - 16*SB*SC : :
X(43419) = 5 X[34755] + 4 X[42630], 5 X[34755] - 6 X[42636], 2 X[42630] + 3 X[42636]

X(43419) lies on the cubic K1229 and these lines: {2, 14}, {3, 43001}, {4, 12821}, {6, 14269}, {13, 398}, {16, 15681}, {17, 3544}, {18, 3530}, {30, 34755}, {61, 3851}, {62, 382}, {376, 16961}, {395, 550}, {396, 11737}, {631, 42798}, {1656, 42934}, {1657, 42964}, {3090, 43199}, {3146, 43244}, {3411, 42164}, {3412, 42920}, {3523, 42513}, {3528, 42157}, {3529, 36968}, {3627, 42935}, {3850, 42777}, {3853, 42965}, {3855, 37640}, {5055, 34754}, {5066, 16960}, {5079, 16644}, {5318, 12817}, {5321, 15687}, {5335, 43250}, {5340, 42612}, {5343, 16965}, {5349, 42990}, {5352, 15720}, {8703, 42778}, {10645, 15707}, {10646, 15688}, {10653, 42629}, {11486, 41972}, {11489, 15710}, {11541, 42891}, {11543, 34200}, {12100, 33606}, {14869, 42147}, {15690, 42796}, {15700, 16645}, {15703, 42690}, {15706, 43301}, {15708, 42954}, {15715, 42119}, {15716, 42519}, {16242, 17504}, {16267, 16809}, {16773, 42797}, {16962, 42915}, {16963, 42085}, {16966, 42923}, {19106, 42800}, {19107, 37641}, {19709, 42952}, {22237, 43012}, {23046, 42692}, {33416, 42415}, {33603, 41119}, {33699, 42521}, {33703, 42517}, {33923, 42890}, {35018, 42163}, {35404, 42682}, {36836, 41971}, {37832, 42125}, {38335, 43367}, {41100, 42940}, {41106, 42520}, {41107, 42093}, {41112, 43226}, {41943, 42095}, {41974, 42941}, {41983, 42684}, {41987, 42693}, {42086, 42901}, {42087, 42497}, {42098, 42902}, {42099, 42507}, {42100, 42983}, {42104, 42897}, {42107, 42633}, {42108, 42899}, {42109, 42416}, {42120, 42533}, {42122, 43005}, {42127, 43400}, {42132, 42976}, {42133, 43031}, {42135, 43228}, {42136, 43015}, {42138, 42904}, {42140, 42429}, {42142, 42506}, {42151, 43330}, {42152, 43021}, {42156, 43232}, {42158, 42634}, {42165, 42994}, {42433, 42801}, {42474, 42995}, {42503, 42628}, {42580, 42925}, {42585, 42792}, {42593, 42773}, {42598, 43009}, {42625, 42989}, {42626, 42818}, {42781, 42896}, {42782, 42943}, {42802, 43024}, {42919, 43007}, {42974, 43251}, {42988, 43017}, {43194, 43333}

X(43419) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 14269, 43418}, {14, 15, 41122}, {14, 5334, 41108}, {14, 10654, 37835}, {14, 16241, 43404}, {14, 16967, 41120}, {14, 41101, 18581}, {14, 41108, 15}, {18, 3530, 42946}, {382, 42780, 62}, {395, 5237, 42893}, {550, 42938, 5237}, {5334, 41113, 14}, {5339, 42975, 36970}, {5352, 42153, 42978}, {10654, 37835, 15}, {10654, 43404, 16241}, {11543, 36967, 41944}, {16241, 43404, 37835}, {16268, 42154, 10646}, {16964, 42993, 5237}, {19106, 43229, 42800}, {34200, 43105, 36967}, {36969, 43196, 15687}, {36970, 42975, 62}, {37835, 41108, 10654}, {41973, 42153, 5352}, {42099, 42507, 42913}, {42099, 42913, 42631}, {42140, 42510, 42429}, {42154, 42816, 16268}, {42613, 42814, 42779}, {42634, 43402, 42158}, {42779, 42814, 546}, {43006, 43399, 16965}

X(43420) = GIBERT (21,4,-28) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 28*a^2*SA + 8*SB*SC : :
X(43420) = 4 X[43329] - 5 X[43333]

X(43420) lies on the cubic K1229 and these lines: {3, 42800}, {4, 16645}, {6, 8703}, {13, 5054}, {16, 15681}, {30, 43329}, {396, 15692}, {547, 42089}, {632, 42151}, {3530, 10653}, {3859, 42910}, {3860, 42086}, {5070, 5237}, {5079, 16242}, {11486, 42799}, {11540, 42118}, {11542, 43304}, {12103, 42154}, {12811, 43239}, {12816, 43371}, {12817, 36968}, {15696, 22238}, {15719, 16644}, {19709, 36969}, {21358, 36769}, {21734, 36836}, {22235, 42148}, {22236, 43008}, {22237, 42940}, {23302, 42508}, {33603, 43402}, {35381, 43033}, {35401, 41944}, {35404, 42123}, {37640, 42685}, {37641, 42087}, {37832, 42958}, {38071, 42137}, {41973, 43331}, {41987, 42121}, {42097, 43198}, {42110, 42477}, {42128, 43295}, {42160, 42913}, {42165, 42475}, {42430, 43335}, {42473, 42941}, {42529, 43009}, {42586, 43404}, {42588, 42933}, {42774, 43403}, {42804, 43228}, {42816, 43325}, {42938, 43017}, {43229, 43243}, {43330, 43400}

X(43420) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 42931, 5054}, {3530, 10653, 43332}, {16645, 43193, 43401}

X(43421) = GIBERT (21,-4,28) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 28*a^2*SA - 8*SB*SC : :
X(43421) = 4 X[43328] - 5 X[43332]

X(43421) lies on the cubic K1229 and these lines: {3, 42799}, {4, 16644}, {6, 8703}, {14, 5054}, {15, 15681}, {30, 43328}, {395, 15692}, {547, 42092}, {632, 42150}, {3530, 10654}, {3859, 42911}, {3860, 42085}, {5070, 5238}, {5079, 16241}, {11485, 42800}, {11540, 42117}, {11543, 43305}, {12103, 42155}, {12811, 43238}, {12816, 36967}, {12817, 43370}, {15696, 22236}, {15719, 16645}, {19709, 36970}, {21734, 36843}, {22235, 42941}, {22237, 42147}, {22238, 43009}, {23303, 42509}, {33602, 43401}, {35381, 43032}, {35401, 41943}, {35404, 42122}, {37640, 42088}, {37641, 42684}, {37835, 42959}, {38071, 42136}, {41974, 43330}, {41987, 42124}, {42096, 43197}, {42107, 42476}, {42125, 43294}, {42161, 42912}, {42164, 42474}, {42429, 43334}, {42472, 42940}, {42528, 43008}, {42587, 43403}, {42589, 42932}, {42773, 43404}, {42803, 43229}, {42815, 43324}, {42939, 43016}, {43228, 43242}, {43331, 43399}

X(43421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 42930, 5054}, {3530, 10654, 43333}, {16644, 43194, 43402}

X(43422) = GIBERT (27,22,6) POINT

Barycentrics    9*Sqrt[3]*a^2*S + 6*a^2*SA + 44*SB*SC : :

X(43422) lies on the cubic K1229 and these lines: {4, 33602}, {13, 5073}, {14, 43033}, {16, 1656}, {17, 42930}, {20, 42502}, {397, 42776}, {398, 43364}, {550, 42156}, {1657, 42632}, {3411, 3851}, {3523, 42155}, {3533, 42166}, {3850, 42153}, {3858, 41112}, {5059, 5318}, {5068, 42599}, {5072, 42994}, {5339, 43226}, {5344, 21735}, {5366, 42096}, {10188, 16965}, {16644, 42959}, {16966, 42981}, {33923, 41119}, {36969, 43000}, {41973, 42815}, {41978, 42817}, {42094, 42630}, {42095, 42922}, {42127, 43326}, {42152, 43328}, {42154, 42992}, {42475, 42935}, {42494, 43242}, {42625, 42979}, {42909, 42988}

X(43422) = {X(5340),X(42128)}-harmonic conjugate of X(43239)

X(43423) = GIBERT (-27,22,6) POINT

Barycentrics    9*Sqrt[3]*a^2*S - 6*a^2*SA - 44*SB*SC : :

X(43423) lies on the cubic K1229 and these lines: {4, 33603}, {13, 43032}, {14, 5073}, {15, 1656}, {18, 42931}, {20, 42503}, {397, 43365}, {398, 42775}, {550, 42153}, {1657, 42631}, {3412, 3851}, {3523, 42154}, {3533, 42163}, {3850, 42156}, {3858, 41113}, {5059, 5321}, {5068, 42598}, {5072, 42995}, {5340, 43227}, {5343, 21735}, {5365, 42097}, {10187, 16964}, {16645, 42958}, {16967, 42980}, {33923, 41120}, {36970, 43001}, {41974, 42816}, {41977, 42818}, {42093, 42629}, {42098, 42923}, {42126, 43327}, {42149, 43329}, {42155, 42993}, {42474, 42934}, {42495, 43243}, {42626, 42978}, {42908, 42989}

X(43423) = {X(5339),X(42125)}-harmonic conjugate of X(43238)

X(43424) = GIBERT (27,20,3) POINT

Barycentrics    9*Sqrt[3]*a^2*S + 3*a^2*SA + 40*SB*SC : :

X(43424) lies on the cubic K1229 and these lines: {4, 12816}, {13, 550}, {15, 5059}, {16, 1656}, {17, 21735}, {61, 43399}, {62, 3850}, {140, 42792}, {397, 42135}, {1657, 16267}, {3523, 16965}, {3533, 5237}, {3830, 42995}, {3851, 41107}, {3854, 41122}, {3858, 42990}, {5068, 37835}, {5072, 42977}, {5073, 22236}, {5238, 43332}, {5318, 42432}, {5334, 43292}, {5335, 22237}, {5351, 42960}, {10188, 42943}, {10299, 41119}, {10646, 42949}, {10653, 42978}, {12817, 43253}, {15720, 41121}, {16645, 42966}, {16963, 33602}, {22235, 42100}, {33703, 42506}, {34755, 42921}, {35018, 41100}, {37832, 42958}, {41973, 42779}, {41991, 42507}, {42094, 42901}, {42112, 43022}, {42116, 42431}, {42141, 42927}, {42150, 42895}, {42151, 43300}, {42155, 42979}, {42156, 42965}, {42161, 42429}, {42166, 43033}, {42801, 42919}, {42802, 42900}, {42813, 42993}, {42918, 43019}, {42946, 42985}

X(43424) = {X(3851),X(41107)}-harmonic conjugate of X(42994)

X(43425) = GIBERT (-27,20,3) POINT

Barycentrics    9*Sqrt[3]*a^2*S - 3*a^2*SA - 40*SB*SC : :

X(43425) lies on the cubic K1229 and these lines: {4, 12817}, {14, 550}, {15, 1656}, {16, 5059}, {18, 21735}, {61, 3850}, {62, 43400}, {140, 42791}, {398, 42138}, {1657, 16268}, {3523, 16964}, {3533, 5238}, {3830, 42994}, {3851, 41108}, {3854, 41121}, {3858, 42991}, {5068, 37832}, {5072, 42976}, {5073, 22238}, {5237, 43333}, {5321, 42431}, {5334, 22235}, {5335, 43293}, {5352, 42961}, {10187, 42942}, {10299, 41120}, {10645, 42948}, {10654, 42979}, {15720, 41122}, {16644, 42967}, {16962, 33603}, {22237, 42099}, {33703, 42507}, {34754, 42920}, {35018, 41101}, {37835, 42959}, {41974, 42780}, {41991, 42506}, {42093, 42900}, {42113, 43023}, {42115, 42432}, {42140, 42926}, {42150, 43301}, {42151, 42894}, {42153, 42964}, {42154, 42978}, {42160, 42430}, {42163, 43032}, {42801, 42901}, {42802, 42918}, {42814, 42992}, {42919, 43018}, {42947, 42984}, {43247, 43253}

X(43425) = {X(3851),X(41108)}-harmonic conjugate of X(42995)

X(43426) = GIBERT (27,10,15) POINT

Barycentrics    9*Sqrt[3]*a^2*S + 15*a^2*SA + 20*SB*SC : :

X(43426) lies on the cubic K1229 and these lines: {3, 42504}, {4, 3412}, {6, 17}, {13, 5073}, {14, 5068}, {15, 5059}, {61, 3850}, {62, 3533}, {396, 550}, {397, 42685}, {631, 42505}, {632, 42533}, {1657, 16962}, {3523, 5237}, {3627, 42976}, {3843, 42532}, {3851, 42991}, {3854, 41108}, {3858, 41121}, {3861, 42502}, {5056, 42952}, {5318, 42802}, {5321, 43018}, {5343, 42103}, {5349, 16808}, {5350, 11542}, {5352, 43244}, {10187, 42488}, {11307, 36366}, {11309, 36386}, {11488, 42779}, {11489, 42530}, {12821, 16964}, {15712, 41943}, {15720, 42990}, {16644, 42596}, {18582, 42776}, {21735, 41974}, {22235, 42432}, {22236, 43245}, {22238, 43199}, {33417, 42998}, {33923, 41107}, {35018, 43228}, {37640, 42581}, {41944, 42480}, {41971, 42777}, {42086, 43334}, {42092, 43295}, {42105, 43016}, {42147, 43400}, {42148, 42959}, {42150, 42909}, {42162, 43399}, {42163, 43232}, {42431, 42895}, {42634, 42979}, {42801, 42954}, {42908, 42925}, {43030, 43239}

X(43426) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17, 43014, 18}, {18, 42817, 17}, {16960, 42988, 17}, {41121, 42995, 3858}

X(43427) = GIBERT (-27,10,15) POINT

Barycentrics    9*Sqrt[3]*a^2*S - 15*a^2*SA - 20*SB*SC : :

X(43427) lies on the cubic K1229 and these lines: {3, 42505}, {4, 3411}, {6, 17}, {13, 5068}, {14, 5073}, {16, 5059}, {61, 3533}, {62, 3850}, {395, 550}, {398, 42684}, {631, 42504}, {632, 42532}, {1657, 16963}, {3523, 5238}, {3627, 42977}, {3843, 42533}, {3851, 42990}, {3854, 41107}, {3858, 41122}, {3861, 42503}, {5056, 42953}, {5318, 43019}, {5321, 42801}, {5344, 42106}, {5349, 11543}, {5350, 16809}, {5351, 43245}, {10188, 42489}, {11308, 36368}, {11310, 36388}, {11488, 42531}, {11489, 42780}, {12820, 16965}, {15712, 41944}, {15720, 42991}, {16645, 42597}, {18581, 42775}, {21735, 41973}, {22236, 43200}, {22237, 42431}, {22238, 43244}, {33416, 42999}, {33923, 41108}, {35018, 43229}, {37641, 42580}, {41943, 42481}, {41972, 42778}, {42085, 43335}, {42089, 43294}, {42104, 43017}, {42147, 42958}, {42148, 43399}, {42151, 42908}, {42159, 43400}, {42166, 43233}, {42432, 42894}, {42633, 42978}, {42802, 42955}, {42909, 42924}, {43031, 43238}

X(43427) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17, 42818, 18}, {18, 43015, 17}, {16961, 42989, 18}, {41122, 42994, 3858}

X(43428) = GIBERT (39,10,26) POINT

Barycentrics    13*Sqrt[3]*a^2*S + 26*a^2*SA + 20*SB*SC : :

X(43428) lies on the cubic K1229 and these lines: {4, 396}, {6, 11539}, {13, 43327}, {16, 15693}, {3412, 16242}, {5340, 42429}, {5352, 42974}, {10109, 41120}, {10653, 34200}, {12108, 42152}, {15689, 16962}, {15701, 42896}, {15703, 16644}, {15721, 37640}, {16267, 42096}, {16645, 42593}, {19710, 41112}, {37641, 42949}, {37832, 42125}, {41121, 43196}, {42091, 43306}, {42153, 42633}, {42165, 42927}, {42507, 42984}, {42516, 42598}, {42610, 42778}, {42626, 42988}, {42802, 43194}, {42817, 42976}, {42892, 42966}, {42932, 42943}, {42979, 43012}, {43028, 43370}

X(43428) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {396, 22236, 43332}, {22236, 43403, 42154}, {42154, 43332, 43403}, {42627, 43247, 42911}

X(43429) = GIBERT (-39,10,26) POINT

Barycentrics    13*Sqrt[3]*a^2*S - 26*a^2*SA - 20*SB*SC : :

X(43429) lies on the cubic K1229 and these lines: {4, 395}, {6, 11539}, {14, 43326}, {15, 15693}, {3411, 16241}, {5339, 42430}, {5351, 42975}, {10109, 41119}, {10654, 34200}, {12108, 42149}, {15689, 16963}, {15701, 42897}, {15703, 16645}, {15721, 37641}, {16268, 42097}, {16644, 42592}, {19710, 41113}, {37640, 42948}, {37835, 42128}, {41122, 43195}, {42090, 43307}, {42156, 42634}, {42164, 42926}, {42506, 42985}, {42517, 42599}, {42611, 42777}, {42625, 42989}, {42801, 43193}, {42818, 42977}, {42893, 42967}, {42933, 42942}, {42978, 43013}, {43029, 43371}

X(43429) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {395, 22238, 43333}, {22238, 43404, 42155}, {42155, 43333, 43404}, {42628, 43246, 42910}

X(43430) = GIBERT (5 SQRT(3),3,5) POINT

Barycentrics    5*a^2*S + 5*a^2*SA + 6*SB*SC : :
X(43430) = 5 X[6429] - 3 X[43339], 5 X[6429] + 6 X[43340], X[43339] + 2 X[43340]

X(43430) lies on the cubic K1229 and these lines: {2, 35770}, {4, 371}, {5, 6431}, {6, 3628}, {20, 6484}, {30, 6429}, {193, 6118}, {230, 19103}, {372, 8972}, {395, 42257}, {396, 42256}, {486, 5055}, {490, 22485}, {548, 6409}, {549, 1152}, {590, 3312}, {615, 6501}, {632, 6432}, {1131, 6478}, {1151, 15704}, {1327, 15684}, {1504, 13711}, {1506, 19104}, {1587, 15717}, {1588, 43343}, {2045, 42779}, {2046, 42780}, {3070, 3534}, {3071, 31487}, {3090, 35771}, {3311, 5072}, {3316, 10577}, {3523, 6487}, {3529, 6480}, {3543, 12818}, {3592, 3857}, {3627, 6437}, {3845, 42642}, {3856, 42215}, {5066, 6470}, {5067, 42558}, {6199, 42273}, {6200, 43336}, {6221, 22644}, {6407, 13665}, {6418, 32789}, {6419, 15022}, {6420, 32785}, {6423, 13651}, {6425, 42275}, {6426, 43315}, {6427, 42583}, {6428, 32790}, {6430, 12108}, {6433, 12103}, {6438, 14869}, {6447, 42271}, {6453, 23249}, {6456, 18512}, {6460, 15698}, {6486, 17538}, {6496, 42259}, {7486, 7585}, {7581, 15709}, {7586, 10194}, {8253, 19117}, {8703, 42568}, {8983, 13607}, {9540, 10304}, {9541, 42540}, {9542, 43376}, {9681, 23251}, {9682, 15750}, {12007, 13910}, {12102, 42643}, {14890, 43322}, {15681, 42572}, {15683, 35820}, {18586, 42778}, {18587, 42777}, {19105, 31463}, {19116, 42603}, {23046, 23261}, {31414, 42267}, {33703, 42570}, {36446, 42564}, {36464, 42562}, {41945, 43380}, {42087, 42249}, {42088, 42248}, {42216, 43338}, {43383, 43408}

X(43430) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 3068, 35815}, {371, 485, 42269}, {371, 8960, 13886}, {371, 13886, 485}, {371, 31412, 22615}, {371, 42269, 6561}, {485, 22615, 31412}, {486, 8976, 42602}, {3068, 8960, 485}, {3068, 13886, 371}, {3316, 19054, 10577}, {3592, 18538, 42268}, {6407, 13665, 42272}, {6407, 42272, 42260}, {6417, 8976, 42582}, {6417, 42582, 486}, {6560, 8981, 9680}, {7583, 13846, 5418}, {8976, 32787, 486}, {9540, 35822, 42261}, {13665, 31454, 42260}, {22615, 31412, 42269}, {31454, 42272, 6407}, {32787, 42582, 6417}

X(43431) = GIBERT (-5 SQRT(3),3,5) POINT

Barycentrics    5*a^2*S - 5*a^2*SA - 6*SB*SC : :
X(43431) = 5 X[6430] - 3 X[43338], 5 X[6430] + 6 X[43341], X[43338] + 2 X[43341]

X(43431) lies on the cubic K1229 and these lines: {2, 35771}, {4, 372}, {5, 6432}, {6, 3628}, {20, 6485}, {30, 6430}, {193, 6119}, {230, 19104}, {371, 10303}, {395, 42255}, {396, 42254}, {485, 5055}, {489, 22484}, {548, 6410}, {549, 1151}, {590, 6500}, {615, 3311}, {632, 6431}, {1132, 6479}, {1152, 15704}, {1328, 15684}, {1505, 13834}, {1506, 19103}, {1587, 43342}, {1588, 9681}, {2045, 42780}, {2046, 42779}, {3071, 3534}, {3090, 35770}, {3312, 5072}, {3317, 10576}, {3523, 6486}, {3529, 6481}, {3543, 12819}, {3594, 3857}, {3627, 6438}, {3845, 42641}, {3856, 42216}, {5066, 6471}, {5067, 42557}, {6395, 42270}, {6396, 43337}, {6398, 22615}, {6408, 13785}, {6417, 32790}, {6419, 32786}, {6420, 15022}, {6424, 13770}, {6425, 43314}, {6426, 42276}, {6427, 32789}, {6428, 42582}, {6429, 12108}, {6434, 12103}, {6437, 14869}, {6448, 42272}, {6454, 23259}, {6455, 18510}, {6459, 15698}, {6487, 17538}, {6497, 42258}, {7486, 7586}, {7582, 15709}, {7585, 10195}, {8252, 19116}, {8703, 42569}, {10304, 13935}, {12007, 13972}, {12102, 42644}, {13607, 13971}, {14890, 43323}, {15681, 42573}, {15683, 35821}, {18586, 42777}, {18587, 42778}, {19117, 42602}, {23046, 23251}, {33703, 42571}, {36447, 42563}, {36465, 42565}, {41946, 43381}, {42087, 42247}, {42088, 42246}, {42215, 43339}, {43382, 43407}

X(43431) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 3069, 35814}, {372, 486, 42268}, {372, 13939, 486}, {372, 42268, 6560}, {372, 42561, 22644}, {485, 13951, 42603}, {486, 22644, 42561}, {3069, 13939, 372}, {3317, 19053, 10576}, {3594, 18762, 42269}, {6408, 13785, 42271}, {6408, 42271, 42261}, {6418, 13951, 42583}, {6418, 42583, 485}, {7584, 13847, 5420}, {13935, 35823, 42260}, {13951, 32788, 485}, {22644, 42561, 42268}, {32788, 42583, 6418}

X(43432) = GIBERT (9 SQRT(3),13,3) POINT

Barycentrics    3*a^2*(3*S+SA)+26*SB*SC : :
X(43432) = 9*a^2*S + 3*a^2*SA + 26*SB*SC : :

X(43432) lies on the cubic K1229 and these lines: {4, 1327}, {140, 6410}, {376, 42608}, {485, 1657}, {486, 3854}, {550, 42639}, {1131, 8960}, {1587, 43377}, {1656, 6522}, {3070, 3851}, {3311, 12818}, {3522, 5418}, {3529, 42525}, {3594, 42640}, {3858, 7584}, {5056, 6564}, {5068, 42603}, {5073, 9681}, {5420, 43379}, {6418, 41953}, {6437, 23251}, {6453, 14241}, {6473, 41964}, {8976, 43314}, {9540, 42540}, {10194, 42273}, {10195, 10299}, {13665, 42271}, {15696, 41952}, {15712, 42602}, {18510, 42268}, {23253, 42522}, {23261, 43313}, {23269, 42277}, {41981, 42264}, {42263, 43340}, {42266, 42570}

X(43432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 43411, 6419}, {6449, 41954, 485}

X(43433) = GIBERT (-9 SQRT(3),13,3) POINT

Barycentrics    9*a^2*S - 3*a^2*SA - 26*SB*SC : :
X(43433) lies on the cubic K1229 and these lines: {4, 1328}, {30, 17852}, {140, 6409}, {376, 42609}, {485, 3854}, {486, 1657}, {550, 42640}, {1132, 22615}, {1588, 43376}, {1656, 6519}, {3071, 3851}, {3312, 12819}, {3522, 5420}, {3529, 42524}, {3592, 42639}, {3858, 7583}, {5056, 6565}, {5068, 42602}, {5073, 43209}, {5418, 43378}, {6417, 41954}, {6438, 23261}, {6454, 14226}, {6472, 41963}, {9691, 41955}, {10194, 10299}, {10195, 42270}, {13785, 42272}, {13935, 42539}, {13951, 43315}, {15696, 41951}, {15712, 42603}, {18512, 42269}, {23251, 43312}, {23263, 42523}, {23275, 42274}, {41981, 42263}, {42264, 43341}, {42267, 42571}

X(43433) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 43412, 6420}, {6450, 41953, 486}

X(43434) = GIBERT (26 SQRT(3),33,13) POINT

Barycentrics    26*a^2*S + 13*a^2*SA + 66*SB*SC : :

X(43434) lies on the cubic K1229 and these lines: {4, 1131}, {372, 10109}, {485, 19710}, {3628, 6477}, {6426, 42277}, {6429, 22644}, {6446, 31412}, {6473, 15703}, {6485, 41958}, {6492, 23251}, {9543, 14241}, {12108, 18538}, {13925, 42272}, {13993, 42273}, {15705, 23269}, {34200, 41948}, {35255, 41954}

X(43434) = {X(7583),X(43376)}-harmonic conjugate of X(43316)

X(43435) = GIBERT (-26 SQRT(3),33,13) POINT

Barycentrics    26*a^2*S - 13*a^2*SA - 66*SB*SC : :

X(43435) lies on the cubic K1229 and these lines: {4, 1132}, {371, 10109}, {486, 19710}, {3628, 6476}, {6425, 42274}, {6430, 22615}, {6445, 42561}, {6472, 15703}, {6484, 41957}, {6493, 23261}, {12108, 18762}, {13925, 42270}, {13993, 42271}, {15705, 23275}, {34200, 41947}, {35256, 41953}

X(43435) = {X(7584),X(43377)}-harmonic conjugate of X(43317)

X(43436) = GIBERT (37 SQRT(3),6,-74) POINT

Barycentrics    37*a^2*S - 74*a^2*SA + 12*SB*SC : :

X(43436) lies on the cubic K1229 and these lines: {4, 615}, {3312, 42524}, {6440, 22615}, {7583, 19711}, {10138, 23261}, {10142, 13993}, {41950, 43376}

X(43436) = {X(42262),X(43319)}-harmonic conjugate of X(41964)

X(43437) = GIBERT (37 SQRT(3),-6,74) POINT

Barycentrics    37*a^2*S + 74*a^2*SA - 12*SB*SC : :

X(43437) lies on the cubic K1229 and these lines: {4, 590}, {3311, 42525}, {6439, 22644}, {7584, 19711}, {9543, 41946}, {9691, 42267}, {10137, 23251}, {10141, 13925}, {41949, 43377}

X(43437) = {X(42265),X(43318)}-harmonic conjugate of X(41963)

X(43438) = GIBERT (45 SQRT(3),46,30) POINT

Barycentrics    45*a^2*S + 30*a^2*SA + 92*SB*SC : :

X(43438) lies on the cubic K1229 and these lines: {4, 3592}, {140, 6434}, {1657, 6484}, {5068, 42572}, {6439, 42260}, {6451, 42267}, {8960, 9691}, {10194, 42265}, {10303, 42418}, {13925, 43340}, {15022, 43411}, {41950, 43338}

X(43439) = GIBERT (-45 SQRT(3),46,30) POINT

Barycentrics    45*a^2*S - 30*a^2*SA - 92*SB*SC : :

X(43439) lies on the cubic K1229 and these lines: {4, 3594}, {140, 6433}, {1657, 6485}, {5068, 42573}, {6440, 42261}, {6452, 42266}, {10195, 42262}, {10303, 42417}, {13993, 43341}, {15022, 43412}, {41949, 43339}

X(43440) = GIBERT (-21,74,147) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 147*a^2*SA - 148*SB*SC : :
Barycentrics    1/(Cot[A] - 7*Sqrt[3]) : :

X(43440) lies on the the Kiepert circumhyperbola and these lines: {13, 5070}, {14, 632}, {547, 12816}, {3530, 12821}, {5054, 12817}, {5056, 42928}, {5079, 12820}, {8703, 42597}, {10188, 43028}, {11540, 42964}, {16239, 42799}, {16963, 42610}, {16967, 42773}, {22235, 42937}, {22237, 42092}, {33417, 41978}, {33603, 42495}, {33607, 42598}, {41981, 42914}, {41984, 42489}, {42118, 42948}, {42144, 42908}, {42161, 42926}, {42431, 42931}, {42591, 42936}, {42956, 42992}, {42958, 43364}, {42986, 43019}, {42989, 43370}

X(43441) = GIBERT (21,74,147) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 147*a^2*SA + 148*SB*SC : :
Barycentrics    1/(Cot[A] + 7*Sqrt[3]) : :

X(43441) lies on the the Kiepert circumhyperbola and these lines: {13, 632}, {14, 5070}, {547, 12817}, {3530, 12820}, {5054, 12816}, {5056, 42929}, {5079, 12821}, {8703, 42596}, {10187, 43029}, {11540, 42965}, {16239, 42800}, {16962, 42611}, {16966, 42774}, {22235, 42089}, {22237, 42936}, {33416, 41977}, {33602, 42494}, {33606, 42599}, {41981, 42915}, {41984, 42488}, {42117, 42949}, {42145, 42909}, {42160, 42927}, {42432, 42930}, {42590, 42937}, {42957, 42993}, {42959, 43365}, {42987, 43018}, {42988, 43371}

X(43442) = GIBERT (-15,38,75) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 75*a^2*SA - 76*SB*SC : :
Barycentrics    1/(Cot[A] - 5*Sqrt[3]) : :

X(43442) lies on the the Kiepert circumhyperbola and these lines: {3, 12821}, {4, 33416}, {5, 12820}, {13, 3628}, {14, 3526}, {17, 43028}, {18, 42124}, {140, 42684}, {398, 33606}, {547, 42965}, {549, 12817}, {1656, 42954}, {2045, 12819}, {2046, 12818}, {3534, 42611}, {5055, 12816}, {5059, 43367}, {5071, 42695}, {5072, 42433}, {6674, 11121}, {6695, 42062}, {7486, 16242}, {10187, 42989}, {10188, 23303}, {11304, 33698}, {14488, 37463}, {15709, 16964}, {15713, 42890}, {16962, 42591}, {16966, 22235}, {16967, 42477}, {33605, 42934}, {35018, 42686}, {42089, 42900}, {42123, 42948}, {42138, 42944}, {42150, 43301}, {42152, 43303}, {42488, 42898}, {42493, 42794}, {42498, 42993}, {42593, 42998}, {42694, 43101}, {42779, 43200}, {42910, 42964}, {42985, 42991}, {43009, 43238}

X(43442) = X(42978)-cross conjugate of X(18)

X(43443) = GIBERT (15,38,75) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 75*a^2*SA + 76*SB*SC : :
Barycentrics    1/(Cot[A] + 5*Sqrt[3]) : :

X(43443) lies on the the Kiepert circumhyperbola and these lines: {3, 12820}, {4, 33417}, {5, 12821}, {13, 3526}, {14, 3628}, {17, 42121}, {18, 43029}, {140, 42685}, {397, 33607}, {547, 42964}, {549, 12816}, {1656, 42955}, {2045, 12818}, {2046, 12819}, {3534, 42610}, {5055, 12817}, {5059, 43366}, {5071, 42694}, {5072, 42434}, {6673, 11122}, {6694, 42063}, {7486, 16241}, {10187, 23302}, {10188, 42988}, {11303, 33698}, {14488, 37464}, {15709, 16965}, {15713, 42891}, {16963, 42590}, {16966, 42476}, {16967, 22237}, {33604, 42935}, {35018, 42687}, {42092, 42901}, {42122, 42949}, {42135, 42945}, {42149, 43302}, {42151, 43300}, {42489, 42899}, {42492, 42793}, {42499, 42992}, {42592, 42999}, {42695, 43104}, {42780, 43199}, {42911, 42965}, {42984, 42990}, {43008, 43239}

X(43443) = X(42979)-cross conjugate of X(17)

X(43444) = GIBERT (-24,49,96) POINT

Barycentrics    4*Sqrt[3]*a^2*S - 48*a^2*SA - 49*SB*SC : :
Barycentrics    1/(Cot[A] - 4*Sqrt[3]) : :

Let L be a line parallel to side BC of a triangle ABC. As a point P traverses L, the locus of X(5)-of-PBC is a parabola. Let L1 and L2 be the parallels to BC such that the corresponding parabolas pass through B and C, respectively. The two parabolas are given by these equations:

2(SC x +a^2 y) (SB x + a^2 z) ± Sqrt[3] a^2 S x (x+y+z) =0

The foci of these parabolas (which are symmetric about BC) are given by

Fa± = (-a^2 : SC ± 4Sqrt[3] S : SB ± 4 Sqrt[3]S).

The lines AFa-, BFb-, CFc- concur in X(43444); the lines AFa+, BFb+, CFc+ concur in X(43445). (Angel Montesdeoca, May 16 2023)

X(43444) lies on the the Kiepert circumhyperbola and these lines: {4, 42774}, {13, 5067}, {14, 3525}, {17, 43019}, {140, 42927}, {397, 33604}, {3523, 42963}, {3524, 12817}, {3528, 12821}, {3533, 22237}, {3544, 12820}, {5056, 42493}, {5068, 42889}, {5071, 5237}, {5344, 42474}, {10188, 11489}, {10299, 42585}, {10645, 42495}, {11289, 18845}, {11290, 38259}, {11486, 22235}, {15022, 42926}, {15702, 33603}, {15709, 43108}, {33602, 43239}, {33605, 42490}, {33606, 42489}, {33607, 41944}, {41106, 42433}, {42089, 42909}, {42134, 42477}, {42142, 42937}, {42151, 42472}, {42775, 42965}, {42921, 43300}

X(43445) = GIBERT (24,49,96) POINT

Barycentrics    4*Sqrt[3]*a^2*S + 48*a^2*SA + 49*SB*SC : :
Barycentrics    1/(Cot[A] - 4*Sqrt[3]) : :

X(43445) lies on the the Kiepert circumhyperbola and these lines: {4, 42773}, {13, 3525}, {14, 5067}, {18, 43018}, {140, 42926}, {398, 33605}, {3523, 42962}, {3524, 12816}, {3528, 12820}, {3533, 22235}, {3544, 12821}, {5056, 42492}, {5068, 42888}, {5071, 5238}, {5343, 42475}, {10187, 11488}, {10299, 42584}, {10646, 42494}, {11289, 38259}, {11290, 18845}, {11485, 22237}, {15022, 42927}, {15702, 33602}, {15709, 43109}, {33603, 43238}, {33604, 42491}, {33606, 41943}, {33607, 42488}, {41106, 42434}, {42092, 42908}, {42133, 42476}, {42139, 42936}, {42150, 42473}, {42776, 42964}, {42920, 43301}

X(43446) = GIBERT (-12,13,24) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 12*a^2*SA - 13*SB*SC : :
Barycentrics    1/(Cot[A] - 2*Sqrt[3]) : :

X(43446) lies on the the Kiepert circumhyperbola and these lines: {2, 42591}, {4, 11481}, {6, 42476}, {13, 3090}, {14, 631}, {17, 11489}, {18, 3533}, {61, 43026}, {62, 33607}, {140, 22237}, {376, 12817}, {395, 42610}, {398, 3525}, {471, 8796}, {550, 42963}, {1131, 2046}, {1132, 2045}, {1327, 36452}, {1328, 36470}, {1656, 22235}, {2996, 11290}, {3424, 37464}, {3522, 42136}, {3523, 42122}, {3524, 5343}, {3529, 12821}, {3544, 5366}, {3545, 12816}, {3850, 42951}, {3851, 43364}, {3855, 12820}, {5056, 42128}, {5059, 42143}, {5067, 16645}, {5068, 42121}, {5071, 5340}, {5334, 42773}, {5395, 11289}, {10187, 42152}, {10188, 11488}, {10299, 18581}, {10653, 43016}, {10654, 42593}, {11001, 42491}, {11121, 37177}, {11304, 41895}, {14484, 37463}, {15682, 42505}, {15698, 42159}, {15702, 33605}, {15709, 33606}, {15715, 42164}, {15719, 16964}, {16241, 42613}, {16242, 33703}, {16808, 41977}, {16967, 41974}, {17538, 43402}, {18582, 42801}, {21735, 42089}, {22236, 42519}, {33416, 42959}, {35018, 42922}, {36843, 41106}, {40693, 42521}, {40694, 42479}, {41099, 42580}, {41973, 42930}, {42104, 42958}, {42133, 42774}, {42141, 42926}, {42157, 42961}, {42160, 43331}, {42162, 43200}, {42431, 42473}, {42775, 42914}, {42818, 43197}, {42908, 43325}, {42915, 43334}, {42949, 42999}, {42991, 43025}

X(43446) = isotomic conjugate of the anticomplement of X(43028)
* X(43446) = X(i)-cross conjugate of X(j) for these (i,j): {42949, 17}, {42999, 4}, {43028, 2}
X(43446) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42089, 42495, 21735}, {42793, 42956, 43239}

X(43447) = GIBERT (12,13,24) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 12*a^2*SA + 13*SB*SC : :
Barycentrics    1/(Cot[A] - 2*Sqrt[3]) : :

X(43447) lies on the the Kiepert circumhyperbola and these lines: {2, 42590}, {4, 11480}, {6, 42476}, {13, 631}, {14, 3090}, {17, 3533}, {18, 11488}, {61, 33606}, {62, 43027}, {140, 22235}, {376, 12816}, {396, 42611}, {397, 3525}, {470, 8796}, {550, 42962}, {1131, 2045}, {1132, 2046}, {1327, 36469}, {1328, 36453}, {1656, 22237}, {2996, 11289}, {3424, 37463}, {3522, 42137}, {3523, 42123}, {3524, 5344}, {3529, 12820}, {3544, 5365}, {3545, 12817}, {3850, 42950}, {3851, 43365}, {3855, 12821}, {5056, 42125}, {5059, 42146}, {5067, 16644}, {5068, 42124}, {5071, 5339}, {5335, 42774}, {5395, 11290}, {10187, 11489}, {10188, 42149}, {10299, 18582}, {10653, 42592}, {10654, 43017}, {11001, 42490}, {11122, 37178}, {11303, 41895}, {14484, 37464}, {15682, 42504}, {15698, 42162}, {15702, 33604}, {15709, 33607}, {15715, 42165}, {15719, 16965}, {16241, 33703}, {16242, 42612}, {16809, 41978}, {16966, 41973}, {17538, 43401}, {18581, 42802}, {21735, 42092}, {22238, 42518}, {33417, 42958}, {35018, 42923}, {36836, 41106}, {40693, 42478}, {40694, 42520}, {41099, 42581}, {41974, 42931}, {42105, 42959}, {42134, 42773}, {42140, 42927}, {42158, 42960}, {42159, 43199}, {42161, 43330}, {42432, 42472}, {42776, 42915}, {42817, 43198}, {42909, 43324}, {42914, 43335}, {42948, 42998}, {42990, 43024}

X(43447) = isotomic conjugate of the anticomplement of X(43029)
X(43447) = X(i)-cross conjugate of X(j) for these (i,j): {42948, 18}, {42998, 4}, {43029, 2}
X(43447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42092, 42494, 21735}, {42794, 42957, 43238}

leftri

Points on the cubic K1230: X(43448)-X(43456)

rightri

This preamble and points X(43448)-X(43456) are contributed by Peter Moses, May 18, 2021. See also the preambles just before X(42085), X(42413), and X(42429) and others

See K1230



X(43448) = X(2)X(99)∩X(4)X(6)

Barycentrics    a^4 - 2*a^2*b^2 - 3*b^4 - 2*a^2*c^2 + 6*b^2*c^2 - 3*c^4 : :
X(43448) = 3 X[2] - 4 X[7844], 2 X[1384] - 3 X[7735], 2 X[7778] - 3 X[33285], X[32817] - 3 X[33285]

In the plane of a triangle ABC, let
G = X(2) = centroid
H = X(4) = orthocenter
Ab = point of intersection, other than B, of BH and circle (G,B,C), and define Bc and Ca cyclically
Ac point of intersection, other than C, of CH and circle (G,B,C), and define Ba and Cb cyclically
A' = BcBa∩CaCb, and define B' and C' cyclically
Then A'B'C' is homothetic to the orthic triangle of ABC, and X(43448) is the homothetic center. (Angel Montesdeoca, January 21, 2023)

X(43448) lies on the cubic K1230 and these lines: {2, 99}, {3, 43291}, {4, 6}, {5, 5024}, {20, 187}, {30, 1384}, {32, 3146}, {39, 3091}, {69, 7841}, {76, 2996}, {83, 32979}, {141, 33190}, {182, 38734}, {183, 32986}, {193, 316}, {194, 14063}, {230, 376}, {232, 6623}, {297, 30227}, {315, 6392}, {325, 16041}, {346, 34542}, {377, 37675}, {381, 7736}, {382, 5305}, {384, 32826}, {385, 33017}, {390, 9664}, {427, 39662}, {439, 7857}, {460, 26864}, {538, 37668}, {546, 9605}, {550, 15655}, {598, 41895}, {599, 5485}, {625, 34511}, {626, 32830}, {631, 3054}, {966, 17677}, {1007, 31859}, {1015, 5274}, {1078, 33023}, {1107, 31418}, {1131, 31411}, {1194, 7378}, {1196, 7396}, {1285, 5306}, {1383, 7519}, {1478, 16785}, {1479, 16784}, {1495, 6620}, {1500, 5261}, {1506, 5068}, {1562, 1899}, {1571, 9780}, {1572, 9812}, {1574, 8165}, {1609, 12082}, {1975, 14064}, {1992, 8352}, {2023, 7709}, {2031, 36998}, {2275, 10591}, {2276, 10590}, {2548, 3832}, {3053, 3529}, {3055, 3090}, {3085, 9598}, {3086, 9597}, {3094, 40330}, {3231, 37190}, {3247, 13161}, {3269, 3981}, {3314, 32836}, {3329, 33016}, {3421, 21956}, {3520, 21397}, {3522, 7756}, {3523, 7746}, {3524, 37637}, {3525, 15815}, {3528, 5585}, {3543, 5008}, {3544, 22332}, {3545, 3815}, {3546, 15075}, {3600, 9651}, {3618, 8370}, {3619, 6656}, {3627, 30435}, {3631, 7784}, {3634, 31421}, {3763, 33230}, {3785, 6655}, {3788, 15301}, {3817, 9592}, {3830, 18907}, {3839, 5475}, {3843, 22246}, {3845, 15484}, {3851, 31406}, {3855, 9607}, {3926, 5025}, {3934, 33202}, {3944, 24247}, {4208, 16589}, {4294, 10987}, {5023, 11742}, {5028, 5921}, {5030, 36670}, {5033, 12203}, {5056, 31401}, {5059, 7755}, {5071, 31489}, {5076, 43136}, {5140, 6467}, {5177, 5283}, {5225, 16502}, {5277, 37435}, {5319, 7747}, {5354, 7391}, {5355, 14075}, {5395, 7878}, {6034, 10485}, {6200, 12123}, {6321, 26316}, {6337, 7887}, {6390, 11318}, {6396, 12124}, {6411, 36703}, {6412, 36701}, {6421, 42561}, {6422, 31412}, {6443, 42262}, {6444, 42265}, {6459, 8375}, {6460, 8376}, {6531, 18850}, {6564, 31403}, {6680, 33201}, {6781, 15683}, {6973, 34460}, {7375, 32790}, {7376, 32789}, {7383, 14806}, {7388, 13934}, {7389, 9600}, {7400, 10979}, {7486, 31455}, {7487, 10985}, {7749, 15717}, {7750, 33238}, {7752, 32980}, {7753, 14930}, {7754, 11008}, {7758, 7825}, {7761, 15589}, {7763, 32972}, {7769, 32988}, {7774, 14041}, {7777, 33006}, {7778, 32817}, {7781, 32831}, {7782, 32989}, {7783, 32829}, {7785, 32996}, {7786, 32987}, {7787, 14068}, {7789, 32822}, {7791, 32828}, {7792, 14033}, {7793, 32997}, {7795, 7861}, {7797, 14035}, {7800, 7872}, {7803, 32971}, {7806, 33007}, {7816, 33181}, {7818, 10513}, {7823, 33279}, {7824, 32838}, {7828, 32973}, {7833, 17008}, {7834, 33198}, {7836, 32824}, {7839, 14062}, {7842, 14023}, {7847, 32832}, {7850, 11054}, {7851, 14001}, {7862, 32835}, {7864, 16924}, {7865, 32874}, {7868, 33223}, {7886, 33203}, {7888, 32841}, {7891, 33248}, {7898, 19570}, {7906, 14045}, {7912, 32825}, {7920, 14042}, {7921, 14044}, {7923, 16898}, {7924, 16990}, {7925, 32837}, {7928, 32868}, {7932, 14037}, {7934, 32833}, {7989, 31396}, {8164, 31477}, {8355, 11165}, {8356, 34229}, {9112, 41112}, {9113, 41113}, {9214, 34169}, {9300, 14482}, {9463, 14957}, {9465, 31099}, {9574, 10175}, {9575, 18483}, {9593, 19925}, {9608, 34484}, {9609, 35921}, {9721, 18347}, {9734, 20398}, {9741, 22110}, {9744, 14639}, {9752, 11676}, {9770, 37350}, {9880, 11179}, {10303, 37512}, {10304, 21843}, {10583, 14031}, {10588, 31448}, {10592, 31461}, {10653, 31710}, {10654, 31709}, {10895, 31402}, {10986, 18533}, {11148, 39785}, {11174, 32983}, {11180, 11646}, {11303, 11488}, {11304, 11489}, {11361, 16989}, {11541, 22331}, {11580, 16063}, {12963, 43408}, {12968, 43407}, {13492, 34165}, {13637, 13832}, {13757, 13831}, {14484, 22682}, {14568, 14907}, {14712, 33192}, {14927, 40825}, {15031, 32991}, {15433, 15437}, {15603, 15696}, {16051, 24855}, {16317, 32216}, {16984, 33255}, {17000, 33032}, {17004, 33008}, {18404, 22121}, {18581, 36252}, {18582, 36251}, {18840, 33232}, {18842, 32532}, {19053, 33456}, {19054, 33457}, {19130, 42852}, {20065, 33019}, {20081, 32452}, {20112, 42849}, {21312, 34809}, {21448, 30739}, {23055, 35955}, {27318, 33057}, {32479, 37809}, {32818, 33292}, {32839, 32967}, {32867, 33001}, {32883, 33015}, {32956, 34573}, {33215, 37688}, {33249, 39143}, {34866, 35473}, {35060, 35687}, {37174, 40814}, {37348, 38732}, {40727, 42850}, {41406, 42086}, {41407, 42085}, {41408, 42113}, {41409, 42112}, {41410, 42275}, {41411, 42276}

X(43448) = reflection of X(32817) in X(7778)
X(43448) = polar conjugate of X(10603)
X(43448) = polar conjugate of the isotomic conjugate of X(16051)
X(43448) = polar conjugate of the isogonal conjugate of X(10602)
X(43448) = X(10602)-cross conjugate of X(16051)
X(43448) = X(i)-isoconjugate of X(j) for these (i,j): {48, 10603}, {9247, 10604}
X(43448) = crosspoint of X(4) and X(5485)
X(43448) = crosssum of X(3) and X(1384)
X(43448) = crossdifference of every pair of points on line {351, 520}
X(43448) = barycentric product X(i)*X(j) for these {i,j}: {4, 16051}, {264, 10602}, {671, 24855}
X(43448) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 10603}, {264, 10604}, {10602, 3}, {16051, 69}, {24855, 524}
X(43448) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 148, 32815}, {2, 671, 7620}, {4, 5254, 5286}, {4, 5523, 393}, {5, 7738, 31400}, {20, 37689, 187}, {39, 3091, 31404}, {39, 18424, 31415}, {115, 2549, 2}, {115, 11648, 2549}, {187, 3767, 37689}, {194, 14063, 32816}, {381, 15048, 7736}, {671, 7790, 11185}, {1992, 8352, 23334}, {2996, 32974, 76}, {3543, 5304, 7737}, {3767, 7748, 20}, {3839, 37665, 5475}, {3855, 9607, 31407}, {5309, 7737, 5304}, {5318, 5321, 36990}, {5334, 5335, 6776}, {5461, 7618, 2}, {5475, 7739, 37665}, {6390, 11318, 37690}, {6392, 32982, 315}, {7739, 39563, 3839}, {7754, 33229, 32006}, {7774, 14041, 32827}, {7783, 32961, 32829}, {7790, 11185, 2}, {7795, 7861, 33180}, {7800, 7872, 33025}, {7847, 32832, 32990}, {7851, 32819, 14001}, {14568, 14907, 37667}, {15589, 33210, 7761}, {18424, 31415, 3091}, {31401, 39565, 5056}, {31859, 33228, 1007}, {32817, 33285, 7778}, {32822, 32951, 7789}, {32830, 33200, 626}, {32834, 33025, 7800}, {33272, 37667, 14907}, {35913, 35914, 6}

X(43449) = X(2)X(4159)∩X(4)X(32)

Barycentrics    a^8 - a^6*b^2 - 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 + a^2*b^2*c^4 - a^2*c^6 + b^2*c^6 - c^8 : :
X(34349) = 4 X[115] - X[7737], X[148] + 2 X[7761], X[2549] + 2 X[11646]

X(43449) lies on the cubics K1225 and K1230 and these lines: {2, 4159}, {4, 32}, {6, 40250}, {13, 9981}, {14, 9982}, {30, 2076}, {39, 147}, {76, 148}, {99, 3096}, {114, 10356}, {187, 40236}, {315, 1916}, {512, 34214}, {542, 7739}, {543, 7865}, {616, 6775}, {617, 6772}, {620, 7914}, {626, 8178}, {671, 7811}, {736, 5207}, {1316, 39691}, {1352, 2549}, {1569, 7738}, {2023, 2548}, {2353, 10828}, {2784, 9620}, {3023, 10874}, {3027, 10873}, {3098, 23698}, {3815, 38743}, {3849, 14568}, {4027, 7803}, {5025, 38907}, {5106, 35922}, {5254, 12188}, {5286, 5984}, {5309, 10336}, {5319, 12829}, {5461, 32983}, {5976, 7800}, {5989, 6656}, {6230, 9994}, {6231, 9995}, {6321, 9821}, {6722, 32968}, {7745, 38744}, {7753, 34681}, {7756, 10357}, {7770, 9478}, {7790, 10347}, {7797, 10346}, {7804, 7828}, {7832, 33021}, {7846, 14061}, {7876, 8290}, {7935, 15821}, {7942, 33020}, {7983, 12495}, {8356, 9890}, {8721, 38642}, {9166, 33016}, {9301, 38732}, {9605, 12830}, {9619, 21636}, {9863, 43183}, {9941, 13178}, {9998, 36163}, {10348, 16989}, {10769, 13235}, {10877, 13183}, {11007, 20998}, {11368, 38220}, {11602, 22746}, {11603, 22745}, {11648, 12243}, {12184, 31409}, {12501, 18332}, {13182, 18957}, {13881, 40279}, {14023, 36849}, {14907, 39652}, {17984, 40889}, {21843, 34473}, {26316, 37348}, {27369, 39857}, {31274, 32960}, {33260, 34885}, {35248, 38730}

X(43449) = anticomplement of X(5149)
X(43449) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 115, 3767}, {98, 9873, 9862}, {148, 2896, 8782}, {2023, 6033, 2548}, {6655, 11606, 148}, {10828, 39832, 41533}, {22512, 22513, 9862}

X(43450) = X(2)X(1501)∩X(4)X(39)

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

X(43450) lies on the cubics K1226 and K1230 and these lines: {2, 1501}, {4, 39}, {5, 39095}, {6, 147}, {69, 35432}, {315, 3972}, {325, 384}, {598, 7799}, {1352, 7735}, {1916, 35705}, {2896, 3053}, {3094, 40236}, {3314, 5017}, {3788, 31982}, {3815, 5116}, {5025, 11174}, {5028, 9993}, {5162, 7737}, {6054, 7753}, {7774, 9865}, {7777, 8290}, {7779, 13330}, {7800, 7915}, {7859, 14064}, {7880, 14039}, {7900, 14037}, {8176, 33285}, {8591, 8716}, {9753, 35388}, {12054, 31404}, {15484, 35930}

{X(2548),X(9744)}-harmonic conjugate of X(7736)

X(43451) = X(4)X(15)∩X(6)X(37332)

Barycentrics    Sqrt[3]*(a^6 - b^6 + 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6) + 2*a^2*(2*a^2 - b^2 - c^2)*S : :

X(43451) lies on the cubic K1230 and these lines: {4, 15}, {6, 37332}, {13, 2549}, {14, 7735}, {16, 1352}, {187, 3818}, {622, 34541}, {3107, 5335}, {3619, 10646}, {3642, 16990}, {5464, 22492}, {5613, 22513}, {6299, 7774}, {6778, 10653}, {11180, 22998}, {14539, 19106}, {16809, 41407}, {18581, 36760}, {20423, 22997}, {36362, 41745}

X(43451) = {X(187),X(3818)}-harmonic conjugate of X(43452)

X(43452) = X(4)X(16)∩X(6)X(37333)

Barycentrics    Sqrt[3]*(a^6 - b^6 + 2*a^2*b^2*c^2 + b^4*c^2 + b^2*c^4 - c^6) - 2*a^2*(2*a^2 - b^2 - c^2)*S : :

X(43452) lies on the cubic K1230 and these lines: {4, 16}, {6, 37333}, {13, 7735}, {14, 2549}, {15, 1352}, {187, 3818}, {621, 34540}, {3106, 5334}, {3619, 10645}, {3643, 16990}, {5463, 22491}, {5617, 22512}, {6298, 7774}, {6777, 10654}, {11180, 22997}, {14538, 19107}, {16808, 41406}, {18582, 36759}, {20423, 22998}, {36363, 41746}

X(43452) = {X(187),X(3818)}-harmonic conjugate of X(43451)

X(43453) = X(2)X(35002)∩X(4)X(69)

Barycentrics    a^8 + a^6*b^2 - a^2*b^6 - b^8 + a^6*c^2 + 5*a^4*b^2*c^2 - 3*a^2*b^4*c^2 + 3*b^6*c^2 - 3*a^2*b^2*c^4 - 4*b^4*c^4 - a^2*c^6 + 3*b^2*c^6 - c^8 : :
X(43453) = 5 X[3] - 6 X[38230], 3 X[4] - 2 X[316], 5 X[4] - 4 X[13449], 4 X[187] - 3 X[376], 5 X[316] - 6 X[13449], 8 X[625] - 9 X[3545], 5 X[631] - 4 X[18860], 5 X[631] - 6 X[38227], 3 X[1513] - 2 X[6390], 21 X[3090] - 20 X[31275], 5 X[3522] - 6 X[38225], 7 X[3523] - 8 X[14693], 4 X[3818] - 3 X[5207], 12 X[5215] - 11 X[15719], 2 X[5999] - 3 X[14651], 3 X[6054] - 2 X[7813], 3 X[6785] - 2 X[14962], 2 X[12188] - 3 X[19570], 8 X[16760] - 9 X[37943], 2 X[18860] - 3 X[38227], 5 X[19708] - 6 X[26613], 4 X[22566] - 3 X[41136], 4 X[31173] - 5 X[41099], 3 X[33265] - 2 X[38730], 5 X[37760] - 4 X[38613]

X(43453) lies on the cubic K1230 and these lines: {2, 35002}, {3, 7797}, {4, 69}, {5, 7931}, {20, 2080}, {30, 148}, {147, 32515}, {187, 376}, {381, 3314}, {382, 9863}, {419, 11064}, {420, 32223}, {549, 16984}, {625, 3545}, {631, 7834}, {671, 9302}, {754, 10722}, {1056, 5148}, {1058, 5194}, {1285, 2031}, {1513, 6390}, {1691, 5286}, {2021, 7738}, {2076, 5254}, {2456, 10359}, {2459, 42637}, {2782, 40236}, {2896, 32521}, {3090, 7822}, {3098, 7790}, {3407, 10788}, {3522, 38225}, {3523, 14693}, {3524, 7884}, {3525, 7943}, {3543, 34623}, {3734, 9993}, {3767, 5162}, {3849, 5485}, {4846, 19222}, {5092, 7827}, {5117, 37638}, {5184, 6361}, {5189, 38953}, {5215, 15719}, {5480, 24273}, {5523, 5667}, {5989, 11676}, {5999, 14651}, {6033, 7779}, {6054, 7813}, {6194, 37242}, {6321, 11606}, {6655, 9821}, {6656, 10357}, {6785, 14962}, {7709, 37182}, {7745, 15514}, {7751, 9873}, {7754, 39899}, {7761, 33706}, {7770, 35458}, {7785, 40279}, {7812, 37517}, {7841, 33878}, {7844, 30270}, {8370, 21850}, {9753, 35925}, {10333, 18502}, {11054, 11645}, {11361, 34615}, {11673, 37190}, {12082, 40947}, {14853, 42534}, {14881, 16044}, {16062, 35462}, {16760, 37943}, {19708, 26613}, {22564, 33017}, {22566, 41136}, {29012, 38664}, {31173, 41099}, {33265, 38730}, {37334, 37688}, {37760, 38613}

X(43453) = reflection of X(i) in X(j) for these {i,j}: {20, 2080}, {5189, 38953}, {6361, 5184}, {7779, 6033}, {9862, 385}, {13172, 11676}, {14712, 9301}
X(43453) = anticomplement of X(35002)
X(43453) = circumcircle-of-anticomplementary-triangle-inverse of X(31670)
X(43453) = crossdifference of every pair of points on line {3049, 10567}
X(43453) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {621, 622, 5207}, {11185, 31670, 4}, {18860, 38227, 631}, {32521, 37243, 2896}

X(43454) = X(2)X(3106)∩X(4)X(13)

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

X(43454) lies on the cubic K1230 and these lines: {2, 3106}, {4, 13}, {6, 20425}, {14, 1352}, {15, 2549}, {16, 7735}, {18, 33410}, {62, 5319}, {376, 39555}, {398, 5873}, {511, 5309}, {533, 33251}, {622, 7766}, {624, 7774}, {633, 7933}, {634, 3181}, {1007, 40335}, {1992, 37171}, {3091, 16631}, {3104, 3767}, {3105, 5286}, {3107, 7739}, {3642, 36252}, {5469, 22491}, {5476, 31702}, {6694, 16898}, {7684, 9744}, {7694, 41036}, {7737, 23005}, {10653, 36759}, {11179, 36757}, {14853, 22694}, {16940, 18581}, {22113, 42999}, {22509, 41746}, {31415, 41094}, {36782, 40922}, {41043, 41108}

X(43454) = reflection of X(43455) in X(5309)
X(43454) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3106, 22510, 2}, {10654, 40693, 6770}

X(43455) = X(2)X(3107)∩X(4)X(14)

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

X(43455) lies on the cubic K1230 and these lines: {2, 3107}, {4, 14}, {6, 20426}, {13, 1352}, {15, 7735}, {16, 2549}, {17, 33411}, {61, 5319}, {376, 39554}, {397, 5872}, {511, 5309}, {532, 33251}, {621, 7766}, {623, 7774}, {633, 3180}, {634, 7933}, {1007, 40334}, {1992, 37170}, {3091, 16630}, {3104, 5286}, {3105, 3767}, {3106, 7739}, {3643, 36251}, {5470, 22492}, {5476, 31701}, {6695, 16898}, {7685, 9744}, {7694, 41037}, {7737, 23004}, {10654, 36760}, {11179, 36758}, {14853, 22693}, {16941, 18582}, {22114, 42998}, {22507, 41745}, {31415, 41098}, {41042, 41107}

X(43455) = reflection of X(43454) in X(5309)
X(43455) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3107, 22511, 2}, {10653, 40694, 6773}

X(43456) = X(4)X(83)∩X(99)X(10168)

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

X(43456) lies on the cubics K1224 and K1230 and these lines: {4, 83}, {99, 10168}, {542, 7919}, {575, 7785}, {1916, 31958}, {2549, 6034}, {5028, 5368}, {5050, 5103}, {6033, 11179}, {7606, 9890}, {8177, 13086}, {11171, 24256}, {14712, 39750}, {16989, 20423}, {26316, 31670}

leftri

Gibert points associated with the KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}}: X(43457)-X(43526)

rightri

This preamble and points X(43457)-X(43526) are contributed by Peter Moses, May 19, 2021. For KHO curves, see the preamble just before X(42561)

The Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}}, given by the equation

(b - c)^2*(b + c)^2*(a^2 - b^2 - c^2)^2*x^2 + (a^2 - c^2)*(b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*c^4)*x*y + (a - c)^2*(a + c)^2*(a^2 - b^2 + c^2)^2*y^2 - (a^2 - b^2)*(b^2 - c^2)*(a^4 - 2*b^4 - 2*a^2*c^2 + c^4)*x*z - (a^2 - b^2)*(a^2 - c^2)*(2*a^4 - b^4 + 2*b^2*c^2 - c^4)*y*z + (a - b)^2*(a + b)^2*(a^2 + b^2 - c^2)^2*z^2 = 0,

passes through X(i) for these i: 2,4,15,16,316,1348,1349,2039,2040,3096,5418,5420,6560,6561,7790,7859,9993,14165,36969,36970,38227,42936,42937,43195,43196, and also the 67 points X(43460)-X(43526).



X(43457) = CENTER OF GIBERT KHO HYPERBOLA {{X(2),X(4),X(15),X(16),X(316)}}

Barycentrics    2*a^4 + 2*a^2*b^2 - 3*b^4 + 2*a^2*c^2 + 6*b^2*c^2 - 3*c^4 : :
X(43457) = 2 X[3055] - 3 X[7603], 3 X[7603] - X[8589]

' X(43457) lies on these lines: {2, 6781}, {3, 18584}, {4, 574}, {5, 187}, {6, 13}, {30, 3055}, {32, 3091}, {39, 546}, {83, 32993}, {111, 7533}, {141, 3363}, {193, 7615}, {216, 10297}, {230, 5066}, {262, 1569}, {302, 8595}, {303, 8594}, {315, 32995}, {316, 7810}, {382, 31455}, {403, 10985}, {543, 7777}, {598, 5461}, {620, 11361}, {625, 7820}, {626, 16044}, {1003, 31274}, {1078, 33024}, {1384, 3851}, {1504, 42268}, {1505, 42269}, {1570, 38136}, {1598, 9700}, {1656, 5210}, {2079, 21308}, {2482, 8176}, {2548, 3832}, {2549, 3839}, {3053, 5072}, {3090, 5206}, {3098, 37348}, {3143, 3613}, {3146, 15515}, {3199, 23047}, {3526, 5585}, {3545, 7737}, {3583, 31476}, {3589, 37350}, {3619, 32983}, {3620, 7818}, {3627, 37512}, {3628, 11614}, {3629, 20112}, {3630, 7845}, {3631, 9466}, {3734, 33016}, {3767, 3855}, {3815, 3845}, {3830, 31489}, {3843, 5024}, {3849, 37688}, {3850, 5008}, {3853, 15602}, {3854, 5368}, {3857, 5007}, {3858, 5254}, {3859, 5305}, {3860, 9300}, {3972, 6722}, {4045, 14041}, {5023, 5079}, {5025, 7889}, {5041, 41991}, {5055, 15655}, {5058, 42273}, {5062, 42270}, {5068, 12815}, {5071, 21843}, {5073, 11742}, {5076, 15815}, {5092, 14160}, {5104, 24206}, {5107, 5480}, {5318, 7685}, {5321, 7684}, {6032, 10418}, {6144, 40727}, {6292, 7825}, {6680, 32966}, {6683, 33229}, {6704, 7933}, {6748, 37984}, {7547, 27371}, {7617, 17008}, {7619, 9855}, {7735, 18362}, {7736, 11648}, {7738, 31417}, {7752, 7863}, {7769, 14042}, {7773, 7794}, {7774, 18546}, {7775, 7813}, {7782, 14066}, {7785, 7890}, {7786, 14062}, {7800, 32991}, {7802, 33002}, {7804, 33228}, {7808, 14063}, {7815, 32962}, {7826, 7843}, {7830, 16921}, {7842, 32992}, {7844, 33006}, {7847, 14044}, {7853, 34573}, {7857, 33011}, {7859, 14045}, {7862, 14035}, {7867, 32971}, {7872, 32996}, {7911, 33020}, {7913, 16041}, {7914, 33269}, {7935, 32968}, {7940, 14034}, {7951, 10987}, {8369, 31275}, {8375, 42265}, {8376, 42262}, {9167, 11159}, {9636, 37697}, {9650, 10896}, {9665, 10895}, {9674, 22615}, {9675, 42277}, {9696, 15033}, {9699, 9818}, {9880, 40277}, {10151, 33843}, {10254, 18472}, {10485, 25555}, {10516, 11173}, {10796, 23514}, {10979, 18531}, {10986, 16868}, {11184, 15300}, {11842, 20398}, {12811, 35007}, {12953, 31501}, {13860, 39838}, {13881, 21309}, {14576, 33842}, {14712, 34506}, {14806, 31723}, {14907, 33005}, {15048, 23046}, {15109, 37924}, {15301, 32819}, {15482, 33017}, {15760, 22052}, {15820, 24855}, {15993, 25561}, {16987, 33291}, {17130, 32816}, {17131, 20080}, {18907, 38071}, {19709, 37637}, {22861, 42111}, {22907, 42114}, {23261, 31481}, {23302, 31694}, {23303, 31693}, {32447, 38734}, {32456, 37647}, {32457, 41624}, {35930, 36519}, {37375, 37675}, {41016, 42101}, {41017, 42102}, {41406, 42918}, {41407, 42919}

X(43457) = reflection of X(8589) in X(3055)
X(43457) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 1506, 7756}, {4, 31415, 574}, {5, 7747, 7749}, {5, 39590, 7747}, {6, 381, 18424}, {6, 18424, 115}, {115, 5475, 7753}, {115, 7753, 5355}, {230, 5066, 39601}, {381, 5475, 115}, {574, 31415, 1506}, {625, 8370, 7820}, {3850, 7745, 39565}, {5008, 39565, 43291}, {5008, 43291, 7755}, {5309, 5475, 15484}, {5475, 18424, 6}, {6564, 6565, 5476}, {7603, 8589, 3055}, {7745, 39565, 7755}, {7745, 43291, 5008}, {7775, 11185, 7813}, {7825, 16924, 6292}, {8176, 11317, 2482}, {14537, 39601, 230}, {16808, 16809, 19130}

X(43458) = PERSPECTOR OF GIBERT KHO HYPERBOLA {{X(2),X(4),X(15),X(16),X(316)}}

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

X(43458) lies on these lines: {232, 3055}, {511, 546}, {3520, 19189}, {9307, 34845}, {13481, 37988}

X(43458) = isotomic conjugate of X(43459)

X(43459) = ISOTOMIC CONJUGATE OF X(43458)

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

X(43459) lies on these lines: {2, 5206}, {3, 76}, {5, 10242}, {20, 32838}, {30, 15031}, {32, 33004}, {36, 25303}, {39, 33273}, {69, 10299}, {83, 187}, {95, 3260}, {115, 33260}, {140, 316}, {194, 15515}, {230, 7847}, {264, 32534}, {274, 13587}, {315, 3523}, {325, 3530}, {376, 32832}, {384, 15513}, {385, 32450}, {549, 7750}, {550, 37688}, {574, 7760}, {620, 2896}, {621, 36959}, {622, 36958}, {625, 16923}, {626, 33259}, {631, 7752}, {668, 5303}, {671, 7756}, {1235, 17506}, {1384, 7878}, {1506, 14712}, {1799, 3266}, {2548, 33012}, {3053, 7786}, {3054, 33229}, {3096, 16925}, {3231, 35277}, {3329, 35007}, {3522, 11185}, {3524, 7763}, {3528, 34229}, {3543, 32867}, {3552, 7815}, {3734, 33014}, {3767, 33008}, {3785, 7796}, {3788, 7883}, {3839, 32883}, {3926, 15692}, {3934, 13586}, {3972, 5023}, {4563, 41462}, {5013, 6179}, {5024, 7894}, {5054, 7773}, {5210, 7770}, {5475, 33015}, {5569, 7746}, {6054, 32151}, {6292, 33225}, {6636, 26235}, {6655, 7749}, {6680, 33021}, {6781, 16044}, {7485, 11059}, {7622, 7903}, {7737, 33001}, {7748, 17004}, {7751, 20105}, {7757, 15815}, {7761, 7899}, {7767, 7799}, {7768, 15712}, {7776, 15693}, {7778, 7936}, {7780, 7783}, {7784, 7940}, {7787, 15482}, {7788, 15700}, {7790, 32965}, {7791, 7857}, {7800, 7835}, {7803, 33215}, {7807, 7831}, {7810, 7836}, {7812, 8182}, {7816, 33276}, {7819, 31268}, {7820, 10159}, {7822, 33246}, {7823, 31455}, {7828, 8356}, {7832, 31168}, {7839, 31652}, {7842, 32967}, {7843, 17005}, {7846, 16043}, {7848, 7947}, {7853, 33245}, {7854, 7891}, {7859, 8359}, {7860, 15720}, {7862, 7898}, {7865, 7945}, {7870, 7879}, {7873, 7925}, {7874, 7928}, {7886, 7924}, {7887, 7910}, {7888, 7929}, {7915, 15810}, {7930, 11288}, {7934, 33233}, {7937, 32954}, {7942, 11287}, {8150, 39652}, {8703, 32819}, {9698, 20088}, {9734, 12251}, {10303, 32884}, {10304, 32828}, {13334, 21445}, {14044, 39601}, {14869, 37647}, {15271, 33235}, {15683, 32897}, {15698, 32833}, {15705, 32830}, {15708, 32839}, {15710, 32822}, {15719, 32823}, {16922, 39590}, {16992, 19537}, {17006, 33256}, {17128, 32456}, {17504, 37671}, {17549, 18140}, {18146, 19704}, {20190, 39099}, {21395, 37814}, {21734, 32815}, {23234, 34510}, {26166, 37941}, {30737, 38448}, {31415, 33003}, {32816, 32871}, {33234, 37637}, {33770, 37522}

X(43459) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7830, 7911}, {3, 183, 7782}, {3, 1078, 99}, {3, 7771, 1078}, {187, 7824, 83}, {549, 7750, 7769}, {574, 7793, 7760}, {620, 2896, 7909}, {631, 14907, 7752}, {3053, 7786, 12150}, {3788, 7904, 7883}, {5023, 11285, 3972}, {6655, 7749, 14061}, {7750, 7769, 7809}, {7761, 7907, 7899}, {7763, 7811, 7917}, {7780, 8589, 7783}, {7791, 7857, 7919}, {7791, 21843, 7857}, {7793, 33022, 574}, {7800, 32964, 7835}, {7807, 7831, 7944}, {7810, 7836, 32027}, {7815, 8588, 3552}, {7874, 40344, 7928}, {7904, 33274, 3788}, {12042, 35464, 98}, {17004, 33275, 7748}, {17006, 33256, 39565}, {32027, 41134, 7836}

X(43460) = GIBERT (2t, t^2 - 1, 2 t^2) POINT, WHERE t = tan(ω)/sqrt(3)

Barycentrics    a^8 + 2*a^6*b^2 - 2*a^4*b^4 - b^8 + 2*a^6*c^2 - a^4*b^2*c^2 + b^6*c^2 - 2*a^4*c^4 + b^2*c^6 - c^8 : :
X(43460) = 3 X[98] - 4 X[230], 2 X[98] - 3 X[38227], 6 X[114] - 5 X[7925], 3 X[147] - X[7779], 2 X[230] - 3 X[1513], 8 X[230] - 9 X[38227], 2 X[325] - 3 X[6054], 3 X[376] - 4 X[32456], 3 X[842] - 4 X[16316], 4 X[1513] - 3 X[38227], 3 X[5999] - 5 X[7925], 2 X[6781] - 3 X[11676], X[7779] + 3 X[40236], 3 X[7799] - 2 X[35002], 2 X[10991] - 3 X[21445], 2 X[12188] - 3 X[14568], 3 X[12243] - 4 X[32457], 3 X[13586] - 2 X[38749], 2 X[14148] - 3 X[14981], 2 X[14830] - 3 X[26613], 3 X[34473] - 4 X[37459]

X(43460) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 1495}, {3, 3096}, {4, 39}, {5, 7859}, {6, 9993}, {15, 1080}, {16, 383}, {20, 7836}, {30, 99}, {69, 33706}, {98, 230}, {114, 5999}, {115, 39095}, {132, 41204}, {140, 6287}, {147, 511}, {182, 7875}, {183, 18440}, {186, 42426}, {187, 9862}, {376, 7761}, {381, 7790}, {385, 542}, {427, 1629}, {626, 7470}, {631, 7915}, {647, 5996}, {858, 16319}, {1281, 29097}, {1352, 16990}, {1529, 6530}, {2039, 6039}, {2040, 6040}, {2794, 5162}, {3014, 32224}, {3016, 12112}, {3098, 3314}, {3258, 7711}, {3329, 19130}, {3398, 40239}, {3424, 7607}, {3815, 12055}, {3830, 11163}, {3849, 9890}, {5000, 34239}, {5001, 34240}, {5111, 12830}, {5116, 13860}, {5167, 6000}, {5171, 9863}, {5188, 7848}, {5304, 6776}, {5418, 6811}, {5420, 6813}, {5477, 35388}, {5988, 29040}, {6194, 34507}, {6787, 14915}, {7000, 8982}, {7374, 26441}, {7735, 39874}, {7768, 9821}, {7774, 31670}, {7788, 33878}, {7828, 14880}, {7837, 37517}, {7840, 19924}, {7847, 37243}, {7849, 10357}, {7858, 14881}, {7876, 10356}, {7908, 30270}, {8356, 34681}, {9300, 14492}, {9418, 15920}, {9745, 35901}, {9749, 36766}, {9770, 15682}, {10168, 16987}, {10991, 21445}, {11171, 40250}, {11178, 16986}, {11179, 16989}, {11180, 15589}, {12110, 18907}, {12188, 14568}, {12243, 32457}, {13334, 37336}, {13586, 38749}, {14148, 14981}, {14484, 14488}, {14614, 39899}, {14660, 38975}, {14830, 26613}, {14853, 14930}, {15819, 18553}, {16988, 24206}, {21850, 41624}, {23208, 35476}, {28470, 41190}, {33971, 37074}, {34175, 36897}, {34473, 37459}, {34615, 41750}, {37451, 39884}, {37463, 42936}, {37464, 42937}

X(43460) = midpoint of X(147) and X(40236)
X(43460) = reflection of X(i) in X(j) for these {i,j}: {98, 1513}, {316, 6033}, {5999, 114}, {9862, 187}
X(43460) = Moses-radical-circle-inverse of X(32526)
X(43460) = crosspoint of X(98) and X(14492)
X(43460) = crosssum of X(511) and X(5092)
X(43460) = crossdifference of every pair of points on line {6041, 9210}
X(43460) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9996, 7831}, {4, 7710, 9744}, {4, 8721, 11257}, {4, 9744, 262}, {5, 12054, 7859}, {98, 1513, 38227}, {1352, 37182, 22712}, {5978, 5979, 7799}, {6033, 35705, 6054}

X(43461) = GIBERT (2t, t^2 - 1, 2 t^2) POINT, WHERE t = sqrt(3) tan(ω)

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

X(43461) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 98}, {3, 316}, {4, 574}, {5, 7786}, {6, 38227}, {15, 37463}, {16, 37464}, {20, 9734}, {39, 37446}, {83, 37466}, {99, 37348}, {115, 7709}, {126, 15921}, {140, 3096}, {183, 11898}, {211, 3567}, {230, 12007}, {262, 1513}, {325, 22712}, {353, 12494}, {376, 7622}, {383, 36969}, {511, 7777}, {549, 41133}, {568, 11675}, {575, 7806}, {598, 37461}, {620, 35925}, {625, 21163}, {626, 631}, {858, 42329}, {1007, 35387}, {1080, 36970}, {1340, 2039}, {1341, 2040}, {1350, 11184}, {1351, 11163}, {1353, 22329}, {1503, 3055}, {1656, 7859}, {2080, 7812}, {2548, 12110}, {2549, 14639}, {3054, 7607}, {3090, 7844}, {3106, 7684}, {3107, 7685}, {3314, 15819}, {3398, 7857}, {3523, 7912}, {3525, 6292}, {3564, 37688}, {3628, 7943}, {3767, 32467}, {3818, 39498}, {3972, 37459}, {4045, 36519}, {5025, 13334}, {5028, 7736}, {5031, 5085}, {5094, 14165}, {5099, 37991}, {5116, 13860}, {5169, 39506}, {5171, 7785}, {5475, 11676}, {5999, 17005}, {6114, 41098}, {6115, 41094}, {6248, 16921}, {6560, 6813}, {6561, 6811}, {6680, 10359}, {7617, 12243}, {7618, 12117}, {7694, 10722}, {7735, 9754}, {7753, 10788}, {7764, 12251}, {7775, 8722}, {7792, 10011}, {7820, 20399}, {7833, 13449}, {7835, 15561}, {7862, 37479}, {7878, 20576}, {7897, 40107}, {7907, 13335}, {7925, 37455}, {7938, 10303}, {9735, 36993}, {9736, 36995}, {9752, 37665}, {9755, 37637}, {9771, 9774}, {9863, 33015}, {9873, 31455}, {9880, 32480}, {9996, 38743}, {10033, 39884}, {11174, 37071}, {11185, 23235}, {11669, 14458}, {11842, 14693}, {12252, 32190}, {14492, 14494}, {15048, 39663}, {15484, 39656}, {15850, 20190}, {16051, 26870}, {32152, 33004}, {32522, 32966}, {34235, 38974}, {37988, 39682}, {38642, 40108}

X(43461) = crosspoint of X(262) and X(7607)
X(43461) = crosssum of X(182) and X(576)
X(43461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9744, 98}, {5, 11171, 7790}, {262, 1513, 9993}, {325, 37451, 22712}, {1513, 3815, 262}

X(43462) = GIBERT (2t, t^2 - 1, 2 t^2) POINT, WHERE t = -sqrt(3) cot A cot B cot C

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + a^6*c^2 + 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 + 3*a^2*c^6 + b^2*c^6 - c^8) : :
Barycentrics    (sec A) ((a^3 cos(B - C) - b^3 cos(C - A) - c^3 cos(A - B)) sec A + 2 a^2 cos(B - C) (b sec B + c sec C)) : :

X(43462) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 95}, {4, 74}, {6, 14165}, {15, 471}, {16, 470}, {53, 2052}, {182, 41203}, {264, 3580}, {297, 7790}, {316, 458}, {340, 15066}, {343, 14615}, {394, 22468}, {427, 9993}, {459, 39284}, {467, 15466}, {472, 36970}, {473, 36969}, {648, 37644}, {1075, 6750}, {1249, 11433}, {1515, 1596}, {1585, 6560}, {1586, 6561}, {1629, 1899}, {3168, 6747}, {5094, 38227}, {5523, 40814}, {7812, 41253}, {7859, 11331}, {8884, 18912}, {11004, 14920}, {11064, 27377}, {14461, 42353}, {17810, 42854}, {23293, 30506}, {26869, 33971}

X(43462) = polar conjugate of the isogonal conjugate of X(5890)
X(43462) = crosssum of X(577) and X(5158)
X(43462) = crossdifference of every pair of points on line {1636, 15451}
X(43462) = barycentric product X(264)*X(5890)
X(43462) = barycentric quotient X(5890)/X(3)

X(43463) = GIBERT (4,3,8) POINT

Barycentrics    2*a^2*S/Sqrt[3] + 4*a^2*SA + 3*SB*SC : :

X(43463) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 11485}, {3, 42627}, {4, 11480}, {6, 3525}, {13, 15698}, {15, 3090}, {16, 631}, {17, 10299}, {20, 42132}, {30, 43364}, {61, 42955}, {140, 42916}, {376, 16241}, {381, 42888}, {396, 15702}, {546, 42950}, {549, 42817}, {632, 43197}, {1656, 42492}, {3091, 42116}, {3146, 42146}, {3522, 42128}, {3523, 11542}, {3524, 5335}, {3528, 5318}, {3529, 10645}, {3530, 42815}, {3533, 11489}, {3544, 36836}, {3545, 16966}, {3628, 42923}, {3832, 42122}, {3839, 42130}, {3855, 42085}, {5056, 42117}, {5067, 5334}, {5068, 42126}, {5071, 5321}, {5072, 43365}, {5238, 42114}, {5344, 42773}, {5352, 42106}, {5365, 42970}, {7051, 8164}, {7486, 42125}, {7494, 37776}, {8889, 10632}, {10109, 42984}, {10188, 42920}, {10303, 11486}, {10304, 42127}, {10634, 16051}, {10646, 43004}, {10653, 15719}, {11001, 42094}, {11541, 42102}, {12812, 42963}, {12816, 43002}, {15022, 42135}, {15682, 37832}, {15692, 42123}, {15701, 42496}, {15704, 42962}, {15708, 42974}, {15709, 16963}, {15712, 22235}, {15715, 42155}, {15717, 42118}, {16239, 42818}, {16268, 42516}, {16808, 33703}, {16962, 43372}, {16964, 42473}, {17538, 42134}, {18581, 42936}, {19106, 42494}, {19107, 41099}, {19708, 33602}, {21734, 42131}, {21735, 42086}, {33416, 37641}, {36968, 42512}, {41106, 42942}, {41974, 43334}, {42104, 42581}, {42115, 42982}, {42150, 42915}, {42161, 42903}, {42162, 42900}, {42580, 42967}, {42931, 42935}, {42949, 42999}, {43200, 43235}

,p> X(43463) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3525, 43464}, {16, 11488, 42986}, {631, 42986, 16}, {5238, 42114, 42140}, {5334, 43029, 5067}, {10645, 42142, 3529}, {11480, 42098, 42108}, {11480, 43296, 42687}, {11485, 43103, 2}, {11488, 42092, 631}, {11489, 33417, 3533}, {15022, 43243, 42135}, {16772, 43029, 5334}, {16966, 42119, 3545}, {19107, 42472, 41099}, {19107, 42911, 42472}, {23302, 42945, 42098}, {33417, 42152, 11489}, {42096, 43296, 11480}, {42108, 42945, 11480}, {42124, 43103, 11485}

X(43464) = GIBERT (-4,3,8) POINT

Barycentrics    2*a^2*S/Sqrt[3] - 4*a^2*SA - 3*SB*SC : :

X(43464) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 11486}, {3, 42628}, {4, 11481}, {6, 3525}, {14, 15698}, {15, 631}, {16, 3090}, {18, 10299}, {20, 42129}, {30, 43365}, {62, 42954}, {140, 42917}, {376, 16242}, {381, 42889}, {395, 15702}, {546, 42951}, {549, 42818}, {632, 43198}, {1656, 42493}, {3091, 42115}, {3146, 42143}, {3522, 42125}, {3523, 11543}, {3524, 5334}, {3528, 5321}, {3529, 10646}, {3530, 42816}, {3533, 11488}, {3544, 36843}, {3545, 16967}, {3628, 42922}, {3832, 42123}, {3839, 42131}, {3855, 42086}, {5056, 42118}, {5067, 5335}, {5068, 42127}, {5071, 5318}, {5072, 43364}, {5237, 42111}, {5343, 42774}, {5351, 42103}, {5366, 42971}, {7486, 42128}, {7494, 37775}, {8164, 19373}, {8889, 10633}, {10109, 42985}, {10187, 42921}, {10303, 11485}, {10304, 42126}, {10635, 16051}, {10645, 43005}, {10654, 15719}, {11001, 42093}, {11541, 42101}, {12812, 42962}, {12817, 43003}, {15022, 42138}, {15682, 37835}, {15692, 42122}, {15701, 42497}, {15704, 42963}, {15708, 42975}, {15709, 16962}, {15712, 22237}, {15715, 42154}, {15717, 42117}, {16239, 42817}, {16267, 42517}, {16809, 33703}, {16963, 43373}, {16965, 42472}, {17538, 42133}, {18582, 42937}, {19106, 41099}, {19107, 42495}, {19708, 33603}, {21734, 42130}, {21735, 42085}, {33417, 37640}, {36967, 42513}, {41106, 42943}, {41973, 43335}, {42105, 42580}, {42116, 42983}, {42151, 42914}, {42159, 42901}, {42160, 42902}, {42581, 42966}, {42930, 42934}, {42948, 42998}, {43199, 43234}

X(43464) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3525, 43463}, {15, 11489, 42987}, {631, 42987, 15}, {5237, 42111, 42141}, {5335, 43028, 5067}, {10646, 42139, 3529}, {11481, 42095, 42109}, {11481, 43297, 42686}, {11486, 43102, 2}, {11488, 33416, 3533}, {11489, 42089, 631}, {15022, 43242, 42138}, {16773, 43028, 5335}, {16967, 42120, 3545}, {19106, 42473, 41099}, {19106, 42910, 42473}, {23303, 42944, 42095}, {33416, 42149, 11488}, {42097, 43297, 11481}, {42109, 42944, 11481}, {42121, 43102, 11486}

X(43465) = GIBERT (4,3,-2) POINT

Barycentrics    2*a^2*S/Sqrt[3] - a^2*SA + 3*SB*SC : :

X(43465) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 5318}, {3, 42627}, {4, 11409}, {6, 3146}, {13, 10304}, {14, 43397}, {15, 20}, {16, 3091}, {30, 42922}, {61, 42113}, {62, 42105}, {376, 11542}, {381, 42628}, {382, 42888}, {395, 42683}, {397, 5059}, {546, 42917}, {548, 42817}, {550, 42815}, {631, 42123}, {1250, 5261}, {3090, 42115}, {3522, 5340}, {3523, 5344}, {3524, 42132}, {3525, 42146}, {3528, 42124}, {3529, 11485}, {3543, 5334}, {3545, 42121}, {3628, 42962}, {3830, 42889}, {3832, 11489}, {3839, 16963}, {3845, 42818}, {3853, 42816}, {3854, 5350}, {3855, 42129}, {3857, 43198}, {5055, 42493}, {5056, 5366}, {5068, 23303}, {5237, 42114}, {5274, 19373}, {5321, 17578}, {5352, 42895}, {5362, 37435}, {5365, 43425}, {5418, 42234}, {5420, 42233}, {6560, 42175}, {6561, 42176}, {6623, 10633}, {6771, 31683}, {6995, 37775}, {7378, 11476}, {7486, 42089}, {8972, 42219}, {10303, 10646}, {10645, 43010}, {10654, 15640}, {11001, 42122}, {11129, 22513}, {11541, 42144}, {12811, 42951}, {12816, 42910}, {13941, 42217}, {14269, 42416}, {14869, 42950}, {15022, 36843}, {15682, 42126}, {15683, 37640}, {15685, 42633}, {15689, 42496}, {15692, 36968}, {15693, 33602}, {15697, 16960}, {15698, 42691}, {15705, 42625}, {15708, 33417}, {15717, 23302}, {15721, 37832}, {16242, 43310}, {16645, 42473}, {16809, 43195}, {17538, 42116}, {19107, 41974}, {19780, 37689}, {21734, 42156}, {22238, 42102}, {23249, 42245}, {23259, 42244}, {33416, 42921}, {33703, 42117}, {34755, 42103}, {35414, 42587}, {36967, 42635}, {36995, 38227}, {37641, 42093}, {38335, 42634}, {41099, 42913}, {41100, 43005}, {41106, 43109}, {41107, 42099}, {41113, 42800}, {41119, 42528}, {42085, 42431}, {42150, 43205}, {42429, 42511}, {42472, 43028}, {42474, 43420}, {42494, 43029}, {42499, 42958}, {42693, 42775}, {42804, 42902}, {42894, 43398}, {42905, 42933}, {42929, 42939}, {42956, 43201}, {42972, 43335}, {43302, 43324}, {43326, 43428}

X(43465) = crosssum of X(11481) and X(22236)
X(43465) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 42987, 42135}, {6, 3146, 43466}, {6, 42109, 42140}, {6, 42141, 3146}, {6, 42165, 42141}, {15, 5335, 42982}, {16, 42134, 3091}, {16, 42161, 42134}, {20, 42982, 15}, {62, 42105, 42133}, {62, 42133, 42983}, {62, 42629, 42105}, {397, 42097, 42119}, {3091, 42134, 43364}, {3091, 43242, 16}, {3522, 5340, 22235}, {5318, 11481, 42142}, {5318, 42120, 2}, {5318, 42155, 42120}, {5318, 42943, 42098}, {5318, 43106, 11481}, {5334, 19106, 3543}, {5335, 42086, 20}, {5340, 42088, 11488}, {5344, 42158, 3523}, {5366, 42151, 5056}, {10653, 19106, 5334}, {11481, 42142, 2}, {11481, 42155, 43106}, {11481, 43106, 42120}, {11485, 42145, 3529}, {11486, 42127, 42137}, {11486, 42135, 42987}, {11486, 42137, 4}, {11488, 42088, 3522}, {11489, 42094, 3832}, {11542, 42131, 376}, {16965, 42086, 5335}, {17538, 42986, 42116}, {22238, 42102, 42139}, {36968, 43403, 15692}, {40693, 42086, 42100}, {42094, 42148, 11489}, {42097, 42119, 5059}, {42109, 42140, 3146}, {42111, 42900, 42134}, {42115, 42138, 3090}, {42116, 42584, 17538}, {42118, 42127, 4}, {42118, 42137, 11486}, {42120, 42142, 11481}, {42123, 42128, 631}, {42140, 42141, 42109}, {42155, 42971, 42142}, {42161, 43242, 43364}, {42211, 42213, 42127}, {42971, 43106, 5318}

X(43466) = GIBERT (4,-3,2) POINT

Barycentrics    2*a^2*S/Sqrt[3] + a^2*SA - 3*SB*SC : :

X(43466) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 5321}, {3, 42628}, {4, 11408}, {6, 3146}, {13, 43398}, {14, 10304}, {15, 3091}, {16, 20}, {30, 42923}, {61, 42104}, {62, 42112}, {376, 11543}, {381, 42627}, {382, 42889}, {396, 42682}, {398, 5059}, {546, 42916}, {548, 42818}, {550, 42816}, {631, 42122}, {3090, 42116}, {3522, 5339}, {3523, 5343}, {3524, 42129}, {3525, 42143}, {3528, 42121}, {3529, 11486}, {3543, 5335}, {3545, 42124}, {3628, 42963}, {3830, 42888}, {3832, 11488}, {3839, 16962}, {3845, 42817}, {3853, 42815}, {3854, 5349}, {3855, 42132}, {3857, 43197}, {5055, 42492}, {5056, 5365}, {5068, 23302}, {5238, 42111}, {5261, 10638}, {5274, 7051}, {5318, 17578}, {5351, 42894}, {5366, 43424}, {5367, 37435}, {5418, 42232}, {5420, 42231}, {6560, 42177}, {6561, 42178}, {6623, 10632}, {6774, 31684}, {6995, 37776}, {7378, 11475}, {7486, 42092}, {8972, 42220}, {10303, 10645}, {10646, 43011}, {10653, 15640}, {11001, 42123}, {11128, 22512}, {11541, 42145}, {12811, 42950}, {12817, 42911}, {13941, 42218}, {14269, 42415}, {14869, 42951}, {15022, 36836}, {15682, 42127}, {15683, 37641}, {15685, 42634}, {15689, 42497}, {15692, 36967}, {15693, 33603}, {15697, 16961}, {15698, 42690}, {15705, 42626}, {15708, 33416}, {15717, 23303}, {15721, 37835}, {16241, 43311}, {16644, 42472}, {16808, 43196}, {17538, 42115}, {19106, 41973}, {19781, 37689}, {21734, 42153}, {22236, 42101}, {23249, 42243}, {23259, 42242}, {33417, 42920}, {33703, 42118}, {34754, 42106}, {35414, 42586}, {36968, 42636}, {36993, 38227}, {37640, 42094}, {38335, 42633}, {41099, 42912}, {41101, 43004}, {41106, 43108}, {41108, 42100}, {41112, 42799}, {41120, 42529}, {42086, 42432}, {42151, 43206}, {42430, 42510}, {42473, 43029}, {42475, 43421}, {42495, 43028}, {42498, 42959}, {42692, 42776}, {42803, 42903}, {42895, 43397}, {42904, 42932}, {42928, 42938}, {42957, 43202}, {42973, 43334}, {43303, 43325}, {43327, 43429}

X(43466) = crosssum of X(11480) and X(22238)
X(43466) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 42986, 42138}, {6, 3146, 43465}, {6, 42108, 42141}, {6, 42140, 3146}, {6, 42164, 42140}, {15, 42133, 3091}, {15, 42160, 42133}, {16, 5334, 42983}, {20, 42983, 16}, {61, 42104, 42134}, {61, 42134, 42982}, {61, 42630, 42104}, {398, 42096, 42120}, {3091, 42133, 43365}, {3091, 43243, 15}, {3522, 5339, 22237}, {5321, 11480, 42139}, {5321, 42119, 2}, {5321, 42154, 42119}, {5321, 42942, 42095}, {5321, 43105, 11480}, {5334, 42085, 20}, {5335, 19107, 3543}, {5339, 42087, 11489}, {5343, 42157, 3523}, {5365, 42150, 5056}, {10654, 19107, 5335}, {11480, 42139, 2}, {11480, 42154, 43105}, {11480, 43105, 42119}, {11485, 42126, 42136}, {11485, 42136, 4}, {11485, 42138, 42986}, {11486, 42144, 3529}, {11488, 42093, 3832}, {11489, 42087, 3522}, {11543, 42130, 376}, {16964, 42085, 5334}, {17538, 42987, 42115}, {22236, 42101, 42142}, {36967, 43404, 15692}, {40694, 42085, 42099}, {42093, 42147, 11488}, {42096, 42120, 5059}, {42108, 42141, 3146}, {42114, 42901, 42133}, {42115, 42585, 17538}, {42116, 42135, 3090}, {42117, 42126, 4}, {42117, 42136, 11485}, {42119, 42139, 11480}, {42122, 42125, 631}, {42140, 42141, 42108}, {42154, 42970, 42139}, {42160, 43243, 43365}, {42212, 42214, 42126}, {42970, 43105, 5321}

X(43467) = GIBERT (5,12,25) POINT

Barycentrics    5*a^2*S/Sqrt[3] + 25*a^2*SA + 24*SB*SC : :

X(43467) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 16961}, {3, 43195}, {4, 33417}, {5, 43196}, {6, 42592}, {13, 11540}, {15, 3628}, {16, 3526}, {62, 42954}, {140, 42797}, {547, 43105}, {548, 42110}, {549, 16966}, {632, 34755}, {3856, 42099}, {3857, 42108}, {5055, 11480}, {5066, 43227}, {5070, 42934}, {5072, 10645}, {5318, 42596}, {5351, 42950}, {5352, 15022}, {7486, 42092}, {10188, 11542}, {10303, 10646}, {10304, 42105}, {11481, 43300}, {11485, 42936}, {11543, 42957}, {12812, 42630}, {14890, 42796}, {15698, 42100}, {15706, 42094}, {15709, 18582}, {15717, 16808}, {15723, 43250}, {16239, 16960}, {16241, 42139}, {16267, 33416}, {16644, 43233}, {16809, 42687}, {17800, 42610}, {23302, 42937}, {33606, 42912}, {33699, 42500}, {36836, 43301}, {37832, 42903}, {40693, 42499}, {41107, 42984}, {41108, 42690}, {41122, 42923}, {41984, 43200}, {42085, 42694}, {42089, 43004}, {42095, 42509}, {42097, 42476}, {42116, 42964}, {42126, 43299}, {42136, 42684}, {42141, 42581}, {42530, 43447}, {42631, 42911}, {42691, 42958}, {42801, 42979}, {42895, 42966}, {42944, 43328}, {42948, 43030}, {42978, 43442}, {42989, 43309}, {43005, 43197}, {43107, 43248}, {43303, 43370}

X(43467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3526, 42488, 42935}, {3628, 42955, 15}, {10188, 42498, 11542}

X(43468) = GIBERT (-5,12,25) POINT

Barycentrics    5*a^2*S/Sqrt[3] - 25*a^2*SA - 24*SB*SC : :

X(43468) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 16960}, {3, 43196}, {4, 33416}, {5, 43195}, {6, 42592}, {14, 11540}, {15, 3526}, {16, 3628}, {61, 42955}, {140, 42798}, {547, 43106}, {548, 42107}, {549, 16967}, {632, 34754}, {3856, 42100}, {3857, 42109}, {5055, 11481}, {5066, 43226}, {5070, 42935}, {5072, 10646}, {5321, 42597}, {5351, 15022}, {5352, 42951}, {7486, 42089}, {10187, 11543}, {10303, 10645}, {10304, 42104}, {11480, 43301}, {11486, 42937}, {11542, 42956}, {12812, 42629}, {14890, 42795}, {15698, 42099}, {15706, 42093}, {15709, 18581}, {15717, 16809}, {15723, 43251}, {16239, 16961}, {16242, 42142}, {16268, 33417}, {16645, 43232}, {16808, 42686}, {17800, 42611}, {23303, 42936}, {33607, 42913}, {33699, 42501}, {36843, 43300}, {37835, 42902}, {40694, 42498}, {41107, 42691}, {41108, 42985}, {41121, 42922}, {41984, 43199}, {42086, 42695}, {42092, 43005}, {42096, 42477}, {42098, 42508}, {42115, 42965}, {42127, 43298}, {42137, 42685}, {42140, 42580}, {42531, 43446}, {42632, 42910}, {42690, 42959}, {42802, 42978}, {42894, 42967}, {42945, 43329}, {42949, 43031}, {42979, 43443}, {42988, 43308}, {43004, 43198}, {43100, 43249}, {43302, 43371}

X(43468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3526, 42489, 42934}, {3628, 42954, 16}, {10187, 42499, 11543}

X(43469) = GIBERT (7,24,49) POINT

Barycentrics    7*a^2*S/Sqrt[3] + 49*a^2*SA + 48*SB*SC : :

X(43469) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {4, 43441}, {6, 43470}, {15, 5070}, {16, 632}, {140, 42928}, {547, 33417}, {3091, 43325}, {3530, 42100}, {5054, 36969}, {5079, 10645}, {5238, 42111}, {8703, 42919}, {11540, 42931}, {11543, 42936}, {12103, 43226}, {12811, 42108}, {15692, 42106}, {15696, 42915}, {15719, 19106}, {16239, 43008}, {16963, 41984}, {16967, 42799}, {21734, 42596}, {33416, 42982}, {41978, 43335}, {42092, 42972}, {42110, 43324}, {42132, 42800}, {42140, 43331}, {42142, 42900}, {42499, 42992}, {42590, 42954}, {42914, 42945}, {42937, 42979}

X(43470) = GIBERT (-7,24,49) POINT

Barycentrics    7*a^2*S/Sqrt[3] - 49*a^2*SA - 48*SB*SC : :

X(43470) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {4, 43440}, {6, 43469}, {15, 632}, {16, 5070}, {140, 42929}, {547, 33416}, {3091, 43324}, {3530, 42099}, {5054, 36970}, {5079, 10646}, {5237, 42114}, {8703, 42918}, {11540, 42930}, {11542, 42937}, {12103, 43227}, {12811, 42109}, {15692, 42103}, {15696, 42914}, {15719, 19107}, {16239, 43009}, {16962, 41984}, {16966, 42800}, {21734, 42597}, {33417, 42983}, {41977, 43334}, {42089, 42973}, {42107, 43325}, {42129, 42799}, {42139, 42901}, {42141, 43330}, {42498, 42993}, {42591, 42955}, {42915, 42944}, {42936, 42978}

X(43471) = GIBERT (7,24,-1) POINT

Barycentrics    7*a^2*S/Sqrt[3] - a^2*SA + 48*SB*SC : :

X(43471) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42100}, {4, 43309}, {13, 42888}, {15, 3627}, {16, 3843}, {30, 42930}, {62, 42900}, {548, 42110}, {1657, 42098}, {3091, 43292}, {3850, 19106}, {3853, 42435}, {5072, 10646}, {5237, 42111}, {5318, 43196}, {10303, 43324}, {10654, 43398}, {11480, 15684}, {11543, 14893}, {12108, 42109}, {12812, 42584}, {12820, 16267}, {14892, 33416}, {15686, 16966}, {15712, 42915}, {16808, 33703}, {16809, 42801}, {16963, 41972}, {17538, 42106}, {18582, 43399}, {19107, 42903}, {23046, 42918}, {34755, 42103}, {36970, 38335}, {41106, 43330}, {41122, 42127}, {41990, 42631}, {42086, 42978}, {42087, 42980}, {42101, 43235}, {42128, 42802}, {42135, 42965}, {42160, 43302}, {42161, 43011}, {42429, 42472}, {42627, 42952}, {42929, 42945}, {42970, 43416}

X(43472) = GIBERT (7,-24,1) POINT

Barycentrics    7*a^2*S/Sqrt[3] + a^2*SA - 48*SB*SC : :

X(43472) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42099}, {4, 43308}, {14, 42889}, {15, 3843}, {16, 3627}, {30, 42931}, {61, 42901}, {548, 42107}, {1657, 42095}, {3091, 43293}, {3850, 19107}, {3853, 42436}, {5072, 10645}, {5238, 42114}, {5321, 43195}, {10303, 43325}, {10653, 43397}, {11481, 15684}, {11542, 14893}, {12108, 42108}, {12812, 42585}, {12821, 16268}, {14892, 33417}, {15686, 16967}, {15712, 42914}, {16808, 42802}, {16809, 33703}, {16962, 41971}, {17538, 42103}, {18581, 43400}, {19106, 42902}, {23046, 42919}, {34754, 42106}, {36969, 38335}, {41106, 43331}, {41121, 42126}, {41990, 42632}, {42085, 42979}, {42088, 42981}, {42102, 43234}, {42125, 42801}, {42138, 42964}, {42160, 43010}, {42161, 43303}, {42430, 42473}, {42628, 42953}, {42928, 42944}, {42971, 43417}

X(43473) = GIBERT (8,15,-2) POINT

Barycentrics    4*a^2*S/Sqrt[3] - a^2*SA + 15*SB*SC : :

X(43473) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42088}, {4, 42816}, {15, 3146}, {16, 3832}, {20, 42132}, {382, 42986}, {546, 43242}, {631, 42889}, {3091, 42115}, {3522, 19106}, {3523, 42584}, {3529, 42627}, {3543, 11485}, {3545, 42933}, {3627, 42982}, {3839, 42127}, {3851, 42926}, {3854, 42120}, {5059, 5350}, {5068, 42086}, {5073, 42916}, {5076, 42923}, {5318, 17578}, {5334, 43196}, {5335, 36970}, {5351, 15022}, {7486, 42131}, {10299, 42492}, {10303, 42145}, {10304, 43103}, {11489, 42683}, {12816, 42090}, {15682, 42496}, {15683, 18582}, {15697, 43246}, {15705, 16966}, {15717, 16808}, {16961, 36969}, {17538, 42962}, {19708, 42984}, {21734, 42097}, {22235, 42096}, {22238, 42102}, {42085, 42435}, {42113, 43294}, {42116, 42907}, {42130, 43328}, {42142, 43298}, {42159, 42900}, {42161, 43195}, {42430, 43403}, {42588, 43304}, {42781, 43402}, {42998, 43398}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42094, 42141, 43364}, {42141, 43364, 2}

X(43474) = GIBERT (8,-15,2) POINT

Barycentrics    4*a^2*S/Sqrt[3] + a^2*SA - 15*SB*SC : :

X(43474) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42087}, {4, 42815}, {15, 3832}, {16, 3146}, {20, 42129}, {382, 42987}, {546, 43243}, {631, 42888}, {3091, 42116}, {3522, 19107}, {3523, 42585}, {3529, 42628}, {3543, 11486}, {3545, 42932}, {3627, 42983}, {3839, 42126}, {3851, 42927}, {3854, 42119}, {5059, 5349}, {5068, 42085}, {5073, 42917}, {5076, 42922}, {5321, 17578}, {5334, 36969}, {5335, 43195}, {5352, 15022}, {7486, 42130}, {10299, 42493}, {10303, 42144}, {10304, 43102}, {11488, 42682}, {12817, 42091}, {15682, 42497}, {15683, 18581}, {15697, 43247}, {15705, 16967}, {15717, 16809}, {16960, 36970}, {17538, 42963}, {19708, 42985}, {21734, 42096}, {22236, 42101}, {22237, 42097}, {38335, 43252}, {42086, 42436}, {42112, 43295}, {42115, 42906}, {42131, 43329}, {42139, 43299}, {42160, 43196}, {42162, 42901}, {42429, 43404}, {42589, 43305}, {42782, 43401}, {42999, 43397}

X(43474) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42093, 42140, 43365}, {42140, 43365, 2}

X(43475) = GIBERT (9,40,-1) POINT

Barycentrics    3*Sqrt[3]*a^2*S - a^2*SA + 80*SB*SC : :
X(43475) = 53 X[42581] - 44 X[42590], 14 X[42581] - 11 X[42936], 56 X[42590] - 53 X[42936]

X(43475) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42113}, {4, 12817}, {13, 43398}, {14, 42782}, {15, 3830}, {16, 3845}, {30, 42581}, {61, 38335}, {381, 5351}, {382, 42979}, {3543, 5238}, {3627, 41943}, {3839, 42431}, {3853, 42960}, {3860, 36968}, {3861, 16963}, {5066, 43226}, {5076, 16267}, {5334, 42481}, {5366, 43252}, {8703, 42919}, {10109, 42100}, {10645, 43399}, {10654, 12820}, {11541, 43002}, {11812, 42429}, {12101, 12816}, {12102, 42992}, {14269, 22238}, {14893, 16268}, {15640, 42106}, {15682, 37832}, {15687, 41101}, {15690, 43292}, {15702, 42514}, {16808, 33699}, {16962, 43013}, {19106, 41099}, {19107, 33607}, {22236, 35401}, {23046, 42489}, {33604, 43301}, {34754, 43400}, {35403, 42973}, {36448, 42177}, {36466, 42178}, {36969, 42125}, {37641, 42900}, {38071, 42948}, {41100, 43005}, {41106, 42105}, {41108, 42094}, {41120, 43227}, {41973, 42520}, {42103, 42588}, {42111, 42933}, {42116, 42952}, {42127, 42977}, {42128, 43366}, {42136, 43232}, {42162, 42589}, {42432, 42695}, {42503, 42683}, {42506, 42940}, {42508, 43429}, {42629, 43109}, {42633, 42905}, {42888, 43021}, {42914, 43295}, {43293, 43369}

X(43475) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {12101, 12816, 36970}, {12101, 42102, 12816}, {16808, 33699, 42632}, {19107, 33607, 43108}, {33607, 43108, 42976}

X(43476) = GIBERT (9,-40,1) POINT

Barycentrics    3*Sqrt[3]*a^2*S + a^2*SA - 80*SB*SC : :
X)43476) = 53 X[42580] - 44 X[42591], 14 X[42580] - 11 X[42937], 56 X[42591] - 53 X[42937]

X(43476) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42112}, {4, 12816}, {13, 42781}, {14, 43397}, {15, 3845}, {16, 3830}, {30, 42580}, {62, 38335}, {381, 5352}, {382, 42978}, {3543, 5237}, {3627, 41944}, {3839, 42432}, {3853, 42961}, {3860, 36967}, {3861, 16962}, {5066, 43227}, {5076, 16268}, {5335, 42480}, {8703, 42918}, {10109, 42099}, {10646, 43400}, {10653, 12821}, {11541, 43003}, {11812, 42430}, {12101, 12817}, {12102, 42993}, {14269, 22236}, {14893, 16267}, {15640, 42103}, {15682, 37835}, {15687, 41100}, {15690, 43293}, {15702, 42515}, {16809, 33699}, {16963, 43012}, {19106, 33606}, {19107, 41099}, {22238, 35401}, {23046, 42488}, {33605, 43300}, {34755, 43399}, {35403, 42972}, {36448, 42176}, {36466, 42175}, {36970, 42128}, {37640, 42901}, {38071, 42949}, {41101, 43004}, {41106, 42104}, {41107, 42093}, {41119, 43226}, {41974, 42521}, {42106, 42589}, {42114, 42932}, {42115, 42953}, {42125, 43367}, {42126, 42976}, {42137, 43233}, {42159, 42588}, {42431, 42694}, {42502, 42682}, {42507, 42941}, {42509, 43428}, {42630, 43108}, {42634, 42904}, {42889, 43020}, {42915, 43294}, {43292, 43368}

X(43476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {12101, 12817, 36969}, {12101, 42101, 12817}, {16809, 33699, 42631}, {19106, 33606, 43109}, {33606, 43109, 42977}

X(43477) = GIBERT (12,35,-2) POINT

Barycentrics    2*Sqrt[3]*a^2*S - a^2*SA + 35*SB*SC : :

X(43477) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42097}, {4, 42975}, {13, 43018}, {15, 3543}, {16, 3839}, {20, 42911}, {30, 43364}, {381, 42889}, {395, 42683}, {3091, 36968}, {3146, 16644}, {3832, 36843}, {5335, 43196}, {10304, 42105}, {10653, 43195}, {11488, 43421}, {12816, 42803}, {12820, 18582}, {14269, 42497}, {15022, 42625}, {15640, 42932}, {15682, 42116}, {15692, 42106}, {15705, 42110}, {17578, 22235}, {33602, 43207}, {34755, 43368}, {36969, 41120}, {36970, 41112}, {37640, 42094}, {37641, 42692}, {38071, 42985}, {42086, 43292}, {42119, 43332}, {42141, 42686}, {42160, 43424}, {42904, 42983}, {42973, 43302}, {43293, 43369}

X(43477) = {X(42094),X(42940)}-harmonic conjugate of X(43201)

X(43478) = GIBERT (12,-35,2) POINT

Barycentrics    2*Sqrt[3]*a^2*S + a^2*SA - 35*SB*SC : :

X(43478) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42096}, {4, 42974}, {14, 43019}, {15, 3839}, {16, 3543}, {20, 42910}, {30, 43365}, {381, 42888}, {396, 42682}, {3091, 36967}, {3146, 16645}, {3832, 36836}, {5318, 43252}, {5334, 43195}, {10304, 42104}, {10654, 43196}, {11489, 43420}, {12817, 42804}, {12821, 18581}, {14269, 42496}, {15022, 42626}, {15640, 42933}, {15682, 42115}, {15692, 42103}, {15705, 42107}, {17578, 22237}, {33603, 43208}, {34754, 43369}, {36969, 41113}, {36970, 41119}, {37640, 42693}, {37641, 42093}, {38071, 42984}, {42085, 43293}, {42120, 43333}, {42140, 42687}, {42161, 43425}, {42905, 42982}, {42972, 43303}, {43292, 43368}

X(43478) = {X(42093),X(42941)}-harmonic conjugate of X(43202)

X(43479) = GIBERT (12,5,18) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 9*a^2*SA + 5*SB*SC : :

X(43479) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 398}, {3, 42496}, {4, 42116}, {6, 43480}, {15, 5056}, {16, 3523}, {17, 20}, {61, 43200}, {62, 15708}, {140, 42917}, {396, 15717}, {631, 42805}, {632, 43446}, {1656, 42492}, {3090, 43417}, {3091, 36970}, {3146, 16644}, {3411, 42892}, {3522, 5340}, {3524, 42924}, {3525, 42912}, {3526, 42497}, {3533, 11485}, {3543, 5238}, {3628, 42969}, {3832, 36836}, {3839, 42432}, {3851, 43365}, {3854, 42119}, {5059, 5350}, {5068, 23302}, {5073, 42627}, {5334, 42936}, {5344, 10645}, {5365, 16966}, {10188, 42111}, {10299, 42988}, {10303, 16241}, {10304, 41112}, {11132, 32829}, {11542, 21735}, {15022, 42147}, {15640, 42434}, {15683, 42166}, {15692, 40693}, {15697, 42161}, {15705, 42148}, {15712, 43197}, {15721, 16962}, {16239, 42985}, {16242, 43018}, {16960, 42959}, {16961, 42092}, {17504, 43207}, {17578, 42598}, {18582, 43195}, {21734, 43332}, {22238, 43428}, {33417, 42983}, {33923, 42817}, {37640, 42490}, {40694, 42593}, {41978, 43335}, {42085, 42979}, {42086, 43424}, {42087, 42775}, {42100, 43016}, {42141, 42687}, {42151, 42928}, {42157, 43196}, {42495, 43029}, {42510, 42797}, {42958, 43014}, {42978, 43022}, {43247, 43445}

X(43479) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 42932, 5352}, {3522, 11488, 22235}, {5352, 43403, 20}, {11488, 42945, 3522}, {22236, 43238, 42949}

X(43480) = GIBERT (-12,5,18) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 9*a^2*SA - 5*SB*SC : :

X(43480) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 397}, {3, 42497}, {4, 42115}, {6, 43479}, {15, 3523}, {16, 5056}, {18, 20}, {61, 15708}, {62, 43199}, {140, 42916}, {395, 15717}, {631, 42806}, {632, 43447}, {1656, 42493}, {3090, 43416}, {3091, 36969}, {3146, 16645}, {3412, 42893}, {3522, 5339}, {3524, 42925}, {3525, 42913}, {3526, 42496}, {3533, 11486}, {3543, 5237}, {3628, 42968}, {3832, 36843}, {3839, 42431}, {3851, 43364}, {3854, 42120}, {5059, 5349}, {5068, 23303}, {5073, 42628}, {5335, 42937}, {5343, 10646}, {5366, 16967}, {10187, 42114}, {10299, 42989}, {10303, 16242}, {10304, 41113}, {11133, 32829}, {11543, 21735}, {15022, 42148}, {15640, 42433}, {15683, 42163}, {15692, 40694}, {15697, 42160}, {15705, 42147}, {15712, 43198}, {15721, 16963}, {16239, 42984}, {16241, 43019}, {16960, 42089}, {16961, 42958}, {17504, 43208}, {17578, 42599}, {18581, 43196}, {21734, 43333}, {22236, 43429}, {33416, 42982}, {33923, 42818}, {37641, 42491}, {40693, 42592}, {41977, 43334}, {42085, 43425}, {42086, 42978}, {42088, 42776}, {42099, 43017}, {42140, 42686}, {42150, 42929}, {42158, 43195}, {42494, 43028}, {42511, 42798}, {42959, 43015}, {42979, 43023}, {43246, 43444}

X(43480) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 42933, 5351}, {3522, 11489, 22237}, {5351, 43404, 20}, {11489, 42944, 3522}, {22238, 43239, 42948}

X(43481) = GIBERT (12,5,-8) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 4*a^2*SA + 5*SB*SC : :

X(43481) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 33602}, {3, 42496}, {4, 395}, {6, 11001}, {13, 631}, {14, 42141}, {15, 376}, {16, 3545}, {20, 42803}, {30, 42923}, {62, 33703}, {140, 42984}, {299, 32817}, {381, 42628}, {382, 42634}, {396, 19708}, {397, 3528}, {398, 11541}, {616, 3096}, {3090, 16965}, {3146, 42924}, {3522, 42912}, {3524, 5335}, {3525, 5340}, {3529, 10654}, {3530, 22235}, {3533, 5237}, {3543, 11486}, {3544, 5366}, {3839, 42127}, {3855, 37835}, {5067, 5344}, {5071, 5318}, {5076, 22237}, {5334, 43106}, {6396, 35737}, {10299, 16241}, {10304, 42123}, {10646, 15719}, {11296, 14929}, {11481, 15702}, {11488, 15698}, {11489, 36969}, {11540, 42950}, {11542, 15692}, {12100, 42815}, {12816, 42111}, {14893, 42818}, {15640, 42145}, {15681, 42416}, {15682, 36970}, {15683, 42131}, {15689, 42633}, {15705, 42124}, {15707, 42627}, {15709, 18582}, {15710, 42930}, {15721, 42132}, {16242, 42142}, {16268, 42105}, {16645, 41106}, {16808, 43300}, {16963, 41972}, {17504, 42817}, {17538, 42942}, {18581, 43195}, {19106, 42902}, {21734, 42988}, {21735, 40693}, {22489, 31683}, {33603, 42133}, {33604, 42685}, {33699, 42816}, {34200, 42922}, {34755, 43399}, {35403, 42889}, {38071, 43364}, {38335, 42497}, {40694, 42517}, {41108, 42113}, {41122, 42629}, {41944, 42106}, {42089, 42973}, {42092, 43418}, {42097, 43229}, {42100, 42800}, {42112, 42589}, {42143, 42689}, {42150, 42935}, {42157, 43006}, {42479, 43008}, {42481, 43325}, {42507, 43400}, {42533, 43032}, {42632, 43030}, {42776, 42805}, {42891, 43330}, {42972, 43020}, {43029, 43420}

X(43481) = crosssum of X(11485) and X(42115)
X(43481) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 11001, 43482}, {631, 42926, 5351}, {3544, 16773, 43446}, {5335, 42943, 3524}, {5344, 36843, 5067}, {5366, 16773, 3544}, {10653, 36968, 37640}, {10653, 42120, 376}, {11481, 43403, 15702}, {11489, 36969, 41099}, {11489, 42588, 36969}, {16645, 42134, 41106}, {22238, 42155, 42941}, {22238, 42941, 43404}, {36968, 37640, 376}, {36969, 42510, 11489}, {37640, 42120, 36968}, {37641, 42086, 15682}, {41100, 42086, 37641}, {42115, 43416, 2}, {42123, 42974, 10304}, {42127, 42913, 3839}, {42155, 43304, 22238}, {42510, 42588, 41099}, {42941, 43404, 4}, {42998, 43193, 17538}, {43246, 43416, 42128}

X(43482) = GIBERT (12,-5,8) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 4*a^2*SA - 5*SB*SC : :

X(43482) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 33603}, {3, 42497}, {4, 396}, {6, 11001}, {13, 42140}, {14, 631}, {15, 3545}, {16, 376}, {20, 42804}, {30, 42922}, {61, 33703}, {140, 42985}, {298, 32817}, {381, 42627}, {382, 42633}, {395, 19708}, {397, 11541}, {398, 3528}, {617, 3096}, {3090, 16964}, {3146, 42925}, {3522, 42913}, {3524, 5334}, {3525, 5339}, {3526, 43253}, {3529, 10653}, {3530, 22237}, {3533, 5238}, {3543, 11485}, {3544, 5365}, {3839, 42126}, {3855, 37832}, {5067, 5343}, {5071, 5321}, {5076, 22235}, {5335, 43105}, {6200, 35737}, {10299, 16242}, {10304, 42122}, {10645, 15719}, {11295, 14929}, {11480, 15702}, {11488, 36970}, {11489, 15698}, {11540, 42951}, {11543, 15692}, {12100, 42816}, {12817, 42114}, {14893, 42817}, {15640, 42144}, {15681, 42415}, {15682, 36969}, {15683, 42130}, {15689, 42634}, {15705, 42121}, {15707, 42628}, {15709, 18581}, {15710, 42931}, {15721, 42129}, {16241, 42139}, {16267, 42104}, {16644, 41106}, {16809, 43301}, {16962, 41971}, {17504, 42818}, {17538, 42943}, {18582, 43196}, {19107, 42903}, {21734, 42989}, {21735, 40694}, {22490, 31684}, {33602, 42134}, {33605, 42684}, {33699, 42815}, {34200, 42923}, {34754, 43400}, {35403, 42888}, {38071, 43365}, {38335, 42496}, {40693, 42516}, {41107, 42112}, {41121, 42630}, {41943, 42103}, {42089, 43419}, {42092, 42972}, {42096, 43228}, {42099, 42799}, {42113, 42588}, {42146, 42688}, {42151, 42934}, {42158, 43007}, {42478, 43009}, {42480, 43324}, {42506, 43399}, {42532, 43033}, {42631, 43031}, {42775, 42806}, {42890, 43331}, {42973, 43021}, {43028, 43421}

X(43482) = crosssum of X(11486) and X(42116)
X(43482) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 11001, 43481}, {631, 42927, 5352}, {3544, 16772, 43447}, {5334, 42942, 3524}, {5343, 36836, 5067}, {5365, 16772, 3544}, {10654, 36967, 37641}, {10654, 42119, 376}, {11480, 43404, 15702}, {11488, 36970, 41099}, {11488, 42589, 36970}, {16644, 42133, 41106}, {22236, 42154, 42940}, {22236, 42940, 43403}, {36967, 37641, 376}, {36970, 42511, 11488}, {37640, 42085, 15682}, {37641, 42119, 36967}, {41101, 42085, 37640}, {42116, 43417, 2}, {42122, 42975, 10304}, {42126, 42912, 3839}, {42154, 43305, 22236}, {42511, 42589, 41099}, {42940, 43403, 4}, {42999, 43194, 17538}, {43247, 43417, 42125}

X(43483) = GIBERT (15,8,25) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 25*a^2*SA + 16*SB*SC : :
X(43483) = 28 X[42687] + 5 X[43195], 2 X[42687] + 5 X[43199], 52 X[42687] - 5 X[43231], 14 X[42795] + 5 X[43195], X[42795] + 5 X[43199], 26 X[42795] - 5 X[43231], X[43195] - 14 X[43199], 13 X[43195] + 7 X[43231], 26 X[43199] + X[43231]

X(43483) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 33606}, {3, 43000}, {4, 5238}, {5, 42947}, {6, 43484}, {13, 10304}, {14, 3628}, {15, 5055}, {16, 396}, {17, 548}, {18, 43007}, {20, 42512}, {30, 42687}, {61, 3526}, {140, 42939}, {381, 43196}, {395, 11540}, {550, 42960}, {619, 7859}, {632, 42780}, {3091, 43245}, {3411, 43018}, {3412, 42913}, {3524, 16960}, {3525, 43200}, {3533, 42516}, {3534, 10645}, {3851, 42694}, {3856, 42581}, {3857, 42157}, {5054, 42636}, {5066, 23302}, {5072, 42154}, {5339, 42592}, {5351, 42490}, {5352, 17800}, {7790, 13083}, {10124, 16961}, {10188, 42159}, {10303, 16242}, {10646, 43420}, {10653, 15717}, {11480, 15684}, {11488, 15698}, {11489, 42532}, {11539, 42635}, {12100, 42685}, {12103, 42798}, {12820, 33703}, {14890, 16963}, {15022, 16964}, {15640, 42932}, {15683, 18582}, {15685, 42952}, {15690, 42629}, {15701, 34755}, {15703, 42690}, {15704, 42529}, {15706, 16267}, {15709, 16962}, {15759, 33607}, {16239, 42778}, {16268, 33417}, {16808, 33699}, {16809, 43301}, {16965, 42959}, {16967, 42799}, {17504, 42777}, {19106, 43201}, {19709, 42688}, {23046, 42919}, {41101, 42914}, {41106, 42630}, {41108, 43029}, {41119, 42504}, {41944, 43429}, {41984, 43110}, {42085, 43293}, {42086, 43033}, {42137, 42530}, {42142, 42430}, {42146, 42791}, {42156, 42965}, {42166, 42429}, {42431, 43403}, {42491, 43428}, {42509, 42963}, {42593, 42596}, {42599, 42995}, {42626, 42695}, {42631, 42815}, {42633, 42802}, {42691, 42973}, {42773, 42968}, {42800, 42988}, {42928, 43109}, {42943, 42992}, {42949, 42991}, {43025, 43028}, {43197, 43228}, {43233, 43239}

X(43483) = reflection of X(42795) in X(42687)
X(43483) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15, 42972, 41971}, {395, 11540, 42954}, {10645, 16644, 41121}, {10653, 15717, 42796}, {16241, 41943, 16}, {16241, 42124, 41943}, {33417, 42912, 16268}, {42596, 42999, 42593}, {42912, 43107, 33417}, {42934, 42936, 3628}

X(43484) = GIBERT (-15,8,25) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 25*a^2*SA - 16*SB*SC : :
X(43484) = 28 X[42686] + 5 X[43196], 2 X[42686] + 5 X[43200], 52 X[42686] - 5 X[43230], 14 X[42796] + 5 X[43196], X[42796] + 5 X[43200], 26 X[42796] - 5 X[43230], X[43196] - 14 X[43200], 13 X[43196] + 7 X[43230], 26 X[43200] + X[43230]

X(43484) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 33607}, {3, 43001}, {4, 5237}, {5, 42946}, {6, 43483}, {13, 3628}, {14, 10304}, {15, 395}, {16, 5055}, {17, 43006}, {18, 548}, {20, 42513}, {30, 42686}, {62, 3526}, {140, 42938}, {381, 43195}, {396, 11540}, {550, 42961}, {618, 7859}, {632, 42779}, {3091, 43244}, {3411, 42912}, {3412, 43019}, {3524, 16961}, {3525, 43199}, {3533, 42517}, {3534, 10646}, {3851, 42695}, {3856, 42580}, {3857, 42158}, {5054, 42635}, {5066, 23303}, {5072, 42155}, {5340, 42593}, {5351, 17800}, {5352, 42491}, {7790, 13084}, {10124, 16960}, {10187, 42162}, {10303, 16241}, {10645, 43421}, {10654, 15717}, {11481, 15684}, {11488, 42533}, {11489, 15698}, {11539, 42636}, {12100, 42684}, {12103, 42797}, {12821, 33703}, {14890, 16962}, {15022, 16965}, {15640, 42933}, {15683, 18581}, {15685, 42953}, {15690, 42630}, {15701, 34754}, {15703, 42691}, {15704, 42528}, {15706, 16268}, {15709, 16963}, {15759, 33606}, {16239, 42777}, {16267, 33416}, {16808, 43300}, {16809, 33699}, {16964, 42958}, {16966, 42800}, {17504, 42778}, {19107, 43202}, {19709, 42689}, {23046, 42918}, {35739, 43338}, {41100, 42915}, {41106, 42629}, {41107, 43028}, {41120, 42505}, {41943, 43428}, {41984, 43111}, {42085, 43032}, {42086, 43292}, {42136, 42531}, {42139, 42429}, {42143, 42792}, {42153, 42964}, {42163, 42430}, {42432, 43404}, {42490, 43429}, {42508, 42962}, {42592, 42597}, {42598, 42994}, {42625, 42694}, {42632, 42816}, {42634, 42801}, {42690, 42972}, {42774, 42969}, {42799, 42989}, {42929, 43108}, {42942, 42993}, {42948, 42990}, {43024, 43029}, {43198, 43229}, {43232, 43238}

X(43484) = reflection of X(42796) in X(42686)
X(43484) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16, 42973, 41972}, {396, 11540, 42955}, {10646, 16645, 41122}, {10654, 15717, 42795}, {16242, 41944, 15}, {16242, 42121, 41944}, {33416, 42913, 16267}, {42597, 42998, 42592}, {42913, 43100, 33416}, {42935, 42937, 3628}

X(43485) = GIBERT (15,8,-9) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 9*a^2*SA + 16*SB*SC : :

X(43485) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 5237}, {3, 43000}, {4, 16961}, {5, 42946}, {6, 43486}, {13, 3530}, {14, 43019}, {15, 397}, {16, 3851}, {17, 10299}, {18, 546}, {20, 43244}, {30, 42935}, {61, 15681}, {62, 382}, {140, 42797}, {376, 42891}, {398, 42630}, {549, 42952}, {3411, 42941}, {3528, 36968}, {3529, 10653}, {3534, 42635}, {3855, 37835}, {5079, 42593}, {5318, 35018}, {5340, 10646}, {5349, 19106}, {5350, 42918}, {5351, 42984}, {5352, 15688}, {5366, 16967}, {11737, 16773}, {12108, 42796}, {12811, 43200}, {12821, 42159}, {14269, 22238}, {14869, 42488}, {15687, 41100}, {15700, 42156}, {15705, 33607}, {15715, 41112}, {16241, 22235}, {16267, 34200}, {16268, 42508}, {16809, 42801}, {16960, 33923}, {16963, 42495}, {16964, 42613}, {16966, 42958}, {17504, 42631}, {18582, 43424}, {22531, 41036}, {35404, 42521}, {36967, 43111}, {37640, 43330}, {37832, 42774}, {38071, 41944}, {38335, 42694}, {41119, 43447}, {41973, 42097}, {42086, 42432}, {42092, 43027}, {42093, 43017}, {42100, 42998}, {42127, 42909}, {42129, 42900}, {42130, 42995}, {42135, 43427}, {42146, 42793}, {42150, 43250}, {42160, 43008}, {42163, 42977}, {42164, 43110}, {42494, 42903}, {42584, 43030}, {42592, 43403}, {42596, 43033}, {42682, 43303}, {42802, 42974}, {42817, 42959}, {42897, 42901}, {42915, 42944}, {42925, 42990}, {42926, 43016}, {42991, 43006}, {43023, 43227}, {43026, 43198}, {43233, 43401}

X(43485) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16, 42978, 41977}, {62, 382, 43419}, {550, 42779, 15}, {550, 43106, 42158}, {3528, 42152, 42798}, {5237, 16965, 42973}, {15687, 41100, 42636}, {15688, 42939, 5352}, {15700, 42156, 42947}, {19106, 42924, 42993}, {36969, 42938, 546}, {41100, 42165, 42814}, {41107, 43193, 5352}, {41974, 42158, 15}, {42118, 42158, 41974}, {42431, 42780, 382}

X(43486) = GIBERT (15,-8,-9) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 9*a^2*SA - 16*SB*SC : :

X(43486) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 5238}, {3, 43001}, {4, 16960}, {5, 42947}, {6, 43485},{13, 43018}, {14, 3530}, {15, 3851}, {16, 398}, {17, 546}, {18, 10299}, {20, 43245}, {30, 42934}, {61, 382}, {62, 15681}, {140, 42798}, {376, 42890}, {397, 42629}, {549, 42953}, {3412, 42940}, {3528, 36967}, {3529, 10654}, {3534, 42636}, {3855, 37832}, {5079, 42592}, {5321, 35018}, {5339, 10645}, {5349, 42919}, {5350, 19107}, {5351, 15688}, {5352, 42985}, {5365, 16966}, {11737, 16772}, {12108, 42795}, {12811, 43199}, {12820, 42162}, {14269, 22236}, {14869, 42489}, {15687, 41101}, {15700, 42153}, {15705, 33606}, {15715, 41113}, {16242, 22237}, {16267, 42509}, {16268, 34200}, {16808, 42802}, {16961, 33923}, {16962, 42494}, {16965, 42612}, {16967, 42959}, {17504, 42632}, {18581, 43425}, {22532, 41037}, {35404, 42520}, {36968, 43110}, {37641, 43331}, {37835, 42773}, {38071, 41943}, {38335, 42695}, {41120, 43446}, {41974, 42096}, {42085, 42431}, {42089, 43026}, {42094, 43016}, {42099, 42999}, {42126, 42908}, {42131, 42994}, {42132, 42901}, {42138, 43426}, {42143, 42794}, {42151, 43251}, {42161, 43009}, {42165, 43111}, {42166, 42976}, {42495, 42902}, {42585, 43031}, {42593, 43404}, {42597, 43032}, {42683, 43302}, {42801, 42975}, {42818, 42958}, {42896, 42900}, {42914, 42945}, {42924, 42991}, {42927, 43017}, {42990, 43007}, {43022, 43226}, {43027, 43197}, {43232, 43402}

X(43486) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15, 42979, 41978}, {61, 382, 43418}, {550, 42780, 16}, {550, 43105, 42157}, {3528, 42149, 42797}, {5238, 16964, 42972}, {15687, 41101, 42635}, {15688, 42938, 5351}, {15700, 42153, 42946}, {19107, 42925, 42992}, {36970, 42939, 546}, {41101, 42164, 42813}, {41108, 43194, 5351}, {41973, 42157, 16}, {42117, 42157, 41973}, {42432, 42779, 382}

X(43487) = GIBERT (20,21,-8) POINT

Barycentrics    10*a^2*S/Sqrt[3] - 4*a^2*SA + 21*SB*SC : :

X(43487) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42123}, {4, 42683}, {15, 3529}, {16, 3855}, {382, 42889}, {546, 42917}, {3528, 5318}, {3544, 36843}, {3832, 42689}, {3851, 43364}, {5079, 42493}, {5335, 43105}, {5340, 42781}, {10299, 42086}, {10653, 12821}, {11001, 42777}, {11543, 42804}, {14269, 42497}, {15022, 42907}, {15688, 42627}, {15710, 18582}, {15715, 42088}, {16965, 43196}, {18581, 42805}, {19107, 43250}, {33416, 43201}, {36969, 42139}, {36970, 42105}, {37641, 42904}, {41120, 43227}, {42090, 42892}, {42103, 43005}, {42119, 42532}, {42120, 42937}, {42133, 42971}, {42142, 42900}, {42159, 43366}, {42431, 42929}, {42531, 43310}

X(43487) = {X(42134),X(43106)}-harmonic conjugate of X(3544)

X(43488) = GIBERT (20,-21,-8) POINT

Barycentrics    10*a^2*S/Sqrt[3] + 4*a^2*SA - 21*SB*SC : :

X(43488) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42122}, {4, 42682}, {15, 3855}, {16, 3529}, {382, 42888}, {546, 42916}, {3528, 5321}, {3544, 36836}, {3832, 42688}, {3851, 43365}, {5079, 42492}, {5334, 43106}, {5339, 42782}, {10299, 42085}, {10654, 12820}, {11001, 42778}, {11542, 42803}, {14269, 42496}, {15022, 42906}, {15688, 42628}, {15710, 18581}, {15715, 42087}, {16964, 43195}, {18582, 42806}, {19106, 43251}, {33417, 43202}, {36969, 42104}, {36970, 42142}, {37640, 42905}, {41119, 43226}, {42091, 42893}, {42106, 43004}, {42119, 42936}, {42120, 42533}, {42134, 42970}, {42139, 42901}, {42162, 43367}, {42432, 42928}, {42530, 43311}

X(43488) = {X(42133),X(43105)}-harmonic conjugate of X(3544)

X(43489) = GIBERT (21,20,49) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 49*a^2*SA + 40*SB*SC : :

X(43489) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 33612}, {3, 43330}, {4, 5352}, {6, 43490}, {13, 3530}, {15, 547}, {16, 5054}, {30, 42930}, {61, 43333}, {62, 43199}, {395, 632}, {396, 11540}, {398, 43441}, {3412, 42946}, {3525, 42801}, {3859, 42945}, {3860, 36967}, {5070, 22236}, {5079, 42592}, {5237, 42500}, {8703, 23302}, {10645, 43399}, {10646, 15719}, {10653, 42931}, {11480, 43331}, {11485, 43372}, {12101, 42929}, {12811, 42942}, {15681, 37832}, {15682, 43292}, {15692, 36968}, {15694, 43308}, {15710, 18582}, {16268, 42985}, {16772, 43419}, {16962, 41984}, {16966, 38071}, {18581, 42803}, {19709, 36970}, {33416, 42957}, {33417, 37640}, {35421, 42693}, {35434, 42098}, {36836, 42984}, {41107, 43420}, {41108, 43029}, {41981, 42941}, {41987, 43104}, {42089, 42636}, {42100, 43201}, {42129, 42892}, {42136, 42997}, {42155, 42979}, {42511, 43032}, {42512, 43334}, {42625, 42965}, {42631, 43024}, {42779, 43008}, {42896, 43100}, {42912, 42993}, {42938, 42947}, {42943, 43328}, {42952, 43416}, {42972, 43305}, {42975, 43012}, {42999, 43440}, {43247, 43370}

X(43489) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5054, 43332, 16}, {5070, 42799, 37835}, {16241, 42911, 5352}, {19709, 43421, 36970}, {42592, 43238, 42814}

X(43490) = GIBERT (-21,20,49) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 49*a^2*SA - 40*SB*SC : :

X(43490) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 33613}, {3, 43331}, {4, 5351}, {6, 43489}, {14, 3530}, {15, 5054}, {16, 547}, {30, 42931}, {61, 43200}, {62, 43332}, {395, 11540}, {396, 632}, {397, 43440}, {3411, 42947}, {3525, 42802}, {3859, 42944}, {3860, 36968}, {5070, 22238}, {5079, 42593}, {5238, 42501}, {8703, 23303}, {10645, 15719}, {10646, 43400}, {10654, 42930}, {11481, 43330}, {11486, 43373}, {12101, 42928}, {12811, 42943}, {15681, 37835}, {15682, 43293}, {15692, 36967}, {15694, 43309}, {15710, 18581}, {16267, 42984}, {16773, 43418}, {16963, 41984}, {16967, 38071}, {18582, 42804}, {19709, 36969}, {33416, 37641}, {33417, 42956}, {35421, 42692}, {35434, 42095}, {36843, 42985}, {41107, 43028}, {41108, 43421}, {41981, 42940}, {41987, 43101}, {42092, 42635}, {42099, 43202}, {42132, 42893}, {42137, 42996}, {42154, 42978}, {42510, 43033}, {42513, 43335}, {42626, 42964}, {42632, 43025}, {42780, 43009}, {42897, 43107}, {42913, 42992}, {42939, 42946}, {42942, 43329}, {42953, 43417}, {42973, 43304}, {42974, 43013}, {42998, 43441}, {43246, 43371}

X(43490) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5054, 43333, 15}, {5070, 42800, 37832}, {16242, 42910, 5351}, {19709, 43420, 36969}, {42593, 43239, 42813}

X(43491) = GIBERT (21,20,-9) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 9*a^2*SA + 40*SB*SC : :

X(43491) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 5351}, {3, 43330}, {4, 43293}, {13, 17538}, {15, 1657}, {16, 3850}, {17, 548}, {61, 33703}, {62, 38335}, {140, 42928}, {316, 33959}, {397, 42629}, {398, 3627}, {550, 43328}, {3146, 42799}, {3843, 22238}, {5072, 42155}, {5238, 15686}, {5318, 15712}, {5344, 10645}, {10654, 42612}, {11480, 43424}, {12102, 43008}, {12108, 36968}, {12812, 42944}, {12816, 14892}, {14093, 42973}, {14891, 42166}, {14893, 16268}, {15684, 41107}, {15689, 41943}, {15718, 42488}, {16808, 42686}, {18581, 42805}, {19106, 41973}, {19107, 42971}, {21735, 42086}, {23046, 42148}, {41974, 42780}, {41983, 42949}, {42088, 42979}, {42105, 42908}, {42115, 42900}, {42118, 43195}, {42150, 42430}, {42151, 42914}, {42152, 42929}, {42157, 43302}, {42433, 42494}, {42496, 42939}, {42580, 42695}, {42585, 43022}, {42635, 43194}, {42773, 42947}, {42776, 43023}, {42779, 43232}, {42959, 43016}, {42964, 42990}, {42981, 43102}

X(43491) = {X(42158),X(42921)}-harmonic conjugate of X(5351)

X(43492) = GIBERT (21,-20,9) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 9*a^2*SA - 40*SB*SC : :

X(43492) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 5352}, {3, 43331}, {4, 43292}, {14, 17538}, {15, 3850}, {16, 1657}, {18, 548}, {61, 38335}, {62, 33703}, {140, 42929}, {316, 33960}, {395, 43253}, {397, 3627}, {398, 42630}, {550, 43329}, {3146, 42800}, {3843, 22236}, {5072, 42154}, {5237, 15686}, {5321, 15712}, {5343, 10646}, {10653, 42613}, {11481, 43425}, {12102, 43009}, {12108, 36967}, {12812, 42945}, {12817, 14892}, {14093, 42972}, {14891, 42163}, {14893, 16267}, {15684, 41108}, {15689, 41944}, {15718, 42489}, {16809, 42687}, {18582, 42806}, {19106, 42970}, {19107, 41974}, {21735, 42085}, {23046, 42147}, {41973, 42779}, {41983, 42948}, {42087, 42978}, {42104, 42909}, {42116, 42901}, {42117, 43196}, {42149, 42928}, {42150, 42915}, {42151, 42429}, {42158, 43303}, {42434, 42495}, {42497, 42938}, {42581, 42694}, {42584, 43023}, {42636, 43193}, {42774, 42946}, {42775, 43022}, {42780, 43233}, {42958, 43017}, {42965, 42991}, {42980, 43103}

X(43492) = {X(42157),X(42920)}-harmonic conjugate of X(5352)

X(43493) = GIBERT (24,7,32) POINT

Barycentrics    4*Sqrt[3]*a^2*S + 16*a^2*SA + 7*SB*SC : :

X(43493) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 33605}, {4, 16644}, {13, 17538}, {15, 5071}, {16, 3524}, {17, 11541}, {376, 11542}, {395, 15702}, {396, 19708}, {631, 42806}, {3090, 43417}, {3522, 42496}, {3525, 16241}, {3528, 36968}, {3533, 42975}, {3534, 43197}, {3545, 42124}, {3627, 42927}, {3839, 42888}, {5067, 10654}, {5365, 42474}, {8703, 42932}, {10304, 42968}, {11001, 11488}, {11485, 15709}, {15682, 42116}, {15683, 42889}, {15688, 42916}, {15693, 42933}, {15694, 42987}, {15708, 42633}, {15710, 42974}, {15715, 42898}, {15759, 43242}, {16267, 43334}, {18582, 43399}, {19709, 43243}, {22236, 43444}, {33602, 42097}, {34200, 42982}, {35381, 43208}, {36970, 41106}, {41943, 42099}, {41971, 42920}, {42089, 42516}, {42092, 43005}, {42109, 43403}, {42115, 42420}, {42119, 43196}, {42134, 42791}, {42142, 42530}, {42150, 43199}, {42161, 42795}, {42500, 42999}, {42589, 42901}, {43101, 43445}, {43238, 43404}

X(43493) = {X(16644),X(36836)}-harmonic conjugate of X(43402)

X(43494) = GIBERT (-24,7,32) POINT

Barycentrics    4*Sqrt[3]*a^2*S - 16*a^2*SA - 7*SB*SC : :

X(43494) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 33604}, {4, 16645}, {14, 17538}, {15, 3524}, {16, 5071}, {18, 11541}, {376, 11543}, {395, 19708}, {396, 15702}, {631, 42805}, {3090, 43416}, {3522, 42497}, {3525, 16242}, {3528, 36967}, {3533, 42974}, {3534, 43198}, {3545, 42121}, {3627, 42926}, {3839, 42889}, {5067, 10653}, {5366, 42475}, {8703, 42933}, {10304, 42969}, {11001, 11489}, {11486, 15709}, {15682, 42115}, {15683, 42888}, {15688, 42917}, {15693, 42932}, {15694, 42986}, {15708, 42634}, {15710, 42975}, {15715, 42899}, {15759, 43243}, {16268, 43335}, {18581, 43400}, {19709, 43242}, {22238, 43445}, {33603, 42096}, {34200, 42983}, {35381, 43207}, {36969, 41106}, {41944, 42100}, {41972, 42921}, {41984, 43252}, {42089, 43004}, {42092, 42517}, {42108, 43404}, {42116, 42419}, {42120, 43195}, {42133, 42792}, {42139, 42531}, {42151, 43200}, {42160, 42796}, {42501, 42998}, {42588, 42900}, {43104, 43444}, {43239, 43403}

X(43494) = {X(16645),X(36843)}-harmonic conjugate of X(43401)

X(43495) = GIBERT (24,7,-18) POINT

Barycentrics    4*Sqrt[3]*a^2*S - 9*a^2*SA + 7*SB*SC : :

X(43495) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 5340}, {4, 42805}, {15, 3522}, {16, 5068}, {18, 43195}, {20, 42804}, {62, 15683}, {398, 5059}, {632, 42933}, {3146, 5343}, {3523, 11542}, {3543, 42989}, {3832, 36969}, {3839, 43109}, {3854, 5350}, {5056, 42118}, {5073, 42983}, {5335, 42936}, {5344, 42114}, {5365, 34755}, {9993, 22531}, {10299, 42982}, {10653, 15717}, {11481, 22235}, {11489, 42683}, {11541, 42634}, {15022, 16965}, {15692, 43252}, {15697, 42420}, {15705, 40693}, {15712, 42926}, {17578, 22237}, {21734, 42943}, {41100, 42150}, {41972, 42432}, {41977, 42910}, {42086, 43011}, {42090, 42994}, {42099, 42999}, {42133, 43017}, {42141, 42692}, {42159, 43023}, {42161, 42695}, {42165, 42776}, {42588, 42599}, {42777, 43238}, {42801, 43404}

X(43495) = {X(42148),X(42166)}-harmonic conjugate of X(42508)

X(43496) = GIBERT (24,-7,18) POINT

Barycentrics    4*Sqrt[3]*a^2*S + 9*a^2*SA - 7*SB*SC : :

X(43496) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 5339}, {4, 42806}, {15, 5068}, {16, 3522}, {17, 43196}, {20, 42803}, {61, 15683}, {397, 5059}, {632, 42932}, {3146, 5344}, {3523, 11543}, {3543, 42988}, {3832, 36970}, {3839, 43108}, {3854, 5349}, {5056, 42117}, {5073, 42982}, {5334, 42937}, {5343, 42111}, {5366, 34754}, {9993, 22532}, {10299, 42983}, {10654, 15717}, {11480, 22237}, {11488, 42682}, {11541, 42633}, {15022, 16964}, {15697, 42419}, {15705, 40694}, {15712, 42927}, {16965, 43252}, {17578, 22235}, {21734, 42942}, {41101, 42151}, {41971, 42431}, {41978, 42911}, {42085, 43010}, {42091, 42995}, {42100, 42998}, {42134, 43016}, {42140, 42693}, {42160, 42694}, {42162, 43022}, {42164, 42775}, {42589, 42598}, {42778, 43239}, {42802, 43403}

X(43496) = {X(42147),X(42163)}-harmonic conjugate of X(42509)

X(43497) = GIBERT (35,12,49) POINT

Barycentrics    35*a^2*S/Sqrt[3] + 49*a^2*SA + 24*SB*SC : :

X(43497) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42799}, {15, 5079}, {16, 3412}, {550, 43328}, {632, 34754}, {3860, 43199}, {5054, 42635}, {5070, 42934}, {5238, 42138}, {8703, 42777}, {10645, 43010}, {11480, 15681}, {11485, 42780}, {11540, 16961}, {11542, 42798}, {12103, 42629}, {12820, 18582}, {14269, 43421}, {15688, 43332}, {15710, 42930}, {15720, 42802}, {16644, 43331}, {16960, 21734}, {33417, 41978}, {36970, 38071}, {41101, 42492}, {41121, 43231}, {41981, 42687}, {42092, 43009}, {42105, 42632}, {42116, 43366}, {42136, 42979}, {42415, 42972}, {42779, 42959}, {42781, 42945}, {42800, 43250}, {42918, 43372}, {42919, 43196}, {42946, 43206}, {42955, 43335}, {43106, 43197}

X(43498) = GIBERT (-35,12,49) POINT

Barycentrics    35*a^2*S/Sqrt[3] - 49*a^2*SA - 24*SB*SC : :

X(43498) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42800}, {15, 3411}, {16, 5079}, {550, 43329}, {632, 34755}, {3860, 43200}, {5054, 42636}, {5070, 42935}, {5237, 42135}, {8703, 42778}, {10646, 43011}, {11481, 15681}, {11486, 42779}, {11540, 16960}, {11543, 42797}, {12103, 42630}, {12821, 18581}, {14269, 43420}, {15688, 43333}, {15710, 42931}, {15720, 42801}, {16645, 43330}, {16961, 21734}, {33416, 41977}, {36969, 38071}, {41100, 42493}, {41122, 43230}, {41981, 42686}, {42089, 43008}, {42104, 42631}, {42115, 43367}, {42137, 42978}, {42416, 42973}, {42780, 42958}, {42782, 42944}, {42799, 43251}, {42918, 43195}, {42919, 43373}, {42947, 43205}, {42954, 43334}, {43105, 43198}

X(43499) = GIBERT (35,12,-25) POINT

Barycentrics    35*a^2*S/Sqrt[3] - 25*a^2*SA + 24*SB*SC : :

X(43499) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {4, 42801}, {6, 43500}, {13, 14890}, {15, 548}, {16, 5072}, {62, 42112}, {3534, 42800}, {3627, 34755}, {3843, 42938}, {5352, 43302}, {10645, 42966}, {10646, 43004}, {11481, 41974}, {11486, 15684}, {11542, 42796}, {12108, 42955}, {14891, 16960}, {15693, 43000}, {15706, 16267}, {15712, 42685}, {16961, 42694}, {16965, 42472}, {18582, 43443}, {19106, 33606}, {21735, 42779}, {23046, 36969}, {36968, 43234}, {41944, 42106}, {42086, 42436}, {42087, 42419}, {42088, 42994}, {42109, 42993}, {42118, 42493}, {42129, 42695}, {42131, 43304}, {42142, 42954}, {42145, 43307}, {42151, 42928}, {42158, 43303}, {42584, 43235}, {42630, 43206}, {42636, 43244}, {42922, 43294}, {42973, 43102}, {43001, 43329}, {43016, 43297}

X(43499) = {X(16),X(43300)}-harmonic conjugate of X(42965)

X(43500) = GIBERT (35,-12,25) POINT

Barycentrics    35*a^2*S/Sqrt[3] + 25*a^2*SA - 24*SB*SC : :

X(43500) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {4, 42802}, {6, 43499}, {14, 14890}, {15, 5072}, {16, 548}, {61, 42113}, {3534, 42799}, {3627, 34754}, {3843, 42939}, {5351, 43303}, {10645, 43005}, {10646, 42967}, {11480, 41973}, {11485, 15684}, {11543, 42795}, {12108, 42954}, {14891, 16961}, {15693, 43001}, {15706, 16268}, {15712, 42684}, {16960, 42695}, {16964, 42473}, {18581, 43442}, {19107, 33607}, {21735, 42780}, {23046, 36970}, {36967, 43235}, {41943, 42103}, {42085, 42435}, {42087, 42995}, {42088, 42420}, {42108, 42992}, {42117, 42492}, {42130, 43305}, {42132, 42694}, {42139, 42955}, {42144, 43306}, {42150, 42929}, {42157, 43302}, {42585, 43234}, {42629, 43205}, {42635, 43245}, {42923, 43295}, {42972, 43103}, {43000, 43328}, {43017, 43296}

X(43500) = {X(15),X(43301)}-harmonic conjugate of X(42964)

X(43501) = GIBERT (36,77,-8) POINT

Barycentrics    6*Sqrt[3]*a^2*S - 4*a^2*SA + 77*SB*SC : :

X(43501) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42145}, {4, 33603}, {15, 12816}, {16, 41099}, {20, 43246}, {376, 42775}, {3543, 42988}, {3545, 42937}, {3830, 42888}, {3839, 43109}, {3845, 42818}, {8703, 42984}, {11001, 42094}, {11541, 42791}, {15693, 43364}, {15698, 42100}, {15719, 19106}, {16241, 42514}, {16962, 42515}, {16963, 42495}, {19708, 42098}, {33602, 42134}, {33604, 42108}, {33703, 41121}, {36969, 43368}, {36970, 43030}, {37641, 42900}, {41106, 42943}, {42105, 42632}, {42141, 43330}, {42162, 42806}, {42511, 43201}, {42629, 43025}, {42803, 43416}, {43242, 43247}

X(43502) = GIBERT (36,-77,8) POINT

Barycentrics    6*Sqrt[3]*a^2*S + 4*a^2*SA - 77*SB*SC : :

X(43502) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42144}, {4, 33602}, {15, 41099}, {16, 12817}, {20, 43247}, {376, 42776}, {3543, 42989}, {3545, 42936}, {3830, 42889}, {3839, 43108}, {3845, 42817}, {8703, 42985}, {11001, 42093}, {11541, 42792}, {15693, 43365}, {15698, 42099}, {15719, 19107}, {16242, 42515}, {16962, 42494}, {16963, 42514}, {19708, 42095}, {33603, 42133}, {33605, 42109}, {33703, 41122}, {36969, 43031}, {36970, 43369}, {37640, 42901}, {41106, 42942}, {42104, 42631}, {42140, 43331}, {42159, 42805}, {42510, 43202}, {42630, 43024}, {42804, 43417}, {43243, 43246}

X(43503) = GIBERT (3 SQRT(3),13,-1) POINT

Barycentrics    3*a^2*S - a^2*SA + 26*SB*SC : :
X(43503) = 13 X[5418] - 10 X[6409], 7 X[5418] - 10 X[42265], 2 X[5418] - 5 X[42269], 4 X[5418] - 5 X[42602], 7 X[6409] - 13 X[42265], 4 X[6409] - 13 X[42269], 8 X[6409] - 13 X[42602], 4 X[42265] - 7 X[42269], 8 X[42265] - 7 X[42602]

X(43403) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42276}, {4, 1328}, {6, 12101}, {30, 5418}, {316, 32808}, {371, 12818}, {376, 35786}, {381, 5420}, {382, 6519}, {485, 3543}, {486, 14269}, {546, 17852}, {615, 17851}, {1151, 35404}, {1152, 23046}, {1327, 3830}, {2043, 42936}, {2044, 42937}, {3070, 38335}, {3071, 35403}, {3091, 43255}, {3146, 9680}, {3311, 43342}, {3312, 42573}, {3316, 35409}, {3534, 42277}, {3545, 42261}, {3592, 43432}, {3594, 42641}, {3839, 35820}, {3843, 41946}, {3845, 6438}, {3860, 42226}, {5055, 42272}, {5066, 42264}, {5071, 42267}, {6200, 15640}, {6396, 41106}, {6410, 11737}, {6412, 42576}, {6418, 12819}, {6431, 43322}, {6437, 42577}, {6442, 43313}, {6472, 42258}, {6564, 15682}, {6565, 42609}, {8253, 19710}, {10195, 17800}, {10576, 15683}, {12816, 36468}, {12817, 36450}, {13846, 33699}, {13966, 41987}, {14893, 42268}, {15681, 42273}, {15684, 41948}, {15687, 19117}, {15689, 42582}, {15693, 42600}, {15695, 32789}, {15698, 42538}, {15704, 43378}, {19709, 43209}, {22615, 23253}, {31412, 42537}, {32788, 41953}, {35434, 42271}, {35735, 42193}, {36448, 42195}, {36449, 36970}, {36466, 42196}, {36467, 36969}, {41099, 42274}, {41945, 43380}

X(43503) = reflection of X(42602) in X(42269)
X(43503) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1327, 3830, 6561}, {3830, 42284, 1327}, {6420, 43343, 43323}, {13846, 33699, 42275}, {15681, 42273, 43254}, {42640, 43312, 3845}, {43323, 43433, 43343}

X(43504) = GIBERT (3 SQRT(3),-13,1) POINT

Barycentrics    3*a^2*S + a^2*SA - 26*SB*SC : :
X(43504) = 13 X[5420] - 10 X[6410], 7 X[5420] - 10 X[42262], 2 X[5420] - 5 X[42268], 4 X[5420] - 5 X[42603], 7 X[6410] - 13 X[42262], 4 X[6410] - 13 X[42268], 8 X[6410] - 13 X[42603], 4 X[42262] - 7 X[42268], 8 X[42262] - 7 X[42603]

X(43504) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42275}, {4, 1327}, {6, 12101}, {30, 5420}, {316, 32809}, {372, 12819}, {376, 35787}, {381, 5418}, {382, 6522}, {485, 14269}, {486, 3543}, {546, 9681}, {1151, 23046}, {1152, 35404}, {1328, 3830}, {2043, 42937}, {2044, 42936}, {3070, 35403}, {3071, 38335}, {3091, 43254}, {3311, 42572}, {3312, 43343}, {3317, 35409}, {3534, 42274}, {3545, 42260}, {3592, 42642}, {3594, 43433}, {3839, 35821}, {3843, 41945}, {3845, 6437}, {3858, 9680}, {3860, 42225}, {5055, 42271}, {5066, 42263}, {5071, 42266}, {6200, 41106}, {6396, 15640}, {6409, 11737}, {6411, 42577}, {6417, 12818}, {6432, 43323}, {6438, 42576}, {6441, 43312}, {6473, 42259}, {6564, 42608}, {6565, 15682}, {8252, 19710}, {8981, 41987}, {10194, 17800}, {10577, 15683}, {12816, 36449}, {12817, 36467}, {13847, 33699}, {14893, 42269}, {15681, 42270}, {15684, 41947}, {15687, 19116}, {15689, 42583}, {15693, 42601}, {15695, 32790}, {15698, 42537}, {15704, 43379}, {19709, 43210}, {22644, 23263}, {32787, 41954}, {35434, 42272}, {35735, 42192}, {36448, 42198}, {36450, 36969}, {36466, 42197}, {36468, 36970}, {41099, 42277}, {41946, 43381}, {42538, 42561}

X(43504) = reflection of X(42603) in X(42268)
X(43504) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1328, 3830, 6560}, {3830, 42283, 1328}, {6419, 43342, 43322}, {13847, 33699, 42276}, {15681, 42270, 43255}, {42639, 43313, 3845}, {43322, 43432, 43342}

X(43505) = GIBERT (4 SQRT(3),11,24) POINT

Barycentrics    2*a^2*S + 12*a^2*SA + 11*SB*SC : :

X(43505) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 3311}, {4, 6411}, {140, 6446}, {316, 7375}, {376, 35786}, {485, 15709}, {631, 6560}, {1131, 14869}, {1132, 15703}, {1587, 3316}, {1588, 43374}, {1656, 9690}, {3068, 35814}, {3071, 5067}, {3090, 6561}, {3523, 42226}, {3524, 23251}, {3526, 13886}, {3528, 42582}, {3533, 5420}, {3545, 42260}, {3854, 6451}, {3855, 42413}, {5071, 23263}, {5073, 43312}, {5418, 23273}, {6396, 42570}, {6434, 43409}, {6459, 43254}, {6473, 15694}, {6477, 10195}, {6492, 42262}, {7376, 7790}, {7585, 16239}, {10299, 42267}, {10303, 43340}, {12819, 42525}, {14226, 42583}, {14241, 15702}, {15710, 22644}, {15721, 43434}, {15723, 19117}, {19708, 42273}, {21735, 42277}, {23261, 42566}, {31414, 42558}, {41948, 43259}, {42274, 42575}, {42524, 42602}

X(43505) = crosssum of X(3311) and X(6428)
X(43505) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {631, 10576, 23269}, {3311, 42527, 7584}, {3525, 8253, 3316}, {3533, 32785, 7581}, {13939, 42522, 7582}

X(43506) = GIBERT (-4 SQRT(3),11,24) POINT

Barycentrics    2*a^2*S - 12*a^2*SA - 11*SB*SC : :

X(43506) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 3312}, {4, 6412}, {140, 6445}, {316, 7376}, {376, 35787}, {486, 15709}, {631, 6561}, {1131, 15703}, {1132, 14869}, {1587, 43375}, {1588, 3317}, {1656, 23269}, {3069, 35815}, {3070, 5067}, {3090, 6560}, {3523, 42225}, {3524, 23261}, {3526, 13939}, {3528, 42583}, {3533, 5418}, {3545, 42261}, {3854, 6452}, {3855, 42414}, {5071, 23253}, {5073, 43313}, {5420, 23267}, {6200, 42571}, {6433, 43410}, {6460, 43255}, {6472, 15694}, {6476, 10194}, {6493, 42265}, {7375, 7790}, {7586, 16239}, {10299, 42266}, {10303, 43341}, {12818, 42524}, {14226, 15702}, {14241, 42582}, {15710, 22615}, {15721, 43435}, {15723, 19116}, {19708, 42270}, {21735, 42274}, {23251, 42567}, {41947, 43258}, {42277, 42574}, {42525, 42603}

X(43506) = crosssum of X(3312) and X(6427)
X(43506) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {631, 10577, 23275}, {3312, 42526, 7583}, {3525, 8252, 3317}, {3533, 32786, 7582}, {13886, 42523, 7581}

X(43507) = GIBERT (4 SQRT(3),11,-2) POINT

Barycentrics    2*a^2*S - a^2*SA + 11*SB*SC : :
X(43507) = 8 X[6445] - 11 X[8972]

X(43507) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6412}, {4, 1132}, {20, 5418}, {30, 6445}, {316, 1270}, {371, 43376}, {381, 43415}, {485, 9542}, {590, 15683}, {615, 3832}, {1131, 3068}, {1152, 3854}, {1327, 6476}, {3069, 41951}, {3070, 17578}, {3091, 5420}, {3316, 15704}, {3522, 8253}, {3523, 42269}, {3529, 35255}, {3543, 6561}, {3545, 42226}, {3590, 5059}, {3591, 42270}, {3627, 18512}, {3830, 23267}, {3839, 6560}, {3853, 7581}, {3856, 6408}, {3861, 13939}, {5056, 35786}, {5068, 42259}, {5073, 6472}, {5076, 7582}, {6199, 33699}, {6395, 14893}, {6398, 41099}, {6433, 41952}, {6440, 43384}, {6446, 38071}, {6447, 43340}, {6470, 41957}, {6471, 42571}, {6493, 42262}, {6565, 42609}, {7374, 38227}, {7486, 42261}, {8981, 11541}, {9543, 41954}, {9692, 13925}, {10303, 42267}, {10304, 42276}, {10576, 12818}, {11001, 18538}, {12101, 18510}, {13665, 15682}, {15022, 42637}, {15684, 43383}, {15687, 23273}, {15692, 42277}, {15705, 32789}, {15717, 42273}, {31414, 42271}, {32787, 42577}, {35256, 41106}, {35815, 43432}, {36445, 42143}, {36463, 42146}, {42263, 42540}, {42268, 42523}, {42274, 43256}, {42283, 42539}, {42541, 43431}

X(43507) = crosssum of X(1151) and X(6412)
X(43507) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3146, 23251, 1131}, {3543, 23249, 7585}, {3839, 6560, 13941}, {22644, 23253, 20}, {35786, 43407, 5056}, {42216, 43317, 3312}, {42273, 42414, 15717}

X(43508) = GIBERT (4 SQRT(3),-11,2) POINT

Barycentrics    2*a^2*S + a^2*SA - 11*SB*SC : :
X(43508) = 8 X[6446] - 11 X[13941]

X(43508) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6411}, {4, 1131}, {20, 5420}, {30, 6446}, {316, 1271}, {372, 43377}, {381, 9690}, {590, 3832}, {615, 15683}, {1132, 3069}, {1151, 3854}, {1328, 6477}, {3068, 41952}, {3071, 17578}, {3091, 5418}, {3317, 15704}, {3522, 8252}, {3523, 42268}, {3529, 35256}, {3543, 6560}, {3545, 42225}, {3590, 42273}, {3591, 5059}, {3627, 18510}, {3830, 23273}, {3839, 6561}, {3853, 7582}, {3856, 6407}, {3861, 13886}, {5056, 35787}, {5068, 42258}, {5073, 6473}, {5076, 7581}, {6199, 14893}, {6221, 41099}, {6395, 33699}, {6434, 41951}, {6439, 43385}, {6445, 38071}, {6448, 43341}, {6470, 42570}, {6471, 41958}, {6492, 42265}, {6564, 42608}, {7000, 38227}, {7486, 42260}, {9542, 42277}, {9681, 42558}, {10303, 42266}, {10304, 42275}, {10577, 12819}, {11001, 18762}, {11541, 13966}, {12101, 18512}, {13785, 15682}, {15684, 43382}, {15687, 23267}, {15692, 42274}, {15705, 32790}, {15717, 42270}, {32788, 42576}, {35255, 41106}, {35733, 42936}, {35814, 43433}, {36445, 42146}, {36463, 42143}, {42264, 42539}, {42269, 42522}, {42284, 42540}, {42542, 43430}

X(43508) = crosssum of X(1152) and X(6411)
X(43508) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3146, 23261, 1132}, {3543, 23259, 7586}, {3839, 6561, 8972}, {9542, 43257, 43383}, {22615, 23263, 20}, {35787, 43408, 5056}, {42215, 43316, 3311}, {42270, 42413, 15717}, {42277, 43257, 9542}

X(43509) = GIBERT (4 SQRT(3),1,8) POINT

Barycentrics    2*a^2*S + 4*a^2*SA + SB*SC : :
X(43509) = 2 X[6445] + X[8972]

X(43509) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6221}, {3, 7581}, {4, 590}, {5, 6407}, {6, 3524}, {10, 9559}, {20, 6449}, {25, 9695}, {30, 6445}, {33, 9633}, {54, 9686}, {55, 9663}, {56, 9648}, {110, 9687}, {113, 10817}, {115, 9684}, {126, 11833}, {140, 13939}, {316, 32806}, {371, 631}, {372, 10299}, {376, 3068}, {381, 9690}, {485, 3529}, {486, 3533}, {491, 26619}, {549, 6199}, {550, 13903}, {615, 6437}, {944, 9615}, {1062, 9634}, {1131, 1657}, {1132, 3628}, {1285, 31403}, {1327, 42525}, {1329, 9688}, {1506, 9685}, {1587, 3528}, {1588, 3317}, {1656, 9691}, {1698, 9585}, {1699, 9584}, {2051, 9558}, {2886, 9689}, {3070, 17538}, {3071, 5067}, {3090, 5418}, {3091, 6519}, {3096, 7375}, {3146, 8976}, {3311, 3523}, {3312, 15717}, {3522, 6455}, {3530, 6417}, {3535, 14165}, {3539, 5407}, {3543, 18538}, {3544, 23261}, {3545, 6480}, {3592, 13935}, {3616, 31439}, {3815, 9602}, {3839, 42225}, {3850, 10137}, {3851, 10145}, {3855, 9681}, {4293, 13901}, {4294, 18965}, {5054, 13941}, {5066, 43383}, {5070, 6472}, {5071, 6468}, {5254, 9601}, {5265, 31474}, {5587, 9617}, {5591, 41491}, {5603, 9616}, {5657, 9583}, {6361, 8983}, {6395, 12100}, {6396, 15698}, {6398, 15692}, {6411, 19708}, {6412, 15715}, {6418, 15712}, {6427, 42523}, {6433, 11001}, {6439, 41106}, {6446, 17504}, {6447, 7584}, {6451, 10304}, {6452, 15705}, {6460, 21735}, {6476, 42274}, {6484, 31412}, {6486, 8960}, {6492, 34091}, {6496, 21734}, {6564, 15682}, {6567, 38227}, {7376, 7859}, {7556, 9682}, {7736, 9675}, {7738, 9674}, {8227, 9618}, {8276, 12088}, {8703, 18512}, {8980, 13172}, {8991, 34781}, {8994, 12383}, {8997, 9862}, {8998, 12244}, {9649, 10895}, {9662, 10896}, {9732, 26516}, {9738, 36703}, {10147, 11541}, {10195, 35787}, {10577, 42600}, {10819, 12317}, {12082, 13889}, {12108, 13961}, {12248, 13922}, {12253, 13923}, {12256, 13650}, {12257, 14227}, {12306, 36702}, {13199, 13913}, {13200, 13918}, {13637, 26615}, {13847, 43375}, {13888, 31730}, {14242, 21736}, {15683, 42540}, {15700, 42643}, {15709, 32786}, {15716, 43415}, {15719, 19053}, {15720, 19116}, {17578, 42604}, {18931, 21640}, {23263, 42582}, {26340, 41490}, {26361, 32419}, {31414, 42267}, {34089, 41959}, {35815, 42261}, {35821, 42558}, {36701, 43120}, {41099, 42277}, {42226, 43316}, {42269, 42413}, {42537, 43405}, {42577, 42606}, {43256, 43386}

X(43509) = crosspoint of X(3317) and X(14241)
X(43509) = crosssum of X(3312) and X(6221)
X(43509) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9542, 6221}, {5, 9692, 9693}, {6, 3524, 43510}, {20, 8981, 13886}, {20, 13886, 23269}, {371, 631, 7582}, {376, 3068, 23267}, {549, 6199, 7586}, {590, 1151, 9541}, {590, 9541, 4}, {1151, 9540, 4}, {1151, 41963, 9540}, {1587, 6409, 3528}, {1588, 3525, 3317}, {1657, 13925, 1131}, {3068, 6200, 376}, {3090, 6459, 23275}, {5071, 43374, 8253}, {5418, 6453, 6459}, {5418, 6459, 3090}, {6221, 35255, 2}, {6409, 31454, 1587}, {6449, 8981, 20}, {6451, 42216, 10304}, {6455, 7583, 3522}, {6468, 8253, 41945}, {6484, 35812, 42260}, {6561, 32785, 3545}, {8253, 23259, 5071}, {8253, 41945, 23259}, {8983, 9582, 6361}, {9540, 9541, 590}, {9615, 13912, 944}, {9663, 31500, 55}, {11001, 13846, 14241}, {15717, 42522, 3312}, {31412, 42260, 33703}, {35812, 42260, 31412}, {41945, 41961, 6468}, {42263, 43318, 1151}, {42265, 43408, 4}, {42267, 43430, 31414}

X(43510) = GIBERT (-4 SQRT(3),1,8) POINT

Barycentrics    2*a^2*S - 4*a^2*SA - SB*SC : :
X(43510) = 2 X[6446] + X[13941]

X(43410) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6398}, {3, 7582}, {4, 615}, {5, 6408}, {6, 3524}, {20, 6450}, {30, 6446}, {113, 10818}, {126, 11834}, {140, 13886}, {316, 32805}, {371, 10299}, {372, 631}, {376, 3069}, {381, 43415}, {485, 3533}, {486, 3529}, {492, 26620}, {549, 6395}, {550, 13961}, {590, 6438}, {944, 13975}, {1131, 3628}, {1132, 1657}, {1328, 42524}, {1587, 3316}, {1588, 3528}, {3070, 5067}, {3071, 17538}, {3090, 5420}, {3091, 6522}, {3096, 7376}, {3146, 13951}, {3311, 9542}, {3312, 3523}, {3522, 6456}, {3530, 6418}, {3536, 14165}, {3540, 5406}, {3543, 18762}, {3544, 17852}, {3545, 6481}, {3594, 9540}, {3839, 42226}, {3850, 10138}, {3851, 10146}, {3855, 10577}, {4293, 13958}, {4294, 18966}, {5054, 8972}, {5055, 17851}, {5066, 43382}, {5070, 6473}, {5071, 6469}, {5590, 41490}, {6199, 12100}, {6200, 15698}, {6221, 15692}, {6361, 13971}, {6411, 15715}, {6412, 9541}, {6417, 15712}, {6428, 42522}, {6434, 11001}, {6440, 41106}, {6445, 17504}, {6448, 7583}, {6451, 15705}, {6452, 10304}, {6455, 9693}, {6459, 21735}, {6471, 31454}, {6477, 42277}, {6479, 31414}, {6485, 33703}, {6493, 34089}, {6496, 9543}, {6497, 21734}, {6565, 15682}, {6566, 38227}, {7375, 7859}, {8277, 12088}, {8376, 31403}, {8703, 18510}, {9690, 15716}, {9733, 26521}, {9739, 36701}, {9862, 13989}, {10148, 11541}, {10194, 35786}, {10576, 42601}, {10820, 12317}, {12082, 13943}, {12108, 13903}, {12244, 13990}, {12248, 13991}, {12253, 13992}, {12256, 14242}, {12257, 13771}, {12305, 36717}, {12383, 13969}, {13172, 13967}, {13199, 13977}, {13200, 13985}, {13757, 26616}, {13846, 43374}, {13942, 31730}, {13980, 34781}, {15683, 42539}, {15700, 42644}, {15709, 32785}, {15719, 19054}, {15720, 19117}, {17578, 42605}, {18931, 21641}, {21736, 39658}, {23253, 42583}, {26339, 41491}, {26362, 32421}, {34091, 41960}, {35814, 42260}, {35820, 42557}, {36703, 43121}, {41099, 42274}, {42225, 43317}, {42266, 43431}, {42268, 42414}, {42538, 43406}, {42576, 42607}, {43257, 43387}

X(43510) = crosspoint of X(3316) and X(14226)
X(43510) = crosssum of X(3311) and X(6398)
X(43510) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3524, 43509}, {20, 13939, 23275}, {20, 13966, 13939}, {372, 631, 7581}, {376, 3069, 23273}, {486, 42637, 3529}, {549, 6395, 7585}, {1152, 13935, 4}, {1152, 41964, 13935}, {1587, 3525, 3316}, {1588, 6410, 3528}, {1657, 13993, 1132}, {3069, 6396, 376}, {3090, 6460, 23269}, {5071, 43375, 8252}, {5420, 6454, 6460}, {5420, 6460, 3090}, {6398, 35256, 2}, {6412, 9541, 19708}, {6412, 32788, 9541}, {6450, 13966, 20}, {6452, 42215, 10304}, {6456, 7584, 3522}, {6469, 8252, 41946}, {6485, 35813, 42261}, {6560, 32786, 3545}, {8252, 23249, 5071}, {8252, 41946, 23249}, {11001, 13847, 14226}, {15717, 42523, 3311}, {35813, 42261, 42561}, {41946, 41962, 6469}, {42261, 42561, 33703}, {42262, 43407, 4}, {42264, 43319, 1152}

X(43511) = GIBERT (4 SQRT(3),1,-6) POINT

Barycentrics    2*a^2*S - 3*a^2*SA + SB*SC : :

X(43511) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 490}, {3, 7581}, {4, 3591}, {5, 6408}, {6, 3522}, {20, 372}, {30, 23275}, {125, 10818}, {140, 6446}, {316, 3593}, {371, 10304}, {376, 3312}, {382, 13939}, {390, 6502}, {485, 10303}, {486, 3543}, {546, 3317}, {547, 10138}, {548, 6418}, {549, 13886}, {550, 6395}, {615, 3832}, {631, 6450}, {1132, 3069}, {1151, 21734}, {1270, 11293}, {1271, 3926}, {1587, 3523}, {1656, 23269}, {1657, 23273}, {1703, 5731}, {3068, 6410}, {3071, 5059}, {3090, 6522}, {3091, 6454}, {3311, 3528}, {3316, 5054}, {3524, 6456}, {3525, 13665}, {3529, 6448}, {3530, 18512}, {3533, 18538}, {3534, 19116}, {3590, 6434}, {3592, 9543}, {3594, 6459}, {3595, 12222}, {3600, 5414}, {3627, 13961}, {3830, 6475}, {3839, 35820}, {3843, 6473}, {3851, 17851}, {3854, 42284}, {5055, 10146}, {5056, 5420}, {5068, 6469}, {5085, 26294}, {5225, 18966}, {5229, 13958}, {5281, 31408}, {5304, 12968}, {5334, 42197}, {5335, 42198}, {5512, 11834}, {6199, 33923}, {6200, 42522}, {6221, 21735}, {6225, 17820}, {6407, 34200}, {6409, 19054}, {6417, 8703}, {6420, 9541}, {6440, 32790}, {6449, 19708}, {6452, 8981}, {6455, 9692}, {6463, 20065}, {6477, 42274}, {6479, 42268}, {6487, 15708}, {6491, 43414}, {6496, 15710}, {6497, 35255}, {6501, 15688}, {6564, 7486}, {6995, 11474}, {7000, 8982}, {7374, 9993}, {7968, 20070}, {8252, 15022}, {8253, 31414}, {8416, 35947}, {9540, 15692}, {9778, 18992}, {9812, 13971}, {11106, 31473}, {11206, 19087}, {11291, 39658}, {11477, 26295}, {11539, 14241}, {12100, 13903}, {12221, 13759}, {12512, 19003}, {13785, 33703}, {13847, 42272}, {13980, 32064}, {14226, 15684}, {15640, 22615}, {15683, 32788}, {15704, 18510}, {15705, 32787}, {17538, 42215}, {17578, 42264}, {19005, 33524}, {19053, 42258}, {22644, 35813}, {23259, 42267}, {23263, 42276}, {26618, 43134}, {33748, 35840}, {35403, 42640}, {39142, 39388}, {41106, 43212}, {43211, 43386}, {43405, 43410}

X(43511) = crosspoint of X(1132) and X(3590)
X(43511) = crosssum of X(1152) and X(3592)
X(43511) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3522, 43512}, {6, 42637, 3522}, {20, 372, 7586}, {20, 42523, 1588}, {372, 1588, 42523}, {372, 42261, 1588}, {486, 43407, 3543}, {550, 6395, 7582}, {1152, 6460, 2}, {1152, 41946, 6460}, {1587, 3523, 8972}, {1587, 6396, 3523}, {1588, 42261, 20}, {1588, 42523, 7586}, {3068, 6410, 15717}, {3069, 3146, 1132}, {3069, 42259, 3146}, {3069, 42414, 23261}, {5420, 23249, 5056}, {6426, 42259, 3069}, {6450, 42216, 631}, {6452, 8981, 10299}, {6454, 6560, 13935}, {6456, 7583, 3524}, {6469, 23251, 41964}, {6560, 10577, 23253}, {6560, 13935, 3091}, {10577, 23253, 3091}, {13935, 23253, 10577}, {13951, 42226, 4}, {23251, 32786, 5068}, {23251, 41964, 32786}, {23261, 42259, 42414}, {23261, 42414, 3146}, {41964, 41970, 6469}, {42226, 43320, 6398}, {42264, 42561, 17578}

X(43512) = GIBERT (4 SQRT(3),-1,6) POINT

Barycentrics    2*a^2*S + 3*a^2*SA - SB*SC : :

X(43512) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 489}, {3, 7582}, {4, 3590}, {5, 6407}, {6, 3522}, {8, 9616}, {10, 9558}, {20, 371}, {25, 9694}, {30, 23269}, {33, 9634}, {54, 9687}, {55, 9662}, {56, 9649}, {110, 9686}, {115, 9685}, {125, 10817}, {140, 6445}, {316, 3595}, {372, 10304}, {376, 3311}, {381, 9691}, {382, 13886}, {390, 2067}, {485, 3543}, {486, 10303}, {546, 3316}, {547, 10137}, {548, 6417}, {549, 13939}, {550, 6199}, {590, 3832}, {631, 6449}, {944, 31439}, {962, 9583}, {1062, 9633}, {1131, 3068}, {1152, 21734}, {1270, 3926}, {1271, 11294}, {1329, 9689}, {1506, 9684}, {1588, 3523}, {1656, 9690}, {1657, 23267}, {1698, 9584}, {1699, 9585}, {1702, 5731}, {2051, 9559}, {2066, 3600}, {2886, 9688}, {3069, 6409}, {3070, 5059}, {3090, 6519}, {3091, 6453}, {3312, 3528}, {3317, 5054}, {3524, 6455}, {3525, 13785}, {3529, 6447}, {3530, 18510}, {3533, 18762}, {3534, 19117}, {3591, 6433}, {3592, 6460}, {3593, 12221}, {3616, 9615}, {3627, 13903}, {3815, 9601}, {3830, 6474}, {3839, 35821}, {3843, 6472}, {3854, 42283}, {4308, 31432}, {5055, 10145}, {5056, 5418}, {5068, 6468}, {5085, 26295}, {5225, 18965}, {5229, 13901}, {5254, 9602}, {5286, 9675}, {5304, 12963}, {5334, 42195}, {5335, 42196}, {5512, 11833}, {5587, 9618}, {6225, 17819}, {6395, 33923}, {6396, 42523}, {6398, 21735}, {6408, 34200}, {6410, 19053}, {6418, 8703}, {6439, 32789}, {6450, 19708}, {6451, 10299}, {6462, 20065}, {6476, 42277}, {6478, 42269}, {6486, 15708}, {6490, 43413}, {6496, 35256}, {6497, 15710}, {6500, 15688}, {6565, 7486}, {6995, 11473}, {7000, 9993}, {7374, 26441}, {7969, 20070}, {8227, 9617}, {8253, 15022}, {8396, 35946}, {8960, 23253}, {8983, 9812}, {8991, 32064}, {9648, 10895}, {9663, 10896}, {9674, 31400}, {9683, 38435}, {9778, 18991}, {11206, 19088}, {11292, 39649}, {11477, 26294}, {11539, 14226}, {12100, 13961}, {12222, 13639}, {12512, 19004}, {13665, 33703}, {13846, 42271}, {13935, 15692}, {14241, 15684}, {15640, 22644}, {15683, 32787}, {15704, 18512}, {15705, 32788}, {17538, 42216}, {17578, 31412}, {19006, 33524}, {19054, 42259}, {22615, 35812}, {23249, 42266}, {26617, 43133}, {31414, 42272}, {33748, 35841}, {35403, 42639}, {39142, 39387}, {41106, 43211}, {43212, 43387}, {43406, 43409}

X(43512) = crosspoint of X(1131) and X(3591)
X(43512) = crosssum of X(1151) and X(3594)
X(43512) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9543, 1151}, {5, 9693, 9692}, {6, 3522, 43511}, {20, 371, 7585}, {20, 42522, 1587}, {371, 1587, 42522}, {371, 9541, 20}, {371, 9681, 9541}, {371, 42260, 1587}, {485, 43408, 3543}, {550, 6199, 7581}, {1151, 6459, 2}, {1151, 41945, 6459}, {1587, 9541, 42260}, {1587, 42260, 20}, {1587, 42522, 7585}, {1588, 3523, 13941}, {1588, 6200, 3523}, {3068, 3146, 1131}, {3068, 42258, 3146}, {3068, 42413, 23251}, {3069, 6409, 15717}, {3091, 9542, 9540}, {5418, 23259, 5056}, {6425, 42258, 3068}, {6449, 42215, 631}, {6451, 13966, 10299}, {6453, 6561, 9540}, {6453, 9540, 9542}, {6455, 7584, 3524}, {6468, 23261, 41963}, {6561, 9540, 3091}, {6561, 10576, 23263}, {8960, 42275, 23253}, {8976, 42225, 4}, {9540, 23263, 10576}, {10576, 23263, 3091}, {23251, 42258, 42413}, {23251, 42413, 3146}, {23261, 32785, 5068}, {23261, 41963, 32785}, {31412, 42263, 17578}, {31454, 42263, 31412}, {41963, 41969, 6468}, {42225, 43321, 6221}

X(43513) = GIBERT (5 SQRT(3),11,25) POINT

Barycentrics    5*a^2*S + 25*a^2*SA + 22*SB*SC : :

X(43513) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42557}, {140, 6430}, {381, 42566}, {485, 10303}, {548, 42269}, {549, 6412}, {590, 3312}, {631, 42558}, {1152, 43316}, {2043, 43195}, {2044, 43196}, {3069, 35815}, {3071, 6472}, {3316, 43411}, {3534, 42277}, {3628, 5418}, {3856, 6409}, {5054, 43342}, {5055, 6445}, {5066, 42263}, {6410, 43340}, {6411, 33699}, {6433, 10109}, {6476, 42274}, {6564, 15698}, {6565, 7486}, {7585, 35814}, {8252, 19116}, {8972, 43255}, {9540, 43377}, {9541, 15022}, {10195, 13665}, {10304, 42276}, {10576, 15717}, {12818, 21735}, {13846, 42601}, {14890, 42216}, {15693, 43380}, {15709, 32785}, {15721, 43382}, {17800, 42582}, {23046, 42275}, {23273, 42609}, {35822, 43315}, {35823, 43374}, {41951, 41965}, {42268, 43339}, {42526, 43415}, {43314, 43385}

X(43513) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {590, 42600, 5420}, {3526, 43430, 5420}, {6564, 15698, 43336}, {32789, 43254, 6561}, {41958, 43409, 13665}

X(43514) = GIBERT (-5 SQRT(3),11,25) POINT

Barycentrics    5*a^2*S - 25*a^2*SA - 22*SB*SC : :

X(43514) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 42558}, {140, 6429}, {381, 42567}, {486, 10303}, {548, 42268}, {549, 6411}, {615, 3311}, {631, 42557}, {1151, 43317}, {2043, 43196}, {2044, 43195}, {3068, 35814}, {3070, 6473}, {3317, 43412}, {3534, 42274}, {3628, 5420}, {3856, 6410}, {5054, 43343}, {5055, 6446}, {5066, 42264}, {6409, 43341}, {6412, 33699}, {6434, 10109}, {6477, 42277}, {6492, 9680}, {6564, 7486}, {6565, 15698}, {7586, 35815}, {8253, 19117}, {9690, 42527}, {10194, 13785}, {10304, 42275}, {10577, 15717}, {12819, 21735}, {13847, 42600}, {13935, 43376}, {13941, 43254}, {14890, 42215}, {15693, 43381}, {15709, 32786}, {15721, 43383}, {17800, 42583}, {23046, 42276}, {23267, 42608}, {35822, 43375}, {35823, 43314}, {41952, 41966}, {42269, 43338}, {43315, 43384}

X(43514) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {615, 42601, 5418}, {3526, 43431, 5418}, {6565, 15698, 43337}, {32790, 43255, 6560}, {41957, 43410, 13785}

X(43515) = GIBERT (5 SQRT(3),11,-3) POINT

Barycentrics    5*a^2*S - 3*a^2*SA + 22*SB*SC : :
X(43515) = 13 X[6429] - 11 X[43339], 8 X[6429] - 11 X[43430], 11 X[43339] - 26 X[43340], 8 X[43339] - 13 X[43430], 16 X[43340] - 11 X[43430]

X(43515) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 12818}, {4, 42571}, {30, 6429}, {316, 32436}, {382, 3070}, {485, 3529}, {486, 14269}, {546, 6426}, {550, 5418}, {615, 6473}, {1151, 43434}, {1152, 38071}, {1327, 8976}, {3523, 43336}, {3528, 6564}, {3530, 42264}, {3544, 35786}, {3851, 5420}, {3854, 6481}, {3855, 10577}, {3856, 6430}, {3861, 43431}, {5079, 42259}, {6431, 33699}, {6477, 42274}, {6480, 42570}, {6492, 9681}, {7581, 22615}, {8981, 43432}, {9690, 42260}, {10299, 42267}, {11541, 35815}, {12811, 43338}, {14869, 42600}, {15687, 19116}, {15688, 42602}, {15704, 42568}, {15707, 42582}, {15720, 42277}, {23249, 42266}, {23269, 43411}, {34200, 42265}, {35018, 42226}, {35400, 42572}, {35787, 42523}, {41946, 42527}

X(43515) = reflection of X(6429) in X(43340)
X(43515) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12818, 42269}, {23253, 35820, 42261}, {23253, 42261, 42269}

X(43516) = GIBERT (5 SQRT(3),-11,3) POINT

Barycentrics    5*a^2*S + 3*a^2*SA - 22*SB*SC : :
X(43516) = 13 X[6430] - 11 X[43338], 8 X[6430] - 11 X[43431], 11 X[43338] - 26 X[43341], 8 X[43338] - 13 X[43431], 16 X[43341] - 11 X[43431]

X(43516) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 12819}, {4, 42570}, {30, 6430}, {316, 32433}, {382, 3071}, {485, 14269}, {486, 3529}, {546, 6425}, {550, 5420}, {590, 6472}, {1151, 38071}, {1152, 43435}, {1328, 13951}, {3523, 43337}, {3528, 6565}, {3530, 42263}, {3544, 35787}, {3851, 5418}, {3854, 6480}, {3855, 9681}, {3856, 6429}, {3861, 43430}, {5079, 42258}, {6432, 33699}, {6476, 42277}, {6481, 42571}, {7582, 22644}, {10299, 42266}, {11541, 35814}, {12811, 43339}, {13966, 43433}, {14869, 42601}, {15687, 19117}, {15688, 42603}, {15704, 42569}, {15707, 42583}, {15720, 42274}, {23259, 42267}, {23275, 43412}, {34200, 42262}, {35018, 42225}, {35400, 42573}, {35739, 43230}, {35786, 42522}, {41945, 42526}, {42261, 43415}

X(43516) = reflection of X(6430) in X(43341)
X(43516) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12819, 42268}, {23263, 35821, 42260}, {23263, 42260, 42268}

X(43517) = GIBERT (8 SQRT(3),13,32) POINT

Barycentrics    4*a^2*S + 16*a^2*SA + 13*SB*SC : :

X(43517) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6199}, {4, 6409}, {316, 32813}, {371, 43412}, {590, 6438}, {631, 6450}, {1587, 17852}, {1656, 6472}, {3068, 3525}, {3090, 6519}, {3316, 41948}, {3524, 6560}, {3528, 6564}, {3533, 7586}, {3543, 43312}, {3544, 35787}, {3545, 42225}, {3590, 6456}, {5054, 17851}, {5067, 5418}, {5071, 6561}, {6200, 41106}, {6398, 43386}, {6412, 14241}, {6437, 14226}, {6459, 43433}, {6487, 43411}, {7582, 34091}, {7585, 43375}, {8972, 15709}, {9543, 35018}, {10303, 18512}, {10576, 17538}, {13665, 15719}, {13941, 43211}, {15698, 18538}, {15715, 23249}, {19053, 42600}, {19708, 42264}, {23267, 42418}, {23273, 41953}, {35812, 42601}, {36969, 42197}, {36970, 42198}, {42602, 43336}

X(43517) = crosssum of X(6199) and X(6418)

X(43518) = GIBERT (-8 SQRT(3),13,32) POINT

Barycentrics    4*a^2*S - 16*a^2*SA - 13*SB*SC : :

X(43518) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6395}, {4, 6410}, {316, 32812}, {372, 43411}, {615, 6437}, {631, 6449}, {1656, 6473}, {3069, 3525}, {3090, 6522}, {3317, 9541}, {3524, 6561}, {3528, 6565}, {3533, 7585}, {3543, 43313}, {3544, 35786}, {3545, 42226}, {3591, 6455}, {5067, 5420}, {5071, 6560}, {6221, 43387}, {6396, 41106}, {6411, 14226}, {6438, 14241}, {6460, 43432}, {6486, 43412}, {7581, 34089}, {7586, 43374}, {8972, 43212}, {9542, 15713}, {10303, 18510}, {10577, 17538}, {13785, 15719}, {13941, 15709}, {15698, 18762}, {15715, 23259}, {19054, 42601}, {19708, 42263}, {23267, 41954}, {23273, 42417}, {35813, 42600}, {36969, 42195}, {36970, 42196}, {42603, 43337}

X(43518) = crosssum of X(6395) and X(6417)

X(43519) = GIBERT (8 SQRT(3),13,-6) POINT

Barycentrics    4*a^2*S - 3*a^2*SA + 13*SB*SC : :
X(43519) = 13 X[42522] - 18 X[43386]

X(43519) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6410}, {4, 6395}, {20, 6449}, {30, 42522}, {376, 42639}, {381, 6473}, {1131, 41954}, {1132, 42573}, {1151, 42572}, {1327, 15705}, {1587, 3146}, {3070, 5059}, {3071, 17578}, {3091, 6522}, {3311, 15640}, {3522, 5418}, {3523, 42226}, {3543, 7582}, {3590, 6411}, {3591, 6438}, {3832, 6560}, {3839, 13951}, {3854, 42284}, {5068, 5420}, {6408, 41106}, {6442, 43412}, {6455, 14241}, {6500, 35404}, {7585, 42272}, {8972, 42414}, {9542, 15704}, {9543, 15683}, {10137, 11001}, {10576, 15717}, {11541, 18512}, {13941, 41947}, {15700, 34089}, {21734, 31412}, {22644, 23263}, {35786, 43256}, {41964, 43382}, {43322, 43408}

X(43519) = crosssum of X(6410) and X(6425)
X(43519) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3070, 6437, 43411}, {21734, 42540, 31412}

X(43520) = GIBERT (8 SQRT(3),-13,6) POINT

Barycentrics    4*a^2*S + 3*a^2*SA - 13*SB*SC : :
X(43520) = 13 X[42523] - 18 X[43387]

X(43520) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6409}, {4, 6199}, {20, 6450}, {30, 42523}, {376, 42640}, {381, 6472}, {1131, 42572}, {1132, 41953}, {1152, 42573}, {1328, 15705}, {1588, 3146}, {1657, 17851}, {3069, 17852}, {3070, 17578}, {3071, 5059}, {3091, 6519}, {3312, 15640}, {3522, 5420}, {3523, 42225}, {3543, 7581}, {3590, 6437}, {3591, 6412}, {3832, 6561}, {3839, 8976}, {3854, 42283}, {3855, 9542}, {3859, 9691}, {5068, 5418}, {6407, 41106}, {6441, 43411}, {6456, 14226}, {6501, 35404}, {7586, 42271}, {8972, 41948}, {9541, 15022}, {10138, 11001}, {10577, 15717}, {11541, 18510}, {13941, 42413}, {15683, 35814}, {15700, 34091}, {21734, 42539}, {22615, 23253}, {35787, 43257}, {41963, 43383}, {42637, 43377}, {43323, 43407}

X(43520) = crosssum of X(6409) and X(6426)
X(43520) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3071, 6438, 43412}, {21734, 42539, 42561}

X(43521) = GIBERT (12 SQRT(3),23,-8) POINT

Barycentrics    6*a^2*S - 4*a^2*SA + 23*SB*SC : :

X(43521) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6452}, {4, 3594}, {30, 23269}, {316, 32810}, {376, 1327}, {1131, 15681}, {3070, 42641}, {3317, 41946}, {3524, 23251}, {3529, 8960}, {3534, 42639}, {3543, 7581}, {3545, 5420}, {3830, 23273}, {3839, 13951}, {3843, 42640}, {3854, 43212}, {5071, 23253}, {6411, 43380}, {6433, 11001}, {6440, 41106}, {6560, 41099}, {6561, 15682}, {6564, 15698}, {7582, 22644}, {7586, 12101}, {8972, 19710}, {9693, 43376}, {11541, 41945}, {13713, 21737}, {13847, 41949}, {13886, 15683}, {13939, 14269}, {13961, 41987}, {15702, 43407}, {15710, 42267}, {15715, 42265}, {19708, 42264}, {21735, 42602}, {32809, 33456}, {33703, 35822}, {35255, 42540}, {35737, 42219}, {42283, 43387}, {43375, 43384}

X(43521) = crosssum of X(6221) and X(6452)
X(43521) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3070, 43257, 43386}, {11001, 23249, 14241}, {42284, 43256, 41106}

X(43522) = GIBERT (12 SQRT(3),-23,-8) POINT

Barycentrics    6*a^2*S + 4*a^2*SA - 23*SB*SC : :

X(43522) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6451}, {4, 3592}, {30, 23275}, {316, 32811}, {376, 1328}, {381, 9691}, {1132, 15681}, {3071, 42642}, {3316, 41945}, {3524, 23261}, {3529, 42537}, {3534, 42640}, {3543, 7582}, {3545, 5418}, {3830, 23267}, {3839, 8976}, {3843, 42639}, {3854, 9693}, {5071, 23263}, {6412, 43381}, {6434, 11001}, {6439, 41106}, {6560, 15682}, {6561, 41099}, {6565, 15698}, {7581, 22615}, {7585, 12101}, {11541, 41946}, {13846, 41950}, {13886, 14269}, {13903, 41987}, {13939, 15683}, {13941, 19710}, {15702, 43408}, {15710, 42266}, {15715, 42262}, {19708, 42263}, {21735, 42603}, {32808, 33457}, {33703, 35823}, {35256, 42539}, {35737, 42218}, {42284, 43386}, {43374, 43385}

X(43522) = crosssum of X(6398) and X(6451)
X(43522) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3071, 43256, 43387}, {11001, 23259, 14226}, {42283, 43257, 41106}

X(43523) = GIBERT (15 SQRT(3),1,27) POINT

Barycentrics    15*a^2*S + 27*a^2*SA + 2*SB*SC : :

X(43523) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6453}, {4, 6480}, {20, 6482}, {30, 10141}, {140, 6429}, {371, 10299}, {382, 6519}, {485, 9542}, {486, 9691}, {546, 9681}, {550, 1151}, {615, 6472}, {1657, 43430}, {3522, 6484}, {3523, 35814}, {3526, 42573}, {3529, 8960}, {3530, 6425}, {3544, 9693}, {3592, 17504}, {3850, 10139}, {3851, 6407}, {5073, 10137}, {5079, 41945}, {5418, 6468}, {5420, 6221}, {6200, 42522}, {6420, 15715}, {6433, 33923}, {6437, 15712}, {6439, 8981}, {6447, 15700}, {6459, 43433}, {6476, 10194}, {6486, 21735}, {6490, 43314}, {6492, 19116}, {9543, 22615}, {9690, 42260}, {10143, 19709}, {10145, 42258}, {12818, 43413}, {14269, 42526}, {15681, 31454}, {15687, 42577}, {15688, 42418}, {15710, 42524}, {42274, 42575}

X(43524) = GIBERT (-15 SQRT(3),1,27) POINT

Barycentrics    15*a^2*S - 27*a^2*SA - 2*SB*SC : :

X(43524) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6454}, {4, 6481}, {20, 6483}, {30, 10142}, {140, 6430}, {372, 10299}, {382, 6522}, {546, 17852}, {550, 1152}, {590, 6473}, {1657, 43431}, {3070, 17851}, {3522, 6485}, {3523, 35815}, {3526, 42572}, {3529, 42537}, {3530, 6426}, {3594, 17504}, {3850, 10140}, {3851, 6408}, {5073, 10138}, {5079, 41946}, {5418, 6398}, {5420, 6469}, {6396, 42523}, {6419, 15715}, {6434, 33923}, {6438, 15712}, {6440, 13966}, {6448, 15700}, {6460, 43432}, {6477, 10195}, {6487, 21735}, {6491, 43315}, {6493, 19117}, {9681, 34200}, {10144, 19709}, {10146, 42259}, {12819, 43414}, {14269, 42527}, {15687, 42576}, {15688, 42417}, {15710, 42525}, {42261, 43415}, {42277, 42574}

X(43525) = GIBERT (15 SQRT(3),1,-25) POINT

Barycentrics    15*a^2*S - 25*a^2*SA + 2*SB*SC : :
X(43525) = 5 X[6430] + X[43338], 35 X[6430] - 2 X[43341], 10 X[6430] - X[43431], 7 X[43338] + 2 X[43341], 2 X[43338] + X[43431], 4 X[43341] - 7 X[43431]

X(43525) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6481}, {4, 6454}, {6, 15759}, {30, 6430}, {140, 10142}, {372, 10304}, {485, 15709}, {486, 15684}, {547, 10140}, {548, 6426}, {549, 1152}, {615, 17851}, {631, 6483}, {1327, 5055}, {1328, 6477}, {3071, 6473}, {3524, 6485}, {3526, 6522}, {3534, 6398}, {3628, 17852}, {3857, 43212}, {5066, 6469}, {5072, 41964}, {6396, 15698}, {6431, 15714}, {6434, 12100}, {6438, 8703}, {6440, 11540}, {6446, 32787}, {6448, 41945}, {6450, 15706}, {6460, 43255}, {6475, 42258}, {6479, 42637}, {6487, 15692}, {6491, 42577}, {6493, 19116}, {10138, 15694}, {10303, 35822}, {13847, 33699}, {14226, 22615}, {15683, 35814}, {15699, 42569}, {15710, 35771}, {19053, 42524}, {23046, 42603}, {35823, 42413}, {41960, 41962}, {42268, 42640}, {42274, 43256}, {42277, 42418}, {42283, 42609}, {42526, 43415}

X(43525) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1328, 43336, 15640}, {3526, 43342, 42602}, {15683, 35814, 43343}, {42216, 43315, 42600}, {42261, 43343, 15683}, {43209, 43381, 15684}

X(43526) = GIBERT (15 SQRT(3),-1,25) POINT

Barycentrics    15*a^2*S + 25*a^2*SA - 2*SB*SC : :
X(43526) = 5 X[6429] + X[43339], 35 X[6429] - 2 X[43340], 10 X[6429] - X[43430], 7 X[43339] + 2 X[43340], 2 X[43339] + X[43430], 4 X[43340] - 7 X[43430]

X(43526) lies on the Gibert KHO hyperbola {{X(2),X(4),X(15),X(16),X(316)}} and these lines: {2, 6480}, {4, 6453}, {6, 15759}, {30, 6429}, {140, 10141}, {371, 10304}, {485, 9691}, {486, 15709}, {547, 10139}, {548, 6425}, {549, 1151}, {631, 6482}, {1327, 6476}, {1328, 5055}, {3070, 6472}, {3524, 6484}, {3526, 6519}, {3534, 6221}, {3628, 9680}, {3857, 43211}, {5066, 6468}, {5072, 41963}, {6200, 15698}, {6432, 15714}, {6433, 12100}, {6437, 8703}, {6439, 11540}, {6445, 32788}, {6447, 41946}, {6449, 15706}, {6459, 43254}, {6474, 42259}, {6486, 15692}, {6490, 42576}, {6492, 19117}, {9542, 42277}, {9543, 15683}, {9690, 42527}, {9692, 15022}, {10137, 15694}, {10303, 35823}, {13846, 33699}, {14241, 22644}, {15699, 42568}, {15710, 35770}, {19054, 42525}, {23046, 42602}, {35822, 42414}, {41959, 41961}, {42269, 42639}, {42274, 42417}, {42284, 42608}

X(43526) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1327, 43337, 15640}, {3526, 43343, 42603}, {15683, 35815, 43342}, {42215, 43314, 42601}, {42260, 43342, 15683}, {43210, 43380, 15684}

X(43527) = GIBERT (2t, t^2 - 1, 2 t^2) POINT, WHERE t = sqrt(3) cot(ω)

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

Let A' be the apex of the isosceles triangle BA'C constructed outward on BC such that angle(A'BC) = angle(A'CB) = ω. Define B' and C' cyclically. Let A" be the centroid of BA'C, and define B" and C" cyclically. The lines AA", BB", CC" concur in X(43527). (Randy Hutson, May 31, 2021)

X(43527) lies on the Kiepert circumhyperbola and these lines: {2, 5007}, {3, 14492}, {4, 5092}, {5, 14458}, {6, 10159}, {10, 17352}, {13, 11290}, {14, 11289}, {76, 3589}, {83, 7784}, {98, 1656}, {140, 262}, {275, 11331}, {315, 18841}, {316, 5395}, {321, 17367}, {458, 39284}, {550, 14488}, {598, 6656}, {620, 1916}, {671, 7770}, {1327, 7388}, {1328, 7389}, {2996, 7803}, {3329, 7869}, {3399, 25555}, {3407, 7808}, {3424, 5056}, {3523, 14484}, {3533, 14494}, {3618, 7894}, {3851, 7919}, {3972, 33021}, {4045, 14034}, {5485, 7827}, {5503, 32954}, {6539, 16816}, {6704, 7755}, {7375, 14241}, {7376, 14226}, {7757, 16895}, {7760, 10302}, {7769, 40824}, {7772, 16896}, {7782, 14037}, {7787, 39784}, {7822, 13571}, {7834, 11606}, {7847, 14031}, {7870, 19694}, {7876, 11057}, {7877, 34573}, {7913, 14045}, {7914, 7926}, {7930, 11174}, {7936, 16897}, {8370, 17503}, {10484, 16923}, {11140, 40814}, {11172, 32975}, {11303, 12817}, {11304, 12816}, {14247, 40425}, {14762, 33010}, {14789, 18316}, {14971, 16921}, {17381, 17758}, {18842, 32956}, {21156, 33423}, {21157, 33422}, {30435, 31268}, {31455, 35005}, {32971, 41895}, {40016, 41259}

X(43527) = isogonal conjugate of X(7772)
X(43527) = isotomic conjugate of X(3763)
X(43527) = polar conjugate of X(5064)
X(43527) = isotomic conjugate of the complement of X(3618)
X(43527) = isotomic conjugate of the isogonal conjugate of X(39955)
X(43527) = X(i)-cross conjugate of X(j) for these (i,j): {3096, 76}, {3800, 99}, {37353, 264}
X(43527) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7772}, {31, 3763}, {48, 5064}, {163, 7950}, {662, 8665}, {1964, 39668}
X(43527) = cevapoint of X(i) and X(j) for these (i,j): {2, 3618}, {6, 7485}
X(43527) = trilinear pole of line {523, 8664}
X(43527) = barycentric product X(i)*X(j) for these {i,j}: {76, 39955}, {850, 7954}
X(43527) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3763}, {4, 5064}, {6, 7772}, {83, 39668}, {512, 8665}, {523, 7950}, {3589, 39784}, {7954, 110}, {39955, 6}
X(43527) = {X(7808),X(16987)}-harmonic conjugate of X(7943)

X(43528) = GIBERT (2t, t^2 - 1, 2 t^2) POINT, WHERE t = sqrt(3) cot(2ω)

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

Let A' be the apex of the isosceles triangle BA'C constructed outward on BC such that angle(A'BC) = angle(A'CB) = 2ω. Define B' and C' cyclically. Let A" be the centroid of BA'C, and define B" and C" cyclically. The lines AA", BB", CC" concur in X(43528). (Randy Hutson, May 31, 2021)

X(43528) lies on the Kiepert circumhyperbola and these lines: {4, 7932}, {6, 43529}, {39, 10290}, {76, 6680}, {83, 625}, {98, 16984}, {140, 3399}, {230, 42006}, {262, 7875}, {384, 671}, {468, 37892}, {597, 42010}, {598, 5025}, {1656, 3406}, {1916, 7792}, {2996, 14037}, {3329, 8781}, {5395, 33283}, {5485, 14001}, {5939, 11606}, {5999, 14492}, {7607, 24206}, {7915, 10159}, {8859, 10302}, {11361, 17503}, {13862, 14458}, {14031, 38259}, {14033, 32532}, {14035, 41895}, {14042, 33698}, {14064, 18842}, {16989, 40824}, {17008, 18840}, {18845, 33290}

X(43528) = isotomic conjugate of X(7931)
X(43528) = X(31)-isoconjugate of X(7931)
X(43528) = barycentric quotient X(2)/X(7931)

X(43529) = GIBERT (2t, t^2 - 1, 2 t^2) POINT, WHERE t = - sqrt(3) cot(2ω)

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

Let A' be the apex of the isosceles triangle BA'C constructed inward on BC such that angle(A'BC) = angle(A'CB) = 2ω. Define B' and C' cyclically. Let A" be the centroid of BA'C, and define B" and C" cyclically. The lines AA", BB", CC" concur in X(43529). (Randy Hutson, May 31, 2021)

X(43529) lies on the Kiepert circumhyperbola and these lines: {4, 7836}, {6, 43528}, {76, 7844}, {83, 3788}, {98, 3314}, {140, 3406}, {262, 7925}, {325, 3407}, {384, 598}, {599, 8587}, {671, 5025}, {1656, 3399}, {1916, 7778}, {2996, 33283}, {5094, 37892}, {5395, 14037}, {5466, 31072}, {5485, 14064}, {5999, 14458}, {7608, 38317}, {7612, 16990}, {7746, 10159}, {7768, 39603}, {7868, 42006}, {7881, 13108}, {7885, 36997}, {7899, 10290}, {7948, 13085}, {10302, 14065}, {10484, 41133}, {13862, 14492}, {14001, 18842}, {14031, 18845}, {14041, 17503}, {14062, 33698}, {14063, 41895}, {16041, 32532}, {33290, 38259}

X(43529) = isotomic conjugate of X(7806)
X(43529) = isotomic conjugate of the complement of X(7897)
X(43529) = X(31)-isoconjugate of X(7806)
X(43529) = cevapoint of X(2) and X(7897)
X(43529) = barycentric quotient X(2)/X(7806)

X(43530) = GIBERT (2t, t^2 - 1, 2 t^2) POINT, WHERE t = sqrt(3) cot A cot B cot C

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^4 - 4*a^2*b^2 + 2*b^4 - a^2*c^2 - b^2*c^2 - c^4)*(2*a^4 - a^2*b^2 - b^4 - 4*a^2*c^2 - b^2*c^2 + 2*c^4) : :
Barycentrics    1/(tan B tan C + 3) : :
Barycentrics    (sec A)/(cos A + 4 cos B cos C) : :

X(43530) lies on the Kiepert circumhyperbola, the cubic K503, and these lines: {2, 340}, {4, 1495}, {6, 16080}, {13, 471}, {14, 470}, {25, 14492}, {76, 11064}, {83, 11331}, {94, 264}, {98, 5094}, {140, 13599}, {262, 468}, {297, 598}, {378, 22455}, {427, 14458}, {458, 671}, {459, 5702}, {472, 12816}, {473, 12817}, {647, 2394}, {1327, 1586}, {1328, 1585}, {1656, 40448}, {1990, 2052}, {1993, 42410}, {2986, 36794}, {3523, 31363}, {3535, 14226}, {3536, 14241}, {4232, 14484}, {7577, 18316}, {8796, 11547}, {9381, 41760}, {10301, 14488}, {11433, 38253}, {14389, 34289}, {18020, 39295}, {37649, 37874}, {37804, 40824}

X(43530) = isogonal conjugate of X(5158)
X(43530) = isotomic conjugate of X(37638)
X(43530) = polar conjugate of X(381)
X(43530) = isotomic conjugate of the complement of X(37645)
X(43530) = isotomic conjugate of the polar conjugate of X(16263)
X(43530) = polar conjugate of the isogonal conjugate of X(3431)
X(43530) = X(i)-cross conjugate of X(j) for these (i,j): {6749, 4}, {7577, 264}, {9209, 107}, {23324, 253}
X(43530) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5158}, {6, 18477}, {31, 37638}, {48, 381}, {63, 34417}, {304, 34416}, {1531, 2159}, {14314, 32678}, {18486, 18877}, {18487, 35200}, {32225, 36060}
X(43530) = cevapoint of X(i) and X(j) for these (i,j): {2, 37645}, {4, 40138}, {6, 378}
X(43530) = trilinear pole of line {523, 9409}
X(43530) = barycentric product X(i)*X(j) for these {i,j}: {69, 16263}, {264, 3431}, {340, 18316}, {3260, 22455}
X(43530) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18477}, {2, 37638}, {4, 381}, {6, 5158}, {25, 34417}, {30, 1531}, {186, 3581}, {265, 18478}, {275, 4993}, {378, 4550}, {468, 32225}, {526, 14314}, {1784, 18486}, {1974, 34416}, {1990, 18487}, {3431, 3}, {6353, 21970}, {16263, 4}, {18316, 265}, {18533, 40909}, {22455, 74}

X(43531) = ISOGONAL CONJUGATE OF X(386)

Barycentrics    (a^2 + a*b + b^2 + a*c + b*c)*(a^2 + a*b + a*c + b*c + c^2) : :
Trilinears    csc(A + U) : : , where cot U = cot(A/2) cot(B/2) cot(C/2)

X(43531) lies on the Kiepert circumhyperbola, the cubic K321, and these lines: {1, 321}, {2, 58}, {3, 2051}, {4, 572}, {5, 6703}, {6, 10}, {8, 1126}, {9, 2215}, {12, 1397}, {13, 37145}, {14, 37144}, {17, 37147}, {18, 37146}, {32, 37148}, {34, 5136}, {35, 11322}, {36, 19769}, {39, 33745}, {56, 226}, {76, 86}, {79, 32776}, {81, 10479}, {83, 16062}, {98, 7380}, {99, 41849}, {106, 835}, {142, 7535}, {145, 19741}, {182, 15973}, {261, 32014}, {262, 6998}, {269, 1446}, {275, 17555}, {292, 5283}, {333, 19280}, {379, 29598}, {386, 1010}, {442, 1751}, {452, 17188}, {474, 14554}, {485, 13333}, {486, 2047}, {498, 36052}, {501, 13584}, {516, 37062}, {519, 2334}, {551, 3445}, {573, 3597}, {596, 17599}, {598, 17677}, {748, 25512}, {938, 13404}, {939, 13405}, {942, 4670}, {977, 17789}, {986, 11611}, {996, 10459}, {998, 19860}, {1001, 22006}, {1011, 5248}, {1027, 29186}, {1029, 5046}, {1089, 5311}, {1100, 5295}, {1167, 3085}, {1203, 31339}, {1210, 19716}, {1215, 30142}, {1220, 30116}, {1411, 30147}, {1413, 7532}, {1431, 5883}, {1438, 13576}, {1460, 10408}, {1468, 19863}, {1698, 5278}, {1743, 19859}, {1834, 5114}, {1985, 3825}, {2052, 8747}, {2163, 3624}, {2279, 16552}, {2285, 12514}, {2336, 17355}, {2476, 24624}, {2983, 5749}, {3216, 16454}, {3244, 19747}, {3338, 29826}, {3424, 7407}, {3452, 16843}, {3589, 5138}, {3617, 19743}, {3618, 32022}, {3625, 19748}, {3626, 19739}, {3634, 19732}, {3635, 19745}, {3636, 19746}, {3679, 19738}, {3695, 17369}, {3741, 19714}, {3743, 3923}, {3814, 5061}, {3822, 37056}, {3828, 19723}, {3831, 19734}, {3840, 19715}, {3841, 25453}, {3874, 10477}, {3878, 43070}, {3881, 29652}, {3912, 19719}, {3972, 35916}, {4011, 27784}, {4049, 4778}, {4065, 5695}, {4185, 12609}, {4195, 4653}, {4205, 5019}, {4245, 15654}, {4252, 19273}, {4255, 19276}, {4257, 19270}, {4292, 16368}, {4383, 16458}, {4388, 19865}, {4417, 24931}, {4444, 15309}, {4648, 18840}, {4658, 10449}, {4871, 19726}, {4894, 29685}, {5047, 5333}, {5125, 40395}, {5192, 18169}, {5247, 19858}, {5263, 40433}, {5264, 26115}, {5267, 19759}, {5268, 39946}, {5294, 39945}, {5475, 37159}, {5640, 37158}, {5712, 37037}, {6685, 11358}, {6744, 10579}, {7390, 14484}, {7410, 14494}, {7741, 29845}, {9277, 24342}, {9780, 19742}, {10159, 17234}, {10200, 26126}, {10436, 33945}, {10478, 37399}, {11019, 19718}, {11108, 15668}, {11320, 17397}, {11342, 16831}, {11346, 25055}, {11347, 12436}, {11357, 19883}, {11599, 17962}, {12512, 37078}, {13161, 24267}, {13411, 37065}, {13741, 40012}, {14005, 32911}, {14007, 17277}, {16394, 19765}, {16456, 17259}, {16844, 19862}, {16859, 28618}, {16928, 20142}, {16992, 17200}, {17023, 19281}, {17056, 17698}, {17194, 27378}, {17697, 28620}, {18134, 37036}, {19749, 19878}, {19755, 25639}, {20859, 33747}, {21077, 37060}, {23892, 35353}, {24220, 37415}, {24275, 34475}, {24902, 31229}, {25466, 36949}, {25507, 37035}, {25669, 30834}, {27785, 32930}, {29637, 31006}, {29825, 37603}, {29850, 41859}, {30115, 40436}, {30172, 32780}, {31191, 37075}, {31397, 42019}, {33944, 41847}, {37069, 37561}, {37079, 39582}, {37129, 37218}, {37156, 40393}, {37632, 40024}, {40718, 40746}

X(43531) = isogonal conjugate of X(386)
X(43531) = isotomic conjugate of X(5224)
X(43531) = polar conjugate of X(469)
X(43531) = isogonal conjugate of the complement of X(10449)
X(43531) = isotomic conjugate of the anticomplement of X(17398)
X(43531) = isotomic conjugate of the complement of X(17379)
X(43531) = X(i)-cross conjugate of X(j) for these (i,j): {4205, 10}, {4813, 190}, {5019, 13478}, {17398, 2}
X(43531) = X(i)-isoconjugate of X(j) for these (i,j): {1, 386}, {6, 28606}, {31, 5224}, {32, 33935}, {41, 33949}, {48, 469}, {56, 3876}, {100, 834}, {101, 14349}, {163, 23879}, {662, 42664}, {667, 33948}, {668, 8637}, {2206, 42714}, {31359, 34281}
X(43531) = cevapoint of X(i) and X(j) for these (i,j): {1, 1698}, {2, 17379}, {6, 1011}, {11, 17418}, {1459, 26933}
X(43531) = trilinear pole of line {523, 649}
X(43531) = crossdifference of every pair of points on line {834, 42664}
X(43531) = barycentric product X(i)*X(j) for these {i,j}: {75, 2214}, {513, 37218}, {514, 835}, {940, 34265}, {28621, 43223}
X(43531) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 28606}, {2, 5224}, {4, 469}, {6, 386}, {7, 33949}, {9, 3876}, {75, 33935}, {190, 33948}, {321, 42714}, {512, 42664}, {513, 14349}, {523, 23879}, {649, 834}, {835, 190}, {1919, 8637}, {2214, 1}, {3730, 26911}, {4024, 23282}, {5019, 34281}, {17379, 41849}, {34265, 34258}, {37218, 668}
X(43531) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 13323, 13478}, {6, 2049, 10}, {405, 19701, 1125}, {405, 19762, 993}, {964, 19684, 1}, {5717, 5750, 10}, {5814, 17303, 10}, {7532, 19727, 9843}, {10449, 17379, 4658}, {11319, 19740, 3616}, {11358, 19763, 25440}

X(43532) = ISOGONAL CONJUGATE OF X(2080)

Barycentrics    (2*a^4*b^2 - 3*a^2*b^4 + b^6 + a^4*c^2 - a^2*b^2*c^2 - 3*b^4*c^2 + a^2*c^4 + 2*b^2*c^4)*(a^4*b^2 + a^2*b^4 + 2*a^4*c^2 - a^2*b^2*c^2 + 2*b^4*c^2 - 3*a^2*c^4 - 3*b^2*c^4 + c^6) : :
X(43532) = 4 X[3934] - X[23235], 2 X[6248] + X[38664], X[7709] - 3 X[14651], 5 X[7786] - 8 X[20398], X[11257] - 4 X[11623], 3 X[14639] - 2 X[22682], 2 X[22475] - 3 X[38220], X[22728] - 3 X[38732], 3 X[38224] - 2 X[40108]

X(43532) lies on the Kiepert circumhyperbola, the cubics K473 and K792, and these lines: {2, 2782}, {4, 11646}, {6, 11170}, {13, 25230}, {14, 25229}, {39, 7608}, {76, 22677}, {83, 575}, {98, 187}, {99, 15819}, {115, 262}, {148, 6194}, {376, 11172}, {511, 671}, {538, 5503}, {542, 598}, {543, 11167}, {726, 34899}, {1153, 19911}, {1569, 11669}, {1916, 15980}, {2023, 14494}, {2794, 14458}, {2996, 12251}, {3023, 22706}, {3027, 22705}, {3399, 5254}, {3406, 39560}, {3407, 9755}, {3424, 9862}, {3569, 5466}, {3906, 14223}, {3934, 15483}, {5485, 5969}, {5939, 35925}, {6033, 22681}, {6321, 11606}, {7578, 18332}, {7607, 7749}, {7612, 38642}, {7786, 20398}, {7790, 11261}, {7881, 13108}, {8587, 37461}, {8704, 9180}, {8787, 14912}, {9756, 38654}, {9880, 17503}, {10484, 32447}, {10753, 14485}, {11185, 31958}, {13182, 18971}, {13183, 22711}, {14484, 38383}, {14492, 14639}, {22475, 38220}, {22655, 39832}, {22676, 23698}, {22678, 43449}, {22728, 38732}, {39099, 39266}

X(43532) = midpoint of X(148) and X(6194)
X(43532) = reflection of X(i) in X(j) for these {i,j}: {99, 15819}, {262, 115}, {6033, 22681}, {9772, 7697}, {11152, 11171}, {22503, 15980}, {32469, 39}
X(43532) = isogonal conjugate of X(2080)
X(43532) = isotomic conjugate of X(39099)
X(43532) = antigonal image of X(262)
X(43532) = antitomic conjugate of X(262)
X(43532) = symgonal image of X(15819)
X(43532) = Kiepert-hyperbola-antipode of X(262)
X(43532) = isotomic conjugate of the anticomplement of X(15993)
X(43532) = X(15993)-cross conjugate of X(2)
X(43532) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2080}, {31, 39099}, {896, 21460}
X(43532) = trilinear pole of line {523, 3815}
X(43532) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 39099}, {6, 2080}, {111, 21460}

X(43533) = ISOGONAL CONJUGATE OF X(4252)

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

X(43533) lies on the Kiepert circumhyperbola and these lines: {2, 1043}, {4, 391}, {8, 226}, {10, 346}, {20, 13478}, {69, 37161}, {75, 1446}, {76, 5232}, {83, 37681}, {98, 7390}, {145, 30588}, {193, 6625}, {262, 7407}, {280, 6734}, {318, 40149}, {321, 341}, {333, 3146}, {377, 37655}, {452, 1751}, {459, 17555}, {1150, 37435}, {1219, 4847}, {1654, 2996}, {2047, 3316}, {2051, 3091}, {2052, 26592}, {2475, 14552}, {2551, 6559}, {3679, 4052}, {3714, 39570}, {3832, 14555}, {3945, 26051}, {4042, 5229}, {4080, 4678}, {4208, 4869}, {4385, 10005}, {5068, 5233}, {5175, 5271}, {5361, 31295}, {5395, 17349}, {5485, 17677}, {5712, 20019}, {6872, 24624}, {6919, 14554}, {6998, 7612}, {7046, 40445}, {7380, 14494}, {7518, 40395}, {8165, 37865}, {13740, 18841}, {14534, 37666}, {16062, 18840}, {17558, 25446}, {18231, 32932}, {24391, 31995}, {28809, 34258}, {37146, 43447}, {37147, 43446}

X(43533) = isogonal conjugate of X(4252)
X(43533) = isotomic conjugate of X(3945)
X(43533) = polar conjugate of X(7490)
X(43533) = isotomic conjugate of the anticomplement of X(966)
X(43533) = X(966)-cross conjugate of X(2)
X(43533) = X(i)-isoconjugate of X(j) for these (i,j): {1, 4252}, {31, 3945}, {48, 7490}, {56, 3601}, {604, 5273}, {1106, 20007}, {1437, 1869}
X(43533) = cevapoint of X(i) and X(j) for these (i,j): {8, 9780}, {10, 5295}
X(43533) = trilinear pole of line {523, 3239}
X(43533) = barycentric product X(312)*X(5665)
X(43533) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3945}, {4, 7490}, {6, 4252}, {8, 5273}, {9, 3601}, {346, 20007}, {1826, 1869}, {5271, 28627}, {5665, 57}
X(43533) = {X(4208),X(10449)}-harmonic conjugate of X(4869)

X(43534) = ISOGONAL CONJUGATE OF X(5009)

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

X(43534) lies on the Kiepert circumhyperbola and these lines: {1, 83}, {2, 38}, {4, 1840}, {10, 762}, {12, 21941}, {37, 4368}, {75, 40024}, {76, 334}, {98, 813}, {149, 4865}, {226, 3971}, {292, 5283}, {295, 2801}, {312, 30953}, {321, 2887}, {518, 17031}, {561, 18066}, {594, 23944}, {660, 17763}, {671, 4562}, {726, 20335}, {740, 3930}, {741, 1961}, {918, 3837}, {983, 985}, {1016, 7983}, {1655, 6625}, {1698, 40093}, {1751, 4362}, {1757, 33295}, {1911, 5311}, {2051, 29671}, {2156, 16277}, {2643, 4033}, {3159, 40515}, {3263, 3836}, {3406, 22061}, {3662, 42006}, {3678, 16825}, {3681, 32914}, {3821, 24326}, {3948, 20703}, {3963, 7237}, {3994, 4080}, {4010, 22043}, {4013, 4049}, {4016, 28593}, {4037, 4071}, {4039, 20715}, {4052, 4135}, {4075, 17758}, {4110, 17891}, {4118, 18040}, {4120, 35353}, {4516, 21100}, {4557, 8301}, {4583, 18157}, {4645, 5992}, {6539, 21020}, {6540, 17175}, {11364, 30113}, {13723, 18265}, {15065, 18003}, {16556, 18048}, {17777, 26098}, {20711, 22220}, {21077, 36907}, {24076, 40521}, {29687, 40013}, {29862, 36801}, {30985, 32925}, {32778, 34258}, {39725, 40163}

X(43534) = midpoint of X(10) and X(22035)
X(43534) = isogonal conjugate of X(5009)
X(43534) = isotomic conjugate of X(33295)
X(43534) = polar conjugate of X(31905)
X(43534) = X(i)-Ceva conjugate of X(j) for these (i,j): {4583, 4444}, {40098, 594}
X(43534) = X(i)-cross conjugate of X(j) for these (i,j): {594, 40098}, {3930, 40217}, {3932, 10}, {18004, 3952}, {20486, 1441}, {20703, 37}
X(43534) = cevapoint of X(i) and X(j) for these (i,j): {10, 6541}, {37, 20715}, {756, 3930}, {3120, 4088}, {3948, 3963}
X(43534) = crosspoint of X(334) and X(335)
X(43534) = crosssum of X(1914) and X(2210)
X(43534) = trilinear pole of line {523, 594}
X(43534) = crossdifference of every pair of points on line {8632, 22384}
X(43534) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5009}, {21, 1428}, {28, 7193}, {31, 33295}, {32, 30940}, {48, 31905}, {58, 238}, {60, 1284}, {81, 1914}, {86, 2210}, {110, 659}, {162, 22384}, {163, 812}, {239, 1333}, {242, 1437}, {249, 39786}, {255, 34856}, {274, 14599}, {284, 1429}, {310, 18892}, {350, 2206}, {593, 2238}, {603, 14024}, {662, 8632}, {740, 849}, {741, 8300}, {757, 3747}, {1178, 1580}, {1326, 40767}, {1408, 3685}, {1412, 3684}, {1447, 2194}, {1474, 20769}, {1509, 41333}, {1576, 3766}, {1691, 40432}, {1790, 2201}, {1933, 32010}, {2150, 16609}, {3573, 3733}, {3975, 16947}, {4366, 18268}, {4433, 7341}, {4435, 4565}, {4556, 21832}, {4570, 27846}, {6385, 18894}, {17940, 38348}, {27950, 34079}, {34252, 38832}
X(43534) = barycentric product X(i)*X(j) for these {i,j}: {10, 335}, {12, 36800}, {37, 334}, {42, 18895}, {190, 35352}, {226, 4518}, {291, 321}, {292, 313}, {337, 1826}, {349, 7077}, {523, 4562}, {594, 18827}, {660, 1577}, {661, 4583}, {694, 1237}, {740, 40098}, {741, 28654}, {756, 40017}, {813, 850}, {876, 4033}, {1089, 37128}, {1215, 1916}, {1441, 4876}, {1581, 3963}, {1840, 40708}, {1911, 27801}, {1934, 2295}, {2311, 34388}, {2321, 7233}, {3572, 27808}, {3948, 30663}, {3952, 4444}, {4024, 4589}, {4036, 4584}, {4122, 37207}, {4613, 23596}, {4639, 4705}, {5378, 16732}, {7178, 36801}, {7237, 40834}, {13576, 40217}, {18896, 20964}, {20948, 34067}, {40085, 40093}, {40848, 42027}
X(43534) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 33295}, {4, 31905}, {6, 5009}, {10, 239}, {12, 16609}, {37, 238}, {42, 1914}, {65, 1429}, {71, 7193}, {72, 20769}, {75, 30940}, {210, 3684}, {213, 2210}, {226, 1447}, {281, 14024}, {291, 81}, {292, 58}, {295, 1790}, {313, 1921}, {321, 350}, {334, 274}, {335, 86}, {337, 17206}, {349, 18033}, {393, 34856}, {512, 8632}, {523, 812}, {594, 740}, {647, 22384}, {660, 662}, {661, 659}, {694, 1178}, {740, 4366}, {741, 593}, {756, 2238}, {758, 27950}, {813, 110}, {872, 41333}, {876, 1019}, {1018, 3573}, {1089, 3948}, {1213, 4974}, {1215, 385}, {1237, 3978}, {1400, 1428}, {1441, 10030}, {1500, 3747}, {1577, 3766}, {1581, 40432}, {1824, 2201}, {1826, 242}, {1840, 419}, {1911, 1333}, {1916, 32010}, {1918, 14599}, {1922, 2206}, {2171, 1284}, {2196, 1437}, {2205, 18892}, {2238, 8300}, {2295, 1580}, {2311, 60}, {2321, 3685}, {2533, 4107}, {2643, 39786}, {2887, 33891}, {3120, 27918}, {3125, 27846}, {3252, 3286}, {3572, 3733}, {3700, 3716}, {3701, 3975}, {3773, 3797}, {3842, 20142}, {3862, 3736}, {3864, 40773}, {3930, 8299}, {3932, 17755}, {3943, 4432}, {3948, 39044}, {3952, 3570}, {3963, 1966}, {3994, 4465}, {4010, 4375}, {4019, 12215}, {4024, 4010}, {4033, 874}, {4037, 4368}, {4041, 4435}, {4062, 4760}, {4064, 24459}, {4071, 1281}, {4079, 4455}, {4080, 27922}, {4120, 4448}, {4122, 4486}, {4368, 6652}, {4377, 4495}, {4444, 7192}, {4518, 333}, {4562, 99}, {4583, 799}, {4589, 4610}, {4639, 4623}, {4705, 21832}, {4838, 4810}, {4841, 4830}, {4876, 21}, {4931, 4800}, {5378, 4567}, {6057, 3985}, {6535, 4037}, {6541, 6651}, {7077, 284}, {7178, 43041}, {7233, 1434}, {7237, 18904}, {8736, 1874}, {9278, 40767}, {11599, 40725}, {13576, 6654}, {14431, 14433}, {16587, 2236}, {16606, 34252}, {18004, 27929}, {18047, 17941}, {18268, 849}, {18827, 1509}, {18895, 310}, {20693, 8298}, {20715, 19557}, {20716, 27916}, {20964, 1691}, {21021, 4039}, {21044, 4124}, {21093, 27912}, {21801, 15507}, {21830, 20663}, {22116, 18206}, {22321, 27943}, {27801, 18891}, {27808, 27853}, {27809, 3253}, {28654, 35544}, {30663, 37128}, {30669, 17103}, {30713, 4087}, {34067, 163}, {35352, 514}, {36081, 4599}, {36800, 261}, {36801, 645}, {36906, 8849}, {37128, 757}, {40017, 873}, {40098, 18827}, {40217, 30941}, {40794, 1931}, {40796, 2106}, {40848, 33296}, {40936, 8623}, {41531, 27644}, {42027, 39914}, {43074, 43075}
X(43534) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 20716, 4368}, {335, 4518, 291}

X(43535) = ISOGONAL CONJUGATE OF X(5104)

Barycentrics    (2*a^4 + a^2*b^2 + 2*b^4 - 2*a^2*c^2 - 2*b^2*c^2 - c^4)*(2*a^4 - 2*a^2*b^2 - b^4 + a^2*c^2 - 2*b^2*c^2 + 2*c^4) : :
X(43535) = 5 X[14061] - 4 X[14762]

X(43535) lies on the Kiepert circumhyperbola and these lines: {2, 353}, {4, 11177}, {76, 543}, {83, 7817}, {98, 8859}, {99, 10302}, {114, 11669}, {115, 598}, {147, 14494}, {148, 5485}, {230, 8587}, {262, 542}, {325, 42010}, {381, 11170}, {385, 671}, {512, 9180}, {524, 1916}, {538, 10290}, {599, 14931}, {804, 5466}, {2482, 16986}, {2782, 32480}, {2796, 34475}, {2996, 9740}, {3329, 8593}, {3399, 32448}, {5032, 5984}, {5461, 7875}, {5503, 7840}, {5989, 21358}, {5999, 19905}, {6036, 11668}, {6054, 7608}, {6055, 7607}, {7777, 25486}, {7824, 10159}, {7932, 18841}, {8591, 16990}, {8596, 15589}, {9302, 14830}, {10484, 11163}, {10488, 11174}, {11172, 17008}, {11599, 28562}, {11606, 36864}, {14061, 14762}, {14223, 23878}, {14971, 16921}, {16989, 18842}, {17503, 36523}, {18840, 33215}, {19569, 32532}, {19911, 33273}, {35005, 41136}

X(43535) = reflection of X(i) in X(j) for these {i,j}: {99, 15810}, {598, 115}, {8592, 2}, {9774, 6055}
X(43535) = isogonal conjugate of X(5104)
X(43535) = isotomic conjugate of X(7840)
X(43535) = isotomic conjugate of complement of X(44367)
X(43535) = antigonal image of X(598)
X(43535) = antitomic conjugate of X(598)
X(43535) = symgonal image of X(15810)
X(43535) = Kiepert-hyperbola-antipode of X(598)
X(43535) = isotomic conjugate of the anticomplement of X(22329)
X(43535) = X(22329)-cross conjugate of X(2)
X(43535) = cevapoint of X(i) and X(j) for these (i,j): {6, 37914}, {115, 2793}
X(43535) = trilinear pole of line {523, 597}
X(43535) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5104}, {31, 7840}, {662, 9208}
X(43535) = barycentric product X(850)*X(32694)
X(43535) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 7840}, {6, 5104}, {512, 9208}, {32694, 110}

X(43536) = ISOGONAL CONJUGATE OF X(6199)

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

X(43536) lies on the Kiepert circumhyperbola and these lines: {2, 6395}, {4, 6425}, {13, 36464}, {14, 36446}, {376, 1131}, {485, 3524}, {486, 5071}, {547, 6501}, {590, 14241}, {631, 3590}, {1132, 3311}, {1152, 3316}, {1327, 6200}, {1328, 3068}, {1587, 34089}, {3070, 15715}, {3090, 3591}, {3317, 32788}, {3525, 10195}, {3533, 6448}, {3543, 6407}, {3544, 8960}, {3839, 13925}, {5067, 6420}, {5490, 32809}, {6199, 42539}, {6439, 43210}, {6452, 15719}, {6471, 42578}, {6472, 35402}, {6474, 38335}, {6480, 42537}, {6564, 43405}, {7581, 34091}, {7585, 43387}, {8253, 41962}, {8972, 15682}, {9540, 41952}, {9542, 33699}, {11541, 35812}, {12818, 31412}, {13665, 15698}, {13935, 41948}, {14226, 32787}, {18538, 41099}, {23267, 42418}, {23269, 43209}, {31414, 43254}, {38071, 42522}, {41967, 43521}, {42216, 42526}

X(43536) = isogonal conjugate of X(6199)
X(43536) = X(i)-cross conjugate of X(j) for these (i,j): {23267, 4}, {42418, 1328}, {42566, 10194}, {42572, 1327}, {43517, 34091}
X(43536) = cevapoint of X(6200) and X(6420)
X(43536) = X(1)-isoconjugate of X(6199)
X(43536) = barycentric quotient X(6)/X(6199)
X(43536) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {590, 14241, 19708}, {1131, 43211, 376}, {1327, 6200, 42538}, {42539, 42542, 6199}

X(43537) = ISOGONAL CONJUGATE OF X(11477)

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

X(43537) lies on the Kiepert circumhyperbola and these lines: {2, 8550}, {3, 5485}, {4, 1384}, {5, 18842}, {20, 671}, {30, 32532}, {32, 14485}, {76, 3523}, {83, 5056}, {140, 18840}, {230, 3424}, {262, 5304}, {383, 33603}, {459, 468}, {542, 10153}, {598, 3091}, {1080, 33602}, {1327, 7374}, {1328, 7000}, {1656, 18841}, {1916, 37667}, {2052, 4232}, {2996, 3522}, {3146, 8859}, {3543, 17503}, {3850, 18844}, {3851, 18843}, {3854, 18845}, {5032, 10484}, {5059, 38259}, {5068, 5395}, {5189, 13579}, {5466, 6587}, {5503, 6055}, {6504, 16063}, {6776, 7607}, {6811, 14241}, {6813, 14226}, {6995, 39284}, {7616, 15692}, {7735, 14484}, {8549, 11580}, {8781, 37668}, {9753, 14488}, {9755, 10155}, {10185, 43461}, {10302, 10303}, {11160, 42010}, {14494, 37665}, {15258, 16080}, {15589, 40824}

X(43537) = isogonal conjugate of X(11477)
X(43537) = X(1)-isoconjugate of X(11477)
X(43537) = barycentric quotient X(6)/X(11477)

X(43538) = ISOGONAL CONJUGATE OF X(36738)

Barycentrics    (a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2 + 2*Sqrt[3]*b^2*S)*(2*a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4 + 2*Sqrt[3]*c^2*S) : :
X(43538) = X[3105] - 3 X[22688], 3 X[14651] - X[32597], 3 X[22693] - 2 X[41052]

X(43538) lies on the Kiepert circumhyperbola, the cubic K1132b, and these lines: {2, 3107}, {4, 3104}, {6, 22702}, {13, 511}, {14, 2782}, {15, 98}, {16, 22708}, {17, 3105}, {18, 39}, {62, 83}, {76, 635}, {99, 42675}, {115, 3094}, {262, 6115}, {275, 16250}, {530, 598}, {538, 21359}, {621, 11606}, {623, 1916}, {2023, 16967}, {2794, 9982}, {3102, 3367}, {3103, 3366}, {3407, 5980}, {5052, 9112}, {5470, 5969}, {5472, 13330}, {5487, 20081}, {6108, 22712}, {6114, 9772}, {6582, 35917}, {6774, 11171}, {7578, 40855}, {7757, 22574}, {8781, 40334}, {11152, 40672}, {11602, 22894}, {11603, 31703}, {12816, 25154}, {12817, 41042}, {14458, 41022}, {14651, 32597}, {15819, 36780}, {16267, 42062}, {16808, 22694}, {16809, 31702}, {16966, 33479}, {18581, 22690}, {22486, 40671}, {22692, 37835}, {22846, 25187}, {33602, 36323}, {33604, 36345}, {33607, 36364}, {36322, 41119}, {36347, 41112}, {36365, 41107}, {36385, 41121}

X(43538) = midpoint of X(4) and X(32596)
X(43538) = reflection of X(i) in X(j) for these {i,j}: {3107, 22691}, {32465, 39}, {36780, 15819}, {43539, 115}
X(43538) = isogonal conjugate of X(36759)
X(43538) = X(1)-isoconjugate of X(36759)
X(43538) = Kiepert-hyperbola-antipode of X(43539)
X(43538) = barycentric quotient X(6)/X(36759)
X(43538) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3094, 7697, 43539}, {16808, 22696, 22694}, {22708, 22714, 16}

X(43539) = ISOGONAL CONJUGATE OF X(36760)

Barycentrics    (a^2*b^2 - b^4 + 2*a^2*c^2 + b^2*c^2 - 2*Sqrt[3]*b^2*S)*(2*a^2*b^2 + a^2*c^2 + b^2*c^2 - c^4 - 2*Sqrt[3]*c^2*S) : :
X(43539) = X[3104] - 3 X[22690], 3 X[14651] - X[32596], 3 X[22694] - 2 X[41053]

X(43539) lies on the Kiepert circumhyperbola, the cubic K1132a, and these lines: {2, 3106}, {4, 3105}, {6, 22701}, {13, 2782}, {14, 511}, {15, 22707}, {16, 98}, {17, 39}, {18, 3104}, {61, 83}, {76, 636}, {99, 42674}, {115, 3094}, {262, 6114}, {275, 16249}, {531, 598}, {538, 21360}, {622, 11606}, {624, 1916}, {2023, 16966}, {2794, 9981}, {3102, 3392}, {3103, 3391}, {3407, 5981}, {5052, 9113}, {5469, 5969}, {5471, 13330}, {5488, 20081}, {6109, 22712}, {6115, 9772}, {6295, 35918}, {6771, 11171}, {7578, 40854}, {7757, 22573}, {8781, 40335}, {11152, 40671}, {11602, 31704}, {11603, 22850}, {12816, 41043}, {12817, 25164}, {14458, 41023}, {14651, 32596}, {16268, 42063}, {16808, 31701}, {16809, 22693}, {16967, 33478}, {18582, 22688}, {22486, 40672}, {22691, 37832}, {22891, 25183}, {33603, 36322}, {33605, 36347}, {33606, 36365}, {36323, 41120}, {36345, 41113}, {36364, 41108}, {36384, 41122}

X(43539) = midpoint of X(4) and X(32597)
X(43539) = reflection of X(i) in X(j) for these {i,j}: {3106, 22692}, {32466, 39}, {43538, 115}
X(43539) = isogonal conjugate of X(36760)
X(43539) = X(1)-isoconjugate of X(36760)
X(43539) = Kiepert-hyperbola-antipode of X(43538)
X(43539) = barycentric quotient X(6)/X(36760)
X(43539) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3094, 7697, 43538}, {16809, 22695, 22693}, {22707, 22715, 15}

X(43540) = GIBERT (12,13,2) POINT

Barycentrics    2*Sqrt[3]*a^2*S + a^2*SA + 13*SB*SC : :
Barycentrics    1/(Sqrt[3] + 6*Cot[A]) : :
X(43540) = 17 X[42817] - 14 X[42916]

X(43540) lies on the Kiepert circumhyperbola and these lines: {2, 5318}, {3, 43447}, {4, 42974}, {5, 43446}, {6, 42478}, {13, 3543}, {14, 3839}, {15, 15640}, {17, 20}, {18, 3091}, {30, 42817}, {61, 43033}, {98, 41061}, {193, 11121}, {376, 42128}, {381, 42497}, {383, 14494}, {396, 3146}, {459, 473}, {542, 31683}, {547, 42962}, {549, 42950}, {616, 38412}, {617, 42036}, {621, 33626}, {631, 43445}, {1080, 7612}, {2043, 3316}, {2044, 3317}, {2996, 3180}, {3090, 43444}, {3412, 43016}, {3424, 41039}, {3522, 42166}, {3523, 10188}, {3524, 42127}, {3545, 42129}, {3627, 43482}, {3830, 33602}, {3832, 5340}, {3845, 33603}, {3860, 42922}, {5054, 42492}, {5055, 43481}, {5056, 10187}, {5059, 42156}, {5066, 42917}, {5068, 16645}, {5071, 42118}, {5334, 12817}, {5350, 17578}, {5487, 40898}, {6221, 36436}, {6398, 36454}, {7486, 16242}, {10109, 42985}, {10303, 43443}, {10304, 18582}, {10654, 12816}, {11001, 42137}, {11303, 18840}, {11304, 18841}, {11486, 41106}, {11488, 15683}, {11489, 42693}, {11542, 15682}, {11668, 36995}, {12820, 36970}, {12821, 42133}, {15022, 42148}, {15684, 42496}, {15685, 42889}, {15687, 42815}, {15688, 43463}, {15689, 42627}, {15692, 42086}, {15697, 41121}, {15698, 42131}, {15702, 42146}, {15705, 42088}, {15708, 36968}, {15709, 42123}, {15717, 42165}, {15721, 42911}, {16241, 42952}, {16267, 42105}, {16644, 42141}, {16808, 41944}, {16967, 41972}, {17504, 43487}, {18581, 42533}, {19106, 41119}, {19708, 42132}, {21467, 40159}, {21734, 42598}, {22513, 42062}, {23046, 42968}, {32827, 40707}, {33605, 41099}, {33606, 41107}, {35409, 43328}, {36967, 42939}, {37640, 42094}, {41113, 43226}, {41943, 42113}, {42090, 42903}, {42096, 42777}, {42099, 42892}, {42110, 42475}, {42112, 43204}, {42119, 43473}, {42126, 42907}, {42139, 42778}, {42149, 43025}, {42151, 43440}, {42152, 43013}, {42158, 43441}, {42510, 42919}, {42514, 42518}, {42942, 43332}, {42975, 43111}, {42998, 43418}

X(43540) = reflection of X(616) in X(38412)
X(43540) = isogonal conjugate of X(11480)
X(43540) = isotomic conjugate of the anticomplement of X(37640)
X(43540) = X(i)-cross conjugate of X(j) for these (i,j): {37640, 2}, {42094, 4}, {42940, 14}, {43466, 22237}
X(43540) = X(1)-isoconjugate of X(11480)
X(43540) = barycentric quotient X(6)/X(11480)
X(43540) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 42134, 3543}, {20, 42932, 42529}, {5344, 42813, 3091}, {5366, 42162, 20}, {5366, 43403, 36969}, {11488, 42941, 15683}, {15022, 42148, 43480}, {36969, 42162, 43403}, {36969, 43403, 20}, {37640, 43201, 42094}, {41107, 42106, 43404}, {42142, 42155, 2}, {42148, 42775, 15022}, {42155, 42792, 42120}, {42165, 42494, 15717}, {42792, 42971, 42155}, {42792, 43104, 42595}

X(43541) = GIBERT (-12,13,2) POINT

Barycentrics    2*Sqrt[3]*a^2*S - a^2*SA - 13*SB*SC : :
Barycentrics    1/(Sqrt[3] - 6*Cot[A]) : :
X(43541) = 17 X[42818] - 14 X[42917]

X(43541) lies on the Kiepert circumhyperbola and these lines: {2, 5321}, {3, 43446}, {4, 42975}, {5, 43447}, {6, 42478}, {13, 3839}, {14, 3543}, {16, 15640}, {17, 3091}, {18, 20}, {30, 42818}, {62, 43032}, {98, 41060}, {193, 11122}, {376, 42125}, {381, 42496}, {383, 7612}, {395, 3146}, {459, 472}, {542, 31684}, {547, 42963}, {549, 42951}, {616, 42035}, {622, 33627}, {631, 43444}, {1080, 14494}, {2043, 3317}, {2044, 3316}, {2996, 3181}, {3090, 43445}, {3411, 43017}, {3424, 41038}, {3522, 42163}, {3523, 10187}, {3524, 42126}, {3545, 42132}, {3627, 43481}, {3830, 33603}, {3832, 5339}, {3845, 33602}, {3860, 42923}, {5054, 42493}, {5055, 43482}, {5056, 10188}, {5059, 42153}, {5066, 42916}, {5068, 16644}, {5071, 42117}, {5335, 12816}, {5349, 17578}, {5488, 40899}, {6221, 36454}, {6398, 36436}, {7486, 16241}, {10109, 42984}, {10303, 43442}, {10304, 18581}, {10653, 12817}, {11001, 42136}, {11303, 18841}, {11304, 18840}, {11485, 41106}, {11488, 42692}, {11489, 15683}, {11543, 15682}, {11668, 36993}, {12820, 42134}, {12821, 36969}, {15022, 42147}, {15684, 42497}, {15685, 42888}, {15687, 42816}, {15688, 43464}, {15689, 42628}, {15692, 42085}, {15697, 41122}, {15698, 42130}, {15702, 42143}, {15705, 42087}, {15708, 36967}, {15709, 42122}, {15717, 42164}, {15721, 42910}, {16242, 42953}, {16268, 42104}, {16645, 42140}, {16809, 41943}, {16966, 41971}, {17504, 43488}, {18582, 42532}, {19107, 41120}, {19708, 42129}, {21466, 40158}, {21734, 42599}, {22512, 42063}, {23046, 42969}, {32827, 40706}, {33604, 41099}, {33607, 41108}, {35409, 43329}, {36968, 42938}, {37641, 42093}, {41112, 43227}, {41944, 42112}, {42091, 42902}, {42097, 42778}, {42100, 42893}, {42107, 42474}, {42113, 43203}, {42120, 43474}, {42127, 42906}, {42142, 42777}, {42149, 43012}, {42150, 43441}, {42152, 43024}, {42157, 43440}, {42511, 42918}, {42515, 42519}, {42943, 43333}, {42974, 43110}, {42999, 43419}

X(43541) = isogonal conjugate of X(11481)
X(43541) = isotomic conjugate of the anticomplement of X(37641)
X(43541) = X(i)-cross conjugate of X(j) for these (i,j): {37641, 2}, {42093, 4}, {42941, 13}, {43465, 22235}
X(43541) = X(1)-isoconjugate of X(11481)
X(43541) = barycentric quotient X(6)/X(11481)
X(43541) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 42133, 3543}, {20, 42933, 42528}, {5343, 42814, 3091}, {5365, 42159, 20}, {5365, 43404, 36970}, {11489, 42940, 15683}, {15022, 42147, 43479}, {36970, 42159, 43404}, {36970, 43404, 20}, {37641, 43202, 42093}, {41108, 42103, 43403}, {42139, 42154, 2}, {42147, 42776, 15022}, {42154, 42791, 42119}, {42164, 42495, 15717}, {42791, 42970, 42154}, {42791, 43101, 42594}

X(43542) = GIBERT (12,7,8) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 4*a^2*SA + 7*SB*SC : :
Barycentrics    1/(2*Sqrt[3] + 3*Cot[A]) : :
X(43542) = 5 X[631] - 8 X[33419], 5 X[42817] - 2 X[42916]

X(43542) lies on the Kiepert circumhyperbola and these lines: {2, 11486}, {3, 22235}, {4, 396}, {5, 22237}, {6, 5071}, {13, 376}, {14, 3545}, {15, 12816}, {16, 15709}, {17, 631}, {18, 3090}, {20, 43416}, {30, 42817}, {61, 3855}, {62, 10187}, {69, 40707}, {298, 32823}, {303, 32817}, {381, 42496}, {383, 14484}, {397, 3525}, {459, 36302}, {473, 8796}, {547, 42951}, {548, 43479}, {549, 42815}, {617, 671}, {619, 42036}, {623, 5863}, {1080, 3424}, {1131, 2043}, {1132, 2044}, {2041, 9692}, {2045, 3590}, {2046, 3591}, {2996, 11303}, {3091, 42988}, {3412, 42921}, {3524, 5335}, {3528, 5340}, {3529, 36969}, {3533, 10188}, {3543, 42128}, {3544, 42999}, {3628, 42985}, {3839, 11485}, {3860, 43365}, {3861, 43478}, {5054, 42627}, {5055, 42497}, {5067, 16645}, {5318, 11001}, {5334, 33603}, {5344, 16772}, {5366, 36836}, {5395, 11304}, {5459, 42035}, {5485, 9763}, {6772, 10611}, {8703, 43465}, {8781, 11128}, {10299, 43418}, {10304, 42124}, {10654, 12817}, {11121, 37170}, {11480, 43487}, {11489, 42911}, {11737, 42816}, {11812, 42922}, {12820, 16962}, {12821, 16808}, {13925, 18587}, {13993, 18586}, {14269, 42415}, {14893, 42962}, {14912, 22893}, {15640, 42122}, {15683, 42116}, {15686, 43197}, {15692, 42118}, {15698, 16241}, {15702, 23302}, {15703, 42634}, {15705, 42123}, {15710, 36968}, {15719, 41107}, {15721, 42115}, {16773, 42595}, {16809, 43007}, {16964, 42775}, {16965, 21735}, {16966, 42478}, {16967, 42480}, {18581, 33606}, {18776, 36875}, {19708, 33604}, {21846, 41746}, {22238, 43445}, {33417, 42510}, {33605, 42098}, {33703, 36967}, {35737, 42174}, {36366, 40334}, {37835, 42506}, {38335, 43364}, {41101, 42106}, {41113, 42919}, {41120, 42473}, {41122, 43014}, {41944, 42517}, {42091, 42588}, {42105, 43201}, {42112, 43331}, {42127, 43328}, {42134, 42587}, {42140, 42511}, {42141, 42429}, {42146, 42975}, {42149, 43442}, {42151, 42796}, {42158, 43483}, {42161, 42529}, {42431, 43033}, {42488, 43443}, {42589, 42976}, {42594, 43029}, {42597, 42994}, {42776, 42991}, {42814, 43426}, {42895, 42928}, {42990, 43441}, {43488, 43502} X(43542) = reflection of X(31683) in X(13)
X(43542) = isogonal conjugate of X(11485)
X(43542) = isotomic conjugate of the anticomplement of X(16644)
X(43542) = X(i)-cross conjugate of X(j) for these (i,j): {5335, 4}, {16644, 2}, {42943, 14}, {43463, 43446}, {43481, 33603}
X(43542) = X(1)-isoconjugate of X(11485)
X(43542) = barycentric quotient X(6)/X(11485)
X(43542) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 42475, 42778}, {13, 11488, 376}, {13, 41943, 42086}, {61, 42494, 3855}, {396, 42156, 43403}, {396, 42166, 42154}, {396, 43403, 4}, {3524, 5335, 43481}, {3524, 16644, 43463}, {3545, 42986, 37640}, {5335, 16644, 3524}, {5344, 16772, 17538}, {10654, 41121, 42142}, {10654, 42142, 41099}, {11486, 42974, 43111}, {11542, 42132, 42982}, {16241, 41112, 42120}, {16241, 42120, 15698}, {16267, 18582, 37640}, {16267, 37640, 42986}, {16960, 41121, 10654}, {18582, 37640, 3545}, {37641, 37832, 3090}, {37832, 40693, 37641}, {42098, 43228, 43404}, {42128, 42912, 3543}, {42598, 42998, 5067}, {42778, 43104, 42475}, {42898, 43101, 6}, {43463, 43481, 3524}

X(43543) = GIBERT (-12,7,8) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 4*a^2*SA - 7*SB*SC : :
Barycentrics    1/(2*Sqrt[3] - 3*Cot[A]) : :
X(43543) = 5 X[631] - 8 X[33418], 5 X[42818] - 2 X[42917]

X(43543) lies on the Kiepert circumhyperbola and these lines: {2, 11485}, {3, 22237}, {4, 395}, {5, 22235}, {6, 5071}, {13, 3545}, {14, 376}, {15, 15709}, {16, 12817}, {17, 3090}, {18, 631}, {20, 43417}, {30, 42818}, {61, 10188}, {62, 3855}, {69, 40706}, {299, 32823}, {302, 32817}, {381, 42497}, {383, 3424}, {398, 3525}, {459, 36303}, {472, 8796}, {547, 42950}, {548, 43480}, {549, 42816}, {616, 671}, {618, 42035}, {624, 5862}, {1080, 14484}, {1131, 2044}, {1132, 2043}, {2042, 9692}, {2045, 3591}, {2046, 3590}, {2996, 11304}, {3091, 42989}, {3411, 42920}, {3524, 5334}, {3528, 5339}, {3529, 36970}, {3533, 10187}, {3543, 42125}, {3544, 42998}, {3628, 42984}, {3839, 11486}, {3860, 43364}, {3861, 43477}, {5054, 42628}, {5055, 42496}, {5067, 16644}, {5321, 11001}, {5335, 33602}, {5343, 16773}, {5365, 36843}, {5395, 11303}, {5460, 42036}, {5485, 9761}, {6775, 10612}, {8703, 43466}, {8781, 11129}, {10299, 43419}, {10304, 42121}, {10653, 12816}, {11122, 37171}, {11481, 43488}, {11488, 42910}, {11737, 42815}, {11812, 42923}, {12820, 16809}, {12821, 16963}, {13925, 18586}, {13993, 18587}, {14269, 42416}, {14893, 42963}, {14912, 22847}, {15640, 42123}, {15683, 42115}, {15686, 43198}, {15692, 42117}, {15698, 16242}, {15702, 23303}, {15703, 42633}, {15705, 42122}, {15710, 36967}, {15719, 41108}, {15721, 42116}, {16772, 42594}, {16808, 43006}, {16964, 21735}, {16965, 42776}, {16966, 42481}, {16967, 42479}, {18582, 33607}, {18777, 36875}, {19708, 33605}, {21845, 41745}, {22236, 43444}, {33416, 42511}, {33604, 42095}, {33703, 36968}, {35737, 42171}, {36368, 40335}, {37832, 42507}, {38335, 43365}, {41100, 42103}, {41112, 42918}, {41119, 42472}, {41121, 43015}, {41943, 42516}, {42090, 42589}, {42104, 43202}, {42113, 43330}, {42126, 43329}, {42133, 42586}, {42140, 42430}, {42141, 42510}, {42143, 42974}, {42150, 42795}, {42152, 43443}, {42157, 43484}, {42160, 42528}, {42432, 43032}, {42489, 43442}, {42588, 42977}, {42595, 43028}, {42596, 42995}, {42775, 42990}, {42813, 43427}, {42894, 42929}, {42991, 43440}, {43487, 43501}

X(43543) = reflection of X(31684) in X(14)
X(43543) = isogonal conjugate of X(11486)
X(43543) = isotomic conjugate of the anticomplement of X(16645)
X(43543) = X(i)-cross conjugate of X(j) for these (i,j): {5334, 4}, {16645, 2}, {42942, 13}, {43464, 43447}, {43482, 33602}
X(43543) = X(1)-isoconjugate of X(11486)
X(43543) = barycentric quotient X(6)/X(11486)
X(43543) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 42474, 42777}, {14, 11489, 376}, {14, 41944, 42085}, {62, 42495, 3855}, {395, 42153, 43404}, {395, 42163, 42155}, {395, 43404, 4}, {3524, 5334, 43482}, {3524, 16645, 43464}, {3545, 42987, 37641}, {5334, 16645, 3524}, {5343, 16773, 17538}, {10653, 41122, 42139}, {10653, 42139, 41099}, {11485, 42975, 43110}, {11543, 42129, 42983}, {16242, 41113, 42119}, {16242, 42119, 15698}, {16268, 18581, 37641}, {16268, 37641, 42987}, {16961, 41122, 10653}, {18581, 37641, 3545}, {37640, 37835, 3090}, {37835, 40694, 37640}, {42095, 43229, 43403}, {42125, 42913, 3543}, {42599, 42999, 5067}, {42777, 43101, 42474}, {42899, 43104, 6}, {43464, 43482, 3524}

X(43544) = GIBERT (15,14,25) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 25*a^2*SA + 28*SB*SC : :
Barycentrics    1/(5*Sqrt[3] + 3*Cot[A]) : :

X(43544) lies on the Kiepert circumhyperbola and these lines: {2, 16960}, {4, 5238}, {6, 43545}, {13, 549}, {14, 5055}, {15, 5066}, {16, 15709}, {17, 3526}, {18, 396}, {20, 42947}, {30, 12820}, {61, 7486}, {62, 10188}, {140, 42935}, {303, 40707}, {381, 12821}, {383, 14488}, {395, 42896}, {397, 42592}, {546, 42890}, {547, 43110}, {548, 36969}, {619, 671}, {623, 36388}, {628, 33414}, {630, 5488}, {631, 42797}, {1327, 42173}, {1328, 42174}, {2043, 12818}, {2044, 12819}, {3090, 42516}, {3392, 35733}, {3411, 43442}, {3534, 12816}, {3857, 16772}, {5054, 42968}, {5056, 42939}, {5071, 34754}, {5072, 16964}, {5318, 15759}, {5463, 42062}, {5466, 35444}, {6669, 11121}, {6670, 42063}, {10109, 43419}, {10124, 34755}, {10187, 16645}, {10303, 10653}, {10304, 18582}, {10645, 15683}, {10654, 33603}, {11486, 42530}, {11488, 42910}, {11540, 11542}, {11602, 22893}, {11603, 34602}, {11812, 42416}, {12100, 42952}, {13083, 17503}, {14093, 42629}, {14890, 42686}, {15022, 42152}, {15684, 16808}, {15690, 43230}, {15691, 42693}, {15698, 33602}, {15699, 42778}, {15700, 43244}, {15706, 36968}, {15717, 42158}, {16239, 42779}, {16267, 33416}, {16809, 41943}, {16963, 42817}, {16967, 42481}, {17800, 42529}, {18581, 33605}, {19711, 43106}, {23046, 42124}, {23303, 43233}, {33417, 33607}, {33475, 42035}, {33604, 41107}, {33606, 37835}, {33699, 42099}, {37640, 43015}, {37641, 43446}, {38071, 43240}, {40693, 42478}, {41122, 42419}, {41944, 42496}, {41984, 42636}, {42097, 43294}, {42106, 42632}, {42111, 42799}, {42121, 42595}, {42138, 42930}, {42146, 42684}, {42149, 43445}, {42154, 42581}, {42155, 42691}, {42433, 42965}, {42435, 42580}, {42472, 43493}, {42504, 42543}, {42586, 43203}, {42590, 42937}, {42625, 42689}, {42912, 42915}, {42954, 43029}, {42969, 43021}, {42973, 43489}, {42976, 43404}, {42977, 43102}, {42984, 43028}, {42988, 43440}, {43027, 43443}

X(43544) = X(i)-cross conjugate of X(j) for these (i,j): {16267, 13}, {33416, 18}, {42627, 17}, {42913, 14}, {43467, 43442}, {43484, 33606}
X(43544) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 42955, 549}, {397, 42592, 42596}, {10124, 42777, 34755}, {11485, 42475, 14}, {11542, 42501, 42800}, {15022, 42152, 42934}, {16242, 42974, 43020}, {16267, 43467, 43484}, {16644, 16966, 16962}, {16808, 42795, 15684}, {37832, 43483, 4}, {41121, 42092, 42528}, {41943, 42911, 16809}, {41944, 42496, 43030}, {42158, 43403, 43033}, {42500, 42685, 549}, {42974, 43020, 42990}

X(43545) = GIBERT (-15,14,25) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 25*a^2*SA - 28*SB*SC : :
Barycentrics    1/(5*Sqrt[3] - 3*Cot[A]) : :

X(43545) lies on the Kiepert circumhyperbola and these lines: {2, 16961}, {4, 5237}, {6, 43544}, {13, 5055}, {14, 549}, {15, 15709}, {16, 5066}, {17, 395}, {18, 3526}, {20, 42946}, {30, 12821}, {61, 10187}, {62, 7486}, {140, 42934}, {302, 40706}, {381, 12820}, {396, 42897}, {398, 42593}, {546, 42891}, {547, 43111}, {548, 36970}, {618, 671}, {624, 36386}, {627, 33415}, {629, 5487}, {631, 42798}, {1080, 14488}, {1327, 42171}, {1328, 42172}, {2043, 12819}, {2044, 12818}, {3090, 42517}, {3412, 43443}, {3534, 12817}, {3857, 16773}, {5054, 42969}, {5056, 42938}, {5071, 34755}, {5072, 16965}, {5321, 15759}, {5464, 42063}, {5466, 35443}, {6669, 42062}, {6670, 11122}, {10109, 43418}, {10124, 34754}, {10188, 16644}, {10303, 10654}, {10304, 18581}, {10646, 15683}, {10653, 33602}, {11485, 42531}, {11489, 42911}, {11540, 11543}, {11603, 22847}, {11812, 42415}, {12100, 42953}, {13084, 17503}, {14093, 42630}, {14890, 42687}, {15022, 42149}, {15684, 16809}, {15690, 43231}, {15691, 42692}, {15698, 33603}, {15699, 42777}, {15700, 43245}, {15706, 36967}, {15717, 42157}, {16239, 42780}, {16268, 33417}, {16808, 41944}, {16962, 42818}, {16966, 42480}, {17800, 42528}, {18582, 33604}, {19711, 43105}, {23046, 42121}, {23302, 43232}, {33416, 33606}, {33474, 42036}, {33605, 41108}, {33607, 37832}, {33699, 42100}, {36770, 42035}, {37640, 43447}, {37641, 43014}, {38071, 43241}, {40694, 42479}, {41121, 42420}, {41943, 42497}, {41984, 42635}, {42096, 43295}, {42103, 42631}, {42114, 42800}, {42124, 42594}, {42135, 42931}, {42143, 42685}, {42152, 43444}, {42154, 42690}, {42155, 42580}, {42434, 42964}, {42436, 42581}, {42473, 43494}, {42505, 42544}, {42587, 43204}, {42591, 42936}, {42626, 42688}, {42913, 42914}, {42955, 43028}, {42968, 43020}, {42972, 43490}, {42976, 43103}, {42977, 43403}, {42985, 43029}, {42989, 43441}, {43026, 43442}

X(43545) = X(i)-cross conjugate of X(j) for these (i,j): {16268, 14}, {33417, 17}, {42628, 18}, {42912, 13}, {43468, 43443}, {43483, 33607}
X(43545) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 42954, 549}, {398, 42593, 42597}, {10124, 42778, 34754}, {11486, 42474, 13}, {11543, 42500, 42799}, {15022, 42149, 42935}, {16241, 42975, 43021}, {16268, 43468, 43483}, {16645, 16967, 16963}, {16809, 42796, 15684}, {37835, 43484, 4}, {41122, 42089, 42529}, {41943, 42497, 43031}, {41944, 42910, 16808}, {42157, 43404, 43032}, {42501, 42684, 549}, {42975, 43021, 42991}

X(43546) = GIBERT (15,14,3) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 3*a^2*SA + 28*SB*SC : :
Barycentrics    1/(Sqrt[3] + 5*Cot[A]) : :
X(43546) = 6 X[2] - 5 X[33387], 3 X[2] - 5 X[33413], 15 X[33607] - 8 X[42939]

X(43546) lies on the Kiepert circumhyperbola and these lines: {2, 5237}, {4, 42779}, {6, 42904}, {13, 382}, {14, 397}, {15, 5366}, {16, 10187}, {17, 550}, {18, 3851}, {20, 42795}, {30, 33607}, {61, 12816}, {62, 3855}, {140, 42685}, {381, 33606}, {396, 43331}, {398, 43226}, {548, 43199}, {549, 42891}, {631, 42965}, {1656, 42954}, {3528, 16241}, {3529, 36969}, {3530, 36968}, {3544, 10653}, {3545, 42935}, {3850, 16961}, {3858, 42693}, {3861, 43110}, {5068, 34755}, {5073, 16960}, {5238, 42546}, {5335, 22237}, {5339, 12817}, {5349, 12821}, {5350, 19107}, {5352, 41119}, {6778, 11602}, {10188, 15720}, {10299, 18582}, {10302, 11303}, {10646, 42494}, {11122, 33465}, {11542, 42802}, {11669, 37464}, {11737, 16963}, {12101, 42964}, {12102, 42934}, {12820, 16964}, {14869, 37832}, {15681, 42156}, {15700, 42433}, {15707, 43193}, {16267, 33604}, {16268, 42420}, {16772, 42429}, {16962, 42587}, {16966, 42774}, {16967, 41974}, {17504, 42598}, {17538, 43230}, {18581, 43019}, {19106, 43004}, {22832, 41021}, {22844, 40707}, {33602, 41101}, {33603, 41112}, {33605, 40694}, {33923, 42960}, {34200, 41121}, {38071, 41107}, {38335, 42520}, {41973, 42102}, {42086, 42903}, {42088, 42979}, {42093, 43292}, {42094, 42630}, {42103, 43250}, {42106, 42993}, {42111, 42801}, {42117, 42781}, {42118, 42948}, {42134, 42432}, {42136, 42995}, {42142, 42937}, {42147, 42506}, {42150, 42909}, {42474, 43239}, {42530, 43487}, {42627, 42959}, {42908, 43367}, {42919, 42924}, {42998, 43031}, {42999, 43419}

X(43546) = reflection of X(33387) in X(33413)
X(43546) = isogonal conjugate of X(5238)
X(43546) = X(i)-cross conjugate of X(j) for these (i,j): {5350, 4}, {19107, 14}, {42925, 18}, {42992, 17}, {43195, 12821}
X(43546) = X(1)-isoconjugate of X(5238)
X(43546) = barycentric quotient X(6)/X(5238)
X(43546) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17, 42629, 550}, {397, 546, 42780}, {631, 42965, 43244}, {3544, 10653, 42938}, {5318, 42124, 42900}, {5350, 42992, 19107}, {41974, 42921, 16967}, {42157, 42988, 43022}, {42162, 42973, 16965}, {42780, 43418, 397}, {42813, 43418, 546}, {42979, 43491, 42088}, {42988, 43022, 3412}, {42992, 43195, 43486}

X(43547) = GIBERT (-15,14,3) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 3*a^2*SA - 28*SB*SC : :
Barycentrics    1/(Sqrt[3] - 5*Cot[A]) : :
X(43547) = 6 X[2] - 5 X[33386], 3 X[2] - 5 X[33412], 15 X[33606] - 8 X[42938]

X(43547) lies on the Kiepert circumhyperbola and these lines: {2, 5238}, {4, 42780}, {6, 42904}, {13, 398}, {14, 382}, {15, 10188}, {16, 5365}, {17, 3851}, {18, 550}, {20, 42796}, {30, 33606}, {61, 3855}, {62, 12817}, {140, 42684}, {381, 33607}, {395, 43330}, {397, 43227}, {548, 43200}, {549, 42890}, {631, 42964}, {1656, 42955}, {3528, 16242}, {3529, 36970}, {3530, 36967}, {3544, 10654}, {3545, 42934}, {3850, 16960}, {3858, 42692}, {3861, 43111}, {5068, 34754}, {5073, 16961}, {5237, 42545}, {5334, 22235}, {5340, 12816}, {5349, 19106}, {5350, 12820}, {5351, 41120}, {6777, 11603}, {10187, 15720}, {10299, 18581}, {10302, 11304}, {10645, 42495}, {11121, 33464}, {11543, 42801}, {11669, 37463}, {11737, 16962}, {12101, 42965}, {12102, 42935}, {12821, 16965}, {14869, 37835}, {15681, 42153}, {15700, 42434}, {15707, 43194}, {16267, 42419}, {16268, 33605}, {16773, 42430}, {16963, 42586}, {16966, 41973}, {16967, 42773}, {17504, 42599}, {17538, 43231}, {18582, 43018}, {19107, 43005}, {22831, 41020}, {22845, 40706}, {33602, 41113}, {33603, 41100}, {33604, 40693}, {33923, 42961}, {34200, 41122}, {38071, 41108}, {38335, 42521}, {41974, 42101}, {42085, 42902}, {42087, 42978}, {42093, 42629}, {42094, 43293}, {42103, 42992}, {42106, 43251}, {42114, 42802}, {42117, 42949}, {42118, 42782}, {42133, 42431}, {42137, 42994}, {42139, 42936}, {42148, 42507}, {42151, 42908}, {42475, 43238}, {42531, 43488}, {42628, 42958}, {42909, 43366}, {42918, 42925}, {42998, 43418}, {42999, 43030}

X(43547) = reflection of X(33386) in X(33412)
X(43547) = isogonal conjugate of X(5237)
X(43547) = X(i)-cross conjugate of X(j) for these (i,j): {5349, 4}, {19106, 13}, {42924, 17}, {42993, 18}, {43196, 12820}
X(43547) = X(1)-isoconjugate of X(5237)
X(43547) = barycentric quotient X(6)/X(5237)
X(43547) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {18, 42630, 550}, {398, 546, 42779}, {631, 42964, 43245}, {3544, 10654, 42939}, {5321, 42121, 42901}, {5349, 42993, 19106}, {41973, 42920, 16966}, {42158, 42989, 43023}, {42159, 42972, 16964}, {42779, 43419, 398}, {42814, 43419, 546}, {42978, 43492, 42087}, {42989, 43023, 3411}, {42993, 43196, 43485}

X(43548) = GIBERT (21,26,49) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 49*a^2*SA + 52*SB*SC : :
Barycentrics    1/(7*Sqrt[3] + 3*Cot[A]) : :

X(43548) lies on the Kiepert circumhyperbola and these lines: {2, 43470}, {4, 5352}, {6, 43549}, {13, 5054}, {14, 547}, {16, 11540}, {17, 632}, {18, 3412}, {62, 43027}, {376, 43324}, {381, 43293}, {395, 10187}, {396, 42897}, {549, 42928}, {618, 42062}, {671, 6669}, {1656, 43009}, {3530, 36968}, {3859, 5238}, {3860, 19107}, {5321, 43497}, {8703, 12816}, {10645, 35404}, {10653, 33604}, {11602, 22892}, {12811, 36970}, {12817, 16966}, {12820, 15681}, {12821, 38071}, {15684, 43292}, {15692, 42086}, {15710, 36969}, {15719, 18582}, {16242, 43004}, {16267, 42530}, {16772, 41971}, {16961, 43232}, {16963, 41984}, {16965, 42592}, {16967, 42479}, {19106, 43298}, {21845, 25156}, {22236, 42969}, {22237, 37835}, {33603, 41101}, {33606, 42532}, {35401, 42626}, {35403, 42929}, {35409, 42106}, {35434, 42950}, {37640, 43446}, {40693, 42893}, {41107, 42996}, {41121, 43103}, {41944, 42512}, {41987, 42919}, {42098, 42430}, {42117, 43372}, {42129, 42520}, {42144, 43104}, {42146, 42429}, {42157, 43421}, {42492, 43229}, {42499, 42913}, {42506, 42627}, {42529, 42930}, {42533, 42817}, {42580, 43022}, {42632, 43204}, {42634, 42898}, {42803, 43419}, {42937, 43445}, {42954, 43029}, {42976, 43011}, {42977, 43302}

X(43548) = X(i)-cross conjugate of X(j) for these (i,j): {16963, 14}, {42496, 13}, {43102, 18}, {43469, 43440}
X(43548) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 43489, 16241}, {17, 632, 43008}, {35401, 42626, 43325}, {41943, 43101, 43021}, {43021, 43101, 14}, {43021, 43199, 41943}, {43469, 43490, 41984}

X(43549) = GIBERT (-21,26,49) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 49*a^2*SA - 52*SB*SC : :
Barycentrics    1/(7*Sqrt[3] - 3*Cot[A]) : :

X(43549) lies on the Kiepert circumhyperbola and these lines: {2, 43469}, {4, 5351}, {6, 43548}, {13, 547}, {14, 5054}, {15, 11540}, {17, 3411}, {18, 632}, {61, 43026}, {376, 43325}, {381, 43292}, {395, 42896}, {396, 10188}, {549, 42929}, {619, 42063}, {671, 6670}, {1656, 43008}, {3530, 36967}, {3859, 5237}, {3860, 19106}, {5318, 43498}, {8703, 12817}, {10646, 35404}, {10654, 33605}, {11121, 36770}, {11603, 22848}, {12811, 36969}, {12816, 16967}, {12820, 38071}, {12821, 15681}, {15684, 43293}, {15692, 42085}, {15710, 36970}, {15719, 18581}, {16241, 43005}, {16268, 42531}, {16773, 41972}, {16960, 43233}, {16962, 41984}, {16964, 42593}, {16966, 42478}, {18582, 43252}, {19107, 43299}, {21846, 25166}, {22235, 37832}, {22238, 42968}, {33602, 41100}, {33607, 42533}, {35401, 42625}, {35403, 42928}, {35409, 42103}, {35434, 42951}, {37641, 43447}, {40694, 42892}, {41108, 42997}, {41122, 43102}, {41943, 42513}, {41987, 42918}, {42095, 42429}, {42118, 43373}, {42132, 42521}, {42143, 42430}, {42145, 43101}, {42158, 43420}, {42493, 43228}, {42498, 42912}, {42507, 42628}, {42528, 42931}, {42532, 42818}, {42581, 43023}, {42631, 43203}, {42633, 42899}, {42804, 43418}, {42936, 43444}, {42955, 43028}, {42976, 43303}, {42977, 43010}

X(43549) = X(i)-cross conjugate of X(j) for these (i,j): {16962, 13}, {42497, 14}, {43103, 17}, {43470, 43441}
X(43549) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 43490, 16242}, {18, 632, 43009}, {35401, 42625, 43324}, {41944, 43104, 43020}, {43020, 43104, 13}, {43020, 43200, 41944}, {43470, 43489, 41984}

X(43550) = GIBERT (21,26,3) POINT

Barycentrics    7*Sqrt[3]*a^2*S + 3*a^2*SA + 52*SB*SC : :
Barycentrics    1/(Sqrt[3] + 7*Cot[A]) : :
X(43550) = 6 X[2] - 7 X[33414]

X(43550) lies on the Kiepert circumhyperbola and these lines: {2, 5351}, {4, 43308}, {6, 43551}, {13, 3627}, {14, 3843}, {16, 43446}, {17, 1657}, {18, 3850}, {61, 43033}, {62, 23046}, {140, 43441}, {381, 42436}, {397, 43227}, {398, 12817}, {548, 36969}, {550, 42930}, {1656, 43440}, {3856, 42800}, {5072, 16965}, {5073, 43325}, {5238, 42514}, {5321, 43424}, {5344, 16809}, {5349, 43030}, {10187, 16808}, {10188, 15712}, {11668, 37463}, {12108, 42433}, {12812, 42937}, {12816, 16964}, {12820, 42779}, {14891, 42488}, {14892, 41977}, {15684, 16962}, {15686, 42166}, {15687, 43009}, {15689, 43238}, {16267, 42890}, {16960, 22235}, {16966, 42476}, {18582, 42959}, {20395, 42063}, {21735, 42092}, {23303, 43499}, {33416, 42693}, {33602, 40693}, {33604, 42511}, {33605, 41107}, {33703, 36967}, {36968, 42610}, {41990, 42599}, {42086, 43445}, {42094, 42630}, {42099, 42909}, {42100, 43294}, {42102, 42896}, {42110, 43485}, {42127, 42928}, {42136, 43471}, {42138, 42944}, {42141, 42979}, {42151, 42472}, {42156, 42430}, {42157, 43010}, {42159, 42695}, {42478, 43418}, {42591, 42965}, {42629, 43370}, {42919, 43242}, {42946, 43109}, {42994, 43005}, {42997, 43403}

X(43550) = isogonal conjugate of X(5352)
X(43550) = X(42136)-cross conjugate of X(14)
X(43550) = X(1)-isoconjugate of X(5352)
X(43550) = barycentric quotient X(6)/X(5352)
X(43550) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 43491, 42158}, {13, 3627, 42435}, {5366, 42813, 42158}

X(43551) = GIBERT (-21,26,3) POINT

Barycentrics    7*Sqrt[3]*a^2*S - 3*a^2*SA - 52*SB*SC : :
Barycentrics    1/(Sqrt[3] - 7*Cot[A]) : :
X(43551) = 6 X[2] - 7 X[33415]

X(43551) lies on the Kiepert circumhyperbola and these lines: {2, 5352}, {4, 43309}, {6, 43550},{13, 3843}, {14, 3627}, {15, 43447}, {17, 3850}, {18, 1657}, {61, 23046}, {62, 43032}, {140, 43440}, {381, 42435}, {397, 12816}, {398, 43226}, {548, 36970}, {550, 42931}, {1656, 43441}, {3856, 42799}, {5072, 16964}, {5073, 43324}, {5237, 42515}, {5318, 43425}, {5343, 16808}, {5350, 43031}, {10187, 15712}, {10188, 16809}, {11668, 37464}, {12108, 42434}, {12812, 42936}, {12817, 16965}, {12821, 42780}, {14891, 42489}, {14892, 41978}, {15684, 16963}, {15686, 42163}, {15687, 43008}, {15689, 43239}, {16268, 42891}, {16961, 22237}, {16967, 42477}, {18581, 42958}, {20394, 42062}, {21735, 42089}, {23302, 43500}, {33417, 42692}, {33603, 40694}, {33604, 41108}, {33605, 42510}, {33703, 36968}, {36967, 42611}, {41990, 42598}, {42085, 43444}, {42093, 42629}, {42099, 43295}, {42100, 42908}, {42101, 42897}, {42107, 43486}, {42126, 42929}, {42135, 42945}, {42137, 43472}, {42140, 42978}, {42150, 42473}, {42153, 42429}, {42158, 43011}, {42162, 42694}, {42479, 43419}, {42590, 42964}, {42630, 43371}, {42918, 43243}, {42947, 43108}, {42995, 43004}, {42996, 43404}

X(43551) = isogonal conjugate of X(5351)
X(43551) = X(42137)-cross conjugate of X(13)
X(43551) = X(1)-isoconjugate of X(5351)
X(43551) = barycentric quotient X(6)/X(5351)
X(43551) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 43492, 42157}, {14, 3627, 42436}, {5365, 42814, 42157}

X(43552) = GIBERT (24,49,2) POINT

Barycentrics    4*Sqrt[3]*a^2*S + a^2*SA + 49*SB*SC : :
Barycentrics    1/(Sqrt[3] + 12*Cot[A]) : :

X(43552) lies on the Kiepert circumhyperbola and these lines: {2, 42088}, {3, 43445}, {4, 42969}, {5, 43444}, {6, 43553}, {13, 42104}, {14, 42134}, {17, 3146}, {18, 3832}, {20, 43447}, {30, 42932}, {376, 42950}, {381, 43198}, {383, 10155}, {473, 38253}, {2043, 34089}, {2044, 34091}, {3091, 43446}, {3522, 10188}, {3528, 42984}, {3543, 42128}, {3544, 42933}, {3830, 33604}, {3839, 11486}, {3845, 33605}, {3854, 42155}, {5059, 42598}, {5068, 5237}, {5334, 12821}, {5335, 12817}, {5350, 22237}, {6770, 21845}, {10645, 15683}, {10653, 33606}, {11488, 42587}, {14269, 42922}, {15022, 43442}, {15640, 42138}, {15684, 43197}, {15697, 43501}, {15698, 42492}, {15705, 19106}, {15709, 42889}, {15717, 43443}, {17578, 22235}, {21734, 42500}, {33602, 42136}, {33603, 42975}, {33607, 42511}, {36968, 43440}, {38335, 42982}, {41974, 43404}, {41987, 42987}, {42119, 42502}, {42142, 43107}, {42166, 43421}, {42430, 43195}, {42528, 42695}, {42634, 42963}, {43109, 43487}, {43201, 43474}

X(43552) = cevapoint of X(11486) and X(22236)

X(43553) = GIBERT (-24,49,2) POINT

Barycentrics    4*Sqrt[3]*a^2*S - a^2*SA - 49*SB*SC : :
Barycentrics    1/(Sqrt[3] - 12*Cot[A]) : :

X(43553) lies on the Kiepert circumhyperbola and these lines: {2, 42087}, {3, 43444}, {4, 42968}, {5, 43445}, {6, 43552}, {13, 42133}, {14, 42105}, {17, 3832}, {18, 3146}, {20, 43446}, {30, 42933}, {376, 42951}, {381, 43197}, {472, 38253}, {1080, 10155}, {2043, 34091}, {2044, 34089}, {3091, 43447}, {3522, 10187}, {3528, 42985}, {3543, 42125}, {3544, 42932}, {3830, 33605}, {3839, 11485}, {3845, 33604}, {3854, 42154}, {5059, 42599}, {5068, 5238}, {5334, 12816}, {5335, 12820}, {5349, 22235}, {6773, 21846}, {10646, 15683}, {10654, 33607}, {11489, 42586}, {14269, 42923}, {15022, 43443}, {15640, 42135}, {15684, 43198}, {15697, 43502}, {15698, 42493}, {15705, 19107}, {15709, 42888}, {15717, 43442}, {17578, 22237}, {21734, 42501}, {33602, 42974}, {33603, 42137}, {33606, 42510}, {36967, 43441}, {38335, 42983}, {41973, 43403}, {41987, 42986}, {42120, 42503}, {42139, 43100}, {42163, 43420}, {42429, 43196}, {42529, 42694}, {42633, 42962}, {43108, 43488}, {43202, 43473}

X(43553) = cevapoint of X(11485) and X(22238)

X(43554) = GIBERT (24,19,32) POINT

Barycentrics    4*Sqrt[3]*a^2*S + 16*a^2*SA + 19*SB*SC : :
Barycentrics    1/(4*Sqrt[3] + 3*Cot[A]) : :

X(43554) lies on the Kiepert circumhyperbola and these lines: {2, 42492}, {4, 16644}, {6, 43555}, {13, 3524}, {14, 5071}, {15, 12821}, {17, 3525}, {18, 5067}, {30, 42932}, {62, 43443}, {376, 42128}, {381, 43197}, {395, 42610}, {549, 43242}, {616, 42062}, {631, 22235}, {3090, 22237}, {3528, 16241}, {3544, 10654}, {3545, 42132}, {3859, 43496}, {5054, 42922}, {5076, 42927}, {5334, 42474}, {5335, 33604}, {5485, 33475}, {5488, 37178}, {6669, 42035}, {10187, 42488}, {10188, 40693}, {10653, 33607}, {11001, 12816}, {11303, 38259}, {11304, 18845}, {11539, 42982}, {11541, 42494}, {11542, 15709}, {12817, 37832}, {12820, 42430}, {15682, 42124}, {15699, 42987}, {15702, 23302}, {15710, 43416}, {15715, 42625}, {15719, 43328}, {15721, 42815}, {16267, 42530}, {16808, 43204}, {16960, 43308}, {16966, 33606}, {18581, 43251}, {19708, 33602}, {33605, 43101}, {36968, 43424}, {37641, 43014}, {41099, 42136}, {41943, 43245}, {42098, 43482}, {42130, 43246}, {42139, 42799}, {42141, 42930}, {42149, 43441}, {42156, 43481}, {42162, 42959}, {42506, 42893}, {42591, 42988}, {42595, 43029}, {42633, 42950}, {42777, 43494}, {42910, 43232}, {42971, 43107}, {42977, 43249}, {42979, 43013}, {42998, 43445}, {43016, 43330}, {43239, 43447}

X(43554) = X(i)-cross conjugate of X(j) for these (i,j): {42777, 13}, {43494, 33605}
X(43554) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37832, 42511, 42472}, {42088, 43403, 33602}, {42529, 42952, 18582}, {42634, 42984, 2}, {42817, 42984, 42634}, {43403, 43463, 19708}

X(43555) = GIBERT (-24,19,32) POINT

Barycentrics    4*Sqrt[3]*a^2*S - 16*a^2*SA - 19*SB*SC : :
Barycentrics    1/(4*Sqrt[3] - 3*Cot[A]) : :

X(43555) lies on the Kiepert circumhyperbola and these lines: {2, 42493}, {4, 16645}, {6, 43554}, {13, 5071}, {14, 3524}, {16, 12820}, {17, 5067}, {18, 3525}, {30, 42933}, {61, 43442}, {376, 42125}, {381, 43198}, {396, 42611}, {549, 43243}, {617, 42063}, {631, 22237}, {3090, 22235}, {3528, 16242}, {3544, 10653}, {3545, 42129}, {3859, 43495}, {5054, 42923}, {5076, 42926}, {5334, 33605}, {5335, 42475}, {5485, 33474}, {5487, 37177}, {6670, 42036}, {10187, 40694}, {10188, 42489}, {10654, 33606}, {11001, 12817}, {11303, 18845}, {11304, 38259}, {11539, 42983}, {11541, 42495}, {11543, 15709}, {12816, 37835}, {12821, 42429}, {15682, 42121}, {15699, 42986}, {15702, 23303}, {15710, 43417}, {15715, 42626}, {15719, 43329}, {15721, 42816}, {16268, 42531}, {16809, 43203}, {16961, 43309}, {16967, 33607}, {18582, 43250}, {19708, 33603}, {33604, 43104}, {36967, 43425}, {37640, 43015}, {41099, 42137}, {41944, 43244}, {42095, 43481}, {42131, 43247}, {42140, 42931}, {42142, 42800}, {42152, 43440}, {42153, 43482}, {42159, 42958}, {42507, 42892}, {42590, 42989}, {42594, 43028}, {42634, 42951}, {42778, 43493}, {42911, 43233}, {42970, 43100}, {42976, 43248}, {42978, 43012}, {42999, 43444}, {43017, 43331}, {43238, 43446}

X(43555) = X(i)-cross conjugate of X(j) for these (i,j): {42778, 14}, {43493, 33604}
X(43555) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37835, 42510, 42473}, {42087, 43404, 33603}, {42528, 42953, 18581}, {42633, 42985, 2}, {42818, 42985, 42633}, {43404, 43464, 19708}

X(43556) = GIBERT (24,19,6) POINT

Barycentrics    4*Sqrt[3]*a^2*S + 3*a^2*SA + 19*SB*SC : :
Barycentrics    1/(Sqrt[3] + 4*Cot[A]) : :

X(43556) lies on the Kiepert circumhyperbola and these lines: {2, 5340}, {4, 42815}, {6, 43557}, {13, 3146}, {14, 3832}, {16, 43442}, {17, 3522}, {18, 5068}, {20, 43416}, {30, 33604}, {61, 12820}, {140, 42926}, {381, 33605}, {397, 3854}, {470, 38253}, {1656, 43444}, {1657, 42916}, {2045, 34089}, {2046, 34091}, {3091, 42989}, {3523, 42123}, {3533, 43242}, {3543, 33602}, {3839, 33603}, {3858, 42983}, {5056, 42128}, {5059, 5318}, {5339, 43364}, {5343, 12817}, {5350, 17578}, {5487, 20080}, {10155, 37464}, {10187, 41977}, {10188, 18582}, {11488, 42794}, {11541, 42496}, {12816, 40693}, {12821, 42779}, {15022, 42149}, {15683, 33607}, {15717, 42158}, {16772, 42518}, {16965, 42592}, {17800, 42927}, {21734, 43238}, {33606, 41112}, {40694, 42612}, {41107, 43023}, {41943, 42161}, {41972, 42581}, {41974, 43440}, {42098, 43480}, {42108, 43473}, {42112, 43426}, {42120, 42949}, {42134, 42432}, {42141, 42684}, {42144, 42988}, {42151, 43300}, {42156, 43479}, {42164, 43201}, {42433, 43024}, {42498, 43441}, {42693, 43365}, {42781, 43466}, {42897, 42920}, {42999, 43030}

X(43556) = isogonal conjugate of X(36836)
X(43556) = X(42108)-cross conjugate of X(14)
X(43556) = X(1)-isoconjugate of X(36836)
X(43556) = barycentric quotient X(6)/X(36836)
X(43556) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5318, 22235, 5059}, {42123, 43447, 3523}

X(43557) = GIBERT (-24,19,6) POINT

Barycentrics    4*Sqrt[3]*a^2*S - 3*a^2*SA - 19*SB*SC : :
Barycentrics    1/(Sqrt[3] - 4*Cot[A]) : :

X(43557) lies on the Kiepert circumhyperbola and these lines: {2, 5339}, {4, 42816}, {13, 3832}, {6, 43556}, {14, 3146}, {15, 43443}, {17, 5068}, {18, 3522}, {20, 43417}, {30, 33605}, {62, 12821}, {140, 42927}, {381, 33604}, {398, 3854}, {471, 38253}, {1656, 43445}, {1657, 42917}, {2045, 34091}, {2046, 34089}, {3091, 42988}, {3523, 42122}, {3533, 43243}, {3543, 33603}, {3839, 33602}, {3858, 42982}, {5056, 42125}, {5059, 5321}, {5340, 43365}, {5344, 12816}, {5349, 17578}, {5488, 20080}, {10155, 37463}, {10187, 18581}, {10188, 41978}, {11489, 42793}, {11541, 42497}, {12817, 40694}, {12820, 42780}, {15022, 42152}, {15683, 33606}, {15717, 42157}, {16773, 42519}, {16964, 42593}, {17800, 42926}, {21734, 43239}, {33607, 41113}, {40693, 42613}, {41108, 43022}, {41944, 42160}, {41971, 42580}, {41973, 43441}, {42095, 43479}, {42109, 43474}, {42113, 43427}, {42119, 42948}, {42133, 42431}, {42140, 42685}, {42145, 42989}, {42150, 43301}, {42153, 43480}, {42165, 43202}, {42434, 43025}, {42499, 43440}, {42692, 43364}, {42782, 43465}, {42896, 42921}, {42998, 43031}

X(43557) = isogonal conjugate of X(36843)
X(43557) = X(42109)-cross conjugate of X(13)
X(43557) = X(1)-isoconjugate of X(36843)
X(43557) = barycentric quotient X(6)/X(36843)
X(43557) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5321, 22237, 5059}, {42122, 43446, 3523}

X(43558) = GIBERT (5 SQRT(3),13,25) POINT

Barycentrics    5*a^2*S + 25*a^2*SA + 26*SB*SC : :
Barycentrics    1/(5 + Cot[A]) : :

X(43558) lies on the Kiepert circumhyperbola and these lines: {2, 35770}, {3, 12818}, {4, 43513}, {5, 6433}, {6, 43559}, {140, 43340}, {371, 14226}, {372, 3590}, {485, 3526}, {486, 3592}, {548, 42277}, {549, 1327}, {590, 6500}, {1131, 10303}, {1132, 7486}, {1151, 43378}, {1152, 11540}, {1328, 5055}, {2043, 12820}, {2044, 12821}, {2996, 6118}, {3068, 34091}, {3070, 42608}, {3312, 43322}, {3316, 5420}, {3317, 6435}, {3525, 6483}, {3533, 42558}, {3534, 42582}, {3843, 42566}, {3856, 43337}, {3857, 42260}, {5066, 22615}, {5072, 42258}, {5490, 32813}, {6409, 23046}, {6432, 43379}, {6448, 41948}, {6460, 14241}, {6471, 7583}, {6479, 43411}, {6497, 43432}, {6561, 15022}, {6564, 43505}, {6813, 14488}, {7375, 18843}, {8976, 43255}, {10109, 42568}, {10140, 11539}, {10304, 42269}, {15692, 43515}, {15717, 35820}, {15759, 42576}, {16239, 42644}, {18538, 43338}, {31414, 43315}

X(43558) = isogonal conjugate of X(35771)
X(43558) = X(1)-isoconjugate of X(35771)
X(43558) = barycentric quotient X(6)/X(35771)
X(43558) = {X(5),X(6433)}-harmonic conjugate of X(12819)

X(43559) = GIBERT (-5 SQRT(3),13,25) POINT

Barycentrics    1/(5 - Cot[A]) : :
Barycentrics    5*a^2*S - 25*a^2*SA - 26*SB*SC : :

X(43559) lies on the Kiepert circumhyperbola and these lines: {2, 35771}, {3, 12819}, {4, 43514}, {5, 6434}, {6, 43558}, {140, 43341}, {371, 3591}, {372, 14241}, {485, 3594}, {486, 3526}, {548, 42274}, {549, 1328}, {615, 6501}, {1131, 7486}, {1132, 9541}, {1151, 11540}, {1152, 43379}, {1327, 5055}, {2043, 12821}, {2044, 12820}, {2996, 6119}, {3069, 34089}, {3071, 42609}, {3311, 43323}, {3316, 6436}, {3317, 5418}, {3525, 6482}, {3533, 42557}, {3534, 42583}, {3843, 42567}, {3856, 43336}, {3857, 42261}, {5066, 22644}, {5072, 42259}, {5491, 32812}, {6410, 23046}, {6431, 43378}, {6447, 41947}, {6459, 14226}, {6470, 7584}, {6478, 43412}, {6496, 43433}, {6560, 15022}, {6565, 43506}, {6811, 14488}, {7376, 18843}, {9543, 42601}, {10109, 42569}, {10139, 11539}, {10304, 42268}, {13951, 43254}, {15692, 43516}, {15717, 35821}, {15759, 42577}, {16239, 42643}, {18762, 43339}

X(43559) = isogonal conjugate of X(35770)
X(43559) = X(1)-isoconjugate of X(35770)
X(43559) = barycentric quotient X(6)/X(35770)
X(43559) = {X(5),X(6434)}-harmonic conjugate of X(12818)

X(43560) = GIBERT (8 SQRT(3),17,2) POINT

Barycentrics    4*a^2*S + a^2*SA + 17*SB*SC : :
Barycentrics    1/(1 + 4*Cot[A]) : :

X(43560) lies on the Kiepert circumhyperbola and these lines: {2, 6410}, {3, 34089}, {4, 6417}, {5, 34091}, {6, 43561}, {20, 3316}, {226, 17802}, {485, 3146}, {486, 3832}, {1131, 6459}, {1132, 3070}, {1327, 35821}, {1328, 1587}, {1585, 38253}, {1588, 12819}, {2045, 43445}, {2046, 43444}, {3091, 3317}, {3424, 14230}, {3522, 6564}, {3543, 14241}, {3590, 5059}, {3591, 3854}, {3830, 42522}, {3839, 7584}, {3855, 13961}, {5068, 10194}, {5073, 9542}, {5418, 42604}, {6492, 43512}, {6560, 15022}, {6813, 10155}, {7000, 14494}, {7374, 7612}, {7585, 43520}, {8981, 15640}, {12222, 42023}, {14236, 14853}, {15683, 22644}, {15705, 42267}, {15708, 43521}, {15717, 35820}, {21734, 42265}, {41957, 43376}, {41962, 43511}, {42271, 42570}

X(43560) = isogonal conjugate of X(6409)
X(43560) = isotomic conjugate of X(32814)
X(43560) = isotomic conjugate of the anticomplement of X(7585)
X(43560) = X(7585)-cross conjugate of X(2)
X(43560) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6409}, {31, 32814}
X(43560) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 32814}, {6, 6409}
X(43560) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 43415, 34091}, {485, 3146, 9543}, {1131, 42284, 17578}, {31412, 43507, 5059}

X(43561) = GIBERT (-8 SQRT(3),17,2) POINT

Barycentrics    4*a^2*S - a^2*SA - 17*SB*SC : :
Barycentrics    1/(1 - 4*Cot[A]) : :

X(43561) lies on the Kiepert circumhyperbola and these lines: {2, 6409}, {3, 34091}, {4, 6418}, {5, 9543}, {6, 43560}, {20, 3317}, {76, 32814}, {226, 17805}, {485, 3832}, {486, 3146}, {1131, 3071}, {1132, 6460}, {1327, 1588}, {1328, 35820}, {1586, 38253}, {1587, 12818}, {2045, 43444}, {2046, 43445}, {3091, 3316}, {3424, 14233}, {3522, 6565}, {3543, 14226}, {3544, 9542}, {3590, 3854}, {3591, 5059}, {3830, 42523}, {3839, 7583}, {3855, 13903}, {5068, 9540}, {5420, 42605}, {6493, 43511}, {6561, 15022}, {6811, 10155}, {7000, 7612}, {7374, 14494}, {7586, 43519}, {12221, 42024}, {13966, 15640}, {14240, 14853}, {15683, 22615}, {15705, 42266}, {15708, 43522}, {15717, 35821}, {21734, 42262}, {41958, 43377}, {41961, 43512}, {42272, 42571}

X(43561) = isogonal conjugate of X(6410)
X(43561) = isotomic conjugate of the anticomplement of X(7586)
X(43561) = X(7586)-cross conjugate of X(2)
X(43561) = X(1)-isoconjugate of X(6410)
X(43561) = barycentric quotient X(6)/X(6410)
X(43561) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 9690, 34089}, {1132, 42283, 17578}, {42561, 43508, 5059}

X(43562) = GIBERT (9 SQRT(3),41,1) POINT

Barycentrics    9*a^2*S + a^2*SA + 82*SB*SC : :
Barycentrics    1/(1 + 9*Cot[A]) : :

X(43562) lies on the Kiepert circumhyperbola and these lines: {2, 42276}, {6, 43563}, {30, 10195}, {381, 10194}, {485, 3830}, {486, 3845}, {547, 42576}, {1131, 22615}, {1327, 6441}, {1328, 18510}, {2043, 10188}, {2044, 10187}, {2996, 22485}, {3316, 15682}, {3317, 41099}, {3534, 42582}, {3543, 3590}, {3591, 3839}, {3843, 42418}, {3860, 42274}, {5066, 22644}, {6561, 14241}, {6564, 43405}, {6811, 10185}, {9681, 35434}, {11001, 34089}, {12819, 23251}, {13687, 14244}, {14232, 14235}, {15640, 42602}, {18538, 33699}, {19709, 42261}, {19710, 42277}, {34091, 41106}, {41961, 42275}, {42558, 43374}

X(43562) = X(43504)-cross conjugate of X(1328)

X(43563) = GIBERT (-9 SQRT(3),41,1) POINT

Barycentrics    9*a^2*S - a^2*SA - 82*SB*SC : :
Barycentrics    1/(1 - 9*Cot[B]) : :

X(43563) lies on the Kiepert circumhyperbola and these lines: {2, 42275}, {6, 43562}, {30, 10194}, {381, 9680}, {485, 3845}, {486, 3830}, {547, 42577}, {1132, 22644}, {1327, 18512}, {1328, 6442}, {2043, 10187}, {2044, 10188}, {2996, 22484}, {3316, 41099}, {3317, 15682}, {3534, 42583}, {3543, 3591}, {3590, 3839}, {3843, 42417}, {3860, 42277}, {5066, 22615}, {6560, 14226}, {6565, 43406}, {6813, 10185}, {11001, 34091}, {12818, 23261}, {13807, 14229}, {14237, 14239}, {15640, 42603}, {18762, 33699}, {19709, 42260}, {19710, 42274}, {34089, 41106}, {41962, 42276}, {42557, 43375}

X(43563) = X(43503)-cross conjugate of X(1327)

X(43564) = GIBERT (12 SQRT(3),37,72) POINT

Barycentrics    6*a^2*S + 36*a^2*SA + 37*SB*SC : :
Barycentrics    1/(6 + Cot[A]) : :

X(43564) lies on the Kiepert circumhyperbola and these lines: {2, 6428}, {4, 6411}, {6, 43565}, {140, 1131}, {485, 3533}, {590, 34091}, {598, 7375}, {631, 1327}, {671, 7376}, {1132, 1656}, {1328, 3090}, {3317, 8253}, {3525, 10148}, {3535, 39284}, {3591, 7582}, {5067, 14226}, {7389, 41895}, {7581, 10195}, {10194, 32785}, {10299, 12818}, {15703, 43377}, {42601, 43414}

X(43564) = isogonal conjugate of X(6427)
X(43564) = X(43506)-cross conjugate of X(3317)
X(43564) = X(1)-isoconjugate of X(6427)
X(43564) = barycentric quotient X(6)/X(6427)

X(43565) = GIBERT (-12 SQRT(3),37,72) POINT

Barycentrics    6*a^2*S - 36*a^2*SA - 37*SB*SC : :
Barycentrics    1/(6 - Cot[A]) : :

X(43565) lies on the Kiepert circumhyperbola and these lines: {2, 6427}, {4, 6412}, {6, 43564}, {140, 1132}, {486, 3533}, {598, 7376}, {615, 34089}, {631, 1328}, {671, 7375}, {1131, 1656}, {1327, 3090}, {3316, 8252}, {3525, 10147}, {3536, 39284}, {3590, 7581}, {5067, 14241}, {7388, 41895}, {7582, 10194}, {10195, 32786}, {10299, 12819}, {15703, 43376}, {42600, 43413}

X(43565) = isogonal conjugate of X(6428)
X(43565) = X(43505)-cross conjugate of X(3316)
X(43565) = X(1)-isoconjugate of X(6428)
X(43565) = barycentric quotient X(6)/X(6428)

X(43566) = GIBERT (12 SQRT(3),37,2) POINT

Barycentrics    6*a^2*S + a^2*SA + 37*SB*SC : :
Barycentrics    1/(1 + 6*Cot[A]) : :

X(43527) lies on the Kiepert circumhyperbola and these lines: {2, 6412}, {4, 6427}, {6, 43567}, {20, 10195}, {30, 3316}, {376, 34089}, {381, 3317}, {485, 3543}, {486, 3839}, {1131, 32787}, {1132, 19053}, {1327, 7585}, {1328, 23249}, {1587, 12819}, {2043, 43447}, {2044, 43446}, {3068, 43380}, {3069, 41956}, {3091, 10194}, {3146, 3590}, {3545, 34091}, {3591, 3832}, {3830, 14241}, {3845, 7586}, {3854, 41946}, {5066, 43521}, {6449, 35409}, {6564, 15640}, {7000, 7608}, {7374, 7607}, {8253, 42538}, {8972, 15682}, {10304, 42269}, {11541, 43211}, {12818, 35822}, {13687, 14232}, {13846, 42537}, {14269, 19116}, {14893, 23269}, {15684, 42639}, {15692, 22644}, {15705, 42272}, {18762, 41099}, {19054, 43508}, {23267, 43313}, {31412, 43210}, {38335, 43522}, {41952, 42413}, {42283, 42540}, {42542, 43257}, {42569, 43384}

X(43566) = isogonal conjugate of X(6411)
X(43566) = isotomic conjugate of the anticomplement of X(19054)
X(43566) = X(i)-cross conjugate of X(j) for these (i,j): {19054, 2}, {43508, 1132}
X(43566) = X(1)-isoconjugate of X(6411)
X(43566) = barycentric quotient X(6)/X(6411)

X(43567) = GIBERT (-12 SQRT(3),37,2) POINT

Barycentrics    6*a^2*S - a^2*SA - 37*SB*SC : :
Barycentrics    1/(1 - 6*Cot[A]) : :

X(43567) lies on the Kiepert circumhyperbola and these lines: {2, 6411}, {4, 6428}, {6, 43566}, {20, 10194}, {30, 3317}, {376, 34091}, {381, 3316}, {485, 3839}, {486, 3543}, {1131, 19054}, {1132, 32788}, {1327, 23259}, {1328, 7586}, {1588, 12818}, {2043, 43446}, {2044, 43447}, {3068, 41955}, {3069, 43381}, {3091, 9681}, {3146, 3591}, {3545, 34089}, {3590, 3832}, {3830, 14226}, {3845, 7585}, {3854, 41945}, {5066, 43522}, {6450, 35409}, {6565, 15640}, {7000, 7607}, {7374, 7608}, {8252, 42537}, {10304, 42268}, {11541, 43212}, {12819, 35823}, {13807, 14237}, {13847, 42538}, {13941, 15682}, {14269, 19117}, {14893, 23275}, {15684, 42640}, {15692, 22615}, {15705, 42271}, {18538, 41099}, {19053, 43507}, {23273, 43312}, {38335, 43521}, {41951, 42414}, {42284, 42539}, {42541, 43256}, {42561, 43209}, {42568, 43385}

X(43567) = isogonal conjugate of X(6412)
X(43567) = isotomic conjugate of the anticomplement of X(19053)
X(43567) = X(i)-cross conjugate of X(j) for these (i,j): {19053, 2}, {43507, 1131}
X(43567) = X(1)-isoconjugate of X(6412)
X(43567) = barycentric quotient X(6)/X(6412)

X(43568) = GIBERT (15 SQRT(3),17,25) POINT

Barycentrics    15*a^2*S + 25*a^2*SA + 34*SB*SC : :
Barycentrics    1/(5 + 3*Cot[A]) : :
X(43568) = X[12818] + 2 X[42568]

X(43568) lies on the Kiepert circumhyperbola and these lines: {2, 42558}, {4, 6453}, {5, 43343}, {6, 43569}, {30, 12818}, {372, 34089}, {381, 12819}, {485, 549}, {486, 5055}, {590, 1327}, {1131, 5418}, {1132, 35815}, {1152, 14890}, {1328, 5066}, {3068, 14226}, {3070, 15706}, {3316, 15709}, {3317, 10576}, {3526, 6448}, {3590, 10303}, {3591, 7486}, {3628, 10194}, {3860, 6437}, {5490, 32811}, {6492, 8981}, {6560, 14241}, {6564, 15640}, {8253, 11540}, {8703, 43336}, {13798, 41895}, {13886, 34091}, {14229, 22645}, {15022, 35823}, {15683, 22644}, {15684, 41948}, {15701, 42572}, {15704, 43211}, {15712, 43438}, {15715, 42570}, {15717, 43256}, {18538, 33699}, {19709, 43381}, {22541, 37637}, {23046, 42265}, {23249, 42608}, {32788, 42606}, {36448, 42692}, {36466, 42693}, {38259, 41491}, {42261, 43340}, {42263, 43312}, {42269, 43210}, {42274, 43317}, {42524, 43382}, {42526, 43415}, {42537, 43405}

X(43568) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {485, 549, 43342}, {42602, 43430, 5055}

X(43569) = GIBERT (-15 SQRT(3),17,25) POINT

Barycentrics    15*a^2*S - 25*a^2*SA - 34*SB*SC : :
Barycentrics    1/(5 - 3*Cot[A]) : :
X[12819] + 2 X[42569]

X(43569) lies on the Kiepert circumhyperbola and these lines: {2, 42557}, {4, 6454}, {5, 43342}, {6, 43568}, {30, 12819}, {371, 34091}, {381, 12818}, {485, 5055}, {486, 549}, {615, 1328}, {1131, 35814}, {1132, 5420}, {1151, 14890}, {1327, 5066}, {3069, 14241}, {3071, 15706}, {3316, 10577}, {3317, 15709}, {3526, 6447}, {3590, 7486}, {3591, 10303}, {3628, 10195}, {3860, 6438}, {5491, 32810}, {6493, 13966}, {6561, 14226}, {6565, 15640}, {8252, 11540}, {8703, 43337}, {9690, 42527}, {13678, 41895}, {13939, 34089}, {14244, 22616}, {15022, 35822}, {15683, 22615}, {15684, 41947}, {15701, 42573}, {15704, 43212}, {15712, 43439}, {15715, 42571}, {15717, 43257}, {18762, 33699}, {19101, 37637}, {19709, 43380}, {23046, 42262}, {23259, 42609}, {32787, 42607}, {36448, 42693}, {36466, 42692}, {38259, 41490}, {42260, 43341}, {42264, 43313}, {42268, 43209}, {42277, 43316}, {42525, 43383}, {42538, 43406}

X(43569) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {486, 549, 43343}, {42603, 43431, 5055}

X(43570) = GIBERT (15 SQRT(3),17,9) POINT

Barycentrics    15*a^2*S + 9*a^2*SA + 34*SB*SC : :
Barycentrics    1/(3 + 5*Cot[A]) : :

X(43570) lies on the Kiepert circumhyperbola and these lines: {2, 6454}, {4, 42570}, {5, 43342}, {6, 43571}, {140, 43340}, {372, 34091}, {382, 1327}, {485, 550}, {486, 3851}, {546, 1328}, {1131, 8960}, {1132, 6564}, {1587, 3591}, {2043, 33607}, {2044, 33606}, {3070, 6452}, {3316, 6560}, {3317, 31412}, {3529, 14241}, {3530, 43254}, {3544, 31414}, {3590, 5418}, {3843, 42572}, {3855, 14226}, {5073, 43430}, {6493, 42216}, {7389, 10302}, {9690, 42260}, {10194, 13966}, {11541, 43526}, {12819, 42269}, {15681, 41963}, {15707, 41952}, {31487, 43503}, {36449, 42613}, {36467, 42612}, {41991, 43343}

X(43570) = isogonal conjugate of X(6453)
X(43570) = X(i)-cross conjugate of X(j) for these (i,j): {42260, 486}, {43515, 12819}
X(43570) = X(1)-isoconjugate of X(6453)
X(43570) = barycentric quotient X(6)/X(6453)
X(43570) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1131, 8960, 43432}, {8960, 43432, 22644}

X(43571) = GIBERT (-15 SQRT(3),17,9) POINT

Barycentrics    15*a^2*S - 9*a^2*SA - 34*SB*SC : :
Barycentrics    1/(3 - 5*Cot[A]) : :

X(43571) lies on the Kiepert circumhyperbola and these lines: {2, 6453}, {4, 42571}, {5, 43343}, {6, 43570}, {140, 43341}, {371, 34089}, {382, 1328}, {485, 3851}, {486, 550}, {546, 1327}, {1131, 6565}, {1132, 22615}, {1588, 3590}, {2043, 33606}, {2044, 33607}, {3071, 6451}, {3316, 42561}, {3317, 6561}, {3529, 14226}, {3530, 43255}, {3544, 8960}, {3591, 5420}, {3843, 42573}, {3855, 14241}, {5073, 43431}, {6492, 42215}, {7388, 10302}, {8981, 10195}, {11541, 43525}, {12818, 42268}, {15681, 41964}, {15707, 41951}, {36450, 42612}, {36468, 42613}, {41991, 43342}, {42261, 43415}

X(43571) = isogonal conjugate of X(6454)
X(43571) = X(i)-cross conjugate of X(j) for these (i,j): {42261, 485}, {43516, 12818}
X(43571) = X(1)-isoconjugate of X(6454)
X(43571) = barycentric quotient X(6)/X(6454)

X(43572) = X(2)X(54)∩X(30)X(110)

Barycentrics    a^2*(3*a^8 - 9*a^6*b^2 + 9*a^4*b^4 - 3*a^2*b^6 - 9*a^6*c^2 + 13*a^4*b^2*c^2 - 5*a^2*b^4*c^2 + b^6*c^2 + 9*a^4*c^4 - 5*a^2*b^2*c^4 - 2*b^4*c^4 - 3*a^2*c^6 + b^2*c^6) : :
X(43572) = 5 X[110] - 2 X[10540], 4 X[110] - X[14157], X[110] + 2 X[22115], 7 X[110] + 2 X[37477], X[110] - 4 X[40111], X[186] + 2 X[3292], 2 X[186] - 5 X[15034], 2 X[399] + X[13445], 2 X[1568] + X[12383], 2 X[2070] + X[23061], 2 X[2071] + X[14094], X[3153] + 2 X[30714], 4 X[3292] + 5 X[15034], X[3448] - 4 X[14156], 2 X[5609] + X[18859], X[5899] - 7 X[15039], 8 X[10540] - 5 X[14157], X[10540] + 5 X[22115], 7 X[10540] + 5 X[37477], X[10540] - 10 X[40111], 4 X[11064] - X[25739], X[14157] + 8 X[22115], 7 X[14157] + 8 X[37477], X[14157] - 16 X[40111], 7 X[15020] - 4 X[15646], 3 X[15035] - 2 X[37941], 7 X[15036] - 4 X[21663], X[15054] - 4 X[34152], 7 X[22115] - X[37477], X[22115] + 2 X[40111], X[23236] + 2 X[37938], 3 X[32609] - X[37922], X[37477] + 14 X[40111]

X(43572) lies on these lines: {2, 54}, {3, 7666}, {24, 37672}, {30, 110}, {49, 549}, {74, 37948}, {140, 9706}, {155, 15078}, {156, 3534}, {182, 15709}, {184, 3524}, {186, 3292}, {215, 5298}, {323, 37940}, {376, 1092}, {381, 13482}, {394, 11464}, {399, 13445}, {511, 37939}, {524, 19128}, {541, 43391}, {547, 13434}, {567, 15699}, {578, 5071}, {1154, 32609}, {1437, 21161}, {1511, 37955}, {1568, 12383}, {2070, 23061}, {2071, 14094}, {2477, 4995}, {3043, 5642}, {3044, 6055}, {3153, 30714}, {3167, 5890}, {3200, 16962}, {3201, 16963}, {3202, 33706}, {3448, 14156}, {3518, 21969}, {3519, 10125}, {3543, 10539}, {3545, 9306}, {3839, 13352}, {3845, 18350}, {5012, 5054}, {5066, 37472}, {5306, 9603}, {5609, 18859}, {5899, 15039}, {6241, 35602}, {6759, 11001}, {7689, 38942}, {7691, 32171}, {7999, 19357}, {9544, 10304}, {9586, 25055}, {9704, 15693}, {9909, 26882}, {10124, 13353}, {10313, 35324}, {10411, 36890}, {10546, 14483}, {10627, 34006}, {10984, 15698}, {11003, 15708}, {11064, 25739}, {11412, 14070}, {11424, 41106}, {11449, 18324}, {11455, 37497}, {11597, 11694}, {11704, 12429}, {12084, 16835}, {12278, 18568}, {13336, 15721}, {13346, 15682}, {13754, 15035}, {15020, 15646}, {15036, 21663}, {15054, 34152}, {15107, 37956}, {15687, 37495}, {15694, 32046}, {15713, 37471}, {16226, 34986}, {21849, 38848}, {22467, 41597}, {23236, 37938}, {37517, 41448}

X(43572) = midpoint of X(323) and X(37940)
X(43572) = reflection of X(i) in X(j) for these {i,j}: {74, 37948}, {15107, 37956}, {16532, 11694}, {37943, 5642}, {37955, 1511}
X(43572) = crosssum of X(11542) and X(11543)
X(43572) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 34148, 13482}, {22115, 40111, 110}

X(43573) = X(2)X(54)∩X(30)X(143)

Barycentrics    2*a^10 - 6*a^8*b^2 + 7*a^6*b^4 - 5*a^4*b^6 + 3*a^2*b^8 - b^10 - 6*a^8*c^2 + 4*a^6*b^2*c^2 + 7*a^4*b^4*c^2 - 8*a^2*b^6*c^2 + 3*b^8*c^2 + 7*a^6*c^4 + 7*a^4*b^2*c^4 + 10*a^2*b^4*c^4 - 2*b^6*c^4 - 5*a^4*c^6 - 8*a^2*b^2*c^6 - 2*b^4*c^6 + 3*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(43573) = X[4] + 2 X[18128], 2 X[5] + X[10116], 3 X[51] - X[7540], 2 X[140] + X[10112], X[1216] + 2 X[13292], X[1511] + 2 X[19481], 5 X[3567] + X[11750], X[3627] - 4 X[40240], 2 X[3628] + X[11264], 2 X[5462] + X[6146], 5 X[5890] - X[34796], 3 X[5943] - 2 X[23410], 3 X[5946] - X[38322], X[6241] + 3 X[37077], 2 X[9729] + X[12370], 3 X[9730] - X[38323], 4 X[10095] - X[13419], X[10111] + 2 X[12900], X[10114] + 2 X[20304], X[10274] + 2 X[32376], 3 X[11245] + X[34664], X[11591] + 2 X[32165], 2 X[11793] + X[32358], 3 X[12022] + X[38323], 4 X[12241] - X[12897], 2 X[12241] + X[40647], X[12897] + 2 X[40647], X[13403] + 2 X[13630], X[13470] + 2 X[16881], 11 X[15024] + X[34799], 3 X[16226] - X[38321], X[21659] + 5 X[37481], X[22962] + 2 X[31985], 6 X[32068] - X[38322]

X(43573) lies on these lines: {2, 54}, {3, 41586}, {4, 15019}, {5, 542}, {30, 143}, {49, 5642}, {51, 7540}, {113, 15032}, {125, 567}, {140, 10112}, {185, 541}, {265, 15037}, {381, 1181}, {524, 1216}, {547, 15806}, {549, 43394}, {576, 14791}, {578, 18281}, {599, 7393}, {1154, 11225}, {1511, 19481}, {1568, 15087}, {1992, 6643}, {2072, 13366}, {2777, 40928}, {2883, 3845}, {3521, 3527}, {3534, 37490}, {3564, 10170}, {3567, 11750}, {3580, 37513}, {3627, 40240}, {3628, 11264}, {4550, 18917}, {5012, 7552}, {5050, 14852}, {5054, 35602}, {5422, 18474}, {5448, 7592}, {5462, 6146}, {5476, 18381}, {5654, 14912}, {5890, 34796}, {5943, 23410}, {5946, 18400}, {5965, 15067}, {6241, 37077}, {6288, 15047}, {6699, 11430}, {6804, 9936}, {6816, 15083}, {7387, 43273}, {7512, 15360}, {7527, 16003}, {7550, 41724}, {7565, 25739}, {7689, 18916}, {7706, 18396}, {9140, 13434}, {9729, 12370}, {9730, 12022}, {9820, 15123}, {9927, 36752}, {10095, 13419}, {10110, 11645}, {10111, 12900}, {10114, 20304}, {10224, 12242}, {10263, 19924}, {10274, 32376}, {11179, 39571}, {11245, 13754}, {11432, 34725}, {11591, 32165}, {11793, 32358}, {12038, 33563}, {12429, 15805}, {13352, 18911}, {13363, 32423}, {13371, 37505}, {13567, 18475}, {13857, 37452}, {14130, 20126}, {14787, 25738}, {14790, 20423}, {14915, 16657}, {15004, 31723}, {15018, 41171}, {15024, 34799}, {16226, 38321}, {16511, 34507}, {19130, 34514}, {20191, 26879}, {20397, 37118}, {21659, 37481}, {22962, 31985}, {23325, 39561}, {26869, 37506}, {31152, 36747}, {32375, 34114}, {37478, 37644}

X(43573) = midpoint of X(i) and X(j) for these {i,j}: {9730, 12022}, {10170, 11232}
X(43573) = reflection of X(5946) in X(32068)
X(43573) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {569, 5449, 6689}, {569, 18912, 5449}, {575, 20301, 25555}, {12241, 40647, 12897}, {14374, 14375, 5446}

X(43574) = X(3)X(54)∩X(30)X(110)

Barycentrics    a^2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - 3*a^6*c^2 + 7*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 - a^2*c^6 - b^2*c^6) : :
X(43574) = 3 X[2] - 4 X[14156], 2 X[3] + X[23061], 3 X[3] - X[32608], 2 X[23] - 5 X[15034], X[74] + 2 X[323], X[74] - 4 X[10564], 3 X[110] - 2 X[10540], X[110] + 2 X[37477], 3 X[110] - 4 X[40111], 2 X[186] - 3 X[15035], X[323] + 2 X[10564], 5 X[631] - 2 X[41586], 4 X[1511] - X[15107], 2 X[1511] + X[37496], 2 X[1533] - 5 X[20125], 4 X[2072] - 3 X[14644], 2 X[3292] + X[7464], 4 X[3292] - X[14094], 2 X[3581] - 5 X[15051], X[5189] + 2 X[30714], 2 X[5609] + X[35001], X[5899] - 3 X[32609], 4 X[5972] - 3 X[37943], 4 X[6699] - X[37779], 2 X[7464] + X[14094], 4 X[7575] - 7 X[15020], X[7691] + 2 X[15137], 4 X[10540] - 3 X[14157], X[10540] - 3 X[22115], X[10540] + 3 X[37477], X[10706] - 4 X[40112], 2 X[11563] - 3 X[14643], X[13851] - 3 X[13857], X[14157] - 4 X[22115], X[14157] + 4 X[37477], 3 X[14157] - 8 X[40111], 7 X[15036] - 4 X[32110], 7 X[15036] - 6 X[37941], 5 X[15040] - 3 X[37922], 5 X[15051] - 4 X[15646], X[15054] - 4 X[37950], 3 X[15055] - 4 X[34152], X[15107] + 2 X[37496], 4 X[15122] - X[41724], 4 X[15462] - 3 X[19128], 2 X[21663] - 3 X[37948], 3 X[22115] - 2 X[40111], 3 X[23061] + 2 X[32608], 2 X[32110] - 3 X[37941], 3 X[35265] - X[37945], 3 X[37477] + 2 X[40111]

X(43574) lies on these lines: {2, 13352}, {3, 54}, {4, 801}, {5, 37495}, {6, 15045}, {20, 1147}, {22, 11464}, {23, 15034}, {24, 33586}, {26, 11449}, {30, 110}, {49, 550}, {52, 22467}, {60, 500}, {68, 23294}, {74, 323}, {112, 2706}, {140, 13434}, {154, 12082}, {155, 6241}, {156, 1657}, {182, 1992}, {184, 376}, {186, 249}, {215, 15326}, {265, 37938}, {283, 7421}, {343, 37118}, {378, 394}, {399, 35452}, {403, 11064}, {417, 2055}, {427, 41171}, {524, 5622}, {538, 11653}, {539, 3448}, {548, 9706}, {549, 567}, {568, 15053}, {569, 3523}, {578, 631}, {754, 15920}, {852, 6760}, {858, 15133}, {1060, 9637}, {1069, 11461}, {1112, 37917}, {1173, 5462}, {1176, 3098}, {1199, 9729}, {1216, 14118}, {1350, 19127}, {1368, 12022}, {1437, 3651}, {1495, 37925}, {1511, 2070}, {1533, 20125}, {1593, 15058}, {1597, 6090}, {1658, 37484}, {1660, 5656}, {1790, 7430}, {1941, 13450}, {1994, 9730}, {2072, 14644}, {2477, 15338}, {2937, 32171}, {2966, 17974}, {2972, 15781}, {3043, 13619}, {3044, 38749}, {3045, 38761}, {3046, 38773}, {3047, 16111}, {3048, 38805}, {3060, 6644}, {3090, 11424}, {3146, 10539}, {3153, 17702}, {3157, 19368}, {3167, 11456}, {3200, 36967}, {3201, 36968}, {3205, 42434}, {3206, 42433}, {3260, 18878}, {3284, 12096}, {3292, 6000}, {3484, 6368}, {3520, 5562}, {3522, 9545}, {3528, 10984}, {3529, 6759}, {3530, 13353}, {3534, 9703}, {3545, 5651}, {3546, 18912}, {3548, 26917}, {3567, 17928}, {3580, 10257}, {3581, 12228}, {3627, 18350}, {3819, 7550}, {3917, 11430}, {5097, 16226}, {5118, 14355}, {5189, 30714}, {5204, 9666}, {5217, 9653}, {5446, 38848}, {5447, 37126}, {5609, 35001}, {5640, 39522}, {5663, 13445}, {5876, 15062}, {5891, 7527}, {5892, 34545}, {5899, 32609}, {5907, 14865}, {5944, 13564}, {5972, 37943}, {6193, 11457}, {6243, 37814}, {6560, 9676}, {6636, 18475}, {6642, 9781}, {6699, 37779}, {6781, 9696}, {6800, 35243}, {7387, 26882}, {7485, 37506}, {7488, 10625}, {7502, 13340}, {7503, 7999}, {7509, 11425}, {7512, 13367}, {7514, 7998}, {7526, 11444}, {7556, 11202}, {7574, 15132}, {7575, 15020}, {7809, 10411}, {8909, 11462}, {9704, 15696}, {9707, 11414}, {9818, 15066}, {9833, 41736}, {10282, 12088}, {10298, 37478}, {10299, 37515}, {10304, 11003}, {10313, 32661}, {10323, 19357}, {10510, 19374}, {10545, 14483}, {10575, 41597}, {10605, 37672}, {10733, 18403}, {11001, 40196}, {11004, 37470}, {11134, 42943}, {11137, 42942}, {11250, 11440}, {11416, 14984}, {11441, 12085}, {11455, 18451}, {11468, 12163}, {11563, 14643}, {11579, 13169}, {11591, 14130}, {11649, 41743}, {11693, 37909}, {11793, 35500}, {11935, 15688}, {12006, 14627}, {12083, 26881}, {12084, 12111}, {12086, 12162}, {12100, 13339}, {12118, 12289}, {12278, 18569}, {12279, 32139}, {12281, 12302}, {12282, 15316}, {12293, 18394}, {12317, 13399}, {12325, 25563}, {12370, 37452}, {12383, 18400}, {12834, 13363}, {13198, 21663}, {13336, 15717}, {13366, 16836}, {13596, 15030}, {13598, 34484}, {13851, 13857}, {14385, 15329}, {14516, 23335}, {14805, 41462}, {14845, 16042}, {14852, 30744}, {14915, 37944}, {15032, 34986}, {15036, 32110}, {15040, 37922}, {15043, 36749}, {15052, 16194}, {15054, 37950}, {15055, 34152}, {15068, 15305}, {15072, 18445}, {15078, 37489}, {15102, 17847}, {15122, 41724}, {15246, 37513}, {15709, 22112}, {15712, 37471}, {16196, 26879}, {16835, 18439}, {16976, 34380}, {17814, 35502}, {17834, 32534}, {18281, 23293}, {18324, 37494}, {18396, 31180}, {18474, 31074}, {18534, 35264}, {18570, 23039}, {18874, 22462}, {19121, 33878}, {26883, 33703}, {27866, 37955}, {30267, 41608}, {32142, 34864}, {33534, 41450}, {33884, 39242}, {34397, 37931}, {35265, 37945}, {37486, 38444}, {37970, 41673}

X(43574) = midpoint of X(i) and X(j) for these {i,j}: {323, 2071}, {399, 35452}, {2070, 37496}, {22115, 37477}
X(43574) = isogonal conjugate of X(43917)
X(43574) = reflection of X(i) in X(j) for these {i,j}: {4, 1568}, {74, 2071}, {110, 22115}, {265, 37938}, {403, 11064}, {2070, 1511}, {2071, 10564}, {3580, 10257}, {3581, 15646}, {10540, 40111}, {10733, 18403}, {12317, 13399}, {13445, 18859}, {13619, 16163}, {14157, 110}, {15107, 2070}, {25739, 858}, {37909, 11693}, {37925, 1495}
X(43574) = X(36053)-anticomplementary conjugate of X(2888)
X(43574) = crosspoint of X(249) and X(18878)
X(43574) = crosssum of X(i) and X(j) for these (i,j): {115, 21731}, {1637, 20975}
X(43574) = trilinear product X(i)*X(j) for these {i,j}: {1101, 3134}, {14213, 43753}
X(43574) = barycentric product X(249)*X(3134)
X(43574) = barycentric quotient X(3134)/X(338)
X(43574) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13352, 15033}, {3, 195, 13630}, {3, 1993, 5890}, {3, 6101, 7691}, {3, 12161, 10574}, {3, 16266, 5889}, {3, 34148, 54}, {20, 1147, 1614}, {20, 1614, 8718}, {54, 7691, 10203}, {140, 37472, 13434}, {155, 11413, 6241}, {184, 37480, 376}, {323, 10564, 74}, {378, 394, 11459}, {394, 37497, 378}, {1092, 13346, 4}, {1147, 1614, 9705}, {1511, 37496, 15107}, {3167, 21312, 11456}, {3292, 7464, 14094}, {3917, 11430, 35921}, {6101, 15137, 23061}, {8718, 9705, 1614}, {10540, 22115, 40111}, {10540, 40111, 110}, {10625, 12038, 7488}, {10627, 43394, 3}, {11250, 18436, 11440}, {11441, 12085, 12290}, {12118, 37444, 12289}, {12219, 12901, 74}, {13352, 15033, 13482}, {13363, 15038, 12834}, {13367, 15644, 7512}, {15460, 15461, 15035}, {17928, 36747, 3567}, {35602, 37498, 24}

X(43575) = X(5)X(49)∩X(30)X(143)

Barycentrics    2*a^10 - 5*a^8*b^2 + 4*a^6*b^4 - 2*a^4*b^6 + 2*a^2*b^8 - b^10 - 5*a^8*c^2 + 6*a^6*b^2*c^2 + 3*a^4*b^4*c^2 - 7*a^2*b^6*c^2 + 3*b^8*c^2 + 4*a^6*c^4 + 3*a^4*b^2*c^4 + 10*a^2*b^4*c^4 - 2*b^6*c^4 - 2*a^4*c^6 - 7*a^2*b^2*c^6 - 2*b^4*c^6 + 2*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(43575) = X[5] + 3 X[12022], 5 X[5] - X[14516], 3 X[3845] + X[34224], 7 X[3851] + X[34799], X[3853] - 3 X[16657], 2 X[3856] + 3 X[12024], 3 X[5066] - X[12134], 3 X[5946] + X[21659], X[11565] + 2 X[40240], X[11819] - 3 X[13451], 15 X[12022] + X[14516], X[12289] + 3 X[38322], 2 X[13163] - 3 X[13364], 3 X[14893] - X[16655], X[31834] - 3 X[34664], X[32358] + 3 X[34664]

X(43575 lies on these lines: {4, 11538}, {5, 49}, {6, 18377}, {30, 143}, {140, 12370}, {185, 11560}, {539, 14128}, {546, 6146}, {548, 32110}, {578, 10224}, {1173, 3521}, {1199, 18403}, {1493, 1568}, {1503, 3861}, {1658, 39571}, {1994, 11803}, {3153, 14627}, {3518, 20193}, {3845, 34224}, {3851, 34799}, {3853, 16657}, {3856, 12024}, {5066, 12134}, {5448, 32136}, {5462, 30522}, {5498, 11430}, {5562, 12899}, {5663, 43392}, {5907, 11264}, {5944, 10096}, {5946, 21659}, {6000, 15807}, {8550, 34155}, {9818, 18356}, {10095, 18400}, {10112, 11591}, {10113, 36153}, {10264, 14130}, {10610, 34577}, {10628, 27552}, {11250, 18952}, {11438, 15332}, {11565, 40240}, {11800, 11802}, {11818, 18945}, {11819, 13451}, {12006, 17702}, {12106, 19467}, {12233, 18567}, {12254, 13621}, {12289, 38322}, {12902, 15047}, {13163, 13364}, {13406, 18390}, {13567, 15331}, {13754, 32165}, {14893, 16655}, {15037, 34007}, {15761, 22466}, {18282, 18475}, {18555, 22352}, {18570, 18912}, {21230, 34864}, {25739, 33332}, {30531, 37505}, {31834, 32358}, {34004, 37513}, {34209, 36161}, {37472, 37938}

X(43575) = midpoint of X(i) and X(j) for these {i,j}: {140, 12370}, {546, 6146}, {5446, 13470}, {5907, 11264}, {10112, 11591}, {12026, 32410}, {13403, 13630}, {31834, 32358}
X(43575) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 49, 10272}, {5, 54, 15806}, {5, 567, 8254}, {5, 36966, 110}, {265, 13434, 5}, {389, 11692, 143}, {3153, 14627, 20424}, {8254, 11801, 5}, {14374, 14375, 143}, {18390, 32046, 13406}, {32358, 34664, 31834}

X(43576) = X(20)X(54)∩X(30)X(110)

Barycentrics    a^2*(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - 3*a^6*c^2 + 15*a^4*b^2*c^2 - 7*a^2*b^4*c^2 - 5*b^6*c^2 + 3*a^4*c^4 - 7*a^2*b^2*c^4 + 10*b^4*c^4 - a^2*c^6 - 5*b^2*c^6) : :
X(43576) = 2 X[23] - 3 X[15035], 7 X[110] - 6 X[10540], 4 X[110] - 3 X[14157], 5 X[110] - 6 X[22115], 11 X[110] - 12 X[40111], 6 X[186] - 7 X[15036], 5 X[631] - 4 X[32223], 4 X[858] - 3 X[14644], 2 X[1351] - 3 X[11416], 4 X[1495] - 5 X[15034], 3 X[2071] - 2 X[32110], 2 X[2080] - 3 X[9218], 3 X[3153] - 2 X[12295], 2 X[3581] - 3 X[15055], 3 X[5899] - 5 X[15040], 4 X[7575] - 5 X[15051], 3 X[10519] - 2 X[41583], 8 X[10540] - 7 X[14157], 5 X[10540] - 7 X[22115], 3 X[10540] - 7 X[37477], 11 X[10540] - 14 X[40111], 4 X[10564] - 3 X[15035], 2 X[10620] - 3 X[13445], X[10620] - 3 X[35452], 2 X[12041] - 3 X[18859], 5 X[14157] - 8 X[22115], 3 X[14157] - 8 X[37477], 11 X[14157] - 16 X[40111], 7 X[15020] - 4 X[37967], 5 X[15034] - 2 X[37946], 3 X[15055] - 4 X[37950], 9 X[19128] - 8 X[32217], 3 X[22115] - 5 X[37477], 11 X[22115] - 10 X[40111], X[23061] + 2 X[35001], 4 X[25338] - 5 X[38794], 4 X[32237] - 3 X[37925], 11 X[37477] - 6 X[40111], 5 X[37760] - 6 X[38793]

X(43576) lies on these lines: {3, 5640}, {4, 5651}, {20, 54}, {23, 10564}, {30, 110}, {74, 511}, {141, 35484}, {182, 376}, {184, 11001}, {186, 15036}, {323, 14094}, {378, 1350}, {394, 11455}, {548, 13339}, {550, 567}, {578, 17538}, {631, 32223}, {858, 14644}, {1092, 33703}, {1147, 5059}, {1154, 10620}, {1173, 9729}, {1296, 2698}, {1351, 5890}, {1495, 15034}, {1511, 37924}, {1614, 3529}, {1657, 8718}, {1994, 14855}, {2071, 11692}, {2080, 9218}, {2420, 10313}, {3153, 12295}, {3200, 42430}, {3201, 42429}, {3292, 12112}, {3431, 35268}, {3524, 22112}, {3528, 11424}, {3534, 5012}, {3545, 16187}, {3567, 37475}, {3581, 15055}, {3917, 13596}, {4550, 33884}, {5085, 41463}, {5118, 7422}, {5189, 17702}, {5663, 23061}, {5899, 15040}, {5965, 12317}, {6101, 15062}, {6241, 37498}, {7492, 39242}, {7574, 10733}, {7575, 15051}, {7691, 13368}, {7998, 31861}, {7999, 35502}, {9306, 15682}, {9686, 23269}, {9705, 17800}, {9818, 21766}, {10295, 15472}, {10510, 10752}, {10519, 41583}, {10625, 12086}, {11002, 37470}, {11412, 12085}, {11413, 37489}, {11440, 37484}, {11454, 12084}, {11456, 11820}, {11459, 11472}, {11464, 12082}, {11468, 17834}, {11541, 26883}, {12038, 12087}, {12041, 13358}, {12103, 37472}, {12111, 16835}, {12279, 16266}, {12383, 29012}, {13203, 18400}, {13348, 35500}, {13491, 15801}, {13598, 38848}, {13754, 37944}, {14538, 18863}, {14539, 18864}, {14810, 35921}, {14865, 15644}, {15019, 40280}, {15020, 37967}, {15066, 16261}, {15080, 33532}, {15291, 32681}, {15704, 37495}, {16003, 37779}, {16163, 29317}, {18392, 31181}, {19124, 35483}, {20791, 39522}, {22750, 35490}, {23582, 35474}, {25338, 38794}, {26882, 39568}, {32237, 37925}, {33750, 38005}, {35479, 41427}, {37478, 41398}, {37760, 38793}

X(43576) = midpoint of X(35001) and X(37496)
X(43576) = reflection of X(i) in X(j) for these {i,j}: {23, 10564}, {74, 7464}, {110, 37477}, {3581, 37950}, {10733, 7574}, {10752, 10510}, {12112, 3292}, {13445, 35452}, {14094, 323}, {15107, 3}, {23061, 37496}, {37779, 16003}, {37924, 1511}, {37946, 1495}
X(43576) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 11003, 8717}, {23, 10564, 15035}, {1657, 34148, 8718}, {3529, 13346, 1614}, {3581, 37950, 15055}, {8717, 13352, 11003}, {10295, 15472, 19128}, {12082, 37497, 11464}, {12084, 37494, 11454}

X(43577) = X(20)X(54)∩X(30)X(143)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^8 - 5*a^4*b^4 + 2*a^2*b^6 + b^8 + 12*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - 4*b^6*c^2 - 5*a^4*c^4 - 2*a^2*b^2*c^4 + 6*b^4*c^4 + 2*a^2*c^6 - 4*b^2*c^6 + c^8) : :
X(43577) = 3 X[9730] - X[18560], X[11381] - 3 X[38321], X[11412] + 3 X[34796], X[11750] - 3 X[15072], X[12162] - 3 X[38323], X[12225] - 3 X[14855], X[12279] + 3 X[18559], 3 X[14855] - 2 X[17712], 3 X[15072] + X[34797], 2 X[18128] + X[18565]

X(43577) lies on these lines: {3, 1568}, {4, 13445}, {5, 1539}, {20, 54}, {30, 143}, {49, 16163}, {74, 34007}, {113, 22467}, {185, 10111}, {511, 43392}, {539, 34783}, {541, 12162}, {542, 40929}, {548, 15806}, {550, 18475}, {569, 35481}, {578, 34350}, {1204, 5449}, {1209, 11440}, {1216, 31829}, {1531, 37452}, {1533, 18378}, {1593, 7706}, {1657, 36749}, {1885, 5462}, {3520, 16111}, {3575, 14915}, {3627, 15873}, {4549, 10996}, {4550, 6815}, {5097, 29317}, {5893, 16238}, {5895, 6642}, {5925, 9818}, {6102, 32375}, {6143, 15055}, {6240, 10575}, {6288, 10620}, {6644, 22800}, {6689, 18570}, {9730, 18560}, {9786, 22466}, {9927, 10605}, {10024, 20191}, {10226, 37853}, {10263, 43393}, {11250, 18388}, {11381, 38321}, {11387, 12279}, {11412, 34796}, {11750, 15072}, {12006, 34584}, {12038, 38726}, {12225, 14855}, {12244, 15062}, {12370, 13382}, {13368, 13491}, {13474, 31830}, {13561, 20417}, {14130, 20127}, {15063, 18350}, {15074, 19924}, {15311, 31833}, {15800, 35452}, {18128, 18565}, {18420, 20427}, {21243, 32138}, {34005, 37513}, {35498, 38788}

X(43577) = midpoint of X(i) and X(j) for these {i,j}: {550, 34798}, {6240, 10575}, {11750, 34797}, {18565, 21659}
X(43577) = reflection of X(i) in X(j) for these {i,j}: {1216, 31829}, {1885, 5462}, {5446, 13568}, {10116, 185}, {12225, 17712}, {12370, 13382}, {12897, 389}, {13403, 13630}, {13474, 31830}, {21659, 18128}
X(43577) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5448, 14156}, {5, 12041, 25563}, {10024, 21663, 20191}, {12225, 14855, 17712}, {14374, 14375, 40647}, {15072, 34797, 11750}

X(43578) = X(3)X(74)∩X(54)X(16003)

Barycentrics    a^2*(a^14 - 4*a^12*b^2 + 5*a^10*b^4 - 5*a^6*b^8 + 4*a^4*b^10 - a^2*b^12 - 4*a^12*c^2 + 12*a^10*b^2*c^2 - 8*a^8*b^4*c^2 - 9*a^6*b^6*c^2 + 15*a^4*b^8*c^2 - 7*a^2*b^10*c^2 + b^12*c^2 + 5*a^10*c^4 - 8*a^8*b^2*c^4 + 21*a^6*b^4*c^4 - 15*a^4*b^6*c^4 - 3*b^10*c^4 - 9*a^6*b^2*c^6 - 15*a^4*b^4*c^6 + 16*a^2*b^6*c^6 + 2*b^8*c^6 - 5*a^6*c^8 + 15*a^4*b^2*c^8 + 2*b^6*c^8 + 4*a^4*c^10 - 7*a^2*b^2*c^10 - 3*b^4*c^10 - a^2*c^12 + b^2*c^12) : :

X(43578) lies on these lines: {3, 74}, {54, 16003}, {182, 11061}, {541, 14157}, {567, 10264}, {1176, 38727}, {2777, 32235}, {3448, 13352}, {5012, 20126}, {5169, 14644}, {5189, 17702}, {7703, 38724}, {7728, 38322}, {7731, 37489}, {8718, 10990}, {9140, 15033}, {11579, 15463}, {11801, 33332}, {12284, 17847}, {12383, 37480}, {13201, 37494}, {13339, 27866}, {13434, 20379}, {15644, 25714}, {16270, 19362}, {17712, 30714}, {19481, 35482}, {32423, 37477}

X(43578) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10620, 11454, 74}, {11454, 15100, 10620}, {15054, 15132, 1614}

X(43579) = X(23)X(54)∩X(30)X(110)

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

X(43579) lies on these lines: {23, 54}, {30, 110}, {186, 16836}, {1147, 20063}, {2070, 5012}, {5899, 26881}, {5907, 7464}, {6403, 19127}, {8705, 19128}, {9781, 37973}, {12284, 32608}, {13434, 25338}, {13754, 43390}, {14915, 43391}, {15067, 18859}, {15305, 35452}, {15516, 37939}, {26882, 37972}, {32046, 37923}, {34148, 37924}

X(43580) = X(3)X(11702)∩X(54)X(74)

Barycentrics    a^2*(a^14 - 6*a^12*b^2 + 13*a^10*b^4 - 10*a^8*b^6 - 5*a^6*b^8 + 14*a^4*b^10 - 9*a^2*b^12 + 2*b^14 - 6*a^12*c^2 + 16*a^10*b^2*c^2 - 16*a^8*b^4*c^2 + 15*a^6*b^6*c^2 - 19*a^4*b^8*c^2 + 13*a^2*b^10*c^2 - 3*b^12*c^2 + 13*a^10*c^4 - 16*a^8*b^2*c^4 + a^6*b^4*c^4 + 5*a^4*b^6*c^4 - 3*b^10*c^4 - 10*a^8*c^6 + 15*a^6*b^2*c^6 + 5*a^4*b^4*c^6 - 8*a^2*b^6*c^6 + 4*b^8*c^6 - 5*a^6*c^8 - 19*a^4*b^2*c^8 + 4*b^6*c^8 + 14*a^4*c^10 + 13*a^2*b^2*c^10 - 3*b^4*c^10 - 9*a^2*c^12 - 3*b^2*c^12 + 2*c^14) : :
X(43580) = 3 X[54] - 4 X[32226], X[74] - 4 X[2914], 3 X[74] - 8 X[32226], 4 X[1112] - 3 X[7730], 4 X[1493] - X[15054], 3 X[2914] - 2 X[32226], 4 X[3574] - 3 X[14644], 2 X[7691] - 3 X[15035], 4 X[8254] - 3 X[15061], 3 X[9140] - 4 X[11804], X[10117] - 3 X[17824], 4 X[10610] - 3 X[15055], X[11271] + 2 X[15063], 4 X[11597] - 3 X[15035], X[14094] + 2 X[15801], 3 X[14643] - 2 X[21230], 3 X[14644] - 2 X[33565], 5 X[15027] - 8 X[30531]

X(43580) lies on these lines: {3, 11702}, {54, 74}, {110, 1154}, {113, 2888}, {195, 5663}, {265, 20424}, {399, 10263}, {539, 10706}, {1112, 7730}, {1173, 3574}, {1216, 40640}, {1493, 15054}, {1511, 12307}, {1614, 7731}, {1624, 3470}, {1986, 2929}, {1993, 15102}, {2777, 12254}, {3043, 10274}, {3627, 7728}, {5609, 5898}, {5890, 17847}, {5965, 9970}, {6241, 12165}, {6286, 10088}, {6288, 11805}, {7356, 10091}, {7691, 11597}, {7727, 35197}, {8254, 15061}, {9140, 11804}, {10203, 12219}, {10264, 22051}, {10610, 15055}, {10721, 18400}, {11271, 15063}, {11455, 12308}, {11562, 43574}, {11579, 19150}, {12010, 14643}, {12161, 15100}, {12281, 15033}, {12300, 15472}, {13248, 32234}, {13417, 14157}, {15027, 30531}, {15087, 15101}, {23061, 34153}, {32352, 38848}

X(43580) = midpoint of X(399) and X(12316)
X(43580) = reflection of X(i) in X(j) for these {i,j}: {3, 11702}, {74, 54}, {265, 20424}, {2888, 113}, {5898, 5609}, {6288, 11805}, {7691, 11597}, {10264, 22051}, {10733, 15800}, {11579, 19150}, {12254, 14049}, {12307, 1511}, {32339, 1986}, {33565, 3574}
X(43580) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {185, 43391, 74}, {3574, 33565, 14644}, {7691, 11597, 15035}, {12281, 19504, 15033}

X(43581) = X(5)X(51)∩X(54)X(74)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 9*a^6*b^2*c^2 - 8*a^4*b^4*c^2 + a^2*b^6*c^2 + b^8*c^2 + 2*a^6*c^4 - 8*a^4*b^2*c^4 + 4*a^2*b^4*c^4 - 2*b^6*c^4 + 2*a^4*c^6 + a^2*b^2*c^6 - 2*b^4*c^6 - 3*a^2*c^8 + b^2*c^8 + c^10) : :
X(43581) = 3 X[4] - X[13423], 5 X[4] - 2 X[13433], 9 X[51] - 8 X[973], 3 X[51] - 4 X[3574], 3 X[51] - 8 X[15739], 3 X[51] - 2 X[32352], 3 X[381] - 2 X[6153], 2 X[973] - 3 X[3574], X[973] - 3 X[15739], 4 X[973] - 3 X[32352], 3 X[3917] - 2 X[7691], 9 X[5650] - 8 X[32348], 3 X[5891] - 2 X[21230], 2 X[6288] - 3 X[15030], X[6293] - 3 X[17824], 3 X[7730] - 4 X[10110], 4 X[8254] - 3 X[9730], 4 X[10115] - 3 X[14831], X[11381] - 4 X[12300], X[11381] + 2 X[21660], 3 X[11459] - X[12325], X[12291] + 2 X[13474], 2 X[12300] + X[21660], 8 X[13365] - 9 X[14845], 5 X[13423] - 6 X[13433], 4 X[14128] - 3 X[21357], 4 X[15739] - X[32352], 2 X[31978] - 3 X[32345]

X(43581) lies on these lines: {4, 13418}, {5, 51}, {54, 74}, {184, 6293}, {195, 13754}, {381, 6153}, {389, 6143}, {511, 32338}, {546, 13368}, {1216, 3581}, {1495, 2917}, {2807, 9905}, {2888, 5907}, {3917, 7691}, {4550, 11424}, {5498, 8254}, {5650, 32348}, {5663, 14049}, {5965, 40316}, {6000, 12254}, {6102, 22051}, {6242, 11808}, {6288, 15030}, {7527, 15801}, {7730, 10110}, {9920, 26883}, {10115, 14831}, {10203, 35921}, {10226, 10610}, {10274, 13367}, {10619, 15105}, {11381, 12300}, {11459, 12325}, {11550, 32346}, {11562, 11702}, {11597, 12038}, {11663, 17578}, {11804, 13561}, {12162, 32423}, {12219, 13434}, {12242, 37118}, {12291, 13474}, {12294, 32340}, {13366, 32341}, {13403, 21650}, {13630, 30507}, {15800, 22815}, {15806, 38898}, {16226, 34331}, {16227, 16239}, {16657, 31834}, {19460, 31978}, {35498, 40647}, {38323, 41590}

X(43581) = midpoint of X(i) and X(j) for these {i,j}: {12316, 18436}, {15800, 22815}, {15801, 41726}
X(43581) = reflection of X(i) in X(j) for these {i,j}: {52, 20424}, {185, 54}, {2888, 5907}, {3574, 15739}, {6102, 22051}, {6242, 11808}, {11562, 11702}, {12254, 40632}, {12307, 1216}, {13368, 546}, {32339, 389}, {32352, 3574}
X(43581) = crossdifference of every pair of points on line {2623, 14391}
X(43581) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 43392, 185}, {3574, 32352, 51}, {12300, 21660, 11381}, {17824, 32333, 184}

X(43582) = X(4)X(54)∩X(30)X(40632)

Barycentrics    2*a^16 - 6*a^14*b^2 + 3*a^12*b^4 + 6*a^10*b^6 - 5*a^8*b^8 - 2*a^6*b^10 + a^4*b^12 + 2*a^2*b^14 - b^16 - 6*a^14*c^2 + 22*a^12*b^2*c^2 - 28*a^10*b^4*c^2 + 9*a^8*b^6*c^2 + 7*a^6*b^8*c^2 + a^4*b^10*c^2 - 9*a^2*b^12*c^2 + 4*b^14*c^2 + 3*a^12*c^4 - 28*a^10*b^2*c^4 + 34*a^8*b^4*c^4 - 5*a^6*b^6*c^4 - 15*a^4*b^8*c^4 + 15*a^2*b^10*c^4 - 4*b^12*c^4 + 6*a^10*c^6 + 9*a^8*b^2*c^6 - 5*a^6*b^4*c^6 + 26*a^4*b^6*c^6 - 8*a^2*b^8*c^6 - 4*b^10*c^6 - 5*a^8*c^8 + 7*a^6*b^2*c^8 - 15*a^4*b^4*c^8 - 8*a^2*b^6*c^8 + 10*b^8*c^8 - 2*a^6*c^10 + a^4*b^2*c^10 + 15*a^2*b^4*c^10 - 4*b^6*c^10 + a^4*c^12 - 9*a^2*b^2*c^12 - 4*b^4*c^12 + 2*a^2*c^14 + 4*b^2*c^14 - c^16 : :
X(43582) = 7 X[13419] - 8 X[32332]

X(43582) lies on these lines: {4, 54}, {30, 40632}, {195, 3521}, {389, 32375}, {1154, 43577}, {6288, 38724}, {10116, 11802}, {12897, 22051}, {13163, 13364}, {13365, 43573}, {17702, 36966}

X(43582) = reflection of X(i) in X(j) for these {i,j}: {12897, 22051}, {13403, 54}
X(43582) = {X(4),X(43393)}-harmonic conjugate of X(13403)

X(43583) = X(54)X(74)∩X(1154)X(43575)

Barycentrics    a^2*(a^18*b^2 - 5*a^16*b^4 + 8*a^14*b^6 - 14*a^10*b^10 + 14*a^8*b^12 - 8*a^4*b^16 + 5*a^2*b^18 - b^20 + a^18*c^2 - 4*a^16*b^2*c^2 + 10*a^14*b^4*c^2 - 22*a^12*b^6*c^2 + 28*a^10*b^8*c^2 - 6*a^8*b^10*c^2 - 26*a^6*b^12*c^2 + 30*a^4*b^14*c^2 - 13*a^2*b^16*c^2 + 2*b^18*c^2 - 5*a^16*c^4 + 10*a^14*b^2*c^4 - 8*a^12*b^4*c^4 + 23*a^10*b^6*c^4 - 55*a^8*b^8*c^4 + 59*a^6*b^10*c^4 - 27*a^4*b^12*c^4 + 3*b^16*c^4 + 8*a^14*c^6 - 22*a^12*b^2*c^6 + 23*a^10*b^4*c^6 + 16*a^8*b^6*c^6 - 33*a^6*b^8*c^6 - 12*a^4*b^10*c^6 + 28*a^2*b^12*c^6 - 8*b^14*c^6 + 28*a^10*b^2*c^8 - 55*a^8*b^4*c^8 - 33*a^6*b^6*c^8 + 34*a^4*b^8*c^8 - 20*a^2*b^10*c^8 - 2*b^12*c^8 - 14*a^10*c^10 - 6*a^8*b^2*c^10 + 59*a^6*b^4*c^10 - 12*a^4*b^6*c^10 - 20*a^2*b^8*c^10 + 12*b^10*c^10 + 14*a^8*c^12 - 26*a^6*b^2*c^12 - 27*a^4*b^4*c^12 + 28*a^2*b^6*c^12 - 2*b^8*c^12 + 30*a^4*b^2*c^14 - 8*b^6*c^14 - 8*a^4*c^16 - 13*a^2*b^2*c^16 + 3*b^4*c^16 + 5*a^2*c^18 + 2*b^2*c^18 - c^20) : :

X(43583) lies on these lines: {54, 74}, {1154, 43575}, {13630, 22051}

X(43583) = reflection of X(43392) in X(54)

leftri

Perpsectors involving KM triangles: X(43584)-X(43596)

rightri

This preamble is contributed by Clark Kimberling and Peter Moses, June 2, 2021.

The Kiss-Moses mapping, denoted by KM and defined in the preamble just before X(43390), is a linear transformation that maps central triangles to central triangles.

The appearance of (T1,T2,n) in the following list means that KM(T1) is perspective to T2 and the perspector is X(n).

(medial, orthocentroidal, 15043)
(medial, 3rd Hazipolakis, 22966)
(medial, anti-orthocentroidal, 43584)
(medial, infinite altitude 40647)
(medial, AOA, 5)
(medial, Ehrmann mid-triangle, 43585)
(medial, Gemini 110, 140)
(anticomplementary, orthocentroidal, 5462)
(anticomplementary, 2nd Euler, 5462)
(anticomplementary, anti-orthocentroidal, 43586)
(anticomplementary, infinite altitude, 10575)
(anticomplementary, 2nd Hyacinth, 43587)
(anticomplementary, anti-Wasat, 5562)
(orthic, 1st Hyacinth, 43588)
(orthic, infinite altitude, 6146)
(orthic, 2nd Hyacinth, 6146)
(orthic, AOA, 43589)
(orthic, anti-AOA, 43590)
(orthic, anti-Wasat, 43591)
(orthic, Hatzipolakis-Moses, 6146)
(tangential, medial, 2883)
(tangential, Euler, 43592)
(tangential, half-altitude, 43593)
(tangential, submedial, 43594)
(tangential, 1st Hyacinth, 43595)
(tangential, infinite altitude, 550)
(tangential, AOA, 5)
(tangential, anti-AOA, 37118)
(tangential, Yiu tangents, 550)
(Euler, orthic, 22948
(Euler, orthocentroidal, 6241
(Euler, 3rd Hatzipolakis, 22948)
(Euler,anti-centroidal, 43596)
(Euler, infinite altitude, 389
(medial of orthic, anti-2nd-Conway, 389



X(43584) = PERSPECTOR OF THESE TRIANGLES: KM(MEDIAL) AND ANTI-ORTHOCENTROIDAL

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

X(43584) lies on these lines: {2, 1568}, {3, 5640}, {4, 10545}, {5, 74}, {6, 2929}, {20, 34417}, {23, 16836}, {24, 15080}, {25, 20791}, {54, 1511}, {110, 9730}, {140, 3581}, {143, 37496}, {185, 15052}, {186, 5892}, {323, 389}, {373, 7527}, {378, 11451}, {381, 13445}, {399, 13630}, {550, 38848}, {567, 15035}, {568, 23061}, {569, 3431}, {575, 15020}, {631, 37478}, {1092, 11004}, {1173, 37495}, {1204, 5056}, {1291, 15537}, {1495, 9729}, {1994, 16226}, {1995, 15072}, {2070, 6030}, {2071, 5943}, {2914, 11802}, {3060, 37483}, {3090, 4550}, {3098, 3523}, {3357, 5068}, {3515, 12017}, {3526, 33533}, {4993, 38605}, {5012, 6644}, {5020, 15305}, {5050, 11443}, {5067, 7689}, {5079, 32138}, {5092, 7488}, {5462, 10564}, {5621, 40670}, {5889, 15066}, {5890, 15068}, {5893, 12379}, {5946, 43574}, {6642, 10546}, {6688, 21663}, {6815, 37643}, {7503, 37487}, {7526, 11465}, {7529, 12279}, {7550, 32110}, {7575, 13339}, {7605, 38727}, {7687, 34007}, {7712, 10984}, {7998, 37489}, {7999, 37490}, {8718, 13621}, {9140, 41171}, {9786, 11444}, {9977, 13367}, {10316, 41414}, {10594, 35237}, {10601, 15078}, {10610, 12380}, {10733, 37648}, {11002, 37480}, {11430, 13434}, {11449, 36752}, {11695, 14118}, {12106, 40280}, {12112, 40647}, {12383, 43573}, {12834, 15033}, {13347, 38435}, {13352, 15019}, {13364, 18859}, {13482, 15038}, {13596, 14845}, {14130, 32205}, {14641, 26863}, {14805, 37814}, {15030, 15054}, {15047, 43394}, {15087, 43572}, {15805, 32534}, {18420, 26913}, {18551, 33541}, {20190, 37957}, {22352, 37940}, {23329, 37353}, {37440, 41448}, {40664, 40684}

X(43584) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {631, 37478, 41462}, {1511, 12006, 15037}, {1511, 15037, 54}, {1995, 37475, 15072}, {6642, 11456, 10546}, {6644, 15045, 5012}, {10546, 10574, 11456}, {11430, 15018, 13434}, {11430, 22467, 15051}, {13434, 15051, 11430}, {15018, 22467, 11430}, {15043, 17928, 34148}

X(43585) = PERSPECTOR OF THESE TRIANGLES: KM(MEDIAL) AND EHRMANN MID-TRIANGLE

Barycentrics    2*a^10 + a^8*b^2 - 13*a^6*b^4 + 13*a^4*b^6 - a^2*b^8 - 2*b^10 + a^8*c^2 + 20*a^6*b^2*c^2 - 16*a^4*b^4*c^2 - 11*a^2*b^6*c^2 + 6*b^8*c^2 - 13*a^6*c^4 - 16*a^4*b^2*c^4 + 24*a^2*b^4*c^4 - 4*b^6*c^4 + 13*a^4*c^6 - 11*a^2*b^2*c^6 - 4*b^4*c^6 - a^2*c^8 + 6*b^2*c^8 - 2*c^10 : :
X(43585) = X[4] - 3 X[3521], 3 X[381] - X[16835], 5 X[1656] - 3 X[15062], X[1657] - 3 X[8718], 5 X[3522] - 3 X[18442], 4 X[3850] - 3 X[18488], 7 X[3851] - 3 X[33541], 4 X[33923] - 3 X[35240]

X(43585) lies on these lines: {4, 3521}, {5, 15105}, {30, 1493}, {113, 140}, {146, 14128}, {381, 16835}, {550, 5944}, {1539, 40647}, {1656, 15062}, {1657, 8718}, {1885, 36153}, {2777, 10610}, {3522, 18442}, {3627, 18128}, {3850, 18488}, {3851, 7703}, {5073, 15087}, {5097, 8550}, {6000, 11802}, {7728, 14861}, {14862, 43577}, {15311, 20376}, {16534, 22966}, {33923, 35240}

X(43585) = reflection of X(22948) in X(13630)

X(43586) = PERSPECTOR OF THESE TRIANGLES: KM(ANTICOMLEMENTARY) AND ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(2*a^8 - 5*a^6*b^2 + 3*a^4*b^4 + a^2*b^6 - b^8 - 5*a^6*c^2 + 8*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + 4*b^6*c^2 + 3*a^4*c^4 - 7*a^2*b^2*c^4 - 6*b^4*c^4 + a^2*c^6 + 4*b^2*c^6 - c^8) : :
X(43586) = X[3] + 3 X[35259], 3 X[25] + X[37483], 5 X[1656] - X[18396], 3 X[6090] + X[37489], 3 X[6644] - X[11438], 3 X[6644] + X[15068], 3 X[9306] + X[11438], 3 X[9306] - X[15068]

X(43586) lies on these lines: {2, 11464}, {3, 1495}, {4, 10546}, {5, 1511}, {6, 1147}, {24, 1216}, {25, 37483}, {26, 3098}, {49, 15037}, {51, 22115}, {52, 323}, {54, 15018}, {68, 37643}, {74, 12162}, {110, 9730}, {113, 38323}, {140, 1503}, {141, 34351}, {156, 9729}, {184, 5892}, {185, 399}, {186, 5891}, {187, 31848}, {373, 567}, {389, 41597}, {427, 14156}, {511, 12106}, {539, 13567}, {541, 20772}, {568, 3292}, {575, 2854}, {631, 15080}, {632, 5944}, {1092, 5446}, {1209, 10018}, {1568, 38321}, {1656, 13367}, {1658, 11793}, {1994, 43572}, {1995, 13352}, {2070, 3917}, {2071, 16194}, {3090, 3431}, {3517, 33878}, {3518, 10625}, {3520, 15051}, {3523, 7712}, {3524, 26881}, {3567, 11004}, {3581, 5562}, {3628, 32171}, {3818, 18281}, {3819, 7502}, {4549, 37460}, {5054, 22352}, {5068, 38942}, {5448, 31833}, {5449, 16238}, {5654, 7706}, {5884, 41192}, {5899, 36987}, {5907, 37814}, {5946, 34986}, {6090, 37489}, {6644, 9306}, {6689, 7405}, {6699, 20771}, {6759, 31978}, {7387, 41424}, {7393, 17821}, {7512, 41462}, {7514, 11202}, {7527, 15035}, {7529, 35602}, {7530, 37480}, {7545, 37477}, {7555, 14810}, {7556, 7998}, {7575, 15067}, {7689, 17814}, {9544, 15045}, {9545, 15024}, {9703, 13366}, {9707, 13336}, {9786, 15083}, {9820, 9825}, {10127, 23292}, {10539, 11456}, {10545, 34148}, {10575, 12112}, {11284, 37506}, {11459, 32110}, {11695, 32046}, {12022, 30714}, {12095, 16269}, {12107, 32142}, {13346, 13861}, {13348, 17714}, {13561, 40685}, {13595, 43574}, {13621, 37496}, {14070, 17811}, {14128, 15331}, {14157, 14855}, {14643, 17701}, {14845, 15033}, {15026, 37505}, {15034, 16042}, {15042, 35498}, {15056, 21844}, {15060, 15646}, {15082, 34513}, {15087, 16226}, {15091, 32352}, {15132, 19140}, {15448, 16618}, {15462, 29959}, {15644, 37440}, {15647, 23328}, {16266, 37517}, {18369, 37495}, {18435, 21663}, {18859, 32062}, {19130, 23410}, {31860, 37498}, {37118, 38793}, {37648, 43573}

X(43586) = midpoint of X(i) and X(j) for these {i,j}: {6644, 9306}, {7530, 37480}, {11438, 15068}
X(43586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11464, 37513}, {3, 5651, 10170}, {3, 26883, 14641}, {5, 1511, 11430}, {24, 15066, 37478}, {74, 15052, 12162}, {1092, 7506, 5446}, {1147, 6642, 5462}, {1511, 11430, 12038}, {5946, 40111, 34986}, {6644, 15068, 11438}, {9306, 11438, 15068}, {10182, 24206, 140}, {10539, 17928, 40647}, {10539, 37470, 11456}, {11456, 17928, 37470}, {11456, 37470, 40647}, {11464, 37513, 18475}, {15052, 22467, 74}, {15066, 37478, 1216}

X(43587) = PERSPECTOR OF THESE TRIANGLES: KM(ANTICOMPLEMENTARY) AND 2ND HYACINTH

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^16*b^2 - 4*a^14*b^4 + 4*a^12*b^6 + 4*a^10*b^8 - 10*a^8*b^10 + 4*a^6*b^12 + 4*a^4*b^14 - 4*a^2*b^16 + b^18 + a^16*c^2 - 12*a^14*b^2*c^2 + 32*a^12*b^4*c^2 - 32*a^10*b^6*c^2 + 6*a^8*b^8*c^2 + 20*a^6*b^10*c^2 - 32*a^4*b^12*c^2 + 24*a^2*b^14*c^2 - 7*b^16*c^2 - 4*a^14*c^4 + 32*a^12*b^2*c^4 - 64*a^10*b^4*c^4 + 52*a^8*b^6*c^4 - 36*a^6*b^8*c^4 + 56*a^4*b^10*c^4 - 56*a^2*b^12*c^4 + 20*b^14*c^4 + 4*a^12*c^6 - 32*a^10*b^2*c^6 + 52*a^8*b^4*c^6 - 8*a^6*b^6*c^6 - 28*a^4*b^8*c^6 + 72*a^2*b^10*c^6 - 28*b^12*c^6 + 4*a^10*c^8 + 6*a^8*b^2*c^8 - 36*a^6*b^4*c^8 - 28*a^4*b^6*c^8 - 72*a^2*b^8*c^8 + 14*b^10*c^8 - 10*a^8*c^10 + 20*a^6*b^2*c^10 + 56*a^4*b^4*c^10 + 72*a^2*b^6*c^10 + 14*b^8*c^10 + 4*a^6*c^12 - 32*a^4*b^2*c^12 - 56*a^2*b^4*c^12 - 28*b^6*c^12 + 4*a^4*c^14 + 24*a^2*b^2*c^14 + 20*b^4*c^14 - 4*a^2*c^16 - 7*b^2*c^16 + c^18) : :

X(43587) lies on these lines: {6, 1147}, {185, 12118}, {511, 12420}, {1885, 12162}, {5925, 13754}, {10606, 12301}, {20302, 23515}

X(43588) = PERSPECTOR OF THESE TRIANGLES: KM(ORTHIC) AND 1ST HYACINTH

Barycentrics    2*a^10 - 7*a^8*b^2 + 10*a^6*b^4 - 8*a^4*b^6 + 4*a^2*b^8 - b^10 - 7*a^8*c^2 + 4*a^6*b^2*c^2 + 6*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 + 10*a^6*c^4 + 6*a^4*b^2*c^4 + 4*a^2*b^4*c^4 - 2*b^6*c^4 - 8*a^4*c^6 - 6*a^2*b^2*c^6 - 2*b^4*c^6 + 4*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(43588) = X[5] - 3 X[11245], 3 X[568] - X[11819], 3 X[568] + X[34224], 5 X[3567] - 3 X[13490], X[5446] - 3 X[11225], 4 X[5462] - 3 X[23410], 9 X[5890] - X[12278], X[5907] - 3 X[43573], 3 X[5946] - X[12134], X[10112] - 3 X[11232], 2 X[10116] + X[31830], 3 X[11232] + X[40647], X[11750] + 3 X[14831], 3 X[12022] + X[34783], 3 X[12241] - 2 X[15807], X[13142] - 3 X[13292], X[13142] + 3 X[18914], X[13142] - 6 X[32165], X[14516] - 5 X[37481], X[17712] - 3 X[18128], X[18914] + 2 X[32165], X[34799] + 3 X[38321], X[37484] + 3 X[41628]

X(43588) l;ies on these on lines: {3, 32358}, {5, 5422}, {6, 32140}, {26, 6776}, {30, 52}, {49, 26879}, {113, 3850}, {140, 141}, {143, 1503}, {155, 18952}, {156, 13567}, {184, 10020}, {195, 858}, {389, 10116}, {427, 2904}, {511, 17712}, {524, 10627}, {539, 9729}, {542, 5462}, {546, 12233}, {550, 37494}, {568, 11819}, {1181, 15761}, {1199, 3448}, {1353, 23335}, {1594, 15087}, {1658, 31804}, {1899, 12161}, {3313, 15074}, {3519, 13339}, {3530, 10610}, {3567, 13490}, {3628, 15806}, {3853, 22802}, {3859, 18418}, {5012, 7568}, {5097, 14864}, {5446, 11225}, {5447, 5965}, {5663, 12241}, {5890, 12278}, {5907, 43573}, {5946, 12134}, {6642, 39899}, {6644, 18916}, {6746, 6756}, {7499, 21230}, {7514, 11411}, {7517, 37644}, {7526, 18917}, {7715, 39871}, {8907, 37814}, {9704, 10018}, {10024, 15032}, {10111, 14708}, {10112, 11232}, {10114, 11806}, {10201, 19347}, {10264, 15463}, {10619, 12899}, {10691, 12363}, {11264, 13630}, {11422, 23294}, {11423, 23293}, {11432, 11818}, {11433, 13861}, {11457, 36749}, {12022, 34783}, {12084, 18909}, {12160, 14791}, {12325, 15246}, {13382, 17702}, {13421, 29181}, {13561, 23292}, {13568, 30522}, {14216, 39522}, {14516, 37481}, {14627, 15559}, {14788, 15037}, {15047, 37990}, {15069, 15805}, {15122, 34148}, {15123, 15130}, {15646, 36966}, {16531, 32171}, {17714, 41588}, {18281, 26944}, {18324, 18925}, {19357, 34477}, {22051, 32351}, {23291, 31283}, {23336, 34115}, {25328, 34155}, {32139, 39571}, {32515, 41655}, {34799, 38321}, {36153, 37649}, {37471, 37636}, {37484, 41628}

X(43588) = midpoint of X(i) and X(j) for these {i,j}: {3, 32358}, {185, 12370}, {389, 10116}, {1353, 26926}, {6102, 6146}, {10111, 14708}, {10112, 40647}, {10114, 11806}, {10619, 12899}, {11264, 13630}, {11819, 34224}, {13292, 18914}
X(43588) = reflection of X(i) in X(j) for these {i,j}: {6756, 16881}, {13292, 32165}, {22663, 32166}, {31830, 389}, {31831, 3628}
X(43588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {568, 34224, 11819}, {1199, 3448, 5576}, {1899, 12161, 13371}, {6776, 18951, 26}, {7592, 25738, 5}, {8550, 12359, 32046}, {11232, 40647, 10112}, {11442, 36753, 5}, {12359, 32046, 140}, {13561, 32136, 23292}, {18445, 18912, 5}

X(43589) = PERSPECTOR OF THESE TRIANGLES: KM(ORTHIC) AND AOA

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

X(43589) lies on these lines: {4, 15121}, {5, 113}, {49, 3548}, {389, 15126}, {1899, 18281}, {5094, 7592}, {5159, 9820}, {5893, 37984}, {6146, 15122}, {8550, 15116}, {10112, 15130}, {10116, 15115}, {10619, 15124}, {12038, 16196}, {12084, 18396}, {12241, 20299}, {15123, 15129}, {21659, 37950}, {22533, 37495}, {26879, 37981}, {26937, 34826}, {37458, 41603}

X(43589) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13630, 15114, 5}, {15129, 40647, 15123}

X(43590) = PERSPECTOR OF THESE TRIANGLES: KM(ORTHIC) AND AAOA

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

X(43590) lies on these lines: {3, 49}, {4, 15135}, {5, 9512}, {6, 23325}, {52, 37972}, {125, 15037}, {195, 6146}, {389, 15139}, {858, 18914}, {1199, 1594}, {1598, 9971}, {1614, 21284}, {1899, 15087}, {5094, 7592}, {6145, 12234}, {6759, 19596}, {6776, 14791}, {8550, 15141}, {9143, 38323}, {10116, 15133}, {10170, 21637}, {10619, 15137}, {10938, 13352}, {11178, 17814}, {11430, 17847}, {11456, 37196}, {11660, 12088}, {12022, 19504}, {12160, 26283}, {12227, 15131}, {13630, 15132}, {15032, 15106}, {15811, 40285}, {16534, 32285}, {18281, 18909}, {18569, 18945}, {18580, 18913}, {22533, 32165}, {34470, 43573}, {34725, 36747}

,p> X(43590) = {X(15136),X(40647)}-harmonic conjugate of X(3)

X(43591) = PERSPECTOR OF THESE TRIANGLES: KM(ORTHIC) AND ANTI-WASAT

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^10*b^2 - 3*a^8*b^4 + 2*a^6*b^6 + 2*a^4*b^8 - 3*a^2*b^10 + b^12 + a^10*c^2 - 14*a^8*b^2*c^2 + 23*a^6*b^4*c^2 - 16*a^4*b^6*c^2 + 14*a^2*b^8*c^2 - 8*b^10*c^2 - 3*a^8*c^4 + 23*a^6*b^2*c^4 + 28*a^4*b^4*c^4 - 11*a^2*b^6*c^4 + 23*b^8*c^4 + 2*a^6*c^6 - 16*a^4*b^2*c^6 - 11*a^2*b^4*c^6 - 32*b^6*c^6 + 2*a^4*c^8 + 14*a^2*b^2*c^8 + 23*b^4*c^8 - 3*a^2*c^10 - 8*b^2*c^10 + c^12) : :
X(43591) = 3 X[51] - 2 X[11817], 5 X[1173] - 4 X[10110], 4 X[5447] - 3 X[34483]

X(43591) lies on these lines: {51, 11817}, {184, 15047}, {185, 13391}, {1173, 1199}, {1204, 33542}, {1843, 6746}, {5447, 34483}, {5562, 10116}, {5622, 12584}, {5890, 12254}, {5900, 18368}, {6101, 21660}, {6146, 21650}, {10619, 34153}, {11381, 13403}, {12121, 21649}, {19467, 21652}

X(43591) = crosspoint of X(1173) and X(34483)
X(43591) = crosssum of X(140) and X(34484)

X(43592) = PERSPECTOR OF THESE TRIANGLES: KM(TANGENTIAL) AND EULER

Barycentrics    3*a^8*b^2 - 18*a^4*b^6 + 24*a^2*b^8 - 9*b^10 + 3*a^8*c^2 - 8*a^6*b^2*c^2 + 18*a^4*b^4*c^2 - 40*a^2*b^6*c^2 + 27*b^8*c^2 + 18*a^4*b^2*c^4 + 32*a^2*b^4*c^4 - 18*b^6*c^4 - 18*a^4*c^6 - 40*a^2*b^2*c^6 - 18*b^4*c^6 + 24*a^2*c^8 + 27*b^2*c^8 - 9*c^10 : :
X(43592) = 3 X[2] + X[15077], 7 X[3523] - 3 X[27082], 11 X[5056] - 3 X[32605]

X(43592) lies on these lines: {2, 14528}, {4, 1192}, {5, 13382}, {125, 2883}, {140, 9927}, {550, 6699}, {1352, 1656}, {3147, 15153}, {3515, 41362}, {3523, 27082}, {3574, 13567}, {3812, 5777}, {3850, 7706}, {3851, 9815}, {5056, 18928}, {5480, 6697}, {6689, 36966}, {6698, 11585}, {7699, 12233}, {11704, 35487}, {12359, 20304}, {15081, 17506}, {15105, 37984}, {15117, 16270}, {15761, 20396}, {15873, 32767}, {17702, 39084}, {32369, 37458}

X(43592) = midpoint of X(4) and X(3532)
X(43592) = X(33585)-complementary conjugate of X(37)

X(43593) = PERSPECTOR OF THESE TRIANGLES: KM(TANGENTIAL) AND HALF-ALTITUDE

Barycentrics    4*a^16 - 23*a^14*b^2 + 49*a^12*b^4 - 39*a^10*b^6 - 15*a^8*b^8 + 51*a^6*b^10 - 37*a^4*b^12 + 11*a^2*b^14 - b^16 - 23*a^14*c^2 + 54*a^12*b^2*c^2 - 49*a^10*b^4*c^2 + 88*a^8*b^6*c^2 - 169*a^6*b^8*c^2 + 142*a^4*b^10*c^2 - 47*a^2*b^12*c^2 + 4*b^14*c^2 + 49*a^12*c^4 - 49*a^10*b^2*c^4 - 82*a^8*b^4*c^4 + 118*a^6*b^6*c^4 - 107*a^4*b^8*c^4 + 75*a^2*b^10*c^4 - 4*b^12*c^4 - 39*a^10*c^6 + 88*a^8*b^2*c^6 + 118*a^6*b^4*c^6 + 4*a^4*b^6*c^6 - 39*a^2*b^8*c^6 - 4*b^10*c^6 - 15*a^8*c^8 - 169*a^6*b^2*c^8 - 107*a^4*b^4*c^8 - 39*a^2*b^6*c^8 + 10*b^8*c^8 + 51*a^6*c^10 + 142*a^4*b^2*c^10 + 75*a^2*b^4*c^10 - 4*b^6*c^10 - 37*a^4*c^12 - 47*a^2*b^2*c^12 - 4*b^4*c^12 + 11*a^2*c^14 + 4*b^2*c^14 - c^16 : :

X(43593) lies on these lines: {6, 26937}, {51, 16622}, {378, 11431}, {389, 5894}, {550, 12236}, {1899, 10019}, {2883, 7687}, {5921, 15435}, {6723, 12359}, {8550, 14913}, {9729, 12235}, {10151, 15752}, {17928, 32621}

X(43594) = PERSPECTOR OF THESE TRIANGLES: KM(TANGENTIAL) AND SUBMEDIAL

Barycentrics    4*a^16 - 27*a^14*b^2 + 65*a^12*b^4 - 59*a^10*b^6 - 15*a^8*b^8 + 71*a^6*b^10 - 53*a^4*b^12 + 15*a^2*b^14 - b^16 - 27*a^14*c^2 + 38*a^12*b^2*c^2 + 31*a^10*b^4*c^2 + 8*a^8*b^6*c^2 - 189*a^6*b^8*c^2 + 206*a^4*b^10*c^2 - 71*a^2*b^12*c^2 + 4*b^14*c^2 + 65*a^12*c^4 + 31*a^10*b^2*c^4 - 178*a^8*b^4*c^4 + 182*a^6*b^6*c^4 - 219*a^4*b^8*c^4 + 123*a^2*b^10*c^4 - 4*b^12*c^4 - 59*a^10*c^6 + 8*a^8*b^2*c^6 + 182*a^6*b^4*c^6 + 132*a^4*b^6*c^6 - 67*a^2*b^8*c^6 - 4*b^10*c^6 - 15*a^8*c^8 - 189*a^6*b^2*c^8 - 219*a^4*b^4*c^8 - 67*a^2*b^6*c^8 + 10*b^8*c^8 + 71*a^6*c^10 + 206*a^4*b^2*c^10 + 123*a^2*b^4*c^10 - 4*b^6*c^10 - 53*a^4*c^12 - 71*a^2*b^2*c^12 - 4*b^4*c^12 + 15*a^2*c^14 + 4*b^2*c^14 - c^16 : :

X(43594) lies on these lines: {5, 18909}, {550, 9826}, {5894, 9729}, {8550, 9822}, {9827, 36966}, {12359, 12900}

X(43595) = PERSPECTOR OF THESE TRIANGLES: KM(TANGENTIAL) AND 1ST HYACINTH

Barycentrics    4*a^10 - 11*a^8*b^2 + 10*a^6*b^4 - 4*a^4*b^6 + 2*a^2*b^8 - b^10 - 11*a^8*c^2 + 16*a^6*b^2*c^2 - 8*a^2*b^6*c^2 + 3*b^8*c^2 + 10*a^6*c^4 + 12*a^2*b^4*c^4 - 2*b^6*c^4 - 4*a^4*c^6 - 8*a^2*b^2*c^6 - 2*b^4*c^6 + 2*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(43595) = 2 X[140] - 3 X[37506]

X(43595) lies on these lines: {3, 6515}, {5, 578}, {6, 12118}, {26, 13142}, {30, 1181}, {49, 235}, {54, 15760}, {68, 11425}, {140, 35602}, {143, 37458}, {156, 1596}, {195, 18563}, {403, 9545}, {427, 37472}, {511, 550}, {548, 37486}, {549, 43394}, {567, 7399}, {576, 34785}, {1199, 38323}, {1493, 2883}, {1658, 41588}, {1885, 18445}, {1906, 10540}, {1993, 12605}, {1994, 6240}, {3516, 18917}, {3564, 7526}, {3575, 35603}, {3858, 10113}, {5446, 34782}, {5944, 10154}, {6146, 13352}, {6193, 9818}, {6247, 10116}, {6756, 39522}, {6776, 12085}, {6823, 32046}, {7387, 18925}, {7403, 14516}, {7405, 13434}, {7583, 12231}, {7584, 12232}, {9704, 11799}, {9707, 37971}, {10112, 11430}, {10226, 32165}, {10257, 18912}, {10539, 16657}, {11232, 23328}, {11424, 12134}, {11426, 18420}, {11429, 18970}, {11585, 12022}, {11819, 21850}, {12038, 13567}, {12084, 18914}, {12162, 15739}, {12228, 22529}, {12233, 17702}, {12236, 34153}, {12362, 16266}, {12428, 19365}, {13367, 32225}, {13383, 19357}, {13403, 22660}, {13488, 32139}, {14627, 38321}, {15134, 37118}, {15559, 34799}, {16196, 18952}, {16238, 39571}, {18533, 37493}, {18570, 32358}, {30714, 41670}, {32534, 37644}, {37490, 37931}

X(43595) = midpoint of X(19467) and X(36747)
X(43595) = reflection of X(i) in X(j) for these {i,j}: {5, 578}, {6823, 32046}, {37486, 548}
X(43595) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 12118, 31833}, {550, 1353, 6102}, {1147, 12241, 5}, {2883, 12897, 3627}, {6146, 13352, 23335}, {6193, 9818, 31831}, {8550, 32284, 1353}, {9820, 18390, 5}, {9927, 23292, 5}, {10112, 11430, 12359}, {12022, 34148, 11585}, {13367, 41587, 34351}, {13403, 34986, 22660}, {14516, 15033, 7403}

X(43596) = PERSPECTOR OF THESE TRIANGLES: KM(EULER) AND ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(a^8 - 7*a^6*b^2 + 15*a^4*b^4 - 13*a^2*b^6 + 4*b^8 - 7*a^6*c^2 - 5*a^4*b^2*c^2 + 13*a^2*b^4*c^2 - b^6*c^2 + 15*a^4*c^4 + 13*a^2*b^2*c^4 - 6*b^4*c^4 - 13*a^2*c^6 - b^2*c^6 + 4*c^8) : :

X(43596) lies on these lines: {4, 14483}, {6, 6241}, {25, 5890}, {49, 15051}, {54, 74}, {146, 43573}, {323, 40647}, {389, 12112}, {399, 13630}, {567, 15054}, {1173, 11381}, {1181, 11464}, {1204, 3431}, {1495, 13382}, {1511, 9705}, {1614, 11438}, {3529, 37517}, {5663, 15037}, {5888, 11591}, {6000, 34565}, {6030, 32608}, {6102, 8718}, {7492, 37478}, {8550, 10752}, {9730, 14094}, {9781, 12174}, {10545, 37481}, {10546, 32139}, {10574, 15068}, {10721, 12022}, {11440, 14805}, {11459, 40916}, {12162, 15018}, {12308, 13363}, {13445, 13482}, {13754, 15246}, {15072, 43576}, {15801, 37496}, {18436, 41462}, {18445, 43572}, {18916, 22970}, {22585, 22750}

X(43596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 15032, 54}, {185, 15032, 74}, {13445, 15087, 13482}

X(43597) = PERSPECTOR OF THESE TRIANGLES: KM(ABC) AND MK(ANTICOMPLEMENTARY)

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

X(43597) lies on these lines: {2, 5448}, {3, 143}, {4, 40196}, {5, 74}, {20, 37470}, {24, 37475}, {26, 20791}, {30, 38848}, {49, 15034}, {54, 5504}, {64, 16261}, {110, 13630}, {155, 5890}, {182, 8537}, {185, 14094}, {186, 9729}, {378, 15024}, {389, 43574}, {546, 13445}, {548, 15107}, {549, 7691}, {567, 15036}, {631, 11438}, {1192, 7509}, {1199, 15012}, {1204, 3090}, {1511, 9706}, {1614, 6644}, {1656, 11440}, {1658, 40280}, {1995, 12290}, {2071, 5462}, {2979, 37490}, {3357, 3545}, {3518, 8718}, {3530, 3581}, {3796, 35479}, {3843, 10545}, {4550, 7486}, {5012, 37814}, {5055, 32138}, {5446, 43576}, {5640, 12084}, {5892, 14118}, {5943, 14865}, {6030, 12107}, {6241, 6642}, {6288, 9140}, {7464, 10110}, {7506, 15072}, {7512, 16836}, {7526, 15028}, {7529, 11455}, {7592, 34966}, {9705, 15032}, {9781, 11413}, {9786, 11412}, {9818, 11465}, {10095, 18859}, {10298, 13336}, {10575, 13595}, {10601, 35477}, {10605, 15058}, {10610, 37955}, {10620, 22462}, {10721, 43577}, {11484, 34469}, {11557, 43391}, {11695, 21663}, {12041, 32205}, {12082, 16936}, {12121, 43575}, {12278, 18952}, {12279, 13861}, {12289, 18911}, {12834, 34152}, {13353, 15646}, {13363, 14130}, {13482, 16226}, {14157, 40647}, {14644, 34007}, {15018, 35497}, {15037, 15051}, {15078, 36752}, {15133, 38323}, {15331, 37471}, {15463, 22962}, {15717, 37478}, {15806, 38794}, {16194, 16835}, {16881, 37477}, {18420, 23294}, {18560, 37648}, {21308, 32137}, {25711, 43578}, {25739, 31833}, {32110, 37126}, {32142, 32608}, {32534, 37514}, {33703, 34417}, {34148, 37481}, {35472, 37476}, {36161, 38700}, {37513, 38448}, {43586, 43596}

X(43597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 12006, 13434}, {3, 15043, 15033}, {54, 22467, 15035}, {6644, 10574, 1614}, {9730, 22467, 54}, {11465, 11468, 9818}, {11695, 21663, 35500}

X(43598) = PERSPECTOR OF THESE TRIANGLES: KM(ABC) AND MK(X(3)-REFLECTION OF ABC)

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

X(43698) lies on these lines: {2, 1614}, {3, 6030}, {4, 801}, {5, 49}, {22, 7999}, {23, 1216}, {24, 11459}, {25, 11412}, {26, 11444}, {52, 13595}, {74, 12162}, {113, 34007}, {140, 10540}, {143, 15801}, {146, 43577}, {154, 7509}, {155, 1995}, {156, 1656}, {182, 5067}, {184, 3090}, {185, 14094}, {186, 5907}, {195, 10095}, {206, 40330}, {215, 7173}, {323, 5446}, {376, 26883}, {381, 13482}, {382, 43576}, {394, 10594}, {399, 13630}, {511, 34484}, {546, 22115}, {547, 13353}, {569, 5056}, {578, 3545}, {631, 5651}, {852, 14152}, {1147, 3091}, {1154, 13621}, {1157, 30482}, {1173, 1994}, {1176, 24206}, {1181, 15045}, {1199, 5943}, {1209, 10203}, {1352, 7505}, {1368, 16659}, {1437, 6920}, {1493, 15038}, {1495, 7512}, {1511, 14130}, {1593, 16261}, {1598, 6090}, {1853, 31282}, {1993, 7529}, {2070, 7691}, {2477, 3614}, {2888, 21451}, {2914, 41671}, {2937, 15067}, {2979, 7517}, {3043, 36518}, {3044, 23514}, {3045, 23513}, {3047, 23515}, {3060, 13861}, {3205, 42581}, {3206, 42580}, {3233, 36161}, {3292, 10110}, {3410, 5449}, {3518, 5562}, {3520, 15030}, {3525, 10984}, {3533, 37515}, {3542, 14826}, {3580, 31831}, {3581, 31834}, {3832, 13352}, {3845, 37495}, {3850, 37472}, {3853, 37477}, {3855, 11424}, {3917, 12088}, {4994, 30506}, {5020, 7592}, {5055, 32046}, {5068, 9545}, {5072, 9703}, {5079, 9704}, {5133, 9820}, {5422, 11423}, {5498, 38794}, {5609, 12006}, {5640, 12161}, {5643, 15047}, {5654, 7544}, {5889, 7506}, {5890, 6642}, {5891, 7488}, {5899, 10627}, {5944, 34864}, {5972, 6143}, {6101, 15107}, {6241, 17928}, {6644, 12111}, {6677, 26879}, {6800, 7393}, {6997, 12318}, {7387, 15066}, {7395, 8780}, {7464, 13474}, {7484, 14530}, {7486, 11003}, {7493, 11487}, {7503, 11464}, {7516, 15080}, {7526, 11449}, {7527, 12038}, {7545, 10263}, {7569, 10516}, {7574, 43579}, {7703, 31283}, {7728, 43391}, {8537, 11188}, {8717, 21734}, {9143, 43573}, {9590, 31751}, {9625, 31752}, {9676, 42268}, {9936, 37644}, {9972, 34155}, {10082, 38458}, {10096, 21230}, {10116, 14683}, {10170, 35265}, {10226, 15051}, {10282, 32401}, {10323, 17811}, {10574, 32139}, {10706, 38323}, {10752, 40929}, {11064, 15559}, {11134, 42599}, {11137, 42598}, {11284, 19347}, {11402, 11484}, {11413, 11455}, {11439, 12084}, {11440, 18435}, {11442, 26917}, {11451, 36753}, {11465, 36752}, {11468, 15078}, {11557, 43580}, {12086, 16194}, {12106, 18436}, {12134, 25739}, {12283, 26206}, {12325, 41586}, {12380, 12606}, {12383, 13403}, {13163, 20424}, {13339, 16239}, {13347, 15702}, {13362, 24573}, {13363, 22462}, {13364, 14627}, {13367, 35500}, {13383, 37636}, {13561, 15059}, {13564, 32142}, {13598, 26863}, {14076, 32379}, {14156, 18488}, {14912, 19137}, {14940, 21243}, {15026, 15087}, {15036, 35497}, {15037, 32205}, {15040, 33539}, {15043, 18445}, {15053, 34783}, {15063, 43578}, {15139, 16252}, {15355, 23128}, {15462, 18553}, {15644, 37925}, {18859, 32137}, {18916, 40132}, {22051, 23409}, {22151, 43130}, {23039, 37440}, {23606, 38281}, {25555, 32255}, {26896, 37068}, {26913, 32140}, {27355, 37505}, {31255, 34780}, {31829, 32111}, {32415, 40276}, {32609, 43394}, {33703, 37480}, {34939, 37649}, {35502, 35602}

X(43598) = reflection of X(43821) in X(5)
X(43598) = X(43821)-of-Johnson-triangle
X(43598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10539, 1614}, {3, 14157, 8718}, {3, 35264, 26882}, {5, 49, 13434}, {5, 110, 54}, {5, 18350, 110}, {24, 17814, 11459}, {49, 13434, 54}, {52, 13595, 38848}, {54, 110, 9705}, {110, 13434, 49}, {155, 1995, 3567}, {156, 1656, 5012}, {195, 21308, 10095}, {381, 43572, 13482}, {399, 43584, 43596}, {567, 9706, 54}, {1147, 3091, 15033}, {1493, 18874, 15038}, {1495, 11793, 7512}, {1993, 7529, 9781}, {2070, 11591, 7691}, {3850, 40111, 37472}, {5020, 7592, 15024}, {5056, 9544, 569}, {5651, 6759, 631}, {5889, 10546, 7506}, {6101, 18378, 15107}, {6642, 11441, 5890}, {7395, 8780, 9707}, {7506, 15068, 5889}, {12162, 22467, 74}, {12162, 43586, 22467}, {15052, 22467, 12162}, {15052, 43586, 74}, {17814, 35259, 24}, {17928, 18451, 6241}, {18435, 37814, 11440}

X(43599) = PERSPECTOR OF THESE TRIANGLES: KM(ABC) AND MK(CIRCUM-ORTHIC)

Barycentrics    3*a^10 - a^8*b^2 - 13*a^6*b^4 + 15*a^4*b^6 - 2*a^2*b^8 - 2*b^10 - a^8*c^2 + 21*a^6*b^2*c^2 - 15*a^4*b^4*c^2 - 11*a^2*b^6*c^2 + 6*b^8*c^2 - 13*a^6*c^4 - 15*a^4*b^2*c^4 + 26*a^2*b^4*c^4 - 4*b^6*c^4 + 15*a^4*c^6 - 11*a^2*b^2*c^6 - 4*b^4*c^6 - 2*a^2*c^8 + 6*b^2*c^8 - 2*c^10 : :
X(43599) = 2 X[5] - 3 X[3521], 4 X[5] - 3 X[15062], 2 X[20] - 3 X[8718], 8 X[548] - 9 X[6030], 4 X[548] - 3 X[18442], 7 X[3528] - 6 X[35240], 7 X[3832] - 6 X[18488], 5 X[3843] - 3 X[33541], 3 X[5890] - 2 X[22948], 3 X[6030] - 2 X[18442], 3 X[11559] - 4 X[20379], 3 X[13630] - 2 X[40930], X[16835] - 4 X[34563]

X(43599) lies on these lines: {3, 43585}, {4, 13399}, {5, 74}, {20, 1147}, {30, 15801}, {54, 2777}, {146, 43577}, {185, 10721}, {382, 3060}, {541, 34007}, {548, 6030}, {1906, 38848}, {2916, 35446}, {3146, 10116}, {3526, 11468}, {3528, 35240}, {3832, 18488}, {3843, 33541}, {3853, 25739}, {3855, 32601}, {5890, 5895}, {6000, 32352}, {6143, 10990}, {8550, 18560}, {9657, 11461}, {9670, 19368}, {10706, 22467}, {11456, 17800}, {11457, 17578}, {11464, 15696}, {11466, 43194}, {11467, 43193}, {11559, 20379}, {12174, 40242}, {12289, 29012}, {12290, 36990}, {13403, 43596}, {13630, 38790}, {14862, 35489}, {15063, 22955}, {15311, 15559}

X(43599) = reflection of X(i) in X(j) for these {i,j}: {3, 43585}, {4, 34563}, {15062, 3521}, {16835, 4}
X(43599) = crosssum of X(3) and X(33541)

X(43600) = PERSPECTOR OF THESE TRIANGLES: KM(MEDIAL) AND MK(ANTICOMPLEMENTARY)

Barycentrics    a^2*(a^8 - 5*a^6*b^2 + 9*a^4*b^4 - 7*a^2*b^6 + 2*b^8 - 5*a^6*c^2 - a^4*b^2*c^2 + 11*a^2*b^4*c^2 - 5*b^6*c^2 + 9*a^4*c^4 + 11*a^2*b^2*c^4 + 6*b^4*c^4 - 7*a^2*c^6 - 5*b^2*c^6 + 2*c^8) : :
X(43600) = 5 X[15047] - X[33539]

X(43600) lies on these lines: {2, 15083}, {3, 34567}, {4, 16622}, {5, 5643}, {30, 1173}, {49, 43584}, {51, 8718}, {54, 5504}, {74, 13434}, {110, 12006}, {186, 15012}, {382, 15019}, {389, 7512}, {399, 32205}, {546, 12834}, {549, 15801}, {567, 10226}, {575, 3520}, {576, 3528}, {895, 33749}, {1181, 15024}, {1199, 9729}, {1614, 7506}, {1658, 5012}, {3167, 7592}, {3518, 16226}, {3529, 15004}, {3530, 23061}, {3567, 7387}, {5422, 6241}, {5462, 14157}, {5609, 22462}, {5663, 15047}, {5889, 7516}, {5890, 7503}, {5946, 18378}, {7691, 37471}, {8254, 15061}, {9706, 15034}, {10574, 12084}, {10601, 15058}, {10733, 43575}, {11017, 12308}, {11412, 37514}, {11423, 17928}, {11432, 37198}, {11441, 11465}, {11451, 32139}, {12162, 15018}, {13382, 35500}, {13482, 37505}, {15028, 18445}, {15036, 43394}, {15053, 32046}, {15107, 16881}, {16270, 19362}, {20791, 36749}, {23060, 37956}, {34007, 43573}, {34545, 40647}

X(43600) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1199, 9729, 43574}, {10574, 36753, 15033}, {13434, 13630, 74}, {13630, 15037, 13434}

X(43601) = PERSPECTOR OF THESE TRIANGLES: KM(MEDIAL) AND MK(EULER)

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

X(43601) lies on these lines: {2, 1204}, {3, 54}, {4, 13445}, {5, 74}, {20, 11438}, {22, 1192}, {24, 15072}, {25, 12279}, {49, 15035}, {51, 12086}, {64, 1995}, {110, 185}, {125, 34007}, {143, 18859}, {186, 40647}, {376, 43573}, {378, 12834}, {389, 2071}, {476, 36179}, {548, 3581}, {549, 15806}, {550, 43575}, {567, 10226}, {569, 35473}, {631, 5654}, {858, 13568}, {895, 40929}, {1105, 35360}, {1113, 14375}, {1114, 14374}, {1181, 11449}, {1199, 37948}, {1511, 9705}, {1593, 5640}, {1614, 37814}, {1620, 3796}, {1656, 32138}, {1899, 12278}, {2070, 8718}, {2888, 43582}, {3060, 9786}, {3091, 3357}, {3098, 21734}, {3515, 26881}, {3516, 5422}, {3518, 10575}, {3520, 9730}, {3528, 37478}, {3532, 17825}, {3567, 12084}, {3580, 31829}, {3627, 38848}, {3832, 10545}, {4550, 5067}, {4846, 7505}, {5020, 34469}, {5133, 6696}, {5446, 7464}, {5462, 14865}, {5498, 38728}, {5562, 43392}, {5643, 7527}, {5892, 35500}, {5894, 37648}, {5944, 37955}, {6030, 7488}, {6143, 6699}, {6241, 6644}, {6288, 10264}, {6642, 15305}, {6776, 40317}, {6800, 15750}, {6815, 18931}, {7493, 15740}, {7503, 11454}, {7506, 12290}, {7512, 32110}, {7526, 11468}, {7699, 31283}, {7703, 40686}, {8567, 10601}, {9140, 38323}, {9706, 12038}, {9729, 14118}, {9818, 15028}, {10116, 12383}, {10263, 43576}, {10298, 10984}, {10605, 12111}, {10606, 11451}, {11250, 15033}, {11381, 13595}, {11416, 37473}, {11424, 15019}, {11430, 35497}, {11433, 30552}, {11442, 18913}, {11444, 12163}, {11455, 13861}, {12006, 12041}, {12088, 14855}, {12162, 15054}, {12174, 35264}, {12241, 16386}, {12254, 18128}, {13363, 15041}, {13367, 37941}, {13482, 14627}, {13491, 14157}, {13567, 22466}, {13598, 37944}, {14094, 18350}, {14641, 37925}, {14861, 18282}, {14915, 34484}, {15012, 34545}, {15037, 35498}, {15080, 37487}, {15246, 17704}, {15717, 41462}, {16835, 18369}, {16836, 37126}, {16881, 37950}, {17506, 18475}, {17578, 34417}, {19771, 37046}, {21308, 33541}, {22647, 32375}, {22750, 37917}, {23040, 39242}, {23293, 26937}, {32184, 32345}, {34152, 37472}, {35477, 36752}, {36159, 38700}, {38898, 43391}

X(43601) = isogonal conjugate of perspector of circle O(3,4)
X(43601) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1204, 11440}, {3, 5890, 34148}, {3, 6102, 43574}, {3, 10574, 5012}, {3, 13630, 54}, {3, 32608, 10627}, {5, 74, 15062}, {64, 1995, 11439}, {185, 22467, 110}, {1181, 15078, 11449}, {1620, 3796, 38438}, {3520, 9730, 13434}, {6102, 43574, 15801}, {7689, 37470, 631}, {9706, 15051, 12038}, {9729, 21663, 14118}, {9786, 11413, 3060}, {10605, 17928, 12111}, {11250, 37481, 15033}, {11468, 15045, 7526}, {12006, 12041, 14130}, {12038, 15032, 9706}, {13434, 15055, 3520}, {15062, 43584, 5}

X(43602) = PERSPECTOR OF THESE TRIANGLES: KM(MEDIAL) AND MK(X(3)-REFLECTION OF ABC

Barycentrics    a^2*(a^8 - 5*a^6*b^2 + 9*a^4*b^4 - 7*a^2*b^6 + 2*b^8 - 5*a^6*c^2 - a^4*b^2*c^2 + 7*a^2*b^4*c^2 - b^6*c^2 + 9*a^4*c^4 + 7*a^2*b^2*c^4 - 2*b^4*c^4 - 7*a^2*c^6 - b^2*c^6 + 2*c^8) : :
X(43602) = 7 X[1199] - 6 X[34566], 3 X[13434] - 4 X[36153]

X(43602) lies on these lines: {3, 9706}, {4, 1173}, {5, 5643}, {6, 12290}, {24, 154}, {49, 15035}, {52, 8718}, {54, 74}, {110, 13630}, {156, 15053}, {184, 21844}, {186, 13382}, {378, 11423}, {389, 14157}, {399, 12006}, {548, 23061}, {550, 15801}, {567, 15062}, {576, 33703}, {1199, 6000}, {1204, 23040}, {1493, 18859}, {1498, 9781}, {1593, 6241}, {1598, 3567}, {1994, 10575}, {2937, 6102}, {3153, 18128}, {3521, 10733}, {3523, 15083}, {3527, 14487}, {3843, 15019}, {3850, 12834}, {5012, 34783}, {5498, 15057}, {5663, 13434}, {5889, 37494}, {6288, 27552}, {6622, 18916}, {6776, 8537}, {7393, 11459}, {7689, 11003}, {7728, 43575}, {7999, 12164}, {8550, 18560}, {9705, 15034}, {9970, 33749}, {10110, 12112}, {10116, 34007}, {10574, 18445}, {10619, 13619}, {10706, 43573}, {10721, 13403}, {11422, 12084}, {11440, 32046}, {11441, 15045}, {11455, 12174}, {11464, 15750}, {11470, 14912}, {12038, 15036}, {12086, 13482}, {12088, 14831}, {12121, 36966}, {12161, 15072}, {12242, 13399}, {12279, 36749}, {12308, 15047}, {13339, 31834}, {13366, 14865}, {13445, 37472}, {13491, 15087}, {13596, 16835}, {13754, 37126}, {14130, 15054}, {15021, 35498}, {15024, 18451}, {15038, 32137}, {15043, 32139}, {15055, 43394}, {15058, 36752}, {15061, 15806}, {15305, 36753}, {16625, 37925}, {16982, 37949}, {17809, 35477}, {18350, 43584}, {18909, 23294}, {18914, 23047}, {19468, 32339}, {26881, 37490}, {40647, 43574}

X(43602) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {54, 185, 74}, {54, 43596, 185}, {185, 15032, 54}, {185, 43392, 7722}, {389, 14157, 38848}, {1181, 5890, 1614}, {2914, 17855, 43391}, {5890, 26882, 9786}, {6241, 7592, 15033}, {9705, 22467, 15034}, {12242, 13399, 35482}, {15032, 43596, 74}, {17855, 43391, 74}

X(43603) = PERSPECTOR OF THESE TRIANGLES: KM(MEDIAL) AND MK(ABC-REFLECTION OF X(3)

Barycentrics    a^2*(a^8 + a^6*b^2 - 9*a^4*b^4 + 11*a^2*b^6 - 4*b^8 + a^6*c^2 + 11*a^4*b^2*c^2 - 17*a^2*b^4*c^2 + 5*b^6*c^2 - 9*a^4*c^4 - 17*a^2*b^2*c^4 - 2*b^4*c^4 + 11*a^2*c^6 + 5*b^2*c^6 - 4*c^8) : :

X(43603) lies on these lines: {3, 34567}, {5, 10706}, {24, 10574}, {54, 15051}, {74, 12006}, {110, 13630}, {185, 15052}, {569, 23040}, {575, 35497}, {1173, 18859}, {1593, 15043}, {1598, 15072}, {2071, 15012}, {3520, 9730}, {3522, 11431}, {3858, 16835}, {5012, 21844}, {5462, 13445}, {5622, 9977}, {5663, 22462}, {5889, 37475}, {8254, 38728}, {9706, 15020}, {9729, 37126}, {9786, 20791}, {10545, 12290}, {10605, 15028}, {10620, 32205}, {11440, 15045}, {12041, 15047}, {12046, 33539}, {12084, 15019}, {12086, 16226}, {12834, 14865}, {14130, 15021}, {16881, 43576}, {18350, 43596}, {34484, 40647}

X(43603) = {X(9706),X(22467)}-harmonic conjugate of X(15020)

X(43604) = PERSPECTOR OF THESE TRIANGLES: KM(ANTICOMPLEMENTARY) AND MK(EULER)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(2*a^6 - a^4*b^2 - 4*a^2*b^4 + 3*b^6 - a^4*c^2 + 10*a^2*b^2*c^2 - 3*b^4*c^2 - 4*a^2*c^4 - 3*b^2*c^4 + 3*c^6) : :
X(43604) = 3 X[3] - X[1092], X[1092] + 3 X[1204], X[10539] - 3 X[15078]

X(43604) lies on these lines: {2, 11468}, {3, 49}, {5, 1539}, {20, 32110}, {24, 14915}, {26, 14641}, {52, 2071}, {54, 35497}, {68, 18931}, {74, 12162}, {140, 32210}, {186, 10575}, {373, 38633}, {378, 5462}, {389, 11250}, {548, 12024}, {567, 35498}, {569, 35477}, {631, 4846}, {1192, 12085}, {1614, 37941}, {1620, 14070}, {3357, 6644}, {3518, 13445}, {3520, 9730}, {3521, 38728}, {3541, 7706}, {5446, 11438}, {5448, 10257}, {5889, 10564}, {5891, 11440}, {5892, 7526}, {5907, 32138}, {5965, 14810}, {6000, 37814}, {6102, 34152}, {6153, 32345}, {6642, 10606}, {6696, 31833}, {7387, 33534}, {7488, 14855}, {7503, 37470}, {8567, 9818}, {8717, 9715}, {9705, 15036}, {9729, 18570}, {9820, 16976}, {9927, 26937}, {9977, 11802}, {10116, 38726}, {10226, 11430}, {10263, 37950}, {10282, 13491}, {10295, 11750}, {10539, 15078}, {10574, 35473}, {10620, 18350}, {11410, 36752}, {11557, 13293}, {11692, 18859}, {11806, 12901}, {12106, 13474}, {12118, 18913}, {12897, 13567}, {13289, 22962}, {13366, 35495}, {13403, 37853}, {13470, 15332}, {13621, 32062}, {13851, 18565}, {14156, 22660}, {14516, 16003}, {14531, 37477}, {14708, 25564}, {14831, 37495}, {14865, 15053}, {15021, 15062}, {15030, 15041}, {15043, 35475}, {15072, 21844}, {15311, 16238}, {15579, 43130}, {15760, 20191}, {16111, 18560}, {16195, 35237}, {16386, 26879}, {17702, 33563}, {18364, 37471}, {18388, 23336}, {18390, 34350}, {18451, 34469}, {20478, 32549}, {20479, 32550}, {21734, 41398}, {31829, 43589}, {32171, 37968}, {34148, 37948}, {34798, 37938}, {35489, 41482}

X(43604) = midpoint of X(3) and X(1204)
X(43604) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 185, 12038}, {3, 7689, 1216}, {3, 10605, 1147}, {3, 40647, 18475}, {74, 22467, 12162}, {631, 11270, 11454}, {6699, 43577, 5}, {10226, 13630, 11430}, {11438, 12084, 5446}, {12162, 22467, 43586}, {13491, 15646, 10282}

X(43605) = PERSPECTOR OF THESE TRIANGLES: KM(ANTICOMPLEMENTARY) AND MK(X(3)-REFLECTION OF ABC)

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 + a^4*b^2*c^2 + 2*a^2*b^4*c^2 + b^6*c^2 + 6*a^4*c^4 + 2*a^2*b^2*c^4 - 4*b^4*c^4 - 4*a^2*c^6 + b^2*c^6 + c^8) : :
X(436005) = 3 X[49] - 2 X[43394], 3 X[3520] - 4 X[43394]

X(43605) lies on these lines: {2, 1181}, {3, 9544}, {4, 1994}, {5, 399}, {6, 1131}, {20, 155}, {22, 12164}, {23, 5889}, {24, 35265}, {49, 3043}, {52, 14157}, {54, 7527}, {74, 9705}, {110, 185}, {113, 10116}, {146, 18560}, {156, 186}, {182, 15056}, {184, 12111}, {193, 19149}, {195, 3627}, {217, 5984}, {378, 9545}, {381, 1199}, {382, 12112}, {389, 13595}, {394, 3522}, {511, 12087}, {546, 15087}, {568, 34484}, {569, 15058}, {578, 15305}, {631, 15068}, {1092, 15072}, {1147, 2071}, {1154, 12088}, {1204, 11449}, {1353, 1906}, {1493, 32137}, {1498, 1993}, {1598, 11002}, {1614, 7488}, {1941, 35311}, {2883, 17824}, {2888, 15760}, {2914, 7728}, {2930, 40929}, {2979, 16661}, {3060, 26883}, {3089, 37644}, {3091, 7592}, {3153, 22660}, {3157, 9538}, {3167, 11413}, {3193, 6895}, {3410, 13160}, {3518, 6102}, {3521, 23236}, {3529, 16266}, {3543, 36747}, {3545, 36753}, {3580, 16252}, {3845, 14627}, {3858, 15038}, {5012, 5907}, {5056, 36752}, {5059, 37498}, {5068, 5422}, {5448, 25739}, {5562, 6636}, {5609, 13630}, {5654, 11457}, {5876, 35921}, {5890, 10539}, {5894, 17847}, {6000, 12086}, {6143, 12317}, {6243, 37925}, {6285, 9637}, {6623, 35603}, {7352, 9638}, {7391, 34781}, {7411, 22136}, {7496, 11793}, {7503, 11003}, {7505, 18917}, {7512, 18436}, {7545, 16881}, {7555, 12307}, {7577, 32140}, {7689, 11464}, {7712, 9715}, {8718, 10625}, {9143, 38323}, {9306, 10574}, {9703, 11250}, {9704, 18570}, {9706, 11430}, {9707, 10298}, {9716, 12315}, {9779, 16472}, {9786, 35264}, {10226, 10620}, {10254, 18356}, {10296, 12289}, {10575, 41597}, {10601, 15022}, {10606, 35494}, {10984, 11444}, {11004, 17578}, {11206, 31304}, {11381, 34986}, {11412, 15083}, {11422, 11424}, {11440, 13367}, {11459, 37126}, {11470, 15531}, {11799, 32358}, {12107, 32608}, {12160, 32063}, {12254, 18563}, {12279, 13346}, {12290, 13352}, {12308, 14130}, {12316, 37924}, {12324, 37645}, {12834, 27355}, {13243, 23070}, {13353, 15060}, {13382, 15053}, {13403, 15063}, {13434, 15030}, {13491, 22115}, {13567, 21451}, {13596, 37472}, {14128, 37471}, {14216, 31074}, {14516, 14683}, {14531, 15107}, {14611, 36179}, {14865, 18439}, {15066, 15717}, {15683, 37672}, {16868, 25738}, {17506, 32171}, {17834, 37913}, {18435, 32046}, {19139, 39874}, {20094, 39820}, {22750, 22952}, {26864, 38444}, {26882, 37940}, {30714, 43577}, {31802, 34603}, {34117, 37784}, {34796, 35471}, {37197, 39899}, {43586, 43596}

X(43605) = reflection of X(i) in X(j) for these {i,j}: {3520, 49}, {7488, 1614}, {11440, 13367}, {12086, 34148}
X(43605) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 155, 323}, {54, 12162, 7527}, {54, 14094, 12162}, {74, 9705, 12038}, {74, 12038, 35497}, {110, 185, 22467}, {155, 11456, 20}, {156, 34783, 186}, {184, 12111, 14118}, {399, 15032, 15052}, {1147, 6241, 2071}, {1181, 11441, 2}, {1204, 11449, 37941}, {1498, 1993, 3146}, {3091, 7592, 34545}, {3167, 12174, 11413}, {5609, 13630, 18350}, {5889, 6759, 23}, {6102, 10540, 3518}, {7503, 19347, 11003}, {7592, 18451, 3091}, {7689, 11464, 38448}, {9706, 15062, 11430}, {9707, 12163, 10298}, {10575, 41597, 43574}, {10984, 11444, 15246}, {11422, 11439, 11424}, {12279, 13346, 37944}, {14683, 34007, 14516}, {15032, 15052, 15018}, {18435, 32046, 35500}, {18445, 32139, 4}, {22660, 34224, 3153}

X(43606) = PERSPECTOR OF THESE TRIANGLES: KM(ORTHIC) AND MK(TANGENTIAL)

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 + 5*a^8*b^2*c^2 + 4*a^6*b^4*c^2 - 12*a^4*b^6*c^2 + 7*a^2*b^8*c^2 - b^10*c^2 + 2*a^8*c^4 + 4*a^6*b^2*c^4 + 30*a^4*b^4*c^4 - 8*a^2*b^6*c^4 + 4*b^8*c^4 + 2*a^6*c^6 - 12*a^4*b^2*c^6 - 8*a^2*b^4*c^6 - 6*b^6*c^6 - 3*a^4*c^8 + 7*a^2*b^2*c^8 + 4*b^4*c^8 + a^2*c^10 - b^2*c^10) : :

X(436) lies on these lines: {3, 33523}, {110, 185}, {184, 15717}, {1181, 20791}, {1614, 15750}, {5012, 18913}, {5622, 33749}, {10605, 38444}, {15033, 26944}, {16270, 19362}, {18909, 34148}, {18914, 43574}

X(43607) = PERSPECTOR OF THESE TRIANGLES: KM(TANGENTIAL) AND MK(ORTHIC)

Barycentrics    2*a^10 - 3*a^8*b^2 - 4*a^6*b^4 + 10*a^4*b^6 - 6*a^2*b^8 + b^10 - 3*a^8*c^2 + 14*a^6*b^2*c^2 - 10*a^4*b^4*c^2 + 2*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 + 10*a^4*c^6 + 2*a^2*b^2*c^6 + 2*b^4*c^6 - 6*a^2*c^8 - 3*b^2*c^8 + c^10 : :
X(43607) = 3 X[11468] + X[18394], X[18394] - 3 X[23294]

X(43607) lies on these lines: {3, 70}, {4, 1192}, {5, 74}, {20, 14852}, {24, 16658}, {30, 11468}, {49, 20126}, {64, 7505}, {125, 18560}, {140, 6241}, {185, 10294}, {186, 6247}, {378, 26879}, {403, 3357}, {468, 12290}, {548, 12289}, {549, 1614}, {550, 25739}, {631, 11456}, {858, 7689}, {1204, 1594}, {1503, 21844}, {1656, 34469}, {1853, 35471}, {1885, 26917}, {1899, 35477}, {2071, 12359}, {2072, 32138}, {2883, 14940}, {3448, 35497}, {3516, 18912}, {3520, 12022}, {3523, 9707}, {3530, 11464}, {3541, 18931}, {3580, 12084}, {5054, 12174}, {5071, 32601}, {5498, 12281}, {6000, 10018}, {6146, 35473}, {6240, 11572}, {6699, 12162}, {7403, 15053}, {7542, 15072}, {7592, 18913}, {8567, 35481}, {9833, 35472}, {9927, 16386}, {10110, 35484}, {10151, 11704}, {10193, 13367}, {10226, 10264}, {10257, 12111}, {10282, 13399}, {10295, 18381}, {10575, 20191}, {10605, 37119}, {11204, 35491}, {11270, 18434}, {11410, 26944}, {11413, 33563}, {11438, 15559}, {11440, 11585}, {11454, 12605}, {11455, 21841}, {11459, 16196}, {11461, 15325}, {11462, 35255}, {11463, 35256}, {12038, 16003}, {12041, 13561}, {12086, 41587}, {12103, 40242}, {12241, 35475}, {12279, 13383}, {12324, 35486}, {13093, 37453}, {13567, 14865}, {13619, 41362}, {13630, 14389}, {14216, 32534}, {15122, 18436}, {15305, 16238}, {15311, 16868}, {15332, 16000}, {16013, 34152}, {17506, 34782}, {18350, 38728}, {18563, 32210}, {20427, 35488}, {22802, 35487}, {23336, 34783}, {31383, 35479}, {32269, 33703}, {33750, 39874}, {34799, 35493}, {37495, 41628}

X(43607) = midpoint of X(11468) and X(23294)
X(43607) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {64, 7505, 32111}, {185, 25563, 37118}, {186, 6247, 16659}, {378, 26937, 26879}, {1204, 23329, 1594}, {20299, 21663, 6240}, {20417, 25563, 185}

X(43608) = PERSPECTOR OF THESE TRIANGLES: KM(TANGENTIAL) AND MK(CIRCUM-ORTHIC)

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

X(43608) lies on these lines: {2, 6241}, {3, 12278}, {4, 11270}, {5, 74}, {20, 18394}, {24, 35217}, {49, 5498}, {51, 35482}, {54, 67}, {125, 3520}, {140, 1614}, {185, 6143}, {186, 20299}, {252, 3484}, {265, 10226}, {376, 40242}, {378, 26917}, {403, 6696}, {498, 19368}, {499, 11461}, {549, 34224}, {631, 1352}, {1204, 7577}, {1594, 13568}, {1595, 38848}, {1853, 32534}, {2071, 5449}, {2072, 11440}, {3357, 16868}, {3448, 12038}, {3526, 11456}, {3541, 3567}, {3542, 11455}, {3546, 7999}, {3548, 11459}, {5054, 9707}, {5055, 34469}, {5418, 11462}, {5420, 11463}, {5576, 15053}, {5889, 18281}, {5890, 26937}, {5894, 10721}, {6000, 14940}, {6240, 23332}, {6247, 10018}, {6288, 38728}, {6639, 15072}, {6640, 12111}, {6699, 22467}, {7404, 11465}, {7488, 20191}, {7505, 12290}, {7526, 26913}, {7527, 20397}, {7569, 37475}, {7699, 18931}, {7749, 13509}, {8567, 35490}, {8703, 30507}, {10193, 21659}, {10201, 12279}, {10255, 32138}, {10257, 31831}, {10606, 35488}, {11381, 37943}, {11449, 32140}, {11454, 18404}, {11466, 42092}, {11467, 42089}, {11750, 38448}, {12163, 30744}, {12359, 43574}, {13445, 15761}, {13595, 18488}, {13619, 18383}, {14216, 26882}, {14516, 15035}, {14644, 18560}, {15033, 26879}, {15311, 35487}, {15331, 41482}, {15873, 35484}, {16194, 21451}, {17506, 18400}, {17702, 35497}, {17854, 34128}, {18381, 21844}, {18390, 35475}, {18403, 32210}, {20126, 34331}, {20379, 43394}, {23324, 38447}, {23325, 34797}, {23336, 32358}, {26958, 35502}, {35498, 38724}

X(43608) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 23294, 25739}, {125, 25563, 3520}, {631, 11457, 11464}, {5498, 10264, 49}, {6247, 10018, 14157}, {13561, 24572, 23293}, {15059, 15062, 5}, {21663, 32767, 4}, {26937, 37119, 5890}

X(43609) = PERSPECTOR OF THESE TRIANGLES: KM(EXCENTRAL) AND MK(1ST CIRCUMPERP)

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

X(43609) lies on these lines: {23, 31817}, {110, 31803}, {1614, 20117}, {1699, 42463}, {2771, 18350}, {2772, 22467}, {5692, 6759}, {5693, 10539}, {5694, 10540}, {9306, 15071}, {14157, 31806}, {15052, 41192}, {22115, 31828}, {31871, 34148}

X(43610) = PERSPECTOR OF THESE TRIANGLES: KM(EXCENTRAL) AND MK(2ND CIRCUMPERP)

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

X(43610) lies on these lines: {1, 36059}, {3, 6149}, {35, 40944}, {36, 30493}, {49, 2771}, {54, 5884}, {110, 31803}, {184, 15071}, {186, 31825}, {323, 31817}, {517, 37495}, {567, 5885}, {569, 15016}, {578, 5902}, {758, 34148}, {1092, 5692}, {1147, 5693}, {2392, 7488}, {2779, 3520}, {5691, 14529}, {5694, 22115}, {5883, 13434}, {6126, 11430}, {9586, 42463}, {10540, 31828}, {11449, 30438}, {13352, 37625}, {15033, 31870}, {31806, 43574}, {31814, 34397}

X(43611) = PERSPECTOR OF THESE TRIANGLES: KM(EULER) AND MK(ANTICOMPLEMENTARY)

Barycentrics    a^2*(a^8 + 3*a^6*b^2 - 15*a^4*b^4 + 17*a^2*b^6 - 6*b^8 + 3*a^6*c^2 + 15*a^4*b^2*c^2 - 21*a^2*b^4*c^2 + 3*b^6*c^2 - 15*a^4*c^4 - 21*a^2*b^2*c^4 + 6*b^4*c^4 + 17*a^2*c^6 + 3*b^2*c^6 - 6*c^8) : :

X(43611) lies on these lines: {49, 15035}, {54, 35497}, {74, 13434}, {185, 14094}, {1173, 13445}, {5663, 22462}, {5890, 11413}, {6241, 7529}, {7514, 10574}, {9706, 15036}, {12006, 15054}, {13382, 43574}, {13491, 38848}, {15041, 36153}, {22467, 43596}

X(43612) = PERSPECTOR OF THESE TRIANGLES: KM(EULER) AND MK(ABC-REFLECTION OF X(3))

Barycentrics    a^2*(a^8 - 7*a^6*b^2 + 15*a^4*b^4 - 13*a^2*b^6 + 4*b^8 - 7*a^6*c^2 - 5*a^4*b^2*c^2 + 15*a^2*b^4*c^2 - 3*b^6*c^2 + 15*a^4*c^4 + 15*a^2*b^2*c^4 - 2*b^4*c^4 - 13*a^2*c^6 - 3*b^2*c^6 + 4*c^8) : :
X(43612) = 7 X[15047] - 3 X[33539]

X(43612) lies on these lines: {5, 43596}, {20, 37517}, {26, 5890}, {49, 15020}, {54, 10226}, {110, 13630}, {155, 10574}, {185, 575}, {1181, 15053}, {1199, 13445}, {1350, 5889}, {5012, 7689}, {5093, 15072}, {5663, 15047}, {8254, 20126}, {8703, 20585}, {9706, 12038}, {10620, 36153}, {10721, 43575}, {10752, 33749}, {12006, 14094}, {12017, 19139}, {12290, 15019}, {12308, 32205}

X(43612) = {X(185),X(13434)}-harmonic conjugate of X(15054)

X(43613) = PERSPECTOR OF THESE TRIANGLES: KM(X(3)-REFLECTION OF ABC) AND MK(ANTICOMPLEMENTARY)

Barycentrics    a^2*(a^8 - a^6*b^2 - 3*a^4*b^4 + 5*a^2*b^6 - 2*b^8 - a^6*c^2 + 7*a^4*b^2*c^2 - a^2*b^4*c^2 - 5*b^6*c^2 - 3*a^4*c^4 - a^2*b^2*c^4 + 14*b^4*c^4 + 5*a^2*c^6 - 5*b^2*c^6 - 2*c^8) : :
X(43613) = 5 X[13434] - 4 X[36153]

X(43613) lies on these lines: {3, 11439}, {4, 14860}, {5, 74}, {20, 4550}, {24, 16261}, {54, 7527}, {110, 14130}, {140, 13445}, {378, 15058}, {381, 11440}, {399, 9706}, {546, 38848}, {1173, 6102}, {1204, 3545}, {1216, 43576}, {1533, 32348}, {1568, 35482}, {1593, 11459}, {1614, 7526}, {2883, 20376}, {2888, 12897}, {3090, 3357}, {3153, 18488}, {3520, 15030}, {3581, 3861}, {3627, 7691}, {3818, 34797}, {3832, 7689}, {3851, 15053}, {3853, 15107}, {3855, 11438}, {5012, 18439}, {5447, 37944}, {5562, 13596}, {5655, 15806}, {5663, 13434}, {5889, 31861}, {5891, 12086}, {5907, 14865}, {6000, 35500}, {6241, 9818}, {6288, 10733}, {6642, 11468}, {7464, 11793}, {7486, 37470}, {7488, 16194}, {7503, 11472}, {7506, 11454}, {7512, 13474}, {7514, 12279}, {7999, 12085}, {8718, 11381}, {9306, 35475}, {9705, 11430}, {9781, 12163}, {9934, 32401}, {10226, 15036}, {10575, 16835}, {10605, 15024}, {10620, 12006}, {10721, 34007}, {11017, 12041}, {11412, 35502}, {11479, 15045}, {12038, 15052}, {12084, 15056}, {12088, 32062}, {12111, 12161}, {13630, 15054}, {14118, 14157}, {14128, 18859}, {14641, 15246}, {14788, 15311}, {14915, 37126}, {15034, 18350}, {15041, 22462}, {15051, 35498}, {15696, 41462}, {15738, 43578}, {17578, 37478}, {17800, 33533}, {18435, 34148}, {18560, 41171}, {20191, 21451}, {22584, 43580}, {23061, 31834}, {32142, 35452}, {33534, 35446}, {35497, 43586}

X(43613) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 15062, 74}, {54, 12162, 14094}, {3851, 32138, 15053}, {5907, 14865, 43574}, {7503, 11472, 12290}, {7526, 15305, 1614}, {7527, 12162, 54}, {11381, 35921, 8718}

X(43614) = PERSPECTOR OF THESE TRIANGLES: KM(X(3)-REFLECTION OF ABC) AND MK(ABC-REFLECTION OF X(3))

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

X(43614) lies on these lines: {2, 6759}, {3, 11439}, {5, 49}, {20, 5651}, {23, 11793}, {24, 10546}, {25, 11444}, {51, 15801}, {64, 15305}, {140, 14157}, {143, 12316}, {155, 5640}, {156, 5055}, {182, 7486}, {184, 5056}, {185, 15052}, {195, 1173}, {323, 10110}, {399, 12006}, {427, 22750}, {546, 43574}, {549, 8718}, {569, 5071}, {578, 5068}, {1092, 3832}, {1147, 3545}, {1154, 18369}, {1181, 15028}, {1199, 12834}, {1209, 37943}, {1216, 15107}, {1495, 37126}, {1498, 20791}, {1511, 11017}, {1598, 15066}, {1614, 1656}, {1993, 3527}, {1995, 5889}, {2070, 14128}, {2979, 10594}, {3060, 7529}, {3090, 5012}, {3091, 9306}, {3153, 32340}, {3518, 5891}, {3520, 15051}, {3521, 10706}, {3523, 26883}, {3567, 10545}, {3628, 10540}, {3839, 13346}, {3850, 22115}, {3851, 15033}, {3853, 43576}, {3855, 13352}, {3858, 37495}, {3861, 37477}, {4550, 21844}, {5020, 11441}, {5066, 37472}, {5079, 32046}, {5422, 11484}, {5446, 23061}, {5447, 37925}, {5562, 13595}, {5609, 32205}, {5622, 18553}, {5899, 32142}, {5921, 19137}, {6101, 7545}, {6642, 12111}, {6644, 11440}, {7387, 7998}, {7393, 15080}, {7395, 35264}, {7503, 17821}, {7506, 11459}, {7509, 26881}, {7512, 10170}, {7514, 26882}, {7517, 7999}, {7527, 15020}, {7592, 11451}, {9544, 15022}, {9818, 11449}, {9934, 25563}, {10095, 41578}, {10192, 20376}, {10203, 12010}, {10574, 18451}, {11412, 13861}, {11416, 43130}, {11591, 12307}, {12046, 36153}, {12082, 33543}, {12084, 16261}, {12161, 15019}, {12162, 15054}, {12315, 15072}, {12811, 40111}, {12900, 27866}, {13160, 15139}, {13289, 15030}, {13348, 37945}, {13353, 35018}, {13482, 38071}, {13630, 14094}, {14130, 15035}, {14156, 35482}, {14627, 18874}, {14845, 41597}, {15024, 18445}, {15034, 43394}, {15036, 35498}, {15045, 32139}, {15067, 18378}, {15699, 37471}, {16252, 35283}, {17578, 37480}, {18358, 19128}, {19121, 40330}, {21841, 37636}, {27355, 34986}, {31831, 41724}

X(43614) = reflection of X(38848) in X(18369)
X(43614) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 110, 13434}, {5, 6288, 14644}, {5, 18350, 54}, {54, 18350, 110}, {110, 13434, 9706}, {195, 13364, 1173}, {399, 22462, 12006}, {1216, 34484, 15107}, {1995, 17814, 5889}, {3090, 10539, 5012}, {3091, 9306, 34148}, {3518, 5891, 7691}, {5020, 11441, 15043}, {6642, 12111, 15053}, {6644, 15058, 11440}, {10546, 15056, 24}, {15030, 22467, 15062}, {15062, 22467, 15055}

X(43615) = PERSPECTOR OF THESE TRIANGLES: KM(ABC-REFLECTION OF X(3)) AND MK(MEDIAL)

Barycentrics    a^2*(2*a^8 - 4*a^6*b^2 + 4*a^2*b^6 - 2*b^8 - 4*a^6*c^2 + 10*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + b^6*c^2 - 7*a^2*b^2*c^4 + 2*b^4*c^4 + 4*a^2*c^6 + b^2*c^6 - 2*c^8) : :
X(43615) = 3 X[3] + X[24], 7 X[3] + X[7517], 5 X[3] - X[11413], X[3] + 3 X[15078], 5 X[3] + X[37440], 7 X[24] - 3 X[7517], 5 X[24] + 3 X[11413], X[24] - 9 X[15078], 5 X[24] - 3 X[37440], X[24] - 3 X[37814], 3 X[376] + X[31725], 3 X[549] - X[11585], 5 X[631] - X[18404], 5 X[1656] - X[35490], 7 X[3523] + X[35471], 9 X[3524] - X[37444], 9 X[5054] - 5 X[31282], 5 X[7517] + 7 X[11413], X[7517] - 21 X[15078], 5 X[7517] - 7 X[37440], X[7517] - 7 X[37814], X[11413] + 15 X[15078], X[11413] + 5 X[37814], 15 X[15078] - X[37440], 3 X[15078] - X[37814], 15 X[15692] + X[31304], 5 X[15693] - X[31180], X[21841] + 2 X[33923], X[37440] - 5 X[37814]

X(43615) lies on these lines: {2, 3}, {49, 15035}, {54, 15051}, {74, 18350}, {182, 40929}, {185, 1511}, {567, 15036}, {1192, 16266}, {1568, 34798}, {3521, 38794}, {5876, 21663}, {5894, 13289}, {5907, 32210}, {5972, 43577}, {6101, 32110}, {6288, 38728}, {6699, 13561}, {7689, 31834}, {9306, 32138}, {9703, 38942}, {9705, 15020}, {9730, 36153}, {10263, 10564}, {10264, 14516}, {10610, 21660}, {11202, 40928}, {11430, 12006}, {11468, 18435}, {11801, 12901}, {12038, 13630}, {12041, 12162}, {12893, 22962}, {13346, 14449}, {13352, 16881}, {13403, 38726}, {15037, 15042}, {15053, 37472}, {15578, 18358}, {18356, 26937}, {19353, 19468}, {22109, 43575}, {27552, 36966}, {32171, 40647}, {32607, 40685}, {34783, 40111}, {40932, 41398}

X(43615) = midpoint of X(i) and X(j) for these {i,j}: {3, 37814}, {235, 550}, {11413, 37440}, {12041, 20771}
X(43615) = reflection of X(16196) in X(3530)
X(43615) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4, 34152}, {3, 5, 10226}, {3, 186, 550}, {3, 1656, 35473}, {3, 1658, 548}, {3, 3851, 35495}, {3, 5055, 35496}, {3, 6644, 11250}, {3, 7488, 8703}, {3, 7502, 33923}, {3, 7525, 34200}, {3, 14130, 35497}, {3, 15078, 37814}, {3, 15646, 15331}, {3, 17928, 18570}, {3, 18324, 7525}, {3, 18571, 7555}, {3, 22467, 5}, {3, 32534, 7502}, {3, 37955, 7488}, {5, 550, 18560}, {24, 37126, 11585}, {140, 37968, 3}, {186, 550, 12107}, {186, 18325, 7575}, {548, 1658, 7555}, {548, 18571, 1658}, {549, 38323, 34331}, {3851, 35495, 35475}, {6644, 11250, 546}, {6823, 34477, 34577}, {7525, 33591, 7555}, {12084, 12106, 3853}, {12086, 13621, 15687}, {14709, 14710, 1656}, {16976, 31833, 23336}, {17928, 18570, 3628}, {18571, 25338, 186}, {23336, 31833, 39504}, {35231, 35232, 403}

X(43616) = PERSPECTOR OF THESE TRIANGLES: KM(CIRCUM-ORTHIC) AND MK(ABC)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^12 - a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 + a^4*b^8 - 5*a^2*b^10 + 2*b^12 - a^10*c^2 + 9*a^8*b^2*c^2 - 4*a^6*b^4*c^2 - 20*a^4*b^6*c^2 + 21*a^2*b^8*c^2 - 5*b^10*c^2 - 4*a^8*c^4 - 4*a^6*b^2*c^4 + 38*a^4*b^4*c^4 - 16*a^2*b^6*c^4 + 2*b^8*c^4 + 6*a^6*c^6 - 20*a^4*b^2*c^6 - 16*a^2*b^4*c^6 + 2*b^6*c^6 + a^4*c^8 + 21*a^2*b^2*c^8 + 2*b^4*c^8 - 5*a^2*c^10 - 5*b^2*c^10 + 2*c^12) : :
X(43616) = 3 X[4] - 4 X[22968], 3 X[2929] - X[22972], 3 X[22750] - 2 X[22972]

X(43616) lies on these lines: {3, 19460}, {4, 22968}, {20, 1204}, {24, 1192}, {25, 36983}, {52, 22952}, {54, 974}, {74, 5894}, {110, 185}, {125, 15062}, {184, 38942}, {376, 18910}, {378, 19360}, {1181, 9705}, {1350, 15073}, {2904, 5890}, {3089, 5878}, {3357, 22538}, {3520, 5622}, {3575, 41738}, {4549, 6643}, {6146, 22951}, {7387, 11820}, {7691, 13348}, {8780, 32139}, {10116, 12118}, {10295, 32330}, {11440, 26913}, {11821, 22581}, {12605, 18442}, {13568, 32125}, {13630, 19362}, {14130, 16270}, {14216, 22483}, {15053, 22800}, {17837, 37487}, {19353, 22948}, {19467, 22953}, {22497, 41715}, {22662, 34782}, {22979, 26944}, {22980, 26956}, {22981, 26955}, {36989, 39874}

X(43616) = reflection of X(i) in X(j) for these {i,j}: {52, 22952}, {22555, 22834}, {22662, 34782}, {22750, 2929}, {22955, 22962}
X(43616) = {X(21652),X(21663)}-harmonic conjugate of X(22978)

X(43617) = PERSPECTOR OF THESE TRIANGLES: KM(CIRCUM-ORTHIC) AND MK(TANGENTIAL)

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

X(43617) lies on these lines: {24, 19149}, {49, 38728}, {54, 67}, {110, 185}, {125, 13434}, {184, 3523}, {578, 23291}, {631, 5157}, {1092, 6776}, {1147, 18909}, {1204, 10298}, {1614, 1620}, {1899, 34148}, {2883, 22750}, {2929, 41589}, {5012, 26937}, {5504, 10116}, {6146, 43574}, {6759, 37460}, {7396, 13346}, {9706, 13198}, {10112, 22533}, {12006, 19362}, {13367, 15246}, {13568, 15139}, {13630, 15132}, {15738, 43578}, {16063, 19467}, {16196, 26926}, {18914, 22115}, {20191, 40441}

X(43618) = GIBERT (cot(ω)/sqrt(3), 1,-1) POINT

Barycentrics    7*a^4 - 2*a^2*b^2 - 3*b^4 - 2*a^2*c^2 + 6*b^2*c^2 - 3*c^4 : :
X(43618) = 4 X[6] - 3 X[2549], 2 X[6] - 3 X[7737], 10 X[6] - 9 X[7739], 7 X[6] - 6 X[15048], 5 X[6] - 6 X[18907], 2 X[141] - 3 X[11159], 5 X[2549] - 6 X[7739], 7 X[2549] - 8 X[15048], 5 X[2549] - 8 X[18907], 4 X[3589] - 3 X[5077], 7 X[3619] - 6 X[7761], 7 X[3619] - 9 X[14033], 5 X[3620] - 6 X[3734], 4 X[4045] - 3 X[33272], 5 X[7737] - 3 X[7739], 7 X[7737] - 4 X[15048], 5 X[7737] - 4 X[18907], 21 X[7739] - 20 X[15048], 3 X[7739] - 4 X[18907], 2 X[7761] - 3 X[14033], 4 X[7804] - 3 X[32986], 9 X[11286] - 8 X[34573], 5 X[15048] - 7 X[18907], X[20080] - 3 X[32815]

X(43618) lies on these lines: {2, 6781}, {3, 3055}, {4, 187}, {5, 5210}, {6, 30}, {20, 574}, {25, 24855}, {32, 3146}, {39, 3529}, {69, 3849}, {76, 33280}, {83, 32997}, {99, 33193}, {111, 7519}, {115, 3543}, {140, 5585}, {141, 11159}, {193, 543}, {230, 3830}, {315, 6658}, {316, 7870}, {317, 39062}, {376, 5475}, {381, 3054}, {382, 1384}, {439, 7862}, {538, 11008}, {546, 5023}, {550, 31401}, {620, 32827}, {625, 32985}, {626, 32981}, {631, 39590}, {754, 20080}, {1007, 32456}, {1078, 14068}, {1285, 5309}, {1352, 5104}, {1383, 5189}, {1478, 10987}, {1503, 11173}, {1504, 43408}, {1505, 43407}, {1506, 3522}, {1572, 28164}, {1657, 5024}, {1992, 32479}, {2071, 9699}, {2482, 23334}, {3053, 3627}, {3070, 8375}, {3071, 8376}, {3090, 15513}, {3091, 5206}, {3096, 14031}, {3524, 7603}, {3528, 31455}, {3534, 3815}, {3589, 5077}, {3619, 7761}, {3620, 3734}, {3788, 33239}, {3793, 34505}, {3832, 7749}, {3845, 37637}, {3851, 15603}, {3853, 13881}, {3972, 33017}, {4045, 33272}, {4302, 31409}, {4316, 9599}, {4324, 9596}, {5007, 11541}, {5008, 5319}, {5013, 11742}, {5052, 14927}, {5059, 7756}, {5067, 11614}, {5073, 5254}, {5304, 11648}, {6337, 7843}, {6423, 42271}, {6424, 42272}, {6680, 32982}, {6683, 33226}, {6776, 33550}, {7615, 17008}, {7618, 7777}, {7694, 11676}, {7735, 15682}, {7736, 9774}, {7751, 32826}, {7752, 33244}, {7753, 15683}, {7758, 7823}, {7759, 15301}, {7763, 33257}, {7765, 14075}, {7769, 33254}, {7771, 33016}, {7773, 33250}, {7779, 19569}, {7786, 33253}, {7787, 19691}, {7790, 33192}, {7795, 19687}, {7800, 7802}, {7803, 33256}, {7804, 32986}, {7806, 8597}, {7808, 33023}, {7815, 32979}, {7816, 32006}, {7825, 32973}, {7828, 33279}, {7830, 32971}, {7834, 33238}, {7835, 33187}, {7842, 14001}, {7845, 32817}, {7847, 33271}, {7853, 14039}, {7855, 32822}, {7857, 32996}, {7867, 33201}, {7889, 33025}, {7898, 19686}, {7910, 16898}, {7911, 14037}, {7913, 33210}, {7916, 32824}, {7919, 33278}, {7928, 14032}, {7934, 33255}, {7935, 33198}, {7938, 19693}, {8182, 11317}, {8352, 37809}, {8353, 11174}, {8553, 31861}, {8591, 10811}, {8703, 31489}, {8744, 34797}, {9300, 15685}, {9620, 28150}, {9675, 23249}, {9700, 12087}, {10483, 16784}, {11057, 16990}, {11114, 37675}, {11185, 14712}, {11286, 34573}, {11295, 23302}, {11296, 23303}, {11361, 14907}, {12103, 15815}, {12963, 22644}, {12968, 22615}, {14023, 32819}, {14042, 32832}, {14581, 33630}, {15075, 18565}, {15484, 15681}, {15515, 31404}, {15696, 31417}, {17538, 37512}, {18546, 37667}, {19106, 41407}, {19107, 41406}, {19780, 42104}, {19781, 42105}, {22512, 42133}, {22513, 42134}, {22664, 39838}, {23698, 37517}, {26255, 39602}, {31173, 37690}, {31411, 42258}, {32837, 35022}, {32962, 43459}, {35606, 36181}, {39601, 41099}

X(43618) = reflection of X(2549) in X(7737)
X(43618) = reflection of X(43619) in X(6)
X(43618) = center of the Pythagorean hyperbola
X(43618) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 7747, 2548}, {381, 15655, 3054}, {3054, 15655, 21843}, {5585, 18584, 140}, {6560, 6561, 20423}, {6781, 43457, 8588}, {7737, 7739, 18907}, {7802, 14035, 7800}, {8588, 43457, 2}, {32827, 35927, 620}, {42085, 42086, 31670}

X(43619) = GIBERT (cot(ω)/sqrt(3), -1,1) POINT

Barycentrics    5*a^4 - 4*a^2*b^2 - 3*b^4 - 4*a^2*c^2 + 6*b^2*c^2 - 3*c^4 : :
X(43619) = 2 X[6] - 3 X[2549], 4 X[6] - 3 X[7737], 8 X[6] - 9 X[7739], 5 X[6] - 6 X[15048], 7 X[6] - 6 X[18907], 2 X[141] - 3 X[5077], 4 X[2549] - 3 X[7739], 5 X[2549] - 4 X[15048], 7 X[2549] - 4 X[18907], 4 X[3589] - 3 X[11159], 7 X[3619] - 6 X[3734], 7 X[3619] - 9 X[32986], 5 X[3620] - 6 X[7761], 5 X[3620] - 3 X[32815], 5 X[3620] - 9 X[33272], 2 X[3734] - 3 X[32986], 4 X[4045] - 3 X[14033], 2 X[7737] - 3 X[7739], 5 X[7737] - 8 X[15048], 7 X[7737] - 8 X[18907], 15 X[7739] - 16 X[15048], 21 X[7739] - 16 X[18907], 2 X[7761] - 3 X[33272], 4 X[7848] - 3 X[32836], 9 X[11287] - 8 X[34573], 7 X[15048] - 5 X[18907], X[32815] - 3 X[33272]

X(43619) lies on these lines: {2, 8589}, {3, 3054}, {4, 574}, {6, 30}, {20, 187}, {32, 3529}, {39, 3146}, {69, 543}, {76, 32997}, {83, 33280}, {99, 33017}, {111, 16063}, {115, 376}, {141, 5077}, {148, 14907}, {183, 8353}, {193, 3849}, {194, 19691}, {230, 3534}, {315, 33256}, {316, 33192}, {381, 3055}, {382, 2548}, {439, 7886}, {538, 20080}, {546, 15815}, {548, 5585}, {550, 5210}, {620, 16041}, {625, 34504}, {626, 33238}, {671, 8182}, {754, 11008}, {1078, 33253}, {1153, 41895}, {1285, 5355}, {1383, 20063}, {1384, 1657}, {1571, 31673}, {1572, 28150}, {1975, 19695}, {2028, 35914}, {2029, 35913}, {2482, 37690}, {2794, 39874}, {2996, 7780}, {3053, 15704}, {3090, 15515}, {3091, 37512}, {3098, 23698}, {3520, 9700}, {3522, 7746}, {3523, 39565}, {3528, 7749}, {3543, 5475}, {3589, 11159}, {3619, 3734}, {3620, 7761}, {3627, 5013}, {3788, 32982}, {3815, 3830}, {3832, 15602}, {3839, 7603}, {3845, 31489}, {3853, 31450}, {3926, 7842}, {3934, 32826}, {3972, 33193}, {4045, 14033}, {4293, 9664}, {4294, 9651}, {4302, 10987}, {5008, 5059}, {5023, 12103}, {5028, 14927}, {5058, 43408}, {5062, 43407}, {5073, 7745}, {5106, 37190}, {5107, 6776}, {5167, 35704}, {5206, 17538}, {5229, 31451}, {5283, 31295}, {5306, 15685}, {5309, 15683}, {5319, 17800}, {5334, 36995}, {5335, 36993}, {6337, 7825}, {6389, 35923}, {6421, 42271}, {6422, 42272}, {6655, 7795}, {6658, 7803}, {6680, 33239}, {6683, 32979}, {6722, 33216}, {6772, 11488}, {6775, 11489}, {6781, 7735}, {7502, 34866}, {7615, 35955}, {7618, 8352}, {7710, 39838}, {7712, 36181}, {7736, 15682}, {7738, 7747}, {7752, 33279}, {7763, 33019}, {7769, 32996}, {7771, 33207}, {7772, 11541}, {7777, 8597}, {7781, 32006}, {7782, 14063}, {7786, 14068}, {7790, 33007}, {7794, 32822}, {7800, 32819}, {7802, 14023}, {7806, 9855}, {7815, 33226}, {7816, 32974}, {7818, 32817}, {7820, 33190}, {7822, 33025}, {7828, 33244}, {7830, 33247}, {7831, 33263}, {7833, 11185}, {7834, 32981}, {7835, 33251}, {7844, 32985}, {7847, 14035}, {7848, 32836}, {7851, 33250}, {7852, 33201}, {7853, 33210}, {7857, 33254}, {7859, 14031}, {7861, 32973}, {7864, 19696}, {7872, 14001}, {7873, 32830}, {7874, 33200}, {7895, 32824}, {7897, 8591}, {7898, 20094}, {7913, 14039}, {7918, 14037}, {7919, 33255}, {7934, 33278}, {7940, 33290}, {8354, 15271}, {8375, 42258}, {8376, 42259}, {8553, 33532}, {8703, 37637}, {9597, 16784}, {9598, 10483}, {9600, 42284}, {9601, 13925}, {9607, 22246}, {9620, 28164}, {9674, 31412}, {9699, 37925}, {10303, 11614}, {10304, 39563}, {10313, 19220}, {10355, 32133}, {10645, 21156}, {10646, 21157}, {10723, 37182}, {10985, 18533}, {10986, 35471}, {11147, 22247}, {11173, 29181}, {11287, 34573}, {11295, 23303}, {11296, 23302}, {11318, 32459}, {12943, 31409}, {13192, 18911}, {14030, 16987}, {14537, 15640}, {14806, 18420}, {14962, 35687}, {15031, 33001}, {15075, 18563}, {15482, 32983}, {15484, 15684}, {15880, 31133}, {16589, 37435}, {17578, 31400}, {17579, 37675}, {17907, 40890}, {18362, 19708}, {18513, 31497}, {18546, 34229}, {18562, 22121}, {19925, 31422}, {23055, 36523}, {23253, 31481}, {24855, 31152}, {31404, 31652}, {31411, 35820}, {32457, 37667}, {32480, 40246}, {32832, 33260}, {33051, 36812}, {35606, 36163}, {41406, 42100}, {41407, 42099}

X(43619) =reflection of X(i) in X(j) for these {i,j}: {7737, 2549}, {32815, 7761}, {43618, 6}
X(43619) ={X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 574, 31415}, {20, 7748, 3767}, {20, 43448, 187}, {115, 376, 21843}, {148, 33264, 14907}, {187, 7748, 43448}, {187, 43448, 3767}, {550, 43291, 5210}, {574, 31415, 31401}, {2549, 7737, 7739}, {5210, 11742, 550}, {6560, 6561, 11179}, {6781, 11648, 7735}, {7735, 11001, 6781}, {7738, 33703, 7747}, {7898, 20094, 32833}, {8589, 18424, 2}, {17578, 31400, 39590}, {31400, 39590, 31417}, {32815, 33272, 7761}, {32819, 33234, 7800}, {32826, 33023, 3934}

X(43620) = GIBERT (-cot(ω)/sqrt(3), 1,1) POINT

Barycentrics    = a^4-2*(b^2+c^2)*a^2+3*(b^2-c^2)^2 : :
X(43620) = 2 X[5210] - 3 X[21843], X[5210] - 3 X[37637]

X(43620) lies on these lines: {2, 99}, {3, 3054}, {4, 187}, {5, 6}, {20, 7749}, {30, 5210}, {32, 3091}, {39, 3090}, {69, 625}, {76, 32961}, {83, 32962}, {98, 7694}, {125, 22111}, {141, 11318}, {182, 20398}, {183, 33228}, {193, 7775}, {230, 381}, {315, 32966}, {316, 17008}, {382, 15655}, {395, 22492}, {396, 22491}, {538, 1007}, {546, 3053}, {547, 15048}, {548, 11742}, {550, 5585}, {599, 8355}, {621, 11488}, {622, 11489}, {626, 3620}, {631, 7748}, {632, 15815}, {754, 32827}, {858, 20481}, {1015, 10589}, {1078, 14063}, {1285, 14537}, {1383, 7533}, {1479, 10987}, {1500, 10588}, {1506, 5056}, {1571, 3634}, {1572, 3817}, {1656, 3055}, {1975, 33249}, {1992, 8176}, {2023, 7697}, {2030, 3818}, {2079, 18570}, {2241, 10591}, {2242, 10590}, {2476, 37675}, {2963, 14791}, {2996, 7781}, {3070, 8376}, {3071, 8375}, {3089, 27371}, {3096, 33283}, {3146, 5206}, {3199, 6622}, {3231, 37988}, {3523, 7756}, {3524, 39563}, {3525, 11614}, {3529, 15513}, {3533, 15602}, {3543, 6781}, {3544, 5007}, {3545, 5008}, {3547, 10979}, {3618, 7817}, {3619, 3934}, {3627, 5023}, {3628, 5013}, {3630, 7776}, {3763, 8360}, {3785, 7825}, {3788, 32969}, {3815, 5055}, {3832, 7747}, {3849, 23055}, {3851, 7745}, {3855, 39590}, {3857, 22331}, {3926, 7862}, {3972, 33016}, {4257, 36659}, {4262, 36526}, {5025, 7800}, {5028, 40330}, {5058, 42561}, {5062, 31412}, {5066, 18907}, {5067, 7738}, {5068, 7755}, {5071, 5309}, {5072, 30435}, {5073, 15603}, {5077, 15597}, {5079, 9605}, {5094, 21448}, {5097, 14162}, {5104, 31670}, {5169, 11580}, {5218, 9664}, {5275, 17530}, {5277, 6871}, {5283, 6933}, {5304, 7753}, {5306, 15484}, {5318, 41040}, {5321, 41041}, {5354, 37353}, {5355, 37665}, {5471, 43404}, {5472, 43403}, {5477, 11180}, {5480, 11173}, {5485, 39785}, {5486, 42007}, {5569, 23053}, {5921, 38745}, {6103, 41370}, {6292, 33180}, {6337, 15301}, {6390, 34505}, {6392, 7764}, {6421, 42583}, {6422, 42582}, {6423, 42273}, {6424, 42270}, {6640, 15075}, {6643, 22052}, {6680, 32971}, {6683, 32975}, {6776, 11623}, {6787, 14113}, {6856, 16589}, {7173, 16502}, {7288, 9651}, {7486, 7765}, {7530, 8553}, {7610, 37350}, {7708, 18911}, {7741, 16784}, {7751, 20080}, {7752, 7758}, {7759, 11008}, {7761, 16041}, {7763, 32967}, {7769, 32998}, {7771, 33017}, {7772, 15022}, {7773, 14023}, {7774, 14568}, {7780, 32006}, {7782, 33000}, {7785, 33011}, {7786, 32999}, {7787, 33024}, {7793, 32993}, {7794, 32834}, {7795, 7887}, {7797, 33002}, {7801, 31275}, {7802, 32996}, {7803, 16921}, {7804, 32983}, {7806, 33013}, {7808, 32987}, {7815, 32838}, {7816, 32970}, {7818, 15589}, {7822, 32951}, {7828, 16924}, {7830, 32982}, {7831, 33251}, {7832, 33248}, {7833, 17006}, {7834, 32968}, {7841, 37688}, {7846, 33269}, {7847, 33001}, {7851, 32992}, {7852, 16045}, {7853, 33285}, {7855, 32823}, {7857, 14035}, {7861, 16043}, {7864, 16922}, {7865, 32885}, {7866, 34573}, {7867, 33199}, {7872, 32867}, {7874, 32955}, {7886, 14001}, {7888, 32830}, {7899, 33277}, {7904, 14045}, {7908, 32836}, {7911, 33290}, {7925, 32833}, {7932, 33020}, {7934, 16990}, {7935, 32870}, {7942, 16898}, {7951, 16785}, {8182, 8352}, {8721, 37446}, {8743, 35487}, {8744, 16868}, {8889, 33843}, {8972, 43134}, {8982, 23249}, {9112, 41121}, {9113, 41122}, {9600, 11313}, {9607, 31467}, {9620, 10175}, {9675, 23259}, {9699, 13595}, {9700, 37126}, {9734, 38734}, {9744, 14651}, {9754, 11676}, {9996, 15092}, {10172, 31441}, {10255, 22121}, {10303, 15515}, {10485, 11179}, {10593, 16781}, {10645, 22843}, {10646, 22890}, {11159, 20112}, {11305, 23302}, {11306, 23303}, {11314, 32790}, {11317, 37809}, {12963, 42268}, {12968, 42269}, {13860, 39663}, {13941, 43133}, {14041, 14907}, {14046, 16986}, {14148, 32837}, {14482, 39593}, {14538, 43276}, {14539, 43277}, {14901, 15081}, {15271, 33184}, {15993, 20423}, {16808, 41406}, {16809, 41407}, {16989, 33005}, {17131, 37668}, {18404, 18472}, {19780, 42106}, {19781, 42103}, {19872, 31421}, {22110, 40727}, {22510, 41098}, {22511, 41094}, {23291, 39913}, {25639, 31416}, {26316, 37348}, {28808, 34542}, {31239, 32956}, {31276, 32452}, {31406, 35018}, {31859, 37647}, {32456, 33216}, {32457, 34803}, {32819, 33233}, {32826, 32989}, {32897, 33025}, {32997, 43459}, {33042, 36812}, {36655, 42283}, {36656, 42284}

X(43620) = midpoint of X(32827) and X(37667)
X(43620) = reflection of X(21843) in X(37637)
X(43620) = X(i)-complementary conjugate of X(j) for these (i,j): {1973, 11165}, {21448, 18589}, {39238, 1214}
X(43620) = crossdifference of every pair of points on line {351, 924}
X(43620) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 115, 2549}, {2, 671, 7618}, {2, 7620, 2482}, {2, 32815, 620}, {2, 43448, 574}, {5, 6, 31415}, {5, 3767, 2548}, {5, 13881, 3767}, {5, 43291, 6}, {6, 13881, 43291}, {6, 31415, 2548}, {6, 43291, 3767}, {69, 32984, 625}, {115, 574, 43448}, {187, 18424, 4}, {187, 39565, 18424}, {230, 381, 7737}, {547, 15048, 31489}, {574, 43448, 2549}, {620, 18546, 32815}, {1656, 5024, 3055}, {1656, 5254, 31401}, {2548, 3767, 5319}, {2996, 32829, 7781}, {3055, 5024, 31401}, {3055, 5254, 5024}, {3545, 7735, 5475}, {3734, 6722, 2}, {3767, 31415, 6}, {3785, 32980, 7825}, {3926, 32988, 7862}, {5025, 32832, 7800}, {5056, 5286, 1506}, {5067, 7738, 31455}, {5071, 7736, 7603}, {5094, 21448, 24855}, {5309, 7603, 7736}, {5461, 7617, 2}, {5475, 39601, 3545}, {7738, 31455, 31450}, {7746, 18424, 187}, {7746, 39565, 4}, {7801, 31275, 37690}, {7857, 15031, 14035}, {8352, 8860, 8182}, {8355, 16509, 599}, {11542, 11543, 1353}, {13711, 42274, 6}, {13834, 42277, 6}, {14041, 17004, 14907}, {16041, 34229, 7761}, {17008, 33006, 316}, {18581, 18582, 1352}, {32828, 32972, 626}, {32838, 32974, 7815}, {33476, 33477, 7622}

X(43621) = GIBERT (-tan(ω)/sqrt(3), -1,1) POINT

Barycentrics    5*a^6 + 5*a^4*b^2 - 7*a^2*b^4 - 3*b^6 + 5*a^4*c^2 + 2*a^2*b^2*c^2 + 3*b^4*c^2 - 7*a^2*c^4 + 3*b^2*c^4 - 3*c^6 : :
X(43621) = 3 X[4] - 2 X[3098], 9 X[4] - 7 X[3619], 5 X[4] - 4 X[24206], 10 X[6] - 9 X[11179], 8 X[6] - 9 X[20423], 5 X[6] - 6 X[21850], 2 X[6] - 3 X[31670], 11 X[6] - 9 X[43273], 3 X[20] - 4 X[5092], 2 X[20] - 3 X[14561], 7 X[20] - 9 X[33750], 9 X[20] - 14 X[42785], X[69] - 3 X[15682], 2 X[141] - 3 X[3830], X[193] + 3 X[15640], 3 X[376] - 4 X[19130], 9 X[381] - 8 X[34573], 9 X[382] - 4 X[3631], 3 X[382] - X[33878], 4 X[546] - 3 X[31884], 2 X[576] + X[11541], 3 X[1350] - 4 X[18358], 9 X[1352] - 8 X[3631], 3 X[1352] - 2 X[33878], 3 X[1657] - 5 X[12017], 5 X[3091] - 4 X[14810], 15 X[3091] - 14 X[42786], 6 X[3098] - 7 X[3619], 5 X[3098] - 6 X[24206], 5 X[3146] - X[5921], 9 X[3146] - X[20080], 5 X[3522] - 6 X[38317], 3 X[3534] - 4 X[3589], 9 X[3543] - 5 X[3620], 3 X[3543] - 2 X[3818], 5 X[3618] - 3 X[11001], 35 X[3619] - 36 X[24206], 5 X[3620] - 6 X[3818], 3 X[3627] - 2 X[18358], 2 X[3630] - 9 X[15684], 2 X[3630] - 3 X[18440], 4 X[3631] - 3 X[33878], 5 X[3763] - 6 X[3845], 7 X[3851] - 6 X[21167], 4 X[3853] - 3 X[10516], X[5059] - 3 X[14853], 3 X[5085] - 2 X[15704], 8 X[5092] - 9 X[14561], 28 X[5092] - 27 X[33750], 6 X[5092] - 7 X[42785], 6 X[5480] - 5 X[12017], 9 X[5921] - 5 X[20080], 3 X[10519] - 5 X[17578], 4 X[11179] - 5 X[20423], 3 X[11179] - 4 X[21850], 3 X[11179] - 5 X[31670], 11 X[11179] - 10 X[43273], 4 X[12101] - 3 X[21358], 2 X[12103] - 3 X[38136], 7 X[14561] - 6 X[33750], 27 X[14561] - 28 X[42785], 6 X[14810] - 7 X[42786], 2 X[15681] - 3 X[38064], 3 X[15684] - X[18440], 2 X[15686] - 3 X[38072], 7 X[15698] - 8 X[25565], X[16496] - 3 X[41869], 6 X[17508] - 5 X[17538], 15 X[20423] - 16 X[21850], 3 X[20423] - 4 X[31670], 11 X[20423] - 8 X[43273], 4 X[21850] - 5 X[31670], 22 X[21850] - 15 X[43273], 11 X[31670] - 6 X[43273], 3 X[33703] + 2 X[37517], 3 X[33703] + X[39874], 81 X[33750] - 98 X[42785]

X(43621) lies on these lines: {4, 3096}, {6, 30}, {20, 5092}, {69, 13603}, {141, 3830}, {182, 3529}, {193, 11645}, {323, 31383}, {376, 19130}, {381, 34573}, {382, 1352}, {511, 3146}, {542, 11008}, {546, 31884}, {576, 11541}, {597, 15685}, {599, 33699}, {1350, 3627}, {1368, 31860}, {1370, 34417}, {1495, 7500}, {1503, 5073}, {1531, 28419}, {1657, 5480}, {2777, 36851}, {3091, 14810}, {3416, 33697}, {3522, 38317}, {3534, 3589}, {3543, 3620}, {3581, 18382}, {3618, 11001}, {3630, 15684}, {3763, 3845}, {3819, 7408}, {3851, 21167}, {3853, 10516}, {5059, 14853}, {5085, 15704}, {5476, 15683}, {5899, 35228}, {6776, 29323}, {7391, 15107}, {7394, 41462}, {7519, 10546}, {7553, 37483}, {7712, 20063}, {10519, 17578}, {10545, 16063}, {11430, 31305}, {11438, 34938}, {12101, 21358}, {12103, 38136}, {12244, 32273}, {12289, 29012}, {13346, 25712}, {14994, 32826}, {15066, 34603}, {15080, 20062}, {15681, 38064}, {15686, 38072}, {15698, 25565}, {16163, 28708}, {16496, 41869}, {16976, 41447}, {17508, 17538}, {18488, 37478}, {35246, 36712}, {35247, 36711}, {35481, 41470}, {35513, 41469}, {36474, 37508}, {41413, 43448}

X(43621) = midpoint of X(11541) and X(14927)
X(43621) = reflection of X(i) in X(j) for these {i,j}: {599, 33699}, {1350, 3627}, {1352, 382}, {1657, 5480}, {3416, 33697}, {3529, 182}, {12244, 32273}, {14927, 576}, {15683, 5476}, {15685, 597}, {39874, 37517}
X(43621) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11179, 31670, 21850}, {42085, 42086, 7737}

X(43622) = GIBERT (SQRT(3/2),1,2) POINT

Barycentrics    a^2*S/Sqrt[2] + 2*a^2*SA + 2*SB*SC : :

X(43622) lies on the cubic K1231 and these lines: {2, 6}, {3, 3373}, {5, 41976}, {140, 42783}, {549, 41980}, {632, 41975}, {1151, 14783}, {1152, 14782}, {3371, 10577}, {3385, 10576}, {3534, 42727}, {3628, 42784}, {3839, 42730}, {6451, 12822}, {14784, 42262}, {14785, 42265}, {15692, 42729}, {15699, 42648}, {15709, 42725}, {19709, 42728}, {42150, 42808}, {42151, 42807}

X(43622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {549, 42647, 41980}

X(43623) = GIBERT (-SQRT(3/2),1,2) POINT

Barycentrics    a^2*S/Sqrt[2] - 2*a^2*SA - 2*SB*SC : :

X(43623) lies on the cubic K1231 and these lines: {2, 6}, {3, 3374}, {5, 41975}, {140, 42784}, {549, 41979}, {632, 41976}, {1151, 14782}, {1152, 14783}, {3372, 10577}, {3386, 10576}, {3534, 42728}, {3628, 42783}, {3839, 42729}, {6452, 12823}, {14784, 42265}, {14785, 42262}, {15692, 42730}, {15699, 42647}, {15709, 42726}, {19709, 42727}, {42150, 42807}, {42151, 42808}

X(43623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {549, 42648, 41979}

X(43624) = GIBERT (SQRT(6),5,-4) POINT

Barycentrics    Sqrt[2]*a^2*S - 4*a^2*SA + 10*SB*SC : :

X(43624) lies on the cubic K1231 and these lines: {6, 33703}, {382, 42784}, {3529, 42645}, {3543, 42728}, {5073, 41980}, {5076, 41975}, {15681, 41976}, {15682, 42646}, {17578, 42729}, {17800, 42783}

X(43625) = GIBERT (SQRT(6),-5,4) POINT

Barycentrics    Sqrt[2]*a^2*S + 4*a^2*SA - 10*SB*SC : :

X(43625) lies on the cubic K1231 and these lines: 6, 33703}, {382, 42783}, {3529, 42646}, {3543, 42727}, {5073, 41979}, {5076, 41976}, {15681, 41975}, {15682, 42645}, {17578, 42730}, {17800, 42784} on K1231

X(43626) = GIBERT (2 SQRT(6),15,-3) POINT

Barycentrics    2*Sqrt[2]*a^2*S - 3*a^2*SA + 30*SB*SC : :

X(43626) lies on the cubic K1231 and these lines: {4, 42648}, {6, 3853}, {382, 42647}, {3843, 42729}, {12101, 41980}, {38335, 42726}

X(43627) = GIBERT (2 SQRT(6),-15,3) POINT

Barycentrics    2*Sqrt[2]*a^2*S + 3*a^2*SA - 30*SB*SC : :

X(43627) lies on the cubic K1231 and these lines: {4, 42647}, {6, 3853}, {382, 42648}, {3843, 42730}, {12101, 41979}, {38335, 42725}

X(43628) = GIBERT (2 SQRT(6),1,-3) POINT

Barycentrics    2*Sqrt[2]*a^2*S - 3*a^2*SA + 2*SB*SC : :

X(43628) lies on the cubic K1231 and these lines: {4, 42648}, {5, 41975}, {6, 550}, {140, 42647}, {549, 42783}, {1657, 42729}, {3316, 14782}, {3317, 14783}, {3372, 42216}, {3386, 42215}, {3627, 42784}, {11488, 42807}, {11489, 42808}, {15684, 42726}, {15693, 42725}, {15704, 41979}, {15712, 41976}

X(43628) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {41975, 41980, 42645}, {41975, 42645, 5}

X(43629) = GIBERT (2 SQRT(6),-1,3) POINT

Barycentrics    2*sqrt(2)*a^2*S+3*SA*a^2-2*SB*SC : :
X(43629) = 2*Sqrt[2]*a^2*S + 3*a^2*SA - 2*SB*SC : :

X(43629) lies on the cubic K1231 and these lines: {4, 42647}, {5, 41976}, {6, 550}, {140, 42648}, {549, 42784}, {1657, 42730}, {3316, 14783}, {3317, 14782}, {3371, 42216}, {3385, 42215}, {3627, 42783}, {11488, 42808}, {11489, 42807}, {15684, 42725}, {15693, 42726}, {15704, 41980}, {15712, 41975}

X(43629) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {41976, 41979, 42646}, {41976, 42646, 5}

leftri

Points on the Pythagorean conic: X(43630)-X(43649)

rightri

This preamble is contributed by Peter Moses, June 7, 2021.

As introduced by Bernard Gibert in K1231, the Pythagorean conic is the set of KHO points (x,y,z) that satisfy z2 = x2 + y2 but not x*y*z = 0. If (x,y,z) is such a point, then so are these seven points:

(-x,y,z),      (x,-y,z),      (x,y,-z),      (y,x,z),     (-y,x,z),      (y,-x,z),     (y,x,-z).

Thus, if (u,v,w) is a Pythagorean triple of integers, then then the Gibert (u,v,w) point lies on the Pythagorean conic.



X(43630) = GIBERT (4,-3,5) POINT

Barycentrics    4*a^2*S/Sqrt[3] + 5*a^2*SA - 6*SB*SC : :
X(43630) = 3 X[5335] - 5 X[11485], 11 X[5335] - 15 X[37640], X[5335] - 5 X[42119], 7 X[5335] - 5 X[42127], X[5335] + 5 X[42130], 9 X[5335] - 5 X[42141], 47 X[5335] - 75 X[42516], 2 X[5335] - 3 X[42633], 13 X[5335] - 15 X[42974], 11 X[11485] - 9 X[37640], X[11485] - 3 X[42119], 7 X[11485] - 3 X[42127], X[11485] + 3 X[42130], 3 X[11485] - X[42141], 47 X[11485] - 45 X[42516], 10 X[11485] - 9 X[42633], 13 X[11485] - 9 X[42974], 3 X[37640] - 11 X[42119], 21 X[37640] - 11 X[42127], 3 X[37640] + 11 X[42130], 27 X[37640] - 11 X[42141], 47 X[37640] - 55 X[42516], 10 X[37640] - 11 X[42633], 13 X[37640] - 11 X[42974], 7 X[42119] - X[42127], 9 X[42119] - X[42141], 47 X[42119] - 15 X[42516], 10 X[42119] - 3 X[42633], 13 X[42119] - 3 X[42974], X[42127] + 7 X[42130], 9 X[42127] - 7 X[42141], 47 X[42127] - 105 X[42516], 10 X[42127] - 21 X[42633], 13 X[42127] - 21 X[42974], 9 X[42130] + X[42141], 47 X[42130] + 15 X[42516], 10 X[42130] + 3 X[42633], 13 X[42130] + 3 X[42974], 47 X[42141] - 135 X[42516], 10 X[42141] - 27 X[42633], 13 X[42141] - 27 X[42974], 50 X[42516] - 47 X[42633], 65 X[42516] - 47 X[42974], 13 X[42633] - 10 X[42974]

X(43630) lies on the Pythagorean conic and these lines: {3, 42628}, {4, 42627}, {5, 11480}, {6, 15704}, {15, 3627}, {16, 398}, {30, 5335}, {61, 42145}, {140, 5365}, {376, 42983}, {381, 42888}, {395, 43245}, {396, 35404}, {546, 42116}, {548, 5334}, {549, 5321}, {632, 10645}, {3146, 42986}, {3411, 42685}, {3412, 5318}, {3522, 42816}, {3525, 42963}, {3528, 42818}, {3529, 43243}, {3530, 42125}, {3534, 42634}, {3543, 42817}, {3544, 43474}, {3628, 42133}, {3830, 43364}, {3845, 19107}, {3853, 11488}, {3857, 5238}, {3858, 23302}, {3860, 42472}, {3861, 42132}, {5079, 43365}, {5343, 42688}, {5349, 33417}, {5350, 42903}, {5352, 42107}, {8703, 11543}, {10646, 42917}, {10653, 43108}, {10654, 15686}, {11486, 12103}, {11489, 33923}, {11539, 42095}, {11541, 42982}, {11542, 42096}, {11812, 43002}, {12100, 42129}, {12102, 42142}, {12817, 42500}, {14869, 42143}, {14891, 43404}, {15681, 42415}, {15682, 42496}, {15687, 18582}, {15688, 42497}, {15690, 42975}, {15691, 37641}, {15699, 36970}, {15701, 43541}, {15711, 42529}, {15712, 18581}, {15714, 16645}, {15759, 42589}, {16268, 42686}, {16809, 42906}, {16964, 42121}, {16966, 38071}, {17504, 42089}, {19710, 41100}, {22236, 42112}, {23303, 42434}, {33699, 41119}, {33703, 42815}, {34754, 42109}, {35738, 42218}, {36836, 42104}, {36968, 43331}, {41101, 43500}, {41981, 42989}, {41984, 43202}, {41991, 42114}, {42086, 42925}, {42097, 43327}, {42099, 42118}, {42115, 43307}, {42153, 43253}, {42159, 43102}, {42191, 42225}, {42193, 42226}, {42430, 43228}, {42509, 43109}, {42510, 43110}, {42580, 42901}, {42590, 43296}, {42682, 42918}, {42683, 42992}, {42687, 42915}, {42692, 42929}, {42781, 43401}, {42902, 42954}, {43111, 43305}, {43306, 43487}

X(43630) = midpoint of X(42119) and X(42130)
X(43630) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 42585, 15704}, {15, 42108, 42138}, {15, 42138, 42916}, {15, 42144, 3627}, {16, 42117, 42923}, {16, 42157, 43105}, {16, 43105, 42117}, {61, 42145, 42922}, {550, 42923, 16}, {3627, 42916, 42138}, {5349, 42684, 33417}, {5352, 42630, 42107}, {10645, 42135, 632}, {10645, 42164, 42135}, {11480, 42085, 42136}, {11480, 42103, 43103}, {11480, 42136, 5}, {11543, 42090, 8703}, {12102, 43197, 42142}, {14869, 42143, 42493}, {19107, 42124, 3845}, {19107, 42942, 42124}, {22236, 42112, 42137}, {33703, 42815, 42889}, {36836, 42104, 42146}, {42085, 42122, 5}, {42085, 43194, 42122}, {42087, 42117, 550}, {42087, 42157, 42117}, {42087, 43105, 16}, {42090, 42154, 11543}, {42096, 42150, 11542}, {42099, 42147, 42118}, {42103, 43103, 5}, {42108, 42138, 3627}, {42116, 42140, 546}, {42122, 42136, 11480}, {42136, 43103, 42103}, {42138, 42144, 42108}, {42626, 43417, 17504}

X(43631) = GIBERT (4,3,-5) POINT

Barycentrics    4*a^2*S/Sqrt[3] - 5*a^2*SA + 6*SB*SC : :

X(43631) = 3 X[5334] - 5 X[11486], 11 X[5334] - 15 X[37641], X[5334] - 5 X[42120], 7 X[5334] - 5 X[42126], X[5334] + 5 X[42131], 9 X[5334] - 5 X[42140], 47 X[5334] - 75 X[42517], 2 X[5334] - 3 X[42634], 13 X[5334] - 15 X[42975], 11 X[11486] - 9 X[37641], X[11486] - 3 X[42120], 7 X[11486] - 3 X[42126], X[11486] + 3 X[42131], 3 X[11486] - X[42140], 47 X[11486] - 45 X[42517], 10 X[11486] - 9 X[42634], 13 X[11486] - 9 X[42975], 3 X[37641] - 11 X[42120], 21 X[37641] - 11 X[42126], 3 X[37641] + 11 X[42131], 27 X[37641] - 11 X[42140], 47 X[37641] - 55 X[42517], 10 X[37641] - 11 X[42634], 13 X[37641] - 11 X[42975], 7 X[42120] - X[42126], 9 X[42120] - X[42140], 47 X[42120] - 15 X[42517], 10 X[42120] - 3 X[42634], 13 X[42120] - 3 X[42975], X[42126] + 7 X[42131], 9 X[42126] - 7 X[42140], 47 X[42126] - 105 X[42517], 10 X[42126] - 21 X[42634], 13 X[42126] - 21 X[42975], 9 X[42131] + X[42140], 47 X[42131] + 15 X[42517], 10 X[42131] + 3 X[42634], 13 X[42131] + 3 X[42975], 47 X[42140] - 135 X[42517], 10 X[42140] - 27 X[42634], 13 X[42140] - 27 X[42975], 50 X[42517] - 47 X[42634], 65 X[42517] - 47 X[42975], 13 X[42634] - 10 X[42975]

X(43631) lies on the Pythagorean conic and these lines: {3, 42627}, {4, 42628}, {5, 11481}, {6, 15704}, {15, 397}, {16, 3627}, {30, 5334}, {62, 42144}, {140, 5366}, {376, 42982}, {381, 42889}, {395, 35404}, {396, 43244}, {546, 42115}, {548, 5335}, {549, 5318}, {632, 10646}, {3146, 42987}, {3411, 5321}, {3412, 42684}, {3522, 42815}, {3525, 42962}, {3528, 42817}, {3529, 43242}, {3530, 42128}, {3534, 42633}, {3543, 42818}, {3544, 43473}, {3628, 42134}, {3830, 43365}, {3845, 19106}, {3853, 11489}, {3857, 5237}, {3858, 23303}, {3860, 42473}, {3861, 42129}, {5079, 43364}, {5344, 42689}, {5349, 42902}, {5350, 33416}, {5351, 42110}, {8703, 11542}, {10645, 42916}, {10653, 15686}, {10654, 43109}, {11485, 12103}, {11488, 33923}, {11539, 42098}, {11541, 42983}, {11543, 42097}, {11812, 43003}, {12100, 42132}, {12102, 42139}, {12816, 42501}, {14869, 42146}, {14891, 43403}, {15681, 42416}, {15682, 42497}, {15687, 18581}, {15688, 42496}, {15690, 42974}, {15691, 37640}, {15699, 36969}, {15701, 43540}, {15711, 42528}, {15712, 18582}, {15714, 16644}, {15759, 42588}, {16267, 42687}, {16808, 42907}, {16965, 42124}, {16967, 38071}, {17504, 42092}, {19710, 41101}, {22238, 42113}, {23302, 42433}, {33699, 41120}, {33703, 42816}, {34755, 42108}, {35738, 42219}, {36843, 42105}, {36967, 43330}, {40694, 43253}, {41100, 43499}, {41981, 42988}, {41984, 43201}, {41991, 42111}, {42085, 42924}, {42096, 43326}, {42100, 42117}, {42116, 43306}, {42162, 43103}, {42192, 42225}, {42194, 42226}, {42429, 43229}, {42508, 43108}, {42511, 43111}, {42581, 42900}, {42591, 43297}, {42682, 42993}, {42683, 42919}, {42686, 42914}, {42693, 42928}, {42782, 43402}, {42903, 42955}, {43110, 43304}, {43307, 43488}

X(43631) = midpoint of X(42120) and X(42131)
X(43631) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 42584, 15704}, {15, 42118, 42922}, {15, 42158, 43106}, {15, 43106, 42118}, {16, 42109, 42135}, {16, 42135, 42917}, {16, 42145, 3627}, {62, 42144, 42923}, {550, 42922, 15}, {3627, 42917, 42135}, {5350, 42685, 33416}, {5351, 42629, 42110}, {10646, 42138, 632}, {10646, 42165, 42138}, {11481, 42086, 42137}, {11481, 42106, 43102}, {11481, 42137, 5}, {11542, 42091, 8703}, {12102, 43198, 42139}, {14869, 42146, 42492}, {19106, 42121, 3845}, {19106, 42943, 42121}, {22238, 42113, 42136}, {33703, 42816, 42888}, {36843, 42105, 42143}, {42086, 42123, 5}, {42086, 43193, 42123}, {42088, 42118, 550}, {42088, 42158, 42118}, {42088, 43106, 15}, {42091, 42155, 11542}, {42097, 42151, 11543}, {42100, 42148, 42117}, {42106, 43102, 5}, {42109, 42135, 3627}, {42115, 42141, 546}, {42123, 42137, 11481}, {42135, 42145, 42109}, {42137, 43102, 42106}, {42625, 43416, 17504}

X(43632) = GIBERT (3,-4,5) POINT

Barycentrics    Sqrt[3]*a^2*S + 5*a^2*SA - 8*SB*SC : :
X(43632) = 5 X[61] - 4 X[397], 3 X[61] - 2 X[16965], 5 X[61] - 6 X[41101], 4 X[61] - 3 X[41107], 3 X[61] - 4 X[42147], 7 X[61] - 4 X[42165], 31 X[61] - 30 X[42520], 7 X[61] - 8 X[42925], 17 X[61] - 24 X[43108], 13 X[61] - 12 X[43228], 6 X[397] - 5 X[16965], 2 X[397] - 3 X[41101], 16 X[397] - 15 X[41107], 3 X[397] - 5 X[42147], 2 X[397] - 5 X[42157], 7 X[397] - 5 X[42165], 8 X[397] - 5 X[42431], 62 X[397] - 75 X[42520], 7 X[397] - 10 X[42925], 17 X[397] - 30 X[43108], 13 X[397] - 15 X[43228], 5 X[16965] - 9 X[41101], 8 X[16965] - 9 X[41107], X[16965] - 3 X[42157], 7 X[16965] - 6 X[42165], 4 X[16965] - 3 X[42431], 31 X[16965] - 45 X[42520], 7 X[16965] - 12 X[42925], 17 X[16965] - 36 X[43108], 13 X[16965] - 18 X[43228], 8 X[41101] - 5 X[41107], 9 X[41101] - 10 X[42147], 3 X[41101] - 5 X[42157], 21 X[41101] - 10 X[42165], 12 X[41101] - 5 X[42431], 31 X[41101] - 25 X[42520], 21 X[41101] - 20 X[42925], 17 X[41101] - 20 X[43108], 13 X[41101] - 10 X[43228], 9 X[41107] - 16 X[42147], 3 X[41107] - 8 X[42157], 21 X[41107] - 16 X[42165], 3 X[41107] - 2 X[42431], 31 X[41107] - 40 X[42520], 21 X[41107] - 32 X[42925], 17 X[41107] - 32 X[43108], 13 X[41107] - 16 X[43228], 2 X[42147] - 3 X[42157], 7 X[42147] - 3 X[42165], 8 X[42147] - 3 X[42431], 62 X[42147] - 45 X[42520], 7 X[42147] - 6 X[42925], 17 X[42147] - 18 X[43108], 13 X[42147] - 9 X[43228], 7 X[42157] - 2 X[42165], 4 X[42157] - X[42431], 31 X[42157] - 15 X[42520], 7 X[42157] - 4 X[42925], 17 X[42157] - 12 X[43108], 13 X[42157] - 6 X[43228], 8 X[42165] - 7 X[42431], 62 X[42165] - 105 X[42520], 17 X[42165] - 42 X[43108], 13 X[42165] - 21 X[43228], 31 X[42431] - 60 X[42520], 7 X[42431] - 16 X[42925], 17 X[42431] - 48 X[43108], 13 X[42431] - 24 X[43228], 105 X[42520] - 124 X[42925], 85 X[42520] - 124 X[43108], 65 X[42520] - 62 X[43228], 17 X[42925] - 21 X[43108], 26 X[42925] - 21 X[43228], 26 X[43108] - 17 X[43228]

X(43632) lies on the Pythagorean conic and these lines: {3, 36970}, {4, 5238}, {5, 10645}, {6, 17800}, {13, 3146}, {14, 550}, {15, 382}, {16, 20}, {17, 3627}, {18, 376}, {30, 61}, {62, 1657}, {140, 42529}, {185, 36981}, {381, 5352}, {395, 12103}, {398, 15704}, {546, 16241}, {548, 5321}, {549, 5349}, {590, 42238}, {615, 42236}, {631, 16809}, {1656, 42626}, {2041, 22644}, {2042, 22615}, {3200, 13346}, {3205, 37495}, {3364, 42264}, {3365, 42263}, {3366, 42172}, {3367, 42171}, {3389, 42266}, {3390, 42267}, {3412, 5318}, {3522, 16242}, {3523, 42580}, {3524, 12817}, {3526, 42093}, {3528, 18581}, {3529, 10654}, {3530, 16967}, {3534, 5237}, {3543, 41121}, {3830, 36836}, {3832, 16966}, {3843, 11480}, {3845, 42581}, {3851, 42610}, {3853, 16772}, {3855, 42092}, {3857, 42795}, {3860, 42590}, {3861, 23302}, {5059, 10653}, {5067, 42103}, {5070, 42918}, {5073, 22236}, {5076, 16644}, {5079, 42773}, {5340, 43018}, {5344, 15640}, {5350, 42912}, {5365, 10304}, {6777, 13172}, {7005, 10483}, {7486, 42596}, {7748, 41407}, {8703, 42163}, {8918, 15743}, {9736, 16628}, {10187, 42501}, {10299, 42910}, {10646, 15696}, {11001, 42151}, {11541, 37640}, {12102, 43024}, {12108, 43101}, {12811, 42949}, {12812, 42500}, {12816, 35404}, {14093, 42774}, {14269, 42947}, {14893, 42791}, {15681, 22238}, {15682, 16962}, {15683, 41100}, {15684, 16267}, {15686, 16963}, {15687, 42598}, {15688, 41122}, {15689, 41944}, {15715, 43202}, {15717, 33416}, {16239, 42107}, {16630, 30560}, {16631, 35229}, {16960, 42105}, {17504, 42948}, {17538, 42149}, {17578, 18582}, {19106, 33703}, {19708, 42495}, {21734, 42089}, {33387, 35304}, {33923, 42599}, {34584, 36208}, {35402, 42952}, {36843, 42993}, {36962, 41055}, {36993, 36994}, {38071, 42798}, {41974, 42995}, {41978, 43475}, {42086, 42990}, {42100, 42117}, {42102, 42695}, {42109, 43306}, {42113, 43009}, {42115, 42938}, {42118, 43105}, {42124, 43226}, {42125, 42491}, {42143, 42682}, {42155, 42799}, {42161, 43418}, {42506, 43022}, {42530, 43292}, {42544, 43229}, {42625, 42989}, {42692, 43102}, {42693, 42916}, {42779, 43232}, {42892, 43403}, {42897, 42923}, {42917, 43253}, {42928, 42970}, {42929, 43472}, {42944, 43417}, {42973, 42976}, {42980, 43479}, {43030, 43465}, {43293, 43294}, {43404, 43547}

X(43632) = reflection of X(i) in X(j) for these {i,j}: {61, 42157}, {16965, 42147}, {42165, 42925}, {42431, 61}

X(43632) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 42432, 36970}, {3, 42814, 42489}, {4, 5238, 37832}, {4, 36967, 5238}, {5, 42087, 42434}, {5, 42434, 10645}, {6, 17800, 43633}, {14, 550, 5351}, {15, 382, 42813}, {15, 42156, 42939}, {18, 42160, 42972}, {20, 16964, 16}, {20, 40694, 42433}, {20, 42085, 16964}, {61, 42431, 41107}, {62, 42154, 41973}, {376, 42160, 18}, {381, 5352, 42936}, {382, 42130, 43194}, {382, 43194, 15}, {397, 41101, 61}, {398, 15704, 36968}, {550, 42164, 14}, {1657, 42154, 62}, {3146, 42150, 13}, {3411, 16964, 5334}, {3522, 42159, 16242}, {3529, 10654, 42158}, {3534, 5339, 5237}, {3627, 42942, 17}, {3843, 11480, 42488}, {3843, 42488, 42919}, {3845, 42945, 42581}, {3853, 16772, 16808}, {3853, 42122, 16772}, {5073, 22236, 36969}, {5237, 5339, 16268}, {15696, 42126, 42153}, {15696, 42153, 10646}, {16268, 42964, 5339}, {16772, 42108, 3853}, {16964, 42099, 20}, {16964, 42433, 40694}, {16965, 42147, 61}, {16965, 42157, 42147}, {17538, 42149, 42528}, {19106, 42119, 34754}, {19107, 33417, 42101}, {19107, 42087, 10645}, {19107, 42434, 5}, {22236, 36969, 42992}, {22238, 41108, 42780}, {33703, 40693, 19106}, {33703, 42119, 40693}, {33703, 42890, 34754}, {36970, 42489, 42814}, {37832, 43331, 36967}, {40693, 42112, 33703}, {40694, 42433, 16}, {42085, 42091, 43466}, {42085, 42099, 16}, {42087, 42144, 19107}, {42090, 42140, 16809}, {42096, 42130, 15}, {42096, 43194, 382}, {42100, 42991, 42148}, {42100, 43008, 42891}, {42108, 42122, 16808}, {42112, 42119, 19106}, {42117, 42148, 42991}, {42158, 42430, 3529}, {42632, 42936, 5352}, {42813, 42939, 42156}, {42891, 42991, 43008}, {42891, 43008, 42148}

X(43633) = GIBERT (3,4,-5) POINT

Barycentrics    Sqrt[3]*a^2*S - 5*a^2*SA + 8*SB*SC : :
X(43633) = 5 X[62] - 4 X[398], 3 X[62] - 2 X[16964], 5 X[62] - 6 X[41100], 4 X[62] - 3 X[41108], 3 X[62] - 4 X[42148], 7 X[62] - 4 X[42164], 31 X[62] - 30 X[42521], 7 X[62] - 8 X[42924], 17 X[62] - 24 X[43109], 13 X[62] - 12 X[43229], 6 X[398] - 5 X[16964], 2 X[398] - 3 X[41100], 16 X[398] - 15 X[41108], 3 X[398] - 5 X[42148], 2 X[398] - 5 X[42158], 7 X[398] - 5 X[42164], 8 X[398] - 5 X[42432], 62 X[398] - 75 X[42521], 7 X[398] - 10 X[42924], 17 X[398] - 30 X[43109], 13 X[398] - 15 X[43229], 5 X[16964] - 9 X[41100], 8 X[16964] - 9 X[41108], X[16964] - 3 X[42158], 7 X[16964] - 6 X[42164], 4 X[16964] - 3 X[42432], 31 X[16964] - 45 X[42521], 7 X[16964] - 12 X[42924], 17 X[16964] - 36 X[43109], 13 X[16964] - 18 X[43229], 8 X[41100] - 5 X[41108], 9 X[41100] - 10 X[42148], 3 X[41100] - 5 X[42158], 21 X[41100] - 10 X[42164], 12 X[41100] - 5 X[42432], 31 X[41100] - 25 X[42521], 21 X[41100] - 20 X[42924], 17 X[41100] - 20 X[43109], 13 X[41100] - 10 X[43229], 9 X[41108] - 16 X[42148], 3 X[41108] - 8 X[42158], 21 X[41108] - 16 X[42164], 3 X[41108] - 2 X[42432], 31 X[41108] - 40 X[42521], 21 X[41108] - 32 X[42924], 17 X[41108] - 32 X[43109], 13 X[41108] - 16 X[43229], 2 X[42148] - 3 X[42158], 7 X[42148] - 3 X[42164], 8 X[42148] - 3 X[42432], 62 X[42148] - 45 X[42521], 7 X[42148] - 6 X[42924], 17 X[42148] - 18 X[43109], 13 X[42148] - 9 X[43229], 7 X[42158] - 2 X[42164], 4 X[42158] - X[42432], 31 X[42158] - 15 X[42521], 7 X[42158] - 4 X[42924], 17 X[42158] - 12 X[43109], 13 X[42158] - 6 X[43229], 8 X[42164] - 7 X[42432], 62 X[42164] - 105 X[42521], 17 X[42164] - 42 X[43109], 13 X[42164] - 21 X[43229], 31 X[42432] - 60 X[42521], 7 X[42432] - 16 X[42924], 17 X[42432] - 48 X[43109], 13 X[42432] - 24 X[43229], 105 X[42521] - 124 X[42924], 85 X[42521] - 124 X[43109], 65 X[42521] - 62 X[43229], 17 X[42924] - 21 X[43109], 26 X[42924] - 21 X[43229], 26 X[43109] - 17 X[43229]

X(43633) lies on the Pythagorean conic and these lines: {3, 36969}, {4, 5237}, {5, 10646}, {6, 17800}, {13, 550}, {14, 3146}, {15, 20}, {16, 382}, {17, 376}, {18, 3627}, {30, 62}, {61, 1657}, {140, 42528}, {185, 36979}, {381, 5351}, {396, 12103}, {397, 15704}, {546, 16242}, {548, 5318}, {549, 5350}, {590, 42237}, {615, 35739}, {631, 16808}, {1656, 42625}, {2041, 22615}, {2042, 22644}, {3201, 13346}, {3206, 37495}, {3364, 42266}, {3365, 42267}, {3389, 42264}, {3390, 42263}, {3391, 42174}, {3392, 42173}, {3411, 5321}, {3522, 16241}, {3523, 42581}, {3524, 12816}, {3526, 42094}, {3528, 18582}, {3529, 10653}, {3530, 16966}, {3534, 5238}, {3543, 41122}, {3830, 36843}, {3832, 16967}, {3843, 11481}, {3845, 42580}, {3851, 42611}, {3853, 16773}, {3855, 42089}, {3857, 42796}, {3860, 42591}, {3861, 23303}, {5059, 10654}, {5067, 42106}, {5070, 42919}, {5073, 22238}, {5076, 16645}, {5079, 42774}, {5339, 43019}, {5343, 15640}, {5349, 42913}, {5366, 10304}, {6778, 13172}, {7006, 10483}, {7486, 42597}, {7748, 41406}, {8703, 42166}, {8919, 11586}, {9735, 16629}, {10188, 42500}, {10299, 42911}, {10645, 15696}, {11001, 42150}, {11541, 37641}, {12102, 43025}, {12108, 43104}, {12811, 42948}, {12812, 42501}, {12817, 35404}, {14093, 42773}, {14269, 42946}, {14893, 42792}, {15681, 22236}, {15682, 16963}, {15683, 41101}, {15684, 16268}, {15686, 16962}, {15687, 42599}, {15688, 41121}, {15689, 41943}, {15715, 43201}, {15717, 33417}, {16239, 42110}, {16630, 35230}, {16631, 30559}, {16961, 42104}, {17504, 42949}, {17538, 42152}, {17578, 18581}, {19107, 33703}, {19708, 42494}, {21734, 42092}, {33386, 35303}, {33923, 42598}, {34584, 36209}, {35402, 42953}, {36836, 42992}, {36961, 41054}, {36992, 36995}, {38071, 42797}, {41973, 42994}, {41977, 43476}, {42085, 42991}, {42099, 42118}, {42101, 42694}, {42108, 43307}, {42112, 43008}, {42116, 42939}, {42117, 43106}, {42121, 43227}, {42128, 42490}, {42146, 42683}, {42154, 42800}, {42160, 43419}, {42507, 43023}, {42531, 43293}, {42543, 43228}, {42626, 42988}, {42692, 42917}, {42693, 43103}, {42780, 43233}, {42893, 43404}, {42896, 42922}, {42928, 43471}, {42929, 42971}, {42945, 43416}, {42972, 42977}, {42981, 43480}, {43031, 43466}, {43292, 43295}, {43403, 43546}
reflection of X(i) in X(j) for these {i,j}: {62, 42158}, {16964, 42148}, {42164, 42924}, {42432, 62}

X(43633) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 42431, 36969}, {3, 42813, 42488}, {4, 5237, 37835}, {4, 36968, 5237}, {5, 42088, 42433}, {5, 42433, 10646}, {6, 17800, 43632}, {13, 550, 5352}, {16, 382, 42814}, {16, 42153, 42938}, {17, 42161, 42973}, {20, 16965, 15}, {20, 40693, 42434}, {20, 42086, 16965}, {61, 42155, 41974}, {62, 42432, 41108}, {376, 42161, 17}, {381, 5351, 42937}, {382, 42131, 43193}, {382, 43193, 16}, {397, 15704, 36967}, {398, 41100, 62}, {550, 42165, 13}, {1657, 42155, 61}, {3146, 42151, 14}, {3412, 16965, 5335}, {3522, 42162, 16241}, {3529, 10653, 42157}, {3534, 5340, 5238}, {3627, 42943, 18}, {3843, 11481, 42489}, {3843, 42489, 42918}, {3845, 42944, 42580}, {3853, 16773, 16809}, {3853, 42123, 16773}, {5073, 22238, 36970}, {5238, 5340, 16267}, {15696, 42127, 42156}, {15696, 42156, 10645}, {16267, 42965, 5340}, {16773, 42109, 3853}, {16964, 42148, 62}, {16964, 42158, 42148}, {16965, 42100, 20}, {16965, 42434, 40693}, {17538, 42152, 42529}, {19106, 33416, 42102}, {19106, 42088, 10646}, {19106, 42433, 5}, {19107, 42120, 34755}, {22236, 41107, 42779}, {22238, 36970, 42993}, {33703, 40694, 19107}, {33703, 42120, 40694}, {33703, 42891, 34755}, {36969, 42488, 42813}, {37835, 43330, 36968}, {40693, 42434, 15}, {40694, 42113, 33703}, {42086, 42090, 43465}, {42086, 42100, 15}, {42088, 42145, 19106}, {42091, 42141, 16808}, {42097, 42131, 16}, {42097, 43193, 382}, {42099, 42990, 42147}, {42099, 43009, 42890}, {42109, 42123, 16809}, {42113, 42120, 19107}, {42118, 42147, 42990}, {42157, 42429, 3529}, {42631, 42937, 5351}, {42814, 42938, 42153}, {42890, 42990, 43009}, {42890, 43009, 42147}

X(43634) = GIBERT (12,-5,13) POINT

Barycentrics    4*Sqrt[3]*a^2*S + 13*a^2*SA - 10*SB*SC : :
X(43634) = 5 X[5340] - 13 X[22236], 9 X[5340] - 13 X[40693], 35 X[5340] - 39 X[41112], X[5340] - 13 X[42150], 17 X[5340] - 13 X[42161], 11 X[5340] - 39 X[42511], 41 X[5340] + 39 X[42587], 3 X[5340] + 13 X[43194], 55 X[5340] - 78 X[43207], 9 X[22236] - 5 X[40693], 7 X[22236] - 3 X[41112], X[22236] - 5 X[42150], 17 X[22236] - 5 X[42161], 11 X[22236] - 15 X[42511], 41 X[22236] + 15 X[42587], 3 X[22236] + 5 X[43194], 11 X[22236] - 6 X[43207], 35 X[40693] - 27 X[41112], X[40693] - 9 X[42150], 17 X[40693] - 9 X[42161], 11 X[40693] - 27 X[42511], 41 X[40693] + 27 X[42587], X[40693] + 3 X[43194], 55 X[40693] - 54 X[43207], 3 X[41112] - 35 X[42150], 51 X[41112] - 35 X[42161], 11 X[41112] - 35 X[42511], 41 X[41112] + 35 X[42587], 9 X[41112] + 35 X[43194], 11 X[41112] - 14 X[43207], 17 X[42150] - X[42161], 11 X[42150] - 3 X[42511], 41 X[42150] + 3 X[42587], 3 X[42150] + X[43194], 55 X[42150] - 6 X[43207], 11 X[42161] - 51 X[42511], 41 X[42161] + 51 X[42587], 3 X[42161] + 17 X[43194], 55 X[42161] - 102 X[43207], 41 X[42511] + 11 X[42587], 9 X[42511] + 11 X[43194], 5 X[42511] - 2 X[43207], 9 X[42587] - 41 X[43194], 55 X[42587] + 82 X[43207], 55 X[43194] + 18 X[43207]

X(43634) lies on the Pythagorean conic and these lines: {2, 42927}, {3, 42497}, {5, 42116}, {15, 3853}, {16, 548}, {17, 12101}, {30, 5340}, {61, 43244}, {62, 15690}, {140, 5352}, {381, 43479}, {397, 42429}, {398, 34200}, {546, 16772}, {547, 5238}, {631, 43253}, {3090, 42932}, {3412, 42137}, {3528, 42415}, {3529, 42633}, {3530, 42089}, {3627, 43403}, {3628, 42154}, {3843, 42888}, {3850, 36836}, {3855, 43474}, {3856, 42124}, {3859, 42136}, {3861, 42085}, {5066, 42164}, {5070, 43466}, {5321, 43241}, {5339, 12108}, {5343, 11539}, {5349, 43245}, {5351, 41982}, {10124, 42159}, {10303, 42985}, {10654, 33923}, {11480, 16239}, {11540, 42773}, {11737, 43238}, {12102, 42152}, {12103, 36967}, {12812, 42945}, {14893, 42432}, {15691, 41101}, {15700, 22237}, {15759, 42149}, {16965, 42585}, {17538, 43496}, {19107, 43197}, {19710, 42998}, {22238, 41981}, {35018, 42160}, {35404, 43201}, {41987, 43476}, {42102, 42939}, {42135, 42490}, {42144, 42156}, {42166, 42695}, {42503, 42946}, {42584, 42990}, {42590, 43489}, {42599, 43486}, {42632, 42944}, {42684, 43102}, {42813, 42912}, {42814, 43105}, {42898, 42965}, {42941, 43424}, {42964, 43101}

X(43634) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5352, 43417, 140}, {36967, 42925, 12103}, {42122, 42147, 548}

X(43635) = GIBERT (12,5,-13) POINT

Barycentrics    4*Sqrt[3]*a^2*S - 13*a^2*SA + 10*SB*SC : :
x(43635) = 5 X[5339] - 13 X[22238], 9 X[5339] - 13 X[40694], 35 X[5339] - 39 X[41113], X[5339] - 13 X[42151], 17 X[5339] - 13 X[42160], 11 X[5339] - 39 X[42510], 41 X[5339] + 39 X[42586], 3 X[5339] + 13 X[43193], 55 X[5339] - 78 X[43208], 9 X[22238] - 5 X[40694], 7 X[22238] - 3 X[41113], X[22238] - 5 X[42151], 17 X[22238] - 5 X[42160], 11 X[22238] - 15 X[42510], 41 X[22238] + 15 X[42586], 3 X[22238] + 5 X[43193], 11 X[22238] - 6 X[43208], 35 X[40694] - 27 X[41113], X[40694] - 9 X[42151], 17 X[40694] - 9 X[42160], 11 X[40694] - 27 X[42510], 41 X[40694] + 27 X[42586], X[40694] + 3 X[43193], 55 X[40694] - 54 X[43208], 3 X[41113] - 35 X[42151], 51 X[41113] - 35 X[42160], 11 X[41113] - 35 X[42510], 41 X[41113] + 35 X[42586], 9 X[41113] + 35 X[43193], 11 X[41113] - 14 X[43208], 17 X[42151] - X[42160], 11 X[42151] - 3 X[42510], 41 X[42151] + 3 X[42586], 3 X[42151] + X[43193], 55 X[42151] - 6 X[43208], 11 X[42160] - 51 X[42510], 41 X[42160] + 51 X[42586], 3 X[42160] + 17 X[43193], 55 X[42160] - 102 X[43208], 41 X[42510] + 11 X[42586], 9 X[42510] + 11 X[43193], 5 X[42510] - 2 X[43208], 9 X[42586] - 41 X[43193], 55 X[42586] + 82 X[43208], 55 X[43193] + 18 X[43208]

X(43635) lies on the Pythagorean conic and these lines: {2, 42926}, {3, 42496}, {5, 42115}, {15, 548}, {16, 3853}, {18, 12101}, {30, 5339}, {61, 15690}, {62, 43245}, {140, 5351}, {381, 43480}, {397, 34200}, {398, 42430}, {546, 16773}, {547, 5237}, {3090, 42933}, {3411, 42136}, {3528, 42416}, {3529, 42634}, {3530, 42092}, {3627, 43404}, {3628, 42155}, {3843, 42889}, {3850, 36843}, {3855, 43473}, {3856, 42121}, {3859, 42137}, {3861, 42086}, {5066, 42165}, {5070, 43465}, {5318, 43240}, {5340, 12108}, {5344, 11539}, {5350, 43244}, {5352, 41982}, {10124, 42162}, {10303, 42984}, {10653, 33923}, {11481, 16239}, {11540, 42774}, {11737, 43239}, {12102, 42149}, {12103, 36968}, {12812, 42944}, {14893, 42431}, {15691, 41100}, {15700, 22235}, {15759, 42152}, {16964, 42584}, {17538, 43495}, {19106, 43198}, {19708, 43252}, {19710, 42999}, {22236, 41981}, {35018, 42161}, {35404, 43202}, {41987, 43475}, {42101, 42938}, {42138, 42491}, {42145, 42153}, {42163, 42694}, {42502, 42947}, {42585, 42991}, {42591, 43490}, {42598, 43485}, {42631, 42945}, {42685, 43103}, {42813, 43106}, {42814, 42913}, {42899, 42964}, {42940, 43425}, {42965, 43104}

X(43635) {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5351, 43416, 140}, {36968, 42924, 12103}, {42123, 42148, 548}

X(43636) = GIBERT (5,-12,13) POINT

Barycentrics    5*a^2*S/Sqrt[3] + 13*a^2*SA - 24*SB*SC) : :
X(3636) = 36 X[42415] - 41 X[43105], 158 X[42415] - 123 X[43111], 104 X[42415] - 123 X[43245], 576 X[42415] - 451 X[43250], 79 X[43105] - 54 X[43111], 26 X[43105] - 27 X[43245], 16 X[43105] - 11 X[43250], 52 X[43111] - 79 X[43245], 864 X[43111] - 869 X[43250], 216 X[43245] - 143 X[43250]

X(43636) lies on the Pythagorean conic and these lines: {3, 43196}, {4, 42798}, {5, 42099}, {6, 42966}, {15, 3146}, {16, 1657}, {30, 42415}, {62, 42144}, {376, 19107}, {381, 43467}, {382, 42695}, {550, 42692}, {3523, 42103}, {3525, 42104}, {3529, 34755}, {3534, 42953}, {3627, 43366}, {3830, 11480}, {3839, 42090}, {3854, 33417}, {5054, 42475}, {5237, 42140}, {5321, 19710}, {5352, 12102}, {10646, 12103}, {11001, 16961}, {11541, 42629}, {12108, 42101}, {12821, 15698}, {14893, 16966}, {15683, 43419}, {15686, 42682}, {15695, 43231}, {15704, 42630}, {16242, 42888}, {16809, 33923}, {16964, 42584}, {16967, 21734}, {18582, 43399}, {33416, 43402}, {35404, 36967}, {35408, 43401}, {35409, 42973}, {35434, 43483}, {36969, 42130}, {41106, 42529}, {41108, 42100}, {41112, 42119}, {42085, 42991}, {42087, 42627}, {42088, 42899}, {42091, 43011}, {42094, 43327}, {42111, 43470}, {42122, 42693}, {42123, 42970}, {42124, 42997}, {42141, 42157}, {42154, 43006}, {42613, 43499}, {42688, 42780}, {42965, 43500}, {43226, 43463}

X(43636) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15, 42105, 42903}, {5237, 42140, 42901}

X(43637) = GIBERT (5,12,-13) POINT

Barycentrics    5*a^2*S/Sqrt[3] - 13*a^2*SA + 24*SB*SC : :
X(43637) = 36 X[42416] - 41 X[43106], 158 X[42416] - 123 X[43110], 104 X[42416] - 123 X[43244], 576 X[42416] - 451 X[43251], 79 X[43106] - 54 X[43110], 26 X[43106] - 27 X[43244], 16 X[43106] - 11 X[43251], 52 X[43110] - 79 X[43244], 864 X[43110] - 869 X[43251], 216 X[43244] - 143 X[43251]

X(43637) lies on the Pythagorean conic and these lines: {3, 43195}, {4, 42797}, {5, 42100}, {6, 42966}, {15, 1657}, {16, 3146}, {30, 42416}, {61, 42145}, {376, 19106}, {381, 43468}, {382, 42694}, {550, 42693}, {3523, 42106}, {3525, 42105}, {3529, 34754}, {3534, 42952}, {3627, 43367}, {3830, 11481}, {3839, 42091}, {3854, 33416}, {5054, 42474}, {5238, 42141}, {5318, 19710}, {5351, 12102}, {10645, 12103}, {11001, 16960}, {11541, 42630}, {12108, 42102}, {12820, 15698}, {14893, 16967}, {15683, 43418}, {15686, 42683}, {15695, 43230}, {15704, 42629}, {16241, 42889}, {16808, 33923}, {16965, 42585}, {16966, 21734}, {18581, 43400}, {33417, 43401}, {35404, 36968}, {35408, 43402}, {35409, 42972}, {35434, 43484}, {36970, 42131}, {41106, 42528}, {41107, 42099}, {41113, 42120}, {42086, 42990}, {42087, 42898}, {42088, 42628}, {42090, 43010}, {42093, 43326}, {42114, 43469}, {42121, 42996}, {42122, 42971}, {42123, 42692}, {42140, 42158}, {42155, 43007}, {42612, 43500}, {42689, 42779}, {42964, 43499}, {43227, 43464}
on the Pythagorean conic (see K1231)
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16, 42104, 42902}, {5238, 42141, 42900}

X(43638) = GIBERT (-7,24,25) POINT

Barycentrics    7*a^2*S/Sqrt[3] - 25*a^2*SA - 48*SB*SC : :
X(43638) = 37 X[33416] - 30 X[42501], 2 X[33416] + 5 X[42918], 9 X[33416] + 5 X[43227], 12 X[42501] + 37 X[42918], 54 X[42501] + 37 X[43227], 9 X[42918] - 2 X[43227]

X(43638) lies on the Pythagorean conic and these lines: {3, 43470}, {5, 43328}, {15, 3090}, {16, 3851}, {30, 33416}, {62, 43241}, {381, 43471}, {398, 42627}, {3523, 42103}, {3526, 42093}, {3528, 42473}, {3832, 16967}, {3857, 5237}, {5321, 43467}, {5335, 37835}, {5365, 33417}, {11480, 15703}, {11543, 42898}, {14869, 42107}, {14892, 42800}, {15702, 19107}, {16809, 42906}, {16961, 41119}, {16966, 42923}, {18581, 43004}, {19106, 42793}, {34755, 42110}, {37832, 41122}, {41100, 42138}, {41974, 43026}, {42086, 42981}, {42094, 43484}, {42129, 42973}, {42137, 42946}, {42492, 43107}, {42531, 43416}, {42581, 42983}, {42814, 43105}, {42816, 43018}, {42957, 43417}, {43366, 43371}

X(43639) = GIBERT (24,-7,25) POINT

Barycentrics    8*Sqrt[3]*a^2*S + 25*a^2*SA - 14*SB*SC : :

X(43639) lies on the Pythagorean conic and these lines: {3, 43494}, {5, 36836}, {14, 14869}, {15, 15687}, {16, 8703}, {30, 42815}, {140, 42985}, {376, 42803}, {381, 43474}, {397, 15704}, {546, 43478}, {549, 5334}, {632, 42495}, {3146, 42806}, {3411, 42797}, {3412, 43331}, {3627, 43403}, {3830, 42916}, {3845, 42119}, {5054, 43243}, {5070, 42932}, {5321, 43467}, {5349, 43483}, {5352, 43025}, {10109, 43466}, {10645, 43100}, {10653, 15686}, {10654, 17504}, {11480, 15713}, {11485, 19710}, {11539, 37835}, {11542, 43428}, {11543, 19711}, {11737, 43488}, {12100, 42923}, {14269, 43197}, {14891, 42917}, {15681, 42922}, {15699, 42116}, {15705, 43198}, {15711, 42975}, {15712, 16242}, {15716, 42983}, {16268, 42684}, {16772, 41991}, {18581, 43421}, {23046, 37832}, {33417, 43241}, {33699, 41119}, {40694, 43305}, {41973, 42501}, {41983, 42816}, {41990, 42911}, {42087, 42898}, {42089, 42509}, {42124, 42682}, {42130, 42496}, {42144, 42693}, {42164, 42979}, {42626, 42925}, {43194, 43416}, {43418, 43491}

X(43639) = {X(36967),X(42633)}-harmonic conjugate of X(15704)

X(43640) = GIBERT (24,7,-25) POINT

Barycentrics    8*Sqrt[3]*a^2*S - 25*a^2*SA + 14*SB*SC : :

X(43640) lies on the Pythagorean conic and these lines: {3, 43493}, {5, 36843}, {13, 14869}, {15, 8703}, {16, 15687}, {30, 42816}, {140, 42984}, {376, 42804}, {381, 43473}, {398, 15704}, {546, 43477}, {549, 5335}, {632, 42494}, {3146, 42805}, {3411, 43330}, {3412, 42798}, {3627, 43404}, {3830, 42917}, {3845, 42120}, {5054, 43242}, {5070, 42933}, {5318, 43468}, {5350, 43484}, {5351, 43024}, {10109, 43465}, {10646, 43107}, {10653, 17504}, {10654, 15686}, {11481, 15713}, {11486, 19710}, {11539, 37832}, {11542, 19711}, {11543, 43429}, {11737, 43487}, {12100, 42922}, {14269, 43198}, {14891, 42916}, {15681, 42923}, {15699, 42115}, {15705, 43197}, {15711, 42974}, {15712, 16241}, {15716, 42982}, {16267, 42685}, {16773, 41991}, {18582, 43420}, {23046, 37835}, {33416, 43240}, {33699, 41120}, {40693, 43304}, {41974, 42500}, {41983, 42815}, {41990, 42910}, {42088, 42899}, {42092, 42508}, {42121, 42683}, {42131, 42497}, {42145, 42692}, {42165, 42978}, {42625, 42924}, {43193, 43417}, {43419, 43492}

,

X(43640) = {X(36968),X(42634)}-harmonic conjugate of X(15704)

X(43641) = GIBERT (7,-24,25) POINT

Barycentrics    7*a^2*S/Sqrt[3] + 25*a^2*SA - 48*SB*SC : :
X(43641) = 405 X[42799] - 374 X[43234]

X(43641) lies on the Pythagorean conic and these lines: {3, 43470}, {15, 5073}, {16, 3529}, {30, 42799}, {381, 43469}, {3146, 43325}, {3412, 42137}, {3522, 33416}, {3524, 42430}, {3534, 37835}, {3543, 37832}, {5076, 10645}, {5238, 42102}, {5365, 42902}, {12101, 42919}, {15640, 43000}, {16242, 43474}, {19106, 42511}, {19107, 42628}, {34200, 42107}, {34754, 42109}, {41119, 42892}, {41121, 42087}, {41973, 43106}, {42097, 43486}, {42101, 43468}, {42108, 43102}, {42119, 43018}, {42132, 43475}, {42584, 42964}, {42683, 42976}, {42798, 43226}

X(43642) = GIBERT (7,24,-25) POINT

Barycentrics    7*a^2*S/Sqrt[3] - 25*a^2*SA + 48*SB*SC : :
X(43642) = 405 X[42800] - 374 X[43235]

X(43642) lies on the Pythagorean conic and these lines: {3, 43469}, {15, 3529}, {16, 5073}, {30, 42800}, {381, 43470}, {3146, 43324}, {3411, 42136}, {3522, 33417}, {3524, 42429}, {3534, 37832}, {3543, 37835}, {5076, 10646}, {5237, 42101}, {5366, 42903}, {12101, 42918}, {15640, 43001}, {16241, 43473}, {19106, 42627}, {19107, 42510}, {34200, 42110}, {34755, 42108}, {41120, 42893}, {41122, 42088}, {41974, 43105}, {42096, 43485}, {42102, 43467}, {42109, 43103}, {42120, 43019}, {42129, 43476}, {42585, 42965}, {42682, 42977}, {42797, 43227}

X(43643) = GIBERT (7,24,25) POINT

Barycentrics    7*a^2*S/Sqrt[3] + 25*a^2*SA + 48*SB*SC : :

X(43643) = 37 X[33417] - 30 X[42500], 2 X[33417] + 5 X[42919], 9 X[33417] + 5 X[43226], 12 X[42500] + 37 X[42919], 54 X[42500] + 37 X[43226], 9 X[42919] - 2 X[43226]

X(43643) lies on the Pythagorean conic and these lines: {3, 43469}, {5, 43329}, {15, 3851}, {16, 3090}, {30, 33417}, {61, 43240}, {381, 43472}, {397, 42628}, {3523, 42106}, {3526, 42094}, {3528, 42472}, {3832, 16966}, {3857, 5238}, {5318, 43468}, {5334, 37832}, {5366, 33416}, {11481, 15703}, {11542, 42899}, {14869, 42110}, {14892, 42799}, {15702, 19106}, {16808, 42907}, {16960, 41120}, {16967, 42922}, {18582, 43005}, {19107, 42794}, {34754, 42107}, {37835, 41121}, {41101, 42135}, {41973, 43027}, {42085, 42980}, {42093, 43483}, {42132, 42972}, {42136, 42947}, {42493, 43100}, {42530, 43417}, {42580, 42982}, {42813, 43106}, {42815, 43019}, {42956, 43416}, {43367, 43370}

X(43644) = GIBERT (-8,15,17) POINT

Barycentrics    -8*a^2*S+(17*SA*a^2+30*SB*SC)*sqrt(3) : :

X(43644) = X[42089] + 7 X[42095], 9 X[42089] + 7 X[42103], 5 X[42089] - 21 X[42910], 9 X[42095] - X[42103], 5 X[42095] + 3 X[42910], 5 X[42103] + 27 X[42910]

X(43644) lies on the Pythagorean conic and these lines: {3, 43474}, {5, 42815}, {15, 3628}, {16, 3850}, {30, 42089}, {140, 5365}, {381, 43473}, {546, 42115}, {547, 11485}, {632, 43466}, {1656, 42923}, {3090, 42916}, {3091, 43198}, {3530, 16967}, {3544, 42922}, {3627, 42951}, {3856, 42121}, {3858, 43480}, {3859, 42473}, {3860, 42918}, {3861, 23303}, {5055, 42983}, {5066, 42129}, {5072, 42917}, {5079, 42986}, {5321, 10124}, {5334, 42492}, {5335, 14892}, {5351, 12102}, {10109, 11543}, {11480, 16239}, {11542, 43240}, {11737, 37835}, {12108, 42135}, {12811, 22238}, {12812, 43307}, {14269, 42933}, {14869, 42963}, {14891, 33416}, {15686, 43478}, {15699, 43463}, {15759, 19107}, {16241, 42415}, {16809, 33923}, {18581, 35018}, {36967, 43470}, {38071, 43364}, {41113, 42124}, {41985, 43417}, {41989, 42599}, {42100, 43490}, {42101, 42591}, {42108, 43102}, {42130, 43202}, {42133, 42493}, {42430, 43196}, {42472, 42634}, {42781, 43015}, {42797, 43227}, {42906, 42920}, {42914, 42991}, {43246, 43328}

X(43644) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {33416, 42888, 14891}, {42111, 42628, 12811}

X(43645) = GIBERT (15,-8,17) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 17*a^2*SA - 16*SB*SC : :

X(43645) = 13 X[34754] - 4 X[42629], 7 X[34754] - 6 X[42635], 14 X[42629] - 39 X[42635], 8 X[42629] - 13 X[43418], 12 X[42635] - 7 X[43418]

X(43645) lies on the Pythagorean conic and these lines: {2, 43241}, {3, 43001}, {4, 42890}, {5, 5238}, {13, 3146}, {14, 12100}, {15, 3830}, {16, 376}, {17, 12102}, {30, 34754}, {61, 1657}, {140, 42795}, {381, 43196}, {395, 33923}, {396, 35404}, {397, 43021}, {546, 43199}, {548, 42780}, {549, 43105}, {550, 42934}, {3523, 16964}, {3530, 43545}, {3545, 42630}, {3627, 42939}, {3839, 37832}, {3850, 12821}, {3854, 42911}, {3860, 42919}, {5054, 10645}, {5318, 42976}, {5321, 10124}, {5351, 42975}, {10109, 42687}, {10299, 42513}, {10303, 43547}, {10304, 43301}, {11480, 15703}, {11539, 42684}, {11737, 42682}, {12103, 36968}, {12108, 42489}, {12817, 42092}, {14893, 19107}, {15682, 16960}, {15686, 43500}, {15689, 34755}, {15693, 42953}, {15698, 43200}, {15704, 43231}, {15705, 16242}, {15713, 43468}, {15722, 41122}, {15759, 42778}, {16239, 42798}, {16267, 42096}, {16268, 42117}, {16644, 42432}, {16809, 43202}, {16961, 34200}, {16965, 43232}, {16967, 43247}, {18582, 43400}, {19106, 42511}, {19710, 41101}, {33417, 42791}, {33699, 43195}, {35409, 42112}, {36836, 42979}, {36969, 42130}, {37640, 42430}, {41099, 43544}, {41100, 43007}, {41107, 42099}, {41108, 42626}, {41983, 42954}, {42098, 43472}, {42127, 42587}, {42137, 42506}, {42144, 42693}, {42148, 42995}, {42156, 43399}, {42429, 42585}, {42474, 43489}, {42488, 42908}, {42496, 42802}, {42500, 42959}, {42509, 42631}, {42580, 43541}, {42589, 42910}, {42599, 43032}, {42692, 42914}, {42774, 43373}, {42800, 43305}, {42813, 42912}, {42941, 42992}, {42943, 43108}, {42986, 43033}, {42994, 43304}, {43006, 43193}

X(43645) = reflection of X(43418) in X(34754)
X(43645) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 42122, 42632}, {15, 41121, 42892}, {10645, 42154, 42972}, {36968, 42147, 42799}, {36970, 42942, 5238}, {37640, 42430, 42431}, {41107, 43331, 42099}, {42117, 42529, 16268}, {42157, 42942, 36970}, {42585, 43228, 42429}

X(43646) = GIBERT (15,8,-17) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 17*a^2*SA + 16*SB*SC : :
X(43646) = 13 X[34755] - 4 X[42630], 7 X[34755] - 6 X[42636], 14 X[42630] - 39 X[42636], 8 X[42630] - 13 X[43419], 12 X[42636] - 7 X[43419]

X(43646) lies on the Pythagorean conic and these lines: {2, 43240}, {3, 43000}, {4, 42891}, {5, 5237}, {13, 12100}, {14, 3146}, {15, 376}, {16, 3830}, {18, 12102}, {30, 34755}, {62, 1657}, {140, 42796}, {381, 43195}, {395, 35404}, {396, 33923}, {398, 43020}, {546, 43200}, {548, 42779}, {549, 43106}, {550, 42935}, {3523, 16965}, {3530, 43544}, {3545, 42629}, {3627, 42938}, {3839, 37835}, {3850, 12820}, {3854, 42910}, {3860, 42918}, {5054, 10646}, {5318, 10124}, {5321, 42977}, {5352, 42974}, {10109, 42686}, {10299, 42512}, {10303, 43546}, {10304, 43300}, {11481, 15703}, {11539, 42685}, {11737, 42683}, {12103, 36967}, {12108, 42488}, {12816, 42089}, {14893, 19106}, {15682, 16961}, {15686, 43499}, {15689, 34754}, {15693, 42952}, {15698, 43199}, {15704, 43230}, {15705, 16241}, {15713, 43467}, {15722, 41121}, {15759, 42777}, {16239, 42797}, {16267, 42118}, {16268, 42097}, {16645, 42431}, {16808, 43201}, {16960, 34200}, {16964, 43233}, {16966, 43246}, {18581, 43399}, {19107, 42510}, {19710, 41100}, {33416, 42792}, {33699, 43196}, {35409, 42113}, {35739, 42569}, {36843, 42978}, {36970, 42131}, {37641, 42429}, {41099, 43545}, {41101, 43006}, {41107, 42625}, {41108, 42100}, {41983, 42955}, {42095, 43471}, {42126, 42586}, {42136, 42507}, {42145, 42692}, {42147, 42994}, {42153, 43400}, {42430, 42584}, {42475, 43490}, {42489, 42909}, {42497, 42801}, {42501, 42958}, {42508, 42632}, {42581, 43540}, {42588, 42911}, {42598, 43033}, {42693, 42915}, {42773, 43372}, {42799, 43304}, {42814, 42913}, {42940, 42993}, {42942, 43109}, {42987, 43032}, {42995, 43305}, {43007, 43194}

X(43646) = reflection of X(43419) in X(34755)
X(43646) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 42123, 42631}, {16, 41122, 42893}, {10646, 42155, 42973}, {36967, 42148, 42800}, {36969, 42943, 5237}, {37641, 42429, 42432}, {41108, 43330, 42100}, {42118, 42528, 16267}, {42158, 42943, 36969}, {42584, 43229, 42430}

X(43647) = GIBERT (8,-15,17) POINT

Barycentrics    8*a^2*S/Sqrt[3] + 17*a^2*SA - 30*SB*SC : :
X(43647) = 7 X[42922] - 6 X[43465], 35 X[42922] - 54 X[43482], 5 X[43465] - 9 X[43482]

X(43647) lies on the Pythagorean conic and these lines: {3, 43474}, {5, 42090}, {15, 5350}, {16, 15704}, {20, 42917}, {30, 42922}, {550, 5365}, {3529, 42923}, {3530, 43365}, {3627, 42116}, {5318, 42976}, {5352, 42108}, {8703, 12817}, {10645, 41991}, {11001, 43208}, {11481, 15686}, {11542, 43428}, {14869, 42107}, {15681, 42987}, {15687, 37832}, {15712, 19107}, {15759, 42985}, {17504, 42093}, {19710, 42126}, {22236, 42112}, {33699, 42122}, {35404, 43403}, {38335, 42932}, {41985, 43478}, {42085, 42924}, {42092, 42587}, {42109, 43306}, {42117, 43106}, {42121, 42902}, {42432, 43005}, {42529, 43472}, {42598, 43292}, {42635, 43401}, {42818, 43488}, {42920, 43102}

X(43648) = GIBERT (8,15,-17) POINT

Barycentrics    8*a^2*S/Sqrt[3] - 17*a^2*SA + 30*SB*SC : :
X(43648) = 7 X[42923] - 6 X[43466], 35 X[42923] - 54 X[43481], 5 X[43466] - 9 X[43481]

X(43648) lies on the Pythagorean conic and these lines: {3, 43473}, {5, 42091}, {15, 15704}, {16, 5349}, {20, 42916}, {30, 42923}, {550, 5366}, {3529, 42922}, {3530, 43364}, {3627, 42115}, {5321, 42977}, {5351, 42109}, {8703, 12816}, {10646, 41991}, {11001, 43207}, {11480, 15686}, {11543, 43429}, {14869, 42110}, {15681, 42986}, {15687, 37835}, {15712, 19106}, {15759, 42984}, {17504, 42094}, {19710, 42127}, {22238, 42113}, {33699, 42123}, {35404, 43404}, {38335, 42933}, {41985, 43477}, {42086, 42925}, {42089, 42586}, {42108, 43307}, {42118, 43105}, {42124, 42903}, {42431, 43004}, {42528, 43471}, {42599, 43293}, {42636, 43402}, {42817, 43487}, {42921, 43103}

X(43649) = GIBERT (8,15,17) POINT

Barycentrics    8*a^2*S/Sqrt[3] + 17*a^2*SA + 30*SB*SC : :
X(43649) = X[42092] + 7 X[42098], 9 X[42092] + 7 X[42106], 5 X[42092] - 21 X[42911], 9 X[42098] - X[42106], 5 X[42098] + 3 X[42911], 5 X[42106] + 27 X[42911]

X(43649) lies on the Pythagorean conic and these lines: {3, 43473}, {5, 42816}, {15, 3850}, {16, 3628}, {30, 42092}, {140, 5366}, {381, 43474}, {546, 42116}, {547, 11486}, {632, 43465}, {1656, 42922}, {3090, 42917}, {3091, 43197}, {3530, 16966}, {3544, 42923}, {3627, 42950}, {3856, 42124}, {3858, 43479}, {3859, 42472}, {3860, 42919}, {3861, 23302}, {5055, 42982}, {5066, 42132}, {5072, 42916}, {5079, 42987}, {5318, 10124}, {5334, 14892}, {5335, 42493}, {5352, 12102}, {10109, 11542}, {11481, 16239}, {11543, 43241}, {11737, 37832}, {12108, 42138}, {12811, 22236}, {12812, 43306}, {14269, 42932}, {14869, 42962}, {14891, 33417}, {15686, 43477}, {15699, 43464}, {15759, 19106}, {16242, 42416}, {16808, 33923}, {18582, 35018}, {36968, 43469}, {38071, 43365}, {41112, 42121}, {41985, 43416}, {41989, 42598}, {42099, 43489}, {42102, 42590}, {42109, 43103}, {42131, 43201}, {42134, 42492}, {42429, 43195}, {42473, 42633}, {42782, 43014}, {42798, 43226}, {42907, 42921}, {42915, 42990}, {43247, 43329}

X(43649) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {33417, 42889, 14891}, {42114, 42627, 12811}

X(43650) = MIDPOINT OF X(5422) AND X(7485)

Barycentrics    = a*(((b+c)*a^8-(b+c)^2*a^7-2*(b^3+c^3)*a^6+(3*b^2-4*b*c+3*c^2)*(b+c)^2*a^5-(2*b-c)*(b-2*c)*(b+c)*b*c*a^4-(3*b^4+3*c^4+b*c*(4*b^2+b*c+4*c^2))*(b-c)^2*a^3+(b^2-c^2)*(b-c)*(2*b^4+2*c^4+(2*b^2-b*c+2*c^2)*b*c)*a^2+(b^4+c^4-(2*b^2-b*c+2*c^2)*b*c)*(b^2-c^2)^2*a-(b^4-c^4)*(b^2-c^2)^2*(b-c))*sqrt(R*(4*R+r))-S*(-a+b+c)*a*(a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))) : :
X(43650) = 2 X[7485] + X[15004]

See Antreas Hatzipolakis and Peter Moses, euclid 1735.

X(43650) lies on these lines: {2, 98}, {3, 51}, {4, 37515}, {5, 10984}, {6, 3917}, {9, 26889}, {20, 9815}, {22, 5092}, {23, 11451}, {24, 11695}, {25, 373}, {32, 10014}, {39, 42295}, {52, 7516}, {54, 3525}, {57, 26890}, {83, 37190}, {140, 343}, {141, 11245}, {154, 10541}, {185, 7395}, {206, 1853}, {216, 426}, {237, 37479}, {251, 41412}, {372, 8962}, {378, 16836}, {381, 13339}, {386, 37247}, {389, 7509}, {394, 5050}, {404, 13323}, {427, 1974}, {441, 26905}, {458, 42400}, {511, 5422}, {549, 13352}, {567, 5054}, {572, 4191}, {574, 20859}, {575, 1993}, {576, 2979}, {578, 631}, {582, 16287}, {612, 1428}, {614, 2330}, {632, 32046}, {692, 4423}, {748, 2175}, {750, 1397}, {852, 26880}, {1011, 13329}, {1147, 3526}, {1176, 19137}, {1199, 7999}, {1204, 7503}, {1209, 18952}, {1216, 36753}, {1342, 15248}, {1343, 15247}, {1350, 9777}, {1351, 34565}, {1368, 19131}, {1370, 14561}, {1437, 16408}, {1495, 3796}, {1501, 5033}, {1503, 37439}, {1583, 43118}, {1584, 43119}, {1598, 27355}, {1599, 43121}, {1600, 43120}, {1611, 40130}, {1613, 5038}, {1614, 5067}, {1619, 10249}, {1627, 5039}, {1656, 10540}, {1790, 16059}, {1915, 39560}, {1994, 7998}, {1995, 6688}, {2052, 37124}, {2194, 37679}, {2267, 22060}, {2328, 16373}, {2450, 7834}, {2909, 7852}, {2931, 14805}, {3051, 5034}, {3060, 3098}, {3066, 9909}, {3090, 6759}, {3292, 11402}, {3305, 7193}, {3306, 3955}, {3357, 35500}, {3518, 11465}, {3523, 13346}, {3524, 15033}, {3574, 6643}, {3618, 7386}, {3628, 10539}, {3681, 43149}, {3734, 39906}, {3818, 37990}, {3830, 8717}, {3855, 8718}, {3873, 43146}, {3980, 5150}, {3981, 5116}, {4011, 24253}, {4121, 7763}, {4383, 5135}, {4413, 20986}, {4418, 24265}, {5028, 8041}, {5071, 14157}, {5097, 21766}, {5133, 38317}, {5138, 32911}, {5158, 13409}, {5206, 13410}, {5354, 42852}, {5398, 16374}, {5437, 26884}, {5447, 36749}, {5480, 7667}, {5562, 7393}, {5640, 6636}, {5643, 7492}, {5888, 11004}, {5890, 7550}, {5946, 37478}, {6030, 10545}, {6090, 17809}, {6243, 15047}, {6617, 26898}, {6640, 6689}, {6644, 37513}, {6676, 37648}, {6677, 13394}, {6747, 17907}, {6803, 19467}, {6815, 21659}, {7308, 26885}, {7383, 39571}, {7391, 19130}, {7392, 25406}, {7394, 29012}, {7396, 19121}, {7488, 15028}, {7494, 18928}, {7499, 13567}, {7502, 13363}, {7512, 15024}, {7514, 9730}, {7525, 15026}, {7527, 20791}, {7530, 14845}, {7569, 32767}, {7592, 11793}, {7689, 34864}, {7808, 37988}, {7888, 16893}, {8029, 8723}, {8408, 8420}, {8549, 34750}, {8889, 19128}, {9687, 13785}, {9723, 21642}, {9826, 18570}, {10110, 10323}, {10132, 26348}, {10133, 26341}, {10170, 18445}, {10219, 35264}, {10278, 39495}, {10298, 43584}, {10303, 34148}, {10329, 22111}, {10358, 14957}, {10691, 18583}, {11002, 12834}, {11059, 37894}, {11225, 40107}, {11328, 12054}, {11381, 11479}, {11413, 17704}, {11432, 14531}, {11438, 15045}, {12161, 13154}, {12174, 33537}, {12215, 40022}, {13340, 15038}, {13367, 37476}, {13482, 15719}, {13595, 15080}, {14133, 16924}, {14153, 21001}, {14788, 18381}, {14789, 25739}, {14810, 21849}, {14855, 31861}, {15037, 23039}, {15041, 16223}, {15043, 37126}, {15066, 34986}, {15141, 38402}, {15302, 34945}, {15473, 35481}, {15515, 20977}, {15520, 33884}, {15693, 37477}, {15694, 22115}, {15720, 37472}, {16063, 25555}, {16226, 37489}, {16659, 34939}, {19129, 30771}, {19136, 31152}, {19708, 43576}, {21163, 41275}, {21663, 37475}, {22076, 36754}, {22109, 39242}, {22234, 23061}, {23292, 30739}, {23332, 37454}, {24264, 32930}, {31274, 39834}, {32068, 37644}, {32205, 37440}, {32608, 37481}, {35707, 40670}, {36741, 40952}, {36745, 37246}, {37309, 37474}, {37517, 41462}

X(43650) = midpoint of X(5422) and X(7485)
X(43650) = reflection of X(15004) in X(5422)
X(43650) = Brocard circle inverse of X(24981)
X(43650) = psi-transform of X(37925)
X(43650) = crossdifference of every pair of points on line {3569, 3800}
X(43650) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 182, 184}, {2, 184, 5651}, {2, 5012, 9306}, {2, 11442, 24206}, {2, 18911, 21243}, {3, 10601, 51}, {5, 10984, 26883}, {5, 13336, 10984}, {6, 7484, 3917}, {22, 5943, 34417}, {25, 5085, 22352}, {25, 17825, 373}, {25, 22352, 35268}, {140, 569, 1092}, {182, 9306, 5012}, {182, 16187, 11003}, {182, 22112, 5651}, {184, 22112, 2}, {373, 5085, 35268}, {373, 22352, 25}, {394, 5050, 13366}, {394, 16419, 5650}, {575, 3819, 1993}, {1350, 9777, 21969}, {1368, 38110, 37649}, {1993, 40916, 3819}, {2979, 34545, 576}, {3060, 15246, 3098}, {3523, 13434, 13346}, {3524, 15033, 37480}, {3526, 13353, 1147}, {3589, 5157, 1974}, {3796, 5020, 1495}, {4383, 5135, 5320}, {5012, 9306, 184}, {5020, 12017, 3796}, {5050, 16419, 394}, {5085, 17825, 25}, {5092, 5943, 22}, {5650, 13366, 394}, {7392, 25406, 31383}, {7393, 36752, 5562}, {7395, 37514, 185}, {7496, 34545, 2979}, {7503, 9729, 1204}, {11402, 17811, 3292}, {13414, 13415, 24981}, {15018, 15246, 3060}, {15045, 35921, 11438}, {32568, 32575, 574}

X(43651) =X(2)X(54)∩X(3)X(143)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1735.

X(43651) lies on these lines: {2, 54}, {3, 143}, {4, 83}, {5, 1614}, {6, 7509}, {20, 13336}, {22, 9781}, {24, 10601}, {26, 5640}, {30, 37471}, {49, 3628}, {51, 7512}, {52, 34545}, {74, 7526}, {110, 1656}, {140, 567}, {155, 11423}, {156, 5055}, {184, 3090}, {185, 35500}, {195, 15067}, {265, 27866}, {373, 10282}, {376, 11424}, {378, 37514}, {389, 35921}, {547, 18350}, {549, 37472}, {550, 13339}, {568, 7691}, {575, 1199}, {578, 631}, {632, 22115}, {1092, 3525}, {1181, 5622}, {1216, 1994}, {1437, 6946}, {1498, 16261}, {1594, 37649}, {1993, 7393}, {1995, 26882}, {2070, 15026}, {2931, 15035}, {2937, 10095}, {2979, 7516}, {3043, 6723}, {3044, 6721}, {3047, 12900}, {3055, 9603}, {3091, 14157}, {3147, 18928}, {3205, 16967}, {3206, 16966}, {3410, 10116}, {3518, 5943}, {3520, 9729}, {3522, 43576}, {3523, 13352}, {3524, 13346}, {3528, 13347}, {3530, 37495}, {3533, 22112}, {3545, 6759}, {3589, 6146}, {3796, 10594}, {3855, 26883}, {3917, 37505}, {4550, 43596}, {5013, 32654}, {5020, 9707}, {5050, 7395}, {5056, 10539}, {5067, 9306}, {5070, 9706}, {5085, 10323}, {5157, 14853}, {5446, 6636}, {5447, 7496}, {5462, 7488}, {5643, 12106}, {5644, 16195}, {5889, 7514}, {5890, 7503}, {5892, 22467}, {5907, 15032}, {5944, 32205}, {6030, 17714}, {6101, 14627}, {6102, 15037}, {6241, 9818}, {6642, 11464}, {6644, 15028}, {6800, 7529}, {6942, 13323}, {6949, 37527}, {7399, 12022}, {7404, 11457}, {7405, 14516}, {7484, 11426}, {7485, 36747}, {7486, 9544}, {7495, 41587}, {7502, 12834}, {7506, 11451}, {7517, 15080}, {7525, 15107}, {7527, 40647}, {7545, 18874}, {7558, 39571}, {7998, 16266}, {8548, 12271}, {9586, 19872}, {9638, 9817}, {9677, 42274}, {9730, 14118}, {10018, 37648}, {10110, 12088}, {10299, 37480}, {10541, 12082}, {10545, 13621}, {10605, 43611}, {10610, 13363}, {10625, 15246}, {10627, 41462}, {11134, 42598}, {11137, 42599}, {11250, 40280}, {11414, 12017}, {11440, 13630}, {11442, 14786}, {11444, 12161}, {11456, 11479}, {11484, 26864}, {11585, 14389}, {11591, 15087}, {11695, 13367}, {11793, 13366}, {12084, 20791}, {12111, 43602}, {12134, 37990}, {12228, 15059}, {12279, 31861}, {12289, 18420}, {12362, 19129}, {13292, 37636}, {13364, 18378}, {13491, 33541}, {13598, 20190}, {13861, 26881}, {14061, 39805}, {14449, 22233}, {14787, 32140}, {14789, 15462}, {14805, 37814}, {15056, 18445}, {15472, 35477}, {15712, 37477}, {15801, 23039}, {17825, 19357}, {18570, 43601}, {18583, 19121}, {18911, 23294}, {18952, 23293}, {23325, 32379}, {31166, 34781}, {31804, 37439}, {31830, 41482}, {32068, 32348}, {37760, 43579}

X(43651) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 569, 54}, {3, 5422, 3567}, {3, 12006, 15053}, {3, 13434, 15033}, {3, 15038, 10263}, {3, 15045, 43597}, {3, 15047, 5946}, {4, 10984, 8718}, {5, 5012, 1614}, {5, 13353, 5012}, {6, 7509, 11412}, {24, 10601, 15024}, {26, 5640, 38848}, {54, 43572, 9545}, {140, 567, 34148}, {156, 5055, 43614}, {182, 3618, 19128}, {182, 14561, 1176}, {184, 3090, 43598}, {575, 5562, 1199}, {578, 631, 43574}, {1181, 15058, 14094}, {1199, 7550, 5562}, {1656, 32046, 110}, {1993, 7393, 7999}, {3589, 6146, 14788}, {3618, 41257, 14561}, {5050, 7395, 7592}, {5056, 11003, 10539}, {5085, 10982, 10323}, {5462, 37513, 7488}, {5890, 36752, 43600}, {6146, 14788, 41171}, {6241, 9818, 43613}, {7395, 7592, 11459}, {7488, 15018, 5462}, {7503, 36752, 5890}, {7514, 36753, 5889}, {7516, 36749, 2979}, {7526, 10574, 74}, {10110, 22352, 12088}, {10601, 37476, 24}, {11424, 37515, 376}, {11464, 11465, 6642}, {11591, 36153, 15087}, {15037, 34864, 6102}, {15805, 37506, 17928}, {34545, 37126, 52}

X(43652) =X(2)X(11424)∩X(3)X(49)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1735.

X(43652) lies on these lines: {2, 11424}, {3, 49}, {4, 5651}, {6, 9686}, {20, 9306}, {22, 13348}, {24, 15644}, {40, 26884}, {51, 37498}, {54, 3524}, {64, 1660}, {69, 18936}, {84, 26885}, {110, 3522}, {125, 3546}, {140, 13142}, {141, 19124}, {154, 9914}, {156, 8703}, {182, 193}, {195, 40280}, {206, 15748}, {212, 7335}, {219, 26927}, {222, 26935}, {323, 10574}, {343, 16196}, {373, 10982}, {376, 6225}, {378, 11793}, {417, 577}, {511, 17928}, {549, 569}, {550, 10539}, {567, 15720}, {576, 15043}, {578, 631}, {603, 6056}, {1209, 18281}, {1350, 1974}, {1495, 11414}, {1498, 6090}, {1511, 7525}, {1578, 21640}, {1579, 21641}, {1593, 17811}, {1614, 3528}, {1656, 37477}, {1941, 15466}, {1968, 40805}, {1993, 9729}, {1995, 13598}, {2071, 11444}, {2194, 37501}, {2937, 33542}, {2979, 22467}, {3043, 15036}, {3098, 7488}, {3357, 11459}, {3520, 7999}, {3525, 15033}, {3526, 37495}, {3529, 43598}, {3530, 13336}, {3534, 18350}, {3538, 18925}, {3543, 43614}, {3574, 6815}, {3819, 7503}, {5012, 13347}, {5054, 37472}, {5056, 16187}, {5157, 21167}, {5210, 9603}, {5320, 36746}, {5504, 38727}, {5650, 7395}, {5891, 12084}, {5892, 36749}, {5907, 11413}, {6102, 37470}, {6455, 9687}, {6636, 11449}, {6639, 14156}, {6642, 34417}, {6643, 21659}, {6644, 10625}, {6823, 11064}, {6986, 13323}, {7386, 19467}, {7387, 36987}, {7464, 15058}, {7484, 11425}, {7509, 11430}, {7512, 11202}, {7517, 43586}, {7526, 10564}, {7592, 16836}, {7667, 34782}, {7691, 33884}, {7824, 42313}, {7998, 14118}, {8273, 20986}, {9544, 21734}, {9545, 15692}, {9730, 16266}, {9786, 14531}, {9927, 37452}, {10112, 18911}, {10167, 42463}, {10282, 10323}, {10303, 13434}, {10540, 15696}, {10575, 15068}, {10627, 37478}, {10996, 37669}, {11250, 15067}, {11284, 27355}, {11381, 17814}, {11410, 41427}, {11412, 11438}, {11439, 37944}, {12085, 15030}, {12086, 15056}, {12160, 37475}, {12241, 30739}, {13366, 37514}, {13416, 32607}, {13482, 15709}, {14157, 17538}, {14528, 34817}, {14855, 32139}, {15004, 36747}, {15693, 37471}, {15712, 32046}, {16226, 37493}, {16661, 26881}, {17704, 34986}, {18383, 31180}, {18435, 33541}, {18570, 32142}, {19708, 43572}, {20125, 43391}, {22138, 30262}, {22424, 30270}, {22955, 30552}, {26889, 37526}, {31807, 41673}, {32348, 41594}, {33524, 35264}, {35259, 39568}, {37112, 37527}, {37517, 43584}

X(43652) = isotomic conjugate of the polar conjugate of X(5065)
X(43652) = isogonal conjugate of the polar conjugate of X(17811)
X(43652) = X(17811)-Ceva conjugate of X(5065)
X(43652) = X(i)-isoconjugate of X(j) for these (i,j): {19, 37874}, {158, 15740}, {1096, 40032}
X(43652) = crosssum of X(4) and X(3089)
X(43652) = barycentric product X(i)*X(j) for these {i,j}: {3, 17811}, {63, 1496}, {69, 5065}, {184, 32830}, {394, 1593}, {577, 32000}, {3796, 40187}, {3917, 26224}
X(43652) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 37874}, {394, 40032}, {577, 15740}, {1496, 92}, {1593, 2052}, {5065, 4}, {17811, 264}, {32000, 18027}, {32830, 18022}
X(43652) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13346, 11424}, {3, 394, 185}, {3, 1092, 184}, {3, 1147, 10984}, {3, 5562, 1204}, {3, 19357, 22352}, {3, 23039, 7689}, {3, 35602, 13367}, {20, 9306, 26883}, {54, 3524, 37515}, {140, 13142, 37648}, {577, 14379, 417}, {631, 43574, 578}, {1092, 10984, 1147}, {1147, 10984, 184}, {3523, 34148, 182}, {5012, 15717, 13347}, {9704, 22115, 1147}, {10282, 10323, 35268}, {10627, 37814, 37478}, {11413, 15066, 5907}, {17814, 21312, 11381}

X(43653) =X(2)X(51)∩X(3)X(68)

Barycentrics    (a^2 - b^2 - c^2)*(a^4 + 2*a^2*b^2 - b^4 + 2*a^2*c^2 + 2*b^2*c^2 - c^4) : :
X(43653) = 4 X[3] - X[19467], 2 X[5] + X[37486], X[69] + 2 X[19126], 4 X[140] - X[36747], 2 X[141] + X[37485], 2 X[578] - 5 X[631], X[1181] - 4 X[16197], 4 X[3530] - X[43595]

See Antreas Hatzipolakis and Peter Moses, euclid 1735.

X(43653) lies on these lines: {2, 51}, {3, 68}, {4, 33522}, {5, 33586}, {6, 7499}, {20, 11550}, {22, 1352}, {25, 141}, {66, 161}, {69, 184}, {125, 7386}, {140, 10601}, {154, 599}, {155, 34002}, {182, 6515}, {185, 7400}, {193, 13366}, {237, 7795}, {376, 11204}, {389, 7383}, {394, 6676}, {418, 6389}, {427, 1350}, {428, 10516}, {460, 7784}, {468, 17811}, {524, 11402}, {549, 37506}, {578, 631}, {1173, 3525}, {1181, 16197}, {1204, 10996}, {1209, 14790}, {1216, 3549}, {1351, 37649}, {1368, 37638}, {1370, 3098}, {1473, 26942}, {1495, 3620}, {1853, 7667}, {1906, 33537}, {1993, 7495}, {2187, 33081}, {3091, 11821}, {3135, 8266}, {3148, 7800}, {3167, 13394}, {3410, 7492}, {3524, 18950}, {3529, 35240}, {3530, 43595}, {3537, 18931}, {3541, 15644}, {3542, 11793}, {3547, 5562}, {3548, 5447}, {3564, 3796}, {3580, 7485}, {3589, 9777}, {3618, 15004}, {3619, 7392}, {3631, 26864}, {3690, 27509}, {3763, 17810}, {3767, 20859}, {3818, 7500}, {4224, 32782}, {5020, 32269}, {5032, 34566}, {5064, 29181}, {5085, 11245}, {5133, 31670}, {5310, 12589}, {5322, 12588}, {5347, 5820}, {5406, 8964}, {5418, 40067}, {5420, 40068}, {5446, 14786}, {5480, 7539}, {5644, 15694}, {5651, 6353}, {5654, 23039}, {6090, 10192}, {6247, 37198}, {6636, 11442}, {6776, 22352}, {6995, 40330}, {6997, 24206}, {7085, 26932}, {7393, 41587}, {7394, 15107}, {7399, 17834}, {7484, 13567}, {7493, 9306}, {7505, 7999}, {7509, 39571}, {7512, 9833}, {7558, 11412}, {7568, 16266}, {7854, 42671}, {9544, 15108}, {10154, 35259}, {10201, 15067}, {10323, 14216}, {10984, 11411}, {11206, 35268}, {11459, 41715}, {11548, 21850}, {13336, 18951}, {13346, 32348}, {14023, 34396}, {14376, 36952}, {14907, 35926}, {15068, 25337}, {15246, 18911}, {15526, 26880}, {16063, 23293}, {16419, 37648}, {16618, 18451}, {17238, 37103}, {17809, 40341}, {18420, 37478}, {18916, 37515}, {18928, 22112}, {19314, 25977}, {20427, 41736}, {20965, 31401}, {21167, 26869}, {21230, 32140}, {23217, 26874}, {23327, 34751}, {23332, 31152}, {26540, 37261}, {26865, 34828}, {26898, 41005}, {26907, 40680}, {26913, 41462}, {26958, 30739}, {27512, 35614}, {32062, 34621}, {33172, 33849}, {34778, 41602}, {37072, 37877}, {37347, 37494}

X(43653) = reflection of X(37506) in X(549)
X(43653) = isotomic conjugate of the polar conjugate of X(2548)
X(43653) = crosspoint of X(69) and X(18840)
X(43653) = crosssum of X(25) and X(30435)
X(43653) = crossdifference of every pair of points on line {3288, 6753}
X(43653) = barycentric product X(69)*X(2548)
X(43653) = barycentric quotient X(2548)/X(4)
X(43653) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3060, 14561}, {2, 10519, 3917}, {3, 343, 1899}, {22, 1352, 31383}, {22, 37636, 1352}, {69, 7494, 184}, {140, 41588, 10601}, {1853, 31884, 7667}, {3098, 21243, 1370}, {3620, 10565, 14826}, {3763, 17810, 37439}, {10565, 14826, 1495}

X(43654) = REFLECTION OF X(2698) IN EULER LINE

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

X(43654) lies on the circumcircle, the cubic K023, and these lines: {30, 805}, {74, 804}, {98, 14270}, {99, 37991}, {110, 1316}, {186, 22456}, {237, 476}, {401, 10420}, {419, 1304}, {523, 2698}, {542, 9160}, {690, 9161}, {691, 11676}, {925, 37918}, {2715, 19627}, {3016, 26714}, {3288, 32730}, {5916, 39423}, {5917, 39422}, {11594, 13241}

X(43654) = reflection of X(2698) in the Euler line
X(43654) = reflection of X(74) in line X(3)X(76)

X(43655) = REFLECTION OF X(953) IN EULER LINE

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

X(43655) lies on the circumcircle, the cubic K275, and these lines: {30, 901}, {74, 900}, {80, 109}, {101, 36910}, {106, 11125}, {108, 14204}, {110, 952}, {186, 1309}, {403, 36067}, {476, 859}, {523, 953}, {934, 18815}, {1290, 6905}, {1304, 37168}, {2166, 26700}, {2720, 40437}, {2737, 7464}, {5627, 36064}, {35011, 38955}

X(43655) = reflection of X(953) in the Euler line
X(43655) = reflection of X(74) in line X(3)X(8)

X(43656) = REFLECTION OF X(33638) IN X(3)

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

X(43656) lies on the circumcircle, the cubics K300 and K304, and these lines: {3, 33638}, {99, 381}, {110, 576}, {476, 37907}, {691, 7575}, {3565, 10298}, {6325, 7417}, {7418, 14388}, {8590, 32694}, {36898, 40118}

X(43656) = reflection of X(i) in X(j) for these {i,j}: {11643, 15744}, {33638, 3}
X(43656) = reflection of X(74) in line X(3)X(9976)

X(43657) = X(5)X(20189)∩X(99)X(40410)

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

X(43657) lies on the circumcircle, the cubic K439, and these lines: {5, 20189}, {99, 40410}, {110, 1173}, {112, 14579}, {140, 930}, {476, 15392}, {691, 11810}, {933, 34484}, {1291, 5899}, {12011, 20185}, {13582, 43351}, {13621, 39168}, {14367, 33639}, {14979, 39180}, {30248, 35482}

X(43657) = X(51)-cross conjugate of X(11071)
X(43657) = X(i)-isoconjugate of X(j) for these (i,j): {140, 1749}, {11063, 20879}, {17438, 37779}
X(43657) = barycentric product X(i)*X(j) for these {i,j}: {288, 1263}, {1173, 13582}, {1291, 39183}, {14579, 40410}
X(43657) = barycentric quotient X(i)/X(j) for these {i,j}: {1173, 37779}, {13582, 1232}, {14579, 140}, {33631, 37943}

X(43658) = ISOGONAL CONJUGATE OF X(11649)

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

X(43658) lies on the circumcircle, the cubic K481, and these lines: {99, 7502}, {110, 34507}, {112, 5475}, {691, 7574}, {3563, 9769}

X(43658) = isogonal conjugate of X(11649)
X(43658) = barycentric quotient X(6)/X(11649)

X(43659) = X(12)X(108)∩X(37)X(112)

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

X(43659) lies on the circumcircle, the cubic K720, and these lines: {12, 108}, {37, 112}, {72, 110}, {99, 20336}, {100, 2915}, {101, 3949}, {107, 41013}, {109, 191}, {337, 36066}, {934, 6356}, {1290, 5080}, {1807, 36069}, {2766, 20989}, {2975, 5606}, {5251, 26700}, {6326, 39633}, {11827, 30238}, {29044, 38871}

X(43659) = X(i)-cross conjugate of X(j) for these (i,j): {2074, 943}, {10693, 80}
X(43659) = X(58)-isoconjugate of X(30447)
X(43659) = cevapoint of X(i) and X(j) for these (i,j): {37, 20989}, {228, 17796}
X(43659) = barycentric quotient X(37)/X(30447)

X(43660) = REFLECTION OF X(1302) IN X(3)

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

X(43660) lies on the circumcircle, the cubic K808, and these lines: {3, 1302}, {4, 9064}, {30, 9060}, {74, 9003}, {105, 7429}, {107, 378}, {110, 376}, {111, 7422}, {112, 5063}, {476, 7464}, {523, 841}, {675, 7440}, {842, 36164}, {925, 21312}, {1301, 18533}, {1304, 10295}, {1311, 7454}, {2071, 16167}, {3651, 9058}, {7414, 9107}, {7418, 9084}, {7421, 9056}, {7425, 9061}, {7430, 9057}, {7444, 9083}, {10102, 36166}, {18877, 32681}

X(43660) = reflection of X(1302) in X(3)
X(43660) = reflection of X(841) in the Euler line
X(43660) = isogonal conjugate of X(14915)
X(43660) = isotomic conjugate of the anticomplement of X(16303)
X(43660) = Thomson-isogonal conjugate of X(8675)
X(43660) = X(16303)-cross conjugate of X(2)
X(43660) = cevapoint of X(40894) and X(40895)
X(43660) = trilinear pole of line {6, 9209}
X(43660) = barycentric quotient X(6)/X(14915)

X(43661) = CEVAPOINT OF X(115) AND X(7669)

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

X(43661) lies on the circumcircle, the cubic K878, and these lines: {476, 30715}, {3448, 33967}

X(43661) = X(6328)-cross conjugate of X(523)
X(43661) = X(1101)-isoconjugate of X(33967)
X(43661) = cevapoint of X(115) and X(7669)
X(43661) = barycentric quotient X(115)/X(33967)

X(43662) = ISOGONAL CONJUGATE OF X(34380)

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

X(43662) lies on the circumcircle, the cubic K943, and these lines: {2, 5522}, {99, 631}, {110, 5020}, {112, 10594}, {476, 37897}, {691, 37925}, {925, 10565}, {3565, 11414}, {7418, 29180}, {8770, 12283}

X(43662) = isogonal conjugate of X(34380)
X(43662) = orthoptic-circle-of-Steiner-inellipe-inverse of X(5522)
X(43662) = trilinear pole, wrt Thomson triangle, of line X(1351)X(3819)
X(43662) = barycentric quotient X(6)/X(34380)

X(43663) = X(99)X(37913)∩X(110)X(16176)

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

X(43663) lies on the circumcircle, the cubic K1167, and these lines: {99, 37913}, {110, 16176}, {112, 37453}, {625, 691}, {1296, 1657}, {2696, 34152}, {7418, 20480}, {7793, 11636}, {21844, 30247}, {35488, 39382}

X(43664) = ISOTOMIC CONJUGATE OF X(32515)

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

X(43664) lies on the Steiner circumellipse, the cubic K757, and these lines: {99, 182}, {183, 670}, {648, 7766}, {6528, 12188}, {18829, 39099}

X(43664) = isotomic conjugate of X(32515)
X(43664) = isogonal conjugate of the complement of X(33873)
X(43664) = isogonal conjugate of the orthogonal projection of X(2) on the Lemoine axis
X(43664) = X(i)-cross conjugate of X(j) for these (i,j): {22735, 98}, {32515, 2}, {33873, 83}
X(43664) = X(i)-isoconjugate of X(j) for these (i,j): {31, 32515}, {63, 33874}
X(43664) = cevapoint of X(2) and X(32515)
X(43664) = trilinear pole of line {2, 3288}
X(43664) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 32515}, {25, 33874}

X(43665) = ISOTOMIC CONJUGATE OF X(2421)

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

X(43665) lies on the Kiepert circumhyperbola, the cubic K027, and these lines: {2, 647}, {4, 512}, {10, 21050}, {76, 525}, {83, 2422}, {94, 9979}, {98, 804}, {262, 523}, {275, 2623}, {287, 2986}, {290, 671}, {338, 14223}, {598, 30491}, {690, 43532}, {826, 3399}, {881, 36897}, {1640, 40814}, {1821, 24624}, {1916, 2799}, {1976, 13307}, {2052, 2501}, {2433, 16080}, {2715, 22456}, {2966, 14592}, {3050, 36199}, {3260, 14977}, {3267, 40824}, {3406, 15917}, {3424, 32472}, {3429, 28470}, {4108, 34098}, {5392, 33294}, {5503, 35522}, {7608, 34291}, {10551, 30505}, {11550, 21646}, {12075, 37892}, {14458, 25423}, {18024, 34087}, {18808, 37778}, {23870, 43538}, {23871, 43539}, {32545, 33695}

X(43665) = reflection of X(9420) in X(6130)
X(43665) = isogonal conjugate of X(14966)
X(43665) = isotomic conjugate of X(2421)
X(43665) = polar conjugate of X(4230)
X(43665) = polar conjugate of the isogonal conjugate of X(879)
X(43665) = pole wrt polar circle of trilinear polar of X(4230) (line X(232)X(511))
X(43665) = isotomic conjugate of the isogonal conjugate of X(2395)
X(43665) = X(i)-Ceva conjugate of X(j) for these (i,j): {22456, 98}, {34536, 338}, {41173, 41760}, {43187, 290}
X(43665) = X(i)-cross conjugate of X(j) for these (i,j): {338, 34536}, {868, 264}, {3124, 36897}, {3569, 523}
X(43665) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14966}, {6, 23997}, {31, 2421}, {48, 4230}, {99, 9417}, {110, 1755}, {162, 3289}, {163, 511}, {232, 4575}, {237, 662}, {240, 32661}, {326, 34859}, {560, 2396}, {692, 17209}, {799, 9418}, {877, 9247}, {1101, 3569}, {1576, 1959}, {2206, 42717}, {2211, 4592}, {2491, 24041}, {2617, 41270}, {2715, 23996}, {2799, 23995}, {2966, 42075}, {4556, 5360}, {9155, 36142}, {9419, 36036}, {11672, 36084}, {32676, 36212}
X(43665) = cevapoint of X(i) and X(j) for these (i,j): {6, 21525}, {523, 3569}, {850, 14295}, {879, 2395}
X(43665) = crosspoint of X(290) and X(43187)
X(43665) = crosssum of X(237) and X(2491)
X(43665) = trilinear pole of line {338, 523}
X(43665) = crossdifference of every pair of points on line {237, 3289}
X(43665) = barycentric product X(i)*X(j) for these {i,j}: {76, 2395}, {98, 850}, {115, 43187}, {125, 22456}, {264, 879}, {287, 14618}, {290, 523}, {336, 24006}, {338, 2966}, {339, 685}, {512, 18024}, {525, 16081}, {878, 18022}, {1109, 36036}, {1502, 2422}, {1577, 1821}, {1910, 20948}, {2715, 23962}, {2799, 34536}, {2970, 17932}, {3267, 6531}, {4609, 15630}, {9154, 35522}, {14208, 36120}, {14295, 36897}, {20031, 36793}, {23994, 36084}
X(43665) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 23997}, {2, 2421}, {4, 4230}, {6, 14966}, {76, 2396}, {98, 110}, {115, 3569}, {125, 684}, {248, 32661}, {264, 877}, {287, 4558}, {290, 99}, {293, 4575}, {321, 42717}, {325, 15631}, {336, 4592}, {338, 2799}, {339, 6333}, {512, 237}, {514, 17209}, {523, 511}, {525, 36212}, {542, 42743}, {647, 3289}, {661, 1755}, {669, 9418}, {685, 250}, {690, 9155}, {798, 9417}, {804, 36213}, {850, 325}, {868, 41167}, {878, 184}, {879, 3}, {882, 14251}, {1577, 1959}, {1821, 662}, {1910, 163}, {1976, 1576}, {2207, 34859}, {2394, 35910}, {2395, 6}, {2422, 32}, {2489, 2211}, {2491, 9419}, {2501, 232}, {2623, 41270}, {2715, 23357}, {2799, 36790}, {2966, 249}, {2970, 16230}, {3124, 2491}, {3267, 6393}, {3569, 11672}, {4705, 5360}, {5466, 5968}, {5967, 5467}, {6531, 112}, {6784, 9420}, {7178, 43034}, {8754, 17994}, {9148, 6786}, {9154, 691}, {10412, 14356}, {12079, 32112}, {14265, 4226}, {14295, 5976}, {14382, 17941}, {14601, 14574}, {14618, 297}, {15628, 5546}, {15630, 669}, {16081, 648}, {16229, 15143}, {16230, 2967}, {18024, 670}, {18070, 3405}, {18808, 35908}, {20021, 1634}, {20031, 23964}, {20975, 39469}, {22456, 18020}, {23105, 868}, {23290, 39569}, {24006, 240}, {30735, 1513}, {31636, 4611}, {34175, 7468}, {34238, 17938}, {34536, 2966}, {35364, 34157}, {35906, 2420}, {36036, 24041}, {36084, 1101}, {36120, 162}, {36822, 5118}, {36874, 11634}, {36897, 805}, {40428, 10425}, {41167, 23098}, {41932, 2715}, {42759, 42751}, {43187, 4590}

X(43666) = ISOGONAL CONJUGATE OF X(14627)

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

X(43666) lies on the Kiepert circumhyperbola, the cubic K067, and these lines: {2, 195}, {3, 13585}, {4, 35895}, {5, 11538}, {94, 32551}, {140, 10277}, {275, 6143}, {631, 13579}, {1029, 6952}, {2052, 14940}, {3525, 6504}, {7383, 38259}, {7505, 8796}, {11140, 21975}, {16336, 40393}, {37943, 39284}

X(43666) = isogonal conjugate of X(14627)
X(43666) = X(i)-cross conjugate of X(j) for these (i,j): {1157, 33565}, {1199, 4}
X(43666) = X(1)-isoconjugate of X(14627)
X(43666) = crosssum of X(195) and X(15047)
X(43666) = barycentric product X(11140)*X(22101)
X(43666) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 14627}, {6748, 35887}, {22101, 1994}

X(43667) = X(2)X(2793)∩X(98)X(5914)

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

X(43667) lies on the Kiepert circumhyperbola, the cubic K088, and these lines: {2, 2793}, {98, 5914}, {523, 5503}, {671, 1499}, {690, 5485}, {804, 11167}, {1916, 8704}, {5466, 6791}, {27550, 42035}, {27551, 42036}, {32472, 43535}

X(43667) = isotomic conjugate of the orthogonal projection of X(99) on its trilinear polar (line X(2)X(6))
X(43667) = X(662)-isoconjugate of X(9486)
X(43667) = barycentric product X(i)*X(j) for these {i,j}: {523, 9487}, {850, 9136}, {5466, 37860}
X(43667) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 9486}, {9136, 110}, {9487, 99}, {37860, 5468}

X(43668) = ISOTOMIC CONJUGATE OF X(34203)

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

X(43668) lies on the Kiepert circumhyperbola, the cubic K089, and these lines: {2, 8644}, {76, 1499}, {512, 5485}, {598, 30217}, {671, 2444}, {804, 5503}, {1916, 2793}, {11167, 25423}

X(43668) = isotomic conjugate of X(34203)
X(43668) = isotomic conjugate of the isogonal conjugate of X(34204)
X(43668) = X(31)-isoconjugate of X(34203)
X(43668) = barycentric product X(76)*X(34204)
X(43668) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 34203}, {34204, 6}

X(43669) = X(2)X(2487)∩X(4)X(28533)

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

X(43669) lies on the Kiepert circumhyperbola, the cubic K090, and these lines: {2, 2487}, {4, 28533}, {98, 28531}, {4024, 4052}

X(43669) = X(163)-isoconjugate of X(28530)
X(43669) = trilinear pole of line {523, 17058}
X(43669) = barycentric product X(850)*X(28531)
X(43669) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 28530}, {28531, 110}

X(43670) = X(2)X(10607)∩X(4)X(3167)

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

X(43670) lies on the Kiepert circumhyperbola, the cubic K182, and these lines: {2, 10607}, {4, 3167}, {20, 13380}, {98, 7396}, {193, 2052}, {262, 7398}, {394, 2996}, {459, 32001}, {1368, 7612}, {1993, 8796}, {5020, 14494}, {5395, 11427}, {11064, 41899}, {18840, 41235}

X(43670) = polar conjugate of X(6622)
X(43670) = isotomic conjugate of the anticomplement of X(37669)
X(43670) = X(i)-cross conjugate of X(j) for these (i,j): {12429, 69}, {15077, 35510}, {37669, 2}
X(43670) = X(i)-isoconjugate of X(j) for these (i,j): {19, 12164}, {48, 6622}, {2155, 32605}
X(43670) = cevapoint of X(i) and X(j) for these (i,j): {6, 39568}, {115, 8057}
X(43670) = trilinear pole of line {523, 16976}
X(43670) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 12164}, {4, 6622}, {20, 32605}

X(43671) = ISOGONAL CONJUGATE OF X(3110)

Barycentrics    (b + c)*(a^4 + b^4 - a^3*c - a^2*b*c - a*b^2*c - b^3*c + 2*a*b*c^2)*(a^4 - a^3*b - a^2*b*c + 2*a*b^2*c - a*b*c^2 - b*c^3 + c^4) : :
X(43671) = 2 X[17761] - 3 X[38220]

X(43671) lies on the Kiepert circumhyperbola, the cubic K359, and these lines: {1, 4444}, {2, 1083}, {76, 874}, {99, 8299}, {115, 13576}, {528, 671}, {1018, 43534}, {1916, 3903}, {17761, 38220}

X(43671) = reflection of X(i) in X(j) for these {i,j}: {99, 8299}, {13576, 115}
X(43671) = isogonal conjugate of X(3110)
X(43671) = antigonal image of X(13576)
X(43671) = antitomic conjugate of X(13576)
X(43671) = symgonal image of X(8299)
X(43671) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3110}, {662, 5098}
X(43671) = trilinear pole of line {523, 2238}
X(43671) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 3110}, {512, 5098}

X(43672) = ISOGONAL CONJUGATE OF X(13329)

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

A construction is given by Ivan Pavlov in Euclid 2420 .

X(43672) lies on the Kiepert circumhyperbola, the cubic K382, and these lines: {2, 991}, {4, 4253}, {5, 14520}, {10, 1146}, {11, 118}, {76, 18738}, {83, 13727}, {103, 673}, {162, 40395}, {275, 14004}, {321, 4712}, {516, 672}, {537, 4052}, {946, 40515}, {990, 24600}, {1111, 1210}, {1751, 7580}, {2051, 4260}, {2310, 24014}, {2808, 17761}, {2826, 4049}, {3693, 29016}, {4080, 26015}, {4297, 28265}, {4334, 40451}, {4551, 13405}, {5030, 36028}, {5540, 31852}, {5779, 24352}, {6245, 36907}, {6539, 25006}, {6712, 26007}, {9355, 23821}, {10175, 14519}, {13478, 19541}, {14554, 37374}, {18840, 36682}, {24203, 38666}, {24624, 36002}, {32022, 36706}

X(43672) = isogonal conjugate of X(13329)
X(43672) = polar conjugate of X(26003)
X(43672) = X(17435)-cross conjugate of X(514)
X(43672) = X(i)-isoconjugate of X(j) for these (i,j): {1, 13329}, {48, 26003}
X(43672) = cevapoint of X(i) and X(j) for these (i,j): {11, 2254}, {672, 14547}
X(43672) = trilinear pole of line {523, 2294}
X(43672) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 26003}, {6, 13329}
X(43672) = {X(5),X(14520)}-harmonic conjugate of X(17758)

X(43673) = ISOTOMIC CONJUGATE OF X(34211)

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

X(43673) lies on the Kiepert circumhyperbola, the parabola {{A,B,C,X(525),X(850)}}, the cubic K406, and these lines: {2, 2419}, {4, 525}, {98, 1297}, {459, 2501}, {514, 3429}, {523, 3424}, {671, 35140}, {850, 2052}, {877, 17932}, {2867, 23977}, {4240, 17708}, {6330, 9979}, {9476, 34765}, {14458, 23878}, {14944, 39473}, {38240, 38253}

X(43673) = isotomic conjugate of X(34211)
X(43673) = polar conjugate of X(2409)
X(43673) = isotomic conjugate of the isogonal conjugate of X(34212)
X(43673) = polar conjugate of the isotomic conjugate of X(2419)
X(43673) = polar conjugate of the isogonal conjugate of X(2435)
X(43673) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {36046, 147}, {36104, 12384}
X(43673) = X(i)-cross conjugate of X(j) for these (i,j): {2435, 2419}, {3150, 264}, {16230, 850}
X(43673) = X(i)-isoconjugate of X(j) for these (i,j): {31, 34211}, {48, 2409}, {63, 2445}, {110, 2312}, {112, 8766}, {162, 8779}, {163, 1503}, {255, 23977}, {441, 32676}, {577, 24024}, {662, 42671}, {4575, 16318}, {6793, 36034}, {9475, 36084}, {35282, 36142}
X(43673) = cevapoint of X(i) and X(j) for these (i,j): {512, 2508}, {525, 2799}, {2435, 34212}
X(43673) = trilinear pole of line {523, 15526}
X(43673) = pole wrt polar circle of trilinear polar of X(2409) (line X(132)X(1503), the Simson line of X(112))
X(43673) = crossdifference of every pair of points on line {8779, 9475}
X(43673) = barycentric product X(i)*X(j) for these {i,j}: {4, 2419}, {76, 34212}, {264, 2435}, {523, 35140}, {525, 6330}, {850, 1297}, {2799, 9476}, {8767, 14208}, {17879, 36092}, {32687, 36793}
X(43673) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 34211}, {4, 2409}, {25, 2445}, {158, 24024}, {393, 23977}, {512, 42671}, {523, 1503}, {525, 441}, {647, 8779}, {656, 8766}, {661, 2312}, {690, 35282}, {850, 30737}, {879, 34156}, {1297, 110}, {1637, 6793}, {2419, 69}, {2435, 3}, {2492, 28343}, {2501, 16318}, {2799, 15595}, {3569, 9475}, {6330, 648}, {7178, 43045}, {8767, 162}, {9476, 2966}, {10412, 43089}, {14977, 36894}, {15526, 39473}, {16230, 132}, {16318, 15639}, {32687, 23964}, {34212, 6}, {35140, 99}, {35909, 40080}, {36092, 24000}, {39265, 4230}

X(43674) = X(2)X(1499)∩X(76)X(8704)

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

X(43674) lies on the Kiepert circumhyperbola, the cubic K408, and these lines: {2, 1499}, {76, 8704}, {512, 11167}, {523, 5485}, {598, 32472}, {671, 2408}, {690, 5503}, {9123, 11162}, {10302, 32473}, {27550, 42036}, {27551, 42035}

X(43674) = X(12036)-isoconjugate of X(36142)
X(43674) = cevapoint of X(27550) and X(27551)
X(43674) = trilinear pole of line {523, 6791}
X(43674) = barycentric quotient X(i)/X(j) for these {i,j}: {690, 12036}, {1499, 37745}

X(43675) = X(2)X(15474)∩X(4)X(912)

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

X(43675) lies on the Kiepert circumhyperbola, the cubic K610, and these lines: {2, 15474}, {4, 912}, {10, 23604}, {63, 1751}, {98, 13397}, {226, 21065}, {286, 40395}, {321, 1234}, {1229, 40013}, {1441, 25254}, {2895, 13583}, {2994, 39695}, {3870, 29016}, {3998, 16732}, {4463, 13576}, {28605, 43533}, {30690, 34772}

X(43675) = isogonal conjugate of X(41332)
X(43675) = isotomic conjugate of X(40571)
X(43675) = polar conjugate of X(30733)
X(43675) = polar conjugate of the isogonal conjugate of X(28787)
X(43675) = X(i)-cross conjugate of X(j) for these (i,j): {72, 1441}, {21530, 264}, {41508, 23604}
X(43675) = X(i)-isoconjugate of X(j) for these (i,j): {1, 41332}, {6, 1780}, {19, 41608}, {31, 40571}, {48, 30733}, {58, 2911}, {163, 15313}, {284, 37579}, {1172, 3215}, {1333, 3811}, {1474, 11517}, {1708, 2194}, {2150, 41538}, {2206, 17776}, {2299, 3173}
X(43675) = cevapoint of X(525) and X(16732)
X(43675) = barycentric product X(i)*X(j) for these {i,j}: {75, 23604}, {264, 28787}, {274, 41508}, {321, 15474}, {349, 39943}, {850, 13397}, {20336, 39267}
X(43675) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1780}, {2, 40571}, {3, 41608}, {4, 30733}, {6, 41332}, {10, 3811}, {12, 41538}, {37, 2911}, {65, 37579}, {72, 11517}, {73, 3215}, {226, 1708}, {321, 17776}, {429, 41609}, {442, 14054}, {523, 15313}, {1214, 3173}, {3668, 4341}, {13397, 110}, {15474, 81}, {21207, 17877}, {23604, 1}, {28787, 3}, {33294, 26217}, {39267, 28}, {39943, 284}, {41508, 37}

X(43676) = X(2)X(7765)∩X(4)X(5965)

Barycentrics    (a^2 + b^2 - 4*c^2)*(a^2 - 4*b^2 + c^2) : :
X(43676) = 9 X[2] - 10 X[12815], 14 X[2] - 15 X[38223], 14 X[3851] - 15 X[38228], 28 X[12815] - 27 X[38223], 14 X[14869] - 15 X[38226], 14 X[15808] - 15 X[38222]

X(43676) lies on the Kiepert circumhyperbola, the cubic K618, and these lines: {2, 7765}, {4, 5965}, {10, 17258}, {13, 22845}, {14, 22844}, {83, 6329}, {98, 550}, {115, 35005}, {226, 29601}, {262, 3851}, {315, 38259}, {382, 14458}, {524, 33698}, {532, 12817}, {533, 12816}, {546, 14492}, {598, 7760}, {627, 43543}, {628, 43542}, {629, 43549}, {630, 43548}, {671, 7768}, {1656, 11669}, {1916, 14045}, {3407, 14034}, {3631, 7911}, {3858, 7905}, {5254, 10159}, {5395, 11185}, {5485, 7883}, {6392, 18845}, {6656, 10302}, {7388, 43569}, {7389, 43568}, {7607, 15720}, {7608, 35018}, {7612, 10299}, {7751, 14976}, {7790, 18840}, {7860, 40341}, {7895, 33293}, {7901, 32457}, {8587, 33276}, {11172, 33226}, {11289, 43544}, {11290, 43545}, {11303, 33607}, {11304, 33606}, {13571, 15031}, {14061, 32820}, {14869, 38226}, {15808, 38222}, {16277, 37900}, {22113, 43540}, {22114, 43541}, {33256, 43535}

X(43676) = reflection of X(i) in X(j) for these {i,j}: {22844, 33464}, {22845, 33465}, {35005, 115}
X(43676) = isogonal conjugate of X(35007)
X(43676) = isotomic conjugate of X(3629)
X(43676) = antigonal image of X(35005)
X(43676) = antitomic conjugate of X(35005)
X(43676) = isogonal conjugate of the complement of X(7860)
X(43676) = isotomic conjugate of the anticomplement of X(3631)
X(43676) = isotomic conjugate of the complement of X(40341)
X(43676) = X(i)-cross conjugate of X(j) for these (i,j): {3631, 2}, {7911, 83}
X(43676) = X(i)-isoconjugate of X(j) for these (i,j): {1, 35007}, {31, 3629}, {163, 32478}
X(43676) = cevapoint of X(i) and X(j) for these (i,j): {2, 40341}, {6, 37913}
X(43676) = trilinear pole of line {523, 7925}
X(43676) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3629}, {6, 35007}, {523, 32478}, {1594, 41599}

X(43677) = X(1)X(14534)∩X(2)X(986)

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

X(43677) lies on the Kiepert circumhyperbola, the cubic K619, and these lines: {1, 14534}, {2, 986}, {4, 740}, {8, 42066}, {10, 21810}, {40, 98}, {75, 6042}, {76, 18697}, {192, 6625}, {226, 3178}, {304, 40017}, {321, 20653}, {341, 2643}, {516, 3429}, {525, 4444}, {714, 42440}, {758, 10441}, {1029, 20060}, {1962, 4195}, {2051, 17748}, {3695, 43534}, {3704, 34528}, {3743, 3923}, {3869, 24624}, {3931, 40718}, {3944, 4647}, {4080, 27558}, {10180, 37176}, {10436, 32014}, {17476, 34860}, {19925, 38309}, {27576, 36907}, {27577, 30588}

X(43677) = anticomplement of X(15349)
X(43677) = isotomic conjugate of the anticomplement of X(34528)
X(43677) = X(i)-cross conjugate of X(j) for these (i,j): {1329, 6757}, {3704, 10}, {34528, 2}
X(43677) = X(i)-isoconjugate of X(j) for these (i,j): {58, 5247}, {163, 6002}, {249, 16613}, {1333, 1999}, {24560, 32676}
X(43677) = cevapoint of X(2643) and X(3700)
X(43677) = Kirikami-Euler image of X(10)
X(43677) = barycentric product X(850)*X(6010)
X(43677) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 1999}, {37, 5247}, {523, 6002}, {525, 24560}, {1211, 39774}, {2643, 16613}, {6010, 110}, {34528, 15349}

X(43678) = X(4)X(66)∩X(24)X(98)

Barycentrics    b^2*c^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^4 + b^4 - c^4)*(a^4 - b^4 + c^4) : :
Barycentrics    (tan A)/(sin 2A - tan ω) : :

X(43678) lies on the Kiepert circumhyperbola, the cubic K620, and these lines: {2, 1235}, {4, 66}, {24, 98}, {25, 16277}, {76, 5523}, {83, 264}, {96, 19189}, {262, 1594}, {275, 40814}, {297, 5392}, {338, 2207}, {419, 40146}, {458, 40393}, {1249, 18841}, {2986, 7754}, {3147, 7612}, {3406, 41204}, {3424, 7487}, {5359, 40357}, {5395, 41370}, {7509, 40448}, {7576, 14458}, {7607, 10018}, {13599, 14788}, {17407, 40178}, {28696, 30737}, {28706, 40824}, {28710, 41676}, {41366, 43527}

X(43678) = isogonal conjugate of X(10316)
X(43678) = isotomic conjugate of X(20806)
X(43678) = polar conjugate of X(22)
X(43678) = isotomic conjugate of the isogonal conjugate of X(13854)
X(43678) = polar conjugate of the isotomic conjugate of X(18018)
X(43678) = polar conjugate of the isogonal conjugate of X(66)
X(43678) = X(i)-cross conjugate of X(j) for these (i,j): {25, 264}, {66, 18018}, {339, 14618}, {3767, 847}, {23556, 75}, {27376, 4}, {38356, 523}
X(43678) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10316}, {3, 2172}, {22, 48}, {31, 20806}, {63, 206}, {69, 17453}, {72, 17186}, {75, 22075}, {77, 4548}, {78, 7251}, {127, 23995}, {163, 8673}, {184, 1760}, {255, 8743}, {304, 20968}, {315, 9247}, {326, 17409}, {560, 34254}, {810, 4611}, {1101, 38356}, {1332, 21122}, {1437, 4456}, {1444, 21034}, {2485, 4575}, {14396, 36034}, {14575, 20641}, {16757, 32656}, {18596, 39172}, {19616, 22135}, {23208, 34055}, {40364, 40372}
X(43678) = cevapoint of X(i) and X(j) for these (i,j): {6, 21213}, {66, 13854}, {338, 2501}, {523, 38356}
X(43678) = crosssum of X(3) and X(23172)
X(43678) = trilinear pole of line {523, 37981}
X(43678) = pole wrt polar circle of trilinear polar of X(22) (line X(2485)X(8673))
X(43678) = perspector of ABC and orthoanticevian triangle of X(18018)
X(43678) = barycentric product X(i)*X(j) for these {i,j}: {4, 18018}, {25, 40421}, {66, 264}, {76, 13854}, {850, 1289}, {1235, 16277}, {1969, 2156}, {2052, 14376}, {2353, 18022}, {8795, 41168}, {15388, 23962}, {16081, 34138}, {17407, 40009}
X(43678) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 20806}, {4, 22}, {6, 10316}, {19, 2172}, {25, 206}, {32, 22075}, {66, 3}, {76, 34254}, {92, 1760}, {115, 38356}, {235, 41580}, {264, 315}, {273, 7210}, {318, 4123}, {331, 17076}, {338, 127}, {393, 8743}, {427, 3313}, {523, 8673}, {607, 4548}, {608, 7251}, {648, 4611}, {1289, 110}, {1474, 17186}, {1637, 14396}, {1826, 4456}, {1843, 23208}, {1969, 20641}, {1973, 17453}, {1974, 20968}, {2052, 17907}, {2156, 48}, {2207, 17409}, {2333, 21034}, {2353, 184}, {2501, 2485}, {6531, 11610}, {8743, 36414}, {13854, 6}, {14376, 394}, {14618, 33294}, {15388, 23357}, {16081, 31636}, {16277, 1176}, {16732, 18187}, {17407, 159}, {17924, 16757}, {18018, 69}, {18022, 40073}, {26284, 27084}, {27372, 418}, {27376, 40938}, {34138, 36212}, {34207, 39172}, {37801, 22151}, {40146, 14575}, {40404, 28724}, {40421, 305}, {41013, 4463}, {41168, 5562}, {41760, 28405}

X(43679) = X(2)X(41334)∩X(3)X(35098)

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

X(43679) lies on the Kiepert circumhyperbola, the cubic K622, and these lines: {2, 41334}, {3, 35098}, {4, 34845}, {98, 1614}, {262, 3567}, {275, 10312}, {2996, 37186}, {11459, 13599}, {13585, 40853}, {30505, 37988}

X(43679) = isogonal conjugate of the anticomplement of X(36952)
X(43679) = X(217)-cross conjugate of X(4)
X(43679) = X(662)-isoconjugate of X(21646)
X(43679) = cevapoint of X(i) and X(j) for these (i,j): {125, 42293}, {647, 7668}, {12077, 34981}
X(43679) = barycentric quotient X(512)/X(21646)

X(43680) = X(2)X(17104)∩X(10)X(2174)

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

X(43680) lies on the Kiepert circumhyperbola, the cubic K679, and these lines: {2, 17104}, {10, 2174}, {35, 321}, {94, 759}, {226, 1399}, {3648, 4080}, {9274, 39295}

X(43680) = isogonal conjugate of X(41329)
X(43680) = X(1)-isoconjugate of X(41329)
X(43680) = barycentric quotient X(6)/X(41329)

X(43681) = X(2)X(9607)∩X(4)X(11898)

Barycentrics    (a^2 + b^2 - 7*c^2)*(a^2 - 7*b^2 + c^2) : :
X(43681) = 10 X[1656] - 9 X[10155]

X(43681) lies on the Kiepert circumhyperbola, the cubic K917, and these lines: {2, 9607}, {4, 11898}, {69, 38259}, {83, 6392}, {98, 3522}, {193, 18845}, {226, 29583}, {262, 5068}, {598, 32979}, {620, 32824}, {671, 32982}, {1656, 10155}, {1916, 33290}, {2996, 7784}, {3146, 14458}, {3407, 14031}, {3424, 5059}, {3523, 7612}, {3832, 14492}, {3854, 14484}, {5056, 14494}, {5189, 40178}, {5286, 43527}, {5485, 32974}, {7389, 43536}, {7620, 33698}, {7754, 18843}, {7860, 17503}, {8781, 32830}, {11148, 33003}, {11172, 32965}, {11289, 43554}, {11290, 43555}, {11303, 33604}, {11304, 33605}, {11331, 38253}, {13571, 32991}, {18842, 32971}, {32457, 32878}, {32997, 43535}, {33283, 40824}, {34505, 41895}, {40898, 43553}, {40899, 43552}, {40900, 43557}, {40901, 43556}

X(43681) = isogonal conjugate of X(22331)
X(43681) = isotomic conjugate of the anticomplement of X(3620)
X(43681) = X(3620)-cross conjugate of X(2)
X(43681) = X(1)-isoconjugate of X(22331)
X(43681) = barycentric quotient X(6)/X(22331)

X(43682) = X(2)X(7110)∩X(4)X(79)

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

X(43682) lies on the Kiepert circumhyperbola, the cubic K972, and these lines: {2, 7110}, {4, 79}, {7, 1029}, {10, 6757}, {13, 554}, {14, 1081}, {57, 24624}, {85, 32014}, {92, 16080}, {98, 26700}, {226, 8818}, {273, 40395}, {516, 41504}, {553, 24208}, {1479, 41496}, {1577, 2394}, {1751, 2160}, {1836, 12904}, {1989, 3772}, {3870, 6742}, {6358, 6539}, {12649, 13583}, {13582, 17483}, {15455, 18743}, {16547, 21367}, {20565, 34258}, {35049, 39295}

X(43682) = isogonal conjugate of X(35192)
X(43682) = polar conjugate of X(11107)
X(43682) = X(i)-cross conjugate of X(j) for these (i,j): {1109, 4077}, {3649, 1441}, {7178, 38340}, {8818, 6757}, {27555, 264}
X(43682) = X(i)-isoconjugate of X(j) for these (i,j): {1, 35192}, {3, 41502}, {6, 35193}, {9, 17104}, {21, 2174}, {35, 284}, {48, 11107}, {50, 6740}, {55, 40214}, {110, 9404}, {163, 35057}, {1098, 21741}, {1333, 4420}, {1399, 2287}, {1812, 14975}, {2003, 2328}, {2150, 3678}, {2175, 34016}, {2193, 6198}, {2194, 3219}, {2206, 42033}, {2326, 22342}, {2341, 6149}, {2594, 7054}, {2605, 5546}, {6741, 23357}
X(43682) = cevapoint of X(21044) and X(23752)
X(43682) = trilinear pole of line {523, 36035}
X(43682) = barycentric product X(i)*X(j) for these {i,j}: {7, 6757}, {65, 20565}, {79, 1441}, {85, 8818}, {94, 18593}, {226, 30690}, {328, 1835}, {338, 35049}, {349, 2160}, {850, 26700}, {1446, 7110}, {1577, 38340}, {2166, 41804}, {4077, 6742}, {7178, 15455}
X(43682) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 35193}, {4, 11107}, {6, 35192}, {10, 4420}, {12, 3678}, {19, 41502}, {56, 17104}, {57, 40214}, {65, 35}, {79, 21}, {85, 34016}, {225, 6198}, {226, 3219}, {265, 1793}, {321, 42033}, {349, 33939}, {442, 31938}, {523, 35057}, {553, 17190}, {661, 9404}, {1042, 1399}, {1109, 6741}, {1254, 2594}, {1365, 2611}, {1400, 2174}, {1425, 22342}, {1427, 2003}, {1441, 319}, {1446, 17095}, {1464, 6149}, {1835, 186}, {1989, 2341}, {2160, 284}, {2166, 6740}, {2611, 3024}, {3336, 35195}, {3615, 1098}, {3649, 3647}, {3668, 1442}, {4017, 2605}, {4077, 4467}, {6186, 2194}, {6354, 16577}, {6358, 3969}, {6742, 643}, {6757, 8}, {7073, 2328}, {7100, 283}, {7110, 2287}, {7178, 14838}, {8818, 9}, {13486, 4636}, {15455, 645}, {18593, 323}, {20565, 314}, {24002, 16755}, {26700, 110}, {30690, 333}, {34301, 15776}, {34922, 5379}, {35049, 249}, {36064, 36034}, {38340, 662}

X(43683) = X(2)X(17861)∩X(4)X(758)

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

X(43683) lies on the Kiepert circumhyperbola, the cubic K973, and these lines: {2, 17861}, {4, 758}, {8, 13583}, {10, 41501}, {63, 24624}, {92, 40395}, {98, 6011}, {200, 1109}, {226, 21069}, {515, 3429}, {1029, 5905}, {1478, 41495}, {3085, 42005}, {3811, 6757}, {4647, 43533}, {8680, 13478}, {30143, 43531}

X(43683) = polar conjugate of X(13739)
X(43683) = X(i)-cross conjugate of X(j) for these (i,j): {9, 6757}, {21677, 1441}, {27687, 264}, {32580, 4}
X(43683) = X(i)-isoconjugate of X(j) for these (i,j): {48, 13739}, {163, 6003}, {222, 41503}, {284, 37583}, {1333, 34772}, {2150, 15556}, {2206, 33116}, {8286, 23357}, {27086, 34079}
X(43683) = cevapoint of X(1109) and X(3700)
X(43683) = barycentric product X(i)*X(j) for these {i,j}: {75, 41501}, {321, 37887}, {850, 6011}, {1441, 6598}
X(43683) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 13739}, {10, 34772}, {12, 15556}, {33, 41503}, {65, 37583}, {321, 33116}, {442, 39772}, {523, 6003}, {758, 27086}, {1109, 8286}, {3649, 41547}, {4077, 31603}, {6011, 110}, {6598, 21}, {34243, 11101}, {37887, 81}, {41013, 5174}, {41495, 229}, {41501, 1}

X(43684) = X(2)X(34021)∩X(10)X(1920)

Barycentrics    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)*(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(43684) lies on the Kiepert circumhyperbola, the cubic K1007, and these lines: {2, 34021}, {10, 1920}, {83, 40770}, {226, 7205}, {321, 18275}, {6374, 34258}, {13576, 30660}, {40718, 40737}

X(43684) = isotomic conjugate of X(21779)
X(43684) = X(i)-cross conjugate of X(j) for these (i,j): {6385, 76}, {7018, 6063}, {17669, 264}
X(43684) = X(i)-isoconjugate of X(j) for these (i,j): {6, 18756}, {31, 21779}, {32, 1045}, {163, 9402}, {560, 1655}, {1973, 23079}, {2205, 39915}, {2206, 21883}, {18900, 40752}
X(43684) = cevapoint of X(i) and X(j) for these (i,j): {6, 20858}, {693, 3124}
X(43684) = barycentric product X(i)*X(j) for these {i,j}: {75, 18298}, {561, 40737}, {1502, 40770}
X(43684) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18756}, {2, 21779}, {69, 23079}, {75, 1045}, {76, 1655}, {310, 39915}, {321, 21883}, {523, 9402}, {871, 40743}, {6385, 34021}, {18298, 1}, {39926, 3747}, {40737, 31}, {40770, 32}, {40778, 40728}

X(43685) = ISOTOMIC CONJUGATE OF X(2106)

Barycentrics    b*c*(b + c)*(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(43685) lies on the Kiepert circumhyperbola, the cubic K1020, and these lines: {2, 3121}, {76, 3125}, {321, 3124}, {1916, 3263}, {1921, 40017}, {2107, 40718}, {2665, 43531}, {6625, 20345}, {9148, 35353}, {18035, 40024}, {18061, 25661}, {34087, 35543}

X(43685) = isotomic conjugate of X(2106)
X(43685) = polar conjugate of X(15148)
X(43685) = X(35544)-cross conjugate of X(321)
X(43685) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2106}, {32, 2669}, {48, 15148}, {58, 21788}, {560, 40874}, {849, 21897}, {1333, 2664}, {1474, 20796}, {1501, 41535}, {2206, 17759}
X(43685) = barycentric product X(i)*X(j) for these {i,j}: {313, 2665}, {321, 39925}, {561, 2107}
X(43685) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2106}, {4, 15148}, {10, 2664}, {37, 21788}, {72, 20796}, {75, 2669}, {76, 40874}, {321, 17759}, {561, 41535}, {594, 21897}, {2107, 31}, {2665, 58}, {3948, 39916}, {35544, 39028}, {39925, 81}, {40769, 5009}, {43534, 40796}
X(42685) = {X(6),X(10304)}-harmonic conjugate of X(42684)

X(43686) = X(2)X(7167)∩X(4)X(6196)

Barycentrics    (b + c)*(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(43686) lies on the Kiepert circumhyperbola, the cubic K1035, and these lines: {2, 7167}, {4, 6196}, {10, 4531}, {76, 3061}, {83, 19557}, {98, 238}, {226, 16584}, {262, 41886}, {321, 20684}, {1916, 33891}, {20335, 40017}

X(43686) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 39092}, {41520, 141}
X(43686) = X(18904)-cross conjugate of X(10)
X(43686) = X(58)-isoconjugate of X(3508)
X(43686) = barycentric product X(321)*X(7167)
X(43686) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 3508}, {7167, 81}, {8927, 13588}, {16609, 39940}

X(43687) = X(2)X(3510)∩X(4)X(3495)

Barycentrics    (b + c)*(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(43687) lies on the Kiepert circumhyperbola, the cubic K1036, and these lines: {2, 3510}, {4, 3495}, {10, 718}, {76, 982}, {83, 171}, {98, 40597}, {226, 19564}, {321, 3778}, {3741, 40024}, {18905, 21238}, {22171, 43534}

X(43687) = X(39953)-complementary conjugate of X(141)
X(43687) = X(i)-cross conjugate of X(j) for these (i,j): {1237, 42027}, {18905, 226}, {21238, 10}
X(43687) = X(i)-isoconjugate of X(j) for these (i,j): {284, 3503}, {1333, 26752}
X(43687) = cevapoint of X(2533) and X(3122)
X(43687) = barycentric product X(i)*X(j) for these {i,j}: {10, 39746}, {1441, 3495}, {39937, 43534}
X(43687) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 26752}, {65, 3503}, {1215, 39929}, {3495, 21}, {39746, 86}, {39937, 33295}

X(43688) = ISOTOMIC CONJUGATE OF X(7766)

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

X(43688) lies on the Kiepert circumhyperbola, the cubic K1037, and these lines: {2, 698}, {4, 7779}, {10, 33890}, {39, 43527}, {69, 11606}, {76, 7849}, {83, 194}, {98, 3098}, {115, 10290}, {262, 9865}, {511, 14458}, {538, 598}, {671, 7818}, {1278, 13576}, {1916, 7897}, {1975, 39089}, {3094, 42006}, {3212, 33889}, {3399, 7697}, {3406, 7709}, {3407, 7766}, {3552, 31981}, {5395, 20105}, {5485, 33251}, {5969, 43535}, {7607, 15819}, {7914, 7919}, {8024, 40162}, {8149, 33002}, {9464, 34087}, {10513, 38259}, {16898, 18841}, {24349, 40718}

X(43688) = reflection of X(10290) in X(115)
X(43688) = isotomic conjugate of X(7766)
X(43688) = anticomplement of X(10335)
X(43688) = antigonal image of X(10290)
X(43688) = antitomic conjugate of X(10290)
X(43688) = isotomic conjugate of the anticomplement of X(3314)
X(43688) = X(3314)-cross conjugate of X(2)
X(43688) = X(i)-isoconjugate of X(j) for these (i,j): {31, 7766}, {163, 25423}, {560, 41259}, {1917, 10010}
X(43688) = cevapoint of X(824) and X(21138)
X(43688) = barycentric product X(850)*X(25424)
X(43688) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 7766}, {76, 41259}, {141, 32449}, {523, 25423}, {1502, 10010}, {3314, 10335}, {25424, 110}

X(43689) = ISOGONAL CONJUGATE OF X(6240)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6 - 3*a^2*b^4 + 2*b^6 - a^4*c^2 + 2*a^2*b^2*c^2 - 3*b^4*c^2 - a^2*c^4 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 + 2*a^2*b^2*c^2 - 3*a^2*c^4 - 3*b^2*c^4 + 2*c^6) : :
X(43689) = X[68] + 2 X[35240], 2 X[7689] + X[15062], 2 X[12359] + X[18442]

X(43689) lies on the Jerabek circumhyperbola, the cubic K126, and these lines: {4, 5449}, {6, 6102}, {20, 70}, {23, 16835}, {26, 64}, {30, 6145}, {54, 13754}, {66, 3357}, {67, 550}, {68, 21659}, {69, 12118}, {74, 7488}, {155, 14528}, {185, 40441}, {265, 12359}, {539, 13418}, {1147, 3431}, {1154, 42059}, {1173, 7527}, {1176, 40647}, {1177, 41725}, {1204, 3549}, {3426, 7517}, {3521, 10024}, {3527, 13321}, {3564, 13622}, {5504, 5562}, {5663, 32379}, {6030, 11270}, {6368, 15328}, {7530, 22334}, {7556, 13452}, {7691, 17702}, {7722, 38534}, {9019, 12085}, {9927, 16000}, {10627, 12302}, {11468, 15103}, {11744, 15761}, {11819, 15321}, {14542, 18388}, {14852, 18379}, {15132, 33282}, {16665, 22115}, {16774, 41464}, {16867, 18436}, {17505, 18323}, {20191, 43601}

X(43689) = isogonal conjugate of X(6240)
X(43689) = isogonal conjugate of the anticomplement of X(12605)
X(43689) = isogonal conjugate of the polar conjugate of X(42410)
X(43689) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6240}, {158, 12038}
X(43689) = cevapoint of X(3) and X(18436)
X(43689) = barycentric product X(3)*X(42410)
X(43689) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 6240}, {577, 12038}, {42410, 264}

X(43690) = ISOGONAL CONJUGATE OF X(10996)

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 - 2*a^4*c^4 + 20*a^2*b^2*c^4 - 2*b^4*c^4 + c^8)*(a^8 - 2*a^4*b^4 + b^8 - 4*a^6*c^2 + 20*a^2*b^4*c^2 + 6*a^4*c^4 - 2*b^4*c^4 - 4*a^2*c^6 + c^8) : :

X(43690) lies on the Jerabek circumhyperbola, the cubic K152, and these lines: {25, 15740}, {68, 1597}, {69, 1593}, {73, 16541}, {1598, 4846}, {2883, 14542}, {3521, 18535}, {5198, 31371}, {5663, 16543}, {10996, 16540}, {11403, 15077}, {31978, 34207}, {34483, 35501}

X(43690) = isogonal conjugate of X(10996)
X(43690) = isogonal conjugate of the anticomplement of X(11479)
X(43690) = barycentric quotient X(6)/X(10996)

X(43691) = ISOGONAL CONJUGATE OF X(5059)

Barycentrics    a^2*(5*a^4 - 10*a^2*b^2 + 5*b^4 + 6*a^2*c^2 + 6*b^2*c^2 - 11*c^4)*(5*a^4 + 6*a^2*b^2 - 11*b^4 - 10*a^2*c^2 + 6*b^2*c^2 + 5*c^4) : :
X(43691) = 4 X[3] - 3 X[15748], 4 X[4] - 5 X[15752], X[3146] - 3 X[15749], 19 X[15022] - 15 X[15751]

X(43691) lies on the Jerabek circumhyperbola, the cubic K156, and these lines: {3, 15748}, {4, 15752}, {6, 34469}, {54, 10606}, {68, 15704}, {74, 1620}, {378, 34567}, {548, 42021}, {1173, 10605}, {1192, 3426}, {1204, 22334}, {1498, 11270}, {1853, 38436}, {3146, 15749}, {3357, 3527}, {3518, 11738}, {3519, 3534}, {3521, 5072}, {3526, 14861}, {3531, 9786}, {3532, 15750}, {3628, 4846}, {5198, 14490}, {6415, 6425}, {6416, 6426}, {10303, 15740}, {11410, 14528}, {11440, 41435}, {11477, 38263}, {14483, 35502}, {15022, 15751}, {15576, 38264}, {15811, 16835}

X(43691) = isogonal conjugate of X(5059)
X(43691) = isogonal conjugate of the anticomplement of X(3146)
X(43691) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5059}, {92, 33636}
X(43691) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5059}, {184, 33636}

X(43692) = ISOGONAL CONJUGATE OF X(3109)

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

X(43692) lies on the Jerabek circumhyperbola, the cubic K165, and these lines: {1, 35050}, {3, 13868}, {4, 42759}, {69, 6790}, {74, 2818}, {110, 34586}, {125, 38955}, {265, 952}, {895, 2810}, {21740, 34800}

X(43692) = reflection of X(i) in X(j) for these {i,j}: {110, 34586}, {38955, 125}
X(43692) = isogonal conjugate of X(3109)
X(43692) = antigonal image of X(38955)
X(43692) = symgonal image of X(34586)
X(43692) = isogonal conjugate of the anticomplement of X(36155)
X(43692) = isogonal conjugate of the complement of X(36154)
X(43692) = trilinear pole of line {647, 2245}
X(43692) = barycentric quotient X(6)/X(3109)

X(43693) = ISOGONAL CONJUGATE OF X(447)

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

X(43693) lies on the Jerabek circumhyperbola, the cubic K224, and these lines: {4, 3120}, {69, 17216}, {71, 3269}, {72, 2632}, {74, 902}, {238, 37142}, {290, 35169}, {1175, 1193}, {1246, 16099}, {1798, 4303}, {5301, 34440}

X(43693) = isogonal conjugate of X(447)
X(43693) = isogonal conjugate of the isotomic conjugate of X(40715)
X(43693) = X(i)-isoconjugate of X(j) for these (i,j): {1, 447}, {28, 16086}, {811, 42662}, {867, 5379}, {1474, 42709}
X(43693) = barycentric product X(i)*X(j) for these {i,j}: {6, 40715}, {71, 16099}, {647, 35169}
X(43693) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 447}, {71, 16086}, {72, 42709}, {3049, 42662}, {35169, 6331}, {40715, 76}

X(43694) = X(4)X(21044)∩X(65)X(3708)

Barycentrics    a^2*(b + c)*(a^2 - b^2 - c^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 - 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(43694) lies on the Jerabek circumhyperbola, the cubic K225, and these lines: {4, 21044}, {65, 3708}, {73, 3269}, {74, 1055}

X(43694) = X(i)-isoconjugate of X(j) for these (i,j): {2, 14192}, {1172, 16091}
X(43694) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 14192}, {73, 16091}

X(43695) = ISOGONAL CONJUGATE OF X(11413)

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

X(43695) lies on the Jerabek circumhyperbola, the cubic K236, and these lines: {3, 1661}, {4, 31978}, {6, 1885}, {20, 1660}, {30, 15316}, {64, 235}, {66, 11381}, {68, 6000}, {69, 6225}, {70, 12290}, {72, 12779}, {73, 12940}, {74, 3542}, {146, 32605}, {185, 14457}, {248, 40320}, {265, 14216}, {382, 38260}, {468, 3532}, {546, 18431}, {895, 3146}, {1204, 22970}, {1439, 12711}, {1503, 6391}, {1853, 22334}, {1899, 22466}, {2435, 3566}, {2777, 5504}, {3147, 11270}, {3426, 6247}, {4846, 9729}, {6001, 28787}, {6816, 15740}, {11403, 23327}, {11433, 22967}, {11550, 38443}, {11572, 38436}, {12324, 15077}, {15749, 32064}, {16835, 26917}, {18381, 32533}, {18928, 31371}, {30443, 34944}, {30552, 37669}, {31670, 38263}

X(43695) = isogonal conjugate of X(11413)
X(43695) = isogonal conjugate of the anticomplement of X(235)
X(43695) = X(i)-cross conjugate of X(j) for these (i,j): {122, 523}, {30443, 64}, {33581, 393}, {34944, 66}
X(43695) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11413}, {19, 2063}, {75, 1660}, {162, 30211}, {775, 36982}, {1097, 33583}, {14390, 18750}
X(43695) = cevapoint of X(i) and X(j) for these (i,j): {512, 1562}, {6457, 6458}
X(43695) = pedal antipodal perspector of X(20)
X(43695) = barycentric product X(i)*X(j) for these {i,j}: {525, 30249}, {18213, 38253}
X(43695) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 2063}, {6, 11413}, {32, 1660}, {647, 30211}, {800, 36982}, {1562, 35968}, {30249, 648}, {33581, 14390}, {41489, 39268}
X(43695) = {X(6225),X(37201)}-harmonic conjugate of X(36982)

X(43696) = ISOGONAL CONJUGATE OF X(6660)

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

X(43696) lies on the Jerabek circumhyperbola, the cubics K252 and K1000, and these lines: {2, 19576}, {3, 147}, {6, 5117}, {66, 3186}, {68, 12251}, {69, 40035}, {71, 21083}, {248, 8623}, {265, 43453}, {315, 16101}, {338, 15321}, {385, 21536}, {420, 19558}, {695, 3269}, {1176, 36213}, {1899, 19222}, {2887, 19557}, {3569, 18010}, {5207, 9467}, {7779, 36214}
X(43696) = isogonal conjugate of X(6660)
X(43696) = isotomic conjugate of X(5207)
X(43696) = isogonal conjugate of the anticomplement of X(21536)
X(43696) = isotomic conjugate of the anticomplement of X(1691)
X(43696) = isotomic conjugate of the isogonal conjugate of X(41533)
X(43696) = anticomplement of X(19576)
X(43696) = X(1691)-cross conjugate of X(2)
X(43696) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6660}, {2, 19559}, {6, 19555}, {31, 5207}, {75, 19558}, {76, 19560}, {163, 14316}, {561, 19556}, {694, 19572}, {1580, 3493}, {1581, 19576}, {1582, 3505}, {1916, 19578}, {1927, 8783}, {1934, 19575}, {1967, 19571}, {9468, 19574}
X(43696) = cevapoint of X(i) and X(j) for these (i,j): {125, 804}, {732, 21248}
X(43696) = crosspoint of X(1031) and X(9473)
X(43696) = trilinear pole of line {647, 1194}
X(43696) = barycentric product X(i)*X(j) for these {i,j}: {76, 41533}, {695, 16101}
X(43696) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 19555}, {2, 5207}, {6, 6660}, {31, 19559}, {32, 19558}, {385, 19571}, {523, 14316}, {560, 19560}, {694, 3493}, {695, 3505}, {1501, 19556}, {1580, 19572}, {1691, 19576}, {1933, 19578}, {1966, 19574}, {3978, 8783}, {14602, 19575}, {16101, 9230}, {41533, 6}

X(43697) = ISOGONAL CONJUGATE OF X(5094)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(2*a^2 + 2*b^2 - c^2)*(2*a^2 - b^2 + 2*c^2) : :
Barycentrics    A'-power of circumcircle : : , where A'B'C' = 4th Brocard triangle
Trilinears    1/(a^2 sec A + 4 b c) : :
Trilinears    1/(sec A + 3 csc A tan ω) : :
Trilinears    1/(3 csc A + sec A cot ω) : :
X(43697) = 2 X[6] + X[7712], 5 X[3618] - 2 X[7703]

X(43697) lies on the Jerabek circumhyperbola, the cubic K283, and these lines: {2, 67}, {3, 22087}, {4, 575}, {6, 23}, {26, 11482}, {54, 576}, {64, 7527}, {66, 3618}, {69, 3292}, {70, 3090}, {74, 182}, {110, 5505}, {184, 895}, {193, 13622}, {248, 5158}, {265, 6776}, {290, 5967}, {511, 3431}, {524, 9716}, {542, 11564}, {597, 5169}, {1173, 22234}, {1176, 11511}, {1177, 5012}, {1352, 20125}, {1503, 18434}, {1899, 18125}, {1992, 5486}, {1995, 19153}, {2930, 9544}, {3049, 10097}, {3091, 6145}, {3426, 5050}, {3519, 3549}, {3527, 7530}, {3532, 10541}, {3619, 19122}, {4846, 25406}, {5092, 20421}, {5609, 11180}, {5622, 34802}, {6391, 19125}, {7488, 11477}, {7492, 10510}, {7519, 22336}, {8538, 40441}, {8599, 15328}, {9138, 15453}, {10168, 38729}, {10296, 43273}, {10546, 12039}, {10752, 39242}, {11270, 20190}, {13472, 22330}, {13623, 35257}, {14002, 18374}, {14483, 39561}, {14491, 15516}, {14498, 36696}, {15019, 19136}, {15303, 16511}, {15582, 42059}, {18124, 19119}, {18323, 18550}, {18580, 32247}, {19126, 41435}, {19155, 40330}, {19459, 38263}, {20806, 34817}

X(43697) = isogonal conjugate of X(5094)
X(43697) = isogonal conjugate of the complement of X(7493)
X(43697) = isotomic conjugate of the polar conjugate of X(1383)
X(43697) = isogonal conjugate of the polar conjugate of X(598)
X(43697) = X(598)-Ceva conjugate of X(1383)
X(43697) = X(30209)-cross conjugate of X(110)
X(43697) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5094}, {4, 36263}, {19, 599}, {38, 32581}, {75, 8541}, {92, 574}, {162, 3906}, {811, 17414}, {1973, 9464}, {3908, 7649}, {4141, 36125}, {9145, 24006}, {10130, 17442}, {13857, 36119}, {36128, 39785}
X(43697) = cevapoint of X(6) and X(19153)
X(43697) = crosssum of X(i) and X(j) for these (i,j): {574, 8541}, {8288, 17414}
X(43697) = trilinear pole of line {647, 9517}
X(43697) = trilinear product X(i)*X(j) for these {i,j}: {48, 598}, {63, 1383}, {656, 11636}, {810, 35138}, {4575, 8599}, {9247, 40826}
X(43697) = trilinear quotient X(i)/X(j) for these (i,j): (1, 5094), (3, 36263), (31, 8541), (48, 574), (63, 599), (304, 9464), (598, 92), (656, 3906), (810, 17414), (1331, 3908), (4575, 9145), (4592, 9146), (5440, 4141), (8599, 24006), (11636, 162), (35138, 811), (40826, 1969)
X(43697) = barycentric product X(i)*X(j) for these {i,j}: {3, 598}, {69, 1383}, {99, 30491}, {184, 40826}, {525, 11636}, {647, 35138}, {1176, 23297}, {1799, 30489}, {3292, 18818}, {4558, 8599}, {10317, 10512}, {10511, 22151}, {15398, 20380}
X(43697) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 599}, {6, 5094}, {32, 8541}, {48, 36263}, {69, 9464}, {184, 574}, {251, 32581}, {598, 264}, {647, 3906}, {895, 42008}, {906, 3908}, {1176, 10130}, {1383, 4}, {3049, 17414}, {3284, 13857}, {3292, 39785}, {4558, 9146}, {8599, 14618}, {10097, 23288}, {10317, 10510}, {11636, 648}, {14908, 42007}, {14961, 19510}, {20380, 34336}, {20975, 8288}, {22356, 4141}, {23297, 1235}, {30489, 427}, {30491, 523}, {32661, 9145}, {35138, 6331}, {40826, 18022}
X(43697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 32217, 11002}, {6800, 32124, 7712}, {10510, 19127, 7492}, {10511, 20380, 11061}

X(43698) = ISOGONAL CONJUGATE OF X(37101)

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

X(43698) lies on the Jerabek circumhyperbola, the cubic K285, and these lines: {2, 1244}, {4, 3948}, {6, 1009}, {869, 1245}

X(43698) = isogonal conjugate of X(37101)
X(43698) = X(i)-isoconjugate of X(j) for these (i,j): {1, 37101}, {1474, 19791}
X(43698) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 37101}, {72, 19791}

X(43699) = X(6)X(3839)∩X(54)X(3855)

Barycentrics    (a^2 - b^2 - c^2)*(7*a^4 + 10*a^2*b^2 + 7*b^4 - 14*a^2*c^2 - 14*b^2*c^2 + 7*c^4)*(7*a^4 - 14*a^2*b^2 + 7*b^4 + 10*a^2*c^2 - 14*b^2*c^2 + 7*c^4) : :
X(43699) = 3 X[15683] - 7 X[41467]

X(43699) lies on the Jerabek circumhyperbola, the cubic K310, and these lines: {6, 3839}, {54, 3855}, {64, 17578}, {69, 13851}, {74, 15682}, {3426, 15687}, {3431, 5071}, {3527, 3861}, {3818, 17040}, {4846, 18918}, {5066, 8780}, {5068, 14528}, {10113, 10293}, {11744, 32064}, {15683, 41467}, {16774, 31670}, {18434, 37644}, {18917, 21400}, {34436, 37945}

X(43700) = ISOGONAL CONJUGATE OF X(30447)

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

X(43700) lies on the Jerabek circumhyperbola, the cubic K340, and these lines: {65, 2906}, {71, 163}, {72, 110}, {73, 501}, {1175, 13198}, {2074, 10693}

X(43700) = isogonal conjugate of X(30447)
X(43700) = isogonal conjugate of the complement of X(1325)
X(43700) = X(i)-cross conjugate of X(j) for these (i,j): {8674, 110}, {34442, 759}
X(43700) = X(1)-isoconjugate of X(30447)
X(43700) = cevapoint of X(184) and X(19622)
X(43700) = trilinear pole of line {647, 1333}
X(43700) = barycentric quotient X(6)/X(30447)

X(43701) = POLAR CONJUGATE OF X(2404)

Barycentrics    (b - c)*(b + c)*(-a^2 + b^2 + c^2)*(a^8 + 2*a^6*b^2 - 6*a^4*b^4 + 2*a^2*b^6 + b^8 - 3*a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 - 3*b^6*c^2 + 3*a^4*c^4 - 4*a^2*b^2*c^4 + 3*b^4*c^4 - a^2*c^6 - b^2*c^6)*(-a^8 + 3*a^6*b^2 - 3*a^4*b^4 + a^2*b^6 - 2*a^6*c^2 - 3*a^4*b^2*c^2 + 4*a^2*b^4*c^2 + b^6*c^2 + 6*a^4*c^4 - 3*a^2*b^2*c^4 - 3*b^4*c^4 - 2*a^2*c^6 + 3*b^2*c^6 - c^8) : :
Barycentrics    (sin^2 A) (sin 2B - sin 2C)/((cos^2 C) (sin 2A - sin 2B) - (cos^2 B) (sin 2C - sin 2A)) : :

X(43701) lies on the Jerabek circumhyperbola, the cubic K406, and these lines: {3, 2416}, {4, 520}, {6, 2430}, {64, 523}, {66, 8675}, {68, 30211}, {74, 1294}, {512, 35512}, {525, 3426}, {526, 11744}, {684, 1942}, {1177, 9003}, {1650, 14380}, {4846, 8673}, {6368, 16835}, {9517, 10293}, {23977, 32646}

X(43701) = polar conjugate of X(2404)
X(43701) = polar conjugate of the isotomic conjugate of X(2416)
X(43701) = polar conjugate of the isogonal conjugate of X(2430)
X(43701) = X(36043)-anticomplementary conjugate of X(146)
X(43701) = X(i)-cross conjugate of X(j) for these (i,j): {1637, 525}, {2430, 2416}
X(43701) = X(i)-isoconjugate of X(j) for these (i,j): {48, 2404}, {63, 2442}, {133, 36034}, {162, 6000}
X(43701) = cevapoint of X(520) and X(9033)
X(43701) = trilinear pole of line {647, 1562}
X(43701) = pole wrt polar circle of trilinear polar of X(2404) (line X(133)X(1515), the Simson line of X(107))
X(43701) = orthocenter of X(3)X(4)X(64)
X(43701) = barycentric product X(i)*X(j) for these {i,j}: {4, 2416}, {264, 2430}, {525, 1294}, {15404, 41079}
X(43701) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 2404}, {25, 2442}, {647, 6000}, {1294, 648}, {1636, 40948}, {1637, 133}, {2416, 69}, {2430, 3}, {6587, 1559}, {9209, 1515}, {32646, 32230}

X(43702) = ISOGONAL CONJUGATE OF X(5999)

Barycentrics    a^2*(2*a^6*b^2 - a^4*b^4 - b^8 + a^6*c^2 - a^2*b^4*c^2 - 2*a^4*c^4 - b^4*c^4 + a^2*c^6 + 2*b^2*c^6)*(a^6*b^2 - 2*a^4*b^4 + a^2*b^6 + 2*a^6*c^2 + 2*b^6*c^2 - a^4*c^4 - a^2*b^2*c^4 - b^4*c^4 - c^8) : :
X(43702) = 2 X[8925] - 3 X[33876]

Let A'B'C' be the cross-triangle of the 1st and 2nd Neuberg triangles. Let A" be the crosspoint of B' and C', and define B" and C" cyclically. The lines AA", BB", CC" concur in X(43702). (Randy Hutson, June 30, 2021)

Let A1B1C1 be the antipedal triangle of the 1st Brocard point, P(1). Let A2B2C2 be the antipedal triangle of the 2nd Brocard point, U(1). A1, B1, C1, A2, B2, C2 lie on a common hyperbola, H, here named the Brocard antipedal hyperbola. X(43702) is the perspector of H. (Randy Hutson, June 30, 2021)

Let A'1B'1C'1 be the polar triangle of H wrt A1B1C1. Let A'2B'2C'2 be the polar triangle of H wrt A2B2C2. Let A"B"C" be the vertex-triangle of A'1B'1C'1 and A'2B'2C'2. The lines AA", BB", CC" concur in X(80345). (Randy Hutson, June 30, 2021)

X(43702) lies on the Jerabek circumhyperbola, the cubic K422, and these lines: {3, 8925}, {20, 25332}, {54, 35476}, {64, 11325}, {69, 147}, {182, 8922}, {185, 695}, {248, 1691}, {290, 1503}, {446, 694}, {511, 8841}, {804, 879}, {895, 14510}, {1176, 19164}, {1439, 7184}, {1853, 38449}, {1987, 34146}, {2435, 39469}, {2781, 9513}, {3521, 37243}, {4846, 37242}, {5480, 42299}, {5999, 8840}, {6776, 19222}, {7791, 15740}, {8923, 8924}

X(43702) = isogonal conjugate of X(5999)
X(43702) = isogonal conjugate of the anticomplement of X(1513)
X(43702) = isogonal conjugate of the complement of X(40236)
X(43702) = X(1)-isoconjugate of X(5999)
X(43702) = crosssum of X(i) and X(j) for these (i,j): {3, 8925}, {147, 6194}, {182, 8922}, {511, 8841}, {8923, 8924}
X(43702) = trilinear pole of line {647, 40130}
X(43702) = perspector of ABC and the vertex-triangle of the antipedal triangles of PU(1)
X(43702) = barycentric quotient X(6)/X(5999)

X(43703) = ISOGONAL CONJUGATE OF X(16049)

Barycentrics    a*(b + c)*(a^4 - 2*a^2*b^2 + b^4 + 2*a^2*b*c + 2*a*b^2*c - 2*a*b*c^2 - c^4)*(a^4 - b^4 + 2*a^2*b*c - 2*a*b^2*c - 2*a^2*c^2 + 2*a*b*c^2 + c^4) : :
X(43703) = 3 X[392] - 2 X[14529]

X(43703) lies on the Jerabek circumhyperbola, the cubic K430, and these lines: {3, 960}, {4, 17869}, {6, 1854}, {21, 1798}, {65, 429}, {68, 517}, {69, 3827}, {71, 21033}, {72, 3704}, {73, 2292}, {74, 31384}, {265, 2778}, {392, 14529}, {518, 6391}, {758, 28787}, {912, 15316}, {1242, 17634}, {1243, 5799}, {1439, 12709}, {1824, 15232}, {1829, 20029}, {2771, 5504}, {3566, 10099}, {4846, 31937}, {5835, 20306}, {6000, 34800}, {20718, 28786}, {34259, 34277}

X(43703) = isogonal conjugate of X(16049)
X(43703) = isogonal conjugate of the anticomplement of X(429)
X(43703) = X(40454)-Ceva conjugate of X(3435)
X(43703) = X(i)-cross conjugate of X(j) for these (i,j): {1402, 37}, {42550, 34434}
X(43703) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16049}, {21, 21147}, {27, 22132}, {58, 3436}, {63, 41364}, {81, 1766}, {86, 197}, {110, 21186}, {205, 274}, {283, 14257}, {332, 17408}, {333, 478}, {593, 21074}, {662, 6588}, {775, 41601}, {1333, 20928}, {2363, 41600}
X(43703) = cevapoint of X(3269) and X(42661)
X(43703) = crosspoint of X(i) and X(j) for these (i,j): {4, 40457}, {8048, 42467}
X(43703) = crosssum of X(197) and X(1766)
X(43703) = barycentric product X(i)*X(j) for these {i,j}: {10, 42467}, {37, 8048}, {65, 34277}, {321, 3435}, {525, 40097}, {1211, 40454}, {39167, 40149}
X(43703) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 16049}, {10, 20928}, {25, 41364}, {37, 3436}, {42, 1766}, {213, 197}, {228, 22132}, {512, 6588}, {661, 21186}, {756, 21074}, {800, 41601}, {1400, 21147}, {1402, 478}, {1880, 14257}, {1918, 205}, {2092, 41600}, {3435, 81}, {8048, 274}, {34277, 314}, {39167, 1812}, {40097, 648}, {40454, 14534}, {42467, 86}

X(43704) = ISOGONAL CONJUGATE OF X(37943)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 3*a^4*c^2 + a^2*b^2*c^2 - 3*b^4*c^2 + 3*a^2*c^4 + 3*b^2*c^4 - c^6)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - a^4*c^2 + a^2*b^2*c^2 + 3*b^4*c^2 - a^2*c^4 - 3*b^2*c^4 + c^6) : :
X)43704) = 3 X[54] - 2 X[1511], 3 X[195] - X[399], 3 X[195] - 2 X[2914], 3 X[2070] - 2 X[12380], 3 X[2888] - 5 X[15081], 3 X[6288] - 4 X[7687], 6 X[10610] - 5 X[15051], 6 X[11804] - 5 X[15081], 4 X[12242] - 3 X[14643], 2 X[13202] - 3 X[15800], 3 X[19150] - 2 X[25556], 3 X[21230] - 4 X[40685], 2 X[25714] - 3 X[32609]

X(43704) lies on the Jerabek circumhyperbola, the cubic K439, and these lines: {3, 11806}, {4, 195}, {6, 3200}, {54, 1511}, {64, 10628}, {65, 6126}, {67, 5965}, {68, 23306}, {69, 39562}, {70, 15106}, {74, 1154}, {110, 1173}, {125, 3519}, {140, 10821}, {155, 21400}, {248, 22121}, {265, 539}, {323, 33565}, {511, 34437}, {542, 15321}, {1147, 15002}, {1176, 14984}, {2070, 12380}, {2888, 11804}, {2937, 12291}, {3448, 11271}, {3521, 17702}, {3527, 32226}, {3532, 37483}, {3564, 18125}, {3830, 17838}, {4846, 19456}, {5073, 17812}, {5622, 41435}, {5663, 15801}, {5900, 10264}, {6288, 7687}, {9545, 13472}, {9704, 12310}, {9935, 15647}, {10272, 15038}, {10540, 13446}, {10610, 15051}, {10619, 12121}, {10620, 13452}, {10677, 11139}, {10678, 11138}, {11270, 12307}, {11559, 13754}, {11577, 13198}, {11702, 14483}, {11744, 18400}, {11800, 13621}, {12234, 30714}, {12242, 14643}, {12308, 22334}, {12364, 18403}, {12383, 15087}, {13202, 15800}, {13392, 34545}, {13418, 21230}, {13432, 16266}, {13623, 16163}, {15032, 36966}, {15061, 34483}, {16003, 16623}, {17847, 38433}, {18445, 18550}, {19150, 22336}, {19348, 42021}, {22584, 34802}, {26861, 38728}, {32639, 40640}, {33878, 34436}, {36752, 38638}, {37513, 40632}, {37917, 38534}

X(43704) = midpoint of X(3448) and X(11271)
X(43704) = reflection of X(i) in X(j) for these {i,j}: {3, 15089}, {110, 1493}, {399, 2914}, {2888, 11804}, {3519, 125}, {5898, 11597}, {9935, 15647}, {12121, 10619}
X(43704) = Jerabek-circumhyperbola-inverse of X(12011)
X(43704) = isogonal conjugate of X(37943)
X(43704) = antigonal image of X(3519)
X(43704) = symgonal image of X(1493)
X(43704) = isotomic conjugate of the polar conjugate of X(14579)
X(43704) = isogonal conjugate of the polar conjugate of X(13582)
X(43704) = X(i)-Ceva conjugate of X(j) for these (i,j): {1263, 14367}, {13582, 14579}, {15392, 3}
X(43704) = X(22115)-cross conjugate of X(3)
X(43704) = X(i)-isoconjugate of X(j) for these (i,j): {1, 37943}, {4, 1749}, {19, 37779}, {92, 11063}, {324, 19306}, {811, 6140}, {1784, 3470}, {2166, 2914}, {8562, 36129}, {10272, 36119}
X(43704) = crosssum of X(6140) and X(10413)
X(43704) = trilinear pole of line {647, 22052}
X(43704) = barycentric product X(i)*X(j) for these {i,j}: {3, 13582}, {69, 14579}, {97, 1263}, {323, 15392}, {525, 1291}, {3471, 14919}
X(43704) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 37779}, {6, 37943}, {48, 1749}, {50, 2914}, {184, 11063}, {1263, 324}, {1291, 648}, {3049, 6140}, {3284, 10272}, {11071, 6344}, {12011, 41628}, {13582, 264}, {14533, 1157}, {14579, 4}, {15392, 94}, {18877, 3470}, {20975, 10413}, {22115, 40604}, {34433, 11584}, {38539, 37766}
X(43704) = {X(195),X(399)}-harmonic conjugate of X(2914)

X(43705) = ISOGONAL CONJUGATE OF X(460)

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

X(43705) lies on the Jerabek circumhyperbola, the cubic K482, and these lines: {3, 42065}, {4, 99}, {6, 2987}, {54, 13335}, {65, 6516}, {66, 40697}, {68, 3926}, {69, 14060}, {73, 6517}, {74, 5866}, {110, 39072}, {248, 36212}, {265, 6390}, {290, 19599}, {684, 35364}, {879, 6333}, {1245, 36051}, {2396, 31635}, {3519, 3933}, {3527, 10983}, {3785, 42021}, {3964, 6391}, {7767, 34483}, {8552, 10097}, {22143, 38263}, {35919, 42299}

X(43705) = isogonal conjugate of X(460)
X(43705) = isotomic conjugate of X(44145)
X(43705) = isotomic conjugate of the isogonal conjugate of X(42065)
X(43705) = isotomic conjugate of the polar conjugate of X(2987)
X(43705) = isogonal conjugate of the polar conjugate of X(8781)
X(43705) = X(i)-Ceva conjugate of X(j) for these (i,j): {8781, 2987}, {40428, 69}
X(43705) = X(i)-cross conjugate of X(j) for these (i,j): {684, 4558}, {42065, 2987}
X(43705) = X(i)-isoconjugate of X(j) for these (i,j): {1, 460}, {4, 8772}, {19, 230}, {25, 1733}, {92, 1692}, {811, 42663}, {1096, 3564}, {5477, 36128}, {6531, 17462}
X(43705) = cevapoint of X(3) and X(36212)
X(43705) = trilinear pole of line {394, 647}
X(43705) = barycentric product X(i)*X(j) for these {i,j}: {3, 8781}, {63, 8773}, {69, 2987}, {76, 42065}, {304, 36051}, {305, 32654}, {394, 35142}, {525, 10425}, {2065, 6393}, {3265, 32697}, {3563, 3926}, {4563, 35364}, {14919, 36891}, {24018, 36105}, {36212, 40428}
X(43705) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 230}, {6, 460}, {48, 8772}, {63, 1733}, {184, 1692}, {287, 14265}, {394, 3564}, {2065, 6531}, {2987, 4}, {3049, 42663}, {3292, 5477}, {3563, 393}, {4558, 4226}, {8773, 92}, {8781, 264}, {10425, 648}, {14919, 36875}, {32654, 25}, {32697, 107}, {34157, 232}, {35142, 2052}, {35364, 2501}, {36051, 19}, {36105, 823}, {36212, 114}, {40428, 16081}, {42065, 6}

X(43706) = ISOGONAL CONJUGATE OF X(11331)

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

X(43706) lies on the Jerabek circumhyperbola, the cubic K487, and these lines: {4, 5007}, {6, 9407}, {32, 74}, {39, 3431}, {54, 7772}, {65, 7296}, {67, 14003}, {69, 3284}, {187, 20421}, {290, 7766}, {577, 41435}, {1176, 5158}, {2992, 37640}, {2993, 37641}, {3049, 14380}, {3426, 30435}, {3531, 43136}, {3532, 22331}, {5008, 11738}, {6391, 23163}, {9513, 37465}, {11270, 35007}, {13472, 41940}, {14075, 14487}, {15594, 17040}, {19151, 41335}, {21458, 42299}

X(43706) = isogonal conjugate of X(11331)
X(43706) = isogonal conjugate of the polar conjugate of X(14458)
X(43706) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11331}, {19, 7788}, {92, 3098}, {811, 9210}
X(43706) = barycentric product X(i)*X(j) for these {i,j}: {3, 14458}, {184, 14387}, {3049, 9211}
X(43706) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 7788}, {6, 11331}, {184, 3098}, {3049, 9210}, {14387, 18022}, {14458, 264}

X(43707) = X(3)X(476)∩X(69)X(35139)

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

X(43707) lies on the Jerabek circumhyperbola, the cubic K597, and these lines: {3, 476}, {69, 35139}, {74, 6344}, {94, 34802}, {248, 32650}, {265, 39985}, {5504, 34210}, {5627, 10412}, {10293, 18384}, {10688, 14508}, {14644, 15453}

X(43707) = X(39985)-cross conjugate of X(477)
X(43707) = X(i)-isoconjugate of X(j) for these (i,j): {5663, 6149}, {22115, 36063}
X(43707) = trilinear pole of line {647, 1989}
X(43707) = barycentric product X(i)*X(j) for these {i,j}: {94, 477}, {850, 32650}, {1577, 36047}, {2166, 36102}, {10412, 30528}, {18817, 32663}, {39985, 40427}
X(43707) = barycentric quotient X(i)/X(j) for these {i,j}: {94, 35520}, {477, 323}, {1989, 5663}, {14220, 8552}, {30528, 10411}, {32650, 110}, {32663, 22115}, {36047, 662}, {36151, 6149}, {39985, 34834}, {40427, 39988}, {41392, 42742}

X(43708) = ISOGONAL CONJUGATE OF X(13739)

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

X(43708) lies on the Jerabek circumhyperbola, the cubic K619, and these lines: {1, 1175}, {3, 18673}, {4, 758}, {6, 2294}, {40, 74}, {55, 34435}, {65, 21949}, {72, 21671}, {73, 41393}, {912, 34800}, {1714, 5902}, {1762, 11101}, {1802, 3708}, {1903, 3962}, {2213, 5221}, {3869, 37142}, {5692, 24933}, {5903, 41495}, {8044, 21270}, {10693, 27553}, {21677, 27687}

X(43708) = isogonal conjugate of X(13739)
X(43708) = X(6598)-Ceva conjugate of X(41501)
X(43708) = X(i)-isoconjugate of X(j) for these (i,j): {1, 13739}, {7, 41503}, {28, 34772}, {29, 37583}, {58, 5174}, {162, 6003}, {250, 8286}, {270, 15556}, {1474, 33116}
X(43708) = barycentric product X(i)*X(j) for these {i,j}: {63, 41501}, {72, 37887}, {525, 6011}, {1214, 6598}
X(43708) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 13739}, {37, 5174}, {41, 41503}, {71, 34772}, {72, 33116}, {647, 6003}, {1409, 37583}, {2197, 15556}, {3708, 8286}, {6011, 648}, {6598, 31623}, {18591, 39772}, {37887, 286}, {41501, 92}

X(43709) = ISOGONAL CONJUGATE OF X(30512)

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

X(43709) lies on the Jerabek circumhyperbola, the cubic K658, and these lines: {3, 924}, {6, 6753}, {68, 523}, {69, 6563}, {74, 1299}, {125, 40048}, {265, 13556}, {512, 34801}, {520, 15316}, {526, 5504}, {3521, 20184}, {3566, 4846}, {6391, 8675}, {15313, 34800}, {15328, 35235}

X(43709) = reflection of X(40048) in X(125)
X(43709) = isogonal conjugate of X(30512)
X(43709) = antigonal image of X(40048)
X(43709) = isogonal conjugate of the anticomplement of X(35235)
X(43709) = X(i)-isoconjugate of X(j) for these (i,j): {1, 30512}, {131, 36114}, {648, 2314}, {662, 16310}
X(43709) = cevapoint of X(i) and X(j) for these (i,j): {512, 686}, {14270, 30451}
X(43709) = trilinear pole of line {647, 39005}
X(43709) = barycentric product X(525)*X(1299)
X(43709) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 30512}, {512, 16310}, {686, 131}, {810, 2314}, {1299, 648}, {30451, 12095}

X(43710) = ISOGONAL CONJUGATE OF X(6638)

Barycentrics    (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 - 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) : :
Trilinears    (sec A)/(csc 2A - csc 2B - csc 2C) : :

X(43710 lies on the Jerabek circumhyperbola, the cubic K675, and these lines: {3, 3164}, {4, 35709}, {6, 436}, {54, 1075}, {64, 33971}, {69, 16089}, {248, 3186}, {393, 1987}, {8795, 19209}, {14361, 17040}

X(43710) = isogonal conjugate of X(6638)
X(43710) = polar conjugate of X(3164)
X(43710) = polar conjugate of the isogonal conjugate of X(1988)
X(43710) = X(1988)-Ceva conjugate of X(4)
X(43710) = X(i)-cross conjugate of X(j) for these (i,j): {2052, 4}, {9307, 34208}
X(43710) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6638}, {48, 3164}, {63, 32445}, {255, 3168}, {2169, 42453}
X(43710) = cevapoint of X(i) and X(j) for these (i,j): {130, 12077}, {523, 34980}
X(43710) = trilinear pole of line {647, 16229}
X(43710) = Steiner image of X(4)
X(43710) = barycentric product X(i)*X(j) for these {i,j}: {264, 1988}, {2052, 40800}
X(43710) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 3164}, {6, 6638}, {25, 32445}, {53, 42453}, {393, 3168}, {1988, 3}, {8882, 26887}, {40800, 394}

X(43711) = X(2)X(1987)∩X(4)X(16089)

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

X(43711) lies on the Jerabek circumhyperbola, the cubic K677, and these lines: {2, 1987}, {4, 16089}, {6, 401}, {54, 7709}, {64, 9756}, {23301, 35364}

X(43711) = isotomic conjugate of the anticomplement of X(30258)
X(43711) = isotomic conjugate of the polar conjugate of X(40815)
X(43711) = X(i)-cross conjugate of X(j) for these (i,j): {262, 42287}, {30258, 2}
X(43711) = X(19)-isoconjugate of X(40805)
X(43711) = barycentric product X(69)*X(40815)
X(43711) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 40805}, {40815, 4}

X(43712) = ISOGONAL CONJUGATE OF X(2915)

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

X(43712) lies on the Jerabek circumhyperbola, the cubic K680, and these lines: {3, 32782}, {6, 2906}, {71, 191}, {72, 2895}, {73, 30115}, {3448, 3868}, {21287, 27801}, {21293, 38535}

X(43712) = isogonal conjugate of X(2915)
X(43712) = isotomic conjugate of X(21287)
X(43712) = cyclocevian conjugate of X(35058)
X(43712) = isotomic conjugate of the anticomplement of X(1333)
X(43712) = X(1333)-cross conjugate of X(2)
X(43712) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2915}, {6, 21376}, {19, 23130}, {31, 21287}, {32, 21595}, {37, 38822}
X(43712) = cevapoint of X(i) and X(j) for these (i,j): {125, 513}, {514, 21253}
X(43712) = trilinear pole of line {647, 31947}
X(43712) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 21376}, {2, 21287}, {3, 23130}, {6, 2915}, {58, 38822}, {75, 21595}

X(43713) = ISOGONAL CONJUGATE OF X(3543)

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

X(43713) lies on the Jerabek circumhyperbola, the cubic K706, and these lines: {4, 8567}, {6, 11410}, {20, 15749}, {25, 14490}, {64, 1495}, {66, 37931}, {68, 548}, {69, 10304}, {72, 35242}, {74, 154}, {186, 11738}, {248, 5210}, {265, 3534}, {378, 14483}, {549, 4846}, {895, 1350}, {1173, 9786}, {1204, 14528}, {1439, 30282}, {1620, 22334}, {3098, 6391}, {3426, 10606}, {3431, 10605}, {3521, 3526}, {3527, 11438}, {3531, 11204}, {5055, 18550}, {5505, 5621}, {6200, 6415}, {6396, 6416}, {6411, 6413}, {6412, 6414}, {10097, 33979}, {10303, 31371}, {11270, 11456}, {11425, 13472}, {11468, 16835}, {11477, 35499}, {11480, 36296}, {11481, 36297}, {11744, 37453}, {12024, 18931}, {12041, 34802}, {13394, 15717}, {13623, 15706}, {14380, 42658}, {15317, 37483}, {15362, 15684}, {15683, 41467}, {15704, 32533}, {17800, 21400}, {33878, 38263}, {34567, 35477}, {37478, 38260}

X(43713) = isogonal conjugate of X(3543)
X(43713) = isogonal conjugate of the anticomplement of X(376)
X(43713) = isogonal conjugate of the complement of X(15683)
X(43713) = X(26864)-cross conjugate of X(6)
X(43713) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3543}, {75, 41424}
X(43713) = barycentric product X(1073)*X(33702)
X(43713) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 3543}, {32, 41424}, {33702, 15466}
X(43713) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3426, 41447, 41424}, {10606, 41447, 3426}

X(43714) = ISOGONAL CONJUGATE OF X(11325)

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

X(43714) lies on the Jerabek circumhyperbola, the cubics K738 and K1010, and these lines: {2, 695}, {3, 3504}, {4, 3978}, {6, 194}, {20, 25332}, {54, 35925}, {64, 5999}, {65, 18832}, {66, 5207}, {74, 3222}, {76, 19222}, {315, 16101}, {1176, 15389}, {1245, 3223}, {1501, 3552}, {3117, 14001}, {3527, 35930}, {3926, 36214}, {4576, 33014}, {5025, 30496}, {5989, 24730}, {15740, 19583}, {32547, 32548}

X(43714) = isogonal conjugate of X(11325)
X(43714) = isotomic conjugate of X(3186)
X(43714) = isotomic conjugate of the isogonal conjugate of X(3504)
X(43714) = isotomic conjugate of the polar conjugate of X(2998)
X(43714) = isogonal conjugate of the polar conjugate of X(40162)
X(43714) = X(i)-Ceva conjugate of X(j) for these (i,j): {3504, 69}, {40162, 2998}
X(43714) = X(i)-cross conjugate of X(j) for these (i,j): {305, 69}, {3504, 2998}, {9289, 34403}, {23216, 4580}, {23479, 1}
X(43714) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11325}, {19, 1613}, {25, 1740}, {31, 3186}, {162, 3221}, {194, 1973}, {561, 41293}, {607, 1424}, {608, 7075}, {648, 23503}, {811, 9491}, {1096, 20794}, {1474, 21877}, {1783, 23572}, {1974, 17149}, {2203, 21080}, {2212, 17082}, {2524, 24019}, {17442, 38834}, {23301, 32676}
X(43714) = barycentric product X(i)*X(j) for these {i,j}: {3, 40162}, {63, 18832}, {69, 2998}, {76, 3504}, {304, 3223}, {305, 3224}, {525, 3222}, {1502, 15389}, {1799, 42551}, {34248, 40364}, {39927, 40708}
X(43714) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3186}, {3, 1613}, {6, 11325}, {63, 1740}, {69, 194}, {72, 21877}, {77, 1424}, {78, 7075}, {304, 17149}, {305, 6374}, {306, 21080}, {348, 17082}, {394, 20794}, {520, 2524}, {525, 23301}, {647, 3221}, {810, 23503}, {1176, 38834}, {1459, 23572}, {1501, 41293}, {2998, 4}, {3049, 9491}, {3222, 648}, {3223, 19}, {3224, 25}, {3504, 6}, {4025, 21191}, {4064, 21056}, {4466, 21144}, {6332, 25128}, {14208, 20910}, {15389, 32}, {15413, 23807}, {18832, 92}, {19606, 27369}, {20336, 22028}, {34248, 1973}, {39927, 419}, {40162, 264}, {40364, 18837}, {40821, 6620}, {42551, 427}
X(43714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2998, 39927, 40821}, {3224, 42551, 2998}, {32547, 35524, 32548}

X(43715) = ISOTOMIC CONJUGATE OF X(3491)

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

X(43715) lies on the Jerabek circumhyperbola, the cubic K743, and these lines: {3, 6374}, {248, 19585}, {695, 17984}, {9230, 36214}, {30496, 41760}

X(43715) = isotomic conjugate of X(3491)
X(43715) = X(9229)-cross conjugate of X(308)
X(43715) = X(31)-isoconjugate of X(3491)
X(43715) = barycentric quotient X(2)/X(3491)

X(43716) = ISOGONAL CONJUGATE OF X(9855)

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

X(43716) lies on the Jerabek circumhyperbola, the cubic K751, and these lines: {3, 40251}, {69, 8591}, {895, 8586}, {8352, 8785}

X(43716) = isogonal conjugate of X(9855)
X(43716) = isogonal conjugate of the anticomplement of X(8352)
X(43716) = isogonal conjugate of the complement of X(40246)
X(43716) = X(1)-isoconjugate of X(9855)
X(43716) = barycentric quotient X(6)/X(9855)

X(43717) = ISOGONAL CONJUGATE OF X(441)

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

X(43717) lies on the Jerabek circumhyperbola, the cubic K785, and these lines: {3, 112}, {4, 1562}, {6, 32713}, {53, 15321}, {64, 2207}, {66, 393}, {67, 1990}, {68, 41361}, {69, 648}, {71, 8750}, {72, 1783}, {73, 32674}, {74, 8744}, {232, 248}, {265, 5523}, {290, 9476}, {879, 6531}, {895, 15262}, {1439, 32714}, {2435, 3569}, {2492, 8749}, {3168, 19222}, {3519, 41366}, {4846, 41370}, {5254, 22466}, {5286, 13526}, {5486, 40138}, {5504, 32708}, {6145, 27376}, {6749, 22336}, {8745, 34207}, {8746, 34436}, {8751, 10099}, {8753, 10097}, {14944, 15005}, {15077, 38664}, {15143, 36214}, {15407, 41363}, {16774, 33630}, {18288, 20232}, {33971, 38449}, {36092, 37142}

X(43717) = isogonal conjugate of X(441)
X(43717) = polar conjugate of X(30737)
X(43717) = isogonal conjugate of the complement of X(297)
X(43717) = isogonal conjugate of the isotomic conjugate of X(6330)
X(43717) = polar conjugate of the isotomic conjugate of X(1297)
X(43717) = X(i)-Ceva conjugate of X(j) for these (i,j): {6330, 1297}, {9476, 4}, {32687, 34212}
X(43717) = X(i)-cross conjugate of X(j) for these (i,j): {1976, 3563}, {3569, 112}, {34212, 32687}, {34854, 4}
X(43717) = X(i)-isoconjugate of X(j) for these (i,j): {1, 441}, {2, 8766}, {48, 30737}, {63, 1503}, {69, 2312}, {75, 8779}, {78, 43045}, {162, 39473}, {248, 17875}, {293, 15595}, {304, 42671}, {326, 16318}, {336, 9475}, {610, 16096}, {656, 34211}, {896, 36894}, {1959, 34156}, {2409, 24018}
X(43717) = cevapoint of X(i) and X(j) for these (i,j): {6, 232}, {2491, 34980}
X(43717) = trilinear pole of line {25, 647}
X(43717) = barycentric product of (real or nonreal) circumcircle intercepts of line X(4)X(525)
X(43717) = barycentric product X(i)*X(j) for these {i,j}: {1, 8767}, {4, 1297}, {6, 6330}, {25, 35140}, {64, 14944}, {98, 39265}, {107, 2435}, {232, 9476}, {525, 32687}, {648, 34212}, {656, 36092}, {850, 32649}, {1577, 36046}, {2419, 32713}, {6530, 15407}
X(43717) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 30737}, {6, 441}, {25, 1503}, {31, 8766}, {32, 8779}, {64, 16096}, {111, 36894}, {112, 34211}, {232, 15595}, {240, 17875}, {608, 43045}, {647, 39473}, {1297, 69}, {1973, 2312}, {1974, 42671}, {1976, 34156}, {2207, 16318}, {2211, 9475}, {2435, 3265}, {6330, 76}, {8767, 75}, {14581, 6793}, {14944, 14615}, {15407, 6394}, {18384, 43089}, {32649, 110}, {32687, 648}, {32713, 2409}, {34212, 525}, {34854, 132}, {35140, 305}, {36046, 662}, {36092, 811}, {39265, 325}
X(43717) = {X(232),X(248)}-harmonic conjugate of X(38867)

X(43718) = ISOGONAL CONJUGATE OF X(458)

Barycentrics    a^2*(a^2 - b^2 - c^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) : :
Barycentrics    sin A sin 2A sec(A - ω) : :

X(43718) lies on the Jerabek circumhyperbola, the cubic K791, and these lines: {2, 290}, {3, 217}, {4, 39}, {6, 160}, {32, 54}, {50, 19151}, {64, 5013}, {65, 2186}, {66, 570}, {67, 566}, {69, 216}, {71, 20753}, {72, 42702}, {74, 574}, {182, 40799}, {184, 248}, {187, 3431}, {393, 8795}, {577, 1176}, {647, 879}, {800, 17040}, {895, 5158}, {1173, 7772}, {1177, 5063}, {1245, 3402}, {1503, 38449}, {1625, 35934}, {1987, 9475}, {2021, 11674}, {3003, 5486}, {3053, 14528}, {3117, 7735}, {3331, 3426}, {3527, 9605}, {3532, 15815}, {3815, 37988}, {3926, 37186}, {4846, 14961}, {5007, 13472}, {5661, 11179}, {6037, 35906}, {6391, 20794}, {7774, 22240}, {8589, 20421}, {10316, 40441}, {10979, 41435}, {11003, 23357}, {11005, 11564}, {11270, 37512}, {13337, 22336}, {13351, 15321}, {13452, 31652}, {14096, 40805}, {15166, 41519}, {15167, 41518}, {15740, 22401}, {15851, 38263}, {16835, 41367}, {16975, 38955}, {22062, 34817}, {22332, 22334}, {31401, 37121}, {32618, 41197}, {32619, 41196}, {37665, 42299}

X(43718) = isogonal conjugate of X(458)
X(43718) = isotomic conjugate of X(44144)
X(43718) = isogonal conjugate of the isotomic conjugate of X(42313)
X(43718) = isotomic conjugate of the polar conjugate of X(263)
X(43718) = isogonal conjugate of the polar conjugate of X(262)
X(43718) = X(i)-Ceva conjugate of X(j) for these (i,j): {262, 263}, {42300, 262}
X(43718) = X(i)-isoconjugate of X(j) for these (i,j): {1, 458}, {19, 183}, {25, 3403}, {63, 33971}, {75, 10311}, {92, 182}, {162, 23878}, {811, 3288}, {1474, 42711}, {1969, 34396}, {1973, 20023}, {2167, 39530}
X(43718) = crosspoint of X(262) and X(42313)
X(43718) = crosssum of X(i) and X(j) for these (i,j): {6, 9756}, {182, 10311}, {1007, 18906}
X(43718) = trilinear pole of line {647, 39469}
X(43718) = crossdifference of every pair of points on line {9420, 23878}
X(43718) = barycentric product X(i)*X(j) for these {i,j}: {3, 262}, {6, 42313}, {63, 2186}, {69, 263}, {184, 327}, {216, 42300}, {304, 3402}, {525, 26714}, {684, 6037}, {3917, 42299}, {3933, 42288}, {6333, 32716}, {6776, 40803}, {14941, 39682}, {35909, 36885}
X(43718) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 183}, {6, 458}, {25, 33971}, {32, 10311}, {51, 39530}, {63, 3403}, {69, 20023}, {72, 42711}, {184, 182}, {262, 264}, {263, 4}, {327, 18022}, {647, 23878}, {2186, 92}, {3049, 3288}, {3402, 19}, {3917, 14994}, {6037, 22456}, {14575, 34396}, {20775, 14096}, {26714, 648}, {32716, 685}, {36214, 8842}, {39682, 16089}, {42288, 32085}, {42300, 276}, {42313, 76}
X(43718) = {X(262),X(39682)}-harmonic conjugate of X(4)

X(43719) = ISOGONAL CONJUGATE OF X(3529)

Barycentrics    a^2*(3*a^4 - 6*a^2*b^2 + 3*b^4 + 4*a^2*c^2 + 4*b^2*c^2 - 7*c^4)*(3*a^4 + 4*a^2*b^2 - 7*b^4 - 6*a^2*c^2 + 4*b^2*c^2 + 3*c^4) : :
X(43719) = 5 X[3] - 4 X[33556], 5 X[3522] - 3 X[25712], 9 X[10937] - 8 X[13382]


X(43719) lies on the Jerabek circumhyperbola, the cubics K814 and K855, and these lines: {3, 33556}, {4, 34469}, {5, 31371}, {6, 3357}, {24, 13452}, {25, 16835}, {30, 15077}, {54, 3516}, {64, 3517}, {68, 1657}, {69, 550}, {70, 37196}, {74, 3515}, {140, 15740}, {265, 5073}, {378, 13472}, {382, 32533}, {895, 12085}, {1173, 1593}, {1204, 3426}, {1598, 22334}, {1656, 4846}, {1853, 38447}, {3431, 35477}, {3521, 3851}, {3522, 25712}, {3527, 10605}, {3529, 14843}, {3532, 6000}, {3627, 18296}, {3830, 17505}, {5504, 10620}, {6247, 38443}, {6391, 12163}, {6413, 6449}, {6414, 6450}, {7517, 34802}, {7547, 18363}, {10606, 14528}, {11270, 12315}, {11426, 34567}, {11438, 14490}, {11744, 20417}, {11820, 34801}, {13399, 17800}, {14530, 17506}, {14810, 34817}, {15311, 43592}, {16774, 41584}, {17040, 32603}, {17856, 38633}, {21841, 35512}

X(43719) = reflection of X(382) in X(32533)
X(43719) = isogonal conjugate of X(3529)
X(43719) = isogonal conjugate of the anticomplement of X(382)
X(43719) = barycentric quotient X(6)/X(3529)

X(43720) = REFLECTION OF X(7712) IN X(12041)

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

X(43720) lies on the Jerabek circumhyperbola, the cubic K914, and these lines: {4, 15027}, {6, 10620}, {30, 11564}, {54, 15054}, {67, 11645}, {69, 12121}, {74, 7575}, {125, 18550}, {541, 7579}, {2777, 18434}, {3426, 33887}, {3431, 5663}, {4846, 15061}, {5505, 8705}, {5655, 18580}, {7703, 7728}, {7712, 12041}, {13472, 38626}, {13623, 38728}, {15021, 15331}, {16219, 37958}, {19151, 19402}, {20127, 33565}, {21400, 36253}

X(43720) = reflection of X(i) in X(j) for these {i,j}: {7712, 12041}, {7728, 7703}, {12121, 35257}, {18550, 125}
X(43720) = antigonal image of X(18550)
X(43720) = isogonal conjugate of the anticomplement of X(18323)
X(43720) = trilinear pole of line {647, 15860}

X(43721) = X(3)X(3492)∩X(69)X(19571)

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

X(43721) lies on the Jerabek circumhyperbola, the cubic K1001, and these lines: {3, 3492}, {69, 19571}, {5989, 24730}, {6660, 36214}, {9513, 10117}

X(43721) = isogonal conjugate of the anticomplement of X(419)
X(43721) = X(i)-isoconjugate of X(j) for these (i,j): {38, 8928}, {1959, 8861}
X(43721) = cevapoint of X(3269) and X(5027)
X(43721) = barycentric quotient X(i)/X(j) for these {i,j}: {251, 8928}, {1976, 8861}

X(43722) = ISOGONAL CONJUGATE OF X(5117)

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

X(43722) lies on the Jerabek circumhyperbola, the cubic K1013, and these lines: {2, 19576}, {3, 40373}, {4, 3398}, {6, 6660}, {32, 695}, {54, 3095}, {65, 985}, {66, 14617}, {69, 14575}, {74, 26316}, {110, 19602}, {182, 8922}, {184, 36214}, {290, 3114}, {3001, 19151}, {3431, 35002}, {7766, 19222}, {15257, 24730}

X(43722) = isogonal conjugate of X(5117)
X(43722) = isotomic conjugate of the polar conjugate of X(18898)
X(43722) = isogonal conjugate of the polar conjugate of X(3407)
X(43722) = X(3407)-Ceva conjugate of X(18898)
X(43722) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5117}, {19, 3314}, {92, 3094}, {264, 3116}, {1969, 3117}, {3721, 31909}
X(43722) = barycentric product X(i)*X(j) for these {i,j}: {3, 3407}, {48, 3113}, {69, 18898}, {184, 3114}, {248, 8840}, {647, 33514}, {1176, 14617}
X(43722) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 3314}, {6, 5117}, {184, 3094}, {3113, 1969}, {3114, 18022}, {3407, 264}, {9247, 3116}, {14575, 3117}, {14617, 1235}, {18898, 4}, {33514, 6331}, {38813, 31909}, {40373, 18899}

X(43723) = X(4)X(2831)∩X(6)X(18210)

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

X(43723) lies on the Jerabek circumhyperbola, the cubic K1050, and these lines: {4, 2831}, {6, 18210}, {71, 2632}, {72, 15526}, {74, 2722}, {1177, 8758}, {7669, 34435}

X(43723) = X(162)-isoconjugate of X(2806)
X(43723) = barycentric product X(525)*X(2722)
X(43723) = barycentric quotient X(i)/X(j) for these {i,j}: {647, 2806}, {2722, 648}

X(43724) = ISOGONAL CONJUGATE OF X(7412)

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

X(43724) lies on the Jerabek circumhyperbola, the cubic K1058, and these lines: {4, 18180}, {6, 3149}, {12, 117}, {54, 1437}, {64, 1012}, {65, 515}, {72, 5562}, {73, 33597}, {74, 6906}, {222, 1771}, {270, 37380}, {286, 8795}, {355, 38955}, {1243, 20420}, {1425, 38554}, {2779, 10693}, {3431, 6942}, {3527, 19541}, {6950, 11270}, {16835, 21669}

X(43724) = isogonal conjugate of X(7412)
X(43724) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7412}, {1897, 39199}
X(43724) = cevapoint of X(656) and X(1364)
X(43724) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 7412}, {22383, 39199}

X(43725) = ISOGONAL CONJUGATE OF X(6997)

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

X(43725) lies on the Jerabek circumhyperbola, the cubic K1109, and these lines: {4, 159}, {66, 19459}, {68, 141}, {69, 7485}, {72, 22769}, {182, 15316}, {184, 34207}, {1173, 6403}, {1176, 1993}, {1177, 19125}, {3527, 9969}, {4846, 35243}, {5050, 15317}, {6391, 32366}, {8550, 42021}, {11745, 15577}, {31371, 33524}, {37488, 40441}

X(43725) = isogonal conjugate of X(6997)
X(43725) = isogonal conjugate of the anticomplement of X(7484)
X(43725) = X(1)-isoconjugate of X(6997)
X(43725) = barycentric quotient X(6)/X(6997)

X(43726) = ISOGONAL CONJUGATE OF X(7485)

Barycentrics    (a^4 + 4*a^2*b^2 + b^4 - c^4)*(a^4 - b^4 + 4*a^2*c^2 + c^4) : :
X(43726) = X[69] - 3 X[15435], 4 X[3589] - 3 X[31521], 5 X[3763] - 3 X[34817], 3 X[9815] + X[31670]

X(43726) lies on the Jerabek circumhyperbola, the cubic K1110, and these lines: {2, 41435}, {3, 3589}, {6, 428}, {51, 66}, {54, 206}, {64, 1907}, {67, 1112}, {68, 3818}, {69, 3060}, {70, 9781}, {248, 13345}, {511, 42021}, {895, 14683}, {1173, 6776}, {1176, 7500}, {1352, 3519}, {1503, 3527}, {1843, 5486}, {1899, 15321}, {2393, 17040}, {2980, 5319}, {3629, 6391}, {3763, 17810}, {6664, 7758}, {9971, 13622}, {10127, 21850}, {10982, 36989}, {14491, 39874}, {15316, 19139}, {15740, 41257}, {18124, 37644}, {23327, 34207}, {38260, 39899} X(43726) = isogonal conjugate of X(7485)
X(43726) = isogonal conjugate of the anticomplement of X(37439)
X(43726) = isogonal conjugate of the complement of X(7394)
X(43726) = isotomic conjugate of the anticomplement of X(7772)
X(43726) = X(i)-cross conjugate of X(j) for these (i,j): {7772, 2}, {33578, 393}
X(43726) = X(1)-isoconjugate of X(7485)
X(43726) = cevapoint of X(i) and X(j) for these (i,j): {125, 7950}, {2474, 3124}
X(43726) = crosspoint of X(4) and X(39978)
X(43726) = crosssum of X(3) and X(31521)
X(43726) = trilinear pole of line {647, 7927}
X(43726) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 7485}, {39951, 14259}

X(43727) = X(3)X(9292)∩X(4)X(9289)

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

X(43727) lies on the Jerabek circumhyperbola, the cubic K1179, and these lines: {3, 9292}, {4, 9289}, {6, 15143}, {64, 40801}, {69, 9307}, {248, 9306}, {290, 23291}, {879, 30476}, {5921, 40803}, {6391, 40802}, {9744, 15740}

X(43727) = X(2)-cross conjugate of X(40803)
X(43727) = X(i)-isoconjugate of X(j) for these (i,j): {1957, 6776}, {1958, 7735}, {4008, 9306}, {17478, 35278}
X(43727) = barycentric product X(i)*X(j) for these {i,j}: {9289, 40801}, {9292, 40824}, {9307, 40802}
X(43727) = barycentric quotient X(i)/X(j) for these {i,j}: {9258, 4008}, {9292, 7735}, {9307, 40814}, {40799, 9306}, {40801, 9308}, {40802, 1975}

X(43728) = X(1)X(522)∩X(4)X(513)

Barycentrics    (a - b - c)*(b - c)*(a^3 - a^2*b - a*b^2 + b^3 + 2*a*b*c - a*c^2 - b*c^2)*(a^3 - a*b^2 - a^2*c + 2*a*b*c - b^2*c - a*c^2 + c^3) : :
X(43728) = X[5603] - 2 X[42757], 3 X[23615] + X[39771]

X(43728) lies on the Feuerbach circumhyperbola, the cubic K027, and these lines: {1, 522}, {4, 513}, {7, 693}, {8, 521}, {9, 652}, {21, 7253}, {80, 3738}, {84, 3667}, {104, 900}, {294, 28132}, {499, 21189}, {514, 3577}, {523, 1389}, {656, 37154}, {1000, 3900}, {1156, 34234}, {1172, 7252}, {1309, 2720}, {1320, 2804}, {1937, 2254}, {2298, 2423}, {2406, 7451}, {2481, 18816}, {3062, 6006}, {3309, 3427}, {3680, 8058}, {3716, 9365}, {4086, 34918}, {4391, 30513}, {4768, 12641}, {4777, 14497}, {4977, 16615}, {5377, 13136}, {5559, 35057}, {5603, 42757}, {6366, 24297}, {9372, 34051}, {10308, 28217}, {10309, 30198}, {10776, 33650}, {14302, 38271}, {14496, 28209}, {15501, 39471}, {15635, 23836}, {23187, 32153}, {23615, 39771}, {23838, 35015}, {28221, 37518}, {36121, 36123}, {36795, 36798}

X(43728) = isogonal conjugate of X(23981)
X(43728) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2222, 153}, {2720, 6224}, {40437, 33650}
X(43728) = X(i)-Ceva conjugate of X(j) for these (i,j): {1309, 104}, {36037, 38955}
X(43728) = X(i)-cross conjugate of X(j) for these (i,j): {11, 40437}, {654, 4560}, {900, 522}, {4530, 40218}
X(43728) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23981}, {3, 23706}, {6, 24029}, {57, 2427}, {59, 1769}, {73, 4246}, {100, 1457}, {101, 1465}, {108, 22350}, {109, 517}, {604, 2397}, {651, 2183}, {692, 22464}, {859, 4551}, {908, 1415}, {1331, 1875}, {1361, 36037}, {1785, 36059}, {1813, 14571}, {2149, 10015}, {2222, 34586}, {2720, 24028}, {2804, 24027}, {3310, 4564}, {4565, 21801}, {7012, 8677}, {14260, 23703}, {16586, 32675}, {23980, 37136}, {26611, 32669}
X(43728) = cevapoint of X(i) and X(j) for these (i,j): {522, 3738}, {1639, 3900}, {4530, 23615}
X(43728) = crosspoint of X(i) and X(j) for these (i,j): {4997, 35174}, {13136, 18816}
X(43728) = crosssum of X(1404) and X(8648)
X(43728) = trilinear pole of line {650, 1146}
X(43728) = crossdifference of every pair of points on line {1457, 2183}
X(43728) = barycentric product X(i)*X(j) for these {i,j}: {8, 2401}, {11, 13136}, {92, 37628}, {104, 4391}, {513, 36795}, {521, 16082}, {522, 34234}, {646, 15635}, {650, 18816}, {909, 35519}, {1309, 26932}, {1809, 17924}, {2250, 18155}, {2342, 3261}, {2423, 3596}, {2720, 23978}, {3904, 40437}, {4397, 34051}, {4560, 38955}, {4858, 36037}, {6332, 36123}, {24026, 37136}, {32641, 34387}
X(43728) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 24029}, {6, 23981}, {8, 2397}, {11, 10015}, {19, 23706}, {55, 2427}, {104, 651}, {513, 1465}, {514, 22464}, {522, 908}, {649, 1457}, {650, 517}, {652, 22350}, {654, 34586}, {663, 2183}, {909, 109}, {1146, 2804}, {1172, 4246}, {1639, 1145}, {1795, 1813}, {1809, 1332}, {2170, 1769}, {2250, 4551}, {2342, 101}, {2401, 7}, {2423, 56}, {2720, 1262}, {2804, 26611}, {3064, 1785}, {3239, 6735}, {3271, 3310}, {3310, 1361}, {3700, 17757}, {3738, 16586}, {4041, 21801}, {4391, 3262}, {4435, 15507}, {4530, 23757}, {4560, 17139}, {4858, 36038}, {6591, 1875}, {7117, 8677}, {7252, 859}, {8735, 39534}, {13136, 4998}, {14578, 36059}, {14776, 7115}, {15635, 3669}, {16082, 18026}, {17197, 23788}, {17435, 42758}, {18344, 14571}, {18816, 4554}, {21132, 42754}, {32641, 59}, {32669, 24027}, {34051, 934}, {34234, 664}, {34858, 1415}, {36037, 4564}, {36110, 7128}, {36123, 653}, {36795, 668}, {36819, 1025}, {37136, 7045}, {37628, 63}, {38955, 4552}, {40437, 655}, {41933, 2720}, {42462, 35015}

X(43729) = ISOGONAL CONJUGATE OF X(41342)

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

X(43729) lies on the Feuerbach circumhyperbola, the cubics K109 and K457, and these lines: {1, 15656}, {4, 579}, {7, 17167}, {8, 15830}, {9, 8021}, {27, 41342}, {63, 2997}, {84, 3286}, {284, 943}, {1751, 39944}, {2481, 8822}

X(43729) = isogonal conjugate of X(41342)
X(43729) = X(i)-cross conjugate of X(j) for these (i,j): {71, 284}, {23207, 1}
X(43729) = X(i)-isoconjugate of X(j) for these (i,j): {1, 41342}, {57, 3191}, {73, 37279}, {81, 15443}, {226, 580}, {1214, 41227}
X(43729) = barycentric product X(86)*X(41509)
X(43729) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 41342}, {42, 15443}, {55, 3191}, {1172, 37279}, {2194, 580}, {2299, 41227}, {41509, 10}

X(43730) = ISOGONAL CONJUGATE OF X(41348)

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

X(43730) lies on the Feuerbach circumhyperbola, the cubic K156, and these lines: {4640, 4866}, {5059, 41348}, {12705, 14497}

X(43730) = isogonal conjugate of X(41348)
X(43730) = barycentric quotient X(6)/X(41348)

X(43731) = X(1)X(1656)∩X(4)X(41684)

Barycentrics    (2*a^2 - 3*a*b + 2*b^2 - 2*c^2)*(2*a^2 - 2*b^2 - 3*a*c + 2*c^2) : :
X(43731) = 6 X[7704] - 5 X[11522]

X(43731) lies on the Feuerbach circumhyperbola, the cubic K194, and these lines: {1, 1656}, {4, 41684}, {7, 5270}, {8, 4125}, {9, 4668}, {10, 2320}, {11, 24302}, {21, 3679}, {40, 3065}, {65, 14841}, {79, 355}, {80, 12701}, {84, 484}, {90, 11010}, {104, 6796}, {140, 37706}, {388, 5551}, {497, 7317}, {517, 5560}, {519, 1392}, {1320, 3632}, {1389, 7704}, {1476, 37587}, {1657, 37006}, {1697, 7161}, {1699, 16615}, {1837, 5559}, {3062, 37001}, {3245, 5073}, {3336, 7284}, {3337, 7091}, {3467, 5119}, {3576, 11279}, {3577, 10893}, {3583, 7319}, {3585, 5556}, {3625, 27131}, {3633, 30852}, {3680, 4677}, {3851, 11009}, {4325, 34627}, {4926, 23838}, {5010, 15446}, {5424, 15174}, {5557, 37710}, {5558, 18391}, {5561, 5903}, {5691, 10308}, {5722, 13602}, {5727, 15175}, {5881, 6924}, {5882, 18395}, {6597, 41229}, {6946, 15179}, {7320, 12647}, {7991, 36599}, {9614, 24297}, {10826, 21398}, {10827, 15173}, {11545, 37707}, {12699, 33696}, {13143, 30323}, {13464, 14497}, {13606, 37702}, {15180, 37708}, {17098, 37714}, {17501, 18514}, {18513, 41687}, {32537, 34747}, {37571, 38176}

X(43731) = reflection of X(i) in X(j) for these {i,j}: {1, 15079}, {24302, 11}
X(43731) = antigonal image of X(24302)
X(43731) = isotomic conjugate of the anticomplement of X(15492)
X(43731) = X(i)-cross conjugate of X(j) for these (i,j): {5697, 1}, {15492, 2}
X(43731) = X(i)-isoconjugate of X(j) for these (i,j): {6, 23958}, {58, 4084}
X(43731) = cevapoint of X(11) and X(28221)
X(43731) = trilinear pole of line {650, 4931}
X(43731) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 23958}, {37, 4084}

X(43732) = X(1)X(1657)∩X(4)X(41690)

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

X(43732) lies on the Feuerbach circumhyperbola, the cubic K194, and these lines: {1, 1657}, {4, 41690}, {7, 4857}, {8, 3901}, {9, 3336}, {21, 25055}, {46, 7161}, {57, 3467}, {65, 14841}, {90, 3337}, {104, 11522}, {388, 7317}, {484, 7162}, {497, 5551}, {941, 32857}, {942, 5561}, {943, 5010}, {1000, 11552}, {1373, 34216}, {1374, 34215}, {1476, 4355}, {1699, 10308}, {1836, 5557}, {2320, 3636}, {2346, 4312}, {3065, 3338}, {3340, 13143}, {3583, 5556}, {3585, 7319}, {3649, 5424}, {3680, 34747}, {4295, 7320}, {4866, 17528}, {5560, 5902}, {5586, 37718}, {5691, 16615}, {5882, 14497}, {7160, 11010}, {7280, 15175}, {9579, 15173}, {9613, 24297}, {10404, 13606}, {12735, 24302}, {15446, 37587}, {17501, 18513}, {19862, 27186}, {33696, 37702}, {40779, 41326}

X(43732) = X(18398)-cross conjugate of X(1)
X(43732) = cevapoint of X(11) and X(28213)
X(43732) = trilinear pole of line {650, 28199}

X(43733) = X(1)X(3529)∩X(4)X(41706)

Barycentrics    (3*a^2 + 4*a*b + 3*b^2 - 3*c^2)*(3*a^2 - 3*b^2 + 4*a*c + 3*c^2) : :
X(43733) = 8 X[3634] - 15 X[41865]

X(43733) lies on the Feuerbach circumhyperbola, the cubic K195, and these lines: {1, 3529}, {4, 41706}, {7, 15008}, {8, 4018}, {9, 3634}, {21, 11544}, {65, 14843}, {79, 5225}, {80, 5229}, {354, 5551}, {388, 5559}, {497, 5557}, {942, 5556}, {943, 5217}, {1000, 4295}, {1056, 7320}, {1058, 5558}, {1156, 5708}, {1320, 31295}, {1836, 3296}, {3062, 18483}, {3255, 13159}, {3600, 38753}, {3680, 12559}, {4860, 10308}, {5128, 8164}, {5902, 17501}, {7319, 31794}, {7321, 30479}, {10390, 43180}, {10593, 21454}, {10595, 37518}, {11551, 33703}, {11552, 12245}, {12116, 34485}, {15909, 36996}, {20214, 32635}, {21169, 34216}

X(43733) = isotomic conjugate of the anticomplement of X(16884)
X(43733) = X(16884)-cross conjugate of X(2)
X(43733) = X(58)-isoconjugate of X(4533)
X(43733) = cevapoint of X(11) and X(28195)
X(43733) = trilinear pole of line {650, 28175}
X(43733) = perspector of ABC and mid-triangle of intouch triangle and reflection triangle of X(1)
X(43733) = barycentric quotient X(37)/X(4533)

X(43734) = X(1)X(3090)∩X(4)X(41687)

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

X(43734) lies on the Feuerbach circumhyperbola, the cubic K195, and these lines: {1, 3090}, {4, 41687}, {7, 355}, {8, 4533}, {9, 3626}, {21, 3617}, {40, 7285}, {65, 14843}, {79, 5229}, {80, 5225}, {84, 5128}, {104, 5204}, {145, 10593}, {388, 5557}, {390, 38175}, {497, 5559}, {517, 7319}, {631, 37711}, {944, 31231}, {1000, 1837}, {1056, 5558}, {1058, 7320}, {1156, 12702}, {1320, 3621}, {1389, 10598}, {1392, 5748}, {1476, 6911}, {2320, 9780}, {2550, 3255}, {3057, 7317}, {3062, 31673}, {3296, 18391}, {3436, 11604}, {3487, 38155}, {3544, 11011}, {3625, 3680}, {4313, 38176}, {4816, 4900}, {4962, 23838}, {5067, 37740}, {5082, 30513}, {5183, 11541}, {5252, 18490}, {5560, 41684}, {5564, 30479}, {5665, 5714}, {6867, 17097}, {7173, 10595}, {7288, 9897}, {7743, 20053}, {7967, 37518}, {9669, 31145}, {10308, 37567}, {10532, 34485}, {10896, 34631}, {11041, 37714}, {11279, 18395}, {12641, 15863}, {12647, 13606}, {13602, 37702}

X(43734) = isotomic conjugate of the anticomplement of X(16885)
X(43734) = X(16885)-cross conjugate of X(2)
X(43734) = X(i)-isoconjugate of X(j) for these (i,j): {58, 4018}, {2163, 4930}
X(43734) = cevapoint of X(11) and X(4926)
X(43734) = trilinear pole of line {650, 28183}
X(43734) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 4018}, {45, 4930}

X(43735) = MIDPOINT OF X(149) AND X(2897)

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

X(43735) lies on the Feuerbach circumhyperbola, the cubic K288, and these lines: {1, 4466}, {4, 2831}, {11, 1172}, {21, 26932}, {100, 18642}, {104, 1503}, {149, 2897}, {858, 8759}, {10705, 42761}
X(43735) = midpoint of X(149) and X(2897)
X(43735) = reflection of X(i) in X(j) for these {i,j}: {100, 18642}, {1172, 11}
X(43735) = antigonal image of X(1172)
X(43735) = symgonal image of X(18642)
X(43735) = X(109)-isoconjugate of X(2806)
X(43735) = barycentric product X(2722)*X(4391)
X(43735) = barycentric quotient X(i)/X(j) for these {i,j}: {650, 2806}, {2722, 651}

X(43736) = ISOGONAL CONJUGATE OF X(41339)

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

X(43736) lies on the Feuerbach circumhyperbola, the cubic K294, and these lines: {1, 103}, {4, 279}, {7, 4626}, {8, 348}, {9, 77}, {21, 1414}, {57, 42317}, {79, 10481}, {80, 1323}, {84, 4350}, {104, 24016}, {241, 294}, {269, 2310}, {314, 4625}, {347, 6601}, {676, 885}, {677, 34894}, {943, 36048}, {1014, 1172}, {1156, 1443}, {1440, 7003}, {1442, 2346}, {2344, 17074}, {2997, 33673}, {3254, 22464}, {3668, 15909}, {3680, 9451}, {3960, 23893}, {4617, 7004}, {4876, 6168}, {5089, 43044}, {5543, 5558}, {5561, 21314}, {7053, 7071}, {7190, 10390}, {7271, 31507}, {26001, 43035}, {26722, 36039}, {31526, 41527}, {39759, 41353}

X(43736) = isogonal conjugate of X(41339)
X(43736) = X(i)-cross conjugate of X(j) for these (i,j): {1, 9503}, {103, 36101}, {1456, 57}, {2254, 651}, {2820, 100}, {34855, 7}, {43044, 279}
X(43736) = X(i)-isoconjugate of X(j) for these (i,j): {1, 41339}, {6, 40869}, {9, 910}, {41, 30807}, {55, 516}, {200, 1456}, {219, 1886}, {220, 43035}, {284, 17747}, {294, 9502}, {522, 2426}, {607, 26006}, {652, 41321}, {663, 2398}, {676, 3939}, {1334, 14953}, {2175, 35517}, {2338, 23972}, {3063, 42719}, {4105, 23973}
X(43736) = cevapoint of X(i) and X(j) for these (i,j): {1, 241}, {57, 1456}, {665, 3022}, {1565, 43042}, {3669, 3675}, {39759, 43047}
X(43736) = trilinear pole of line {57, 650}
X(43736) = barycentric product X(i)*X(j) for these {i,j}: {7, 36101}, {57, 18025}, {85, 103}, {273, 1815}, {331, 36056}, {348, 36122}, {651, 2400}, {677, 24002}, {911, 6063}, {1088, 2338}, {2424, 4554}, {4391, 24016}, {4564, 15634}, {9436, 9503}, {32668, 35519}
X(43736) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40869}, {6, 41339}, {7, 30807}, {34, 1886}, {56, 910}, {57, 516}, {65, 17747}, {77, 26006}, {85, 35517}, {103, 9}, {108, 41321}, {269, 43035}, {651, 2398}, {664, 42719}, {677, 644}, {911, 55}, {1014, 14953}, {1407, 1456}, {1415, 2426}, {1456, 23972}, {1458, 9502}, {1815, 78}, {2078, 28345}, {2338, 200}, {2400, 4391}, {2424, 650}, {3669, 676}, {3675, 1566}, {4617, 23973}, {4626, 24015}, {9503, 14942}, {15634, 4858}, {18025, 312}, {24016, 651}, {32657, 212}, {32668, 109}, {34855, 39063}, {36039, 3939}, {36056, 219}, {36101, 8}, {36122, 281}, {43035, 24014}

X(43737) = POLAR CONJUGATE OF X(2405)

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

X(43737) lies on the Feuerbach circumhyperbola, the cubic K406, and these lines: {1, 8058}, {4, 521}, {7, 4131}, {8, 30201}, {9, 14331}, {21, 2417}, {84, 522}, {104, 1295}, {513, 10309}, {900, 34256}, {1172, 2431}, {1896, 7253}, {3427, 3900}, {3676, 8809}, {4581, 40454}, {10015, 36121}, {23987, 36044}

X(43737) = polar conjugate of X(2405)
X(43737) = polar conjugate of the isotomic conjugate of X(2417)
X(43737) = polar conjugate of the isogonal conjugate of X(2431)
X(43737) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {36044, 153}, {36110, 34550}
X(43737) = X(2431)-cross conjugate of X(2417)
X(43737) = X(i)-isoconjugate of X(j) for these (i,j): {48, 2405}, {63, 2443}, {73, 7435}, {101, 43058}, {109, 6001}, {14312, 24027}, {23706, 39175}
X(43737) = cevapoint of X(i) and X(j) for these (i,j): {517, 15252}, {521, 2804}, {6129, 8677}
X(43737) = trilinear pole of line {650, 5514}
X(43737) = pole wrt polar circle of trilinear polar of X(2405) (line X(1528)X(6001), the Simson line of X(108))
X(43737) = barycentric product X(i)*X(j) for these {i,j}: {4, 2417}, {264, 2431}, {1295, 4391}
X(43737) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 2405}, {25, 2443}, {513, 43058}, {650, 6001}, {1146, 14312}, {1172, 7435}, {1295, 651}, {2417, 69}, {2431, 3}, {36044, 7128}

X(43738) = ISOGONAL CONJUGATE OF X(8924)

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

X(43738) lies on the Feuerbach circumhyperbola, the cubic K422, and these lines: {1, 8925}, {3, 3495}, {4, 3503}, {98, 7167}, {182, 2344}, {511, 3508}, {2481, 29057}, {3402, 7350}, {3403, 6210}, {3404, 7351}, {3405, 6211}, {5999, 8924}, {6194, 7155}

X(43738) = isogonal conjugate of X(8924)
X(43738) = barycentric quotient X(6)/X(8924)

X(43739) = ISOGONAL CONJUGATE OF X(1764)

Barycentrics    a*(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(43739) lies on the Feuerbach circumhyperbola, the cubic K430, and these lines: {1, 14749}, {3, 34278}, {7, 10478}, {8, 573}, {9, 3185}, {21, 572}, {57, 10435}, {104, 38855}, {314, 1764}, {1172, 4264}, {1630, 38871}, {1896, 37390}, {5816, 30513}, {7091, 10862}, {33847, 37499}

X(43739) = isogonal conjugate of X(1764)
X(43739) = isotomic conjugate of X(21596)
X(43739) = isogonal conjugate of the anticomplement of X(2051)
X(43739) = X(1402)-cross conjugate of X(1)
X(43739) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1764}, {2, 23361}, {4, 23131}, {6, 20245}, {31, 21596}, {58, 22020}, {81, 22299}, {86, 3588}, {101, 23799}, {333, 40611}, {3666, 40455}
X(43739) = cevapoint of X(i) and X(j) for these (i,j): {649, 11998}, {661, 38345}, {798, 2310}
X(43739) = crosssum of X(3588) and X(22299)
X(43739) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 20245}, {2, 21596}, {6, 1764}, {31, 23361}, {37, 22020}, {42, 22299}, {48, 23131}, {213, 3588}, {513, 23799}, {1402, 40611}
X(43739) = {X(10437),X(16574)}-harmonic conjugate of X(1764)

X(43740) = ISOGONAL CONJUGATE OF X(37579)

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

X(43740) lies on the Feuerbach circumhyperbola, the cubic K617, and these lines: {1, 224}, {2, 943}, {4, 912}, {7, 7702}, {9, 2478}, {10, 7162}, {11, 1259}, {12, 42885}, {20, 104}, {21, 497}, {57, 41565}, {63, 90}, {65, 41710}, {69, 2997}, {79, 10052}, {80, 3436}, {84, 10431}, {119, 10524}, {145, 1389}, {225, 1041}, {315, 2481}, {388, 17097}, {496, 37248}, {528, 11510}, {950, 37155}, {962, 3427}, {983, 5230}, {987, 11269}, {1000, 3885}, {1012, 10943}, {1039, 40950}, {1063, 1068}, {1069, 2990}, {1071, 5553}, {1156, 5225}, {1172, 3193}, {1392, 12536}, {1476, 11240}, {1478, 11520}, {1837, 10522}, {1937, 37591}, {1998, 5715}, {2298, 41508}, {2320, 4313}, {2346, 2550}, {2475, 11036}, {2551, 32635}, {3062, 5735}, {3086, 37300}, {3187, 37181}, {3218, 6851}, {3467, 18232}, {3555, 18517}, {3577, 5881}, {3583, 36599}, {3621, 24297}, {3813, 10966}, {4208, 10587}, {4292, 7284}, {4294, 37285}, {4654, 5665}, {4857, 31424}, {5080, 7319}, {5086, 10629}, {5259, 15175}, {5438, 37462}, {5555, 41871}, {5687, 25962}, {5709, 6836}, {5720, 6835}, {6598, 31938}, {6601, 41228}, {6826, 34772}, {6837, 10530}, {6849, 31053}, {6850, 18444}, {6897, 24299}, {6916, 10806}, {6925, 41854}, {6993, 10528}, {7080, 34894}, {7160, 24987}, {8809, 22464}, {9669, 37358}, {9799, 10309}, {9812, 10429}, {9965, 10308}, {10198, 41859}, {10267, 20075}, {10305, 11220}, {10597, 14497}, {10680, 18499}, {10947, 10959}, {10957, 11235}, {13243, 34256}, {15171, 20835}, {15179, 37435}, {15314, 21279}, {16465, 37820}, {16615, 20060}, {17584, 27509}, {17781, 38271}, {18543, 40295}, {18544, 37447}, {20066, 37105}, {21398, 41702}, {24390, 37228}, {24541, 37704}, {31775, 32214}, {35976, 37579}, {37163, 37518}

X(43740) = anticomplement of X(11517)
X(43740) = isogonal conjugate of X(37579)
X(43740) = cyclocevian conjugate of X(41514)
X(43740) = anticomplement of the isogonal conjugate of X(39267)
X(43740) = isotomic conjugate of the anticomplement of X(219)
X(43740) = isotomic conjugate of the complement of X(20110)
X(43740) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {13397, 20294}, {15474, 4329}, {39267, 8}
X(43740) = X(i)-cross conjugate of X(j) for these (i,j): {219, 2}, {8735, 4391}, {39943, 15474}
X(43740) = X(i)-isoconjugate of X(j) for these (i,j): {1, 37579}, {4, 3215}, {6, 1708}, {19, 3173}, {34, 11517}, {55, 4341}, {56, 3811}, {57, 2911}, {58, 41538}, {65, 1780}, {73, 30733}, {109, 15313}, {225, 41608}, {226, 41332}, {604, 17776}, {1400, 40571}
X(43740) = cevapoint of X(i) and X(j) for these (i,j): {1, 5709}, {2, 20110}, {11, 521}, {3900, 6506}, {23604, 28787}
X(43740) = crosspoint of X(2994) and X(39695)
X(43740) = barycentric product X(i)*X(j) for these {i,j}: {8, 15474}, {75, 39943}, {261, 41508}, {333, 23604}, {345, 39267}, {4391, 13397}, {28787, 31623}
X(43740) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1708}, {3, 3173}, {6, 37579}, {8, 17776}, {9, 3811}, {21, 40571}, {37, 41538}, {48, 3215}, {55, 2911}, {57, 4341}, {219, 11517}, {284, 1780}, {650, 15313}, {1172, 30733}, {2193, 41608}, {2194, 41332}, {4373, 27815}, {4858, 17877}, {8735, 5521}, {13397, 651}, {15474, 7}, {23604, 226}, {28787, 1214}, {39267, 278}, {39943, 1}, {40937, 14054}, {41508, 12}
X(43740) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {149, 10529, 12116}, {1837, 10522, 30513}, {5905, 12649, 14054}

X(43741) = X(1)X(27186)∩X(104)X(550)

Barycentrics    (a - b - c)*(a^3 + a^2*b + a*b^2 + b^3 - a^2*c - 3*a*b*c - b^2*c - a*c^2 - b*c^2 + c^3)*(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(43741) lies on the Feuerbach circumhyperbola, the cubic K618, and these lines: {1, 27186}, {21, 3058}, {79, 3874}, {104, 550}, {149, 3065}, {496, 943}, {983, 24883}, {2346, 3826}, {2481, 7768}, {3219, 3467}, {3296, 3434}, {4294, 15446}, {5080, 5560}, {6597, 24392}, {7161, 37162}, {10944, 17097}, {11112, 15179}, {16615, 37705}

X(43741) = cevapoint of X(i) and X(j) for these (i,j): {1, 24468}, {11, 35057}

X(43742) = X(1)X(406)∩X(24)X(104)

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

X(43742) lies on the Feuerbach circumhyperbola, the cubic K620, and these lines: {1, 406}, {4, 17869}, {7, 8048}, {21, 34277}, {24, 104}, {25, 40454}, {34, 20266}, {84, 7713}, {123, 7219}, {281, 2298}, {318, 30513}, {1146, 2207}, {1476, 35973}, {1890, 3062}, {3194, 34279}, {8759, 12649}, {18391, 40396}

X(43742) = polar conjugate of the isotomic conjugate of X(34277)
X(43742) = X(i)-cross conjugate of X(j) for these (i,j): {25, 281}, {22760, 7040}
X(43742) = X(i)-isoconjugate of X(j) for these (i,j): {3, 21147}, {57, 22132}, {63, 478}, {73, 16049}, {77, 197}, {123, 24027}, {205, 348}, {222, 1766}, {255, 14257}, {326, 17408}, {603, 3436}, {1813, 6588}, {21186, 36059}, {40152, 41364}
X(43742) = cevapoint of X(1146) and X(18344)
X(43742) = barycentric product X(i)*X(j) for these {i,j}: {4, 34277}, {281, 8048}, {318, 42467}, {2052, 39167}, {3435, 7017}, {4391, 40097}, {15385, 23978}
X(43742) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 21147}, {25, 478}, {33, 1766}, {55, 22132}, {281, 3436}, {318, 20928}, {393, 14257}, {607, 197}, {1146, 123}, {1172, 16049}, {2207, 17408}, {2212, 205}, {3064, 21186}, {3435, 222}, {8048, 348}, {15385, 1262}, {18344, 6588}, {34277, 69}, {39167, 394}, {40097, 651}, {42467, 77}

X(43743) = X(3)X(35097)∩X(4)X(15622)

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

X(43743) lies on the Feuerbach circumhyperbola, the cubic K622, and these lines: {3, 35097}, {4, 15622}, {104, 1614}

X(43743) = X(664)-isoconjugate of X(21645)
X(43743) = cevapoint of X(1946) and X(11998)
X(43743) = barycentric quotient X(3063)/X(21645)

X(43744) = X(1)X(963)∩X(4)X(269)

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

X(43744) lies on the Feuerbach circumhyperbola, the cubic K713, and these lines: {1, 963}, {4, 269}, {8, 77}, {9, 222}, {79, 7271}, {294, 610}, {885, 21172}, {1039, 1467}, {1172, 1412}, {1422, 7003}, {1442, 7320}, {1443, 7319}, {2481, 33673}, {3296, 4328}, {3427, 4341}, {4350, 10429}, {5557, 7274}, {5558, 7190}, {8270, 42470}, {8809, 34855}

X(43744) = X(i)-cross conjugate of X(j) for these (i,j): {221, 57}, {40953, 189}, {40971, 41790}
X(43744) = X(i)-isoconjugate of X(j) for these (i,j): {6, 27508}, {8, 20991}, {9, 2270}, {41, 20921}, {55, 962}, {281, 22124}, {284, 21068}, {3939, 7661}
X(43744) = cevapoint of X(3942) and X(6129)
X(43744) = barycentric product X(85)*X(963)
X(43744) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 27508}, {7, 20921}, {56, 2270}, {57, 962}, {65, 21068}, {603, 22124}, {604, 20991}, {963, 9}, {3669, 7661}

X(43745) = X(1)X(37462)∩X(21)X(10385)

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

X(43745) lies on the Feuerbach circumhyperbola, the cubic K917, and these lines: {1, 37462}, {21, 10385}, {79, 3434}, {90, 10624}, {104, 3522}, {497, 32635}, {519, 17098}, {1389, 20013}, {2478, 4866}, {3296, 3889}, {3305, 7162}, {3436, 5560}, {3621, 16615}, {5557, 10044}, {5665, 37709}, {6904, 15179}, {7160, 12620}, {7161, 18233}, {10308, 20078}, {17781, 36599}

X(43746) = ISOGONAL CONJUGATE OF X(41349)

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

X(43746) lies on the Feuerbach circumhyperbola, the cubic K954, and these lines: {4, 2791}, {7, 18210}, {21, 3270}, {104, 2714}, {314, 2968}, {1172, 14936}, {1896, 42069}, {10006, 14224}

X(43746) = isogonal conjugate of X(41349)
X(43746) = X(i)-isoconjugate of X(j) for these (i,j): {1, 41349}, {65, 23695}, {73, 425}, {109, 2798}
X(43746) = trilinear pole of line {650, 1858}
X(43746) = barycentric product X(2714)*X(4391)
X(43746) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 41349}, {284, 23695}, {650, 2798}, {1172, 425}, {2714, 651}

X(43747) = ISOGONAL CONJUGATE OF X(18788)

Barycentrics    a*(a^4 - a^3*b - a*b^3 + b^4 + a^3*c + a^2*b*c + a*b^2*c + b^3*c - 2*a^2*c^2 - a*b*c^2 - 2*b^2*c^2 + a*c^3 + b*c^3 - c^4)*(a^4 + a^3*b - 2*a^2*b^2 + a*b^3 - b^4 - a^3*c + a^2*b*c - 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(43747) lies on the Feuerbach circumhyperbola, the cubics K960 and K1025, and these lines: {1, 40765}, {8, 1281}, {9, 8245}, {21, 8847}, {256, 34253}, {294, 1580}, {846, 40779}, {885, 4107}, {1447, 7261}, {1757, 23605}, {1768, 14947}, {1929, 8926}, {2298, 12725}, {3509, 4447}, {7155, 17738}
X(43747) = isogonal conjugate of X(18788)
X(43747) = X(i)-cross conjugate of X(j) for these (i,j): {1429, 1}, {3512, 1929}
X(43747) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18788}, {55, 41352}, {291, 8932}, {8848, 41531}
X(43747) = cevapoint of X(i) and X(j) for these (i,j): {659, 2310}, {2238, 42446}
X(43747) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 18788}, {57, 41352}, {1914, 8932}

X(43748) = X(1)X(295)∩X(4)X(291)

Barycentrics    a*(a - b - c)*(-b^2 + a*c)*(a*b - c^2)*(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(43748) lies on the Feuerbach circumhyperbola, the cubic K990, and these lines: {1, 295}, {4, 291}, {7, 3123}, {9, 22205}, {21, 1808}, {38, 41527}, {256, 36214}, {983, 1582}, {1172, 2311}, {2196, 2201}, {2227, 7261}, {2310, 7155}, {2997, 17157}

X(43748) = X(i)-isoconjugate of X(j) for these (i,j): {6, 39930}, {1284, 13588}, {1403, 14199}, {1428, 32937}, {1429, 3501}, {1447, 34247}
X(43748) = trilinear pole of line {650, 20359}
X(43748) = barycentric product X(i)*X(j) for these {i,j}: {1581, 39936}, {3500, 4518}
X(43748) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 39930}, {2311, 13588}, {2319, 14199}, {3500, 1447}, {4518, 17786}, {4876, 32937}, {7077, 3501}, {39936, 1966}

X(43749) = ISOGONAL CONJUGATE Of X(41346)

Barycentrics    (a - b - c)*(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(43749) lies on the Feuerbach circumhyperbola, the cubic K1000, and these lines: {1, 2896}, {2, 983}, {4, 4812}, {7, 40038}, {8, 12589}, {9, 3705}, {38, 256}, {69, 41527}, {75, 7261}, {80, 4692}, {104, 37331}, {497, 7155}, {894, 29655}, {941, 41269}, {943, 29964}, {2298, 24512}, {2346, 29839}, {3112, 7224}, {3551, 29844}, {4876, 17452}, {5749, 9599}, {7161, 30171}, {17282, 29634}, {17291, 29656}, {29838, 33123}, {35975, 41346}

X(43749) = isogonal conjugate of X(41346)
X(43749) = isotomic conjugate of the anticomplement of X(2329)
X(43749) = isotomic conjugate of {X(7),X(8)}-harmonic conjugate of X(3212)
X(43749) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {39724, 30660}, {40432, 20934}
X(43749) = X(40038)-Ceva conjugate of X(39724)
X(43749) = X(i)-cross conjugate of X(j) for these (i,j): {2329, 2}, {4514, 8}
X(43749) = X(i)-isoconjugate of X(j) for these (i,j): {1, 41346}, {56, 3961}, {604, 17280}, {1397, 33938}, {1402, 33954}, {1403, 3494}, {1423, 34249}
X(43749) = cevapoint of X(11) and X(3907)
X(43749) = trilinear pole of line {650, 3810}
X(43749) = barycentric product X(i)*X(j) for these {i,j}: {8, 39724}, {9, 40038}, {312, 7194}, {3502, 27424}
X(43749) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 41346}, {8, 17280}, {9, 3961}, {312, 33938}, {333, 33954}, {2053, 34249}, {2319, 3494}, {3502, 1423}, {7081, 17741}, {7194, 57}, {18155, 18077}, {39724, 7}, {40038, 85}

X(43750) = X(1)X(9446)∩X(8)X(2898)

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

X(43750) lies on the Feuerbach circumhyperbola, the cubic K1011, and these lines: {1, 9446}, {8, 2898}, {9, 3177}, {279, 9442}, {294, 3212}, {658, 38285}, {3062, 42309}, {3160, 40779}, {3680, 27829}, {7155, 40704}, {7320, 31527}

X(43750) = X(i)-cross conjugate of X(j) for these (i,j): {1088, 7}, {9311, 27818}
X(43750) = X(i)-isoconjugate of X(j) for these (i,j): {9, 20995}, {33, 20793}, {41, 3177}, {55, 1742}, {220, 34497}, {284, 21856}, {1212, 38835}, {1253, 31526}, {2175, 20935}, {2194, 21084}, {14827, 40593}
X(43750) = cevapoint of X(i) and X(j) for these (i,j): {514, 3022}, {3676, 4014}
X(43750) = trilinear pole of line {650, 21195}
X(43750) = Steiner image of X(7)
X(43750) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 3177}, {56, 20995}, {57, 1742}, {65, 21856}, {85, 20935}, {222, 20793}, {226, 21084}, {269, 34497}, {279, 31526}, {1088, 40593}, {3676, 21195}

X(43751) = X(1)X(2114)∩X(8)X(17755)

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

X(43751) lies on the Feuerbach circumhyperbola, the cubic K1041, and these lines: {1, 2114}, {8, 17755}, {9, 1282}, {21, 8932}, {144, 7155}, {238, 294}, {256, 14100}, {390, 41527}, {516, 2481}, {518, 4876}, {812, 885}, {971, 9442}, {984, 40779}, {1001, 2344}, {1423, 3062}, {2801, 14947}, {6601, 20539}, {7290, 42317}

X(43751) = X(4649)-isoconjugate of X(18789)
X(43751) = barycentric quotient X(25426)/X(18789)

X(43752) = X(3)X(95)∩X(97)X(2052)

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

X(43752) lies on these lines: {3, 95}, {97, 2052}, {250, 41202}, {275, 5422}, {317, 18912}, {340, 520}, {687, 40427}, {37871, 40684}

X(43752) = cevapoint of X(97) and X(19193)
X(43752) = trilinear pole of line {1636, 14920}
X(43752) = crossdifference of every pair of points on line {217, 42293}
X(43752) = polar conjugate of isogonal conjugate of X(43768)
X(43752) = X(i)-isoconjugate of X(j) for these (i,j): {51, 35200}, {216, 2159}, {217, 2349}, {418, 36119}, {810, 36831}, {1953, 18877}, {2179, 14919}, {2290, 11079}, {15451, 36034}, {17434, 36131}
X(43752) = barycentric product X(i)*X(j) for these {i,j}: {30, 276}, {275, 3260}, {1990, 34384}, {8795, 11064}, {9033, 42405}, {14206, 40440}, {18831, 41079}
X(43752) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 216}, {54, 18877}, {95, 14919}, {275, 74}, {276, 1494}, {648, 36831}, {933, 32640}, {1141, 11079}, {1495, 217}, {1637, 15451}, {1784, 1953}, {1990, 51}, {2167, 35200}, {2190, 2159}, {2407, 23181}, {3260, 343}, {3284, 418}, {4240, 1625}, {6357, 30493}, {8795, 16080}, {8882, 40352}, {8884, 8749}, {9033, 17434}, {9409, 42293}, {11064, 5562}, {14391, 34983}, {14581, 40981}, {14920, 1154}, {15412, 14380}, {16813, 1304}, {24001, 2617}, {35201, 2290}, {36789, 1568}, {38808, 15291}, {40440, 2349}, {41079, 6368}, {42405, 16077}
X(43752) = {X(95),X(8795)}-harmonic conjugate of X(264)

X(43753) = X(50)X(14533)∩X(54)X(3003)

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

X)43753) lies on these lines: {50, 14533}, {54, 3003}, {3284, 8882}, {9380, 14587}, {14586, 18365}

X(43753) = barycentric product X(i)*X(j) for these {i,j}: {54, 43574}, {3134, 14587}
X(43753) = barycentric quotient X(43574)/X(311)

X(43754) = ISOGONAL CONJUGATE OF X(16230)

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

X(43754) lies on the MacBeath circumconic, the cubic K147, and these lines: {98, 858}, {110, 647}, {248, 895}, {249, 39201}, {250, 523}, {287, 441}, {340, 31635}, {511, 1976}, {520, 4558}, {651, 36084}, {677, 17943}, {691, 9409}, {827, 6037}, {879, 43083}, {933, 22456}, {1634, 14587}, {2001, 22391}, {3265, 4563}, {3292, 14919}, {4230, 34212}, {5467, 14380}, {5489, 14366}, {6531, 16310}, {9218, 42658}, {9517, 32662}, {11064, 41175}, {13136, 17944}, {14355, 33927}, {14601, 41909}, {15407, 36212}, {15451, 33803}, {17708, 34761}, {17939, 23220}, {17941, 41173}

X(43754) = reflection of X(15407) in X(39085)
X(43754) = isogonal conjugate of X(16230)
X(43754) = isogonal conjugate of the isotomic conjugate of X(17932)
X(43754) = isotomic conjugate of the polar conjugate of X(2715)
X(43754) = isogonal conjugate of the polar conjugate of X(2966)
X(43754) = X(2966)-Ceva conjugate of X(2715)
X(43754) = X(i)-cross conjugate of X(j) for these (i,j): {520, 15407}, {684, 3}, {878, 248}, {3289, 249}
X(43754) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16230}, {19, 2799}, {75, 17994}, {92, 3569}, {158, 684}, {162, 868}, {232, 1577}, {240, 523}, {297, 661}, {511, 24006}, {512, 40703}, {656, 6530}, {823, 41172}, {877, 2643}, {1096, 6333}, {1109, 4230}, {1755, 14618}, {1784, 32112}, {1959, 2501}, {1969, 2491}, {2211, 20948}, {2616, 39569}, {2618, 19189}, {2970, 23997}, {14208, 34854}, {35088, 36104}, {35908, 36035}, {36120, 41167}
X(43754) = cevapoint of X(i) and X(j) for these (i,j): {3, 684}, {248, 878}, {3289, 39201}, {42295, 42663}
X(43754) = crosspoint of X(2966) and X(17932)
X(43754) = crosssum of X(3569) and X(17994)
X(43754) = trilinear pole of line {3, 248}
X(43754) = crossdifference of every pair of points on line {868, 41172}
X(43754) = barycentric product X(i)*X(j) for these {i,j}: {3, 2966}, {6, 17932}, {48, 36036}, {63, 36084}, {69, 2715}, {98, 4558}, {99, 248}, {110, 287}, {112, 6394}, {163, 336}, {184, 43187}, {249, 879}, {290, 32661}, {293, 662}, {326, 36104}, {394, 685}, {577, 22456}, {648, 17974}, {670, 14600}, {878, 4590}, {1821, 4575}, {1910, 4592}, {1976, 4563}, {3926, 32696}, {3964, 20031}, {15391, 17941}, {15407, 34211}, {36212, 41173}, {39201, 41174}
X(43754) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 2799}, {6, 16230}, {32, 17994}, {98, 14618}, {110, 297}, {112, 6530}, {163, 240}, {184, 3569}, {248, 523}, {249, 877}, {287, 850}, {293, 1577}, {336, 20948}, {394, 6333}, {577, 684}, {647, 868}, {662, 40703}, {684, 35088}, {685, 2052}, {878, 115}, {879, 338}, {1332, 42703}, {1576, 232}, {1625, 39569}, {1910, 24006}, {1976, 2501}, {2395, 2970}, {2422, 8754}, {2715, 4}, {2966, 264}, {3289, 41167}, {4230, 36426}, {4558, 325}, {4575, 1959}, {6394, 3267}, {10317, 33752}, {14574, 2211}, {14575, 2491}, {14585, 39469}, {14586, 19189}, {14600, 512}, {14601, 2489}, {14908, 8430}, {14966, 2967}, {15407, 43673}, {17932, 76}, {17974, 525}, {18877, 32112}, {20031, 1093}, {22456, 18027}, {23357, 4230}, {32640, 35908}, {32661, 511}, {32662, 14356}, {32696, 393}, {35912, 41079}, {36036, 1969}, {36084, 92}, {36104, 158}, {39201, 41172}, {41173, 16081}, {43187, 18022}
X(43754) = {X(38861),X(43113)}-harmonic conjugate of X(32696)

X(43755) = CEVAPOINT OF X(3) AND X(686)

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

X(43755) lies on the MacBeath circumconic, the cubic K256, and these lines: {110, 924}, {249, 648}, {895, 5504}, {2986, 11064}, {2987, 14910}, {10411, 18879}

X(43755) = isotomic conjugate of the polar conjugate of X(10420)
X(43755) = isogonal conjugate of the polar conjugate of X(18878)
X(43755) = X(18878)-Ceva conjugate of X(10420)
X(43755) = X(i)-cross conjugate of X(j) for these (i,j): {526, 69}, {647, 10419}, {686, 3}, {11064, 249}
X(43755) = X(i)-isoconjugate of X(j) for these (i,j): {92, 21731}, {158, 686}, {403, 661}, {1096, 6334}, {1725, 2501}, {2643, 16237}, {3003, 24006}, {12828, 23894}, {16221, 32678}, {36114, 39021}
X(43755) = cevapoint of X(i) and X(j) for these (i,j): {3, 686}, {394, 8552}
X(43755) = trilinear pole of line {3, 974}
X(43755) = barycentric product X(i)*X(j) for these {i,j}: {3, 18878}, {69, 10420}, {99, 5504}, {249, 15421}, {326, 36114}, {394, 687}, {525, 18879}, {2986, 4558}, {3926, 32708}, {4563, 14910}, {4592, 36053}, {10411, 12028}, {32661, 40832}
X(43755) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 403}, {184, 21731}, {249, 16237}, {394, 6334}, {526, 16221}, {577, 686}, {686, 39021}, {687, 2052}, {2986, 14618}, {4558, 3580}, {4575, 1725}, {5467, 12828}, {5504, 523}, {10419, 18808}, {10420, 4}, {12028, 10412}, {13398, 16172}, {14910, 2501}, {15328, 2970}, {15421, 338}, {15470, 35235}, {18878, 264}, {18879, 648}, {32661, 3003}, {32708, 393}, {36053, 24006}, {36114, 158}

X(43756) = ISOGONAL CONJUGATE OF X(16310)

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

X(43756) lies on the MacBeath circumconic, the cubics K500 and X1169, and these lines: {24, 110}, {68, 136}, {74, 35465}, {648, 6515}, {895, 43709}, {1332, 42700}, {1993, 4558}, {3580, 16310}, {4563, 7763}, {10733, 18781}

X(43756) = isogonal conjugate of X(16310)
X(43756) = isotomic conjugate of the polar conjugate of X(1299)
X(43756) = X(14910)-cross conjugate of X(74)
X(43756) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16310}, {4, 2314}, {661, 30512}
X(43756) = cevapoint of X(i) and X(j) for these (i,j): {6, 13754}, {50, 1147}, {520, 2088}, {2245, 3157}
X(43756) = trilinear pole of line {3, 924}
X(43756) = barycentric product X(i)*X(j) for these {i,j}: {69, 1299}, {99, 43709}
X(43756) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 16310}, {48, 2314}, {110, 30512}, {155, 27087}, {1147, 12095}, {1299, 4}, {13754, 131}, {39373, 39170}, {43709, 523}

X(43757) = X(2)X(4604)∩X(11)X(32631)

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

X(43757) lies on the circumconic with center X(9), the curve Q059, and these lines: {2, 4604}, {11, 32631}, {88, 4508}, {100, 993}, {190, 1150}, {651, 5219}, {662, 5235}, {3257, 4396}, {20568, 24593}, {24618, 37222}, {28910, 37131}, {30590, 37211}

X(43757) = X(28160)-cross conjugate of X(7)
X(43757) = X(101)-isoconjugate of X(14315)
X(43757) = trilinear pole of line {1, 4777}
X(43757) = barycentric product X(903)*X(36818)
X(43757) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 14315}, {4715, 25398}, {36818, 519}

X(43758) = X(2)X(37211)∩X(100)X(1698)

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

X(43758) lies on the circumconic with center X(9), the curve Q060, and these lines: {2, 37211}, {100, 1698}, {162, 31902}, {190, 5278}, {651, 4654}, {662, 5333}, {4604, 17379}, {37212, 43260}

X(43758) = X(28146)-cross conjugate of X(7)
X(43758) = trilinear pole of line {1, 4802}

X(43759) = X(100)X(958)∩X(190)X(3929)

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

X(43759) lies on the circumconic with center X(9), the curve Q061, and these lines: {100, 958}, {190, 3929}, {651, 940}, {653, 5307}

X(43759) = X(28164)-cross conjugate of X(7)
X(43759) = X(931)-isoconjugate of X(14415)
X(43759) = cevapoint of X(11) and X(4773)
X(43759) = trilinear pole of line {1, 17418}

X(43760) = ISOGONAL CONJUGATE OF X(2348)

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

X(43760) lies on the circumconic with center X(9), the cubics K294 and K981, and these lines: {1, 42315}, {2, 37206}, {7, 190}, {9, 19604}, {57, 100}, {88, 37626}, {162, 1396}, {241, 1279}, {269, 651}, {479, 658}, {653, 1119}, {655, 30379}, {662, 1014}, {673, 2402}, {1155, 14201}, {1156, 2827}, {2346, 37597}, {3218, 6078}, {3257, 37787}, {3675, 28071}, {3911, 31226}, {17107, 25082}, {21446, 37223}, {27818, 42318}, {34253, 37138}, {37139, 37789}

X(43760) = reflection of X(i) in X(j) for these {i,j}: {7, 40617}, {27834, 9}
X(43760) = isogonal conjugate of X(2348)
X(43760) = X(35160)-Ceva conjugate of X(1280)
X(43760) = X(i)-cross conjugate of X(j) for these (i,j): {105, 43736}, {518, 7}, {650, 39272}, {2348, 1}
X(43760) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2348}, {2, 8647}, {6, 5853}, {9, 1279}, {55, 3008}, {281, 20780}, {513, 23704}, {1438, 40609}, {1477, 35111}, {2195, 16593}, {3699, 8659}, {3939, 6084}, {14942, 20662}
X(43760) = cevapoint of X(i) and X(j) for these (i,j): {1, 2348}, {57, 241}, {650, 3675}, {665, 1357}, {40615, 43042}
X(43760) = trilinear pole of line {1, 3309}
X(43760) = barycentric product X(i)*X(j) for these {i,j}: {1, 35160}, {7, 1280}, {57, 36807}, {75, 1477}, {190, 37626}, {273, 1810}, {664, 35355}, {6078, 24002}, {39272, 43042}
X(43760) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 5853}, {6, 2348}, {31, 8647}, {56, 1279}, {57, 3008}, {101, 23704}, {241, 16593}, {518, 40609}, {603, 20780}, {1279, 3021}, {1280, 8}, {1477, 1}, {1810, 78}, {2348, 35111}, {3669, 6084}, {6078, 644}, {35160, 75}, {35355, 522}, {36807, 312}, {37626, 514}, {39272, 36802}

X(43761) = ISOGONAL CONJUGATE OF X(2227)

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

X(43761) lies on the circumconic with center X(9), the cubics K432 and K989, and these lines: {31, 799}, {75, 34248}, {82, 18270}, {100, 699}, {171, 4598}, {190, 1918}, {560, 662}, {660, 18278}, {1403, 37137}, {1580, 1927}, {8858, 37215}

X(43761) = isogonal conjugate of X(2227)
X(43761) = X(i)-cross conjugate of X(j) for these (i,j): {1966, 82}, {1967, 1910}, {2227, 1}
X(43761) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2227}, {2, 3229}, {6, 698}, {32, 35524}, {76, 32748}, {325, 32540}, {523, 41337}, {524, 36821}, {670, 9429}, {694, 39080}
X(43761) = cevapoint of X(i) and X(j) for these (i,j): {1, 2227}, {31, 1580}, {43, 3747}
X(43761) = trilinear pole of line {1, 1924}
X(43761) = barycentric product X(i)*X(j) for these {i,j}: {1, 3225}, {19, 8858}, {75, 699}, {1581, 32544}
X(43761) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 698}, {6, 2227}, {31, 3229}, {75, 35524}, {163, 41337}, {560, 32748}, {699, 1}, {923, 36821}, {1580, 39080}, {1924, 9429}, {3225, 75}, {8858, 304}, {32544, 1966}

X(43762) = X(7)X(100)∩X(85)X(190)

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

X(43762) lies on the circumconic with center X(9), the cubic K660, and these lines: {7, 100}, {9, 37206}, {85, 190}, {218, 279}, {320, 35160}, {653, 1847}, {658, 1445}, {660, 7233}, {662, 1434}, {1156, 2826}, {1358, 6068}, {2369, 2742}, {4598, 7209}, {6172, 27818}, {10509, 41572}, {22464, 36086}, {23772, 42014}, {30379, 37139}, {31638, 34085}, {37143, 37780}

X(43762) = reflection of X(i) in X(j) for these {i,j}: {7, 40615}, {37206, 9}
X(43762) = X(i)-cross conjugate of X(j) for these (i,j): {527, 7}, {5526, 21453}, {43050, 664}
X(43762) = X(i)-isoconjugate of X(j) for these (i,j): {6, 15733}, {41, 26015}, {55, 43065}, {220, 3660}, {1253, 30379}, {2175, 37788}, {10427, 18889}, {14827, 38468}
X(43762) = cevapoint of X(i) and X(j) for these (i,j): {7, 37787}, {57, 1323}, {1358, 1638}
X(43762) = trilinear pole of line {1, 3676}
X(43762) = barycentric product X(i)*X(j) for these {i,j}: {75, 15728}, {1088, 34894}
X(43762) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 15733}, {7, 26015}, {57, 43065}, {85, 37788}, {269, 3660}, {279, 30379}, {1088, 38468}, {1323, 10427}, {2742, 3939}, {3676, 2826}, {10426, 4845}, {10481, 41555}, {15728, 1}, {34894, 200}

X(43763) = ISOGONAL CONJUGATE OF X(2236)

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

X(43763) lies on the circumconic with center X(9), the cubics K864 and K990, and these lines: {31, 4599}, {38, 799}, {75, 37204}, {82, 662}, {100, 733}, {190, 256}, {651, 1431}, {660, 694}, {1580, 34054}, {3405, 17799}, {16889, 37133}, {19559, 36084}

X(43763) = isogonal conjugate of X(2236)
X(43763) = X(i)-cross conjugate of X(j) for these (i,j): {2236, 1}, {3405, 82}
X(43763) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2236}, {2, 8623}, {6, 732}, {32, 35540}, {38, 1580}, {39, 385}, {141, 1691}, {419, 3917}, {688, 880}, {804, 1634}, {1843, 12215}, {1914, 16720}, {1923, 1926}, {1930, 1933}, {1964, 1966}, {3005, 17941}, {3051, 3978}, {4039, 17187}, {4093, 17103}, {4164, 4553}, {4576, 5027}, {4590, 41178}, {8024, 14602}, {9019, 36820}, {11183, 36827}, {14603, 41331}, {17984, 20775}, {20021, 36213}, {21752, 30940}, {24284, 35325}, {33295, 40936}
X(43763) = cevapoint of X(i) and X(j) for these (i,j): {1, 2236}, {82, 34054}, {1581, 1967}
X(43763) = trilinear pole of line {1, 2084}
X(43763) = barycentric product X(i)*X(j) for these {i,j}: {1, 14970}, {75, 733}, {82, 1916}, {83, 1581}, {251, 1934}, {308, 1967}, {661, 41209}, {694, 3112}, {805, 18070}, {881, 37204}, {882, 4593}, {1927, 40016}, {3405, 36897}, {9468, 18833}, {9477, 34054}
X(43763) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 732}, {6, 2236}, {31, 8623}, {75, 35540}, {82, 385}, {83, 1966}, {251, 1580}, {291, 16720}, {308, 1926}, {694, 38}, {733, 1}, {881, 2084}, {882, 8061}, {1581, 141}, {1916, 1930}, {1927, 3051}, {1934, 8024}, {1967, 39}, {3112, 3978}, {3405, 5976}, {4593, 880}, {4599, 17941}, {8789, 1923}, {9468, 1964}, {10566, 14296}, {14970, 75}, {17970, 4020}, {17980, 17442}, {18070, 14295}, {18098, 4039}, {18108, 4107}, {18833, 14603}, {34054, 8290}, {34055, 12215}, {34238, 3404}, {36081, 18047}, {37134, 4576}, {39276, 17103}, {40729, 4093}, {41209, 799}

X(43764) = X(3)X(7040)∩X(4)X(651)

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

X(43764) lies on the circumconic with center X(9), the cubic K1185, and these lines: {3, 7040}, {4, 651}, {29, 662}, {46, 158}, {100, 281}, {162, 8748}, {190, 318}, {243, 8758}, {273, 658}, {823, 3559}, {1898, 7016}, {36123, 37136}, {37141, 37258}

X(43764) = polar conjugate of the isotomic conjugate of X(8777)
X(43764) = X(i)-cross conjugate of X(j) for these (i,j): {1936, 29}, {1937, 8764}, {5179, 92}
X(43764) = X(i)-isoconjugate of X(j) for these (i,j): {3, 8758}, {63, 8776}
X(43764) = cevapoint of X(4) and X(243)
X(43764) = trilinear pole of line {1, 3064}
X(43764) = barycentric product X(i)*X(j) for these {i,j}: {4, 8777}, {75, 20624}, {92, 8759}
X(43764) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 8758}, {25, 8776}, {8759, 63}, {8777, 69}, {20624, 1}

X(43765) = X(3)X(76)∩X(6)X(804)

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

X(43765) lies on the Brocard circle, the cubic K552, and these lines:{3, 76}, {6, 804}, {30, 31513}, {115, 9468}, {542, 33755}, {1316, 5027}, {5106, 22735}, {8429, 39906}, {11646, 39087}, {15920, 18332}

X(43765) = reflection of X(38947) in X(115)
X(43765) = circumcircle-inverse of X(21444)
X(43765) = crossdifference of every pair of points on line {2491, 34383}
X(43765) = {X(98),X(99)}-harmonic conjugate of X(21444)

X(43766) = X(2)X(19180)∩X(4)X(8901)

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

X(43766) lies on the Kiepert circumhyperbola and these lines: {2, 19180}, {4, 8901}, {83, 4993}, {97, 801}, {110, 40448}, {10574, 13599}

X(43766) = X(i)-cross conjugate of X(j) for these (i,j): {3003, 54}, {6000, 8795}
X(43766) = X(i)-isoconjugate of X(j) for these (i,j): {1087, 43753}, {1953, 43574}
X(43766) = trilinear pole of line {389, 523}
X(43766) = polar conjugate of isogonal conjugate of X(43918)
X(43766) = barycentric quotient X(i)/X(j) for these {i,j}: {54, 43574}, {8901, 3134}

X(43767) = X(2)X(19180)∩X(264)X(5890)

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

X(43767) lies on these lines: {2, 19180}, {264, 5890}

X(43767) = isotomic conjugate of isogonal conjugate of X(43918)
X(43767) = X(13754)-cross conjugate of X(97)
X(43767) = X(2181)-isoconjugate of X(43574)
X(43767) = barycentric quotient X(97)/X(43574)

X(43768) = X(2)X(95)∩X(20)X(54)

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

X(43768) lies on these lines: {2, 95}, {4, 19176}, {20, 54}, {22, 16030}, {23, 19189}, {52, 19168}, {146, 19193}, {147, 39814}, {148, 39843}, {323, 401}, {441, 40512}, {511, 19167}, {858, 8901}, {933, 2697}, {1141, 3153}, {1383, 42300}, {1993, 19180}, {1994, 8613}, {2167, 17483}, {3060, 21638}, {3091, 4994}, {3146, 8884}, {3152, 35196}, {3164, 11004}, {3284, 43752}, {3448, 19208}, {5059, 16251}, {6243, 19211}, {7391, 19174}, {8794, 41894}, {9536, 19181}, {9539, 19182}, {9544, 26887}, {9792, 11002}, {10217, 16770}, {10218, 16771}, {11413, 16035}, {11422, 42329}, {12086, 19172}, {13150, 27423}, {14533, 37645}, {17578, 19169}, {19166, 37644}, {19774, 19778}, {19775, 19779}, {23295, 31074}, {23357, 23582}, {23958, 26931}, {31610, 39286}, {32428, 35311}, {32830, 34386}, {35360, 41202}

X(43768) = anticomplement of X(14918)
X(43768) = anticomplement of the isogonal conjugate of X(11077)
X(43768) = isotomic conjugate of the anticomplement of X(14920)
X(43768) = isogonal conjugate of the polar conjugate of X(43752)
X(43768) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1141, 21270}, {2148, 12383}, {2168, 39118}, {2169, 1272}, {11077, 8}
X(43768) = X(i)-cross conjugate of X(j) for these (i,j): {30, 43752}, {1636, 4240}, {14920, 2}, {41079, 2407}
X(43768) = X(i)-isoconjugate of X(j) for these (i,j): {5, 2159}, {51, 2349}, {53, 35200}, {74, 1953}, {216, 36119}, {661, 36831}, {1393, 15627}, {1494, 2179}, {2181, 14919}, {2290, 5627}, {2433, 2617}, {2618, 32640}, {6368, 36131}, {12077, 36034}, {14213, 40352}, {18695, 40354}, {33805, 40981}
X(43768) = cevapoint of X(30) and X(3284)
X(43768) = trilinear pole of line {1511, 9033}
X(43768) = crossdifference of every pair of points on line {51, 15451}
X(43768) = isotomic conjugate of trilinear pole of line X(5)X(6368) (the line through X(5) parallel to the trilinear polar of X(5))
X(43768) = barycentric product X(i)*X(j) for these {i,j}: {3, 43752}, {30, 95}, {54, 3260}, {275, 11064}, {276, 3284}, {1141, 6148}, {1495, 34384}, {1636, 42405}, {1990, 34386}, {2167, 14206}, {2407, 15412}, {6739, 39277}, {9033, 18831}, {16813, 41077}, {18315, 41079}
X(43768) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 5}, {54, 74}, {95, 1494}, {97, 14919}, {110, 36831}, {275, 16080}, {933, 1304}, {1141, 5627}, {1157, 3470}, {1495, 51}, {1511, 1154}, {1636, 17434}, {1637, 12077}, {1650, 35442}, {1990, 53}, {2148, 2159}, {2167, 2349}, {2169, 35200}, {2173, 1953}, {2190, 36119}, {2407, 14570}, {2420, 1625}, {2623, 2433}, {3260, 311}, {3284, 216}, {3471, 1263}, {3484, 38933}, {4240, 35360}, {5642, 41586}, {5664, 41078}, {6110, 6117}, {6111, 6116}, {6148, 1273}, {8882, 8749}, {8901, 12079}, {9033, 6368}, {9406, 2179}, {9407, 40981}, {9409, 15451}, {10564, 5891}, {11064, 343}, {11077, 11079}, {11125, 21102}, {11589, 8798}, {14206, 14213}, {14401, 14391}, {14533, 18877}, {14581, 3199}, {14586, 32640}, {14920, 14918}, {15412, 2394}, {16163, 1568}, {16813, 15459}, {18653, 17167}, {18831, 16077}, {19189, 35908}, {23286, 14380}, {33629, 15291}, {36035, 2618}, {36134, 36034}, {38808, 10152}, {39176, 11062}, {40634, 16243}, {41079, 18314}, {41887, 33529}, {41888, 33530}, {43752, 264}
X(43768) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {95, 275, 4993}, {95, 4993, 2}, {97, 275, 2}, {97, 4993, 95}, {4994, 19179, 3091}

leftri

Gibert points on the cubic K1232: X(43769)-X(43802)

rightri

This preamble and points X(43769)-X(43802) are contributed by Peter Moses, June 15-17, 2021. See also the preambles just before X(42085), X(42413), and X(42429).

See K1232, a crunodal KHO-cubic



X(43769) = GIBERT (6,5,-6) POINT

Barycentrics    Sqrt[3]*a^2*S - 3*a^2*SA + 5*SB*SC : :
X(43769) = 9 X[42589] - 14 X[42999]

X(43769) lies on the cubic K1232 and these lines: {2, 42165}, {3, 5344}, {4, 16}, {6, 5059}, {13, 3528}, {15, 42927}, {17, 21735}, {20, 397}, {30, 42589}, {61, 11001}, {62, 33703}, {140, 5366}, {376, 5352}, {382, 5365}, {395, 17578}, {398, 42097}, {550, 5335}, {631, 36968}, {1656, 42123}, {1657, 42118}, {3090, 36969}, {3091, 42943}, {3146, 5339}, {3412, 42806}, {3522, 5340}, {3523, 5318}, {3524, 42162}, {3525, 42813}, {3529, 10653}, {3533, 10646}, {3543, 5349}, {3544, 16242}, {3545, 5237}, {3627, 42497}, {3832, 36843}, {3839, 16773}, {3845, 43635}, {3850, 42115}, {3851, 42137}, {3853, 43404}, {3854, 23303}, {3855, 42946}, {5056, 5350}, {5067, 5351}, {5068, 42094}, {5072, 42985}, {5073, 5334}, {5076, 42913}, {5321, 43242}, {5343, 11486}, {10299, 18582}, {10304, 42156}, {11541, 16964}, {12103, 42974}, {14269, 43247}, {15022, 42491}, {15682, 40694}, {15683, 42147}, {15684, 43109}, {15688, 43002}, {15691, 43207}, {15692, 42598}, {15698, 42973}, {15704, 43634}, {15707, 42590}, {15709, 42581}, {15710, 41119}, {15712, 42128}, {15715, 41121}, {15717, 42166}, {15721, 43003}, {16241, 42965}, {16644, 21734}, {16772, 42932}, {16960, 41978}, {16963, 43012}, {16967, 42909}, {17538, 40693}, {22237, 42093}, {35400, 42515}, {36970, 42517}, {41100, 42160}, {41106, 42489}, {41113, 42514}, {41972, 42436}, {41973, 42112}, {41974, 42100}, {42089, 42629}, {42102, 42473}, {42104, 42993}, {42106, 42937}, {42109, 43474}, {42111, 43446}, {42113, 42432}, {42129, 42889}, {42133, 42989}, {42153, 43401}, {42167, 42637}, {42416, 42923}, {42510, 42814}, {42586, 43228}, {42634, 43253}, {42683, 42793}, {42773, 43556}, {42779, 43022}, {42890, 43203}, {42900, 43550}, {42918, 43292}, {42978, 43226}, {42987, 43551}, {43194, 43496}

X(43769) = crosspoint of X(22235) and X(43557)
X(43769) = crosssum of X(22236) and X(36843)
X(43769) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 11489, 42776}, {4, 42149, 42139}, {4, 42158, 42120}, {6, 5059, 43770}, {17, 42091, 21735}, {140, 5366, 42142}, {140, 42127, 5366}, {1657, 42118, 42998}, {1657, 42998, 42119}, {3146, 42148, 37641}, {3522, 5340, 11488}, {3522, 22235, 42945}, {3522, 43465, 5340}, {3523, 5318, 42494}, {5073, 42924, 5334}, {5340, 42088, 3522}, {5340, 42945, 22235}, {5350, 11481, 5056}, {5352, 16965, 41112}, {10646, 42921, 3533}, {10653, 42429, 43482}, {10653, 43633, 3529}, {19106, 42149, 4}, {22235, 42945, 11488}, {33703, 43481, 62}, {36843, 42941, 3832}, {36968, 42161, 631}, {41974, 42100, 42150}, {42086, 42120, 42141}, {42086, 42151, 42431}, {42086, 42158, 4}, {42088, 43465, 11488}, {42094, 42944, 5068}, {42120, 42141, 11489}, {42120, 42431, 42495}, {42145, 42924, 5073}, {42151, 42431, 4}, {42151, 42920, 16}, {42157, 43485, 10653}, {42158, 42431, 42151}, {42162, 42433, 3524}, {42165, 43193, 2}, {42166, 42625, 15717}, {42683, 43028, 43364}, {43485, 43633, 42157}

X(43770) = GIBERT (6,-5,6) POINT

Barycentrics    Sqrt[3]*a^2*S + 3*a^2*SA - 5*SB*SC : :
X(43770) = 9 X[42588] - 14 X[42998]

X(43770) lies on the cubic K1232 and these lines: {2, 42164}, {3, 5343}, {4, 15}, {6, 5059}, {14, 3528}, {16, 42926}, {18, 21735}, {20, 398}, {30, 42588}, {61, 33703}, {62, 11001}, {140, 5365}, {376, 5351}, {382, 5366}, {396, 17578}, {397, 42096}, {550, 5334}, {631, 36967}, {1656, 42122}, {1657, 42117}, {3090, 36970}, {3091, 42942}, {3146, 5340}, {3411, 42805}, {3522, 5339}, {3523, 5321}, {3524, 42159}, {3525, 42814}, {3529, 10654}, {3533, 10645}, {3543, 5350}, {3544, 16241}, {3545, 5238}, {3627, 42496}, {3832, 36836}, {3839, 16772}, {3845, 43634}, {3850, 42116}, {3851, 42136}, {3853, 43403}, {3854, 23302}, {3855, 42947}, {5056, 5349}, {5067, 5352}, {5068, 42093}, {5072, 42984}, {5073, 5335}, {5076, 42912}, {5318, 43243}, {5344, 11485}, {10299, 18581}, {10304, 42153}, {11541, 16965}, {12103, 42975}, {14269, 43246}, {15022, 42490}, {15682, 40693}, {15683, 42148}, {15684, 43108}, {15688, 43003}, {15691, 43208}, {15692, 42599}, {15698, 42972}, {15704, 43635}, {15707, 42591}, {15709, 42580}, {15710, 41120}, {15712, 42125}, {15715, 41122}, {15717, 42163}, {15721, 43002}, {16242, 42964}, {16645, 21734}, {16773, 42933}, {16961, 41977}, {16962, 43013}, {16966, 42908}, {17538, 40694}, {22235, 42094}, {35400, 42514}, {36969, 42516}, {41101, 42161}, {41106, 42488}, {41112, 42515}, {41971, 42435}, {41973, 42099}, {41974, 42113}, {42092, 42630}, {42101, 42472}, {42103, 42936}, {42105, 42992}, {42108, 43473}, {42112, 42431}, {42114, 43447}, {42132, 42888}, {42134, 42988}, {42156, 43402}, {42169, 42637}, {42415, 42922}, {42511, 42813}, {42587, 43229}, {42682, 42794}, {42774, 43557}, {42780, 43023}, {42891, 43204}, {42901, 43551}, {42919, 43293}, {42979, 43227}, {42986, 43550}, {43193, 43495}, {43228, 43252}

X(43770) = crosspoint of X(22237) and X(43556)
X(43770) = crosssum of X(22238) and X(36836)
X(43770) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 11488, 42775}, {4, 42152, 42142}, {4, 42157, 42119}, {6, 5059, 43769}, {18, 42090, 21735}, {140, 5365, 42139}, {140, 42126, 5365}, {1657, 42117, 42999}, {1657, 42999, 42120}, {3146, 42147, 37640}, {3522, 5339, 11489}, {3522, 22237, 42944}, {3522, 43466, 5339}, {3523, 5321, 42495}, {5073, 42925, 5335}, {5339, 42087, 3522}, {5339, 42944, 22237}, {5349, 11480, 5056}, {5351, 16964, 41113}, {10645, 42920, 3533}, {10654, 42430, 43481}, {10654, 43632, 3529}, {19107, 42152, 4}, {22237, 42944, 11489}, {33703, 43482, 61}, {36836, 42940, 3832}, {36967, 42160, 631}, {41973, 42099, 42151}, {42085, 42119, 42140}, {42085, 42150, 42432}, {42085, 42157, 4}, {42087, 43466, 11489}, {42093, 42945, 5068}, {42119, 42140, 11488}, {42119, 42432, 42494}, {42144, 42925, 5073}, {42150, 42432, 4}, {42150, 42921, 15}, {42157, 42432, 42150}, {42158, 43486, 10654}, {42159, 42434, 3524}, {42163, 42626, 15717}, {42164, 43194, 2}, {42682, 43029, 43365}, {43486, 43632, 42158}

X(43771) = GIBERT (10,9,2) POINT

Barycentrics    5*a^2*S/Sqrt[3] + a^2*SA + 9*SB*SC : :

X(43771) lies on the cubic K1232 and these lines: {2, 42686}, {4, 42779}, {6, 18296}, {13, 15682}, {15, 11541}, {16, 3090}, {20, 5318}, {140, 5344}, {376, 43483}, {381, 5335}, {396, 42587}, {397, 42983}, {550, 42691}, {3524, 18582}, {3530, 42689}, {3543, 43105}, {3544, 34755}, {3627, 11485}, {3832, 42693}, {3860, 42690}, {3861, 5334}, {5059, 42683}, {5066, 42517}, {5067, 43240}, {5068, 5340}, {5070, 42118}, {5073, 5366}, {5076, 42907}, {5350, 43422}, {8703, 42127}, {10303, 43106}, {10654, 43033}, {11486, 12811}, {12816, 43471}, {14269, 42906}, {14892, 42129}, {15640, 42777}, {15685, 42817}, {15689, 42124}, {15701, 42123}, {15702, 43467}, {15721, 42155}, {16808, 42436}, {16960, 33703}, {16961, 41106}, {16963, 43638}, {17538, 42629}, {21735, 42086}, {22235, 42087}, {33416, 43481}, {36969, 43004}, {37640, 42094}, {41099, 43418}, {41119, 42100}, {41987, 42478}, {42088, 42957}, {42090, 43542}, {42098, 42948}, {42102, 42970}, {42103, 42813}, {42104, 42895}, {42108, 43473}, {42112, 43010}, {42136, 42815}, {42137, 43328}, {42152, 43016}, {42166, 43465}, {42429, 43493}, {42510, 43373}, {42532, 43501}, {42612, 43303}, {42921, 42978}, {42923, 42974}, {42972, 43227}, {43242, 43297}

X(43771) = crosspoint of X(43540) and X(43556)
X(43771) = crosssum of X(11480) and X(36836)
X(43771) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 42105, 42986}, {5335, 42138, 42139}, {5344, 42128, 42120}, {37640, 43540, 43201}, {42105, 42986, 42119}, {42120, 42128, 42494}

X(43772) = GIBERT (-10,9,2) POINT

Barycentrics    5*a^2*S/Sqrt[3] - a^2*SA - 9*SB*SC : :

X(43772) lies on the cubic K1232 and these lines: {2, 42687}, {4, 42780}, {6, 18296}, {14, 15682}, {15, 3090}, {16, 11541}, {20, 5321}, {140, 5343}, {376, 43484}, {381, 5334}, {395, 42586}, {398, 42982}, {550, 42690}, {3524, 18581}, {3530, 42688}, {3543, 43106}, {3544, 34754}, {3627, 11486}, {3832, 42692}, {3860, 42691}, {3861, 5335}, {5059, 42682}, {5066, 42516}, {5067, 43241}, {5068, 5339}, {5070, 42117}, {5073, 5365}, {5076, 42906}, {5349, 43423}, {8703, 42126}, {10303, 43105}, {10653, 43032}, {11485, 12811}, {12817, 43472}, {14269, 42907}, {14892, 42132}, {15640, 42778}, {15685, 42818}, {15689, 42121}, {15701, 42122}, {15702, 43468}, {15721, 42154}, {16809, 42435}, {16960, 41106}, {16961, 33703}, {16962, 43643}, {17538, 42630}, {21735, 42085}, {22237, 42088}, {33417, 43482}, {36970, 43005}, {37641, 42093}, {41099, 43419}, {41120, 42099}, {41987, 42479}, {42087, 42956}, {42091, 43543}, {42095, 42949}, {42101, 42971}, {42105, 42894}, {42106, 42814}, {42109, 43474}, {42113, 43011}, {42136, 43329}, {42137, 42816}, {42149, 43017}, {42163, 43466}, {42430, 43494}, {42511, 43372}, {42533, 43502}, {42613, 43302}, {42920, 42979}, {42922, 42975}, {42973, 43226}, {43243, 43296}, {43253, 43649}

X(43772) = crosspoint of X(43541) and X(43557)
X(43772) = crosssum of X(11481) and X(36843)
X(43772) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 42104, 42987}, {5334, 42135, 42142}, {5343, 42125, 42119}, {37641, 43541, 43202}, {42104, 42987, 42120}, {42119, 42125, 42495}

X(43773) = GIBERT (15,7,6) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 6*a^2*SA + 14*SB*SC : :

X(43773) lies on the cubic K1232 and these lines: {3, 42777}, {4, 42682}, {5, 42778}, {6, 5068}, {13, 3627}, {16, 17}, {20, 396}, {61, 3861}, {62, 15699}, {381, 398}, {395, 3090}, {547, 33607}, {548, 43418}, {549, 42797}, {550, 16960}, {2043, 42572}, {2044, 42573}, {3411, 43025}, {3412, 43416}, {3522, 42687}, {3524, 42148}, {3851, 42781}, {3853, 43486}, {3858, 42692}, {5070, 42149}, {5073, 5318}, {5238, 15691}, {5335, 21735}, {5344, 42087}, {5349, 42128}, {5351, 43107}, {5366, 15682}, {8703, 16267}, {10109, 42502}, {11488, 42773}, {11541, 42941}, {12101, 42506}, {12103, 42939}, {14869, 42935}, {14891, 41107}, {14892, 41121}, {14893, 42934}, {15685, 42161}, {15686, 42965}, {15689, 41112}, {15702, 42518}, {15712, 42685}, {15721, 36843}, {16809, 43328}, {16964, 43476}, {16965, 42496}, {16966, 42801}, {18582, 42989}, {22238, 43445}, {23303, 42982}, {33465, 37352}, {33923, 43106}, {34754, 43546}, {36969, 43639}, {41974, 42124}, {41977, 42488}, {41981, 43334}, {41984, 43013}, {41988, 43368}, {41991, 43419}, {41992, 43484}, {42088, 42152}, {42099, 43424}, {42102, 42888}, {42107, 43010}, {42108, 43473}, {42110, 42999}, {42121, 43023}, {42122, 42802}, {42132, 42948}, {42144, 42909}, {42151, 42817}, {42155, 43493}, {42162, 42940}, {42163, 43403}, {42431, 42895}, {42434, 43491}, {42436, 42591}, {42492, 43441}, {42791, 43633}, {42805, 43236}, {42893, 42937}, {42946, 42952}, {42971, 42980}, {42993, 43307}, {42995, 43226}, {43000, 43111}

X(43773) = crosspoint of X(17) and X(43556)
X(43773) = crosssum of X(61) and X(36836)
X(43773) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5068, 43774}, {17, 397, 42944}, {17, 42924, 42949}, {17, 42944, 23302}, {397, 42949, 42924}, {11542, 42992, 397}, {40693, 42166, 43228}, {42088, 42152, 42794}, {42888, 42905, 42102}, {42895, 43426, 42431}, {42924, 42949, 42944}

X(43774) = GIBERT (-15,7,6) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 6*a^2*SA - 14*SB*SC : :

X(43774) lies on the cubic K1232 and these lines: {3, 42778}, {4, 42683}, {5, 42777}, {6, 5068}, {14, 3627}, {15, 18}, {20, 395}, {61, 15699}, {62, 3861}, {381, 397}, {396, 3090}, {547, 33606}, {548, 43419}, {549, 42798}, {550, 16961}, {2043, 42573}, {2044, 42572}, {3411, 43417}, {3412, 43024}, {3522, 42686}, {3524, 42147}, {3851, 42782}, {3853, 43485}, {3858, 42693}, {5070, 42152}, {5073, 5321}, {5237, 15691}, {5334, 21735}, {5343, 42088}, {5350, 42125}, {5352, 43100}, {5365, 15682}, {8703, 16268}, {10109, 42503}, {11489, 42774}, {11541, 42940}, {12101, 42507}, {12103, 42938}, {14869, 42934}, {14891, 41108}, {14892, 41122}, {14893, 42935}, {15685, 42160}, {15686, 42964}, {15689, 41113}, {15702, 42519}, {15712, 42684}, {15721, 36836}, {16808, 43329}, {16964, 42497}, {16965, 43475}, {16967, 42802}, {18581, 42988}, {22236, 43444}, {23302, 42983}, {33464, 37351}, {33923, 43105}, {34755, 43547}, {36970, 43640}, {41973, 42121}, {41978, 42489}, {41981, 43335}, {41984, 43012}, {41988, 43369}, {41991, 43418}, {41992, 43483}, {42087, 42149}, {42100, 43425}, {42101, 42889}, {42107, 42998}, {42109, 43474}, {42110, 43011}, {42123, 42801}, {42124, 43022}, {42129, 42949}, {42145, 42908}, {42150, 42818}, {42154, 43494}, {42159, 42941}, {42166, 43404}, {42432, 42894}, {42433, 43492}, {42435, 42590}, {42493, 43440}, {42792, 43632}, {42806, 43237}, {42892, 42936}, {42947, 42953}, {42970, 42981}, {42992, 43306}, {42994, 43227}, {43001, 43110}

X(43774) = crosspoint of X(18) and X(43557)
X(43774) = crosssum of X(62) and X(36843)
X(43774) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5068, 43773}, {18, 398, 42945}, {18, 42925, 42948}, {18, 42945, 23303}, {398, 42948, 42925}, {11543, 42993, 398}, {40694, 42163, 43229}, {42087, 42149, 42793}, {42889, 42904, 42101}, {42894, 43427, 42432}, {42925, 42948, 42945}

X(43775) = GIBERT (15,4,-3) POINT

Barycentrics    5*Sqrt[3]*a^2*S - 3*a^2*SA + 8*SB*SC : :
X(43775) = 3 X[42934] - 2 X[43486]

X(54775) lies on the cubic K1232 and these lines: {3, 42612}, {4, 42780}, {5, 43418}, {6, 5073}, {13, 3090}, {14, 3861}, {15, 43018}, {16, 17}, {18, 5068}, {20, 61}, {30, 42934}, {62, 381}, {376, 42635}, {382, 42964}, {395, 12811}, {398, 3627}, {548, 43111}, {550, 34754}, {631, 42947}, {1656, 34755}, {1657, 43485}, {3411, 42162}, {3412, 42943}, {3523, 16960}, {3524, 5351}, {3530, 43483}, {3544, 42517}, {3830, 42965}, {3839, 42521}, {3850, 16961}, {3856, 42778}, {5055, 42938}, {5070, 22238}, {5076, 43419}, {5237, 42974}, {5238, 8703}, {5334, 42908}, {5343, 42161}, {5344, 16809}, {5366, 40694}, {7486, 43200}, {10109, 16963}, {10124, 33607}, {10645, 21735}, {10646, 42773}, {10654, 11541}, {11486, 42801}, {11737, 42953}, {12101, 42972}, {12103, 42891}, {12108, 43199}, {12812, 43545}, {12816, 41987}, {14869, 42777}, {14891, 16772}, {14892, 42436}, {15682, 16964}, {15683, 42890}, {15685, 43633}, {15686, 42520}, {15689, 22236}, {15691, 42434}, {15696, 43646}, {15699, 41121}, {15701, 16267}, {15703, 42946}, {15704, 43231}, {15721, 42510}, {16808, 42922}, {16962, 43495}, {19106, 42999}, {19709, 42636}, {22235, 42089}, {22844, 37352}, {33703, 42545}, {33923, 43205}, {35018, 42960}, {36968, 43232}, {37640, 42433}, {41977, 42815}, {41981, 42416}, {41988, 43475}, {42091, 42896}, {42093, 42900}, {42098, 42978}, {42100, 42925}, {42102, 42897}, {42118, 42157}, {42120, 43030}, {42121, 42895}, {42123, 43014}, {42124, 43426}, {42134, 43015}, {42137, 43031}, {42152, 42959}, {42154, 42967}, {42155, 42799}, {42165, 42991}, {42491, 43013}, {42495, 43427}, {42581, 42913}, {42592, 43024}, {42691, 43240}, {42774, 42817}, {42814, 43006}, {42816, 43017}, {42904, 43557}, {42910, 43026}, {42918, 43019}, {42962, 43422}, {43020, 43403}

X(43775) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5073, 43776}, {6, 41974, 42431}, {6, 42431, 41973}, {16, 397, 42992}, {16, 42992, 42936}, {17, 42924, 16}, {17, 42949, 42979}, {62, 41107, 42813}, {62, 42813, 16268}, {62, 42973, 42153}, {397, 42924, 17}, {5351, 40693, 41943}, {10653, 42990, 61}, {10653, 42998, 42158}, {11542, 42949, 17}, {16961, 43546, 3850}, {40693, 41100, 5351}, {42158, 42990, 42998}, {42158, 42998, 61}, {42562, 42563, 43004}, {43019, 43424, 42918}

X(43776) = GIBERT (15,-4,3) POINT

Barycentrics    5*Sqrt[3]*a^2*S + 3*a^2*SA + 8*SB*SC : :
X(43776) = 3 X[42935] - 2 X[43485]

X(43776) lies on the cubic K1232 and these lines: {3, 42613}, {4, 42779}, {5, 43419}, {6, 5073}, {13, 3861}, {14, 3090}, {15, 18}, {16, 43019}, {17, 5068}, {20, 62}, {30, 42935}, {61, 381}, {376, 42636}, {382, 42965}, {396, 12811}, {397, 3627}, {548, 43110}, {550, 34755}, {631, 42946}, {1656, 34754}, {1657, 43486}, {3411, 42942}, {3412, 42159}, {3523, 16961}, {3524, 5352}, {3530, 43484}, {3544, 42516}, {3830, 42964}, {3839, 42520}, {3850, 16960}, {3856, 42777}, {5055, 42939}, {5070, 22236}, {5076, 43418}, {5237, 8703}, {5238, 42975}, {5335, 42909}, {5343, 16808}, {5344, 42160}, {5365, 40693}, {7486, 43199}, {10109, 16962}, {10124, 33606}, {10645, 42774}, {10646, 21735}, {10653, 11541}, {11485, 42802}, {11737, 42952}, {12101, 42973}, {12103, 42890}, {12108, 43200}, {12812, 43544}, {12817, 41987}, {14869, 42778}, {14891, 16773}, {14892, 42435}, {15682, 16965}, {15683, 42891}, {15685, 43632}, {15686, 42521}, {15689, 22238}, {15691, 42433}, {15696, 43645}, {15699, 41122}, {15701, 16268}, {15703, 42947}, {15704, 43230}, {15721, 42511}, {16809, 42923}, {16963, 43496}, {19107, 42998}, {19709, 42635}, {22237, 42092}, {22845, 37351}, {33703, 42546}, {33923, 43206}, {35018, 42961}, {35739, 42228}, {36967, 43233}, {37641, 42434}, {41978, 42816}, {41981, 42415}, {41988, 43476}, {42090, 42897}, {42094, 42901}, {42095, 42979}, {42099, 42924}, {42101, 42896}, {42117, 42158}, {42119, 43031}, {42121, 43427}, {42122, 43015}, {42124, 42894}, {42133, 43014}, {42136, 43030}, {42149, 42958}, {42154, 42800}, {42155, 42966}, {42164, 42990}, {42490, 43012}, {42494, 43426}, {42580, 42912}, {42593, 43025}, {42690, 43241}, {42773, 42818}, {42813, 43007}, {42815, 43016}, {42905, 43556}, {42911, 43027}, {42919, 43018}, {42963, 43423}, {43021, 43404}

X(43776) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5073, 43775}, {6, 41973, 42432}, {6, 42432, 41974}, {15, 398, 42993}, {15, 42993, 42937}, {18, 42925, 15}, {18, 42948, 42978}, {61, 41108, 42814}, {61, 42814, 16267}, {61, 42972, 42156}, {398, 42925, 18}, {5352, 40694, 41944}, {10654, 42991, 62}, {10654, 42999, 42157}, {11543, 42948, 18}, {16960, 43547, 3850}, {40694, 41101, 5352}, {42157, 42991, 42999}, {42157, 42999, 62}, {42564, 42565, 43005}, {43018, 43425, 42919}

X(43777) = GIBERT (20,9,-8) POINT

Barycentrics    10*a^2*S/Sqrt[3] - 4*a^2*SA + 9*SB*SC : :

X(43777) lies on the cubic K1232 and these lines: {4, 42683}, {6, 11541}, {16, 3090}, {20, 11485}, {381, 43364}, {1656, 42416}, {3524, 5335}, {3528, 42781}, {3627, 43465}, {5068, 42138}, {5073, 43466}, {5344, 43446}, {8703, 43207}, {10653, 15682}, {11543, 43473}, {14891, 42817}, {14892, 43540}, {15685, 43630}, {15719, 43418}, {15721, 43103}, {16268, 42103}, {16965, 42139}, {17538, 43106}, {17578, 42689}, {21735, 41974}, {41100, 42531}, {42090, 42532}, {42094, 43543}, {42119, 43203}, {42127, 42983}, {42148, 42610}, {42155, 43482}, {42161, 42987}, {42472, 42510}, {42905, 43638}, {43242, 43328}

X(43778) = GIBERT (20,-9,8) POINT

Barycentrics    10*a^2*S/Sqrt[3] + 4*a^2*SA - 9*SB*SC : :

X(43778) lies on the cubic K1232 and these lines: {4, 42682}, {6, 11541}, {15, 3090}, {20, 11486}, {381, 43365}, {1656, 42415}, {3524, 5334}, {3528, 42782}, {3627, 43466}, {5068, 42135}, {5070, 43253}, {5073, 43465}, {5343, 43447}, {8703, 43208}, {10654, 15682}, {11542, 43474}, {14891, 42818}, {14892, 43541}, {15685, 43631}, {15719, 43419}, {15721, 43102}, {16267, 42106}, {16964, 42142}, {17538, 43105}, {17578, 42688}, {21735, 41973}, {41101, 42530}, {42091, 42533}, {42093, 43542}, {42120, 43204}, {42126, 42982}, {42147, 42611}, {42154, 43481}, {42160, 42986}, {42473, 42511}, {42904, 43643}, {43243, 43329}

X(43779) = GIBERT (23,45,2) POINT

Barycentrics    23*a^2*S/Sqrt[3] + 2*a^2*SA + 90*SB*SC : :

X(43779) lies on the cubic K1232 and these lines: {16, 3857}, {20, 23302}, {396, 42691}, {5318, 14893}, {5350, 11486}, {11539, 42941}, {12816, 43007}, {15759, 19106}, {19709, 42106}, {33416, 35018}, {41121, 42087}, {42102, 42160}, {42140, 43477}, {42152, 42693}, {42163, 42966}, {42584, 43240}, {43008, 43226}, {43201, 43474}, {43292, 43307}

X(43780) = GIBERT (-23,45,-2) POINT

Barycentrics    23*a^2*S/Sqrt[3] - 2*a^2*SA - 90*SB*SC : :

X(43780) lies on the cubic K1232 and these lines: {15, 3857}, {20, 23303}, {395, 42690}, {5321, 14893}, {5349, 11485}, {11539, 42940}, {12817, 43006}, {15759, 19107}, {19709, 42103}, {33417, 35018}, {41122, 42088}, {42101, 42161}, {42141, 43478}, {42149, 42692}, {42166, 42967}, {42585, 43241}, {43009, 43227}, {43202, 43473}, {43293, 43306}

X(43781) = GIBERT (25,36,3) POINT

Barycentrics    25*a^2*S/Sqrt[3] + 3*a^2*SA + 72*SB*SC : :

X(43781) lies on the cubic K1232 and these lines: {16, 12811}, {20, 10645}, {140, 42629}, {381, 34755}, {397, 43292}, {3090, 43468}, {3627, 34754}, {3830, 43301}, {3851, 43300}, {5079, 43298}, {5344, 42894}, {8703, 42693}, {10109, 42954}, {12101, 12816}, {14891, 42146}, {15699, 16808}, {15701, 36969}, {21735, 42955}, {35410, 42626}, {41973, 43550}, {41990, 42118}, {42094, 42992}, {42099, 42927}, {42105, 43325}, {42115, 42900}, {42139, 43005}, {42145, 42936}, {42149, 42473}, {42431, 42962}, {42494, 43294}, {42588, 42914}, {42598, 43324}, {42632, 43493}, {42684, 43231}, {42799, 43540}, {42889, 42979}, {42892, 42942}, {42916, 43641}, {42934, 43366}, {42947, 43637}, {42964, 43205}, {42965, 43241}, {42967, 42982}

X(43782) = GIBERT (-25,36,3) POINT

Barycentrics    25*a^2*S/Sqrt[3] - 3*a^2*SA - 72*SB*SC : :

X(43782) lies on the cubic K1232 and these lines: {15, 12811}, {20, 10646}, {140, 42630}, {381, 34754}, {398, 43293}, {3090, 43467}, {3627, 34755}, {3830, 43300}, {3851, 43301}, {5079, 43299}, {5343, 42895}, {8703, 42692}, {10109, 42955}, {12101, 12817}, {14891, 42143}, {15699, 16809}, {15701, 36970}, {21735, 42954}, {35410, 42625}, {41974, 43551}, {41990, 42117}, {42093, 42993}, {42100, 42926}, {42104, 43324}, {42116, 42901}, {42142, 43004}, {42144, 42937}, {42152, 42472}, {42432, 42963}, {42495, 43295}, {42589, 42915}, {42599, 43325}, {42631, 43494}, {42685, 43230}, {42800, 43541}, {42888, 42978}, {42893, 42943}, {42917, 43642}, {42935, 43367}, {42946, 43636}, {42964, 43240}, {42965, 43206}, {42966, 42983}

X(43783) = GIBERT (57,40,15) POINT

Barycentrics    19*Sqrt[3]*a^2*S + 15*a^2*SA + 80*SB*SC : :

X(43783) lies on the cubic K1232 and these lines: {13, 20}, {16, 42948}, {18, 42142}, {61, 38335}, {397, 5066}, {5079, 16645}, {5237, 15694}, {5318, 42802}, {5340, 42979}, {5349, 42813}, {5350, 19107}, {10645, 43424}, {12108, 42936}, {16808, 43329}, {16965, 17504}, {18582, 43469}, {35404, 42157}, {40693, 43400}, {41973, 42895}, {41984, 42597}, {42096, 42988}, {42134, 43018}, {42151, 42797}, {42158, 43463}, {42162, 42972}, {42432, 43422}, {42584, 42687}, {42596, 43403}, {42815, 43016}, {42921, 43427}, {42978, 43643}, {42998, 43303}, {43416, 43634}

X(43784) = GIBERT (-57,40,15) POINT

Barycentrics    19*Sqrt[3]*a^2*S - 15*a^2*SA - 80*SB*SC : :

X(43784) lies on the cubic K1232 and these lines: {14, 20}, {15, 42949}, {17, 42139}, {62, 38335}, {398, 5066}, {5079, 16644}, {5238, 15694}, {5321, 42801}, {5339, 42978}, {5349, 19106}, {5350, 42814}, {10646, 43425}, {12108, 42937}, {16809, 43328}, {16964, 17504}, {18581, 43470}, {35404, 42158}, {40694, 43399}, {41974, 42894}, {41984, 42596}, {42097, 42989}, {42133, 43019}, {42150, 42798}, {42157, 43464}, {42159, 42973}, {42431, 43423}, {42585, 42686}, {42597, 43404}, {42816, 43017}, {42920, 43426}, {42979, 43638}, {42999, 43302}, {43245, 43253}, {43417, 43635}

X(43785) = GIBERT (3 SQRT(3),11,-18) POINT

Barycentrics    3*a^2*S - 18*a^2*SA + 22*SB*SC : :
X(43785) = 44 X[35813] - 39 X[41951], 12 X[35813] - 13 X[41964], 31 X[35813] - 39 X[42524], 9 X[41951] - 11 X[41964], 31 X[41951] - 44 X[42524], 31 X[41964] - 36 X[42524]

X(43785) lies on the cubic K1232 and these lines: {4, 6412}, {20, 6425}, {30, 35813}, {485, 41965}, {550, 590}, {1657, 3312}, {3069, 5059}, {3070, 6445}, {3522, 8253}, {3529, 32788}, {3534, 9680}, {3591, 42637}, {5073, 42268}, {6440, 42571}, {6450, 43410}, {6476, 42226}, {6564, 41981}, {8960, 12103}, {8972, 42414}, {10195, 42276}, {11541, 41968}, {13785, 41960}, {13886, 41963}, {15686, 31454}, {15689, 42526}, {15704, 43209}, {17800, 43343}, {21735, 42273}, {22644, 43513}, {23275, 41970}, {33923, 42284}, {35407, 43504}, {35770, 41957}, {35821, 43317}, {41947, 42283}, {41958, 42258}, {42099, 42223}, {42100, 42224}, {42261, 43415}, {42413, 42574}

X(43785) = crosssum of X(6425) and X(6454)
X(43785) = {X(42261),X(43516)}-harmonic conjugate of X(43415)

X(43786) = GIBERT (3 SQRT(3),-11,18) POINT

Barycentrics    3*a^2*S + 18*a^2*SA - 22*SB*SC : :
X(43786) = 44 X[35812] - 39 X[41952], 12 X[35812] - 13 X[41963], 31 X[35812] - 39 X[42525], 9 X[41952] - 11 X[41963], 31 X[41952] - 44 X[42525], 31 X[41963] - 36 X[42525]

X(43786) lies on the cubic K1232 and these lines: {4, 6411}, {20, 6426}, {30, 35812}, {486, 41966}, {550, 615}, {1657, 3311}, {3068, 5059}, {3071, 6446}, {3522, 8252}, {3529, 32787}, {5073, 42269}, {6439, 42570}, {6449, 43409}, {6477, 42225}, {6492, 9541}, {6565, 41981}, {8960, 43340}, {9690, 42260}, {10194, 42275}, {11541, 41967}, {12103, 42573}, {13665, 41959}, {13939, 41964}, {13941, 42413}, {15686, 42524}, {15689, 42527}, {15704, 43210}, {17800, 43342}, {21735, 42270}, {22615, 43514}, {23269, 41969}, {33923, 42283}, {35407, 43503}, {35771, 41958}, {35820, 43316}, {41948, 42284}, {41957, 42259}, {42099, 42221}, {42100, 42222}, {42414, 42575}

X(43786) = crosssum of X(6426) and X(6453)
X(43786) = {X(42260),X(43515)}-harmonic conjugate of X(9690)

X(43787) = GIBERT (4 SQRT(3),9,-24) POINT

Barycentrics    2*a^2*S - 12*a^2*SA + 9*SB*SC : :

X(43787) lies on the cubic K1232 and these lines: {4, 6412}, {6, 17538}, {20, 6398}, {372, 43337}, {376, 3068}, {548, 8972}, {550, 6199}, {631, 35786}, {1587, 6468}, {1657, 13941}, {3069, 43343}, {3071, 6440}, {3146, 6452}, {3316, 3528}, {3317, 42283}, {3522, 8976}, {3524, 42284}, {3529, 6396}, {3534, 43382}, {5059, 18762}, {6395, 12103}, {6410, 11541}, {6411, 43407}, {6417, 43383}, {6434, 11001}, {6436, 6459}, {6437, 42259}, {6438, 43408}, {6442, 42258}, {6446, 13939}, {6451, 13886}, {6564, 15710}, {7582, 42261}, {7585, 15689}, {7586, 15686}, {9690, 15696}, {10299, 42277}, {10304, 18538}, {12100, 43507}, {14241, 43209}, {15682, 42274}, {15685, 42640}, {15697, 42216}, {19708, 42264}, {19711, 43566}, {21735, 32785}, {23251, 42566}, {23253, 43505}, {23275, 42275}, {32786, 33703}, {35771, 42575}

X(43787) = crosssum of X(6398) and X(6447)
X(43787) = {X(6459),X(42574)}-harmonic conjugate of X(6436)

X(43788) = GIBERT (4 SQRT(3),-9,24) POINT

Barycentrics    2*a^2*S + 12*a^2*SA - 9*SB*SC : :

X(43788) lies on the cubic K1232 and these lines: {4, 6411}, {6, 17538}, {20, 6221}, {371, 43336}, {376, 3069}, {548, 13941}, {550, 6395}, {631, 35787}, {1588, 6469}, {1657, 8972}, {3068, 43342}, {3070, 6439}, {3146, 6451}, {3316, 42284}, {3317, 3528}, {3522, 13951}, {3524, 42283}, {3529, 6200}, {3534, 43383}, {5059, 18538}, {6199, 12103}, {6409, 11541}, {6412, 43408}, {6418, 43382}, {6433, 11001}, {6435, 6460}, {6437, 43407}, {6438, 42258}, {6441, 42259}, {6445, 13886}, {6452, 13939}, {6565, 15710}, {7581, 42260}, {7585, 15686}, {7586, 15689}, {8960, 23269}, {10299, 42274}, {10304, 18762}, {12100, 43508}, {14226, 43210}, {15682, 42277}, {15685, 42639}, {15696, 43415}, {15697, 42215}, {19708, 42263}, {19711, 43567}, {21735, 32786}, {23261, 42567}, {23263, 43506}, {32785, 33703}, {35770, 42574}

X(43788) = crosssum of X(6221) and X(6448)
X(43788) = {X(6460),X(42575)}-harmonic conjugate of X(6435)

X(43789) = GIBERT (7 SQRT(3),13,2) POINT

Barycentrics    7*a^2*S + 2*a^2*SA + 26*SB*SC : :

X(43789) lies on the cubic K1232 and these lines: {2, 43384}, {6, 42478}, {20, 590}, {485, 6519}, {546, 3070}, {549, 6564}, {615, 3545}, {1131, 42271}, {1152, 43518}, {1327, 3830}, {1656, 6450}, {3068, 43383}, {3069, 3854}, {3311, 12818}, {3525, 42259}, {3853, 43316}, {5420, 10138}, {6200, 42639}, {6221, 41954}, {6436, 42573}, {6437, 14241}, {6468, 15640}, {6472, 31454}, {7585, 43520}, {8252, 15022}, {8253, 15705}, {8960, 42258}, {10109, 35256}, {10299, 42265}, {13785, 43323}, {13846, 43507}, {13951, 42269}, {15690, 18538}, {15716, 43209}, {17851, 41946}, {18510, 43343}, {19708, 42264}, {22644, 41963}, {23253, 42263}, {23267, 43387}, {23269, 42270}, {31414, 43508}, {33923, 35820}, {41950, 43211}, {42216, 42640}, {42283, 43312}, {42582, 42600}, {43407, 43505}

X(43789) = crosspoint of X(1327) and X(43560)
X(43789) = crosssum of X(6200) and X(6409)
X(43789) = {X(12818),X(43432)}-harmonic conjugate of X(3311)

X(43790) = GIBERT (-7 SQRT(3),13,2) POINT

Barycentrics    7*a^2*S - 2*a^2*SA - 26*SB*SC : :

X(43790) lies on the cubic K1232 and these lines: {2, 43385}, {6, 42478}, {20, 615}, {486, 6522}, {546, 3071}, {549, 6565}, {590, 3545}, {1132, 42272}, {1151, 43517}, {1328, 3830}, {1656, 6449}, {3068, 3854}, {3069, 43382}, {3312, 12819}, {3525, 42258}, {3853, 43317}, {5418, 10137}, {6396, 42640}, {6398, 41953}, {6435, 42572}, {6438, 14226}, {6469, 15640}, {7586, 43519}, {8252, 15705}, {8253, 15022}, {8976, 42268}, {10109, 35255}, {10299, 42262}, {13665, 43322}, {13847, 43508}, {15690, 18762}, {15716, 43210}, {18512, 43342}, {19708, 42263}, {22615, 41964}, {23263, 42264}, {23273, 43386}, {23275, 42273}, {33923, 35821}, {41949, 43212}, {42215, 42639}, {42284, 43313}, {42583, 42601}, {43408, 43506}

X(43790) = crosspoint of X(1328) and X(43561)
X(43790) = crosssum of X(6396) and X(6410)
X(43790) = {X(12819),X(43433)}-harmonic conjugate of X(3312)

X(43791) = GIBERT (7 SQRT(3),9,3) POINT

Barycentrics    7*a^2*S + 3*a^2*SA + 18*SB*SC : :

X(43791) lies on the cubic K1232 and these lines: {2, 43315}, {6, 546}, {20, 485}, {30, 6468}, {371, 42575}, {372, 15022}, {549, 6412}, {550, 43314}, {590, 15688}, {1327, 3830}, {1587, 3854}, {1656, 3070}, {3069, 3545}, {3525, 6396}, {3628, 6469}, {5418, 33923}, {6221, 22644}, {6250, 39874}, {6395, 42273}, {6408, 42567}, {6411, 43434}, {6433, 13925}, {6434, 16239}, {6437, 23251}, {6442, 18762}, {6445, 42272}, {6446, 42582}, {6470, 12102}, {6471, 12811}, {6476, 8960}, {6480, 13886}, {7582, 43433}, {9690, 42260}, {10109, 42216}, {10299, 23269}, {12818, 35821}, {13770, 43457}, {15687, 43316}, {15690, 42264}, {18512, 43342}, {19053, 42609}, {19708, 43374}, {19711, 43384}, {23259, 35822}, {23273, 31414}, {23275, 43411}, {35740, 42248}, {41954, 41967}, {42184, 42236}, {42186, 42235}, {42225, 43340}, {42240, 42249}, {42259, 42566}, {42569, 43320}, {43209, 43568}, {43313, 43322}

X(43791) = crosspoint of X(1327) and X(43570)
X(43791) = crosssum of X(6200) and X(6453)
X(43791) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 546, 43792}, {485, 23249, 42276}, {485, 35820, 9680}, {1327, 13665, 6561}, {6564, 23267, 42274}, {8972, 23249, 35820}

X(43792) = GIBERT (-7 SQRT(3),9,3) POINT

Barycentrics    7*a^2*S - 3*a^2*SA - 18*SB*SC : :

X(43792) lies on the cubic K1232 and these lines: {2, 43314}, {6, 546}, {20, 486}, {30, 6469}, {371, 15022}, {372, 42574}, {549, 6411}, {550, 43315}, {615, 15688}, {1328, 3830}, {1588, 3854}, {1656, 3071}, {3068, 3545}, {3525, 6200}, {3628, 6468}, {5420, 33923}, {6199, 42270}, {6251, 39874}, {6398, 22615}, {6407, 42566}, {6412, 43435}, {6433, 9681}, {6434, 13993}, {6438, 23261}, {6441, 18538}, {6445, 42583}, {6446, 42271}, {6470, 12811}, {6471, 12102}, {6477, 42571}, {6481, 13939}, {7581, 43432}, {10109, 42215}, {10299, 23275}, {12819, 35820}, {13651, 43457}, {15687, 43317}, {15690, 42263}, {18510, 43343}, {19054, 42608}, {19708, 43375}, {19711, 43385}, {23249, 35823}, {23267, 35787}, {23269, 43412}, {41953, 41968}, {42183, 42238}, {42185, 42237}, {42226, 43341}, {42239, 42247}, {42241, 42246}, {42258, 42567}, {42261, 43415}, {42568, 43321}, {43210, 43569}, {43312, 43323}

X(43792) = crosspoint of X(1328) and X(43571)
X(43792) = crosssum of X(6396) and X(6454)
X(43792) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 546, 43791}, {486, 23259, 42275}, {1328, 13785, 6560}, {6565, 23273, 42277}, {13941, 23259, 35821}

X(43793) = GIBERT (21 SQRT(3),5,-45) POINT

Barycentrics    21*a^2*S - 45*a^2*SA + 10*SB*SC : :

X(43793) lies on the cubic K1232 and these lines: {5, 43384}, {6, 33923}, {20, 6454}, {486, 43414}, {546, 10148}, {1656, 6450}, {3068, 10299}, {3591, 42267}, {3830, 41964}, {6396, 10195}, {6426, 15690}, {6446, 10194}, {6453, 19708}, {6481, 23275}, {15705, 42524}, {35018, 43315}, {42261, 43415}, {42601, 43432}

X(43794) = GIBERT (21 SQRT(3),-5,45) POINT

Barycentrics    21*a^2*S + 45*a^2*SA - 10*SB*SC : :

X(43794) lies on the cubic K1232 and these lines: {5, 43385}, {6, 33923}, {20, 6453}, {485, 43413}, {546, 9680}, {549, 9681}, {1656, 6449}, {3069, 10299}, {3590, 42266}, {3830, 41963}, {3854, 9541}, {6200, 10194}, {6425, 15690}, {6445, 10195}, {6454, 19708}, {6480, 23269}, {9690, 42260}, {15705, 42525}, {35018, 43314}, {42600, 43433}

X(43795) = GIBERT (23 SQRT(3),55,5) POINT

Barycentrics    23*a^2*S + 5*a^2*SA + 110*SB*SC : :

X(43795) lies on the cubic K1232 and these lines: {6, 14893}, {20, 5418}, {485, 6472}, {3857, 23251}, {6412, 11539}, {6445, 35400}, {6449, 43409}, {6450, 43514}, {6560, 19709}, {12818, 43516}, {13846, 42608}, {15700, 32789}, {15759, 43513}, {18512, 43504}, {23269, 35787}, {35018, 42269}, {41958, 42274}, {42268, 43317}, {42557, 43414}, {42641, 43315}, {43432, 43560}

X(43796) = GIBERT (-23 SQRT(3),55,5) POINT

Barycentrics    23*a^2*S - 5*a^2*SA - 110*SB*SC : :

X(43796) lies on the cubic K1232 and these lines: {6, 14893}, {20, 5420}, {486, 6473}, {3857, 23261}, {6411, 11539}, {6446, 35400}, {6449, 43513}, {6450, 43410}, {6561, 9690}, {12819, 43515}, {13847, 42609}, {15700, 32790}, {15759, 43514}, {18510, 43503}, {23275, 35786}, {35018, 42268}, {41957, 42277}, {42269, 43316}, {42558, 43413}, {42642, 43314}, {43433, 43561}

X(43797) = GIBERT (28 SQRT(3),11,-8) POINT

Barycentrics    14*a^2*S - 4*a^2*SA + 11*SB*SC : :

X(43797) lies on the cubic K1232 and these lines: {2, 43316}, {20, 3311}, {372, 43506}, {546, 7586}, {549, 6446}, {1587, 3316}, {1656, 43376}, {3068, 10299}, {3069, 3545}, {3312, 3854}, {3830, 23273}, {6395, 10109}, {6411, 19708}, {6418, 43507}, {7582, 35820}, {7585, 9690}, {11001, 43384}, {13951, 42541}, {14226, 23249}, {15022, 43340}, {15705, 35255}, {23275, 43515}, {31412, 42557}, {32790, 41952}, {35822, 42601}, {41957, 42264}, {42268, 42571}, {42523, 43434}, {42582, 43565}

X(43798) = GIBERT (28 SQRT(3),-11,8) POINT

Barycentrics    14*a^2*S + 4*a^2*SA - 11*SB*SC : :

X(43798) lies on the cubic K1232 and these lines: {2, 43317}, {20, 3312}, {371, 43505}, {546, 7585}, {549, 6445}, {1588, 3317}, {1656, 43377}, {3068, 3545}, {3069, 10299}, {3311, 3854}, {3830, 23267}, {6199, 10109}, {6412, 9541}, {6417, 43508}, {6472, 9692}, {7581, 35821}, {7586, 15688}, {8976, 42542}, {11001, 43385}, {14241, 23259}, {15022, 43341}, {15705, 35256}, {23269, 43516}, {32789, 41951}, {35823, 42600}, {41958, 42263}, {42269, 42570}, {42522, 43435}, {42558, 42561}, {42583, 43564}

X(43799) = GIBERT (34 SQRT(3),99,6) POINT

Barycentrics    17*a^2*S + 3*a^2*SA + 99*SB*SC : :

X(43799) lies on the cubic K1232 and these lines: {20, 6411}, {1587, 43313}, {3311, 12102}, {3858, 13951}, {5072, 6446}, {6199, 43434}, {6221, 33699}, {6396, 43506}, {6426, 42574}, {6477, 6560}, {9690, 31412}, {12818, 31414}, {14269, 18510}, {15709, 43336}, {15715, 42277}, {19054, 43508}, {23251, 42571}, {32786, 43519}, {42225, 42575}, {42276, 43505}

X(43800) = GIBERT (-34 SQRT(3),99,6) POINT

Barycentrics    17*a^2*S - 3*a^2*SA - 99*SB*SC : :

X(43800) lies on the cubic K1232 and these lines: {20, 6412}, {1588, 43312}, {3312, 12102}, {3858, 8976}, {5072, 6445}, {6200, 43505}, {6395, 43435}, {6398, 33699}, {6425, 42575}, {6476, 6561}, {14269, 18512}, {15709, 43337}, {15715, 42274}, {19053, 43507}, {23261, 42570}, {32785, 43520}, {42226, 42574}, {42275, 43506}, {42561, 43415}

X(43801) = GIBERT (51 SQRT(3),13,-9) POINT

Barycentrics    51*a^2*S - 9*a^2*SA + 26*SB*SC : :

X(43801) lies on the cubic K1232 and these lines: {20, 6419}, {3069, 43411}, {3594, 42639}, {3858, 7584}, {5072, 32788}, {5073, 41955}, {5420, 6395}, {6420, 41106}, {6428, 43503}, {6449, 43523}, {6522, 15693}, {8960, 15709}, {9680, 15715}, {12102, 43504}, {12818, 43412}, {13846, 14869}, {35770, 43433}, {42602, 43386}

X(43802) = GIBERT (51 SQRT(3),-13,9) POINT

Barycentrics    51*a^2*S + 9*a^2*SA - 26*SB*SC : :

X(43802) lies on the cubic K1232 and these lines: {20, 6420}, {3068, 43412}, {3592, 42640}, {3858, 7583}, {5072, 32787}, {5073, 41956}, {5418, 6199}, {6419, 41106}, {6427, 43504}, {6450, 43524}, {6519, 15693}, {9680, 13847}, {12102, 43503}, {12819, 43411}, {35771, 43432}, {42603, 43387}

leftri

Special KM and MK perspectors: X(43803)-X(43815)

rightri

This preamble is contributed by Peter Moses and Clark Kimberling, June 20, 2021.

Let KM and MK be the Kiss-Moses mapping and its inverse, as introduced in the preabmle just before X(43390). For many pairs of triangles U and V, the triangle KM(U) is perspective to MK(V) and KM(V) is perspective to MK(U). In some cases, the two perspectors are the same point. This section presents several such points.

The appearance of (i,U,V) in the following list means that KM(U) is perspective to MK(V) and KM(V) is perspective to MK(U) and that in both cases, the perspector is X(i).

(54, ABC, Kosnita), (54, ABC, 3rd Hatzipolakis), (54, ABC, Hatzipolaks-Moses), (54, circum-medial, Gemini 44), (54, circum-orthic, anti-Conway), (54, circum-orthic, Gemini 113), (54, antipedal triangle of X(13), maximal-area-circumscribed equilateral triangle), (54, antipedal triangle of X(14), minimal-area-circumscribed equilateral triangle), (54, pedal triangle of X(15), minimal-area-circumscribed equilateral triangle), (54, pedal triangle of X(16), maximal-area-circumscribed equilateral triangle), (54, Kosnita, 3rd Hatzipolakis), (54, Kosnita, Hatzipolakis-Moses), (54, 3rd Hatzipolakis, Hatzipolakis-Moses), (54, orthic-of-anticomplementary, Gemini 113), (54, anti-Conway, 1st anti-Sharygin), (54, inner Conway, Gemini 30), (54, Garcia reflection triangle, Gemini 8)

(43598, ABC, O-reflection of ABC), (43598, anticomplementary, anti-1st-Euler), (43598, tangential, anti-Hutson-intouch), (43598, excentral, hexyl), (43598, orthic of anticomplementary), (43598) 1st circumperp, 2nd circumperp), (43598, tangential triangle of 1st circumperp, tangential triangle of 2nd circumperp), (43598, circumtangential, circumnormal). (43598, Kosnita, Trihn), (43598, anti-3rd-Euler, anti-4th-Euler)

(43601, Carnot, X(5)-reflection of ABC [aka Johnson triangle]), (43601, medial, Euler), (43601, anticomplementary, ABC-reflection-of O), (43601, orthic, 2nd Euler), (43601, circum-orthic, Ehrmann side-triangle), (43601, inner Napoleon, Fermat-Dao), (43601, outer Napoleon, Fermat-Dao), (43601, Kosnita, Ehrmann vertex triangle), (43601, 3rd Euler, 4th Euler), (43601, anti-incircle-circes triangle, tangential-of-anticomplementary)

(43803, ABC, outer Garcia), (43803, anticomplementary, Aquila), (43803, ABC-sides-reflection of X(1), inner Conway), (43808, ABC-sides-reflection of X(1), Gemini 30)

(43804, ABC, Gemini 107), (43804, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi), (43804, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi), (43804, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi), (43804, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi)

(43805, medial, anti-Aquila), (43805, 2nd circumperp, Wasat), (43805, incircle-circles triangle, 2nd Zaniah)

(43806, orthic, 5th-mixtilinear-of-orthic)

(43807, Euler, Ehrmann mid-triangle)

(43808, circum-orthic, anti-Wasat)

(43809, circumnormal, complement of Stammler)

(43810, Kosnita, 2nd Ehrmann)

(43811, Trinh, anti-Honsberger)

(43812, 2nd Ehrmann, anti-Honsberger)

(43813, anti-incircle-circles triangle, 1st excosine)

(43814, Ehrmann vertex triangle, anti-Honsberger)

(43815, 7th Brocard, 10 Brocard)



X(43803) = X(3)X(30438)∩X(74)X(31803)

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

Let U = ABC and V = outer Garcia triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43803). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

The same holds for these choices of {U,V}: {ABC, Gemini 107}, {ABC-side-reflections of X(1), inner Conway}, {ABC-side-reflections of X(1), Gemini 30}.

X(43803) lies on these lines: {3, 30438}, {74, 31803}, {2771, 43601}, {2779, 43598}, {5884, 43597}, {5885, 43584}, {13445, 31828}, {14094, 43609}, {15035, 43610}, {31825, 43574}, {41192, 43596}

X(43804) = X(3)X(5640)∩X(5)X(10721)

Barycentrics    a^2*(3*a^8 - 5*a^6*b^2 - 3*a^4*b^4 + 9*a^2*b^6 - 4*b^8 - 5*a^6*c^2 + 17*a^4*b^2*c^2 - 17*a^2*b^4*c^2 + 5*b^6*c^2 - 3*a^4*c^4 - 17*a^2*b^2*c^4 - 2*b^4*c^4 + 9*a^2*c^6 + 5*b^2*c^6 - 4*c^8) : :
X(43804) = X[550] + 2 X[20193], X[43598] + 2 X[43601]

Let U = ABC and V = Gemini 107. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43804). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

The same holds for these choices of {U,V}: {1st inner-Fermat-Dao-Nhi triangle, 2nd inner-Fermat-Dao-Nhi triangle}, {3rd inner-Fermat-Dao-Nhi triangle, 4th inner-Fermat-Dao-Nhi triangle}, {1st outer-Fermat-Dao-Nhi triangle, 2nd outer-Fermat-Dao-Nhi triangle}, {3rd outer-Fermat-Dao-Nhi triangle, 4th outer-Fermat-Dao-Nhi triangle}.

X(43804) lies on these lines: {3, 5640}, {5, 10721}, {49, 43603}, {54, 5504}, {74, 15030}, {110, 43596}, {186, 16836}, {373, 3520}, {550, 20193}, {567, 15051}, {568, 15053}, {1192, 7999}, {1656, 18550}, {3167, 5890}, {3567, 37497}, {5071, 11204}, {5085, 6403}, {5646, 37487}, {5663, 43598}, {5892, 37941}, {5943, 37948}, {5946, 13482}, {6030, 37922}, {6241, 35259}, {6642, 16261}, {6644, 14157}, {7712, 37470}, {9705, 12284}, {10299, 25555}, {11430, 15036}, {11459, 12163}, {11464, 37475}, {11465, 35477}, {13203, 25563}, {13339, 18571}, {13434, 43615}, {14094, 43586}, {14644, 38323}, {15032, 15034}, {15041, 15062}, {15045, 15078}, {16223, 22962}, {22462, 38633}, {23515, 34007}, {32205, 35498}, {35265, 40647}, {37513, 37952}, {37814, 40280}, {39242, 43651}, {43604, 43613}, {43605, 43611}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9730, 15035, 54}, {9730, 22467, 15035}, {12038, 43600, 54}, {15035, 43597, 9730}, {22467, 43597, 54}

X(43805) = X(1)X(3)∩X(2071)X(31870)

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

Let U = medial triangle and V = anti-Aquila triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43805). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

The same holds for these choices of {U,V}: {2nd circumperp, Wasat}, {incircle-circles triangle, 2nd Zaniah}.

X(43805 lies on these lines: {1, 3}, {2071, 31870}, {2772, 43598}, {2779, 43601}, {3520, 5883}, {3833, 35500}, {5693, 17928}, {5884, 22467}, {6644, 15071}, {9590, 13369}, {9625, 9943}, {9626, 10167}, {9730, 43610}, {15053, 31825}, {43586, 43609}

X(43806) = X(3)X(7666)∩X(54)X(74)

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

Let U = orthic triangle and V = 5th mixtilinear triangle of orthic triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43806). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

X(43806) lies on these linese: {3, 7666}, {4, 13399}, {5, 10706}, {20, 10116}, {24, 1192}, {49, 15055}, {54, 74}, {64, 3567}, {110, 43615}, {184, 23040}, {567, 43612}, {1173, 13596}, {1181, 11468}, {1204, 1614}, {1593, 5890}, {1598, 12290}, {2937, 8718}, {3357, 15033}, {3448, 43577}, {3516, 11423}, {3521, 10264}, {5012, 32138}, {5663, 43598}, {5889, 43576}, {6000, 34484}, {6102, 13445}, {6143, 20417}, {7527, 43600}, {7592, 34469}, {7689, 41398}, {7699, 40686}, {9706, 10226}, {9730, 43611}, {9786, 11455}, {10095, 33541}, {10575, 12087}, {10620, 13630}, {11381, 38848}, {11438, 41448}, {11456, 15750}, {12162, 43597}, {12174, 26882}, {12244, 13403}, {13366, 35478}, {13382, 14865}, {14094, 22467}, {14130, 36153}, {15035, 43604}, {15041, 43394}, {15053, 18439}, {15801, 18859}, {16003, 34007}, {18913, 26917}, {22462, 43584}, {22949, 32345}, {34783, 43574}, {37126, 40647}

X(43806) = reflection of X(43598) in X(43601)
X(43806) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {54, 185, 43596}, {74, 185, 54}, {74, 7722, 43391}, {74, 43602, 3520}, {185, 3520, 43602}, {3520, 43602, 54}, {9706, 15021, 10226}, {10620, 13630, 15062}, {43604, 43605, 15035}, {43611, 43613, 9730}

X(43807) = X(3)X(49)∩X(5)X(146)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6 + a^4*b^2 - 5*a^2*b^4 + 3*b^6 + a^4*c^2 + 11*a^2*b^2*c^2 - 3*b^4*c^2 - 5*a^2*c^4 - 3*b^2*c^4 + 3*c^6) : :
X(43807) = X[43598] - 3 X[43601]

Let U = Euler triangle and V = Ehrmann mid-triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43807). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

X(43807) lies on these lines: {3, 49}, {5, 146}, {52, 35452}, {54, 12041}, {64, 3843}, {74, 13434}, {125, 3521}, {143, 13445}, {195, 2071}, {265, 43577}, {381, 23294}, {382, 26869}, {399, 22467}, {546, 33541}, {548, 11271}, {550, 32608}, {567, 17835}, {1539, 43599}, {1614, 37955}, {1658, 7712}, {1899, 18565}, {2070, 13491}, {2937, 15072}, {3357, 37481}, {3520, 15041}, {3830, 9786}, {5012, 18364}, {5070, 37475}, {5073, 37490}, {5643, 12006}, {5663, 43598}, {5889, 37496}, {5890, 14627}, {5899, 10575}, {6000, 13621}, {6102, 18859}, {6288, 16003}, {6639, 18931}, {7527, 15047}, {7545, 12290}, {7579, 40686}, {10116, 12121}, {10226, 15032}, {10254, 26937}, {10263, 35001}, {10264, 34007}, {10574, 32138}, {10606, 36753}, {11003, 11270}, {11017, 38626}, {11250, 15087}, {11438, 18378}, {11440, 34864}, {11468, 32046}, {12308, 18350}, {12316, 37477}, {13363, 43603}, {13382, 37472}, {13403, 20127}, {14449, 37944}, {14677, 43575}, {14865, 15038}, {15021, 43612}, {15030, 22462}, {15053, 18369}, {15054, 43597}, {15055, 43394}, {15131, 25563}, {15689, 37486}, {16386, 43588}, {17800, 37489}, {26879, 31726}, {32609, 43605}

X(43807) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {49, 43604, 3}, {54, 12041, 35498}, {74, 13630, 14130}, {74, 43611, 13434}, {185, 43604, 49}, {5012, 32210, 18364}, {13434, 43611, 13630}, {13630, 14130, 15037}, {15055, 43602, 43394}, {43603, 43613, 13363}, {43605, 43615, 32609}

X(43808) = X(2)X(49)∩X(4)X(51)

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

Let U = circum-orthic triangle and V = anti-Wasat triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43808). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

Let P=X(3) and Q=X(4). Let PA = the reflection of P in QA, QA = the reflection of Q in PA, MA = the midpoint of PAQA. Define MB and MC cyclically. Then MAMBMC is homothetic to ABC at X(49) and to the anticomplementary triangle at X(43808). (see Anopolis #2584, Antreas Hatzipolakis 5/29/2015) (Randy Hutson, June 30, 2021)

X(43808 lies on these lines: {2, 49}, {4, 51}, {5, 399}, {20, 3581}, {24, 26869}, {54, 125}, {68, 631}, {70, 11427}, {74, 13403}, {93, 338}, {110, 10116}, {140, 2888}, {184, 14940}, {186, 2917}, {195, 32165}, {265, 13630}, {323, 11271}, {376, 43604}, {378, 26944}, {403, 18914}, {542, 43598}, {567, 13561}, {569, 23293}, {578, 23294}, {858, 13292}, {1147, 26913}, {1181, 16868}, {1199, 1594}, {1216, 12325}, {1352, 5067}, {1503, 34484}, {1614, 37943}, {1656, 3410}, {1994, 13371}, {2071, 12370}, {2072, 43588}, {2088, 18335}, {3090, 11442}, {3091, 32140}, {3153, 6102}, {3167, 31282}, {3482, 11584}, {3518, 13567}, {3519, 15108}, {3520, 12022}, {3521, 10113}, {3541, 43589}, {3580, 7512}, {5012, 5449}, {5050, 7569}, {5189, 10263}, {5576, 34545}, {5972, 9705}, {6101, 37779}, {6247, 13596}, {6288, 12006}, {6639, 11003}, {6640, 9545}, {6644, 34799}, {6696, 35478}, {6776, 7505}, {7577, 7592}, {7687, 43596}, {9140, 13434}, {9706, 15059}, {9707, 26958}, {9786, 18559}, {9927, 10574}, {10018, 31804}, {10095, 37349}, {10112, 43574}, {10224, 15087}, {10264, 14130}, {10540, 21451}, {10733, 43577}, {11262, 32353}, {11264, 22115}, {11270, 18931}, {11416, 12585}, {11430, 43608}, {11438, 12289}, {11804, 27552}, {12079, 36161}, {12088, 41587}, {12160, 31180}, {12162, 12317}, {12241, 14865}, {12244, 18560}, {12359, 35921}, {12383, 22467}, {12897, 13445}, {13202, 43599}, {13358, 36853}, {13366, 32767}, {13418, 40632}, {13419, 38848}, {13452, 14457}, {13619, 21659}, {14641, 18555}, {14644, 43602}, {14683, 18350}, {14790, 37644}, {15033, 20299}, {15038, 33332}, {15043, 18474}, {15061, 43394}, {15062, 16003}, {15109, 18212}, {15463, 43617}, {15472, 43606}, {15873, 16658}, {16266, 31101}, {16655, 26863}, {17702, 43601}, {17854, 22466}, {18125, 20301}, {18396, 34797}, {18913, 35481}, {18945, 35471}, {18951, 37444}, {19467, 21844}, {21243, 43651}, {21650, 43392}, {23291, 37119}, {26937, 35473}, {31074, 36749}, {32337, 32395}

X(43808) = crosspoint of X(4) and X(13418)
X(43808) = crosssum of X(3) and X(13621)
X(43808) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {54, 125, 6143}, {68, 18911, 631}, {184, 26917, 14940}, {186, 6146, 12254}, {265, 13630, 34007}, {323, 32358, 11271}, {389, 25739, 4}, {1216, 41724, 12325}, {1594, 11245, 1199}, {1656, 18356, 3410}, {1899, 18912, 4}, {1899, 39571, 11457}, {3519, 32142, 15108}, {3567, 18381, 4}, {3581, 13470, 20}, {6146, 26879, 186}, {6241, 18390, 4}, {9781, 11550, 4}, {10264, 43575, 14130}, {10821, 15032, 15037}, {11457, 18912, 39571}, {11457, 39571, 4}, {13353, 34826, 2}, {13567, 34224, 3518}, {15033, 20299, 35482}, {18952, 25738, 2}, {32165, 37938, 195}, {32358, 37452, 323}

X(43809) = X(2)X(3)∩X(39)X(2079)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 5*a^4*b^2*c^2 - 5*a^2*b^4*c^2 + 2*b^6*c^2 - 5*a^2*b^2*c^4 - 2*b^4*c^4 + 2*a^2*c^6 + 2*b^2*c^6 - c^8) : :
X(43809) = 3 X[3] + 2 X[34484], 3 X[13621] - 2 X[34484]

Let U = circumnormal triangle and V = complement of Stammler triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43809). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

X(43809) lies on these lines: {2, 3}, {39, 2079}, {49, 9730}, {51, 37495}, {54, 1511}, {74, 43614}, {110, 13630}, {113, 3521}, {125, 6288}, {143, 43574}, {156, 10574}, {185, 399}, {195, 389}, {233, 15109}, {252, 11815}, {323, 12316}, {394, 37490}, {567, 2931}, {568, 1092}, {1105, 34334}, {1147, 15087}, {1204, 18435}, {1216, 3581}, {1324, 35220}, {1351, 40929}, {1384, 9608}, {2917, 37513}, {3172, 21397}, {3312, 9682}, {3574, 14156}, {5012, 32171}, {5023, 9699}, {5446, 37477}, {5462, 15038}, {5562, 32608}, {5621, 18553}, {5651, 7689}, {5663, 43598}, {5892, 13353}, {5894, 9919}, {5898, 36966}, {5946, 14627}, {6102, 15053}, {6451, 9683}, {6759, 7729}, {7592, 9703}, {7666, 13366}, {7691, 32142}, {7728, 43577}, {8276, 18512}, {8277, 18510}, {9306, 34783}, {9590, 13624}, {9625, 31663}, {9626, 17502}, {9641, 11399}, {9706, 15034}, {9932, 11935}, {10110, 10564}, {10116, 23236}, {10117, 33539}, {10263, 37496}, {10312, 22121}, {10540, 40647}, {10546, 12290}, {10610, 41578}, {10620, 12162}, {11202, 13336}, {11438, 18436}, {11440, 15060}, {11449, 15045}, {11597, 11802}, {11793, 32110}, {12017, 15577}, {12041, 15062}, {12121, 13403}, {12310, 37648}, {12584, 33749}, {12893, 38794}, {13171, 43607}, {13289, 25563}, {13321, 36747}, {13363, 13434}, {13445, 32137}, {13561, 41171}, {14861, 14862}, {15026, 15033}, {15030, 15041}, {15055, 43613}, {15058, 32138}, {15567, 33695}, {16035, 40631}, {18475, 37471}, {19176, 38605}, {19362, 19403}, {20791, 26882}, {23850, 35221}, {32063, 40928}, {32345, 32767}, {34153, 43575}, {34866, 39565}, {35602, 36749}, {37484, 43652}, {38739, 39854}, {38750, 39825}

X(43809) = midpoint of X(i) and X(j) for these {i,j}: {3, 13621}, {43598, 43601}
X(43809) = circumcircle-inverse of X(43893)
X(43809) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 34864}, {2, 37814, 3}, {3, 4, 18859}, {3, 5, 14130}, {3, 24, 2937}, {3, 25, 1657}, {3, 2070, 13564}, {3, 3516, 35495}, {3, 3517, 12083}, {3, 3830, 11413}, {3, 3843, 12084}, {3, 3851, 378}, {3, 5055, 7526}, {3, 5070, 7503}, {3, 5899, 550}, {3, 6642, 381}, {3, 7387, 15696}, {3, 7506, 382}, {3, 7517, 3534}, {3, 7545, 35001}, {3, 11414, 15688}, {3, 12106, 37924}, {3, 14130, 35498}, {3, 15694, 7509}, {3, 18378, 20}, {3, 37814, 37955}, {3, 37922, 7488}, {5, 140, 6143}, {5, 10226, 7527}, {5, 22467, 3}, {5, 43615, 3520}, {20, 12106, 18378}, {20, 18378, 37924}, {24, 2937, 2070}, {24, 21844, 21284}, {54, 12006, 15037}, {54, 43584, 12006}, {110, 43597, 13630}, {110, 43603, 43602}, {140, 186, 3}, {140, 3575, 37452}, {185, 18350, 399}, {185, 43586, 18350}, {382, 7506, 7545}, {389, 22115, 195}, {549, 7488, 3}, {550, 3518, 5899}, {631, 1658, 3}, {631, 7544, 18281}, {632, 15331, 35921}, {1147, 37481, 15087}, {1216, 3581, 12307}, {1511, 12006, 54}, {1511, 43584, 15037}, {1995, 12084, 3843}, {3520, 22467, 43615}, {3520, 43615, 3}, {3523, 7502, 3}, {3524, 7525, 3}, {3530, 7512, 3}, {3530, 7575, 7512}, {3575, 7574, 382}, {3575, 37452, 7574}, {3628, 15646, 14118}, {3850, 34152, 14865}, {5462, 37472, 15038}, {5892, 13367, 13353}, {5946, 34148, 14627}, {6636, 15712, 3}, {6644, 17928, 3}, {7393, 15750, 3}, {7509, 18324, 3}, {7514, 32534, 3}, {7516, 38444, 3}, {7526, 15078, 3}, {7550, 18571, 3}, {9825, 10257, 5576}, {11413, 13861, 3830}, {11449, 15045, 32046}, {11585, 38321, 31724}, {12100, 37940, 34006}, {12107, 15712, 6636}, {13363, 43394, 13434}, {13434, 15035, 43394}, {14118, 15646, 3}, {14709, 14710, 140}, {15034, 43600, 9706}, {15331, 35921, 3}, {16042, 22467, 35497}, {18369, 18859, 4}, {18564, 35471, 1657}, {18859, 37917, 2070}, {22462, 43615, 14130}, {34864, 37955, 3}, {43597, 43602, 43603}, {43602, 43603, 13630}

X(43810) = X(5)X(11579)∩X(54)X(69)

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

Let U = Kosnita triangle and V = 2nd Ehrmann triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43810). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

X(43810) lies on these lines: {5, 11579}, {6, 12084}, {49, 8550}, {54, 69}, {155, 38402}, {185, 575}, {511, 43601}, {542, 43598}, {567, 23328}, {895, 43597}, {1216, 32599}, {3521, 5480}, {5085, 43394}, {6288, 25328}, {8584, 37495}, {9972, 39562}, {9976, 43584}, {11179, 39571}, {11470, 39561}, {15033, 22234}, {15037, 25711}, {15806, 38110}, {25556, 43596}, {31670, 43577}

X(43810) = {X(182),X(33749)}-harmonic conjugate of X(54)

X(43811) = X(5)X(15133)∩X(6)X(1493)

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

Let U = Trihn and V = anti-Honsberger triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43811). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

X(43811) lies on these lines: {5, 15133}, {6, 1493}, {49, 597}, {54, 25555}, {110, 373}, {140, 18374}, {182, 1614}, {206, 13336}, {542, 43598}, {578, 7401}, {1092, 20423}, {1352, 5449}, {1656, 32379}, {1974, 3147}, {3526, 19127}, {3589, 12134}, {3763, 19154}, {3819, 37977}, {5092, 11381}, {5476, 34148}, {5480, 37495}, {5622, 18553}, {6143, 32239}, {6816, 26883}, {8550, 18350}, {9019, 13621}, {9306, 11225}, {9968, 37470}, {9977, 32260}, {10203, 14940}, {10539, 11179}, {11188, 11458}, {11511, 11663}, {11579, 15027}, {19140, 43584}, {22462, 40670}, {22830, 22955}, {29959, 32245}, {34397, 35283}

X(43811) = {X(5622),X(43614)}-harmonic conjugate of X(18553)

X(43812) = X(3)X(15531)∩X(54)X(67)

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

Let U = 2nd Ehrmann triangle and V = anti-Honsberger triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43812). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

X(43812) lies on these lines: {3, 15531}, {6, 6241}, {54, 67}, {182, 3525}, {206, 1614}, {542, 43598}, {575, 11579}, {578, 14912}, {1353, 37495}, {2071, 32284}, {3520, 40673}, {3567, 8549}, {5012, 38397}, {5050, 11441}, {5890, 8537}, {6102, 11416}, {6193, 13336}, {6403, 9786}, {8548, 10574}, {9705, 15462}, {9972, 9976}, {11061, 33749}, {11432, 39588}, {11477, 43576}, {13382, 21639}, {13630, 39562}, {14984, 43601}, {26883, 39874}, {37784, 40647}

X(43812) = {X(5622),X(8550)}-harmonic conjugate of X(54)

X(43813) = X(3)X(41715)∩X(54)X(74)

Barycentrics    a^2*(a^14 - 4*a^12*b^2 + 5*a^10*b^4 - 5*a^6*b^8 + 4*a^4*b^10 - a^2*b^12 - 4*a^12*c^2 + 19*a^10*b^2*c^2 - 21*a^8*b^4*c^2 - 10*a^6*b^6*c^2 + 26*a^4*b^8*c^2 - 9*a^2*b^10*c^2 - b^12*c^2 + 5*a^10*c^4 - 21*a^8*b^2*c^4 + 54*a^6*b^4*c^4 - 30*a^4*b^6*c^4 - 11*a^2*b^8*c^4 + 3*b^10*c^4 - 10*a^6*b^2*c^6 - 30*a^4*b^4*c^6 + 42*a^2*b^6*c^6 - 2*b^8*c^6 - 5*a^6*c^8 + 26*a^4*b^2*c^8 - 11*a^2*b^4*c^8 - 2*b^6*c^8 + 4*a^4*c^10 - 9*a^2*b^2*c^10 + 3*b^4*c^10 - a^2*c^12 - b^2*c^12) : :

Let U = anti-incircle-circles triangle and V = 1st Excosine triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43813). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

X(43813) lies on these lines: {3, 41715}, {54, 74}, {64, 394}, {110, 5894}, {206, 21734}, {323, 31978}, {376, 6225}, {2777, 43598}, {2781, 43601}, {2935, 15062}, {3357, 43574}, {5012, 8567}, {10606, 34148}, {11424, 11433}, {12315, 15068}, {12324, 37480}, {13434, 23328}, {15472, 43607}, {18350, 20127}, {18381, 43576}, {38323, 43614}

X(43814) = X(74)X(575)∩X(182)X(11440)

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

Let U = Ehrmann vertex triangle and V = anti-Honsberger triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43814). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

X(43814) lies on these lines: {74, 575}, {182, 11440}, {185, 15462}, {542, 43601}, {1204, 11179}, {1352, 18913}, {5092, 43596}, {5621, 13630}, {9972, 11579}, {15062, 25555}, {15579, 37481}, {18553, 43597}

X(43815) = X(4)X(83)∩X(54)X(575)

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

Let U = 7th Brocard triangle and V = 10th Brocard triangle. Then KM(U) is perpsective to MK(V), and KM(V) is perspective to MK(U), and the perspectors are both X(43815). (KM denotes the Kiss-Moses mapping, and MK, its inverse.)

X(43815) lies on these lines: {4, 83}, {5, 5622}, {6, 2929}, {20, 19136}, {54, 575}, {110, 8550}, {154, 1995}, {184, 18928}, {373, 13198}, {389, 22151}, {542, 43598}, {567, 19138}, {576, 43574}, {597, 13434}, {682, 3398}, {858, 37649}, {1092, 1992}, {1177, 7527}, {1352, 26917}, {1614, 11179}, {2781, 43601}, {3546, 19131}, {5050, 6642}, {5085, 11413}, {5133, 41738}, {5621, 15062}, {5943, 37777}, {6644, 15073}, {6776, 10539}, {7464, 20190}, {7544, 23327}, {9306, 18950}, {9705, 33749}, {10541, 19127}, {10574, 34117}, {11579, 18553}, {11585, 19129}, {12017, 12085}, {12160, 20806}, {15053, 37473}, {16051, 43650}, {19140, 43596}, {21460, 39169}, {26206, 41716}, {26913, 34118}

X(43815) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 1974, 25406}, {182, 19128, 1176}, {575, 15462, 54}

leftri

Special KM and MK perspectors: X(43816)-X(43839)

rightri

This preamble is contributed by Peter Moses and Clark Kimberling, June 21, 2021.

Let KM be the Kiss-Moses mapping, as introduced in the preabmle just before X(43390).

The appearance of (T,i) in the following list means that KM(KM(T)) is perspective to ABC, and the perspector is X(i).

(ABC,54), (medial,43816), (anticomplementary,43817), (Euler,43818), (tangential-triangle-of-1st-circumperp,43819), (tangential triangle of 2nd circumperp,43820), (X(5)-reflection of ABC,43821), (Aquila,43822),A(ara,43823), (Caelum,43824), (inner Grebe,43825), (outer Grebe,43826), (outer Garcia,43827), (5th Brocard, 43828), (intouch-of-orthic,43829), (anti-Aquila,43830), (anti-1st-Euler,43831), (inner Johnson,43832), (outer Johnson,43833), (anti-Conway,43834), (Ehrmann mid-triangle,43835), (Gemini 107, 43836), (Gemini 109, 43837), (Gemini 110,43838), (Gemini 111,43839)



X(43816) = X(2)X(54)∩X(5)X(399)

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

X(43816) lies on these lines: {2, 54}, {3, 43575}, {4, 3521}, {5, 399}, {20, 11438}, {64, 37077}, {113, 43602}, {125, 13434}, {146, 185}, {184, 22533}, {265, 12006}, {323, 13292}, {389, 3153}, {542, 43614}, {567, 6143}, {578, 26913}, {631, 14805}, {1199, 2072}, {1216, 37779}, {1352, 7486}, {1594, 34545}, {1614, 21451}, {1656, 15806}, {1899, 3091}, {1994, 11585}, {2071, 12241}, {2889, 3917}, {2931, 12022}, {3090, 3410}, {3146, 43577}, {3527, 31133}, {3545, 32140}, {3574, 32068}, {3580, 37126}, {3832, 11457}, {3839, 14216}, {5055, 18356}, {5056, 11442}, {5189, 5446}, {5462, 25739}, {5640, 18381}, {5972, 9706}, {6288, 13363}, {6636, 41587}, {6642, 34799}, {6643, 37644}, {6816, 18950}, {7488, 13567}, {7503, 26869}, {7505, 11003}, {7574, 16881}, {7577, 36753}, {7693, 34514}, {7706, 18394}, {8254, 33565}, {9143, 18350}, {9730, 34007}, {9927, 15045}, {10116, 14683}, {10126, 11584}, {10296, 13568}, {10574, 18390}, {10721, 43611}, {10733, 43603}, {11002, 14790}, {11225, 15801}, {11426, 30744}, {11433, 37444}, {11793, 41724}, {11802, 36853}, {12111, 43392}, {12325, 15067}, {13595, 34224}, {13851, 15012}, {14118, 26879}, {14157, 18128}, {14374, 14807}, {14375, 14808}, {14516, 37648}, {14627, 37938}, {14644, 43600}, {14940, 32046}, {15024, 18474}, {15053, 21659}, {15740, 22466}, {16003, 43613}, {16226, 18383}, {17702, 43597}, {20304, 36153}, {23325, 32337}, {31101, 36747}, {31180, 37493}, {32142, 34483}, {32609, 36966}, {34193, 36179}, {36794, 42877}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {569, 26917, 2}, {3090, 25738, 3410}, {5449, 43651, 2}, {10116, 43598, 14683}, {13403, 43601, 20}, {15047, 38724, 5}, {18911, 39571, 20}

X(43817) = X(2)X(54)∩X(5)X(113)

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

X(43817) lies on these lines: {2, 54}, {3, 2929}, {4, 13445}, {5, 113}, {24, 11750}, {49, 5972}, {51, 13371}, {52, 11585}, {64, 381}, {67, 25555}, {110, 10116}, {140, 12370}, {143, 37938}, {155, 26869}, {182, 6639}, {184, 18952}, {195, 11225}, {235, 10575}, {389, 2072}, {403, 40647}, {511, 37452}, {542, 18350}, {567, 6723}, {575, 24572}, {578, 6640}, {631, 39242}, {858, 5446}, {1216, 3580}, {1312, 14375}, {1313, 14374}, {1368, 10625}, {1506, 41334}, {1568, 6102}, {1594, 5462}, {1614, 18128}, {1656, 17814}, {1853, 7529}, {1899, 10539}, {1993, 31282}, {2071, 12897}, {2904, 5422}, {2937, 32223}, {3090, 23293}, {3091, 23294}, {3292, 32358}, {3448, 43598}, {3520, 6699}, {3526, 37506}, {3548, 13352}, {3549, 13336}, {3574, 5946}, {3628, 15806}, {3851, 18418}, {5012, 14940}, {5050, 5070}, {5448, 5890}, {5498, 25487}, {5576, 5943}, {5654, 18916}, {5891, 12359}, {5892, 13160}, {5907, 43392}, {6101, 41586}, {6143, 13434}, {6146, 16238}, {6247, 16194}, {6288, 38724}, {6642, 18474}, {6643, 37478}, {6677, 12134}, {6697, 14561}, {6759, 41603}, {7393, 37638}, {7403, 14845}, {7505, 18911}, {7506, 18381}, {7527, 20397}, {7542, 37513}, {7547, 7706}, {7575, 13470}, {7577, 15043}, {7765, 10413}, {8254, 32226}, {9140, 43614}, {9306, 25738}, {9729, 10024}, {9781, 31074}, {9820, 11245}, {9927, 17928}, {10018, 18475}, {10112, 22115}, {10125, 10610}, {10201, 10984}, {10226, 38727}, {10255, 18388}, {10257, 12241}, {10297, 13568}, {10564, 16196}, {10574, 16868}, {10619, 32171}, {11064, 13292}, {11264, 40111}, {11424, 18281}, {11438, 18404}, {11550, 13861}, {11572, 31830}, {11695, 37347}, {11704, 15045}, {12022, 12038}, {12088, 17712}, {12163, 16072}, {12227, 15037}, {12242, 32068}, {12301, 14852}, {12585, 22151}, {12605, 32110}, {12827, 38795}, {12900, 15032}, {13293, 14130}, {13364, 33332}, {13419, 13621}, {13754, 26879}, {14076, 15047}, {14118, 20191}, {14156, 34148}, {14157, 21451}, {14516, 43586}, {14644, 34007}, {15025, 34802}, {15026, 39504}, {15081, 43584}, {15125, 22967}, {16111, 18560}, {16163, 43615}, {16222, 32743}, {16534, 43605}, {17702, 22467}, {18378, 29012}, {18383, 38321}, {18451, 26944}, {21659, 37814}, {22104, 36159}, {22955, 32375}, {25641, 36179}, {26156, 34382}, {30771, 36747}, {32263, 33563}, {32340, 38322}, {35498, 38728}

X(43817) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5449, 1209}, {2, 18912, 1147}, {2, 26917, 5449}, {2, 43651, 6689}, {4, 43601, 43577}, {5, 185, 113}, {140, 43575, 43394}, {381, 20299, 18488}, {1368, 41587, 10625}, {3548, 39571, 13352}, {5943, 32767, 5576}, {5946, 10224, 3574}, {10255, 37481, 18388}, {11585, 13567, 52}, {12006, 20304, 5}, {13434, 15059, 6143}, {14130, 15061, 25563}, {14644, 43597, 34007}, {18560, 43604, 16111}

X(43818) = X(2)X(43394)∩X(4)X(54)

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

X(43818) lies on these lines: {2, 43394}, {3, 43575}, {4, 54}, {5, 12383}, {6, 34797}, {20, 568}, {30, 1199}, {113, 9706}, {185, 7731}, {186, 12241}, {376, 43573}, {381, 15806}, {389, 13619}, {399, 36966}, {542, 43613}, {567, 34007}, {631, 39242}, {1899, 35475}, {1994, 18563}, {2777, 43602}, {3090, 12118}, {3146, 3521}, {3153, 37472}, {3431, 7505}, {3448, 14130}, {3518, 15873}, {3520, 12022}, {3529, 43577}, {5189, 13470}, {6143, 11430}, {6146, 14865}, {6241, 43392}, {7577, 11425}, {9705, 20125}, {9781, 34785}, {10116, 12317}, {10540, 15807}, {11245, 35491}, {11270, 35485}, {11271, 18436}, {11402, 35490}, {11426, 35480}, {11433, 35503}, {12006, 12121}, {12112, 13488}, {12281, 43581}, {12370, 14118}, {13292, 34005}, {13367, 37943}, {13434, 17702}, {13445, 18128}, {13567, 17506}, {13596, 34224}, {14374, 15160}, {14375, 15161}, {14940, 18390}, {15032, 18560}, {15520, 33749}, {16163, 43597}, {16657, 34484}, {18912, 35473}, {21451, 32171}, {21844, 39571}, {25739, 35482}, {30714, 43614}, {31985, 43616}, {38848, 40240}

X(43818) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {54, 13403, 4}, {10116, 15062, 12317}, {11424, 12289, 4}, {13403, 43393, 21659}, {15033, 21659, 4}

X(43819) = X(1)X(13630)∩X(54)X(55)

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

X(43819) lies on these lines: {1, 13630}, {5, 3024}, {12, 3270}, {35, 43394}, {54, 55}, {56, 43601}, {185, 3028}, {389, 10149}, {1478, 3521}, {3058, 43573}, {5160, 5446}, {6284, 13403}, {7354, 43577}, {7951, 32168}, {9652, 19354}, {10065, 14130}, {10895, 11461}, {12903, 34007}, {15171, 43575}, {33964, 36179}

X(43819) = {X(1),X(13630)}-harmonic conjugate of X(43820)

X(43820) = X(1)X(13630)∩X(54)X(56)

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

X(43820) lies on these lines: {1, 13630}, {5, 3028}, {11, 1425}, {36, 43394}, {54, 56}, {55, 43601}, {185, 3024}, {1479, 3521}, {3025, 30493}, {5434, 43573}, {5446, 7286}, {6284, 43577}, {7354, 13403}, {7741, 32143}, {9667, 19349}, {10081, 14130}, {10149, 40647}, {10896, 19368}, {12904, 34007}, {15325, 15806}, {18990, 43575}, {33965, 36179}

X(43820) = {X(1),X(13630)}-harmonic conjugate of X(43819)

X(43821) = X(2)X(43394)∩X(5)X(49)

Barycentrics    a^10 - 2*a^8*b^2 + a^6*b^4 - a^4*b^6 + 2*a^2*b^8 - b^10 - 2*a^8*c^2 + 3*a^6*b^2*c^2 + 2*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 + a^6*c^4 + 2*a^4*b^2*c^4 + 8*a^2*b^4*c^4 - 2*b^6*c^4 - 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(43821) lies on these lines: {1, 43832}, {2, 43394}, {3, 2929}, {4, 3521}, {5, 49}, {23, 13470}, {30, 43601}, {51, 31724}, {125, 14130}, {143, 3153}, {185, 7728}, {195, 1568}, {381, 1181}, {382, 43577}, {389, 13376}, {399, 10116}, {546, 25739}, {568, 18404}, {569, 10254}, {578, 10255}, {1656, 7666}, {1899, 18439}, {2072, 12241}, {2888, 14128}, {3519, 11591}, {3520, 15061}, {3567, 18377}, {3574, 15038}, {3581, 12605}, {3818, 33749}, {3832, 34514}, {3843, 12315}, {3851, 18474}, {5012, 13406}, {5446, 7574}, {5448, 15087}, {5462, 13851}, {5498, 15059}, {5640, 18394}, {5655, 43605}, {5944, 37943}, {6143, 20304}, {6146, 10540}, {6243, 18531}, {6639, 14805}, {6643, 13340}, {6699, 35498}, {7506, 18396}, {7527, 13561}, {7528, 18918}, {7540, 15873}, {7687, 15037}, {9140, 43613}, {10024, 13353}, {10113, 12006}, {10224, 15033}, {10226, 38728}, {10264, 15062}, {10733, 43597}, {10750, 14374}, {10751, 14375}, {11250, 26913}, {11438, 18562}, {11585, 37495}, {11692, 32352}, {11750, 18378}, {11800, 43583}, {11805, 27552}, {12038, 38794}, {12106, 12289}, {12121, 22467}, {12162, 43392}, {12234, 14627}, {12254, 21451}, {12307, 41586}, {12370, 22115}, {12897, 18859}, {12902, 43393}, {12956, 38458}, {13399, 33541}, {13567, 18563}, {13568, 18323}, {13621, 18400}, {14865, 15807}, {15024, 18392}, {15026, 18379}, {15058, 18356}, {15644, 18555}, {15760, 37471}, {16868, 32046}, {16881, 18572}, {18364, 20191}, {18435, 25738}, {18560, 20127}, {18570, 26917}, {18874, 22804}, {18912, 34783}, {19552, 34356}, {21308, 43582}, {31726, 40647}, {31834, 41724}, {34826, 35500}, {37452, 37477}, {38723, 43615}, {38788, 43604}

,p> X(43821) = reflection of X(43598) in X(5)
X(43821) = X(43598)-of-Johnson-triangle
X(43821) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 13630, 3521}, {5, 49, 14643}, {5, 265, 6288}, {5, 12022, 49}, {5, 36966, 10272}, {5, 43575, 54}, {143, 3153, 15800}, {2072, 12241, 37472}, {10113, 12006, 34007}, {10272, 36966, 9705}, {13403, 18390, 22466}, {13434, 14644, 5}, {18404, 39571, 568}, {43832, 43833, 1}

X(43822) = X(1)X(54)∩X(5)X(11720)

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

X(43822) lies on these lines: {1, 54}, {5, 11720}, {185, 11709}, {517, 43394}, {551, 43573}, {946, 13403}, {952, 15806}, {1385, 13630}, {2948, 9705}, {3521, 18481}, {3576, 43601}, {4297, 43577}, {5901, 43575}, {6143, 13211}, {7984, 9706}, {10116, 13605}, {24301, 31738}

X(43823) = X(4)X(3521)∩X(25)X(54)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10 + a^8*c^2 - 4*a^6*b^2*c^2 + a^4*b^4*c^2 + 6*a^2*b^6*c^2 - 4*b^8*c^2 - 4*a^6*c^4 + a^4*b^2*c^4 - 4*a^2*b^4*c^4 + 3*b^6*c^4 + 6*a^4*c^6 + 6*a^2*b^2*c^6 + 3*b^4*c^6 - 4*a^2*c^8 - 4*b^2*c^8 + c^10) : :
X(43823) = 7 X[9781] + X[26882]

X(43823) lies on these lines: {4, 3521}, {5, 1112}, {24, 43394}, {25, 54}, {51, 235}, {143, 403}, {156, 15317}, {185, 11746}, {378, 15026}, {389, 10151}, {428, 43573}, {468, 5446}, {1154, 16868}, {1593, 5640}, {1594, 13364}, {1885, 5462}, {3516, 15024}, {3520, 13363}, {3567, 37197}, {3575, 10110}, {3851, 9827}, {6102, 35488}, {6622, 11002}, {6756, 43575}, {7505, 10263}, {7577, 18874}, {10018, 13391}, {10019, 13754}, {10627, 14940}, {11410, 15028}, {11470, 16776}, {11591, 35487}, {11807, 25563}, {12006, 18560}, {12052, 36179}, {12162, 13148}, {12300, 13365}, {13451, 15806}, {13473, 40647}, {13598, 37931}, {13851, 41589}, {14542, 22466}, {16881, 37984}, {19504, 43598}, {32205, 37118}, {34397, 34484}, {37472, 37951}

X(43823) = {X(51),X(235)}-harmonic conjugate of X(6746)

X(43824) = X(1)X(54)∩X(5)X(7984)

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

X(43824) lies on these lines: {1, 54}, {5, 7984}, {185, 7978}, {517, 43601}, {944, 13403}, {962, 43577}, {1482, 13630}, {1483, 43575}, {2102, 14374}, {2103, 14375}, {3241, 43573}, {3521, 22791}, {6143, 11735}, {9705, 11720}, {10246, 43394}, {10283, 15806}

X(43825) = X(5)X(19052)∩X(6)X(24)

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) + 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)*S) : :

X(43825) lies on these lines: {5, 19052}, {6, 24}, {49, 19111}, {185, 19059}, {372, 43601}, {1588, 13403}, {3311, 43394}, {3312, 13630}, {3520, 19060}, {3521, 42216}, {6460, 43577}, {15806, 19117}, {19053, 43573}, {19116, 43575}, {33749, 42832}

X(43826) = X(5)X(19051)∩X(6)X(24)

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) - 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)*S) : :

X(43826) lies on these lines: {5, 19051}, {6, 24}, {49, 19110}, {185, 19060}, {371, 43601}, {1587, 13403}, {3311, 13630}, {3312, 43394}, {3520, 19059}, {3521, 42215}, {6459, 43577}, {15806, 19116}, {19054, 43573}, {19117, 43575}, {33749, 42833}

X(43827) = X(5)X(13211)∩X(10)X(54)

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

X(43827) lies on these lines: {5, 13211}, {10, 54}, {40, 13403}, {185, 12368}, {355, 13630}, {515, 43601}, {2948, 10116}, {3521, 18480}, {3679, 43573}, {5690, 43575}, {5691, 43577}, {15806, 38042}, {26446, 43394}

X(43828) = X(5)X(13193)∩X(32)X(54)

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

X(43828) lies on these lines: {5, 13193}, {32, 54}, {182, 43601}, {185, 12192}, {2080, 43394}, {3398, 13630}, {3521, 14880}, {12110, 13403}, {12150, 43573}, {12203, 43577}, {32134, 43575}

X(43829) = X(5)X(12310)∩X(25)X(54)

Barycentrics    a^2*(a^14 - 3*a^12*b^2 + a^10*b^4 + 5*a^8*b^6 - 5*a^6*b^8 - a^4*b^10 + 3*a^2*b^12 - b^14 - 3*a^12*c^2 + 3*a^10*b^2*c^2 + 5*a^8*b^4*c^2 - 8*a^6*b^6*c^2 + 9*a^4*b^8*c^2 - 11*a^2*b^10*c^2 + 5*b^12*c^2 + a^10*c^4 + 5*a^8*b^2*c^4 - 10*a^6*b^4*c^4 - 8*a^4*b^6*c^4 + 21*a^2*b^8*c^4 - 9*b^10*c^4 + 5*a^8*c^6 - 8*a^6*b^2*c^6 - 8*a^4*b^4*c^6 - 26*a^2*b^6*c^6 + 5*b^8*c^6 - 5*a^6*c^8 + 9*a^4*b^2*c^8 + 21*a^2*b^4*c^8 + 5*b^6*c^8 - a^4*c^10 - 11*a^2*b^2*c^10 - 9*b^4*c^10 + 3*a^2*c^12 + 5*b^2*c^12 - c^14) : :

X(43829) lies on these lines: {3, 2929}, {5, 12310}, {6, 18378}, {25, 54}, {26, 43575}, {185, 9919}, {389, 5899}, {578, 13621}, {1112, 19362}, {1498, 43392}, {1593, 18394}, {2070, 12241}, {2937, 39571}, {3521, 18534}, {5020, 32048}, {5446, 37972}, {6642, 43394}, {7387, 13630}, {7517, 11432}, {9909, 43573}, {11414, 43601}, {11433, 17714}, {11746, 15047}, {13564, 13567}, {13568, 37924}, {13861, 15806}, {16868, 32333}, {18369, 23292}, {34785, 43393}, {39568, 43577}

X(43830) = X(1)X(54)∩X(5)X(2948)

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

X(43830) lies on these lines: {1, 54}, {5, 2948}, {40, 13630}, {165, 43601}, {185, 9904}, {355, 43575}, {2100, 14374}, {2101, 14375}, {3521, 41869}, {3576, 43394}, {3624, 9928}, {3679, 43573}, {5691, 13403}, {5886, 15806}, {9706, 11720}, {12006, 12778}, {14130, 33535}, {34464, 37732}

X(43831) = X(4)X(54)∩X(5)X(113)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^6*b^2 - 3*a^4*b^4 + b^8 + 2*a^6*c^2 + 6*a^4*b^2*c^2 - 4*b^6*c^2 - 3*a^4*c^4 + 6*b^4*c^4 - 4*b^2*c^6 + c^8) : :
X(43831) = 3 X[51] - 2 X[6746]

X(43831) lies on these lines: {2, 1204}, {3, 1568}, {4, 54}, {5, 113}, {6, 17837}, {11, 1425}, {12, 3270}, {20, 35268}, {30, 5944}, {39, 1562}, {49, 17702}, {51, 235}, {52, 15761}, {64, 5094}, {74, 6143}, {110, 34007}, {115, 217}, {140, 21663}, {143, 11563}, {146, 15062}, {154, 12173}, {265, 10116}, {287, 16044}, {378, 22802}, {381, 1181}, {382, 1533}, {389, 403}, {399, 6288}, {427, 2883}, {468, 13568}, {542, 43605}, {546, 6146}, {1092, 5654}, {1192, 37453}, {1209, 5876}, {1312, 14374}, {1313, 14375}, {1495, 3575}, {1498, 7507}, {1503, 11572}, {1506, 3269}, {1514, 13488}, {1516, 31381}, {1531, 12605}, {1594, 6000}, {1595, 32062}, {1656, 10605}, {1853, 12174}, {1885, 5893}, {1899, 3091}, {1906, 5480}, {2072, 40647}, {2777, 3520}, {3070, 21641}, {3071, 21640}, {3089, 34417}, {3090, 26937}, {3258, 36179}, {3331, 27371}, {3357, 37119}, {3516, 5895}, {3526, 32620}, {3541, 5878}, {3545, 18909}, {3548, 4846}, {3613, 17703}, {3614, 26956}, {3832, 6776}, {3839, 18945}, {3843, 18396}, {3845, 31804}, {3850, 18914}, {3917, 6823}, {5056, 18913}, {5064, 15811}, {5067, 18931}, {5068, 23291}, {5072, 26944}, {5169, 11439}, {5181, 40929}, {5318, 21648}, {5321, 21647}, {5422, 18418}, {5446, 11799}, {5449, 10254}, {5475, 39643}, {5498, 12041}, {5562, 15760}, {5622, 25555}, {5642, 38323}, {5651, 6815}, {5655, 43590}, {5889, 41586}, {5890, 16868}, {5899, 15800}, {5907, 13160}, {5925, 11410}, {5972, 22467}, {6053, 41171}, {6102, 13406}, {6225, 8889}, {6240, 10282}, {6241, 7577}, {6623, 15004}, {6639, 7689}, {6804, 22112}, {6816, 43650}, {7173, 26955}, {7505, 11438}, {7506, 7706}, {7527, 38791}, {7539, 33537}, {7547, 11456}, {7592, 18390}, {7687, 15032}, {7699, 12290}, {7728, 14130}, {7745, 8779}, {7747, 14585}, {7777, 9289}, {8550, 32250}, {9544, 12278}, {9705, 12383}, {9706, 10733}, {9707, 34785}, {9714, 40909}, {9927, 18445}, {10019, 11245}, {10020, 32110}, {10024, 13754}, {10151, 12241}, {10182, 21844}, {10193, 11468}, {10224, 13491}, {10226, 16111}, {10272, 17701}, {10575, 13371}, {10706, 43613}, {10895, 19354}, {10896, 19349}, {10984, 18531}, {10990, 37118}, {11064, 31829}, {11202, 35471}, {11430, 13202}, {11457, 23325}, {11464, 34797}, {11558, 22051}, {11750, 18377}, {12038, 16163}, {12087, 29317}, {12111, 21243}, {12244, 43599}, {12279, 31074}, {12281, 14076}, {12362, 22352}, {12897, 31726}, {13198, 13434}, {13382, 26879}, {13417, 43581}, {13470, 18572}, {13474, 15559}, {14516, 24981}, {14644, 43602}, {14826, 32605}, {14831, 41587}, {15043, 18504}, {15056, 24206}, {15081, 43596}, {15126, 22967}, {15331, 34798}, {15740, 16051}, {16072, 37514}, {16198, 16654}, {16534, 18350}, {16665, 18550}, {17821, 37196}, {17845, 26864}, {17854, 32743}, {17928, 22962}, {18347, 31864}, {18383, 34224}, {18392, 34799}, {18474, 32139}, {18475, 18563}, {18488, 39504}, {18559, 26882}, {19125, 36990}, {19355, 23261}, {19356, 23251}, {19363, 42093}, {19364, 42094}, {19457, 38789}, {20127, 35498}, {20417, 43608}, {20424, 21660}, {21969, 31802}, {23358, 37932}, {31978, 32125}, {32137, 33332}, {35497, 37853}, {38727, 43604}, {38793, 43615}, {43584, 43616}, {43614, 43617}

X(43831) = midpoint of X(4) and X(1614)
X(43831) = reflection of X(i) in X(j) for these {i,j}: {11572, 23047}, {43394, 15806}
X(43831) = complement of X(11440)
X(43831) = crosspoint of X(14374) and X(14375)
X(43831) = crosssum of X(i) and X(j) for these (i,j): {3, 34148}, {14709, 14710}
X(43831) = excentral-to-ABC functional image of X(2975)
X(43831) = X(2975)-of-orthic-triangle if ABC is acute
X(43831) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3521, 43577}, {3, 5448, 1568}, {4, 54, 13403}, {4, 184, 21659}, {4, 14157, 13419}, {4, 18388, 3574}, {5, 185, 125}, {74, 6143, 25563}, {184, 21659, 10619}, {235, 12233, 51}, {427, 2883, 11381}, {546, 6146, 13851}, {1498, 7507, 11550}, {3575, 16252, 1495}, {3843, 19347, 18396}, {5893, 23292, 1885}, {6241, 7577, 20299}, {6241, 20299, 13399}, {7547, 11456, 18381}, {7592, 35488, 18390}, {9707, 35480, 34785}, {10254, 34783, 5449}, {13419, 14862, 14157}, {15559, 32111, 13474}, {15760, 22660, 5562}, {22968, 31985, 22466}, {31726, 37472, 12897}, {43395, 43396, 21650}

X(43832) = X(5)X(10088)∩X(11)X(54)

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

X(43832) lies on these lines: {1, 43821}, {5, 10088}, {11, 54}, {56, 13403}, {65, 3521}, {73, 19472}, {185, 12374}, {496, 43575}, {499, 43394}, {1479, 13630}, {6284, 43601}, {10593, 15806}, {10896, 19349}, {11238, 43573}, {12953, 43577}

X(43832) = {X(1),X(43821)}-harmonic conjugate of X(43833)

X(43833) = X(5)X(10091)∩X(12)X(54)

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

X(43833) lies on these lines: {1, 43821}, {5, 10091}, {12, 54}, {55, 13403}, {185, 12373}, {495, 43575}, {498, 43394}, {1478, 13630}, {3521, 3585}, {7354, 43601}, {9627, 22466}, {10592, 15806}, {10895, 19354}, {11237, 43573}, {12943, 43577}

X(43833) = {X(1),X(43821)}-harmonic conjugate of X(43832)

X(43834) = X(3)X(11225)∩X(52)X(14861)

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

X(43834) lies on the Jerabek hyhperbola and these lines: {3, 11225}, {52, 14861}, {68, 14128}, {973, 38006}, {1173, 15873}, {1176, 12007}, {3410, 15077}, {3426, 13403}, {3519, 11793}, {3521, 13598}, {4846, 10263}, {5972, 43704}, {6146, 16835}, {6293, 35512}, {6391, 24206}, {15316, 17825}, {32165, 43689}

X(43835) = X(3)X(2929)∩X(54)X(156)

Barycentrics    3*a^10 - 6*a^8*b^2 + 2*a^6*b^4 + 3*a^2*b^8 - 2*b^10 - 6*a^8*c^2 + 11*a^6*b^2*c^2 + a^4*b^4*c^2 - 12*a^2*b^6*c^2 + 6*b^8*c^2 + 2*a^6*c^4 + a^4*b^2*c^4 + 18*a^2*b^4*c^4 - 4*b^6*c^4 - 12*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(438)35 lies on these lines: {3, 2929}, {4, 11538}, {5, 12383}, {54, 156}, {185, 38790}, {382, 3567}, {1539, 43602}, {1656, 43394}, {1657, 43601}, {3091, 15806}, {3521, 3527}, {3843, 18396}, {5055, 12293}, {5073, 43577}, {7545, 12289}, {10113, 13434}, {10116, 12308}, {10296, 16881}, {10733, 12006}, {12022, 38789}, {12241, 14627}, {12897, 35452}, {13470, 37924}, {13561, 14130}, {13621, 21659}, {15047, 34007}, {15807, 25739}, {18369, 30522}, {18376, 32402}, {18439, 43392}, {18561, 37490}, {18562, 39571}, {21308, 43393}, {33749, 36990}

X(43835) = {X(12241),X(18403)}-harmonic conjugate of X(14627)

X(43836) = X(2)X(54)∩X(5)X(5643)

Barycentrics    a^10 - 3*a^8*b^2 + 5*a^6*b^4 - 7*a^4*b^6 + 6*a^2*b^8 - 2*b^10 - 3*a^8*c^2 - a^6*b^2*c^2 + 11*a^4*b^4*c^2 - 13*a^2*b^6*c^2 + 6*b^8*c^2 + 5*a^6*c^4 + 11*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - 4*b^6*c^4 - 7*a^4*c^6 - 13*a^2*b^2*c^6 - 4*b^4*c^6 + 6*a^2*c^8 + 6*b^2*c^8 - 2*c^10 : :

X(43836) lies on these lines: {2, 54}, {5, 5643}, {30, 43601}, {113, 43596}, {125, 43578}, {185, 10706}, {265, 43584}, {376, 13403}, {381, 6241}, {542, 43598}, {549, 43575}, {567, 15059}, {575, 32234}, {1173, 13371}, {1614, 18952}, {3521, 3845}, {3543, 43577}, {3545, 18909}, {5054, 43394}, {5055, 11441}, {5067, 11178}, {5446, 10989}, {5462, 7565}, {5642, 9705}, {6225, 41099}, {7505, 11179}, {7512, 32225}, {7540, 38848}, {9143, 10116}, {9730, 14644}, {9781, 31133}, {10545, 34514}, {10719, 14374}, {10720, 14375}, {11061, 25555}, {11459, 26869}, {11645, 34484}, {11694, 36966}, {11704, 36752}, {12022, 15035}, {12834, 39504}, {13292, 40112}, {13363, 38724}, {14787, 23293}, {15033, 18281}, {15037, 20304}, {15062, 20126}, {15133, 38323}, {15699, 15806}, {18128, 21451}, {22750, 37943}, {26879, 34664}, {37648, 41171}

X(43836) = {X(2),X(43573)}-harmonic conjugate of X(54)

X(43837) = X(2)X(54)∩X(4)X(32068)

Barycentrics    3*a^10 - 9*a^8*b^2 + 11*a^6*b^4 - 9*a^4*b^6 + 6*a^2*b^8 - 2*b^10 - 9*a^8*c^2 + 5*a^6*b^2*c^2 + 13*a^4*b^4*c^2 - 15*a^2*b^6*c^2 + 6*b^8*c^2 + 11*a^6*c^4 + 13*a^4*b^2*c^4 + 18*a^2*b^4*c^4 - 4*b^6*c^4 - 9*a^4*c^6 - 15*a^2*b^2*c^6 - 4*b^4*c^6 + 6*a^2*c^8 + 6*b^2*c^8 - 2*c^10 : :

X(43837) lies on these lines: {2, 54}, {4, 32068}, {382, 3567}, {546, 25739}, {550, 43575}, {3521, 15687}, {3529, 11433}, {3530, 3580}, {3618, 33749}, {3851, 5422}, {12022, 43597}, {13434, 13561}, {15033, 18952}, {15720, 43394}, {18560, 43611}, {24981, 43598}

X(43838) = X(2)X(54)∩X(4)X(11538)

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

X(43838) lies on these lines: {2, 54}, {4, 11538}, {5, 14683}, {20, 568}, {146, 43602}, {184, 21451}, {265, 36153}, {567, 13561}, {1199, 3153}, {2777, 43612}, {3090, 15806}, {3146, 13403}, {3448, 13434}, {3521, 3543}, {3522, 43601}, {3523, 43394}, {3832, 6776}, {5059, 43577}, {5422, 34799}, {5446, 20063}, {5946, 12254}, {6146, 34545}, {6643, 11004}, {7550, 32358}, {7691, 11225}, {8254, 38724}, {8550, 43605}, {9143, 43614}, {10619, 32068}, {11003, 39571}, {11245, 14118}, {11271, 15067}, {11426, 31074}, {11572, 15516}, {12006, 12383}, {12022, 34007}, {13142, 16661}, {13292, 37126}, {13595, 31804}, {14516, 15018}, {15047, 32423}, {16111, 43611}, {16163, 43603}, {17702, 43600}, {19481, 27866}, {22466, 43697}, {23236, 32205}, {32165, 34864}, {34224, 37349}, {35500, 43588}

X(43838) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2888, 43651, 2}, {13292, 37126, 37779}

X(43839) = X(2)X(54)∩X(3)X(1568)

Barycentrics    (a^2 - b^2 - c^2)*(2*a^8 - 4*a^6*b^2 + a^4*b^4 + 2*a^2*b^6 - b^8 - 4*a^6*c^2 - 2*a^2*b^4*c^2 + 4*b^6*c^2 + a^4*c^4 - 2*a^2*b^2*c^4 - 6*b^4*c^4 + 2*a^2*c^6 + 4*b^2*c^6 - c^8) : :
X)43839) = 9 X[2] - X[68], 3 X[2] + X[1147], 15 X[2] + X[6193], X[68] + 3 X[1147], X[68] - 3 X[5449], 5 X[68] + 3 X[6193], X[155] + 7 X[3526], 3 X[549] + X[22660], 5 X[631] + 3 X[5654], 5 X[631] - X[7689], 5 X[632] - X[12359], 5 X[632] + X[41597], 5 X[1147] - X[6193], 5 X[1656] - X[9927], X[1658] - 3 X[10182], 7 X[3090] + X[12118], 11 X[3525] + X[15083], 17 X[3533] - X[11411], 7 X[3624] + X[9928], 9 X[5054] - X[12163], 9 X[5055] - X[12293], 11 X[5070] - 3 X[14852], 5 X[5449] + X[6193], 3 X[5654] + X[7689], 3 X[5972] + X[15115], X[6759] + 3 X[18281], 7 X[9780] + X[9933], 2 X[9820] + X[20191], X[9896] - 17 X[19872], 3 X[10192] + X[23335], 3 X[10193] - X[32138], 3 X[10201] + X[13346], 3 X[11202] + X[18569], X[12164] + 15 X[15694], X[12259] - 5 X[19862], X[12893] - 5 X[38794], X[12901] + 3 X[14643], X[13561] - 3 X[34331], 3 X[15035] + X[19479], X[18381] - 5 X[31283], 3 X[23329] + X[32139]

X(43839) lies on these lines: {2, 54}, {3, 1568}, {5, 1511}, {30, 32903}, {49, 125}, {52, 10018}, {110, 6143}, {113, 3520}, {140, 9729}, {155, 3526}, {156, 20299}, {184, 6640}, {185, 6699}, {403, 12897}, {468, 5446}, {511, 10020}, {542, 13561}, {549, 22660}, {631, 5654}, {632, 12359}, {1092, 6639}, {1154, 10125}, {1216, 7542}, {1493, 11225}, {1503, 32144}, {1506, 32661}, {1656, 7666}, {1658, 10182}, {2072, 13367}, {2777, 10226}, {3090, 12118}, {3258, 36159}, {3448, 9705}, {3525, 15083}, {3533, 11411}, {3564, 16239}, {3589, 34382}, {3624, 9928}, {3628, 43575}, {3819, 7568}, {5020, 32048}, {5054, 12163}, {5055, 12293}, {5070, 14852}, {5447, 6676}, {5462, 16238}, {5498, 5663}, {5504, 13434}, {5642, 18350}, {5944, 37938}, {5946, 12242}, {6000, 23336}, {6288, 32609}, {6368, 8562}, {6680, 40489}, {6759, 18281}, {7393, 19908}, {7505, 13352}, {7527, 38795}, {7577, 11449}, {7728, 35498}, {8252, 8909}, {8253, 13909}, {8254, 13363}, {9544, 23294}, {9706, 15059}, {9707, 30744}, {9780, 9933}, {9896, 19872}, {9908, 16419}, {10096, 13446}, {10192, 23335}, {10193, 32138}, {10201, 13346}, {10224, 18400}, {10255, 21659}, {10257, 40647}, {10263, 32223}, {10282, 13371}, {10539, 37119}, {10610, 43582}, {10627, 34577}, {10628, 32415}, {10661, 33416}, {10662, 33417}, {11202, 18569}, {11425, 22466}, {11464, 11750}, {11585, 18475}, {12162, 16534}, {12164, 15694}, {12235, 37649}, {12259, 19862}, {12310, 22462}, {12893, 38794}, {12901, 14130}, {13348, 25337}, {13391, 18282}, {14915, 16252}, {14940, 34148}, {14984, 25555}, {15018, 32263}, {15035, 19479}, {15067, 32348}, {15316, 17825}, {15800, 37922}, {16003, 43605}, {16111, 35497}, {16223, 43581}, {16532, 20424}, {16665, 21400}, {18381, 31283}, {18388, 37814}, {18952, 32539}, {19061, 32786}, {19062, 32785}, {19131, 28408}, {22467, 38793}, {23128, 31455}, {23329, 32139}, {26882, 31074}, {31379, 36179}, {33563, 37648}, {34826, 40111}, {36747, 37453}

X(43839) = midpoint of X(i) and X(j) for these {i,j}: {3, 5448}, {5, 12038}, {140, 9820}, {156, 20299}, {1147, 5449}, {1511, 33547}, {10224, 32171}, {10282, 13371}, {12359, 41597}
X(43839) = reflection of X(i) in X(j) for these {i,j}: {20191, 140}, {25563, 5498}
X(43839) = complement of X(5449)
X(43839) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1147, 5449}, {2, 9545, 26917}, {5, 43394, 13403}, {49, 125, 10116}, {140, 15806, 13630}, {631, 5654, 7689}, {7542, 11064, 1216}, {8252, 8909, 13970}, {9729, 43392, 13630}, {16238, 23292, 5462}, {43605, 43608, 16003}

X(43840) = X(4)X(19170)∩X(6)X(13450)

Barycentrics    a^2*(a^18*b^2 - 8*a^16*b^4 + 28*a^14*b^6 - 56*a^12*b^8 + 70*a^10*b^10 - 56*a^8*b^12 + 28*a^6*b^14 - 8*a^4*b^16 + a^2*b^18 + a^18*c^2 - 10*a^16*b^2*c^2 + 35*a^14*b^4*c^2 - 55*a^12*b^6*c^2 + 29*a^10*b^8*c^2 + 29*a^8*b^10*c^2 - 55*a^6*b^12*c^2 + 35*a^4*b^14*c^2 - 10*a^2*b^16*c^2 + b^18*c^2 - 8*a^16*c^4 + 35*a^14*b^2*c^4 - 50*a^12*b^4*c^4 + 11*a^10*b^6*c^4 + 22*a^8*b^8*c^4 + 17*a^6*b^10*c^4 - 54*a^4*b^12*c^4 + 33*a^2*b^14*c^4 - 6*b^16*c^4 + 28*a^14*c^6 - 55*a^12*b^2*c^6 + 11*a^10*b^4*c^6 + 10*a^8*b^6*c^6 + 10*a^6*b^8*c^6 + 29*a^4*b^10*c^6 - 49*a^2*b^12*c^6 + 16*b^14*c^6 - 56*a^12*c^8 + 29*a^10*b^2*c^8 + 22*a^8*b^4*c^8 + 10*a^6*b^6*c^8 - 4*a^4*b^8*c^8 + 25*a^2*b^10*c^8 - 26*b^12*c^8 + 70*a^10*c^10 + 29*a^8*b^2*c^10 + 17*a^6*b^4*c^10 + 29*a^4*b^6*c^10 + 25*a^2*b^8*c^10 + 30*b^10*c^10 - 56*a^8*c^12 - 55*a^6*b^2*c^12 - 54*a^4*b^4*c^12 - 49*a^2*b^6*c^12 - 26*b^8*c^12 + 28*a^6*c^14 + 35*a^4*b^2*c^14 + 33*a^2*b^4*c^14 + 16*b^6*c^14 - 8*a^4*c^16 - 10*a^2*b^2*c^16 - 6*b^4*c^16 + a^2*c^18 + b^2*c^18) : :

See Antreas Hatzipolakis and Peter Moses, euclid 1752.

X(43840) lies on these lines: {4, 19170}, {6, 13450}, {24, 184}, {436, 1199}, {1614, 9792}, {5890, 31381}, {6641, 12161}, {7668, 18912}

X(43841) = X(2)X(389)∩X(4)X(154)

Barycentrics    3*a^10 - 13*a^8*b^2 + 18*a^6*b^4 - 6*a^4*b^6 - 5*a^2*b^8 + 3*b^10 - 13*a^8*c^2 + 12*a^6*b^2*c^2 + 6*a^4*b^4*c^2 + 4*a^2*b^6*c^2 - 9*b^8*c^2 + 18*a^6*c^4 + 6*a^4*b^2*c^4 + 2*a^2*b^4*c^4 + 6*b^6*c^4 - 6*a^4*c^6 + 4*a^2*b^2*c^6 + 6*b^4*c^6 - 5*a^2*c^8 - 9*b^2*c^8 + 3*c^10 : :
X(43841) = X[4] + 2 X[14528], 7 X[3090] - 4 X[16254]

See Antreas Hatzipolakis and Peter Moses, euclid 1752.

X(43841) lies on the Thomson-Gibert-Moses hyperbola and these lines: {2, 389}, {3, 41465}, {4, 154}, {5, 3167}, {6, 3090}, {20, 6030}, {54, 18945}, {110, 578}, {354, 3086}, {378, 9914}, {393, 3462}, {427, 34781}, {631, 1192}, {973, 6242}, {974, 7722}, {1181, 8889}, {1594, 6776}, {1656, 5644}, {2888, 5056}, {3088, 5656}, {3089, 11387}, {3146, 7712}, {3524, 13568}, {3525, 5646}, {3527, 37942}, {3541, 6241}, {3542, 6403}, {3545, 12241}, {3547, 10625}, {3549, 6243}, {3574, 7487}, {3628, 5544}, {3832, 18504}, {3839, 13403}, {3855, 15752}, {5067, 11431}, {5068, 18390}, {5094, 18909}, {5489, 34291}, {5648, 32246}, {5654, 7404}, {5888, 10303}, {5925, 35483}, {5972, 9815}, {6622, 10982}, {6623, 11424}, {6756, 35260}, {6759, 7378}, {6803, 11064}, {6804, 37649}, {6816, 14389}, {6833, 33883}, {7396, 10984}, {7399, 37669}, {7400, 13348}, {7401, 9820}, {7507, 18925}, {7558, 10519}, {7577, 20303}, {7581, 19039}, {7582, 19040}, {7592, 19360}, {7999, 19161}, {9716, 15022}, {10272, 15436}, {10590, 19365}, {10591, 11429}, {11469, 15063}, {11818, 15806}, {12236, 15026}, {12319, 34153}, {12358, 37481}, {13160, 37645}, {13472, 15081}, {14530, 16198}, {14561, 14913}, {14643, 15465}, {15030, 32605}, {15033, 22750}, {15118, 18912}, {16051, 37514}, {18533, 34472}, {18916, 43593}, {19347, 32064}

X(43841) = {X(3628),X(11432)}-harmonic conjugate of X(37643)

X(43842) = X(4)X(288)∩X(25)X(54)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1752.

X(43842) lies on these lines: {4, 288}, {25, 54}, {933, 13472}, {13527, 18912}

X(43843) = X(3)X(6)∩X(4)X(30505)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1752.

X(43843) lies on these lines: {3, 6}, {4, 30505}, {5, 20965}, {49, 14153}, {140, 3051}, {143, 20859}, {217, 18914}, {384, 34545}, {632, 3231}, {1180, 3567}, {1184, 15805}, {1194, 5462}, {1199, 34945}, {1595, 2211}, {1613, 3526}, {1625, 2548}, {1993, 11285}, {1994, 7824}, {2937, 10329}, {3124, 15026}, {3289, 31406}, {3499, 15047}, {3525, 9463}, {5422, 7770}, {5946, 11205}, {6101, 8041}, {7592, 13860}, {7736, 11411}, {7999, 15302}, {9465, 15024}, {10014, 10358}, {10095, 13410}, {11360, 27374}, {11427, 28407}, {12160, 39951}, {15484, 32445}, {20976, 32136}, {31467, 40805}, {34482, 37455}, {35325, 37119}

X(43843) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {{371, 372, 41328}

X(43844) = MIDPOINT OF X(34148) AND X(43605)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(2*a^6 - 5*a^4*b^2 + 4*a^2*b^4 - b^6 - 5*a^4*c^2 - 4*a^2*b^2*c^2 + b^4*c^2 + 4*a^2*c^4 + b^2*c^4 - c^6) : :
X(43844) = X[3] - 3 X[49], 2 X[3] - 3 X[13367], 3 X[1614] - X[12088], 2 X[3628] - 3 X[15806], 4 X[3628] - 3 X[34826], X[12086] - 3 X[34148], X[12086] + 3 X[43605]

See Antreas Hatzipolakis and Peter Moses, euclid 1752.

X(43844) lies on these lines: {3, 49}, {4, 34986}, {5, 11264}, {23, 15801}, {24, 14831}, {26, 14531}, {51, 10539}, {52, 156}, {54, 5907}, {110, 389}, {113, 137}, {125, 9820}, {154, 12160}, {159, 11477}, {186, 9705}, {195, 5446}, {323, 15644}, {373, 36753}, {399, 37472}, {403, 10112}, {511, 1614}, {539, 10024}, {542, 1594}, {547, 36153}, {569, 15068}, {575, 1352}, {576, 1843}, {578, 11441}, {895, 1173}, {1199, 5943}, {1531, 21659}, {1568, 6146}, {1885, 15063}, {1993, 6759}, {1994, 10110}, {2072, 10116}, {3047, 10628}, {3091, 11422}, {3146, 5656}, {3448, 32767}, {3518, 16625}, {3529, 40196}, {3544, 13472}, {3549, 9936}, {3564, 21637}, {3627, 30522}, {3628, 15806}, {5012, 11793}, {5092, 7999}, {5097, 9781}, {5133, 12242}, {5448, 13851}, {5462, 15087}, {5642, 16238}, {5650, 13336}, {5651, 36752}, {5889, 9544}, {5891, 32046}, {5972, 26879}, {6000, 12086}, {6090, 37514}, {6467, 8538}, {6636, 15606}, {6642, 16226}, {7395, 17809}, {7517, 21969}, {7529, 15004}, {7558, 34507}, {7592, 9306}, {9545, 11430}, {9706, 14118}, {9729, 15032}, {10111, 36253}, {10170, 13353}, {10272, 32165}, {10564, 13491}, {10610, 31834}, {10619, 12605}, {10661, 21648}, {10662, 21647}, {10665, 21641}, {10666, 21640}, {11003, 11444}, {11064, 18914}, {11232, 14643}, {11381, 13352}, {11402, 17814}, {11414, 37672}, {11424, 18451}, {11432, 35259}, {11456, 13346}, {11563, 18555}, {11591, 37513}, {12174, 37497}, {13293, 15054}, {13382, 22467}, {13383, 41586}, {13421, 37947}, {13598, 14157}, {13630, 40111}, {14094, 14865}, {14216, 37645}, {14516, 18388}, {14530, 33586}, {14641, 37477}, {14845, 34566}, {14864, 31074}, {14915, 37495}, {15066, 37515}, {16003, 23336}, {17834, 26864}, {18128, 37452}, {18383, 34799}, {19150, 43129}, {21849, 34484}, {25555, 34939}, {26883, 36747}, {32110, 32171}, {34417, 37493}, {34545, 43614}, {35268, 37486}, {37481, 43586}, {37948, 43806}, {43572, 43602}

X(43844) = midpoint of X(34148) and X(43605)
X(43844) = reflection of X(i) in X(j) for these {i,j}: {13367, 49}, {34826, 15806}
X(43844) = crosssum of X(4) and X(10018)
X(43844) = barycentric product X(394)*X(21841)
X(43844) = barycentric quotient X(21841)/X(2052)
X(43844) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 41597, 3292}, {52, 156, 1495}, {110, 12227, 16223}, {155, 184, 5562}, {195, 10540, 5446}, {394, 19347, 10984}, {578, 11441, 15030}, {1147, 18445, 185}, {1181, 3167, 1092}, {1199, 43598, 5943}, {1493, 5609, 546}, {3090, 11423, 575}, {3091, 11422, 37505}, {3574, 24981, 12134}, {5889, 9544, 10282}, {9545, 12111, 11430}, {9703, 34783, 12038}, {9704, 18436, 18475}, {10539, 12161, 51}, {12038, 34783, 21663}, {13352, 32139, 11381}, {15087, 18350, 5462}, {21659, 22660, 1531}

leftri

Special KM and MK perspectors: X(43845)-X(43868)

rightri

This preamble is contributed by Peter Moses and Clark Kimberling, June 23, 2021.

Let KM be the Kiss-Moses mapping, as introduced in the preamble just before X(43390). The appearance of (T,i) in the following list means that KM(KM(ABC)) is perspective to T, and the perspector is X(i).

(ABC, 54), (medial, 43817), (anticomplementary, 43816), (Euler, 43831), {O-reflection of ABC, 43601), (ABC-reflection of O in ABC, 43845), (Kosnita, 54), (X(5)-reflection of ABC, 43821), (Aquila, 43830), (Ara, 43829), (Caelum, 43824), (Mandart-incircle triangle, 43819), (3rd Hatzipolakis, 54), (intouch-of-orthic, 43823), (anti-Aquila, 43822), (anti-1st-Euler, 43822), (1st Johnson-Yff, 43833), (2nd Johnson-Yff, 43832), (infinite altitude, 13403), (anti-5th-Brocard, 43828), (anti-inner-Grebe, 43825), (anti-outer-Grebe, 43826), (2nd anti-circumperp-tangential, 43820), (Gemini 107, 43836), (Gemini 110, 43839), (Hatzipolakis-Moses, 54), (Gemini 111, 43838), (circum-orthic, 43846), (tangential triangle of 1st circumperp, 43847), (tangential triangle of 2nd circumperp, 43848), (Gossard, 43849), (1st Auriga, 43850), (2nd Auriga, 43851), (inner Grebe, 434852), (outer Grebe, 43853), (5th Brocard, 43854), (orthc-of intouch, 43855), (tangential-of-excentral, 43856), (inner Yff, 43857), (outer Yff, 43858), (inner Johnson, 43859), (outer Johnson, 43860), (inner Yff tangents, 43861), (outer Yff tangents, 43862), (3rd tri-squares central, 43863), (4th tri-squares central, 43864), (Ehrmann mid-triangle, 43865), (Gemini 109, 43866), (1st Kenmotu free vertices triangle, 43867), (2nd Kenmotu free vertices triangle, 43868)

For triangles T such that ABC is perspective to K(K(T)), see the preamble just before X(43816).



X(43845) = X(2)X(15806)∩X(3)X(54)

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 + a^4*b^2*c^2 + 5*a^2*b^4*c^2 - 2*b^6*c^2 + 6*a^4*c^4 + 5*a^2*b^2*c^4 + 2*b^4*c^4 - 4*a^2*c^6 - 2*b^2*c^6 + c^8) : :
X(43845) = X[399] - 4 X[40640], 3 X[13434] - X[43613], 2 X[36153] + X[43602], 6 X[36153] - X[43613], 3 X[43602] + X[43613]

X(43845) lies on these lines: {2, 15806}, {3, 54}, {4, 11538}, {5, 399}, {6, 382}, {23, 16881}, {30, 1199}, {49, 9730}, {52, 13564}, {74, 43612}, {110, 12006}, {143, 5899}, {155, 3526}, {156, 15043}, {182, 18436}, {184, 37481}, {185, 567}, {323, 3530}, {381, 1181}, {389, 2070}, {394, 15720}, {517, 43830}, {546, 34545}, {548, 37496}, {550, 1994}, {568, 2937}, {569, 34783}, {575, 12162}, {999, 43820}, {1092, 40280}, {1216, 13339}, {1351, 17710}, {1498, 18376}, {1511, 9706}, {1597, 35603}, {1598, 43823}, {1614, 5946}, {1656, 17814}, {1657, 36749}, {1658, 11003}, {2079, 9697}, {2904, 3516}, {3295, 43819}, {3520, 15041}, {3528, 11004}, {3534, 36747}, {3567, 18378}, {3574, 18128}, {3843, 11456}, {3851, 5422}, {3861, 12112}, {5050, 43810}, {5054, 37514}, {5055, 11441}, {5070, 15068}, {5072, 18451}, {5073, 39522}, {5076, 10982}, {5079, 10601}, {5446, 37924}, {5462, 10540}, {5562, 37471}, {5576, 18914}, {5609, 32205}, {5663, 13434}, {5790, 43827}, {5876, 43651}, {5944, 37922}, {6241, 33541}, {6243, 10984}, {6288, 10116}, {6417, 43826}, {6418, 43825}, {6639, 18916}, {6644, 9704}, {6759, 7545}, {7506, 19347}, {7517, 11432}, {7550, 31834}, {7689, 14805}, {8254, 10264}, {8550, 39562}, {8718, 37949}, {9654, 43833}, {9669, 43832}, {9703, 17928}, {9705, 43584}, {9729, 22115}, {10024, 11245}, {10095, 14157}, {10246, 43822}, {10247, 43824}, {10254, 18912}, {10255, 18952}, {10575, 37505}, {10625, 33542}, {11430, 35498}, {11597, 11806}, {11802, 21649}, {11842, 43828}, {11935, 22962}, {12083, 37493}, {12227, 15061}, {12233, 31724}, {12241, 31726}, {12315, 34117}, {12383, 36966}, {12834, 18874}, {12902, 34007}, {13160, 43588}, {13336, 23039}, {13353, 13754}, {13363, 22462}, {13366, 18859}, {13367, 37955}, {13382, 18364}, {13474, 15516}, {13491, 15033}, {14374, 15154}, {14375, 15155}, {14528, 16665}, {14926, 15056}, {15026, 21308}, {15035, 43603}, {15040, 22467}, {15053, 32171}, {15055, 43611}, {15062, 43596}, {15083, 43650}, {15106, 43608}, {15700, 37672}, {16270, 43617}, {17824, 20299}, {17835, 32401}, {17847, 25563}, {18381, 32395}, {22146, 41334}, {26201, 35197}, {27552, 33565}, {31804, 38321}, {34153, 43704}, {36179, 38581}, {37509, 37732}, {38638, 43804}

X(43845) = midpoint of X(13434) and X(43602)
X(43845) = reflection of X(i) in X(j) for these {i,j}: {13434, 36153}, {14627, 1199}, {34864, 13353}
X(43845) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5889, 12307}, {3, 6102, 32608}, {3, 7592, 15087}, {3, 12316, 6101}, {3, 15087, 195}, {4, 43575, 43835}, {4, 43838, 43575}, {5, 15037, 15047}, {5, 43808, 38724}, {49, 9730, 43809}, {49, 43809, 32609}, {54, 13630, 3}, {54, 43601, 43394}, {110, 43600, 12006}, {185, 567, 14130}, {185, 14130, 10620}, {399, 15047, 5}, {1181, 36753, 381}, {1614, 5946, 13621}, {3520, 43807, 15041}, {3521, 13403, 382}, {5012, 6102, 3}, {5422, 32139, 3851}, {5462, 10540, 18369}, {5609, 32205, 43614}, {5890, 7592, 32341}, {5890, 32046, 3}, {7517, 11432, 13321}, {9706, 43597, 1511}, {13363, 43598, 22462}, {13366, 40647, 37472}, {13630, 43394, 43601}, {15032, 15037, 399}, {18445, 36752, 1656}, {37472, 40647, 18859}, {43394, 43601, 3}, {43573, 43831, 43821}, {43821, 43831, 381}, {43867, 43868, 6}

X(43846) = X(4)X(3521)∩X(54)X(6000)

Barycentrics    a^2*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10 + a^8*c^2 + 3*a^6*b^2*c^2 - 6*a^4*b^4*c^2 - a^2*b^6*c^2 + 3*b^8*c^2 - 4*a^6*c^4 - 6*a^4*b^2*c^4 + 17*a^2*b^4*c^4 - 4*b^6*c^4 + 6*a^4*c^6 - a^2*b^2*c^6 - 4*b^4*c^6 - 4*a^2*c^8 + 3*b^2*c^8 + c^10) : :
X(43846) = 3 X[3521] - 4 X[13630], 3 X[5890] - 2 X[34563], 2 X[6101] - 3 X[18442], 5 X[11439] - 6 X[18488], 2 X[12162] - 3 X[15062]

X(43846) lies on these lines: {4, 3521}, {30, 6242}, {54, 6000}, {110, 3520}, {185, 10721}, {186, 8718}, {378, 9704}, {3518, 10575}, {5890, 34563}, {6030, 17506}, {6101, 18442}, {6143, 12292}, {6193, 35481}, {6241, 13403}, {6403, 29012}, {6776, 43818}, {7577, 11439}, {7699, 12290}, {7722, 18560}, {9544, 18439}, {11387, 12279}, {12133, 32205}, {15072, 43817}, {15103, 35240}, {15305, 43839}, {15462, 43613}, {17854, 22466}, {18435, 38942}, {31834, 35491}

X(43846) = reflection of X(i) in X(j) for these {i,j}: {4, 22948}, {15103, 35240}, {43599, 185}

X(43847) = X(5)X(13204)∩X(54)X(55)

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

X(43847) lies on these lines: {5, 13204}, {35, 43830}, {54, 55}, {56, 43824}, {100, 43816}, {185, 12327}, {197, 43829}, {1001, 43839}, {1376, 43817}, {3295, 43822}, {4421, 43573}, {5687, 43827}, {10267, 43394}, {10310, 43601}, {11248, 13630}, {11383, 43823}, {11490, 43828}, {11491, 43818}, {11496, 43831}, {11499, 43821}, {11500, 13403}, {11501, 43833}, {11502, 43832}, {11509, 43820}, {18524, 43835}, {18999, 43825}, {19000, 43826}, {32141, 43575}

X(43848) = X(5)X(22586)∩X(54)X(56)

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 + 2*a^9*b*c - a^8*b^2*c - 2*a^7*b^3*c + 6*a^6*b^4*c - 6*a^5*b^5*c - 2*a^4*b^6*c + 10*a^3*b^7*c - 5*a^2*b^8*c - 4*a*b^9*c + 3*b^10*c - 3*a^9*c^2 - a^8*b*c^2 + 13*a^7*b^2*c^2 - 5*a^6*b^3*c^2 - 12*a^5*b^4*c^2 + 12*a^4*b^5*c^2 - 3*a^3*b^6*c^2 - 5*a^2*b^7*c^2 + 5*a*b^8*c^2 - b^9*c^2 + 3*a^8*c^3 - 2*a^7*b*c^3 - 5*a^6*b^2*c^3 + 14*a^5*b^3*c^3 - 8*a^4*b^4*c^3 - 14*a^3*b^5*c^3 + 15*a^2*b^6*c^3 + 2*a*b^7*c^3 - 5*b^8*c^3 + 2*a^7*c^4 + 6*a^6*b*c^4 - 12*a^5*b^2*c^4 - 8*a^4*b^3*c^4 + 20*a^3*b^4*c^4 - 8*a^2*b^5*c^4 - 6*a*b^6*c^4 + 6*b^7*c^4 - 2*a^6*c^5 - 6*a^5*b*c^5 + 12*a^4*b^2*c^5 - 14*a^3*b^3*c^5 - 8*a^2*b^4*c^5 + 4*a*b^5*c^5 - 2*b^6*c^5 + 2*a^5*c^6 - 2*a^4*b*c^6 - 3*a^3*b^2*c^6 + 15*a^2*b^3*c^6 - 6*a*b^4*c^6 - 2*b^5*c^6 - 2*a^4*c^7 + 10*a^3*b*c^7 - 5*a^2*b^2*c^7 + 2*a*b^3*c^7 + 6*b^4*c^7 - 3*a^3*c^8 - 5*a^2*b*c^8 + 5*a*b^2*c^8 - 5*b^3*c^8 + 3*a^2*c^9 - 4*a*b*c^9 - b^2*c^9 + a*c^10 + 3*b*c^10 - c^11) : :

X(43848) lies on these lines: {5, 22586}, {36, 43830}, {54, 56}, {55, 43824}, {104, 43818}, {185, 22583}, {956, 43827}, {958, 43817}, {999, 43822}, {2975, 43816}, {3428, 43601}, {10269, 43394}, {10966, 43819}, {11194, 43573}, {11249, 13630}, {12114, 13403}, {19013, 43825}, {19014, 43826}, {22479, 43823}, {22520, 43828}, {22654, 43829}, {22753, 43831}, {22758, 43821}, {22759, 43833}, {22760, 43832}, {25524, 43839}, {26321, 43835}, {32153, 43575}

X(43849) = X(5)X(13212)∩X(54)X(402)

Barycentrics    (2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(a^12*b^6 - 6*a^10*b^8 + 15*a^8*b^10 - 20*a^6*b^12 + 15*a^4*b^14 - 6*a^2*b^16 + b^18 + a^12*b^4*c^2 + 4*a^10*b^6*c^2 - 28*a^8*b^8*c^2 + 52*a^6*b^10*c^2 - 43*a^4*b^12*c^2 + 16*a^2*b^14*c^2 - 2*b^16*c^2 + a^12*b^2*c^4 - 4*a^10*b^4*c^4 + 15*a^8*b^6*c^4 - 34*a^6*b^8*c^4 + 29*a^4*b^10*c^4 - 2*a^2*b^12*c^4 - 5*b^14*c^4 + a^12*c^6 + 4*a^10*b^2*c^6 + 15*a^8*b^4*c^6 + 4*a^6*b^6*c^6 - a^4*b^8*c^6 - 40*a^2*b^10*c^6 + 17*b^12*c^6 - 6*a^10*c^8 - 28*a^8*b^2*c^8 - 34*a^6*b^4*c^8 - a^4*b^6*c^8 + 64*a^2*b^8*c^8 - 11*b^10*c^8 + 15*a^8*c^10 + 52*a^6*b^2*c^10 + 29*a^4*b^4*c^10 - 40*a^2*b^6*c^10 - 11*b^8*c^10 - 20*a^6*c^12 - 43*a^4*b^2*c^12 - 2*a^2*b^4*c^12 + 17*b^6*c^12 + 15*a^4*c^14 + 16*a^2*b^2*c^14 - 5*b^4*c^14 - 6*a^2*c^16 - 2*b^2*c^16 + c^18) : :

X(43849) lies on these lines: {5, 13212}, {30, 43601}, {54, 402}, {185, 12369}, {1650, 43817}, {1651, 43573}, {4240, 43816}, {11251, 13630}, {11831, 43822}, {11832, 43823}, {11839, 43828}, {11845, 43818}, {11852, 43830}, {11853, 43829}, {11897, 43831}, {11900, 43827}, {11905, 43833}, {11906, 43832}, {11909, 43819}, {11910, 43824}, {12113, 13403}, {15183, 43839}, {18508, 43835}, {18958, 43820}, {19017, 43825}, {19018, 43826}, {26451, 43394}, {32162, 43575}

X(43850) = X(5)X(13208)∩X(54)X(5597)

Barycentrics    a*(a^12 - a^11*b - 3*a^10*b^2 + 3*a^9*b^3 + 2*a^8*b^4 - 2*a^7*b^5 + 2*a^6*b^6 - 2*a^5*b^7 - 3*a^4*b^8 + 3*a^3*b^9 + a^2*b^10 - a*b^11 - a^11*c + 3*a^9*b^2*c - 2*a^7*b^4*c - 2*a^5*b^6*c + 3*a^3*b^8*c - a*b^10*c a*((a^8*b - a^7*b^2 - 2*a^6*b^3 + 3*a^5*b^4 - 3*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9 + a^8*c - 2*a^7*b*c + 2*a^5*b^3*c - 2*a^4*b^4*c + 2*a^3*b^5*c - 2*a*b^7*c + b^8*c - a^7*c^2 - 2*a^5*b^2*c^2 + 3*a^4*b^3*c^2 + 4*a^3*b^4*c^2 - 5*a^2*b^5*c^2 - a*b^6*c^2 + 2*b^7*c^2 - 2*a^6*c^3 + 2*a^5*b*c^3 + 3*a^4*b^2*c^3 - 6*a^3*b^3*c^3 + 3*a^2*b^4*c^3 + 2*a*b^5*c^3 - 2*b^6*c^3 + 3*a^5*c^4 - 2*a^4*b*c^4 + 4*a^3*b^2*c^4 + 3*a^2*b^3*c^4 + 2*a^3*b*c^5 - 5*a^2*b^2*c^5 + 2*a*b^3*c^5 - 3*a^3*c^6 - a*b^2*c^6 - 2*b^3*c^6 + 2*a^2*c^7 - 2*a*b*c^7 + 2*b^2*c^7 + a*c^8 + b*c^8 - c^9)*Sqrt[R*(r + 4*R)] + a*(a - b - c)*(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)*S) : :

X(43850) lies on these lines: {5, 13208}, {54, 5597}, {185, 12365}, {5598, 43824}, {5599, 43817}, {5601, 43816}, {8186, 43830}, {8190, 43829}, {8196, 43831}, {8197, 43827}, {8200, 43821}, {9834, 13403}, {11207, 43573}, {11252, 13630}, {11366, 43822}, {11384, 43823}, {11822, 43601}, {11837, 43828}, {11843, 43818}, {11869, 43833}, {11871, 43832}, {11873, 43819}, {18955, 43820}, {19007, 43825}, {19008, 43826}, {32146, 43575}

X(43851) = X(5)X(13209)∩X(54)X(5598)

Barycentrics    a*((a^8*b - a^7*b^2 - 2*a^6*b^3 + 3*a^5*b^4 - 3*a^3*b^6 + 2*a^2*b^7 + a*b^8 - b^9 + a^8*c - 2*a^7*b*c + 2*a^5*b^3*c - 2*a^4*b^4*c + 2*a^3*b^5*c - 2*a*b^7*c + b^8*c - a^7*c^2 - 2*a^5*b^2*c^2 + 3*a^4*b^3*c^2 + 4*a^3*b^4*c^2 - 5*a^2*b^5*c^2 - a*b^6*c^2 + 2*b^7*c^2 - 2*a^6*c^3 + 2*a^5*b*c^3 + 3*a^4*b^2*c^3 - 6*a^3*b^3*c^3 + 3*a^2*b^4*c^3 + 2*a*b^5*c^3 - 2*b^6*c^3 + 3*a^5*c^4 - 2*a^4*b*c^4 + 4*a^3*b^2*c^4 + 3*a^2*b^3*c^4 + 2*a^3*b*c^5 - 5*a^2*b^2*c^5 + 2*a*b^3*c^5 - 3*a^3*c^6 - a*b^2*c^6 - 2*b^3*c^6 + 2*a^2*c^7 - 2*a*b*c^7 + 2*b^2*c^7 + a*c^8 + b*c^8 - c^9)*Sqrt[R*(r + 4*R)] - a*(a - b - c)*(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)*S) : :

X(43851) lies on these lines: {5, 13209}, {54, 5598}, {185, 12366}, {5597, 43824}, {5600, 43817}, {5602, 43816}, {8187, 43830}, {8191, 43829}, {8203, 43831}, {8204, 43827}, {8207, 43821}, {9835, 13403}, {11208, 43573}, {11253, 13630}, {11367, 43822}, {11385, 43823}, {11823, 43601}, {11838, 43828}, {11844, 43818}, {11870, 43833}, {11872, 43832}, {11874, 43819}, {18956, 43820}, {19009, 43825}, {19010, 43826}, {32147, 43575}

X(43852) = X(5)X(7732)∩X(6)X(24)

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

X(43852) lies on these lines: {5, 7732}, {6, 24}, {185, 7725}, {1161, 13630}, {1271, 43816}, {5589, 43830}, {5591, 43817}, {5595, 43829}, {5605, 43824}, {5689, 43827}, {5861, 43573}, {5871, 13403}, {5875, 43575}, {6202, 43831}, {6215, 43821}, {10783, 43818}, {10792, 43828}, {10923, 43833}, {10925, 43832}, {10927, 43819}, {11370, 43822}, {11388, 43823}, {11824, 43601}, {18959, 43820}, {26336, 43835}, {26341, 43394}, {33749, 42858}

X(43853) = X(5)X(7733)∩X(6)X(24)

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

X(43853) lies on these lines: {5, 7733}, {6, 24}, {185, 7726}, {1160, 13630}, {1270, 43816}, {5588, 43830}, {5590, 43817}, {5594, 43829}, {5604, 43824}, {5688, 43827}, {5860, 43573}, {5870, 13403}, {5874, 43575}, {6201, 43831}, {6214, 43821}, {10784, 43818}, {10793, 43828}, {10924, 43833}, {10926, 43832}, {10928, 43819}, {11371, 43822}, {11389, 43823}, {11825, 43601}, {18960, 43820}, {26346, 43835}, {26348, 43394}, {33749, 42859}

X(43854) = X(5)X(13210)∩X(32)X(54)

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

X(43854) lies on these lines: {5, 13210}, {32, 54}, {185, 9984}, {2896, 43816}, {3096, 43817}, {3098, 21734}, {3099, 43830}, {7811, 43573}, {7846, 43839}, {7865, 43836}, {9821, 13630}, {9857, 43827}, {9862, 43818}, {9873, 13403}, {9993, 43831}, {9996, 43821}, {9997, 43824}, {10828, 43829}, {10873, 43833}, {10874, 43832}, {10877, 43819}, {11368, 43822}, {11386, 43823}, {18503, 43835}, {18957, 43820}, {19011, 43825}, {19012, 43826}, {26316, 43394}, {32151, 43575}

X(43855) = X(1)X(43601)∩X(54)X(57)

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

X(43855) lies on these lines: {1, 43601}, {7, 43816}, {54, 57}, {56, 43822}, {65, 43820}, {226, 43817}, {354, 43819}, {388, 43827}, {553, 43573}, {942, 13630}, {950, 43577}, {1210, 43831}, {1836, 43832}, {1876, 43823}, {3339, 43830}, {3340, 43824}, {3521, 5722}, {3911, 43839}, {4292, 13403}, {4654, 43836}, {10404, 43833}, {15806, 34753}, {18541, 43835}, {21454, 43838}, {24470, 43575}, {37582, 43394}

X(43856) = X(9)X(43817)∩X(54)X(57)

Barycentrics    a*(a^12 - 4*a^10*b^2 + 5*a^8*b^4 - 5*a^4*b^8 + 4*a^2*b^10 - b^12 - 2*a^10*b*c + 6*a^8*b^3*c - 8*a^6*b^5*c + 8*a^4*b^7*c - 6*a^2*b^9*c + 2*b^11*c - 4*a^10*c^2 + 11*a^8*b^2*c^2 - 11*a^6*b^4*c^2 + 7*a^4*b^6*c^2 - 5*a^2*b^8*c^2 + 2*b^10*c^2 + 6*a^8*b*c^3 - 2*a^6*b^3*c^3 - 12*a^4*b^5*c^3 + 14*a^2*b^7*c^3 - 6*b^9*c^3 + 5*a^8*c^4 - 11*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*b*c^5 - 12*a^4*b^3*c^5 - 16*a^2*b^5*c^5 + 4*b^7*c^5 + 7*a^4*b^2*c^6 + a^2*b^4*c^6 - 4*b^6*c^6 + 8*a^4*b*c^7 + 14*a^2*b^3*c^7 + 4*b^5*c^7 - 5*a^4*c^8 - 5*a^2*b^2*c^8 + b^4*c^8 - 6*a^2*b*c^9 - 6*b^3*c^9 + 4*a^2*c^10 + 2*b^2*c^10 + 2*b*c^11 - c^12) : :

X(43856) lies on these lines: {9, 43817}, {40, 43601}, {46, 43830}, {54, 57}, {63, 43816}, {84, 13403}, {1697, 43824}, {3218, 43838}, {3220, 43829}, {3333, 43822}, {3928, 43573}, {3929, 43836}, {5437, 43839}, {5709, 13630}, {7330, 43821}, {24467, 43575}, {30223, 43832}, {37534, 43394}, {37550, 43820}

X(43857) = X(1)X(54)∩X(3)X(43820)

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

X(43857) lies on these lines: {1, 54}, {3, 43820}, {5, 10088}, {12, 43821}, {35, 43601}, {49, 10091}, {55, 13630}, {56, 43394}, {185, 10065}, {388, 43818}, {495, 43575}, {496, 15806}, {498, 43817}, {499, 43839}, {1478, 13403}, {1479, 43831}, {2330, 43810}, {3028, 14130}, {3085, 43816}, {3295, 43819}, {3299, 43825}, {3301, 43826}, {3520, 10081}, {3521, 6284}, {3584, 43836}, {4302, 43577}, {9654, 43835}, {10037, 43829}, {10039, 43827}, {10056, 43573}, {10801, 43828}, {11398, 43823}, {12896, 34007}, {15062, 19470}

X(43857) = {X(495),X(43575)}-harmonic conjugate of X(43833)

X(43858) = X(1)X(54)∩X(3)X(43819)

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

X(43858) lies on these lines: {1, 54}, {3, 43819}, {5, 10091}, {11, 43821}, {36, 43601}, {49, 10088}, {55, 43394}, {56, 13630}, {185, 10081}, {495, 15806}, {496, 43575}, {497, 43818}, {498, 43839}, {499, 43817}, {999, 43820}, {1428, 43810}, {1478, 43831}, {1479, 13403}, {1737, 43827}, {3024, 14130}, {3086, 43816}, {3299, 43826}, {3301, 43825}, {3520, 10065}, {3521, 7354}, {3582, 43836}, {4299, 43577}, {7727, 15062}, {9669, 43835}, {10046, 43829}, {10072, 43573}, {10149, 37472}, {10802, 43828}, {11399, 43823}, {14986, 43838}, {18968, 34007}

X(43858) = {X(496),X(43575)}-harmonic conjugate of X(43832)

X(43859) = X(5)X(13213)∩X(11)X(54)

Barycentrics    a^13 - a^12*b - 3*a^11*b^2 + 3*a^10*b^3 + 3*a^9*b^4 - 3*a^8*b^5 - 2*a^7*b^6 + 2*a^6*b^7 + 3*a^5*b^8 - 3*a^4*b^9 - 3*a^3*b^10 + 3*a^2*b^11 + a*b^12 - b^13 - a^12*c + 2*a^11*b*c + 3*a^10*b^2*c - 6*a^9*b^3*c - 3*a^8*b^4*c + 8*a^7*b^5*c - 8*a^5*b^7*c + 3*a^4*b^8*c + 6*a^3*b^9*c - 3*a^2*b^10*c - 2*a*b^11*c + b^12*c - 3*a^11*c^2 + 3*a^10*b*c^2 + 3*a^9*b^2*c^2 - 3*a^8*b^3*c^2 + 2*a^7*b^4*c^2 - 4*a^6*b^5*c^2 - 3*a^5*b^6*c^2 + 9*a^4*b^7*c^2 + 3*a^3*b^8*c^2 - 9*a^2*b^9*c^2 - 2*a*b^10*c^2 + 4*b^11*c^2 + 3*a^10*c^3 - 6*a^9*b*c^3 - 3*a^8*b^2*c^3 + 2*a^7*b^3*c^3 + 2*a^6*b^4*c^3 + 12*a^5*b^5*c^3 - 7*a^4*b^6*c^3 - 14*a^3*b^7*c^3 + 9*a^2*b^8*c^3 + 6*a*b^9*c^3 - 4*b^10*c^3 + 3*a^9*c^4 - 3*a^8*b*c^4 + 2*a^7*b^2*c^4 + 2*a^6*b^3*c^4 - 8*a^5*b^4*c^4 - 2*a^4*b^5*c^4 + 12*a^2*b^7*c^4 - a*b^8*c^4 - 5*b^9*c^4 - 3*a^8*c^5 + 8*a^7*b*c^5 - 4*a^6*b^2*c^5 + 12*a^5*b^3*c^5 - 2*a^4*b^4*c^5 + 16*a^3*b^5*c^5 - 12*a^2*b^6*c^5 - 4*a*b^7*c^5 + 5*b^8*c^5 - 2*a^7*c^6 - 3*a^5*b^2*c^6 - 7*a^4*b^3*c^6 - 12*a^2*b^5*c^6 + 4*a*b^6*c^6 + 2*a^6*c^7 - 8*a^5*b*c^7 + 9*a^4*b^2*c^7 - 14*a^3*b^3*c^7 + 12*a^2*b^4*c^7 - 4*a*b^5*c^7 + 3*a^5*c^8 + 3*a^4*b*c^8 + 3*a^3*b^2*c^8 + 9*a^2*b^3*c^8 - a*b^4*c^8 + 5*b^5*c^8 - 3*a^4*c^9 + 6*a^3*b*c^9 - 9*a^2*b^2*c^9 + 6*a*b^3*c^9 - 5*b^4*c^9 - 3*a^3*c^10 - 3*a^2*b*c^10 - 2*a*b^2*c^10 - 4*b^3*c^10 + 3*a^2*c^11 - 2*a*b*c^11 + 4*b^2*c^11 + a*c^12 + b*c^12 - c^13 : :

X(43859) lies on these lines: {5, 13213}, {11, 54}, {185, 12371}, {355, 43821}, {1376, 43817}, {3434, 43816}, {10525, 13630}, {10785, 43818}, {10794, 43828}, {10826, 43830}, {10829, 43829}, {10893, 43831}, {10914, 43827}, {10943, 43575}, {10944, 43824}, {10947, 43819}, {11235, 43573}, {11373, 43822}, {11390, 43823}, {11826, 43601}, {12114, 13403}, {18519, 43835}, {18961, 43820}, {19023, 43825}, {19024, 43826}, {26492, 43394}, {34612, 43836}

X(43860) = X(5)X(13214)∩X(12)X(54)

Barycentrics    a^13 - a^12*b - 3*a^11*b^2 + 3*a^10*b^3 + 3*a^9*b^4 - 3*a^8*b^5 - 2*a^7*b^6 + 2*a^6*b^7 + 3*a^5*b^8 - 3*a^4*b^9 - 3*a^3*b^10 + 3*a^2*b^11 + a*b^12 - b^13 - a^12*c + 2*a^11*b*c - a^10*b^2*c - 2*a^9*b^3*c + 5*a^8*b^4*c - 4*a^7*b^5*c + 4*a^5*b^7*c - 5*a^4*b^8*c + 2*a^3*b^9*c + a^2*b^10*c - 2*a*b^11*c + b^12*c - 3*a^11*c^2 - a^10*b*c^2 + 11*a^9*b^2*c^2 - 3*a^8*b^3*c^2 - 6*a^7*b^4*c^2 + 4*a^6*b^5*c^2 - 11*a^5*b^6*c^2 + 9*a^4*b^7*c^2 + 11*a^3*b^8*c^2 - 13*a^2*b^9*c^2 - 2*a*b^10*c^2 + 4*b^11*c^2 + 3*a^10*c^3 - 2*a^9*b*c^3 - 3*a^8*b^2*c^3 + 10*a^7*b^3*c^3 - 10*a^6*b^4*c^3 - 4*a^5*b^5*c^3 + 13*a^4*b^6*c^3 - 10*a^3*b^7*c^3 + a^2*b^8*c^3 + 6*a*b^9*c^3 - 4*b^10*c^3 + 3*a^9*c^4 + 5*a^8*b*c^4 - 6*a^7*b^2*c^4 - 10*a^6*b^3*c^4 + 16*a^5*b^4*c^4 - 14*a^4*b^5*c^4 - 8*a^3*b^6*c^4 + 20*a^2*b^7*c^4 - a*b^8*c^4 - 5*b^9*c^4 - 3*a^8*c^5 - 4*a^7*b*c^5 + 4*a^6*b^2*c^5 - 4*a^5*b^3*c^5 - 14*a^4*b^4*c^5 + 16*a^3*b^5*c^5 - 12*a^2*b^6*c^5 - 4*a*b^7*c^5 + 5*b^8*c^5 - 2*a^7*c^6 - 11*a^5*b^2*c^6 + 13*a^4*b^3*c^6 - 8*a^3*b^4*c^6 - 12*a^2*b^5*c^6 + 4*a*b^6*c^6 + 2*a^6*c^7 + 4*a^5*b*c^7 + 9*a^4*b^2*c^7 - 10*a^3*b^3*c^7 + 20*a^2*b^4*c^7 - 4*a*b^5*c^7 + 3*a^5*c^8 - 5*a^4*b*c^8 + 11*a^3*b^2*c^8 + a^2*b^3*c^8 - a*b^4*c^8 + 5*b^5*c^8 - 3*a^4*c^9 + 2*a^3*b*c^9 - 13*a^2*b^2*c^9 + 6*a*b^3*c^9 - 5*b^4*c^9 - 3*a^3*c^10 + a^2*b*c^10 - 2*a*b^2*c^10 - 4*b^3*c^10 + 3*a^2*c^11 - 2*a*b*c^11 + 4*b^2*c^11 + a*c^12 + b*c^12 - c^13 : :

X(43860) lies on these lines: {5, 13214}, {12, 54}, {72, 43827}, {185, 12372}, {355, 43821}, {958, 43817}, {3436, 43816}, {10526, 13630}, {10786, 43818}, {10795, 43828}, {10827, 43830}, {10830, 43829}, {10894, 43831}, {10942, 43575}, {10950, 43824}, {10953, 43819}, {11236, 43573}, {11374, 43822}, {11391, 43823}, {11500, 13403}, {11827, 43601}, {18518, 43835}, {18962, 43820}, {19025, 43825}, {19026, 43826}, {26487, 43394}, {34606, 43836}

X(43861) = X(1)X(54)∩X(5)X(13217)

Barycentrics    a^2*(a^11 - a^10*b - 4*a^9*b^2 + 4*a^8*b^3 + 6*a^7*b^4 - 6*a^6*b^5 - 4*a^5*b^6 + 4*a^4*b^7 + a^3*b^8 - a^2*b^9 - a^10*c + 6*a^8*b^2*c - 4*a^7*b^3*c - 8*a^6*b^4*c + 12*a^5*b^5*c - 2*a^4*b^6*c - 12*a^3*b^7*c + 9*a^2*b^8*c + 4*a*b^9*c - 4*b^10*c - 4*a^9*c^2 + 6*a^8*b*c^2 + a^7*b^2*c^2 - 3*a^6*b^3*c^2 + 3*a^5*b^4*c^2 - 9*a^4*b^5*c^2 + 7*a^3*b^6*c^2 + 3*a^2*b^7*c^2 - 7*a*b^8*c^2 + 3*b^9*c^2 + 4*a^8*c^3 - 4*a^7*b*c^3 - 3*a^6*b^2*c^3 - 8*a^5*b^3*c^3 + 11*a^4*b^4*c^3 + 16*a^3*b^5*c^3 - 21*a^2*b^6*c^3 - 4*a*b^7*c^3 + 9*b^8*c^3 + 6*a^7*c^4 - 8*a^6*b*c^4 + 3*a^5*b^2*c^4 + 11*a^4*b^3*c^4 - 24*a^3*b^4*c^4 + 10*a^2*b^5*c^4 + 7*a*b^6*c^4 - 5*b^7*c^4 - 6*a^6*c^5 + 12*a^5*b*c^5 - 9*a^4*b^2*c^5 + 16*a^3*b^3*c^5 + 10*a^2*b^4*c^5 - 3*b^6*c^5 - 4*a^5*c^6 - 2*a^4*b*c^6 + 7*a^3*b^2*c^6 - 21*a^2*b^3*c^6 + 7*a*b^4*c^6 - 3*b^5*c^6 + 4*a^4*c^7 - 12*a^3*b*c^7 + 3*a^2*b^2*c^7 - 4*a*b^3*c^7 - 5*b^4*c^7 + a^3*c^8 + 9*a^2*b*c^8 - 7*a*b^2*c^8 + 9*b^3*c^8 - a^2*c^9 + 4*a*b*c^9 + 3*b^2*c^9 - 4*b*c^10) : :

X(43861) lies on these lines: {1, 54}, {5, 13217}, {185, 12381}, {5552, 43817}, {10528, 43816}, {10531, 43831}, {10679, 13630}, {10803, 43828}, {10805, 43818}, {10834, 43829}, {10915, 43827}, {10942, 43821}, {10956, 43833}, {10958, 43832}, {10965, 43819}, {11239, 43573}, {11248, 43601}, {11400, 43823}, {11509, 43820}, {12115, 13403}, {16203, 43394}, {18545, 43835}, {19047, 43825}, {19048, 43826}, {32213, 43575}

X(43862) = X(1)X(54)∩X(5)X(13218)

Barycentrics    a^2*(a^11 - a^10*b - 4*a^9*b^2 + 4*a^8*b^3 + 6*a^7*b^4 - 6*a^6*b^5 - 4*a^5*b^6 + 4*a^4*b^7 + a^3*b^8 - a^2*b^9 - a^10*c + 4*a^9*b*c - 2*a^8*b^2*c - 8*a^7*b^3*c + 8*a^6*b^4*c - 2*a^4*b^6*c + 8*a^3*b^7*c - 7*a^2*b^8*c - 4*a*b^9*c + 4*b^10*c - 4*a^9*c^2 - 2*a^8*b*c^2 + 17*a^7*b^2*c^2 - 3*a^6*b^3*c^2 - 13*a^5*b^4*c^2 + 7*a^4*b^5*c^2 - 9*a^3*b^6*c^2 + 3*a^2*b^7*c^2 + 9*a*b^8*c^2 - 5*b^9*c^2 + 4*a^8*c^3 - 8*a^7*b*c^3 - 3*a^6*b^2*c^3 + 20*a^5*b^3*c^3 - 13*a^4*b^4*c^3 - 12*a^3*b^5*c^3 + 19*a^2*b^6*c^3 - 7*b^8*c^3 + 6*a^7*c^4 + 8*a^6*b*c^4 - 13*a^5*b^2*c^4 - 13*a^4*b^3*c^4 + 24*a^3*b^4*c^4 - 14*a^2*b^5*c^4 - 9*a*b^6*c^4 + 11*b^7*c^4 - 6*a^6*c^5 + 7*a^4*b^2*c^5 - 12*a^3*b^3*c^5 - 14*a^2*b^4*c^5 + 8*a*b^5*c^5 - 3*b^6*c^5 - 4*a^5*c^6 - 2*a^4*b*c^6 - 9*a^3*b^2*c^6 + 19*a^2*b^3*c^6 - 9*a*b^4*c^6 - 3*b^5*c^6 + 4*a^4*c^7 + 8*a^3*b*c^7 + 3*a^2*b^2*c^7 + 11*b^4*c^7 + a^3*c^8 - 7*a^2*b*c^8 + 9*a*b^2*c^8 - 7*b^3*c^8 - a^2*c^9 - 4*a*b*c^9 - 5*b^2*c^9 + 4*b*c^10) : :

X(43862) lies on these lines: {1, 54}, {5, 13218}, {185, 12382}, {10527, 43817}, {10529, 43816}, {10532, 43831}, {10680, 13630}, {10804, 43828}, {10806, 43818}, {10835, 43829}, {10916, 43827}, {10943, 43821}, {10957, 43833}, {10959, 43832}, {10966, 43819}, {11240, 43573}, {11249, 43601}, {11401, 43823}, {12116, 13403}, {16202, 43394}, {18543, 43835}, {18967, 43820}, {19049, 43825}, {19050, 43826}, {32214, 43575}

X(43863) = X(2)X(43826)∩X(54)X(3068)

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

X(43863) lies on these lines: {2, 43826}, {5, 8998}, {6, 43839}, {54, 3068}, {185, 8994}, {371, 43831}, {485, 13403}, {590, 43817}, {1151, 43577}, {3521, 6221}, {6143, 19111}, {7583, 43394}, {7585, 43825}, {8972, 43816}, {8976, 43821}, {8981, 13630}, {9540, 43601}, {13846, 43573}, {13883, 43822}, {13884, 43823}, {13885, 43828}, {13886, 43818}, {13888, 43830}, {13889, 43829}, {13893, 43827}, {13897, 43833}, {13898, 43832}, {13901, 43819}, {13902, 43824}, {13925, 43575}, {18965, 43820}

X(43864) = X(2)X(43825)∩X(54)X(3069)

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

X(43864) lies on these lines: {2, 43825}, {5, 13990}, {6, 43839}, {54, 3069}, {185, 13969}, {372, 43831}, {486, 13403}, {615, 43817}, {1152, 43577}, {3521, 6398}, {6143, 19110}, {7584, 43394}, {7586, 43826}, {13630, 13966}, {13847, 43573}, {13935, 43601}, {13936, 43822}, {13937, 43823}, {13938, 43828}, {13939, 43818}, {13941, 43816}, {13942, 43830}, {13943, 43829}, {13947, 43827}, {13951, 43821}, {13954, 43833}, {13955, 43832}, {13958, 43819}, {13959, 43824}, {13993, 43575}, {18966, 43820}

X(43865) = X(4)X(3521)∩X(54)X(156)

Barycentrics    2*a^10 - 3*a^8*b^2 - a^6*b^4 + a^4*b^6 + 3*a^2*b^8 - 2*b^10 - 3*a^8*c^2 + 8*a^6*b^2*c^2 - 11*a^2*b^6*c^2 + 6*b^8*c^2 - a^6*c^4 + 16*a^2*b^4*c^4 - 4*b^6*c^4 + a^4*c^6 - 11*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(43865) lies on these lines: {4, 3521}, {5, 1511}, {30, 43817}, {51, 18567}, {54, 156}, {68, 5876}, {143, 18403}, {185, 1539}, {382, 43601}, {403, 5944}, {546, 6146}, {973, 18377}, {1478, 43832}, {1479, 43833}, {1493, 5448}, {1514, 3861}, {1594, 15807}, {2883, 3845}, {3091, 43818}, {3520, 20304}, {3583, 43819}, {3585, 43820}, {3627, 15873}, {3830, 43836}, {3832, 18430}, {3839, 43838}, {3843, 11456}, {3850, 15806}, {3851, 18392}, {5446, 18572}, {5498, 23515}, {6102, 18390}, {6153, 43583}, {7728, 43808}, {9818, 43829}, {9927, 15060}, {9955, 43822}, {10226, 34128}, {10263, 18404}, {10610, 13406}, {10721, 43807}, {10733, 43809}, {11017, 41171}, {11799, 13470}, {12041, 18560}, {12241, 23323}, {12699, 43827}, {12897, 37938}, {12902, 43598}, {13363, 34007}, {13567, 34798}, {13665, 43826}, {13785, 43825}, {14130, 14644}, {14269, 43837}, {15059, 35498}, {15062, 38724}, {18386, 35603}, {18492, 43830}, {18502, 43828}, {18525, 43824}, {20396, 43608}, {25739, 32137}, {26917, 32210}, {32046, 35488}, {32533, 43834}, {36990, 43810}, {38136, 41729}, {38790, 43806}

X(43865) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 43816, 3521}, {4, 43821, 13630}, {5, 13403, 43394}, {381, 9704, 18504}, {381, 18379, 22804}, {381, 43835, 54}, {546, 43575, 43831}, {3521, 43816, 13630}, {3521, 43821, 43816}

X(43866) = X(2)X(54)∩X(5)X(74)

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

X(43866) lies on these lines: {2, 54}, {5, 74}, {10, 43824}, {113, 43806}, {125, 43598}, {140, 43821}, {590, 43826}, {615, 43825}, {631, 13403}, {632, 43575}, {1125, 43827}, {1614, 26913}, {1656, 12111}, {3090, 26937}, {3091, 43577}, {3520, 22962}, {3525, 43818}, {3526, 43394}, {3545, 20427}, {3624, 43822}, {5054, 43835}, {5070, 15068}, {5094, 43823}, {5432, 43832}, {5433, 43833}, {5446, 30745}, {5640, 31283}, {5972, 9705}, {6030, 18282}, {6143, 6723}, {6640, 15033}, {7484, 43829}, {7723, 12006}, {7808, 43828}, {8718, 37943}, {9140, 18350}, {9781, 30744}, {10255, 15053}, {10721, 43604}, {10733, 43615}, {11412, 26958}, {11704, 17928}, {12900, 43596}, {12901, 14644}, {13371, 38848}, {13561, 43614}, {14130, 34128}, {16238, 25739}, {16261, 40686}, {20304, 43809}, {23515, 34007}, {24206, 43810}, {34330, 37471}

X(43866) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 43816, 43839}, {2, 43817, 54}, {5, 15061, 15062}, {5, 43608, 43613}, {54, 43817, 43836}, {54, 43836, 43837}, {5972, 43808, 9705}, {26958, 31282, 11412}, {43816, 43839, 54}, {43817, 43839, 43816}

X(43867) = X(6)X(382)∩X(54)X(372)

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

X(43867) lies on these lines: {5, 12375}, {6, 382}, {54, 372}, {185, 35826}, {371, 13630}, {485, 43816}, {615, 15806}, {1587, 43838}, {3070, 43575}, {6200, 43601}, {6396, 43394}, {6419, 43826}, {6560, 43818}, {6564, 43821}, {6565, 43831}, {9706, 10820}, {10576, 43817}, {10665, 43839}, {10819, 43597}, {14130, 35827}, {19060, 43612}, {19111, 43600}, {23251, 43835}, {34007, 35835}, {35762, 43822}, {35764, 43823}, {35766, 43828}, {35768, 43820}, {35770, 43825}, {35774, 43830}, {35776, 43829}, {35788, 43827}, {35800, 43833}, {35802, 43832}, {35808, 43819}, {35810, 43824}, {35822, 43573}, {42266, 43577}

X(43867) = {X(6),X(43845)}-harmonic conjugate of X(43868)

X(43868) = X(6)X(382)∩X(54)X(371)

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

X(43868) lies on these lines: {5, 12376}, {6, 382}, {54, 371}, {185, 35827}, {372, 13630}, {486, 43816}, {590, 15806}, {1588, 43838}, {3071, 43575}, {6200, 43394}, {6396, 43601}, {6420, 43825}, {6561, 43818}, {6564, 43831}, {6565, 43821}, {9706, 10819}, {10577, 43817}, {10666, 43839}, {10820, 43597}, {14130, 35826}, {19059, 43612}, {19110, 43600}, {23261, 43835}, {34007, 35834}, {35763, 43822}, {35765, 43823}, {35767, 43828}, {35769, 43820}, {35771, 43826}, {35775, 43830}, {35777, 43829}, {35789, 43827}, {35801, 43833}, {35803, 43832}, {35809, 43819}, {35811, 43824}, {35823, 43573}, {42267, 43577}

X(43868) = {X(6),X(43845)}-harmonic conjugate of X(43867)

leftri

Gibert points on the cubic K1234: X(43869)-X(43890)

rightri

This preamble and points X(43869)-X(43890) are contributed by Peter Moses, June 23, 2021. See also the preambles just before X(42085), X(42413), and X(42429) and others.

See K1234.



X(43869) = GIBERT (4,1,10) POINT

Barycentrics    2*Sqrt[3]*a^2*S + 15*a^2*SA + 3*SB*SC : :
X(43869) = X[43364] - 4 X[43463], 4 X[43364] - 3 X[43477], 16 X[43463] - 3 X[43477]

X(43869) lies on the cubic K1234 and these lines: {2, 5321}, {4, 42585}, {6, 15717}, {15, 3523}, {16, 15692}, {20, 10645}, {30, 43364}, {140, 43778}, {376, 42124}, {631, 11543}, {3090, 42122}, {3091, 5352}, {3146, 23302}, {3522, 5340}, {3524, 11485}, {3525, 42117}, {3528, 11542}, {3529, 42132}, {3533, 42125}, {3534, 42627}, {3543, 16241}, {3545, 42130}, {3832, 42087}, {3839, 16966}, {3853, 42950}, {3855, 42144}, {3860, 42984}, {4232, 11475}, {5055, 43630}, {5056, 42085}, {5059, 42142}, {5067, 42126}, {5068, 42140}, {5071, 42136}, {5238, 5334}, {5265, 10638}, {5281, 7051}, {5335, 10304}, {5365, 42914}, {7486, 33417}, {8703, 42817}, {10299, 11486}, {10654, 15721}, {11001, 42138}, {11489, 36836}, {11540, 43639}, {11812, 42923}, {12108, 42818}, {14869, 42816}, {15022, 42093}, {15640, 37832}, {15683, 42094}, {15688, 43542}, {15694, 43482}, {15697, 42100}, {15698, 42912}, {15702, 42129}, {15705, 37640}, {15706, 42633}, {15708, 16268}, {15709, 42690}, {15710, 42974}, {15720, 43464}, {16644, 42141}, {16772, 21734}, {16808, 42798}, {16961, 42511}, {17538, 42128}, {17578, 42098}, {18581, 43243}, {19708, 42123}, {19709, 42492}, {19781, 37665}, {21735, 42118}, {22237, 23303}, {33607, 43330}, {33703, 42146}, {33923, 42815}, {34200, 42916}, {40693, 43242}, {42104, 42936}, {42105, 42529}, {42107, 43770}, {42108, 42472}, {42109, 42494}, {42110, 42626}, {42111, 43294}, {42112, 42488}, {42114, 42434}, {42150, 42959}, {42152, 42982}, {42155, 43296}, {42164, 42473}, {42260, 42562}, {42261, 42563}, {42475, 43202}, {42510, 42896}, {42632, 43227}, {42682, 43194}, {42779, 42928}, {42802, 42998}, {42919, 42929}, {42925, 42987}, {42949, 43474}, {42955, 43632}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3522, 11488, 43465}, {3522, 42945, 43479}, {3522, 43479, 22235}, {5056, 42085, 43365}, {11488, 43465, 22235}, {15708, 42983, 42089}, {15710, 43493, 42974}, {19708, 42986, 42123}, {33417, 42133, 7486}, {42130, 43103, 3545}, {42139, 42589, 5321}, {42140, 43029, 5068}, {42492, 42888, 19709}, {43465, 43479, 11488}

X(43870) = GIBERT (-4,1,10) POINT

Barycentrics    2*Sqrt[3]*a^2*S - 15*a^2*SA - 3*SB*SC : :
X(43870) = X[43365] - 4 X[43464], 4 X[43365] - 3 X[43478], 16 X[43464] - 3 X[43478]

X(43870) lies on the cubic K1234 and these lines: {2, 5318}, {4, 42584}, {6, 15717}, {15, 15692}, {16, 3523}, {20, 10646}, {30, 43365}, {140, 43777}, {376, 42121}, {631, 11542}, {1250, 5265}, {3090, 42123}, {3091, 5351}, {3146, 23303}, {3522, 5339}, {3524, 11486}, {3525, 42118}, {3528, 11543}, {3529, 42129}, {3533, 42128}, {3534, 42628}, {3543, 16242}, {3545, 42131}, {3832, 42088}, {3839, 16967}, {3853, 42951}, {3855, 42145}, {3860, 42985}, {4232, 11476}, {5055, 43631}, {5056, 42086}, {5059, 42139}, {5067, 42127}, {5068, 42141}, {5071, 42137}, {5237, 5335}, {5281, 19373}, {5334, 10304}, {5366, 42915}, {7486, 33416}, {8703, 42818}, {10299, 11485}, {10653, 15721}, {11001, 42135}, {11488, 36843}, {11540, 43640}, {11812, 42922}, {12108, 42817}, {14869, 42815}, {15022, 42094}, {15640, 37835}, {15683, 42093}, {15688, 43543}, {15694, 43481}, {15697, 42099}, {15698, 42913}, {15702, 42132}, {15705, 37641}, {15706, 42634}, {15708, 16267}, {15709, 42691}, {15710, 42975}, {15720, 43463}, {16645, 42140}, {16773, 21734}, {16809, 42797}, {16960, 42510}, {17538, 42125}, {17578, 42095}, {18582, 43242}, {19708, 42122}, {19709, 42493}, {19780, 37665}, {21735, 42117}, {22235, 23302}, {33606, 43331}, {33703, 42143}, {33923, 42816}, {34200, 42917}, {40694, 43243}, {42104, 42528}, {42105, 42937}, {42107, 42625}, {42108, 42495}, {42109, 42473}, {42110, 43769}, {42111, 42433}, {42113, 42489}, {42114, 43295}, {42149, 42983}, {42151, 42958}, {42154, 43297}, {42165, 42472}, {42260, 42564}, {42261, 42565}, {42474, 43201}, {42511, 42897}, {42631, 43226}, {42683, 43193}, {42777, 43252}, {42780, 42929}, {42801, 42999}, {42918, 42928}, {42924, 42986}, {42948, 43473}, {42954, 43633}

X(43870) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3522, 11489, 43466}, {3522, 42944, 43480}, {3522, 43480, 22237}, {5056, 42086, 43364}, {11489, 43466, 22237}, {15708, 42982, 42092}, {15710, 43494, 42975}, {19708, 42987, 42122}, {33416, 42134, 7486}, {42131, 43102, 3545}, {42141, 43028, 5068}, {42142, 42588, 5318}, {42493, 42889, 19709}, {43466, 43480, 11489}

X(43871) = GIBERT (10,3,-69) POINT

Barycentrics    10*Sqrt[3]*a^2*S - 207*a^2*SA + 18*SB*SC : :

X(43871) lies on the cubic K1234 and these lines: {30, 43367}, {548, 42630}, {550, 42089}, {3528, 11543}, {3530, 33417}, {8703, 42519}, {10299, 42132}, {10646, 34200}, {11737, 42429}, {12100, 42955}, {14869, 42114}, {14891, 43199}, {15688, 43404}, {15707, 42134}, {15710, 42116}, {15715, 42118}, {15720, 42145}, {15759, 34754}, {16961, 33923}, {17504, 42155}, {41982, 43419}, {42087, 43012}, {42123, 43485}, {42144, 43464}, {43102, 43472}, {43103, 43487}, {43105, 43198}

X(43872) = GIBERT (10,-3,69) POINT

Barycentrics    10*Sqrt[3]*a^2*S + 207*a^2*SA - 18*SB*SC : :

X(43872) lies on the cubic K1234 and these lines: {30, 43366}, {548, 42629}, {550, 42092}, {3528, 11542}, {3530, 33416}, {8703, 42518}, {10299, 42129}, {10645, 34200}, {11737, 42430}, {12100, 42954}, {14869, 42111}, {14891, 43200}, {15688, 43403}, {15707, 42133}, {15710, 42115}, {15715, 42117}, {15720, 42144}, {15759, 34755}, {16960, 33923}, {17504, 42154}, {41982, 43418}, {42088, 43013}, {42122, 43486}, {42145, 43463}, {43102, 43488}, {43103, 43471}, {43106, 43197}

X(43873) = GIBERT (11,11,20) POINT

Barycentrics    11*Sqrt[3]*a^2*S + 60*a^2*SA + 66*SB*SC : :

X(43873) lies on the cubic K1234 and these lines: {3, 5318}, {30, 42957}, {140, 43010}, {396, 16961}, {398, 42802}, {3545, 42970}, {3854, 42119}, {3856, 42101}, {10109, 16966}, {10188, 42801}, {10299, 42971}, {11539, 43004}, {11543, 42488}, {14890, 43248}, {14893, 36967}, {15713, 42996}, {16267, 33416}, {16772, 42133}, {16809, 42415}, {16960, 42590}, {23046, 43372}, {33417, 42686}, {33699, 37832}, {36970, 38071}, {41099, 42942}, {42089, 42777}, {42094, 43107}, {42114, 42682}, {42138, 42429}, {42147, 42950}, {42432, 43649}, {42585, 42945}, {42594, 43554}, {42948, 42998}, {43401, 43473}, {43426, 43468}, {43483, 43630}

X(43873) = crosspoint of X(43447) and X(43544)
X(43873) = {X(42124),X(43104)}-harmonic conjugate of X(43105)

X(43874) = GIBERT (-11,11,20) POINT

Barycentrics    11*Sqrt[3]*a^2*S - 60*a^2*SA - 66*SB*SC : :

X(43874) lies on the cubic K1234 and these lines: {3, 5321}, {30, 42956}, {140, 43011}, {395, 16960}, {397, 42801}, {3545, 42971}, {3854, 42120}, {3856, 42102}, {10109, 16967}, {10187, 42802}, {10299, 42970}, {11539, 43005}, {11542, 42489}, {14890, 43249}, {14893, 36968}, {15713, 42997}, {16268, 33417}, {16773, 42134}, {16808, 42416}, {16961, 42591}, {23046, 43373}, {33416, 42687}, {33699, 37835}, {36969, 38071}, {41099, 42943}, {42092, 42778}, {42093, 43100}, {42111, 42683}, {42135, 42430}, {42148, 42951}, {42431, 43644}, {42584, 42944}, {42595, 43555}, {42949, 42999}, {43402, 43474}, {43427, 43467}, {43484, 43631}

X(43874) = crosspoint of X(43446) and X(43545)
X(43874) = {X(42121),X(43101)}-harmonic conjugate of X(43106)

X(43875) = GIBERT (26,39,75) POINT

Barycentrics    26*Sqrt[3]*a^2*S + 225*a^2*SA + 234*SB*SC : :

X(43875) lies on the cubic K1234 and these lines: {3, 42134}, {6, 43558}, {30, 43370}, {3859, 19107}, {5321, 43301}, {10188, 16960}, {10645, 12101}, {11488, 42985}, {11540, 41100}, {11737, 42630}, {12108, 42903}, {16268, 23302}, {41106, 43478}, {42101, 42592}, {42111, 42511}, {42117, 42984}, {42533, 43198}, {42627, 42954}, {42913, 43029}

X(43876) = GIBERT (-26,39,75) POINT

Barycentrics    26*Sqrt[3]*a^2*S - 225*a^2*SA - 234*SB*SC : :

X(43876) lies on the cubic K1234 and these lines: {3, 42133}, {6, 43558}, {30, 43371}, {3859, 19106}, {5318, 43300}, {10187, 16961}, {10646, 12101}, {11489, 42984}, {11540, 41101}, {11737, 42629}, {12108, 42902}, {16267, 23303}, {41106, 43477}, {42102, 42593}, {42114, 42510}, {42118, 42985}, {42532, 43197}, {42628, 42955}, {42912, 43028}

X(43877) = GIBERT (39,26,40) POINT

Barycentrics    13*Sqrt[3]*a^2*S + 40*a^2*SA + 52*SB*SC : :

X(43877) lies on the cubic K1234 and these lines: {3, 13}, {16, 42518}, {396, 42474}, {3534, 42903}, {3859, 22236}, {5321, 41106}, {11486, 43548}, {11488, 42940}, {11540, 42627}, {11543, 42911}, {11737, 42114}, {12101, 18582}, {15640, 42094}, {15694, 43370}, {16267, 43373}, {16268, 42132}, {16645, 42496}, {16966, 43333}, {19709, 43428}, {23046, 42093}, {35404, 42112}, {41119, 42584}, {42098, 42972}, {42110, 42509}, {42134, 42626}, {42153, 43232}, {42154, 43196}, {42475, 42915}, {42500, 43542}, {42502, 43463}, {42683, 42932}, {42777, 43494}, {42799, 43425}, {42815, 43304}, {42913, 43029}, {42914, 43001}, {42955, 42996}, {42999, 43101}, {43006, 43239}, {43028, 43332}

X(43878) = GIBERT (-39,26,40) POINT

Barycentrics    13*Sqrt[3]*a^2*S - 40*a^2*SA - 52*SB*SC : :

X(43878) lies on the cubic K1234 and these lines: {3, 14}, {15, 42519}, {395, 42475}, {3534, 42902}, {3859, 22238}, {5318, 41106}, {11485, 43549}, {11489, 42941}, {11540, 42628}, {11542, 42910}, {11737, 42111}, {12101, 18581}, {15640, 42093}, {15694, 43371}, {16267, 42129}, {16268, 43372}, {16644, 42497}, {16967, 43332}, {19709, 43429}, {23046, 42094}, {35404, 42113}, {41120, 42585}, {42095, 42973}, {42107, 42508}, {42133, 42625}, {42155, 43195}, {42156, 43233}, {42474, 42914}, {42501, 43543}, {42503, 43464}, {42682, 42933}, {42778, 43493}, {42800, 43424}, {42816, 43305}, {42912, 43028}, {42915, 43000}, {42954, 42997}, {42998, 43104}, {43007, 43238}, {43029, 43333}

X(43879) = GIBERT (3 SQRT(3),3,4) POINT

Barycentrics    3*a^2*S + 4*a^2*SA + 6*SB*SC : :
X)43879) = 2 X[35812] + 3 X[41952], 11 X[35812] - 3 X[42525], 14 X[35812] - X[43786], 3 X[41952] + X[41963], 11 X[41952] + 2 X[42525], 21 X[41952] + X[43786], 11 X[41963] - 6 X[42525], 7 X[41963] - X[43786], 42 X[42525] - 11 X[43786]

X(43879) lies on the cubic K1234 and these lines: {2, 3590}, {3, 485}, {4, 6425}, {5, 6419}, {6, 3090}, {30, 35812}, {140, 6454}, {371, 546}, {372, 632}, {382, 6519}, {486, 5079}, {548, 43211}, {549, 42418}, {615, 3628}, {631, 41946}, {1131, 41954}, {1151, 2671}, {1152, 10303}, {1327, 1657}, {1587, 3316}, {1588, 3544}, {1656, 6428}, {3055, 12969}, {3068, 3071}, {3303, 13897}, {3304, 13898}, {3311, 5072}, {3312, 32790}, {3364, 42194}, {3389, 42193}, {3522, 43209}, {3523, 31414}, {3526, 6448}, {3528, 14241}, {3529, 9540}, {3627, 6453}, {3746, 9646}, {3830, 9681}, {3839, 42417}, {3851, 31487}, {3857, 35815}, {5056, 19054}, {5067, 13847}, {5076, 6221}, {5159, 8280}, {5420, 18512}, {5563, 9661}, {5609, 13915}, {6199, 42268}, {6200, 15704}, {6248, 22720}, {6396, 12108}, {6407, 42275}, {6409, 17538}, {6410, 23267}, {6417, 42274}, {6429, 43408}, {6431, 42561}, {6432, 32786}, {6437, 42575}, {6447, 6561}, {6449, 22644}, {6451, 43791}, {6455, 42276}, {6459, 43508}, {6470, 23273}, {6483, 41970}, {6489, 43511}, {6501, 43431}, {6565, 12811}, {7486, 19053}, {7581, 8252}, {7584, 12812}, {7585, 15022}, {7772, 31481}, {7821, 32491}, {7982, 13911}, {7991, 13893}, {9542, 42413}, {10141, 41961}, {10142, 15702}, {10147, 11541}, {10194, 15703}, {10577, 19117}, {11292, 13663}, {12102, 35786}, {12103, 35255}, {13637, 32489}, {13908, 14981}, {13909, 15083}, {14869, 42216}, {15025, 19111}, {15685, 42608}, {15688, 43570}, {15694, 42526}, {15717, 43376}, {15720, 43254}, {15765, 35730}, {17800, 43380}, {18585, 41101}, {18762, 35771}, {19106, 42202}, {19107, 42200}, {22883, 33425}, {22928, 33426}, {35732, 42153}, {35738, 42913}, {35740, 42163}, {35787, 41991}, {41949, 42579}, {42156, 42282}, {42159, 42183}, {42162, 42185}, {42166, 42240}, {42225, 43312}, {42228, 42921}, {42230, 42920}, {42280, 42813}, {42281, 42814}, {42601, 43558}, {43383, 43406}

X(43879) = reflection of X(41963) in X(35812)
X(43879) = crosspoint of X(485) and X(3316)
X(43879) = crosssum of X(371) and X(3311)
X(43879) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 13846, 31454}, {4, 31454, 41945}, {5, 8960, 32787}, {6, 3090, 43880}, {6, 42582, 42583}, {371, 18538, 42273}, {371, 42273, 42283}, {485, 590, 3070}, {485, 5418, 13665}, {485, 8976, 590}, {590, 42259, 5418}, {1151, 31412, 42284}, {1327, 9680, 1657}, {1587, 3316, 8253}, {1587, 3525, 6426}, {1587, 43505, 42569}, {3068, 3091, 3592}, {3068, 42265, 3071}, {3091, 3592, 3071}, {3311, 42277, 42270}, {3592, 42265, 3091}, {3627, 6453, 42258}, {3627, 8981, 6453}, {3628, 6420, 615}, {3628, 7583, 6420}, {5079, 6427, 486}, {5418, 13665, 42259}, {6221, 42269, 42271}, {6420, 10576, 3628}, {6426, 8253, 3525}, {6453, 6564, 3627}, {6564, 8981, 42258}, {7583, 10576, 615}, {8972, 31412, 1151}, {9542, 42413, 43339}, {13665, 42259, 3070}, {13925, 18538, 371}, {42252, 42253, 485}, {42277, 43430, 3311}, {42598, 42599, 42582}

X(43880) = GIBERT (-3 SQRT(3),3,4) POINT

Barycentrics    3*a^2*S - 4*a^2*SA - 6*SB*SC : :
X(43880) = 2 X[35813] + 3 X[41951], 11 X[35813] - 3 X[42524], 14 X[35813] - X[43785], 3 X[41951] + X[41964], 11 X[41951] + 2 X[42524], 21 X[41951] + X[43785], 11 X[41964] - 6 X[42524], 7 X[41964] - X[43785], 42 X[42524] - 11 X[43785]

X(43880) lies on the cubic K1234 and these lines: X(438) lies on these lines: {2, 3591}, {3, 486}, {4, 6426}, {5, 6420}, {6, 3090}, {30, 35813}, {140, 6453}, {371, 632}, {372, 546}, {382, 6522}, {485, 5079}, {547, 8960}, {548, 43212}, {549, 42417}, {590, 3628}, {631, 41945}, {1132, 41953}, {1151, 10303}, {1152, 2672}, {1328, 1657}, {1587, 3544}, {1588, 3317}, {1656, 6427}, {3055, 12962}, {3069, 3070}, {3303, 13954}, {3304, 13955}, {3311, 32789}, {3312, 5072}, {3365, 42192}, {3390, 42191}, {3522, 43210}, {3523, 42573}, {3526, 6447}, {3528, 14226}, {3529, 13935}, {3627, 6454}, {3839, 42418}, {3857, 35814}, {5056, 19053}, {5067, 13846}, {5076, 6398}, {5159, 8281}, {5418, 18510}, {5609, 13979}, {6200, 12108}, {6248, 22721}, {6395, 42269}, {6396, 15704}, {6408, 42276}, {6409, 23273}, {6410, 17538}, {6418, 42277}, {6430, 43407}, {6431, 32785}, {6432, 31412}, {6438, 42574}, {6448, 6560}, {6450, 22615}, {6452, 43792}, {6456, 42275}, {6460, 43507}, {6471, 23267}, {6482, 41969}, {6488, 43512}, {6489, 42637}, {6500, 43430}, {6564, 12811}, {7486, 19054}, {7582, 8253}, {7583, 12812}, {7586, 15022}, {7821, 32490}, {7982, 13973}, {7991, 13947}, {9680, 15694}, {9681, 15720}, {10141, 15702}, {10142, 41962}, {10148, 11541}, {10195, 15703}, {10576, 19116}, {11291, 13783}, {12102, 35787}, {12103, 35256}, {13757, 32488}, {13968, 14981}, {13970, 15083}, {14869, 42215}, {15025, 19110}, {15685, 42609}, {15688, 43571}, {15717, 43377}, {15765, 41101}, {17800, 43381}, {18538, 35770}, {18585, 41100}, {19106, 42201}, {19107, 42199}, {19876, 31440}, {22882, 33427}, {22927, 33424}, {35732, 42156}, {35738, 42912}, {35739, 42211}, {35786, 41991}, {41950, 42578}, {42153, 42282}, {42159, 42184}, {42162, 42186}, {42163, 42241}, {42166, 42239}, {42226, 43313}, {42227, 42921}, {42229, 42920}, {42280, 42814}, {42281, 42813}, {42414, 43338}, {42600, 43559}, {43382, 43405}

X(43880) = reflection of X(41964) in X(35813)
X(43880) = crosspoint of X(486) and X(3317)
X(43880) = crosssum of X(372) and X(3312)
X(43880) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3090, 43879}, {6, 42583, 42582}, {372, 18762, 42270}, {372, 42270, 42284}, {486, 615, 3071}, {486, 5420, 13785}, {486, 13951, 615}, {615, 42258, 5420}, {1152, 42561, 42283}, {1588, 3317, 8252}, {1588, 3525, 6425}, {1588, 43506, 42568}, {3069, 3091, 3594}, {3069, 42262, 3070}, {3091, 3594, 3070}, {3312, 42274, 42273}, {3594, 42262, 3091}, {3627, 6454, 42259}, {3627, 13966, 6454}, {3628, 6419, 590}, {3628, 7584, 6419}, {5079, 6428, 485}, {5420, 13785, 42258}, {6398, 42268, 42272}, {6419, 10577, 3628}, {6425, 8252, 3525}, {6454, 6565, 3627}, {6565, 13966, 42259}, {7584, 10577, 590}, {9681, 43255, 15720}, {13785, 42258, 3071}, {13941, 42561, 1152}, {13993, 18762, 372}, {15703, 31487, 10195}, {42250, 42251, 486}, {42274, 43431, 3312}, {42598, 42599, 42583}

X(43881) = GIBERT (8 SQRT(3),12,21) POINT

Barycentrics    8*a^2*S + 21*a^2*SA + 24*SB*SC : :

X(43881) lies on the cubic K1234 and these lines: {3, 18538}, {6, 5070}, {30, 43374}, {140, 43415}, {381, 9690}, {485, 6446}, {590, 5055}, {1656, 7582}, {3068, 15703}, {3091, 9691}, {3316, 3526}, {3534, 43507}, {3590, 43505}, {3628, 6500}, {3830, 6200}, {3843, 6445}, {3850, 43520}, {3851, 6221}, {3859, 9543}, {5054, 23267}, {5073, 5418}, {5079, 23273}, {5420, 6395}, {6398, 8253}, {6407, 42283}, {6408, 43315}, {6412, 15707}, {6418, 32790}, {6451, 17800}, {6501, 13925}, {6560, 15718}, {6564, 15689}, {9542, 38071}, {12100, 43517}, {13665, 15701}, {13903, 18762}, {14269, 35255}, {15681, 42284}, {16239, 34089}, {19708, 42604}, {19709, 23259}, {32787, 42527}, {41946, 43513}, {42129, 42174}, {42132, 42172}, {42600, 43568}, {43211, 43321}, {43254, 43791}

X(43881) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6445, 42277, 3843}, {8976, 32789, 6395}

X(43882) = GIBERT (-8 SQRT(3),12,21) POINT

Barycentrics    8*a^2*S - 21*a^2*SA - 24*SB*SC : :

X(43882) lies on the cubic K1234 and these lines: {3, 18762}, {6, 5070}, {30, 43375}, {140, 9690}, {381, 43415}, {486, 6445}, {615, 5055}, {1656, 7581}, {3069, 15703}, {3317, 3526}, {3534, 43508}, {3591, 43506}, {3628, 6501}, {3830, 6396}, {3843, 6446}, {3850, 43519}, {3851, 6398}, {5054, 23273}, {5073, 5420}, {5079, 23267}, {5418, 6199}, {6221, 8252}, {6407, 43314}, {6408, 42284}, {6411, 15707}, {6417, 32789}, {6452, 17800}, {6500, 8972}, {6561, 15718}, {6565, 15689}, {9542, 11540}, {12100, 43518}, {13785, 15701}, {13935, 17851}, {13961, 18538}, {14269, 35256}, {15681, 42283}, {16239, 34091}, {19708, 42605}, {19709, 23249}, {31454, 43559}, {32788, 42526}, {41945, 43514}, {42129, 42173}, {42132, 42171}, {42601, 43569}, {43212, 43320}, {43255, 43792}

X(43882) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6446, 42274, 3843}, {13951, 32790, 6199}

X(43883) = GIBERT (12 SQRT(3),3,14) POINT

Barycentrics    6*a^2*S + 7*a^2*SA + 3*SB*SC : :

X(43883) lies on the cubic K1234 and these lines: {2, 3591}, {3, 7581}, {4, 6447}, {20, 6453}, {30, 43376}, {371, 3091}, {376, 9692}, {546, 13903}, {590, 1132}, {631, 6427}, {632, 7582}, {1131, 3068}, {1587, 9542}, {1657, 9693}, {3070, 9543}, {3090, 8981}, {3241, 31440}, {3311, 3525}, {3316, 5072}, {3522, 32787}, {3523, 6420}, {3529, 6221}, {3543, 8960}, {3544, 42215}, {3545, 42526}, {3590, 3832}, {3593, 7769}, {3627, 13886}, {3628, 6199}, {5056, 35812}, {5079, 23273}, {5420, 6419}, {6407, 12103}, {6417, 14869}, {6426, 15717}, {6428, 35255}, {6437, 31412}, {6451, 43382}, {6459, 43508}, {6470, 32786}, {6480, 43407}, {6519, 7583}, {6522, 10299}, {7486, 43377}, {9541, 35815}, {9680, 15692}, {10147, 42259}, {11541, 13665}, {12811, 23275}, {12962, 37689}, {15683, 31414}, {17578, 41945}, {42538, 43786}, {43383, 43408}

X(43883) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3068, 6425, 3146}, {3068, 43512, 1131}, {3146, 6425, 43512}, {3832, 13846, 3590}, {6419, 9540, 10303}, {6419, 10303, 7586}, {6519, 7583, 17538}, {9540, 42522, 7586}, {10303, 42522, 6419}, {19054, 41963, 15717}, {43507, 43512, 42258}

X(43884) = GIBERT (-12 SQRT(3),3,14) POINT

Barycentrics    6*a^2*S - 7*a^2*SA - 3*SB*SC : :

X(43884) lies on the cubic K1234 and these lines: {2, 3590}, {3, 7582}, {4, 6448}, {20, 6454}, {30, 43377}, {372, 3091}, {546, 13961}, {615, 1131}, {631, 6428}, {632, 7581}, {1132, 3069}, {3090, 13665}, {3312, 3525}, {3317, 5072}, {3522, 32788}, {3523, 6419}, {3529, 6398}, {3544, 42216}, {3545, 42527}, {3591, 3832}, {3595, 7769}, {3627, 13939}, {3628, 6395}, {5056, 35813}, {5079, 23267}, {5418, 6420}, {6408, 12103}, {6418, 14869}, {6425, 15717}, {6427, 35256}, {6438, 42561}, {6452, 43383}, {6460, 43507}, {6471, 32785}, {6481, 43408}, {6519, 10299}, {6522, 7584}, {7486, 43376}, {9692, 15712}, {9693, 17504}, {10148, 42258}, {11541, 13785}, {12811, 23269}, {12969, 37689}, {17578, 41946}, {17852, 42637}, {42537, 43785}, {43382, 43407}

X(43884) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3069, 6426, 3146}, {3069, 43511, 1132}, {3146, 6426, 43511}, {3832, 13847, 3591}, {6420, 10303, 7585}, {6420, 13935, 10303}, {6522, 7584, 17538}, {10303, 42523, 6420}, {13935, 42523, 7585}, {19053, 41964, 15717}, {43508, 43511, 42259}

X(43885) = GIBERT (15 SQRT(3),30,56) POINT

Barycentrics    15*a^2*S + 56*a^2*SA + 60*SB*SC : :

X(43885) lies on the cubic K1234 and these lines: {3, 3366}, {5, 43523}, {30, 43378}, {140, 43342}, {3091, 6433}, {3525, 6430}, {3543, 43786}, {3594, 10195}, {3628, 6431}, {5056, 6425}, {5067, 43387}, {5068, 42642}, {5072, 42568}, {6429, 23259}, {6432, 41992}, {6437, 43792}, {6483, 42558}, {7581, 34089}, {9543, 10141}, {15702, 42418}, {15723, 42526}, {41991, 43314}

X(43886) = GIBERT (-15 SQRT(3),30,56) POINT

Barycentrics    15*a^2*S - 56*a^2*SA - 60*SB*SC : :

X(43886) lies on the cubic K1234 and these lines: {3, 3367}, {5, 43524}, {30, 43379}, {140, 43343}, {3091, 6434}, {3525, 6429}, {3543, 43785}, {3592, 10194}, {3628, 6432}, {5056, 6426}, {5067, 43386}, {5068, 42641}, {5072, 42569}, {6430, 23249}, {6431, 41992}, {6438, 43791}, {6482, 42557}, {7582, 34091}, {9680, 11539}, {10142, 23251}, {15702, 42417}, {15723, 42527}, {41991, 43315}

X(43887) = GIBERT (15 SQRT(3),5,28) POINT

Barycentrics    15*a^2*S + 28*a^2*SA + 10*SB*SC : :
X(43887) = 18 X[6484] + 5 X[43380]

X(43887) lies on the cubic K1234 and these lines: {2, 6437}, {3, 9680}, {4, 10141}, {6, 15719}, {30, 6484}, {371, 11539}, {381, 43516}, {547, 3071}, {549, 35771}, {590, 3845}, {1132, 6492}, {1151, 3543}, {1327, 6445}, {1328, 6221}, {3524, 42568}, {3534, 42572}, {3545, 6429}, {3592, 43413}, {3830, 43568}, {3843, 43523}, {3850, 6453}, {3853, 6482}, {5067, 6425}, {6200, 15690}, {6407, 42602}, {6409, 43256}, {6411, 42418}, {6431, 15708}, {6433, 11001}, {6438, 19054}, {6439, 42606}, {6447, 42603}, {6468, 43257}, {6481, 12100}, {6486, 8981}, {7582, 13847}, {7583, 41982}, {8252, 43387}, {8976, 43503}, {9542, 42283}, {9543, 43258}, {10137, 42273}, {11812, 32788}, {13663, 13798}, {15655, 22541}, {15689, 43430}, {16239, 35823}, {23267, 43384}, {32785, 41965}, {34200, 35815}, {35400, 41952}, {35770, 41983}, {35812, 42639}, {38335, 42258}, {43318, 43566}

X(43887) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3545, 6429, 41945}, {6433, 13846, 11001}

X(43888) = GIBERT (-15 SQRT(3),5,28) POINT

Barycentrics    15*a^2*S - 28*a^2*SA - 10*SB*SC : :
X(43888) = 18 X[6485] + 5 X[43381]

X(43888) lies on the cubic K1234 and these lines: {2, 6438}, {3, 9681}, {4, 10142}, {6, 15719}, {30, 6485}, {372, 11539}, {381, 43515}, {547, 3070}, {549, 35770}, {615, 3845}, {1131, 6493}, {1152, 3543}, {1327, 6398}, {1328, 6446}, {3524, 42569}, {3534, 42573}, {3545, 6430}, {3594, 43414}, {3830, 43569}, {3843, 43524}, {3850, 6454}, {3853, 6483}, {5067, 6426}, {6396, 15690}, {6408, 42603}, {6410, 43257}, {6412, 42417}, {6432, 15708}, {6434, 11001}, {6437, 19053}, {6440, 42607}, {6448, 42602}, {6469, 43256}, {6480, 12100}, {6487, 13966}, {7581, 13846}, {7584, 41982}, {8253, 43386}, {10138, 42270}, {11812, 32787}, {13678, 13783}, {13951, 43504}, {15655, 19101}, {15689, 43431}, {16239, 35822}, {23273, 43385}, {32786, 41966}, {34200, 35814}, {35400, 41951}, {35771, 41983}, {35813, 42640}, {38335, 42259}, {42606, 43536}, {43319, 43567}

X(43888) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3545, 6430, 41946}, {6434, 13847, 11001}

X(43889) = GIBERT (20 SQRT(3),15,6) POINT

Barycentrics    10*a^2*S + 3*a^2*SA + 15*SB*SC : :

X(43889) lies on the cubic K1234 and these lines: {2, 6438}, {3, 8972}, {6, 1131}, {20, 6480}, {30, 43383}, {485, 6481}, {547, 6395}, {1327, 6435}, {1587, 5056}, {1588, 43791}, {1656, 42644}, {3068, 6433}, {3070, 5059}, {3091, 35770}, {3316, 6446}, {3522, 42568}, {3523, 43382}, {3533, 6398}, {3543, 6561}, {3545, 7586}, {3590, 6434}, {3839, 43342}, {3845, 18512}, {3850, 7581}, {3854, 43439}, {3855, 43340}, {5067, 18538}, {5068, 42570}, {6199, 23269}, {6221, 11001}, {6396, 15708}, {6430, 32789}, {6431, 42284}, {6432, 31412}, {6441, 42540}, {6468, 42414}, {6485, 10303}, {6486, 43407}, {7583, 33703}, {8960, 43314}, {9542, 42525}, {15690, 43509}, {15697, 43336}, {15702, 42216}, {15719, 43316}, {15723, 43510}, {17800, 42643}, {19054, 43508}, {19117, 43313}, {23259, 35771}, {41981, 43787}, {42215, 43386}, {42242, 42983}, {42244, 42982}, {42275, 42522}, {43406, 43520}

X(43889) = crosspoint of X(3590) and X(43566)
X(43889) = crosssum of X(3592) and X(6411)

X(43890) = GIBERT (-20 SQRT(3),15,6) POINT

Barycentrics    10*a^2*S - 3*a^2*SA - 15*SB*SC : :

X(43890) lies on the cubic K1234 and these lines: {2, 6437}, {3, 13939}, {6, 1131}, {20, 6481}, {30, 43382}, {486, 6480}, {547, 6199}, {1328, 6436}, {1587, 43792}, {1588, 5056}, {1656, 42643}, {3069, 6434}, {3071, 5059}, {3091, 35771}, {3317, 6445}, {3522, 42569}, {3523, 43383}, {3533, 6221}, {3543, 6560}, {3545, 7585}, {3591, 6433}, {3839, 43343}, {3845, 18510}, {3850, 7582}, {3854, 43438}, {3855, 43341}, {5067, 18762}, {5068, 42571}, {6200, 15708}, {6395, 23275}, {6398, 11001}, {6429, 32790}, {6431, 42561}, {6432, 42283}, {6442, 42539}, {6469, 42413}, {6484, 10303}, {6487, 43408}, {7584, 33703}, {15690, 43510}, {15697, 43337}, {15702, 42215}, {15719, 43317}, {15723, 43509}, {17800, 42644}, {19053, 43507}, {19116, 43312}, {23249, 35770}, {41981, 43788}, {42216, 43387}, {42243, 42983}, {42245, 42982}, {42276, 42523}, {42637, 43786}, {43405, 43519}

X(43890) = crosspoint of X(3591) and X(43567)
X(43890) = crosssum of X(3594) and X(6412)

X(43891) = PERSPECTOR OF ABC and KM(KM(KM(ABC)))

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

The mapping KM is introduced in the preamble just before X(43390)

X(43891) lies on the Jerabek circumhyperbola and these lines: {3, 43575}, {4, 43392}, {5, 43704}, {54, 37943}, {74, 13403}, {143, 3521}, {1176, 43810}, {1199, 11563}, {1899, 13452}, {3431, 39571}, {3519, 11591}, {5504, 13434}, {11270, 18912}, {11457, 11738}, {13630, 14861}, {15002, 15038}, {33565, 43581}, {38848, 43582}

X(43891) = isogonal conjugate of X(43809)

X(43892) = PERSPECTOR OF ABC AND MK(MK(MK(ABC)))

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

The mapping MK is introduced in the preamble just before X(43390)

X(43892) lies on the Jerabek circumhyperbola and these lines: {4, 43391}, {6, 32325}, {74, 43390}, {110, 14861}, {3519, 10264}, {3521, 43598}, {11559, 13445}, {15463, 34567}, {16835, 21650}, {43574, 43704}

X(43892) = isogonal conjugate of X(43893)

X(43893) = ISOGONAL CONJUGATE OF X(43892)

Barycentrics    a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 + 8*a^6*b^2*c^2 - 3*a^4*b^4*c^2 - 9*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 3*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - 2*b^6*c^4 - 9*a^2*b^2*c^6 - 2*b^4*c^6 + 2*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(43893) = 2 X[3] - 3 X[16532], 3 X[5] - 4 X[403], 7 X[5] - 4 X[858], 5 X[5] - 4 X[2072], X[5] - 4 X[11799], 3 X[5] - 2 X[37938], X[20] - 3 X[37922], 2 X[23] + X[3627], 2 X[140] - 3 X[37943], 3 X[381] + X[37949], X[382] + 3 X[37956], 7 X[403] - 3 X[858], 5 X[403] - 3 X[2072], 2 X[403] - 3 X[11563], X[403] - 3 X[11799], 8 X[468] - 5 X[15712], 2 X[546] + X[37924], 2 X[548] - 5 X[37760], 2 X[548] - 3 X[37955], 3 X[549] - 2 X[2071], X[550] + 2 X[18325], X[550] - 4 X[25338], 5 X[632] - 2 X[7464], 5 X[858] - 7 X[2072], 2 X[858] - 7 X[11563], X[858] - 7 X[11799], 6 X[858] - 7 X[37938], 2 X[1533] + X[10264], 3 X[1533] + X[13399], X[1657] - 3 X[35489], 3 X[2070] - X[13619], 7 X[2070] - 9 X[37909], 2 X[2072] - 5 X[11563], X[2072] - 5 X[11799], 6 X[2072] - 5 X[37938], X[3146] + 5 X[37923], 4 X[3628] - X[35001], 5 X[3843] + X[20063], 3 X[3845] - 2 X[18403], 3 X[3845] + 2 X[37925], 4 X[3850] - X[5189], 7 X[3857] + 2 X[37946], 5 X[3858] - 2 X[7574], 5 X[3858] + 2 X[37945], X[5899] + 2 X[11558], 4 X[7426] - X[15686], 4 X[7575] - X[15704], 3 X[7575] - 2 X[37931], 3 X[8703] - 4 X[15646], 5 X[8703] - 8 X[18579], 9 X[8703] - 16 X[37935], 4 X[10096] - 3 X[16532], 8 X[10257] - 9 X[11539], 3 X[10264] - 2 X[13399], 8 X[10297] - 11 X[41991], 3 X[11563] - X[37938], 6 X[11799] - X[37938], 2 X[12103] - 5 X[37958], 8 X[13473] - 9 X[15687], 2 X[13473] + 3 X[37947], 7 X[13619] - 27 X[37909], X[14677] - 4 X[32223], 7 X[14869] - 4 X[37950], 2 X[14893] + X[37901], 4 X[15350] - X[37944], 5 X[15646] - 6 X[18579], 3 X[15646] - 4 X[37935], 3 X[15687] + 4 X[37947], 3 X[15704] - 8 X[37931], X[15704] - 8 X[37971], 5 X[15712] - 4 X[34152], X[18325] + 2 X[25338], 9 X[18579] - 10 X[37935], X[18859] - 3 X[37943], 4 X[22249] - 3 X[37941], 9 X[23046] - 8 X[23323], 5 X[37760] - 3 X[37955], X[37931] - 3 X[37971]

X(43893) lies on these lines: {2, 3}, {113, 13391}, {146, 32608}, {1154, 13417}, {1263, 18319}, {1533, 10264}, {1614, 36966}, {5944, 12897}, {8901, 19651}, {10272, 43574}, {11264, 18555}, {11649, 21850}, {11692, 13446}, {11792, 25641}, {11805, 11807}, {13474, 34826}, {14157, 32423}, {14677, 32223}, {14861, 43603}, {20424, 21660}, {30210, 34979}, {36153, 40240}

X(43893) = midpoint of X(i) and X(j) for these {i,j}: {4, 5899}, {23, 31726}, {146, 32608}, {186, 18325}, {3153, 37924}, {7574, 37945}, {18403, 37925}
X(43893) = reflection of X(i) in X(j) for these {i,j}: {3, 10096}, {4, 11558}, {5, 11563}, {186, 25338}, {550, 186}, {3153, 546}, {3627, 31726}, {7575, 37971}, {11563, 11799}, {11692, 13446}, {15122, 37942}, {16386, 18571}, {18572, 10151}, {18859, 140}, {34152, 468}, {37936, 16619}, {37938, 403}, {43574, 10272}
X(43893) = reflection of X(34152) in the orthic axis
X(43893) = isogonal conjugate of X(43892)
X(43893) = complement of X(35452)
X(43893) = circumcircle-inverse of X(43809)
X(43893) = nine-point-circle-inverse of X(3850)
X(43893) = polar-circle-inverse of X(14865)
X(43893) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10096, 16532}, {4, 37913, 18564}, {5, 15686, 1368}, {23, 11799, 15761}, {235, 550, 5}, {403, 37938, 5}, {550, 3627, 18560}, {1113, 1114, 43809}, {1312, 1313, 3850}, {3627, 15761, 5}, {3845, 15760, 5}, {3853, 10024, 33332}, {3857, 7399, 5}, {5899, 37932, 17714}, {7502, 37954, 15646}, {10024, 33332, 5}, {11563, 37938, 403}, {11799, 18325, 235}, {12107, 18560, 550}, {18325, 25338, 550}, {18859, 37943, 140}

X(43894) = X(5)X(43617)∩X(110)X(3520)

Barycentrics    a^2*(a^14 - 4*a^12*b^2 + 5*a^10*b^4 - 5*a^6*b^8 + 4*a^4*b^10 - a^2*b^12 - 4*a^12*c^2 + 11*a^10*b^2*c^2 - 7*a^8*b^4*c^2 - 6*a^6*b^6*c^2 + 10*a^4*b^8*c^2 - 5*a^2*b^10*c^2 + b^12*c^2 + 5*a^10*c^4 - 7*a^8*b^2*c^4 + 14*a^6*b^4*c^4 - 6*a^4*b^6*c^4 - 3*a^2*b^8*c^4 - 3*b^10*c^4 - 6*a^6*b^2*c^6 - 6*a^4*b^4*c^6 + 18*a^2*b^6*c^6 + 2*b^8*c^6 - 5*a^6*c^8 + 10*a^4*b^2*c^8 - 3*a^2*b^4*c^8 + 2*b^6*c^8 + 4*a^4*c^10 - 5*a^2*b^2*c^10 - 3*b^4*c^10 - a^2*c^12 + b^2*c^12) : :

X(43894) lies on these lines: {5, 43617}, {110, 3520}, {113, 43614}, {376, 10539}, {5878, 9306}, {9140, 13434}, {9730, 43606}, {10706, 38323}, {11413, 12290}, {12111, 19908}, {12134, 43574}, {15462, 25563}, {18350, 20127}, {25711, 43578}

X(43895) = X(3)X(17711)∩X(4)X(14831)

Barycentrics    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 - a^6*b^2*c^2 + 3*a^4*b^4*c^2 - a^2*b^6*c^2 + 3*b^8*c^2 + 7*a^6*c^4 + 3*a^4*b^2*c^4 - 6*a^2*b^4*c^4 - 2*b^6*c^4 - 7*a^4*c^6 - a^2*b^2*c^6 - 2*b^4*c^6 + 4*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(43895) = 3 X[1614] - 4 X[7542]

X(43895) lies on these lines: {3, 17711}, {4, 14831}, {5, 5643}, {68, 12290}, {74, 14516}, {110, 43608}, {185, 12317}, {343, 8718}, {382, 41724}, {399, 13561}, {539, 12086}, {542, 3520}, {1181, 7569}, {1614, 7542}, {1899, 15058}, {1994, 18488}, {2888, 10575}, {3410, 40647}, {3448, 12162}, {3519, 15704}, {3528, 34507}, {3567, 18917}, {5890, 7544}, {6241, 11442}, {6247, 43574}, {6643, 11457}, {7527, 10116}, {9705, 37118}, {10112, 13596}, {10226, 23236}, {10264, 18350}, {11412, 14216}, {11441, 23294}, {12022, 43613}, {12038, 14683}, {12111, 18404}, {12359, 14157}, {15030, 43808}, {15035, 43607}, {15045, 18909}, {15052, 43817}, {15083, 31074}, {15305, 25738}, {16003, 22467}, {16261, 39571}, {18356, 18439}, {18451, 26917}, {18914, 43651}, {20126, 43615}, {23293, 32139}, {24981, 25563}, {30714, 35497}, {34986, 35482}, {38323, 43806}
{X(12111),X(32140)}-harmonic conjugate of X(25739)

X(43896) = X(3)X(34439)∩X(24)X(34146)

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 - 4*a^10*b^2*c^2 + 3*a^8*b^4*c^2 + 4*a^6*b^6*c^2 - 5*a^4*b^8*c^2 + b^12*c^2 - 4*a^10*c^4 + 3*a^8*b^2*c^4 - 12*a^6*b^4*c^4 + 10*a^4*b^6*c^4 + 3*b^10*c^4 + 5*a^8*c^6 + 4*a^6*b^2*c^6 + 10*a^4*b^4*c^6 - 8*a^2*b^6*c^6 - 3*b^8*c^6 - 5*a^4*b^2*c^8 - 3*b^6*c^8 - 5*a^4*c^10 + 3*b^4*c^10 + 4*a^2*c^12 + b^2*c^12 - c^14)

X(43896) lies on these lines: {3, 34439}, {24, 34146}, {49, 13171}, {51, 23294}, {54, 74}, {70, 11550}, {376, 5562}, {511, 11457}, {539, 10625}, {541, 12162}, {1216, 11456}, {1614, 3917}, {3147, 41715}, {3567, 12294}, {5446, 31133}, {5447, 9707}, {6000, 35471}, {9730, 43607}, {10018, 41580}, {10996, 11459}, {11381, 18559}, {11412, 12058}, {11413, 13754}, {12174, 23039}, {13433, 14864}, {15106, 18350}, {15559, 19161}, {21663, 41725}, {27365, 32140}, {34469, 34783}

X(43897) = X(54)X(74)∩X(1204)X(19708)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^12 - a^10*b^2 - 4*a^8*b^4 + 6*a^6*b^6 + a^4*b^8 - 5*a^2*b^10 + 2*b^12 - a^10*c^2 + 9*a^8*b^2*c^2 - 22*a^6*b^4*c^2 + 18*a^4*b^6*c^2 - a^2*b^8*c^2 - 3*b^10*c^2 - 4*a^8*c^4 - 22*a^6*b^2*c^4 - 38*a^4*b^4*c^4 + 6*a^2*b^6*c^4 - 6*b^8*c^4 + 6*a^6*c^6 + 18*a^4*b^2*c^6 + 6*a^2*b^4*c^6 + 14*b^6*c^6 + a^4*c^8 - a^2*b^2*c^8 - 6*b^4*c^8 - 5*a^2*c^10 - 3*b^2*c^10 + 2*c^12) : :

X(43897) lies on these lines: {54, 74}, {1204, 19708}, {1899, 38848}, {15034, 43617}, {15035, 43606}

X(43898) = X(3)X(64)∩X(5)X(12295)

Barycentrics    a^2*(4*a^8 - 9*a^6*b^2 + 3*a^4*b^4 + 5*a^2*b^6 - 3*b^8 - 9*a^6*c^2 + 18*a^4*b^2*c^2 - 11*a^2*b^4*c^2 + 2*b^6*c^2 + 3*a^4*c^4 - 11*a^2*b^2*c^4 + 2*b^4*c^4 + 5*a^2*c^6 + 2*b^2*c^6 - 3*c^8)

X(43898) lies on these lines: {3, 64}, {5, 12295}, {24, 10564}, {49, 15040}, {52, 37814}, {54, 5504}, {110, 43604}, {140, 21659}, {185, 1511}, {186, 10625}, {548, 20725}, {549, 1209}, {1092, 32110}, {1147, 15078}, {1216, 21844}, {3520, 15051}, {3523, 43608}, {3525, 32533}, {3917, 15331}, {5447, 10298}, {5562, 15646}, {5876, 37968}, {5890, 38942}, {6101, 18571}, {6240, 14156}, {6644, 11424}, {6699, 14516}, {9703, 13382}, {9715, 33543}, {10226, 15030}, {11250, 16194}, {11270, 12111}, {11381, 34152}, {11430, 43809}, {11449, 40647}, {11750, 16196}, {12107, 36987}, {12134, 16976}, {12307, 37955}, {13371, 32340}, {14641, 26882}, {15020, 43601}, {15034, 43605}, {15036, 35497}, {15056, 23040}, {15058, 35493}, {15750, 37478}, {17800, 32237}, {18324, 43652}, {18534, 41427}, {18560, 38726}, {18564, 32903}, {19357, 37470}, {33539, 35498}, {37476, 38260}, {38323, 43839}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10282, 14855}, {1511, 43615, 185}, {12038, 22467, 9730}, {14855, 36982, 10575}, {15035, 22467, 12038}, {15036, 43598, 35497}

X(43899) = X(5)X(43611)∩X(54)X(5504)

Barycentrics    a^2*(a^8 + 3*a^6*b^2 - 15*a^4*b^4 + 17*a^2*b^6 - 6*b^8 + 3*a^6*c^2 + 15*a^4*b^2*c^2 - 29*a^2*b^4*c^2 + 11*b^6*c^2 - 15*a^4*c^4 - 29*a^2*b^2*c^4 - 10*b^4*c^4 + 17*a^2*c^6 + 11*b^2*c^6 - 6*c^8) : :

X(43899) lies on these lines: {5, 43611}, {54, 5504}, {64, 15024}, {74, 12006}, {7395, 15045}, {10574, 13861}, {13434, 35498}, {13630, 14094}, {14845, 16835}, {15012, 43574}, {15034, 43845}, {15047, 15055}, {15051, 36153}, {15054, 32205}, {18350, 43584}, {38323, 43837}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9730, 43597, 43600}, {12006, 43603, 74}, {43597, 43600, 15035}

X(43900) = X(2771)X(43612)∩X(2772)X(43600)

Barycentrics    a^2*(a^8 - 7*a^6*b^2 + 15*a^4*b^4 - 13*a^2*b^6 + 4*b^8 - 2*a^5*b^2*c + 2*a^4*b^3*c + 4*a^3*b^4*c - 4*a^2*b^5*c - 2*a*b^6*c + 2*b^7*c - 7*a^6*c^2 - 2*a^5*b*c^2 - 5*a^4*b^2*c^2 - 2*a^3*b^3*c^2 + 15*a^2*b^4*c^2 + 4*a*b^5*c^2 - 3*b^6*c^2 + 2*a^4*b*c^3 - 2*a^3*b^2*c^3 + 4*a^2*b^3*c^3 - 2*a*b^4*c^3 - 2*b^5*c^3 + 15*a^4*c^4 + 4*a^3*b*c^4 + 15*a^2*b^2*c^4 - 2*a*b^3*c^4 - 2*b^4*c^4 - 4*a^2*b*c^5 + 4*a*b^2*c^5 - 2*b^3*c^5 - 13*a^2*c^6 - 2*a*b*c^6 - 3*b^2*c^6 + 2*b*c^7 + 4*c^8) : :

X(43900) lies on these lines: {2771, 43612}, {2772, 43600}, {5884, 43596}

X(43901) = X(3)X(3647)∩X(74)X(43610)

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

X(43901) lies on these lines: {3, 3647}, {74, 43610}, {378, 31870}, {758, 11250}, {2071, 31806}, {2771, 10226}, {2772, 12038}, {3520, 5884}, {5694, 34152}, {5883, 14130}, {5902, 35475}, {7527, 43805}, {10564, 31817}, {15035, 43609}, {15071, 35473}, {15646, 31828}, {21663, 31825}, {31871, 37814}

X(43902) = X(110)X(185)∩X(8550)X(43813)

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 + 5*a^8*b^2*c^2 + 12*a^6*b^4*c^2 - 28*a^4*b^6*c^2 + 15*a^2*b^8*c^2 - b^10*c^2 + 2*a^8*c^4 + 12*a^6*b^2*c^4 + 62*a^4*b^4*c^4 - 16*a^2*b^6*c^4 + 4*b^8*c^4 + 2*a^6*c^6 - 28*a^4*b^2*c^6 - 16*a^2*b^4*c^6 - 6*b^6*c^6 - 3*a^4*c^8 + 15*a^2*b^2*c^8 + 4*b^4*c^8 + a^2*c^10 - b^2*c^10) : :

X(43902) lies on these lines: {110, 185}, {8550, 43813}

X(43902) = {X(185),X(43606)}-harmonic conjugate of X(110)

X(43903) = X(2)X(34469)∩X(5)X(74)

Barycentrics    4*a^10 - 5*a^8*b^2 - 10*a^6*b^4 + 20*a^4*b^6 - 10*a^2*b^8 + b^10 - 5*a^8*c^2 + 28*a^6*b^2*c^2 - 20*a^4*b^4*c^2 - 3*b^8*c^2 - 10*a^6*c^4 - 20*a^4*b^2*c^4 + 20*a^2*b^4*c^4 + 2*b^6*c^4 + 20*a^4*c^6 + 2*b^4*c^6 - 10*a^2*c^8 - 3*b^2*c^8 + c^10 : :

X(43903) lies on these lines: {2, 34469}, {3, 31831}, {5, 74}, {20, 41467}, {64, 468}, {125, 5894}, {185, 15151}, {235, 3357}, {427, 1204}, {428, 1192}, {548, 11457}, {549, 6241}, {550, 11468}, {1205, 40929}, {1368, 11440}, {1593, 18931}, {1614, 15712}, {1620, 31383}, {1853, 3532}, {1885, 10606}, {1899, 8567}, {1907, 11438}, {3147, 13093}, {3516, 11245}, {3523, 12174}, {3530, 11456}, {3542, 35450}, {3627, 23294}, {5056, 32601}, {5622, 43813}, {5895, 10019}, {5925, 13473}, {6146, 11204}, {6225, 37453}, {6247, 21663}, {8703, 34224}, {9707, 12100}, {10151, 20427}, {10154, 12279}, {10295, 11270}, {11250, 32358}, {11410, 18909}, {11441, 16976}, {11585, 32138}, {12086, 41588}, {12315, 35486}, {12324, 15750}, {13171, 22467}, {13399, 34782}, {13403, 20417}, {13470, 32210}, {14216, 37931}, {14516, 15055}, {15106, 43605}, {15704, 25739}, {15717, 26864}, {18914, 35477}, {19710, 40242}, {21734, 39874}, {23047, 40686}, {31804, 35473}, {35492, 43818}

{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 43607, 5}, {1204, 6696, 427}, {3516, 18913, 11245}, {10606, 26937, 1885}

X(43904) = X(4)X(32184)∩X(5)X(17854)

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 + 2*a^10*b^2*c^2 - 4*a^8*b^4*c^2 - 12*a^6*b^6*c^2 + 25*a^4*b^8*c^2 - 14*a^2*b^10*c^2 + 2*b^12*c^2 - 4*a^10*c^4 - 4*a^8*b^2*c^4 + 30*a^6*b^4*c^4 - 20*a^4*b^6*c^4 - 2*a^2*b^8*c^4 + 5*a^8*c^6 - 12*a^6*b^2*c^6 - 20*a^4*b^4*c^6 + 24*a^2*b^6*c^6 - b^8*c^6 + 25*a^4*b^2*c^8 - 2*a^2*b^4*c^8 - b^6*c^8 - 5*a^4*c^10 - 14*a^2*b^2*c^10 + 4*a^2*c^12 + 2*b^2*c^12 - c^14) : :

X(43904) lies on these lines: {4, 32184}, {5, 17854}, {74, 13434}, {185, 10294}, {974, 3520}, {1204, 12234}, {1656, 6241}, {3516, 5890}, {5663, 43608}, {6000, 35487}, {6102, 11468}, {6288, 11457}, {7505, 7729}, {9707, 20791}, {9818, 10574}, {10254, 13491}, {10721, 43823}, {11456, 43598}, {12162, 12900}, {13160, 40647}, {15081, 43846}, {17855, 43831}, {31978, 32111}

X(43905) = X(3)X(49)∩X(74)X(43606)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^12 - 2*a^10*b^2 - a^8*b^4 + 4*a^6*b^6 - a^4*b^8 - 2*a^2*b^10 + b^12 - 2*a^10*c^2 + 7*a^8*b^2*c^2 - a^6*b^4*c^2 - 13*a^4*b^6*c^2 + 11*a^2*b^8*c^2 - 2*b^10*c^2 - a^8*c^4 - a^6*b^2*c^4 + 28*a^4*b^4*c^4 - 9*a^2*b^6*c^4 - b^8*c^4 + 4*a^6*c^6 - 13*a^4*b^2*c^6 - 9*a^2*b^4*c^6 + 4*b^6*c^6 - a^4*c^8 + 11*a^2*b^2*c^8 - b^4*c^8 - 2*a^2*c^10 - 2*b^2*c^10 + c^12) : :

X(43905) lies on these lines: {3, 49}, {74, 43606}, {378, 26944}, {974, 43845}, {1593, 43589}, {2071, 18914}, {2931, 43577}, {2935, 13403}, {5621, 32401}, {5663, 43617}, {6146, 18859}, {6623, 22497}, {6776, 36966}, {9920, 35471}, {10116, 12302}, {11250, 18909}, {12168, 22467}, {13434, 16270}, {13630, 19362}, {15033, 19361}, {16252, 37933}, {18560, 43829}, {18570, 18913}, {21659, 35452}, {32333, 35473}

X(43906) = X(49)X(15035)∩X(74)X(43612)

Barycentrics    a^2*(a^8 - 13*a^6*b^2 + 33*a^4*b^4 - 31*a^2*b^6 + 10*b^8 - 13*a^6*c^2 - 17*a^4*b^2*c^2 + 35*a^2*b^4*c^2 - 5*b^6*c^2 + 33*a^4*c^4 + 35*a^2*b^2*c^4 - 10*b^4*c^4 - 31*a^2*c^6 - 5*b^2*c^6 + 10*c^8) : :

X(43906) lies on these lines: {49, 15035}, {74, 43612}, {185, 43600}, {13630, 14094}, {43586, 43596}

X(43906) = {X(43602),X(43611)}-harmonic conjugate of X(15035)

X(43907) = X(3)X(64)∩X(5)X(13202)

Barycentrics    a^2*(4*a^8 - 7*a^6*b^2 - 3*a^4*b^4 + 11*a^2*b^6 - 5*b^8 - 7*a^6*c^2 + 22*a^4*b^2*c^2 - 13*a^2*b^4*c^2 - 2*b^6*c^2 - 3*a^4*c^4 - 13*a^2*b^2*c^4 + 14*b^4*c^4 + 11*a^2*c^6 - 2*b^2*c^6 - 5*c^8) : :

X(43907) lies on these lines: {3, 64}, {5, 13202}, {20, 18394}, {49, 15041}, {52, 11250}, {74, 9705}, {113, 5894}, {185, 10226}, {548, 11750}, {550, 13561}, {569, 11410}, {1204, 12161}, {1216, 11454}, {2071, 10625}, {2904, 35477}, {3520, 9730}, {3627, 30507}, {5449, 16386}, {5462, 35475}, {5562, 32210}, {5889, 11270}, {5890, 35494}, {6241, 35493}, {6699, 18560}, {7689, 10564}, {10024, 10193}, {10298, 14641}, {11381, 15646}, {11430, 35498}, {11440, 37948}, {11468, 13754}, {11562, 25564}, {12084, 32110}, {13445, 17506}, {14516, 38726}, {14915, 21844}, {15030, 43615}, {15053, 35478}, {15062, 43586}, {15072, 23040}, {15578, 37511}, {16194, 37814}, {17702, 43607}, {18565, 32767}, {20299, 24572}, {22467, 43613}, {25563, 37853}, {34783, 35495}, {35473, 40647}, {37118, 43577}, {38633, 43807}

X(43907) = midpoint of X(20) and X(18394)
X(43907) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10606, 10539}, {74, 35497, 12038}, {3520, 15055, 43604}, {3520, 43604, 9730}, {10226, 12041, 185}, {11250, 21663, 52}, {32210, 34152, 5562}

X(43908) = ISOGONAL CONJUGATE OF X(3090)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1763.

X(43908) lies on the Jerabek circumhyperbola and these lines: {3, 13366}, {4, 11402}, {5, 15077}, {6, 3517}, {24, 13472}, {25, 1173}, {26, 11482}, {30, 31371}, {49, 38260}, {54, 3515}, {64, 578}, {66, 8550}, {68, 1656}, {69, 140}, {70, 5094}, {72, 10246}, {74, 3516}, {182, 34817}, {184, 3527}, {185, 43719}, {248, 9605}, {265, 3851}, {378, 13452}, {381, 32533}, {389, 14528}, {546, 18296}, {550, 15740}, {567, 12164}, {895, 6642}, {1147, 6391}, {1176, 1351}, {1181, 3426}, {1199, 3431}, {1439, 37545}, {1493, 7393}, {1498, 14490}, {1593, 11423}, {1597, 22334}, {1598, 17809}, {1657, 4846}, {3090, 14843}, {3311, 6414}, {3312, 6413}, {3519, 6689}, {3521, 5073}, {3531, 10982}, {3532, 11204}, {3567, 34567}, {3843, 17505}, {3850, 15749}, {3858, 43699}, {5462, 38263}, {5504, 15040}, {6145, 12242}, {6415, 6418}, {6416, 6417}, {7395, 11422}, {7715, 19125}, {9818, 32136}, {11270, 35477}, {11427, 38442}, {11430, 43713}, {11431, 37935}, {11456, 13603}, {11485, 32586}, {11486, 32585}, {11738, 13093}, {12017, 16266}, {12315, 15033}, {14483, 14530}, {14491, 26864}, {14912, 16774}, {15087, 43689}, {15316, 36753}, {15720, 42021}, {18363, 35480}, {18388, 38447}, {19153, 38005}, {23324, 38443}, {30435, 43718}, {34483, 34564}, {37493, 40441}

X(43908) = isogonal conjugate of X(3090)
X(43908) = isogonal conjugate of the anticomplement of X(3526)
X(43908) = isogonal conjugate of the complement of X(3523)
X(43908) = isogonal conjugate of the isotomic conjugate of X(36948)
X(43908) = X(19357)-cross conjugate of X(3)

X(43909) = X(7)X(59)∩X(11)X(3667)

Barycentrics    (b - c)^2*(2*a^3 - 2*a^2*b - a*b^2 + b^3 - 2*a^2*c + 4*a*b*c - b^2*c - a*c^2 - b*c^2 + c^3) : :
X(43909) = X[1155] + 2 X[4887]

See Antreas Hatzipolakis and Peter Moses, euclid 1774.

X(43909) lies on these lines: {7, 59}, {11, 3667}, {36, 1284}, {56, 37815}, {57, 2957}, {244, 3259}, {513, 1086}, {516, 1319}, {517, 24231}, {901, 33148}, {1155, 4887}, {1357, 3326}, {1358, 3328}, {1365, 3025}, {1486, 38530}, {3120, 6075}, {3315, 31512}, {3662, 24250}, {3782, 34583}, {3821, 19890}, {4440, 39185}, {4542, 4926}, {4934, 24237}, {5048, 37743}, {6547, 6550}, {17114, 31849}, {17719, 22102}, {33646, 38357}

X(43909) = midpoint of X(i) and X(j) for these {i,j}: {36, 32857}, {4440, 39185}
X(43909) = reflection of X(i) in X(j) for these {i,j}: {2957, 40654}, {7336, 1086}
X(43909) = X(3035)-Ceva conjugate of X(21105)
X(43909) = X(i)-isoconjugate of X(j) for these (i,j): {9, 38809}, {41, 31619}, {101, 31628}, {765, 18771}
X(43909) = crosspoint of X(i) and X(j) for these (i,j): {7, 1086}, {3035, 21105}
X(43909) = crosssum of X(55) and X(1252)
X(43909) = barycentric product X(i)*X(j) for these {i,j}: {244, 20881}, {514, 21105}, {651, 42547}, {1086, 3035}, {1111, 17439}, {2973, 22055}, {3120, 18645}, {11124, 24002}, {17205, 21013}, {20958, 23989}
X(43909) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 31619}, {56, 38809}, {513, 31628}, {1015, 18771}, {3035, 1016}, {7336, 31611}, {11124, 644}, {17439, 765}, {18645, 4600}, {20881, 7035}, {20958, 1252}, {21105, 190}, {42547, 4391}

X(43910) = (name pending)

Barycentrics    (2*a^2 - b^2 - c^2)*(a^2 + b^2 - 3*b*c + c^2)*(a^2 + b^2 + 3*b*c + c^2)*(2*a^6 - 6*a^4*b^2 - 21*a^2*b^4 + 5*b^6 - 6*a^4*c^2 + 60*a^2*b^2*c^2 - 9*b^4*c^2 - 21*a^2*c^4 - 9*b^2*c^4 + 5*c^6 ) : :

See Elias M. Hagos and Peter Moses, euclid 1779.

X(43910) lies on this line: {18800, 37745}

X(43911) = X(4)X(5627)∩X(30)X(1990)

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

See Elias M. Hagos and Peter Moses, euclid 1779.

X(43911) lies on these lines: {4, 5627}, {30, 1990}, {133, 10151}, {186, 3258}, {403, 16240}, {1986, 6000}, {7687, 34329}

X(43912) = (name pending)

Barycentrics    (a^6 - a^4*b^2 - a^2*b^4 + b^6 + 2*a^2*b^3*c - 2*b^5*c - a^4*c^2 - a^2*b^2*c^2 - b^4*c^2 + 2*a^2*b*c^3 + 4*b^3*c^3 - a^2*c^4 - b^2*c^4 - 2*b*c^5 + c^6)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - 2*a^2*b^3*c + 2*b^5*c - a^4*c^2 - a^2*b^2*c^2 - b^4*c^2 - 2*a^2*b*c^3 - 4*b^3*c^3 - a^2*c^4 - b^2*c^4 + 2*b*c^5 + c^6)*(2*a^10 - 5*a^8*b^2 + 4*a^6*b^4 - 2*a^4*b^6 + 2*a^2*b^8 - b^10 - 5*a^8*c^2 + 6*a^6*b^2*c^2 - a^4*b^4*c^2 - 3*a^2*b^6*c^2 + 3*b^8*c^2 + 4*a^6*c^4 - a^4*b^2*c^4 + 2*a^2*b^4*c^4 - 2*b^6*c^4 - 2*a^4*c^6 - 3*a^2*b^2*c^6 - 2*b^4*c^6 + 2*a^2*c^8 + 3*b^2*c^8 - c^10)*(a^18 - 5*a^16*b^2 + 9*a^14*b^4 - 3*a^12*b^6 - 17*a^10*b^8 + 39*a^8*b^10 - 45*a^6*b^12 + 31*a^4*b^14 - 12*a^2*b^16 + 2*b^18 - 5*a^16*c^2 + 21*a^14*b^2*c^2 - 35*a^12*b^4*c^2 + 33*a^10*b^6*c^2 - 36*a^8*b^8*c^2 + 59*a^6*b^10*c^2 - 67*a^4*b^12*c^2 + 39*a^2*b^14*c^2 - 9*b^16*c^2 + 9*a^14*c^4 - 35*a^12*b^2*c^4 + 47*a^10*b^4*c^4 - 24*a^8*b^6*c^4 - 15*a^6*b^8*c^4 + 50*a^4*b^10*c^4 - 47*a^2*b^12*c^4 + 15*b^14*c^4 - 3*a^12*c^6 + 33*a^10*b^2*c^6 - 24*a^8*b^4*c^6 + 11*a^6*b^6*c^6 - 14*a^4*b^8*c^6 + 29*a^2*b^10*c^6 - 11*b^12*c^6 - 17*a^10*c^8 - 36*a^8*b^2*c^8 - 15*a^6*b^4*c^8 - 14*a^4*b^6*c^8 - 18*a^2*b^8*c^8 + 3*b^10*c^8 + 39*a^8*c^10 + 59*a^6*b^2*c^10 + 50*a^4*b^4*c^10 + 29*a^2*b^6*c^10 + 3*b^8*c^10 - 45*a^6*c^12 - 67*a^4*b^2*c^12 - 47*a^2*b^4*c^12 - 11*b^6*c^12 + 31*a^4*c^14 + 39*a^2*b^2*c^14 + 15*b^4*c^14 - 12*a^2*c^16 - 9*b^2*c^16 + 2*c^18) : :

See Elias M. Hagos and Peter Moses, euclid 1779.

X(43912) lies on these lines: { }

X(43913) = (name pending)

Barycentrics    (2*a^2 - b^2 - c^2)*(a^2 + b^2 - 3*b*c + c^2)*(a^2 + b^2 + 3*b*c + c^2)*(2*a^8 - 6*a^6*b^2 - 11*a^4*b^4 - 2*a^2*b^6 + b^8 - 6*a^6*c^2 + 40*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - 11*a^4*c^4 - 2*a^2*b^2*c^4 - 2*b^4*c^4 - 2*a^2*c^6 + c^8 ) : :

See Elias M. Hagos and Peter Moses, euclid 1779.

X(43913) lies on these lines: { }

X(43914) = X(241)X(516)∩X(1458)X(43066)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1781.

X(43914) lies on these lines: {241, 516}, {1458, 43066}, {5083, 21104}

X(43915) = X(7)X(13476)∩X(37)X(65)

Barycentrics    a*(a + b - c)*(a - b + c)*(b + c)*(a^2 - a*b - a*c - b*c)*(a*b - b^2 + a*c + 2*b*c - c^2) : :
X(43915) = 3 X[354] - X[2293], 3 X[354] - 2 X[40636]

See Antreas Hatzipolakis and Peter Moses, euclid 1782.

X(43915) lies on the cubic K1089 and these lines: {7, 13476}, {37, 65}, {57, 8053}, {226, 22277}, {354, 1418}, {516, 942}, {674, 5173}, {1439, 15320}, {1486, 5228}, {1839, 1876}, {11246, 22440}

X(43915) = midpoint of X(65) and X(42289)
X(43915) = reflection of X(2293) in X(40636)
X(43915) = X(i)-isoconjugate of X(j) for these (i,j): {6605, 39950}, {10482, 39734}
X(43915) = barycentric product X(i)*X(j) for these {i,j}: {1418, 4651}, {3294, 10481}, {17169, 20616}, {21039, 33765}
X(43915) = barycentric quotient X(i)/X(j) for these {i,j}: {1418, 39734}, {10481, 40004}
X(43915) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {65, 11553, 15443}, {354, 2293, 40636}

X(43916) = X(4)X(9)∩X(269)X(2191)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1782.

X(43916) lies on these lines: {4, 9}, {55, 34813}, {269, 2191}, {497, 7289}, {927, 30705}, {948, 1486}, {1284, 28015}, {1633, 4000}, {3056, 17642}, {4224, 20992}, {4644, 21746}, {28079, 28080}, {37800, 40577}

X(43916) = X(7)-Ceva conjugate of X(4000)
X(43916) = X(7123)-isoconjugate of X(41790)
X(43916) = barycentric product X(i)*X(j) for these {i,j}: {1, 41787}, {1633, 25009}, {4000, 17784}
X(43916) = barycentric quotient X(i)/X(j) for these {i,j}: {614, 41790}, {17784, 30701}, {41787, 75}

X(43917) = ISOGONAL CONJUGATE OF X(43574)

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

X(43917) lies on the circumconic {{A,B,C,X(4),X(5)}} and these lines: {4, 8901}, {5, 113}, {30, 39986}, {53, 115}, {74, 3134}, {235, 2970}, {311, 339}, {381, 17500}, {399, 9512}, {403, 12079}, {546, 40449}, {1141, 14157}, {1263, 18319}, {1300, 40352}, {1624, 14894}, {1907, 36809}, {3150, 10745}, {3331, 43291}, {3613, 18388}, {6759, 22261}, {6823, 27356}, {7668, 7687}, {8797, 43767}, {11563, 34209}, {13419, 15619}, {15761, 15912}, {20975, 34334}, {21011, 21046}, {26883, 34449}

X(43917) = isogonal conjugate of X(43574)
X(43917) = X(i)-isoconjugate of X(j) for these (i,j): {1, 43574}, {1101, 3134}, {14213, 43753}
X(43917) = cevapoint of X(i) and X(j) for these (i,j): {115, 21731}, {1637, 20975}
X(43917) = barycentric product X(i)*X(j) for these {i,j}: {5, 43766}, {53, 43767}
X(43917) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 43574}, {115, 3134}, {43766, 95}, {43767, 34386}

X(43918) = CROSSPOINT OF X(43766) AND X(43767)

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

X(43918) lies on the Jerabek circumhyperbola and these lines: {4, 8901}, {69, 43767}, {1141, 43707}, {1157, 43892}, {3431, 16030}, {14220, 23286}

X(43918) = isogonal conjugate of the isotomic conjugate of X(43767)
X(43918) = isogonal conjugate of the polar conjugate of X(43766)
X(43918) = crosspoint of X(43766) and X(43767)
X(43918) = barycentric product X(i)*X(j) for these {i,j}: {3, 43766}, {6, 43767}
X(43918) = barycentric quotient X(i)/X(j) for these {i,j}: {14533, 43574}, {43766, 264}, {43767, 76}

X(43919) = REFLECTION OF X(3) IN X(1624)

Barycentrics    a^2*(a^12*b^2 - 5*a^10*b^4 + 10*a^8*b^6 - 10*a^6*b^8 + 5*a^4*b^10 - a^2*b^12 + a^12*c^2 - 6*a^10*b^2*c^2 + 3*a^8*b^4*c^2 + 14*a^6*b^6*c^2 - 15*a^4*b^8*c^2 + 3*b^12*c^2 - 5*a^10*c^4 + 3*a^8*b^2*c^4 - 20*a^6*b^4*c^4 + 10*a^4*b^6*c^4 + 21*a^2*b^8*c^4 - 9*b^10*c^4 + 10*a^8*c^6 + 14*a^6*b^2*c^6 + 10*a^4*b^4*c^6 - 40*a^2*b^6*c^6 + 6*b^8*c^6 - 10*a^6*c^8 - 15*a^4*b^2*c^8 + 21*a^2*b^4*c^8 + 6*b^6*c^8 + 5*a^4*c^10 - 9*b^4*c^10 - a^2*c^12 + 3*b^2*c^12) : :

In the plane of a triangle ABC, let
TaTbTc = tangential triangle;
Oa = line through X(3) parallel to BC;
Ua = Oa∩TbTc;
La = line through Ua perpendicular to BC, and define Lb and Lc cyclically;
A' = Lb ∩Lc, and define B' and C' cyclically.
Then A'B'C' is perspective to TaTbTc, and the perspector is X(43919). See X(43919). (Angel Montesedeoca, March 15, 2022)

X(43919) lies on these lines: {3, 113}, {4, 8901}, {115, 8573}, {146, 15329}, {381, 34845}, {382, 17703}, {399, 526}, {1384, 9412}, {1561, 1597}, {1576, 9934}, {1596, 40981}, {1625, 15905}, {1634, 6053}, {2790, 34334}, {6086, 38577}, {7731, 14264}, {11641, 12918}, {13093, 38281}, {15063, 23181}, {15472, 40352}, {35450, 38283}, {38585, 38595}

X(43919) = reflection of X(3) in X(1624)
X(43919) = X(43768)-Ceva conjugate of X(6)
X(43919) = crosssum of X(i) and X(j) for these (i,j): {1154, 31378}, {6368, 16177}
X(43919) = {X(2935),X(14703)}-harmonic conjugate of X(3)

X(43920) = X(98)*X(1015)/X(6)

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

X(43920) lies on the circumparabola {{A,B,C,X(513),X(649)}} and these lines: {98, 901}, {125, 26080}, {237, 1284}, {290, 889}, {513, 4459}, {649, 3120}, {660, 1821}, {867, 35365}, {1086, 3733}, {1976, 32735}, {1977, 2969}, {2395, 3572}, {3937, 7192}, {6650, 14953}, {17139, 17929}

X(43920) = X(1821)-Ceva conjugate of X(2395)
X(43920) = X(i)-isoconjugate of X(j) for these (i,j): {101, 42717}, {237, 7035}, {325, 1110}, {511, 765}, {1016, 1755}, {1018, 2421}, {1252, 1959}, {3952, 23997}, {4033, 14966}, {4600, 5360}, {9417, 31625}
X(43920) = cevapoint of X(3271) and X(39786)
X(43920) = barycentric product X(i)*X(j) for these {i,j}: {98, 1086}, {244, 1821}, {248, 2973}, {287, 2969}, {290, 1015}, {879, 17925}, {1111, 1910}, {1358, 15628}, {1565, 6531}, {1976, 23989}, {1977, 18024}, {2395, 7192}, {3733, 43665}, {3937, 16081}, {3942, 36120}, {8034, 43187}
X(43920) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 1016}, {244, 1959}, {290, 31625}, {513, 42717}, {878, 4574}, {1015, 511}, {1086, 325}, {1357, 43034}, {1565, 6393}, {1821, 7035}, {1910, 765}, {1976, 1252}, {1977, 237}, {2395, 3952}, {2422, 4557}, {2969, 297}, {3121, 5360}, {3248, 1755}, {3733, 2421}, {3937, 36212}, {6531, 15742}, {7192, 2396}, {8034, 3569}, {14601, 23990}, {15628, 4076}, {15630, 1500}, {16732, 42703}, {17925, 877}, {22096, 3289}, {42067, 232}, {43665, 27808}

leftri

Points on circumparabola with center X(513): X(42921)-X(43933)

rightri

This preamble and points X(42921)-X(43933) are contributed by Peter Moses, July 2, 2021.

Suppose that U = u : v : w is a point in the plane of a triangle ABC. The locus of of a point X = x : y : z such that the circumconic {{A,B,C,U,X}} is a parabola is given by the quartic equation

f(u,v,w,x,y,z) + f(v,w,u,y,z,x) + f(w,u,v,z,x,y) = 0, where

f(u,v,w,x,y,z) = u^2 (v + w)^2 y^2 z^2 - 2 v w (-v w + u(u + v + w)x^2 y z).

If U lies on the line at infinity, then U = (b - c)(1 + b t + c t) : (c - a)(1 + c t + a t) : (a - b)(1 + a t + b t)

for some function t that is symmetric in a,b,c and has degree 0 of homogeneity. In this case,

f(x,y,z,u,v,w) = ((b - c)^2 (1 + b t + c t)^2 y z)^2.

The appearance of i, {j1, j2,..., jk}

in the following list means that the circumparabola with center X(i) passes through the points X(j1),X(j2),..., X(jk):

30, {30,476,3233,4240,9141,16077}
511, {511,805,877,14966,15631}
512, {512,669,805,875,881,886,15630,32729,38241}
513, {513,649,660,889,901,3572,3733,4581,7192,15635,17929,17940,23345,23836,32735,35365,38242,42921---43933}
514, {514,693,927,3676,4444,4555,4583,4608,4817,6548,6549,7192,15634,17925,17930,37143}
516, {516,927,3234,23973,41321}
517, {517,901,15632,23981,38243}
518, {518,660,677,883,2284,6078}
519, {519,4555,6079,17780,38244}
521, {521,677,4131,6081,7253,23090,43737}
522, {522,693,1309,2400,3239,4397,7253,15633,17926,17931,28132,35157,36802,43728}
523, {476,523,685,850,892,2395,2501,4024,4036,4581,4608,5466,8599,10412,12065,12079,13636,13722,14775,15328,18808,20578,20579,30508,30509,31065,34246,39240,39241}
524, {524,892,5468,6082,9141,17708,38245}
525, {525,850,2867,3265,16077,17708,17932,34767,43673}
690, {690,1648,1649,5466,5468,20404,34763}
900, {900,1647,6544,6548,17780,23836,34764,39771}
1503, {685,1503,2867,15639,23977}
3667, {3667,3676,6079,15637,31182}
9033, {1650,4240,9033,14401,34767,43083,43701}

{{A,B,C,523,476}} is the "X-parabola of ABC", as in X(12065).

See Michel Bataille, Forum Geometricorum 11 (2011) 57-63, On the Foci of Circumparabolas and Bernard Gibert, Q077

If PP is one of these circumparabolas, let P' be its perspector. Then if P'' is a point on the circumcircle, then the point P''*P'/X(6) is on PP. Various choices of P'' yeild the points X(42921)-X(43933).



X(43921) = X(105)*X(1015)/X(6)

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

X(43921) lies on the circumparabola {{A,B,C,X(513),X(649)}} and these lines: {11, 4885}, {44, 18785}, {88, 105}, {238, 20367}, {239, 335}, {244, 649}, {513, 1086}, {884, 42753}, {885, 23836}, {889, 2481}, {1024, 3675}, {1027, 16507}, {1279, 2223}, {1405, 36267}, {1428, 1456}, {1438, 7113}, {1646, 29956}, {2832, 6549}, {3572, 27846}, {3733, 16726}, {3742, 6654}, {3880, 36802}, {4363, 16482}, {4459, 40528}, {5880, 14267}, {6547, 8678}, {7192, 16727}, {13576, 29824}, {14839, 40538}, {24482, 42697}

X(43921) = X(105)-Ceva conjugate of X(1027)
X(43921) = X(i)-isoconjugate of X(j) for these (i,j): {59, 3717}, {100, 1026}, {101, 42720}, {190, 2284}, {518, 765}, {644, 1025}, {665, 6632}, {672, 1016}, {883, 3939}, {1110, 3263}, {1252, 3912}, {1458, 4076}, {1818, 15742}, {2223, 7035}, {2283, 3699}, {2340, 4998}, {3693, 4564}, {3930, 4567}, {3932, 4570}, {4578, 41353}, {4600, 20683}, {4601, 39258}, {4712, 5377}, {5376, 14439}, {5378, 8299}, {6065, 9436}, {9454, 31625}
X(43921) = cevapoint of X(244) and X(27846)
X(43921) = crosspoint of X(i) and X(j) for these (i,j): {105, 1027}, {291, 35355}
X(43921) = crosssum of X(i) and X(j) for these (i,j): {518, 1026}, {2223, 2284}
X(43921) = trilinear pole of line {764, 1015}
X(43921) = crossdifference of every pair of points on line {1026, 2284}
X(43921) = barycentric product X(i)*X(j) for these {i,j}: {11, 1462}, {105, 1086}, {244, 673}, {294, 1358}, {514, 1027}, {666, 764}, {884, 24002}, {885, 3669}, {1015, 2481}, {1024, 3676}, {1111, 1438}, {1357, 36796}, {1416, 4858}, {1565, 8751}, {1814, 2969}, {2973, 32658}, {3248, 18031}, {3271, 34018}, {3675, 6185}, {3942, 36124}, {6545, 36086}, {8027, 36803}, {10099, 17925}, {13576, 16726}, {17205, 18785}, {21132, 36146}, {23100, 32666}, {23760, 36041}, {32735, 40166}
X(43921) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 1016}, {244, 3912}, {294, 4076}, {513, 42720}, {649, 1026}, {667, 2284}, {673, 7035}, {764, 918}, {884, 644}, {885, 646}, {1015, 518}, {1024, 3699}, {1027, 190}, {1086, 3263}, {1357, 241}, {1358, 40704}, {1416, 4564}, {1438, 765}, {1462, 4998}, {1977, 2223}, {2170, 3717}, {2481, 31625}, {3121, 20683}, {3122, 3930}, {3125, 3932}, {3248, 672}, {3271, 3693}, {3669, 883}, {3675, 4437}, {3937, 25083}, {4014, 40883}, {8027, 665}, {8034, 24290}, {8042, 23829}, {8751, 15742}, {16726, 30941}, {17205, 18157}, {21143, 2254}, {22096, 20752}, {27846, 17755}, {29956, 3799}, {32735, 31615}, {35505, 23102}, {36086, 6632}, {41934, 5377}, {42067, 5089}

X(43922) = X(106)*X(1015)/X(6)

Barycentrics    a^2*(a + b - 2*c)*(b - c)^2*(a - 2*b + c) : :
X(43922) = 3 X[244] - X[38979]

X(43922) lies on the circumparabola {{A,B,C,X(513),X(649)}} and these lines: {1, 39264}, {2, 36814}, {36, 106}, {42, 34230}, {88, 291}, {244, 513}, {350, 889}, {519, 4674}, {649, 1015}, {1022, 27846}, {1086, 4379}, {1201, 14260}, {1357, 8054}, {1416, 32735}, {1646, 3572}, {1647, 23836}, {1914, 17969}, {2308, 40215}, {3120, 40451}, {4080, 4871}, {6549, 7192}, {7292, 17960}, {19945, 23352}

X(43922) = isogonal conjugate of the isotomic conjugate of X(6549)
X(43922) = X(i)-Ceva conjugate of X(j) for these (i,j): {106, 23345}, {903, 1022}, {2226, 649}, {36592, 4893}
X(43922) = X(8661)-cross conjugate of X(649)
X(43922) = X(i)-isoconjugate of X(j) for these (i,j): {44, 1016}, {59, 4723}, {100, 17780}, {101, 24004}, {190, 1023}, {519, 765}, {651, 30731}, {662, 4169}, {668, 23344}, {902, 7035}, {1110, 3264}, {1252, 4358}, {1319, 4076}, {1635, 6632}, {1639, 31615}, {2251, 31625}, {2325, 4564}, {3251, 6635}, {3689, 4998}, {3699, 23703}, {3943, 4567}, {3992, 4570}, {4370, 5376}, {4432, 5378}, {4439, 5384}, {4600, 21805}, {4738, 9268}, {4908, 5385}, {5440, 15742}, {42084, 42372}
X(43922) = crosspoint of X(i) and X(j) for these (i,j): {106, 23345}, {903, 1022}
X(43922) = crosssum of X(i) and X(j) for these (i,j): {519, 17780}, {902, 1023}
X(43922) = trilinear pole of line {1015, 21143}
X(43922) = crossdifference of every pair of points on line {1023, 4169}
X(43922) = barycentric product X(i)*X(j) for these {i,j}: {6, 6549}, {88, 244}, {106, 1086}, {513, 1022}, {514, 23345}, {649, 6548}, {679, 2087}, {764, 3257}, {901, 6545}, {903, 1015}, {1111, 9456}, {1357, 4997}, {1358, 2316}, {1417, 4858}, {1565, 8752}, {1647, 2226}, {1797, 2969}, {2973, 32659}, {3248, 20568}, {3669, 23838}, {3733, 4049}, {3937, 6336}, {3942, 36125}, {4555, 21143}, {4615, 8034}, {4638, 6550}, {4674, 16726}, {10428, 42754}, {14442, 39414}, {23100, 32719}
X(43922) = barycentric quotient X(i)/X(j) for these {i,j}: {88, 7035}, {106, 1016}, {244, 4358}, {512, 4169}, {513, 24004}, {649, 17780}, {663, 30731}, {667, 1023}, {764, 3762}, {901, 6632}, {903, 31625}, {1015, 519}, {1022, 668}, {1086, 3264}, {1357, 3911}, {1417, 4564}, {1647, 36791}, {1919, 23344}, {1977, 902}, {2087, 4738}, {2170, 4723}, {2316, 4076}, {2441, 43290}, {3121, 21805}, {3122, 3943}, {3125, 3992}, {3248, 44}, {3249, 1960}, {3271, 2325}, {3937, 3977}, {4049, 27808}, {4638, 6635}, {6548, 1978}, {6549, 76}, {8027, 1635}, {8034, 4120}, {8661, 6544}, {8752, 15742}, {9456, 765}, {16726, 30939}, {21143, 900}, {22096, 22356}, {23345, 190}, {23838, 646}, {33917, 14437}, {39786, 4783}, {41935, 9268}, {42067, 8756}, {42752, 21942}
X(43922) = {X(14260),X(17109)}-harmonic conjugate of X(1201)

X(43923) = X(108)*X(1015)/X(6)

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

The trilinear polar of X(43923) passes through X(1015) and the polar conjugate of X(7035).

X(43923) lies on the circumparabola {{A,B,C,X(513),X(649)}}, the inscribed parabola with focus X(108), and these lines: {4, 23836}, {34, 23345}, {56, 34948}, {57, 23800}, {65, 15313}, {108, 901}, {513, 1835}, {649, 4017}, {653, 660}, {764, 1398}, {889, 18026}, {1357, 2969}, {1767, 42758}, {1880, 3572}, {1946, 6129}, {2358, 42462}, {2501, 8672}, {2827, 16231}, {2849, 7661}, {3064, 14300}, {3669, 3733}, {3937, 38362}, {4014, 42069}, {4581, 17924}, {7192, 24002}, {8678, 21108}, {9001, 21121}, {9373, 21119}, {10940, 14257}, {32714, 32735}

X(43923) = reflection of X(18344) in X(7649)
X(43923) = isogonal conjugate of X(4571)
X(43923) = polar conjugate of X(646)
X(43923) = polar conjugate of the isotomic conjugate of X(3669)
X(43923) = X(39946)-anticomplementary conjugate of X(34188)
X(43923) = X(i)-Ceva conjugate of X(j) for these (i,j): {108, 34}, {653, 1880}, {1118, 2969}, {18026, 278}, {32714, 608}
X(43923) = X(i)-cross conjugate of X(j) for these (i,j): {764, 2969}, {1357, 1398}, {42067, 608}
X(43923) = cevapoint of X(764) and X(1357)
X(43923) = crosspoint of X(i) and X(j) for these (i,j): {34, 108}, {278, 18026}, {1119, 32714}
X(43923) = crosssum of X(i) and X(j) for these (i,j): {63, 24562}, {78, 521}, {219, 1946}, {522, 10395}, {652, 2318}
X(43923) = crossdifference of every pair of points on line {78, 219}
X(43923) = pole wrt polar circle of trilinear polar of X(646) (line X(8)X(210))
X(43923) = X(i)-isoconjugate of X(j) for these (i,j): {1, 4571}, {2, 4587}, {3, 3699}, {8, 1331}, {9, 1332}, {48, 646}, {55, 4561}, {63, 644}, {69, 3939}, {71, 645}, {72, 643}, {73, 7256}, {77, 4578}, {78, 100}, {99, 2318}, {101, 345}, {109, 1265}, {110, 3710}, {190, 219}, {200, 6516}, {210, 4592}, {212, 668}, {222, 6558}, {228, 7257}, {283, 3952}, {306, 5546}, {312, 906}, {332, 4557}, {333, 4574}, {341, 36059}, {346, 1813}, {521, 765}, {651, 3692}, {652, 1016}, {662, 3694}, {664, 1260}, {692, 3718}, {1018, 1812}, {1043, 23067}, {1110, 35518}, {1214, 7259}, {1252, 6332}, {1259, 1897}, {1264, 8750}, {1334, 4563}, {1409, 7258}, {1444, 4069}, {1459, 4076}, {1461, 30681}, {1783, 3719}, {1790, 30730}, {1792, 4551}, {1796, 30729}, {1797, 30731}, {1802, 4554}, {1811, 23705}, {1818, 36802}, {1946, 7035}, {2149, 15416}, {2193, 4033}, {2289, 6335}, {2321, 4558}, {2327, 4552}, {3596, 32656}, {3682, 36797}, {3695, 4636}, {3701, 4575}, {3949, 4612}, {3977, 5548}, {4025, 6065}, {4567, 8611}, {4582, 22356}, {4855, 31343}, {5376, 14418}, {6517, 7046}, {6632, 7117}, {7193, 36801}, {8706, 22072}, {30713, 32661}, {31615, 34591}
X(43923) = barycentric product X(i)*X(j) for these {i,j}: {4, 3669}, {7, 6591}, {11, 32714}, {19, 3676}, {25, 24002}, {27, 4017}, {28, 7178}, {29, 7216}, {34, 514}, {56, 17924}, {57, 7649}, {65, 17925}, {108, 1086}, {225, 1019}, {244, 653}, {269, 3064}, {273, 649}, {278, 513}, {279, 18344}, {286, 7180}, {331, 667}, {522, 1435}, {523, 1396}, {608, 693}, {650, 1119}, {651, 2969}, {663, 1847}, {905, 1118}, {934, 8735}, {1014, 2501}, {1015, 18026}, {1022, 1877}, {1027, 5236}, {1111, 32674}, {1357, 6335}, {1358, 1783}, {1395, 3261}, {1398, 4391}, {1408, 14618}, {1412, 24006}, {1415, 2973}, {1426, 4560}, {1474, 4077}, {1824, 17096}, {1826, 7203}, {1875, 2401}, {1880, 7192}, {2170, 36118}, {3271, 13149}, {3733, 40149}, {3942, 36127}, {4554, 42067}, {4617, 42069}, {5317, 17094}, {6545, 7012}, {7128, 21132}, {7250, 31623}, {7337, 15413}, {8712, 11546}, {8751, 43042}, {17922, 20615}, {23345, 37790}, {30725, 36125}, {34051, 39534}, {36110, 42754}, {37141, 38362}, {38374, 40117}
X(43923) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 646}, {6, 4571}, {11, 15416}, {19, 3699}, {25, 644}, {27, 7257}, {28, 645}, {29, 7258}, {31, 4587}, {33, 6558}, {34, 190}, {56, 1332}, {57, 4561}, {108, 1016}, {225, 4033}, {244, 6332}, {273, 1978}, {278, 668}, {331, 6386}, {512, 3694}, {513, 345}, {514, 3718}, {604, 1331}, {607, 4578}, {608, 100}, {649, 78}, {650, 1265}, {653, 7035}, {661, 3710}, {663, 3692}, {667, 219}, {764, 26932}, {798, 2318}, {905, 1264}, {1014, 4563}, {1015, 521}, {1019, 332}, {1086, 35518}, {1106, 1813}, {1118, 6335}, {1119, 4554}, {1172, 7256}, {1357, 905}, {1358, 15413}, {1395, 101}, {1396, 99}, {1397, 906}, {1398, 651}, {1402, 4574}, {1407, 6516}, {1408, 4558}, {1412, 4592}, {1426, 4552}, {1435, 664}, {1459, 3719}, {1474, 643}, {1783, 4076}, {1824, 30730}, {1828, 25268}, {1847, 4572}, {1875, 2397}, {1876, 42720}, {1877, 24004}, {1880, 3952}, {1919, 212}, {1973, 3939}, {1977, 1946}, {2203, 5546}, {2299, 7259}, {2333, 4069}, {2355, 30729}, {2423, 1809}, {2489, 210}, {2501, 3701}, {2969, 4391}, {3063, 1260}, {3064, 341}, {3122, 8611}, {3248, 652}, {3669, 69}, {3676, 304}, {3733, 1812}, {3900, 30681}, {4017, 306}, {4077, 40071}, {5317, 36797}, {5338, 30728}, {6545, 17880}, {6591, 8}, {7012, 6632}, {7099, 6517}, {7178, 20336}, {7180, 72}, {7203, 17206}, {7216, 307}, {7250, 1214}, {7252, 1792}, {7337, 1783}, {7649, 312}, {8027, 7117}, {8042, 17219}, {8735, 4397}, {8751, 36802}, {16947, 4575}, {17924, 3596}, {17925, 314}, {18026, 31625}, {18191, 15411}, {18344, 346}, {21143, 7004}, {22096, 36054}, {22383, 1259}, {24002, 305}, {24006, 30713}, {32674, 765}, {32714, 4998}, {34406, 42380}, {36125, 4582}, {40149, 27808}, {40983, 35341}, {42067, 650}

X(43924) = X(109)*X(1015)/X(6)

Barycentrics    a^2*(b - c)*(a + b - c)*(a - b + c) : :
X(43924) = 3 X[663] - 4 X[2605], 3 X[1459] - 2 X[2605], 4 X[4057] - 5 X[8656], 2 X[6129] - 3 X[14413], X[6615] - 3 X[14413], 5 X[8656] + 4 X[23345], X[30572] - 4 X[30719]

X(43924) lies on the circumparabola {{A,B,C,X(513),X(649)}} and these lines: {1, 3667}, {34, 7649}, {36, 39225}, {56, 4057}, {59, 109}, {77, 23465}, {106, 43081}, {222, 35365}, {244, 15635}, {269, 1027}, {513, 663}, {514, 4581}, {521, 2254}, {522, 4318}, {523, 7286}, {604, 1919}, {649, 854}, {651, 660}, {652, 43060}, {656, 9001}, {657, 665}, {659, 43051}, {661, 40134}, {664, 889}, {667, 6363}, {764, 1042}, {876, 41350}, {900, 30726}, {905, 17420}, {1038, 20315}, {1201, 15999}, {1357, 8054}, {1400, 3572}, {1414, 17929}, {1422, 23615}, {1428, 3733}, {1443, 1447}, {1461, 24027}, {1477, 9097}, {2171, 17458}, {2285, 21389}, {2484, 21123}, {2517, 4474}, {3716, 24666}, {3738, 23800}, {3766, 17215}, {3924, 23764}, {3939, 38828}, {3960, 21189}, {4040, 28225}, {4296, 20294}, {4322, 6161}, {4498, 23579}, {4565, 17940}, {4786, 5256}, {4905, 6003}, {4977, 7178}, {6085, 8643}, {6614, 23971}, {7212, 29362}, {7628, 9623}, {7951, 39508}, {8648, 23224}, {8686, 12029}, {10571, 14812}, {17072, 20293}, {21105, 21147}, {22108, 39521}, {22379, 34948}, {22384, 23568}, {24002, 43041}, {24720, 37764}, {24749, 25380}, {26983, 37762}, {28195, 43052}, {28209, 30724}, {29328, 42289}

X(43924) = midpoint of X(4057) and X(23345)
X(43924) = reflection of X(i) in X(j) for these {i,j}: {663, 1459}, {4017, 3669}, {4474, 2517}, {4724, 3737}, {6615, 6129}, {17418, 21173}, {17420, 905}, {20293, 17072}, {21119, 21186}, {21132, 7649}, {21189, 3960}, {42312, 1}
X(43924) = reflection of X(42312) in the Nagel line
X(43924) = isogonal conjugate of X(3699)
X(43924) = isogonal conjugate of the anticomplement of X(3756)
X(43924) = isotomic conjugate of the anticomplement of X(16614)
X(43924) = isogonal conjugate of the isotomic conjugate of X(3676)
X(43924) = X(979)-anticomplementary conjugate of X(33650)
X(43924) = X(i)-Ceva conjugate of X(j) for these (i,j): {34, 244}, {56, 1357}, {109, 56}, {651, 1400}, {664, 57}, {1293, 16945}, {1407, 1015}, {1413, 3937}, {1422, 2170}, {1461, 604}, {3669, 649}, {4551, 32636}, {4626, 28017}, {6614, 1407}, {7203, 3669}, {36118, 36570}, {38828, 6}
X(43924) = X(i)-cross conjugate of X(j) for these (i,j): {667, 649}, {1015, 1407}, {1357, 56}, {3248, 604}, {3271, 608}, {6363, 513}, {7180, 3669}, {16614, 2}, {17071, 3445}, {17477, 1}, {23751, 514}
X(43924) = cevapoint of X(i) and X(j) for these (i,j): {1, 16576}, {649, 8643}, {3248, 21143}, {3669, 43051}, {6363, 42336}
X(43924) = crosspoint of X(i) and X(j) for these (i,j): {1, 1293}, {56, 109}, {57, 664}, {269, 1461}, {651, 1014}, {1407, 6614}
X(43924) = crosssum of X(i) and X(j) for these (i,j): {1, 3667}, {2, 4468}, {8, 522}, {9, 663}, {200, 3239}, {210, 650}, {346, 4163}, {514, 4859}, {644, 4578}, {1229, 4391}, {1639, 4152}, {2325, 4543}, {3161, 4943}, {3700, 4046}, {3701, 4397}, {3939, 4587}, {4041, 21033}, {4069, 30730}, {4105, 28070}, {4521, 6555}, {6332, 27509}, {6745, 38376}
X(43924) = trilinear pole of line {1015, 1357}
X(43924) = crossdifference of every pair of points on line {8, 9}
X(43924) = barycentric product X(i)*X(j) for these {i,j}: {1, 3669}, {6, 3676}, {7, 649}, {11, 1461}, {21, 7216}, {31, 24002}, {34, 905}, {37, 7203}, {42, 17096}, {56, 514}, {57, 513}, {58, 7178}, {59, 6545}, {65, 1019}, {73, 17925}, {77, 6591}, {81, 4017}, {85, 667}, {86, 7180}, {87, 43051}, {101, 1358}, {106, 30725}, {108, 3942}, {109, 1086}, {190, 1357}, {222, 7649}, {225, 7254}, {226, 3733}, {241, 1027}, {244, 651}, {269, 650}, {273, 22383}, {278, 1459}, {279, 663}, {292, 43041}, {333, 7250}, {479, 657}, {512, 1434}, {521, 1435}, {522, 1407}, {523, 1412}, {552, 4079}, {603, 17924}, {604, 693}, {608, 4025}, {652, 1119}, {653, 3937}, {656, 1396}, {658, 3271}, {661, 1014}, {664, 1015}, {738, 3900}, {741, 7212}, {764, 4564}, {850, 16947}, {875, 10030}, {876, 1429}, {918, 1416}, {934, 2170}, {951, 29162}, {1020, 18191}, {1022, 1319}, {1024, 34855}, {1042, 4560}, {1088, 3063}, {1106, 4391}, {1111, 1415}, {1118, 4091}, {1126, 30724}, {1146, 6614}, {1262, 21132}, {1279, 37626}, {1293, 40617}, {1333, 4077}, {1365, 4556}, {1395, 15413}, {1397, 3261}, {1398, 6332}, {1400, 7192}, {1401, 10566}, {1402, 7199}, {1404, 6548}, {1408, 1577}, {1411, 3960}, {1413, 14837}, {1414, 3125}, {1417, 3762}, {1422, 6129}, {1427, 3737}, {1428, 4444}, {1431, 4369}, {1432, 4367}, {1438, 43042}, {1447, 3572}, {1457, 2401}, {1462, 2254}, {1469, 4817}, {1474, 17094}, {1477, 6084}, {1565, 32674}, {1769, 34051}, {1813, 2969}, {1847, 1946}, {1919, 6063}, {1977, 4572}, {1980, 20567}, {2163, 43052}, {2191, 43049}, {2226, 39771}, {2310, 4617}, {2334, 30723}, {2423, 22464}, {2424, 43035}, {2488, 10509}, {2720, 42754}, {2973, 32660}, {3064, 7053}, {3120, 4565}, {3121, 4625}, {3122, 4573}, {3239, 7023}, {3248, 4554}, {3309, 17107}, {3445, 30719}, {3667, 40151}, {3668, 7252}, {3675, 36146}, {3756, 38828}, {3777, 7132}, {3911, 23345}, {4024, 7341}, {4063, 20615}, {4083, 7153}, {4089, 32675}, {4394, 19604}, {4397, 7366}, {4462, 16945}, {4516, 4637}, {4551, 16726}, {4559, 17205}, {4619, 7336}, {4620, 8034}, {4626, 14936}, {4638, 14027}, {4724, 42290}, {4750, 7316}, {4998, 21143}, {6363, 40420}, {6364, 13438}, {6365, 13460}, {6610, 35348}, {6612, 8058}, {6728, 7370}, {6729, 7371}, {7004, 32714}, {7091, 8712}, {7117, 36118}, {7177, 18344}, {7200, 29055}, {7202, 26700}, {7209, 8640}, {7233, 8632}, {7249, 20981}, {7337, 30805}, {7339, 42462}, {8641, 23062}, {8643, 27818}, {8659, 35160}, {9262, 17089}, {14413, 34056}, {15635, 24029}, {16079, 31182}, {16610, 37627}, {18815, 21758}, {23355, 43040}, {23615, 23971}, {23892, 43037}, {24027, 40166}, {30722, 41434}, {32017, 42336}, {36049, 38374}, {37136, 42753}
X(43924) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 646}, {6, 3699}, {7, 1978}, {21, 7258}, {31, 644}, {32, 3939}, {34, 6335}, {41, 4578}, {42, 30730}, {48, 4571}, {55, 6558}, {56, 190}, {57, 668}, {58, 645}, {59, 6632}, {65, 4033}, {81, 7257}, {85, 6386}, {101, 4076}, {106, 4582}, {109, 1016}, {181, 4103}, {184, 4587}, {213, 4069}, {222, 4561}, {226, 27808}, {244, 4391}, {269, 4554}, {279, 4572}, {284, 7256}, {292, 36801}, {512, 2321}, {513, 312}, {514, 3596}, {523, 30713}, {603, 1332}, {604, 100}, {608, 1897}, {647, 3710}, {649, 8}, {650, 341}, {651, 7035}, {652, 1265}, {657, 5423}, {659, 3975}, {661, 3701}, {663, 346}, {664, 31625}, {665, 3717}, {667, 9}, {669, 1334}, {693, 28659}, {738, 4569}, {757, 4631}, {764, 4858}, {798, 210}, {810, 3694}, {812, 4087}, {849, 4612}, {875, 4876}, {884, 6559}, {902, 30731}, {905, 3718}, {1014, 799}, {1015, 522}, {1019, 314}, {1027, 36796}, {1041, 42384}, {1042, 4552}, {1086, 35519}, {1106, 651}, {1122, 21580}, {1201, 25268}, {1319, 24004}, {1333, 643}, {1356, 4079}, {1357, 514}, {1358, 3261}, {1395, 1783}, {1396, 811}, {1397, 101}, {1398, 653}, {1400, 3952}, {1401, 4568}, {1402, 1018}, {1403, 4595}, {1404, 17780}, {1405, 4767}, {1407, 664}, {1408, 662}, {1411, 36804}, {1412, 99}, {1414, 4601}, {1415, 765}, {1416, 666}, {1417, 3257}, {1423, 36863}, {1428, 3570}, {1429, 874}, {1431, 27805}, {1434, 670}, {1435, 18026}, {1438, 36802}, {1447, 27853}, {1455, 42718}, {1456, 42719}, {1457, 2397}, {1458, 42720}, {1459, 345}, {1461, 4998}, {1469, 3807}, {1474, 36797}, {1635, 4723}, {1646, 14430}, {1919, 55}, {1946, 3692}, {1960, 2325}, {1977, 663}, {1980, 41}, {2087, 4768}, {2170, 4397}, {2194, 7259}, {2206, 5546}, {2308, 30729}, {2484, 3974}, {2605, 42033}, {3049, 2318}, {3052, 30720}, {3063, 200}, {3121, 4041}, {3122, 3700}, {3125, 4086}, {3248, 650}, {3249, 3271}, {3250, 3790}, {3261, 40363}, {3271, 3239}, {3310, 6735}, {3451, 8706}, {3572, 4518}, {3669, 75}, {3676, 76}, {3709, 4082}, {3733, 333}, {3768, 4009}, {3900, 30693}, {3937, 6332}, {3942, 35518}, {4017, 321}, {4077, 27801}, {4079, 6057}, {4083, 4110}, {4091, 1264}, {4128, 4140}, {4367, 17787}, {4378, 4494}, {4455, 3985}, {4556, 6064}, {4565, 4600}, {4724, 28809}, {4775, 4873}, {4790, 4673}, {4822, 42712}, {4832, 4061}, {4834, 4007}, {4979, 3702}, {6363, 3452}, {6371, 3687}, {6377, 4147}, {6545, 34387}, {6591, 318}, {6614, 1275}, {6729, 7027}, {7004, 15416}, {7023, 658}, {7099, 6516}, {7143, 4605}, {7146, 4505}, {7153, 18830}, {7178, 313}, {7180, 10}, {7192, 28660}, {7199, 40072}, {7203, 274}, {7212, 35544}, {7216, 1441}, {7234, 4095}, {7248, 33946}, {7250, 226}, {7252, 1043}, {7254, 332}, {7341, 4610}, {7342, 4556}, {7366, 934}, {7649, 7017}, {8027, 2170}, {8034, 21044}, {8632, 3685}, {8640, 3208}, {8641, 728}, {8643, 3161}, {8659, 5853}, {8661, 4530}, {8662, 1697}, {9002, 5233}, {14936, 4163}, {16726, 18155}, {16945, 27834}, {16947, 110}, {17094, 40071}, {17096, 310}, {17477, 20317}, {18344, 7101}, {20979, 27538}, {20981, 7081}, {21007, 3996}, {21123, 3703}, {21132, 23978}, {21143, 11}, {21747, 30727}, {21758, 4511}, {22096, 652}, {22383, 78}, {23224, 3719}, {23345, 4997}, {23355, 36799}, {23751, 1329}, {23892, 36798}, {24002, 561}, {24027, 31615}, {30724, 1269}, {30725, 3264}, {32674, 15742}, {32739, 6065}, {37627, 36805}, {38266, 31343}, {39771, 36791}, {40436, 42380}, {41280, 32739}, {42067, 3064}, {42336, 3752}, {43041, 1921}, {43051, 6376}
X(43924) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3699}, {2, 644}, {4, 4571}, {6, 646}, {7, 4578}, {8, 100}, {9, 190}, {10, 643}, {21, 3952}, {33, 4561}, {37, 645}, {41, 1978}, {42, 7257}, {44, 4582}, {55, 668}, {57, 6558}, {59, 4397}, {65, 7256}, {72, 36797}, {75, 3939}, {78, 1897}, {81, 30730}, {86, 4069}, {88, 30731}, {92, 4587}, {99, 210}, {101, 312}, {108, 1265}, {109, 341}, {110, 3701}, {145, 31343}, {162, 3710}, {163, 30713}, {200, 664}, {219, 6335}, {220, 4554}, {226, 7259}, {238, 36801}, {261, 40521}, {281, 1332}, {284, 4033}, {294, 42720}, {314, 4557}, {318, 1331}, {321, 5546}, {333, 1018}, {345, 1783}, {346, 651}, {390, 37223}, {391, 4606}, {480, 4569}, {513, 4076}, {518, 36802}, {521, 15742}, {522, 765}, {594, 4612}, {648, 3694}, {650, 1016}, {653, 3692}, {658, 728}, {660, 3685}, {662, 2321}, {663, 7035}, {666, 3693}, {692, 3596}, {693, 6065}, {789, 4517}, {799, 1334}, {811, 2318}, {813, 3975}, {835, 3876}, {874, 7077}, {883, 28071}, {898, 4009}, {901, 4723}, {906, 7017}, {931, 3714}, {932, 27538}, {934, 5423}, {960, 8707}, {1023, 4997}, {1025, 6559}, {1026, 14942}, {1043, 4551}, {1089, 4636}, {1110, 35519}, {1120, 23705}, {1146, 31615}, {1252, 4391}, {1253, 4572}, {1255, 30729}, {1260, 18026}, {1261, 21272}, {1275, 4130}, {1310, 3974}, {1320, 17780}, {1400, 7258}, {1414, 4082}, {1461, 30693}, {1492, 3790}, {1500, 4631}, {1639, 5376}, {1813, 7101}, {2053, 36863}, {2170, 6632}, {2175, 6386}, {2185, 4103}, {2194, 27808}, {2284, 36796}, {2287, 4552}, {2316, 24004}, {2319, 4595}, {2320, 4767}, {2323, 36804}, {2325, 3257}, {2329, 27805}, {2338, 42719}, {2344, 3807}, {2427, 36795}, {3057, 8706}, {3059, 6606}, {3061, 4621}, {3063, 31625}, {3161, 27834}, {3208, 4598}, {3239, 4564}, {3570, 4876}, {3573, 4518}, {3680, 43290}, {3683, 6540}, {3684, 4562}, {3686, 37212}, {3687, 36147}, {3689, 4555}, {3700, 4567}, {3702, 8701}, {3706, 8708}, {3709, 4601}, {3711, 4597}, {3712, 5380}, {3713, 32038}, {3715, 32042}, {3716, 5378}, {3717, 36086}, {3718, 8750}, {3786, 4613}, {3871, 8050}, {3877, 9059}, {3880, 6079}, {3886, 37138}, {3900, 4998}, {3902, 28210}, {3903, 7081}, {3965, 6648}, {3985, 4584}, {4007, 37211}, {4012, 8269}, {4041, 4600}, {4046, 4596}, {4061, 4614}, {4070, 5386}, {4086, 4570}, {4087, 34067}, {4095, 4603}, {4102, 35342}, {4110, 34071}, {4152, 4618}, {4157, 5389}, {4163, 7045}, {4171, 4620}, {4358, 5548}, {4420, 6742}, {4427, 32635}, {4433, 4589}, {4451, 4579}, {4513, 30610}, {4515, 4573}, {4521, 5382}, {4522, 5384}, {4526, 5381}, {4574, 31623}, {4585, 36910}, {4604, 4873}, {4623, 7064}, {4627, 42712}, {4671, 5549}, {4673, 8694}, {4705, 6064}, {4752, 30608}, {4768, 9268}, {4903, 29227}, {4944, 5385}, {5547, 42721}, {6012, 30615}, {6066, 40495}, {6135, 13425}, {6136, 13458}, {6516, 7046}, {6574, 18228}, {6733, 7027}, {6735, 36037}, {7033, 40499}, {7058, 21859}, {7080, 13138}, {7115, 15416}, {7124, 42384}, {8056, 30720}, {8693, 28809}, {8851, 23354}, {11607, 42552}, {15627, 42716}, {15628, 42717}, {15629, 42718}, {23343, 36798}, {23617, 25268}, {23704, 36807}, {25430, 30728}, {28659, 32739}, {30236, 42020}, {30681, 32714}, {30727, 40434}, {30732, 39962}, {32008, 35341}, {32041, 37658}, {39272, 40609}
X(43924) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {665, 20980, 657}, {6615, 14413, 6129}

X(43925) = X(112)*X(1015)/X(6)

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

X(43925) lies on the circumparabola {{A,B,C,X(513),X(649)}} and these lines: {25, 3572}, {27, 17921}, {58, 35365}, {112, 901}, {162, 660}, {422, 2501}, {513, 1430}, {525, 17498}, {647, 21789}, {648, 889}, {649, 21122}, {1021, 1734}, {1172, 23836}, {1474, 23345}, {1977, 2969}, {2423, 5317}, {7192, 7254}, {15150, 17926}

X(43925) = isogonal conjugate of the isotomic conjugate of X(17925)
X(43925) = polar conjugate of X(27808)
X(43925) = polar conjugate of the isotomic conjugate of X(3733)
X(43925) = X(i)-Ceva conjugate of X(j) for these (i,j): {112, 1474}, {162, 25}, {648, 28}, {17925, 3733}, {36419, 2969}, {36420, 1015}
X(43925) = X(i)-cross conjugate of X(j) for these (i,j): {1015, 36420}, {3248, 1398}, {8034, 2969}
X(43925) = cevapoint of X(1977) and X(8034)
X(43925) = crosspoint of X(i) and X(j) for these (i,j): {28, 648}, {112, 1474}, {2983, 29014}
X(43925) = crosssum of X(i) and X(j) for these (i,j): {72, 647}, {306, 525}, {656, 3949}, {905, 4001}, {29013, 40940}
X(43925) = trilinear pole of line {1015, 22096}
X(43925) = crossdifference of every pair of points on line {72, 306}
X(43925) = X(i)-isoconjugate of X(j) for these (i,j): {3, 4033}, {10, 1332}, {37, 4561}, {48, 27808}, {63, 3952}, {69, 1018}, {71, 668}, {72, 190}, {73, 646}, {75, 4574}, {77, 30730}, {78, 4552}, {99, 3949}, {100, 306}, {101, 20336}, {201, 645}, {226, 4571}, {228, 1978}, {304, 4557}, {307, 644}, {312, 23067}, {313, 906}, {321, 1331}, {332, 21859}, {345, 4551}, {348, 4069}, {525, 765}, {594, 4592}, {643, 26942}, {647, 7035}, {651, 3710}, {656, 1016}, {662, 3695}, {664, 3694}, {692, 40071}, {756, 4563}, {799, 3690}, {810, 31625}, {823, 4158}, {1020, 1265}, {1089, 4558}, {1110, 3267}, {1214, 3699}, {1231, 3939}, {1252, 14208}, {1310, 3610}, {1425, 7258}, {1439, 6558}, {1441, 4587}, {1444, 4103}, {1792, 4605}, {1799, 35309}, {1813, 3701}, {1897, 3998}, {2197, 7257}, {2200, 6386}, {2318, 4554}, {2321, 6516}, {3682, 6335}, {3692, 4566}, {3718, 4559}, {3903, 4019}, {3958, 6540}, {4064, 4567}, {4101, 4606}, {4575, 28654}, {4998, 8611}, {5376, 14429}, {5378, 24459}, {6356, 7259}, {6632, 18210}, {7256, 37755}, {15742, 24018}, {17206, 40521}, {22057, 42384}, {23139, 40033}, {27801, 32656}, {30713, 36059}, {37212, 41014}
X(43925) = barycentric product X(i)*X(j) for these {i,j}: {4, 3733}, {6, 17925}, {19, 1019}, {25, 7192}, {27, 649}, {28, 513}, {33, 7203}, {34, 3737}, {58, 7649}, {81, 6591}, {99, 42067}, {107, 3937}, {108, 18191}, {110, 2969}, {112, 1086}, {162, 244}, {270, 4017}, {278, 7252}, {286, 667}, {393, 7254}, {514, 1474}, {525, 36420}, {593, 2501}, {607, 17096}, {608, 4560}, {647, 36419}, {648, 1015}, {650, 1396}, {693, 2203}, {764, 5379}, {811, 3248}, {849, 24006}, {905, 5317}, {1014, 18344}, {1021, 1435}, {1111, 32676}, {1118, 23189}, {1119, 21789}, {1172, 3669}, {1333, 17924}, {1357, 36797}, {1395, 18155}, {1398, 7253}, {1407, 17926}, {1412, 3064}, {1459, 8747}, {1509, 2489}, {1565, 32713}, {1576, 2973}, {1783, 16726}, {1973, 7199}, {1977, 6331}, {2162, 17921}, {2189, 7178}, {2204, 24002}, {2207, 15419}, {2299, 3676}, {2326, 7216}, {3572, 31905}, {3942, 24019}, {4246, 15635}, {4565, 8735}, {6528, 22096}, {8034, 18020}, {8750, 17205}, {17197, 32674}, {17442, 39179}, {23345, 37168}, {40574, 43060}
X(43925) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 27808}, {19, 4033}, {25, 3952}, {27, 1978}, {28, 668}, {32, 4574}, {58, 4561}, {112, 1016}, {162, 7035}, {244, 14208}, {270, 7257}, {286, 6386}, {512, 3695}, {513, 20336}, {514, 40071}, {593, 4563}, {607, 30730}, {608, 4552}, {648, 31625}, {649, 306}, {663, 3710}, {667, 72}, {669, 3690}, {798, 3949}, {849, 4592}, {1015, 525}, {1019, 304}, {1086, 3267}, {1172, 646}, {1333, 1332}, {1357, 17094}, {1395, 4551}, {1396, 4554}, {1397, 23067}, {1398, 4566}, {1408, 6516}, {1474, 190}, {1919, 71}, {1973, 1018}, {1974, 4557}, {1977, 647}, {1980, 228}, {2189, 645}, {2194, 4571}, {2203, 100}, {2204, 644}, {2206, 1331}, {2212, 4069}, {2299, 3699}, {2326, 7258}, {2332, 6558}, {2333, 4103}, {2484, 3610}, {2489, 594}, {2501, 28654}, {2969, 850}, {3063, 3694}, {3064, 30713}, {3122, 4064}, {3248, 656}, {3669, 1231}, {3733, 69}, {3737, 3718}, {3937, 3265}, {5317, 6335}, {6591, 321}, {7180, 26942}, {7192, 305}, {7199, 40364}, {7203, 7182}, {7250, 6356}, {7252, 345}, {7254, 3926}, {7649, 313}, {8027, 18210}, {8034, 125}, {16726, 15413}, {16947, 1813}, {17921, 6382}, {17924, 27801}, {17925, 76}, {18191, 35518}, {18344, 3701}, {20981, 4019}, {21143, 4466}, {21789, 1265}, {22096, 520}, {22383, 3998}, {23189, 1264}, {31905, 27853}, {32676, 765}, {32713, 15742}, {36419, 6331}, {36420, 648}, {39201, 4158}, {42067, 523}

X(43926) = X(691)*X(1015)/X(6)

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

X(43926) lies on the circumparabola {{A,B,C,X(513),X(649)}} and these lines: {58, 649}, {81, 513}, {111, 741}, {593, 3733}, {660, 36085}, {691, 901}, {889, 892}, {1171, 9178}, {1509, 7192}, {4581, 5466}, {17929, 18015}, {17940, 18001}, {19623, 35353}, {32729, 32735}, {35365, 42744}

X(43926) = X(36085)-Ceva conjugate of X(111)
X(43926) = X(i)-isoconjugate of X(j) for these (i,j): {42, 42721}, {100, 4062}, {101, 42713}, {187, 4033}, {190, 21839}, {351, 7035}, {524, 1018}, {594, 23889}, {690, 765}, {756, 5468}, {896, 3952}, {922, 27808}, {1016, 2642}, {1089, 5467}, {1110, 35522}, {1500, 24039}, {2748, 16597}, {3712, 4551}, {3949, 4235}, {4069, 7181}, {4103, 16702}, {4557, 14210}, {6629, 40521}
X(43926) = crosssum of X(i) and X(j) for these (i,j): {351, 21839}, {690, 4062}
X(43926) = trilinear pole of line {1015, 3733}
X(43926) = crossdifference of every pair of points on line {4062, 21839}
X(43926) = barycentric product X(i)*X(j) for these {i,j}: {111, 7192}, {244, 36085}, {593, 5466}, {671, 3733}, {691, 1086}, {757, 23894}, {892, 1015}, {895, 17925}, {897, 1019}, {923, 7199}, {1111, 36142}, {1509, 9178}, {4560, 7316}, {5380, 16726}, {5547, 17096}, {7254, 17983}, {8753, 15419}, {23989, 32729}
X(43926) = barycentric quotient X(i)/X(j) for these {i,j}: {81, 42721}, {111, 3952}, {513, 42713}, {593, 5468}, {649, 4062}, {667, 21839}, {671, 27808}, {691, 1016}, {757, 24039}, {849, 23889}, {892, 31625}, {897, 4033}, {923, 1018}, {1015, 690}, {1019, 14210}, {1086, 35522}, {1977, 351}, {3248, 2642}, {3733, 524}, {3937, 14417}, {5466, 28654}, {5547, 30730}, {7192, 3266}, {7252, 3712}, {7254, 6390}, {7316, 4552}, {8034, 1648}, {9178, 594}, {10097, 3695}, {14908, 4574}, {23894, 1089}, {32729, 1252}, {32740, 4557}, {36085, 7035}, {36142, 765}, {42067, 14273}

X(43927) = X(835)*X(1015)/X(6)

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

X(43927) lies on the circumparabola {{A,B,C,X(513),X(649)}, the cubic K1072, and these lines: {513, 1577}, {514, 3733}, {522, 31010}, {523, 649}, {660, 37218}, {835, 901}, {3261, 7192}, {3572, 6133}, {4049, 4778}, {4840, 4932}, {4977, 7178}, {6590, 23282}, {17940, 35148}, {21111, 29120}

X(43927) = reflection of X(i) in X(j) for these {i,j}: {4840, 4932}, {23282, 6590}
X(43927) = isotomic conjugate of X(33948)
X(43927) = X(835)-Ceva conjugate of X(43531)
X(43927) = X(8672)-cross conjugate of X(513)
X(43927) = X(i)-isoconjugate of X(j) for these (i,j): {31, 33948}, {100, 386}, {101, 28606}, {109, 3876}, {469, 906}, {692, 5224}, {765, 834}, {1101, 23282}, {1252, 14349}, {1576, 42714}, {4567, 42664}, {7035, 8637}, {32739, 33935}
X(43927) = cevapoint of X(i) and X(j) for these (i,j): {513, 4802}, {514, 4932}
X(43927) = crosspoint of X(i) and X(j) for these (i,j): {835, 43531}, {32042, 37870}
X(43927) = crosssum of X(i) and X(j) for these (i,j): {386, 834}, {513, 43220}
X(43927) = trilinear pole of line {1015, 3120}
X(43927) = crossdifference of every pair of points on line {386, 28622}
X(43927) = barycentric product X(i)*X(j) for these {i,j}: {244, 37218}, {514, 43531}, {693, 2214}, {835, 1086}
X(43927) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 33948}, {115, 23282}, {244, 14349}, {513, 28606}, {514, 5224}, {649, 386}, {650, 3876}, {693, 33935}, {835, 1016}, {1015, 834}, {1577, 42714}, {1977, 8637}, {2214, 100}, {3120, 23879}, {3122, 42664}, {3676, 33949}, {4932, 41849}, {6586, 26911}, {7649, 469}, {37218, 7035}, {43531, 190}

X(43928) = X(898)*X(1015)/X(6)

Barycentrics    a*(b - c)*(2*a*b - a*c - b*c)*(a*b - 2*a*c + b*c) : :
X(43928) = X[2] + 2 X[8027], X[2] - 4 X[38238], X[149] + 8 X[38018], 3 X[8027] + X[14434], X[8027] + 2 X[38238], X[14434] - 3 X[14474], X[14434] - 6 X[38238]

X(43928) lies on the conic {{A,B,C,X(1),X(2), the circumparabola {{A,B,C,X(513),X(649)}, the cubics K015 and K635, and these lines: {1, 649}, {2, 513}, {81, 3733}, {88, 659}, {89, 4782}, {105, 739}, {149, 38018}, {274, 7192}, {291, 1635}, {330, 17494}, {512, 27811}, {514, 36871}, {660, 875}, {667, 17126}, {876, 8661}, {889, 41314}, {890, 25569}, {891, 3227}, {898, 901}, {957, 30234}, {1022, 27846}, {1646, 16507}, {2401, 15635}, {2832, 34578}, {2978, 39738}, {3887, 34892}, {4581, 30710}, {4724, 39963}, {4784, 40434}, {5468, 17929}, {8056, 21173}, {14399, 16100}, {14419, 17946}, {16495, 21143}, {18197, 39950}, {21297, 31002}, {23825, 30957}, {23836, 36798}, {32718, 32735}, {39698, 41683}

X(43928) = midpoint of X(8027) and X(14474)
X(43928) = reflection of X(i) in X(j) for these {i,j}: {2, 14474}, {14474, 38238}
X(43928) = isogonal conjugate of X(23343)
X(43928) = isotomic conjugate of X(41314)
X(43928) = isotomic conjugate of the anticomplement of X(1646)
X(43928) = isotomic conjugate of the isogonal conjugate of X(23349)
X(43928) = complement of X(44008)
X(43928) = anticomplement of X(14434)
X(43928) = X(34075)-anticomplementary conjugate of X(39360)
X(43928) = X(i)-Ceva conjugate of X(j) for these (i,j): {889, 3227}, {898, 37129}
X(43928) = X(i)-cross conjugate of X(j) for these (i,j): {891, 513}, {1646, 2}, {16507, 1}, {33917, 1015}
X(43928) = cevapoint of X(i) and X(j) for these (i,j): {513, 891}, {536, 27076}, {1015, 33917}, {1646, 8027}
X(43928) = crosspoint of X(i) and X(j) for these (i,j): {889, 3227}, {898, 37129}
X(43928) = crosssum of X(i) and X(j) for these (i,j): {890, 3230}, {891, 899}, {3994, 14430}
X(43928) = trilinear pole of line {513, 1015}
X(43928) = crossdifference of every pair of points on line {899, 3230}
X(43928) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23343}, {6, 23891}, {31, 41314}, {59, 14430}, {100, 899}, {101, 536}, {109, 4009}, {110, 3994}, {190, 3230}, {692, 6381}, {765, 891}, {813, 4465}, {890, 7035}, {898, 42083}, {1016, 3768}, {1252, 4728}, {1646, 6632}, {2284, 36816}, {3939, 43037}, {4526, 4564}, {4570, 14431}, {4588, 4937}, {4600, 14404}, {4706, 8694}, {5376, 14437}, {9268, 30583}, {13466, 34075}, {32739, 35543}
X(43928) = barycentric product X(i)*X(j) for these {i,j}: {75, 23892}, {76, 23349}, {81, 35353}, {244, 4607}, {513, 3227}, {514, 37129}, {649, 31002}, {693, 739}, {764, 5381}, {889, 1015}, {898, 1086}, {1019, 41683}, {1022, 36872}, {1111, 34075}, {3669, 36798}, {23989, 32718}
X(43928) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 23891}, {2, 41314}, {6, 23343}, {244, 4728}, {513, 536}, {514, 6381}, {649, 899}, {650, 4009}, {659, 4465}, {661, 3994}, {667, 3230}, {693, 35543}, {739, 100}, {889, 31625}, {891, 13466}, {898, 1016}, {1015, 891}, {1027, 36816}, {1646, 14434}, {1977, 890}, {2087, 30583}, {2170, 14430}, {3121, 14404}, {3125, 14431}, {3227, 668}, {3248, 3768}, {3271, 4526}, {3669, 43037}, {3768, 42083}, {4607, 7035}, {4790, 4706}, {4893, 4937}, {6377, 14426}, {8027, 1646}, {14434, 8031}, {14474, 36847}, {21143, 19945}, {23349, 6}, {23892, 1}, {27846, 14433}, {31002, 1978}, {32718, 1252}, {33917, 39011}, {34075, 765}, {35353, 321}, {36798, 646}, {36872, 24004}, {37129, 190}, {41683, 4033}, {42753, 42764}
{X(8027),X(38238)}-harmonic conjugate of X(2)

X(43929) = X(919)*X(1015)/X(6)

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

X(43929) lies on the circumparabola {{A,B,C,X(513),X(649)}} and these lines: {6, 513}, {31, 649}, {81, 6654}, {105, 739}, {294, 23836}, {604, 1919}, {650, 1376}, {654, 35365}, {660, 2284}, {665, 2195}, {666, 889}, {673, 20332}, {764, 16502}, {885, 2298}, {901, 919}, {918, 1814}, {1022, 16784}, {1333, 3733}, {1438, 8658}, {1911, 3572}, {2221, 4790}, {2423, 15635}, {2481, 18825}, {2483, 28615}, {3287, 23617}, {4448, 5275}, {4976, 24115}, {7033, 21611}, {20172, 27855}, {32655, 32658}

X(43929) = isogonal conjugate of X(42720)
X(43929) = isogonal conjugate of the anticomplement of X(27918)
X(43929) = X(i)-Ceva conjugate of X(j) for these (i,j): {666, 105}, {919, 1438}, {1027, 884}, {39272, 55}, {41934, 1015}
X(43929) = X(i)-cross conjugate of X(j) for these (i,j): {875, 23355}, {1015, 41934}, {8659, 649}
X(43929) = cevapoint of X(649) and X(8632)
X(43929) = crosspoint of X(i) and X(j) for these (i,j): {105, 666}, {919, 1438}, {1462, 32735}
X(43929) = crosssum of X(i) and X(j) for these (i,j): {518, 665}, {812, 3008}, {918, 3912}, {2254, 3930}
X(43929) = trilinear pole of line {667, 1015}
X(43929) = crossdifference of every pair of points on line {518, 3717}
X(43929) = X(i)-isoconjugate of X(j) for these (i,j): {1, 42720}, {2, 1026}, {8, 1025}, {9, 883}, {75, 2284}, {99, 3930}, {100, 3912}, {101, 3263}, {190, 518}, {241, 3699}, {306, 4238}, {312, 2283}, {346, 41353}, {644, 9436}, {646, 1458}, {651, 3717}, {660, 17755}, {662, 3932}, {664, 3693}, {665, 7035}, {666, 4712}, {668, 672}, {670, 39258}, {765, 918}, {799, 20683}, {874, 3252}, {1016, 2254}, {1018, 30941}, {1332, 1861}, {1818, 6335}, {1897, 25083}, {1978, 2223}, {2340, 4554}, {2397, 36819}, {2414, 3870}, {3286, 4033}, {3570, 22116}, {3573, 40217}, {3675, 6632}, {3939, 40704}, {3952, 18206}, {4088, 4567}, {4437, 36086}, {4447, 27805}, {4555, 14439}, {4557, 18157}, {4561, 5089}, {4562, 8299}, {4571, 5236}, {4600, 24290}, {4606, 4684}, {4899, 27834}, {4925, 5382}, {4966, 37212}, {6386, 9454}, {6558, 34855}, {17464, 35574}, {24004, 34230}, {27853, 40730}, {34253, 36801}, {36803, 42079}
X(43929) = barycentric product X(i)*X(j) for these {i,j}: {1, 1027}, {7, 884}, {11, 32735}, {28, 10099}, {34, 23696}, {56, 885}, {57, 1024}, {105, 513}, {244, 36086}, {277, 2440}, {294, 3669}, {514, 1438}, {522, 1416}, {649, 673}, {650, 1462}, {665, 6185}, {666, 1015}, {667, 2481}, {764, 5377}, {905, 8751}, {918, 41934}, {919, 1086}, {927, 3271}, {1019, 18785}, {1111, 32666}, {1357, 36802}, {1407, 28132}, {1459, 36124}, {1814, 6591}, {1919, 18031}, {1977, 36803}, {2170, 36146}, {2195, 3676}, {3063, 34018}, {3572, 6654}, {3733, 13576}, {4904, 32644}, {7649, 36057}, {14621, 29956}, {15382, 23770}, {17924, 32658}, {23892, 36816}
X(43929) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 42720}, {31, 1026}, {32, 2284}, {56, 883}, {105, 668}, {294, 646}, {512, 3932}, {513, 3263}, {604, 1025}, {649, 3912}, {663, 3717}, {665, 4437}, {666, 31625}, {667, 518}, {669, 20683}, {673, 1978}, {798, 3930}, {875, 22116}, {884, 8}, {885, 3596}, {919, 1016}, {1015, 918}, {1019, 18157}, {1024, 312}, {1027, 75}, {1106, 41353}, {1357, 43042}, {1397, 2283}, {1416, 664}, {1438, 190}, {1462, 4554}, {1919, 672}, {1924, 39258}, {1977, 665}, {1980, 2223}, {2195, 3699}, {2203, 4238}, {2440, 344}, {2481, 6386}, {3063, 3693}, {3121, 24290}, {3122, 4088}, {3248, 2254}, {3572, 40217}, {3669, 40704}, {3733, 30941}, {6185, 36803}, {6654, 27853}, {8027, 3675}, {8632, 17755}, {8643, 4899}, {8659, 16593}, {8751, 6335}, {10099, 20336}, {13576, 27808}, {15382, 35574}, {18785, 4033}, {20980, 40883}, {22383, 25083}, {23696, 3718}, {29956, 3661}, {32658, 1332}, {32666, 765}, {32735, 4998}, {36057, 4561}, {36086, 7035}, {41934, 666}

X(43930) = X(927)*X(1015)/X(6)

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

X(43930) lies on the circumparabola {{A,B,C,X(513),X(649)}} and these lines: {4, 30204}, {7, 513}, {57, 649}, {105, 15728}, {269, 1027}, {279, 764}, {514, 21446}, {660, 883}, {673, 2402}, {693, 3434}, {901, 927}, {1014, 3733}, {1022, 1323}, {2481, 23836}, {3572, 43041}, {3669, 42290}, {4106, 9812}, {4453, 35365}, {4581, 31643}, {4927, 14942}, {8814, 10099}, {9269, 31721}, {21279, 23819}, {23973, 32735}, {29956, 43051}

X(43930) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1477, 39353}, {39272, 329}
X(43930) = X(i)-isoconjugate of X(j) for these (i,j): {9, 2284}, {41, 42720}, {55, 1026}, {100, 2340}, {101, 3693}, {200, 2283}, {220, 1025}, {480, 41353}, {518, 3939}, {643, 20683}, {644, 672}, {645, 39258}, {646, 9454}, {692, 3717}, {765, 926}, {883, 1253}, {1458, 4578}, {2223, 3699}, {2254, 6065}, {2318, 4238}, {2356, 4571}, {3286, 4069}, {3930, 5546}, {4587, 5089}, {5548, 14439}, {7035, 8638}, {36802, 42079}
X(43930) = cevapoint of X(i) and X(j) for these (i,j): {513, 6084}, {884, 2440}, {3676, 43041}
X(43930) = crosssum of X(926) and X(2340)
X(43930) = trilinear pole of line {1015, 1358}
X(43930) = barycentric product X(i)*X(j) for these {i,j}: {85, 1027}, {105, 24002}, {244, 34085}, {279, 885}, {479, 28132}, {513, 34018}, {666, 1358}, {673, 3676}, {693, 1462}, {927, 1086}, {1024, 1088}, {1111, 36146}, {1357, 36803}, {1416, 3261}, {1847, 23696}, {2402, 40154}, {2481, 3669}, {6185, 43042}, {6545, 39293}, {13576, 17096}, {23989, 32735}
X(43930) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 42720}, {56, 2284}, {57, 1026}, {105, 644}, {269, 1025}, {279, 883}, {294, 4578}, {513, 3693}, {514, 3717}, {649, 2340}, {666, 4076}, {673, 3699}, {738, 41353}, {764, 17435}, {884, 220}, {885, 346}, {919, 6065}, {927, 1016}, {1015, 926}, {1024, 200}, {1027, 9}, {1357, 665}, {1358, 918}, {1396, 4238}, {1407, 2283}, {1416, 101}, {1438, 3939}, {1462, 100}, {1814, 4571}, {1977, 8638}, {2440, 6600}, {2481, 646}, {3669, 518}, {3676, 3912}, {4017, 3930}, {6084, 40609}, {6185, 36802}, {7178, 3932}, {7180, 20683}, {7203, 18206}, {10099, 3694}, {13576, 30730}, {14942, 6558}, {17096, 30941}, {18785, 4069}, {23696, 3692}, {24002, 3263}, {28132, 5423}, {29956, 4517}, {30719, 4899}, {30723, 4684}, {30724, 4966}, {32735, 1252}, {34018, 668}, {34085, 7035}, {36057, 4587}, {36146, 765}, {39293, 6632}, {40154, 2414}, {40617, 4925}, {43041, 17755}, {43042, 4437}

X(43931) = X(932)*X(1015)/X(6)

Barycentrics    a*(b - c)*(a*b - a*c - b*c)*(a*b - a*c + b*c) : :
X(43931) = X[650] - 3 X[38238], X[693] + 3 X[8027], 9 X[14474] - 5 X[31209], X[20983] - 5 X[27013]

X(43931) lies on the circumparabola {{A,B,C,X(513),X(649)}} and these lines: {2, 27466}, {87, 16495}, {330, 17494}, {513, 3716}, {514, 21128}, {649, 4083}, {650, 3572}, {659, 43051}, {660, 3699}, {693, 6384}, {889, 18830}, {890, 23506}, {901, 932}, {2319, 9443}, {2527, 9040}, {3676, 3808}, {3733, 4782}, {3798, 30665}, {4411, 6383}, {4724, 27837}, {4777, 42027}, {6085, 8689}, {6373, 25142}, {7155, 23836}, {7192, 16737}, {9366, 10912}, {14474, 31209}, {20983, 27013}, {24755, 27345}, {25098, 40783}, {27424, 30061}, {27451, 27453}, {27452, 28372}, {27455, 28374}

X(43931) = reflection of X(i) in X(j) for these {i,j}: {21128, 21197}, {25142, 31286}
X(43931) = isotomic conjugate of X(36863)
X(43931) = X(i)-Ceva conjugate of X(j) for these (i,j): {932, 87}, {4598, 16606}, {18830, 330}
X(43931) = X(i)-cross conjugate of X(j) for these (i,j): {244, 6384}, {514, 513}, {2170, 27498}, {3125, 27447}, {3249, 16726}, {23456, 6}
X(43931) = X(i)-isoconjugate of X(j) for these (i,j): {6, 4595}, {31, 36863}, {43, 100}, {59, 4147}, {101, 192}, {109, 27538}, {110, 3971}, {190, 2176}, {213, 36860}, {644, 1423}, {646, 41526}, {651, 3208}, {662, 20691}, {668, 2209}, {692, 6376}, {765, 4083}, {1016, 20979}, {1018, 27644}, {1110, 20906}, {1252, 3835}, {1403, 3699}, {1415, 4110}, {1783, 22370}, {1897, 20760}, {3212, 3939}, {3573, 41531}, {3952, 38832}, {4557, 33296}, {4567, 21834}, {4570, 21051}, {4621, 20284}, {4734, 8694}, {4970, 8701}, {5376, 14408}, {6377, 6632}, {6382, 32739}, {7035, 8640}, {15742, 22090}
X(43931) = cevapoint of X(i) and X(j) for these (i,j): {244, 8027}, {513, 29226}
X(43931) = crosspoint of X(i) and X(j) for these (i,j): {87, 932}, {330, 18830}
X(43931) = crosssum of X(i) and X(j) for these (i,j): {43, 4083}, {2176, 8640}, {3971, 4147}
X(43931) = trilinear pole of line {1015, 3123}
X(43931) = crossdifference of every pair of points on line {43, 2176}
X(43931) = barycentric product X(i)*X(j) for these {i,j}: {87, 514}, {244, 4598}, {330, 513}, {522, 7153}, {649, 6384}, {663, 7209}, {667, 6383}, {693, 2162}, {764, 5383}, {876, 39914}, {932, 1086}, {1015, 18830}, {1019, 42027}, {1111, 34071}, {2053, 24002}, {2319, 3676}, {3123, 32039}, {3261, 7121}, {3669, 7155}, {4367, 27447}, {4444, 34252}, {4449, 27498}, {4581, 27455}, {7192, 16606}, {7199, 23493}, {17924, 23086}
X(43931) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4595}, {2, 36863}, {86, 36860}, {87, 190}, {244, 3835}, {330, 668}, {512, 20691}, {513, 192}, {514, 6376}, {522, 4110}, {649, 43}, {650, 27538}, {661, 3971}, {663, 3208}, {667, 2176}, {693, 6382}, {764, 21138}, {876, 40848}, {932, 1016}, {1015, 4083}, {1019, 33296}, {1086, 20906}, {1357, 43051}, {1459, 22370}, {1646, 14426}, {1919, 2209}, {1977, 8640}, {2053, 644}, {2162, 100}, {2170, 4147}, {2319, 3699}, {3122, 21834}, {3123, 23886}, {3125, 21051}, {3248, 20979}, {3249, 38986}, {3572, 41531}, {3669, 3212}, {3676, 30545}, {3733, 27644}, {3777, 33890}, {3835, 8026}, {3937, 25098}, {4367, 17752}, {4369, 41318}, {4598, 7035}, {4790, 4734}, {4979, 4970}, {6377, 25142}, {6378, 40521}, {6383, 6386}, {6384, 1978}, {7121, 101}, {7148, 4103}, {7153, 664}, {7155, 646}, {7192, 31008}, {7209, 4572}, {8027, 6377}, {8042, 23824}, {15373, 1331}, {16606, 3952}, {16726, 17217}, {16737, 27891}, {17448, 25312}, {18191, 27527}, {18830, 31625}, {21143, 3123}, {21759, 4557}, {22381, 4574}, {22383, 20760}, {23086, 1332}, {23493, 1018}, {27499, 21272}, {29226, 40598}, {34071, 765}, {34252, 3570}, {39914, 874}, {40495, 40367}, {40881, 23354}, {42027, 4033}

X(43932) = X(934)*X(1015)/X(6)

Barycentrics    a*(b - c)*(a + b - c)^2*(a - b + c)^2 : :
X(43932) = 3 X[1638] - X[14298], X[4131] + 3 X[4453]

X(43932) lies on the circumparabola {{A,B,C,X(513),X(649)}} and these lines: {7, 4106}, {56, 8642}, {57, 4394}, {269, 23345}, {513, 676}, {649, 3669}, {658, 660}, {738, 764}, {889, 4569}, {901, 934}, {942, 30199}, {1358, 15635}, {1427, 3572}, {1435, 6591}, {1638, 14298}, {2473, 8678}, {2516, 43050}, {3361, 30234}, {3733, 7203}, {3900, 4025}, {4017, 7659}, {4131, 4453}, {4298, 28475}, {4380, 21454}, {4581, 24002}, {4616, 17929}, {4617, 7339}, {4637, 17940}, {4897, 31605}, {7177, 35365}, {7658, 40137}, {9048, 24471}, {14300, 21104}

X(43932) = midpoint of X(14300) and X(21104)
X(43932) = reflection of X(i) in X(j) for these {i,j}: {17115, 17427}, {40137, 7658}
X(43932) = isogonal conjugate of X(4578)
X(43932) = isotomic conjugate of the anticomplement of X(17071)
X(43932) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2137, 37781}, {8051, 33650}
X(43932) = X(i)-Ceva conjugate of X(j) for these (i,j): {658, 1427}, {934, 269}, {1119, 1358}, {4569, 279}, {4617, 1407}
X(43932) = X(i)-cross conjugate of X(j) for these (i,j): {244, 1435}, {1357, 1407}, {3937, 6612}, {17071, 2}
X(43932) = cevapoint of X(7216) and X(7250)
X(43932) = crosspoint of X(i) and X(j) for these (i,j): {269, 934}, {279, 4569}, {479, 4617}
X(43932) = crosssum of X(i) and X(j) for these (i,j): {55, 4162}, {200, 3900}, {220, 8641}, {480, 4130}, {522, 24389}, {4082, 4163}
X(43932) = crossdifference of every pair of points on line {200, 220}
X(43932) = X(i)-isoconjugate of X(j) for these (i,j): {1, 4578}, {6, 6558}, {8, 3939}, {9, 644}, {21, 4069}, {33, 4571}, {37, 7259}, {41, 646}, {42, 7256}, {55, 3699}, {59, 4163}, {100, 200}, {101, 346}, {109, 5423}, {110, 4082}, {190, 220}, {210, 643}, {213, 7258}, {281, 4587}, {284, 30730}, {341, 692}, {480, 664}, {522, 6065}, {645, 1334}, {651, 728}, {657, 1016}, {662, 4515}, {663, 4076}, {668, 1253}, {765, 3900}, {906, 7101}, {1018, 2287}, {1026, 28071}, {1043, 4557}, {1098, 40521}, {1110, 4397}, {1252, 3239}, {1260, 1897}, {1265, 8750}, {1293, 6555}, {1331, 7046}, {1332, 7079}, {1415, 30693}, {1783, 3692}, {1802, 6335}, {1978, 14827}, {2284, 6559}, {2316, 30731}, {2318, 36797}, {2321, 5546}, {2322, 4574}, {2325, 5548}, {2328, 3952}, {2340, 36802}, {3119, 31615}, {3158, 31343}, {3965, 36147}, {4103, 7054}, {4105, 4998}, {4130, 4564}, {4171, 4567}, {4524, 4600}, {4528, 9268}, {4554, 6602}, {4561, 7071}, {4619, 23970}, {4636, 6057}, {4873, 5549}, {4936, 27834}, {5376, 14427}, {6066, 35519}, {6605, 35341}, {6632, 14936}, {7035, 8641}, {30681, 32674}, {30728, 34820}, {30729, 33635}
X(43932) = barycentric product X(i)*X(j) for these {i,j}: {7, 3669}, {11, 4617}, {56, 24002}, {57, 3676}, {65, 17096}, {86, 7216}, {226, 7203}, {244, 658}, {269, 514}, {274, 7250}, {279, 513}, {479, 650}, {522, 738}, {644, 41292}, {649, 1088}, {651, 1358}, {663, 23062}, {693, 1407}, {764, 1275}, {905, 1119}, {934, 1086}, {1014, 7178}, {1015, 4569}, {1019, 3668}, {1020, 17205}, {1042, 7199}, {1106, 3261}, {1111, 1461}, {1357, 4554}, {1396, 17094}, {1398, 15413}, {1412, 4077}, {1426, 15419}, {1427, 7192}, {1434, 4017}, {1435, 4025}, {1439, 17925}, {1446, 3733}, {1459, 1847}, {1462, 43042}, {1565, 32714}, {2170, 4626}, {3120, 4637}, {3122, 4635}, {3125, 4616}, {3271, 36838}, {3937, 13149}, {3942, 36118}, {4391, 7023}, {4566, 16726}, {4817, 7204}, {4858, 6614}, {6545, 7045}, {6591, 7056}, {6612, 17896}, {7053, 17924}, {7177, 7649}, {7339, 40166}, {7366, 35519}, {17107, 31605}, {18344, 30682}, {19604, 30719}, {23100, 24027}, {23971, 42455}, {24013, 42462}, {37141, 38374}, {40154, 43049}
X(43932) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 6558}, {6, 4578}, {7, 646}, {56, 644}, {57, 3699}, {58, 7259}, {65, 30730}, {81, 7256}, {86, 7258}, {222, 4571}, {244, 3239}, {269, 190}, {279, 668}, {479, 4554}, {512, 4515}, {513, 346}, {514, 341}, {521, 30681}, {522, 30693}, {552, 4631}, {603, 4587}, {604, 3939}, {649, 200}, {650, 5423}, {651, 4076}, {658, 7035}, {661, 4082}, {663, 728}, {667, 220}, {738, 664}, {764, 1146}, {905, 1265}, {934, 1016}, {1014, 645}, {1015, 3900}, {1019, 1043}, {1027, 6559}, {1042, 1018}, {1086, 4397}, {1088, 1978}, {1106, 101}, {1119, 6335}, {1122, 25268}, {1254, 4103}, {1319, 30731}, {1357, 650}, {1358, 4391}, {1396, 36797}, {1398, 1783}, {1400, 4069}, {1407, 100}, {1408, 5546}, {1410, 4574}, {1412, 643}, {1415, 6065}, {1417, 5548}, {1420, 30720}, {1427, 3952}, {1434, 7257}, {1435, 1897}, {1446, 27808}, {1459, 3692}, {1461, 765}, {1462, 36802}, {1565, 15416}, {1919, 1253}, {1977, 8641}, {1980, 14827}, {2087, 4528}, {2170, 4163}, {3063, 480}, {3121, 4524}, {3122, 4171}, {3248, 657}, {3271, 4130}, {3361, 30728}, {3668, 4033}, {3669, 8}, {3676, 312}, {3733, 2287}, {4017, 2321}, {4077, 30713}, {4394, 6555}, {4569, 31625}, {4616, 4601}, {4617, 4998}, {4637, 4600}, {6371, 3965}, {6545, 24026}, {6591, 7046}, {6612, 13138}, {6614, 4564}, {7023, 651}, {7045, 6632}, {7053, 1332}, {7099, 1331}, {7143, 21859}, {7177, 4561}, {7178, 3701}, {7180, 210}, {7203, 333}, {7204, 3807}, {7216, 10}, {7250, 37}, {7254, 1792}, {7339, 31615}, {7341, 4612}, {7366, 109}, {7649, 7101}, {8027, 14936}, {8034, 36197}, {8643, 4936}, {16726, 7253}, {17096, 314}, {21143, 2310}, {22383, 1260}, {23062, 4572}, {24002, 3596}, {27846, 4148}, {30722, 3902}, {30723, 4673}, {30724, 3702}, {30725, 4723}, {32636, 30729}, {32714, 15742}, {34399, 42380}, {34855, 42720}, {40151, 31343}, {41292, 24002}, {42336, 2347}, {43041, 3975}, {43051, 27538}
X(43932) = {X(57),X(43049)}-harmonic conjugate of X(4394)

X(43933) = X(1309)*X(1015)/X(6)

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

X(43933) lies on the circumparabola {{A,B,C,X(513),X(649)}, the cubic K406, and these lines: {2, 42769}, {4, 513}, {19, 649}, {28, 2401}, {34, 7649}, {104, 915}, {286, 7192}, {514, 37628}, {522, 1158}, {877, 17929}, {885, 14776}, {901, 1309}, {1643, 40138}, {1785, 23838}, {2423, 5317}, {7952, 24457}, {11023, 39267}, {20293, 34406}, {23345, 36123}, {23987, 36110}, {34234, 35365}

X(43933) = anticomplement of X(42769)
X(43933) = polar conjugate of X(2397)
X(43933) = polar conjugate of the isotomic conjugate of X(2401)
X(43933) = polar conjugate of the isogonal conjugate of X(2423)
X(43933) = X(36106)-anticomplementary conjugate of X(153)
X(43933) = X(1309)-Ceva conjugate of X(36123)
X(43933) = X(i)-cross conjugate of X(j) for these (i,j): {2423, 2401}, {6550, 2969}
X(43933) = crosspoint of X(1309) and X(36123)
X(43933) = crosssum of X(8677) and X(22350)
X(43933) = trilinear pole of line {1015, 6591}
X(43933) = pole wrt polar circle of trilinear polar of X(2397) (line X(119)X(517))
X(43933) = crossdifference of every pair of points on line {22350, 38353}
X(43933) = X(i)-isoconjugate of X(j) for these (i,j): {48, 2397}, {63, 2427}, {78, 23981}, {100, 22350}, {219, 24029}, {517, 1331}, {765, 8677}, {906, 908}, {1259, 23706}, {1332, 2183}, {1457, 4571}, {1465, 4587}, {1795, 15632}, {3262, 32656}, {3682, 4246}, {4558, 21801}, {4575, 17757}, {6735, 36059}, {7035, 23220}
X(43933) = barycentric product X(i)*X(j) for these {i,j}: {4, 2401}, {104, 17924}, {264, 2423}, {278, 43728}, {513, 16082}, {514, 36123}, {1086, 1309}, {2969, 13136}, {2973, 32641}, {4858, 36110}, {6335, 15635}, {6591, 18816}, {7649, 34234}, {14776, 23989}, {17925, 38955}, {21132, 39294}, {32702, 34387}
X(43933) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 2397}, {25, 2427}, {34, 24029}, {104, 1332}, {608, 23981}, {649, 22350}, {909, 1331}, {1015, 8677}, {1309, 1016}, {1977, 23220}, {2342, 4587}, {2401, 69}, {2423, 3}, {2501, 17757}, {2969, 10015}, {3064, 6735}, {5317, 4246}, {6591, 517}, {7649, 908}, {8735, 2804}, {14571, 15632}, {14776, 1252}, {15635, 905}, {16082, 668}, {17924, 3262}, {17925, 17139}, {32702, 59}, {34051, 6516}, {34234, 4561}, {34858, 906}, {36110, 4564}, {36123, 190}, {37628, 3719}, {39534, 26611}, {42067, 3310}, {43728, 345}

X(43934) = 59TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    (a^2 - b^2 - c^2)*(2*a^8 - a^6*b^2 - 3*a^4*b^4 + a^2*b^6 + b^8 - a^6*c^2 - 30*a^4*b^2*c^2 - a^2*b^4*c^2 - 4*b^6*c^2 - 3*a^4*c^4 - a^2*b^2*c^4 + 6*b^4*c^4 + a^2*c^6 - 4*b^2*c^6 + c^8) : :
X(43934) = 7 X[2] - X[34613], X[3] + 2 X[10691], 7 X[3] + 2 X[12362], 8 X[3] + X[12605], 23 X[3] + X[18561], 35 X[3] + X[18562], 17 X[3] + X[18563], 11 X[3] + X[18564], 37 X[3] - X[18565], 11 X[3] - 2 X[31829], 4 X[140] - X[428], X[381] - 4 X[7734], 2 X[549] + X[7667], 10 X[631] - X[7553], 5 X[631] - 2 X[10127], X[1885] + 8 X[33923], 7 X[3523] - X[7576], 7 X[3524] - X[38320], 7 X[3526] - 4 X[10128], 17 X[3533] - 8 X[23411], X[3575] - 10 X[15712], 2 X[3845] + X[34614], 2 X[6756] - 11 X[15720], X[7540] - 7 X[15701], X[7553] - 4 X[10127], 2 X[8703] + X[34664], 13 X[10299] - X[18559], 7 X[10691] - X[12362], 16 X[10691] - X[12605], 46 X[10691] - X[18561], 70 X[10691] - X[18562], 34 X[10691] - X[18563], 22 X[10691] - X[18564], 74 X[10691] + X[18565], 11 X[10691] + X[31829], 4 X[11812] - X[13490], 16 X[12362] - 7 X[12605], 46 X[12362] - 7 X[18561], 10 X[12362] - X[18562], 34 X[12362] - 7 X[18563], 22 X[12362] - 7 X[18564], 74 X[12362] + 7 X[18565], 11 X[12362] + 7 X[31829], 23 X[12605] - 8 X[18561], 35 X[12605] - 8 X[18562], 17 X[12605] - 8 X[18563], 11 X[12605] - 8 X[18564], 37 X[12605] + 8 X[18565], 11 X[12605] + 16 X[31829], 8 X[13361] - 11 X[15723], 7 X[15698] - X[38323], 7 X[15700] - X[38321], 7 X[15702] - X[34603], 5 X[15713] - 2 X[23410], 11 X[15717] - 2 X[31833], 35 X[18561] - 23 X[18562], 17 X[18561] - 23 X[18563], 11 X[18561] - 23 X[18564], 37 X[18561] + 23 X[18565], 11 X[18561] + 46 X[31829], 17 X[18562] - 35 X[18563], 11 X[18562] - 35 X[18564], 37 X[18562] + 35 X[18565], 11 X[18562] + 70 X[31829], 11 X[18563] - 17 X[18564], 37 X[18563] + 17 X[18565], 11 X[18563] + 34 X[31829], 37 X[18564] + 11 X[18565], X[18564] + 2 X[31829], 11 X[18565] - 74 X[31829], 7 X[19711] - X[38322]

See Antreas Hatzipolakis and Peter Moses, euclid 1787.

X(43934) lies on these lines: {2, 3}, {11515, 16962}, {11516, 16963}

X(43934) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 7387}, {2, 34938, 381}, {3, 7386, 15760}, {549, 8703, 1658}, {549, 23335, 2}, {5054, 15688, 10245}, {10212, 14891, 12100}, {12100, 23336, 549}, {34551, 34552, 17714}

leftri

Points associated with circumparabola with infinite center: X(42935)-X(43945)

rightri

This preamble and points X(42935)-X(43945) are contributed by Peter Moses, July 5, 2021.

In the following table each nmber k represents the triangle center X(k):

center focus vertex perspector
30 38246 43941 3163
511 43935 43942 11672
512 38017 1084
513 38018 1015
514 38019 43943 1086
516 23972
517 43936 23980
518 43937 43944 6184
519 43938 4370
521 43939 35072
522 43940 1146
523 12064 115
524 38020 43345 2482
525 38233 15526
690 38233 23992
900 35092
1503 23976
3667 40621
9033 39008

Barycentrics for the vertex of the circumparabola with center U = u : v : w are given by

(v + w)*(2*c^2*v^3 - 3*(a^2 - b^2 - c^2)*v^2*w - (a^2 - 5*b^2 - c^2)*v*w^2 + 2*b^2*w^3)*(2*c^2*v^3 - (a^2 - b^2 - 5*c^2)*v^2*w - 3*(a^2 - b^2 - c^2)*v*w^2 + 2*b^2*w^3) : : ,

this being the combo U'-(cross conjugate of U), where U' = orthocpoint of U.

See Bernard Gibert, Q077 and Q079. See also the preamble just before X(42921).



X(43935) = FOCUS OF CIRCUMPARABOLA WITH CENTER X(511)

Barycentrics    a^2*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^16*b^4 - 5*a^14*b^6 + 11*a^12*b^8 - 14*a^10*b^10 + 11*a^8*b^12 - 5*a^6*b^14 + a^4*b^16 + 3*a^16*b^2*c^2 - 13*a^14*b^4*c^2 + 24*a^12*b^6*c^2 - 22*a^10*b^8*c^2 + 7*a^8*b^10*c^2 + 3*a^6*b^12*c^2 - 2*a^4*b^14*c^2 + a^16*c^4 - 13*a^14*b^2*c^4 + 24*a^12*b^4*c^4 - 22*a^10*b^6*c^4 + 9*a^8*b^8*c^4 - 3*a^6*b^10*c^4 + 2*a^4*b^12*c^4 + 2*a^2*b^14*c^4 - 5*a^14*c^6 + 24*a^12*b^2*c^6 - 22*a^10*b^4*c^6 + 15*a^8*b^6*c^6 - 3*a^6*b^8*c^6 - 4*a^4*b^10*c^6 - 6*a^2*b^12*c^6 + b^14*c^6 + 11*a^12*c^8 - 22*a^10*b^2*c^8 + 9*a^8*b^4*c^8 - 3*a^6*b^6*c^8 + 6*a^4*b^8*c^8 + 4*a^2*b^10*c^8 - 4*b^12*c^8 - 14*a^10*c^10 + 7*a^8*b^2*c^10 - 3*a^6*b^4*c^10 - 4*a^4*b^6*c^10 + 4*a^2*b^8*c^10 + 6*b^10*c^10 + 11*a^8*c^12 + 3*a^6*b^2*c^12 + 2*a^4*b^4*c^12 - 6*a^2*b^6*c^12 - 4*b^8*c^12 - 5*a^6*c^14 - 2*a^4*b^2*c^14 + 2*a^2*b^4*c^14 + b^6*c^14 + a^4*c^16) : :
X(43935) = X[98] + 3 X[23611]

X(43935) lies on the curve Q077 and these lines: {98, 23611}, {230, 511}

X(43936) = FOCUS OF CIRCUMPARABOLA WITH CENTER X(517)

Barycentrics    a^2*(a^2*b - b^3 + a^2*c - 2*a*b*c + b^2*c + b*c^2 - c^3)*(a^12*b^2 - a^11*b^3 - 5*a^10*b^4 + 5*a^9*b^5 + 10*a^8*b^6 - 10*a^7*b^7 - 10*a^6*b^8 + 10*a^5*b^9 + 5*a^4*b^10 - 5*a^3*b^11 - a^2*b^12 + a*b^13 + 3*a^12*b*c - 9*a^11*b^2*c - 2*a^10*b^3*c + 33*a^9*b^4*c - 22*a^8*b^5*c - 42*a^7*b^6*c + 48*a^6*b^7*c + 18*a^5*b^8*c - 37*a^4*b^9*c + 3*a^3*b^10*c + 10*a^2*b^11*c - 3*a*b^12*c + a^12*c^2 - 9*a^11*b*c^2 + 28*a^10*b^2*c^2 - 16*a^9*b^3*c^2 - 70*a^8*b^4*c^2 + 102*a^7*b^5*c^2 + 32*a^6*b^6*c^2 - 120*a^5*b^7*c^2 + 29*a^4*b^8*c^2 + 43*a^3*b^9*c^2 - 20*a^2*b^10*c^2 - a^11*c^3 - 2*a^10*b*c^3 - 16*a^9*b^2*c^3 + 73*a^8*b^3*c^3 - 18*a^7*b^4*c^3 - 144*a^6*b^5*c^3 + 96*a^5*b^6*c^3 + 78*a^4*b^7*c^3 - 69*a^3*b^8*c^3 - 6*a^2*b^9*c^3 + 8*a*b^10*c^3 + b^11*c^3 - 5*a^10*c^4 + 33*a^9*b*c^4 - 70*a^8*b^2*c^4 - 18*a^7*b^3*c^4 + 132*a^6*b^4*c^4 - 4*a^5*b^5*c^4 - 98*a^4*b^6*c^4 - 6*a^3*b^7*c^4 + 41*a^2*b^8*c^4 - 5*a*b^9*c^4 + 5*a^9*c^5 - 22*a^8*b*c^5 + 102*a^7*b^2*c^5 - 144*a^6*b^3*c^5 - 4*a^5*b^4*c^5 + 46*a^4*b^5*c^5 + 34*a^3*b^6*c^5 - 4*a^2*b^7*c^5 - 9*a*b^8*c^5 - 4*b^9*c^5 + 10*a^8*c^6 - 42*a^7*b*c^6 + 32*a^6*b^2*c^6 + 96*a^5*b^3*c^6 - 98*a^4*b^4*c^6 + 34*a^3*b^5*c^6 - 40*a^2*b^6*c^6 + 8*a*b^7*c^6 - 10*a^7*c^7 + 48*a^6*b*c^7 - 120*a^5*b^2*c^7 + 78*a^4*b^3*c^7 - 6*a^3*b^4*c^7 - 4*a^2*b^5*c^7 + 8*a*b^6*c^7 + 6*b^7*c^7 - 10*a^6*c^8 + 18*a^5*b*c^8 + 29*a^4*b^2*c^8 - 69*a^3*b^3*c^8 + 41*a^2*b^4*c^8 - 9*a*b^5*c^8 + 10*a^5*c^9 - 37*a^4*b*c^9 + 43*a^3*b^2*c^9 - 6*a^2*b^3*c^9 - 5*a*b^4*c^9 - 4*b^5*c^9 + 5*a^4*c^10 + 3*a^3*b*c^10 - 20*a^2*b^2*c^10 + 8*a*b^3*c^10 - 5*a^3*c^11 + 10*a^2*b*c^11 + b^3*c^11 - a^2*c^12 - 3*a*b*c^12 + a*c^13) : :

X(43936) lies on the curve Q077 and these lines: {517, 1387}, {23981, 38579}

X(43937) = FOCUS OF CIRCUMPARABOLA WITH CENTER X(518)

Barycentrics    a^2*(a*b - b^2 + a*c - c^2)*(a^8*b^2 - 3*a^7*b^3 + 3*a^6*b^4 - a^5*b^5 - a^4*b^6 + 3*a^3*b^7 - 3*a^2*b^8 + a*b^9 + 3*a^8*b*c - 7*a^7*b^2*c + 4*a^6*b^3*c + 5*a^5*b^4*c - 13*a^4*b^5*c + 11*a^3*b^6*c - 2*a^2*b^7*c - a*b^8*c + a^8*c^2 - 7*a^7*b*c^2 + 18*a^5*b^3*c^2 - 23*a^4*b^4*c^2 + 9*a^3*b^5*c^2 - 2*a^2*b^6*c^2 + 4*a*b^7*c^2 - 3*a^7*c^3 + 4*a^6*b*c^3 + 18*a^5*b^2*c^3 - 17*a^4*b^3*c^3 + 9*a^3*b^4*c^3 - 4*a^2*b^5*c^3 - 8*a*b^6*c^3 + b^7*c^3 + 3*a^6*c^4 + 5*a^5*b*c^4 - 23*a^4*b^2*c^4 + 9*a^3*b^3*c^4 + 6*a^2*b^4*c^4 + 4*a*b^5*c^4 - 4*b^6*c^4 - a^5*c^5 - 13*a^4*b*c^5 + 9*a^3*b^2*c^5 - 4*a^2*b^3*c^5 + 4*a*b^4*c^5 + 6*b^5*c^5 - a^4*c^6 + 11*a^3*b*c^6 - 2*a^2*b^2*c^6 - 8*a*b^3*c^6 - 4*b^4*c^6 + 3*a^3*c^7 - 2*a^2*b*c^7 + 4*a*b^2*c^7 + b^3*c^7 - 3*a^2*c^8 - a*b*c^8 + a*c^9) : :
X(43937) = X[105] + 3 X[23612]

X(43937) lies on the curve Q077 and these lines: {105, 7077}, {518, 6714}

X(43938) = FOCUS OF CIRCUMPARABOLA WITH CENTER X(519)

Barycentrics    (2*a - b - c)*(5*a^6 - 10*a^5*b - 14*a^4*b^2 + 15*a^3*b^3 + 8*a^2*b^4 - 5*a*b^5 + b^6 - 10*a^5*c + 42*a^4*b*c + 7*a^3*b^2*c - 43*a^2*b^3*c + 3*a*b^4*c + b^5*c - 14*a^4*c^2 + 7*a^3*b*c^2 - 21*a^2*b^2*c^2 + 34*a*b^3*c^2 - 5*b^4*c^2 + 15*a^3*c^3 - 43*a^2*b*c^3 + 34*a*b^2*c^3 - 10*b^3*c^3 + 8*a^2*c^4 + 3*a*b*c^4 - 5*b^2*c^4 - 5*a*c^5 + b*c^5 + c^6) : :
X(43938) = X[106] + 3 X[8028], 9 X[17780] - X[21290]

X(43938) lies on the curve Q077 and these lines: {106, 8028}, {519, 6715}, {4152, 41529}, {6224, 17780}

X(43939) = FOCUS OF CIRCUMPARABOLA WITH CENTER X(521)

Barycentrics    a^2*(a - b - c)*(b - c)*(a^2 - b^2 - c^2)*(a^16*b^2 - 3*a^15*b^3 - a^14*b^4 + 11*a^13*b^5 - 7*a^12*b^6 - 11*a^11*b^7 + 15*a^10*b^8 - 5*a^9*b^9 - 5*a^8*b^10 + 15*a^7*b^11 - 11*a^6*b^12 - 7*a^5*b^13 + 11*a^4*b^14 - a^3*b^15 - 3*a^2*b^16 + a*b^17 - 3*a^16*b*c + 5*a^15*b^2*c + 14*a^14*b^3*c - 31*a^13*b^4*c - 9*a^12*b^5*c + 57*a^11*b^6*c - 36*a^10*b^7*c - 19*a^9*b^8*c + 59*a^8*b^9*c - 49*a^7*b^10*c - 18*a^6*b^11*c + 51*a^5*b^12*c - 15*a^4*b^13*c - 13*a^3*b^14*c + 8*a^2*b^15*c - a*b^16*c + a^16*c^2 + 5*a^15*b*c^2 - 32*a^14*b^2*c^2 + 22*a^13*b^3*c^2 + 75*a^12*b^4*c^2 - 113*a^11*b^5*c^2 - 2*a^10*b^6*c^2 + 132*a^9*b^7*c^2 - 137*a^8*b^8*c^2 - 13*a^7*b^9*c^2 + 132*a^6*b^10*c^2 - 58*a^5*b^11*c^2 - 35*a^4*b^12*c^2 + 25*a^3*b^13*c^2 - 2*a^2*b^14*c^2 - 3*a^15*c^3 + 14*a^14*b*c^3 + 22*a^13*b^2*c^3 - 119*a^12*b^3*c^3 + 67*a^11*b^4*c^3 + 178*a^10*b^5*c^3 - 272*a^9*b^6*c^3 + 37*a^8*b^7*c^3 + 243*a^7*b^8*c^3 - 198*a^6*b^9*c^3 - 34*a^5*b^10*c^3 + 83*a^4*b^11*c^3 - 19*a^3*b^12*c^3 + 6*a^2*b^13*c^3 - 4*a*b^14*c^3 - b^15*c^3 - a^14*c^4 - 31*a^13*b*c^4 + 75*a^12*b^2*c^4 + 67*a^11*b^3*c^4 - 310*a^10*b^4*c^4 + 164*a^9*b^5*c^4 + 290*a^8*b^6*c^4 - 386*a^7*b^7*c^4 + 59*a^6*b^8*c^4 + 161*a^5*b^9*c^4 - 113*a^4*b^10*c^4 + 31*a^3*b^11*c^4 - 4*a^2*b^12*c^4 - 6*a*b^13*c^4 + 4*b^14*c^4 + 11*a^13*c^5 - 9*a^12*b*c^5 - 113*a^11*b^2*c^5 + 178*a^10*b^3*c^5 + 164*a^9*b^4*c^5 - 488*a^8*b^5*c^5 + 190*a^7*b^6*c^5 + 280*a^6*b^7*c^5 - 317*a^5*b^8*c^5 + 107*a^4*b^9*c^5 + 35*a^3*b^10*c^5 - 66*a^2*b^11*c^5 + 30*a*b^12*c^5 - 2*b^13*c^5 - 7*a^12*c^6 + 57*a^11*b*c^6 - 2*a^10*b^2*c^6 - 272*a^9*b^3*c^6 + 290*a^8*b^4*c^6 + 190*a^7*b^5*c^6 - 488*a^6*b^6*c^6 + 204*a^5*b^7*c^6 + 137*a^4*b^8*c^6 - 175*a^3*b^9*c^6 + 82*a^2*b^10*c^6 - 4*a*b^11*c^6 - 12*b^12*c^6 - 11*a^11*c^7 - 36*a^10*b*c^7 + 132*a^9*b^2*c^7 + 37*a^8*b^3*c^7 - 386*a^7*b^4*c^7 + 280*a^6*b^5*c^7 + 204*a^5*b^6*c^7 - 350*a^4*b^7*c^7 + 117*a^3*b^8*c^7 + 52*a^2*b^9*c^7 - 56*a*b^10*c^7 + 17*b^11*c^7 + 15*a^10*c^8 - 19*a^9*b*c^8 - 137*a^8*b^2*c^8 + 243*a^7*b^3*c^8 + 59*a^6*b^4*c^8 - 317*a^5*b^5*c^8 + 137*a^4*b^6*c^8 + 117*a^3*b^7*c^8 - 146*a^2*b^8*c^8 + 40*a*b^9*c^8 + 8*b^10*c^8 - 5*a^9*c^9 + 59*a^8*b*c^9 - 13*a^7*b^2*c^9 - 198*a^6*b^3*c^9 + 161*a^5*b^4*c^9 + 107*a^4*b^5*c^9 - 175*a^3*b^6*c^9 + 52*a^2*b^7*c^9 + 40*a*b^8*c^9 - 28*b^9*c^9 - 5*a^8*c^10 - 49*a^7*b*c^10 + 132*a^6*b^2*c^10 - 34*a^5*b^3*c^10 - 113*a^4*b^4*c^10 + 35*a^3*b^5*c^10 + 82*a^2*b^6*c^10 - 56*a*b^7*c^10 + 8*b^8*c^10 + 15*a^7*c^11 - 18*a^6*b*c^11 - 58*a^5*b^2*c^11 + 83*a^4*b^3*c^11 + 31*a^3*b^4*c^11 - 66*a^2*b^5*c^11 - 4*a*b^6*c^11 + 17*b^7*c^11 - 11*a^6*c^12 + 51*a^5*b*c^12 - 35*a^4*b^2*c^12 - 19*a^3*b^3*c^12 - 4*a^2*b^4*c^12 + 30*a*b^5*c^12 - 12*b^6*c^12 - 7*a^5*c^13 - 15*a^4*b*c^13 + 25*a^3*b^2*c^13 + 6*a^2*b^3*c^13 - 6*a*b^4*c^13 - 2*b^5*c^13 + 11*a^4*c^14 - 13*a^3*b*c^14 - 2*a^2*b^2*c^14 - 4*a*b^3*c^14 + 4*b^4*c^14 - a^3*c^15 + 8*a^2*b*c^15 - b^3*c^15 - 3*a^2*c^16 - a*b*c^16 + a*c^17) : :
X(43939) = X[108] + 3 X[23614]

X(43939) lies on the curve Q077 and these lines: {108, 23614}, {521, 6717}

X(43940) = FOCUS OF CIRCUMPARABOLA WITH CENTER X(522)

Barycentrics    (a - b - c)*(b - c)*(a^10 - 2*a^9*b - 2*a^8*b^2 + 7*a^7*b^3 - 3*a^6*b^4 - 5*a^5*b^5 + 7*a^4*b^6 - 3*a^3*b^7 - 2*a^2*b^8 + 3*a*b^9 - b^10 - 2*a^9*c + 10*a^8*b*c - 9*a^7*b^2*c - 13*a^6*b^3*c + 25*a^5*b^4*c - 11*a^4*b^5*c - 7*a^3*b^6*c + 13*a^2*b^7*c - 7*a*b^8*c + b^9*c - 2*a^8*c^2 - 9*a^7*b*c^2 + 33*a^6*b^2*c^2 - 20*a^5*b^3*c^2 - 25*a^4*b^4*c^2 + 39*a^3*b^5*c^2 - 17*a^2*b^6*c^2 - 2*a*b^7*c^2 + 3*b^8*c^2 + 7*a^7*c^3 - 13*a^6*b*c^3 - 20*a^5*b^2*c^3 + 58*a^4*b^3*c^3 - 29*a^3*b^4*c^3 - 17*a^2*b^5*c^3 + 18*a*b^6*c^3 - 4*b^7*c^3 - 3*a^6*c^4 + 25*a^5*b*c^4 - 25*a^4*b^2*c^4 - 29*a^3*b^3*c^4 + 46*a^2*b^4*c^4 - 12*a*b^5*c^4 - 2*b^6*c^4 - 5*a^5*c^5 - 11*a^4*b*c^5 + 39*a^3*b^2*c^5 - 17*a^2*b^3*c^5 - 12*a*b^4*c^5 + 6*b^5*c^5 + 7*a^4*c^6 - 7*a^3*b*c^6 - 17*a^2*b^2*c^6 + 18*a*b^3*c^6 - 2*b^4*c^6 - 3*a^3*c^7 + 13*a^2*b*c^7 - 2*a*b^2*c^7 - 4*b^3*c^7 - 2*a^2*c^8 - 7*a*b*c^8 + 3*b^2*c^8 + 3*a*c^9 + b*c^9 - c^10) : :
X(43940 = X[109] + 3 X[23615]

X(43940) lies on the curve Q077 and these lines: {109, 23615}, {522, 6718}

X(43941) = VERTEX OF CIRCUMPARABOLA WITH CENTER X(30)

Barycentrics    (a^2 - b^2)*(a^2 - c^2)*(2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(4*a^8 - a^6*b^2 - 6*a^4*b^4 - a^2*b^6 + 4*b^8 - 7*a^6*c^2 + 13*a^4*b^2*c^2 + 13*a^2*b^4*c^2 - 7*b^6*c^2 - 3*a^4*c^4 - 23*a^2*b^2*c^4 - 3*b^4*c^4 + 11*a^2*c^6 + 11*b^2*c^6 - 5*c^8)*(4*a^8 - 7*a^6*b^2 - 3*a^4*b^4 + 11*a^2*b^6 - 5*b^8 - a^6*c^2 + 13*a^4*b^2*c^2 - 23*a^2*b^4*c^2 + 11*b^6*c^2 - 6*a^4*c^4 + 13*a^2*b^2*c^4 - 3*b^4*c^4 - a^2*c^6 - 7*b^2*c^6 + 4*c^8) : :
X(43941) = 3 X[3081] + X[12079], 9 X[4240] - X[14611], X[31945] - 3 X[34582]

X(43941) lies on the curve Q079 and these lines: {30, 6699}, {3081, 12079}, {4240, 14611}, {31945, 34582}

X(43941) = X(523)-cross conjugate of X(30)
X(43941) = cevapoint of X(1637) and X(3081)
X(43941) = trilinear pole of line {3163, 13202}
X(43941) = barycentric quotient X(2420)/X(15051)

X(43942) = VERTEX OF CIRCUMPARABOLA WITH CENTER X(511)

Barycentrics    a^2*(a^2 - b^2)*(a^2 - c^2)*(a^2*b^2 - b^4 + a^2*c^2 - c^4)*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8 + 3*a^6*c^2 - 3*a^4*b^2*c^2 + a^2*b^4*c^2 + 3*b^6*c^2 - 2*a^4*c^4 - 3*a^2*b^2*c^4 - 3*b^4*c^4 + 3*a^2*c^6 + b^2*c^6)*(3*a^6*b^2 - 2*a^4*b^4 + 3*a^2*b^6 + a^6*c^2 - 3*a^4*b^2*c^2 - 3*a^2*b^4*c^2 + b^6*c^2 - 3*a^4*c^4 + a^2*b^2*c^4 - 3*b^4*c^4 + 3*a^2*c^6 + 3*b^2*c^6 - c^8) : :
X(43942) = X[15630] + 3 X[23611]

X(43942) lies on the curve Q079 and these lines: {230, 511}, {15630, 23611}

X(43942) = X(512)-cross conjugate of X(511)
X(43942) = cevapoint of X(2491) and X(23611)

X(43943) = VERTEX OF CIRCUMPARABOLA WITH CENTER X(514)

Barycentrics    (b - c)*(2*a^5 - a^4*b - a^3*b^2 - a^2*b^3 - a*b^4 + 2*b^5 - 5*a^4*c + 4*a^3*b*c + 2*a^2*b^2*c + 4*a*b^3*c - 5*b^4*c + 3*a^3*c^2 - 2*a^2*b*c^2 - 2*a*b^2*c^2 + 3*b^3*c^2 - a^2*c^3 - 4*a*b*c^3 - b^2*c^3 + 3*a*c^4 + 3*b*c^4 - 2*c^5)*(-2*a^5 + 5*a^4*b - 3*a^3*b^2 + a^2*b^3 - 3*a*b^4 + 2*b^5 + a^4*c - 4*a^3*b*c + 2*a^2*b^2*c + 4*a*b^3*c - 3*b^4*c + a^3*c^2 - 2*a^2*b*c^2 + 2*a*b^2*c^2 + b^3*c^2 + a^2*c^3 - 4*a*b*c^3 - 3*b^2*c^3 + a*c^4 + 5*b*c^4 - 2*c^5) : :
X(43943) = X[3234] + 3 X[6545]

X(43943) lies on the curve Q079 and these lines: {514, 6710}, {3234, 6545}, {31647, 41308}

X(43943) = reflection of X(31647) in X(41308)
X(43943) = X(516)-cross conjugate of X(514)
X(43943) = cevapoint of X(676) and X(6545)
X(43943) = trilinear pole of line {1086, 23730}

X(43944) = VERTEX OF CIRCUMPARABOLA WITH CENTER X(518)

Barycentrics    a*(a - b)*(a - c)*(a*b - b^2 + a*c - c^2)*(a^5*b - 3*a^4*b^2 + 4*a^3*b^3 - 4*a^2*b^4 + 3*a*b^5 - b^6 + 3*a^5*c - 7*a^4*b*c + 8*a^3*b^2*c - 4*a^2*b^3*c - 3*a*b^4*c + 3*b^5*c - 6*a^4*c^2 + 2*a^3*b*c^2 + 4*a^2*b^2*c^2 - 4*a*b^3*c^2 - 4*b^4*c^2 + 6*a^3*c^3 + 2*a^2*b*c^3 + 8*a*b^2*c^3 + 4*b^3*c^3 - 6*a^2*c^4 - 7*a*b*c^4 - 3*b^2*c^4 + 3*a*c^5 + b*c^5)*(3*a^5*b - 6*a^4*b^2 + 6*a^3*b^3 - 6*a^2*b^4 + 3*a*b^5 + a^5*c - 7*a^4*b*c + 2*a^3*b^2*c + 2*a^2*b^3*c - 7*a*b^4*c + b^5*c - 3*a^4*c^2 + 8*a^3*b*c^2 + 4*a^2*b^2*c^2 + 8*a*b^3*c^2 - 3*b^4*c^2 + 4*a^3*c^3 - 4*a^2*b*c^3 - 4*a*b^2*c^3 + 4*b^3*c^3 - 4*a^2*c^4 - 3*a*b*c^4 - 4*b^2*c^4 + 3*a*c^5 + 3*b*c^5 - c^6) : :
X(43944) = X[15636] + 3 X[23612]

X(43944) lies on the curve Q079 and these lines: {518, 6714}, {15636, 23612}

X(43944) = X(3309)-cross conjugate of X(518)

X(43945) = VERTEX OF CIRCUMPARABOLA WITH CENTER X(525)

Barycentrics    (b^2 - c^2)*(-a^2 + b^2 + c^2)*(-2*a^14 + a^12*b^2 + 5*a^10*b^4 - 4*a^8*b^6 + a^4*b^10 - 3*a^2*b^12 + 2*b^14 + 5*a^12*c^2 - 8*a^10*b^2*c^2 - a^8*b^4*c^2 + 4*a^6*b^6*c^2 - a^4*b^8*c^2 + 4*a^2*b^10*c^2 - 3*b^12*c^2 - 3*a^10*c^4 + 7*a^8*b^2*c^4 - 4*a^6*b^4*c^4 - a^2*b^8*c^4 + b^10*c^4 - 4*a^4*b^4*c^6 + 4*a^2*b^6*c^6 + 7*a^4*b^2*c^8 - a^2*b^4*c^8 - 4*b^6*c^8 - 3*a^4*c^10 - 8*a^2*b^2*c^10 + 5*b^4*c^10 + 5*a^2*c^12 + b^2*c^12 - 2*c^14)*(2*a^14 - 5*a^12*b^2 + 3*a^10*b^4 + 3*a^4*b^10 - 5*a^2*b^12 + 2*b^14 - a^12*c^2 + 8*a^10*b^2*c^2 - 7*a^8*b^4*c^2 - 7*a^4*b^8*c^2 + 8*a^2*b^10*c^2 - b^12*c^2 - 5*a^10*c^4 + a^8*b^2*c^4 + 4*a^6*b^4*c^4 + 4*a^4*b^6*c^4 + a^2*b^8*c^4 - 5*b^10*c^4 + 4*a^8*c^6 - 4*a^6*b^2*c^6 - 4*a^2*b^6*c^6 + 4*b^8*c^6 + a^4*b^2*c^8 + a^2*b^4*c^8 - a^4*c^10 - 4*a^2*b^2*c^10 - b^4*c^10 + 3*a^2*c^12 + 3*b^2*c^12 - 2*c^14) : :
X(43945) = X[15639] + 3 X[23616]

X(43945) lies on the curve Q079 and these lines: {525, 6720}, {15639, 23616}

X(43945) = X(1503)-cross conjugate of X(525)

X(43946) = PERSPECTOR OF THE FEUERBACH CIRCUMHYPERBOLA OF THE MEDIAL TRIANGLE

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

X(43946) lies on these lines: {1376, 14589}, {3035, 4885}

X(43947) = PERSPECTOR OF THE KIEPERT CIRCUMHYPERBOLA OF THE INTOUCH TRIANGLE

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

X(43847) lies on these lines: {65, 34230}, {513, 43914}, {517, 1458}, {518, 6735}, {522, 5083}, {651, 18771}, {672, 3660}, {840, 40577}, {1037, 5091}, {1319, 3286}, {1362, 7336}, {1785, 1876}, {18839, 22464}, {38269, 38530}

X(43947) = X(43909)-cross conjugate of X(513)
X(43947) = cevapoint of X(i) and X(j) for these (i,j): {1362, 3675}, {2446, 2447}
X(43947) = X(i)-isoconjugate of X(j) for these (i,j): {55, 24203}, {522, 1618}, {7012, 34949}
X(43947) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 24203}, {1415, 1618}, {7117, 34949}

X(43948) = PERSPECTOR OF THE JERABEK CIRCUMHYPERBOLA OF THE INTOUCH TRIANGLE

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

X(43948) lies on these lines: {226, 24198}, {3911, 36954}, {5083, 43932}

X(43948) = cevapoint of X(57) and X(37736)
X(43948) = X(i)-isoconjugate of X(j) for these (i,j): {41, 27191}, {55, 3315}, {3063, 32028}
X(43948) = barycentric product X(7)*X(36954)
X(43948) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 27191}, {57, 3315}, {664, 32028}, {1358, 31647}, {3911, 20042}, {36954, 8}

X(43949) = PERSPECTOR OF THE PYTHAGOREAN CONIC

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

See the preamble just before X(43630) for the definition of the Pythagorean conic and reference for its connection with the cubic K1231.

X(43949) lies on on the Jerabek circumhyperbola and these lines: {67, 18382}, {68, 18394}, {70, 18383}, {265, 18568}, {568, 17505}, {3521, 11457}, {3532, 18405}, {4846, 25739}, {7687, 38534}, {12022, 43908}, {14528, 18396}, {39874, 43697}
X(43949) = isogonal conjugate of X(18324)
X(43949) = X(18376)-cross conjugate of X(4)
X(43949) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18324}, {6149, 18576}
X(43949) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 18324}, {1989, 18576}

X(43950) = PERSPECTOR OF THE MOSES CIRCLE

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

X(43950) lies on these lines: {187, 14096}, {512, 13410}, {524, 5052}, {5475, 20021}, {27366, 39590}

X(43951) = PERSPECTOR OF THE OTHOPTIC CIRCLE OF THE STEINER CIRCUMELLIPSE

Barycentrics    (3*a^4 + 10*a^2*b^2 + 3*b^4 + 2*a^2*c^2 + 2*b^2*c^2 - 5*c^4)*(3*a^4 + 2*a^2*b^2 - 5*b^4 + 10*a^2*c^2 + 2*b^2*c^2 + 3*c^4) : :
X(43951) = 5 X[3091] - 2 X[18840]

X(43951) lies on the Kiepert circumhyperbola and these lines: {2, 21167}, {4, 14930}, {20, 18841}, {76, 3832}, {83, 3146}, {98, 9748}, {275, 7408}, {383, 43554}, {427, 38253}, {459, 7378}, {1080, 43555}, {1513, 10155}, {1699, 4052}, {2052, 7409}, {3091, 18840}, {3316, 7000}, {3317, 7374}, {3424, 5480}, {3522, 43527}, {3543, 18842}, {3839, 5485}, {5068, 10159}, {5395, 7864}, {6201, 14237}, {6202, 14232}, {6504, 37349}, {6811, 34091}, {6813, 34089}, {7607, 9752}, {7710, 14484}, {7779, 43681}, {9754, 11668}, {9756, 43537}, {14458, 14853}, {37463, 43444}, {37464, 43445}

X(43951) = isotomic conjugate of the anticomplement of X(37665)
X(43951) = isogonal conjugate of {X(3),X(6)}-harmonic conjugate of X(31884)
X(43951) = isogonal conjugate of {X(1151),X(1152)}-harmonic conjugate of X(39)
X(43951) = X(37665)-cross conjugate of X(2)

X(43952) = PERSPECTOR OF THE MOSES-RADICAL CIRCLE

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

X(43952) lies on these lines: {852, 38999}, {1503, 6130}, {3331, 9408}, {6000, 9409}

X(43952) = cevapoint of X(1495) and X(8779)

X(43953) = PERSPECTOR OF CIRCUMCIRCLE OF THE INNER NAPOLEON TRIANGLE

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

X(43953) lies on the Kiepert circumhyperbola and these lines: {13, 14853}, {14, 41458}, {18, 40921}, {98, 5334}, {5480, 43954}, {6776, 9113}, {7685, 9752}, {22491, 42036}

X(43954) = PERSPECTOR OF CIRCUMCIRCLE OF THE OUTER NAPOLEON TRIANGLE

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

X(43954) lies on the Kiepert circumhyperbola and these lines: {13, 36761}, {14, 14853}, {17, 40922}, {98, 5335}, {5480, 43953}, {6776, 9112}, {7684, 9752}, {22492, 42035}

X(43955) = PERSPECTOR OF LUCAS-CIRCLES RADICAL CIRCLE

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

X(43955) lies on these lines: {5408, 6221}, {32810, 32837}

X(43956) = PERSPECTOR OF ANTI-ARTZT CIRCLE

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

X(43956) lies on these lines: {30, 5050}, {1499, 15484}

X(43956) = barycentric product X(599)*X(39453)
X(43956) = barycentric quotient X(39453)/X(598)

X(43957) = 60TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    2*a^6 + a^4*b^2 - 2*a^2*b^4 - b^6 + a^4*c^2 - 12*a^2*b^2*c^2 + b^4*c^2 - 2*a^2*c^4 + b^2*c^4 - c^6 : :
X(43957) = 2 X[1] + X[34656], 4 X[2] - X[428], 2 X[2] + X[7667], X[2] - 4 X[7734], 7 X[2] - 4 X[10128], X[2] + 2 X[10691], 11 X[2] - 8 X[13361], 7 X[2] - X[34603], 8 X[3] + X[1885], 2 X[3] + X[34664], 2 X[4] + X[34614], 2 X[8] + X[34667], 2 X[10] + X[34634], 10 X[140] - X[11819], X[428] + 2 X[7667], X[428] - 16 X[7734], 7 X[428] - 16 X[10128], X[428] + 8 X[10691], 11 X[428] - 32 X[13361], 7 X[428] - 4 X[34603], 10 X[631] - X[3575], 10 X[632] - X[7553], 5 X[632] - 2 X[23410], X[1885] - 4 X[34664], 7 X[3090] - X[34613], 7 X[3523] + 2 X[12362], 7 X[3523] - X[38323], 11 X[3525] - 2 X[6756], 7 X[3526] - X[7540], 7 X[3528] + 2 X[13488], 8 X[3530] + X[12605], 7 X[3624] - X[34657], 2 X[3917] + X[11245], 2 X[5447] + X[43573], X[7553] - 4 X[23410], X[7576] - 7 X[15702], X[7667] + 8 X[7734], 7 X[7667] + 8 X[10128], X[7667] - 4 X[10691], 11 X[7667] + 16 X[13361], 7 X[7667] + 2 X[34603], 7 X[7734] - X[10128], 2 X[7734] + X[10691], 11 X[7734] - 2 X[13361], 28 X[7734] - X[34603], 2 X[7812] + X[34660], 2 X[7883] + X[34650], 7 X[7999] + 2 X[18914], 7 X[9780] - X[34668], 4 X[9825] - 13 X[10303], 4 X[10124] - X[13490], 2 X[10127] - 5 X[15694], 2 X[10128] + 7 X[10691], 11 X[10128] - 14 X[13361], 4 X[10128] - X[34603], 3 X[10304] + X[37077], 11 X[10691] + 4 X[13361], 14 X[10691] + X[34603], 2 X[11235] + X[34654], 2 X[11236] + X[34662], 8 X[11592] + X[12370], 2 X[12362] + X[38323], 56 X[13361] - 11 X[34603], 7 X[14869] - X[38322], 7 X[15701] - X[38321], 11 X[15717] - 2 X[31829], 11 X[15718] + X[18564], 11 X[15720] - 2 X[31833], 2 X[34606] + X[34652], 2 X[34609] + X[34658], 2 X[34612] + X[34665]

See Antreas Hatzipolakis and Peter Moses, euclid 1810.

X(43957) lies on these lines: {1, 34656}, {2, 3}, {8, 34667}, {10, 34634}, {125, 33851}, {126, 15822}, {305, 37671}, {373, 29181}, {394, 11179}, {524, 3917}, {542, 3819}, {597, 43650}, {599, 1899}, {612, 5434}, {614, 3058}, {1184, 7739}, {1503, 5650}, {1853, 21358}, {3003, 9300}, {3098, 37648}, {3266, 7767}, {3564, 7998}, {3580, 41462}, {3624, 34657}, {5012, 40112}, {5063, 5306}, {5092, 11064}, {5297, 18990}, {5447, 43573}, {5480, 22112}, {5486, 15533}, {5642, 22352}, {5646, 36990}, {5888, 18358}, {5943, 19924}, {6090, 25406}, {7191, 15170}, {7292, 15171}, {7738, 40126}, {7750, 11059}, {7812, 34660}, {7883, 34650}, {7904, 30793}, {7999, 18914}, {8589, 24855}, {9140, 37636}, {9780, 34668}, {10168, 37649}, {10519, 26869}, {10601, 20423}, {11235, 34654}, {11236, 34662}, {11592, 12370}, {12017, 37645}, {13394, 17508}, {13857, 23292}, {14810, 32269}, {15051, 32227}, {15082, 29012}, {17811, 43273}, {18911, 21766}, {26866, 26939}, {26867, 26929}, {32237, 33751}, {33750, 35260}, {33884, 34380}, {34606, 34652}, {34612, 34665}, {35254, 37470}, {37775, 42122}, {37776, 42123}, {37803, 43459}

X(43957) = reflection of X(35283) in X(15082)
X(43957) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 25}, {2, 381, 37439}, {2, 549, 7499}, {2, 1370, 381}, {2, 3543, 7392}, {2, 5133, 547}, {2, 6636, 7426}, {2, 7378, 5071}, {2, 7386, 31152}, {2, 7426, 6677}, {2, 7485, 549}, {2, 7667, 428}, {2, 8703, 37904}, {2, 10691, 7667}, {2, 10989, 5133}, {2, 15683, 7398}, {2, 15692, 7494}, {2, 16063, 31133}, {2, 16951, 6661}, {2, 31133, 5}, {2, 31152, 427}, {2, 34603, 10128}, {3, 30739, 468}, {20, 11284, 10301}, {140, 858, 37454}, {140, 10300, 858}, {381, 16419, 2}, {549, 1368, 2}, {550, 1995, 37899}, {858, 7496, 140}, {1368, 7485, 7499}, {1370, 16419, 37439}, {3530, 5159, 7495}, {6804, 37198, 1906}, {7386, 7484, 427}, {7396, 7539, 427}, {7484, 31152, 2}, {7496, 10300, 37454}, {7734, 10691, 2}, {8889, 15702, 2}, {10124, 11548, 2}, {16063, 40916, 5}, {31133, 40916, 2}, {33923, 37897, 7492}, {34551, 34552, 12106}

X(43958) = X(125)X(523)∩X(128)X(1154)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1812.

X(43958) lies on these lines: {125, 523}, {128, 1154}, {137, 6368}, {1511, 14049}

X(43958) = X(13418)-Ceva conjugate of X(526)
X(43958) = crosspoint of X(1273) and X(18314)
X(43958) = barycentric product X(i)*X(j) for these {i,j}: {1273, 10413}, {8562, 18314}
X(43958) = barycentric quotient X(i)/X(j) for these {i,j}: {2081, 1291}, {8562, 18315}, {10413, 1141}, {41221, 11071}

X(43959) = X(2310)X(6608)∩X(3119)X(15607)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1812.

X(43959) lies on these lines: {2310, 6608}, {3119, 15607}

X(43959) = X(34919)-Ceva conjugate of X(6362)
X(43959) = barycentric quotient X(10581)/X(20219)

X(43960) = X(11)X(1146)∩X(57)X(28344)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1812.

X(43960) lies on these lines: {11, 1146}, {57, 28344}, {650, 1086}, {652, 38991}, {3064, 42069}, {3259, 38959}, {3271, 14298}, {3700, 4953}, {4014, 14300}, {4521, 17059}, {5540, 5660}, {12035, 17330}, {13405, 28345}, {14936, 38357}, {17718, 40131}, {28292, 38387}

X(43960) = X(34525)-complementary conjugate of X(3835)
X(43960) = X(12848)-Ceva conjugate of X(28292)
X(43960) = X(651)-isoconjugate of X(28291)
X(43960) = crosspoint of X(i) and X(j) for these (i,j): {514, 34919}, {12848, 28292}
X(43960) = crosssum of X(101) and X(37541)
X(43960) = crossdifference of every pair of points on line {109, 28291}
X(43960) = barycentric product X(i)*X(j) for these {i,j}: {522, 28292}, {1146, 12848}
X(43960) = barycentric quotient X(i)/X(j) for these {i,j}: {663, 28291}, {12848, 1275}, {28292, 664}

X(43961) = X(2)X(18777)∩X(115)X(23871)

Barycentrics    (b^2 - c^2)^2*(Sqrt[3]*(a^2 - b^2 - c^2) - 2*S)^2 : :
Barycentrics    O'a-power of inner-Le Viet An circle : :, where O'aO'bO'c is the outer-Le Viet An triangle
Barycentrics    O'a-power of circumcircle : :, where O'aO'bO'c is the outer-Le Viet An triangle
X(43961) = X[23895] + 3 X[43091]

See Antreas Hatzipolakis and Peter Moses, euclid 1812.

The inner- and outer- Le Viet An circles are here defined as the circumcircles of the inner- and outer- Le Viet An triangles, with centers X(14169) and X(14170), respectively. These circles are tangent to each other and to the circumcircle at X(110). (Randy Hutson, July 16, 2021)

X(43961) lies on the Steiner inellipse and these lines: {2, 18777}, {115, 23871}, {125, 523}, {298, 6148}, {302, 40854}, {338, 30452}, {395, 23967}, {396, 3163}, {524, 41887}, {531, 618}, {5099, 27551}, {5641, 11085}, {9204, 30465}, {11080, 19776}, {11672, 40695}, {15357, 27550}, {34540, 38403}, {40710, 40879}

X(43961) = midpoint of X(i) and X(j) for these {i,j}: {2, 43091}, {298, 11092}, {19776, 36308}
X(43961) = complement of X(23895)
X(43961) = complement of the isogonal conjugate of X(6137)
X(43961) = complement of the isotomic conjugate of X(23870)
X(43961) = X(i)-complementary conjugate of X(j) for these (i,j): {15, 4369}, {31, 23870}, {298, 42327}, {470, 21259}, {661, 623}, {798, 396}, {2151, 523}, {2154, 526}, {2624, 619}, {6137, 10}, {8739, 8062}, {17402, 21254}, {23870, 2887}, {30465, 21253}, {34394, 14838} X(43961) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 23870}, {2993, 526}, {19776, 523}
X(43961) = X(i)-isoconjugate of X(j) for these (i,j): {163, 36839}, {1095, 23588}, {1101, 11080}
X(43961) = crosspoint of X(2) and X(23870)
X(43961) = crosssum of X(i) and X(j) for these (i,j): {6, 5995}, {110, 41472}
X(43961) = crossdifference of every pair of points on line {2420, 5995}
X(43961) = isotomic conjugate of trilinear pole of line X(2407)X(17402)
X(43961) = polar conjugate of trilinear pole of line X(4240)X(36306)
X(43961) = barycentric square of X(23870)
X(43961) = barycentric product X(i)*X(j) for these {i,j}: {115, 11129}, {298, 30465}, {299, 30463}, {338, 11131}, {1094, 23994}, {3268, 23284}, {11085, 23965}, {23870, 23870}
X(43961) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 11080}, {125, 10217}, {523, 36839}, {1094, 1101}, {2088, 11081}, {6137, 5995}, {11085, 23588}, {11092, 39295}, {11129, 4590}, {11131, 249}, {20578, 5618}, {23284, 476}, {23870, 23895}, {23965, 11128}, {30463, 14}, {30465, 13}, {30467, 42001}, {30468, 36211}

X(43962) = X(2)X(18776)∩X(115)X(23870)

Barycentrics    (b^2 - c^2)^2*(Sqrt[3]*(a^2 - b^2 - c^2) + 2*S)^2 : :
Barycentrics    Oa-power of outer-Le Viet An circle : :, where OaObOc is the inner-Le Viet An triangle
Barycentrics    Oa-power of circumcircle : :, where OaObOc is the inner-Le Viet An triangle
X(43962)= X[23896] + 3 X[43092]

See Antreas Hatzipolakis and Peter Moses, euclid 1812.

X(43962) lies on the Steiner inellipse and these lines: {2, 18776}, {115, 23870}, {125, 523}, {299, 6148}, {303, 40855}, {338, 30453}, {395, 3163}, {396, 23967}, {524, 41888}, {530, 619}, {5099, 27550}, {5641, 11080}, {9205, 30468}, {11085, 19777}, {11672, 40696}, {15357, 27551}, {34541, 38404}, {40709, 40879}

X(43962) = midpoint of X(i) and X(j) for these {i,j}: {2, 43092}, {299, 11078}, {19777, 36311}
X(43962) = complement of X(23896)
X(43962) = complement of the isogonal conjugate of X(6138)
X(43962) = complement of the isotomic conjugate of X(23871)
X(43962) = X(i)-complementary conjugate of X(j) for these (i,j): {16, 4369}, {31, 23871}, {299, 42327}, {471, 21259}, {661, 624}, {798, 395}, {2152, 523}, {2153, 526}, {2624, 618}, {6138, 10}, {8740, 8062}, {17403, 21254}, {23871, 2887}, {30468, 21253}, {34395, 14838}
X(43962) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 23871}, {2992, 526}, {19777, 523}
X(43962) = X(i)-isoconjugate of X(j) for these (i,j): {163, 36840}, {1094, 23588}, {1101, 11085}
X(43962) = crosspoint of X(2) and X(23871)
X(43962) = crosssum of X(i) and X(j) for these (i,j): {6, 5994}, {110, 41473}
X(43962) = crossdifference of every pair of points on line {2420, 5994}
X(43962) = isotomic conjugate of trilinear pole of line X(2407)X(17403)
X(43962) = polar conjugate of trilinear pole of line X(4240)X(36309)
X(43962) = barycentric square of X(23871)
X(43962) = barycentric product X(i)*X(j) for these {i,j}: {115, 11128}, {298, 30460}, {299, 30468}, {338, 11130}, {1095, 23994}, {3268, 23283}, {11080, 23965}, {23871, 23871}
X(43962) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 11085}, {125, 10218}, {523, 36840}, {1095, 1101}, {2088, 11086}, {6138, 5994}, {11078, 39295}, {11080, 23588}, {11128, 4590}, {11130, 249}, {20579, 5619}, {23283, 476}, {23871, 23896}, {23965, 11129}, {30460, 13}, {30465, 36210}, {30468, 14}, {30470, 42002}

X(43963) = X(115)X(5521)∩X(122)X(26933)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1812.

X(43963) lies on these lines: {115, 5521}, {122, 26933}, {661, 2310}, {1562, 7117}, {2631, 2632}

X(43963) = X(648)-isoconjugate of X(36516)
X(43963) = barycentric quotient X(810)/X(36516)

X(43964) = X(4)X(38940)∩X(5)X(1499)

Barycentrics    a^8*b^2 - 14*a^6*b^4 + 12*a^4*b^6 + 2*a^2*b^8 - b^10 + a^8*c^2 + 16*a^6*b^2*c^2 - 3*a^4*b^4*c^2 - 33*a^2*b^6*c^2 + 7*b^8*c^2 - 14*a^6*c^4 - 3*a^4*b^2*c^4 + 54*a^2*b^4*c^4 - 6*b^6*c^4 + 12*a^4*c^6 - 33*a^2*b^2*c^6 - 6*b^4*c^6 + 2*a^2*c^8 + 7*b^2*c^8 - c^10 : :
X(43964) = 3 X[4] + X[38940], 3 X[5] - 2 X[32525], 3 X[381] - X[6792], 3 X[381] + X[18346], 2 X[546] + X[15098]

See Antreas Hatzipolakis and Peter Moses, euclid 1833.

X(43964) lies on these lines: {4, 38940}, {5, 1499}, {30, 5108}, {381, 6792}, {524, 3818}, {546, 15098}, {3830, 14916}, {5066, 9169}, {6787, 20326}, {9146, 22338}, {14856, 33962}, {15539, 15547}

X(43964) = midpoint of X(i) and X(j) for these {i,j}: {3830, 14916}, {6792, 18346}, {9146, 22338}
X(43964) = reflection of X(9169) in X(5066)
X(43964) = orthocentroidal circle inverse of X(18346)
X(43964) = {X(381),X(18346)}-harmonic conjugate of X(6792)

X(43965) = X(110)X(476)∩X(930)X(6368)

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

See Antreas Hatzipolakis and Peter Moses, euclid 1833.

X(43965) lies on these lines: {110, 476}, {930, 6368}, {1141, 1154}, {5965, 34308}, {8254, 39390}, {14980, 32423}

X(43965) = X(2624)-isoconjugate of X(11538)
X(43965) = cevapoint of X(523) and X(24385)
X(43965) = trilinear pole of line {15109, 34520}
X(43965) = barycentric product X(i)*X(j) for these {i,j}: {476, 15108}, {15109, 35139}
X(43965) = barycentric quotient X(i)/X(j) for these {i,j}: {476, 11538}, {9697, 14270}, {15108, 3268}, {15109, 526}, {21230, 41078}

X(43966) = X(4)X(195)∩X(113)X(25150)

Barycentrics    a^20*b^2 - 7*a^18*b^4 + 23*a^16*b^6 - 48*a^14*b^8 + 70*a^12*b^10 - 70*a^10*b^12 + 42*a^8*b^14 - 8*a^6*b^16 - 7*a^4*b^18 + 5*a^2*b^20 - b^22 + a^20*c^2 - 6*a^18*b^2*c^2 + 16*a^16*b^4*c^2 - 23*a^14*b^6*c^2 + 9*a^12*b^8*c^2 + 26*a^10*b^10*c^2 - 34*a^8*b^12*c^2 - 11*a^6*b^14*c^2 + 48*a^4*b^16*c^2 - 34*a^2*b^18*c^2 + 8*b^20*c^2 - 7*a^18*c^4 + 16*a^16*b^2*c^4 - 10*a^14*b^4*c^4 - 3*a^10*b^8*c^4 + 2*a^8*b^10*c^4 + 50*a^6*b^12*c^4 - 118*a^4*b^14*c^4 + 98*a^2*b^16*c^4 - 28*b^18*c^4 + 23*a^16*c^6 - 23*a^14*b^2*c^6 + 10*a^10*b^6*c^6 - a^8*b^8*c^6 - 42*a^6*b^10*c^6 + 136*a^4*b^12*c^6 - 158*a^2*b^14*c^6 + 55*b^16*c^6 - 48*a^14*c^8 + 9*a^12*b^2*c^8 - 3*a^10*b^4*c^8 - a^8*b^6*c^8 + 22*a^6*b^8*c^8 - 59*a^4*b^10*c^8 + 169*a^2*b^12*c^8 - 62*b^14*c^8 + 70*a^12*c^10 + 26*a^10*b^2*c^10 + 2*a^8*b^4*c^10 - 42*a^6*b^6*c^10 - 59*a^4*b^8*c^10 - 160*a^2*b^10*c^10 + 28*b^12*c^10 - 70*a^10*c^12 - 34*a^8*b^2*c^12 + 50*a^6*b^4*c^12 + 136*a^4*b^6*c^12 + 169*a^2*b^8*c^12 + 28*b^10*c^12 + 42*a^8*c^14 - 11*a^6*b^2*c^14 - 118*a^4*b^4*c^14 - 158*a^2*b^6*c^14 - 62*b^8*c^14 - 8*a^6*c^16 + 48*a^4*b^2*c^16 + 98*a^2*b^4*c^16 + 55*b^6*c^16 - 7*a^4*c^18 - 34*a^2*b^2*c^18 - 28*b^4*c^18 + 5*a^2*c^20 + 8*b^2*c^20 - c^22 : :
X(43966) = X[930] - 3 X[14643], X[10264] - 3 X[25147], X[20127] - 3 X[38710], 2 X[20304] - 3 X[23516], X[38587] + 3 X[38789], 3 X[38706] - 5 X[38794]

See Antreas Hatzipolakis and Peter Moses, euclid 1833.

X(43966) lies on these lines: {4, 195}, {113, 25150}, {137, 5663}, {930, 14643}, {1141, 7728}, {2777, 38618}, {5972, 38615}, {10264, 25147}, {12041, 34837}, {20127, 38710}, {20304, 23516}, {38706, 38794}

X(43966) = midpoint of X(1141) and X(7728)
X(43966) = reflection of X(i) in X(j) for these {i,j}: {12041, 34837}, {38615, 5972}

X(43967) = X(13)X(5611)∩X(115)X(30452)

Barycentrics    (b^2 - c^2)^2*(-a^2 + b^2 + c^2 - 2*Sqrt[3]*S)*(3*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) + 4*S*(Sqrt[3]*a^2 + S)) : :
X(43967) = X[8173] - 5 X[16960]

See Antreas Hatzipolakis, Elias M. Hagos and Peter Moses, euclid 1834.

X(43967) lies on these lines: {13, 5611}, {115, 30452}, {1989, 15930}, {2381, 11082}, {5965, 11601}, {5995, 11080}, {6105, 11142}, {6772, 36515}, {8173, 16960}, {8737, 11060}, {10677, 11139}, {15610, 23873}, {15929, 36211}, {18803, 34325}, {25220, 25222}

X(43967) = X(11082)-Ceva conjugate of X(20578)
X(43967) = X(i)-isoconjugate of X(j) for these (i,j): {249, 3384}, {1101, 19778}
X(43967) = crosspoint of X(11082) and X(20578)
X(43967) = crosssum of X(11127) and X(17402)
X(43967) = barycentric product X(i)*X(j) for these {i,j}: {115, 16770}, {303, 30452}, {338, 11142}, {1109, 3383}, {11582, 30460}, {11601, 42000}, {20578, 23873}
X(43967) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 19778}, {2643, 3384}, {3383, 24041}, {11142, 249}, {15610, 14921}, {16770, 4590}, {20578, 32037}, {30452, 18}

X(43968) = X(14)X(5615)∩X(115)X(30453)

Barycentrics    (b^2 - c^2)^2*(-a^2 + b^2 + c^2 + 2*Sqrt[3]*S)*(3*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2) - 4*S*(Sqrt[3]*a^2 - S)) : :
X(43968) = X[8172] - 5 X[16961]

See Antreas Hatzipolakis, Elias M. Hagos and Peter Moses, euclid 1834.

X(43968) lies on these lines: {14, 5615}, {115, 30453}, {1989, 15929}, {2380, 11087}, {5965, 11600}, {5994, 11085}, {6104, 11141}, {6775, 36514}, {8172, 16961}, {8738, 11060}, {10678, 11138}, {15609, 23872}, {15930, 36210}, {18804, 34326}, {25219, 25221}

X(43968) = X(11087)-Ceva conjugate of X(20579)
X(43968) = X(i)-isoconjugate of X(j) for these (i,j): {249, 3375}, {1101, 19779}
X(43968) = crosspoint of X(11087) and X(20579)
X(43968) = crosssum of X(11126) and X(17403)
X(43968) = barycentric product X(i)*X(j) for these {i,j}: {115, 16771}, {302, 30453}, {338, 11141}, {1109, 3376}, {11581, 30463}, {11600, 41999}, {20579, 23872}
X(43968) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 19779}, {2643, 3375}, {3376, 24041}, {11141, 249}, {15609, 14922}, {16771, 4590}, {20579, 32036}, {30453, 17}

X(43969) = X(110)X(1291)∩X(128)X(539)

Barycentrics    a^2*(a - b)*(a + b)*(a - c)*(a + c)*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - c^2)*(2*a^8 - 4*a^6*b^2 + 3*a^4*b^4 - 2*a^2*b^6 + b^8 - 4*a^6*c^2 + 2*a^2*b^4*c^2 - 4*b^6*c^2 + 3*a^4*c^4 + 2*a^2*b^2*c^4 + 6*b^4*c^4 - 2*a^2*c^6 - 4*b^2*c^6 + c^8) : :
X(43969) = 3 X[110] + X[1291], X[1157] + 3 X[43572], X[14979] - 5 X[15034]

See Antreas Hatzipolakis, Elias M. Hagos and Peter Moses, euclid 1834.

X(43969) lies on these lines: {110, 1291}, {128, 539}, {186, 323}, {1157, 43572}, {2623, 35324}, {14979, 15034}, {15537, 43586}

X(43969) = X(2618)-isoconjugate of X(15401)
X(43969) = crosspoint of X(10411) and X(18315)
X(43969) = crosssum of X(12077) and X(15475)
X(43969) = crossdifference of every pair of points on line {10413, 14582}
X(43969) = barycentric product X(i)*X(j) for these {i,j}: {128, 18315}, {231, 10411}, {539, 14590}
X(43969) = barycentric quotient X(i)/X(j) for these {i,j}: {128, 18314}, {231, 10412}, {539, 14592}, {14586, 15401}, {14591, 2383}

leftri

Points associated with Vijay parallel transforms: X(43970)-X(44010)

rightri

This preamble is contributed by Clark Kimberling (July 18, 2021), based on notes from Dasari Naga Vijay Krishna, July 13, 2021.

Let U = u : v : w be a point in the plane of a triangle ABC. Let
Ia = line through U parallel to line BC, and define Ib and Ic cyclically;
Ab = Ic∩BC, and define Bc and Ca cyclically;
Ac = Ic∩BC, and define Ba and Cb cyclically;
Ua = reflection of U in line BC, and define Ub and Uc cyclically;
Pa = line through Ua parallel to the line BC, and define pb and pc cyclically,
A'B'C' = anticomplementary triangle of ABC;
A'b=AbBa∩C'A', and define B'c and C'a cyclically;
A'c=AcAa∩B'A', and define B'a and C'b cyclically.

Define 9 points based on the preceding constructions as follows:

A1 = BcCa∩CbBa , B1 = CaAb∩AcCb, C1 = AbBc∩BaAc
A2 = AbBc∩AcCb, B2 = BcCa∩BaAc, C2 = CaAb∩CbBa
A3 = AbCb∩AcBc, B3 = AcBc∩BaCa, C3 = BaCa∩AbCb
A4 = B'cB'a∩C'aC'b, B4 = C'aC'b∩A'bA'c, C4 = A'bA'c∩B'cB'a
A5 = BA'c∩CA'b, B5 = CB'a∩AB'c, C5 = AC'b∩BC'a
A6 = AbA'c∩AcA'b, B6 = BcB'a∩BaB'c, C6 = CaC'b∩CbC'a
A7 = BC4∩CB4, B7 = AC4∩CA4 , C7 = AB4∩BA4
A8 = AbC4∩AcB4, B8 = BcA4∩BaC4 , C8 = CaB4∩CbA4
A9 = Pb∩Pc , B9 = Pc∩Pa , C9 = Pa∩Pb.

Barycentrics for the 9 points and others:

Ab = 0 : u + v : w, Ac = 0 : v : u + w
A'b = -w : u + v + w : w, A'c = -v : v : u + v + w
A' = -1 : 1 : 1
A1 = (v + w)*(u*v + v*w + w*u) - u*v*w : (v + w)*v^2 : (v + w)*w^2
A2 = u^2 : (v + w)*(v + u) : (w + u)*(w + v)
A3 = -u^2 : v*(v + w) : w*(v + w)
A4 = -(u + v + w)^2 - u^2 : w*(u + v + w) - u*v : v*(u + v + w) - u*w
A5 = -v*w : v*(u + v + w) : w*(u + v + w)
A6 = -u*v*w : v*(v*w + 2*u*w + u*v + u^2) : w*(v*w + u*w + 2*u*v + u^2)
A7 = -(w*(u + v + w) - u*v)*(v*(u + v + w) - u*w) : (v*(u + v + w) - w*u)*((u + v + w)^2 + v^2) : (w*(u + v + w) -u*v)*((u + v + w)^2 + w^2)
A8 = -u*(v*(u + v + w) - w*u)*(w*(u + v + w) - u*v) : 2*v^2*w^3 + 3*u*v*w^3 - u^2*w^3 + 4*v^3*w^2 + 9*u*v^2*w^2 + 3*u^2*v*w^2 - 2*u^3*w^2 + 2*v^4*w + 8*u*v^3*w+ 6*u^2*v^2*w + u^3*v*w -u^4*w + 2*u*v^4 + 4*u^2*v^3 + 3*u^3*v^2 + u^4*v : 2*v*w^4 + 2*u*w^4 + 4*v^2*w^3 + 8*u*v*w^3 + 4*u^2*w^3 + 2*v^3*w^2 + 9*u*v^2*w^2 + 6*u^2*v*w^2 + 3*u^3*w^2 + 3*u*v^3*w + 3*u^2*v^2*w + u^3*v*w + u^4*w - u^2*v^3 - 2*u^3*v^2 - u^4*v
A9 = -(u + 2*v + 2*w) : v : w

Related triangles are named as follows:

A1B1C1 = 1st Vijay parallel transform triangle of U
A2B2C2 = 2nd Vijay parallel transform triangle of U
A3B3C3 = 3rd Vijay parallel transform triangle of U
A4B4C4= 4th Vijay parallel transform triangle of U
A5B5C5 = 5th Vijay parallel transform triangle of U
A6B6C6 = 6th Vijay parallel transform triangle of U
A7B7C7 = 7th Vijay parallel transform triangle of U
A8B8C8 = 8th Vijay parallel transform triangle of U
A9B9C9 = 9th Vijay parallel transform triangle of U

Collinearities:

U, A, A3, A5, A9 are collinear.
U, A1, A2 are collinear.
A3, A4, A8 are collinear.

Perspectors:

AA3A5A9U∩BB3B5B9U∩CC3C5C9U = A1A2U∩B1B2U∩C1C2U = A4A'∩B4B'∩C4C' = U
AA1∩BB1∩CC1 = u^2 : v^2 : w^2 = barycentric square of U
A5A6∩B5B6∩C5C6 = vw : uw : uv = 1/u : 1/v : 1/w = isotomic conjugate of U
A9A'∩B9B'∩C9C' = v+w : w+u : u+v = complement point U
AA2∩BB2∩CC2 = (u+v)(u+w) : (v+w)(v+u) : (w+u)(w+v) = 1/(v+w) : 1/(u+w) : 1/(u+v) = isotomic conjugate of complement of U
A6A'∩B6B'∩C6C' = uv-vw+wu : uv+vw-wu : -uv+vw+wu = 1/v + 1/w -1/u : 1/w + 1/u -1/v : 1/u + 1/v -1/w = X(2)-Ceva conjugate of U
AA4∩BB4∩CC4 = Vijay 1st parallel transform of U
AA7∩BB7∩CC7 = Vijay 2nd parallel transform of U
A1A3∩B1B3∩C1C3 = Vijay 3rd parallel transform of U
A2A3∩B2B3∩C2C3 = Vijay 4th parallel transform of U
A2A'∩B2B'∩C2C' = Vijay 5th parallel transform of U
A5A'∩B5B'∩C5C' = Vijay 6th parallel transform of U
A1A8∩B1B8∩C1C8 = Vijay 7th parallel transform of U
A3A4∩B3B4∩C3C4 = A3A8∩B3B8∩C3C8 = A4A8∩B4B8∩C4C8 = Vijay 8th parallel transform of U
A3A7∩B3B7∩C3C7 = Vijay 9th parallel transform of U
A4A7∩B4B7∩C4C7 = Vijay 10th parallel transform of U
A2A9∩B2B9∩C2C9 = Vijay 11th parallel transform of U
A4A9∩B4B9∩C4C9 = Vijay 12th parallel transform of U
A7A'∩B7B' ? C7C' = Vijay 13th parallel transform of U

Barycentrics for Vijay parallel transforms:

Vijay 1st parallel transform triangle of U
= 1/ (u*(u + v + w) - v*w) : :
= perspector of ABC and 4th Vijay parallel transform triangle of U

Vijay 2nd parallel transform of U:
(u*(u + v + w) - v*w)*((u + v + w)^2 + u^2) : :
= perspector of ABC and 7th Vijay parallel transform triangle of U

Vijay 3rd parallel transform of U:
u^2*(u + v)*(u + w)*(v^2 + w^2 + v*w) : :
= perspector of 1st and 3rd Vijay parallel transform triangles of U

Vijay 4th parallel transform of U:
u*(2*v*w + u*w + u*v - u^2) : :
= perspector of 2nd and 3rd Vijay parallel transform triangles of U
= center of the parallels-conic of U; see the preamble just before X(10001)

Vijay 5th parallel transform of U:
2*u^2 + u*v + v*w + w*u : :
= perspector of anticomplementary triangle of ABC and 2nd Vijay parallel transform tirangle of U

Vijay 6th parallel transform of U:
(u + v + w)*(u*v - v*w + w*u) - u*v*w : :
= perspector of anticomplementary triangle of ABC and 5th Vijay parallel transform triangle of U

Vijay 7th parallel transform of U:
u*(-v^3*w^5 + 2*u*v^2*w^5 + 5*u^2*v*w^5 + 2*u^3*w^5 - 2*v^4*w^4 + 2*u*v^3*w^4 + 17*u^2*v^2*w^4 + 15*u^3*v*w^4 + 4*u^4*w^4 - v^5*w^3 + 2*u*v^4*w^3 + 20*u^2*v^3*w^3 + 29*u^3*v^2*w^3 + 14*u^4*v*w^3 + 2*u^5*w^3 + 2*u*v^5*w^2 + 17*u^2*v^4*w^2 + 29*u^3*v^3*w^2 + 20*u^4*v^2*w^2 + 4*u^5*v*w^2 + 5*u^2*v^5*w + 15*u^3*v^4*w + 14*u^4*v^3*w + 4*u^5*v^2*w + 2*u^3*v^5 + 4*u^4*v^4 + 2*u^5*v^3) : :
= perspector of 1st and 8th Vijay parallel transform triangles of U

Vijay 8th parallel transform of U:
-v*w^3 + u*w^3 - 2*v^2*w^2 + u*v*w^2 + 3*u^2*w^2 -v^3*w + u*v^2*w + 2*u^2*v*w + 2*u^3*w + u*v^3 + 3*u^2*v^2 + 2*u^3*v : :
= perspector of each pair of these: 3rd, 4th, and 8th Vijay parallel transform triangles of U

Vijay 9th parallel transform of U:
v*w^3 - u*w^3 + 2*v^2*w^2 + u*v*w^2 - u^2*w^2 + v^3*w + u*v^2*w - 2*u^3*w - u*v^3 - u^2*v^2 - 2*u^3*v - 2*u^4 : :
= perspector of 3rd and 7th Vijay parallel transform triangles of U

Vijay 10th parallel transform of U:
-v*w^3 + u*w^3 - 2*v^2*w^2 + 2*u^2*w^2 - v^3*w + u^2*v*w + 2*u^3*w + u*v^3 + 2*u^2*v^2 + 2*u^3*v + u^4 : :
= perspector of 4th and 7th Vijay parallel transform triangles of U

Vijay 11th parallel transform of U:
2*v*w^2 + 2*u*w^2 + 2*v^2*w + 5*u*v*w + 3*u^2*w + 2*u*v^2 + 3*u^2*v + 2*u^3 : :
= perspector of 2nd and 9th Vijay parallel transform triangles of U

Vijay 12th parallel transform of U:
v*w^2 - 3*u*w^2 + v^2*w + 2*u*v*w + u^2*w - 3*u*v^2 + u^2*v : :
= perspector of 4th and 9th Vijay parallel transform triangles of U

Vijay 13th parallel transform of U:
-2*v*w^6 + 2*u*w^6 - 8*v^2*w^5 + 8*u^2*w^5 - 14*v^3*w^4 - 9*u*v^2*w^4 + 10*u^2*v*w^4 + 13*u^3*w^4 - 14*v^4*w^3 - 14*u*v^3*w^3 + 4*u^2*v^2*w^3 + 14*u^3*v*w^3 + 10*u^4*w^3 - 8*v^5*w^2 - 9*u*v^4*w^2 + 4*u^2*v^3*w^2 + 10*u^3*v^2*w^2 + 4*u^4*v*w^2 + 3*u^5*w^2 - 2*v^6*w + 10*u^2*v^4*w + 14*u^3*v^3*w + 4*u^4*v^2*w - 2*u^5*v*w + 2*u*v^6 + 8*u^2*v^5 + 13*u^3*v^4 + 10*u^4*v^3 + 3*u^5*v^2 : :
= perspector of anticomplementary triangle of ABC and 7th Vijay parallel transform triangle of U

Constructions as downloadable pdfs:

Vijay 1st parallel transform
Vijay 2nd parallel transform
Vijay 3rd parallel transform
Vijay 4thd parallel transform
Vijay 5th parallel transform
Vijay 6th parallel transform
Vijay 7th parallel transform
Vijay 8th parallel transform
Vijay 9th parallel transform
Vijay 10th parallel transform
Vijay 11th parallel transform
Vijay 12th parallel transform
Vijay 13th parallel transform

The appearance of {i,j} in the following list means that the 1st Vijay parallel transform of X(i) is X(j):

{1,596}, {2,2}, {3,6662}, {4,68}, {6,6664}, {7,6601}, {8,4}, {20,3346}, {69,66}, {75,13476}, {76,27375}, {99,36955}, {144,42483}, {145,6553}, {192,2998}, {193,6339}, {194,42486}, {264,42487}, {329,34546}, {3869,42485}, {4329,42484}, {4560,15412}, {5905,6504}, {6360,34287}, {7057,8}, {16017,189}, {16018,39694}, {20346,7357}, {20534,7}, {40383,330}
Also, if X is on the line at infinity, then the 1st Vijay parallel transform of X is X.

The appearance of {i,j} in the following list means that the 2nd Vijay parallel transform of X(i) is X(j): {2,2}
Also, if X is on the line at infinity, then the 2nd Vijay parallel transform of X is X.

The appearance of {i,j} in the following list means that the 3rd Vijay parallel transform of X(i) is X(j):

{1,3736}, {2,2}, {13,16459}, {14,16460}, {99,4590}, {190,1016}, {648,23582}, {664,1275}, {668,31625}, {1494,31621}

As noted above the 4th Vijay parallel transform of U is the center of the parallels-conic of U. The appearance of {i,j} in the following list means that the 4th Vijay parallel transform of X(i) is X(j):

{1,1001}, {2,2}, {3,182}, {4,10002}, {5,10003}, {6,182}, {7,10004}, {8,10005}, {9,1001}, {10,3842}, {11,10006}, {13,10217}, {14,10218}, {25,42820}, {32,42826}, {37,3842}, {39,10007}, {55,42834}, {56,42828}, {69,10008}, {75,10009}, {76,10010}, {99,4590}, {100,38310}, {114,10011}, {115,523}, {125,22264}, {141,10007}, {142,10012}, {190,1016}, {206,42826}, {216,10003}, {230,10011}, {239,20142}, {298,11133}, {299,11132}, {371,42866}, {372,42864}, {381,42830}, {395,6672}, {396,6671}, {478,42828}, {618,6671}, {619,6672}, {647,22264}, {648,23582}, {650,10006}, {664,1275}, {668,31625}, {1015,513}, {1084,512}, {1086,514}, {1146,522}, {1212,10012}, {1249,10002}, {1494,31621}, {2482,524}, {3068,42838}, {3069,42840}, {3160,10004}, {3161,10005}, {3162,42820}, {3163,30}, {4370,519}, {5375,38310}, {5452,42834}, {6184,518}, {6337,10008}, {6374,10010}, {6376,10009}, {6631,1016}, {6651,20142}, {7026,14358}, {7043,14359}, {9296,31625}, {9410,31621}, {10001,1275}, {10853,4857}, {10960,42864}, {10962,42866}, {11672,511}, {13466,536}, {13636,8371}, {13722,8371}, {15166,2574}, {15167,2575}, {15449,826}, {15525,3566}, {15526,525}, {15527,7927}, {17416,3906}, {17429,17430}, {18334,526}, {20532,726}, {23967,542}, {23972,516}, {23976,1503}, {23980,517}, {23986,515}, {23992,690}, {30471,11133}, {30472,11132}, {31998,4590}, {33364,42838}, {33365,42840}, {35066,17768}, {35067,3564}, {35068,740}, {35069,758}, {35070,35101}, {35071,520}, {35072,521}, {35073,538}, {35074,35102}, {35075,8680}, {35076,4977}, {35077,5969}, {35078,804}, {35079,2787}, {35080,2786}, {35081,2792}, {35082,2784}, {35083,2783}, {35084,2795}, {35085,2796}, {35086,2785}, {35087,543}, {35088,2799}, {35089,35103}, {35090,8674}, {35091,6366}, {35092,900}, {35093,5845}, {35094,918}, {35095,35104}, {35110,527}, {35111,5853}, {35113,528}, {35114,17770}, {35116,2801}, {35119,812}, {35121,545}, {35123,537}, {35124,4715}, {35125,3887}, {35126,9055}, {35128,3738}, {35129,2802}, {35133,1499}, {35135,4160}, {35508,3900}, {36668,3911}, {36669,3911}, {39008,9033}, {39010,888}, {39011,891}, {39013,924}, {39014,926}, {39015,6371}, {39016,834}, {39017,928}, {39018,1510}, {39019,6368}, {39020,8057}, {39022,3414}, {39023,3413}, {39062,23582}, {40578,10217}, {40579,10218}, {40610,4083}, {40621,3667}, {41887,11064}, {41888,11064}, {43961,23870}, {43962,23871}
Also, if X is on the line at infinity, then the 4th Vijay parallel transform of X is X.

The appearance of {i,j} in the following list means that the 5th Vijay parallel transform of X(i) is X(j):

{1,17379}, {2,2}, {6,7787}, {8,4461}, {30,39358}, {69,32830}, {75,34284}, {99,4590}, {190,1016}, {511,39355}, {512,25054}, {513,9263}, {514,4440}, {518,39350}, {519,17487}, {522,39351}, {523,148}, {524,8591}, {525,39352}, {527,39357}, {528,39363}, {536,39360}, {538,39361}, {648,23582}, {664,1275}, {668,31625}, {690,39356}, {726,39354}, {740,39367}, {788,39347}, {812,39362}, {824,39345}, {826,39346}, {900,39349}, {918,39353}, {1494,31621}, {2786,39368}, {2799,39359}, {3413,39366}, {3414,39365}, {4777,39364}, {4977,39348}, {16839,22739}
Also, if X is on the line at infinity, then the 5th Vijay parallel transform of X is on the ellipse E(X(4440)), which is the anticomplement of the Steiner circumellipse; see the preamble just before X(39345).

The appearance of {i,j} in the following list means that the 6th Vijay parallel transform of X(i) is X(j):

{1,17147}, {2,2}, {4,6515}, {6,8267}, {7,36845}, {8,329}, {69,1370}, {75,17135}, {192,41840}, {193,18287}, {693,3434}, {850,11442}, {2592,6515}, {2593,6515}, {4560,18662}, {7192,17140}, {17494,40637}, {22339,1370}, {22340,1370}, {31296,40642}
Also, if X is on the line at infinity, then the 6th Vijay parallel transform of X is X(2).

The appearance of {i,j} in the following list means that the 7th Vijay parallel transform of X(i) is X(j):

{2,2}, {99,4590}, {190,1016}, {648,23582}, {664,1275}, {668,31625}, {1494,31621}, {38026,43027}
Also, if X is on the line at infinity, then the 7th Vijay parallel transform of X is X.

The appearance of {i,j} in the following list means that the 8th Vijay parallel transform of X(i) is X(j):

{2,2}, {8,3421}
Also, if X is on the line at infinity, then the 8th Vijay parallel transform of X is X.

The appearance of {i,j} in the following list means that the 9th Vijay parallel transform of X(i) is X(j):

{2,2}
Also, if X is on the line at infinity, then the 9th Vijay parallel transform of X is X.

The appearance of {i,j} in the following list means that the 10th Vijay parallel transform of X(i) is X(j):

{2,2}, {8,7270}
Also, if X is on the line at infinity, then the 10th Vijay parallel transform of X is X.

The appearance of {i,j} in the following list means that the 11th Vijay parallel transform of X(i) is X(j):

{2,2}, {99,4590}, {190,1016}, {648,23582}, {664,1275}, {668,31625}, {1494,31621}
Also, if X is on the line at infinity, then the 11th Vijay parallel transform of X is X.

The appearance of {i,j} in the following list means that the 12th Vijay parallel transform of X(i) is X(j):

{1,17154}, {4,3448}, {6,25047}, {7,149}, {8,149}, {20,34186}, {69,3448}, {75,17154}, {76,25047}, {192,21224}, {253,34186}, {330,21224}, {519,20042}, {903,20042}, {2408,9485}, {2418,9485}, {4240,9033}, {5466,690}, {5468,690}, {6548,900}, {9214,9143}, {13386,37781}, {13387,37781}, {17780,900}, {30508,523}, {30509,523}, {34760,33921}, {34762,33920}, {34763,33921}, {34764,33920}, {34767,9033}, {36890,9143}, {41314,891}, {43928,891}
Also, if X is on the line at infinity, then the 11th Vijay parallel transform of X is X, and if F(X) denotes this transform, then F(X) = F(X*), where X* = isotomic conjugate of X. See the note at X(44007).

The appearance of {i,j} in the following list means that the 13th Vijay parallel transform of X(i) is X(j):

{2,2}
Also, if X is on the line at infinity, then the 13th Vijay parallel transform of X is X.

The Vijay 1st parallel transform of U is the isogonal conjugate of the Vu tangential transform of U, and the perspector of ABC and the reflection of the cevian triangle of U in the centroid of ABCU. It is also the anticomplement of the centroid of {{[complement of U], [vertices of anticevain triangle of complement of U]}}, and also the isogonal conjugate of the TCC-perspector of [isogonal conjugate of complement of U]. (Randy Hutson, August 24, 2021)



X(43970) = VIJAY 1ST PARALLEL TRANSFORM OF X(5)

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

X(43970) lies on these lines: {30, 14978}, {233, 3284}, {520, 32142}, {3530, 10610}, {3850, 31505}, {11589, 33923}, {41008, 43752}

X(43970) is the perspector of ABC and the reflection of the cevian triangle of X(5) in the centroid of {{A,B,C,X(5)}}. (Randy Hutson, August 24, 2021)

X(43970) = isogonal conjugate of X(38848)
X(43970) = isotomic conjugate of the anticomplement of X(36422)
X(43970) = X(i)-cross conjugate of X(j) for these (i,j): {36422, 2}, {39019, 525}
X(43970) = X(1)-isoconjugate of X(38848)
X(43970) = trilinear pole of line {1636, 35441}
X(43970) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 38848}, {17434, 34987}

X(43971) = VIJAY 1ST PARALLEL TRANSFORM OF X(9)

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

X(43971) is the perspector of ABC and the reflection of the cevian triangle of X(9) in the centroid of {{A,B,C,X(9)}}. (Randy Hutson, August 24, 2021)

X(43971) lies on these lines: {514, 42356}, {527, 3059}, {1212, 1323}, {1855, 38461}

X(43971) = isogonal conjugate of X(38849)
X(43971) = isotomic conjugate of X(32024)
X(43971) = X(35508)-cross conjugate of X(522)
X(43971) = X(i)-isoconjugate of X(j) for these (i,j): {1, 38849}, {6, 7676}, {31, 32024}
X(43971) = cevapoint of X(3119) and X(6362)
X(43971) = trilinear pole of line {1638, 6608}
X(43971) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 7676}, {2, 32024}, {6, 38849}

X(43972) = VIJAY 1ST PARALLEL TRANSFORM OF X(10)

Barycentrics    (2*a^2 + 3*a*b + 2*b^2 + a*c + b*c - c^2)*(2*a^2 + a*b - b^2 + 3*a*c + b*c + 2*c^2) : :
X(43972) = X[1125] - 3 X[23812]

X(43972) is the perspector of ABC and the reflection of the cevian triangle of X(10) in the centroid of {{A,B,C,X(10)}}. (Randy Hutson, August 24, 2021)

X(43972) lies on these lines: {10, 20290}, {44, 1213}, {519, 2650}, {751, 24046}, {1125, 6536}, {1269, 3664}, {1319, 3636}, {2392, 33815}, {6538, 32846}, {23823, 36250}

X(43972) = isogonal conjugate of X(33771)
X(43972) = isotomic conjugate of X(32025)
X(43972) = X(115)-cross conjugate of X(514)
X(43972) = X(i)-isoconjugate of X(j) for these (i,j): {1, 33771}, {6, 33761}, {31, 32025}, {32, 33775}, {692, 17161}, {18158, 32739}
X(43972) = cevapoint of X(i) and X(j) for these (i,j): {11, 21106}, {1086, 23731}, {3120, 4977}
X(43972) = trilinear pole of line {1635, 2527}
X(43972) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 33761}, {2, 32025}, {6, 33771}, {75, 33775}, {514, 17161}, {693, 18158}

X(43973) = VIJAY 1ST PARALLEL TRANSFORM OF X(68)

Barycentrics    tan 4A : tan 4B : tan 4C
Barycentrics    (a^2 - b^2 - c^2)*(a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + c^4)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 4*a^4*b^2*c^2 + 8*a^2*b^4*c^2 - 4*b^6*c^2 - 4*a^2*b^2*c^4 + 6*b^4*c^4 - 4*b^2*c^6 + c^8)*(a^8 + b^8 - 4*a^6*c^2 - 4*a^4*b^2*c^2 - 4*a^2*b^4*c^2 - 4*b^6*c^2 + 6*a^4*c^4 + 8*a^2*b^2*c^4 + 6*b^4*c^4 - 4*a^2*c^6 - 4*b^2*c^6 + c^8) : :

X(43973) is the perspector of ABC and the reflection of the cevian triangle of X(68) in the centroid of {{A,B,C,X(68)}}. (Randy Hutson, August 24, 2021)

X(43973) lies on these lines: {577, 5449}, {5562, 9927}

X(43974) = VIJAY 1ST PARALLEL TRANSFORM OF X(100)

Barycentrics    (b - c)*(a^3*b - a^2*b^2 - a*b^3 + b^4 + a^3*c - a^2*b*c + 3*a*b^2*c - b^3*c - 2*a^2*c^2 - a*b*c^2 - b^2*c^2 + a*c^3 + b*c^3)*(a^3*b - 2*a^2*b^2 + a*b^3 + a^3*c - a^2*b*c - a*b^2*c + b^3*c - a^2*c^2 + 3*a*b*c^2 - b^2*c^2 - a*c^3 - b*c^3 + c^4) : :
X(43974) = 5 X[31235] - 3 X[42454]

X(43974) is the perspector of ABC and the reflection of the cevian triangle of X(100) in the centroid of {{A,B,C,X(100)}}. (Randy Hutson, August 24, 2021)

X(43974) lies on these lines: {514, 14740}, {522, 5083}, {528, 42552}, {650, 3035}, {2254, 2804}, {2826, 4120}, {31235, 42454}, {36038, 43042}

X(43974) = reflection of X(15914) in X(3035)
X(43974) = isogonal conjugate of X(1618)
X(43974) = X(i)-cross conjugate of X(j) for these (i,j): {6184, 918}, {21942, 3762}, {42547, 11}
X(43974) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1618}, {692, 24203}
X(43974) = cevapoint of X(6550) and X(23757)
X(43974) = trilinear pole of line {17435, 34530}
X(43974) = barycentric product X(4391)*X(43947)
X(43974) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 1618}, {514, 24203}, {43947, 651}

X(43975) = VIJAY 3RD PARALLEL TRANSFORM OF X(3)

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

X(43975) lies on these lines: {3, 95}, {97, 110}, {160, 6759}, {275, 6638}, {426, 40913}, {577, 1147}, {852, 4993}, {9792, 30258}, {16030, 38396}, {19188, 38283}

X(43975) = crossdifference of every pair of points on line {23290, 42293}
X(43975) = barycentric product X(i)*X(j) for these {i,j}: {97, 30258}, {394, 9792}
X(43975) = barycentric quotient X(i)/X(j) for these {i,j}: {9792, 2052}, {30258, 324}
X(43975) = {X(95),X(26902)}-harmonic conjugate of X(3)

X(43976) = VIJAY 3RD PARALLEL TRANSFORM OF X(4)

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

X(43976) lies on these lines: {4, 69}, {24, 33802}, {25, 98}, {30, 30262}, {182, 419}, {235, 6530}, {237, 42329}, {242, 31394}, {324, 6995}, {338, 36990}, {393, 800}, {460, 39871}, {847, 10594}, {1503, 41760}, {1513, 40822}, {1974, 41204}, {2353, 8884}, {2367, 39382}, {3088, 7795}, {3146, 26179}, {3541, 7832}, {3542, 7828}, {3575, 9873}, {5117, 24206}, {6353, 15466}, {6620, 6776}, {6623, 10002}, {7378, 40684}, {7487, 34285}, {7505, 7942}, {7930, 37119}, {9747, 9752}, {11257, 11325}, {19124, 37124}, {32451, 39931}, {36794, 39588}, {39646, 39879}

X(43976) = midpoint of X(4) and X(3186)
X(43976) = polar conjugate of X(40802)
X(43976) = isotomic conjugate of the isogonal conjugate of X(6620)
X(43976) = polar conjugate of the isotomic conjugate of X(40814)
X(43976) = polar conjugate of the isogonal conjugate of X(7735)
X(43976) = X(7735)-cross conjugate of X(40814)
X(43976) = cevapoint of X(6620) and X(7735)
X(43976) = pole wrt polar circle of trilinear polar of X(40802) (line X(512)X(684))
X(43976) = X(i)-isoconjugate of X(j) for these (i,j): {48, 40802}, {63, 40799}, {255, 40801}, {304, 40823}, {810, 35575}, {9247, 40824}
X(43976) = barycentric product X(i)*X(j) for these {i,j}: {4, 40814}, {25, 40822}, {76, 6620}, {92, 4008}, {264, 7735}, {648, 30735}, {1093, 37188}, {1513, 16081}, {2052, 6776}, {8794, 42353}, {9752, 42298}, {14618, 35278}, {18022, 40825}
X(43976) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 40802}, {25, 40799}, {264, 40824}, {393, 40801}, {648, 35575}, {1513, 36212}, {1974, 40823}, {3186, 40811}, {4008, 63}, {6620, 6}, {6776, 394}, {7735, 3}, {30735, 525}, {35278, 4558}, {37188, 3964}, {40814, 69}, {40821, 3504}, {40822, 305}, {40825, 184}
X(43976) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {264, 17984, 76}, {14249, 21447, 6530}

X(43977) = VIJAY 3RD PARALLEL TRANSFORM OF X(6)

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

X(43977) lies on these lines: {6, 76}, {32, 206}, {110, 251}, {182, 30495}, {695, 1176}, {737, 827}, {1196, 10551}, {1207, 3589}, {1613, 1799}, {3094, 18899}, {3231, 10130}, {3721, 21751}, {5480, 34294}, {7787, 10340}, {10339, 12206}, {10796, 19139}, {20965, 39668}, {28724, 34870}, {38817, 39080}, {38908, 39674}

X(43977) = midpoint of X(6) and X(3499)
X(43977) = cevapoint of X(3117) and X(18899)
X(43977) = crosspoint of X(83) and X(42288)
X(43977) = crosssum of X(39) and X(14994)
X(43977) = crossdifference of every pair of points on line {688, 23285}
X(43977) = isogonal conjugate of isotomic conjugate of isogonal conjugate of X(14617)
X(43977) = barycentric product X(i)*X(j) for these {i,j}: {82, 3116}, {83, 3117}, {251, 3094}, {308, 18899}, {689, 9006}, {4577, 17415}, {5117, 10547}
X(43977) = X(i)-isoconjugate of X(j) for these (i,j): {38, 3114}, {75, 14617}, {141, 3113}, {1930, 3407}, {2084, 9063}
X(43977) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 14617}, {251, 3114}, {3094, 8024}, {3116, 1930}, {3117, 141}, {4577, 9063}, {4630, 33514}, {9006, 3005}, {17415, 826}, {18899, 39}
X(43977) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 33786, 42534}, {1176, 38834, 1691}

X(43978) = VIJAY 3RD PARALLEL TRANSFORM OF X(100)

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

X(43978) lies on these lines: {55, 5377}, {100, 693}, {1252, 23988}, {1621, 31633}, {2078, 4564}

X(43979) = VIJAY 4TH PARALLEL TRANSFORM OF X(101)

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

X(43979) lies on these lines: {59, 36942}, {101, 6586}, {859, 4570}, {1936, 6066}

X(43979) = midpoint of X(101) and X(39026)

X(43980) = VIJAY 5TH PARALLEL TRANSFORM OF X(3)

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

X(43980) lies on these lines: {2, 95}, {3, 3164}, {140, 27377}, {182, 193}, {183, 10607}, {194, 37126}, {264, 22052}, {287, 3620}, {385, 7485}, {401, 36748}, {648, 10979}, {2322, 22359}, {3186, 37457}, {7495, 7777}, {15692, 39358}, {15705, 17037}, {15905, 37067}, {17008, 19577}, {39352, 40680}

X(43980) = X(19)-isoconjugate of X(17039)
X(43980) = barycentric quotient X(3)/X(17039)
X(43980) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 40897, 317}, {95, 577, 2}

X(43981) = VIJAY 5TH PARALLEL TRANSFORM OF X(4)

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

X(43981) lies on these lines: {2, 216}, {4, 193}, {20, 33971}, {25, 37667}, {53, 69}, {297, 3620}, {317, 20080}, {385, 6995}, {458, 1249}, {648, 3087}, {1785, 17257}, {1968, 32981}, {1990, 3618}, {1992, 6748}, {2207, 32971}, {3091, 6530}, {3199, 32828}, {3538, 18853}, {3543, 16264}, {3832, 10002}, {4232, 17008}, {5032, 40065}, {6524, 7398}, {6994, 37683}, {7378, 7774}, {7392, 14569}, {7404, 14978}, {7757, 39662}, {8796, 37192}, {8801, 17983}, {11160, 32001}, {11427, 41244}, {14853, 39530}, {18027, 36434}, {18666, 37421}, {18928, 37873}, {20079, 41761}, {27371, 32816}, {27376, 32974}, {32817, 35920}, {36426, 39352}, {36794, 40138}, {39569, 40330}

X(43981) = anticomplement of X(40680)
X(43981) = polar conjugate of X(17040)
X(43981) = anticomplement of the isotomic conjugate of X(1217)
X(43981) = polar conjugate of the isogonal conjugate of X(5020)
X(43981) = X(1217)-anticomplementary conjugate of X(6327)
X(43981) = X(1217)-Ceva conjugate of X(2)
X(43981) = X(48)-isoconjugate of X(17040)
X(43981) = pole wrt polar circle of trilinear polar of X(17040) (line X(647)X(3566))
X(43981) = barycentric product X(264)*X(5020)
X(43981) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 17040}, {5020, 3}
X(43981) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 40896, 6527}, {4, 9308, 193}, {53, 69, 37174}, {264, 393, 2}, {297, 32000, 3620}

X(43982) = VIJAY 5TH PARALLEL TRANSFORM OF X(5)

Barycentrics    a^8 - 5*a^6*b^2 + 10*a^4*b^4 - 9*a^2*b^6 + 3*b^8 - 5*a^6*c^2 + 9*a^4*b^2*c^2 + 9*a^2*b^4*c^2 - 13*b^6*c^2 + 10*a^4*c^4 + 9*a^2*b^2*c^4 + 20*b^4*c^4 - 9*a^2*c^6 - 13*b^2*c^6 + 3*c^8 : :

X(43982) lies on these lines: {2, 10979}, {5, 17035}, {193, 11178}, {1972, 8797}, {3090, 3164}, {5071, 39358}, {5079, 9308}

X(43982) = X(2148)-isoconjugate of X(17041)
X(43982) = barycentric quotient X(5)/X(17041)
X(43982) = {X(36412),X(40410)}-harmonic conjugate of X(2)

X(43983) = VIJAY 5TH PARALLEL TRANSFORM OF X(7)

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

X(43983) lies on these lines: {1, 32086}, {2, 85}, {7, 145}, {8, 10481}, {10, 21314}, {57, 24599}, {144, 42309}, {226, 29621}, {239, 21454}, {269, 19860}, {312, 32882}, {346, 21605}, {388, 1358}, {519, 32098}, {664, 3623}, {738, 3306}, {1111, 14986}, {1323, 3616}, {1418, 4875}, {1434, 16704}, {1565, 3091}, {1997, 40014}, {3146, 17170}, {3160, 3622}, {3188, 17576}, {3476, 24796}, {3522, 5088}, {3598, 7176}, {3600, 7195}, {3617, 9436}, {3621, 6604}, {3632, 20121}, {3665, 5261}, {3674, 17316}, {4080, 4624}, {4403, 5286}, {4454, 4513}, {4461, 40704}, {4488, 4936}, {4666, 41918}, {4747, 6610}, {4853, 7271}, {4872, 17578}, {5068, 17181}, {5252, 24797}, {5543, 25716}, {6737, 21296}, {7177, 27003}, {7183, 23958}, {10405, 26531}, {10586, 34060}, {16749, 26818}, {17089, 39775}, {18600, 25059}, {20014, 32007}, {20059, 20111}, {20618, 26871}, {20924, 32830}, {25719, 31145}, {32869, 33939}

X(43983) = X(5437)-cross conjugate of X(31995)
X(43983) = X(41)-isoconjugate of X(7320)
X(43983) = cevapoint of X(5437) and X(7271)
X(43983) = barycentric product X(i)*X(j) for these {i,j}: {7, 31995}, {75, 7271}, {85, 5437}, {1088, 4853}, {3304, 6063}
X(43983) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 7320}, {3304, 55}, {3698, 210}, {4853, 200}, {5437, 9}, {7271, 1}, {31995, 8}
X(43983) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20089, 30695}, {7, 9312, 145}, {85, 279, 2}, {85, 1088, 26563}, {85, 17079, 279}, {3160, 40719, 3622}, {7195, 7223, 3600}, {9436, 31994, 3617}, {25719, 32003, 31145}

X(43984) = VIJAY 5TH PARALLEL TRANSFORM OF X(9)

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

X(43984) lies on these lines: {2, 220}, {9, 3177}, {145, 1001}, {218, 27253}, {239, 3305}, {631, 38572}, {644, 27304}, {1212, 32088}, {3617, 14942}, {3730, 4209}, {4384, 4936}, {4473, 40861}, {4513, 17277}, {4875, 17335}, {5819, 26790}, {6603, 31269}, {6737, 25101}, {17244, 37684}, {17260, 19860}, {17316, 37652}, {17368, 24564}, {17691, 39350}, {20089, 32024}, {26653, 27288}, {29621, 37683}

X(43984) = {X(220),X(32008)}-harmonic conjugate of X(2)

X(43985) = VIJAY 5TH PARALLEL TRANSFORM OF X(10)

Barycentrics    a^2 + 3*a*b + 3*b^2 + 3*a*c + 7*b*c + 3*c^2 : :

X(43985) lies on these lines: {2, 594}, {10, 894}, {86, 4478}, {192, 3842}, {335, 4699}, {524, 32101}, {756, 24372}, {1213, 32089}, {1698, 6541}, {2345, 4473}, {3617, 17379}, {3634, 17319}, {3739, 29591}, {3759, 17303}, {3828, 4431}, {3943, 31248}, {3963, 25458}, {4007, 29612}, {4033, 25457}, {4060, 29580}, {4429, 28556}, {4440, 5224}, {4470, 17343}, {4472, 20090}, {4535, 19877}, {4751, 29587}, {4967, 17302}, {5564, 29586}, {6542, 28639}, {6687, 17289}, {7227, 31144}, {16816, 28635}, {17239, 26806}, {17248, 19875}, {17251, 31300}, {17257, 17487}, {17280, 29576}, {17299, 29592}, {17300, 29593}, {17385, 29590}, {17398, 20016}, {23913, 27798}, {26045, 26764}, {29621, 42335}

X(43985) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 28604, 1654}, {594, 1268, 2}, {4472, 32025, 20090}, {4967, 29610, 17302}

X(43986) = VIJAY 5TH PARALLEL TRANSFORM OF X(100)

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

X(43986) lies on these lines: {2, 1252}, {100, 17494}, {101, 27013}, {666, 26777}, {693, 14589}, {765, 20072}, {901, 26853}, {5218, 6066}, {5375, 27115}, {14513, 31290}, {20295, 41405}, {26985, 40865}

X(43986) = barycentric product X(i)*X(j) for these {i,j}: {1016, 17365}, {4998, 5432}
X(43986) = barycentric quotient X(i)/X(j) for these {i,j}: {5432, 11}, {17365, 1086}
X(43986) = {X(1252),X(4998)}-harmonic conjugate of X(2)

X(43987) = VIJAY 5TH PARALLEL TRANSFORM OF X(101)

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

X(43987) lies on these lines: {2, 23990}, {59, 17349}, {101, 21225}

X(43988) = VIJAY 6TH PARALLEL TRANSFORM OF X(3)

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

X(43988) lies on these lines: {2, 216}, {3, 6662}, {20, 6193}, {323, 8613}, {394, 14570}, {401, 1994}, {467, 41005}, {852, 42453}, {1993, 19180}, {2979, 42329}, {5392, 43766}, {6638, 35360}, {13409, 32428}, {18301, 39352}, {23606, 35311}, {30258, 30506}, {35941, 41676}

X(43988) = anticomplement of X(324)
X(43988) = anticomplement of the isogonal conjugate of X(14533)
X(43988) = anticomplement of the isotomic conjugate of X(97)
X(43988) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 2888}, {54, 21270}, {97, 6327}, {2148, 4}, {2167, 11442}, {2168, 68}, {2169, 69}, {2190, 317}, {8882, 5906}, {9247, 17035}, {14533, 8}, {14573, 21216}, {14586, 7253}, {15958, 7192}, {18315, 21300}, {19210, 4329}, {23286, 21294}, {34386, 21275}, {36134, 850}
X(43988) = X(97)-Ceva conjugate of X(2)
X(43988) = X(2148)-isoconjugate of X(42466)
X(43988) = barycentric product X(95)*X(15912)
X(43988) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 42466}, {15912, 5}
X(43988) = {X(216),X(40684)}-harmonic conjugate of X(2)

X(43989) = VIJAY 6TH PARALLEL TRANSFORM OF X(9)

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

X(43989) lies on these lines: {2, 85}, {144, 4661}, {3732, 7411}, {3870, 25237}, {3957, 10025}, {5698, 30622}, {6605, 32024}, {17147, 21218}, {25297, 42720}

X(43989) = anticomplement of the isotomic conjugate of X(6605)
X(43989) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {55, 2890}, {1174, 3434}, {2346, 21285}, {6605, 6327}, {10482, 69}, {32008, 21280}
X(43989) = X(i)-Ceva conjugate of X(j) for these (i,j): {6605, 2}, {32024, 9}

X(43990) = VIJAY 6TH PARALLEL TRANSFORM OF X(10)

Barycentrics    2*a^3 + a^2*b - 3*a*b^2 - 2*b^3 + a^2*c - 4*a*b*c - 3*b^2*c - 3*a*c^2 - 3*b*c^2 - 2*c^3 : :
X(43990) = 3 X[2] - 4 X[41809]

X(43990) lies on these lines: {2, 6}, {8, 24068}, {10, 20290}, {145, 26064}, {210, 3909}, {319, 3995}, {321, 4690}, {1029, 27797}, {1330, 3617}, {1655, 20055}, {2475, 3421}, {3219, 3882}, {3621, 26117}, {3686, 17184}, {3770, 28605}, {3969, 17332}, {4030, 20058}, {4359, 17344}, {4418, 31301}, {4425, 17162}, {4427, 21085}, {4440, 41821}, {4643, 17147}, {4651, 32948}, {4683, 17163}, {4886, 17495}, {4938, 10180}, {6539, 32025}, {6542, 24051}, {8013, 17770}, {9534, 17690}, {17011, 17252}, {17257, 20017}, {17270, 26223}, {17275, 32859}, {17287, 27065}, {17328, 28606}, {17331, 32858}, {17491, 21020}, {17499, 29593}, {17588, 41014}, {19998, 33083}, {24697, 27804}, {27812, 33097}, {28652, 28653}, {30564, 33113}, {31025, 33066}

X(43990) = reflection of X(8025) in X(41809)
X(43990) = reflection of X(43990) in the line X(2)X(6)
X(43990) = anticomplement of X(8025)
X(43990) = anticomplement of the isotomic conjugate of X(6539)
X(43990) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {37, 2891}, {42, 41821}, {798, 39348}, {1126, 75}, {1171, 17140}, {1255, 17135}, {1268, 17137}, {1796, 20243}, {4596, 17159}, {4629, 17166}, {6538, 21287}, {6539, 6327}, {6540, 17217}, {8701, 7192}, {28615, 1}, {30582, 20290}, {31010, 21293}, {32018, 17138}, {32635, 20245}, {33635, 3869}, {37212, 512}, {40438, 17143}
X(43990) = X(i)-Ceva conjugate of X(j) for these (i,j): {6539, 2}, {32025, 10}
X(43990) = crosspoint of X(4590) and X(6540)
X(43990) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20086, 26860}, {81, 27081, 2}, {81, 41816, 27081}, {333, 31037, 2}, {333, 31143, 31037}, {1211, 3578, 16704}, {1211, 16704, 2}, {1654, 2895, 2}, {4683, 17163, 44006}, {4683, 42334, 17163}, {5224, 19717, 2}, {5278, 31017, 2}, {8025, 41809, 2}, {16738, 27041, 2}, {17346, 32782, 19742}, {19742, 32782, 2}, {26044, 37635, 2}, {26772, 27163, 2}, {37653, 37656, 2}

X(43991) = VIJAY 6TH PARALLEL TRANSFORM OF X(100)

Barycentrics    (b - c)*(-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 + 2*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(43991) lies on these lines: {2, 650}, {63, 514}, {81, 2401}, {522, 3870}, {885, 1621}, {1001, 42454}, {3210, 17496}, {4391, 17776}, {5552, 35100}, {6938, 8760}, {10006, 10584}, {12647, 29066}, {17594, 23811}, {17784, 30613}, {36038, 43050}

X(43991) = reflection of X(36038) in X(43050)
X(43991) = anticomplement of X(40166)
X(43991) = anticomplement of the isotomic conjugate of X(31615)
X(43991) = X(31615)-Ceva conjugate of X(2)
X(43991) = crosssum of X(649) and X(21742)
X(43991) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {59, 150}, {1110, 37781}, {1252, 33650}, {2149, 149}, {4564, 21293}, {4619, 3434}, {23990, 39351}, {31615, 6327}, {32739, 17036}
X(43991) = barycentric product X(4998)*X(15914)
X(43991) = barycentric quotient X(15914)/X(11)

X(43992) = VIJAY 6TH PARALLEL TRANSFORM OF X(101)

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

X(43992) lies on these lines: {2, 2412}, {3190, 25259}

X(43992) = anticomplement of the isotomic conjugate of X(31616)
X(43992) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {15378, 21293}, {31616, 6327}
X(43992) = X(31616)-Ceva conjugate of X(2)

X(43993) = VIJAY 10TH PARALLEL TRANSFORM OF X(1)

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

X(43993) lies on these lines: {1, 75}, {10, 32924}, {58, 17150}, {81, 596}, {145, 17690}, {386, 3891}, {595, 17147}, {726, 1203}, {1089, 29821}, {1125, 1224}, {1724, 31036}, {1739, 41261}, {1961, 6533}, {1999, 3953}, {2891, 20016}, {2901, 7191}, {3187, 24632}, {3210, 5264}, {3216, 32926}, {3244, 5425}, {3454, 32842}, {3555, 4852}, {3746, 4970}, {3773, 19881}, {3791, 6763}, {3874, 41723}, {4066, 32944}, {4075, 37680}, {4361, 25499}, {4658, 17140}, {5312, 32920}, {6742, 39697}, {10479, 17599}, {17061, 25645}, {20045, 33771}, {20083, 33089}, {24068, 32911}, {24165, 37559}, {25431, 25501}, {30145, 32860}, {30148, 32915}, {32844, 36250}

X(43993) = {X(1),X(24325)}-harmonic conjugate of X(28619)

X(43994) = VIJAY 10TH PARALLEL TRANSFORM OF X(3)

Barycentrics    a^16 - 6*a^14*b^2 + 16*a^12*b^4 - 25*a^10*b^6 + 25*a^8*b^8 - 16*a^6*b^10 + 6*a^4*b^12 - a^2*b^14 - 6*a^14*c^2 + 21*a^12*b^2*c^2 - 26*a^10*b^4*c^2 + 9*a^8*b^6*c^2 + 8*a^6*b^8*c^2 - 7*a^4*b^10*c^2 + b^14*c^2 + 16*a^12*c^4 - 26*a^10*b^2*c^4 + 8*a^6*b^6*c^4 + 2*a^4*b^8*c^4 + 6*a^2*b^10*c^4 - 6*b^12*c^4 - 25*a^10*c^6 + 9*a^8*b^2*c^6 + 8*a^6*b^4*c^6 - 2*a^4*b^6*c^6 - 5*a^2*b^8*c^6 + 15*b^10*c^6 + 25*a^8*c^8 + 8*a^6*b^2*c^8 + 2*a^4*b^4*c^8 - 5*a^2*b^6*c^8 - 20*b^8*c^8 - 16*a^6*c^10 - 7*a^4*b^2*c^10 + 6*a^2*b^4*c^10 + 15*b^6*c^10 + 6*a^4*c^12 - 6*b^4*c^12 - a^2*c^14 + b^2*c^14 : :

X(43994) lies on these lines: {3, 95}, {97, 6662}, {140, 14938}, {550, 13445}

X(43995) = VIJAY 10TH PARALLEL TRANSFORM OF X(4)

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

X(43995) lies on these lines: {4, 69}, {5, 275}, {24, 5962}, {68, 2052}, {99, 8905}, {107, 41587}, {297, 6146}, {324, 2888}, {467, 8884}, {1147, 14165}, {1209, 37127}, {1288, 18401}, {1298, 39418}, {1629, 12134}, {3462, 34986}, {6193, 11547}, {6642, 43462}, {7488, 14918}, {8613, 10600}, {8883, 41679}, {10112, 39569}, {10282, 41203}, {12429, 41365}, {14788, 36794}, {15466, 18912}

X(43995) = reflection of X(2055) in X(5)
X(43995) = X(2055)-of-Johnson-triangle
X(43995) = {X(467),X(14516)}-harmonic conjugate of X(8884)

X(43996) = VIJAY 10TH PARALLEL TRANSFORM OF X(6)

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

X(43996) lies on these lines: {6, 76}, {251, 6664}, {3108, 3589}

X(43997) = VIJAY 11TH PARALLEL TRANSFORM OF X(1)

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

X(43997) lies on these lines: {1, 75}, {2, 2308}, {6, 1698}, {10, 17363}, {31, 5333}, {36, 1001}, {43, 19684}, {69, 19856}, {87, 43531}, {142, 29646}, {171, 19701}, {238, 3624}, {750, 4279}, {964, 36646}, {968, 13174}, {984, 4670}, {1125, 3662}, {1203, 27623}, {1386, 40328}, {1757, 39586}, {2245, 30585}, {3416, 4798}, {3550, 43223}, {3576, 39549}, {3616, 24248}, {3634, 17349}, {3679, 4649}, {3751, 36531}, {3758, 3842}, {3764, 24923}, {3771, 26109}, {3775, 17378}, {3821, 17397}, {3836, 17381}, {3923, 16826}, {3993, 29570}, {4648, 29637}, {4655, 17322}, {4672, 4687}, {4716, 16884}, {4751, 4974}, {4758, 29659}, {4991, 16816}, {5061, 5219}, {5145, 9902}, {5248, 28620}, {5251, 37507}, {5259, 20992}, {5290, 7175}, {5691, 37474}, {5698, 28641}, {5711, 28365}, {5750, 29674}, {5988, 29634}, {6703, 33111}, {7290, 36554}, {8025, 31330}, {8053, 39578}, {9345, 31137}, {9780, 37677}, {9791, 29592}, {11108, 36635}, {14621, 29603}, {14996, 30970}, {16469, 31312}, {16477, 17259}, {16503, 38052}, {16738, 19858}, {16779, 29633}, {17045, 33149}, {17244, 24295}, {17248, 17770}, {17284, 20131}, {17303, 32846}, {17308, 20132}, {17321, 32857}, {17392, 33087}, {17398, 32784}, {17591, 29644}, {17592, 37869}, {19717, 26037}, {20134, 27020}, {20145, 29610}, {23812, 27184}, {25354, 29612}, {25496, 25502}, {26102, 31005}, {27169, 30107}, {27804, 30562}, {29827, 37633}, {31423, 37510}, {32853, 42028}, {33084, 37631}, {40031, 40718}

X(43997) = reflection of X(1) in X(17394)
X(43997) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 25528, 18792}, {2, 33682, 16468}, {86, 25526, 18792}, {238, 15668, 3624}

X(43998) = VIJAY 11TH PARALLEL TRANSFORM OF X(3)

Barycentrics    2*a^12 - 9*a^10*b^2 + 17*a^8*b^4 - 17*a^6*b^6 + 9*a^4*b^8 - 2*a^2*b^10 - 9*a^10*c^2 + 23*a^8*b^2*c^2 - 14*a^6*b^4*c^2 - 7*a^4*b^6*c^2 + 9*a^2*b^8*c^2 - 2*b^10*c^2 + 17*a^8*c^4 - 14*a^6*b^2*c^4 - 4*a^4*b^4*c^4 - 7*a^2*b^6*c^4 + 8*b^8*c^4 - 17*a^6*c^6 - 7*a^4*b^2*c^6 - 7*a^2*b^4*c^6 - 12*b^6*c^6 + 9*a^4*c^8 + 9*a^2*b^2*c^8 + 8*b^4*c^8 - 2*a^2*c^10 - 2*b^2*c^10 : :

X(43998) lies on these lines: {3, 95}, {182, 599}, {577, 1656}, {5070, 36794}

X(43999) = VIJAY 11TH PARALLEL TRANSFORM OF X(4)

Barycentrics    (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^8 - 2*a^4*b^4 + b^8 - 8*a^4*b^2*c^2 + 16*a^2*b^4*c^2 - 8*b^6*c^2 - 2*a^4*c^4 + 16*a^2*b^2*c^4 + 14*b^4*c^4 - 8*b^2*c^6 + c^8) : :
X(43999) = 5 X[631] - 4 X[36751]

X(43999) lies on these lines: {2, 14489}, {4, 69}, {53, 10519}, {324, 7386}, {376, 33971}, {393, 631}, {1217, 34208}, {1249, 37124}, {3090, 6530}, {3525, 17907}, {3545, 10002}, {3619, 39569}, {7392, 40684}, {8801, 18854}, {9308, 14912}, {14978, 34938}, {15702, 37765}, {16264, 33703}

X(44000) = VIJAY 11TH PARALLEL TRANSFORM OF X(6)

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

X(44000) lies on these lines: {2, 42421}, {6, 76}, {32, 3763}, {141, 7787}, {182, 381}, {597, 39141}, {599, 12212}, {625, 1691}, {1350, 10796}, {1501, 39668}, {1503, 10359}, {1656, 39750}, {2076, 10345}, {3094, 7804}, {3098, 18501}, {3242, 10791}, {3329, 4048}, {3398, 10516}, {3589, 5025}, {3618, 16044}, {3844, 10789}, {3972, 10007}, {5017, 40842}, {5031, 7846}, {5033, 33241}, {5039, 40341}, {5041, 41747}, {5116, 11174}, {7793, 34573}, {7822, 15870}, {7889, 38905}, {10387, 10798}, {11842, 24206}, {12110, 31884}, {12150, 21358}, {14535, 40825}, {14561, 40279}, {15588, 41928}

X(44000) = reflection of X(6) in X(7878)
X(44000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {83, 42534, 6}

This is the end of PART 22: Centers X(42001) - X(44000)

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)