ENCYCLOPEDIA OF TRIANGLE CENTERS Part24

X(46001) lies on these lines: {6, 11186}, {110, 9124}, {351, 523}, {512, 2030}, {526, 7625}, {597, 1499}, {598, 25423}, {669, 1383}, {691, 1576}, {882, 9009}, {3566, 14279}, {6088, 8644}, {8704, 11621}, {9044, 9208}, {9155, 9164}, {9182, 18829}, {11580, 17414}, {11622, 32217}, {14606, 18818}, {19127, 39518}, {23297, 23301}, {35364, 43697}

X(46001) = midpoint of X(i) and X(j) for these {i, j}: {6, 11186}, {669, 9178}, {8599, 23287}
X(46001) = reflection of X(32231) in X(11621)
X(46001) = isogonal conjugate of X(9146)
X(46001) = polar conjugate of the isotomic conjugate of X(30491)
X(46001) = barycentric product X(i)*X(j) for these {i, j}: {4, 30491}, {6, 8599}, {111, 23287}, {115, 11636}, {351, 18818}, {512, 598}
X(46001) = barycentric quotient X(i)/X(j) for these (i, j): (32, 9145), (213, 3908), (351, 39785), (512, 599), (523, 9464), (598, 670)
X(46001) = trilinear product X(i)*X(j) for these {i, j}: {19, 30491}, {31, 8599}, {598, 798}, {661, 1383}, {923, 23287}, {1924, 40826}
X(46001) = trilinear quotient X(i)/X(j) for these (i, j): (31, 9145), (42, 3908), (512, 36263), (598, 799), (661, 599), (798, 574)
X(46001) = trilinear pole of the line {3124, 9135}
X(46001) = perspector of the circumconic {{A, B, C, X(598), X(1383)}}
X(46001) = inverse of X(24976) in Kiepert parabola
X(46001) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(2030)}} and {{A, B, C, X(25), X(7426)}}
X(46001) = cevapoint of X(512) and X(8644)
X(46001) = crossdifference of every pair of points on line {X(574), X(599)}
X(46001) = crosspoint of X(i) and X(j) for these (i, j): {1296, 39389}, {1383, 11636}
X(46001) = crosssum of X(i) and X(j) for these (i, j): {523, 16509}, {597, 1499}, {599, 3906}
X(46001) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 9464), (206, 9145), (512, 17414), (1084, 599)
X(46001) = X(i)-isoconjugate-of-X(j) for these {i, j}: {75, 9145}, {86, 3908}, {99, 36263}, {163, 9464}
X(46001) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (32, 9145), (213, 3908), (351, 39785), (512, 599)
X(46001) = center of circle {{X(2), X(6), X(23)}}
X(46001) = X(11621)-of-anti-McCay triangle
X(46001) = X(2492)-of-4th anti-Brocard triangle
X(46001) = X(1383)-vertex conjugate of-X(11580)

X(46002) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(5) AND X(54)

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

X(46002) lies on these lines: {137, 8901}, {523, 10096}, {526, 11702}, {1510, 42650}, {8254, 45147}, {8562, 11701}

X(46002) = isogonal conjugate of X(43965)
X(46002) = barycentric product X(526)*X(11538)
X(46002) = barycentric quotient X(i)/X(j) for these (i, j): (526, 15108), (2081, 21230)
X(46002) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(523)}} and {{A, B, C, X(137), X(933)}}
X(46002) = crossdifference of every pair of points on line {X(15109), X(34520)}
X(46002) = crosspoint of X(1291) and X(39390)
X(46002) = crosssum of X(523) and X(24385)
X(46002) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {5, 54, 1157}, {19651, 20424, 30481}
X(46002) = X(526)-reciprocal conjugate of-X(15108)

X(46003) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(7) AND X(55)

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

X(46003) = isogonal conjugate of the anticomplement of X(43959)
X(46003) = center of circle {{X(7), X(55), X(1155)}}
X(46003) = barycentric quotient X(2488)/X(34522)

X(46004) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(8) AND X(56)

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

X(46004) = center of circle {{X(8), X(56), X(1319)}}
X(46004) = crossdifference of every pair of points on line {X(34524), X(34543)}

X(46005) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(20) AND X(64)

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

X(46005) lies on these lines: {523, 14329}, {525, 5894}, {2489, 2881}, {9178, 41894}, {15292, 39201}

X(46005) = isogonal conjugate of the anticomplement of X(1562)
X(46005) = barycentric product X(i)*X(j) for these {i, j}: {523, 41894}, {647, 18848}
X(46005) = barycentric quotient X(i)/X(j) for these (i, j): (512, 26958), (647, 40995), (661, 18691)
X(46005) = trilinear product X(i)*X(j) for these {i, j}: {661, 41894}, {810, 18848}
X(46005) = trilinear quotient X(i)/X(j) for these (i, j): (523, 18691), (656, 40995), (661, 26958), (810, 1204)
X(46005) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(18778)}} and {{A, B, C, X(25), X(16386)}}
X(46005) = cevapoint of X(512) and X(42658)
X(46005) = crossdifference of every pair of points on line {X(26958), X(40995)}
X(46005) = crosssum of X(525) and X(5894)
X(46005) = X(i)-Dao conjugate of X(j) for these (i, j): (125, 40995), (244, 18691), (1084, 26958)
X(46005) = X(i)-isoconjugate-of-X(j) for these {i, j}: {110, 18691}, {162, 40995}, {662, 26958}, {811, 1204}
X(46005) = center of circle {{X(20), X(64), X(2071)}}
X(46005) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (512, 26958), (647, 40995), (661, 18691)

X(46006) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(9) AND X(57)

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

X(46006) = midpoint of X(23351) and X(23865)
X(46006) = isogonal conjugate of the anticomplement of X(43960)
X(46006) = barycentric product X(513)*X(34525)
X(46006) = trilinear product X(649)*X(34525)
X(46006) = trilinear quotient X(657)/X(34526)
X(46006) = center of circle {{X(9), X(57), X(2078)}}
X(46006) = X(658)-isoconjugate-of-X(34526)

X(46007) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(11) AND X(59)

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

X(46008) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(186) AND X(265)

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

X(46008) lies on these lines: {403, 523}, {526, 10113}, {5448, 9033}, {39235, 45147}

X(46008) = center of circle {{X(4), X(186), X(265)}}
X(46008) = crosssum of X(526) and X(6102)

X(46009) = X(1)X(37413)∩X(2)X(1804)

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

X(46009) lies on the cubic K1245 and these lines: {1, 37413}, {2, 1804}, {4, 11}, {6, 57}, {19, 43058}, {28, 1035}, {196, 6046}, {225, 37818}, {226, 7011}, {278, 6611}, {940, 7125}, {1014, 5932}, {1214, 1766}, {1410, 4185}, {1470, 37310}, {1617, 40960}, {3075, 11425}, {3911, 5120}, {5706, 7114}, {5909, 37582}, {6516, 30828}, {7053, 34050}, {7532, 19762}, {8748, 40837}, {8808, 13478}, {10400, 16580}, {13737, 15654}, {24030, 43160}, {37046, 37583}

X(46010) = X(2)X(1444)∩X(3)X(37)

Barycentrics a^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(46010) lies on the conic {{A,B,C,X(2),X(6)}}, the cubics K321 and K1245, and on these lines: {2, 1444}, {3, 37}, {6, 1437}, {19, 3435}, {25, 1333}, {28, 393}, {42, 48}, {56, 1880}, {284, 45129}, {478, 603}, {941, 2303}, {958, 19285}, {967, 5115}, {1036, 2214}, {1108, 3420}, {1427, 7053}, {1791, 14624}, {3433, 5322}, {4252, 14553}, {4254, 39974}, {4261, 37257}, {5069, 39951}, {5110, 39967}, {5120, 39798}, {5124, 39982}, {5301, 11365}, {10037, 22118}, {13478, 24005}, {15668, 16580}, {16606, 23086}, {40144, 45786}

X(46010) = isogonal conjugate of X(5739)
X(46010) = isogonal conjugate of the anticomplement of X(940)
X(46010) = X(i)-cross conjugate of X(j) for these (i,j): {2281, 2214}, {5019, 6}
X(46010) = cevapoint of X(3124) and X(8639)
X(46010) = trilinear pole of line {512, 22383}
X(46010) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5739}, {2, 12514}, {8, 45126}, {10, 27174}, {58, 42707}, {63, 406}, {75, 36744}, {304, 44086}, {345, 1452}, {612, 14258}
X(46010) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5739}, {25, 406}, {31, 12514}, {32, 36744}, {37, 42707}, {604, 45126}, {1333, 27174}, {1395, 1452}, {1974, 44086}, {2221, 14258}
X(46010) = {X(2303),X(11337)}-harmonic conjugate of X(36744)

X(46011) = X(3)X(281)∩X(4)X(6)

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

X(46011) lies on the cubic K1245 and these lines: {3, 281}, {4, 6}, {19, 1158}, {48, 515}, {57, 5307}, {92, 3101}, {278, 41007}, {412, 2322}, {572, 5136}, {860, 5816}, {961, 40836}, {966, 37414}, {1754, 1957}, {1766, 41013}, {1857, 37538}, {1880, 17102}, {5236, 24220}, {8755, 37530}

X(46011) = polar conjugate of the isotomic conjugate of X(24537)
X(46011) = barycentric product X(4)*X(24537)
X(46011) = barycentric quotient X(24537)/X(69)

X(46012) = X(3)X(9)∩X(19)X(18237)

Barycentrics a^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 - 3*b^2*c - a*c^2 - 3*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(46012) lies on the cubic K1245 and these lines: {3, 9}, {19, 18237}, {189, 1150}, {285, 11344}, {391, 411}, {572, 16293}, {940, 1422}, {961, 40836}, {3149, 5120}, {8808, 13478}, {12114, 40942}

X(46012) = barycentric product X(84)*X(19860)
X(46012) = barycentric quotient X(19860)/X(322)
X(46012) = {X(1436),X(1903)}-harmonic conjugate of X(268)

X(46013) = X(4)X(961)∩X(6)X(42467)

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)*(a^9 + 2*a^8*b - 2*a^6*b^3 - 2*a^5*b^4 - 2*a^4*b^5 + 2*a^2*b^7 + a*b^8 + 2*a^8*c + 4*a^7*b*c + 2*a^6*b^2*c - 6*a^5*b^3*c - 8*a^4*b^4*c + 2*a^2*b^6*c + 2*a*b^7*c + 2*b^8*c + 2*a^6*b*c^2 - 4*a^5*b^2*c^2 + 2*a^4*b^3*c^2 - 4*a^3*b^4*c^2 - 6*a^2*b^5*c^2 + 8*a*b^6*c^2 + 2*b^7*c^2 - 2*a^6*c^3 - 6*a^5*b*c^3 + 2*a^4*b^2*c^3 - 8*a^3*b^3*c^3 + 2*a^2*b^4*c^3 - 2*a*b^5*c^3 - 2*b^6*c^3 - 2*a^5*c^4 - 8*a^4*b*c^4 - 4*a^3*b^2*c^4 + 2*a^2*b^3*c^4 - 18*a*b^4*c^4 - 2*b^5*c^4 - 2*a^4*c^5 - 6*a^2*b^2*c^5 - 2*a*b^3*c^5 - 2*b^4*c^5 + 2*a^2*b*c^6 + 8*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 + 2*b*c^8) : :

X(46013) lies on the cubic K1245 and these lines: {4, 961}, {6, 42467}, {572, 34279}, {13478, 24005}

X(46014) = X(4)X(960)∩X(57)X(573)

Barycentrics (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 - 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(46014) lies on the cubic K1246 and these lines: {4, 960}, {57, 573}, {189, 5739}, {581, 937}, {3194, 37410}, {36100, 37419}

X(46014) = X(1436)-isoconjugate of X(19860)
X(46014) = barycentric quotient X(40)/X(19860)

X(46015) = X(6)X(104)∩X(57)X(2051)

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

X(46015) lies on the cubic K1246 and these lines: {6, 104}, {57, 2051}, {515, 2183}, {573, 38955}

X(46016) = X(1)X(25490)∩X(4)X(386)

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

X(46016) lies on the cubic K1246 and these lines: {1, 25490}, {4, 386}, {6, 859}, {9, 22350}, {42, 5727}, {57, 959}, {995, 37642}, {4312, 5313}

X(46017) = X(1)X(9786)∩X(4)X(65)

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

X(46017) lies on the cubic K1246 and these lines: {1, 9786}, {4, 65}, {6, 57}, {7, 11433}, {19, 34032}, {46, 37413}, {51, 1876}, {56, 37310}, {77, 11350}, {169, 34048}, {208, 5706}, {221, 7713}, {226, 6708}, {241, 44708}, {278, 2262}, {354, 11436}, {389, 942}, {573, 1214}, {578, 37582}, {950, 13568}, {1155, 11429}, {1192, 3601}, {1210, 12233}, {1425, 1829}, {1452, 19349}, {1767, 2285}, {1892, 1899}, {1901, 10379}, {2051, 8808}, {2183, 37755}, {2807, 5173}, {2982, 32677}, {3340, 10373}, {3911, 23292}, {4254, 7011}, {4292, 12241}, {5122, 11430}, {5219, 26958}, {5226, 37643}, {5435, 11427}, {5708, 11432}, {5746, 40837}, {5836, 6358}, {5930, 44662}, {5932, 36850}, {7053, 34052}, {7066, 45120}, {10391, 20122}, {10903, 10969}, {10974, 18641}, {11399, 40658}, {11425, 15803}, {11426, 37545}, {11438, 24929}, {17106, 34499}, {17441, 45963}, {19365, 32636}, {20617, 44548}, {23982, 40940}, {30282, 37487}, {43915, 44546}

X(46017) = X(i)-complementary conjugate of X(j) for these (i,j): {947, 6389}, {40396, 18589}
X(46017) = crossdifference of every pair of points on line {3900, 36054}
X(46017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {65, 19366, 44547}, {1439, 14557, 223}, {1452, 19349, 40660}, {13437, 13459, 4295}

X(46018) = X(2)X(2245)∩X(6)X(859)

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

X(46018) lies on the conic {{A,B,C,X(2),X(6)}}, the cubic K1246, and these lines: {2, 2245}, {6, 859}, {9, 45095}, {32, 34079}, {37, 517}, {42, 2183}, {44, 16606}, {251, 4290}, {579, 39798}, {583, 39956}, {941, 4271}, {960, 19257}, {966, 14624}, {967, 40153}, {995, 28658}, {1169, 4275}, {1400, 1457}, {1875, 1880}, {2176, 14260}, {2278, 4216}, {2350, 5165}, {4253, 39981}, {4254, 45129}, {4266, 39974}, {4270, 28625}, {4285, 39961}, {5036, 39982}, {5043, 39960}

X(46018) = isogonal conjugate of X(1150)
X(46018) = isogonal conjugate of the anticomplement of X(5718)
X(46018) = isogonal conjugate of the complement of X(31034)
X(46018) = X(4274)-cross conjugate of X(6)
X(46018) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1150}, {2, 993}, {63, 5136}, {75, 2278}, {13136, 14299}
X(46018) = trilinear pole of line {512, 3310}
X(46018) = barycentric product X(i)*X(j) for these {i,j}: {1, 994}, {58, 45095}
X(46018) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 1150}, {25, 5136}, {31, 993}, {32, 2278}, {994, 75}, {45095, 313}

X(46019) = X(4)X(6)∩X(19)X(946)

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

X(46019) lies on the cubic K1246 and these lines: {4, 6}, {19, 946}, {20, 2326}, {33, 10445}, {57, 1848}, {281, 517}, {406, 573}, {608, 41344}, {959, 2358}, {1474, 37395}, {1712, 39579}, {1753, 5750}, {3213, 4292}, {10478, 37388}, {24220, 37382}, {24553, 37378}, {26118, 45786}

X(46020) = X(4)X(959)∩X(6)X(2050)

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

X(46020) lies on the cubic K1246 and these lines: {4, 959}, {6, 2050}, {573, 19608}, {10478, 40160}, {19607, 23512}

X(46021) = X(4)X(57)∩X(271)X(5739)

X(46021) lies on the cubic K1246 and these lines: {4, 57}, {271, 5739}, {282, 573}, {285, 411}, {581, 1433}

X(46022) = X(3)X(9)∩X(189)X(5739)

X(46022) lies on the cubic K1246 and these lines: {3, 9}, {189, 5739}, {959, 2358}, {2051, 8808}, {3427, 7003}, {5798, 37544}, {6001, 40942}, {6245, 9119}

X(46022) = barycentric product X(84)*X(24987)
X(46022) = barycentric quotient X(24987)/X(322)

X(46023) = ISOGONAL CONJUGATE OF X(1340)

X(46023) lies on the Keipert circumhyperbola, the cubics K055 and K281, and these lines: {2, 1380}, {3, 14633}, {4, 14631}, {5, 6177}, {6, 3414}, {30, 182}, {32, 6178}, {76, 3558}, {83, 2558}, {98, 31863}, {262, 1341}, {381, 3413}, {671, 31862}, {1340, 3972}, {1349, 5475}, {1379, 10788}, {2559, 12110}, {3399, 13326}, {3424, 35913}, {7787, 14630}

X(46023) = reflection of X(46024) in X(5476)
X(46023) = isogonal conjugate of X(1340)
X(46023) = X(i)-cross conjugate of X(j) for these (i,j): (1349,6178), (5475, 46024)
X(46023) = X(1)-isoconjugate of X(1340)
X(46023) = trilinear pole of line {523, 5638}
X(46023) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 1340}, {1341, 7998}, {45819, 46024}
X(46023) = {X(182),X(10796)}-harmonic conjugate of X (46024)

X(46024) = ISOGONAL CONJUGATE OF X(1341)

X(46024) lies on the Keipert circumhyperbola, the cubics K055 and K281, and these lines: {2, 1379}, {3, 14632}, {4, 14630}, {5, 6178}, {6, 3413}, {30, 182}, {32, 6177}, {76, 3557}, {83, 2559}, {98, 31862}, {262, 1340}, {381, 3414}, {671, 31863}, {1341, 3972}, {1348, 5475}, {1380, 10788}, {2558, 12110}, {3399, 13325}, {3424, 35914}, {7787, 14631}

X(46024) = reflection of X(46023) in X(5476)
X(46024) = isogonal conjugate of X(1341)
X(46024) = X(i)-cross conjugate of X(j) for these (i,j): (1348,6177), (5475, 46023)
X(46024) = X(1)-isoconjugate of X(1341)
X(46024) = trilinear pole of line {523, 5639}
X(46024) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 1341}, {1340, 7998}, {45819, 46023}
X(46024) = {X(182),X(10796)}-harmonic conjugate of X(46023)

X(46025) = X(3)X(54)∩X(5)X(53)

X(46025) = 3 X[3] - X[31388], X[3] - 3 X[32078], 2 X[140] - 3 X[12012], 2 X[546] - 3 X[14635], 5 X[632] - 6 X[44914], 5 X[1656] - 3 X[11197], 4 X[3628] - 3 X[10184], X[31388] - 9 X[32078], X[31388] + 3 X[42441], 3 X[32078] + X[42441]

X(46025) lies on these lines: {2, 14978}, {3, 54}, {5, 53}, {26, 26898}, {30, 35717}, {52, 26907}, {140, 12012}, {143, 418}, {155, 36751}, {156, 6641}, {546, 14635}, {549, 33549}, {568, 26876}, {632, 6509}, {852, 32205}, {1216, 45112}, {1578, 18940}, {1579, 18939}, {1656, 11197}, {2072, 34768}, {3060, 26896}, {3567, 26895}, {3628, 10184}, {5609, 41212}, {5647, 10539}, {5663, 26897}, {6243, 26874}, {6638, 15026}, {7393, 40681}, {7526, 23709}, {10263, 30258}, {11793, 34990}, {13371, 26905}, {13856, 37452}, {14790, 26870}, {15869, 21230}, {16239, 44436}, {19347, 44200}, {22804, 36245}, {26865, 37493}, {26880, 37440}

X(46025) = midpoint of X(i) and X(j) for these {i,j}: {3, 42441}, {30258, 42556}
X(46025) = reflection of X(35719) in X(5)
X(46025) = complement of X(14978)
X(46025) = complement of the isogonal conjugate of X(20574)
X(46025) = X(i)-complementary conjugate of X(j) for these (i,j): {288, 20305}, {20574, 10}, {39181, 21253}
X(46025) = X(35311)-Ceva conjugate of X(520)
X(46025) = X(2190)-isoconjugate of X(14938)
X(46025) = crossdifference of every pair of points on line {12077, 23286}
X(46025) = barycentric product X(343)*X(1199)
X(46025) = barycentric quotient X(i)/X(j) for these {i,j}: {216, 14938}, {1199, 275}
X(46025) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 195, 97}, {3, 13409, 10627}, {32078, 42441, 3}

X(46026) = X(4)X(83)∩X(141)X(427)

X(46026) = 3*X(1176)-5*X(3618), X(18440)+3*X(45034), 3*X(18488)+2*X(21850), 6*X(38136)-X(44866)

X(46026) lies on these lines: {2, 41464}, {4, 83}, {6, 5064}, {25, 2916}, {51, 23300}, {52, 1595}, {125, 9969}, {141, 427}, {155, 18440}, {159, 38396}, {185, 1907}, {193, 7378}, {264, 40035}, {378, 32600}, {428, 3589}, {511, 6152}, {542, 2914}, {858, 9822}, {1162, 3128}, {1163, 3127}, {1503, 3574}, {1568, 3818}, {1593, 35240}, {1594, 11817}, {1597, 40909}, {1829, 1861}, {2904, 39588}, {3564, 13431}, {5092, 7576}, {5094, 5646}, {5095, 32455}, {5133, 11574}, {5169, 12220}, {5895, 11403}, {5965, 13420}, {6030, 6995}, {6287, 22138}, {6292, 22078}, {6329, 44102}, {6697, 9971}, {7391, 19126}, {7394, 19137}, {8754, 39931}, {10294, 32250}, {10594, 38317}, {12167, 40341}, {14216, 14853}, {14865, 29317}, {15062, 15741}, {15583, 40673}, {15809, 37648}, {15812, 31099}, {16198, 36153}, {19125, 36990}, {20184, 38359}, {22970, 23047}, {26177, 28665}, {27366, 27371}, {31267, 44082}, {31390, 39691}, {32587, 45478}, {32588, 45479}, {38136, 44866}

X(46026) = midpoint of X(6) and X(15321)
X(46026) = complement of X(41464)
X(46026) = polar conjugate of X(40425)
X(46026) = crosspoint of X(i) and X(j) for these (i, j): {4, 427}, {428, 44142}
X(46026) = crosssum of X(3) and X(1176)
X(46026) = X(i)-Ceva conjugate of-X(j) for these (i, j): (4, 428), (427, 28666)
X(46026) = X(141)-Dao conjugate of X(41435)
X(46026) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 40425}, {82, 41435}
X(46026) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 40425), (39, 41435), (427, 10159), (428, 83)
X(46026) = perspector of the circumconic {{A, B, C, X(41676), X(42396)}}
X(46026) = Jerabek-circumhyperbola-inverse of X(9969)
X(46026) = polar-circle-inverse of X(38946)
X(46026) = pole wrt polar circle of trilinear polar of X(40425) (line X(826)X(14318))
X(46026) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(28666)}} and {{A, B, C, X(6), X(14247)}}
X(46026) = Zosma transform of X(82)
X(46026) = barycentric product X(i)*X(j) for these {i, j}: {4, 6292}, {19, 20898}, {25, 42554}, {27, 21038}, {39, 44142}, {83, 28666}
X(46026) = barycentric quotient X(i)/X(j) for these (i, j): (4, 40425), (39, 41435), (427, 10159), (428, 83), (1843, 3108)
X(46026) = trilinear product X(i)*X(j) for these {i, j}: {4, 17457}, {19, 6292}, {25, 20898}, {27, 21817}, {28, 21038}, {38, 428}
X(46026) = trilinear quotient X(i)/X(j) for these (i, j): (38, 41435), (92, 40425), (428, 82)
X(46026)= {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (427, 3867, 1843), (428, 3589, 44091)

X(46027) = X(6)X(382)∩X(143)X(185)

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

X(46027) = 3*X(4)-X(15062), 3*X(381)-X(18442), 2*X(382)+X(44866), X(3529)-3*X(6030), 2*X(3627)+X(34563), 5*X(3627)+X(44755), 5*X(5076)-X(33541), 2*X(15062)-3*X(18488), 5*X(17578)+X(43599), 5*X(34563)-2*X(44755)

X(46027) lies on these lines: {4, 5449}, {5, 35240}, {6, 382}, {30, 3574}, {113, 3575}, {143, 185}, {155, 12173}, {381, 18442}, {539, 13420}, {546, 44106}, {1112, 11560}, {1531, 31830}, {1568, 45971}, {1843, 12162}, {1986, 5446}, {2904, 35480}, {2914, 17702}, {3060, 16880}, {3146, 8718}, {3153, 43597}, {3529, 6030}, {3589, 12605}, {3830, 5895}, {3853, 10113}, {5076, 33541}, {5448, 18559}, {5663, 32340}, {5889, 15110}, {6152, 13754}, {6240, 12038}, {6756, 22970}, {7487, 15751}, {10110, 18323}, {10294, 30714}, {10539, 32605}, {11457, 17578}, {11559, 38447}, {13431, 44665}, {13474, 40949}, {16835, 32533}, {18128, 43612}, {18376, 37490}, {18377, 43817}, {23047, 32110}, {32478, 38359}, {34564, 43585}

X(46027) = midpoint of X(i) and X(j) for these {i, j}: {382, 3521}, {3146, 8718}
X(46027) = reflection of X(i) in X(j) for these (i, j): (11560, 1112), (18488, 4), (35240, 5), (44866, 3521)
X(46027) = crosspoint of X(4) and X(6240)
X(46027) = X(4)-Ceva conjugate of-X(546)
X(46027) = anti-excenters-incenter-reflections-to-orthic similarity image of X(18488)
X(46027) = Ehrmann-side-to-orthic similarity image of X(18442)
X(46027) = X(546)-reciprocal conjugate of-X(42410)
X(46027) = barycentric quotient X(546)/X(42410)

X(46028) = EULER LINE INTERCEPT OF X(11)X(16137)

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

X(46028) = 3*X(4)+5*X(15674), 7*X(4)+9*X(31669), 3*X(5)-X(442), 5*X(5)-X(5499), 3*X(5)+X(16160), 7*X(5)-X(37401), 5*X(5)+X(37447), X(21)+3*X(381), X(21)-3*X(44257), X(382)+3*X(21161), 5*X(442)-3*X(5499), X(442)+3*X(6841), 7*X(442)-3*X(37401), 5*X(442)+3*X(37447), 2*X(546)+X(12104), 3*X(547)-X(11277), X(550)-3*X(28465), 5*X(632)-X(31651)

X(46028) lies on these lines: {2, 3}, {11, 16137}, {12, 15174}, {758, 9955}, {1699, 16139}, {3585, 5427}, {3649, 7741}, {3817, 33592}, {3899, 21677}, {5424, 5560}, {5426, 18492}, {7173, 11544}, {7988, 16132}, {8227, 33858}, {8261, 31937}, {10113, 16164}, {11263, 22798}, {12558, 40273}, {16118, 31231}, {16125, 22936}, {16126, 38021}, {16159, 19919}, {18253, 25639}, {18357, 44669}, {18480, 35016}, {18493, 34195}, {22938, 35204}, {33857, 37692}

X(46028) = midpoint of X(i) and X(j) for these {i, j}: {3, 44258}, {4, 5428}, {5, 6841}, {381, 44257}, {442, 16160}, {546, 10021}, {3627, 44238}, {3845, 15670}, {3861, 44254}, {5499, 37447}, {8261, 31937}, {10113, 16164}, {11263, 22798}, {15687, 44255}, {16125, 22936}, {16159, 19919}, {18480, 35016}, {21677, 22791}, {22938, 35204}, {31649, 37230}
X(46028) = reflection of X(i) in X(j) for these (i, j): (11276, 16239), (12104, 10021)
X(46028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 550, 6829), (5, 632, 6991), (5, 3845, 2476), (5, 3857, 6941), (5, 3858, 6980), (5, 6831, 3628), (5, 8226, 3850), (5, 16160, 442), (21, 5141, 442), (381, 6873, 5), (5154, 19709, 5)

X(46029) = EULER LINE INTERCEPT OF X(113)X(15060)

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

X(46029) = 9*X(2)-X(35481), 3*X(3)+X(35480), 3*X(5)-X(427), 3*X(5)-2*X(13413), X(22)+3*X(381), X(22)-3*X(44262), X(378)-5*X(1656), 3*X(381)-X(44288), X(382)+3*X(44837), X(427)+3*X(15760), 2*X(427)-3*X(39504), 2*X(546)+X(7555), 3*X(547)-X(44236), 3*X(549)-X(44249)

X(46029) lies on these lines: {2, 3}, {113, 15060}, {182, 11801}, {184, 32423}, {185, 34826}, {265, 5012}, {399, 3410}, {569, 43575}, {578, 8254}, {1147, 15806}, {1154, 18388}, {1181, 18356}, {1209, 5876}, {1263, 15367}, {1352, 25336}, {1568, 15067}, {1614, 6288}, {2781, 24206}, {2979, 7699}, {3521, 11440}, {3574, 10263}, {3818, 19127}, {5448, 11591}, {5449, 13630}, {5663, 21243}, {6243, 20424}, {6689, 13403}, {7592, 32165}, {7731, 11805}, {9019, 19130}, {9306, 10272}, {9927, 32046}, {10112, 32136}, {10113, 16165}, {10193, 32743}, {10264, 12270}, {10540, 41171}, {10610, 21659}, {11204, 23315}, {11804, 12902}, {12281, 18435}, {13399, 13491}, {13470, 18383}, {13561, 40647}, {13565, 14076}, {13851, 37513}, {16000, 34224}, {16252, 40276}, {16789, 21850}, {16837, 22335}, {16881, 41587}, {18436, 21230}, {18475, 30522}, {20584, 26883}, {22660, 31834}, {26913, 40280}, {26958, 44754}, {32171, 44516}, {32210, 43577}, {32351, 34786}, {37470, 40685}, {43651, 43821}

X(46029) = midpoint of X(i) and X(j) for these {i, j}: {3, 44263}, {4, 7502}, {5, 15760}, {22, 44288}, {381, 44262}, {546, 25337}, {3627, 44239}, {3818, 19127}, {3845, 44210}, {10113, 16165}, {15687, 44261}, {16789, 21850}, {18572, 37969}
X(46029) = reflection of X(i) in X(j) for these (i, j): (427, 13413), (7555, 25337), (39504, 5)
X(46029) = complement of X(18570)
X(46029) = inverse of X(18572) in: MacBeath inconic, nine-point circle
X(46029) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 10254, 5), (3, 381, 3153), (3, 1656, 6143), (3, 34797, 550), (5, 235, 3850), (5, 549, 2072), (5, 550, 1594), (5, 3627, 5576), (5, 3845, 5133), (5, 7399, 3628), (5, 11563, 381), (5, 15761, 546), (22, 37353, 427), (140, 37968, 549), (381, 5899, 4), (403, 37347, 5), (1656, 16868, 5), (3628, 44912, 547), (5133, 11799, 3845), (6823, 13371, 548), (7577, 35480, 427), (10024, 13160, 5), (10024, 37347, 403), (34577, 45971, 1658), (44262, 44288, 22)

X(46030) = EULER LINE INTERCEPT OF X(51)X(113)

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

X(46030) = 3*X(5)-X(1368), X(25)+3*X(381), X(25)-3*X(44275), 2*X(546)+X(12106), X(1368)+3*X(1596), X(1370)-9*X(3545)

X(46030) lies on these lines: {2, 3}, {51, 113}, {125, 16194}, {143, 15873}, {156, 12241}, {343, 15060}, {399, 45968}, {1353, 45016}, {1498, 18952}, {1531, 44106}, {1533, 14855}, {2393, 19130}, {2883, 13630}, {3580, 18435}, {3818, 19136}, {5448, 10110}, {5449, 44870}, {5480, 14984}, {5504, 10272}, {5654, 34966}, {5663, 13567}, {5876, 41587}, {6053, 11225}, {6247, 32137}, {8263, 9971}, {9220, 9722}, {9955, 44662}, {10095, 12233}, {10113, 20772}, {10169, 18583}, {10539, 12370}, {10540, 12022}, {11381, 43817}, {11439, 26917}, {11441, 32358}, {11455, 26913}, {11472, 26958}, {11579, 11801}, {12359, 45959}, {14389, 40114}, {15032, 45967}, {15807, 32171}, {16252, 32046}, {16261, 23293}, {16534, 34986}, {18439, 26879}, {20300, 36201}, {20304, 23332}, {31804, 43575}, {32139, 39571}, {34224, 43821}

X(46030) = midpoint of X(i) and X(j) for these {i, j}: {3, 44276}, {4, 6644}, {5, 1596}, {381, 44275}, {546, 44233}, {3627, 44241}, {3818, 19136}, {3845, 44212}, {7530, 18531}, {8263, 21850}, {10113, 20772}, {14791, 18534}, {15687, 44273}, {44260, 44288}, {44263, 44274}
X(46030) = reflection of X(i) in X(j) for these (i, j): (12106, 44233), (44920, 3850)
X(46030) = complement of the circumperp conjugate of X(11799)
X(46030) = nine-point-circle-inverse of X(47336)
X(46030) = 1st-Droz-Farny-circle-inverse X(7464)
X(46030) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 3845, 427), (5, 3858, 7403), (5, 6823, 3628), (5, 43893, 549), (25, 5133, 1368), (381, 403, 5), (381, 10254, 5133), (381, 11818, 546), (546, 31830, 4), (546, 44235, 5), (1906, 11585, 3627), (3091, 10024, 5), (3545, 37347, 5), (3832, 16868, 5576), (3850, 13406, 5), (3851, 13160, 5), (3861, 10224, 1595), (5072, 14788, 5), (5133, 10254, 5), (5576, 16868, 5), (7576, 18403, 3627), (9818, 10201, 140), (13490, 23323, 4), (18494, 18568, 3853), (18570, 44270, 468), (19709, 37990, 5), (34664, 37971, 7502)

X(46031) = EULER LINE INTERCEPT OF X(113)X(16227)

X(46031) = 3*X(2)+X(31726), 7*X(5)-X(858), 3*X(5)-X(2072), 3*X(5)+X(11563), 5*X(5)+X(11799), 5*X(5)-X(37938), 7*X(5)+X(43893), 2*X(5)+X(44961), X(23)+11*X(5072), 3*X(140)-2*X(16976), X(140)+2*X(37984), X(186)+3*X(381), X(186)-3*X(44282), 3*X(381)+2*X(44900), X(382)+3*X(37941), 7*X(403)+X(858), 3*X(403)+X(2072), 3*X(403)-X(11563), 5*X(403)-X(11799), 5*X(403)+X(37938), 7*X(403)-X(43893)

X(46031) lies on these lines: {2, 3}, {113, 16227}, {523, 39510}, {1514, 40685}, {1539, 21663}, {3564, 34155}, {6000, 20304}, {7687, 30522}, {7951, 10149}, {10095, 32411}, {10272, 44665}, {10540, 14644}, {11704, 18439}, {11745, 20193}, {11793, 13446}, {12241, 15806}, {12290, 45622}, {13367, 43865}, {13754, 41671}, {14643, 40111}, {16328, 36412}, {18504, 34783}, {26917, 45957}, {32137, 32767}

X(46031) = midpoint of X(i) and X(j) for these {i, j}: {3, 44283}, {4, 15646}, {5, 403}, {381, 44282}, {468, 23323}, {546, 44234}, {858, 43893}, {1539, 21663}, {2070, 18572}, {2071, 44267}, {2072, 11563}, {3153, 37936}, {3627, 44246}, {3845, 44214}, {7574, 37947}, {7575, 18403}, {10151, 44452}, {11793, 13446}, {11799, 37938}, {15687, 44280}, {31726, 34152}, {37984, 44911}, {44263, 44281}
X(46031) = reflection of X(i) in X(j) for these (i, j): (140, 44911), (186, 44900), (10096, 37942), (10257, 3628), (13473, 3861), (18571, 44234), (23323, 3850), (32411, 10095), (37931, 22249), (37968, 44452), (44452, 15350), (44961, 403)
X(46031) = complement of X(34152)
X(46031) = inverse of X(3627) in: MacBeath inconic, nine-point circle
X(46031) = inverse of X(21844) in polar circle
X(46031) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 10024, 3628), (5, 11563, 2072), (5, 13406, 140), (5, 44235, 546), (235, 10224, 3853), (1312, 1313, 3627), (3628, 31829, 140), (3850, 31830, 546), (5066, 44233, 546), (10255, 44958, 3627), (18570, 34330, 140)

X(46032) = X(8)X(291)∩X(10)X(75)

X(46032) lies on these lines: {1, 3795}, {8, 291}, {10, 75}, {38, 29593}, {238, 3501}, {244, 17230}, {312, 20340}, {518, 21868}, {536, 24456}, {594, 4446}, {728, 39954}, {982, 3661}, {1107, 3097}, {1278, 4941}, {1376, 3507}, {1574, 14839}, {1698, 21264}, {1706, 3751}, {1740, 4649}, {2321, 17065}, {2345, 24478}, {3061, 3864}, {3123, 4740}, {3293, 22327}, {3617, 21219}, {3679, 24464}, {3701, 20440}, {3912, 17063}, {3967, 25125}, {4041, 4444}, {4051, 22116}, {4078, 30063}, {4110, 42027}, {4438, 27321}, {4443, 4665}, {4445, 7241}, {4704, 22174}, {4904, 20255}, {5687, 8298}, {6382, 19567}, {11364, 25440}, {12263, 27091}, {13178, 38499}, {16476, 16549}, {17143, 32020}, {17889, 20486}, {20456, 29617}, {20917, 24165}, {24575, 42696}, {27255, 40328}, {27299, 33159}, {29659, 35101}, {32921, 41240}

X(46032) = midpoint of X(8) and X(330)
X(46032) = reflection of X(i) in X(j) for these (i, j): (1, 16604), (6376, 10)
X(46032) = X(8)-Beth conjugate of-X(6376)
X(46032) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10009)}} and {{A, B, C, X(291), X(6376)}}
X(46032) = {X(10), X(12782)}-harmonic conjugate of X(984)

X(46033) = X(4)X(14941)∩X(5)X(264)

X(46033) lies on these lines: {3, 38297}, {4, 14941}, {5, 264}, {127, 14059}, {35709, 40800}, {38974, 40804}

X(46034) = X(4)X(6)∩X(20)X(1078)

X(46034) lies on these lines: {4,6}, {20,1078}, {30,7620}, {147,32827}, {193,38664}, {316,5921}, {376,9756}, {381,7710}, {458,35260}, {542,23334}, {543,22664}, {671,2794}, {3091,7790}, {3146,14712}, {3524,8719}, {3545,15428}, {3839,7694}, {3926,39266}, {4232,41254}, {5024,40927}, {5188,32834}, {5309,9748}, {5999,32815}, {7739,22682}, {8370,25406}, {9752,14651}, {10516,33190}, {10991,43618}, {11257,31400}, {11623,37689}, {12203,32971}, {20079,32002}, {22575,41023}, {22576,41022}, {29181,34505}, {32064,39908}, {34473,35927}

X(46034) = midpoint of X(3424) and X(3543)
X(46034) = reflection of X(i) in X(j) for these {i,j}: {376,9756}, {7710,381}

X(46035) = X(3)X(2133)∩X(4)X(1138)

X(46035) lies on the cubic K005 and these lines: {3, 2133}, {4, 1138}, {5, 20123}, {3336, 38934}, {3463, 38935}, {15774, 15791}

X(46035) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(2132)}} and {{A, B, C, X(4), X(2133)}}

X(46036) = X(3)X(2132)∩X(4)X(2133)

X(46036) lies on the cubic K005 and these lines: {3, 2132}, {4, 2133}, {5, 20123}, {3462, 3471}, {8918, 8919}, {15773, 15790}

X(46037) = ISOGONAL CONJUGATE OF X(38934)

X(46037) lies on the cubic K005 and these lines: {1, 3470}, {3, 5677}, {4, 1768}, {5, 34299}, {195, 3469}, {3461, 38935}, {7344, 8929}, {7345, 8930}

X(46037) = isogonal conjugate of X(38934)
X(46037) = X(484)-isoconjugate-of-X(3466)
X(46037) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(3464)}} and {{A, B, C, X(4), X(3465)}}

X(46038) = X(2)X(914)∩(3)X(2164)

X(46038) lies on the cubic K1242 and these lines: {2, 914}, {3, 2164}, {6, 1069}, {90, 1172}

X(46038) = X(1068)-isoconjugate of X(45127)
X(46038) = barycentric product X(i)*X(j) for these {i,j}: {90, 377}, {1448, 36626}, {20570, 37538}
X(46038) = barycentric quotient X(i)/X(j) for these {i,j}: {377, 20930}, {36082, 13395}, {37538, 46}, {43214, 21077}

X(46039) = X(4)X(804)∩X(99)X(511)

X(46039) lies on the cubic K289 and these lines: {4, 804}, {99, 511}, {1976, 41173}, {7417, 44420}

X(46039) = antigonal conjugate of the isotomic conjugate of X(35364)
X(46039) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(99)}} and {{A, B, C, X(114), X(511)}}
X(46039) = barycentric quotient X(230)/X(2782)
X(46039) = trilinear product X(1733)*X(2698)
X(46039) = trilinear quotient X(1733)/X(2782)

X(46040) = X(4)X(804)∩X(98)X(512)

X(46040) lies on Kiepert circumhyperbola and these lines: {2, 3569}, {4, 804}, {76, 2799}, {83, 16069}, {98, 512}, {115, 43665}, {262, 690}, {523, 43532}, {525, 1916}, {671, 8430}, {878, 12176}, {3399, 9479}, {6321, 35098}, {9420, 37991}, {23870, 43539}, {23871, 43538}, {39295, 40866}

X(46040) = reflection of X(43665) in X(115)
X(46040) = antigonal conjugate of X(43665)
X(46040) = antipode of X(43665) in Kiepert circumhyperbola
X(46040) = intersection, other than A, B, C, of circumconics Kiepert hyperbola and {{A, B, C, X(99), X(15412)}}
X(46040) = trilinear pole of the line {523, 44114}
X(46040) = barycentric product X(850)*X(2698)
X(46040) = barycentric quotient X(i)/X(j) for these (i, j): (523, 2782), (882, 16068)
X(46040) = trilinear product X(1577)*X(2698)
X(46040) = trilinear quotient X(1577)/X(2782)

X(46041) = X(1)X(1769)∩X(4)X(900)

X(46041) lies on Feuerbach circumhyperbola and these lines: {1, 1769}, {4, 900}, {7, 4453}, {8, 2804}, {9, 14418}, {11, 43728}, {80, 522}, {84, 2827}, {104, 953}, {108, 35011}, {521, 1320}, {1000, 6366}, {1389, 8674}, {2826, 3427}, {3577, 3887}, {3900, 24297}, {4926, 23959}, {7004, 23838}, {8058, 12641}, {8677, 38513}, {10090, 21189}, {10698, 42757}, {10738, 35097}, {13143, 35057}, {30198, 34256}

X(46041) = reflection of X(i) in X(j) for these (i, j): (10698, 42757), (43728, 11)
X(46041) = antigonal conjugate of X(43728)
X(46041) = antipode of X(43728) in Feuerbach circumhyperbola
X(46041) = intersection, other than A, B, C, of circumconics Feuerbach hyperbola and {{A, B, C, X(11), X(108)}}
X(46041) = barycentric product X(953)*X(4391)
X(46041) = barycentric quotient X(i)/X(j) for these (i, j): (513, 43043), (650, 952), (663, 2265), (953, 651)
X(46041) = trilinear product X(i)*X(j) for these {i, j}: {104, 37629}, {522, 953}
X(46041) = trilinear quotient X(i)/X(j) for these (i, j): (514, 43043), (522, 952), (650, 2265), (953, 109)

X(46042) = X(4)X(926)∩X(103)X(514)

X(46042) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(103)}} and {{A, B, C, X(116), X(514)}}
X(46042) = trilinear product X(1734)*X(2724)
X(46042) = trilinear quotient X(1734)/X(2808)

X(46043) = X(4)X(2457)∩X(519)X(1293)

X(46044) = X(4)X(14266)∩X(100)X(517)

Barycentrics a*((b^2+c^2)*a^10-(b+c)^3*a^9-(4*b^4+4*c^4-(7*b^2+6*b*c+7*c^2)*b*c)*a^8+4*(b^4-3*b^2*c^2+c^4)*(b+c)*a^7+2*(3*b^6+3*c^6-(10*b^4+10*c^4-3*(b^2+3*b*c+c^2)*b*c)*b*c)*a^6-2*(b^2-c^2)*(b-c)*(3*b^4-8*b^2*c^2+3*c^4)*a^5-2*(2*b^6+2*c^6-(5*b^4+5*c^4-2*(2*b^2+7*b*c+2*c^2)*b*c)*b*c)*(b-c)^2*a^4+4*(b^2-c^2)^2*(b+c)*(b^4+c^4-(4*b^2-7*b*c+4*c^2)*b*c)*a^3+(b^6+c^6-(4*b^4+4*c^4-(19*b^2-34*b*c+19*c^2)*b*c)*b*c)*(b^2-c^2)^2*a^2-(b^2-c^2)^4*(b-c)^2*b*c-(b^2-c^2)^3*(b-c)*(b^4+c^4-2*(2*b-c)*(b-2*c)*b*c)*a) : :

X(46044) lies on these lines: {4, 14266}, {100, 517}, {104, 14115}, {108, 18838}, {119, 34151}, {901, 12775}, {912, 15343}, {2818, 3259}, {2829, 3025}, {6941, 31847}, {6950, 34583}, {12248, 33647}, {12776, 14511}, {15313, 18341}

X(46044) = reflection of X(i) in X(j) for these (i, j): (104, 14115), (34151, 119)

X(46045) = X(4)X(523)∩X(30)X(110)

Barycentrics 2*a^16-4*(b^2+c^2)*a^14-3*((b^2-c^2)^2-4*b^2*c^2)*a^12+(b^2+c^2)*(7*b^4-18*b^2*c^2+7*c^4)*a^10+(10*b^8+10*c^8-3*(13*b^4-20*b^2*c^2+13*c^4)*b^2*c^2)*a^8-2*(b^4-c^4)*(b^2-c^2)*(11*b^4-16*b^2*c^2+11*c^4)*a^6+(9*b^8+9*c^8+2*(7*b^4-16*b^2*c^2+7*c^4)*b^2*c^2)*(b^2-c^2)^2*a^4+(b^4-c^4)*(b^2-c^2)^3*(3*b^4-14*b^2*c^2+3*c^4)*a^2-(b^2-c^2)^6*(2*b^4+3*b^2*c^2+2*c^4) : :

X(46045) = 4*X(125)-3*X(40630), 3*X(403)-2*X(11657), 3*X(3845)-2*X(21316), 4*X(3850)-3*X(21315), 4*X(12068)-3*X(38700), 2*X(12079)-3*X(14644), 5*X(14934)-2*X(21317), 3*X(15035)-4*X(31945), 2*X(22104)-3*X(36518), 3*X(31378)-2*X(38726), X(36193)-3*X(38789)

X(46045) lies on these lines: {4, 523}, {30, 110}, {74, 3154}, {107, 403}, {113, 7471}, {125, 32417}, {146, 17511}, {186, 1624}, {476, 36169}, {546, 34209}, {1539, 16168}, {1553, 38791}, {2777, 3258}, {3845, 21316}, {3850, 21315}, {3853, 21269}, {5663, 10689}, {6070, 7687}, {10295, 16319}, {10733, 14480}, {10745, 37985}, {12068, 38700}, {12079, 14644}, {14611, 17702}, {14731, 36172}, {14983, 16334}, {15035, 31945}, {16111, 31379}, {18560, 38936}, {18809, 43911}, {22104, 36518}, {31378, 38726}, {34584, 38610}, {36161, 43831}, {36193, 38789}, {44990, 44992}

X(46045) = midpoint of X(i) and X(j) for these {i, j}: {110, 44967}, {146, 17511}, {477, 10721}, {7728, 20957}, {10733, 14480}, {14731, 36172}
X(46045) = reflection of X(i) in X(j) for these (i, j): (74, 3154), (476, 36169), (1553, 38791), (6070, 7687), (7471, 113), (10295, 16319), (16111, 31379), (21269, 3853), (34150, 4), (34153, 33505), (34209, 546), (36164, 3258)
X(46045) = perspector of the circumconic {{A, B, C, X(16080), X(30528)}}

X(46046) = X(4)X(512)∩X(99)X(511)

X(46046) lies on these lines: {4, 512}, {98, 14113}, {99, 511}, {112, 1692}, {114, 12833}, {13860, 41330}, {31848, 37446}

X(46046) = reflection of X(i) in X(j) for these (i, j): (98, 14113), (12833, 114), (13137, 31850)

X(46047) = X(4)X(525)∩X(112)X(1503)

X(46048) = X(2)X(98)∩X(3081)X(8029)

Barycentrics (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)^3 : :

X(46048) lies on the cubic K656 and these lines: {2, 98}, {3081, 8029}, {8030, 23616}, {14583, 23968}

X(46048) = X(542)^3
X(46048) = X(542)-Ceva conjugate of X(23967)
X(46048) = crosspoint of X(542) and X(23967)
X(46048) = barycentric product X(542)*X(23967)
X(46048) = barycentric quotient X(23967)/X(5641)

X(46049) = X(2)X(690)∩X(524)X(10190)

X(46049) = 50X[2] - 3 X[34763], 7 X[2] - 3 X[45294], 3 X[1648] - X[8029], 3 X[1649] - X[8030], 2 X[8029] - 3 X[14423], 7 X[34763] - X[45294]

X(46049) lies on the cubic K656 and these lines: {2, 690}, {524, 10190}, {1641, 33906}, {1648, 8029}, {1649, 8030}, {5468, 37880}, {11123, 33921}, {14443, 14444}

X(46049) = midpoint of X(14443) and X(14444)
X(46049) = reflection of X(14423) in X(1648)
X(46049) = X(690)^3
X(46049) = X(i)-Ceva conjugate of X(j) for these (i,j): {690, 23992}, {33915, 14444}, {33919, 14443}, {34763, 41176}
X(46049) = X(34539)-isoconjugate of X(36085)
X(46049) = crosspoint of X(i) and X(j) for these (i,j): {690, 23992}, {1648, 1649}, {14443, 33919}, {14444, 33915}
X(46049) = crosssum of X(691) and X(34539)
X(46049) = crossdifference of every pair of points on line {249, 2502}
X(46049) = barycentric product X(i)*X(j) for these {i,j}: {115, 33915}, {523, 14444}, {524, 14443}, {690, 23992}, {1648, 1649}, {2482, 33919}, {8029, 8030}, {22260, 23106}, {34763, 41176}
X(46049) = barycentric quotient X(i)/X(j) for these {i,j}: {351, 34539}, {8030, 31614}, {14443, 671}, {14444, 99}, {21906, 34574}, {23992, 892}, {33915, 4590}, {39689, 45773}, {41176, 34760}

X(46050) = X(2)X(900)∩X(519)X(10196)

X(46050) = X[2] - 3 X[34764], 7 X[2] - 3 X[45295], 3 X[1647] - X[6545], 5 X[1647] + X[40472], 3 X[6544] - X[8028], 5 X[6545] + 3 X[40472], 7 X[34764] - X[45295]

X(46050) lies on the cubic K656 and these lines: {2, 900}, {519, 10196}, {764, 1647}, {1644, 33905}, {1960, 40172}, {3251, 4543}, {6546, 33920}

X(46050) = isotomic conjugate of the isogonal conjugate of X(14637)
X(46050) = X(i)-Ceva conjugate of X(j) for these (i,j): {900, 35092}, {6550, 14442}
X(46050) = X(i)-isoconjugate of X(j) for these (i,j): {679, 6551}, {765, 39414}, {4618, 9268}, {4638, 5376}
X(46050) = crosspoint of X(i) and X(j) for these (i,j): {900, 35092}, {1647, 6544}, {6550, 14442}
X(46050) = crosssum of X(4638) and X(9268)
X(46050) = crossdifference of every pair of points on line {1252, 2226}
X(46050) = barycentric product X(i)*X(j) for these {i,j}: {76, 14637}, {519, 14442}, {900, 35092}, {1086, 33922}, {1639, 14027}, {1647, 6544}, {3762, 42084}, {4370, 6550}, {4530, 39771}, {4542, 30725}, {6545, 8028}, {8661, 36791}
X(46050) = barycentric quotient X(i)/X(j) for these {i,j}: {1015, 39414}, {1017, 6551}, {2087, 4618}, {3251, 5376}, {4370, 6635}, {4542, 4582}, {8028, 6632}, {8661, 2226}, {14442, 903}, {14637, 6}, {14835, 1023}, {33922, 1016}, {35092, 4555}, {42084, 3257}
X(46050) = X(900)^3

X(46051) = X(2)X(812)∩X(4375)X(27855)

X(46051) lies on the cubic K656 and these lines: {2, 812}, {4375, 27855}, {6545, 8027}, {6654, 8632}, {8028, 8031}

X(46051) = X(812)^3
X(46051) = X(812)-Ceva conjugate of X(35119)
X(46051) = crosspoint of X(812) and X(35119)
X(46051) = barycentric product X(i)*X(j) for these {i,j}: {812, 35119}, {4375, 27918}, {6545, 6652}, {27846, 27855}
X(46051) = barycentric quotient X(i)/X(j) for these {i,j}: {6652, 6632}, {35119, 4562}

X(46052) = X(2)X(1637)∩X(2395)X(43673)

X(46052) lies on the cubic K656 and these lines: {2, 1637}, {2395, 43673}, {3081, 8030}, {8029, 23616}, {14966, 40173}

X(46052) = X(2799)^3
X(46052) = X(2799)-Ceva conjugate of X(35088)
X(46052) = crosspoint of X(2799) and X(35088)
X(46052) = barycentric product X(2799)*X(35088)
X(46052) = barycentric quotient X(i)/X(j) for these {i,j}: {868, 41173}, {35088, 2966}

X(46053) = X(2)X(14)∩X(16)X(115)

In the construction described at X(46054), if the first Fermat point F1 is replaced by the second Fermat point F2, then triangle LaLbLc is homothetic to the 2nd isodynamic-Dao triangle at X(46053). (Randy Hutson, November 30, 2021)

X(46053) lies on these lines: {2, 14}, {3, 23004}, {4, 33389}, {6, 22510}, {13, 41094}, {16, 115}, {17, 6783}, {18, 3104}, {61, 1506}, {62, 3767}, {182, 11646}, {230, 36760}, {542, 37832}, {622, 25235}, {624, 6782}, {671, 13084}, {2023, 3107}, {2782, 36766}, {5238, 16002}, {5321, 20253}, {5469, 6775}, {5470, 10653}, {5472, 25560}, {5475, 36759}, {5479, 19107}, {5613, 6777}, {6117, 16249}, {6321, 9736}, {6672, 35918}, {6773, 6778}, {6781, 30559}, {7835, 42675}, {9117, 32909}, {9873, 33420}, {10612, 22856}, {10646, 21157}, {11087, 40696}, {11480, 13102}, {11488, 16529}, {11542, 22893}, {11602, 33813}, {14137, 16961}, {16644, 22997}, {16808, 41023}, {16809, 22512}, {16962, 41746}, {16963, 43276}, {21843, 30560}, {22797, 42919}, {22846, 43620}, {22998, 33476}, {25164, 36967}, {31709, 36968}, {31710, 45880}, {32628, 36301}, {33416, 36772}

X(46053) = midpoint of X(14) and X(16241)
X(46053) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (14, 16967, 6114), (14, 22490, 37835), (16, 22891, 115), (115, 6774, 16), (5460, 6109, 14), (5469, 16242, 6775), (6114, 6670, 16967), (6773, 18582, 6778), (6777, 16966, 5613)

X(46054) = X(2)X(13)∩X(15)X(115)

From a post by Tran Quang Hung (ADGEOM #5186, February 28, 2019): Let ABC be a triangle with the first Fermat point F1. Let La, Lb, Lc be centers of Lester circles of triangles F1BC, F1CA, F1AB respectively. Then LaLbLc is an equilateral triangle. X(46054) is the homothetic center of LaLbLc and the 1st isodynamic-Dao triangle. (Randy Hutson, November 30, 2021)

X(46054) lies on these lines: {2, 13}, {3, 23005}, {4, 33388}, {6, 22511}, {14, 41098}, {15, 115}, {17, 3105}, {18, 6782}, {61, 3767}, {62, 1506}, {182, 11646}, {230, 36759}, {542, 37835}, {621, 25236}, {623, 6783}, {671, 13083}, {2023, 3106}, {5237, 16001}, {5238, 36772}, {5318, 20252}, {5469, 10654}, {5470, 6772}, {5471, 25559}, {5475, 36760}, {5478, 19106}, {5617, 6778}, {6116, 16250}, {6321, 9735}, {6671, 35917}, {6770, 6777}, {6781, 30560}, {7835, 42674}, {9115, 32907}, {9873, 33421}, {10611, 22900}, {10645, 21156}, {11082, 40695}, {11481, 13103}, {11489, 16530}, {11543, 22847}, {11603, 33813}, {14136, 16960}, {16645, 22998}, {16808, 22513}, {16809, 41022}, {16962, 43277}, {16963, 41745}, {21843, 30559}, {22796, 42918}, {22891, 43620}, {22997, 33477}, {25154, 36968}, {31709, 45879}, {31710, 36967}, {32627, 36300}, {36765, 42914}, {36782, 42092}

X(46054) = midpoint of X(13) and X(16242)
X(46054) = {X(i), X(j)}-harmonic conjugate of X(k) for these (i, j, k): (13, 16966, 6115), (13, 22489, 37832), (15, 22846, 115), (115, 6771, 15), (5459, 6108, 13), (5470, 16241, 6772), (6115, 6669, 16966), (6770, 18581, 6777), (6778, 16967, 5617), (11646, 38224, 46053)

X(46055) = X(14)X(36248)∩X(15)X(302)

X(46055) = intersection, other than A, B, C, of circumconics {{A, B, C, X(14), X(302)}} and {{A, B, C, X(15), X(618)}}
X(46055) = barycentric quotient X(396)/X(34509)

X(46056) = X(13)X(36249)∩X(16)X(303)

X(46056) = intersection, other than A, B, C, of circumconics {{A, B, C, X(13), X(303)}} and {{A, B, C, X(16), X(619)}}
X(46056) = barycentric quotient X(395)/X(34508)

X(46057) = X(4)X(51)∩X(520)X(6587)

X(46057) lies on these lines: {4, 51}, {6, 34147}, {520, 6587}, {1192, 11589}, {6760, 11426}, {9786, 34109}, {11425, 12096}

X(46057) = crossdifference of every pair of points on line {X(1498), X(32320)}
X(46057) = perspector of the circumconic {{A, B, C, X(3346), X(15352)}}
X(46057) = inverse of X(14361) in polar circle

X(46058) = X(13)X(2992)∩X(14)X(14372)

X(46058) lies on the cubic K261a and these lines: {13, 2992}, {14, 14372}, {15, 5682}, {62, 8919}, {619, 39377}, {3438, 6104}, {6116, 16459}

X(46059) = X(13)X(14373)∩X(14)X(2993)

X(46059) lies on the cubic K261b and these lines: {13, 14373}, {14, 2993}, {16, 5681}, {61, 8918}, {618, 39378}, {3439, 6105}, {6117, 16460}

X(46060) = X(14)X(19776)∩X(16)X(3440)

X(46060) lies on the cubic K261b and these lines: {14, 19776}, {16, 3440}, {18, 32461}, {618, 6110}, {3170, 36209}

X(46061) = X(13)X(19777)∩X(15)X(3441)

X(46061) lies on the cubic K261a and these lines: {13, 19777}, {15, 3441}, {17, 32460}, {619, 6111}, {3171, 36208}

X(46062) = X(30)X(511)∩X(9409)X(11587)

X(46062) = isogonal conjugate of the anticomplement of X(35592)
X(46062) = complementary conjugate of X(35592)
X(46062) = circumtangential-isogonal conjugate of the anticomplement of X(35592)
X(46062) = crossdifference of every pair of points on line {X(6), X(39019)}
X(46062) = crosspoint of X(933) and X(18401)
X(46062) = X(4)-Ceva conjugate of-X(35592)
X(46062) = X(1)-complementary conjugate of-X(35592)

X(46063) = X(30)X(511)∩X(1301)X(32713)

X(46063) = crossdifference of every pair of points on line {X(6), X(39020)}
X(46063) = crosspoint of X(1301) and X(5897)

X(46064) = X(30)X(3484)∩X(54)X(3575)

X(46064) lies on these lines: {30, 3484}, {54, 3575}, {97, 37636}, {275, 1971}, {323, 401}, {858, 15958}, {933, 1503}, {1540, 18400}, {1614, 36842}, {2167, 17043}, {4993, 33629}, {11064, 18315}, {25044, 34224}, {25739, 40631}

X(46064) = reflection of X(1540) in X(18402)
X(46064) = crossdifference of every pair of points on line {X(51), X(34983)}
X(46064) = X(340)-Ceva conjugate of-X(40631)
X(46064) = X(1953)-isoconjugate-of-X(18401)
X(46064) = X(54)-reciprocal conjugate of-X(18401)
X(46064) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(1540)}} and {{A, B, C, X(275), X(525)}}
X(46064) = barycentric product X(95)*X(18400)
X(46064) = barycentric quotient X(54)/X(18401)
X(46064) = trilinear product X(2167)*X(18400)
X(46064) = trilinear quotient X(2167)/X(18401)

X(46065) = X(2)X(1032)∩X(393)X(459)

X(46065) lies on these lines: {2, 1032}, {4, 28785}, {64, 3089}, {253, 37643}, {393, 459}, {525, 3239}, {1073, 13567}, {1301, 1503}, {2184, 18634}, {6247, 41085}, {6393, 44326}, {6696, 39268}, {12241, 14379}, {26937, 31942}

X(46065) = X(610)-isoconjugate-of-X(5897)
X(46065) = X(64)-reciprocal conjugate of-X(5897)
X(46065) = barycentric product X(253)*X(15311)
X(46065) = barycentric quotient X(64)/X(5897)
X(46065) = trilinear product X(2184)*X(15311)
X(46065) = trilinear quotient X(2184)/X(5897)

X(46066) = EULER LINE INTERCEPT OF X(1511)X(18800)

X(46066) lies on these lines: {2, 3}, {1511, 18800}, {2793, 9126}, {6055, 14650}, {6699, 19662}, {7622, 18122}, {9775, 14653}, {10264, 11161}

X(46067) = EULER LINE INTERCEPT OF X(113)X(18800)

X(46067) lies on these lines: {2, 3}, {113, 18800}, {115, 45331}, {265, 11161}, {2793, 18309}, {5655, 8593}, {6054, 10748}, {7615, 40879}, {7687, 19662}, {10113, 40915}

X(46067) = reflection of X(14694) in X(5)
X(46067) = {X(31693), X(31694)}-harmonic conjugate of X(868)

X(46068) = EULER LINE INTERCEPT OF X(10272)X(18800)

X(46068) lies on these lines: {2, 3}, {10272, 18800}, {13162, 22110}, {19662, 20304}

X(46069) = EULER LINE INTERCEPT OF X(16163)X(18800)

Barycentrics 14*a^10-25*(b^2+c^2)*a^8-(7*b^4-80*b^2*c^2+7*c^4)*a^6+(b^2+c^2)*(29*b^4-77*b^2*c^2+29*c^4)*a^4-(7*b^8+7*c^8+2*b^2*c^2*(5*b^4-21*b^2*c^2+5*c^4))*a^2+(b^4-c^4)*(b^2-c^2)*(-4*b^4+7*b^2*c^2-4*c^4) : :

X(46069) lies on these lines: {2, 3}, {74, 11161}, {2793, 14977}, {11177, 14654}, {16111, 40915}, {16163, 18800}, {19662, 37853}

X(46069) = reflection of X(4) in X(14694)
X(46069) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 8598, 4235), (35931, 35932, 4226)

X(46070) = EULER LINE INTERCEPT OF X(16165)X(18800)

X(46071) = X(13)-CEVA CONJUGATE OF X(39153)

X(46071) lies on the cubic K261a and these lines: {13, 37773}, {14, 79}, {15, 3464}, {16, 18593}, {36, 6104}, {62, 2306}, {2153, 5620}, {11076, 14158}, {36211, 39151}

X(46071) = X(13)-Ceva conjugate of X(39153)
X(46071) = X(14)-isoconjugate of X(7343)
X(46071) = barycentric product X(i)*X(j) for these {i,j}: {13, 40612}, {299, 11076}, {17484, 39153}
X(46071) = barycentric quotient X(i)/X(j) for these {i,j}: {2152, 7343}, {3457, 11075}, {11076, 14}, {26744, 44688}, {39153, 21739}, {40612, 298}

X(46072) = ISOGONAL CONJUGATE OF X(5616)

X(46072) lies on the cubics K561a and K439 and on these lines: {13, 5612}, {14, 1117}, {15, 1263}, {62, 3471}, {231, 1989}, {300, 11133}, {532, 11118}, {619, 11119}, {1291, 39424}, {8737, 10633}, {10677, 11139}, {11600, 34308}

X(46072) = isogonal conjugate of X(5616)
X(46072) = X(16)-cross conjugate of X(13)
X(46072) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5616}, {15, 1749}, {2151, 37779}, {2154, 40604}, {19306, 33529}
X(46072) = cevapoint of X(6138) and X(30452)
X(46072) = barycentric product X(i)*X(j) for these {i,j}: {13, 13582}, {299, 11071}, {300, 14579}, {471, 15392}, {3471, 36308}
X(46072) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5616}, {13, 37779}, {16, 40604}, {1263, 33529}, {1291, 17402}, {2153, 1749}, {3457, 11063}, {3471, 41887}, {6138, 8562}, {8737, 37943}, {8740, 2914}, {11071, 14}, {11081, 5612}, {13582, 298}, {14579, 15}, {15392, 40710}, {20578, 45147}, {23871, 45790}, {30452, 10413}, {36299, 10272}, {43704, 44718}

X(46073) = ISOGONAL CONJUGATE OF X(39152)

X(46073) lies on the cubics K058 and K261a and on these lines: {1, 62}, {10, 36931}, {13, 226}, {14, 80}, {15, 3465}, {16, 559}, {35, 6104}, {37, 101}, {55, 42616}, {65, 42680}, {203, 2801}, {519, 5240}, {1126, 11073}, {1251, 3383}, {3678, 7005}, {3961, 7088}, {3969, 40714}, {5995, 15168}, {7150, 10638}, {36737, 39150}, {37772, 39787}

X(46073) = isogonal conjugate of X(39152)
X(46073) = X(80)-Ceva conjugate of X(39151)
X(46073) = X(5357)-cross conjugate of X(42677)
X(46073) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39152}, {14, 36}, {15, 79}, {298, 6186}, {320, 3458}, {2151, 30690}, {2154, 3218}, {3179, 42680}, {4707, 5994}, {5240, 33654}, {7051, 36932}, {8738, 22128}, {17923, 36297}, {20565, 34394}, {21828, 23896}, {33653, 37773}, {39150, 41225}
X(46073) = cevapoint of X(35) and X(5357)
X(46073) = trilinear product X(i)*X(j) for these {i,j}: {13, 35}, {16, 80}, {299, 6187}, {319, 3457}, {559, 19551}, {2152, 18359}, {2153, 3219}, {5357, 14358}, {5995, 7265}, {20566, 34395}
X(46073) = barycentric product X(i)*X(j) for these {i,j}: {13, 3219}, {16, 18359}, {299, 2161}, {300, 2174}, {319, 2153}, {471, 1807}, {559, 7026}, {2003, 44690}, {2006, 44689}, {2152, 20566}, {3457, 33939}, {6198, 40709}, {33655, 40714}, {39153, 41226}
X(46073) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39152}, {13, 30690}, {16, 3218}, {299, 20924}, {1807, 40710}, {2152, 36}, {2153, 79}, {2161, 14}, {2174, 15}, {3219, 298}, {3457, 2160}, {5995, 13486}, {6187, 2154}, {6198, 470}, {7126, 36932}, {8740, 1870}, {10638, 5240}, {11081, 39153}, {14975, 8739}, {18359, 301}, {21824, 30465}, {33655, 554}, {34395, 7113}, {35194, 33529}, {36296, 7100}, {36910, 44691}, {42624, 39150}, {44689, 32851}
X(46073) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11789, 202}, {1, 19551, 39151}, {37, 24929, 46077}

X(46074) = X(13)-CEVA CONJUGATE OF X(14)

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)*(2*(5*a^8 - 14*a^6*b^2 + 12*a^4*b^4 - 2*a^2*b^6 - b^8 - 14*a^6*c^2 + 17*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + 4*b^6*c^2 + 12*a^4*c^4 - 7*a^2*b^2*c^4 - 6*b^4*c^4 - 2*a^2*c^6 + 4*b^2*c^6 - c^8) + 4*Sqrt[3]*(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(46074) lies on the cubic K261a and these lines: {13, 14993}, {14, 16}, {15, 1138}, {17, 32460}, {62, 8015}, {186, 8738}, {231, 1989}, {476, 2381}, {523, 16529}, {532, 11092}, {533, 23896}, {3129, 14583}, {3411, 11556}, {5612, 18285}, {5627, 11601}, {5899, 11141}, {6116, 37943}, {6672, 11120}, {8918, 42157}, {11300, 43086}, {16962, 18776}, {21311, 37949}, {21360, 40710}, {22827, 36758}, {36209, 37496}

X(46074) = midpoint of X(15743) and X(36210)
X(46074) = reflection of X(i) in X(j) for these {i,j}: {14, 36210}, {36210, 11549}
X(46074) = X(13)-Ceva conjugate of X(14)
X(46074) = barycentric product X(8173)*X(8836)
X(46074) = barycentric quotient X(11088)/X(8456)
X(46074) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 45779, 36968}, {16, 11085, 14}, {395, 11582, 14}, {10218, 36970, 14}, {11549, 15743, 14}, {15442, 40579, 14}

X(46075) = X(13)X(79)∩X(14)X(37772)

X(46075) lies on the cubic K261b and these lines: {13, 79}, {14, 37772}, {15, 18593}, {16, 3464}, {36, 6105}, {61, 3336}, {2154, 5620}, {11076, 14158}, {36210, 39150}

X(46075) = X(14)-Ceva conjugate of X(39152)
X(46075) = X(13)-isoconjugate of X(7343)
X(46075) = barycentric product X(i)*X(j) for these {i,j}: {14, 40612}, {298, 11076}, {17484, 39152}
X(46075) = barycentric quotient X(i)/X(j) for these {i,j}: {2151, 7343}, {3458, 11075}, {11076, 13}, {26744, 44689}, {39152, 21739}, {40612, 299}

X(46076) = ISOGONAL CONJUGATE OF X(5612)

X(46076) lies on the cubics K261b and K439 and on these lines: {13, 1117}, {14, 5616}, {16, 1263}, {61, 3471}, {231, 1989}, {301, 11132}, {533, 11117}, {618, 11120}, {1291, 39425}, {8738, 10632}, {10678, 11138}, {11601, 34308}

X(46076) = isogonal conjugate of X(5612)
X(46076) = X(15)-cross conjugate of X(14)
X(46076) = X(i)-isoconjugate of X(j) for these (i,j): {1, 5612}, {16, 1749}, {2152, 37779}, {2153, 40604}, {19306, 33530}
X(46076) = cevapoint of X(6137) and X(30453)
X(46076) = barycentric product X(i)*X(j) for these {i,j}: {14, 13582}, {298, 11071}, {301, 14579}, {470, 15392}, {3471, 36311}
X(46076) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 5612}, {14, 37779}, {15, 40604}, {1263, 33530}, {1291, 17403}, {2154, 1749}, {3458, 11063}, {3471, 41888}, {6137, 8562}, {8738, 37943}, {8739, 2914}, {11071, 13}, {11086, 5616}, {13582, 299}, {14579, 16}, {15392, 40709}, {20579, 45147}, {23870, 45790}, {30453, 10413}, {36298, 10272}, {43704, 44719}

X(46077) = X(13)-ISOCONJUGATE OF X(36)

X(46077) lies on the cubics K058 and K261b and on these lines: {1, 61}, {10, 36930}, {13, 80}, {14, 226}, {15, 1082}, {16, 3465}, {35, 6105}, {37, 101}, {65, 42677}, {202, 2801}, {519, 5239}, {1126, 11072}, {3295, 42624}, {3376, 33653}, {3678, 7006}, {3961, 7089}, {3969, 40713}, {5994, 15168}, {36738, 39151}, {37773, 39788}

X(46077) = isogonal conjugate of X(39153)
X(46077) = X(80)-Ceva conjugate of X(39150)
X(46077) = X(5353)-cross conjugate of X(42680)
X(46077) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39153}, {13, 36}, {16, 79}, {299, 6186}, {320, 3457}, {1081, 7127}, {1251, 37772}, {2152, 30690}, {2153, 3218}, {2306, 5239}, {3179, 39151}, {4707, 5995}, {8737, 22128}, {17923, 36296}, {19373, 36933}, {20565, 34395}, {21828, 23895}, {41225, 42677}
X(46077) = cevapoint of X(35) and X(5353)
X(46077) = trilinear product X(i)*X(j) for these {i,j}: {14, 35}, {15, 80}, {298, 6187}, {319, 3458}, {1082, 7126}, {2151, 18359}, {2154, 3219}, {2307, 7043}, {5353, 14359}, {5994, 7265}, {20566, 34394}
X(46077) = barycentric product X(i)*X(j) for these {i,j}: {14, 3219}, {15, 18359}, {298, 2161}, {301, 2174}, {319, 2154}, {470, 1807}, {1082, 7043}, {2003, 44691}, {2006, 44688}, {2151, 20566}, {3458, 33939}, {6198, 40710}, {7052, 40713}, {39152, 41226}
X(46077) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39153}, {14, 30690}, {15, 3218}, {298, 20924}, {1250, 5239}, {1807, 40709}, {2151, 36}, {2154, 79}, {2161, 13}, {2174, 16}, {2307, 37772}, {3219, 299}, {3458, 2160}, {5994, 13486}, {6187, 2153}, {6198, 471}, {7052, 1081}, {8739, 1870}, {11086, 39152}, {14975, 8740}, {18359, 300}, {19551, 36933}, {21824, 30468}, {34394, 7113}, {35194, 33530}, {36297, 7100}, {36910, 44690}, {42624, 42677}, {44688, 32851}
X(46077) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7126, 39150}, {1, 7150, 7052}, {1, 11752, 203}, {37, 24929, 46073}, {7052, 7126, 7150}, {7052, 7150, 39150}

X(46078) = X(14)-CEVA CONJUGATE OF X(13)

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)*(2*(5*a^8 - 14*a^6*b^2 + 12*a^4*b^4 - 2*a^2*b^6 - b^8 - 14*a^6*c^2 + 17*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + 4*b^6*c^2 + 12*a^4*c^4 - 7*a^2*b^2*c^4 - 6*b^4*c^4 - 2*a^2*c^6 + 4*b^2*c^6 - c^8) - 4*Sqrt[3]*(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(46078) lies on the cubic K261b and these lines: {13, 15}, {14, 14993}, {16, 1138}, {18, 32461}, {61, 8014}, {186, 8737}, {231, 1989}, {476, 2380}, {523, 16530}, {532, 23895}, {533, 11078}, {3130, 14583}, {3412, 11555}, {5616, 18285}, {5627, 11600}, {5899, 11142}, {6117, 37943}, {6671, 11119}, {8919, 42158}, {11299, 43085}, {16963, 18777}, {21310, 37949}, {21359, 40709}, {22826, 36757}, {36208, 37496}

X(46078) = midpoint of X(11586) and X(36211)
X(46078) = reflection of X(i) in X(j) for these {i,j}: {13, 36211}, {36211, 11537}
X(46078) = X(14)-Ceva conjugate of X(13)
X(46078) = barycentric product X(8172)*X(8838)
X(46078) = barycentric quotient X(11083)/X(8446)
X(46078) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 45778, 36967}, {15, 11080, 13}, {396, 11581, 13}, {10217, 36969, 13}, {11537, 11586, 13}, {15441, 40578, 13}

X(46079) = X(16)X(3815)∩X(381)X(396)

X(46079) lies on these lines: {16, 3815}, {182, 46080}, {381, 396}, {597, 11543}, {624, 3849}, {3054, 36759}, {5306, 46054}, {5478, 42138}, {5480, 11542}, {6771, 18907}, {7684, 42117}, {9996, 42627}, {10613, 43457}, {11480, 44465}, {22846, 22856}, {22861, 23302}

X(46080) = X(15)X(3815)∩X(381)X(395)

X(46080) lies on these lines: {15, 3815}, {182, 46079}, {381, 395}, {597, 11542}, {623, 3849}, {3054, 36760}, {5306, 46053}, {5479, 42135}, {5480, 11543}, {6774, 18907}, {7685, 42118}, {9996, 42628}, {10614, 43457}, {11481, 44461}, {22891, 22900}, {22907, 23303}

X(46081) = ISOGONAL CONJUGATE OF X(15034)

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

X(46081) = 3*X(125)-X(41522), X(477)-5*X(12079), 3*X(1138)-7*X(3154), 9*X(6070)-X(10990)

X(46081) lies on these lines: {5, 9214}, {30, 6070}, {125, 41522}, {140, 15454}, {477, 12079}, {1138, 3154}, {1990, 12003}, {3471, 35018}, {3850, 14254}, {17986, 32230}

X(46081) = isogonal conjugate of X(15034)
X(46081) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(9139)}} and {{A, B, C, X(4), X(30)}}

X(46082) = ISOGONAL CONJUGATE OF X(39229)

X(46082) lies on Kiepert circumhyperbola, cubics K043, K599, K811 and these lines: {5, 542}, {671, 39229}, {7608, 39230}

X(46083) = ISOGONAL CONJUGATE OF X(39230)

X(46083) lies on Kiepert circumhyperbola, cubics K043, K599, K811 and these lines: {5, 542}, {671, 39230}, {7608, 39229}

X(46084) = X(3)X(143)∩X(113)X(3850)

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

X(46084) = X(3)+5*X(1173), X(3)-5*X(15047), 9*X(3)-5*X(33542), 9*X(1173)+X(33542), 5*X(2889)-17*X(3533), 4*X(3850)+5*X(34564), 4*X(10095)-X(11817), 9*X(15047)-X(33542)

X(46084) lies on these lines: {2, 34483}, {3, 143}, {5, 11225}, {110, 34567}, {113, 3850}, {141, 5097}, {206, 15580}, {547, 1209}, {578, 33556}, {960, 33179}, {1147, 15026}, {1199, 5609}, {1493, 5943}, {1511, 5462}, {2883, 3845}, {2889, 3533}, {3519, 7605}, {3628, 34565}, {3853, 44866}, {4550, 6102}, {5041, 11672}, {5067, 45794}, {5640, 9704}, {5876, 33537}, {6101, 15004}, {6644, 15748}, {8718, 14483}, {10095, 11817}, {10627, 15018}, {10960, 35771}, {10962, 35770}, {11597, 13365}, {12041, 35478}, {12834, 14627}, {13596, 13630}, {14449, 44107}, {16239, 41586}, {18583, 34826}, {22949, 33541}, {23409, 24981}, {32068, 33332}, {34199, 43817}

X(46084) = midpoint of X(1173) and X(15047)
X(46084) = complement of X(34483)
X(46084) = complementary conjugate of the complement of X(34484)
X(46084) = inverse of X(34567) in Stammler hyperbola
X(46084) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1199, 18874, 5609), (10095, 34545, 36153), (12834, 14627, 32205)

X(46085) = X(3)X(125)∩X(68)X(110)

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

X(46085) = 3*X(154)-X(12419), X(155)-3*X(14643), X(265)-3*X(14852), X(2931)+3*X(14852), 2*X(5448)-3*X(36518), 2*X(12038)-3*X(38793), X(12118)-3*X(15035), X(12302)-3*X(15061), X(12310)+3*X(38724), X(12319)-5*X(15081), X(12429)+3*X(32609), X(15133)-3*X(38724), 4*X(20191)-3*X(38727), 3*X(23515)+X(32263), 3*X(23515)-2*X(33547), X(32263)+2*X(33547), 5*X(38795)-2*X(41597)

X(46085) lies on the bicevian conic of X(2) and X(110) and on these lines: {2, 5504}, {3, 125}, {5, 11746}, {6, 12900}, {26, 41674}, {30, 11598}, {52, 45177}, {68, 110}, {74, 44440}, {113, 403}, {140, 22966}, {141, 14984}, {154, 12419}, {155, 14643}, {184, 10111}, {206, 542}, {343, 12358}, {468, 20771}, {511, 15116}, {539, 5642}, {541, 11744}, {567, 43839}, {568, 5448}, {960, 12261}, {974, 15760}, {1112, 41587}, {1147, 5972}, {1209, 10170}, {1493, 9820}, {1511, 44452}, {2072, 45780}, {2777, 7689}, {2883, 5663}, {3549, 13198}, {3564, 6593}, {3581, 13202}, {4550, 7687}, {5181, 34382}, {5654, 37644}, {6723, 15115}, {7728, 12163}, {8542, 12596}, {9826, 13567}, {10018, 30714}, {10020, 32391}, {10055, 10091}, {10071, 10088}, {10113, 34826}, {10264, 15151}, {10539, 32539}, {10639, 10663}, {10640, 10664}, {10733, 23293}, {10960, 12891}, {10962, 12892}, {11585, 41673}, {11672, 39021}, {12022, 12038}, {12041, 44158}, {12118, 15035}, {12140, 18474}, {12295, 18560}, {12319, 15081}, {12429, 32609}, {13383, 15647}, {13561, 23328}, {14915, 41603}, {15051, 26913}, {15088, 16254}, {15114, 23315}, {16003, 17854}, {19061, 19111}, {19062, 19110}, {20299, 34350}, {32227, 37453}, {37197, 37489}, {38795, 41597}

X(46085) = midpoint of X(i) and X(j) for these {i, j}: {68, 110}, {265, 2931}, {7728, 12163}, {9927, 12893}, {12121, 12293}, {12310, 15133}
X(46085) = reflection of X(i) in X(j) for these (i, j): (26, 41674), (125, 5449), (1147, 5972), (12041, 44158), (12901, 6699), (15115, 6723), (15647, 13383), (19479, 7687), (23306, 20304), (23315, 15114)
X(46085) = complement of X(5504)
X(46085) = complementary conjugate of X(10257)
X(46085) = center of the circumconic {{A, B, C, X(68), X(110)}}
X(46085) = inverse of X(38534) in Stammler hyperbola
X(46085) = antipode of X(1147) in bicevian conic of X(2) and X(110)
X(46085) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(1986)}} and {{A, B, C, X(125), X(16221)}}
X(46085) = barycentric product X(2072)*X(3580)
X(46085) = barycentric quotient X(2072)/X(2986)
X(46085) = trilinear product X(1725)*X(2072)
X(46085) = trilinear quotient X(i)/X(j) for these (i, j): (1725, 38534), (2072, 36053)
X(46085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (113, 12828, 11557), (265, 37638, 6699), (403, 12825, 113), (2931, 14852, 265), (12310, 38724, 15133)

X(46086) = X(2)X(38861)∩X(468)X(14052)

X(46086) lies on these lines: {2,38861}, {468,14052}, {1656,34810}, {2072,36519}, {3447,16760}

X(46086) = complement of X(46087)
X(46086) = complement of the isogonal conjugate of X(1112)
X(46086) = complementary conjugate of X(13416)
X(46086) = X(i)-complementary conjugate of X(j) for these (i,j): (1,13416), (1112,10)

X(46087) = ISOGONAL CONJUGATE OF X(1112)

X(46087) lies on these lines: {2,38861}, {3,39193}, {50,230}, {186,30716}, {476,3447}, {523,14060}, {631,14385}, {2165,36163}, {3564,5622}, {4558,34978}, {6036,40118}, {34178,38701}

X(46087) = reflection of X(30717) in the Euler line
X(46087) = isogonal conjugate of X(1112)
X(46087) = anticomplement of X(46086)
X(46087) = anticomplement of the complementary conjugate of X(13416)
X(46087) = X(i)-isoconjugate of X(j) for these (i,j): (19,34990), (158,23217), (2333,16734)
X(46087) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {3,34990}, {6,1112}, {577,23217}, {1444,16734}
X(46087) = cevapoint of X(i)and X(j) for these {i,j}: {3,125}, {647,34982}
X(46087) = barycentric quotient X(i)/X(j) for these {i,j}: {3,34990}, {577,23217}, {1444,16734}
X(46087) = trilinear quotient X(i)/X(j) for these (i,j): (63,34990), (255,23217)

X(46088) = X(50)X(647)∩X(97)X(2525)

X(46088) lies on these lines: {50, 647}, {97, 2525}, {571, 16040}, {577, 17434}, {933, 23964}, {1637, 15422}, {5063, 14346}, {11077, 32663}, {14586, 32640}, {15412, 44427}, {30451, 39201}

X(46088) = isogonal conjugate of the polar conjugate of X(23286)
X(46088) = crossdifference of every pair of points on line {X(5), X(324)}
X(46088) = crosspoint of X(i) and X(j) for these (i, j): {54, 16813}, {97, 15958}
X(46088) = crosssum of X(i) and X(j) for these (i, j): {5, 17434}, {53, 23290}, {324, 18314}, {525, 40684}
X(46088) = X(933)-Ceva conjugate of-X(184)
X(46088) = X(i)-Dao conjugate of X(j) for these (i, j): (125, 324), (130, 36412), (525, 15415), (1147, 14570)
X(46088) = X(i)-isoconjugate-of-X(j) for these {i, j}: {5, 823}, {53, 811}, {92, 35360}, {107, 14213}
X(46088) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (54, 6528), (97, 6331), (184, 35360), (520, 311)
X(46088) = perspector of the circumconic {{A, B, C, X(54), X(14533)}}
X(46088) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(44886)}} and {{A, B, C, X(50), X(577)}}
X(46088) = barycentric product X(i)*X(j) for these {i, j}: {3, 23286}, {32, 15414}, {54, 520}, {95, 39201}, {97, 647}, {125, 15958}
X(46088) = barycentric quotient X(i)/X(j) for these (i, j): (54, 6528), (97, 6331), (184, 35360), (520, 311), (577, 14570), (647, 324)
X(46088) = trilinear product X(i)*X(j) for these {i, j}: {48, 23286}, {54, 822}, {97, 810}, {255, 2623}, {520, 2148}, {560, 15414}
X(46088) = trilinear quotient X(i)/X(j) for these (i, j): (48, 35360), (54, 823), (97, 811), (255, 14570), (520, 14213), (577, 2617)
X(46088) = {X(2623), X(23286)}-harmonic conjugate of X(647)

X(46089) = X(54)X(186)∩X(125)X(252)

X(46089) lies on these lines: {3, 15958}, {50, 14533}, {54, 186}, {97, 1216}, {125, 252}, {184, 20574}, {185, 1157}, {933, 1614}, {1141, 21659}, {1594, 46064}, {2169, 22342}, {3459, 24862}, {3484, 3520}, {6146, 40631}, {14585, 14586}, {19210, 22115}

X(46089) = X(6)-Dao conjugate of X(45793)
X(46089) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 1087}, {19, 45793}, {53, 14213}, {92, 36412}
X(46089) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 45793), (48, 1087), (54, 324), (97, 311)
X(46089) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(50)}} and {{A, B, C, X(4), X(389)}}
X(46089) = barycentric product X(i)*X(j) for these {i, j}: {54, 97}, {95, 14533}, {275, 19210}, {2167, 2169}
X(46089) = barycentric quotient X(i)/X(j) for these (i, j): (3, 45793), (48, 1087), (54, 324), (97, 311), (184, 36412), (217, 23607)
X(46089) = trilinear product X(i)*X(j) for these {i, j}: {54, 2169}, {97, 2148}, {2167, 14533}, {2190, 19210}
X(46089) = trilinear quotient X(i)/X(j) for these (i, j): (3, 1087), (48, 36412), (63, 45793), (97, 14213), (603, 41279), (2148, 53)

X(46090) = X(54)X(74)∩X(417)X(15958)

X(46090) lies on these lines: {54, 74}, {417, 15958}, {3043, 34980}, {8884, 10152}, {11815, 13489}, {14533, 14586}, {15781, 44715}, {19189, 32715}, {25044, 39174}, {40353, 43753}

X(46090) = X(1147)-Dao conjugate of X(1568)
X(46090) = X(i)-isoconjugate-of-X(j) for these {i, j}: {5, 1784}, {53, 14206}, {158, 1568}, {324, 2173}
X(46090) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (74, 324), (97, 3260), (577, 1568)
X(46090) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(3520)}} and {{A, B, C, X(4), X(185)}}
X(46090) = barycentric product X(i)*X(j) for these {i, j}: {54, 14919}, {74, 97}, {95, 18877}, {1494, 14533}, {2167, 35200}, {2169, 2349}
X(46090) = barycentric quotient X(i)/X(j) for these (i, j): (74, 324), (97, 3260), (577, 1568), (2148, 1784), (2169, 14206)
X(46090) = trilinear product X(i)*X(j) for these {i, j}: {54, 35200}, {74, 2169}, {97, 2159}, {2148, 14919}, {2167, 18877}
X(46090) = trilinear quotient X(i)/X(j) for these (i, j): (54, 1784), (97, 14206), (255, 1568), (822, 14391), (2148, 1990), (2159, 53)

X(46091) = (name pending)

X(46091) = X(97)-reciprocal conjugate of-X(44135)
X(46091) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(13139)}} and {{A, B, C, X(54), X(14533)}}
X(46091) = barycentric product X(97)*X(3431)
X(46091) = barycentric quotient X(97)/X(44135)
X(46091) = trilinear product X(2169)*X(3431)
X(46091) = trilinear quotient X(2169)/X(381)

X(46092) = (name pending)

X(46092) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(32534)}} and {{A, B, C, X(54), X(14533)}}
X(46092) = barycentric product X(97)*X(14528)
X(46092) = trilinear product X(2169)*X(14528)
X(46092) = trilinear quotient X(2169)/X(3091)

X(46093) = X(3)X(6663)∩X(23195)X(39071)

X(46093) = X(2)-Ceva conjugate of-X(32320)
X(46093) = X(i)-complementary conjugate of-X(j) for these (i, j): (31, 32320), (810, 36412)
X(46093) = X(520)-Dao conjugate of X(6662)
X(46093) = X(1614)-reciprocal conjugate of-X(34538)
X(46093) = center of the circumconic {{A, B, C, X(3), X(95)}}
X(46093) = barycentric quotient X(1614)/X(34538)
X(46093) = trilinear quotient X(1614)/X(24021)

X(46094) = X(125)X(23195)∩X(160)X(7710)

X(46094) lies on the Johnson circumconic of the medial triangle and on these lines: {2, 23181}, {3, 36952}, {125, 23195}, {160, 7710}, {418, 2972}, {684, 9420}, {5664, 42731}, {5866, 39100}, {13367, 17423}, {14713, 15577}, {19161, 36790}, {22089, 33813}

X(46094) = complement of X(35098)
X(46094) = X(2)-Ceva conjugate of-X(3289)
X(46094) = X(31)-complementary conjugate of-X(3289)
X(46094) = center of the circumconic {{A, B, C, X(3), X(99)}}

X(46095) = X(2972)X(22080)∩X(10167)X(22390)

X(46096) = X(6)X(35088)∩X(325)X(44099)

X(46096) lies on the Vijay orthic-medial conic and these lines: {6, 35088}, {325, 44099}, {30717, 43705}

X(46097) = X(6)X(35088)∩X(297)X(8779)

X(46097) lies on the Vijay orthic-medial conic and these lines: {6, 35088}, {297, 8779}, {520, 23583}, {525, 6720}, {40550, 45327}

X(46097) = midpoint of X(297) and X(8779)
X(46097) = X(36092)-complementary conjugate of X(36471)

X(46098) = X(5)X(2794)∩X(6)X(39645)

X(46098) lies on the Vijay orthic-medial conic and these lines: {5, 2794}, {6, 39645}, {2871, 14913}, {36163, 43705}

X(46099) = X(6)X(39645)∩X(41369)X(44499)

X(46099) lies on the Vijay orthic-medial conic and these lines: {6, 39645}, {41369, 44499}

X(46100) = COMPLEMENT OF X(59)

X(46100) lies on these lines: {2, 59}, {9, 2957}, {10, 6073}, {11, 521}, {36, 856}, {123, 14115}, {124, 3259}, {125, 6075}, {513, 21252}, {518, 1737}, {1086, 21186}, {1618, 21293}, {2238, 2323}, {3041, 35967}, {3326, 24026}, {4086, 4092}, {6667, 33562}, {15635, 26933}, {19953, 38406}, {20335, 26013}

X(46100) = midpoint of X(1618) and X(21293)
X(46100) = reflection of X(i) in X(j) for these {i,j}: {59, 40531}, {33562, 6667}
X(46100) = anticomplement of X(40531)
X(46100) = complement of X(59)
X(46100) = complement of the isogonal conjugate of X(11)
X(46100) = complement of the isotomic conjugate of X(34387)
X(46100) = medial isogonal conjugate of X(3035)
X(46100) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 13006}, {44184, 522}
X(46100) = crosspoint of X(2) and X(34387)
X(46100) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 3035}, {2, 21232}, {6, 16578}, {8, 24003}, {9, 4422}, {11, 10}, {19, 36949}, {31, 13006}, {34, 15252}, {41, 23988}, {55, 24036}, {56, 24025}, {57, 17044}, {58, 34977}, {60, 16598}, {105, 24980}, {158, 3042}, {200, 3039}, {244, 1}, {261, 21254}, {270, 5972}, {312, 27076}, {341, 3038}, {479, 24009}, {513, 522}, {514, 4885}, {521, 20315}, {522, 513}, {604, 23585}, {644, 10196}, {649, 905}, {650, 514}, {661, 1577}, {663, 650}, {667, 6589}, {693, 17072}, {738, 23587}, {764, 3756}, {876, 25380}, {885, 3716}, {1015, 3752}, {1019, 17069}, {1022, 44902}, {1024, 918}, {1027, 676}, {1086, 142}, {1109, 34829}, {1111, 2886}, {1118, 24030}, {1146, 3452}, {1358, 11019}, {1422, 40555}, {1565, 34822}, {1647, 1145}, {2150, 34990}, {2170, 2}, {2185, 620}, {2189, 16599}, {2217, 6718}, {2254, 3126}, {2310, 9}, {2968, 34823}, {2969, 1210}, {3063, 6586}, {3119, 6554}, {3120, 442}, {3122, 2092}, {3123, 41886}, {3125, 17056}, {3239, 20317}, {3248, 17053}, {3271, 37}, {3669, 7658}, {3676, 3900}, {3700, 4129}, {3737, 523}, {3756, 12640}, {3900, 4521}, {3937, 17102}, {3942, 17073}, {4017, 656}, {4041, 661}, {4086, 31946}, {4124, 17793}, {4391, 3835}, {4435, 27929}, {4466, 18642}, {4516, 1213}, {4530, 16594}, {4560, 4369}, {4858, 141}, {4895, 6544}, {4939, 2885}, {6545, 4904}, {6591, 14837}, {7004, 3}, {7117, 1214}, {7129, 40535}, {7199, 17066}, {7252, 14838}, {7649, 521}, {8027, 16614}, {8034, 16613}, {8735, 226}, {9503, 40554}, {14430, 14434}, {14837, 20314}, {14935, 25066}, {14936, 1212}, {15635, 44675}, {16726, 3946}, {16727, 17050}, {16732, 17052}, {17197, 3739}, {17205, 3742}, {17435, 16593}, {17880, 1368}, {18101, 1215}, {18108, 4142}, {18155, 512}, {18191, 1125}, {18210, 18641}, {18344, 3239}, {21044, 1211}, {21132, 11}, {21138, 20528}, {23615, 5514}, {23838, 900}, {23893, 45326}, {23978, 21244}, {23989, 17046}, {24010, 5574}, {24026, 1329}, {26856, 21233}, {26932, 18589}, {27424, 40562}, {33676, 40538}, {34387, 2887}, {35015, 119}, {35348, 6366}, {35355, 4925}, {35519, 21260}, {36197, 38930}, {36800, 40548}, {38357, 6260}, {38362, 20264}, {40166, 116}, {40451, 5836}, {40528, 17355}, {42067, 20227}, {42069, 20262}, {42455, 124}, {42462, 26932}, {43923, 21172}, {43924, 6129}, {44426, 20316}
X(46100) = barycentric product X(13006)*X(34387)
X(46100) = barycentric quotient X(13006)/X(59)
X(46100) = {X(2),X(59)}-harmonic conjugate of X(40531)

X(46101) = COMPLEMENT OF X(4998)

Barycentrics (a - b - c)*(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(46101) lies on these lines: {2, 1252}, {6, 34530}, {11, 650}, {44, 40869}, {115, 35128}, {516, 9356}, {649, 3259}, {661, 6075}, {1015, 6506}, {1086, 7658}, {1146, 4521}, {1647, 17435}, {2238, 2323}, {3008, 6547}, {3035, 14589}, {3290, 5121}, {3452, 27942}, {3816, 5701}, {3825, 9367}, {4885, 35094}, {5375, 31272}, {5514, 5516}, {5548, 26074}, {9374, 10893}, {14298, 33646}, {21104, 40629}, {22102, 41405}, {27010, 28833}, {35113, 35509}

X(46101) = midpoint of X(4998) and X(17036)
X(46101) = reflection of X(9356) in the Gergonne line
X(46101) = isogonal conjugate of X(38809)
X(46101) = isotomic conjugate of X(31619)
X(46101) = complement of X(4998)
X(46101) = complement of the isogonal conjugate of X(3271)
X(46101) = complement of the isotomic conjugate of X(11)
X(46101) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 3035}, {3035, 11124}, {6630, 522}, {40520, 21132}
X(46101) = X(i)-isoconjugate of X(j) for these (i,j): {1, 38809}, {31, 31619}, {109, 31628}, {4564, 18771}
X(46101) = crosspoint of X(2) and X(11)
X(46101) = crosssum of X(6) and X(59)
X(46101) = X(11)-Ceva conjugate of Danneels point of X(11)
X(46101) = trilinear product X(i)*X(j) for these {i,j}: {11, 17439}, {514, 11124}, {650, 21105}, {2170, 3035}
X(46101) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 21232}, {9, 27076}, {11, 2887}, {31, 3035}, {32, 16578}, {41, 4422}, {55, 24003}, {60, 21254}, {200, 3038}, {244, 2886}, {513, 17072}, {522, 21260}, {560, 13006}, {604, 17044}, {649, 4885}, {650, 3835}, {657, 20317}, {663, 513}, {667, 522}, {764, 17059}, {798, 1577}, {875, 25380}, {884, 3716}, {1015, 142}, {1019, 17066}, {1027, 926}, {1086, 17046}, {1096, 3042}, {1111, 17047}, {1146, 21244}, {1253, 3039}, {1357, 11019}, {1395, 15252}, {1397, 24025}, {1919, 905}, {1946, 20315}, {1973, 36949}, {1977, 3752}, {1980, 6589}, {2150, 620}, {2170, 141}, {2175, 24036}, {2206, 34977}, {2310, 1329}, {2311, 40548}, {2319, 40562}, {2643, 34829}, {3063, 514}, {3121, 17056}, {3122, 442}, {3123, 20338}, {3125, 17052}, {3248, 1}, {3270, 34823}, {3271, 10}, {3709, 4129}, {3737, 512}, {3937, 34822}, {3942, 18639}, {4041, 31946}, {4124, 20542}, {4391, 21262}, {4435, 27854}, {4516, 3454}, {4560, 42327}, {4858, 626}, {6377, 20528}, {7004, 1368}, {7023, 24009}, {7117, 18589}, {7252, 4369}, {7337, 24030}, {7366, 23587}, {8027, 3756}, {8034, 8286}, {8641, 4521}, {8735, 20305}, {9447, 23988}, {14936, 3452}, {16726, 17050}, {17197, 21240}, {17435, 20540}, {18101, 21238}, {18155, 23301}, {18191, 3741}, {18344, 20316}, {21044, 21245}, {21132, 21252}, {21138, 20547}, {21143, 4904}, {22096, 17102}, {24012, 5574}, {34387, 21235}, {38365, 40607}, {38986, 41886}, {42067, 1210}, {43924, 3900}
X(46101) = barycentric product X(i)*X(j) for these {i,j}: {8, 43909}, {11, 3035}, {100, 42547}, {522, 21105}, {693, 11124}, {2170, 20881}, {4858, 17439}, {14589, 40166}, {17197, 21013}, {18645, 21044}, {20958, 34387}
X(46101) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 31619}, {6, 38809}, {650, 31628}, {3035, 4998}, {3271, 18771}, {11124, 100}, {14589, 31615}, {17439, 4564}, {18645, 4620}, {20958, 59}, {21105, 664}, {22055, 44717}, {42547, 693}, {43909, 7}
X(46101) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17036, 4998}, {1647, 33573, 17435}

X(46102) = POLAR CONJUGATE OF X(11)

X(46102) lies on these lines: {2, 1262}, {4, 5377}, {34, 5378}, {59, 5080}, {108, 898}, {109, 17072}, {278, 5376}, {608, 5381}, {648, 35174}, {651, 4391}, {653, 3257}, {664, 6332}, {666, 1783}, {765, 1861}, {908, 4564}, {1016, 37790}, {1025, 1981}, {1275, 1944}, {2397, 2405}, {4551, 36797}, {4567, 4998}, {4585, 24035}, {7017, 34048}, {7045, 37774}, {21301, 32735}, {23984, 24032}, {37768, 43043}

X(46102) = isogonal conjugate of X(7117)
X(46102) = isotomic conjugate of X(26932)
X(46102) = polar conjugate of X(11)
X(46102) = isotomic conjugate of the anticomplement of X(36949)
X(46102) = isotomic conjugate of the complement of X(651)
X(46102) = isotomic conjugate of the isogonal conjugate of X(7115)
X(46102) = polar conjugate of the isotomic conjugate of X(4998)
X(46102) = polar conjugate of the isogonal conjugate of X(59)
X(46102) = pole wrt polar circle of trilinear polar of X(11) (line X(4530)X(14393))
X(46102) = perspector of ABC and orthoanticevian triangle of X(4998)
X(46102) = X(4998)-Ceva conjugate of X(44699)
X(46102) = X(i)-cross conjugate of X(j) for these (i,j): {2, 6335}, {4, 18026}, {8, 664}, {9, 36797}, {59, 4998}, {92, 648}, {219, 100}, {278, 653}, {281, 1897}, {321, 6648}, {329, 190}, {608, 108}, {3434, 4569}, {3436, 668}, {3681, 6606}, {3869, 99}, {4318, 927}, {5057, 35157}, {5080, 35174}, {5176, 4555}, {5279, 8707}, {5739, 32038}, {7078, 6516}, {11109, 811}, {14923, 6613}, {17913, 6331}, {20557, 18830}, {23541, 75}, {26668, 30610}, {26942, 4552}, {27382, 3699}, {27540, 646}, {28739, 4554}, {28950, 645}, {30807, 666}, {34040, 934}, {34048, 651}, {36949, 2}, {37279, 823}
X(46102) = cevapoint of X(i) and X(j) for these (i,j): {2, 651}, {4, 1783}, {9, 4551}, {12, 4559}, {59, 7115}, {100, 219}, {108, 608}, {190, 4417}, {278, 653}, {281, 1897}, {644, 7080}, {664, 33298}, {4552, 26942}
X(46102) = trilinear pole of line {100, 108}
X(46102) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7117}, {3, 2170}, {6, 7004}, {9, 3937}, {11, 48}, {19, 1364}, {31, 26932}, {32, 17880}, {34, 35072}, {41, 1565}, {55, 3942}, {56, 34591}, {57, 3270}, {60, 3708}, {63, 3271}, {71, 18191}, {77, 14936}, {78, 1015}, {125, 2150}, {184, 4858}, {212, 1086}, {213, 17219}, {219, 244}, {222, 2310}, {228, 17197}, {255, 8735}, {270, 3269}, {273, 39687}, {278, 2638}, {283, 3125}, {284, 18210}, {312, 22096}, {332, 3121}, {345, 3248}, {513, 652}, {514, 1946}, {521, 649}, {522, 22383}, {603, 1146}, {604, 2968}, {608, 24031}, {647, 3737}, {650, 1459}, {656, 7252}, {661, 23189}, {663, 905}, {665, 23696}, {667, 6332}, {764, 4587}, {810, 4560}, {906, 21132}, {909, 35014}, {1357, 3692}, {1358, 1802}, {1395, 23983}, {1437, 21044}, {1789, 20982}, {1790, 4516}, {1808, 39786}, {1812, 3122}, {1919, 35518}, {1977, 3718}, {2185, 20975}, {2189, 2632}, {2193, 3120}, {2194, 4466}, {2196, 4124}, {2204, 17216}, {2208, 16596}, {2289, 2969}, {2318, 16726}, {3022, 7177}, {3049, 18155}, {3063, 4025}, {3064, 23224}, {3119, 7053}, {3310, 37628}, {3719, 42067}, {3733, 8611}, {4017, 23090}, {4020, 18101}, {4041, 7254}, {4081, 7099}, {4091, 18344}, {4459, 7116}, {4530, 36058}, {4571, 21143}, {7125, 42069}, {7202, 8606}, {7289, 14935}, {7649, 36054}, {9247, 34387}, {14418, 23345}, {14578, 35015}, {15451, 39177}, {17435, 36057}, {22086, 23838}, {22386, 27424}, {24012, 30682}, {32656, 40166}, {32660, 42455}, {34434, 38344}, {36059, 42462}, {40527, 40958}
X(46102) = barycentric product X(i)*X(j) for these {i,j}: {4, 4998}, {7, 15742}, {12, 18020}, {34, 7035}, {59, 264}, {75, 7012}, {76, 7115}, {78, 24032}, {92, 4564}, {100, 18026}, {108, 668}, {190, 653}, {201, 23999}, {225, 4600}, {250, 34388}, {253, 44699}, {273, 765}, {278, 1016}, {281, 1275}, {312, 7128}, {318, 7045}, {319, 34922}, {331, 1252}, {345, 23984}, {608, 31625}, {644, 13149}, {646, 32714}, {648, 4552}, {651, 6335}, {664, 1897}, {811, 4551}, {908, 39294}, {1119, 4076}, {1262, 7017}, {1441, 5379}, {1783, 4554}, {1826, 4620}, {1861, 39293}, {1880, 4601}, {1969, 2149}, {1978, 32674}, {2052, 44717}, {3699, 36118}, {3718, 24033}, {4242, 35174}, {4559, 6331}, {4561, 36127}, {4566, 36797}, {4567, 40149}, {4572, 8750}, {4590, 8736}, {5376, 37790}, {6528, 23067}, {7140, 7340}, {8795, 44710}, {17924, 31615}, {23582, 26942}
X(46102) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 7004}, {2, 26932}, {3, 1364}, {4, 11}, {6, 7117}, {7, 1565}, {8, 2968}, {9, 34591}, {12, 125}, {19, 2170}, {25, 3271}, {27, 17197}, {28, 18191}, {33, 2310}, {34, 244}, {55, 3270}, {56, 3937}, {57, 3942}, {59, 3}, {65, 18210}, {75, 17880}, {78, 24031}, {86, 17219}, {92, 4858}, {100, 521}, {101, 652}, {108, 513}, {109, 1459}, {110, 23189}, {112, 7252}, {162, 3737}, {181, 20975}, {190, 6332}, {201, 2632}, {212, 2638}, {219, 35072}, {225, 3120}, {226, 4466}, {242, 4124}, {250, 60}, {264, 34387}, {273, 1111}, {278, 1086}, {281, 1146}, {307, 17216}, {318, 24026}, {329, 16596}, {331, 23989}, {345, 23983}, {388, 26933}, {393, 8735}, {517, 35014}, {572, 38344}, {607, 14936}, {608, 1015}, {645, 15411}, {646, 15416}, {648, 4560}, {651, 905}, {653, 514}, {664, 4025}, {668, 35518}, {692, 1946}, {765, 78}, {811, 18155}, {906, 36054}, {1016, 345}, {1018, 8611}, {1023, 14418}, {1110, 212}, {1118, 2969}, {1119, 1358}, {1252, 219}, {1262, 222}, {1275, 348}, {1309, 43728}, {1361, 35012}, {1395, 3248}, {1396, 16726}, {1397, 22096}, {1398, 1357}, {1415, 22383}, {1783, 650}, {1785, 35015}, {1804, 7215}, {1812, 16731}, {1813, 4091}, {1824, 4516}, {1825, 2611}, {1826, 21044}, {1846, 3259}, {1857, 42069}, {1875, 42753}, {1876, 3675}, {1877, 1647}, {1880, 3125}, {1897, 522}, {2149, 48}, {2171, 3708}, {2197, 3269}, {2594, 22094}, {2969, 7336}, {3064, 42462}, {3085, 26956}, {3436, 123}, {3695, 7068}, {3869, 34588}, {4076, 1265}, {4242, 3738}, {4417, 40626}, {4551, 656}, {4552, 525}, {4554, 15413}, {4559, 647}, {4564, 63}, {4565, 7254}, {4566, 17094}, {4567, 1812}, {4570, 283}, {4573, 15419}, {4600, 332}, {4619, 1813}, {4620, 17206}, {4998, 69}, {5089, 17435}, {5379, 21}, {5546, 23090}, {6065, 1260}, {6335, 4391}, {6356, 1367}, {6358, 20902}, {6516, 4131}, {6648, 15420}, {7009, 4459}, {7012, 1}, {7017, 23978}, {7035, 3718}, {7045, 77}, {7046, 4081}, {7066, 2972}, {7071, 3022}, {7079, 3119}, {7080, 7358}, {7115, 6}, {7128, 57}, {7140, 4092}, {7337, 42067}, {7339, 7053}, {7649, 21132}, {7719, 38375}, {7952, 38357}, {8736, 115}, {8750, 663}, {8756, 4530}, {11109, 34589}, {13149, 24002}, {14594, 23874}, {15385, 3435}, {15742, 8}, {17555, 124}, {17906, 21120}, {17916, 38358}, {17924, 40166}, {18020, 261}, {18026, 693}, {21664, 3326}, {23067, 520}, {23586, 30682}, {23706, 1769}, {23964, 2189}, {23981, 8677}, {23984, 278}, {23985, 608}, {24000, 270}, {24027, 603}, {24032, 273}, {24033, 34}, {26942, 15526}, {27382, 40616}, {31615, 1332}, {32085, 18101}, {32674, 649}, {32702, 2423}, {32714, 3669}, {33298, 40618}, {34388, 339}, {34922, 79}, {36037, 37628}, {36059, 23224}, {36086, 23696}, {36118, 3676}, {36127, 7649}, {36794, 27010}, {36797, 7253}, {37993, 41214}, {39293, 31637}, {39294, 34234}, {40149, 16732}, {40399, 40527}, {40446, 40451}, {42069, 5532}, {42070, 4542}, {43923, 764}, {44426, 42455}, {44699, 20}, {44710, 5562}, {44717, 394}, {44724, 44722}

X(46103) = POLAR CONJUGATE OF X(12)

X(46103) lies on these lines: {2, 7054}, {4, 1798}, {21, 23207}, {27, 86}, {28, 37870}, {29, 270}, {33, 1808}, {81, 286}, {83, 39281}, {92, 648}, {110, 20242}, {162, 14004}, {163, 1746}, {261, 2189}, {275, 24624}, {314, 1172}, {331, 37543}, {422, 1824}, {448, 1214}, {469, 36794}, {593, 26856}, {940, 11341}, {1396, 1509}, {1826, 18812}, {1891, 41258}, {2193, 25515}, {5174, 19808}, {7518, 37666}, {10319, 37089}, {17907, 37181}, {18134, 40414}, {18139, 27418}, {31905, 32010}, {31909, 40415}, {39280, 39284}, {40574, 44129}

X(46103) = isogonal conjugate of X(2197)
X(46103) = isotomic conjugate of X(26942)
X(46103) = polar conjugate of X(12)
X(46103) = isotomic conjugate of the isogonal conjugate of X(2189)
X(46103) = polar conjugate of the isotomic conjugate of X(261)
X(46103) = polar conjugate of the isogonal conjugate of X(60)
X(46103) = X(i)-cross conjugate of X(j) for these (i,j): {60, 261}, {81, 2185}, {1172, 270}, {23542, 75}, {26932, 4560}
X(46103) = cevapoint of X(i) and X(j) for these (i,j): {11, 7252}, {27, 81}, {29, 1172}, {60, 2189}, {270, 2326}, {4560, 26932}, {18134, 32939}
X(46103) = trilinear pole of line {4560, 14024}
X(46103) = pole wrt polar circle of trilinear polar of X(12) (line X(2610)X(4024))
X(46103) = perspector of ABC and orthoanticevian triangle of X(261)
X(46103) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2197}, {3, 2171}, {6, 201}, {9, 1425}, {10, 1409}, {12, 48}, {19, 7066}, {31, 26942}, {37, 73}, {41, 6356}, {42, 1214}, {55, 37755}, {56, 3949}, {57, 3690}, {59, 3708}, {63, 181}, {65, 71}, {72, 1400}, {77, 1500}, {125, 2149}, {184, 6358}, {212, 6354}, {213, 307}, {219, 1254}, {222, 756}, {225, 3990}, {226, 228}, {227, 41087}, {255, 8736}, {281, 7138}, {306, 1402}, {348, 872}, {594, 603}, {604, 3695}, {647, 4551}, {656, 4559}, {661, 23067}, {810, 4552}, {1042, 3694}, {1231, 1918}, {1253, 20618}, {1260, 7147}, {1334, 1439}, {1410, 2321}, {1415, 4064}, {1427, 2318}, {1441, 2200}, {1459, 21859}, {1802, 6046}, {1813, 4705}, {1824, 40152}, {1826, 22341}, {1880, 3682}, {1946, 4605}, {2196, 7235}, {2198, 28786}, {2259, 41393}, {2632, 7115}, {2643, 44717}, {3215, 41508}, {3269, 7012}, {3692, 7143}, {4017, 4574}, {4024, 36059}, {4036, 32660}, {4055, 40149}, {4079, 6516}, {4564, 20975}, {6057, 7099}, {7064, 7177}, {7100, 21794}, {7109, 7182}, {7116, 7211}, {7125, 7140}, {8818, 22342}, {9247, 34388}, {23286, 35307}
X(46103) = barycentric product X(i)*X(j) for these {i,j}: {4, 261}, {11, 18020}, {21, 286}, {25, 18021}, {27, 333}, {28, 314}, {29, 86}, {33, 873}, {58, 44130}, {60, 264}, {75, 270}, {76, 2189}, {81, 31623}, {85, 2326}, {92, 2185}, {162, 18155}, {250, 34387}, {273, 1098}, {274, 1172}, {278, 7058}, {281, 1509}, {284, 44129}, {310, 2299}, {318, 757}, {331, 7054}, {332, 8747}, {345, 36419}, {348, 36421}, {552, 7046}, {593, 7017}, {645, 17925}, {648, 4560}, {811, 3737}, {1434, 2322}, {1444, 1896}, {1474, 28660}, {1969, 2150}, {2203, 40072}, {2204, 6385}, {2969, 6064}, {3064, 4610}, {4573, 17926}, {4590, 8735}, {4612, 17924}, {4623, 18344}, {4631, 6591}, {5931, 44698}, {6331, 7252}, {6336, 30606}, {6528, 23189}, {7004, 23999}, {7192, 36797}, {7340, 42069}, {8748, 17206}, {14006, 32010}, {14024, 18827}, {14616, 17515}, {17880, 24000}, {23582, 26932}, {31905, 36800}, {37870, 44734}
X(46103) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 201}, {2, 26942}, {3, 7066}, {4, 12}, {6, 2197}, {7, 6356}, {8, 3695}, {9, 3949}, {11, 125}, {19, 2171}, {21, 72}, {25, 181}, {27, 226}, {28, 65}, {29, 10}, {33, 756}, {34, 1254}, {55, 3690}, {56, 1425}, {57, 37755}, {58, 73}, {60, 3}, {81, 1214}, {86, 307}, {92, 6358}, {110, 23067}, {112, 4559}, {162, 4551}, {242, 7235}, {249, 44717}, {250, 59}, {261, 69}, {264, 34388}, {270, 1}, {272, 28786}, {274, 1231}, {278, 6354}, {279, 20618}, {281, 594}, {283, 3682}, {284, 71}, {286, 1441}, {314, 20336}, {318, 1089}, {333, 306}, {393, 8736}, {497, 21015}, {522, 4064}, {552, 7056}, {593, 222}, {603, 7138}, {607, 1500}, {648, 4552}, {653, 4605}, {757, 77}, {849, 603}, {873, 7182}, {942, 41393}, {950, 21671}, {1014, 1439}, {1021, 8611}, {1043, 3710}, {1098, 78}, {1119, 6046}, {1172, 37}, {1259, 4158}, {1333, 1409}, {1364, 2972}, {1396, 1427}, {1398, 7143}, {1408, 1410}, {1435, 7147}, {1437, 22341}, {1440, 6355}, {1474, 1400}, {1509, 348}, {1565, 1367}, {1783, 21859}, {1790, 40152}, {1812, 3998}, {1857, 7140}, {1896, 41013}, {2150, 48}, {2170, 3708}, {2185, 63}, {2189, 6}, {2193, 3990}, {2194, 228}, {2203, 1402}, {2204, 213}, {2212, 872}, {2287, 3694}, {2299, 42}, {2322, 2321}, {2326, 9}, {2328, 2318}, {2332, 1334}, {2905, 27691}, {2907, 3178}, {2968, 7068}, {2969, 1365}, {3064, 4024}, {3086, 26955}, {3194, 227}, {3271, 20975}, {3559, 21077}, {3737, 656}, {4183, 210}, {4211, 40961}, {4233, 41539}, {4248, 4848}, {4267, 22076}, {4556, 1813}, {4560, 525}, {4612, 1332}, {4636, 1331}, {4858, 20902}, {5317, 1880}, {5324, 17441}, {5546, 4574}, {6061, 1260}, {6727, 7591}, {7004, 2632}, {7009, 7211}, {7017, 28654}, {7046, 6057}, {7054, 219}, {7058, 345}, {7071, 7064}, {7117, 3269}, {7140, 6058}, {7192, 17094}, {7252, 647}, {7341, 7053}, {8735, 115}, {8747, 225}, {8748, 1826}, {11107, 3678}, {13739, 15556}, {14006, 1215}, {14024, 740}, {17104, 22342}, {17188, 21912}, {17197, 4466}, {17219, 17216}, {17515, 758}, {17519, 3753}, {17880, 17879}, {17925, 7178}, {17926, 3700}, {18020, 4998}, {18021, 305}, {18155, 14208}, {18191, 18210}, {18344, 4705}, {21044, 21046}, {21132, 21134}, {23189, 520}, {23964, 7115}, {24000, 7012}, {26856, 26932}, {26932, 15526}, {27958, 4019}, {28660, 40071}, {30606, 3977}, {30733, 41538}, {31623, 321}, {31900, 3649}, {31903, 3671}, {31905, 16609}, {31906, 5244}, {31909, 16603}, {31917, 16888}, {34387, 339}, {34856, 1874}, {36419, 278}, {36420, 608}, {36421, 281}, {36797, 3952}, {37168, 40663}, {37265, 8896}, {37390, 10408}, {37908, 20683}, {40950, 21674}, {41227, 15443}, {42069, 4092}, {43925, 7180}, {44129, 349}, {44130, 313}, {44426, 4036}, {44428, 6370}, {44698, 5930}, {44734, 31993}
X(46103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {27, 2905, 1848}, {33, 14006, 36797}, {1172, 44734, 31623}

X(46104) = POLAR CONJUGATE OF X(39)

X(46104) lies on these lines: {4, 18022}, {25, 183}, {51, 290}, {53, 16890}, {76, 33586}, {83, 458}, {251, 324}, {327, 43653}, {393, 37876}, {419, 44142}, {427, 6331}, {428, 17984}, {511, 34384}, {689, 3563}, {1176, 8795}, {1824, 40717}, {5640, 44176}, {6524, 17500}, {6995, 44144}, {6997, 40822}, {8753, 32581}, {10130, 40684}, {10550, 14593}, {10551, 39530}, {14486, 43976}, {17994, 17995}, {18384, 18817}, {23962, 37349}, {30505, 30506}, {38817, 39931}

X(46104) = isogonal conjugate of X(20775)
X(46104) = isotomic conjugate of X(3917)
X(46104) = polar conjugate of X(39)
X(46104) = isotomic conjugate of the anticomplement of X(5943)
X(46104) = isotomic conjugate of the complement of X(3060)
X(46104) = isotomic conjugate of the isogonal conjugate of X(32085)
X(46104) = polar conjugate of the isotomic conjugate of X(308)
X(46104) = polar conjugate of the isogonal conjugate of X(83)
X(46104) = X(i)-cross conjugate of X(j) for these (i,j): {4, 32085}, {83, 308}, {419, 16081}, {2501, 6331}, {5943, 2}, {10551, 251}, {17500, 83}, {17867, 75}, {44142, 264}
X(46104) = cevapoint of X(i) and X(j) for these (i,j): {2, 3060}, {4, 264}, {83, 32085}, {324, 30506}, {1843, 37125}
X(46104) = crosssum of X(3) and X(23174)
X(46104) = trilinear pole of line {2489, 4580}
X(46104) = pole wrt polar circle of trilinear polar of X(39) (line X(688)X(3005))
X(46104) = perspector of ABC and orthoanticevian triangle of X(308)
X(46104) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20775}, {3, 1964}, {6, 4020}, {31, 3917}, {38, 184}, {39, 48}, {63, 3051}, {69, 1923}, {141, 9247}, {212, 1401}, {222, 40972}, {228, 17187}, {255, 1843}, {304, 41331}, {326, 27369}, {560, 3933}, {577, 17442}, {603, 3688}, {688, 4592}, {810, 1634}, {822, 35325}, {906, 21123}, {1178, 22367}, {1437, 21035}, {1444, 41267}, {1790, 21814}, {1930, 14575}, {2084, 4558}, {2200, 16696}, {2236, 17970}, {2530, 32656}, {3005, 4575}, {3289, 3404}, {4100, 27376}, {8061, 32661}, {14585, 20883}, {23225, 35333}
X(46104) = barycentric product X(i)*X(j) for these {i,j}: {4, 308}, {19, 18833}, {25, 40016}, {53, 41488}, {76, 32085}, {82, 1969}, {83, 264}, {92, 3112}, {251, 18022}, {276, 17500}, {324, 39287}, {669, 42395}, {689, 2501}, {811, 18070}, {850, 42396}, {1176, 18027}, {1799, 2052}, {2489, 42371}, {4577, 14618}, {4580, 6528}, {4593, 24006}, {14970, 17984}, {16081, 20022}, {18082, 44129}, {18097, 44130}, {32581, 40826}, {39289, 40684}, {40425, 44142}, {42299, 44144}
X(46104) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4020}, {2, 3917}, {4, 39}, {6, 20775}, {19, 1964}, {25, 3051}, {27, 17187}, {33, 40972}, {76, 3933}, {82, 48}, {83, 3}, {92, 38}, {107, 35325}, {158, 17442}, {251, 184}, {264, 141}, {275, 16030}, {278, 1401}, {281, 3688}, {286, 16696}, {308, 69}, {318, 33299}, {331, 3665}, {393, 1843}, {419, 8623}, {427, 8041}, {428, 11205}, {458, 14096}, {648, 1634}, {689, 4563}, {733, 17970}, {827, 32661}, {850, 2525}, {1093, 27376}, {1176, 577}, {1235, 7794}, {1799, 394}, {1824, 21814}, {1826, 21035}, {1840, 40936}, {1969, 1930}, {1973, 1923}, {1974, 41331}, {2052, 427}, {2207, 27369}, {2295, 22367}, {2333, 41267}, {2489, 688}, {2501, 3005}, {2970, 39691}, {3112, 63}, {3199, 27374}, {3589, 22078}, {4577, 4558}, {4580, 520}, {4593, 4592}, {4599, 4575}, {4628, 32656}, {4972, 22077}, {6331, 4576}, {6335, 4553}, {6353, 3787}, {6528, 41676}, {6656, 22424}, {7017, 3703}, {7649, 21123}, {8024, 4175}, {8743, 23208}, {8753, 41272}, {8794, 19174}, {10312, 3203}, {10547, 14585}, {10548, 13367}, {10549, 23635}, {10550, 570}, {10566, 1459}, {13450, 27371}, {14618, 826}, {14970, 36214}, {16081, 20021}, {16889, 20727}, {16890, 20819}, {17500, 216}, {17907, 3313}, {17924, 2530}, {17984, 732}, {18022, 8024}, {18027, 1235}, {18070, 656}, {18082, 71}, {18083, 22069}, {18084, 22057}, {18085, 22394}, {18086, 22072}, {18087, 22053}, {18088, 22070}, {18089, 22060}, {18090, 22404}, {18091, 22065}, {18092, 22062}, {18093, 22409}, {18094, 22412}, {18095, 22064}, {18096, 22420}, {18097, 73}, {18098, 228}, {18099, 22061}, {18101, 7117}, {18102, 22066}, {18103, 20730}, {18105, 3049}, {18106, 22387}, {18107, 22090}, {18108, 22383}, {18109, 22067}, {18110, 22091}, {18111, 22093}, {18112, 22098}, {18700, 22399}, {18701, 22400}, {18704, 22402}, {18705, 22403}, {18833, 304}, {20022, 36212}, {20965, 23210}, {21447, 41584}, {21458, 8779}, {21459, 2393}, {24006, 8061}, {24243, 45594}, {24244, 26347}, {26224, 43652}, {27067, 22076}, {28724, 1092}, {32085, 6}, {32581, 574}, {34055, 255}, {34294, 20975}, {35360, 35319}, {36120, 3404}, {36794, 41328}, {37765, 9019}, {38817, 23174}, {38946, 22121}, {39182, 23286}, {39287, 97}, {39289, 31626}, {40016, 305}, {40425, 41435}, {41013, 3954}, {41488, 34386}, {41884, 22138}, {42037, 3796}, {42299, 43718}, {42395, 4609}, {42396, 110}, {44129, 16887}, {44142, 6292}, {44144, 14994}, {44146, 7813}
X(46104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {264, 32085, 308}, {428, 42394, 17984}

X(46105) = POLAR CONJUGATE OF X(23)

X(46105) lies on the Kiepert circumhyperbola and these lines: {2, 339}, {4, 67}, {83, 648}, {94, 297}, {98, 186}, {262, 7577}, {264, 598}, {275, 41254}, {328, 39295}, {458, 7578}, {468, 10511}, {671, 44146}, {1236, 22151}, {1289, 9076}, {2986, 17708}, {3406, 36820}, {3424, 18533}, {7550, 40448}, {7607, 14357}, {8744, 37778}, {10718, 18866}, {11606, 40889}, {13599, 14789}, {14223, 14618}, {14458, 18559}, {14830, 38552}, {35486, 43537}, {40393, 40684}, {40814, 43530}, {41079, 43673}, {43665, 44427}

X(46105) = isogonal conjugate of X(10317)
X(46105) = isotomic conjugate of X(22151)
X(46105) = polar conjugate of X(23)
X(46105) = isotomic conjugate of the isogonal conjugate of X(8791)
X(46105) = polar conjugate of the isotomic conjugate of X(18019)
X(46105) = polar conjugate of the isogonal conjugate of X(67)
X(46105) = X(i)-cross conjugate of X(j) for these (i,j): {67, 18019}, {468, 264}, {5523, 4}, {23557, 75}, {43291, 847}
X(46105) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10317}, {23, 48}, {31, 22151}, {63, 18374}, {163, 9517}, {184, 16568}, {255, 8744}, {316, 9247}, {560, 37804}, {662, 42659}, {2159, 16165}, {2492, 4575}, {6593, 36060}, {10547, 18715}, {14575, 20944}
X(46105) = cevapoint of X(i) and X(j) for these (i,j): {6, 21284}, {67, 8791}, {1235, 44146}, {1843, 14580}, {5523, 39269}
X(46105) = trilinear pole of line {427, 523} (the radical axis of the anticomplementary circle and tangential circle)
X(46105) = anticomplement of isotomic conjugate of polar conjugate of X(40949)
X(46105) = pole wrt polar circle of trilinear polar of X(23) (line X(2492)X(6593))
X(46105) = barycentric product X(i)*X(j) for these {i,j}: {4, 18019}, {67, 264}, {76, 8791}, {850, 935}, {1235, 9076}, {1969, 2157}, {2052, 34897}, {2373, 39269}, {3455, 18022}, {5094, 10512}, {10415, 44146}, {11605, 18018}, {14618, 17708}, {20883, 37221}
X(46105) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 22151}, {4, 23}, {6, 10317}, {25, 18374}, {30, 16165}, {67, 3}, {76, 37804}, {92, 16568}, {264, 316}, {331, 17088}, {393, 8744}, {403, 12824}, {427, 9019}, {468, 6593}, {512, 42659}, {523, 9517}, {935, 110}, {1969, 20944}, {2052, 37765}, {2157, 48}, {2501, 2492}, {3455, 184}, {5094, 10510}, {8744, 36415}, {8791, 6}, {9076, 1176}, {10415, 895}, {10511, 43697}, {11605, 22}, {14357, 3292}, {14618, 9979}, {16230, 33752}, {16318, 28343}, {17708, 4558}, {17983, 14246}, {18019, 69}, {18022, 40074}, {20883, 18715}, {34897, 394}, {37221, 34055}, {37981, 40949}, {39269, 858}, {43678, 37801}, {44146, 7664}

X(46106) = POLAR CONJUGATE OF X(74)

X(46106) lies on these lines: {2, 216}, {3, 13450}, {4, 4846}, {5, 44732}, {20, 1093}, {23, 107}, {30, 34334}, {53, 37648}, {92, 445}, {94, 16080}, {97, 8794}, {110, 450}, {111, 16081}, {125, 39569}, {133, 1533}, {186, 476}, {250, 36188}, {275, 34545}, {297, 525}, {311, 37638}, {317, 37644}, {323, 648}, {339, 44216}, {340, 37779}, {343, 1232}, {373, 39530}, {401, 23582}, {421, 19128}, {436, 5012}, {459, 5392}, {467, 13567}, {468, 2970}, {470, 8838}, {471, 8836}, {511, 35360}, {847, 3147}, {852, 32428}, {858, 6530}, {1075, 5889}, {1235, 11331}, {1249, 37645}, {1368, 14569}, {1370, 6524}, {1495, 4240}, {1629, 13595}, {1896, 2475}, {1947, 3219}, {1948, 3218}, {1990, 3260}, {1995, 33971}, {2207, 26212}, {2864, 20624}, {2986, 15262}, {3060, 3168}, {3146, 14249}, {3266, 6331}, {3284, 43752}, {3292, 35311}, {3628, 14978}, {4232, 43976}, {4993, 8795}, {5943, 30506}, {6330, 18019}, {6335, 32849}, {6515, 6820}, {6525, 7500}, {6528, 40885}, {6800, 37070}, {7017, 28605}, {8744, 41253}, {8796, 37874}, {8884, 44802}, {9308, 15066}, {9381, 18366}, {10002, 31099}, {11078, 11094}, {11092, 11093}, {11433, 37192}, {13409, 42453}, {14363, 45186}, {14919, 15459}, {14957, 34854}, {15018, 36794}, {15107, 35474}, {15351, 40853}, {16082, 21907}, {17484, 18026}, {17825, 41244}, {17928, 41365}, {18022, 39998}, {18027, 26166}, {18484, 23097}, {25987, 41013}, {26164, 27376}, {26235, 44144}, {31621, 44579}, {32205, 35719}, {34287, 35061}, {36192, 44096}, {37127, 43651}, {37174, 40814}, {37643, 41760}, {40506, 44578}, {40512, 44334}

X(46106) = isogonal conjugate of X(18877)
X(46106) = isotomic conjugate of X(14919)
X(46106) = anticomplement of X(44436)
X(46106) = polar conjugate of X(74)
X(46106) = isotomic conjugate of the isogonal conjugate of X(1990)
X(46106) = polar conjugate of the isotomic conjugate of X(3260)
X(46106) = polar conjugate of the isogonal conjugate of X(30)
X(46106) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19, 34549}, {1294, 4329}, {32646, 7253}, {36043, 850}
X(46106) = X(i)-Ceva conjugate of X(j) for these (i,j): {94, 324}, {264, 34334}, {18817, 14254}, {43752, 30}
X(46106) = X(i)-cross conjugate of X(j) for these (i,j): {30, 3260}, {1637, 4240}, {3163, 14254}, {5664, 648}, {34334, 264}
X(46106) = cevapoint of X(i) and X(j) for these (i,j): {6, 14703}, {30, 1990}, {186, 15262}, {1650, 14391}, {3003, 6000}
X(46106) = crosspoint of X(i) and X(j) for these (i,j): {687, 23582}, {18027, 18817}
X(46106) = crosssum of X(686) and X(3269)
X(46106) = trilinear pole of line {113, 133}
X(46106) = crossdifference of every pair of points on line {184, 39201}
X(46106) = pole wrt polar circle of trilinear polar of X(74) (line X(6)X(647))
X(46106) = perspector of ABC and orthoanticevian triangle of X(3260)
X(46106) = trilinear product X(i)*X(j) for these {i,j}: {2, 1784}, {4, 14206}, {19, 3260}, {30, 92}, {75, 1990}, {158, 11064}, {264, 2173}, {273, 7359}, {318, 6357}, {561, 14581}, {811, 1637}, {823, 9033}, {1099, 16080}, {1495, 1969}, {1577, 4240}, {2166, 14920}, {2631, 6528}, {6335, 11125}, {9406, 18022}, {14400, 18026}
X(46106) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18877}, {3, 2159}, {6, 35200}, {31, 14919}, {48, 74}, {63, 40352}, {163, 14380}, {184, 2349}, {255, 8749}, {326, 40354}, {520, 36131}, {577, 36119}, {603, 15627}, {647, 36034}, {656, 32640}, {810, 44769}, {822, 1304}, {1094, 39380}, {1095, 39381}, {1494, 9247}, {1953, 46090}, {2148, 44715}, {2151, 39377}, {2152, 39378}, {2315, 10419}, {2433, 4575}, {6149, 11079}, {9717, 36060}, {14575, 33805}, {15291, 19614}, {24018, 32715}
X(46106) = barycentric product X(i)*X(j) for these {i,j}: {4, 3260}, {5, 43752}, {30, 264}, {75, 1784}, {76, 1990}, {92, 14206}, {94, 14920}, {300, 6110}, {301, 6111}, {324, 43768}, {331, 7359}, {340, 14254}, {648, 41079}, {811, 36035}, {850, 4240}, {1494, 34334}, {1495, 18022}, {1502, 14581}, {1511, 18817}, {1568, 8795}, {1577, 24001}, {1637, 6331}, {1969, 2173}, {2052, 11064}, {2407, 14618}, {3284, 18027}, {6148, 6344}, {6357, 7017}, {6528, 9033}, {9214, 44146}, {9407, 44161}, {14391, 42405}, {15352, 41077}, {15454, 44138}, {16080, 36789}, {17924, 42716}, {20573, 39176}, {23347, 44173}, {35906, 44132}, {36891, 44145}
X(46106) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 35200}, {2, 14919}, {4, 74}, {5, 44715}, {6, 18877}, {13, 39377}, {14, 39378}, {19, 2159}, {25, 40352}, {30, 3}, {54, 46090}, {92, 2349}, {107, 1304}, {112, 32640}, {113, 13754}, {133, 6000}, {158, 36119}, {162, 36034}, {186, 14385}, {264, 1494}, {281, 15627}, {297, 35910}, {318, 44693}, {393, 8749}, {403, 14264}, {468, 9717}, {523, 14380}, {648, 44769}, {850, 34767}, {1249, 15291}, {1294, 15404}, {1300, 10419}, {1495, 184}, {1511, 22115}, {1514, 10605}, {1568, 5562}, {1636, 32320}, {1637, 647}, {1650, 2972}, {1784, 1}, {1969, 33805}, {1989, 11079}, {1990, 6}, {2052, 16080}, {2173, 48}, {2207, 40354}, {2407, 4558}, {2420, 32661}, {2501, 2433}, {2631, 822}, {2970, 12079}, {3163, 3284}, {3184, 12096}, {3258, 16186}, {3260, 69}, {3284, 577}, {3471, 43704}, {4240, 110}, {5642, 3292}, {5664, 8552}, {6000, 39174}, {6110, 15}, {6111, 16}, {6344, 5627}, {6357, 222}, {6528, 16077}, {6529, 32695}, {6530, 35908}, {6761, 38933}, {6793, 8779}, {7359, 219}, {7687, 34329}, {8749, 40353}, {9033, 520}, {9214, 895}, {9406, 9247}, {9407, 14575}, {9409, 39201}, {11064, 394}, {11080, 39380}, {11085, 39381}, {11125, 1459}, {11251, 5663}, {11589, 14379}, {13202, 21663}, {14206, 63}, {14249, 10152}, {14254, 265}, {14391, 17434}, {14395, 36054}, {14397, 30451}, {14398, 3049}, {14399, 22383}, {14400, 652}, {14401, 1636}, {14581, 32}, {14618, 2394}, {14920, 323}, {15144, 6090}, {15352, 15459}, {15454, 5504}, {15459, 34568}, {16080, 40384}, {16230, 32112}, {16240, 1495}, {16263, 22455}, {17983, 9139}, {18384, 40355}, {18486, 18477}, {18487, 5158}, {18507, 12041}, {18653, 1790}, {20772, 41615}, {23097, 16163}, {23347, 1576}, {24001, 662}, {24019, 36131}, {32713, 32715}, {34104, 34333}, {34170, 38937}, {34297, 8431}, {34334, 30}, {35201, 6149}, {35360, 36831}, {35906, 248}, {35912, 17974}, {36035, 656}, {36298, 36297}, {36299, 36296}, {36417, 40351}, {36789, 11064}, {36891, 43705}, {37943, 3470}, {38605, 6760}, {38956, 11589}, {39176, 50}, {39375, 12028}, {41079, 525}, {41392, 32662}, {41887, 44718}, {41888, 44719}, {42716, 1332}, {42750, 8677}, {43752, 95}, {43768, 97}, {44145, 36875}, {44146, 36890}, {44203, 30209}, {44721, 44727}
X(46106) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 324, 40684}, {2, 2052, 324}, {2, 37766, 14165}, {2, 43988, 6509}, {297, 3580, 14918}, {450, 41204, 110}, {468, 2970, 44145}, {2052, 15466, 2}, {5943, 42400, 30506}, {6331, 44132, 3266}, {6820, 14361, 6515}, {14165, 37765, 37766}

X(46107) = POLAR CONJUGATE OF X(101)

X(46107) lies on these lines: {4, 20295}, {25, 26277}, {27, 649}, {92, 3064}, {273, 3676}, {297, 525}, {469, 3835}, {521, 23683}, {693, 17094}, {1577, 23595}, {3004, 39534}, {3261, 4025}, {3766, 18344}, {4106, 16228}, {4374, 43923}, {4467, 44428}, {6528, 35169}, {6994, 26853}, {7490, 27013}, {14208, 18076}, {17494, 17926}, {17496, 17925}, {17861, 21184}, {18026, 35174}, {21666, 23989}, {24032, 36118}, {25924, 26003}

X(46107) = isogonal conjugate of X(32656)
X(46107) = isotomic conjugate of X(1331)
X(46107) = polar conjugate of X(101)
X(46107) = isotomic conjugate of the isogonal conjugate of X(7649)
X(46107) = polar conjugate of the isotomic conjugate of X(3261)
X(46107) = polar conjugate of the isogonal conjugate of X(514)
X(46107) = pole wrt polar circle of trilinear polar of X(101) (line X(6)X(31))
X(46107) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1305, 4329}, {1751, 34188}
X(46107) = X(264)-Ceva conjugate of X(2973)
X(46107) = X(i)-cross conjugate of X(j) for these (i,j): {514, 3261}, {1111, 273}, {2973, 264}, {3120, 27}, {4077, 693}, {17877, 75}, {21102, 514}, {21108, 7649}, {21666, 2052}, {23752, 1577}, {24006, 17924}
X(46107) = cevapoint of X(i) and X(j) for these (i,j): {514, 7649}, {6586, 8676}, {14618, 24006}, {16732, 42455}, {17924, 44426}, {23595, 23752}
X(46107) = crosspoint of X(286) and X(18026)
X(46107) = crosssum of X(i) and X(j) for these (i,j): {3, 23093}, {228, 1946}
X(46107) = trilinear pole of line {116, 2973}
X(46107) = crossdifference of every pair of points on line {184, 2200}
X(46107) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32656}, {3, 692}, {6, 906}, {9, 32660}, {31, 1331}, {32, 1332}, {37, 32661}, {41, 1813}, {42, 4575}, {48, 101}, {55, 36059}, {59, 1946}, {63, 32739}, {71, 163}, {72, 1576}, {100, 184}, {108, 6056}, {109, 212}, {110, 228}, {112, 3990}, {162, 4055}, {190, 9247}, {213, 4558}, {219, 1415}, {255, 8750}, {560, 4561}, {577, 1783}, {603, 3939}, {604, 4587}, {652, 2149}, {662, 2200}, {668, 14575}, {810, 4570}, {901, 23202}, {905, 23990}, {919, 20752}, {1023, 32659}, {1110, 1459}, {1252, 22383}, {1333, 4574}, {1397, 4571}, {1409, 5546}, {1437, 4557}, {1461, 1802}, {1818, 32666}, {1918, 4592}, {2175, 6516}, {2193, 4559}, {2194, 23067}, {2205, 4563}, {2212, 6517}, {2253, 35182}, {2284, 32658}, {2289, 32674}, {2426, 36056}, {2427, 14578}, {2715, 42702}, {3049, 4567}, {3063, 44717}, {3682, 32676}, {3781, 34069}, {4020, 4628}, {4064, 23995}, {4553, 10547}, {5360, 43754}, {5377, 23225}, {5379, 39201}, {5380, 23200}, {5440, 32719}, {6335, 14585}, {6386, 40373}, {7078, 32652}, {7115, 36054}, {7193, 34067}, {8685, 20753}, {8687, 22074}, {8701, 23201}, {14574, 20336}, {14600, 42717}, {15439, 23207}, {15958, 21807}, {20818, 34080}, {22134, 32653}, {22345, 32736}, {22356, 32665}, {23344, 36058}
X(46107) = barycentric product X(i)*X(j) for these {i,j}: {4, 3261}, {19, 40495}, {27, 850}, {28, 20948}, {75, 17924}, {76, 7649}, {85, 44426}, {86, 14618}, {92, 693}, {158, 15413}, {190, 2973}, {264, 514}, {273, 4391}, {274, 24006}, {276, 21102}, {278, 35519}, {286, 1577}, {308, 21108}, {310, 2501}, {313, 17925}, {318, 24002}, {331, 522}, {513, 1969}, {523, 44129}, {561, 6591}, {648, 21207}, {649, 18022}, {653, 34387}, {658, 21666}, {811, 16732}, {1093, 30805}, {1111, 6335}, {1235, 10566}, {1459, 18027}, {1474, 44173}, {1847, 4397}, {1897, 23989}, {1919, 44161}, {1978, 2969}, {2052, 4025}, {2970, 4610}, {3064, 6063}, {3120, 6331}, {3267, 8747}, {3676, 7017}, {4077, 31623}, {4131, 6521}, {4444, 40717}, {4466, 6528}, {4572, 8735}, {4858, 18026}, {7178, 44130}, {7199, 41013}, {13149, 24026}, {15352, 17216}, {15742, 23100}, {16082, 36038}, {16747, 18070}, {18155, 40149}, {18344, 20567}, {21178, 43678}, {23595, 40422}, {23978, 36118}, {28659, 43923}
X(46107) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 906}, {2, 1331}, {4, 101}, {6, 32656}, {7, 1813}, {8, 4587}, {10, 4574}, {11, 652}, {19, 692}, {25, 32739}, {27, 110}, {28, 163}, {29, 5546}, {34, 1415}, {56, 32660}, {57, 36059}, {58, 32661}, {75, 1332}, {76, 4561}, {81, 4575}, {85, 6516}, {86, 4558}, {92, 100}, {108, 2149}, {158, 1783}, {225, 4559}, {226, 23067}, {244, 22383}, {264, 190}, {273, 651}, {274, 4592}, {278, 109}, {281, 3939}, {286, 662}, {310, 4563}, {312, 4571}, {318, 644}, {331, 664}, {338, 4064}, {348, 6517}, {393, 8750}, {423, 17943}, {512, 2200}, {513, 48}, {514, 3}, {521, 2289}, {522, 219}, {523, 71}, {525, 3682}, {647, 4055}, {648, 4570}, {649, 184}, {650, 212}, {652, 6056}, {653, 59}, {656, 3990}, {661, 228}, {664, 44717}, {667, 9247}, {693, 63}, {811, 4567}, {812, 7193}, {823, 5379}, {824, 3781}, {850, 306}, {876, 2196}, {900, 22356}, {905, 255}, {917, 35182}, {918, 1818}, {1019, 1437}, {1022, 36058}, {1027, 32658}, {1086, 1459}, {1111, 905}, {1118, 32674}, {1119, 1461}, {1235, 4568}, {1459, 577}, {1474, 1576}, {1565, 4091}, {1577, 72}, {1635, 23202}, {1647, 22086}, {1783, 1110}, {1785, 2427}, {1826, 4557}, {1839, 35327}, {1847, 934}, {1861, 2284}, {1870, 1983}, {1886, 2426}, {1897, 1252}, {1919, 14575}, {1969, 668}, {2052, 1897}, {2170, 1946}, {2254, 20752}, {2400, 1815}, {2401, 1795}, {2424, 32657}, {2489, 1918}, {2501, 42}, {2517, 5227}, {2530, 4020}, {2533, 22061}, {2786, 17976}, {2969, 649}, {2970, 4024}, {2973, 514}, {3004, 22097}, {3064, 55}, {3120, 647}, {3122, 3049}, {3125, 810}, {3239, 1260}, {3261, 69}, {3663, 23113}, {3667, 20818}, {3669, 603}, {3676, 222}, {3700, 2318}, {3737, 2193}, {3762, 5440}, {3766, 20769}, {3776, 3784}, {3798, 3167}, {3801, 20727}, {3835, 20760}, {3837, 20785}, {3900, 1802}, {3942, 23224}, {4017, 1409}, {4024, 3690}, {4025, 394}, {4036, 3949}, {4077, 1214}, {4086, 3694}, {4091, 1092}, {4131, 6507}, {4142, 23150}, {4369, 3955}, {4391, 78}, {4397, 3692}, {4425, 23139}, {4444, 295}, {4453, 22128}, {4458, 20741}, {4462, 4855}, {4466, 520}, {4560, 283}, {4581, 2359}, {4608, 1796}, {4750, 3292}, {4785, 23095}, {4791, 3940}, {4801, 4652}, {4815, 4047}, {4823, 3927}, {4858, 521}, {4962, 22147}, {4977, 22054}, {4978, 3916}, {4979, 23201}, {4988, 22080}, {5190, 8676}, {5236, 2283}, {5317, 32676}, {6006, 23073}, {6084, 20780}, {6331, 4600}, {6332, 1259}, {6335, 765}, {6336, 901}, {6544, 22371}, {6545, 3937}, {6548, 1797}, {6590, 7085}, {6591, 31}, {7004, 36054}, {7017, 3699}, {7101, 4578}, {7129, 32652}, {7141, 4103}, {7178, 73}, {7192, 1790}, {7199, 1444}, {7200, 22093}, {7202, 23226}, {7216, 1410}, {7253, 2327}, {7649, 6}, {7658, 22117}, {7661, 22124}, {8714, 22126}, {8735, 663}, {8747, 112}, {8750, 23990}, {8751, 32666}, {8752, 32719}, {8754, 4079}, {8756, 23344}, {10015, 22350}, {10566, 1176}, {11125, 3284}, {11263, 23084}, {13149, 7045}, {14208, 3998}, {14618, 10}, {14775, 2259}, {14837, 7078}, {15413, 326}, {16082, 36037}, {16732, 656}, {16892, 3917}, {17094, 40152}, {17167, 23181}, {17171, 1634}, {17197, 23189}, {17205, 7254}, {17420, 22074}, {17498, 1801}, {17761, 22160}, {17921, 38832}, {17922, 595}, {17924, 1}, {17925, 58}, {17926, 2328}, {17982, 2702}, {18022, 1978}, {18026, 4564}, {18155, 1812}, {18210, 822}, {18344, 41}, {20504, 20728}, {20505, 20730}, {20507, 20731}, {20508, 20732}, {20509, 20733}, {20510, 20734}, {20511, 20735}, {20512, 20736}, {20513, 20737}, {20515, 20738}, {20516, 20740}, {20517, 20739}, {20518, 20742}, {20519, 20743}, {20520, 20744}, {20521, 20745}, {20522, 20746}, {20525, 20747}, {20526, 20748}, {20883, 4553}, {20906, 22370}, {20948, 20336}, {20974, 22388}, {21102, 216}, {21103, 22052}, {21104, 22053}, {21105, 22055}, {21106, 22056}, {21107, 22057}, {21108, 39}, {21109, 14961}, {21110, 20819}, {21111, 22058}, {21112, 22059}, {21113, 22062}, {21114, 22064}, {21115, 22067}, {21116, 22068}, {21117, 22069}, {21118, 22070}, {21119, 22071}, {21120, 22072}, {21121, 22073}, {21122, 22075}, {21123, 20775}, {21124, 22076}, {21125, 22077}, {21126, 22078}, {21127, 22079}, {21128, 22081}, {21129, 22082}, {21130, 22083}, {21131, 20975}, {21132, 7117}, {21133, 22084}, {21134, 3269}, {21135, 22085}, {21136, 22087}, {21137, 22089}, {21138, 22090}, {21139, 22091}, {21140, 22092}, {21141, 22094}, {21142, 22095}, {21143, 22096}, {21144, 2524}, {21145, 22098}, {21146, 22099}, {21172, 15905}, {21173, 22118}, {21174, 22119}, {21175, 22120}, {21176, 22121}, {21178, 20806}, {21179, 22122}, {21180, 22123}, {21181, 22162}, {21182, 22125}, {21183, 22129}, {21184, 22130}, {21185, 22131}, {21186, 22132}, {21187, 22133}, {21188, 3157}, {21189, 22134}, {21190, 22135}, {21191, 20794}, {21192, 22136}, {21193, 22137}, {21194, 22138}, {21195, 20793}, {21196, 22139}, {21197, 22140}, {21198, 22141}, {21199, 22142}, {21200, 22143}, {21201, 22144}, {21202, 22145}, {21203, 22146}, {21204, 22148}, {21205, 22151}, {21206, 22152}, {21207, 525}, {21208, 22154}, {21209, 22156}, {21210, 22157}, {21211, 22158}, {21212, 22161}, {21665, 3234}, {21666, 3239}, {23100, 1565}, {23105, 21046}, {23224, 4100}, {23290, 21011}, {23345, 32659}, {23595, 942}, {23681, 35350}, {23726, 39796}, {23735, 22411}, {23748, 22440}, {23751, 23196}, {23752, 18591}, {23756, 20755}, {23772, 22443}, {23785, 23124}, {23799, 23131}, {23801, 23114}, {23803, 23160}, {23806, 23171}, {23824, 23092}, {23989, 4025}, {24002, 77}, {24006, 37}, {24220, 23161}, {24225, 23146}, {24237, 23187}, {24720, 22163}, {25381, 20797}, {26705, 15378}, {27918, 22384}, {28209, 22357}, {29013, 42463}, {30591, 3958}, {30805, 3964}, {31605, 23144}, {31623, 643}, {32085, 4628}, {32714, 24027}, {34387, 6332}, {34948, 563}, {35518, 3719}, {35519, 345}, {36118, 1262}, {36122, 36039}, {36123, 32641}, {36124, 919}, {36125, 32665}, {36127, 7115}, {36613, 29217}, {37203, 6099}, {37790, 23703}, {38357, 10397}, {38461, 23890}, {38462, 1023}, {39534, 2183}, {40149, 4551}, {40166, 7004}, {40445, 29163}, {40495, 304}, {40573, 15439}, {40627, 23212}, {40703, 42717}, {40717, 3570}, {40836, 36049}, {41013, 1018}, {42067, 1919}, {42069, 657}, {42455, 34591}, {42462, 3270}, {42754, 8677}, {43923, 604}, {43925, 2206}, {43931, 15373}, {43932, 7099}, {43933, 909}, {44129, 99}, {44130, 645}, {44143, 4115}, {44173, 40071}, {44312, 23093}, {44426, 9}, {44428, 2323}, {44721, 30720}, {45674, 23166}

X(46108) = POLAR CONJUGATE OF X(105)

X(46108) lies on these lines: {2, 17916}, {4, 8}, {19, 3729}, {27, 19835}, {29, 4968}, {37, 17913}, {75, 281}, {76, 331}, {107, 2754}, {112, 44330}, {225, 4044}, {239, 1783}, {240, 726}, {273, 1229}, {278, 312}, {297, 525}, {536, 14571}, {664, 45798}, {666, 8751}, {860, 3948}, {1013, 26227}, {1016, 37790}, {1089, 1838}, {1430, 17763}, {1435, 30567}, {1441, 26165}, {1748, 32933}, {1826, 20236}, {1861, 3717}, {1957, 4362}, {2223, 4238}, {2331, 3875}, {3006, 37371}, {3187, 8743}, {3263, 5089}, {3673, 17862}, {3701, 5125}, {3705, 37372}, {3757, 4183}, {3912, 5236}, {4054, 30687}, {4219, 7081}, {4358, 17923}, {4384, 7079}, {5307, 24630}, {6335, 37788}, {6656, 26153}, {7076, 32914}, {7172, 37104}, {7283, 41227}, {7414, 26243}, {7719, 33937}, {7770, 26203}, {7952, 20173}, {8756, 20881}, {13727, 23661}, {14954, 20045}, {16747, 31909}, {17442, 17760}, {17858, 20239}, {17859, 40942}, {17863, 17918}, {17903, 30699}, {17917, 18743}, {18026, 35158}, {18689, 26006}, {20336, 25252}, {20880, 37448}, {23581, 25935}, {24199, 25993}, {31130, 37102}, {31623, 31926}, {32714, 40862}, {32851, 37799}, {43675, 43678}

X(46108) = isogonal conjugate of X(32658)
X(46108) = isotomic conjugate of X(1814)
X(46108) = polar conjugate of X(105)
X(46108) = isotomic conjugate of the isogonal conjugate of X(5089)
X(46108) = polar conjugate of the isotomic conjugate of X(3263)
X(46108) = polar conjugate of the isogonal conjugate of X(518)
X(46108) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {26703, 4329}, {32688, 522}, {36093, 693}
X(46108) = X(264)-Ceva conjugate of X(34337)
X(46108) = X(i)-cross conjugate of X(j) for these (i,j): {518, 3263}, {24290, 4238}, {34337, 264}
X(46108) = cevapoint of X(i) and X(j) for these (i,j): {518, 5089}, {3290, 3827}
X(46108) = trilinear pole of line {120, 20621}
X(46108) = crossdifference of every pair of points on line {184, 22383}
X(46108) = pole wrt polar circle of trilinear polar of X(105) (line X(6)X(513))
X(46108) = perspector of the circumconic through the polar conjugates of PU(46) and PU(54)
X(46108) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32658}, {3, 1438}, {6, 36057}, {31, 1814}, {32, 31637}, {48, 105}, {163, 10099}, {184, 673}, {212, 1462}, {219, 1416}, {222, 2195}, {255, 8751}, {294, 603}, {577, 36124}, {652, 32735}, {884, 1813}, {885, 32660}, {905, 32666}, {906, 1027}, {919, 1459}, {1024, 36059}, {1331, 43929}, {1415, 23696}, {1437, 18785}, {1818, 41934}, {1946, 36146}, {2481, 9247}, {7099, 28071}, {14575, 18031}, {22383, 36086}
X(46108) = barycentric product X(i)*X(j) for these {i,j}: {4, 3263}, {75, 1861}, {76, 5089}, {92, 3912}, {241, 7017}, {264, 518}, {273, 3717}, {281, 40704}, {286, 3932}, {312, 5236}, {318, 9436}, {321, 15149}, {331, 3693}, {561, 2356}, {672, 1969}, {811, 4088}, {850, 4238}, {883, 44426}, {918, 6335}, {1826, 18157}, {1876, 3596}, {2052, 25083}, {2223, 18022}, {2481, 34337}, {3930, 44129}, {6331, 24290}, {9455, 44161}, {17924, 42720}, {18027, 20752}, {22116, 40717}, {30941, 41013}
X(46108) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36057}, {2, 1814}, {4, 105}, {6, 32658}, {19, 1438}, {33, 2195}, {34, 1416}, {75, 31637}, {92, 673}, {108, 32735}, {120, 34381}, {158, 36124}, {241, 222}, {264, 2481}, {278, 1462}, {281, 294}, {318, 14942}, {331, 34018}, {393, 8751}, {518, 3}, {522, 23696}, {523, 10099}, {653, 36146}, {665, 22383}, {672, 48}, {883, 6516}, {918, 905}, {926, 1946}, {1025, 1813}, {1026, 1331}, {1458, 603}, {1783, 919}, {1818, 255}, {1826, 18785}, {1861, 1}, {1876, 56}, {1897, 36086}, {1969, 18031}, {2223, 184}, {2254, 1459}, {2283, 36059}, {2284, 906}, {2340, 212}, {2356, 31}, {2969, 43921}, {3064, 1024}, {3252, 2196}, {3263, 69}, {3286, 1437}, {3675, 3937}, {3693, 219}, {3717, 78}, {3827, 34160}, {3912, 63}, {3930, 71}, {3932, 72}, {4088, 656}, {4238, 110}, {4437, 25083}, {4447, 3955}, {4684, 4652}, {4712, 1818}, {4899, 4855}, {4966, 3916}, {5089, 6}, {5236, 57}, {6184, 20752}, {6335, 666}, {6554, 23601}, {6591, 43929}, {7017, 36796}, {7046, 28071}, {7101, 6559}, {7649, 1027}, {8299, 7193}, {8750, 32666}, {8751, 41934}, {9436, 77}, {9454, 9247}, {9455, 14575}, {10029, 27832}, {14439, 22356}, {15149, 81}, {15344, 15382}, {15742, 5377}, {17435, 7117}, {17755, 20769}, {18026, 927}, {18157, 17206}, {18206, 1790}, {18344, 884}, {20621, 3827}, {20683, 228}, {20752, 577}, {22116, 295}, {23612, 20776}, {24290, 647}, {25083, 394}, {26706, 35185}, {30941, 1444}, {34230, 36058}, {34337, 518}, {34855, 7053}, {36819, 1795}, {37908, 2194}, {39258, 2200}, {40704, 348}, {41013, 13576}, {42071, 2223}, {42341, 22091}, {42720, 1332}, {42758, 8677}, {44426, 885}

X(46109) = POLAR CONJUGATE OF X(106)

X(46109) lies on these lines: {4, 21282}, {27, 19811}, {80, 5081}, {92, 264}, {107, 2760}, {242, 17987}, {281, 17740}, {297, 525}, {318, 6736}, {321, 41883}, {331, 40029}, {1145, 4723}, {1897, 32927}, {1904, 41013}, {2052, 4052}, {2997, 7003}, {3264, 3977}, {3995, 18677}, {4358, 37790}, {6335, 17923}, {6528, 35161}, {14206, 35516}, {17147, 18676}, {17495, 17906}, {17555, 37716}, {17861, 24177}, {21270, 32001}, {40013, 40149}

X(46109) = isogonal conjugate of X(32659)
X(46109) = isotomic conjugate of X(1797)
X(46109) = polar conjugate of X(106)
X(46109) = isotomic conjugate of the isogonal conjugate of X(8756)
X(46109) = polar conjugate of the isotomic conjugate of X(3264)
X(46109) = polar conjugate of the isogonal conjugate of X(519)
X(46109) = X(2370)-anticomplementary conjugate of X(4329)
X(46109) = X(519)-cross conjugate of X(3264)
X(46109) = pole wrt polar circle of trilinear polar of X(106) (line X(6)X(649))
X(46109) = cevapoint of X(i) and X(j) for these (i,j): {519, 8756}, {2390, 8610}
X(46109) = trilinear pole of line {121, 4768}
X(46109) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32659}, {3, 9456}, {6, 36058}, {31, 1797}, {48, 106}, {88, 184}, {219, 1417}, {255, 8752}, {577, 36125}, {603, 2316}, {810, 4591}, {901, 22383}, {903, 9247}, {905, 32719}, {906, 23345}, {1022, 32656}, {1459, 32665}, {2226, 23202}, {3049, 4622}, {5376, 22096}, {5440, 41935}, {14260, 14578}, {14575, 20568}, {23838, 32660}, {32658, 34230}
X(46109) = barycentric product X(i)*X(j) for these {i,j}: {4, 3264}, {44, 1969}, {75, 38462}, {76, 8756}, {92, 4358}, {264, 519}, {273, 4723}, {286, 3992}, {312, 37790}, {313, 37168}, {331, 2325}, {902, 18022}, {1877, 3596}, {2052, 3977}, {3762, 6335}, {3911, 7017}, {3943, 44129}, {4120, 6331}, {4768, 18026}, {6336, 36791}, {6528, 14429}, {9459, 44161}, {17924, 24004}, {18027, 22356}, {30939, 41013}, {40663, 44130}
X(46109) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36058}, {2, 1797}, {4, 106}, {6, 32659}, {19, 9456}, {34, 1417}, {44, 48}, {92, 88}, {158, 36125}, {264, 903}, {281, 2316}, {318, 1320}, {393, 8752}, {519, 3}, {648, 4591}, {678, 23202}, {811, 4622}, {900, 1459}, {902, 184}, {1023, 906}, {1145, 22350}, {1319, 603}, {1635, 22383}, {1639, 652}, {1647, 3937}, {1783, 32665}, {1785, 14260}, {1846, 1457}, {1861, 34230}, {1870, 16944}, {1877, 56}, {1878, 17109}, {1897, 901}, {1969, 20568}, {2052, 6336}, {2251, 9247}, {2325, 219}, {2969, 43922}, {2973, 6549}, {3264, 69}, {3689, 212}, {3762, 905}, {3911, 222}, {3943, 71}, {3977, 394}, {3992, 72}, {4120, 647}, {4169, 4574}, {4358, 63}, {4370, 22356}, {4432, 7193}, {4434, 3955}, {4439, 3781}, {4448, 22384}, {4487, 4855}, {4530, 7117}, {4723, 78}, {4730, 810}, {4738, 5440}, {4742, 4652}, {4759, 23095}, {4768, 521}, {4895, 1946}, {4922, 22093}, {4969, 22054}, {4975, 3916}, {5151, 1149}, {5440, 255}, {6331, 4615}, {6335, 3257}, {6336, 2226}, {6544, 22086}, {7017, 4997}, {7141, 4013}, {7649, 23345}, {8028, 22371}, {8750, 32719}, {8752, 41935}, {8756, 6}, {9459, 14575}, {14407, 3049}, {14418, 36054}, {14429, 520}, {14439, 20752}, {14618, 4049}, {15742, 9268}, {16704, 1790}, {17460, 23205}, {17780, 1331}, {17923, 40215}, {17924, 1022}, {20619, 2390}, {21805, 228}, {22356, 577}, {23344, 32656}, {23703, 36059}, {23757, 8677}, {24004, 1332}, {30731, 4587}, {30939, 1444}, {31011, 1796}, {32704, 35186}, {34587, 23169}, {36123, 10428}, {36791, 3977}, {36944, 1795}, {37168, 58}, {37790, 57}, {38462, 1}, {40101, 15383}, {40663, 73}, {40717, 27922}, {41013, 4674}, {42070, 902}, {44426, 23838}, {45144, 32657}

X(46110) = POLAR CONJUGATE OF X(109)

X(46110) lies on these lines: {4, 21302}, {29, 663}, {92, 514}, {107, 2769}, {158, 21185}, {286, 4406}, {297, 525}, {318, 44448}, {2804, 4397}, {3064, 6332}, {4040, 39585}, {5125, 17072}, {6335, 36804}, {17922, 37770}

X(46110) = isogonal conjugate of X(32660)
X(46110) = isotomic conjugate of X(1813)
X(46110) = polar conjugate of X(109)
X(46110) = isotomic conjugate of the isogonal conjugate of X(3064)
X(46110) = polar conjugate of the isotomic conjugate of X(35519)
X(46110) = polar conjugate of the isogonal conjugate of X(522)
X(46110) = X(41906)-anticomplementary conjugate of X(4329)
X(46110) = X(i)-Ceva conjugate of X(j) for these (i,j): {264, 21666}, {331, 34387}
X(46110) = X(i)-cross conjugate of X(j) for these (i,j): {522, 35519}, {1577, 4391}, {4858, 92}, {21044, 29}, {21666, 264}, {23104, 34387}
X(46110) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32660}, {3, 1415}, {6, 36059}, {31, 1813}, {32, 6516}, {48, 109}, {56, 906}, {57, 32656}, {59, 22383}, {65, 32661}, {73, 163}, {77, 32739}, {101, 603}, {108, 577}, {110, 1409}, {112, 22341}, {184, 651}, {212, 1461}, {222, 692}, {228, 4565}, {255, 32674}, {521, 23979}, {604, 1331}, {652, 24027}, {664, 9247}, {667, 44717}, {1106, 4587}, {1214, 1576}, {1231, 14574}, {1262, 1946}, {1332, 1397}, {1333, 23067}, {1400, 4575}, {1402, 4558}, {1408, 4574}, {1410, 5546}, {1414, 2200}, {1437, 4559}, {1459, 2149}, {1783, 7335}, {1802, 6614}, {1973, 6517}, {2283, 32658}, {2425, 36055}, {3939, 7099}, {4100, 36127}, {4554, 14575}, {6056, 32714}, {6510, 32728}, {7011, 32652}, {7114, 36049}, {7115, 23224}, {7125, 8750}, {8687, 22345}, {14578, 23981}, {14585, 18026}, {14597, 15439}, {20752, 32735}, {22096, 31615}, {22350, 32669}, {23207, 32651}, {23703, 32659}, {32676, 40152}, {40518, 44085}
X(46110) = cevapoint of X(i) and X(j) for these (i,j): {522, 3064}, {1577, 14618}
X(46110) = crosspoint of X(6335) and X(31623)
X(46110) = crosssum of X(1409) and X(22383)
X(46110) = trilinear pole of line {124, 20620}
X(46110) = crossdifference of every pair of points on line {184, 23197}
X(46110) = pole wrt polar circle of trilinear polar of X(109) (line X(6)X(41))
X(46110) = barycentric product X(i)*X(j) for these {i,j}: {4, 35519}, {29, 850}, {33, 40495}, {75, 44426}, {76, 3064}, {92, 4391}, {158, 35518}, {264, 522}, {273, 4397}, {281, 3261}, {286, 4086}, {312, 17924}, {314, 24006}, {318, 693}, {331, 3239}, {333, 14618}, {349, 17926}, {514, 7017}, {523, 44130}, {561, 18344}, {650, 1969}, {652, 18027}, {653, 23978}, {663, 18022}, {664, 21666}, {1172, 20948}, {1577, 31623}, {1896, 14208}, {1897, 34387}, {1978, 8735}, {2052, 6332}, {2299, 44173}, {2501, 28660}, {2973, 3699}, {3267, 8748}, {3596, 7649}, {3700, 44129}, {4572, 42069}, {4858, 6335}, {6331, 21044}, {6591, 28659}, {7020, 17896}, {7101, 24002}, {17925, 30713}, {18026, 24026}, {18155, 41013}, {20566, 44428}, {21207, 36797}
X(46110) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36059}, {2, 1813}, {4, 109}, {6, 32660}, {8, 1331}, {9, 906}, {10, 23067}, {11, 1459}, {19, 1415}, {21, 4575}, {27, 4565}, {29, 110}, {33, 692}, {55, 32656}, {69, 6517}, {75, 6516}, {92, 651}, {108, 24027}, {158, 108}, {190, 44717}, {264, 664}, {273, 934}, {278, 1461}, {281, 101}, {284, 32661}, {286, 1414}, {312, 1332}, {314, 4592}, {318, 100}, {331, 658}, {333, 4558}, {341, 4571}, {346, 4587}, {393, 32674}, {415, 17942}, {513, 603}, {514, 222}, {521, 255}, {522, 3}, {523, 73}, {525, 40152}, {607, 32739}, {650, 48}, {652, 577}, {653, 1262}, {656, 22341}, {661, 1409}, {663, 184}, {693, 77}, {850, 307}, {885, 36057}, {905, 7125}, {1021, 2193}, {1024, 32658}, {1093, 36127}, {1119, 6614}, {1146, 652}, {1172, 163}, {1459, 7335}, {1577, 1214}, {1639, 22356}, {1783, 2149}, {1785, 23981}, {1826, 4559}, {1839, 36075}, {1847, 4617}, {1855, 35326}, {1857, 8750}, {1861, 2283}, {1896, 162}, {1897, 59}, {1969, 4554}, {2052, 653}, {2170, 22383}, {2299, 1576}, {2310, 1946}, {2321, 4574}, {2322, 5546}, {2501, 1400}, {2517, 1038}, {2785, 17975}, {2804, 22350}, {2969, 43924}, {2973, 3676}, {3063, 9247}, {3064, 6}, {3239, 219}, {3261, 348}, {3452, 23113}, {3596, 4561}, {3669, 7099}, {3676, 7053}, {3700, 71}, {3709, 2200}, {3716, 7193}, {3737, 1437}, {3810, 3784}, {3900, 212}, {3904, 22128}, {3907, 3955}, {3910, 22097}, {4017, 1410}, {4024, 2197}, {4025, 1804}, {4036, 201}, {4041, 228}, {4064, 7066}, {4077, 1439}, {4086, 72}, {4124, 22384}, {4130, 1802}, {4140, 22061}, {4147, 20760}, {4163, 1260}, {4391, 63}, {4397, 78}, {4459, 22093}, {4468, 23144}, {4516, 810}, {4521, 20818}, {4522, 3781}, {4530, 22086}, {4543, 22371}, {4560, 1790}, {4768, 5440}, {4811, 4652}, {4858, 905}, {4895, 23202}, {4976, 22054}, {4985, 3916}, {5190, 43060}, {5514, 10397}, {6129, 7114}, {6331, 4620}, {6332, 394}, {6335, 4564}, {6362, 22053}, {6590, 2286}, {6591, 604}, {6608, 22079}, {6615, 22344}, {7003, 36049}, {7004, 23224}, {7008, 32652}, {7017, 190}, {7020, 13138}, {7040, 36082}, {7046, 3939}, {7101, 644}, {7253, 283}, {7649, 56}, {8058, 7078}, {8611, 3990}, {8735, 649}, {8748, 112}, {8755, 2425}, {9581, 35350}, {14331, 15905}, {14400, 3284}, {14432, 3292}, {14618, 226}, {14837, 7011}, {15313, 3215}, {15411, 6514}, {15413, 7183}, {15416, 3719}, {16082, 37136}, {16231, 34040}, {17197, 7254}, {17420, 22345}, {17880, 4131}, {17896, 7013}, {17899, 7364}, {17924, 57}, {17925, 1412}, {17926, 284}, {18022, 4572}, {18026, 7045}, {18155, 1444}, {18344, 31}, {20948, 1231}, {21044, 647}, {21102, 30493}, {21108, 1401}, {21119, 23154}, {21132, 3937}, {21207, 17094}, {21666, 522}, {23104, 2968}, {23615, 3270}, {23710, 23346}, {23752, 39791}, {23838, 36058}, {23978, 6332}, {24002, 7177}, {24006, 65}, {24026, 521}, {25128, 20794}, {26704, 15386}, {26932, 4091}, {28660, 4563}, {31623, 662}, {32674, 23979}, {32706, 35187}, {34387, 4025}, {34589, 23187}, {34591, 36054}, {35015, 8677}, {35196, 15958}, {35518, 326}, {35519, 69}, {36054, 4100}, {36118, 7339}, {36121, 36040}, {36123, 2720}, {36124, 32735}, {36797, 4570}, {37805, 23890}, {38462, 23703}, {39534, 1457}, {40149, 1020}, {40166, 3942}, {40495, 7182}, {40573, 32651}, {40836, 8059}, {41013, 4551}, {42069, 663}, {42337, 22072}, {42455, 7004}, {42462, 7117}, {43728, 1795}, {43923, 1106}, {43925, 16947}, {44129, 4573}, {44130, 99}, {44426, 1}, {44428, 36}, {44721, 43290}

X(46111) = POLAR CONJUGATE OF X(187)

X(46111) lies on these lines: {4, 41911}, {111, 16081}, {264, 2970}, {324, 42008}, {468, 8827}, {671, 2052}, {895, 8795}, {8753, 32581}, {8791, 18818}, {16089, 16092}

X(46111) = isogonal conjugate of X(23200)
X(46111) = isotomic conjugate of X(3292)
X(46111) = polar conjugate of X(187)
X(46111) = isotomic conjugate of the complement of X(41724)
X(46111) = isotomic conjugate of the isogonal conjugate of X(17983)
X(46111) = polar conjugate of the isotomic conjugate of X(18023)
X(46111) = polar conjugate of the isogonal conjugate of X(671)
X(46111) = pole wrt polar circle of trilinear polar of X(187) (line X(351)X(39689))
X(46111) = X(i)-cross conjugate of X(j) for these (i,j): {671, 18023}, {23679, 75}, {44146, 264}
X(46111) = X(i)-isoconjugate of X(j) for these (i,j): {1, 23200}, {3, 922}, {31, 3292}, {48, 187}, {63, 14567}, {184, 896}, {255, 44102}, {351, 4575}, {524, 9247}, {560, 6390}, {810, 5467}, {2200, 16702}, {2642, 32661}, {3049, 23889}, {14210, 14575}, {14419, 32656}, {14908, 42081}, {36060, 39689}
X(46111) = cevapoint of X(i) and X(j) for these (i,j): {2, 41724}, {4, 37765}, {264, 44146}, {671, 17983}
X(46111) = trilinear pole of line {264, 8430}
X(46111) = barycentric product X(i)*X(j) for these {i,j}: {4, 18023}, {76, 17983}, {111, 18022}, {264, 671}, {561, 36128}, {892, 14618}, {895, 18027}, {897, 1969}, {1502, 8753}, {2052, 30786}, {5466, 6331}, {6528, 14977}, {9154, 44132}, {32740, 44161}
X(46111) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3292}, {4, 187}, {6, 23200}, {19, 922}, {25, 14567}, {76, 6390}, {92, 896}, {111, 184}, {264, 524}, {286, 16702}, {297, 9155}, {324, 41586}, {331, 7181}, {393, 44102}, {468, 39689}, {648, 5467}, {671, 3}, {691, 32661}, {811, 23889}, {850, 14417}, {892, 4558}, {895, 577}, {897, 48}, {923, 9247}, {1235, 7813}, {1969, 14210}, {2052, 468}, {2501, 351}, {2970, 1648}, {5380, 906}, {5466, 647}, {5968, 3289}, {6331, 5468}, {6528, 4235}, {7017, 3712}, {8430, 39469}, {8753, 32}, {8754, 21906}, {9139, 18877}, {9154, 248}, {9178, 3049}, {9214, 3284}, {10097, 39201}, {10561, 42659}, {10630, 14908}, {14246, 10317}, {14618, 690}, {14908, 14585}, {14977, 520}, {16080, 9717}, {16081, 5967}, {17924, 14419}, {17983, 6}, {17984, 5026}, {18022, 3266}, {18023, 69}, {18027, 44146}, {18312, 39474}, {18817, 43084}, {18818, 43697}, {19626, 40373}, {23894, 810}, {24006, 2642}, {30786, 394}, {31125, 3917}, {32740, 14575}, {34336, 8030}, {36085, 4575}, {36128, 31}, {36307, 36296}, {36310, 36297}, {37765, 6593}, {37778, 5095}, {40717, 4760}, {41013, 21839}, {44129, 6629}, {44145, 5477}, {44146, 2482}, {44173, 45807}, {44427, 44814}

X(46112) = BARYCENTRIC PRODUCT X(3)*X(15)

X(46112) lies on these lines: {3, 36297}, {6, 3132}, {15, 186}, {16, 5890}, {18, 252}, {50, 11136}, {61, 3567}, {62, 1199}, {184, 418}, {298, 17402}, {323, 40156}, {396, 32461}, {477, 5994}, {1568, 40682}, {3131, 11244}, {3166, 11464}, {3284, 36296}, {5063, 34395}, {5669, 35469}, {6137, 15470}, {8738, 42157}, {10640, 11453}, {11146, 40580}, {16645, 30542}, {21648, 22052}, {26882, 41089}, {34327, 40695}, {36760, 37641}

X(46112) = isogonal conjugate of the isotomic conjugate of X(44718)
X(46112) = isotomic conjugate of the polar conjugate of X(34394)
X(46112) = isogonal conjugate of the polar conjugate of X(15)
X(46112) = X(15)-Ceva conjugate of X(34394)
X(46112) = X(i)-isoconjugate of X(j) for these (i,j): {13, 92}, {19, 300}, {75, 8737}, {158, 40709}, {264, 2153}, {278, 44690}, {471, 2166}, {811, 20578}, {1577, 36306}, {1784, 36308}, {1969, 3457}, {2152, 18817}, {2184, 44702}, {23871, 36129}, {23895, 24006}
X(46112) = crosspoint of X(i) and X(j) for these (i,j): {15, 44718}, {32586, 36296}
X(46112) = crosssum of X(i) and X(j) for these (i,j): {13, 8737}, {470, 472}, {6111, 36299}
X(46112) = crossdifference of every pair of points on line {6116, 14618}
X(46112) = barycentric product X(i)*X(j) for these {i,j}: {3, 15}, {6, 44718}, {14, 22115}, {50, 40710}, {54, 44711}, {63, 2151}, {69, 34394}, {184, 298}, {323, 36297}, {394, 8739}, {470, 577}, {526, 38413}, {603, 44688}, {647, 17402}, {1511, 39378}, {4558, 6137}, {5616, 43704}, {5994, 8552}, {6117, 19210}, {6782, 42065}, {11086, 44719}, {11127, 32586}, {11131, 36296}, {11136, 40711}, {11137, 40712}, {11146, 32585}, {14379, 44700}, {14533, 33529}, {18877, 41887}, {23870, 32661}
X(46112) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 300}, {14, 18817}, {15, 264}, {32, 8737}, {50, 471}, {154, 44702}, {184, 13}, {212, 44690}, {298, 18022}, {418, 44713}, {470, 18027}, {577, 40709}, {1576, 36306}, {2151, 92}, {3049, 20578}, {3458, 6344}, {6137, 14618}, {8739, 2052}, {9247, 2153}, {11136, 472}, {11137, 473}, {14575, 3457}, {14585, 36296}, {14908, 36307}, {17402, 6331}, {18877, 36308}, {19627, 8740}, {22115, 299}, {32661, 23895}, {34394, 4}, {34980, 41997}, {36297, 94}, {38413, 35139}, {40710, 20573}, {44711, 311}, {44718, 76}
X(46112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15, 3165, 186}, {50, 11137, 11136}, {418, 577, 46113}, {11136, 11137, 34394}, {21648, 22052, 32586}

X(46113) = BARYCENTRIC PRODUCT X(3)*X(16)

X(46113) lies on these lines: {3, 36296}, {6, 3131}, {15, 5890}, {16, 186}, {17, 252}, {50, 11134}, {61, 1199}, {62, 3567}, {184, 418}, {299, 17403}, {323, 40157}, {395, 32460}, {477, 5995}, {1568, 40683}, {3132, 11243}, {3165, 11464}, {3284, 36297}, {5063, 34394}, {5668, 35470}, {6138, 15470}, {8737, 42158}, {10639, 11452}, {11145, 40581}, {16644, 30542}, {21647, 22052}, {26882, 41090}, {34328, 40696}, {36759, 37640}

X(46113) = isogonal conjugate of the isotomic conjugate of X(44719)
X(46113) = isotomic conjugate of the polar conjugate of X(34395)
X(46113) = isogonal conjugate of the polar conjugate of X(16)
X(46113) = X(16)-Ceva conjugate of X(34395)
X(46113) = X(i)-isoconjugate of X(j) for these (i,j): {14, 92}, {19, 301}, {75, 8738}, {158, 40710}, {264, 2154}, {278, 44691}, {470, 2166}, {811, 20579}, {1577, 36309}, {1784, 36311}, {1969, 3458}, {2151, 18817}, {2184, 44703}, {23870, 36129}, {23896, 24006}
X(46113) = crosspoint of X(i) and X(j) for these (i,j): {16, 44719}, {32585, 36297}
X(46113) = crosssum of X(i) and X(j) for these (i,j): {14, 8738}, {471, 473}, {6110, 36298}
X(46113) = crossdifference of every pair of points on line {6117, 14618}
X(46113) = barycentric product X(i)*X(j) for these {i,j}: {3, 16}, {6, 44719}, {13, 22115}, {50, 40709}, {54, 44712}, {63, 2152}, {69, 34395}, {184, 299}, {323, 36296}, {394, 8740}, {471, 577}, {526, 38414}, {603, 44689}, {647, 17403}, {1511, 39377}, {4558, 6138}, {5612, 43704}, {5995, 8552}, {6116, 19210}, {6783, 42065}, {11081, 44718}, {11126, 32585}, {11130, 36297}, {11134, 40711}, {11135, 40712}, {11145, 32586}, {14379, 44701}, {14533, 33530}, {18877, 41888}, {23871, 32661}
X(46113) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 301}, {13, 18817}, {16, 264}, {32, 8738}, {50, 470}, {154, 44703}, {184, 14}, {212, 44691}, {299, 18022}, {418, 44714}, {471, 18027}, {577, 40710}, {1576, 36309}, {2152, 92}, {3049, 20579}, {3457, 6344}, {6138, 14618}, {8740, 2052}, {9247, 2154}, {11134, 472}, {11135, 473}, {14575, 3458}, {14585, 36297}, {14908, 36310}, {17403, 6331}, {18877, 36311}, {19627, 8739}, {22115, 298}, {32661, 23896}, {34395, 4}, {34980, 41998}, {36296, 94}, {38414, 35139}, {40709, 20573}, {44712, 311}, {44719, 76}
X(46113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16, 3166, 186}, {50, 11134, 11135}, {418, 577, 46112}, {11134, 11135, 34395}, {21647, 22052, 32585}

X(46114) = X(30)X(113)∩X(140)X(389)

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

X(46114) = {3 X[140] - 2 X[44673], X[323] + 2 X[40685], X[399] + 3 X[44450], 5 X[631] - X[32608], 5 X[632] + X[23061], X[10272] - 4 X[11064], X[11694] + 2 X[13857], 3 X[14156] - X[44673], 3 X[14643] - X[43893], 4 X[16239] - X[41586], 3 X[16532] - 5 X[38794], 3 X[22115] + X[25739], X[25739] - 3 X[37938], X[37496] + 3 X[37943]}

X(46114) lies on these lines: {2, 15038}, {3, 15806}, {5, 37495}, {30, 113}, {110, 43390}, {140, 389}, {323, 10821}, {343, 34331}, {399, 44450}, {511, 44234}, {546, 44686}, {548, 9820}, {631, 32608}, {632, 23061}, {858, 40111}, {1092, 10224}, {2072, 11801}, {3153, 34153}, {3628, 13142}, {5446, 20193}, {5447, 34004}, {5498, 5562}, {5972, 10096}, {6101, 10125}, {6143, 13420}, {6640, 45794}, {6677, 13451}, {9703, 31101}, {10124, 37649}, {10625, 18282}, {10627, 34577}, {11539, 14389}, {11563, 37477}, {11566, 37951}, {11585, 45970}, {13346, 44235}, {14449, 16238}, {14643, 43893}, {15137, 15426}, {15330, 37478}, {16239, 41586}, {16252, 32903}, {16266, 26958}, {16532, 38794}, {18281, 37669}, {18377, 35602}, {20424, 43809}, {22115, 25739}, {23336, 31834}, {32269, 44900}, {34148, 43575}, {37483, 44278}, {37496, 37943}

X(46114) = midpoint of X(i) and X(j) for these {i,j}: {5, 43574}, {858, 40111}, {3153, 34153}, {11563, 37477}, {22115, 37938}
X(46114) = reflection of X(i) in X(j) for these {i,j}: {140, 14156}, {10096, 5972}, {11801, 2072}, {32269, 44900}
X(46114) = X(2148)-complementary conjugate of X(40604)
X(46114) = X(2159)-isoconjugate of X(11538)
X(46114) = barycentric product X(i)*X(j) for these {i,j}: {30, 15108}, {3260, 15109}, {5664, 43965}, {6143, 11064}, {21230, 43768}
X(46114) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 11538}, {3471, 30526}, {6143, 16080}, {9697, 40352}, {15108, 1494}, {15109, 74}, {43965, 39290}
X(46114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {140, 22051, 12006}, {10627, 43839, 34577}

X(46115) = X(2)X(40470)∩X(5)X(35912)

See Tran Quang Hung, Francisco Javier García Capitán and Peter Moses, euclid 3387.

X(46115) lies on these lines: {2, 40470}, {5, 35912}, {30, 39569}, {297, 43768}, {525, 23583}, {3800, 40542}, {11064, 44334}, {15526, 40512}

X(46115) = reflection of X(15526) in X(40512)
X(46115) = X(23616)-cross conjugate of X(648)
X(46115) = X(2159)-isoconjugate of X(45289)
X(46115) = cevapoint of X(i) and X(j) for these (i,j): {868, 9475}, {1650, 3163}, {2454, 2455}
X(46115) = trilinear pole of line {9033, 24981}
X(46115) = barycentric quotient X(30)/X(45289)

This preamble and centers X(46116)-X(46122) were contributed by César Eliud Lozada, November 30, 2021.

Let F₀ be a geometric figure and L₁, L₂, L₃ three distinct lines in an Euclidean plane. Let F₁ be the reflection of F₀ in L₁, F₂ the reflection of F₁ in L₂ and F₃ the reflection of F₂ in L₃. Then F₃ is a reflection of F₀ if, and only if, L₁, L₂, L₃ are concurrent.

The preceeding statement is known as the Three Reflections Theorem. Abundant information on this theorem can be found in the web. As a special reference, see Gunter Weiss, The Three Reflections Theorem Revisited, in this link, in which the theorem is extended to other geometries.

Centers X(46116)-X(46122) refer to tripoles of the final axis of reflection of F₀ and F₃, after succesive reflections of ABC in the indicated concurrent lines and in the order these lines are given.

X(46116) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(2), X(1)X(6), X(1)X(3)

X(46116) lies on these lines: {88, 1358}, {100, 30725}, {3257, 3676}, {3960, 46117}, {10015, 46122}, {43055, 43760}

X(46117) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(3), X(1)X(2), X(1)X(6)

X(46117) lies on these lines: {190, 43050}, {3669, 37143}, {3960, 46116}, {10015, 46121}

X(46117) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}} and {{A, B, C, X(109), X(3669)}}

X(46118) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(2), X(1)X(4), X(1)X(3)

X(46118) lies on these lines: {88, 3942}, {653, 30725}, {905, 3257}, {3960, 46119}, {34234, 43055}, {43050, 46122}

X(46118) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}} and {{A, B, C, X(106), X(1461)}}

X(46119) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(3), X(1)X(2), X(1)X(4)

X(46119) lies on these lines: {88, 16560}, {100, 1769}, {190, 10015}, {1086, 34234}, {3669, 37136}, {3960, 46118}, {33129, 37222}, {43050, 46120}

X(46119) = barycentric quotient X(i)/X(j) for these (i, j): (100, 6790), (1769, 45940)
X(46119) = trilinear quotient X(190)/X(6790)
X(46119) = intersection, other than A, B, C, of circumconics {{A, B, C, X(88), X(100)}} and {{A, B, C, X(278), X(2397)}}
X(46119) = X(649)-isoconjugate-of-X(6790)
X(46119) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (100, 6790), (1769, 45940)

X(46120) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(2), X(1)X(4), X(1)X(6)

X(46121) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(2), X(1)X(6), X(1)X(4)

X(46122) = TRIPOLE OF THE 3rd-REFLECTION-AXIS OF ABC IN LINES X(1)X(4), X(1)X(2), X(1)X(6)

X(46123) = PERSPECTOR OF THIS ELLIPSE: X(2)-LINE CONJUGATE OF THE LINE AT IINFINITY

The center of this ellipse is X(597). The axes are parallel to the asymptotes of the Jerabek hyperbola, and it passes through X(i) for these i: 2, 6, 16482, 44889, 46124, 46125, 46126, 46127, 46128, 46129, 46130, 46131.

X(46124) = X(2)-LINE CONJUGATE OF X(511)

X(46124) lies on these lines: {2, 51}, {4, 38520}, {6, 523}, {182, 4226}, {468, 20977}, {597, 45662}, {868, 5480}, {1649, 44889}, {1976, 35278}, {2396, 18906}, {5108, 11284}, {5201, 37827}, {5468, 5651}, {5969, 9155}, {7417, 34417}, {7698, 23061}, {10753, 41254}, {11007, 21850}, {14223, 14932}, {14694, 20192}, {22735, 33876}, {31670, 36163}

X(46124) = crossdifference of every pair of points on line {511, 3288}
X(46124) = X(i)-line conjugate of X(j) for these (i,j): {2, 511}, {6, 3288}
X(46124) = {X(6),X(1316)}-harmonic conjugate of X(5967)

X(46125) = X(2)-LINE CONJUGATE OF X(514)

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

X(46125) lies on these lines: {2, 514}, {6, 31}, {649, 24484}, {661, 5701}, {1635, 34583}, {2225, 9037}, {2810, 20974}, {31136, 34362}

X(46125) = crossdifference of every pair of points on line {514, 902}
X(46125) = X(i)-line conjugate of X(j) for these (i,j): {2, 514}, {6, 902}

X(46126) = X(2)-LINE CONJUGATE OF X(519)

X(46126) lies on these lines: {1, 2}, {6, 649}, {31, 16493}, {55, 16492}, {100, 8054}, {896, 16467}, {999, 17109}, {1100, 9360}, {1834, 3141}, {2177, 16501}, {2309, 16495}, {2810, 23644}, {3722, 17477}, {4360, 7035}, {4813, 24289}, {14752, 16576}, {17187, 34583}, {24696, 36872}

X(46126) = crosssum of X(1) and X(9458)
X(46126) = crossdifference of every pair of points on line {519, 649}
X(46126) = X(i)-line conjugate of X(j) for these (i,j): {1, 519} (and {X,519) for evey X on X(1)X(2)) , {6, 649}
X(46126) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 43, 17780}, {1, 3216, 6789}, {16493, 23832, 31}

X(46127) = X(2)-LINE CONJUGATE OF X(523)

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

X(46127) = X[3] + 2 X[18114], X[1634] + 2 X[20975], X[1634] - 4 X[34990], X[3001] + 2 X[3003], 2 X[3001] + X[5201], 4 X[3003] - X[5201], 2 X[7668] + X[14570], X[20975] + 2 X[34990]

X(46127) is the diagonal crosspoint of the cyclic quadrilateral X(2)X(15)X(16)X(9213). (Randy Hutson, January 11, 2022)

X(46127) lies on these lines: {2, 523}, {3, 6}, {110, 9142}, {114, 3014}, {237, 8705}, {373, 44114}, {524, 22087}, {549, 45331}, {597, 45662}, {599, 45330}, {868, 18122}, {895, 9145}, {1576, 14060}, {1624, 41670}, {1634, 2854}, {1645, 34811}, {1989, 38224}, {2421, 7998}, {2452, 40879}, {3018, 6036}, {3124, 40283}, {3163, 38737}, {3589, 15000}, {3733, 24500}, {5191, 6593}, {5502, 35259}, {5640, 15329}, {5650, 16186}, {5651, 9717}, {5972, 41359}, {5999, 32224}, {6128, 23698}, {6235, 13531}, {6771, 18776}, {6774, 18777}, {6787, 23099}, {7668, 14570}, {7820, 14357}, {9027, 36212}, {9171, 44814}, {9465, 14898}, {9513, 14380}, {11184, 32216}, {11216, 35302}, {11284, 14685}, {11416, 39231}, {14169, 35329}, {14170, 35330}, {14830, 34319}, {15921, 34235}, {16776, 23635}, {19663, 33237}, {23181, 45237}, {23347, 36176}, {32217, 37916}, {33962, 44468}, {34989, 41221}, {35268, 44127}

X(46127) = midpoint of X(9155) and X(20975)
X(46127) = reflection of X(i) in X(j) for these {i,j}: {1634, 9155}, {9155, 34990}
X(46127) = Brocard circle inverse of X(5467)
X(46127) = psi-transform of X(9138)
X(46127) = X(896)-isoconjugate of X(39450)
X(46127) = crosssum of X(523) and X(15359)
X(46127) = crossdifference of every pair of points on line {187, 523}
X(46127) = X(i)-line conjugate of X(j) for these (i,j): {2, 523}, {3, 187}
X(46127) = barycentric product X(249)*X(15359)
X(46127) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 39450}, {15359, 338}
X(46127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6, 5467}, {3, 1351, 15919}, {39, 21906, 6}, {3001, 3003, 5201}, {5191, 6593, 35357}, {5968, 33927, 34291}, {20975, 34990, 1634}

X(46128) = X(2)-LINE CONJUGATE OF X(525)

X(46128) lies on these lines: {2, 525}, {6, 25}, {22, 2420}, {39, 44889}, {1196, 2088}, {1560, 1562}, {2781, 35325}, {3124, 12099}, {3269, 44467}, {5254, 35235}, {5890, 7418}, {6000, 14580}, {6792, 18950}, {32064, 35902}, {35906, 36178}, {37930, 44415}

X(46128) = crossdifference of every pair of points on line {525, 1495}
X(46128) = X(i)-line conjugate of X(j) for these (i,j): {2, 525}, {6, 1495}

X(46129) = X(2)-LINE CONJUGATE OF X(526)

Barycentrics a^12*b^2 - 6*a^10*b^4 + 11*a^8*b^6 - 7*a^6*b^8 + a^2*b^12 + a^12*c^2 + 4*a^10*b^2*c^2 - 5*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 - 6*a^10*c^4 - 5*a^8*b^2*c^4 + 18*a^6*b^4*c^4 - 9*a^4*b^6*c^4 + 7*a^2*b^8*c^4 - 3*b^10*c^4 + 11*a^8*c^6 - 6*a^6*b^2*c^6 - 9*a^4*b^4*c^6 - 6*a^2*b^6*c^6 + 2*b^8*c^6 - 7*a^6*c^8 + 10*a^4*b^2*c^8 + 7*a^2*b^4*c^8 + 2*b^6*c^8 - 5*a^2*b^2*c^10 - 3*b^4*c^10 + a^2*c^12 + b^2*c^12 : :

X(46129) lies on these lines: {2, 526}, {6, 13}, {524, 36189}, {804, 9144}, {1634, 5642}, {5648, 34383}, {7668, 9140}, {9143, 25051}, {20126, 41330}

X(46129) = midpoint of X(9143) and X(25051)
X(46129) = reflection of X(i) in X(j) for these {i,j}: {1634, 5642}, {9140, 7668}
X(46129) = crossdifference of every pair of points on line {526, 3016}
X(46129) = X(i)-line conjugate of X(j) for these (i,j): {2, 526}, {6, 3016}
X(46129) = {X(6),X(18332)}-harmonic conjugate of X(14559)

X(46130) = X(2)-LINE CONJUGATE OF X(542)

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

X(46130) lies on these lines: {2, 98}, {3, 42743}, {6, 526}, {74, 37991}, {111, 34235}, {246, 2781}, {351, 44889}, {511, 7468}, {804, 1316}, {895, 9513}, {974, 38551}, {1503, 36189}, {1634, 2854}, {3124, 12099}, {5505, 43718}, {9129, 11284}, {11061, 25314}, {14984, 36790}, {20976, 35325}, {25051, 25320}

X(46130) = midpoint of X(3448) and X(25046)
X(46130) = reflection of X(i) in X(j) for these {i,j}: {110, 36213}, {20021, 125}
X(46130) = Brocard-circle inverse of X(5967)
X(46130) = psi-transform of X(7418)
X(46130) = crossdifference of every pair of points on line {542, 3569}
X(46130) = X(i)-line conjugate of X(j) for these (i,j): {2, 542}, {6, 3569}
X(46130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 5622, 1976}, {13414, 13415, 5967}

X(46131) = X(2)-LINE CONJUGATE OF X(690)

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

X(46131) lies on the cubic K793 and these lines: {2, 690}, {6, 110}, {23, 9181}, {2088, 9176}, {4576, 5972}, {7665, 25047}, {9140, 9169}, {9155, 40283}, {9775, 22265}, {10836, 13248}, {14999, 36168}, {15035, 37930}, {20975, 40282}, {31655, 38395}, {38523, 39576}

X(46131) = psi-transform of X(9178)
X(46131) = crossdifference of every pair of points on line {690, 2502}
X(46131) = X(i)-line conjugate of X(j) for these (i,j): {2, 690}, {6, 2502} X(46131) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 9129, 110}, {2502, 6593, 110}

X(46132) = ISOTOMIC CONJUGATE OF X(788)

X(46132) lies on the Steiner circumellipse and these lines: {2, 39347}, {75, 43096}, {99, 789}, {190, 6386}, {292, 18277}, {310, 18827}, {561, 31134}, {666, 5388}, {670, 3888}, {752, 30875}, {794, 4586}, {815, 9063}, {825, 9065}, {870, 3226}, {871, 903}, {985, 18824}, {1492, 4577}, {1502, 43099}, {1920, 7245}, {1978, 4562}, {2887, 14945}, {3225, 40747}, {3227, 43266}, {4645, 14603}, {6327, 40362}, {14621, 18825}, {18826, 40718}, {33514, 34069}

X(46132) = reflection of X(i) in X(j) for these {i,j}: {14945, 2887}, {43095, 2}
X(46132) = isogonal conjugate of X(8630)
X(46132) = isotomic conjugate of X(788)
X(46132) = isotomic conjugate of the isogonal conjugate of X(789)
X(46132) = complement of X(39347)
X(46132) = X(4586)-anticomplementary conjugate of X(39347)
X(46132) = X(i)-cross conjugate of X(j) for these (i,j): {788, 2}, {4441, 31625}, {30639, 334}, {30870, 561}, {30872, 40362}
X(46132) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8630}, {31, 788}, {32, 3250}, {513, 18900}, {560, 1491}, {649, 40728}, {667, 869}, {669, 3736}, {824, 1501}, {984, 1980}, {1919, 2276}, {1924, 40773}, {2205, 4481}, {4486, 18897}, {4522, 41280}, {7104, 45882}, {9006, 40415}, {9426, 30966}, {9454, 29956}, {9456, 14436}, {9468, 30654}, {14598, 30665}, {14599, 30671}, {17415, 38813}, {18894, 23596}, {20979, 40736}
X(46132) = cevapoint of X(i) and X(j) for these (i,j): {2, 788}, {513, 21264}, {561, 30870}, {824, 2887}, {4586, 43289}, {6327, 30872}, {20333, 30665}
X(46132) = trilinear pole of line {2, 561}
X(46132) = barycentric product X(i)*X(j) for these {i,j}: {75, 37133}, {76, 789}, {190, 871}, {561, 4586}, {693, 5388}, {825, 1928}, {870, 1978}, {1492, 1502}, {1921, 41072}, {3721, 9063}, {4602, 40718}, {4609, 40747}, {4613, 6385}, {6386, 14621}, {18891, 37207}, {30664, 44169}, {34069, 40362}
X(46132) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 788}, {6, 8630}, {75, 3250}, {76, 1491}, {100, 40728}, {101, 18900}, {190, 869}, {310, 4481}, {334, 30671}, {519, 14436}, {561, 824}, {646, 4517}, {668, 2276}, {670, 40773}, {752, 14402}, {789, 6}, {799, 3736}, {825, 560}, {870, 649}, {871, 514}, {874, 16514}, {932, 40736}, {985, 1919}, {1492, 32}, {1909, 45882}, {1920, 3805}, {1921, 30665}, {1966, 30654}, {1978, 984}, {2481, 29956}, {3261, 4475}, {3721, 17415}, {3888, 3117}, {3952, 3774}, {4554, 1469}, {4572, 7146}, {4583, 3862}, {4586, 31}, {4602, 30966}, {4613, 213}, {4817, 3248}, {5384, 32739}, {5388, 100}, {6386, 3661}, {9063, 38810}, {14603, 30639}, {14621, 667}, {16584, 9006}, {18891, 4486}, {27801, 4122}, {27853, 3783}, {28659, 4522}, {30664, 1922}, {30670, 7104}, {30874, 33904}, {31625, 3799}, {33946, 3116}, {34069, 1501}, {37133, 1}, {37207, 1911}, {40362, 30870}, {40718, 798}, {40746, 1980}, {40747, 669}, {41072, 292}, {43266, 8027}, {43289, 32664}, {44172, 23596}

X(46133) = ISOTOMIC CONJUGATE OF X(912)

X(46133) lies on the Steiner circumellipse and these lines: {69, 2973}, {92, 190}, {99, 286}, {264, 668}, {273, 664}, {290, 3657}, {317, 18026}, {340, 35156}, {648, 2990}, {913, 4586}, {2966, 32655}, {5081, 35174}

X(46133) = isotomic conjugate of X(912)
X(46133) = polar conjugate of X(8609)
X(46133) = isotomic conjugate of the isogonal conjugate of X(915)
X(46133) = polar conjugate of the isogonal conjugate of X(2990)
X(46133) = X(i)-cross conjugate of X(j) for these (i,j): {912, 2}, {3262, 264}, {4511, 31623}, {44428, 6335}
X(46133) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2252}, {31, 912}, {32, 914}, {48, 8609}, {184, 1737}, {212, 18838}, {810, 3658}
X(46133) = cevapoint of X(i) and X(j) for these (i,j): {2, 912}, {92, 5081}, {525, 3139}, {915, 2990}, {2969, 10015}
X(46133) = trilinear pole of line {2, 17924}
X(46133) = barycentric product X(i)*X(j) for these {i,j}: {75, 37203}, {76, 915}, {264, 2990}, {331, 45393}, {561, 913}, {1969, 36052}, {3261, 36106}, {3657, 6331}, {18022, 32655}, {32698, 40495}
X(46133) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2252}, {2, 912}, {4, 8609}, {75, 914}, {92, 1737}, {278, 18838}, {648, 3658}, {913, 31}, {915, 6}, {2990, 3}, {3657, 647}, {6099, 906}, {10015, 42769}, {15381, 14578}, {16082, 14266}, {17923, 11570}, {32655, 184}, {32698, 692}, {36052, 48}, {36106, 101}, {37203, 1}, {37790, 12832}, {37805, 12831}, {45393, 219}

X(46134) = ISOTOMIC CONJUGATE OF X(924)

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

X(46134) lies on the Steiner circumellipse and these lines: {2, 39013}, {68, 290}, {76, 847}, {91, 18827}, {99, 925}, {316, 5962}, {648, 30450}, {671, 5392}, {850, 18878}, {1236, 5641}, {1494, 14615}, {2165, 3228}, {2966, 4611}, {4577, 32734}, {4586, 36145}, {6331, 18831}, {7763, 34853}, {8920, 43664}, {11185, 14593}, {14616, 20571}, {20573, 34385}

X(46134) = isogonal conjugate of X(34952)
X(46134) = isotomic conjugate of X(924)
X(46134) = anticomplement of X(39013)
X(46134) = polar conjugate of X(6753)
X(46134) = isotomic conjugate of the isogonal conjugate of X(925)
X(46134) = isotomic conjugate of the polar conjugate of X(30450)
X(46134) = X(2)-cross conjugate of polar conjugate of X(6754)
X(46134) = X(i)-cross conjugate of X(j) for these (i,j): {924, 2}, {925, 30450}, {4558, 6331}, {6334, 40832}, {11412, 249}, {14618, 76}, {25739, 39295}, {37444, 23582}, {44128, 18020}, {45780, 18879}, {45794, 4590}
X(46134) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34952}, {19, 30451}, {24, 810}, {31, 924}, {42, 34948}, {47, 512}, {48, 6753}, {560, 6563}, {563, 2501}, {571, 661}, {656, 44077}, {669, 44179}, {798, 1993}, {822, 8745}, {1748, 3049}, {1919, 42700}, {1924, 7763}, {2159, 14397}, {2180, 2623}, {4079, 18605}, {14574, 17881}, {36145, 39013}
X(46134) = cevapoint of X(i) and X(j) for these (i,j): {2, 924}, {69, 850}, {343, 523}, {512, 7746}, {525, 11585}, {847, 14618}
X(46134) = trilinear pole of line {2, 311}
X(46134) = barycentric product X(i)*X(j) for these {i,j}: {68, 6331}, {69, 30450}, {76, 925}, {91, 799}, {99, 5392}, {561, 36145}, {648, 20563}, {662, 20571}, {670, 2165}, {847, 4563}, {1502, 32734}, {14570, 34385}, {35139, 37802}
X(46134) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 924}, {3, 30451}, {4, 6753}, {6, 34952}, {30, 14397}, {68, 647}, {76, 6563}, {81, 34948}, {91, 661}, {94, 43088}, {96, 2623}, {99, 1993}, {107, 8745}, {110, 571}, {112, 44077}, {317, 15423}, {323, 44808}, {648, 24}, {662, 47}, {668, 42700}, {670, 7763}, {799, 44179}, {811, 1748}, {847, 2501}, {924, 39013}, {925, 6}, {1820, 810}, {2165, 512}, {2351, 3049}, {2617, 2180}, {4558, 1147}, {4563, 9723}, {4575, 563}, {5392, 523}, {6331, 317}, {6528, 11547}, {6753, 6754}, {14570, 52}, {14593, 2489}, {14618, 136}, {16391, 32320}, {18020, 41679}, {20563, 525}, {20571, 1577}, {20948, 17881}, {30450, 4}, {32734, 32}, {34385, 15412}, {35139, 18883}, {35360, 14576}, {36145, 31}, {37802, 526}, {38342, 14111}, {39289, 39184}, {39416, 39109}, {43187, 31635}, {44174, 32661}

X(46135) = ISOTOMIC CONJUGATE OF X(926)

X(46135) lies on the Steiner circumellipse and these lines: {2, 39014}, {76, 35158}, {85, 35167}, {99, 927}, {190, 3261}, {349, 35163}, {664, 4449}, {668, 40495}, {885, 14727}, {889, 43930}, {1121, 18031}, {1416, 18824}, {1441, 35152}, {1462, 18825}, {2481, 18033}, {3227, 34018}, {4554, 32041}, {4577, 32735}, {4586, 36146}, {6063, 18821}, {6606, 36802}, {18025, 35517}

X(46135) = isogonal conjugate of X(8638)
X(46135) = isotomic conjugate of X(926)
X(46135) = isotomic conjugate of the isogonal conjugate of X(927)
X(46135) = anticomplement of X(39014)
X(46135) = X(34085)-anticomplementary conjugate of X(14732)
X(46135) = X(i)-cross conjugate of X(j) for these (i,j): {883, 4554}, {926, 2}, {2398, 31624}, {3766, 85}, {20347, 1275}, {20556, 46102}, {43930, 34018}
X(46135) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8638}, {31, 926}, {33, 23225}, {41, 665}, {522, 9455}, {650, 9454}, {663, 2223}, {667, 2340}, {672, 3063}, {810, 37908}, {884, 42079}, {918, 9447}, {1024, 39686}, {1458, 8641}, {1919, 3693}, {1946, 2356}, {1980, 3717}, {2175, 2254}, {7252, 39258}, {15615, 36086}, {17435, 32739}, {36146, 39014}
X(46135) = cevapoint of X(i) and X(j) for these (i,j): {2, 926}, {518, 4885}, {522, 20335}, {693, 40704}, {883, 4554}, {918, 2886}, {3261, 35517}, {3900, 34852}, {34018, 43930}
X(46135) = trilinear pole of line {2, 4554}
X(46135) = barycentric product X(i)*X(j) for these {i,j}: {7, 36803}, {75, 34085}, {76, 927}, {561, 36146}, {664, 18031}, {666, 6063}, {668, 34018}, {673, 4572}, {919, 41283}, {1462, 6386}, {1502, 32735}, {2481, 4554}, {3261, 39293}, {4569, 36796}, {20567, 36086}, {31625, 43930}
X(46135) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 926}, {6, 8638}, {7, 665}, {85, 2254}, {105, 3063}, {109, 9454}, {190, 2340}, {222, 23225}, {294, 8641}, {349, 4088}, {528, 14411}, {648, 37908}, {651, 2223}, {653, 2356}, {658, 1458}, {664, 672}, {665, 15615}, {666, 55}, {668, 3693}, {673, 663}, {693, 17435}, {883, 6184}, {885, 14936}, {919, 2175}, {926, 39014}, {927, 6}, {1025, 42079}, {1275, 2283}, {1415, 9455}, {1416, 1919}, {1441, 24290}, {1462, 667}, {1814, 1946}, {1978, 3717}, {2283, 39686}, {2481, 650}, {4551, 39258}, {4552, 20683}, {4554, 518}, {4569, 241}, {4572, 3912}, {4573, 3286}, {4624, 14626}, {4625, 18206}, {4998, 2284}, {6063, 918}, {6185, 884}, {6516, 20752}, {6559, 4105}, {10015, 42771}, {13149, 1876}, {13576, 3709}, {14625, 8653}, {14942, 657}, {18026, 5089}, {18031, 522}, {24002, 3675}, {28132, 3022}, {31637, 652}, {32666, 9447}, {32735, 32}, {34018, 513}, {34085, 1}, {35333, 40972}, {36086, 41}, {36146, 31}, {36796, 3900}, {36802, 220}, {36803, 8}, {36838, 34855}, {39293, 101}, {40704, 3126}, {43042, 35505}, {43930, 1015}

X(46136) = ISOTOMIC CONJUGATE OF X(952)

X(4613) lies on the Steiner circumellipse and these lines: {69, 4555}, {75, 35174}, {99, 953}, {190, 908}, {320, 664}, {648, 16704}, {668, 3262}, {693, 18816}, {903, 4025}, {2481, 46041}, {2861, 35011}, {3663, 35169}, {4597, 5088}, {14616, 18155}, {35157, 42697}

X(46136) = isotomic conjugate of X(952)
X(46136) = isotomic conjugate of the isogonal conjugate of X(953)
X(46136) = X(952)-cross conjugate of X(2)
X(46136) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2265}, {31, 952}, {41, 43043}, {1110, 6075}
X(46136) = cevapoint of X(i) and X(j) for these (i,j): {2, 952}, {8, 30566}
X(46136) = trilinear pole of line {2, 3904}
X(46136) = barycentric product X(i)*X(j) for these {i,j}: {76, 953}, {4554, 46041}
X(46136) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2265}, {2, 952}, {7, 43043}, {953, 6}, {1086, 6075}, {10015, 35013}, {26611, 6073}, {35011, 32641}, {43043, 3319}, {46041, 650}

X(46137) = ISOTOMIC CONJUGATE OF X(971)

X(46137) lies on the Steiner circumellipse and these lines: {8, 18026}, {69, 4569}, {78, 664}, {85, 271}, {99, 972}, {190, 322}, {648, 2287}, {666, 40863}, {668, 1265}, {1809, 30806}, {3262, 35157}, {7358, 13149}

X(46137) = isotomic conjugate of X(971)
X(46137) = isotomic conjugate of the isogonal conjugate of X(972)
X(46137) = X(971)-cross conjugate of X(2)
X(46137) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2272}, {31, 971}, {41, 43044}
X(46137) = cevapoint of X(i) and X(j) for these (i,j): {2, 971}, {8, 30807}
X(46137) = trilinear pole of line {2, 17896}
X(46137) = barycentric product X(76)*X(972)
X(46137) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2272}, {2, 971}, {7, 43044}, {972, 6}, {10015, 42772}, {37780, 28344}

X(46138) = ISOTOMIC CONJUGATE OF X(1154)

X(46138) lies on the Steiner circumellipse and these lines: {94, 275}, {95, 99}, {264, 18831}, {265, 6528}, {300, 32036}, {301, 32037}, {338, 18315}, {664, 20565}, {670, 34384}, {1989, 42300}, {2966, 11077}, {4577, 39287}, {14859, 35139}, {16077, 43752}, {20573, 34385}, {33513, 39286}

X(46138) = isotomic conjugate of X(1154)
X(46138) = polar conjugate of X(11062)
X(46138) = isotomic conjugate of the isogonal conjugate of X(1141)
X(46138) = X(i)-cross conjugate of X(j) for these (i,j): {3, 40427}, {526, 18315}, {1154, 2}, {37779, 31617}, {41079, 42405}, {43768, 276}
X(46138) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2290}, {31, 1154}, {48, 11062}, {50, 1953}, {51, 6149}, {163, 2081}, {323, 2179}, {560, 1273}, {1625, 2624}, {2181, 22115}, {2617, 14270}, {9247, 14918}, {14213, 19627}, {34397, 44706}
X(46138) = cevapoint of X(i) and X(j) for these (i,j): {2, 1154}, {94, 265}, {264, 43752}, {338, 526}
X(46138) = trilinear pole of line {2, 2413}
X(46138) = barycentric product X(i)*X(j) for these {i,j}: {54, 20573}, {76, 1141}, {94, 95}, {97, 18817}, {265, 276}, {275, 328}, {1989, 34384}, {6344, 34386}, {7799, 14859}, {11077, 18022}, {14592, 18831}, {15412, 35139}, {18883, 34385}, {42405, 43083}
X(46138) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2290}, {2, 1154}, {4, 11062}, {54, 50}, {76, 1273}, {94, 5}, {95, 323}, {97, 22115}, {264, 14918}, {265, 216}, {275, 186}, {276, 340}, {300, 33530}, {301, 33529}, {328, 343}, {476, 1625}, {523, 2081}, {850, 41078}, {930, 2439}, {933, 14591}, {1141, 6}, {1989, 51}, {2166, 1953}, {2167, 6149}, {2413, 1510}, {2616, 2624}, {2623, 14270}, {4993, 3581}, {6344, 53}, {8795, 14165}, {8882, 34397}, {8901, 2088}, {10412, 12077}, {11060, 40981}, {11077, 184}, {14582, 15451}, {14592, 6368}, {14859, 1989}, {15412, 526}, {18359, 35194}, {18384, 3199}, {18817, 324}, {18831, 14590}, {18883, 52}, {20573, 311}, {30529, 143}, {32680, 2617}, {34384, 7799}, {34385, 37802}, {35139, 14570}, {39277, 40214}, {39290, 36831}, {40709, 44712}, {40710, 44711}, {43083, 17434}, {43084, 41586}, {43752, 14920}, {43768, 1511}

X(46139) = ISOTOMIC CONJUGATE OF X(1510)

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

X(46139) lies on the Steiner circumellipse and these lines: {2, 39018}, {76, 25043}, {93, 1235}, {99, 930}, {252, 1078}, {290, 3519}, {311, 25148}, {316, 19552}, {648, 38342}, {671, 11140}, {2962, 18827}, {2963, 3228}, {4577, 32737}, {4586, 36148}, {7750, 35888}, {7769, 21975}, {10411, 18831}, {11117, 34390}, {11118, 34389}

X(46139) = isogonal conjugate of anticomplement of X(39512)
X(46139) = isogonal conjugate of circumcircle pole of Napoleon axis
X(46139) = isotomic conjugate of X(1510)
X(46139) = isotomic conjugate of the isogonal conjugate of X(930)
X(46139) = isotomic conjugate of the polar conjugate of X(38342)
X(46139) = anticomplement of X(39018)
X(46139) = X(i)-cross conjugate of X(j) for these (i,j): {930, 38342}, {1510, 2}, {6101, 249}, {18314, 76}
X(46139) = X(i)-isoconjugate of X(j) for these (i,j): {31, 1510}, {512, 2964}, {560, 41298}, {661, 2965}, {798, 1994}, {810, 3518}, {1096, 37084}, {1924, 7769}, {36148, 39018}
X(46139) = cevapoint of X(i) and X(j) for these (i,j): {2, 1510}, {523, 37636}, {525, 37452}, {635, 23873}, {636, 23872}, {850, 1232}, {1273, 45790}, {18314, 25043}
X(46139) = trilinear pole of line {2, 1225}
X(46139) = barycentric product X(i)*X(j) for these {i,j}: {69, 38342}, {76, 930}, {93, 4563}, {99, 11140}, {561, 36148}, {670, 2963}, {799, 2962}, {1502, 32737}, {3519, 6331}, {4558, 20572}, {32036, 34390}, {32037, 34389}
X(46139) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 1510}, {76, 41298}, {93, 2501}, {99, 1994}, {110, 2965}, {252, 2623}, {311, 20577}, {323, 44809}, {394, 37084}, {648, 3518}, {662, 2964}, {670, 7769}, {930, 6}, {1510, 39018}, {2962, 661}, {2963, 512}, {3519, 647}, {4558, 49}, {4563, 44180}, {6331, 32002}, {11140, 523}, {14111, 6753}, {14570, 143}, {18314, 137}, {18315, 25044}, {20572, 14618}, {25043, 12077}, {32036, 62}, {32037, 61}, {32737, 32}, {34389, 23873}, {34390, 23872}, {35139, 30529}, {35360, 14577}, {36148, 31}, {38342, 4}, {41677, 6152}

X(46140) = ISOTOMIC CONJUGATE OF X(2393)

X(46140) lies on the Steiner circumellipse and these lines: {4, 40421}, {22, 99}, {76, 648}, {190, 4456}, {315, 670}, {316, 11605}, {668, 4463}, {892, 1236}, {1177, 4577}, {2966, 11610}, {3267, 10718}, {6528, 11185}, {14615, 35179}, {16084, 18829}, {18831, 34384}, {33769, 35138}, {34360, 36793}

X(46140) = isotomic conjugate of X(2393)
X(46140) = polar conjugate of X(14580)
X(46140) = isotomic conjugate of the isogonal conjugate of X(2373)
X(46140) = X(i)-cross conjugate of X(j) for these (i,j): {23, 308}, {2393, 2}, {18019, 18023}, {44146, 76}
X(46140) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2393}, {32, 18669}, {48, 14580}, {560, 858}, {1236, 1917}, {1501, 20884}, {1973, 14961}, {2205, 17172}, {5523, 9247}, {32676, 42665}
X(46140) = cevapoint of X(i) and X(j) for these (i,j): {2, 2393}, {69, 3266}, {76, 316}, {35522, 36793}
X(46140) = trilinear pole of line {2, 2485}
X(46140) = barycentric product X(i)*X(j) for these {i,j}: {75, 37220}, {76, 2373}, {1177, 1502}, {18022, 18876}, {18024, 36823}
X(46140) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2393}, {4, 14580}, {69, 14961}, {75, 18669}, {76, 858}, {264, 5523}, {310, 17172}, {313, 21017}, {525, 42665}, {561, 20884}, {895, 34158}, {1177, 32}, {1502, 1236}, {2373, 6}, {3261, 21109}, {3266, 5181}, {9464, 19510}, {10422, 32740}, {18876, 184}, {36095, 32676}, {36823, 237}, {37220, 1}, {37765, 20410}, {41511, 14908}, {44146, 1560}, {46104, 21459}

X(46141) = ISOTOMIC CONJUGATE OF X(2771)

X(4613) lies on the Steiner circumellipse and these lines: {69, 35156}, {99, 2687}, {190, 14206}, {286, 16077}, {314, 35139}, {316, 39991}, {319, 35174}, {340, 18026}, {648, 37783}, {664, 17791}, {668, 3260}, {693, 1494}, {850, 18816}, {2481, 14224}

X(46141) = isotomic conjugate of X(2771)
X(46141) = isotomic conjugate of the isogonal conjugate of X(2687)
X(46141) = X(2771)-cross conjugate of X(2)
X(46141) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2771}, {810, 37966}
X(46141) = cevapoint of X(2) and X(2771)
X(46141) = barycentric product X(i)*X(j) for these {i,j}: {76, 2687}, {4554, 14224}
X(46141) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2771}, {648, 37966}, {2687, 6}, {14224, 650}, {39991, 8609}

X(46142) = ISOTOMIC CONJUGATE OF X(2782)

X(46142) lies on the Steiner circumellipse and these lines: {6, 2966}, {69, 18829}, {99, 511}, {183, 892}, {232, 385}, {290, 523}, {317, 39359}, {325, 670}, {671, 8430}, {1494, 32112}, {4019, 4562}, {4577, 39093}, {4580, 14970}, {5641, 23350}, {6528, 6530}, {10313, 39097}, {14356, 35139}, {16077, 35908}, {18831, 19189}, {20423, 30226}, {20975, 36897}, {38987, 43187}, {40801, 41074}

X(46142) = isotomic conjugate of X(2782)
X(46142) = isotomic conjugate of the isogonal conjugate of X(2698)
X(46142) = X(2782)-cross conjugate of X(2)
X(46142) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2782}, {1580, 16068}, {6071, 24041}
X(46142) = cevapoint of X(2) and X(2782)
X(46142) = trilinear pole of line {2, 3569}
X(46142) = Steiner-circumellipse-X(6)-antipode of X(2966)
X(46142) = barycentric product X(i)*X(j) for these {i,j}: {76, 2698}, {99, 46040}, {1916, 16069}, {8781, 46039}
X(46142) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2782}, {694, 16068}, {2698, 6}, {3124, 6071}, {16069, 385}, {36790, 6072}, {46039, 230}, {46040, 523}

X(46143) = ISOTOMIC CONJUGATE OF X(2789)

X(46143) lies on the Steiner circumellipse and these lines: {69, 35153}, {99, 2705}, {183, 35165}, {190, 14321}, {290, 3264}, {325, 903}, {668, 4404}, {671, 17132}, {3226, 39099}, {9487, 31144}, {14829, 35155}, {35150, 37668}

X(46143) = isotomic conjugate of X(2789)
X(46143) = isotomic conjugate of the isogonal conjugate of X(2705)
X(46143) = X(2789)-cross conjugate of X(2)
X(46143) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2789}, {667, 37764}, {798, 37792}, {4394, 17967}, {8643, 17958}
X(46143) = cevapoint of X(i) and X(j) for these (i,j): {2, 2789}, {8, 45661}
X(46143) = trilinear pole of line {2, 15903}
X(46143) = barycentric product X(i)*X(j) for these {i,j}: {76, 2705}, {99, 34899}
X(46143) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2789}, {99, 37792}, {190, 37764}, {1293, 17967}, {2705, 6}, {27834, 17958}, {34899, 523}

X(46144) = ISOTOMIC CONJUGATE OF X(2793)

X(46144) lies on the Steiner circumellipse and these lines: {2, 9487}, {69, 18823}, {99, 1499}, {183, 35146}, {290, 3266}, {325, 671}, {523, 35179}, {648, 9182}, {892, 2396}, {2418, 43674}, {2966, 5468}, {3228, 39099}, {4590, 35138}, {5641, 37668}, {6082, 9123}, {7840, 11162}, {17952, 22110}, {18829, 34203}, {33799, 42367}

X(46144) = reflection of X(i) in X(j) for these {i,j}: {9487, 2}, {17952, 22110}
X(46144) = isogonal conjugate of X(9135)
X(46144) = isotomic conjugate of X(2793)
X(46144) = isotomic conjugate of the isogonal conjugate of X(2709)
X(46144) = X(i)-cross conjugate of X(j) for these (i,j): {2793, 2}, {7840, 4590}, {34246, 5503}, {39905, 76}
X(46144) = X(i)-isoconjugate of X(j) for these (i,j): {1, 9135}, {31, 2793}, {661, 2030}, {798, 22329}, {8644, 17959}, {17999, 36277}
X(46144) = cevapoint of X(i) and X(j) for these (i,j): {2, 2793}, {523, 22110}, {5503, 34246}
X(46144) = trilinear pole of line {2, 5503}
X(46144) = barycentric product X(i)*X(j) for these {i,j}: {76, 2709}, {99, 5503}, {4590, 34246}
X(46144) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2793}, {6, 9135}, {99, 22329}, {110, 2030}, {1296, 17968}, {2709, 6}, {4590, 34245}, {5468, 18800}, {5485, 18012}, {5503, 523}, {6082, 18775}, {11163, 14327}, {21448, 17999}, {34246, 115}, {35179, 17952}, {37216, 17959}

X(46145) = ISOTOMIC CONJUGATE OF X(2794)

X(46145) lies on the Steiner circumellipse and these lines: {4, 46096}, {69, 2966}, {99, 1503}, {290, 3267}, {325, 648}, {393, 35088}, {523, 35140}, {670, 30737}, {892, 37668}, {4577, 21458}, {6528, 44132}, {15526, 41932}, {16077, 32815}, {35139, 43089}, {40824, 41074}

X(46145) = isotomic conjugate of X(2794)
X(46145) = isotomic conjugate of the isogonal conjugate of X(2710)
X(46145) = X(2794)-cross conjugate of X(2)
X(46145) = X(31)-isoconjugate of X(2794)
X(46145) = cevapoint of X(2) and X(2794)
X(46145) = trilinear pole of line {2, 6333}
X(46145) = barycentric product X(76)*X(2710)
X(46145) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2794}, {287, 41175}, {2710, 6}

X(46146) = (name pending)

X(46147) = CROSSPOINT OF X(74) AND X(1494)

X(46147) lies on these lines: {2, 25045}, {3, 74}, {39, 35325}, {67, 9003}, {262, 5094}, {305, 670}, {660, 2349}, {694, 2433}, {858, 12079}, {1304, 21284}, {1634, 3917}, {2781, 44889}, {3933, 4576}, {7495, 16243}, {7574, 34150}, {8749, 39951}, {9515, 40351}, {10152, 12173}, {14424, 20021}, {16063, 36875}

X(46147) = complement of X(25045)
X(46147) = X(32640)-Ceva conjugate of X(14380)
X(46147) = X(i)-isoconjugate of X(j) for these (i,j): {30, 82}, {83, 2173}, {251, 14206}, {308, 9406}, {827, 36035}, {1176, 1784}, {1495, 3112}, {1637, 4599}, {1990, 34055}, {2420, 18070}, {2631, 42396}, {3405, 35906}, {4593, 14398}, {9407, 18833}, {18098, 18653}, {34072, 41079}
X(46147) = crosspoint of X(74) and X(1494)
X(46147) = crosssum of X(30) and X(1495)
X(46147) = barycentric product X(i)*X(j) for these {i,j}: {38, 2349}, {39, 1494}, {74, 141}, {427, 14919}, {826, 44769}, {1235, 18877}, {1304, 2525}, {1634, 2394}, {1930, 2159}, {1964, 33805}, {2433, 4576}, {3665, 15627}, {3917, 16080}, {3933, 8749}, {7813, 9139}, {8024, 40352}, {9717, 31125}, {14380, 41676}, {20021, 35910}, {20883, 35200}, {23285, 32640}, {34767, 35325}
X(46147) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 14206}, {39, 30}, {74, 83}, {141, 3260}, {427, 46106}, {688, 14398}, {826, 41079}, {1304, 42396}, {1401, 6357}, {1494, 308}, {1634, 2407}, {1843, 1990}, {1923, 9406}, {1964, 2173}, {2159, 82}, {2349, 3112}, {3005, 1637}, {3051, 1495}, {3688, 7359}, {3917, 11064}, {4553, 42716}, {8061, 36035}, {8749, 32085}, {14380, 4580}, {14919, 1799}, {16030, 43768}, {16080, 46104}, {17187, 18653}, {17442, 1784}, {18877, 1176}, {20775, 3284}, {21123, 11125}, {27369, 14581}, {32640, 827}, {33805, 18833}, {35200, 34055}, {35325, 4240}, {35910, 20022}, {36034, 4599}, {40352, 251}, {41331, 9407}, {44769, 4577}
X(46147) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 14919, 40352}, {14919, 40352, 9717}

X(46148) = CROSSPOINT OF X(101) AND X(190)

X(46148) lies on these lines: {1, 38346}, {2, 25049}, {6, 8054}, {9, 30942}, {37, 18191}, {38, 17456}, {42, 694}, {67, 71}, {100, 649}, {101, 110}, {190, 670}, {513, 35310}, {518, 2225}, {672, 20785}, {896, 39258}, {1018, 4427}, {1755, 3930}, {2308, 28643}, {2350, 32913}, {2810, 20974}, {3219, 6651}, {3231, 21830}, {3404, 15523}, {3508, 17763}, {3588, 5279}, {3730, 17230}, {3835, 27134}, {3909, 7239}, {3937, 6184}, {3938, 20665}, {4020, 33299}, {4379, 4554}, {4553, 35309}, {4557, 35326}, {4568, 4576}, {4584, 4610}, {4600, 4603}, {4621, 35009}, {5364, 32912}, {6377, 46126}, {7075, 32925}, {8620, 21760}, {9026, 43046}, {15487, 20588}, {16550, 21382}, {17135, 21369}, {17187, 21814}, {17449, 20459}, {20295, 26795}, {20372, 29824}, {21362, 35341}, {25924, 26692}, {28743, 30835}

X(46148) = reflection of X(i) in X(j) for these {i,j}: {20974, 23988}, {25049, 44312}, {46158, 141}
X(46148) = isogonal conjugate of X(10566)
X(46148) = complement of X(25049)
X(46148) = anticomplement of X(44312)
X(46148) = isogonal conjugate of the isotomic conjugate of X(4568)
X(46148) = X(i)-Ceva conjugate of X(j) for these (i,j): {190, 4568}, {4600, 42}, {4603, 100}, {35334, 35309}
X(46148) = X(21123)-cross conjugate of X(39)
X(46148) = cevapoint of X(39) and X(21123)
X(46148) = crosspoint of X(101) and X(190)
X(46148) = crosssum of X(i) and X(j) for these (i,j): {514, 649}, {4375, 21832}
X(46148) = trilinear pole of line {39, 1964}
X(46148) = crossdifference of every pair of points on line {3120, 4107}
X(46148) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10566}, {2, 18108}, {10, 39179}, {28, 4580}, {58, 18070}, {82, 514}, {83, 513}, {87, 18107}, {251, 693}, {256, 18111}, {274, 18105}, {308, 667}, {649, 3112}, {651, 18101}, {689, 3121}, {733, 14296}, {827, 16732}, {905, 32085}, {1019, 18082}, {1111, 4628}, {1176, 17924}, {1799, 6591}, {1919, 18833}, {1980, 40016}, {3120, 4599}, {3122, 4593}, {3125, 4577}, {3737, 18097}, {4010, 39276}, {4107, 43763}, {4164, 14970}, {7192, 18098}, {7649, 34055}, {9309, 18110}, {16277, 16757}, {18113, 27834}, {18180, 39182}, {18210, 42396}, {21207, 34072}, {22383, 46104}, {27918, 36081}
X(46148) = barycentric product X(i)*X(j) for these {i,j}: {1, 4553}, {6, 4568}, {10, 1634}, {38, 100}, {39, 190}, {42, 4576}, {71, 41676}, {81, 35309}, {99, 21035}, {101, 141}, {109, 3703}, {110, 15523}, {306, 35325}, {427, 1331}, {518, 35333}, {651, 33299}, {662, 3954}, {664, 3688}, {668, 1964}, {670, 41267}, {692, 1930}, {765, 2530}, {799, 21814}, {826, 4570}, {906, 20883}, {1016, 21123}, {1018, 16696}, {1235, 32656}, {1252, 16892}, {1293, 4884}, {1332, 17442}, {1401, 3699}, {1843, 4561}, {1897, 3917}, {1923, 6386}, {1978, 3051}, {2084, 4601}, {2346, 35335}, {3005, 4600}, {3404, 42717}, {3665, 3939}, {3666, 35334}, {3933, 8750}, {3952, 17187}, {4020, 6335}, {4062, 36827}, {4093, 4589}, {4554, 40972}, {4557, 16887}, {4558, 21016}, {4567, 8061}, {4574, 17171}, {4594, 40936}, {4603, 16587}, {4628, 7794}, {7260, 21752}, {7953, 21038}, {8024, 32739}
X(46148) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 10566}, {31, 18108}, {37, 18070}, {38, 693}, {39, 514}, {71, 4580}, {100, 3112}, {101, 83}, {141, 3261}, {172, 18111}, {190, 308}, {427, 46107}, {663, 18101}, {668, 18833}, {688, 3122}, {692, 82}, {826, 21207}, {906, 34055}, {1331, 1799}, {1333, 39179}, {1401, 3676}, {1634, 86}, {1843, 7649}, {1897, 46104}, {1918, 18105}, {1923, 667}, {1930, 40495}, {1964, 513}, {1978, 40016}, {2084, 3125}, {2176, 18107}, {2236, 14296}, {2530, 1111}, {3005, 3120}, {3051, 649}, {3313, 21178}, {3688, 522}, {3703, 35519}, {3787, 3798}, {3917, 4025}, {3954, 1577}, {4020, 905}, {4079, 34294}, {4093, 4010}, {4553, 75}, {4557, 18082}, {4559, 18097}, {4567, 4593}, {4568, 76}, {4570, 4577}, {4576, 310}, {4600, 689}, {4601, 37204}, {8041, 16892}, {8061, 16732}, {8623, 4107}, {8643, 18113}, {8750, 32085}, {9019, 21205}, {9310, 18110}, {15523, 850}, {16696, 7199}, {16892, 23989}, {17187, 7192}, {17442, 17924}, {17456, 27712}, {20775, 1459}, {21016, 14618}, {21035, 523}, {21108, 2973}, {21123, 1086}, {21814, 661}, {23990, 4628}, {32656, 1176}, {32739, 251}, {33299, 4391}, {35309, 321}, {35319, 17167}, {35325, 27}, {35326, 18087}, {35333, 2481}, {35334, 30710}, {35335, 20880}, {40936, 2533}, {40972, 650}, {41267, 512}, {41331, 1919}, {41676, 44129}
X(46148) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 25049, 44312}, {101, 1331, 32739}, {3909, 42723, 7239}, {20974, 23988, 46125}

X(46149) = CROSSPOINT OF X(105) AND X(2481)

X(46149) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46149) lies on these lines: {1, 39957}, {2, 25050}, {6, 13476}, {38, 17456}, {65, 1462}, {67, 8674}, {69, 25048}, {81, 105}, {141, 3688}, {239, 335}, {291, 39979}, {314, 670}, {1086, 2876}, {1100, 1438}, {1279, 2195}, {1634, 16696}, {3056, 40505}, {3057, 28071}, {3271, 5845}, {3416, 4863}, {3589, 25323}, {3618, 25316}, {4437, 14839}, {4576, 16703}, {4974, 34378}, {5091, 20468}, {14942, 21334}, {20670, 38989}, {32658, 41332}, {36057, 40959}

X(46149) = midpoint of X(69) and X(25048)
X(46149) = reflection of X(i) in X(j) for these {i,j}: {4553, 141}, {25323, 3589}
X(46149) = complement of X(25050)
X(46149) = crosspoint of X(105) and X(2481)
X(46149) = crosssum of X(i) and X(j) for these (i,j): {238, 40910}, {518, 2223}
X(46149) = trilinear pole of line {39, 2530}
X(46149) = X(i)-isoconjugate of X(j) for these (i,j): {82, 518}, {83, 672}, {251, 3912}, {308, 9454}, {827, 4088}, {918, 4628}, {1026, 18108}, {1176, 1861}, {1799, 2356}, {1818, 32085}, {2223, 3112}, {2284, 10566}, {3286, 18082}, {4599, 24290}, {5089, 34055}, {9455, 18833}, {18098, 18206}
X(46149) = barycentric product X(i)*X(j) for these {i,j}: {38, 673}, {39, 2481}, {105, 141}, {294, 3665}, {427, 1814}, {514, 35333}, {666, 2530}, {1027, 4568}, {1235, 32658}, {1401, 36796}, {1438, 1930}, {1462, 3703}, {1964, 18031}, {3688, 34018}, {3933, 8751}, {10099, 41676}, {13576, 16696}, {16887, 18785}, {16892, 36086}, {17442, 31637}, {20883, 36057}
X(46149) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 3912}, {39, 518}, {105, 83}, {141, 3263}, {427, 46108}, {673, 3112}, {1027, 10566}, {1401, 241}, {1438, 82}, {1814, 1799}, {1843, 5089}, {1923, 9454}, {1964, 672}, {2481, 308}, {2530, 918}, {3005, 24290}, {3051, 2223}, {3665, 40704}, {3688, 3693}, {3917, 25083}, {3954, 3932}, {4020, 1818}, {4553, 42720}, {8061, 4088}, {8751, 32085}, {10099, 4580}, {16696, 30941}, {16887, 18157}, {17187, 18206}, {17442, 1861}, {18031, 18833}, {18785, 18082}, {20775, 20752}, {21035, 3930}, {21123, 2254}, {21814, 20683}, {32658, 1176}, {32666, 4628}, {33299, 3717}, {35325, 4238}, {35333, 190}, {36057, 34055}, {40972, 2340}, {41267, 39258}, {41331, 9455}, {43929, 18108}

X(46150) = CROSSPOINT OF X(106) AND X(903)

X(46150) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46150) lies on these lines: {8, 596}, {38, 4553}, {58, 106}, {88, 291}, {310, 670}, {320, 17449}, {901, 28485}, {902, 1623}, {1015, 23552}, {1320, 45989}, {1634, 17187}, {2810, 23644}, {3831, 4013}, {4080, 30942}, {4576, 16887}, {4615, 41209}

X(46150) = crosspoint of X(106) and X(903)
X(46150) = crosssum of X(519) and X(902)
X(46150) = trilinear pole of line {39, 21123}
X(46150) = X(i)-isoconjugate of X(j) for these (i,j): {44, 83}, {82, 519}, {251, 4358}, {308, 2251}, {902, 3112}, {1023, 10566}, {1176, 38462}, {3762, 4628}, {4120, 4599}, {4169, 39179}, {4448, 36081}, {4577, 4730}, {4593, 14407}, {5440, 32085}, {8756, 34055}, {9459, 18833}, {16704, 18098}, {17780, 18108}, {23202, 46104}
X(46150) = barycentric product X(i)*X(j) for these {i,j}: {38, 88}, {39, 903}, {106, 141}, {427, 1797}, {826, 4591}, {901, 16892}, {1022, 4553}, {1235, 32659}, {1401, 4997}, {1634, 4049}, {1930, 9456}, {1964, 20568}, {2084, 4634}, {2316, 3665}, {2530, 3257}, {3005, 4615}, {3917, 6336}, {3933, 8752}, {4080, 17187}, {4555, 21123}, {4568, 23345}, {4622, 8061}, {4674, 16696}, {20883, 36058}
X(46150) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 4358}, {39, 519}, {88, 3112}, {106, 83}, {141, 3264}, {427, 46109}, {688, 14407}, {903, 308}, {1401, 3911}, {1797, 1799}, {1843, 8756}, {1923, 2251}, {1964, 44}, {2084, 4730}, {2530, 3762}, {3005, 4120}, {3051, 902}, {3688, 2325}, {3917, 3977}, {3954, 3992}, {4020, 5440}, {4553, 24004}, {4591, 4577}, {4615, 689}, {4622, 4593}, {4634, 37204}, {6336, 46104}, {8752, 32085}, {9456, 82}, {16696, 30939}, {17187, 16704}, {17442, 38462}, {20568, 18833}, {20775, 22356}, {21035, 3943}, {21123, 900}, {21814, 21805}, {23345, 10566}, {32659, 1176}, {32719, 4628}, {33299, 4723}, {36058, 34055}, {40972, 3689}, {41331, 9459}

X(46151) = CROSSPOINT OF X(107) AND X(6528)

X(46151) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46151) lies on these lines: {4, 67}, {25, 9512}, {69, 41766}, {107, 110}, {112, 1289}, {132, 15526}, {141, 41375}, {393, 694}, {523, 37937}, {660, 823}, {670, 877}, {685, 16813}, {1075, 15258}, {1235, 27373}, {1576, 2409}, {1634, 41676}, {1843, 20021}, {2493, 6353}, {3168, 40138}, {4226, 41679}, {4230, 14570}, {6525, 14826}, {8057, 39192}, {8749, 11596}, {10002, 40330}, {11444, 14249}, {12358, 34334}, {15255, 39998}, {15435, 32000}, {16039, 44770}, {27376, 41585}, {34854, 37778}

X(46151) = reflection of X(46164) in X(141)
X(46151) = anticomplement of X(47413)
X(46151) = pole wrt polar circle of trilinear polar of X(4580) (line X(125)X(127))
X(46151) = polar conjugate of X(4580)
X(46151) = polar conjugate of the isotomic conjugate of X(41676)
X(46151) = polar conjugate of the isogonal conjugate of X(35325)
X(46151) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {15388, 6360}, {23582, 21288}, {23964, 21215}, {24000, 5596}, {44183, 4329}
X(46151) = X(23964)-Ceva conjugate of X(4)
X(46151) = X(i)-cross conjugate of X(j) for these (i,j): {826, 427}, {23881, 41375}, {35325, 41676}
X(46151) = cevapoint of X(i) and X(j) for these (i,j): {141, 23881}, {427, 826}, {523, 9969}, {6676, 8673}
X(46151) = crosspoint of X(107) and X(6528)
X(46151) = crosssum of X(520) and X(39201)
X(46151) = trilinear pole of line {39, 427}
X(46151) = X(i)-isoconjugate of X(j) for these (i,j): {48, 4580}, {82, 520}, {83, 822}, {251, 24018}, {326, 18105}, {577, 18070}, {647, 34055}, {656, 1176}, {661, 28724}, {810, 1799}, {827, 2632}, {3112, 39201}, {3269, 4599}, {3682, 18108}, {3990, 10566}, {4091, 18098}, {4630, 17879}, {10547, 14208}, {15526, 34072}, {18082, 23224}, {18097, 36054}, {37754, 42396}
X(46151) = barycentric product X(i)*X(j) for these {i,j}: {4, 41676}, {38, 823}, {39, 6528}, {99, 27376}, {107, 141}, {112, 1235}, {162, 20883}, {264, 35325}, {393, 4576}, {427, 648}, {811, 17442}, {826, 23582}, {1634, 2052}, {1783, 16747}, {1843, 6331}, {1897, 17171}, {1930, 24019}, {2525, 32230}, {3917, 15352}, {3933, 6529}, {4568, 8747}, {8024, 32713}, {8061, 23999}, {8795, 35319}, {14570, 19174}, {18831, 27371}, {23285, 23964}, {36827, 37778}, {41375, 44766}
X(46151) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 4580}, {38, 24018}, {39, 520}, {107, 83}, {110, 28724}, {112, 1176}, {141, 3265}, {158, 18070}, {162, 34055}, {427, 525}, {648, 1799}, {823, 3112}, {826, 15526}, {1235, 3267}, {1289, 40404}, {1634, 394}, {1843, 647}, {1964, 822}, {2207, 18105}, {3005, 3269}, {3051, 39201}, {3933, 4143}, {4553, 3998}, {4576, 3926}, {5317, 18108}, {6528, 308}, {6529, 32085}, {8061, 2632}, {8747, 10566}, {8884, 39182}, {15352, 46104}, {16696, 4131}, {16747, 15413}, {16813, 39287}, {16887, 30805}, {16892, 17216}, {17171, 4025}, {17187, 4091}, {17442, 656}, {19174, 15412}, {20775, 32320}, {20883, 14208}, {21016, 4064}, {21108, 4466}, {23285, 36793}, {23582, 4577}, {23964, 827}, {23977, 21458}, {23999, 4593}, {24000, 4599}, {24019, 82}, {27369, 3049}, {27371, 6368}, {27373, 2485}, {27374, 42293}, {27376, 523}, {32230, 42396}, {32713, 251}, {35319, 5562}, {35325, 3}, {36127, 18097}, {39691, 5489}, {40938, 8673}, {41375, 33294}, {41676, 69}, {41937, 4630}, {42405, 41488}
X(46151) = {X(107),X(648)}-harmonic conjugate of X(32713)

X(46152) = CROSSPOINT OF X(108) AND X(18026)

X(46152) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46152) lies on these lines: {65, 67}, {108, 110}, {427, 1401}, {513, 8750}, {653, 660}, {670, 18026}, {694, 1880}, {1463, 1876}, {1469, 1892}, {1897, 3888}, {4242, 4579}, {20621, 26932}

X(46152) = X(2530)-cross conjugate of X(427)
X(46152) = cevapoint of X(1401) and X(2530)
X(46152) = crosspoint of X(108) and X(18026)
X(46152) = crosssum of X(521) and X(1946)
X(46152) = trilinear pole of line {39, 17442}
X(46152) = X(i)-isoconjugate of X(j) for these (i,j): {78, 18108}, {82, 521}, {83, 652}, {219, 10566}, {251, 6332}, {284, 4580}, {332, 18105}, {522, 1176}, {650, 34055}, {663, 1799}, {1331, 18101}, {1946, 3112}, {2193, 18070}, {3064, 28724}, {3694, 39179}, {4628, 26932}, {10547, 35519}, {18082, 23189}, {18097, 23090}
X(46152) = barycentric product X(i)*X(j) for these {i,j}: {34, 4568}, {38, 653}, {39, 18026}, {65, 41676}, {108, 141}, {109, 20883}, {278, 4553}, {427, 651}, {664, 17442}, {1235, 1415}, {1401, 6335}, {1414, 21016}, {1441, 35325}, {1634, 40149}, {1783, 3665}, {1843, 4554}, {1880, 4576}, {1930, 32674}, {2530, 46102}, {3688, 13149}, {3703, 32714}, {4551, 17171}, {4559, 16747}, {4564, 21108}, {5236, 35333}, {6516, 27376}, {7012, 16892}, {33299, 36118}
X(46152) = barycentric quotient X(i)/X(j) for these {i,j}: {34, 10566}, {38, 6332}, {39, 521}, {65, 4580}, {108, 83}, {109, 34055}, {141, 35518}, {225, 18070}, {427, 4391}, {608, 18108}, {651, 1799}, {653, 3112}, {1401, 905}, {1415, 1176}, {1634, 1812}, {1843, 650}, {1964, 652}, {2530, 26932}, {3051, 1946}, {3665, 15413}, {3703, 15416}, {4553, 345}, {4568, 3718}, {6591, 18101}, {16892, 17880}, {17171, 18155}, {17442, 522}, {18026, 308}, {20775, 36054}, {20883, 35519}, {21016, 4086}, {21035, 8611}, {21108, 4858}, {21123, 7004}, {27369, 3063}, {27376, 44426}, {32674, 82}, {35309, 3710}, {35325, 21}, {36059, 28724}, {41676, 314}

X(46153) = CROSSPOINT OF X(109) AND X(664)

X(46153) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46153) lies on these lines: {1, 24237}, {6, 38991}, {65, 16726}, {67, 73}, {109, 110}, {292, 694}, {651, 660}, {663, 1633}, {664, 670}, {692, 1459}, {934, 29052}, {2875, 22084}, {3000, 45932}, {4014, 45937}, {4296, 39035}, {4551, 8050}, {4553, 35335}, {4620, 41209}, {17136, 35338}, {39046, 39047}

X(46153) = X(4620)-Ceva conjugate of X(1400)
X(46153) = X(2530)-cross conjugate of X(17187)
X(46153) = cevapoint of X(1964) and X(21123)
X(46153) = crosspoint of X(109) and X(664)
X(46153) = crosssum of X(522) and X(663)
X(46153) = trilinear pole of line {39, 1401}
X(46153) = crossdifference of every pair of points on line {18101, 21044}
X(46153) = X(i)-isoconjugate of X(j) for these (i,j): {8, 18108}, {9, 10566}, {82, 522}, {83, 650}, {100, 18101}, {251, 4391}, {284, 18070}, {308, 3063}, {314, 18105}, {521, 32085}, {663, 3112}, {1021, 18097}, {1172, 4580}, {1176, 44426}, {1799, 18344}, {1946, 46104}, {2319, 18107}, {2321, 39179}, {3064, 34055}, {3737, 18082}, {4124, 36081}, {4516, 4577}, {4560, 18098}, {4599, 21044}, {4612, 34294}, {4628, 4858}, {18113, 31343}
X(46153) = barycentric product X(i)*X(j) for these {i,j}: {38, 651}, {39, 664}, {56, 4568}, {57, 4553}, {59, 16892}, {73, 41676}, {101, 3665}, {109, 141}, {190, 1401}, {226, 1634}, {241, 35333}, {307, 35325}, {427, 1813}, {653, 3917}, {658, 3688}, {934, 33299}, {1014, 35309}, {1170, 35335}, {1235, 32660}, {1400, 4576}, {1414, 3954}, {1415, 1930}, {1461, 3703}, {1964, 4554}, {2530, 4564}, {3005, 4620}, {3051, 4572}, {3933, 32674}, {4020, 18026}, {4551, 16696}, {4552, 17187}, {4559, 16887}, {4565, 15523}, {4569, 40972}, {4573, 21035}, {4625, 21814}, {4628, 41285}, {4884, 38828}, {4998, 21123}, {6516, 17442}, {6517, 27376}, {16720, 29055}, {17171, 23067}, {20883, 36059}, {21108, 44717}, {24471, 35334}
X(46153) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 4391}, {39, 522}, {56, 10566}, {65, 18070}, {73, 4580}, {109, 83}, {141, 35519}, {427, 46110}, {604, 18108}, {649, 18101}, {651, 3112}, {653, 46104}, {664, 308}, {1401, 514}, {1403, 18107}, {1408, 39179}, {1415, 82}, {1634, 333}, {1813, 1799}, {1843, 3064}, {1923, 3063}, {1964, 650}, {2084, 4516}, {2530, 4858}, {3005, 21044}, {3051, 663}, {3665, 3261}, {3688, 3239}, {3917, 6332}, {3954, 4086}, {4020, 521}, {4553, 312}, {4554, 18833}, {4559, 18082}, {4568, 3596}, {4572, 40016}, {4576, 28660}, {4620, 689}, {9316, 18110}, {16696, 18155}, {16892, 34387}, {17187, 4560}, {17442, 44426}, {20775, 652}, {21035, 3700}, {21123, 11}, {21814, 4041}, {23845, 18086}, {32660, 1176}, {32674, 32085}, {33299, 4397}, {35309, 3701}, {35325, 29}, {35333, 36796}, {35335, 1229}, {36059, 34055}, {40936, 4140}, {40972, 3900}, {41267, 3709}, {41676, 44130}

X(46154) = CROSSPOINT OF X(111) AND X(671)

X(46154) = X[193] - 3 X[25315], 3 X[599] + X[25334], 3 X[599] - 2 X[36792], 2 X[6593] - 3 X[46131], 3 X[21358] - 2 X[45672], X[25334] + 2 X[36792]

X(46154) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46154) lies on these lines: {2, 17413}, {6, 110}, {39, 1634}, {67, 690}, {69, 6664}, {76, 338}, {115, 5181}, {141, 4576}, {193, 25315}, {524, 20977}, {660, 897}, {691, 755}, {694, 882}, {826, 36824}, {892, 14970}, {1648, 25328}, {1691, 12367}, {1843, 35325}, {1916, 23342}, {2353, 3053}, {2393, 3291}, {2916, 8869}, {3051, 30489}, {3094, 14609}, {3231, 8705}, {3589, 25325}, {3763, 30786}, {3954, 4553}, {5013, 15268}, {5017, 41443}, {5104, 17964}, {5106, 46127}, {5648, 6034}, {6698, 8288}, {6792, 32255}, {8050, 40085}, {8586, 9872}, {9019, 36827}, {9023, 17993}, {9225, 10510}, {9971, 13330}, {10418, 15118}, {10558, 45843}, {19596, 32729}, {19626, 30435}, {21358, 42008}, {27376, 41585}, {32241, 35902}, {32251, 35901}

X(46154) = midpoint of X(69) and X(25047)
X(46154) = reflection of X(i) in X(j) for these {i,j}: {6, 3124}, {4576, 141}, {25325, 3589}
X(46154) = complement of X(25052)
X(46154) = isotomic conjugate of the isogonal conjugate of X(41272)
X(46154) = isogonal conjugate of the isotomic conjugate of X(31125)
X(46154) = X(i)-Ceva conjugate of X(j) for these (i,j): {111, 41272}, {671, 31125}, {892, 9178}, {32729, 10097}
X(46154) = X(9019)-cross conjugate of X(6)
X(46154) = X(i)-isoconjugate of X(j) for these (i,j): {82, 524}, {83, 896}, {187, 3112}, {251, 14210}, {308, 922}, {351, 4593}, {468, 34055}, {662, 22105}, {690, 4599}, {2642, 4577}, {3405, 5967}, {5026, 43763}, {5467, 18070}, {6593, 37221}, {6629, 18098}, {14567, 18833}, {16702, 18082}, {18105, 24039}, {34072, 35522}
X(46154) = crosspoint of X(i) and X(j) for these (i,j): {111, 671}, {34539, 39413}
X(46154) = crosssum of X(187) and X(524)
X(46154) = trilinear pole of line {39, 3005}
X(46154) = crossdifference of every pair of points on line {690, 5026}
X(46154) = barycentric product X(i)*X(j) for these {i,j}: {6, 31125}, {38, 897}, {39, 671}, {76, 41272}, {111, 141}, {427, 895}, {523, 36827}, {691, 826}, {892, 3005}, {923, 1930}, {1235, 14908}, {1634, 5466}, {1843, 30786}, {2530, 5380}, {3051, 18023}, {3665, 5547}, {3703, 7316}, {3917, 17983}, {3933, 8753}, {4576, 9178}, {5968, 20021}, {7813, 10630}, {8024, 32740}, {8061, 36085}, {9019, 10415}, {10097, 41676}, {14424, 34574}, {14977, 35325}, {20775, 46111}, {20883, 36060}, {23285, 32729}, {23297, 42007}, {30489, 42008}
X(46154) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 14210}, {39, 524}, {111, 83}, {141, 3266}, {427, 44146}, {512, 22105}, {671, 308}, {688, 351}, {691, 4577}, {826, 35522}, {892, 689}, {895, 1799}, {897, 3112}, {923, 82}, {1401, 7181}, {1634, 5468}, {1843, 468}, {1923, 922}, {1964, 896}, {2084, 2642}, {2525, 45807}, {3005, 690}, {3051, 187}, {3688, 3712}, {3787, 32459}, {3917, 6390}, {3954, 42713}, {4553, 42721}, {5968, 20022}, {7813, 36792}, {8041, 7813}, {8623, 5026}, {8753, 32085}, {8877, 38946}, {9019, 7664}, {10097, 4580}, {14908, 1176}, {16696, 16741}, {17187, 6629}, {17983, 46104}, {18023, 40016}, {20775, 3292}, {21035, 4062}, {21123, 4750}, {21814, 21839}, {23894, 18070}, {27369, 44102}, {27376, 37778}, {31125, 76}, {32729, 827}, {32740, 251}, {35325, 4235}, {36060, 34055}, {36085, 4593}, {36142, 4599}, {36827, 99}, {38303, 31128}, {41272, 6}, {41331, 14567}, {42007, 10130}
X(46154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {111, 895, 32740}, {111, 42007, 6}, {895, 32740, 6}, {2502, 3124, 46131}, {32740, 42007, 895}

X(46155) = CROSSPOINT OF X(476) AND X(35139)

X(46155) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46155) lies on these lines: {67, 265}, {110, 476}, {231, 32223}, {660, 32680}, {670, 14221}, {694, 1989}, {826, 1634}, {2420, 23968}, {4576, 23285}, {9019, 20021}, {14254, 15067}, {14356, 24206}, {16776, 43084}, {29959, 36824}

X(46155) = reflection of X(265) in X(43087)
X(46155) = reflection of X(46157) in X(141)
X(46155) = crosspoint of X(476) and X(35139)
X(46155) = crosssum of X(526) and X(14270)
X(46155) = trilinear pole of line {39, 35319}
X(46155) = crossdifference of every pair of points on line {2088, 39495}
X(46155) = X(i)-isoconjugate of X(j) for these (i,j): {50, 18070}, {82, 526}, {83, 2624}, {251, 32679}, {2088, 4599}, {2290, 39182}, {3112, 14270}, {39495, 43763}
X(46155) = barycentric product X(i)*X(j) for these {i,j}: {38, 32680}, {39, 35139}, {94, 1634}, {141, 476}, {265, 41676}, {328, 35325}, {826, 39295}, {1235, 32662}, {1930, 32678}, {1989, 4576}, {8024, 14560}, {14559, 31125}, {20883, 36061}, {35319, 46138}, {36827, 43084}
X(46155) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 32679}, {39, 526}, {141, 3268}, {265, 4580}, {427, 44427}, {476, 83}, {1141, 39182}, {1634, 323}, {1964, 2624}, {2166, 18070}, {3005, 2088}, {3051, 14270}, {3917, 8552}, {3933, 45792}, {4553, 42701}, {4576, 7799}, {7813, 45808}, {8623, 39495}, {11060, 18105}, {14560, 251}, {15475, 34294}, {32662, 1176}, {32678, 82}, {32680, 3112}, {35139, 308}, {35319, 1154}, {35325, 186}, {36061, 34055}, {39295, 4577}, {41676, 340}

X(46156) = CROSSPOINT OF X(729) AND X(3228)

X(46156) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46156) lies on these lines: {2, 670}, {6, 38998}, {32, 110}, {39, 4576}, {67, 36255}, {351, 694}, {660, 37132}, {733, 9150}, {886, 40858}, {1634, 3051}, {3117, 14608}, {3231, 5201}, {4553, 21814}, {5468, 9468}, {8623, 36827}, {20021, 35366}, {20081, 42486}, {23584, 32973}, {27369, 35325}, {31125, 41178}

X(46156) = X(14406)-cross conjugate of X(4576)
X(46156) = crosspoint of X(729) and X(3228)
X(46156) = crosssum of X(538) and X(3231)
X(46156) = trilinear pole of line {39, 688} (the line through X(39) parallel to the trilinear polar of X(39))
X(46156) = crossdifference of every pair of points on line {887, 9148}
X(46156) = X(i)-isoconjugate of X(j) for these (i,j): {82, 538}, {83, 2234}, {887, 37204}, {888, 4593}, {3112, 3231}, {3405, 36822}, {4599, 9148}, {5118, 18070}, {18833, 33875}
X(46156) = barycentric product X(i)*X(j) for these {i,j}: {38, 37132}, {39, 3228}, {110, 35366}, {141, 729}, {688, 886}, {826, 32717}, {3005, 9150}, {3051, 34087}, {8061, 36133}, {31125, 41309}
X(46156) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 538}, {141, 30736}, {688, 888}, {729, 83}, {886, 42371}, {1634, 23342}, {1964, 2234}, {3005, 9148}, {3051, 3231}, {3228, 308}, {9150, 689}, {9494, 887}, {16696, 30938}, {32717, 4577}, {34087, 40016}, {35366, 850}, {36133, 4593}, {37132, 3112}, {41272, 14609}, {41331, 33875}

X(46157) = CROSSPOINT OF X(842) AND X(5641)

X(46157) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46157) lies on these lines: {23, 110}, {67, 523}, {670, 3260}, {694, 9210}, {826, 20021}, {1634, 9019}, {3917, 36827}, {6035, 41209}, {20859, 46128}, {32154, 46127}, {38939, 40107}, {38987, 44895}

X(46157) = reflection of X(46155) in X(141)
X(46157) = X(6035)-Ceva conjugate of X(14998)
X(46157) = crosspoint of X(842) and X(5641)
X(46157) = crosssum of X(542) and X(5191)
X(46157) = X(i)-isoconjugate of X(j) for these (i,j): {82, 542}, {83, 2247}, {1640, 4599}, {3112, 5191}, {3405, 34369}, {4593, 6041}, {6103, 34055}, {18312, 34072}
X(46157) = barycentric product X(i)*X(j) for these {i,j}: {39, 5641}, {141, 842}, {826, 5649}, {1634, 14223}, {3005, 6035}, {4576, 14998}, {35909, 41676}
X(46157) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 542}, {688, 6041}, {826, 18312}, {842, 83}, {1634, 14999}, {1843, 6103}, {1964, 2247}, {3005, 1640}, {3051, 5191}, {5641, 308}, {5649, 4577}, {6035, 689}, {35325, 7473}, {35909, 4580}

X(46158) = CROSSPOINT OF X(675) AND X(43093)

X(46158) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46158) lies on these lines: {6, 44312}, {67, 2774}, {69, 8050}, {86, 110}, {320, 334}, {670, 33297}, {1634, 16887}, {1930, 4553}, {2224, 41239}, {4675, 17750}, {17171, 35325}

X(46158) = midpoint of X(69) and X(25049)
X(46158) = reflection of X(6) in X(44312)
X(46158) = reflection of X(46148) in X(141)
X(46158) = crosspoint of X(675) and X(43093)
X(46158) = crosssum of X(674) and X(8618)
X(46158) = trilinear pole of line {39, 16892}
X(46158) = X(i)-isoconjugate of X(j) for these (i,j): {82, 674}, {83, 2225}, {3112, 8618}, {14964, 18098}
X(46158) = barycentric product X(i)*X(j) for these {i,j}: {38, 37130}, {39, 43093}, {141, 675}, {1930, 2224}
X(46158) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 674}, {141, 3006}, {675, 83}, {1401, 43039}, {1964, 2225}, {2224, 82}, {3051, 8618}, {4553, 42723}, {16892, 23887}, {17187, 14964}, {32682, 4628}, {35325, 4249}, {37130, 3112}, {43093, 308}

X(46159) = CROSSPOINT OF X(741) AND X(18827)

X(46159) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46159) lies on these lines: {31, 110}, {38, 4576}, {75, 670}, {291, 4651}, {660, 1757}, {694, 3572}, {745, 36066}, {1634, 1964}, {4553, 16696}, {17187, 21814}, {17208, 40017}, {41209, 43763}

X(46159) = X(4093)-cross conjugate of X(39)
X(46159) = cevapoint of X(39) and X(4093)
X(46159) = crosspoint of X(741) and X(18827)
X(46159) = crosssum of X(740) and X(3747)
X(46159) = trilinear pole of line {39, 2084}
X(46159) = X(i)-isoconjugate of X(j) for these (i,j): {82, 740}, {83, 2238}, {238, 18082}, {239, 18098}, {251, 3948}, {308, 41333}, {862, 1799}, {874, 18105}, {3112, 3747}, {3684, 18097}, {4154, 43763}, {4155, 4577}, {18099, 18786}, {35068, 39276}
X(46159) = barycentric product X(i)*X(j) for these {i,j}: {38, 37128}, {39, 18827}, {141, 741}, {291, 16696}, {292, 16887}, {295, 17171}, {335, 17187}, {1401, 36800}, {1634, 4444}, {1911, 16703}, {1930, 18268}, {1964, 40017}, {2196, 16747}, {2311, 3665}, {2530, 4584}, {3572, 4576}, {4589, 21123}, {8061, 36066}
X(46159) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 3948}, {39, 740}, {141, 35544}, {292, 18082}, {741, 83}, {876, 18070}, {1401, 16609}, {1634, 3570}, {1911, 18098}, {1923, 41333}, {1964, 2238}, {2084, 4155}, {3051, 3747}, {3688, 3985}, {4093, 35068}, {4576, 27853}, {8623, 4154}, {16696, 350}, {16703, 18891}, {16887, 1921}, {17171, 40717}, {17187, 239}, {18268, 82}, {18827, 308}, {21035, 4037}, {21123, 4010}, {36066, 4593}, {37128, 3112}, {40017, 18833}, {40972, 4433}

X(46160) = CROSSPOINT OF X(759) AND X(14616)

X(46160) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46160) lies on these lines: {1, 60}, {38, 1634}, {80, 8050}, {561, 670}, {660, 17763}, {1930, 4576}, {4553, 15523}, {17442, 35325}, {18165, 29683}, {18191, 22321}, {37536, 45926}

X(46160) = crosspoint of X(759) and X(14616)
X(46160) = crosssum of X(758) and X(3724)
X(46160) = trilinear pole of line {39, 8061}
X(46160) = X(i)-isoconjugate of X(j) for these (i,j): {36, 18082}, {82, 758}, {83, 2245}, {251, 3936}, {827, 6370}, {860, 1176}, {1799, 44113}, {1983, 18070}, {2323, 18097}, {2610, 4599}, {3112, 3724}, {3218, 18098}, {4577, 42666}, {4628, 4707}
X(46160) = barycentric product X(i)*X(j) for these {i,j}: {38, 24624}, {39, 14616}, {80, 16696}, {141, 759}, {826, 37140}, {1807, 17171}, {1930, 34079}, {2161, 16887}, {2341, 3665}, {6187, 16703}, {17187, 18359}, {23285, 32671}
X(46160) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 3936}, {39, 758}, {141, 35550}, {759, 83}, {1401, 18593}, {1411, 18097}, {1634, 4585}, {1964, 2245}, {2084, 42666}, {2161, 18082}, {2530, 4707}, {3005, 2610}, {3051, 3724}, {6187, 18098}, {8061, 6370}, {14616, 308}, {16696, 320}, {16703, 40075}, {16887, 20924}, {17187, 3218}, {17442, 860}, {21035, 4053}, {24624, 3112}, {32671, 827}, {34079, 82}, {35325, 4242}, {36069, 4599}, {37140, 4577}

X(46161) = CROSSPOINT OF X(805) AND X(18229)

X(46161) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46161) lies on these lines: {67, 3001}, {110, 669}, {511, 694}, {523, 670}, {660, 37134}, {688, 1634}, {732, 20021}, {3005, 4576}, {5201, 9468}, {14251, 38987}, {14607, 17415}, {18872, 46127}, {39292, 41209}

X(46161) = X(39292)-Ceva conjugate of X(694)
X(46161) = X(35319)-cross conjugate of X(39291)
X(46161) = crosspoint of X(805) and X(18829)
X(46161) = crosssum of X(804) and X(5027)
X(46161) = trilinear pole of line {39, 3118}
X(46161) = X(i)-isoconjugate of X(j) for these (i,j): {82, 804}, {659, 18099}, {1691, 18070}, {1966, 18105}, {2086, 4593}, {2238, 18111}, {3112, 5027}, {4039, 18108}, {4107, 18098}, {4164, 18082}
X(46161) = barycentric product X(i)*X(j) for these {i,j}: {38, 37134}, {39, 18829}, {141, 805}, {694, 4576}, {1634, 1916}, {3005, 39292}, {8024, 17938}, {8041, 41209}, {35325, 40708}, {36214, 41676}
X(46161) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 804}, {141, 14295}, {688, 2086}, {741, 18111}, {805, 83}, {813, 18099}, {882, 34294}, {1581, 18070}, {1634, 385}, {2531, 41178}, {3051, 5027}, {3917, 24284}, {4576, 3978}, {9468, 18105}, {16696, 14296}, {17187, 4107}, {17938, 251}, {18829, 308}, {18872, 22105}, {35325, 419}, {36214, 4580}, {37134, 3112}, {39292, 689}, {41676, 17984}

X(46162) = CROSSPOINT OF X(901) AND X(4555)

X(46162) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46162) lies on these lines: {67, 41327}, {106, 33844}, {110, 901}, {660, 876}, {670, 4555}, {1320, 32922}, {2530, 4553}, {3242, 34230}, {3699, 8050}, {4674, 18792}, {5289, 14260}, {21007, 25577}

X(46162) = crosspoint of X(901) and X(4555)
X(46162) = crosssum of X(900) and X(1960)
X(46162) = X(i)-isoconjugate of X(j) for these (i,j): {44, 10566}, {82, 900}, {83, 1635}, {251, 3762}, {519, 18108}, {1960, 3112}, {3285, 18070}, {3943, 39179}, {18101, 23703}, {18105, 30939}
X(46162) = barycentric product X(i)*X(j) for these {i,j}: {38, 3257}, {39, 4555}, {88, 4553}, {106, 4568}, {141, 901}, {1401, 4582}, {1634, 4080}, {1930, 32665}, {2530, 5376}, {3665, 5548}, {3954, 4622}, {4591, 15523}, {4615, 21035}, {4634, 21814}, {8024, 32719}, {9268, 16892}
X(46162) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 3762}, {39, 900}, {106, 10566}, {901, 83}, {1401, 30725}, {1634, 16704}, {1964, 1635}, {2441, 18113}, {3051, 1960}, {3257, 3112}, {3688, 1639}, {4553, 4358}, {4555, 308}, {4568, 3264}, {4674, 18070}, {9456, 18108}, {20775, 22086}, {21035, 4120}, {21123, 1647}, {21814, 4730}, {32665, 82}, {32719, 251}, {33299, 4768}, {35309, 3992}, {35325, 37168}, {40972, 4895}, {41267, 14407}

X(46163) = CROSSPOINT OF X(666) AND X(919)

X(46163) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46163) lies on these lines: {6, 38989}, {67, 17796}, {110, 919}, {645, 666}, {660, 2284}, {692, 21007}, {694, 21788}, {4553, 35333}, {4559, 32735}, {5452, 30825}, {28743, 28834}, {32666, 35327}

X(46163) = crosspoint of X(666) and X(919)
X(46163) = crosssum of X(665) and X(918)
X(46163) = trilinear pole of line {39, 20969}
X(46163) = X(i)-isoconjugate of X(j) for these (i,j): {82, 918}, {83, 2254}, {518, 10566}, {665, 3112}, {1025, 18101}, {3286, 18070}, {3912, 18108}, {3932, 39179}, {18098, 23829}, {18105, 18157}
X(46163) = barycentric product X(i)*X(j) for these {i,j}: {1, 35333}, {38, 36086}, {39, 666}, {105, 4553}, {141, 919}, {927, 3688}, {1401, 36802}, {1438, 4568}, {1634, 13576}, {1930, 32666}, {2530, 5377}, {3051, 36803}, {3703, 32735}, {33299, 36146}, {34085, 40972}
X(46163) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 918}, {666, 308}, {884, 18101}, {919, 83}, {1401, 43042}, {1438, 10566}, {1634, 30941}, {1964, 2254}, {3051, 665}, {4553, 3263}, {17187, 23829}, {18785, 18070}, {21035, 4088}, {21814, 24290}, {32666, 82}, {35325, 15149}, {35333, 75}, {36086, 3112}, {36803, 40016}

X(46164) = CROSSPOINT OF X(1297) AND X(35140)

X(46164) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46164) lies on these lines: {22, 110}, {67, 2435}, {141, 41375}, {511, 44894}, {670, 14615}, {694, 34212}, {1634, 3313}, {1853, 18018}, {3917, 35325}, {6330, 11331}, {34817, 43717}

X(46164) = reflection of X(46151) in X(141)
X(46164) = isogonal conjugate of X(21458)
X(46164) = crosspoint of X(1297) and X(35140)
X(46164) = crosssum of X(1503) and X(42671)
X(46164) = perspector of ABC and unary cofactor triangle of 1st orthosymmedial triangle
X(46164) = X(i)-isoconjugate of X(j) for these (i,j): {1, 21458}, {82, 1503}, {83, 2312}, {3112, 42671}, {8766, 32085}, {16318, 34055}, {28343, 37221}
X(46164) = barycentric product X(i)*X(j) for these {i,j}: {39, 35140}, {141, 1297}, {1634, 43673}, {2419, 35325}, {2435, 41676}, {2525, 44770}, {3917, 6330}, {3933, 43717}, {4576, 34212}
X(46164) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 21458}, {39, 1503}, {141, 30737}, {1297, 83}, {1401, 43045}, {1634, 34211}, {1843, 16318}, {1964, 2312}, {2435, 4580}, {3051, 42671}, {3917, 441}, {4020, 8766}, {6330, 46104}, {20775, 8779}, {35140, 308}, {35325, 2409}, {43717, 32085}, {44770, 42396}

X(46165) = CROSSPOINT OF X(2373) AND X(46140)

X(46165) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46165) lies on these lines: {32, 14376}, {67, 9517}, {69, 110}, {141, 35325}, {315, 670}, {327, 44134}, {339, 32246}, {599, 36823}, {660, 37220}, {694, 9035}, {1235, 27373}, {1634, 3933}, {2892, 13219}, {3313, 4576}, {5201, 40996}, {39129, 41584}

X(46165) = midpoint of X(69) and X(25053)
X(46165) = reflection of X(35325) in X(141)
X(46165) = polar conjugate of X(21459)
X(46165) = X(37220)-anticomplementary conjugate of X(11061)
X(46165) = cevapoint of X(i) and X(j) for these (i,j): {141, 9019}, {3917, 7813}
X(46165) = crosspoint of X(2373) and X(46140)
X(46165) = trilinear pole of line {39, 2525}
X(46165) = X(i)-isoconjugate of X(j) for these (i,j): {48, 21459}, {82, 2393}, {251, 18669}, {14580, 34055}
X(46165) = barycentric product X(i)*X(j) for these {i,j}: {38, 37220}, {39, 46140}, {141, 2373}, {1177, 8024}, {1235, 18876}
X(46165) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 21459}, {38, 18669}, {39, 2393}, {141, 858}, {427, 5523}, {1177, 251}, {1843, 14580}, {1930, 20884}, {2373, 83}, {3917, 14961}, {7813, 5181}, {8024, 1236}, {15523, 21017}, {16887, 17172}, {16892, 21109}, {18876, 1176}, {37220, 3112}, {46140, 308}

X(46166) = CROSSPOINT OF X(1113) AND X(15164)

X(46166) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46166) lies on these lines: {67, 2575}, {110, 1113}, {141, 427}, {468, 44126}, {511, 1312}, {524, 20405}, {660, 2580}, {670, 15164}, {694, 8106}, {1345, 1350}, {1346, 6403}, {1347, 7998}, {2781, 14500}, {13415, 15162}, {14808, 25408}

X(46166) = midpoint of X(14808) and X(25408)
X(46166) = reflection of X(46167) in X(141)
X(46166) = crosspoint of X(1113) and X(15164)
X(46166) = crosssum of X(2574) and X(42668)
X(46166) = X(i)-isoconjugate of X(j) for these (i,j): {82, 2574}, {83, 2578}, {251, 2582}, {1176, 2588}, {2577, 4580}, {2584, 32085}, {3112, 42668}, {8105, 34055}
X(46166) = barycentric product X(i)*X(j) for these {i,j}: {38, 2580}, {39, 15164}, {141, 1113}, {427, 8115}, {826, 39298}, {1634, 2593}, {1822, 20883}, {1930, 2576}, {2575, 41676}, {4576, 8106}, {8024, 44123}, {22340, 35325}
X(46166) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 2582}, {39, 2574}, {141, 22339}, {427, 2592}, {1113, 83}, {1634, 8116}, {1822, 34055}, {1843, 8105}, {1964, 2578}, {2575, 4580}, {2576, 82}, {2580, 3112}, {2589, 18070}, {3051, 42668}, {4020, 2584}, {8115, 1799}, {15164, 308}, {17442, 2588}, {35325, 1114}, {39298, 4577}, {41676, 15165}, {44123, 251}
X(46166) = {X(1113),X(8115)}-harmonic conjugate of X(44123)

X(46167) = CROSSPOINT OF X(1114) AND X(15165)

X(46167) lies on the circumellipse centered at X(141) (ellipse {{A,B,C,X(67),X(110)}}, which is the barycentric product X(141)*circumcircle); this is true for X(k) for k = 46149, 46150,...,46167.

X(46167) lies on these lines: {67, 2574}, {110, 1114}, {141, 427}, {468, 44125}, {511, 1313}, {524, 20406}, {660, 2581}, {670, 15165}, {694, 8105}, {1344, 1350}, {1346, 7998}, {1347, 6403}, {2781, 14499}, {13414, 15163}, {14807, 25407}

X(46167) = midpoint of X(14807) and X(25407)
X(46167) = reflection of X(46166) in X(141)
X(46167) = crosspoint of X(1114) and X(15165)
X(46167) = crosssum of X(2575) and X(42667)
X(46167) = X(i)-isoconjugate of X(j) for these (i,j): {82, 2575}, {83, 2579}, {251, 2583}, {1176, 2589}, {2576, 4580}, {2585, 32085}, {3112, 42667}, {8106, 34055}
X(46167) = barycentric product X(i)*X(j) for these {i,j}: {38, 2581}, {39, 15165}, {141, 1114}, {427, 8116}, {826, 39299}, {1634, 2592}, {1823, 20883}, {1930, 2577}, {2574, 41676}, {4576, 8105}, {8024, 44124}, {22339, 35325}
X(46167) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 2583}, {39, 2575}, {141, 22340}, {427, 2593}, {1114, 83}, {1634, 8115}, {1823, 34055}, {1843, 8106}, {1964, 2579}, {2574, 4580}, {2577, 82}, {2581, 3112}, {2588, 18070}, {3051, 42667}, {4020, 2585}, {8116, 1799}, {15165, 308}, {17442, 2589}, {35325, 1113}, {39299, 4577}, {41676, 15164}, {44124, 251}
X(46167) = {X(1114),X(8116)}-harmonic conjugate of X(44124)

X(46168) = (name pending)

X(46168) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(547)}} and {{A, B, C, X(3), X(550)}}

X(46169) = X(511)X(548)∩X(512)X(547)

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

X(46169) = 5*X(140)-2*X(31848), 5*X(3111)-X(31848), 3*X(6785)-7*X(41330), X(12103)+2*X(31850), 4*X(16239)-X(18321)

X(46169) lies on these lines: {30, 6785}, {140, 3111}, {511, 548}, {512, 547}, {3628, 6787}, {12103, 31850}, {16239, 18321}

X(46169) = reflection of X(i) in X(j) for these (i, j): (140, 3111), (6787, 3628)

X(46170) = X(525)X(548)∩X(547)X(1503)

Barycentrics 18*a^14-33*(b^2+c^2)*a^12+2*(10*b^4+19*b^2*c^2+10*c^4)*a^10-(b^2+c^2)*(29*b^4-43*b^2*c^2+29*c^4)*a^8+3*(b^2-c^2)^2*(10*b^4+17*b^2*c^2+10*c^4)*a^6+(b^4-c^4)*(b^2-c^2)*(b^4-9*b^2*c^2+c^4)*a^4-(b^2-c^2)^2*(4*b^8+4*c^8+3*b^2*c^2*(3*b^2+c^2)*(b^2+3*c^2))*a^2+(b^4-c^4)*(b^2-c^2)^3*(-3*b^4-8*b^2*c^2-3*c^4) : :

X(46170) = 5*X(140)-2*X(43389), 7*X(546)-4*X(43280), 5*X(3859)-2*X(43279), X(12103)+2*X(18338)

X(46170) lies on these lines: {30, 6794}, {140, 43389}, {525, 548}, {546, 43280}, {547, 1503}, {3859, 43279}, {12103, 18338}

X(46171) = X(140)X(31847)∩X(517)X(548)

Barycentrics a*(2*(2*b-c)*(b-2*c)*a^7+2*(b+c)*b*c*a^6-(12*b^4+12*c^4-(29*b^2-22*b*c+29*c^2)*b*c)*a^5-(b+c)*(5*b^2+4*b*c+5*c^2)*b*c*a^4+(12*b^6+12*c^6-(28*b^4+28*c^4-(25*b^2-4*b*c+25*c^2)*b*c)*b*c)*a^3+2*(b^2-c^2)*(b-c)*(b+2*c)*(2*b+c)*b*c*a^2-(b^2-c^2)^2*(4*b^4+4*c^4-3*(3*b^2-5*b*c+3*c^2)*b*c)*a-(b^2-c^2)^3*(b-c)*b*c) : :

X(46172) = X(32)X(143)∩X(98)X(5663)

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

X(46172) = X(98)+3*X(41330), 3*X(3111)-X(33813), 3*X(6785)+X(38741), 5*X(14061)-X(18321), X(18322)+3*X(21445), X(31848)-3*X(34127)

X(46172) lies on these lines: {32, 143}, {83, 32205}, {98, 5663}, {182, 12893}, {1078, 32142}, {2023, 14113}, {2080, 13391}, {2387, 14693}, {2698, 14734}, {2854, 32135}, {2882, 18583}, {3111, 33813}, {3398, 12006}, {5946, 11842}, {6101, 7793}, {6785, 38741}, {7787, 15026}, {8590, 11649}, {9517, 20304}, {10095, 32134}, {10104, 11591}, {10796, 13364}, {12042, 31850}, {14061, 18321}, {15074, 39560}, {18322, 21445}, {19155, 41277}, {21152, 39477}, {31848, 34127}, {32046, 32661}, {32515, 35060}

X(46173) = X(30)X(44909)∩X(542)X(547)

X(46173) lies on these lines: {30, 44909}, {542, 547}, {17974, 32046}, {18338, 38608}

X(46174) = X(5)X(3937)∩X(143)X(34753)

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

X(46174) lies on these lines: {5, 3937}, {143, 34753}, {1387, 14115}, {2841, 5901}, {2850, 20304}, {3025, 8068}, {5663, 13226}, {5844, 35059}, {6914, 36058}, {6971, 26914}, {6980, 26910}, {31847, 34126}, {31849, 38602}, {32046, 36059}, {33814, 34583}

X(46174) = midpoint of X(i) and X(j) for these {i, j}: {5, 3937}, {31849, 38602}

X(46175) = X(2)X(594)∩X(7)X(299)

X(46175) lies on these lines: {2,594}, {7,299}, {8,302}, {75, 303}, {298,319}, {300,34388}, {396,7227}, {1086,34541}, {4399,23303}, {4431,5243}, {4445,34540}, {4665,23302}, {7231,33458}, {9763,17118}, {11289,33941}, {17365,40901}, {34387,34390}

X(46176) = X(2)X(594)∩X(7)X(298)

X(46176) lies on these lines: {2,594}, {7,298}, {8, 303|, {75, 302}, {299,319}, {301,34388}, {395,7227}, {1086,34540}, {4399,23302}, {4431,5242}, {4445,34541}, {4665,23303}, {7231,33459}, {9761,17118}, {11290,33941}, {17365,40900}, {34387,34389}

X(46177) = CROSSPOINT OF X(101) AND X(664)

X(46177) lies on these lines: {1, 2140}, {42, 21725}, {55, 14714}, {100, 3903}, {101, 663}, {109, 43344}, {664, 4449}, {672, 3010}, {2340, 45932}, {2389, 43039}, {2398, 4551}, {3732, 4724}, {3900, 21859}, {5540, 38365}, {17072, 27135}, {17136, 35338}, {17439, 42079}, {21302, 26796}

X(46177) = X(39293)-Ceva conjugate of X(672)
X(46177) = crosspoint of X(i) and X(j) for these (i,j): {1, 9322}, {101, 664}
X(46177) = crosssum of X(i) and X(j) for these (i,j): {1, 9317}, {514, 663}, {17761, 21132}
X(46177) = trilinear pole of line {16588, 21746}
X(46177) = crossdifference of every pair of points on line {24237, 38991}
X(46177) = X(i)-isoconjugate of X(j) for these (i,j): {513, 40419}, {693, 3449}
X(46177) = barycentric product X(i)*X(j) for these {i,j}: {100, 17451}, {101, 2886}, {109, 40997}, {110, 21029}, {190, 21746}, {662, 21804}, {664, 16588}, {692, 20236}, {1018, 18165}, {1252, 21118}, {1897, 22070}, {4551, 16699}, {4572, 9449}, {4625, 21819}
X(46177) = barycentric quotient X(i)/X(j) for these {i,j}: {101, 40419}, {2886, 3261}, {9449, 663}, {16588, 522}, {16699, 18155}, {17451, 693}, {18165, 7199}, {20236, 40495}, {21029, 850}, {21118, 23989}, {21746, 514}, {21804, 1577}, {21819, 4041}, {22070, 4025}, {22368, 652}, {32739, 3449}, {40997, 35519}

X(46178) = CROSSPOINT OF X(105) AND X(1280)

X(46178) lies on these lines: {1, 39}, {55, 244}, {56, 20871}, {100, 3744}, {105, 910}, {612, 44304}, {1054, 3749}, {1086, 39047}, {1280, 3693}, {1282, 5332}, {2087, 10695}, {3242, 4712}, {3315, 3666}, {3722, 17017}, {3772, 26246}, {9507, 42819}, {10987, 35227}, {12740, 13277}, {14942, 27918}, {20999, 23847}, {33127, 36481}

X(46178) = X(39272)-Ceva conjugate of X(513)
X(46178) = crosspoint of X(i) and X(j) for these (i,j): {1, 9452}, {105, 1280}
X(46178) = crosssum of X(i) and X(j) for these (i,j): {1, 9451}, {518, 1279}
X(46178) = crossdifference of every pair of points on line {659, 3126}

X(46179) = X(30)X(511)∩X(39)X(226)

X(46179) lies on these lines: {30, 511}, {39, 226}, {48, 24263}, {63, 76}, {194, 5905}, {349, 4020}, {993, 12263}, {1478, 12782}, {3095, 37826}, {3934, 5745}, {7757, 31164}, {7786, 31266}, {11257, 18446}, {20078, 20081}, {20785, 44150}, {21165, 22712}, {21403, 22065}, {22001, 22036}

X(46180) = X(30)X(511)∩X(39)X(1212)

X(46180) lies on these lines: {1, 24333}, {7, 24247}, {9, 24249}, {10, 12933}, {30, 511}, {39, 1212}, {57, 24266}, {63, 194}, {76, 85}, {99, 5060}, {192, 10027}, {350, 33946}, {894, 24291}, {993, 22779}, {1055, 17136}, {1086, 21331}, {1111, 20335}, {1149, 24403}, {1334, 25237}, {1423, 25252}, {1475, 20247}, {1478, 9902}, {1575, 21138}, {1737, 24318}, {1916, 11608}, {2275, 24172}, {2321, 33936}, {2347, 20248}, {2549, 33869}, {3061, 3673}, {3212, 3501}, {3419, 24694}, {3509, 5088}, {3663, 3735}, {3665, 17046}, {3684, 3732}, {3693, 21232}, {3721, 24214}, {3726, 7200}, {3729, 24282}, {3741, 24255}, {3761, 21101}, {3831, 16720}, {3905, 7754}, {3930, 21139}, {3933, 4136}, {3934, 6706}, {4511, 9318}, {4566, 6168}, {4568, 6381}, {4694, 7208}, {4920, 5254}, {5074, 21090}, {5145, 30117}, {5289, 24352}, {5440, 24685}, {5905, 6542}, {7709, 21165}, {7751, 8669}, {7757, 31169}, {7781, 8720}, {7786, 31269}, {7805, 41656}, {8545, 40872}, {9311, 17158}, {9466, 41141}, {12053, 13110}, {12251, 18446}, {13108, 37826}, {16609, 25083}, {17050, 17451}, {17266, 31266}, {17310, 31164}, {17333, 27492}, {17355, 24254}, {17861, 20258}, {20016, 20078}, {20236, 30097}, {20432, 30055}, {20590, 23682}, {20893, 21443}, {21044, 33864}, {22034, 22036}, {24477, 42050}, {25254, 40886}, {25568, 42048}, {26563, 33299}, {29960, 33930}, {29968, 33943}, {29991, 33944}, {30030, 33933}, {30038, 33940}, {32453, 40859}, {32921, 37492}, {35957, 41773}, {44562, 44570}

X(46180) = crossdifference of every pair of points on line {6, 23655}
X(46180) = isotomic conjugate of trilinear pole of line X(2)X(663)
X(46180) = isotomic conjugate of Steiner-circumellipse-X(6)-antipode of X(664)
X(46180) = barycentric quotient X(13829)/X(13040)
X(46180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3212, 25242, 3501}, {3665, 40997, 17046}, {3693, 43037, 21232}, {3930, 21139, 30806}, {17451, 20880, 17050}

X(46181) = X(19)X(76)∩X(30)X(511)

X(46181) lies on these lines: {19, 76}, {30, 511}, {39, 18589}, {194, 4329}, {1486, 9917}, {3934, 40530}, {7757, 31158}, {7786, 31261}, {11257, 30265}, {20061, 20081}, {21160, 22712}

X(46182) = X(27)X(76)∩X(30)X(511)

X(46182) lies on these lines: {27, 76}, {30, 511}, {39, 440}, {194, 3151}, {3934, 6678}, {5188, 44243}, {6248, 15762}, {7757, 31153}, {7786, 31256}, {9917, 20834}, {11257, 30266}, {20081, 31292}, {21162, 22712}

X(46183) = X(30)X(511)∩X(38)X(76)

X(46193) lies on these lines: {30, 511}, {38, 76}, {39, 1215}, {194, 17165}, {1221, 17157}, {3934, 6682}, {4692, 12782}, {7757, 31161}, {7786, 31264}, {11257, 30272}, {20068, 20081}, {22024, 22036}

X(46184) = X(2)X(2986)∩X(114)X(1576)

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

X(46184) lies on the Vijay orthic medial conic and these lines: {2, 2986}, {114, 1576}, {126, 8791}, {140, 12235}, {141, 40484}, {441, 44389}, {468, 44899}, {526, 5972}, {597, 6680}, {620, 2492}, {868, 22085}, {2987, 3618}, {3018, 14570}, {3284, 44388}, {6036, 7668}, {6593, 20399}, {6722, 34989}, {9034, 36949}, {9164, 44401}, {10112, 23702}, {15526, 40879}, {19136, 37466}, {23698, 34981}, {34843, 34844}, {38393, 38736}, {38394, 38734}, {40544, 40556}

X(46184) = complement of complement of X(4558)
X(46184) = X(i)-complementary conjugate of X(j) for these (i,j): {163, 136}, {925, 21253}, {32734, 8287}, {36145, 125}, {44174, 18589}
X(46184) = crossdifference of every pair of points on line {7669, 21731}
X(46184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {620, 23583, 34990}, {24975, 34990, 23583}

X(46185) = COMPLEMENT OF X(34980)

X(46185) lies on the Vijay orthic medial conic and these lines: {2, 34980}, {511, 44228}, {520, 23583}, {526, 5972}, {620, 34839}, {1576, 9306}, {2781, 5893}, {2871, 14913}, {2882, 3491}, {15595, 34383}

X(46185) = complement of X(34980)
X(46185) = X(i)-complementary conjugate of X(j) for these (i,j): {107, 16573}, {162, 35071}, {250, 828}, {648, 16595}, {811, 122}, {823, 15526}, {1093, 24040}, {1784, 42306}, {2617, 38976}, {6520, 23991}, {6528, 34846}, {6529, 16592}, {15352, 8287}, {23582, 1214}, {23590, 16583}, {23999, 3}, {24000, 216}, {24021, 6}, {24022, 1196}, {32230, 37}, {34538, 226}, {36126, 115}

X(46186) = X(2)X(112)∩X(2781)X(5893)

Barycentrics (a^2 - b^2 - c^2)*(2*a^14 - 2*a^12*b^2 - 7*a^10*b^4 + 7*a^8*b^6 + 8*a^6*b^8 - 8*a^4*b^10 - 3*a^2*b^12 + 3*b^14 - 2*a^12*c^2 + 16*a^10*b^2*c^2 - 7*a^8*b^4*c^2 - 38*a^6*b^6*c^2 + 18*a^4*b^8*c^2 + 22*a^2*b^10*c^2 - 9*b^12*c^2 - 7*a^10*c^4 - 7*a^8*b^2*c^4 + 60*a^6*b^4*c^4 - 10*a^4*b^6*c^4 - 45*a^2*b^8*c^4 + 9*b^10*c^4 + 7*a^8*c^6 - 38*a^6*b^2*c^6 - 10*a^4*b^4*c^6 + 52*a^2*b^6*c^6 - 3*b^8*c^6 + 8*a^6*c^8 + 18*a^4*b^2*c^8 - 45*a^2*b^4*c^8 - 3*b^6*c^8 - 8*a^4*c^10 + 22*a^2*b^2*c^10 + 9*b^4*c^10 - 3*a^2*c^12 - 9*b^2*c^12 + 3*c^14) : :

X(46186) lies on the Vijay orthic medial conic and these lines: {2, 112}, {2781, 5893}, {2794, 44241}, {10151, 12145}, {16976, 34841}, {41369, 44499}

Centers X(46187) - X(46190) were contributed by César Eliud Lozada, December 7, 2021.

Bicentric points P(197) and U(197) are the real foci of the De Longchamps ellipse. (See definition of this ellipse in Wolfram's Mathworld and coordinates of its real foci in PU(197)).

X(46187) = ISOGONAL CONJUGATE OF X(5253)

X(46187) lies on these lines: {35, 3293}, {60, 6043}, {88, 46188}, {319, 17751}, {519, 960}, {1183, 38882}, {1193, 1319}, {1825, 1829}, {2392, 13752}, {3450, 20986}, {3754, 43972}, {8679, 20617}, {20615, 24443}, {23638, 34434}

X(46187) = isogonal conjugate of X(5253)
X(46187) = barycentric quotient X(i)/X(j) for these (i, j): (10, 27792), (37, 17164)
X(46187) = trilinear quotient X(i)/X(j) for these (i, j): (10, 17164), (321, 27792)
X(46187) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(519)}} and {{A, B, C, X(2), X(35652)}}
X(46187) = cevapoint of X(42) and X(2347)
X(46187) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 17164), (37, 27792)
X(46187) = X(i)-isoconjugate-of-X(j) for these {i, j}: {58, 17164}, {1333, 27792}
X(46187) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (10, 27792), (37, 17164)
X(46187) = cevapoint of PU(197)

X(46188) = X(583)X(992) ∩ X(942)X(3244)

X(46188) lies on these lines: {88, 46187}, {583, 992}, {942, 3244}, {3337, 31855}

X(46189) = X(6)X(101) ∩ X(39)X(1449)

X(46189) lies on these lines: {6, 101}, {37, 15828}, {39, 1449}, {1100, 1500}, {1475, 20228}, {1574, 5839}, {2087, 2171}, {2092, 16666}, {2220, 9341}, {2241, 5120}, {2275, 4263}, {3623, 39975}, {4253, 21785}, {4700, 28244}, {4860, 17071}, {4890, 22343}, {4969, 39798}, {5042, 16502}, {7757, 20168}, {8610, 16671}, {20090, 24625}, {20456, 23532}, {21746, 23524}

X(46189) = barycentric product X(1)*X(46190)
X(46189) = trilinear product X(6)*X(46190)
X(46189) = barycentric product of PU(197)
X(46189) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 1015, 21796), (2275, 16667, 4263)

X(46190) = X(1)X(88) ∩ X(12)X(1647)

X(46190) lies on these lines: {1, 88}, {12, 1647}, {31, 3333}, {37, 23649}, {38, 3616}, {42, 17609}, {56, 4332}, {145, 17063}, {354, 1201}, {495, 28096}, {518, 28352}, {551, 2292}, {595, 9340}, {596, 4975}, {756, 1125}, {902, 32636}, {942, 1149}, {960, 17449}, {978, 3889}, {982, 3622}, {986, 38314}, {999, 28082}, {1015, 21808}, {1056, 28074}, {1058, 33094}, {1193, 5045}, {1254, 1319}, {1388, 1393}, {1476, 2647}, {1616, 4860}, {1739, 3635}, {1962, 37592}, {2310, 11376}, {2975, 29820}, {2999, 30343}, {3086, 33127}, {3120, 37722}, {3123, 25557}, {3216, 3892}, {3241, 24174}, {3244, 4695}, {3290, 17474}, {3304, 3924}, {3337, 40091}, {3338, 3915}, {3555, 21805}, {3623, 9335}, {3636, 3670}, {3726, 39244}, {3742, 10459}, {3756, 15888}, {3873, 21214}, {3914, 21625}, {3930, 16604}, {3938, 25524}, {4075, 39697}, {4188, 17715}, {4666, 10448}, {4696, 4871}, {4714, 6532}, {4999, 29689}, {5221, 16486}, {5492, 5901}, {5542, 22172}, {6765, 9350}, {7191, 26261}, {7278, 21208}, {10586, 33144}, {11019, 21935}, {11037, 28016}, {11263, 23869}, {12005, 32486}, {17164, 42053}, {17448, 21921}, {17469, 37607}, {17480, 30947}, {21620, 28018}, {22167, 24325}, {24178, 33136}, {24216, 24987}, {24911, 25650}, {25055, 42039}, {25253, 42055}, {25591, 31161}, {26093, 32931}, {26111, 32937}, {27003, 37588}, {28257, 34790}, {28403, 38053}, {29818, 37539}, {31435, 36263}, {32856, 41012}, {32925, 34860}

X(46190) = barycentric product X(75)*X(46189)
X(46190) = trilinear product X(2)*X(46189)
X(46190) = crosspoint of X(1) and X(20615)
X(46190) = crosssum of X(1) and X(3871)
X(46190) = trilinear product of PU(197)
X(46190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 244, 4642), (1, 404, 3722), (354, 1201, 2650), (551, 3953, 2292), (2292, 3953, 42038), (3333, 28011, 31), (3555, 27627, 21805), (3616, 3976, 38), (3623, 9335, 24440), (11019, 23675, 21935)

Contributed by César Eliud Lozada, December 7, 2021.

X(46191) = MIDPOINT OF PU(160)

X(46192) = X(30)X(511) ∩ X(1019)X(6626)

X(46192) = crossdifference of every pair of points on line {X(6), X(46195)}
X(46192) = ideal point of PU(160)

X(46193) = X(81)X(6651) ∩ X(757)X(4094)

X(46193) lies on these lines: {81, 6651}, {757, 4094}, {873, 18059}, {1961, 40439}, {2054, 17731}, {4594, 20090}, {6542, 37128}

X(46193) = isogonal conjugate of X(46195)
X(46193) = barycentric quotient X(i)/X(j) for these (i, j): (48, 20782), (1326, 20668), (1757, 20687)
X(46193) = trilinear quotient X(i)/X(j) for these (i, j): (3, 20782), (1931, 20668)
X(46193) = trilinear pole of the line {1019, 6626}
X(46193) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2054)}} and {{A, B, C, X(81), X(86)}}
X(46193) = cevapoint of X(i) and X(j) for these (i, j): {1, 17731}, {86, 740}
X(46193) = X(4)-isoconjugate-of-X(20782)
X(46193) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (48, 20782), (1326, 20668)
X(46193) = trilinear pole of PU(160)

X(46194) = X(58)X(291) ∩ X(99)X(1475)

X(46194) lies on these lines: {42, 40408}, {58, 291}, {81, 1500}, {83, 2350}, {86, 3294}, {99, 1475}, {213, 37128}, {274, 39252}, {662, 17745}, {757, 5280}, {1018, 32004}, {1334, 33770}, {1724, 24923}, {3842, 25526}, {4253, 17103}, {5525, 33953}, {16549, 17731}, {17754, 34016}, {18206, 36483}

X(46195) = ISOGONAL CONJUGATE OF X(46193)

X(46195) lies on these lines: {1, 6626}, {37, 42}, {292, 3747}, {740, 20947}, {741, 36066}, {1149, 4128}, {1621, 1964}, {1914, 5147}, {1961, 4434}, {2643, 3290}, {3122, 20461}, {4079, 7234}, {8299, 38978}, {9277, 40433}, {9507, 20360}, {16784, 23648}, {21254, 33891}

X(46195) = isogonal conjugate of X(46193)
X(46195) = barycentric product X(92)*X(20782)
X(46195) = trilinear product X(4)*X(20782)
X(46195) = intersection, other than A, B, C, of circumconics {{A, B, C, X(37), X(9506)}} and {{A, B, C, X(292), X(20529)}}
X(46195) = crossdifference of every pair of points on line {X(1019), X(6626)}
X(46195) = crosspoint of X(i) and X(j) for these (i, j): {1, 2054}, {42, 741}
X(46195) = crosssum of X(i) and X(j) for these (i, j): {1, 17731}, {86, 740}
X(46195) = X(1)-line conjugate of-X(6626)
X(46195) = crossdifference of PU(160)

X(46196) = COMPLEMENT OF X(17169)

X(46196) lies on these lines: {1, 1573}, {2, 2350}, {6, 16842}, {9, 46}, {10, 1018}, {21, 35342}, {37, 762}, {45, 24429}, {58, 37675}, {101, 5260}, {169, 857}, {200, 4204}, {210, 3970}, {274, 29460}, {333, 29456}, {350, 29773}, {405, 4258}, {429, 7719}, {518, 25086}, {573, 3091}, {668, 29383}, {740, 24049}, {756, 16600}, {758, 21921}, {846, 46198}, {860, 7079}, {942, 17746}, {966, 4266}, {1019, 6626}, {1125, 3691}, {1211, 7308}, {1400, 3947}, {1475, 19862}, {1500, 31855}, {1577, 32008}, {1724, 5275}, {1764, 36662}, {1765, 37112}, {2092, 3731}, {2292, 16611}, {2294, 24048}, {2328, 28062}, {2503, 6537}, {3125, 21879}, {3216, 5283}, {3247, 4272}, {3496, 37049}, {3501, 19875}, {3624, 21384}, {3646, 41014}, {3678, 21808}, {3679, 4050}, {3684, 5259}, {3730, 9780}, {3739, 4721}, {3740, 16601}, {3760, 3948}, {3770, 25458}, {3882, 31144}, {3921, 4515}, {3930, 4015}, {3952, 22011}, {3983, 3991}, {3985, 4647}, {4002, 21872}, {4115, 17164}, {4199, 8580}, {4205, 17742}, {4251, 5047}, {4262, 16865}, {4424, 16605}, {4651, 21070}, {4754, 36812}, {5022, 16862}, {5030, 17531}, {5224, 17671}, {5257, 21061}, {5299, 17123}, {5506, 5540}, {5816, 6836}, {6707, 18164}, {7377, 21363}, {10176, 17451}, {10455, 26045}, {11108, 16783}, {15485, 41333}, {16503, 25542}, {16569, 21838}, {16572, 17056}, {16788, 34812}, {17129, 20138}, {17163, 24044}, {17185, 26044}, {17256, 21362}, {17260, 20372}, {17266, 31037}, {17277, 18046}, {17289, 20605}, {17292, 21383}, {17736, 41229}, {17744, 36478}, {18133, 29486}, {18230, 27039}, {20337, 36483}, {20367, 24603}, {21033, 25081}, {21372, 27065}, {21753, 26102}, {24045, 33108}, {24051, 27804}, {25088, 40967}, {25280, 29699}, {27033, 27091}, {29399, 29405}, {29440, 37686}, {29742, 30963}, {29812, 31238}, {32431, 37433}, {33557, 37508}

X(46196) = complement of X(17169)
X(46196) = barycentric product X(i)*X(j) for these {i, j}: {1, 17163}, {10, 5284}, {75, 4068}, {81, 24044}
X(46196) = trilinear product X(i)*X(j) for these {i, j}: {2, 4068}, {6, 17163}, {37, 5284}, {58, 24044}
X(46196) = perspector of the circumconic {{A, B, C, X(6742), X(46193)}}
X(46196) = crossdifference of every pair of points on line {X(2605), X(46195)}
X(46196) = X(i)-complementary conjugate of-X(j) for these (i, j): (1170, 17050), (1174, 3739), (1400, 45226)
X(46196) = X(i)-Zayin conjugate of-X(j) for these (i, j): (2, 3219), (514, 1019), (1255, 81)
X(46196) = bicentric sum of PU(160)
X(46196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 17499, 17175), (9, 1698, 16549), (37, 3697, 4006), (1125, 3691, 45751), (1213, 38930, 442), (2238, 16589, 1), (5283, 37673, 3216), (11108, 37658, 16783), (17277, 18140, 29433)

X(46197) = X(2)X(6) ∩ X(9)X(21783)

X(46197) = barycentric product X(1)*X(46198)
X(46197) = trilinear product X(6)*X(46198)
X(46197) = barycentric product of PU(160)

X(46198) = X(1)X(75) ∩ X(8)X(5539)

X(46198) lies on these lines: {1, 75}, {8, 5539}, {846, 46196}, {1574, 3571}, {2640, 17744}, {4418, 17499}, {21816, 24450}

X(46198) = barycentric product X(75)*X(46197)
X(46198) = trilinear product X(2)*X(46197)
X(46198) = trilinear product of PU(160)

X(46199) = ISOGONAL CONJUGATE OF X(10539)

X(46199) lies on these lines: {20, 6193}, {403, 14249}, {925, 44752}, {1249, 3003}, {2986, 46200}, {7871, 14615}, {9307, 26879}, {10152, 14264}, {11585, 40698}, {19185, 32534}

X(46199) = isogonal conjugate of X(10539)
X(46199) = trilinear quotient X(91)/X(46200)
X(46199) = trilinear pole of the line {686, 6587}
X(46199) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3147)}} and {{A, B, C, X(3), X(403)}}
X(46199) = cevapoint of X(3) and X(44752)
X(46199) = X(47)-isoconjugate-of-X(46200)
X(46199) = cevapoint of PU(161)

X(46200) = X(3)X(847) ∩ X(30)X(64)

X(46200) lies on these lines: {3, 847}, {5, 8906}, {26, 2351}, {30, 64}, {96, 14070}, {155, 34757}, {156, 32734}, {382, 5962}, {1899, 44209}, {1975, 46134}, {2165, 13383}, {2986, 46199}, {5392, 7387}, {6642, 40698}, {7529, 39116}, {12084, 16391}, {13292, 39111}, {16238, 32132}, {27367, 35930}

X(46200) = reflection of X(68) in the line X(523)X(20302)
X(46200) = trilinear product X(91)*X(10539)
X(46200) = trilinear quotient X(91)/X(46199)
X(46200) = X(925)-beth conjugate of-X(221)
X(46200) = X(47)-isoconjugate-of-X(46199)
X(46200) = crosspoint of PU(161)
X(46200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (847, 925, 3), (14593, 34853, 5)

X(46201) = X(4)X(15021) ∩ X(2986)X(44569)

X(46201) lies on the Kiepert circumhyperbola and these lines: {4, 15021}, {2986, 44569}, {17503, 41254}, {40112, 44877}

X(46201) = isogonal conjugate of X(46203)
X(46201) = trilinear pole of the line {523, 3830}
X(46201) = cevapoint of X(6) and X(18571)
X(46201) = trilinear pole of PU(162)

X(46202) = X(110)X(20421) ∩ X(2930)X(3098)

X(46202) lies on these lines: {110, 20421}, {389, 46221}, {2930, 3098}, {3357, 37496}, {4550, 15045}, {7689, 12112}, {10170, 37470}, {11438, 18369}, {11738, 15107}

X(46203) = ISOGONAL CONJUGATE OF X(46201)

X(46203) lies on these lines: {3, 6}, {625, 45331}, {5306, 39602}, {6128, 43291}, {9142, 21639}, {13192, 23357}

X(46203) = isogonal conjugate of X(46201)
X(46203) = perspector of the circumconic {{A, B, C, X(110), X(20421)}}
X(46203) = crossdifference of every pair of points on line {X(523), X(3830)}
X(46203) = crosssum of X(6) and X(18571)
X(46203) = X(2)-Ceva conjugate of-X(39083)
X(46203) = X(31)-complementary conjugate of-X(39083)
X(46203) = crossdifference of PU(162)
X(46203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (50, 3003, 46222), (187, 40349, 5585), (3284, 34569, 50), (5024, 10317, 187), (15166, 15167, 18573)

X(46204) = X(6)X(1327) ∩ X(2165)X(18487)

X(46204) lies on these lines: {6, 1327}, {37, 46205}, {216, 46223}, {2165, 18487}, {3018, 15682}, {22165, 40802}

X(46204) = barycentric product X(i)*X(j) for these {i, j}: {1, 46205}, {1327, 1328}
X(46204) = barycentric quotient X(i)/X(j) for these (i, j): (25, 35472), (1327, 32809), (1328, 32808)
X(46204) = trilinear product X(6)*X(46205)
X(46204) = trilinear quotient X(19)/X(35472)
X(46204) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(3845)}}
X(46204) = X(63)-isoconjugate-of-X(35472)
X(46204) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 35472), (1327, 32809), (1328, 32808)
X(46204) = barycentric product of PU(162)

X(46205) = X(37)X(46204) ∩ X(91)X(18486)

X(46205) = barycentric product X(75)*X(46204)
X(46205) = barycentric quotient X(19)/X(35472)
X(46205) = trilinear product X(i)*X(j) for these {i, j}: {2, 46204}, {1327, 1328}
X(46205) = trilinear quotient X(i)/X(j) for these (i, j): (4, 35472), (1328, 6200)
X(46205) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}} and {{A, B, C, X(318), X(33696)}}
X(46205) = X(3)-isoconjugate-of-X(35472)
X(46205) = X(19)-reciprocal conjugate of-X(35472)
X(46205) = trilinear product of PU(162)

X(46206) = ISOGONAL CONJUGATE OF X(34569)

X(46206) lies on the Kiepert circumhyperbola and these lines: {4, 6723}, {98, 37911}, {648, 38253}, {38259, 41254}, {44569, 46210}

X(46206) = isogonal conjugate of X(34569)
X(46206) = isotomic conjugate of complement of X(47296)
X(46206) = polar conjugate of X(13473)
X(46206) = barycentric quotient X(4)/X(13473)
X(46206) = trilinear quotient X(92)/X(13473)
X(46206) = trilinear pole of the line {523, 3146}
X(46206) = intersection, other than A, B, C, of circumconics Kiepert hyperbola and {{A, B, C, X(287), X(6723)}}
X(46206) = cevapoint of X(6) and X(37941)
X(46206) = X(48)-isoconjugate-of-X(13473)
X(46206) = X(4)-reciprocal conjugate of-X(13473)
X(46206) = trilinear pole of PU(163)

X(46207) = X(110)X(3532) ∩ X(1498)X(2781)

X(46207) lies on these lines: {6, 44870}, {110, 3532}, {389, 46215}, {1192, 10539}, {1498, 2781}, {1993, 22334}, {5907, 10541}, {12160, 15811}, {18369, 18451}, {27082, 41467}

X(46207) = crosssum of PU(163)
X(46207) = {X(110), X(3532)}-harmonic conjugate of X(15748)

X(46208) = ISOTOMIC CONJUGATE OF X(32841)

X(46208) lies on these lines: {6, 1131}, {37, 46209}, {216, 46217}, {18487, 46212}, {32840, 42407}, {33630, 45004}

X(46208) = isotomic conjugate of X(32841)
X(46208) = polar conjugate of the anticomplement of X(38292)
X(46208) = barycentric product X(i)*X(j) for these {i, j}: {1, 46209}, {4, 15749}, {1131, 1132}
X(46208) = barycentric quotient X(i)/X(j) for these (i, j): (25, 15750), (1131, 1271), (1132, 1270)
X(46208) = trilinear product X(i)*X(j) for these {i, j}: {6, 46209}, {19, 15749}
X(46208) = trilinear quotient X(19)/X(15750)
X(46208) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(3832)}}
X(46208) = X(63)-isoconjugate-of-X(15750)
X(46208) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 15750), (1131, 1271), (1132, 1270)
X(46208) = barycentric product of PU(163)
X(46208) = {X(1131), X(1132)}-harmonic conjugate of X(15749)

X(46209) = X(37)X(46208) ∩ X(65)X(15749)

X(46209) lies on these lines: {37, 46208}, {65, 15749}, {18486, 46213}, {44706, 46218}

X(46209) = barycentric product X(i)*X(j) for these {i, j}: {75, 46208}, {92, 15749}
X(46209) = barycentric quotient X(i)/X(j) for these (i, j): (19, 15750), (75, 32841)
X(46209) = trilinear product X(i)*X(j) for these {i, j}: {2, 46208}, {4, 15749}, {1131, 1132}
X(46209) = trilinear quotient X(i)/X(j) for these (i, j): (4, 15750), (76, 32841), (1131, 1152), (1132, 1151)
X(46209) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(10)}} and {{A, B, C, X(341), X(18815)}}
X(46209) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 15750}, {32, 32841}, {1151, 1152}
X(46209) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (19, 15750), (75, 32841)
X(46209) = trilinear product of PU(163)

X(46210) = TRILINEAR POLE OF LINE PU(164)

X(46210) = isogonal conjugate of X(46211)
X(46210) = trilinear pole of the line {523, 11001}
X(46210) = trilinear pole of PU(164)

X(46211) = ISOGONAL CONJUGATE OF X(46210)

X(46211) = isogonal conjugate of X(46210)
X(46211) = crossdifference of every pair of points on line {X(523), X(11001)}
X(46211) = crossdifference of PU(164)
X(46211) = {X(187), X(5024)}-harmonic conjugate of X(40349)

X(46212) = X(6)X(14226) ∩ X(18487)X(46208)

X(46212) = barycentric product X(1)*X(46213)
X(46212) = trilinear product X(6)*X(46213)
X(46212) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(41106)}}
X(46212) = barycentric product of PU(164)

X(46213) = X(37)X(46212) ∩ X(18486)X(46209)

X(46213) = barycentric product X(75)*X(46212)
X(46213) = trilinear product X(2)*X(46212)
X(46213) = trilinear product of PU(164)

X(46214) = TRILINEAR POLE OF LINE PU(165)

X(46214) = isogonal conjugate of X(46216)
X(46214) = trilinear pole of the line {523, 3525}
X(46214) = trilinear pole of line PU(165)

X(46215) = X(389)X(46207) ∩ X(399)X(7529)

X(46215) lies on these lines: {3, 6688}, {389, 46207}, {399, 7529}, {1598, 15045}, {3066, 10984}, {3531, 17928}, {5020, 10263}, {10170, 11484}, {12160, 43614}, {15606, 17810}, {20417, 38790}

X(46216) = ISOGONAL CONJUGATE OF X(46214)

X(46216) is the Brocard axis intercept of the line through the X(3311)-Ceva conjugate of X(3312) and the X(3312)-Ceva conjugate of X(3311). (Randy Hutson, January 11, 2022)

X(46216) = isogonal conjugate of X(46214)
X(46216) = crossdifference of every pair of points on line {X(523), X(3525)}
X(46216) = crossdifference of PU(165)
X(46216) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (50, 3003, 34569), (50, 46222, 187), (3003, 18365, 40135)

X(46217) = ISOTOMIC CONJUGATE OF X(32839)

X(46217) lies on these lines: {6, 3316}, {37, 46218}, {216, 46208}, {308, 32867}, {8882, 12815}, {32829, 42332}, {32838, 42407}

X(46217) = isotomic conjugate of X(32839)
X(46217) = barycentric product X(1)*X(46218)
X(46217) = trilinear product X(6)*X(46218)
X(46217) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(4), X(5067)}}
X(46217) = barycentric product of PU(165)

X(46218) = X(37)X(46217) ∩ X(44706)X(46209)

X(46218) = barycentric product X(75)*X(46217)
X(46218) = barycentric quotient X(75)/X(32839)
X(46218) = trilinear product X(2)*X(46217)
X(46218) = trilinear quotient X(76)/X(32839)
X(46218) = X(32)-isoconjugate-of-X(32839)
X(46218) = X(75)-reciprocal conjugate of-X(32839)
X(46218) = trilinear product of PU(165)

X(46219) = EULER LINE INTERCEPT OF X(6)X(11614)

X(46219) = 9*X(3)+4*X(4)
X(46219) = 12*X(2)+X(3) = 15*X(2)-2*X(5) = 9*X(2)+4*X(140) = 14*X(2)-X(381) = 17*X(2)-4*X(547) = 11*X(2)+2*X(549) = 3*X(2)+10*X(632) = 18*X(2)-5*X(1656) = 15*X(2)+11*X(3525) = 6*X(2)+7*X(3526) = 9*X(2)+17*X(3533) = 10*X(2)+3*X(5054) = 16*X(2)-3*X(5055) = 9*X(2)-X(5068) = 6*X(2)-X(5079) = 5*X(2)+8*X(10124) = 9*X(2)+X(10299) = 3*X(2)+X(10303) = 7*X(2)+6*X(11539) = 8*X(2)+5*X(15694) = 19*X(2)-6*X(15699) = 19*X(2)+7*X(15702) = 20*X(2)-7*X(15703) = 17*X(2)+9*X(15709) = 2*X(2)+11*X(15723) = 3*X(2)-16*X(16239) = 15*X(2)+X(21734)

X(46219) lies on these lines: {2, 3}, {6, 11614}, {10, 37624}, {13, 42491}, {14, 42490}, {17, 10188}, {18, 10187}, {49, 43650}, {54, 14841}, {61, 42978}, {62, 42979}, {69, 32884}, {76, 10185}, {143, 7998}, {154, 14864}, {182, 9704}, {183, 7871}, {195, 15066}, {230, 31467}, {265, 38638}, {371, 42557}, {372, 42558}, {373, 5447}, {395, 42594}, {396, 42595}, {397, 42089}, {398, 42092}, {399, 34128}, {485, 41950}, {486, 41949}, {498, 7294}, {499, 5326}, {517, 34595}, {568, 11695}, {575, 21358}, {590, 6418}, {615, 6417}, {952, 19877}, {1001, 20107}, {1073, 22268}, {1125, 10247}, {1147, 22112}, {1154, 15028}, {1159, 24914}, {1351, 25555}, {1384, 1506}, {1385, 37712}, {1482, 3624}, {1649, 10279}, {1698, 10246}, {1853, 45185}, {1993, 15047}, {2055, 37877}, {2888, 20585}, {2979, 13421}, {3035, 31493}, {3054, 31401}, {3055, 21309}, {3060, 32205}, {3068, 6501}, {3069, 6500}, {3070, 6446}, {3071, 6445}, {3167, 43839}, {3311, 8252}, {3312, 8253}, {3519, 6689}, {3527, 26861}, {3567, 32142}, {3576, 30315}, {3589, 5093}, {3590, 43564}, {3591, 43565}, {3619, 11898}, {3622, 38112}, {3634, 5790}, {3655, 31399}, {3763, 5050}, {3815, 43136}, {3819, 6243}, {3828, 37727}, {3933, 32839}, {4413, 37621}, {4423, 11849}, {5023, 7603}, {5024, 7746}, {5085, 18553}, {5219, 37545}, {5309, 31492}, {5334, 42951}, {5335, 42950}, {5339, 16967}, {5340, 16966}, {5343, 42143}, {5344, 42146}, {5349, 42111}, {5350, 42114}, {5351, 43646}, {5352, 43645}, {5365, 42122}, {5366, 42123}, {5418, 6199}, {5420, 6395}, {5433, 31479}, {5462, 5650}, {5550, 5690}, {5640, 10627}, {5644, 42021}, {5646, 37494}, {5655, 38729}, {5708, 31231}, {5734, 38022}, {5886, 19878}, {5891, 13382}, {5892, 18436}, {5895, 10193}, {5907, 40280}, {5943, 37484}, {5946, 7999}, {6033, 38634}, {6101, 13321}, {6221, 10577}, {6321, 38635}, {6337, 32883}, {6390, 32838}, {6398, 10576}, {6407, 13785}, {6408, 13665}, {6427, 13847}, {6428, 13846}, {6447, 35823}, {6448, 35822}, {6449, 42262}, {6450, 42265}, {6451, 23261}, {6452, 23251}, {6455, 6565}, {6456, 6564}, {6472, 43377}, {6473, 43376}, {6474, 43509}, {6475, 43510}, {6496, 35821}, {6497, 35820}, {6667, 10993}, {6683, 32447}, {6684, 18493}, {6688, 10625}, {6721, 10991}, {6722, 10992}, {6723, 30714}, {7308, 37612}, {7607, 7940}, {7608, 43527}, {7610, 7764}, {7619, 34505}, {7728, 38633}, {7739, 31470}, {7749, 30435}, {7754, 17006}, {7755, 9605}, {7760, 8860}, {7767, 34803}, {7769, 32821}, {7776, 37647}, {7780, 11184}, {7781, 40727}, {7815, 11842}, {7869, 15271}, {7888, 8556}, {7988, 31663}, {7989, 17502}, {8148, 13464}, {8371, 32204}, {8550, 34573}, {8724, 38740}, {8972, 43505}, {8981, 32786}, {9140, 15039}, {9167, 20398}, {9306, 37471}, {9342, 32141}, {9540, 18510}, {9690, 18762}, {9691, 42215}, {9703, 13353}, {9755, 16988}, {9780, 12645}, {9956, 19872}, {10072, 31480}, {10156, 40263}, {10165, 18525}, {10168, 15069}, {10170, 34783}, {10172, 18481}, {10192, 34780}, {10198, 12001}, {10200, 12000}, {10219, 15644}, {10222, 38066}, {10263, 11451}, {10539, 13339}, {10540, 37515}, {10541, 11178}, {10574, 14128}, {10601, 14627}, {10605, 33540}, {10738, 38636}, {10742, 38637}, {10749, 38639}, {10982, 37496}, {10990, 12900}, {11017, 11455}, {11171, 31239}, {11230, 11522}, {11412, 13363}, {11426, 26958}, {11432, 12242}, {11444, 12006}, {11480, 42959}, {11481, 42958}, {11482, 40107}, {11488, 43102}, {11489, 43103}, {11591, 15045}, {11623, 15561}, {11632, 38751}, {11793, 37481}, {12017, 24206}, {12041, 15046}, {12174, 43608}, {12308, 15061}, {12315, 14862}, {12331, 34126}, {12815, 13881}, {12902, 38793}, {13108, 40108}, {13188, 34127}, {13336, 18350}, {13348, 14845}, {13432, 21230}, {13571, 17004}, {13935, 18512}, {13941, 43506}, {13966, 32785}, {14449, 33884}, {14530, 20299}, {14643, 20417}, {14861, 43719}, {14978, 44914}, {15034, 20396}, {15037, 15805}, {15040, 20304}, {15043, 15067}, {15051, 15088}, {15059, 32609}, {15178, 19875}, {15533, 22234}, {16241, 42153}, {16242, 42156}, {16772, 42975}, {16773, 42974}, {16836, 18439}, {16960, 42954}, {16961, 42955}, {16962, 43427}, {16963, 43426}, {17606, 37606}, {17811, 36753}, {17821, 32767}, {17825, 36749}, {17851, 23267}, {18526, 38042}, {18538, 42570}, {18581, 42945}, {18582, 42944}, {19854, 31235}, {19883, 34718}, {20104, 25524}, {20126, 38795}, {20400, 38069}, {20418, 38752}, {20791, 45959}, {21001, 43843}, {21154, 38756}, {22235, 42492}, {22236, 42489}, {22237, 42493}, {22238, 42488}, {22246, 30122}, {23236, 45311}, {23294, 26864}, {23302, 42149}, {23303, 42152}, {24926, 43731}, {25542, 26285}, {25563, 35450}, {28198, 31425}, {31162, 31447}, {31188, 34753}, {31274, 38224}, {31275, 38225}, {31276, 32519}, {31454, 43254}, {31487, 32788}, {32063, 40686}, {32149, 44453}, {32817, 32897}, {32818, 32898}, {32820, 32832}, {32824, 32867}, {32825, 34229}, {33520, 38774}, {33521, 38767}, {33537, 33887}, {33878, 38317}, {34565, 44749}, {35814, 43379}, {35815, 43378}, {36750, 37679}, {36754, 37682}, {36836, 37835}, {36843, 37832}, {36990, 42786}, {37509, 37674}, {37714, 38083}, {38727, 38790}, {38733, 38748}, {38737, 38744}, {38848, 41462}, {41943, 42593}, {41944, 42592}, {41967, 43323}, {41968, 43322}, {42095, 42157}, {42098, 42158}, {42117, 42495}, {42118, 42494}, {42121, 42817}, {42124, 42818}, {42125, 42150}, {42126, 42692}, {42127, 42693}, {42128, 42151}, {42135, 43770}, {42138, 43769}, {42144, 42473}, {42145, 42472}, {42147, 42910}, {42148, 42911}, {42154, 42580}, {42155, 42581}, {42160, 43101}, {42161, 43104}, {42163, 42500}, {42166, 42501}, {42431, 42915}, {42432, 42914}, {42474, 42528}, {42475, 42529}, {42476, 42895}, {42477, 42894}, {42522, 43374}, {42523, 43375}, {42572, 42602}, {42573, 42603}, {42627, 43447}, {42628, 43446}, {42688, 42798}, {42689, 42797}, {42779, 43467}, {42780, 43468}, {42795, 42890}, {42796, 42891}, {42815, 42924}, {42816, 42925}, {42896, 43370}, {42897, 43371}, {42982, 43445}, {42983, 43444}, {43006, 43024}, {43007, 43025}

X(46219) = midpoint of X(i) and X(j) for these {i, j}: {2045, 2046}, {3534, 35402}, {5067, 10303}, {5068, 10299}, {14893, 35421}, {15693, 35382}, {17800, 35406}
X(46219) = reflection of X(i) in X(j) for these (i, j): (5079, 5067), (11818, 7505), (18494, 13620)
X(46219) = complement of X(5067)
X(46219) = perspector of the circumconic {{A, B, C, X(648), X(46220)}}
X(46219) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5), X(14841)}} and {{A, B, C, X(20), X(22268)}}
X(46219) = crossdifference of every pair of points on line {X(647), X(46222)}
X(46219) = midpoint of PU(166)
X(46219) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 3526, 3), (4, 15720, 3), (5, 5054, 3), (20, 15693, 3), (140, 1656, 3), (381, 631, 3), (382, 549, 3), (548, 15700, 3), (549, 41984, 2), (632, 16239, 2), (1506, 44535, 1384), (1657, 3523, 3), (2070, 7516, 3), (2937, 7485, 3), (3524, 15696, 3), (3528, 15706, 3), (3530, 3534, 3), (3624, 11231, 1482), (3843, 15701, 3), (5070, 15694, 3), (5072, 14869, 3), (5079, 10303, 3), (6883, 45976, 3), (7484, 7506, 3), (7509, 45735, 3), (7514, 43809, 3), (7542, 30771, 3), (7998, 11465, 143), (13846, 35813, 6428), (13847, 35812, 6427), (14093, 44682, 3), (15688, 15717, 3), (15707, 17800, 3), (15723, 16239, 3), (17928, 34864, 3), (42936, 42937, 6), (43028, 43238, 18), (43029, 43239, 17)

X(46220) = TRILINEAR POLE OF LINE PU(166)

X(46220) = isogonal conjugate of X(46222)
X(46220) = trilinear pole of the line {523, 46219}
X(46220) = trilinear pole of line PU(166)

X(46221) = X(3)X(21849) ∩ X(389)X(46202)

X(46222) = ISOGONAL CONJUGATE OF X(46220)

X(46222) = isogonal conjugate of X(46220)
X(46222) = crossdifference of every pair of points on line {X(523), X(46219)}
X(46222) = crossdifference of PU(166)
X(46222) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (50, 3003, 46203), (187, 46216, 50)

X(46223) = X(6)X(10194) ∩ X(216)X(46204)

X(46223) lies on these lines: {6, 10194}, {37, 46224}, {216, 46204}, {32832, 42332}

X(46223) = barycentric product X(1)*X(46224)
X(46223) = trilinear product X(6)*X(46224)
X(46223) = barycentric product of PU(166)

X(46224) = X(37)X(46223) ∩ X(44706)X(46205)

X(46224) = barycentric product X(75)*X(46223)
X(46224) = trilinear product X(2)*X(46223)
X(46224) = trilinear product of PU(166)

X(46225) = ISOTOMIC CONJUGATE OF X(40000)

X(46225) lies on these lines: {2, 14370}, {6, 2896}, {141, 28677}, {755, 7832}, {3589, 46227}, {6656, 14970}, {7859, 40850}, {17949, 46226}

X(46225) = isogonal conjugate of X(46227)
X(46225) = isotomic conjugate of X(40000)
X(46225) = barycentric product X(6)*X(40043)
X(46225) = barycentric quotient X(141)/X(46226)
X(46225) = trilinear product X(31)*X(40043)
X(46225) = trilinear quotient X(1930)/X(46226)
X(46225) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(17192)}} and {{A, B, C, X(2), X(2896)}}
X(46225) = X(39)-Dao conjugate of X(46226)
X(46225) = X(141)-reciprocal conjugate of-X(46226)
X(46225) = cevapoint of PU(167)

X(46226) = X(2)X(39) ∩ X(3)X(16986)

X(46226) lies on these lines: {2, 39}, {3, 16986}, {4, 7938}, {5, 7931}, {6, 16895}, {20, 3818}, {30, 7928}, {32, 19689}, {69, 7787}, {83, 7779}, {99, 6292}, {115, 7944}, {140, 12188}, {141, 384}, {148, 6656}, {183, 7892}, {230, 14043}, {316, 7849}, {385, 7819}, {420, 12143}, {599, 7893}, {621, 635}, {622, 636}, {625, 33024}, {626, 16044}, {631, 14880}, {733, 35567}, {754, 32027}, {1003, 7904}, {1078, 7820}, {1352, 35422}, {1506, 7909}, {1930, 17280}, {1975, 3763}, {2548, 7897}, {3053, 14036}, {3096, 3734}, {3314, 7770}, {3329, 3933}, {3407, 7793}, {3552, 7800}, {3589, 7839}, {3619, 7791}, {3620, 20065}, {3785, 14037}, {3815, 7947}, {3972, 7854}, {4195, 17232}, {5025, 7868}, {5189, 31124}, {5224, 33827}, {5254, 7948}, {5475, 7922}, {5989, 7789}, {6658, 7761}, {6661, 7767}, {6704, 7813}, {7737, 7929}, {7745, 7939}, {7747, 7883}, {7748, 7937}, {7751, 7846}, {7752, 7869}, {7753, 7917}, {7754, 7875}, {7760, 7889}, {7768, 7804}, {7774, 16045}, {7777, 7881}, {7778, 16921}, {7783, 8362}, {7784, 11361}, {7788, 7921}, {7790, 7914}, {7792, 17129}, {7796, 7808}, {7802, 7865}, {7806, 33217}, {7812, 7896}, {7815, 7835}, {7816, 7831}, {7823, 7879}, {7826, 12150}, {7830, 31168}, {7833, 11164}, {7847, 20094}, {7855, 7878}, {7856, 17131}, {7858, 7895}, {7885, 8370}, {7891, 11285}, {7898, 14035}, {7901, 46236}, {7906, 11174}, {7907, 15271}, {7910, 19691}, {7912, 16924}, {7923, 8364}, {7924, 32819}, {7925, 32992}, {7933, 11185}, {7934, 32993}, {7936, 19693}, {8591, 20582}, {8724, 9302}, {9301, 44237}, {9862, 44224}, {9873, 11178}, {9939, 21356}, {10007, 32476}, {10304, 14458}, {10328, 35214}, {11293, 43407}, {11294, 43408}, {12110, 40107}, {13881, 14065}, {14069, 17008}, {14376, 37186}, {16897, 34573}, {16922, 44377}, {16984, 33185}, {17000, 17540}, {17004, 32954}, {17234, 17688}, {17238, 17691}, {17279, 33943}, {17300, 33953}, {17302, 39722}, {17358, 25242}, {17383, 19784}, {17681, 31090}, {17949, 46225}, {18358, 44251}, {20335, 30175}, {24206, 37336}, {24249, 30177}, {30174, 30949}, {32816, 33269}, {32999, 37690}, {33245, 37688}, {40000, 46227}

X(46226) = isogonal conjugate of X(46287)
X(46226) = anticomplement of X(7859)
X(46226) = crosssum of PU(183)
X(46226) = barycentric product X(141)*X(40000)
X(46226) = barycentric quotient X(141)/X(46225)
X(46226) = trilinear quotient X(40000)/X(82)
X(46226) = trilinear product X(38)*X(40000)
X(46226) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(14370)}} and {{A, B, C, X(76), X(1031)}}
X(46226) = X(39)-Dao conjugate of X(46225)
X(46226) = X(141)-reciprocal conjugate of-X(46225)
X(46226) = crosspoint of PU(167)
X(46226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 76, 7797), (2, 7795, 7836), (2, 20081, 7803), (2, 31078, 19577), (69, 16898, 7787), (76, 7797, 19570), (76, 7822, 2), (76, 7943, 5309), (83, 7794, 7779), (99, 6292, 33021), (141, 384, 2896), (141, 24273, 5207), (384, 2896, 14712), (385, 7819, 10583), (1078, 7820, 33225), (1975, 3763, 7876), (3096, 3734, 6655), (3314, 7770, 7785), (3329, 3933, 13571), (3934, 7832, 2), (6656, 17128, 148), (7746, 7930, 2), (7769, 31239, 2), (7828, 7915, 2), (7839, 16896, 3589), (7879, 11286, 7823), (7880, 31239, 7769), (7914, 17130, 7790), (7915, 9466, 7828), (14001, 16990, 7793), (14001, 18840, 16990), (17129, 19694, 7792), (17280, 39724, 1930)

X(46227) = ISOGONAL CONJUGATE OF X(46225)

X(46227) lies on these lines: {2, 32}, {3, 41295}, {6, 14370}, {39, 46228}, {112, 28666}, {148, 8856}, {384, 28677}, {827, 5007}, {1176, 13331}, {3589, 46225}, {4577, 7839}, {5149, 28674}, {7765, 38946}, {7772, 14247}, {16896, 40425}, {18907, 28664}, {40000, 46226}

X(46227) = isogonal conjugate of X(46225)
X(46227) = isotomic conjugate of X(40043)
X(46227) = barycentric product X(i)*X(j) for these {i, j}: {6, 40000}, {251, 46226}
X(46227) = trilinear product X(31)*X(40000)
X(46227) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(14370)}} and {{A, B, C, X(6), X(2896)}}
X(46227) = crosssum of PU(167)
X(46227) = {X(251), X(9481)}-harmonic conjugate of X(32)

X(46228) = ISOGONAL CONJUGATE OF X(17949)

X(46228) lies on the cubics K222, K789 and these lines: {2, 1031}, {3, 9481}, {6, 22}, {32, 14247}, {39, 46227}, {83, 4045}, {115, 38946}, {187, 827}, {385, 4577}, {543, 38888}, {689, 35524}, {699, 783}, {733, 1691}, {1627, 8265}, {2076, 24973}, {3005, 18105}, {4628, 17735}, {7779, 40850}, {7794, 40003}, {8623, 9480}, {8928, 40236}, {9076, 16102}, {10130, 16986}, {13236, 34214}, {14712, 16095}, {14970, 39089}

X(46228) = isogonal conjugate of X(17949)
X(46228) = barycentric product X(i)*X(j) for these {i, j}: {1, 34054}, {6, 40850}, {82, 17799}, {83, 2076}, {99, 17997}, {110, 18010}
X(46228) = barycentric quotient X(i)/X(j) for these (i, j): (31, 17957), (251, 11606), (420, 1235), (733, 9477)
X(46228) = trilinear product X(i)*X(j) for these {i, j}: {6, 34054}, {31, 40850}, {82, 2076}, {163, 18010}, {251, 17799}, {662, 17997}
X(46228) = trilinear quotient X(i)/X(j) for these (i, j): (6, 17957), (82, 11606), (420, 20883)
X(46228) = trilinear pole of the line {5113, 17997}
X(46228) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(10329)}} and {{A, B, C, X(6), X(1031)}}
X(46228) = cevapoint of X(6) and X(9480)
X(46228) = crossdifference of every pair of points on line {X(826), X(6292)}
X(46228) = X(733)-Ceva conjugate of-X(251)
X(46228) = X(385)-Dao conjugate of X(35540)
X(46228) = X(i)-Hirst inverse of-X(j) for these (i, j): {6, 251}, {32, 14885}, {251, 6}
X(46228) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 17957}, {38, 11606}
X(46228) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (31, 17957), (251, 11606), (420, 1235), (733, 9477)
X(46228) = X(251)-vertex conjugate of-X(3005)
X(46228) = crossdifference of PU(167)
X(46228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 41295, 251), (32, 14247, 14885)

X(46229) = ISOGONAL CONJUGATE OF X(32681)

X(46229) lies on these lines: {30, 511}, {684, 42733}, {1637, 5664}, {1651, 9155}, {2394, 2986}, {8552, 14566}, {11007, 42736}, {32836, 45792}, {44564, 45681}

X(46229) = isogonal conjugate of X(32681)
X(46229) = barycentric product X(i)*X(j) for these {i, j}: {30, 30474}, {850, 10564}, {1637, 32833}
X(46229) = barycentric quotient X(i)/X(j) for these (i, j): (1, 36083), (30, 1302), (378, 1304), (1495, 32738), (1637, 34288)
X(46229) = trilinear product X(1577)*X(10564)
X(46229) = trilinear quotient X(i)/X(j) for these (i, j): (2, 36083), (30, 36149), (378, 36131)
X(46229) = crossdifference of every pair of points on line {X(6), X(32738)}
X(46229) = X(9)-Dao conjugate of X(36083)
X(46229) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 36083}, {74, 36149}, {1302, 2159}
X(46229) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 36083), (30, 1302), (378, 1304)
X(46229) = ideal point of line PU(168)

X(46230) = TRILINEAR POLE OF LINE PU(168)

X(46230) = isogonal conjugate of X(46233)
X(46230) = barycentric quotient X(30)/X(6795)
X(46230) = trilinear pole of the line {113, 46229}
X(46230) = X(30)-reciprocal conjugate of-X(6795)
X(46230) = trilinear pole of line PU(168)

X(46231) = X(113)X(40832) ∩ X(146)X(3260)

X(46231) lies on these lines: {113, 40832}, {146, 3260}, {148, 41760}, {1975, 46247}

X(46232) = X(6)X(34178) ∩ X(10419)X(32681)

X(46233) = ISOGONAL CONJUGATE OF X(46230)

X(46233) = isogonal conjugate of X(46230)
X(46233) = barycentric product X(74)*X(6795)
X(46233) = perspector of the circumconic {{A, B, C, X(10419), X(32681)}}
X(46233) = crossdifference of every pair of points on line {X(113), X(46229)}
X(46233) = X(6)-Hirst inverse of-X(40352)
X(46233) = crossdifference of PU(168)

X(46234) = ISOTOMIC CONJUGATE OF X(2159)

X(46234) lies on these lines: {75, 1725}, {76, 43682}, {92, 304}, {799, 36102}, {824, 1577}, {14210, 23994}

X(46234) = isotomic conjugate of X(2159)
X(46234) = barycentric product X(i)*X(j) for these {i, j}: {30, 561}, {75, 3260}, {76, 14206}, {304, 46106}, {305, 1784}, {670, 36035}
X(46234) = barycentric quotient X(i)/X(j) for these (i, j): (1, 40352), (19, 40354), (30, 31), (63, 18877), (69, 35200), (75, 74)
X(46234) = trilinear product X(i)*X(j) for these {i, j}: {2, 3260}, {30, 76}, {69, 46106}, {75, 14206}, {94, 6148}, {99, 41079}
X(46234) = trilinear quotient X(i)/X(j) for these (i, j): (2, 40352), (4, 40354), (25, 40351), (30, 32), (69, 18877), (76, 74)
X(46234) = intersection, other than A, B, C, of circumconics {{A, B, C, X(30), X(824)}} and {{A, B, C, X(92), X(1577)}}
X(46234) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 40352), (30, 9406), (133, 1973), (1511, 9247)
X(46234) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 40354}, {6, 40352}, {25, 18877}, {32, 74}
X(46234) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 40352), (19, 40354), (30, 31), (63, 18877)
X(46234) = trilinear product of PU(168)

X(46235) = X(114)X(39931) ∩ X(147)X(385)

X(46235) lies on the cubic K776 and these lines: {114, 39931}, {147, 385}, {287, 44534}, {297, 19599}

X(46235) = isogonal conjugate of X(46237)
X(46235) = barycentric quotient X(325)/X(46236)
X(46235) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(147)}} and {{A, B, C, X(69), X(46236)}}
X(46235) = X(69)-cross conjugate of-X(297)
X(46235) = X(325)-reciprocal conjugate of-X(46236)
X(46235) = cevapoint of PU(169)

X(46236) = X(4)X(99) ∩ X(69)X(98)

X(46236) lies on the cubic K780 and these lines: {2, 694}, {4, 99}, {69, 98}, {76, 14651}, {115, 7795}, {141, 44531}, {147, 325}, {148, 1975}, {193, 12829}, {297, 19599}, {305, 46247}, {315, 5152}, {384, 3815}, {543, 16041}, {620, 7808}, {626, 8178}, {631, 12176}, {671, 33285}, {1078, 10357}, {1281, 7179}, {1569, 34511}, {1987, 43714}, {2482, 14033}, {2548, 5149}, {2782, 3926}, {2794, 32006}, {3407, 10353}, {3705, 7061}, {3785, 12042}, {3933, 12188}, {4027, 7774}, {5490, 13873}, {5491, 13926}, {5939, 5984}, {5985, 45962}, {5986, 40123}, {6033, 32816}, {6036, 34229}, {6321, 32815}, {6330, 6340}, {6390, 13188}, {6394, 34841}, {7735, 36849}, {7736, 10352}, {7777, 8290}, {7788, 11177}, {7799, 39266}, {7868, 9478}, {7901, 46226}, {7912, 32528}, {8591, 14041}, {8724, 32837}, {9723, 39803}, {9766, 12830}, {9888, 32986}, {11164, 11184}, {11606, 43529}, {11632, 32836}, {12243, 32833}, {13137, 15631}, {14036, 42849}, {14039, 41134}, {14046, 41135}, {14061, 32951}, {14063, 20094}, {15561, 19910}, {16089, 44132}, {16925, 39652}, {22103, 34238}, {22505, 32827}, {22515, 32826}, {32828, 38224}, {32838, 34127}, {33290, 35369}

X(46236) = reflection of X(148) in X(44518)
X(46236) = anticomplement of X(44534)
X(46236) = barycentric quotient X(325)/X(46235)
X(46236) = X(297)-Ceva conjugate of-X(69)
X(46236) = X(325)-reciprocal conjugate of-X(46235)
X(46236) = crosspoint of PU(169)
X(46236) = X(3767)-of-1st anti-Brocard triangle
X(46236) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (98, 32458, 69), (99, 8781, 114), (114, 8781, 1007), (315, 5152, 9862), (325, 5989, 147), (325, 5999, 5207), (626, 8178, 43449), (1916, 5976, 18906), (1916, 34999, 8782), (33340, 33341, 4)

X(46237) = ISOGONAL CONJUGATE OF X(46235)

X(46237) lies on the cubic K782 and these lines: {6, 34130}, {98, 2458}, {232, 1692}, {237, 694}, {248, 511}, {287, 5207}, {2456, 17974}, {5034, 14355}, {5999, 41932}, {11610, 35388}

X(46237) = isogonal conjugate of X(46235)
X(46237) = barycentric product X(1976)*X(46236)
X(46237) = X(25)-Ceva conjugate of-X(248)
X(46237) = crosssum of PU(169)
X(46237) = {X(2065), X(2715)}-harmonic conjugate of X(1692)

X(46238) = ISOTOMIC CONJUGATE OF X(1910)

X(46238) lies on the cubic K1023 and these lines: {1, 75}, {19, 1102}, {38, 20627}, {63, 20641}, {76, 20236}, {190, 20643}, {240, 23996}, {325, 42703}, {518, 35551}, {561, 14213}, {668, 35150}, {726, 20629}, {746, 8624}, {799, 14206}, {824, 1577}, {1109, 20904}, {1284, 5977}, {1920, 6358}, {1921, 4858}, {1928, 1969}, {3926, 25252}, {4137, 16891}, {6382, 20237}, {10030, 20924}, {11683, 17206}, {16703, 20896}, {16706, 24786}, {16887, 21421}, {17289, 30103}, {17787, 33939}, {17871, 18056}, {17874, 18059}, {17884, 18064}, {17890, 18068}, {17897, 18075}, {18275, 18895}, {18837, 21406}, {20437, 40017}, {20879, 33764}, {20887, 35543}, {20911, 21442}, {24037, 46254}, {27801, 40564}, {30886, 30892}

X(46238) = isotomic conjugate of X(1910)
X(46238) = barycentric product X(i)*X(j) for these {i, j}: {63, 44132}, {69, 40703}, {75, 325}, {76, 1959}, {86, 42703}, {92, 6393}
X(46238) = barycentric quotient X(i)/X(j) for these (i, j): (1, 1976), (31, 14601), (48, 14600), (63, 248), (69, 293), (75, 98)
X(46238) = trilinear product X(i)*X(j) for these {i, j}: {2, 325}, {3, 44132}, {4, 6393}, {63, 40703}, {69, 297}, {75, 1959}
X(46238) = trilinear quotient X(i)/X(j) for these (i, j): (2, 1976), (3, 14600), (6, 14601), (69, 248), (76, 98), (99, 2715)
X(46238) = perspector of the circumconic {{A, B, C, X(561), X(799)}}
X(46238) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(240)}} and {{A, B, C, X(75), X(20948)}}
X(46238) = crosspoint of X(75) and X(1934)
X(46238) = crosssum of X(31) and X(1933)
X(46238) = X(i)-daleth conjugate of-X(j) for these (i, j): (75, 1930), (304, 18695)
X(46238) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 1976), (39, 3404), (132, 1973), (230, 8772)
X(46238) = X(i)-Hirst inverse of-X(j) for these (i, j): {75, 304}, {304, 75}
X(46238) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 14601}, {4, 14600}, {6, 1976}, {25, 248}
X(46238) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 1976), (31, 14601), (48, 14600), (63, 248)
X(46238) = trilinear product of PU(169)
X(46238) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (75, 304, 3403), (75, 1966, 1733), (75, 18156, 4008), (799, 20944, 14206), (1733, 14210, 1966)

X(46239) = ISOTOMIC CONJUGATE OF X(15013)

X(46239) lies on these lines: {2, 46151}, {69, 41676}, {127, 264}, {232, 2373}, {287, 2393}, {648, 1799}, {1289, 1843}, {3186, 41769}, {15526, 18018}, {46240, 46241}

X(46239) = reflection of X(i) in X(j) for these (i, j): (648, 40938), (18018, 15526)
X(46239) = isogonal conjugate of X(46243)
X(46239) = isotomic conjugate of X(15013)
X(46239) = trilinear pole of the line {427, 525}
X(46239) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(69)}} and {{A, B, C, X(22), X(46240)}}
X(46239) = cevapoint of X(2) and X(40889)
X(46239) = trilinear pole of line PU(170)

X(46240) = X(194)X(7391) ∩ X(8788)X(28408)

X(46240) = isogonal conjugate of X(46242)
X(46240) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(7391)}} and {{A, B, C, X(4), X(28412)}}
X(46240) = cevapoint of PU(170)

X(46241) = X(22)X(16097) ∩ X(25)X(40421)

X(46241) lies on these lines: {22, 16097}, {25, 40421}, {2998, 13854}, {7391, 18018}, {46239, 46240}

X(46242) = ISOGONAL CONJUGATE OF X(46240)

X(46242) lies on these lines: {6, 34436}, {66, 46243}, {112, 1176}, {1691, 1968}, {5157, 17409}, {5596, 22075}, {7737, 24270}, {8778, 19125}, {19126, 36879}

X(46242) = isogonal conjugate of X(46240)
X(46242) = barycentric product X(206)*X(46241)
X(46242) = crosssum of PU(170)

X(46243) = ISOGONAL CONJUGATE OF X(46239)

X(46243) lies on these lines: {2, 22075}, {6, 25}, {23, 34137}, {66, 46242}, {125, 1691}, {287, 2373}, {647, 8673}, {1501, 1899}, {1799, 40404}, {2548, 14585}, {3269, 8627}, {5523, 15388}, {6638, 22391}, {10766, 15107}, {11064, 32661}, {13198, 14567}, {15139, 35325}

X(46243) = isogonal conjugate of X(46239)
X(46243) = barycentric product X(i)*X(j) for these {i, j}: {6, 15013}, {206, 16097}
X(46243) = trilinear product X(31)*X(15013)
X(46243) = perspector of the circumconic {{A, B, C, X(112), X(1176)}}
X(46243) = inverse of X(184) in MacBeath circumconic
X(46243) = intersection, other than A, B, C, of circumconics {{A, B, C, X(25), X(15013)}} and {{A, B, C, X(184), X(15388)}}
X(46243) = crossdifference of every pair of points on line {X(427), X(525)}
X(46243) = crosssum of X(2) and X(40889)
X(46243) = X(2)-Ceva conjugate of-X(39086)
X(46243) = X(6)-daleth conjugate of-X(21637)
X(46243) = X(i)-Hirst inverse of-X(j) for these (i, j): {6, 206}, {206, 6}
X(46243) = X(206)-vertex conjugate of-X(647)
X(46243) = crossdifference of PU(170)
X(46243) = {X(23), X(34137)}-harmonic conjugate of X(38356)

X(46244) = ISOGONAL CONJUGATE OF X(17453)

X(46244) lies on these lines: {19, 37220}, {66, 21280}, {75, 17870}, {92, 39733}, {304, 18669}, {336, 44179}, {561, 1760}, {18018, 20336}, {18051, 18716}, {20884, 40364}, {21017, 40071}

X(46244) = isogonal conjugate of X(17453)
X(46244) = isotomic conjugate of X(2172)
X(46244) = barycentric product X(i)*X(j) for these {i, j}: {1, 40421}, {66, 561}, {75, 18018}, {304, 43678}, {1502, 2156}
X(46244) = barycentric quotient X(i)/X(j) for these (i, j): (1, 206), (9, 4548), (19, 17409), (31, 20968), (37, 21034), (38, 23208)
X(46244) = trilinear product X(i)*X(j) for these {i, j}: {2, 18018}, {6, 40421}, {66, 76}, {69, 43678}, {264, 14376}, {276, 41168}
X(46244) = trilinear quotient X(i)/X(j) for these (i, j): (2, 206), (3, 22075), (4, 17409), (6, 20968), (7, 7251), (8, 4548)
X(46244) = trilinear pole of the line {14208, 17901}
X(46244) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1760)}} and {{A, B, C, X(19), X(1577)}}
X(46244) = cevapoint of X(i) and X(j) for these (i, j): {1, 2156}, {2, 17492}, {75, 20915}
X(46244) = X(1)-cross conjugate of-X(561)
X(46244) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 4548), (9, 206), (10, 21034), (223, 7251)
X(46244) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 20968}, {3, 17409}, {4, 22075}, {6, 206}
X(46244) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 206), (9, 4548), (19, 17409), (31, 20968)
X(46244) = trilinear product of PU(170)

X(46245) = ISOTOMIC CONJUGATE OF X(40866)

X(46245) lies on these lines: {2, 879}, {297, 523}, {325, 525}, {327, 18312}, {512, 40077}, {647, 2966}, {850, 35088}, {4580, 20022}, {5641, 23878}, {9141, 36900}, {13485, 31296}, {15421, 35923}, {46246, 46247}

X(46245) = midpoint of X(31296) and X(39359)
X(46245) = reflection of X(i) in X(j) for these (i, j): (850, 35088), (2966, 647)
X(46245) = isogonal conjugate of X(46249)
X(46245) = isotomic conjugate of X(40866)
X(46245) = barycentric product X(850)*X(9513)
X(46245) = barycentric quotient X(i)/X(j) for these (i, j): (98, 43113), (512, 44127), (523, 1316), (850, 44155), (868, 31953)
X(46245) = trilinear product X(1577)*X(9513)
X(46245) = trilinear quotient X(i)/X(j) for these (i, j): (661, 44127), (1577, 1316)
X(46245) = Gibert-Simson transform of X(9513)
X(46245) = trilinear pole of the line {125, 2799}
X(46245) = inverse of X(9513) in Steiner circumellipse
X(46245) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(297)}} and {{A, B, C, X(110), X(23962)}}
X(46245) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 1316), (1084, 44127)
X(46245) = X(2)-Hirst inverse of-X(9513)
X(46245) = X(i)-isoconjugate-of-X(j) for these {i, j}: {163, 1316}, {662, 44127}
X(46245) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (98, 43113), (512, 44127), (523, 1316), (850, 44155)
X(46245) = trilinear pole of line PU(171)

X(46246) = ISOTOMIC CONJUGATE OF X(9514)

X(46246) = isogonal conjugate of X(46248)
X(46246) = isotomic conjugate of X(9514)
X(46246) = barycentric quotient X(i)/X(j) for these (i, j): (523, 9512), (850, 46247)
X(46246) = trilinear quotient X(1577)/X(9512)
X(46246) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3448)}} and {{A, B, C, X(110), X(23962)}}
X(46246) = X(115)-Dao conjugate of X(9512)
X(46246) = X(163)-isoconjugate-of-X(9512)
X(46246) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (523, 9512), (850, 46247)
X(46246) = cevapoint of PU(171)

X(46247) = X(2)X(11794) ∩ X(99)X(23217)

X(46247) lies on these lines: {2, 11794}, {99, 23217}, {110, 23962}, {125, 290}, {184, 18022}, {305, 46236}, {311, 11056}, {850, 3448}, {1495, 17984}, {1975, 46231}, {3292, 44137}, {3978, 39266}, {5651, 40822}, {23292, 42394}, {31074, 44176}, {35319, 39355}, {46245, 46246}

X(46247) = isotomic conjugate of X(46603)
X(46247) = anticomplement of X(45215)
X(46247) = isotomic conjugate of the isogonal conjugate of X(9512)
X(46247) = barycentric product X(i)*X(j) for these {i, j}: {76, 9512}, {311, 39843}, {850, 9514}
X(46247) = barycentric quotient X(850)/X(46246)
X(46247) = trilinear product X(i)*X(j) for these {i, j}: {75, 9512}, {1577, 9514}
X(46247) = X(850)-reciprocal conjugate of-X(46246)
X(46247) = crosspoint of PU(171)
X(46247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (110, 23962, 44155), (290, 6331, 125)

X(46248) = ISOGONAL CONJUGATE OF X(46246)

X(46248) lies on these lines: {6, 3447}, {250, 2715}, {523, 23963}, {1576, 3050}, {3288, 38861}, {20975, 46252}

X(46248) = reflection of X(46249) in X(23963)
X(46248) = isogonal conjugate of X(46246)
X(46248) = barycentric product X(i)*X(j) for these {i, j}: {6, 9514}, {110, 9512}, {1576, 46247}, {1625, 39843}
X(46248) = trilinear product X(i)*X(j) for these {i, j}: {31, 9514}, {163, 9512}
X(46248) = crosssum of PU(171)
X(46248) = {X(250), X(2715)}-harmonic conjugate of X(3049)

X(46249) = ISOGONAL CONJUGATE OF X(46245)

X(46249) lies on these lines: {6, 157}, {110, 112}, {246, 17847}, {250, 2451}, {523, 23963}, {1640, 35278}, {2485, 34947}, {2502, 9408}, {2715, 3288}, {3049, 38861}, {3269, 13198}, {5027, 14574}, {9157, 46128}

X(46249) = reflection of X(46248) in X(23963)
X(46249) = isogonal conjugate of X(46245)
X(46249) = barycentric product X(i)*X(j) for these {i, j}: {6, 40866}, {99, 44127}, {110, 1316}, {511, 43113}, {1576, 44155}
X(46249) = barycentric quotient X(i)/X(j) for these (i, j): (1316, 850), (1576, 9513)
X(46249) = trilinear product X(i)*X(j) for these {i, j}: {31, 40866}, {163, 1316}, {662, 44127}
X(46249) = trilinear quotient X(i)/X(j) for these (i, j): (163, 9513), (1316, 1577)
X(46249) = perspector of the circumconic {{A, B, C, X(250), X(2715)}}
X(46249) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(1316)}} and {{A, B, C, X(99), X(38947)}}
X(46249) = crossdifference of every pair of points on line {X(125), X(2799)}
X(46249) = X(6)-Hirst inverse of-X(1576)
X(46249) = X(1316)-reciprocal conjugate of-X(850)
X(46249) = crossdifference of PU(171)
X(46249) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (110, 112, 3569), (5191, 9475, 8429)

X(46250) = TRILINEAR POLE OF LINE PU(172)

X(46250) = reflection of X(18020) in X(35088)
X(46250) = isogonal conjugate of X(46253)
X(46250) = isotomic conjugate of the anticomplement of X(40866)
X(46250) = trilinear pole of the line {2799, 5972}
X(46250) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(297)}} and {{A, B, C, X(30), X(18823)}}
X(46250) = trilinear pole of line PU(172)

X(46251) = CROSSPOINT OF PU(172)

X(46252) = X(6)X(523) ∩ X(20975)X(46248)

X(46253) = ISOGONAL CONJUGATE OF X(46250)

X(46253) lies on these lines: {6, 157}, {74, 2502}, {110, 3269}, {112, 3124}, {250, 46252}, {1648, 9862}, {2079, 3569}, {3050, 30715}, {5027, 39857}

X(46253) = isogonal conjugate of X(46250)
X(46253) = crossdifference of every pair of points on line {X(2799), X(5972)}
X(46253) = X(6)-Hirst inverse of-X(20975)
X(46253) = crossdifference of PU(172)

X(46254) = ISOTOMIC CONJUGATE OF X(3708)

X(46254) lies on these lines: {75, 1101}, {422, 4601}, {662, 20948}, {811, 24006}, {1275, 7058}, {20944, 23999}, {20953, 36142}, {24001, 24039}, {24037, 46238}

X(46254) = isotomic conjugate of X(3708)
X(46254) = polar conjugate of X(2643)
X(46254) = barycentric product X(i)*X(j) for these {i, j}: {4, 24037}, {19, 34537}, {27, 4601}, {69, 23999}, {75, 18020}, {92, 4590}
X(46254) = barycentric quotient X(i)/X(j) for these (i, j): (1, 20975), (4, 2643), (19, 3124), (27, 3125), (28, 3122), (29, 4516)
X(46254) = trilinear product X(i)*X(j) for these {i, j}: {2, 18020}, {4, 4590}, {19, 24037}, {25, 34537}, {27, 4600}, {28, 4601}
X(46254) = trilinear quotient X(i)/X(j) for these (i, j): (2, 20975), (4, 3124), (25, 1084), (27, 3122), (28, 3121), (32, 23216)
X(46254) = trilinear pole of the line {162, 799} (the tangent to conic {A,B,C,X(811),X(823)} at X(811))
X(46254) = intersection, other than A, B, C, of circumconics {{A, B, C, X(27), X(422)}} and {{A, B, C, X(28), X(15147)}}
X(46254) = cevapoint of X(i) and X(j) for these (i, j): {4, 17914}, {75, 662}, {92, 811}, {99, 7058}
X(46254) = X(i)-cross conjugate of-X(j) for these (i, j): (92, 811), (304, 799), (561, 4593)
X(46254) = X(9)-Dao conjugate of X(20975)
X(46254) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 3124}, {6, 20975}, {25, 3269}, {32, 125}
X(46254) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 20975), (4, 2643), (19, 3124), (27, 3125)
X(46254) = trilinear product of PU(172)

X(46255) = ISOGONAL CONJUGATE OF X(11454)

X(46255) = isogonal conjugate of X(11454)
X(46255) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(35480)}} and {{A, B, C, X(4), X(30)}}
X(46255) = cevapoint of PU(174)

X(46256) = X(3830)X(23324) ∩ X(16080)X(46255)

X(46257) = X(6)X(14269) ∩ X(115)X(393)

X(46257) lies on these lines: {6, 14269}, {115, 393}, {574, 44218}, {1285, 40136}, {5158, 9220}, {5206, 46262}, {18362, 18487}

X(46257) = barycentric product X(1)*X(46258)
X(46257) = trilinear product X(6)*X(46258)
X(46257) = barycentric product of PU(174)

X(46258) = X(158)X(1109) ∩ X(9219)X(18477)

X(46258) = barycentric product X(75)*X(46257)
X(46258) = trilinear product X(2)*X(46257)
X(46258) = trilinear product of PU(174)

X(46259) = X(376)X(2979) ∩ X(3003)X(35486)

X(46259) lies on these lines: {376, 2979}, {2986, 46260}, {3003, 35486}, {7796, 44133}

X(46259) = isogonal conjugate of X(46261)
X(46259) = trilinear pole of the line {686, 9209}
X(46259) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(35486)}} and {{A, B, C, X(3), X(403)}}
X(46259) = cevapoint of PU(175)

X(46260) = X(30)X(1853) ∩ X(2453)X(15068)

X(46260) lies on these lines: {30, 1853}, {2453, 15068}, {2986, 46259}, {13881, 16618}

X(46261) = ISOGONAL CONJUGATE OF X(46259)

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

X(46261) = X(3)-3*X(35259) = 3*X(25)-X(37489) = 3*X(381)-X(18396) = 3*X(6090)-X(37483) = 3*X(9306)-X(37480) = 3*X(18451)+X(37489) = 3*X(19136)-2*X(44490) = 3*X(35259)-2*X(43586)

X(46261) lies on these lines: {2, 14157}, {3, 1495}, {4, 110}, {5, 182}, {20, 43598}, {22, 5891}, {23, 11459}, {24, 7689}, {25, 13754}, {26, 5907}, {30, 9306}, {32, 3016}, {49, 3843}, {51, 18445}, {52, 10594}, {54, 3832}, {64, 43604}, {68, 3089}, {140, 16187}, {141, 16618}, {146, 43578}, {154, 9818}, {155, 1351}, {156, 546}, {184, 381}, {185, 7506}, {186, 11454}, {235, 9927}, {343, 37971}, {378, 16194}, {382, 1092}, {389, 13861}, {394, 18534}, {399, 568}, {403, 18474}, {511, 7530}, {542, 19136}, {569, 1614}, {571, 45938}, {576, 2854}, {590, 9687}, {631, 43614}, {632, 13347}, {692, 18491}, {858, 16658}, {1181, 3066}, {1204, 10620}, {1216, 1350}, {1344, 32550}, {1345, 32549}, {1437, 37234}, {1498, 6642}, {1568, 31723}, {1593, 12038}, {1595, 9820}, {1596, 41619}, {1597, 8780}, {1625, 10311}, {1656, 10984}, {1657, 43652}, {1658, 45959}, {1660, 18400}, {1968, 2420}, {1974, 14852}, {1995, 9730}, {2070, 18435}, {2071, 11455}, {2072, 11550}, {2080, 5167}, {2883, 31833}, {2979, 37925}, {3090, 13336}, {3098, 15067}, {3146, 43576}, {3147, 20191}, {3167, 18535}, {3199, 23128}, {3357, 12041}, {3517, 12163}, {3518, 12111}, {3520, 11439}, {3523, 8718}, {3527, 38263}, {3541, 43839}, {3542, 5449}, {3543, 43574}, {3545, 5012}, {3547, 40330}, {3567, 43605}, {3627, 13346}, {3628, 37515}, {3830, 22115}, {3839, 9544}, {3850, 32046}, {3855, 13434}, {3917, 12083}, {4846, 5656}, {5020, 5892}, {5055, 43650}, {5068, 43651}, {5072, 13353}, {5076, 37495}, {5079, 37471}, {5097, 10110}, {5198, 36747}, {5320, 45923}, {5422, 14845}, {5447, 11414}, {5544, 11484}, {5562, 7517}, {5640, 15032}, {5663, 11438}, {5876, 37440}, {5878, 43577}, {5889, 34484}, {5890, 13595}, {5899, 23039}, {5972, 18281}, {6000, 6644}, {6090, 37483}, {6153, 17824}, {6241, 44802}, {6247, 16238}, {6643, 14927}, {6689, 7404}, {6699, 9934}, {6723, 20299}, {6756, 22660}, {6776, 43573}, {6785, 33803}, {6800, 37513}, {7487, 22750}, {7488, 15058}, {7502, 15060}, {7512, 15056}, {7525, 14128}, {7526, 10282}, {7527, 11464}, {7547, 15432}, {7550, 15080}, {7555, 33533}, {7565, 7699}, {8541, 45016}, {8542, 44493}, {8547, 15581}, {9703, 14269}, {10116, 39571}, {10154, 44201}, {10182, 18580}, {10201, 21243}, {10254, 44078}, {10274, 22804}, {10323, 21766}, {10535, 37697}, {10546, 12112}, {10575, 17928}, {10665, 35765}, {10666, 35764}, {10982, 44863}, {11064, 16654}, {11178, 44262}, {11202, 18570}, {11204, 15646}, {11206, 18537}, {11232, 39899}, {11250, 20773}, {11430, 31861}, {11440, 44879}, {11444, 12088}, {11449, 14865}, {11457, 43817}, {11479, 14530}, {11579, 36253}, {11585, 16655}, {11591, 17714}, {11692, 34751}, {11793, 14810}, {11801, 44235}, {11818, 18388}, {11935, 37472}, {12039, 44480}, {12082, 15066}, {12084, 13474}, {12085, 15811}, {12133, 12901}, {12272, 12364}, {12290, 22467}, {12308, 13621}, {12359, 21841}, {13292, 15873}, {13340, 37924}, {13419, 18569}, {13509, 15355}, {13567, 44233}, {13598, 16266}, {14002, 14094}, {14118, 26882}, {14156, 44441}, {14529, 31937}, {14560, 39170}, {14791, 29012}, {14831, 44106}, {15004, 15087}, {15062, 21844}, {15063, 32235}, {15132, 38791}, {15448, 34351}, {15687, 40111}, {16619, 34507}, {16621, 23335}, {17811, 35243}, {18358, 19126}, {18369, 37481}, {18376, 18418}, {18378, 18436}, {18390, 46030}, {18488, 37119}, {18531, 31383}, {19347, 21637}, {20725, 44240}, {20772, 44274}, {21451, 26917}, {23293, 37943}, {23329, 44452}, {23332, 44911}, {26864, 37506}, {26881, 35921}, {26885, 37584}, {26888, 37696}, {32111, 38323}, {32217, 44470}, {34117, 43130}, {34986, 39522}, {35266, 44218}, {36749, 43844}, {36987, 44457}, {37625, 43609}, {37897, 44683}, {42426, 43389}

X(46261) = midpoint of X(i) and X(j) for these {i, j}: {25, 18451}, {394, 18534}, {7530, 15068}, {18531, 31383}
X(46261) = reflection of X(i) in X(j) for these (i, j): (3, 43586), (11438, 12106), (13567, 44233), (18390, 46030)
X(46261) = isogonal conjugate of X(46259)
X(46261) = crossdifference of every pair of points on line {X(686), X(9209)}
X(46261) = crosssum of PU(175)
X(46261) = center of circle {{X(394), X(18534), X(36192)}}
X(46261) = X(18396)-of-Ehrmann-mid triangle
X(46261) = X(43586)-of-X3-ABC reflections triangle
X(46261) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 15030, 4550), (3, 35259, 43586), (4, 110, 13352), (4, 10539, 1147), (4, 12118, 12897), (5, 34514, 23325), (23, 11459, 37478), (23, 15052, 11459), (24, 12162, 7689), (49, 3843, 11424), (52, 11441, 15083), (110, 13352, 1147), (113, 12140, 19479), (154, 9818, 18475), (155, 1598, 5446), (156, 546, 578), (235, 12134, 9927), (381, 10540, 184), (382, 18350, 1092), (399, 7545, 568), (568, 7545, 34417), (1181, 7529, 5462), (1495, 15030, 3), (1498, 6642, 40647), (1614, 3091, 569), (7387, 17814, 1216), (10282, 44870, 7526), (10539, 13352, 110), (10984, 22112, 13339), (11464, 16261, 7527), (13861, 32139, 389), (18439, 45735, 1204)

X(46262) = X(2)X(6) ∩ X(4)X(50)

X(46262) lies on these lines: {2, 6}, {3, 16310}, {4, 50}, {53, 18533}, {115, 577}, {186, 393}, {231, 3767}, {338, 37188}, {376, 1989}, {562, 2963}, {566, 631}, {571, 7737}, {647, 15328}, {1285, 2965}, {1609, 6644}, {1990, 35486}, {2072, 9722}, {2493, 7493}, {3018, 21843}, {3087, 7577}, {3147, 11062}, {3284, 7746}, {3525, 41335}, {5023, 37460}, {5054, 14836}, {5158, 7749}, {5206, 46257}, {5286, 7550}, {6036, 11511}, {6587, 38401}, {7514, 15048}, {7612, 18919}, {7755, 33871}, {9862, 41761}, {15484, 37347}, {15655, 44265}, {16051, 44529}, {16303, 44214}, {18324, 42459}, {35952, 44532}, {36748, 44526}, {38872, 44440}

X(46262) = barycentric product X(1)*X(46263)
X(46262) = trilinear product X(6)*X(46263)
X(46262) = inverse of X(37638) in Evans conic
X(46262) = crosssum of X(6) and X(37489)
X(46262) = barycentric product of PU(175)
X(46262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (231, 5063, 3767), (590, 615, 37638), (3068, 3069, 37644)

X(46263) = X(1)X(75) ∩ X(91)X(255)

X(46263) = barycentric product X(75)*X(46262)
X(46263) = trilinear product X(2)*X(46262)
X(46263) = trilinear product of PU(175)

X(46264) = REFLECTION OF X(4) IN X(182)

X(46264) = 3 X[2] - 4 X[5092], 5 X[2] - 4 X[25561], 15 X[2] - 14 X[42786], 3 X[3] - 2 X[141], 3 X[3] - X[18440], 7 X[3] - 6 X[21167], 3 X[4] - 5 X[3618], 2 X[4] - 3 X[14561], 3 X[4] - 4 X[19130], X[4] - 3 X[25406], 5 X[4] - 8 X[25555], 2 X[5] - 3 X[5085], 2 X[6] - 3 X[11179], 4 X[6] - 3 X[20423], 3 X[6] - 2 X[21850], X[6] - 3 X[43273], 4 X[6] - X[43621], 3 X[20] + X[193], X[69] - 3 X[376], 2 X[113] - 3 X[15462], 4 X[140] - 3 X[10516], 4 X[141] - 3 X[1352], 7 X[141] - 9 X[21167], X[141] - 3 X[44882], 3 X[165] - X[39885], 6 X[182] - 5 X[3618], 4 X[182] - 3 X[14561], 2 X[182] + X[14927], 3 X[182] - 2 X[19130], 2 X[182] - 3 X[25406], 5 X[182] - 4 X[25555], X[193] - 3 X[6776], 2 X[355] - 3 X[38116], 3 X[376] - 2 X[3098], 3 X[376] + X[39874], 3 X[381] - 4 X[3589], 3 X[381] - 5 X[12017], 2 X[381] - 3 X[38064], X[382] - 3 X[5050], 3 X[382] - 8 X[6329], 4 X[546] - 7 X[10541], 2 X[546] - 3 X[38110], 4 X[548] - X[15069], 4 X[548] - 3 X[31884], 6 X[549] - 5 X[3763], 3 X[549] - 2 X[18358], 6 X[550] - X[40341], 4 X[575] - X[3146], 4 X[575] - 3 X[14853], 2 X[576] + X[3529], 2 X[576] - 3 X[14912], 5 X[631] - 6 X[17508], 5 X[631] - 4 X[24206], 2 X[946] - 3 X[38029], 3 X[1350] - X[40341], 3 X[1351] - 4 X[32455], 3 X[1352] - 2 X[18440]

X(46264) lies on the cubic K1249 and these lines: {2, 1495}, {3, 66}, {4, 83}, {5, 5085}, {6, 30}, {20, 185}, {22, 1899}, {23, 18911}, {25, 37648}, {26, 35217}, {35, 12588}, {36, 12589}, {51, 7500}, {67, 12041}, {68, 34436}, {69, 74}, {98, 17008}, {110, 16063}, {113, 206}, {114, 7710}, {115, 5033}, {125, 7493}, {140, 10516}, {146, 19140}, {147, 7897}, {154, 1368}, {165, 39885}, {184, 1370}, {315, 7470}, {317, 35474}, {355, 38116}, {381, 3589}, {382, 5050}, {389, 31305}, {394, 7667}, {427, 3796}, {428, 10601}, {458, 16264}, {516, 24257}, {518, 18481}, {524, 3534}, {546, 10541}, {548, 15069}, {549, 3763}, {550, 1350}, {572, 36474}, {575, 3146}, {576, 3529}, {578, 34938}, {597, 3830}, {599, 8703}, {611, 7354}, {613, 6284}, {623, 33381}, {624, 33380}, {631, 17508}, {732, 8725}, {858, 6800}, {946, 38029}, {1147, 17712}, {1351, 1657}, {1353, 11477}, {1386, 12699}, {1428, 1479}, {1469, 4299}, {1478, 2330}, {1498, 12362}, {1511, 14982}, {1568, 28708}, {1595, 37476}, {1691, 3767}, {1692, 7748}, {1843, 18533}, {1853, 6676}, {1885, 44503}, {1975, 44251}, {1992, 11001}, {2030, 43448}, {2072, 31267}, {2393, 14855}, {2697, 2715}, {2777, 9970}, {2781, 17710}, {2792, 24728}, {2794, 12177}, {2854, 12121}, {2892, 13293}, {2916, 2931}, {2930, 34153}, {2937, 22550}, {3054, 40248}, {3056, 4302}, {3060, 20062}, {3066, 10301}, {3070, 19145}, {3071, 19146}, {3091, 20190}, {3242, 34773}, {3313, 13754}, {3416, 3579}, {3424, 15819}, {3431, 45835}, {3448, 7492}, {3522, 5921}, {3523, 18553}, {3524, 3619}, {3528, 33751}, {3543, 5476}, {3545, 7919}, {3546, 10282}, {3547, 18381}, {3587, 5227}, {3620, 10304}, {3627, 18583}, {3629, 15681}, {3630, 15689}, {3631, 15688}, {3785, 14994}, {3819, 14826}, {3853, 38136}, {3867, 18494}, {3923, 29040}, {4232, 32237}, {4260, 6869}, {4265, 5820}, {4549, 5663}, {5002, 32619}, {5003, 32618}, {5012, 7391}, {5026, 6033}, {5028, 7756}, {5034, 7747}, {5054, 34573}, {5059, 5097}, {5064, 37649}, {5093, 12007}, {5094, 13394}, {5116, 31401}, {5138, 5800}, {5157, 18420}, {5181, 38726}, {5182, 10722}, {5189, 11003}, {5204, 39892}, {5207, 7763}, {5217, 39891}, {5224, 13634}, {5241, 19544}, {5254, 40825}, {5422, 34603}, {5486, 8547}, {5596, 6000}, {5622, 10733}, {5640, 7519}, {5652, 32472}, {5654, 14791}, {5731, 39898}, {5805, 38115}, {5816, 36477}, {5846, 12702}, {5847, 31730}, {5848, 38761}, {5870, 21737}, {5871, 33347}, {5878, 12605}, {5890, 44831}, {5907, 34781}, {5943, 6995}, {5965, 12254}, {5967, 36163}, {5969, 38730}, {5972, 16051}, {5984, 6194}, {5999, 7777}, {6030, 23293}, {6034, 22515}, {6101, 9936}, {6144, 15686}, {6146, 11414}, {6193, 15644}, {6240, 39588}, {6241, 41716}, {6403, 11663}, {6459, 39875}, {6460, 39876}, {6593, 7728}, {6636, 11442}, {6643, 6759}, {6644, 20987}, {6655, 39141}, {6688, 7398}, {6698, 38728}, {6756, 9815}, {6803, 13347}, {6804, 44862}, {6816, 26883}, {6985, 36741}, {6997, 43650}, {7171, 7289}, {7386, 9306}, {7387, 39571}, {7395, 16655}, {7401, 13419}, {7467, 15652}, {7487, 9729}, {7488, 26937}, {7494, 21243}, {7509, 16659}, {7512, 11457}, {7525, 32140}, {7528, 13336}, {7553, 36752}, {7581, 42833}, {7582, 42832}, {7612, 35021}, {7694, 15980}, {7714, 18928}, {7716, 37458}, {7735, 41412}, {7791, 9873}, {7813, 30270}, {8177, 12188}, {8182, 9830}, {8229, 31229}, {8546, 35001}, {8584, 15685}, {8588, 19905}, {8717, 11579}, {8722, 10991}, {9053, 18526}, {9730, 9969}, {9738, 12257}, {9739, 12256}, {9753, 39750}, {9756, 37451}, {9822, 16836}, {9909, 13567}, {9924, 44241}, {9967, 10575}, {9993, 16989}, {10024, 20300}, {10065, 32243}, {10081, 32297}, {10154, 26958}, {10192, 21968}, {10201, 20304}, {10249, 15760}, {10323, 34224}, {10356, 32956}, {10565, 23291}, {10574, 31304}, {10605, 26926}, {10691, 17811}, {10721, 32271}, {10748, 14688}, {10783, 42858}, {10784, 42859}, {11002, 20063}, {11061, 12244}, {11064, 26864}, {11160, 15697}, {11245, 33586}, {11427, 44442}, {11433, 34608}, {11456, 20806}, {11464, 28408}, {11479, 16621}, {11541, 22234}, {11585, 23041}, {11646, 12042}, {11649, 13619}, {11676, 35424}, {11750, 19131}, {11898, 15696}, {12022, 12082}, {12054, 42534}, {12088, 18912}, {12100, 21358}, {12103, 34380}, {12167, 37196}, {12225, 44469}, {12241, 39568}, {12294, 44479}, {12295, 15118}, {12902, 25328}, {12918, 28343}, {13329, 36674}, {13331, 14881}, {13346, 18925}, {13354, 31958}, {13369, 24476}, {13403, 43810}, {13470, 19154}, {13564, 25738}, {13608, 31731}, {13635, 17234}, {13665, 13910}, {13748, 18539}, {13749, 26438}, {13785, 13972}, {14227, 36703}, {14242, 36701}, {14389, 31133}, {14538, 41021}, {14539, 41020}, {14683, 33884}, {14708, 40949}, {14848, 15684}, {14852, 16618}, {14893, 38079}, {15035, 41737}, {15041, 32306}, {15061, 32274}, {15074, 34350}, {15078, 26156}, {15107, 37644}, {15160, 41519}, {15161, 41518}, {15311, 34774}, {15326, 39873}, {15338, 39897}, {15516, 33748}, {15520, 33749}, {15533, 15690}, {15534, 19710}, {15595, 37188}, {15687, 38072}, {15693, 20582}, {15695, 22165}, {15988, 17579}, {16010, 32423}, {16165, 32227}, {16190, 39886}, {16196, 17821}, {16237, 18880}, {16370, 26543}, {16475, 41869}, {16491, 31162}, {16661, 34799}, {16776, 40280}, {16964, 36758}, {16965, 36757}, {17714, 18952}, {17810, 45298}, {17834, 18914}, {17845, 31829}, {18128, 18951}, {18325, 32217}, {18382, 19127}, {18400, 19126}, {18475, 44441}, {18480, 38047}, {18482, 38186}, {18483, 38049}, {18510, 36718}, {18512, 36734}, {18536, 32063}, {18537, 19137}, {18563, 34117}, {18564, 38790}, {18580, 34513}, {18917, 37478}, {18935, 35513}, {19118, 44438}, {19161, 40647}, {19459, 21312}, {19708, 21356}, {19925, 38118}, {20021, 37184}, {20477, 44252}, {20771, 38794}, {20791, 43129}, {21659, 37201}, {21732, 22260}, {21736, 43120}, {22338, 28662}, {22486, 33193}, {22683, 44667}, {22685, 44666}, {22687, 41022}, {22689, 41023}, {22791, 38315}, {22793, 38035}, {22796, 37170}, {22797, 37171}, {23292, 34609}, {24248, 29097}, {24309, 29046}, {24695, 29301}, {25320, 32273}, {25562, 41134}, {25565, 41106}, {25898, 37038}, {26118, 37527}, {26341, 36712}, {26348, 36711}, {26361, 45554}, {26362, 45555}, {26869, 32269}, {30739, 35259}, {31804, 37498}, {32191, 37481}, {32216, 35266}, {32218, 37958}, {32223, 37643}, {32250, 38727}, {32599, 33532}, {33703, 39561}, {33851, 38723}, {34511, 35002}, {34778, 44249}, {34787, 44240}, {35243, 37485}, {35422, 35925}, {35423, 35930}, {35840, 42267}, {35841, 42266}, {35934, 41328}, {36181, 46124}, {36213, 37190}, {36696, 44987}, {36709, 43119}, {36714, 43118}, {36883, 38623}, {37342, 45552}, {37343, 45553}, {37466, 40278}, {37638, 44210}, {37665, 44422}, {37689, 38010}, {37931, 41584}, {38040, 40273}, {39560, 40279}, {41005, 44248}, {41424, 44212}, {41482, 41714}, {41614, 44458}, {43407, 44502}, {43408, 44501}

X(46264) = midpoint of X(i) and X(j) for these {i,j}: {4, 14927}, {20, 6776}, {69, 39874}, {1351, 1657}, {1353, 15704}, {1992, 11001}, {6241, 41716}, {9967, 10575}, {11061, 12244}, {33878, 39899}
X(46264) = reflection of X(i) in X(j) for these {i,j}: {3, 44882}, {4, 182}, {66, 44883}, {67, 12041}, {69, 3098}, {146, 19140}, {194, 32429}, {382, 5480}, {599, 8703}, {1350, 550}, {1351, 8550}, {1352, 3}, {2892, 13293}, {2930, 34153}, {3242, 34773}, {3416, 3579}, {3448, 32305}, {3543, 5476}, {3627, 18583}, {3818, 5092}, {3830, 597}, {5181, 38726}, {5486, 8547}, {5596, 34776}, {5878, 19149}, {5921, 34507}, {6033, 5026}, {7728, 6593}, {9833, 36989}, {10721, 32271}, {10748, 14688}, {11179, 43273}, {11477, 1353}, {11646, 12042}, {11663, 6403}, {12294, 44479}, {12295, 15118}, {12699, 1386}, {12902, 25328}, {12918, 28343}, {14561, 25406}, {14982, 1511}, {18325, 32217}, {18438, 17710}, {18440, 141}, {19161, 40647}, {20423, 11179}, {22338, 28662}, {24476, 13369}, {31670, 6}, {34118, 15578}, {34507, 14810}, {34775, 23300}, {36883, 38623}, {36990, 5}, {39879, 34782}, {39884, 140}, {40107, 33751}, {40949, 14708}, {41735, 6759}, {43621, 31670}, {44439, 15074}, {44456, 3629}
X(46264) = anticomplement of X(3818)
X(46264) = crossdifference of every pair of points on line {2451, 2485}
X(46264) = X(182)-of-anti-Euler-triangle
X(46264) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 18437, 6389}, {3, 18440, 141}, {4, 182, 14561}, {4, 3618, 19130}, {4, 25406, 182}, {6, 31670, 20423}, {69, 376, 3098}, {125, 35268, 7493}, {140, 39884, 10516}, {141, 18440, 1352}, {182, 7790, 43456}, {182, 19130, 3618}, {376, 9862, 14907}, {376, 39874, 69}, {381, 12017, 3589}, {382, 5050, 5480}, {549, 18358, 3763}, {616, 617, 32833}, {3522, 5921, 10519}, {3522, 10519, 14810}, {3534, 39899, 33878}, {3589, 12017, 38064}, {3618, 19130, 14561}, {3620, 11180, 43150}, {3818, 5092, 2}, {3818, 42786, 25561}, {4299, 39900, 1469}, {4302, 39901, 3056}, {5085, 36990, 5}, {5921, 10519, 34507}, {6560, 6561, 2549}, {6636, 11442, 43653}, {6756, 37514, 9815}, {7386, 11206, 9306}, {7494, 32064, 21243}, {8982, 26441, 11257}, {10249, 34775, 23300}, {10653, 10654, 7739}, {10984, 19124, 182}, {11179, 31670, 6}, {11550, 22352, 2}, {13419, 37515, 7401}, {14810, 34507, 10519}, {14927, 25406, 4}, {16051, 35260, 5972}, {17508, 24206, 631}, {20423, 43621, 31670}, {26864, 31152, 11064}, {33750, 40330, 3523}, {41979, 41980, 15048}, {42085, 42086, 43619}

X(46265) = X(2)X(18376)∩X(5)X(32903)

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

X(46265) = 5*X(2)-X(18376), 2*X(5)+X(32903), 4*X(140)-X(32767), X(154)+7*X(15701), 3*X(549)+X(10192), 3*X(549)-X(10193), 5*X(549)-X(23328), 5*X(631)+X(10282), 15*X(631)+X(11206), 5*X(631)-X(23329), 3*X(10182)-X(10192), 3*X(10182)+X(10193), 5*X(10182)+X(23328), 5*X(10192)+3*X(23328), 5*X(10193)-3*X(23328), 3*X(10282)-X(11206), 5*X(10282)+X(14216), 5*X(11206)+3*X(14216), X(11206)+3*X(23329), X(14216)-5*X(23329)

X(46265) lies on these lines: {2, 18376}, {5, 32903}, {140, 13470}, {154, 15701}, {511, 34477}, {549, 6000}, {631, 10282}, {632, 23324}, {1503, 11812}, {1853, 5054}, {2777, 12100}, {3523, 12250}, {3525, 34785}, {3526, 18383}, {3530, 15311}, {3819, 10628}, {5892, 44325}, {5943, 44214}, {6759, 15720}, {7568, 32415}, {10168, 10169}, {10303, 18381}, {10606, 15707}, {11204, 15693}, {11245, 44673}, {12108, 25563}, {13289, 15246}, {13367, 43808}, {14864, 17821}, {14869, 20299}, {15694, 23325}, {15713, 23332}, {15717, 22802}, {15722, 35450}, {34786, 46219}

X(46265) = midpoint of X(i) and X(j) for these {i, j}: {549, 10182}, {10192, 10193}, {10282, 23329}
X(46265) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (549, 10192, 10193), (10182, 10193, 10192)

X(46266) = X(2)X(38710)∩X(3090)X(32536)

Barycentrics 2*a^16-16*(b^2+c^2)*a^14+12*(5*b^4+7*b^2*c^2+5*c^4)*a^12-3*(b^2+c^2)*(43*b^4+10*b^2*c^2+43*c^4)*a^10+11*(15*b^8+15*c^8+8*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^8-(b^4-c^4)*(b^2-c^2)*(122*b^4+29*b^2*c^2+122*c^4)*a^6+(46*b^8+46*c^8-(49*b^4+68*b^2*c^2+49*c^4)*b^2*c^2)*(b^2-c^2)^2*a^4-(b^4-c^4)*(b^2-c^2)^3*(5*b^4-39*b^2*c^2+5*c^4)*a^2-(b^4+9*b^2*c^2+c^4)*(b^2-c^2)^6 : :
Barycentrics 19*S^4+(R^2*(116*R^2-5*SA-84*SW)+2*SA^2-5*SB*SC+13*SW^2)*S^2+(R^2*(36*R^2-31*SW)+7*SW^2)*SB*SC : :

X(46266) = 7*X(3090)-X(32536), 4*X(3628)-X(34598), 11*X(5070)+X(30484), 2*X(16239)+X(32904)

X(46266) lies on these lines: {2, 38710}, {3090, 32536}, {3628, 34598}, {5070, 30484}, {10124, 18400}, {16239, 32904}, {25150, 34479}, {35728, 41992}

X(46267) = X(2)X(575)∩X(182)X(381)

Barycentrics 8*a^6-11*(b^2+c^2)*a^4+(b^4-24*b^2*c^2+c^4)*a^2+2*(b^4-c^4)*(b^2-c^2) : :

X(46267) = 5*X(2)-X(34507), 3*X(6)+5*X(15694), 2*X(140)+X(22330), 3*X(182)+X(381), 11*X(182)+X(36990), 5*X(182)-X(43273), X(376)+15*X(3618), X(376)-3*X(5092), X(376)+3*X(5476), 5*X(376)+3*X(31670), X(376)-9*X(38064), 11*X(381)-3*X(36990), 5*X(381)+3*X(43273), 5*X(575)+X(34507), 5*X(3618)+X(5092), 5*X(3618)-X(5476), 5*X(3618)+3*X(38064), 5*X(5092)+X(31670), X(5092)-3*X(38064), X(20190)+2*X(25555), 5*X(36990)+11*X(43273)

X(46267) lies on these lines: {2, 575}, {6, 15694}, {30, 20190}, {140, 22330}, {182, 381}, {376, 3618}, {511, 549}, {524, 10124}, {542, 547}, {576, 5054}, {599, 15723}, {632, 22165}, {1003, 39498}, {1350, 15718}, {1503, 11737}, {2030, 7753}, {3055, 41672}, {3098, 14848}, {3526, 15534}, {3543, 14561}, {3628, 33749}, {3830, 10541}, {3849, 8590}, {5050, 11178}, {5055, 18553}, {5071, 11179}, {5085, 15681}, {5097, 15702}, {5480, 15686}, {5643, 37907}, {5943, 7426}, {5965, 20582}, {7603, 10485}, {7708, 30516}, {8550, 15699}, {8584, 11539}, {8787, 34127}, {9466, 32149}, {9729, 44218}, {10169, 10182}, {11477, 15701}, {11649, 13363}, {11812, 41153}, {11842, 15810}, {12017, 15684}, {13334, 37461}, {13846, 44657}, {13847, 44656}, {14093, 17508}, {14537, 39560}, {14762, 32135}, {14810, 15692}, {14893, 29012}, {15018, 32225}, {15082, 40112}, {15687, 19130}, {15691, 29317}, {15714, 21850}, {16241, 44497}, {16242, 44498}, {16962, 44511}, {16963, 44512}, {18583, 19924}, {20301, 37347}, {21401, 35303}, {21402, 35304}, {22352, 37901}, {22486, 43147}, {31152, 44491}, {32787, 44481}, {32788, 44482}, {32907, 37351}, {32909, 37352}, {35404, 44882}, {44214, 44479}

X(46267) = midpoint of X(i) and X(j) for these {i, j}: {2, 575}, {597, 10168}, {5092, 5476}, {8584, 40107}, {10169, 10182}, {11179, 25561}, {14810, 20423}, {22486, 43147}
X(46267) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (597, 38110, 10168), (3618, 38064, 5476), (5476, 38064, 5092), (8584, 11539, 40107), (11179, 38317, 25561)

X(46268) = (name pending)

X(46269) = (name pending)

Centers X(46270)-X(46328) were contributed by César Eliud Lozada, December 8, 2021.

X(46270) = ISOGONAL CONJUGATE OF X(9412)

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

X(46270) lies on the cubic K860 and these lines: {2, 9410}, {30, 39358}, {10304, 35912}, {11064, 44575}, {23582, 36435}, {31621, 39008}, {44577, 46106}

X(46270) = reflection of X(31621) in X(39008)
X(46270) = anticomplement of X(9410)
X(46270) = isogonal conjugate of X(9412)
X(46270) = isotomic conjugate of X(39358)
X(46270) = barycentric quotient X(i)/X(j) for these (i, j): (30, 34582), (1494, 9410)
X(46270) = trilinear pole of the line {9033, 11049}
X(46270) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(30)}} and {{A, B, C, X(3), X(44577)}}
X(46270) = cevapoint of X(525) and X(39008)
X(46270) = X(1494)-cross conjugate of-X(2)
X(46270) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (30, 34582), (1494, 9410)
X(46270) = cevapoint of PU(176)

X(46271) = ISOTOMIC CONJUGATE OF X(39355)

X(46271) lies on the cubic K355 and these lines: {2, 39058}, {182, 32545}, {385, 41204}, {401, 12215}, {511, 39355}

X(46271) = anticomplement of X(39058)
X(46271) = isogonal conjugate of X(46272)
X(46271) = isotomic conjugate of X(39355)
X(46271) = cyclocevian conjugate of the anticomplement of X(40601)
X(46271) = barycentric quotient X(i)/X(j) for these (i, j): (1, 39342), (290, 39058)
X(46271) = trilinear quotient X(2)/X(39342)
X(46271) = trilinear pole of the line {6130, 24284}
X(46271) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(182)}} and {{A, B, C, X(4), X(401)}}
X(46271) = cevapoint of X(525) and X(38974)
X(46271) = X(290)-cross conjugate of-X(2)
X(46271) = X(9)-Dao conjugate of X(39342)
X(46271) = X(6)-isoconjugate-of-X(39342)
X(46271) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 39342), (290, 39058)
X(46271) = cevapoint of PU(177)

X(46272) = ISOGONAL CONJUGATE OF X(46271)

X(46272) lies on these lines: {3, 1625}, {6, 98}, {25, 694}, {217, 37334}, {1691, 9418}, {1979, 2352}, {2076, 13236}, {2421, 5989}, {3053, 9431}, {3289, 5999}, {3331, 11676}, {5116, 5621}, {9259, 23383}, {9862, 45910}, {13330, 33983}

X(46272) = isogonal conjugate of X(46271)
X(46272) = barycentric product X(i)*X(j) for these {i, j}: {1, 39342}, {6, 39355}, {237, 39058}
X(46272) = trilinear product X(i)*X(j) for these {i, j}: {6, 39342}, {31, 39355}
X(46272) = intersection, other than A, B, C, of circumconics {{A, B, C, X(25), X(32542)}} and {{A, B, C, X(98), X(39683)}}
X(46272) = crossdifference of every pair of points on line {X(6130), X(24284)}
X(46272) = crosssum of X(525) and X(38974)
X(46272) = crosspoint of PU(89)
X(46272) = X(237)-Ceva conjugate of-X(6)
X(46272) = X(290)-Dao conjugate of X(18024)
X(46272) = X(6)-Hirst inverse of-X(9419)
X(46272) = crosssum of PU(177)
X(46272) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (98, 9419, 6), (98, 26714, 9419)

X(46273) = ISOGONAL CONJUGATE OF X(9417)

X(46273) lies on the cubics K865, K1023 and these lines: {1, 336}, {63, 561}, {72, 290}, {75, 23996}, {98, 789}, {293, 1966}, {304, 1928}, {306, 1978}, {850, 30995}, {1214, 1920}, {1910, 4593}, {1926, 46238}, {1956, 40703}, {22456, 26702}, {40017, 43665}

X(46273) = isogonal conjugate of X(9417)
X(46273) = isotomic conjugate of X(1755)
X(46273) = polar conjugate of the isogonal conjugate of X(336)
X(46273) = barycentric product X(i)*X(j) for these {i, j}: {1, 18024}, {75, 290}, {76, 1821}, {98, 561}, {264, 336}, {287, 1969}
X(46273) = barycentric quotient X(i)/X(j) for these (i, j): (1, 237), (10, 5360), (19, 2211), (31, 9418), (63, 3289), (75, 511)
X(46273) = trilinear product X(i)*X(j) for these {i, j}: {2, 290}, {6, 18024}, {69, 16081}, {75, 1821}, {76, 98}, {92, 336}
X(46273) = trilinear quotient X(i)/X(j) for these (i, j): (2, 237), (4, 2211), (6, 9418), (69, 3289), (76, 511), (95, 41270)
X(46273) = trilinear pole of the line {75, 656}
X(46273) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(63)}} and {{A, B, C, X(75), X(3403)}}
X(46273) = cevapoint of X(i) and X(j) for these (i, j): {1, 16564}, {75, 1959}, {312, 35544}, {336, 1821}
X(46273) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 237), (37, 5360), (244, 2491), (290, 39342)
X(46273) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 9418}, {3, 2211}, {6, 237}, {25, 3289}
X(46273) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 237), (10, 5360), (19, 2211), (31, 9418)
X(46273) = trilinear product of PU(177)

X(46274) = ISOGONAL CONJUGATE OF X(9431)

X(46274) lies on these lines: {2, 9428}, {512, 25054}, {3231, 40858}, {38294, 44371}, {39010, 44168}

X(46274) = reflection of X(44168) in X(39010)
X(46274) = anticomplement of X(9428)
X(46274) = isogonal conjugate of X(9431)
X(46274) = isotomic conjugate of X(25054)
X(46274) = cyclocevian conjugate of the anticomplement of X(38996)
X(46274) = antigonal conjugate of the isogonal conjugate of X(9430)
X(46274) = barycentric quotient X(i)/X(j) for these (i, j): (1, 39337), (3, 23180), (512, 38237), (670, 9428)
X(46274) = trilinear quotient X(i)/X(j) for these (i, j): (2, 39337), (63, 23180), (661, 38237)
X(46274) = trilinear pole of the line {888, 36950}
X(46274) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1655)}} and {{A, B, C, X(2), X(512)}}
X(46274) = cevapoint of X(538) and X(39010)
X(46274) = X(670)-cross conjugate of-X(2)
X(46274) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 23180), (9, 39337), (1084, 38237)
X(46274) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 39337}, {19, 23180}, {662, 38237}
X(46274) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 39337), (3, 23180), (512, 38237), (670, 9428)
X(46274) = cevapoint of PU(178)

X(46275) = ISOTOMIC CONJUGATE OF X(8591)

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

X(46275) lies on the curve Q124 and these lines: {2, 39061}, {148, 18823}, {468, 8859}, {523, 41135}, {524, 8591}, {543, 35511}, {3266, 41136}, {5032, 5967}, {5486, 32480}, {34763, 44010}

X(46275) = anticomplement of X(39061)
X(46275) = isogonal conjugate of X(46276)
X(46275) = isotomic conjugate of X(8591)
X(46275) = cyclocevian conjugate of X(67)
X(46275) = barycentric quotient X(i)/X(j) for these (i, j): (1, 39339), (111, 41404), (524, 38239), (671, 39061)
X(46275) = trilinear quotient X(i)/X(j) for these (i, j): (2, 39339), (897, 41404)
X(46275) = trilinear pole of the line {690, 5461}
X(46275) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(468)}} and {{A, B, C, X(4), X(9855)}}
X(46275) = cevapoint of X(i) and X(j) for these (i, j): {2, 8596}, {523, 23992}
X(46275) = X(671)-cross conjugate of-X(2)
X(46275) = X(9)-Dao conjugate of X(39339)
X(46275) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 39339}, {896, 41404}, {922, 39061}, {923, 38239}
X(46275) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 39339), (111, 41404), (524, 38239), (671, 39061)
X(46275) = cevapoint of PU(180)

X(46276) = ISOGONAL CONJUGATE OF X(46275)

X(46276) lies on these lines: {2, 8786}, {3, 40251}, {6, 110}, {25, 41911}, {31, 5168}, {48, 10987}, {154, 5191}, {184, 8585}, {187, 9225}, {351, 39232}, {352, 2076}, {353, 5116}, {524, 7665}, {574, 2936}, {599, 7664}, {843, 9217}, {1384, 1613}, {1495, 5104}, {1511, 45723}, {1641, 14360}, {1648, 9143}, {1915, 5008}, {1979, 5163}, {2030, 3506}, {2434, 10355}, {3053, 9486}, {3292, 8586}, {3569, 9412}, {3763, 40915}, {5026, 35279}, {5029, 21781}, {5108, 31128}, {5642, 11646}, {6437, 7598}, {6438, 7599}, {6439, 7601}, {6440, 7602}, {6719, 18800}, {8566, 37457}, {8591, 38239}, {9830, 30786}, {9872, 18374}, {9966, 15871}, {10540, 40115}, {10552, 15534}, {11061, 44915}, {11580, 14567}, {13192, 15514}, {14729, 45769}, {15504, 41424}, {15993, 35266}, {20481, 39560}, {37477, 40237}, {38623, 45722}, {40350, 44496}

X(46276) = midpoint of X(7665) and X(10553)
X(46276) = isogonal conjugate of X(46275)
X(46276) = barycentric product X(i)*X(j) for these {i, j}: {1, 39339}, {6, 8591}, {111, 38239}, {187, 39061}, {524, 41404}
X(46276) = trilinear product X(i)*X(j) for these {i, j}: {6, 39339}, {31, 8591}, {896, 41404}, {922, 39061}, {923, 38239}
X(46276) = perspector of the circumconic {{A, B, C, X(691), X(41404)}}
X(46276) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(38239)}} and {{A, B, C, X(111), X(8591)}}
X(46276) = crossdifference of every pair of points on line {X(690), X(5461)}
X(46276) = crosspoint of X(110) and X(34539)
X(46276) = crosspoint of PU(107)
X(46276) = crosssum of X(i) and X(j) for these (i, j): {2, 8596}, {523, 23992}
X(46276) = X(187)-Ceva conjugate of-X(6)
X(46276) = X(671)-Dao conjugate of X(18023)
X(46276) = X(i)-Hirst inverse of-X(j) for these (i, j): {6, 39689}, {187, 41449}
X(46276) = X(351)-vertex conjugate of-X(39689)
X(46276) = crosssum of PU(180)
X(46276) = X(20998)-of-circumsymmedial triangle
X(46276) = X(41911)-of-Ara triangle
X(46276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 2502, 20998), (110, 111, 39689), (110, 2502, 6), (111, 39689, 6), (184, 8585, 10485), (2502, 39689, 111), (6593, 42007, 6)

X(46277) = ISOGONAL CONJUGATE OF X(922)

X(46277) lies on these lines: {75, 799}, {92, 811}, {111, 789}, {313, 1978}, {321, 668}, {523, 30992}, {561, 4602}, {892, 14616}, {923, 3112}, {1441, 4554}, {1821, 14206}, {1966, 17955}, {2157, 16568}, {4583, 31125}, {5466, 40017}, {14210, 18075}

X(46277) = isogonal conjugate of X(922)
X(46277) = isotomic conjugate of X(896)
X(46277) = complement of anticomplementary conjugate of X(21298)
X(46277) = anticomplement of complementary conjugate of X(21256)
X(46277) = trilinear pole of the line {75, 1577}
X(46277) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2157)}} and {{A, B, C, X(2), X(29615)}}
X(46277) = cevapoint of X(i) and X(j) for these (i, j): {1, 16568}, {2, 17491}, {6, 23862}, {10, 22047}
X(46277) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 187), (37, 21839), (115, 2642), (244, 351)
X(46277) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 14567}, {3, 44102}, {4, 23200}, {6, 187}
X(46277) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 187), (10, 21839), (19, 44102), (31, 14567)
X(46277) = trilinear product of PU(180)
X(46277) = barycentric product X(i)*X(j) for these {i, j}: {1, 18023}, {63, 46111}, {75, 671}, {76, 897}, {92, 30786}, {111, 561}
X(46277) = barycentric quotient X(i)/X(j) for these (i, j): (1, 187), (10, 21839), (19, 44102), (31, 14567), (48, 23200), (63, 3292)
X(46277) = trilinear product X(i)*X(j) for these {i, j}: {2, 671}, {3, 46111}, {4, 30786}, {6, 18023}, {69, 17983}, {75, 897}
X(46277) = trilinear quotient X(i)/X(j) for these (i, j): (2, 187), (3, 23200), (4, 44102), (6, 14567), (69, 3292), (76, 524)
X(46277) = {X(1109), X(20939)}-harmonic conjugate of X(799)

X(46278) = ISOGONAL CONJUGATE OF X(39087)

X(46278) lies on these lines: {385, 706}, {736, 3978}, {3114, 35078}, {20026, 40858}, {46279, 46282}

X(46278) = reflection of X(3114) in X(35078)
X(46278) = isogonal conjugate of X(39087)
X(46278) = trilinear pole of the line {804, 24256}
X(46278) = trilinear pole of line PU(181)

X(46279) = X(3114)X(18906) ∩ X(24256)X(41073)

X(46280) = X(6)X(17970) ∩ X(1915)X(23209)

X(46281) = ISOTOMIC CONJUGATE OF X(3116)

X(46281) lies on the cubic K1031 and these lines: {1, 1925}, {31, 561}, {42, 7033}, {75, 1967}, {213, 3114}, {304, 46309}, {741, 9063}, {870, 23493}, {871, 1402}, {875, 4374}, {1969, 1973}, {3402, 3403}, {18833, 46289}

X(46281) = isotomic conjugate of X(3116)
X(46281) = barycentric product X(i)*X(j) for these {i, j}: {75, 3114}, {76, 3113}, {561, 3407}, {661, 9063}, {871, 17743}
X(46281) = barycentric quotient X(i)/X(j) for these (i, j): (1, 3117), (31, 18899), (75, 3094), (82, 43977), (561, 3314), (661, 17415)
X(46281) = trilinear product X(i)*X(j) for these {i, j}: {2, 3114}, {75, 3113}, {76, 3407}, {290, 8840}, {308, 14617}, {512, 9063}
X(46281) = trilinear quotient X(i)/X(j) for these (i, j): (2, 3117), (6, 18899), (76, 3094), (83, 43977), (512, 9006), (523, 17415)
X(46281) = trilinear pole of the line {798, 20948}
X(46281) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31)}} and {{A, B, C, X(75), X(1926)}}
X(46281) = cevapoint of X(1) and X(3403)
X(46281) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 3117), (244, 17415)
X(46281) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 18899}, {6, 3117}, {32, 3094}, {39, 43977}
X(46281) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 3117), (31, 18899), (75, 3094), (82, 43977)
X(46281) = trilinear product of PU(181)

X(46282) = ISOGONAL CONJUGATE OF X(46280)

X(46283) = X(3)X(6) ∩ X(76)X(148)

X(46283) lies on these lines: {3, 6}, {76, 148}, {141, 15821}, {194, 14023}, {262, 31455}, {315, 8149}, {384, 10347}, {524, 41756}, {538, 7811}, {626, 5976}, {698, 7767}, {732, 7826}, {736, 7750}, {1078, 1916}, {1506, 14881}, {1569, 38749}, {2023, 7749}, {2549, 12251}, {2782, 7756}, {2979, 3117}, {3060, 8570}, {3096, 3934}, {3097, 31422}, {3099, 12782}, {3229, 3917}, {3399, 12110}, {3767, 6194}, {3785, 31981}, {3972, 10346}, {5077, 14711}, {5149, 10350}, {5254, 32521}, {5309, 33706}, {5346, 10336}, {5969, 7810}, {6248, 9996}, {6292, 24256}, {6309, 7855}, {6636, 14602}, {6656, 18806}, {6683, 7846}, {7603, 9993}, {7746, 10357}, {7760, 32476}, {7768, 9865}, {7786, 10583}, {7800, 18906}, {7801, 9890}, {7804, 10345}, {7816, 10000}, {7827, 22564}, {7841, 7865}, {7842, 39266}, {7887, 7914}, {7889, 10007}, {7890, 41651}, {7893, 10335}, {7998, 9998}, {8623, 20859}, {9482, 10332}, {9651, 10063}, {9664, 10079}, {9862, 11257}, {9873, 22678}, {9941, 14839}, {9984, 38520}, {12503, 38529}, {12837, 31451}, {13108, 44526}, {13210, 38523}, {13235, 38521}, {13236, 38525}, {14537, 34733}, {27375, 39684}, {31400, 44434}, {32450, 33275}, {33274, 44562}, {34885, 39652}, {35700, 37004}, {39590, 40279}

X(46283) = midpoint of X(9821) and X(40252)
X(46283) = reflection of X(i) in X(j) for these (i, j): (7890, 41651), (46313, 39)
X(46283) = perspector of the circumconic {{A, B, C, X(110), X(46284)}}
X(46283) = inverse of X(2076) in 2nd Brocard circle
X(46283) = Moses-circle-inverse of Gallatly-circle-inverse of X(3)
X(46283) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(11606)}} and {{A, B, C, X(54), X(44423)}}
X(46283) = crossdifference of every pair of points on line {X(523), X(39089)}
X(46283) = midpoint of PU(182)
X(46283) = X(39)-of-5th Brocard triangle
X(46283) = X(24256)-of-6th Brocard triangle
X(46283) = X(46283)-of-circumsymmedial triangle
X(46283) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 32452, 39), (3, 44453, 32452), (32, 3094, 39), (32, 35248, 15513), (39, 5052, 5041), (39, 5188, 187), (39, 8589, 13334), (39, 15513, 2021), (39, 35007, 13357), (39, 46321, 5007), (76, 7854, 44772), (574, 3095, 39), (1078, 1916, 32189), (1670, 1671, 2076), (2896, 8782, 76), (3094, 9821, 32), (3095, 9821, 9301), (3098, 9821, 5188), (13325, 13326, 6)

X(46284) = ISOGONAL CONJUGATE OF X(39089)

X(46284) = isogonal conjugate of X(39089)
X(46284) = trilinear pole of the line {512, 46283}
X(46284) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(39), X(737)}}
X(46284) = trilinear pole of line PU(182)

X(46285) = X(3)X(16986) ∩ X(76)X(10997)

X(46285) lies on these lines: {3, 16986}, {76, 10997}, {99, 39090}, {194, 5989}, {3552, 11606}, {3818, 10998}

X(46286) = ISOGONAL CONJUGATE OF X(7779)

X(46286) lies on the cubics K252, K1001 and these lines: {2, 4048}, {6, 3506}, {37, 19557}, {42, 19561}, {110, 3108}, {111, 8627}, {237, 46306}, {251, 3124}, {308, 338}, {694, 2076}, {1976, 35006}, {2502, 39389}, {2987, 15514}, {2998, 8177}, {3589, 39938}, {3750, 9281}, {5027, 17997}, {9178, 14428}, {16606, 40597}, {21513, 36213}, {23868, 34249}, {34572, 39024}, {40802, 44453}, {46227, 46287}

X(46286) = isogonal conjugate of X(7779)
X(46286) = barycentric product X(i)*X(j) for these {i, j}: {6, 11606}, {82, 17957}, {251, 17949}
X(46286) = barycentric quotient X(i)/X(j) for these (i, j): (25, 420), (31, 17799), (32, 2076), (251, 40850), (512, 9479), (669, 5113)
X(46286) = trilinear product X(i)*X(j) for these {i, j}: {31, 11606}, {251, 17957}
X(46286) = trilinear quotient X(i)/X(j) for these (i, j): (6, 17799), (19, 420), (31, 2076), (82, 40850), (251, 34054), (661, 9479)
X(46286) = trilinear pole of the line {512, 5007}
X(46286) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(3), X(36615)}}
X(46286) = crossdifference of every pair of points on line {X(5113), X(9479)}
X(46286) = crosssum of X(732) and X(15573)
X(46286) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 2076), (1084, 9479)
X(46286) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 17799}, {38, 40850}, {63, 420}, {75, 2076}
X(46286) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 420), (31, 17799), (32, 2076), (251, 40850)
X(46286) = X(694)-vertex conjugate of-X(694)
X(46286) = trilinear pole of line PU(183)

X(46287) = ISOGONAL CONJUGATE OF X(46226)

X(46287) lies on these lines: {6, 2896}, {32, 10329}, {213, 21880}, {1974, 11386}, {3224, 5359}, {14885, 46288}, {24273, 40043}, {26454, 44605}, {26461, 44604}, {46227, 46286}

X(46287) = isogonal conjugate of X(46226)
X(46287) = barycentric product X(251)*X(46225)
X(46287) = barycentric quotient X(251)/X(40000)
X(46287) = trilinear quotient X(82)/X(40000)
X(46287) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(21512)}} and {{A, B, C, X(6), X(32)}}
X(46287) = X(38)-isoconjugate-of-X(40000)
X(46287) = X(251)-reciprocal conjugate of-X(40000)
X(46287) = cevapoint of PU(183)

X(46288) = ISOGONAL CONJUGATE OF X(8024)

X(46288) lies on the cubic K486 and these lines: {6, 22}, {32, 206}, {53, 6531}, {69, 9516}, {82, 40747}, {83, 316}, {110, 39449}, {141, 1799}, {182, 10014}, {213, 14599}, {308, 3114}, {427, 46242}, {524, 40405}, {571, 40799}, {597, 42037}, {694, 18903}, {729, 827}, {1184, 8793}, {1333, 45785}, {1485, 41382}, {1576, 9468}, {1918, 18892}, {1974, 17409}, {2373, 40404}, {2422, 18105}, {2965, 32654}, {2980, 3767}, {3053, 28724}, {3224, 38834}, {3225, 4577}, {3629, 41909}, {3763, 10130}, {4630, 32740}, {5116, 46227}, {6664, 38826}, {7735, 21458}, {9418, 46308}, {9969, 10551}, {10328, 42554}, {12212, 39674}, {14575, 46319}, {14600, 42288}, {14601, 40981}, {14885, 46287}, {15321, 39691}, {16519, 34055}, {18268, 34072}, {18374, 18902}, {19125, 22075}, {19137, 41412}, {19156, 40825}, {22331, 40322}, {26926, 46243}, {32661, 41413}, {33739, 44166}

X(46288) = isogonal conjugate of X(8024)
X(46288) = polar conjugate of the isotomic conjugate of X(10547)
X(46288) = barycentric product X(i)*X(j) for these {i, j}: {1, 46289}, {4, 10547}, {6, 251}, {25, 1176}, {31, 82}, {32, 83}
X(46288) = barycentric quotient X(i)/X(j) for these (i, j): (25, 1235), (31, 1930), (32, 141), (82, 561), (83, 1502), (184, 3933)
X(46288) = trilinear product X(i)*X(j) for these {i, j}: {6, 46289}, {19, 10547}, {31, 251}, {32, 82}, {83, 560}, {163, 18105}
X(46288) = trilinear quotient X(i)/X(j) for these (i, j): (6, 1930), (19, 1235), (25, 20883), (31, 141), (32, 38), (41, 3703)
X(46288) = trilinear pole of the line {669, 14602}
X(46288) = perspector of the circumconic {{A, B, C, X(827), X(4630)}}
X(46288) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1180)}} and {{A, B, C, X(4), X(20960)}}
X(46288) = cevapoint of X(i) and X(j) for these (i, j): {32, 1501}, {251, 38834}
X(46288) = crossdifference of every pair of points on line {X(826), X(23285)}
X(46288) = crosspoint of X(83) and X(16277)
X(46288) = crosssum of X(i) and X(j) for these (i, j): {2, 1369}, {39, 3313}, {75, 20933}, {76, 40035}
X(46288) = X(251)-Ceva conjugate of-X(10547)
X(46288) = X(32)-cross conjugate of-X(251)
X(46288) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 141), (512, 39691), (626, 16893), (1084, 23285)
X(46288) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 1930}, {10, 16703}, {38, 76}, {39, 561}
X(46288) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 1235), (31, 1930), (32, 141), (82, 561)
X(46288) = X(308)-vertex conjugate of-X(40416)
X(46288) = barycentric product of PU(183)
X(46288) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 2916, 23642), (32, 206, 16285), (251, 1176, 6), (251, 33632, 1176), (8627, 23642, 2916)

X(46289) = ISOGONAL CONJUGATE OF X(1930)

Let A'B'C' be the 1st orthosymmedial triangle. Let A" be the trilinear product B'*C', and define B" and C" cyclically. The lines AA", BB", CC" concur in X(46289). (Randy Hutson, January 11, 2022)

X(46289) lies on the cubic K1030 and these lines: {1, 82}, {6, 20969}, {10, 26270}, {31, 1917}, {38, 40398}, {42, 251}, {83, 16889}, {163, 1923}, {213, 14599}, {741, 827}, {923, 34072}, {1176, 1203}, {1402, 10547}, {1580, 3112}, {1582, 1930}, {1799, 32783}, {2206, 40148}, {2964, 36051}, {3402, 9247}, {4577, 18826}, {4599, 37132}, {5299, 7122}, {9417, 46309}, {17192, 24707}, {17442, 32676}, {18693, 37220}, {18833, 46281}, {23493, 38834}

X(46289) = isogonal conjugate of X(1930)
X(46289) = complement of anticomplementary conjugate of X(17489)
X(46289) = trilinear pole of the line {798, 1933}
X(46289) = perspector of the circumconic {{A, B, C, X(4599), X(4628)}}
X(46289) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31)}} and {{A, B, C, X(4), X(33720)}}
X(46289) = cevapoint of X(31) and X(560)
X(46289) = crossdifference of every pair of points on line {X(16892), X(23885)}
X(46289) = crosssum of X(i) and X(j) for these (i, j): {1, 21378}, {2, 21289}, {10, 22025}, {37, 22303}
X(46289) = X(i)-cross conjugate of-X(j) for these (i, j): (31, 82), (661, 32676)
X(46289) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 8024), (206, 38), (244, 23285), (251, 21598)
X(46289) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 1930}, {2, 141}, {3, 1235}, {4, 3933}, {6, 8024}
X(46289) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 8024), (19, 1235), (25, 20883), (31, 141)
X(46289) = trilinear product of PU(183)
X(46289) = barycentric product X(i)*X(j) for these {i, j}: {1, 251}, {6, 82}, {25, 34055}, {31, 83}, {32, 3112}, {48, 32085}
X(46289) = barycentric quotient X(i)/X(j) for these (i, j): (1, 8024), (19, 1235), (25, 20883), (31, 141), (32, 38), (41, 3703)
X(46289) = trilinear product X(i)*X(j) for these {i, j}: {2, 46288}, {4, 10547}, {6, 251}, {25, 1176}, {31, 82}, {32, 83}
X(46289) = trilinear quotient X(i)/X(j) for these (i, j): (2, 8024), (3, 3933), (4, 1235), (6, 141), (19, 20883), (25, 427)
X(46289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 21378, 21336), (6, 20994, 20969), (82, 34055, 1), (1923, 1932, 163), (2244, 21336, 21378)

X(46290) = X(524)X(2076) ∩ X(9293)X(17997)

X(46290) lies on these lines: {385, 46291}, {524, 2076}, {8290, 46293}, {9293, 17997}, {15014, 39927}

X(46290) = isogonal conjugate of X(46292)
X(46290) = barycentric product X(i)*X(j) for these {i, j}: {385, 35511}, {804, 37880}
X(46290) = barycentric quotient X(i)/X(j) for these (i, j): (385, 148), (804, 10278), (1580, 2640)
X(46290) = trilinear product X(i)*X(j) for these {i, j}: {385, 9395}, {1580, 35511}
X(46290) = trilinear quotient X(385)/X(2640)
X(46290) = X(i)-isoconjugate-of-X(j) for these {i, j}: {148, 1967}, {694, 2640}, {882, 2644}
X(46290) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (385, 148), (804, 10278)
X(46290) = cevapoint of PU(185)

X(46291) = X(99)X(112) ∩ X(385)X(46290)

X(46291) lies on these lines: {99, 112}, {385, 46290}, {804, 17941}, {4027, 46293}, {4577, 17997}, {9218, 31998}

X(46291) = barycentric product X(i)*X(j) for these {i, j}: {148, 17941}, {385, 31998}, {804, 31632}, {880, 20998}
X(46291) = barycentric quotient X(i)/X(j) for these (i, j): (385, 9293), (1580, 9396)
X(46291) = trilinear product X(i)*X(j) for these {i, j}: {385, 2644}, {1580, 31998}
X(46291) = trilinear quotient X(385)/X(9396)
X(46291) = perspector of the circumconic {{A, B, C, X(18020), X(31632)}}
X(46291) = intersection, other than A, B, C, of circumconics {{A, B, C, X(112), X(9218)}} and {{A, B, C, X(148), X(41676)}}
X(46291) = crossdifference of every pair of points on line {X(19610), X(20975)}
X(46291) = X(385)-Ceva conjugate of-X(17941)
X(46291) = X(99)-Dao conjugate of X(1916)
X(46291) = X(804)-Hirst inverse of-X(17941)
X(46291) = X(i)-isoconjugate-of-X(j) for these {i, j}: {694, 9396}, {882, 9395}
X(46291) = X(385)-reciprocal conjugate of-X(9293)
X(46291) = crosspoint of PU(185)

X(46292) = ISOGONAL CONJUGATE OF X(46290)

X(46292) lies on these lines: {111, 694}, {232, 16068}, {732, 1916}, {882, 10097}, {1967, 9506}

X(46292) = isogonal conjugate of X(46290)
X(46292) = barycentric product X(i)*X(j) for these {i, j}: {148, 694}, {805, 10278}, {882, 31998}, {1581, 2640}
X(46292) = barycentric quotient X(i)/X(j) for these (i, j): (148, 3978), (694, 35511), (805, 37880), (882, 9293)
X(46292) = trilinear product X(i)*X(j) for these {i, j}: {148, 1967}, {694, 2640}, {882, 2644}, {1581, 20998}
X(46292) = trilinear quotient X(i)/X(j) for these (i, j): (148, 1966), (694, 9395), (882, 9396)
X(46292) = X(882)-Ceva conjugate of-X(694)
X(46292) = X(99)-Dao conjugate of X(880)
X(46292) = X(385)-isoconjugate-of-X(9395)
X(46292) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (148, 3978), (694, 35511), (805, 37880), (882, 9293)
X(46292) = crosssum of PU(185)

X(46293) = X(99)X(25054) ∩ X(543)X(5034)

X(46293) lies on these lines: {99, 25054}, {543, 5034}, {804, 4107}, {4027, 46291}, {8290, 46290}

X(46293) = X(45914)-of-6th anti-Brocard triangle
X(46293) = bicentric sum of PU(185)

X(46294) = X(99)X(249) ∩ X(110)X(18829)

X(46294) lies on these lines: {99, 249}, {110, 18829}, {325, 19576}, {385, 14602}, {523, 4577}, {1576, 4590}, {4027, 35078}, {11183, 14959}

X(46294) = barycentric product X(i)*X(j) for these {i, j}: {1, 46295}, {99, 4027}, {385, 17941}, {880, 1691}
X(46294) = barycentric quotient X(i)/X(j) for these (i, j): (110, 41517), (880, 18896), (1691, 882)
X(46294) = trilinear product X(i)*X(j) for these {i, j}: {6, 46295}, {662, 4027}, {880, 1933}
X(46294) = trilinear quotient X(i)/X(j) for these (i, j): (662, 41517), (880, 1934)
X(46294) = X(i)-Dao conjugate of X(j) for these (i, j): (732, 2528), (804, 8029)
X(46294) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 41517}, {881, 1934}, {882, 1581}
X(46294) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (110, 41517), (880, 18896)
X(46294) = barycentric product of PU(185)

X(46295) = X(163)X(24037) ∩ X(799)X(4575)

X(46295) lies on these lines: {163, 24037}, {799, 4575}, {1577, 4593}, {1933, 1966}, {19572, 46238}

X(46295) = barycentric product X(i)*X(j) for these {i, j}: {75, 46294}, {799, 4027}, {880, 1580}, {1966, 17941}
X(46295) = barycentric quotient X(i)/X(j) for these (i, j): (662, 41517), (880, 1934), (1580, 882), (1933, 881)
X(46295) = trilinear product X(i)*X(j) for these {i, j}: {2, 46294}, {99, 4027}, {385, 17941}, {880, 1691}
X(46295) = trilinear quotient X(i)/X(j) for these (i, j): (99, 41517), (385, 882), (880, 1916), (1691, 881)
X(46295) = X(i)-isoconjugate-of-X(j) for these {i, j}: {512, 41517}, {694, 882}, {881, 1916}
X(46295) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (662, 41517), (880, 1934), (1580, 882)
X(46295) = trilinear product of PU(185)

X(46296) = TRILINEAR POLE OF LINE PU(186)

X(46296) = isogonal conjugate of X(46298)
X(46296) = trilinear pole of the line {690, 7753}
X(46296) = trilinear pole of line PU(186)

X(46297) = X(3)X(5640) ∩ X(2076)X(32154)

X(46297) lies on these lines: {3, 5640}, {2076, 32154}, {5012, 38661}, {5116, 32740}, {10168, 13586}, {12215, 16511}

X(46298) = ISOGONAL CONJUGATE OF X(46296)

X(46298) lies on these lines: {6, 110}, {183, 9140}, {323, 34383}, {385, 542}, {399, 32595}, {526, 3005}, {1384, 38661}, {2871, 15107}, {3329, 5642}, {5008, 13193}, {5092, 12192}, {5663, 9301}, {6784, 15018}, {7766, 9143}, {7998, 9145}, {9142, 15080}, {9976, 15920}, {13210, 14901}, {33878, 38653}

X(46298) = isogonal conjugate of X(46296)
X(46298) = crossdifference of every pair of points on line {X(690), X(7753)}
X(46298) = X(385)-of-anti-orthocentroidal triangle
X(46298) = crossdifference of PU(186)

X(46299) = X(6)X(30) ∩ X(385)X(1383)

X(46299) lies on these lines: {6, 30}, {385, 1383}, {3124, 45819}, {7766, 20099}

X(46299) = barycentric product X(1)*X(46300)
X(46299) = trilinear product X(6)*X(46300)
X(46299) = barycentric product of PU(186)

X(46300) = TRILINEAR PRODUCT OF PU(186)

X(46300) = barycentric product X(75)*X(46299)
X(46300) = trilinear product X(2)*X(46299)
X(46300) = trilinear product of PU(186)

X(46301) = X(6)X(13) ∩ X(32)X(110)

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

X(46301) lies on the Moses circle, cubic K291 and these lines: {6, 13}, {32, 110}, {39, 5663}, {74, 574}, {112, 3043}, {125, 217}, {146, 2549}, {187, 1511}, {216, 12358}, {230, 10272}, {232, 1986}, {323, 754}, {690, 1569}, {1015, 3028}, {1112, 3199}, {1495, 2387}, {1500, 3024}, {1561, 12112}, {1571, 9904}, {1572, 2948}, {1692, 6593}, {1968, 15463}, {2021, 38650}, {2207, 19504}, {2211, 5095}, {2241, 10088}, {2242, 10091}, {2275, 19470}, {2276, 7727}, {2421, 2482}, {2493, 15544}, {2548, 3448}, {2777, 7756}, {2854, 5052}, {2914, 8744}, {2931, 9699}, {3031, 9561}, {3047, 9697}, {3053, 32609}, {3055, 40685}, {3231, 5642}, {3289, 6781}, {3331, 13202}, {3569, 9408}, {3815, 10264}, {5007, 5609}, {5013, 10620}, {5017, 12584}, {5023, 15040}, {5028, 9970}, {5033, 15462}, {5034, 11579}, {5206, 15035}, {5585, 15042}, {5972, 7749}, {6126, 16784}, {7343, 16785}, {7603, 20304}, {7722, 39575}, {7728, 7748}, {7735, 20125}, {7736, 12317}, {7737, 12383}, {7745, 32423}, {7746, 14643}, {7747, 17702}, {7755, 16534}, {7765, 15063}, {7772, 14094}, {7810, 15066}, {7812, 11004}, {8588, 15051}, {9560, 34453}, {9605, 12308}, {9619, 33535}, {9635, 10118}, {9636, 12888}, {9650, 12903}, {9651, 12373}, {9664, 12374}, {9665, 12904}, {9675, 10819}, {9684, 10817}, {9698, 16003}, {9700, 10117}, {10065, 31451}, {10113, 39590}, {10294, 41358}, {10706, 11648}, {10721, 41367}, {12041, 37512}, {12133, 33843}, {12165, 45141}, {12219, 22240}, {15039, 22331}, {15041, 15815}, {15055, 15515}, {15061, 31455}, {15081, 31415}, {22401, 44573}, {23357, 32730}, {23515, 41334}, {32452, 38520}, {38632, 41940}, {38789, 44518}, {38790, 44526}

X(46301) = perspector of the circumconic {{A, B, C, X(476), X(32717)}}
X(46301) = touchpoint of the line {526, 46301} and Moses circle
X(46301) = intersection, other than A, B, C, of circumconics {{A, B, C, X(115), X(32730)}} and {{A, B, C, X(323), X(14901)}}
X(46301) = crossdifference of every pair of points on line {X(526), X(9140)}
X(46301) = midpoint of PU(187)
X(46301) = X(39)-of-anti-orthocentroidal triangle
X(46301) = reflection of X(39) in the line X(526)X(2491)
X(46301) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 399, 14901), (6, 1625, 3016), (6, 3016, 115), (12375, 12376, 19140), (36208, 36209, 25556)

X(46302) = X(98)X(17938) ∩ X(237)X(804)

X(46302) lies on these lines: {98, 17938}, {237, 804}, {511, 11052}, {523, 5106}, {524, 36213}, {1691, 5967}, {3231, 11176}, {3266, 5976}, {4230, 17984}, {5201, 23342}

X(46302) = midpoint of X(5201) and X(23342)
X(46302) = isogonal conjugate of X(46303)
X(46302) = trilinear pole of the line {690, 1569}
X(46302) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(468)}} and {{A, B, C, X(4), X(44215)}}
X(46302) = cevapoint of X(i) and X(j) for these (i, j): {237, 3231}, {385, 13586}, {887, 2086}
X(46302) = trilinear pole of line PU(187)

X(46303) = ISOGONAL CONJUGATE OF X(46302)

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

X(46303) = X(805)-4*X(15630) = 3*X(6784)-X(6786) = 2*X(13137)+X(14510) = X(13188)-4*X(46172) = 4*X(14113)-X(14509) = 2*X(31850)+X(38664)

X(46303) lies on these lines: {2, 6784}, {6, 110}, {98, 385}, {99, 3111}, {115, 6787}, {141, 13518}, {183, 7998}, {290, 879}, {373, 3329}, {512, 671}, {524, 33873}, {526, 9140}, {542, 6785}, {694, 2086}, {888, 3228}, {2387, 14568}, {2782, 41330}, {2871, 3060}, {2979, 8667}, {3225, 14970}, {3511, 9155}, {4609, 33769}, {5201, 9142}, {5663, 12188}, {5969, 9828}, {6772, 25173}, {6775, 25178}, {7766, 11002}, {9027, 39099}, {9218, 14908}, {9418, 35265}, {9855, 32442}, {11163, 13240}, {11174, 12093}, {11673, 22329}, {13188, 46172}, {14113, 14509}, {15072, 39646}, {15271, 33879}, {23004, 31707}, {23005, 31708}, {31850, 38664}, {32547, 44518}, {38650, 44468}, {43664, 46142}

X(46303) = midpoint of X(385) and X(13207)
X(46303) = reflection of X(i) in X(j) for these (i, j): (2, 6784), (99, 3111), (6787, 115), (9855, 32442), (11673, 22329)
X(46303) = anticomplement of X(6786)
X(46303) = isogonal conjugate of X(46302)
X(46303) = perspector of the circumconic {{A, B, C, X(691), X(39291)}}
X(46303) = intersection, other than A, B, C, of circumconics {{A, B, C, X(110), X(35146)}} and {{A, B, C, X(111), X(36897)}}
X(46303) = crossdifference of every pair of points on line {X(690), X(1569)}
X(46303) = crosspoint of X(i) and X(j) for these (i, j): {290, 3228}, {886, 39292}
X(46303) = crosssum of X(i) and X(j) for these (i, j): {237, 3231}, {385, 13586}, {887, 2086}
X(46303) = crossdifference of PU(187)
X(46303) = X(385)-of-orthocentroidal triangle
X(46303) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (98, 512, 11632), (110, 2780, 9144), (111, 2780, 11632)
X(46303) = {X(6), X(9149)}-harmonic conjugate of X(110)

X(46304) = BARYCENTRIC PRODUCT OF PU(187)

X(46305) = X(3)X(6) ∩ X(51)X(3117)

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

X(46305) lies on these lines: {3, 6}, {51, 3117}, {76, 2548}, {83, 39101}, {115, 38383}, {194, 14035}, {230, 11272}, {262, 3767}, {325, 1506}, {538, 7753}, {698, 41651}, {726, 41662}, {736, 7838}, {1569, 19687}, {1572, 12782}, {1916, 7839}, {1992, 13085}, {2023, 5305}, {2782, 7745}, {3229, 5943}, {3399, 39095}, {3933, 24256}, {5254, 14881}, {5309, 44422}, {5475, 6248}, {6033, 39590}, {6194, 31400}, {6309, 18906}, {6660, 14153}, {6683, 7749}, {7736, 12251}, {7737, 11257}, {7757, 33007}, {7764, 18806}, {7778, 31239}, {7785, 39266}, {7786, 16989}, {7804, 10349}, {7805, 32189}, {7819, 44380}, {7837, 9983}, {7855, 14994}, {8992, 31481}, {9225, 21513}, {9419, 42442}, {9466, 9766}, {9596, 10063}, {9599, 10079}, {9865, 13571}, {12837, 16502}, {13108, 15484}, {13366, 14602}, {13410, 37338}, {15819, 31455}, {18907, 32448}, {19090, 31411}, {22486, 34511}, {22712, 31401}, {31276, 31404}, {31406, 32521}, {31981, 32451}

X(46305) = midpoint of X(39) and X(46313)
X(46305) = perspector of the circumconic {{A, B, C, X(110), X(46306)}}
X(46305) = crossdifference of every pair of points on line {X(523), X(39093)}
X(46305) = midpoint of PU(188)
X(46305) = X(46305)-of-circumsymmedial triangle
X(46305) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 13330, 46321), (6, 3095, 39), (32, 39, 2021), (39, 187, 13334), (39, 5007, 13357), (39, 5052, 32), (39, 5188, 574), (39, 46321, 3), (576, 13356, 43183), (3094, 9605, 39), (7772, 32452, 39), (13357, 44500, 5007)

X(46306) = ISOGONAL CONJUGATE OF X(39093)

X(46306) lies on these lines: {237, 46286}, {420, 16081}, {2395, 5113}, {20027, 39292}, {30535, 36213}

X(46306) = isogonal conjugate of X(39093)
X(46306) = trilinear pole of the line {512, 46305}
X(46306) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(98), X(34214)}}
X(46306) = trilinear pole of line PU(188)

X(46307) = X(99)X(39094) ∩ X(1975)X(5116)

X(46307) lies on these lines: {99, 39094}, {1975, 5116}, {3399, 39093}, {5989, 14651}, {7750, 37334}, {7824, 46236}, {12215, 46226}

X(46308) = X(69)X(3114) ∩ X(83)X(511)

X(46308) lies on these lines: {6, 20885}, {69, 3114}, {83, 511}, {213, 46309}, {688, 2422}, {729, 41413}, {1843, 6531}, {1974, 18899}, {3224, 5017}, {3225, 33755}, {5028, 10014}, {9418, 46288}, {9468, 40981}, {14601, 41331}, {39099, 40405}

X(46308) = barycentric product X(i)*X(j) for these {i, j}: {1, 46309}, {32, 3399}
X(46308) = barycentric quotient X(1501)/X(3398)
X(46308) = trilinear product X(i)*X(j) for these {i, j}: {6, 46309}, {560, 3399}
X(46308) = trilinear quotient X(560)/X(3398)
X(46308) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(32)}} and {{A, B, C, X(25), X(20885)}}
X(46308) = X(561)-isoconjugate-of-X(3398)
X(46308) = barycentric product of PU(188)

X(46309) = X(1)X(3400) ∩ X(213)X(46308)

X(46309) lies on these lines: {1, 3400}, {213, 46308}, {304, 46281}, {1959, 3112}, {1967, 2179}, {3399, 7594}, {9417, 46289}, {17442, 36120}

X(46309) = barycentric product X(i)*X(j) for these {i, j}: {31, 3399}, {75, 46308}, {694, 3400}
X(46309) = barycentric quotient X(560)/X(3398)
X(46309) = trilinear product X(i)*X(j) for these {i, j}: {2, 46308}, {32, 3399}
X(46309) = trilinear quotient X(i)/X(j) for these (i, j): (32, 3398), (694, 20027)
X(46309) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(31)}} and {{A, B, C, X(304), X(9247)}}
X(46309) = X(i)-isoconjugate-of-X(j) for these {i, j}: {76, 3398}, {385, 20027}
X(46309) = X(560)-reciprocal conjugate of-X(3398)
X(46309) = trilinear product of PU(188)

X(46310) = ISOGONAL CONJUGATE OF X(39095)

X(46310) lies on these lines: {25, 36213}, {263, 3095}, {287, 8842}, {393, 39931}, {694, 36212}, {1976, 2456}, {2395, 24284}, {3978, 16081}

X(46310) = isogonal conjugate of X(39095)
X(46310) = barycentric quotient X(511)/X(38383)
X(46310) = trilinear pole of the line {512, 5188}
X(46310) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(76), X(182)}}
X(46310) = X(511)-reciprocal conjugate of-X(38383)
X(46310) = trilinear pole of line PU(189)

X(46311) = X(99)X(39096) ∩ X(384)X(1503)

X(46311) lies on these lines: {99, 39096}, {384, 1503}, {574, 11257}, {1975, 5999}, {3424, 3552}, {7710, 7770}, {7738, 13860}, {7824, 9756}, {11381, 17970}, {33198, 35423}

X(46312) = X(2)X(6) ∩ X(3511)X(15905)

X(46313) = X(3)X(6) ∩ X(51)X(3229)

Barycentrics a^2*((b^2+c^2)*a^4+(b^4+4*b^2*c^2+c^4)*a^2-b^6-c^6) : :
Trilinears sin A - sin 3ω cos(A + ω) : :

X(46313) lies on these lines: {3, 6}, {51, 3229}, {69, 31982}, {76, 5475}, {115, 14881}, {193, 31981}, {194, 6658}, {262, 7746}, {325, 18806}, {385, 32189}, {538, 7812}, {698, 41756}, {732, 7890}, {736, 7762}, {881, 8711}, {1569, 10992}, {1916, 7760}, {1994, 14602}, {2023, 7755}, {2241, 12837}, {2242, 12836}, {2548, 12251}, {2782, 7747}, {3060, 3117}, {3180, 6581}, {3181, 6294}, {3202, 19558}, {3314, 3934}, {3734, 18548}, {3815, 32521}, {5286, 44434}, {5969, 41651}, {5976, 7764}, {6194, 31401}, {6248, 39590}, {6660, 45843}, {6683, 7857}, {7745, 32515}, {7749, 11272}, {7757, 33265}, {7758, 18906}, {7774, 8149}, {7775, 7788}, {7794, 24256}, {7801, 22486}, {7843, 39266}, {7862, 7868}, {7877, 9983}, {7905, 9865}, {8782, 13571}, {9650, 10063}, {9665, 10079}, {14251, 27375}, {18501, 44539}, {22712, 31455}, {22728, 44518}, {31276, 31415}, {32450, 33257}

X(46313) = midpoint of X(7877) and X(9983)
X(46313) = reflection of X(i) in X(j) for these (i, j): (39, 46305), (46283, 39)
X(46313) = perspector of the circumconic {{A, B, C, X(110), X(46314)}}
X(46313) = inverse of X(5116) in 2nd Brocard circle
X(46313) = crossdifference of every pair of points on line {X(523), X(39097)}
X(46313) = crosssum of X(2) and X(8177)
X(46313) = circle-{{X(4),X(194),X(3557),X(3558)}}-inverse of X(3094)
X(46313) = midpoint of PU(190)
X(46313) = X(46313)-of-circumsymmedial triangle
X(46313) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 32452, 39), (32, 3095, 39), (39, 5008, 13357), (39, 5052, 5007), (39, 5188, 37512), (39, 15513, 13334), (39, 35007, 2021), (39, 46321, 187), (576, 3095, 35437), (576, 13330, 5052), (1670, 1671, 5116), (3094, 7772, 39), (3095, 13330, 32), (3102, 3103, 44423), (3557, 3558, 3094), (5052, 35439, 1570)

X(46314) = ISOGONAL CONJUGATE OF X(39097)

X(46314) = isogonal conjugate of X(39097)
X(46314) = trilinear pole of the line {512, 46313}
X(46314) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(98), X(41517)}}
X(46314) = trilinear pole of line PU(190)

X(46315) = X(3)X(148) ∩ X(99)X(39098)

X(46315) lies on these lines: {3, 148}, {99, 39098}, {9737, 10998}, {32189, 34885}

X(46316) = ISOGONAL CONJUGATE OF X(39099)

X(46316) lies on the cubic K756 and these lines: {2, 2782}, {6, 6784}, {25, 34096}, {110, 30535}, {111, 237}, {263, 3124}, {308, 37688}, {351, 2395}, {468, 16081}, {694, 3291}, {1383, 5191}, {1976, 14567}, {2433, 9208}, {2491, 9178}, {2502, 11166}, {2987, 14510}, {2998, 17008}, {3228, 22329}, {5106, 21448}, {7610, 9462}, {8644, 14606}, {8770, 20885}, {8842, 39292}, {8901, 42300}, {11284, 36213}, {14998, 17414}, {16092, 18818}, {27809, 37764}, {37439, 37876}, {46317, 46320}

X(46316) = isogonal conjugate of X(39099)
X(46316) = barycentric product X(6)*X(43532)
X(46316) = barycentric quotient X(32)/X(2080)
X(46316) = trilinear product X(31)*X(43532)
X(46316) = trilinear quotient X(i)/X(j) for these (i, j): (31, 2080), (923, 21460)
X(46316) = trilinear pole of the line {512, 5052}
X(46316) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(32), X(7607)}}
X(46316) = X(206)-Dao conjugate of X(2080)
X(46316) = X(75)-isoconjugate-of-X(2080)
X(46316) = X(32)-reciprocal conjugate of-X(2080)
X(46316) = X(25)-vertex conjugate of-X(694)
X(46316) = trilinear pole of line PU(191)

X(46317) = X(262)X(5028) ∩ X(263)X(3148)

X(46317) lies on these lines: {262, 5028}, {263, 3148}, {5034, 14252}, {5052, 26714}, {46316, 46320}

X(46318) = X(2)X(12215) ∩ X(3)X(32815)

X(46318) lies on these lines: {2, 12215}, {3, 32815}, {69, 13860}, {76, 9737}, {98, 13354}, {99, 15819}, {141, 44531}, {183, 1350}, {230, 384}, {262, 39099}, {385, 13330}, {1003, 23055}, {1007, 40330}, {1078, 7470}, {1975, 7824}, {2076, 13468}, {4048, 37637}, {5017, 37667}, {5152, 6055}, {5976, 14931}, {5989, 37455}, {6337, 11285}, {7610, 11164}, {7612, 35925}, {8290, 17006}, {8591, 11168}, {9466, 9888}, {9752, 35930}, {11185, 11676}, {11286, 16509}, {11356, 43291}, {32832, 38907}, {35021, 35422}

X(46318) = isogonal conjugate of X(46320)
X(46318) = crosssum of PU(191)
X(46318) = {X(5989), X(37688)}-harmonic conjugate of X(37455)

X(46319) = ISOGONAL CONJUGATE OF X(20023)

X(46319) lies on the cubic K1057 and these lines: {3, 83}, {6, 160}, {25, 6531}, {32, 3202}, {39, 10014}, {183, 327}, {213, 3402}, {385, 37465}, {669, 2422}, {729, 1384}, {1501, 14601}, {1974, 41331}, {2186, 21010}, {2207, 27369}, {3053, 3224}, {3225, 3511}, {3329, 37184}, {5201, 9516}, {6037, 36822}, {9468, 41278}, {11159, 38889}, {14252, 30435}, {14575, 46288}, {15271, 37338}, {22331, 36615}, {23210, 39951}, {32740, 34416}, {33875, 39238}, {37344, 42313}, {39646, 39682}

X(46319) = isogonal conjugate of X(20023)
X(46319) = barycentric product X(i)*X(j) for these {i, j}: {1, 3402}, {6, 263}, {25, 43718}, {31, 2186}, {32, 262}, {39, 42288}
X(46319) = barycentric quotient X(i)/X(j) for these (i, j): (25, 44144), (31, 3403), (32, 183), (213, 42711), (262, 1502), (263, 76)
X(46319) = trilinear product X(i)*X(j) for these {i, j}: {6, 3402}, {31, 263}, {32, 2186}, {262, 560}, {327, 1917}, {798, 26714}
X(46319) = trilinear quotient X(i)/X(j) for these (i, j): (6, 3403), (19, 44144), (31, 183), (42, 42711), (262, 561), (263, 75)
X(46319) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(14575)}} and {{A, B, C, X(6), X(32)}}
X(46319) = X(206)-Dao conjugate of X(183)
X(46319) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 3403}, {63, 44144}, {75, 183}, {86, 42711}
X(46319) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 44144), (31, 3403), (32, 183), (213, 42711)
X(46319) = barycentric product of PU(191)

X(46320) = ISOGONAL CONJUGATE OF X(46318)

X(46320) = isogonal conjugate of X(46318)
X(46320) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(5017)}} and {{A, B, C, X(182), X(46316)}}
X(46320) = cevapoint of PU(191)

X(46321) = X(3)X(6) ∩ X(51)X(8623)

X(46321) = 3*X(32)-2*X(13357) = 3*X(32)-X(32452) = 3*X(39)-4*X(13357) = 3*X(39)-2*X(32452) = 4*X(626)-5*X(31239) = 3*X(9466)-4*X(18806) = 4*X(13335)-3*X(21163) = 3*X(14711)-2*X(37004)

X(46321) lies on these lines: {3, 6}, {51, 8623}, {76, 7737}, {193, 6309}, {194, 33244}, {230, 14881}, {315, 3934}, {538, 33007}, {626, 7603}, {736, 19687}, {754, 8370}, {1506, 15819}, {2056, 20854}, {2548, 22712}, {3229, 3787}, {3399, 22521}, {3629, 41651}, {5477, 41756}, {5976, 7762}, {6248, 7747}, {6683, 33001}, {7746, 9753}, {7749, 20576}, {7757, 33208}, {7767, 24256}, {7786, 21843}, {7804, 10350}, {7805, 36849}, {7823, 39266}, {7826, 14994}, {11159, 14711}, {12829, 23718}, {14153, 21512}, {15993, 44230}, {18502, 44530}, {18907, 32521}, {22564, 34604}, {22682, 39565}, {31415, 33261}, {32450, 33254}, {36212, 41278}

X(46321) = midpoint of X(76) and X(20065)
X(46321) = reflection of X(i) in X(j) for these (i, j): (39, 32), (315, 3934), (5052, 35432), (5188, 35430), (32452, 13357), (35439, 35431)
X(46321) = perspector of the circumconic {{A, B, C, X(110), X(46322)}}
X(46321) = inverse of X(2024) in: Brocard inellipse, Moses circle
X(46321) = crossdifference of every pair of points on line {X(523), X(39101)}
X(46321) = X(6)-daleth conjugate of-X(2024)
X(46321) = midpoint of PU(192)
X(46321) = Brocard axis intercept, other than X(182), of circle {{X(182),PU(39)}}
X(46321) = center of circle {{X(76), X(20065), X(38527)}}
X(46321) = X(46321)-of-circumsymmedial triangle
X(46321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 13330, 46305), (3, 46305, 39), (32, 5162, 13335), (32, 32452, 13357), (32, 43183, 5007), (39, 15513, 21163), (187, 46313, 39), (2021, 3095, 39), (2028, 2029, 2024), (3053, 3095, 2021), (5007, 46283, 39), (5052, 5188, 39), (5162, 13335, 15513), (13357, 32452, 39), (35430, 35432, 32)

X(46322) = ISOGONAL CONJUGATE OF X(39101)

X(46322) = isogonal conjugate of X(39101)
X(46322) = trilinear pole of the line {512, 46321}
X(46322) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(6)}} and {{A, B, C, X(232), X(36213)}}
X(46322) = trilinear pole of line PU(192)

X(46323) = X(99)X(39102) ∩ X(148)X(7470)

X(46323) lies on these lines: {99, 39102}, {148, 7470}, {194, 37334}, {6337, 7824}

X(46324) = ISOGONAL CONJUGATE OF X(40461)

X(46324) = isogonal conjugate of X(40461)
X(46324) = trilinear pole of the line {39541, 40458}
X(46324) = trilinear pole of line PU(195)

X(46325) = MIDPOINT OF PU(196)

X(46326) = ISOTOMIC CONJUGATE OF X(16187)

X(46326) = isogonal conjugate of X(46327)
X(46326) = isotomic conjugate of X(16187)
X(46326) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(297)}} and {{A, B, C, X(125), X(22112)}}
X(46326) = cevapoint of PU(196)

X(46327) = ISOGONAL CONJUGATE OF X(46326)

X(46327) lies on these lines: {6, 157}, {237, 33871}, {5640, 22143}, {14930, 44089}, {20968, 41940}, {23200, 33872}

X(46327) = isogonal conjugate of X(46326)
X(46327) = barycentric product X(6)*X(16187)
X(46327) = trilinear product X(31)*X(16187)
X(46327) = crosssum of PU(196)

X(46328) = X(2)X(6331) ∩ X(125)X(327)

X(46328) lies on these lines: {2, 6331}, {76, 37648}, {125, 327}, {264, 30739}, {1502, 11059}, {7386, 46104}, {11284, 17984}, {11433, 34384}, {16187, 44155}, {22112, 46247}

X(46328) = barycentric product X(1285)*X(1502)
X(46328) = barycentric quotient X(1285)/X(32)
X(46328) = trilinear product X(561)*X(1285)
X(46328) = trilinear quotient X(1285)/X(560)
X(46328) = X(1285)-reciprocal conjugate of-X(32)
X(46328) = barycentric product of PU(196)

X(46329) = (name pending)

X(46330) = X(6)X(57)∩X(85)X(189)

X(46330) lies on these lines: {6, 57}, {77, 6611}, {85, 189}, {142, 6708}, {241, 28274}, {515, 942}, {940, 1435}, {1119, 40149}, {1456, 4224}, {1876, 10391}, {2182, 34035}, {3666, 37755}, {4340, 34231}, {4349, 11018}, {4359, 4566}, {5745, 20201}, {7248, 37566}, {8808, 21239}, {9940, 40657}, {20197, 41867}, {37523, 40933}, {43058, 44708}

X(46330) = barycentric product X(3668)*X(10461)
X(46330) = barycentric quotient X(10461)/X(1043)
X(46330) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {57, 223, 15509}, {942, 40644, 9942}

X(46331) = X(38)X(65)∩X(141)X(226)

X(46331) lies on these lines: {38, 65}, {57, 16696}, {85, 16703}, {141, 226}, {1407, 20617}, {7341, 17074}, {10473, 46149}

X(46331) = X(i)-isoconjugate of X(j) for these (i,j): {8, 4264}, {219, 37390}, {284, 26115}, {7054, 10408}
X(46331) = trilinear pole of line {2530, 4017}
X(46331) = barycentric quotient X(i)/X(j) for these {i,j}: {34, 37390}, {65, 26115}, {604, 4264}, {1254, 10408}

X(46332) = EULER LINE INTERCEPT OF X(5318)X(42952)

X(46332) = X(2)+3*X(548), 13*X(2)+3*X(1657), 9*X(2)+7*X(3534), 11*X(2)-3*X(3627), 15*X(2)-7*X(3845), 5*X(2)-3*X(3850), 13*X(2)-7*X(3860), 11*X(2)-7*X(5066), X(2)+7*X(8703), 9*X(2)-7*X(10109), 6*X(2)-7*X(11540), 5*X(2)-7*X(11812), 3*X(2)-7*X(12100), 19*X(2)-7*X(12101), 2*X(2)-3*X(12108), 19*X(2)-15*X(12812), X(2)+15*X(14093), 7*X(2)-9*X(14890), X(2)-3*X(14891), 13*X(2)-9*X(14892), 7*X(2)-3*X(14893), 19*X(2)-3*X(15684), 5*X(2)+3*X(15686), 7*X(2)+9*X(15689), 5*X(2)+7*X(15690), 7*X(2)-15*X(15712), X(2)-7*X(15759), 17*X(2)+15*X(17538), 17*X(2)+7*X(19710), 17*X(2)-9*X(23046), 5*X(2)-9*X(41983), 4*X(2)-7*X(44580), 11*X(2)-9*X(45757), 8*X(2)-9*X(45758), X(2)-9*X(45759), 13*X(2)-15*X(45760)

X(46332) lies on these lines: {2, 3}, {5318, 42952}, {5321, 42953}, {6484, 41946}, {6485, 41945}, {9300, 15602}, {9681, 10142}, {28212, 31662}, {34754, 42791}, {34755, 42792}, {35770, 42524}, {35771, 42525}, {41943, 42891}, {41944, 42890}, {42087, 43200}, {42088, 43199}, {42508, 43635}, {42509, 43634}, {42528, 43109}, {42529, 43108}, {42532, 42924}, {42533, 42925}, {42631, 42912}, {42632, 42913}, {42906, 43247}, {42907, 43246}, {42942, 42977}, {42943, 42976}

X(46332) = midpoint of X(i) and X(j) for these {i, j}: {376, 3530}, {548, 14891}, {549, 44245}, {550, 10124}, {3534, 10109}, {3628, 15691}, {3850, 15686}, {8703, 15759}, {11737, 12103}, {11812, 15690}, {12102, 15681}, {14890, 15689}, {33923, 34200}
X(46332) = reflection of X(i) in X(j) for these (i, j): (3856, 10124), (11540, 12100), (12108, 14891), (35018, 549), (41988, 35018)
X(46332) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 8703, 548), (3, 15688, 3543), (140, 3855, 3628), (376, 15706, 3627), (548, 12812, 550), (549, 35400, 547), (3545, 41992, 547), (3832, 11539, 547), (3850, 11812, 2), (5066, 15711, 3530), (8703, 15711, 376), (8703, 45759, 2), (11001, 19711, 547), (11539, 15686, 3627), (11541, 15702, 3545), (11812, 15759, 3), (12100, 15701, 3530), (14093, 45759, 548), (14891, 45757, 3530), (15684, 15693, 2), (15686, 45759, 3), (15688, 15714, 140), (15688, 17800, 376), (15697, 15716, 5), (15698, 17538, 2), (15698, 19710, 140), (15718, 23046, 140), (33923, 44245, 3528), (34200, 41982, 3), (44245, 45760, 1657)

X(46333) = EULER LINE INTERCEPT OF X(397)X(42586)

X(46333) = 11*X(2)-14*X(3), 10*X(2)-7*X(4), X(2)-7*X(20), 4*X(2)-7*X(376), 17*X(2)-14*X(381), 5*X(2)-8*X(548), X(2)+2*X(1657), 19*X(2)-7*X(3146), 6*X(2)-7*X(3524), 8*X(2)+7*X(3529), 5*X(2)-14*X(3534), 13*X(2)-7*X(3543), 8*X(2)-7*X(3545), 7*X(2)-4*X(3627), 9*X(2)-7*X(3839), 13*X(2)-10*X(3843), 19*X(2)-16*X(3850), 13*X(2)-14*X(5054), 15*X(2)-14*X(5055), 17*X(2)+7*X(5059), 5*X(2)-7*X(10304), 2*X(2)+7*X(11001), 7*X(2)-10*X(14093), 19*X(2)-14*X(14269), 15*X(2)-16*X(14890), 13*X(2)-16*X(14891), 9*X(2)-8*X(14892), 11*X(2)-8*X(14893), X(2)+14*X(15681), 16*X(2)-7*X(15682), 5*X(2)+7*X(15683), 5*X(2)-2*X(15684), 13*X(2)+14*X(15685), X(2)-4*X(15686), 9*X(2)-14*X(15688), 5*X(2)-6*X(15706), 17*X(2)-20*X(15712), 2*X(2)-5*X(17538), 8*X(2)-11*X(21735), 5*X(2)-4*X(23046), 4*X(2)-X(33703), 7*X(2)-11*X(35418), 7*X(2)-8*X(41983), 17*X(2)-16*X(45757), 3*X(2)-4*X(45759)

X(46333) lies on these lines: {2, 3}, {397, 42586}, {398, 42587}, {485, 43521}, {486, 43522}, {3068, 43342}, {3069, 43343}, {3592, 43785}, {3594, 43786}, {3625, 34638}, {3633, 6361}, {3653, 28154}, {4324, 10385}, {4668, 31730}, {5731, 28202}, {6435, 43336}, {6436, 43337}, {6449, 43340}, {6450, 43341}, {6451, 43507}, {6452, 43508}, {6470, 43384}, {6471, 43385}, {6486, 42570}, {6487, 42571}, {7739, 14075}, {7750, 32877}, {7811, 32822}, {7850, 32817}, {7967, 28198}, {8591, 14692}, {9778, 28208}, {10653, 43300}, {10654, 43301}, {11488, 42929}, {11489, 42928}, {13702, 42520}, {14226, 35821}, {14241, 35820}, {14912, 19924}, {16962, 42090}, {16963, 42091}, {18481, 34631}, {19053, 42266}, {19054, 42267}, {19106, 43201}, {19107, 43202}, {19875, 28172}, {20053, 34632}, {28146, 38314}, {28158, 38021}, {28164, 38074}, {28190, 38066}, {31412, 43568}, {32455, 43273}, {32787, 43339}, {32788, 43338}, {32878, 37671}, {33606, 42149}, {33607, 42152}, {33750, 38072}, {35822, 42414}, {35823, 42413}, {36969, 42795}, {36970, 42796}, {37640, 42100}, {37641, 42099}, {38742, 41135}, {41100, 42934}, {41101, 42935}, {41107, 42435}, {41108, 42436}, {41112, 42434}, {41113, 42433}, {41121, 43550}, {41122, 43551}, {41945, 43407}, {41946, 43408}, {42093, 43100}, {42094, 43107}, {42096, 42685}, {42097, 42684}, {42108, 43299}, {42109, 43298}, {42112, 42528}, {42113, 42529}, {42119, 43481}, {42120, 43482}, {42140, 42430}, {42141, 42429}, {42258, 43256}, {42259, 43257}, {42271, 43381}, {42272, 43380}, {42275, 43510}, {42276, 43509}, {42472, 43467}, {42473, 43468}, {42480, 42966}, {42481, 42967}, {42514, 43002}, {42515, 43003}, {42521, 43486}, {42561, 43569}, {42588, 43633}, {42589, 43632}, {42631, 43492}, {42632, 43491}, {42637, 43431}, {42638, 43430}, {42686, 42940}, {42687, 42941}, {43463, 43544}, {43464, 43545}

X(46333) = midpoint of X(i) and X(j) for these {i, j}: {1657, 15689}, {3529, 3545}, {5054, 15685}, {10304, 15683}
X(46333) = reflection of X(i) in X(j) for these (i, j): (2, 15689), (4, 10304), (382, 15699), (3146, 14269), (3543, 5054), (3545, 376), (3627, 41983), (3830, 17504), (3839, 15688), (5054, 550), (10304, 3534), (14269, 8703), (15682, 3545), (15684, 23046), (15689, 15686), (15699, 15690), (17504, 15691), (23046, 548), (37907, 44246), (38335, 45759), (41135, 38742)
X(46333) = anticomplement of X(38335)
X(46333) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 15684, 4), (2, 17538, 376), (3, 14893, 2), (4, 3534, 376), (20, 11001, 376), (20, 15704, 4), (376, 33703, 2), (376, 41099, 3), (381, 15712, 2), (382, 15022, 4), (548, 15684, 2), (549, 5072, 2), (549, 15640, 4), (550, 19708, 376), (1657, 15686, 2), (3146, 3526, 4), (3528, 15697, 376), (3534, 15683, 4), (3543, 5066, 4), (3627, 14093, 2), (3843, 14891, 2), (3845, 41989, 381), (3850, 15718, 2), (5055, 14890, 2), (5059, 15697, 381), (15681, 19710, 20), (15691, 15702, 376), (15693, 41990, 2), (15706, 23046, 2), (38335, 45759, 2)

X(46334) = REFLECTION OF X(41108) IN X(41100)

Barycentrics -19*a^4 + 11*a^2*b^2 + 8*b^4 + 11*a^2*c^2 - 16*b^2*c^2 + 8*c^4 - 6*Sqrt[3]*a^2*S : :

X(46334) = 11 X[62] - 8 X[398], 7 X[62] - 4 X[16964], 3 X[62] - 4 X[41100], 3 X[62] - 2 X[41108], 5 X[62] - 8 X[42148], X[62] - 4 X[42158], 17 X[62] - 8 X[42164], 5 X[62] - 2 X[42432], 21 X[62] - 20 X[42521], 13 X[62] - 16 X[42924], 9 X[62] - 16 X[43109], 9 X[62] - 8 X[43229], X[62] + 2 X[43633], 14 X[398] - 11 X[16964], 6 X[398] - 11 X[41100], 12 X[398] - 11 X[41108], 5 X[398] - 11 X[42148], 2 X[398] - 11 X[42158], 17 X[398] - 11 X[42164], 20 X[398] - 11 X[42432], 42 X[398] - 55 X[42521], 13 X[398] - 22 X[42924], 9 X[398] - 22 X[43109], 9 X[398] - 11 X[43229], 4 X[398] + 11 X[43633], 3 X[16964] - 7 X[41100], 6 X[16964] - 7 X[41108], 5 X[16964] - 14 X[42148], X[16964] - 7 X[42158], 17 X[16964] - 14 X[42164], 10 X[16964] - 7 X[42432], 3 X[16964] - 5 X[42521], 13 X[16964] - 28 X[42924], 9 X[16964] - 28 X[43109], 9 X[16964] - 14 X[43229], 2 X[16964] + 7 X[43633], 5 X[41100] - 6 X[42148], X[41100] - 3 X[42158], 17 X[41100] - 6 X[42164], 10 X[41100] - 3 X[42432], 7 X[41100] - 5 X[42521], 13 X[41100] - 12 X[42924], 3 X[41100] - 4 X[43109], 3 X[41100] - 2 X[43229], 2 X[41100] + 3 X[43633], 5 X[41108] - 12 X[42148], X[41108] - 6 X[42158], 17 X[41108] - 12 X[42164], 5 X[41108] - 3 X[42432], 7 X[41108] - 10 X[42521], 13 X[41108] - 24 X[42924], 3 X[41108] - 8 X[43109], 3 X[41108] - 4 X[43229], X[41108] + 3 X[43633], 2 X[42148] - 5 X[42158], 17 X[42148] - 5 X[42164], 4 X[42148] - X[42432], 42 X[42148] - 25 X[42521], 13 X[42148] - 10 X[42924], 9 X[42148] - 10 X[43109], 9 X[42148] - 5 X[43229], 4 X[42148] + 5 X[43633], 17 X[42158] - 2 X[42164], 10 X[42158] - X[42432], 21 X[42158] - 5 X[42521], 13 X[42158] - 4 X[42924], 9 X[42158] - 4 X[43109], 9 X[42158] - 2 X[43229], 2 X[42158] + X[43633], 20 X[42164] - 17 X[42432], 42 X[42164] - 85 X[42521], 13 X[42164] - 34 X[42924], 9 X[42164] - 34 X[43109], 9 X[42164] - 17 X[43229], 4 X[42164] + 17 X[43633], 21 X[42432] - 50 X[42521], 13 X[42432] - 40 X[42924], 9 X[42432] - 40 X[43109], 9 X[42432] - 20 X[43229], X[42432] + 5 X[43633], 65 X[42521] - 84 X[42924], 15 X[42521] - 28 X[43109], 15 X[42521] - 14 X[43229], 10 X[42521] + 21 X[43633], 9 X[42924] - 13 X[43109], 18 X[42924] - 13 X[43229], 8 X[42924] + 13 X[43633], 8 X[43109] + 9 X[43633], 4 X[43229] + 9 X[43633]

X(46334) lies on these lines: {2, 10646}, {3, 41121}, {4, 41944}, {5, 42909}, {6, 15685}, {13, 8703}, {14, 15682}, {15, 3534}, {16, 3830}, {17, 10304}, {18, 15687}, {20, 41974}, {30, 62}, {61, 15681}, {376, 5352}, {381, 5237}, {382, 16268}, {395, 12817}, {396, 15690}, {397, 15686}, {530, 11129}, {549, 42165}, {550, 16962}, {1657, 42586}, {3090, 42958}, {3146, 42993}, {3180, 33611}, {3412, 17538}, {3524, 42161}, {3525, 43201}, {3543, 16963}, {3545, 42937}, {3843, 42978}, {3845, 19106}, {3849, 5858}, {3850, 43100}, {3860, 23303}, {5054, 42813}, {5055, 5351}, {5059, 42991}, {5066, 16242}, {5238, 15689}, {5318, 12100}, {5321, 42507}, {5334, 43233}, {5335, 15697}, {5340, 15688}, {5343, 42436}, {5350, 15699}, {5366, 15708}, {5863, 35695}, {6778, 8591}, {6779, 36363}, {7865, 11296}, {8353, 12155}, {10109, 42137}, {10645, 15695}, {10653, 11001}, {10654, 42429}, {11480, 43418}, {11481, 19709}, {11486, 41972}, {11488, 33604}, {11540, 43104}, {11541, 42515}, {11648, 41406}, {11812, 16966}, {12101, 16809}, {12811, 42793}, {14093, 42156}, {14269, 36843}, {14855, 30439}, {14891, 42598}, {14893, 16773}, {15640, 19107}, {15683, 42157}, {15684, 22238}, {15692, 42162}, {15693, 37832}, {15696, 42992}, {15698, 18582}, {15700, 42936}, {15702, 42581}, {15704, 42990}, {15706, 43491}, {15709, 42921}, {15711, 23302}, {15712, 42592}, {15714, 43107}, {15715, 43546}, {15716, 42128}, {15719, 33417}, {15759, 43416}, {15764, 42562}, {16241, 19708}, {16967, 41106}, {17504, 42166}, {19710, 36967}, {23046, 42580}, {25235, 36344}, {33458, 35696}, {33923, 43424}, {34755, 36970}, {35434, 42519}, {36450, 42275}, {36467, 42276}, {36994, 41029}, {37641, 42113}, {38071, 42944}, {40694, 42636}, {41099, 42141}, {42085, 43481}, {42089, 42505}, {42099, 43106}, {42108, 42634}, {42109, 42913}, {42115, 43475}, {42125, 43400}, {42126, 43637}, {42130, 42509}, {42135, 43640}, {42140, 43499}, {42143, 43025}, {42147, 44903}, {42154, 42508}, {42159, 42801}, {42163, 42694}, {42430, 43006}, {42434, 42779}, {42497, 44016}, {42501, 42683}, {42532, 42584}, {42596, 43550}, {42689, 43483}, {42900, 43029}, {42910, 43226}, {42911, 44015}, {42912, 43207}, {42967, 43632}, {43002, 43004}, {43011, 43541}, {43031, 43324}, {43108, 43300}, {43194, 43775}, {43237, 43402}, {43310, 44245}, {43326, 43331}

X(46334) = reflection of X(i) in X(j) for these {i,j}: {41108, 41100}, {43229, 43109}
X(46334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36968, 42631}, {2, 42631, 10646}, {14, 42510, 42977}, {16, 3830, 41122}, {376, 16267, 5352}, {376, 16965, 16267}, {376, 42588, 41112}, {395, 33699, 12817}, {3534, 41107, 15}, {3534, 42155, 41107}, {3543, 16963, 42814}, {3543, 42151, 16963}, {5066, 42123, 42792}, {5066, 42792, 16242}, {5340, 15688, 41943}, {8703, 42502, 42504}, {10653, 11001, 41101}, {15640, 41113, 19107}, {15682, 42120, 42510}, {15682, 42510, 14}, {15684, 22238, 42972}, {16809, 43401, 43399}, {16964, 41100, 42521}, {19106, 42943, 37835}, {19107, 42533, 41113}, {19708, 41119, 16241}, {19710, 42118, 43228}, {19710, 43228, 36967}, {36968, 36969, 10646}, {36968, 42086, 36969}, {36969, 42631, 2}, {41100, 41108, 62}, {41101, 42100, 11001}, {41107, 42976, 42974}, {41112, 42588, 16965}, {41119, 42091, 19708}, {41972, 43419, 11486}, {42100, 43244, 10653}, {42107, 43200, 37835}, {42123, 42941, 16242}, {42127, 42625, 37832}, {42148, 42432, 62}, {42158, 43633, 62}, {42431, 43193, 5237}, {42792, 42941, 5066}, {43109, 43229, 41100}

X(46335) = REFLECTION OF X(41107) IN X(41101)

Barycentrics -19*a^4 + 11*a^2*b^2 + 8*b^4 + 11*a^2*c^2 - 16*b^2*c^2 + 8*c^4 + 6*Sqrt[3]*a^2*S : :

X(46335) 11 X[61] - 8 X[397], 7 X[61] - 4 X[16965], 3 X[61] - 4 X[41101], 3 X[61] - 2 X[41107], 5 X[61] - 8 X[42147], X[61] - 4 X[42157], 17 X[61] - 8 X[42165], 5 X[61] - 2 X[42431], 21 X[61] - 20 X[42520], 13 X[61] - 16 X[42925], 9 X[61] - 16 X[43108], 9 X[61] - 8 X[43228], X[61] + 2 X[43632], 14 X[397] - 11 X[16965], 6 X[397] - 11 X[41101], 12 X[397] - 11 X[41107], 5 X[397] - 11 X[42147], 2 X[397] - 11 X[42157], 17 X[397] - 11 X[42165], 20 X[397] - 11 X[42431], 42 X[397] - 55 X[42520], 13 X[397] - 22 X[42925], 9 X[397] - 22 X[43108], 9 X[397] - 11 X[43228], 4 X[397] + 11 X[43632], 3 X[16965] - 7 X[41101], 6 X[16965] - 7 X[41107], 5 X[16965] - 14 X[42147], X[16965] - 7 X[42157], 17 X[16965] - 14 X[42165], 10 X[16965] - 7 X[42431], 3 X[16965] - 5 X[42520], 13 X[16965] - 28 X[42925], 9 X[16965] - 28 X[43108], 9 X[16965] - 14 X[43228], 2 X[16965] + 7 X[43632], 5 X[41101] - 6 X[42147], X[41101] - 3 X[42157], 17 X[41101] - 6 X[42165], 10 X[41101] - 3 X[42431], 7 X[41101] - 5 X[42520], 13 X[41101] - 12 X[42925], 3 X[41101] - 4 X[43108], 3 X[41101] - 2 X[43228], 2 X[41101] + 3 X[43632], 5 X[41107] - 12 X[42147], X[41107] - 6 X[42157], 17 X[41107] - 12 X[42165], 5 X[41107] - 3 X[42431], 7 X[41107] - 10 X[42520], 13 X[41107] - 24 X[42925], 3 X[41107] - 8 X[43108], 3 X[41107] - 4 X[43228], X[41107] + 3 X[43632], 2 X[42147] - 5 X[42157], 17 X[42147] - 5 X[42165], 4 X[42147] - X[42431], 42 X[42147] - 25 X[42520], 13 X[42147] - 10 X[42925], 9 X[42147] - 10 X[43108], 9 X[42147] - 5 X[43228], 4 X[42147] + 5 X[43632], 17 X[42157] - 2 X[42165], 10 X[42157] - X[42431], 21 X[42157] - 5 X[42520], 13 X[42157] - 4 X[42925], 9 X[42157] - 4 X[43108], 9 X[42157] - 2 X[43228], 2 X[42157] + X[43632], 20 X[42165] - 17 X[42431], 42 X[42165] - 85 X[42520], 13 X[42165] - 34 X[42925], 9 X[42165] - 34 X[43108], 9 X[42165] - 17 X[43228], 4 X[42165] + 17 X[43632], 21 X[42431] - 50 X[42520], 13 X[42431] - 40 X[42925], 9 X[42431] - 40 X[43108], 9 X[42431] - 20 X[43228], X[42431] + 5 X[43632], 65 X[42520] - 84 X[42925], 15 X[42520] - 28 X[43108], 15 X[42520] - 14 X[43228], 10 X[42520] + 21 X[43632], 9 X[42925] - 13 X[43108], 18 X[42925] - 13 X[43228], 8 X[42925] + 13 X[43632], 8 X[43108] + 9 X[43632], 4 X[43228] + 9 X[43632]

X(46335) lies on these lines: {2, 10645}, {3, 41122}, {4, 41943}, {5, 42908}, {6, 15685}, {13, 15682}, {14, 8703}, {15, 3830}, {16, 3534}, {17, 15687}, {18, 10304}, {20, 41973}, {30, 61}, {62, 15681}, {376, 5351}, {381, 5238}, {382, 16267}, {395, 15690}, {396, 12816}, {398, 15686}, {531, 11128}, {549, 42164}, {550, 16963}, {1657, 42587}, {3090, 42959}, {3146, 42992}, {3181, 33610}, {3411, 17538}, {3524, 42160}, {3525, 43202}, {3543, 16962}, {3545, 42936}, {3843, 42979}, {3845, 19107}, {3849, 5859}, {3850, 43107}, {3860, 23302}, {5054, 42814}, {5055, 5352}, {5059, 42990}, {5066, 16241}, {5237, 15689}, {5318, 42506}, {5321, 12100}, {5334, 15697}, {5335, 43232}, {5339, 15688}, {5344, 42435}, {5349, 15699}, {5365, 15708}, {5862, 35691}, {6777, 8591}, {6780, 36362}, {7865, 11295}, {8353, 12154}, {10109, 42136}, {10646, 15695}, {10653, 42430}, {10654, 11001}, {11480, 19709}, {11481, 43419}, {11485, 41971}, {11489, 33605}, {11540, 43101}, {11541, 42514}, {11648, 41407}, {11812, 16967}, {12101, 16808}, {12811, 42794}, {14093, 42153}, {14269, 36836}, {14855, 30440}, {14891, 42599}, {14893, 16772}, {15640, 19106}, {15683, 42158}, {15684, 22236}, {15692, 42159}, {15693, 37835}, {15696, 42993}, {15698, 18581}, {15700, 42937}, {15702, 42580}, {15704, 42991}, {15706, 43492}, {15709, 42920}, {15711, 23303}, {15712, 42593}, {15714, 43100}, {15715, 43547}, {15716, 42125}, {15719, 33416}, {15759, 43417}, {15764, 42565}, {16242, 19708}, {16966, 41106}, {17504, 42163}, {19710, 36968}, {23046, 42581}, {25236, 36319}, {33459, 35692}, {33923, 43425}, {34754, 36969}, {35434, 42518}, {36449, 42276}, {36468, 42275}, {36775, 44678}, {36992, 41028}, {37640, 42112}, {38071, 42945}, {40693, 42635}, {41099, 42140}, {42086, 43482}, {42092, 42504}, {42100, 43105}, {42108, 42912}, {42109, 42633}, {42116, 43476}, {42127, 43636}, {42128, 43399}, {42131, 42508}, {42138, 43639}, {42141, 43500}, {42146, 43024}, {42148, 44903}, {42155, 42509}, {42162, 42802}, {42166, 42695}, {42429, 43007}, {42433, 42780}, {42496, 44015}, {42500, 42682}, {42533, 42585}, {42597, 43551}, {42688, 43484}, {42901, 43028}, {42910, 44016}, {42911, 43227}, {42913, 43208}, {42966, 43633}, {43003, 43005}, {43010, 43540}, {43030, 43325}, {43109, 43301}, {43193, 43776}, {43236, 43401}, {43311, 44245}, {43327, 43330}

X(46335) = reflection of X(i) in X(j) for these {i,j}: {41107, 41101}, {43228, 43108}
X(46335) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36967, 42632}, {2, 42632, 10645}, {13, 42511, 42976}, {15, 3830, 41121}, {376, 16268, 5351}, {376, 16964, 16268}, {376, 42589, 41113}, {396, 33699, 12816}, {3534, 41108, 16}, {3534, 42154, 41108}, {3543, 16962, 42813}, {3543, 42150, 16962}, {5066, 42122, 42791}, {5066, 42791, 16241}, {5339, 15688, 41944}, {8703, 42503, 42505}, {10654, 11001, 41100}, {15640, 41112, 19106}, {15682, 42119, 42511}, {15682, 42511, 13}, {15684, 22236, 42973}, {16808, 43402, 43400}, {16965, 41101, 42520}, {19106, 42532, 41112}, {19107, 42942, 37832}, {19708, 41120, 16242}, {19710, 42117, 43229}, {19710, 43229, 36968}, {36967, 36970, 10645}, {36967, 42085, 36970}, {36970, 42632, 2}, {41100, 42099, 11001}, {41101, 41107, 61}, {41108, 42977, 42975}, {41113, 42589, 16964}, {41120, 42090, 19708}, {41971, 43418, 11485}, {42099, 43245, 10654}, {42110, 43199, 37832}, {42122, 42940, 16241}, {42126, 42626, 37835}, {42147, 42431, 61}, {42157, 43632, 61}, {42432, 43194, 5238}, {42791, 42940, 5066}, {43108, 43228, 41101}

X(46336) = EULER LINE INTERCEPT OF X(69)X(3266)

X(46336) lies on these lines: {2, 3}, {69, 3266}, {110, 25406}, {141, 8547}, {146, 10293}, {182, 37645}, {251, 40320}, {315, 11059}, {323, 14912}, {373, 31670}, {388, 5297}, {394, 8550}, {497, 7292}, {1216, 18916}, {1350, 37648}, {1352, 5650}, {1899, 3819}, {1992, 23061}, {1993, 44503}, {2549, 3291}, {2896, 30793}, {2979, 11433}, {3003, 7736}, {3060, 18928}, {3066, 29181}, {3218, 26939}, {3219, 26929}, {3292, 11179}, {3434, 19804}, {3448, 44833}, {3580, 10519}, {3619, 5888}, {3620, 18935}, {3763, 45303}, {3818, 15082}, {3917, 6515}, {4549, 37470}, {4857, 5272}, {5012, 37669}, {5063, 7735}, {5085, 11064}, {5157, 28708}, {5181, 9140}, {5268, 5270}, {5314, 20266}, {5422, 44492}, {5646, 10516}, {5651, 46264}, {5800, 37633}, {5972, 17508}, {6504, 7607}, {6776, 15066}, {7703, 15435}, {7738, 9465}, {7768, 40123}, {7771, 37803}, {7800, 30749}, {7999, 11411}, {8024, 19583}, {8585, 43619}, {9214, 15899}, {10159, 40178}, {10192, 34944}, {10327, 44720}, {10717, 25051}, {11003, 41615}, {11444, 18909}, {11457, 11487}, {11677, 16706}, {12324, 15056}, {13857, 38064}, {14561, 22112}, {15048, 40126}, {15051, 18933}, {15067, 18917}, {15080, 35260}, {15820, 31455}, {16187, 29012}, {17008, 19577}, {18950, 45794}, {19467, 44862}, {20481, 43448}, {23291, 37636}, {31884, 32269}, {32064, 44299}, {32273, 45311}, {32821, 45201}, {33884, 37644}, {35259, 44882}, {35283, 36990}, {37643, 41462}, {37775, 42119}, {37776, 42120}, {43650, 44470}

X(46336) = anticomplement of X(11284)
X(46336) = isotomic conjugate of the isogonal conjugate of X(32621)
X(46336) = barycentric product X(76)*X(32621)
X(46336) = barycentric quotient X(32621)/X(6)
X(46336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 7493}, {2, 20, 1995}, {2, 23, 40132}, {2, 376, 26255}, {2, 1370, 6997}, {2, 3522, 4232}, {2, 3523, 7495}, {2, 4189, 26256}, {2, 4190, 4239}, {2, 5169, 3090}, {2, 6636, 6353}, {2, 7378, 37990}, {2, 7386, 1370}, {2, 7391, 7392}, {2, 7396, 5133}, {2, 7496, 631}, {2, 7500, 5020}, {2, 7519, 16042}, {2, 10304, 7426}, {2, 10989, 3545}, {2, 15246, 7494}, {2, 16063, 4}, {2, 31099, 5}, {2, 31100, 6856}, {2, 31101, 8889}, {2, 31105, 5071}, {2, 31106, 5084}, {2, 31107, 14064}, {2, 32965, 26257}, {3, 140, 35486}, {3, 1656, 16618}, {3, 3526, 34351}, {3, 6816, 37201}, {3, 30739, 2}, {3, 34664, 20}, {4, 7386, 16063}, {4, 7392, 7533}, {4, 16063, 1370}, {5, 10300, 31152}, {5, 31152, 31099}, {23, 40132, 26255}, {140, 1368, 5094}, {140, 5094, 2}, {376, 40132, 23}, {377, 2478, 17677}, {427, 16419, 2}, {549, 32216, 2}, {631, 6643, 6815}, {631, 16051, 2}, {858, 40916, 2}, {1368, 3548, 16051}, {1368, 7484, 2}, {1368, 7734, 7484}, {1370, 7493, 37201}, {1656, 16618, 3542}, {1657, 5020, 10301}, {1657, 10301, 7500}, {2045, 2046, 7383}, {3522, 4232, 22}, {3526, 37454, 2}, {3538, 6804, 20}, {3548, 7516, 631}, {3580, 21766, 10519}, {5002, 5003, 35513}, {5020, 7667, 7500}, {5094, 7484, 140}, {6676, 31255, 2}, {6804, 34664, 6816}, {6816, 7493, 6997}, {6921, 30776, 2}, {7386, 16051, 6643}, {7386, 30739, 6816}, {7391, 7533, 4}, {7484, 7516, 7496}, {7485, 7495, 3523}, {7493, 30552, 22}, {7496, 37126, 7485}, {7499, 30771, 2}, {7574, 18420, 4}, {7667, 10301, 1657}, {7907, 30777, 2}, {7998, 18911, 69}, {8359, 11336, 2}, {10303, 30769, 2}, {10303, 37444, 6803}, {14813, 14814, 7529}, {15692, 44440, 3537}, {15702, 30775, 2}, {18537, 26255, 6997}, {30739, 43957, 3}

X(46337) = X(6)X(23)∩X(39)X(524)

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

X(46337) lies on these lines: {6, 23}, {39, 524}, {141, 15302}, {597, 9465}, {1180, 8584}, {2493, 25488}, {3291, 3589}, {8542, 42852}, {9019, 44500}, {9872, 39389}, {11580, 38402}, {11594, 15048}, {20965, 46154}, {32621, 40689}

X(46338) = X(5)X(14357)∩X(30)X(67)

X(46338) lies on the cubic K1251 and these lines: {5, 14357}, {30, 67}, {111, 468}, {523, 18907}, {3455, 7575}, {7426, 10511}, {10295, 46105}, {10297, 34897}

X(46339) = X(2)X(11657)∩X(4)X(541)

X(46339) lies on the Hutson-Parry circle, the cubics K876 and K1251, and on these lines: on lines {2, 11657}, {4, 541}, {111, 1302}, {376, 9159}, {1992, 9003}, {4240, 40138}, {7493, 11628}, {15360, 43453}

X(46340) = X(30)X(112)∩X(1297)X(8749)

X(46340) lies on the cubic K1251 and these lines: {30, 112}, {1297, 8749}, {16165, 28343}, {18876, 46105}

X(46340) = barycentric product X(23)*X(2697)
X(46340) = barycentric quotient X(i)/X(j) for these {i,j}: {2697, 18019}, {18374, 2781}

X(46341) = X(4)X(6128)∩X(74)X(46233)

X(46341) lies on the cubic K1251 and these lines: {4, 6128}, {74, 46233}, {113, 6794}, {2394, 2986}, {7464, 32640}, {14094, 15291}, {14915, 32681}, {15738, 18877}, {40352, 44468}

X(46342) = X(13)X(15)∩X(62)X(32906)

X(46342) lies on the cubic K1251 and these lines: {13, 15}, {62, 32906}, {111, 3457}, {187, 11142}, {5523, 8737}, {8739, 16459}, {16461, 36757}, {21466, 37775}

X(46342) = barycentric product X(i)*X(j) for these {i,j}: {13, 37776}, {476, 11617}, {11081, 21468}
X(46342) = barycentric quotient X(i)/X(j) for these {i,j}: {11617, 3268}, {37776, 298}
X(46342) = {X(3457),X(5995)}-harmonic conjugate of X(41406)

X(46343) = X(14)X(16)∩X(61)X(32908)

X(46343) lies on the cubic K1251 and these lines: {14, 16}, {61, 32908}, {111, 3458}, {187, 11141}, {5523, 8738}, {8740, 16460}, {16462, 36758}, {21467, 37776}

X(46343) = barycentric product X(i)*X(j) for these {i,j}: {14, 37775}, {476, 11618}, {11086, 21469}
X(46343) = barycentric quotient X(i)/X(j) for these {i,j}: {11618, 3268}, {37775, 299}
X(46343) = {X(3458),X(5994)}-harmonic conjugate of X(41407)

X(46344) = X(1)X(8074)∩X(2)X(77)

X(46344) lies on the cubic K1251 and these lines: {1, 8074}, {2, 77}, {9, 109}, {19, 25}, {614, 3554}, {1035, 1212}, {1038, 6554}, {1742, 1750}, {2270, 33849}, {4296, 27541}, {5819, 9817}, {7129, 40943}, {8270, 40869}, {9502, 28043}, {15849, 26020}, {16589, 37324}, {21147, 23058}

X(46345) = X(2)X(7)∩X(11)X(19)

X(46345) lies on the cubic K1252 and these lines: {2, 7}, {11, 19}, {25, 1436}, {56, 7079}, {282, 604}, {610, 33849}, {612, 2256}, {614, 1108}, {936, 9310}, {1210, 2082}, {1723, 5121}, {1781, 7988}, {2272, 30223}, {2347, 33995}, {3086, 7719}, {3554, 38375}, {3673, 29464}, {3692, 5205}, {6700, 17742}, {21153, 41423}, {37697, 43065}

X(46345) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 40127, 40131}

X(46346) = X(2)X(253)∩X(25)X(28782)

X(46346) lies on the cubic K1252 and these lines: {2, 253}, {25, 28782}, {122, 393}, {2060, 8778}, {3344, 14642}, {15341, 18337}

X(46347) = X(2)X(1032)∩X(25)X(393)

X(46347) lies on the cubic K1252 and these lines: {2, 1032}, {25, 393}, {1249, 1301}, {14092, 45141}, {37487, 37689}

X(46348) = X(2)X(77)∩X(25)X(7037)

X(46348) lies on the cubic K1252 and these lines: {2, 77}, {25, 7037}, {34, 5514}, {3342, 7118}, {40131, 45141}

X(46349) = X(4)X(10545)∩X(20)X(64)

Barycentrics 5*a^10 - 5*a^8*b^2 - 14*a^6*b^4 + 22*a^4*b^6 - 7*a^2*b^8 - b^10 - 5*a^8*c^2 + 72*a^6*b^2*c^2 - 46*a^4*b^4*c^2 - 24*a^2*b^6*c^2 + 3*b^8*c^2 - 14*a^6*c^4 - 46*a^4*b^2*c^4 + 62*a^2*b^4*c^4 - 2*b^6*c^4 + 22*a^4*c^6 - 24*a^2*b^2*c^6 - 2*b^4*c^6 - 7*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(46349) = 7 X[3528] - 4 X[46261], X[5059] + 2 X[18396], 3 X[10304] - 2 X[35259], 11 X[21735] - 8 X[43586]

X(46349) lies on these lines: {4, 10545}, {20, 64}, {30, 26869}, {376, 5891}, {1370, 2777}, {1593, 38110}, {2071, 35260}, {2854, 37749}, {3153, 40196}, {3528, 46261}, {3543, 20192}, {5059, 18396}, {5656, 11413}, {7464, 37645}, {10304, 35259}, {11001, 17702}, {11738, 42021}, {12244, 41465}, {13445, 35513}, {14912, 15072}, {15080, 35483}, {15683, 44555}, {16111, 34802}, {18911, 45088}, {21735, 43586}, {35237, 35485}

X(46350) = X(2)X(280)∩X(9)X(271)

X(46350) lies on the curve Q172 and these lines: {2, 280}, {9, 271}, {329, 14365}, {5587, 39130}, {7078, 13138}

X(46350) = cevapoint of X(1490) and X(3341)
X(46350) = crosspoint of X(312) and X(33672)
X(46350) = X(i)-isoconjugate of X(j) for these (i,j): {56, 3342}, {221, 3345}, {223, 7152}, {2199, 41514}, {2360, 8811}, {7114, 7149}
X(46350) = barycentric product X(i)*X(j) for these {i,j}: {282, 33672}, {312, 3341}, {1490, 34404}, {3176, 44189}, {14302, 44327}
X(46350) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 3342}, {280, 41514}, {282, 3345}, {1035, 6611}, {1490, 223}, {1903, 8811}, {2192, 7152}, {3176, 196}, {3197, 221}, {3341, 57}, {5932, 14256}, {7003, 7149}, {7367, 7037}, {13614, 1817}, {14302, 14837}, {33672, 40702}

X(46351) = X(2)X(253)∩X(3)X(15394)

X(46351) lies on the curves K099 and Q172 and these lines: {2, 253}, {3, 15394}, {20, 2130}, {77, 271}, {216, 40813}, {3343, 6617}, {5085, 14379}, {6527, 6616}, {14615, 44326}, {34403, 40680}

X(46351) = isogonal conjugate of polar conjugate of X(47435)
X(46351) = isotomic conjugate of X(46353)
X(46351) = isotomic conjugate of the polar conjugate of X(3343)
X(46351) = X(i)-Ceva conjugate of X(j) for these (i,j): {69, 15394}, {34415, 64}
X(46351) = X(i)-cross conjugate of X(j) for these (i,j): {1498, 6617}, {41085, 1073}
X(46351) = cevapoint of X(i) and X(j) for these (i,j): {1073, 2130}, {1498, 3343}
X(46351) = crosspoint of X(69) and X(6527)
X(46351) = X(i)-isoconjugate of X(j) for these (i,j): {19, 3344}, {204, 3346}, {3213, 8805}, {7156, 8810}
X(46351) = barycentric product X(i)*X(j) for these {i,j}: {69, 3343}, {253, 6617}, {1073, 6527}, {1498, 34403}, {3926, 41085}, {14361, 15394}
X(46351) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 3344}, {1033, 6525}, {1073, 3346}, {1498, 1249}, {3343, 4}, {6527, 15466}, {6617, 20}, {14361, 14249}, {14379, 28783}, {15394, 1032}, {41085, 393}
X(46351) = {X(16096),X(41005)}-harmonic conjugate of X(253)

X(46352) = X(2)X(342)∩X(7)X(1034)

X(46352) lies on the curve Q172 and these lines: {2, 342}, {7, 1034}, {77, 3345}, {3342, 7013}

X(46352) = X(57)-cross conjugate of X(14256)
X(46352) = cevapoint of X(57) and X(3345)
X(46352) = X(i)-isoconjugate of X(j) for these (i,j): {55, 3341}, {282, 3197}, {1490, 2192}, {2188, 3176}, {2357, 13614}, {14302, 32652}
X(46352) = barycentric product X(i)*X(j) for these {i,j}: {85, 3342}, {347, 41514}, {1034, 14256}, {3345, 40702}
X(46352) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 3341}, {196, 3176}, {221, 3197}, {223, 1490}, {1817, 13614}, {3342, 9}, {3345, 282}, {6611, 1035}, {7037, 7367}, {7149, 7003}, {7152, 2192}, {8811, 1903}, {14256, 5932}, {14837, 14302}, {40702, 33672}, {41514, 280}

X(46353) = X(2)X(3346)∩X(4)X(1032)

X(46353) lies on the curves K647 and Q172 and these lines: {2, 3346}, {4, 1032}, {20, 3344}, {264, 34403}, {1105, 20792}, {2052, 31943}, {6616, 37669}

X(46353) = isotomic conjugate of X(46351)
X(46353) = polar conjugate of X(3343)
X(46353) = polar conjugate of the isogonal conjugate of X(3344)
X(46353) = X(4)-cross conjugate of X(14249)
X(46353) = cevapoint of X(4) and X(3346)
X(46353) = X(i)-isoconjugate of X(j) for these (i,j): {48, 3343}, {255, 41085}, {1498, 19614}, {1712, 14379}, {2155, 6617}
X(46353) = barycentric product X(i)*X(j) for these {i,j}: {264, 3344}, {1032, 14249}, {3346, 15466}
X(46353) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 3343}, {20, 6617}, {393, 41085}, {1032, 15394}, {1249, 1498}, {3344, 3}, {3346, 1073}, {6525, 1033}, {14249, 14361}, {15466, 6527}, {28783, 14379}

X(46354) = X(3)X(15474)∩X(942)X(39267)

X(46354) lies on these lines: {3, 15474}, {942, 39267}, {4303, 28082}, {7742, 13397}

X(46354) = X(i)-isoconjugate of X(j) for these (i,j): {1708, 2911}, {1780, 41538}, {3811, 37579}
X(46354) = barycentric product X(15474)*X(43740)
X(46354) = barycentric quotient X(i)/X(j) for these {i,j}: {39943, 3811}, {43740, 17776}

X(46355) = X(1)X(280)∩X(4)X(189)

X(46355) lies on the Feuerbach circumhyperbola and these lines: {1, 280}, {4, 189}, {7, 309}, {8, 44189}, {9, 271}, {84, 44075}, {282, 40957}, {285, 1172}, {1413, 9372}, {1433, 40396}, {1440, 8809}, {3577, 39130}, {7157, 17097}, {7338, 10538}, {27383, 44327}, {36121, 40836}

X(46355) = X(i)-cross conjugate of X(j) for these (i,j): {84, 280}, {7003, 189}
X(46355) = cevapoint of X(84) and X(1256)
X(46355) = X(i)-isoconjugate of X(j) for these (i,j): {6, 40212}, {40, 221}, {56, 1103}, {198, 223}, {208, 7078}, {227, 2360}, {329, 2199}, {347, 2187}, {2324, 6611}, {2331, 7011}, {3195, 7013}, {3318, 24027}, {7114, 7952}
X(46355) = barycentric product X(i)*X(j) for these {i,j}: {84, 34404}, {189, 280}, {282, 309}, {312, 1256}, {2192, 44190}, {7020, 41081}, {7058, 7157}, {40836, 44189}
X(46355) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40212}, {9, 1103}, {84, 223}, {189, 347}, {268, 7078}, {280, 329}, {282, 40}, {285, 1817}, {309, 40702}, {1146, 3318}, {1256, 57}, {1413, 6611}, {1433, 7011}, {1436, 221}, {1440, 14256}, {1903, 227}, {2192, 198}, {2208, 2199}, {7003, 7952}, {7008, 2331}, {7118, 2187}, {7129, 208}, {7151, 3209}, {7154, 3195}, {7157, 6354}, {7367, 7074}, {34404, 322}, {40836, 196}, {41081, 7013}

X(46356) = X(1)X(44301)∩X(8)X(8051)

X(46356) lies on the Feuerbach circumhyperbola and these lines: {1, 44301}, {8, 8051}, {9, 2137}, {3680, 6553}

X(46356) = X(1616)-isoconjugate of X(2136)
X(46356) = barycentric product X(6553)*X(8051)
X(46356) = barycentric quotient X(i)/X(j) for these {i,j}: {2137, 23511}, {6553, 8055}, {8051, 4452}

X(46357) = 1ST INTERCEPT, OTHER THAN X(3), OF LINE X(3)X(2574) AND McCAY CUBIC

See Antreas Hatzipolakis, Francisco Javier García Capitán, César Lozada, and Bernard Gibert, euclid 3550.

X(46357) lies on cubics K003, K019, K187, K376, K443, K810, K851; curves Q007, Q008, Q009, Q010, Q020, Q063, Q113; and this line: {3, 2574}

X(46357) = reflection of X(46358) in X(3)
X(46357) = isogonal conjugate of X(46358)
X(46357) = X(3)-vertex conjugate of-X(46358)
X(46357) = 1st focus of the inconic centered at X(3) (see cubic K003)

X(46358) = 2ND INTERCEPT, OTHER THAN X(3), OF LINE X(3)X(2574) AND McCAY CUBIC

See Antreas Hatzipolakis, Francisco Javier García Capitán, César Lozada, and Bernard Gibert, euclid 3550.

X(46358) lies on cubics K003, K019, K187, K376, K443, K810, K851; curves Q007, Q008, Q009, Q010, Q020, Q063, Q113; and this line: {3, 2574}

X(46358) = reflection of X(46350) in X(3)
X(46358) = isogonal conjugate of X(46357)
X(46358) = X(3)-vertex conjugate of-X(46357)
X(46358) = 2nd focus of the inconic centered at X(3) (see cubic K003)

X(46359) = BARYCENTRIC QUOTIENT X(39)/X(515)

X(46359) lies on these lines: {38, 46152}, {102, 110}, {660, 23691}, {670, 34393}, {3917, 46153}

X(46359) = crosspoint of X(102) and X(34393)
X(46359) = X(i)-isoconjugate of X(j) for these (i,j): {82, 515}, {83, 2182}, {8755, 34055}
X(46359) = barycentric product X(i)*X(j) for these {i,j}: {38, 36100}, {39, 34393}, {102, 141}, {1930, 32677}, {2399, 46153}, {3665, 15629}, {20883, 36055}
X(46359) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 515}, {102, 83}, {141, 35516}, {1401, 34050}, {1843, 8755}, {1964, 2182}, {4553, 42718}, {32677, 82}, {34393, 308}, {35325, 7452}, {36055, 34055}, {36100, 3112}, {46152, 24035}, {46153, 2406}

X(46360) = X(4)X(3527)∩X(8573)X(11433)

X(46361) = (name (pending)

X(46362) = X(1)X(4014)∩X(40)X(550)

X(46362) = lies on these lines: {1,4014}, {40,550}, {1385,32486}, {5258,31662}, {5400,7987}, {10609,21362}, {11372,40256}

X(46363) = X(3)X(6)∩X(51)X(3089)

X(46363) = lies on these lines: {3,6}, {51,3089}, {185,12250}, {373,43841}, {1596,10110} {2393,11745}, {3567,6353}, {5462,6677}, {5562,6804}, {5907,11411}, {6000,12241}, {6403,17040}, {6467,7487}, {7392,12282}, {7401,14913}, {9306,12166}, {9825,34382}, {11431,14531}, {11695,23292}, {11793,13567}, {12007,41589}, {12161,41619}, {12242,22530}, {12294,18909}, {13474,34780}, {15585,32191}, {18925,40673}, {32366,34782}, {32411,37971}

X(46364) = (name pending)

X(46365) = (name pending)

X(46366) = X(1)X(3)∩X(920)X(1069)

Let A' = X(1)-line conjugate of the anticevian triangle of X(3), and define B' and C' cyclically. Then A'B'C' is perspective to the cevian triangle of X(920), and the perspector is X(46366).

X(46366) = crosspoint of X(1068) and X(3193)
X(46366) = barycentric product X(i)*X(j) for these {i,j}: {46, 45206}, {1195, 20930}, {1858, 5905}
X(46366) = barycentric quotient X(i)/X(j) for these {i,j}: {1195, 90}, {1858, 2994}, {45206, 20570}

X(46367) = X(6)X(9050)∩X(7)X(145)

Let A' = X(1)-line conjugate of the anticevian triangle of X(9), and define B' and C' cyclically. Then A'B'C' is perspective to the cevian triangle of X(19604), and the perspector is X(46367).

X(46367) = crosssum of X(3158) and X(6555)
X(46367) = X(i)-isoconjugate of X(j) for these (i,j): {145, 1261}, {1222, 3158}, {1476, 6555}, {3161, 23617}, {4162, 8706}, {4936, 40420}, {40528, 44724}
X(46367) = barycentric product X(i)*X(j) for these {i,j}: {1, 45205}, {1122, 8056}, {1201, 27818}, {1828, 27832}, {3663, 40151}, {3752, 19604}, {16079, 45204}, {16945, 26563}
X(46367) = barycentric quotient X(i)/X(j) for these {i,j}: {1122, 18743}, {1201, 3161}, {2347, 6555}, {3663, 44723}, {3752, 44720}, {6363, 4521}, {16945, 23617}, {19604, 32017}, {20228, 3158}, {23845, 30720}, {38266, 1261}, {38828, 8706}, {40151, 1222}, {42336, 4394}, {45205, 75}

X(46368) = X(81)X(213)∩X(354)X(10458)

Let A' = X(1)-line conjugate of the anticevian triangle of X(42), and define B' and C' cyclically. Then A'B'C' is perspective to the cevian triangle of X(81), and the perspector is X(46368).

X(46368) lies on these lines: {81, 213}, {354, 10458}, {1206, 16819}, {3720, 18166}

X(46368) = X(81)-Ceva conjugate of X(1206)
X(46368) = barycentric product X(i)*X(j) for these {i,j}: {1206, 16748}, {16819, 18166}, {17175, 45223}

X(46369) = X(1)X(39)∩X(99)X(4367)

Let A' = X(1)-line conjugate of the anticevian triangle of X(512), and define B' and C' cyclically. Then A'B'C' is perspective to the cevian triangle of X(1), and the perspector is X(46369).

X(46369) lies on these lines: {1, 39}, {99, 4367}, {3903, 4879}, {4436, 17136}, {4553, 46177}, {21051, 27133}

X(46369) = X(39292)-Ceva conjugate of X(2238)
X(46369) = crosspoint of X(i) and X(j) for these (i,j): {1, 9424}, {99, 3903}
X(46369) = crosssum of X(i) and X(j) for these (i,j): {1, 7170}, {512, 4367}

X(46370) = X(1)X(167)∩X(4)X(8140)

Let H_A be the hyperbola through X(1) with foci B and C, and define H_B and H_C cyclically. The three hyperbolas meet in X(1) and X(46370). (Peter Moses, December 18, 2021)

X(46370) lies on the curve Q104 and these lines: {1, 167}, {4, 8140}, {40, 43192}, {1490, 15502}

X(46370) = reflection of X(1) in X(13443)
X(46370) = isogonal conjugate of X(46705)
X(46370) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {177, 6585, 1}, {7590, 16012, 1}, {8091, 8351, 8422}

X(46371) = X(4)X(512)∩X(235)X(523)

X(46371) lies on these lines: {4, 512}, {107, 13494}, {235, 523}, {525, 41587}, {2501, 5254}, {3574, 23290}, {5664, 39606}, {10018, 44814}, {14249, 18504}, {14457, 15328}, {16230, 41079}

X(46371) = crossdifference of every pair of points on line {X(3289), X(41615)}
X(46371) = trilinear product X(2501)*X(17882)
X(46371) = {X(4), X(14618)}-harmonic conjugate of X(23105)

X(46372) = X(3)-OF-ANTICEVIAN TRIANGLE OF X(3)

X(46372) lies on these lines: {3, 22658}, {4, 6}, {64, 2063}, {154, 22467}, {155, 15311}, {184, 36982}, {394, 5894}, {399, 13093}, {1147, 6000}, {1619, 12174}, {1993, 5895}, {2072, 14216}, {2777, 16266}, {2781, 9914}, {3292, 30443}, {3357, 15068}, {3515, 15647}, {3548, 6247}, {5020, 32184}, {5504, 12085}, {5663, 32321}, {5878, 18445}, {5907, 44883}, {6225, 43605}, {6241, 43617}, {6644, 6759}, {6696, 17814}, {7506, 32063}, {7517, 9934}, {7729, 17928}, {8567, 15066}, {9306, 31978}, {10249, 33537}, {10605, 45172}, {11477, 32602}, {12161, 12897}, {12163, 45171}, {13371, 40285}, {13861, 15012}, {17837, 22647}, {18381, 18418}, {18390, 22968}, {18439, 18466}, {22972, 26958}, {32284, 34779}, {34148, 36983}, {39568, 44668}

X(46372) = midpoint of X(9914) and X(12164)
X(46372) = reflection of X(46373) in X(46374)
X(46372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1181, 1498, 2883}, {1181, 2883, 34117}, {8550, 19149, 34117}

X(46373) = X(4)-OF-ANTICEVIAN TRIANGLE OF X(3)

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 + 18*a^10*b^2*c^2 - 13*a^8*b^4*c^2 - 36*a^6*b^6*c^2 + 51*a^4*b^8*c^2 - 14*a^2*b^10*c^2 - 3*b^12*c^2 + a^10*c^4 - 13*a^8*b^2*c^4 + 82*a^6*b^4*c^4 - 50*a^4*b^6*c^4 - 35*a^2*b^8*c^4 + 15*b^10*c^4 + 5*a^8*c^6 - 36*a^6*b^2*c^6 - 50*a^4*b^4*c^6 + 92*a^2*b^6*c^6 - 11*b^8*c^6 - 5*a^6*c^8 + 51*a^4*b^2*c^8 - 35*a^2*b^4*c^8 - 11*b^6*c^8 - a^4*c^10 - 14*a^2*b^2*c^10 + 15*b^4*c^10 + 3*a^2*c^12 - 3*b^2*c^12 - c^14) : :

X(46373) lies on the Feuerbach circumhyperbola of the tangential triangle and these lines: {1, 7169}, {3, 1661}, {4, 45045}, {6, 64}, {20, 159}, {25, 2929}, {30, 9937}, {66, 43690}, {154, 16936}, {155, 6000}, {184, 30443}, {195, 13093}, {378, 12250}, {394, 36982}, {399, 12315}, {541, 19908}, {610, 3556}, {1092, 1498}, {1103, 12335}, {1204, 44079}, {1503, 19588}, {1597, 6247}, {1619, 6225}, {1853, 11403}, {1885, 34944}, {2071, 32605}, {2777, 2931}, {2916, 35240}, {2917, 5925}, {2918, 35243}, {2930, 17845}, {2935, 15063}, {3343, 33583}, {3357, 9729}, {5020, 5893}, {5663, 12301}, {5898, 17800}, {6642, 22802}, {6696, 11479}, {6759, 35237}, {7395, 10606}, {7484, 8567}, {7503, 15740}, {10117, 15750}, {11441, 36983}, {15047, 35450}, {15066, 43813}, {15136, 40285}, {17837, 17847}, {18916, 35502}, {32125, 37197}, {32357, 32401}, {37201, 41602}

X(46373) = reflection of X(46372) in X(46374)
X(46373) = reflection of X(i) in X(j) for these {i,j}: {9914, 3}, {43695, 2883}
X(46373) = isotomic conjugate of the polar conjugate of X(17807)
X(46373) = tangential isogonal conjugate of X(3515)
X(46373) = X(i)-Ceva conjugate of X(j) for these (i,j): {1619, 159}, {6225, 1498}, {11413, 3}, {37669, 6}
X(46373) = X(17807)-cross conjugate of X(40221)
X(46373) = crosssum of X(i) and X(j) for these (i,j): {512, 39020}, {523, 35968}
X(46373) = barycentric product X(i)*X(j) for these {i,j}: {20, 40221}, {69, 17807}
X(46373) = barycentric quotient X(i)/X(j) for these {i,j}: {17807, 4}, {40221, 253}
X(46373) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 64, 31978}, {6225, 11413, 1619}, {6293, 12379, 64}

X(46374) = X(5)-OF-ANTICEVIAN TRIANGLE OF X(3)

X(46374) lies on these lines: {3, 1177}, {6, 32184}, {49, 20427}, {54, 10606}, {64, 34148}, {110, 5895}, {154, 33524}, {156, 2777}, {184, 5894}, {569, 23328}, {578, 6696}, {974, 2904}, {1092, 2883}, {1147, 15311}, {1498, 43574}, {1503, 13346}, {1614, 5925}, {1620, 19128}, {2071, 6293}, {2935, 6241}, {3088, 34118}, {3146, 15139}, {3292, 36982}, {3357, 45957}, {3534, 32379}, {5012, 8567}, {5878, 22115}, {5893, 9306}, {6000, 41597}, {6247, 13352}, {6759, 15704}, {9786, 19142}, {9833, 37477}, {10117, 11449}, {10192, 43652}, {10323, 32391}, {10628, 32138}, {11424, 23332}, {11425, 44883}, {11468, 17835}, {11598, 15463}, {12041, 34114}, {12111, 17847}, {13198, 34469}, {13348, 35228}, {14216, 37495}, {15033, 40686}, {15072, 17824}, {17704, 41593}, {31978, 34986}, {37498, 44668}

X(46374) = midpoint of X(46372) and X(46373)
X(46374) = {X(5012),X(43813)}-harmonic conjugate of X(8567)

X(46375) = X(6)-OF-ANTICEVIAN TRIANGLE OF X(3)

X(46375) lies on these lines: {5, 6}, {14642, 14961}, {15905, 32661}, {20233, 22120}

X(46376) = X(55)X(1151)∩X(57)X(30279)

X(46376) lies on the cubic K1253 and these lines: {55, 1151}, {57, 30279}, {165, 6213}, {198, 1615}, {222, 2066}, {354, 16214}, {5273, 30303}, {7177, 13389}

X(46376) = X(34125)-cross conjugate of X(6502)
X(46376) = X(i)-isoconjugate of X(j) for these (i,j): {175, 7133}, {2362, 30413}
X(46376) = barycentric product X(i)*X(j) for these {i,j}: {6502, 40699}, {13389, 15891}
X(46376) = barycentric quotient X(i)/X(j) for these {i,j}: {1124, 31547}, {2066, 30413}, {6502, 175}, {30336, 7090}

X(46377) = X(55)X(1152)∩X(57)X(7133)

X(46377) lies on the cubic K1253 and these lines: {55, 1152}, {57, 7133}, {165, 6212}, {198, 1615}, {222, 5414}, {354, 16213}, {1155, 13455}, {5273, 30302}, {7177, 13388}

X(46377) = isogonal conjugate of the anticomplement of X(45704)
X(46377) = X(34121)-cross conjugate of X(2067)
X(46377) = X(i)-isoconjugate of X(j) for these (i,j): {176, 42013}, {16232, 30412}
X(46377) = barycentric product X(i)*X(j) for these {i,j}: {2067, 40700}, {13388, 15892}
X(46377) = barycentric quotient X(i)/X(j) for these {i,j}: {1335, 31548}, {2067, 176}, {5414, 30412}, {30335, 14121}

X(46378) = X(19)X(25)∩X(57)X(2067)

X(46378) lies on the cubic K1253 and these lines: {19, 25}, {57, 2067}, {165, 6213}, {610, 5414}, {2066, 2270}, {5273, 7090}, {7291, 13388}, {7348, 30385}, {9778, 30413}, {11051, 13456}, {11349, 13389}, {16441, 30557}

X(46378) = X(6213)-Ceva conjugate of X(7133)
X(46378) = X(i)-isoconjugate of X(j) for these (i,j): {6502, 40699}, {13389, 15891}
X(46378) = barycentric product X(i)*X(j) for these {i,j}: {175, 7133}, {2362, 30413}
X(46378) = barycentric quotient X(7133)/X(40699)
X(46378) = {X(19),X(34121)}-harmonic conjugate of X(7133)
X(46378) = {X(19),X(5338)}-harmonic conjugate of X(46379)

X(46379) = X(19)X(25)∩X(57)X(6502)

X(46379) lies on the cubic K1253 and these lines: {19, 25}, {57, 6502}, {165, 6212}, {610, 2066}, {2270, 5414}, {5273, 14121}, {7291, 13389}, {7347, 30386}, {9778, 30412}, {11051, 13427}, {11349, 13388}, {16440, 30556}

X(46379) = X(6212)-Ceva conjugate of X(42013)
X(46379) = X(i)-isoconjugate of X(j) for these (i,j): {2067, 40700}, {13388, 15892}
X(46379) = barycentric product X(i)*X(j) for these {i,j}: {176, 42013}, {16232, 30412}
X(46379) = barycentric quotient X(42013)/X(40700)
X(46379) = {X(19),X(34125)}-harmonic conjugate of X(42013)
X(46379) = {X(19),X(5338)}-harmonic conjugate of X(46378)

This preamble is contributed by Clark Kimberling and Peter Moses, December 21, 2021. The appearance of (j,k) in the following list means that the crossdifference of X(1) and X(j) is X(k):

(2,649), (3,650), (4,652), (5,654), (6,513), (7,657), (8,649), (9,513), (10,649), (11,654), (12,654), (19,656), (20,657), (21,661), (22,46380), (23,46381), (25,2522), (27,46382), (28,656), (29,822), (30,9404), (31,661), (32,1491), (33,652), (34,652), (35,650), (36,650), (37,513), (38,661), (39,659), (40,650), (41,2254), (42,649), (43,649), (44,513), (45,513), (46,650), (47,661), (48,656), (50,18116), (54,2600), (55,650), (56,650), (57,650), (58,661), (592,46383), (60,2610), (63,661), (65,650), (69,2484), (71,46384), (72,513), (73,652), (75,798), (76,46385), (77,657), (78,649), (79,9404), (80,654), (81,661), (82,8061), (83,46386), (84,14298), (85,46387), (86,798), (87,20979), (88,1635), (89,4893), (90,46388), (92,822), (99,46389), (100,1635), (102,46390), (103,46391), (104,46392), (108,46393), (109,46394)

For every point U, the crossdifference of X(1) and U lies on the anti-orthic axis, X(44) X(513).

X(46380) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(22)

X(46380) lies on these lines: {44, 513}, {647, 826}, {665, 2523}, {824, 16757}, {905, 16892}, {4024, 6591}, {4025, 14838}, {4705, 8646}, {6588, 11125}, {6590, 16612}, {8635, 8678}, {16751, 30913}, {21122, 21761}, {29021, 45745}

X(46380) = X(839)-complementary conjugate of X(21235)
X(46380) = X(14542)-Ceva conjugate of X(3270)
X(46380) = crossdifference of every pair of points on line {1, 22}
X(46380) = barycentric product X(i)*X(j) for these {i,j}: {521, 11392}, {1577, 4280}
X(46380) = barycentric quotient X(i)/X(j) for these {i,j}: {4280, 662}, {11392, 18026}
X(46380) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 2509, 661}, {650, 2522, 649}

X(46381) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(23)

X(46381) lies on these lines: {39, 647}, {44, 513}, {1021, 16549}, {3700, 17369}, {3960, 16892}, {4024, 16612}, {4750, 14838}, {26035, 26080}

X(46382) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(27)

X(46382) lies on these lines: {44, 513}, {647, 810}, {1021, 1577}, {21761, 43925}, {22382, 23189}, {24018, 24562}

X(46382) = crosssum of X(7490) and X(17925)
X(46382) = crossdifference of every pair of points on line {1, 27}
X(46382) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36077}, {286, 36080}, {811, 2215}
X(46382) = barycentric product X(i)*X(j) for these {i,j}: {71, 23882}, {405, 656}, {520, 39585}, {647, 5271}, {649, 42706}, {810, 44140}, {1459, 5295}, {5320, 14208}, {8611, 37543}
X(46382) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36077}, {405, 811}, {2200, 36080}, {3049, 2215}, {5271, 6331}, {5320, 162}, {23882, 44129}, {39585, 6528}, {42706, 1978}
X(46382) = {X(652),X(656)}-harmonic conjugate of X(822)

X(46383) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(51)

X(46383) lies on these lines: {6, 4976}, {44, 513}, {323, 401}, {522, 22383}, {647, 21173}, {693, 28983}, {900, 7252}, {1021, 22086}, {2298, 2423}, {2523, 21189}, {4024, 21758}, {4391, 26652}, {15150, 17926}, {20293, 21719}, {20980, 45745}

X(46383) = isotomic conjugate of trilinear pole of line X(5)X(75)
X(46383) = crossdifference of every pair of points on line {1, 51}
X(46383) = barycentric product X(i)*X(j) for these {i,j}: {649, 19811}, {693, 26890}
X(46383) = barycentric quotient X(i)/X(j) for these {i,j}: {19811, 1978}, {26890, 100}

X(46384) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(59)

X(46384) lies on these lines: {44, 513}, {514, 22464}, {1443, 3960}, {1769, 8609}, {2323, 3738}, {3737, 4282}, {4530, 14393}

X(46384) = X(i)-Ceva conjugate of X(j) for these (i,j): {523, 41218}, {10015, 1647}, {23838, 2310}
X(46384) = crosspoint of X(655) and X(40450)
X(46384) = crosssum of X(59) and X(1983)
X(46384) = crossdifference of every pair of points on line {1, 59}
X(46384) = perspector of hyperbola {{A,B,C,X(1),X(11)}}
X(46384) = X(i)-isoconjugate of X(j) for these (i,j): {59, 655}, {80, 4619}, {1411, 31615}, {2149, 35174}, {2222, 4564}, {4998, 32675}, {24027, 36804}
X(46384) = barycentric product X(i)*X(j) for these {i,j}: {11, 3738}, {36, 42455}, {654, 4858}, {1146, 3960}, {1443, 23615}, {2170, 3904}, {2245, 40213}, {2310, 4453}, {2323, 40166}, {2610, 26856}, {3218, 42462}, {3900, 4089}, {4511, 21132}, {7004, 44428}, {8648, 34387}, {21666, 22379}, {21758, 23978}
X(46384) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 35174}, {654, 4564}, {1146, 36804}, {2170, 655}, {2323, 31615}, {3271, 2222}, {3738, 4998}, {3960, 1275}, {4089, 4569}, {7113, 4619}, {8648, 59}, {21132, 18815}, {21758, 1262}, {35128, 4585}, {42455, 20566}, {42462, 18359}
X(46384) = {X(654),X(2600)}-harmonic conjugate of X(2610)

X(46385) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(71)

X(46385) = X[650] - X[7655], 3 X[656] - 2 X[7655], 3 X[2457] - 4 X[14837], X[4498] + 2 X[4833]

X(46385) lies on these lines: {1, 28147}, {44, 513}, {242, 514}, {522, 3465}, {523, 663}, {667, 8672}, {693, 8062}, {832, 4705}, {834, 4498}, {2402, 23696}, {2457, 4778}, {2517, 29051}, {2533, 6133}, {2605, 4449}, {3716, 7650}, {4041, 15313}, {4063, 7654}, {4086, 29066}, {4139, 4775}, {4379, 30911}, {4468, 23874}, {4490, 38469}, {4560, 28623}, {4762, 45686}, {4777, 42312}, {4794, 28161}, {4824, 23655}, {4874, 28116}, {4977, 7178}, {7199, 17215}, {7253, 17494}, {14838, 23800}, {21007, 45755}, {25667, 27416}

X(46385) = midpoint of X(i) and X(j) for these {i,j}: {4724, 17418}, {7253, 17494}
X(46385) = reflection of X(i) in X(j) for these {i,j}: {656, 650}, {693, 8062}, {1459, 3737}, {2533, 6133}, {4449, 2605}, {7650, 3716}, {23752, 7649}, {23800, 14838}
X(46385) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36080}, {72, 36077}, {190, 2215}, {651, 2335}
X(46385) = crossdifference of every pair of points on line {1, 71}
X(46385) = barycentric product X(i)*X(j) for these {i,j}: {1, 23882}, {42, 15417}, {405, 514}, {513, 5271}, {522, 37543}, {649, 44140}, {905, 39585}, {1019, 5295}, {1451, 4391}, {3261, 5320}, {14549, 17494}
X(46385) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36080}, {405, 190}, {663, 2335}, {667, 2215}, {1451, 651}, {1474, 36077}, {5271, 668}, {5295, 4033}, {5320, 101}, {15417, 310}, {23882, 75}, {37543, 664}, {39585, 6335}, {44140, 1978}

X(46386) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(76)

X(46386) lies on these lines: {44, 513}, {213, 667}, {514, 21763}, {669, 688}, {788, 14436}, {790, 40495}, {802, 18197}, {838, 2084}, {1107, 4083}, {1924, 8637}, {2978, 4079}, {3063, 8640}, {3250, 16514}, {4063, 16552}, {4367, 23572}, {7192, 21225}, {8631, 16695}, {17458, 20598}, {20981, 22384}

X(46386) = isogonal conjugate of X(37133)
X(46386) = isogonal conjugate of the isotomic conjugate of X(3250)
X(46386) = isotomic conjugate of trilinear pole of line X(75)X(1502)
X(46386) = X(i)-Ceva conjugate of X(j) for these (i,j): {1492, 40935}, {2279, 3248}, {37133, 1}
X(46386) = X(17415)-cross conjugate of X(1491)
X(46386) = X(i)-isoconjugate of X(j) for these (i,j): {1, 37133}, {2, 789}, {6, 46132}, {75, 4586}, {76, 1492}, {101, 871}, {190, 870}, {239, 41072}, {274, 4613}, {350, 37207}, {513, 5388}, {561, 825}, {668, 14621}, {670, 40747}, {799, 40718}, {985, 1978}, {1502, 34069}, {1920, 30670}, {1921, 30664}, {2344, 4572}, {3113, 33946}, {3114, 3888}, {3261, 5384}, {4817, 7035}, {6386, 40746}, {9063, 16584}, {20234, 33514}
X(46386) = cevapoint of X(1) and X(39338)
X(46386) = crosspoint of X(1) and X(37133)
X(46386) = crosssum of X(i) and X(j) for these (i,j): {649, 21352}, {870, 4817}, {1491, 3721}
X(46386) = crossdifference of every pair of points on line {1, 76}
X(46386) = barycentric product X(i)*X(j) for these {i,j}: {1, 788}, {6, 3250}, {31, 1491}, {32, 824}, {75, 8630}, {88, 14436}, {213, 4481}, {512, 3736}, {513, 869}, {514, 40728}, {649, 2276}, {663, 1469}, {667, 984}, {669, 30966}, {672, 29956}, {692, 4475}, {693, 18900}, {694, 30654}, {798, 40773}, {875, 3783}, {893, 45882}, {904, 3805}, {1019, 3774}, {1397, 4522}, {1911, 30665}, {1914, 30671}, {1917, 30870}, {1919, 3661}, {1922, 4486}, {1927, 30639}, {1977, 3807}, {1980, 33931}, {2206, 4122}, {3049, 31909}, {3063, 7146}, {3248, 3799}, {3572, 16514}, {3835, 40736}, {3862, 8632}, {4517, 43924}, {7204, 8641}, {8640, 45782}, {14599, 23596}, {17415, 40415}
X(46386) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 46132}, {6, 37133}, {31, 789}, {32, 4586}, {101, 5388}, {513, 871}, {560, 1492}, {667, 870}, {669, 40718}, {788, 75}, {824, 1502}, {869, 668}, {984, 6386}, {1469, 4572}, {1491, 561}, {1501, 825}, {1911, 41072}, {1917, 34069}, {1918, 4613}, {1919, 14621}, {1922, 37207}, {1924, 40747}, {1977, 4817}, {1980, 985}, {2276, 1978}, {3117, 33946}, {3249, 43266}, {3250, 76}, {3736, 670}, {3774, 4033}, {4475, 40495}, {4481, 6385}, {4486, 44169}, {4522, 40363}, {8630, 1}, {9006, 3778}, {14436, 4358}, {14598, 30664}, {16514, 27853}, {17415, 2887}, {18900, 100}, {23596, 44170}, {29956, 18031}, {30654, 3978}, {30665, 18891}, {30671, 18895}, {30966, 4609}, {40370, 43289}, {40415, 9063}, {40728, 190}, {40736, 4598}, {40773, 4602}, {45882, 1920}
X(46386) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 20979, 659}, {16695, 21791, 8631}

X(46387) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(83)

X(46387) lies on these lines: {44, 513}, {688, 3005}, {3249, 14419}, {3271, 6377}, {3570, 21362}, {3716, 29955}, {3777, 23572}, {4380, 20906}, {4553, 35309}, {8632, 22384}, {17277, 29546}, {29428, 37686}, {29545, 33295}

X(46387) = X(i)-Ceva conjugate of X(j) for these (i,j): {660, 40936}, {3572, 2084}, {35333, 1964}
X(46387) = crosspoint of X(i) and X(j) for these (i,j): {660, 40432}, {812, 8632}, {1019, 3572}
X(46387) = crosssum of X(i) and X(j) for these (i,j): {659, 2295}, {813, 4562}, {1018, 3570}
X(46387) = crossdifference of every pair of points on line {1, 83}
X(46387) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36081}, {82, 4562}, {83, 660}, {251, 4583}, {308, 34067}, {334, 4628}, {813, 3112}, {2295, 41209}, {3952, 39276}, {4579, 14970}, {4584, 18082}, {4589, 18098}, {4599, 43534}, {5378, 10566}, {18047, 43763}, {18099, 37134}
X(46387) = barycentric product X(i)*X(j) for these {i,j}: {38, 659}, {39, 812}, {141, 8632}, {238, 2530}, {239, 21123}, {427, 22384}, {826, 5009}, {1401, 3716}, {1914, 16892}, {1964, 3766}, {2084, 30940}, {3005, 33295}, {3688, 43041}, {4010, 17187}, {4093, 7192}, {4124, 46153}, {4448, 46150}, {4455, 16887}, {4553, 27846}, {7193, 21108}, {16696, 21832}, {20663, 35367}, {27918, 46148}, {35333, 38989}
X(46387) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36081}, {38, 4583}, {39, 4562}, {659, 3112}, {812, 308}, {1178, 41209}, {1923, 34067}, {1964, 660}, {2530, 334}, {3005, 43534}, {3051, 813}, {3688, 36801}, {3766, 18833}, {4093, 3952}, {4455, 18082}, {5009, 4577}, {5027, 18099}, {8623, 18047}, {8632, 83}, {14599, 4628}, {16696, 4639}, {16892, 18895}, {17187, 4589}, {21123, 335}, {22384, 1799}, {30940, 37204}, {33295, 689}, {39786, 18070}

X(46388) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(85)

X(46388) lies on these lines: {6, 22384}, {9, 3716}, {41, 8648}, {44, 513}, {101, 34905}, {512, 10581}, {665, 20662}, {692, 2874}, {928, 14825}, {1025, 4763}, {1334, 4895}, {1475, 14413}, {1919, 8642}, {2488, 3709}, {2491, 3725}, {3063, 8641}, {3271, 6139}, {3572, 23569}, {3691, 14430}, {3730, 3887}, {3762, 16552}, {3960, 4253}, {4010, 28143}, {4079, 33525}, {4369, 21390}, {4775, 17425}, {5013, 22437}, {8632, 20672}, {9436, 31286}, {9605, 23141}, {16560, 21382}, {17463, 21339}, {17754, 25380}, {18155, 21388}, {40978, 42666}

X(46388) = isogonal conjugate of X(34085)
X(46388) = X(i)-Ceva conjugate of X(j) for these (i,j): {101, 42079}, {103, 24012}, {813, 55}, {1024, 663}, {34085, 1}, {36039, 31}, {40730, 15615}
X(46388) = crosspoint of X(i) and X(j) for these (i,j): {1, 34085}, {101, 2195}, {663, 1024}, {665, 926}, {692, 911}, {813, 40730}
X(46388) = crosssum of X(i) and X(j) for these (i,j): {57, 43041}, {514, 9436}, {650, 20358}, {658, 24015}, {664, 1025}, {666, 927}, {672, 4449}, {693, 30807}, {2254, 17451}, {4077, 16609}
X(46388) = crossdifference of every pair of points on line {1, 85}
X(46388) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34085}, {2, 927}, {6, 46135}, {7, 666}, {56, 36803}, {75, 36146}, {76, 32735}, {85, 36086}, {100, 34018}, {105, 4554}, {109, 18031}, {279, 36802}, {294, 4569}, {514, 39293}, {651, 2481}, {653, 31637}, {658, 14942}, {664, 673}, {668, 1462}, {883, 6185}, {885, 1275}, {919, 6063}, {934, 36796}, {1016, 43930}, {1416, 1978}, {1438, 4572}, {1814, 18026}, {4573, 13576}, {4625, 18785}, {4626, 6559}, {5222, 41075}, {5377, 24002}, {6180, 14727}, {20567, 32666}, {21609, 36041}, {28071, 36838}
X(46388) = barycentric product X(i)*X(j) for these {i,j}: {1, 926}, {9, 665}, {41, 918}, {55, 2254}, {75, 8638}, {101, 17435}, {241, 657}, {284, 24290}, {318, 23225}, {513, 2340}, {518, 663}, {521, 2356}, {522, 2223}, {649, 3693}, {650, 672}, {652, 5089}, {656, 37908}, {667, 3717}, {884, 4712}, {885, 42079}, {1024, 6184}, {1025, 14936}, {1026, 3271}, {1253, 43042}, {1458, 3900}, {1566, 36039}, {1818, 18344}, {1861, 1946}, {2170, 2284}, {2194, 4088}, {2195, 3126}, {2283, 2310}, {2342, 42758}, {2428, 38375}, {3022, 41353}, {3063, 3912}, {3064, 20752}, {3252, 4435}, {3286, 4041}, {3675, 3939}, {3709, 18206}, {3716, 40730}, {3737, 20683}, {3930, 7252}, {4105, 34855}, {4391, 9454}, {4560, 39258}, {4895, 34230}, {8641, 9436}, {9439, 42341}, {9455, 35519}, {14411, 37131}, {23351, 35293}, {23696, 42071}, {34085, 39014}, {36037, 42771}
X(46388) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 46135}, {6, 34085}, {9, 36803}, {31, 927}, {32, 36146}, {41, 666}, {518, 4572}, {560, 32735}, {649, 34018}, {650, 18031}, {657, 36796}, {663, 2481}, {665, 85}, {672, 4554}, {692, 39293}, {918, 20567}, {926, 75}, {1253, 36802}, {1458, 4569}, {1919, 1462}, {1946, 31637}, {1980, 1416}, {2175, 36086}, {2223, 664}, {2254, 6063}, {2340, 668}, {2356, 18026}, {3063, 673}, {3248, 43930}, {3286, 4625}, {3693, 1978}, {3717, 6386}, {8638, 1}, {8641, 14942}, {9439, 14727}, {9447, 919}, {9448, 32666}, {9454, 651}, {9455, 109}, {15615, 2254}, {17435, 3261}, {23225, 77}, {24290, 349}, {37908, 811}, {39258, 4552}, {39686, 1025}, {42079, 883}, {42771, 36038}

X(46389) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(90)

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

X(46389) = 3 X[650] - 2 X[14300], 3 X[650] - 4 X[40137], X[13401] - 4 X[14298], 3 X[13401] - 4 X[14300], 3 X[13401] - 8 X[40137], 3 X[14298] - X[14300], 3 X[14298] - 2 X[40137]

X(46389) lies on these lines: {6, 3657}, {44, 513}, {198, 42769}, {521, 3700}, {924, 2501}, {926, 2520}, {1252, 34151}, {3064, 15313}, {3239, 3738}, {3309, 11927}, {3900, 4820}, {4017, 10397}, {4106, 5928}, {4131, 4885}, {4776, 28834}, {6003, 14331}, {6588, 22383}, {6590, 9001}, {8676, 18344}, {12664, 30199}, {14115, 46101}, {14330, 42325}, {14589, 15632}, {20980, 36054}, {34032, 43049}, {42762, 43932}

X(46389) = reflection of X(i) in X(j) for these {i,j}: {650, 14298}, {4131, 4885}, {11934, 2520}, {13401, 650}, {14300, 40137}
X(46389) = X(i)-complementary conjugate of X(j) for these (i,j): {42, 136}, {91, 21252}, {925, 3741}, {1918, 39013}, {2165, 116}, {2351, 2968}, {8750, 1147}, {32734, 1125}, {36145, 3739}, {41271, 44311}
X(46389) = X(i)-Ceva conjugate of X(j) for these (i,j): {651, 3157}, {1813, 65}, {3064, 650}, {13397, 55}, {36599, 2310}
X(46389) = crosspoint of X(i) and X(j) for these (i,j): {4, 651}, {1800, 1813}
X(46389) = crosssum of X(i) and X(j) for these (i,j): {3, 650}, {6, 34948}
X(46389) = crossdifference of every pair of points on line {1, 90}
X(46389) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36082}, {90, 651}, {101, 7318}, {108, 6513}, {109, 2994}, {653, 1069}, {658, 7072}, {664, 2164}, {1415, 20570}, {1461, 36626}, {1813, 7040}, {4636, 7363}, {6512, 36127}, {13395, 46038}
X(46389) = barycentric product X(i)*X(j) for these {i,j}: {9, 21188}, {46, 522}, {513, 5552}, {521, 1068}, {523, 3193}, {650, 5905}, {651, 6506}, {656, 3559}, {661, 31631}, {663, 20930}, {1406, 4397}, {1800, 24006}, {2178, 4391}, {3064, 6505}, {3157, 44426}, {3737, 21077}, {4560, 21853}
X(46389) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36082}, {46, 664}, {513, 7318}, {522, 20570}, {650, 2994}, {652, 6513}, {663, 90}, {1068, 18026}, {1406, 934}, {1800, 4592}, {1946, 1069}, {2178, 651}, {3063, 2164}, {3157, 6516}, {3193, 99}, {3559, 811}, {3900, 36626}, {5552, 668}, {5905, 4554}, {6506, 4391}, {8641, 7072}, {18344, 7040}, {20930, 4572}, {21188, 85}, {21853, 4552}, {31631, 799}, {36054, 6512}
X(46389) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {652, 661, 650}, {14298, 14300, 40137}, {14300, 40137, 650}

X(46390) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(99)

X(46390) lies on these lines: {44, 513}, {351, 865}, {645, 3570}, {812, 39028}, {891, 16589}, {1213, 3837}, {1960, 20970}, {2533, 22224}, {3709, 4093}, {4010, 4839}, {4079, 8663}, {14436, 21838}, {14838, 21763}, {17990, 18001}, {21385, 46196}

X(46390) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 38978}, {2107, 11}
X(46390) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 38978}, {1018, 4094}, {3570, 4093}, {3572, 512}, {18001, 8663}, {18785, 2643}, {18793, 4117}, {21832, 4155}, {27853, 740}, {37128, 4128}
X(46390) = X(2086)-cross conjugate of X(2238)
X(46390) = crosspoint of X(i) and X(j) for these (i,j): {512, 3572}, {740, 27853}, {3903, 37128}, {4455, 21832}
X(46390) = crosssum of X(i) and X(j) for these (i,j): {99, 3570}, {1019, 33295}, {2238, 4367}, {3572, 46159}, {4444, 18827}, {4584, 4589}
X(46390) = crossdifference of every pair of points on line {1, 99}
X(46390) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36066}, {56, 36806}, {58, 4639}, {81, 4589}, {86, 4584}, {99, 37128}, {110, 40017}, {291, 4610}, {292, 4623}, {334, 4556}, {593, 4583}, {660, 1509}, {662, 18827}, {670, 18268}, {741, 799}, {757, 4562}, {805, 8033}, {813, 873}, {875, 34537}, {876, 4590}, {1414, 36800}, {2311, 4625}, {3572, 24037}, {4367, 39292}, {4444, 24041}, {4576, 39276}, {4593, 46159}, {4612, 7233}, {17103, 37134}
X(46390) = barycentric product X(i)*X(j) for these {i,j}: {1, 4155}, {10, 4455}, {37, 21832}, {42, 4010}, {181, 3716}, {238, 4705}, {239, 4079}, {512, 740}, {523, 3747}, {594, 8632}, {649, 4037}, {656, 862}, {659, 756}, {661, 2238}, {663, 7235}, {669, 35544}, {798, 3948}, {812, 1500}, {872, 3766}, {876, 4094}, {882, 4154}, {1018, 39786}, {1084, 27853}, {1284, 4041}, {1334, 7212}, {1577, 41333}, {1914, 4024}, {2086, 27805}, {2171, 4435}, {2210, 4036}, {2333, 24459}, {2643, 3573}, {3124, 3570}, {3572, 35068}, {3709, 16609}, {3985, 7180}, {4017, 4433}, {7064, 43041}, {7140, 22384}, {9402, 39926}, {27846, 40521}, {36815, 42666}
X(46390) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 36806}, {31, 36066}, {37, 4639}, {42, 4589}, {213, 4584}, {238, 4623}, {512, 18827}, {659, 873}, {661, 40017}, {669, 741}, {688, 46159}, {740, 670}, {756, 4583}, {798, 37128}, {862, 811}, {872, 660}, {1084, 3572}, {1284, 4625}, {1500, 4562}, {1914, 4610}, {1924, 18268}, {2086, 4369}, {2238, 799}, {3124, 4444}, {3570, 34537}, {3573, 24037}, {3684, 4631}, {3709, 36800}, {3716, 18021}, {3747, 99}, {3948, 4602}, {4010, 310}, {4024, 18895}, {4036, 44172}, {4037, 1978}, {4079, 335}, {4093, 4576}, {4094, 874}, {4117, 875}, {4154, 880}, {4155, 75}, {4433, 7257}, {4455, 86}, {4705, 334}, {5027, 17103}, {7064, 36801}, {7109, 813}, {7235, 4572}, {8632, 1509}, {14599, 4556}, {21727, 40094}, {21832, 274}, {27853, 44168}, {35068, 27853}, {35544, 4609}, {39786, 7199}, {40729, 37134}, {41333, 662}

X(46391) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(102)

X(46391) lies on these lines: {44, 513}, {109, 1783}, {1636, 18675}, {7004, 7117}, {8611, 36054}, {14331, 21186}, {22383, 40628}

X(46391) = isogonal conjugate of the polar conjugate of X(14304)
X(46391) = X(i)-Ceva conjugate of X(j) for these (i,j): {2765, 55}, {24035, 515}, {36044, 33}, {36050, 42076}
X(46391) = crosspoint of X(i) and X(j) for these (i,j): {63, 36037}, {515, 24035}, {905, 37628}, {13138, 36100}
X(46391) = crosssum of X(i) and X(j) for these (i,j): {19, 1769}, {652, 1457}, {1783, 23706}, {2182, 6129}, {32667, 36040}
X(46391) = crossdifference of every pair of points on line {1, 102}
X(46391) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36067}, {75, 32667}, {92, 36040}, {102, 653}, {108, 36100}, {196, 6081}, {264, 32643}, {651, 36121}, {15629, 36118}, {17080, 36108}, {18026, 32677}, {32674, 34393}
X(46391) = barycentric product X(i)*X(j) for these {i,j}: {1, 39471}, {3, 14304}, {271, 6087}, {515, 521}, {1809, 42755}, {1946, 35516}, {2182, 6332}, {2406, 34591}, {7117, 42718}, {10017, 36037}, {23987, 24031}, {24035, 35072}
X(46391) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36067}, {32, 32667}, {184, 36040}, {515, 18026}, {521, 34393}, {652, 36100}, {663, 36121}, {1455, 36118}, {1946, 102}, {2182, 653}, {2188, 6081}, {2425, 7128}, {6087, 342}, {9247, 32643}, {10017, 36038}, {14304, 264}, {23986, 24035}, {23987, 24032}, {34050, 13149}, {34591, 2399}, {39471, 75}, {42076, 23987}

X(46392) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(103)

X(46392) lies on these lines: {44, 513}, {294, 2338}, {676, 9502}, {1212, 14414}, {2310, 3119}, {3716, 28132}, {4105, 4171}

X(46392) = X(i)-Ceva conjugate of X(j) for these (i,j): {294, 2310}, {1783, 42077}, {24015, 516}, {36146, 4319}
X(46392) = crosspoint of X(i) and X(j) for these (i,j): {516, 24015}, {658, 14942}
X(46392) = crosssum of X(i) and X(j) for these (i,j): {651, 41353}, {657, 1458}
X(46392) = crossdifference of every pair of points on line {1, 103}
X(46392) = X(i)-isoconjugate of X(j) for these (i,j): {2, 24016}, {75, 32668}, {103, 658}, {279, 677}, {651, 43736}, {911, 4569}, {934, 36101}, {1088, 36039}, {1262, 2400}, {1275, 2424}, {1461, 18025}, {1815, 36118}, {2338, 4626}, {4619, 15634}, {7056, 40116}, {9503, 41353}, {13149, 36056}
X(46392) = barycentric product X(i)*X(j) for these {i,j}: {200, 676}, {516, 3900}, {522, 41339}, {650, 40869}, {657, 30807}, {910, 3239}, {1021, 17747}, {1456, 4163}, {2310, 2398}, {2426, 24026}, {4130, 43035}, {4171, 14953}, {7079, 39470}, {8641, 35517}, {9502, 28132}, {14936, 42719}, {23973, 24010}, {24015, 35508}, {34591, 41321}
X(46392) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 24016}, {32, 32668}, {516, 4569}, {657, 36101}, {663, 43736}, {676, 1088}, {910, 658}, {1253, 677}, {1456, 4626}, {1886, 13149}, {2310, 2400}, {2426, 7045}, {3900, 18025}, {8641, 103}, {14827, 36039}, {14953, 4635}, {23972, 24015}, {23973, 24011}, {40869, 4554}, {41339, 664}, {42077, 23973}, {43035, 36838}
X(46392) = {X(650),X(4724)}-harmonic conjugate of X(21127)

X(46393) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(1)X(104)

X(46393) lies on these lines: {9, 14418}, {11, 1146}, {44, 513}, {55, 14392}, {101, 108}, {908, 36038}, {972, 2291}, {1459, 40134}, {1512, 14330}, {1637, 2294}, {1769, 3310}, {2161, 2432}, {2316, 3738}, {2814, 5400}, {2821, 3030}, {3064, 3239}, {3700, 42337}, {3762, 14554}, {4105, 11934}, {4120, 42462}, {4171, 4944}, {4521, 14331}, {4728, 40166}, {6139, 11124}, {6591, 10397}, {8677, 42772}, {10015, 42762}, {13576, 28132}, {21801, 42763}, {23893, 24297}, {25666, 28834}, {25900, 31287}, {25924, 28984}, {26545, 27014}, {39534, 42756}

X(46393) = isogonal conjugate of X(37136)
X(46393) = isotomic conjugate of trilinear pole of line X(75)X(77)
X(46393) = polar conjugate of trilinear pole of line X(57)X(92)
X(46393) = X(31)-complementary conjugate of X(38981)
X(46393) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 38981}, {57, 35065}, {80, 2310}, {514, 23757}, {908, 35015}, {1465, 35014}, {2222, 55}, {2316, 2170}, {2427, 21801}, {3738, 4895}, {10015, 1769}, {14554, 11}, {24029, 517}, {32665, 17452}, {34234, 7004}, {36106, 212}, {37136, 1}
X(46393) = crosspoint of X(i) and X(j) for these (i,j): {1, 37136}, {514, 23838}, {517, 24029}, {651, 1320}, {1465, 23706}, {1897, 34234}, {2804, 10015}
X(46393) = crosssum of X(i) and X(j) for these (i,j): {56, 21786}, {57, 3960}, {101, 23703}, {650, 1319}, {1459, 2183}, {2720, 32641}
X(46393) = crossdifference of every pair of points on line {1, 104}
X(46393) = Stevanovic-circle-inverse of X(45884)
X(46393) = X(i)-isoconjugate of X(j) for these (i,j): {1, 37136}, {2, 2720}, {7, 32641}, {56, 13136}, {57, 36037}, {59, 2401}, {63, 36110}, {69, 32702}, {75, 32669}, {100, 34051}, {104, 651}, {109, 34234}, {222, 1309}, {348, 14776}, {653, 1795}, {658, 2342}, {664, 909}, {901, 40218}, {1262, 43728}, {1414, 2250}, {1415, 18816}, {1459, 39294}, {1809, 32714}, {1813, 36123}, {2405, 15405}, {2423, 4998}, {4554, 34858}, {4565, 38955}, {7128, 37628}, {14578, 18026}, {15501, 37141}, {15635, 31615}, {16082, 36059}, {35011, 43043}, {36146, 36819}, {43933, 44717}
X(46393) = barycentric product X(i)*X(j) for these {i,j}: {1, 2804}, {8, 1769}, {9, 10015}, {55, 36038}, {78, 39534}, {100, 35015}, {210, 23788}, {312, 3310}, {318, 8677}, {513, 6735}, {517, 522}, {521, 1785}, {643, 42759}, {644, 42754}, {650, 908}, {663, 3262}, {859, 4086}, {952, 37629}, {1145, 23838}, {1146, 24029}, {1320, 23757}, {1457, 4397}, {1465, 3239}, {1897, 35014}, {2170, 2397}, {2183, 4391}, {2427, 4858}, {2968, 23706}, {3326, 36037}, {3699, 42753}, {3737, 17757}, {3900, 22464}, {4041, 17139}, {4551, 14010}, {4560, 21801}, {4768, 14260}, {6332, 14571}, {6740, 42768}, {7257, 42752}, {8851, 42766}, {14942, 42758}, {21664, 37628}, {22350, 44426}, {23981, 24026}, {24028, 43728}, {41798, 42762}, {42750, 44693}
X(46393) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 37136}, {9, 13136}, {25, 36110}, {31, 2720}, {32, 32669}, {33, 1309}, {41, 32641}, {55, 36037}, {517, 664}, {522, 18816}, {649, 34051}, {650, 34234}, {663, 104}, {859, 1414}, {908, 4554}, {926, 36819}, {1457, 934}, {1465, 658}, {1635, 40218}, {1769, 7}, {1783, 39294}, {1785, 18026}, {1875, 36118}, {1946, 1795}, {1973, 32702}, {2170, 2401}, {2183, 651}, {2212, 14776}, {2310, 43728}, {2427, 4564}, {2804, 75}, {3063, 909}, {3064, 16082}, {3239, 36795}, {3262, 4572}, {3270, 37628}, {3310, 57}, {3326, 36038}, {3709, 2250}, {4041, 38955}, {4814, 36921}, {4895, 36944}, {6735, 668}, {8641, 2342}, {8677, 77}, {10015, 85}, {14010, 18155}, {14571, 653}, {17139, 4625}, {18344, 36123}, {21801, 4552}, {22350, 6516}, {22464, 4569}, {23220, 603}, {23980, 24029}, {23981, 7045}, {24029, 1275}, {35014, 4025}, {35015, 693}, {36038, 6063}, {37629, 46136}, {39534, 273}, {42072, 23706}, {42078, 23981}, {42752, 4017}, {42753, 3676}, {42754, 24002}, {42757, 22464}, {42758, 9436}, {42759, 4077}, {42762, 37780}, {42768, 41804}, {42771, 2254}
X(46393) = trilinear product X(i)*X(j) for these {i,j}: {6, 2804}, {8, 3310}, {9, 1769}, {11, 2427}, {41, 36038}, {55, 10015}, {101, 35015}, {281, 8677}, {517, 650}, {521, 14571}, {522, 2183}, {649, 6735}, {652, 1785}, {657, 22464}, {663, 908}, {859, 3700}, {1146, 23981}, {1334, 23788}, {1457, 3239}, {1465, 3900}, {1639, 14260}, {1783, 35014}, {2310, 24029}, {2316, 23757}, {2397, 3271}, {2431, 25640}, {3063, 3262}, {3064, 22350}, {3259, 5548}, {3326, 32641}, {3709, 17139}, {3737, 21801}, {4559, 14010}, {7017, 23220}, {7252, 17757}, {23706, 34591}
X(46393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 654, 1635}, {650, 14298, 652}, {657, 4893, 650}, {2590, 2591, 652}

X(46394) = BARYCENTRIC SQUARE OF X(216)

X(46394) lies on these lines: {3, 1625}, {5, 53}, {32, 26880}, {39, 12233}, {184, 36433}, {217, 418}, {327, 37186}, {2207, 26898}, {3164, 18027}, {3331, 26897}, {6292, 6509}, {8571, 39170}, {14374, 15167}, {14375, 15166}, {15526, 36952}, {26907, 40588}

X(46394) = complement of the isotomic conjugate of X(42487)
X(46394) = X(42487)-complementary conjugate of X(2887)
X(46394) = crosspoint of X(i) and X(j) for these (i,j): {2, 42487}, {216, 418}
X(46394) = crosssum of X(i) and X(j) for these (i,j): {6, 1629}, {275, 8795}
X(46394) = crossdifference of every pair of points on line {6130, 23286}
X(46394) = barycentric square of X(216)
X(46394) = X(i)-isoconjugate of X(j) for these (i,j): {275, 40440}, {276, 2190}, {2167, 8795}, {2616, 42405}
X(46394) = barycentric product X(i)*X(j) for these {i,j}: {5, 418}, {51, 5562}, {110, 34983}, {216, 216}, {217, 343}, {250, 41212}, {311, 44088}, {577, 36412}, {1625, 17434}, {6056, 41279}, {14570, 42293}, {14585, 45793}, {15451, 23181}, {19210, 23607}, {23357, 39019}, {30493, 44707}
X(46394) = barycentric quotient X(i)/X(j) for these {i,j}: {51, 8795}, {216, 276}, {217, 275}, {418, 95}, {1625, 42405}, {3199, 8794}, {5562, 34384}, {27374, 19174}, {34983, 850}, {36412, 18027}, {39019, 23962}, {40981, 8884}, {41212, 339}, {42293, 15412}, {44088, 54}

X(46395) = PERSPECTOR OF THE PRIVALOV CONIC

X(46395 lies on the cubic K925 and these lines: {11, 5452}, {3434, 23989}, {5101, 12586}, {10947, 11927}, {17625, 30617}, {17658, 30615}

X(46395) = isotomic conjugate of the anticomplement of X(16283)
X(46395) = X(i)-cross conjugate of X(j) for these (i,j): {14935, 650}, {16283, 2}

X(46396) = COMPLEMENT OF X(652)

X(46396) lies on these lines: {2, 652}, {141, 8999}, {142, 7658}, {226, 3239}, {306, 17894}, {513, 3716}, {520, 6130}, {522, 23806}, {812, 28984}, {1459, 26146}, {2550, 4105}, {3900, 20314}, {4025, 5249}, {4728, 29005}, {6589, 17056}, {8611, 17896}, {8676, 17072}, {9240, 34831}, {16612, 23724}, {17069, 21195}, {17924, 24018}, {18134, 35519}, {18589, 20319}, {25259, 31019}, {25604, 41867}, {26571, 27014}, {26596, 27193}

X(46396) = midpoint of X(i) and X(j) for these {i,j}: {8611, 17896}, {17924, 24018}
X(46396) = complement of X(652)
X(46396) = complement of the isogonal conjugate of X(653)
X(46396) = medial isogonal conjugate of X(16596)
X(46396) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 16596}, {2, 123}, {4, 26932}, {6, 35072}, {9, 40616}, {19, 1146}, {27, 34589}, {28, 4858}, {33, 13609}, {34, 1086}, {57, 2968}, {65, 15526}, {73, 16595}, {81, 34588}, {92, 124}, {107, 6708}, {108, 2}, {109, 1214}, {112, 40937}, {162, 5745}, {190, 34823}, {196, 7358}, {225, 8287}, {226, 34846}, {273, 116}, {278, 11}, {281, 5514}, {331, 21252}, {393, 6506}, {607, 35508}, {608, 1015}, {644, 42018}, {648, 960}, {651, 3}, {653, 10}, {658, 34822}, {662, 34851}, {664, 18589}, {811, 21246}, {823, 34831}, {934, 17073}, {1020, 18641}, {1041, 1565}, {1119, 4904}, {1172, 34591}, {1214, 122}, {1395, 6377}, {1396, 244}, {1400, 16573}, {1409, 35071}, {1411, 42761}, {1415, 216}, {1426, 17058}, {1435, 3756}, {1441, 127}, {1461, 17102}, {1465, 10017}, {1783, 9}, {1847, 17059}, {1876, 35094}, {1880, 115}, {1897, 3452}, {2405, 25640}, {4551, 440}, {4552, 21530}, {4554, 1368}, {4559, 18591}, {4564, 20315}, {4565, 37565}, {4566, 18642}, {4569, 18639}, {5089, 1566}, {6335, 1329}, {6516, 6389}, {6529, 9119}, {6591, 46101}, {6648, 37613}, {7012, 514}, {7115, 650}, {7128, 522}, {8735, 34530}, {8750, 1212}, {8751, 17435}, {13149, 2886}, {15742, 20317}, {17080, 38977}, {17924, 46100}, {18026, 141}, {23984, 521}, {23985, 6588}, {24019, 40942}, {24033, 14837}, {24035, 117}, {30456, 39020}, {32647, 14571}, {32660, 828}, {32667, 8607}, {32674, 37}, {32688, 5089}, {32702, 8609}, {32714, 1}, {32726, 33572}, {34051, 35014}, {36044, 34050}, {36059, 6509}, {36067, 1465}, {36099, 958}, {36110, 3911}, {36118, 142}, {36127, 226}, {37790, 3259}, {37799, 5520}, {40117, 281}, {40149, 125}, {40397, 7004}, {40446, 24237}, {41207, 37370}, {43923, 6547}, {46102, 513}, {46152, 6292}
X(46396) = crossdifference of every pair of points on line {2176, 10537}
X(46396) = barycentric product X(514)*X(25252)
X(46396) = barycentric quotient X(25252)/X(190)

X(46397) = COMPLEMENT OF X(654)

X(46397) lies on these lines: {2, 654}, {116, 124}, {118, 31844}, {142, 44902}, {226, 918}, {513, 3716}, {908, 1639}, {924, 30476}, {926, 2886}, {1638, 5249}, {2826, 21635}, {3310, 5718}, {3452, 45326}, {4106, 28984}, {4453, 31019}, {5880, 9511}, {6139, 6690}, {17069, 23806}, {22086, 35466}, {24462, 33111}, {25511, 26596}, {30565, 31053}

X(46397) = reflection of X(6139) in X(6690)
X(46397) = complement of X(654)
X(46397) = complement of the isogonal conjugate of X(655)
X(46397) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 35128}, {80, 26932}, {109, 16586}, {651, 214}, {655, 10}, {759, 4858}, {1020, 6739}, {1411, 1086}, {1807, 16596}, {2006, 11}, {2161, 1146}, {2222, 2}, {2341, 34591}, {4552, 31845}, {4559, 35069}, {14628, 3259}, {16577, 3258}, {18359, 124}, {18815, 116}, {21741, 18334}, {23592, 3738}, {24624, 34589}, {32675, 37}, {34242, 40626}, {35174, 141}, {36069, 16579}, {36078, 16577}, {36804, 1329}, {36910, 5514}, {37140, 4999}, {43048, 35587}
X(46397) = crossdifference of every pair of points on line {2176, 45937}

X(46398) = COMPLEMENT OF X(655)

X(46398) lies on these lines: {2, 655}, {7, 37136}, {11, 522}, {214, 516}, {338, 1577}, {514, 26932}, {523, 46100}, {527, 39063}, {905, 1086}, {908, 1465}, {1861, 21664}, {2972, 34588}, {3126, 42757}, {3218, 14920}, {4466, 38372}, {5289, 14260}, {5886, 24410}, {6739, 45022}, {11729, 38617}, {13136, 46136}, {23593, 45274}

X(46398) = midpoint of X(908) and X(22464)
X(46398) = reflection of X(655) in X(40536)
X(46398) = complement of X(655)
X(46398) = anticomplement of X(40536)
X(46398) = complement of the isogonal conjugate of X(654)
X(46398) = complement of the isotomic conjugate of X(3904)
X(46398) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 3738}, {31, 10015}, {36, 4885}, {41, 1639}, {522, 21237}, {649, 1737}, {650, 3814}, {654, 10}, {663, 908}, {1333, 21180}, {1983, 3035}, {2148, 6369}, {2150, 6370}, {2323, 513}, {2361, 514}, {2423, 12736}, {2600, 1209}, {2610, 34829}, {3063, 44}, {3218, 17072}, {3724, 1577}, {3738, 141}, {3904, 2887}, {3960, 2886}, {4282, 523}, {4453, 17046}, {4511, 3835}, {7113, 522}, {7252, 758}, {8648, 2}, {16944, 44902}, {17515, 30476}, {21758, 1}, {21828, 442}, {22379, 17073}, {32851, 21260}, {44428, 20305}
X(46398) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 10015}, {7, 3738}, {264, 6369}, {36917, 522}
X(46398) = X(i)-isoconjugate of X(j) for these (i,j): {2149, 40437}, {2222, 32641}, {32675, 36037}, {35321, 36078}
X(46398) = crosspoint of X(2) and X(3904)
X(46398) = crosssum of X(6) and X(32675)
X(46398) = barycentric product X(i)*X(j) for these {i,j}: {320, 35015}, {331, 38353}, {1845, 17880}, {2804, 4453}, {3738, 36038}, {3904, 10015}, {4089, 6735}, {4858, 16586}, {14010, 41804}, {18155, 42768}, {32851, 42754}, {34387, 34586}, {45950, 46136}
X(46398) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 40437}, {654, 32641}, {1769, 2222}, {1845, 7012}, {2600, 35321}, {3259, 14584}, {3310, 32675}, {3738, 36037}, {3904, 13136}, {3960, 37136}, {10015, 655}, {14010, 6740}, {16586, 4564}, {17923, 39294}, {21758, 32669}, {34586, 59}, {35014, 1807}, {35015, 80}, {36038, 35174}, {38353, 219}, {42753, 1411}, {42754, 2006}, {42768, 4551}, {44428, 1309}, {45950, 952}
X(46398) = {X(2),X(655)}-harmonic conjugate of X(40536)

X(46399) = COMPLEMENT OF X(657)

Barycentrics (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) : :

X(46399) lies on these lines: {2, 657}, {57, 22443}, {116, 46100}, {141, 9000}, {142, 522}, {226, 21960}, {513, 3716}, {514, 40465}, {656, 7658}, {693, 21127}, {926, 17066}, {1021, 25604}, {1024, 17282}, {1459, 4648}, {3239, 15413}, {3261, 17234}, {3912, 20907}, {4106, 17410}, {4131, 26017}, {4147, 9443}, {4728, 23819}, {4791, 17758}, {4869, 20293}, {4927, 23769}, {6586, 17245}, {7650, 23806}, {9029, 21262}, {26571, 26854}

X(46399) = midpoint of X(i) and X(j) for these {i,j}: {693, 21127}, {4106, 17410}
X(46399) = reflection of X(21195) in X(142)
X(46399) = complement of X(657)
X(46399) = complement of the isogonal conjugate of X(658)
X(46399) = medial-isogonal conjugate of X(13609)
X(46399) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 13609}, {2, 5514}, {6, 35508}, {7, 26932}, {57, 1146}, {63, 40616}, {77, 16596}, {81, 34591}, {85, 124}, {100, 6554}, {109, 1212}, {220, 17426}, {222, 35072}, {241, 1566}, {269, 1086}, {278, 6506}, {279, 11}, {348, 123}, {479, 4904}, {644, 5574}, {651, 9}, {653, 20262}, {658, 10}, {664, 3452}, {738, 3756}, {927, 34852}, {934, 2}, {1014, 4858}, {1020, 1213}, {1042, 16592}, {1086, 34530}, {1088, 116}, {1106, 6377}, {1170, 3119}, {1212, 38973}, {1254, 6627}, {1262, 650}, {1275, 513}, {1332, 42018}, {1407, 1015}, {1414, 5745}, {1415, 16588}, {1426, 6388}, {1427, 115}, {1434, 34589}, {1439, 15526}, {1446, 125}, {1461, 37}, {1462, 17435}, {3668, 8287}, {3669, 46101}, {4350, 40615}, {4551, 38930}, {4554, 1329}, {4564, 4521}, {4565, 40937}, {4566, 1211}, {4569, 141}, {4572, 21244}, {4573, 960}, {4616, 3739}, {4617, 1}, {4619, 24036}, {4625, 21246}, {4626, 142}, {4635, 3741}, {4637, 1125}, {4998, 20317}, {6610, 35091}, {6614, 3752}, {7045, 514}, {7128, 3239}, {7177, 2968}, {7339, 905}, {7365, 5517}, {7366, 16614}, {8269, 17279}, {13149, 5}, {14256, 7358}, {17093, 5511}, {18026, 41883}, {23062, 17059}, {23586, 3900}, {23971, 6129}, {23973, 39063}, {23984, 14298}, {24002, 46100}, {24013, 7658}, {24015, 118}, {24016, 241}, {24027, 6586}, {31615, 3039}, {32668, 8608}, {32674, 20310}, {32714, 6}, {34056, 33573}, {34855, 35094}, {36079, 1427}, {36118, 226}, {36146, 40869}, {36838, 2886}, {37139, 5199}, {37141, 281}, {38459, 40629}, {38859, 40619}, {41353, 16593}, {43932, 6547}
X(46399) = crossdifference of every pair of points on line {2176, 3010}
X(46399) = barycentric product X(514)*X(25242)
X(46399) = barycentric quotient X(25242)/X(190)

X(46400) = ANTICOMPLEMENT OF X(652)

X(46400) lies on these lines: {2, 652}, {7, 4025}, {8, 17894}, {69, 8999}, {320, 350}, {329, 3239}, {340, 520}, {521, 17896}, {522, 16091}, {1021, 23806}, {3664, 23801}, {3738, 4077}, {3900, 20297}, {4105, 17784}, {4329, 20298}, {5712, 6589}, {5905, 25259}, {7658, 9776}, {8676, 21302}, {14298, 25009}, {21173, 23725}, {21189, 23724}, {22383, 26146}, {34408, 43933}

X(46400) = reflection of X(1021) in X(23806)
X(46400) = anticomplement of X(652)
X(46400) = anticomplement of the isogonal conjugate of X(653)
X(46400) = isotomic conjugate of the anticomplement of X(38983)
X(46400) = isotomic conjugate of the isogonal conjugate of X(39199)
X(46400) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2, 34188}, {4, 37781}, {19, 39351}, {34, 4440}, {65, 39352}, {92, 33650}, {107, 92}, {108, 2}, {109, 6360}, {162, 63}, {225, 21221}, {273, 150}, {278, 149}, {331, 21293}, {608, 9263}, {648, 3869}, {651, 20}, {653, 8}, {664, 4329}, {811, 20245}, {934, 347}, {1020, 3152}, {1214, 34186}, {1395, 21224}, {1396, 17154}, {1414, 17134}, {1415, 3164}, {1441, 13219}, {1783, 144}, {1876, 39353}, {1880, 148}, {1897, 329}, {2405, 34550}, {4551, 3151}, {4554, 1370}, {4559, 18666}, {4564, 20294}, {4565, 20222}, {4566, 2897}, {4573, 20243}, {4625, 18659}, {5089, 14732}, {6335, 3436}, {6516, 6527}, {6591, 17036}, {7012, 514}, {7115, 17494}, {7128, 522}, {8750, 3177}, {13149, 3434}, {15742, 4462}, {18026, 69}, {23984, 521}, {24035, 151}, {32674, 192}, {32714, 145}, {34922, 1577}, {36093, 7291}, {36098, 3101}, {36110, 3218}, {36118, 7}, {36127, 5905}, {36146, 3100}, {36797, 18750}, {37136, 10538}, {37141, 280}, {40149, 3448}, {41207, 14956}, {46102, 513}, {46152, 2896}
X(46400) = X(38983)-cross conjugate of X(2)
X(46400) = X(8750)-isoconjugate of X(43724)
X(46400) = crosspoint of X(i) and X(j) for these (i,j): {86, 18026}, {95, 664}, {668, 40424}
X(46400) = crosssum of X(i) and X(j) for these (i,j): {42, 1946}, {51, 663}, {667, 40958}, {8641, 40957}
X(46400) = crossdifference of every pair of points on line {213, 217}
X(46400) = barycentric product X(i)*X(j) for these {i,j}: {76, 39199}, {7412, 15413}
X(46400) = barycentric quotient X(i)/X(j) for these {i,j}: {905, 43724}, {7412, 1783}, {38983, 652}, {39199, 6}

X(46401) = ANTICOMPLEMENT OF X(654)

X(46401) lies on these lines: {2, 654}, {7, 4453}, {150, 928}, {320, 350}, {329, 30565}, {812, 43991}, {850, 924}, {918, 5905}, {926, 3434}, {1639, 31018}, {2826, 9809}, {3738, 36038}, {3909, 21272}, {9034, 40166}, {20525, 32946}, {22086, 24597}, {23725, 23801}

X(46401) = anticomplement of X(654)
X(46401) = anticomplement of the isogonal conjugate of X(655)
X(46401) = isotomic conjugate of the anticomplement of X(38984)
X(46401) = isotomic conjugate of the isogonal conjugate of X(39200)
X(46401) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {80, 37781}, {476, 14213}, {651, 6224}, {655, 8}, {934, 41803}, {1411, 4440}, {2006, 149}, {2161, 39351}, {2222, 2}, {16577, 14731}, {18359, 33650}, {18815, 150}, {23592, 3738}, {32675, 192}, {35174, 69}, {36069, 18662}, {36078, 17479}, {36804, 3436}, {37136, 36944}, {37140, 2975}
X(46401) = X(38984)-cross conjugate of X(2)
X(46401) = crosspoint of X(i) and X(j) for these (i,j): {86, 35174}, {99, 39277}
X(46401) = crosssum of X(i) and X(j) for these (i,j): {42, 8648}, {663, 20962}
X(46401) = crossdifference of every pair of points on line {213, 45937}
X(46401) = barycentric product X(76)*X(39200)
X(46401) = barycentric quotient X(i)/X(j) for these {i,j}: {38984, 654}, {39200, 6}
X(46401) = {X(4106),X(4131)}-harmonic conjugate of X(693)

X(46402) = ANTICOMPLEMENT OF X(657)

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

X(46402) lies on these lines: {2, 657}, {7, 522}, {8, 20907}, {69, 3261}, {320, 350}, {521, 24002}, {926, 4374}, {1024, 3662}, {1459, 3945}, {3664, 21173}, {4380, 17410}, {4449, 41352}, {4474, 36854}, {4648, 6586}, {5232, 20316}, {8058, 30181}, {9029, 21304}, {9443, 20906}, {17096, 23800}, {17300, 21225}, {17494, 21127}, {20294, 30805}, {21195, 45755}, {34399, 43930}

X(46402) = reflection of X(i) in X(j) for these {i,j}: {4380, 17410}, {17494, 21127}, {45755, 21195}
X(46402) = anticomplement of X(657)
X(46402) = anticomplement of the isogonal conjugate of X(658)
X(46402) = isotomic conjugate of the anticomplement of X(14714)
X(46402) = isotomic conjugate of the isogonal conjugate of X(44408)
X(46402) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {7, 37781}, {57, 39351}, {85, 33650}, {99, 18750}, {100, 30695}, {108, 30694}, {109, 3177}, {241, 14732}, {269, 4440}, {279, 149}, {348, 34188}, {651, 144}, {653, 5942}, {658, 8}, {662, 45738}, {664, 329}, {927, 30807}, {934, 2}, {1020, 1654}, {1042, 21220}, {1088, 150}, {1106, 21224}, {1170, 44005}, {1262, 17494}, {1275, 513}, {1407, 9263}, {1414, 63}, {1415, 21218}, {1427, 148}, {1439, 39352}, {1446, 3448}, {1461, 192}, {3668, 21221}, {3669, 17036}, {4554, 3436}, {4564, 4468}, {4566, 2895}, {4569, 69}, {4572, 21286}, {4573, 3869}, {4616, 75}, {4617, 145}, {4625, 20245}, {4626, 7}, {4635, 17135}, {4637, 1}, {4998, 4462}, {6613, 312}, {6614, 3210}, {6648, 43216}, {7045, 514}, {7128, 25259}, {7204, 39345}, {7339, 17496}, {8269, 346}, {13149, 4}, {17093, 34547}, {23586, 3900}, {24013, 4025}, {24015, 152}, {24027, 21225}, {32714, 193}, {34056, 45293}, {34855, 39353}, {36048, 3219}, {36079, 18663}, {36118, 5905}, {36146, 10025}, {36838, 3434}, {41353, 20533}
X(46402) = X(14714)-cross conjugate of X(2)
X(46402) = crosspoint of X(i) and X(j) for these (i,j): {86, 4569}, {664, 40419}
X(46402) = crosssum of X(i) and X(j) for these (i,j): {42, 8641}, {649, 23653}, {663, 21746}, {667, 20978}, {669, 40984}
X(46402) = crossdifference of every pair of points on line {213, 3010}
X(46402) = barycentric product X(i)*X(j) for these {i,j}: {76, 44408}, {693, 37659}, {4219, 15413}, {7192, 45744}
X(46402) = barycentric quotient X(i)/X(j) for these {i,j}: {4219, 1783}, {14714, 657}, {37659, 100}, {44408, 6}, {45744, 3952}
X(46402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 3261, 20293}, {693, 4131, 7192}

X(46403) = ANTICOMPLEMENT OF X(659)

X(46403) = 3 X[2] - 4 X[3837], 9 X[2] - 10 X[30795], 5 X[2] - 4 X[45314], 7 X[2] - 8 X[45340], 5 X[631] - 4 X[44805], 2 X[650] - 3 X[44429], 3 X[659] - 5 X[30795], 5 X[659] - 6 X[45314], 7 X[659] - 12 X[45340], 2 X[676] - 3 X[4927], 4 X[676] - 3 X[44433], 3 X[693] - 2 X[7662], 3 X[1635] - 2 X[4830], 3 X[1635] - 4 X[25380], 4 X[1960] - 5 X[3616], 7 X[3622] - 6 X[25569], 2 X[3716] - 3 X[4728], 2 X[3762] - 3 X[30709], 6 X[3837] - 5 X[30795], 5 X[3837] - 3 X[45314], 7 X[3837] - 6 X[45340], 2 X[4010] - 3 X[21297], 2 X[4458] - 3 X[6545], 2 X[4491] - 3 X[26144], 4 X[4782] - 5 X[27013], 4 X[4806] - 5 X[26798], 2 X[4809] - 3 X[6548], 4 X[4874] - 5 X[26985], 2 X[5592] - 3 X[14432], X[6161] - 3 X[30592], 2 X[9508] - 3 X[36848], 2 X[13246] - 3 X[21204], 3 X[14419] - 4 X[19947], 3 X[16173] - 2 X[41191], 3 X[30574] - 4 X[44314], 25 X[30795] - 18 X[45314], 35 X[30795] - 36 X[45340], 7 X[45314] - 10 X[45340]

X(46403) lies on these lines: {2, 659}, {4, 2826}, {8, 891}, {10, 21385}, {11, 13266}, {145, 21343}, {149, 900}, {291, 812}, {320, 350}, {388, 30725}, {514, 4088}, {522, 4382}, {523, 2528}, {631, 44805}, {649, 24720}, {650, 44429}, {667, 23815}, {669, 26854}, {676, 4927}, {764, 2787}, {804, 5992}, {814, 3777}, {830, 4978}, {876, 30669}, {918, 20539}, {962, 2821}, {1019, 23789}, {1491, 17494}, {1635, 4830}, {1734, 29302}, {1960, 3616}, {2526, 4762}, {2530, 4560}, {2550, 4925}, {2788, 42758}, {2789, 21105}, {2827, 34789}, {2832, 3762}, {3120, 17197}, {3254, 23836}, {3436, 24128}, {3621, 25574}, {3622, 25569}, {3716, 4728}, {3733, 18108}, {3766, 20345}, {3835, 4724}, {3904, 29240}, {3909, 3952}, {4080, 23345}, {4083, 21302}, {4120, 4778}, {4170, 42325}, {4367, 31291}, {4449, 28470}, {4458, 6545}, {4491, 26144}, {4498, 17072}, {4782, 27013}, {4784, 26853}, {4789, 28209}, {4801, 8678}, {4806, 26798}, {4809, 6548}, {4874, 26985}, {4876, 23656}, {4895, 28521}, {4905, 29013}, {4963, 28213}, {4977, 18004}, {5080, 6550}, {5592, 14432}, {6008, 7659}, {6084, 20344}, {6085, 17777}, {6161, 30592}, {6373, 17794}, {9508, 36848}, {13246, 21204}, {14349, 29186}, {14419, 19947}, {16173, 41191}, {17418, 30094}, {18197, 23791}, {19882, 23814}, {20060, 24097}, {20293, 20983}, {21118, 28487}, {21173, 23803}, {21176, 21201}, {21303, 30665}, {21612, 33931}, {23765, 29324}, {23818, 27345}, {23838, 46150}, {30574, 44314}, {30578, 44008}

X(46403) = reflection of X(i) in X(j) for these {i,j}: {145, 21343}, {649, 24720}, {659, 3837}, {667, 23815}, {1019, 23789}, {3733, 40086}, {4498, 17072}, {4560, 2530}, {4724, 3835}, {4830, 25380}, {7192, 21146}, {13266, 11}, {17166, 4978}, {17494, 1491}, {17496, 3777}, {20295, 24719}, {21222, 764}, {21385, 10}, {26853, 4784}, {31291, 4367}, {44433, 4927}
X(46403) = anticomplement of X(659)
X(46403) = circumcircle-of-anticomplementary-triangle-inverse of X(10773)}
X(46403) = anticomplement of the isogonal conjugate of X(660)
X(46403) = anticomplement of the isotomic conjugate of X(4583)
X(46403) = isotomic conjugate of the anticomplement of X(40623)
X(46403) = isotomic conjugate of the isogonal conjugate of X(21003)
X(46403) = polar conjugate of the isogonal conjugate of X(22155)
X(46403) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {6, 39362}, {100, 17794}, {101, 33888}, {190, 20345}, {291, 149}, {292, 4440}, {334, 21293}, {335, 150}, {660, 8}, {668, 20554}, {692, 30667}, {741, 17154}, {805, 38}, {813, 2}, {1911, 9263}, {1922, 21224}, {3252, 39353}, {3862, 39345}, {4518, 33650}, {4557, 39367}, {4562, 69}, {4583, 6327}, {4584, 75}, {4589, 17135}, {4639, 17137}, {4876, 37781}, {5378, 513}, {7077, 39351}, {8684, 32937}, {18047, 25332}, {18829, 17153}, {30664, 24349}, {34067, 192}, {36066, 17140}, {36081, 17165}, {36801, 3436}, {37134, 17152}, {37207, 4441}, {43534, 3448}
X(46403) = X(4583)-Ceva conjugate of X(2)
X(46403) = X(40623)-cross conjugate of X(2)
X(46403) = X(i)-isoconjugate of X(j) for these (i,j): {101, 39979}, {692, 39714}
X(46403) = cevapoint of X(21003) and X(22155)
X(46403) = crosspoint of X(i) and X(j) for these (i,j): {86, 4562}, {668, 673}, {18827, 37205}
X(46403) = crosssum of X(i) and X(j) for these (i,j): {42, 8632}, {649, 20456}, {667, 672}
X(46403) = crossdifference of every pair of points on line {213, 5007}
X(46403) = barycentric product X(i)*X(j) for these {i,j}: {1, 20950}, {76, 21003}, {264, 22155}, {514, 32922}, {693, 33854}, {4583, 40623}
X(46403) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 39979}, {514, 39714}, {20950, 75}, {21003, 6}, {22155, 3}, {29955, 3783}, {32922, 190}, {33854, 100}, {40623, 659}
X(46403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 3837, 2}, {659, 28399, 27675}, {4830, 25380, 1635}, {27015, 27140, 2}, {27075, 27194, 2}, {27294, 27347, 2}

X(46404) = ISOTOMIC CONJUGATE OF X(652)

X(46404) lies on these lines: {75, 24031}, {76, 40701}, {85, 1969}, {92, 18031}, {108, 789}, {109, 22456}, {226, 46273}, {264, 21666}, {273, 31002}, {278, 32020}, {331, 20568}, {349, 33805}, {653, 799}, {658, 3261}, {664, 811}, {668, 18026}, {1441, 14009}, {1813, 42405}, {1897, 46107}, {4554, 6335}, {4593, 32674}, {6063, 7017}, {16089, 16091}, {17984, 17985}, {18033, 46108}, {40017, 40149}, {46111, 46277}

X(46404) = isotomic conjugate of X(652)
X(46404) = polar conjugate of X(663)
X(46404) = isotomic conjugate of the isogonal conjugate of X(653)
X(46404) = polar conjugate of the isotomic conjugate of X(4572)
X(46404) = polar conjugate of the isogonal conjugate of X(664)
X(46404) = X(6331)-Ceva conjugate of X(4554)
X(46404) = X(i)-cross conjugate of X(j) for these (i,j): {664, 4572}, {3261, 1969}, {4391, 44130}, {6332, 75}, {18134, 4998}, {21957, 10}, {35519, 6063}, {46110, 264}
X(46404) = cevapoint of X(i) and X(j) for these (i,j): {65, 21348}, {75, 6332}, {85, 3261}, {92, 46107}, {264, 46110}, {514, 17861}, {653, 664}, {693, 17862}, {1441, 4391}, {1577, 18692}, {3239, 17860}, {6335, 18026}, {7017, 35519}
X(46404) = trilinear pole of line {75, 225}
X(46404) = X(i)-isoconjugate of X(j) for these (i,j): {3, 3063}, {6, 1946}, {21, 3049}, {25, 36054}, {31, 652}, {32, 521}, {41, 1459}, {48, 663}, {55, 22383}, {78, 1919}, {108, 39687}, {184, 650}, {212, 649}, {213, 23189}, {219, 667}, {222, 8641}, {228, 7252}, {283, 798}, {284, 810}, {294, 23225}, {332, 1924}, {345, 1980}, {512, 2193}, {520, 2204}, {522, 9247}, {560, 6332}, {577, 18344}, {603, 657}, {607, 23224}, {644, 22096}, {647, 2194}, {669, 1812}, {692, 7117}, {822, 2299}, {884, 20752}, {905, 2175}, {906, 3271}, {926, 32658}, {1172, 39201}, {1402, 23090}, {1409, 21789}, {1415, 3270}, {1437, 3709}, {1501, 35518}, {1802, 43924}, {1814, 8638}, {1977, 4571}, {2170, 32656}, {2200, 3737}, {2206, 8611}, {2208, 10397}, {2212, 4091}, {2310, 32660}, {2637, 34078}, {2638, 32674}, {3248, 4587}, {4025, 9447}, {4105, 7099}, {4391, 14575}, {4516, 32661}, {4631, 23216}, {4895, 32659}, {6056, 6591}, {7004, 32739}, {7107, 21761}, {9448, 15413}, {9454, 23696}, {14395, 40352}, {14585, 44426}, {14936, 36059}, {15416, 41280}, {23614, 23985}, {32727, 33572}
X(46404) = barycentric product X(i)*X(j) for these {i,j}: {4, 4572}, {34, 6386}, {75, 18026}, {76, 653}, {85, 6335}, {92, 4554}, {108, 561}, {109, 18022}, {190, 331}, {225, 670}, {226, 6331}, {264, 664}, {273, 668}, {278, 1978}, {305, 36127}, {307, 6528}, {312, 13149}, {318, 4569}, {349, 648}, {646, 1847}, {651, 1969}, {658, 7017}, {799, 40149}, {811, 1441}, {823, 1231}, {1275, 46110}, {1502, 32674}, {1783, 20567}, {1813, 18027}, {1861, 46135}, {1880, 4602}, {1897, 6063}, {3261, 46102}, {3596, 36118}, {4552, 44129}, {4566, 44130}, {4620, 14618}, {4625, 41013}, {4998, 46107}, {5236, 36803}, {7012, 40495}, {7101, 36838}, {8750, 41283}, {18833, 46152}, {24032, 35518}, {28659, 32714}, {34085, 46108}, {40701, 44327}
X(46404) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1946}, {2, 652}, {4, 663}, {7, 1459}, {19, 3063}, {27, 7252}, {29, 21789}, {33, 8641}, {34, 667}, {57, 22383}, {59, 32656}, {63, 36054}, {65, 810}, {73, 39201}, {75, 521}, {76, 6332}, {77, 23224}, {85, 905}, {86, 23189}, {92, 650}, {99, 283}, {100, 212}, {107, 2299}, {108, 31}, {109, 184}, {158, 18344}, {162, 2194}, {190, 219}, {225, 512}, {226, 647}, {264, 522}, {273, 513}, {278, 649}, {281, 657}, {286, 3737}, {307, 520}, {318, 3900}, {321, 8611}, {329, 10397}, {331, 514}, {333, 23090}, {342, 6129}, {348, 4091}, {349, 525}, {514, 7117}, {521, 2638}, {522, 3270}, {561, 35518}, {608, 1919}, {644, 1802}, {645, 2327}, {646, 3692}, {648, 284}, {651, 48}, {652, 39687}, {653, 6}, {658, 222}, {662, 2193}, {664, 3}, {668, 78}, {670, 332}, {693, 7004}, {799, 1812}, {811, 21}, {823, 1172}, {883, 1818}, {927, 36057}, {934, 603}, {1016, 4587}, {1020, 1409}, {1025, 20752}, {1119, 43924}, {1214, 822}, {1231, 24018}, {1262, 32660}, {1275, 1813}, {1309, 2342}, {1331, 6056}, {1332, 2289}, {1395, 1980}, {1400, 3049}, {1414, 1437}, {1415, 9247}, {1434, 7254}, {1441, 656}, {1442, 23226}, {1443, 22379}, {1447, 22384}, {1457, 23220}, {1458, 23225}, {1783, 41}, {1813, 577}, {1826, 3709}, {1847, 3669}, {1855, 10581}, {1861, 926}, {1870, 8648}, {1874, 4455}, {1877, 1960}, {1880, 798}, {1897, 55}, {1940, 21761}, {1943, 22382}, {1969, 4391}, {1978, 345}, {1981, 1951}, {2052, 3064}, {2356, 8638}, {2481, 23696}, {2973, 21132}, {3064, 14936}, {3212, 22090}, {3261, 26932}, {3676, 3937}, {3699, 1260}, {3732, 7124}, {3882, 22074}, {3888, 20753}, {3911, 22086}, {3952, 2318}, {4025, 1364}, {4033, 3694}, {4077, 18210}, {4242, 2361}, {4358, 14418}, {4391, 34591}, {4551, 228}, {4552, 71}, {4554, 63}, {4559, 2200}, {4561, 1259}, {4563, 6514}, {4564, 906}, {4566, 73}, {4569, 77}, {4572, 69}, {4573, 1790}, {4589, 1808}, {4605, 2197}, {4617, 7099}, {4620, 4558}, {4625, 1444}, {4626, 7053}, {4998, 1331}, {5125, 8676}, {5236, 665}, {5930, 42658}, {6063, 4025}, {6331, 333}, {6332, 35072}, {6335, 9}, {6386, 3718}, {6516, 255}, {6517, 1092}, {6528, 29}, {6648, 2359}, {6649, 3955}, {6742, 8606}, {7012, 692}, {7017, 3239}, {7035, 4571}, {7045, 36059}, {7046, 4105}, {7101, 4130}, {7115, 32739}, {7128, 1415}, {7176, 22093}, {7182, 4131}, {7257, 1792}, {7282, 2605}, {7649, 3271}, {8736, 4079}, {8750, 2175}, {9312, 22091}, {13138, 2188}, {13149, 57}, {14206, 14395}, {14594, 7085}, {14618, 21044}, {15352, 8748}, {15418, 6518}, {15466, 14331}, {15742, 3939}, {17136, 22361}, {17496, 38344}, {17862, 40628}, {17906, 2347}, {17923, 654}, {17924, 2170}, {17985, 5075}, {18020, 4636}, {18022, 35519}, {18026, 1}, {18027, 46110}, {18816, 37628}, {18831, 35196}, {20567, 15413}, {21272, 22072}, {21609, 24562}, {21666, 23615}, {22464, 8677}, {23067, 4055}, {23703, 23202}, {23710, 6139}, {23984, 32674}, {24002, 3942}, {24006, 4516}, {24019, 2204}, {24031, 23614}, {24032, 108}, {24035, 2182}, {27808, 3710}, {28659, 15416}, {28660, 15411}, {30545, 25098}, {30806, 14414}, {31623, 1021}, {32660, 14585}, {32674, 32}, {32714, 604}, {34085, 1814}, {34388, 4064}, {35154, 17973}, {35174, 1807}, {35312, 22053}, {35338, 22079}, {35516, 39471}, {35518, 24031}, {35519, 2968}, {36038, 35014}, {36110, 34858}, {36118, 56}, {36124, 884}, {36127, 25}, {36146, 32658}, {36797, 2328}, {36838, 7177}, {37136, 14578}, {37137, 7116}, {37790, 1635}, {38461, 14413}, {38462, 4895}, {39060, 2636}, {39294, 32641}, {40117, 7118}, {40149, 661}, {40152, 32320}, {40495, 17880}, {40701, 14837}, {40717, 3716}, {41013, 4041}, {41207, 2249}, {43040, 22092}, {43923, 3248}, {43924, 22096}, {44129, 4560}, {44130, 7253}, {44146, 14432}, {44327, 268}, {44426, 2310}, {44721, 4546}, {46102, 101}, {46106, 14400}, {46107, 11}, {46109, 1639}, {46110, 1146}, {46135, 31637}, {46152, 1964}, {46153, 20775}, {46177, 22368}, {46254, 4612}
X(46404) = {X(6335),X(13149)}-harmonic conjugate of X(4554)

X(46405) = ISOTOMIC CONJUGATE OF X(654)

X(46405) lies on these lines: {655, 799}, {668, 35174}, {789, 2222}, {850, 4998}, {2006, 32020}, {3261, 4554}, {4593, 32675}, {18031, 18359}, {18815, 31002}, {20566, 35517}, {20920, 21587}

X(46405) = isotomic conjugate of X(654)
X(46405) = isotomic conjugate of the isogonal conjugate of X(655)
X(46405) = X(i)-cross conjugate of X(j) for these (i,j): {3904, 75}, {3936, 4998}
X(46405) = X(i)-isoconjugate of X(j) for these (i,j): {6, 8648}, {31, 654}, {32, 3738}, {36, 3063}, {55, 21758}, {512, 4282}, {560, 3904}, {607, 22379}, {649, 2361}, {663, 7113}, {667, 2323}, {1919, 4511}, {1980, 32851}, {1983, 3271}, {2150, 42666}, {2175, 3960}, {2194, 21828}, {3049, 17515}, {3724, 7252}, {4453, 9447}, {9247, 44428}
X(46405) = cevapoint of X(i) and X(j) for these (i,j): {75, 3904}, {514, 24209}, {850, 3936}, {3262, 4391}, {35174, 36804}
X(46405) = trilinear pole of line {75, 311} (the isotomic conjugate of the isogonal conjugate of line X(1)X(5))
X(46405) = barycentric product X(i)*X(j) for these {i,j}: {75, 35174}, {76, 655}, {80, 4572}, {85, 36804}, {561, 2222}, {664, 20566}, {668, 18815}, {1411, 6386}, {1502, 32675}, {1978, 2006}, {4554, 18359}, {4625, 15065}, {35139, 40999}
X(46405) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8648}, {2, 654}, {12, 42666}, {57, 21758}, {75, 3738}, {76, 3904}, {77, 22379}, {80, 663}, {85, 3960}, {100, 2361}, {190, 2323}, {226, 21828}, {264, 44428}, {311, 6369}, {349, 4707}, {651, 7113}, {655, 6}, {662, 4282}, {664, 36}, {668, 4511}, {811, 17515}, {1411, 667}, {1807, 1946}, {1978, 32851}, {2006, 649}, {2161, 3063}, {2222, 31}, {2594, 14270}, {3904, 35128}, {4453, 3025}, {4551, 3724}, {4552, 2245}, {4554, 3218}, {4564, 1983}, {4566, 1464}, {4569, 1443}, {4572, 320}, {4585, 34544}, {6063, 4453}, {6358, 2610}, {6369, 41218}, {6740, 21789}, {14213, 2600}, {14584, 1960}, {14616, 3737}, {14628, 1635}, {15065, 4041}, {16577, 2624}, {18026, 1870}, {18359, 650}, {18815, 513}, {20566, 522}, {23592, 32675}, {24624, 7252}, {32675, 32}, {34388, 6370}, {35139, 3615}, {35174, 1}, {36804, 9}, {36910, 657}, {37140, 2150}, {40999, 526}, {41226, 9404}

X(46406) = ISOTOMIC CONJUGATE OF X(657)

X(46406) lies on these lines: {75, 24010}, {85, 17451}, {279, 32020}, {658, 799}, {664, 4449}, {668, 883}, {789, 934}, {811, 4625}, {1088, 31002}, {1446, 40017}, {1461, 4593}, {3732, 34085}, {4554, 36838}, {6063, 34387}, {20567, 20925}

X(46406) = isotomic conjugate of X(657)
X(46406) = isotomic conjugate of the isogonal conjugate of X(658)
X(46406) = X(i)-cross conjugate of X(j) for these (i,j): {3239, 75}, {3261, 6063}, {4554, 4572}, {15413, 310}, {17234, 4998}, {18153, 31625}, {20946, 7035}, {30805, 7182}
X(46406) = cevapoint of X(i) and X(j) for these (i,j): {75, 3239}, {514, 3673}, {693, 20905}, {3261, 6063}, {3676, 41777}, {4391, 20880}, {4554, 4569}, {7182, 30805}
X(46406) = trilinear pole of line {75, 1088} (the isotomic conjugate of the isogonal conjugate of the Soddy line)
X(46406) = X(i)-isoconjugate of X(j) for these (i,j): {6, 8641}, {31, 657}, {32, 3900}, {41, 663}, {55, 3063}, {200, 1919}, {213, 21789}, {220, 667}, {294, 8638}, {346, 1980}, {513, 14827}, {522, 9447}, {560, 3239}, {604, 4105}, {607, 1946}, {649, 1253}, {650, 2175}, {652, 2212}, {669, 2287}, {692, 14936}, {798, 2328}, {810, 2332}, {1021, 1918}, {1043, 1924}, {1333, 4524}, {1397, 4130}, {1415, 3022}, {1461, 24012}, {1501, 4397}, {1576, 36197}, {1977, 4578}, {2194, 3709}, {2205, 7253}, {2206, 4171}, {2310, 32739}, {3049, 4183}, {4148, 14598}, {4391, 9448}, {4435, 18265}, {4477, 7104}, {4612, 7063}, {6059, 36054}, {6139, 18889}, {6602, 43924}, {7071, 22383}, {9455, 28132}, {15416, 44162}
X(46406) = barycentric product X(i)*X(j) for these {i,j}: {7, 4572}, {75, 4569}, {76, 658}, {85, 4554}, {109, 41283}, {269, 6386}, {279, 1978}, {304, 13149}, {305, 36118}, {310, 4566}, {312, 36838}, {313, 4616}, {321, 4635}, {349, 4573}, {561, 934}, {646, 23062}, {651, 20567}, {664, 6063}, {668, 1088}, {670, 3668}, {799, 1446}, {1020, 6385}, {1042, 4609}, {1275, 3261}, {1427, 4602}, {1441, 4625}, {1461, 1502}, {3596, 4626}, {4397, 24011}, {4617, 28659}, {4637, 27801}, {6614, 40363}, {7045, 40495}, {7182, 18026}, {7204, 46132}, {9436, 46135}, {32714, 40364}, {34085, 40704}
X(46406) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8641}, {2, 657}, {7, 663}, {8, 4105}, {10, 4524}, {57, 3063}, {75, 3900}, {76, 3239}, {77, 1946}, {85, 650}, {86, 21789}, {99, 2328}, {100, 1253}, {101, 14827}, {108, 2212}, {109, 2175}, {142, 10581}, {190, 220}, {226, 3709}, {269, 667}, {273, 18344}, {274, 1021}, {279, 649}, {310, 7253}, {312, 4130}, {321, 4171}, {331, 3064}, {348, 652}, {349, 3700}, {479, 43924}, {514, 14936}, {522, 3022}, {555, 6729}, {561, 4397}, {644, 6602}, {646, 728}, {648, 2332}, {651, 41}, {653, 607}, {658, 6}, {664, 55}, {668, 200}, {670, 1043}, {693, 2310}, {799, 2287}, {811, 4183}, {883, 2340}, {927, 2195}, {934, 31}, {1020, 213}, {1042, 669}, {1088, 513}, {1106, 1980}, {1231, 8611}, {1262, 32739}, {1269, 4990}, {1275, 101}, {1323, 6139}, {1332, 1802}, {1407, 1919}, {1414, 2194}, {1415, 9447}, {1427, 798}, {1434, 7252}, {1439, 810}, {1441, 4041}, {1443, 8648}, {1446, 661}, {1458, 8638}, {1461, 32}, {1577, 36197}, {1847, 6591}, {1897, 7071}, {1909, 4477}, {1920, 4529}, {1921, 4148}, {1978, 346}, {3239, 35508}, {3261, 1146}, {3264, 4528}, {3596, 4163}, {3668, 512}, {3671, 8653}, {3673, 17115}, {3676, 3271}, {3699, 480}, {3732, 30706}, {3900, 24012}, {4025, 3270}, {4033, 4515}, {4077, 4516}, {4091, 39687}, {4131, 2638}, {4320, 8646}, {4350, 8642}, {4358, 14427}, {4391, 3119}, {4397, 24010}, {4552, 1334}, {4554, 9}, {4561, 1260}, {4563, 2327}, {4566, 42}, {4569, 1}, {4572, 8}, {4573, 284}, {4601, 7259}, {4605, 1500}, {4610, 7054}, {4616, 58}, {4617, 604}, {4619, 23990}, {4620, 5546}, {4623, 1098}, {4624, 34820}, {4625, 21}, {4626, 56}, {4635, 81}, {4637, 1333}, {4847, 6607}, {4998, 3939}, {5249, 33525}, {6063, 522}, {6173, 17425}, {6331, 2322}, {6335, 7079}, {6354, 4079}, {6359, 21761}, {6386, 341}, {6516, 212}, {6517, 6056}, {6606, 10482}, {6614, 1397}, {6649, 2330}, {7035, 4578}, {7045, 692}, {7056, 1459}, {7177, 22383}, {7182, 521}, {7183, 36054}, {7196, 3287}, {7204, 788}, {7205, 3907}, {7216, 3121}, {7243, 4501}, {7340, 4636}, {7365, 2484}, {8269, 7084}, {9436, 926}, {10030, 4435}, {10481, 2488}, {13149, 19}, {15413, 34591}, {15467, 23289}, {17078, 654}, {17095, 9404}, {17206, 23090}, {18026, 33}, {18031, 28132}, {18033, 3716}, {19804, 4827}, {20567, 4391}, {20880, 6608}, {23062, 3669}, {23586, 1461}, {23989, 42462}, {24002, 2170}, {24011, 934}, {24015, 910}, {27808, 4082}, {30805, 35072}, {30806, 14392}, {31625, 6558}, {32714, 1973}, {33765, 21007}, {34018, 1024}, {34085, 294}, {34387, 23615}, {35157, 4845}, {35171, 42064}, {35312, 2293}, {35341, 8551}, {35519, 4081}, {36079, 33581}, {36118, 25}, {36127, 6059}, {36803, 6559}, {36838, 57}, {37139, 18889}, {37141, 7118}, {37757, 22108}, {38459, 8645}, {39126, 4162}, {40364, 15416}, {40495, 24026}, {40702, 14298}, {41283, 35519}, {41353, 2223}, {43932, 3248}, {44129, 17926}, {44327, 7367}, {46107, 42069}, {46135, 14942}

X(46407) = CIRCUMCIRCLE-INVERSE OF X(649)

X(46407) lies on the Brocard circle and these lines: {2, 5991}, {3, 649}, {6, 31}, {901, 38884}, {1252, 3730}, {1316, 24275}, {1331, 10756}, {2265, 14439}, {3735, 4414}, {4813, 36280}, {4988, 36205}, {20999, 46148}, {23988, 32739}, {24047, 41405}, {39640, 43079}

X(46407) = circumcircle-inverse of X(649)
X(46407) = psi-transform of X(101)
X(46407) = crossdifference of every pair of points on line {514, 3011}
X(46407) = isogonal conjugate of antitomic conjugate of X(675)
X(46407) = X(675)-of-1st-Brocard-triangle

X(46408) = CIRCUMCIRCLE-INVERSE OF X(650)

X(46408) lies on these lines: {3, 650}, {19, 25}, {1465, 14878}, {5514, 6174}, {14667, 14936}, {22108, 41155}

X(46408) = circumcircle-inverse of X(650)
X(46408) = Stevanovic-circle-inverse of X(3)

X(46409) = CIRCUMCIRCLE-INVERSE OF X(659)

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

X(46409) = (X[104] - 3 X[38694], X[1292] - 3 X[34474], X[5540] + 3 X[15015], X[10743] - 3 X[38752], 2 X[11730] - 3 X[34123]

X(46409) = lies on these lines: {2, 11}, {3, 659}, {104, 38694}, {214, 2809}, {952, 38603}, {1083, 3887}, {1292, 34474}, {1358, 6516}, {2795, 35204}, {2802, 11716}, {2836, 34583}, {5150, 24494}, {5220, 14191}, {5511, 5840}, {5540, 15015}, {10743, 38752}, {11730, 34123}, {28915, 33814}

X(46409) = midpoint of X(100) and X(105)
X(46409) = reflection of X(i) in X(j) for these {i,j}: {11, 6714}, {120, 3035}
X(46409) = complement of X(10773)
X(46409) = circumcircle-inverse of X(659)
X(46409) = psi-transform of X(3573)

X(46410) = CIRCUMCIRCLE-INVERSE OF X(663)

X(46410) lies on the Brocard circle and these lines: {3, 663}, {6, 41}, {1262, 10571}, {1813, 10764}, {9317, 19950}, {24248, 24279}

X(46410) = circumcircle-inverse of X(663)
X(46410) = psi-transform of X(109)
X(46410) = X(1311)-of-1st-Brocard-triangle

X(46411) = PERSPECTOR OF THE 1ST LOZADA CONIC

X(46412) = X(3)X(6749)∩X(394)X(549)

X(46412) lies on these lines: {3, 6749}, {97, 3524}, {376, 31626}, {394, 549}, {631, 14919}, {1073, 5054}, {3926, 44148}, {15701, 36609}

X(46412) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3)}} and {{A, B, C, X(4), X(549)}}

X(46413) = X(114)X(34349)∩X(2679)X(2881)

X(46413) lies on the nine-point circle and these lines: {114, 34349}, {804, 33504}, {2679, 2881}, {2794, 41175}, {2799, 36471}

X(46414) = X(526)X(35588)∩X(17702)X(42424)

X(46414) lies on the nine-point circle and these lines: {526, 35588}, {17702, 42424}

X(46415) = COMPLEMENT OF X(14733)

X(46415) lies on the nine-point circle and these lines: {2, 14733}, {11, 3900}, {115, 656}, {116, 46100}, {118, 3814}, {119, 971}, {120, 5123}, {124, 17072}, {513, 5514}, {517, 44993}, {1566, 3126}, {1861, 25640}, {2550, 33331}, {3820, 31841}

X(46415) = complement of X(14733)
X(46415) = complementary conjugate of X(6366)
X(46415) = center of the circumconic {{A, B, C, X(4), X(10426)}}
X(46415) = Poncelet point of X(10426)

X(46416) = X(114)X(35282)∩X(125)X(40550)

X(46416) lies on the nine-point circle and these lines: {114, 35282}, {125, 40550}, {3258, 14417}, {6334, 38971}, {7473, 42426}, {16177, 45689}, {23967, 38975}, {24284, 36471}, {32313, 35582}

X(46417) = X(525)X(22239)∩X(1301)X(39447)

X(46418) = X(514)X(1309)∩X(653)X(1845)

X(46419) = X(6)X(1012)∩X(73)X(4304)

X(46419) lies on these lines: {6,1012}, {30,34586}, {73,4304}, {946,1201}, {1777,3157}, {2650,2800}, {2823,18675}, {7004,10122}, {22300,23845}, {33811,37195}

X(46420) = (name pending)

Let A'B'C' be the intouch triangle, Oa the circumcenter of AB'C' and Ac, Ab the reflections of Oa in A'B', A'C', resp. Define Ba, Bc, Cb, Ca cyclically. The six points lie on a conic centered at X(942). Its perspector is X(46420)

X(46421) = X(2)X(175)∩X(8)X(20)

X(46421) lies on the cubic K332 and these lines: {2, 175}, {8, 20}, {144, 13387}, {176, 6360}, {190, 13458}, {200, 31563}, {329, 31547}, {1271, 4329}, {2324, 3084}, {3666, 19066}, {4641, 19065}, {6347, 20262}, {11680, 16028}, {13425, 14829}, {17134, 32793}, {17594, 26300}, {20223, 31550}

X(46421) = anticomplement of X(13390)
X(46421) = anticomplement of the isogonal conjugate of X(5414)
X(46421) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 176}, {55, 13386}, {212, 46413}, {606, 175}, {1805, 75}, {2066, 31552}, {2067, 7}, {5414, 8}, {7090, 21270}, {7133, 4}, {13388, 3434}, {30557, 69}
X(46421) = X(i)-Ceva conjugate of X(j) for these (i,j): {329, 46422}, {31547, 144}
X(46421) = barycentric product X(75)*X(32556)
X(46421) = barycentric quotient X(i)/X(j) for these {i,j}: {30557, 34907}, {32556, 1}, {34910, 14121}
X(46421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 63, 46422}, {40, 189, 46422}, {13388, 14121, 2}

X(46422) = X(2)X(176)∩X(8)X(20)

X(46422) lies on the cubic K332 and these lines: {2, 176}, {8, 20}, {69, 13461}, {144, 13386}, {165, 8984}, {175, 6360}, {190, 13425}, {200, 31564}, {329, 31548}, {1270, 4329}, {2324, 3083}, {3666, 19065}, {4641, 19066}, {6348, 20262}, {11681, 16028}, {13458, 14829}, {17134, 32794}, {17594, 26301}, {20223, 31549}

X(46422) = anticomplement of X(1659)
X(46422) = anticomplement of the isogonal conjugate of X(2066)
X(46422) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {48, 175}, {55, 13387}, {212, 46412}, {605, 176}, {1806, 75}, {2066, 8}, {5414, 31551}, {6502, 7}, {13389, 3434}, {14121, 21270}, {30556, 69}, {42013, 4}
X(46422) = X(i)-Ceva conjugate of X(j) for these (i,j): {329, 46421}, {31548, 144}
X(46422) = cevapoint of X(40) and X(38004)
X(46422) = barycentric product X(75)*X(32555)
X(46422) = barycentric quotient X(i)/X(j) for these {i,j}: {30556, 34908}, {32555, 1}, {34909, 7090}
X(46422) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 63, 46421}, {40, 189, 46421}, {7090, 13389, 2}

X(46423) = ISOGONAL CONJUGATE OF X(7728)

X(46423) lies on these lines: {3, 34209}, {4, 46424}, {50, 15262}, {186, 34170}, {477, 6344}, {2071, 5663}, {3520, 14385}, {10564, 31941}, {12028, 38701}, {36164, 43917}

X(46423) = reflection of X(4) in X(46424)
X(46423) = isogonal conjugate of X(7728)
X(46423) = cevapoint of X(3) and X(12302)
X(46423) = X(i)-vertex conjugate of-X(j) for these (i, j): {4, 30}, {64, 186}
X(46423) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(50)}} and {{A, B, C, X(4), X(2071)}}

X(46424) = X(5)X(14385)∩X(2072)X(5663)

X(46424) lies on these lines: {4, 46423}, {5, 14385}, {2072, 5663}, {16177, 17854}

X(46425) = X(115)X(122)∩X(230)X(231)

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

X(46425) lies on these lines: {6, 1636}, {25, 2881}, {111, 1297}, {112, 1301}, {115, 122}, {186, 15292}, {230, 231}, {526, 686}, {1196, 2508}, {2079, 3569}, {2395, 40347}, {5972, 13526}, {6128, 45319}, {7663, 10278}, {8552, 14566}, {8770, 14998}, {14346, 32320}, {15421, 41079}, {23292, 45325}, {44564, 44817}

X(46425) = midpoint of X(i) and X(j) for these {i, j}: {25, 42665}, {15421, 41079}
X(46425) = complement of the isogonal conjugate of X(32715)
X(46425) = crossdifference of every pair of points on line {X(3), X(113)}
X(46425) = crosspoint of X(i) and X(j) for these (i, j): {2, 1304}, {107, 2986}, {112, 34570}
X(46425) = crosssum of X(i) and X(j) for these (i, j): {6, 9033}, {30, 6587}, {520, 3003}
X(46425) = X(2)-Ceva conjugate of-X(16177)
X(46425) = X(i)-complementary conjugate of-X(j) for these (i, j): (31, 16177), (560, 39008), (1304, 2887)
X(46425) = X(i)-Dao conjugate of X(j) for these (i, j): (403, 16237), (1084, 11744)
X(46425) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 22239}, {662, 11744}, {823, 40082}
X(46425) = X(i)-line conjugate of-X(j) for these (i, j): (112, 1624), (115, 122), (1301, 1624)
X(46425) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 22239), (512, 11744)
X(46425) = perspector of the circumconic {{A, B, C, X(4), X(2071)}}
X(46425) = center of the circumconic {{A, B, C, X(15421), X(41079)}}
X(46425) = intersection, other than A, B, C, of circumconics {{A, B, C, X(111), X(16318)}} and {{A, B, C, X(112), X(6587)}}
X(46425) = midpoint of hyperbola {{A,B,C,X(2),X(3)}} intercepts of the orthic axis
X(46425) = barycentric product X(i)*X(j) for these {i, j}: {520, 34170}, {523, 2071}, {525, 15262}, {1304, 16177}
X(46425) = barycentric quotient X(i)/X(j) for these (i, j): (25, 22239), (512, 11744), (2071, 99)
X(46425) = trilinear product X(i)*X(j) for these {i, j}: {656, 15262}, {661, 2071}, {822, 34170}
X(46425) = trilinear quotient X(i)/X(j) for these (i, j): (19, 22239), (661, 11744), (822, 40082), (2071, 662)
X(46425) = {X(647), X(6587)}-harmonic conjugate of X(16040)

X(46426) = ISOGONAL CONJUGATE OF X(5972)

X(46426) lies on these lines: {4, 39190}, {6, 38861}, {232, 15262}, {250, 20975}, {264, 2452}, {325, 5159}, {511, 2071}, {523, 11596}, {648, 34978}, {974, 2693}, {1316, 9307}, {1593, 35908}, {2407, 46087}, {2715, 46252}, {3091, 14356}, {5020, 5968}, {6530, 10151}, {11007, 22468}, {13479, 30716}, {19189, 37917}, {34233, 36176}

X(46426) = isogonal conjugate of X(5972)
X(46426) = antigonal conjugate of the isogonal conjugate of X(14673)
X(46426) = Cevapoint of X(i) and X(j) for these (i, j): {6, 20975}, {523, 34978}
X(46426) = crosssum of X(402) and X(31945)
X(46426) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 17882), (136, 46371)
X(46426) = X(i)-isoconjugate-of-X(j) for these {i, j}: {2, 17468}, {6, 17882}
X(46426) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 17882), (31, 17468)
X(46426) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(10422)}} and {{A, B, C, X(3), X(10151)}}
X(46426) = trilinear pole of the line {2079, 3569}
X(46426) = 1st Saragossa point of X(250)
X(46426) = barycentric quotient X(i)/X(j) for these (i, j): (1, 17882), (31, 17468)
X(46426) = trilinear quotient X(i)/X(j) for these (i, j): (2, 17882), (6, 17468)

X(46427) = ISOGONAL CONJUGATE OF X(14643)

Let P and U be the intersections of the 1st and 2nd Droz-Farny circles. Then X(46427) is the cevapoint of P and U. (Randy Hutson, January 11, 2022)

X(46427) lies on these lines: {5, 14611}, {137, 18809}, {974, 46423}, {1154, 2071}, {11062, 15262}, {14865, 38937}

X(46427) = isogonal conjugate of X(14643)
X(46427) = crosssum of X(5) and X(33505)
X(46427) = trilinear pole of line X(2081)X(46425)
X(46427) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(5627)}} and {{A, B, C, X(4), X(2071)}}
X(46427) = barycentric quotient X(1989)/X(10688)
X(46427) = trilinear quotient X(2166)/X(10688)

X(46428) = ISOGONAL CONJUGATE OF X(38794)

X(46428) = isogonal conjugate of X(38794)
X(46428) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(2071)}} and {{A, B, C, X(6), X(186)}}

X(46429) = ISOGONAL CONJUGATE OF X(16111)

X(46429) = isogonal conjugate of X(16111)
X(46429) = anticomplement of complementary conjugate of X(46686)
X(46429) = X(i)-vertex conjugate of-X(j) for these (i, j): {3, 10419}, {250, 46423}
X(46429) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(2071)}} and {{A, B, C, X(24), X(30)}}

X(46430) = X(4)X(974)∩X(125)X(389)

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

X(46430) = X(3)+2*X(12236), X(4)+2*X(974), X(4)-4*X(11746), 2*X(4)+X(17854), 4*X(5)-X(12825), X(52)+2*X(6699), X(74)+2*X(1112), X(74)+5*X(3567), X(74)-4*X(16270), X(110)-4*X(9826), X(110)-7*X(15043), X(974)+2*X(11746), 4*X(974)-X(17854), 2*X(1112)-5*X(3567), X(1112)+2*X(16270), X(1511)-4*X(12006), X(1511)+2*X(13358), 5*X(3567)+4*X(16270), 8*X(11746)+X(17854), 2*X(12006)+X(13358)

X(46430) lies on these lines: {3, 12236}, {4, 974}, {5, 12825}, {6, 15463}, {24, 13198}, {51, 2777}, {52, 6699}, {54, 1511}, {74, 1112}, {110, 6642}, {113, 5462}, {125, 389}, {143, 12041}, {182, 22109}, {185, 7687}, {186, 44668}, {265, 14708}, {381, 5640}, {511, 38727}, {526, 42731}, {542, 16223}, {568, 15061}, {569, 12893}, {631, 41673}, {973, 10821}, {1154, 34128}, {1199, 3043}, {1503, 16227}, {1539, 10095}, {1899, 44795}, {2781, 14853}, {2854, 14912}, {2931, 36752}, {2935, 10982}, {3047, 20771}, {3060, 15055}, {3448, 7544}, {3518, 15647}, {5050, 14914}, {5446, 16111}, {5504, 17928}, {5562, 6723}, {5622, 39588}, {5876, 11704}, {5889, 12358}, {5892, 38793}, {5943, 36518}, {5972, 21649}, {6102, 7723}, {6241, 12133}, {6243, 38728}, {6746, 7730}, {6776, 32246}, {7401, 18932}, {7722, 15081}, {9729, 11800}, {9730, 12022}, {9781, 10721}, {9786, 19457}, {9934, 10594}, {10110, 13202}, {10111, 14516}, {10113, 13630}, {10574, 10733}, {10990, 11807}, {11245, 32423}, {11402, 32609}, {11412, 13416}, {11424, 13293}, {11432, 19504}, {11438, 32607}, {11557, 16003}, {11561, 13365}, {11562, 36253}, {11598, 14865}, {11709, 31760}, {12052, 46045}, {12140, 34224}, {12228, 36753}, {12244, 15151}, {12273, 15028}, {12281, 13148}, {12284, 15024}, {12295, 40647}, {13160, 46085}, {13201, 15057}, {13321, 15041}, {13366, 17701}, {13417, 20417}, {13474, 17856}, {13754, 23515}, {14049, 34564}, {14831, 45311}, {15063, 41671}, {15085, 15805}, {15118, 19161}, {16625, 38729}, {18560, 43904}, {20379, 38898}, {21663, 32411}, {23315, 45089}, {25487, 37472}, {31763, 32311}, {32111, 44084}, {32191, 40949}, {33547, 43817}, {37853, 45186}, {38723, 40280}

X(46430) = midpoint of X(i) and X(j) for these {i, j}: {568, 15061}, {3060, 15055}, {5890, 14644}
X(46430) = reflection of X(i) in X(j) for these (i, j): (12824, 16222), (14644, 12099), (16222, 5946), (36518, 5943), (38793, 5892)
X(46430) = crosssum of X(3) and X(14643)
X(46430) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 974, 17854), (4, 17854, 46431), (74, 3567, 1112), (110, 15043, 9826), (125, 389, 1986), (125, 3574, 32743), (185, 7687, 12292), (265, 37481, 14708), (974, 11746, 4), (1112, 16270, 74), (3047, 44802, 20771), (5462, 11806, 113), (5889, 15059, 12358), (6102, 20304, 7723), (6642, 19456, 110), (7722, 15081, 15738), (9729, 11800, 16163), (10110, 17855, 13202), (10574, 10733, 44573), (12006, 13358, 1511), (15151, 16105, 12244)

X(46431) = X(4)X(974)∩X(25)X(74)

Barycentrics a^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^4-11*b^2*c^2+5*c^4)*a^8-2*(3*b^2-4*c^2)*(4*b^2-3*c^2)*b^2*c^2*a^6-(b^4-c^4)*(b^2-c^2)*(5*b^4-28*b^2*c^2+5*c^4)*a^4+2*(b^2-c^2)^2*(2*b^8+2*c^8+b^2*c^2*(b^4-15*b^2*c^2+c^4))*a^2-(b^4-c^4)*(b^2-c^2)^3*(b^4+7*b^2*c^2+c^4)) : :

X(46431) = 3*X(4)-2*X(974), 5*X(4)-4*X(11746), X(74)-3*X(11455), 5*X(974)-6*X(11746), 4*X(974)-3*X(17854), 3*X(1539)-2*X(11561), 4*X(1539)-3*X(12824), 3*X(1986)-4*X(11807), 3*X(3830)-2*X(12236), 2*X(6699)-3*X(16194), 2*X(7687)-3*X(32062), X(7731)-3*X(10721), X(7731)+3*X(12290), 3*X(11381)-X(21650), 3*X(11455)-2*X(12133), 8*X(11561)-9*X(12824), 8*X(11746)-5*X(17854), 2*X(11807)-3*X(13202), 2*X(12140)-3*X(16658), 3*X(12292)-2*X(21650)

X(46431) lies on these lines: {4, 974}, {25, 74}, {30, 12825}, {110, 12085}, {113, 858}, {125, 13474}, {146, 7391}, {186, 11598}, {265, 44276}, {378, 9934}, {382, 5663}, {389, 17856}, {541, 34603}, {1112, 6241}, {1495, 25564}, {1498, 15463}, {1511, 14157}, {1539, 11561}, {1986, 6000}, {2071, 20771}, {2777, 6240}, {2781, 9973}, {3028, 9629}, {3043, 12112}, {3520, 15647}, {3529, 41673}, {3830, 12236}, {5946, 18550}, {6699, 16194}, {7687, 32062}, {7722, 16105}, {7723, 18565}, {7728, 18569}, {9826, 15072}, {10540, 25487}, {10628, 13433}, {10706, 34609}, {10752, 34777}, {11439, 15055}, {11456, 15472}, {11559, 16835}, {12041, 32137}, {12244, 15738}, {12279, 44573}, {12315, 19504}, {12358, 15305}, {12900, 14855}, {13198, 35502}, {13293, 26883}, {13416, 15058}, {13491, 16222}, {14641, 38793}, {15030, 37853}, {15081, 15151}, {16659, 17702}, {17812, 19457}, {18781, 19223}, {38727, 44870}

X(46431) = midpoint of X(10721) and X(12290)
X(46431) = reflection of X(i) in X(j) for these (i, j): (74, 12133), (125, 13474), (1986, 13202), (3529, 41673), (6241, 1112), (7722, 16105), (12041, 32137), (12244, 15738), (12279, 44573), (12292, 11381), (17854, 4), (17856, 389)
X(46431) = crosssum of X(3) and X(20127)
X(46431) = {X(74), X(11455)}-harmonic conjugate of X(12133)
X(46431) = {X(4), X(17854)}-harmonic conjugate of X(46430)

X(46432) = X(3)X(6)∩X(115)X(393)

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 3630.

In the plane of a triangle ABC, let
I = X(1) = incenter
Ia, Ib, Ic = excenters
DEF = anticomplementary triangle
A1B1C1 = 1st circumperp triangle of DEF
A2B2C2 = 2nd circumperp triangle of DEF
A' = point of intersection, other than X(147), of the circles {{A1,Ib, IC}} and {{A2, X1,Ia}}, and define B' and C' cyclically.
The finite fixed point of the affine transformation from ABC to A'B'C' is X(46432). (Angel Montesdeoca, October 15, 2023)

X(46432) lies on these lines: {3,6}, {53,44226}, {115,393}, {232,34481}, {419,9307}, {608,14936}, {1033,14581}, {1196,45141}, {1249,3767}, {1843,33578}, {1974,20975}, {1990,44960}, {2197,14827}, {2207,31942}, {3087,7747}, {3186,11596}, {3269,14642}, {5475,44920}, {7735,38282} ,{7737,40065}, {7748,42459}, {7755,40138}, {8541,40981}, {9722,18362}, {15525,23976}, {19118,42671}, {20232,42295}, {23583,41770}, {26958,40995}, {30457,35508}, {33581,44079}, {36212,40318}, {37689,45245}

X(46433) = ISOGONAL CONJUGATE OF X(32555)

X(46433) lies on the cubics K332 and K414 and on these lines: {40, 30556}, {196, 13390}, {223, 13389}, {282, 2262}, {329, 31548}, {946, 7090}, {1703, 7348}, {2956, 6212}, {6213, 15892}, {14256, 31540}, {34495, 42872}

X(46433) = isogonal conjugate of X(32555)
X(46433) = X(34908)-Ceva conjugate of X(1)
X(46433) = X(2362)-cross conjugate of X(1)
X(46433) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32555}, {6, 46422}, {6502, 34909}
X(46433) = barycentric product X(1659)*X(34908)
X(46433) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 46422}, {6, 32555}, {7133, 34909}
X(46433) = {X(40),X(38004)}-harmonic conjugate of X(32555)

X(46434) = ISOGONAL CONJUGATE OF X(32556)

X(46434) lies on the cubics K332 and K414 and on these lines: {40, 30557}, {196, 1659}, {223, 13388}, {282, 2262}, {329, 31547}, {946, 14121}, {1702, 7347}, {2956, 6213}, {6212, 15891}, {14256, 31541}, {34494, 42872}

X(46434) = isogonal conjugate of X(32556)
X(46434) = X(34907)-Ceva conjugate of X(1)
X(46434) = X(16232)-cross conjugate of X(1)
X(46434) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32556}, {6, 46421}, {2067, 34910}
X(46434) = barycentric product X(13390)*X(34907)
X(46434) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 46421}, {6, 32556}, {42013, 34910}

X(46435) = ISOGONAL CONJUGATE OF X(2077)

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

X(46435) = 3 X[5658] - X[13199], 3 X[5660] - 2 X[12332], 4 X[6702] - 3 X[14647], 4 X[6705] - 5 X[31272], X[7992] - 3 X[37718], 2 X[12114] - 3 X[16173]

X(46435) lies on the Feuerbach circumhyperbola, the cubic K1254, and on these lines: {1, 1537}, {4, 12736}, {7, 15528}, {8, 153}, {9, 119}, {11, 84}, {21, 10165}, {30, 6596}, {80, 6001}, {90, 1768}, {100, 6260}, {104, 1519}, {149, 6223}, {515, 1320}, {516, 25438}, {517, 12641}, {528, 42470}, {908, 2077}, {943, 12775}, {946, 1476}, {952, 3680}, {971, 3254}, {1000, 12115}, {1156, 10265}, {1317, 12678}, {1389, 10728}, {1490, 5840}, {1699, 7284}, {1709, 8068}, {1836, 3577}, {1877, 36121}, {2771, 6598}, {2801, 6601}, {2802, 12667}, {2827, 43728}, {3035, 10270}, {3065, 11219}, {3255, 10202}, {3296, 10531}, {3667, 46041}, {3738, 43737}, {5424, 16154}, {5533, 10085}, {5559, 12749}, {5658, 13199}, {5660, 12332}, {5787, 22938}, {6003, 14224}, {6245, 10308}, {6246, 7319}, {6261, 12119}, {6700, 21635}, {6702, 14647}, {6705, 31272}, {7160, 10956}, {7285, 13226}, {7992, 36599}, {10073, 15071}, {10269, 12611}, {10596, 18490}, {10742, 22792}, {11609, 29057}, {12019, 33576}, {12114, 16173}, {12247, 43734}, {12619, 45631}, {12680, 13274}, {12687, 37726}, {12688, 13273}, {12750, 41690}, {12764, 18838}, {15017, 16209}, {15446, 22775}, {16127, 43740}, {18391, 38307}, {24703, 38759}, {37826, 43166}

X(46435) = midpoint of X(149) and X(6223)
X(46435) = reflection of X(i) in X(j) for these {i,j}: {80, 12761}, {84, 11}, {100, 6260}, {2950, 119}, {5787, 22938}, {10742, 22792}, {12119, 6261}, {12665, 34293}, {12751, 6256}
X(46435) = isogonal conjugate of X(2077)
X(46435) = antigonal image of X(84)
X(46435) = symgonal image of X(6260)
X(46435) = X(i)-cross conjugate of X(j) for these (i,j): {909, 2006}, {12764, 80}, {18838, 1}
X(46435) = cevapoint of X(513) and X(35015)
X(46435) = trilinear pole of line {650, 1108}
X(46435) = Feuerbach-hyperbola-antipode of X(84)
X(46435) = inner-Garcia-to-ABC similarity image of X(12666)
X(46435) = X(i)-isoconjugate of X(j) for these (i,j): {1, 2077}, {3, 15500}, {12665, 36052}
X(46435) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 2077}, {19, 15500}, {8609, 12665}
X(46435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {153, 39776, 12751}, {12676, 12679, 84}

X(46436) = X(2)X(477)∩X(4)X(841)

X(46436) lies on the nine-point circle and these lines: {2, 477}, {4, 841}, {113, 858}, {115, 3154}, {125, 8675}, {127, 37985}, {128, 30745}, {131, 5159}, {133, 468}, {427, 18809}, {1368, 42424}, {1560, 1990}, {1650, 38971}, {3134, 5099}, {4549, 16167}, {5094, 14685}, {5512, 36189}, {14672, 37987}, {14995, 31655}, {16188, 30739}, {25642, 37167}

X(46436) = midpoint of X(4) and X(841)
X(46436) = complement of X(9060)
X(46436) = orthoptic-circle-of-Steiner-inellipse-inverse of X(477)
X(46436) = complement of the isogonal conjugate of X(9003)
X(46436) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 9003}, {656, 10297}, {661, 44569}, {9003, 10}, {10295, 8062}, {40112, 4369} X(46436) = X(4)-Ceva conjugate of X(9003)

X(46437) = X(133)X(186)∩X(137)X(3154)

X(46437) lies on the nine-point circle and these lines: {2, 16166}, {113, 37938}, {114, 30745}, {133, 186}, {137, 3154}, {140, 25641}, {858, 44953}, {1594, 18809}, {20625, 37985}, {36189, 45161}, {37452, 42424}

X(46437) = complement of X(16166)
X(46437) = X(i)-complementary conjugate of X(j) for these (i,j): {656, 18403}, {13619, 8062}, {18365, 14838}

X(46438) = X(114)X(7426)∩X(115)X(6070)

X(46438) lies on the nine-point circle and these lines: {113, 41586}, {114, 7426}, {115, 6070}, {126, 34827}, {131, 18323}, {3845, 25641}, {5169, 16188}, {10254, 42424}, {10301, 42426}, {13413, 45180}, {14120, 34113}

X(46438) = X(i)-complementary conjugate of X(j) for these (i,j): {661, 40112}, {44555, 4369}

X(46439) = X(23)X(114)∩X(30)X(128)

Barycentrics (b - c)^2*(b + c)^2*(-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)*(-a^8 + 2*a^6*b^2 - 2*a^2*b^6 + b^8 + 2*a^6*c^2 - a^4*b^2*c^2 + a^2*b^4*c^2 - 2*b^6*c^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(46439) = 3 X[381] - X[14980], X[1157] - 3 X[37943], 3 X[5642] - 2 X[43969], 3 X[16532] - X[35729]

X(46439) lies on the nine-point circle and these lines: {2, 1291}, {4, 14979}, {5, 45180}, {23, 114}, {30, 128}, {113, 1154}, {115, 12077}, {125, 1510}, {131, 18403}, {137, 523}, {381, 14980}, {403, 10214}, {428, 42426}, {546, 25641}, {858, 31843}, {1157, 37943}, {1209, 33333}, {2070, 19552}, {5133, 16188}, {5642, 43969}, {6070, 8902}, {6150, 44234}, {10024, 42424}, {10096, 10227}, {14140, 43893}, {14857, 43958}, {15169, 19939}, {16532, 35729}, {20392, 34836}, {30436, 31841}, {30446, 42422}, {31655, 37454}, {33545, 36161}

X(46439) = midpoint of X(i) and X(j) for these {i,j}: {4, 14979}, {2070, 19552}, {14140, 43893}, {14857, 43958}
X(46439) = reflection of X(i) in X(j) for these {i,j}: {6150, 44234}, {16337, 403}, {45180, 5}
X(46439) = complement of X(1291)
X(46439) = reflection of X(137) in the Euler line
X(46439) -= complement of the isogonal conjugate of X(45147)
X(46439) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 45147}, {661, 323}, {1749, 523}, {2616, 46114}, {2618, 16336}, {6140, 37}, {10413, 8287}, {11063, 14838}, {37779, 4369}, {37943, 8062}, {45147, 10}
X(46439) = X(4)-Ceva conjugate of X(45147)
X(46439) = X(1141)-of-(reflection of Euler triangle in Euler line)
X(46439) = barycentric product X(24978)*X(45147)
X(46439) = barycentric quotient X(10413)/X(33565)

X(46440) = CENTER OF THE HATZIPOLAKIS - SUPPA ELLIPSE

Let P be a point on the Euler line and A'B'C' the cevian triangle of P. Let Ra be the radical axis of the circumcircles of the triangles PBC' and PCB'. Define Rb, Rc cyclically. The reflections of Ra, Rb, Rc in BC, CA, AB, resp. concur at a point on an ellipse passing through X(i) for these i: {4, 5, 6, 399, 11061, 11441, 14627}. This ellipse is named here Hatzipolakis-Suppa ellipse. Its perspector is X(323) and its center X(46440)

X(46440) lies on these lines: {23,110}, {146,12605}, {399,546}, {428,9143}, {1994,5480}, {2914,5609}, {3448,5133}, {5663,13353}, {5898,14449}, {7527,15102}, {7550,15101}, {10192,17847}, {11819,12383}, {12022,43605}, {12308,15032}, {15018,45303}, {25329,37784}

X(46441) = X(1)X(21)∩X(60)X(65)

X(46441) lies on the Hatzipolakis-Suppa ellipse and these lines: {1,21}, {4,1029}, {6,2476}, {10,37783}, {46,37294}, {60,65}, {110,942}, {229,5902}, {399,6841}, {411,5396}, {484,15792}, {501,3336}, {757,1442}, {940,24936}, {1210,3615}, {1393,23692}, {1411,17097}, {1812,14005}, {1963,27577}, {3017,17577}, {4278,14799}, {5425,37816}, {5707,6828}, {5814,40571}, {5903,9275}, {6175,41501}, {6842,14627}, {6852,45931}, {6853,37509}, {6856,24898}, {6857,14996}, {7424,37730}, {7548,45926}, {8614,18625}, {12047,24624}, {13746,18391}, {14009,33142}, {22136,37635}, {24880,32911}, {24902,37680}, {36279,37405}, {37369,39542}, {37418,37584}

X(46441) = X(661)-he conjugate of X(2640)
X(46441) = X(i)-isoconjugate of X(j) for these (i,j): (65,15910), (523,39630)
X(46441) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {163,39630}, {284,15910}
X(46441) = barycentric product X(333)*X(15932)
X(46441) = barycentric quotient X(i)/X(j) for these {i,j}: {163,39630}, {284,15910}
X(46441) = trilinear product X(21)*X(15932)
X(46441) = trilinear quotient X(i)/X(j) for these (i,j): (21,15910), (110,39630)
X(46441) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (46,40214,37294), (60,65,1325), (5902,17104,229)

X(46442) = X(4)X(193)∩X(22)X(69)

Barycentrics 2 a^8-a^6 b^2-a^4 b^4+a^2 b^6-b^8-a^6 c^2+a^2 b^4 c^2-a^4 c^4+a^2 b^2 c^4+2 b^4 c^4+a^2 c^6-c^8 : :
Barycentrics S^2 (SW-2 R^2) (2 SA-SW)+SB SC SW^2 : :

X(46442) lies on the Hatzipolakis-Suppa ellipse and these lines: {2,13562}, {4,193}, {6,5133}, {22,69}, {66,858}, {67,110}, {343,19121}, {399,15760}, {511,14516}, {524,9973}, {542,6467}, {648,41375}, {1352,11441}, {1353,7403}, {1370,20079}, {1503,12111}, {1594,19139}, {1899,26206}, {1974,3580}, {3164,9863}, {3547,31831}, {3589,19122}, {3620,7494}, {3630,12367}, {3933,5938}, {5093,32358}, {6403,12134}, {6776,7503}, {7387,11898}, {7404,14912}, {7500,20080}, {7553,34380}, {7566,14853}, {8681,40316}, {9306,26156}, {9818,39899}, {9967,34224}, {11160,34608}, {11416,15583}, {11440,44882}, {11443,32455}, {12168,12317}, {12278,29181}, {12359,19128}, {12412,45170}, {12827,41593}, {14003,23163}, {15066,15812}, {15069,19149}, {16386,34778}, {19126,37636}, {19132,37638}, {19155,34826}, {21243,21637}, {22151,23300}, {28708,30744}, {33878,44831}, {37491,45794}, {37900,40317}, {40867,41237}, {45016,45178}

X(46442) = reflection of X(i) in X(j) for these (i,j): (6403,12134), (12225,41716), (26926,13562), (34224,9967)
X(46442) = anticomplement of X(26926)
X(46442) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (66,20806,858), (69,5596,22), (141,1176,7495), (343,34774,19121), (13562,26926,2), (19122,23293,3589)

X(46443) = X(6)X(70)∩X(68)X(403)

X(46443) lies on the Hatzipolakis-Suppa ellipse and these lines: {4,13292}, {6,70}, {24,6193}, {25,32358}, {52,1986}, {68,403}, {235,399}, {343,10018}, {378,18909}, {427,14627}, {569,37118}, {1593,43588}, {1595,32165}, {1614,41729}, {3518,18947}, {3541,11245}, {3542,3564}, {6146,6241}, {6225,35490}, {6247,15472}, {6776,34207}, {10295,17834}, {12235,14516}, {13371,19504}, {14111,27376}, {18356,37981}, {22750,32234}

X(46444) = X(6)X(666)∩X(25)X(193)

Barycentrics (a^2+b^2-c^2) (a^2-b^2+c^2) (4 a^4-3 a^2 b^2+b^4-3 a^2 c^2+2 b^2 c^2+c^4) : :
Barycentrics SB SC (4 SA^2-3 SA SW+SW^2) : :

X(46444) lies on the Hatzipolakis-Suppa ellipse and these lines: {4,1353}, {6,66}, {24,34380}, {25,193}, {69,468}, {110,40316}, {141,44102}, {235,3564}, {399,1596}, {428,1992}, {460,9308}, {524,1974}, {1112,1843}, {1351,3575}, {1503,11470}, {1570,27376}, {1593,14912}, {1595,14627}, {1885,6225}, {1906,39871}, {1907,39588}, {1994,15809}, {3542,11898}, {3589,15471}, {3620,37453}, {3751,12135}, {3867,8584}, {3933,44162}, {5032,5064}, {5052,12143}, {5186,5477}, {5596,10602}, {5921,37197}, {6353,20080}, {6467,34774}, {7399,35603}, {7716,15534}, {8541,32455}, {8550,12294}, {10151,18440}, {10733,12596}, {11363,34379}, {11443,39884}, {12007,19124}, {13562,41614}, {14853,23047}, {14913,44084}, {15069,45004}, {15583,21639}, {18438,44239}, {18533,44456}, {18919,20079}, {19121,34397}, {19459,35219}, {19504,25321}, {21213,37491}, {26206,30739}, {33878,37931}, {35264,40317}, {39874,44438}, {41585,44091}

X(46444) = reflection of X(41584) in X(1974)
X(46444) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (69,19118,468), (1843,5095,3629)

X(46445) = X(110)X(1209)∩X(399)X(3153)

X(46445) lies on the Hatzipolakis - Suppa ellipse and these lines: {5,14683}, {110,1209}, {399,3153}, {511,7731}, {2070,5898}, {3448,13353}, {3518,18947}, {5900,15246}, {6152,23236}, {9143,34397}, {10114,24981}, {12168,12317}, {14627,32423}

X(46446) = X(110)X(34483)∩X(399)X(43893)

X(46446) lies on the Hatzipolakis - Suppa ellipse and these lines: {110,34483}, {140,5900}, {399,43893}

X(46447) = X(110)X(34437)∩X(399)X(511)

X(46447) lies on the Hatzipolakis - Suppa ellipse and these lines: {5,25335}, {110,34437}, {399,511}, {542,14627}, {599,11441}, {13353,16010}

X(46448) = X(110)X(18125)∩X(399)X(18358)

X(46448) lies on the Hatzipolakis - Suppa ellipse and these lines: {4,69}, {6,3410}, {66,3619}, {110,18125}, {141,2916}, {399,18358}, {1503,37126}, {1614,24206}, {2888,5480}, {3448,3589}, {3564,14627}, {3618,11442}, {3620,20062}, {3763,6800}, {5189,15321}, {6776,13353}, {7514,18440}, {10516,11441}, {11646,23642}, {13562,22151}, {14826,28408}, {19140,33565}, {20021,40425}, {20079,34118}, {32255,32366}, {37334,45799}, {38317,43808}

X(46448) = reflection of X(i) in X(j) for these (i,j): (11061,46440), (6776,13353)

X(46449) = X(5663)X(14627)∩X(7731)X(18859)

X(46449) lies on the Hatzipolakis - Suppa ellipse and these lines: {5663,14627}, {7731,18859}, {43704,44056}

X(46450) = EULER LINE INTERCEPT OF X(52)X(43808)

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^2-3 a^6 b^2 c^2+2 a^4 b^4 c^2-a^2 b^6 c^2+3 b^8 c^2-2 a^6 c^4+2 a^4 b^2 c^4-2 b^6 c^4+2 a^4 c^6-a^2 b^2 c^6-2 b^4 c^6+a^2 c^8+3 b^2 c^8-c^10 : :
Barycentrics 2 R^2 S^2+SB SC (3 R^2-2 SW) : :

X(46450) = 3*X(2)-4*X(37938),9*X(2)-8*X(44234),4*X(3)-3*X(35489),2*X(3)-3*X(44450),X(4)+2*X(5189),X(4)-4*X(7574),7*X(4)-4*X(18325),3*X(4)-4*X(18403),5*X(4)-8*X(18572),5*X(4)-4*X(31726),9*X(4)-8*X(44283),4*X(5)-X(20063),4*X(23)-7*X(3090),2*X(23)-3*X(37943),4*X(140)-3*X(37922),4*X(186)-5*X(631),3*X(186)-4*X(10257),3*X(376)-4*X(2071),X(376)-4*X(10989),3*X(376)-2*X(13619),9*X(376)-8*X(44246),3*X(381)-X(37949),3*X(381)-2*X(43893),8*X(403)-9*X(3545),4*X(468)-3*X(37939),5*X(631)-8*X(858),3*X(858)-2*X(10257),5*X(1656)-4*X(10096),5*X(1656)-3*X(37956),3*X(2070)-4*X(44234),X(2071)-3*X(10989),3*X(2071)-2*X(44246),8*X(2072)-7*X(3090),4*X(2072)-3*X(37943),3*X(3060)-4*X(11692),7*X(3090)-6*X(37943),5*X(3091)-4*X(11563),5*X(3091)-2*X(37924),X(3146)+2*X(35001),7*X(3153)-2*X(18325),3*X(3153)-2*X(18403),5*X(3153)-4*X(18572),5*X(3153)-2*X(31726),9*X(3153)-4*X(44283),7*X(3523)-6*X(37955),9*X(3524)-8*X(15646),7*X(3526)-6*X(16532),7*X(3528)-8*X(34152),X(3529)-4*X(7464),9*X(3545)-4*X(37925),8*X(3628)-5*X(37923),5*X(3843)-4*X(11558),5*X(5071)-2*X(37901),8*X(5159)-5*X(37953),X(5189)+2*X(7574),7*X(5189)+2*X(18325),3*X(5189)+2*X(18403),5*X(5189)+4*X(18572),5*X(5189)+2*X(31726),9*X(5189)+4*X(44283),4*X(6676)-3*X(37932),3*X(7426)-4*X(44911),7*X(7574)-X(18325),3*X(7574)-X(18403),5*X(7574)-2*X(18572),5*X(7574)-X(31726),9*X(7574)-2*X(44283),7*X(9781)-8*X(13376),4*X(10096)-3*X(37956),2*X(10295)-3*X(37948),4*X(10296)-X(33703),4*X(10297)-X(37946),4*X(10540)-5*X(20125),6*X(10989)-X(13619),9*X(10989)-2*X(44246),3*X(13619)-4*X(44246),5*X(15081)-2*X(15107),4*X(15122)-3*X(37941),9*X(15709)-8*X(44214),9*X(15710)-8*X(44280),8*X(16531)-7*X(37957),5*X(17538)-8*X(37950),3*X(18325)-7*X(18403),5*X(18325)-7*X(31726),5*X(18403)-6*X(18572),5*X(18403)-3*X(31726),3*X(18403)-2*X(44283),9*X(18572)-5*X(44283),5*X(30745)-3*X(37940),5*X(30745)-4*X(44452),9*X(31726)-10*X(44283),3*X(32609)-4*X(46114),X(33703)+4*X(37944),5*X(37760)-4*X(37936),3*X(37901)-4*X(37947),3*X(37909)-4*X(44282),3*X(37938)-2*X(44234),3*X(37940)-4*X(44452)

X(46450) lies on these lines: {2,3}, {52,43808}, {54,44829}, {69,11649}, {110,44407}, {143,43816}, {265,5900}, {511,25739}, {523,15099}, {539,23061}, {543,15070}, {758,15095}, {1058,10149}, {1154,3448}, {1157,14651}, {1272,1273}, {1568,14157}, {2888,6101}, {2979,18474}, {3060,11692}, {3289,15340}, {3410,23039}, {3818,44834}, {3917,41171}, {6000,13203}, {6288,10627}, {7706,20791}, {8718,43831}, {9306,43579}, {9781,13376}, {10116,15801}, {10264,32608}, {10540,20125}, {11412,12325}, {11433,32411}, {11459,11550}, {11572,15644}, {11750,12254}, {12038,41482}, {12244,13445}, {12289,13346}, {12290,22555}, {12317,12319}, {12383,18400}, {13419,43598}, {13470,37472}, {13630,15800}, {13851,18933}, {14627,43838}, {14644,29317}, {14864,43895}, {15077,17711}, {15081,15107}, {16266,34799}, {20424,43845}, {23293,37478}, {25563,32365}, {30522,37477}, {32609,46114}

X(46450) = midpoint of X(i) and X(j) for these {i,j}: {3153,5189}, {10296,37944}
X(46450) = reflection of X(i) in X(j) for these (i,j): (4,3153), (20,18859), (23,2072), (186,858), (2070,37938), (3153,7574), (5899,5), (12244,13445), (12383,43574), (13619,2071), (14157,1568), (20063,5899), (31726,18572), (32608,10264), (35489,44450), (37899,37942), (37900,37971), (37910,44912), (37924,11563), (37925,403), (37945,11799), (37949,43893), (37967,46031)
X(46450) = reflection of X(1325) in X(523)
X(46450) = anticomplement of X(2070)
X(46450) = anticomplementary conjugate of the anticomplement of X(33565)
X(46450) = circumperp conjugate of X(14118)
X(46450) = anticomplementary-circle-inverse of X(3)
X(46450) = de-Longchamps-circle-inverse of X(7488)
X(46450) = polar-circle-inverse of X(6756)
X(46450) = X(i)-vertex conjugate of X(j) for these (i,j): (523,7512), (7512,523)
X(46450) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,20,7502), (2,31723,4), (2,44831,7556), (3,382,45971), (3,31181,31074), (3,39504,2), (4,1370,376), (4,3524,18420), (4,3525,7544), (4,5067,7528), (4,5071,7394), (4,6643,3090), (4,6816,3855), (4,11001,44440), (4,18537,41099), (4,34938,33703), (20,3146,18565), (20,18569,4), (20,35473,376), (20,44441,35473), (22,7577,7552), (23,2072,37943), (186,45181,37943), (376,3090,7494), (376,8889,631), (381,7485,14789), (381,37949,43893), (550,31724,34007), (1113,1114,7512), (1312,1313,14788), (1656,37956,10096), (2070,18403,11818), (2070,37938,2), (2071,13619,376), (2072,37943,3090), (3146,18404,4), (3548,31304,44879), (5189,7574,4), (5189,10296,34938), (5189,10989,1370), (7391,18531,4), (7391,37444,18531), (7488,13371,6143), (7565,15246,37347), (7574,35001,18404), (10750,10751,546), (11750,34148,12254), (11819,37452,44802), (12225,23335,3520), (12362,15559,35500), (14784,14785,2937), (14790,18531,7391), (14790,37444,4), (14791,31723,2), (14807,14808,3), (14864,45187,43895), (16063,18420,3524), (21312,34725,35480), (23039,34514,3410), (30745,37940,44452), (31724,34007,4), (35732,42282,17714)

X(46451) = EULER LINE INTERCEPT OF X(146)X(32223)

Barycentrics 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^2-3 a^6 b^2 c^2+9 a^2 b^6 c^2-3 b^8 c^2+2 a^6 c^4-12 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 : :
Barycentrics 6 R^2 SB SC+S^2 (7 R^2-2 SW) : :

X(46451) = X(2)+8*X(44266),5*X(2)-8*X(44282),X(3)-4*X(10096),X(3)+2*X(43893),X(4)+2*X(2070),X(4)-4*X(11563),X(4)+8*X(25338),2*X(5)+X(5899),8*X(5)+X(20063),X(20)-4*X(186),X(20)+8*X(11799),X(20)-10*X(37760),5*X(20)-8*X(44246),X(23)+2*X(403),4*X(23)+5*X(3091),2*X(23)+X(3153),5*X(23)+4*X(10297),X(23)-4*X(37971),4*X(140)-X(35452),X(146)+8*X(32223),X(186)+2*X(11799),2*X(186)-5*X(37760),5*X(186)-2*X(44246),X(382)-4*X(11558),X(382)+8*X(44264),8*X(403)-5*X(3091),4*X(403)-X(3153),5*X(403)-2*X(10297),X(403)+2*X(37971),4*X(468)-X(2071),5*X(468)-2*X(16976),4*X(546)+5*X(37923),5*X(631)-2*X(18859),5*X(631)-8*X(44234),X(858)-4*X(37942),2*X(858)+X(37945),2*X(1533)+X(13445),X(1533)+2*X(44673),2*X(1568)+X(15107),5*X(1656)+X(37949),X(2070)+2*X(11563),X(2070)-4*X(25338),4*X(2071)-7*X(3523),5*X(2071)-8*X(16976),4*X(2072)-X(5189),X(2072)+2*X(16619),2*X(2072)+X(37925),7*X(3090)+2*X(37924),7*X(3090)-4*X(37938),5*X(3091)-2*X(3153),X(3146)+8*X(7575),X(3146)+2*X(13619),X(3146)-4*X(31726),5*X(3153)-8*X(10297),X(3153)+8*X(37971),X(3448)+2*X(14157),5*X(3522)-8*X(15646),5*X(3522)+4*X(18325),X(3529)-10*X(37958),X(3543)+8*X(7426),X(3543)+4*X(37940),7*X(3832)-4*X(18403),7*X(3832)+8*X(37936),X(3839)+2*X(37909),3*X(3839)+4*X(37939),X(5059)+8*X(44267),X(5189)+8*X(16619),X(5189)+2*X(37925),4*X(5899)-X(20063),X(5921)+8*X(32217),X(7464)-4*X(44452),X(7574)+2*X(37947),X(7574)-4*X(46031),4*X(7575)-X(13619),2*X(7575)+X(31726),7*X(9781)-4*X(11692),2*X(10096)+X(43893),4*X(10151)-X(10296),X(10151)+2*X(37897),4*X(10257)-X(37944),X(10296)+8*X(37897),X(10297)+5*X(37971),X(10304)-4*X(37907),3*X(10304)-4*X(37941),4*X(10540)-X(14683),X(11558)+2*X(44264),X(11563)+2*X(25338),4*X(11799)+5*X(37760),5*X(11799)+X(44246),X(13445)-4*X(44673),X(13619)+2*X(31726),X(13851)+2*X(32237),4*X(14156)-X(43576),X(15640)+8*X(44265),2*X(15646)+X(18325),5*X(15692)-4*X(37948),5*X(15692)-8*X(44214),5*X(15697)-8*X(44280),X(16386)-4*X(37935),2*X(16386)-5*X(37952),4*X(16619)-X(37925),5*X(17578)-8*X(44283),X(18403)+2*X(37936),X(18403)-4*X(44961),X(18859)-4*X(44234),5*X(30745)-8*X(44911),3*X(37907)-X(37941),3*X(37909)-2*X(37939),X(37924)+2*X(37938),4*X(37931)-7*X(37957),8*X(37935)-5*X(37952),X(37936)+2*X(44961),8*X(37942)+X(37945),X(37943)+4*X(44266),5*X(37943)-4*X(44282),4*X(37943)-X(44450),X(37947)+2*X(46031),X(37950)-4*X(44900),5*X(44266)+X(44282)

As a point on the Euler line, X(46451) has Shinagawa coefficients (e + 8f, -6e).

X(46451) lies on these lines: {2,3}, {146,32223}, {343,15052}, {539,9143}, {1533,13445}, {1568,15107}, {3410,46261}, {3448,14157}, {3582,4351}, {3584,4354}, {5655,38898}, {5921,32217}, {5944,43818}, {7605,14845}, {8718,43817}, {9140,9934}, {9781,11692}, {10540,14683}, {11177,21458}, {11649,14853}, {13391,14643}, {13851,32237}, {14156,43576}, {14644,44407}, {18390,26881}, {35265,44665}, {41587,43605}

X(46451) = midpoint of X(i) and X(j) for these {i,j}: {381,37956}, {16532,43893}
X(46451) = reflection of X(i) in X(j) for these (i,j): (2,37943), (3,16532), (376,37955), (16532,10096), (35489,37922), (37940,7426), (37948,44214), (44450,2)
X(46451) = complement of the circumperp conjugate of X(35500)
X(46451) = anticomplement of the circumperp conjugate of X(12086)
X(46451) = X(523)-vertex conjugate of X(44802)
X(46451) = barycentric product X(94)*X(40640)
X(46451) = trilinear product X(2166)*X(40640)
X(46451) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (2,3146,44441), (4,10201,2), (23,403,3153), (381,7552,2), (381,44278,7552), (403,3153,3091), (403,37971,23), (1113,1114,44802), (1533,44673,13445), (2070,11563,4), (2072,16619,37925), (2072,37925,5189), (3518,15761,34007), (6143,34330,2), (7505,44441,2), (7575,31726,13619), (10096,43893,3), (10201,44275,10254), (11563,25338,2070), (11799,37760,20), (13406,18378,4), (13406,44278,10201), (13619,31726,3146), (16386,37935,37952), (18531,37913,20), (18859,44234,631), (37936,44961,18403), (37947,46031,7574), (44211,44458,22467)

X(46452) = ISOGONAL CONJUGATE OF X(22233)

X(46452) = isogonal conjugate of X(22233)
X(46452) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(140)}} and {{A, B, C, X(3), X(11539)}}

X(46453) = X(4)X(230)∩X(32)X(631)

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 3660.

X(46453) lies on these lines: {2,1285}, {3,5304}, {4,230}, {6,3524}, {30,37689}, {32,631}, {39,10299}, {69,7835}, {112,2374}, {115,15682}, {183,14039}, {186,1249}, {187,376}, {193,35297}, {315,33189}, {385,32817}, {439,7754}, {549,21309}, {571,40065}, {574,14482}, {598,23053}, {599,20194}, {609,5218}, {626,33195}, {691,36877}, {754,37690}, {966,33628}, {1003,37667}, {1007,7926}, {1078,16045}, {1620,41369}, {1627,7494}, {1691,14912}, {1992,2030}, {2420,6792}, {2548,3533}, {2996,33250}, {3003,5702}, {3089,8778}, {3090,5475}, {3147,40320}, {3291,33885}, {3314,33224}, {3407,7793}, {3522,5305}, {3523,14930}, {3525,22331}, {3528,5023}, {3529,3767}, {3530,43136}, {3543,43291}, {3545,7737}, {3552,32822}, {3618,7771}, {3620,33220}, {3734,37809}, {3785,7868}, {3793,11288}, {3815,15702}, {3855,7746}, {3933,33205}, {3972,34229}, {4045,8182}, {4232,16317}, {4262,37642}, {5008,15719}, {5024,15692}, {5067,7745}, {5071,37637}, {5206,5355}, {5210,5306}, {5254,17538}, {5277,16845}, {5319,15513}, {5485,11164}, {6179,6337}, {6392,33235}, {6423,44594}, {6424,44597}, {6636,40179}, {6680,33194}, {6722,44678}, {7031,7288}, {7426,41394}, {7581,12968}, {7582,12963}, {7714,10986}, {7739,8588}, {7750,32951}, {7761,33196}, {7762,32989}, {7767,33181}, {7773,32958}, {7774,33216}, {7776,33203}, {7778,33231}, {7779,10351}, {7784,32953}, {7785,32977}, {7787,32978}, {7797,33226}, {7799,11008}, {7806,32986}, {7812,34803}, {7823,32969}, {7831,7943}, {7848,33197}, {7857,32006}, {7875,16043}, {7898,14064}, {7904,33221}, {7908,14023}, {7919,14907}, {7921,33206}, {7925,20065}, {7941,33262}, {8369,15589}, {8587,32532}, {8779,18931}, {9605,15717}, {9741,22253}, {10304,15048}, {11001,43448}, {11179,38010}, {11580,26255}, {12082,34809}, {13638,26619}, {13758,26620}, {14033,17008}, {14712,16041}, {15603,34200}, {15700, 22246}, {16318,37460}, {16976,38292}, {16984,33223}, {16989,33215}, {17004,32983}, {17561,37675}, {18841,32960}, {18843,32883}, {20088,33000}, {23334,44401}, {31404,44535}, {31859,35287}, {32640,36875}, {32816,32959}, {38282,41370}, {41099,43620}, {41134,41672}

X(46454) = X(54)X(549)∩X(235)X(933)

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 3660.

X(46454) lies on these lines: {5,23338}, {54,549}, {235,933}, {252,632}, {550,1157}, {1141,3627}, {1166,7405}, {6150,35720}, {7399,19179}, {8901,13371}, {15801,38710}, {16035,22467}, {25042,44682}

X(46455) = X(3146)X(4993)∩X(5056)X(37638)

X(46456) = ISOTOMIC CONJUGATE OF X(8552)

X(46456) lies on these lines: {94,16080}, {107,476}, {250,23290}, {264,34370}, {328,6330}, {648,14618}, {653,7115}, {685,10412}, {687,14590}, {1897,36129}, {1989,16081}, {2410,16237}, {6344,17983}, {6528,41392}, {14165,18883}, {14570,38342}, {14592,15459}, {16813,23582}, {22456,23969}, {30529,37766}, {41079,44769}

X(46456) = isotomic conjugate of X(8552)
X(46456) = polar conjugate of X(526)
X(46456) = X(i)-cross conjugate of X(j) for these (i,j): (476,35139), (4240,6528)
X(46456) = X(i)-isoconjugate of X(j) for these (i,j): (3,2624), (31,8552), (48,526), (50,656), (63,14270)
X(46456) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {2,8552}, {4,526}, {19,2624}, {24,44808}, {25,14270}
X(46456) = X(1745)-Zayin conjugate of X(2624)
X(46456) = cevapoint of X(i)and X(j) for these {i,j}: {2,41079}, {94,14592}, {403,2501}, {647,13851}, {1625,15329}
X(46456) = pole wrt polar circle of trilinear polar of X(526) (line X(2088)X(16186))
X(46456) = trilinear pole of line X(4)X(94)
X(46456) = barycentric product X(i)*X(j) for these (i,j): (4,35139), (75,36129), (92,32680), (94,648), (99,6344)
X(46456) = barycentric quotient X(i)/X(j) for these {i,j}: {4,526}, {19,2624}, {24,44808}, {25,14270}, {53,2081}
X(46456) = trilinear product X(i)*X(j) for these (i,j): (2,36129), (4,32680), (19,35139), (92,476), (94,162)
X(46456) = trilinear quotient X(i)/X(j) for these (i,j): (4,2624), (19,14270), (75,8552), (92,526), (94,656)

X(46457) = X(99)X(101)∩X(115)X(2642)

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

X(46457) lies on the cubic K1255 and these lines: {99, 101}, {115, 2642}, {545, 4750}, {900, 1635}, {903, 45674}, {6084, 40520}, {24506, 24956}, {30190, 44432}, {41138, 45661}

X(46457) = reflection of X(i) in X(j) for these {i,j}: {903, 45674}, {4120, 4370}, {14442, 1635}, {30190, 44432}
X(46457) = crossdifference of every pair of points on line {106, 3122}
X(46457) = barycentric product X(4530)*X(45273)
X(46457) = barycentric quotient X(i)/X(j) for these {i,j}: {5170, 4591}, {42084, 39155}

X(46458) = X(11)X(244)∩X(86)X(99)

X(46458) lies on the cubic K1255 and these lines: {11, 244}, {86, 99}, {190, 17719}, {537, 24222}, {1411, 24836}, {2643, 6089}, {3125, 14442}, {4427, 4440}, {7200, 21135}, {21035, 21725}, {21200, 24185}

X(46458) = midpoint of X(4427) and X(4440)
X(46458) = reflection of X(3120) in X(1086)
X(46458) = X(6551)-isoconjugate of X(39155)
X(46458) = crossdifference of every pair of points on line {101, 14407}
X(46458) = barycentric product X(i)*X(j) for these {i,j}: {5170, 21207}, {21132, 45273}
X(46458) = barycentric quotient X(5170)/X(4570)
X(46458) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {244, 1086, 24188}, {244, 1769, 3122}, {4440, 33148, 24416}

X(46459) = X(69)X(74)∩X(122)X(125)

X(46459) lies on the cubic K1255 and these lines: {69, 74}, {110, 39352}, {122, 125}, {648, 5972}, {2799, 16278}, {9530, 13202}, {30211, 34950}

X(46459) = midpoint of X(110) and X(39352)
X(46459) = reflection of X(i) in X(j) for these {i,j}: {125, 15526}, {648, 5972}
X(46459) = crossdifference of every pair of points on line {112, 14398}
X(46459) = barycentric product X(3267)*X(42654)
X(46459) = barycentric quotient X(42654)/X(112)

X(46460) = X(81)X(99)∩X(244)X(665)

X(46460) lies on the cubic K1255 and these lines: {81, 99}, {244, 665}, {291, 21888}, {668, 36226}, {812, 7200}, {4128, 4155}, {9263, 33888}

X(46460) = reflection of X(3125) in X(1015)
X(46460) = crossdifference of every pair of points on line {100, 14404}
X(46460) = barycentric product X(693)*X(42655)
X(46460) = barycentric quotient X(42655)/X(100)

X(46461) = X(6)X(99)∩X(351)X(865)

X(46461) lies on the cubic K1255 and these lines: {6, 99}, {351, 865}, {694, 2854}, {4576, 25054}, {45672, 45914}

X(46461) = midpoint of X(4576) and X(25054)
X(46461) = reflection of X(3124) in X(1084)
X(46461) = X(799)-isoconjugate of X(39442)
X(46461) = crossdifference of every pair of points on line {99, 888}
X(46461) = barycentric quotient X(669)/X(39442)

X(46462) = X(99)X(1380)∩X(523)X(13636)

X(46462) lies on the cubic K1255 and these lines: {99, 1380}, {523, 13636}, {1648, 1649}, {2028, 3906}, {2793, 14502}, {3413, 9180}, {5639, 5648}, {13722, 44398}, {30508, 39366}

X(46462) = midpoint of X(30508) and X(39366)
X(46462) = reflection of X(13636) in X(39023)
X(46462) = reflection of X(46463) in X(1649)
X(46462) = X(22245)-Ceva conjugate of X(13722)
X(46462) = crossdifference of every pair of points on line {691, 1379}
X(46462) = X(i)-isoconjugate of X(j) for these (i,j): {1379, 36085}, {6190, 36142}
X(46462) = barycentric product X(i)*X(j) for these {i,j}: {524, 13636}, {690, 3413}, {1648, 6189}, {5638, 35522}
X(46462) = barycentric quotient X(i)/X(j) for these {i,j}: {351, 1379}, {690, 6190}, {1648, 3414}, {3413, 892}, {5638, 691}, {13636, 671}, {21906, 5639}, {33919, 13722}
X(46462) = {X(1648),X(23992)}-harmonic conjugate of X(46463)

X(46463) = X(99)X(1379)∩X(523)X(13722)

X(46463) lies on the cubic K1255 and these lines: {99, 1379}, {523, 13722}, {1648, 1649}, {2029, 3906}, {2793, 14501}, {3414, 9180}, {5638, 5648}, {13636, 44398}, {30509, 39365}

X(46463) = midpoint of X(30509) and X(39365)
X(46463) = reflection of X(46462) in X(1649)
X(46463) = reflection of X(13722) in X(39022)
X(46463) = X(22244)-Ceva conjugate of X(13636)
X(46463) = crossdifference of every pair of points on line {691, 1380}
X(46463) = X(i)-isoconjugate of X(j) for these (i,j): {1380, 36085}, {6189, 36142}
X(46463) = barycentric product X(i)*X(j) for these {i,j}: {524, 13722}, {690, 3414}, {1648, 6190}, {5639, 35522}
X(46463) = barycentric quotient X(i)/X(j) for these {i,j}: {351, 1380}, {690, 6189}, {1648, 3413}, {3414, 892}, {5639, 691}, {13722, 671}, {21906, 5638}, {33919, 13636}
X(46463) = {X(1648),X(23992)}-harmonic conjugate of X(46462)

X(46464) = X(99)X(524)∩X(892)X(11053)

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

X(46464) lies on the cubic K1255 and these lines: {99, 524}, {892, 11053}, {1648, 1649}, {5468, 39356}, {33919, 41177}, {42344, 44398}

X(46464) = midpoint of X(5468) and X(39356)
X(46464) = reflection of X(i) in X(j) for these {i,j}: {892, 11053}, {1648, 23992}
X(46464) = crossdifference of every pair of points on line {691, 9171}
X(46464) = barycentric product X(i)*X(j) for these {i,j}: {1648, 44372}, {35522, 39527}
X(46464) = barycentric quotient X(39527)/X(691)

X(46465) = X(4)X(14)∩X(13)X(125)

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

X(46465) = 2 X[2] + X[41092], 7 X[2] - X[41132], X[5668] + 2 X[6111], 2 X[5668] + X[38944], 4 X[6111] - X[38944], 7 X[41092] + 2 X[41132]

X(46465) lies on the the circumcircle of the outer Napoleon triangle, the cubics K874, K884, K952, and these lines: {2, 41092}, {3, 5623}, {4, 14}, {13, 125}, {16, 16319}, {17, 39377}, {61, 23721}, {477, 5995}, {2777, 3163}, {5335, 30465}, {5464, 23871}, {5890, 30439}, {17702, 41889}, {18777, 42155}, {25641, 40579}, {36186, 36839}, {41040, 41066}

X(46465) = midpoint of X(13) and X(36788)
X(46465) = reflection of X(46466) in X(3163)
X(46465) = {X(5668),X(6111)}-harmonic conjugate of X(38944)

X(46466) = X(4)X(13)∩X(14)X(125)

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

X(46466) lies on the the circumcircle of the outer Napoleon triangle, the cubics K874, K884, K952, and these lines: {3, 5624}, {4, 13}, {14, 125}, {15, 16319}, {18, 39378}, {62, 23722}, {477, 5994}, {2777, 3163}, {5334, 30468}, {5463, 23870}, {5663, 41889}, {5890, 30440}, {18776, 42154}, {25641, 40578}, {36185, 36840}, {41041, 41067}

X(46466) = reflection of X(46465) in X(3163)
X(46466) = {X(5669),X(6110)}-harmonic conjugate of X(38943)

X(46467) = EULER LINE INTERCEPT OF X(33)X(500)

As a point on the Euler line, X(46467) has Shinagawa coefficients (4 r^2 (r+2 R)^2 - S^2, 5 S^2 -4 r^2 (r+2 R) (r+6 R)).

X(46467) lies on these lines: {2,3}, {19,9958} ,{33,500}, {225,6357}, {511,1872}, {1770,1882}, {1824,13754}, {1826,3579}, {1838,18400}, {1839,15946}, {1844,17637}, {1865,45930}, {1868,37585}, {1869,18480}, {1871,6000}, {5307,12699}, {5453,6198}, {37826,44665}

X(46467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,27,15763), (4,28,44225), (4,7414,430), (4,14016,6841), (4,14018,381), (4,31902,15762), (4,37381,546), (4,37395,7524)

X(46468) = EULER LINE INTERCEPT OF X(500)X(1442)

As a point on the Euler line, X(46468) has Shinagawa coefficients (4 r^2 (r+2 R)^2 - S^2, 4S^2 -8 r^2 (r+2 R) (r+3 R)).

X(46468) lies on these lines: {2,3}, {500,1442}, {516,23555}, {1068,13408}, {1770,40149}, {1825,41562}, {1826,31730}, {1838,35201}, {1869,31673}, {5307,41869}, {5905,44665}, {6000,42448}, {6637,37755}, {12528,13754}, {14206,41013}, {18400,42759}

X(46468) = X(29)-beth conjugate of X(44225)
X(46468) = X(92)-Ceva conjugate of X(40942)
X(46468) = trilinear product X(4292)*X(6198)
X(46468) = trilinear quotient X(4292)/X(7100)
X(46468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (4,7554,37372), (4,31900,15763), (4,37168,44225), (2475,3559,860)

X(46469) = X(4)X(65)∩X(521)X(8062)

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 3708.

X(46470) = EULER LINE INTERCEPT OF X(13)X(74)

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

X(46470) lies on these lines: {2, 3}, {13, 74}, {15, 36299}, {617, 15928}, {5890, 30439}, {8919, 16962}, {16163, 22796}

X(46471) = EULER LINE INTERCEPT OF X(14)X(74)

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

X(46471) lies on these lines: {2, 3}, {14, 74}, {16, 36298}, {616, 15928}, {5890, 30440}, {8918, 16963}, {16163, 22797}

X(46472) = EULER LINE INTERCEPT OF X(1294)X(34601)

Barycentrics (2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*(2*a^12-2*(b^2+c^2)*a^10-(11*b^4-24*b^2*c^2+11*c^4)*a^8+24*(b^4-c^4)*(b^2-c^2)*a^6-16*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)*a^4+2*(b^4-c^4)*(b^2-c^2)*(b^4+10*b^2*c^2+c^4)*a^2+(b^4+4*b^2*c^2+c^4)*(b^2-c^2)^4) : :

X(46472) = 4*X(3)-3*X(1651), 2*X(4)-3*X(1650), 4*X(140)-3*X(11251), 16*X(140)-15*X(15183), 3*X(376)-2*X(15774), 6*X(402)-7*X(3523), 4*X(550)-3*X(12113), 2*X(550)-3*X(35241

X(46472) lies on these lines: {2, 3}, {1294, 34601}, {3184, 16240}, {5882, 12626}, {9033, 10990}, {11623, 13179}, {12244, 38591}, {12369, 16534}, {12438, 43174}, {12696, 13464}, {13212, 20417}, {13268, 20418}, {15354, 38791}, {34507, 39886}, {41963, 44610}, {41964, 44611}

X(46472) = reflection of X(i) in X(j) for these (i, j): (3081, 376), (12113, 35241), (34601, 1294)

X(46473) = X(1587)X(3388)∩X(1588)X(3374)

X(46473) lies on the Kiepert circumhyperbola, the cubics K329, K1227 and these lines: {3,42647}, {4,41979}, {6,3091}, {20,42645}, {376,41976}, {381,42725}, {631,41980}, {1587,3388}, {1588,3374}, {3146,42730}, {3371,23259}, {3385,23249}, {3387,9541}, {3523,43622}, {3526,43628}, {3545,42784}, {3830,43629}, {3839,42646}, {5066,42726}, {5067,41975}, {5072,42648}, {7486,43623}, {8981,14785}, {13665,14782}, {13785,14783}, {13966,14784}, {15683,43624}

X(46474) = X(3)X(42647)∩X(5)X(11425)

X(46475) = X(1)X(256)∩X(3)X(37)

X(46475) lies on these lines: {1, 256}, {3, 37}, {4, 17321}, {5, 4657}, {9, 182}, {10, 24257}, {30, 41312}, {31, 11203}, {40, 31395}, {44, 5050}, {45, 5085}, {63, 37527}, {75, 6998}, {140, 17279}, {238, 38029}, {344, 631}, {355, 4026}, {381, 41311}, {474, 25099}, {549, 41313}, {575, 1743}, {576, 1449}, {581, 37819}, {612, 37619}, {692, 15296}, {726, 31981}, {971, 1001}, {988, 9737}, {1100, 1351}, {1108, 37492}, {1279, 10246}, {1350, 16777}, {1352, 4357}, {1486, 7387}, {1503, 4364}, {1621, 15503}, {1656, 17384}, {1961, 20368}, {2456, 36405}, {2808, 6176}, {3098, 3247}, {3526, 17357}, {3553, 4260}, {3564, 4643}, {3576, 7611}, {3666, 19544}, {3672, 7390}, {3717, 38116}, {3723, 33878}, {3731, 5092}, {3932, 26446}, {4078, 6684}, {4220, 28606}, {4223, 24554}, {4664, 13634}, {4687, 21554}, {5054, 41310}, {5093, 16666}, {5097, 16667}, {5138, 8557}, {5145, 9619}, {5171, 37552}, {5287, 37521}, {5480, 17045}, {5587, 29061}, {5751, 37615}, {6776, 17257}, {6889, 28420}, {6940, 28978}, {7330, 13323}, {7380, 17322}, {7385, 17302}, {7609, 16468}, {8424, 9959}, {8550, 17332}, {8609, 36740}, {10516, 17325}, {10519, 17316}, {11108, 25887}, {11477, 16884}, {11482, 16668}, {11898, 17344}, {12017, 16814}, {12610, 36674}, {13727, 30273}, {14561, 17023}, {14810, 16673}, {14853, 26626}, {15069, 17253}, {16434, 44307}, {16593, 38122}, {16670, 39561}, {16672, 31884}, {16676, 17508}, {17073, 25365}, {17272, 34507}, {17296, 40107}, {17306, 24206}, {18589, 43160}, {20336, 37151}, {20872, 32613}, {24320, 40937}, {24328, 34381}, {24357, 29010}, {24547, 37149}, {24701, 41007}, {26635, 33849}, {29077, 36663}, {29598, 38317}, {32555, 43121}, {32556, 43120}

X(46475) = reflection of X(37474) in X(1385)
X(46475) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 8245, 6210), (3, 20430, 1766)

X(46476) = X(3)X(42648)∩X(4)X(41980)

X(46476) lies on the Kiepert circumhyperbola, the cubics K329 and K1227, and these lines: {3, 42648}, {4, 41980}, {6, 3091}, {20, 42646}, {376, 41975}, {381, 42726}, {631, 41979}, {1587, 3387}, {1588, 3373}, {3146, 42729}, {3372, 23259}, {3386, 23249}, {3388, 9541}, {3523, 43623}, {3526, 43629}, {3545, 42783}, {3830, 43628}, {3839, 42645}, {5066, 42725}, {5067, 41976}, {5072, 42647}, {7486, 43622}, {8981, 14784}, {13665, 14783}, {13785, 14782}, {13966, 14785}, {15683, 43625}

X(46476) = X(i)-cross conjugate of X(j) for these (i,j): {20, 46473}, {42646, 4}
X(46476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3091, 46473}, {42163, 42983, 46473}, {42166, 42982, 46473}

X(46477) = X(3)X(42648)∩X(5)X(11425)

X(46477) lies on these lines: {3, 42648}, {5, 11425}, {578, 42647}, {1192, 42784}

X(46478) = X(1)X(14749)∩X(11)X(1402)

X(46479) = (name pending)

X(46479) is the perspector of the conic defined in the following posting: Floor van Lamoen and Peter Moses, euclid 3752.

X(46480) = X(4427)X(4551)∩X(17301)X(39974)

X(46480) = trilinear pole of the line {65,1125}
X(46480) = X(5434)-cross conjugate of X(4998)
X(46480) = X(i)-isoconjugate of X(j) for these (i,j): (522,5035), (663,37633), (2175,4828), (4828,2175) ,(5035,522)
X(46480) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {85,4828}, {651,37633}, {1415,5035}, {4552,31025}
X(46480) = cevapoint of X(i)and X(j) for these {i,j}: {226,43052}, {514,5718}, {3669,4031}
X(46480) = barycentric product X(i)*X(j) for these (i,j): (664,42285), (4554,39974)
X(46480) = barycentric quotient X(i)/X(j) for these {i,j}: {85,4828}, {651,37633}, {1415,5035}, {4552,31025}
X(46480) = trilinear product X(i)*X(j) for these (i,j): (651,42285), (664,39974)
X(46480) = trilinear quotient X(i) /X(j) for these (i,j): (109,5035), (664,37633)

X(46481) = (name pending)

X(46482) = (name pending)

X(46483) = X(4)X(81)∩X(30)X(944)

X(46483) lies on these lines: {3, 3936}, {4, 81}, {8, 3564}, {20, 17778}, {30, 944}, {58, 8229}, {182, 4202}, {184, 24984}, {221, 388}, {377, 6776}, {511, 3868}, {515, 2650}, {631, 30831}, {860, 1437}, {964, 1352}, {1330, 4220}, {1899, 24537}, {2292, 2792}, {2975, 4388}, {3146, 20090}, {3487, 13442}, {4340, 26118}, {4683, 8235}, {5051, 37527}, {5767, 6917}, {6193, 6850}, {6998, 26064}, {7413, 26131}, {9306, 25017}, {11064, 27686}, {11179, 17679}, {12115, 44665}, {13407, 39572}, {13731, 29984}, {13732, 18139}, {16066, 26540}, {20077, 37443}, {23536, 39870}, {36496, 36746}

X(46483) = reflection of X(4) in X(13408)
X(46483) = X(13408)-of-anti-Euler triangle
X(46483) = {X(37527), X(37823)}-harmonic conjugate of X(5051)

X(46484) = EULER LINE INTERCEPT OF X(522)X(1491)

X(46484) lies on these lines: {2, 3}, {522, 1491}, {1764, 21243}, {1961, 2647}, {29821, 33178}

X(46485) = EULER LINE INTERCEPT OF X(1491)X(4728)

X(46486) = EULER LINE INTERCEPT OF X(1491)X(4802)

X(46487) = EULER LINE INTERCEPT OF X900)X(1491)

X(46487) lies on these lines: {2, 3}, {900, 1491}, {1764, 37636}, {3704, 3869}, {3712, 5057}, {3743, 12047}, {3936, 17139}, {17011, 45230}, {24624, 35466}

X(46488) = EULER LINE INTERCEPT OF X(1491)X(2977)

X(46489) = EULER LINE INTERCEPT OF X(1491)X(4926)

X(46490) = EULER LINE INTERCEPT OF X(1491)X(28195)

X(46491) = EULER LINE INTERCEPT OF X(1491)X(28138)

X(46492) = EULER LINE INTERCEPT OF X(1491)X(28175)

X(46493) = EULER LINE INTERCEPT OF X(1491)X(28138)

X(46493) lies on these lines: {2, 3}, {3978, 10330}, {5027, 7927}, {19596, 25051}, {26881, 40814}

X(46494) = (name pending)

X(46495) = EULER LINE INTERCEPT OF X(2407)X(11123)

X(46495) lies on these lines: {2, 3}, {2407, 11123}, {5467, 10190}, {5468, 31614}, {23342, 37879}

X(46496) = (name pending)

X(46497) = EULER LINE INTERCEPT OF X(115)X(5991)

X(46497) lies on these lines: {2, 3}, {115, 5991}, {349, 4456}, {664, 14963}, {798, 812}, {3732, 39690}, {16600, 18097}

X(46498) = EULER LINE INTERCEPT OF X(812)X(1019)

X(46499) = EULER LINE INTERCEPT OF X(190)X(646)

X(46500) = (name pending)

X(46501) = EULER LINE INTERCEPT OF X(100)X(3948)

X(46501) lies on these lines: {2, 3}, {100, 3948}, {294, 39690}, {651, 44112}, {661, 830}, {1376, 27040}, {1633, 2245}, {2238, 20672}, {7676, 22369}

X(46502) = EULER LINE INTERCEPT OF X(100)X(29511)

X(46503) = EULER LINE INTERCEPT OF X(112)X(743)

X(46503) lies on these lines: {2, 3}, {19, 16872}, {31, 1932}, {112, 743}, {292, 1474}, {648, 43095}, {893, 2299}, {2309, 2354}

X(46504) = EULER LINE INTERCEPT OF X(112)X(721)

X(46505) = EULER LINE INTERCEPT OF X(112)X(707)

X(46505) lies on these lines: {2, 3}, {112, 707}, {1501, 40372}, {1843, 45210}, {1974, 9468}, {3186, 3511}, {16584, 22364}, {41293, 41331}

X(46506) = EULER LINE INTERCEPT OF X(1928)X(1969)

X(46507) = X(1)X(19)∩(X(75)X(9239)

X(46507) lies on these lines: {1, 19}, {75, 9239}, {92, 1934}, {1928, 1969}, {2201, 41269}, {3056, 3721}, {3708, 4008}, {16706, 20272}, {17473, 17871}

X(46508) = EULER LINE INTERCEPT OF X(626)X(20819)

X(46508) lies on these lines: {2, 3}, {626, 20819}, {7852, 44099}, {7853, 40325}, {14820, 39691}, {40359, 40360}

X(46509) = EULER LINE INTERCEPT OF X(8265)X(23209)

X(46510) = EULER LINE INTERCEPT OF X(1897)X(17987)

X(46511) = EULER LINE INTERCEPT OF X(232)X(538)

X(46511) lies on these lines: {2, 3}, {232, 538}, {264, 33885}, {287, 14157}, {385, 8744}, {393, 9462}, {524, 2211}, {1235, 3199}, {1992, 36879}, {2207, 8667}, {2489, 4580}, {3934, 44142}, {3972, 10986}, {5182, 19128}, {6403, 22486}, {7757, 39575}, {7773, 28417}, {7804, 10985}, {8743, 14614}, {10312, 12150}, {28441, 32823}

X(46512) = EULER LINE INTERCEPT OF X(39)X(35606)

X(46512) lies on these lines: {2, 3}, {39, 35606}, {76, 5468}, {83, 5466}, {110, 38664}, {338, 6593}, {476, 38680}, {575, 5967}, {576, 46124}, {597, 9214}, {1078, 34245}, {1648, 7745}, {2930, 25051}, {3329, 36822}, {5254, 41939}, {5640, 31850}, {5972, 38734}, {6033, 31127}, {7762, 45291}, {7793, 40871}, {9168, 11638}, {11183, 23105}, {11422, 40814}, {35282, 38740}, {35360, 41253}

X(46513) = EULER LINE INTERCEPT OF X(649)X(834)

X(46513) lies on these lines: {2, 3}, {649, 834}, {896, 23363}, {1403, 2206}, {3187, 23160}, {3670, 18202}, {20878, 29632}, {23197, 40940}

X(46514) = EULER LINE INTERCEPT OF X(116)X(14964)

X(46514) lies on these lines: {2, 3}, {116, 14964}, {514, 1921}, {16699, 17181}, {17911, 18659}, {18180, 26531}

X(46515) = EULER LINE INTERCEPT OF X(11)X(16752)

X(46516) = EULER LINE INTERCEPT OF X(768)X(3261)

X(46517) = EULER LINE INTERCEPT OF X(66)X(40341)

X(46517) lies on these lines: {2, 3}, {66, 40341}, {125, 29181}, {325, 33799}, {523, 2525}, {570, 16308}, {576, 11245}, {1503, 3292}, {1899, 11477}, {3098, 45303}, {3258, 44955}, {3284, 16318}, {3313, 3631}, {3448, 34380}, {3564, 23061}, {3629, 15826}, {3793, 31125}, {5157, 32217}, {5522, 16188}, {5972, 29323}, {7756, 15820}, {7998, 18358}, {11064, 29012}, {14927, 26864}, {15019, 45298}, {15066, 39884}, {15437, 39951}, {15581, 41602}, {15598, 16325}, {18390, 44935}, {18911, 21850}, {20190, 37649}, {24855, 40350}, {29317, 32269}, {30737, 40996}, {37775, 42136}, {37776, 42137}, {40126, 43448}, {42426, 46662}

X(46517) = reflection of X(468) in X(858)
X(46517) = reflection of X(37899) in X(468)
X(46517) = reflection of X(47312) in X(2)
X(46517) = reflection of X(37899) in the orthic axis
X(46517) = complement of X(37900)
X(46517) = anticomplement of X(37897)

X(46518) = EULER LINE INTERCEPT OF X(99)X(20022)

X(46518) lies on these lines: {2, 3}, {99, 20022}, {263, 46264}, {511, 25046}, {512, 14712}, {2387, 20065}, {3060, 11257}, {4324, 40790}, {5012, 12110}, {5201, 25051}, {6781, 8623}, {7748, 41278}, {9019, 14570}, {17500, 41328}, {20021, 29012}, {22735, 38741}, {29317, 36213}

X(46519) = EULER LINE INTERCEPT OF X(42)X(1770)

X(46519) lies on these lines: {2, 3}, {42, 1770}, {43, 4333}, {148, 5990}, {390, 37635}, {513, 4380}, {2895, 17784}, {4294, 26131}, {4295, 17018}, {4299, 11269}, {4305, 29814}, {4316, 33140}, {4324, 29640}, {4338, 42042}, {5088, 37782}, {17778, 20075}, {18663, 20011}, {18666, 20061}, {18668, 44661}, {26013, 28164}

X(46520) = EULER LINE INTERCEPT OF X(513)X(4382)

X(46520) lies on these lines: {2, 3}, {513, 4382}, {11269, 12953}, {26013, 28150}

X(46521) = EULER LINE INTERCEPT OF X(513)X(4379)

X(46521) lies on these lines: {2, 3}, {513, 4379}, {1464, 3720}, {3683, 30970}, {4683, 24703}, {8299, 30981}, {11238, 11269}, {17605, 22053}, {26013, 28194}, {30979, 30980}, {30996, 30999}, {31136, 31165}

X(46522) = EULER LINE INTERCEPT OF X(39)X(40325)

X(46522) lies on these lines: {2, 3}, {39, 40325}, {112, 5970}, {160, 44526}, {187, 44099}, {232, 2971}, {512, 1692}, {682, 3767}, {1843, 33843}, {1968, 44162}, {1974, 5033}, {2386, 20975}, {2387, 5028}, {2549, 20775}, {2782, 44145}, {3289, 5167}, {3331, 9418}, {3455, 39644}, {5186, 44146}, {6392, 19597}, {7737, 40981}, {7748, 23208}, {7761, 22062}, {8744, 44090}, {8749, 16098}, {8753, 17980}, {9917, 32006}, {12143, 44142}, {15270, 44518}, {16084, 17984}, {38294, 44371}

X(46523) = EULER LINE INTERCEPT OF X(514)X(4374)

X(46524) = EULER LINE INTERCEPT OF X(649)X(4083)

X(46525) = EULER LINE INTERCEPT OF X(824)X(4391)

X(46526) = EULER LINE INTERCEPT OF X(321)X(693)

X(46527) = EULER LINE INTERCEPT OF X(824)X(4791)

X(46528) = EULER LINE INTERCEPT OF X(824)X(4823)

X(46529) = EULER LINE INTERCEPT OF X(824)X(3762)

X(46530) = EULER LINE INTERCEPT OF X(824)X(4978)

X(46531) = EULER LINE INTERCEPT OF X(824)X(6586)

X(46532) = EULER LINE INTERCEPT OF X(4024)X(4705)

X(46533) = EULER LINE INTERCEPT OF X(918)X(1086)

X(46534) = EULER LINE INTERCEPT OF X(850)X(1577)

X(46535) = EULER LINE INTERCEPT OF X(1111)X(3120)

X(46536) = EULER LINE INTERCEPT OF X(115)X(2223)

X(46536) lies on these lines: {2, 3}, {115, 2223}, {512, 661}, {4433, 10026}, {4436, 44396}, {4447, 23947}, {5949, 8053}, {8299, 20337}, {8818, 15624}, {20975, 44670}, {21010, 23903}

X(46537) = EULER LINE INTERCEPT OF X(812)X(1015))

X(46538) = EULER LINE INTERCEPT OF X(8061)X(16892)

X(46539) = EULER LINE INTERCEPT OF X(826)X(2474)

X(46539) lies on these lines: {2, 3}, {826, 2474}, {3917, 14378}, {6030, 8725}, {8623, 39691}, {9821, 23293}, {9918, 28436}, {12144, 26177}, {17949, 20021}

X(46540) = EULER LINE INTERCEPT OF X(2084)X(2530)

X(46541) = EULER LINE INTERCEPT OF X(99)X(9088)

X(46541) lies on these lines: {2, 3}, {99, 9088}, {107, 1293}, {108, 34594}, {110, 32704}, {112, 9059}, {162, 190}, {902, 46109}, {933, 26713}, {1304, 2692}, {4781, 17906}, {16077, 35169}

X(46542) = EULER LINE INTERCEPT OF X(242)X(514)

X(46543) = EULER LINE INTERCEPT OF X(112)X(9069)

X(46544) = EULER LINE INTERCEPT OF X(339)X(44089)

X(46544) lies on these lines: {2, 3}, {339, 44089}, {2548, 16335}, {2549, 31267}, {16313, 30435}

X(46545) = (name pending)

X(46546) = EULER LINE INTERCEPT OF X(32)X(20859)

X(46546) lies on these lines: {2, 3}, {32, 20859}, {39, 1501}, {141, 33801}, {157, 22062}, {160, 2916}, {184, 30270}, {206, 20819}, {511, 34396}, {574, 8627}, {577, 9475}, {594, 7087}, {626, 4159}, {1086, 1631}, {1634, 35707}, {3001, 19127}, {3060, 3398}, {3094, 18898}, {3095, 5012}, {3098, 3506}, {3117, 5162}, {3313, 14575}, {3917, 42671}, {4414, 8628}, {5007, 21969}, {5989, 20023}, {6664, 8177}, {7795, 10328}, {8588, 41273}, {9155, 35268}, {12203, 39906}, {12220, 37893}, {14602, 32452}, {15080, 35002}, {15107, 26316}, {16893, 23208}, {19126, 23635}, {37485, 40947}

X(46547) = (name pending)

X(46548) = EULER LINE INTERCEPT OF X(56)X(43066)

X(46548) lies on these lines: {2, 3}, {56, 43066}, {238, 28283}, {514, 659}, {528, 23854}, {4433, 32847}, {4653, 5277}, {5045, 29819}, {21808, 24929}

X(46549) = EULER LINE INTERCEPT OF X(55)X(13097)

X(46549) lies on these lines: {2, 3}, {55, 13097}, {522, 659}, {846, 7322}, {1283, 1284}, {1697, 11533}, {3556, 3913}, {8666, 29844}, {24928, 29818}, {25968, 29291}

X(46550) = EULER LINE INTERCEPT OF X(513)X(4088)

X(46551) = EULER LINE INTERCEPT OF X(513)X(168922)

X(46552) = EULER LINE INTERCEPT OF X(513)X(4468)

X(46553) = EULER LINE INTERCEPT OF X(63)X(3966)

X(46553) lies on these lines: {2, 3}, {63, 3966}, {513, 3004}, {3743, 10624}, {26013, 28845}

X(46554) = EULER LINE INTERCEPT OF X(650)X(4802)

X(46555) = EULER LINE INTERCEPT OF X(37)X(650)

X(46555) lies on these lines: {2, 3}, {37, 650}, {1104, 1647}, {1125, 42753}, {3695, 17780}, {9458, 32777}

X(46556) = (name pending)

X(46557) = EULER LINE INTERCEPT OF X(1826)X(7649)

X(46558) = EULER LINE INTERCEPT OF X(242)X(8735)

X(46559) = EULER LINE INTERCEPT OF X(1874)X(5236)

X(46560) = EULER LINE INTERCEPT OF X(316)X(44089)

X(46560) lies on these lines: {2, 3}, {316, 44089}, {16221, 44947}, {35524, 44146}

X(46561) = EULER LINE INTERCEPT OF X(3906)X(9148)

X(46561) lies on these lines: {2, 3}, {3906, 9148}, {7697, 7703}, {30789, 35002}, {31127, 32515}

X(46562) = (name pending)

X(46563) = EULER LINE INTERCEPT OF X(313)X(3261)

X(46564) = EULER LINE INTERCEPT OF X(650)X(3250)

X(46565) = EULER LINE INTERCEPT OF X(29017)X(35519)

X(46566) = EULER LINE INTERCEPT OF X(42)X(649)

X(46567) = (name pending)

X(46568) = EULER LINE INTERCEPT OF X(37)X(513)

X(46568) lies on these lines: {2, 3}, {37, 513}, {1104, 27846}, {3695, 23354}, {20777, 26012}

X(46569) = EULER LINE INTERCEPT OF X(1577)X(1930)

X(46570) = EULER LINE INTERCEPT OF X(14208)X(20910)

X(46571) = EULER LINE INTERCEPT OF X(6)X(44136)

X(46571) lies on these lines: {2, 3}, {6, 44136}, {287, 44768}, {323, 1236}, {338, 22151}, {1994, 7894}, {3260, 37784}, {3978, 23962}, {6748, 26156}, {9544, 39646}, {10358, 11451}, {13449, 15059}

X(46572) = (name pending)

X(46573) = (name pending)

X(46574) = EULER LINE INTERCEPT OF X(649)X(693)

X(46574) lies on these lines: {2, 3}, {649, 693}, {673, 17963}, {3002, 5088}, {17026, 21370}, {24592, 24633}

X(46575) = EULER LINE INTERCEPT OF X(812)X(4391)

X(46576) = EULER LINE INTERCEPT OF X(513)X(3261)

X(46577) = EULER LINE INTERCEPT OF X(3766)X(4083)

X(46578) = EULER LINE INTERCEPT OF X(513)X(1919)

X(46579) = EULER LINE INTERCEPT OF X(650)X(8632)

X(46580) = EULER LINE INTERCEPT OF X(918)X(3837)

X(46581) = EULER LINE INTERCEPT OF X(3910)X(4486)

X(46582) = EULER LINE INTERCEPT OF X(150)X(14964)

X(46583) = EULER LINE INTERCEPT OF X(513)X(894)

X(46584) = EULER LINE INTERCEPT OF X(f239)X(18107)

This preamble is contributed by Clark Kimberling and Peter Moses, January 11, 2022. In the plane of a triangle ABC with circumcircle (O) and Euler line L, let U1 be a point on (O), and let

U1 = an arbitrary point on (O), and T1 = line tangent to (O) at U1;
U2 = reflection of U1 in L, and T2 = line tangent to (O) at U2;
U3 = antipode of U1, and T3 = line tangent to (O) at U3;
U4 = antipode of U2, and T4 = line tangent to (O) at U4;
P1 = T1∩T2; P2 = T2∩T3; P3 = T3∩T4; P4 = T4∩T1.

The points P1, P2, P3, P4 are the vertices of a parallelogram. The following table shows results for several choices of the point U1. In the table, each index k represents the triangle center X(k).

U1	U2	U3	U4	P1	P2	P3	P4
74	477	110	476	46585	46616	15329	46608
98	842	99	691	7418	46609	11634	44823
100	1290	104	2687	13583	46610	14127	46611
101	2690	103	2688	46595		46596
105	2752	1292	2691	46586		46593
107	1304	1294	2693	46587		46614	46613
108	2766	1295	2694	46588
111	2770	1296	2770	46589
112	935	1297	2697	46592	46614	46594	46615
930	1291	1141	14979	46590
933	972	18401	945	46591

The midpoints of segments U1U2, U2U3, U3U4, U4U1 are vertices of another parallelogram, as represented by the following table.

U1	m(U1,U2)	m(U2,U3)	m(U3,U4)	m(U4,U1)
74	36164	14934	7471	46632
98	36166	46634	7472	46333
100	36167	46636	46618	46635
112	46619	46631	46620	46637

If you have Geogebra, you can download Three Parallelograms. (The vertices are U1, U2, U3, U4; P1, P2, P3, P4; m1, m2, m3, m4. Drag D to vary the line OD; drag U1 to vary the 12 vertices.)

X(46585) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(74)

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 + 4*a^10*b^2*c^2 - 7*a^8*b^4*c^2 - 10*a^6*b^6*c^2 + 17*a^4*b^8*c^2 - 2*a^2*b^10*c^2 - 3*b^12*c^2 - 5*a^10*c^4 - 7*a^8*b^2*c^4 + 38*a^6*b^4*c^4 - 22*a^4*b^6*c^4 - 13*a^2*b^8*c^4 + 9*b^10*c^4 + 10*a^8*c^6 - 10*a^6*b^2*c^6 - 22*a^4*b^4*c^6 + 32*a^2*b^6*c^6 - 6*b^8*c^6 - 10*a^6*c^8 + 17*a^4*b^2*c^8 - 13*a^2*b^4*c^8 - 6*b^6*c^8 + 5*a^4*c^10 - 2*a^2*b^2*c^10 + 9*b^4*c^10 - a^2*c^12 - 3*b^2*c^12) : :

X(46585) lies on these lines: {2, 3}, {74, 526}, {98, 43660}, {477, 16171}, {841, 842}, {1294, 1300}, {1299, 5897}, {1495, 7740}, {1624, 10721}, {1986, 40948}, {2693, 32710}, {2777, 39985}, {2972, 12292}, {5467, 43576}, {5502, 14157}, {6000, 14264}, {9717, 12112}, {12041, 14933}, {14915, 33927}, {15035, 42742}, {15055, 39987}, {21663, 39174}, {39434, 39437}

X(46585) = reflection of X(i) in X(j) for these {i,j}: {4, 3134}, {14264, 16186}, {14933, 12041}, {15329, 3}
X(46585) = circumcircle-inverse of X(36164)
X(46585) = crosspoint of X(74) and X(477)
X(46585) = crosssum of X(i) and X(j) for these (i,j): {30, 5663}, {9033, 37985}
X(46585) = crossdifference of every pair of points on line {647, 3163}
X(46585) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 7464, 11634}, {1113, 1114, 36164}, {3651, 36001, 13589}, {7440, 7454, 7429}, {14157, 14385, 5502}, {40894, 40895, 4230}, {42789, 42790, 4240}

X(46586) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(105)

X(46586) lies on these lines: {2, 3}, {104, 9061}, {105, 659}, {111, 759}, {2373, 39439}, {2374, 39435}, {2770, 12030}, {7292, 42753}, {9078, 28476}, {15344, 26703}, {24403, 41230}, {24822, 27543}

X(46586) = crosspoint of X(105) and X(2752)
X(46586) = crosssum of X(518) and X(2836)
X(46586) = crossdifference of every pair of points on line {647, 6184}
X(46586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 23, 13589}, {21, 1325, 11634}, {468, 867, 2}, {4228, 7469, 15329}, {7423, 7458, 7448}

X(46587) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(107)

X(46587) lines on these lines: {2, 3}, {107, 1624}, {110, 1301}, {111, 38867}, {112, 9064}, {476, 22239}, {685, 878}, {925, 30249}, {1289, 1302}, {1304, 5502}, {1495, 43952}, {5667, 43919}, {6000, 39174}, {9060, 10423}, {16186, 35908}, {23181, 30441}, {30510, 40596}, {39575, 46128}

X(46587) = circumcircle-inverse of X(31510)
X(46587) = polar-circle-inverse of X(37985)
X(46587) = isogonal conjugate of X(43701)
X(46587) = isotomic conjugate of the polar conjugate of X(2442)
X(46587) = isogonal conjugate of the polar conjugate of X(2404)
X(46587) = X(i)-Ceva conjugate of X(j) for these (i,j): {250, 40948}, {2404, 2442}, {44769, 112}
X(46587) = X(i)-isoconjugate of X(j) for these (i,j): {1, 43701}, {19, 2416}, {92, 2430}, {656, 1294}, {2972, 36043}, {15404, 36035}
X(46587) = crosspoint of X(107) and X(1304)
X(46587) = crosssum of X(520) and X(9033)
X(46587) = crossdifference of every pair of points on line {647, 1562}
X(46587) = barycentric product X(i)*X(j) for these {i,j}: {3, 2404}, {69, 2442}, {107, 44436}, {133, 44769}, {648, 6000}, {15459, 40948}
X(46587) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 2416}, {6, 43701}, {112, 1294}, {133, 41079}, {184, 2430}, {2404, 264}, {2442, 4}, {6000, 525}, {32640, 15404}, {40948, 41077}, {44436, 3265}
X(46587) = trilinear product X(i)*X(j) for these {i,j}: {48, 2404}, {63, 2442}, {133, 36034}, {162, 6000}
X(46587) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 468, 7418}, {25, 44889, 4}, {28, 2074, 14127}, {235, 36179, 4}, {1113, 1114, 31510}, {4230, 7473, 11634}, {4240, 7480, 15329}, {4240, 15329, 4230}, {4246, 37966, 13589}

X(46588) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(108)

X(46588) lies on these lines: {2, 3}, {100, 40097}, {107, 30250}, {108, 676}, {1289, 9070}, {1301, 6011}, {1870, 42753}, {2222, 23706}, {9107, 26706}, {30249, 44065}, {36110, 36113}

X(46588) = X(37140)-Ceva conjugate of X(112)
X(46588) = X(656)-isoconjugate of X(39435)
X(46588) = crosspoint of X(108) and X(2766)
X(46588) = crosssum of X(521) and X(2850)
X(46588) = crossdifference of every pair of points on line {647, 35072}
X(46588) = barycentric product X(653)*X(45272)
X(46588) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 39435}, {45272, 6332}
X(46588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 186, 14127}, {4238, 7476, 11634}, {4242, 37964, 13589}, {4246, 37966, 15329}

X(46589) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(111)

X(46589) lies on these lines: {2, 3}, {98, 9084}, {111, 351}, {842, 10102}, {2373, 2374}, {14700, 15916}, {23342, 26276}, {40282, 44420}

X(46589) = circumcircle-inverse of X(36168)
X(46589) = crosspoint of X(111) and X(2770)
X(46589) = crosssum of X(524) and X(2854)
X(46589) = crossdifference of every pair of points on line {647, 2482}
X(46589) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 23, 11634}, {468, 3143, 2}, {1113, 1114, 36168}, {1995, 7426, 15329}

X(46590) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(930)

X(46590) lies on these lines: {2, 3}, {110, 33639}, {925, 30248}, {930, 25149}, {933, 20185}, {6799, 13398}, {10420, 13863}

X(46590) = crosspoint of X(930) and X(1291)
X(46590) = crosssum of X(1510) and X(45147)
X(46590) = crossdifference of every pair of points on line {647, 39018}

X(46591) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(933)

X(46591) lies on these lines: {2, 3}, {107, 30248}, {110, 6799}, {930, 20626}, {933, 46062}, {1301, 33639}, {1304, 13863}

X(46591) = crossdifference of every pair of points on line {647, 39019}
X(46591) = X(656)-isoconjugate of X(39431)
X(46591) = barycentric product X(18315)*X(44057)
X(46591) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 39431}, {10214, 24978}, {44057, 18314}

X(46592) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(935)

X(46592) lies on these lines: {2, 3}, {99, 1289}, {107, 30247}, {110, 39382}, {112, 1576}, {159, 35902}, {691, 10423}, {925, 30251}, {1296, 1301}, {1304, 10098}, {1986, 38551}, {2420, 2445}, {2696, 22239}, {3565, 39417}, {10097, 32729}, {14580, 34158}, {20187, 30249}, {20626, 44061}, {32649, 32662}, {32696, 32708}, {34131, 39841}

X(46592) = isogonal conjugate of orthocenter of X(3)X(6)X(66)
X(46592) = circumcircle-inverse of X(46619)
X(46592) = X(691)-Ceva conjugate of X(112)
X(46592) = X(42665)-cross conjugate of X(2393)
X(46592) = cevapoint of X(i) and X(j) for these (i,j): {2393, 42665}, {42659, 44102}
X(46592) = crosspoint of X(112) and X(935)
X(46592) = crosssum of X(i) and X(j) for these (i,j): {520, 14417}, {525, 9517}
X(46592) = trilinear pole of line {2393, 14580}
X(46592) = crossdifference of every pair of points on line {647, 15526}
X(46592) = X(i)-isoconjugate of X(j) for these (i,j): {647, 37220}, {656, 2373}, {810, 46140}, {1177, 14208}, {1577, 18876}, {10423, 17879}, {15526, 36095}
X(46592) = barycentric product X(i)*X(j) for these {i,j}: {99, 14580}, {107, 14961}, {110, 5523}, {112, 858}, {162, 18669}, {648, 2393}, {691, 1560}, {1634, 21459}, {8750, 17172}, {12827, 32708}, {17708, 20410}, {20884, 32676}, {23582, 42665}
X(46592) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 2373}, {162, 37220}, {648, 46140}, {858, 3267}, {1560, 35522}, {1576, 18876}, {2393, 525}, {5181, 45807}, {5523, 850}, {14580, 523}, {14961, 3265}, {18669, 14208}, {20410, 9979}, {32729, 41511}, {35325, 46165}, {41937, 10423}, {42665, 15526}

X(46593) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(1292)

X(46593) lies on these lines: {2, 3}, {99, 30257}, {1292, 6084}, {1296, 6011}, {9070, 30256}, {20187, 30250}, {30247, 44065}

X(46593) = crosspoint of X(1292) and X(2691)
X(46593) = crosssum of X(2775) and X(3309)

X(46594) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(1297)

X(46594) lies on these lines: {2, 3}, {98, 34168}, {111, 5897}, {684, 1297}, {1294, 2373}, {1300, 39436}, {2374, 39434}

X(46594) = circumcircle-inverse of X(46620)
X(46594) = crosspoint of X(1297) and X(2697)
X(46594) = crosssum of X(1503) and X(2781)
X(46594) = crossdifference of every pair of points on line {647, 23976}

X(46595) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(101)

X(46595)lies on these lines: {2, 3}, {101, 692}, {1305, 26705}, {1983, 21789}, {9057, 44876}

X(46595) = X(656)-isoconjugate of X(39438)
X(46595) = crosspoint of X(101) and X(2690)
X(46595) = crosssum of X(514) and X(2774)
X(46595) = crossdifference of every pair of points on line {647, 1086}
X(46595) = barycentric quotient X(112)/X(39438)

X(46596) = EULER LINE INTERCEPT OF LINE TANGENT TO CIRCUMCIRCLE AT X(2688)

X(46596) = crosspoint of X(103) and X(2688)
X(46596) = crosssum of X(516) and X(2772)
X(46596) = crossdifference of every pair of points on line {647, 23972}

X(46597) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(190)

X(46597) lies on these lines: {2, 3}, {36, 27846}, {99, 27853}, {100, 932}, {101, 29329}, {109, 29325}, {110, 6010}, {667, 3573}, {3572, 17940}, {3733, 4585}, {3799, 8671}, {9058, 39631}, {18266, 40155}

X(46597) = crosspoint of X(2702) and X(34071)
X(46597) = crosssum of X(2786) and X(3835)
X(46597) = crossdifference of every pair of points on line {647, 6377}

X(46598) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(670)

X(46598) lies on these lines: {2, 3}, {99, 3222}, {110, 30254}, {669, 2396}, {17938, 17941}, {21006, 23342}

X(46599) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(671)

X(46599) lies on these lines: {2, 3}, {187, 5968}, {2079, 33900}, {3455, 34010}, {11643, 23288}, {14263, 40350}, {14995, 26613}, {21445, 34810}

X(46599) = circumcircle-inverse of X(36196)
X(46599) = crosssum of X(i) and X(j) for these (i,j): {125, 33921}, {543, 625}

X(46600) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(6189)

X(46600) lies on these lines: {2, 3}, {110, 1380}, {323, 38597}, {669, 30509}, {1340, 5640}, {1341, 15080}, {1379, 15107}, {1634, 6189}, {3060, 3557}, {3414, 36829}, {3558, 11422}, {5012, 14631}, {5201, 6190}, {6141, 11673}, {14630, 15019}

X(46600) = crosssum of X(512) and X(13636)
X(46600) = crossdifference of every pair of points on line {647, 13722}
X(46600) = barycentric product X(3557)*X(6189)
X(46600) = barycentric quotient X(i)/X(j) for these {i,j}: {1380, 6177}, {3557, 3414}
X(46600) = {X(2),X(237)}-harmonic conjugate of X(46601)
X(46600) = {X(3),X(23)}-harmonic conjugate of X(46601)

X(46601) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(6190)

X(46601) lies on these lines: {2, 3}, {110, 1379}, {323, 38596}, {669, 30508}, {1340, 15080}, {1341, 5640}, {1380, 15107}, {1634, 6190}, {3060, 3558}, {3413, 36829}, {3557, 11422}, {5012, 14630}, {5201, 6189}, {6142, 11673}, {14631, 15019}

X(46601) = crosssum of X(512) and X(13722)
X(46601) = crossdifference of every pair of points on line {647, 13636}
X(46601) = barycentric product X(3558)*X(6190)
X(46601) = barycentric quotient X(i)/X(j) for these {i,j}: {1379, 6178}, {3558, 3413}
X(46601) = {X(2),X(237)}-harmonic conjugate of X(46600)
X(46601) = {X(3),X(23)}-harmonic conjugate of X(46600)

X(46602) = EULER LINE INTERCEPT OF LINE TANGENT TO STEINER CIRCUMELLIPSE AT X(43091)

X(46602) lies on these lines: {2, 3}, {1495, 33927}, {5467, 15107}, {6800, 14687}, {9717, 35265}, {15080, 46127}

X(46603) = ISOGONAL CONJUGATE OF X(9512)

X(46603) lies on these lines: {3448, 14721}, {5012, 36830}, {9513, 9514}, {21243, 44155}

X(46603) = isogonal conjugate of X(9512)
X(46603) = isotomic conjugate of X(46247)
X(46603) = X(i)-isoconjugate-of-X(j) for these {i, j}: {661, 9514}, {1577, 46248}
X(46603) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (54, 39843), (110, 9514), (1576, 46248)
X(46603) = cevapoint of PU(145)
X(46603) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(5012)}} and {{A, B, C, X(3), X(41203)}}
X(46603) = barycentric product X(110)*X(46246)
X(46603) = barycentric quotient X(i)/X(j) for these (i, j): (54, 39843), (110, 9514), (1576, 46248)
X(46603) = trilinear product X(163)*X(46246)
X(46603) = trilinear quotient X(i)/X(j) for these (i, j): (163, 46248), (662, 9514), (2167, 39843)

X(46604) = X(311)X(930)∩X(570)X(8603)

X(46604) lies on these lines: {140, 21394}, {311, 930}, {570, 8603}, {34507, 39171}

X(46604) = center of the circumconic {{A, B, C, X(930), X(32737)}}
X(46604) = center of the perspeconic of these triangles: ABC and Kosnita

X(46605) = (name pending)

X(46606) = X(2)X(14265)∩X(2421)X(4226)

X(46606) lies on the curve Q066 and these lines: {2,14265}, {147,34174}, {2421,4226}, {5968,7736}, {25046,46039}, {35910,35922}

X(46606) = isotomic conjugate of the anticomplement of X(2395)
X(46606) = X(2395)-cross conjugate of X(2)
X(46606) = X(i)-vertex conjugate of X(j) for these (i,j): (4226,4230) ,(4230,4226)
X(46606) = cevapoint of X(i)and X(j) for these {i,j}: {114,523}, {512,11672}
X(46606) = trilinear pole of line X(230)X(511) (the axis of parabola {{A,B,C,X(511),X(805)}}, and the Simson line of X(115) wrt the medial triangle)
X(46606) = barycentric product X(290)*X(43942)
X(46606) = trilinear product X(1821)*X(43942)

X(46607) = (name pending)

X(46607) = cevapoint of X(113) and X(647)
X(46607) = trilinear pole of line X(30)X(974) (the Simson line of X(125) wrt the orthic triangle)

X(46608) = CROSSPOINT OF X(74) AND X(476)

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

X(46608) lies on the cubic K723 and these lines: {3, 523}, {74, 526}, {157, 669}, {186, 18808}, {476, 10412}, {512, 4550}, {520, 7689}, {924, 3357}, {1510, 15062}, {1609, 45801}, {2433, 11074}, {3005, 5888}, {3050, 18573}, {3098, 8675}, {5961, 13289}, {7691, 14329}, {8057, 9938}, {8266, 45839}, {9003, 32305}, {9033, 12901}, {14977, 35296}, {16868, 34963}, {18310, 37344}

X(46608) = reflection of X(3) in X(14809)
X(46608) = circumcircle-inverse of X(46632)
X(46608) = X(39290)-Ceva conjugate of X(6)
X(46608) = crosspoint of X(i) and X(j) for these (i,j): {74, 476}, {1304, 38534}
X(46608) = crosssum of X(i) and X(j) for these (i,j): {30, 526}, {512, 6128}, {523, 20304}, {2072, 9033}
X(46608) = crossdifference of every pair of points on line {3003, 3163}

X(46609) = CROSSPOINT OF X(99) AND X(842)

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

X(46609) = 3 X[3] - 2 X[44821], X[44821] - 3 X[44822], 4 X[44821] - 3 X[44823], 4 X[44822] - X[44823]

X(46609) lies on these lines: {3, 523}, {6, 39495}, {22, 669}, {23, 9168}, {25, 10190}, {26, 32204}, {99, 670}, {159, 3566}, {511, 8723}, {512, 3098}, {690, 11616}, {842, 7418}, {1499, 33532}, {1649, 1995}, {2422, 3094}, {2793, 44826}, {2799, 14270}, {3050, 44453}, {3534, 25423}, {5466, 7496}, {7484, 10278}, {7485, 8029}, {7492, 44010}, {8266, 21395}, {8371, 40916}, {9479, 41078}, {9723, 22089}, {10189, 16419}, {10280, 13154}, {23301, 31152}, {39513, 39560}

X(46609) = reflection of X(i) in X(j) for these {i,j}: {3, 44822}, {6, 39495}, {44823, 3}
X(46609) = reflection of X(44823) in the Euler line
X(46609) = circumcircle-inverse of X(46634)
X(46609) = X(6035)-Ceva conjugate of X(6)
X(46609) = crosspoint of X(99) and X(842)
X(46609) = crosssum of X(512) and X(542)
X(46609) = crossdifference of every pair of points on line {1084, 3003}

X(46610) = CROSSPOINT OF X(104) AND X(1290)

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

X(46610) lies on these lines: {1, 13868}, {3, 523}, {104, 900}, {513, 1385}, {659, 1623}, {1290, 13589}, {2320, 4367}, {2605, 21842}, {3733, 11101}, {12262, 15313}, {13743, 28217}, {27685, 31946}, {39478, 44805}

X(46610) = reflection of X(39478) in X(44807)
X(46610) = circumcircle-inverse of X(46636)
X(46610) = crosspoint of X(104) and X(1290)
X(46610) = crosssum of X(i) and X(j) for these (i,j): {517, 8674}, {8677, 18455}
X(46610) = crossdifference of every pair of points on line {3003, 23980}

X(46611) = CROSSPOINT OF X(100) AND X(2687)

X(46611) lies on these lines: {3, 523}, {100, 190}, {513, 3579}, {526, 12778}, {2605, 5697}, {2687, 14127}, {2804, 39478}, {3733, 37405}, {3737, 11010}, {8674, 44812}, {15313, 40660}, {16117, 28217}, {27553, 31946}

X(46611) = circumcircle-inverse of X(46635)
X(46611) = crosspoint of X(100) and X(2687)
X(46611) = crosssum of X(i) and X(j) for these (i,j): {512, 3013}, {513, 2771}
X(46611) = crossdifference of every pair of points on line {1015, 3003}

X(46612) = CROSSPOINT OF X(1294) AND X(1304)

X(46612) lies on these lines: {3, 523}, {26, 8057}, {159, 9007}, {206, 8675}, {520, 6759}, {526, 9934}, {1294, 6086}, {1304, 5502}, {9033, 13289}, {23286, 38808}

X(46612) = crosspoint of X(1294) and X(1304)
X(46612) = crosssum of X(i) and X(j) for these (i,j): {520, 34842}, {6000, 9033}
X(46612) = crossdifference of every pair of points on line {3003, 39008}

X(46613) = CROSSPOINT OF X(107) AND X(2693)

X(46613) lies on these lines: {3, 523}, {107, 1624}, {520, 3357}, {8057, 12084}, {9033, 13293}, {14380, 38937}

X(46613) = crosspoint of X(107) and X(2693)
X(46613) = crosssum of X(520) and X(2777)
X(46613) = crossdifference of every pair of points on line {3003, 35071}

X(46614) = CROSSPOINT OF X(935) AND X(1297)

X(46614) lies on these lines: {3, 523}, {161, 23616}, {525, 15577}, {684, 1297}, {935, 46592}, {2799, 39854}, {3265, 26283}

X(46614) = circumcircle-inverse of X(46631)
X(46614) = crosspoint of X(935) and X(1297)
X(46614) = crosssum of X(1503) and X(9517)
X(46614) = crossdifference of every pair of points on line {3003, 23976}

X(46615) = CROSSPOINT OF X(112) AND X(2697)

X(46615) lies on these lines: {3, 523}, {25, 6587}, {112, 1576}, {157, 21397}, {206, 512}, {525, 44883}, {571, 42658}, {1968, 2485}, {2697, 46594}, {2799, 39860}, {2848, 44806}, {9178, 41890}, {25644, 34217}

X(46615) = circumcircle-inverse of X(46637)
X(46615) = crosspoint of X(112) and X(2697)
X(46615) = crosssum of X(525) and X(2781)
X(46615) = crossdifference of every pair of points on line {3003, 15526}

X(46616) = CROSSPOINT OF X(110) AND X(477)

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

X(46616) lies on these lines: {3, 523}, {54, 8562}, {110, 351}, {182, 8675}, {477, 16171}, {512, 8717}, {520, 1147}, {647, 5063}, {924, 6759}, {1510, 8718}, {2436, 32663}, {3520, 18808}, {5926, 15577}, {8057, 9932}, {9003, 12584}, {9033, 12893}, {13293, 13496}, {22962, 37084}

X(46616) = circumcircle-inverse of X(14934)
X(46616) = X(30528)-Ceva conjugate of X(6)
X(46616) = crosspoint of X(110) and X(477)
X(46616) = crosssum of X(i) and X(j) for these (i,j): {512, 3018}, {523, 5663}
X(46616) = crossdifference of every pair of points on line {115, 3003}
X(46616) = barycentric product X(525)*X(15463)
X(46616) = barycentric quotient X(15463)/X(648)

X(46617) = EULER LINE INTERCEPT OF X(542)X(3416)

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

As a point on the Euler line, X(46617) has Shinagawa coefficients (r*R+2s^2,3*(r^2+r*R-s^2)) .

X(46618) = MIDPOINT OF X(104) AND X(2687)

X(46618) lies on these lines: {2, 3}, {36, 29008}, {74, 6003}, {104, 523}, {477, 759}, {517, 31523}, {915, 2694}, {1290, 38693}, {2693, 39439}, {2695, 14987}, {2716, 43655}, {2829, 5520}, {6713, 42422}, {32710, 39435}

X(46618) = midpoint of X(i) and X(j) for these {i,j}: {20, 36175}, {104, 2687}, {1325, 6909}
X(46618) = reflection of X(i) in X(j) for these {i,j}: {1532, 44898}, {36167, 3}, {42422, 6713}
X(46618) = circumcircle-inverse of X(14127)

X(46619) = MIDPOINT OF X(112) AND X(935)

X(46619) lies on these lines: {2, 3}, {99, 250}, {107, 10098}, {112, 523}, {476, 39382}, {691, 1289}, {1296, 22239}, {1301, 2696}, {1304, 30247}, {1554, 2777}, {2697, 38699}, {2794, 42426}, {6720, 38971}, {10420, 30251}, {34978, 39832}

X(46619) = midpoint of X(112) and X(935)
X(46619) = reflection of X(38971) in X(6720)
X(46619) = circumcircle-inverse of X(46592)
X(46619) = isogonal conjugate of orthocenter of X(4)X(6)X(67)
X(46619) = Euler line intercept, other than X(2), of circle {{X(2),X(107),X(112)}}

X(46620) = MIDPOINT OF X(1297) AND X(2697)

X(46620) lies on these lines: {2, 3}, {523, 1297}, {842, 34168}, {935, 38717}, {1554, 5972}, {2373, 2693}, {2770, 5897}, {32710, 39436}, {34841, 42426}, {39434, 40119}

X(46620) = midpoint of X(i) and X(j) for these {i,j}: {1297, 2697}
X(46620) = reflection of X(i) in X(j) for these {i,j}: {1529, 5159}, {1554, 5972}, {42426, 34841}
X(46620) = circumcircle-inverse of X(46594)

X(46621) = X(4)X(371)∩X(54)X(216)

X(46621) lies on these lines: {4, 371}, {54, 216}, {186, 8954}, {324, 16032}, {1151, 10605}, {1199, 32589}, {1589, 6515}, {1599, 8909}, {3090, 10960}, {3156, 3311}, {3364, 46112}, {3389, 46113}, {5012, 8961}, {6200, 6458}, {6419, 26894}, {6425, 12964}, {8908, 11463}, {8963, 43651}, {18909, 44616}, {21640, 26916}

X(46621) = X(13450)-Ceva conjugate of X(46622)
X(46621) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54, 216, 46622), (371, 6413, 4)

X(46622) = X(4)X(372)∩X(54)X(216)

X(46622) lies on these lines: {4, 372}, {54, 216}, {186, 32589}, {324, 16037}, {1152, 10605}, {1199, 8954}, {1590, 6515}, {3090, 10962}, {3155, 3312}, {3365, 46112}, {3390, 46113}, {6396, 6457}, {6420, 26919}, {6426, 12970}, {8961, 34148}, {18909, 44617}

X(46622) = X(13450)-Ceva conjugate of X(46621)
X(46622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {54, 216, 46621}, {372, 6414, 4}

X(46623) = X(1)X(3)∩X(4)X(25446)

X(46623) lies on the cubic K1256 and these lines: {1, 3}, {4, 25446}, {20, 19642}, {58, 37425}, {184, 23059}, {185, 411}, {283, 851}, {404, 5650}, {511, 3651}, {573, 19548}, {580, 4192}, {582, 19543}, {1006, 15488}, {1150, 5178}, {1408, 15447}, {1444, 5929}, {1792, 10381}, {2328, 28258}, {3781, 25440}, {3917, 35976}, {4220, 35203}, {5752, 6102}, {5907, 6905}, {5972, 24882}, {6045, 7580}, {9306, 37264}, {13323, 37400}, {13329, 19513}, {18180, 37286}, {19771, 20846}, {21363, 36558}, {22076, 35979}, {37510, 37732}

X(46623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 45923, 1385}

X(46624) = X(1885)-CEVA CONJUGATE OF X(4)

X(46624) lies on the cubic K1256 and these lines: {4, 40196}, {20, 3186}, {378, 3462}, {1249, 1968}, {3068, 26936}, {5254, 5894}, {5667, 18560}

X(46625) = X(20)X(3186)∩X(147)X(185)

X(46625) lies on the Steiner/Wallace right hyperbola, the Kiepert circumhyperbola of the anticomplementary triangle, the cubic K1256, and these lines: {20, 3186}, {147, 185}, {2896, 8920}, {3504, 17928}, {6815, 45029}, {32974, 41914}

X(46626) = X(147)X(185)∩X(3493)X(8841)

X(46627) = X(32)X(512)∩X(114)X(325)

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

X(46627) lies on the cubic K1257 and these lines: {32, 512}, {114, 325}, {2794, 44011}, {9753, 13137}, {32484, 35436}

X(46628) = X(4)X(39299)∩X(114)X(4558)

X(46628) lies on the cubic K1257 and these lines: {4, 39299}, {114, 4558}, {230, 1313}, {511, 1114}, {1113, 44099}, {13414, 44127}

X(46628) = orthic-isogonal conjugate of X(13414)
X(46628) = X(4)-Ceva conjugate of X(13414)

X(46629) = X(4)X(39298)∩X(114)X(4558)

X(46629) lies on the cubic K1257 and these lines: {4, 39298}, {114, 4558}, {230, 1312}, {511, 1113}, {1114, 44099}, {13415, 44127}

X(46629) = orthic-isogonal conjugate of X(13415)
X(46629) = X(4)-Ceva conjugate of X(13415)

X(46630) = X(511)X(38642)∩X(1976)X(2396)

X(46631) = MIDPOINT OF X(935) AND X(1297)

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

X(46631) lies on these lines: {3, 523}, {30, 935}, {339, 36166}, {2072, 38953}, {2697, 38717}, {10242, 18323}, {34841, 38971}, {38624, 46620}, {38741, 44246}

X(46631) = midpoint of X(935) and X(1297)
X(46631) = reflection of X(i) in X(j) for these {i,j}: {38971, 34841}, {46620, 38624}, {46637, 3}
X(46631) = reflection of X(46637) in the Euler line
X(46631) = circumcircle inverse of X(46614)

X(46632) = MIDPOINT OF X(74) AND X(476)

Barycentrics 2*a^16 - 6*a^14*b^2 + 3*a^12*b^4 + 5*a^10*b^6 - 12*a^6*b^10 + 11*a^4*b^12 - 3*a^2*b^14 - 6*a^14*c^2 + 22*a^12*b^2*c^2 - 21*a^10*b^4*c^2 - 15*a^8*b^6*c^2 + 40*a^6*b^8*c^2 - 24*a^4*b^10*c^2 + 3*a^2*b^12*c^2 + b^14*c^2 + 3*a^12*c^4 - 21*a^10*b^2*c^4 + 48*a^8*b^4*c^4 - 30*a^6*b^6*c^4 - 3*a^4*b^8*c^4 + 9*a^2*b^10*c^4 - 6*b^12*c^4 + 5*a^10*c^6 - 15*a^8*b^2*c^6 - 30*a^6*b^4*c^6 + 32*a^4*b^6*c^6 - 9*a^2*b^8*c^6 + 15*b^10*c^6 + 40*a^6*b^2*c^8 - 3*a^4*b^4*c^8 - 9*a^2*b^6*c^8 - 20*b^8*c^8 - 12*a^6*c^10 - 24*a^4*b^2*c^10 + 9*a^2*b^4*c^10 + 15*b^6*c^10 + 11*a^4*c^12 + 3*a^2*b^2*c^12 - 6*b^4*c^12 - 3*a^2*c^14 + b^2*c^14 : :

X(467632) = 3 X[74] - X[14508], X[110] - 3 X[38700], 3 X[476] + X[14508], X[477] - 3 X[15055], 2 X[546] - 3 X[21315], 2 X[3154] - 3 X[15061], 3 X[5627] - X[10733], 2 X[10264] - 3 X[40630], 4 X[12068] - 3 X[14643], X[14480] - 3 X[15035], 3 X[14644] - X[44967], 3 X[14993] + X[20127], 5 X[15021] + X[38677], 5 X[15040] - 2 X[30221], 3 X[15041] + X[38580], 3 X[15061] - X[20957], 2 X[16319] - 3 X[44214], 2 X[21269] - 3 X[34150], X[21269] - 3 X[34209], 2 X[31379] - 3 X[38727], 4 X[31945] - 5 X[38794]

X(46632) lies on the cubic K905 and these lines: {3, 523}, {5, 46045}, {30, 74}, {110, 38700}, {113, 22104}, {125, 36184}, {185, 36159}, {399, 3233}, {477, 15055}, {541, 1553}, {546, 21315}, {1511, 14611}, {1552, 11251}, {2072, 10745}, {2777, 25641}, {2780, 9179}, {3154, 15061}, {3258, 6699}, {3627, 21316}, {5663, 7471}, {6070, 17702}, {7728, 36169}, {10620, 36193}, {11657, 11799}, {12041, 16168}, {12068, 14643}, {12103, 21317}, {12236, 16978}, {12244, 36172}, {13630, 36161}, {14480, 15035}, {14644, 44967}, {14830, 44265}, {15021, 38677}, {15040, 30221}, {15041, 38580}, {16171, 39987}, {16319, 44214}, {31379, 38727}, {31945, 38794}, {36177, 40280}

X(46632) = midpoint of X(i) and X(j) for these {i,j}: {74, 476}, {10620, 36193}, {12244, 36172}, {14677, 18319}
X(46632) = reflection of X(i) in X(j) for these {i,j}: {113, 22104}, {265, 12079}, {399, 3233}, {3258, 6699}, {3627, 21316}, {7471, 38609}, {7728, 36169}, {11799, 11657}, {14611, 1511}, {14934, 3}, {16978, 12236}, {20957, 3154}, {21317, 12103}, {34150, 34209}, {36164, 12041}, {36184, 125}, {46045, 5}
X(46632) = reflection of X(14934) in the Euler line
X(46632) = circumcircle-inverse of X(46608)
X(46632) = {X(15061),X(20957)}-harmonic conjugate of X(3154)

X(46633) = MIDPOINT OF X(98) AND X(691)

Barycentrics 2*a^14 - 6*a^12*b^2 + 5*a^10*b^4 + 2*a^8*b^6 - 6*a^6*b^8 + 4*a^4*b^10 - a^2*b^12 - 6*a^12*c^2 + 18*a^10*b^2*c^2 - 18*a^8*b^4*c^2 + 15*a^6*b^6*c^2 - 9*a^4*b^8*c^2 + a^2*b^10*c^2 - b^12*c^2 + 5*a^10*c^4 - 18*a^8*b^2*c^4 + 3*a^4*b^6*c^4 + 5*a^2*b^8*c^4 + 3*b^10*c^4 + 2*a^8*c^6 + 15*a^6*b^2*c^6 + 3*a^4*b^4*c^6 - 10*a^2*b^6*c^6 - 2*b^8*c^6 - 6*a^6*c^8 - 9*a^4*b^2*c^8 + 5*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(46633) = X[23] - 3 X[21445], X[99] - 3 X[38702], X[842] - 3 X[34473], 2 X[14120] - 3 X[38224], 3 X[14639] - X[44969], 3 X[14651] - X[36174], 2 X[16320] - 3 X[44214], 2 X[16760] - 3 X[38737], 2 X[36180] - 3 X[38225]

X(46633) lies on these lines: {3, 523}, {23, 21445}, {30, 98}, {99, 38702}, {114, 40544}, {230, 11799}, {325, 15122}, {385, 7464}, {524, 11579}, {542, 9181}, {842, 34473}, {1499, 18332}, {2072, 10749}, {2420, 34369}, {2682, 33511}, {2782, 7472}, {2794, 16188}, {3398, 36157}, {3564, 15545}, {5099, 6036}, {5191, 7471}, {5663, 14999}, {6033, 36170}, {9155, 14611}, {9179, 15566}, {9862, 36173}, {10104, 36165}, {10796, 36183}, {12042, 36166}, {14120, 38224}, {14639, 44969}, {14651, 36174}, {14666, 44265}, {16320, 44214}, {16760, 38737}, {22104, 35282}, {23967, 25641}, {26316, 36177}, {32515, 37950}, {34209, 39295}, {34365, 43090}, {36180, 38225}, {38552, 46619}, {38553, 46620}

X(46633) = midpoint of X(i) and X(j) for these {i,j}: {98, 691}, {385, 7464}, {9862, 36173}, {38741, 38953}
X(46633) = reflection of X(i) in X(j) for these {i,j}: {114, 40544}, {325, 15122}, {2682, 33511}, {5099, 6036}, {6033, 36170}, {7472, 38611}, {11799, 230}, {36166, 12042}
X(46633) = circumcircle-inverse of X(44823)

X(46634) = MIDPOINT OF X(99) AND X(842)

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

X(46634) = X[98] - 3 X[38704], 3 X[186] - X[385], 2 X[230] - 3 X[44214], X[691] - 3 X[21166], 3 X[2072] - 4 X[44377], 3 X[15561] - 2 X[36170], 3 X[15561] - X[38953], 3 X[21445] - 5 X[37952], 3 X[38748] - 2 X[40544]

X(46634) lies on these lines: {3, 523}, {30, 99}, {98, 38704}, {115, 16760}, {186, 385}, {230, 44214}, {524, 3581}, {525, 18332}, {549, 16092}, {620, 16188}, {691, 21166}, {1511, 14999}, {2072, 44377}, {2080, 36180}, {2782, 36166}, {2967, 46619}, {3095, 36156}, {5099, 23698}, {5191, 14611}, {6023, 15452}, {6321, 14120}, {7471, 9155}, {7472, 33813}, {7575, 32515}, {7782, 38528}, {7789, 43090}, {11171, 36177}, {11649, 14962}, {11799, 16320}, {13172, 36174}, {15561, 36170}, {18579, 22329}, {21445, 37952}, {23967, 31378}, {30717, 34978}, {31859, 37930}, {38748, 40544}

X(46634) = midpoint of X(i) and X(j) for these {i,j}: {99, 842}, {13172, 36174}
X(46634) = reflection of X(i) in X(j) for these {i,j}: {115, 16760}, {2080, 36180}, {6321, 14120}, {7472, 33813}, {11799, 16320}, {14999, 1511}, {16092, 549}, {16188, 620}, {22329, 18579}, {36166, 38613}, {38953, 36170}
X(46634) = circumcircle-inverse of X(46609)
X(46634) = crossdifference of every pair of points on line {3003, 6041}
X(46634) = {X(15561),X(38953)}-harmonic conjugate of X(36170)

X(46635) = MIDPOINT OF X(100) AND X(2687)

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

X(46635) lies on these lines: {3, 523}, {30, 100}, {186, 1897}, {758, 12778}, {952, 46618}, {1290, 34474}, {2677, 17702}, {3035, 42422}, {3109, 11849}, {5520, 5840}, {13199, 36175}, {13869, 37535}, {33814, 36167}

X(46635) = midpoint of X(i) and X(j) for these {i,j}: {100, 2687}, {13199, 36175}
X(46635) = reflection of X(i) in X(j) for these {i,j}: {36167, 33814}, {42422, 3035}
X(46635) = circumcircle-inverse of X(46611)

X(46636) = MIDPOINT OF X(104) AND X(1290)

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

X(46636) lies on these lines: {3, 523}, {30, 104}, {100, 38711}, {952, 36167}, {1623, 7575}, {2072, 10746}, {2677, 6699}, {2687, 38693}, {2829, 42422}, {3109, 37535}, {5520, 6713}, {11849, 13869}, {32153, 36154}, {38602, 46618}

X(46636) = midpoint of X(104) and X(1290)
X(46636) = reflection of X(i) in X(j) for these {i,j}: {2677, 6699}, {5520, 6713}, {46618, 38602}
X(46636) = circumcircle-inverse of X(46610)

X(46637) = MIDPOINT OF X(112) AND X(2697)

Barycentrics (a^2 - b^2 - c^2)*(2*a^18 - 4*a^16*b^2 - a^14*b^4 + 6*a^12*b^6 - 3*a^10*b^8 + a^6*b^12 - 2*a^4*b^14 + a^2*b^16 - 4*a^16*c^2 + 14*a^14*b^2*c^2 - 10*a^12*b^4*c^2 - a^10*b^6*c^2 + 5*a^8*b^8*c^2 - 12*a^6*b^10*c^2 + 8*a^4*b^12*c^2 - a^2*b^14*c^2 + b^16*c^2 - a^14*c^4 - 10*a^12*b^2*c^4 + 10*a^10*b^4*c^4 - 5*a^8*b^6*c^4 + 25*a^6*b^8*c^4 - 8*a^4*b^10*c^4 - 6*a^2*b^12*c^4 - 5*b^14*c^4 + 6*a^12*c^6 - a^10*b^2*c^6 - 5*a^8*b^4*c^6 - 28*a^6*b^6*c^6 + 2*a^4*b^8*c^6 + 17*a^2*b^10*c^6 + 9*b^12*c^6 - 3*a^10*c^8 + 5*a^8*b^2*c^8 + 25*a^6*b^4*c^8 + 2*a^4*b^6*c^8 - 22*a^2*b^8*c^8 - 5*b^10*c^8 - 12*a^6*b^2*c^10 - 8*a^4*b^4*c^10 + 17*a^2*b^6*c^10 - 5*b^8*c^10 + a^6*c^12 + 8*a^4*b^2*c^12 - 6*a^2*b^4*c^12 + 9*b^6*c^12 - 2*a^4*c^14 - a^2*b^2*c^14 - 5*b^4*c^14 + a^2*c^16 + b^2*c^16) : :

X(46637) lies on these lines: {3, 523}, {30, 112}, {935, 38699}, {2071, 41676}, {2072, 6033}, {2794, 38971}, {5159, 9775}, {6720, 42426}, {38608, 46619}

X(46637) = midpoint of X(112) and X(2697)
X(46637) = reflection of X(i) in X(j) for these {i,j}: {42426, 6720}, {46619, 38608}
X(46637) = reflection of X(46631) in the Euler line
X(46637) = circumcircle-inverse of X(46615)

X(46638) = ISOGONAL CONJUGATE OF X(8610)

X(46638) lies on MacBeath circumconic and these lines: {6, 36791}, {110, 4248}, {145, 595}, {519, 15383}, {651, 3187}, {1332, 18743}, {1797, 2403}, {1813, 5435}, {2316, 39698}, {4558, 41629}, {7754, 43190}, {9059, 23644}

X(46638) = isogonal conjugate of X(8610)
X(46638) = isotomic conjugate of the anticomplement of X(3977)
X(46638) = Cevapoint of X(6) and X(519)
X(46638) = X(6)-cross conjugate of-X(15383)
X(46638) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 1739), (214, 17465)
X(46638) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 1739}, {42, 16753}, {44, 39264}, {88, 23644}
X(46638) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 1739), (44, 17465), (81, 16753), (106, 39264)
X(46638) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(145)}} and {{A, B, C, X(6), X(16947)}}
X(46638) = trilinear pole of the line {3, 3667}
X(46638) = orthocorrespondent of X(121)
X(46638) = barycentric product X(69)*X(40101)
X(46638) = barycentric quotient X(i)/X(j) for these (i, j): (1, 1739), (44, 17465), (81, 16753), (106, 39264), (519, 121), (902, 23644)
X(46638) = trilinear product X(63)*X(40101)
X(46638) = trilinear quotient X(i)/X(j) for these (i, j): (2, 1739), (44, 23644), (86, 16753), (88, 39264), (519, 17465)

X(46639) = ISOGONAL CONJUGATE OF X(6587)

X(46639) lies on MacBeath circumconic and these lines: {6, 15394}, {64, 895}, {69, 14390}, {110, 1301}, {162, 13138}, {193, 253}, {394, 3343}, {459, 2986}, {520, 15384}, {648, 2404}, {1073, 1993}, {1332, 7259}, {1813, 5546}, {1992, 34403}, {2063, 40221}, {2987, 40318}, {3964, 14092}, {4563, 34211}, {8798, 15801}, {10733, 38956}, {11064, 46065}, {11441, 41085}, {12111, 39268}, {12164, 31942}, {12272, 33584}, {13157, 41628}, {14362, 36413}, {14379, 34148}, {15905, 46351}, {28785, 35602}, {34570, 37672}, {41679, 44769}

X(46639) = isogonal conjugate of X(6587)
X(46639) = isotomic conjugate of the polar conjugate of X(1301)
X(46639) = Cevapoint of X(i) and X(j) for these (i, j): {6, 520}, {58, 23090}, {112, 1301}, {521, 9119}
X(46639) = X(i)-cross conjugate of-X(j) for these (i, j): (6, 15384), (112, 110), (520, 15394), (1461, 662)
X(46639) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 17898), (125, 1562), (1511, 14345)
X(46639) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 17898}, {19, 8057}, {20, 661}, {37, 21172}, {57, 14308}
X(46639) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 17898), (25, 44705), (55, 14308), (58, 21172)
X(46639) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(2404)}} and {{A, B, C, X(6), X(2445)}}
X(46639) = trilinear pole of the line {3, 64} (the line through X(3) perpendicular to the trilinear polar of X(3))
X(46639) = 1st Saragossa point of X(32713)
X(46639) = orthocorrespondent of X(122)
X(46639) = barycentric product X(i)*X(j) for these {i, j}: {6, 44326}, {64, 99}, {69, 1301}, {107, 15394}, {109, 5931}, {110, 253}
X(46639) = barycentric quotient X(i)/X(j) for these (i, j): (1, 17898), (25, 44705), (55, 14308), (58, 21172), (64, 523), (99, 14615)
X(46639) = trilinear product X(i)*X(j) for these {i, j}: {31, 44326}, {63, 1301}, {64, 662}, {99, 2155}, {110, 2184}, {112, 19611}
X(46639) = trilinear quotient X(i)/X(j) for these (i, j): (2, 17898), (9, 14308), (19, 44705), (21, 14331), (48, 42658), (64, 661)

X(46640) = ISOGONAL CONJUGATE OF X(6588)

X(46640) lies on MacBeath circumconic and these lines: {{6, 23983}, {110, 7435}, {193, 1814}, {521, 15385}, {651, 2405}, {895, 43703}, {1783, 44765}, {1797, 42467}, {1813, 3882}, {1993, 23122}, {2988, 3187}, {2990, 6515}, {2991, 40318}, {8759, 12649}, {11609, 40454}

X(46640) = isogonal conjugate of X(6588)
X(46640) = isotomic conjugate of the polar conjugate of X(40097)
X(46640) = Cevapoint of X(i) and X(j) for these (i, j): {6, 521}, {520, 2092}, {522, 24005}, {650, 22760}
X(46640) = X(i)-cross conjugate of-X(j) for these (i, j): (6, 15385), (1415, 100)
X(46640) = X(9)-Dao conjugate of X(21186)
X(46640) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 21186}, {123, 32674}, {197, 514}, {205, 693}
X(46640) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 21186), (100, 3436), (101, 1766), (108, 14257)
X(46640) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(2405)}} and {{A, B, C, X(81), X(32714)}}
X(46640) = trilinear pole of the line {3, 960}
X(46640) = orthocorrespondent of X(123)
X(46640) = barycentric product X(i)*X(j) for these {i, j}: {69, 40097}, {99, 43703}, {190, 42467}, {651, 34277}, {668, 3435}
X(46640) = barycentric quotient X(i)/X(j) for these (i, j): (1, 21186), (100, 3436), (101, 1766), (108, 14257), (109, 21147), (110, 16049)
X(46640) = trilinear product X(i)*X(j) for these {i, j}: {63, 40097}, {100, 42467}, {109, 34277}, {190, 3435}, {653, 39167}, {662, 43703}
X(46640) = trilinear quotient X(i)/X(j) for these (i, j): (2, 21186), (100, 1766), (101, 197), (109, 478), (162, 41364), (190, 3436)

X(46641) = X(2)X(3603)∩X(356)X(357)

X(46642) = X(2)X(3602)∩X(356)X(1134)

X(46643) = X(2)X(3604)∩X(1136)X(1137)

X(46644) = X(2)X(664)∩X(1155)X(1156)

X(46644) = X(1055)-isoconjugate-of-X(34919)
X(46644) = X(1156)-reciprocal conjugate of-X(34919)
X(46644) = trilinear pole of the line {8545, 14077}
X(46644) = orthocorrespondent of X(1156)
X(46644) = barycentric product X(i)*X(j) for these {i, j}: {1121, 8545}, {1996, 41798}
X(46644) = barycentric quotient X(i)/X(j) for these (i, j): (1156, 34919), (1996, 37780)
X(46644) = trilinear product X(i)*X(j) for these {i, j}: {1121, 37541}, {1156, 8545}, {1996, 4845}
X(46644) = trilinear quotient X(i)/X(j) for these (i, j): (1121, 34919), (1996, 1323)

X(46645) = X(67)X(32424)∩X(599)X(2549)

X(46645) lies on these lines: {67, 32424}, {599, 2549}, {5094, 22110}, {10130, 42850}

X(46645) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(67)}} and {{A, B, C, X(69), X(9164)}}

X(46646) = X(530)X(11119)∩X(5472)X(11080)

X(46647) = X(531)X(11120)∩X(5471)X(11085)

X(46648) = X(542)X(34238)∩X(2065)X(2782)

X(46649) = ISOGONAL CONJUGATE OF X(3025)

X(46649) lies on these lines: {59, 952}, {80, 23592}, {528, 36590}, {655, 900}, {14204, 18815}

X(46649) = isogonal conjugate of X(3025)
X(46649) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(528)}} and {{A, B, C, X(8), X(952)}}
X(46649) = perspector of ABC and the reflection of the intouch triangle in line X(1)X(5)
X(46649) = barycentric product X(i)*X(j) for these {i, j}: {8, 23592}, {765, 34535}
X(46649) = barycentric quotient X(i)/X(j) for these (i, j): (55, 35128), (655, 4453), (1110, 34544), (1252, 4996)
X(46649) = trilinear product X(i)*X(j) for these {i, j}: {9, 23592}, {1252, 34535}
X(46649) = trilinear quotient X(i)/X(j) for these (i, j): (9, 35128), (655, 3960), (765, 4996), (1110, 215), (1252, 34544)

X(46650) = COMPLEMENT OF X(5995)

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

X(46650) lies on the nine-point circle and these lines: {2, 5995}, {113, 623}, {114, 618}, {115, 23871}, {132, 7684}, {512, 46651}, {624, 16188}, {5668, 40334}, {6111, 31705}, {7685, 45158}, {15526, 23872}, {15609, 25173}

X(46650) = midpoint of X(623) and X(33501)
X(46650) = complement of X(5995)
X(46650) = complement of the isogonal conjugate of X(23870)
X(46650) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23870}, {15, 14838}, {298, 4369}, {470, 8062}, {661, 396}, {1577, 623}, {2151, 647}, {2154, 1637}, {2624, 40696}, {3384, 23873}, {6137, 37}, {8739, 16612}, {9204, 16597}, {17402, 16598}, {23870, 10}, {30465, 8287}, {32679, 619}, {39152, 21192}
X(46650) = X(4)-Ceva conjugate of X(23870)

X(46651) = COMPLEMENT OF X(5994)

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

X(46651) lies on the nine-point circle and these lines: {2, 5994}, {113, 624}, {114, 619}, {115, 23870}, {132, 7685}, {512, 46650}, {623, 16188}, {5669, 40335}, {6110, 31706}, {7684, 45158}, {15526, 23873}, {15610, 25178}

X(46651) = midpoint of X(624) and X(33499)
X(46651) = complement of X(5994)
X(46651) = complement of the isogonal conjugate of X(23871)
X(46651) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23871}, {16, 14838}, {299, 4369}, {471, 8062}, {661, 395}, {1577, 624}, {2152, 647}, {2153, 1637}, {2624, 40695}, {3375, 23872}, {6138, 37}, {8740, 16612}, {9205, 16597}, {17403, 16598}, {23871, 10}, {30468, 8287}, {32679, 618}, {39153, 21192}
X(46651) = X(4)-Ceva conjugate of X(23871)

X(46652) = COMPLEMENT OF X(16806)

X(46652) lies on the nine-point circle and these lines: {2, 16806}, {114, 629}, {128, 618}, {636, 31843}, {32552, 33526}, {33496, 41022}

X(46652) = complement of X(16806)
X(46652) = complement of the isogonal conjugate of X(23872)
X(46652) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23872}, {61, 14838}, {302, 4369}, {473, 8062}, {656, 465}, {661, 23302}, {1577, 635}, {3376, 23871}, {10642, 16612}, {23872, 10}
X(46652) = X(4)-Ceva conjugate of X(23872)

X(46653) = COMPLEMENT OF X(16807)

X(46653) lies on the nine-point circle and these lines: {2, 16807}, {114, 630}, {128, 619}, {635, 31843}, {32553, 33527}, {33497, 41023}

X(46653) = complement of X(16807)
X(46653) = complement of the isogonal conjugate of X(23873)
X(46653) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23873}, {62, 14838}, {303, 4369}, {472, 8062}, {656, 466}, {661, 23303}, {1577, 636}, {3383, 23870}, {10641, 16612}, {23873, 10}
X(46653) = X(4)-Ceva conjugate of X(23873)

X(46654) = COMPLEMENT OF X(827)

X(46654) lies on the nine-point circle and these lines: {2, 827}, {4, 14378}, {5, 44953}, {20, 44943}, {113, 37347}, {114, 140}, {115, 9479}, {126, 21248}, {132, 1594}, {133, 42874}, {137, 868}, {186, 42426}, {339, 23285}, {826, 35584}, {3005, 3258}, {3143, 45161}, {3150, 20625}, {3269, 33504}, {3934, 13499}, {4577, 26197}, {5971, 30745}, {6143, 33695}, {7574, 25641}, {7759, 28672}, {7845, 15573}, {7853, 44947}, {7858, 28688}, {8623, 38975}, {10173, 45163}, {16188, 37938}, {21249, 31845}, {31842, 37452}, {35605, 36471}, {36189, 46439}

X(46654) = midpoint of X(i) and X(j) for these {i,j}: {4, 29011}, {20, 44943}
X(46654) = reflection of X(44953) in X(5)
X(46654) = complement of X(827)
X(46654) = orthoptic-circle-of-Steiner-inellipse-inverse of X(9076)
X(46654) = complement of the isogonal conjugate of X(826)
X(46654) = complement of the isotomic conjugate of X(23285)
X(46654) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 826}, {41513, 523}
X(46654) = crosspoint of X(i) and X(j) for these (i,j): {2, 23285}, {427, 31067}
X(46654) = crosssum of X(6) and X(4630)
X(46654) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 826}, {2, 8060}, {38, 523}, {39, 14838}, {65, 4142}, {141, 4369}, {427, 8062}, {512, 16600}, {513, 29654}, {523, 1215}, {561, 688}, {594, 29512}, {656, 6676}, {661, 3589}, {688, 16584}, {798, 1194}, {826, 10}, {850, 21238}, {897, 32193}, {1109, 7668}, {1235, 21259}, {1577, 3934}, {1581, 5113}, {1634, 16598}, {1843, 16612}, {1910, 14316}, {1928, 42291}, {1930, 512}, {1964, 647}, {2084, 39}, {2156, 23881}, {2525, 18589}, {2528, 21249}, {2530, 1125}, {2642, 7664}, {2643, 3124}, {3005, 37}, {3125, 21208}, {3404, 2799}, {3708, 339}, {3954, 514}, {4017, 17061}, {4077, 17049}, {4576, 21254}, {7178, 17048}, {8024, 42327}, {8061, 2}, {14208, 11574}, {14424, 16597}, {15523, 513}, {16696, 21196}, {16732, 44312}, {16892, 3739}, {17187, 31947}, {17442, 525}, {17957, 9479}, {20883, 30476}, {21035, 650}, {21108, 942}, {21123, 3666}, {21814, 6586}, {23285, 2887}, {23881, 21247}, {24006, 5943}, {31067, 28595}, {35309, 4422}, {35325, 16599}, {39691, 8287}, {46149, 4458}, {46151, 23998}, {46153, 34977}, {46160, 6370}
X(46654) = barycentric product X(i)*X(j) for these {i,j}: {7768, 39691}, {8061, 18076}
X(46654) = barycentric quotient X(i)/X(j) for these {i,j}: {15449, 14378}, {18076, 4593}, {37085, 4630}, {39691, 15321}

X(46655) = COMPLEMENT OF X(32692)

X(46655) lies on the nine-point circle and these lines: {2, 32692}, {114, 12134}, {128, 6069}, {132, 5446}, {1209, 31842}, {18314, 38970}

X(46655) = complement of X(32692)
X(46655) = circumcircle-inverse of X(112)-of-tangential-triangle
X(46655) = X(i)-complementary conjugate of X(j) for these (i,j): {52, 14838}, {467, 8062}, {924, 16577}, {1577, 1216}, {1748, 6368}, {1953, 2501}, {2180, 647}, {2617, 46184}, {2618, 343}, {6368, 18588}, {6563, 21231}, {14213, 924}, {14576, 16612}, {18314, 34825}, {21011, 46389}, {39113, 4369}

X(46656) = COMPLEMENT OF X(26714)

X(46656) lies on the nine-point circle and these lines: {2, 26714}, {4, 14383}, {114, 141}, {132, 19130}, {625, 33330}, {1560, 37648}, {3580, 38975}, {6388, 35971}, {15526, 38974}

X(46656) = complement of X(26714)
X(46656) = complement of the isogonal conjugate of X(23878)
X(46656) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 23878}, {182, 14838}, {183, 4369}, {458, 8062}, {523, 16603}, {661, 3815}, {798, 3117}, {897, 45336}, {1577, 24206}, {1755, 33569}, {2349, 45319}, {3288, 37}, {3403, 512}, {6784, 16592}, {10311, 16612}, {20023, 42327}, {23878, 10}, {24018, 42353}, {39680, 18904}, {42711, 3835}, {44144, 21259}
X(46656) = X(4)-Ceva conjugate of X(23878)

X(46657) = COMPLEMENT OF X(11636)

X(46657) lies on the nine-point circle and these lines: {2, 6325}, {4, 14388}, {113, 24206}, {114, 549}, {115, 17416}, {126, 626}, {132, 7577}, {141, 13234}, {1506, 1560}, {3096, 9999}, {5031, 44956}, {5094, 15922}, {7818, 30789}, {10295, 42426}, {10748, 11569}, {15357, 35582}, {15526, 38971}, {36189, 46438}

X(46657) = midpoint of X(4) and X(14388)
X(46657) = complement of X(11636)
X(46657) = orthoptic-circle-of-Steiner-inellipse-inverse of X(6325)
X(46657) = complement of isogonal conjugate of X(3906)
X(46657) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 3906}, {574, 14838}, {599, 4369}, {661, 597}, {798, 9465}, {2643, 6791}, {3906, 10}, {5094, 8062}, {8288, 8287}, {8541, 16612}, {9145, 16598}, {9146, 21254}, {9464, 42327}, {10130, 8060}, {17414, 37}, {23288, 4892}, {36263, 523}
X(46657) = X(4)-Ceva conjugate of X(3906)
X(46657) = crossdifference of every pair of points on line {35357, 36828}
X(46657) = barycentric product X(i)*X(j) for these {i,j}: {599, 38361}, {7850, 8288}
X(46657) = barycentric quotient X(38361)/X(598)

X(46658) = X(113)X(389)∩X(114)X(6677)

X(46658) lies on the nine-point circle and these lines: {113, 389}, {114, 6677}, {128, 43809}, {133, 44226}, {2970, 16178}, {3124, 33504}, {25641, 31726}, {37777, 42426}

X(46658) = X(i)-complementary conjugate of X(j) for these (i,j): {235, 8062}, {656, 16196}, {774, 523}, {800, 14838}, {1624, 16598}, {2643, 3269}, {13567, 4369}, {17858, 512}, {18603, 21196}, {24006, 5907}, {44079, 16612}, {44131, 21259}

X(46659) = MIDPOINT OF X(4) AND X(843)

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

X(46659) lies on the nine-point circle and these lines: {2, 2709}, {4, 843}, {5, 44956}, {20, 44946}, {114, 524}, {115, 1499}, {126, 511}, {352, 38227}, {512, 5512}, {542, 16341}, {1648, 9193}, {2793, 35586}, {3849, 11569}, {5476, 9169}, {5480, 16188}, {6092, 7617}, {6791, 8704}, {6792, 9753}, {9152, 24206}, {20389, 35605}

X(46659) = complement of X(2709)
X(46659) = midpoint of X(i) and X(j) for these {i,j}: {4, 843}, {20, 44946}
X(46659) = reflection of X(44956) in X(5)
X(46659) = complement of the isogonal conjugate of X(2793)
X(46659) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2793}, {661, 22110}, {2030, 14838}, {2793, 10}, {9135, 37}, {17959, 1499}, {22329, 4369}, {23894, 19662}, {34245, 21254}
X(46659) = X(4)-Ceva conjugate of X(2793)
X(46659) = X(843)-of-Euler-triangle
X(46659) = X(44956)-of-Johnson-triangle
X(46659) = barycentric product X(2793)*X(39905)
X(46659) = barycentric quotient X(39905)/X(46144)

X(46660) = MIDPOINT OF X(4) AND X(28173)

X(46660) lies on the nine-point circle and these lines: {2, 8701}, {4, 28173}, {114, 41820}, {115, 244}, {119, 9947}, {121, 3831}, {1086, 38960}, {1125, 27592}, {1566, 4988}, {1647, 15611}, {3756, 5515}, {5511, 26933}, {5520, 6075}

X(46660) = complement of X(8701)
X(46660) = midpoint of X(4) and X(28173)
X(46660) = orthoptic-circle-of-Steiner-inellipse inverse of X(9108)
X(46660) = X(28173)-of-Euler-triangle
X(46660) = complement of the isogonal conjugate of X(4977)
X(46660) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 4977}, {58, 8043}, {244, 3120}, {513, 3634}, {514, 17239}, {553, 4885}, {649, 44307}, {661, 41809}, {757, 6367}, {1015, 16726}, {1019, 6707}, {1100, 514}, {1125, 513}, {1213, 4129}, {1269, 21260}, {1962, 661}, {2308, 650}, {2355, 3239}, {3683, 4521}, {3686, 20317}, {3733, 3743}, {3737, 18253}, {3916, 20315}, {4359, 3835}, {4427, 24003}, {4647, 31946}, {4976, 3452}, {4977, 10}, {4978, 141}, {4979, 2}, {4983, 1213}, {4984, 16594}, {4985, 1329}, {4988, 1211}, {4992, 34832}, {7192, 27798}, {8025, 4369}, {16709, 512}, {16726, 24185}, {30581, 21196}, {30591, 3454}, {30724, 142}, {31900, 8062}, {32636, 522}, {35327, 24036}, {35342, 4422}, {36075, 16578}, {46542, 942}
X(46660) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 4977}, {13476, 6367}

X(46661) = X(2)X(43658)∩X(113)X(15060)

X(46661) lies on the nine-point circle and these lines: {2, 43658}, {113, 15060}, {114, 7495}, {6070, 38971}, {18572, 25641}, {37969, 42426}

X(46661) = orthoptic-circle-of-Steiner-inellipse-inverse of X(43658)
X(46661) = X(i)-complementary conjugate of X(j) for these (i,j): {566, 14838}, {661, 14389}, {7577, 8062}, {18117, 37}, {24006, 5946}, {36829, 16598}

X(46662) = X(113)X(6823)∩X(114)X(7386)

X(46662) lies on the nine-point circle and these lines: {113, 6823}, {114, 7386}, {115, 2972}, {132, 37439}, {133, 3091}, {1650, 15613}, {3937, 31653}

X(46662) = X(i)-complementary conjugate of X(j) for these (i,j): {631, 8062}, {656, 1656}, {661, 11433}, {11402, 16612}, {36748, 14838}, {44149, 21259}

X(46663) = COMPLEMENT OF X(8059)

X(46663) lies on the nine-point circle and these lines: {2, 8059}, {10, 25640}, {11, 7358}, {117, 1329}, {118, 20307}, {119, 6260}, {123, 44313}, {223, 30757}, {2550, 20622}, {3452, 44993}, {5513, 38015}, {7952, 20619}, {20206, 21244}

X(46663) = complement of X(8059)
X(46663) = complement of the isogonal conjugate of X(8058)
X(46663) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 8058}, {33, 14331}, {37, 24018}, {40, 522}, {65, 17898}, {198, 905}, {208, 21172}, {221, 6129}, {223, 7658}, {227, 656}, {322, 17072}, {329, 4885}, {346, 20318}, {347, 3900}, {513, 3086}, {522, 946}, {650, 57}, {651, 40555}, {663, 1108}, {1783, 40535}, {1817, 17069}, {2187, 6589}, {2324, 514}, {2331, 14837}, {3195, 6588}, {3239, 20205}, {3318, 7358}, {3900, 281}, {4041, 1901}, {4391, 21239}, {4397, 20306}, {5514, 26932}, {6129, 1}, {7074, 650}, {7080, 513}, {7358, 123}, {7952, 521}, {8058, 10}, {10397, 1214}, {14298, 2}, {14302, 20210}, {14837, 142}, {15501, 2804}, {17896, 2886}, {21871, 1577}, {27398, 4369}, {38357, 11}, {40702, 46399}, {40971, 3239}
X(46663) = X(4)-Ceva conjugate of X(8058)

X(46664) = X(3)X(14980)∩X(23)X(132)

X(46664) lies on the nine-point circle and these lines: {3, 14980}, {23, 132}, {30, 18402}, {113, 10540}, {115, 16040}, {125, 6368}, {128, 2072}, {133, 11563}, {523, 20625}, {546, 18809}, {1650, 46437}, {5133, 42426}, {5159, 31843}, {6676, 16188}, {10024, 12091}, {12605, 42424}, {12606, 33333}, {24977, 46439}

X(46664) = reflection of X(20625) in the Euler line
X(46664) = X(i)-complementary conjugate of X(j) for these (i,j): {656, 37938}, {810, 50}, {2070, 8062}, {9380, 14838}, {24978, 20305}

X(46665) = COMPLEMENT OF X(7953)

X(46665) lies on the nine-point circle and these lines: {2, 7953}, {4, 14381}, {5, 45165}, {20, 45155}, {114, 3628}, {115, 15527}, {132, 15559}, {868, 11792}, {2679, 35605}, {19577, 31655}, {25641, 37924}, {37943, 42426}

X(46665) = midpoint of X(i) and X(j) for these {i,j}: {4, 29316}, {20, 45155}
X(46665) = reflection of X(45165) in X(5)
X(46665) = complement of X(7953)
X(46665) = complement of the isogonal conjugate of X(7927)
X(46665) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 7927}, {428, 8062}, {512, 28594}, {523, 28595}, {656, 10691}, {661, 34573}, {1577, 7849}, {2642, 31128}, {2643, 39691}, {3589, 4369}, {5007, 14838}, {7927, 10}, {8664, 37}, {10330, 21254}, {17457, 3005}, {17469, 523}, {21802, 514}, {39998, 42327}, {44091, 16612}, {44142, 21259}
X(46665) = X(4)-Ceva conjugate of X(7927)
X(46665) = X(29316)-of-Euler-triangle
X(46665) = X(45165)-of-Johnson-triangle
X(46665) = barycentric quotient X(15527)/X(14381)

X(46666) = COMPLEMENT OF X(36515)

X(46666) lies on the nine-point circle and these lines: {2, 36515}, {114, 1080}, {115, 30452}, {512, 15610}, {621, 1338}, {623, 33498}, {3440, 14372}

X(46666) = midpoint of X(i) and X(j) for these {i,j}: {621, 1338}, {3440, 14372}
X(46666) = reflection of X(33498) in X(623)
X(46666) = complement of X(36515)
X(46666) = X(i)-complementary conjugate of X(j) for these (i,j): {661, 298}, {3180, 4369}, {19780, 14838}

X(46667) = COMPLEMENT OF X(36514)

X(46667) lies on the nine-point circle and these lines: {2, 36514}, {114, 383}, {115, 30453}, {512, 15609}, {622, 1337}, {624, 33500}, {3441, 14373}

X(46667) = midpoint of X(i) and X(j) for these {i,j}: {622, 1337}, {3441, 14373}
X(46667) = reflection of X(33500) in X(624)
X(46667) = complement of X(36514)
X(46667) = X(i)-complementary conjugate of X(j) for these (i,j): {661, 299}, {3181, 4369}, {19781, 14838}

X(46668) = COMPLEMENT OF X(2702)

X(46668) lies on the nine-point circle and these lines: {2, 2702}, {4, 2700}, {11, 4369}, {114, 516}, {115, 514}, {116, 512}, {118, 511}, {121, 625}, {125, 3835}, {126, 20339}, {2681, 2786}, {5031, 20551}, {5074, 20529}, {5513, 6651}, {7683, 45158}, {20541, 20546}, {41323, 41324}

X(46668) = midpoint of X(4) and X(2700)
X(46668) = complement of X(2702)
X(46668) = complement of the isogonal conjugate of X(2786)
X(46668) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2786}, {423, 8062}, {513, 239}, {523, 20337}, {661, 10026}, {1326, 14838}, {1577, 20546}, {1757, 514}, {1931, 523}, {2786, 10}, {5029, 37}, {6541, 4129}, {6542, 513}, {8298, 27929}, {9508, 2}, {17731, 4369}, {17735, 650}, {17990, 16589}, {18004, 1211}, {18266, 6586}, {20693, 661}, {20947, 3835}, {27929, 17793}, {28602, 16594}, {38348, 17755}, {40740, 30665}, {40794, 812}
X(46668) = X(4)-Ceva conjugate of X(2786)
X(46668) = polar conjugate of isogonal conjugate of X(47428)
X(46668) = X(2700)-of-Euler-triangle

X(46669) = X(114)X(5999)∩X(115)X(826)

X(46669) lies on the nine-point circle and these lines: {114, 5999}, {115, 826}, {511, 44953}, {647, 35971}, {5103, 13499}, {5207, 19558}

X(46669) = Moses-radical-circle-inverse of X(35971)
X(46669) = complement of the isogonal conjugate of X(9479)
X(46669) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 9479}, {420, 8062}, {661, 385}, {1577, 5103}, {2076, 14838}, {5113, 37}, {7779, 4369}, {8061, 15573}, {9479, 10}, {17799, 523}, {17997, 16600}, {18010, 1215}, {34054, 826}, {40850, 8060}, {44090, 16612}
X(46669) = X(4)-Ceva conjugate of X(9479)
X(46669) = complement of X(46970)
X(46669) = barycentric product X(9479)*X(14316)

X(46670) = COMPLEMENT OF X(2701)

X(4666) lies on the nine-point circle and these lines: {2, 2701}, {4, 2708}, {114, 515}, {115, 522}, {116, 17066}, {117, 511}, {124, 512}, {125, 17072}, {625, 31844}, {20546, 31845}

X(46670) = midpoint of X(4) and X(2708)
X(46670) = complement of X(2701)
X(46670) = complement of the isogonal conjugate of X(2785)
X(46670) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2785}, {415, 8062}, {513, 33140}, {650, 1944}, {1758, 522}, {2651, 523}, {2785, 10}, {4516, 41182}, {5060, 14838}, {5075, 37}, {17942, 34977}, {17950, 4885}, {17966, 905}, {17985, 521}, {17992, 2092}, {18006, 442}, {40882, 4369}
X(46670) = X(4)-Ceva conjugate of X(2785)
X(46670) = X(2708)-of-Euler-triangle

X(46671) = COMPLEMENT OF X(2703)

X(46671) lies on the nine-point circle and these lines: {2, 2703}, {4, 2699}, {11, 512}, {114, 517}, {115, 513}, {116, 42327}, {119, 511}, {125, 21260}, {2680, 2787}, {3110, 37715}, {3814, 45162}, {3836, 31845}, {5006, 5061}, {5164, 38472}, {5958, 11792}, {6547, 15611}

X(46671) = midpoint of X(4) and X(2699)
X(46671) = reflection of X(5164) in X(38472)
X(46671) = complement of X(2703)
X(46671) = complement of the isogonal conjugate of X(2787)
X(46671) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2787}, {42, 2511}, {422, 8062}, {661, 44396}, {2787, 10}, {5006, 14838}, {5040, 37}, {5061, 522}, {5209, 512}, {5291, 514}, {17763, 513}, {17790, 3835}, {17977, 20315}, {17987, 20316}, {17989, 1213}, {18003, 3454}, {19623, 4369}
X(46671) = X(4)-Ceva conjugate of X(2787)
X(46671) = X(2699)-of-Euler-triangle
X(46671) = barycentric quotient X(2787)/X(43189)

X(46672) = (name pending)

X(46673) = X(3)X(13378)∩X(5)X(10168)

Barycentrics 12*a^10-19*(b^2+c^2)*a^8-5*(b^4+4*b^2*c^2+c^4)*a^6-3*(b^2+c^2)*(b^4+4*b^2*c^2+c^4)*a^4+(29*b^8+29*c^8-2*(8*b^4+21*b^2*c^2+8*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)*(-14*b^4+32*b^2*c^2-14*c^4) : :

X(46673) = X(3)-3*X(13378), 3*X(381)-X(31748), 3*X(10162)-X(31731), X(31729)-3*X(34512)

X(46673) lies on these lines: {3, 13378}, {5, 10168}, {381, 31748}, {9830, 31749}, {10162, 31731}, {31729, 34512}

X(46674) = X(5)X(539)∩X(54)X(21265)

X(46674) lies on these lines: {5,539}, {54,21265}, {143,36412}, {265,40448}, {1173,3078}, {15780,33664}, {18370,39284}, {30483,34826}

X(46675) = X(165)X(2324)∩X(480)X(19605)

X(46675) lies on these lines: {165,2324}, {480,19605}, {1174,8012}, {3256,6602}, {5537,11051}, {6244,7368}, {10310,45721}, {11227,34867}

X(46676) = X(10)X(4682)∩X(12)X(21081)

X(46676) lies on these lines: {10,4682}, {12,21081}, {306,39583}, {502,6057}, {1126,1224}

X(46677) = X(3)X(200)∩X(8)X(210)

X(46677) lies on these lines: {3,200}, {8,210}, {10,17658}, {40,18239}, {56,2057}, {65,6735}, {72,1145}, {78,1319}, {100,12680}, {354,5552}, {404,9850}, {452,18247}, {480,11510}, {517,45631}, {518,1788}, {1158,5687}, {1259,3689}, {1260,1728}, {1329,17642}, {1532,21075}, {1864,3913}, {3059,5220}, {3436,7957}, {3522,12125}, {3555,6745}, {3697,4187}, {3698,4197}, {3711,10966}, {3832,14923}, {3870,25875}, {3871,14100}, {3872,25917}, {3873,27525}, {3895,9848}, {3967,23528}, {3983,6734}, {4420,37605}, {4853,5044}, {4861,17536}, {4882,5119}, {5176,6895}, {5177,5836}, {5815,6925}, {6762,41426}, {7962,15347}, {9954,12526}, {10395,38211}, {11678,20070}, {12053,18236}, {12688,17615}, {15558,17648}, {17609,27385}, {17857,18237}, {27383,34791}, {34619,44547}, {35460,40263}

X(46677) = reflection of X(37566) in X(37828)
X(46677) = crossdifference of every pair of points on line X(7661)-X(43924)
X(46677) = extouch-isogonal conjugate of X(8)
X(46677) = {X(6736),X(14740)}-harmonic conjugate of X(72)

X(46678) = X(9)X(55)∩X(220)X(15931)

X(46678) lies on these lines: {9,55}, {220,15931}, {2078,6602}, {8012,38849}, {10857,34867}, {11508,15662}, {34526,41338}

X(46679) = X(10)X(37)∩X(8013)X(33771)

X(46680) = X(6)X(1092)∩X(54)X(1249)

X(46680) lies on these lines: {6,1092}, {32,23606}, {54,1249}, {83,11427}, {184,2207}, {578,1217}, {1970,10984}, {1974,14585}, {7763,40405}

X(46680) = X(i)-isoconjugate of X(j) for these (i,j): (75,11433), (92,40680), (304,3089), (561,8573), (1181,1969)
X(46680) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {32,11433}, {184,40680}, {1217,18022}, {1501,8573}, {1974,3089}
X(46680) = barycentric product X(184)*X(1217)
X(46680) = barycentric quotient X(i)/X(j) for these {i,j}: {32,11433}, {184,40680}, {1217,18022}, {1501,8573}, {1974,3089}
X(46680) = trilinear product X(1217)*X(9247)
X(46680) = trilinear quotient X(i)/X(j) for these (i,j): (31,11433), (48,40680), (560,8573), (1217,1969), (1973,3089)

This preamble and centers X(46681)-X(46696) were contributed by César Eliud Lozada, January 14, 2022.

Let T'=A'B'C' and T"=A"B"C" be two triangles, A₁ the reflection of A' in B"C" and A₂ the reflection of A" in B'C'. Define B₁, B₂, C₁, C₂ cyclically. For some selected pairs of triangles T' and T", these six points lie on a conic, here named the mutual-reflections conic of T' and T" or, shortly, the MR-conic of T' and T".

The appearance of (T', T", n) in the following partial list means that the center of the MR-conic of triangles T' and T" is X(n):

(ABC, ABC-X3 reflections, 3), (ABC, anticomplementary, 3), (ABC, outer-Garcia, 10), (ABC, Gossard, 402), (ABC, intouch, 5083), (ABC, medial, 5), (ABC, 5th mixtilinear, 1), (ABC, tangential, 125), (ABC-X3 reflections, anti-Euler, 3), (ABC-X3 reflections, anti-Hutson intouch, 16163), (anti-Aquila, Ehrmann-mid, 9955), (anti-Aquila, incircle-circles, 46681), (anti-Aquila, medial, 1125), (anti-Ara, orthic, 46682), (anti-Ascella, 2nd anti-extouch, 12161), (1st anti-Auriga, 2nd anti-Auriga, 1), (2nd anti-circumperp-tangential, anti-tangential-midarc, 46683), (2nd anti-circumperp-tangential, Mandart-incircle, 1), (1st anti-circumperp, 3rd anti-Euler, 3), (1st anti-circumperp, circumorthic, 3), (anti-Conway, 2nd anti-extouch, 32046), (2nd anti-Conway, orthic, 143), (anti-Ehrmann-mid, anti-Euler, 5), (anti-Ehrmann-mid, Aquila, 18480), (4th anti-Euler, circumorthic, 3), (anti-excenters-reflections, orthic, 4), (anti-Honsberger, anti-Ursa minor, 3589), (anti-Honsberger, Ehrmann-vertex, 19130), (anti-Honsberger, 2nd Ehrmann, 6), (anti-Honsberger, Trinh, 5092), (anti-Hutson intouch, tangential, 3), (anti-incircle-circles, anti-inverse-in-incircle, 5), (anti-incircle-circles, 1st excosine, 6759), (anti-incircle-circles, X3-ABC reflections, 265), (anti-inverse-in-incircle, anticomplementary, 110), (anti-Mandart-incircle, 2nd circumperp tangential, 3), (anti-Mandart-incircle, 1st circumperp, 46684), (1st anti-Parry, 2nd anti-Parry, 3), (anti-tangential-midarc, intangents, 1), (anti-Ursa minor, Kosnita, 140), (anti-Ursa minor, medial, 5972), (anti-Wasat, circumorthic, 389), (anti-Wasat, orthic, 5), (anti-X3-ABC reflections, Ehrmann-mid, 5), (anti-X3-ABC reflections, Kosnita, 6699), (anti-inner-Yff, outer-Johnson, 5), (anti-outer-Yff, inner-Johnson, 5), (anticomplementary, Aquila, 10), (anticomplementary, inner-Conway, 46685), (anticomplementary, X3-ABC reflections, 5), (Aquila, outer-Garcia, 355), (1st Auriga, 2nd Auriga, 55), (7th Brocard, 10th Brocard, 182), (circumorthic, Ehrmann-side, 5), (2nd circumperp tangential, 2nd circumperp, 214), (1st circumperp, 2nd circumperp, 3), (1st circumperp, excentral, 3), (2nd circumperp, hexyl, 3), (2nd circumperp, Wasat, 1125), (inner-Conway, Honsberger, 9), (3rd Conway, inverse-in-Conway, 10441), (Ehrmann-mid, Ehrmann-vertex, 46686), (Ehrmann-vertex, Kosnita, 5), (2nd Ehrmann, Kosnita, 575), (Euler, Johnson, 5), (Euler, medial, 5), (2nd Euler, orthic, 5), (3rd Euler, 4th Euler, 5), (3rd Euler, Wasat, 5), (excenters-reflections, excentral, 1), (excentral, 6th mixtilinear, 40), (1st excosine, tangential, 26), (inner-Fermat, 1st half-diamonds, 18), (outer-Fermat, 2nd half-diamonds, 17), (Garcia-reflection, 2nd Schiffler, 11), (1st half-squares, outer-Vecten, 641), (2nd half-squares, inner-Vecten, 642), (Honsberger, Ursa-minor, 5572), (Hutson intouch, intouch, 1), (Hutson intouch, 5th mixtilinear, 15558), (incircle-circles, 2nd Zaniah, 1125), (intangents, Mandart-incircle, 46687), (intouch, inverse-in-incircle, 942), (intouch, Ursa-minor, 1), (Johnson, X3-ABC reflections, 4), (1st Kenmotu-centers, 1st Kenmotu diagonals, 46688), (2nd Kenmotu-centers, 2nd Kenmotu diagonals, 46689), (Kosnita, Trinh, 3), (Lucas central, Lucas tangents, 46690), (Lucas(-1) central, Lucas(-1) tangents, 46691), (Lucas inner, Lucas inner tangential, 46692), (Lucas(-1) inner, Lucas(-1) inner tangential, 46693), (medial, 2nd Zaniah, 46694), (midarc, 2nd midarc, 1), (midarc, tangential-midarc, 46695), (2nd midarc, 2nd tangential-midarc, 46696)

X(46681) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: ANTI-AQUILA AND INCIRCLE-CIRCLES

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

X(46681) = 3*X(1)+X(11570) = 7*X(1)+X(11571) = 5*X(1)-X(12758) = 3*X(1)-X(15558) = X(11)-5*X(17609) = X(214)+3*X(3892) = 3*X(354)+X(1317) = 3*X(354)-X(12736) = 9*X(354)-X(17636) = 3*X(1317)+X(17636) = 3*X(5083)-X(11570) = 7*X(5083)-X(11571) = 5*X(5083)+X(12758) = 3*X(5083)+X(15558) = 7*X(11570)-3*X(11571) = 5*X(11570)+3*X(12758) = 5*X(11571)+7*X(12758) = 3*X(11571)+7*X(15558) = 3*X(12736)-X(17636) = 3*X(12758)-5*X(15558)

X(46681) lies on these lines: {1, 104}, {7, 14217}, {11, 17609}, {80, 1056}, {100, 3333}, {119, 11019}, {149, 11037}, {153, 10580}, {214, 999}, {226, 16174}, {354, 1317}, {388, 6246}, {495, 6702}, {551, 18254}, {758, 25405}, {938, 12751}, {942, 2802}, {952, 5045}, {1058, 34789}, {1125, 46694}, {1210, 10956}, {1320, 11529}, {1387, 2801}, {1537, 14100}, {2829, 16215}, {3035, 34791}, {3036, 3742}, {3085, 38133}, {3241, 39776}, {3295, 46684}, {3304, 12739}, {3338, 10087}, {3361, 34474}, {3487, 16173}, {3555, 14740}, {3600, 12119}, {3616, 46685}, {3660, 28234}, {3881, 24928}, {3947, 23513}, {4298, 5840}, {4314, 38761}, {5434, 12743}, {5531, 30343}, {5533, 13407}, {5541, 10980}, {5542, 21630}, {6049, 37625}, {6265, 7373}, {6326, 11025}, {6713, 13405}, {6767, 12515}, {7993, 30350}, {8083, 8098}, {9654, 38161}, {9850, 38038}, {9946, 12737}, {9951, 10569}, {10090, 41553}, {10265, 41556}, {10404, 13274}, {11021, 35636}, {11033, 12748}, {11035, 15009}, {11038, 12757}, {11041, 26726}, {11374, 32557}, {12019, 12128}, {12532, 38314}, {12665, 40269}, {12832, 31397}, {15888, 20118}, {17644, 38156}, {18527, 22799}, {18530, 38756}, {21625, 21635}, {35620, 38484}

X(46681) = midpoint of X(i) and X(j) for these {i, j}: {1, 5083}, {942, 12735}, {1317, 12736}, {3035, 34791}, {3555, 14740}, {9946, 12737}, {11570, 15558}, {15528, 25485}
X(46681) = reflection of X(i) in X(j) for these (i, j): (18240, 5045), (46694, 1125)
X(46681) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 11570, 15558), (354, 1317, 12736), (3555, 34123, 14740), (5083, 15558, 11570), (17609, 17624, 21620)

X(46682) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: ANTI-ARA AND ORTHIC

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

X(46682) = 3*X(428)-X(1112) = 3*X(7540)+X(7723) = 3*X(7576)+X(12292) = 3*X(13490)-X(14708) = 3*X(16658)+X(17854) = X(16659)+3*X(46430)

X(46682) lies on these lines: {4, 110}, {24, 6699}, {25, 125}, {30, 13416}, {33, 46687}, {34, 46683}, {67, 7716}, {74, 7487}, {235, 7687}, {265, 1598}, {378, 38726}, {403, 44407}, {427, 5972}, {428, 542}, {468, 6723}, {541, 7576}, {974, 16655}, {1495, 37981}, {1503, 11746}, {1511, 1595}, {1560, 20998}, {1593, 16163}, {1594, 12900}, {1596, 10113}, {1597, 12121}, {1843, 13417}, {1974, 15118}, {2777, 3575}, {3088, 15035}, {3089, 14644}, {3448, 6995}, {3515, 38727}, {3517, 15061}, {3518, 20397}, {3541, 38793}, {3542, 23515}, {3867, 6593}, {5064, 5642}, {5095, 12167}, {5412, 46688}, {5413, 46689}, {5663, 6756}, {6353, 15059}, {6800, 35488}, {7408, 14683}, {7507, 36518}, {7540, 7723}, {7553, 12358}, {7713, 13211}, {7714, 9140}, {7715, 10264}, {7718, 7984}, {7728, 18494}, {10018, 17712}, {10151, 18400}, {10272, 16198}, {10594, 36253}, {11363, 11735}, {11382, 32241}, {11744, 15811}, {12041, 37458}, {12173, 13202}, {12902, 18535}, {13198, 31383}, {13490, 14708}, {15066, 35490}, {15080, 16868}, {15088, 37942}, {15115, 20771}, {16003, 37122}, {16111, 18533}, {16658, 17854}, {16659, 46430}, {18405, 37197}, {19504, 24981}, {20304, 21841}, {21243, 41674}, {21659, 26864}, {22970, 32340}, {32257, 41584}, {33547, 45179}

X(46682) = midpoint of X(i) and X(j) for these {i, j}: {4, 12140}, {974, 16655}, {1843, 32239}, {3575, 12133}, {7553, 12358}, {7687, 13419}
X(46682) = reflection of X(15473) in X(6756)
X(46682) = crosssum of X(3) and X(41673)

X(46683) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: 2nd ANTI-CIRCUMPERP-TANGENTIAL AND ANTI-TANGENTIAL-MIDARC

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

X(46683) = 3*X(1)-X(12896) = X(3028)-3*X(5434) = X(12896)+3*X(18968) = 2*X(12896)-3*X(46687) = 2*X(18968)+X(46687)

X(46683) lies on these lines: {1, 12888}, {11, 7687}, {12, 5972}, {34, 46682}, {35, 38726}, {36, 6699}, {55, 16163}, {56, 125}, {57, 13211}, {74, 4293}, {110, 388}, {113, 1478}, {226, 11720}, {265, 999}, {495, 1511}, {496, 10113}, {497, 10733}, {498, 38793}, {499, 23515}, {541, 7727}, {542, 3023}, {1056, 12383}, {1319, 11735}, {1354, 4092}, {1428, 15118}, {1469, 32243}, {1479, 12295}, {1870, 12140}, {2067, 46688}, {2192, 11744}, {2777, 3024}, {3085, 15035}, {3086, 14644}, {3295, 12121}, {3304, 12904}, {3333, 12407}, {3448, 3600}, {3476, 7984}, {3585, 46686}, {4295, 7978}, {4299, 10065}, {4311, 11709}, {4315, 13605}, {4317, 10081}, {5181, 12588}, {5204, 38727}, {5218, 15051}, {5270, 16534}, {5298, 45311}, {5433, 6723}, {5563, 36253}, {5642, 11237}, {5663, 18990}, {6502, 46689}, {7286, 29012}, {7288, 15059}, {7373, 12902}, {7728, 9655}, {7951, 12900}, {8998, 31472}, {9033, 11905}, {9613, 12368}, {9654, 14643}, {9657, 12373}, {9659, 22109}, {9672, 32607}, {10054, 11656}, {10088, 30714}, {10117, 18954}, {10832, 19457}, {10895, 36518}, {11723, 12047}, {12261, 24928}, {12374, 12943}, {13182, 16278}, {13990, 44622}, {15325, 20304}, {15326, 37853}, {19111, 31408}, {19472, 32378}, {19505, 36201}, {31479, 38794}, {32250, 39892}

X(46683) = midpoint of X(i) and X(j) for these {i, j}: {1, 18968}, {1469, 32243}, {3024, 7354}
X(46683) = reflection of X(46687) in X(1)
X(46683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (56, 12903, 125), (1478, 10091, 113), (4299, 10065, 16111), (12374, 12943, 13202)

X(46684) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: ANTI-MANDART-INCIRCLE AND 1st CIRCUMPERP

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

X(46684) = X(1)-3*X(38693) = 3*X(3)-X(6265) = 2*X(4)-3*X(38161) = 2*X(5)-3*X(38133) = 3*X(40)+X(6264) = X(100)-3*X(165) = 3*X(100)-X(5531) = 3*X(100)+X(13243) = 3*X(104)-X(6264) = X(149)+3*X(9778) = X(149)-3*X(11219) = 3*X(165)+X(1768) = 9*X(165)-X(5531) = 9*X(165)+X(13243) = 3*X(214)-2*X(6265) = X(214)+2*X(12515) = 3*X(1768)+X(5531) = 3*X(1768)-X(13243) = X(6265)+3*X(12515) = 4*X(6702)-3*X(38161)

Let O_A, O_B, O_C be the circles with collinear centers described at X(5531) and Hyacinthos #21433 (Barry Wolk, January 2013). Let A'B'C' be the triangle formed by the radical axes of these circles and the corresponding mixtilinear excircle. Then X(46684) = X(6)-of-A'B'C'. (Randy Hutson, April 16, 2022)

X(46684) lies on these lines: {1, 38693}, {2, 34789}, {3, 214}, {4, 6702}, {5, 38133}, {10, 2829}, {11, 516}, {20, 80}, {30, 6246}, {35, 11570}, {36, 12758}, {40, 104}, {46, 10058}, {55, 5083}, {56, 15558}, {57, 18240}, {63, 100}, {109, 24025}, {119, 3647}, {140, 12611}, {149, 9778}, {210, 17661}, {355, 38213}, {376, 12119}, {381, 38104}, {484, 6909}, {515, 15863}, {517, 4973}, {519, 13528}, {528, 13226}, {546, 38182}, {548, 952}, {659, 2827}, {758, 2077}, {946, 6713}, {950, 12832}, {962, 16173}, {991, 17601}, {993, 3359}, {1125, 1537}, {1145, 3916}, {1156, 2951}, {1158, 5720}, {1317, 37568}, {1320, 7991}, {1376, 5779}, {1385, 25485}, {1387, 4301}, {1519, 6681}, {1699, 9352}, {1702, 19081}, {1703, 19082}, {1764, 38484}, {1770, 8068}, {2096, 45701}, {2771, 9943}, {2821, 41191}, {2950, 10270}, {2975, 39776}, {3035, 3452}, {3036, 34862}, {3057, 41554}, {3065, 33557}, {3070, 8988}, {3071, 13976}, {3218, 5537}, {3295, 46681}, {3522, 6224}, {3534, 12747}, {3576, 10698}, {3651, 12691}, {3678, 12665}, {3683, 31235}, {3754, 6906}, {3814, 32554}, {3817, 6667}, {3874, 11248}, {3881, 26877}, {3884, 37561}, {3887, 19921}, {3892, 10679}, {3898, 10269}, {4299, 10057}, {4302, 10073}, {4868, 37469}, {5010, 11571}, {5119, 10074}, {5184, 9441}, {5204, 12740}, {5217, 12739}, {5248, 12775}, {5250, 16209}, {5267, 31788}, {5445, 37437}, {5480, 38197}, {5493, 20418}, {5541, 38669}, {5587, 10728}, {5657, 12248}, {5660, 9809}, {5731, 7972}, {5805, 38207}, {5840, 10265}, {5851, 6594}, {5884, 26285}, {6154, 7964}, {6174, 13257}, {6244, 13205}, {6284, 20118}, {6326, 12520}, {6361, 14217}, {6459, 19077}, {6460, 19078}, {6840, 15228}, {7004, 23703}, {7987, 13253}, {8148, 38637}, {9616, 19113}, {9841, 38665}, {9951, 13279}, {9955, 34126}, {9956, 22799}, {9964, 37105}, {10165, 11729}, {10167, 17660}, {10427, 43151}, {10434, 35649}, {10724, 37718}, {10742, 26446}, {11012, 18861}, {11218, 26842}, {11717, 41343}, {11849, 12005}, {12512, 24466}, {12532, 15071}, {12699, 16174}, {12702, 12737}, {12729, 16190}, {12743, 15338}, {12764, 24914}, {12767, 15015}, {13464, 38032}, {13624, 19907}, {14110, 17654}, {14151, 31508}, {15326, 18976}, {15599, 37998}, {15626, 23832}, {16128, 38752}, {17009, 34339}, {18232, 34293}, {18481, 19914}, {18483, 23513}, {19925, 34122}, {20095, 43161}, {22938, 28146}, {26364, 46435}, {28174, 41347}, {30329, 37541}, {31445, 38757}, {31806, 38722}, {33709, 38038}, {33898, 37828}, {35445, 37736}

X(46684) = midpoint of X(i) and X(j) for these {i, j}: {3, 12515}, {20, 80}, {40, 104}, {100, 1768}, {355, 38753}, {484, 6909}, {1155, 17613}, {1156, 2951}, {1320, 7991}, {3065, 33557}, {3218, 5537}, {5493, 21630}, {5531, 13243}, {5541, 38669}, {6361, 14217}, {6840, 15228}, {9778, 11219}, {10265, 31730}, {12119, 12247}, {12248, 12751}, {12532, 15071}, {12702, 12737}, {14110, 17654}, {18481, 19914}
X(46684) = reflection of X(i) in X(j) for these (i, j): (4, 6702), (119, 6684), (214, 3), (946, 6713), (1145, 43174), (1519, 6681), (1537, 1125), (3874, 15528), (4297, 38759), (4301, 1387), (6246, 12619), (10427, 43151), (11715, 38602), (12611, 140), (12665, 3678), (12699, 16174), (19907, 13624), (21630, 20418), (21635, 3035), (22799, 9956), (24466, 12512), (25485, 1385), (31803, 18254), (33814, 31663), (35016, 17009)
X(46684) = complement of X(34789)
X(46684) = X(643)-beth conjugate of-X(14740)
X(46684) = X(1026)-Zayin conjugate of-X(516)
X(46684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 40256, 3878), (4, 6702, 38161), (46, 10058, 12736), (63, 100, 14740), (100, 13243, 5531), (165, 1768, 100), (376, 12247, 12119), (946, 6713, 32557), (1158, 25440, 31803), (1537, 21154, 1125), (1768, 5531, 13243), (5657, 12248, 12751), (6326, 35242, 34474), (10164, 21635, 3035), (12767, 16192, 15015), (19914, 38754, 18481)

X(46685) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: ANTICOMPLEMENTARY AND INNER-CONWAY

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

X(46685) = 3*X(2)-4*X(46694) = X(100)-3*X(3681) = X(149)+3*X(4661) = 3*X(210)-2*X(3035) = 3*X(210)-X(17660) = 3*X(354)-4*X(6667) = 3*X(392)-2*X(12735) = 2*X(942)-3*X(34122) = 5*X(3616)-4*X(46681) = 3*X(3679)-X(11571) = 3*X(3681)-2*X(14740) = 6*X(3740)-5*X(31235) = 2*X(3754)-3*X(38213) = 3*X(3873)-4*X(18240) = 3*X(3873)-5*X(31272) = 2*X(3881)-3*X(32557) = 3*X(4134)-X(33337) = 4*X(5044)-3*X(34123) = 2*X(12532)+X(39776) = 4*X(18240)-5*X(31272)

X(46685) lies on these lines: {1, 18254}, {2, 5083}, {8, 153}, {9, 37736}, {10, 11570}, {11, 518}, {63, 100}, {65, 3036}, {72, 952}, {78, 104}, {80, 3436}, {119, 6734}, {144, 20095}, {145, 15558}, {149, 329}, {210, 3035}, {214, 2975}, {354, 6667}, {392, 12735}, {517, 38389}, {519, 12758}, {528, 17781}, {529, 18976}, {758, 1109}, {912, 6735}, {914, 3717}, {942, 34122}, {956, 6265}, {958, 12739}, {960, 1317}, {997, 10074}, {1145, 2771}, {1156, 34784}, {1320, 11682}, {1329, 20118}, {1331, 2342}, {1387, 3555}, {1537, 5777}, {2098, 11256}, {2284, 38358}, {2802, 3632}, {2810, 22321}, {2829, 14872}, {3059, 5851}, {3219, 41553}, {3305, 14151}, {3419, 10742}, {3421, 12247}, {3434, 34789}, {3616, 46681}, {3679, 11571}, {3687, 34458}, {3699, 34234}, {3738, 4088}, {3740, 31235}, {3754, 38213}, {3811, 10058}, {3868, 12736}, {3870, 30223}, {3871, 41562}, {3872, 10698}, {3873, 18240}, {3874, 6702}, {3881, 32557}, {3916, 33814}, {3927, 12331}, {3935, 41166}, {3940, 12773}, {3951, 38665}, {3962, 17636}, {3984, 38669}, {4134, 33337}, {4420, 17100}, {4430, 5748}, {4468, 37998}, {4511, 11715}, {4551, 16586}, {4651, 20879}, {4652, 34474}, {4847, 21635}, {4853, 13253}, {4855, 38693}, {4861, 20117}, {4863, 13271}, {4882, 12767}, {4996, 12757}, {5044, 34123}, {5080, 6246}, {5220, 41701}, {5231, 15017}, {5249, 38211}, {5289, 20586}, {5440, 38602}, {5533, 21616}, {5541, 12526}, {5552, 15528}, {5686, 12755}, {5687, 12515}, {5692, 7972}, {5730, 12737}, {5794, 12763}, {5795, 41558}, {5815, 9803}, {5854, 17638}, {6174, 27778}, {6583, 38182}, {6713, 27385}, {6765, 13278}, {7330, 12775}, {7672, 31164}, {7686, 38156}, {7993, 10971}, {8068, 21077}, {9024, 43216}, {9802, 9804}, {10057, 41686}, {10087, 12514}, {10265, 21075}, {10427, 40659}, {10707, 11678}, {10916, 39692}, {10956, 24987}, {11415, 14217}, {11679, 35649}, {11680, 15064}, {12005, 27529}, {12513, 12740}, {12607, 20612}, {12611, 24390}, {12619, 17757}, {12675, 21154}, {12680, 38759}, {12831, 25006}, {12832, 24982}, {13265, 44694}, {13274, 24703}, {14213, 17165}, {14923, 31803}, {15104, 44447}, {15556, 20060}, {17658, 17661}, {18253, 33667}, {19907, 31835}, {20116, 38216}, {24465, 41539}, {34339, 38128}, {35614, 38484}, {39778, 40661}, {45393, 45632}

X(46685) = midpoint of X(i) and X(j) for these {i, j}: {8, 12532}, {80, 5904}, {1156, 34784}, {3869, 12531}, {3962, 17636}
X(46685) = reflection of X(i) in X(j) for these (i, j): (1, 18254), (65, 3036), (100, 14740), (145, 15558), (214, 3678), (908, 17615), (1145, 34790), (1317, 960), (1537, 5777), (3555, 1387), (3868, 12736), (3874, 6702), (5083, 46694), (9809, 13227), (10427, 40659), (11570, 10), (12680, 38759), (17660, 3035), (19907, 31835), (25485, 20117), (33667, 18253), (39776, 8), (39778, 40661), (41558, 5795)
X(46685) = anticomplement of X(5083)
X(46685) = X(8)-beth conjugate of-X(11570)
X(46685) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (100, 3681, 14740), (200, 1768, 100), (210, 17660, 3035), (3873, 31272, 18240), (5083, 46694, 2)

X(46686) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: EHRMANN-MID AND EHRMANN-VERTEX

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

X(46686) = 3*X(2)+X(10721) = X(3)-3*X(36518) = 3*X(4)+X(110) = 5*X(4)-X(10733) = 3*X(4)-X(12295) = 7*X(4)+X(12383) = 2*X(4)+X(16534) = 11*X(4)+5*X(20125) = 5*X(4)+X(30714) = X(110)-3*X(113) = 5*X(110)+3*X(10733) = 7*X(110)-3*X(12383) = 2*X(110)-3*X(16534) = 11*X(110)-15*X(20125) = 5*X(110)-3*X(30714) = 5*X(113)+X(10733) = 3*X(113)+X(12295) = 7*X(113)-X(12383) = 11*X(113)-5*X(20125) = 5*X(113)-X(30714) = 2*X(12900)+X(13202) = 2*X(12900)-3*X(36518) = X(13202)+3*X(36518)

X(46686) lies on these lines: {2, 10721}, {3, 12900}, {4, 110}, {5, 1539}, {20, 15036}, {25, 12893}, {30, 5972}, {52, 12825}, {74, 3091}, {125, 381}, {140, 34584}, {146, 3832}, {182, 19506}, {185, 16222}, {235, 15473}, {265, 3527}, {382, 14643}, {389, 546}, {399, 36749}, {403, 32110}, {427, 33547}, {515, 11723}, {542, 1353}, {567, 43831}, {974, 5462}, {1112, 10151}, {1495, 18323}, {1511, 3627}, {1514, 10297}, {1531, 11799}, {1533, 7574}, {1553, 36184}, {1568, 31726}, {1593, 12901}, {1595, 23306}, {1597, 12302}, {1598, 2931}, {1656, 20127}, {1657, 15046}, {1699, 12368}, {1986, 12162}, {2574, 32549}, {2575, 32550}, {2771, 5806}, {2794, 33511}, {2935, 6642}, {3047, 15033}, {3090, 15055}, {3146, 15035}, {3448, 3839}, {3526, 38788}, {3529, 15029}, {3544, 15021}, {3545, 12244}, {3574, 15089}, {3583, 46687}, {3585, 46683}, {3817, 11709}, {3818, 32271}, {3830, 5642}, {3850, 20304}, {3851, 10990}, {3853, 10272}, {3856, 13566}, {3858, 10264}, {3859, 20396}, {3861, 6053}, {5055, 38728}, {5066, 15088}, {5072, 15041}, {5073, 38723}, {5076, 32609}, {5095, 18440}, {5181, 31670}, {5198, 12168}, {5446, 44226}, {5449, 35488}, {5655, 12902}, {5892, 44920}, {5893, 9826}, {5907, 11807}, {5943, 17855}, {6000, 14708}, {6033, 16278}, {6560, 13990}, {6561, 8998}, {6564, 46688}, {6565, 46689}, {6644, 13293}, {6759, 12228}, {7517, 22109}, {7526, 13289}, {7699, 37077}, {7722, 15305}, {7723, 13417}, {8717, 18531}, {8994, 42265}, {9140, 41099}, {9730, 17854}, {9818, 10117}, {9919, 11479}, {9927, 45010}, {9955, 11735}, {10110, 12236}, {10114, 18379}, {10118, 37697}, {10170, 13416}, {10257, 20725}, {10575, 46431}, {10628, 44870}, {10657, 43227}, {10658, 43226}, {10750, 14500}, {10751, 14499}, {10752, 32275}, {10819, 22615}, {10820, 22644}, {10895, 12374}, {10896, 12373}, {10982, 19456}, {11381, 16223}, {11454, 16868}, {11558, 13391}, {11561, 32137}, {11562, 12292}, {11563, 41674}, {11597, 32340}, {11720, 31673}, {11744, 37475}, {11805, 22804}, {12038, 20771}, {12133, 23047}, {12219, 15058}, {12227, 32139}, {12242, 15807}, {12281, 16261}, {12310, 18535}, {12358, 16105}, {12811, 40685}, {12891, 35764}, {12892, 35765}, {12896, 18514}, {13203, 18537}, {13211, 18492}, {13419, 18567}, {13488, 15115}, {13568, 15114}, {13969, 42262}, {14448, 22584}, {14853, 41737}, {15054, 15081}, {15101, 16776}, {15118, 19130}, {15123, 37984}, {15647, 18475}, {15687, 34153}, {17812, 37514}, {18358, 32257}, {18376, 34155}, {18403, 44407}, {18451, 19504}, {18513, 18968}, {18560, 43839}, {18572, 29012}, {19059, 42561}, {19060, 31412}, {19110, 23249}, {19111, 23259}, {19481, 40240}, {19505, 37696}, {22251, 33699}, {23698, 33512}, {25564, 37814}, {25641, 46045}, {32223, 44961}, {34484, 46027}, {37197, 37489}, {44673, 46031}

X(46686) = midpoint of X(i) and X(j) for these {i, j}: {3, 13202}, {4, 113}, {5, 1539}, {52, 12825}, {110, 12295}, {125, 7728}, {146, 16003}, {265, 15063}, {382, 16163}, {1495, 18323}, {1511, 3627}, {1514, 10297}, {1531, 11799}, {1533, 7574}, {1553, 36184}, {1568, 31726}, {1986, 12162}, {3818, 32271}, {3830, 5642}, {3853, 10272}, {5095, 18440}, {5181, 31670}, {5907, 11807}, {6033, 16278}, {7687, 38791}, {7723, 13417}, {10575, 46431}, {10721, 16111}, {10733, 30714}, {10750, 14500}, {10751, 14499}, {10752, 32275}, {10990, 38790}, {11561, 32137}, {11562, 12292}, {11597, 32340}, {11720, 31673}, {11805, 22804}, {12133, 25711}, {12358, 16105}, {12824, 16194}, {12902, 24981}, {14448, 22584}, {25641, 46045}
X(46686) = reflection of X(i) in X(j) for these (i, j): (3, 12900), (74, 20397), (974, 5462), (6699, 5), (7687, 546), (11735, 9955), (11806, 11746), (12041, 6723), (12236, 10110), (14708, 41671), (15118, 19130), (16534, 113), (19481, 40240), (20304, 3850), (20417, 20304), (32223, 44961), (32257, 18358), (36253, 7687), (37853, 140), (38726, 5972), (40647, 9826), (40685, 12811), (44673, 46031), (45311, 5066)
X(46686) = complement of X(16111)
X(46686) = complementary conjugate of the complement of X(46429)
X(46686) = inverse of X(10151) in Hatzipolakis-Lozada hyperbola
X(46686) = X(113)-of-Euler-triangle
X(46686) = X(6699)-of-Johnson-triangle
X(46686) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 10721, 16111), (3, 36518, 12900), (4, 110, 12295), (4, 5448, 12897), (5, 12041, 6723), (5, 14677, 34128), (74, 3091, 23515), (74, 23515, 20397), (113, 12295, 110), (146, 3832, 14644), (146, 14644, 16003), (265, 38789, 15063), (381, 7728, 125), (382, 14643, 16163), (546, 38791, 36253), (1656, 20127, 38727), (1657, 15046, 38794), (3545, 12244, 15059), (3843, 38789, 265), (3851, 38790, 15061), (5655, 12902, 24981), (6723, 12041, 6699), (11562, 16194, 12292), (12292, 12824, 11562), (13202, 36518, 3), (13417, 15030, 7723), (15061, 38790, 10990), (20304, 20417, 38725)

X(46687) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: INTANGENTS AND MANDART-INCIRCLE

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

X(46687) = 3*X(1)-X(18968) = X(3024)-3*X(3058) = 3*X(12896)+X(18968) = 2*X(12896)+X(46683) = 2*X(18968)-3*X(46683)

X(46687) lies on these lines: {1, 12888}, {11, 5972}, {12, 7687}, {33, 46682}, {35, 6699}, {36, 38726}, {55, 125}, {56, 16163}, {67, 10387}, {74, 4294}, {110, 497}, {113, 1479}, {221, 11744}, {265, 3295}, {388, 10733}, {390, 3448}, {495, 10113}, {496, 1511}, {498, 23515}, {499, 38793}, {541, 19470}, {542, 3024}, {999, 12121}, {1058, 12383}, {1365, 6062}, {1456, 6357}, {1478, 12295}, {1697, 13211}, {2066, 46688}, {2293, 38535}, {2330, 15118}, {2646, 11735}, {2771, 31795}, {2777, 3028}, {3056, 32297}, {3057, 10693}, {3085, 14644}, {3086, 15035}, {3303, 12903}, {3486, 7984}, {3583, 46686}, {3586, 12368}, {3746, 36253}, {4302, 10081}, {4304, 11709}, {4309, 10065}, {4314, 13605}, {4857, 16534}, {4995, 45311}, {5160, 29012}, {5181, 12589}, {5217, 38727}, {5218, 15059}, {5414, 46689}, {5432, 6723}, {5642, 11238}, {5663, 15171}, {5722, 12778}, {6198, 12140}, {6767, 12902}, {7288, 15051}, {7728, 9668}, {7741, 12900}, {7978, 30305}, {8998, 44623}, {9033, 11906}, {9140, 10385}, {9659, 32607}, {9669, 14643}, {9670, 12374}, {9672, 22109}, {10070, 11656}, {10091, 30714}, {10117, 10833}, {10118, 36201}, {10149, 18400}, {10264, 10386}, {10831, 19457}, {10896, 36518}, {11720, 12053}, {11723, 30384}, {12261, 24929}, {12310, 16541}, {12373, 12953}, {12407, 31393}, {13183, 16278}, {13990, 44624}, {15172, 32423}, {15338, 37853}, {19052, 31474}, {22954, 32350}, {32250, 39891}

X(46687) = midpoint of X(i) and X(j) for these {i, j}: {1, 12896}, {3028, 6284}, {3056, 32297}
X(46687) = reflection of X(46683) in X(1)
X(46687) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (55, 12904, 125), (1479, 10088, 113), (4302, 10081, 16111), (12373, 12953, 13202)

X(46688) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: 1st KENMOTU-CENTERS AND 1st KENMOTU DIAGONALS

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

X(46688) lies on these lines: {2, 13990}, {3, 8994}, {4, 19044}, {5, 13915}, {6, 67}, {49, 43863}, {74, 1587}, {110, 3068}, {113, 485}, {141, 32303}, {265, 3311}, {371, 12891}, {372, 6699}, {486, 23515}, {541, 35822}, {542, 32787}, {590, 5972}, {615, 6723}, {1151, 16163}, {1152, 38727}, {1511, 8981}, {1588, 14644}, {1986, 12239}, {2066, 46687}, {2067, 46683}, {2777, 3070}, {3024, 19030}, {3028, 19028}, {3069, 15059}, {3071, 7687}, {3312, 13969}, {3448, 7585}, {3594, 38729}, {5412, 46682}, {5418, 10820}, {5465, 13908}, {5504, 19062}, {5622, 39875}, {5642, 13846}, {5663, 7583}, {6143, 43825}, {6199, 12902}, {6200, 38726}, {6221, 12121}, {6398, 38728}, {6417, 19051}, {6419, 36253}, {6420, 20397}, {6427, 15027}, {6449, 38723}, {6459, 10733}, {6460, 15055}, {6560, 16111}, {6561, 12295}, {6564, 46686}, {6593, 13910}, {7581, 19059}, {7582, 15081}, {7584, 20304}, {7728, 13665}, {7735, 13654}, {7736, 13774}, {7968, 11735}, {7984, 19066}, {8960, 12376}, {8976, 14643}, {8983, 11720}, {8991, 11598}, {8995, 11597}, {9140, 19054}, {9540, 15035}, {10088, 13905}, {10091, 13904}, {10113, 42215}, {10117, 44598}, {10264, 19117}, {10272, 13925}, {10576, 12900}, {10620, 18512}, {10721, 23249}, {10778, 19113}, {10817, 42638}, {10819, 30714}, {10880, 12140}, {11005, 19056}, {11006, 19058}, {11744, 19088}, {12041, 42216}, {12240, 46430}, {12244, 23267}, {12903, 18996}, {12904, 19038}, {13171, 19006}, {13202, 23251}, {13211, 18991}, {13287, 36201}, {13903, 32609}, {13909, 46085}, {13966, 34128}, {13979, 19116}, {15088, 18762}, {19096, 33565}, {23236, 31487}, {32788, 45311}, {35770, 38725}, {36518, 42265}, {37853, 42259}, {43808, 43826}

X(46688) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 19110, 13990), (6, 125, 46689), (110, 3068, 8998), (3312, 15061, 13969), (3448, 7585, 19111), (5418, 10820, 38793), (6417, 38724, 19051)

X(46689) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: 2nd KENMOTU-CENTERS AND 2nd KENMOTU DIAGONALS

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

X(46689) lies on these lines: {2, 8998}, {3, 13969}, {4, 19043}, {5, 13979}, {6, 67}, {49, 43864}, {74, 1588}, {110, 3069}, {113, 486}, {141, 32304}, {265, 3312}, {371, 6699}, {372, 12892}, {485, 23515}, {541, 35823}, {542, 32788}, {590, 6723}, {615, 5972}, {1151, 38727}, {1152, 16163}, {1511, 13966}, {1587, 14644}, {1986, 12240}, {2777, 3071}, {3024, 19029}, {3028, 19027}, {3068, 15059}, {3070, 7687}, {3311, 8994}, {3448, 7586}, {3592, 38729}, {5413, 46682}, {5414, 46687}, {5420, 10819}, {5465, 13968}, {5504, 19061}, {5622, 39876}, {5642, 13847}, {5663, 7584}, {6143, 43826}, {6221, 38728}, {6395, 12902}, {6396, 38726}, {6398, 12121}, {6418, 19052}, {6419, 20397}, {6420, 36253}, {6428, 15027}, {6450, 38723}, {6459, 15055}, {6460, 10733}, {6502, 46683}, {6560, 12295}, {6561, 16111}, {6565, 46686}, {6593, 13972}, {7581, 15081}, {7582, 19060}, {7583, 20304}, {7728, 13785}, {7735, 13774}, {7736, 13654}, {7969, 11735}, {7984, 19065}, {8981, 34128}, {9140, 19053}, {10088, 13963}, {10091, 13962}, {10113, 42216}, {10117, 44599}, {10264, 19116}, {10272, 13993}, {10577, 12900}, {10620, 18510}, {10721, 23259}, {10778, 19112}, {10818, 42637}, {10820, 30714}, {10881, 12140}, {11005, 19055}, {11006, 19057}, {11597, 13986}, {11598, 13980}, {11720, 13971}, {11744, 19087}, {12041, 42215}, {12239, 46430}, {12244, 23273}, {12375, 16534}, {12903, 18995}, {12904, 19037}, {13171, 19005}, {13202, 23261}, {13211, 18992}, {13288, 36201}, {13915, 19117}, {13935, 15035}, {13951, 14643}, {13961, 32609}, {13970, 46085}, {15088, 18538}, {19095, 33565}, {32787, 45311}, {35771, 38725}, {36518, 42262}, {37853, 42258}, {43808, 43825}

X(46689) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 19111, 8998), (6, 125, 46688), (110, 3069, 13990), (3311, 15061, 8994), (3448, 7586, 19110), (5420, 10819, 38793), (6418, 38724, 19052)

X(46690) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: LUCAS CENTRAL AND LUCAS TANGENTS

Barycentrics (-4*a^12+b^12+c^12+17*(b^2+c^2)*a^10-2*(11*b^4+4*b^2*c^2+11*c^4)*a^8+(b^2+c^2)*(23*b^4-113*b^2*c^2+23*c^4)*a^6-(19*b^8+19*c^8-2*(52*b^4+61*b^2*c^2+52*c^4)*b^2*c^2)*a^4+(8*b^8+8*c^8-(9*b^4+16*b^2*c^2+9*c^4)*b^2*c^2)*b^2*c^2+(b^2+c^2)*(4*b^8+4*c^8-(75*b^4-82*b^2*c^2+75*c^4)*b^2*c^2)*a^2+(22*(b^2+c^2)*a^8-2*(17*b^4+74*b^2*c^2+17*c^4)*a^6+2*(b^2+c^2)*(14*b^4+27*b^2*c^2+14*c^4)*a^4-2*(15*b^8+15*c^8+2*(2*b^4-27*b^2*c^2+2*c^4)*b^2*c^2)*a^2+2*(b^2+c^2)*(3*b^8+3*c^8-(9*b^4+8*b^2*c^2+9*c^4)*b^2*c^2))*S)*a^2 : :

X(46691) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: LUCAS(-1) CENTRAL AND LUCAS(-1) TANGENTS

Barycentrics a^2*(-4*a^12+b^12+c^12+17*(b^2+c^2)*a^10-2*(11*b^4+4*b^2*c^2+11*c^4)*a^8+(b^2+c^2)*(23*b^4-113*b^2*c^2+23*c^4)*a^6-(19*b^8+19*c^8-2*(52*b^4+61*b^2*c^2+52*c^4)*b^2*c^2)*a^4+(8*b^8+8*c^8-(9*b^4+16*b^2*c^2+9*c^4)*b^2*c^2)*b^2*c^2+(b^2+c^2)*(4*b^8+4*c^8-(75*b^4-82*b^2*c^2+75*c^4)*b^2*c^2)*a^2-(22*(b^2+c^2)*a^8-2*(17*b^4+74*b^2*c^2+17*c^4)*a^6+2*(b^2+c^2)*(14*b^4+27*b^2*c^2+14*c^4)*a^4-2*(15*b^8+15*c^8+2*(2*b^4-27*b^2*c^2+2*c^4)*b^2*c^2)*a^2+2*(b^2+c^2)*(3*b^8+3*c^8-(9*b^4+8*b^2*c^2+9*c^4)*b^2*c^2))*S) : :

X(46692) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: LUCAS INNER AND LUCAS INNER TANGENTIAL

Barycentrics a^2*(400*a^12-490*b^12-490*c^12-2090*(b^2+c^2)*a^10+20*(173*b^4+166*b^2*c^2+173*c^4)*a^8-2*(b^2+c^2)*(1195*b^4-2341*b^2*c^2+1195*c^4)*a^6-2*(25*b^8+25*c^8+2*(1481*b^4+755*b^2*c^2+1481*c^4)*b^2*c^2)*a^4+2*(134*b^8+134*c^8+(1353*b^4-2164*b^2*c^2+1353*c^4)*b^2*c^2)*b^2*c^2+2*(b^2+c^2)*(580*b^8+580*c^8+(1767*b^4-2678*b^2*c^2+1767*c^4)*b^2*c^2)*a^2-(600*a^10+590*(b^2+c^2)*a^8-10*(377*b^4+734*b^2*c^2+377*c^4)*a^6+2*(b^2+c^2)*(2530*b^4-81*b^2*c^2+2530*c^4)*a^4-(3270*b^8+3270*c^8+(277*b^4-4182*b^2*c^2+277*c^4)*b^2*c^2)*a^2+(b^2+c^2)*(390*b^8+390*c^8-(4173*b^4-5614*b^2*c^2+4173*c^4)*b^2*c^2))*S) : :

X(46693) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: LUCAS(-1) INNER AND LUCAS(-1) INNER TANGENTIAL

Barycentrics a^2*(400*a^12-490*b^12-490*c^12-2090*(b^2+c^2)*a^10+20*(173*b^4+166*b^2*c^2+173*c^4)*a^8-2*(b^2+c^2)*(1195*b^4-2341*b^2*c^2+1195*c^4)*a^6-2*(25*b^8+25*c^8+2*(1481*b^4+755*b^2*c^2+1481*c^4)*b^2*c^2)*a^4+2*(134*b^8+134*c^8+(1353*b^4-2164*b^2*c^2+1353*c^4)*b^2*c^2)*b^2*c^2+2*(b^2+c^2)*(580*b^8+580*c^8+(1767*b^4-2678*b^2*c^2+1767*c^4)*b^2*c^2)*a^2+(600*a^10+590*(b^2+c^2)*a^8-10*(377*b^4+734*b^2*c^2+377*c^4)*a^6+2*(b^2+c^2)*(2530*b^4-81*b^2*c^2+2530*c^4)*a^4-(3270*b^8+3270*c^8+(277*b^4-4182*b^2*c^2+277*c^4)*b^2*c^2)*a^2+(b^2+c^2)*(390*b^8+390*c^8-(4173*b^4-5614*b^2*c^2+4173*c^4)*b^2*c^2))*S) : :

X(46694) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: MEDIAL AND 2nd ZANIAH

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

X(46694) = 3*X(2)+X(46685) = X(11)+3*X(210) = X(72)+3*X(34122) = 3*X(210)-X(14740) = X(1145)-5*X(3697) = X(1317)-5*X(25917) = 5*X(1698)-X(11570) = X(3035)-3*X(3740) = 5*X(3617)-X(39776) = 3*X(3679)+X(12758) = 3*X(3681)+5*X(31272) = X(3878)+3*X(38213) = 7*X(3983)+X(17638) = X(5887)+3*X(38128) = 7*X(9780)+X(12532) = X(9946)-3*X(38752) = 3*X(10176)+X(15863) = X(12736)-3*X(34122) = 3*X(15064)+X(46684) = X(15528)-3*X(38133)

X(46694) lies on these lines: {2, 5083}, {8, 4939}, {9, 100}, {10, 119}, {11, 210}, {72, 12736}, {80, 2551}, {104, 936}, {149, 18228}, {214, 958}, {518, 6667}, {527, 24465}, {528, 18227}, {756, 16579}, {758, 5123}, {952, 5044}, {960, 2802}, {997, 11715}, {1125, 46681}, {1145, 3697}, {1158, 34293}, {1215, 41797}, {1317, 25917}, {1320, 15829}, {1329, 3678}, {1376, 5779}, {1387, 34790}, {1698, 11570}, {1768, 8580}, {2284, 25069}, {2550, 34789}, {2801, 3035}, {2827, 4925}, {3305, 41553}, {3617, 39776}, {3679, 12758}, {3681, 30827}, {3754, 10592}, {3820, 12619}, {3878, 11928}, {3911, 17615}, {3928, 11678}, {3952, 4858}, {3983, 17638}, {4521, 37998}, {4551, 16578}, {4662, 5854}, {4679, 13274}, {5234, 15015}, {5325, 6174}, {5438, 38693}, {5531, 30393}, {5660, 38057}, {5770, 15528}, {5784, 17661}, {5791, 9946}, {5811, 46435}, {5840, 12572}, {6265, 9708}, {6700, 6713}, {7308, 37736}, {8582, 12832}, {9519, 38390}, {9623, 10698}, {9709, 12515}, {9780, 12532}, {9951, 13996}, {10090, 41229}, {10176, 15863}, {11571, 19875}, {11681, 15556}, {12059, 24914}, {12611, 31419}, {14110, 38156}, {14872, 21154}, {16174, 21616}, {17660, 31235}, {18229, 35649}, {18976, 34606}, {19113, 31438}, {19861, 41554}, {21630, 21631}, {24003, 34589}, {24025, 24433}, {25096, 38358}, {25681, 32557}, {30294, 34711}, {31165, 38099}, {31424, 34474}, {31445, 33814}, {31803, 37828}, {34894, 42015}, {35628, 38484}

X(46694) = midpoint of X(i) and X(j) for these {i, j}: {8, 15558}, {10, 18254}, {11, 14740}, {72, 12736}, {960, 3036}, {1158, 34293}, {1387, 34790}, {1768, 13227}, {3678, 6702}, {3911, 17615}, {5083, 46685}, {9951, 13996}
X(46694) = reflection of X(i) in X(j) for these (i, j): (18240, 6667), (46681, 1125)
X(46694) = complement of X(5083)
X(46694) = inverse of X(124) in Spieker circle
X(46694) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 46685, 5083), (11, 210, 14740), (72, 34122, 12736), (210, 18236, 3452)

X(46695) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: MIDARC AND TANGENTIAL-MIDARC

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

X(46695) lies on these lines: {1, 6724}, {177, 10501}, {5045, 5571}, {10491, 10506}, {13092, 13560}

X(46695) = midpoint of X(177) and X(10501)
X(46695) = reflection of X(46696) in X(1)
X(46695) = X(125)-of-midarc-triangle

X(46696) = CENTER OF THE MR-CONIC OF THESE TRIANGLES: 2ND MIDARC AND 2ND TANGENTIAL-MIDARC

Barycentrics a*(4*b*c*(b-c)*(2*a^3-(2*b^2+7*b*c+2*c^2)*a+b*c*(b+c))*sin(A/2)+2*c*((5*b-c)*a^4+(11*b+c)*c*a^3-(6*b^3-c^3+b*c*(b+10*c))*a^2+(b^2-c^2)*(3*b+c)*c*a+(b^2-c^2)^2*b)*sin(B/2)+2*b*((b-5*c)*a^4-(b+11*c)*b*a^3-(b^3-6*c^3-b*c*(10*b+c))*a^2+(b^2-c^2)*(b+3*c)*b*a-(b^2-c^2)^2*c)*sin(C/2)-(b-c)*(a^5-(b+c)*a^4+13*b*c*a^3-13*(b+c)*b*c*a^2-(b^4+c^4+b*c*(b^2-12*b*c+c^2))*a+(b^2-c^2)*(b-c)*(b^2+3*b*c+c^2))) : :

X(46696) lies on these lines: {1, 6724}, {8422, 10506}, {10501, 11234}, {31766, 31792}

X(46696) = midpoint of X(8422) and X(10506)
X(46696) = reflection of X(46695) in X(1)
X(46696) = X(125)-of-2nd-midarc-triangle

X(46697) = (name pending)

X(46698) = NINE-POINT-CIRCLE-INVERSE OF X(1113)

X(46698) = midpoint of PU(199)
X(46698) = nine-point-circle-inverse of X(1113)
X(46698) = crosssum of X(184) and X(15166)

X(46699) = NINE-POINT-CIRCLE-INVERSE OF X(1114)

X(46699) = midpoint of PU(200)
X(46699) = nine-point-circle-inverse of X(1114)
X(46699) = crosssum of X(184) and X(15167)

X(46700) = X(4)X(6)∩X(253)X(7398)

X(46700) lies on these lines: {4, 6}, {25, 15594}, {107, 35283}, {253, 7398}, {1368, 20204}, {3589, 32713}, {5020, 15259}, {6525, 32000}, {9825, 15312}, {13562, 27373}, {14615, 34412}

X(46700) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(34412)}} and {{A, B, C, X(253), X(5286)}}

X(46701) = (name pending)

X(46701) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(25)}} and {{A, B, C, X(66), X(76)}}

X(46702) = EULER LINE INTERCEPT OF X(577)X(6116)

X(46702) lies on these lines: {2, 3}, {577, 6116}, {1092, 41888}, {3643, 11793}, {5872, 40665}, {5889, 11078}, {6759, 41023}, {10654, 39571}, {11543, 42459}, {18381, 41022}, {23325, 44666}

X(46702) = reflection of X(46703) in X(5)
X(46702) = X(46703)-of-Johnson-triangle
X(46702) = intersection, other than A, B, C, of circumconics {{A, B, C, X(68), X(19773)}} and {{A, B, C, X(265), X(46703)}}
X(46702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 19772, 3), (18586, 18587, 473)

X(46703) = EULER LINE INTERCEPT OF X(577)X(6117)

X(46703) lies on these lines: {2, 3}, {577, 6117}, {1092, 41887}, {3642, 11793}, {5873, 40666}, {5889, 11092}, {6759, 41022}, {10653, 39571}, {11542, 42459}, {18381, 41023}, {23325, 44667}

X(46703) = reflection of X(46702) in X(5)
X(46703) = X(46702)-of-Johnson-triangle
X(46703) = intersection, other than A, B, C, of circumconics {{A, B, C, X(68), X(19772)}} and {{A, B, C, X(265), X(46702)}}
X(46703) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 19773, 3), (18586, 18587, 472)

X(46704) = 68TH HATZIPOLAKIS-MOSES-EULER POINT

X(46704) lies on these lines: {2, 3}, {171, 3585}, {355, 511}, {500, 515}, {517, 4647}, {944, 5453}, {946, 36250}, {1460, 18961}, {1478, 5711}, {1503, 13408}, {3436, 5774}, {4299, 15447}, {4442, 22791}, {5492, 29057}, {5786, 36742}, {7009, 18447}, {7683, 45926}, {9958, 10526}, {10888, 37531}, {16792, 29012}, {18492, 20368}, {18513, 37603}, {26446, 35203}

X(46704) = midpoint X(4) and X(15971)
X(46704) = reflection of X(i) in X(j) for these {i,j}: {3,15973}, {944,5453}, {9840,5}
X(46704) = X(15971)-of-Euler-triangle
X(46704) = X(9840)-of-Johnson-triangle

X(46705) = ISOGONAL CONJUGATE OF X(46370)

This preamble is contributed by Clark Kimberling and Peter Moses, January 18, 2022.

Let P = p : q : r be a point that is not on a sideline BC, CA, AB of a triangle ABC. Let A' be the point, other than A, in which the cevian line AP intersects the Steiner circumellipse, and define B' and C' cyclically. Then

A' = -a q r : (b r + c q) q : (b r + c q) r

Let A'' be the points, other than A, in which the anticevian line of P intersects the Steiner circumellipse, and define B'' and C'' cyclically. Then

A" = a q r : (c q - b r) q : (b r - c q) r

Then A'B'C' is perspective to the anticomplementary triangle, and the perspector is the point

U(P) = p^2*q^2 + p^2*r^2 - q^2*r^2 : :

Moreover, A''B''C'' is also perspective to the anticomplementary triangle, with perspector U(P), which is the anticomplement of isotomic conjugate of P^2. The appearance of (i,j) in the following list means that if X(i) = p:q:r, then X(j) = U(P).

(1,194), (2,2), (4,6392), (6,8264), (7,4452), (8,30695), (31,40382), (32,40381), (66,33785), (69,6527), (75,69), (76,315), (83,7760), (85,6604), (86,4360), (87,32033), (92,6515), (98,36849), (99,99), (174,3210), (188,3177), (190,190), (264,317), (274,17143), (290,290), (308,33769), (335,6653), (365,17486), (366,192), (508,145), (556,329), (561,33796), (648,648), (662,14570), (664,664), (666,666), (668,668), (670,670), (671,671), (673,32029), (799,4576), (886,886), (889,889), (892,892), (903,903),

Note that i = j if and only if X(i) lies on the Steiner circumellipse.

X(46706) = X(220)-CEVA CONJUGATE OF X(2)

X(46706) lies on these lines: {2, 31618}, {9, 3177}, {144, 4499}, {192, 3870}, {1655, 30695}, {7674, 20111}, {11677, 14732}, {25243, 43989}, {26125, 30694}

X(46706) = anticomplement of isogonal conjugate of X(14827)
X(46706) = anticomplement of isotomic conjugate of X(220)
X(46706) = anticomplement of polar conjugate of X(7071)
X(46706) = anticomplement of barycentric square of X(85)
X(46706) = isotomic conjugate of isogonal conjugate of X(35215)
X(46706) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {9, 21280}, {31, 6604}, {32, 36845}, {41, 3434}, {55, 21285}, {200, 315}, {220, 6327}, {341, 33796}, {346, 21275}, {480, 21286}, {560, 4452}, {657, 21293}, {692, 46402}, {1253, 69}, {1501, 17480}, {1802, 1370}, {2175, 7}, {2194, 20244}, {2206, 17158}, {2287, 17138}, {2328, 17137}, {2332, 20242}, {4524, 21294}, {4578, 21304}, {6066, 21272}, {6602, 3436}, {7071, 21270}, {7079, 11442}, {7256, 21305}, {7259, 44445}, {8641, 150}, {9447, 145}, {9448, 3210}, {14827, 8}, {24027, 4569}, {32739, 3900}
X(46706) = X(220)-Ceva conjugate of X(2)
X(46706) = barycentric product X(76)*X(35215)
X(46706) = barycentric quotient X(35215)/X(6)

X(46707) = X(594)-CEVA CONJUGATE OF X(2)

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

X(46707) lies on these lines: {1, 20536}, {2, 1171}, {8, 148}, {10, 894}, {69, 27269}, {194, 5739}, {315, 17343}, {333, 20337}, {524, 23905}, {596, 39348}, {599, 26147}, {1655, 2895}, {2134, 35216}, {3578, 19570}, {4643, 44370}, {6626, 10026}, {14555, 27318}, {16826, 17778}, {17344, 25994}, {17346, 26081}, {17685, 33297}, {17781, 29615}, {20090, 33770}, {21220, 37656}, {23942, 41135}, {24051, 24090}, {24504, 33299}, {26064, 40721}, {35511, 36223}

X(46707) = reflection of X(i) in X(j) for these {i,j}: {1509, 6537}, {32004, 23905}
X(46707) = anticomplement of X(1509)
X(46707) = anticomplement of isogonal conjugate of X(1500)
X(46707) = anticomplement of isotomic conjugate of X(594)
X(46707) = isotomic conjugate of isogonal conjugate of X(35216)
X(46707) = anticomplementary isogonal conjugate of X(17143)
X(46707) = X(594)-Ceva conjugate of X(2)
X(46707) = X(58)-isoconjugate of X(2135)
X(46707) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 17143}, {6, 17140}, {9, 35614}, {10, 17137}, {12, 21285}, {31, 4360}, {37, 17135}, {41, 2975}, {42, 75}, {43, 34086}, {55, 21273}, {65, 20244}, {71, 20243}, {72, 18659}, {100, 17159}, {101, 17166}, {181, 7}, {210, 20245}, {213, 1}, {228, 17134}, {321, 17138}, {594, 6327}, {692, 17161}, {756, 69}, {762, 1330}, {765, 4576}, {798, 17154}, {813, 4155}, {872, 2}, {1018, 512}, {1042, 17158}, {1089, 315}, {1110, 99}, {1245, 39731}, {1252, 21295}, {1254, 6604}, {1334, 3869}, {1400, 3873}, {1402, 3875}, {1500, 8}, {1824, 17220}, {1826, 20242}, {1918, 17147}, {2171, 3434}, {2175, 18662}, {2194, 18654}, {2200, 20222}, {2205, 17148}, {2333, 3868}, {2350, 13476}, {3690, 4329}, {3949, 1370}, {3952, 17217}, {4024, 21293}, {4033, 44445}, {4037, 20554}, {4079, 149}, {4103, 21301}, {4551, 4374}, {4557, 7192}, {4705, 150}, {6057, 21286}, {6187, 39765}, {6358, 21280}, {6378, 10453}, {6535, 21287}, {6541, 20560}, {7035, 670}, {7064, 329}, {7109, 192}, {7140, 21270}, {7148, 21281}, {18098, 17142}, {20693, 20351}, {21759, 17155}, {21803, 30660}, {21816, 2891}, {21859, 21302}, {23493, 17144}, {23990, 6758}, {27808, 21305}, {28654, 21275}, {28658, 17146}, {34857, 17139}, {40504, 8049}, {40521, 20295}, {40607, 40007}, {40729, 38}
X(46707) = barycentric product X(i)*X(j) for these {i,j}: {76, 35216}, {321, 2134}
X(46707) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 2135}, {2134, 81}, {35216, 6}
X(46707) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1509, 6537, 2}, {1654, 6625, 10}

X(46708) = X(11080)-CEVA CONJUGATE OF X(2)

X(46708) lies on these lines: {2, 2981}, {13, 533}, {115, 40901}, {146, 148}, {194, 616}, {299, 5025}, {303, 22847}, {315, 40899}, {395, 30471}, {628, 22511}, {3411, 36781}, {5617, 13571}, {6298, 22496}, {6772, 40898}, {7785, 22796}, {14145, 16530}, {20088, 41745}, {33255, 37641}

X(46708) = anticomplement of X(11129)
X(46708) = anticomplement of isotomic conjugate of X(11080)
X(46708) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {11080, 6327}, {36839, 17217}
X(46708) = X(11080)-Ceva conjugate of X(2)
X(46708) = {X(3180),X(11121)}-harmonic conjugate of X(13)

X(46709) = X(11085)-CEVA CONJUGATE OF X(2)

X(46709) lies on these lines: {2, 6151}, {14, 532}, {115, 40900}, {146, 148}, {194, 617}, {298, 5025}, {302, 22893}, {315, 40898}, {396, 30472}, {627, 22510}, {3412, 44029}, {5613, 13571}, {6299, 22495}, {6775, 40899}, {7785, 22797}, {14144, 16529}, {20088, 41746}, {33255, 37640}

X(46709) = anticomplement of X(11128)
X(46709) = anticomplement of isotomic conjugate of X(11085)
X(46709) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {11085, 6327}, {36840, 17217}
X(46709) = X(11085)-Ceva conjugate of X(2)
X(46709) = {X(3181),X(11122)}-harmonic conjugate of X(14)

X(46710) = X(17)X(623)∩X(148)X(16001)

X(46710) lies on these lines: {17, 623}, {148, 16001}, {182, 193}, {194, 617}, {299, 7939}, {315, 40901}, {2996, 21845}, {3181, 16241}, {7764, 40900}, {7826, 40899}

X(46711) = X(18)X(624)∩X(148)X(16002)

X(46711) lies on these lines: {18, 624}, {148, 16002}, {182, 193}, {194, 616}, {298, 7939}, {315, 40900}, {2996, 21846}, {3180, 16242}, {7764, 40901}, {7826, 40898}

X(46712) = X(2207)-CEVA CONJUGATE OF X(2)

X(46712) lies on these lines: {2, 40831}, {6, 194}, {19, 21216}, {69, 3981}, {148, 36851}, {193, 1843}, {385, 37491}, {393, 6339}, {3618, 4074}, {7766, 36432}, {7793, 37485}, {30676, 30688}

X(46712) = anticomplement of isogonal conjugate of X(36417)
X(46712) = anticomplement of isotomic conjugate of X(2207)
X(46712) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {107, 21305}, {158, 33796}, {393, 21275}, {560, 6527}, {1096, 315}, {1924, 34186}, {1973, 1370}, {1974, 4329}, {2203, 18659}, {2207, 6327}, {5317, 17138}, {6059, 21286}, {7337, 21285}, {24000, 670}, {24019, 44445}, {32713, 17217}, {36417, 8}, {41937, 21295}, {44162, 6360}
X(46712) = X(2207)-Ceva conjugate of X(2)

X(46713) = X(36421)-CEVA CONJUGATE OF X(2)

X(46713) lies on these lines: {29, 3868}, {63, 26647}, {193, 20008}, {1993, 3177}, {3732, 5889}, {6225, 20061}, {6515, 30694}, {17147, 40571}, {31294, 39351}

X(46713) = anticomplement of isotomic conjugate of X(36421)
X(46713) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2204, 3152}, {2299, 2897}, {2326, 1370}, {24022, 18026}, {36420, 36845}, {36421, 6327}
X(46713) = X(36421)-Ceva conjugate of X(2)

X(46714) = X(1500)-CEVA CONJUGATE OF X(2)

X(46714) lies on these lines: {2, 34022}, {37, 1655}, {192, 25054}, {194, 966}, {1654, 4651}, {2663, 17499}, {17300, 21220}, {21226, 24437}, {24478, 24505}

X(46714) = anticomplement of isogonal conjugate of X(7109)
X(46714) = anticomplement of isotomic conjugate of X(1500)
X(46714) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {31, 17143}, {32, 17140}, {37, 17138}, {41, 35614}, {42, 17137}, {181, 21285}, {213, 17135}, {228, 18659}, {560, 4360}, {594, 21275}, {692, 17159}, {756, 315}, {765, 670}, {872, 69}, {1018, 44445}, {1089, 33796}, {1110, 4576}, {1402, 20244}, {1500, 6327}, {1918, 75}, {1924, 17154}, {2171, 21280}, {2175, 21273}, {2200, 20243}, {2205, 1}, {2209, 34086}, {2333, 20242}, {3952, 21305}, {4079, 21293}, {4557, 17217}, {7064, 21286}, {7109, 8}, {9447, 2975}, {9448, 18662}, {18267, 18827}, {23990, 21295}, {32739, 17166}, {40521, 21304}, {40729, 17153}
X(46714) = X(1500)-Ceva conjugate of X(2)

X(46715) = X(8041)-CEVA CONJUGATE OF X(2)

X(46715) lies on these lines: {2, 689}, {38, 21217}, {1369, 7779}, {2896, 3118}, {3410, 39346}, {7791, 40382}, {33021, 39953}

X(46715) = anticomplement of isotomic conjugate of X(8041)
X(46715) = anticomplementary isogonal conjugate of X(33769)
X(46715) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 33769}, {31, 33798}, {39, 21278}, {560, 7760}, {1923, 6}, {1964, 76}, {2084, 25051}, {2531, 21221}, {3051, 17165}, {4020, 12220}, {7794, 21275}, {8041, 6327}, {9247, 19121}, {23995, 4577}, {41267, 3770}, {41331, 17489}
X(46715) = X(8041)-Ceva conjugate of X(2)

X(46716) = X(1407)-CEVA CONJUGATE OF X(2)

X(46716) lies on these lines: {2, 32017}, {57, 1999}, {192, 5256}, {194, 712}, {4320, 17480}, {9263, 9965}, {17143, 24621}, {17490, 27002}, {19825, 27318}, {29529, 37652}

X(46716) = anticomplement of isotomic conjugate of X(1407)
X(46716) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {56, 21286}, {269, 315}, {279, 21275}, {560, 30695}, {604, 3436}, {738, 21280}, {934, 21304}, {1042, 21287}, {1088, 33796}, {1106, 69}, {1397, 329}, {1398, 21270}, {1407, 6327}, {1408, 20245}, {1435, 11442}, {1461, 21301}, {2206, 18750}, {4616, 21305}, {4637, 44445}, {7023, 21285}, {7099, 1370}, {7250, 21294}, {7342, 21273}, {7366, 3434}, {16947, 3869}, {23979, 3952}, {24027, 668}, {41280, 3177}
X(46716) = X(1407)-Ceva conjugate of X(2)
X(46716) = {X(3210),X(39694)}-harmonic conjugate of X(57)

X(46717) = X(394)-CEVA CONJUGATE OF X(2)

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

X(46717) lies on the Steiner/Wallace right hyperbola (Kiepert circumhyperbola of anticomplementary triangle) and these lines: {1, 10538}, {2, 216}, {4, 13409}, {20, 2979}, {22, 6194}, {63, 1943}, {69, 8612}, {147, 1370}, {148, 6504}, {194, 401}, {253, 41914}, {394, 8613}, {426, 41204}, {627, 19772}, {628, 19773}, {631, 32078}, {852, 3168}, {1075, 41481}, {1764, 7560}, {3552, 46625}, {3917, 42329}, {5905, 44354}, {6503, 40888}, {7396, 9742}, {7493, 7616}, {8782, 40870}, {12012, 40329}, {14361, 41678}, {14461, 41588}, {14570, 37669}, {14919, 35061}, {38283, 42453}, {39352, 45794}

X(46717) = reflection of X(2052) in X(6509)
X(46717) = isotomic conjugate of X(34287)
X(46717) = anticomplement of X(2052)
X(46717) = anticomplement of isogonal conjugate of X(577)
X(46717) = anticomplement of isotomic conjugate of X(394)
X(46717) = isotomic conjugate of isogonal conjugate of X(41373)
X(46717) = isotomic conjugate of polar conjugate of X(1075)
X(46717) = anticomplementary isogonal conjugate of X(317)
X(46717) = X(38257)-complementary conjugate of X(20305)
X(46717) = X(i)-Ceva conjugate of X(j) for these (i,j): {394, 2}, {20477, 20}
X(46717) = X(41373)-cross conjugate of X(1075)
X(46717) = X(i)-isoconjugate of X(j) for these (i,j): {19, 13855}, {31, 34287}
X(46717) = crossdifference of every pair of points on line {30442, 39201}
X(46717) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 317}, {3, 21270}, {6, 5906}, {31, 6515}, {48, 4}, {63, 11442}, {163, 520}, {184, 5905}, {255, 69}, {326, 315}, {394, 6327}, {520, 21294}, {560, 6392}, {563, 6193}, {577, 8}, {822, 3448}, {906, 20293}, {1092, 4329}, {1259, 21286}, {1437, 17220}, {1790, 20242}, {1804, 21285}, {1820, 68}, {2148, 5889}, {2169, 264}, {2289, 3436}, {3682, 21287}, {3926, 21275}, {3990, 1330}, {4055, 2895}, {4091, 21293}, {4100, 20}, {4558, 21300}, {4575, 850}, {6056, 329}, {6507, 1370}, {7125, 3434}, {7183, 21280}, {7335, 7}, {9247, 193}, {14575, 21216}, {14585, 192}, {18604, 17135}, {19210, 21271}, {19614, 32001}, {22341, 2893}, {23224, 150}, {23606, 6360}, {23995, 648}, {24000, 6528}, {24027, 18026}, {28724, 21278}, {32656, 4391}, {32660, 521}, {32661, 7253}, {35200, 340}, {36054, 33650}, {36059, 46400}, {36060, 41724}, {39201, 21221}
X(46717) = barycentric product X(i)*X(j) for these {i,j}: {69, 1075}, {76, 41373}, {95, 41481}
X(46717) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 34287}, {3, 13855}, {1075, 4}, {41373, 6}, {41481, 5}
X(46717) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 40896, 324}, {2, 43988, 3164}, {394, 20477, 8613}, {2052, 6509, 2}, {6360, 7361, 63}, {6389, 11547, 2}, {15466, 44436, 2}

X(46718) = X(2)X(18023)∩X(67)X(14712)

X(46718) lies on these lines: {2, 18023}, {67, 14712}, {895, 39356}, {1632, 39346}, {2453, 32528}, {7836, 45809}, {11061, 40871}

X(46719) = X(2)X(4403)∩X(80)X(20072)

X(46719) lies on these lines: {2, 4403}, {80, 20072}, {148, 3732}, {194, 30694}, {1320, 39349}, {6224, 40860}, {14206, 19570}, {17279, 18159}, {20085, 39364}

X(46720) = X(593)-CEVA CONJUGATE OF X(2)

X(46720) lies on these lines: {2, 1240}, {75, 18601}, {81, 4360}, {192, 19717}, {239, 33792}, {3210, 23958}, {3264, 26747}, {3995, 41242}, {8267, 17486}, {9263, 20086}, {10330, 33767}, {14829, 17495}, {16049, 20222}, {17143, 18171}, {17160, 29766}, {18654, 18662}, {31036, 32026}

X(46720) = anticomplement of X(28654)
X(46720) = anticomplement of isotomic conjugate of X(593)
X(46720) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {58, 21287}, {60, 21286}, {593, 6327}, {757, 315}, {763, 17138}, {849, 69}, {873, 33796}, {1101, 668}, {1333, 1330}, {1408, 2893}, {1509, 21275}, {2150, 3436}, {2206, 2895}, {3733, 21294}, {4556, 21301}, {7341, 21285}, {7342, 7}, {16947, 2475}, {23357, 3952}, {23995, 190}, {36420, 5906}
X(46720) = X(593)-Ceva conjugate of X(2)
X(46720) = {X(17147),X(35058)}-harmonic conjugate of X(81)

X(46721) = X(6)X(6664)∩X(69)X(20859)

X(46721) lies on these lines: {6, 6664}, {69, 20859}, {82, 17489}, {193, 2854}, {194, 3618}, {1974, 41676}, {8264, 14570}, {27375, 32451}, {43996, 46288}

X(46721) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {46288, 21289}, {46289, 1369}
X(46721) = crosssum of X(3005) and X(38996)
X(46721) = {X(6),X(6664)}-harmonic conjugate of X(33798)

X(46722) = X(2226)-CEVA CONJUGATE OF X(2)

X(46722) lies on these lines: {2, 646}, {88, 17160}, {190, 17147}, {194, 21224}, {519, 46150}, {668, 26844}, {1797, 2403}, {3210, 23958}, {4576, 33296}, {9263, 20092}, {14570, 41629}, {16726, 42051}

X(46722) = anticomplement of X(36791)
X(46722) = anticomplement of isogonal conjugate of X(41935)
X(46722) = anticomplement of isotomic conjugate of X(2226)
X(46722) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {679, 315}, {1318, 21286}, {2226, 6327}, {4618, 21304}, {4638, 21301}, {9456, 21290}, {41935, 8}
X(46722) = X(2226)-Ceva conjugate of X(2)
X(46722) = crossdifference of every pair of points on line {8660, 23644}
X(46722) = {X(17495),X(39698)}-harmonic conjugate of X(88)

X(46723) = X(2)X(2986)∩X(94)X(11071)

X(46723) lies on these lines: {2, 2986}, {94, 11071}, {648, 14129}, {2407, 30529}, {18122, 40604}, {18300, 36853}, {32027, 41254}

X(46723) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2166, 1272}, {14595, 6360}, {14859, 21271}, {23588, 6758}
X(46723) = {X(13582),X(37779)}-harmonic conjugate of X(94)

X(46724) = ANTICOMPLEMENT OF X(36412)

X(46724) lies on these lines: {2, 10979}, {3, 95}, {6, 35941}, {20, 317}, {30, 32002}, {69, 74}, {76, 10323}, {97, 43988}, {141, 35937}, {160, 1632}, {183, 16276}, {186, 44131}, {206, 35278}, {216, 401}, {286, 6906}, {290, 8266}, {297, 34828}, {305, 15574}, {311, 1078}, {315, 40697}, {316, 39113}, {325, 7667}, {340, 550}, {418, 16089}, {458, 36751}, {548, 41008}, {577, 648}, {1232, 18354}, {1238, 7768}, {1609, 40814}, {1799, 20564}, {1843, 11676}, {1975, 37198}, {3148, 32085}, {3260, 44180}, {3522, 6527}, {3525, 8797}, {3528, 32000}, {3589, 40884}, {3964, 44133}, {4226, 19121}, {6394, 46546}, {6636, 30737}, {7488, 44138}, {7771, 44837}, {7782, 9723}, {7802, 44128}, {8553, 41760}, {8719, 9924}, {9308, 36748}, {9737, 44443}, {9822, 35919}, {11057, 38434}, {11257, 40947}, {15696, 40995}, {17538, 32001}, {17907, 37188}, {19126, 35926}, {30716, 37918}, {37688, 44210}, {37765, 42459}, {39352, 40897}, {39646, 44200}, {40896, 43980}, {40996, 44245}, {43459, 44135}

X(46724) = reflection of X(32002) in X(45198)
X(46724) = isotomic conjugate of X(6662)
X(46724) = isotomic conjugate of anticomplement of X(6663)
X(46724) = isotomic conjugate of isogonal conjugate of X(1614)
X(46724) = isogonal conjugate of perspector of Steiner circumellipse of orthic triangle
X(46724) = anticomplement of X(36412)
X(46724) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2148, 17035}, {2167, 2888}, {46089, 6360}
X(46724) = X(6663)-cross conjugate of X(2)
X(46724) = X(31)-isoconjugate of X(6662)
X(46724) = cevapoint of X(3) and X(43988)
X(46724) = crosssum of X(15451) and X(34980)
X(46724) = crossdifference of every pair of points on line {14398, 42293}
X(46724) = barycentric product X(76)*X(1614)
X(46724) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 6662}, {1614, 6}, {6663, 36412}, {46093, 35071}
X(46724) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 264, 95}, {3, 20477, 264}, {20, 40680, 317}, {216, 401, 36794}, {577, 3164, 648}, {7782, 14615, 9723}

X(46725) = X(1252)-CEVA CONJUGATE OF X(2)

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

X(46725) lies on these lines: {2, 4554}, {100, 17494}, {194, 21224}, {514, 46148}, {693, 27134}, {1331, 2398}, {1621, 40637}, {2481, 26846}, {4576, 33946}, {4586, 10330}, {4762, 35310}, {5701, 27190}, {6758, 31296}, {8267, 17486}, {14570, 43191}, {17147, 32029}, {20095, 39350}, {20974, 25049}, {26795, 26824}, {26985, 28743}, {44312, 46125}

X(46725) = reflection of X(i) in X(j) for these {i,j}: {23989, 23988}, {25049, 20974}
X(46725) = isotomic conjugate of trilinear pole of line X(116)X(926) (the tangent to the nine-point circle at X(116))
X(46725) = anticomplement of X(23989)
X(46725) = anticomplement of isogonal conjugate of X(23990)
X(46725) = anticomplement of isotomic conjugate of X(1252)
X(46725) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {59, 21285}, {101, 21293}, {692, 150}, {765, 315}, {1016, 21275}, {1101, 17143}, {1110, 69}, {1252, 6327}, {2149, 3434}, {4557, 21294}, {4564, 21280}, {4567, 17138}, {4570, 17137}, {6065, 21286}, {6066, 329}, {7035, 33796}, {9447, 17036}, {23357, 17140}, {23979, 36845}, {23990, 8}, {23995, 4360}, {24027, 6604}, {32739, 149}
X(46725) = X(1252)-Ceva conjugate of X(2)
X(46725) = X(513)-isoconjugate of X(2141)
X(46725) = cevapoint of X(17494) and X(40637)
X(46725) = crosspoint of X(190) and X(31624)
X(46725) = crossdifference of every pair of points on line {8638, 20974}
X(46725) = barycentric product X(i)*X(j) for these {i,j}: {190, 2140}, {765, 19594}
X(46725) = barycentric quotient X(i)/X(j) for these {i,j}: {101, 2141}, {2140, 514}, {19594, 1111}
X(46725) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5701, 40619, 27190}, {23988, 23989, 2}

X(46726) = X(23357)-CEVA CONJUGATE OF X(2)

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

X(46726) lies on these lines: {2, 6331}, {110, 9514}, {194, 11004}, {850, 45215}, {3164, 7492}, {4226, 35311}, {5012, 40642}, {5661, 36901}, {8267, 36849}, {10330, 14570}, {14683, 39355}, {23878, 35319}

X(46726) = reflection of X(23962) in X(23584)
X(46726) = isogonal conjugate of X(36198)
X(46726) = anticomplement of X(23962)
X(46726) = anticomplement of isogonal conjugate of X(23963)
X(46726) = anticomplement of isotomic conjugate of X(23357)
X(46726) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {249, 21275}, {1101, 315}, {1576, 21294}, {14574, 21221}, {23357, 6327}, {23963, 8}, {23995, 69}, {24037, 33797}, {24041, 33796}, {41937, 5906}
X(46726) = X(23357)-Ceva conjugate of X(2)
X(46726) = cevapoint of X(31296) and X(40642)
X(46726) = trilinear product X(662)*X(34845)
X(46726) = trilinear quotient X(34845)/X(661)
X(46726) = barycentric product X(i)*X(j) for these {i,j}: {99, 34845}, {249, 36199}
X(46726) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 36198}, {34845, 523}, {36199, 338}
X(46726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11794, 31296, 110}, {23584, 23962, 2}

X(46727) = X(2)X(9833)∩X(262)X(6146)

X(46727) lies on the Kiepert circumhyperbola and these lines: {2, 9833}, {262, 6146}, {1503, 13599}, {2052, 6756}, {3517, 16080}, {7566, 40393}, {10982, 14492}, {13380, 16655}, {18396, 45300}, {31363, 34781}

X(46728) = X(3)X(6)∩X(20)X(2888)

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 - 4*a^4*b^2*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 + 5*a^2*c^6 + 2*b^2*c^6 - 2*c^8) : :
Barycentrics Sin[A]^2*(Cot[A] + 1 / (Csc[A]*Csc[B]*Csc[C] - 3*Cot[w])) : :

X(46728) = 3 X[3] - X[36747], 5 X[3] - 3 X[37506], X[4] - 3 X[43653], 3 X[376] - X[19467], 3 X[578] - 2 X[36747], X[578] + 2 X[37486], 5 X[578] - 6 X[37506], 3 X[3796] - X[12160], 3 X[8703] - X[43595], 3 X[19126] - 2 X[44480], X[36747] + 3 X[37486], 5 X[36747] - 9 X[37506], 5 X[37486] + 3 X[37506]

X(46728) lies on these lines: {3, 6}, {4, 33522}, {20, 2888}, {22, 5562}, {23, 11444}, {24, 3917}, {25, 11793}, {26, 1216}, {51, 7509}, {68, 44829}, {69, 9833}, {74, 17538}, {110, 38435}, {141, 6756}, {156, 7555}, {184, 7512}, {185, 10323}, {186, 43652}, {343, 18381}, {376, 1204}, {394, 9715}, {524, 31804}, {546, 33533}, {548, 43588}, {550, 7689}, {599, 34726}, {1092, 2979}, {1147, 5944}, {1154, 7525}, {1209, 31723}, {1297, 6570}, {1352, 13419}, {1370, 20299}, {1595, 29181}, {1614, 35268}, {1658, 10627}, {2777, 37201}, {2937, 10539}, {3060, 37126}, {3088, 46026}, {3089, 11821}, {3090, 34417}, {3091, 15107}, {3292, 9707}, {3517, 17811}, {3518, 5651}, {3546, 44673}, {3547, 18388}, {3567, 43650}, {3574, 7558}, {3627, 4550}, {3796, 12160}, {3818, 7553}, {3819, 6642}, {5059, 15062}, {5067, 38848}, {5446, 7514}, {5447, 6644}, {5449, 14791}, {5462, 7516}, {5889, 6636}, {5891, 7517}, {5907, 7387}, {5921, 41464}, {5943, 7393}, {6000, 11414}, {6247, 44683}, {6800, 43844}, {7395, 10110}, {7404, 31670}, {7484, 11695}, {7487, 10519}, {7496, 15028}, {7499, 45089}, {7503, 45186}, {7528, 24206}, {7540, 11178}, {7550, 9781}, {7592, 14531}, {7998, 44802}, {8542, 12061}, {8567, 17822}, {8703, 43595}, {8717, 13491}, {9545, 23061}, {9818, 13598}, {9909, 17814}, {9927, 34115}, {10170, 13861}, {10274, 41590}, {10299, 43597}, {10303, 41462}, {10304, 43601}, {10605, 37198}, {11003, 15801}, {11204, 11413}, {11381, 12082}, {11411, 46264}, {11424, 35921}, {11439, 37945}, {11456, 45187}, {11459, 12088}, {11591, 17714}, {12083, 12162}, {12087, 15305}, {12103, 32138}, {12106, 32142}, {12111, 41466}, {12134, 16789}, {12163, 35243}, {12225, 34786}, {12233, 16197}, {12307, 34783}, {12362, 18390}, {13289, 41673}, {13322, 34850}, {13367, 44837}, {13474, 39568}, {13564, 18436}, {14641, 33532}, {14786, 19130}, {14790, 21243}, {15004, 43651}, {15024, 22112}, {15043, 15246}, {15053, 15717}, {15058, 37925}, {15067, 37440}, {15072, 16661}, {15682, 43613}, {16266, 18475}, {16618, 22660}, {18534, 44870}, {18535, 33537}, {18570, 32196}, {18912, 41586}, {18914, 44882}, {20427, 35513}, {20806, 23042}, {21230, 34514}, {21735, 34564}, {22549, 33542}, {23325, 37444}, {23335, 44201}, {32767, 37638}, {34779, 41716}, {34785, 44239}, {34788, 41614}, {35228, 41589}, {35240, 35481}, {35475, 43576}, {43598, 44082}

X(46728) = midpoint of X(i) and X(j) for these {i,j}: {3, 37486}, {1350, 37485}
X(46728) = reflection of X(i) in X(j) for these {i,j}: {576, 44491}, {578, 3}, {12233, 16197}
X(46728) = isogonal conjugate of X(46727)
X(46728) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 52, 182}, {3, 389, 37515}, {3, 568, 13336}, {3, 1350, 15644}, {3, 1351, 37476}, {3, 6243, 569}, {3, 9730, 13347}, {3, 9786, 16836}, {3, 10625, 13346}, {3, 11432, 5085}, {3, 13336, 17508}, {3, 15644, 37480}, {3, 17834, 389}, {3, 33878, 37498}, {3, 36749, 37513}, {3, 36752, 5092}, {3, 37484, 13352}, {3, 37489, 9729}, {3, 37494, 52}, {3, 37495, 39242}, {3, 37498, 11430}, {22, 5562, 6759}, {26, 1216, 9306}, {394, 9715, 10282}, {569, 6243, 576}, {1092, 7488, 11202}, {1351, 37476, 37505}, {1352, 31305, 13419}, {2937, 23039, 10539}, {2979, 7488, 1092}, {3098, 37478, 11438}, {3518, 7999, 5651}, {5092, 16625, 36752}, {5889, 6636, 10984}, {6101, 7502, 1147}, {7395, 33586, 10110}, {7512, 11412, 184}, {9729, 14810, 3}, {9786, 31884, 3}, {10282, 15606, 394}, {11459, 12088, 26883}, {11591, 17714, 46261}, {14531, 22352, 7592}

X(46729) = X(2)X(11449)∩X(275)X(7507)

X(46729) lies on the Kiepert circumhyperbola and these lines: {2, 11449}, {76, 12362}, {262, 12241}, {275, 7507}, {671, 34725}, {1503, 13380}, {2052, 3575}, {3515, 16080}, {5392, 12225}, {6146, 13599}, {6776, 31363}, {9825, 37874}, {18396, 40448}, {38444, 42410}

X(46729) = isogonal conjugate of X(46730)
X(46729) = X(41362)-cross conjugate of X(4)

X(46730) = X(3)X(6)∩X(22)X(185)

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 - a^2*b^4*c^2 + 2*b^6*c^2 - 3*a^4*c^4 - a^2*b^2*c^4 + 5*a^2*c^6 + 2*b^2*c^6 - 2*c^8) : :
Barycentrics Sin[A]^2*(Cot[A] + 1 / (2*Csc[A]*Csc[B]*Csc[C] - 3*Cot[w])) : :

X(46730) = 5 X[3] - 3 X[37497], 3 X[3] - X[37498], 3 X[26] - X[32139], 3 X[154] - X[12164], 3 X[154] - 5 X[16195], X[155] - 3 X[14070], 3 X[182] - 2 X[44469], 2 X[1147] - 3 X[11202], 3 X[1147] - 4 X[32171], X[1498] - 3 X[9909], 4 X[1658] - 3 X[11202], 3 X[1658] - 2 X[32171], 3 X[3167] - 5 X[17821], 3 X[3357] - 4 X[32138], 2 X[5448] - 3 X[10201], 4 X[5449] - 3 X[23325], 3 X[6759] - 2 X[32139], 3 X[7689] - 2 X[32138], 2 X[9820] - 3 X[34351], 3 X[10154] - 2 X[16252], 3 X[10192] - 4 X[44277], 7 X[10244] - 3 X[32063], 9 X[10245] - 5 X[14530], 2 X[10282] - 3 X[14070], 9 X[11202] - 8 X[32171], 3 X[11204] - 2 X[12084], 2 X[12038] - 3 X[18324], 4 X[12107] - X[15083], X[12164] - 5 X[16195], X[12250] + 3 X[34621], X[12324] + 3 X[34608], X[13346] + 2 X[17834], 5 X[13346] - 6 X[37497], 3 X[13346] - 2 X[37498], 3 X[14852] - 2 X[18383], X[16266] - 3 X[18324], 5 X[17834] + 3 X[37497], 3 X[17834] + X[37498], 3 X[18281] - 4 X[20191], 2 X[18569] - 3 X[23325], 2 X[19139] - 3 X[23042], 3 X[23329] - 2 X[23335], 3 X[23329] - 4 X[44158], 4 X[25563] - 3 X[44441], 3 X[34609] - 5 X[40686], 3 X[34726] + X[34780], 3 X[37488] - X[44492], 9 X[37497] - 5 X[37498]

X(46730) lies on these lines: {2, 3574}, {3, 6}, {4, 14860}, {5, 11745}, {20, 1204}, {22, 185}, {23, 12111}, {24, 5562}, {25, 5907}, {26, 6759}, {30, 3357}, {51, 7503}, {64, 39568}, {68, 18400}, {74, 3529}, {110, 14448}, {113, 41674}, {125, 37444}, {141, 9825}, {154, 12164}, {155, 10282}, {156, 12107}, {184, 5889}, {186, 1092}, {206, 41589}, {235, 32269}, {323, 11449}, {343, 3575}, {376, 18916}, {378, 45186}, {394, 3515}, {517, 8144}, {542, 9833}, {546, 4550}, {548, 45969}, {550, 12370}, {1147, 1154}, {1181, 9715}, {1216, 6644}, {1352, 7487}, {1370, 26937}, {1495, 11441}, {1498, 9909}, {1531, 35488}, {1568, 7505}, {1593, 13598}, {1598, 44870}, {1614, 7556}, {1974, 41716}, {1986, 22109}, {1993, 13367}, {2070, 10539}, {2904, 16879}, {2931, 10628}, {2937, 32608}, {2979, 22467}, {3060, 11424}, {3088, 31670}, {3091, 34417}, {3146, 11440}, {3147, 5972}, {3167, 17821}, {3517, 17814}, {3518, 11459}, {3522, 43601}, {3523, 15053}, {3524, 43597}, {3542, 32223}, {3543, 15062}, {3545, 38848}, {3548, 44673}, {3549, 18388}, {3564, 34776}, {3567, 35921}, {3580, 12225}, {3628, 33533}, {3818, 6756}, {3917, 17928}, {5059, 13445}, {5446, 7526}, {5448, 10201}, {5449, 18569}, {5462, 7514}, {5651, 11444}, {5663, 17714}, {5876, 37440}, {5890, 7512}, {5891, 7506}, {5892, 7516}, {5899, 18439}, {5943, 7395}, {5965, 6193}, {6000, 7387}, {6101, 37814}, {6102, 7502}, {6146, 44239}, {6241, 12088}, {6515, 10112}, {6636, 10574}, {6642, 11793}, {6676, 12233}, {6696, 23300}, {6815, 43653}, {6823, 13568}, {7393, 11695}, {7401, 24206}, {7404, 19130}, {7412, 10441}, {7464, 11468}, {7507, 37638}, {7517, 12162}, {7525, 13630}, {7550, 15024}, {7592, 14831}, {8263, 34507}, {8548, 34788}, {8681, 34787}, {9545, 15801}, {9707, 43844}, {9714, 18451}, {9781, 35500}, {9818, 10110}, {9820, 34351}, {10154, 16252}, {10192, 44277}, {10244, 32063}, {10245, 14530}, {10263, 18570}, {10298, 34148}, {10303, 43584}, {10311, 22416}, {10545, 15022}, {10575, 12083}, {10594, 15030}, {10605, 11414}, {10982, 21849}, {10996, 33522}, {11204, 12084}, {11250, 13391}, {11413, 21663}, {11442, 31304}, {11454, 12086}, {11457, 44831}, {11479, 17810}, {11591, 12106}, {11645, 34726}, {11750, 25738}, {11800, 19457}, {12038, 16266}, {12087, 12279}, {12160, 19357}, {12161, 18475}, {12241, 41588}, {12250, 34621}, {12290, 37925}, {12307, 23039}, {12310, 17835}, {12324, 34608}, {12362, 13567}, {12412, 15085}, {12429, 17845}, {12605, 18390}, {13148, 16165}, {13383, 22660}, {13399, 20062}, {13434, 15004}, {13474, 18534}, {13595, 15056}, {14216, 29012}, {14790, 20299}, {14852, 18383}, {15028, 22112}, {15043, 37126}, {15058, 34484}, {15578, 32184}, {15750, 35602}, {16163, 35503}, {16261, 26863}, {18281, 20191}, {18378, 18435}, {18418, 44960}, {18909, 46264}, {19139, 23042}, {19506, 46085}, {20417, 32273}, {21230, 38322}, {21844, 43574}, {23292, 31802}, {23294, 46450}, {23329, 23335}, {25563, 44441}, {26881, 43605}, {29317, 34938}, {30552, 37853}, {32140, 44407}, {32345, 34751}, {34609, 40686}, {34785, 44665}, {34799, 41482}, {34826, 44288}, {35268, 38435}, {38443, 43689}

X(46730) = midpoint of X(i) and X(j) for these {i,j}: {3, 17834}, {64, 39568}, {1350, 37491}, {7387, 12163}, {9833, 11411}, {12310, 17835}, {12412, 15085}, {12429, 17845}, {14216, 31305}
X(46730) = reflection of X(i) in X(j) for these {i,j}: {113, 41674}, {155, 10282}, {156, 12107}, {576, 44470}, {1147, 1658}, {3357, 7689}, {6759, 26}, {13346, 3}, {14790, 20299}, {15083, 156}, {16266, 12038}, {18381, 12359}, {18569, 5449}, {19506, 46085}, {22660, 13383}, {23335, 44158}, {34786, 9927}, {34788, 8548}
X(46730) = isogonal conjugate of X(46729)
X(46730) = X(20)-of-Kosnita-triangle
X(46730) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 52, 578}, {3, 389, 182}, {3, 568, 569}, {3, 1350, 13348}, {3, 1351, 11425}, {3, 6243, 13352}, {3, 9729, 13347}, {3, 9730, 37515}, {3, 9786, 9729}, {3, 10625, 37480}, {3, 11432, 37476}, {3, 14627, 14805}, {3, 36747, 11430}, {3, 36753, 37513}, {3, 37472, 39242}, {3, 37475, 17704}, {3, 37481, 13336}, {3, 37486, 15644}, {3, 37489, 389}, {3, 37490, 9730}, {3, 37493, 37506}, {3, 37494, 10625}, {3, 37514, 5092}, {3, 37515, 17508}, {20, 1899, 44829}, {23, 12111, 26883}, {24, 5562, 9306}, {52, 578, 576}, {155, 14070, 10282}, {186, 11412, 1092}, {1147, 1658, 11202}, {1192, 1350, 3}, {1495, 45187, 11441}, {1593, 33586, 13598}, {1993, 38444, 13367}, {2070, 18436, 10539}, {2937, 32608, 34783}, {2979, 22467, 43652}, {3060, 14118, 11424}, {3581, 37478, 11438}, {5092, 15012, 37514}, {5449, 18569, 23325}, {5876, 37440, 46261}, {5889, 7488, 184}, {5890, 7512, 10984}, {6515, 19467, 10112}, {10625, 32110, 3}, {11432, 37476, 575}, {11438, 37478, 3098}, {11440, 15107, 3146}, {11444, 44802, 5651}, {12160, 19357, 34986}, {12164, 16195, 154}, {12307, 45735, 23039}, {12605, 41587, 18390}, {13367, 14531, 1993}, {14810, 17704, 3}, {15043, 37126, 43650}, {16266, 18324, 12038}, {23335, 44158, 23329}, {32110, 37494, 37480}, {36752, 37498, 44469}, {37493, 37505, 15520}, {37493, 37506, 37505}, {41482, 41724, 34799}

X(46731) = (name pending)

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 4016.

X(46732) = X(4)X(575)∩X(20)X(13378)

See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 4016.

X(46733) = X(4)X(50)∩X(32)X(3567)

X(46734) = X(2)X(9872)∩X(111)X(5476)

X(46735) = X(3)X(3186)∩X(194)X(394)

X(46735) lies on these lines: {3, 3186}, {194, 394}, {1073, 41235}, {3682, 21080}, {3926, 6374}, {3998, 22028}

X(46735) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3)}} and {{A, B, C, X(6), X(40830)}}
X(46735) = trilinear pole of the line {520, 23301}

X(46736) = PERSPECTOR OF THE TAYLOR CIRCLE

X(46736) = isogonal conjugate of X(46760)
X(46736) = perspector of the Taylor circle
X(46736) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(389)}} and {{A, B, C, X(6), X(51)}}

X(46737) = MIDPOINT OF X(3162) AND X(15255)

This preamble is contributed by Clark Kimberling and Peter Moses, January 24, 2022.

In the plane of a triangle ABC, let L, given by l x + m y + n z = 0, be a line, and let P = p : q : r be a point not on L and not on a sideline BC, CA, AB. Let

Ap = L∩AP, Bp = L∩BP, Cp = L∩CP.

Let A'B'C' be the cevian triangle of a point X = x : y : z, so that

A' = 0 : y : z , B' = x : 0 : z, C' = x : y : 0.

The locus of X such that A'B'C' is perspective to the (degenerate) triangle ApBpCp is the cubic pK(m^2 n^2, m^2 n^2 q r), given by

p (m^2 q y^2 z - n^2 r y z^2) + (cyclic) = 0.

The appearance of {{i,j}, {{Knnn}, {h₁, h₂, ...}}} in the following list means that if l : m : n = X(i) and P = X(j), then the cubic is Knnn in Bernard Gibert's catalogue (CTC), and that the cubic passes through the points X(h₁), X(h₂), . . .

{{1,1},{{},{1,75,92,304,561,1760,46244}}}
{{1,2},{{K184},{2,69,75,76,85,264,312,15466,34403,34404,40702}}}
{{1,4},{{},{2,4,75,76,253,305,341,1088,1370,14615,20914,40009,40015,46738,46739,46740,46741}}}
{{1,10},{{},{2,10,75,76,310,4043,17135,40004,40005}}}
{{1,20},{{},{20,75,253,14615,15466,34403,41530}}}
{{1,63},{{},{63,75,92,304,1969,20571,44179}}}
{{1,69},{{},{69,75,264,491,492,20570,20930,24243,24244,34391,34392,40697,46742,46743,46744,46745,46746}}}
{{1,76},{{},{2,75,76,2998,6374,6376,6384}}}
{{1,83},{{},{2,75,76,83,1031,1369,8024,20933,33938,40035,40036,40037,40038,46747,46748}}}
{{1,92},{{},{75,85,92,304,309,312,322,18750}}}
{{1,94},{{},{2,75,76,94,1272,7799,40705}}}
{{1,95},{{},{69,75,95,264,302,303,311,19712,19713,34389,34390,45799,46749,46750,46751,46752,46753,46754,46755,46756,46757,46758,}}}
{1,523,{{},{75,141,308,523,670,4033,6189,6190,7199}}}
{{2,1},{{K034},{1,2,7,8,63,75,92,280,347,1895,19611}}}
{{2,3},{{K045},{2,3,4,69,254,264,1993,5392,40697,40698}}}
{{2,4},{{K007},{2,4,7,8,20,69,189,253,329,1032,1034,5932,14361,14362,14365,34162,39158,39159,39160,39161,41080,42427,42428}}}
{{2,6},{{K141},{2,4,6,22,69,76,1670,1671,18018,19613,41361}}}
{{2,7},{{K200},{2,7,8,144,175,176,1143,1274,10405,13386,13387,20534,31527,40699,40700}}}
{{2,8},{{K1078},{2,7,8,145,4373,7048,7057,8051,8055,24313,24314}}}
{{2,10},{{},{1,2,10,75,86,3995,18133,39747,39748}}}
{{2,19},{{K605},{1,2,19,75,279,304,346,2184,4329,7219,10327,18596,18750,39732,39733}}}
{{2,21},{{},{2,7,8,21,1441,2475,3219,30690,34772,41808}}}
{{2,37},{{},{1,2,37,75,274,4651,16552,39734,39735}}}
{{2,39},{{},{2,6,39,76,308,8266,30505}}}
{{2,40},{{K133},{2,40,77,189,280,309,318,329,347,962}}}
{{2,52},{{},{2,52,54,68,311,317,1993,5392,11412,34385}}}
{{2,54},{{},{2,4,54,69,311,1994,2888,3459,7488,11140,45799}}}
{{2,63},{{},{2,63,92,2994,5905,13386,13387,19217,19218}}}
{{2,64},{{K235},{2,4,64,69,394,2052,3346,6225,6527,11413,14615}}}
{{2,65},{{K254},{1,2,4,65,69,75,81,314,321,1764,2995,3869,16049,17751,20028}}}
{{2,66},{{},{2,4,66,69,315,1370,5596,13575}}}
{{2,67},{{K008},{2,4,67,69,316,524,671,858,2373,11061,13574,14360,14364,34163,34164,34165,34166,39157}}}
{{2,68},{{},{2,4,68,69,317,6193,6504,6515}}}
{{2,69},{{K170},{2,4,69,193,487,488,2996,13386,13387,13428,13439,19583,24243,24244}}}
{{2,70},{{},{2,4,69,70,13579,37444,44128,44177,45794}}}
{{2,71},{{},{2,4,69,71,4184,17220,17911,44129}}}
{{2,72},{{K610},{2,4,21,63,69,72,92,286,1441,2997,3868,40571,43675}}}
{{2,74},{{K279},{2,4,69,74,94,146,323,1138,1272,2071,3260}}}
{{2,75},{{},{1,2,75,192,330,3223,17149}}}
{{2,79},{{K455},{2,7,8,10,79,86,319,1029,2895,3648,17781}}}
{{2,80},{{K311},{2,7,8,80,320,369,519,903,908,3232,6224,8046,30578,34234,36917,36918}}}
{{2,81},{{},{2,81,321,1029,2895,13386,13387}}}
{{2,82},{{},{1,2,75,82,1930,17280,20934,21289,21378,33091,39724,39725,39726,39727,39728,46759}}}
{{2,84},{{K154},{2,7,8,78,84,273,322,6223,41514}}}
{{2,91},{{},{1,2,75,91,5552,7318,44179}}}
{{2,95},{{},{2,5,95,627,628,11143,11144,17035,19712,19713}}}
{{2,104},{{},{2,7,8,104,153,3262,4511,18815}}}
{{2,113},{{},{2,74,113,2986,3260,3580,5627,6148,15454,40423}}}
{2,523,{{K242},{2,99,523,1113,1114,3413,3414,6189,6190,22339,22340,30508,30509}}}
{{3,4},{{},{4,76,264,2052,16246,17907,18022,40009}}}
{{3,92},{{},{75,92,264,331,1969,7017,40701}}}
{{3,94},{{},{76,94,264,2052,40705,44138,46106}}}
{{3,98},{{},{76,98,264,305,1093,2052,6330,35142}}}
{{4,1},{{},{1,63,69,304,1265,7056,19611}}}
{{4,2},{{},{2,69,345,348,3926,6527,34403,37669}}}
{{4,3},{{},{2,3,69,305,1370,3926,20806}}}
{{4,39},{{},{3,39,69,305,1176,14376,34254}}}
{{4,63},{{},{63,69,75,304,326,345,348,18750,44189}}}
{{6,2},{{},{2,76,264,305,315,1502,40421}}}
{{6,75},{{},{75,76,304,561,1969,3596,6063}}}
{{7,9},{{},{2,8,9,78,312,318,329,346,46350}}}
{{7,33},{{},{7,8,9,33,312,3718,5423,27540,41791,44692}}}
{{7,37},{{},{8,9,21,37,281,312,345,3701}}}
{{8,1},{{},{1,2,7,279,1088,1445,36845}}}
{{8,2},{{},{2,7,279,4452,5435,18886,21456,27818}}}
{{8,34},{{},{7,8,34,57,85,479,7182,8809,28739,33673}}}
{{8,57},{{},{2,7,57,77,85,189,273,279,14256,44697,46352}}}
{{8,81},{{},{2,7,81,279,1029,1442,1446,18625}}}
{{8,88},{{},{2,7,88,279,1443,8046,18815,37789}}}
{{8,105},{{},{2,7,8,105,279,479,4318,7291,43736,43760}}}
{{9,7},{{},{7,75,85,309,331,348,1088,6063}}}
{{10,57},{{},{27,57,75,81,86,274,757,14829,17206}}}
{{10,63},{{},{27,63,85,86,286,1444,2185,17206}}}
{{10,81},{{},{81,86,274,286,333,1434,1444}}}
{{19,69},{{},{69,76,304,305,3718,3926,7182,14615}}}
{{27,72},{{},{72,306,307,321,3710,3998,20336}}}
{{31,76},{{},{76,305,561,1502,18022,20567,28659}}}
{{37,7},{{},{7,76,86,274,286,310,1509,18021}}}
{{37,69},{{},{69,261,274,286,6063,17206,44129}}}
{{42,85},{{},{85,274,310,561,873,6385,44129}}}
{{57,8},{{},{8,75,312,322,341,345,3596,7017}}}
{{57,10},{{},{8,10,312,318,333,3596,3718,30713}}}
{{63,4},{{K647},{2,4,92,253,264,273,318,342,2052,7020,14249,46353}}}
{{63,10},{{},{2,10,29,75,92,158,2052,5125}}}
{{63,76},{{},{2,76,92,393,2052,2998,6392}}}
{{65,2},{{},{2,261,314,333,3596,28660,31623}}}
{{69,1},{{},{1,4,158,920,1068,1123,1336,7040}}}
{{69,2},{{K1046},{2,4,393,1123,1336,3068,3069,6353,6392,13429,13440,34208}}}
{{69,6},{{K621},{2,4,6,24,393,847,2052,6515}}}
{{69,10},{{},{1,4,10,158,1714,8747,39748}}}
{{69,19},{{},{1,4,19,92,158,196,278,281,2184,7003}}}
{{69,24},{{},{4,24,847,7505,10880,10881,13429,13440}}}
{{69,25},{{},{2,4,25,264,393,8743,13575,41766,43678}}}
{{69,37},{{},{1,2,4,37,158,393,1172,1713,30733,40149}}}
{{69,54},{{},{4,54,3459,13429,13440,13450,46621,46622}}}
{{69,75},{{},{1,4,75,158,1096,3223,33781}}}
{{69,111},{{},{2,4,111,393,8744,13574,37777,37778,46105}}}
{{75,2},{{K102},{1,2,6,43,87,194,3224,15963,15964,15965,15966,15967,15968,39641,39642,40139}}}
{{75,3},{{K006},{1,3,4,46,90,155,254,371,372,485,486,487,488,6212,6213,8946,8947,8948,8949}}}
{{75,4},{{K003},{1,3,4,1075,1745,3362,13855,39641,39642,46357,46358}}}
{{75,6},{{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}}}
{{75,9},{{K1079},{1,9,57,173,258,1743,2136,2137,8056,8078,24242}}}
{{75,10},{{},{1,10,58,3216,39641,39642,39748}}}
{{75,16},{{},{1,14,16,17,61,7150,41225}}}
{{75,19},{{K343},{1,9,19,40,57,63,84,610,1712,2184}}}
{{75,25},{{K169},{1,2,6,20,25,64,69,159,200,269,1763,2138,2139,7097,13575,17742,40187,40188,40189,40190,40219,40220,40221,40222,40223,40224,40225,40226,40227}}}
{{75,31},{{K968},{1,19,31,63,75,2172,19616}}}
{{75,32},{{K1027},{1,32,76,1670,1671,1676,1677,1759,7096,18796,18797,18798,18799,19612}}}
{{75,37},{{},{1,2,6,37,81,3293,17147,39949,39964}}}
{{75,39},{{},{1,39,83,1342,1343,5403,5404,16549}}}
{{75,42},{{},{1,2,6,42,86,3294,8049,8053,39950}}}
{{75,48},{{},{1,19,47,48,63,91,92}}}
{{75,54},{{K005},{1,3,4,5,17,18,54,61,62,195,627,628,2120,2121,3336,3459,3460,3461,3462,3463,3467,3468,3469,3470,3471,3489,3490,6191,6192,7344,7345,8837,8839,8918,8919,8929,8930,38931,38932,38933,38934,38935,39261,39262,46035,46036,46037}}}
{{75,55},{{K1059},{1,7,9,55,57,218,277,3174}}}
{{75,56},{{K692},{1,8,40,56,84,2122,2123}}}
{{75,57},{{K351},{1,9,57,165,364,2124,2125,3062,6212,6213,7001,7010,15891,15892}}}
{{75,58},{{},{1,10,58,191,267,2126,2127,6212,6213}}}
{{75,61},{{},{1,17,61,3389,3390,3391,3392}}}
{{75,62},{{},{1,18,62,3364,3365,3366,3367}}}
{{75,63},{{K1039},{1,19,63,1707,2128,2129,3377,3378,6203,6204,6212,6213,7347,7348,8769,19213,19214,19215,19216,19217,19218}}}
{{75,64},{{K004},{1,3,4,20,40,64,84,1490,1498,2130,2131,3182,3183,3345,3346,3347,3348,3353,3354,3355,3472,3473,3637,40851,40852,40993,40994,42411,42412}}}
{{75,66},{{},{1,3,4,22,66,159,8270,13575}}}
{{75,67},{{},{1,3,4,23,67,2930,13574}}}
{{75,69},{{},{1,3,4,25,69,1716,3186,3504,7093,19588}}}
{{75,71},{{K109},{1,3,4,19,27,63,71,226,284,579,1751,1780,23604,41342,43729}}}
{{75,74},{{K001},{1,3,4,13,14,15,16,30,74,370,399,484,616,617,1138,1157,1263,1276,1277,1337,1338,2132,2133,3065,3440,3441,3464,3465,3466,3479,3480,3481,3482,3483,3484,5623,5624,5667,5668,5669,5670,5671,5672,5673,5674,5675,5676,5677,5678,5679,5680,5681,5682,5683,5684,5685,7059,7060,7164,7165,7325,7326,7327,7328,7329,8172,8173,8174,8175,8431,8432,8433,8434,8435,8436,8437,8438,8439,8440,8441,8442,8443,8444,8445,8446,8447,8448,8449,8450,8451,8452,8453,8454,8455,8456,8457,8458,8459,8460,8461,8462,8463,8464,8465,8466,8467,8468,8469,8470,8471,8472,8473,8474,8475,8476,8477,8478,8479,8480,8481,8482,8483,8484,8485,8486,8487,8488,8489,8490,8491,8492,8493,8494,8495,8496,8497,8498,8499,8500,8501,8502,8503,8504,8505,8506,8507,8508,8509,8510,8511,8512,8513,8514,8515,8516,8517,8518,8519,8520,8521,8522,8523,8524,8525,8526,8527,8528,8529,8530,8531,8532,8533,8534,8535,8536,16882,16883}}}
{{75,81},{{K1146},{1,37,81,846,2134,2135,13610,42677,42680}}}
{{75,84},{{K414},{1,40,84,164,505,2956,3645,6212,6213,32555,32556,34494,34495,46433,46434}}}
{{75,88},{{},{1,44,88,9324,9325,39150,39151}}}
{{75,99},{{K021},{1,99,512,2142,2143,5539,7315}}}
{{75,102},{{K269},{1,36,40,80,84,102,515,6326,8072,8073,10692,39146,39147}}}
{{75,103},{{},{1,103,516,6212,6213,32622,32623,39144,39145}}}
{{75,104},{{},{1,104,517,11752,11789,39150,39151}}}
{{75,111},{{K1156},{1,2,6,111,524,2930,5524,5525,7312,7313,8591,13574}}}
{{76,1},{{},{1,6,31,1740,2162,2176,34248}}}
{{76,3},{{K171},{3,6,25,3053,8770,8946,8948,10132,10133,15369,19588,20032,34121,34125,44192,44193}}}
{{76,21},{{},{6,21,55,56,172,893,1402}}}
{{76,24},{{},{6,24,2351,3155,3156,44192,44193}}}
{{76,25},{{K172},{3,6,25,55,56,64,154,198,1033,1035,1436,7037,28781,28782,28783,28784,28785,34167}}}
{{76,31},{{K175},{1,6,19,31,48,55,56,204,221,2192,19614}}}
{{76,32},{{K177},{2,3,6,25,32,66,206,1676,1677,3162,19615,41378,41379}}}
{{76,41},{{},{6,41,55,56,57,2191,21059}}}
{{76,48},{{},{6,19,48,2164,2178,19215,19216,34121,34125}}}
{{76,56},{{},{6,55,56,3207,11051,20673,30335,30336,34121,34125}}}
{{76,63},{{},{6,19,48,63,1973,2129,21775}}}
{{76,74},{{},{6,74,1495,3440,3441,9412,11081,11086}}}
{{76,98},{{},{3,6,25,98,237,694,1691,1971,1987,3511,46272}}}
{{76,103},{{},{6,103,1458,2195,3207,9500,11051,20672}}}
{{76,105},{{},{6,55,56,105,292,1914,2110,2223}}}
{{81,12},{{},{2,10,12,313,321,3436,3596,20336,22020,28654,41013}}}
{514,6,{{},{6,190,4360,14087,31625}}}
{514,7,{{},{7,190,344,4076,14087}}}
{523,1,{{},{1,99,1016,1509,4593,14089,24037}}}
{523,2,{{},{2,99,4590,6189,6190,14089,39298,39299}}}
{523,20,{{},{20,99,3926,14089,23582}}}

Each of these cubics is unicursal with node and singularity m n : n l : l m. As noted above, each cubic is of type pK(m^2 n^2, m^2 n^2 q r), which is equivalent to cK(# m n , m^2, n^2 q r). See Special Isocubics in the Triangle Plane). (Bernard Gibert, January 28, 2022)

X(46738) = ISOTOMIC CONJUGATE OF X(40188)

X(46738) lies on the cubic pK(76,305) and these lines: {2, 37}, {4, 341}, {82, 4676}, {85, 18040}, {92, 30713}, {190, 1760}, {304, 17233}, {322, 4033}, {1111, 18065}, {1861, 3710}, {1930, 17286}, {1978, 40364}, {2064, 14615}, {2298, 3758}, {2550, 3701}, {3596, 20927}, {3673, 18044}, {3717, 12618}, {3769, 33760}, {3994, 17872}, {4110, 17788}, {4150, 20914}, {4385, 5263}, {4494, 20236}, {5016, 44720}, {7283, 13730}, {10327, 11677}, {17315, 18156}, {17353, 33937}, {17381, 39731}, {17446, 32925}, {17786, 17789}, {18133, 33736}, {20179, 33938}, {20915, 20920}, {28739, 41786}, {28753, 30701}

X(46738) = isotomic conjugate of X(40188)
X(46738) = isotomic conjugate of the isogonal conjugate of X(17742)
X(46738) = X(i)-Ceva conjugate of X(j) for these (i,j): {305, 341}, {15742, 4033}
X(46738) = X(11677)-cross conjugate of X(75)
X(46738) = X(i)-isoconjugate of X(j) for these (i,j): {31, 40188}, {32, 39732}, {1397, 41791}, {1472, 40184}, {2206, 36907}
X(46738) = barycentric product X(i)*X(j) for these {i,j}: {75, 10327}, {76, 17742}, {305, 23050}, {312, 28739}, {561, 12329}, {1978, 2509}, {3596, 8270}, {4033, 17498}
X(46738) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 40188}, {75, 39732}, {312, 41791}, {321, 36907}, {1801, 1437}, {2345, 40184}, {2509, 649}, {8270, 56}, {10327, 1}, {11677, 614}, {12329, 31}, {15487, 16502}, {17498, 1019}, {17742, 6}, {20613, 608}, {23050, 25}, {28409, 7289}, {28739, 57}, {41786, 28017}
X(46738) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 17371, 19804}, {75, 18743, 16706}, {321, 2345, 75}, {322, 30693, 4033}, {4033, 20444, 322}, {17786, 17789, 20930}

X(46739) = ISOTOMIC CONJUGATE OF X(40222)

X(46739) lies on the cubic pK(76,305) and these lines: {2, 3933}, {69, 14259}, {907, 3926}, {8801, 44142}, {14615, 40009}, {40123, 40189}

X(46739) = isotomic conjugate of X(40222)
X(46739) = isotomic conjugate of the isogonal conjugate of X(40189)
X(46739) = X(31)-isoconjugate of X(40222)
X(46739) = barycentric product X(i)*X(j) for these {i,j}: {76, 40189}, {18840, 40123}
X(46739) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 40222}, {18840, 40178}, {37485, 30435}, {40123, 3618}, {40189, 6}

X(46740) = ISOTOMIC CONJUGATE OF X(17742)

X(46740) lies on the cubic pK(76,305) and these lines: {75, 1370}, {76, 5179}, {85, 16706}, {274, 40188}, {286, 16750}, {334, 20930}, {1760, 7182}, {17370, 40044}, {27826, 40014}, {39733, 40015}

X(46740) = isotomic conjugate of X(17742)
X(46740) = polar conjugate of X(23050)
X(46740) = isotomic conjugate of the isogonal conjugate of X(40188)
X(46740) = X(i)-cross conjugate of X(j) for these (i,j): {4, 1088}, {4000, 75}, {12610, 7}, {23537, 310}, {36907, 39732}
X(46740) = X(i)-isoconjugate of X(j) for these (i,j): {6, 12329}, {31, 17742}, {32, 10327}, {41, 8270}, {48, 23050}, {212, 20613}, {692, 2509}, {1801, 2333}, {2175, 28739}, {7084, 15487}
X(46740) = cevapoint of X(39732) and X(41791)
X(46740) = trilinear pole of line {693, 21174}
X(46740) = barycentric product X(i)*X(j) for these {i,j}: {75, 39732}, {76, 40188}, {85, 41791}, {274, 36907}
X(46740) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 12329}, {2, 17742}, {4, 23050}, {7, 8270}, {75, 10327}, {85, 28739}, {278, 20613}, {514, 2509}, {1444, 1801}, {3673, 11677}, {4000, 15487}, {7199, 17498}, {36907, 37}, {39732, 1}, {40188, 6}, {41791, 9}

X(46741) = ISOTOMIC CONJUGATE OF X(2139)

X(46741) lies on the cubic pK(76,305) and these lines: {2, 253}, {75, 17903}, {76, 17907}, {193, 15262}, {393, 41760}, {441, 1033}, {648, 28419}, {1075, 3541}, {1619, 15259}, {1853, 46700}, {3542, 41204}, {3618, 8743}, {5596, 32713}, {6225, 39268}, {6527, 41678}, {36794, 41370}, {41766, 45279}

X(46741) = isotomic conjugate of X(2139)
X(46741) = polar conjugate of X(42484)
X(46741) = isotomic conjugate of the isogonal conjugate of X(2138)
X(46741) = polar conjugate of the isogonal conjugate of X(1619)
X(46741) = X(305)-Ceva conjugate of X(4)
X(46741) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2139}, {48, 42484}, {19614, 40186}
X(46741) = cevapoint of X(1619) and X(2138)
X(46741) = barycentric product X(i)*X(j) for these {i,j}: {76, 2138}, {264, 1619}, {305, 15259}
X(46741) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2139}, {4, 42484}, {1249, 40186}, {1619, 3}, {2138, 6}, {15259, 25}
X(46741) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {459, 1249, 32000}, {6527, 42458, 41678}

X(46742) = ISOTOMIC CONJUGATE OF X(8948)

X(46742) lies on the cubic pK(76,264) and these lines: {69, 305}, {76, 485}, {264, 3127}, {1270, 3266}, {1271, 8024}, {3068, 8222}, {3595, 39998}, {11059, 32805}, {32806, 40022}, {44149, 45806}

X(46742) = isotomic conjugate of X(8948)
X(46742) = isotomic conjugate of the isogonal conjugate of X(488)
X(46742) = polar conjugate of the isogonal conjugate of X(8222)
X(46742) = X(45805)-Ceva conjugate of X(76)
X(46742) = X(i)-isoconjugate of X(j) for these (i,j): {19, 26454}, {31, 8948}, {32, 19218}, {493, 1973}, {560, 24244}
X(46742) = cevapoint of X(488) and X(8222)
X(46742) = barycentric product X(i)*X(j) for these {i,j}: {76, 488}, {264, 8222}, {305, 3068}, {561, 19215}, {670, 17431}, {1502, 10132}, {6423, 40050}, {24246, 45805}
X(46742) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8948}, {3, 26454}, {69, 493}, {75, 19218}, {76, 24244}, {305, 5490}, {487, 45596}, {488, 6}, {3068, 25}, {3933, 26347}, {4563, 1306}, {5200, 2207}, {5408, 8950}, {5590, 26373}, {6423, 1974}, {8222, 3}, {10132, 32}, {17431, 512}, {19215, 31}, {24246, 8577}, {26503, 8946}, {33364, 5411}, {39387, 5413}, {42022, 26461}
X(46742) = {X(69),X(305)}-harmonic conjugate of X(46743)

X(46743) = ISOTOMIC CONJUGATE OF X(8946)

X(46743) lies on the cubic pK(76,264) and these lines: {69, 305}, {76, 486}, {264, 3128}, {1270, 8024}, {1271, 3266}, {3069, 8223}, {3593, 39998}, {9464, 32814}, {11059, 32806}, {32805, 40022}, {44149, 45805}

X(46743) = isotomic conjugate of X(8946)
X(46743) = isotomic conjugate of the isogonal conjugate of X(487)
X(46743) = polar conjugate of the isogonal conjugate of X(8223)
X(46743) = X(45806)-Ceva conjugate of X(76)
X(46743) = X(i)-isoconjugate of X(j) for these (i,j): {19, 26461}, {31, 8946}, {32, 19217}, {494, 1973}, {560, 24243}
X(46743) = cevapoint of X(487) and X(8223)
X(46743) = barycentric product X(i)*X(j) for these {i,j}: {76, 487}, {264, 8223}, {305, 3069}, {561, 19216}, {670, 17432}, {1502, 10133}, {6424, 40050}, {24245, 45806}
X(46743) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8946}, {3, 26461}, {69, 494}, {75, 19217}, {76, 24243}, {305, 5491}, {487, 6}, {488, 45595}, {3069, 25}, {3933, 45594}, {4563, 1307}, {5591, 26374}, {6424, 1974}, {8222, 42022}, {8223, 3}, {10133, 32}, {17432, 512}, {19216, 31}, {24245, 8576}, {26494, 8948}, {33365, 5410}, {39388, 5412}
X(46743) = {X(69),X(305)}-harmonic conjugate of X(46742)

X(46744) = ISOTOMIC CONJUGATE OF X(6213)

X(46744) lies on the cubic pK(76,264) and these lines: {69, 13386}, {75, 492}, {86, 3083}, {92, 264}, {348, 1267}, {491, 14121}, {6212, 17206}, {13453, 34400}, {20930, 34392}, {24243, 41013}

X(46744) = isotomic conjugate of X(6213)
X(46744) = isotomic conjugate of the anticomplement of X(31591)
X(46744) = isotomic conjugate of the complement of X(31552)
X(46744) = isotomic conjugate of the isogonal conjugate of X(6212)
X(46744) = polar conjugate of the isogonal conjugate of X(3083)
X(46744) = X(31591)-cross conjugate of X(2)
X(46744) = X(i)-isoconjugate of X(j) for these (i,j): {6, 34121}, {19, 606}, {25, 1335}, {31, 6213}, {32, 13387}, {184, 1123}, {212, 13438}, {603, 13456}, {1973, 3084}, {1974, 5391}, {6135, 22383}
X(46744) = cevapoint of X(i) and X(j) for these (i,j): {2, 31552}, {3083, 6212}
X(46744) = barycentric product X(i)*X(j) for these {i,j}: {75, 13386}, {76, 6212}, {92, 1267}, {264, 3083}, {273, 13425}, {304, 1336}, {318, 13453}, {561, 34125}, {605, 18022}, {1124, 1969}, {3718, 13459}, {7182, 13426}
X(46744) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 34121}, {2, 6213}, {3, 606}, {63, 1335}, {69, 3084}, {75, 13387}, {92, 1123}, {273, 13437}, {278, 13438}, {281, 13456}, {304, 5391}, {318, 13454}, {605, 184}, {1124, 48}, {1267, 63}, {1336, 19}, {1897, 6135}, {3083, 3}, {3718, 13458}, {4025, 6365}, {6136, 8750}, {6212, 6}, {6364, 1459}, {7182, 13436}, {13386, 1}, {13389, 2067}, {13390, 2362}, {13424, 6212}, {13425, 78}, {13426, 33}, {13427, 607}, {13453, 77}, {13459, 34}, {13460, 608}, {14121, 7133}, {22107, 3942}, {30556, 5414}, {34125, 31}
X(46744) = {X(92),X(264)}-harmonic conjugate of X(46745)
X(46744) = {X(312),X(322)}-harmonic conjugate of X(46745)

X(46745) = ISOTOMIC CONJUGATE OF X(6212)

X(46745) lies on the cubic pK(76,264) and these lines: {69, 13387}, {75, 491}, {86, 3084}, {92, 264}, {348, 5391}, {492, 7090}, {6213, 17206}, {13436, 34400}, {20930, 34391}, {24244, 41013}

X(46745) = isotomic conjugate of X(6212)
X(46745) = isotomic conjugate of the anticomplement of X(31590)
X(46745) = isotomic conjugate of the complement of X(31551)
X(46745) = isotomic conjugate of the isogonal conjugate of X(6213)
X(46745) = polar conjugate of the isogonal conjugate of X(3084)
X(46745) = X(31590)-cross conjugate of X(2)
X(46745) = X(i)-isoconjugate of X(j) for these (i,j): {6, 34125}, {19, 605}, {25, 1124}, {31, 6212}, {32, 13386}, {184, 1336}, {212, 13460}, {603, 13427}, {1267, 1974}, {1973, 3083}, {6136, 22383}
X(46745) = cevapoint of X(i) and X(j) for these (i,j): {2, 31551}, {3084, 6213}
X(46745) = barycentric product X(i)*X(j) for these {i,j}: {75, 13387}, {76, 6213}, {92, 5391}, {264, 3084}, {273, 13458}, {304, 1123}, {318, 13436}, {561, 34121}, {606, 18022}, {1335, 1969}, {3718, 13437}, {7182, 13454}
X(46745) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 34125}, {2, 6212}, {3, 605}, {63, 1124}, {69, 3083}, {75, 13386}, {92, 1336}, {273, 13459}, {278, 13460}, {281, 13427}, {304, 1267}, {318, 13426}, {606, 184}, {1123, 19}, {1335, 48}, {1659, 16232}, {1897, 6136}, {3084, 3}, {3718, 13425}, {4025, 6364}, {5391, 63}, {6135, 8750}, {6213, 6}, {6365, 1459}, {7090, 42013}, {7182, 13453}, {13387, 1}, {13388, 6502}, {13435, 6213}, {13436, 77}, {13437, 34}, {13438, 608}, {13454, 33}, {13456, 607}, {13458, 78}, {22106, 3942}, {26871, 38003}, {30557, 2066}, {34121, 31}
X(46745) = {X(92),X(264)}-harmonic conjugate of X(46744)
X(46745) = {X(312),X(322)}-harmonic conjugate of X(46744)

X(46746) = ISOTOMIC CONJUGATE OF X(155)

X(46746) lies on the cubic pK(76,264) and these lines: {254, 264}, {317, 2052}, {847, 9723}, {2970, 3964}, {8795, 15316}, {16081, 31635}, {39109, 46104}

X(46746) = isotomic conjugate of X(155)
X(46746) = polar conjugate of X(1609)
X(46746) = isotomic conjugate of the anticomplement of X(12359)
X(46746) = isotomic conjugate of the complement of X(11411)
X(46746) = isotomic conjugate of the isogonal conjugate of X(254)
X(46746) = polar conjugate of the isogonal conjugate of X(6504)
X(46746) = X(i)-cross conjugate of X(j) for these (i,j): {69, 264}, {5392, 76}, {8800, 6504}, {12359, 2}
X(46746) = X(i)-isoconjugate of X(j) for these (i,j): {31, 155}, {48, 1609}, {184, 920}, {560, 40697}, {1973, 6503}, {6515, 9247}, {14575, 33808}
X(46746) = cevapoint of X(i) and X(j) for these (i,j): {2, 11411}, {254, 6504}, {525, 2970}
X(46746) = trilinear pole of line {6563, 14618}
X(46746) = barycentric product X(i)*X(j) for these {i,j}: {76, 254}, {264, 6504}, {276, 8800}, {921, 1969}, {1502, 39109}, {15316, 18027}, {16172, 40832}, {34384, 41536}, {34385, 39114}
X(46746) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 155}, {4, 1609}, {69, 6503}, {76, 40697}, {92, 920}, {254, 6}, {264, 6515}, {275, 8883}, {324, 41587}, {921, 48}, {1969, 33808}, {2052, 3542}, {2986, 15478}, {5392, 34853}, {6504, 3}, {6515, 454}, {8800, 216}, {11547, 35603}, {13398, 32661}, {13579, 18126}, {15316, 577}, {16172, 3003}, {34756, 571}, {39109, 32}, {39114, 52}, {39117, 41523}, {39416, 32734}, {41536, 51}, {44427, 44816}

X(46747) = X(2)X(37)∩X(76)X(40044)

X(46747) lies on the cubic pK(76,8024) and these lines: {2, 37}, {76, 40044}, {82, 32930}, {83, 30133}, {190, 16566}, {304, 17240}, {341, 5015}, {1089, 5263}, {1930, 17285}, {3596, 18151}, {3701, 32850}, {3718, 17336}, {3994, 17446}, {4033, 17788}, {4385, 30145}, {4429, 36250}, {7283, 20833}, {17233, 20445}, {17352, 33937}, {17763, 33760}, {17786, 17791}, {17789, 18040}, {20915, 20928}, {20919, 28654}, {20933, 21064}, {21598, 40035}

X(46747) = isotomic conjugate of the isogonal conjugate of X(17744)
X(46747) = X(8024)-Ceva conjugate of X(33938)
X(46747) = X(32)-isoconjugate of X(39728)
X(46747) = barycentric product X(i)*X(j) for these {i,j}: {75, 33091}, {76, 17744}, {312, 28780}
X(46747) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 39728}, {17744, 6}, {28780, 57}, {33091, 1}
X(46747) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 312, 40001}, {75, 18743, 17370}, {312, 19799, 18743}, {321, 4358, 33155}, {321, 17289, 75}, {17786, 20444, 17791}

X(46748) = X(2)X(3108)∩X(76)X(40045)

X(46748) lies on the cubic pK(76,8024) and these lines: {2, 3108}, {69, 14250}, {76, 40045}, {315, 39989}, {3933, 7953}, {7768, 35137}, {40035, 40036}

X(46749) = ISOTOMIC CONJUGATE OF X(3467)

X(46749) lies on the cubic pK(76,311) and these lines: {7, 8}, {76, 20932}, {264, 40716}, {304, 30596}, {311, 20565}, {313, 20924}, {870, 40044}, {1111, 4360}, {3673, 17393}, {4089, 33943}, {5361, 19804}, {9312, 44179}, {16732, 17300}, {17234, 18151}, {17241, 20927}, {17263, 30807}, {17271, 18698}, {17297, 20236}, {17322, 26563}, {17378, 17861}, {17387, 20171}, {17483, 21863}, {17788, 18143}, {17789, 18040}, {18032, 39735}, {18041, 30985}, {18133, 18159}, {18139, 20919}, {20444, 20917}, {20920, 31019}, {20951, 44188}, {21609, 33808}, {25647, 38941}, {35550, 44139}

X(46749) = isotomic conjugate of X(3467)
X(46749) = isotomic conjugate of the isogonal conjugate of X(3336)
X(46749) = X(20565)-Ceva conjugate of X(75)
X(46749) = cevapoint of X(17483) and X(27529)
X(46749) = barycentric product X(i)*X(j) for these {i,j}: {75, 17483}, {76, 3336}, {85, 27529}, {310, 21863}, {561, 21773}, {1969, 23070}, {11069, 40075}
X(46749) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3467}, {3336, 6}, {11069, 6187}, {14452, 11075}, {17483, 1}, {21773, 31}, {21863, 42}, {23070, 48}, {27529, 9}, {35195, 35192}, {35197, 2174}, {42649, 3063}
X(46749) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 20930, 17791}, {85, 20930, 75}, {320, 1441, 75}, {3262, 7321, 75}, {5564, 20880, 75}, {18139, 30690, 20919}, {18143, 20956, 17788}, {20444, 20917, 40001}

X(46750) = ISOTOMIC CONJUGATE OF X(3336)

X(46750) lies on the cubic pK(76,311) and these lines: {69, 40716}, {75, 45799}, {264, 17791}, {309, 17361}, {311, 20565}, {312, 37656}, {314, 3467}, {17360, 20570}

X(46750) = isotomic conjugate of X(3336)
X(46750) = isotomic conjugate of the isogonal conjugate of X(3467)
X(46750) = X(319)-cross conjugate of X(75)
X(46750) = X(i)-isoconjugate of X(j) for these (i,j): {6, 21773}, {25, 23070}, {31, 3336}, {32, 17483}, {109, 42649}, {1333, 21863}, {1397, 27529}, {6186, 35197}, {7113, 11069}
X(46750) = barycentric product X(76)*X(3467)
X(46750) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 21773}, {2, 3336}, {10, 21863}, {63, 23070}, {75, 17483}, {80, 11069}, {312, 27529}, {650, 42649}, {3219, 35197}, {3467, 6}, {19658, 11076}

X(46751) = ISOTOMIC CONJUGATE OF X(3471)

X(46751) lies on the cubic pK(76,311) and these lines: {69, 74}, {264, 40705}, {3629, 44769}, {3763, 35910}, {16076, 45198}, {16077, 32002}, {34767, 40410}, {46757, 46758}

X(46751) = isotomic conjugate of X(3471)
X(46751) = isotomic conjugate of the isogonal conjugate of X(3470)
X(46751) = X(10272)-cross conjugate of X(37779)
X(46751) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3471}, {2173, 14579}, {9406, 13582}
X(46751) = cevapoint of X(10272) and X(37779)
X(46751) = barycentric product X(i)*X(j) for these {i,j}: {76, 3470}, {1494, 37779}, {1749, 33805}, {10272, 31621}, {39290, 45790}
X(46751) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3471}, {74, 14579}, {1494, 13582}, {1749, 2173}, {2914, 39176}, {3470, 6}, {5627, 11071}, {6140, 14398}, {10272, 3163}, {11063, 1495}, {14451, 11070}, {14919, 43704}, {36308, 46072}, {36311, 46076}, {37779, 30}, {37943, 1990}, {40604, 1511}, {44769, 1291}, {45147, 1637}, {45790, 5664}

X(46752) = ISOTOMIC CONJUGATE OF X(3469)

X(46752) lies on the cubic pK(76,311) and these lines: {75, 225}, {85, 1804}, {320, 1439}, {4554, 18695}, {7535, 20914}, {18747, 27471}

X(46752) = isotomic conjugate of X(3469)
X(46752) = isotomic conjugate of the isogonal conjugate of X(3468)
X(46752) = barycentric product X(i)*X(j) for these {i,j}: {76, 3468}, {349, 15777}, {20924, 34300}
X(46752) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3469}, {3468, 6}, {15777, 284}, {17483, 7165}, {30690, 34303}, {34300, 2161}
X(46752) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 40702, 18749}, {349, 45797, 75}

X(46753) = X(5)X(302)∩X(95)X(303)

X(46753) lies on the cubic pK(76,311) and these lines: {5, 302}, {69, 19772}, {95, 303}, {264, 298}, {299, 465}, {343, 8613}, {32002, 33529}

X(46753) = isotomic conjugate of the isogonal conjugate of X(8837)
X(46753) = X(311)-Ceva conjugate of X(303)
X(46753) = barycentric product X(76)*X(8837)
X(46753) = barycentric quotient X(8837)/X(6)
X(46753) = {X(95),X(33530)}-harmonic conjugate of X(303)

X(46754) = X(5)X(303)∩X(95)X(302)

X(46754) lies on the cubic pK(76,311) and these lines: {5, 303}, {69, 19773}, {95, 302}, {264, 299}, {298, 466}, {343, 8613}, {32002, 33530}

X(46754) = isotomic conjugate of the isogonal conjugate of X(8839)
X(46754) = X(311)-Ceva conjugate of X(302)
X(46754) = barycentric product X(76)*X(8839)
X(46754) = barycentric quotient X(8839)/X(6)
X(46754) = {X(95),X(33529)}-harmonic conjugate of X(302)

X(46755) = ISOTOMIC CONJUGATE OF X(3489)

X(46755) lies on the cubic pK(76,311) and these lines: {17, 76}, {69, 2993}, {95, 183}, {99, 1606}, {264, 38428}, {299, 40035}, {311, 19712}

X(46755) = isotomic conjugate of X(3489)
X(46755) = isotomic conjugate of the isogonal conjugate of X(627)
X(46755) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3489}, {560, 19712}
X(46755) = barycentric product X(76)*X(627)
X(46755) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3489}, {76, 19712}, {627, 6}, {34389, 40167}, {41000, 39134}
X(46755) = {X(305),X(44149)}-harmonic conjugate of X(46756)

X(46756) = ISOTOMIC CONJUGATE OF X(3490)

X(46756) lies on the cubic pK(76,311) and these lines: {18, 76}, {69, 2992}, {95, 183}, {99, 1605}, {264, 38427}, {298, 40035}, {311, 19713}

X(46756) = isotomic conjugate of X(3490)
X(46756) = isotomic conjugate of the isogonal conjugate of X(628)
X(46756) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3490}, {560, 19713}
X(46756) = barycentric product X(76)*X(628)
X(46756) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3490}, {76, 19713}, {628, 6}, {34390, 40168}, {41001, 39135}
X(46756) = {X(305),X(44149)}-harmonic conjugate of X(46755)

X(46757) = ISOTOMIC CONJUGATE OF X(38932)

X(46757) lies on the cubic pK(76,311) and these lines: {13, 99}, {69, 19777}, {264, 38427}, {302, 11120}, {622, 39261}, {19712, 45799}, {46751, 46758}

X(46757) = isotomic conjugate of X(38932)
X(46757) = isotomic conjugate of the isogonal conjugate of X(39261)
X(46757) = barycentric product X(i)*X(j) for these {i,j}: {76, 39261}, {622, 40706}
X(46757) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 38932}, {622, 395}, {6151, 3439}, {11094, 23715}, {14369, 19295}, {38404, 40157}, {39261, 6}, {40706, 2993}

X(46758) = ISOTOMIC CONJUGATE OF X(38931)

X(46758) lies on the cubic pK(76,311) and these lines: {14, 99}, {69, 19776}, {264, 38428}, {303, 11119}, {621, 39262}, {19713, 45799}, {46751, 46757}

X(46758) = isotomic conjugate of X(38931)
X(46758) = isotomic conjugate of the isogonal conjugate of X(39262)
X(46758) = barycentric product X(i)*X(j) for these {i,j}: {76, 39262}, {621, 40707}
X(46758) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 38931}, {621, 396}, {2981, 3438}, {11093, 23714}, {14368, 19294}, {38403, 40156}, {39262, 6}, {40707, 2992}

X(46759) = X(1)X(39725)∩X(2)X(39726)

X(46759) lies on the cubic pK(76,311) and these lines: {1, 39725}, {2, 39726}, {75, 39727}, {39724, 39728}

X(46759) = X(1930)-Ceva conjugate of X(82)
X(46759) = barycentric product X(3112)*X(35213)
X(46759) = barycentric quotient X(35213)/X(38)

X(46760) = ISOGONAL CONJUGATE OF X(46736)

X(46760) lies on these lines: {2, 95}, {3, 2052}, {76, 6503}, {107, 6641}, {140, 2055}, {324, 46724}, {343, 1078}, {418, 1629}, {578, 631}, {3524, 14361}, {7484, 22712}, {7509, 40814}, {7786, 10601}, {8613, 22052}, {8884, 26876}, {14165, 26906}, {15466, 37068}, {26865, 33971}, {26907, 41204}, {35941, 41244}, {38283, 43998}

X(46760) = isogonal conjugate of X(46736)
X(46760) = {X(2),X(577)}-harmonic conjugate of X (275)

X(46761) = (name pending)

X(46762) = ISOGONAL CONJUGATE OF X(46761)

X(46763) = X(4)X(46358)∩X(6)X(1344)

X(46764) = X(4)X(46357)∩X(6)X(1344)

X(46765) = X(4)X(251)∩X(32)X(66)

X(46765) lies on the Jerabek circumhyperbola, the cubic K1258, and these lines: {3, 22075}, {4, 251}, {6, 2353}, {32, 66}, {54, 34945}, {69, 10316}, {248, 27372}, {290, 11610}, {1176, 34137}, {1799, 28405}, {7819, 34138}, {8793, 40938}, {10312, 43678}, {21458, 41361}, {34207, 46288}, {38834, 43696}

X(46765) = isogonal conjugate of the isotomic conjugate of X(40404)
X(46765) = isogonal conjugate of the polar conjugate of X(16277)
X(46765) = X(i)-cross conjugate of X(j) for these (i,j): {32, 10547}, {40947, 1799}
X(46765) = X(i)-isoconjugate of X(j) for these (i,j): {10, 16715}, {22, 20883}, {38, 17907}, {63, 41375}, {75, 40938}, {92, 3313}, {162, 23881}, {304, 27373}, {315, 17442}, {427, 1760}, {1235, 2172}, {1843, 20641}, {1930, 8743}, {1969, 23208}, {4456, 16747}, {4463, 17171}, {11605, 18715}
X(46765) = cevapoint of X(32) and X(2353)
X(46765) = crosspoint of X(16277) and X(40404)
X(46765) = crosssum of X(i) and X(j) for these (i,j): {427, 19595}, {3313, 40938}
X(46765) = barycentric product X(i)*X(j) for these {i,j}: {3, 16277}, {6, 40404}, {66, 1176}, {251, 14376}, {1799, 2353}, {2156, 34055}, {10547, 18018}, {13854, 28724}, {27372, 39287}
X(46765) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 41375}, {32, 40938}, {66, 1235}, {184, 3313}, {251, 17907}, {647, 23881}, {1176, 315}, {1333, 16715}, {1799, 40073}, {1974, 27373}, {2156, 20883}, {2353, 427}, {10547, 22}, {14376, 8024}, {14575, 23208}, {16277, 264}, {28724, 34254}, {34055, 20641}, {40146, 1843}, {40404, 76}, {46288, 8743}
X(46765) = {X(16277),X(40357)}-harmonic conjugate of X(13854)

X(46766) = X(6)X(34427)∩X(32)X(66)

X(46766) lies on the cubic K1258 and these lines: {6, 34427}, {25, 46288}, {32, 66}, {251, 13575}, {1370, 40357}, {7735, 16277}

X(46766) = isogonal conjugate of the isotomic conjugate of X(40357)
X(46766) = X(i)-isoconjugate of X(j) for these (i,j): {1760, 39129}, {1930, 40358}, {3313, 39733}
X(46766) = barycentric product X(i)*X(j) for these {i,j}: {6, 40357}, {66, 8793}, {159, 16277}, {1176, 17407}, {3162, 40404}
X(46766) = barycentric quotient X(i)/X(j) for these {i,j}: {2353, 39129}, {8793, 315}, {16277, 40009}, {17407, 1235}, {40357, 76}, {46288, 40358}

X(46767) = X(6)X(17409)∩X(251)X(13575)

X(46767) lies on the cubics K429 and K1258 and these lines: {6, 17409}, {251, 13575}, {10316, 39172}, {20806, 36414}

X(46767) = isogonal conjugate of the isotomic conjugate of X(40358)
X(46767) = polar conjugate of the isotomic conjugate of X(39172)
X(46767) = X(40358)-Ceva conjugate of X(39172)
X(46767) = X(32)-cross conjugate of X(17409)
X(46767) = X(i)-isoconjugate of X(j) for these (i,j): {66, 21582}, {159, 46244}, {304, 17407}, {1930, 40357}, {18018, 18596}
X(46767) = barycentric product X(i)*X(j) for these {i,j}: {4, 39172}, {6, 40358}, {22, 34207}, {206, 13575}, {8673, 39417}, {17453, 39733}, {20806, 40144}, {20968, 40009}
X(46767) = barycentric quotient X(i)/X(j) for these {i,j}: {206, 1370}, {1974, 17407}, {2172, 21582}, {7251, 18629}, {10316, 28419}, {13575, 40421}, {17409, 41361}, {17453, 18596}, {20968, 159}, {22075, 23115}, {34207, 18018}, {39172, 69}, {40144, 43678}, {40358, 76}, {46288, 40357}

X(46768) = X(6)X(34427)∩X(32)X(19615)

X(46768) lies on the cubic K1258 and these lines: {6, 34427}, {32, 19615}, {251, 40358}, {10547, 17409}

X(46768) = X(20931)-isoconjugate of X(39129)
X(46768) = barycentric product X(i)*X(j) for these {i,j}: {8793, 34427}, {19615, 40357}
X(46768) = barycentric quotient X(22262)/X(39129)

X(46769) = X(6)X(39172)∩X(25)X(40144)

X(46769) lies on the cubic K1258 and these lines: {6, 39172}, {25, 40144}, {251, 40358}, {8743, 39417}, {34207, 46288}

X(46769) = X(40358)-Ceva conjugate of X(34207)
X(46769) = X(21582)-isoconjugate of X(34427)
X(46769) = barycentric product X(i)*X(j) for these {i,j}: {5596, 34207}, {13575, 20993}, {28696, 40144}
X(46769) = barycentric quotient X(i)/X(j) for these {i,j}: {16544, 21582}, {20993, 1370}, {22135, 28419}

X(46770) = X(32)X(184)∩X(251)X(1343)

X(46770) lies on the cubic K1258 and these lines: {32, 184}, {251, 1343}, {1342, 5012}, {1670, 6636}, {1671, 34945}, {1976, 12050}

X(46770) = isogonal conjugate of the isotomic conjugate of X(1342)
X(46770) = X(75)-isoconjugate of X(5403)
X(46770) = barycentric product X(6)*X(1342)
X(46770) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 5403}, {1342, 76}
X(46770) = {X(32),X(184)}-harmonic conjugate of X(41379)
X(46770) = {X(32),X(1501)}-harmonic conjugate of X(46771)
X(46770) = {X(184),X(34396)}-harmonic conjugate of X(46771)

X(46771) = X(32)X(184)∩X(251)X(1342)

X(46771) lies on the cubic K1258 and these lines: {32, 184}, {251, 1342}, {1343, 5012}, {1670, 34945}, {1671, 6636}, {1976, 12051}

X(46771) = isogonal conjugate of the isotomic conjugate of X(1343)
X(46771) = X(75)-isoconjugate of X(5404)
X(46771) = barycentric product X(i)*X(j) for these {i,j}: {6, 1343}, {184, 16245}
X(46771) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 5404}, {1343, 76}, {16245, 18022}
X(46771) = {X(32),X(184)}-harmonic conjugate of X(41378)
X(46771) = {X(32),X(1501)}-harmonic conjugate of X(46770)
X(46771) = {X(184),X(34396)}-harmonic conjugate of X(46770)

X(46772) = ISOGONAL CONJUGATE OF X(39673)

X(46772) lies on these lines: {1, 3696}, {2, 39737}, {19, 1889}, {37, 4365}, {65, 22271}, {75, 4981}, {82, 18089}, {210, 40504}, {536, 17038}, {759, 6013}, {876, 4802}, {984, 39708}, {994, 44663}, {3896, 4751}, {4688, 13476}, {4699, 39739}, {4739, 39742}, {4967, 39712}, {22316, 27798}, {31238, 37593}, {42027, 43224}

X(46772) = isogonal conjugate of X(39673)
X(46772) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39673}, {21, 16878}, {58, 17018}, {99, 8655}, {110, 6005}, {1333, 4687}
X(46772) = trilinear pole of line {661, 21836}
X(46772) = trilinear product X(i)*X(j) for these {i,j}: {10, 10013}, {523, 6013}
X(46772) = barycentric product X(i)*X(j) for these {i,j}: {321, 10013}, {1577, 6013}
X(46772) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39673}, {10, 4687}, {37, 17018}, {661, 6005}, {798, 8655}, {1400, 16878}, {6013, 662}, {10013, 81}

X(46773) = X(58)X(40589)∩X(65)X(4649)

X(46774) = (name pending)

X(46775) = X(6)X(17)∩X(30259)X(45971)

X(46776) = X(4)X(6)∩X(648)X(5895)

X(46776) lies on these lines: {4, 6}, {648, 5895}, {8567, 44134}, {30549, 44247}

X(46777) = X(2)X(6)∩X(98)X(804)

X(46777) lies on these lines: {2, 6}, {98, 804}, {237, 36822}, {3053, 10684}, {4108, 46589}, {6785, 13240}, {9753, 36183}, {9755, 15920}

X(46777) = crossdifference of every pair of points on line {X(512), X(11672)}
X(46777) = crosssum of X(511) and X(34383)
X(46777) = X(98)-daleth conjugate of-X(804)
X(46777) = perspector of the circumconic {{A, B, C, X(99), X(34536)}}
X(46777) = intersection, other than A, B, C, of circumconics {{A, B, C, X(98), X(2421)}} and {{A, B, C, X(325), X(43665)}}
X(46777) = {X(2), X(385)}-harmonic conjugate of X(2421)

X(46778) = X(6)X(523)∩X(99)X(670)

X(46778) lies on these lines: {6, 523}, {99, 670}, {183, 669}, {308, 18105}, {512, 3734}, {599, 25423}, {888, 33755}, {1975, 14824}, {3098, 32472}, {3314, 44445}, {7610, 45317}, {7770, 23099}, {7778, 23301}, {8266, 21006}, {33799, 39292}, {37637, 44451}

X(46778) = crossdifference of every pair of points on line {X(511), X(1084)}
X(46778) = crosssum of X(512) and X(34383)
X(46778) = X(99)-daleth conjugate of-X(804)
X(46778) = perspector of the circumconic {{A, B, C, X(98), X(34537)}}
X(46778) = inverse of X(6) in Kiepert parabola

This preamble is contributed by Clark Kimberling and Peter Moses, January 27, 2022.

In the plane of a triangle ABC, let L, given by l x + m y + n z = 0, be a line, and let P = p : q : r be a point not on L and not on a sideline BC, CA, AB. Let

Ap = L∩AP, Bp = L∩BP, Cp = L∩CP.

Let A'B'C' be the cocevian triangle (TCCT, p. 200) of a point X = x : y : z, so that

A' = 0 : y : -z, B' = -x : 0 : z, C' = x :-y : 0.

The locus of X such that A'B'C' is perspective to the (degenerate) triangle ApBpCp is the cubic, given by

m^2 p q y^2 z + n^2 p r y z^2 + (cyclic) - 2(m n q r + n l r p + l m p q) x y z = 0.

The appearance of (k, Knnn) in the following list means that if L is the line x + y + z = 0 at infinity and P = X(k), then the cubic is Knnn in Bernard Gibert's catalogue (CTC):

(2, K015), (4, K010), (99, K185), (190, K296), (648, K953), (876, K286), (4373, K090), (5485, K408)

The appearance of {{i,j}, {h1, h2, ...}}} in the following list means that if l : m : n = X(i) and P = X(j), then the cubic passes through the points X(h₁), X(h₂), . . .

{1,{2,1022,1026,3572,4585,24004,24015,24029,24035,27853,46779,46780,46781,46782,}
{76,{2,4230,17941,23288,23342,23354,30508,30509}
{100,{2,88,3218,3935,4358,18359,37780,37783,41798}
{110,{2,23,94,111,323,3266,14919,18019,21907,32849,37798,46106,46783,46784,46785,46786,46787,46788,46789}. This is the isogonal conjugate of the cubic K381)
{650,{2,57,200,312,1088,1812,40149,46644}
{664,{2,527,673,1121,1948,3912,11608,14943,40843,40846,40864,40873,40875,40882,44331,46790,46791,46792,46793,,46794. This is the isogonal conjugate of the cubic K225
{666,{2,7,8,528,14947,18821,36887,43671}
{668,{2,239,335,536,3227,11611,19623,29908,40844,40862,40874,40881,44330,46795,46796,46797,46798,46799,46800,46801,46802,46803,46804,46805}
{670,{2,385,538,1916,3228,15014,17759,39925,40859,40887}
{671,{2,99,523,7473,9180,9182,14606,30508,30509}
{693,{2,81,321,4945,6605,13386,13387,43260}
{850,{2,97,251,324,8024,11078,11092,11143,11144,13428,13439,42008,46806,46807,46808,46809}
{879,{2,4,69,393,3926,6776,43718,44144}
{882,{2,6,32,76,1502,3094,3114,11325,14609}
{885,{2,7,8,279,346,390,16713,40779}
{2394,{2,4,69,3431,5967,27558,30508,30509,44135}
{2574,{2,1114,2593,8106,8116,8426,16071,22340,39298,41519,46810,46811,46812}
{2575,{2,1113,2592,8105,8115,8427,16070,22339,39299,41518,46813,46814,46815}
{2966,{2,4,69,542,5641,9214,9513,36890,44155}
{4025,{2,27,63,92,306,13386,13387,19799}
{4367,{2,256,694,1432,1909,3978,17787,28369,40790}
{4374,{2,257,385,894,1916,17752,27447,40738}
{4581,{2,7,8,941,4198,30589,30590,31011,34262,34284}
{5466,{2,1383,4232,9464,21466,21467,30508,30509}
{6332,{2,29,77,78,273,307,318,13386,13387}

X(46779) = X(2)X(45)∩X(1022)X(1023)

X(46779) lies on these lines: {2, 45}, {1022, 1023}, {1026, 23838}, {3573, 39154}, {4582, 24004}, {17109, 24397}, {23343, 23352}

X(46779) = isotomic conjugate of X(46781)
X(46779) = crossdifference of every pair of points on line {1960, 42084}
X(46779) = X(i)-isoconjugate of X(j) for these (i,j): {1635, 2718}, {1960, 37222}
X(46779) = barycentric product X(i)*X(j) for these {i,j}: {2802, 4555}, {3257, 30566}, {4582, 43048}
X(46779) = barycentric quotient X(i)/X(j) for these {i,j}: {901, 2718}, {2802, 900}, {3257, 37222}, {4555, 35175}, {24457, 1647}, {30566, 3762}, {37630, 14584}, {43048, 30725}
X(46779) = {X(3257),X(5376)}-harmonic conjugate of X(4585)

X(46780) = X(2)X(668)∩X(889)X(3572)

X(46780) lies on these lines: {2, 668}, {889, 3572}, {1022, 27853}, {4585, 5381}, {4607, 23891}, {23354, 43928}

X(46780) = isotomic conjugate of X(46782)
X(46780) = X(2382)-isoconjugate of X(3768)
X(46780) = barycentric product X(537)*X(889)
X(46780) = barycentric quotient X(i)/X(j) for these {i,j}: {537, 891}, {889, 18822}, {898, 2382}, {20331, 3768}, {36848, 19945}
X(46780) = {X(3227),X(30866)}-harmonic conjugate of X(31002)

X(46781) = X(2)X(3762)∩X(1000)X(3887)

X(46781) lies on these lines: {2, 3762}, {1000, 3887}, {1016, 4585}, {2718, 2726}, {14628, 30725}, {35168, 35175}

X(46781) = isotomic conjugate of X(46779)
X(46781) = X(i)-isoconjugate of X(j) for these (i,j): {2802, 32665}, {30566, 32719}
X(46781) = trilinear pole of line {900, 34590}
X(46781) = barycentric product X(i)*X(j) for these {i,j}: {900, 35175}, {3762, 37222}
X(46781) = barycentric quotient X(i)/X(j) for these {i,j}: {900, 2802}, {1647, 24457}, {2718, 901}, {3762, 30566}, {14584, 37630}, {30725, 43048}, {35175, 4555}, {37222, 3257}

X(46782) = X(2)X(812)∩X(513)X(16507)

X(46782) lies on these lines: {2, 812}, {513, 16507}, {536, 14433}, {899, 14434}, {1022, 3572}, {2382, 9081}, {6381, 27855}, {24004, 27853}

X(46782) = isotomic conjugate of X(46780)
X(46782) = X(i)-isoconjugate of X(j) for these (i,j): {537, 34075}, {898, 20331}
X(46782) = barycentric product X(891)*X(18822)
X(46782) = barycentric quotient X(i)/X(j) for these {i,j}: {891, 537}, {2382, 898}, {3768, 20331}, {18822, 889}, {19945, 36848}

X(46783) = X(2)X(523)∩X(6)X(10560)

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

X(46783) = X(4678) lies on the cubic K792 and these lines: {2, 523}, {6, 10560}, {23, 111}, {323, 895}, {352, 42007}, {511, 36827}, {512, 46131}, {538, 42008}, {671, 10989}, {858, 31125}, {892, 5971}, {1236, 3266}, {1994, 10559}, {3231, 8705}, {7417, 46633}, {7468, 44420}, {7482, 44467}, {7664, 40544}, {8753, 37962}, {9139, 14919}, {9465, 14609}, {10558, 34545}, {10754, 14515}, {14246, 16042}, {14263, 36182}, {14908, 37980}, {15018, 21460}, {17983, 46106}, {17993, 20403}, {32729, 35265}, {34169, 36174}, {38526, 39576}

X(46783) = X(9177)-cross conjugate of X(2854)
X(46783) = X(i)-isoconjugate of X(j) for these (i,j): {524, 36150}, {896, 2770}, {14210, 32741}
X(46783) = cevapoint of X(2854) and X(9177)
X(46783) = crossdifference of every pair of points on line {187, 1649}
X(46783) = barycentric product X(i)*X(j) for these {i,j}: {671, 2854}, {5968, 37858}, {7482, 14977}, {30786, 44467}
X(46783) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 2770}, {923, 36150}, {2854, 524}, {7482, 4235}, {9177, 2482}, {14263, 34171}, {32740, 32741}, {44467, 468}, {46154, 36824}
X(46783) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {111, 691, 23}, {111, 15899, 691}, {671, 34320, 10989}, {691, 15398, 111}, {895, 32583, 323}, {15398, 15899, 23}

X(46784) = X(2)X(650)∩X(23)X(105)

X(46784) lies on these lines: {2, 650}, {23, 105}, {111, 927}, {323, 1814}, {673, 24585}, {4442, 14942}, {6185, 14953}, {6654, 33150}, {18019, 32849}

X(46784) = X(672)-isoconjugate of X(2752)
X(46784) = barycentric product X(2481)*X(2836)
X(46784) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 2752}, {2836, 518}, {7476, 4238}

X(46785) = X(2)X(1577)∩X(23)X(759)

X(46785) lies on these lines: {2, 1577}, {23, 759}, {80, 33139}, {2006, 18593}, {6740, 33305}, {14194, 24916}, {18359, 37759}, {24624, 35466}, {33134, 36815}, {34172, 36175}, {36002, 45926}

X(46785) = X(2245)-isoconjugate of X(12030)
X(46785) = barycentric quotient X(i)/X(j) for these {i,j}: {759, 12030}, {37964, 4242}

X(46786) = X(2)X(647)∩X(23)X(94)

X(46786) lies on these lines: {2, 647}, {23, 94}, {111, 16081}, {248, 290}, {287, 323}, {542, 36885}, {1976, 18372}, {2697, 40079}, {3266, 14919}, {5191, 7473}, {5967, 11422}, {11673, 20021}, {14999, 34369}, {15080, 35912}, {35606, 40814}

X(46786) = isotomic conjugate of X(46787)
X(46786) = isotomic conjugate of the isogonal conjugate of X(34369)
X(46786) = X(i)-isoconjugate of X(j) for these (i,j): {163, 23350}, {842, 1755}, {5641, 9417}, {6149, 34370}, {14998, 23997}
X(46786) = trilinear pole of line {542, 18312}
X(46786) = barycentric product X(i)*X(j) for these {i,j}: {76, 34369}, {290, 542}, {850, 34761}, {1640, 43187}, {2247, 46273}, {2966, 18312}, {5191, 18024}, {14999, 43665}
X(46786) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 842}, {290, 5641}, {523, 23350}, {542, 511}, {850, 34765}, {879, 35909}, {1640, 3569}, {1989, 34370}, {2247, 1755}, {2395, 14998}, {2966, 5649}, {5191, 237}, {6041, 2491}, {6103, 232}, {7473, 4230}, {14265, 34174}, {14999, 2421}, {16092, 5968}, {17986, 35908}, {18312, 2799}, {20021, 46157}, {34156, 40080}, {34175, 38939}, {34369, 6}, {34761, 110}, {43087, 14356}, {43187, 6035}, {43665, 14223}, {45662, 9155}
X(46786) = {X(16081),X(22456)}-harmonic conjugate of X(46106)

X(46787) = X(2)X(1637)∩X(23)X(110)

X(46787) lies on these lines: {2, 1637}, {23, 110}, {94, 18019}, {111, 14919}, {147, 34174}, {325, 34370}, {684, 5968}, {877, 7664}, {1297, 40080}, {1916, 39291}, {2396, 32458}, {2421, 36790}, {2967, 4230}, {3266, 6331}, {3569, 35910}, {5641, 7840}, {9513, 35909}, {14966, 36415}

X(46787) = isogonal conjugate of X(34369)
X(46787) = isotomic conjugate of X(46786)
X(46787) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34369}, {98, 2247}, {293, 6103}, {542, 1910}, {661, 34761}, {1640, 36084}, {1821, 5191}, {6041, 36036}, {36132, 45321}
X(46787) = trilinear pole of line {511, 23350}
X(46787) = crossdifference of every pair of points on line {1640, 5191}
X(46787) = trilinear product X(i)*X(j) for these {i,j}: {662, 23350}, {842, 1959}, {1755, 5641}, {14223, 23997}
X(46787) = barycentric product X(i)*X(j) for these {i,j}: {99, 23350}, {110, 34765}, {325, 842}, {511, 5641}, {877, 35909}, {2396, 14998}, {2421, 14223}, {2799, 5649}, {3569, 6035}, {7799, 34370}, {20022, 46157}
X(46787) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34369}, {110, 34761}, {232, 6103}, {237, 5191}, {511, 542}, {842, 98}, {1755, 2247}, {2421, 14999}, {2491, 6041}, {2799, 18312}, {3569, 1640}, {4230, 7473}, {5641, 290}, {5649, 2966}, {5968, 16092}, {6035, 43187}, {9155, 45662}, {14223, 43665}, {14356, 43087}, {14998, 2395}, {23350, 523}, {34174, 14265}, {34370, 1989}, {34765, 850}, {35908, 17986}, {35909, 879}, {38939, 34175}, {40080, 34156}, {46157, 20021}

X(46788) = X(2)X(525)∩X(23)X(74)

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

X(46788) lies on these lines: {2, 525}, {23, 74}, {94, 16080}, {323, 3284}, {511, 36831}, {852, 44715}, {1304, 35265}, {1494, 44555}, {2693, 15055}, {3448, 17986}, {5627, 14854}, {5663, 7480}, {11002, 35908}, {14118, 38933}, {14380, 33927}, {15072, 39174}, {17511, 34150}

X(46788) = isotomic conjugate of X(46789)
X(46788) = X(i)-isoconjugate of X(j) for these (i,j): {30, 36151}, {477, 2173}, {1495, 36102}, {1784, 32663}, {1990, 36062}, {3284, 36130}, {14401, 36117}
X(46788) = barycentric product X(i)*X(j) for these {i,j}: {74, 35520}, {1494, 5663}, {7480, 34767}, {14264, 39988}
X(46788) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 477}, {1553, 23097}, {2159, 36151}, {2349, 36102}, {2437, 41392}, {5627, 43707}, {5663, 30}, {7480, 4240}, {11251, 34334}, {14264, 39985}, {14380, 14220}, {14385, 34210}, {18877, 32663}, {34209, 14254}, {35200, 36062}, {35520, 3260}, {36063, 1784}, {36119, 36130}, {39986, 15454}, {42742, 3233}, {44769, 30528}
X(46788) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14919, 44769, 323}, {40384, 44769, 14919}

X(46789) = X(2)X(2411)∩X(23)X(477)

X(46789) lies on these lines: {2, 2411}, {23, 477}, {94, 14919}, {146, 39985}, {323, 648}, {1511, 4240}, {2407, 36789}, {5504, 34210}, {36102, 38340}

X(46789) = isotomic conjugate of X(46788)
X(46789) = X(32162)-cross conjugate of X(43752)
X(46789) = X(i)-isoconjugate of X(j) for these (i,j): {2159, 5663}, {18877, 36063}
X(46789) = barycentric product X(i)*X(j) for these {i,j}: {477, 3260}, {6148, 43707}, {14206, 36102}, {30528, 41079}, {36151, 46234}
X(46789) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 5663}, {477, 74}, {1784, 36063}, {3233, 42742}, {3260, 35520}, {4240, 7480}, {14220, 14380}, {14254, 34209}, {15454, 39986}, {23097, 1553}, {30528, 44769}, {32663, 18877}, {34210, 14385}, {34334, 11251}, {36062, 35200}, {36102, 2349}, {36130, 36119}, {36151, 2159}, {39985, 14264}, {41392, 2437}, {43707, 5627}

X(46790) = X(2)X(514)∩X(80)X(519)

Barycentrics (a + b - 2*c)*(a - 2*b + 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(46790) lies on these lines: {2, 514}, {80, 519}, {88, 3008}, {239, 4080}, {527, 666}, {528, 14190}, {679, 17067}, {1121, 3912}, {3218, 21372}, {3911, 17078}, {4887, 9326}, {5723, 35113}, {6336, 26003}, {6633, 30566}, {17023, 27922}, {17310, 31051}, {17556, 36205}, {19636, 28534}, {26136, 39349}, {27739, 34362}, {29590, 35596}, {30575, 33129}, {30849, 30857}, {31222, 31226}, {35092, 37691}

X(46790) = midpoint of X(i) and X(j) for these {i,j}: {903, 3257}, {10707, 36236}
X(46790) = isotomic conjugate of X(46791)
X(46790) = X(i)-isoconjugate of X(j) for these (i,j): {6, 14191}, {44, 840}, {902, 37131}, {2251, 18821}
X(46790) = barycentric product X(i)*X(j) for these {i,j}: {75, 14190}, {528, 903}, {1022, 42722}, {2246, 20568}, {4997, 5723}
X(46790) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14191}, {88, 37131}, {106, 840}, {528, 519}, {903, 18821}, {1642, 14439}, {1643, 1635}, {2246, 44}, {5723, 3911}, {14190, 1}, {42722, 24004}, {42763, 23757}
X(46790) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3008, 6549, 88}, {4555, 4997, 3912}

X(46791) = X(2)X(918)∩X(190)X(320)

X(46791) lies on these lines: {2, 918}, {190, 320}, {673, 1121}, {840, 9059}, {903, 36910}, {1227, 24004}, {3904, 36887}, {4152, 6174}, {4370, 41801}, {4437, 30731}

X(46791) = isotomic conjugate of X(46790)
X(46791) = X(i)-isoconjugate of X(j) for these (i,j): {6, 14190}, {106, 2246}, {528, 9456}, {901, 1643}
X(46791) = trilinear pole of line {519, 4543}
X(46791) = barycentric product X(i)*X(j) for these {i,j}: {75, 14191}, {519, 18821}, {840, 3264}, {4358, 37131}
X(46791) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14190}, {44, 2246}, {519, 528}, {840, 106}, {1635, 1643}, {3911, 5723}, {14191, 1}, {14439, 1642}, {18821, 903}, {23757, 42763}, {24004, 42722}, {37131, 88}

X(46792) = X(2)X(650)∩X(518)X(30807)

X(46792) lies on these lines: {2, 650}, {518, 30807}, {527, 2481}, {666, 2323}, {673, 10030}, {1861, 33676}, {3912, 14943}, {3975, 36803}

X(46792) = isotomic conjugate of X(46793)
X(46792) = X(672)-isoconjugate of X(12032)
X(46792) = barycentric product X(i)*X(j) for these {i,j}: {75, 14197}, {2481, 28850}, {28143, 34085}
X(46792) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 12032}, {14197, 1}, {28850, 518}

X(46793) = X(100)X(2340)∩X(527)X(32041)

X(46793) lies on these lines: {100, 2340}, {527, 32041}, {673, 14943}, {1025, 6184}, {3738, 14947}, {3912, 4554}, {4876, 31637}

X(46793) = reflection of X(1025) in X(6184)
X(46793) = isotomic conjugate of X(46792)
X(46793) = antitomic conjugate of X(1025)
X(46793) = X(i)-isoconjugate of X(j) for these (i,j): {6, 14197}, {1438, 28850}, {28143, 32735}
X(46793) = barycentric product X(3263)*X(12032)
X(46793) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14197}, {518, 28850}, {12032, 105}

X(46794) = X(2)X(905)∩X(517)X(38955)

X(46794) lies on these lines: {2, 905}, {517, 38955}, {527, 18816}, {673, 1948}, {3912, 36795}, {6996, 34234}, {16082, 26001}

X(46794) = barycentric product X(75)*X(14198)
X(46794) = barycentric quotient X(14198)/X(1)

X(46795) = X(2)X(514)∩X(88)X(239)

X(46795) lies on these lines: {2, 514}, {88, 239}, {335, 536}, {519, 4674}, {3912, 4080}, {4358, 4945}, {4850, 35962}, {4997, 17266}, {9460, 16610}, {16826, 27922}, {23345, 36872}, {24183, 35092}, {29607, 31201}

X(46795) = isotomic conjugate of X(46797)
X(46795) = X(i)-isoconjugate of X(j) for these (i,j): {44, 2382}, {2251, 18822}
X(46795) = trilinear pole of line {537, 36848}
X(46795) = barycentric product X(i)*X(j) for these {i,j}: {537, 903}, {4555, 36848}, {20331, 20568}
X(46795) = barycentric quotient X(i)/X(j) for these {i,j}: {106, 2382}, {537, 519}, {903, 18822}, {20331, 44}, {36848, 900}, {42765, 23757}
X(46795) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {88, 4555, 239}, {3912, 6549, 4080}

X(46796) = X(2)X(513)∩X(44)X(4607)

X(46796) lies on these lines: {2, 513}, {44, 4607}, {239, 37129}, {536, 889}, {13466, 40552}, {31002, 41144}

X(46796) = midpoint of X(889) and X(3227)
X(46796) = reflection of X(13466) in X(40552)
X(46796) = isotomic conjugate of X(46801)
X(46796) = X(36847)-cross conjugate of X(33908)
X(46796) = cevapoint of X(33908) and X(36847)
X(46796) = trilinear pole of line {14474, 33908}
X(46796) = barycentric product X(i)*X(j) for these {i,j}: {889, 14474}, {3227, 33908}
X(46796) = barycentric quotient X(i)/X(j) for these {i,j}: {14474, 891}, {33908, 536}, {36847, 13466}

X(46797) = X(2)X(812)∩X(44)X(190)

X(46797) lies on these lines: {2, 812}, {44, 190}, {335, 2087}, {678, 4432}, {900, 36872}, {903, 24625}, {1023, 4366}, {2382, 9059}, {4370, 24004}, {6632, 6652}

X(46797) = reflection of X(24004) in X(4370)
X(46797) = isotomic conjugate of X(46795)
X(46797) = antitomic conjugate of X(24004)
X(46797) = X(i)-isoconjugate of X(j) for these (i,j): {106, 20331}, {537, 9456}, {32665, 36848}
X(46797) = trilinear pole of line {519, 3251}
X(46797) = barycentric product X(i)*X(j) for these {i,j}: {519, 18822}, {2382, 3264}
X(46797) = barycentric quotient X(i)/X(j) for these {i,j}: {44, 20331}, {519, 537}, {900, 36848}, {2382, 106}, {18822, 903}, {23757, 42765}

X(46798) = X(2)X(650)∩X(44)X(666)

X(46798) lies on these lines: {2, 650}, {44, 666}, {105, 26247}, {239, 335}, {241, 34085}, {536, 2481}, {1921, 34852}, {4384, 35026}, {4702, 14942}, {5222, 36221}, {6185, 36802}, {10030, 39979}, {17023, 36219}

X(46798) = midpoint of X(33674) and X(33676)
X(46798) = isotomic conjugate of X(46802)
X(46798) = X(672)-isoconjugate of X(14665)
X(46798) = barycentric product X(i)*X(j) for these {i,j}: {2481, 14839}, {36796, 43063}
X(46798) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 14665}, {14839, 518}, {43063, 241}

X(46799) = X(2)X(523)∩X(239)X(897)

X(46799) lies on these lines: {2, 523}, {239, 897}, {524, 17497}, {536, 671}, {892, 3227}, {3263, 42008}

X(46799) = X(i)-isoconjugate of X(j) for these (i,j): {896, 35107}, {922, 35155}
X(46799) = barycentric product X(i)*X(j) for these {i,j}: {671, 35103}, {5163, 18023}
X(46799) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 35107}, {671, 35155}, {5163, 187}, {35103, 524}

X(46800) = X(2)X(1577)∩X(239)X(11611)

X(46800) lies on these lines: {2, 1577}, {239, 11611}, {335, 2161}, {536, 14616}, {758, 16704}, {30908, 34079}

X(46801) = X(2)X(891)∩X(239)X(37209)

X(46801) lies on these lines: {2, 891}, {239, 37209}, {536, 668}, {1646, 3227}, {13466, 41314}, {23891, 42083}

X(46801) = reflection of X(i) in X(j) for these {i,j}: {3227, 1646}, {41314, 13466}
X(46801) = isotomic conjugate of X(46796)
X(46801) = antitomic conjugate of X(41314)
X(46801) = X(36847)-cross conjugate of X(536)
X(46801) = X(14474)-isoconjugate of X(34075)
X(46801) = cevapoint of X(536) and X(36847)
X(46801) = trilinear pole of line {536, 14434}
X(46801) = barycentric quotient X(i)/X(j) for these {i,j}: {536, 33908}, {891, 14474}, {13466, 36847}

X(46802) = X(2)X(665)∩X(100)X(239)

X(46802) lies on these lines: {2, 665}, {100, 239}, {241, 4554}, {292, 2481}, {335, 3675}, {536, 32041}, {900, 14947}, {1025, 39775}, {1026, 17755}, {4876, 39714}, {6184, 42720}

X(46802) = reflection of X(i) in X(j) for these {i,j}: {2481, 27918}, {42720, 6184}
X(46802) = isotomic conjugate of X(46798)
X(46802) = antitomic conjugate of X(42720)
X(46802) = X(i)-isoconjugate of X(j) for these (i,j): {1438, 14839}, {2195, 43063}
X(46802) = barycentric product X(3263)*X(14665)
X(46802) = barycentric quotient X(i)/X(j) for these {i,j}: {241, 43063}, {518, 14839}, {14665, 105}

X(46803) = X(2)X(649)∩X(239)X(20332)

X(46803) lies on these lines: {2, 649}, {239, 20332}, {335, 20363}, {536, 3226}, {726, 23579}, {894, 3253}

X(46804) = X(2)X(905)∩X(104)X(517)

X(46804) lies on these lines: {2, 905}, {104, 517}, {239, 34234}, {335, 40862}, {536, 18816}, {3872, 35046}

X(46804) = isotomic conjugate of X(46805)
X(46804) = X(2183)-isoconjugate of X(2726)
X(46804) = barycentric product X(2810)*X(18816)
X(46804) = barycentric quotient X(i)/X(j) for these {i,j}: {104, 2726}, {2810, 517}, {45919, 42757}

X(46805) = X(2)X(3310)∩X(239)X(651)

X(46805) lies on these lines: {2, 3310}, {239, 651}, {2397, 23980}, {2726, 9058}, {6335, 14571}, {9456, 18816}

X(46805) = reflection of X(2397) in X(23980)
X(46805) = isotomic conjugate of X(46804)
X(46805) = antitomic conjugate of X(2397)
X(46805) = X(909)-isoconjugate of X(2810)
X(46805) = barycentric product X(2726)*X(3262)
X(46805) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 2810}, {2726, 104}, {42757, 45919}

X(46806) = X(2)X(98)∩X(97)X(8024)

X(46806) lies on these lines: {2, 98}, {97, 8024}, {248, 290}, {251, 324}, {458, 9755}, {1297, 1972}, {1916, 2987}, {2395, 9979}, {3329, 30535}, {3407, 39685}, {3424, 37174}, {5304, 6531}, {5989, 36790}, {6394, 15589}, {7925, 40428}, {9769, 43113}, {11610, 44176}, {14601, 41231}, {16989, 31636}, {16990, 31635}, {22329, 34369}, {35909, 46245}, {36897, 39097}, {41194, 41201}, {41195, 41200}

X(46806) = isotomic conjugate of X(46807)
X(46806) = crosspoint of X(41074) and X(41174)
X(46806) = trilinear pole of line {182, 23878}
X(46806) = X(i)-isoconjugate of X(j) for these (i,j): {240, 43718}, {262, 1755}, {263, 1959}, {325, 3402}, {327, 9417}, {511, 2186}, {36132, 41167}, {46238, 46319}
X(46806) = barycentric product X(i)*X(j) for these {i,j}: {98, 183}, {182, 290}, {248, 44144}, {287, 458}, {1910, 3403}, {1976, 20023}, {2966, 23878}, {3288, 43187}, {6394, 33971}, {8842, 40820}, {18024, 34396}
X(46806) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 262}, {182, 511}, {183, 325}, {248, 43718}, {287, 42313}, {290, 327}, {458, 297}, {1910, 2186}, {1976, 263}, {2715, 26714}, {3288, 3569}, {3403, 46238}, {6784, 44114}, {9755, 1513}, {10311, 232}, {14601, 46319}, {23878, 2799}, {32545, 39682}, {33971, 6530}, {34396, 237}, {34761, 36885}, {39530, 39569}, {39683, 40804}, {41173, 6037}, {42711, 42703}, {44144, 44132}
X(46806) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5984, 40867}, {2, 40870, 110}, {98, 287, 2}, {98, 40820, 1976}, {1976, 17974, 5012}

X(46807) = X(2)X(51)∩X(97)X(251)

X(46807) lies on these lines: {2, 51}, {97, 251}, {147, 39682}, {237, 38383}, {297, 2967}, {323, 2857}, {324, 8024}, {325, 36790}, {327, 3314}, {385, 2987}, {401, 1297}, {850, 2525}, {1972, 30737}, {4108, 39469}, {5641, 7840}, {7774, 22240}, {7779, 9473}, {10352, 35296}, {18020, 26276}, {20022, 36212}, {37174, 37668}

X(46807) = isotomic conjugate of X(46806)
X(46807) = trilinear pole of line {2799, 41167}
X(46807) = X(i)-isoconjugate of X(j) for these (i,j): {182, 1910}, {293, 10311}, {1821, 34396}, {3288, 36084}, {3403, 14601}
X(46807) = crossdifference of every pair of points on line {3288, 34396}
X(46807) = barycentric product X(i)*X(j) for these {i,j}: {262, 325}, {297, 42313}, {327, 511}, {2186, 46238}, {34765, 36885}, {43718, 44132}
X(46807) = barycentric quotient X(i)/X(j) for these {i,j}: {232, 10311}, {237, 34396}, {262, 98}, {263, 1976}, {297, 458}, {325, 183}, {327, 290}, {511, 182}, {1513, 9755}, {2186, 1910}, {2799, 23878}, {3569, 3288}, {6037, 41173}, {6530, 33971}, {26714, 2715}, {36885, 34761}, {39569, 39530}, {39682, 32545}, {40804, 39683}, {42313, 287}, {42703, 42711}, {43718, 248}, {44114, 6784}, {44132, 44144}, {46238, 3403}, {46319, 14601}
X(46807) = {X(262),X(42313)}-harmonic conjugate of X(2)

X(46808) = X(2)X(648)∩X(30)X(74)

X(46808) lies on these lines: {2, 648}, {30, 74}, {297, 16076}, {1304, 37907}, {2394, 9979}, {2799, 34767}, {5055, 44715}, {7426, 17986}, {9410, 14918}, {10298, 22455}, {16077, 40885}, {31621, 44579}, {34288, 36889}, {35910, 36886}, {44555, 44769}

X(46808) = isotomic conjugate of X(46809)
X(46808) = X(40423)-Ceva conjugate of X(4550)
X(46808) = X(18487)-cross conjugate of X(381)
X(46808) = X(2173)-isoconjugate of X(3431)
X(46808) = cevapoint of X(i) and X(j) for these (i,j): {381, 18487}, {3581, 5158}
X(46808) = barycentric product X(i)*X(j) for these {i,j}: {74, 44135}, {381, 1494}, {16080, 37638}, {18487, 31621}
X(46808) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 3431}, {381, 30}, {1531, 16163}, {3581, 1511}, {4550, 10564}, {4993, 43768}, {5158, 3284}, {5627, 18316}, {16080, 43530}, {18486, 1099}, {18487, 3163}, {32225, 5642}, {34416, 9407}, {34417, 1495}, {36430, 18487}, {37638, 11064}, {44135, 3260}, {46090, 46091}
X(46808) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1494, 14919}, {2, 39358, 14920}, {1494, 16080, 2}, {11078, 11092, 10733}, {13212, 20126, 9140}, {36308, 36311, 74}

X(46809) = X(2)X(340)∩X(30)X(14920)

X(46809) lies on these lines: {2, 340}, {30, 14920}, {323, 1494}, {376, 3431}, {525, 1636}, {2071, 22455}, {2697, 10989}, {2986, 12028}, {3163, 46106}, {3543, 16263}, {6148, 11064}, {7552, 15786}, {10217, 11078}, {10218, 11092}, {11050, 13857}, {14919, 31621}, {15351, 44651}, {15683, 16251}, {23582, 40885}, {40506, 44576}, {40512, 44346}, {44216, 46115}

X(46809) = isotomic conjugate of X(46808)
X(46809) = X(46229)-cross conjugate of X(2407)
X(46809) = cevapoint of X(3284) and X(10564)
X(46809) = trilinear pole of line {5664, 9033}
X(46809) = X(i)-isoconjugate of X(j) for these (i,j): {381, 2159}, {2349, 34417}, {5158, 36119}, {8749, 18477}, {18486, 40353}, {33805, 34416}
X(46809) = barycentric product X(i)*X(j) for these {i,j}: {3260, 3431}, {6148, 18316}, {11064, 43530}
X(46809) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 381}, {1099, 18486}, {1495, 34417}, {1511, 3581}, {3163, 18487}, {3260, 44135}, {3284, 5158}, {3431, 74}, {5642, 32225}, {9407, 34416}, {10564, 4550}, {11064, 37638}, {16163, 1531}, {18316, 5627}, {18487, 36430}, {43530, 16080}, {43768, 4993}, {46091, 46090}

X(46810) = X(2)X(39)∩X(99)X(11114)

X(46810) lis on the cubic K106 and these lines: {2, 39}, {69, 41519}, {99, 1114}, {316, 14808}, {325, 1312}, {1345, 1975}, {1346, 7752}, {2581, 37215}, {2592, 8781}, {4563, 8116}, {4590, 39298}, {7809, 10720}, {8858, 42668}, {12215, 13415}, {22339, 30786}

X(46810) = isotomic conjugate of X(8106)
X(46810) = isotomic conjugate of the complement of X(22340)
X(46810) = isotomic conjugate of the isogonal conjugate of X(8116)
X(46810) = isotomic conjugate of the polar conjugate of X(15165)
X(46810) = X(i)-cross conjugate of X(j) for these (i,j): {525, 15164}, {8116, 15165}, {22340, 305}
X(46810) = X(i)-isoconjugate of X(j) for these (i,j): {19, 42667}, {25, 2579}, {31, 8106}, {32, 2589}, {512, 2576}, {560, 2593}, {661, 44123}, {669, 2580}, {798, 1113}, {1822, 2489}, {1924, 15164}, {1973, 2575}, {1974, 2583}, {2207, 2585}, {2577, 44125}, {2586, 3049}
X(46810) = cevapoint of X(2) and X(22340)
X(46810) = trilinear pole of line {69, 2574}
X(46810) = barycentric product X(i)*X(j) for these {i,j}: {69, 15165}, {76, 8116}, {99, 22339}, {304, 2581}, {305, 1114}, {561, 1823}, {670, 2574}, {799, 2582}, {2577, 40364}, {2578, 4602}, {2592, 4563}, {3267, 39299}, {4609, 42668}, {40050, 44124}
X(46810) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8106}, {3, 42667}, {63, 2579}, {69, 2575}, {75, 2589}, {76, 2593}, {99, 1113}, {110, 44123}, {304, 2583}, {305, 22340}, {326, 2585}, {662, 2576}, {670, 15164}, {799, 2580}, {811, 2586}, {850, 39241}, {1114, 25}, {1823, 31}, {2574, 512}, {2575, 44125}, {2577, 1973}, {2578, 798}, {2581, 19}, {2582, 661}, {2584, 810}, {2587, 1096}, {2592, 2501}, {4563, 8115}, {4576, 46166}, {4590, 39298}, {4592, 1822}, {8105, 2489}, {8116, 6}, {10411, 44067}, {15165, 4}, {15460, 44124}, {22339, 523}, {22340, 1312}, {39240, 8754}, {39298, 41941}, {39299, 112}, {42668, 669}, {44068, 34397}, {44124, 1974}, {46167, 1843}
X(46810) = {X(2),X(3266)}-harmonic conjugate of X(46813)
X(46810) = {X(76),X(7799)}-harmonic conjugate of X(46813)

X(46811) = X(2)X(2593)∩X(3)X(2575)

X(46811) lies the Kiepert circumhyperbola of the medial triangle and these lines: {2, 2593}, {3, 2575}, {99, 44333}, {114, 1313}, {441, 525}, {684, 2574}, {1113, 1297}, {1214, 2583}, {1344, 40801}, {2482, 15166}, {2585, 3682}, {2799, 8105}, {4558, 8116}, {8115, 14919}, {8299, 34592}, {15167, 15526}

X(46811) = reflection of X(46814) in X(8552)
X(46811) = isotomic conjugate of X(46812)
X(46811) = complement of X(2593)
X(46811) = complement of the isotomic conjugate of X(8116)
X(46811) = isotomic conjugate of the polar conjugate of X(2575)
X(46811) = isogonal conjugate of the polar conjugate of X(22340)
X(46811) = X(i)-complementary conjugate of X(j) for these (i,j): {48, 1312}, {163, 2574}, {1114, 20305}, {1823, 141}, {2574, 21253}, {2577, 5}, {2578, 125}, {2581, 21243}, {2584, 127}, {8116, 2887}, {9247, 15167}, {39299, 21259}, {42668, 8287}, {44124, 226}
X(46811) = X(i)-Ceva conjugate of X(j) for these (i,j): {99, 2574}, {8116, 394}, {22340, 2575}, {39298, 8115}
X(46811) = X(i)-cross conjugate of X(j) for these (i,j): {3269, 2574}, {15167, 3}
X(46811) = X(i)-isoconjugate of X(j) for these (i,j): {4, 2577}, {6, 2587}, {19, 1114}, {25, 2581}, {92, 44124}, {107, 2578}, {112, 2588}, {162, 8105}, {393, 1823}, {823, 42668}, {1096, 8116}, {1973, 15165}, {2574, 24019}, {2582, 32713}, {2584, 6529}, {2589, 41942}, {2592, 32676}
X(46811) = cevapoint of X(15167) and X(23110)
X(46811) = crosspoint of X(i) and X(j) for these (i,j): {2, 8116}, {8115, 39298}
X(46811) = crosssum of X(i) and X(j) for these (i,j): {6, 8106}, {2489, 44126}
X(46811) = crossdifference of every pair of points on line {25, 8105}
X(46811) = barycentric product X(i)*X(j) for these {i,j}: {3, 22340}, {63, 2583}, {69, 2575}, {75, 2585}, {304, 2579}, {305, 42667}, {326, 2589}, {394, 2593}, {520, 15164}, {525, 8115}, {1113, 3265}, {1822, 14208}, {2580, 24018}, {3926, 8106}, {15526, 39298}
X(46811) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2587}, {3, 1114}, {48, 2577}, {63, 2581}, {69, 15165}, {125, 39240}, {184, 44124}, {255, 1823}, {394, 8116}, {520, 2574}, {525, 2592}, {647, 8105}, {656, 2588}, {822, 2578}, {1113, 107}, {1822, 162}, {2575, 4}, {2576, 24019}, {2579, 19}, {2580, 823}, {2583, 92}, {2585, 1}, {2586, 36126}, {2589, 158}, {2593, 2052}, {3265, 22339}, {3917, 46167}, {4558, 39299}, {8106, 393}, {8115, 648}, {15164, 6528}, {15167, 8106}, {22115, 44068}, {22340, 264}, {23110, 1312}, {24018, 2582}, {39201, 42668}, {39298, 23582}, {42667, 25}, {44123, 32713}, {46166, 46151}

X(46812) = X(2)X(216)∩X(4)X(41519)

X(46812) lies on these lines: {2, 216}, {4, 41519}, {107, 1114}, {297, 15164}, {450, 13415}, {648, 2593}, {653, 2581}, {685, 39240}, {687, 39299}, {1313, 6530}, {1344, 33971}, {1897, 2587}, {2592, 16080}, {6330, 22339}, {8105, 16081}, {13414, 41204}, {23582, 39298}

X(46812) = isotomic conjugate of X(46811)
X(46812) = polar conjugate of X(2575)
X(46812) = isotomic conjugate of the complement of X(2593)
X(46812) = polar conjugate of the isotomic conjugate of X(15165)
X(46812) = polar conjugate of the isogonal conjugate of X(1114)
X(46812) = X(i)-cross conjugate of X(j) for these (i,j): {523, 15164}, {1114, 15165}, {2593, 2052}, {8106, 4}
X(46812) = X(i)-isoconjugate of X(j) for these (i,j): {3, 2579}, {6, 2585}, {48, 2575}, {63, 42667}, {184, 2583}, {255, 8106}, {520, 2576}, {577, 2589}, {647, 1822}, {810, 8115}, {822, 1113}, {1823, 15167}, {2580, 39201}, {2586, 32320}, {9247, 22340}, {24018, 44123}
X(46812) = cevapoint of X(i) and X(j) for these (i,j): {2, 2593}, {4, 8106}, {1313, 2501}, {8105, 39240}
X(46812) = trilinear pole of line {4, 2574}
X(46812) = barycentric product X(i)*X(j) for these {i,j}: {4, 15165}, {75, 2587}, {92, 2581}, {107, 22339}, {264, 1114}, {648, 2592}, {811, 2588}, {823, 2582}, {1969, 2577}, {2052, 8116}, {2574, 6528}, {6331, 8105}, {14618, 39299}, {18020, 39240}, {18022, 44124}, {18817, 44068}, {46104, 46167}
X(46812) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2585}, {4, 2575}, {19, 2579}, {25, 42667}, {92, 2583}, {107, 1113}, {158, 2589}, {162, 1822}, {264, 22340}, {393, 8106}, {648, 8115}, {823, 2580}, {1114, 3}, {1312, 23110}, {1823, 255}, {2052, 2593}, {2574, 520}, {2577, 48}, {2578, 822}, {2581, 63}, {2582, 24018}, {2587, 1}, {2588, 656}, {2592, 525}, {6528, 15164}, {8105, 647}, {8106, 15167}, {8116, 394}, {15165, 69}, {22339, 3265}, {23582, 39298}, {24019, 2576}, {32713, 44123}, {36126, 2586}, {39240, 125}, {39299, 4558}, {42668, 39201}, {44068, 22115}, {44124, 184}, {46151, 46166}, {46167, 3917}
X(46812) = {X(2),X(46106)}-harmonic conjugate of X(46815)

X(46813) = X(2)X(39)∩X(69)X(41518)

X(46813) lies on the cubic K106 and these lines: {2, 39}, {69, 41518}, {99, 1113}, {316, 14807}, {325, 1313}, {1344, 1975}, {1347, 7752}, {2580, 37215}, {2593, 8781}, {4563, 8115}, {4590, 39299}, {7809, 10719}, {8858, 42667}, {12215, 13414}, {22340, 30786}

X(46813) = isotomic conjugate of X(8105)
X(46813) = isotomic conjugate of the complement of X(22339)
X(46813) = isotomic conjugate of the isogonal conjugate of X(8115)
X(46813) = isotomic conjugate of the polar conjugate of X(15164)
X(46813) = cevapoint of X(2) and X(22339)
X(46813) = trilinear pole of line {69, 2575}
X(46813) = X(i)-cross conjugate of X(j) for these (i,j): {525, 15165}, {8115, 15164}, {22339, 305}
X(46813) = X(i)-isoconjugate of X(j) for these (i,j): {19, 42668}, {25, 2578}, {31, 8105}, {32, 2588}, {512, 2577}, {560, 2592}, {661, 44124}, {669, 2581}, {798, 1114}, {1823, 2489}, {1924, 15165}, {1973, 2574}, {1974, 2582}, {2207, 2584}, {2576, 44126}, {2587, 3049}
X(46813) = barycentric product X(i)*X(j) for these {i,j}: {69, 15164}, {76, 8115}, {99, 22340}, {304, 2580}, {305, 1113}, {561, 1822}, {670, 2575}, {799, 2583}, {2576, 40364}, {2579, 4602}, {2593, 4563}, {3267, 39298}, {4609, 42667}, {40050, 44123}
X(46813) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 8105}, {3, 42668}, {63, 2578}, {69, 2574}, {75, 2588}, {76, 2592}, {99, 1114}, {110, 44124}, {304, 2582}, {305, 22339}, {326, 2584}, {662, 2577}, {670, 15165}, {799, 2581}, {811, 2587}, {850, 39240}, {1113, 25}, {1822, 31}, {2574, 44126}, {2575, 512}, {2576, 1973}, {2579, 798}, {2580, 19}, {2583, 661}, {2585, 810}, {2586, 1096}, {2593, 2501}, {4563, 8116}, {4576, 46167}, {4590, 39299}, {4592, 1823}, {8106, 2489}, {8115, 6}, {10411, 44068}, {15164, 4}, {15461, 44123}, {22339, 1313}, {22340, 523}, {39241, 8754}, {39298, 112}, {39299, 41942}, {42667, 669}, {44067, 34397}, {44123, 1974}, {46166, 1843}
X(46813) = {X(2),X(3266)}-harmonic conjugate of X(46810)
X(46813) = {X(76),X(7799)}-harmonic conjugate of X(46810)

X(46814) = X(2)X(2592)∩X(3)X(2574)

X(46814) lies on the Kiepert circumhyperbola of the medial triangle and these lines: {2, 2592}, {3, 2574}, {99, 44332}, {114, 1312}, {441, 525}, {684, 2575}, {1114, 1297}, {1214, 2582}, {1345, 40801}, {2482, 15167}, {2584, 3682}, {2799, 8106}, {4558, 8115}, {8116, 14919}, {8299, 34593}, {15166, 15526}

X(46814) = reflection of X(46811) in X(8552)
X(46814) = isotomic conjugate of X(46815)
X(46814) = complement of X(2592)
X(46814) = complement of the isotomic conjugate of X(8115)
X(46814) = isotomic conjugate of the polar conjugate of X(2574)
X(46814) = isogonal conjugate of the polar conjugate of X(22339)
X(46814) = X(i)-complementary conjugate of X(j) for these (i,j): {48, 1313}, {163, 2575}, {1113, 20305}, {1822, 141}, {2575, 21253}, {2576, 5}, {2579, 125}, {2580, 21243}, {2585, 127}, {8115, 2887}, {9247, 15166}, {39298, 21259}, {42667, 8287}, {44123, 226}
X(46814) = X(i)-Ceva conjugate of X(j) for these (i,j): {99, 2575}, {8115, 394}, {22339, 2574}, {39299, 8116}
X(46814) = X(i)-cross conjugate of X(j) for these (i,j): {3269, 2575}, {15166, 3}
X(46814) = cevapoint of X(15166) and X(23109)
X(46814) = crosspoint of X(i) and X(j) for these (i,j): {2, 8115}, {8116, 39299}
X(46814) = crosssum of X(i) and X(j) for these (i,j): {6, 8105}, {2489, 44125}
X(46814) = crossdifference of every pair of points on line {25, 8106}
X(46814) = X(i)-isoconjugate of X(j) for these (i,j): {4, 2576}, {6, 2586}, {19, 1113}, {25, 2580}, {92, 44123}, {107, 2579}, {112, 2589}, {162, 8106}, {393, 1822}, {823, 42667}, {1096, 8115}, {1973, 15164}, {2575, 24019}, {2583, 32713}, {2585, 6529}, {2588, 41941}, {2593, 32676}
X(46814) = barycentric product X(i)*X(j) for these {i,j}: {3, 22339}, {63, 2582}, {69, 2574}, {75, 2584}, {304, 2578}, {305, 42668}, {326, 2588}, {394, 2592}, {520, 15165}, {525, 8116}, {1114, 3265}, {1823, 14208}, {2581, 24018}, {3926, 8105}, {15526, 39299}
X(46814) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2586}, {3, 1113}, {48, 2576}, {63, 2580}, {69, 15164}, {125, 39241}, {184, 44123}, {255, 1822}, {394, 8115}, {520, 2575}, {525, 2593}, {647, 8106}, {656, 2589}, {822, 2579}, {1114, 107}, {1823, 162}, {2574, 4}, {2577, 24019}, {2578, 19}, {2581, 823}, {2582, 92}, {2584, 1}, {2587, 36126}, {2588, 158}, {2592, 2052}, {3265, 22340}, {3917, 46166}, {4558, 39298}, {8105, 393}, {8116, 648}, {15165, 6528}, {15166, 8105}, {22115, 44067}, {22339, 264}, {23109, 1313}, {24018, 2583}, {39201, 42667}, {39299, 23582}, {42668, 25}, {44124, 32713}, {46167, 46151}

X(46815) = X(2)X(216)∩X(4)X(41518)

X(46815) lies on these lines: {2, 216}, {4, 41518}, {107, 1113}, {297, 15165}, {450, 13414}, {648, 2592}, {653, 2580}, {685, 39241}, {687, 39298}, {1312, 6530}, {1345, 33971}, {1897, 2586}, {2593, 16080}, {6330, 22340}, {8106, 16081}, {13415, 41204}, {23582, 39299}

X(46815) = isotomic conjugate of X(46814)
X(46815) = polar conjugate of X(2574)
X(46815) = isotomic conjugate of the complement of X(2592)
X(46815) = polar conjugate of the isotomic conjugate of X(15164)
X(46815) = polar conjugate of the isogonal conjugate of X(1113)
X(46815) = X(i)-cross conjugate of X(j) for these (i,j): {523, 15165}, {1113, 15164}, {2592, 2052}, {8105, 4}
X(46815) = X(i)-isoconjugate of X(j) for these (i,j): {3, 2578}, {6, 2584}, {48, 2574}, {63, 42668}, {184, 2582}, {255, 8105}, {520, 2577}, {577, 2588}, {647, 1823}, {810, 8116}, {822, 1114}, {1822, 15166}, {2581, 39201}, {2587, 32320}, {9247, 22339}, {24018, 44124}
X(46815) = cevapoint of X(i) and X(j) for these (i,j): {2, 2592}, {4, 8105}, {1312, 2501}, {8106, 39241}
X(46815) = trilinear pole of line {4, 2575}
X(46815) = barycentric product X(i)*X(j) for these {i,j}: {4, 15164}, {75, 2586}, {92, 2580}, {107, 22340}, {264, 1113}, {648, 2593}, {811, 2589}, {823, 2583}, {1969, 2576}, {2052, 8115}, {2575, 6528}, {6331, 8106}, {14618, 39298}, {18020, 39241}, {18022, 44123}, {18817, 44067}, {46104, 46166}
X(46815) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2584}, {4, 2574}, {19, 2578}, {25, 42668}, {92, 2582}, {107, 1114}, {158, 2588}, {162, 1823}, {264, 22339}, {393, 8105}, {648, 8116}, {823, 2581}, {1113, 3}, {1313, 23109}, {1822, 255}, {2052, 2592}, {2575, 520}, {2576, 48}, {2579, 822}, {2580, 63}, {2583, 24018}, {2586, 1}, {2589, 656}, {2593, 525}, {6528, 15165}, {8105, 15166}, {8106, 647}, {8115, 394}, {15164, 69}, {22340, 3265}, {23582, 39299}, {24019, 2577}, {32713, 44124}, {36126, 2587}, {39241, 125}, {39298, 4558}, {42667, 39201}, {44067, 22115}, {44123, 184}, {46151, 46167}, {46166, 3917}
X(46815) = {X(2),X(46106)}-harmonic conjugate of X(46812)

X(46816) = CENTER OF ALTINTAS-MOSES-NEUBERG HYPERBOLA

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

X(46816) = 3 X[21] - X[100], 3 X[36] - 4 X[5427], X[79] - 3 X[16173], 2 X[100] - 3 X[35204], X[149] + 3 X[15677], 3 X[191] + X[12653], 3 X[442] - 4 X[6667], 2 X[3035] - 3 X[15670], 3 X[5426] - X[34600], 3 X[6175] - 5 X[31272], 6 X[6675] - 5 X[31235], 2 X[6701] - 3 X[32557], X[12773] + 3 X[13743], 3 X[16173] - 2 X[33593], X[33557] - 3 X[38693]

Let I be the incenter. The Neuberg cubics of IBC, ICA, IAB intersect pairwise at 8 real points, other than A, B, C. The points X(1), X(3065) and 6 others. These 8 points lie on a hyperbola, here named as Altintas-Moses-Neuberg Hyperbola. Its center is X(46816)

X(46816) lies on these lines: {1, 399}, {3, 15079}, {4, 14804}, {10, 21}, {11, 30}, {55, 9897}, {56, 16118}, {79, 104}, {90, 6596}, {119, 16617}, {149, 993}, {153, 37719}, {191, 956}, {214, 5259}, {405, 15015}, {442, 6667}, {484, 6797}, {517, 1749}, {528, 17525}, {758, 2611}, {952, 3746}, {958, 5541}, {1001, 5426}, {1012, 1768}, {1145, 18253}, {1156, 5424}, {1317, 15174}, {1320, 5288}, {1387, 3649}, {1479, 11604}, {1484, 4857}, {1621, 33337}, {1698, 2932}, {1699, 22775}, {2077, 12619}, {2078, 18976}, {2098, 13465}, {2475, 7741}, {2646, 45764}, {2802, 3647}, {2829, 37447}, {2975, 21630}, {3035, 15670}, {3057, 22936}, {3245, 41166}, {3560, 6326}, {3584, 11698}, {3585, 16160}, {3586, 37286}, {3612, 3646}, {3648, 8666}, {3651, 10090}, {3652, 12737}, {3679, 13205}, {4297, 34890}, {5010, 28443}, {5119, 11525}, {5248, 6224}, {5253, 33709}, {5425, 11571}, {5428, 12019}, {5442, 37403}, {5443, 14526}, {5450, 37720}, {5542, 10074}, {5885, 16767}, {5903, 22760}, {6174, 15673}, {6175, 31272}, {6246, 44425}, {6264, 22758}, {6265, 33857}, {6675, 31235}, {6701, 32557}, {6702, 17100}, {6713, 37401}, {6841, 8068}, {6906, 10265}, {6912, 21635}, {6913, 15017}, {7280, 16117}, {7489, 22935}, {7688, 28460}, {7727, 23341}, {7972, 28461}, {8674, 35055}, {9957, 45065}, {10122, 11570}, {10483, 37433}, {10707, 15678}, {10738, 11012}, {10826, 37308}, {11009, 16141}, {11010, 17636}, {11238, 18515}, {11263, 37735}, {11496, 13253}, {12104, 33814}, {12119, 15931}, {12332, 37721}, {12515, 41697}, {12532, 41696}, {12611, 38063}, {12740, 30538}, {12747, 32613}, {12764, 37230}, {13273, 37583}, {13995, 37737}, {14217, 16113}, {16125, 16174}, {16132, 21842}, {16140, 20586}, {16143, 37618}, {16152, 33594}, {16154, 26725}, {18254, 31938}, {20831, 34442}, {24926, 35016}, {24929, 41689}, {25439, 37706}, {30282, 36835}, {32760, 37006}, {33557, 38693}

X(46816) = midpoint of X(i) and X(j) for these {i,j}: {1, 3065}, {80, 5441}, {104, 21669}, {1320, 11684}, {3652, 12737}, {10707, 15678}, {11604, 15680}, {14217, 16113}, {17637, 17638}
X(46816) = reflection of X(i) in X(j) for these {i,j}: {79, 33593}, {119, 16617}, {484, 41542}, {1145, 18253}, {1317, 15174}, {3649, 1387}, {3651, 17009}, {6174, 15673}, {11570, 10122}, {16125, 16174}, {31938, 18254}, {33814, 12104}, {35204, 21}, {37401, 6713}, {39778, 35016}
X(46816) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 5441, 35}, {79, 16173, 33593}, {80, 10058, 35}, {104, 16173, 5563}, {13743, 26321, 26202}
X(46816) = center of Altintas-Moses-Neuberg hyperbola

X(46817) = X(5)X(182)∩X(30)X(113)

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

X(46817) = 3 X[2] + X[12112], X[4] + 3 X[35265], X[74] - 3 X[44214], 3 X[113] - X[1531], X[146] + 3 X[186], X[265] - 3 X[403], X[265] + 3 X[10540], X[323] - 5 X[20125], X[858] - 3 X[14643], 3 X[1495] + X[1531], X[1514] + 3 X[35266], X[1533] + 3 X[5642], X[3581] + 3 X[5655], X[3581] - 3 X[7426], 3 X[5642] - X[10564], 2 X[6699] - 3 X[44452], X[10264] - 3 X[44282], 7 X[10272] - 3 X[46114], 7 X[11064] - 6 X[46114], X[12244] - 5 X[37952], X[12317] - 9 X[37943], X[14677] - 3 X[15646], X[14982] + 3 X[18374], 2 X[15152] + X[37938], 2 X[16534] + X[16619], X[18325] + 3 X[32609], X[20127] - 3 X[44280], 3 X[34128] - 4 X[37911], X[37496] - 3 X[40112], X[37779] - 9 X[46451]

X(46817) lies on these lines: {2, 12112}, {3, 32111}, {4, 35265}, {5, 182}, {6, 44275}, {30, 113}, {69, 15068}, {74, 44214}, {110, 11799}, {140, 10575}, {141, 44262}, {146, 186}, {155, 6144}, {156, 235}, {184, 46030}, {185, 44232}, {230, 3016}, {265, 403}, {323, 20125}, {343, 44278}, {381, 14389}, {399, 3580}, {468, 5663}, {511, 16534}, {524, 19140}, {541, 18579}, {546, 21659}, {548, 20725}, {549, 4550}, {597, 39487}, {858, 14643}, {1154, 37971}, {1353, 15471}, {1499, 11176}, {1596, 44080}, {1885, 32171}, {1990, 14254}, {2070, 12168}, {2072, 14157}, {2883, 37814}, {3089, 12161}, {3431, 37077}, {3542, 18917}, {3564, 5609}, {3581, 5655}, {3627, 9820}, {3845, 23292}, {3856, 8254}, {3861, 15806}, {4846, 6644}, {5066, 37649}, {5448, 11819}, {5654, 7530}, {5876, 13383}, {5891, 25337}, {5946, 44233}, {5972, 14915}, {6000, 6699}, {6053, 13754}, {6102, 21841}, {6146, 44235}, {6676, 15060}, {6703, 44257}, {7502, 35254}, {7517, 8907}, {7542, 45959}, {7552, 15052}, {7575, 12893}, {7728, 10295}, {9407, 34104}, {9934, 32125}, {9970, 32113}, {10018, 18439}, {10019, 18379}, {10020, 12162}, {10024, 41171}, {10113, 37984}, {10151, 12140}, {10192, 18570}, {10201, 18451}, {10224, 16655}, {10255, 16659}, {10264, 44282}, {10539, 15761}, {10706, 44265}, {11381, 23336}, {11472, 18580}, {11563, 44665}, {12134, 13406}, {12236, 44084}, {12242, 44863}, {12244, 37952}, {12317, 37943}, {13289, 14677}, {13371, 26883}, {13474, 43839}, {13488, 43394}, {13490, 18388}, {13491, 16238}, {13567, 44270}, {14128, 34002}, {14862, 40647}, {14982, 18374}, {15063, 32110}, {15067, 16618}, {15152, 37938}, {16194, 44236}, {16531, 21663}, {18325, 32609}, {18400, 23323}, {18445, 37644}, {18563, 26882}, {19118, 39899}, {19155, 39871}, {19479, 44283}, {20127, 44280}, {21650, 44234}, {22660, 37440}, {25338, 32269}, {29181, 37967}, {31830, 43831}, {32366, 43129}, {32423, 44961}, {33533, 44210}, {34128, 37911}, {34153, 44267}, {37472, 44803}, {37496, 40112}, {37779, 46451}, {40111, 43893}, {40909, 41424}, {44076, 44958}, {44516, 44870}

X(46817) = midpoint of X(i) and X(j) for these {i,j}: {3, 32111}, {110, 11799}, {113, 1495}, {399, 3580}, {403, 10540}, {1533, 10564}, {2072, 14157}, {5655, 7426}, {6053, 32223}, {7728, 10295}, {9934, 32125}, {9970, 32113}, {10706, 44265}, {15063, 32110}, {34153, 44267}, {40111, 43893}
X(46817) = reflection of X(i) in X(j) for these {i,j}: {1353, 15471}, {7575, 15448}, {10113, 37984}, {11064, 10272}, {12236, 44084}, {15122, 5972}, {20725, 548}, {21663, 16531}, {32269, 25338}
X(46817) = crosssum of X(8675) and X(16186)
X(46817) = barycentric product X(i)*X(j) for these {i,j}: {30, 37644}, {18445, 46106}
X(46817) = barycentric quotient X(i)/X(j) for these {i,j}: {18445, 14919}, {37644, 1494}
X(46817) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {156, 235, 12370}, {1533, 5642, 10564}

X(46818) = X(22)X(69)∩X(30)X(146)

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

X(46818) = 3 X[23] - X[37779], 2 X[74] - 3 X[44280], 3 X[110] - 2 X[11064], 3 X[186] - X[12317], 2 X[265] - 3 X[403], X[265] - 3 X[10540], X[316] - 3 X[33803], X[323] - 3 X[9143], 2 X[468] - 3 X[35265], 3 X[858] - 4 X[11064], 4 X[1495] - 3 X[7426], 3 X[1495] - 2 X[32223], 5 X[1495] - 3 X[32225], 7 X[1495] - 6 X[32267], 3 X[2072] - 4 X[10272], X[3448] - 3 X[35265], 2 X[3580] - 3 X[7426], 3 X[3580] - 4 X[32223], 5 X[3580] - 6 X[32225], 7 X[3580] - 12 X[32267], 9 X[7426] - 8 X[32223], 5 X[7426] - 4 X[32225], 7 X[7426] - 8 X[32267], 2 X[10264] - 3 X[44214], 2 X[14677] - 3 X[44246], 3 X[14683] + X[37779], 2 X[15122] - 3 X[32609], 4 X[16163] - 3 X[16386], 4 X[24981] + X[37900], 10 X[32223] - 9 X[32225], 7 X[32223] - 9 X[32267], 7 X[32225] - 10 X[32267], 4 X[44084] - 3 X[45237]

X(46818) lies on these lines: {2, 8780}, {4, 43595}, {5, 11003}, {20, 11820}, {22, 69}, {23, 3564}, {24, 18917}, {25, 37644}, {30, 146}, {49, 15559}, {68, 32145}, {74, 44280}, {110, 858}, {141, 15080}, {154, 11442}, {156, 1594}, {184, 3818}, {186, 12317}, {235, 34799}, {265, 403}, {316, 33803}, {343, 26881}, {427, 9544}, {428, 1994}, {462, 16771}, {463, 16770}, {468, 3448}, {511, 24981}, {524, 12367}, {542, 1495}, {550, 33884}, {1147, 16659}, {1238, 33801}, {1351, 7519}, {1352, 6800}, {1353, 10301}, {1514, 10733}, {1531, 6053}, {1539, 30522}, {1595, 9545}, {1614, 12134}, {1629, 32002}, {1899, 35264}, {1993, 31383}, {1995, 6776}, {2071, 12168}, {2072, 10272}, {2854, 32220}, {2883, 12278}, {3047, 37981}, {3060, 3629}, {3091, 31804}, {3167, 7391}, {3292, 29012}, {3410, 6676}, {3431, 44218}, {3566, 6562}, {3575, 43605}, {3589, 5012}, {3615, 9958}, {3627, 9716}, {3763, 3796}, {3861, 36966}, {4846, 11456}, {5169, 39884}, {5480, 11422}, {5562, 45185}, {5640, 8550}, {5663, 10295}, {5921, 7493}, {5938, 6390}, {6000, 12825}, {6090, 16063}, {6144, 33586}, {6240, 32139}, {6247, 11449}, {6393, 10330}, {6759, 14516}, {6995, 12167}, {6997, 18935}, {7394, 11402}, {7485, 14826}, {7488, 44683}, {7512, 31831}, {7533, 18583}, {7544, 19347}, {7550, 44834}, {7576, 18445}, {7693, 34545}, {7712, 44210}, {7998, 44882}, {8627, 15993}, {8907, 32321}, {9140, 35266}, {9833, 11441}, {9909, 45794}, {10018, 32140}, {10192, 23293}, {10264, 44214}, {10539, 34224}, {10546, 37648}, {10619, 44870}, {11004, 21850}, {11161, 35295}, {11225, 44106}, {11245, 13595}, {11413, 34781}, {11459, 35254}, {11645, 40112}, {11799, 32423}, {12007, 15019}, {12022, 46261}, {12111, 34782}, {12162, 34005}, {12164, 31304}, {12272, 34774}, {12279, 44762}, {12359, 26882}, {12370, 44803}, {13171, 37978}, {13292, 34484}, {13352, 16658}, {13353, 34939}, {13419, 43844}, {13490, 15087}, {13621, 43588}, {14157, 44665}, {14677, 22584}, {14915, 30714}, {15037, 23410}, {15052, 34664}, {15066, 46264}, {15122, 32609}, {15583, 19122}, {16655, 34148}, {17702, 32111}, {18378, 32358}, {18439, 35491}, {18911, 35259}, {18914, 44802}, {18932, 37951}, {19130, 44109}, {21243, 44110}, {23061, 29181}, {25406, 40916}, {26283, 39879}, {27365, 41580}, {30744, 32064}, {31133, 37645}, {31166, 41614}, {32063, 44440}, {32237, 41586}, {32269, 41724}, {34380, 37899}, {34507, 35268}, {35311, 44704}, {35996, 37656}, {37636, 43150}, {37766, 44228}, {37904, 44555}, {43895, 44158}, {44067, 44309}, {44068, 44310}, {44084, 45237}

X(46818) = midpoint of X(i) and X(j) for these {i,j}: {23, 14683}, {12112, 12383}
X(46818) = reflection of X(i) in X(j) for these {i,j}: {403, 10540}, {858, 110}, {1531, 6053}, {3448, 468}, {3580, 1495}, {9140, 35266}, {10733, 1514}, {41586, 32237}, {41724, 32269}, {44555, 37904}
X(46818) = reflection of X(14731) in the orthic axis
X(46818) = cevapoint of X(159) and X(399)
X(46818) = crosssum of X(512) and X(16186)
X(46818) = crosspoint, wrt excentral or tangential triangle, of X(159) and X(399)
X(46818) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 39899, 37644}, {184, 3818, 14389}, {1352, 6800, 7495}, {1353, 10301, 11002}, {1495, 3580, 7426}, {1614, 12134, 13160}, {1993, 31383, 34603}, {3448, 35265, 468}, {3818, 14389, 5133}, {9833, 11441, 12225}, {18440, 26864, 2}, {37644, 39899, 45968}

X(46819) = X(80)X(109)∩X(100)X(6126)

X(46819) lies on these lines: {1, 12515}, {79, 18360}, {80, 109}, {100, 6126}, {750, 37701}, {5902, 17126}, {5903, 11700}, {11571, 33649}, {24025, 37572}

X(46819) = isogonal conjugate of the perspector of the Altintas-Moses-Neuberg hyperbola

X(46820) = X(1)X(3)∩X(1054)X(9897)

X(46820) lies on the Altintas-Moses-Neuberg hyperbola and these lines: {1, 3}, {1054, 9897}, {1647, 3583}, {3065, 23838}, {3582, 35015}, {14584, 36975}

X(46820) = isogonal conjugate of X(46821)
X(46820) = barycentric product X(3218)*X(16173)
X(46820) = barycentric quotient X(16173)/X(18359)
X(46820) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5131, 23703}

X(46821) = ISOGONAL CONJUGATE OF X(46820)

X(46821) lies on the Feuerbach circumhyperbola and these lines: {484, 23838}, {1411, 24302}, {3065, 23703}, {5559, 14584}, {13602, 34232}

X(46821) = isogonal conjugate of X(46820)
X(46821) = X(36)-isoconjugate of X(16173)
X(46821) = barycentric quotient X(2161)/X(16173)

X(46822) = X(3)X(1126)∩X(42)X(572)

X(46822) lies on these lines: {3, 1126}, {42, 572}, {55, 20958}, {996, 7967}, {1385, 4849}, {1746, 29822}, {13244, 31264}, {13323, 33771}, {22276, 24047}

X(46823) = X(1)X(4271)∩X(37)X(101)

X(46823) lies on these lines: {1, 4271}, {6, 17440}, {37, 101}, {198, 1953}, {572, 26287}, {1030, 2171}, {1100, 15178}, {1251, 11142}, {1962, 20989}, {2294, 19297}, {3723, 31792}, {4053, 38871}, {4268, 37525}, {4289, 40968}, {5356, 22054}, {5755, 37615}, {11063, 21801}, {11141, 33653}, {13145, 21863}, {16548, 17454}, {17796, 21811}, {24323, 25241}

X(46823) = isogonal conjugate of the perspector of the Hutson ellipse
X(46823) = {X(37),X(284)}-harmonic conjugate of X(2161)

X(46824) = EULER LINE INTERCEPT OF X(110)X(5463)

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

X(46824) lies on these lines: {2, 3}, {13, 46646}, {15, 15360}, {110, 5463}, {298, 35314}, {396, 21466}, {531, 14185}, {542, 14170}, {5467, 37786}, {5640, 33957}, {5642, 11131}, {8014, 16267}, {8838, 25154}, {9140, 40709}, {9177, 9885}, {10168, 41478}, {13350, 32225}, {13857, 36755}, {30465, 36967}, {36839, 40578}

X(46824) = complement of X(46856)
X(46824) = anticomplement of X(46858)
X(46824) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 44466, 381), (549, 32461, 2)

X(46825) = EULER LINE INTERCEPT OF X(110)X(5464)

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

X(46825) lies on these lines: {2, 3}, {14, 46647}, {16, 15360}, {110, 5464}, {299, 35315}, {395, 21467}, {530, 14187}, {542, 14169}, {5467, 37785}, {5640, 33958}, {5642, 11130}, {8015, 16268}, {8836, 25164}, {9140, 40710}, {9177, 9886}, {10168, 41477}, {13349, 32225}, {13857, 36756}, {30468, 36968}, {36840, 41889}

X(46825) = complement of X(46857)
X(46825) = anticomplement of X(46859)
X(46825) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 44462, 381), (549, 32460, 2)

In the plane of a triangle ABC, let L, given by l x + m y + n z = 0, be a line, and let P = p : q : r be a point not on L and not on a sideline BC, CA, AB. Let

Ap = L∩AP, Bp = L∩BP, Cp = L∩CP.

Let A'B'C' be the generalized Gemini triangle 34 a point X = x : y : z; that is,

A' = -x : z : y, B' = z : -y : x, C' = y : x : -z .

The locus of X such that A'B'C' is perspective to the (degenerate) triangle ApBpCp is the cubic, given by

l p (n r - m q) x^3 - (l m p r + m^2 q r + l^2 p q + m n p q) y^2 z + (l n p q + n^2 q r + l^2 p r + m n p r) y z^2 + (cyclic) = 0.

This section exemplifies the cubic for three cases:

Case 1: L = 1 : 1 : 1 (the line at infinity). Here, the cubic is given by

p (r - q) x^2 - (p r + q r + 2 p q) y^2 z + ) p q + q r + 2 p r) y z^2 + (cyclic) = 0.

Case 2: P = 1 : 1 : 1 (centroid). Here, the cubic is given by

l (n - m) x^3 - (m^2 + l^2 + l m + m n) y^2 z + (n^2 + l^2 + l n + m n) y z^2 + (cyclic) = 0. Case 2: P = 1 : 1 : 1 (centroid). Here, the cubic is given by

a^2 ( c^2 - b^2) x^3 - (a^2 b (a + c) + b^2 c (a + b)) y^2 z + (a^2 c (a + b) + b c^2 (a + c)) y z^2 = 0.

Examples for Case 1 are indicated in the next list, where the appearance of {{i}, {h1, h2, ...}} means that if l : m : n = 1 : 1 : 1 and P = X(j), then the cubic passes through the points X(h₁), X(h₂), . . .

{56,{2,10,1329,3452,3596,20258,34832,46826,46827,46828}}
{76,{2,6,37,39,216,1212,3752,46829,46830,46831}}
{94,{2,323,16585,16586,34834,41887,41888,44436,46832,46833,46834}}
{274,{2,37,1212,1213,16589,17056,18592,46835,46836,46837}}
{286,{2,37,72,440,1212,18591,1864,146838,46839}}
{290,{2,39,114,216,511,3229,11672,15595,146840,46841}}
{292,{2,10,1921,3739,3836,3846,17793,19563,20333,20530,34832,34852,46842,46843,46834}}
{300,{2,15,39,216,396,618,23303,40695}}
{301,{2,16,39,216,395,619,23302,40696}}
{334,{2,37,238,1125,1212,3008,17755,19563}}
{393,{2,3,3926,6389,30771,45472,45473}}

Examples for Case 2:

{8,{2,192,3752,17760}}
{192,{2,8,3840,17792}}
{193,{2,20,30549,30771}}
{523,{2,148,39365,39366}}

Example for Case 3: This cubic passes through X(75) and X(333).

X(46826) = X(2)X(261)∩X(75)X(115)

X(46826) lies on these lines: {1, 27556}, {2, 261}, {9, 16565}, {10, 14873}, {37, 44396}, {75, 115}, {125, 17047}, {141, 8287}, {142, 20337}, {314, 17669}, {626, 5224}, {645, 1654}, {894, 27707}, {1211, 3452}, {1213, 17353}, {1738, 37159}, {2092, 26601}, {2160, 24704}, {2321, 23947}, {3454, 34832}, {3596, 40099}, {3662, 17058}, {3739, 5949}, {3875, 23903}, {3879, 10026}, {3912, 34528}, {3936, 17312}, {4363, 8818}, {4967, 23897}, {5031, 15985}, {5277, 21287}, {6627, 27805}, {7794, 18133}, {13178, 24374}, {17257, 27704}, {17279, 30860}, {20654, 42713}, {21249, 31946}, {23942, 32087}, {25536, 25662}, {25687, 27958}, {35960, 45212}

X(46826) = X(i)-complementary conjugate of X(j) for these (i,j): {256, 3739}, {257, 3741}, {661, 40608}, {694, 740}, {740, 39080}, {893, 1125}, {904, 3666}, {1178, 17045}, {1431, 3946}, {1432, 3742}, {2238, 19563}, {3747, 5976}, {3903, 4369}, {4451, 21246}, {7018, 21240}, {7116, 37565}, {7249, 17050}, {27805, 512}, {29055, 17069}, {37134, 4155}, {40729, 37}, {46390, 35078}

X(46827) = X(1)X(2)∩X(5)X(3836)

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

X(46827) lies on these lines: {1, 2}, {5, 3836}, {46, 4011}, {65, 25079}, {72, 24003}, {142, 3934}, {171, 13741}, {226, 17114}, {244, 3701}, {312, 24174}, {341, 3976}, {515, 19549}, {596, 4125}, {726, 20923}, {750, 5192}, {964, 17124}, {986, 18743}, {1054, 7283}, {1089, 24165}, {1215, 5439}, {1329, 41682}, {1574, 2321}, {1575, 21071}, {2277, 3950}, {2476, 25961}, {2841, 11814}, {2887, 4187}, {3263, 24172}, {3454, 34832}, {3579, 4432}, {3663, 24170}, {3670, 3971}, {3714, 16602}, {3717, 27680}, {3814, 14058}, {3817, 35663}, {3846, 17527}, {3874, 4090}, {3953, 3992}, {3987, 4975}, {4066, 20891}, {4075, 29982}, {4135, 24168}, {4193, 25957}, {4297, 19513}, {4358, 24443}, {4385, 17063}, {4974, 24742}, {5047, 32918}, {5708, 32935}, {6381, 24215}, {6541, 27633}, {6684, 31394}, {7741, 21241}, {8258, 17353}, {9709, 32941}, {10164, 13731}, {11108, 32916}, {13740, 17122}, {15271, 25500}, {16604, 21025}, {17048, 30748}, {17205, 28660}, {17536, 32917}, {17541, 24602}, {17674, 21935}, {17697, 37603}, {18135, 24214}, {19730, 43531}, {19806, 23537}, {20255, 20530}, {20336, 24173}, {20892, 22220}, {21246, 21255}, {22190, 23414}, {23821, 36798}, {24068, 24167}, {24914, 38286}, {25992, 37634}, {26127, 32947}, {30811, 31246}

X(46827) = midpoint of X(341) and X(3976)
X(46827) = complement of X(978)
X(46827) = complement of the isogonal conjugate of X(979)
X(46827) = X(i)-complementary conjugate of X(j) for these (i,j): {979, 10}, {39694, 141}, {39701, 2885}
X(46827) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 25492, 1125}, {2, 3831, 10}, {2, 17751, 27627}, {1698, 3741, 10}, {1722, 30567, 17733}, {3741, 4871, 30947}, {20340, 29674, 10}

X(46828) = X(2)X(261)∩X(10)X(12)

X(46828) lies on these lines: {2, 261}, {10, 12}, {57, 27688}, {115, 312}, {125, 25957}, {626, 18134}, {894, 41809}, {1230, 20234}, {1368, 34846}, {1999, 3936}, {2064, 3948}, {2999, 27556}, {3687, 34528}, {3752, 44396}, {3840, 20546}, {5949, 44417}, {6627, 36800}, {7058, 26081}, {10472, 32782}, {17056, 21245}, {24210, 37159}, {30811, 32431}

X(46828) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 15349}, {523, 44950}, {6010, 523}, {43677, 141}
X(46828) = crossdifference of every pair of points on line {7252, 42661}
X(46828) = {X(1211),X(20337)}-harmonic conjugate of X(226)

X(46829) = X(2)X(34403)∩X(4)X(6)

X(46829) lies on these lines: {2, 34403}, {3, 23976}, {4, 6}, {64, 16318}, {112, 5925}, {1033, 9914}, {1192, 7735}, {1562, 3172}, {3053, 44248}, {3767, 20207}, {5013, 31377}, {5304, 13568}, {5305, 9786}, {6554, 23982}, {6793, 8778}, {8779, 17845}, {11348, 23292}, {11425, 15048}, {13526, 13613}, {14482, 43841}, {18017, 38292}, {28785, 46347}

X(46829) = complement of X(34403)
X(46829) = polar conjugate of X(34407)
X(46829) = complement of the isogonal conjugate of X(3172)
X(46829) = complement of the isotomic conjugate of X(1249)
X(46829) = isotomic conjugate of the isogonal conjugate of X(20232)
X(46829) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 20309}, {19, 23332}, {31, 20208}, {154, 18589}, {204, 141}, {610, 1368}, {692, 20319}, {798, 13611}, {1249, 2887}, {1394, 18639}, {1395, 18634}, {1895, 626}, {1973, 4}, {1974, 1427}, {3172, 10}, {3213, 2886}, {6525, 20305}, {7121, 20261}, {7156, 1329}, {9406, 3184}, {15466, 21235}, {44695, 21244}, {44696, 17046}, {44697, 17047}, {44698, 21240}, {44705, 21253}
X(46829) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 20208}, {20208, 1853}, {44766, 8057}
X(46829) = X(i)-isoconjugate of X(j) for these (i,j): {48, 34407}, {2155, 34412}
X(46829) = crosspoint of X(2) and X(1249)
X(46829) = crosssum of X(6) and X(1073)
X(46829) = barycentric product X(i)*X(j) for these {i,j}: {1, 20322}, {20, 1853}, {76, 20232}, {1249, 20208}
X(46829) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 34407}, {20, 34412}, {1853, 253}, {20208, 34403}, {20232, 6}, {20322, 75}
X(46829) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 41369, 6}, {1249, 20265, 6}, {1562, 3172, 5895}, {15341, 41361, 1498}, {41369, 44909, 4}

X(46830) = X(2)X(85)∩X(6)X(282)

X(46830) lies on these lines: {2, 85}, {6, 282}, {9, 474}, {11, 1855}, {37, 216}, {39, 20310}, {56, 7079}, {65, 34591}, {78, 4513}, {169, 6918}, {220, 936}, {281, 1108}, {910, 3149}, {1146, 1210}, {1418, 18634}, {1466, 7367}, {1475, 3119}, {1901, 20263}, {2272, 12688}, {3452, 37326}, {3624, 40937}, {3693, 27383}, {5088, 29464}, {5179, 6922}, {6506, 6831}, {6700, 25066}, {7719, 22753}, {8558, 37582}, {9843, 41006}, {12680, 22088}, {16293, 32561}, {17857, 22153}, {20205, 20311}, {21384, 41796}, {23058, 43065}, {25583, 27509}

X(46830) = complement of X(40702)
X(46830) = complement of the isogonal conjugate of X(7118)
X(46830) = complement of the isotomic conjugate of X(282)
X(46830) = isotomic conjugate of the isogonal conjugate of X(20230)
X(46830) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 20307}, {31, 20206}, {32, 7952}, {41, 6260}, {84, 17046}, {189, 17047}, {268, 1368}, {280, 626}, {282, 2887}, {285, 21240}, {657, 46663}, {692, 20314}, {1413, 21258}, {1433, 18639}, {1436, 2886}, {1973, 20264}, {2175, 223}, {2188, 18589}, {2192, 141}, {2208, 142}, {2357, 17052}, {3063, 7358}, {7003, 21243}, {7008, 20305}, {7118, 10}, {7121, 20260}, {7151, 16608}, {7154, 5}, {7367, 1329}, {8059, 46399}, {9447, 40943}, {14827, 38015}, {32652, 4885}, {34404, 21235}, {36049, 17072}
X(46830) = X(2)-Ceva conjugate of X(20206)
X(46830) = crosspoint of X(2) and X(282)
X(46830) = crosssum of X(6) and X(223)
X(46830) = crossdifference of every pair of points on line {8641, 39199}
X(46830) = barycentric product X(i)*X(j) for these {i,j}: {76, 20230}, {282, 20206}
X(46830) = barycentric quotient X(i)/X(j) for these {i,j}: {20206, 40702}, {20230, 6}
X(46830) = {X(17102),X(25063)}-harmonic conjugate of X(37)

X(46831) = X(2)X(216)∩X(3)X(13474)

X(46831) lies on these lines: {2, 216}, {3, 13474}, {6, 1073}, {51, 2972}, {57, 35072}, {64, 1661}, {122, 427}, {141, 45200}, {184, 34147}, {185, 8798}, {220, 7011}, {268, 1407}, {373, 13409}, {378, 12096}, {389, 14059}, {394, 3284}, {418, 5650}, {426, 5651}, {441, 7789}, {511, 38283}, {577, 6617}, {647, 23616}, {800, 20208}, {852, 3917}, {1192, 40675}, {1212, 1214}, {1593, 14379}, {1853, 37072}, {1885, 33553}, {1994, 14919}, {3199, 44334}, {3452, 44360}, {3819, 6638}, {5158, 17825}, {5188, 44894}, {5422, 15860}, {5646, 26909}, {6354, 16596}, {6611, 30457}, {6688, 30258}, {6760, 11430}, {7484, 26880}, {11348, 34861}, {13567, 15526}, {13611, 23332}, {15644, 38281}, {17810, 33924}, {21482, 25878}, {26874, 44299}, {33843, 35071}, {36412, 37873}

X(46831) = complement of X(15466)
X(46831) = complement of the isogonal conjugate of X(14642)
X(46831) = complement of the isotomic conjugate of X(1073)
X(46831) = isotomic conjugate of the isogonal conjugate of X(20233)
X(46831) = isotomic conjugate of the polar conjugate of X(11381)
X(46831) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 20308}, {31, 20207}, {48, 2883}, {64, 20305}, {184, 36908}, {822, 35968}, {1073, 2887}, {1973, 20265}, {2155, 5}, {2184, 21243}, {4100, 31377}, {9247, 1249}, {14379, 18589}, {14642, 10}, {19611, 626}, {19614, 141}, {33581, 226}, {34403, 21235}, {46639, 21259}
X(46831) = X(2)-Ceva conjugate of X(20207)
X(46831) = X(20233)-cross conjugate of X(11381)
X(46831) = crosspoint of X(2) and X(1073)
X(46831) = crosssum of X(6) and X(1249)
X(46831) = barycentric product X(i)*X(j) for these {i,j}: {69, 11381}, {76, 20233}, {1073, 20207}
X(46831) = barycentric quotient X(i)/X(j) for these {i,j}: {11381, 4}, {20207, 15466}, {20233, 6}
X(46831) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6509, 216}, {2, 44436, 6509}, {6617, 17811, 577}

X(46832) = X(2)X(216)∩X(3)X(49)

Barycentrics a^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 - 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) : :

X(46832) lies on these lines: {2, 216}, {3, 49}, {5, 6747}, {22, 26880}, {39, 11427}, {51, 6638}, {95, 37871}, {97, 323}, {140, 12012}, {182, 426}, {275, 401}, {276, 37872}, {297, 46394}, {343, 26906}, {373, 38283}, {389, 42441}, {408, 15489}, {417, 9729}, {418, 511}, {427, 42353}, {441, 37649}, {465, 41888}, {466, 41887}, {570, 23292}, {577, 1993}, {800, 11433}, {852, 5943}, {1214, 16586}, {1350, 26909}, {1368, 26905}, {1589, 45508}, {1590, 45509}, {1594, 10600}, {1624, 45979}, {1994, 3284}, {2972, 3819}, {2979, 26874}, {3003, 13567}, {3219, 35072}, {3781, 26901}, {3784, 26900}, {5158, 5422}, {5249, 44360}, {5907, 26897}, {6617, 10601}, {6641, 9306}, {7386, 9744}, {7494, 22712}, {8613, 46724}, {8798, 15056}, {10979, 15066}, {10996, 13380}, {11412, 26876}, {11550, 18437}, {11572, 36245}, {14919, 31626}, {15526, 34834}, {17811, 36751}, {20806, 26899}, {21638, 43975}, {23061, 39243}, {23158, 34382}, {23606, 34986}, {30506, 44924}, {31383, 44437}, {32428, 42400}, {34833, 37452}, {34836, 45198}, {36748, 37672}, {37648, 45200}

X(46832) = midpoint of X(i) and X(j) for these {i,j}: {324, 43988}, {418, 13409}
X(46832) = isogonal conjugate of X(40402)
X(46832) = complement of X(324)
X(46832) = complement of the isogonal conjugate of X(14533)
X(46832) = complement of the isotomic conjugate of X(97)
X(46832) = isotomic conjugate of the polar conjugate of X(389)
X(46832) = isogonal conjugate of the polar conjugate of X(45198)
X(46832) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 34836}, {48, 1209}, {54, 20305}, {97, 2887}, {563, 34835}, {822, 20625}, {2148, 5}, {2167, 21243}, {2168, 5449}, {2169, 141}, {4100, 10600}, {9247, 233}, {14533, 10}, {14573, 16583}, {14586, 8062}, {15958, 4369}, {18315, 21259}, {19210, 18589}, {23286, 21253}, {33629, 20308}, {34386, 21235}, {36134, 30476}, {46088, 34846}, {46089, 21231}
X(46832) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 34836}, {14570, 525}, {18831, 520}, {45198, 389}
X(46832) = X(42441)-cross conjugate of X(45198)
X(46832) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40402}, {19, 40448}, {1973, 42333}
X(46832) = crosspoint of X(i) and X(j) for these (i,j): {2, 97}, {69, 276}
X(46832) = crosssum of X(i) and X(j) for these (i,j): {4, 436}, {6, 53}, {25, 217}
X(46832) = crossdifference of every pair of points on line {2501, 39201}
X(46832) = barycentric product X(i)*X(j) for these {i,j}: {3, 45198}, {63, 45224}, {69, 389}, {95, 42441}, {97, 34836}, {326, 45225}, {343, 19170}
X(46832) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 40448}, {6, 40402}, {69, 42333}, {389, 4}, {6750, 13450}, {19170, 275}, {34836, 324}, {42441, 5}, {45198, 264}, {45224, 92}, {45225, 158}
X(46832) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3164, 2052}, {2, 6509, 44436}, {2, 40684, 14767}, {2, 43988, 324}, {2, 46717, 264}, {3, 49, 37081}, {216, 6509, 2}, {2979, 26895, 26874}, {3917, 26907, 3}, {5408, 5409, 1092}, {6638, 30258, 51}, {26906, 41005, 343}, {40680, 40681, 216}

X(46833) = X(2)X(13)∩X(15)X(33529)

X(46833) lies on these lines: {2, 13}, {15, 33529}, {125, 128}, {323, 10677}, {343, 42124}, {471, 8741}, {570, 23303}, {629, 34834}, {635, 11130}, {1216, 15962}, {1526, 3581}, {3580, 6671}, {3619, 18929}, {6694, 15018}, {11290, 41254}, {15768, 22796}, {19294, 23302}, {34540, 44719}, {41022, 41472}, {41888, 43961}, {43962, 44386}

X(46833) = complement of X(8838)
X(46833) = complement of the isogonal conjugate of X(8603)
X(46833) = isotomic conjugate of the polar conjugate of X(31687)
X(46833) = X(i)-complementary conjugate of X(j) for these (i,j): {2151, 629}, {2152, 33526}, {8603, 10}
X(46833) = X(32036)-Ceva conjugate of X(23870)
X(46833) = crosssum of X(6) and X(11083)
X(46833) = barycentric product X(i)*X(j) for these {i,j}: {69, 31687}, {298, 11542}
X(46833) = barycentric quotient X(i)/X(j) for these {i,j}: {11542, 13}, {11555, 11581}, {31687, 4}
X(46833) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 618, 41887}, {2, 11078, 6669}

X(46834) = X(2)X(14)∩X(16)X(33530)

X(46834) lies on these lines: {2, 14}, {16, 33530}, {125, 128}, {323, 10678}, {343, 42121}, {470, 8742}, {570, 23302}, {630, 34834}, {636, 11131}, {1216, 15961}, {1527, 3581}, {3580, 6672}, {3619, 18930}, {6695, 15018}, {11289, 41254}, {15769, 22797}, {19295, 23303}, {34541, 44718}, {41023, 41473}, {41887, 43962}, {43961, 44386}

X(46834) = complement of X(8836)
X(46834) = complement of the isogonal conjugate of X(8604)
X(46834) = isotomic conjugate of the polar conjugate of X(31688)
X(46834) = X(i)-complementary conjugate of X(j) for these (i,j): {2151, 33527}, {2152, 630}, {8604, 10}
X(46834) = X(32037)-Ceva conjugate of X(23871)
X(46834) = crosssum of X(6) and X(11088)
X(46834) = barycentric product X(i)*X(j) for these {i,j}: {69, 31688}, {299, 11543}
X(46834) = barycentric quotient X(i)/X(j) for these {i,j}: {11543, 14}, {11556, 11582}, {31688, 4}
X(46834) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 619, 41888}, {2, 11092, 6670}

X(46835) = X(2)X(85)∩X(9)X(46)

X(46835) lies on these lines: {1, 1146}, {2, 85}, {3, 5179}, {4, 910}, {5, 169}, {6, 1210}, {8, 6603}, {9, 46}, {10, 220}, {11, 2082}, {12, 208}, {19, 235}, {34, 46344}, {37, 158}, {40, 17747}, {41, 1837}, {55, 1855}, {75, 27547}, {78, 40997}, {101, 355}, {141, 27384}, {198, 1826}, {218, 1737}, {219, 17275}, {226, 26958}, {230, 16968}, {312, 27526}, {346, 27525}, {388, 40127}, {405, 32561}, {427, 15487}, {430, 15496}, {498, 16601}, {499, 43065}, {515, 3207}, {594, 2324}, {650, 42455}, {672, 24914}, {853, 22368}, {936, 34526}, {946, 8074}, {950, 4258}, {958, 19309}, {966, 27382}, {1104, 7735}, {1107, 9367}, {1111, 20269}, {1125, 5199}, {1211, 27413}, {1229, 27507}, {1475, 17728}, {1802, 21029}, {1836, 21912}, {1944, 4643}, {2170, 11376}, {2329, 29659}, {2345, 27508}, {2348, 17606}, {2654, 40957}, {3061, 25681}, {3086, 40133}, {3091, 5819}, {3119, 17718}, {3142, 39690}, {3198, 4207}, {3416, 4109}, {3436, 26258}, {3452, 29604}, {3496, 24703}, {3501, 37828}, {3553, 21933}, {3579, 17732}, {3665, 30742}, {3693, 5552}, {3730, 26446}, {3732, 17181}, {3739, 27509}, {3752, 5286}, {3767, 3772}, {3911, 5022}, {3925, 28070}, {3965, 27522}, {3991, 45701}, {4193, 33950}, {4251, 5722}, {4363, 40880}, {4513, 6735}, {4515, 7080}, {4675, 26932}, {4858, 7264}, {4875, 10527}, {5011, 12699}, {5123, 25610}, {5219, 13609}, {5224, 27420}, {5228, 26001}, {5252, 9310}, {5283, 19721}, {5526, 18395}, {5540, 7741}, {5546, 13746}, {5574, 25525}, {5657, 21872}, {5687, 21073}, {5743, 27411}, {5745, 19744}, {5942, 24553}, {6559, 40724}, {6684, 42316}, {6690, 41795}, {6734, 37658}, {7289, 21239}, {7680, 7719}, {7705, 26074}, {8715, 21090}, {8804, 37499}, {9312, 17044}, {9318, 30617}, {10025, 33298}, {11108, 15288}, {11375, 17451}, {12609, 31896}, {15853, 19855}, {16318, 36103}, {16588, 16589}, {17048, 38186}, {17278, 24774}, {17355, 34524}, {17439, 37738}, {17675, 34847}, {17720, 28836}, {17742, 17757}, {18140, 36796}, {20205, 37674}, {21258, 40483}, {24249, 31284}, {24954, 39244}, {25003, 26223}, {25066, 26364}, {25082, 27529}, {25086, 40937}, {26059, 28653}, {26531, 31640}, {27040, 32777}, {27396, 27524}, {27523, 32851}, {27539, 44417}, {27540, 31993}, {27542, 28054}, {27546, 44720}, {28118, 41339}, {28143, 33528}, {28734, 30806}, {28794, 30818}

X(46835) = midpoint of X(348) and X(30694)
X(46835) = complement of X(348)
X(46835) = polar conjugate of X(34398)
X(46835) = complement of the isogonal conjugate of X(607)
X(46835) = complement of the isotomic conjugate of X(281)
X(46835) = medial isogonal conjugate of X(18639)
X(46835) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 17073}, {17188, 4336}, {18026, 3900}, {43190, 522}
X(46835) = X(4336)-cross conjugate of X(1836)
X(46835) = X(i)-isoconjugate of X(j) for these (i,j): {48, 34398}, {57, 37741}, {604, 34409}
X(46835) = crosspoint of X(2) and X(281)
X(46835) = crosssum of X(6) and X(222)
X(46835) = crossdifference of every pair of points on line {2605, 8641}
X(46835) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 18639}, {4, 17046}, {6, 34822}, {9, 1368}, {19, 2886}, {25, 142}, {28, 17050}, {29, 21240}, {31, 17073}, {32, 17102}, {33, 141}, {34, 21258}, {41, 3}, {42, 18642}, {55, 18589}, {92, 17047}, {108, 46399}, {162, 17066}, {212, 6389}, {213, 18641}, {220, 34823}, {281, 2887}, {318, 626}, {607, 10}, {608, 11019}, {657, 123}, {1096, 16608}, {1172, 3741}, {1334, 21530}, {1395, 4000}, {1402, 18643}, {1474, 3742}, {1783, 17072}, {1824, 17052}, {1857, 20305}, {1918, 18592}, {1973, 1}, {1974, 3752}, {2175, 1214}, {2203, 3946}, {2204, 1125}, {2207, 1210}, {2212, 2}, {2299, 3739}, {2331, 20307}, {2332, 960}, {2333, 442}, {2356, 17060}, {2489, 8286}, {3063, 2968}, {3064, 21252}, {3195, 20206}, {3709, 34846}, {4041, 127}, {4183, 21246}, {6059, 226}, {6591, 17059}, {6602, 42018}, {7008, 21239}, {7017, 21235}, {7046, 21244}, {7071, 3452}, {7079, 1329}, {7154, 946}, {7156, 2883}, {8641, 16596}, {8750, 4885}, {9447, 216}, {18344, 116}, {30457, 20309}, {32674, 3900}, {32676, 17069}, {36417, 20227}, {36797, 42327}, {40983, 45226}
X(46835) = barycentric product X(i)*X(j) for these {i,j}: {1, 17860}, {8, 1836}, {10, 17188}, {29, 21912}, {75, 4336}, {281, 17073}, {318, 20277}, {668, 2520}, {4521, 27833}
X(46835) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 34398}, {8, 34409}, {55, 37741}, {1836, 7}, {2520, 513}, {4336, 1}, {17073, 348}, {17188, 86}, {17860, 75}, {20277, 77}, {21912, 307}, {36838, 42388}
X(46835) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 23058, 1146}, {2, 3177, 17095}, {2, 6554, 1212}, {2, 26793, 26690}, {2, 27541, 6554}, {2, 28827, 34852}, {2, 30694, 348}, {10, 40869, 220}, {41, 21044, 1837}, {1125, 5199, 41006}, {1125, 41006, 34522}, {3767, 16583, 3772}, {5011, 24045, 12699}, {20262, 40942, 6}

X(46836) = X(1)X(15849)∩X(2)X(34404)

X(46836) lies on these lines: {1, 15849}, {2, 34404}, {6, 20263}, {9, 23986}, {37, 158}, {223, 5219}, {2331, 5514}, {3767, 20227}, {3772, 24005}, {6260, 34261}, {7358, 17275}, {13612, 46344}

X(46836) = complement of the isogonal conjugate of X(3195)
X(46836) = complement of the isotomic conjugate of X(7952)
X(46836) = X(i)-complementary conjugate of X(j) for these (i,j): {19, 21239}, {25, 946}, {33, 20306}, {40, 1368}, {196, 17046}, {198, 18589}, {208, 2886}, {221, 34822}, {223, 18639}, {342, 17047}, {607, 20205}, {1395, 3086}, {1973, 57}, {1974, 1108}, {2187, 3}, {2199, 17073}, {2212, 281}, {2331, 141}, {3194, 3741}, {3195, 10}, {3209, 142}, {6059, 20263}, {7074, 34823}, {7952, 2887}, {40971, 1329}, {41083, 21240}, {41088, 20309}
X(46836) = X(44765)-Ceva conjugate of X(8058)
X(46836) = X(2208)-isoconjugate of X(34411)
X(46836) = crosspoint of X(2) and X(7952)
X(46836) = crosssum of X(6) and X(1433)
X(46836) = barycentric product X(1)*X(20321)
X(46836) = barycentric quotient X(i)/X(j) for these {i,j}: {329, 34411}, {20321, 75}
X(46836) = {X(7952),X(38015)}-harmonic conjugate of X(40943)

X(46837) = X(2)X(216)∩X(3)X(4877)

X(46837) lies on these lines: {2, 216}, {3, 4877}, {9, 856}, {282, 3330}, {440, 5316}, {577, 965}, {1212, 1213}, {1901, 20263}, {2092, 16573}, {2287, 3284}, {15526, 18635}, {35072, 40942}

X(46837) = X(i)-complementary conjugate of X(j) for these (i,j): {73, 20307}, {228, 6260}, {268, 21246}, {810, 7358}, {1402, 20264}, {1409, 20206}, {1433, 3741}, {1436, 34830}, {1903, 20305}, {2188, 960}, {2192, 34831}, {2200, 223}, {2208, 942}, {2357, 5}, {7118, 6708}, {13138, 21259}, {32652, 8062}, {36049, 30476}, {39130, 21243}, {41081, 21240}, {41086, 20308}, {41087, 141}
X(46837) = crosssum of X(6) and X(3194)

X(46838) = X(1)X(21858)∩X(2)X(37)

X(46838) lies on these lines: {1, 21858}, {2, 37}, {6, 474}, {9, 4286}, {11, 22071}, {39, 1213}, {44, 579}, {69, 16726}, {71, 27627}, {216, 18641}, {239, 29453}, {244, 3949}, {274, 33769}, {292, 39693}, {386, 1100}, {387, 21896}, {404, 1333}, {573, 19550}, {583, 2238}, {594, 1574}, {665, 24920}, {714, 25120}, {750, 2214}, {869, 22279}, {899, 2260}, {966, 5069}, {980, 17327}, {992, 2245}, {1015, 17362}, {1054, 1761}, {1108, 1714}, {1627, 2220}, {1778, 37680}, {2092, 17398}, {2178, 16414}, {2197, 5433}, {2275, 17275}, {2303, 17531}, {2321, 8610}, {3723, 20691}, {4016, 24443}, {4033, 40010}, {4272, 24512}, {4426, 16453}, {4526, 24959}, {5013, 19527}, {5124, 21004}, {5165, 16669}, {5224, 16696}, {5227, 11512}, {5291, 21773}, {5301, 25440}, {5750, 20108}, {7484, 36744}, {7536, 18591}, {9534, 17448}, {10090, 22118}, {10449, 21868}, {11347, 37500}, {16700, 32782}, {16710, 26756}, {16716, 33833}, {16736, 18134}, {16753, 31017}, {17239, 37596}, {17245, 31198}, {17369, 21796}, {17443, 21951}, {18040, 27044}, {18143, 27095}, {18144, 24621}, {18148, 30473}, {20174, 26959}, {21245, 37096}, {21897, 24923}, {24580, 37650}, {28611, 40986}, {36743, 37257}, {37654, 39956}, {39960, 39983}

X(46838) = complement of X(18147)
X(46838) = X(i)-complementary conjugate of X(j) for these (i,j): {15376, 3741}, {29014, 3835}, {39700, 626}
X(46838) = crosssum of X(6) and X(1724)
X(46838) = crossdifference of every pair of points on line {667, 4132}
X(46838) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4261, 37}, {1574, 17053, 594}, {1575, 28244, 37}, {2277, 17303, 37}, {5224, 24598, 16696}, {16604, 21857, 1100}, {38312, 38313, 3175}

X(46839) = X(2)X(85)∩X(212)X(650)

X(46839) lies on these lines: {2, 85}, {212, 650}, {220, 7580}, {573, 910}, {1104, 9367}, {3190, 6603}, {6602, 35310}, {16588, 17056}

X(46839) = X(15393)-complementary conjugate of X(3741)
X(46839) = X(37659)-Ceva conjugate of X(1)

X(46840) = X(2)X(36897)∩X(114)X(325)

X(46840) lies on these lines: {2, 36897}, {114, 325}, {230, 3229}, {327, 14382}, {385, 36213}, {18829, 41520}, {21536, 35088}, {39080, 44377}

X(46840) = midpoint of X(18829) and X(41520)
X(46840) = complement of X(36897)
X(46840) = complement of the isogonal conjugate of X(36213)
X(46840) = complement of the isotomic conjugate of X(5976)
X(46840) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 2023}, {237, 18904}, {1580, 511}, {1691, 16609}, {1755, 325}, {1933, 230}, {1959, 5031}, {1966, 21531}, {2679, 24040}, {5976, 2887}, {9417, 3229}, {23997, 804}, {24041, 22103}, {36213, 10}, {39931, 20305}
X(46840) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 2023}, {41520, 511}, {46606, 804}
X(46840) = crosspoint of X(2) and X(5976)
X(46840) = crosssum of X(6) and X(34238)
X(46840) = crossdifference of every pair of points on line {2422, 39680}
X(46840) = barycentric product X(2023)*X(5976)
X(46840) = barycentric quotient X(2023)/X(36897)

X(46841) = X(2)X(216)∩X(3)X(38297)

X(46841) lies on these lines: {2, 216}, {3, 38297}, {6, 38283}, {30, 35071}, {32, 9243}, {114, 38974}, {140, 46394}, {418, 1495}, {441, 11672}, {511, 14941}, {520, 647}, {577, 1971}, {8724, 14961}

X(46841) = complement of X(16089)
X(46841) = complement of the isotomic conjugate of X(14941)
X(46841) = X(i)-complementary conjugate of X(j) for these (i,j): {1956, 21243}, {1987, 20305}, {14941, 2887}
X(46841) = X(401)-Ceva conjugate of X(511)
X(46841) = crosspoint of X(2) and X(14941)
X(46841) = crosssum of X(6) and X(41204)
X(46841) = crossdifference of every pair of points on line {4, 39201}
X(46841) = {X(6638),X(40805)}-harmonic conjugate of X(577)

X(46842) = X(2)X(799)∩X(10)X(20694)

X(46842) lies on these lines: {2, 799}, {10, 20694}, {11, 1211}, {37, 20496}, {115, 26582}, {141, 8287}, {668, 16613}, {1086, 1213}, {1368, 34846}, {1921, 3797}, {2238, 4396}, {3836, 20337}, {3934, 6537}, {3936, 30967}, {4489, 4716}, {5224, 10472}, {6374, 30830}, {6389, 16595}, {6651, 40548}, {7212, 16591}, {7257, 26138}, {10026, 20530}, {16589, 25994}, {16593, 30860}, {16888, 27691}, {17302, 26772}, {17322, 27042}, {20484, 20681}, {21093, 31993}, {21246, 26932}, {23897, 25107}, {23905, 25102}, {24505, 36800}, {25530, 25685}, {26563, 27698}, {30097, 40617}, {30863, 32746}, {35070, 35078}

X(46842) = complement of X(37128)
X(46842) = complement of the isogonal conjugate of X(2238)
X(46842) = complement of the isotomic conjugate of X(3948)
X(46842) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 740}, {10, 20541}, {37, 3836}, {42, 3912}, {101, 9508}, {213, 1575}, {238, 3739}, {239, 3741}, {242, 34830}, {350, 21240}, {659, 17761}, {662, 4155}, {740, 141}, {765, 40548}, {798, 39786}, {813, 40549}, {862, 226}, {874, 42327}, {1018, 3837}, {1284, 142}, {1400, 1738}, {1428, 3946}, {1429, 3742}, {1438, 9507}, {1447, 17050}, {1824, 26012}, {1874, 16608}, {1914, 1125}, {2201, 942}, {2210, 3666}, {2238, 10}, {3570, 512}, {3573, 4369}, {3684, 960}, {3685, 21246}, {3747, 2}, {3948, 2887}, {3952, 21261}, {3985, 1329}, {4010, 116}, {4037, 3454}, {4093, 6292}, {4154, 39080}, {4155, 8287}, {4368, 20333}, {4433, 3452}, {4435, 34589}, {4455, 1086}, {4557, 812}, {4559, 25380}, {5009, 17045}, {6651, 20339}, {7212, 17059}, {7235, 17052}, {8298, 20529}, {8632, 244}, {16609, 2886}, {20681, 20343}, {20964, 1966}, {21759, 20363}, {21832, 11}, {27853, 23301}, {35068, 45162}, {35544, 626}, {40729, 18904}, {41333, 37}, {46390, 115}
X(46842) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 740}, {670, 4155}
X(46842) = X(2311)-isoconjugate of X(35108)
X(46842) = crosspoint of X(2) and X(3948)
X(46842) = crosssum of X(6) and X(18268)
X(46842) = barycentric quotient X(1284)/X(35108)

X(46843) = X(1)X(2)∩X(76)X(17063)

X(46843) lies on these lines: {1, 2}, {76, 17063}, {142, 21257}, {244, 3948}, {982, 30830}, {3264, 21100}, {3778, 29982}, {3816, 20255}, {3835, 6005}, {3836, 20544}, {3846, 21240}, {3944, 24190}, {4044, 24165}, {4297, 19545}, {4368, 20367}, {5267, 16372}, {6381, 19567}, {6682, 16589}, {9335, 31060}, {12782, 18743}, {16420, 25440}, {17065, 20923}, {17241, 31337}, {17245, 21238}, {17758, 43687}, {20683, 24003}, {20892, 22172}, {21255, 34832}, {22190, 30045}, {24688, 34824}, {30819, 30982}

X(46843) = complement of X(2664)
X(46843) = complement of the isogonal conjugate of X(2665)
X(46843) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 39028}, {2107, 1213}, {2665, 10}, {3733, 38978}, {39925, 141}, {40769, 17793}, {43685, 21245}
X(46843) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3741, 4871, 30967}, {3741, 24603, 10}, {3912, 20340, 10}, {4871, 20340, 3912}

X(46844) = X(2)X(85)∩X(960)X(17793)

X(46844) lies on these lines: {2, 85}, {960, 17793}, {1146, 30038}, {1329, 3836}, {2329, 25102}, {3061, 20530}, {6603, 17752}, {15985, 34831}, {20317, 27929}, {25104, 34371}

X(46844) = complement of X(28391)
X(46844) = X(i)-complementary conjugate of X(j) for these (i,j): {18299, 17046}, {39924, 141}

X(46845) = X(1)X(6)∩X(551)X(594)

X(46845) lies on these lines: {1,6}, {86,4686}, {192,31313}, {354,21863}, {536,17394}, {551,594}, {573,33179}, {966,20057}, {1125,4060}, {1149,5153}, {1213,3244}, {1255,35595}, {1418,7269}, {1575,29814}, {1766,37624}, {2174,9327}, {2178,6767}, {2269,33176}, {3218,37595}, {3241,17275}, {3290,29815}, {3306,20182}, {3616,17299}, {3622,4727}, {3635,17362}, {3636,17398}, {3689,5311}, {3739,17393}, {3746,21773}, {3752,17019}, {3759,4755}, {3763,29602}, {3834,17396}, {3969,41850}, {3986,4969}, {4021,17392}, {4357,22165}, {4360,4688}, {4361,29597}, {4393,4698}, (4657,29585}, (4670,4718}, (4681,17379}, (4708,17377}, (4725,17248}, (4726,41847}, (4851,21356}, (4852,16826}, (4889,5224}, (4908,5749}, {4909,17365}, {4980,30562}, {5206,5266}, {5287,16602}, {5564,29592}, {6542,25498}, {11160,17344}, {11278,37508}, {16200,37499}, {16605,30145}, (17011,37687}, {17021,31197}, {17045,17231}, {17229,17397}, {17235,17391}, {17237,17390}, {17239,17389}, {17278,29624}, {17283,29625}, {17307,29619}, {17309,29603}, {17314,38314}, {17315,17385}, {17316,17384}, {17317,17382}, {17320,17376}, {17321,17374}, {17322,17372}, {17323,31138}, {17327,29605}, {17348,29584}, {17356,29569}, {17357,26626}, {17609,21853}, {19684,22034}, {21866,44840}, {28484,43997}, {28633,29612}, {28640,42696}, {29601,34573}, {29817,44798}, {37512,37592}

X(46846) = X(1)X(39)∩X(1384)X(31451)

X(46847) = X(3)X(5646)∩X(4)X(69)

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

X(46847) = 2*X(3)-3*X(15082), 5*X(4)+X(5562), 2*X(4)+X(5907), 11*X(4)+X(11412), 3*X(4)+X(11459), 4*X(4)-X(13598), 7*X(4)+5*X(15058), X(4)+3*X(16261), X(4)+2*X(44870), 7*X(4)-X(45186), 4*X(3818)-X(14913), 2*X(5562)-5*X(5907), 11*X(5562)-5*X(11412), 3*X(5562)-5*X(11459), 4*X(5562)+5*X(13598), X(5562)-5*X(15030), X(5562)-15*X(16261), X(5562)-10*X(44870), 7*X(5562)+5*X(45186), 11*X(5907)-2*X(11412), 3*X(5907)-2*X(11459), 2*X(5907)+X(13598), 7*X(5907)-10*X(15058), X(5907)-6*X(16261), X(5907)-4*X(44870), 7*X(5907)+2*X(45186)

X(46847) lies on these lines: {2, 32062}, {3, 5646}, {4, 69}, {5, 13474}, {20, 5650}, {30, 3819}, {51, 3839}, {185, 3832}, {235, 45303}, {373, 3091}, {381, 1853}, {382, 11793}, {389, 546}, {542, 16657}, {548, 11017}, {568, 3843}, {575, 11456}, {1154, 14893}, {1181, 39561}, {1216, 3853}, {1495, 7527}, {1498, 5050}, {1593, 35259}, {1594, 36518}, {1596, 21243}, {1597, 9306}, {1885, 46682}, {2842, 31871}, {2883, 23300}, {3090, 12045}, {3146, 7998}, {3292, 15052}, {3357, 7529}, {3426, 37475}, {3522, 33879}, {3543, 3917}, {3545, 6688}, {3581, 18551}, {3627, 15067}, {3628, 14641}, {3830, 5891}, {3845, 13754}, {3850, 13363}, {3851, 10575}, {3854, 10574}, {3855, 12290}, {3856, 13630}, {3857, 13491}, {3858, 5462}, {3859, 12006}, {3860, 13364}, {3861, 5446}, {4550, 7530}, {5055, 14855}, {5066, 5892}, {5068, 12279}, {5071, 10219}, {5076, 10625}, {5085, 11479}, {5102, 12164}, {5198, 46730}, {5656, 14561}, {5890, 41099}, {5946, 23046}, {6090, 11403}, {6102, 44863}, {6225, 9815}, {6241, 15012}, {6759, 37506}, {6800, 26883}, {7387, 32620}, {7395, 17508}, {7503, 35268}, {7528, 22802}, {7545, 32110}, {9976, 14094}, {10182, 44218}, {10193, 44211}, {10282, 39242}, {10982, 15520}, {11002, 12111}, {11430, 31861}, {11438, 11472}, {11454, 14002}, {11591, 12102}, {11645, 16658}, {12082, 14810}, {12101, 13391}, {12133, 41670}, {12233, 38136}, {12292, 41671}, {12362, 16656}, {13334, 44437}, {13367, 35265}, {13382, 18439}, {13402, 15102}, {13451, 41987}, {13487, 31978}, {13595, 21663}, {14269, 18435}, {14531, 16981}, {14865, 15035}, {15026, 41991}, {15032, 15516}, {15041, 18369}, {15045, 41106}, {15055, 44802}, {15056, 17578}, {15060, 15687}, {15682, 36987}, {16621, 44829}, {16654, 29012}, {16776, 34146}, {18451, 34986}, {18488, 23515}, {18492, 23841}, {23039, 38335}, {23306, 33332}, {23328, 44212}, {31884, 33537}, {32139, 37505}, {34484, 43613}, {44233, 44673}, {44665, 44804}

X(46847) = midpoint of X(i) and X(j) for these {i, j}: {2, 32062}, {4, 15030}, {51, 15305}, {381, 16194}, {568, 12162}, {3543, 3917}, {3627, 15067}, {3830, 5891}, {11188, 12294}, {11381, 15072}, {12133, 41670}, {13363, 32137}, {13474, 16836}, {15060, 15687}, {15682, 36987}, {16654, 34664}
X(46847) = reflection of X(i) in X(j) for these (i, j): (51, 13570), (568, 10110), (5892, 5066), (5907, 15030), (5943, 381), (13363, 3850), (13364, 3860), (15030, 44870), (15072, 9729), (15644, 15067), (16836, 5), (40647, 13363), (45956, 5462)
X(46847) = X(9730)-of-Ehrmann-mid triangle
X(46847) = X(15030)-of-Euler triangle
X(46847) = X(16836)-of-Johnson triangle
X(46847) = X(37853)-of-orthocentroidal triangle
X(46847) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 5907, 13598), (4, 15058, 45186), (4, 16261, 15030), (4, 44870, 5907), (51, 3839, 13570), (373, 11381, 15072), (373, 15072, 9729), (3091, 11381, 9729), (3091, 15072, 373), (3832, 11439, 185), (3839, 15305, 51), (3843, 12162, 10110), (3850, 32137, 40647), (3851, 10575, 11695), (3853, 45958, 1216), (3854, 10574, 27355), (3861, 45959, 5446), (15030, 16261, 44870), (31861, 46261, 11430)

X(46848) = ISOGONAL CONJUGATE OF X(33923)

X(46848) lies on the Jerabek circumhyperbola and these lines: {3, 11017}, {30, 26861}, {54, 32062}, {64, 38848}, {74, 26863}, {265, 12102}, {389, 14487}, {546, 14861}, {1173, 13474}, {3146, 42021}, {3431, 26883}, {3519, 3627}, {3527, 11455}, {3531, 6241}, {3532, 10594}, {3830, 14841}, {3857, 13623}, {5198, 43719}, {5900, 10721}, {11381, 14483}, {11403, 43908}, {14094, 43704}, {14528, 35502}

X(46848) = isogonal conjugate of X(33923)
X(46848) = intersection, other than A, B, C, of circumconics Jerabek hyperbola and {{A, B, C, X(30), X(26863)}}

X(46849) = X(4)X(52)∩X(30)X(5447)

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

X(46849) = X(3)+3*X(32062), 5*X(4)-X(52), 11*X(4)-3*X(3060), 3*X(4)-X(5446), 9*X(4)-X(5889), 3*X(4)+5*X(11439), 5*X(4)-2*X(12002), 7*X(4)+X(12111), 3*X(4)+X(12162), 5*X(4)+3*X(15305), X(4)+3*X(16194), 11*X(52)-15*X(3060), 3*X(52)-5*X(5446), 9*X(52)-5*X(5889), 7*X(52)+5*X(12111), 3*X(52)+5*X(12162), X(52)+3*X(15305), X(52)+15*X(16194), 9*X(3060)-11*X(5446), 9*X(3060)+11*X(12162), 5*X(3060)+11*X(15305), X(3060)+11*X(16194)

X(46849) lies on these lines: {2, 14641}, {3, 32062}, {4, 52}, {5, 13474}, {20, 10170}, {23, 43613}, {30, 5447}, {51, 18439}, {113, 15559}, {143, 14893}, {185, 3843}, {381, 11381}, {382, 1216}, {389, 3845}, {403, 18488}, {511, 3853}, {541, 13568}, {546, 5462}, {547, 17704}, {1147, 1597}, {1154, 12102}, {1495, 14130}, {1593, 12038}, {1595, 5448}, {1596, 5449}, {1598, 7689}, {1885, 45286}, {2777, 31830}, {3090, 14855}, {3091, 5892}, {3146, 5891}, {3357, 13861}, {3530, 11017}, {3543, 10625}, {3544, 20791}, {3545, 12279}, {3627, 5907}, {3819, 15704}, {3830, 5562}, {3832, 9730}, {3839, 6241}, {3850, 9729}, {3854, 15045}, {3855, 15072}, {3856, 12006}, {3858, 5943}, {3859, 13363}, {3860, 18874}, {3861, 5663}, {3917, 5073}, {4550, 7387}, {5066, 11695}, {5076, 18435}, {5650, 15696}, {5876, 13598}, {5878, 7706}, {6243, 38335}, {6688, 12811}, {6696, 44233}, {6759, 31861}, {7393, 8717}, {7464, 43614}, {7506, 43604}, {9818, 15811}, {10095, 13382}, {10116, 16657}, {10219, 44904}, {10539, 35502}, {10564, 43598}, {10574, 14845}, {10627, 40247}, {11403, 18451}, {11444, 15682}, {11459, 17578}, {11557, 12292}, {11645, 13470}, {11750, 16658}, {11818, 22802}, {12084, 43586}, {12112, 13434}, {12133, 23047}, {12134, 12897}, {12163, 18535}, {12241, 44804}, {12289, 37077}, {12605, 16654}, {12606, 18323}, {12900, 32144}, {13488, 17702}, {13621, 21663}, {14269, 34783}, {15026, 23046}, {15028, 41106}, {15043, 41099}, {15056, 33703}, {15060, 15644}, {15062, 32110}, {15082, 44682}, {15083, 44413}, {16621, 44407}, {18475, 26883}, {20191, 21841}, {20299, 46030}, {21969, 35403}, {22804, 44283}, {23325, 31978}, {23515, 46431}, {25563, 44232}, {32767, 44235}, {33537, 35243}, {33539, 37924}, {34382, 39884}, {40240, 43588}, {40929, 43130}

X(46849) = midpoint of X(i) and X(j) for these {i, j}: {5, 13474}, {382, 1216}, {546, 32137}, {1885, 45286}, {3627, 5907}, {3853, 45959}, {5446, 12162}, {5876, 13598}, {5892, 11455}, {11381, 40647}, {11557, 12292}, {12133, 46686}, {12134, 12897}
X(46849) = reflection of X(i) in X(j) for these (i, j): (52, 12002), (389, 44863), (3530, 11017), (5462, 546), (9729, 3850), (10110, 3861), (10627, 40247), (11793, 45958), (12006, 3856), (13348, 14128), (13382, 10095), (43588, 40240)
X(46849) = complement of X(14641)
X(46849) = X(13607)-of-orthic triangle, when ABC is acute
X(46849) = X(40647)-of-Ehrmann-mid triangle
X(46849) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 11439, 12162), (4, 12162, 5446), (4, 15305, 52), (381, 11381, 40647), (382, 15030, 1216), (389, 3845, 44863), (1593, 46261, 12038), (1598, 11472, 7689), (3091, 10575, 5892), (3091, 11455, 10575), (3543, 15058, 10625), (3832, 12290, 9730), (3858, 13491, 5943), (5076, 18435, 45186), (5876, 15687, 13598), (11793, 44870, 45958), (12162, 16194, 11439), (13364, 15012, 5462), (13382, 13570, 10095), (15062, 34484, 32110)

X(46850) = X(3)X(64)∩X(20)X(185)

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

X(46850) = 9*X(2)-5*X(11439), 3*X(2)+X(12279), 3*X(2)-4*X(17704), 4*X(3)-3*X(3819), 5*X(3)-3*X(5891), 3*X(3)-2*X(11793), 3*X(3)-X(12162), X(3)-3*X(14855), 7*X(3)-3*X(18435), 5*X(3)-X(18439), 7*X(3)-4*X(40247), 3*X(154)-X(36982), 5*X(3819)-4*X(5891), 3*X(3819)-2*X(5907), 3*X(3819)+4*X(10575), 9*X(3819)-8*X(11793), 9*X(3819)-4*X(12162), X(3819)-4*X(14855), 7*X(3819)-4*X(18435), 15*X(3819)-4*X(18439), 3*X(11381)-5*X(11439), X(11381)-4*X(17704), 5*X(11439)+3*X(12279), 5*X(11439)-12*X(17704), 5*X(11439)-6*X(44870), X(12279)+4*X(17704), X(12279)+2*X(44870)

Let (A) be the circle centered at A that cuts off a segment of line BC equal to 2|BC|. Define (B) and (C) cyclically. X(46850) is the radical center of circles (A), (B), (C). (Randy Hutson, April 16, 2022)

X(46850) lies on these lines: {2, 11381}, {3, 64}, {4, 5943}, {5, 13474}, {20, 185}, {22, 1204}, {23, 43601}, {24, 32237}, {30, 143}, {39, 31952}, {49, 10564}, {51, 3146}, {52, 1657}, {54, 7464}, {72, 2808}, {74, 7512}, {113, 37452}, {140, 45958}, {155, 37480}, {170, 1695}, {182, 1593}, {184, 11413}, {186, 8718}, {373, 3832}, {376, 5562}, {378, 10984}, {381, 11695}, {382, 9730}, {394, 12174}, {411, 15489}, {512, 46626}, {546, 5892}, {548, 1216}, {550, 6101}, {568, 17800}, {575, 11424}, {578, 12085}, {631, 12290}, {858, 43831}, {916, 31793}, {970, 7580}, {971, 29958}, {974, 11800}, {1038, 6285}, {1040, 7355}, {1092, 11456}, {1105, 41204}, {1154, 12103}, {1176, 30100}, {1181, 13346}, {1192, 9909}, {1350, 16936}, {1352, 10996}, {1368, 2883}, {1425, 3100}, {1495, 22467}, {1503, 14913}, {1597, 37514}, {1598, 11820}, {1656, 16194}, {1658, 43604}, {1660, 46372}, {1843, 14927}, {1899, 37201}, {1906, 37648}, {1907, 19130}, {1986, 16624}, {2071, 13367}, {2393, 22967}, {2777, 12605}, {2781, 32392}, {2807, 4297}, {2810, 12680}, {2937, 32110}, {2944, 39156}, {2979, 45187}, {3060, 5059}, {3090, 11455}, {3091, 6688}, {3098, 37198}, {3270, 4296}, {3292, 43605}, {3491, 8721}, {3516, 3796}, {3521, 7574}, {3522, 3917}, {3523, 15305}, {3524, 15058}, {3528, 11459}, {3529, 5890}, {3530, 10170}, {3534, 10625}, {3543, 15043}, {3549, 23329}, {3567, 33703}, {3575, 12144}, {3581, 43807}, {3627, 5462}, {3628, 32137}, {3781, 37551}, {3784, 9841}, {3818, 6815}, {3839, 15028}, {3843, 40280}, {3853, 12006}, {3861, 13363}, {4260, 37537}, {4550, 7516}, {4846, 14542}, {5012, 12086}, {5020, 15811}, {5056, 10219}, {5067, 16261}, {5073, 37481}, {5092, 7503}, {5160, 43820}, {5447, 5876}, {5640, 17578}, {5650, 15056}, {5691, 23841}, {5878, 6643}, {5894, 11574}, {5895, 41580}, {5944, 34152}, {5972, 16196}, {5999, 13500}, {6102, 15704}, {6225, 7386}, {6243, 15681}, {6247, 6823}, {6293, 9967}, {6310, 37182}, {6636, 11440}, {6676, 6696}, {6689, 44236}, {6699, 10020}, {6723, 12133}, {6795, 36162}, {6836, 15488}, {7286, 43819}, {7387, 11438}, {7393, 11472}, {7395, 13347}, {7411, 22076}, {7486, 12045}, {7488, 21663}, {7506, 37470}, {7525, 32138}, {7527, 20190}, {7542, 25563}, {7550, 43613}, {7552, 43608}, {7689, 8717}, {7691, 16661}, {7729, 17845}, {7957, 9052}, {7998, 21734}, {7999, 21735}, {9441, 10822}, {9781, 15682}, {9786, 39568}, {9818, 37515}, {9822, 36990}, {9825, 16621}, {9961, 42448}, {10024, 32767}, {10112, 18914}, {10263, 45956}, {10304, 11444}, {10601, 11403}, {10605, 11414}, {10627, 44245}, {10628, 12606}, {10721, 16223}, {10990, 35240}, {11001, 14831}, {11179, 44495}, {11220, 23154}, {11225, 13142}, {11250, 18475}, {11412, 17538}, {11430, 12084}, {11441, 43652}, {11449, 44110}, {11557, 34584}, {11562, 20127}, {11572, 34007}, {11573, 31805}, {11591, 33923}, {11598, 32391}, {11645, 38323}, {11799, 43817}, {11807, 14708}, {12058, 30552}, {12100, 14128}, {12102, 13364}, {12112, 43598}, {12163, 35243}, {12239, 42264}, {12240, 42263}, {12292, 38727}, {12294, 25406}, {12362, 15311}, {12370, 18128}, {12584, 15054}, {12825, 17856}, {13202, 41671}, {13366, 37944}, {13383, 44673}, {13419, 31833}, {13445, 14118}, {13596, 43651}, {14130, 37513}, {14864, 18474}, {14893, 18874}, {15026, 15687}, {15055, 21650}, {15060, 15712}, {15062, 32600}, {15122, 43839}, {15575, 44518}, {15606, 15696}, {15683, 21969}, {15726, 42450}, {15760, 20299}, {15812, 41735}, {16163, 17854}, {16195, 37487}, {16197, 32348}, {16225, 44988}, {16419, 33537}, {16618, 20417}, {17702, 17855}, {17928, 26883}, {18325, 43821}, {18388, 23335}, {18488, 37347}, {18531, 22802}, {18909, 35513}, {19149, 46373}, {19347, 37497}, {19513, 33811}, {19924, 34614}, {22401, 32445}, {22549, 41615}, {23336, 44516}, {28158, 31757}, {28172, 31760}, {29957, 37544}, {32142, 34200}, {32903, 44246}, {34224, 44458}, {34484, 43597}, {34622, 43273}, {34664, 44862}, {34782, 44241}, {35001, 43845}, {35268, 38444}, {35452, 37472}, {36518, 46431}, {37490, 44457}, {37950, 43394}, {43574, 43844}, {43576, 43602}, {43865, 44267}, {43903, 44210}

X(46850) = midpoint of X(i) and X(j) for these {i, j}: {3, 10575}, {20, 185}, {52, 1657}, {550, 13491}, {1843, 14927}, {3529, 45186}, {5562, 6241}, {6101, 45957}, {6102, 15704}, {6225, 30443}, {9961, 42448}, {10625, 34783}, {11001, 14831}, {11381, 12279}, {11562, 20127}, {12825, 17856}, {14641, 40647}, {15683, 21969}, {16163, 17854}
X(46850) = reflection of X(i) in X(j) for these (i, j): (4, 9729), (52, 13382), (382, 10110), (389, 40647), (1216, 548), (3627, 5462), (3853, 12006), (5446, 13630), (5562, 13348), (5691, 23841), (5876, 5447), (5907, 3), (10112, 18914), (10627, 44245), (11381, 44870), (11573, 31805), (11574, 44882), (11591, 33923), (11800, 974), (11807, 14708), (12133, 6723), (12162, 11793), (12370, 18128), (13202, 41671), (13419, 31833), (13474, 5), (13598, 389), (15644, 550), (16621, 9825), (18436, 15606), (32062, 6688), (32137, 3628), (36990, 9822), (44870, 17704), (45186, 16625), (45959, 3530)
X(46850) = complement of X(11381)
X(46850) = anticomplement of X(44870)
X(46850) = crossdifference of every pair of points on line {X(2451), X(6587)} >br> X(46850) = perspector of the circumconic {{A, B, C, X(43188), X(46639)}}
X(46850) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(9306)}} and {{A, B, C, X(64), X(9307)}}
X(46850) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {20, 185, 36179}, {52, 1657, 36160}
X(46850) = X(5907)-of-ABC-X3 reflections triangle
X(46850) = X(9729)-of-anti-Euler triangle
X(46850) = X(10575)-of-anti-X3-ABC reflections triangle
X(46850) = X(13474)-of-Johnson triangle
X(46850) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 11381, 44870), (2, 12279, 11381), (3, 1498, 9306), (3, 5907, 3819), (3, 12162, 11793), (3, 12315, 17814), (3, 18439, 5891), (4, 9729, 5943), (20, 15072, 185), (51, 10574, 15012), (376, 5562, 13348), (376, 6241, 5562), (382, 9730, 10110), (389, 13598, 21849), (550, 45957, 6101), (631, 12290, 15030), (1181, 13346, 34986), (1181, 21312, 13346), (3146, 10574, 51), (5446, 13630, 389), (5446, 40647, 13630), (5876, 8703, 5447), (6101, 13491, 45957), (10575, 14855, 3), (10996, 12324, 1352), (11793, 12162, 5907), (13474, 16836, 5), (13570, 15045, 5943), (15056, 15717, 5650), (16196, 16252, 5972), (17704, 44870, 2), (18435, 40247, 5907), (20791, 32062, 6688)

X(46851) = X(185)X(14487)∩X(1173)X(32062)

X(46851) lies on the Jerabek circumhyperbola and these lines: {185, 14487}, {1173, 32062}, {3426, 43806}, {3521, 14893}, {3531, 12290}, {3856, 13623}, {6415, 6494}, {6416, 6495}, {13418, 32340}, {13474, 14483}, {14157, 14528}, {14491, 43596}, {15740, 41099}, {33699, 34483}

X(46851) = isogonal conjugate of X(46853)
X(46851) = X(54)-vertex conjugate of-X(14528)

X(46852) = X(143)X(546)∩X(185)X(381)

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

X(46852) = 3*X(4)+X(1216), 13*X(4)+3*X(2979), 5*X(4)+3*X(5891), 7*X(4)+X(10625), 11*X(4)+5*X(11444), 9*X(4)+7*X(15056), 3*X(5)+X(13474), 7*X(5)-3*X(16836), X(52)-9*X(3839), X(143)-5*X(546), 3*X(143)-5*X(10110), 11*X(143)-15*X(13451), X(143)-3*X(13570), 7*X(143)-5*X(16625), 2*X(143)-5*X(44863), X(143)+5*X(44870), 3*X(143)-10*X(44871), 3*X(143)+5*X(45959), 13*X(1216)-9*X(2979), 5*X(1216)-9*X(5891), 7*X(1216)-3*X(10625), 11*X(1216)-15*X(11444), 3*X(1216)-7*X(15056), 5*X(2979)-13*X(5891), 11*X(11017)-3*X(11592), 7*X(13474)+9*X(16836)

X(46852) lies on these lines: {4, 1216}, {5, 13474}, {30, 11017}, {52, 3839}, {143, 546}, {185, 381}, {382, 10170}, {389, 3858}, {511, 3861}, {1154, 12002}, {1209, 44803}, {1593, 43586}, {1598, 4550}, {1656, 14641}, {1995, 43604}, {3091, 12290}, {3410, 18555}, {3544, 12279}, {3545, 10575}, {3567, 3832}, {3581, 33539}, {3627, 5447}, {3818, 22661}, {3843, 5446}, {3845, 5907}, {3850, 6000}, {3851, 5892}, {3853, 11793}, {3854, 6241}, {3855, 9730}, {3856, 5663}, {3857, 5943}, {3859, 13630}, {3860, 10095}, {3917, 5076}, {5056, 14855}, {5066, 9729}, {5068, 11455}, {5448, 23307}, {5650, 17800}, {5946, 41991}, {6102, 23046}, {7706, 18920}, {10546, 43898}, {10564, 43614}, {10574, 41106}, {10627, 12101}, {10996, 18489}, {11591, 14893}, {11695, 12046}, {12038, 31861}, {12102, 14128}, {12111, 41099}, {13364, 13382}, {13391, 40247}, {13487, 16270}, {13491, 38071}, {13598, 15060}, {14269, 45186}, {14449, 41987}, {15012, 18874}, {15311, 23411}, {15644, 15687}, {15738, 46686}, {16619, 32348}, {17704, 35018}, {18369, 21663}, {19357, 46261}, {20191, 44233}, {32110, 43613}, {43575, 45734}

X(46852) = midpoint of X(i) and X(j) for these {i, j}: {546, 44870}, {3627, 5447}, {3853, 11793}, {3861, 45958}, {9729, 32137}, {10110, 45959}, {12102, 14128}
X(46852) = reflection of X(i) in X(j) for these (i, j): (10110, 44871), (11695, 12811), (15012, 18874), (17704, 35018), (44863, 546)
X(46852) = X(5462)-of-Ehrmann-mid triangle
X(46852) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (143, 546, 13570), (546, 10110, 44871), (546, 45959, 10110), (1656, 32062, 14641), (3091, 16194, 40647), (3832, 16261, 12162), (3851, 11381, 5892), (3854, 6241, 14845), (3855, 11439, 9730), (5066, 32137, 9729), (10110, 44870, 45959), (10110, 44871, 44863)

X(46853) = ISOGONAL CONJUGATE OF X(46851)

X(46854) = 3*X(2)-13*X(3), 18*X(2)-13*X(5), 7*X(2)+13*X(376), 8*X(2)-13*X(549), 12*X(2)+13*X(550), 9*X(2)-13*X(631), 12*X(2)-13*X(632), 15*X(2)-13*X(1656), 3*X(2)+13*X(3522), 17*X(2)+13*X(3534), 12*X(2)-7*X(3857), 9*X(2)-4*X(3861), 17*X(2)-13*X(5071), 2*X(2)+13*X(8703), 3*X(2)+2*X(12103), X(2)+13*X(14093), 5*X(2)-13*X(15692), 7*X(2)-13*X(15693), 11*X(2)-13*X(15694), 5*X(2)+13*X(15695), 9*X(2)+13*X(15696), 11*X(2)+13*X(15697), 4*X(2)-13*X(15711), 6*X(2)-13*X(15712), 10*X(2)-13*X(15713), 2*X(2)-13*X(15714), 15*X(2)+13*X(17538), 9*X(2)+X(17800), X(2)-13*X(19708), 19*X(2)-13*X(19709), 4*X(2)+X(44903)

X(46853) lies on these lines: {2, 3}, {6, 43320}, {17, 43372}, {18, 43373}, {36, 10386}, {141, 33751}, {143, 36987}, {165, 37727}, {187, 9607}, {355, 31425}, {397, 42528}, {398, 42529}, {495, 4325}, {496, 4330}, {515, 31447}, {952, 4816}, {1152, 9681}, {1216, 45957}, {1353, 3098}, {1385, 28228}, {1483, 3579}, {1587, 6496}, {1588, 6497}, {1698, 28190}, {3411, 10646}, {3412, 10645}, {3616, 28216}, {3767, 5585}, {4293, 31480}, {4297, 37705}, {4301, 10283}, {4309, 5204}, {4316, 10592}, {4317, 5217}, {4324, 10593}, {4338, 37737}, {4652, 9945}, {4746, 5690}, {5010, 15888}, {5023, 5319}, {5206, 5346}, {5210, 5305}, {5237, 43233}, {5238, 43232}, {5267, 9710}, {5318, 42957}, {5321, 42956}, {5351, 42942}, {5352, 42943}, {5447, 13491}, {5650, 45958}, {5734, 28212}, {5881, 16192}, {5891, 11592}, {5901, 9589}, {5946, 17704}, {5965, 14810}, {5984, 38635}, {6101, 45956}, {6102, 13348}, {6199, 9693}, {6200, 19117}, {6396, 19116}, {6411, 7583}, {6412, 7584}, {6433, 43338}, {6434, 43339}, {6449, 42637}, {6450, 42638}, {6451, 6460}, {6452, 6459}, {6456, 9541}, {6684, 38138}, {7280, 37722}, {7581, 9692}, {7737, 31492}, {7738, 15655}, {7745, 31457}, {7765, 15513}, {7796, 14929}, {7987, 28174}, {8227, 28182}, {8589, 9698}, {9588, 18481}, {9606, 18907}, {9670, 15325}, {10193, 32903}, {10263, 16836}, {10264, 38726}, {10272, 15036}, {10575, 32142}, {11362, 31663}, {11542, 43193}, {11543, 43194}, {11591, 14855}, {11698, 38759}, {11749, 38701}, {12111, 44324}, {12121, 15057}, {12244, 13392}, {12512, 17502}, {13561, 30507}, {13630, 14531}, {13925, 31414}, {14073, 38706}, {14641, 15060}, {14677, 15063}, {14683, 38633}, {15051, 22251}, {15055, 23236}, {15072, 31834}, {15300, 38627}, {15326, 37719}, {15338, 37720}, {15515, 31406}, {15606, 40647}, {15935, 37582}, {16003, 34153}, {16163, 20379}, {16226, 16982}, {16772, 16960}, {16773, 16961}, {16881, 40280}, {16962, 42794}, {16963, 42793}, {16964, 42121}, {16965, 42124}, {17508, 21850}, {18990, 31452}, {19862, 28154}, {20094, 38634}, {20095, 38637}, {20396, 38727}, {20585, 43611}, {20791, 37484}, {21167, 39884}, {21663, 31804}, {23238, 38615}, {23302, 43633}, {23303, 43632}, {24470, 30282}, {25042, 40634}, {28160, 31399}, {28186, 37714}, {28194, 31666}, {31454, 42216}, {31730, 38028}, {33543, 37475}, {33750, 33878}, {34753, 37723}, {35255, 42261}, {35256, 42260}, {35812, 42259}, {35813, 42258}, {36836, 42633}, {36843, 42634}, {36967, 42778}, {36968, 42777}, {37572, 37728}, {37640, 43640}, {37641, 43639}, {40107, 44882}, {40111, 43652}, {40693, 42123}, {40694, 42122}, {42085, 42491}, {42086, 42490}, {42087, 43295}, {42088, 43294}, {42089, 42585}, {42090, 42153}, {42091, 42156}, {42092, 42584}, {42096, 43102}, {42097, 43103}, {42103, 42611}, {42106, 42610}, {42130, 42628}, {42131, 42627}, {42135, 42489}, {42138, 42488}, {42144, 42682}, {42145, 42683}, {42149, 42626}, {42150, 42913}, {42151, 42912}, {42152, 42625}, {42159, 42774}, {42162, 42773}, {42492, 43240}, {42493, 43241}, {42512, 43238}, {42513, 43239}, {42532, 42994}, {42533, 42995}, {42580, 43402}, {42581, 43401}, {42590, 42921}, {42591, 42920}, {42694, 43636}, {42695, 43637}, {42888, 43647}, {42889, 43648}, {42928, 43008}, {42929, 43009}, {42936, 42941}, {42937, 42940}, {43197, 43869}, {43198, 43870}, {43291, 44519}

X(46853) = midpoint of X(i) and X(j) for these {i, j}: {3, 3522}, {20, 3843}, {376, 15693}, {550, 632}, {631, 15696}, {1656, 17538}, {3534, 5071}, {5059, 35407}, {8703, 15714}, {11001, 35434}, {14093, 19708}, {15692, 15695}, {15694, 15697}, {15699, 36670}
X(46853) = reflection of X(i) in X(j) for these (i, j): (4, 12812), (5, 631), (549, 15711), (632, 15712), (3091, 140), (3627, 3858), (3858, 632), (3859, 45760), (8703, 14093), (15686, 15697), (15687, 19709), (15694, 12100), (15696, 548), (15711, 15714), (15712, 3), (15713, 15692), (15714, 19708), (17578, 3859), (19708, 34200), (22251, 15051)
X(46853) = isogonal conjugate of X(46851)
X(46853) = complement of X(5076)
X(46853) = X(3522)-of-anti-X3-ABC reflections triangle
X(46853) = X(12812)-of-anti-Euler triangle
X(46853) = X(15712)-of-ABC-X3 reflections triangle
X(46853) = X(31274)-of-Moses-Steiner osculatory triangle
X(46853) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 3861, 5), (3, 376, 140), (3, 548, 5), (3, 15688, 4), (4, 16239, 5), (20, 3530, 5), (140, 382, 5), (140, 15759, 3), (376, 5067, 20), (382, 15717, 140), (546, 5070, 5), (548, 3530, 20), (550, 44682, 5), (550, 45759, 3), (1656, 3859, 5), (3091, 15693, 140), (3522, 19708, 3), (3523, 15710, 3), (3526, 3853, 5), (3528, 21734, 3), (3628, 3832, 5), (3843, 15696, 20), (3850, 7486, 5), (3856, 5067, 5), (12100, 44245, 4), (14869, 15686, 4), (15036, 38788, 10272), (15712, 15714, 3), (17578, 45760, 5), (21734, 33923, 5), (33923, 34200, 3), (43320, 43321, 6)

X(46854) = X(4)X(14)∩X(16)X(115)

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

X(46854) lies on these lines: {2, 5470}, {3, 22510}, {4, 14}, {6, 13102}, {13, 2782}, {15, 2549}, {16, 115}, {17, 619}, {18, 16630}, {30, 12204}, {61, 7765}, {140, 22893}, {148, 22689}, {182, 6034}, {202, 10077}, {203, 18975}, {376, 30560}, {383, 22692}, {395, 20253}, {542, 41107}, {574, 46054}, {617, 16529}, {633, 46709}, {635, 11128}, {3105, 20425}, {3458, 44462}, {5237, 21157}, {5309, 36759}, {5335, 6778}, {5460, 16963}, {5464, 16267}, {5469, 41100}, {5978, 32466}, (6034, 6321, 46855), {6109, 36968}, {6114, 16808}, {6780, 37640}, {6783, 16941}, {7005, 13075}, {7006, 10061}, {7790, 22687}, {9166, 13084}, {9736, 38224}, {9750, 41036}, {9763, 22571}, {9886, 22489}, {9981, 22513}, {10612, 16268}, {10614, 39563}, {11085, 11626}, {11179, 41108}, {13083, 32480}, {14651, 33389}, {14905, 34509}, {19106, 22512}, {22490, 37171}, {22797, 42813}, {22847, 38229}, {22848, 42489}, {22997, 42974}, {25166, 41746}, {29012, 36758}, {33813, 36782}, {35230, 42943}, {35692, 36763}, {37178, 42488}, {41043, 42973}

X(46854) = midpoint of X(i) and X(j) for these {i, j}: {14, 16965}, {633, 46709}
X(46854) = reflection of X(i) in X(j) for these (i, j): (14, 36252), (11128, 635)
X(46854) = inverse of X(14705) in outer-Napoleon circle
X(46854) = inverse of X(31704) in Kiepert circumhyperbola
X(46854) = inner-Napoleon-to-outer-Napoleon similarity image of X(61); see X(46855)
X(46854) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (16, 115, 46053), (16, 22891, 6774), (115, 6774, 22891), (182, 11648, 46855), (617, 40693, 16529), (5479, 14137, 14), (6774, 22891, 46053), (10653, 43455, 62), (14137, 31709, 5479), (35850, 35851, 23004), (43454, 44461, 15)

X(46855) = X(4)X(13)∩X(15)X(115)

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

X(46855) lies on these lines: {2, 5469}, {3, 22511}, {4, 13}, {6, 13103}, {14, 2782}, {15, 115}, {16, 2549}, {17, 16631}, {18, 618}, {30, 12205}, {62, 7765}, {140, 22847}, {148, 22687}, {182, 6034}, {202, 18974}, {203, 10078}, {376, 30559}, {396, 20252}, {542, 41108}, {574, 46053}, {616, 16530}, {634, 46708}, {636, 11129}, {1080, 22691}, {3104, 20426}, {3457, 44466}, {5238, 21156}, {5309, 36760}, {5334, 6777}, {5459, 16962}, {5463, 16268}, {5470, 41101}, {5979, 32465}, {6108, 36967}, {6115, 16809}, {6779, 37641}, {6782, 16940}, {7005, 10062}, {7006, 13076}, {7790, 22689}, {9166, 13083}, {9735, 38224}, {9749, 41037}, {9761, 22572}, {9885, 22490}, {9982, 22512}, {10611, 16267}, {10613, 39563}, {10645, 36772}, {11080, 11624}, {11179, 41107}, {13084, 32480}, {14651, 33388}, {14904, 34508}, {18581, 36766}, {19107, 22513}, {22489, 37170}, {22796, 42814}, {22892, 42488}, {22893, 38229}, {22998, 42975}, {25156, 41745}, {29012, 36757}, {35229, 42942}, {36763, 37832}, {36769, 42507}, {36770, 37177}, {36771, 42919}, {41042, 42972}

X(46855) = midpoint of X(i) and X(j) for these {i, j}: {13, 16964}, {634, 46708}
X(46855) = reflection of X(i) in X(j) for these (i, j): (13, 36251), (11129, 636)
X(46855) = inverse of X(14704) in inner-Napoleon circle
X(46855) = inverse of X(31703) in Kiepert circumhyperbola
X(46855) = outer-Napoleon-to-inner-Napoleon similarity image of X(62); see X(46854)
X(46855) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (15, 115, 46054), (15, 22846, 6771), (115, 6771, 22846), (182, 11648, 46854), (616, 40694, 16530), (5478, 14136, 13), (6034, 6321, 46854), (6771, 22846, 46054), (10654, 43454, 61), (14136, 31710, 5478), (35753, 35754, 23005), (43455, 44465, 16)

X(46856) = EULER LINE INTERCEPT OF X(3180)X(9214)

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

X(46856) lies on these lines: {2, 3}, {3180, 9214}, {9140, 16770}, {16771, 20423}, {21466, 30465}, {33884, 33957}

X(46856) = reflection of X(46857) in X(18867)
X(46856) = complement of X(46860)
X(46856) = anticomplement of X(46824)
X(46856) = {X(4),X(31105)}-harmonic conjugate of X(46857)
X(46856) = {X(381), X(36186)}-harmonic conjugate of X(2)

X(46857) = EULER LINE INTERCEPT OF X(3181)X(9214)

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

X(46857) lies on these lines: {2, 3}, {3181, 9214}, {9140, 16771}, {16770, 20423}, {21467, 30468}, {33884, 33958}

X(46857) = reflection of X(46856) in X(18867)
X(46857) = complement of X(46861)
X(46857) = anticomplement of X(46825)
X(46857) = {X(381), X(36185)}-harmonic conjugate of X(2)
X(46857) = {X(4),X(31105)}-harmonic conjugate of X(46856)

X(46858) = EULER LINE INTERCEPT OF X(125)X(5459)

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

X(46858) lies on these lines: {2, 3}, {125, 5459}, {396, 18777}, {623, 13857}, {5650, 33957}, {6669, 34296}, {7684, 32225}, {8838, 9140}, {21466, 43416}, {25154, 40709}

X(46858) = midpoint of X(18867) and X(46825)
X(46858) = complement of X(46824)
X(46858) = anticomplement of X(46862)
X(46858) = {X(2), X(36186)}-harmonic conjugate of X(549)

X(46859) = EULER LINE INTERCEPT OF X(125)X(5460)

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

X(46859) lies on these lines: {2, 3}, {125, 5460}, {395, 18776}, {624, 13857}, {5650, 33958}, {6670, 34295}, {7685, 32225}, {8836, 9140}, {21467, 43417}, {25164, 40710}

X(46859) = midpoint of X(18867) and X(46824)
X(46859) = complement of X(46825)
X(46859) = anticomplement of X(46863)
X(46859) = {X(2), X(36185)}-harmonic conjugate of X(549)

X(46860) = EULER LINE INTERCEPT OF X(16981)X(33957)

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

X(46860) lies on these lines: {2, 3}, {16981, 33957}, {21466, 36967}, {25154, 41472}

X(46860) = anticomplement of X(46856)
X(46860) = anticomplement of the anticomplement of X(46824)
X(46860) = {X(376), X(44466)}-harmonic conjugate of X(2)

X(46861) = EULER LINE INTERCEPT OF X(16981)X(33958)

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

X(46861) lies on these lines: {2, 3}, {16981, 33958}, {21467, 36968}, {25164, 41473}

X(46861) = anticomplement of X(46857)
X(46861) = anticomplement of the anticomplement of X(46825)
X(46861) = {X(376), X(44462)}-harmonic conjugate of X(2)

X(46862) = EULER LINE INTERCEPT OF X(5642)X(46833)

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

X(46862) = complement of X(46858)
X(46862) = complement of the complement of X(46824)
X(46862) = {X(2), X(32461)}-harmonic conjugate of X(547)

X(46863) = EULER LINE INTERCEPT OF X(5642)X(46834)

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

X(46863) = complement of X(46859)
X(46863) = complement of the complement of X(46825)
X(46863) = {X(2), X(32460)}-harmonic conjugate of X(547)

X(46864) = (name pending)

X(46865) = ISOGONAL CONJUGATE OF X(46864)

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 + a^4*b^2*c^2 + 17*a^2*b^4*c^2 - 9*b^6*c^2 + 9*a^4*c^4 + 17*a^2*b^2*c^4 + 18*b^4*c^4 - 3*a^2*c^6 - 9*b^2*c^6) : :

X(46865) = (20 - 3*J^2)*X[3] + 12*X[143], (12 - 3*J^2)*X[54] + 20*X[632], 3*J^2*X[110] - 32*X[3628], 3*(9 - J^2)*X[182] + 5*X[3091]

X(46865) lies on these lines: {2, 9706}, {3, 143}, {54, 632}, {110, 3628}, {182, 3091}, {567, 14869}, {569, 3525}, {575, 15801}, {1614, 5079}, {3090, 5012}, {3518, 5643}, {3529, 13336}, {3627, 37471}, {5050, 11444}, {6689, 15059}, {7496, 37505}, {7512, 12834}, {7565, 46267}, {7605, 13419}, {9545, 22112}, {9729, 13417}, {10303, 34148}, {11562, 15054}, {12103, 13339}, {12108, 43574}, {12811, 14157}, {13160, 32233}, {13482, 15712}, {14118, 43603}, {15028, 37476}, {16239, 43572}, {16625, 37126}, {27866, 36253}, {34864, 43600}, {36749, 41462}

X(46866) = X(3)X(6)∩X(4)X(6752)

X(46866) lies on these lines: {3, 6}, {4, 6752}, {24, 44088}, {51, 42374}, {184, 19170}, {185, 33971}, {3060, 8613}, {5890, 41204}, {11427, 37872}, {18925, 19197}

X(46866) = perspector of the circumconic {{A, B, C, X(110), X(42401)}}
X(46866) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(42374)}} and {{A, B, C, X(182), X(37872)}}

X(46867) = (name pending)

Barycentrics 5*(b^2+c^2)*a^16-2*(11*b^4+14*b^2*c^2+11*c^4)*a^14+3*(b^2+c^2)*(11*b^4+8*b^2*c^2+11*c^4)*a^12-(10*b^8+10*c^8+b^2*c^2*(59*b^4+46*b^2*c^2+59*c^4))*a^10-(b^2+c^2)*(25*b^8+25*c^8-b^2*c^2*(72*b^4-61*b^2*c^2+72*c^4))*a^8+(b^2-c^2)^2*(30*b^8+30*c^8+b^2*c^2*(4*b^2+5*b*c+4*c^2)*(4*b^2-5*b*c+4*c^2))*a^6-(b^4-c^4)*(b^2-c^2)*(13*b^8+13*c^8-5*b^2*c^2*(4*b^4-3*b^2*c^2+4*c^4))*a^4+(b^2-c^2)^4*(2*b^8+2*c^8-5*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^2+2*(b^2-c^2)^6*(b^2+c^2)*b^2*c^2 : :

X(46868) = EULER LINE INTERCEPT OF X(6)X(14611)

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

X(46868) lies on these lines: {2, 3}, {6, 14611}, {110, 46129}, {476, 10545}, {523, 5640}, {1302, 41254}, {1304, 36794}, {2453, 3066}, {3233, 10546}, {3258, 19130}, {7693, 14731}, {7706, 46045}, {14389, 16319}, {14480, 15019}

X(46868) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (381, 44889, 2), (1316, 1995, 7471)

X(46869) = EULER LINE INTERCEPT OF X(69)X(3233)

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

X(46869) lies on these lines: {2, 3}, {69, 3233}, {523, 35260}, {542, 46808}, {2453, 15448}, {6776, 11657}, {12079, 39874}, {22104, 46264}

X(46869) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 1651, 2), (381, 44891, 2), (3081, 44891, 381)

X(46870) = EULER LINE INTERCEPT OF X(7)X(41574)

As a point on the Euler line, X(46870) has Shinagawa coefficients (6*R*r+2*r^2+E, 8*R*r+6*r^2).

X(46870) lies on these lines: {2, 3}, {7, 41574}, {226, 5086}, {329, 10895}, {758, 9612}, {1864, 8261}, {3485, 5175}, {3486, 11281}, {3586, 35016}, {3869, 40661}, {4867, 6737}, {6045, 41723}, {6738, 11263}, {7701, 15239}, {10572, 26725}

X(46870) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 442, 21), (4, 6843, 6828), (4, 6856, 452), (4, 6874, 6913)

X(46871) = X(3)X(142)∩X(141)X(31399)

X(46871) lies on these lines: {3, 142}, {141, 31399}, {3739, 38127}, {4648, 5882}, {4859, 13464}, {10175, 21255}

X(46872) = X(8)X(4072)∩X(10)X(38255)

X(46872) lies on these lines: {8, 4072}, {10, 38255}, {85, 45789}, {312, 4678}, {333, 3621}, {3617, 6557}, {3623, 30608}, {20052, 30711}

X(46872) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(8)}} and {{A, B, C, X(9), X(45789)}}
X(46872) = trilinear pole of the line {522, 14350}

X(46873) = X(2)X(7)∩X(8)X(3817)

X(46873) lies on these lines: {2, 7}, {8, 3817}, {20, 22792}, {72, 5056}, {78, 3832}, {145, 1837}, {200, 9779}, {354, 11678}, {936, 37161}, {962, 27525}, {1997, 4869}, {2886, 3614}, {2894, 6896}, {2975, 8167}, {3091, 3419}, {3146, 27383}, {3436, 3622}, {3485, 8165}, {3522, 27385}, {3543, 5440}, {3545, 3940}, {3600, 25681}, {3621, 24392}, {3672, 37662}, {3698, 3740}, {3816, 11038}, {3838, 40333}, {3854, 5175}, {3912, 6557}, {3927, 5067}, {4187, 11036}, {4358, 20921}, {4417, 29616}, {4430, 17615}, {4678, 11682}, {4855, 5059}, {4997, 18141}, {5129, 11374}, {5180, 5552}, {5223, 10171}, {5281, 24703}, {5550, 12527}, {5714, 17580}, {5815, 8227}, {5828, 7982}, {6554, 28656}, {6734, 15022}, {6745, 9812}, {6945, 7956}, {6987, 37713}, {7672, 18236}, {7988, 21060}, {9581, 20008}, {9945, 15682}, {10157, 41228}, {11037, 25522}, {11106, 13411}, {11813, 34619}, {12125, 17609}, {12526, 19877}, {14986, 21077}, {17300, 41913}, {17604, 30628}, {18743, 30807}, {20060, 24558}, {26136, 37683}, {27340, 30812}, {29627, 30695}, {30694, 30833}, {30711, 37656}

X(46873) = anticomplement of the isotomic conjugate of X(38255)
X(46873) = perspector of the circumconic {{A, B, C, X(664), X(42408)}}
X(46873) = intersection, other than A, B, C, of circumconics {{A, B, C, X(57), X(11531)}} and {{A, B, C, X(144), X(6557)}}
X(46873) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 20059, 5435), (7, 30827, 2), (226, 5328, 2), (329, 5748, 30852), (329, 30852, 2), (908, 5748, 2), (908, 30852, 329), (3452, 5226, 2), (5087, 25568, 5274), (5219, 18228, 2), (5274, 25568, 145), (5435, 28609, 20059)

X(46874) = X(4)X(80)∩X(109)X(1698)

X(46874) lies on these lines: {4, 80}, {109, 1698}, {3454, 6700}, {5932, 21296}, {13539, 20262}

X(46875) = X(145)X(17056)∩X(3622)X(3752)

X(46876) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MALFATTI-TOUCHPOINTS TO BCI

Let A' be the touchpoint of the B- and C-Malfatti circles and define B', C' cyclically. The triangle A'B'C' is named here the Malfatti-touchpoints triangle of ABC. Barycentric coordinates of A' are:

A' = a*(1+y)*(1+z)/(1+x) : b*(1+z)^2 : c*(1+y)^2, where {x, y, z} = {cos(A/2), cos(B/2), cos(C/2)}

Malfatti-touchpoints triangle is perspective to the following triangles with the indicated perspector: (ABC, X(179)), (excentral, X(180)), (Malfatti, X(31495)), (2nd tangential-midarc, X(483)).

Malfatti-touchpoints triangle is orthologic to the following triangles with the given centers: (BCI, X(46876), X(483)), (Malfatti, X(483), X(483)).

X(46877) = X(1)X(333)∩X(9)X(21)

X(46877) lies on these lines: {1, 333}, {9, 21}, {29, 27411}, {56, 18206}, {57, 37442}, {58, 997}, {63, 4225}, {72, 859}, {73, 4416}, {81, 19861}, {86, 8583}, {101, 1791}, {200, 341}, {213, 37539}, {274, 40719}, {386, 13725}, {391, 4270}, {573, 34259}, {936, 1010}, {960, 4267}, {978, 25527}, {1038, 24632}, {1193, 4357}, {1490, 7415}, {1792, 2328}, {2271, 5283}, {3216, 5233}, {3419, 37357}, {3616, 16713}, {3687, 40976}, {3811, 4653}, {3882, 22076}, {3940, 29531}, {3984, 7419}, {4184, 4855}, {4276, 12514}, {5044, 19259}, {5208, 11523}, {5235, 19860}, {5289, 18178}, {5438, 13588}, {5440, 17524}, {5730, 18180}, {5739, 46016}, {5741, 24984}, {6282, 37422}, {7963, 18186}, {9581, 37373}, {10381, 28258}, {10449, 25513}, {10470, 16552}, {10477, 28383}, {10479, 25519}, {11103, 27412}, {11115, 27064}, {11679, 25515}, {11682, 41723}, {12635, 18165}, {13738, 16574}, {14011, 30827}, {15829, 18163}, {16454, 27381}, {17588, 34772}, {24931, 28810}, {25526, 31631}, {27622, 29472}, {28920, 37522}, {30282, 37296}, {31424, 37303}, {31623, 39585}

X(46877) = X(i)-Ceva conjugate of X(j) for these (i,j): {333, 2269}, {3699, 7253}
X(46877) = crosspoint of X(1043) and X(1098)
X(46877) = crosssum of X(1042) and X(1254)
X(46877) = X(i)-isoconjugate of X(j) for these (i,j): {65, 961}, {1042, 1220}, {1169, 6354}, {1254, 2363}, {1402, 31643}, {1407, 14624}, {1426, 1791}, {1427, 2298}, {4017, 36098}, {6648, 7180}, {7178, 8687}, {7216, 36147}, {7250, 8707}, {20617, 40453}
X(46877) = barycentric product X(i)*X(j) for these {i,j}: {8, 17185}, {21, 3687}, {86, 3965}, {200, 16705}, {220, 16739}, {261, 21033}, {312, 4267}, {314, 2269}, {333, 960}, {341, 40153}, {643, 3910}, {645, 17420}, {1043, 3666}, {1098, 1211}, {1792, 1848}, {2185, 3704}, {2287, 4357}, {2292, 7058}, {2328, 20911}, {3004, 7259}, {3882, 7253}, {6061, 45196}, {6371, 7258}, {7054, 18697}, {20967, 28660}, {22074, 44130}
X(46877) = barycentric quotient X(i)/X(j) for these {i,j}: {200, 14624}, {284, 961}, {333, 31643}, {643, 6648}, {960, 226}, {1021, 4581}, {1043, 30710}, {1098, 14534}, {1193, 1427}, {2092, 1254}, {2269, 65}, {2287, 1220}, {2292, 6354}, {2300, 1042}, {2327, 1791}, {2328, 2298}, {2354, 1426}, {3666, 3668}, {3687, 1441}, {3704, 6358}, {3882, 4566}, {3910, 4077}, {3965, 10}, {4267, 57}, {4357, 1446}, {5546, 36098}, {6371, 7216}, {7054, 2363}, {7259, 8707}, {16705, 1088}, {17185, 7}, {17420, 7178}, {18235, 4032}, {20967, 1400}, {21033, 12}, {22074, 73}, {22076, 37755}, {22097, 1439}, {40153, 269}, {40966, 2171}, {40976, 1880}
X(46877) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {72, 859, 10461}, {960, 4267, 17185}

Let Ap, Bp,Cp be as in the preambles just before X(46738) and X(46779). The locus of a point X = x : y : z such that the anticevian triangle of X is perspective to the triangle ApBpCp is given by the following cubic:

p(m q + n r)(m y^2 z - n y z^2) + (cyclic) = 0,

which, in the Gibert classification system, is pK(-m n p (m q + n r) : : , m n : : ).

In the following list, the appearance of {j,{Knnn},{{h1, h2, ...}} means that if P = X(1) and L is given by l x + m y + n z = 0, Where l : m : n = X(j), then the cubic passes through the points X(h₁), X(h₂), . . .

{2,{K345},{1,2,9,10,37,226,281,1214,7952,39131}}
{4,{},{1,69,72,306,1439,1763,7289,17170,17441}}
{8,{},{1,7,57,142,354,10481,15185,40154}}
{10,{},{1,2,86,3720,17175,18166,39734}}
{69,{},{1,4,46,65,225,2362,16232}}
{83,{},{1,141,3954,15523,16555,17192,17456,18183}}
{85,{},{1,9,55,165,220,2066,4166,5414}}
{92,{},{1,3,48,63,219,222,255,268,610,7011}}
{226,{},{1,8,9,283,284,333,573,2269,3687,4267,17185,46877,46878,46879,46880,46881}}
{253,{},{1,20,1394,3182,5930,40933,44696}}
{305,{},{1,25,1402,1716,7083,40934,40987}}
{306,{},{1,27,57,58,278,579,1474,1838,2260,5249,46882,46883,46884,46885,46886,46887}}
{312,{},{1,6,56,57,266,289,1743,40151}}
{329,{},{1,4,57,189,1422,2262,2270,7003,20262}}
{333,{},{1,37,65,226,442,1781,2294,8818}}
{368,{},{1,2,9,10,37,226,281,1214,7952,39131}}
{370,{},{1,2,9,10,37,226,281,1214,7952,39131}}
{556,{K748},{1,173,174,177,236,7707,12646,16015,41799}}
{693,{},{1,100,513,1381,1382,3307,3308}}
{918,{},{1,239,294,644,666,885,3573,4435,4560}}

In the following list, the appearance of {j,{Knnn},{{h1, h2, ...}} means that if P = X(2) and L is given by l x + m y + n z = 0, Where l : m : n = X(j), then the cubic passes through the points X(h₁), X(h₂), . . .

{1,{K366},{2,8,10,75,307,318,321,1441}}
{3,{K674},{2,4,5,264,311,324,847,39113,39114,39115,39116,39117}}
{4,{K099},{2,3,20,63,69,77,78,271,394,7013,15394,46351}}
{7,{},{2,8,9,144,200,4182,30556,30557}}
{8,{K365},{1,2,7,57,145,174,1488,2089,19604,44301}}
{10,{},{1,2,86,1125,8025,16709,39949}}
{19,{},{2,304,306,4329,17170,18589,20336,28409}}
{21,{},{2,10,226,442,1441,2475,6757}}
{37,{},{2,75,274,3739,16748,17175,29773,40004}}
{40,{},{2,7,92,309,946,962,1440,7020,23528}}
{52,{},{2,69,97,1216,11412,20563,34385}}
{54,{},{2,5,311,343,1209,1225,2888,25043}}
{63,{},{2,92,226,1659,5905,13390,40149}}
{64,{},{2,20,2883,6225,14249,14615,37669}}
{65,{},{2,8,21,312,314,960,1812,3869,17185}}
{66,{},{2,22,206,315,5596,8743,20806,36414}}
{67,{},{2,23,316,6593,7664,11061,14246,22151}}
{68,{},{2,24,317,1147,1993,6193,9723,34756}}
{69,{K233},{2,4,6,25,193,371,372,2362,7133,14248,16232,20034,41515,41516,42013}}
{72,{},{2,7,28,81,273,286,942,3868,39267}}
{74,{},{2,30,113,146,3260,11064,14254}}
{79,{},{2,319,3219,3578,3647,3648,4420}}
{80,{},{2,214,320,3218,4511,6224,41801}}
{82,{},{2,1930,15523,17192,21249,21289,28676}}
{84,{},{2,322,329,342,6223,6260,7080}}
{95,{},{2,5,233,3078,17035,36300,36301}}
{113,{},{2,69,74,6699,12028,40423,40630}}
{191,{},{2,86,11263,14450,30690,42005,44188}}
{257,{},{2,894,1909,17103,27697,28369,41318}}
{265,{},{2,186,323,340,1511,6148,12383,14920,38936}}
{290,{},{2,237,511,2967,3289,11672,14251,23611,36790,39355,46888}}
{304,{},{2,19,1400,1880,2082,8020,16583,21216,30677}}
{306,{},{2,27,57,278,3187,40574,40940}}
{320,{},{2,44,80,7126,19551,20072,40172}}
{511,{},{2,290,511,32618,32619,44780,44781}}
{523,{K242},{2,99,523,1113,1114,3413,3414,6189,6190,22339,22340,30508,30509}}
{525,{},{2,525,648,2479,2480,2592,2593,8115,8116}}
{659,{},{2,693,3263,3837,4444,4583,43534,46403}}
{684,{},{2,98,107,6130,16089,22456,43665}}
{690,{K240},{2,99,523,524,671,690,892,5466,5468}}
{850,{},{2,110,184,647,5638,5639,31296}}
{888,{},{2,512,538,670,886,888,3228}}
{891,{},{2,513,536,668,889,891,3227,41314,43928}}
{900,{},{2,190,514,519,900,903,4555,6548,17780}}

In the following list, the appearance of {j,{Knnn},{{h1, h2, ...}} means that if P = X(6) and L is given by l x + m y + n z = 0, Where l : m : n = X(j), then the cubic passes through the points X(h₁), X(h₂), . . .

{2,{K836},{2,3,6,39,141,427,5403,5404,14376,40938}}
{69,{K350},{4,5,6,25,51,52,53,14593}}
{75,{K362},{1,6,33,37,42,55,65,73,2331,41086,41087,41088}}
{92,{},{6,63,71,72,1473,3556,7289,23620}}
{253,{},{6,20,154,1661,2883,6525,15905}}
{264,{K576},{3,6,48,154,184,212,577,603,2188,7114,14379}}
{304,{},{6,19,1400,1880,2178,6203,6204}}
{306,{},{6,27,58,1474,1860,14377,23383,34830,40955}}
{312,{},{6,56,57,354,1418,1475,17107}}
{322,{},{6,19,56,84,1413,7008,20991}}
{328,{},{6,50,186,1511,14385,34397,39176}}
{368,{},{2,3,6,39,141,427,5403,5404,14376,40938}}
{370,{},{2,3,6,39,141,427,5403,5404,14376,40938}}
{427,{},{3,6,69,1799,10547,15270,45201}}
{850,{K1067},{6,110,512,1379,1380,2574,2575,5638,5639,41880,41881,44123,44124}}

In the following list, the appearance of {j,{Knnn},{{h1, h2, ...}} means that if P = X(75) and L is given by l x + m y + n z = 0, Where l : m : n = X(j), then the cubic passes through the points X(h₁), X(h₂), . . .

{6,{},{75,76,312,313,321,349,1231,7017}}
{9,{},{2,7,75,85,4146,18743,27818,27828}}
{19,{},{63,69,75,304,326,345,348,18750,44189}}
{63,{},{1,19,75,92,1659,7090,13390,14121,18156}}
{71,{},{27,75,85,86,331,5249,18134,44129}}
{144,{},{7,75,9311,10405,11019,36620,41006}}
{333,{},{37,65,75,226,1211,2292,41003}}
{673,{},{75,518,3693,3912,4437,4712,22116}}
{812,{},{75,513,876,1575,2254,3252,4562,30941,42720}}
{900,{},{75,320,664,903,4453,4555,6548,7192}}

In the following list, the appearance of {j,{Knnn},{{h1, h2, ...}} means that if P = X(76) and L is given by l x + m y + n z = 0, Where l : m : n = X(j), then the cubic passes through the points X(h₁), X(h₂), . . .

{3,{},{2,4,76,264,491,492,34208}}
{20,{},{4,76,253,459,9307,13567,41005}}
{21,{},{10,76,226,1211,1441,18697,45196}}
{25,{},{69,76,304,305,3718,3926,7182,14615}}
{98,{},{76,325,511,23098,32458,36212,36790,40810}}
{105,{},{76,3263,3717,3912,4437,23102,40217}}
{523,{},{3,76,99,525,2479,2480,3413,3414}}
{659,{},{76,514,726,918,4444,4583,18157,22116,43534}}
{684,{},{76,98,1289,14618,22456,43665,44145}}
{690,{},{76,316,648,671,892,5466,9979,14246}}
{804,{},{76,512,882,2396,3229,3569,14251,18829,20022}}

X(46878) = X(1)X(406)∩X(2)X(34)

X(46878) lies on these lines: {1, 406}, {2, 34}, {4, 9}, {8, 33}, {11, 40964}, {12, 1875}, {20, 34822}, {21, 34851}, {24, 993}, {25, 958}, {28, 5745}, {29, 270}, {47, 1724}, {63, 1452}, {65, 13567}, {72, 1905}, {78, 28807}, {92, 225}, {108, 10106}, {124, 1845}, {132, 5514}, {162, 2363}, {186, 5267}, {204, 5716}, {208, 388}, {219, 5814}, {221, 10361}, {232, 1107}, {235, 2886}, {264, 6376}, {297, 26558}, {307, 20914}, {318, 341}, {378, 25440}, {403, 25639}, {405, 11398}, {427, 1329}, {429, 960}, {442, 6708}, {451, 1125}, {458, 25007}, {461, 4847}, {468, 4999}, {475, 1698}, {515, 1610}, {519, 6198}, {607, 37658}, {860, 1838}, {908, 1866}, {942, 26932}, {950, 4183}, {956, 11399}, {1040, 27505}, {1146, 1834}, {1172, 3686}, {1210, 1453}, {1213, 1841}, {1235, 6381}, {1330, 1944}, {1376, 1593}, {1377, 3093}, {1378, 3092}, {1398, 25524}, {1426, 5236}, {1441, 25017}, {1448, 20266}, {1528, 12672}, {1573, 3199}, {1574, 33843}, {1585, 6348}, {1586, 6347}, {1594, 3814}, {1595, 3820}, {1596, 31419}, {1597, 9709}, {1598, 9708}, {1783, 5280}, {1785, 10039}, {1824, 1904}, {1835, 5249}, {1852, 3683}, {1859, 21677}, {1862, 3036}, {1867, 1894}, {1868, 31993}, {1872, 5690}, {1874, 25978}, {1876, 3812}, {1877, 5294}, {1878, 1883}, {1887, 40663}, {1888, 3925}, {1902, 5836}, {1906, 9710}, {1907, 9711}, {1968, 4386}, {2212, 3883}, {2262, 5799}, {2303, 3194}, {2332, 3684}, {2355, 18253}, {2478, 11393}, {2975, 35973}, {3035, 12138}, {3041, 5185}, {3089, 19843}, {3195, 5710}, {3422, 10570}, {3436, 11392}, {3452, 5142}, {3541, 26364}, {3542, 26363}, {3687, 40976}, {3704, 3965}, {3714, 40997}, {3741, 4213}, {3869, 30687}, {3878, 41722}, {3913, 7071}, {3975, 31623}, {4109, 40869}, {4185, 5155}, {4186, 5090}, {4196, 26037}, {4198, 5273}, {4200, 9780}, {4205, 40937}, {4207, 31330}, {4222, 5795}, {4267, 19608}, {4297, 37441}, {4357, 45196}, {4426, 10311}, {4858, 23537}, {5016, 27410}, {5101, 17516}, {5125, 5342}, {5174, 14004}, {5190, 45162}, {5255, 8750}, {5275, 46835}, {5289, 11396}, {5302, 37398}, {5307, 31339}, {5412, 31453}, {5791, 7497}, {5794, 37194}, {5837, 39579}, {6245, 37028}, {6353, 30478}, {6559, 36124}, {6623, 31418}, {6684, 37305}, {6736, 7046}, {6995, 29667}, {7378, 8165}, {7414, 17647}, {7511, 31445}, {7531, 14058}, {7952, 31397}, {9284, 9367}, {9895, 30444}, {9943, 12136}, {12294, 17792}, {13161, 20883}, {15149, 24603}, {16832, 37382}, {17171, 21246}, {17923, 24564}, {18344, 20317}, {19808, 37087}, {20323, 23711}, {20888, 44146}, {24474, 41587}, {25640, 45776}, {25681, 30811}, {26001, 37448}, {26153, 27022}, {27091, 37337}, {28076, 36568}, {31424, 37395}, {32777, 37318}, {34589, 35201}, {34591, 39039}, {37391, 37828}

X(46878) = complement of X(4296)
X(46878) = isotomic conjugate of the isogonal conjugate of X(40976)
X(46878) = isotomic conjugate of cevapoint of X(63) and X(73)
X(46878) = polar conjugate of the isotomic conjugate of X(3687)
X(46878) = polar conjugate of the isogonal conjugate of X(2269)
X(46878) = X(i)-complementary conjugate of X(j) for these (i,j): {8615, 1}, {15314, 2886}
X(46878) = X(162)-Ceva conjugate of X(522)
X(46878) = X(i)-cross conjugate of X(j) for these (i,j): {2269, 3687}, {2292, 960}
X(46878) = cevapoint of X(i) and X(j) for these (i,j): {429, 2292}, {2269, 40976}
X(46878) = crosspoint of X(i) and X(j) for these (i,j): {29, 318}, {92, 44130}
X(46878) = crosssum of X(73) and X(603)
X(46878) = X(i)-isoconjugate of X(j) for these (i,j): {3, 961}, {56, 1791}, {57, 2359}, {65, 1798}, {73, 2363}, {184, 31643}, {222, 2298}, {603, 1220}, {905, 8687}, {1169, 1214}, {1409, 14534}, {1415, 15420}, {1459, 36098}, {4581, 36059}, {6648, 22383}
X(46878) = barycentric product X(i)*X(j) for these {i,j}: {4, 3687}, {8, 1848}, {27, 3704}, {29, 1211}, {33, 20911}, {76, 40976}, {92, 960}, {264, 2269}, {273, 3965}, {281, 4357}, {286, 21033}, {312, 1829}, {318, 3666}, {333, 429}, {1172, 18697}, {1193, 7017}, {1228, 2299}, {1897, 3910}, {1969, 20967}, {2092, 44130}, {2292, 31623}, {2322, 41003}, {2354, 3596}, {3674, 7046}, {3882, 44426}, {4183, 45196}, {6335, 17420}, {7101, 24471}, {17185, 41013}, {17555, 19608}, {20653, 46103}, {21124, 36797}, {28660, 44092}, {40966, 44129}
X(46878) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 1791}, {19, 961}, {29, 14534}, {33, 2298}, {55, 2359}, {92, 31643}, {281, 1220}, {284, 1798}, {318, 30710}, {429, 226}, {444, 7175}, {522, 15420}, {960, 63}, {1172, 2363}, {1193, 222}, {1211, 307}, {1682, 22097}, {1783, 36098}, {1829, 57}, {1848, 7}, {1897, 6648}, {2092, 73}, {2269, 3}, {2292, 1214}, {2299, 1169}, {2300, 603}, {2354, 56}, {3064, 4581}, {3666, 77}, {3674, 7056}, {3687, 69}, {3704, 306}, {3725, 1409}, {3882, 6516}, {3910, 4025}, {3965, 78}, {4267, 1790}, {4357, 348}, {7017, 1240}, {8750, 8687}, {17185, 1444}, {17420, 905}, {18697, 1231}, {20653, 26942}, {20911, 7182}, {20967, 48}, {21033, 72}, {21124, 17094}, {21810, 201}, {22074, 255}, {22076, 40152}, {22097, 1804}, {22345, 7125}, {24471, 7177}, {40966, 71}, {40976, 6}, {41609, 1708}, {41611, 1445}, {44092, 1400}, {44130, 40827}
X(46878) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 10, 1861}, {4, 242, 1842}, {4, 5657, 1753}, {4, 7713, 1890}, {8, 4194, 33}, {25, 5130, 1891}, {29, 2907, 46103}, {29, 5081, 40950}, {92, 17555, 225}, {429, 1829, 1848}, {451, 1870, 1125}, {7090, 14121, 19}, {11105, 41013, 1785}

X(46879) = X(1)X(6)∩X(572)X(9562)

X(46879) lies on these lines: {1, 6}, {572, 9562}, {573, 23361}, {992, 1329}, {2269, 4267}, {3686, 34831}, {3687, 19608}, {3965, 22074}, {5783, 5793}, {37659, 41245}

X(46879) = X(333)-Ceva conjugate of X(4267)
X(46879) = X(i)-isoconjugate of X(j) for these (i,j): {226, 40453}, {961, 2051}
X(46879) = barycentric product X(i)*X(j) for these {i,j}: {572, 3687}, {960, 2975}, {2269, 14829}, {3965, 17074}, {4267, 17751}, {17185, 21061}
X(46879) = barycentric quotient X(i)/X(j) for these {i,j}: {2194, 40453}, {2269, 2051}, {2975, 31643}, {4267, 20028}, {20967, 34434}, {20986, 961}

X(46880) = X(2)X(573)∩X(21)X(1220)

X(46880) lies on these lines: {2, 573}, {21, 1220}, {81, 34234}, {85, 16705}, {86, 40420}, {92, 18662}, {284, 19607}, {941, 34267}, {1311, 17188}, {3877, 31359}, {3995, 18359}, {5235, 25515}, {8777, 28942}, {18031, 31008}, {18135, 40011}, {18165, 26095}, {19767, 26091}

X(46880) = X(i)-cross conjugate of X(j) for these (i,j): {37, 21}, {2262, 1896}, {2269, 8}, {2654, 7}, {3057, 314}, {14749, 1}, {19608, 34277}
X(46880) = X(i)-isoconjugate of X(j) for these (i,j): {6, 37558}, {42, 17074}, {56, 21061}, {65, 572}, {225, 22118}, {226, 20986}, {284, 20617}, {604, 17751}, {1400, 2975}, {1402, 14829}, {1409, 11109}, {1412, 14973}, {4559, 21173}
X(46880) = trilinear pole of line {522, 14310}
X(46880) = barycentric product X(i)*X(j) for these {i,j}: {8, 20028}, {314, 34434}, {333, 2051}
X(46880) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 37558}, {8, 17751}, {9, 21061}, {21, 2975}, {29, 11109}, {65, 20617}, {81, 17074}, {210, 14973}, {284, 572}, {333, 14829}, {2051, 226}, {2193, 22118}, {2194, 20986}, {3737, 21173}, {4560, 17496}, {17197, 24237}, {20028, 7}, {23189, 23187}, {27527, 27346}, {34434, 65}, {40453, 961}

X(46881) = X(1)X(84)∩X(20)X(13138)

X(46881) lies on these lines: {1, 84}, {20, 13138}, {48, 268}, {271, 10884}, {1490, 3341}, {3348, 7011}, {5768, 40836}, {8059, 8886}, {9799, 41084}

X(46881) = X(63)-Ceva conjugate of X(268)
X(46881) = crosssum of X(19) and X(7007)
X(46881) = X(i)-isoconjugate of X(j) for these (i,j): {4, 3342}, {33, 46352}, {40, 7149}, {208, 1034}, {223, 40838}, {342, 7037}, {347, 7007}, {2331, 41514}, {3194, 8806}, {3345, 7952}
X(46881) = barycentric product X(i)*X(j) for these {i,j}: {63, 3341}, {222, 46350}, {268, 5932}, {1035, 44189}, {1490, 41081}
X(46881) = barycentric quotient X(i)/X(j) for these {i,j}: {48, 3342}, {222, 46352}, {268, 1034}, {1035, 196}, {1433, 41514}, {1436, 7149}, {2192, 40838}, {3197, 7952}, {3341, 92}, {5932, 40701}, {7118, 7007}, {41087, 8806}, {46350, 7017}

X(46882) = X(1)X(15656)∩X(3)X(6)

X(46882) lies on these lines: {1, 15656}, {3, 6}, {7, 27}, {9, 17194}, {19, 18180}, {21, 219}, {37, 35194}, {48, 859}, {60, 2189}, {71, 17524}, {86, 25521}, {218, 1778}, {220, 4877}, {269, 18164}, {380, 18163}, {906, 2259}, {940, 7522}, {942, 1841}, {1394, 1449}, {1400, 20122}, {1437, 1474}, {2194, 7083}, {2256, 4653}, {2260, 4303}, {2264, 18191}, {2287, 27383}, {2303, 25516}, {3211, 36011}, {3664, 17197}, {3990, 24929}, {4340, 5802}, {5208, 22163}, {5707, 7534}, {7419, 23073}, {7560, 37685}, {7573, 32911}, {8021, 14547}, {8748, 41344}, {11110, 22127}, {13730, 44101}, {15149, 16608}, {16470, 18724}, {17171, 41004}, {17440, 21743}, {17560, 22153}, {18603, 45126}, {19350, 37227}, {20857, 40954}

X(46882) = X(i)-Ceva conjugate of X(j) for these (i,j): {21, 23207}, {81, 942}, {651, 3737}, {13486, 21789}
X(46882) = X(37993)-cross conjugate of X(942)
X(46882) = cevapoint of X(2260) and X(14597)
X(46882) = crosspoint of X(i) and X(j) for these (i,j): {21, 46103}, {60, 81}
X(46882) = crosssum of X(i) and X(j) for these (i,j): {12, 37}, {65, 2197}, {226, 16577}
X(46882) = X(i)-isoconjugate of X(j) for these (i,j): {10, 2982}, {65, 40435}, {72, 40573}, {73, 40447}, {201, 40395}, {226, 943}, {1175, 6358}, {1400, 40422}, {1441, 2259}, {1577, 15439}, {1794, 40149}, {2171, 40412}, {3700, 36048}, {4086, 32651}, {15412, 35320}
X(46882) = barycentric product X(i)*X(j) for these {i,j}: {7, 8021}, {21, 942}, {29, 4303}, {58, 6734}, {60, 442}, {81, 40937}, {86, 14547}, {261, 40952}, {283, 1838}, {284, 5249}, {286, 23207}, {314, 40956}, {333, 2260}, {500, 3615}, {757, 40967}, {1172, 18607}, {1444, 1859}, {1789, 1844}, {1812, 1841}, {2185, 2294}, {4573, 33525}, {4636, 23752}, {14597, 31623}, {18591, 46103}, {37993, 40412}
X(46882) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 40422}, {60, 40412}, {284, 40435}, {442, 34388}, {500, 40999}, {942, 1441}, {1172, 40447}, {1333, 2982}, {1474, 40573}, {1576, 15439}, {1841, 40149}, {1859, 41013}, {2189, 40395}, {2194, 943}, {2260, 226}, {2294, 6358}, {4303, 307}, {5249, 349}, {6734, 313}, {8021, 8}, {14547, 10}, {14597, 1214}, {18591, 26942}, {18607, 1231}, {23207, 72}, {33525, 3700}, {37993, 442}, {39791, 6356}, {40937, 321}, {40952, 12}, {40956, 65}, {40967, 1089}, {40978, 2171}
X(46882) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {27, 81, 37543}, {58, 284, 2193}, {58, 991, 3286}

X(46883) = X(1)X(27)∩X(4)X(991)

X(46883) lies on these lines: {1, 27}, {4, 991}, {10, 15149}, {28, 34}, {29, 17194}, {33, 31902}, {222, 18180}, {269, 1847}, {278, 4306}, {286, 10436}, {386, 7490}, {387, 37102}, {500, 15762}, {859, 22341}, {940, 37377}, {942, 1841}, {1038, 25516}, {1172, 4658}, {1722, 14013}, {1838, 4303}, {1870, 31900}, {1888, 17524}, {2193, 37697}, {2360, 34036}, {4185, 44105}, {4198, 4340}, {4296, 37113}, {5292, 37388}, {7431, 11471}, {7497, 18165}, {7543, 37732}

X(46883) = X(i)-Ceva conjugate of X(j) for these (i,j): {27, 2260}, {36118, 17925}
X(46883) = crosssum of X(2318) and X(3949)
X(46883) = crossdifference of every pair of points on line {8611, 46382}
X(46883) = X(i)-isoconjugate of X(j) for these (i,j): {10, 1794}, {71, 40435}, {72, 943}, {228, 40422}, {306, 2259}, {1175, 3695}, {2982, 3694}, {3690, 40412}, {3990, 40447}, {40161, 40572}
X(46883) = barycentric product X(i)*X(j) for these {i,j}: {27, 942}, {28, 5249}, {81, 1838}, {86, 1841}, {110, 23595}, {286, 2260}, {757, 1865}, {1396, 6734}, {1434, 1859}, {1847, 8021}, {8747, 18607}, {40956, 44129}
X(46883) = barycentric quotient X(i)/X(j) for these {i,j}: {27, 40422}, {28, 40435}, {942, 306}, {1333, 1794}, {1474, 943}, {1838, 321}, {1841, 10}, {1844, 3969}, {1859, 2321}, {1865, 1089}, {2203, 2259}, {2260, 72}, {2294, 3695}, {4303, 3998}, {5249, 20336}, {8021, 3692}, {8747, 40447}, {14547, 3694}, {14597, 3682}, {23595, 850}, {40937, 3710}, {40952, 3949}, {40956, 71}, {40978, 3690}, {44095, 3678}
X(46883) = {X(28),X(1396)}-harmonic conjugate of X(58)

X(46884) = X(1)X(19)∩X(4)X(579)

X(46884) lies on these lines: {1, 19}, {4, 579}, {6, 1243}, {9, 29}, {27, 57}, {58, 5317}, {142, 15149}, {270, 2150}, {286, 18206}, {393, 5292}, {942, 1841}, {965, 37393}, {1108, 1871}, {1827, 37908}, {1838, 2260}, {1859, 8021}, {1865, 15762}, {1901, 15763}, {2189, 4282}, {2193, 36011}, {2257, 8747}, {2287, 17519}, {2299, 39943}, {2326, 17515}, {4183, 4877}, {4198, 5802}, {4233, 40131}, {4269, 5709}, {5742, 37321}, {5755, 7510}, {7120, 37583}, {11341, 16574}, {11679, 31623}, {17185, 46103}, {27626, 31909}

X(46884) = X(i)-Ceva conjugate of X(j) for these (i,j): {27, 1838}, {29, 14547}
X(46884) = cevapoint of X(1841) and X(2260)
X(46884) = crosspoint of X(27) and X(270)
X(46884) = crosssum of X(71) and X(201)
X(46884) = X(i)-isoconjugate of X(j) for these (i,j): {72, 2982}, {73, 40435}, {226, 1794}, {307, 2259}, {525, 15439}, {943, 1214}, {1175, 26942}, {1409, 40422}, {2197, 40412}, {3682, 40573}, {7066, 40395}, {8611, 36048}, {22341, 40447}, {28786, 40572}
X(46884) = barycentric product X(i)*X(j) for these {i,j}: {21, 1838}, {27, 40937}, {28, 6734}, {29, 942}, {86, 1859}, {270, 442}, {273, 8021}, {286, 14547}, {333, 1841}, {1172, 5249}, {1844, 3615}, {1865, 2185}, {1896, 4303}, {2260, 31623}, {2294, 46103}, {5546, 23595}, {8748, 18607}, {17515, 45926}, {40956, 44130}
X(46884) = barycentric quotient X(i)/X(j) for these {i,j}: {29, 40422}, {270, 40412}, {942, 307}, {1172, 40435}, {1474, 2982}, {1838, 1441}, {1841, 226}, {1844, 40999}, {1859, 10}, {1865, 6358}, {2194, 1794}, {2204, 2259}, {2260, 1214}, {2294, 26942}, {2299, 943}, {5249, 1231}, {5317, 40573}, {6734, 20336}, {8021, 78}, {8748, 40447}, {14547, 72}, {14597, 40152}, {23207, 3682}, {32676, 15439}, {33525, 8611}, {40937, 306}, {40952, 201}, {40956, 73}, {40967, 3695}, {40978, 2197}, {44095, 16577}
X(46884) = {X(28),X(1172)}-harmonic conjugate of X(284)

X(46885) = X(1)X(21)∩X(7)X(17173)

X(46885) lies on these lines: {1, 21}, {7, 17173}, {333, 20930}, {1708, 40571}, {1943, 16704}, {2260, 5249}, {3218, 26830}, {3286, 16465}, {17167, 24316}

X(46885) = X(27)-Ceva conjugate of X(5249)
X(46885) = X(i)-isoconjugate of X(j) for these (i,j): {1175, 41508}, {2259, 23604}
X(46885) = barycentric product X(i)*X(j) for these {i,j}: {86, 14054}, {5249, 40571}
X(46885) = barycentric quotient X(i)/X(j) for these {i,j}: {942, 23604}, {1780, 943}, {2294, 41508}, {4303, 28787}, {5249, 43675}, {14054, 10}, {40571, 40435}, {41332, 2259}, {41608, 1794}

X(46886) = X(9)X(5190)∩X(19)X(46)

X(46886) lies on these lines: {9, 5190}, {19, 46}, {25, 1841}, {48, 913}, {608, 1406}, {1829, 45130}, {1839, 43740}, {5307, 43675}, {7465, 9085}

X(46886) = X(i)-cross conjugate of X(j) for these (i,j): {31, 34}, {2260, 1474}
X(46886) = X(i)-isoconjugate of X(j) for these (i,j): {2, 11517}, {3, 17776}, {8, 3173}, {63, 3811}, {69, 2911}, {72, 40571}, {78, 1708}, {306, 1780}, {312, 3215}, {321, 41608}, {345, 37579}, {1332, 15313}, {1812, 41538}, {3692, 4341}, {3998, 30733}, {20336, 41332}
X(46886) = barycentric product X(i)*X(j) for these {i,j}: {1, 39267}, {19, 15474}, {28, 23604}, {34, 43740}, {278, 39943}, {1474, 43675}, {7649, 13397}, {8747, 28787}
X(46886) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 17776}, {25, 3811}, {31, 11517}, {604, 3173}, {608, 1708}, {1395, 37579}, {1397, 3215}, {1398, 4341}, {1474, 40571}, {1973, 2911}, {2203, 1780}, {2206, 41608}, {2969, 17877}, {13397, 4561}, {15474, 304}, {23604, 20336}, {39267, 75}, {39943, 345}, {43675, 40071}, {43740, 3718}

X(46887) = X(1)X(3)∩X(27)X(19850)

X(46887) lies on these lines: {1, 3}, {27, 19850}, {48, 16453}, {500, 37993}, {582, 6056}, {1451, 7420}, {2260, 4303}, {2360, 20470}, {3286, 4292}, {4293, 37093}, {7522, 19762}

X(46887) = barycentric product X(i)*X(j) for these {i,j}: {81, 45038}, {580, 5249}, {4303, 37279}, {18607, 41227}
X(46887) = barycentric quotient X(i)/X(j) for these {i,j}: {580, 40435}, {41227, 40447}, {45038, 321}

X(46888) = X(2)X(6)∩X(147)X(8925)

X(46888) lies on these lines: {2, 6}, {147, 8925}, {315, 45910}, {446, 511}, {7759, 45915}, {7845, 45901}, {9419, 32458}, {11672, 16725}, {12215, 32542}, {25332, 39355}, {46236, 46272}

X(46888) = X(i)-Ceva conjugate of X(j) for these (i,j): {511, 36790}, {3978, 5976}
X(46888) = crosspoint of X(i) and X(j) for these (i,j): {511, 36213}, {3978, 5976}
X(46888) = crosssum of X(i) and X(j) for these (i,j): {98, 36897}, {385, 10352}, {9468, 34238}
X(46888) = crossdifference of every pair of points on line {512, 34238}
X(46888) = X(i)-isoconjugate of X(j) for these (i,j): {661, 18858}, {1581, 41932}, {1821, 34238}, {1910, 36897}, {1967, 34536}, {15391, 36120}
X(46888) = barycentric product X(i)*X(j) for these {i,j}: {325, 36213}, {385, 36790}, {511, 5976}, {804, 15631}, {1691, 32458}, {1926, 42075}, {1966, 23996}, {2967, 12215}, {3978, 11672}, {6072, 16069}, {9419, 14603}, {14382, 23098}, {17941, 41167}, {18901, 36425}, {36212, 39931}
X(46888) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 18858}, {237, 34238}, {385, 34536}, {511, 36897}, {1691, 41932}, {2421, 39291}, {3289, 15391}, {5976, 290}, {9419, 9468}, {11672, 694}, {15631, 18829}, {23098, 40810}, {23611, 14251}, {23996, 1581}, {32458, 18896}, {33569, 39680}, {36213, 98}, {36425, 8789}, {36790, 1916}, {39931, 16081}, {42075, 1967}

X(46889) = X(6)X(21)∩X(9)X(16699)

X(46889) lies on these lines: {6, 21}, {9, 16699}, {29, 965}, {55, 219}, {63, 18603}, {86, 5228}, {220, 346}, {283, 1333}, {394, 27174}, {572, 17524}, {573, 859}, {604, 3286}, {692, 2359}, {940, 37265}, {960, 22074}, {1010, 37537}, {1409, 4640}, {1449, 17194}, {1498, 37418}, {1817, 17811}, {1974, 37908}, {2193, 39167}, {2256, 2303}, {2269, 4267}, {2300, 3666}, {2911, 4273}, {3285, 35193}, {3794, 21785}, {3796, 4184}, {3877, 16685}, {4000, 17183}, {4225, 37499}, {5816, 37357}, {6180, 8822}, {12514, 22134}, {14953, 37659}, {16054, 25878}, {17182, 24789}, {19732, 25515}, {21769, 37549}, {21997, 26657}, {25649, 28818}, {27398, 28830}, {36754, 37322}, {37373, 37673}

X(46889) = X(i)-Ceva conjugate of X(j) for these (i,j): {21, 20967}, {644, 1021}, {2287, 3965}, {17185, 4267}
X(46889) = cevapoint of X(2269) and X(22074)
X(46889) = crosspoint of X(i) and X(j) for these (i,j): {21, 7058}, {2287, 7054}
X(46889) = crosssum of X(1427) and X(6354)
X(46889) = crossdifference of every pair of points on line {7178, 7250}
X(46889) = X(i)-isoconjugate of X(j) for these (i,j): {226, 961}, {269, 14624}, {1020, 4581}, {1042, 30710}, {1220, 1427}, {1254, 14534}, {1400, 31643}, {2298, 3668}, {2363, 6354}, {4017, 6648}, {4077, 8687}, {7178, 36098}, {7216, 8707}
X(46889) = barycentric product X(i)*X(j) for these {i,j}: {8, 4267}, {9, 17185}, {21, 960}, {60, 3704}, {81, 3965}, {220, 16705}, {261, 40966}, {284, 3687}, {314, 20967}, {332, 40976}, {333, 2269}, {346, 40153}, {643, 17420}, {1021, 3882}, {1043, 1193}, {1098, 2292}, {1211, 7054}, {1253, 16739}, {1792, 1829}, {1848, 2327}, {2092, 7058}, {2185, 21033}, {2287, 3666}, {2322, 22097}, {2328, 4357}, {3910, 5546}, {6061, 41003}, {6371, 7256}, {22074, 31623}
X(46889) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 31643}, {220, 14624}, {960, 1441}, {1043, 1240}, {1193, 3668}, {1682, 41003}, {2092, 6354}, {2194, 961}, {2269, 226}, {2287, 30710}, {2300, 1427}, {2328, 1220}, {3666, 1446}, {3687, 349}, {3704, 34388}, {3725, 1254}, {3965, 321}, {4267, 7}, {5546, 6648}, {7054, 14534}, {7058, 40827}, {17185, 85}, {17420, 4077}, {20967, 65}, {21033, 6358}, {21789, 4581}, {22074, 1214}, {22076, 6356}, {22345, 1439}, {23090, 15420}, {40153, 279}, {40966, 12}, {40976, 225}
X(46889) = {X(1043),X(2287)}-harmonic conjugate of X(3713)

X(46890) = X(6)X(28)∩X(27)X(940)

X(46890) lies on these lines: {6, 28}, {19, 13476}, {27, 940}, {56, 608}, {141, 15149}, {577, 859}, {942, 1841}, {1119, 1396}, {1172, 3296}, {1778, 4233}, {4269, 37581}, {4675, 17171}, {5165, 44103}, {8021, 18591}, {36080, 40572}

X(46890) = X(28)-Ceva conjugate of X(40956)
X(46890) = crosspoint of X(28) and X(36419)
X(46890) = crosssum of X(3694) and X(3695)
X(46890) = X(i)-isoconjugate of X(j) for these (i,j): {71, 40422}, {72, 40435}, {306, 943}, {321, 1794}, {2259, 20336}, {2982, 3710}, {3682, 40447}, {3949, 40412}
X(46890) = barycentric product X(i)*X(j) for these {i,j}: {27, 2260}, {28, 942}, {58, 1838}, {81, 1841}, {163, 23595}, {286, 40956}, {593, 1865}, {1014, 1859}, {1119, 8021}, {1396, 40937}, {1474, 5249}, {4303, 8747}, {5317, 18607}, {18591, 36419}
X(46890) = barycentric quotient X(i)/X(j) for these {i,j}: {28, 40422}, {942, 20336}, {1474, 40435}, {1838, 313}, {1841, 321}, {1859, 3701}, {1865, 28654}, {2203, 943}, {2206, 1794}, {2260, 306}, {5249, 40071}, {5317, 40447}, {8021, 1265}, {14547, 3710}, {14597, 3998}, {23595, 20948}, {36420, 40395}, {40952, 3695}, {40956, 72}, {40978, 3949}, {44095, 3969}

X(46891) = INNER MOSES-MALFATTI PERSPECTOR

In the plane of a triangle ABC, let Ab be the touchpoint of the A-Malfatti circle and side AB, and define Bc and Ca cyclically. Let Ac be the touchpoint of the same circle with side AC, and define Ba and Cb cyclically. The lines AbAc, BcBa, CaCb form a triangle perspective to the intouch triangle, and the perspector is X(46891). (Peter Moses, February 7, 2022)

X(46891) = cevapoint of X(174) and X(558)
X(46891) = X(174)-cross conjugate of X(46892)
X(46891) = barycentric product X(1143)*X(46892)
X(46891) = barycentric quotient X (i)/X(j) for these {i,j}: {174, 41885}, {558, 1489}, {1489, 7028}, {18886, 46892}, {46892, 1274}
X(46891) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7057, 46892}, {234, 2089, 46892}

X(46892) = OUTER MOSES-MALFATTI PERSPECTOR

In the plane of a triangle ABC, let Ab be the touchpoint of the outer A-Malfatti circle and side AB, and define Bc and Ca cyclically. Let Ac be the touchpoint of the same circle with side AC, and define Ba and Cb cyclically. The lines AbAc, BcBa, CaCb form a triangle perspective to the intouch triangle, and the perspector is X(46892). The triangles defined at X(446891) at and X(446892) are homothetic. (Peter Moses, February 7, 2022)

X(46892) = cevapoint of X(174) and X(557)
X(46892) = X(174)-cross conjugate of X(46891)
X(46892) = barycentric product X(1274)*X(46891)
X(46892) = barycentric quotient X (i)/X(j) for these {i,j}: {174, 1489}, {557, 41885}, {41885, 7028}
X(46892) = barycentric quotient X(i)/X(j) for these {i,j}: {174, 1489}, {557, 41885}, {18886, 46891}, {41885, 7028}, {46891, 1143}
X(46892) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7057, 46891}, {234, 2089, 46891}

X(46893) = THURNHEER POINT

X(46893) = 2 X[2] - 3 X[1153], X[2] - 3 X[5569], 5 X[2] - 3 X[8176], X[2] + 3 X[8182], 11 X[2] - 3 X[23334], 5 X[2] - X[44678], 5 X[3] + X[7751], 2 X[3] + X[7780], 7 X[3] - X[7781], 3 X[3] + X[8667], 5 X[3] - X[8716], 4 X[140] - X[7843], 5 X[1153] - 2 X[8176], X[1153] + 2 X[8182], 11 X[1153] - 2 X[23334], 15 X[1153] - 2 X[44678], 7 X[3523] - X[7759], 4 X[3530] - X[7764], X[3534] + 3 X[7610], X[3830] - 3 X[7617], X[3845] - 3 X[15597], 3 X[5054] - X[7775], 5 X[5569] - X[8176], 11 X[5569] - X[23334], 15 X[5569] - X[44678], 3 X[7610] - X[18546], 3 X[7615] + X[11001], 3 X[7618] - 7 X[15698], 3 X[7619] - 4 X[11812], 3 X[7620] + 5 X[15697], 3 X[7622] - X[9766], 3 X[7622] - 5 X[15693], 2 X[7751] - 5 X[7780], 7 X[7751] + 5 X[7781], 3 X[7751] - 5 X[8667], X[7758] - 13 X[10299], 7 X[7780] + 2 X[7781], 3 X[7780] - 2 X[8667], 5 X[7780] + 2 X[8716], 3 X[7781] + 7 X[8667], 5 X[7781] - 7 X[8716], X[8176] + 5 X[8182], 11 X[8176] - 5 X[23334], 3 X[8176] - X[44678], 11 X[8182] + X[23334], 15 X[8182] + X[44678], 5 X[8667] + 3 X[8716], X[9766] - 5 X[15693], 3 X[9770] - 11 X[15719], 3 X[9771] - 5 X[15713], 3 X[10304] - X[34504], 3 X[11165] - 11 X[15716], 3 X[11184] - 7 X[15701], 3 X[12040] - 7 X[19711], X[14023] + 11 X[15717], 3 X[15688] + X[34505], 5 X[15692] - X[34511], 5 X[15695] + 3 X[40727], 3 X[16509] + X[19710], 3 X[20112] - X[33699], 15 X[23334] - 11 X[44678]

This point is collinear with the centroid and the center of the van Lamoen circle, X(1153). Contributed by Peter Thurnheer and Peter Moses, February 8, 2022.

X(46893) lies on these lines: {2, 187}, {3, 538}, {30, 34506}, {32, 44562}, {39, 33273}, {99, 14711}, {115, 8353}, {140, 7843}, {183, 8588}, {230, 8354}, {385, 8589}, {524, 5092}, {543, 8703}, {549, 754}, {574, 14614}, {597, 41413}, {620, 7848}, {1003, 3934}, {1078, 7816}, {1384, 15482}, {2080, 44422}, {2482, 37671}, {3053, 6683}, {3098, 13708}, {3111, 3917}, {3523, 7759}, {3530, 7764}, {3534, 7610}, {3734, 5210}, {3785, 7895}, {3788, 33216}, {3830, 7617}, {3845, 15597}, {4045, 8358}, {5007, 33004}, {5023, 7815}, {5026, 22165}, {5054, 7775}, {5309, 33008}, {5939, 15300}, {5969, 14810}, {6179, 31652}, {6295, 36755}, {6582, 36756}, {6781, 37688}, {7615, 11001}, {7618, 15698}, {7619, 11812}, {7620, 15697}, {7622, 9766}, {7746, 33017}, {7748, 33207}, {7749, 7842}, {7757, 7793}, {7758, 10299}, {7800, 33191}, {7810, 7880}, {7811, 33274}, {7817, 8356}, {7821, 33259}, {7824, 12150}, {7825, 44535}, {7830, 7886}, {7849, 16925}, {7854, 32964}, {7861, 32986}, {7865, 11288}, {7873, 7907}, {7874, 7904}, {7915, 8368}, {8860, 18362}, {9770, 15719}, {9771, 15713}, {10304, 34504}, {11165, 15716}, {11184, 15701}, {11648, 35955}, {12040, 19711}, {14023, 15717}, {15271, 15655}, {15301, 17131}, {15515, 32450}, {15688, 34505}, {15692, 34511}, {15695, 40727}, {15819, 38225}, {16509, 19710}, {17006, 39601}, {17008, 32457}, {18860, 33706}, {20112, 33699}, {21163, 21445}, {23878, 44821}, {32832, 33193}, {33264, 39563}, {33458, 36769}

X(46893) = midpoint of X(i) and X(j) for these {i,j}: {3534, 18546}, {5569, 8182}, {7751, 8716}, {8703, 13468}
X(46893) = reflection of X(1153) in X(5569)
X(46893) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11057, 31173}, {2, 44678, 8176}, {183, 8588, 32456}, {1078, 13586, 9466}, {1078, 15513, 7816}, {3534, 7610, 18546}, {6179, 33022, 31652}, {7793, 37512, 7805}, {7810, 35297, 7880}, {9466, 13586, 7816}, {9466, 15513, 13586}, {9766, 15693, 7622}, {13708, 13828, 3098}

The preamble and centers X(46894)-X(46919) are contributed by Clark Kimberling and Peter Moses, February 9-10, 2022.

In the plane of a triangle ABC, suppose that L1, given by l1 x + m1 y + n1 z = 0, is a line, and P1 = p1:q1:r1 is a point not on L1 and not on a sideline BC, CA, AB. The cevians of P1 are the lines AP1, BP1, CP1, for which coefficients are

0 : q : r, p : 0 : r, p : q : 0, respectively. Let

Ap = L1∩AP1, Bp = L2∩BP1, Cp = L2∩CP1

Similarly, suppose that L2, given by l2 x + m2 y + n2 z = 0, is another line, and that P2 = p2:q2:r2 is a point not on L2 and not on a sideline BC, CA, AB. Let

Au = L2∩AP2, Bu = L2∩BP2, Cu = L2∩CP2

By Pappus's Theorem, the points

BpCu∩CpBu, CpAu∩ApCu, ApBu∩BpAu

are collinear (on the Pappus line of the configuration). The Type 1 Pappus Point of L1, P1, L2, P2 is the point whose barycentrics are coefficients of the Pappus line. Barycentrics for this point follow:

l2 p2 q1 r1 (m1 q2 + n1 r2) + l1 p1 q1 r2 (l2 p2 + n2 r2) + l1 p1 q2 r1 (l2 p2 + m2 q2) : :

X(46894) = PAPPUS POINT (X(2),X(2),X(75),X(514))

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

X(46894) = X[1018] + 2 X[1111], X[1018] - 4 X[21232], X[1111] + 2 X[21232], 2 X[17761] + X[21272], X[21139] + 2 X[24036], 2 X[30806] + X[45751]

X(46894) lies on these lines: {1, 16377}, {2, 514}, {75, 23891}, {85, 1025}, {190, 20568}, {518, 599}, {664, 25532}, {1018, 1111}, {1023, 9318}, {1086, 1145}, {1150, 3306}, {1698, 19978}, {3035, 43057}, {3294, 26563}, {3661, 31017}, {4089, 24318}, {4403, 20331}, {4760, 24261}, {5219, 7146}, {6372, 24494}, {7278, 17048}, {8257, 21373}, {9317, 35342}, {16506, 25034}, {16820, 27912}, {17294, 27476}, {17761, 21272}, {17789, 29401}, {20432, 29716}, {20448, 33934}, {20955, 29433}, {21139, 24036}, {29375, 33943}, {29381, 33930}, {29383, 33944}, {29440, 41875}, {29691, 33933}, {29699, 33940}, {31183, 31187}, {34123, 35110}

X(46894) = barycentric product X(75)*X(24405)
X(46894) = barycentric quotient X(24405)/X(1)
X(46894) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1111, 21232, 1018}, {27918, 36226, 1}

X(46895) = PAPPUS POINT (X(2),X(2),X(75),X(10))

X(46895) = X[1] + 2 X[4647], 2 X[10] + X[17164], 2 X[10] - 3 X[27812], 4 X[1125] - 3 X[27811], 5 X[1698] - 2 X[2292], 2 X[1962] - 3 X[25055], 2 X[2650] + X[3632], 5 X[3616] - 2 X[4065], 7 X[3624] - 4 X[3743], X[17164] + 3 X[27812], 3 X[19875] - 4 X[27798]

X(46895) lies on these lines: {1, 75}, {10, 3120}, {40, 16124}, {191, 37369}, {392, 4688}, {519, 17163}, {523, 1022}, {551, 27804}, {758, 3679}, {956, 17118}, {994, 39708}, {1125, 17495}, {1215, 4714}, {1698, 2292}, {1738, 19867}, {1739, 44417}, {1962, 25055}, {2650, 3632}, {3159, 19874}, {3216, 28612}, {3616, 4065}, {3624, 3743}, {3678, 22294}, {3720, 4717}, {3761, 35544}, {3971, 19870}, {4424, 31993}, {5692, 20718}, {5904, 31327}, {11231, 27747}, {11263, 20653}, {11552, 33082}, {13745, 28530}, {16821, 17116}, {19875, 27798}, {24161, 25669}, {26725, 33160}, {27714, 36250}, {28605, 30116}, {31178, 44671}

X(46895) = reflection of X(i) in X(j) for these {i,j}: {3679, 21020}, {27804, 551}
X(46895) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1215, 4714, 31855}, {28619, 41813, 1}

X(46896) = PAPPUS POINT (X(2),X(2),X(10),X(10))

X(46896) lies on these lines: {2, 740}, {10, 16704}, {100, 1268}, {1125, 42437}, {1213, 4427}, {1961, 6539}, {2475, 3647}, {3952, 28604}, {4046, 41818}, {4733, 17162}, {8013, 8025}, {14007, 27558}, {17491, 24342}, {17495, 19856}, {17768, 41809}, {26860, 42334}, {28653, 29822}

X(46896) = X(28615)-isoconjugate of X(44572)
X(46896) = barycentric quotient X(1125)/X(44572)
X(46896) = {X(24342),X(27081)}-harmonic conjugate of X(17491)

X(46897) = PAPPUS POINT (X(2),X(2),X(1),X(1))

X(46897) = X[38] - 4 X[6685], 2 X[42] + X[321], X[42] + 2 X[1215], 4 X[42] - X[3896], 5 X[42] + X[4365], X[321] - 4 X[1215], 2 X[321] + X[3896], 5 X[321] - 2 X[4365], 8 X[1215] + X[3896], 10 X[1215] - X[4365], 2 X[3666] + X[17165], 2 X[3706] + X[20011], 2 X[3741] - 5 X[31264], 5 X[3896] + 4 X[4365], X[4450] + 2 X[41011], X[17135] - 4 X[44417]

X(46897) lies on these lines: {1, 996}, {2, 210}, {6, 26227}, {8, 5725}, {10, 2650}, {11, 29835}, {31, 29670}, {37, 3121}, {38, 6685}, {42, 321}, {43, 4359}, {55, 26223}, {65, 22294}, {72, 26115}, {75, 3240}, {81, 7081}, {86, 3699}, {100, 894}, {141, 26251}, {142, 24988}, {145, 3714}, {182, 39572}, {226, 4972}, {238, 41241}, {312, 17018}, {320, 33086}, {386, 4968}, {512, 35353}, {612, 19684}, {726, 31161}, {748, 29651}, {756, 4090}, {846, 32938}, {899, 24325}, {902, 4672}, {942, 26030}, {964, 3811}, {1010, 4420}, {1150, 3751}, {1220, 34772}, {1386, 20045}, {1441, 4551}, {1442, 14594}, {1621, 27064}, {1757, 32917}, {1962, 3971}, {2177, 3923}, {2229, 3774}, {2667, 22016}, {3006, 5718}, {3120, 4085}, {3175, 27804}, {3263, 37632}, {3416, 31034}, {3589, 17724}, {3618, 26228}, {3666, 17165}, {3679, 31179}, {3685, 41242}, {3694, 5749}, {3696, 19998}, {3697, 19874}, {3706, 20011}, {3741, 31264}, {3745, 19717}, {3750, 32930}, {3752, 17140}, {3755, 4054}, {3757, 32911}, {3758, 17126}, {3769, 37685}, {3771, 26061}, {3773, 4062}, {3821, 32856}, {3844, 31017}, {3846, 29685}, {3870, 24552}, {3881, 19864}, {3891, 5256}, {3909, 17792}, {3935, 5263}, {3938, 25496}, {3953, 20108}, {3956, 19870}, {3957, 32942}, {3961, 32772}, {3967, 3995}, {3969, 4028}, {3979, 32943}, {3989, 42054}, {3993, 3994}, {3999, 17146}, {4003, 17154}, {4009, 15569}, {4015, 16828}, {4026, 26580}, {4096, 10180}, {4104, 41809}, {4202, 13407}, {4385, 19767}, {4413, 26627}, {4414, 32935}, {4417, 29667}, {4423, 26688}, {4427, 4689}, {4429, 31019}, {4438, 29678}, {4450, 41011}, {4514, 33107}, {4646, 17164}, {4649, 17763}, {4651, 4849}, {4660, 24725}, {4663, 16704}, {4670, 17780}, {4682, 8025}, {4685, 21020}, {4687, 9330}, {4709, 4946}, {4723, 30116}, {4756, 17261}, {4767, 16826}, {4850, 24349}, {4871, 17450}, {4980, 32860}, {5014, 26098}, {5045, 26094}, {5051, 21077}, {5205, 37633}, {5294, 13405}, {5302, 17588}, {5524, 24342}, {5712, 10327}, {5905, 32950}, {6155, 22036}, {9011, 44429}, {9053, 17726}, {9347, 17379}, {11319, 37080}, {11322, 15624}, {14439, 35263}, {16342, 41229}, {16496, 29826}, {16606, 21814}, {16706, 33148}, {16823, 37680}, {17011, 32926}, {17012, 32922}, {17017, 32920}, {17125, 24331}, {17135, 44417}, {17147, 28555}, {17175, 25585}, {17279, 29830}, {17289, 33175}, {17353, 24542}, {17483, 33068}, {17484, 24723}, {17557, 32635}, {17592, 32925}, {17594, 32933}, {17596, 32940}, {17602, 29833}, {17717, 33120}, {17719, 29631}, {17720, 29829}, {17723, 29832}, {17725, 29636}, {17778, 33078}, {18059, 41318}, {18098, 21750}, {18134, 29679}, {18743, 29814}, {19786, 33153}, {20683, 41249}, {21101, 21840}, {22277, 27042}, {24003, 30950}, {25253, 37548}, {25385, 33136}, {25453, 33127}, {25760, 29659}, {26034, 32859}, {26073, 26806}, {26128, 29663}, {26234, 37678}, {28606, 32937}, {28968, 37541}, {29301, 37619}, {29632, 33159}, {29633, 32775}, {29640, 33115}, {29643, 33165}, {29671, 33162}, {29673, 33105}, {29821, 32923}, {29824, 30818}, {29839, 33157}, {29846, 32780}, {29849, 33169}, {29850, 33130}, {29857, 30834}, {29873, 41878}, {31053, 32773}, {32774, 33144}, {32776, 33101}, {32781, 33064}, {32784, 33065}, {32843, 33076}, {32850, 33112}, {32851, 33170}, {32912, 32916}, {32913, 32918}, {32915, 42042}, {32946, 33074}, {32947, 33096}, {32948, 33097}, {32949, 33079}, {33066, 33083}, {33069, 33174}, {33071, 33090}, {33073, 33091}, {33103, 33125}, {33111, 33117}, {33113, 33163}, {33116, 33166}, {41013, 44113}

X(46897) = X(3758)-Ceva conjugate of X(3997)
X(46897) = X(i)-isoconjugate of X(j) for these (i,j): {58, 4492}, {2206, 30635}, {4833, 8695}
X(46897) = barycentric product X(i)*X(j) for these {i,j}: {10, 3758}, {75, 3997}, {190, 4761}, {313, 609}, {321, 17126}, {333, 7276}, {740, 43262}, {1018, 4406}
X(46897) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 4492}, {321, 30635}, {609, 58}, {3758, 86}, {3809, 40773}, {3997, 1}, {4406, 7199}, {4761, 514}, {7208, 17205}, {7276, 226}, {17126, 81}, {43262, 18827}
X(46897) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 32931, 4358}, {2, 3681, 4981}, {42, 321, 3896}, {42, 1215, 321}, {43, 32771, 4359}, {86, 3699, 5297}, {899, 24325, 24589}, {3589, 17724, 26230}, {3696, 21870, 19998}, {3751, 29828, 1150}, {3755, 4054, 4442}, {3952, 29822, 37}, {3967, 37593, 3995}, {3994, 21806, 3993}, {4009, 15569, 31035}, {4090, 43223, 756}, {4689, 17351, 4427}, {4849, 31993, 4651}, {17718, 38047, 2}, {19998, 31025, 3696}

X(46898) = PAPPUS POINT (X(2),X(2),X(1),X(6))

X(46898) lies on these lines: {1, 3264}, {2, 674}, {31, 30882}, {76, 36289}, {313, 730}, {1269, 1740}, {2234, 12263}, {3009, 24327}, {22277, 26963}, {26176, 44412}

X(46899) = PAPPUS POINT (X(2),X(2),X(6),X(1))

X(46899) lies on these lines: {1, 17755}, {2, 758}, {6, 14210}, {10, 4766}, {21, 30127}, {31, 30108}, {35, 35292}, {38, 30106}, {79, 17680}, {141, 21839}, {191, 16060}, {213, 742}, {239, 5315}, {894, 5526}, {960, 16818}, {1046, 29473}, {1089, 17033}, {1111, 24514}, {1125, 26689}, {1724, 16822}, {2238, 24254}, {2251, 4797}, {2887, 30915}, {2975, 30132}, {3263, 3997}, {3336, 33828}, {3868, 30110}, {3869, 30107}, {3874, 27097}, {3878, 26965}, {3912, 41249}, {3992, 30114}, {4084, 26562}, {4692, 40859}, {4975, 17027}, {5025, 30165}, {5903, 27299}, {5904, 27248}, {6679, 30886}, {15556, 28777}, {17671, 30119}, {17696, 37571}, {19871, 31322}, {20894, 24330}, {21879, 25499}, {22836, 33819}, {24995, 40690}, {25079, 29438}, {25591, 29455}, {30131, 34195}, {30139, 33817}, {33936, 37657}

X(46900) = PAPPUS POINT (X(2),X(2),X(6),X(6))

X(46900) lies on these lines: {2, 51}, {6, 3266}, {39, 4576}, {76, 9463}, {83, 4563}, {110, 384}, {141, 23297}, {184, 16949}, {251, 37894}, {597, 45672}, {688, 35366}, {732, 3051}, {1003, 6800}, {1196, 33798}, {1235, 35325}, {1613, 39998}, {1993, 11324}, {2056, 10328}, {3231, 24256}, {3329, 9146}, {3552, 15080}, {3618, 15302}, {3787, 8891}, {5012, 16951}, {5017, 26233}, {5052, 30749}, {5468, 7804}, {6090, 11286}, {6636, 35277}, {6661, 40112}, {7770, 15066}, {7807, 14389}, {7816, 10330}, {7824, 41462}, {8369, 9155}, {8370, 40915}, {9306, 16932}, {9464, 32451}, {9465, 18906}, {9544, 16953}, {11285, 21766}, {11422, 39141}, {14001, 37645}, {14994, 31078}, {15107, 26257}, {16055, 34417}, {17686, 26637}, {32957, 44833}

X(46900) = X(i)-isoconjugate of X(j) for these (i,j): {82, 30495}, {44558, 46289}
X(46900) = barycentric product X(i)*X(j) for these {i,j}: {141, 3972}, {4108, 4576}
X(46900) = barycentric quotient X(i)/X(j) for these {i,j}: {39, 30495}, {141, 44558}, {3972, 83}
X(46900) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 35288, 33879}, {3051, 4074, 8024}, {3231, 24256, 26235}

X(46901) = PAPPUS POINT (X(2),X(2),X(1),X(76))

X(46901) = 2 X[38] + X[42], X[38] + 2 X[3666], X[42] - 4 X[3666], X[321] - 4 X[6682], 2 X[321] - 5 X[31241], 4 X[3741] - X[4365], 2 X[3741] + X[17147], X[4365] + 2 X[17147], 2 X[4970] + X[17135], 8 X[6682] - 5 X[31241], 4 X[6685] - X[17165]

X(46901) lies on these lines: {1, 89}, {2, 726}, {6, 36263}, {10, 17495}, {11, 17246}, {31, 17599}, {37, 244}, {38, 42}, {39, 8620}, {43, 7226}, {45, 17125}, {57, 5311}, {63, 2308}, {75, 30964}, {81, 17600}, {100, 17593}, {141, 32848}, {171, 29816}, {190, 32944}, {192, 30942}, {210, 42039}, {226, 29688}, {321, 6682}, {333, 32924}, {345, 24943}, {354, 1962}, {392, 1201}, {551, 27811}, {649, 24286}, {672, 41269}, {740, 31136}, {750, 17595}, {756, 3752}, {846, 7191}, {896, 1386}, {899, 984}, {968, 3677}, {980, 3009}, {982, 3720}, {986, 10459}, {988, 35262}, {1054, 5297}, {1064, 2771}, {1125, 3977}, {1150, 32921}, {1193, 5692}, {1621, 17598}, {1647, 24318}, {1757, 17012}, {1961, 27003}, {2177, 3242}, {2293, 7004}, {2611, 17447}, {2632, 22063}, {2802, 4424}, {2886, 33145}, {3006, 3821}, {3011, 4353}, {3120, 3663}, {3159, 19864}, {3210, 31330}, {3219, 29821}, {3244, 17145}, {3315, 16484}, {3550, 29815}, {3662, 29643}, {3670, 5883}, {3672, 11269}, {3703, 32781}, {3705, 32776}, {3722, 4689}, {3724, 35289}, {3729, 29826}, {3739, 30955}, {3740, 42041}, {3741, 4365}, {3742, 42040}, {3743, 3953}, {3782, 33105}, {3840, 3995}, {3842, 24589}, {3873, 17592}, {3891, 32916}, {3914, 29690}, {3920, 17596}, {3938, 17594}, {3944, 29680}, {3993, 29824}, {3994, 30818}, {3999, 15569}, {4083, 38349}, {4360, 32919}, {4389, 25760}, {4427, 29823}, {4430, 42042}, {4438, 29867}, {4442, 21242}, {4519, 4718}, {4640, 17469}, {4655, 33070}, {4660, 29832}, {4661, 42043}, {4671, 29827}, {4683, 33071}, {4699, 31000}, {4704, 30947}, {4772, 17038}, {4860, 9345}, {4865, 32950}, {4871, 31035}, {4884, 33162}, {4970, 17135}, {5057, 17722}, {5211, 9791}, {5249, 29682}, {5256, 32912}, {5263, 32845}, {5287, 18193}, {5294, 29684}, {5718, 32856}, {6646, 32843}, {6685, 17165}, {8054, 22343}, {8616, 17024}, {8720, 11115}, {9335, 25502}, {10180, 42053}, {10448, 37549}, {11680, 33154}, {14829, 32928}, {15015, 30115}, {16468, 17025}, {16491, 36277}, {16666, 39251}, {16706, 33115}, {16828, 24176}, {17011, 32913}, {17123, 33761}, {17140, 43223}, {17154, 29822}, {17184, 29671}, {17187, 35623}, {17276, 17723}, {17301, 33128}, {17302, 29631}, {17304, 29857}, {17459, 21327}, {17490, 26037}, {17612, 35293}, {17717, 33151}, {17726, 17768}, {17763, 24627}, {17776, 29677}, {17889, 29664}, {18133, 25618}, {18201, 37633}, {19785, 24892}, {19786, 29863}, {21020, 42051}, {21342, 37593}, {21352, 40773}, {21674, 23536}, {23958, 37604}, {24177, 38204}, {24248, 33104}, {24552, 32934}, {24723, 32844}, {25496, 32933}, {26034, 32854}, {26098, 33098}, {26128, 29865}, {26223, 29650}, {26840, 32949}, {27184, 29849}, {27804, 42057}, {28582, 31161}, {29580, 35292}, {29633, 33170}, {29637, 32849}, {29640, 33148}, {29641, 33125}, {29652, 32929}, {29657, 31019}, {29663, 33163}, {29676, 33134}, {29678, 33144}, {29840, 32947}, {29869, 33116}, {30957, 41839}, {32772, 32939}, {32775, 32851}, {32782, 32855}, {32783, 33168}, {32784, 33089}, {32842, 33082}, {32847, 33086}, {32857, 33112}, {32862, 33174}, {32866, 33083}, {32914, 38000}, {32917, 32922}, {32918, 32926}, {32936, 32942}, {33067, 33073}, {33068, 33072}, {33080, 33088}, {33085, 33093}, {33092, 33172}, {33099, 33107}, {33100, 33106}, {33102, 33109}, {33108, 33149}, {33111, 33146}, {33138, 33150}, {33140, 33155}, {35261, 38314}, {35271, 37599}, {36565, 37574}

X(46901) = crosspoint of X(1) and X(4492)
X(46901) = crosssum of X(1) and X(17126)
X(46901) = barycentric product X(1)*X(17237)
X(46901) = barycentric quotient X(17237)/X(75)
X(46901) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4392, 17449}, {1, 4414, 902}, {31, 17599, 29819}, {37, 244, 30950}, {37, 4003, 244}, {38, 3666, 42}, {63, 17017, 2308}, {321, 6682, 31241}, {896, 1386, 21747}, {982, 28606, 3720}, {984, 4850, 899}, {1621, 17598, 29818}, {1962, 42038, 354}, {2292, 37592, 1201}, {3663, 29639, 3120}, {3741, 17147, 4365}, {3999, 15569, 17450}, {4438, 32774, 29867}, {4860, 16777, 9345}, {17276, 17723, 24725}, {19786, 33119, 29863}, {26128, 33113, 29865}, {33116, 33123, 29869}

X(46902) = PAPPUS POINT (X(2),X(2),X(1),X(561))

X(46902) = X[213] + 2 X[3721], X[213] - 4 X[16600], X[3721] + 2 X[16600], X[17489] + 2 X[21240]

X(46902) lies on these lines: {1, 2251}, {2, 712}, {6, 3894}, {31, 36283}, {37, 1018}, {65, 21802}, {210, 3954}, {213, 758}, {228, 1962}, {762, 3921}, {1759, 16974}, {2176, 3899}, {2238, 4134}, {2295, 3919}, {3230, 3735}, {3509, 5429}, {3726, 3892}, {3727, 3898}, {3873, 20963}, {3956, 16611}, {3968, 21951}, {3997, 4744}, {4376, 30105}, {4904, 17246}, {5309, 33143}, {8619, 24513}, {16589, 20966}, {17456, 21750}, {17489, 21240}, {21965, 38058}, {22036, 27040}

X(46902) = barycentric product X(37)*X(17290)
X(46902) = barycentric quotient X(17290)/X(274)
X(46902) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3721, 16600, 213}, {3735, 26242, 3230}

X(46903) = PAPPUS POINT (X(2),X(2),X(1),X(1502))

X(46903) lies on these lines: {1, 9459}, {2, 696}, {37, 4475}, {760, 1918}, {12194, 18722}

X(46904) = PAPPUS POINT (X(2),X(2),X(6),X(75))

Barycentrics a*(2*a*b + b^2 + 2*a*c + c^2) : :
Trilinears (B-power of C-Longuet-Higgins circle) + (C-power of B-Longuet-Higgins circle) : :

X(46904) = X[1] + 2 X[4868], X[38] + 2 X[42], X[38] - 4 X[3666], X[42] + 2 X[3666], X[321] + 2 X[4970], X[321] - 4 X[6685], 2 X[321] - 5 X[31264], 2 X[1215] + X[17147], 2 X[3706] - 5 X[31241], 2 X[3741] + X[3896], X[4365] - 4 X[44417], X[4970] + 2 X[6685], 4 X[4970] + 5 X[31264], 4 X[6682] - X[17135], 8 X[6685] - 5 X[31264]

X(46904) lies on these lines: {1, 88}, {2, 740}, {6, 896}, {10, 32848}, {31, 5256}, {37, 899}, {38, 42}, {39, 3121}, {43, 756}, {55, 5096}, {63, 4722}, {69, 4938}, {81, 1326}, {141, 4062}, {149, 17722}, {171, 17011}, {192, 3994}, {210, 3989}, {226, 33145}, {238, 17012}, {239, 32917}, {306, 32781}, {319, 14459}, {321, 4970}, {345, 26061}, {354, 42040}, {386, 2292}, {392, 1193}, {513, 39974}, {528, 17726}, {614, 37553}, {726, 31161}, {748, 968}, {846, 32911}, {894, 32845}, {902, 1386}, {982, 17018}, {984, 3240}, {986, 2650}, {1100, 1155}, {1125, 24589}, {1126, 6763}, {1201, 4719}, {1215, 17147}, {1255, 9342}, {1376, 5311}, {1402, 35289}, {1442, 9364}, {1465, 42289}, {1500, 6377}, {1621, 29821}, {1635, 14402}, {1999, 32918}, {2275, 39247}, {2276, 14439}, {2293, 9371}, {2308, 4640}, {2667, 21330}, {2702, 2721}, {2771, 5396}, {2886, 29688}, {3006, 4085}, {3011, 3946}, {3120, 5718}, {3178, 4202}, {3187, 32916}, {3210, 32771}, {3216, 3743}, {3218, 4649}, {3336, 4658}, {3589, 3712}, {3616, 24620}, {3663, 32856}, {3681, 42039}, {3685, 32944}, {3696, 30970}, {3706, 31241}, {3720, 3752}, {3724, 5132}, {3736, 25060}, {3739, 4706}, {3741, 3896}, {3744, 29819}, {3748, 29818}, {3749, 17782}, {3750, 7191}, {3751, 36263}, {3755, 29639}, {3757, 32924}, {3771, 32774}, {3772, 29678}, {3773, 26251}, {3774, 8620}, {3791, 45222}, {3807, 4664}, {3821, 3936}, {3873, 17591}, {3875, 29828}, {3886, 29826}, {3891, 29670}, {3914, 33105}, {3920, 17600}, {3924, 19765}, {3925, 29682}, {3930, 41269}, {3938, 17599}, {3957, 17598}, {3980, 19684}, {3993, 4358}, {4003, 17449}, {4009, 4681}, {4021, 6745}, {4023, 4364}, {4028, 33081}, {4038, 27003}, {4065, 20108}, {4343, 10177}, {4359, 43223}, {4360, 17763}, {4365, 44417}, {4389, 33065}, {4413, 16777}, {4417, 32776}, {4425, 5741}, {4427, 4672}, {4429, 21026}, {4442, 25385}, {4646, 10459}, {4650, 37685}, {4655, 31034}, {4660, 33070}, {4685, 4981}, {4695, 30116}, {4697, 19717}, {4743, 21242}, {4831, 32455}, {4854, 37662}, {4972, 29671}, {5051, 17748}, {5161, 7122}, {5205, 17319}, {5262, 37573}, {5268, 9350}, {5287, 17124}, {5429, 17549}, {5432, 29683}, {5530, 21935}, {5743, 6536}, {6051, 27627}, {6682, 17135}, {7081, 32928}, {7264, 40619}, {7292, 16484}, {8728, 27577}, {8758, 21346}, {9316, 45126}, {9348, 40401}, {9352, 37604}, {10458, 25059}, {13728, 20653}, {15569, 16610}, {16482, 46126}, {16706, 29632}, {16972, 41423}, {17013, 17126}, {17015, 37617}, {17019, 17122}, {17020, 17123}, {17024, 17715}, {17063, 29814}, {17301, 17718}, {17302, 32775}, {17380, 29636}, {17395, 17602}, {17495, 24325}, {17717, 33134}, {17719, 33155}, {17723, 33104}, {17749, 27785}, {17778, 33067}, {17779, 37680}, {18059, 34020}, {18134, 33125}, {18139, 24169}, {19270, 27368}, {19785, 33127}, {19786, 29846}, {20331, 36409}, {22392, 31803}, {24003, 31035}, {24177, 38054}, {24248, 24725}, {24504, 40776}, {24552, 29650}, {24627, 32919}, {24629, 26626}, {24697, 37656}, {24715, 33112}, {24723, 32843}, {24789, 29661}, {25453, 33113}, {25496, 32929}, {25800, 25817}, {25805, 25834}, {25806, 25811}, {26034, 32852}, {26098, 33094}, {26223, 32934}, {26227, 32921}, {27064, 32936}, {28581, 31136}, {29631, 32851}, {29633, 32779}, {29640, 33129}, {29657, 33108}, {29659, 33089}, {29663, 32777}, {29664, 32865}, {29667, 32855}, {29679, 33092}, {29680, 33141}, {29839, 33123}, {29849, 32773}, {29850, 33116}, {30834, 31280}, {31019, 33149}, {31053, 33154}, {31177, 31179}, {32772, 32932}, {32780, 33168}, {32784, 33077}, {32842, 33076}, {32846, 33086}, {32849, 33159}, {32858, 33174}, {32861, 33083}, {32864, 38000}, {32946, 32950}, {32947, 33071}, {32948, 33073}, {32949, 33068}, {33074, 33088}, {33079, 33093}, {33095, 33107}, {33096, 33100}, {33097, 33102}, {33111, 33131}, {33130, 33150}, {33161, 38047}, {33162, 38191}, {34122, 37715}, {35263, 38049}, {36250, 37693}

X(46904) = isotomic conjugate of trilinear pole of line X(3762)X(28840)
X(46904) = crosspoint of X(1) and X(751)
X(46904) = crosssum of X(1) and X(750)
X(46904) = crossdifference of every pair of points on line {1635, 4160}
X(46904) = barycentric product X(i)*X(j) for these {i,j}: {1, 4364}, {57, 4023}
X(46904) = barycentric quotient X(i)/X(j) for these {i,j}: {4023, 312}, {4364, 75}
X(46904) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 244, 17450}, {1, 1054, 37633}, {1, 2177, 3722}, {1, 3306, 9345}, {1, 4850, 244}, {2, 4734, 32860}, {2, 17592, 1962}, {2, 32860, 21020}, {6, 4414, 896}, {42, 3666, 38}, {43, 28606, 756}, {55, 17017, 17469}, {192, 32931, 3994}, {210, 3989, 42041}, {244, 21806, 1}, {321, 6685, 31264}, {968, 2999, 748}, {984, 3240, 21805}, {986, 19767, 2650}, {1376, 20182, 5311}, {1386, 4689, 902}, {3752, 37593, 3720}, {3755, 29639, 33136}, {3873, 17591, 42038}, {4429, 29643, 21026}, {4649, 17593, 3218}, {4719, 37548, 1201}, {4850, 21806, 17450}, {4970, 6685, 321}, {5256, 17594, 31}, {5256, 35258, 16475}, {15569, 16610, 30950}, {16475, 17594, 35258}, {16475, 35258, 31}, {17301, 17718, 33143}, {17495, 29822, 24325}, {17591, 42042, 3873}

X(46905) = PAPPUS POINT (X(2),X(2),X(6),X(76))

X(46905) lies on these lines: {2, 714}, {6, 922}, {39, 3122}, {560, 35267}, {674, 1964}, {869, 4484}, {872, 2277}, {2228, 37596}, {2234, 4443}, {2275, 3248}, {2643, 24443}, {2667, 4261}, {3009, 4735}, {3097, 4664}, {3728, 46838}, {3747, 4286}, {4022, 27633}, {4446, 17445}, {17053, 21035}, {17148, 21238}, {17157, 25505}, {17399, 17591}, {18148, 25619}, {20913, 25347}, {24494, 24513}, {24530, 24575}, {25092, 25422}, {35270, 40934}

X(46905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2275, 3764, 3248}, {4443, 24598, 2234}

X(46906) = PAPPUS POINT (X(2),X(2),X(6),X(1502))

X(46906) lies on these lines: {2, 698}, {6, 23}, {39, 373}, {51, 11205}, {125, 7765}, {141, 46721}, {217, 38356}, {511, 1194}, {1180, 3981}, {1184, 31884}, {1196, 5650}, {1501, 35268}, {1613, 33884}, {1648, 11007}, {2076, 5354}, {2086, 46127}, {3094, 3231}, {3221, 38366}, {3291, 15082}, {5038, 39024}, {5085, 42295}, {5254, 39691}, {5968, 45914}, {5969, 46900}, {7772, 34417}, {9463, 44453}, {9607, 37648}, {10007, 26235}, {10329, 35006}, {12212, 15107}, {20976, 44499}, {32225, 39593}, {34945, 35265}, {46124, 46128}

X(46906) = isogonal conjugate of the isotomic conjugate of X(7853)
X(46906) = crosspoint of X(6) and X(30495)
X(46906) = crosssum of X(2) and X(3972)
X(46906) = crossdifference of every pair of points on line {3906, 9147}
X(46906) = barycentric product X(6)*X(7853)
X(46906) = barycentric quotient X(7853)/X(76)
X(46906) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1180, 3981, 20965}, {1180, 5640, 13331}, {1194, 20859, 3051}, {3094, 9465, 3231}, {3981, 13331, 5640}, {5640, 13331, 20965}

X(46907) = PAPPUS POINT (X(2),X(2),X(561),X(75))

X(46907) lies on these lines: {1, 9351}, {2, 742}, {6, 3726}, {9, 29821}, {10, 21802}, {31, 2243}, {37, 42}, {38, 44}, {41, 16974}, {45, 4383}, {172, 5429}, {213, 758}, {614, 36404}, {712, 46899}, {1100, 2348}, {2176, 3727}, {2246, 17469}, {2295, 3753}, {2325, 4970}, {2887, 4144}, {3125, 3919}, {3230, 3898}, {3247, 3979}, {3290, 3742}, {3589, 26234}, {3618, 26274}, {3720, 36409}, {3735, 3899}, {3752, 20331}, {3880, 41015}, {3890, 36647}, {3892, 20963}, {3896, 3943}, {3954, 4134}, {3956, 28594}, {3957, 16777}, {3968, 16611}, {3970, 20970}, {4070, 6679}, {4359, 17369}, {4512, 16970}, {4525, 21839}, {4661, 37657}, {4731, 16605}, {4766, 25345}, {4881, 21008}, {4981, 17330}, {5257, 29653}, {5320, 16972}, {7296, 16478}, {17281, 32860}, {18785, 40747}, {21803, 22232}, {21814, 21835}, {23652, 40936}, {24592, 25368}

X(46907) = midpoint of X(213) and X(46902)
X(46907) = reflection of X(i) in X(j) for these {i,j}: {3721, 46902}, {46902, 16600}
X(46907) = X(17367)-Ceva conjugate of X(4085)
X(46907) = X(7192)-isoconjugate of X(28883)
X(46907) = crossdifference of every pair of points on line {1019, 6004}
X(46907) = barycentric product X(i)*X(j) for these {i,j}: {1, 4085}, {37, 17367}, {321, 5332}, {1018, 28882}, {3949, 31908}
X(46907) = barycentric quotient X(i)/X(j) for these {i,j}: {4085, 75}, {5332, 81}, {17367, 274}, {28882, 7199}
X(46907) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 26242, 3726}, {37, 21904, 3930}, {213, 16600, 3721}, {2295, 16583, 21951}

X(46908) = PAPPUS POINT (X(2),X(2),X(561),X(76))

X(46908) lies on these lines: {1, 24598}, {2, 730}, {31, 36}, {39, 3009}, {42, 1015}, {551, 1962}, {674, 1964}, {714, 46898}, {869, 2275}, {902, 8589}, {1055, 2308}, {1125, 20913}, {1193, 20985}, {1201, 3747}, {2210, 21008}, {2276, 16526}, {2277, 7032}, {2309, 17053}, {2810, 20663}, {3122, 23634}, {3616, 24621}, {3752, 27846}, {3795, 17389}, {4191, 22520}, {4263, 23532}, {4443, 36289}, {5299, 18266}, {7757, 32925}, {12194, 19308}, {13331, 19586}, {18170, 24530}, {21796, 22343}, {35269, 46904}

X(46908) = midpoint of X(1964) and X(46905)
X(46908) = reflection of X(3778) in X(46905)
X(46908) = crosssum of X(2) and X(32935)
X(46908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {869, 2275, 20456}, {2277, 7032, 23659}, {2309, 17053, 22172}

X(46909) = PAPPUS POINT (X(2),X(2),X(75),X(6))

X(46909) = 2 X[38] + X[321], X[38] + 2 X[3741], X[42] - 4 X[6682], X[321] - 4 X[3741], 2 X[1215] - 5 X[31241], 4 X[3666] - X[3896], 2 X[3666] + X[17135], 2 X[3706] + X[17147], X[3896] + 2 X[17135], X[3902] + 2 X[4424], X[17165] - 4 X[44417], X[24690] + 2 X[25368]

X(46909) lies on these lines: {1, 1150}, {2, 210}, {8, 4850}, {10, 244}, {11, 26580}, {31, 29652}, {37, 29824}, {38, 321}, {42, 6682}, {63, 24552}, {69, 33070}, {75, 4392}, {100, 24627}, {141, 3006}, {149, 24723}, {312, 7226}, {319, 32842}, {320, 33112}, {333, 7191}, {519, 46904}, {524, 17726}, {614, 5278}, {740, 31136}, {748, 29668}, {750, 24593}, {756, 3840}, {846, 32943}, {982, 4359}, {984, 4358}, {1125, 17450}, {1215, 31241}, {1386, 16704}, {1621, 38000}, {1647, 4407}, {1654, 5211}, {1757, 32944}, {1962, 42057}, {2886, 17184}, {2887, 29690}, {2895, 33071}, {3120, 21242}, {3121, 17448}, {3187, 17599}, {3218, 5263}, {3219, 32942}, {3242, 26227}, {3244, 21806}, {3246, 30564}, {3315, 5235}, {3338, 16454}, {3416, 29832}, {3434, 32950}, {3555, 26115}, {3616, 24597}, {3617, 17480}, {3622, 31359}, {3660, 17077}, {3661, 33089}, {3662, 33108}, {3663, 4442}, {3666, 3896}, {3677, 5271}, {3678, 19864}, {3696, 4003}, {3705, 32782}, {3706, 17147}, {3715, 26688}, {3728, 20892}, {3739, 3999}, {3745, 37639}, {3751, 29826}, {3752, 4651}, {3756, 5241}, {3759, 17025}, {3769, 5372}, {3791, 29819}, {3821, 33136}, {3833, 19870}, {3842, 30950}, {3844, 31079}, {3874, 19863}, {3891, 11679}, {3902, 4424}, {3920, 14829}, {3923, 36263}, {3936, 29639}, {3938, 32916}, {3952, 30818}, {3961, 32918}, {3971, 42039}, {3976, 31339}, {4026, 29835}, {4201, 5178}, {4357, 26015}, {4389, 33134}, {4414, 32941}, {4417, 29680}, {4438, 24943}, {4514, 33083}, {4643, 17721}, {4655, 33104}, {4657, 29829}, {4683, 33106}, {4688, 27812}, {4847, 4972}, {4852, 17162}, {4860, 26627}, {4865, 33080}, {4968, 10479}, {4980, 17155}, {5014, 26034}, {5044, 26094}, {5051, 10916}, {5057, 6646}, {5086, 5484}, {5192, 41229}, {5361, 17024}, {5439, 19874}, {5737, 17597}, {5741, 24239}, {6679, 29686}, {7292, 17277}, {9330, 30829}, {9342, 27002}, {9347, 37684}, {10453, 28606}, {10707, 17254}, {11680, 27184}, {16347, 37080}, {16496, 29828}, {16706, 33139}, {16727, 16887}, {16830, 37633}, {17017, 32853}, {17063, 26037}, {17140, 21342}, {17145, 29822}, {17154, 31025}, {17163, 42051}, {17165, 44417}, {17227, 25959}, {17237, 27918}, {17289, 33170}, {17308, 24629}, {17319, 38473}, {17345, 17491}, {17449, 24325}, {17591, 32860}, {17596, 32945}, {17598, 32914}, {17717, 33065}, {17722, 32843}, {17723, 31034}, {17884, 20882}, {18134, 29664}, {18398, 19858}, {19284, 32636}, {19786, 33142}, {19812, 29864}, {20292, 26840}, {20905, 26013}, {21020, 24165}, {24167, 28611}, {24616, 30653}, {24690, 25368}, {24892, 26128}, {25385, 32856}, {25496, 32912}, {25531, 35595}, {25760, 29676}, {26030, 34790}, {26098, 32859}, {26126, 41538}, {26230, 35466}, {26234, 30966}, {26563, 40619}, {27798, 42053}, {29637, 33115}, {29641, 33172}, {29643, 33087}, {29671, 33081}, {29673, 32781}, {29821, 32864}, {29827, 32931}, {29840, 33075}, {29849, 33084}, {29855, 31229}, {29874, 41806}, {30867, 31272}, {30967, 31323}, {32772, 32913}, {32774, 33137}, {32775, 33140}, {32776, 33141}, {32783, 33119}, {32784, 33120}, {32844, 33082}, {32850, 33086}, {32851, 33175}, {32863, 33073}, {32865, 33125}, {33064, 33105}, {33066, 33107}, {33067, 33109}, {33068, 33110}, {33069, 33111}, {33072, 33085}, {33113, 33171}, {33116, 33173}, {33117, 33174}, {33123, 33138}

X(46909) = midpoint of X(31136) and X(46901)
X(46909) = reflection of X(46897) in X(2)
X(46909) = crosssum of X(31) and X(2242)
X(46909) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 244, 24589}, {38, 3741, 321}, {982, 31330, 4359}, {984, 30942, 4358}, {1757, 32944, 41241}, {3242, 37660, 26227}, {3315, 5235, 16823}, {3666, 17135, 3896}, {3696, 4003, 17495}, {5372, 29815, 3769}, {16704, 29823, 1386}, {17449, 30970, 24325}, {21020, 42038, 24165}, {21342, 31993, 17140}, {29840, 37653, 33075}

X(46910) = PAPPUS POINT (X(2),X(2),X(75),X(561))

X(46910) lies on these lines: {2, 674}, {6, 26232}, {10, 3122}, {313, 714}, {349, 16889}, {730, 46905}, {1269, 4446}, {1400, 18082}, {1631, 26222}, {1737, 4008}, {3264, 4443}, {3765, 4484}, {3948, 4735}, {3971, 21035}, {4026, 40663}, {5224, 18052}, {17234, 24239}, {17792, 26979}, {21022, 42027}, {21352, 25347}, {22172, 28593}, {22277, 26772}, {23633, 24327}, {25048, 26959}, {36494, 38191}

X(46910) = reflection of X(46898) in X(2)
X(46910) = {X(3778),X(21238)}-harmonic conjugate of X(313)

X(46911) = PAPPUS POINT (X(2),X(2),X(1),X(141))

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

X(46911) lies on these lines: {86, 18183}, {522, 17320}, {551, 46903}, {2244, 12264}, {17457, 18082}, {17599, 30882}, {46898, 46901}

X(46912) = PAPPUS POINT (X(2),X(2),X(1),X(523))

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

X(46912) lies on these lines: {2, 523}, {86, 24345}, {99, 897}, {190, 2643}, {512, 24482}, {740, 3679}, {2611, 25531}, {4128, 37129}, {4132, 16482}, {4422, 21295}, {5263, 36815}, {6758, 24988}, {18082, 21804}, {26227, 26242}, {29857, 30758}, {31079, 31087}

X(46913) = PAPPUS POINT (X(2),X(2),X(6),X(10))

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

X(46913) lies on these lines: {1, 2}, {6, 6629}, {39, 597}, {58, 21937}, {524, 16887}, {662, 1509}, {3664, 25470}, {4278, 35276}, {4568, 21840}, {4658, 33828}, {16436, 19762}, {17200, 18755}, {17205, 40721}, {24915, 25723}, {35085, 36234}, {46899, 46904}

X(46914) = PAPPUS POINT (X(2),X(2),X(6),X(514))

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

X(46914) = 2 X[1015] + X[4568], 2 X[4103] + X[9263], X[21138] - 4 X[40479], 2 X[21208] - 5 X[27195], 2 X[21208] + X[33946], X[24427] - 3 X[25055], 5 X[27195] + X[33946]

X(46914) lies on these lines: {1, 42720}, {2, 514}, {10, 19933}, {106, 190}, {551, 726}, {667, 24492}, {1015, 4568}, {2786, 24508}, {3227, 3807}, {3570, 6789}, {3730, 35286}, {4103, 9263}, {4850, 17023}, {6381, 20917}, {6788, 30225}, {16826, 19740}, {16887, 39244}, {17063, 24196}, {17205, 18061}, {21138, 40479}, {21208, 27195}, {24427, 25055}, {24497, 28846}, {31191, 31233}

X(46914) = midpoint of X(3227) and X(3807)
X(46914) = {X(27195),X(33946)}-harmonic conjugate of X(21208)

X(46915) = PAPPUS POINT (X(2),X(2),X(514),X(10))

X(46915) = 2 X[661] + X[17161], 4 X[3004] - X[26824], 4 X[4369] - X[4608], X[4467] + 2 X[4841], 2 X[4467] + X[31290], 4 X[4500] - 7 X[27138], 2 X[4786] - 3 X[27486], X[4838] - 4 X[25666], 4 X[4841] - X[31290], 4 X[4976] - X[26853], 2 X[4988] + X[7192], X[4988] + 2 X[21196], 4 X[6590] - 7 X[27115], X[7192] - 4 X[21196], X[14779] + 8 X[17069], X[17494] - 4 X[45745], X[17494] + 2 X[45746], 2 X[45745] + X[45746]

X(46915) lies on these lines: {2, 523}, {239, 514}, {661, 17161}, {3004, 26824}, {3737, 17011}, {3797, 4010}, {4024, 45661}, {4359, 7199}, {4369, 4608}, {4467, 4841}, {4500, 27138}, {4770, 29593}, {4838, 25666}, {4931, 45315}, {4976, 26853}, {6548, 27483}, {6590, 27115}, {14779, 17069}, {24124, 27929}, {27757, 28169}, {28894, 31150}

X(46915) = midpoint of X(4750) and X(4988)
X(46915) = reflection of X(i) in X(j) for these {i,j}: {4024, 45661}, {4750, 21196}, {4931, 45315}, {7192, 4750}
X(46915) = anticomplement of X(4789)
X(46915) = anticomplement of the isotomic conjugate of X(37210)
X(46915) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {8691, 69}, {32672, 524}, {34914, 21293}, {34916, 150}, {35181, 315}, {36070, 17491}, {37210, 6327}
X(46915) = X(37210)-Ceva conjugate of X(2)
X(46915) = crosspoint of X(274) and X(35181)
X(46915) = crossdifference of every pair of points on line {42, 187}
X(46915) = barycentric product X(514)*X(31144)
X(46915) = barycentric quotient X(31144)/X(190)
X(46915) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4467, 4841, 31290}, {4988, 21196, 7192}, {45745, 45746, 17494}

X(46916) = PAPPUS POINT (X(2),X(2),X(10),X(8))

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

X(46916) = 8 X[10] + X[10106], 2 X[210] + X[553], X[950] - 10 X[1698], 5 X[3697] + 4 X[12436], 5 X[3698] + 4 X[12447], 7 X[3983] + 2 X[4298], 13 X[34595] - 4 X[40270]

X(46916) lies on these lines: {2, 3158}, {10, 56}, {55, 38059}, {57, 5686}, {100, 6666}, {165, 5817}, {200, 38053}, {210, 553}, {226, 8580}, {515, 3524}, {519, 4731}, {950, 1698}, {1125, 3689}, {1376, 13615}, {2550, 5316}, {3306, 24393}, {3474, 30393}, {3634, 17590}, {3651, 6684}, {3697, 12436}, {3698, 12447}, {3699, 24199}, {3711, 5542}, {3740, 17768}, {3826, 6745}, {3828, 6174}, {3925, 20103}, {3946, 5297}, {3982, 21060}, {3983, 4298}, {4031, 5223}, {4357, 26073}, {4689, 25072}, {5219, 40333}, {5745, 35977}, {6692, 9342}, {9779, 38092}, {17718, 38204}, {18230, 35445}, {26007, 29604}, {26251, 46896}, {28526, 42056}, {31140, 38201}, {34123, 41553}, {34595, 40270}

X(46916) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 4413, 3911}, {8580, 26040, 226}, {9342, 25006, 6692}

X(46917) = PAPPUS POINT (X(2),X(2),X(8),X(8))

X(46917) = 4 X[10] - X[5727], X[40] + 2 X[5720], X[57] + 2 X[200], X[57] - 4 X[1376], X[200] + 2 X[1376], X[497] - 4 X[20103], 2 X[497] - 5 X[20196], 4 X[997] - X[7962], 5 X[1698] - 2 X[5722], X[1750] + 2 X[6244], X[2093] + 2 X[3940], 4 X[3452] - X[9580], 2 X[3452] + X[17784], X[3474] + 2 X[21060], X[3586] - 4 X[3820], X[5768] - 4 X[6684], 4 X[6692] - X[36845], 2 X[7171] - 5 X[35242], 5 X[7987] - 2 X[30283], X[7994] + 2 X[19541], X[9580] + 2 X[17784], X[18528] + 2 X[35238], 8 X[20103] - 5 X[20196]

X(46917) lies on these lines: {1, 3689}, {2, 3158}, {8, 1420}, {9, 100}, {10, 3486}, {40, 5692}, {43, 5269}, {55, 7308}, {56, 4882}, {57, 200}, {72, 5128}, {75, 43290}, {78, 1706}, {165, 210}, {390, 5316}, {392, 936}, {404, 6762}, {474, 6765}, {480, 37541}, {497, 20103}, {516, 31142}, {549, 952}, {612, 46904}, {614, 9350}, {678, 17125}, {899, 7290}, {902, 15601}, {956, 35271}, {997, 2802}, {1054, 16496}, {1155, 3711}, {1260, 3256}, {1319, 4915}, {1419, 4551}, {1449, 3240}, {1574, 16780}, {1698, 5722}, {1699, 34612}, {1743, 37540}, {1750, 6244}, {1788, 6743}, {1962, 10158}, {2093, 3940}, {2136, 19861}, {2321, 40127}, {2550, 5219}, {2771, 3359}, {2999, 38315}, {3030, 3056}, {3035, 5231}, {3174, 10177}, {3189, 8582}, {3243, 3306}, {3247, 5297}, {3293, 37554}, {3419, 34122}, {3434, 30827}, {3452, 9580}, {3474, 21060}, {3475, 38054}, {3586, 3820}, {3587, 18524}, {3617, 4855}, {3622, 4917}, {3646, 3746}, {3677, 3961}, {3681, 3928}, {3683, 30393}, {3697, 31424}, {3699, 3729}, {3722, 35227}, {3731, 4689}, {3740, 4421}, {3744, 23511}, {3749, 16569}, {3751, 5524}, {3811, 5883}, {3870, 5437}, {3872, 41553}, {3886, 5205}, {3900, 35348}, {3913, 8583}, {3921, 16370}, {3938, 5573}, {3983, 5217}, {3996, 30567}, {4420, 11523}, {4654, 25568}, {4659, 9318}, {4666, 9342}, {4668, 37618}, {4678, 45036}, {4679, 6154}, {4711, 11194}, {4847, 31231}, {4848, 20007}, {4859, 17724}, {4866, 16192}, {4901, 17740}, {5082, 6700}, {5084, 41864}, {5268, 25430}, {5281, 5809}, {5436, 9780}, {5440, 9623}, {5534, 37526}, {5537, 11372}, {5691, 21031}, {5744, 24393}, {5768, 6684}, {6048, 37552}, {6692, 36845}, {6736, 37709}, {7080, 9578}, {7171, 35242}, {7174, 46901}, {7262, 9337}, {7322, 17594}, {7966, 38665}, {7987, 30283}, {7988, 31140}, {7994, 19541}, {8056, 17597}, {8270, 36636}, {8275, 13996}, {8715, 31435}, {9579, 21075}, {9588, 21677}, {9708, 30282}, {10164, 38210}, {10270, 14872}, {10980, 41711}, {11500, 37551}, {11519, 20323}, {12526, 41348}, {12625, 24982}, {12629, 17614}, {13405, 26040}, {15803, 34790}, {16491, 17779}, {16670, 17126}, {17282, 26073}, {17284, 26007}, {17718, 38052}, {17857, 37560}, {18164, 35983}, {18528, 35238}, {18540, 35000}, {19604, 31343}, {19605, 28070}, {21283, 37762}, {24391, 26062}, {26015, 31190}, {28043, 35293}, {30318, 37789}, {30852, 33110}, {34607, 40998}, {39948, 42043}

X(46917) = reflection of X(1) in X(35272)
X(46917) = X(6)-isoconjugate of X(44559)
X(46917) = barycentric quotient X(1)/X(44559)
X(46917) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3158, 10389}, {8, 5438, 1420}, {9, 100, 35445}, {55, 8580, 7308}, {78, 1706, 3340}, {165, 210, 3929}, {200, 1376, 57}, {497, 20103, 20196}, {936, 5687, 1697}, {1155, 3711, 5223}, {2550, 6745, 5219}, {3189, 8582, 37723}, {3306, 3935, 3243}, {3452, 17784, 9580}, {3689, 4413, 1}, {3740, 4421, 4512}, {3870, 5437, 44841}, {3913, 8583, 37556}, {3983, 5217, 5234}, {5268, 37553, 25430}, {5440, 9623, 13384}, {13405, 26040, 41867}, {30393, 31508, 3683}

X(46918) = PAPPUS POINT (X(2),X(2),X(8),X(10))

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

X(46918) = X[81] + 2 X[4046], 4 X[1211] - X[33100], X[2895] + 2 X[4418], X[2895] - 4 X[21085], X[4418] + 2 X[21085], 4 X[4697] - X[20086], 2 X[4854] - 5 X[31247], 2 X[32945] + X[33090]

X(46918) lies on these lines: {2, 740}, {8, 58}, {10, 32849}, {75, 33122}, {81, 4046}, {100, 594}, {346, 9330}, {846, 8013}, {896, 42334}, {1211, 28530}, {1654, 4427}, {2321, 5297}, {2345, 3240}, {2475, 20653}, {2805, 17281}, {2895, 4418}, {3617, 23937}, {3661, 33086}, {3679, 15677}, {3687, 33107}, {3696, 32779}, {3712, 4733}, {3775, 32845}, {3896, 19808}, {3923, 37656}, {3980, 32863}, {4023, 41242}, {4034, 36277}, {4062, 24342}, {4359, 33173}, {4442, 30832}, {4651, 33166}, {4683, 28546}, {4697, 20086}, {4699, 29830}, {4709, 29631}, {4732, 33115}, {4854, 31247}, {4980, 33126}, {5263, 32842}, {6539, 38836}, {8715, 27787}, {9347, 17299}, {9791, 27081}, {14459, 33682}, {15674, 42437}, {17018, 19822}, {17117, 26230}, {17285, 24988}, {17483, 33084}, {17765, 32945}, {17768, 31143}, {20095, 33076}, {21027, 29862}, {21081, 26131}, {21919, 26040}, {24161, 24946}, {26051, 27558}, {26228, 32087}, {26842, 33081}, {28566, 33075}, {28604, 29822}, {28605, 33153}, {31330, 33168}, {32778, 33110}, {32782, 33102}, {32783, 33150}, {32914, 41821}, {32932, 33083}, {33077, 33112}, {40592, 41811}

X(46918) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 33175, 33148}, {3696, 32779, 33139}, {3712, 4733, 5235}, {4062, 24342, 37635}, {4418, 21085, 2895}, {21020, 33160, 2}, {27811, 46896, 2}

X(46919) = PAPPUS POINT (X(2),X(2),X(514),X(8))

X(46919) = 3 X[2] + X[27486], 2 X[650] + X[3676], X[650] + 2 X[7658], 5 X[650] + X[21104], 4 X[905] - X[30719], 5 X[1638] - X[21104], X[3004] + 2 X[43061], X[3239] + 2 X[17069], X[3239] - 4 X[31287], X[3676] - 4 X[7658], 5 X[3676] - 2 X[21104], X[3798] + 2 X[25666], X[4025] + 2 X[4521], X[4025] + 5 X[31209], X[4468] - 7 X[27115], 2 X[4521] - 5 X[31209], X[4765] + 2 X[4885], X[4976] + 5 X[31250], X[6590] - 7 X[31207], 10 X[7658] - X[21104], X[11068] + 2 X[21212], X[14837] + 2 X[14838], X[17069] + 2 X[31287], 5 X[24924] + X[45745], X[30565] - 5 X[31209], X[44551] + 2 X[44567], 2 X[44551] + X[45670], 4 X[44563] - X[45320], 4 X[44567] - X[45670], 2 X[45334] + X[45669]

X(46919) lies on these lines: {2, 522}, {57, 657}, {226, 21195}, {241, 514}, {676, 4777}, {812, 44432}, {824, 45675}, {900, 10006}, {918, 44551}, {1459, 2999}, {2254, 4776}, {2487, 28902}, {3239, 17069}, {3752, 6586}, {3798, 25666}, {3835, 45679}, {4025, 4521}, {4077, 27417}, {4468, 27115}, {4762, 44902}, {4765, 4885}, {4789, 21180}, {4814, 5308}, {4893, 28878}, {4944, 45334}, {4976, 31250}, {5222, 30573}, {6548, 42318}, {6590, 31207}, {11350, 39226}, {14425, 30520}, {14475, 39963}, {19804, 20907}, {21173, 23511}, {21183, 31150}, {23876, 45683}, {24924, 45745}, {28846, 45674}, {29144, 45691}, {31947, 40940}, {37269, 39199}, {44563, 45320}

X(46919) = midpoint of X(i) and X(j) for these {i,j}: {650, 1638}, {3835, 45679}, {4025, 30565}, {4776, 4786}, {4944, 45669}, {17069, 45326}, {21183, 31150}
X(46919) = reflection of X(i) in X(j) for these {i,j}: {1638, 7658}, {3239, 45326}, {3676, 1638}, {4944, 45334}, {30565, 4521}, {45326, 31287}
X(46919) = X(i)-complementary conjugate of X(j) for these (i,j): {1415, 15346}, {14074, 141}
X(46919) = X(30181)-Ceva conjugate of X(28292)
X(46919) = X(14074)-isoconjugate of X(25411)
X(46919) = crossdifference of every pair of points on line {55, 1055}
X(46919) = barycentric product X(i)*X(j) for these {i,j}: {514, 6172}, {693, 35445}, {4569, 23056}
X(46919) = barycentric quotient X(i)/X(j) for these {i,j}: {6172, 190}, {23056, 3900}, {35445, 100}
X(46919) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 905, 43050}, {650, 7658, 3676}, {3676, 43050, 30719}, {4025, 31209, 4521}, {17069, 31287, 3239}, {44551, 44567, 45670}

X(46920) = X(1)X(3)∩X(4)X(6224)

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

X(46920) = 7 X[1] + X[6769], 3 X[1] - 2 X[26087], 3 X[1] + X[37531], X[3] - 4 X[35597], 3 X[1385] - X[37623], 3 X[3655] + X[5812], 3 X[5603] - X[10525], X[6769] + 14 X[11567], 3 X[6769] + 14 X[26087], 3 X[6769] - 7 X[37531], 3 X[10246] - X[11249], 3 X[10246] - 4 X[33657], 3 X[10247] + X[10306], X[11249] - 4 X[33657], 3 X[11567] - X[26087], 6 X[11567] + X[37531], X[22770] - 5 X[37624], 2 X[26087] + X[37531], 3 X[26286] - 2 X[37623]

X(46920) lies on these lines: {1, 3}, {4, 6224}, {5, 30144}, {8, 6952}, {30, 40257}, {80, 6971}, {140, 30147}, {145, 6972}, {214, 6924}, {355, 4511}, {404, 1389}, {758, 32153}, {944, 6840}, {952, 12607}, {997, 9956}, {1490, 28208}, {1656, 17057}, {1766, 4287}, {1807, 39270}, {1872, 40985}, {2320, 6875}, {2475, 5603}, {2476, 5886}, {2771, 12114}, {3476, 5761}, {3560, 5289}, {3616, 6853}, {3655, 5812}, {3656, 17579}, {3874, 11715}, {3878, 6914}, {4999, 5690}, {5443, 6980}, {5450, 14988}, {5499, 10283}, {5657, 37291}, {5693, 26321}, {5694, 5730}, {5731, 14450}, {5840, 19907}, {5841, 34773}, {5844, 22837}, {5901, 25466}, {6261, 22792}, {6326, 18525}, {6842, 15950}, {6882, 10950}, {6903, 7967}, {6922, 37728}, {6931, 38182}, {6943, 34772}, {6951, 10595}, {6958, 10573}, {7681, 11729}, {9955, 10893}, {10943, 44669}, {11230, 19861}, {11231, 19860}, {11236, 28204}, {11499, 22935}, {12747, 45764}, {16159, 39778}, {18391, 26492}, {18480, 45770}, {18481, 21740}, {30143, 38028}, {30212, 35050}, {31828, 41704}

X(46920) = midpoint of X(i) and X(j) for these {i,j}: {944, 10526}, {1482, 11248}
X(46920) = reflection of X(i) in X(j) for these {i,j}: {1, 11567}, {3, 26287}, {40, 26086}, {26286, 1385}, {26287, 35597}
X(46920) = X(18567)-of-excentral-triangle
X(46920) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5538, 11014}, {1, 37533, 10222}, {3, 1482, 5903}, {3, 2099, 35004}, {3, 10679, 14882}, {3, 34471, 1385}, {3, 37567, 10225}, {40, 37616, 3}, {145, 6972, 12247}, {1385, 10222, 942}, {1385, 10284, 8071}, {1385, 23960, 17437}, {2077, 11009, 25413}, {2077, 14800, 3}, {2098, 10679, 10284}, {5538, 11014, 12702}, {5730, 22758, 5694}, {6958, 10573, 12619}, {7982, 37618, 37532}, {10222, 35004, 2099}, {11012, 14799, 3}, {13601, 16193, 942}, {21842, 37625, 22765}, {37531, 37615, 37623}

X(46921) = (name pending)

X(46922) = X(1)X(190)∩X(2)X(6)

X(46922) = X(319)-4*X(5750), X(894)+2*X(1100), 2*X(894)+X(4360), 4*X(1100)-X(4360), 2*X(4649)+X(5263), X(4649)+2*X(33682), X(5263)-4*X(33682), X(17277)-4*X(20147)

X(46922) lies on these lines: {1, 190}, {2, 6}, {7, 17380}, {9, 17394}, {32, 21937}, {37, 17120}, {42, 41142}, {44, 4755}, {45, 29570}, {61, 21898}, {62, 21869}, {75, 1449}, {87, 40433}, {182, 13635}, {187, 22351}, {192, 16884}, {216, 22359}, {238, 551}, {239, 4670}, {261, 33766}, {319, 5750}, {320, 4667}, {335, 36409}, {354, 46911}, {376, 37474}, {511, 13634}, {519, 4649}, {527, 16503}, {536, 894}, {545, 4366}, {549, 37510}, {553, 7175}, {574, 22355}, {575, 21554}, {576, 6998}, {594, 28337}, {645, 33770}, {648, 11109}, {662, 1509}, {673, 2364}, {757, 4264}, {903, 4586}, {999, 19255}, {1001, 6172}, {1043, 16394}, {1125, 16477}, {1268, 17275}, {1404, 41245}, {1740, 42043}, {1743, 4687}, {1911, 43262}, {1961, 42056}, {1964, 2663}, {2220, 30593}, {2345, 17377}, {3241, 28503}, {3247, 17336}, {3286, 17549}, {3664, 16706}, {3686, 28653}, {3699, 9347}, {3723, 17261}, {3729, 17393}, {3739, 16668}, {3759, 10436}, {3834, 29630}, {3873, 9020}, {3879, 17289}, {3943, 29588}, {3946, 7321}, {4203, 18185}, {4234, 5145}, {4263, 24530}, {4277, 24598}, {4349, 32850}, {4363, 4393}, {4364, 20072}, {4384, 41847}, {4389, 4644}, {4416, 17322}, {4422, 29569}, {4428, 20992}, {4440, 17395}, {4472, 4969}, {4643, 17397}, {4657, 17273}, {4658, 7760}, {4663, 16830}, {4665, 20016}, {4675, 17367}, {4690, 29610}, {4698, 16671}, {4700, 4758}, {4708, 29609}, {4715, 17254}, {4725, 29615}, {4741, 17325}, {4747, 17014}, {4753, 36531}, {4798, 29576}, {4851, 17285}, {4852, 17116}, {4856, 4967}, {5007, 16060}, {5132, 13587}, {5158, 21940}, {5327, 11114}, {5733, 36652}, {5749, 17233}, {6419, 21909}, {6420, 21992}, {6542, 17369}, {6631, 35962}, {6646, 7277}, {6687, 29626}, {7113, 40744}, {7232, 17383}, {7379, 8550}, {7474, 11422}, {7772, 16061}, {7812, 17677}, {7878, 17681}, {9055, 31314}, {9345, 25531}, {10022, 40891}, {11038, 38048}, {11329, 37503}, {12150, 16712}, {16370, 37507}, {16371, 37502}, {16393, 19767}, {16403, 44094}, {16468, 25055}, {16495, 17450}, {16669, 17260}, {16670, 16831}, {16675, 31313}, {16777, 17350}, {16779, 17274}, {16829, 20963}, {16885, 27268}, {17011, 20176}, {17021, 41241}, {17227, 29598}, {17237, 29614}, {17246, 31300}, {17250, 29603}, {17252, 25498}, {17264, 29574}, {17272, 17400}, {17276, 17396}, {17279, 17391}, {17280, 17390}, {17281, 17389}, {17284, 17387}, {17286, 17386}, {17287, 17385}, {17288, 17384}, {17291, 17376}, {17292, 17374}, {17293, 17373}, {17296, 17371}, {17298, 17370}, {17302, 17365}, {17303, 17363}, {17306, 17361}, {17308, 17360}, {17310, 17359}, {17311, 17358}, {17312, 17357}, {17315, 17355}, {17316, 17354}, {17317, 17353}, {17319, 17351}, {17321, 17347}, {17324, 17345}, {17326, 17344}, {17333, 41312}, {17342, 29573}, {17362, 28604}, {17366, 26806}, {17682, 33955}, {17809, 37103}, {18046, 44139}, {18147, 34283}, {18170, 23532}, {18816, 32040}, {18825, 40735}, {19322, 37492}, {19325, 36741}, {19326, 36740}, {19875, 43997}, {20170, 41834}, {20179, 37756}, {20924, 30892}, {21849, 40954}, {22343, 45223}, {23812, 33132}, {24345, 35148}, {24358, 31349}, {25496, 31137}, {25528, 36634}, {25529, 26738}, {26223, 34064}, {26685, 31333}, {26821, 26976}, {27064, 37595}, {28619, 37035}, {29575, 41310}, {29590, 34824}, {30710, 39948}, {31136, 32772}, {31161, 32926}, {31178, 32922}, {35110, 40861}, {36494, 38315}, {36646, 39972}, {37128, 39974}, {39971, 39982}, {41138, 41313}

X(46922) = midpoint of X(894) and X(29584)
X(46922) = reflection of X(i) in X(j) for these (i, j): (4360, 29584), (17254, 41311), (17271, 2), (29584, 1100)
X(46922) = perspector of the circumconic {{A, B, C, X(99), X(4607)}}
X(46922) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(29822)}} and {{A, B, C, X(81), X(37129)}}
X(46922) = barycentric product X(86)*X(29822)
X(46922) = trilinear product X(81)*X(29822)
X(46922) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3758, 190), (2, 1992, 17346), (2, 5032, 37654), (2, 17346, 31144), (2, 17378, 17297), (6, 86, 17277), (6, 15668, 17349), (6, 17379, 86), (69, 17381, 17307), (320, 17023, 17305), (597, 17392, 2), (894, 1100, 4360), (3589, 17300, 17283), (3618, 3945, 17234), (3629, 17398, 1654), (3739, 16668, 17121), (3879, 17289, 17295), (4363, 4393, 17160), (4644, 26626, 4389), (4649, 33682, 5263), (4657, 17364, 17273), (4667, 17023, 320), (4670, 16666, 239), (4675, 17367, 27191), (6144, 17327, 17343), (7277, 17045, 6646), (8025, 19743, 32911), (10436, 16667, 3759), (17379, 37677, 6), (19684, 37685, 333), (20072, 29586, 4364)

X(46923) = X(7)X(17198)∩X(57)X(33100)

X(46923) lies on these lines: {7, 17198}, {57, 33100}, {1756, 37635}, {3218, 9791}, {3338, 14450}, {6007, 35983}, {9811, 42744}

X(46924) = X(2)X(216)∩X(53)X(1994)

X(46924) lies on these lines: {2, 216}, {4, 13585}, {53, 1994}, {297, 15108}, {467, 37779}, {648, 14129}, {1217, 21734}, {1990, 34545}, {3448, 6747}, {6524, 14002}, {6530, 37349}, {13450, 21451}, {13595, 14569}, {30529, 41678}

X(46924) = polar conjugate of X(13418)
X(46924) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 13418}, {822, 30248}
X(46924) = X(107)-reciprocal conjugate of-X(30248)
X(46924) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(13621)}} and {{A, B, C, X(324), X(30526)}}
X(46924) = barycentric product X(264)*X(13621)
X(46924) = barycentric quotient X(107)/X(30248)
X(46924) = trilinear product X(i)*X(j) for these {i, j}: {92, 13621}, {823, 30210}
X(46924) = trilinear quotient X(i)/X(j) for these (i, j): (92, 13418), (823, 30248)
X(46924) = {X(324), X(37766)}-harmonic conjugate of X(2)

X(46925) = X(4)X(13)∩X(472)X(1994)

X(46925) lies on these lines: {4, 13}, {186, 11537}, {393, 1989}, {472, 1994}, {3518, 11142}, {6104, 44879}, {10594, 21310}, {11080, 36302}, {11139, 13472}, {11586, 13619}, {35489, 46078}, {36211, 37943}

X(46925) = polar conjugate of X(19778)
X(46925) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 3384}, {48, 19778}
X(46925) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 19778), (13, 40711), (19, 3384), (62, 44718)
X(46925) = barycentric product X(i)*X(j) for these {i, j}: {4, 16770}, {13, 472}, {92, 3383}, {264, 11142}, {300, 10641}, {303, 8737}
X(46925) = barycentric quotient X(i)/X(j) for these (i, j): (4, 19778), (13, 40711), (19, 3384), (62, 44718), (462, 40668), (472, 298)
X(46925) = trilinear product X(i)*X(j) for these {i, j}: {4, 3383}, {19, 16770}, {92, 11142}, {472, 2153}
X(46925) = trilinear quotient X(i)/X(j) for these (i, j): (4, 3384), (92, 19778), (2153, 32586)
X(46925) = {X(1989),X(6344)}-harmonic conjugate of X(46926)

X(46926) = X(4)X(14)∩X(473)X(1994)

X(46926) lies on these lines: {4, 14}, {186, 11549}, {393, 1989}, {473, 1994}, {3518, 11141}, {6105, 44879}, {10594, 21311}, {11085, 36303}, {11138, 13472}, {13619, 15743}, {35489, 46074}, {36210, 37943}

X(46926) = polar conjugate of X(19779)
X(46926) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 3375}, {48, 19779}
X(46926) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 19779), (14, 40712), (19, 3375), (61, 44719)
X(46926) = barycentric product X(i)*X(j) for these {i, j}: {4, 16771}, {14, 473}, {92, 3376}, {264, 11141}, {301, 10642}, {302, 8738}
X(46926) = barycentric quotient X(i)/X(j) for these (i, j): (4, 19779), (14, 40712), (19, 3375), (61, 44719), (463, 40667), (473, 299)
X(46926) = trilinear product X(i)*X(j) for these {i, j}: {4, 3376}, {19, 16771}, {92, 11141}, {473, 2154}
X(46926) = trilinear quotient X(i)/X(j) for these (i, j): (4, 3375), (92, 19779), (2154, 32585)
X(46926) = {X(1989),X(6344)}-harmonic conjugate of X(46925)

X(46927) = X(2)X(216)∩X(69)X(459)

X(46927) lies on these lines: {2, 216}, {4, 40196}, {20, 6526}, {69, 459}, {107, 1370}, {154, 46776}, {297, 26958}, {317, 13567}, {441, 20207}, {450, 1899}, {648, 14361}, {671, 38253}, {1093, 3546}, {1948, 20266}, {3079, 14927}, {3926, 42468}, {5523, 14939}, {6036, 38282}, {6330, 6340}, {6331, 34254}, {6504, 16080}, {6524, 16051}, {6525, 7396}, {6530, 30771}, {6677, 33971}, {6820, 37643}, {14615, 46741}, {16081, 40323}, {17811, 44134}, {18026, 27540}, {18928, 36794}, {20477, 45200}, {37192, 43462}, {37774, 44697}

X(46927) = polar conjugate of X(43695)
X(46927) = crossdifference of every pair of points on line {X(33968), X(39201)}
X(46927) = X(235)-Dao conjugate of X(800)
X(46927) = X(i)-isoconjugate-of-X(j) for these {i, j}: {48, 43695}, {822, 30249}
X(46927) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 43695), (107, 30249), (1660, 184)
X(46927) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(2063)}} and {{A, B, C, X(232), X(1660)}}
X(46927) = barycentric product X(i)*X(j) for these {i, j}: {264, 11413}, {1660, 18022}, {2052, 2063}
X(46927) = barycentric quotient X(i)/X(j) for these (i, j): (4, 43695), (107, 30249), (1660, 184), (2063, 394)
X(46927) = trilinear product X(i)*X(j) for these {i, j}: {92, 11413}, {158, 2063}, {823, 30211}, {1660, 1969}
X(46927) = trilinear quotient X(i)/X(j) for these (i, j): (92, 43695), (823, 30249), (1660, 9247), (2063, 255)
X(46927) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 15466, 17907), (2, 46106, 11547), (14361, 37669, 648)

X(46928) = ISOGONAL CONJUGATE OF X(46921)

Barycentrics a^2*(5*a^8 - 24*a^6*b^2 + 42*a^4*b^4 - 32*a^2*b^6 + 9*b^8 - 24*a^6*c^2 + 34*a^4*b^2*c^2 + 32*a^2*b^4*c^2 - 42*b^6*c^2 + 42*a^4*c^4 + 32*a^2*b^2*c^4 + 66*b^4*c^4 - 32*a^2*c^6 - 42*b^2*c^6 + 9*c^8) : :

X(46928) lies on these lines: {3, 143}, {6, 14491}, {378, 44107}, {524, 5071}, {3527, 14157}, {6000, 15004}, {7592, 34565}, {9707, 17810}, {9781, 14530}, {10594, 44111}, {14483, 32063}

X(46929) = X(4)X(3917)∩X(53)X(39662)

X(46930) = X(1)X(2)∩X(20)X(38140)

X(46930) = 18*X(1)+11*X(8), 11*X(1)+18*X(38098), 9*X(2)+20*X(1698), 13*X(2)+16*X(3828), 15*X(2)+14*X(9780), 17*X(2)+12*X(19875), 20*X(8)+9*X(145), 17*X(8)+12*X(3244), 14*X(8)+15*X(3623), 15*X(10)+14*X(1125), 20*X(10)+9*X(38314), 19*X(145)+10*X(3621), 13*X(145)+16*X(3625), 14*X(145)+15*X(31145), 20*X(1125)+9*X(3679), 19*X(1125)+10*X(4691), 17*X(1698)+12*X(31253), 14*X(3244)+15*X(4816), 16*X(3616)+13*X(3617), 15*X(3617)+14*X(3622)

X(46930) lies on these lines: {1, 2}, {20, 38140}, {165, 3854}, {632, 18526}, {1268, 32105}, {1376, 17570}, {3090, 20070}, {3091, 11231}, {3146, 31423}, {3296, 31479}, {3522, 10175}, {3523, 18480}, {3525, 34773}, {3533, 38042}, {3826, 5141}, {3832, 31425}, {3847, 33108}, {3871, 16854}, {4189, 9342}, {4373, 28650}, {4413, 16865}, {4751, 31302}, {5056, 12699}, {5059, 7989}, {5067, 18493}, {5068, 6684}, {5224, 32093}, {5303, 17572}, {5687, 17546}, {7486, 26446}, {7967, 16239}, {9330, 24174}, {9709, 17534}, {9956, 10303}, {10164, 17578}, {10172, 15022}, {10588, 21454}, {11680, 34501}, {12690, 16845}, {15692, 38083}, {15702, 18357}, {15709, 18525}, {15721, 18481}, {16980, 33879}, {17559, 33110}, {18253, 31888}, {19925, 21734}, {23841, 44299}, {26040, 37162}

X(46930) = intersection, other than A, B, C, of circumconics {{A, B, C, X(79), X(19872)}} and {{A, B, C, X(145), X(28650)}}
X(46930) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 3621, 3624), (2, 4678, 5550), (2, 9780, 145), (10, 31145, 3617), (145, 1125, 3622), (1125, 1698, 9780), (3616, 19872, 2), (3617, 3622, 20054), (3622, 31145, 3623), (3828, 19872, 3616), (4816, 19875, 10), (5550, 19875, 4678), (5550, 31253, 2), (9780, 38314, 10), (19875, 31253, 5550)

X(46931) = X(1)X(2)∩X(20)X(11231)

X(46931) = 14*X(1)+9*X(8), 5*X(1)+18*X(10), 8*X(1)+15*X(3617), 20*X(1)+3*X(3621), 17*X(1)+6*X(3625), 11*X(1)+12*X(3626), 15*X(2)+8*X(10), 3*X(2)+20*X(1698), 18*X(2)+5*X(3617), 19*X(2)+4*X(3679), 7*X(2)+16*X(3828), 9*X(2)+14*X(9780), 11*X(2)+12*X(19875), 16*X(8)+7*X(145), 7*X(8)+16*X(3636), 3*X(8)+20*X(19862), 5*X(8)+18*X(25055), 13*X(10)+10*X(1125), 20*X(10)+3*X(3241), 16*X(10)+7*X(3622), 3*X(10)+20*X(3634), 12*X(10)+11*X(5550), 6*X(10)+17*X(19872), 14*X(10)+9*X(25055), 10*X(10)+13*X(34595)

X(46931) lies on these lines: {1, 2}, {20, 11231}, {35, 17544}, {40, 15022}, {100, 17570}, {149, 17559}, {442, 20084}, {631, 18357}, {962, 10172}, {1213, 26039}, {1268, 3672}, {1376, 16859}, {1574, 46846}, {3090, 12702}, {3091, 3579}, {3146, 10175}, {3295, 17546}, {3305, 5128}, {3522, 31423}, {3523, 9956}, {3525, 38042}, {3526, 37705}, {3533, 5790}, {3543, 38083}, {3614, 3826}, {3620, 4663}, {3628, 8148}, {3697, 4430}, {3832, 6684}, {3842, 4772}, {3854, 9778}, {3868, 4539}, {3871, 16853}, {3876, 31794}, {3889, 3921}, {3890, 4731}, {3925, 5154}, {4188, 9342}, {4189, 4413}, {4197, 10592}, {4346, 17249}, {4536, 5902}, {4661, 5439}, {4967, 32105}, {5046, 26040}, {5056, 20070}, {5059, 10164}, {5068, 18483}, {5070, 12245}, {5129, 20066}, {5187, 15254}, {5204, 5260}, {5217, 16865}, {5220, 10585}, {5221, 10588}, {5225, 37162}, {5232, 28650}, {5251, 37307}, {5261, 32636}, {5281, 17606}, {5302, 8165}, {5551, 5708}, {5587, 15717}, {5657, 7486}, {5687, 17534}, {5731, 31399}, {5818, 10303}, {6666, 30332}, {6920, 35251}, {6946, 35252}, {7173, 33108}, {7967, 46219}, {7989, 17578}, {8193, 16042}, {9330, 24443}, {9578, 31188}, {9588, 9779}, {9708, 17535}, {9709, 17536}, {9963, 12019}, {10124, 18526}, {10590, 37524}, {11319, 19744}, {14002, 37557}, {15683, 18492}, {15692, 18480}, {15697, 33697}, {15702, 18525}, {15708, 18481}, {15709, 34773}, {16456, 37639}, {16704, 17551}, {16948, 17589}, {16980, 44299}, {17558, 17619}, {17580, 20067}, {17582, 20060}, {20059, 38204}, {20085, 34122}, {21454, 24914}, {24988, 26070}, {30340, 38057}, {34748, 41984}, {37436, 37582}

X(46931) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 10, 3622), (2, 3621, 5550), (2, 3623, 3624), (2, 4678, 1125), (2, 9780, 3617), (2, 20049, 19883), (2, 29576, 24599), (8, 38098, 4678), (10, 1125, 4677), (10, 3621, 3617), (10, 3634, 19872), (10, 5550, 3621), (10, 19872, 5550), (10, 25055, 8), (10, 34595, 3241), (1698, 19876, 10), (1698, 19877, 2), (3617, 3622, 3621), (3617, 31145, 3626), (3621, 5550, 3622), (3633, 19875, 10), (3634, 3828, 19862), (3634, 9780, 2), (4677, 20050, 3621), (5550, 9780, 10), (5550, 19872, 2), (9780, 19872, 3621), (9780, 19877, 3634), (19862, 25055, 5550), (19872, 19876, 3634)

X(46932) = X(1)X(2)∩X(20)X(9956)

X(46932) = 10*X(1)+7*X(8), 3*X(1)+14*X(10), 5*X(1)+12*X(4745), 9*X(1)+8*X(4746), X(1)-7*X(19872), 20*X(1)-3*X(20049), 12*X(1)+5*X(20052), 16*X(1)+X(20054), 3*X(1)-20*X(31253), 15*X(2)+2*X(8), 9*X(2)+8*X(10), 18*X(2)-X(145), 3*X(2)-20*X(1698), 19*X(2)-2*X(3241), 12*X(2)+5*X(3617), 13*X(2)+4*X(3679), X(2)+16*X(3828), 3*X(2)+14*X(9780), 3*X(2)-4*X(19872), 5*X(2)+12*X(19875), 16*X(2)+X(31145)

X(46932) lies on these lines: {1, 2}, {4, 28182}, {5, 20070}, {12, 21454}, {20, 9956}, {40, 5068}, {55, 17570}, {100, 16859}, {144, 3826}, {165, 17578}, {193, 3844}, {319, 28650}, {341, 24589}, {346, 16677}, {355, 10303}, {390, 17606}, {391, 16671}, {442, 31888}, {452, 7705}, {516, 3854}, {517, 7486}, {631, 18525}, {632, 7967}, {944, 31662}, {952, 3533}, {956, 17535}, {958, 9342}, {962, 15022}, {986, 9330}, {1211, 41913}, {1268, 4373}, {1278, 3842}, {1329, 18231}, {1376, 16865}, {2475, 26040}, {2550, 37162}, {3035, 20085}, {3090, 22791}, {3091, 6361}, {3146, 6684}, {3295, 17534}, {3522, 5587}, {3523, 5818}, {3524, 18357}, {3525, 5790}, {3544, 28174}, {3579, 3839}, {3620, 38047}, {3628, 12245}, {3649, 10588}, {3697, 4661}, {3739, 31302}, {3740, 3962}, {3812, 4005}, {3820, 4197}, {3822, 20078}, {3832, 10175}, {3868, 4533}, {3869, 3922}, {3871, 16842}, {3873, 3983}, {3876, 4018}, {3877, 4002}, {3925, 5141}, {3947, 5586}, {3956, 18398}, {3988, 5902}, {4004, 5044}, {4188, 4413}, {4293, 5442}, {4430, 5439}, {4452, 5936}, {4454, 4708}, {4547, 5883}, {4731, 14923}, {4747, 17251}, {5047, 9709}, {5056, 5657}, {5059, 19925}, {5067, 5690}, {5070, 10595}, {5071, 12702}, {5084, 33110}, {5123, 20067}, {5129, 17619}, {5154, 33108}, {5232, 17361}, {5235, 17589}, {5251, 17548}, {5261, 24914}, {5302, 9352}, {5441, 15676}, {5445, 10590}, {5686, 25557}, {5687, 17536}, {5691, 21734}, {5698, 6871}, {5710, 37687}, {5711, 14997}, {5734, 38127}, {5772, 17291}, {5791, 37436}, {6548, 32212}, {6702, 20095}, {6767, 16856}, {6857, 9945}, {7226, 24174}, {7321, 17250}, {7496, 9798}, {7989, 9778}, {7998, 23841}, {8025, 17551}, {8148, 15699}, {8165, 26066}, {8972, 13973}, {9588, 9812}, {9708, 17531}, {9779, 43174}, {10032, 18253}, {10106, 31188}, {10304, 18480}, {10592, 43733}, {11015, 17558}, {11024, 31018}, {11036, 31479}, {11539, 18526}, {12645, 16239}, {12699, 38083}, {13624, 15721}, {13911, 13941}, {13996, 31272}, {14007, 16704}, {15254, 38092}, {15492, 17303}, {15683, 35242}, {15694, 37705}, {15702, 34773}, {15717, 31399}, {15720, 38138}, {15723, 38081}, {16981, 31737}, {17057, 37256}, {17321, 32105}, {17327, 26104}, {17567, 38058}, {17676, 26073}, {18491, 37105}, {20060, 37462}, {20073, 28604}, {21075, 27186}, {23958, 41229}, {24988, 30577}, {25498, 28635}, {26062, 37161}, {27578, 30436}, {31298, 40533}, {31992, 44314}, {32089, 42696}

X(46932) = reflection of X(29626) in X(5550)
X(46932) = anticomplement of the anticomplement of X(19872)
X(46932) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 4745, 8), (1, 20052, 145), (2, 10, 145), (2, 3617, 3622), (2, 3621, 1125), (2, 4678, 3616), (8, 3616, 3635), (8, 3634, 2), (10, 145, 3617), (10, 1125, 4668), (10, 3616, 4678), (10, 3624, 8), (10, 3634, 3624), (10, 3636, 3679), (10, 19877, 2), (10, 19878, 3632), (10, 31253, 1), (1698, 19875, 3634), (3244, 41150, 1), (3616, 4678, 145), (3621, 20057, 145), (3623, 20053, 145), (3624, 3635, 3616), (3624, 19875, 10), (3632, 19878, 3616), (3634, 19875, 8), (3636, 20053, 3623), (3679, 5550, 3623), (4413, 5260, 4188), (4668, 20057, 3621), (5550, 20053, 3636), (5818, 11231, 3523)

X(46933) = X(1)X(2)∩X(20)X(5818)

X(46933) = 4*X(1)-15*X(2), 6*X(1)+5*X(8), X(1)+10*X(10), 16*X(1)-5*X(145), 9*X(1)-20*X(1125), 13*X(1)+20*X(3626), 17*X(1)+5*X(3632), 7*X(1)+15*X(3679), X(1)-12*X(3828), 5*X(1)+6*X(4669), 4*X(1)+7*X(4678), 3*X(1)+8*X(4691), 7*X(1)+4*X(4701), 2*X(1)-5*X(5550), 2*X(1)-13*X(19877), 5*X(1)-16*X(19878), 7*X(1)-18*X(19883), 12*X(1)-X(20014), 10*X(1)+X(20053), 8*X(1)+3*X(31145)

X(46933) lies on these lines: {1, 2}, {3, 38138}, {4, 28178}, {9, 41348}, {20, 5818}, {21, 9709}, {40, 3832}, {55, 16859}, {56, 9342}, {69, 1268}, {79, 10590}, {100, 16865}, {140, 18526}, {144, 5880}, {149, 5084}, {153, 6897}, {165, 5059}, {193, 38047}, {320, 3823}, {333, 17589}, {341, 4359}, {346, 1213}, {355, 3523}, {376, 18357}, {390, 17358}, {391, 16669}, {404, 9708}, {442, 27081}, {443, 20060}, {452, 20066}, {495, 3296}, {515, 15717}, {517, 5056}, {547, 8148}, {594, 16674}, {631, 5790}, {632, 12645}, {756, 24440}, {942, 3921}, {944, 10303}, {946, 15022}, {952, 3525}, {956, 17531}, {958, 4188}, {960, 4731}, {962, 5068}, {966, 16885}, {984, 4772}, {993, 37307}, {999, 17535}, {1191, 37687}, {1219, 39962}, {1265, 31247}, {1329, 5141}, {1376, 4189}, {1420, 31188}, {1478, 26060}, {1482, 5067}, {1483, 46219}, {1512, 37434}, {1621, 17570}, {1656, 12245}, {1706, 3305}, {1724, 30652}, {1788, 5261}, {1837, 5281}, {2049, 19742}, {2276, 25614}, {2292, 9330}, {2325, 5296}, {2345, 16814}, {2475, 2551}, {2476, 3820}, {2478, 33110}, {2550, 5046}, {2886, 5154}, {2975, 4413}, {2979, 23841}, {3090, 5690}, {3091, 5657}, {3097, 20105}, {3146, 5587}, {3219, 37161}, {3295, 17536}, {3336, 31410}, {3421, 37462}, {3434, 37162}, {3436, 26040}, {3522, 6684}, {3524, 18525}, {3526, 7967}, {3533, 10246}, {3543, 3579}, {3545, 12702}, {3600, 24914}, {3620, 3844}, {3628, 10595}, {3646, 3895}, {3650, 6175}, {3662, 5772}, {3681, 3812}, {3695, 6539}, {3696, 27268}, {3697, 3868}, {3698, 3740}, {3701, 28605}, {3707, 5749}, {3715, 11684}, {3753, 3876}, {3817, 30315}, {3826, 5686}, {3839, 6361}, {3842, 4704}, {3847, 9710}, {3854, 7989}, {3855, 28174}, {3871, 11108}, {3873, 4662}, {3913, 5284}, {3918, 5692}, {3925, 9711}, {3927, 32635}, {3945, 17360}, {3956, 5904}, {3968, 5903}, {3992, 28612}, {4000, 28633}, {4002, 5044}, {4015, 5902}, {4034, 4982}, {4190, 26066}, {4193, 31419}, {4197, 17757}, {4208, 9965}, {4232, 5090}, {4293, 5445}, {4295, 26792}, {4302, 5560}, {4307, 26083}, {4308, 31231}, {4346, 17250}, {4357, 4373}, {4371, 25498}, {4392, 24174}, {4395, 17327}, {4429, 28556}, {4430, 34790}, {4452, 4967}, {4454, 4748}, {4461, 17248}, {4470, 17251}, {4472, 4747}, {4480, 7229}, {4533, 31794}, {4540, 5883}, {4657, 28635}, {4663, 11160}, {4679, 5187}, {4696, 19804}, {4699, 31302}, {4711, 17609}, {4779, 31311}, {4848, 5226}, {4869, 17239}, {4873, 5257}, {4913, 21052}, {4916, 28640}, {4917, 38316}, {4997, 5835}, {5047, 5687}, {5054, 37705}, {5057, 5123}, {5070, 5844}, {5071, 22791}, {5072, 28212}, {5122, 5791}, {5129, 20075}, {5218, 10543}, {5224, 32089}, {5235, 11115}, {5248, 17544}, {5250, 35595}, {5252, 5265}, {5263, 8692}, {5264, 30653}, {5273, 37435}, {5274, 17606}, {5328, 5837}, {5330, 40587}, {5435, 9578}, {5493, 10248}, {5603, 7486}, {5698, 38092}, {5710, 37680}, {5731, 31423}, {5737, 19284}, {5744, 44848}, {5745, 37267}, {5774, 19280}, {5775, 21075}, {5795, 46916}, {5828, 27003}, {5905, 11024}, {6687, 32850}, {6767, 16854}, {6872, 37828}, {6910, 10609}, {6919, 7705}, {7226, 24443}, {7373, 16864}, {7409, 7713}, {7492, 8185}, {7585, 13973}, {7586, 13911}, {7982, 10172}, {7987, 38155}, {7991, 9779}, {7998, 16980}, {8025, 14007}, {8055, 39800}, {8164, 11036}, {8192, 40916}, {8193, 13595}, {8227, 38127}, {8972, 19065}, {9540, 35789}, {9588, 9778}, {9798, 15246}, {9947, 11220}, {10164, 21734}, {10171, 11531}, {10436, 32093}, {10585, 21677}, {10588, 40663}, {11319, 19732}, {11365, 16042}, {11499, 37106}, {12135, 38282}, {12531, 31235}, {12541, 24386}, {13624, 15708}, {13935, 35788}, {13941, 19066}, {14005, 16704}, {14923, 25917}, {15683, 31673}, {15692, 18481}, {15694, 38081}, {15699, 34631}, {15720, 28224}, {15721, 28204}, {16062, 19825}, {16137, 31254}, {16239, 37624}, {16458, 37639}, {16668, 17275}, {17125, 37588}, {17164, 27538}, {17252, 20059}, {17289, 27132}, {17293, 31285}, {17330, 26039}, {17355, 31722}, {17372, 28641}, {17548, 25440}, {17580, 20076}, {17718, 18221}, {17776, 43533}, {18230, 38200}, {18483, 34632}, {19324, 37580}, {21226, 41836}, {21735, 28186}, {21896, 44307}, {24344, 24850}, {24697, 28546}, {25244, 27288}, {25278, 31997}, {25439, 25542}, {25466, 34501}, {25590, 45789}, {26131, 43990}, {27448, 45782}, {27549, 32784}, {28461, 35251}, {30578, 41921}, {30711, 33078}, {31245, 45085}, {32087, 32105}, {32900, 38176}, {37557, 37913}, {38116, 40330}, {38177, 38762}

X(46933) = reflection of X(25979) in X(8)
X(46933) = anticomplement of X(5550)
X(46933) = X(513)-isoconjugate-of-X(28156)
X(46933) = X(101)-reciprocal conjugate of-X(28156)
X(46933) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(16673)}} and {{A, B, C, X(4), X(3634)}}
X(46933) = barycentric product X(i)*X(j) for these {i, j}: {75, 16673}, {190, 28155}
X(46933) = barycentric quotient X(101)/X(28156)
X(46933) = trilinear product X(i)*X(j) for these {i, j}: {2, 16673}, {100, 28155}
X(46933) = trilinear quotient X(100)/X(28156)
X(46933) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 4691, 8), (1, 19877, 2), (1, 19883, 3616), (1, 31145, 145), (2, 3617, 145), (2, 3621, 3616), (2, 3623, 1125), (2, 4678, 1), (8, 1698, 2), (8, 3616, 3244), (8, 3622, 145), (10, 1698, 8), (10, 3828, 1), (10, 9780, 2), (3244, 3679, 8), (3616, 3634, 2), (3617, 3622, 8), (3623, 20054, 145), (3624, 3626, 3241), (3679, 34595, 3244), (3812, 3983, 3681), (4668, 19872, 551), (4669, 19878, 1), (4678, 20014, 8), (4701, 19883, 1), (5552, 19855, 2), (5657, 9956, 3091), (5818, 26446, 20), (7989, 9812, 3854), (19853, 26030, 2), (19854, 27529, 2), (19876, 38314, 2), (24603, 29611, 2), (27026, 27299, 2), (38057, 40333, 144)

X(46934) = X(1)X(2)∩X(20)X(5886)

X(46934) = 4*X(1)+9*X(2), 10*X(1)+3*X(8), 7*X(1)+6*X(10), 16*X(1)-3*X(145), 5*X(1)-18*X(551), X(1)+12*X(1125), 11*X(1)+15*X(1698), 19*X(1)-6*X(3244), 2*X(1)-15*X(3616), 8*X(1)+5*X(3617), 12*X(1)+X(3621), 11*X(1)+2*X(3625), 9*X(1)+4*X(3626), 5*X(1)+8*X(3634), 17*X(1)+9*X(3679), 2*X(1)+11*X(5550), 6*X(1)+7*X(9780), X(1)-14*X(15808), 3*X(1)+10*X(19862), 9*X(1)+17*X(19872), 2*X(1)+3*X(19877), 14*X(1)-X(20050), X(1)+3*X(34595)

X(46934) lies on these lines: {1, 2}, {3, 28216}, {4, 28190}, {20, 5886}, {21, 11544}, {55, 17572}, {56, 5284}, {86, 16948}, {140, 8148}, {142, 30332}, {144, 15254}, {149, 443}, {153, 6898}, {214, 31418}, {346, 16672}, {355, 7486}, {376, 18493}, {377, 37606}, {388, 37162}, {390, 11376}, {391, 16666}, {392, 31794}, {405, 19740}, {452, 5126}, {496, 4197}, {515, 5068}, {516, 21734}, {517, 10303}, {547, 18526}, {631, 5901}, {632, 10247}, {940, 19333}, {944, 5056}, {946, 3522}, {952, 5067}, {956, 17536}, {958, 17570}, {962, 9624}, {984, 46190}, {986, 9335}, {999, 5047}, {1001, 4189}, {1006, 35252}, {1010, 19823}, {1058, 33110}, {1159, 7483}, {1191, 37633}, {1219, 40434}, {1319, 5261}, {1385, 3091}, {1386, 3620}, {1388, 10588}, {1420, 5226}, {1478, 26127}, {1482, 3525}, {1483, 5070}, {1621, 4188}, {1656, 7967}, {1699, 5059}, {1724, 19741}, {2320, 17501}, {2475, 5225}, {2476, 10593}, {2646, 5274}, {2975, 4423}, {3057, 3848}, {3090, 10246}, {3146, 3576}, {3218, 31435}, {3219, 3333}, {3295, 17531}, {3304, 5260}, {3306, 5128}, {3485, 5265}, {3523, 3579}, {3524, 22791}, {3526, 10283}, {3529, 38034}, {3533, 5690}, {3543, 3653}, {3545, 34773}, {3598, 17084}, {3600, 11375}, {3614, 3816}, {3619, 38315}, {3628, 37624}, {3646, 27065}, {3647, 15676}, {3649, 10032}, {3650, 15675}, {3656, 15708}, {3681, 17609}, {3731, 23649}, {3742, 3869}, {3812, 3890}, {3817, 30389}, {3832, 5731}, {3833, 5697}, {3839, 18481}, {3854, 5691}, {3871, 16408}, {3873, 25917}, {3876, 4430}, {3877, 5439}, {3889, 4661}, {3897, 6919}, {3911, 4323}, {3913, 9342}, {3945, 17322}, {3976, 7226}, {3984, 44841}, {3993, 4821}, {4000, 28640}, {4190, 28628}, {4193, 10592}, {4208, 17614}, {4293, 5443}, {4294, 37735}, {4297, 9779}, {4299, 5561}, {4305, 23708}, {4307, 26150}, {4308, 5219}, {4344, 17291}, {4346, 7321}, {4357, 32093}, {4364, 4747}, {4373, 10436}, {4454, 41312}, {4653, 28618}, {4657, 27006}, {4673, 24589}, {4696, 30829}, {4699, 15569}, {4704, 24325}, {4758, 35578}, {4772, 40328}, {4848, 31188}, {4855, 38316}, {4860, 11281}, {4869, 28639}, {4881, 37435}, {4896, 45789}, {5046, 5229}, {5071, 18525}, {5079, 28224}, {5084, 20060}, {5129, 20076}, {5141, 7173}, {5220, 11038}, {5221, 7288}, {5232, 17394}, {5248, 17548}, {5249, 17576}, {5250, 27003}, {5289, 18231}, {5296, 16670}, {5303, 40726}, {5333, 11115}, {5557, 20078}, {5563, 17544}, {5592, 6548}, {5657, 11278}, {5687, 17535}, {5708, 6857}, {5719, 17552}, {5734, 6684}, {5749, 16676}, {5818, 15178}, {5844, 46219}, {5921, 38029}, {6049, 9578}, {6147, 17561}, {6175, 9669}, {6224, 32557}, {6361, 15692}, {6636, 11365}, {6767, 16862}, {6854, 38033}, {6872, 37605}, {6883, 45977}, {6884, 10785}, {6889, 35459}, {6892, 11729}, {6904, 20066}, {6910, 36279}, {6920, 16203}, {6933, 12019}, {6940, 35251}, {6946, 16202}, {7373, 16842}, {7378, 11363}, {7496, 8193}, {7518, 17923}, {7585, 13959}, {7586, 13902}, {7968, 8972}, {7969, 13941}, {7987, 9812}, {8025, 11110}, {8236, 20195}, {8273, 35986}, {8666, 25542}, {9708, 17534}, {9778, 11522}, {9965, 17558}, {10179, 14923}, {10180, 17164}, {10299, 28174}, {10304, 12699}, {10531, 37163}, {10589, 34471}, {10590, 21842}, {10591, 37525}, {11004, 16472}, {11036, 37737}, {11037, 31018}, {11106, 31019}, {11160, 38023}, {11319, 19701}, {11396, 38282}, {11415, 26842}, {11451, 16980}, {11539, 34631}, {11831, 45289}, {12410, 40916}, {12514, 23958}, {12536, 24386}, {13199, 38044}, {14150, 37582}, {14996, 16466}, {15601, 17257}, {15668, 19284}, {15671, 16137}, {15680, 26725}, {15683, 38021}, {15705, 31162}, {16173, 20095}, {16343, 37639}, {16475, 20080}, {16477, 37677}, {16704, 17557}, {16781, 37675}, {16844, 19742}, {17051, 21677}, {17124, 37588}, {17127, 37607}, {17140, 19582}, {17303, 39260}, {17324, 30424}, {17381, 31333}, {17514, 27081}, {17538, 40273}, {17539, 25526}, {17580, 20075}, {17589, 25507}, {17728, 18221}, {19327, 37580}, {19925, 30392}, {20059, 43180}, {20094, 38220}, {21620, 27131}, {24178, 33134}, {24542, 26070}, {24929, 37436}, {25261, 27340}, {25557, 38025}, {25719, 31721}, {25723, 31994}, {26139, 37691}, {26860, 28619}, {27268, 31302}, {27541, 34522}, {28629, 37568}, {30275, 37583}, {30571, 39740}, {30652, 37522}, {31017, 37039}, {31313, 31334}, {32785, 44636}, {32786, 44635}, {33108, 37722}, {36996, 38043}, {37291, 37567}, {37339, 37589}, {37542, 37682}, {40333, 42819}

X(46934) = reflection of X(19877) in X(34595)
X(46934) = anticomplement of X(19877)
X(46934) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(4691)}} and {{A, B, C, X(10), X(30712)}}
X(46934) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 2, 3617), (1, 3617, 145), (1, 3625, 3241), (1, 3634, 8), (1, 5550, 2), (1, 27627, 3240), (2, 3622, 145), (2, 3623, 10), (2, 4678, 1698), (8, 3616, 551), (8, 3624, 2), (551, 3624, 8), (551, 3634, 1), (1125, 3616, 2), (1125, 15808, 1), (3241, 19883, 2), (3241, 20054, 145), (3616, 5550, 1), (3617, 3622, 1), (3623, 31145, 145), (3625, 3636, 1), (3635, 19875, 8), (3636, 19883, 1698), (5308, 29603, 2), (5731, 8227, 3832), (9624, 10165, 962), (9780, 19862, 2), (15254, 30340, 144), (16672, 26039, 346), (17316, 29609, 2), (19877, 34595, 2), (20050, 38314, 1), (25492, 26115, 2), (26626, 29612, 2), (27148, 27248, 2)

X(46935) = EULER LINE INTERCEPT OF X(145)X(38176)

X(46935) = 13*X(2)+16*X(547), 9*X(2)+20*X(1656), 15*X(2)+14*X(3090), 17*X(2)+12*X(5055), 18*X(2)+11*X(5056), 19*X(2)+10*X(5071), 12*X(2)+17*X(7486), 18*X(3)+11*X(4), 12*X(3)+17*X(3854), 13*X(3)+16*X(3856), 17*X(3)+12*X(14893), 11*X(3)+18*X(38071), 14*X(3)+15*X(41099), 20*X(4)+9*X(20), 17*X(4)+12*X(550), 14*X(4)+15*X(3522), 9*X(4)+20*X(15712), 13*X(4)+16*X(33923), 15*X(5)+14*X(140), 20*X(5)+9*X(3524), 12*X(5)+17*X(3533), 16*X(5)+13*X(10303), 17*X(5)+12*X(11812), 14*X(5)+15*X(15694), 18*X(5)+11*X(15720)

X(46935) lies on these lines: {2, 3}, {145, 38176}, {193, 25555}, {325, 32897}, {371, 43377}, {372, 43376}, {1007, 32870}, {1125, 30315}, {1132, 9542}, {1506, 14075}, {1975, 32898}, {3019, 24902}, {3316, 6499}, {3317, 6498}, {3590, 6436}, {3591, 6435}, {3592, 43410}, {3594, 43409}, {3616, 10172}, {3617, 11230}, {3620, 38317}, {3623, 38042}, {3634, 11522}, {3828, 5734}, {4857, 5281}, {5265, 5270}, {5304, 34571}, {5334, 42936}, {5335, 42937}, {5343, 42092}, {5344, 42089}, {5349, 42473}, {5350, 42472}, {5355, 12815}, {5365, 42111}, {5366, 42114}, {5395, 10185}, {5493, 7988}, {5550, 5882}, {5731, 19878}, {6053, 15059}, {6221, 43505}, {6398, 43506}, {6437, 42571}, {6438, 42570}, {6688, 11444}, {6776, 42786}, {7320, 31434}, {7586, 8960}, {7752, 32883}, {7755, 37665}, {7769, 32824}, {7917, 15589}, {9748, 16988}, {9780, 13464}, {10110, 44299}, {10170, 11465}, {10171, 19872}, {10187, 22235}, {10188, 22237}, {10283, 20052}, {11185, 32884}, {11480, 42776}, {11481, 42775}, {11488, 43873}, {11489, 43874}, {13382, 15056}, {15082, 27355}, {16187, 34148}, {16808, 42958}, {16809, 42959}, {16966, 42998}, {16967, 42999}, {18538, 43565}, {18581, 43776}, {18582, 43775}, {18762, 43564}, {23302, 42983}, {23303, 42982}, {31399, 38314}, {31412, 41964}, {32785, 42522}, {32786, 42523}, {32820, 32835}, {32821, 32834}, {32825, 32832}, {32830, 37647}, {33416, 42921}, {33417, 42920}, {33748, 40330}, {33879, 45186}, {35786, 42601}, {35787, 42600}, {35822, 43884}, {35823, 43883}, {38751, 41135}, {40693, 42978}, {40694, 42979}, {41963, 42561}, {42095, 42949}, {42098, 42948}, {42107, 42773}, {42110, 42774}, {42119, 42794}, {42120, 42793}, {42125, 43778}, {42128, 43777}, {42139, 42945}, {42142, 42944}, {42150, 42914}, {42151, 42915}, {42157, 43869}, {42158, 43870}, {42164, 42475}, {42165, 42474}, {42274, 43512}, {42277, 43511}, {42431, 43364}, {42432, 43365}, {42490, 42932}, {42491, 42933}, {42492, 42816}, {42493, 42815}, {42494, 43239}, {42495, 43238}, {42557, 43430}, {42558, 43431}, {42590, 42975}, {42591, 42974}, {42598, 42611}, {42599, 42610}, {42803, 43404}, {42804, 43403}, {42805, 43198}, {42806, 43197}, {42910, 42993}, {42911, 42992}, {42924, 43464}, {42925, 43463}, {42960, 43442}, {42961, 43443}, {43004, 43019}, {43005, 43018}, {43102, 43556}, {43103, 43557}, {43240, 43546}, {43241, 43547}, {43527, 43537}

X(46935) = midpoint of X(5055) and X(37038)
X(46935) = intersection, other than A, B, C, of circumconics {{A, B, C, X(68), X(12812)}} and {{A, B, C, X(253), X(3526)}}
X(46935) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 3090, 20), (2, 5068, 140), (2, 15022, 631), (2, 15717, 632), (5, 15711, 546), (5, 15720, 4), (5, 44245, 381), (140, 1656, 3090), (140, 5068, 20), (140, 12811, 550), (140, 15699, 1656), (632, 35403, 631), (632, 44904, 1657), (1656, 3851, 547), (1656, 5070, 140), (3090, 3524, 5), (3090, 5070, 2), (3091, 15721, 20), (3146, 8703, 20), (3522, 5073, 20), (3524, 3533, 140), (3628, 5067, 2), (3851, 33923, 4), (3861, 15717, 20), (5055, 5076, 5), (5070, 15699, 3090), (5079, 16239, 376), (8703, 41986, 381), (35018, 46219, 4), (38071, 45760, 3)

X(46936) = EULER LINE INTERCEPT OF X(8)X(10172)

X(46936) = 15*X(2)+8*X(5), 19*X(2)+4*X(381), 7*X(2)+16*X(547), 3*X(2)+20*X(1656), 9*X(2)+14*X(3090), 18*X(2)+5*X(3091), 17*X(2)+6*X(3545), 20*X(2)+3*X(3839), 11*X(2)+12*X(5055), 12*X(2)+11*X(5056), 13*X(2)+10*X(5071), 6*X(2)+17*X(7486), 9*X(2)-8*X(41992), 14*X(3)+9*X(4), 5*X(3)+18*X(5), 11*X(3)+12*X(546), 8*X(3)+15*X(3091), 20*X(3)+3*X(3146), 6*X(3)+17*X(3544), 17*X(3)+6*X(3627), 9*X(3)+14*X(3857), 15*X(3)+8*X(12102), 7*X(3)+16*X(12811), 3*X(3)+20*X(12812), 4*X(3)+19*X(15022), X(3)-6*X(41992)

X(46936) lies on these lines: {2, 3}, {8, 10172}, {10, 16189}, {13, 42593}, {14, 42592}, {61, 42983}, {62, 42982}, {69, 32897}, {99, 32884}, {144, 38318}, {145, 11230}, {146, 15029}, {147, 38740}, {148, 38751}, {149, 38319}, {150, 38775}, {151, 38787}, {184, 46865}, {185, 10219}, {193, 22330}, {315, 32883}, {325, 32870}, {373, 11444}, {397, 42611}, {398, 42610}, {485, 42523}, {486, 42522}, {551, 30315}, {575, 40330}, {576, 3620}, {962, 10171}, {1125, 37712}, {1131, 5420}, {1132, 5418}, {1151, 42566}, {1152, 42567}, {1506, 5304}, {1587, 43884}, {1588, 43883}, {1699, 31253}, {1975, 32871}, {3054, 22331}, {3055, 22332}, {3068, 43880}, {3069, 43879}, {3071, 9542}, {3241, 31399}, {3303, 10589}, {3304, 10588}, {3316, 13951}, {3317, 8976}, {3448, 38795}, {3589, 33748}, {3592, 32785}, {3594, 32786}, {3617, 10222}, {3619, 11477}, {3621, 38042}, {3622, 9956}, {3634, 7991}, {3746, 5274}, {3817, 19872}, {3951, 5748}, {4301, 19876}, {4678, 5901}, {5007, 31404}, {5032, 25555}, {5225, 5326}, {5229, 7294}, {5237, 42114}, {5238, 42111}, {5261, 5563}, {5265, 7951}, {5281, 7741}, {5319, 12815}, {5334, 42580}, {5335, 42581}, {5343, 16241}, {5344, 16242}, {5351, 42134}, {5352, 42133}, {5395, 11668}, {5550, 10175}, {5643, 43841}, {5651, 9545}, {5704, 11518}, {5731, 34595}, {5734, 19875}, {5818, 15178}, {5889, 6688}, {5891, 11465}, {5972, 15025}, {5984, 34127}, {6337, 32898}, {6392, 17005}, {6419, 8972}, {6420, 13941}, {6425, 32789}, {6426, 31412}, {6427, 13939}, {6428, 13886}, {6447, 23273}, {6448, 23267}, {6453, 42274}, {6454, 42277}, {6459, 41955}, {6460, 17852}, {6484, 43383}, {6485, 43382}, {6667, 38669}, {6721, 23235}, {6722, 38664}, {6723, 15054}, {7585, 10577}, {7586, 10576}, {7746, 37665}, {7752, 32867}, {7755, 31407}, {7796, 32885}, {7871, 32832}, {7982, 9780}, {7989, 19878}, {7999, 11002}, {8227, 19877}, {8798, 14572}, {8981, 43317}, {9543, 23275}, {9612, 31188}, {9742, 11174}, {9779, 31423}, {9781, 33884}, {10095, 16981}, {10170, 15024}, {10283, 20014}, {10545, 46728}, {10645, 43365}, {10646, 43364}, {10653, 43480}, {10654, 43479}, {11231, 20070}, {11451, 11793}, {11482, 20080}, {11485, 42590}, {11486, 42591}, {11488, 42599}, {11489, 42598}, {11695, 15056}, {12045, 15072}, {12111, 40284}, {12816, 42958}, {12817, 42959}, {12900, 14094}, {13966, 43316}, {14061, 20399}, {14360, 38807}, {14643, 38632}, {14683, 15027}, {14843, 44731}, {14924, 32605}, {15012, 15028}, {15021, 36518}, {15034, 23515}, {15043, 45187}, {15052, 37514}, {15061, 38626}, {15561, 38628}, {15644, 33879}, {15801, 32396}, {15805, 43605}, {16772, 42495}, {16773, 42494}, {16808, 43870}, {16809, 43869}, {17809, 43592}, {18221, 37701}, {18362, 31450}, {19855, 31263}, {19862, 30389}, {19883, 37714}, {20049, 38022}, {20054, 38176}, {20059, 38171}, {20085, 38182}, {20400, 31272}, {20401, 31273}, {22234, 24206}, {22235, 37832}, {22237, 37835}, {23249, 43315}, {23259, 43314}, {31145, 38083}, {31415, 35007}, {31454, 42573}, {31652, 43448}, {32817, 32873}, {32818, 32872}, {32821, 32874}, {32830, 34803}, {32831, 37647}, {32838, 37668}, {33416, 42161}, {33417, 42160}, {34754, 43335}, {34755, 43334}, {35255, 43505}, {35256, 43506}, {35369, 38229}, {36836, 42139}, {36843, 42142}, {37640, 43333}, {37641, 43332}, {38224, 38627}, {38629, 38752}, {38630, 38764}, {40410, 40680}, {41951, 43412}, {41952, 43411}, {41953, 42262}, {41954, 42265}, {42085, 42930}, {42086, 42931}, {42119, 42692}, {42120, 42693}, {42143, 43463}, {42146, 43464}, {42149, 43008}, {42150, 43441}, {42151, 43440}, {42152, 43009}, {42159, 42914}, {42162, 42915}, {42163, 43029}, {42166, 43028}, {42266, 42600}, {42267, 42601}, {42488, 42910}, {42489, 42911}, {42490, 43421}, {42491, 43420}, {42528, 43477}, {42529, 43478}, {42596, 43331}, {42597, 43330}, {42627, 42951}, {42628, 42950}, {42775, 42943}, {42776, 42942}, {42779, 43545}, {42780, 43544}, {42799, 43404}, {42800, 43403}, {42920, 42932}, {42921, 42933}, {42954, 43240}, {42955, 43241}, {43101, 43238}, {43104, 43239}, {43614, 43650}, {44299, 45186}

X(46936) = intersection, other than A, B, C, of circumconics {{A, B, C, X(68), X(35018)}} and {{A, B, C, X(253), X(3525)}}
X(46936) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 3832, 140), (2, 5056, 20), (2, 15022, 3), (3, 12811, 4), (4, 5070, 2), (4, 15692, 20), (5, 5054, 4), (140, 45757, 5), (547, 5070, 4), (631, 11541, 3), (632, 5079, 4), (632, 12811, 3), (1656, 5067, 2), (1656, 15703, 5), (1657, 5055, 5), (3090, 3525, 5), (3090, 3628, 2), (3091, 10303, 20), (3522, 15640, 20), (3523, 3839, 20), (3530, 19709, 4), (3839, 5056, 5), (3859, 15681, 4), (3861, 35401, 4), (12100, 35018, 5), (12102, 12812, 5), (15029, 38729, 146), (15696, 38071, 4), (16922, 32998, 2), (32975, 33249, 2), (32976, 32992, 2)

X(46937) = X(1)X(341)∩X(8)X(392)

X(46937) lies on these lines: {1, 341}, {2, 3701}, {3, 5205}, {4, 2899}, {5, 29641}, {8, 392}, {10, 312}, {34, 14594}, {37, 25629}, {40, 30568}, {43, 37042}, {46, 190}, {65, 4009}, {72, 27538}, {75, 1089}, {76, 30758}, {85, 3947}, {92, 5142}, {100, 4222}, {145, 4723}, {158, 6335}, {191, 17336}, {192, 26029}, {210, 10449}, {235, 34337}, {304, 6376}, {318, 406}, {321, 9780}, {344, 3085}, {355, 36926}, {405, 7081}, {442, 3948}, {497, 5100}, {498, 33116}, {499, 37758}, {517, 19582}, {519, 44720}, {612, 13740}, {668, 18156}, {726, 24174}, {740, 6048}, {938, 5423}, {942, 32937}, {962, 8055}, {964, 5297}, {975, 1220}, {978, 24003}, {982, 46827}, {984, 3831}, {986, 3971}, {999, 9369}, {1010, 5268}, {1111, 33780}, {1125, 17725}, {1210, 3717}, {1265, 18391}, {1329, 3932}, {1376, 7283}, {1479, 32850}, {1714, 18147}, {1724, 3769}, {1837, 16086}, {1997, 3086}, {1999, 11353}, {2136, 4939}, {2478, 5015}, {3006, 4193}, {3090, 30741}, {3091, 39570}, {3178, 17786}, {3214, 32915}, {3239, 14825}, {3263, 3673}, {3501, 3985}, {3596, 4078}, {3616, 4696}, {3617, 3702}, {3621, 4742}, {3624, 4692}, {3632, 4975}, {3633, 4738}, {3634, 4125}, {3679, 4673}, {3685, 5687}, {3695, 3820}, {3699, 3811}, {3704, 9711}, {3705, 4187}, {3706, 3983}, {3710, 24982}, {3714, 3740}, {3718, 44735}, {3753, 4903}, {3757, 11108}, {3758, 37559}, {3812, 3967}, {3814, 30172}, {3828, 4066}, {3868, 3952}, {3876, 17751}, {3902, 4678}, {3912, 17671}, {3920, 5192}, {3931, 41839}, {3950, 30693}, {3976, 4871}, {4011, 5255}, {4082, 8582}, {4110, 6541}, {4359, 19877}, {4429, 46738}, {4487, 20050}, {4518, 29983}, {4646, 35652}, {4647, 19875}, {4676, 5264}, {4866, 35613}, {4986, 17158}, {5045, 30947}, {5046, 5300}, {5047, 26227}, {5051, 29679}, {5129, 7172}, {5247, 29649}, {5266, 17697}, {5292, 33118}, {5439, 24349}, {5711, 27064}, {5734, 28661}, {6533, 19872}, {7101, 17916}, {7881, 30798}, {7887, 30763}, {7951, 20927}, {9709, 32932}, {9959, 26446}, {10453, 34790}, {10459, 25591}, {10479, 18137}, {11110, 29828}, {12699, 17777}, {13161, 33833}, {13407, 17234}, {13735, 37552}, {14210, 16284}, {14829, 41229}, {16062, 19799}, {16466, 41261}, {16823, 16842}, {17551, 30599}, {17566, 37762}, {17602, 25992}, {17748, 33092}, {17752, 35274}, {17790, 26066}, {18134, 21077}, {18145, 33933}, {18146, 33940}, {19280, 39586}, {19843, 28808}, {19853, 44417}, {20925, 20943}, {21290, 32049}, {21935, 42709}, {24046, 24068}, {24443, 32925}, {25066, 27523}, {25583, 32830}, {25660, 38047}, {26030, 28606}, {26364, 32851}, {27529, 33113}, {28082, 32927}, {29376, 29511}, {29633, 30963}, {30179, 33046}, {30740, 32818}, {33091, 37162}, {34208, 41013}, {38471, 44723}

X(46937) = barycentric product X(i)*X(j) for these {i, j}: {75, 17314}, {312, 1788}, {313, 1778}, {561, 14974}, {1016, 17888}
X(46937) = barycentric quotient X(i)/X(j) for these (i, j): (1778, 58), (1788, 57)
X(46937) = trilinear product X(i)*X(j) for these {i, j}: {2, 17314}, {8, 1788}, {76, 14974}, {321, 1778}, {765, 17888}, {1897, 20315}
X(46937) = trilinear quotient X(i)/X(j) for these (i, j): (1778, 1333), (1788, 56)
X(46937) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 341, 4737), (1, 3992, 341), (2, 3701, 4385), (341, 18743, 1), (1089, 1698, 75), (2478, 10327, 5015), (3263, 18135, 3673), (3714, 3740, 9534), (3828, 4066, 28612), (3992, 18743, 4737), (4066, 28612, 42029), (6376, 20947, 304), (6381, 33942, 85), (18140, 33932, 75), (20943, 33943, 20925), (30963, 33938, 39731)

X(46938) = X(2)X(37)∩X(8)X(3898)

X(46938) lies on these lines: {2, 37}, {8, 3898}, {9, 5372}, {76, 29599}, {145, 4723}, {190, 23958}, {226, 40021}, {341, 3623}, {726, 9335}, {1089, 5550}, {1227, 4473}, {1698, 4717}, {1999, 14997}, {2895, 18228}, {2899, 20060}, {3218, 25734}, {3219, 30567}, {3241, 3992}, {3452, 32858}, {3616, 4692}, {3617, 3902}, {3622, 3701}, {3741, 9330}, {3760, 29626}, {3761, 29620}, {3816, 32862}, {3840, 7226}, {3873, 4009}, {3891, 25531}, {3912, 27131}, {3948, 29572}, {3952, 4430}, {3971, 4392}, {3994, 17063}, {4011, 17126}, {4044, 29581}, {4066, 34595}, {4078, 29680}, {4125, 25055}, {4487, 20049}, {4661, 27538}, {4679, 33078}, {4693, 9350}, {4742, 31145}, {4767, 41711}, {4865, 24709}, {4871, 32925}, {4903, 17165}, {5361, 27065}, {5695, 9342}, {5737, 30563}, {5748, 14211}, {5905, 8055}, {6381, 29582}, {6557, 30690}, {7283, 17572}, {11679, 35595}, {11814, 29849}, {14829, 24616}, {14996, 27064}, {17013, 34064}, {17056, 27794}, {17127, 29649}, {17140, 26103}, {17230, 30830}, {17242, 27130}, {17244, 31060}, {17267, 30831}, {17484, 18141}, {17719, 29870}, {18134, 30566}, {18135, 20924}, {18153, 23989}, {18359, 38255}, {19872, 42031}, {20014, 44720}, {24003, 32915}, {25378, 28595}, {25417, 32017}, {25958, 29687}, {26105, 33090}, {26745, 36805}, {26791, 31034}, {27757, 30827}, {28809, 29569}, {29814, 32931}, {29864, 33159}, {31018, 32863}, {31242, 46901}, {34255, 37656}, {37674, 41242}, {39698, 39703}

X(46938) = X(i)-beth conjugate of-X(j) for these (i, j): (312, 20942), (645, 23958)
X(46938) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3633)}} and {{A, B, C, X(27), X(19831)}}
X(46938) = barycentric product X(75)*X(3633)
X(46938) = trilinear product X(2)*X(3633)
X(46938) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 312, 28605), (312, 28605, 4671), (321, 4358, 20942), (321, 30829, 2), (1997, 17776, 2), (1999, 26688, 14997), (3971, 30957, 4392), (4358, 18743, 2), (4903, 30947, 17165), (5905, 8055, 30578), (18743, 20942, 30829), (20942, 30829, 321), (27538, 29824, 4661), (30861, 41839, 2), (33113, 37758, 2)

X(46939) = EULER LINE INTERCEPT OF X(155)X(17835)

X(46939) lies on these lines: {2, 3}, {155, 17835}, {9932, 32423}, {12893, 18381}, {25487, 25711}

X(46939) = midpoint of X(3) and X(38450)
X(46939) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (26, 12084, 382), (26, 38444, 1658), (1658, 11250, 5), (1658, 18377, 24), (1885, 7542, 5), (3575, 10257, 5), (10226, 15331, 3530), (11250, 44279, 378)

X(46940) = EULER LINE INTERCEPT OF X(16665)X(34148)

X(46941) = X(3)X(598)∩X(538)X(3524)

X(46941) lies on these lines: {3, 598}, {99, 15693}, {538, 3524}, {9774, 33273}, {11645, 33004}, {12100, 26316}, {15717, 20190}

X(46942) = CIRCUMCIRCLE-INVERSE OF X(232)

X(46942) lies on these lines: {3, 232}, {25, 647}, {132, 44534}, {378, 34235}, {8743, 33695}, {8779, 11470}

X(46942) = circumcircle-inverse of X(232)
X(46942) = Moses-radical-circle inverse of X(25)

X(46943) = X(1)X(2)∩X(3)X(7963)

X(46943) lies on the cubic K1262 and these lines: {1, 2}, {3, 7963}, {36, 20991}, {40, 45047}, {105, 28295}, {106, 3973}, {238, 13462}, {517, 8056}, {958, 15839}, {999, 1696}, {1420, 34048}, {1616, 5438}, {1706, 45219}, {3158, 16486}, {3361, 4650}, {3445, 6762}, {4859, 5603}, {5289, 5573}, {6282, 32486}, {7962, 16610}, {7991, 11512}, {11194, 15601}, {11522, 24178}, {11531, 24174}, {15479, 17053}, {17063, 18421}

X(46943) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 6048, 11519}, {1, 16569, 4915}, {200, 1149, 1}, {1201, 8583, 1}

X(46944) = X(1)X(3598)∩X(2)X(1350)

X(46944) lies on the Steiner/Wallace right hyperbola (= Kiepert circumhyperbola of the anticomplementary triangle), the cubic K1262, and these lines: {1, 3598}, {2, 1350}, {3, 14482}, {20, 7767}, {63, 7172}, {147, 10513}, {194, 3522}, {376, 11148}, {511, 14930}, {1370, 41914}, {2896, 3146}, {3098, 10336}, {5304, 31884}, {5984, 8591}, {7766, 21734}, {9742, 37182}, {15705, 18860}, {15717, 30270}, {31670, 43951}, {36413, 37485}

X(46944) = reflection of X(14482) in X(3)
X(46944) = anticomplement of X(14484)
X(46944) = anticomplement of the isogonal conjugate of X(5085)
X(46944) = anticomplement of the isotomic conjugate of X(15589)
X(46944) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {5085, 8}, {15589, 6327}
X(46944) = X(15589)-Ceva conjugate of X(2)

X(46945) = X(3)X(5646)∩X(6)X(376)

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 - 116*a^4*b^2*c^2 + 100*a^2*b^4*c^2 + 20*b^6*c^2 + 6*a^4*c^4 + 100*a^2*b^2*c^4 - 42*b^4*c^4 - 4*a^2*c^6 + 20*b^2*c^6 + c^8) : :

X(46945) lies on the Feuerbach circumhyperbola of the tangential triangle, the cubic K1262, and these lines: {3, 5646}, {6, 376}, {22, 41447}, {74, 2930}, {155, 548}, {159, 10606}, {195, 37483}, {399, 15688}, {550, 15805}, {1498, 3522}, {2929, 10323}, {2935, 15051}, {3098, 19588}, {3216, 37426}, {3528, 16936}, {3534, 17825}, {6411, 8939}, {6412, 8943}, {8703, 17811}, {10601, 15697}, {15047, 15696}, {15695, 37672}, {15811, 21735}, {17821, 46373}, {21312, 31521}, {22829, 36987}, {37198, 37487}, {37514, 44245}

X(46945) = reflection of X(5646) in X(3)
X(46945) = X(10304)-Ceva conjugate of X(3)

X(46946) = X(1)X(2137)∩X(3)X(7963)

X(46946) lies on the cubic K1262 and these lines: {1, 2137}, {3, 7963}, {40, 376}, {57, 3021}, {165, 2348}, {649, 24771}, {1292, 17222}, {1293, 3158}, {2955, 37560}, {3576, 16486}, {4512, 5646}, {7982, 38496}

X(46946) = excentral-isogonal conjugate of X(3973)
X(46946) = X(3161)-Ceva conjugate of X(1)

X(46947) = X(1)X(5316)∩X(9)X(999)

X(46947) lies on the Jerabek circumhyperbola of the excentral triangle, the cubic K1262, and these lines: {1, 5316}, {9, 999}, {21, 16009}, {40, 392}, {78, 12658}, {191, 3361}, {376, 2951}, {452, 1490}, {936, 2136}, {956, 3646}, {997, 3174}, {1000, 8580}, {1387, 9623}, {2950, 21164}, {5528, 9945}, {5541, 9819}, {5732, 35272}, {12629, 17527}, {13144, 19875}, {18237, 31435}, {34123, 38399}

X(46948) = X(2)X(39)∩X(3)X(8617)

X(46948) lies on the cubic K1261 and these lines: {2, 39}, {3, 8617}, {111, 30270}, {647, 39647}, {1084, 11160}, {3053, 3231}, {5106, 5206}, {6090, 9463}, {9210, 21733}, {9821, 9998}, {10983, 21448}, {21001, 37184}, {21356, 34811}

X(46949) = X(2)X(6)∩X(111)X(1350)

X(46949) lies on the cubic K1260 and these lines: {2, 6}, {111, 1350}, {187, 35259}, {511, 21448}, {647, 21733}, {1351, 22111}, {1384, 5651}, {1495, 15655}, {2030, 6090}, {2502, 5210}, {3066, 8585}, {5024, 5650}, {9306, 38010}, {11472, 40115}, {11477, 39576}, {15082, 42852}, {15694, 30516}

X(46949) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {352, 8617, 20481}, {352, 20481, 6}, {1350, 33979, 111}, {8585, 11173, 3066}, {11580, 15066, 6}

X(46950) = X(6)X(1296)∩X(376)X(524)

X(46950) lies on the cubic K1260 and these lines: {6, 1296}, {376, 524}, {3066, 11159}, {5024, 39236}, {9871, 33979}, {35259, 45722}

X(46951) = X(2)X(39)∩X(69)X(381)

Barycentrics    (a^2 - b^2 - 4*b*c - c^2)*(a^2 - b^2 + 4*b*c - c^2) : :
Barycentrics    1 + 3 Csc[A]^2 : :
Barycentrics    (a^2 - b^2 - c^2)^2 - 16 b^2 c^2 : :

X(46951) lies on these lines: {2, 39}, {4, 37671}, {30, 3785}, {69, 381}, {99, 15692}, {115, 3620}, {141, 33223}, {148, 33263}, {183, 376}, {193, 7753}, {230, 33224}, {298, 37171}, {299, 37170}, {315, 3839}, {325, 5071}, {339, 1272}, {524, 32983}, {547, 1007}, {549, 34229}, {599, 16041}, {631, 32824}, {671, 33210}, {1078, 10304}, {1368, 41927}, {1975, 3524}, {2896, 33278}, {2996, 7800}, {3090, 32825}, {3091, 7809}, {3146, 11057}, {3525, 32820}, {3543, 7811}, {3545, 7788}, {3734, 37667}, {3760, 10056}, {3761, 10072}, {3830, 7767}, {3832, 7768}, {3845, 32006}, {3933, 5055}, {4479, 34619}, {5032, 41748}, {5054, 6337}, {5056, 7796}, {5066, 7776}, {5067, 32821}, {5475, 20080}, {5976, 12243}, {6194, 46034}, {6390, 15694}, {6623, 44134}, {6661, 7735}, {7610, 33216}, {7615, 7818}, {7620, 33017}, {7697, 14853}, {7750, 15682}, {7751, 32971}, {7758, 32987}, {7759, 32991}, {7773, 41106}, {7780, 32981}, {7782, 15705}, {7793, 33187}, {7794, 18362}, {7802, 15640}, {7810, 33272}, {7814, 15022}, {7837, 16924}, {7840, 33005}, {7851, 18840}, {7854, 32982}, {7865, 32974}, {7924, 16990}, {7946, 32995}, {8356, 42850}, {8556, 33215}, {8667, 14033}, {8716, 11168}, {8781, 14971}, {9166, 32458}, {9300, 32968}, {10008, 21356}, {11001, 32819}, {11008, 15484}, {11288, 23055}, {13468, 32985}, {13571, 31407}, {14023, 14537}, {14039, 22329}, {14068, 19569}, {14893, 14929}, {14907, 15683}, {14994, 20423}, {15598, 44526}, {15702, 32817}, {15703, 34803}, {17008, 33246}, {17079, 20925}, {17128, 33255}, {17130, 32973}, {19708, 32822}, {19843, 20943}, {31156, 37670}, {32986, 34505}, {32994, 41136}, {33023, 40344}

X(46951) = reflection of X(33215) in X(8556)
X(46951) = barycentric product X(i)*X(j) for these {i,j}: {305, 18535}, {3305, 20925}, {17079, 42032}, {42696, 42697}
X(46951) = barycentric quotient X(i)/X(j) for these {i,j}: {3295, 34446}, {18535, 25}, {42032, 36916}, {42696, 1000}, {42697, 3296}
X(46951) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 76, 32836}, {2, 6392, 7739}, {2, 7799, 32829}, {2, 19570, 5286}, {2, 32828, 32885}, {2, 32830, 7799}, {2, 32833, 32837}, {2, 32836, 3926}, {2, 32869, 32833}, {2, 32874, 76}, {2, 32885, 32838}, {76, 32828, 3926}, {76, 32830, 32878}, {76, 32832, 32830}, {76, 32833, 32869}, {76, 32834, 32828}, {76, 32836, 32892}, {76, 32838, 32877}, {76, 32868, 32888}, {76, 32870, 32890}, {76, 32872, 32829}, {76, 32886, 32838}, {76, 32893, 32837}, {3543, 15589, 7811}, {3545, 7788, 32816}, {3926, 32828, 32838}, {3926, 32838, 32839}, {3926, 32883, 32829}, {3926, 32884, 7763}, {3926, 32885, 2}, {3926, 32886, 32828}, {3926, 32887, 32831}, {3926, 32888, 76}, {3926, 32892, 32836}, {3934, 7739, 2}, {7763, 32867, 32884}, {7763, 32898, 32829}, {7769, 32890, 3926}, {7799, 32830, 32896}, {7799, 32832, 2}, {7799, 32896, 3926}, {7811, 11185, 3543}, {13571, 33261, 31407}, {19570, 31276, 2}, {32828, 32829, 32832}, {32828, 32830, 32883}, {32828, 32834, 32886}, {32828, 32836, 2}, {32828, 32868, 76}, {32828, 32874, 32892}, {32828, 32878, 32829}, {32828, 32882, 32887}, {32829, 32830, 3926}, {32829, 32832, 32883}, {32829, 32836, 32896}, {32829, 32878, 32830}, {32829, 32896, 7799}, {32830, 32832, 32829}, {32830, 32834, 32872}, {32830, 32872, 32832}, {32830, 32894, 76}, {32831, 32875, 3926}, {32832, 32872, 32828}, {32832, 32878, 3926}, {32832, 32883, 32838}, {32832, 32894, 32878}, {32832, 32898, 32867}, {32833, 32837, 3926}, {32833, 32869, 32836}, {32834, 32868, 3926}, {32834, 32869, 32893}, {32834, 32874, 2}, {32834, 32888, 32838}, {32834, 32894, 32832}, {32836, 32837, 32833}, {32836, 32896, 32830}, {32837, 32893, 32885}, {32839, 32877, 3926}, {32840, 32870, 7769}, {32868, 32878, 32894}, {32869, 32893, 2}, {32870, 32890, 32889}, {32872, 32878, 32883}, {32872, 32894, 32830}, {32872, 32896, 32885}, {32874, 32893, 32869}, {32878, 32896, 32836}, {32885, 32888, 32892}, {32885, 32892, 3926}, {32886, 32888, 3926}, {32886, 32892, 32885}

X(46952) = X(6)X(631)∩X(39)X(393)

X(46952) lies on the circumconic {{A, B, C, X(2), X(6)}} and these lines: {2, 44149}, {4, 34818}, {6, 631}, {25, 3087}, {37, 3086}, {39, 393}, {42, 3554}, {53, 39662}, {193, 30535}, {251, 577}, {308, 3926}, {493, 3069}, {494, 3068}, {570, 34288}, {588, 7586}, {589, 7585}, {1907, 7738}, {2165, 5286}, {2548, 33631}, {2963, 13337}, {3108, 5304}, {3618, 40802}, {3815, 8770}, {5065, 8882}, {7735, 39951}, {7746, 46217}, {8577, 31403}, {11245, 34285}, {13341, 31401}, {14930, 39955}, {32785, 41437}, {32786, 41438}, {32829, 42407}, {32884, 42332}, {33871, 41890}, {37689, 39389}, {40138, 41489}, {40680, 40815}

X(46952) = isogonal conjugate of X(10601)
X(46952) = isotomic conjugate of X(32828)
X(46952) = isotomic conjugate of the anticomplement of X(31401)
X(46952) = X(i)-cross conjugate of X(j) for these (i,j): {9777, 4}, {13341, 6}, {31401, 2}
X(46952) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10601}, {2, 1497}, {31, 32828}, {63, 1598}, {92, 10984}
X(46952) = trilinear pole of line {512, 6562}
X(46952) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 32828}, {6, 10601}, {25, 1598}, {31, 1497}, {184, 10984}

X(46953) = X(3)X(512)∩X(230)X(231)

X(46953) lies on these lines: {2, 30735}, {3, 512}, {230, 231}, {235, 16229}, {351, 8675}, {520, 8651}, {525, 11615}, {526, 8644}, {669, 684}, {1499, 8552}, {1510, 3804}, {2510, 7652}, {2793, 7624}, {3542, 14618}, {3906, 6140}, {4108, 7493}, {5926, 9517}, {5996, 46336}, {7630, 32472}, {7651, 8574}, {8673, 34952}, {9027, 40282}, {21731, 30209}, {25423, 45319}, {32112, 40352}, {42658, 44680}

X(46953) = midpoint of X(669) and X(684)
X(46953) = reflection of X(i) in X(j) for these {i,j}: {647, 6132}, {6130, 44451}, {42658, 44680}
X(46953) = complement of X(30735)
X(46953) = complement of the isotomic conjugate of X(35575)
X(46953) = X(i)-complementary conjugate of X(j) for these (i,j): {35575, 2887}, {40799, 8287}, {40802, 21253}, {40823, 16592}
X(46953) = X(i)-line conjugate of X(j) for these (i,j): {231, 230}, {512, 3}
X(46953) = crosspoint of X(i) and X(j) for these (i,j): {2, 35575}, {110, 3425}
X(46953) = crosssum of X(i) and X(j) for these (i,j): {523, 1352}, {525, 7778}, {8057, 34808}
X(46953) = crossdifference of every pair of points on line {3, 230}
X(46953) = {X(647),X(2491)}-harmonic conjugate of X(2485)

X(46954) = X(2)X(18016)∩X(5)X(51)

Barycentrics (-(b^2-c^2)^2+a^2*(b^2+c^2))*(a^12-4*b^2*c^2*(b^2-c^2)^4-7*a^10*(b^2+c^2)+2*a^8*(9*b^4+10*b^2*c^2+9*c^4)-11*a^6*(2*b^6+b^4*c^2+b^2*c^4+2*c^6)-a^2*(b^2-c^2)^2*(3*b^6-10*b^4*c^2-10*b^2*c^4+3*c^6)+a^4*(13*b^8-14*b^6*c^2-7*b^4*c^4-14*b^2*c^6+13*c^8)) : :
Barycentrics (S^2+SB*SC)*(17*R^4+4*S^2-5*R^2*SA-13*R^2*SW+2*SA*SW+2*SW^2) : :

X(46954) = 3*X(547)-X(13856), 5*X(1656)-X(15345), 7*X(3090)+X(25043), 3*X(10109)-2*X(34599), 9*X(15699)-X(35720)

X(46954) lies on these lines: {2,18016}, {5,51}, {30,32904}, {511,17727}, {547,13856}, {1656,15345}, {3090,25043}, {3628,25150}, {5965,34597}, {6689,12026}, {7604,19553}, {10109,34599}, {10615,23280}, {12010,32428}, {12242,24385}, {13391,21473}, {13467,34577}, {13469,15425}, {13621,34292}, {14143,20414}, {15699,35720}, {15957,32744}, {18400,36837}, {34768,35018}, {35719,37943}

X(46954) = midpoint of X(i) and X(j) for these {i,j}: {5,32551}, {14143,20414}
X(46954) = reflection of X(i) in X(j) for these (i,j): (15425,13469), (34768,35018)
X(46954) = complement of X(18016)

X(46955) = X(4)X(69)∩X(1078)X(5403)

X(46955) lies on these lines: {4, 69}, {1078, 5403}, {1670, 7752}, {1671, 7802}, {1676, 38721}, {7769, 8160}

X(46956) = X(4)X(69)∩X(1078)X(5404)

X(46956) lies on these lines: {4, 69}, {1078, 5404}, {1670, 7802}, {1671, 7752}, {1677, 38720}, {7769, 8161}

X(46957) = X(4)X(519)∩X(3667)X(3669)

X(46958) = X(4)X(524)∩X(1499)X(8355)

X(46959) = X(4)X(524)∩X(1499)X(7652)

X(46959) lies on these lines: {4, 524}, {858, 37746}, {1499, 7652}, {1503, 10734}, {1995, 37745}, {5181, 16183}

X(46960) = X(4)X(527)∩X(28292)X(30235)

This preamble is contributed by Clark Kimberling and Peter Moses, February 20, 2022.

For an introduction to inverse triangles, see the preambles just before X(42005), X(43280), and X(43343). This present section extends the section consisting of X(43344)-X(43363).

Let O = X(3) = circumcenter fo ABC, and suppose that P is a point not on a sideline BC, CA, AB. Let T be the circumcevian triangle of P, and let T' be the inverse of T, as defined in the preamble just before X(42005). Then T and T' are perspective, and the perspector is the point on the circumcircle whose isogonal conjugate is the infinite point of intersection of all the lines perpendicular to OP. (Francisco Javier García Capitán, February 19, 2022)

Continuing, let U be the isogonal conjugate just mentioned. The line OP meets the infinity line in the orthogonal conjugate of U. For a discussion of orthogonal conjugates, see Clark Kimberling, "Polynomial triangle centers on the line at infinity": Journal of Geometry 111, Article 10)

The appearance of (h,j,k) in the following list means that X(j) is the perspector of the circumcevian triangle of X(h) and its inverse triangle, as defined near in the preamble just before X(42005), and that X(j) is the trilinear pole of X(6)X(j).

(1,100,1), (2,110,3), (4,110,3), (5,110,3), (6,99,2), (7,43344,13404), (8,901,101), (9,934,57), (10,109,41), (11,6099,906), (12,43345,8071), (13,10409,2981), (14,10410,6151), (15,99,2), (16,99,2), (17,10409,2981), (18,10410,6151), (19,13395,1214), (20,110,3), (21,110,3), (22,110,3), (23,110,3), (24,110,3), (25,110,3), (26,110,3), (27,110,3), (28,110,3), (29,110,3), (30,110,3), (31,835,10), (32,99,2), (33,43346,1741), (34,43347,46973), (35,100,1), (36,100,1), (37,1310,63), (38,43348,3874), (39,99,2), (40,100,1), (41,43349,142), (42,46961,1125), (43,43350,978), (45,13396,2243), (46,100,1), (48,1305,226), (49,925,5), (50,99,2), (51,43351,140), (52,99,2), (53,43352,46832), (54,930,17), (55,100,1), (56,100,1), (57,100,1), (58,99,2), (59,43353,34530), (60,43354,24880), (61,99,2), (62,99,2), (63,13397,169), (64,107,4), (65,100,1), (66,112,25), (67,691,110), (68,13398,1147), (69,3565,1196), (70,46963,49), (71,1305,226), (72,13397,169), (73,41906,1210), (74,476,13), (75,815,9017), (76,805,694), (77,46964,20310), (78,13397,169), (80,43355,34544), (81,43356,4658), (83,43357,8623), (84,934,57), (85,43358,20793), (86,43359,16058), (87,43360,22140), (88,43361,22141), (90,30240,17700), (95,1303,6638), (96,46965,xx), (97,930,17), (98,805,694), (99,805,694), (100,901,101), (101,927,7), (102,1309,281), (103,927,7), (104,901,101), (105,6078,3939), (106,6079,644), (107,6080,35071), (108,6081,268), (109,1309,281), (110,476,13), (111,6082,2482), (112,2867,15526), (113,1304,74), (114,2715,157), (115,10425,2987), (116,35182,32656), (117,35183,32653), (118,35184,22084), (119,2720,909), (120,35185,3433), (121,35186,32659), (122,1304,74), (123,2720,909), (124,35187,32660), (125,10420,1511), (126,35188,14908), (127,2715,157), (131,10420,1511), (132,46967,46164), (133,46968,xx), (136,46969,xx), (140,110,3), (141,112,25), (142,101,31), (143,20189,3411), (145,28218,7373), (146,16166,11559), (147,46970,3506), (154,107,4), (155,925,5), (156,476,13), (157,112,25), (159,112,25), (160,112,25), (161,933,24), (165,100,1), (169,6183,77),

X(46961) = TRILINEAR POLE OF X(6)X(1125)

X(46961) lies on the circumcircle and these lines: {2, 38960}, {101, 4427}, {106, 3622}, {109, 4781}, {190, 8701}, {664, 5545}, {759, 16824}, {835, 4436}, {1018, 29303}, {1331, 6577}, {2718, 38475}, {3699, 28210}, {3952, 8694}, {4610, 6578}, {17780, 28226}

X(46961) = anticomplement of X(38960)
X(46961) = isotomic conjugate of the anticomplement of X(45745)
X(46961) = Collings transform of X(i) for these i: {1213, 3931, 15668, 26066}
X(46961) = X(i)-cross conjugate of X(j) for these (i,j): {16884, 1016}, {45745, 2}
X(46961) = cevapoint of X(i) and X(j) for these (i,j): {513, 3931}, {514, 15668}, {522, 26066}
X(46961) = trilinear pole of line {6, 1125}
X(46961) = Ψ(X(6), X(1125))
X(46961) = barycentric product X(645)*X(35576)
X(46961) = barycentric quotient X(i)/X(j) for these {i,j}: {35576, 7178}, {45745, 38960}

X(46962) = TRILINEAR POLE OF X(6)X(3306)

X(46962) lies on the circumcircle and these lines: {2, 38962}, {7, 8686}, {644, 6017}, {668, 6079}, {759, 1444}, {1633, 13396}, {2222, 6516}, {2320, 39428}, {2370, 17134}, {2384, 3218}, {2726, 5088}, {12652, 28848}

X(46962) = anticomplement of X(38962)
X(46962) = Collings transform of X(i) for these i: {16594, 17595}
X(46962) = X(16486)-cross conjugate of X(1016)
X(46962) = cevapoint of X(513) and X(17595)
X(46962) = trilinear pole of line {6, 3306}
X(46962) = Ψ(X(6), X(3306))

X(46963) = TRILINEAR POLE OF X(6)X(49)

X(46963) lies on the circumcircle and these lines: {4, 15241}, {74, 5889}, {98, 7391}, {111, 26284}, {477, 44246}, {842, 37978}, {930, 4558}, {1141, 8883}, {1286, 4226}, {1288, 41679}, {1299, 18126}, {1300, 35471}, {3563, 21213}, {30510, 44060}, {37981, 40118}

X(46963) = polar-circle inverse of X(15241)
X(46963) = Collings transform of X(i) for these i: {571, 13371}
X(46963) = X(7517)-cross conjugate of X(250)
X(46963) = X(i)-isoconjugate of X(j) for these (i,j): {656, 7505}, {661, 45794}, {1577, 8553}
X(46963) = cevapoint of X(i) and X(j) for these (i,j): {512, 571}, {523, 13371}
X(46963) = trilinear pole of line {6, 49}
X(46963) = Ψ(X(6), X(49))
X(46963) = barycentric product X(i)*X(j) for these {i,j}: {110, 13579}, {648, 15317}, {18315, 27361}
X(46963) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 45794}, {112, 7505}, {1576, 8553}, {13579, 850}, {15317, 525}, {27361, 18314}

X(46964) = TRILINEAR POLE OF X(6)X(20310)

X(46964) lies on the circumcircle and these lines: {2, 38966}, {20, 972}, {102, 36984}, {103, 10085}, {915, 1012}, {917, 37048}, {2723, 10538}, {3100, 13529}, {15344, 37254}, {16049, 26702}

X(46964) = anticomplement of X(38966)
X(46964) = Collings transform of X(34822)
X(46964) = cevapoint of X(i) and X(j) for these (i,j): {3, 3900}, {522, 34822}
X(46964) = trilinear pole of line {6, 20310}
X(46964) = Ψ(X(6), X(20310))

X(46965) = (name pending)

X(46965) lies on the circumcircle and these lines: {2, 134}, {3, 45135}, {1141, 11412}, {1299, 7691}, {1300, 10625}, {2383, 37478}, {2979, 23233}

X(46965) = reflection of X(45135) in X(3)
X(46965) = anticomplement of X(134)
X(46965) = Collings transform of X(1216)
X(46965) = cevapoint of X(924) and X(1216)
X(46965) = circumperp conjugate of X(45135)
X(46965) = X(107)-of-dual-of-orthic-triangle

X(46966) = TRILINEAR POLE OF X(6)X(11077)

X(46966) is the intersection, other than X(1141), of the circumcircle and the tangent to hyperbola {{A,B,C,X(4),X(5)}} at X(1141). (Randy Hutson, April 16, 2022)

X(46966) lies on the circumcircle and these lines: {54, 14979}, {74, 1157}, {110, 14587}, {265, 39431}, {477, 46089}, {930, 6368}, {933, 1510}, {1141, 16337}, {1154, 18401}, {2383, 15401}, {15907, 25044}, {18315, 43969}

X(46966) = midpoint of X(1157) and X(3484)
X(46966) = Λ(X(137), X(20625))
X(46966) = Ψ(X(5), X(49))
X(46966) = Ψ(X(6), X(11077))
X(46966) = X(i)-cross conjugate of X(j) for these (i,j): {1510, 15401}, {1614, 15395}
X(46966) = X(i)-isoconjugate of X(j) for these (i,j): {526, 1087}, {1154, 2618}, {1953, 41078}, {2081, 14213}, {2290, 18314}, {2599, 6369}, {2624, 45793}, {32679, 36412}
X(46966) = trilinear pole of line {6, 11077}
X(46966) = barycentric product X(i)*X(j) for these {i,j}: {1141, 18315}, {11077, 18831}, {14586, 46138}, {46089, 46456}
X(46966) = barycentric quotient X(i)/X(j) for these {i,j}: {54, 41078}, {476, 45793}, {933, 14918}, {1141, 18314}, {11077, 6368}, {14560, 36412}, {14586, 1154}, {18315, 1273}, {32678, 1087}, {46089, 8552}, {46138, 15415}

X(46967) = TRILINEAR POLE OF X(6)X(46164)

X(46967) lies on the circumcircle and these lines: {66, 2697}, {98, 15407}, {107, 33294}, {112, 8673}, {525, 1289}, {1297, 19158}, {1503, 34168}, {2353, 2710}, {2435, 10423}, {14376, 18337}, {32649, 39417}

X(46967) = reflection of X(34237) in X(34138)
X(46967) = Collings transform of X(i) for these i: {34138, 42671}
X(46967) = X(i)-cross conjugate of X(j) for these (i,j): {525, 15407}, {684, 18018}
X(46967) = X(2312)-isoconjugate of X(33294)
X(46967) = cevapoint of X(i) and X(j) for these (i,j): {520, 42671}, {525, 34138}
X(46967) = trilinear pole of line {6, 46164}
X(46967) = Λ(perspectrix of ABC and 1st orthosymmedial triangle)
X(46967) = Ψ(X(6), X(46164))
X(46967) = barycentric product X(i)*X(j) for these {i,j}: {1297, 44766}, {2419, 15388}, {2435, 44183}, {14376, 44770}
X(46967) = barycentric quotient X(i)/X(j) for these {i,j}: {1297, 33294}, {2435, 127}, {15388, 2409}, {32649, 8743}, {44766, 30737}, {44770, 17907}, {46164, 23881}

X(46968) = (name pending)

X(46968) lies on the circumcircle and these lines: {64, 2693}, {74, 11589}, {107, 8057}, {520, 1301}, {1294, 15311}, {2430, 32687}, {2706, 33581}, {5897, 6000}, {9064, 46639}, {14379, 44874}, {15324, 34147}, {22239, 43701}

X(46968) = Collings transform of X(11589)
X(46968) = X(i)-cross conjugate of X(j) for these (i,j): {520, 15404}, {1636, 1073}
X(46968) = X(i)-isoconjugate of X(j) for these (i,j): {656, 1559}, {6000, 17898}
X(46968) = cevapoint of X(520) and X(11589)
X(46968) = barycentric product X(i)*X(j) for these {i,j}: {394, 39464}, {1294, 46639}, {2416, 15384}, {2430, 44181}, {15394, 32646}
X(46968) = barycentric quotient X(i)/X(j) for these {i,j}: {112, 1559}, {2430, 122}, {15384, 2404}, {32646, 14249}, {39464, 2052}

X(46969) = (name pending)

X(46969) lies on the circumcircle and these lines: {68, 16221}, {110, 44174}, {924, 13398}, {1299, 13754}, {1300, 5962}, {2501, 39416}, {3563, 43756}, {3580, 39437}, {10420, 43709}, {12163, 32710}

X(46969) = X(13754)-cross conjugate of X(44174)
X(46969) = X(12095)-isoconjugate of X(24006)
X(46969) = cevapoint of X(686) and X(2351)
X(46969) = barycentric product X(925)*X(43756)
X(46969) = barycentric quotient X(i)/X(j) for these {i,j}: {32661, 12095}, {32734, 16310}, {43756, 6563}

X(46970) = TRILINEAR POLE OF X(6)X(3506)

X(46970) lies on the circumcircle and these lines: {2, 46669}, {6, 24973}, {74, 9301}, {98, 8784}, {99, 826}, {110, 3005}, {111, 8627}, {187, 755}, {249, 7953}, {511, 29011}, {512, 827}, {689, 850}, {733, 1691}, {842, 5092}, {843, 5008}, {1326, 28485}, {2076, 9482}, {2698, 3398}, {2710, 5188}, {2770, 32525}, {4558, 25424}, {9076, 17949}, {9150, 35366}, {9181, 12074}, {14712, 39938}, {36827, 45773}, {38946, 39427}

X(46970) = reflection of X(827) in the Brocard axis
X(46970) = isogonal conjugate of X(9479)
X(46970) = anticomplement of X(46669)
X(46970) = Schoutte circle inverse of X(755)
X(46970) = Collings transform of X(i) for these i: {1691, 21536}
X(46970) = X(i)-cross conjugate of X(j) for these (i,j): {882, 1976}, {5113, 6}, {20854, 250}
X(46970) = X(i)-isoconjugate of X(j) for these (i,j): {1, 9479}, {38, 18010}, {75, 5113}, {420, 656}, {523, 17799}, {661, 7779}, {826, 34054}, {1577, 2076}, {1930, 17997}, {8061, 40850}, {14208, 44090}
X(46970) = cevapoint of X(i) and X(j) for these (i,j): {6, 5113}, {512, 1691}, {523, 21536}, {3005, 9482}
X(46970) = trilinear pole of line {6, 3506}
X(46970) = Λ(PU(136))
X(46970) = Λ(X(9478), X(9479))
X(46970) = Ψ(X(6), X(3506))
X(46970) = barycentric product X(i)*X(j) for these {i,j}: {99, 46286}, {110, 11606}, {827, 17949}, {4599, 17957}
X(46970) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 9479}, {32, 5113}, {110, 7779}, {112, 420}, {163, 17799}, {251, 18010}, {827, 40850}, {1576, 2076}, {4630, 46228}, {11606, 850}, {17949, 23285}, {34072, 34054}, {46286, 523}, {46288, 17997}

X(46971) = X(10)X(4478)∩X(37)X(4722)

X(46971) lies on these lines: {10, 4478}, {37, 4722}, {4649, 25431}, {9278, 17467}

X(46971) = X(6)-isoconjugate of X(31248)
X(46971) = barycentric quotient X(1)/X(31248)

X(46972) = X(44)X(3290)∩X(244)X(765)

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

X(46972) lies on these lines: {44, 3290}, {244, 765}, {388, 14584}, {513, 3315}, {519, 1738}, {1319, 4318}, {3257, 9282}

X(46972) = isogonal conjugate of X(3722)
X(46972) = isotomic conjugate of X(4986)
X(46972) = X(1023)-cross conjugate of X(88)
X(46972) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3722}, {3, 1862}, {6, 4422}, {31, 4986}, {100, 6161}, {101, 6546}, {649, 32094}, {901, 33905}, {1252, 6547}
X(46972) = cevapoint of X(1) and X(244)
X(46972) = trilinear pole of line {1054, 1635}
X(46972) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4422}, {2, 4986}, {6, 3722}, {19, 1862}, {100, 32094}, {244, 6547}, {513, 6546}, {649, 6161}, {1635, 33905}

X(46973) = X(36)X(518)∩X(100)X(513)

X(46973) = 5 X[100] + X[3257], 3 X[100] + X[6163], 5 X[765] - X[3257], 3 X[765] - X[6163], 3 X[3257] - 5 X[6163]

X(46973) lies on these lines: {36, 518}, {44, 3684}, {55, 16482}, {100, 513}, {101, 2748}, {190, 4926}, {238, 31855}, {404, 46188}, {521, 3939}, {660, 37211}, {678, 45233}, {1026, 23344}, {1279, 3880}, {1618, 6065}, {4057, 4557}, {4606, 36086}, {4777, 39185}, {4802, 36236}, {32094, 33905}

X(46973) = midpoint of X(100) and X(765)
X(46973) = X(i)-Ceva conjugate of X(j) for these (i,j): {88, 1023}, {100, 6161}, {2991, 2284}
X(46973) = X(6161)-cross conjugate of X(3722)
X(46973) = cevapoint of X(3722) and X(6161)
X(46973) = crosssum of X(513) and X(764)
X(46973) = barycentric product X(i)*X(j) for these {i,j}: {1, 32094}, {100, 4422}, {101, 4986}, {190, 3722}, {765, 6546}, {1016, 6161}, {1332, 1862}, {5376, 33905}
X(46973) = barycentric quotient X(i)/X(j) for these {i,j}: {1862, 17924}, {3722, 514}, {4422, 693}, {4986, 3261}, {6161, 1086}, {6546, 1111}, {32094, 75}

X(46974) = ISOGONAL CONJUGATE OF X(36121)

X(46974) lies on these lines: {1, 3}, {2, 5081}, {9, 15905}, {20, 7952}, {21, 40396}, {30, 1785}, {33, 1012}, {34, 3149}, {37, 577}, {44, 3284}, {58, 44547}, {72, 255}, {73, 33597}, {78, 271}, {109, 2733}, {117, 515}, {123, 17757}, {162, 15776}, {201, 22361}, {208, 36986}, {216, 1100}, {221, 6261}, {222, 18446}, {225, 37468}, {227, 6796}, {239, 21940}, {268, 2324}, {411, 4296}, {440, 39595}, {441, 3912}, {498, 34120}, {518, 39026}, {519, 2968}, {521, 656}, {601, 12711}, {603, 1071}, {612, 25907}, {614, 25947}, {758, 12016}, {912, 1795}, {938, 27407}, {971, 3465}, {976, 1496}, {997, 17811}, {1068, 6934}, {1074, 11112}, {1104, 1210}, {1158, 1854}, {1262, 3100}, {1279, 44675}, {1324, 44662}, {1394, 1490}, {1399, 1858}, {1465, 1870}, {1532, 1877}, {1737, 35466}, {1743, 38292}, {1777, 12688}, {1809, 4511}, {1824, 37397}, {1828, 28077}, {1829, 37259}, {1838, 20420}, {1895, 7538}, {1897, 10538}, {1905, 11334}, {1935, 5777}, {1951, 5089}, {2072, 8068}, {2193, 2303}, {3074, 5044}, {3157, 37700}, {3194, 13614}, {3468, 40262}, {3546, 10321}, {3548, 10320}, {3560, 37696}, {3562, 34772}, {3616, 25876}, {3664, 6356}, {3694, 22132}, {3723, 22052}, {3879, 41005}, {3916, 44706}, {3940, 22117}, {3973, 33636}, {4292, 6354}, {4293, 7365}, {4339, 10996}, {4357, 41008}, {4641, 18397}, {4648, 17073}, {4851, 6389}, {4855, 6505}, {5158, 16666}, {5222, 25932}, {5287, 21482}, {5703, 37180}, {5720, 34048}, {6198, 6906}, {6603, 35072}, {6643, 10629}, {6676, 24239}, {6826, 37695}, {6831, 40950}, {6911, 37697}, {6913, 9817}, {6914, 37729}, {6918, 19372}, {8070, 10024}, {9370, 17857}, {10391, 37469}, {10393, 36746}, {10523, 11585}, {10571, 37837}, {11363, 28348}, {11398, 37034}, {11399, 13730}, {11500, 21147}, {12362, 13161}, {13006, 14961}, {13411, 17056}, {15526, 17374}, {15851, 16667}, {16777, 36748}, {16869, 38357}, {16884, 36751}, {17074, 18444}, {17296, 20208}, {17316, 37188}, {17390, 34828}, {18391, 37642}, {19904, 21228}, {20803, 22345}, {21578, 43036}, {22359, 29584}, {22753, 34036}, {23115, 25066}, {27402, 40836}, {27622, 40985}, {28150, 44901}, {31397, 34822}, {31895, 36280}, {35012, 39756}, {36984, 40971}, {37043, 38462}, {37306, 40937}, {40616, 40869}

X(46974) = midpoint of X(i) and X(j) for these {i,j}: {109, 45272}, {1897, 10538}, {3100, 7012}, {4511, 36037}
X(46974) = reflection of X(i) in X(j) for these {i,j}: {1455, 11700}, {1785, 15252}, {38357, 16869}
X(46974) = isogonal conjugate of X(36121)
X(46974) = complement of X(5081)
X(46974) = isotomic conjugate of the polar conjugate of X(2182)
X(46974) = X(i)-complementary conjugate of X(j) for these (i,j): {73, 31845}, {603, 214}, {759, 34831}, {1399, 1511}, {1410, 6739}, {1411, 5}, {1807, 1329}, {2006, 20305}, {2161, 41883}, {2222, 20316}, {6187, 20262}, {18815, 21243}, {22383, 46398}, {34079, 6708}
X(46974) = X(i)-Ceva conjugate of X(j) for these (i,j): {1809, 3}, {4242, 2850}, {4511, 912}, {36037, 521}
X(46974) = X(i)-isoconjugate of X(j) for these (i,j): {1, 36121}, {4, 102}, {19, 36100}, {25, 34393}, {92, 32677}, {158, 36055}, {278, 15629}, {522, 36067}, {653, 2432}, {2399, 32674}, {4391, 32667}, {21189, 36108}, {32085, 46359}, {32643, 46110}, {36040, 44426}
X(46974) = crosssum of X(i) and X(j) for these (i,j): {1, 1735}, {33, 14571}, {3270, 3310}
X(46974) = crossdifference of every pair of points on line {19, 650}
X(46974) = circumconic-centered-at-X(1)-inverse of X(40)
X(46974) = barycentric product X(i)*X(j) for these {i,j}: {48, 35516}, {63, 515}, {69, 2182}, {78, 34050}, {326, 8755}, {345, 1455}, {521, 2406}, {651, 39471}, {664, 46391}, {1459, 42718}, {1813, 14304}, {2425, 35518}, {7452, 24018}, {36100, 38554}
X(46974) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 36100}, {6, 36121}, {48, 102}, {63, 34393}, {184, 32677}, {212, 15629}, {515, 92}, {521, 2399}, {577, 36055}, {1415, 36067}, {1455, 278}, {1946, 2432}, {2182, 4}, {2406, 18026}, {2425, 108}, {4020, 46359}, {7452, 823}, {8755, 158}, {11700, 17923}, {14304, 46110}, {32653, 36108}, {32660, 36040}, {34050, 273}, {34591, 15633}, {35516, 1969}, {39471, 4391}, {42076, 8755}, {46391, 522}
X(46974) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3, 17102}, {1, 1771, 65}, {1, 3075, 942}, {1, 8071, 37592}, {1, 11507, 3931}, {1, 37607, 16193}, {3, 1060, 1214}, {3, 18447, 37565}, {1870, 6905, 1465}, {23703, 45269, 13528}, {38292, 42018, 1743}

X(46975) = X(4)X(25650)∩X(30)X(1125)

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

X(46975) lies on these lines: {4, 25650}, {10, 38330}, {30, 1125}, {381, 24931}, {511, 31937}, {542, 22791}, {3683, 35203}, {18480, 21081}, {19862, 38430}

X(46976) = X(4)X(1798)∩X(10)X(30)

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

X(46976) lies on these lines: {3, 31872}, {4, 1798}, {10, 30}, {511, 22036}, {524, 28645}, {542, 12699}, {1125, 38330}, {3017, 3830}, {3634, 38430}, {10733, 19642}, {17702, 42463}, {18653, 27555}, {25645, 46828}, {30436, 37405}

X(46977) = EULER LINE INTERCEPT OF X(6663)X(9781)

Barycentrics 2*(b^2+c^2)*a^14-3*(3*b^4+4*b^2*c^2+3*c^4)*a^12+15*(b^2+c^2)*(b^4+c^4)*a^10-(10*b^8+10*c^8-(b^4-10*b^2*c^2+c^4)*b^2*c^2)*a^8-2*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^6+(3*b^8+3*c^8-2*(3*b^4-b^2*c^2+3*c^4)*b^2*c^2)*(b^2-c^2)^2*a^4-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^3*(b^4-c^4)*a^2-(b^2-c^2)^6*b^2*c^2 : :
Barycentrics S^4+(2*R^2*(12*R^2-5*SW)-3*SB*SC+SW^2)*S^2+3*(2*R^2+SW)*(4*R^2-SW)*SB*SC : :

X(46978) = X(1)X(3349)∩X(3)X(3473)

X(46978) lies on the cubic K002 and these lines: {1, 3349}, {3, 3473}, {4, 3342}, {6, 3352}, {9, 3356}, {57, 3344}, {282, 1073}

X(46978) = X(31)-complementary conjugate of X(3352)
X(46978) = X(2)-Ceva conjugate of X(3352)
X(46978) = barycentric product X(3353)*X(41080)
X(46978) = barycentric quotient X(i)/X(j) for these {i,j}: {3353, 34162}, {34167, 3354}

X(46979) = X(1)X(14481)∩X(3)X(3351)

X(46979) lies on the cubic K002 and these lines: {1, 14481}, {3, 3351}, {4, 3473}, {9, 3350}, {223, 3343}, {1249, 3341}

X(46979) = X(6)-cross conjugate of X(3351)
X(46979) = barycentric product X(3354)*X(34162)
X(46979) = barycentric quotient X(i)/X(j) for these {i,j}: {3354, 41080}, {28784, 3353}

X(46980) = VERTEX V OF RECTANGLE WITH VERTICES V, X(230), X(468), X(2)

Barycentrics 4*a^10 - 8*a^8*b^2 + a^6*b^4 + 4*a^4*b^6 - 5*a^2*b^8 + 4*b^10 - 8*a^8*c^2 + 22*a^6*b^2*c^2 - 12*a^4*b^4*c^2 + 13*a^2*b^6*c^2 - 11*b^8*c^2 + a^6*c^4 - 12*a^4*b^2*c^4 - 12*a^2*b^4*c^4 + 7*b^6*c^4 + 4*a^4*c^6 + 13*a^2*b^2*c^6 + 7*b^4*c^6 - 5*a^2*c^8 - 11*b^2*c^8 + 4*c^10 : :

X(46980) = X[691] + 3 X[9166], 3 X[5054] - X[46634], X[5099] - 3 X[14971], X[7840] - 5 X[30745], 3 X[8859] + X[10989], 3 X[9166] - X[36196], 2 X[16092] + X[46986], X[16316] - 4 X[44381], X[16320] - 3 X[41139], 3 X[22510] + X[34313], 3 X[22511] + X[34314], 3 X[26614] - X[38613], 4 X[44401] - X[46992], 2 X[46633] + X[46988], 2 X[46981] + X[46982]

X(46980) lies on these lines: {2, 523}, {30, 115}, {98, 1551}, {125, 524}, {381, 46633}, {468, 8754}, {542, 36170}, {543, 40544}, {549, 46987}, {671, 7472}, {691, 9166}, {858, 7668}, {1499, 5465}, {2452, 11184}, {3566, 9144}, {5054, 46634}, {5099, 14971}, {5159, 15526}, {5461, 14120}, {5912, 34320}, {6795, 40248}, {7426, 41125}, {7610, 36194}, {7817, 36157}, {7840, 30745}, {8859, 10989}, {8860, 9832}, {9140, 14999}, {9164, 10415}, {9165, 15899}, {9182, 30786}, {11007, 11168}, {16316, 44381}, {16320, 41139}, {22510, 34313}, {22511, 34314}, {23055, 36163}, {26614, 38613}, {31858, 39511}, {32216, 40879}, {34369, 35912}

X(46980) = midpoint of X(i) and X(j) for these {i,j}: {2, 16092}, {98, 1551}, {381, 46633}, {671, 7472}, {691, 36196}, {858, 22329}, {5912, 34320}, {6055, 16188}, {9140, 14999}
X(46980) = reflection of X(i) in X(j) for these {i,j}: {468, 44401}, {14120, 5461}, {22110, 5159}, {46986, 2}, {46987, 549}, {46988, 381}, {46992, 468}, {46998, 230}
X(46980) = orthoptic-circle-of-Steiner-inellipse-inverse of X(5466)
X(46980) = crossdifference of every pair of points on line {187, 34291}
X(46980) = X(i)-line conjugate of X(j) for these (i,j): {2, 34291}, {30, 187}
X(46980) = radical trace of circles O(13,14) and O(15,16)
X(46980) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {115, 230, 5914}, {691, 9166, 36196}, {6108, 6109, 5915}

X(46981) = VERTEX V OF RECTANGLE WITH VERTICES V, X(230), X(468), X(3)

Barycentrics 4*a^14 - 12*a^12*b^2 + 11*a^10*b^4 + 2*a^8*b^6 - 12*a^6*b^8 + 10*a^4*b^10 - 3*a^2*b^12 - 12*a^12*c^2 + 34*a^10*b^2*c^2 - 34*a^8*b^4*c^2 + 27*a^6*b^6*c^2 - 17*a^4*b^8*c^2 + 3*a^2*b^10*c^2 - b^12*c^2 + 11*a^10*c^4 - 34*a^8*b^2*c^4 + 6*a^6*b^4*c^4 + 3*a^4*b^6*c^4 + 7*a^2*b^8*c^4 + 3*b^10*c^4 + 2*a^8*c^6 + 27*a^6*b^2*c^6 + 3*a^4*b^4*c^6 - 14*a^2*b^6*c^6 - 2*b^8*c^6 - 12*a^6*c^8 - 17*a^4*b^2*c^8 + 7*a^2*b^4*c^8 - 2*b^6*c^8 + 10*a^4*c^10 + 3*a^2*b^2*c^10 + 3*b^4*c^10 - 3*a^2*c^12 - b^2*c^12 : :

X(46981) = 3 X[3] - X[46634], X[98] + 3 X[38702], X[385] + 3 X[2071], X[691] + 3 X[34473], X[5099] - 3 X[38737], X[7464] + 3 X[21445], X[7472] - 3 X[38702], 3 X[10257] - 2 X[44377], 5 X[14061] - X[44969], 3 X[34473] - X[36166], 3 X[38742] + X[38953], 3 X[46633] + X[46634], 2 X[46633] + X[46987], 2 X[46634] - 3 X[46987], 3 X[46980] - X[46982]

X(46981) lies on these lines: {3, 523}, {5, 46988}, {30, 115}, {74, 14999}, {98, 7472}, {127, 10257}, {376, 16092}, {385, 2071}, {468, 46993}, {524, 10564}, {549, 46986}, {691, 34473}, {2696, 5912}, {2794, 36170}, {3233, 5191}, {3288, 46983}, {3564, 15357}, {3566, 18332}, {3972, 36183}, {5099, 38737}, {6036, 14120}, {7464, 21445}, {12068, 35282}, {13335, 36157}, {14061, 44969}, {18122, 44218}, {18579, 46992}, {38742, 38953}

X(46981) = midpoint of X(i) and X(j) for these {i,j}: {3, 46633}, {74, 14999}, {98, 7472}, {376, 16092}, {691, 36166}, {2696, 5912}, {12042, 38611}, {16188, 38749}
X(46981) = reflection of X(i) in X(j) for these {i,j}: {14120, 6036}, {36170, 40544}, {46986, 549}, {46987, 3}, {46988, 5}, {46992, 18579}, {46993, 468}, {46999, 230}
X(46981) = crossdifference of every pair of points on line {3003, 34291}
X(46981) = X(46988)-of-Johnson-triangle
X(46981) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 38702, 7472}, {691, 34473, 36166}

X(46982) = VERTEX V OF RECTANGLE WITH VERTICES V, X(230), X(468), X(4)

Barycentrics 4*a^14 - 8*a^12*b^2 + a^10*b^4 + 10*a^8*b^6 - 12*a^6*b^8 + 2*a^4*b^10 + 7*a^2*b^12 - 4*b^14 - 8*a^12*c^2 + 22*a^10*b^2*c^2 - 18*a^8*b^4*c^2 + 5*a^6*b^6*c^2 + 13*a^4*b^8*c^2 - 31*a^2*b^10*c^2 + 17*b^12*c^2 + a^10*c^4 - 18*a^8*b^2*c^4 + 18*a^6*b^4*c^4 - 15*a^4*b^6*c^4 + 49*a^2*b^8*c^4 - 27*b^10*c^4 + 10*a^8*c^6 + 5*a^6*b^2*c^6 - 15*a^4*b^4*c^6 - 50*a^2*b^6*c^6 + 14*b^8*c^6 - 12*a^6*c^8 + 13*a^4*b^2*c^8 + 49*a^2*b^4*c^8 + 14*b^6*c^8 + 2*a^4*c^10 - 31*a^2*b^2*c^10 - 27*b^4*c^10 + 7*a^2*c^12 + 17*b^2*c^12 - 4*c^14 : :

X(46982) = 3 X[381] - X[46634], 3 X[10151] - X[16316], X[10295] - 3 X[39663], 3 X[14639] - X[36166], 3 X[14639] + X[44972], 2 X[46634] - 3 X[46986], 3 X[46980] - 2 X[46981]

X(46982) lies on these lines: {4, 523}, {5, 46987}, {30, 115}, {381, 46634}, {382, 46633}, {460, 16319}, {468, 46994}, {524, 1531}, {1503, 16278}, {1550, 3566}, {3543, 16092}, {5139, 10151}, {5203, 13473}, {5641, 9410}, {7472, 10723}, {10295, 39663}, {10733, 14999}, {14639, 36166}, {16320, 37984}, {23698, 36170}, {34664, 44386}

X(46982) = midpoint of X(i) and X(j) for these {i,j}: {382, 46633}, {3543, 16092}, {7472, 10723}, {10733, 14999}, {16188, 39809}, {36166, 44972}
X(46982) = reflection of X(i) in X(j) for these {i,j}: {16320, 37984}, {46986, 381}, {46987, 5}, {46988, 4}, {46994, 468}, {47000, 230}
X(46982) = crossdifference of every pair of points on line {3284, 34291}
X(46982) = X(46987)-of-Johnson-triangle
X(46982) = {X(14639),X(44972)}-harmonic conjugate of X(36166)

X(46983) = VERTEX V OF RECTANGLE WITH VERTICES V, X(468), X(647), X(2)

Barycentrics (b^2 - c^2)*(4*a^10 - 11*a^8*b^2 + 3*a^6*b^4 + 11*a^4*b^6 - 7*a^2*b^8 - 11*a^8*c^2 + 30*a^6*b^2*c^2 - 22*a^4*b^4*c^2 + 2*a^2*b^6*c^2 + b^8*c^2 + 3*a^6*c^4 - 22*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - b^6*c^4 + 11*a^4*c^6 + 2*a^2*b^2*c^6 - b^4*c^6 - 7*a^2*c^8 + b^2*c^8) : :

X(46983) lies on these lines: {2, 523}, {30, 647}, {381, 46991}, {468, 44560}, {512, 35266}, {525, 13857}, {549, 46990}, {858, 36900}, {2433, 20423}, {3265, 7799}, {3288, 46981}, {5159, 31174}, {22264, 44569}

X(46983) = midpoint of X(858) and X(36900)
X(46983) = reflection of X(i) in X(j) for these {i,j}: {468, 44560}, {31174, 5159}, {44569, 22264}, {46989, 2}, {46990, 549}, {46991, 381}, {46995, 468}, {47001, 647}
X(46983) = crossdifference of every pair of points on line {187, 44889}

X(46984) = VERTEX V OF RECTANGLE WITH VERTICES V, X(468), X(647), X(3)

Barycentrics (b^2 - c^2)*(-4*a^14 + 13*a^12*b^2 - 11*a^10*b^4 - 6*a^8*b^6 + 14*a^6*b^8 - 7*a^4*b^10 + a^2*b^12 + 13*a^12*c^2 - 46*a^10*b^2*c^2 + 47*a^8*b^4*c^2 - 8*a^6*b^6*c^2 - 5*a^4*b^8*c^2 - 2*a^2*b^10*c^2 + b^12*c^2 - 11*a^10*c^4 + 47*a^8*b^2*c^4 - 56*a^6*b^4*c^4 + 16*a^4*b^6*c^4 + 7*a^2*b^8*c^4 - 3*b^10*c^4 - 6*a^8*c^6 - 8*a^6*b^2*c^6 + 16*a^4*b^4*c^6 - 12*a^2*b^6*c^6 + 2*b^8*c^6 + 14*a^6*c^8 - 5*a^4*b^2*c^8 + 7*a^2*b^4*c^8 + 2*b^6*c^8 - 7*a^4*c^10 - 2*a^2*b^2*c^10 - 3*b^4*c^10 + a^2*c^12 + b^2*c^12) : :

X(46984) lies on these lines: {3, 523}, {5, 46991}, {30, 647}, {468, 46996}, {525, 10564}, {549, 46989}, {2071, 31296}, {3288, 35237}, {10257, 30476}, {14273, 44202}, {14685, 40856}, {18312, 44218}, {18579, 46995}

X(46984) = reflection of X(i) in X(j) for these {i,j}: {46989, 549}, {46990, 3}, {46991, 5}, {46995, 18579}, {46996, 468}, {47002, 647}
X(46984) = crossdifference of every pair of points on line {3003, 44889}
X(46984) = X(46991)-of-Johnson-triangle

X(46985) = VERTEX V OF RECTANGLE WITH VERTICES V, X(468), X(647), X(4)

Barycentrics (b^2 - c^2)*(-a^2 + b^2 + c^2)*(4*a^12 - 3*a^10*b^2 - 10*a^8*b^4 + 8*a^6*b^6 + 6*a^4*b^8 - 5*a^2*b^10 - 3*a^10*c^2 + 20*a^8*b^2*c^2 - 7*a^6*b^4*c^2 - 31*a^4*b^6*c^2 + 18*a^2*b^8*c^2 + 3*b^10*c^2 - 10*a^8*c^4 - 7*a^6*b^2*c^4 + 50*a^4*b^4*c^4 - 13*a^2*b^6*c^4 - 12*b^8*c^4 + 8*a^6*c^6 - 31*a^4*b^2*c^6 - 13*a^2*b^4*c^6 + 18*b^6*c^6 + 6*a^4*c^8 + 18*a^2*b^2*c^8 - 12*b^4*c^8 - 5*a^2*c^10 + 3*b^2*c^10) : :

X(46985) lies on these lines: {4, 523}, {5, 46990}, {30, 647}, {381, 46989}, {468, 46997}, {512, 1514}, {525, 1531}, {4846, 10097}, {10297, 30209}

X(46985) = reflection of X(i) in X(j) for these {i,j}: {46989, 381}, {46990, 5}, {46991, 4}, {46997, 468}, {47003, 647}
X(46985) = crossdifference of every pair of points on line {3284, 44889}
X(46985) = X(46990)-of-Johnson-triangle

X(46986) = REFLECTION OF X(46980) IN THE ORTHIC AXIS

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

X(46986) = X[842] + 3 X[23234], X[858] - 3 X[41133], X[1551] - 3 X[23234], 3 X[5054] - X[46633], X[7472] - 3 X[41134], X[7840] + 3 X[37907], 5 X[7925] - X[10989], 2 X[16092] - 3 X[46980], X[16316] + 2 X[44377], 2 X[22110] + X[46992], 5 X[37760] + 3 X[41136], 4 X[37911] - 3 X[41139], 2 X[46634] + X[46982], 2 X[46987] + X[46988]

X(46986) lies on these lines: {2, 523}, {5, 14357}, {30, 114}, {99, 36196}, {126, 3258}, {230, 3163}, {325, 3233}, {381, 46634}, {468, 524}, {525, 5465}, {542, 16760}, {543, 14120}, {547, 13162}, {549, 46981}, {842, 1551}, {858, 41133}, {1316, 11184}, {2770, 9164}, {3566, 11006}, {3815, 34094}, {3849, 36180}, {5054, 46633}, {5641, 7473}, {5914, 10418}, {6054, 36166}, {6719, 40486}, {7472, 41134}, {7775, 36156}, {7778, 36194}, {7840, 37907}, {7870, 36165}, {7874, 40517}, {7925, 10989}, {9760, 16180}, {9762, 16179}, {16279, 37071}, {16315, 44401}, {22247, 40544}, {30718, 34320}, {32113, 41146}, {37760, 41136}, {37911, 41139}

X(46986) = midpoint of X(i) and X(j) for these {i,j}: {99, 36196}, {325, 7426}, {381, 46634}, {842, 1551}, {2482, 5099}, {5641, 7473}, {6054, 36166}, {16320, 22110}, {22566, 38613}, {32113, 41146}
X(46986) = reflection of X(i) in X(j) for these {i,j}: {16315, 44401}, {40544, 22247}, {46980, 2}, {46981, 549}, {46982, 381}, {46992, 16320}, {46998, 468}
X(46986) = complement of X(16092)
X(46986) = orthoptic-circle-of-Steiner-inellipse-inverse of X(9168)
X(46986) = X(i)-complementary conjugate of X(j) for these (i,j): {842, 4892}, {896, 16188}, {922, 23967}, {5641, 21256}
X(46986) = X(5641)-Ceva conjugate of X(524)
X(46986) = crossdifference of every pair of points on line {187, 10097}
X(46986) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {842, 23234, 1551}, {10418, 44398, 5914}

X(46987) = REFLECTION OF X(46981) IN THE ORTHIC AXIS

Barycentrics 4*a^14 - 12*a^12*b^2 + 13*a^10*b^4 - 2*a^8*b^6 - 12*a^6*b^8 + 14*a^4*b^10 - 5*a^2*b^12 - 12*a^12*c^2 + 30*a^10*b^2*c^2 - 30*a^8*b^4*c^2 + 21*a^6*b^6*c^2 - 15*a^4*b^8*c^2 + 5*a^2*b^10*c^2 + b^12*c^2 + 13*a^10*c^4 - 30*a^8*b^2*c^4 + 18*a^6*b^4*c^4 - 3*a^4*b^6*c^4 + a^2*b^8*c^4 - 3*b^10*c^4 - 2*a^8*c^6 + 21*a^6*b^2*c^6 - 3*a^4*b^4*c^6 - 2*a^2*b^6*c^6 + 2*b^8*c^6 - 12*a^6*c^8 - 15*a^4*b^2*c^8 + a^2*b^4*c^8 + 2*b^6*c^8 + 14*a^4*c^10 + 5*a^2*b^2*c^10 - 3*b^4*c^10 - 5*a^2*c^12 + b^2*c^12 : :

X(46987) = 3 X[3] - X[46633], X[99] + 3 X[38704], X[385] - 5 X[37952], X[842] + 3 X[21166], X[1551] - 3 X[41134], 3 X[3524] - X[16092], 2 X[5159] - 3 X[10256], X[7472] - 3 X[21166], 5 X[7925] - X[10296], X[14999] - 3 X[15035], X[16188] - 3 X[38748], X[36166] - 3 X[38704], 5 X[38750] - X[38953], X[46633] + 3 X[46634], 2 X[46633] - 3 X[46981], 2 X[46634] + X[46981], 3 X[46986] - X[46988]

X(46987) lies on these lines: {3, 523}, {5, 46982}, {30, 114}, {99, 36166}, {325, 10295}, {385, 37952}, {468, 46999}, {511, 36180}, {524, 32110}, {549, 46980}, {574, 36177}, {620, 36170}, {842, 7472}, {1551, 41134}, {3233, 9155}, {3524, 16092}, {5159, 10256}, {7925, 10296}, {9737, 36156}, {10257, 31842}, {10297, 44377}, {12117, 36196}, {14120, 16760}, {14999, 15035}, {16188, 38748}, {18571, 32515}, {18579, 46998}, {31945, 35282}, {38750, 38953}

X(46987) = midpoint of X(i) and X(j) for these {i,j}: {3, 46634}, {99, 36166}, {325, 10295}, {842, 7472}, {5099, 38738}, {12117, 36196}, {33813, 38613}
X(46987) = reflection of X(i) in X(j) for these {i,j}: {10297, 44377}, {14120, 16760}, {36170, 620}, {46980, 549}, {46981, 3}, {46982, 5}, {46993, 16320}, {46998, 18579}, {46999, 468}
X(46987) = X(46982)-of-Johnson-triangle
X(46987) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 38704, 36166}, {842, 21166, 7472}

X(46988) = REFLECTION OF X(46982) IN THE ORTHIC AXIS

Barycentrics 4*a^14 - 8*a^12*b^2 - a^10*b^4 + 14*a^8*b^6 - 12*a^6*b^8 - 2*a^4*b^10 + 9*a^2*b^12 - 4*b^14 - 8*a^12*c^2 + 26*a^10*b^2*c^2 - 22*a^8*b^4*c^2 + 11*a^6*b^6*c^2 + 11*a^4*b^8*c^2 - 33*a^2*b^10*c^2 + 15*b^12*c^2 - a^10*c^4 - 22*a^8*b^2*c^4 + 6*a^6*b^4*c^4 - 9*a^4*b^6*c^4 + 55*a^2*b^8*c^4 - 21*b^10*c^4 + 14*a^8*c^6 + 11*a^6*b^2*c^6 - 9*a^4*b^4*c^6 - 62*a^2*b^6*c^6 + 10*b^8*c^6 - 12*a^6*c^8 + 11*a^4*b^2*c^8 + 55*a^2*b^4*c^8 + 10*b^6*c^8 - 2*a^4*c^10 - 33*a^2*b^2*c^10 - 21*b^4*c^10 + 9*a^2*c^12 + 15*b^2*c^12 - 4*c^14 : :

X(46988) = 3 X[381] - X[46633], 3 X[3839] - X[16092], 3 X[10151] - X[16315], 2 X[46633] - 3 X[46980], 3 X[46986] - 2 X[46987]

X(46988) lies on these lines: {4, 523}, {5, 46981}, {30, 114}, {132, 10151}, {230, 37984}, {381, 46633}, {382, 46634}, {460, 11657}, {468, 47000}, {1503, 2682}, {2794, 14120}, {3566, 11005}, {3839, 16092}, {7472, 44969}, {10722, 36166}, {16308, 33874}

X(46988) = midpoint of X(i) and X(j) for these {i,j}: {382, 46634}, {5099, 39838}, {7472, 44969}, {10722, 36166}
X(46988) = reflection of X(i) in X(j) for these {i,j}: {230, 37984}, {46980, 381}, {46981, 5}, {46982, 4}, {46994, 16320}, {47000, 468}
X(46988) = X(46981)-of-Johnson-triangle

X(46989) = REFLECTION OF X(46983) IN THE ORTHIC AXIS

Barycentrics (b^2 - c^2)*(4*a^10 - 5*a^8*b^2 - 3*a^6*b^4 + 5*a^4*b^6 - a^2*b^8 - 5*a^8*c^2 + 18*a^6*b^2*c^2 - 10*a^4*b^4*c^2 - 10*a^2*b^6*c^2 + 7*b^8*c^2 - 3*a^6*c^4 - 10*a^4*b^2*c^4 + 26*a^2*b^4*c^4 - 7*b^6*c^4 + 5*a^4*c^6 - 10*a^2*b^2*c^6 - 7*b^4*c^6 - a^2*c^8 + 7*b^2*c^8) : :

X(46989) lies on these lines: {2, 523}, {30, 31174}, {381, 46985}, {468, 23878}, {525, 32225}, {549, 46984}, {850, 7426}, {10989, 31072}, {14568, 41357}, {37648, 45321}

X(46989) = midpoint of X(850) and X(7426)
X(46989) = reflection of X(i) in X(j) for these {i,j}: {44552, 41357}, {46983, 2}, {46984, 549}, {46985, 381}, {47001, 468}

X(46990) = REFLECTION OF X(46984) IN THE ORTHIC AXIS

Barycentrics (b^2 - c^2)*(4*a^14 - 11*a^12*b^2 + 5*a^10*b^4 + 10*a^8*b^6 - 10*a^6*b^8 + a^4*b^10 + a^2*b^12 - 11*a^12*c^2 + 34*a^10*b^2*c^2 - 33*a^8*b^4*c^2 + 19*a^4*b^8*c^2 - 10*a^2*b^10*c^2 + b^12*c^2 + 5*a^10*c^4 - 33*a^8*b^2*c^4 + 48*a^6*b^4*c^4 - 24*a^4*b^6*c^4 + 7*a^2*b^8*c^4 - 3*b^10*c^4 + 10*a^8*c^6 - 24*a^4*b^4*c^6 + 4*a^2*b^6*c^6 + 2*b^8*c^6 - 10*a^6*c^8 + 19*a^4*b^2*c^8 + 7*a^2*b^4*c^8 + 2*b^6*c^8 + a^4*c^10 - 10*a^2*b^2*c^10 - 3*b^4*c^10 + a^2*c^12 + b^2*c^12) : :

X(46990) lies on these lines: {3, 523}, {5, 46985}, {30, 31174}, {468, 30209}, {525, 32110}, {549, 46983}, {850, 10295}, {10296, 31072}, {10297, 30476}, {11472, 32120}, {18579, 47001}, {31296, 37952}, {33752, 44218}

X(46990) = midpoint of X(850) and X(10295)
X(46990) = reflection of X(i) in X(j) for these {i,j}: {10297, 30476}, {46983, 549}, {46984, 3}, {46985, 5}, {47001, 18579}, {47002, 468}
X(46990) = X(46985)-of-Johnson-triangle

X(46991) = REFLECTION OF X(46985) IN THE ORTHIC AXIS

Barycentrics (b^2 - c^2)*(-4*a^14 + 9*a^12*b^2 + a^10*b^4 - 14*a^8*b^6 + 6*a^6*b^8 + 5*a^4*b^10 - 3*a^2*b^12 + 9*a^12*c^2 - 38*a^10*b^2*c^2 + 31*a^8*b^4*c^2 + 24*a^6*b^6*c^2 - 29*a^4*b^8*c^2 - 2*a^2*b^10*c^2 + 5*b^12*c^2 + a^10*c^4 + 31*a^8*b^2*c^4 - 72*a^6*b^4*c^4 + 24*a^4*b^6*c^4 + 31*a^2*b^8*c^4 - 15*b^10*c^4 - 14*a^8*c^6 + 24*a^6*b^2*c^6 + 24*a^4*b^4*c^6 - 52*a^2*b^6*c^6 + 10*b^8*c^6 + 6*a^6*c^8 - 29*a^4*b^2*c^8 + 31*a^2*b^4*c^8 + 10*b^6*c^8 + 5*a^4*c^10 - 2*a^2*b^2*c^10 - 15*b^4*c^10 - 3*a^2*c^12 + 5*b^2*c^12) : :

X(46991) lies on these lines: {4, 523}, {5, 46984}, {30, 31174}, {381, 46983}, {468, 47003}, {647, 37984}

X(46991) = reflection of X(i) in X(j) for these {i,j}: {647, 37984}, {46983, 381}, {46984, 5}, {46985, 4}, {47003, 468}
X(46991) = X(46984)-of-Johnson-triangle

X(46992) = REFLECTION OF X(46980) IN X(468)

Barycentrics 8*a^10 - 10*a^8*b^2 + 5*a^6*b^4 + 8*a^4*b^6 - 13*a^2*b^8 + 2*b^10 - 10*a^8*c^2 + 2*a^6*b^2*c^2 - 6*a^4*b^4*c^2 + 23*a^2*b^6*c^2 - b^8*c^2 + 5*a^6*c^4 - 6*a^4*b^2*c^4 - 24*a^2*b^4*c^4 - b^6*c^4 + 8*a^4*c^6 + 23*a^2*b^2*c^6 - b^4*c^6 - 13*a^2*c^8 - b^2*c^8 + 2*c^10 : :

X(46992) = 3 X[23] + X[7840], 3 X[468] - 2 X[44401], 3 X[7426] - X[22329], X[16092] - 3 X[37907], 3 X[16320] - X[22110], 2 X[22110] - 3 X[46986], 2 X[22329] - 3 X[46998], 9 X[37909] - X[44367], 4 X[44401] - 3 X[46980], 2 X[46993] + X[46994]

X(46992) lies on these lines: {2, 38393}, {23, 1634}, {30, 114}, {230, 18487}, {351, 523}, {468, 8754}, {524, 1495}, {597, 44114}, {1084, 16308}, {1316, 42849}, {16092, 37907}, {18579, 46981}, {37909, 44367}, {44265, 47000}, {44266, 46999}

X(46992) = midpoint of X(16316) and X(37904)
X(46992) = reflection of X(i) in X(j) for these {i,j}: {46980, 468}, {46981, 18579}, {46986, 16320}, {46998, 7426}, {46999, 44266}, {47000, 44265}

X(46993) = REFLECTION OF X(46981) IN X(468)

Barycentrics 2*a^12*b^2 - 7*a^10*b^4 + 8*a^8*b^6 - 8*a^4*b^10 + 7*a^2*b^12 - 2*b^14 + 2*a^12*c^2 + 10*a^10*b^2*c^2 - 14*a^8*b^4*c^2 + 7*a^6*b^6*c^2 + 13*a^4*b^8*c^2 - 25*a^2*b^10*c^2 + 7*b^12*c^2 - 7*a^10*c^4 - 14*a^8*b^2*c^4 + 6*a^6*b^4*c^4 - 9*a^4*b^6*c^4 + 45*a^2*b^8*c^4 - 9*b^10*c^4 + 8*a^8*c^6 + 7*a^6*b^2*c^6 - 9*a^4*b^4*c^6 - 54*a^2*b^6*c^6 + 4*b^8*c^6 + 13*a^4*b^2*c^8 + 45*a^2*b^4*c^8 + 4*b^6*c^8 - 8*a^4*c^10 - 25*a^2*b^2*c^10 - 9*b^4*c^10 + 7*a^2*c^12 + 7*b^2*c^12 - 2*c^14 : :

X(46993) lies on these lines: {30, 114}, {468, 46981}, {523, 11799}, {1555, 16316}, {5512, 25641}, {7575, 47000}, {18325, 46634}, {44266, 46998}

X(46993) = midpoint of X(18325) and X(46634)
X(46993) = reflection of X(i) in X(j) for these {i,j}: {46981, 468}, {46987, 16320}, {46998, 44266}, {46999, 11799}, {47000, 7575}

X(46994) = REFLECTION OF X(46982) IN X(468)

Barycentrics 8*a^14 - 22*a^12*b^2 + 19*a^10*b^4 + 4*a^8*b^6 - 24*a^6*b^8 + 20*a^4*b^10 - 3*a^2*b^12 - 2*b^14 - 22*a^12*c^2 + 46*a^10*b^2*c^2 - 38*a^8*b^4*c^2 + 25*a^6*b^6*c^2 - 17*a^4*b^8*c^2 - 3*a^2*b^10*c^2 + 9*b^12*c^2 + 19*a^10*c^4 - 38*a^8*b^2*c^4 + 18*a^6*b^4*c^4 - 3*a^4*b^6*c^4 + 11*a^2*b^8*c^4 - 15*b^10*c^4 + 4*a^8*c^6 + 25*a^6*b^2*c^6 - 3*a^4*b^4*c^6 - 10*a^2*b^6*c^6 + 8*b^8*c^6 - 24*a^6*c^8 - 17*a^4*b^2*c^8 + 11*a^2*b^4*c^8 + 8*b^6*c^8 + 20*a^4*c^10 - 3*a^2*b^2*c^10 - 15*b^4*c^10 - 3*a^2*c^12 + 9*b^2*c^12 - 2*c^14 : :

X(46994) lies on these lines: {30, 114}, {230, 37934}, {468, 46982}, {523, 9409}, {7575, 46999}, {16315, 37931}, {44265, 46998}

X(46994) = reflection of X(i) in X(j) for these {i,j}: {230, 37934}, {46982, 468}, {46988, 16320}, {46998, 44265}, {46999, 7575}, {47000, 10295}

X(46995) = REFLECTION OF X(46983) IN X(468)

Barycentrics (b^2 - c^2)*(8*a^10 - 7*a^8*b^2 - 9*a^6*b^4 + 7*a^4*b^6 + a^2*b^8 - 7*a^8*c^2 + 18*a^6*b^2*c^2 - 2*a^4*b^4*c^2 - 14*a^2*b^6*c^2 + 5*b^8*c^2 - 9*a^6*c^4 - 2*a^4*b^2*c^4 + 22*a^2*b^4*c^4 - 5*b^6*c^4 + 7*a^4*c^6 - 14*a^2*b^2*c^6 - 5*b^4*c^6 + a^2*c^8 + 5*b^2*c^8) : :

X(46995) = 3 X[468] - 2 X[44560], 3 X[7426] - X[36900], 2 X[31174] - 3 X[46989], 2 X[36900] - 3 X[47001], 4 X[44560] - 3 X[46983], 2 X[46996] + X[46997]

X(46995) lies on these lines: {30, 31174}, {351, 523}, {468, 44560}, {512, 44569}, {18579, 46984}, {20192, 45321}, {23878, 37904}, {44265, 47003}, {44266, 47002}

X(46995) = reflection of X(i) in X(j) for these {i,j}: {46983, 468}, {46984, 18579}, {47001, 7426}, {47002, 44266}, {47003, 44265}

X(46996) = REFLECTION OF X(46984) IN X(468)

Barycentrics (b^2 - c^2)*(-(a^12*b^2) + 3*a^10*b^4 - 2*a^8*b^6 - 2*a^6*b^8 + 3*a^4*b^10 - a^2*b^12 - a^12*c^2 - 14*a^10*b^2*c^2 + 17*a^8*b^4*c^2 + 12*a^6*b^6*c^2 - 11*a^4*b^8*c^2 - 6*a^2*b^10*c^2 + 3*b^12*c^2 + 3*a^10*c^4 + 17*a^8*b^2*c^4 - 48*a^6*b^4*c^4 + 12*a^4*b^6*c^4 + 25*a^2*b^8*c^4 - 9*b^10*c^4 - 2*a^8*c^6 + 12*a^6*b^2*c^6 + 12*a^4*b^4*c^6 - 36*a^2*b^6*c^6 + 6*b^8*c^6 - 2*a^6*c^8 - 11*a^4*b^2*c^8 + 25*a^2*b^4*c^8 + 6*b^6*c^8 + 3*a^4*c^10 - 6*a^2*b^2*c^10 - 9*b^4*c^10 - a^2*c^12 + 3*b^2*c^12) : :

X(46996) lies on these lines: {30, 31174}, {132, 25641}, {468, 46984}, {523, 11799}, {1499, 16003}, {5099, 14672}, {7575, 47003}, {15760, 33752}, {44266, 47001}

X(46996) = reflection of X(i) in X(j) for these {i,j}: {46984, 468}, {47001, 44266}, {47002, 11799}, {47003, 7575}

X(46997) = REFLECTION OF X(46985) IN X(468)

Barycentrics (b^2 - c^2)*(-8*a^14 + 21*a^12*b^2 - 7*a^10*b^4 - 22*a^8*b^6 + 18*a^6*b^8 + a^4*b^10 - 3*a^2*b^12 + 21*a^12*c^2 - 58*a^10*b^2*c^2 + 47*a^8*b^4*c^2 + 12*a^6*b^6*c^2 - 37*a^4*b^8*c^2 + 14*a^2*b^10*c^2 + b^12*c^2 - 7*a^10*c^4 + 47*a^8*b^2*c^4 - 72*a^6*b^4*c^4 + 36*a^4*b^6*c^4 - a^2*b^8*c^4 - 3*b^10*c^4 - 22*a^8*c^6 + 12*a^6*b^2*c^6 + 36*a^4*b^4*c^6 - 20*a^2*b^6*c^6 + 2*b^8*c^6 + 18*a^6*c^8 - 37*a^4*b^2*c^8 - a^2*b^4*c^8 + 2*b^6*c^8 + a^4*c^10 + 14*a^2*b^2*c^10 - 3*b^4*c^10 - 3*a^2*c^12 + b^2*c^12) : :

X(46997) lies on these lines: {30, 31174}, {468, 46985}, {523, 9409}, {647, 37934}, {1499, 10990}, {7575, 47002}, {16240, 39533}, {33752, 44285}, {44265, 47001}

X(46997) = reflection of X(i) in X(j) for these {i,j}: {647, 37934}, {46985, 468}, {47001, 44265}, {47002, 7575}, {47003, 10295}

X(46998) = REFLECTION OF X(46980) IN THE EULER LINE

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

X(46998) = X[23] + 3 X[8859], X[385] + 3 X[37907], X[1551] - 3 X[38227], 2 X[5159] - 3 X[41139], X[7472] - 3 X[26613], 3 X[8859] - X[16092], 2 X[22329] + X[46992], 2 X[46999] + X[47000]

X(46998) lies on these lines: {2, 5467}, {23, 8859}, {30, 115}, {351, 523}, {385, 37907}, {468, 524}, {543, 36180}, {549, 9177}, {1316, 7610}, {1551, 38227}, {3849, 14120}, {5159, 41139}, {5306, 21906}, {6784, 8705}, {7417, 14995}, {7472, 26613}, {9465, 11628}, {11168, 34094}, {14694, 45331}, {14999, 15360}, {16315, 37904}, {18579, 46987}, {22110, 45312}, {34506, 36157}, {44265, 46994}, {44266, 46993}, {45163, 46438}

X(46998) = midpoint of X(i) and X(j) for these {i,j}: {23, 16092}, {7426, 22329}, {14999, 15360}, {16315, 37904}
X(46998) = reflection of X(i) in X(j) for these {i,j}: {46980, 230}, {46986, 468}, {46987, 18579}, {46992, 7426}, {46993, 44266}, {46994, 44265}
X(46998) = crossdifference of every pair of points on line {574, 10097}
X(46998) = {X(23),X(8859)}-harmonic conjugate of X(16092)

X(46999) = REFLECTION OF X(46981) IN THE EULER LINE

Barycentrics 2*a^12*b^2 - 5*a^10*b^4 + 4*a^8*b^6 - 4*a^4*b^10 + 5*a^2*b^12 - 2*b^14 + 2*a^12*c^2 + 6*a^10*b^2*c^2 - 10*a^8*b^4*c^2 + a^6*b^6*c^2 + 15*a^4*b^8*c^2 - 23*a^2*b^10*c^2 + 9*b^12*c^2 - 5*a^10*c^4 - 10*a^8*b^2*c^4 + 18*a^6*b^4*c^4 - 15*a^4*b^6*c^4 + 39*a^2*b^8*c^4 - 15*b^10*c^4 + 4*a^8*c^6 + a^6*b^2*c^6 - 15*a^4*b^4*c^6 - 42*a^2*b^6*c^6 + 8*b^8*c^6 + 15*a^4*b^2*c^8 + 39*a^2*b^4*c^8 + 8*b^6*c^8 - 4*a^4*c^10 - 23*a^2*b^2*c^10 - 15*b^4*c^10 + 5*a^2*c^12 + 9*b^2*c^12 - 2*c^14 : :

X(46999) = X[325] - 3 X[403], X[858] - 3 X[39663], X[7472] - 3 X[38227], 3 X[10256] - 4 X[37911], 3 X[10257] - 4 X[44381], 3 X[46998] - X[47000]

X(46999) lies on these lines: {30, 115}, {113, 524}, {247, 32269}, {325, 403}, {381, 40879}, {468, 46987}, {511, 14120}, {523, 11799}, {858, 39663}, {3143, 14356}, {7472, 38227}, {7575, 46994}, {10256, 37911}, {10257, 44381}, {15760, 18122}, {18325, 46633}, {23698, 36180}, {32515, 44961}, {44266, 46992}

X(46999) = midpoint of X(18325) and X(46633)
X(46999) = reflection of X(i) in X(j) for these {i,j}: {46981, 230}, {46987, 468}, {46992, 44266}, {46993, 11799}, {46994, 7575}
X(46999) = crossdifference of every pair of points on line {5063, 34291}

X(47000) = REFLECTION OF X(46982) IN THE EULER LINE

Barycentrics 8*a^14 - 22*a^12*b^2 + 17*a^10*b^4 + 8*a^8*b^6 - 24*a^6*b^8 + 16*a^4*b^10 - a^2*b^12 - 2*b^14 - 22*a^12*c^2 + 50*a^10*b^2*c^2 - 42*a^8*b^4*c^2 + 31*a^6*b^6*c^2 - 19*a^4*b^8*c^2 - 5*a^2*b^10*c^2 + 7*b^12*c^2 + 17*a^10*c^4 - 42*a^8*b^2*c^4 + 6*a^6*b^4*c^4 + 3*a^4*b^6*c^4 + 17*a^2*b^8*c^4 - 9*b^10*c^4 + 8*a^8*c^6 + 31*a^6*b^2*c^6 + 3*a^4*b^4*c^6 - 22*a^2*b^6*c^6 + 4*b^8*c^6 - 24*a^6*c^8 - 19*a^4*b^2*c^8 + 17*a^2*b^4*c^8 + 4*b^6*c^8 + 16*a^4*c^10 - 5*a^2*b^2*c^10 - 9*b^4*c^10 - a^2*c^12 + 7*b^2*c^12 - 2*c^14 : :

X(47000) = X[325] - 3 X[44280], 5 X[7925] - 9 X[37941], X[16316] - 3 X[37931], 3 X[46998] - 2 X[46999]

X(47000) lies on these lines: {30, 115}, {325, 44280}, {468, 46988}, {523, 9409}, {524, 16163}, {2794, 36180}, {7575, 46993}, {7925, 37941}, {16316, 37931}, {16320, 37934}, {18122, 44285}, {36825, 40080}, {44265, 46992}

X(47000) = reflection of X(i) in X(j) for these {i,j}: {16320, 37934}, {46982, 230}, {46988, 468}, {46992, 44265}, {46993, 7575}, {46994, 10295}
X(47000) = crossdifference of every pair of points on line {5158, 34291}

X(47001) = REFLECTION OF X(46983) IN THE EULER LINE

Barycentrics (b^2 - c^2)*(-8*a^10 + 13*a^8*b^2 + 3*a^6*b^4 - 13*a^4*b^6 + 5*a^2*b^8 + 13*a^8*c^2 - 30*a^6*b^2*c^2 + 14*a^4*b^4*c^2 + 2*a^2*b^6*c^2 + b^8*c^2 + 3*a^6*c^4 + 14*a^4*b^2*c^4 - 10*a^2*b^4*c^4 - b^6*c^4 - 13*a^4*c^6 + 2*a^2*b^2*c^6 - b^4*c^6 + 5*a^2*c^8 + b^2*c^8) : :

X(47001) lies on these lines: {30, 647}, {351, 523}, {468, 23878}, {525, 5642}, {2433, 11179}, {6055, 9209}, {13394, 45321}, {18579, 46990}, {31296, 37907}, {35266, 42654}, {44265, 46997}, {44266, 46996}

X(47001) = midpoint of X(7426) and X(36900)
X(47001) = reflection of X(i) in X(j) for these {i,j}: {35266, 42654}, {46983, 647}, {46989, 468}, {46990, 18579}, {46995, 7426}, {46996, 44266}, {46997, 44265}
X(47001) = crossdifference of every pair of points on line {574, 44889}

X(47002) = REFLECTION OF X(46984) IN THE EULER LINE

X(47002) lies on these lines: {30, 647}, {113, 525}, {403, 850}, {468, 30209}, {523, 11799}, {2433, 4846}, {7575, 46997}, {14273, 44203}, {15760, 18312}, {31277, 44911}, {44266, 46995}

X(47002) = reflection of X(i) in X(j) for these {i,j}: {46984, 647}, {46990, 468}, {46995, 44266}, {46996, 11799}, {46997, 7575}
X(47002) = crossdifference of every pair of points on line {5063, 44889}

X(47003) = REFLECTION OF X(46985) IN THE EULER LINE

Barycentrics (b^2 - c^2)*(-a^2 + b^2 + c^2)*(8*a^12 - 15*a^10*b^2 - 2*a^8*b^4 + 16*a^6*b^6 - 6*a^4*b^8 - a^2*b^10 - 15*a^10*c^2 + 40*a^8*b^2*c^2 - 23*a^6*b^4*c^2 - 11*a^4*b^6*c^2 + 6*a^2*b^8*c^2 + 3*b^10*c^2 - 2*a^8*c^4 - 23*a^6*b^2*c^4 + 34*a^4*b^4*c^4 - 5*a^2*b^6*c^4 - 12*b^8*c^4 + 16*a^6*c^6 - 11*a^4*b^2*c^6 - 5*a^2*b^4*c^6 + 18*b^6*c^6 - 6*a^4*c^8 + 6*a^2*b^2*c^8 - 12*b^4*c^8 - a^2*c^10 + 3*b^2*c^10) : :

X(47003) = X[850] - 3 X[44280], 5 X[31072] - 9 X[37941], 3 X[47001] - 2 X[47002]

X(47003) lies on these lines: {30, 647}, {468, 46991}, {523, 9409}, {525, 16163}, {850, 44280}, {1514, 42654}, {7575, 46996}, {18312, 44285}, {31072, 37941}, {44265, 46995}

X(47003) = reflection of X(i) in X(j) for these {i,j}: {1514, 42654}, {46985, 647}, {46991, 468}, {46995, 44265}, {46996, 7575}, {46997, 10295}
X(47003) = crossdifference of every pair of points on line {5158, 44889}

X(47004) = REFLECTION OF X(647) IN THE EULER LINE

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

X(47004) = 3 X[1637] - 4 X[41357], 4 X[5159] - 5 X[31277], X[5189] - 5 X[31072], X[31174] + 2 X[46995], X[31296] - 5 X[37760], X[36900] - 3 X[37907]

X(47004) lies on these lines: {2, 33752}, {23, 850}, {30, 31174}, {98, 2770}, {107, 935}, {125, 512}, {230, 231}, {237, 31953}, {250, 9514}, {373, 40550}, {520, 41586}, {525, 32269}, {858, 30476}, {1995, 18312}, {2453, 44889}, {5159, 31277}, {5189, 31072}, {7426, 23878}, {8371, 15000}, {8599, 10511}, {8675, 32113}, {9030, 32217}, {10415, 10561}, {11799, 30209}, {12073, 42736}, {13558, 14729}, {14417, 44813}, {23105, 44895}, {28729, 37977}, {31296, 37760}, {36900, 37907}, {37934, 47003}, {37984, 46985}, {42659, 44806}

X(47004) = midpoint of X(i) and X(j) for these {i,j}: {23, 850}, {46989, 46995}, {46990, 46996}, {46991, 46997}
X(47004) = reflection of X(i) in X(j) for these {i,j}: {647, 468}, {858, 30476}, {31174, 46989}, {46985, 37984}, {47003, 37934}
X(47004) = reflection of X(647) in the Euler line
X(47004) = Dao-Moses-Telv-circle-inverse of X(2492)
X(47004) = Moses-radical-circle-inverse of X(47233)
X(47004) = barycentric product X(523)*X(40856)
X(47004) = barycentric quotient X(40856)/X(99)
X(47004) = {X(24007),X(24008)}-harmonic conjugate of X(2492)

X(47005) = X(2)X(39)∩X(30)X(3096)

X(47005) lies on these lines: {2, 39}, {3, 10159}, {30, 3096}, {83, 7788}, {99, 3763}, {141, 3972}, {376, 3619}, {381, 7868}, {384, 7865}, {549, 7835}, {574, 16988}, {598, 7818}, {599, 12150}, {1003, 21358}, {1078, 33220}, {3314, 7753}, {3552, 40344}, {3642, 11299}, {3643, 11300}, {3734, 7924}, {3830, 7911}, {5013, 31268}, {5054, 14880}, {5055, 7899}, {5071, 43453}, {5207, 14039}, {5306, 7846}, {5980, 11302}, {5981, 11301}, {5989, 41134}, {6179, 7819}, {6292, 7782}, {6704, 7906}, {7751, 19694}, {7761, 19686}, {7768, 16898}, {7770, 7809}, {7771, 7820}, {7772, 16896}, {7781, 16897}, {7794, 7837}, {7796, 9300}, {7798, 16987}, {7800, 33255}, {7804, 7850}, {7808, 7871}, {7810, 14036}, {7814, 7869}, {7849, 7860}, {7854, 19689}, {7858, 16045}, {7873, 19569}, {7883, 11286}, {7889, 7894}, {7901, 18362}, {7914, 7918}, {7933, 39563}, {7944, 33219}, {7948, 17130}, {8356, 20582}, {8366, 8556}, {10000, 11178}, {11185, 33223}, {12188, 15694}, {41443, 41462}

X(47005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 76, 7884), (2, 7739, 7859), (2, 7795, 7799), (2, 7799, 7786), (2, 7884, 7943), (2, 19570, 7834), (2, 32836, 7803), (141, 6661, 7811), (384, 7865, 11057), (6661, 7811, 3972), (7772, 16896, 43527), (7794, 16895, 7878), (7820, 16986, 7771), (7822, 46226, 76), (7865, 11057, 7936), (7914, 17128, 7918), (7915, 31276, 7942)

This preamble and centers X(47006)-X(47025) were contributed by César Eliud Lozada, February 26, 2022.

Let ABC be a triangle, A_iB_iC_i the intouch triangle of ABC and P a point in the line at infinity. Let A'B'C' be the reflection of A_iB_iC_i in the line X(1)P. Then A'B'C' is perspective to ABC and Q(P), the isogonal-conjugate of the perspector, lies on the incircle of ABC.

The point Q is named here the infinity-incircle-transform of P. If P = x : y : z (barycentrics) then

Q(P) = a^2*(a - b + c)*(a + b - c)*(c*y - b*z)^2 : :

The appearance of (i, j) in the following partial list means that Q( X(i) ) = X(j):

(30, 3024), (511, 3023), (512, 3027), (513, 1317), (514, 1362), (515, 1364), (516, 3022), (517, 11), (518, 1358), (519, 1357), (520, 3324), (521, 1359), (522, 1361), (523, 3028), (524, 3325), (525, 3320), (526, 33964), (527, 47006), (528, 47007), (529, 47008), (530, 47009), (531, 47010), (532, 47011), (533, 47012), (534, 47013), (535, 47014), (536, 47015), (537, 47016), (538, 7333), (539, 47017), (540, 47018), (541, 47019), (542, 6027), (543, 47020), (544, 47021), (545, 47022), (674, 33966), (680, 47023), (688, 7334), (690, 6023), (696, 47024), (698, 47025), (740, 1356), (758, 1365), (900, 13756), (952, 3025), (1154, 3327), (1499, 6019), (1503, 6020), (1510, 7159), (2771, 31522), (2782, 44042), (2800, 3326), (2801, 3328), (2802, 14027), (2808, 44043), (2809, 3323), (2818, 44044), (3307, 2447), (3308, 2446), (3309, 3021), (3667, 6018), (3738, 3319), (3887, 3322), (3900, 1360), (3907, 1355), (4160, 1366), (5663, 33965), (6000, 7158), (6001, 3318), (6003, 34194), (8674, 31524), (14077, 3321), (16168, 44050), (25150, 44053), (28234, 5577), (28292, 5580), (28294, 6024), (28475, 6021), (28849, 31892), (28850, 15615), (28915, 44045), (29311, 3026), (32472, 6022), (33962, 44048), (35057, 1354), (44661, 1367)

X(47006) = INFINITY-INCIRCLE-TRANSFORM OF X(527)

X(47006) lies on the incircle and these lines: {1, 5580}, {12, 31844}, {55, 28291}, {56, 2291}, {65, 3321}, {1317, 8581}, {1319, 15746}, {1361, 1469}, {1362, 2099}, {3021, 5919}, {3028, 44764}, {3271, 47007}, {3328, 4014}, {3675, 5577}

X(47006) = reflection of X(5580) in X(1)
X(47006) = antipode of X(5580) in incircle
X(47006) = X(30247)-of-intouch triangle
X(47006) = X(28291)-of-Mandart-incircle triangle
X(47006) = X(14672)-of-Ursa-minor triangle
X(47006) = X(5580)-of-5th mixtilinear triangle
X(47006) = X(2373)-of-Hutson intouch triangle
X(47006) = X(2291)-of-2nd anti-circumperp-tangential triangle
X(47006) = X(1)-beth conjugate of-X(3321)

X(47007) = INFINITY-INCIRCLE-TRANSFORM OF X(528)

X(47007) lies on the incircle and these lines: {11, 3309}, {55, 2742}, {56, 840}, {65, 3322}, {513, 1358}, {517, 3021}, {518, 1317}, {1155, 5580}, {1284, 3028}, {1319, 1362}, {1360, 18838}, {2078, 5526}, {2099, 13756}, {3022, 35604}, {3025, 3675}, {3271, 47006}, {3321, 3660}

X(47007) = barycentric product X(7)*X(35125)
X(47007) = trilinear product X(57)*X(35125)
X(47007) = touchpoint of the tripolar of X(43050) and incircle
X(47007) = crosspoint of X(7) and X(43050)
X(47007) = X(1)-beth conjugate of-X(3322)
X(47007) = reflection of X(11) in the line X(1)X(6)
X(47007) = X(38971)-of-Ursa-minor triangle
X(47007) = X(2742)-of-Mandart-incircle triangle
X(47007) = X(2697)-of-Hutson intouch triangle
X(47007) = X(935)-of-intouch triangle
X(47007) = X(840)-of-2nd anti-circumperp-tangential triangle
X(47007) = X(7)-Ceva conjugate of-X(43050)

X(47008) = INFINITY-INCIRCLE-TRANSFORM OF X(529)

X(47008) lies on the incircle and these lines: {55, 39635}, {56, 38882}, {14027, 18191}

X(47008) = X(38882)-of-2nd anti-circumperp-tangential triangle
X(47008) = X(39635)-of-Mandart-incircle triangle

X(47009) = INFINITY-INCIRCLE-TRANSFORM OF X(530)

X(47009) lies on the incircle and these lines: {55, 9202}, {56, 2378}, {512, 47010}, {531, 3027}, {3023, 27550}, {18975, 33964}

X(47009) = X(2378)-of-2nd anti-circumperp-tangential triangle
X(47009) = X(9202)-of-Mandart-incircle triangle

X(47010) = INFINITY-INCIRCLE-TRANSFORM OF X(531)

X(47010) lies on the incircle and these lines: {55, 9203}, {56, 2379}, {512, 47009}, {530, 3027}, {3023, 27551}, {18974, 33964}

X(47010) = X(2379)-of-2nd anti-circumperp-tangential triangle
X(47010) = X(9203)-of-Mandart-incircle triangle

X(47011) = INFINITY-INCIRCLE-TRANSFORM OF X(532)

X(47011) lies on the incircle and these lines: {55, 39636}, {56, 2380}, {3027, 18975}, {7159, 18972}

X(47011) = X(2380)-of-2nd anti-circumperp-tangential triangle
X(47011) = X(39636)-of-Mandart-incircle triangle

X(47012) = INFINITY-INCIRCLE-TRANSFORM OF X(533)

X(47012) lies on the incircle and these lines: {55, 39637}, {56, 2381}, {3027, 18974}, {7159, 18973}

X(47012) = X(2381)-of-2nd anti-circumperp-tangential triangle
X(47012) = X(39637)-of-Mandart-incircle triangle

X(47013) = INFINITY-INCIRCLE-TRANSFORM OF X(534)

X(47014) = INFINITY-INCIRCLE-TRANSFORM OF X(535)

X(47015) = INFINITY-INCIRCLE-TRANSFORM OF X(536)

X(47015) lies on the incircle and these lines: {1, 6021}, {55, 28474}, {56, 739}, {1317, 1469}, {3027, 35103}

X(47015) = reflection of X(6021) in X(1)
X(47015) = reflection of X(11) in the line X(1)X(9024)
X(47015) = X(28474)-of-Mandart-incircle triangle
X(47015) = X(6021)-of-5th mixtilinear triangle
X(47015) = X(739)-of-2nd anti-circumperp-tangential triangle
X(47015) = antipode of X(6021) in incircle

X(47016) = INFINITY-INCIRCLE-TRANSFORM OF X(537)

X(47016) lies on the incircle and these lines: {11, 24232}, {55, 28520}, {56, 2382}, {1317, 1463}, {1356, 4017}, {1357, 3669}, {4009, 6381}

X(47016) = barycentric product X(i)*X(j) for these {i, j}: {7, 39011}, {1357, 13466}, {1646, 43037}
X(47016) = barycentric quotient X(1646)/X(36798)
X(47016) = trilinear product X(i)*X(j) for these {i, j}: {57, 39011}, {664, 14441}, {1357, 42083}
X(47016) = touchpoint of the line {19945, 47016} and incircle
X(47016) = X(891)-Dao conjugate of X(8)
X(47016) = reflection of X(11) in the line X(1)X(19945)
X(47016) = X(28520)-of-Mandart-incircle triangle
X(47016) = X(2382)-of-2nd anti-circumperp-tangential triangle
X(47016) = X(1646)-reciprocal conjugate of-X(36798)

X(47017) = INFINITY-INCIRCLE-TRANSFORM OF X(539)

X(47017) lies on the incircle and these lines: {55, 20185}, {56, 2383}, {7159, 7354}

X(47017) = X(2383)-of-2nd anti-circumperp-tangential triangle
X(47017) = X(20185)-of-Mandart-incircle triangle

X(47018) = INFINITY-INCIRCLE-TRANSFORM OF X(540)

X(47019) = INFINITY-INCIRCLE-TRANSFORM OF X(541)

X(47019) lies on the incircle and these lines: {11, 46436}, {55, 9060}, {56, 841}, {3024, 8675}, {3028, 5160}, {3058, 33964}

X(47019) = X(841)-of-2nd anti-circumperp-tangential triangle
X(47019) = X(9060)-of-Mandart-incircle triangle

X(47020) = INFINITY-INCIRCLE-TRANSFORM OF X(543)

X(47020) lies on the incircle and these lines: {11, 46659}, {12, 44956}, {55, 2709}, {56, 843}, {511, 6019}, {512, 3325}, {524, 3027}, {1469, 6023}, {1499, 3023}, {3028, 5194}, {12953, 44946}

X(47020) = X(843)-of-2nd anti-circumperp-tangential triangle
X(47020) = X(2709)-of-Mandart-incircle triangle

X(47021) = INFINITY-INCIRCLE-TRANSFORM OF X(544)

X(47021) lies on the incircle and these lines: {55, 39640}, {56, 38884}, {514, 33966}, {516, 6025}, {674, 1362}

X(47021) = X(38884)-of-2nd anti-circumperp-tangential triangle
X(47021) = X(39640)-of-Mandart-incircle triangle

X(47022) = INFINITY-INCIRCLE-TRANSFORM OF X(545)

X(47022) lies on the incircle and these lines: {1, 6024}, {55, 28293}, {56, 2384}, {1469, 13756}

X(47022) = reflection of X(6024) in X(1)
X(47022) = X(28293)-of-Mandart-incircle triangle
X(47022) = X(6024)-of-5th mixtilinear triangle
X(47022) = X(2384)-of-2nd anti-circumperp-tangential triangle
X(47022) = antipode of X(6024) in incircle

X(47023) = INFINITY-INCIRCLE-TRANSFORM OF X(680)

X(47024) = INFINITY-INCIRCLE-TRANSFORM OF X(696)

X(47024) lies on the incircle and these lines: {1, 6028}, {12, 35972}, {56, 697}

X(47024) = reflection of X(6028) in X(1)
X(47024) = X(6028)-of-5th mixtilinear triangle
X(47024) = X(697)-of-2nd anti-circumperp-tangential triangle
X(47024) = antipode of X(6028) in incircle

X(47025) = INFINITY-INCIRCLE-TRANSFORM OF X(698)

X(47025) lies on the incircle and these lines: {55, 30254}, {56, 699}, {14691, 18957}

X(47025) = X(699)-of-2nd anti-circumperp-tangential triangle
X(47025) = X(30254)-of-Mandart-incircle triangle

X(47026) = X(623)X(858)∩X(624)X(6787)

X(47026) lies on these lines: {4, 15441}, {5, 16536}, {15, 1080}, {623, 858}, {624, 6787}, {5478, 5618}, {7684, 32111}, {33529, 33957}, {36961, 45779}

X(47027) = X(623)X(6787)∩X(624)X(858)

X(47027) lies on these lines: {4, 15442}, {5, 16537}, {16, 383}, {623, 6787}, {624, 858}, {5479, 5619}, {7685, 32111}, {33530, 33958}, {36962, 45779}

X(47028) = X(396)X(15609)∩X(623)X(33499)

X(47028) lies on these lines: {5, 36312}, {396, 15609}, {623, 33499}, {7684, 13754}, {33529, 33957}

X(47029) = X(395)X(15610)∩X(624)X(33501)

X(47029) lies on these lines: {5, 36313}, {395, 15610}, {624, 33501}, {7685, 13754}, {33530, 33958}

X(47030) = X(5)X(9530)∩X(122)X(5894)

X(47030) lies on these lines: {5, 9530}, {122, 5894}, {1503, 33546}, {3832, 33924}, {14059, 23324}, {20329, 33531}

X(47031) = MIDPOINT OF X(20) AND X(7426)

Barycentrics    22*a^10 - 39*a^8*b^2 - 10*a^6*b^4 + 44*a^4*b^6 - 12*a^2*b^8 - 5*b^10 - 39*a^8*c^2 + 92*a^6*b^2*c^2 - 52*a^4*b^4*c^2 - 16*a^2*b^6*c^2 + 15*b^8*c^2 - 10*a^6*c^4 - 52*a^4*b^2*c^4 + 56*a^2*b^4*c^4 - 10*b^6*c^4 + 44*a^4*c^6 - 16*a^2*b^2*c^6 - 10*b^4*c^6 - 12*a^2*c^8 + 15*b^2*c^8 - 5*c^10::
Barycentrics    9*SA*SB*SC*(2*S^2 - 3*SB*SC) - S^4*SW : :
Barycentrics    22 a^10 - 39 a^8 (b^2 + c^2) - 5 (b^2 - c^2)^4 (b^2 + c^2) - 4 a^2 (b - c)^2 (b + c)^2 (3 b^2 + c^2) (b^2 + 3 c^2) - 2 a^6 (5 b^4 - 46 b^2 c^2 + 5 c^4) + 4 a^4 (b^2 + c^2) (11 b^4 - 24 b^2 c^2 + 11 c^4)

X(47031) = (-9 + 5*J^2)*X[2] - 9*(J^2 - 1)*X[3]
X(47031) = 5 X[2] - 9 X[37941], X[2] - 3 X[44280], X[20] + 2 X[37934], 5 X[20] + 7 X[37957], 3 X[186] + X[11001], 5 X[376] - X[7464], 3 X[403] - X[15682], 5 X[468] - 8 X[18571], 3 X[468] - 4 X[18579], 13 X[468] - 16 X[22249], 11 X[468] - 8 X[44961], 5 X[550] + X[37967], X[858] - 3 X[10304], 3 X[2070] + 5 X[3534], 6 X[2070] - 5 X[37904], and many others

X(47031) lies on these lines: {2, 3}, {523, 14290}, {524, 16163}, {2777, 35266}, {11645, 37853}, {14831, 41149}, {16227, 21849}, {16312, 38749}, {23878, 47003}, {44401, 46982}, {44560, 46985}

X(47031) = midpoint of X(i) and X(j) for these {i,j}: {20, 7426}, {376, 10295}, {3534, 44265}, {7575, 15686}, {11799, 15681}, {19710, 44266}, {44267, 44903}
X(47031) = reflection of X(i) in X(j) for these {i,j}: {3543, 37984}, {7426, 37934}, {10151, 44214}, {10297, 549}, {15122, 34200}, {37904, 44265}, {46982, 44401}, {46985, 44560}
X(47031) = orthoptic-circle-of-Steiner-inellipse-inverse of X(30775)
X(47031) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3534, 8703, 7667}, {3534, 9909, 11001}, {5066, 12100, 34478}, {10295, 44246, 44239}, {35931, 35932, 40884}, {37904, 37931, 44265}, {44246, 44265, 3534}, {44265, 44280, 44268}

X(47032) = EULER LINE INTERCEPT OF X(79)X(517)

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

X(47032) lies on these lines: {2,3}, {8,16116}, {10,3652}, {12,35000}, {35,13273}, {40,16118}, {46,18977}, {65,16152}, {79,517}, {80,13145}, {388,8148}, {498,35249}, {758,25413}, {1385,4857}, {1478,12702}, {1482,3649}, {1737,16141}, {2771,12751}, {2886,26321}, {3057,16153}, {3065,12619}, {3295,18961}, {3359,7701}, {3434,18526}, {3436,3650}, {3579,3585}, {3583,13624}, {3647,26446}, {3648,5657}, {3698,18480}, {3884,12699}, {4413,45631}, {4999,38761}, {5119,16142}, {5260,10728}, {5434,27197}, {5557,6583}, {5587,22798}, {5690,11684}, {5790,6256}, {5794,40266}, {5800,44456}, {5840,37621}, {5882,12737}, {5886,6701}, {6244,11929}, {9579,37584}, {9654,35448}, {9709,18542}, {9956,26202}, {10039,16140}, {10246,10525}, {10247,16137}, {10270,30315}, {10308,18357}, {10441,13340}, {10895,35238}, {11010,17662}, {11263,13464}, {11522,33592}, {11573,18330}, {11604,37518}, {11826,11849}, {12047,35459}, {12115,12645}, {12513,34698}, {12761,38752}, {12773,24390}, {12943,35239}, {13391,41723}, {13465,21677}, {13528,45065}, {15174,37624}, {15908,22765}, {16005,34918}, {16128,20117}, {16139,43174}, {16154,17637}, {18253,37821}, {18406,33697}, {18513,35242}, {18515,26363}, {18525,40587}, {24466,31659}, {28174,34352}, {31479,35251}, {33110,37705}, {33668,34195}, {35610,35855}, {35611,35854}, {37561,46816}

X(47032) = midpoint of X(i) and X(j) for these {i,j}: {8, 16116}, {40, 16118}, {12702, 16150}
X(47032) = reflection of X(i) in X(j) for these {i,j}: {3, 37401}, {21, 5499}, {1482, 3649}, {3065, 12619}, {3652, 10}, {5441, 1385}, {11684, 5690}, {12699, 16125}, {13465, 21677}, {13743, 442}, {15678, 549}, {15680, 5428}, {16113, 3579}, {17637, 34339}, {21669, 5}, {26202, 9956}, {34195, 33668}, {37230, 2475}

X(47033) = X(8)X(79)∩X(10)X(21)

X(47033) lies on these lines: {1,442}, {2,15079}, {4,5692}, {8,79}, {10,21}, {30,40}, {36,6734}, {46,10042}, {63,10483}, {72,3585}, {78,7951}, {101,21029}, {140,15015}, {145,6701}, {149,3884}, {165,44238}, {200,10827}, {201,38945}, {210,18480}, {226,41696}, {284,21675}, {377,5902}, {388,12777}, {392,4857}, {404,14804}, {452,41872}, {484,33961}, {498,17057}, {515,3651}, {517,37230}, {518,5270}, {519,5178}, {528,37563}, {594,16548}, {936,10826}, {946,31159}, {950,5259}, {952,5499}, {958,37286}, {960,3583}, {997,7741}, {1089,16086}, {1125,31254}, {1145,13089}, {1224,41506}, {1376,17665}, {1479,5175}, {1482,31140}, {1698,1837}, {1733,2550}, {1749,8256}, {1768,31775}, {1788,41547}, {1869,31902}, {2093,10045}, {2476,22836}, {2771,12751}, {2795,13178}, {2802,5559}, {2893,18698}, {2975,36975}, {3035,38411}, {3036,3065}, {3189,10056}, {3216,37717}, {3245,3626}, {3255,43731}, {3336,11112}, {3338,41574}, {3340,3632}, {3434,5697}, {3486,19854}, {3582,17614}, {3612,5705}, {3617,3647}, {3624,5722}, {3625,32634}, {3633,4863}, {3648,4678}, {3678,5080}, {3746,24987}, {3753,8261}, {3754,20612}, {3811,37719}, {3822,34772}, {3824,44840}, {3828,15671}, {3872,37707}, {3894,10404}, {3899,12699}, {3916,4316}, {3925,37730}, {3927,12943}, {3940,10895}, {4018,11552}, {4084,20292}, {4127,17484}, {4187,37718}, {4188,5442}, {4190,37524}, {4197,30143}, {4208,41862}, {4292,4880}, {4317,24477}, {4324,4640}, {4511,5443}, {4653,21674}, {4668,5223}, {4669,15679}, {4677,32049}, {4720,21081}, {4745,15678}, {4816,11544}, {4847,5288}, {4853,37708}, {4861,7972}, {4867,6737}, {4999,10609}, {5010,26066}, {5046,10176}, {5082,10629}, {5231,37618}, {5234,18253}, {5312,5725}, {5425,12609}, {5427,24914}, {5428,26446}, {5445,25440}, {5537,21669}, {5538,6831}, {5563,10916}, {5587,6841}, {5693,6923}, {5730,18393}, {5771,30264}, {5777,41698}, {5779,37001}, {5790,11248}, {5836,16152}, {5842,15910}, {5881,16132}, {5884,6951}, {5887,34789}, {6174,31650}, {6326,6842}, {6596,8068}, {6684,21161}, {6700,31263}, {6762,34690}, {6763,7354}, {6850,15071}, {6901,31870}, {6917,37625}, {6940,10265}, {7110,21018}, {7270,35616}, {8715,31660}, {9623,37711}, {9708,37292}, {9780,15674}, {9803,37163}, {9897,13146}, {9956,33596}, {10021,38042}, {10057,10914}, {10122,11024}, {10527,21842}, {10590,20007}, {10950,31419}, {11045,12649}, {11219,37561}, {11277,34773}, {11321,30119}, {11680,30144}, {12245,16125}, {12635,17532}, {12762,18908}, {13465,41691}, {15670,19875}, {15792,37152}, {15955,33136}, {16117,18525}, {16143,37712}, {16160,18357}, {16173,24387}, {17052,24435}, {17688,30165}, {18514,24703}, {18743,44784}, {19861,37720}, {19925,31160}, {20172,30124}, {20653,37369}, {21014,37508}, {21033,32431}, {21692,44253}, {21935,30115}, {22793,31165}, {22798,35448}, {22936,37829}, {25006,35989}, {26363,37525}, {26726,33593}, {28186,31651}, {28465,31423}, {30135,33045}, {30147,33108}, {30150,33825}, {31262,38410}, {31493,34471}, {31803,37437}, {33557,35099}, {37447,37714}, {37721,44256}, {40663,41697}

X(47033) = midpoint of X(i) and X(j) for these {i,j}: {8, 2475}, {3632, 16126}, {5881, 16132}, {9897, 13146}, {16117, 18525}
X(47033) = reflection of X(i) in X(j) for these {i,j}: {1, 442}, {21, 10}, {79, 2475}, {191, 21677}, {1482, 33592}, {3746, 24987}, {5441, 21}, {7972, 39778}, {10543, 6675}, {15680, 3647}, {16113, 16139}, {16126, 3649}, {16132, 37401}, {16139, 5690}, {16160, 18357}, {33858, 5499}, {34195, 11263}, {34773, 11277}, {41691, 13465}
X(47033) = isogonal conjugate of X(1)-vertex conjugate of X(65)

X(47034) = X(65)X(79)∩X(119)X(191)

X(47034) lies on these lines: {4,6599}, {5,1768}, {21,10165}, {30,6265}, {65,79}, {104,11263}, {119,191}, {153,14450}, {546,12600}, {758,12751}, {952,16126}, {2475,2800}, {2829,16132}, {3065,6841}, {4301,10698}, {5426,11729}, {5443,12611}, {5499,12515}, {5531,37826}, {5840,13146}, {6326,37468}, {6831,12615}, {6839,9809}, {6842,13089}, {6905,21635}, {7491,16143}, {7548,10265}, {9964,11604}, {10021,38410}, {10058,14526}, {10074,33593}, {10266,13729}, {12761,17653}, {12764,17637}, {12913,31870}, {13465,38755}, {16113,35204}, {16118,45764}, {16152,33594}, {16173,33592}, {22937,38752}

X(47034) = midpoint of X(153) and X(14450)
X(47034) = reflection of X(i) in X(j) for these {i,j}: {80, 37230}, {104, 11263}, {191, 119}, {3065, 6841}, {11604, 16125}, {12119, 34600}, {12515, 5499}, {13743, 12611}, {16113, 35204}, {46816, 33594}

X(47035) = MIDPOINT OF X(3) AND X(3440)

Barycentrics a^2*(2*(a^8-3*(b^2+c^2)*a^6+3*(b^4+c^4)*a^4-(b^2+c^2)*(b^4+3*b^2*c^2+c^4)*a^2+7*(b^2-c^2)^2*b^2*c^2)*S+sqrt(3)*(a^10-2*(b^2+c^2)*a^8+2*(b^4+c^4)*a^6-(b^2+c^2)*(4*b^4-5*b^2*c^2+4*c^4)*a^4+(5*b^8+5*c^8-2*(2*b^4+3*b^2*c^2+2*c^4)*b^2*c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(2*b^4-3*b^2*c^2+2*c^4))) : :
Barycentrics (SB+SC)*(3*(12*R^2-2*SA-5*SW)*S^2-3*(6*R^2+3*SA-4*SW)*SA*SW+S*sqrt(3)*(SA*(18*R^2-9*SA+2*SW)-7*S^2)) : :

X(47035) lies on these lines: {3, 3440}, {18, 15441}, {30, 5463}, {110, 3129}, {11080, 22511}, {11086, 36759}, {14670, 14687}

X(47036) = MIDPOINT OF X(3) AND X(3441)

Barycentrics a^2*(-2*(a^8-3*(b^2+c^2)*a^6+3*(b^4+c^4)*a^4-(b^2+c^2)*(b^4+3*b^2*c^2+c^4)*a^2+7*(b^2-c^2)^2*b^2*c^2)*S+sqrt(3)*(a^10-2*(b^2+c^2)*a^8+2*(b^4+c^4)*a^6-(b^2+c^2)*(4*b^4-5*b^2*c^2+4*c^4)*a^4+(5*b^8+5*c^8-2*(2*b^4+3*b^2*c^2+2*c^4)*b^2*c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(2*b^4-3*b^2*c^2+2*c^4))) : :
Barycentrics (SB+SC)*(3*(12*R^2-2*SA-5*SW)*S^2-3*(6*R^2+3*SA-4*SW)*SA*SW-S*sqrt(3)*(SA*(18*R^2-9*SA+2*SW)-7*S^2)) : :

X(47036) lies on these lines: {3, 3441}, {17, 15442}, {30, 5464}, {110, 3130}, {11081, 36760}, {11085, 22510}, {14670, 14687}

X(47037) = X(2)X(6)∩X(3)X(33985)

X(47037) lies on the cubic K1263 and these lines: {2, 6}, {3, 33985}, {36, 36871}, {45, 26247}, {55, 536}, {405, 7751}, {442, 14023}, {474, 7780}, {538, 16370}, {754, 17532}, {956, 33908}, {958, 4400}, {1001, 4396}, {3011, 4643}, {3052, 24330}, {3053, 34284}, {3684, 16833}, {4252, 4754}, {4363, 26227}, {4364, 26228}, {4386, 4688}, {4419, 26245}, {4670, 29828}, {4690, 29857}, {4708, 29855}, {4713, 26237}, {4760, 5695}, {6179, 11321}, {7483, 7758}, {7781, 19535}, {8716, 17549}, {9909, 20875}, {11114, 34505}, {16394, 19761}, {16825, 24685}, {16919, 22331}, {17318, 20045}, {17360, 30763}, {19705, 46893}, {20065, 33031}, {34511, 37298}

X(47037) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {385, 16992, 5275}, {385, 16994, 16995}, {385, 16996, 16992}, {17002, 37670, 6}

X(47038) = X(3)X(6)∩X(35)X(43146)

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

X(47038) lies on the cubic K1263 and these lines: {3, 6}, {35, 43146}, {55, 2810}, {69, 11111}, {452, 3620}, {518, 25439}, {993, 9025}, {1005, 10477}, {1352, 6930}, {1386, 5126}, {1420, 16491}, {1468, 4787}, {1469, 2078}, {1480, 2818}, {1697, 16496}, {2097, 15934}, {2979, 5320}, {3056, 43149}, {3242, 17461}, {3589, 17564}, {3619, 5084}, {3751, 35445}, {3781, 5526}, {3827, 9957}, {5820, 29012}, {6636, 44104}, {6970, 14561}, {10761, 41451}, {14996, 15107}, {14997, 41462}, {17197, 36477}, {17527, 34573}, {17576, 20080}, {24929, 34371}, {33849, 34417}

X(47038) = reflection of X(5138) in X(36740)
X(47038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1350, 37492, 4260}, {4265, 37516, 182}

X(47039) = X(2)X(5030)∩X(63)X(16834)

X(47039) lies on the cubic K1263 and these lines: {2, 5030}, {63, 16834}, {99, 17346}, {101, 6172}, {527, 551}, {8074, 17729}, {9741, 37654}, {13635, 22712}, {16394, 19868}

X(47040) = X(1)X(16393)∩X(2)X(4256)

X(47040) lies on the cubic K1263 and these lines: {1, 16393}, {2, 4256}, {55, 519}, {99, 17378}, {386, 13735}, {536, 24929}, {551, 4356}, {940, 16401}, {996, 2177}, {2901, 3601}, {3175, 33595}, {3241, 17126}, {3244, 4252}, {3679, 32917}, {3950, 37504}, {4234, 5145}, {4421, 19251}, {4664, 30115}, {4891, 17502}, {5132, 19255}, {5426, 32860}, {8715, 28348}, {9945, 17243}, {13634, 22712}, {16394, 19765}, {16397, 37522}, {16418, 37502}, {16834, 37817}, {19346, 42057}, {24552, 25055}

X(47041) = X(31)X(999)∩X(55)X(2810)

X(47041) lies on the cubic K1263 and these lines: {31, 999}, {55, 2810}, {57, 238}, {63, 517}, {109, 24320}, {222, 36942}, {329, 7413}, {513, 1376}, {601, 42461}, {654, 5452}, {896, 36279}, {1473, 10269}, {2093, 16570}, {3452, 4703}, {3820, 26034}, {4640, 34371}, {5020, 9316}, {7085, 35238}, {9965, 37103}, {10310, 29958}, {16466, 23085}, {23845, 45729}

X(47042) = X(3)X(142)∩X(7)X(109)

X(47042) lies on the cubic K1263 and these lines: {3, 142}, {7, 109}, {9, 2225}, {379, 35338}, {929, 38884}, {10436, 35258}, {17197, 37580}, {17810, 41797}

X(47043) = X(1)X(514)∩X(2)X(6075)

X(47043) lies on the cubic K1263 and these lines: {1, 514}, {2, 6075}, {3, 8}, {20, 14512}, {840, 929}, {1055, 4530}, {1319, 4124}, {2726, 14733}, {5698, 5845}, {5723, 16020}, {16825, 45749}, {30305, 38503}

X(47044) = X(2)X(512)∩X(3)X(76)

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

X(47044) lies on the cubic K1264 and these lines: {2, 512}, {3, 76}, {187, 4226}, {249, 40820}, {262, 41330}, {385, 5118}, {691, 1316}, {5085, 33989}, {7735, 14700}, {7757, 35146}, {7786, 14251}, {7792, 36157}, {7804, 46512}, {11634, 46777}, {26316, 36177}, {44823, 46778}

X(47044) = crossdifference of every pair of points on line {2491, 3231}
X(47044) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 36822, 99}, {3111, 5652, 14608}

X(47045) = X(2)X(513)∩X(3)X(8)

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

X(47045) lies on the cubic K1264 and these lines: {2, 513}, {3, 8}, {59, 40218}, {1788, 14584}, {3286, 3658}, {3616, 14260}, {4257, 6788}, {17126, 36086}

X(47045) = crossdifference of every pair of points on line {3230, 3310}
X(47045) = {X(3),X(45145)}-harmonic conjugate of X(100)

X(47046) = X(2)X(1499)∩X(3)X(111)

Barycentrics a^2*(a^10*b^2 + 6*a^8*b^4 + 2*a^6*b^6 - 8*a^4*b^8 - 3*a^2*b^10 + 2*b^12 + a^10*c^2 - 34*a^8*b^2*c^2 + 41*a^6*b^4*c^2 - 71*a^4*b^6*c^2 + 50*a^2*b^8*c^2 - 19*b^10*c^2 + 6*a^8*c^4 + 41*a^6*b^2*c^4 + 12*a^4*b^4*c^4 + 9*a^2*b^6*c^4 + 44*b^8*c^4 + 2*a^6*c^6 - 71*a^4*b^2*c^6 + 9*a^2*b^4*c^6 - 86*b^6*c^6 - 8*a^4*c^8 + 50*a^2*b^2*c^8 + 44*b^4*c^8 - 3*a^2*c^10 - 19*b^2*c^10 + 2*c^12) : :

X(47046) lies on the cubics K793 and K1264 and these lines: {2, 1499}, {3, 111}, {6, 2709}, {511, 14898}, {5085, 33928}, {5968, 9175}, {5969, 7610}, {7418, 9176}, {14684, 32447}, {37930, 38702}

X(47047) = X(2)X(99)∩X(3)X(669)

X(47047) lies on the cubic K1265 and these lines: {2, 99}, {3, 669}, {32, 40517}, {55, 46369}, {69, 23992}, {187, 5468}, {237, 41337}, {385, 2396}, {843, 6082}, {868, 44377}, {1641, 27088}, {1648, 6390}, {3552, 40871}, {4226, 11052}, {5026, 5967}, {5099, 36163}, {5969, 9486}, {6792, 14515}, {7417, 18860}, {7778, 36194}, {7795, 14357}, {7813, 45291}, {7816, 46512}, {7870, 40877}, {8369, 41939}, {9125, 15566}, {9169, 11165}, {9214, 40553}, {11053, 32459}, {13586, 34245}, {15271, 36822}, {18311, 39078}

X(47047) = X(i)-complementary conjugate of X(j) for these (i,j): {2642, 36472}, {2987, 4892}, {8773, 625}, {8781, 21256}, {32654, 16611}, {36051, 524}
X(47047) = X(i)-Ceva conjugate of X(j) for these (i,j): {98, 524}, {39292, 5468}
X(47047) = crosssum of X(3124) and X(8430)
X(47047) = crossdifference of every pair of points on line {351, 3291}
X(47047) = barycentric product X(i)*X(j) for these {i,j}: {524, 10754}, {5468, 34290}, {6390, 36898}
X(47047) = barycentric quotient X(i)/X(j) for these {i,j}: {10754, 671}, {34290, 5466}, {36898, 17983}
X(47047) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 99, 35606}, {187, 45330, 5468}, {11053, 32459, 45662}

X(47048) = X(1)X(16449)∩X(2)X(11)

X(47048) lies on the cubic K1265 and these lines: {1, 16449}, {2, 11}, {3, 667}, {35, 16450}, {36, 1023}, {56, 4564}, {574, 6184}, {840, 6078}, {991, 24498}, {5217, 16448}, {37660, 45145}

X(47048) = X(i)-complementary conjugate of X(j) for these (i,j): {1818, 42423}, {2254, 15608}, {2990, 20335}, {6099, 3716}, {32655, 3008}, {36052, 518}
X(47048) = X(i)-Ceva conjugate of X(j) for these (i,j): {104, 518}, {5376, 2284}
X(47048) = crossdifference of every pair of points on line {665, 3290}

X(47049) = X(2)X(98)∩X(3)X(512)

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

X(47049) lies on the cubic K1265 and these lines: {2, 98}, {3, 512}, {30, 5118}, {32, 45901}, {55, 45235}, {511, 2421}, {574, 3016}, {576, 6785}, {577, 38974}, {805, 842}, {1495, 15329}, {2088, 13754}, {2882, 35387}, {3134, 11064}, {3569, 40083}, {3818, 36183}, {5108, 6795}, {5650, 33927}, {6787, 37991}, {7775, 13352}, {7809, 10411}, {7818, 35088}, {7865, 31378}, {9177, 14915}, {10539, 43389}, {14811, 17508}, {17811, 33988}, {34359, 40805}, {35259, 44889}

X(47049) = midpoint of X(2421) and X(7418)
X(47049) = psi-transform of X(7468)
X(47049) = X(i)-complementary conjugate of X(j) for these (i,j): {240, 46085}, {14910, 16609}, {36053, 511}, {36114, 6130}
X(47049) = X(i)-Ceva conjugate of X(j) for these (i,j): {74, 511}, {18878, 2799}, {39295, 14966}
X(47049) = crossdifference of every pair of points on line {230, 3569}
X(47049) = barycentric product X(34810)*X(35910)
X(47049) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15920, 182}

X(47050) = X(2)X(74)∩X(3)X(523)

X(47050) lies on the cubic K1265 and these lines: {2, 74}, {3, 523}, {4, 14508}, {376, 476}, {549, 31945}, {574, 3163}, {2407, 10564}, {3524, 31378}, {7422, 32110}, {15469, 35912}, {16177, 18531}

X(47050) = Thomson-isogonal conjugate of X(33927)
X(47050) = X(43660)-Ceva conjugate of X(30)

X(47051) = X(2)X(104)∩X(3)X(513)

X(47051) lies on the cubic K1265 and these lines: {2, 104}, {3, 513}, {55, 1480}, {574, 23980}, {901, 35238}, {999, 33646}

X(47052) = X(3)X(3734)∩X(32)X(39684)

X(47052) lies on the cubic K1266 and these lines: {3, 3734}, {32, 39684}, {39, 10014}, {99, 20023}, {160, 3098}, {187, 6195}, {237, 574}, {669, 8723}, {3357, 15270}, {5206, 32518}, {8588, 21444}, {11328, 15482}, {21512, 39857}, {33981, 37916}, {35704, 43718}

X(47053) = X(3)X(143)∩X(50)X(15360)

X(47053) lies on the cubic K130 and these lines: {3, 143}, {50, 15360}, {97, 44891}, {110, 351}, {476, 1291}, {2617, 13486}, {3470, 15766}, {4226, 14884}, {4240, 14590}, {10420, 16166}, {11800, 14652}, {14966, 36830}, {15919, 41462}, {16186, 23061}, {16962, 46824}, {16963, 46825}, {23217, 27866}

X(47053) = X(476)-Ceva conjugate of X(110)
X(47053) = X(i)-cross conjugate of X(j) for these (i,j): {6140, 11063}, {8562, 3470}, {45147, 1157}
X(47053) = X(i)-isoconjugate of X(j) for these (i,j): {661, 13582}, {1109, 1291}, {1263, 2616}, {1577, 14579}, {11071, 32679}, {24006, 43704}
X(47053) = cevapoint of X(i) and X(j) for these (i,j): {523, 10277}, {6140, 11063}
X(47053) = crosssum of X(i) and X(j) for these (i,j): {2088, 8029}, {2610, 12071}
X(47053) = trilinear pole of line {5612, 5616}
X(47053) = barycentric product X(i)*X(j) for these {i,j}: {99, 11063}, {110, 37779}, {249, 45147}, {476, 40604}, {662, 1749}, {1157, 14570}, {2407, 3470}, {2420, 46751}, {4558, 37943}, {4590, 6140}, {5612, 23896}, {5616, 23895}, {8562, 39295}, {10272, 44769}
X(47053) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 13582}, {1157, 15412}, {1576, 14579}, {1625, 1263}, {1749, 1577}, {2420, 3471}, {2914, 44427}, {3470, 2394}, {5612, 23871}, {5616, 23870}, {5994, 46076}, {5995, 46072}, {6140, 115}, {10272, 41079}, {10413, 23105}, {11063, 523}, {14560, 11071}, {15766, 14566}, {19306, 2616}, {23357, 1291}, {32661, 43704}, {32662, 15392}, {37779, 850}, {37943, 14618}, {40604, 3268}, {45147, 338}
X(47053) = {X(1576),X(36829)}-harmonic conjugate of X(110)

X(47054) = X(1)X(60)∩X(30)X(80)

X(47054) lies on the cubic K130 and these lines: {1, 60}, {30, 80}, {35, 35194}, {191, 6740}, {265, 7701}, {267, 2166}, {3336, 45926}, {10260, 34871}

X(47055) = X(2)X(1138)∩X(3)X(74)

Barycentrics a^2*(a^2 - b^2 - b*c - c^2)*(a^2 - b^2 + b*c - 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 - 5*a^4*b^4*c^2 + 3*a^2*b^6*c^2 - 3*b^8*c^2 - 4*a^6*c^4 - 5*a^4*b^2*c^4 + 2*a^2*b^4*c^4 + 2*b^6*c^4 + 6*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(47055) = 3 X[3] + X[14264], X[3] + 3 X[33927], X[14264] - 3 X[14670], X[14264] - 9 X[33927], X[14670] - 3 X[33927], 5 X[38794] - X[41512]

X(47055) lies on the cubics K130 and K258 and these lines: {2, 1138}, {3, 74}, {5, 3258}, {39, 18334}, {140, 523}, {526, 23108}, {549, 18285}, {1154, 16186}, {6663, 10125}, {13363, 18114}, {13364, 44889}, {13391, 15329}, {15766, 37496}, {16241, 40579}, {16242, 40578}, {18573, 44535}, {20304, 39170}, {38794, 41512}

X(47055) = midpoint of X(3) and X(14670)
X(47055) = complement of X(14254)
X(47055) = complement of the isogonal conjugate of X(14385)
X(47055) = X(i)-complementary conjugate of X(j) for these (i,j): {2159, 3580}, {2349, 34827}, {6149, 113}, {14385, 10}, {35200, 2072}, {36034, 526}
X(47055) = X(476)-Ceva conjugate of X(526)
X(47055) = crosssum of X(i) and X(j) for these (i,j): {6, 14583}, {36208, 46078}, {36209, 46074}
X(47055) = crossdifference of every pair of points on line {1637, 11063}
X(47055) = barycentric product X(323)*X(10264)
X(47055) = barycentric quotient X(10264)/X(94)
X(47055) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14385, 1511}, {3, 33927, 14670}, {1511, 12041, 15468}

X(47056) = X(2)X(45)∩X(81)X(4638)

X(47056) lies on the cubic K134 and these lines: {2, 45}, {81, 4638}, {106, 29820}, {679, 37520}, {1320, 3938}, {1647, 37375}, {1999, 4555}, {2226, 27003}, {3257, 4641}, {3961, 4792}, {6548, 30724}, {6549, 39595}, {32911, 40594}, {40940, 46790}

X(47056) = X(i)-isoconjugate of X(j) for these (i,j): {3285, 34895}, {17455, 36935}
X(47056) = barycentric product X(i)*X(j) for these {i,j}: {88, 37759}, {1168, 41873}, {4080, 37791}
X(47056) = barycentric quotient X(i)/X(j) for these {i,j}: {1168, 36935}, {4674, 34895}, {36926, 4723}, {37759, 4358}, {37791, 16704}, {41873, 1227}
X(47056) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {}

X(47057) = X(1)X(30)∩X(2)X(21739)

X(47057) lies on the cubic K134 and these lines: {1, 30}, {2, 21739}, {7, 41819}, {9, 6505}, {34, 1873}, {55, 9904}, {57, 77}, {63, 323}, {65, 2940}, {73, 30115}, {191, 8614}, {223, 5219}, {226, 1029}, {501, 2906}, {553, 1443}, {651, 16577}, {664, 6358}, {991, 20277}, {1048, 37558}, {1214, 2003}, {1419, 18675}, {1421, 29820}, {1458, 29819}, {1461, 37755}, {1697, 34498}, {2323, 18607}, {2895, 41808}, {3182, 3601}, {3911, 17020}, {3938, 36482}, {3982, 7269}, {4303, 8555}, {5287, 26738}, {16554, 21367}, {18652, 45206}, {23511, 31231}, {41804, 42045}, {41807, 41816}

X(47057) = X(i)-Ceva conjugate of X(j) for these (i,j): {226, 57}, {1442, 1}, {41808, 191}
X(47057) = X(1030)-cross conjugate of X(191)
X(47057) = X(i)-isoconjugate of X(j) for these (i,j): {8, 3444}, {9, 267}, {21, 21353}, {41, 44188}, {55, 1029}, {210, 40143}, {284, 502}, {2341, 39149}
X(47057) = cevapoint of X(1030) and X(8614)
X(47057) = crosspoint of X(651) and X(35049)
X(47057) = crossdifference of every pair of points on line {4041, 9404}
X(47057) = barycentric product X(i)*X(j) for these {i,j}: {1, 41808}, {7, 191}, {56, 20932}, {57, 2895}, {75, 8614}, {77, 451}, {85, 1030}, {226, 40592}, {273, 22136}, {307, 2906}, {501, 1441}, {651, 21192}, {664, 31947}, {1014, 21081}, {1412, 42710}, {1434, 21873}, {4625, 42653}, {7182, 44097}
X(47057) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 44188}, {56, 267}, {57, 1029}, {65, 502}, {191, 8}, {451, 318}, {501, 21}, {604, 3444}, {1030, 9}, {1400, 21353}, {1412, 40143}, {1464, 39149}, {2895, 312}, {2906, 29}, {8614, 1}, {20932, 3596}, {21081, 3701}, {21192, 4391}, {21873, 2321}, {22136, 78}, {31947, 522}, {40592, 333}, {41808, 75}, {42653, 4041}, {42710, 30713}, {44097, 33}
X(47057) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 16143, 38336}, {77, 45126, 57}, {81, 18593, 57}, {500, 7100, 1}, {1443, 17011, 553}, {4303, 8555, 33178}, {18625, 37635, 226}

X(47058) = X(2)X(8046)∩X(57)X(88)

X(47058) lies on the cubic K134 and these lines: {2, 8046}, {57, 88}, {81, 4638}, {226, 26743}, {321, 4555}, {329, 36887}, {679, 17012}, {903, 17483}, {1022, 1255}, {1029, 4080}, {1168, 5425}, {1320, 5561}, {2226, 3752}, {3219, 3257}, {3748, 14190}, {4622, 40592}, {4945, 31053}, {4997, 18139}, {5249, 46790}, {14260, 33151}, {19684, 27922}, {27064, 46795}, {31143, 33079}

X(47058) = cevapoint of X(6126) and X(19297)
X(47058) = X(i)-isoconjugate of X(j) for these (i,j): {44, 3065}, {214, 11075}, {519, 19302}, {902, 21739}, {1639, 34921}, {2251, 40716}
X(47058) = barycentric product X(i)*X(j) for these {i,j}: {88, 17484}, {106, 17791}, {484, 903}, {19297, 20568}
X(47058) = barycentric quotient X(i)/X(j) for these {i,j}: {88, 21739}, {106, 3065}, {484, 519}, {903, 40716}, {6126, 214}, {9456, 19302}, {17484, 4358}, {17791, 3264}, {19297, 44}, {21864, 3943}, {23071, 5440}, {42657, 4895}

X(47059) = X(2)X(1029)∩X(21)X(6536)

X(47059) lies on the cubic K134 and these lines: {2, 1029}, {21, 6536}, {48, 28606}, {56, 229}, {57, 37791}, {81, 4556}, {409, 993}, {21674, 37294}

X(47059) = X(226)-Ceva conjugate of X(81)
X(47059) = {X(34053),X(40592)}-harmonic conjugate of X(2)

X(47060) = ISOGONAL CONJUGATE OF X(47061)

X(47060) = isogonal conjugate of X(47061)
X(47060) = intersection, other than A, B, C, of circumconics Jerabek hyperbola and {{A, B, C, X(25), X(11317)}}

X(47061) = EULER LINE INTERCEPT OF X(69)X(7618)

X(47061) lies on these lines: {2, 3}, {69, 7618}, {99, 42850}, {115, 23053}, {148, 16508}, {543, 34229}, {574, 1992}, {597, 5210}, {1007, 7622}, {1153, 43620}, {2482, 11161}, {2549, 5569}, {3448, 14653}, {3618, 8588}, {3785, 15533}, {3926, 22165}, {5013, 8584}, {5024, 5032}, {6337, 7810}, {7617, 43619}, {7620, 37688}, {7771, 11054}, {7826, 15515}, {8593, 25406}, {8860, 43448}, {9740, 31859}, {9770, 14907}, {9771, 32827}, {11147, 15810}, {11160, 11165}, {11168, 32815}, {15534, 15815}, {15597, 44526}, {15655, 19661}, {17008, 32480}, {21358, 32459}, {31173, 34803}

X(47061) = isogonal conjugate of X(47060)
X(47061) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 8597, 3545), (549, 5077, 2), (5054, 37350, 2), (5999, 10304, 376), (8354, 15693, 2), (33188, 33267, 3855), (35303, 35304, 5054), (37172, 37173, 3525)

X(47062) = X(23)X(7665)∩X(187)X(2393)

X(47063) = X(524)X(13493)∩X(1499)X(11616)

X(47064) = X(4)X(195)∩X(323)X(25150)

X(47064) lies on these lines: {4, 195}, {323, 25150}, {1141, 15032}, {1511, 18016}, {11438, 13505}, {11464, 34418}, {12026, 15037}, {13504, 37478}, {15052, 31656}, {15412, 45147}

X(47065) = X(3)X(1263)∩X(4)X(137)

Barycentrics a^16-4*(b^2+c^2)*a^14+2*(3*b^4+5*b^2*c^2+3*c^4)*a^12-6*(b^2+c^2)*(b^4+c^4)*a^10+(10*b^8+10*c^8-b^2*c^2*(6*b^4-b^2*c^2+6*c^4))*a^8-2*(b^4-c^4)*(b^2-c^2)*(8*b^4-3*b^2*c^2+8*c^4)*a^6+(14*b^8+14*c^8-b^2*c^2*(8*b^4+5*b^2*c^2+8*c^4))*(b^2-c^2)^2*a^4-2*(b^4-c^4)*(b^2-c^2)^3*(3*b^4-5*b^2*c^2+3*c^4)*a^2+(b^2-c^2)^8 : :
Barycentrics 3*S^4-(R^2*(12*R^2+5*SA-12*SW)-2*SA^2-SB*SC+3*SW^2)*S^2+(R^2*(9*R^2-7*SW)+SW^2)*SB*SC : :

X(47065) = X(3)+2*X(1263), 2*X(3)+X(11671), X(3)-4*X(12026), X(4)-4*X(137), X(4)+2*X(1141), 5*X(4)-2*X(44981), 2*X(5)+X(38587), X(20)-4*X(38618), 2*X(52)+X(13504), 4*X(128)-7*X(3090), 2*X(128)+X(38683), 2*X(137)+X(1141), 10*X(137)-X(44981), 4*X(140)-X(13512), X(146)-4*X(43966), 5*X(1141)+X(44981), 4*X(1263)-X(11671), X(1263)+2*X(12026), 7*X(3090)+2*X(38683), X(11671)+8*X(12026)

X(47065) lies on these lines: {2, 25150}, {3, 1263}, {4, 137}, {5, 38587}, {20, 38618}, {24, 34418}, {26, 14652}, {52, 13504}, {56, 14101}, {128, 3090}, {140, 13512}, {146, 43966}, {376, 38710}, {381, 9143}, {389, 13505}, {631, 930}, {1138, 39180}, {1493, 15307}, {1656, 14072}, {3085, 7159}, {3086, 3327}, {3091, 31656}, {3518, 15959}, {3523, 38615}, {3524, 38706}, {3525, 13372}, {3526, 6592}, {3529, 44976}, {3545, 23516}, {3628, 14073}, {5055, 23237}, {5070, 23238}, {5079, 25339}, {10594, 15960}, {12254, 27196}, {12316, 31674}, {15081, 45258}, {15392, 27357}, {15693, 38640}, {23320, 44879}, {42731, 45147}

X(47065) = reflection of X(i) in X(j) for these (i, j): (376, 38710), (381, 25147)
X(47065) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 1263, 11671), (137, 1141, 4), (930, 34837, 631), (1263, 12026, 3)

X(47066) = X(3)X(6)∩X(4)X(616)

X(47066) = 3*X(3)-X(5865), 4*X(3)-3*X(9735), 2*X(3)-3*X(9736), 3*X(5864)+X(5865), 4*X(5864)+3*X(9735), 2*X(5864)+3*X(9736), 4*X(5865)-9*X(9735), 2*X(5865)-9*X(9736), 5*X(22234)-6*X(44478)

X(47066) lies on these lines: {3, 6}, {4, 616}, {5, 3643}, {17, 20425}, {20, 6773}, {30, 33459}, {184, 11126}, {194, 32596}, {298, 9989}, {383, 37825}, {530, 7775}, {532, 5873}, {542, 22570}, {617, 36959}, {621, 7802}, {622, 7752}, {623, 7825}, {624, 7862}, {629, 7684}, {633, 7811}, {634, 5613}, {635, 7865}, {636, 7869}, {2902, 2925}, {2979, 11145}, {3060, 11146}, {3130, 9306}, {3132, 44719}, {3534, 22496}, {5463, 37333}, {5473, 16530}, {5476, 37340}, {5872, 41022}, {6582, 33421}, {6770, 13571}, {6771, 40693}, {6774, 42149}, {7755, 43454}, {7765, 43455}, {11004, 41472}, {11131, 34417}, {11178, 37332}, {12110, 44460}, {13102, 42432}, {13103, 42813}, {14561, 37177}, {14881, 22687}, {16001, 42162}, {16002, 22512}, {16628, 36970}, {16631, 18362}, {17130, 25167}, {20423, 37172}, {22843, 42528}, {22861, 42159}, {22869, 33389}, {22870, 29012}, {22871, 35688}, {22890, 42157}, {22914, 33420}, {34507, 41034}, {35747, 42257}, {35917, 36384}, {35918, 36365}, {40694, 44465}, {42151, 44461}

X(47066) = midpoint of X(3) and X(5864)
X(47066) = reflection of X(9735) in X(9736)
X(47066) = reflection of X(47068) in X(3)
X(47066) = circumnormal-isogonal conjugate of the anticomplement of X(16630)
X(47066) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(40707)}} and {{A, B, C, X(6), X(38428)}}
X(47066) = X(5864)-of-anti-X3-ABC reflections triangle
X(47066) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 62, 182), (3, 1351, 22236), (3, 5611, 5238), (3, 5615, 62), (3, 14540, 3098), (3, 22236, 13350), (3, 36843, 13349), (4, 627, 5617), (16, 3104, 32), (16, 14540, 3), (62, 3095, 576), (62, 3106, 7772), (62, 14538, 3), (1350, 36843, 3), (3130, 44718, 9306), (5237, 14541, 3), (5351, 14539, 3), (5615, 14538, 182), (9738, 9739, 9736), (11126, 34008, 184), (11481, 33878, 36756)

X(47067) = X(76)X(618)∩X(302)X(3642)

X(47067) lies on these lines: {3, 40707}, {13, 22911}, {76, 618}, {298, 11132}, {299, 16530}, {302, 3642}, {395, 7786}, {623, 11057}, {629, 7814}, {631, 633}, {7811, 44383}, {7860, 11289}, {7934, 23303}, {42158, 44030}

X(47068) = X(3)X(6)∩X(4)X(617)

X(47068) = 3*X(3)-X(5864), 2*X(3)-3*X(9735), 4*X(3)-3*X(9736), X(5864)+3*X(5865), 2*X(5864)-9*X(9735), 4*X(5864)-9*X(9736), 2*X(5865)+3*X(9735), 4*X(5865)+3*X(9736), 5*X(22234)-6*X(44477)

X(47068) lies on these lines: {3, 6}, {4, 617}, {5, 3642}, {18, 20426}, {20, 6770}, {30, 33458}, {184, 11127}, {194, 32597}, {299, 9988}, {531, 7775}, {533, 5872}, {542, 22568}, {616, 36958}, {621, 7752}, {622, 7802}, {623, 7862}, {624, 7825}, {630, 7685}, {633, 5617}, {634, 7811}, {635, 7869}, {636, 7865}, {1080, 37824}, {2903, 2926}, {2979, 11146}, {3060, 11145}, {3129, 9306}, {3131, 44718}, {3534, 22495}, {5464, 37332}, {5474, 16529}, {5476, 37341}, {5873, 41023}, {6295, 33420}, {6771, 42152}, {6773, 13571}, {6774, 40694}, {7755, 43455}, {7765, 43454}, {11004, 41473}, {11130, 34417}, {11178, 37333}, {12110, 44464}, {13102, 42814}, {13103, 42431}, {14561, 37178}, {14881, 22689}, {16001, 22513}, {16002, 42159}, {16629, 36969}, {16630, 18362}, {17130, 25157}, {20423, 37173}, {22843, 42158}, {22869, 33421}, {22890, 42529}, {22907, 42162}, {22914, 33388}, {22915, 29012}, {22916, 35689}, {34507, 41035}, {35759, 42246}, {35917, 36364}, {35918, 36385}, {40693, 44461}, {42148, 44250}, {42150, 44465}

X(47068) = midpoint of X(3) and X(5865)
X(47068) = reflection of X(9736) in X(9735)
X(47068) = reflection of X(47066) in X(3)
X(47068) = circumnormal-isogonal conjugate of the anticomplement of X(16631)
X(47068) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(40706)}} and {{A, B, C, X(6), X(38427)}}
X(47068) = X(5865)-of-anti-X3-ABC reflections triangle
X(47068) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 61, 182), (3, 1351, 22238), (3, 5611, 61), (3, 5615, 5237), (3, 14541, 3098), (3, 22238, 13349), (3, 36836, 13350), (4, 628, 5613), (15, 3105, 32), (15, 14541, 3), (61, 3095, 576), (61, 3107, 7772), (61, 14539, 3), (1350, 36836, 3), (3129, 44719, 9306), (5238, 14540, 3), (5352, 14538, 3), (5611, 14539, 182), (9738, 9739, 9735), (11480, 33878, 36755)

X(47069) = X(76)X(619)∩X(303)X(3643)

X(47069) lies on these lines: {3, 40706}, {14, 22866}, {76, 619}, {298, 16529}, {299, 11133}, {303, 3643}, {396, 7786}, {624, 11057}, {630, 7814}, {631, 634}, {7811, 44382}, {7860, 11290}, {7934, 23302}, {42157, 44032}

X(47070) = X(2)X(812)∩X(239)X(4375)

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

X(47070) lies on the cubic K015 and these lines: {2, 812}, {239, 4375}, {350, 4448}, {659, 27922}, {874, 7035}, {2382, 9073}, {6548, 43928}

X(47070) = X(i)-isoconjugate of X(j) for these (i,j): {537, 34067}, {813, 20331}
X(47070) = trilinear pole of line {812, 35119}
X(47070) = barycentric product X(812)*X(18822)
X(47070) = barycentric quotient X(i)/X(j) for these {i,j}: {659, 20331}, {812, 537}, {2382, 813}, {18822, 4562}, {27918, 36848}

X(47071) = X(2)X(9033)∩X(30)X(14401)

X(47071) lies on the cubic K015 and these lines: {2, 9033}, {30, 14401}, {402, 46115}, {525, 1650}, {4240, 23582}, {15184, 40512}, {15351, 45289}, {31621, 34767}, {41433, 43701}, {45292, 46270}

X(47071) = trilinear pole of line {9033, 39008}
X(47071) = X(16076)-isoconjugate of X(32676)
X(47071) = barycentric product X(525)*X(16075)
X(47071) = barycentric quotient X(i)/X(j) for these {i,j}: {525, 16076}, {14401, 1651}, {16075, 648}, {41433, 34568}

X(47072) = X(13)X(5916)∩X(15)X(110)

X(47072) lies on the cubic K018 and these lines: {13, 5916}, {15, 110}, {111, 2088}, {524, 11092}, {5663, 37776}, {11131, 17402}, {14094, 14816}

X(47072) = isogonal conjugate of X(11537)
X(47072) = trilinear pole of line {15, 44814}
X(47072) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11537}, {530, 2153}
X(47072) = crossdifference of every pair of points on line {9200, 42001}
X(47072) = intersection of tangents at X(13) and X(15) to Brocard (second) cubic K018
X(47072) = X(1976)-vertex conjugate of X(47073)
X(47072) = barycentric product X(i)*X(j) for these {i,j}: {15, 43091}, {298, 2378}, {11131, 36316}, {16256, 38403}
X(47072) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 11537}, {15, 530}, {2378, 13}, {6137, 9200}, {8739, 23712}, {11086, 18776}, {16256, 43085}, {43091, 300}

X(47073) = X(14)X(5917)∩X(16)X(110)

X(47073) lies on the cubic K018 and these lines: {14, 5917}, {16, 110}, {111, 2088}, {524, 11078}, {5655, 44219}, {5663, 37775}, {11130, 17403}, {14094, 14817}

X(47073) = isogonal conjugate of X(11549)
X(47073) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11549}, {531, 2154}
X(47073) = trilinear pole of line {16, 44814}
X(47073) = crossdifference of every pair of points on line {9201, 42002}
X(47073) = intersection of tangents at X(14) and X(16) to Brocard (second) cubic K018
X(47073) = X(1976)-vertex conjugate of X(47072)
X(47073) = barycentric product X(i)*X(j) for these {i,j}: {16, 43092}, {299, 2379}, {11130, 36317}, {16255, 38404}
X(47073) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 11549}, {16, 531}, {2379, 14}, {6138, 9201}, {8740, 23713}, {11081, 18777}, {16255, 43086}, {43092, 301}

X(47074) = X(2)X(187)∩X(30)X(14866)

X(47074) lies on these lines: {2,187}, {30,14866}, {140,31840}, {376,12505}, {381,31606}, {519,31746}, {542,32311}, {543,44574}, {549,12506}, {3524,31762}, {3917,38239}, {5055,31749}, {5181,22165}, {6322,8667}, {6325,12074}, {6636,14682}, {8703,32424}, {8704,11123}, {10304,34792}, {11056,40246}, {11539,32156}, {11594,37904}, {14153,15534}, {16226,31763}, {16836,31743}, {19883,31755}, {26233,39785}, {27088,30749}, {28194,31747}, {31758,38068}

X(47074) = midpoint of X(i) and X(j) for these {i,j}: {376,12505}, {6031,9829}
X(47074) = reflection of X(i) in X(j) for these {i,j}: {381,31606}, {10162,10163}, {10163,9829}, {12506,549}, {31743,16836}, {31840,140}, {31961,31762}

X(47075) = X(2)X(187)∩X(22)X(2930)

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

X(47075) lies on these lines: {2,187}, {3,31961}, {22,2930}, {30,12505}, {376,31729}, {381,31744}, {1180,8584}, {1296,3534}, {2979,8030}, {3524,12506}, {3543,14866}, {3545,31606}, {3679,31746}, {5054,31840}, {5071,31749}, {6082,9831}, {6322,14614}, {7492,39785}, {8704,33706}, {9140,32311}, {9855,26233}, {9909,34992}, {10717,44574}, {15684,31824}, {15692,31762}, {15694,32156}, {20791,31743}, {31162,31747}, {34554,35734}

X(47075) = reflection of X(i) in X(j) for these {i,j}: {376,31729}, {381,31744}, {3543,14866}, {3679,31746}, {6032,9829}, {9140,32311}, {9829,6031}, {10717,44574}, {15684,31824}, {31162,31747}, {31961,3}, {34792,376}
X(47075) = X(2)-of-circlecevian-triangle-of-X(2)

X(47076) = X(2)X(3)∩X(74)X(115)

X(47076) lies on these lines: {2, 3}, {69, 15928}, {74, 115}, {193, 34810}, {247, 541}, {393, 35908}, {477, 5099}, {1640, 21733}, {1989, 2781}, {3018, 10752}, {3566, 42733}, {5309, 5890}, {5622, 6128}, {6033, 12383}, {7753, 15033}, {9466, 18304}, {12188, 12317}, {14356, 31670}

X(47076) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {46470, 46471, 376}

X(47077) = X(2)X(34169)∩X(3)X(669)

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

X(47077) lies on the cubic K038 and these lines: {2, 34169}, {3, 669}, {30, 126}, {99, 5912}, {187, 524}, {543, 5914}, {620, 46986}, {2770, 7472}, {5099, 44377}, {5913, 7664}, {5971, 13586}, {6792, 32985}, {8369, 32525}, {8598, 26276}, {16341, 16508}, {32456, 36180}, {34205, 41134}, {35287, 38940}, {37512, 40517}

X(47077) = complement of X(34169)
X(47077) = midpoint of X(i) and X(j) for these {i,j}: {99, 5912}, {2770, 7472}
X(47077) = complement of the isogonal conjugate of X(40078)
X(47077) = X(40078)-complementary conjugate of X(10)
X(47077) = X(2770)-Ceva conjugate of X(524)
X(47077) = crossdifference of every pair of points on line {3291, 9178}
X(47077) = barycentric product X(36696)*X(36792)
X(47077) = barycentric quotient X(36696)/X(10630)
X(47077) = {X(2482),X(23992)}-harmonic conjugate of X(6390)

X(47078) = X(2)X(34171)∩X(3)X(351)

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

X(47078) lies on the cubic K038 and these lines: {2, 34171}, {3, 351}, {30, 5512}, {111, 11634}, {187, 1084}, {2854, 9177}, {3143, 6719}, {5467, 14908}, {7418, 38698}, {22143, 34106}

X(47078) = midpoint of X(111) and X(11634)
X(47078) = reflection of X(3143) in X(6719)
X(47078) = complement of X(34171)
X(47078) = X(111)-Ceva conjugate of X(2854)
X(47078) = crosspoint of X(111) and X(36696)

X(47079) = X(3)X(512)∩X(30)X(114)

X(47079) lies on the cubic K038 and these lines: {2, 34175}, {3, 512}, {30, 114}, {131, 36471}, {187, 1511}, {237, 511}, {842, 7468}, {2080, 22115}, {5092, 40810}, {5106, 39528}, {6785, 37465}, {16760, 36189}, {38974, 40349}

X(47079) = midpoint of X(842) and X(7468)
X(47079) = reflection of X(i) in X(j) for these {i,j}: {187, 44221}, {36189, 16760}
X(47079) = complement of X(34175)
X(47079) = complement of the isogonal conjugate of X(40083)
X(47079) = X(40083)-complementary conjugate of X(10)
X(47079) = X(842)-Ceva conjugate of X(511)
X(47079) = crossdifference of every pair of points on line {230, 2395}

X(47080) = X(3)X(667)∩X(30)X(120)

X(47080) lies on the cubic K038 and these lines: {2, 34173}, {3, 667}, {30, 120}, {35, 22116}, {36, 2482}, {187, 1017}, {518, 2223}, {2752, 7475}

X(47080) = midpoint of X(2752) and X(7475)
X(47080) = complement of X(34173)
X(47080) = complement of the isogonal conjugate of X(40084)
X(47080) = X(40084)-complementary conjugate of X(10)
X(47080) = X(2752)-Ceva conjugate of X(518)

X(47081) = X(3)X(513)∩X(30)X(119)

X(47081) lies on the cubic K038 and these lines: {2, 38952}, {3, 513}, {30, 119}, {35, 45828}, {36, 1464}, {187, 23980}, {517, 859}, {2687, 7477}, {13744, 26285}

X(47081) = midpoint of X(2687) and X(7477)
X(47081) = complement of X(38952)
X(47081) = X(2687)-Ceva conjugate of X(517)
X(47081) = barycentric product X(10058)*X(16586)

X(47082) = X(3)X(690)∩X(30)X(115)

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

X(47082) lies on the cubic K038 and these lines: {2, 34174}, {3, 690}, {30, 115}, {98, 4226}, {114, 35282}, {248, 14966}, {265, 14830}, {542, 5191}, {868, 6036}, {1511, 2482}, {2793, 15566}, {2799, 40080}, {5027, 47049}, {6795, 8429}, {7422, 34473}, {37916, 38997}

X(47082) = midpoint of X(98) and X(4226)
X(47082) = reflection of X(868) in X(6036)
X(47082) = complement of X(34174)
X(47082) = X(36051)-complementary conjugate of X(542)
X(47082) = X(98)-Ceva conjugate of X(542)
X(47082) = crossdifference of every pair of points on line {2493, 14998}

X(47083) = X(3)X(2775)∩X(30)X(5511)

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

X(47083) lies on the cubic K038 and these lines: {3, 2775}, {30, 5511}, {36, 187}, {105, 4236}, {2482, 35204}, {2787, 46409}, {2836, 42747}, {3140, 6714}, {7425, 38694}

X(47083) = midpoint of X(105) and X(4236)
X(47083) = reflection of X(3140) in X(6714)
X(47083) = complement of X(47104)
X(47083) = X(105)-Ceva conjugate of X(2836)

X(47084) = X(3)X(523)∩X(30)X(113)

Barycentrics (2*a^4 - a^2*b^2 - b^4 - a^2*c^2 + 2*b^2*c^2 - c^4)*(2*a^12 - 5*a^10*b^2 + 10*a^6*b^6 - 10*a^4*b^8 + 3*a^2*b^10 - 5*a^10*c^2 + 18*a^8*b^2*c^2 - 17*a^6*b^4*c^2 + a^4*b^6*c^2 + 2*a^2*b^8*c^2 + b^10*c^2 - 17*a^6*b^2*c^4 + 22*a^4*b^4*c^4 - 5*a^2*b^6*c^4 - 4*b^8*c^4 + 10*a^6*c^6 + a^4*b^2*c^6 - 5*a^2*b^4*c^6 + 6*b^6*c^6 - 10*a^4*c^8 + 2*a^2*b^2*c^8 - 4*b^4*c^8 + 3*a^2*c^10 + b^2*c^10) : :

X(47084) = 3 X[3] - X[46632], 3 X[5] - X[21269], 3 X[110] + X[14508], X[110] + 3 X[38701], X[113] - 3 X[31378], X[476] - 5 X[15051], X[477] + 3 X[15035], 3 X[549] - X[34209], 5 X[632] - 3 X[21315], X[1553] - 3 X[5642], X[3233] + 2 X[38610], X[6070] - 3 X[38727], X[7471] - 3 X[15035], 2 X[12041] + X[30221], 2 X[12068] - 3 X[38793], X[14480] + 3 X[15055], X[14508] - 3 X[36164], X[14508] - 9 X[38701], 3 X[14934] + X[46632], 7 X[15036] - 3 X[38700], 5 X[15040] - X[36193], X[20957] + 3 X[38723], X[25641] - 3 X[38793], 3 X[31378] - 2 X[31945], X[36164] - 3 X[38701]

X(47084) lies on the cubic K038 and these lines: {2, 34150}, {3, 523}, {5, 21269}, {20, 46045}, {30, 113}, {74, 14611}, {110, 14508}, {131, 10257}, {187, 3163}, {476, 15051}, {477, 7471}, {549, 34209}, {632, 21315}, {3154, 17702}, {3184, 12095}, {3627, 21317}, {3628, 21316}, {5915, 10418}, {5972, 36169}, {6070, 38727}, {6699, 12079}, {10295, 14920}, {11537, 42943}, {11549, 42942}, {12038, 36179}, {12041, 30221}, {12068, 25641}, {12121, 36184}, {14480, 15055}, {15036, 38700}, {15040, 36193}, {16311, 18571}, {16340, 34153}, {20957, 38723}, {32417, 37853}, {36177, 39242}

X(47084) = midpoint of X(i) and X(j) for these {i,j}: {3, 14934}, {20, 46045}, {74, 14611}, {110, 36164}, {477, 7471}, {1511, 38610}, {3258, 16163}, {3627, 21317}, {12121, 36184}, {16340, 34153}
X(47084) = reflection of X(i) in X(j) for these {i,j}: {113, 31945}, {3154, 31379}, {3233, 1511}, {12079, 6699}, {21316, 3628}, {25641, 12068}, {36169, 5972}
X(47084) = complement of X(34150)
X(47084) = complement of the isogonal conjugate of X(15469)
X(47084) = X(15469)-complementary conjugate of X(10)
X(47084) = X(i)-Ceva conjugate of X(j) for these (i,j): {477, 30}, {15035, 32162}
X(47084) = crossdifference of every pair of points on line {2433, 3003}
X(47084) = barycentric product X(39987)*X(46789)
X(47084) = barycentric quotient X(39987)/X(46788)
X(47084) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 34810, 47050}, {110, 38701, 36164}, {113, 31378, 31945}, {477, 15035, 7471}, {15454, 47050, 34810}, {25641, 38793, 12068}

X(47085) = X(3)X(525)∩X(30)X(132)

X(47085) lies on the cubic K038 and these lines: {3, 525}, {30, 132}, {187, 3184}, {441, 1503}, {2482, 12096}, {2697, 7473}, {5523, 44252}, {9475, 15639}

X(47085) = midpoint of X(i) and X(j) for these {i,j}: {2697, 7473}, {5523, 44252}
X(47085) = complement of X(47105)
X(47085) = complement of the isogonal conjugate of X(40080)
X(47085) = X(i)-complementary conjugate of X(j) for these (i,j): {8766, 16188}, {40080, 10}
X(47085) = X(2697)-Ceva conjugate of X(1503)
X(47085) = crossdifference of every pair of points on line {232, 34212}

X(47086) = X(3)X(8674)∩X(11)X(30)

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

X(47086) lies on the cubic K038 and these lines: {2, 39991}, {3, 8674}, {11, 30}, {104, 3658}, {1511, 35204}, {2771, 42746}, {3139, 6713}, {7429, 38693}

X(47086) = midpoint of X(104) and X(3658)
X(47086) = reflection of X(3139) in X(6713)
X(47086) = complement of X(39991)
X(47086) = X(36052)-complementary conjugate of X(2771)
X(47086) = X(104)-Ceva conjugate of X(2771)

X(47087) = X(3)X(9033)∩X(30)X(122)

Barycentrics (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 - 5*a^6*b^4 + 7*a^4*b^6 - a^2*b^8 - b^10 - 2*a^8*c^2 + 12*a^6*b^2*c^2 - 7*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 - 5*a^6*c^4 - 7*a^4*b^2*c^4 + 14*a^2*b^4*c^4 - 2*b^6*c^4 + 7*a^4*c^6 - 6*a^2*b^2*c^6 - 2*b^4*c^6 - a^2*c^8 + 3*b^2*c^8 - c^10)*(a^12 - a^10*b^2 - 6*a^8*b^4 + 14*a^6*b^6 - 11*a^4*b^8 + 3*a^2*b^10 - a^10*c^2 + 13*a^8*b^2*c^2 - 14*a^6*b^4*c^2 - 6*a^4*b^6*c^2 + 7*a^2*b^8*c^2 + b^10*c^2 - 6*a^8*c^4 - 14*a^6*b^2*c^4 + 34*a^4*b^4*c^4 - 10*a^2*b^6*c^4 - 4*b^8*c^4 + 14*a^6*c^6 - 6*a^4*b^2*c^6 - 10*a^2*b^4*c^6 + 6*b^6*c^6 - 11*a^4*c^8 + 7*a^2*b^2*c^8 - 4*b^4*c^8 + 3*a^2*c^10 + b^2*c^10) : :

X(47087) = X[107] - 3 X[11845], 2 X[6716] - 3 X[26451], 3 X[11911] - X[22337], 3 X[16190] + X[34601]

X(47087) lies on the cubic K038 and these lines: {3, 9033}, {30, 122}, {107, 11845}, {133, 402}, {1294, 4240}, {1511, 3184}, {1650, 7687}, {2777, 7740}, {5655, 23240}, {6716, 26451}, {10745, 18508}, {11853, 14703}, {11911, 22337}, {16190, 34601}

X(47087) = midpoint of X(i) and X(j) for these {i,j}: {1294, 4240}, {10745, 18508}
X(47087) = reflection of X(i) in X(j) for these {i,j}: {133, 402}, {1650, 34842}
X(47087) = complement of X(47111)
X(47087) = X(35200)-complementary conjugate of X(2777)
X(47087) = X(1294)-Ceva conjugate of X(2777)

X(47088) = X(2)X(1341)∩X(3)X(3414)

X(47088) lies on the cubic K038 and these lines: {2, 1341}, {3, 3414}, {30, 2039}, {141, 542}, {187, 39023}, {376, 31862}, {1379, 6189}, {1380, 6040}, {2040, 44377}, {14502, 19660}, {14631, 14633}, {22245, 46024}

X(47088) = midpoint of X(i) and X(j) for these {i,j}: {376, 31862}, {1379, 6189}, {1380, 6040}
X(47088) = midpoint of circumcircle-intercepts of line X(2)X(1341)
X(47088) = complement of X(31863)
X(47088) = psi-transform of X(30509)
X(47088) = {X(39162),X(39163)}-harmonic conjugate of X(30509)

X(47089) = X(2)X(1340)∩X(3)X(3413)

X(47089) lies on the cubic K038 and these lines: {2, 1340}, {3, 3413}, {30, 2040}, {141, 542}, {187, 39022}, {376, 31863}, {1379, 6039}, {1380, 6190}, {2039, 44377}, {14501, 19659}, {14630, 14632}, {22244, 46023}

X(47089) = midpoint of X(i) and X(j) for these {i,j}: {376, 31863}, {1379, 6039}, {1380, 6190}
X(47089) = midpoint of circumcircle intercepts of line X(2)X(1340)
X(47089) = complement of X(31862)
X(47089) = psi-transform of X(30508)

This preamble, based on notes by Kiminari Shinagawa, is contributed by Clark Kimberling and Peter Moses, March 8, 2022.

The Euler coordinate system consists of an x-axis (the Euler line) and y-axis (the orthic axis). The axes meet in the origin, X(468) = (0,0). Points on the x-axis and on the same side of (0,0) as the centroid, G, have positive x-coordinates. Points on the y-axis and on the same side of (0,0) as the bicentric point P(201) have positive y-coordinates.

A point with barycentrics p : q : r has Euler coordinates (x,y) given by

x = (SA*p + SB*q + SC*r)/(p+q+r)
y = (SA(SB-SC)*p + SB(SC-SA)*q +SC(SA - SB)*r)/(p+q+r).

To convert from Euler coordinates (x,y) to barycentrics p : q : r, let

S^2 = SB*SC + SC*SA + SA*SB = 4*(area of ABC)^2
E = (SB + SC)(SC + SA)(SA + SB)/S^2
F = SA*SB*SC/S^2.

Then

p = (E+F)*SB*SC - 3F S^2 - (3SB*SC-S^2)x + (SB-SC)y
q = (E+F)*SC*SA - 3F S^2 - (3SC*SA-S^2)x + (SC-SA)y
r = (E+F)*SA*SB - 3F S^2 - (3SA*SB-S^2)x + (SA-SB)y

Note that x must have degree 2 in a,b,c, and y must have degree 4.

The appearance of (x,0;n) in the following list means that the point with Euler coordinates (x,0) is X(n):

{(E/2,0); 10257}, {(-E/2,0); 37971}, {(E+F,0); 858}, {(2(E+F),0); 46517}, {(3(E+F),0); 5189}, {((E+F)/4,0);37911}, {(E-F,0); 2071}, {(F,0); 403}, {(2F,0); 10151}, {(4F,0); 13473}, {(F/2,0); 37942}, {(F/3,0); 37779}, {(-F,0); 186}, {(-2F,0); 37931}, {(-F/2,0); 37935}

The appearance of ($f(a,b,c)$,0;n) in the next list means that the point with Euler coordinates (f(a,b,c)+f(b,c,a)+f(c,a,b),0) is X(n), and that the point lies on the positive x-axis for all non-equilateral triangles:

{($a^2$,0); 46517}, {($a^2$/4,0); 5159}, {($a^2$/6,0); 2}, {($aSA$/$a$,0);3109}}

For more examples, see Euler Coordinates.

See also the preambles just before X(47332) and X(47488).

X(47090) = SHINAGAWA-EULER POINT (-E,0)

X(47090) lies on these lines: {2, 3}, {343, 23329}, {523, 21668}, {570, 16303}, {907, 2697}, {1092, 6247}, {1350, 23327}, {1568, 15311}, {1899, 37497}, {2979, 44683}, {3100, 15325}, {3292, 13399}, {3564, 43574}, {5562, 6696}, {6000, 6053}, {6390, 30737}, {6699, 12099}, {9730, 12058}, {9820, 10575}, {10420, 45138}, {10564, 44665}, {10625, 44158}, {11245, 13352}, {11412, 43607}, {11417, 35255}, {11418, 35256}, {12160, 18913}, {12163, 43903}, {13142, 26879}, {13292, 37495}, {14156, 14915}, {14216, 35602}, {14389, 20791}, {14641, 43839}, {14961, 16318}, {15033, 45298}, {15045, 18583}, {15644, 25563}, {15740, 43841}, {16324, 45114}, {16836, 37649}, {18914, 34148}, {26937, 37498}, {29181, 38727}, {32269, 44673}, {34380, 39562}, {40664, 44704}, {41372, 46927}

X(47090) = complement of X(47096)
X(47090) = anticomplement of X(37942)
X(47090) = radical trace of circumcircle and 1st Steiner circle
X(47090) = center of inverse-in-de-Longchamps-circle-of-orthocentroidal-circle
X(47090) = circumcircle-inverse of X(11414)
X(47090) = orthoptic-circle-of-Steiner-inellipse-inverse of X(7386)
X(47090) = polar-circle-inverse of X(3089)

X(47091) = SHINAGAWA-EULER POINT (-2E,0)

X(47091) lies on these lines: {2, 3}, {524, 13399}, {5421, 16303}, {5642, 15152}, {13567, 44935}, {17834, 43903}, {18583, 20791}, {21663, 29181}

X(47092) = SHINAGAWA-EULER POINT (-3E,0)

X(47092) lies on these lines: {2, 3}, {3564, 43576}, {11820, 37645}, {44762, 46374}

X(47092) = reflection of X(37899) in X(3)
X(47092) = radical trace of orthoptic circle of Steiner inellipse and 1st Steiner circle

X(47093) = SHINAGAWA-EULER POINT (E,0)

X(47093) lies on these lines: {2, 3}, {524, 15152}, {1533, 15311}, {1568, 29181}, {1614, 13142}, {3564, 14157}, {6000, 32269}, {6515, 32063}, {10984, 15873}, {11456, 41588}, {13352, 44935}, {13391, 46817}, {13399, 32225}, {15305, 44683}, {16194, 44201}, {16252, 45186}, {16654, 21243}

X(47093) = radical trace of every pair of {Grebe circle, polar circle, 1st Steiner circle}
X(47093) = polar-circle-inverse of X(3088)

X(47094) = SHINAGAWA-EULER POINT (2E,0)

X(47094) lies on these lines: {2, 3}, {184, 44935}, {3292, 15152}, {11455, 44683}

X(47095) = SHINAGAWA-EULER POINT (-4(E+F),0)

X(47095) lies on these lines: {2, 3}, {98, 46214}, {4348, 7286}, {5160, 7221}, {11064, 29323}, {11594, 16327}, {29181, 41586}

X(47096) = SHINAGAWA-EULER POINT (E-F,0)

X(47096 lies on these lines: {2, 3}, {343, 15305}, {495, 9539}, {1209, 46849}, {1514, 15107}, {1515, 14918}, {1533, 3580}, {2883, 5889}, {5012, 16657}, {5099, 44955}, {5522, 25641}, {5523, 40234}, {5656, 6515}, {6241, 41587}, {9927, 16659}, {10116, 18555}, {10575, 26879}, {11456, 45968}, {12290, 12359}, {13567, 15072}, {13598, 43831}, {13754, 32111}, {13851, 29012}, {14157, 44665}, {14516, 26883}, {14641, 43817}, {14862, 43844}, {15030, 37636}, {15043, 15873}, {15311, 32269}, {16252, 34148}, {16658, 18474}, {18809, 46662}, {19149, 32220}, {20791, 37648}, {21243, 32062}, {21663, 32223}, {22115, 46817}, {32113, 41716}, {46085, 46431}

X(47096) = complement of X(37944)
X(47096) = anticomplement of X(47090)
X(47096) = circumcircle-inverse of X(17928)
X(47096) = nine-point-circle-inverse of X(3091)
X(47096) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(6995)
X(47096) = orthoptic-circle-of-Steiner-inellipse-inverse of X(5020)
X(47096) = polar-circle-inverse of X(1593)

X(47097) = SHINAGAWA-EULER POINT (-$(1/3)a^2$,0)

X(47097) is the common radical trace of the harmonic circles of pairs of the power circles. (Randy Hutson, April 16, 2022)

X(47097) lies on these lines: {2, 3}, {114, 46436}, {115, 16317}, {120, 30781}, {125, 524}, {126, 3258}, {141, 16325}, {230, 6128}, {323, 39562}, {325, 892}, {511, 12099}, {523, 7625}, {542, 11064}, {599, 17813}, {614, 10149}, {1007, 16326}, {1503, 5642}, {1560, 3163}, {1992, 26869}, {2393, 15113}, {2452, 9770}, {2696, 38951}, {3564, 9140}, {3815, 16303}, {3819, 11649}, {3849, 40544}, {5476, 37648}, {5650, 8705}, {5913, 43291}, {5972, 11645}, {6090, 11180}, {6723, 19924}, {7703, 18358}, {7753, 15820}, {7778, 16312}, {7809, 37803}, {8791, 34570}, {9300, 16306}, {9745, 15048}, {10162, 11594}, {10718, 34320}, {11059, 16327}, {11178, 45303}, {14961, 44467}, {15059, 15360}, {15106, 22151}, {15131, 34319}, {15361, 34128}, {15826, 22165}, {16272, 29639}, {16304, 29857}, {16305, 30768}, {16313, 30749}, {16322, 30741}, {16331, 30747}, {19662, 37745}, {21358, 32113}, {22112, 32217}, {23878, 46983}, {25561, 35283}, {30476, 46989}, {30737, 34336}, {30778, 30780}, {33878, 40920}, {34315, 40334}, {34316, 40335}, {34380, 44555}, {37649, 46267}, {37775, 43417}, {37776, 43416}, {44401, 46998}, {44560, 47001}

X(47097) = midpoint of X(2) and X(858) (the harmonic traces of the power circles)
X(47097) = reflection of X(47332) in X(5)
X(47097) = complement of X(7426)
X(47097) = radical trace of nine-point circle and de Longchamps circle
X(47097) = nine-point-circle-inverse of X(30739)
X(47097) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(15683)
X(47097) = orthoptic-circle-of-Steiner-inellipse-inverse of X(376)
X(47097) = polar-circle-inverse of X(4232)
X(47097) = inverse of X(47597) in: orthocentroidal circle, Yff hyperbola
X(47097) = X(47332)-of-Johnson-triangle
X(47097) = {X(2),X(4)}-harmonic conjugate of X(47597)

X(47098) = SHINAGAWA-EULER POINT (-(a+b+c)^2,0)

X(47099) = SHINAGAWA-EULER POINT (-$bc$,0)

X(47100) = SHINAGAWA-EULER POINT (-$bc/2$,0)

X(47100) lies on these lines: {2, 3}, {516, 32223}, {523, 3716}, {3979, 10149}, {5160, 5524}

X(47101) = X(2)X(187)∩X(3)X(754)

X(47101) lies on these lines: {2,187}, {3,754}, {20,7780}, {30,5171}, {32,8356}, {39,33008}, {69,32456}, {76,33265}, {183,6781}, {315,15513}, {325,8588}, {376,538}, {381,32152}, {524,3098}, {543,3534}, {546,38619}, {548,7781}, {549,7775}, {550,7751}, {574,41624}, {591,6396}, {597,8358}, {620,5210}, {626,5023}, {631,7843}, {1003,7810}, {1078,11361}, {1350,14645}, {1384,4045}, {1991,6200}, {2482,7788}, {3053,7830}, {3522,14023}, {3528,7758}, {3552,7854}, {3767,33272}, {3785,7816}, {3788,5206}, {3793,7798}, {3830,7610}, {3845,7617}, {3917,32442}, {3934,14033}, {5007,32965}, {5066,15597}, {5306,8354}, {5309,7833}, {5319,33226}, {5346,7847}, {5858,36329}, {5859,35751}, {6179,33260}, {6337,7882}, {7615,15682}, {7618,19708}, {7619,15701}, {7622,12100}, {7746,7802}, {7747,44543}, {7748,7793}, {7755,33234}, {7757,46283}, {7760,33275}, {7762,15515}, {7768,33014}, {7774,8589}, {7778,15655}, {7782,7855}, {7791,35007}, {7794,33235}, {7796,33276}, {7799,9939}, {7800,14039}, {7801,7811}, {7809,33274}, {7812,33273}, {7817,32986}, {7821,32964}, {7822,7904}, {7823,31455}, {7829,22331}, {7838,15815}, {7842,16041}, {7849,32973}, {7857,14046}, {7858,31457}, {7860,33259}, {7861,33210}, {7865,8369}, {7873,16925}, {7880,32985}, {7883,33246}, {7886,33285}, {7908,14929}, {7936,33225}, {8352,18362}, {8353,11648}, {8556,11159}, {8598,37671}, {8716,15688}, {9466,33007}, {9738,32421}, {9739,32419}, {9740,15697}, {9770,15698}, {9771,11812}, {9862,9890}, {10159,14038}, {10304,34511}, {11001,32479}, {11055,44367}, {11184,15693}, {12040,15711}, {12101,20112}, {12974,41491}, {12975,41490}, {14148,40341}, {14614,35955}, {15482,18907}, {15533,36521}, {15681,34505}, {15685,40727}, {16509,33699}, {17004,18424}, {17130,33250}, {18324,34217}, {20065,37512}, {22253,44541}, {32457,37667}, {32833,33208}, {33005,39590}, {33192,39563}, {33215,44562}, {34229,43618}, {34733,37334}

X(47101) = midpoint of X(i) and X(j) for these {i,j}: {3534,8667}, {9862,9890}, {15681,34505}
X(47101) = reflection of X(i) in X(j) for these {i,j}: {381,34506}, {5569,8182}, {7775,549}, {8176,5569}, {18546,13468}, {34504,376}

X(47102) = X(6)X(8354)∩X(20)X(538)

X(47102) lies on these lines: {6,8354}, {20,538}, {30,8667}, {32,32986}, {69,6781}, {76,33193}, {183,43618}, {315,7891}, {376,754}, {385,43619}, {439,7821}, {524,3534}, {543,9862}, {550,7758}, {626,33191}, {1003,7750}, {1007,8588}, {1078,33016}, {1285,4045}, {2549,8353}, {3053,33184}, {3146,7780}, {3522,7759}, {3523,7843}, {3524,7775}, {3528,7764}, {3529,7751}, {3545,34506}, {3767,7802}, {3785,9466}, {3793,44526}, {3830,7615}, {3845,7610}, {5007,33023}, {5077,5306}, {5206,32006}, {5309,33272}, {5319,33234}, {5862,33611}, {5863,33610}, {5969,38741}, {6179,32997}, {6680,33196}, {7617,41099}, {7618,8703}, {7620,15640}, {7622,15698}, {7739,7833}, {7747,32983}, {7753,33215}, {7755,33238}, {7756,41748}, {7757,20065}, {7760,33253}, {7765,33247}, {7768,33244}, {7772,33226}, {7781,17538}, {7784,8368}, {7788,8598}, {7791,12150}, {7794,33239}, {7796,33254}, {7799,33208}, {7800,11286}, {7801,35927}, {7810,14033}, {7811,33007}, {7812,33008}, {7817,33210}, {7818,32985}, {7823,31401}, {7827,33263}, {7844,46453}, {7849,33201}, {7854,32981}, {7860,32964}, {7865,14039}, {7870,33266}, {7873,32973}, {7883,33255}, {7936,14037}, {8177,43621}, {8357,22331}, {8358,18907}, {9699,34883}, {9740,32479}, {9764,22676}, {9770,19708}, {9771,15701}, {9821,18768}, {9888,38749}, {9939,32833}, {11165,15695}, {11184,12100}, {12040,15759}, {12101,16509}, {13086,34510}, {14568,33192}, {14711,32815}, {15513,32816}, {15597,19709}, {15655,44377}, {15682,18546}, {18362,23055}, {31417,33001}, {32456,37668}, {32974,35007}, {35955,41624}, {36345,36995}, {36347,36993}, {36775,42632}

X(47102) = reflection of X(i) in X(j) for these {i,j}: {3830,13468}, {7758,8716}, {8716,550}, {9766,8703}, {9888,38749}, {15682,18546}, {23334,5569}, {34511,376}

X(47103) = X(4)X(4846)∩X(30)X(841)

X(47103) lies on the cubic K025 and these lines: {4, 4846}, {30, 841}, {316, 39985}, {671, 9139}, {7464, 46436}, {9060, 11799}, {34174, 38951}, {34288, 43448}

X(47103) = reflection of X(i) in X(j) for these {i,j}: {7464, 46436}, {9060, 11799}
X(47103) = antigonal image of X(7464)
X(47103) = symgonal image of X(11799)
X(47103) = barycentric product X(7464)*X(34289)
X(47103) = barycentric quotient X(i)/X(j) for these {i,j}: {7464, 15066}, {34288, 10293}, {40114, 5063}

X(47104) = X(2)X(47083)∩X(4)X(2775)

X(47104) lies on the cubic K025 and these lines: {2, 47083}, {4, 2775}, {30, 1292}, {105, 3140}, {120, 4236}, {316, 668}, {671, 11604}, {2787, 10773}, {5203, 38949}, {7475, 40084}, {39990, 41521}

X(47104) = reflection of X(i) in X(j) for these {i,j}: {105, 3140}, {4236, 120}
X(47104) = anticomplement of X(47083)
X(47104) = antigonal image of X(4236)
X(47104) = symgonal image of X(3140)
X(47104) = barycentric quotient X(i)/X(j) for these {i,j}: {2752, 2991}, {3290, 2836}, {14267, 46784}

X(47105) = X(2)X(47085)∩X(4)X(525)

X(47105) lies on the cubics K025 and K715 and these lines: {2, 47085}, {4, 525}, {30, 935}, {265, 5523}, {287, 297}, {316, 10152}, {403, 32649}, {542, 35907}, {671, 34170}, {1300, 46967}, {2697, 37987}, {4230, 40079}, {7473, 42426}, {37200, 43279}

X(47105) = reflection of X(i) in X(j) for these {i,j}: {2697, 37987}, {5523, 44228}, {7473, 42426}
X(47105) = isogonal conjugate of X(40080)
X(47105) = anticomplement of X(47085)
X(47105) = antigonal image of X(7473)
X(47105) = symgonal image of X(37987)
X(47105) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40080}, {842, 8766}
X(47105) = trilinear product X(i)*X(j) for these {i,j}: {542, 8767}, {2247, 6330}, {18312, 36046}
X(47105) = barycentric product X(i)*X(j) for these {i,j}: {542, 6330}, {2419, 35907}, {6103, 35140}, {7473, 43673}, {18312, 44770}, {39265, 46786}
X(47105) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40080}, {542, 441}, {2247, 8766}, {2435, 35911}, {5191, 8779}, {6103, 1503}, {6330, 5641}, {7473, 34211}, {16092, 36894}, {34212, 35909}, {34369, 34156}, {35907, 2409}, {39265, 46787}, {43717, 842}, {44770, 5649}

X(47106) = X(4)X(912)∩X(30)X(13397)

ZX(47106) lies on the cubic K025 and these lines: {4, 912}, {30, 13397}, {1717, 23604}, {10152, 38952}, {11605, 34173}, {14775, 15313}, {34170, 39991}, {34172, 39990}

X(47106) = polar-circle inverse of X(14054)
X(47106) = antigonal image of X(2074)
X(47106) = X(17796)-cross conjugate of X(37799)
X(47106) = X(i)-isoconjugate of X(j) for these (i,j): {3215, 11604}, {5620, 41608}
X(47106) = barycentric product X(i)*X(j) for these {i,j}: {2074, 43675}, {32849, 39267}, {37799, 43740}
X(47106) = barycentric quotient X(i)/X(j) for these {i,j}: {2074, 40571}, {5172, 3173}, {17796, 11517}, {19622, 41608}, {39267, 21907}
X(47106) = {X(4),X(43740)}-harmonic conjugate of X(39267)

X(47107) = X(4)X(514)∩X(30)X(103)

X(47107) lies on the cubic K025 and these lines: {4, 514}, {30, 103}, {265, 5134}, {316, 18025}, {381, 45144}, {1300, 35184}, {2688, 37167}, {5088, 15634}, {17734, 32642}

X(47107) = reflection of X(2688) in X(37167)
X(47107) = antigonal image of X(7479)
X(47107) = symgonal image of X(37167)

X(47108) = X(4)X(3566)∩X(30)X(3563)

X(47108) lies on the cubic K025 and these lines: {4, 3566}, {30, 3563}, {265, 5203}, {316, 1300}, {403, 32697}, {671, 5962}, {2987, 3564}, {11605, 16172}

X(47109) = X(4)X(64)∩X(30)X(1301)

X(47109) lies on the cubic K025 and these lines: {4, 64}, {30, 1301}, {382, 41085}, {403, 11589}, {1073, 44438}, {1300, 46968}, {5896, 10151}, {14379, 18560}, {16172, 39985}

X(47109) = reflection of X(22239) in X(10151)
X(47109) = polar-circle inverse of X(5895)
X(47109) = antigonal image of X(16386)
X(47109) = symgonal image of X(10151)
X(47109) = barycentric product X(459)*X(16386)
X(47109) = barycentric quotient X(16386)/X(37669)

X(47110) = X(4)X(9517)∩X(30)X(112)

X(47110) lies on the cubic K025 and these lines: {4, 9517}, {30, 112}, {132, 4230}, {265, 11605}, {316, 6528}, {671, 10152}, {1297, 3150}, {2799, 35908}, {7473, 40080}, {16230, 39265}, {20410, 34334}

X(47110) = reflection of X(i) in X(j) for these {i,j}: {1297, 3150}, {4230, 132}
X(47110) = isogonal conjugate of X(40079)
X(47110) = antigonal image of X(4230)
X(47110) = symgonal image of X(3150)
X(47110) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40079}, {293, 2781}
X(47110) = barycentric product X(297)*X(2697)
X(47110) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40079}, {232, 2781}, {2697, 287}

X(47111) = X(2)X(47087)∩X(4)X(9033)

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

X(47111) lies on the cubic K025 and these lines: {2, 47087}, {4, 9033}, {30, 107}, {133, 4240}, {265, 10152}, {648, 12369}, {1294, 1650}, {6716, 11845}, {10714, 18317}, {11251, 14643}, {12113, 23239}, {18508, 38605}, {34549, 45289}

X(47111) = midpoint of X(34549) and X(45289)
X(47111) = reflection of X(i) in X(j) for these {i,j}: {1294, 1650}, {4240, 133}, {10152, 18507}, {18508, 38605}
X(47111) = anticomplement of X(47087)
X(47111) = antigonal image of X(4240)
X(47111) = symgonal image of X(1650)
X(47111) = X(i)-isoconjugate of X(j) for these (i,j): {255, 1552}, {2777, 35200}
X(47111) = cevapoint of X(30) and X(11251)
X(47111) = trilinear pole of line {1990, 14401}
X(47111) = barycentric product X(2693)*X(46106)
X(47111) = barycentric quotient X(i)/X(j) for these {i,j}: {393, 1552}, {1990, 2777}, {2693, 14919}, {3163, 12113}, {39176, 7740}

X(47112) = MIDPOINT OF X(1) AND X(1339)

X(47113) = MIDPOINT OF X(3) AND X(187)

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

X(47113) = 3*X(3)+X(2080), 7*X(3)+X(9301), 3*X(3)-X(18860), 5*X(3)-X(35002), X(3)+3*X(38225), X(15)+3*X(21159), X(16)+3*X(21158), X(182)+3*X(35375), 3*X(187)-X(2080), 7*X(187)-X(9301), 3*X(187)+X(18860), 5*X(187)+X(35002), X(187)-3*X(38225), X(1350)+3*X(1691), X(1351)-3*X(1692), X(1351)+3*X(35383), 3*X(2030)-4*X(8590), 7*X(2080)-3*X(9301), 5*X(2080)+3*X(35002), X(2080)-9*X(38225)

X(47113) lies on these lines: {2, 13449}, {3, 6}, {20, 38227}, {23, 38702}, {24, 5140}, {30, 5461}, {35, 5148}, {36, 5194}, {40, 38221}, {98, 13586}, {99, 21445}, {110, 23700}, {114, 35297}, {140, 625}, {186, 691}, {230, 23698}, {237, 32237}, {316, 631}, {325, 38748}, {376, 26613}, {381, 5215}, {385, 21166}, {439, 5921}, {441, 6723}, {512, 5926}, {538, 33813}, {542, 27088}, {549, 3849}, {550, 38230}, {842, 37952}, {1007, 41400}, {1296, 14659}, {1352, 32985}, {1495, 35298}, {1513, 38749}, {2386, 39854}, {2705, 28527}, {2782, 32456}, {2794, 37459}, {3515, 14248}, {3523, 14712}, {3526, 7935}, {3528, 43453}, {3552, 6248}, {3564, 32459}, {3576, 5184}, {4558, 32127}, {5054, 31173}, {5099, 44214}, {5167, 37114}, {5476, 37809}, {5943, 37457}, {5965, 6390}, {6055, 8598}, {6109, 44250}, {6671, 44667}, {6672, 44666}, {6771, 35304}, {6774, 35303}, {6776, 35287}, {6781, 15980}, {7575, 14650}, {7771, 15819}, {7807, 32152}, {7816, 10104}, {8369, 24206}, {8681, 9145}, {8859, 12117}, {9306, 35302}, {10124, 10150}, {10295, 16188}, {10411, 14253}, {10788, 44422}, {11257, 33014}, {11645, 37461}, {11676, 34473}, {12221, 26521}, {12222, 26516}, {13172, 14568}, {14162, 43457}, {15646, 38608}, {15692, 46941}, {16187, 37344}, {17974, 21663}, {20403, 44820}, {20428, 37173}, {20429, 37172}, {32964, 36998}, {32973, 40330}, {33274, 43461}, {33748, 40925}, {35276, 37527}, {35305, 45555}, {35306, 45554}, {36170, 47000}, {36180, 46981}, {37955, 38583}, {38064, 47061}, {38734, 43291}, {39663, 39809}

X(47113) = midpoint of X(i) and X(j) for these {i, j}: {3, 187}, {1513, 38749}, {1692, 35383}, {2080, 18860}, {6055, 8598}, {6109, 44250}, {6781, 15980}, {7575, 38611}, {9181, 32110}, {10295, 16188}, {13349, 13350}, {36170, 47000}, {36180, 46981}
X(47113) = reflection of X(i) in X(j) for these (i, j): (625, 140), (38734, 43291), (44496, 575)
X(47113) = complement of X(13449)
X(47113) = isogonal conjugate of the isotomic conjugate of X(44369)
X(47113) = circumperp conjugate of X(33878)
X(47113) = crossdifference of every pair of points on line {X(523), X(37637)}
X(47113) = X(i)-Hirst inverse of-X(j) for these (i, j): {6, 1351}, {1351, 6}
X(47113) = X(512)-vertex conjugate of-X(1351)
X(47113) = inverse of X(1351) in circumcircle
X(47113) = inverse of X(5107) in Schoute circle
X(47113) = inverse of X(9734) in Brocard circle
X(47113) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(9734)}} and {{A, B, C, X(6), X(23700)}}
X(47113) = barycentric product X(6)*X(44369)
X(47113) = trilinear product X(31)*X(44369)
X(47113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 9734), (3, 2080, 18860), (3, 3053, 9737), (3, 3398, 37512), (3, 5023, 5171), (3, 8722, 14810), (3, 11171, 8589), (3, 13335, 13334), (3, 26316, 21163), (3, 38225, 187), (15, 16, 5107), (39, 11842, 15516), (182, 576, 44504), (187, 1692, 3053), (187, 18860, 2080), (187, 37512, 10631), (1379, 1380, 1351), (1691, 5023, 187), (2459, 2460, 1692), (5008, 32447, 22330), (5085, 5585, 3), (6781, 38737, 15980), (7771, 35925, 15819), (21163, 26316, 20190), (43120, 43121, 575)

X(47114) = MIDPOINT OF X(20) AND X(10151)

Barycentrics (-a^2+b^2+c^2)*(10*a^8-9*(b^2+c^2)*a^6-(11*b^4-30*b^2*c^2+11*c^4)*a^4+9*(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^4) : :

X(47114) = 5*X(3)-X(2072), 4*X(3)-X(5159), 3*X(3)-X(10257), 7*X(3)-X(10297), 13*X(3)-X(18323), 9*X(3)-X(18403), 3*X(3)+X(44246), X(20)+2*X(37911), X(186)+7*X(3528), 3*X(376)+X(403), X(468)+5*X(3522), X(468)-3*X(37941), 7*X(548)+X(11558), 4*X(548)+X(37942), 3*X(548)+X(44234), 5*X(548)+X(44961), 3*X(549)-X(23323), 2*X(550)+X(37984), 3*X(550)+X(44283), X(858)-13*X(21734)

X(47114) lies on these lines: {2, 3}, {1038, 10149}, {3184, 31945}, {3564, 21663}, {6000, 13416}, {12134, 43907}, {15311, 37853}, {16227, 36987}, {16303, 36748}, {16836, 32411}, {18914, 43604}, {31831, 32210}, {37487, 41588}, {38726, 44665}

X(47114) = midpoint of X(i) and X(j) for these {i, j}: {20, 10151}, {468, 16386}, {548, 37968}, {550, 44452}, {2071, 37931}, {10257, 44246}, {12103, 46031}, {16227, 36987}, {37899, 37944}
X(47114) = reflection of X(i) in X(j) for these (i, j): (4, 44912), (5159, 16976), (10151, 37911), (16976, 3), (37897, 186), (37935, 15646), (37984, 44452)
X(47114) = complement of X(13473)
X(47114) = circumperp conjugate of X(39568)
X(47114) = perspector of the circumconic {{A, B, C, X(648), X(41899)}}
X(47114) = inverse of X(20) in the complement of the polar circle
X(47114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 376, 1368), (3, 15696, 3546), (3, 44240, 140), (3, 44241, 6676), (376, 38282, 20), (548, 13383, 550), (3522, 10565, 376), (7502, 8703, 548), (16196, 37984, 5159), (16386, 37941, 468)

X(47115) = MIDPOINT OF X(1) AND X(11700)

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

X(47115) = 3*X(1)+X(109), 5*X(1)-X(10703), 5*X(109)+3*X(10703), X(109)-3*X(11700), X(124)-3*X(551), 3*X(1385)-X(38600), 3*X(3576)+X(10696), 5*X(3616)-X(13532), 9*X(3653)-5*X(38786), 3*X(3655)+X(10740), 3*X(3656)+X(38777), X(7982)+3*X(38697), 3*X(10246)-X(11713), 9*X(10246)-X(38573), X(10703)+5*X(11700), X(10732)-5*X(11522), X(10764)-5*X(16491), 3*X(11713)-X(38573), 5*X(18398)-X(34242), 7*X(30389)-3*X(38691)

X(47115) lies on these lines: {1, 104}, {117, 5882}, {124, 551}, {515, 11727}, {519, 6718}, {952, 29008}, {1385, 2817}, {1482, 14690}, {1845, 21842}, {2802, 33649}, {2818, 15178}, {3576, 10696}, {3616, 13532}, {3636, 11734}, {3653, 38786}, {3655, 10740}, {3656, 38777}, {3738, 14315}, {4301, 38785}, {7982, 38697}, {10222, 38607}, {10246, 11713}, {10732, 11522}, {10764, 16491}, {11809, 21578}, {18398, 34242}, {28194, 38783}, {30389, 38691}, {33650, 38314}

X(47115) = midpoint of X(i) and X(j) for these {i, j}: {1, 11700}, {117, 5882}, {1482, 14690}, {4301, 38785}, {10222, 38607}
X(47115) = reflection of X(11734) in X(3636)
X(47115) = inverse of X(11571) in incircle

X(47116) = MIDPOINT OF X(5) AND X(11701)

Barycentrics 2*a^22-14*(b^2+c^2)*a^20+2*(19*b^4+31*b^2*c^2+19*c^4)*a^18-(b^2+c^2)*(47*b^4+54*b^2*c^2+47*c^4)*a^16+2*(9*b^8+9*c^8+(36*b^4+41*b^2*c^2+36*c^4)*b^2*c^2)*a^14+2*(b^2+c^2)*(7*b^8+7*c^8-(16*b^4-3*b^2*c^2+16*c^4)*b^2*c^2)*a^12-(14*b^12+14*c^12+(13*b^8+13*c^8-2*(13*b^4-8*b^2*c^2+13*c^4)*b^2*c^2)*b^2*c^2)*a^10+(b^4-c^4)*(b^2-c^2)*(12*b^8+12*c^8+(25*b^4+11*b^2*c^2+25*c^4)*b^2*c^2)*a^8-(b^2-c^2)^2*(28*b^12+28*c^12+(10*b^8+10*c^8+(25*b^4-8*b^2*c^2+25*c^4)*b^2*c^2)*b^2*c^2)*a^6+(b^4-c^4)*(b^2-c^2)^3*(32*b^8+32*c^8-(6*b^4-41*b^2*c^2+6*c^4)*b^2*c^2)*a^4-(b^2-c^2)^6*(16*b^8+16*c^8+23*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^2+3*(b^4+b^2*c^2+c^4)*(b^2+c^2)*(b^2-c^2)^8 : :

X(47116) lies on these lines: {5, 11701}, {3090, 8157}, {3628, 10628}, {14940, 18402}

X(47117) = MIDPOINT OF X(54) AND X(11702)

Barycentrics (4*a^14-17*(b^2+c^2)*a^12+24*(b^2+c^2)^2*a^10-5*(b^2+c^2)*(b^4+8*b^2*c^2+c^4)*a^8-(20*b^8+20*c^8-(21*b^4+26*b^2*c^2+21*c^4)*b^2*c^2)*a^6+3*(b^2+c^2)*(7*b^8+7*c^8-13*(b^4-b^2*c^2+c^4)*b^2*c^2)*a^4-(b^2-c^2)^2*(8*b^8+8*c^8+(b^4+5*b^2*c^2+c^4)*b^2*c^2)*a^2+(b^6+c^6)*(b^2-c^2)^4)*a^2 : :

X(47117) = 5*X(1493)+X(25714), 3*X(10274)-X(15647), 5*X(11597)-X(25714), X(12316)+3*X(15035), X(12325)-5*X(38794), X(13368)-3*X(16222)

X(47117) lies on these lines: {5, 14049}, {54, 5663}, {110, 13364}, {113, 36966}, {195, 1511}, {1154, 14708}, {1493, 11597}, {1539, 12254}, {2914, 10610}, {3043, 12006}, {3850, 7687}, {6689, 12043}, {8254, 20304}, {10203, 11592}, {10274, 15647}, {10619, 11805}, {11557, 40632}, {11591, 12228}, {12041, 43580}, {12316, 15035}, {12325, 38794}, {13368, 16222}, {14984, 19150}, {17702, 22051}, {17847, 32046}, {20396, 33565}

X(47117) = midpoint of X(i) and X(j) for these {i, j}: {5, 14049}, {54, 11702}, {113, 36966}, {195, 1511}, {1493, 11597}, {1539, 12254}, {2914, 10610}, {10619, 11805}, {11557, 40632}, {12041, 43580}
X(47117) = reflection of X(i) in X(j) for these (i, j): (20304, 8254), (33565, 20396)

X(47118) = X(17)X(33421)∩(186)X(6104)

X(47118) lies on these lines: {17, 33421}, {186, 6104}, {619, 40581}, {5668, 16241}, {5995, 6671}, {6107, 6109}

X(47119) = X(18)X(33420)∩(186)X(6105)

X(47119) lies on these lines: {18, 33420}, {186, 6105}, {618, 40580}, {5669, 16242}, {5994, 6672}, {6106, 6108}

X(47120) = {X(3369), X(3396)}-HARMONIC CONJUGATE OF X(574)

X(47120) = reflection of X(576) in X(47121)
X(47120) = {X(3369), X(3396)}-harmonic conjugate of X(574)

X(47121) = MIDPOINT OF X(576) AND X(47120)

This preamble is contributed by Clark Kimberling and Peter Moses, March 12, 2022.

This section consists of five types of points on the orthic axis:

(1) Points X(47122)-X(47139). Suppose that X = x : y : z, and let D(X) = SB z - SC y : : . Then D(X) lies on the orthic axis; indeed,

D(X) = crossdifference of every pair of points on the line X(3)X*, where X* = isogonal conjugate of isotomic conjugate of X. (Note that SB z - SC y : : lies on the orthic axis, whereas SB y - SC z : : lies on the line at infinity.

The appearance of {h,k} in the following list means that X(k) = D(X(h)): {1,6590}, {2,523}, {3,2501}, {4,647}, {5, 47122}, {6,523}, {7,650}, {8,650}, {9,47123}, {10,45745}, {20,6587}, {21,47124}, {22,47125}, {30,9209}, {32, 47126}, {37,7662}, {38, 47127}, {39,47128}, {42,47129}, {43,47130}, {44,47131}, {45,47132}, {51,47133}, {54,12077}, [55,47134}, {56,47135}, {57,47136}, {63,7649}, {64,6587}, {65,650}, {66,2485}, {67,2492}, {68,6753}, {71,7649}, {72,6591}, {73,3064}, {74,1637}, {75,650}, {76,647}, {77,3064}, {78,3064}, {81,523}, {83,3806}, {85,650}, {86,523}, {95,12077}, {99,1637}, {100,47137}, {110,47138}, {111,47139}, {115,45687}, {125,14273}

(2) Points X(47140)-X(47192). The appearance of {h,k} in the following list means that the line through X(h) parallel to the Euler line meets the orthic axis in X(k):

{1,16272}, {6,16303}, {8,16304}, {10,16305}, {11,47140}, {12,47160}, {13,47141}, {14,47142}, {19,47161}, {32,16306}, {37,16307}, {39,16308}, {40,16309}, {50,16310}, {51,16311}, {52,47143}, {53,47144}, {54,47145}, {58,47163}, {64,47164}, {67,47165}, {69,16312}, {74,47146}, {76,16313}, {79,16272}, {83,16314}, {98,16315}, {99,16316}, {107,47147}, {110,47148}, {111,16317}, {112,16318}, {113,16319}, {114,16320}, {115,230}, {119,47149}, {122,47166}, {125,11657}, {126,47170}, {127,47150}, {132,47151}, {133,47152}, {141,16321}, {143,47153}, {145,16322}, {147,47154}, {148,47155}, {165,16323}, {182,16324}, {183,16325}, {187,230}, {191,16309}, {193,16326}, {194,16327}, {216,16328}, {225,47156}, {233,47157}, {250,47157},{262,16329}, {264,16330}{351,47159}, {389,47171}, {393,47162}, {570,47167}, {571,47168}, {574,47169}, {620,47171}, {648,47172}, {669, 47173}, {693,47174}, {850,47175}, {905},47176}, {935,47177}, {1072,47178}, {1112,47179}, {1180,47180}, {1194,47181}, {1196,47182}, {1249,47183}, {1384,47184}, {1465,47185}, (1506,47186}, {1560,47187}, {1576,47188}, {1609,47189}, {1649,47190}, {1785,47191}, {1879,47192}

(3) Points X(47193)-X(47195). The appearance of {i, j; k} in the following list means that X(k) = X(i)-line conjugate of X(j):

{230, 231; 47193}
{230, 232; 47194}
{230, 2501; 47195}
{231, 230; 46953}
{232, 230; 46953}
{230, 647; 468}
{647, 230; 46953}
{230, 650; 8758}
{650, 230; 46953}
{647, 650; 8758}
{650, 647; 468}
{230, 468; 647}
{468, 230; 46953}
{468, 647; 468}
{647, 468; 647}
{468, 650; 8758}
{650, 468; 647}
{2501, 468; 647}

(4) Points X(47196)-X(47198). The appearance of {h, i; j, k} in the following list means that X(k) = {X(i), X(j)-harmonic conjugate of X(h), so that also, X(h) = {X(i), X(j)-harmonic conjugate of X(k): {230,231,232 47196}, {230,231,468,47197}, {230,468, 647,47198}

(5) Points X(47199)-X(47236). Four circles with center on the orthic axis are these: Stevanovic circle, Dao-Moses-Telv circle, Moses radical circle, and Moses-Parry circle. If P is a point on the orthic axis and (O) is a circle with center on the orthic axis, then the (O)(-inverse of P is also on the orthic axis, as exemplified by X(47199)-X(47236).

X(47122) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(51)

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

X(47122) = 5 X[647] - 3 X[1637], 3 X[647] - 2 X[6587], 4 X[647] - 3 X[9209], 3 X[647] - X[12077], 6 X[1637] - 5 X[2501], 9 X[1637] - 10 X[6587], 4 X[1637] - 5 X[9209], 9 X[1637] - 5 X[12077], 3 X[2501] - 4 X[6587], 2 X[2501] - 3 X[9209], 3 X[2501] - 2 X[12077], 8 X[6587] - 9 X[9209], 9 X[9209] - 4 X[12077], 3 X[32320] + X[35441], X[33294] - 3 X[36900], 3 X[36900] + X[41298]

X(47122) lies on these lines: {230, 231}, {323, 401}, {512, 6562}, {661, 30572}, {1640, 44010}, {2395, 11123}, {2799, 41300}, {3050, 30451}, {3265, 23878}, {3569, 3800}, {8057, 14461}, {10562, 14536}, {14480, 36830}, {14611, 23357}, {15451, 44705}, {33294, 36900}

X(47122) = midpoint of X(i) and X(j) for these {i,j}: {6563, 31296}, {14325, 14326}, {33294, 41298}
X(47122) = reflection of X(i) in X(j) for these {i,j}: {2501, 647}, {12077, 6587}, {44705, 15451}
X(47122) = complement of the isotomic conjugate of X(43351)
X(47122) = X(17040)-anticomplementary conjugate of X(21294)
X(47122) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 5522}, {43351, 2887}
X(47122) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 5522}, {37872, 8901}
X(47122) = X(i)-isoconjugate of X(j) for these (i,j): {163, 8797}, {662, 3527}, {4575, 8796}, {4592, 34818}
X(47122) = crosspoint of X(i) and X(j) for these (i,j): {2, 43351}, {648, 1217}
X(47122) = crosssum of X(i) and X(j) for these (i,j): {520, 10979}, {647, 1181}
X(47122) = crossdifference of every pair of points on line {3, 51}
X(47122) = barycentric product X(i)*X(j) for these {i,j}: {512, 44149}, {523, 631}, {525, 3087}, {850, 11402}, {5522, 43351}, {14618, 36748}
X(47122) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 3527}, {523, 8797}, {631, 99}, {2489, 34818}, {2501, 8796}, {3087, 648}, {6755, 35360}, {11402, 110}, {26907, 23181}, {36748, 4558}, {44149, 670}
X(47122) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {647, 2501, 9209}, {647, 12077, 6587}, {3288, 32320, 2623}, {6587, 12077, 2501}, {36900, 41298, 33294}

X(47123) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(41)

Barycentrics (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(47123) = 2 X[4163] - 3 X[21052], 3 X[4449] - X[21105], X[4814] - 3 X[30574], X[21105] + 3 X[21118], 3 X[21183] - 2 X[24720], 3 X[21185] - 2 X[21201]

X(47123) lies on these lines: {1, 514}, {11, 42770}, {230, 231}, {513, 11934}, {522, 693}, {656, 23687}, {659, 8642}, {905, 34958}, {1491, 29639}, {1638, 4777}, {1734, 21188}, {2499, 8672}, {3239, 4088}, {3667, 46403}, {3669, 6362}, {3716, 4468}, {3900, 7178}, {4041, 14837}, {4105, 8058}, {4147, 24987}, {4151, 20517}, {4163, 21052}, {4379, 11269}, {4397, 24622}, {4786, 24623}, {4789, 21180}, {4814, 30574}, {4895, 28292}, {6332, 23877}, {6366, 43052}, {6734, 17072}, {7650, 23874}, {7658, 21186}, {7661, 17420}, {10015, 14077}, {10196, 29675}, {12649, 21302}, {17418, 21172}, {21146, 23811}, {21175, 29164}, {21179, 28147}, {21204, 29676}, {22388, 39199}, {23732, 29142}, {26357, 44408}

X(47123) = midpoint of X(4449) and X(21118)
X(47123) = reflection of X(i) in X(j) for these {i,j}: {650, 676}, {905, 34958}, {1734, 21188}, {2254, 3676}, {4025, 4458}, {4041, 14837}, {4088, 3239}, {4468, 3716}, {6590, 7662}, {17418, 21172}, {17420, 7661}, {44448, 17072}
X(47123) = isotomic conjugate of trilinear pole of line X(9)X(69)
X(47123) = complement of the isotomic conjugate of X(43349)
X(47123) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {28847, 329}, {39954, 33650}
X(47123) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 38959}, {43349, 2887}
X(47123) = X(2)-Ceva conjugate of X(38959)
X(47123) = X(i)-isoconjugate of X(j) for these (i,j): {55, 6183}, {100, 3423}, {101, 39273}, {651, 949}, {1492, 45974}
X(47123) = crosspoint of X(i) and X(j) for these (i,j): {2, 43349}, {664, 27475}
X(47123) = crosssum of X(663) and X(2280)
X(47123) = crossdifference of every pair of points on line {3, 41}
X(47123) = barycentric product X(i)*X(j) for these {i,j}: {85, 6182}, {514, 2550}, {522, 948}, {523, 16054}, {693, 40131}, {2263, 4391}, {3261, 37580}, {24002, 28043}, {38959, 43349}
X(47123) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 6183}, {513, 39273}, {649, 3423}, {663, 949}, {948, 664}, {2263, 651}, {2550, 190}, {3250, 45974}, {6182, 9}, {16054, 99}, {28043, 644}, {37580, 101}, {40131, 100}
X(47123) = {X(4017),X(6608)}-harmonic conjugate of X(2254)

X(47124) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(1779)

X(47124) lies on these lines: {230, 231}, {512, 11934}, {520, 46389}, {525, 1577}, {656, 4024}, {661, 23752}, {693, 33294}, {2457, 4931}, {3265, 4885}, {4762, 44552}, {4820, 7655}, {7252, 44409}, {8057, 36054}, {14837, 23879}, {17094, 23749}

X(47124) = midpoint of X(693) and X(33294)
X(47124) = reflection of X(i) in X(j) for these {i,j}: {650, 6587}, {3265, 4885}
X(47124) = X(i)-isoconjugate of X(j) for these (i,j): {162, 45127}, {284, 13395}
X(47124) = crossdifference of every pair of points on line {3, 1779}
X(47124) = barycentric product X(i)*X(j) for these {i,j}: {377, 523}, {693, 43214}, {850, 37538}, {1448, 4086}, {23879, 45999}
X(47124) = barycentric quotient X(i)/X(j) for these {i,j}: {65, 13395}, {377, 99}, {647, 45127}, {1448, 1414}, {37538, 110}, {43214, 100}
X(47124) = {X(6590),X(7649)}-harmonic conjugate of X(650)

X(47125) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(206)

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

X(47125) lies on these lines: {6, 8057}, {107, 23975}, {141, 4143}, {230, 231}, {525, 23285}, {2079, 30715}, {2165, 34212}, {2881, 44705}, {3265, 23881}, {3267, 33294}, {9178, 40323}, {10279, 21732}, {13881, 14566}, {21006, 34952}

X(47125) = midpoint of X(3267) and X(33294)
X(47125) = reflection of X(i) in X(j) for these {i,j}: {2485, 6587}, {4143, 141}
X(47125) = complement of the isotomic conjugate of X(1289)
X(47125) = isotomic conjugate of trilinear pole of line X(22)X(69)
X(47125) = X(i)-complementary conjugate of X(j) for these (i,j): {112, 21247}, {1289, 2887}, {2156, 127}, {2353, 34846}, {13854, 21253}, {15388, 4369}, {32676, 206}, {40146, 16573}, {44183, 42327}
X(47125) = X(i)-Ceva conjugate of X(j) for these (i,j): {1289, 17407}, {3267, 523}, {33294, 525}
X(47125) = X(i)-isoconjugate of X(j) for these (i,j): {63, 39417}, {163, 13575}, {662, 34207}, {1576, 39733}, {4592, 40144}, {34072, 39129}
X(47125) = crosspoint of X(i) and X(j) for these (i,j): {2, 1289}, {76, 107}
X(47125) = crosssum of X(i) and X(j) for these (i,j): {6, 8673}, {32, 520}
X(47125) = crossdifference of every pair of points on line {3, 206}
X(47125) = barycentric product X(i)*X(j) for these {i,j}: {159, 850}, {523, 1370}, {525, 41361}, {661, 21582}, {1577, 18596}, {2501, 28419}, {3162, 3267}, {3265, 41766}, {3700, 18629}, {8793, 23285}, {14618, 23115}, {23881, 40357}
X(47125) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 39417}, {159, 110}, {512, 34207}, {523, 13575}, {826, 39129}, {850, 40009}, {1370, 99}, {1577, 39733}, {2485, 40358}, {2489, 40144}, {3162, 112}, {8793, 827}, {17407, 1289}, {18596, 662}, {18629, 4573}, {21582, 799}, {23115, 4558}, {28419, 4563}, {33584, 1301}, {41361, 648}, {41766, 107}
X(47125) = {X(6587),X(46425)}-harmonic conjugate of X(9209)

X(47126) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(1501)

X(47126) = 4 X[647] - 3 X[45687], 2 X[850] - 3 X[9134], X[2528] - 3 X[9148], 9 X[5466] - X[31065], X[8664] - 3 X[14420], 3 X[9134] - 4 X[12075], 9 X[9189] - 8 X[44451], 5 X[31072] - 6 X[45688]

X(47126) lies on these lines: {230, 231}, {512, 33294}, {690, 44445}, {826, 850}, {2525, 23301}, {2528, 9148}, {2799, 3005}, {5027, 7927}, {5466, 10159}, {6368, 30735}, {8664, 14420}, {8665, 32473}, {31072, 45688}

X(47126) = midpoint of X(3806) and X(12077)
X(47126) = reflection of X(i) in X(j) for these {i,j}: {850, 12075}, {2525, 23301}
X(47126) = isotomic conjugate of the isogonal conjugate of X(2514)
X(47126) = X(i)-Ceva conjugate of X(j) for these (i,j): {308, 115}, {1235, 338}, {37892, 125}
X(47126) = X(560)-isoconjugate of X(35567)
X(47126) = crosssum of X(1576) and X(1634)
X(47126) = crossdifference of every pair of points on line {3, 1501}
X(47126) = barycentric product X(i)*X(j) for these {i,j}: {76, 2514}, {523, 6656}, {850, 1194}, {1577, 17446}, {2501, 45201}, {4036, 16735}, {11574, 14618}, {18070, 21336}, {24006, 45220}
X(47126) = barycentric quotient X(i)/X(j) for these {i,j}: {76, 35567}, {850, 1241}, {1194, 110}, {2514, 6}, {6656, 99}, {11574, 4558}, {17446, 662}, {21248, 4576}, {23642, 1634}, {45201, 4563}, {45220, 4592}
X(47126) = {X(850),X(12075)}-harmonic conjugate of X(9134)

X(47127) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(1964)

X(47127) lies on these lines: {230, 231}, {649, 2517}, {786, 8060}, {798, 812}, {824, 21178}, {830, 21099}, {1919, 3907}, {2483, 4036}, {2484, 4391}, {3250, 8062}, {3261, 4369}, {3716, 4079}, {4979, 44444}, {21113, 43041}, {21225, 26248}

X(47127) = crossdifference of every pair of points on line {3, 1964}
X(47127) = barycentric product X(i)*X(j) for these {i,j}: {523, 14012}, {26924, 46107}
X(47127) = barycentric quotient X(i)/X(j) for these {i,j}: {14012, 99}, {26924, 1331}

X(47128) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(3051)

X(47128) = 3 X[351] - 2 X[41300], 5 X[647] - 6 X[11176], 3 X[647] - 4 X[44451], 3 X[850] - X[44445], 3 X[1637] - X[3806], 3 X[3005] - 5 X[31279], 3 X[4108] - 2 X[8651], 3 X[4108] - X[31296], 3 X[5996] - 5 X[31072], 9 X[8599] + X[31065], X[8665] - 3 X[9148], 9 X[11176] - 10 X[44451], 2 X[23301] - 3 X[31174], 6 X[30476] - 5 X[31279]

X(47128) lies on these lines: {230, 231}, {316, 512}, {351, 41300}, {669, 23878}, {804, 3804}, {826, 33294}, {3005, 30476}, {3800, 9134}, {4108, 8651}, {5113, 7950}, {5466, 43527}, {5996, 31072}, {7927, 12075}, {8599, 31065}, {8664, 32472}, {8665, 9148}, {23301, 31174}

X(47128) = reflection of X(i) in X(j) for these {i,j}: {3005, 30476}, {31296, 8651}
X(47128) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {162, 8892}, {5395, 21221}
X(47128) = X(i)-complementary conjugate of X(j) for these (i,j): {10014, 8287}, {34816, 21253}
X(47128) = X(163)-isoconjugate of X(31360)
X(47128) = crosspoint of X(670) and X(18840)
X(47128) = crosssum of X(669) and X(30435)
X(47128) = crossdifference of every pair of points on line {3, 3051}
X(47128) = barycentric product X(i)*X(j) for these {i,j}: {523, 7770}, {14618, 19126}
X(47128) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 31360}, {7770, 99}, {8891, 4576}, {19126, 4558}
X(47128) = {X(4108),X(31296)}-harmonic conjugate of X(8651)

X(47129) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(1918)

X(47129) lies on these lines: {230, 231}, {514, 1921}, {522, 798}, {649, 28623}, {661, 2517}, {768, 4025}, {2484, 4581}, {3239, 4079}, {4813, 44444}, {8061, 17072}, {17159, 25259}, {20906, 30061}, {21178, 21196}, {22044, 28161}, {22388, 23399}, {26049, 45746}

X(47129) = midpoint of X(17159) and X(25259)
X(47129) = reflection of X(4079) in X(3239)
X(47129) = crossdifference of every pair of points on line {3, 1918}

X(47130) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(2209)

X(47130) lies on these lines: {230, 231}, {514, 4374}, {522, 20979}, {661, 4397}, {693, 30093}, {816, 30183}, {3239, 21834}, {3261, 18071}, {11068, 21225}, {17159, 28846}, {17894, 20910}, {22044, 28169}

X(47130) = reflection of X(i) in X(j) for these {i,j}: {21225, 11068}, {21834, 3239}
X(47130) = crossdifference of every pair of points on line {3, 2209}

X(47131) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(2251)

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

X(47131) = 3 X[676] - 2 X[2490], 2 X[4394] - 3 X[4809], 2 X[6590] - 3 X[7662], 2 X[11068] - 3 X[26275]

X(47131) lies on these lines: {75, 693}, {230, 231}, {513, 41794}, {522, 3776}, {2496, 4802}, {2505, 28183}, {3801, 3900}, {3803, 29098}, {4162, 29082}, {4394, 4809}, {4820, 29370}, {4885, 30748}, {4926, 46403}, {9001, 11927}, {11068, 26275}, {17494, 26274}, {21185, 29288}, {21212, 28161}, {29144, 43067}

X(47132) = X(230)X(231)∩X(693)X(900)

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

X(47132) = 4 X[2490] - 3 X[2977], 2 X[2490] - 3 X[4874], 3 X[4809] - X[4976], 4 X[4885] - 3 X[30792], X[6590] - 3 X[7662], X[17494] - 3 X[26275], X[26824] + 3 X[44433]

X(47132) lies on these lines: {230, 231}, {693, 900}, {784, 34958}, {2804, 15584}, {4777, 17069}, {4809, 4976}, {4885, 30792}, {4977, 23770}, {14779, 28179}, {17494, 26275}, {26824, 44433}, {39386, 46403}

X(47133) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(3618)

X(47133) = 3 X[647] - 2 X[2485], 7 X[647] - 4 X[2492], 4 X[2485] - 3 X[2489], 7 X[2485] - 6 X[2492], 7 X[2489] - 8 X[2492], 3 X[8644] - 2 X[18105]

X(47133) lies on these lines: {230, 231}, {520, 3288}, {826, 7652}, {2395, 46952}, {3050, 8675}, {3267, 7799}, {3804, 21006}, {4580, 41300}, {8644, 18105}

X(47133) = reflection of X(i) in X(j) for these {i,j}: {2489, 647}, {3804, 21006}, {4580, 41300}
X(47133) = crosssum of X(525) and X(3619)
X(47133) = crossdifference of every pair of points on line {3, 3618}
X(47133) = barycentric product X(523)*X(7484)
X(47133) = barycentric quotient X(7484)/X(99)

X(47134) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(2175)

X(47134) lies on these lines: {230, 231}, {824, 14837}, {885, 2298}, {918, 3261}, {2517, 3700}, {3063, 44409}, {17069, 21178}, {20504, 21131}, {20906, 25009}, {21114, 43042}, {21118, 21127}

X(47135) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(1397)

X(47135) lies on these lines: {230, 231}, {661, 21119}, {834, 46389}, {918, 20952}, {3700, 3910}, {4024, 17420}, {4083, 14298}, {4581, 21786}, {4976, 40500}, {28832, 28834}

X(47135) = X(30710)-Ceva conjugate of X(11)
X(47135) = crosspoint of X(4391) and X(4581)
X(47135) = crossdifference of every pair of points on line {3, 1397}
X(47135) = barycentric product X(i)*X(j) for these {i,j}: {522, 13161}, {37613, 44426}
X(47135) = barycentric quotient X(i)/X(j) for these {i,j}: {13161, 664}, {37613, 6516}

X(47136) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(604)

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

X(47136) = 2 X[4397] - 3 X[7628], 2 X[14353] - 3 X[41800], 3 X[17418] - X[21106], X[21106] + 3 X[21119]

X(47136) lies on these lines: {230, 231}, {513, 21120}, {514, 4581}, {522, 3717}, {657, 21832}, {663, 8058}, {693, 25022}, {4017, 14837}, {4025, 20906}, {4105, 42312}, {4449, 21172}, {4777, 40500}, {14077, 44409}, {14282, 28132}, {14353, 41800}, {14413, 21180}, {20315, 28834}, {21175, 29260}, {21179, 28169}, {21185, 28161}

X(47136) = midpoint of X(17418) and X(21119)
X(47136) = reflection of X(i) in X(j) for these {i,j}: {4017, 14837}, {4449, 21172}
X(47136) = crossdifference of every pair of points on line {3, 604}
X(47136) = barycentric product X(i)*X(j) for these {i,j}: {514, 2551}, {7649, 23600}, {10319, 44426}
X(47136) = barycentric quotient X(i)/X(j) for these {i,j}: {2551, 190}, {10319, 6516}, {23600, 4561}

X(47137) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(692)

X(47137) lies on these lines: {37, 2804}, {230, 231}, {918, 1086}, {1024, 2161}, {1769, 42462}, {2345, 23678}, {2509, 21186}, {3261, 26546}, {21102, 21127}, {21133, 43042}, {23972, 23986}

X(47137) = complement of the isotomic conjugate of X(929)
X(47137) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 15612}, {560, 39017}, {929, 2887}
X(47137) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 15612}, {20624, 8735}
X(47137) = X(i)-isoconjugate of X(j) for these (i,j): {101, 43363}, {692, 37214}
X(47137) = crosspoint of X(2) and X(929)
X(47137) = crosssum of X(6) and X(928)
X(47137) = crossdifference of every pair of points on line {3, 692}
X(47137) = barycentric product X(i)*X(j) for these {i,j}: {514, 5179}, {523, 14956}, {693, 44670}, {929, 15612}
X(47137) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 43363}, {514, 37214}, {5179, 190}, {14956, 99}, {44670, 100}

X(47138) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(1177)

Barycentrics (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(47138) = 3 X[1637] - 2 X[2492], 3 X[1637] - X[14273], 3 X[2485] - 4 X[6587], 5 X[3620] - 3 X[45792], X[14277] - 3 X[23288], X[14278] - 6 X[23288]

X(47138) lies on these lines: {6, 9033}, {24, 44806}, {30, 44205}, {67, 690}, {111, 2373}, {112, 1289}, {115, 127}, {141, 6333}, {230, 231}, {248, 2395}, {526, 45801}, {804, 13187}, {1560, 42665}, {1640, 9003}, {1989, 34212}, {2079, 7669}, {2165, 14998}, {2502, 14697}, {2549, 46229}, {2793, 10991}, {2881, 13166}, {3163, 23976}, {3267, 23881}, {3569, 32312}, {3620, 45792}, {5181, 21109}, {9035, 14316}, {9178, 40347}, {9517, 32246}, {14417, 18310}, {18311, 44564}

X(47138) = midpoint of X(9979) and X(14977)
X(47138) = reflection of X(i) in X(j) for these {i,j}: {6333, 141}, {6334, 18312}, {14273, 2492}, {14278, 14277}, {14417, 18310}, {18311, 44564}
X(47138) = isotomic conjugate of trilinear pole of line X(69)X(110)
X(47138) = polar circle pole of line X(2)X(112)
X(47138) = orthogonal projection of X(44205) on the orthic axis
X(47138) = Moses-Parry-circle-inverse of X(2485)
X(47138) = complement of the isotomic conjugate of X(935)
X(47138) = polar conjugate of the isogonal conjugate of X(42665)
X(47138) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {691, 21288}, {32729, 21215}, {36142, 5596}
X(47138) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 38971}, {935, 2887}, {2157, 127}, {3455, 34846}, {8791, 21253}, {32676, 6593}
X(47138) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 38971}, {111, 115}, {9979, 690}, {14977, 523}, {46105, 125}
X(47138) = X(i)-isoconjugate of X(j) for these (i,j): {3, 36095}, {63, 10423}, {162, 18876}, {163, 2373}, {662, 1177}, {1576, 37220}, {10422, 23889}, {34072, 46165}, {36084, 36823}
X(47138) = crosspoint of X(i) and X(j) for these (i,j): {2, 935}, {107, 671}, {892, 1502}, {5466, 14618}
X(47138) = crosssum of X(i) and X(j) for these (i,j): {6, 9517}, {187, 520}, {351, 1501}, {5467, 32661}
X(47138) = crossdifference of every pair of points on line {3, 1177}
X(47138) = barycentric product X(i)*X(j) for these {i,j}: {10, 21109}, {264, 42665}, {339, 46592}, {512, 1236}, {514, 21017}, {523, 858}, {525, 5523}, {661, 20884}, {850, 2393}, {935, 38971}, {1560, 14977}, {1577, 18669}, {2525, 21459}, {3267, 14580}, {4024, 17172}, {5181, 5466}, {8599, 19510}, {9517, 39269}, {12827, 15328}, {14618, 14961}
X(47138) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 36095}, {25, 10423}, {512, 1177}, {523, 2373}, {647, 18876}, {826, 46165}, {850, 46140}, {858, 99}, {1236, 670}, {1560, 4235}, {1577, 37220}, {2393, 110}, {3569, 36823}, {5181, 5468}, {5523, 648}, {9178, 10422}, {10097, 41511}, {14580, 112}, {14961, 4558}, {17172, 4610}, {18669, 662}, {19510, 9146}, {20884, 799}, {21017, 190}, {21109, 86}, {21459, 42396}, {42665, 3}, {46592, 250}
X(47138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1637, 14273, 2492}, {8105, 8106, 2485}

X(47139) = CROSSDIFFERENCE OF EVERY PAIR OF POINTS ON X(3)X(15268)

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

X(47139) lies on these lines: {3, 2793}, {69, 39904}, {230, 231}, {351, 14272}, {690, 5181}, {804, 14278}, {1632, 4235}, {5652, 9003}, {6088, 9134}, {7493, 9123}, {9131, 14977}, {9178, 44564}

X(47139) = midpoint of X(i) and X(j) for these {i,j}: {69, 39904}, {9131, 14977}
X(47139) = reflection of X(i) in X(j) for these {i,j}: {9134, 18310}, {9178, 44564}
X(47139) = X(2793)-line conjugate of X(3)
X(47139) = crossdifference of every pair of points on line {3, 15268}

X(47140) = ORTHIC AXIS INTERCEPT OF X(11)X(30)

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

X(47140) lies on these lines: {2, 14686}, {11, 30}, {105, 7426}, {108, 403}, {186, 14667}, {230, 231}, {758, 15904}, {2006, 11809}, {10149, 40663}, {10773, 36167}, {11799, 46636}, {15251, 16619}, {15252, 44452}, {44214, 46635}

(47140) = midpoint of X(i) and X(j) for these {i,j}: {10149, 40663}, {11799, 46636}
X(47140) = orthogonal projection of X(11) on the orthic axis
X(47140) = {X(468),X(16272)}-harmonic conjugate of X(47160)

X(47141) = ORTHIC AXIS INTERCEPT OF X(13)X(15)

Barycentrics (2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 3*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) + 2*Sqrt[3]*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)^2*S : :

X(47141) lies on these lines: {6, 32461}, {13, 15}, {186, 36302}, {230, 231}, {524, 41888}, {3580, 23895}, {11488, 36186}, {30465, 36299}, {30467, 41995}

X(47141) = midpoint of X(i) and X(j) for these {i,j}: {396, 11537}, {3580, 23895}
X(47141) = reflection of X(47142) in X(230)
X(47141) = orthogonal projection of X(13) on the orthic axis
X(47141) = inverse of X(5318) in the pedal circle of X(15)
X(47141) = {{X(468),X(16303)}-harmonic conjugate of X(47142)
X(47141) = {{X(3003),X(16319)}-harmonic conjugate of X(47142)
X(47141) = {X(36211),X(40578)}-harmonic conjugate of X(11537)

X(47142) = ORTHIC AXIS INTERCEPT OF X(14)X(16)

Barycentrics (2*a^4 - a^2*b^2 + b^4 - a^2*c^2 - 2*b^2*c^2 + c^4)*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - a^4*c^2 + 3*a^2*b^2*c^2 - b^4*c^2 - a^2*c^4 - b^2*c^4 + c^6) - 2*Sqrt[3]*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)^2*S : :

X(47142) lies on these lines: {6, 32460}, {14, 16}, {186, 36303}, {230, 231}, {524, 41887}, {3580, 23896}, {11489, 36185}, {30468, 36298}, {30470, 41996}

X(47142) = midpoint of X(i) and X(j) for these {i,j}: {395, 11549}, {3580, 23896}
X(47142) = reflection of X(47141) in X(230)
X(47142) = orthogonal projection of X(14) on the orthic axis
X(47142) = inverse of X(5321) in the pedal circle of X(16)
X(47142) = {{X(468),X(16303)}-harmonic conjugate of X(47141)
X(47142) = {{X(3003),X(16319)}-harmonic conjugate of X(47141)
X(47142) = {X(36210),X(40579)}-harmonic conjugate of X(11549)

X(47143) = ORTHIC AXIS INTERCEPT OF X(30)X(52)

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

X(47143) lies on these lines: {30, 52}, {184, 42453}, {186, 1075}, {230, 231}, {403, 847}, {1316, 9490}, {2452, 41202}, {5189, 44434}, {6795, 37929}, {13558, 41204}, {14894, 16227}

X(47143) = orthogonal projection of X(52) on the orthic axis
X(47143) = {X(15912),X(45195)}-harmonic conjugate of X(6146)

X(47144) = ORTHIC AXIS INTERCEPT OF X(30)X(53)

X(47144) lies on these lines: {6, 403}, {30, 53}, {186, 393}, {216, 44452}, {230, 231}, {297, 40879}, {1249, 37943}, {1552, 18877}, {1609, 37917}, {1989, 5523}, {3199, 16619}, {5206, 37934}, {5475, 6749}, {6748, 10151}, {7735, 37962}, {9699, 44272}, {10018, 18573}, {14356, 44228}, {14577, 37971}, {15646, 42459}, {15905, 31726}, {16386, 36748}, {18487, 18579}, {23323, 36412}, {32113, 36191}, {37855, 45331}, {37942, 46432}

X(47144) = orthogonal projection of X(53) on the orthic axis
X(47144) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {232, 3018, 1990}, {468, 16303, 16328}, {468, 16330, 16321}, {1990, 16328, 16303}

X(47145) = ORTHIC AXIS INTERCEPT OF X(30)X(54)

X(47145) lies on these lines: {30, 54}, {230, 231}, {6750, 10151}, {10257, 46025}, {13473, 35717}, {33549, 37931}, {37974, 42924}, {37975, 42925}, {41202, 42459}

X(47146) = ORTHIC AXIS INTERCEPT OF X(30)X(74)

Barycentrics 2*a^12 - 3*a^10*b^2 - a^8*b^4 + 6*a^4*b^8 - 5*a^2*b^10 + b^12 - 3*a^10*c^2 + 8*a^8*b^2*c^2 - a^6*b^4*c^2 - 16*a^4*b^6*c^2 + 12*a^2*b^8*c^2 - a^8*c^4 - a^6*b^2*c^4 + 20*a^4*b^4*c^4 - 7*a^2*b^6*c^4 - 9*b^8*c^4 - 16*a^4*b^2*c^6 - 7*a^2*b^4*c^6 + 16*b^6*c^6 + 6*a^4*c^8 + 12*a^2*b^2*c^8 - 9*b^4*c^8 - 5*a^2*c^10 + c^12 : :

X(47146) lies on these lines: {30, 74}, {133, 10151}, {230, 231}, {403, 35372}, {1316, 6792}, {1503, 6070}, {1514, 32417}, {1651, 9717}, {3564, 7471}, {4240, 36875}, {6795, 44210}, {9064, 40118}, {11064, 22104}, {11245, 36178}, {11542, 32460}, {11543, 32461}, {13292, 36159}, {16188, 47097}, {22353, 44234}, {26864, 46869}, {32409, 32411}, {36162, 43903}, {37984, 46045}

X(47146) = midpoint of X(476) and X(3580)
X(47146) = reflection of X(i) in X(j) for these {i,j}: {468, 11657}, {11064, 22104}, {46045, 37984}
X(47146) = orthogonal projection of X(74) on the orthic axis

X(47147) = ORTHIC AXIS INTERCEPT OF X(30)X(107)

X(47147) lies on these lines: {30, 107}, {125, 10151}, {132, 47097}, {230, 231}, {403, 40664}, {1503, 14847}, {1552, 16080}, {6000, 24930}, {6523, 36162}, {6525, 18870}, {34131, 37969}

X(47147) = midpoint of X(403) and X(40664)
X(47147) = reflection of X(1552) in X(37984)
X(47147) = orthogonal projection of X(107) on the orthic axis

X(47148) = ORTHIC AXIS INTERCEPT OF X(30)X(110)

Barycentrics 2*a^12 - 3*a^10*b^2 - 5*a^8*b^4 + 12*a^6*b^6 - 6*a^4*b^8 - a^2*b^10 + b^12 - 3*a^10*c^2 + 16*a^8*b^2*c^2 - 13*a^6*b^4*c^2 - 4*a^4*b^6*c^2 + 8*a^2*b^8*c^2 - 4*b^10*c^2 - 5*a^8*c^4 - 13*a^6*b^2*c^4 + 20*a^4*b^4*c^4 - 7*a^2*b^6*c^4 + 7*b^8*c^4 + 12*a^6*c^6 - 4*a^4*b^2*c^6 - 7*a^2*b^4*c^6 - 8*b^6*c^6 - 6*a^4*c^8 + 8*a^2*b^2*c^8 + 7*b^4*c^8 - a^2*c^10 - 4*b^2*c^10 + c^12 : :

X(47148) lies on these lines: {30, 110}, {54, 14896}, {114, 46436}, {136, 10151}, {230, 231}, {352, 5112}, {868, 9717}, {1304, 6530}, {1316, 6794}, {1503, 3258}, {3154, 11005}, {3564, 14611}, {3580, 14480}, {6090, 36163}, {6795, 30739}, {14731, 35265}, {15122, 34834}, {16168, 46817}, {17511, 46818}, {18583, 46868}, {18883, 34209}, {19165, 37969}, {32460, 42912}, {32461, 42913}, {34150, 37984}

X(47148) = midpoint of X(i) and X(j) for these {i,j}: {477, 32111}, {3580, 14480}, {9158, 40112}, {17511, 46818}
X(47148) = reflection of X(i) in X(j) for these {i,j}: {468, 16319}, {34150, 37984}
X(47148) = orthogonal projection of X(110) on the orthic axis

X(47149) = ORTHIC AXIS INTERCEPT OF X(30)X(119)

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

X(47149) lies on these lines: {30, 119}, {230, 231}, {403, 915}, {758, 32126}, {1495, 2677}, {1718, 35466}, {2752, 7426}, {5432, 15737}, {11799, 46635}, {17757, 20989}, {37799, 37989}, {44214, 46636}

X(47149) = midpoint of X(i) and X(j) for these {i,j}: {1495, 2677}, {11799, 46635}
X(47149) = Stevanovic-circle inverse of X(8609)
X(47149) = orthogonal projection of X(119) on the orthic axis

X(47150) = ORTHIC AXIS INTERCEPT OF X(30)X(127)

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

X(47150) lies on these lines: {30, 127}, {186, 9862}, {230, 231}, {325, 7473}, {403, 842}, {858, 30716}, {1304, 1494}, {1971, 32113}, {10295, 43460}, {11799, 46631}, {32112, 32122}, {44214, 46637}

X(47150) = midpoint of X(11799) and X(46631)
X(47150) = Moses-radical-circle-inverse of X(14580)
X(47150) = orthogonal projection of X(127) on the orthic axis
X(47150) = {X(468),X(16316)}-harmonic conjugate of X(232)

X(47151) = ORTHIC AXIS INTERCEPT OF X(30)X(132)

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

X(47151) lies on these lines: {30, 132}, {98, 403}, {107, 7426}, {125, 44102}, {186, 34131}, {230, 231}, {250, 858}, {5099, 14581}, {5523, 46619}, {6530, 36166}, {7735, 36191}, {9832, 17907}, {11799, 46637}, {27376, 36156}, {37981, 44089}, {44214, 46631}

X(47151) = midpoint of X(i) and X(j) for these {i,j}: {468, 16318}, {5523, 46619}, {11799, 46637}
X(47151) = orthogonal projection of X(132) on the orthic axis

X(47152) = ORTHIC AXIS INTERCEPT OF X(30)X(133)

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

X(47152) lies on these lines: {30, 133}, {74, 403}, {186, 34178}, {230, 231}, {1503, 31510}, {1651, 23347}, {2697, 7426}, {11251, 47050}, {15139, 40596}, {37943, 40664}

X(47153) = ORTHIC AXIS INTERCEPT OF X(30)X(143)

Barycentrics a^8*b^4 - 3*a^6*b^6 + 3*a^4*b^8 - a^2*b^10 + 2*a^8*b^2*c^2 + a^6*b^4*c^2 - 7*a^4*b^6*c^2 + 3*a^2*b^8*c^2 + b^10*c^2 + a^8*c^4 + a^6*b^2*c^4 + 8*a^4*b^4*c^4 - 2*a^2*b^6*c^4 - 4*b^8*c^4 - 3*a^6*c^6 - 7*a^4*b^2*c^6 - 2*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(47153) lies on these lines: {6, 41202}, {30, 143}, {230, 231}, {397, 37975}, {398, 37974}, {403, 13450}, {6795, 37928}, {10282, 45195}, {11746, 32428}, {13567, 42453}

X(47154) = ORTHIC AXIS INTERCEPT OF X(30)X(147)

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

X(47154) = 4 X[230] - 5 X[468], 6 X[230] - 5 X[16315], 2 X[230] - 5 X[16316], 3 X[230] - 5 X[16320], 3 X[468] - 2 X[16315], 3 X[468] - 4 X[16320], 5 X[5099] - 3 X[39563], 3 X[13473] - 4 X[46988], X[16315] - 3 X[16316], 3 X[16316] - 2 X[16320], 6 X[41133] - 5 X[47097]

X(47154) lies on these lines: {30, 147}, {230, 231}, {325, 33799}, {385, 37897}, {524, 24981}, {1316, 37665}, {5099, 39563}, {7779, 37900}, {13473, 46988}, {36207, 44210}, {41133, 47097}

X(47154) = midpoint of X(7779) and X(37900)
X(47154) = reflection of X(i) in X(j) for these {i,j}: {385, 37897}, {468, 16316}, {16315, 16320}, {46517, 325}
X(47154) = orthogonal projection of X(147) on the orthic axis
X(47154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16315, 16316, 16320}, {16315, 16320, 468}, {16321, 16329, 468}

X(47155) = ORTHIC AXIS INTERCEPT OF X(30)X(148)

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

X(47155) = 4 X[230] - 3 X[468], 2 X[230] - 3 X[16315], 5 X[230] - 3 X[16320], X[325] - 3 X[16092], 2 X[325] - 3 X[47097], 3 X[468] - 2 X[16316], 5 X[468] - 4 X[16320], 3 X[858] - X[7779], 6 X[5159] - 5 X[7925], 3 X[13473] - 4 X[46982], 3 X[16315] - X[16316], 5 X[16315] - 2 X[16320], 5 X[16316] - 6 X[16320], 3 X[21445] - 2 X[37934], 2 X[44377] - 3 X[46980], 4 X[44381] - 3 X[46986]

X(47155) lies on these lines: {30, 148}, {230, 231}, {325, 892}, {858, 7779}, {1316, 5304}, {1550, 3564}, {2452, 7736}, {5159, 7925}, {5203, 13473}, {11007, 16990}, {15589, 36194}, {16989, 34094}, {21445, 37934}, {22329, 37904}, {30739, 36207}, {40879, 43957}, {44377, 46980}, {44381, 46986}

X(47155) = reflection of X(i) in X(j) for these {i,j}: {468, 16315}, {16316, 230}, {37904, 22329}, {47097, 16092}
X(47155) = crossdifference of every pair of points on line {3, 10567}
X(47155) = orthogonal projection of X(148) on the orthic axis
X(47155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {230, 16316, 468}, {16303, 16325, 468}, {16306, 16313, 468}, {16315, 16316, 230}

X(47156) = ORTHIC AXIS INTERCEPT OF X(30)X(225)

X(47156) lies on these lines: {1, 403}, {30, 225}, {186, 1068}, {230, 231}, {10151, 40950}, {26228, 37962}, {37565, 44452}, {37579, 37917}, {37943, 38295}

X(47156) = orthogonal projection of X(225) on the orthic axis
X(47156) = {X(186),X(1068)}-harmonic conjugate of X(11809)

X(47157) = ORTHIC AXIS INTERCEPT OF X(30)X(233)

X(47157) lies on these lines: {30, 233}, {53, 37943}, {186, 6748}, {216, 10096}, {230, 231}, {577, 16532}, {8882, 30537}, {10151, 35895}, {10979, 43893}, {36751, 46451}

X(47158) = ORTHIC AXIS INTERCEPT OF X(30)X(250)

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

X(47158) lies on these lines: {30, 250}, {230, 231}, {297, 46250}, {393, 1316}, {403, 6761}, {1249, 2452}, {1503, 10151}, {3575, 18121}, {6524, 37926}, {11007, 17907}, {14120, 35907}, {14569, 36178}, {16810, 32411}, {37981, 44090}, {44089, 45279}

X(47158) = midpoint of X(403) and X(41204)
X(47158) = orthogonal projection of X(250) on the orthic axis
X(47158) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {468, 16318, 16315}, {1249, 36191, 2452}

X(47159) = ORTHIC AXIS INTERCEPT OF X(30)X(351)

Barycentrics (b^2 - c^2)*(6*a^10 - 11*a^8*b^2 - a^6*b^4 + 11*a^4*b^6 - 5*a^2*b^8 - 11*a^8*c^2 + 32*a^6*b^2*c^2 - 20*a^4*b^4*c^2 + 2*a^2*b^6*c^2 + b^8*c^2 - a^6*c^4 - 20*a^4*b^2*c^4 + 10*a^2*b^4*c^4 - b^6*c^4 + 11*a^4*c^6 + 2*a^2*b^2*c^6 - b^4*c^6 - 5*a^2*c^8 + b^2*c^8) : :

X(47159) lies on these lines: {30, 351}, {230, 231}, {512, 35266}, {690, 11064}, {804, 47097}, {858, 9147}, {1649, 5664}, {3564, 36255}, {5159, 9148}, {7426, 9213}, {9138, 40112}, {10257, 16235}, {17414, 44215}, {20403, 37904}, {34291, 45331}

X(47159) =midpoint of X(i) and X(j) for these {i,j}: {858, 9147}, {7426, 9213}, {9138, 40112}
X(47159) =reflection of X(i) in X(j) for these {i,j}: {468, 11176}, {9148, 5159}
X(47159) = orthogonal projection of X(351) on the orthic axis

X(47160) = ORTHIC AXIS INTERCEPT OF X(12)X(30)

X(47160) lies on these lines: {12, 30}, {230, 231}, {403, 41227}, {1781, 17718}, {1852, 10151}, {13405, 20129}

X(47160) = orthogonal projection of X(12) on the orthic axis
X(47160) = {X(468),X(16272)}-harmonic conjugate of X(47140)

X(47161) = ORTHIC AXIS INTERCEPT OF X(19)X(30)

X(47161) = orthogonal projection of X(19) on the orthic axis
X(47161) lies on these lines: {19, 30}, {230, 231}, {281, 403}, {1826, 10151}, {1839, 13473}, {10257, 40937}

X(47162) = ORTHIC AXIS INTERCEPT OF X(30)X(393)

X(47162) lies on these lines: {6, 10151}, {30, 393}, {53, 13473}, {186, 33630}, {230, 231}, {403, 1249}, {1033, 37917}, {8573, 37951}, {8749, 43291}, {18487, 47031}, {34809, 37777}, {34810, 44228}, {37984, 40138}

X(47162) = orthogonal projection of X(393) on the orthic axis
X(47162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1990, 3018, 16318}, {16317, 16318, 6103}

X(47163) = ORTHIC AXIS INTERCEPT OF X(30)X(58)

X(47163) lies on these lines: {6, 33329}, {30, 58}, {230, 231}, {387, 36026}, {403, 8747}, {5196, 37642}, {37646, 44908}

X(47164) = ORTHIC AXIS INTERCEPT OF X(30)X(64)

X(47164) lies on these lines: {30, 64}, {186, 15512}, {230, 231}, {403, 6523}, {5159, 33924}, {15312, 32125}

X(47164) = orthogonal projection of X(64) on the orthic axis
X(47164) = {X(468),X(47143)}-harmonic conjugate of X(16303)

X(47165) = ORTHIC AXIS INTERCEPT OF X(30)X(67)

X(47165) lies on these lines: {5, 16279}, {30, 67}, {230, 231}, {2453, 7737}, {7575, 7669}, {10297, 15526}

X(47165) = reflection of X(i) in X(j) for these {i,j}: {16303, 11657}, {47148, 16321}
X(47165) = orthogonal projection of X(67) on the orthic axis

X(47166) = ORTHIC AXIS INTERCEPT OF X(30)X(122)

Barycentrics (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(2*a^14 - 3*a^12*b^2 - 10*a^10*b^4 + 29*a^8*b^6 - 26*a^6*b^8 + 7*a^4*b^10 + 2*a^2*b^12 - b^14 - 3*a^12*c^2 + 26*a^10*b^2*c^2 - 30*a^8*b^4*c^2 - 17*a^6*b^6*c^2 + 36*a^4*b^8*c^2 - 13*a^2*b^10*c^2 + b^12*c^2 - 10*a^10*c^4 - 30*a^8*b^2*c^4 + 86*a^6*b^4*c^4 - 43*a^4*b^6*c^4 - 6*a^2*b^8*c^4 + 3*b^10*c^4 + 29*a^8*c^6 - 17*a^6*b^2*c^6 - 43*a^4*b^4*c^6 + 34*a^2*b^6*c^6 - 3*b^8*c^6 - 26*a^6*c^8 + 36*a^4*b^2*c^8 - 6*a^2*b^4*c^8 - 3*b^6*c^8 + 7*a^4*c^10 - 13*a^2*b^2*c^10 + 3*b^4*c^10 + 2*a^2*c^12 + b^2*c^12 - c^14) : :

X(47166) lies on these lines: {30, 122}, {186, 10117}, {230, 231}, {403, 477}, {1297, 7426}, {1304, 1503}, {1552, 10295}, {7480, 11064}

X(47166) = midpoint of X(1552) and X(10295)
X(47166) = reflection of X(47152) in X(468)
X(47166) = reflection of X(47152) in the Euler line
X(47166) = orthogonal projection of X(122) on the orthic axis

X(47167) = ORTHIC AXIS INTERCEPT OF X(30)X(570)

X(47167) lies on these lines: {6, 2070}, {30, 570}, {186, 571}, {216, 2072}, {230, 231}, {403, 1879}, {566, 5475}, {1656, 18573}, {2071, 14806}, {2165, 37943}, {5063, 45171}, {8745, 37970}, {22240, 37980}

X(47167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {232, 3003, 3018}, {16303, 16328, 3003}, {16308, 16328, 16303}
X(47167) = orthogonal projection of X(570) on the orthic axis

X(47168) = ORTHIC AXIS INTERCEPT OF X(30)X(571)

X(47168) lies on these lines: {6, 2072}, {30, 571}, {216, 44907}, {230, 231}, {393, 37951}, {403, 2165}, {570, 10257}, {1609, 2070}, {1879, 10151}, {1989, 41336}, {5523, 14910}, {7735, 37980}, {14806, 16976}, {34809, 37972}

X(47168) = orthogonal projection of X(571) on the orthic axis
X(47168) = {X(16310),X(16318)}-harmonic conjugate of X(3018)

X(47169) = ORTHIC AXIS INTERCEPT OF X(30)X(574)

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

X(47169) lies on these lines: {6, 7426}, {23, 7736}, {30, 574}, {39, 16619}, {186, 41370}, {187, 18579}, {230, 231}, {858, 31489}, {2549, 11799}, {3055, 47097}, {5304, 37760}, {7575, 9699}, {7735, 37907}, {7737, 44265}, {9300, 37904}, {10151, 42391}, {15048, 44266}, {21843, 44214}, {31400, 37946}, {31406, 37967}, {33871, 37897}, {37665, 37909}

X(47169) = orthogonal projection of X(574) on the orthic axis
X(47169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {230, 16303, 16306}, {230, 16308, 16303}, {468, 16303, 230}, {468, 16308, 16306}, {468, 16316, 16321}, {468, 16329, 16324}, {3003, 10418, 230}

X(47170) = ORTHIC AXIS INTERCEPT OF X(30)X(126)

Barycentrics 2*a^12 - 7*a^10*b^2 - 6*a^8*b^4 + 11*a^6*b^6 + 3*a^4*b^8 - 4*a^2*b^10 + b^12 - 7*a^10*c^2 + 42*a^8*b^2*c^2 - 24*a^6*b^4*c^2 - 41*a^4*b^6*c^2 + 27*a^2*b^8*c^2 - 5*b^10*c^2 - 6*a^8*c^4 - 24*a^6*b^2*c^4 + 84*a^4*b^4*c^4 - 23*a^2*b^6*c^4 - b^8*c^4 + 11*a^6*c^6 - 41*a^4*b^2*c^6 - 23*a^2*b^4*c^6 + 10*b^6*c^6 + 3*a^4*c^8 + 27*a^2*b^2*c^8 - b^4*c^8 - 4*a^2*c^10 - 5*b^2*c^10 + c^12 : :

X(47170) lies on these lines: {30, 126}, {99, 7426}, {230, 231}, {403, 2374}, {7665, 9870}, {32114, 32225}

X(47170) = {X(468),X(16316)}-harmonic conjugate of X(10418)
X(47170) = orthogonal projection of X(126) on the orthic axis

X(47171) = ORTHIC AXIS INTERCEPT OF X(30)X(620)

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

X(47171) = 3 X[23] + 5 X[7925], 3 X[186] - X[47000], X[230] - 3 X[468], 5 X[230] - 3 X[16315], X[230] + 3 X[16320], X[325] + 3 X[7426], X[325] - 3 X[46986], X[385] - 9 X[37907], X[385] - 3 X[46998], 3 X[403] - X[46982], 5 X[468] - X[16315], 3 X[468] + X[16316], 3 X[5099] + X[6781], X[6781] - 3 X[36180], X[7779] + 15 X[37760], 3 X[16315] + 5 X[16316], X[16315] + 5 X[16320], X[16316] - 3 X[16320], 3 X[36166] + X[43460], 3 X[37907] - X[46998], 3 X[44214] - X[46981]

X(47171) lies on these lines: {2, 38393}, {3, 46993}, {4, 46994}, {23, 7925}, {30, 620}, {186, 47000}, {230, 231}, {325, 3233}, {385, 37907}, {403, 46982}, {524, 32223}, {1316, 31489}, {5099, 6781}, {5475, 36156}, {6353, 23347}, {6676, 44386}, {6719, 22104}, {7779, 37760}, {7835, 36165}, {7868, 9832}, {10295, 46988}, {11799, 46987}, {15491, 34094}, {18122, 44212}, {22110, 37904}, {36166, 43460}, {44214, 46981}, {46634, 46999}

X(47171) = midpoint of X(i) and X(j) for these {i,j}: {2, 46992}, {3, 46993}, {4, 46994}, {230, 16316}, {468, 16320}, {5099, 36180}, {7426, 46986}, {10295, 46988}, {11799, 46987}, {22110, 37904}, {46634, 46999}
X(47171) = reflection of X(47239) in the Euler line
X(47171) = orthogonal projection of X(620) on the orthic axis
X(47171) = X(46993)-line conjugate of X(3)
X(47171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {230, 468, 47244}, {230, 16320, 16316}, {468, 16316, 230}

X(47172) = ORTHIC AXIS INTERCEPT OF X(30)X(648)

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

X(47172) = lies on these lines: {4, 2452}, {30, 648}, {230, 231}, {1316, 40138}, {1503, 5095}, {5667, 10295}, {6530, 9139}, {8754, 10151}, {11007, 44134}

X(47172) = reflection of X(i) in X(j) for these {i,j}: {468, 1990}, {17986, 37984}
X(47172) = orthogonal projection of X(648) on the orthic axis
X(47172) = barycentric product X(648)*X(42736)
X(47172) = barycentric quotient X(42736)/X(525)
X(47172) = {X(6530),X(17986)}-harmonic conjugate of X(37984)

X(47173) = ORTHIC AXIS INTERCEPT OF X(30)X(669)

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

X(47173) = 3 X[468] - 4 X[44451], X[850] + 3 X[9137], 3 X[858] - X[44445], 6 X[5159] - 5 X[31279], 3 X[10989] + X[31299], 2 X[23301] - 3 X[47097]

X(47173) lies on these lines: {30, 669}, {140, 1649}, {230, 231}, {351, 41079}, {512, 11064}, {850, 9137}, {858, 44445}, {3005, 31945}, {5159, 31279}, {5652, 10097}, {6563, 16387}, {6676, 11123}, {6677, 8029}, {7495, 9168}, {7499, 10190}, {7542, 8151}, {8723, 13394}, {10989, 31299}, {15328, 34291}, {23301, 47097}, {30219, 34380}, {30739, 44823}, {32204, 34002}, {37904, 45317}, {43957, 44821}, {44210, 46609}

X(47173) = reflection of X(37904) in X(45317)
X(47173) = orthogonal projection of X(669) on the orthic axis

X(47174) = ORTHIC AXIS INTERCEPT OF X(30)X(693)

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

X(47174) = 3 X[23] + X[26824], 3 X[468] - 2 X[650], 3 X[858] - 5 X[26985], 4 X[4885] - 3 X[47097], 3 X[7426] - X[17494], 5 X[26777] - 9 X[37907]

X(47174) lies on these lines: {23, 26824}, {30, 693}, {230, 231}, {858, 26985}, {1375, 4789}, {4762, 37904}, {4885, 47097}, {7426, 17494}, {26777, 37907}

X(47175) = ORTHIC AXIS INTERCEPT OF X(30)X(850)

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

X(47175) = 3 X[468] - 2 X[647], X[647] - 3 X[47004], 3 X[858] - 5 X[31072], 3 X[7426] - X[31296], 3 X[10151] - 2 X[46985], 2 X[30476] - 3 X[46989], 4 X[30476] - 3 X[47097], 3 X[37931] - 2 X[47003], 2 X[41300] - 3 X[47001]

X(47175) lies on these lines: {30, 850}, {230, 231}, {858, 31072}, {5466, 15000}, {7426, 31296}, {10151, 46985}, {12079, 36189}, {23878, 37904}, {30209, 46996}, {30476, 46989}, {33752, 37454}, {34093, 43665}, {37931, 47003}, {41300, 47001}

X(47175) = reflection of X(i) in X(j) for these {i,j}: {468, 47004}, {37904, 46995}, {47097, 46989}
X(47175) = reflection of X(47248) in the Euler line
X(47175) = orthogonal projection of X(850) on the orthic axis

X(47176) = ORTHIC AXIS INTERCEPT OF X(30)X(905)

X(47176) lies on these lines: {11, 3258}, {30, 905}, {105, 842}, {108, 1304}, {186, 1946}, {230, 231}, {513, 1495}, {2070, 22160}, {2071, 22091}, {3900, 10149}, {8672, 42654}, {14165, 44426}, {15904, 32112}, {20621, 42426}, {43460, 44429}

X(47176) = reflection of X(47199) in the Euler line
X(47176) = orthogonal projection of X(905) on the orthic axis
X(47176) = Moses-radical-circle-inverse of X(650)

X(47177) = ORTHIC AXIS INTERCEPT OF X(30)X(935)

X(47177) lies on these lines: {23, 40996}, {30, 935}, {122, 47097}, {230, 231}, {325, 30716}, {427, 2453}, {1301, 2770}, {1529, 42426}, {5099, 10151}, {6390, 7482}, {10117, 19596}

X(47177) = reflection of X(i) in X(j) for these {i,j}: {1529, 42426}, {16318, 468}
X(47177) = reflection of X(16318) in the Euler line
X(47177) = orthogonal projection of X(935) on the orthic axis

X(47178) = ORTHIC AXIS INTERCEPT OF X(30)X(1072)

X(47178) lies on these lines: {1, 858}, {23, 11809}, {30, 1072}, {230, 231}, {1068, 37777}, {5159, 29639}, {16977, 37565}, {21284, 37579}, {36152, 37978}

X(47179) = ORTHIC AXIS INTERCEPT OF X(30)X(1112)

Barycentrics (a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*(a^10*b^4 - 4*a^8*b^6 + 6*a^6*b^8 - 4*a^4*b^10 + a^2*b^12 + 2*a^10*b^2*c^2 - 2*a^8*b^4*c^2 - 5*a^6*b^6*c^2 + 7*a^4*b^8*c^2 - a^2*b^10*c^2 - b^12*c^2 + a^10*c^4 - 2*a^8*b^2*c^4 + 10*a^6*b^4*c^4 - 5*a^4*b^6*c^4 - 5*a^2*b^8*c^4 + 3*b^10*c^4 - 4*a^8*c^6 - 5*a^6*b^2*c^6 - 5*a^4*b^4*c^6 + 10*a^2*b^6*c^6 - 2*b^8*c^6 + 6*a^6*c^8 + 7*a^4*b^2*c^8 - 5*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(47179) lies on these lines: {30, 1112}, {186, 14934}, {230, 231}, {403, 2970}, {476, 19128}, {6663, 14894}, {7471, 34397}, {12052, 32428}, {16221, 39569}

X(47180) = ORTHIC AXIS INTERCEPT OF X(30)X(1180)

X(47180) lies on these lines: {23, 30435}, {30, 1180}, {39, 46517}, {230, 231}, {858, 31406}, {5359, 37936}, {9465, 37897}, {18907, 37900}, {37931, 40938}

X(47181) = ORTHIC AXIS INTERCEPT OF X(30)X(1194)

X(47181) lies on these lines: {23, 32}, {30, 1194}, {39, 858}, {230, 231}, {1180, 10989}, {1184, 2070}, {1196, 7426}, {2549, 5189}, {3051, 11649}, {3053, 21284}, {5206, 37978}, {6795, 13515}, {8585, 15355}, {15268, 15899}, {15302, 30745}, {30435, 37972}

X(47181) = orthogonal projection of X(1194) on the orthic axis
X(47181) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3003, 14580, 3291}, {16306, 16308, 3003}

X(47182) = ORTHIC AXIS INTERCEPT OF X(30)X(1196)

X(47182) lies on these lines: {23, 3053}, {30, 1196}, {39, 5159}, {111, 41336}, {186, 1611}, {230, 231}, {858, 5254}, {1184, 37980}, {1194, 47097}, {2207, 37777}, {8770, 37962}, {9745, 30745}, {15398, 32740}

X(47182) = orthogonal projection of X(1196) on the orthic axis
X(47182) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2493, 16306, 16308}, {3291, 14580, 2493}

X(47183) = ORTHIC AXIS INTERCEPT OF X(30)X(1249)

X(47183) lies on these lines: {6, 13473}, {30, 1249}, {112, 47031}, {186, 1033}, {230, 231}, {393, 10151}, {403, 33630}, {2331, 10149}, {37935, 42458}, {45141, 47097}

X(47184) = ORTHIC AXIS INTERCEPT OF X(30)X(1384)

X(47184) lies on these lines: {6, 47097}, {23, 34809}, {30, 1384}, {187, 47031}, {230, 231}, {858, 5304}, {1609, 37969}, {3163, 24855}, {5159, 7736}, {5355, 47090}, {7426, 37689}, {8573, 37980}, {10295, 46453}, {10297, 18907}, {10311, 13473}, {14930, 30745}

X(47184) = orthogonal projection of X(1384) on the orthic axis
X(47184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {230, 1990, 10418}, {230, 3018, 16317}, {230, 16303, 468}, {230, 16306, 16303}, {468, 16326, 16316}, {16317, 16318, 3018}

X(47185) = ORTHIC AXIS INTERCEPT OF X(30)X(1465)

X(47185) lies on these lines: {30, 1465}, {33, 15737}, {36, 186}, {106, 2766}, {230, 231}, {403, 1785}, {1784, 37799}, {1830, 24025}, {2752, 9088}, {5520, 20619}

X(47185) = orthogonal projection of X(1465) on the orthic axis
X(47185) = Stevanovic-circle-inverse of X(8756)

X(47186) = ORTHIC AXIS INTERCEPT OF X(30)X(1506)

X(47186) lies on these lines: {6, 32218}, {23, 3815}, {30, 1506}, {39, 25338}, {187, 22249}, {230, 231}, {858, 3055}, {2070, 2548}, {5189, 31489}, {5305, 10096}, {5306, 37907}, {5899, 31467}, {7426, 9300}, {7575, 7745}, {7737, 37958}, {7738, 46451}, {7748, 11563}, {7749, 44234}, {9609, 37973}, {13881, 37943}, {31401, 37924}

X(47186) = {X(468),X(16308)}-harmonic conjugate of X(230)
X(47186) = orthogonal projection of X(1506) on the orthic axis

X(47187) = ORTHIC AXIS INTERCEPT OF X(30)X(1560)

X(47187) lies on these lines: {2, 5523}, {4, 9745}, {25, 7737}, {30, 1560}, {111, 403}, {112, 7426}, {186, 5913}, {230, 231}, {1503, 35901}, {2549, 5094}, {3162, 6353}, {6677, 40938}, {6791, 44102}, {7665, 15014}, {9475, 44892}, {10018, 39576}, {13854, 21448}, {15262, 40132}, {15341, 46128}, {21213, 40326}, {26255, 41370}, {32269, 35325}

X(47187) = X(9084)-Ceva conjugate of X(25)
X(47187) = orthogonal projection of X(1560) on the orthic axis
X(47187) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {232, 6103, 16303}, {232, 10418, 468}, {468, 44467, 230}

X(47188) = ORTHIC AXIS INTERCEPT OF X(30)X(1576)

X(47188) lies on these lines: {5, 15928}, {30, 1576}, {113, 1503}, {230, 231}, {1300, 6530}, {5502, 14995}, {7575, 14703}, {10151, 34981}, {10257, 34990}

X(47189) = ORTHIC AXIS INTERCEPT OF X(30)X(1609)

X(47189) lies on these lines: {6, 10257}, {30, 1609}, {230, 231}, {571, 47090}, {2072, 8573}, {7735, 16387}, {9722, 10151}, {18573, 34002}, {38872, 41336}, {44452, 46262}

X(47189) = {X(16306),X(16328)}-harmonic conjugate of X(16303)
X(47189) = orthogonal projection of X(1609) on the orthic axis

X(47190) = ORTHIC AXIS INTERCEPT OF X(30)X(1649)

Barycentrics (b^2 - c^2)*(22*a^10 - 35*a^8*b^2 - 5*a^6*b^4 + 31*a^4*b^6 - 17*a^2*b^8 + 4*b^10 - 35*a^8*c^2 + 88*a^6*b^2*c^2 - 48*a^4*b^4*c^2 - 2*a^2*b^6*c^2 + b^8*c^2 - 5*a^6*c^4 - 48*a^4*b^2*c^4 + 42*a^2*b^4*c^4 - 5*b^6*c^4 + 31*a^4*c^6 - 2*a^2*b^2*c^6 - 5*b^4*c^6 - 17*a^2*c^8 + b^2*c^8 + 4*c^10) : :

X(47190) lies on these lines: {30, 1649}, {230, 231}, {669, 18571}, {690, 35266}, {3906, 47001}, {5652, 36180}, {7426, 9168}, {10190, 37904}, {37907, 44010}

X(47190) = midpoint of X(7426) and X(9168)
X(47190) = orthogonal projection of X(1649) on the orthic axis

X(47191) = ORTHIC AXIS INTERCEPT OF X(30)X(1785)

X(47191) lies on these lines: {11, 403}, {30, 1785}, {105, 37962}, {108, 186}, {230, 231}, {1877, 10151}, {10149, 15500}, {14667, 37917}, {15253, 37942}

X(47192) = ORTHIC AXIS INTERCEPT OF X(30)X(1879)

X(47192) lies on these lines: {30, 1879}, {186, 2165}, {230, 231}, {403, 571}, {570, 44452}, {577, 2072}, {2070, 8553}, {21843, 45171}, {37951, 41758}

X(47193) = X(230)-LINE CONJUGATE OF X(231)

X(47193) lies on these lines: {3, 1510}, {230, 231}, {512, 44816}, {526, 34952}, {924, 5926}, {3542, 23290}, {6140, 6368}

X(47193) = crossdifference of every pair of points on line {3, 231}
X(47193) = X(i)-line conjugate of X(j) for these (i,j): {230, 231}, {1510, 3}

X(47194) = X(230)-LINE CONJUGATE OF X(232)

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

X(47194) lies on these lines: {3, 525}, {230, 231}, {235, 44705}, {520, 3265}, {684, 8057}, {1499, 9409}, {1513, 30735}, {2394, 35485}, {3566, 42658}, {3800, 15451}, {5486, 14380}, {8675, 35371}, {9007, 14417}, {9033, 22264}, {14999, 43754}, {30474, 46336}, {32640, 46619}

X(47194) = reflection of X(i) in X(j) for these {i,j}: {2501, 6130}, {16230, 6587}
X(47194) = X(i)-Ceva conjugate of X(j) for these (i,j): {7612, 125}, {19222, 34980}, {35278, 6776}, {42313, 3269}
X(47194) = crosspoint of X(6776) and X(35278)
X(47194) = crossdifference of every pair of points on line {3, 232}
X(47194) = X(i)-line conjugate of X(j) for these (i,j): {230, 232}, {525, 3}
X(47194) = X(i)-isoconjugate of X(j) for these (i,j): {162, 40801}, {823, 40799}, {1096, 35575}, {24019, 40802}
X(47194) = barycentric product X(i)*X(j) for these {i,j}: {394, 30735}, {520, 40814}, {523, 37188}, {525, 6776}, {3265, 7735}, {4008, 24018}, {4143, 6620}, {15412, 42353}, {15526, 35278}, {39201, 40822}
X(47194) = barycentric quotient X(i)/X(j) for these {i,j}: {287, 41074}, {394, 35575}, {520, 40802}, {647, 40801}, {3265, 40824}, {4008, 823}, {6620, 6529}, {6776, 648}, {7735, 107}, {30735, 2052}, {35278, 23582}, {37188, 99}, {39201, 40799}, {40814, 6528}, {40825, 32713}, {42353, 14570}, {43976, 15352}

X(47195) = X(230)-LINE CONJUGATE OF X(2501)

X(47195) lies on these lines: {1, 7105}, {3, 49}, {125, 44436}, {131, 32123}, {230, 231}, {235, 6747}, {254, 1093}, {421, 1632}, {454, 15316}, {852, 20975}, {1075, 3147}, {1495, 13558}, {1624, 44084}, {1899, 6509}, {2351, 9306}, {2393, 44886}, {6090, 44200}, {7669, 15139}, {9744, 46336}, {10608, 35259}, {11799, 21667}, {23181, 34382}, {43754, 43756}

X(47195) = crosspoint of X(i) and X(j) for these (i,j): {3, 1942}, {7040, 37142}
X(47195) = crosssum of X(i) and X(j) for these (i,j): {4, 450}, {851, 3157}, {32320, 35236}
X(47195) = crossdifference of every pair of points on line {3, 2501}
X(47195) = X(i)-line conjugate of X(j) for these (i,j): {49, 3}, {230, 2501}

X(47196) = {X(230), X(231)-HARMONIC CONJUGATE OF X(232)

X(47197) = {X(230), X(231)-HARMONIC CONJUGATE OF X(468)

X(47197) lies on these lines: {230, 231}, {1656, 7735}, {2165, 10301}, {7574, 43291}

X(47198) = {X(230), X(468)-HARMONIC CONJUGATE OF X(647)

X(47198) lies on these lines: {2, 14966}, {112, 44893}, {115, 237}, {187, 36189}, {230, 231}, {3231, 40601}, {3289, 41586}, {7746, 44895}, {7749, 15000}, {13410, 41939}, {37637, 44889}, {44529, 44886}, {44533, 44890}

X(47199) = STEVANOVIC-CIRCLE-INVERSE OF X(647)

X(47199) lies on these lines: {30, 45664}, {98, 2752}, {107, 2766}, {125, 513}, {230, 231}, {905, 44898}, {1325, 4391}, {1946, 2074}, {4036, 20989}, {32119, 32126}

X(47199) = midpoint of X(1325) and X(4391)
X(47199) = reflection of X(i) in X(j) for these {i,j}: {905, 44898}, {47176, 468}
X(47199) = reflection of X(47176) in the Euler line
X(47199) = Stevanovic-circle-inverse of X(647)
X(47199) = orthogonal projection of X(45664) on the orthic axis
X(47199) = Dao-Moses-Telv-circle-inverse of X(47227)
X(47199) = {X(24007),X(24008)}-harmonic conjugate of X(47227)

X(47200) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(230)

X(47200) lies on these lines: {2, 98}, {4, 35278}, {25, 132}, {107, 3563}, {112, 36191}, {115, 1316}, {187, 5112}, {230, 231}, {325, 3292}, {351, 31953}, {373, 7792}, {385, 41586}, {427, 39071}, {543, 45662}, {620, 9155}, {868, 2794}, {1495, 1513}, {1627, 13195}, {1632, 8754}, {1634, 46184}, {1649, 42738}, {1974, 41770}, {1989, 2453}, {1995, 3425}, {2450, 42671}, {2452, 3163}, {2770, 23969}, {2777, 7422}, {2854, 24975}, {2972, 34841}, {2974, 34844}, {3014, 11284}, {3233, 36170}, {3258, 36166}, {4226, 23698}, {4232, 9752}, {4563, 46236}, {5094, 9756}, {5181, 40879}, {5650, 37450}, {5915, 14120}, {6090, 7778}, {6108, 32461}, {6109, 32460}, {6593, 18122}, {6676, 46832}, {6680, 37338}, {6791, 6793}, {7426, 30685}, {7471, 16188}, {7495, 15819}, {7612, 16080}, {7668, 40559}, {8770, 39645}, {9168, 14223}, {9172, 14995}, {9214, 44556}, {9512, 15526}, {9753, 34417}, {11007, 12042}, {11056, 46318}, {11623, 15000}, {13394, 37451}, {14361, 38282}, {14559, 34310}, {14651, 41254}, {14693, 44215}, {14769, 37990}, {15576, 37453}, {18020, 40428}, {20398, 46512}, {20975, 23583}, {20998, 44534}, {21637, 45198}, {22329, 32225}, {24987, 37047}, {34229, 35520}, {34473, 35922}, {35259, 37071}, {35268, 37182}, {36163, 38749}, {36181, 39809}, {41626, 41721}

X(47200) = midpoint of X(i) and X(j) for these {i,j}: {868, 5191}, {3018, 41359}
X(47200) = Dao-Moses-Telv-circle-inverse of X(230)
X(47200) = orthoptic-circle-of-Steiner-inellipse-inverse of X(11005)
X(47200) = complement of the isotomic conjugate of X(2857)
X(47200) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 38975}, {2857, 2887}
X(47200) = X(2)-Ceva conjugate of X(38975)
X(47200) = crosspoint of X(2) and X(2857)
X(47200) = crosssum of X(6) and X(2871)
X(47200) = crossdifference of every pair of points on line {3, 3569}
X(47200) = barycentric product X(2857)*X(38975)
X(47200) = Thomson-Gibert-Moses-hyperbola-inverse of X(114)
X(47200) = PU(4)-harmonic conjugate of X(16230)
X(47200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 98, 125}, {2, 110, 114}, {2, 3448, 30789}, {115, 35282, 1316}, {468, 16315, 11657}, {5972, 6036, 2}, {6103, 10418, 1637}, {6130, 6132, 16230}, {10418, 45687, 41360}, {24007, 24008, 230}

X(47201) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(231)

X(47201) lies on these lines: {4, 11587}, {17, 8839}, {18, 8837}, {96, 10018}, {98, 7495}, {107, 2383}, {110, 34310}, {125, 128}, {230, 231}, {3471, 45195}, {6104, 6106}, {6105, 6107}, {12099, 40559}, {15912, 18282}, {16240, 21841}, {32225, 44347}, {34218, 36190}

X(47201) = Dao-Moses-Telv-circle-inverse of X(231)
X(47201) = {X(24007),X(24008)}-harmonic conjugate of X(231)

X(47202) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(232)

X(47202) is the diagonal crosspoint of the cyclic quadrilateral X(98)X(107)X(125)X(132). (Randy Hutson, April 16, 2022)

Let (O₁) be the circle internally tangent to the nine-point circle at X(125) and to the circumcircle at X(107). Let (O₂) be the circle externally tangent to the nine-point circle at X(132) and to the circumcircle at X(98). Then X(47202) is the exsimilicenter of circles (O₁) and (O₂). The insimilicenter is X(2). (Randy Hutson, April 16, 2022)

Let (O₃) be the circle externally tangent to the nine-point circle at X(125) and to the circumcircle at X(98). Let (O₄) be the circle internally tangent to the nine-point circle at X(132) and to the circumcircle at X(107). Then X(47202) is the insimilicenter of circles (O₃) and (O₄). The exsimilicenter of X(4). (Randy Hutson, April 16, 2022)

X(47202) lies on these lines: {2, 1972}, {25, 98}, {51, 125}, {112, 1316}, {230, 231}, {262, 5094}, {385, 450}, {421, 44089}, {428, 8902}, {458, 10796}, {648, 36207}, {694, 13854}, {852, 30737}, {1235, 37338}, {2409, 5191}, {2452, 8749}, {2782, 4230}, {5112, 5523}, {5943, 45123}, {5976, 6331}, {6070, 42426}, {7473, 46633}, {7480, 38552}, {9155, 41676}, {9419, 35325}, {9512, 32713}, {9755, 37070}, {10184, 37990}, {10301, 16240}, {10313, 41202}, {12042, 36176}, {13558, 21213}, {20975, 46151}, {26869, 37074}, {44096, 44375}

X(47202) = X(2)-Ceva conjugate of X(38974)
X(47202) = PU(4)-harmonic conjugate of X(6130)
X(47202) = Dao-Moses-Telv-circle-inverse of X(232)
X(47202) = barycentric product X(232)*X(16083)
X(47202) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 35360, 2967}, {25, 2970, 12131}, {98, 107, 25}, {125, 132, 427}, {1637, 6103, 44467}, {13558, 34131, 21213}, {24007, 24008, 232}

X(47203) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(650)

X(47203) is the insimilicenter of circles {{X(11),X(105),X(108),X(20621)}} and {{X(98),X(107),X(125),X(132)}}. The exsimilicenter is X(47212). (Randy Hutson, April 16, 2022)

X(47203) lies on these lines: {11, 125}, {21, 2798}, {98, 105}, {107, 108}, {132, 20621}, {230, 231}, {442, 2806}, {1937, 2006}, {1946, 17924}, {2803, 36035}, {3651, 9520}, {3835, 6003}, {8062, 30864}, {13558, 14667}, {15904, 32119}, {26013, 35057}

X(47203) = complement of the isotomic conjugate of X(2864)
X(47203) = X(2864)-complementary conjugate of X(2887)
X(47203) = crosspoint of X(2) and X(2864)
X(47203) = crosssum of X(6) and X(2878)
X(47203) = Dao-Moses-Telv-circle-inverse of X(650)
X(47203) = midpoint of Feuerbach hyperbola intercepts of the orthic axis
X(47203) = PU(4)-harmonic conjugate of X(47212)
X(47203) = barycentric product X(i)*X(j) for these {i,j}: {448, 523}, {650, 16090}, {1577, 23692}
X(47203) = barycentric quotient X(i)/X(j) for these {i,j}: {448, 99}, {16090, 4554}, {23692, 662}
X(47203) = {X(24007),X(24008)}-harmonic conjugate of X(650)

X(47204) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(1990)

X(47204) is the centroid of the intersections of the trilinear polar of X(4) (the orthic axis) and the cevians of X(4) (the altitudes). (Randy Hutson, April 16, 2022)

Let A_B, A_C, B_C, B_A, C_A, C_B be the points on the Montesdeoca conic as defined at X(5702). Let A' be the intersection of tangents to the Montesdeoca conic at A_B and A_C, and define B' and C' cyclically. A', B', C' are collinear on the orthic axis and perspective with ABC at X(4). X(47204) is the centroid of A'B'C'. A' is also the polar-circle-inverse of the A-vertex of the orthocentroidal triangle, and cyclically for B', C'. (Randy Hutson, April 16, 2022)

X(47204) lies on these lines: {2, 42830}, {4, 74}, {98, 4232}, {132, 5094}, {136, 18384}, {230, 231}, {297, 32225}, {340, 450}, {403, 32417}, {459, 31383}, {524, 15144}, {541, 11251}, {542, 4240}, {648, 5642}, {1650, 9530}, {2972, 6716}, {3515, 13558}, {5651, 44134}, {5972, 14920}, {6070, 17986}, {6110, 32461}, {6111, 32460}, {6531, 6791}, {6699, 34334}, {6793, 40138}, {9880, 37174}, {10018, 14363}, {11331, 39604}, {16244, 21841}, {23583, 44891}, {32223, 46106}, {44228, 44569}

X(47204) = crossdifference of every pair of points on line {3, 1636}
X(47204) = barycentric product X(i)*X(j) for these {i,j}: {648, 42733}, {1651, 16080}, {1990, 16076}
X(47204) = Dao-Moses-Telv-circle-inverse of X(1990)
X(47204) = X(i)-isoconjugate of X(j) for these (i,j): {16075, 35200}, {36034, 47071}
X(47204) = barycentric quotient X(i)/X(j) for these {i,j}: {1637, 47071}, {1651, 11064}, {1990, 16075}, {8749, 41433}, {42733, 525}
X(47204) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 107, 16240}, {4, 16080, 125}, {107, 16080, 4}, {125, 16240, 4}, {24007, 24008, 1990}

X(47205) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(2485)

X(47205) lies on these lines: {2, 42665}, {98, 2373}, {107, 1289}, {125, 127}, {230, 231}, {427, 2881}, {686, 879}, {804, 42659}, {3265, 44205}, {3268, 44813}, {5489, 14420}, {9148, 9409}, {13558, 21525}, {31174, 42658}, {42736, 45693}

X(47205) = Dao-Moses-Telv-circle-inverse of X(2485)
X(47205) = X(163)-isoconjugate of X(46239)
X(47205) = crossdifference of every pair of points on line {3, 23584}
X(47205) = barycentric product X(i)*X(j) for these {i,j}: {523, 15013}, {850, 46243}, {2485, 16097}
X(47205) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 46239}, {15013, 99}, {46243, 110}
X(47205) = {X(24007),X(24008)}-harmonic conjugate of X(2485)

X(47206) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(2489)

X(47206) lies on these lines: {2, 17994}, {4, 9148}, {25, 804}, {98, 2374}, {99, 107}, {125, 5139}, {126, 132}, {230, 231}, {351, 6353}, {427, 45689}, {526, 12828}, {1596, 2780}, {4232, 9147}, {6676, 44817}, {6720, 34844}, {9023, 41585}, {9126, 37935}, {11615, 21841}, {14420, 44427}, {16229, 31174}, {32114, 32119}

X(47206) = Dao-Moses-Telv-circle-inverse of X(2489)
X(47206) = polar conjugate of the isotomic conjugate of X(9035)
X(47206) = X(i)-isoconjugate of X(j) for these (i,j): {63, 9091}, {4592, 16098}
X(47206) = barycentric product X(i)*X(j) for these {i,j}: {4, 9035}, {523, 15014}, {865, 6331}, {2489, 16084}
X(47206) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 9091}, {865, 647}, {2489, 16098}, {9035, 69}, {15014, 99}
X(47206) = PU(4)-harmonic conjugate of X(47211)
X(47206) = {X(24007),X(24008)}-harmonic conjugate of X(2489)

X(47207) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(2493)

X(47207) lies on these lines: {2, 16186}, {23, 94}, {32, 1316}, {51, 36183}, {107, 37777}, {125, 511}, {132, 16221}, {230, 231}, {385, 9514}, {403, 34854}, {1513, 6070}, {2452, 5158}, {3292, 14999}, {6792, 46124}, {11005, 41724}, {11257, 37918}, {13558, 21284}, {14221, 37803}, {16092, 32225}, {22353, 45848}, {34310, 46155}, {37911, 45847}, {37991, 40814}

X(47207) = Dao-Moses-Telv-circle-inverse of X(2493)
X(47207) = PU(4)-harmonic conjugate of Dao-Moses-Telv-circle-inverse of X(47230)
X(47207) = {X(24007),X(24008)}-harmonic conjugate of X(2493)

X(47208) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(3003)

X(47208) lies on these lines: {3, 36789}, {5, 113}, {24, 107}, {98, 1302}, {230, 231}, {338, 44889}, {1075, 7505}, {1624, 2970}, {1968, 27359}, {2781, 3134}, {3124, 3767}, {6793, 40130}, {7575, 16168}, {7668, 12099}, {8901, 11746}, {12106, 14254}, {14264, 16080}, {15363, 33927}, {16240, 37458}, {18883, 34310}

X(47208) = midpoint of X(15363) and X(33927)
X(47208) = Dao-Moses-Telv-circle-inverse of X(3003)
X(47208) = {X(24007),X(24008)}-harmonic conjugate of X(3003)

X(47209) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(3011)

X(47209) lies on these lines: {2, 1762}, {10, 98}, {107, 9085}, {125, 1213}, {132, 1842}, {230, 231}, {2173, 8229}, {2247, 2792}, {2607, 5988}, {2822, 7433}, {3006, 22356}, {3756, 6793}, {3924, 7735}

X(47209) = Dao-Moses-Telv-circle-inverse of X(3011)
X(47209) = crossdifference of every pair of points on line {3, 42662}
X(47209) = {X(24007),X(24008)}-harmonic conjugate of X(3011)

X(47210) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(3064)

X(47210) lies on these lines: {4, 30574}, {29, 2785}, {92, 4458}, {107, 109}, {125, 20620}, {230, 231}, {281, 4088}, {1844, 2774}, {4142, 46110}, {4707, 39585}, {6197, 42657}, {7498, 14432}

X(47210) = crossdifference of every pair of points on line {3, 43694}
X(47210) = Dao-Moses-Telv-circle-inverse of X(3064)
X(47210) = X(662)-isoconjugate of X(43694)
X(47210) = barycentric product X(i)*X(j) for these {i,j}: {523, 44331}, {1577, 14192}, {3064, 16091}
X(47210) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 43694}, {14192, 662}, {44331, 99}
X(47210) = {X(24007),X(24008)}-harmonic conjugate of X(3064)

X(47211) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(3291)

X(47211) lies on these lines: {2, 16098}, {3, 76}, {25, 1632}, {107, 2374}, {125, 126}, {132, 235}, {157, 13558}, {230, 231}, {2453, 44533}, {2790, 7418}, {3164, 7493}, {5968, 9307}, {6353, 41678}, {7735, 9475}, {13468, 44210}, {14908, 40856}, {16990, 46336}, {32119, 32121}, {34338, 41770}, {36157, 44468}, {40102, 43084}

X(47211) = complement of the isotomic conjugate of X(2868)
X(47211) = X(2868)-complementary conjugate of X(2887)
X(47211) = crosspoint of X(2) and X(2868)
X(47211) = crosssum of X(6) and X(2882)
X(47211) = crossdifference of every pair of points on line {3, 2491}
X(47211) = Dao-Moses-Telv-circle-inverse of X(3291)
X(47211) = PU(4)-harmonic conjugate of X(47206)
X(47211) = {X(24007),X(24008)}-harmonic conjugate of X(3291)

X(47212) = DAO-MOSES-TELV-CIRCLE-INVERSE OF X(5089)

X(47212) is the exsimilicenter of circles {{X(11),X(105),X(108),X(20621)}} and {{X(98),X(107),X(125),X(132)}}. The insimilicenter is X(47203). (Randy Hutson, April 16, 2022)

X(47212) lies on these lines: {11, 132}, {98, 108}, {105, 107}, {125, 15904}, {230, 231}, {243, 1447}, {811, 5977}, {1281, 36797}, {2795, 4238}, {14667, 34131}

X(47212) = Dao-Moses-Telv-circle-inverse of X(5089)
X(47212) = barycentric product X(5089)*X(16087)
X(47212) = PU(4)-harmonic conjugate of X(47203)
X(47212) = {X(24007),X(24008)}-harmonic conjugate of X(5089)

X(47213) = MOSES-RADICAL-CIRCLE-INVERSE OF X(230)

X(47213) lies on these lines: {23, 110}, {25, 5502}, {30, 36212}, {39, 1316}, {114, 858}, {136, 37981}, {184, 37930}, {230, 231}, {566, 2453}, {1304, 3563}, {1555, 18325}, {1995, 18114}, {3260, 37804}, {3917, 15915}, {5159, 44436}, {5189, 43460}, {7418, 16186}, {11284, 14685}, {14165, 44145}, {15302, 34235}, {18883, 43087}, {19165, 21284}, {34854, 37937}, {37918, 38528}

X(47213) = Moses-radical-circle-inverse of X(230)
X(47213) = crossdifference of every pair of points on line {3, 1640}
X(47213) = orthogonal projection of X(36212) on the orthic axis
X(47213) = PU(4)-harmonic conjugate of X(47221)

X(47214) = MOSES-RADICAL-CIRCLE-INVERSE OF X(1637)

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

X(47214) lies on these lines: {23, 684}, {30, 8552}, {186, 9409}, {230, 231}, {402, 22104}, {525, 46817}, {526, 1495}, {842, 7418}, {1304, 5502}, {2797, 11799}, {3134, 3258}, {5099, 38974}, {7575, 9517}, {8675, 42654}, {9033, 32223}, {12112, 42656}, {18571, 44810}, {38613, 41167}, {44214, 44818}

X(47214) = midpoint of X(i) and X(j) for these {i,j}: {23, 684}, {1495, 32112}
X(47214) = reflection of X(i) in X(j) for these {i,j}: {6130, 468}, {44810, 18571}
X(47214) = reflection of X(6130) in the Euler line
X(47214) = Moses-radical-circle-inverse of X(1637)
X(47214) = X(36034)-complementary conjugate of X(16188)
X(47214) = crosspoint of X(842) and X(1304)
X(47214) = crosssum of X(542) and X(9033)
X(47214) = crossdifference of every pair of points on line {3, 23967}
X(47214) = orthogonal projection of X(8552) on the orthic axis
X(47214) = PU(4)-harmonic conjugate of X(47223)
X(47214) = {X(232),X(647)}-harmonic conjugate of X(2492)

X(47215) = MOSES-RADICAL-CIRCLE-INVERSE OF X(1990)

X(47215) lies on these lines: {25, 14685}, {30, 44436}, {74, 186}, {133, 403}, {230, 231}, {250, 3292}, {450, 30716}, {457, 37496}, {511, 7480}, {842, 9064}, {1138, 14165}, {1316, 33843}, {5651, 36176}, {6509, 37926}, {9717, 23347}, {14896, 35717}, {16186, 35908}, {18870, 46831}, {33885, 36191}, {37934, 44437}

X(47215) = Moses-radical-circle-inverse of X(1990)
X(47215) = crossdifference of every pair of points on line {3, 14401}
X(47215) = orthogonal projection of X(44436) on the orthic axis
X(47215) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {186, 1304, 1495}, {468, 47146, 47152}

X(47216) = MOSES-RADICAL-CIRCLE-INVERSE OF X(2485)

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

X(47216) lies on these lines: {30, 3265}, {127, 3258}, {230, 231}, {525, 1495}, {669, 39857}, {826, 42654}, {842, 2373}, {1289, 1304}, {1499, 10990}, {7426, 33294}, {7473, 9514}, {8057, 41586}, {11550, 38240}, {23616, 31383}, {23964, 46619}, {30474, 43460}

X(47216) = Moses-radical-circle-inverse of X(2485)
X(47216) = crossdifference of every pair of points on line {3, 46128}
X(47216) = orthogonal projection of X(3265) on the orthic axis

X(47217) = MOSES-RADICAL-CIRCLE-INVERSE OF X(2489)

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

X(47217) = 3 X[468] - X[2501], 2 X[2501] - 3 X[41357], X[6563] + 3 X[7426], X[47173] - 9 X[47190]

X(47217) lies on these lines: {4, 1649}, {25, 10190}, {99, 1304}, {126, 42426}, {186, 669}, {230, 231}, {351, 44427}, {420, 17414}, {525, 42654}, {842, 2374}, {1495, 3566}, {1499, 37934}, {3258, 5139}, {4232, 9168}, {6353, 11123}, {6563, 7426}, {7665, 33294}, {8029, 38282}, {9007, 32112}, {10278, 37453}, {21841, 32204}, {39495, 44080}

X(47217) = midpoint of X(47122) and X(47175)
X(47217) = reflection of X(41357) in X(468)
X(47217) = reflection of X(41357) in the Euler line
X(47217) = Moses-radical-circle-inverse of X(2489)

X(47218) = MOSES-RADICAL-CIRCLE-INVERSE OF X(2491)

X(47218) lies on these lines: {30, 24284}, {230, 231}, {804, 1495}, {1304, 22456}, {2679, 3258}, {2799, 32223}, {5112, 32120}, {9148, 43460}, {14165, 17994}, {23878, 42654}, {32112, 32225}, {32224, 35522}

X(47218) = midpoint of X(i) and X(j) for these {i,j}: {5112, 32120}, {32224, 35522}
X(47218) = Moses-radical-circle-inverse of X(2491)
X(47218) = orthogonal projection of X(24284) on the orthic axis

X(47219) = MOSES-RADICAL-CIRCLE-INVERSE OF X(2492)

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

X(47219) lies on these lines: {23, 3268}, {30, 14417}, {186, 42659}, {230, 231}, {525, 35266}, {690, 1495}, {842, 2770}, {868, 1649}, {935, 1304}, {2453, 14685}, {2799, 7426}, {3906, 42654}, {9003, 32112}, {9033, 32225}, {9191, 43460}, {9979, 37907}, {10190, 20403}, {18579, 44202}

X(47219) = midpoint of X(23) and X(3268)
X(47219) = reflection of X(i) in X(j) for these {i,j}: {1637, 468}, {9125, 47190}, {44202, 18579}
X(47219) = reflection of X(1637) in the Euler line
X(47219) = Moses-radical-circle-inverse of X(2492)
X(47219) = orthogonal projection of X(14417) on the orthic axis

X(47220) = MOSES-RADICAL-CIRCLE-INVERSE OF X(2493)

X(47220) lies on these lines: {2, 476}, {23, 43460}, {25, 16221}, {98, 6070}, {114, 7471}, {125, 1550}, {230, 231}, {428, 34145}, {542, 1495}, {935, 36191}, {1304, 6353}, {1316, 5099}, {1555, 11799}, {2715, 2770}, {5642, 14999}, {6114, 32461}, {6115, 32460}, {11007, 38613}, {14559, 32227}, {16619, 44437}, {17511, 30789}, {34841, 37985}, {35088, 36825}, {35922, 38704}

X(47220) = Moses-radical-circle-inverse of X(2493)
X(47220) = PU(4)-harmonic conjugate of Moses-radical-circle-inverse of X(47230)
X(47220) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 476, 16188}, {2, 842, 3258}, {468, 16316, 16319}, {468, 47146, 230}, {16760, 22104, 2}

X(47221) = MOSES-RADICAL-CIRCLE-INVERSE OF X(2501)

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

X(47221) lies on these lines: {25, 34291}, {110, 250}, {114, 7630}, {136, 3258}, {186, 512}, {230, 231}, {378, 44814}, {403, 16229}, {842, 3563}, {924, 1495}, {3542, 46371}, {6140, 44427}, {7505, 23105}, {8574, 39575}, {8675, 44102}, {14618, 37943}, {18403, 44918}, {36176, 41167}

X(47221) = reflection of X(i) in X(j) for these {i,j}: {16229, 403}, {18403, 44918}
X(47221) = Moses-radical-circle-inverse of X(2501)
X(47221) = crosssum of X(523) and X(5877)
X(47221) = PU(4)-harmonic conjugate of X(47213)
X(47221) = barycentric product X(246)*X(648)
X(47221) = barycentric quotient X(246)/X(525)

X(47222) = MOSES-RADICAL-CIRCLE-INVERSE OF X(3018)

X(47222) lies on these lines: {5, 3258}, {24, 1304}, {230, 231}, {842, 1995}, {1495, 5663}, {5651, 38613}, {7471, 34834}, {10297, 44436}, {12106, 14670}

X(47223) = MOSES-RADICAL-CIRCLE-INVERSE OF X(6103)

X(47223) lies on these lines: {2, 38552}, {25, 842}, {186, 5191}, {230, 231}, {427, 3258}, {935, 1316}, {1495, 2781}, {2967, 7480}, {5099, 33842}, {7473, 46634}, {7482, 9155}, {36176, 38613}, {44436, 47097}

X(47223) = Moses-radical-circle-inverse of X(6103)
X(47223) = PU(4)-harmonic conjugate of X(47214)
X(47223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {232, 647, 44467}, {842, 1304, 25}, {3258, 42426, 427}, {16319, 47150, 468}

X(47224) = MOSES-RADICAL-CIRCLE-INVERSE OF X(6586)

X(47224) lies on these lines: {30, 4025}, {116, 3258}, {186, 22388}, {230, 231}, {514, 1495}, {675, 842}, {1304, 26705}, {2070, 23093}, {43460, 44435}

X(47224) = Moses-radical-circle-inverse of X(6586)
X(47224) = orthogonal projection of X(4025) on the orthic axis

X(47225) = MOSES-RADICAL-CIRCLE-INVERSE OF X(6587)

X(47225) lies on these lines: {122, 3258}, {186, 42658}, {230, 231}, {512, 21663}, {520, 1495}, {842, 1297}, {924, 3447}, {1301, 1304}, {2070, 8673}, {8057, 32269}, {8675, 18374}, {30211, 41615}

X(47225) = reflection of X(42658) in X(186)
X(47225) = Moses-radical-circle-inverse of X(6587)
X(47225) = crossdifference of every pair of points on line {3, 6794}
X(47225) = PU(4)-harmonic conjugate of Moses-radical-circle-inverse of X(16318)

X(47226) = MOSES-PARRY-CIRCLE-INVERSE OF X(231)

X(47226) lies on these lines: {6, 3200}, {50, 45737}, {112, 2383}, {115, 128}, {216, 1989}, {230, 231}, {571, 2079}, {3163, 39018}, {5421, 6128}, {8882, 14586}, {10314, 44533}, {14806, 34866}

X(47226) = Moses-Parry-circle-inverse of X(231)
X(47226) = complement of the isotomic conjugate of X(14979)
X(47226) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 45180}, {14979, 2887}
X(47226) = X(2)-Ceva conjugate of X(45180)
X(47226) = crosspoint of X(2) and X(14979)
X(47226) = crosssum of X(6) and X(32423)
X(47226) = crossdifference of every pair of points on line {3, 44809}
X(47226) = barycentric product X(14979)*X(45180)
X(47226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {230, 47167, 3003}, {231, 11062, 3003}, {8105, 8106, 231}

X(47227) = MOSES-PARRY-CIRCLE-INVERSE OF X(650)

X(47227) is the insimilicenter the Moses-Parry circle and circle {{X(11),X(105),X(108),X(20621)}}; the exsimilicenter is X(47232). (Randy Hutson, April 16, 2022)

X(47227) lies on these lines: {6, 14399}, {11, 115}, {81, 9034}, {105, 111}, {108, 112}, {230, 231}, {513, 21758}, {654, 1769}, {661, 2605}, {905, 4823}, {1560, 20621}, {1639, 17724}, {2079, 14667}, {2509, 4944}, {2522, 4820}, {2610, 8674}, {2850, 40584}, {2878, 40952}, {3163, 23980}, {3569, 15904}, {3669, 29126}, {3700, 16612}, {3960, 4927}, {4120, 24506}, {4220, 9523}, {4221, 9531}, {4885, 16757}, {4931, 46381}, {13006, 15252}, {14910, 32655}, {17439, 46393}

X(47227) = Moses-Parry-circle-inverse of X(650)
X(47227) = complement of the isotomic conjugate of X(1290)
X(47227) = polar conjugate of the isotomic conjugate of X(2850)
X(47227) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 5520}, {560, 35090}, {1290, 2887}, {2206, 38982}, {35156, 21235}
X(47227) = X(2)-Ceva conjugate of X(5520)
X(47227) = X(i)-isoconjugate of X(j) for these (i,j): {63, 2766}, {190, 34442}, {662, 10693}
X(47227) = crosspoint of X(i) and X(j) for these (i,j): {2, 1290}, {108, 2006}
X(47227) = crosssum of X(i) and X(j) for these (i,j): {6, 8674}, {521, 2323}
X(47227) = crossdifference of every pair of points on line {3, 191}
X(47227) = Dao-Moses-Telv-circle-inverse of X(47199)
X(47227) = PU(4)-harmonic conjugate of X(47232)
X(47227) = barycentric product X(i)*X(j) for these {i,j}: {1, 21180}, {4, 2850}, {513, 5080}, {514, 16548}, {523, 1325}, {649, 20920}, {650, 37798}, {693, 20989}, {1019, 21066}, {1290, 5520}, {12826, 15328}, {17924, 22123}
X(47227) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 2766}, {512, 10693}, {667, 34442}, {1325, 99}, {2850, 69}, {5080, 668}, {16548, 190}, {20920, 1978}, {20989, 100}, {21066, 4033}, {21180, 75}, {22123, 1332}, {37798, 4554}, {40584, 4585}
X(47227) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6588, 6591, 650}, {8105, 8106, 650}, {24007, 24008, 47199}

X(47228) = MOSES-PARRY-CIRCLE-INVERSE OF X(1990)

X(47228) lies on these lines: {6, 74}, {25, 9142}, {50, 15262}, {53, 115}, {111, 9064}, {216, 549}, {230, 231}, {338, 41678}, {393, 1989}, {566, 40138}, {648, 34990}, {1033, 8746}, {1249, 46262}, {1560, 3815}, {1609, 14910}, {2854, 4230}, {2965, 36423}, {2967, 46127}, {3284, 37950}, {5191, 23347}, {5702, 13337}, {6128, 6748}, {6749, 18907}, {7669, 32713}, {8791, 34288}, {11079, 23964}, {18487, 44266}, {18573, 39575}, {30685, 37766}, {32663, 32712}, {32690, 32710}

X(47228) = Moses-Parry-circle-inverse of X(1990)
X(47228) = complement of the isotomic conjugate of X(2693)
X(47228) = polar conjugate of the isotomic conjugate of X(5663)
X(47228) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 18809}, {2693, 2887}
X(47228) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 18809}, {32710, 25}
X(47228) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36062}, {3, 36102}, {63, 477}, {69, 36151}, {75, 32663}, {394, 36130}, {656, 30528}, {662, 14220}, {2411, 36061}, {8552, 36047}, {35200, 46789}, {36117, 41077}
X(47228) = crosspoint of X(2) and X(2693)
X(47228) = crosssum of X(6) and X(2777)
X(47228) = crossdifference of every pair of points on line {3, 9033}
X(47228) = PU(4)-harmonic conjugate of crossdifference of X(3) and X(541)
X(47228) = barycentric product X(i)*X(j) for these {i,j}: {1, 36063}, {4, 5663}, {25, 35520}, {74, 11251}, {186, 34209}, {250, 6070}, {403, 39986}, {523, 7480}, {1990, 46788}, {2437, 44427}, {2693, 18809}, {18808, 42742}, {25641, 32710}, {39988, 44084}
X(47228) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 36102}, {25, 477}, {31, 36062}, {32, 32663}, {112, 30528}, {512, 14220}, {1096, 36130}, {1973, 36151}, {1990, 46789}, {5663, 69}, {6070, 339}, {7480, 99}, {11251, 3260}, {18384, 43707}, {34209, 328}, {34397, 34210}, {35520, 305}, {36063, 75}, {44084, 39985}
X(47228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 112, 39176}, {112, 8749, 6}, {230, 1990, 47144}, {232, 3003, 16328}, {232, 6103, 44467}, {232, 16328, 11062}, {232, 44467, 2493}, {1990, 3003, 11062}, {1990, 16328, 232}, {8105, 8106, 1990}, {16303, 16318, 1990}, {16310, 47189, 230}

X(47229) = MOSES-PARRY-CIRCLE-INVERSE OF X(2491)

Barycentrics (b^2 - c^2)*(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(47229) lies on these lines: {32, 23105}, {111, 4108}, {112, 2966}, {115, 512}, {230, 231}, {325, 30476}, {385, 850}, {524, 31174}, {1968, 46371}, {2395, 6041}, {2451, 3289}, {3815, 10567}, {7755, 8574}, {7779, 31072}, {8371, 41939}, {8430, 16092}, {8675, 15993}, {8859, 36900}, {12079, 44398}, {22329, 23878}, {23991, 34978}, {30735, 41932}, {31277, 44377}, {34291, 37637}, {39482, 43457}

X(47229) = midpoint of X(i) and X(j) for these {i,j}: {385, 850}, {47155, 47175}
X(47229) = reflection of X(i) in X(j) for these {i,j}: {325, 30476}, {647, 230}
X(47229) = Moses-Parry-circle-inverse of X(2491)
X(47229) = X(40866)-Ceva conjugate of X(1316)
X(47229) = X(i)-isoconjugate of X(j) for these (i,j): {662, 9513}, {1101, 46245}, {37134, 40077}
X(47229) = crosspoint of X(1316) and X(40866)
X(47229) = crossdifference of every pair of points on line {3, 2421}
X(47229) = barycentric product X(i)*X(j) for these {i,j}: {98, 31953}, {115, 40866}, {338, 46249}, {512, 44155}, {523, 1316}, {804, 38947}, {850, 44127}, {868, 43113}
X(47229) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 46245}, {512, 9513}, {1316, 99}, {5027, 40077}, {31953, 325}, {38947, 18829}, {40866, 4590}, {44127, 110}, {44155, 670}, {46249, 249}
X(47229) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2395, 7735, 6041}, {2501, 16318, 2489}, {8105, 8106, 2491}

X(47230) = MOSES-PARRY-CIRCLE-INVERSE OF X(2501)

X(47230) lies on these lines: {2, 44817}, {4, 9147}, {6, 686}, {25, 351}, {50, 15470}, {110, 112}, {111, 3563}, {114, 1560}, {115, 136}, {186, 9126}, {230, 231}, {378, 2780}, {427, 804}, {525, 15423}, {526, 2081}, {1304, 23969}, {2395, 8791}, {2433, 8749}, {2510, 44468}, {2881, 42659}, {3265, 7630}, {3268, 5664}, {5094, 9148}, {7663, 9134}, {8428, 19165}, {8541, 9023}, {9188, 44102}, {10294, 11215}, {14592, 18883}, {14618, 30685}, {16235, 37118}, {18344, 42653}, {20403, 37969}, {21731, 40352}, {32662, 32708}, {32695, 32712}, {37742, 45688}, {39469, 42651}

X(47230) = Moses-Parry-circle-inverse of X(2501)
X(47230) = polar conjugate of X(35139)
X(47230) = complement of the isotomic conjugate of X(10420)
X(47230) = isogonal conjugate of the isotomic conjugate of X(44427)
X(47230) = polar conjugate of the isotomic conjugate of X(526)
X(47230) = polar conjugate of the isogonal conjugate of X(14270)
X(47230) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 16221}, {560, 39021}, {10420, 2887}, {14910, 21253}, {18878, 21235}, {18879, 42327}, {32676, 46085}, {32708, 20305}, {36114, 21243}
X(47230) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 16221}, {112, 39176}, {648, 1986}, {1304, 25}, {4240, 44084}, {14165, 35235}, {14590, 186}, {14591, 11062}, {16237, 30}, {18808, 512}, {32708, 6}, {44427, 526}, {46456, 4}
X(47230) = X(14270)-cross conjugate of X(526)
X(47230) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36061}, {3, 32680}, {48, 35139}, {63, 476}, {69, 32678}, {75, 32662}, {94, 4575}, {163, 328}, {255, 46456}, {265, 662}, {304, 14560}, {394, 36129}, {655, 1789}, {656, 39295}, {1101, 14592}, {1793, 38340}, {1989, 4592}, {2166, 4558}, {2410, 36062}, {14582, 24041}, {34055, 46155}
X(47230) = cevapoint of X(14398) and X(21731)
X(47230) = crosspoint of X(i) and X(j) for these (i,j): {2, 10420}, {4, 46456}, {110, 43756}, {112, 8749}, {186, 14590}, {393, 32695}, {648, 1300}, {2433, 2623}
X(47230) = crosssum of X(i) and X(j) for these (i,j): {265, 14582}, {394, 41077}, {523, 16310}, {525, 11064}, {647, 13754}, {1989, 43088}, {2407, 14570}
X(47230) = crossdifference of every pair of points on line {3, 125}
X(47230) = pole wrt polar circle of trilinear polar of X(35139) (line X(2)X(94))
X(47230) = Dao-Moses-Telv-circle-inverse of PU(4)-harmonic conjugate of X(47207)
X(47230) = Moses-radical-circle-inverse of PU(4)-harmonic conjugate of X(47220)
X(47230) = PU(4)-harmonic conjugate of X(2493)
X(47230) = intersection of trilinear polars of X(8739) and X(8740)
X(47230) = barycentric product X(i)*X(j) for these {i,j}: {4, 526}, {6, 44427}, {19, 32679}, {25, 3268}, {50, 14618}, {92, 2624}, {93, 44809}, {107, 16186}, {110, 35235}, {115, 14590}, {186, 523}, {254, 44816}, {264, 14270}, {275, 2081}, {323, 2501}, {338, 14591}, {340, 512}, {393, 8552}, {403, 15470}, {468, 9213}, {470, 6138}, {471, 6137}, {562, 1510}, {647, 14165}, {648, 2088}, {847, 44808}, {850, 34397}, {860, 2605}, {924, 5962}, {1304, 3258}, {1511, 18808}, {1825, 3738}, {1835, 35057}, {1986, 15328}, {2207, 45792}, {2394, 39176}, {2433, 14920}, {2489, 7799}, {2594, 44428}, {2611, 4242}, {2623, 14918}, {3043, 10412}, {4467, 44113}, {5664, 8749}, {6143, 46002}, {6149, 24006}, {6591, 42701}, {6753, 37802}, {8739, 23871}, {8740, 23870}, {8753, 45808}, {8754, 10411}, {8882, 41078}, {10420, 16221}, {11062, 15412}, {13754, 14222}, {14314, 16263}, {14355, 16230}, {14592, 36423}, {17983, 44814}, {18334, 46456}, {39240, 44067}, {39241, 44068}
X(47230) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 35139}, {19, 32680}, {25, 476}, {31, 36061}, {32, 32662}, {50, 4558}, {112, 39295}, {115, 14592}, {186, 99}, {323, 4563}, {340, 670}, {393, 46456}, {512, 265}, {523, 328}, {526, 69}, {562, 46139}, {1096, 36129}, {1825, 35174}, {1843, 46155}, {1973, 32678}, {1974, 14560}, {2081, 343}, {2088, 525}, {2489, 1989}, {2501, 94}, {2624, 63}, {2971, 15475}, {3043, 10411}, {3124, 14582}, {3268, 305}, {5962, 46134}, {6137, 40710}, {6138, 40709}, {6149, 4592}, {6753, 18883}, {8552, 3926}, {8648, 1789}, {8739, 23896}, {8740, 23895}, {8749, 39290}, {8754, 10412}, {9213, 30786}, {11062, 14570}, {14165, 6331}, {14270, 3}, {14273, 43084}, {14355, 17932}, {14581, 41392}, {14590, 4590}, {14591, 249}, {14618, 20573}, {16186, 3265}, {17994, 14356}, {18334, 8552}, {19627, 32661}, {20975, 43083}, {21731, 39170}, {32679, 304}, {32715, 15395}, {34394, 38413}, {34395, 38414}, {34397, 110}, {34952, 5961}, {35235, 850}, {36423, 14590}, {38936, 18878}, {39176, 2407}, {39495, 12215}, {41078, 28706}, {44084, 41512}, {44102, 14559}, {44113, 6742}, {44427, 76}, {44808, 9723}, {44809, 44180}, {44814, 6390}, {44816, 40697}
X(47230) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {351, 17994, 25}, {647, 1637, 46425}, {647, 2485, 9209}, {647, 6753, 2501}, {686, 14397, 6}, {2492, 6132, 2493}, {2492, 46425, 1637}, {8105, 8106, 2501}

X(47231) = MOSES-PARRY-CIRCLE-INVERSE OF X(3290)

X(47231) lies on these lines: {2, 16732}, {23, 15586}, {37, 100}, {112, 15344}, {115, 120}, {230, 231}, {1560, 1841}, {1880, 40347}, {2079, 20832}, {2503, 2836}, {2831, 7423}, {7469, 19622}, {8287, 25344}, {40129, 40133}, {40131, 44533}

X(47231) = Moses-Parry-circle-inverse of X(3290)
X(47231) = complement of the isotomic conjugate of X(2752)
X(47231) = X(2752)-complementary conjugate of X(2887)
X(47231) = X(673)-isoconjugate of X(40084)
X(47231) = crosspoint of X(2) and X(2752)
X(47231) = crosssum of X(6) and X(2836)
X(47231) = crossdifference of every pair of points on line {3, 2775}
X(47231) = PU(4)-harmonic conjugate of X(47235)
X(47231) = barycentric product X(i)*X(j) for these {i,j}: {518, 34173}, {523, 7475}
X(47231) = barycentric quotient X(i)/X(j) for these {i,j}: {2223, 40084}, {7475, 99}, {34173, 2481}
X(47231) = {X(8105),X(8106)}-harmonic conjugate of X(3290)

X(47232) = MOSES-PARRY-CIRCLE-INVERSE OF X(5089)

X(47232) is the exsimilicenter the Moses-Parry circle and circle {{X(11),X(105),X(108),X(20621)}}; the insimilicenter is X(47227). (Randy Hutson, April 16, 2022)

X(47232) lies on these lines: {6, 10100}, {11, 1560}, {28, 105}, {37, 8791}, {108, 111}, {115, 429}, {230, 231}, {427, 2486}, {451, 17916}, {608, 1421}, {8428, 14667}

X(47232) = Moses-Parry-circle-inverse of X(5089)
X(47232) = polar conjugate of the isotomic conjugate of X(2836)
X(47232) = X(63)-isoconjugate of X(2752)
X(47232) = barycentric product X(i)*X(j) for these {i,j}: {4, 2836}, {523, 7476}, {5089, 46784}
X(47232) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 2752}, {2836, 69}, {7476, 99}
X(47232) = PU(4)-harmonic conjugate of X(47227)
X(47232) = {X(8105),X(8106)}-harmonic conjugate of X(5089)

X(47233) = MOSES-PARRY-CIRCLE-INVERSE OF X(6130)

X(47233) lies on these lines: {112, 39201}, {115, 34984}, {230, 231}, {1971, 3049}, {2079, 9431}, {2393, 42654}, {5489, 39575}, {23964, 38861}, {34212, 34291}

X(47233) = midpoint of X(232) and X(647)
X(47233) = Moses-radical-circle-inverse of X(47004)
X(47233) = Moses-Parry-circle-inverse of X(6130)
X(47233) = crosssum of X(520) and X(5661)
X(47233) = crossdifference of every pair of points on line {3, 34360}
X(47233) = barycentric product X(523)*X(37918)
X(47233) = barycentric quotient X(37918)/X(99)
X(47233) = {X(8105),X(8106)}-harmonic conjugate of X(6130)

X(47234) = MOSES-PARRY-CIRCLE-INVERSE OF X(6586)

X(47234) lies on these lines: {2, 21205}, {6, 11125}, {37, 21180}, {111, 675}, {112, 26705}, {115, 116}, {230, 231}, {3163, 23972}, {4025, 45659}, {5029, 21131}

X(47234) = midpoint of X(5029) and X(21131)
X(47234) = Moses-Parry-circle-inverse of X(6586)
X(47234) = complement of the isotomic conjugate of X(2690)
X(47234) = X(2690)-complementary conjugate of X(2887)
X(47234) = X(100)-isoconjugate of X(40076)
X(47234) = crosspoint of X(2) and X(2690)
X(47234) = crosssum of X(6) and X(2774)
X(47234) = crossdifference of every pair of points on line {3, 2772}
X(47234) = barycentric product X(i)*X(j) for these {i,j}: {514, 5134}, {523, 5196}
X(47234) = barycentric quotient X(i)/X(j) for these {i,j}: {649, 40076}, {5134, 190}, {5196, 99}
X(47234) = {X(8105),X(8106)}-harmonic conjugate of X(6586)

X(47235) = MOSES-PARRY-CIRCLE-INVERSE OF X(6591)

X(47235) lies on these lines: {100, 112}, {111, 15344}, {115, 5521}, {120, 1560}, {230, 231}, {2203, 5040}, {2788, 37362}, {2830, 4227}, {17924, 31150}

X(47235) = Moses-Parry-circle-inverse of X(6591)
X(47235) = polar conjugate of X(35156)
X(47235) = polar conjugate of the isotomic conjugate of X(8674)
X(47235) = polar conjugate of the isogonal conjugate of X(42670)
X(47235) = pole wrt polar circle of trilinear polar of X(35156) (line X(2)X(16732))
X(47235) = PU(4)-harmonic conjugate of X(47231)
X(47235) = X(2766)-Ceva conjugate of X(25)
X(47235) = X(42670)-cross conjugate of X(8674)
X(47235) = crosssum of X(905) and X(22128)
X(47235) = crossdifference of every pair of points on line {3, 18210}
X(47235) = X(i)-isoconjugate of X(j) for these (i,j): {48, 35156}, {63, 1290}, {1331, 21907}, {1813, 11604}, {4558, 5620}
X(47235) = barycentric product X(i)*X(j) for these {i,j}: {4, 8674}, {264, 42670}, {523, 2074}, {650, 37799}, {2501, 37783}, {2766, 5520}, {5127, 24006}, {5172, 44426}, {6591, 32849}, {14618, 19622}, {15313, 47106}, {16164, 18808}, {17796, 17924}, {41013, 42741}
X(47235) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 35156}, {25, 1290}, {2074, 99}, {5127, 4592}, {5172, 6516}, {6591, 21907}, {8674, 69}, {17796, 1332}, {18344, 11604}, {19622, 4558}, {37783, 4563}, {37799, 4554}, {42670, 3}, {42741, 1444}
X(47235) = {X(8105),X(8106)}-harmonic conjugate of X(6591)

X(47236) = MOSES-PARRY-CIRCLE-INVERSE OF X(6753)

Barycentrics (b^2 - c^2)*(-a^2 + b^2 - c^2)*(a^2 + b^2 - c^2)*(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(47236) lies on these lines: {6, 40048}, {111, 40120}, {112, 925}, {115, 135}, {230, 231}, {427, 9134}, {686, 12828}, {1560, 2967}, {3569, 14391}, {5094, 45688}, {6353, 9131}, {8029, 17994}, {8428, 39828}, {13854, 14998}, {15475, 18384}, {23588, 32711}, {44427, 46229}

X(47236) = Moses-Parry-circle-inverse of X(6753)
X(47236) = isogonal conjugate of X(43755)
X(47236) = polar conjugate of X(18878)
X(47236) = polar conjugate of the isogonal conjugate of X(21731)
X(47236) = X(31)-complementary conjugate of X(16178)
X(47236) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 16178}, {476, 25}, {648, 113}, {687, 4}, {2407, 10151}, {6344, 8754}, {8749, 115}, {16237, 403}, {46106, 35235}
X(47236) = crosspoint of X(i) and X(j) for these (i,j): {4, 687}, {403, 16237}, {14618, 18808}
X(47236) = crosssum of X(i) and X(j) for these (i,j): {3, 686}, {394, 8552}
X(47236) = crossdifference of every pair of points on line {3, 974}
X(47236) = X(i)-isoconjugate of X(j) for these (i,j): {1, 43755}, {48, 18878}, {63, 10420}, {255, 687}, {326, 32708}, {394, 36114}, {656, 18879}, {662, 5504}, {1101, 15421}, {2986, 4575}, {4558, 36053}, {4592, 14910}
X(47236) = barycentric product X(i)*X(j) for these {i,j}: {113, 18808}, {115, 16237}, {264, 21731}, {393, 6334}, {403, 523}, {476, 16221}, {512, 44138}, {686, 2052}, {687, 39021}, {850, 44084}, {1725, 24006}, {1986, 10412}, {2501, 3580}, {2970, 15329}, {3003, 14618}, {5466, 12828}, {35235, 41512}
X(47236) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 18878}, {6, 43755}, {25, 10420}, {112, 18879}, {115, 15421}, {393, 687}, {403, 99}, {512, 5504}, {686, 394}, {1096, 36114}, {1725, 4592}, {1986, 10411}, {2207, 32708}, {2489, 14910}, {2501, 2986}, {3003, 4558}, {3580, 4563}, {6334, 3926}, {8754, 15328}, {12828, 5468}, {14618, 40832}, {15475, 12028}, {16221, 3268}, {16237, 4590}, {18808, 40423}, {21731, 3}, {39021, 6334}, {44084, 110}, {44138, 670}
X(47236) = {X(8105),X(8106)}-harmonic conjugate of X(6753)

X(47237) = ORTHIC AXIS INTERCEPT OF X(30)X(8859)

Barycentrics 6*a^10 - 9*a^8*b^2 - a^6*b^4 + 6*a^4*b^6 - 5*a^2*b^8 + 3*b^10 - 9*a^8*c^2 + 20*a^6*b^2*c^2 - 9*a^4*b^4*c^2 + 14*a^2*b^6*c^2 - 10*b^8*c^2 - a^6*c^4 - 9*a^4*b^2*c^4 - 18*a^2*b^4*c^4 + 7*b^6*c^4 + 6*a^4*c^6 + 14*a^2*b^2*c^6 + 7*b^4*c^6 - 5*a^2*c^8 - 10*b^2*c^8 + 3*c^10 : :

X(47237) = 4 X[230] - X[468], 2 X[230] + X[16315], 10 X[230] - X[16316], 7 X[230] - X[16320], 16 X[230] - X[47154], 8 X[230] + X[47155], 11 X[230] - 2 X[47171], X[385] + 2 X[5159], X[468] + 2 X[16315], 5 X[468] - 2 X[16316], 7 X[468] - 4 X[16320], 4 X[468] - X[47154], 2 X[468] + X[47155], 11 X[468] - 8 X[47171], 2 X[16092] + X[37904], 5 X[16315] + X[16316], 7 X[16315] + 2 X[16320], 8 X[16315] + X[47154], 4 X[16315] - X[47155], 11 X[16315] + 4 X[47171], 7 X[16316] - 10 X[16320], 8 X[16316] - 5 X[47154], 4 X[16316] + 5 X[47155], 11 X[16316] - 20 X[47171], 16 X[16320] - 7 X[47154], 8 X[16320] + 7 X[47155], 11 X[16320] - 14 X[47171], 2 X[22329] + X[47097], X[47154] + 2 X[47155], 11 X[47154] - 32 X[47171], 11 X[47155] + 16 X[47171]

X(47237) lies on these lines: {30, 8859}, {230, 231}, {385, 5159}, {1316, 37689}, {10151, 39663}, {10257, 32515}, {11007, 17008}, {16092, 37904}, {22329, 47097}

X(47237) = reflection of X(10151) in X(39663)
X(47237) = orthogonal projection of X(8859) on the orthic axis
X(47237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {230, 16315, 468}, {468, 16315, 47155}, {468, 47155, 47154}

X(47238) = ORTHIC AXIS INTERCEPT OF X(23)X(8859)

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

X(47238) = X[23] - 9 X[8859], X[23] + 3 X[16092], X[23] - 3 X[46998], 3 X[230] - X[468], 7 X[230] - X[16316], 5 X[230] - X[16320], 11 X[230] - X[47154], 5 X[230] + X[47155], 4 X[230] - X[47171], 3 X[385] + 5 X[30745], X[468] + 3 X[16315], 7 X[468] - 3 X[16316], 5 X[468] - 3 X[16320], 11 X[468] - 3 X[47154], 5 X[468] + 3 X[47155], 4 X[468] - 3 X[47171], X[858] + 3 X[22329], X[858] - 3 X[46980], X[7472] + 3 X[14568], 3 X[8859] + X[16092], 3 X[8859] - X[46998], 3 X[14999] + X[41724], 7 X[16315] + X[16316], 5 X[16315] + X[16320], 11 X[16315] + X[47154], 5 X[16315] - X[47155], 4 X[16315] + X[47171], 5 X[16316] - 7 X[16320], 11 X[16316] - 7 X[47154], 5 X[16316] + 7 X[47155], 4 X[16316] - 7 X[47171], 11 X[16320] - 5 X[47154], 4 X[16320] - 5 X[47171], X[18325] + 3 X[46633], X[18325] - 3 X[46999], 3 X[21445] - X[47000], 5 X[37760] - 3 X[46992], 2 X[37911] - 3 X[44401], 3 X[39663] - X[46988], 5 X[47154] + 11 X[47155], 4 X[47154] - 11 X[47171], 4 X[47155] + 5 X[47171]

X(47238) lies on these lines: {23, 8859}, {30, 11623}, {230, 231}, {385, 30745}, {524, 5159}, {858, 7668}, {2452, 37637}, {5189, 35727}, {7472, 14568}, {7755, 36157}, {9182, 37803}, {11007, 13468}, {14999, 41724}, {18325, 46633}, {21445, 47000}, {23583, 37911}, {37760, 46992}, {39663, 46988}

X(47238) = midpoint of X(i) and X(j) for these {i,j}: {230, 16315}, {16092, 46998}, {16320, 47155}, {22329, 46980}, {46633, 46999}
X(47238) = orthogonal projection of X(11623) on the orthic axis
X(47238) = {X(230),X(468)}-harmonic conjugate of X(47241)
X(47238) = {X(8859),X(16092)}-harmonic conjugate of X(46998)

X(47239) = ORTHIC AXIS INTERCEPT OF X(2)X(5467)

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

X(47239) = 3 X[186] - X[46994], 3 X[230] - X[16315], 5 X[230] + X[16316], 3 X[230] + X[16320], 9 X[230] + X[47154], 7 X[230] - X[47155], 2 X[230] + X[47171], 3 X[403] - X[46988], 3 X[468] + X[16315], 5 X[468] - X[16316], 3 X[468] - X[16320], 9 X[468] - X[47154], 7 X[468] + X[47155], X[10295] + 3 X[39663], X[16092] + 3 X[37907], 5 X[16315] + 3 X[16316], 3 X[16315] + X[47154], 7 X[16315] - 3 X[47155], 2 X[16315] + 3 X[47171], 3 X[16316] - 5 X[16320], 9 X[16316] - 5 X[47154], 7 X[16316] + 5 X[47155], 2 X[16316] - 5 X[47171], 3 X[16320] - X[47154], 7 X[16320] + 3 X[47155], 2 X[16320] - 3 X[47171], 3 X[26613] + X[36196], X[36166] + 3 X[38227], 3 X[37907] - X[46992], 3 X[39663] - X[46982], 3 X[41139] - X[47097], 3 X[44214] - X[46987], 7 X[47154] + 9 X[47155], 2 X[47154] - 9 X[47171], 2 X[47155] + 7 X[47171]

X(47239) lies on these lines: {2, 5467}, {3, 46999}, {4, 47000}, {30, 5461}, {115, 36180}, {186, 46994}, {187, 14120}, {230, 231}, {403, 46988}, {524, 5972}, {1316, 37637}, {1624, 37962}, {5159, 44381}, {7417, 38393}, {7426, 41125}, {7746, 36156}, {7749, 36157}, {7857, 36165}, {10295, 39663}, {11799, 46981}, {14588, 37803}, {15597, 34094}, {16092, 37907}, {22329, 46986}, {26613, 36196}, {31644, 40350}, {36166, 38227}, {37911, 44377}, {41139, 47097}, {44214, 46987}, {46633, 46993}

X(47239) = midpoint of X(i) and X(j) for these {i,j}: {2, 46998}, {3, 46999}, {4, 47000}, {115, 36180}, {187, 14120}, {230, 468}, {7426, 46980}, {10295, 46982}, {11799, 46981}, {16092, 46992}, {16315, 16320}, {22329, 46986}, {46633, 46993}
X(47239) = reflection of X(i) in X(j) for these {i,j}: {5159, 44381}, {44377, 37911}, {47171, 468}
X(47239) = reflection of X(47171) in the Euler line
X(47239) = orthogonal projection of X(5461) on the orthic axis
X(47239) = PU(4)-harmonic conjugate of X(2501)
X(47239) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {230, 16320, 16315}, {468, 16315, 16320}, {10295, 39663, 46982}, {16092, 37907, 46992}

X(47240) = ORTHIC AXIS INTERCEPT OF X(30)X(9166)

Barycentrics 6*a^10 - 9*a^8*b^2 + a^6*b^4 + 6*a^4*b^6 - 7*a^2*b^8 + 3*b^10 - 9*a^8*c^2 + 16*a^6*b^2*c^2 - 9*a^4*b^4*c^2 + 16*a^2*b^6*c^2 - 8*b^8*c^2 + a^6*c^4 - 9*a^4*b^2*c^4 - 18*a^2*b^4*c^4 + 5*b^6*c^4 + 6*a^4*c^6 + 16*a^2*b^2*c^6 + 5*b^4*c^6 - 7*a^2*c^8 - 8*b^2*c^8 + 3*c^10 : :

X(47240) = 2 X[230] + X[468], 4 X[230] - X[16315], 8 X[230] + X[16316], 5 X[230] + X[16320], 14 X[230] + X[47154], 10 X[230] - X[47155], 7 X[230] + 2 X[47171], X[325] - 4 X[37911], 2 X[468] + X[16315], 4 X[468] - X[16316], 5 X[468] - 2 X[16320], 7 X[468] - X[47154], 5 X[468] + X[47155], 7 X[468] - 4 X[47171], 2 X[16315] + X[16316], 5 X[16315] + 4 X[16320], 7 X[16315] + 2 X[47154], 5 X[16315] - 2 X[47155], 7 X[16315] + 8 X[47171], 5 X[16316] - 8 X[16320], 7 X[16316] - 4 X[47154], 5 X[16316] + 4 X[47155], 7 X[16316] - 16 X[47171], 14 X[16320] - 5 X[47154], 2 X[16320] + X[47155], 7 X[16320] - 10 X[47171], X[36180] + 2 X[43291], X[37904] + 2 X[46980], 2 X[44401] + X[46998], 4 X[44401] - X[47097], 2 X[46998] + X[47097], 5 X[47154] + 7 X[47155], X[47154] - 4 X[47171], 7 X[47155] + 20 X[47171]

X(47240) lies on these lines: {30, 9166}, {230, 231}, {325, 37911}, {403, 21445}, {2452, 37689}, {8860, 34094}, {32515, 44452}, {36180, 43291}, {37904, 46980}, {44401, 46998}

X(47240) = midpoint of X(403) and X(21445)
X(47240) = orthogonal projection of X(9166) on the orthic axis
X(47240) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {230, 468, 16315}, {468, 16315, 16316}, {468, 47154, 47171}, {468, 47155, 16320}, {44401, 46998, 47097}

X(47241) = ORTHIC AXIS INTERCEPT OF X(23)X(46980)

Barycentrics 8*a^10 - 12*a^8*b^2 + a^6*b^4 + 8*a^4*b^6 - 9*a^2*b^8 + 4*b^10 - 12*a^8*c^2 + 22*a^6*b^2*c^2 - 12*a^4*b^4*c^2 + 21*a^2*b^6*c^2 - 11*b^8*c^2 + a^6*c^4 - 12*a^4*b^2*c^4 - 24*a^2*b^4*c^4 + 7*b^6*c^4 + 8*a^4*c^6 + 21*a^2*b^2*c^6 + 7*b^4*c^6 - 9*a^2*c^8 - 11*b^2*c^8 + 4*c^10 : :

X(47241) = X[23] + 3 X[46980], 3 X[230] + X[468], 5 X[230] - X[16315], 11 X[230] + X[16316], 7 X[230] + X[16320], 19 X[230] + X[47154], 13 X[230] - X[47155], 5 X[230] + X[47171], 5 X[468] + 3 X[16315], 11 X[468] - 3 X[16316], 7 X[468] - 3 X[16320], 19 X[468] - 3 X[47154], 13 X[468] + 3 X[47155], 5 X[468] - 3 X[47171], X[858] + 3 X[46998], X[5159] - 3 X[44401], 3 X[8859] + X[46986], 3 X[16092] + 5 X[37760], 11 X[16315] + 5 X[16316], 7 X[16315] + 5 X[16320], 19 X[16315] + 5 X[47154], 13 X[16315] - 5 X[47155], 7 X[16316] - 11 X[16320], 19 X[16316] - 11 X[47154], 13 X[16316] + 11 X[47155], 5 X[16316] - 11 X[47171], 19 X[16320] - 7 X[47154], 13 X[16320] + 7 X[47155], 5 X[16320] - 7 X[47171], X[18325] + 3 X[46981], 3 X[21445] + X[46988], 3 X[39663] + X[47000], 13 X[47154] + 19 X[47155], 5 X[47154] - 19 X[47171], 5 X[47155] + 13 X[47171]

X(47241) lies on these lines: {23, 46980}, {30, 20398}, {230, 231}, {524, 32300}, {858, 46998}, {5159, 9165}, {7607, 36183}, {8859, 46986}, {16092, 37760}, {18325, 46981}, {21445, 46988}, {39663, 47000}

X(47241) = midpoint of X(16315) and X(47171)
X(47241) = orthogonal projection of X(20398) on the orthic axis
X(47241) = {X(230),X(468)}-harmonic conjugate of X(47238)

X(47242) = ORTHIC AXIS INTERCEPT OF X(23)X(7669)

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

X(47242) = X[23] - 3 X[22329], 3 X[230] - 2 X[468], 5 X[230] - 2 X[16316], 7 X[230] - 2 X[47154], X[230] + 2 X[47155], 7 X[230] - 4 X[47171], 3 X[325] - 5 X[30745], 3 X[385] + X[5189], X[468] - 3 X[16315], 5 X[468] - 3 X[16316], 4 X[468] - 3 X[16320], 7 X[468] - 3 X[47154], X[468] + 3 X[47155], 7 X[468] - 6 X[47171], X[858] - 3 X[16092], 4 X[5159] - 3 X[22110], 2 X[5159] - 3 X[46980], 9 X[8859] - 5 X[37760], 5 X[16315] - X[16316], 4 X[16315] - X[16320], 7 X[16315] - X[47154], 7 X[16315] - 2 X[47171], 4 X[16316] - 5 X[16320], 7 X[16316] - 5 X[47154], X[16316] + 5 X[47155], 7 X[16316] - 10 X[47171], 7 X[16320] - 4 X[47154], X[16320] + 4 X[47155], 7 X[16320] - 8 X[47171], 2 X[37897] - 3 X[46998], 8 X[37911] - 9 X[41139], 4 X[37911] - 3 X[46986], 3 X[41139] - 2 X[46986], X[47154] + 7 X[47155], 7 X[47155] + 2 X[47171]

X(47242) lies on these lines: {23, 7669}, {30, 10991}, {67, 524}, {230, 231}, {325, 30745}, {385, 5189}, {892, 37803}, {1316, 5306}, {2452, 3815}, {2453, 7735}, {3564, 16188}, {5099, 43291}, {5159, 15526}, {6390, 40544}, {8667, 36163}, {8859, 37760}, {9832, 13468}, {15398, 17948}, {37897, 46998}, {37911, 41139}, {40879, 46336}

X(47242) = midpoint of X(16315) and X(47155)
X(47242) = reflection of X(i) in X(j) for these {i,j}: {230, 16315}, {5099, 43291}, {6390, 40544}, {16320, 230}, {22110, 46980}, {47154, 47171}
X(47242) = orthogonal projection of X(10991) on the orthic axis
X(47242) = {X(468),X(16333)}-harmonic conjugate of X(16308)

X(47243) = ORTHIC AXIS INTERCEPT OF X(30)X(5215)

Barycentrics 6*a^10 - 9*a^8*b^2 + 2*a^6*b^4 + 6*a^4*b^6 - 8*a^2*b^8 + 3*b^10 - 9*a^8*c^2 + 14*a^6*b^2*c^2 - 9*a^4*b^4*c^2 + 17*a^2*b^6*c^2 - 7*b^8*c^2 + 2*a^6*c^4 - 9*a^4*b^2*c^4 - 18*a^2*b^4*c^4 + 4*b^6*c^4 + 6*a^4*c^6 + 17*a^2*b^2*c^6 + 4*b^4*c^6 - 8*a^2*c^8 - 7*b^2*c^8 + 3*c^10 : :

X(47243) = X[230] + 2 X[468], 5 X[230] - 2 X[16315], 7 X[230] + 2 X[16316], 2 X[230] + X[16320], 13 X[230] + 2 X[47154], 11 X[230] - 2 X[47155], 5 X[230] + 4 X[47171], 5 X[468] + X[16315], 7 X[468] - X[16316], 4 X[468] - X[16320], 13 X[468] - X[47154], 11 X[468] + X[47155], 5 X[468] - 2 X[47171], X[858] - 4 X[44381], X[7426] + 2 X[44401], 7 X[16315] + 5 X[16316], 4 X[16315] + 5 X[16320], 13 X[16315] + 5 X[47154], 11 X[16315] - 5 X[47155], X[16315] + 2 X[47171], 4 X[16316] - 7 X[16320], 13 X[16316] - 7 X[47154], 11 X[16316] + 7 X[47155], 5 X[16316] - 14 X[47171], 13 X[16320] - 4 X[47154], 11 X[16320] + 4 X[47155], 5 X[16320] - 8 X[47171], X[21445] + 3 X[37943], X[22110] + 2 X[46998], X[32220] + 2 X[44395], 2 X[37934] + X[46982], 2 X[37984] + X[47000], 11 X[47154] + 13 X[47155], 5 X[47154] - 26 X[47171], 5 X[47155] + 22 X[47171]

X(47243) lies on these lines: {30, 5215}, {186, 39663}, {230, 231}, {858, 44381}, {1316, 3054}, {7426, 44401}, {9754, 37930}, {10256, 44452}, {21445, 37943}, {22110, 45312}, {32220, 44395}, {32515, 44234}, {37934, 46982}, {37984, 47000}

X(47243) = midpoint of X(186) and X(39663)
X(47243) = reflection of X(10256) in X(44452)
X(47243) = orthogonal projection of X(5215) on the orthic axis
X(47243) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {230, 468, 16320}, {468, 16315, 47171}

X(47244) = ORTHIC AXIS INTERCEPT OF X(2)X(35345)

Barycentrics 8*a^10 - 12*a^8*b^2 + 3*a^6*b^4 + 8*a^4*b^6 - 11*a^2*b^8 + 4*b^10 - 12*a^8*c^2 + 18*a^6*b^2*c^2 - 12*a^4*b^4*c^2 + 23*a^2*b^6*c^2 - 9*b^8*c^2 + 3*a^6*c^4 - 12*a^4*b^2*c^4 - 24*a^2*b^4*c^4 + 5*b^6*c^4 + 8*a^4*c^6 + 23*a^2*b^2*c^6 + 5*b^4*c^6 - 11*a^2*c^8 - 9*b^2*c^8 + 4*c^10 : :

X(47244) = 3 X[186] + X[46982], X[230] + 3 X[468], 7 X[230] - 3 X[16315], 3 X[230] + X[16316], 5 X[230] + 3 X[16320], 17 X[230] + 3 X[47154], 5 X[230] - X[47155], X[325] + 3 X[46998], X[385] + 3 X[46986], 3 X[403] + X[47000], 7 X[468] + X[16315], 9 X[468] - X[16316], 5 X[468] - X[16320], 17 X[468] - X[47154], 15 X[468] + X[47155], 3 X[468] - X[47171], X[6781] + 3 X[14120], 9 X[16315] + 7 X[16316], 5 X[16315] + 7 X[16320], 17 X[16315] + 7 X[47154], 15 X[16315] - 7 X[47155], 3 X[16315] + 7 X[47171], 5 X[16316] - 9 X[16320], 17 X[16316] - 9 X[47154], 5 X[16316] + 3 X[47155], X[16316] - 3 X[47171], 17 X[16320] - 5 X[47154], 3 X[16320] + X[47155], 3 X[16320] - 5 X[47171], X[37904] + 3 X[41139], 3 X[37907] + X[46980], 3 X[39663] + X[46994], 3 X[44214] + X[46999], 15 X[47154] + 17 X[47155], 3 X[47154] - 17 X[47171], X[47155] + 5 X[47171]

X(47244) lies on these lines: {2, 35345}, {30, 6722}, {186, 46982}, {230, 231}, {325, 46998}, {385, 46986}, {403, 47000}, {6677, 44386}, {6781, 14120}, {37904, 41139}, {37907, 46980}, {39663, 46994}, {44214, 46999}

X(47244) = midpoint of X(230) and X(47171)
X(47244) = orthogonal projection of X(6722) on the orthic axis
X(47244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {230, 468, 47171}, {230, 16320, 47155}

X(47245) = ORTHIC AXIS INTERCEPT OF X(23)X(524)

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

X(47245) = 3 X[230] - 4 X[468], 5 X[230] - 4 X[16315], X[230] - 4 X[16316], X[230] + 4 X[47154], 7 X[230] - 4 X[47155], 5 X[230] - 8 X[47171], 3 X[325] - X[5189], 5 X[468] - 3 X[16315], X[468] - 3 X[16316], 2 X[468] - 3 X[16320], X[468] + 3 X[47154], 7 X[468] - 3 X[47155], 5 X[468] - 6 X[47171], 2 X[858] - 3 X[22110], 2 X[5159] - 3 X[46986], 3 X[7840] + X[20063], 2 X[16092] - 3 X[41139], X[16315] - 5 X[16316], 2 X[16315] - 5 X[16320], X[16315] + 5 X[47154], 7 X[16315] - 5 X[47155], 7 X[16316] - X[47155], 5 X[16316] - 2 X[47171], X[16320] + 2 X[47154], 7 X[16320] - 2 X[47155], 5 X[16320] - 4 X[47171], 3 X[22329] - 5 X[37760], 5 X[30745] - 6 X[44377], 2 X[37897] - 3 X[46992], 4 X[37911] - 3 X[46980], 7 X[47154] + X[47155], 5 X[47154] + 2 X[47171], 5 X[47155] - 14 X[47171]

X(47245) lies on these lines: {23, 524}, {30, 10992}, {230, 231}, {325, 5189}, {691, 32459}, {842, 1503}, {858, 10717}, {1316, 9300}, {2453, 3815}, {5159, 46986}, {7426, 14480}, {7789, 38526}, {7840, 20063}, {8550, 37930}, {9766, 36181}, {9872, 32113}, {10416, 17948}, {16092, 41139}, {22329, 37760}, {23992, 40350}, {30745, 44377}, {37897, 46992}, {37911, 46980}

X(47245) = midpoint of X(16316) and X(47154)
X(47245) = reflection of X(i) in X(j) for these {i,j}: {230, 16320}, {691, 32459}, {16315, 47171}, {16320, 16316}
X(47245) = orthogonal projection of X(10992) on the orthic axis

X(47246) = ORTHIC AXIS INTERCEPT OF X(23)X(44377)

Barycentrics 6*a^10 - 9*a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 - 10*a^2*b^8 + 3*b^10 - 9*a^8*c^2 + 10*a^6*b^2*c^2 - 9*a^4*b^4*c^2 + 19*a^2*b^6*c^2 - 5*b^8*c^2 + 4*a^6*c^4 - 9*a^4*b^2*c^4 - 18*a^2*b^4*c^4 + 2*b^6*c^4 + 6*a^4*c^6 + 19*a^2*b^2*c^6 + 2*b^4*c^6 - 10*a^2*c^8 - 5*b^2*c^8 + 3*c^10 : :

X(47246) = X[23] + 2 X[44377], X[230] - 4 X[468], 7 X[230] - 4 X[16315], 5 X[230] + 4 X[16316], X[230] + 2 X[16320], 11 X[230] + 4 X[47154], 13 X[230] - 4 X[47155], X[230] + 8 X[47171], X[325] + 5 X[37760], 7 X[468] - X[16315], 5 X[468] + X[16316], 2 X[468] + X[16320], 11 X[468] + X[47154], 13 X[468] - X[47155], X[468] + 2 X[47171], 2 X[7426] + X[22110], 5 X[16315] + 7 X[16316], 2 X[16315] + 7 X[16320], 11 X[16315] + 7 X[47154], 13 X[16315] - 7 X[47155], X[16315] + 14 X[47171], 2 X[16316] - 5 X[16320], 11 X[16316] - 5 X[47154], 13 X[16316] + 5 X[47155], X[16316] - 10 X[47171], 11 X[16320] - 2 X[47154], 13 X[16320] + 2 X[47155], X[16320] - 4 X[47171], 2 X[32218] + X[44380], 2 X[37934] + X[46988], 3 X[37943] - X[39663], 2 X[37984] + X[46994], 13 X[47154] + 11 X[47155], X[47154] - 22 X[47171], X[47155] + 26 X[47171]

X(47246) lies on these lines: {23, 44377}, {30, 9167}, {230, 231}, {325, 37760}, {524, 25321}, {1316, 3055}, {2453, 3054}, {7426, 22110}, {10096, 32515}, {32218, 44380}, {37909, 41133}, {37934, 46988}, {37943, 39663}, {37984, 46994}

X(47246) = midpoint of X(37909) and X(41133)
X(47246) = orthogonal projection of X(9167) on the orthic axis
X(47246) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {468, 16320, 230}, {468, 47171, 16320}

X(47247) = ORTHIC AXIS INTERCEPT OF X(23)X(47001)

Barycentrics (b^2 - c^2)*(-4*a^10 + 9*a^8*b^2 - a^6*b^4 - 9*a^4*b^6 + 5*a^2*b^8 + 9*a^8*c^2 - 22*a^6*b^2*c^2 + 14*a^4*b^4*c^2 - 2*a^2*b^6*c^2 + b^8*c^2 - a^6*c^4 + 14*a^4*b^2*c^4 - 6*a^2*b^4*c^4 - b^6*c^4 - 9*a^4*c^6 - 2*a^2*b^2*c^6 - b^4*c^6 + 5*a^2*c^8 + b^2*c^8) : :

X(47247) = X[23] - 3 X[47001], X[468] - 3 X[647], 5 X[468] - 3 X[47004], 7 X[468] - 3 X[47175], 5 X[647] - X[47004], 7 X[647] - X[47175], X[858] + 3 X[36900], X[858] - 3 X[46983], X[18325] - 3 X[47002], 5 X[30745] + 3 X[31296], 5 X[37760] - 3 X[46995], 2 X[37911] - 3 X[44560], 7 X[47004] - 5 X[47175]

X(47247) lies on these lines: {23, 47001}, {230, 231}, {858, 36900}, {5159, 23878}, {10190, 15000}, {18325, 47002}, {30745, 31296}, {37760, 46995}, {37911, 44560}

X(47248) = ORTHIC AXIS INTERCEPT OF X(30)X(36900)

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

X(47248) = 3 X[468] - 2 X[47004], 3 X[647] - X[47004], 4 X[647] - X[47175], 3 X[9209] - 2 X[41357], 3 X[10151] - 2 X[46991], 3 X[37931] - 2 X[46997], 4 X[41300] + X[46517], 4 X[47004] - 3 X[47175]

X(47248) lies on these lines: {30, 36900}, {230, 231}, {850, 5159}, {858, 31296}, {2452, 44889}, {8901, 9213}, {9168, 15000}, {10151, 46991}, {18312, 37454}, {23878, 46983}, {30209, 46984}, {37904, 47001}, {37931, 46997}, {41300, 46517}, {44560, 46989}

X(47248) = midpoint of X(858) and X(31296)
X(47248) = reflection of X(i) in X(j) for these {i,j}: {468, 647}, {850, 5159}, {37904, 47001}, {46989, 44560}, {47097, 46983}, {47175, 468}
X(47248) = orthogonal projection of X(36900) on the orthic axis
X(47248) = reflection of X(47175) in the Euler line

X(47249) = ORTHIC AXIS INTERCEPT OF X(2)X(47001)

Barycentrics (b^2 - c^2)*(4*a^10 - 7*a^8*b^2 - a^6*b^4 + 7*a^4*b^6 - 3*a^2*b^8 - 7*a^8*c^2 + 18*a^6*b^2*c^2 - 10*a^4*b^4*c^2 - 2*a^2*b^6*c^2 + b^8*c^2 - a^6*c^4 - 10*a^4*b^2*c^4 + 10*a^2*b^4*c^4 - b^6*c^4 + 7*a^4*c^6 - 2*a^2*b^2*c^6 - b^4*c^6 - 3*a^2*c^8 + b^2*c^8) : :

X(47249) = 3 X[186] - X[46997], 3 X[403] - X[46991], 3 X[468] - X[47004], 5 X[468] - X[47175], 3 X[647] + X[47004], 5 X[647] + X[47175], 3 X[9210] + X[32120], 3 X[37907] - X[46995], 3 X[44214] - X[46990], 5 X[47004] - 3 X[47175]

X(47249) lies on these lines: {2, 47001}, {3, 47002}, {4, 47003}, {30, 44560}, {186, 46997}, {230, 231}, {403, 46991}, {512, 15448}, {525, 5972}, {1503, 22264}, {1624, 37937}, {7426, 46983}, {9210, 32120}, {10295, 46985}, {11799, 46984}, {30476, 37911}, {33752, 44212}, {36900, 46989}, {37907, 46995}, {44214, 46990}, {44889, 46616}

X(47249) = midpoint of X(i) and X(j) for these {i,j}: {2, 47001}, {3, 47002}, {4, 47003}, {468, 647}, {7426, 46983}, {10295, 46985}, {11799, 46984}, {22264, 42654}, {36900, 46989} X(47249) = reflection of X(30476) in X(37911)
X(47249) = crosssum of X(520) and X(46127)
X(47249) = orthogonal projection of X(44560) on the orthic axis

X(47250) = ORTHIC AXIS INTERCEPT OF X(23)X(36900)

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

X(47250) = X[23] - 3 X[36900], 2 X[468] - 3 X[647], 4 X[468] - 3 X[47004], 5 X[468] - 3 X[47175], 5 X[647] - 2 X[47175], 3 X[850] - 5 X[30745], 4 X[5159] - 3 X[31174], 2 X[5159] - 3 X[46983], X[5189] + 3 X[31296], 2 X[37897] - 3 X[47001], X[37900] - 6 X[41300], 4 X[37911] - 3 X[46989], 5 X[47004] - 4 X[47175]

X(47250) lies on these lines: {23, 36900}, {110, 33754}, {230, 231}, {850, 30745}, {858, 23878}, {5159, 31174}, {5189, 31296}, {9213, 10415}, {11123, 15000}, {37897, 47001}, {37900, 41300}, {37911, 46989}

X(47250) = reflection of X(i) in X(j) for these {i,j}: {31174, 46983}, {47004, 647}

X(47251) = ORTHIC AXIS INTERCEPT OF X(125)X(42654)

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

X(47251) = X[125] + 2 X[42654], 2 X[468] + X[647], 4 X[468] - X[47004], 7 X[468] - X[47175], 2 X[647] + X[47004], 7 X[647] + 2 X[47175], X[1495] + 2 X[22264], X[7426] + 2 X[44560], X[12077] - 4 X[41357], X[31174] + 2 X[47001], 5 X[31277] - 8 X[37911], 2 X[37934] + X[46985], 2 X[37984] + X[47003], 7 X[47004] - 4 X[47175]

X(47251) lies on these lines: {125, 42654}, {230, 231}, {520, 5642}, {1495, 22264}, {7426, 44560}, {15000, 42733}, {30209, 44214}, {31174, 47001}, {31277, 37911}, {35278, 37937}, {37934, 46985}, {37984, 47003}

X(47252) = ORTHIC AXIS INTERCEPT OF X(2)X(46995)

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

X(47252) = 3 X[23] + 5 X[31072], 3 X[186] - X[47003], 3 X[403] - X[46985], 3 X[468] - X[647], 3 X[468] + X[47175], X[647] + 3 X[47004], X[850] + 3 X[7426], X[850] - 3 X[46989], 5 X[31277] - 3 X[47097], X[31296] - 9 X[37907], X[31296] - 3 X[47001], 3 X[37907] - X[47001], 3 X[44214] - X[46984], 3 X[47004] - X[47175]

X(47252) lies on these lines: {2, 46995}, {3, 46996}, {4, 46997}, {23, 31072}, {30, 30476}, {186, 47003}, {230, 231}, {403, 46985}, {525, 32223}, {850, 7426}, {1499, 20417}, {6720, 14341}, {10295, 46991}, {11799, 46990}, {18312, 44212}, {23301, 36189}, {31174, 37904}, {31277, 47097}, {31296, 37907}, {38401, 44891}, {44214, 46984}, {44889, 46608}

X(47252) = midpoint of X(i) and X(j) for these {i,j}: {2, 46995}, {3, 46996}, {4, 46997}, {468, 47004}, {647, 47175}, {7426, 46989}, {10295, 46991}, {11799, 46990}, {31174, 37904}
X(47252) = orthogonal projection of X(30476) on the orthic axis
X(47252) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {468, 647, 47253}, {468, 47175, 647}, {647, 47004, 47175}

X(47253) = ORTHIC AXIS INTERCEPT OF X(186)X(46985)

Barycentrics (b^2 - c^2)*(8*a^10 - 13*a^8*b^2 - 3*a^6*b^4 + 13*a^4*b^6 - 5*a^2*b^8 - 13*a^8*c^2 + 34*a^6*b^2*c^2 - 18*a^4*b^4*c^2 - 6*a^2*b^6*c^2 + 3*b^8*c^2 - 3*a^6*c^4 - 18*a^4*b^2*c^4 + 22*a^2*b^4*c^4 - 3*b^6*c^4 + 13*a^4*c^6 - 6*a^2*b^2*c^6 - 3*b^4*c^6 - 5*a^2*c^8 + 3*b^2*c^8) : :

X(47253) = 3 X[186] + X[46985], 3 X[403] + X[47003], 3 X[468] + X[647], 5 X[468] - X[47004], 9 X[468] - X[47175], 5 X[647] + 3 X[47004], 3 X[647] + X[47175], X[850] + 3 X[47001], X[31296] + 3 X[46989], 3 X[37907] + X[46983], 3 X[44214] + X[47002], 9 X[47004] - 5 X[47175]

X(47253) lies on these lines: {186, 46985}, {230, 231}, {403, 47003}, {620, 40557}, {850, 47001}, {3265, 7664}, {15448, 22264}, {31296, 46989}, {37907, 46983}, {44214, 47002}

X(47253) = midpoint of X(15448) and X(22264)
X(47253) = {X(468),X(647)}-harmonic conjugate of X(47252)

X(47254) = ORTHIC AXIS INTERCEPT OF X(23)X(23878)

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

X(47254) = 4 X[468] - 3 X[647], 2 X[468] - 3 X[47004], X[468] - 3 X[47175], X[647] - 4 X[47175], 3 X[850] - X[5189], 2 X[858] - 3 X[31174], 2 X[5159] - 3 X[46989], 6 X[30476] - 5 X[30745], 3 X[36900] - 5 X[37760], 2 X[37897] - 3 X[46995], 4 X[37911] - 3 X[46983]

X(47254) lies on these lines: {23, 23878}, {230, 231}, {850, 5189}, {858, 31174}, {3580, 33754}, {5159, 46989}, {6070, 36189}, {8029, 15000}, {8430, 10415}, {18325, 30209}, {30476, 30745}, {36900, 37760}, {37897, 46995}, {37911, 46983}

X(47254) = reflection of X(i) in X(j) for these {i,j}: {647, 47004}, {47004, 47175}

X(47255) = ORTHIC AXIS INTERCEPT OF X(23)X(30476)

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

X(47255) = X[23] + 2 X[30476], 4 X[468] - X[647], 2 X[468] + X[47004], 5 X[468] + X[47175], X[647] + 2 X[47004], 5 X[647] + 4 X[47175], X[850] + 5 X[37760], 2 X[858] - 5 X[31277], 2 X[7426] + X[31174], 2 X[37934] + X[46991], 2 X[37984] + X[46997], 5 X[47004] - 2 X[47175]

X(47255) lies on these lines: {23, 30476}, {230, 231}, {520, 32225}, {850, 37760}, {858, 31277}, {7426, 31174}, {23878, 37907}, {37934, 46991}, {37984, 46997}

X(47256) = X(30)X(511)∩X(468)X(850)

X(47256) lies on these lines: {23, 47175}, {30, 511}, {140, 18312}, {468, 850}, {546, 33752}, {647, 5159}, {858, 31296}, {2395, 11007}, {2485, 43291}, {3267, 6390}, {4580, 34978}, {18358, 41167}, {30476, 37911}, {31174, 47001}, {36900, 47097}, {37897, 47004}, {37934, 46990}, {37984, 47002}

X(47257) = X(23)X(46995)∩X(468)X(850)

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

X(47257) = 5 X[23] - 6 X[46995], 2 X[468] - 3 X[850], 4 X[5159] - 3 X[36900], 5 X[30745] - 3 X[31296], 5 X[37760] - 6 X[46989], 2 X[37910] - 3 X[47175]

X(47257) lies on these lines: {23, 46995}, {468, 850}, {523, 2528}, {525, 41724}, {858, 23878}, {5159, 36900}, {30745, 31296}, {37760, 46989}, {37910, 47175}

X(47258) = X(110)X(525)∩X(468)X(850)

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

X(47258) = 3 X[186] - 2 X[46990], 3 X[7426] - 2 X[47004], X[37900] + 4 X[41300], 3 X[37907] - 2 X[46989], 3 X[37909] - 2 X[46995]

X(47258) lies on these lines: {2, 47001}, {4, 47002}, {20, 47003}, {23, 385}, {30, 36900}, {110, 525}, {186, 46990}, {468, 850}, {647, 858}, {879, 6800}, {2395, 9832}, {2433, 18911}, {2986, 9180}, {7426, 23878}, {7464, 46984}, {7495, 18312}, {8675, 32220}, {9030, 32113}, {10295, 30209}, {10296, 46985}, {10989, 46983}, {32119, 32124}, {37897, 47175}, {37900, 41300}, {37907, 46989}, {37909, 46995}, {38675, 38678}

X(47258) = midpoint of X(23) and X(31296)
X(47258) = reflection of X(i) in X(j) for these {i,j}: {2, 47001}, {4, 47002}, {20, 47003}, {850, 468}, {858, 647}, {7464, 46984}, {10296, 46985}, {10989, 46983}, {47175, 37897}
X(47258) = crossdifference of every pair of points on line {39, 44895}

X(47259) = X(2)X(523)∩X(468)X(850)

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

X(47259) = 5 X[2] - 2 X[46983], X[2] + 2 X[46989], X[4] + 2 X[46990], X[20] + 2 X[46991], X[23] + 5 X[31072], 2 X[468] + X[850], 5 X[631] - 2 X[46984], X[858] - 4 X[30476], X[858] + 2 X[47004], 5 X[3091] - 2 X[46985], 2 X[5159] + X[47175], X[7426] + 2 X[31174], X[7464] + 2 X[46996], X[10296] + 2 X[46997], X[10989] + 2 X[46995], 2 X[30476] + X[47004], X[33294] - 4 X[41357], 5 X[37952] - 2 X[47003], X[46983] + 5 X[46989]

X(47259) lies on these lines: {2, 523}, {4, 46990}, {20, 46991}, {23, 31072}, {403, 30209}, {468, 850}, {520, 3580}, {631, 46984}, {858, 30476}, {2501, 13114}, {3091, 46985}, {5159, 47175}, {7426, 31174}, {7464, 46996}, {7703, 32120}, {10296, 46997}, {10989, 46995}, {19577, 33294}, {37952, 47003}

X(47260) = X(30)X(31296)∩X(468)X(850)

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

X(47260) = 3 X[468] - 2 X[850], 4 X[647] - 3 X[47097], 3 X[10151] - 4 X[47002], 2 X[30476] - 3 X[47001], 5 X[37904] - 4 X[46995], 3 X[37904] - 2 X[47175], 8 X[41300] - 3 X[46517], 6 X[46995] - 5 X[47175]

X(47260) lies on these lines: {30, 31296}, {468, 850}, {523, 3804}, {647, 47097}, {7499, 18312}, {10151, 47002}, {23878, 37904}, {30476, 47001}, {41300, 46517}

X(47261) = X(30)X(647)∩X(468)X(850)

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

X(47261) = 3 X[351] - X[47173], 3 X[468] - X[850], 5 X[647] - 3 X[46983], X[647] - 3 X[47001], 3 X[7426] + X[31296], 3 X[7426] - X[47175], 5 X[31277] - 6 X[37911], 3 X[37897] + 2 X[41300], X[46983] - 5 X[47001]

X(47261) lies on these lines: {30, 647}, {351, 41079}, {468, 850}, {523, 8651}, {525, 42654}, {6676, 18312}, {7426, 31296}, {30209, 37934}, {31277, 37911}, {36900, 37904}

X(47261) = midpoint of X(i) and X(j) for these {i,j}: {31296, 47175}, {36900, 37904}
X(47261) = crossdifference of every pair of points on line {5013, 44889}
X(47261) = {X(468),X(850)}-harmonic conjugate of X(47262)
X(47261) = {X(7426),X(31296)}-harmonic conjugate of X(47175)

X(47262) = X(2)X(47175)∩X(468)X(850)

Barycentrics (b^2 - c^2)*(6*a^10 - 9*a^8*b^2 - 3*a^6*b^4 + 9*a^4*b^6 - 3*a^2*b^8 - 9*a^8*c^2 + 28*a^6*b^2*c^2 - 16*a^4*b^4*c^2 - 10*a^2*b^6*c^2 + 7*b^8*c^2 - 3*a^6*c^4 - 16*a^4*b^2*c^4 + 30*a^2*b^4*c^4 - 7*b^6*c^4 + 9*a^4*c^6 - 10*a^2*b^2*c^6 - 7*b^4*c^6 - 3*a^2*c^8 + 7*b^2*c^8) : :

X(47262) = 3 X[2] + X[47175], 3 X[468] + X[850], X[647] + 3 X[46989], 3 X[5159] - 5 X[31277], 3 X[7426] + 5 X[31072], 5 X[31277] + 3 X[47004], 3 X[37942] - X[47002]

X(47262) lies on these lines: {2, 47175}, {30, 30476}, {468, 850}, {523, 14341}, {647, 46989}, {5159, 31277}, {6677, 18312}, {7426, 31072}, {37942, 47002}, {37984, 46990}

X(47262) = midpoint of X(i) and X(j) for these {i,j}: {5159, 47004}, {37984, 46990}
X(47262) = {X(468),X(850)}-harmonic conjugate of X(47261)

X(47263) = X(23)X(647)∩X(468)X(850)

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

X(47263) = X[23] + 2 X[647], X[110] - 4 X[42654], 4 X[351] - X[9137], 4 X[468] - X[850], 2 X[7426] + X[36900], 5 X[7426] - 2 X[46995], X[7426] + 2 X[47001], X[10295] + 2 X[47002], X[10989] - 4 X[44560], X[31296] + 5 X[37760], X[31296] + 2 X[47004], 5 X[36900] + 4 X[46995], X[36900] - 4 X[47001], 5 X[37760] - 2 X[47004], X[46995] + 5 X[47001]

X(47263) lies on these lines: {23, 647}, {110, 250}, {111, 2485}, {186, 30209}, {351, 523}, {468, 850}, {924, 9138}, {2433, 6800}, {3267, 7664}, {3569, 32124}, {6368, 14697}, {10295, 47002}, {10546, 41167}, {10989, 44560}, {13318, 30210}, {14002, 33752}, {20998, 30715}, {23878, 37907}, {31296, 37760}

X(47263) = Parry-circle-inverse of X(9979)
X(47263) = crossdifference of every pair of points on line {574, 15000}
X(47263) = X(2071)-of-1st-Parry-triangle
X(47263) = X(186)-of-2nd-Parry-triangle
X(47263) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7426, 47001, 36900}, {31296, 37760, 47004}

X(47264) = X(2)X(33752)∩X(468)X(850)

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

X(47264) = 3 X[2] + 2 X[47004], X[23] + 4 X[30476], 3 X[403] + 2 X[46990], 4 X[468] + X[850], 3 X[9979] - 8 X[41357], 2 X[31174] + 3 X[37907], X[36900] + 4 X[46989], 4 X[37911] + X[47175], 3 X[44280] + 2 X[46991]

X(47264) lies on these lines: {2, 33752}, {23, 30476}, {403, 46990}, {468, 850}, {512, 15059}, {523, 31209}, {9979, 41357}, {30745, 31277}, {31072, 37760}, {31174, 37907}, {36900, 46989}, {37911, 47175}, {44280, 46991}

X(47264) = midpoint of X(31072) and X(37760)
X(47264) = reflection of X(30745) in X(31277)
X(47264) = {X(468),X(850)}-harmonic conjugate of X(47263)

X(47265) = X(3)X(5106)∩X(15)X(99)

X(47265) lies on the cubic K1270 and these lines: {3, 5106}, {15, 99}, {62, 729}, {9431, 11486}, {33757, 35918}

X(47266) = X(3)X(5106)∩X(16)X(99)

X(47266) lies on the cubic K1270 and these lines: {3, 5106}, {16, 99}, {61, 729}, {9431, 11485}, {33757, 35917}

X(47267) = (name pending)

X(47268) = (name pending)

X(47269) = X(290)X(6527)∩X(648)X(1624)

X(47269) lies on Steiner circumellipse and these lines: {290,6527}, {648,1624}, {671,13380}, {6528,41678}

X(47269) = X(661)-isoconjugate of X(13346)
X(47269) = X(110)-reciprocal conjugate of X(13346)
X(47269) = cevapoint of X(i)and X(j) for these {i,j}: {20,647}, {525,45200}
X(47269) = barycentric product X(99)*X(13380)
X(47269) = barycentric quotient X(110)/X(13346)
X(47269) = trilinear product X(662)*X(13380)
X(47269) = trilinear quotient X(662)/X(13346

X(47270) = X(1)X(523)∩X(30)X(40)

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

X(47270) = 3 X[1] - 2 X[13869], 3 X[165] - 2 X[36158], 5 X[1698] - 4 X[36155], 3 X[3109] - X[13869]

X(47270) lies on these lines: {1, 523}, {2, 38514}, {5, 5520}, {8, 36171}, {10, 36154}, {21, 38570}, {23, 26227}, {30, 40}, {80, 21381}, {165, 36158}, {186, 37812}, {267, 7354}, {318, 37964}, {404, 1290}, {405, 2453}, {468, 11809}, {476, 6757}, {477, 35056}, {514, 24347}, {550, 2940}, {691, 11104}, {759, 1109}, {858, 29857}, {952, 2948}, {1008, 38526}, {1010, 46912}, {1146, 16562}, {1316, 1724}, {1325, 2975}, {1329, 30447}, {1698, 36155}, {2074, 41227}, {2687, 2689}, {2688, 37048}, {2690, 2752}, {2695, 2766}, {3258, 27685}, {3878, 7424}, {4427, 21290}, {5099, 37049}, {5189, 31079}, {5433, 39751}, {5445, 36195}, {5450, 46618}, {5620, 24916}, {6741, 13211}, {6742, 11720}, {10944, 31524}, {13743, 38580}, {16320, 37047}, {25440, 36167}, {26285, 46635}, {32612, 46636}, {37702, 46037}, {38588, 45976}

X(47270) = midpoint of X(8) and X(36171)
X(47270) = reflection of X(i) in X(j) for these {i,j}: {1, 3109}, {2948, 14985}, {6742, 11720}, {11809, 468}, {13211, 6741}, {36154, 10}, {39751, 44898}
X(47270) = reflection of X(1) in the Euler line
X(47270) = complement of X(38514)
X(47270) = incircle-inverse of X(39540)
X(47270) = Conway-circle-inverse of X(39547)
X(47270) = reflection of X(47321) in the orthic axis
X(47270) = X(110)-of-inner-Garcia-triangle

X(47271) = X(1)X(30)∩X(225)X(468)

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

X(47271) lies on these lines: {1, 30}, {23, 37579}, {225, 468}, {523, 43052}, {858, 26481}, {1068, 10295}, {1070, 47092}, {3011, 37904}, {7464, 26357}, {7575, 36152}, {10297, 37565}, {33925, 37946}, {37899, 47178}, {37931, 47156}

X(47272) = X(1)X(523)∩X(8)X(30)

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

X(47272) = 2 X[1] - 3 X[3109], 4 X[1] - 3 X[13869], 4 X[3579] - 3 X[36158], 5 X[3617] - 3 X[36154], X[3621] + 3 X[36171], 7 X[9780] - 6 X[36155], 7 X[9780] - 3 X[38514

X(47272) lies on these lines: {1, 523}, {8, 30}, {468, 1068}, {952, 23236}, {3579, 36158}, {3617, 36154}, {3621, 36171}, {5520, 7173}, {9780, 36155}, {11809, 16305}, {16316, 37047}, {18357, 20957}, {24880, 39751}

X(47272) = reflection of X(i) in X(j) for these {i,j}: {11809, 16305}, {13869, 3109}, {38514, 36155}
X(47272) = reflection of X(13869) in the Euler line

X(47273) = X(1)X(523)∩X(30)X(4677)

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

X(47273) = 3 X[1] - 4 X[3109], 5 X[1] - 4 X[13869], 5 X[3109] - 3 X[13869], 3 X[3679] - 2 X[36154], 9 X[19875] - 8 X[36155

X(47273) lies on these lines: {1, 523}, {10, 38514}, {30, 4677}, {519, 36171}, {993, 38570}, {1290, 25440}, {1325, 8666}, {1724, 2453}, {2687, 5450}, {3679, 36154}, {5196, 6763}, {5520, 7741}, {11376, 31522}, {11809, 16309}, {19875, 36155}, {24914, 39751}, {31524, 37738}, {37047, 47245}

X(47273) = reflection of X(i) in X(j) for these {i,j}: {11809, 16309}, {38514, 10}

X(47274) = X(1)X(523)∩X(30)X(7982)

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

X(47274) = 3 X[1] - 2 X[3109], X[3109] - 3 X[13869], 3 X[3241] - X[36171], 3 X[3679] - 4 X[36155

X(47274) lies on these lines: {1, 523}, {30, 7982}, {145, 38514}, {496, 5520}, {519, 36154}, {952, 12407}, {1290, 3871}, {1724, 2452}, {3241, 36171}, {3679, 36155}, {3874, 5196}, {6070, 27685}, {7991, 36158}, {8715, 36167}, {10942, 42422}, {10950, 31522}, {11101, 14480}, {12607, 30447}, {26285, 46636}, {32612, 46635}, {37047, 47242}

X(47274) = midpoint of X(145) and X(38514)
X(47274) = reflection of X(i) in X(j) for these {i,j}: {1, 13869}, {7991, 36158}

X(47275) = X(6)X(30)∩X(23)X(230)

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

X(47275) =3 X[6] - 4 X[16303], 3 X[2453] - 4 X[16321], 3 X[5112] - 2 X[16321], 2 X[16312] - 3 X[32113

X(47275) lies on these lines: {4, 13531}, {6, 30}, {23, 230}, {50, 3018}, {53, 186}, {187, 1989}, {216, 18403}, {393, 13619}, {523, 39232}, {566, 5475}, {858, 31489}, {1609, 5899}, {1990, 18365}, {2070, 8553}, {2071, 15109}, {2072, 36751}, {2165, 37936}, {2453, 5112}, {2502, 9158}, {3003, 18325}, {3053, 47168}, {3054, 37907}, {3284, 19656}, {3569, 16171}, {3767, 37967}, {3815, 10989}, {5189, 7736}, {5210, 44265}, {5254, 37946}, {5304, 20063}, {5355, 13338}, {7426, 37637}, {7575, 21843}, {7735, 37901}, {7747, 41335}, {8573, 37949}, {8588, 36430}, {9722, 43893}, {9855, 45331}, {10295, 47144}, {11594, 36163}, {13881, 16619}, {14460, 47153}, {14533, 19651}, {16306, 37900}, {16312, 32113}, {24975, 35933}, {30745, 47186}, {32217, 36181}, {35296, 44386}, {36188, 41939}, {36748, 44246}, {37899, 47184}, {37974, 47142}, {37975, 47141}, {43620, 44266}

X(47275) = reflection of X(i) in X(j) for these {i,j}: {2453, 5112}, {36181, 32217}
X(47275) = crossdifference of every pair of points on line {575, 8675}
X(47275) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {858, 47169, 31489}, {3018, 6781, 50}

X(47276) = X(6)X(468)∩X(23)X(524)

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

X(47276) =3 X[6] - 4 X[468], 3 X[69] - X[5189], 6 X[141] - 5 X[30745], 3 X[186] - 2 X[8550], 2 X[468] - 3 X[32113], 3 X[599] - 2 X[858], 3 X[1352] - 2 X[18572], 3 X[1992] - 5 X[37760], 2 X[3292] - 3 X[5648], 2 X[5095] - 3 X[18374], 3 X[5112] - 2 X[16333], 8 X[5159] - 9 X[21358], 2 X[8584] - 3 X[37907], 3 X[11160] + X[20063], 3 X[11179] - 4 X[18571], 3 X[15993] - 2 X[47242], X[16176] - 3 X[19596], 3 X[18403] - 4 X[18553], 3 X[20423] - 4 X[44961], 2 X[25329] - 3 X[35265], 2 X[37900] + 3 X[40341], 3 X[41721] - X[41724

X(47276) lies on these lines: {2, 15826}, {4, 12061}, {6, 468}, {23, 524}, {30, 15069}, {50, 41359}, {67, 1205}, {69, 5189}, {141, 30745}, {155, 16619}, {186, 8550}, {193, 32217}, {511, 7728}, {523, 39232}, {599, 858}, {895, 8262}, {1192, 31804}, {1352, 18572}, {1503, 12244}, {1992, 37760}, {2854, 41721}, {3292, 5648}, {3564, 15085}, {3629, 32218}, {5095, 18374}, {5099, 8586}, {5112, 16333}, {5159, 21358}, {5181, 10510}, {6144, 32220}, {7426, 15534}, {7574, 11649}, {8584, 37907}, {8675, 47254}, {9969, 13622}, {10295, 10605}, {10415, 42007}, {10989, 22165}, {11160, 20063}, {11179, 18571}, {11477, 11799}, {11645, 32272}, {14023, 37905}, {15993, 47242}, {18403, 18553}, {20423, 44961}, {23061, 30718}, {25329, 35265}, {25336, 46818}, {32274, 44668}, {32621, 37920}, {37777, 41585}, {37900, 40317}, {41583, 41615}, {41596, 41617}

X(47276) = anticomplement of X(15826)
X(47276) = reflection of X(i) in X(j) for these {i,j}: {6, 32113}, {193, 32217}, {895, 8262}, {3629, 32218}, {6144, 32220}, {7574, 34507}, {8586, 5099}, {10510, 5181}, {10989, 22165}, {11477, 11799}, {15534, 7426}, {25336, 46818}
X(47276) = crosssum of X(23) and X(16042)
X(47276) = crossdifference of every pair of points on line {575, 30209}

X(47277) = X(6)X(468)∩X(125)X(524)

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

X(47277) = 3 X[6] - X[32113], X[125] - 3 X[21639], 3 X[468] - 2 X[32113], 3 X[1570] - X[5099], 3 X[1992] - X[32220], 3 X[2072] - X[11898], 5 X[3618] - 4 X[37911], 4 X[3629] + X[46517], 3 X[5032] - X[7426], 3 X[5093] - X[11799], 4 X[5480] - 3 X[10151], 3 X[8584] - X[32217], 4 X[8584] - X[37904], X[10295] - 3 X[14912], 8 X[12007] - 3 X[37931], 3 X[13473] - 2 X[36990], 3 X[14853] - 2 X[37984], 2 X[15448] - 3 X[44102], 4 X[15826] - X[46517], 2 X[15993] - 3 X[47237], X[20080] - 5 X[30745], 3 X[20583] - X[32218], 3 X[25321] - X[46818], 4 X[32217] - 3 X[37904], 8 X[32455] - X[37899], 9 X[33748] - 5 X[37952

X(47277) lies on these lines: {6, 468}, {23, 19459}, {30, 1351}, {69, 5159}, {125, 524}, {184, 8584}, {193, 858}, {265, 895}, {287, 9190}, {427, 11216}, {511, 974}, {568, 15073}, {1112, 2393}, {1316, 16312}, {1495, 15471}, {1503, 5095}, {1570, 5099}, {1899, 15534}, {2072, 11898}, {3618, 37911}, {3629, 15826}, {5032, 7426}, {5093, 11799}, {5189, 18935}, {5480, 8541}, {5622, 37477}, {6467, 8705}, {7728, 41720}, {8675, 47248}, {8779, 16316}, {10257, 41614}, {10295, 14912}, {11179, 47031}, {12007, 19161}, {13473, 17813}, {14853, 37984}, {15122, 19348}, {15341, 44496}, {15448, 44102}, {15993, 47237}, {16387, 37784}, {18323, 39899}, {19119, 37900}, {19125, 37897}, {19457, 32599}, {19504, 41744}, {20080, 30745}, {20583, 32218}, {25321, 46818}, {32245, 41613}, {32621, 37969}, {33748, 37952}, {34777, 46444}, {37491, 37929}, {41359, 46203}

X(47277) = midpoint of X(i) and X(j) for these {i,j}: {193, 858}, {3629, 15826}, {18323, 39899}
X(47277) = reflection of X(i) in X(j) for these {i,j}: {69, 5159}, {468, 6}, {1495, 15471}, {16312, 1316}, {47031, 11179}
X(47277) = crosssum of X(3) and X(32127)
X(47277) = crossdifference of every pair of points on line {1351, 30209}
X(47277) = {X(2104),X(2105)}-harmonic conjugate of X(10602)

X(47278) = X(6)X(468)∩X(30)X(5921)

Barycentrics -6*a^8 + 21*a^6*b^2 + a^4*b^4 - 21*a^2*b^6 + 5*b^8 + 21*a^6*c^2 - 38*a^4*b^2*c^2 + 21*a^2*b^4*c^2 + a^4*c^4 + 21*a^2*b^2*c^4 - 10*b^4*c^4 - 21*a^2*c^6 + 5*c^8 : :

X(47278) = 4 X[6] - 5 X[468], 3 X[6] - 5 X[32113], 3 X[468] - 4 X[32113], 2 X[6776] - 3 X[37931], 6 X[21356] - 5 X[47097], 5 X[32218] - 3 X[41149], 2 X[32220] - 3 X[37904

X(47278) lies on these lines: {6, 468}, {23, 19588}, {30, 5921}, {69, 46517}, {193, 37897}, {399, 34380}, {524, 24981}, {3531, 37984}, {6776, 37931}, {8705, 47095}, {12294, 13473}, {20080, 37900}, {21356, 47097}, {32218, 41149}, {32220, 37904}

X(47278) = midpoint of X(20080) and X(37900)
X(47278) = reflection of X(i) in X(j) for these {i,j}: {193, 37897}, {46517, 69}

X(47279) = X(6)X(468)∩X(30)X(69)

Barycentrics -2*a^8 + 11*a^6*b^2 - a^4*b^4 - 11*a^2*b^6 + 3*b^8 + 11*a^6*c^2 - 18*a^4*b^2*c^2 + 11*a^2*b^4*c^2 - a^4*c^4 + 11*a^2*b^2*c^4 - 6*b^4*c^4 - 11*a^2*c^6 + 3*c^8 : :

X(47279) = 2 X[6] - 3 X[468], X[6] - 3 X[32113], 3 X[23] + X[20080], 4 X[141] - 3 X[47097], X[193] - 3 X[7426], 3 X[858] - 5 X[3620], 7 X[3619] - 6 X[5159], 4 X[3630] + 3 X[37899], 8 X[3631] - 3 X[46517], 3 X[10295] - X[39874], 3 X[10297] - 4 X[18358], X[11008] - 3 X[32220], X[11008] - 6 X[37897], 3 X[11799] - X[44456], X[39899] - 3 X[44265], 2 X[46264] - 3 X[47031

X(47279) lies on these lines: {6, 468}, {23, 20080}, {30, 69}, {141, 16325}, {159, 37969}, {186, 19459}, {193, 7426}, {511, 1514}, {524, 1495}, {858, 3620}, {1503, 10990}, {1843, 10151}, {1992, 21970}, {2070, 19588}, {3313, 3631}, {3564, 3581}, {3619, 5159}, {3630, 16331}, {5095, 15448}, {5655, 10752}, {6776, 37934}, {8263, 15066}, {8675, 47175}, {9001, 47174}, {9007, 47216}, {9030, 47260}, {10295, 39874}, {10297, 11188}, {10602, 37643}, {11008, 32220}, {11550, 22165}, {11649, 14913}, {11799, 44456}, {13169, 20127}, {15533, 31383}, {15993, 47155}, {16619, 34380}, {26926, 37931}, {34417, 41585}, {39899, 44265}, {46264, 47031}

X(47279) = reflection of X(i) in X(j) for these {i,j}: {468, 32113}, {5095, 15448}, {6776, 37934}, {32220, 37897}, {47155, 15993}
X(47279) = crossdifference of every pair of points on line {5050, 30209}
X(47279) = {X(6),X(468)}-harmonic conjugate of X(47456)

X(47280) = X(6)X(468)∩X(30)X(11477)

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

X(47280) = 3 X[6] - 2 X[468], X[23] - 3 X[1992], 3 X[69] - 5 X[30745], 3 X[193] + X[5189], 4 X[468] - 3 X[32113], 4 X[575] - 3 X[44214], 3 X[599] - 4 X[5159], 3 X[895] - X[41724], 3 X[1351] - X[18325], 3 X[2072] - 2 X[34507], 3 X[2452] - 2 X[16333], 6 X[3629] - X[37900], 9 X[5032] - 5 X[37760], 2 X[15118] - 3 X[21639], 4 X[15471] - 3 X[18374], 3 X[15993] - 4 X[47238], 3 X[32220] - X[37900

X(47280) lies on these lines: {6, 468}, {23, 1992}, {30, 11477}, {52, 11649}, {67, 524}, {69, 30745}, {141, 11443}, {193, 5189}, {403, 8537}, {511, 16111}, {542, 18323}, {575, 44214}, {576, 11799}, {599, 5159}, {1351, 18325}, {1503, 10721}, {2072, 8538}, {2393, 5095}, {2452, 16333}, {3284, 41359}, {3564, 18572}, {3629, 8705}, {5032, 37760}, {5094, 11216}, {5099, 44496}, {5621, 32599}, {5890, 8550}, {7426, 8584}, {8541, 37981}, {8548, 15122}, {8675, 47250}, {9030, 47257}, {9786, 37934}, {10297, 15069}, {12161, 16619}, {12596, 32123}, {13248, 32125}, {15118, 21639}, {15471, 18374}, {15533, 47097}, {15993, 47238}, {21284, 32621}, {22165, 38397}, {25329, 46818}, {32217, 32455}, {35282, 46203}

X(47280) = reflection of X(i) in X(j) for these {i,j}: {858, 15826}, {5099, 44496}, {7426, 8584}, {10295, 8550}, {11799, 576}, {15069, 10297}, {15533, 47097}, {32113, 6}, {32123, 12596}, {32125, 13248}, {32217, 32455}, {32220, 3629}, {46818, 25329}
X(47280) = crossdifference of every pair of points on line {576, 30209}
X(47280) = {X(6),X(468)}-harmonic conjugate of X(47458)

X(47281) = X(6)X(468)∩X(30)X(193)

Barycentrics 10*a^8 - 19*a^6*b^2 - 7*a^4*b^4 + 19*a^2*b^6 - 3*b^8 - 19*a^6*c^2 + 42*a^4*b^2*c^2 - 19*a^2*b^4*c^2 - 7*a^4*c^4 - 19*a^2*b^2*c^4 + 6*b^4*c^4 + 19*a^2*c^6 - 3*c^8 : :

X(47281) = 4 X[6] - 3 X[468], 5 X[6] - 3 X[32113], 2 X[69] - 3 X[47097], 5 X[468] - 4 X[32113], 3 X[858] - X[20080], 5 X[3620] - 6 X[5159], X[3630] - 3 X[15826], 2 X[11008] + 3 X[46517], 3 X[14912] - 2 X[37934

X(47281) lies on these lines: {6, 468}, {30, 193}, {69, 47097}, {511, 20725}, {524, 47155}, {858, 20080}, {1992, 26864}, {3620, 5159}, {3630, 15826}, {8705, 16327}, {10151, 12167}, {11008, 46517}, {14912, 37934}, {17040, 37935}, {19459, 37969}, {19588, 37980}, {32220, 37899}, {34380, 37496}

X(47281) = reflection of X(i) in X(j) for these {i,j}: {37899, 32220}, {37904, 1992}
X(47281) = crossdifference of every pair of points on line {5093, 30209}

X(47282) = X(30)X(69)∩X(468)X(7736)

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

X(47282) = 3 X[1316] - 4 X[16321], 3 X[2452] - 4 X[16303], 3 X[5112] - 2 X[16303], 2 X[16321] - 3 X[32113

X(47282) lies on these lines: {4, 16330}, {23, 7779}, {30, 69}, {186, 20775}, {340, 43460}, {468, 7736}, {511, 1555}, {523, 39232}, {524, 32224}, {754, 32114}, {858, 16325}, {1316, 16321}, {2070, 20794}, {2071, 22062}, {2452, 5112}, {2782, 41721}, {3289, 16319}, {5189, 16313}, {5899, 22152}, {6148, 35002}, {7426, 7774}, {9996, 11188}, {16328, 43718}, {16331, 37900}

X(47282) = reflection of X(i) in X(j) for these {i,j}: {1316, 32113}, {2452, 5112}

X(47283) = X(6)X(523)∩X(30)X(5921)

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

X(47283) = 4 X[6] - 5 X[1316], 6 X[6] - 5 X[2452], 3 X[6] - 5 X[2453], 3 X[1316] - 2 X[2452], 3 X[1316] - 4 X[2453], 5 X[6795] - 6 X[17508], 6 X[21356] - 5 X[36194

X(47283) lies on these lines: {2, 47154}, {6, 523}, {30, 5921}, {5112, 16312}, {6795, 17508}, {21356, 36194}, {37667, 37897}, {37668, 46517}, {37911, 40809}

X(47283) = reflection of X(i) in X(j) for these {i,j}: {2452, 2453}, {5112, 16312}
X(47283) = {X(2452),X(2453)}-harmonic conjugate of X(1316)

X(47284) = X(6)X(523)∩X(30)X(15069)

Barycentrics X(47284) = a^8 - a^6*b^2 + 3*a^4*b^4 - 3*a^2*b^6 - a^6*c^2 - 5*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + 4*b^6*c^2 + 3*a^4*c^4 + 3*a^2*b^2*c^4 - 8*b^4*c^4 - 3*a^2*c^6 + 4*b^2*c^6 : :

X(47284) = 3 X[6] - 4 X[1316], 5 X[6] - 4 X[2452], 3 X[599] - 2 X[36163], 5 X[1316] - 3 X[2452], 2 X[1316] - 3 X[2453], 2 X[2452] - 5 X[2453], 7 X[10541] - 8 X[36177], 8 X[11007] - 9 X[21358

X(47284) lies on these lines: {2, 47245}, {6, 523}, {23, 8667}, {30, 15069}, {157, 3447}, {394, 36188}, {476, 35259}, {524, 36181}, {599, 36163}, {842, 9756}, {868, 15356}, {1989, 41359}, {5023, 36180}, {5189, 7788}, {5858, 44466}, {5859, 44462}, {8556, 9832}, {9308, 30716}, {10541, 36177}, {10605, 15111}, {10606, 36164}, {10607, 39193}, {11007, 21358}, {11472, 16168}, {16181, 36836}, {16182, 36843}, {16312, 32113}, {16320, 37637}, {18451, 36193}, {18573, 47213}, {19596, 37921}, {22331, 36156}, {22332, 36157}, {30549, 30715}, {33924, 37985}, {38552, 40801}, {39560, 44058}, {44889, 47254}

X(47284) = reflection of X(i) in X(j) for these {i,j}: {6, 2453}, {32113, 16312}

X(47285) = X(6)X(523)∩X(30)X(69)

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

X(47285) = 2 X[6] - 3 X[1316], 4 X[6] - 3 X[2452], X[6] - 3 X[2453], 4 X[141] - 3 X[36194], X[2452] - 4 X[2453], 5 X[3618] - 6 X[34094], 7 X[3619] - 6 X[11007], 5 X[3620] - 3 X[36163], 4 X[5092] - 3 X[6795], 5 X[12017] - 6 X[36177], 3 X[16279] - 4 X[19130], X[20080] + 3 X[36181

X(47285) lies on these lines: {2, 16316}, {6, 523}, {23, 16313}, {30, 69}, {74, 2790}, {111, 47211}, {125, 2847}, {141, 36194}, {186, 16330}, {216, 47213}, {264, 842}, {338, 9142}, {393, 468}, {476, 10546}, {543, 32114}, {858, 16331}, {1249, 47172}, {1384, 36156}, {1494, 10722}, {1495, 37926}, {1632, 5191}, {3054, 16320}, {3055, 47245}, {3260, 35002}, {3618, 34094}, {3619, 11007}, {3620, 36163}, {4226, 36207}, {5024, 36157}, {5033, 44058}, {5092, 6795}, {5099, 18424}, {5112, 16334}, {5888, 9159}, {6033, 35520}, {6148, 38730}, {7426, 16325}, {7473, 9308}, {7610, 46992}, {7703, 34312}, {7735, 47155}, {7897, 10989}, {8177, 9462}, {9139, 9307}, {9530, 13202}, {9717, 18808}, {11188, 12157}, {11488, 32460}, {11489, 32461}, {12017, 36177}, {14685, 47216}, {14977, 40856}, {15066, 36192}, {15356, 38393}, {15655, 36180}, {15915, 22062}, {16179, 42128}, {16180, 42125}, {16181, 42116}, {16182, 42115}, {16261, 38677}, {16279, 19130}, {16315, 37689}, {20080, 36181}, {20208, 37987}, {20775, 37991}, {20975, 41254}, {23200, 38294}, {26864, 36178}, {33630, 47158}, {34540, 36185}, {34541, 36186}, {37637, 47171}, {37690, 47097}, {37930, 40947}, {40900, 44466}, {40901, 44462}, {43618, 44915}, {44889, 47175}

X(47285) = reflection of X(i) in X(j) for these {i,j}: {1316, 2453}, {2452, 1316}, {5112, 16334}
X(47285) = reflection of X(2452) in the Euler line

X(47286) = X(30)X(148)∩X(99)X(230)

Barycentrics a^2*b^2 + b^4 + a^2*c^2 - 4*b^2*c^2 + c^4 : :
Barycentrics cot^2 A - cot^2 B - cot^2 C + cot B cot C : :

X(47286) = 3 X[2] - 4 X[43291], X[99] - 3 X[14568], 3 X[99] - 4 X[32459], 2 X[99] - 3 X[35297], 2 X[114] - 3 X[39663], 3 X[115] - 2 X[625], 3 X[115] - X[7813], 4 X[115] - 3 X[33228], 4 X[141] - 3 X[6393], 3 X[148] + 2 X[3793], 3 X[148] + X[14712], X[148] + 3 X[19570], 4 X[187] - 3 X[8598], 2 X[187] - 3 X[22329], 2 X[230] - 3 X[14568], 3 X[230] - 2 X[32459], 4 X[230] - 3 X[35297], X[316] - 3 X[671], 2 X[316] - 3 X[8352], X[316] + 3 X[11054], 3 X[325] - 4 X[625], 3 X[325] - 2 X[7813], X[325] - 4 X[32457], 2 X[325] - 3 X[33228], 3 X[385] - 2 X[3793], 3 X[385] - X[14712], X[385] - 3 X[19570], X[625] - 3 X[32457], 8 X[625] - 9 X[33228], 3 X[2482] - 2 X[15301], 5 X[3618] - 3 X[12215], 2 X[3793] - 9 X[19570], 3 X[5215] - 2 X[36521], 6 X[5461] - 5 X[31275], 4 X[5461] - 3 X[41133], 3 X[6034] - 2 X[44380], 4 X[6329] - 3 X[13196], 3 X[6784] - 2 X[35060], X[7779] - 3 X[14041], 3 X[7799] - 5 X[14061], 3 X[7799] - 4 X[44377], X[7813] - 6 X[32457], 4 X[7813] - 9 X[33228], X[7840] - 3 X[41135], X[7845] - 3 X[39563], X[8352] + 2 X[11054], X[8591] - 3 X[8859], 3 X[8859] - 2 X[27088], 3 X[9166] - 2 X[22110], 3 X[11632] - X[35002], 3 X[12243] + X[43453], X[13172] - 3 X[21445], 3 X[13586] - X[20094], 5 X[14061] - 4 X[44377], 9 X[14568] - 4 X[32459], X[14712] - 9 X[19570], X[23235] - 3 X[38227], 5 X[31275] - 3 X[39785], 10 X[31275] - 9 X[41133], 8 X[32457] - 3 X[33228], 8 X[32459] - 9 X[35297], 3 X[33265] + X[35369], 2 X[37350] - 3 X[41135], 6 X[38224] - 5 X[40336], 2 X[39785] - 3 X[41133], 3 X[41134] - 4 X[44401

X(47286) lies on these lines: {2, 2418}, {3, 17008}, {4, 193}, {5, 194}, {6, 8370}, {12, 25264}, {23, 5938}, {30, 148}, {32, 19687}, {39, 32992}, {69, 7841}, {76, 141}, {83, 6329}, {99, 230}, {113, 39931}, {114, 39663}, {115, 325}, {126, 3291}, {140, 7783}, {183, 2549}, {187, 543}, {192, 495}, {274, 33034}, {287, 15341}, {297, 525}, {315, 33229}, {316, 524}, {330, 496}, {338, 1236}, {376, 37667}, {381, 7774}, {382, 20065}, {384, 5305}, {403, 41676}, {442, 1655}, {458, 37645}, {468, 7665}, {511, 6071}, {532, 31710}, {533, 31709}, {546, 7785}, {547, 17005}, {549, 17004}, {550, 7793}, {574, 37688}, {598, 8584}, {623, 36251}, {624, 36252}, {668, 21956}, {691, 47242}, {732, 39266}, {858, 31125}, {894, 37715}, {1003, 7735}, {1384, 33007}, {1503, 38664}, {1506, 32450}, {1513, 2782}, {1654, 17677}, {1834, 17499}, {1916, 15980}, {1975, 3767}, {1992, 7620}, {2030, 14928}, {2421, 45938}, {2482, 15301}, {2896, 8357}, {3053, 33250}, {3180, 43416}, {3181, 43417}, {3314, 33184}, {3589, 7827}, {3618, 5286}, {3620, 33190}, {3627, 7823}, {3629, 7812}, {3630, 7850}, {3631, 7883}, {3729, 25978}, {3734, 5309}, {3760, 26561}, {3761, 26590}, {3785, 33234}, {3788, 32820}, {3815, 7757}, {3845, 7837}, {3850, 13571}, {3926, 7887}, {3933, 5025}, {3934, 7765}, {3972, 5306}, {3978, 9428}, {4045, 9466}, {4173, 6310}, {4442, 17497}, {4754, 23903}, {5013, 32832}, {5133, 8267}, {5140, 8681}, {5167, 34383}, {5215, 36521}, {5283, 33033}, {5304, 14033}, {5355, 7804}, {5461, 31275}, {5475, 7798}, {5480, 32451}, {5866, 5941}, {5965, 13449}, {5969, 15993}, {6034, 44380}, {6248, 19130}, {6321, 36849}, {6337, 33233}, {6381, 26582}, {6462, 13886}, {6463, 13939}, {6531, 17932}, {6655, 7767}, {6722, 14148}, {6784, 35060}, {7388, 13951}, {7389, 8976}, {7472, 16315}, {7615, 11163}, {7618, 8860}, {7619, 11614}, {7709, 37451}, {7736, 44543}, {7737, 14614}, {7738, 11285}, {7739, 11174}, {7745, 7760}, {7746, 7781}, {7747, 7805}, {7748, 7750}, {7755, 7816}, {7756, 7780}, {7758, 7773}, {7761, 11648}, {7763, 13881}, {7764, 39565}, {7766, 11361}, {7771, 13468}, {7775, 18424}, {7776, 14063}, {7778, 32833}, {7779, 14041}, {7786, 9607}, {7789, 7828}, {7794, 7861}, {7795, 7851}, {7797, 7819}, {7799, 14061}, {7801, 7844}, {7806, 8369}, {7817, 7820}, {7822, 7902}, {7825, 7855}, {7826, 7842}, {7834, 17130}, {7836, 8361}, {7838, 39590}, {7839, 16044}, {7840, 37350}, {7843, 7890}, {7845, 39563}, {7846, 19702}, {7853, 14711}, {7854, 7872}, {7858, 15031}, {7863, 7886}, {7864, 8362}, {7879, 32974}, {7881, 14064}, {7893, 33019}, {7898, 14929}, {7900, 14062}, {7906, 20105}, {7921, 33018}, {7923, 8364}, {7931, 8360}, {7932, 33185}, {7941, 32993}, {7945, 33186}, {8353, 8667}, {8368, 16984}, {8588, 34504}, {8589, 34506}, {8591, 8859}, {8596, 9855}, {8597, 44367}, {8716, 37637}, {8728, 27269}, {8744, 37784}, {9149, 37927}, {9166, 22110}, {9605, 16924}, {9891, 33343}, {9893, 33342}, {10583, 19697}, {10592, 32107}, {10593, 32005}, {10845, 35947}, {10846, 35946}, {10992, 47113}, {11053, 22254}, {11064, 41254}, {11112, 16997}, {11113, 16998}, {11114, 17002}, {11159, 21309}, {11164, 37809}, {11286, 16989}, {11287, 16990}, {11303, 11542}, {11304, 11543}, {11580, 14360}, {11623, 18860}, {11632, 35002}, {11634, 36874}, {13172, 21445}, {13188, 37459}, {13586, 20094}, {13638, 35953}, {14035, 30435}, {14042, 20088}, {14645, 44369}, {14880, 44251}, {14970, 33666}, {15014, 16318}, {15484, 33016}, {15589, 32986}, {15655, 33208}, {16041, 37668}, {16043, 32834}, {16052, 31090}, {16921, 31406}, {17001, 17579}, {17527, 27318}, {17669, 40908}, {17670, 18135}, {17739, 24851}, {17747, 40859}, {17757, 17759}, {17983, 41909}, {18287, 38282}, {18840, 43681}, {19569, 33699}, {20888, 26558}, {21226, 24390}, {21531, 40858}, {22495, 22576}, {22496, 22575}, {23000, 25195}, {23009, 25191}, {23235, 38227}, {23537, 25994}, {24855, 30786}, {25242, 25984}, {31060, 37096}, {31173, 36523}, {31419, 41838}, {31467, 32999}, {32818, 32972}, {32822, 32973}, {32823, 32980}, {32831, 32969}, {32835, 32976}, {32836, 33219}, {32840, 33199}, {32869, 33223}, {32983, 37665}, {32985, 37689}, {33265, 35369}, {33314, 34953}, {34511, 43620}, {34518, 38294}, {35927, 46453}, {36196, 44373}, {37648, 40814}, {38224, 40336}, {39355, 44227}, {39646, 46264}, {41134, 44401}

X(47286) = midpoint of X(i) and X(j) for these {i,j}: {148, 385}, {671, 11054}, {8596, 9855}, {8597, 44367}
X(47286) = reflection of X(i) in X(j) for these {i,j}: {99, 230}, {115, 32457}, {325, 115}, {691, 47242}, {6390, 43291}, {7472, 16315}, {7813, 625}, {7840, 37350}, {8352, 671}, {8591, 27088}, {8598, 22329}, {10992, 47113}, {13188, 37459}, {13449, 38734}, {14148, 6722}, {14712, 3793}, {14928, 2030}, {18860, 11623}, {31173, 36523}, {35297, 14568}, {39785, 5461}
X(47286) = isotomic conjugate of X(41909)
X(47286) = anticomplement of X(6390)
X(47286) = polar conjugate of X(2374)
X(47286) = anticomplement of the isogonal conjugate of X(8753)
X(47286) = anticomplement of the isotomic conjugate of X(17983)
X(47286) = complement of the isotomic conjugate of X(9227)
X(47286) = isotomic conjugate of the isogonal conjugate of X(3291)
X(47286) = polar conjugate of the isogonal conjugate of X(8681)
X(47286) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19, 14360}, {111, 4329}, {158, 34518}, {897, 1370}, {923, 20}, {1973, 8591}, {8753, 8}, {17983, 6327}, {23894, 13219}, {32676, 44010}, {32740, 6360}, {36060, 6527}, {36128, 69}, {36142, 6563}, {46111, 21275}
X(47286) = X(i)-complementary conjugate of X(j) for these (i,j): {9227, 2887}, {38279, 18589}
X(47286) = X(i)-Ceva conjugate of X(j) for these (i,j): {671, 14263}, {17983, 2}
X(47286) = X(i)-isoconjugate of X(j) for these (i,j): {31, 41909}, {48, 2374}, {896, 15387}, {922, 44182}, {923, 34161}
X(47286) = cevapoint of X(i) and X(j) for these (i,j): {193, 7665}, {3291, 8681}
X(47286) = crosspoint of X(i) and X(j) for these (i,j): {2, 9227}, {76, 671}
X(47286) = crosssum of X(i) and X(j) for these (i,j): {6, 9225}, {32, 187}, {647, 21906}
X(47286) = trilinear pole of line {126, 9134}
X(47286) = crossdifference of every pair of points on line {184, 8644}
X(47286) = barycentric product X(i)*X(j) for these {i,j}: {76, 3291}, {99, 9134}, {126, 671}, {264, 8681}, {305, 5140}, {321, 16756}, {325, 36874}, {850, 11634}, {3266, 14263}, {17466, 46277}
X(47286) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 41909}, {4, 2374}, {111, 15387}, {126, 524}, {325, 36892}, {524, 34161}, {671, 44182}, {3291, 6}, {5140, 25}, {8681, 3}, {9134, 523}, {11634, 110}, {14263, 111}, {16756, 81}, {17466, 896}, {21905, 351}, {34171, 2770}, {36874, 98}
X(47286) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 6392, 7754}, {4, 7754, 7762}, {6, 11185, 8370}, {6, 34505, 11185}, {32, 32819, 19687}, {69, 43448, 7841}, {76, 5254, 6656}, {76, 7790, 141}, {99, 230, 35297}, {99, 14568, 230}, {115, 325, 33228}, {115, 7813, 625}, {141, 5254, 7790}, {141, 7790, 6656}, {148, 19570, 385}, {183, 2549, 8356}, {315, 44518, 33229}, {381, 22253, 7774}, {385, 14712, 3793}, {625, 7813, 325}, {671, 892, 34169}, {1975, 3767, 7807}, {1992, 7620, 11317}, {2996, 6392, 4}, {3734, 5309, 7792}, {3734, 7792, 6661}, {5025, 20081, 3933}, {5461, 39785, 41133}, {5475, 7798, 41624}, {5523, 44146, 297}, {6390, 43291, 2}, {6655, 17129, 7767}, {7735, 32815, 1003}, {7738, 32828, 11285}, {7748, 7750, 19695}, {7748, 7751, 7750}, {7761, 17131, 37671}, {7763, 13881, 33249}, {7766, 11361, 18907}, {7795, 7851, 8363}, {7797, 17128, 7819}, {7798, 18546, 5475}, {7799, 14061, 44377}, {7840, 41135, 37350}, {7864, 31276, 8362}, {7923, 46226, 8364}, {8591, 8859, 27088}, {8667, 44526, 14907}, {11648, 17131, 7761}, {14064, 32830, 7881}, {14907, 44526, 8353}, {20105, 32966, 7906}

X(47287) = X(30)X(7779)∩X(99)X(230)

X(47287) = 3 X[99] - 2 X[230], 5 X[99] - 3 X[14568], 5 X[99] - 4 X[32459], 4 X[99] - 3 X[35297], 3 X[148] - 5 X[7925], 2 X[148] - 3 X[33228], 10 X[230] - 9 X[14568], 5 X[230] - 6 X[32459], 8 X[230] - 9 X[35297], 4 X[325] - 3 X[8352], 3 X[325] - 4 X[14148], 7 X[325] - 6 X[31173], 5 X[325] - 6 X[39785], X[385] - 3 X[8591], 2 X[385] - 3 X[8598], 3 X[671] - 4 X[44377], 3 X[2482] - 2 X[32457], 2 X[3793] - 3 X[33265], 6 X[6390] - 5 X[7925], 4 X[6390] - 3 X[33228], 3 X[6393] - 2 X[11646], 3 X[7472] - 2 X[47155], X[7779] + 3 X[20094], 10 X[7925] - 9 X[33228], 9 X[8352] - 16 X[14148], 7 X[8352] - 8 X[31173], 5 X[8352] - 8 X[39785], 3 X[14041] - X[35369], 14 X[14148] - 9 X[31173], 10 X[14148] - 9 X[39785], 3 X[14568] - 4 X[32459], 4 X[14568] - 5 X[35297], 3 X[15300] - 2 X[32456], 3 X[22329] - 4 X[32456], 3 X[23235] - X[43460], 5 X[31173] - 7 X[39785], 16 X[32459] - 15 X[35297], 9 X[41134] - 8 X[44381

X(47287) lies on these lines: {4, 9742}, {30, 7779}, {69, 8353}, {76, 15598}, {99, 230}, {115, 15301}, {148, 6390}, {194, 18907}, {298, 35691}, {299, 35695}, {325, 543}, {385, 8591}, {524, 45018}, {538, 6781}, {548, 17129}, {550, 20081}, {671, 44377}, {1003, 5304}, {1513, 13188}, {1975, 2549}, {2482, 32457}, {2996, 33233}, {3564, 13172}, {3627, 7906}, {3629, 11055}, {3630, 11057}, {3793, 33265}, {3853, 7941}, {3926, 33229}, {3933, 7898}, {5254, 7835}, {5355, 7816}, {5475, 7781}, {6337, 33249}, {6392, 33235}, {6393, 11646}, {6661, 7875}, {7472, 47155}, {7620, 34803}, {7736, 8370}, {7748, 7908}, {7754, 33250}, {7756, 7848}, {7770, 32822}, {7783, 32992}, {7788, 43619}, {7789, 7919}, {7803, 19702}, {7841, 32817}, {7881, 32824}, {7893, 15704}, {8356, 16990}, {8596, 37350}, {8716, 11185}, {9741, 11317}, {11001, 20080}, {12429, 14952}, {14033, 14930}, {14041, 35369}, {14929, 33264}, {15300, 22329}, {15589, 35955}, {16986, 32480}, {16989, 35954}, {17131, 34504}, {18546, 37647}, {20105, 33257}, {21309, 33187}, {22253, 33007}, {23235, 43460}, {32830, 33234}, {32833, 44526}, {32840, 33238}, {33227, 45017}, {41134, 44381}

X(47287) = reflection of X(i) in X(j) for these {i,j}: {115, 15301}, {148, 6390}, {1513, 13188}, {8596, 37350}, {8598, 8591}, {22329, 15300}
X(47287) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 14568, 32459}, {148, 6390, 33228}, {31859, 32815, 8370}

X(47288) = X(30)X(23235)∩X(99)X(523)

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

X(47288) = 2 X[98] - 3 X[38704], 3 X[99] - 2 X[7472], 4 X[468] - 3 X[14568], 3 X[671] - 4 X[14120], 3 X[691] - 4 X[7472], 2 X[858] - 3 X[7799], 3 X[9166] - 4 X[46986], 3 X[12151] - 2 X[15826], 3 X[14651] - 4 X[16760], 2 X[15342] - 3 X[33803], 2 X[16092] - 3 X[41134], 3 X[19570] - 5 X[37760], 3 X[21166] - 2 X[46633], 2 X[23235] + X[38680], 4 X[33813] - 3 X[38702], 3 X[34473] - 4 X[46987], 3 X[35297] - 2 X[47242], 3 X[38704] - 4 X[46634

X(47288) lies on these lines: {2, 10415}, {23, 538}, {30, 23235}, {76, 9832}, {98, 38704}, {99, 523}, {110, 3906}, {148, 5099}, {249, 826}, {250, 827}, {468, 14568}, {476, 12074}, {525, 15342}, {543, 36174}, {648, 46619}, {671, 14120}, {842, 2782}, {858, 7799}, {1287, 7953}, {1316, 7757}, {1975, 38526}, {2452, 3972}, {2453, 31859}, {4226, 14366}, {6033, 44972}, {6070, 35922}, {7426, 11054}, {7482, 23878}, {7760, 36156}, {7781, 36182}, {7796, 36187}, {7950, 9218}, {9166, 46986}, {10422, 16276}, {10989, 39785}, {12151, 15826}, {12188, 38613}, {14611, 35278}, {14651, 16760}, {14981, 36173}, {16092, 41134}, {19570, 37760}, {20063, 31068}, {21166, 46633}, {23698, 44969}, {32833, 36163}, {33813, 38702}, {34473, 46987}, {35297, 47242}, {36166, 38664}

X(47288) = reflection of X(i) in X(j) for these {i,j}: {98, 46634}, {148, 5099}, {691, 99}, {10989, 39785}, {11054, 7426}, {12188, 38613}, {36173, 14981}, {38664, 36166}, {44972, 6033}
X(47288) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 46634, 38704}, {935, 41676, 250}

X(47289) = X(30)X(7779)∩X(99)X(523)

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

X(47289) = 5 X[99] - 3 X[691], 4 X[99] - 3 X[7472], 2 X[148] - 3 X[36196], 4 X[620] - 3 X[16092], 4 X[691] - 5 X[7472], 2 X[12042] - 3 X[46634], 2 X[12188] - 3 X[36166], 5 X[14061] - 6 X[46986], 3 X[14568] - 4 X[47171], 3 X[35297] - 2 X[47155], X[35369] - 3 X[36174

X(47289) lies on these lines: {30, 7779}, {99, 523}, {148, 36196}, {476, 907}, {620, 16092}, {826, 14999}, {7426, 9870}, {7473, 14611}, {7766, 36156}, {11054, 46992}, {12042, 46634}, {12188, 36166}, {14061, 46986}, {14568, 47171}, {30221, 35278}, {35297, 47155}, {35369, 36174}, {36187, 37668}

X(47290) = X(30)X(11054)∩X(99)X(523)

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

X(47290) = 3 X[99] - 4 X[7472], 3 X[671] - 2 X[36174], 3 X[691] - 2 X[7472], 2 X[842] - 3 X[34473], 4 X[858] - 3 X[7809], 4 X[5099] - 5 X[14061], 9 X[9166] - 8 X[14120], 3 X[9166] - 4 X[16092], 2 X[14120] - 3 X[16092], 3 X[14568] - 4 X[47242], 3 X[21166] - 4 X[38611], 3 X[34473] - 4 X[46633], 3 X[35297] - 2 X[47245], X[38664] + 2 X[38679], 3 X[38702] - 2 X[46634], 3 X[38704] - 4 X[46981

X(47290) lies on these lines: {2, 8877}, {30, 11054}, {99, 523}, {110, 12073}, {112, 1287}, {249, 3800}, {476, 8599}, {512, 15342}, {648, 7482}, {671, 36174}, {754, 5189}, {842, 34473}, {858, 7809}, {1078, 9832}, {1316, 12150}, {2453, 3972}, {2696, 33638}, {2770, 46783}, {2782, 38582}, {4226, 14884}, {5099, 14061}, {5649, 18556}, {5912, 10630}, {6179, 37915}, {7468, 14480}, {7760, 36182}, {7811, 36163}, {7927, 9218}, {9166, 14120}, {10722, 38953}, {11007, 31168}, {12042, 38583}, {12203, 38528}, {14568, 47242}, {15398, 36168}, {21166, 38611}, {30735, 35139}, {35297, 47245}, {36166, 38680}, {38702, 46634}, {38704, 46981}

X(47290) = reflection of X(i) in X(j) for these {i,j}: {99, 691}, {842, 46633}, {10722, 38953}, {38583, 12042}, {38680, 36166}
X(47290) = barycentric product X(648)*X(25320)
X(47290) = barycentric quotient X(25320)/X(525)
X(47290) = {X(842),X(46633)}-harmonic conjugate of X(34473)

X(47291) = X(30)X(148)∩X(99)X(523)

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

X(47291) = X[99] - 3 X[691], 2 X[99] - 3 X[7472], 2 X[115] - 3 X[16092], 4 X[115] - 3 X[36196], 3 X[1551] - 2 X[6033], 3 X[5099] - 4 X[6722], 4 X[12042] - 3 X[36166], 2 X[12042] - 3 X[46633], X[12188] + 3 X[38582], 5 X[14061] - 6 X[46980], 2 X[16316] - 3 X[35297], 3 X[26613] - 2 X[46992], 5 X[31274] - 6 X[40544], 3 X[34473] - X[38680], 3 X[38227] - 2 X[46993], 3 X[38702] - 2 X[46987

X(47391) lies on these lines: {30, 148}, {98, 38679}, {99, 523}, {112, 476}, {115, 5912}, {183, 36165}, {376, 34810}, {512, 14999}, {842, 46981}, {858, 5971}, {1551, 6033}, {2407, 11634}, {2696, 3565}, {2770, 15899}, {3329, 36157}, {3800, 9218}, {5099, 6722}, {5914, 10630}, {7426, 11580}, {7468, 14611}, {7766, 36182}, {7771, 38526}, {9181, 12073}, {12042, 36166}, {14061, 46980}, {16316, 35297}, {26613, 46992}, {31274, 40544}, {34473, 38680}, {36168, 46783}, {38227, 46993}, {38611, 46634}, {38702, 46987}, {44969, 46982}

X(47291) = midpoint of X(98) and X(38679)
X(47291) = reflection of X(i) in X(j) for these {i,j}: {842, 46981}, {7472, 691}, {36166, 46633}, {36196, 16092}, {44969, 46982}, {46634, 38611}
X(47291) = crossdifference of every pair of points on line {10567, 16186}

X(47292) = X(30)X(5984)∩X(99)X(523)

Barycentrics (a^2 - b^2)*(a^2 - c^2)*(2*a^6 - 2*a^4*b^2 - 7*a^2*b^4 - 3*b^6 - 2*a^4*c^2 + 16*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(47292) = 3 X[99] - 5 X[691], 4 X[99] - 5 X[7472], 4 X[691] - 3 X[7472], 5 X[5099] - 6 X[5461], 2 X[5099] - 3 X[16092], 4 X[5461] - 5 X[16092], 9 X[9167] - 10 X[40544], 3 X[35297] - 2 X[47154], 3 X[36166] - 2 X[38583], 5 X[36196] - 6 X[41135], 2 X[38613] - 3 X[46633

X(47292) lies on these lines: {30, 5984}, {99, 523}, {110, 3800}, {3793, 20099}, {5099, 5461}, {7473, 35360}, {7927, 9181}, {9167, 40544}, {12073, 14999}, {12317, 34380}, {35297, 47154}, {36166, 38583}, {36196, 41135}, {38613, 46633}

X(47293) = X(30)X(147)∩X(99)X(523)

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

X(47293) = 3 X[99] - X[691], 2 X[691] - 3 X[7472], 3 X[1551] - 2 X[38953], 3 X[2482] - 2 X[40544], 4 X[5099] - 3 X[36196], 3 X[6054] - X[44972], 3 X[8724] - X[38953], 3 X[13188] + X[38583], 3 X[14568] - 4 X[47239], 3 X[16092] - 4 X[40544], 2 X[16315] - 3 X[35297], 3 X[21166] - 2 X[46981], 3 X[36166] - 4 X[38613], 2 X[38613] - 3 X[46634], X[38664] - 3 X[38704], 3 X[41134] - 2 X[46980

X(47293) lies on these lines: {30, 147}, {98, 46987}, {99, 523}, {110, 525}, {148, 14120}, {194, 36156}, {385, 36180}, {468, 7665}, {543, 5099}, {671, 46986}, {698, 32217}, {826, 9181}, {842, 23235}, {858, 6390}, {1003, 2452}, {1287, 12074}, {1316, 31859}, {1551, 8724}, {1975, 36165}, {2453, 8716}, {2482, 16092}, {2782, 36166}, {3564, 10295}, {3906, 14999}, {3926, 36187}, {4226, 14611}, {6054, 44972}, {7482, 47256}, {7709, 36177}, {7783, 36157}, {10723, 46988}, {11054, 46998}, {11104, 13869}, {12079, 35922}, {12215, 25052}, {13574, 37900}, {14568, 47239}, {16315, 35297}, {18311, 23348}, {20094, 36174}, {21166, 46981}, {31128, 46783}, {32459, 47242}, {32817, 36163}, {33813, 46633}, {38664, 38704}, {41134, 46980}, {41676, 46619}

X(47293) = midpoint of X(i) and X(j) for these {i,j}: {842, 23235}, {20094, 36174}
X(47293) = reflection of X(i) in X(j) for these {i,j}: {98, 46987}, {148, 14120}, {385, 36180}, {671, 46986}, {858, 6390}, {1551, 8724}, {7472, 99}, {10723, 46988}, {11054, 46998}, {16092, 2482}, {36166, 46634}, {46633, 33813}, {47242, 32459}
X(47293) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {250, 17491}, {1101, 858}, {4235, 21294}, {18020, 21298}, {23889, 13219}, {24000, 41724}, {32676, 45291}
X(47293) = trilinear pole of line {32257, 44915}
X(47293) = barycentric product X(i)*X(j) for these {i,j}: {648, 32257}, {892, 44915}
X(47293) = barycentric quotient X(i)/X(j) for these {i,j}: {32257, 525}, {44915, 690}

X(47294) = X(30)X(99)∩X(126)X(468)

Barycentrics (2*a^2 - b^2 - c^2)*(3*a^8 - 5*a^6*b^2 - 4*a^4*b^4 + 5*a^2*b^6 + b^8 - 5*a^6*c^2 + 19*a^4*b^2*c^2 - 7*a^2*b^4*c^2 - 9*b^6*c^2 - 4*a^4*c^4 - 7*a^2*b^2*c^4 + 16*b^4*c^4 + 5*a^2*c^6 - 9*b^2*c^6 + c^8) : :

X(47294) lies on these lines: {30, 99}, {126, 468}, {858, 7665}, {1503, 32114}, {5139, 13473}, {7472, 16315}, {10418, 47097}, {14417, 47217}, {14712, 16103}, {37904, 47170}

X(47294) = reflection of X(i) in X(j) for these {i,j}: {16315, 7472}, {16316, 99}, {47295,468}

X(47295) = X(30)X(98)∩X(126)X(468)

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

X(47295) = 5 X[468] - 4 X[32459], 5 X[691] - 9 X[14568], 2 X[691] - 3 X[16315], 5 X[5099] - 3 X[39785], 2 X[7472] - 3 X[47240], 6 X[14568] - 5 X[16315

X(47295) lies on these lines: {30, 98}, {126, 468}, {1503, 32127}, {3291, 46517}, {5099, 39785}, {7472, 47240}, {16229, 41357}, {19577, 37900}, {37803, 37897}

X(47296) = X(2)X(6)∩X(125)X(468)

Barycentrics 2*a^6 - a^4*b^2 - 4*a^2*b^4 + 3*b^6 - a^4*c^2 + 8*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(47296) = 9 X[2] - X[323], 3 X[2] + X[3580], 15 X[2] + X[37779], 5 X[2] - X[40112], 7 X[2] + X[44555], X[74] + 3 X[403], 3 X[125] + X[1495], 2 X[125] + X[15448], 3 X[186] + 5 X[15081], X[265] + 3 X[44214], X[323] + 3 X[3580], X[323] - 3 X[11064], 5 X[323] + 3 X[37779], 5 X[323] - 9 X[40112], 7 X[323] + 9 X[44555], X[323] + 9 X[44569], 3 X[403] - X[1514], 3 X[468] - X[1495], X[858] - 5 X[15059], 3 X[858] + X[15107], 2 X[1495] - 3 X[15448], X[1511] - 3 X[44452], X[1986] - 3 X[16227], 3 X[2072] + X[3581], 5 X[3580] - X[37779], 5 X[3580] + 3 X[40112], 7 X[3580] - 3 X[44555], X[3580] - 3 X[44569], 7 X[3619] + X[41617], 5 X[3620] + 3 X[37784], X[7687] + 3 X[44673], 3 X[9140] + X[46818], 3 X[10151] - X[13202], 3 X[10257] - X[10564], X[10264] + 3 X[44282], X[10295] + 3 X[14644], X[10297] - 3 X[23515], X[10733] + 3 X[44280], 5 X[11064] + X[37779], 5 X[11064] - 3 X[40112], 7 X[11064] + 3 X[44555], X[11064] + 3 X[44569], X[11799] + 3 X[15061], X[12112] - 9 X[37943], 2 X[12900] - 3 X[44911], X[13202] + 3 X[21663], 3 X[15055] - X[20725], 15 X[15059] + X[15107], 5 X[15059] + X[32269], X[15107] - 3 X[32269], X[15122] - 3 X[34128], X[15153] + 2 X[37935], 3 X[21639] - X[47281], 3 X[23515] + X[32110], X[32223] + 3 X[45311], 3 X[35266] - X[46818], X[37779] + 3 X[40112], 7 X[37779] - 15 X[44555], X[37779] - 15 X[44569], 7 X[40112] + 5 X[44555], X[40112] + 5 X[44569], 3 X[44282] - X[46817], X[44555] - 7 X[44569]

X(47296) lies on these lines: {2, 6}, {4, 8567}, {5, 4550}, {25, 23332}, {30, 6699}, {64, 6622}, {74, 403}, {111, 2867}, {115, 44216}, {125, 468}, {140, 11430}, {154, 23291}, {186, 15081}, {187, 441}, {235, 6696}, {265, 44214}, {297, 39062}, {338, 46106}, {373, 19161}, {389, 3628}, {427, 34417}, {440, 37508}, {459, 33630}, {465, 10645}, {466, 10646}, {470, 5318}, {471, 5321}, {472, 42101}, {473, 42102}, {511, 5159}, {512, 47252}, {523, 22264}, {525, 3239}, {546, 32210}, {547, 18388}, {549, 18390}, {578, 632}, {858, 15059}, {902, 25968}, {914, 17044}, {1146, 17923}, {1192, 3091}, {1204, 5893}, {1350, 16051}, {1368, 3098}, {1511, 44452}, {1585, 42284}, {1586, 42283}, {1589, 6411}, {1590, 6412}, {1594, 11745}, {1596, 23329}, {1620, 3146}, {1656, 12233}, {1853, 6353}, {1899, 10192}, {1986, 16227}, {1990, 14165}, {1995, 45303}, {2072, 3581}, {2777, 37984}, {2781, 44084}, {2854, 35371}, {2883, 26937}, {2929, 14118}, {3003, 44436}, {3089, 40686}, {3090, 9786}, {3147, 34782}, {3154, 11657}, {3258, 47146}, {3331, 44893}, {3357, 44960}, {3431, 12022}, {3515, 41362}, {3525, 11425}, {3526, 39571}, {3530, 13403}, {3535, 23249}, {3536, 23259}, {3541, 15873}, {3542, 6247}, {3548, 37483}, {3564, 5972}, {3634, 44547}, {3818, 44212}, {4232, 36990}, {5092, 6676}, {5094, 5480}, {5133, 10545}, {5191, 44887}, {5210, 37188}, {5254, 11331}, {5326, 11429}, {5446, 32144}, {5449, 16238}, {5621, 37962}, {5640, 37473}, {5894, 37197}, {5943, 21851}, {6000, 15151}, {6070, 47148}, {6146, 10018}, {6240, 11704}, {6393, 37803}, {6623, 10606}, {6640, 41587}, {6677, 18358}, {6688, 11548}, {6741, 16272}, {6748, 43462}, {6756, 32767}, {7294, 19365}, {7493, 44882}, {7505, 11456}, {7542, 37513}, {7998, 44439}, {8550, 26869}, {8705, 32246}, {8780, 21974}, {8889, 17810}, {9140, 35266}, {9410, 44576}, {9826, 12900}, {10114, 13392}, {10117, 37777}, {10151, 11598}, {10182, 12024}, {10257, 10564}, {10264, 44282}, {10295, 14644}, {10297, 23515}, {10300, 14810}, {10516, 40132}, {10546, 23293}, {10733, 44280}, {10752, 15131}, {10979, 26906}, {11245, 44109}, {11561, 15350}, {11585, 37478}, {11799, 15061}, {11801, 18571}, {12079, 16319}, {12112, 37943}, {12359, 15068}, {12901, 15646}, {13160, 43584}, {13289, 44272}, {13292, 43839}, {13394, 18911}, {13488, 25563}, {13561, 44232}, {13851, 37931}, {14915, 20397}, {14924, 43841}, {14940, 15032}, {15055, 20725}, {15080, 26913}, {15122, 34128}, {15139, 19128}, {15153, 18400}, {15269, 34806}, {15595, 41181}, {15760, 37470}, {16531, 30522}, {16621, 20299}, {16655, 23294}, {16657, 37118}, {17809, 18950}, {18396, 35486}, {18405, 37460}, {18474, 44211}, {18533, 23324}, {18593, 18644}, {19772, 42087}, {19773, 42088}, {20391, 23047}, {21167, 46336}, {21639, 47281}, {21970, 31670}, {23315, 37981}, {23325, 37458}, {23327, 41585}, {29012, 37897}, {29323, 37910}, {30771, 33878}, {31255, 43653}, {32225, 47097}, {33533, 44201}, {34310, 40355}, {34609, 43621}, {37517, 41588}, {40135, 40996}, {40867, 46276}, {42654, 47253}, {43607, 44958}, {43903, 45004}, {43961, 47141}, {43962, 47142}, {44277, 44829}, {44877, 46206}

X(47296) = midpoint of X(i) and X(j) for these {i,j}: {2, 44569}, {74, 1514}, {125, 468}, {858, 32269}, {3154, 11657}, {3258, 47146}, {3580, 11064}, {6070, 47148}, {6741, 16272}, {9140, 35266}, {10151, 21663}, {10264, 46817}, {10297, 32110}, {11801, 18571}, {12079, 16319}, {13851, 37931}, {32225, 47097}, {43961, 47141}, {43962, 47142}
X(47296) = reflection of X(i) in X(j) for these {i,j}: {5159, 6723}, {5972, 37911}, {15448, 468}, {42654, 47253}
X(47296) = isogonal conjugate of X(34570)
X(47296) = isotomic conjugate of X(44877)
X(47296) = complement of X(11064)
X(47296) = complement of the isogonal conjugate of X(8749)
X(47296) = anticomplement of the isotomic conjugate of X(46206)
X(47296) = complement of the isotomic conjugate of X(16080)
X(47296) = isotomic conjugate of the isogonal conjugate of X(40135)
X(47296) = isotomic conjugate of the polar conjugate of X(10151)
X(47296) = polar conjugate of the isotomic conjugate of X(40996)
X(47296) = polar conjugate of the isogonal conjugate of X(21663)
X(47296) = X(46206)-anticomplementary conjugate of X(6327)
X(47296) = cevapoint of X(21663) and X(40135)
X(47296) = crosspoint of X(2) and X(16080)
X(47296) = crosssum of X(6) and X(3284)
X(47296) = crossdifference of every pair of points on line {154, 512}
X(47296) = X(i)-complementary conjugate of X(j) for these (i,j): {19, 113}, {74, 18589}, {661, 16177}, {798, 39008}, {1304, 4369}, {1973, 3163}, {2155, 3184}, {2159, 3}, {2349, 1368}, {2433, 34846}, {8749, 10}, {15459, 21259}, {15627, 34823}, {16077, 42327}, {16080, 2887}, {18808, 21253}, {32676, 5664}, {32695, 8062}, {32715, 14838}, {35200, 6389}, {36119, 141}, {36131, 523}, {40351, 16584}, {40352, 1214}, {40354, 37}
X(47296) = X(i)-Ceva conjugate of X(j) for these (i,j): {16077, 523}, {46206, 2}
X(47296) = X(i)-cross conjugate of X(j) for these (i,j): {21663, 40996}, {40135, 10151}
X(47296) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34570}, {31, 44877}, {610, 5896}
X(47296) = barycentric product X(i)*X(j) for these {i,j}: {1, 18699}, {4, 40996}, {69, 10151}, {76, 40135}, {264, 21663}, {850, 5502}, {1494, 13202}
X(47296) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 44877}, {6, 34570}, {64, 5896}, {5502, 110}, {10151, 4}, {11598, 2071}, {13202, 30}, {18699, 75}, {21663, 3}, {40135, 6}, {40996, 69}
X(47296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3580, 11064}, {2, 13567, 23292}, {2, 26958, 13567}, {2, 37638, 141}, {2, 37643, 6}, {2, 37648, 3589}, {6, 26958, 37643}, {6, 37643, 13567}, {74, 403, 1514}, {343, 15066, 3631}, {1899, 37453, 10192}, {3580, 40112, 37779}, {8115, 8116, 37672}, {10018, 26917, 6146}, {10264, 44282, 46817}, {11064, 44569, 3580}, {20299, 21841, 16621}, {23291, 38282, 154}, {23515, 32110, 10297}

X(47297) = X(115)X(468)∩X(187)X(47091)

X(47297) lies on these lines: {115, 468}, {187, 47091}, {230, 47090}, {460, 39832}, {1285, 35484}, {2549, 7499}, {6676, 43448}, {7735, 39662}, {10257, 43291}

X(47298) = X(50)X(230)∩X(115)X(468)

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

X(47298) lies on these lines: {2, 1975}, {6, 45303}, {22, 44528}, {32, 427}, {39, 37454}, {50, 230}, {115, 468}, {187, 46517}, {325, 19577}, {1184, 8889}, {1370, 5023}, {1503, 14567}, {3053, 31099}, {3054, 40916}, {3055, 13351}, {3265, 23881}, {3266, 40511}, {3291, 5159}, {3767, 5094}, {3933, 30747}, {5038, 37649}, {5169, 7745}, {5319, 15880}, {5913, 30745}, {6034, 44569}, {6329, 23297}, {6656, 11056}, {6749, 7735}, {6781, 47095}, {7493, 44518}, {7499, 37512}, {7667, 15513}, {7746, 30739}, {7748, 44210}, {7749, 43957}, {7755, 15820}, {8357, 15822}, {8361, 30749}, {8791, 37981}, {9225, 11064}, {10415, 47245}, {10416, 34169}, {10418, 37911}, {11059, 33249}, {11284, 43620}, {14061, 37803}, {16315, 23991}, {16318, 40135}, {16320, 31644}, {17129, 45201}, {21243, 44499}, {23332, 42295}, {30744, 40326}, {31125, 32459}, {32740, 37801}, {34866, 37929}, {37637, 46336}, {37804, 47286}, {37904, 39563}, {39884, 44116}, {41139, 42008}, {44398, 47242}, {45212, 47155}

X(47298) = X(i)-complementary conjugate of X(j) for these (i,j): {111, 21247}, {923, 206}, {2156, 126}, {2353, 16597}, {32740, 16582}
X(47298) = crosssum of X(3167) and X(14961)
X(47298) = crossdifference of every pair of points on line {8651, 20993}
X(47298) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3291, 5159, 24855}, {5159, 43291, 3291}

X(47299) = X(1)X(198)∩X(37)X(57)

X(47299) lies on the cubic K1112 and these lines: {1, 198}, {2, 28616}, {7, 21068}, {9, 1125}, {37, 57}, {40, 2294}, {46, 16673}, {101, 1449}, {346, 3306}, {354, 1696}, {612, 33588}, {942, 2324}, {966, 6762}, {1056, 20262}, {1202, 2257}, {1486, 5269}, {1697, 16777}, {1706, 17314}, {1766, 37526}, {1778, 18164}, {2178, 3601}, {2345, 5437}, {2650, 33589}, {3220, 27802}, {3304, 33590}, {3338, 3731}, {3339, 21871}, {3553, 11518}, {3723, 37556}, {5128, 16672}, {5436, 38871}, {6590, 42462}, {9578, 24005}, {10389, 36744}, {11028, 18216}, {11037, 27508}, {15624, 37553}, {16970, 28014}, {25124, 26244}

X(47299) = complement of X(28616)
X(47299) = X(47299) = barycentric product X(1)*X(11024)
X(47299) = barycentric quotient X(11024)/X(75)

X(47300) = X(3)X(3158)∩X(6)X(1334)

X(47300) lies on the cubic K1112 and these lines: {3, 3158}, {6, 1334}, {519, 37062}, {612, 3304}, {1293, 28193}, {12513, 19649}

X(47301) = 69TH HATZIPOLAKIS-MOSES-EULER POINT

X(47301) lies on these lines: {2,3}, {373,14640}, {389,41481}, {5946,42453}, {9730,32428}

X(47302) = X(1)X(2137)∩X(3)X(11506)

X(47302) lies on the cubic K1271 and these lines: {1, 2137}, {3, 11506}, {40, 3880}, {1293, 2136}, {4221, 5358}, {7982, 10700}

X(47303) = X(1)X(289)∩X(40)X(12518)

Barycentrics a*(b*(a - b - c)*(3*a - b - c)*(b - c)*(a + b - c)*c*(a - b + c)*(a + b + c) - 8*a*b*(a - b - c)*(b - c)*c*(a^2*b - b^3 + a^2*c - a*b*c - c^3)*Sin[A/2] - 2*a*c*(a - b + c)*(a^5 + a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 + b^5 + 2*a^3*b*c - 6*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 + 10*a*b^2*c^2 - 4*b^3*c^2 - 2*a*b*c^3 - 2*b^2*c^3 + a*c^4 + 3*b*c^4)*Sin[B/2] + 2*a*b*(a + b - c)*(a^5 - 2*a^3*b^2 + a*b^4 + a^4*c + 2*a^3*b*c - 4*a^2*b^2*c - 2*a*b^3*c + 3*b^4*c + 2*a^3*c^2 - 6*a^2*b*c^2 + 10*a*b^2*c^2 - 2*b^3*c^2 - 2*a^2*c^3 + 2*a*b*c^3 - 4*b^2*c^3 - 3*a*c^4 + 2*b*c^4 + c^5)*Sin[C/2])::

X(47303) = 3 X[1] - X[11527] (*= reflection of the (midpoint of x[1] and x[11527]) in x[1]*)

X(47303) lies on the cubic K1271 and these lines: {1, 289}, {40, 12518}, {3659, 12646}, {8110, 16192}, {12513, 12523}

X(47304) = X(3)X(3462)∩X(4)X(8431)

X(47304) lies on the cubic K005 and these lines: {3,3462}, {4,8431}, {5,34298}, {195,46035}, {250,2055}, {389,520}, {2120,3471}, {3460,46037}, {8837,8919}, {8839,8918}

X(47304) = isogonal conjugate of X(38933)
X(47304) = X(54)-cross conjugate of X(3471)
X(47304) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {1990,6761}, {3284,15781}
X(47304) = barycentric quotient X(i)/X(j) for these {i,j}: {1990,6761}, {3284,15781}
X(47304) = trilinear quotient X(1784)/X(6761)

X(47305) = X(3)X(1138)∩X(4)X(5670)

X(47305) lies on the cubic K005 and these lines: {3,1138}, {4,5670}, {5,14451}, {54,46035}, {140,40662}, {3459,38933}, {3467,46037}

X(47306) = X(3)X(5677)∩X(4)X(7327)

X(47306) lies on the cubic K005 and these lines: {1,46035}, {3,5677}, {4,7327}, {3467,38933}, {3468,3471}

X(47307) = X(3)X(3065)∩X(4)X(5677)

X(47307) lies on the cubic K005 and these lines: {1,3471}, {3,3065}, {4,5677}, {5,14452}, {54,46037}, {3459,3468}, {3461,38933}, {3469,46035}

X(47308) = SHINAGAWA-EULER POINT ((E-8F)/2,0)

Barycentrics (a^2 - b^2 - c^2)*(10*a^8 - 7*a^6*b^2 - 13*a^4*b^4 + 7*a^2*b^6 + 3*b^8 - 7*a^6*c^2 + 30*a^4*b^2*c^2 - 7*a^2*b^4*c^2 - 12*b^6*c^2 - 13*a^4*c^4 - 7*a^2*b^2*c^4 + 18*b^4*c^4 + 7*a^2*c^6 - 12*b^2*c^6 + 3*c^8) : :

X(47308) = 5 X[3] - 3 X[2072], 3 X[3] - 2 X[5159], 4 X[3] - 3 X[10257], 7 X[3] - 6 X[16976], 3 X[3] - X[18323], 7 X[3] - 3 X[18403], X[3] - 3 X[44246], 5 X[3] - 6 X[47114], X[4] - 3 X[44280], 3 X[20] + X[23], X[23] - 3 X[10295], 3 X[186] + X[3529], 3 X[376] - X[858], 3 X[381] - 4 X[37911], X[382] - 3 X[44214], 3 X[403] - X[3146], 3 X[403] - 5 X[37952], 3 X[468] - 4 X[18571], 5 X[468] - 6 X[18579], 7 X[468] - 8 X[22249], 5 X[468] - 4 X[44961], X[468] - 3 X[47031], 5 X[468] - 3 X[47310], 4 X[546] - 3 X[13473], 2 X[546] - 3 X[44452], 3 X[550] - X[37950], 6 X[550] - X[46517], X[1657] + 2 X[37934], 3 X[1657] + 5 X[37958], 3 X[1657] + 4 X[47316], 9 X[2072] - 10 X[5159], 4 X[2072] - 5 X[10257], 6 X[2072] - 5 X[10297], 7 X[2072] - 10 X[16976], 9 X[2072] - 5 X[18323], 7 X[2072] - 5 X[18403], X[2072] - 5 X[44246], 5 X[3091] - 9 X[37941], 5 X[3091] - 6 X[44911], X[3146] - 5 X[37952], 5 X[3522] - X[10296], 9 X[3534] - X[35001], 2 X[3627] - 3 X[10151], X[3627] - 3 X[15646], 4 X[3628] - 3 X[23323], 2 X[3628] - 3 X[37968], 11 X[5072] - 12 X[44912], 8 X[5159] - 9 X[10257], 4 X[5159] - 3 X[10297], 7 X[5159] - 9 X[16976], 14 X[5159] - 9 X[18403], 2 X[5159] - 9 X[44246], 5 X[5159] - 9 X[47114], X[7464] + 3 X[13619], X[7464] - 3 X[16386], X[7464] - 5 X[17538], X[7574] - 5 X[15696], 2 X[7575] - 3 X[37931], 4 X[7575] - 3 X[37971], 5 X[7575] - 3 X[43893], and many others

X(47308) lies on these lines: {2, 3}, {511, 44573}, {1060, 5160}, {1062, 7286}, {1503, 16111}, {3284, 6781}, {3292, 16163}, {3564, 12121}, {5446, 16227}, {8705, 37511}, {9716, 34796}, {11063, 47189}, {11064, 38726}, {11645, 32257}, {12244, 46818}, {12295, 47296}, {12358, 14915}, {13169, 32272}, {13851, 38729}, {14961, 16308}, {15012, 32411}, {15826, 44882}, {30209, 47003}, {32124, 41470}, {34109, 47164}, {34584, 46817}, {35520, 40996}, {43273, 47280}

X(47308) = midpoint of X(i) and X(j) for these {i,j}: {20, 10295}, {1657, 11799}, {7426, 11001}, {7575, 15704}, {12244, 46818}, {13619, 16386}, {15681, 44265}, {32124, 41470}, {44266, 44903}
X(47308) = reflection of X(i) in X(j) for these {i,j}: {382, 37984}, {2072, 47114}, {10151, 15646}, {10297, 3}, {11064, 38726}, {11799, 37934}, {12295, 47296}, {13473, 44452}, {15122, 548}, {18323, 5159}, {18325, 37897}, {18403, 16976}, {23323, 37968}, {31726, 37935}, {37971, 37931}, {44283, 16531}, {46517, 37950}, {47097, 8703}, {47309, 468}, {47310, 18579}
X(47308) = X(46201)-complementary conjugate of X(20305)
X(47308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 10297, 10257}, {3, 18323, 5159}, {20, 12082, 15704}, {20, 44240, 12605}, {382, 44214, 37984}, {468, 47310, 44961}, {3146, 37952, 403}, {5159, 18323, 10297}, {7464, 17538, 16386}, {7542, 15122, 10257}, {10295, 44246, 44240}, {11799, 37958, 47316}, {13619, 17538, 7464}, {15122, 44452, 5498}, {15160, 15161, 7500}, {18325, 44265, 37897}, {18579, 44961, 468}, {37934, 47316, 37958}

X(47309) = SHINAGAWA-EULER POINT ((-E+8F)/2,0)

X(47309) lies on these lines: {2, 3}, {265, 41738}, {974, 14915}, {1499, 19918}, {1503, 12295}, {1514, 17702}, {3564, 7728}, {3580, 10721}, {6699, 20725}, {9644, 10149}, {10733, 12419}, {11064, 46686}, {11598, 32110}, {11745, 22833}, {13202, 41586}, {13754, 16105}, {15063, 44665}, {15262, 47183}, {15311, 16003}, {16111, 47296}, {16227, 40647}, {16303, 40135}, {21850, 47277}, {22530, 32411}, {30209, 46991}, {44084, 44573}

X(47310) = SHINAGAWA-EULER POINT ((-E+8F)/3,0)

Barycentrics 10*a^10 - 9*a^8*b^2 - 22*a^6*b^4 + 20*a^4*b^6 + 12*a^2*b^8 - 11*b^10 - 9*a^8*c^2 + 68*a^6*b^2*c^2 - 28*a^4*b^4*c^2 - 64*a^2*b^6*c^2 + 33*b^8*c^2 - 22*a^6*c^4 - 28*a^4*b^2*c^4 + 104*a^2*b^4*c^4 - 22*b^6*c^4 + 20*a^4*c^6 - 64*a^2*b^2*c^6 - 22*b^4*c^6 + 12*a^2*c^8 + 33*b^2*c^8 - 11*c^10 : :

11 X[4] + X[37946], X[376] - 3 X[403], 5 X[376] - 6 X[47114], 5 X[381] - 3 X[2072], 2 X[381] - 3 X[10151], 11 X[381] - 3 X[18859], X[381] + 3 X[31726], 8 X[381] - 3 X[47090], 5 X[403] - 2 X[47114], 11 X[468] - 8 X[18571], 5 X[468] - 4 X[18579], 19 X[468] - 16 X[22249], 5 X[468] - 8 X[44961], 5 X[468] - 2 X[47308], X[468] + 2 X[47309], 4 X[547] - 3 X[10257], X[858] - 3 X[3839], 3 X[2070] + 5 X[35434], 2 X[2072] - 5 X[10151], 11 X[2072] - 5 X[18859], X[2072] + 5 X[31726], 8 X[2072] - 5 X[47090], 6 X[2072] - 5 X[47097], X[3146] + 3 X[37907], X[3146] + 2 X[37934], 3 X[3524] - 4 X[37911], 11 X[3543] + 9 X[37940], 7 X[3543] + 9 X[46451], 3 X[3545] - 2 X[5159], 2 X[3830] + X[37904], 11 X[3830] + 5 X[37923], 8 X[3845] - X[47092], 4 X[3845] - X[47311], 2 X[3853] + X[16619], and many others

X(47310) lies on these lines: {2, 3}, {115, 47184}, {524, 46988}, {542, 1514}, {1494, 1552}, {1531, 41583}, {1561, 46999}, {2777, 44569}, {3163, 47162}, {3564, 10706}, {5523, 47183}, {6128, 16303}, {12099, 14915}, {12112, 39562}, {13202, 32225}, {16326, 34150}, {20423, 47277}, {21850, 47281}, {23878, 46991}, {31670, 47279}, {39358, 47286}

X(47310) = reflection of X(2) in X(37984)
X(47310) = reflection of X(47308) in X(18579)

X(47311) = SHINAGAWA-EULER POINT ((4/3)(E+F),0)

X(47311) lies on these lines: {2, 3}, {524, 47155}, {599, 47279}, {612, 7286}, {614, 5160}, {1503, 13857}, {1853, 15533}, {1899, 15534}, {3917, 8705}, {5306, 47184}, {8584, 11245}, {9300, 16303}, {9766, 16326}, {11064, 11645}, {15431, 44833}, {16316, 22110}, {16317, 39602}, {19924, 44569}, {22165, 47278}, {25423, 47173}, {29012, 35266}, {29181, 32225}, {29323, 32267}, {29639, 47271}, {30476, 46995}, {31174, 47175}, {31655, 47295}, {32217, 43650}, {32269, 45311}, {36900, 47260}, {44377, 46992}, {45320, 47174}, {46980, 47237}

X(47311) = midpoint of X(i) and X(j) for these {i,j}: {2,47314}, {382, 44265}, {3543, 7426}, {3627, 44266}, {3830, 11799}, {3845, 44267}, {7575, 33699}, {10295, 15682}, {10296, 47313}, {13202, 32225}
X(47311) = reflection of X(i) in X(j) for these {i,j}: {2, 37984}, {10297, 3845}, {15122, 5066}, {18579, 44961}, {37904, 2}, {44280, 37942}, {47031, 468}, {47092, 47311}, {47097, 381}, {47277, 20423}, {47308, 18579}, {47312, 468}
X(47311) = complement of X(47313)
X(47311) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 15684, 44441}, {403, 10295, 38282}, {10151, 47097, 381}, {10719, 15159, 20408}, {10720, 15158, 20409}, {36437, 36455, 44438}, {44961, 47308, 468}

X(47312) = SHINAGAWA-EULER POINT ((-4/3)(E+F),0)

X(47312) lies on these lines: {2, 3}, {524, 24981}, {597, 35268}, {1194, 47180}, {3629, 47281}, {4995, 7302}, {5298, 5370}, {5642, 29181}, {8185, 34656}, {8705, 20583}, {9143, 34380}, {9740, 47283}, {11064, 32267}, {11363, 34642}, {11645, 32269}, {13857, 15448}, {16326, 32224}, {19924, 32237}, {29012, 44569}, {29323, 45311}, {40341, 47279}, {46998, 47237}

X(47312) = midpoint of X(2) and X(37900)
X(47312) = reflection of X(2) in X(37897)
X(47312) = reflection of X(46517) in X(2)
X(47312) = reflection of X(47311) in X(468)
X(47312) = reflection of X(47313) in X(37910)

X(47313) = SHINAGAWA-EULER POINT ((-5/3)(E+F),0)

Let P and P' be circumcircle antipodes. Let Q, Q' be the reflections of X(2) in P, P' resp. The rectangular hyperbola passing through P, P', Q, Q' has center X(47313) for all P. (Randy Hutson, April 16, 2022)

X(47313) lies on these lines: {2, 3}, {325, 46992}, {524, 12367}, {597, 15080}, {850, 46995}, {1180, 16308}, {1383, 15048}, {1495, 19924}, {1503, 15360}, {3060, 8584}, {3580, 11645}, {3582, 5370}, {3584, 7302}, {3793, 9870}, {3920, 5160}, {5012, 32217}, {5476, 35268}, {5642, 32237}, {5913, 6781}, {6800, 20423}, {7191, 7286}, {7712, 21850}, {7840, 16316}, {9140, 32269}, {9157, 9158}, {9745, 43618}, {11160, 47279}, {11594, 47075}, {11649, 21969}, {13857, 29317}, {14614, 32224}, {15534, 32220}, {20192, 44882}, {22165, 32113}, {26228, 47271}, {29012, 32225}, {29181, 35266}, {32896, 40123}, {34106, 47291}, {37775, 42943}, {37776, 42942}, {41133, 47171}, {41149, 47280}, {46983, 47263}

X(47313) = reflection of X(2) in X(37904)
X(47313) = reflection of X(10989) in X(468)
X(47313) = reflection of X(47312) in X(37910)
X(47313) = reflection of X(47314) in X(2)
X(47313) = anticomplement of X(47311)
X(47313) = circumcircle-inverse of X(40916)

X(47314) = SHINAGAWA-EULER POINT ((7/3)(E+F),0)

X(47314) lies on these lines: {2, 3}, {2979, 8705}, {3580, 19924}, {3920, 7286}, {5160, 7191}, {8280, 42525}, {8281, 42524}, {8584, 32220}, {9745, 43619}, {11442, 15533}, {11645, 40112}, {13857, 29012}, {15107, 44569}, {15360, 29181}, {15534, 45968}, {15826, 41149}, {20582, 41462}, {29317, 32225}, {37775, 42940}, {37776, 42941}, {41133, 46992}, {44367, 47155}

X(47314) = reflection of X(2) in X(47311)
X(47314) = reflection of X(37901) in X(468)
X(47314) = reflection of X(47312) in X(5159)
X(47314) = reflection of X(47313) in X(2)
X(47314) = anticomplement of X(37904)

X(47315) = SHINAGAWA-EULER POINT ((3/2)(E+F),0)

X(47315) lies on these lines: {2, 3}, {3630, 15583}, {3793, 19577}, {6144, 47280}, {8280, 41963}, {8281, 41964}, {8705, 14913}, {15448, 29323}, {15480, 47242}, {15815, 15880}, {29317, 47296}, {34380, 41724}, {47250, 47256}

X(47315) = reflection of X(2) in (reflection of X(47316) in X(2))
X(47315) = reflection of X(37910) in X(468)
X(47315) = reflection of (reflection of X(2) in X(47316)) in X(2)
X(47315) = complement of X(37899)

X(47316) = SHINAGAWA-EULER POINT ((-1/4)(E+F),0)

X(47316) lies on these lines: {2, 3}, {576, 10192}, {800, 16308}, {1353, 21970}, {3292, 32269}, {3564, 15448}, {3630, 32217}, {6144, 32113}, {15480, 16320}, {15585, 32218}, {31860, 38136}, {32237, 47296}, {35266, 41586}, {39884, 41424}, {40350, 43291}, {46992, 47242}, {46995, 47250}, {46998, 47245}, {47001, 47254}, {47004, 47261}, {47175, 47263}, {47252, 47256}

X(47316) = midpoint of X(2) and (reflection of X(47315) in X(2))
X(47316) = reflection of X(37911) in X(468)
X(47316) = reflection of (midpoint of X(2) and X(47315)) in X(2)
X(47316) = complement of X(47315)

X(47317) = X(6742)X(36037)∩X(13136)X(15455)

X(47317) = X(i)-isoconjugate of X(j) for these (i,j): (35,46393), (517,9404), (2174,2804), (2183,35057), (2804,2174)
X(47317) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {79,2804}, {104,35057}, {909,9404}, {2160,46393}, {2720,35}
X(47317) = barycentric product X(2720)*X(20565)
X(47317) = barycentric quotient X(i)/X(j) for these {i,j}: {79,2804}, {104,35057}, {909,9404}, {2160,46393}, {2720,35}
X(47317) = trilinear product X(i)*X(j) for these (i,j): (79,37136), (104,38340), (2720,30690)
X(47317) = trilinear quotient X(i)/X(j) for these (i,j): (79,46393), (104,9404), (2720,2174)

X(47318) = ISOGONAL CONJUGATE OF X(21828)

X(47318) lies on the Hutson-Moses hyperbola and these lines: {80,5380}, {99,5385}, {190,4567}, {335,2161}, {476,8652}, {522,4570}, {643,765}, {645,1016}, {648,35174}, {651,32680}, {655,662}, {666,2341}, {759,898}, {835,36069}, {931,2222}, {1275,4573}, {1897,5379}, {1978,4601}, {2651,14204}, {3257,4080}, {3936,46785}, {4613,5384}, {4620,16755}, {4629,31010}, {13136,30939}, {18359,37783}, {27809,34079}

X(47318) = isogonal conjugate of X(21828)
X(47318) = isotomic conjugate of X(4707)
X(47318) = trilinear pole of line X(10)X(21)
X(47318) = X(645)-beth conjugate of X(4567)
X(47318) = X(i)-cross conjugate of X(j) for these (i,j): (519,4600), (2323,4570)
X(47318) = X(i)-isoconjugate of X(j) for these (i,j): (10,21758), (31,4707), (42,3960), (58,2610),(65,654)
X(47318) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {2,4707}, {10,6370}, {21,3738}, {29,44428}, {35,526}
X(47318) = X(i)-Zayin conjugate of X(j) for these {i,j}: {1046,654}, {1054,2245}, {3216,2610}, {3336,2624}
X(47318) = cevapoint of X(i)and X(j) for these {i,j}: {37,8674}, {514,33129}, {522,2323}, {4560,16704}
X(47318) = barycentric product X(i)*X(j) for these (i,j): (21,35174), (35,35139), (80,99), (81,36804), (100,14616)
X(47318) = barycentric quotient X(i)/X(j) for these {i,j}: {10,6370}, {21,3738}, {29,44428}, {35,526}, {37,2610}
X(47318) = trilinear product X(i)*X(j) for these (i,j): (10,37140), (21,655), (35,32680), (58,36804), (80,662)
X(47318) = trilinear quotient X(i)/X(j) for these (i,j): (10,2610), (21,654), (35,2624), (37,42666),(58,21758)

X(47319) = X(1)X(21)∩X(10)X(8261)

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

X(47319) = 2*X(442)-3*X(5883), X(2475)-3*X(5902), 6*X(3833)-5*X(31254), X(3869)-3*X(5426), 3*X(3873)-X(16126), X(3878)-4*X(10122), 2*X(4757)+X(5441),3*X(5692)-5*X(15674), 4*X(6675)-3*X(10176)

X(47319) lies on these lines: {1,21}, {10,8261}, {30,5884}, {65,33667}, {79,11570}, {442,5883}, {942,3838}, {946,1484}, {950,17637}, {1125,44782}, {1479,14450}, {1737,41550}, {2475,5902}, {3337,34600}, {3651,5535}, {3754,20612}, {3814,44547}, {3833,31254}, {4757,5441}, {4973,33857}, {5172,15556}, {5428,31806}, {5499,5885}, {5563,39778}, {5692,15674}, {5694,10021}, {5787,16159}, {5880,30329}, {5903,20066}, {6675,10176}, {6841,31803}, {6894,15096}, {7702,41710}, {12005,22765}, {13146,35982}, {14526,41557}, {14795,31660}, {14804,27086}, {15071,37433}, {16139,37621}, {22836,37308}, {31870,37230}, {31938,41859}, {33961,37730}, {34772,35204}

X(47319) = midpoint of X(i) and X(j) for these {i,j}: {191,3868}, {15071,37433}
X(47319) = reflection of X(i) in X(j) for these (i,j): (10,8261), (3874,39772), (3878,35016), (5499,5885), (5694,10021), (11263,942), (31803,6841), (31806,5428), (33858,12005), (34195,3881), (35016,10122), (37230,31870), (44782,1125)
X(47319) = X(661)-he conjugate of X(2640)
X(47319) = {X(11604),X(12913)}-harmonic conjugate of X(79)

X(47320) = X(9)X(48)∩X(80)X(758)

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

X(47320) = 2*X(119)-3*X(15064), 2*X(214)-3*X(10176), 3*X(354)-4*X(33709), 3*X(392)-2*X(33812), 2*X(1317)-3*X(3898), 4*X(1387)-3*X(3892), 3*X(3681)-X(5541), X(3868)-3*X(37718), 5*X(3876)-3*X(15015), 2*X(3881)-3*X(16173), 6*X(4532)-X(9963), 3*X(4661)+X(9802), 2*X(5083)-3*X(32557),3*X(5660)-X(9964), 3*X(5692)-X(6224), 3*X(5883)-4*X(6702), 3*X(5883)-2*X(11570),3*X(10176)-4*X(18254), X(12690)-3*X(33519),3*X(17638)-X(17652), X(27778)-3*X(34123)

X(47320) lies on these lines: {3,36866}, {9,48}, {10,2771}, {11,3874}, {21,41689}, {80,758}, {100,191}, {119,15064}, {149,5904}, {354,33709}, {355,2800}, {392,33812}, {518,21630}, {519,17638}, {912,3814}, {952,3878}, {960,33337}, {1125,17660}, {1317,3898}, {1387,3892}, {1484,11813}, {1768,12528}, {2802,3632}, {2842,22321}, {2975,45764}, {3219,35204}, {3647,12738}, {3681,5541}, {3754,11571}, {3868,37718}, {3876,15015}, {3881,16173}, {3884,7972}, {3988,31938}, {4084,6797}, {4532,9963}, {4661,9802}, {4973,10090}, {5083,11375}, {5251,39778}, {5267,22935}, {5531,12514},{5660,9964},{5692,6224},{5693,12247},{5777,21635},{5883,6702},{5884,12619},{6265,20117},{6796,46684},{8068,18389},{8674,22037},{10058,41562}, {10592,38219}, {12515,18524}, {12690,33519}, {12736,31164}, {12739,35016}, {12758,37706}, {12773,30144}, {13273,15556}, {15528,37713}, {15558,37740}, {17647,17661}, {26066,46694}, {27778,34123}, {31871,34789}, {34772,46816}

X(47320) = midpoint of X(i) and X(j) for these {i,j}: {80,12532}, {149,5904}, {1768,12528}, {3869,9897}, {5693,12247}, {12665,12691}
X(47320) = reflection of X(i) in X(j) for these (i,j): (100,3678), (214,18254), (3874,11), (4084,6797), (5884,12619), (6265,20117), (7972,3884), (11570,6702), (11571,3754), (17660,1125), (21635,5777), (22935,31835), (33337,960), (34789,31871)
X(47320) = reflection of X(i) in X(j)X(k) for these (i,j,k): (10,8674,18004), (101,3678,3887)
X(47320) = X(3738)-he conjugate of X(34464)
X(47320) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (214,18254,10176), (993,6326,214), (6702,11570,5883)

X(47321) = X(1)X(468)∩X(8)X(23)

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

X(47321) = X[145] - 5 X[37760], 3 X[186] - X[944], 3 X[403] - 2 X[946], 2 X[1385] - 3 X[44214], 5 X[1698] - 4 X[5159], 3 X[1699] - 4 X[37984], 3 X[2070] + X[12645], 3 X[2072] - 4 X[9956], X[3241] - 3 X[37907], 5 X[3617] - X[5189], 7 X[3624] - 8 X[37911], 4 X[3626] + X[37900], X[3632] + 4 X[37897], X[3633] - 8 X[47316], 2 X[4297] - 3 X[44280], 5 X[4668] + 2 X[37899], 2 X[4669] + X[47313], X[4677] + 2 X[37904], 7 X[4678] + X[20063], 4 X[4745] - X[47314], 3 X[5587] - 2 X[10297], 3 X[5657] - X[7464], 3 X[5731] - 5 X[37952], 3 X[5790] - X[7574], 2 X[5901] - 3 X[44282], 7 X[9780] - 5 X[30745], 6 X[10257] - 7 X[31423], 5 X[10595] - 9 X[37943], 4 X[12512] - 3 X[16386], 2 X[15122] - 3 X[26446], 3 X[18374] - X[32298], X[18526] - 5 X[37958], 3 X[19875] - 2 X[47097], X[31145] + 3 X[37909]

The points X(1), X(11809), X(47321), X(47270) are vertices of a rectangle with center X(486). In Euler coordinates with X(1) = (x,y), the four vertices are (x,y), (-x,y), (-x,-y), (x,-y).

X(47321) lies on these lines: {1, 468}, {8, 23}, {10, 858}, {30, 40}, {145, 37760}, {186, 944}, {403, 946}, {515, 10295}, {517, 11799}, {518, 32113}, {519, 7426}, {523, 10015}, {524, 32278}, {758, 41742}, {952, 7575}, {1385, 44214}, {1503, 13211}, {1698, 5159}, {1699, 37984}, {1829, 37981}, {2070, 12645}, {2072, 9956}, {2948, 3564}, {3109, 16305}, {3241, 37907}, {3617, 5189}, {3624, 37911}, {3626, 37900}, {3632, 37897}, {3633, 47316}, {3655, 18579}, {4297, 44280}, {4663, 47280}, {4668, 37899}, {4669, 47313}, {4677, 37904}, {4678, 20063}, {4745, 47314}, {5587, 10297}, {5657, 7464}, {5731, 37952}, {5790, 7574}, {5844, 25338}, {5846, 32217}, {5847, 32220}, {5901, 44282}, {7286, 40663}, {8192, 37920}, {8193, 37928}, {9053, 32218}, {9780, 30745}, {9798, 21284}, {10149, 45081}, {10257, 31423}, {10595, 37943}, {12410, 37973}, {12512, 16386}, {12702, 18325}, {13407, 37989}, {13869, 16332}, {15122, 26446}, {15177, 45171}, {16272, 47274}, {16304, 47273}, {18323, 18480}, {18357, 18572}, {18374, 32298}, {18526, 37958}, {18571, 34773}, {19875, 47097}, {22791, 44961}, {28174, 44267}, {28204, 44265}, {31145, 37909}, {32123, 32126}, {34628, 47031}, {37557, 37929}, {41869, 47309}, {44898, 47160}

X(47321) = midpoint of X(i) and X(j) for these {i,j}: {8, 23}, {12702, 18325}
X(47321) = reflection of X(i) in X(j) for these {i,j}: {1, 468}, {858, 10}, {3109, 16305}, {3655, 18579}, {13869, 16332}, {18323, 18480}, {18572, 18357}, {22791, 44961}, {34628, 47031}, {34773, 18571}, {41869, 47309}, {47270, 16309}, {47273, 16304}, {47274, 16272}, {47280, 4663}
X(47321) = reflection of X(11809) in the Euler line
X(47321) = reflection of X(47270) in the orthic axis

X(47322) = X(6)X(30)∩X(111)X(230)

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

The points X(6), X(47322), X(32113), X(2453) are vertices of a rectangle with center X(486). In Euler coordinates with X(6) = (x,y), the four vertices are (x,y), (-x,y), (-x,-y), (x,-y).

X(47322) lies on the Moses-Parry circle and these lines: {2, 47169}, {5, 18573}, {6, 30}, {23, 7735}, {50, 112}, {53, 403}, {111, 230}, {115, 3003}, {186, 393}, {187, 3018}, {216, 2072}, {232, 1560}, {297, 16237}, {468, 2453}, {523, 3569}, {566, 858}, {577, 44246}, {1249, 13619}, {1316, 16324}, {1609, 2070}, {2079, 7575}, {2450, 38393}, {2452, 16333}, {2492, 16171}, {2493, 5913}, {2963, 47157}, {3163, 6781}, {3767, 16619}, {5023, 37934}, {5158, 18323}, {5189, 37665}, {5286, 37946}, {5304, 37901}, {5305, 37967}, {5306, 47313}, {5523, 47228}, {5899, 8573}, {7574, 15484}, {7736, 10989}, {7745, 41335}, {8428, 16318}, {8598, 45331}, {8609, 11809}, {8749, 14989}, {8882, 19651}, {9300, 47314}, {9722, 11563}, {10257, 36751}, {11586, 41406}, {13338, 37900}, {14995, 37461}, {15109, 34152}, {15743, 41407}, {15980, 46127}, {16321, 47285}, {16326, 47279}, {16334, 47284}, {18579, 21843}, {31489, 47097}, {32460, 47141}, {32461, 47142}, {33630, 35489}, {37689, 37909}, {37904, 47184}, {37931, 47162}, {37971, 47189}, {43291, 44266}, {46257, 47192}

X(47322) = midpoint of X(i) and X(j) for these {i,j}: {6, 47275}, {16326, 47279}
X(47322) = reflection of X(i) in X(j) for these {i,j}: {6, 16303}, {1316, 16324}, {2452, 16333}, {2453, 468}, {32113, 5112}, {47280, 2452}, {47284, 16334}, {47285, 16321}
X(47322) = reflection of X(6) in the orthic axis
X(47322) = reflection of X(32113) in the Euler line
X(47322) = 2nd-Lemoine-circle inverse of X(39522)
X(47322) = crossdifference of every pair of points on line {182, 8675}
X(47322) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {50, 19656, 1990}, {53, 16328, 403}, {186, 393, 47144}, {187, 18487, 3018}, {2549, 34288, 6}, {11537, 11549, 7426}, {14836, 18907, 6}

X(47323) = X(4)X(2453)∩X(30)X(74)

Barycentrics 3*a^14*b^2 - 13*a^12*b^4 + 21*a^10*b^6 - 15*a^8*b^8 + 5*a^6*b^10 - 3*a^4*b^12 + 3*a^2*b^14 - b^16 + 3*a^14*c^2 + 8*a^12*b^2*c^2 - 12*a^10*b^4*c^2 - 30*a^8*b^6*c^2 + 35*a^6*b^8*c^2 + 12*a^4*b^10*c^2 - 18*a^2*b^12*c^2 + 2*b^14*c^2 - 13*a^12*c^4 - 12*a^10*b^2*c^4 + 84*a^8*b^4*c^4 - 40*a^6*b^6*c^4 - 63*a^4*b^8*c^4 + 36*a^2*b^10*c^4 + 8*b^12*c^4 + 21*a^10*c^6 - 30*a^8*b^2*c^6 - 40*a^6*b^4*c^6 + 108*a^4*b^6*c^6 - 21*a^2*b^8*c^6 - 34*b^10*c^6 - 15*a^8*c^8 + 35*a^6*b^2*c^8 - 63*a^4*b^4*c^8 - 21*a^2*b^6*c^8 + 50*b^8*c^8 + 5*a^6*c^10 + 12*a^4*b^2*c^10 + 36*a^2*b^4*c^10 - 34*b^6*c^10 - 3*a^4*c^12 - 18*a^2*b^2*c^12 + 8*b^4*c^12 + 3*a^2*c^14 + 2*b^2*c^14 - c^16 : :

The points X(74), X(47323), X(32111), X(477) are vertices of a rectangle with center X(486). In Euler coordinates with X(6) = (x,y), the four vertices are (x,y), (-x,y), (-x,-y), (x,-y).

X(47323) lies on these lines: {4, 2453}, {23, 34193}, {30, 74}, {133, 403}, {186, 34178}, {468, 477}, {523, 32111}, {858, 25641}, {1596, 15111}, {5523, 47228}, {10295, 47204}, {11563, 11749}, {11657, 36164}, {11799, 16168}, {18325, 38580}, {36162, 43607}, {38610, 44214}, {44967, 47309}

X(47323) = midpoint of X(i) and X(j) for these {i,j}: {23, 34193}, {18325, 38580}
X(47323) = reflection of X(i) in X(j) for these {i,j}: {74, 47146}, {477, 468}, {858, 25641}, {36164, 11657}, {44967, 47309}
X(47323) = reflection of X(74) in the orthic axis
X(47323) = reflection of X(32111) in the Euler line
X(47323) = {X(133),X(47215)}-harmonic conjugate of X(403)

X(47324) = X(2)X(2453)∩X(30)X(110)

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

X(47324) lies on these lines: {2, 2453}, {5, 15112}, {23, 12384}, {30, 110}, {114, 858}, {136, 403}, {468, 476}, {511, 44830}, {523, 3580}, {868, 33927}, {1316, 14389}, {1503, 17511}, {1514, 36172}, {2072, 14769}, {2493, 5913}, {2986, 10723}, {3564, 14480}, {5468, 36891}, {5523, 47230}, {6132, 16171}, {6530, 7480}, {7426, 30685}, {7471, 16319}, {9123, 19912}, {9159, 30739}, {10749, 14919}, {11064, 36188}, {11799, 16168}, {13434, 14896}, {14165, 30716}, {14670, 39235}, {14989, 47309}, {15066, 36163}, {15111, 15760}, {18319, 44961}, {18325, 38581}, {36181, 37645}, {36190, 37636}, {36193, 46817}, {37638, 47284}, {38609, 44214}, {39569, 47215}

X(47324) = midpoint of X(i) and X(j) for these {i,j}: {23, 14731}, {9158, 34312}, {18325, 38581}
X(47324) = reflection of X(i) in X(j) for these {i,j}: {110, 47148}, {476, 468}, {858, 3258}, {7471, 16319}, {14989, 47309}, {18319, 44961}, {36172, 1514}, {36188, 11064}, {36193, 46817}
X(47324) = reflection of X(110) in the orthic axis
X(47324) = reflection of X(3580) in the Euler line

X(47325) = X(2)X(2453)∩X(30)X(1296)

Barycentrics 3*a^10*b^2 + a^8*b^4 - 4*a^6*b^6 + a^2*b^10 - b^12 + 3*a^10*c^2 - 20*a^8*b^2*c^2 + 13*a^6*b^4*c^2 + 18*a^4*b^6*c^2 - 14*a^2*b^8*c^2 + 4*b^10*c^2 + a^8*c^4 + 13*a^6*b^2*c^4 - 42*a^4*b^4*c^4 + 13*a^2*b^6*c^4 + b^8*c^4 - 4*a^6*c^6 + 18*a^4*b^2*c^6 + 13*a^2*b^4*c^6 - 8*b^6*c^6 - 14*a^2*b^2*c^8 + b^4*c^8 + a^2*c^10 + 4*b^2*c^10 - c^12 : :

X(47325) = -3 X[186] - X[14654], 3 X[403] - 2 X[5512], 3 X[2072] - 4 X[40340], 2 X[14650] - 3 X[44214], 3 X[16386] - 4 X[38803], X[20099] - 5 X[37760], 3 X[31726] - X[38800], 5 X[38806] - 6 X[44452]

The points X(110), X(47324), X(3580), X(476) are vertices of a rectangle with center X(486). In Euler coordinates with X(6) = (x,y), the four vertices are (x,y), (-x,y), (-x,-y), (x,-y).

X(47325) lies on these lines: {2, 2453}, {23, 5866}, {30, 1296}, {111, 468}, {126, 625}, {186, 14654}, {403, 5512}, {523, 5913}, {543, 7426}, {2072, 40340}, {2780, 32111}, {2793, 47219}, {2854, 3580}, {10295, 23699}, {11580, 47242}, {11799, 33962}, {14650, 44214}, {14666, 18579}, {16386, 38803}, {18325, 38593}, {20099, 37760}, {24855, 47245}, {31644, 47246}, {31726, 38800}, {32424, 44265}, {36168, 47170}, {38806, 44452}, {44987, 47309}

X(47325) = midpoint of X(i) and X(j) for these {i,j}: {23, 14360}, {18325, 38593}
X(47325) = reflection of X(i) in X(j) for these {i,j}: {111, 468}, {858, 126}, {14666, 18579}, {36168, 47170}, {44987, 47309}
X(47325) = orthoptic-circle-of-Steiner-inellipse inverse of X(2453)
X(47325) = reflection of X(2770) in the orthic axis
X(47325) = reflection of X(5913) in the Euler line

X(47326) = X(23)X(99)∩X(30)X(114)

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

X(47326) = X[98] - 3 X[186], X[148] - 5 X[37760], X[671] - 3 X[37907], X[691] - 3 X[13586], 3 X[2070] + X[13188], 3 X[2072] - 4 X[6721], 4 X[5159] - 5 X[31274], 3 X[5215] - 2 X[46980], X[5999] - 3 X[38704], 2 X[6036] - 3 X[44214], X[6781] + 2 X[16316], X[7464] - 3 X[21166], X[7574] - 3 X[15561], X[8591] + 3 X[37909], 3 X[9167] - 2 X[47097], 2 X[10297] - 3 X[36519], X[10989] - 3 X[41134], X[10991] - 4 X[37934], X[10992] + 2 X[16619], X[12188] - 5 X[37958], 2 X[15122] - 3 X[38748], X[15300] + 2 X[37904], X[15342] - 3 X[35265], X[23235] + 5 X[37953], 3 X[34473] - 5 X[37952], 4 X[35022] + X[37900], 3 X[35297] - 2 X[40544], 2 X[36521] + X[47313], 7 X[37957] - X[38664], 2 X[38747] - 3 X[44280], 2 X[43291] - 3 X[47243]

The points X(111), X(5913), X(47325), X(2770) are vertices of a rectangle with center X(486). In Euler coordinates with X(6) = (x,y), the four vertices are (x,y), (-x,y), (-x,-y), (x,-y).

X(47326) lies on the circle {{X(935),X(2453),X(2770),X(5099)}} (the reflection of the Moses-Parry circle in the Euler line) and these lines: {2, 11628}, {3, 2453}, {23, 99}, {30, 114}, {32, 2452}, {39, 36156}, {98, 186}, {115, 468}, {148, 37760}, {187, 523}, {232, 46619}, {237, 31953}, {385, 47288}, {476, 35298}, {511, 46634}, {538, 47293}, {542, 32110}, {543, 7426}, {574, 1316}, {620, 858}, {671, 37907}, {690, 1495}, {691, 13586}, {842, 11676}, {1503, 15357}, {2070, 2936}, {2072, 6721}, {2088, 5967}, {2782, 7575}, {2794, 10295}, {3552, 38526}, {3734, 9832}, {3788, 36187}, {4226, 9177}, {5026, 8705}, {5112, 47220}, {5159, 31274}, {5160, 15452}, {5189, 31132}, {5206, 47283}, {5210, 47284}, {5215, 46980}, {5866, 39193}, {5938, 30715}, {5969, 32217}, {5999, 38704}, {6036, 44214}, {6055, 18579}, {6781, 16316}, {7464, 21166}, {7472, 32456}, {7574, 15561}, {7782, 36182}, {7816, 36165}, {7820, 11007}, {8588, 47285}, {8591, 37909}, {9167, 47097}, {9876, 37922}, {10297, 36519}, {10989, 41134}, {10991, 37934}, {10992, 16619}, {11616, 11644}, {11629, 35917}, {11630, 35918}, {11649, 32135}, {11799, 23698}, {12042, 18571}, {12131, 44281}, {12188, 37958}, {13175, 37973}, {14120, 47171}, {14645, 32220}, {15122, 38748}, {15300, 37904}, {15342, 35265}, {15980, 16760}, {16188, 37459}, {16319, 35282}, {18325, 38730}, {21163, 36177}, {21284, 39857}, {22515, 44961}, {23235, 37953}, {31726, 39818}, {32459, 36953}, {32479, 36196}, {34473, 37952}, {35022, 37900}, {35297, 40544}, {36157, 37512}, {36521, 47313}, {37023, 47270}, {37920, 39832}, {37931, 47177}, {37957, 38664}, {38609, 44221}, {38747, 44280}, {41672, 47280}, {43291, 47243}, {46633, 47113}

X(47326) = midpoint of X(i) and X(j) for these {i,j}: {23, 99}, {385, 47288}, {842, 11676}, {18325, 38730}
X(47326) = reflection of X(i) in X(j) for these {i,j}: {115, 468}, {187, 36180}, {858, 620}, {5099, 16320}, {6055, 18579}, {7472, 32456}, {12042, 18571}, {14120, 47171}, {15980, 16760}, {16188, 37459}, {18860, 46987}, {22515, 44961}, {31173, 46986}, {46633, 47113}, {47280, 41672}
X(47326) = reflection of X(187) in the Euler line
X(47326) = reflection of X(5099) in the orthic axis
X(47326) = antipode of X(115) in rectangular hyperbola {{X(98),X(99),X(114),X(115),X(31953)}}
X(47326) = circumcircle-inverse of X(2453)

X(47327) = X(23)X(94)∩X(30)X(125)

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

X(47327) = 3 X[186] - X[477], 3 X[2070] + X[38580], X[7464] - 3 X[38700], X[9158] - 3 X[37909], X[14480] - 3 X[35265], X[14731] - 5 X[37760], 2 X[31379] - 3 X[44214], X[34312] - 3 X[37907], 5 X[37952] - 3 X[38701], 5 X[37953] + X[38677], 7 X[37957] - X[38678], 5 X[37958] - X[38581]

The points X(115), X(187), X(47326), X(5099) are vertices of a rectangle with center X(486). In Euler coordinates with X(6) = (x,y), the four vertices are (x,y), (-x,y), (-x,-y), (x,-y).

X(47327) lies on these lines: {3, 23097}, {23, 94}, {25, 2453}, {30, 125}, {51, 36178}, {107, 186}, {132, 468}, {184, 2452}, {187, 1637}, {237, 31953}, {373, 36177}, {511, 7471}, {523, 1495}, {858, 22104}, {1316, 34417}, {1503, 6070}, {1513, 47220}, {1531, 36169}, {2070, 13558}, {3233, 3292}, {3581, 36193}, {4240, 16186}, {5446, 36159}, {6130, 16171}, {6793, 16303}, {6795, 35268}, {7426, 30685}, {7464, 38700}, {7492, 9159}, {7575, 16168}, {7684, 32460}, {7685, 32461}, {9158, 37909}, {10110, 36161}, {10295, 47204}, {11005, 15360}, {14480, 35265}, {14731, 37760}, {14915, 46632}, {14989, 16080}, {15107, 36188}, {15448, 47148}, {16315, 37904}, {18571, 38610}, {21284, 34131}, {25338, 47201}, {31379, 44214}, {31510, 47215}, {32111, 32417}, {34093, 44106}, {34312, 37907}, {37931, 47147}, {37952, 38701}, {37953, 38677}, {37957, 38678}, {37958, 38581}, {37969, 47202}, {38613, 44215}, {40885, 44972}, {41424, 47284}, {44082, 47283}

X(47327) = midpoint of X(i) and X(j) for these {i,j}: {23, 476}, {3581, 36193}, {15107, 36188}
X(47327) = reflection of X(i) in X(j) for these {i,j}: {125, 11657}, {858, 22104}, {1531, 36169}, {3258, 468}, {3292, 3233}, {6070, 47146}, {38610, 18571}, {47148, 15448}
X(47327) = Dao-Moses-Telv-circle-inverse of X(187)

X(47328) = X(4)X(52)∩X(6)X(25)

Barycentrics a^2*((b^2+c^2)*a^4-2*(b^4+b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
Trilinears (tan A) (sin A + sin 2A cos(B - C)) : :

X(47328) = 3*X(51)-X(184), X(161)+3*X(34751), 3*X(3060)+X(11442), 3*X(41578)-X(41594)

Let A'B'C' be the reflection triangle. Let A_B and A_C be the orthogonal projections of A' on lines CA and AB, resp. Define B_C, B_A, C_A, C_B cyclically. Let A" = B_CB_A∩C_AC_B, and define B" and, C" cyclically. Triangle A"B"C" is perspective to ABC at X(6), and homothetic to the orthic triangle at X(47328). (Randy Hutson, April 16, 2022)

Let A'B'C' be the reflection triangle. Let A_B be the orthogonal projection of A' on CA, and define B_C and C_A cyclically. Let A_C be the orthogonal projection of A' on BA, and define B_A and C_B cyclically. Then A"B"C" is perspective to ABC at X(6), and homothetic to the orthic triangle at X(47328). (Randy Hutson, April 16, 2022)

X(47328) lies on these lines: {2, 6403}, {4, 52}, {5, 31807}, {6, 25}, {22, 19131}, {24, 569}, {125, 32316}, {129, 136}, {140, 9827}, {143, 6756}, {182, 21213}, {185, 12173}, {186, 5892}, {216, 3135}, {235, 10110}, {251, 41363}, {263, 13854}, {275, 421}, {323, 41713}, {343, 427}, {373, 37453}, {378, 37478}, {389, 973}, {403, 11692}, {418, 23635}, {428, 542}, {460, 2387}, {468, 5943}, {568, 18494}, {570, 23195}, {571, 2351}, {1209, 1216}, {1370, 37511}, {1593, 17834}, {1595, 10263}, {1598, 18445}, {1824, 2875}, {1853, 37473}, {1885, 13598}, {1899, 19161}, {1993, 27365}, {1994, 8537}, {1995, 8538}, {2356, 20961}, {2917, 13367}, {2970, 42400}, {2979, 8889}, {3051, 14580}, {3089, 9781}, {3131, 10635}, {3132, 10634}, {3148, 10316}, {3155, 10898}, {3156, 10897}, {3271, 14975}, {3313, 43653}, {3515, 37476}, {3518, 15019}, {3541, 10625}, {3567, 7487}, {3917, 5094}, {5064, 12294}, {5447, 37119}, {5562, 7507}, {5640, 6353}, {5907, 23047}, {5946, 37458}, {6145, 11572}, {6240, 11750}, {6293, 11381}, {6755, 18130}, {6995, 11002}, {7409, 16981}, {7494, 12220}, {7499, 11574}, {7577, 10170}, {7691, 30100}, {7730, 25739}, {8882, 41271}, {9306, 41714}, {9730, 18533}, {9822, 37439}, {9926, 41619}, {9937, 36747}, {10095, 21841}, {10169, 35371}, {10192, 12061}, {10594, 35603}, {11188, 14826}, {11396, 16980}, {11410, 36987}, {11427, 15073}, {11451, 38282}, {11550, 34146}, {11557, 12140}, {11807, 12133}, {12058, 34609}, {12160, 21651}, {12236, 15473}, {12827, 32263}, {12828, 45237}, {13363, 37935}, {13364, 37942}, {14449, 16198}, {14569, 14715}, {14641, 34797}, {14915, 35480}, {15030, 18386}, {15045, 37460}, {15809, 41588}, {16776, 41585}, {16836, 37931}, {19128, 34545}, {20411, 31688}, {20412, 31687}, {20962, 40976}, {21284, 22352}, {21852, 37644}, {23158, 41169}, {23292, 44668}, {30506, 44145}, {31383, 41580}, {32196, 34826}, {32340, 32392}, {32379, 45110}, {33586, 37488}, {33798, 44146}, {35488, 44863}, {44886, 46832}, {45179, 45780}

X(47328) = midpoint of X(i) and X(j) for these {i, j}: {52, 18474}, {1843, 8541}, {1993, 27365}
X(47328) = reflection of X(i) in X(j) for these (i, j): (18388, 10110), (18475, 5462), (45118, 5)
X(47328) = isogonal conjugate of the isotomic conjugate of X(1594)
X(47328) = polar conjugate of the isotomic conjugate of X(570)
X(47328) = pole wrt polar circle of line X(850)X(924)
X(47328) = crossdifference of every pair of points on line {X(525), X(30451)}
X(47328) = crosspoint of X(i) and X(j) for these (i, j): {4, 8882}, {6, 6145}
X(47328) = crosssum of X(i) and X(j) for these (i, j): {2, 7488}, {3, 343}, {69, 44180}
X(47328) = X(1594)-Ceva conjugate of-X(570)
X(47328) = X(i)-Dao conjugate of-X(j) for these (i, j): (206, 40441), (570, 28706), (1209, 69)
X(47328) = X(i)-isoconjugate-of-X(j) for these {i, j}: {63, 40393}, {69, 2216}, {75, 40441}, {326, 1179}
X(47328) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (25, 40393), (32, 40441), (570, 69), (1209, 28706)
X(47328) = perspector of the circumconic {{A, B, C, X(112), X(30450)}}
X(47328) = inverse of X(34397) in orthic inconic
X(47328) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(44077)}} and {{A, B, C, X(6), X(570)}}
X(47328) = X(184)-of-anti-Ara triangle
X(47328) = X(226)-of-orthic triangle, when ABC is acute
X(47328) = X(45118)-of-Johnson triangle
X(47328) = barycentric product X(i)*X(j) for these {i, j}: {4, 570}, {6, 1594}, {25, 37636}, {39, 10550}, {393, 1216}, {512, 41677}
X(47328) = barycentric quotient X(i)/X(j) for these (i, j): (25, 40393), (32, 40441), (570, 69), (1209, 28706), (1216, 3926), (1594, 76)
X(47328) = trilinear product X(i)*X(j) for these {i, j}: {19, 570}, {31, 1594}, {158, 23195}, {798, 41677}, {1096, 1216}, {1964, 10550}
X(47328) = trilinear quotient X(i)/X(j) for these (i, j): (19, 40393), (25, 2216), (31, 40441), (570, 63), (1096, 1179), (1209, 18695)
X(47328) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 25, 44077), (6, 161, 184), (25, 51, 44084), (51, 1843, 25), (973, 6146, 389), (3060, 6515, 52), (3575, 6746, 389), (5446, 12235, 52), (5943, 44479, 37649), (6152, 41578, 41599), (6746, 11576, 3575), (44125, 44126, 34397)

X(47329) = X(30)-LINE CONJUGATE OF X(528)

X(47329) lies on these lines: {6, 665}, {30, 511}, {69, 3766}, {354, 26275}, {599, 45338}, {876, 7077}, {3250, 23650}, {3271, 7202}, {3681, 31131}, {3740, 30792}, {3873, 44433}, {3908, 23343}, {4435, 16973}, {4809, 30704}, {9508, 43050}, {22769, 39200}

X(47329) = crossdifference of every pair of points on line {6, 528}
X(47329) = X(i)-line conjugate of X(j) for these (i,j): {30, 528}, {665, 6}
X(47329) = barycentric quotient X(29176)/X(14770)

X(47330) = X(30)-LINE CONJUGATE OF X(537)

X(47330) lies on these lines: {6, 3768}, {30, 511}, {69, 21303}, {141, 21261}, {659, 14404}, {1635, 24577}, {3271, 16507}, {3572, 3862}, {3888, 4033}, {14426, 45666}, {22384, 23866}, {23656, 46387}

X(47330) = X(i)-line conjugate of X(j) for these (i,j): {30, 537}, {3768, 6}
X(47330) = crossdifference of every pair of points on line {6, 537}

X(47331) = X(30)-LINE CONJUGATE OF X(539)

X(47331) lies on these lines: {30, 511}, {1176, 43709}, {15321, 15328}, {15453, 34437}, {18125, 40048}, {34952, 44816}

X(47331) = X(30)-line conjugate of X(539)
X(47331) = crossdifference of every pair of points on line {6, 539}

This preamble is contributed by Peter Moses, Kiminari Shinagawa, and Clark Kimberling, April 1, 2022.

Suppose that P and U are points, neither on the line at infinity, and that normed (i.e., "normalized") barycentrcis are given by P= (p,q,r) and U = (u,v,w) Then the point P-U defined by the combo p-u : q - v : r - w is on the line at infinity. Let T(P,U) denote the point with Euler coordinates (x,y) given by

x = SA*(p-u) + SB*(q - r) + SC*(r - w)
y = SA*(SB - SC)*(p-u) + SB*(SC - SA)*(q - r) + SC*(SA - SB)*(r - w)

If P and U are on the Euler line, then y = 0, and P - U = X(30), and T(P,U) lies on the Euler line. The appearance of (i,j;k) in the following list means that T(X(i),X(j)) = X(k).

(2,3; 47332), (2,4; 47031), (2,5; 18579), (2,23; 47311), (2,376; 47310), (2,381; 47333), (3,2; 47333), (3,4; 47308), (3,5; 47335), (3,20; 47309), (3,140; 18571), (3,186; 10257), (3,376; 47332), (3,381; 47031), (4,2; 47310), (4,3; 47309), (4,5; 47336), (4,23; 47339), (4,186; 13473), (4,381; 47332), (4,382; 47308), (4,403; 10151), (5,2; 47334), (5,3;47336), (5,4; 47335), (5,23; 47341), (5,140; 44961), (5,186; 23323), (5,381; 18579), (5,403; 44452), (20,3; 47308), (20,376; 47031), (23,2; 47312), (23,4; 47340), (23,5;47342), (23,186; 47093), (140,3; 44961), (140,5; 18571), (140,403; 37968), (186,3;37971), (186,23; 47090), (186,403; 37931), (376,2; 47031), (376,3; 47333), (376,20; 47310), (376,381; 47308), (381,2; 47332), (381,3; 47310), (381,4; 47333), (381,5; 47334), (381,376; 47309), (382,4; 47309), (403,4; 37931), (403,186; 10151)

See also the preambles just before X(47090), X(47488), and X(47629).

X(47332) = SHINAGAWA-EULER POINT (-E/6 + 4F/3, 0)

Barycentrics 2*a^10 + 3*a^8*b^2 - 14*a^6*b^4 + 4*a^4*b^6 + 12*a^2*b^8 - 7*b^10 + 3*a^8*c^2 + 28*a^6*b^2*c^2 - 8*a^4*b^4*c^2 - 44*a^2*b^6*c^2 + 21*b^8*c^2 - 14*a^6*c^4 - 8*a^4*b^2*c^4 + 64*a^2*b^4*c^4 - 14*b^6*c^4 + 4*a^4*c^6 - 44*a^2*b^2*c^6 - 14*b^4*c^6 + 12*a^2*c^8 + 21*b^2*c^8 - 7*c^10 : :

X(47332) = X[2] - 3 X[403], 7 X[2] - 3 X[2071], 4 X[2] - 3 X[10257], 5 X[2] - 6 X[44911], 7 X[4] + 5 X[37953], X[23] + 3 X[3839], 3 X[186] + X[15682], 5 X[381] - X[7574], 7 X[381] + X[37924], X[382] + 2 X[37934], 7 X[403] - X[2071], 4 X[403] - X[10257], 5 X[403] - 2 X[44911], 7 X[468] - 4 X[18571], 3 X[468] - 2 X[18579], 11 X[468] - 8 X[22249], X[468] - 4 X[44961], 3 X[468] - X[47031], 4 X[468] - X[47308], 2 X[468] + X[47309], 2 X[546] + X[16619], 4 X[546] + X[47312], X[858] - 3 X[3545], 4 X[2071] - 7 X[10257], 5 X[2071] - 14 X[44911], 3 X[2072] - 5 X[19709], 5 X[3091] - X[10989], X[3534] + 3 X[31726], X[3534] - 6 X[37942], X[3534] - 3 X[44214], X[3543] + 3 X[37907], 7 X[3830] + 9 X[37922], 7 X[3832] + X[37901], 2 X[3845] - 3 X[10151], X[3845] + 3 X[11563], 2 X[3845] + X[37904], 7 X[3845] + 3 X[37936], 4 X[3845] + 3 X[37971], 11 X[3855] + X[37946], 5 X[3858] + X[37967], 4 X[3860] - 3 X[23323], 8 X[3860] + 3 X[47093], 2 X[3861] + X[12105], 3 X[5054] - 4 X[37911], 3 X[5055] - 2 X[5159], 3 X[5055] + X[18325], 4 X[5066] - X[47311], 5 X[5071] - X[7464], 2 X[5159] + X[18325], 7 X[7426] - 5 X[37953], 2 X[7574] - 5 X[10297], X[7574] + 5 X[11799], 7 X[7574] + 5 X[37924], X[7574] - 10 X[37984], X[8703] - 3 X[44282], and many others

X(47332) lies on these lines: {2, 3}, {113, 524}, {115, 16303}, {399, 37784}, {523, 44203}, {541, 1514}, {1539, 15361}, {3564, 5655}, {3580, 10706}, {5099, 16334}, {5512, 25641}, {7687, 11645}, {7706, 20192}, {7728, 15362}, {9140, 32111}, {11180, 32220}, {12295, 15448}, {13857, 36518}, {14672, 18809}, {16092, 39663}, {17702, 35266}, {21850, 47279}, {23878, 47002}, {26613, 44969}, {30209, 46989}, {32269, 46686}, {34315, 41036}, {34316, 41037}, {34334, 37778}, {43291, 47184}, {44401, 46981}, {44560, 46984}, {46982, 46992}, {46985, 46995}, {46988, 46998}, {46991, 47001}

X(47332) = midpoint of X(i) and X(j) for these {i,j}: {4, 7426}, {381, 11799}, {468, 47310}, {549, 44267}, {1513, 36196}, {1514, 44569}, {1539, 15361}, {3543, 10295}, {3580, 10706}, {3830, 44265}, {3845, 44266}, {7575, 15687}, {9140, 32111}, {11180, 32220}, {14893, 25338}, {31726, 44214}, {46982, 46992}, {46985, 46995}, {46988, 46998}, {46991, 47001}
X(47332) = reflection of X(i) in X(j) for these {i,j}: {381, 37984}, {10297, 381}, {15122, 547}, {37904, 44266}, {44214, 37942}, {46981, 44401}, {46984, 44560}, {47031, 18579}, {47097, 5}, {47309, 47310}, {47312, 16619}, {47333, 468}
X(47332) = polar-circle-inverse of X(35485)
X(47332) = orthoptic-circle-of-Steiner-inellipse-inverse of X(26255)
X(47332) = X(7426)-of-Euler-triangle
X(47332) = X(47097)-of-Johnson-triangle
X(47332) = reflection of X(47333) in the orthic axis
X(47332) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 44458, 12100}, {403, 6623, 37984}, {403, 11799, 15760}, {468, 47031, 18579}, {468, 47309, 47308}, {1596, 11563, 11799}, {1596, 37984, 10151}, {3543, 37907, 10295}, {3845, 11563, 44266}, {3845, 33699, 18566}, {10151, 11563, 37971}, {10297, 15760, 10257}, {11799, 37984, 10297}, {37904, 44266, 37971}, {44266, 44282, 44278}

X(47333) = SHINAGAWA-EULER POINT (E/6 - 4F/3, 0)

Barycentrics 14*a^10 - 27*a^8*b^2 - 2*a^6*b^4 + 28*a^4*b^6 - 12*a^2*b^8 - b^10 - 27*a^8*c^2 + 52*a^6*b^2*c^2 - 32*a^4*b^4*c^2 + 4*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 32*a^4*b^2*c^4 + 16*a^2*b^4*c^4 - 2*b^6*c^4 + 28*a^4*c^6 + 4*a^2*b^2*c^6 - 2*b^4*c^6 - 12*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(47333) = 5 X[2] - X[10296], X[2] - 5 X[37952], X[3] + 2 X[37934], X[20] + 3 X[37907], X[23] + 3 X[10304], 3 X[186] + X[376], 3 X[186] - X[7426], 5 X[186] + X[16386], 4 X[186] - X[37971], 7 X[186] - X[47096], 5 X[376] - 3 X[16386], 4 X[376] + 3 X[37971], X[376] - 3 X[44280], 7 X[376] + 3 X[47096], X[381] - 9 X[37955], X[381] - 3 X[44214], 3 X[403] - X[3543], X[468] - 4 X[18571], 5 X[468] - 8 X[22249], 7 X[468] - 4 X[44961], 2 X[468] + X[47308], 4 X[468] - X[47309], 3 X[468] - X[47310], 2 X[547] - 3 X[44452], 2 X[548] + X[16619], 4 X[549] - 3 X[10257], X[549] - 3 X[15646], 2 X[549] + 3 X[37931], 7 X[549] - 3 X[37938], X[858] - 3 X[3524], X[1551] - 3 X[35297], 3 X[2070] + 5 X[14093], X[2070] + 2 X[47114], 3 X[2071] + X[37901], 3 X[2072] - 5 X[15694], 3 X[3153] - 11 X[15721], 5 X[3522] + 3 X[37909], 5 X[3522] + 7 X[37957], 7 X[3528] + 5 X[37953], 3 X[5054] - 2 X[5159], 3 X[5055] - X[18323], 3 X[5055] - 4 X[37911], 5 X[5071] + 3 X[13619], 5 X[5071] - 6 X[44911], X[5189] - 9 X[15705], 5 X[7426] + 3 X[16386], 4 X[7426] - 3 X[37971], X[7426] + 3 X[44280], 7 X[7426] - 3 X[47096], X[7464] - 5 X[19708], X[7574] - 5 X[15693], 2 X[8703] + X[37904], 3 X[10151] - 2 X[15687], X[10151] - 4 X[16531], X[10257] - 4 X[15646], X[10257] + 2 X[37931], 7 X[10257] - 4 X[37938], 3 X[10257] - 2 X[47097], 5 X[10295] + X[10296], 2 X[10295] + X[10297], X[10295] + 5 X[37952], 2 X[10296] - 5 X[10297], X[10296] - 25 X[37952], X[10297] - 10 X[37952], X[10989] - 5 X[15692], X[10989] - 9 X[37941], 5 X[10989] - 9 X[44450], 3 X[11539] - X[18572], 3 X[11563] + X[44903], 4 X[11737] - 3 X[23323], 4 X[12100] - X[47311], X[12105] + 2 X[33923], 3 X[13473] - 4 X[14893], X[13473] - 4 X[44234], X[13619] + 2 X[44911], 5 X[14093] - 6 X[47114], 2 X[14891] - 3 X[37968], 8 X[14891] - 3 X[47090], X[14893] - 3 X[44234], 2 X[15646] + X[37931], 7 X[15646] - X[37938], 6 X[15646] - X[47097], X[15681] + 6 X[37935], X[15681] - 3 X[44246], X[15684] - 6 X[37942], X[15687] - 6 X[16531], X[15687] - 3 X[44282], 3 X[15688] + 2 X[37897], 3 X[15688] + 5 X[37958], 3 X[15689] + X[18325], 3 X[15689] + 4 X[47316], 5 X[15692] - 9 X[37941], 25 X[15692] - 9 X[44450], and many others

X(47333) lies on these lines: {2, 3}, {187, 3163}, {523, 44202}, {524, 32110}, {541, 35266}, {597, 39242}, {1499, 47190}, {2482, 45312}, {5585, 47275}, {6148, 6390}, {9126, 47159}, {11649, 16836}, {12042, 16325}, {14961, 16328}, {15035, 40112}, {15448, 16111}, {16163, 32225}, {16279, 37809}, {16312, 46632}, {17702, 44569}, {23878, 46990}, {30209, 47001}, {32113, 43273}, {32267, 37853}, {32269, 38726}, {46980, 46994}, {46983, 46997}, {46986, 47000}, {46989, 47003}

X(47333) = midpoint of X(i) and X(j) for these {i,j}: {2, 10295}, {3, 44265}, {186, 44280}, {376, 7426}, {468, 47031}, {550, 44266}, {3534, 11799}, {7464, 47313}, {7575, 8703}, {8598, 36166}, {15690, 25338}, {16163, 32225}, {19710, 44267}, {32113, 43273}, {32267, 37853}, {37969, 44285}, {46980, 46994}, {46983, 46997}, {46986, 47000}, {46989, 47003}
X(47333) = reflection of X(i) in X(j) for these {i,j}: {468, 18579}, {3830, 37984}, {10151, 44282}, {10297, 2}, {15122, 12100}, {18579, 18571}, {37904, 7575}, {44265, 37934}, {44282, 16531}, {47097, 549}, {47159, 9126}, {47308, 47031}, {47311, 15122}, {47332, 468}
X(47333) = reflection of X(47332) in the orthic axis
X(47333) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {22, 186, 7575}, {22, 41463, 35243}, {186, 376, 7426}, {376, 15078, 549}, {468, 47308, 47309}, {549, 47097, 10257}, {7426, 44214, 44211}, {7426, 44280, 376}, {7499, 15122, 10257}, {10304, 41463, 8703}, {10989, 37941, 15692}, {15646, 37931, 10257}, {35472, 37952, 15646}, {36439, 36457, 44285}, {44265, 44280, 44261}

X(47334) = SHINAGAWA-EULER POINT (-E/12 + 2F/3, 0)

Barycentrics 2*a^10 - 9*a^8*b^2 + 10*a^6*b^4 + 4*a^4*b^6 - 12*a^2*b^8 + 5*b^10 - 9*a^8*c^2 - 8*a^6*b^2*c^2 - 2*a^4*b^4*c^2 + 34*a^2*b^6*c^2 - 15*b^8*c^2 + 10*a^6*c^4 - 2*a^4*b^2*c^4 - 44*a^2*b^4*c^4 + 10*b^6*c^4 + 4*a^4*c^6 + 34*a^2*b^2*c^6 + 10*b^4*c^6 - 12*a^2*c^8 - 15*b^2*c^8 + 5*c^10 : :

X(47334) = 5 X[2] - X[7464], X[4] + 3 X[37907], 5 X[4] + 7 X[37957], 2 X[5] + X[16619], 5 X[5] + X[37967], X[23] + 3 X[3545], 3 X[186] + X[3543], 5 X[376] - 9 X[37941], X[376] - 9 X[37943], X[376] - 3 X[44214], X[381] - 3 X[403], 5 X[381] + 3 X[2070], 7 X[381] - 3 X[18403], 4 X[381] - 3 X[23323], 5 X[403] + X[2070], 3 X[403] + X[7426], 7 X[403] - X[18403], 4 X[403] - X[23323], 5 X[468] - 2 X[18571], 7 X[468] - 4 X[22249], X[468] + 2 X[44961], 5 X[468] - X[47031], 7 X[468] - X[47308], 5 X[468] + X[47309], 3 X[468] + X[47310], X[549] + 3 X[11563], 7 X[549] - 6 X[16976], 5 X[549] - 3 X[34152], X[549] - 6 X[37942], X[549] - 3 X[44282], 2 X[549] - 3 X[44452], X[858] - 3 X[5055], 3 X[2070] - 5 X[7426], 7 X[2070] + 5 X[18403], 4 X[2070] + 5 X[23323], 3 X[2071] - 7 X[15702], 3 X[2072] - 5 X[5071], 3 X[2072] - X[10989], 5 X[2072] + X[37945], 5 X[3091] + 3 X[37909], X[3627] + 2 X[37934], 7 X[3832] + 5 X[37953], 3 X[3839] - X[18323], 3 X[3839] + 5 X[37760], 2 X[3850] + X[12105], 3 X[5054] + X[18325], 11 X[5056] + X[37946], 2 X[5066] + X[37904], 5 X[5071] - X[10989], 25 X[5071] + 3 X[37945], 2 X[5159] - 3 X[15699], 7 X[7426] + 3 X[18403], 4 X[7426] + 3 X[23323], X[7464] + 5 X[11799], 2 X[7464] - 5 X[15122], X[7574] - 5 X[19709], X[7575] + 2 X[37984], 2 X[10096] + X[10151], 3 X[10096] + X[14893], 4 X[10109] - X[47311], 4 X[10124] - 3 X[10257]and many more

X(47334) lies on these lines: {2, 3}, {113, 32225}, {115, 47169}, {523, 44204}, {542, 46817}, {1989, 16303}, {3163, 47144}, {3564, 34319}, {3580, 5655}, {5663, 44569}, {7687, 32267}, {10113, 15448}, {11579, 18374}, {14643, 40112}, {14915, 45311}, {20126, 32111}, {20423, 32113}, {30685, 47148}, {41617, 45016}, {44203, 47219}, {46980, 46993}, {46983, 46996}, {46986, 46999}, {46989, 47002}

X(47334) = midpoint of X(i) and X(j) for these {i,j}: {2, 11799}, {4, 44265}, {5, 44266}, {113, 32225}, {381, 7426}, {3580, 5655}, {3830, 10295}, {3845, 7575}, {3860, 44264}, {5066, 25338}, {7574, 47313}, {7687, 32267}, {8703, 44267}, {10297, 37904}, {11563, 44282}, {20126, 32111}, {20423, 32113}, {31726, 44280}, {36196, 37461}, {37924, 47314}, {44203, 47219}, {46980, 46993}, {46983, 46996}, {46986, 46999}, {46989, 47002}, {47031, 47309}
X(47334) = reflection of X(i) in X(j) for these {i,j}: {3845, 37984}, {10297, 5066}, {15122, 2}, {16619, 44266}, {18579, 468}, {37904, 25338}, {44280, 16531}, {44282, 37942}, {44452, 44282}, {47031, 18571}, {47097, 547}
X(47334) = reflection of X(18579) in the orthic axis
X(47334) = X(44265)-of-Euler-triangle
X(47334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 37907, 44265}, {25, 403, 37984}, {381, 7576, 14893}, {381, 10201, 549}, {403, 7426, 381}, {403, 11799, 46030}, {468, 47308, 22249}, {468, 47309, 18571}, {5071, 10989, 2072}, {5655, 15362, 3580}, {7426, 44214, 44213}, {11563, 37942, 44452}, {13626, 13627, 39487}, {15122, 46030, 23323}, {44266, 44282, 44262}

X(47335) = SHINAGAWA-EULER POINT (E/4 - 2F, 0)

Barycentrics 6*a^10 - 11*a^8*b^2 - 2*a^6*b^4 + 12*a^4*b^6 - 4*a^2*b^8 - b^10 - 11*a^8*c^2 + 24*a^6*b^2*c^2 - 14*a^4*b^4*c^2 - 2*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 14*a^4*b^2*c^4 + 12*a^2*b^4*c^4 - 2*b^6*c^4 + 12*a^4*c^6 - 2*a^2*b^2*c^6 - 2*b^4*c^6 - 4*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(47335) = 3 X[3] - X[858], 5 X[3] - X[7574], X[3] - 3 X[44280], X[4] - 5 X[37952], X[4] - 3 X[44214], X[5] - 3 X[15646], 4 X[5] - 3 X[23323], 3 X[5] - 4 X[37911], 2 X[5] - 3 X[44452], 5 X[5] - 6 X[44911], 11 X[5] - 12 X[44912], X[20] + 3 X[186], 3 X[20] + 5 X[37760], X[20] - 3 X[44246], 7 X[20] + 9 X[46451], X[23] + 3 X[376], X[23] - 3 X[44265], 3 X[186] - X[11799], 9 X[186] - 5 X[37760], 7 X[186] - 3 X[46451], X[382] - 3 X[403], X[382] - 6 X[16531], X[382] - 9 X[37955], X[403] - 3 X[37955], 2 X[468] - 3 X[18579], 3 X[468] - 4 X[22249], 3 X[468] - 2 X[44961], X[468] + 3 X[47031], 3 X[468] - X[47309], 7 X[468] - 3 X[47310], 6 X[548] + X[37899], 2 X[548] + 3 X[37931], 3 X[549] - 2 X[5159], 3 X[549] - X[18572], 2 X[550] + X[16619], 3 X[550] + 2 X[37897], X[550] + 2 X[37934], 5 X[631] - 3 X[2072], 5 X[631] - X[10296], 5 X[631] + 3 X[13619], 5 X[631] - 9 X[37941], 5 X[858] - 3 X[7574], X[858] + 3 X[10295], 2 X[858] - 3 X[15122], X[858] - 9 X[44280], 3 X[2070] + 5 X[15696], 3 X[2071] - 7 X[3528], X[2071] + 3 X[35489], 3 X[2072] - X[10296], X[2072] - 3 X[37941], 3 X[3153] - 11 X[15717], and many more

X(47335) lies on these lines: {2, 3}, {50, 16303}, {143, 16227}, {187, 16306}, {511, 14708}, {523, 44205}, {1495, 16111}, {1503, 12041}, {1514, 34584}, {1531, 38793}, {2777, 46817}, {3564, 32233}, {3580, 12121}, {3581, 38723}, {5160, 37729}, {6781, 47169}, {9820, 34798}, {9934, 14677}, {10113, 47296}, {10620, 46818}, {11179, 47280}, {12134, 32210}, {12228, 37477}, {12244, 35265}, {13346, 34114}, {13568, 43394}, {14915, 37853}, {15057, 25739}, {15136, 40111}, {16003, 21663}, {16163, 32110}, {19924, 32300}, {20127, 32111}, {20379, 30522}, {22463, 38608}, {23328, 34514}, {32113, 46264}, {32124, 35257}, {32220, 33878}, {43273, 47276}, {46981, 46994}, {46984, 46997}, {46987, 47000}, {46990, 47003}

X(47335) = complement of X(18323)
X(47335) = midpoint of X(i) and X(j) for these {i,j}: {3, 10295}, {20, 11799}, {186, 44246}, {376, 44265}, {468, 47308}, {550, 7575}, {1495, 16111}, {2070, 16386}, {2072, 13619}, {3534, 7426}, {3580, 12121}, {10620, 46818}, {12103, 25338}, {15686, 44266}, {15704, 44267}, {16163, 32110}, {20127, 32111}, {32113, 46264}, {32124, 35257}, {32220, 33878}, {35001, 37900}, {37969, 44249}, {46981, 46994}, {46984, 46997}, {46987, 47000}, {46990, 47003}
X(47335) = reflection of X(i) in X(j) for these {i,j}: {403, 16531}, {468, 18571}, {3627, 37984}, {7575, 37934}, {10113, 47296}, {10151, 44234}, {10257, 37968}, {10297, 140}, {11563, 37935}, {13473, 46031}, {15122, 3}, {16619, 7575}, {18572, 5159}, {23323, 44452}, {34152, 47114}, {37938, 16976}, {44283, 37942}, {44452, 15646}, {44961, 22249}, {47097, 12100}, {47309, 44961}, {47336, 468}
X(47335) = reflection of X(47336) in the orthic axis
X(47335) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3534, 16063}, {3, 6240, 23336}, {3, 7495, 12100}, {3, 35471, 13371}, {3, 35503, 44242}, {3, 37196, 18281}, {3, 38323, 140}, {4, 37952, 44214}, {20, 186, 11799}, {26, 186, 7575}, {26, 33532, 12083}, {186, 35503, 10295}, {376, 33532, 550}, {403, 10295, 35471}, {403, 37955, 16531}, {468, 18571, 18579}, {468, 47031, 47308}, {468, 47309, 44961}, {549, 18572, 5159}, {550, 37934, 16619}, {631, 10296, 2072}, {631, 13619, 10296}, {858, 21284, 37897}, {3534, 37958, 18325}, {3627, 44282, 37984}, {7568, 15122, 10257}, {7575, 15646, 37814}, {10295, 44246, 44242}, {10295, 44280, 3}, {10296, 37941, 631}, {10300, 21841, 34199}, {11799, 44246, 20}, {13619, 37941, 2072}, {15332, 43615, 12605}, {16532, 44283, 37942}, {18281, 37196, 3627}, {18325, 37958, 7426}, {18571, 44961, 22249}, {22249, 44961, 468}, {31664, 31665, 18579}, {35231, 35232, 18570}, {35473, 38321, 44236}, {44246, 44265, 12083}

X(47336) = SHINAGAWA-EULER POINT (-E/4 + 2F, 0)

Barycentrics 2*a^10 - a^8*b^2 - 6*a^6*b^4 + 4*a^4*b^6 + 4*a^2*b^8 - 3*b^10 - a^8*c^2 + 16*a^6*b^2*c^2 - 6*a^4*b^4*c^2 - 18*a^2*b^6*c^2 + 9*b^8*c^2 - 6*a^6*c^4 - 6*a^4*b^2*c^4 + 28*a^2*b^4*c^4 - 6*b^6*c^4 + 4*a^4*c^6 - 18*a^2*b^2*c^6 - 6*b^4*c^6 + 4*a^2*c^8 + 9*b^2*c^8 - 3*c^10 : :

X(47336) = X[3] - 3 X[403], 5 X[3] - 3 X[16386], X[3] + 3 X[31726], 2 X[3] - 3 X[44452], 3 X[4] + X[23], 5 X[4] - X[10296], 2 X[4] + X[16619], 3 X[4] - X[18323], 3 X[5] - 2 X[5159], 3 X[5] - X[37950], X[20] - 3 X[44214], 5 X[23] + 3 X[10296], X[23] - 3 X[11799], 2 X[23] - 3 X[16619], 3 X[186] + X[3146], 3 X[381] - X[858], 3 X[381] + X[18325], 9 X[381] - X[35001], 3 X[382] + 5 X[37958], 5 X[403] - X[16386], 3 X[468] - 2 X[18571], 4 X[468] - 3 X[18579], 5 X[468] - 4 X[22249], 7 X[468] - 3 X[47031], 3 X[468] - X[47308], X[468] + 3 X[47310], 2 X[546] - 3 X[10151], X[546] + 3 X[11558], 4 X[546] - 3 X[23323], 6 X[546] - X[46517], 3 X[549] - 4 X[37911], X[550] - 3 X[44282], 5 X[632] - 3 X[34152], 5 X[632] - 6 X[44911], 3 X[858] - X[35001], X[1657] - 3 X[44280], 3 X[2070] + 5 X[5076], 3 X[2071] - 7 X[3090], 3 X[2072] - 5 X[3091], 3 X[2072] - X[7464], 5 X[2072] - 3 X[44450], 5 X[3091] - X[7464], 25 X[3091] - 9 X[44450], 3 X[3153] + X[37946], X[3529] - 6 X[16531], X[3529] - 9 X[37943], X[3529] - 5 X[37952], X[3529] - 3 X[44246], 3 X[3543] + 5 X[37760], 9 X[3545] - 5 X[30745], X[3627] + 3 X[11563], X[3627] - 3 X[44283], 3 X[3627] + 4 X[47316], 4 X[3628] - 3 X[10257], 2 X[3628] - 3 X[46031], 9 X[3839] - X[5189], 5 X[3843] - X[7574], 3 X[3845] - X[18572], and many more

X(47336) lies on these lines: {2, 3}, {113, 3292}, {115, 16306}, {265, 32111}, {511, 46686}, {524, 32271}, {1493, 32364}, {1495, 12295}, {1503, 10113}, {1514, 5663}, {1539, 46085}, {1853, 18431}, {2777, 15126}, {3284, 47144}, {3564, 9970}, {3580, 7728}, {3818, 8542}, {5480, 15826}, {5609, 44665}, {5893, 6102}, {6000, 36253}, {7687, 14915}, {10264, 11744}, {10564, 36518}, {10706, 41724}, {11645, 15118}, {11801, 17854}, {12041, 47296}, {12902, 46818}, {13202, 32110}, {13445, 15025}, {13446, 16625}, {13630, 16227}, {13754, 38791}, {14708, 44084}, {15012, 22968}, {15044, 25739}, {15120, 16252}, {15125, 18400}, {16303, 19656}, {16308, 44468}, {16655, 18379}, {16658, 18430}, {17702, 46817}, {18440, 32220}, {18809, 34147}, {19510, 19924}, {20423, 47280}, {31670, 32113}, {38227, 44969}, {39663, 46633}, {40996, 44138}, {41336, 43291}, {46982, 46993}, {46985, 46996}, {46988, 46999}, {46991, 47002}

X(47336) = midpoint of X(i) and X(j) for these {i,j}: {4, 11799}, {5, 44267}, {23, 18323}, {265, 32111}, {382, 10295}, {403, 31726}, {468, 47309}, {858, 18325}, {1495, 12295}, {3543, 44265}, {3580, 7728}, {3627, 7575}, {3830, 7426}, {3853, 25338}, {11563, 44283}, {12902, 46818}, {13202, 32110}, {13473, 37971}, {15687, 44266}, {18403, 47096}, {18440, 32220}, {31670, 32113}, {46982, 46993}, {46985, 46996}, {46988, 46999}, {46991, 47002}
X(47336) = reflection of X(i) in X(j) for these {i,j}: {5, 37984}, {468, 44961}, {10257, 46031}, {10297, 546}, {12041, 47296}, {14708, 44084}, {15122, 5}, {15646, 37942}, {16387, 46029}, {16619, 11799}, {23323, 10151}, {34152, 44911}, {37931, 10096}, {37950, 5159}, {44246, 16531}, {44452, 403}, {47097, 5066}, {47308, 18571}, {47335, 468}
X(47336) = nine-point-circle-inverse of X(46030)
X(47336) = polar-circle-inverse of X(35481)
X(47336) = 2nd-Droz-Farny-circle-inverse of X(381)
X(47336) = reflection of X(47335) in the orthic axis
X(47336) = X(11799)-of-Euler-triangle
X(47336) = X(15122)-of-Johnson-triangle
X(47336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 23, 18323}, {4, 7519, 3830}, {4, 7530, 3627}, {4, 7540, 3853}, {5, 37950, 5159}, {23, 31861, 37950}, {23, 37981, 5159}, {381, 3830, 31105}, {381, 18325, 858}, {403, 10295, 7505}, {403, 11799, 15761}, {403, 37197, 37984}, {403, 37917, 37942}, {468, 47308, 18571}, {468, 47310, 47309}, {546, 10297, 23323}, {858, 11284, 5159}, {1312, 1313, 46030}, {1596, 44263, 13490}, {3091, 7464, 2072}, {3529, 37943, 37952}, {3529, 37952, 44246}, {3627, 7530, 11819}, {3627, 11563, 7575}, {3853, 10020, 18560}, {5159, 37950, 15122}, {7526, 45171, 34152}, {7527, 10024, 3628}, {7556, 18563, 12103}, {7575, 44283, 3627}, {10024, 45181, 46031}, {10151, 10297, 546}, {10750, 10751, 7391}, {11558, 44226, 44267}, {11799, 18323, 23}, {11799, 44283, 11819}, {18323, 37981, 31861}, {30524, 30525, 37440}, {31105, 44440, 35481}, {31725, 35488, 13371}, {31829, 37984, 46031}, {37943, 44246, 16531}, {37984, 44226, 10151}, {37984, 44267, 15122}, {42280, 42281, 13371}, {44267, 44283, 44271}

X(47337) = SHINAGAWA-EULER POINT (3E/2 - 3F/2, 0)

Barycentrics 10*a^10 - 19*a^8*b^2 - 2*a^6*b^4 + 20*a^4*b^6 - 8*a^2*b^8 - b^10 - 19*a^8*c^2 + 80*a^6*b^2*c^2 - 44*a^4*b^4*c^2 - 20*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 - 44*a^4*b^2*c^4 + 56*a^2*b^4*c^4 - 2*b^6*c^4 + 20*a^4*c^6 - 20*a^2*b^2*c^6 - 2*b^4*c^6 - 8*a^2*c^8 + 3*b^2*c^8 - c^10 : :

X(47337) = X[4] - 3 X[47090], 4 X[5] - 5 X[5159], 3 X[5] - 5 X[15122], X[5] - 5 X[37950], 6 X[5] - 5 X[37984], 9 X[5] - 5 X[44267], 5 X[23] - 13 X[21734], 4 X[140] - 3 X[37942], 3 X[376] + 5 X[7464], 9 X[376] - 5 X[10295], 7 X[376] - 5 X[47031], 9 X[376] + 5 X[47092], X[468] - 3 X[2071], 5 X[468] - 7 X[3523], 2 X[468] - 3 X[16976], 11 X[468] - 9 X[46451], 5 X[468] - 3 X[47096], 5 X[858] - X[3146], 3 X[1657] + 5 X[7574], X[1657] + 15 X[18859], 2 X[1657] + 5 X[47315], 15 X[2071] - 7 X[3523], 11 X[2071] - 3 X[46451], 5 X[2071] - X[47096], 5 X[3522] - X[37900], 5 X[3522] - 3 X[37931], 5 X[3522] + 3 X[37944], 14 X[3523] - 15 X[16976], 77 X[3523] - 45 X[46451], 7 X[3523] - 3 X[47096], 11 X[3525] - 10 X[37911], 3 X[3830] - 5 X[10297], 3 X[3839] - 5 X[47097], 17 X[3854] - 15 X[10151], 17 X[3854] - 25 X[30745], 9 X[5054] - 5 X[11799], 3 X[5159] - 4 X[15122], X[5159] - 4 X[37950], 3 X[5159] - 2 X[37984], 9 X[5159] - 4 X[44267], X[5189] + 3 X[16386], X[5189] - 3 X[47091], 5 X[7426] - 9 X[15705], 3 X[7464] + X[10295], 7 X[7464] + 3 X[47031], 3 X[7464] - X[47092], X[7574] - 9 X[18859], 2 X[7574] - 3 X[47315], 5 X[7575] - 9 X[45759], 3 X[10151] - 5 X[30745], 3 X[10257] - X[18325], 15 X[10257] - 13 X[46219], 7 X[10295] - 9 X[47031], X[10296] - 3 X[47311], 3 X[10304] - X[47312], 9 X[12100] - 5 X[25338], X[13473] - 3 X[44450], X[15122] - 3 X[37950], 3 X[15122] - X[44267], X[16619] - 3 X[34152], 2 X[16619] - 3 X[37935], 11 X[16976] - 6 X[46451], 5 X[16976] - 2 X[47096], 5 X[18325] - 13 X[46219], 6 X[18859] - X[47315], 11 X[21735] - 3 X[37925], 16 X[33923] - 5 X[37910], 8 X[33923] - 5 X[37934], 16 X[33923] - 15 X[47114], X[37899] - 3 X[44280], X[37900] - 3 X[37931], X[37900] + 3 X[37944], 3 X[37904] - 5 X[37952], X[37910] - 3 X[47114], 2 X[37934] - 3 X[47114], 3 X[37941] - X[47094], 3 X[37948] - X[47093], 6 X[37950] - X[37984], 9 X[37950] - X[44267], 3 X[37984] - 2 X[44267], 7 X[41106] - 5 X[47310], 15 X[46451] - 11 X[47096], 9 X[47031] + 7 X[47092]

X(47337) lies on these lines: {2, 3}, {74, 34380}, {511, 15151}, {841, 43351}, {2696, 29180}, {15118, 29181}, {26864, 46349}

X(47337) = midpoint of X(i) and X(j) for these {i,j}: {20, 46517}, {10295, 47092}, {16386, 47091}, {37931, 37944}
X(47337) = reflection of X(i) in X(j) for these {i,j}: {16976, 2071}, {37897, 3}, {37910, 37934}, {37935, 34152}, {37984, 15122}, {47338, 468}
X(47337) = reflection of X(47338) in the orthic axis
X(47337) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3522, 37900, 37931}, {3522, 37944, 37900}, {3523, 47096, 468}, {7464, 10295, 47092}, {15122, 37984, 5159}, {21312, 35485, 550}, {30552, 37196, 550}, {37910, 47114, 37934}

X(47338) = SHINAGAWA-EULER POINT (-3E/2 + 3F/2, 0)

Barycentrics 2*a^10 + a^8*b^2 - 10*a^6*b^4 + 4*a^4*b^6 + 8*a^2*b^8 - 5*b^10 + a^8*c^2 + 64*a^6*b^2*c^2 - 28*a^4*b^4*c^2 - 52*a^2*b^6*c^2 + 15*b^8*c^2 - 10*a^6*c^4 - 28*a^4*b^2*c^4 + 88*a^2*b^4*c^4 - 10*b^6*c^4 + 4*a^4*c^6 - 52*a^2*b^2*c^6 - 10*b^4*c^6 + 8*a^2*c^8 + 15*b^2*c^8 - 5*c^10 : :

X(47338) = 5 X[4] + 3 X[37946], X[20] - 3 X[37904], 9 X[23] - X[5059], 3 X[403] - X[47092], 5 X[468] - 3 X[2071], 9 X[468] - 7 X[3523], 4 X[468] - 3 X[16976], 7 X[468] - 9 X[46451], X[468] - 3 X[47096], 5 X[550] - 9 X[7575], X[550] - 3 X[16619], 4 X[550] - 9 X[37897], 2 X[550] - 3 X[37934], 9 X[858] - 13 X[5068], 10 X[1656] - 9 X[5159], 5 X[1656] - 9 X[11799], 25 X[1656] - 9 X[35001], 27 X[2071] - 35 X[3523], 4 X[2071] - 5 X[16976], 7 X[2071] - 15 X[46451], X[2071] - 5 X[47096], 5 X[3522] - 9 X[7426], 28 X[3523] - 27 X[16976], 49 X[3523] - 81 X[46451], 7 X[3523] - 27 X[47096], 17 X[3533] - 9 X[7464], 17 X[3533] - 18 X[37911], 8 X[3850] - 9 X[37984], 17 X[3854] - 9 X[10989], 11 X[5056] - 9 X[47097], 5 X[5073] + 27 X[5899], X[5073] - 9 X[18325], 2 X[5073] + 9 X[37910], 5 X[5159] - 2 X[35001], X[5189] - 3 X[10151], 3 X[5899] + 5 X[18325], 6 X[5899] - 5 X[37910], 3 X[7575] - 5 X[16619], 4 X[7575] - 5 X[37897], 6 X[7575] - 5 X[37934], 5 X[10295] - 9 X[37939], X[10295] - 3 X[47093], X[10990] - 3 X[32269], 5 X[11799] - X[35001], 2 X[15122] - 3 X[37942], X[15122] - 3 X[43893], 5 X[15712] - 9 X[44266], 4 X[16619] - 3 X[37897], 7 X[16976] - 12 X[46451], X[16976] - 4 X[47096], 2 X[18325] + X[37910], 4 X[25338] - 3 X[37935], 5 X[25338] - 3 X[37968], 5 X[30745] - 6 X[44912], 5 X[30745] - 3 X[47091], 3 X[37897] - 2 X[37934], X[37900] - 3 X[47094], 5 X[37935] - 4 X[37968], 3 X[37939] - 5 X[47093], 5 X[37953] - 3 X[47031], 3 X[37955] - 5 X[37971], 6 X[37955] - 5 X[47114], 7 X[44904] - 9 X[44961], 3 X[46451] - 7 X[47096]

X(47338) lies on these lines: {2, 3}, {1533, 3564}, {8705, 13598}, {10990, 32269}, {32111, 34380}

X(47338) = midpoint of X(13473) and X(37945)
X(47338) = reflection of X(i) in X(j) for these {i,j}: {5159, 11799}, {7464, 37911}, {37934, 16619}, {37942, 43893}, {47091, 44912}, {47114, 37971}, {47337, 468}
X(47338) = reflection of X(47337) in the orthic axis
X(47338) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 34621, 1657}, {3515, 5059, 550}, {16619, 37934, 37897}

X(47339) = SHINAGAWA-EULER POINT (E + 4F, 0)

Barycentrics 6*a^10 - 7*a^8*b^2 - 10*a^6*b^4 + 12*a^4*b^6 + 4*a^2*b^8 - 5*b^10 - 7*a^8*c^2 + 12*a^6*b^2*c^2 - 4*a^4*b^4*c^2 - 16*a^2*b^6*c^2 + 15*b^8*c^2 - 10*a^6*c^4 - 4*a^4*b^2*c^4 + 24*a^2*b^4*c^4 - 10*b^6*c^4 + 12*a^4*c^6 - 16*a^2*b^2*c^6 - 10*b^4*c^6 + 4*a^2*c^8 + 15*b^2*c^8 - 5*c^10 : :

X(47339) = 4 X[3] - 3 X[47031], 2 X[3] - 3 X[47097], 5 X[4] - X[37946], 4 X[5] - 3 X[468], 5 X[5] - 3 X[7575], 2 X[5] - 3 X[10297], X[5] - 3 X[18572], 11 X[5] - 9 X[44282], X[20] - 3 X[858], 5 X[20] - 9 X[2071], X[20] - 9 X[3153], X[20] + 3 X[10296], 7 X[20] - 9 X[16386], 11 X[20] - 27 X[44450], 4 X[20] - 9 X[47090], 3 X[23] - 7 X[3832], 9 X[186] - 13 X[5067], 3 X[186] - 4 X[37911], X[382] + 3 X[7574], X[382] - 3 X[18323], 5 X[382] + 3 X[35001], 2 X[382] + 3 X[46517], 4 X[382] + 3 X[47092], 9 X[403] - 11 X[3855], 3 X[403] - 2 X[37897], 5 X[403] - 3 X[37939], 5 X[468] - 4 X[7575], X[468] - 4 X[18572], 11 X[468] - 12 X[44282], 2 X[548] - 3 X[15122], 5 X[631] - 6 X[5159], 5 X[631] - 3 X[10295], 5 X[858] - 3 X[2071], X[858] - 3 X[3153], 7 X[858] - 3 X[16386], 11 X[858] - 9 X[44450], 4 X[858] - 3 X[47090], 3 X[1531] - X[15063], 5 X[1656] - 3 X[44265], X[2071] - 5 X[3153], 3 X[2071] + 5 X[10296], 7 X[2071] - 5 X[16386], 11 X[2071] - 15 X[44450], 4 X[2071] - 5 X[47090], 9 X[2072] - 7 X[3526], 5 X[2072] - 3 X[37955], 5 X[3091] - 3 X[7426], X[3146] + 3 X[10989], 3 X[3153] + X[10296], 7 X[3153] - X[16386], 11 X[3153] - 3 X[44450], 4 X[3153] - X[47090], 14 X[3526] - 9 X[37931], 35 X[3526] - 27 X[37955], 8 X[3530] - 9 X[10257], 10 X[3530] - 9 X[37968], 9 X[3545] - 5 X[37953], 4 X[3628] - 3 X[18579], 7 X[3832] - 6 X[37984], 25 X[3843] - 9 X[5899], 10 X[3843] - 9 X[10151], 5 X[3843] - 3 X[11799], 5 X[3843] - 9 X[18403], 10 X[3843] - 3 X[37899], 20 X[3843] - 9 X[47093], 3 X[3845] - X[37967], 8 X[3853] - 9 X[13473], 8 X[3853] + 3 X[47095], 17 X[3854] - 9 X[37909], 11 X[3855] - 6 X[37897], 55 X[3855] - 27 X[37939], 8 X[3856] - 9 X[23323], 16 X[3856] - 9 X[37971], 4 X[3856] - 3 X[44961], 5 X[3858] - 3 X[44266], 5 X[3859] - 3 X[25338], 11 X[5056] - 7 X[37957], 13 X[5067] - 12 X[37911], 13 X[5068] - 9 X[37907], 11 X[5070] - 9 X[44214], 3 X[5189] + 5 X[17578], 2 X[5899] - 5 X[10151], 3 X[5899] - 5 X[11799], X[5899] - 5 X[18403], 6 X[5899] - 5 X[37899], 4 X[5899] - 5 X[47093], 3 X[7464] + X[33703], 5 X[7574] - X[35001], 4 X[7574] - X[47092], 2 X[7575] - 5 X[10297], X[7575] - 5 X[18572], 11 X[7575] - 15 X[44282], 3 X[10151] - 2 X[11799], 3 X[10151] - X[37899], 5 X[10257] - 4 X[37968], 7 X[10296] + 3 X[16386], 11 X[10296] + 9 X[44450], 4 X[10296] + 3 X[47090], 11 X[10297] - 6 X[44282], X[11799] - 3 X[18403], 4 X[11799] - 3 X[47093], 3 X[13473] + X[47095], 3 X[13851] - X[41586], 7 X[15044] - 3 X[15360], 2 X[15448] - 3 X[36518], 11 X[15717] - 15 X[30745], 11 X[15717] - 9 X[44280], 4 X[16239] - 3 X[18571], 11 X[16386] - 21 X[44450], 4 X[16386] - 7 X[47090], 5 X[18323] + X[35001], 2 X[18323] + X[46517], 4 X[18323] + X[47092], 6 X[18403] - X[37899], 4 X[18403] - X[47093], 11 X[18572] - 3 X[44282], X[20063] - 3 X[47096], 5 X[22248] - 6 X[44900], 3 X[23323] - 2 X[44961], 5 X[30745] - 3 X[44280], 2 X[35001] - 5 X[46517], 4 X[35001] - 5 X[47092], 5 X[37760] - 6 X[37942], 10 X[37897] - 9 X[37939], 2 X[37899] - 3 X[47093], 5 X[37931] - 6 X[37955], 9 X[37938] - 5 X[46853], 3 X[37971] - 4 X[44961], 2 X[44264] - 3 X[46031], 12 X[44450] - 11 X[47090]

X(47339) lies on these lines: {2, 3}, {32, 47184}, {343, 18376}, {511, 15738}, {1352, 47279}, {1503, 1531}, {1514, 29012}, {3564, 47281}, {5160, 9643}, {5907, 11649}, {7687, 32269}, {7745, 16303}, {8262, 29181}, {8705, 15030}, {8743, 47183}, {11416, 14094}, {11459, 47278}, {11645, 38791}, {12220, 16261}, {13851, 41586}, {14915, 25711}, {15044, 15360}, {15069, 18405}, {15448, 36518}, {18396, 47277}, {27376, 47162}, {30476, 46997}, {38397, 44683}, {44377, 46994}

X(47339) = midpoint of X(i) and X(j) for these {i,j}: {858, 10296}, {7574, 18323}
X(47339) = reflection of X(i) in X(j) for these {i,j}: {23, 37984}, {468, 10297}, {10151, 18403}, {10295, 5159}, {10297, 18572}, {12105, 3850}, {13619, 16976}, {16619, 546}, {32269, 7687}, {37899, 11799}, {37904, 381}, {37931, 2072}, {37971, 23323}, {46517, 7574}, {46994, 44377}, {46997, 30476}, {47031, 47097}, {47092, 46517}, {47093, 10151}, {47279, 1352}, {47340, 468}
X(47339) = anticomplement of X(37934)
X(47339) = circumcircle-of-anticomplementary-triangle-inverse of X(35513)
X(47339) = de-Longchamps-circle-inverse of X(10304)
X(47339) = reflection of X(47340) in the orthic axis
X(47339) = Johnson-circle-inverse of X(18420)
X(47339) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 382, 3575}, {5, 548, 7542}, {382, 18404, 5}, {631, 7547, 5}, {2041, 2042, 37196}, {2071, 37946, 11414}, {3153, 10296, 858}, {3832, 7503, 5}, {10151, 37899, 11799}, {10750, 10751, 18420}, {11799, 37899, 47093}, {12605, 18377, 23047}, {14807, 14808, 35513}, {37454, 37904, 468}, {45994, 45995, 34664}, {47031, 47093, 37969}

X(47340) = SHINAGAWA-EULER POINT (-E - 4F, 0)

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

X(47340) = 2 X[3] - 3 X[37931], 4 X[3] - 3 X[47090], 4 X[5] - 5 X[468], 3 X[5] - 5 X[7575], 6 X[5] - 5 X[10297], 7 X[5] - 5 X[18572], 13 X[5] - 15 X[44282], 5 X[23] - X[3146], 4 X[23] - 3 X[47093], 5 X[23] - 3 X[47096], 15 X[186] - 11 X[3525], 3 X[186] - 2 X[5159], 9 X[376] - 5 X[7464], 3 X[376] - 5 X[10295], 4 X[376] - 5 X[47031], 12 X[376] - 5 X[47092], 3 X[403] - 5 X[37953], 3 X[468] - 4 X[7575], 3 X[468] - 2 X[10297], 7 X[468] - 4 X[18572], 13 X[468] - 12 X[44282], 5 X[632] - 6 X[16531], 5 X[858] - 7 X[3523], 3 X[858] - 5 X[37952], 2 X[1657] + 5 X[37899], 3 X[1657] + 5 X[37924], 3 X[2070] - X[18323], 3 X[2072] - 5 X[37958], 5 X[3091] - 9 X[37940], 5 X[3091] - 6 X[37942], 4 X[3146] - 15 X[47093], X[3146] - 3 X[47096], 3 X[3153] - 7 X[37957], 15 X[3153] - 23 X[46936], 7 X[3523] - 10 X[37934], 21 X[3523] - 25 X[37952], 11 X[3525] - 10 X[5159], X[3529] + 3 X[37925], X[3627] - 3 X[37936], 3 X[3830] - 5 X[11799], 2 X[3830] - 5 X[37904], 9 X[3830] - 25 X[37923], 3 X[3839] - 5 X[7426], 9 X[3839] - 5 X[10296], 9 X[3839] - 10 X[37984], 17 X[3854] - 25 X[37760], 3 X[3860] - 5 X[44264], 9 X[5054] - 5 X[7574], 3 X[5054] - 5 X[44265], 6 X[5054] - 5 X[47097], and many others

X(47340) lies on these lines: {2, 3}, {973, 15012}, {1503, 41583}, {1514, 32237}, {1531, 15448}, {3564, 47278}, {6090, 41465}, {6593, 16163}, {8705, 19161}, {12383, 34380}, {15531, 47281}, {18914, 41482}, {29323, 37853}

X(47340) = midpoint of X(20) and X(37900)
X(47340) = reflection of X(i) in X(j) for these {i,j}: {4, 37897}, {858, 37934}, {1514, 32237}, {1531, 15448}, {3153, 37935}, {10151, 2070}, {10296, 37984}, {10297, 7575}, {13473, 37971}, {46450, 16976}, {46517, 3}, {47090, 37931}, {47097, 44265}, {47339, 468}

X(47340) = reflection of X(47339) in the orthic axis
X(47340) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 46517, 47090}, {20, 37458, 34664}, {23, 3146, 47096}, {3575, 37931, 468}, {7426, 10296, 37984}, {7575, 10297, 468}, {12106, 15704, 12605}, {37931, 44239, 47031}, {37931, 46517, 3}

X(47341) = SHINAGAWA-EULER POINT (5E/4 + 2F, 0)

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

X(47341) = 9 X[2] - 5 X[37953], X[3] - 3 X[858], X[3] + 3 X[7574], 5 X[3] - 3 X[10295], 2 X[3] - 3 X[15122], 11 X[3] - 9 X[44280], X[4] + 3 X[10989], 3 X[5] - X[37967], 5 X[5] - 3 X[44266], X[23] - 3 X[2072], 3 X[23] - 7 X[3090], 5 X[23] - 9 X[37943], X[23] + 3 X[46450], 4 X[140] - 3 X[18579], 2 X[140] - 3 X[47097], 9 X[186] - 13 X[10303], 3 X[316] + X[38679], 9 X[403] - 11 X[5072], 3 X[403] - X[37924], 3 X[468] - 4 X[3628], 3 X[468] - 2 X[12105], 5 X[468] - 4 X[44264], 10 X[546] - 9 X[10151], 2 X[546] - 3 X[10297], 13 X[546] - 9 X[11558], 8 X[546] - 9 X[23323], 2 X[546] + 3 X[46517], 3 X[549] - 2 X[37934], 5 X[631] - 3 X[44265], 5 X[632] - 6 X[5159], 5 X[632] - 3 X[7575], 35 X[632] - 27 X[16532], 25 X[632] - 18 X[37935], 5 X[632] - 9 X[37938], 10 X[632] - 9 X[44452], 5 X[858] - X[10295], 11 X[858] - 3 X[44280], 3 X[1495] - 5 X[38795], 5 X[1656] - 3 X[7426], 9 X[2071] - 5 X[17538], 9 X[2072] - 7 X[3090], 5 X[2072] - 3 X[37943], 35 X[3090] - 27 X[37943], 7 X[3090] + 9 X[46450], 5 X[3091] + 3 X[5189], 5 X[3091] - 3 X[11799], 5 X[3091] - X[37946], X[3146] - 9 X[3153], X[3146] + 3 X[7464], X[3146] - 3 X[18323], 3 X[3153] + X[7464], 3 X[3153] - X[18323], 11 X[3525] - 15 X[30745], 11 X[3525] - 7 X[37957], 11 X[3525] - 9 X[44214], and many others

X(47341) lies on these lines: {2, 3}, {50, 43291}, {316, 38679}, {511, 36253}, {1216, 11649}, {1495, 38795}, {1503, 5609}, {1506, 47169}, {3564, 10510}, {3580, 15027}, {5007, 16306}, {8705, 15067}, {11482, 32220}, {11645, 16534}, {12900, 32237}, {13857, 30714}, {14915, 38791}, {15025, 15107}, {15131, 34153}, {15139, 40111}, {15826, 32358}, {16303, 41335}, {20304, 32269}, {20396, 44569}, {22330, 43573}, {23061, 25739}, {23236, 40112}, {27371, 47144}, {29012, 46817}, {32110, 38729}, {32217, 44491}, {33533, 45303}

X(47341) = midpoint of X(i) and X(j) for these {i,j}: {858, 7574}, {2072, 46450}, {5189, 11799}, {7464, 18323}, {10297, 46517}
X(47341) = reflection of X(i) in X(j) for these {i,j}: {7575, 5159}, {12105, 3628}, {15122, 858}, {16619, 5}, {18579, 47097}, {32237, 12900}, {32269, 20304}, {37899, 25338}, {37904, 547}, {37936, 44911}, {37947, 37942}, {44452, 37938}, {47093, 46031}, {47342, 468}
X(47341) = reflection of X(15122) in the De Longchamps axis
X(47341) = reflection of X(47342) in the orthic axis
X(47341) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1594, 3628}, {3, 3529, 44242}, {3, 3628, 7568}, {3, 5079, 7558}, {3, 12225, 12103}, {3, 18569, 3627}, {5, 550, 44262}, {3091, 5189, 37946}, {3091, 37946, 11799}, {3153, 7464, 18323}, {3525, 37957, 44214}, {3628, 12102, 13163}, {3628, 12105, 468}, {3628, 23410, 16042}, {5159, 7575, 44452}, {7495, 7579, 547}, {7575, 37938, 5159}, {12103, 23336, 3}, {13154, 37946, 7575}, {18531, 31099, 31861}, {30745, 37957, 3525}, {31181, 31861, 31099}

X(47342) = SHINAGAWA-EULER POINT (-5E/4 - 2F, 0)

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

X(47342) = X[4] - 5 X[23], 9 X[4] - 5 X[10296], 3 X[4] - 5 X[11799], 2 X[4] - 5 X[16619], 7 X[4] - 5 X[18323], X[5] - 3 X[37936], 5 X[5] - 6 X[37942], X[20] + 3 X[37925], 9 X[23] - X[10296], 3 X[23] - X[11799], 7 X[23] - X[18323], 15 X[186] - 11 X[15717], 3 X[186] + X[20063], X[382] - 3 X[47096], X[403] - 3 X[37956], 5 X[468] - 4 X[3628], 3 X[468] - 4 X[44264], 2 X[548] + 5 X[37899], 2 X[548] - 3 X[37931], 3 X[549] - 5 X[7575], 6 X[549] - 5 X[15122], 4 X[549] - 5 X[18579], 5 X[631] - 6 X[16531], 5 X[631] - 9 X[37940], X[858] - 3 X[2070], 5 X[858] - 7 X[3526], 2 X[858] - 3 X[44452], 15 X[2070] - 7 X[3526], 15 X[2072] - 17 X[7486], 3 X[2072] - 5 X[37760], X[2072] - 3 X[37939], 14 X[3526] - 15 X[44452], 7 X[3528] - 3 X[37944], 4 X[3530] - 3 X[47090], 3 X[3534] - 5 X[10295], 3 X[3534] + 5 X[37924], 2 X[3628] - 5 X[12105], 3 X[3628] - 5 X[44264], 16 X[3856] - 15 X[23323], 8 X[3856] - 15 X[37971], 4 X[3856] - 5 X[44961], 7 X[3857] - 5 X[18572], 3 X[5055] - 5 X[7426], 9 X[5055] - 5 X[7574], 9 X[5055] - 25 X[37923], 6 X[5066] - 5 X[10297], 3 X[5066] - 5 X[25338], 2 X[5066] - 5 X[37904], 5 X[5189] - 13 X[10303], X[5189] - 5 X[37953], X[5189] - 3 X[44214], 15 X[5899] + X[17800], and many others

X(47342) lies on these lines: {2, 3}, {1511, 29181}, {3564, 12367}, {5480, 34513}, {6699, 29323}, {8705, 12007}, {11061, 34380}, {11649, 32284}, {13338, 16303}, {32237, 46817}

X(47342) = midpoint of X(i) and X(j) for these {i,j}: {3, 37900}, {10295, 37924}, {16386, 37949}, {37901, 44265}, {37945, 44246}
X(47342) = reflection of X(i) in X(j) for these {i,j}: {5, 37897}, {468, 12105}, {10297, 25338}, {15122, 7575}, {16619, 23}, {23323, 37971}, {37950, 37934}, {37967, 37910}, {44452, 2070}, {46517, 140}, {46817, 32237}, {47091, 37968}, {47341, 468}
X(47342) = reflection of X(47341) in the orthic axis
X(47342) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 37936, 37897}, {23, 26, 37936}, {23, 31304, 47096}, {23, 37925, 7517}, {382, 14070, 18580}, {5189, 37953, 44214}, {7540, 7556, 140}, {7574, 37923, 7426}, {7575, 15122, 18579}, {10297, 37904, 25338}

X(47343) = X(30)-LINE CONJUGATE OF X(541)

X(47343) lies on these lines: {30, 511}, {5486, 14220}, {5505, 14380}, {8547, 44810}, {9126, 46616}

X(47343) = X(30)-line conjugate of X(541)
X(47343) = crossdifference of every pair of points on line {6, 541}
X(47343) = barycentric product X(2146)*X(34058)

X(47344) = X(3)X(7169)∩X(9)X(478)

X(47344 lies on the cubic K1272 and these lines: {3, 7169}, {9, 478}, {10, 20308}, {57, 44692}, {78, 7111}, {318, 377}, {1426, 34846}, {1712, 40169}

X(47344) = crosssum of X(3556) and X(36103)
X(47344) = X(1400)-cross conjugate of X(1214)
X(47344) = X(i)-isoconjugate of X(j) for these (i,j): {21, 36103}, {29, 3556}, {284, 17903}, {333, 21148}, {1172, 1763}, {1474, 27540}, {2189, 21062}, {2204, 20914}, {2299, 4329}, {8748, 22119}
X(47344) = barycentric product X(i)*X(j) for these {i,j}: {73, 40015}, {307, 7097}, {1214, 7219}, {1231, 7169}
X(47344) = barycentric quotient X(i)/X(j) for these {i,j}: {65, 17903}, {72, 27540}, {73, 1763}, {201, 21062}, {307, 20914}, {1214, 4329}, {1400, 36103}, {1402, 21148}, {1409, 3556}, {7097, 29}, {7169, 1172}, {7219, 31623}, {22341, 22119}, {40015, 44130}, {40169, 8748}

X(47345) = X(57)X(5307)∩X(65)X(1826)

X(47345) lies on the cubic K1272 and these lines: {57, 5307}, {65, 1826}, {281, 3485}, {653, 8822}, {1108, 1880}, {5816, 14257}, {23986, 30456}

X(47345) = complement of the isogonal conjugate of X(10537)
X(47345) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 225}, {10537, 10}
X(47345) = X(2)-Ceva conjugate of X(225)
X(47345) = barycentric quotient X(10537)/X(283)

X(47346) = VERTEX V OF PARALLELOGRAM WITH VERTICES X(3109), X(16272), V, X(16309)

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

X(47346) lies on these lines: {1, 16332}, {2, 3}, {511, 6739}, {523, 10015}, {952, 3580}, {7286, 45763}, {13869, 16272}, {16305, 47270}, {16309, 47271}

X(47346) = midpoint of X(i) and X(j) for these {i,j}: {23, 36154}, {11809, 47321}, {16309, 47271}
X(47346) = reflection of X(i) in X(j) for these {i,j}: {1, 16332}, {858, 36155}, {3109, 468}, {13869, 16272}, {47270, 16305}, {47272, 16309}
X(47346) = reflection of X(3109) in the orthic axis
X(47346) = circumcircle-inverse of X(11334)
X(47346) = polar-circle-inverse of X(5136)
X(47346) = crossdifference of every pair of points on line {647, 2278}
X(47346) = {X(1113),X(1114)}-harmonic conjugate of X(11334)

X(47347) = VERTEX V OF PARALLELOGRAM WITH VERTICES X(36164), X(47146), V, X(47148)

Barycentrics 3*a^14*b^2 - 12*a^12*b^4 + 16*a^10*b^6 - 5*a^8*b^8 - 5*a^6*b^10 + 2*a^4*b^12 + 2*a^2*b^14 - b^16 + 3*a^14*c^2 + 6*a^12*b^2*c^2 - 7*a^10*b^4*c^2 - 37*a^8*b^6*c^2 + 45*a^6*b^8*c^2 + 4*a^4*b^10*c^2 - 17*a^2*b^12*c^2 + 3*b^14*c^2 - 12*a^12*c^4 - 7*a^10*b^2*c^4 + 78*a^8*b^4*c^4 - 40*a^6*b^6*c^4 - 60*a^4*b^8*c^4 + 39*a^2*b^10*c^4 + 2*b^12*c^4 + 16*a^10*c^6 - 37*a^8*b^2*c^6 - 40*a^6*b^4*c^6 + 108*a^4*b^6*c^6 - 24*a^2*b^8*c^6 - 19*b^10*c^6 - 5*a^8*c^8 + 45*a^6*b^2*c^8 - 60*a^4*b^4*c^8 - 24*a^2*b^6*c^8 + 30*b^8*c^8 - 5*a^6*c^10 + 4*a^4*b^2*c^10 + 39*a^2*b^4*c^10 - 19*b^6*c^10 + 2*a^4*c^12 - 17*a^2*b^2*c^12 + 2*b^4*c^12 + 2*a^2*c^14 + 3*b^2*c^14 - c^16 : :

X(47347) lies on these lines: {2, 3}, {74, 11657}, {477, 16319}, {511, 1553}, {523, 32111}, {1503, 34150}, {1514, 46045}, {1533, 16278}, {2777, 47327}, {6000, 6070}, {6794, 16303}, {14915, 16280}, {14934, 46817}, {18809, 47215}

X(47347) = midpoint of X(i) and X(j) for these {i,j}: {23, 36172}, {18325, 36193}, {32111, 47323}
X(47347) = reflection of X(i) in X(j) for these {i,j}: {74, 11657}, {477, 16319}, {858, 36169}, {14934, 46817}, {16340, 44961}, {36164, 468}, {46045, 1514}
X(47347) = reflection of X(36164) in the orthic axis

X(47348) = VERTEX V OF PARALLELOGRAM WITH VERTICES X(7471), X(47148), V, X(47146)

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

X(47348) lies on these lines: {2, 3}, {110, 16319}, {250, 14165}, {476, 11657}, {511, 3258}, {523, 3580}, {1648, 47322}, {2452, 37644}, {2453, 37638}, {3564, 14611}, {3581, 20957}, {6792, 16303}, {6795, 18911}, {9140, 9158}, {10564, 31379}, {12079, 46788}, {13754, 44830}, {14480, 41724}, {15360, 34312}, {32223, 47327}, {37766, 47158}

X(47348) = midpoint of X(i) and X(j) for these {i,j}: {23, 17511}, {3580, 47324}, {3581, 20957}, {9140, 9158}, {14480, 41724}, {15360, 34312}
X(47348) = reflection of X(i) in X(j) for these {i,j}: {110, 16319}, {476, 11657}, {858, 3154}, {7471, 468}, {10564, 31379}, {14611, 47148}, {47327, 32223}
X(47348) = reflection of X(7471) in the orthic axis
X(47348) = complement of X(36188)
X(47348) = crossdifference of every pair of points on line {647, 32761}
X(47348) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 10989, 40236}, {468, 47097, 10011}, {858, 7426, 1513}, {1316, 36194, 37242}

X(47349) = VERTEX V OF PARALLELOGRAM WITH VERTICES X(36168), X(16317), V, X(47350)

X(47349) lies on these lines: {2, 3}, {523, 5913}, {1648, 32113}, {2770, 47170}, {5099, 39602}, {5468, 32220}, {5914, 47239}, {8705, 32525}, {10418, 47326}, {11053, 32217}, {11580, 16315}, {16320, 24855}

X(47349) = midpoint of X(5913) and X(47325)
X(47349) = reflection of X(i) in X(j) for these {i,j}: {2770, 47170}, {5914, 47239}, {36168, 468}
X(47349) = reflection of X(36168) in the orthic axis
X(47349) = {X(468),X(36180)}-harmonic conjugate of X(7426)

X(47350) = VERTEX V OF PARALLELOGRAM WITH VERTICES X(36168), X(16317), X(47349), V

Barycentrics 2*a^12 - 7*a^10*b^2 - 7*a^8*b^4 + 10*a^6*b^6 + 4*a^4*b^8 - 3*a^2*b^10 + b^12 - 7*a^10*c^2 + 44*a^8*b^2*c^2 - 23*a^6*b^4*c^2 - 42*a^4*b^6*c^2 + 26*a^2*b^8*c^2 - 6*b^10*c^2 - 7*a^8*c^4 - 23*a^6*b^2*c^4 + 84*a^4*b^4*c^4 - 23*a^2*b^6*c^4 - b^8*c^4 + 10*a^6*c^6 - 42*a^4*b^2*c^6 - 23*a^2*b^4*c^6 + 12*b^6*c^6 + 4*a^4*c^8 + 26*a^2*b^2*c^8 - b^4*c^8 - 3*a^2*c^10 - 6*b^2*c^10 + c^12 : :

X(47350) lies on these lines: {30, 1296}, {230, 231}, {5099, 47097}, {7426, 47293}, {9870, 37760}, {14729, 37969}, {15300, 37904}

X(47350) = midpoint of X(2770) and X(47325)
X(47350) = reflection of X(i) in X(j) for these {i,j}: {468, 47170}, {16317, 468}
X(47350) = reflection of X(16317) in the Euler line
X(47350) = orthogonal projection of X(1296) on the orthic axis

X(47351) = VERTEX V OF PARALLELOGRAM WITH VERTICES X(3154), X(11657), V, X(16319)

Barycentrics 4*a^12 - 6*a^10*b^2 - 3*a^8*b^4 + 5*a^6*b^6 + 3*a^4*b^8 - 3*a^2*b^10 - 6*a^10*c^2 + 18*a^8*b^2*c^2 - 7*a^6*b^4*c^2 - 13*a^4*b^6*c^2 + 7*a^2*b^8*c^2 + b^10*c^2 - 3*a^8*c^4 - 7*a^6*b^2*c^4 + 20*a^4*b^4*c^4 - 4*a^2*b^6*c^4 - 4*b^8*c^4 + 5*a^6*c^6 - 13*a^4*b^2*c^6 - 4*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 - 3*a^2*c^10 + b^2*c^10 : :

X(47351) = 3 X[23] + X[36188], 3 X[186] - X[36164], 3 X[2070] + X[36193], 3 X[7471] - X[36188], X[17511] - 5 X[37760], X[14611] - 3 X[35265]

X(47351) lies on these lines: {2, 3}, {187, 9209}, {511, 3233}, {523, 1495}, {1503, 11657}, {2452, 26864}, {2453, 41424}, {5191, 9185}, {14611, 35265}, {15448, 16319}, {16303, 35901}, {22104, 29012}

X(47351) = midpoint of X(i) and X(j) for these {i,j}: {23, 7471}, {1495, 47327}
X(47351) = reflection of X(i) in X(j) for these {i,j}: {858, 12068}, {3154, 468}, {12079, 11657}, {16319, 15448}
X(47351) = reflection of X(3154) in the orthic axis
X(47351) = circumcircle-inverse of X(44889)
X(47351) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 37123, 37969}, {25, 36178, 34093}, {25, 37926, 36178}, {186, 31510, 468}, {1113, 1114, 44889}, {1513, 7426, 468}

X(47352) = X(1)X(41310) ∩ X(2)X(6)

X(47352) = 2 X[2] + X[6], 7 X[2] - X[69], 5 X[2] - 2 X[141], 11 X[2] + X[193], X[2] + 2 X[597], 4 X[2] - X[599], 5 X[2] + X[1992], X[2] - 4 X[3589], X[2] + 5 X[3618], 13 X[2] - 7 X[3619], 17 X[2] - 5 X[3620], 13 X[2] + 2 X[3629], 23 X[2] - 2 X[3630], 19 X[2] - 4 X[3631], 8 X[2] - 5 X[3763], 3 X[2] + X[5032], 20 X[2] + X[6144], 7 X[2] + 8 X[6329], 7 X[2] + 2 X[8584], 29 X[2] + X[11008], 13 X[2] - X[11160], 10 X[2] - X[15533], 8 X[2] + X[15534], 25 X[2] - X[20080], 7 X[2] - 4 X[20582], 11 X[2] + 4 X[20583], 11 X[2] - 2 X[22165], 17 X[2] + 4 X[32455], 11 X[2] - 8 X[34573], 16 X[2] - X[40341], 23 X[2] + 4 X[41149], 35 X[2] - 8 X[41152], 11 X[2] + 16 X[41153], 7 X[6] + 2 X[69], 5 X[6] + 4 X[141], 11 X[6] - 2 X[193], X[6] - 4 X[597], 2 X[6] + X[599], 5 X[6] - 2 X[1992], X[6] + 8 X[3589], X[6] - 10 X[3618], 13 X[6] + 14 X[3619], 17 X[6] + 10 X[3620], 13 X[6] - 4 X[3629], 23 X[6] + 4 X[3630], 19 X[6] + 8 X[3631], 4 X[6] + 5 X[3763], 3 X[6] - 2 X[5032], 10 X[6] - X[6144], 7 X[6] - 16 X[6329], 7 X[6] - 4 X[8584], 29 X[6] - 2 X[11008], 13 X[6] + 2 X[11160], 5 X[6] + X[15533], 4 X[6] - X[15534], 25 X[6] + 2 X[20080], 7 X[6] + 8 X[20582], 11 X[6] - 8 X[20583], 3 X[6] + 2 X[21356], 11 X[6] + 4 X[22165], 17 X[6] - 8 X[32455], 11 X[6] + 16 X[34573], 8 X[6] + X[40341], 23 X[6] - 8 X[41149], 35 X[6] + 16 X[41152], 11 X[6] - 32 X[41153], 5 X[69] - 14 X[141], 11 X[69] + 7 X[193], X[69] + 14 X[597], 4 X[69] - 7 X[599], 5 X[69] + 7 X[1992], X[69] - 28 X[3589], X[69] + 35 X[3618], 13 X[69] - 49 X[3619], 17 X[69] - 35 X[3620], 13 X[69] + 14 X[3629], 23 X[69] - 14 X[3630], 19 X[69] - 28 X[3631], 8 X[69] - 35 X[3763], 3 X[69] + 7 X[5032], 20 X[69] + 7 X[6144], X[69] + 8 X[6329], X[69] + 2 X[8584], 29 X[69] + 7 X[11008], 13 X[69] - 7 X[11160], 10 X[69] - 7 X[15533], 8 X[69] + 7 X[15534], 25 X[69] - 7 X[20080], X[69] - 4 X[20582], 11 X[69] + 28 X[20583], 3 X[69] - 7 X[21356], 2 X[69] - 7 X[21358], 11 X[69] - 14 X[22165], 17 X[69] + 28 X[32455], 11 X[69] - 56 X[34573], 16 X[69] - 7 X[40341], 23 X[69] + 28 X[41149], 5 X[69] - 8 X[41152], 11 X[69] + 112 X[41153], 22 X[141] + 5 X[193], and many others

X(47352) lies on these lines: {1, 41310}, {2, 6}, {3, 5476}, {4, 10541}, {5, 11179}, {9, 41311}, {30, 5085}, {32, 15810}, {39, 11165}, {44, 17325}, {45, 17023}, {67, 15303}, {83, 598}, {115, 14535}, {125, 25336}, {140, 11477}, {154, 23327}, {182, 381}, {373, 2393}, {376, 5480}, {382, 20190}, {384, 11164}, {458, 37765}, {487, 6470}, {488, 6471}, {511, 5054}, {518, 4539}, {519, 38023}, {527, 38086}, {528, 38048}, {529, 38091}, {530, 11297}, {531, 11298}, {538, 13331}, {541, 5621}, {542, 5050}, {543, 5149}, {547, 1352}, {549, 1350}, {551, 3242}, {575, 1656}, {576, 3526}, {611, 3582}, {613, 3584}, {618, 22580}, {619, 22579}, {671, 5026}, {702, 9462}, {1003, 5116}, {1030, 16431}, {1078, 9731}, {1086, 35578}, {1100, 17267}, {1153, 6683}, {1351, 15694}, {1386, 3679}, {1405, 31230}, {1428, 11237}, {1449, 17311}, {1503, 3545}, {1691, 3849}, {1692, 33240}, {1743, 17253}, {1853, 19153}, {1974, 5064}, {1995, 19596}, {2030, 7913}, {2076, 26613}, {2330, 11238}, {2453, 34094}, {2482, 5024}, {2548, 8360}, {2781, 15045}, {2916, 9909}, {2930, 5642}, {3053, 8182}, {3066, 7426}, {3090, 8550}, {3094, 7622}, {3098, 15693}, {3228, 39080}, {3313, 21849}, {3416, 3828}, {3524, 14853}, {3534, 5092}, {3543, 44882}, {3564, 15699}, {3624, 4663}, {3758, 17290}, {3759, 17293}, {3767, 8367}, {3818, 19709}, {3830, 12017}, {3839, 25406}, {3844, 19876}, {3845, 46264}, {3867, 7714}, {3943, 17014}, {3972, 35955}, {4027, 43535}, {4045, 5077}, {4265, 16371}, {4361, 17368}, {4363, 17367}, {4393, 17269}, {4422, 16672}, {4445, 17121}, {4657, 16885}, {4675, 31191}, {4677, 16491}, {4912, 17382}, {4969, 29611}, {4995, 10387}, {5013, 7618}, {5017, 5569}, {5023, 33215}, {5033, 14537}, {5034, 12151}, {5038, 7617}, {5070, 34507}, {5071, 6776}, {5079, 18553}, {5094, 44102}, {5096, 16370}, {5097, 15723}, {5102, 11539}, {5104, 15482}, {5124, 16436}, {5135, 17528}, {5157, 34609}, {5182, 7884}, {5210, 37809}, {5220, 29646}, {5222, 17119}, {5254, 7620}, {5286, 5485}, {5309, 24273}, {5339, 11303}, {5340, 11304}, {5459, 42098}, {5460, 42095}, {5461, 10488}, {5463, 11486}, {5464, 11485}, {5477, 19662}, {5544, 5648}, {5585, 47061}, {5640, 9019}, {5643, 11416}, {5655, 16010}, {5749, 17118}, {5943, 9971}, {5969, 33220}, {6292, 43136}, {6425, 11291}, {6426, 11292}, {6593, 9140}, {6661, 8716}, {6680, 7619}, {6687, 16831}, {6688, 29959}, {6694, 43239}, {6695, 43238}, {6698, 13169}, {6800, 7605}, {7232, 17120}, {7493, 20192}, {7496, 37827}, {7566, 46865}, {7569, 43836}, {7745, 23334}, {7753, 40825}, {7757, 24256}, {7760, 10302}, {7770, 7827}, {7775, 7866}, {7784, 7812}, {7786, 22486}, {7790, 11317}, {7801, 7889}, {7803, 8370}, {7804, 11159}, {7807, 31492}, {7810, 30435}, {7813, 22246}, {7819, 34511}, {7834, 8176}, {7844, 10485}, {7846, 8366}, {7851, 33013}, {7870, 33217}, {7876, 34604}, {7878, 7883}, {7924, 42421}, {8355, 31415}, {8365, 31406}, {8368, 12040}, {8541, 37453}, {8546, 16042}, {8592, 19120}, {8593, 14061}, {8598, 44541}, {8623, 34097}, {8703, 31670}, {8705, 37907}, {8787, 11161}, {8976, 44657}, {9041, 38314}, {9055, 41138}, {9143, 25328}, {9148, 9188}, {9171, 45693}, {9178, 11183}, {9466, 40332}, {9606, 14069}, {9607, 33198}, {9855, 11742}, {9924, 31267}, {10169, 17813}, {10182, 23048}, {10304, 29181}, {10352, 44536}, {10484, 43528}, {10510, 32225}, {10519, 15709}, {10542, 31401}, {10554, 20976}, {10583, 33274}, {10717, 28662}, {10718, 28343}, {10989, 32217}, {11147, 32973}, {11188, 40670}, {11295, 42155}, {11296, 42154}, {11301, 13084}, {11302, 13083}, {11305, 42153}, {11306, 42156}, {11311, 34508}, {11312, 34509}, {11405, 16511}, {11451, 16776}, {11465, 15073}, {11480, 35303}, {11481, 35304}, {11482, 40107}, {11737, 39884}, {11898, 15516}, {12007, 40330}, {12036, 34898}, {12039, 21639}, {12100, 21850}, {13167, 34226}, {13337, 36212}, {13394, 26255}, {13595, 35707}, {13633, 37474}, {13857, 22112}, {13903, 44473}, {13951, 44656}, {13961, 44474}, {14001, 22332}, {14269, 29012}, {14608, 36821}, {14711, 41747}, {14787, 36752}, {14810, 15700}, {14928, 36523}, {15047, 44494}, {15059, 41720}, {15074, 32205}, {15274, 37124}, {15302, 45672}, {15595, 40477}, {15685, 42785}, {15688, 17508}, {15689, 29317}, {15701, 33878}, {15703, 24206}, {15708, 21167}, {15805, 18281}, {15815, 32985}, {16043, 22331}, {16267, 36758}, {16268, 36757}, {16279, 36177}, {16417, 36740}, {16418, 36741}, {16475, 19875}, {16666, 17284}, {16667, 17231}, {16668, 17296}, {16669, 17306}, {16670, 17237}, {16671, 17272}, {16674, 25101}, {16675, 17045}, {16777, 17353}, {16833, 16972}, {16834, 17359}, {16884, 17279}, {17132, 17301}, {17133, 17281}, {17255, 17383}, {17256, 25503}, {17262, 17380}, {17263, 29622}, {17289, 29617}, {17309, 17358}, {17318, 17354}, {17323, 17350}, {17335, 29614}, {17342, 29584}, {17394, 29620}, {17399, 24441}, {17809, 37439}, {17810, 44210}, {18311, 45327}, {18440, 25561}, {19127, 31133}, {19132, 23300}, {19136, 31152}, {19145, 35823}, {19146, 35822}, {19151, 21400}, {19154, 31181}, {19694, 32821}, {19710, 43621}, {20112, 32983}, {21509, 36743}, {21526, 37503}, {21539, 36744}, {22111, 30516}, {22236, 37341}, {22238, 37340}, {22491, 37352}, {22492, 37351}, {23332, 41719}, {23583, 41145}, {24599, 26039}, {25326, 39361}, {25566, 32305}, {26619, 41946}, {26620, 41945}, {27759, 29856}, {28194, 38035}, {28204, 38029}, {29607, 41847}, {30537, 40802}, {30734, 44300}, {31139, 36404}, {31183, 31244}, {31400, 33197}, {31407, 32953}, {31467, 44499}, {31860, 37904}, {32046, 43811}, {32069, 47075}, {32740, 42008}, {32979, 41895}, {33007, 44519}, {33219, 35006}, {34117, 40686}, {34360, 44649}, {35931, 42625}, {35932, 42626}, {36386, 42521}, {36388, 42520}, {36836, 37173}, {36843, 37172}, {37475, 44218}, {37911, 47280}, {37943, 39588}, {38040, 38116}, {38046, 38194}, {38115, 38166}, {38117, 38143}, {38282, 41585}, {38425, 38426}, {39232, 45336}, {39957, 39960}, {40334, 42818}, {40335, 42817}

X(47352) = midpoint of X(i) and X(j) for these {i,j}: {6, 21358}, {3524, 14853}, {3839, 25406}, {5032, 21356}, {5050, 5055}, {5054, 14848}, {5085, 38072}, {5182, 9166}, {8859, 41137}, {14561, 38064}, {16475, 19875}, {38023, 38047}, {38049, 38089}, {38079, 38110}, {38087, 38315}, {38088, 38186}
X(47352) = reflection of X(i) in X(j) for these {i,j}: {599, 21358}, {2076, 26613}, {5055, 38317}, {5085, 38064}, {10516, 5055}, {14561, 38079}, {15688, 17508}, {21358, 2}, {31884, 3524}, {38023, 38049}, {38047, 38089}, {38064, 38110}, {38072, 14561}, {38086, 38186}, {38087, 38047}, {38315, 38023}
X(47352) = complement of X(21356)
X(47352) = complement of the isotomic conjugate of X(18842)
X(47352) = X(18842)-complementary conjugate of X(2887)
X(47352) = crosspoint of X(2) and X(18842)
X(47352) = crosssum of X(i) and X(j) for these (i,j): {6, 5024}, {1015, 2515}
X(47352) = centroid of X(3)X(6)X(381)
X(47352) = X(5182)-of-McCay-triangle
X(47352) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 599}, {2, 69, 20582}, {2, 597, 6}, {2, 599, 3763}, {2, 1992, 141}, {2, 3329, 11163}, {2, 3618, 597}, {2, 5032, 21356}, {2, 5304, 42850}, {2, 5306, 8556}, {2, 7735, 11168}, {2, 7736, 22110}, {2, 7806, 8860}, {2, 7840, 7868}, {2, 11160, 3619}, {2, 11163, 7778}, {2, 11174, 42849}, {2, 13637, 45473}, {2, 13639, 5591}, {2, 13663, 8253}, {2, 13757, 45472}, {2, 13759, 5590}, {2, 13783, 8252}, {2, 16989, 22329}, {2, 17349, 31144}, {2, 22329, 15271}, {2, 31144, 17327}, {2, 31179, 30811}, {2, 42849, 31489}, {2, 44367, 16986}, {2, 46922, 17313}, {6, 141, 6144}, {6, 599, 15534}, {6, 3763, 40341}, {6, 15533, 1992}, {44, 29598, 17325}, {69, 6329, 6}, {141, 1992, 15533}, {141, 15533, 599}, {182, 381, 43273}, {381, 43273, 36990}, {384, 32480, 11164}, {395, 396, 7736}, {549, 18583, 20423}, {549, 20423, 1350}, {575, 1656, 15069}, {597, 3589, 2}, {597, 8584, 6329}, {599, 6144, 15533}, {599, 15534, 40341}, {1449, 17357, 17311}, {1743, 17384, 17253}, {1992, 6144, 15534}, {1992, 15533, 6144}, {3589, 3618, 6}, {3758, 29630, 17290}, {3763, 15534, 599}, {3818, 25565, 19709}, {4422, 26626, 16672}, {5038, 7617, 33683}, {5050, 38317, 10516}, {5222, 17369, 17119}, {5461, 18800, 11646}, {5476, 10168, 3}, {5749, 17366, 17118}, {6329, 20582, 8584}, {7617, 7808, 14762}, {7770, 7827, 34505}, {7817, 14762, 7617}, {7840, 16987, 2}, {8182, 19661, 3053}, {8359, 19661, 8182}, {8584, 20582, 69}, {9761, 9763, 9766}, {10168, 25555, 5476}, {11183, 45690, 9178}, {11482, 46219, 40107}, {11646, 18800, 10488}, {14561, 38110, 5085}, {15303, 45311, 67}, {15491, 44401, 2}, {16644, 16645, 31489}, {16989, 44380, 6}, {17045, 26685, 16675}, {17120, 17370, 7232}, {17121, 17371, 4445}, {20582, 41152, 141}, {20583, 22165, 193}, {20583, 34573, 22165}, {22489, 22490, 5055}, {32300, 45311, 15303}, {34573, 41153, 20583}, {37640, 37641, 14930}, {38023, 38089, 38087}, {38029, 38167, 38144}, {38047, 38049, 38315}, {38064, 38079, 38072}, {43622, 43623, 3055}

X(47353) = X(4)X(524) ∩ X(6)X(13)

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

X(47353) = 4 X[2] - 3 X[5085], 2 X[2] - 3 X[10516], 5 X[2] - 3 X[25406], 5 X[5085] - 4 X[25406], 3 X[5085] - 2 X[43273], 5 X[10516] - 2 X[25406], 3 X[10516] - X[43273], 6 X[25406] - 5 X[43273], X[3] - 4 X[18553], 2 X[3] - 3 X[21358], 4 X[11178] - 3 X[21358], 8 X[18553] - 3 X[21358], 4 X[4] - X[11477], 2 X[4] + X[15069], 4 X[11180] + X[11477], X[11477] + 2 X[15069], X[6] - 4 X[3818], 3 X[6] - 4 X[5476], 5 X[6] - 6 X[14848], X[6] + 2 X[18440], 5 X[6] - 8 X[19130], 2 X[6] - 3 X[38072], 5 X[6] - 2 X[39899], 19 X[6] - 28 X[42785], 3 X[381] - 2 X[5476], 5 X[381] - 3 X[14848], 5 X[381] - 4 X[19130], 4 X[381] - 3 X[38072], 5 X[381] - X[39899], 19 X[381] - 14 X[42785], 3 X[3818] - X[5476], 10 X[3818] - 3 X[14848], 2 X[3818] + X[18440], 5 X[3818] - 2 X[19130], 8 X[3818] - 3 X[38072], 10 X[3818] - X[39899], 19 X[3818] - 7 X[42785], 10 X[5476] - 9 X[14848], 2 X[5476] + 3 X[18440], 5 X[5476] - 6 X[19130], 8 X[5476] - 9 X[38072], 10 X[5476] - 3 X[39899], 19 X[5476] - 21 X[42785], 3 X[14848] + 5 X[18440], 3 X[14848] - 4 X[19130], 4 X[14848] - 5 X[38072], 3 X[14848] - X[39899], 57 X[14848] - 70 X[42785], 5 X[18440] + 4 X[19130], 4 X[18440] + 3 X[38072], 5 X[18440] + X[39899], and many others

X(47353) lies on these lines: {2, 154}, {3, 11178}, {4, 524}, {5, 11179}, {6, 13}, {20, 11164}, {25, 32225}, {30, 599}, {64, 34118}, {67, 541}, {69, 3543}, {141, 376}, {147, 11163}, {182, 5055}, {382, 19924}, {383, 9761}, {394, 31133}, {511, 3830}, {547, 38064}, {549, 3763}, {575, 3851}, {576, 3843}, {597, 3545}, {1080, 9763}, {1351, 14269}, {1353, 23046}, {1386, 38021}, {1513, 7610}, {1550, 33987}, {1634, 32444}, {1656, 10168}, {1657, 40107}, {1692, 18362}, {1992, 3839}, {1995, 9140}, {2070, 44751}, {2393, 15030}, {2502, 9759}, {2781, 11188}, {2794, 11159}, {2854, 16261}, {2930, 31861}, {3058, 12588}, {3066, 3448}, {3091, 8550}, {3098, 15681}, {3242, 28204}, {3363, 7694}, {3410, 33586}, {3416, 28194}, {3524, 20582}, {3534, 29012}, {3541, 45248}, {3564, 3845}, {3580, 31860}, {3589, 5071}, {3619, 15692}, {3620, 15683}, {3832, 5032}, {3860, 38136}, {4265, 28444}, {4550, 12367}, {4663, 18492}, {5013, 37345}, {5026, 23234}, {5028, 39563}, {5050, 19709}, {5054, 24206}, {5064, 37672}, {5066, 14561}, {5070, 20190}, {5072, 25555}, {5092, 15694}, {5094, 5642}, {5133, 17809}, {5169, 9143}, {5207, 7788}, {5210, 37461}, {5434, 12589}, {5478, 22580}, {5479, 22579}, {5621, 6644}, {5648, 17702}, {5651, 32216}, {5868, 11304}, {5869, 11303}, {5890, 16776}, {5907, 34725}, {5913, 33979}, {5968, 14833}, {5969, 34681}, {6000, 29959}, {6054, 9830}, {6055, 37071}, {6090, 13857}, {6144, 14893}, {6278, 36657}, {6281, 36658}, {6288, 44492}, {7426, 37638}, {7503, 15581}, {7540, 17834}, {7565, 11441}, {7576, 7716}, {8176, 38745}, {8359, 8721}, {8541, 18386}, {8584, 14853}, {8681, 46847}, {8719, 35955}, {8724, 25562}, {9019, 11459}, {9041, 34627}, {9308, 42854}, {9744, 42849}, {9924, 34775}, {9969, 14831}, {9971, 13754}, {9974, 35786}, {9975, 35787}, {10109, 38110}, {10304, 14927}, {10488, 12177}, {10519, 11001}, {10542, 44518}, {10602, 13851}, {10606, 36201}, {10989, 15066}, {11161, 11317}, {11165, 14981}, {11177, 13862}, {11237, 39892}, {11238, 39891}, {11295, 41022}, {11296, 41023}, {11425, 12134}, {11442, 17810}, {11550, 17811}, {11737, 38079}, {11898, 38335}, {12017, 15703}, {12101, 34380}, {12162, 37473}, {12163, 38322}, {12586, 34697}, {12587, 34746}, {13419, 34726}, {13663, 45511}, {13783, 45510}, {14070, 20987}, {14118, 15582}, {14157, 19127}, {14787, 37476}, {14810, 15689}, {14852, 44275}, {14912, 41106}, {15045, 40670}, {15052, 22151}, {15074, 45958}, {15078, 44883}, {15271, 43460}, {15578, 37941}, {15579, 22467}, {15682, 22165}, {15684, 33878}, {15685, 29323}, {15687, 31670}, {15701, 17508}, {15702, 34573}, {15719, 33750}, {16176, 32271}, {16475, 30308}, {16621, 34621}, {16645, 44219}, {17813, 23049}, {18323, 47276}, {18374, 46261}, {18387, 41617}, {18437, 36751}, {18583, 38071}, {19708, 21167}, {19905, 35930}, {20194, 37689}, {21243, 32267}, {21733, 32472}, {22236, 37333}, {22238, 37332}, {22491, 41017}, {22492, 41016}, {22575, 41060}, {22576, 41061}, {23410, 32140}, {25330, 39487}, {26255, 44569}, {26543, 31156}, {26958, 44212}, {28538, 31162}, {31105, 40112}, {31383, 44210}, {32284, 46852}, {33537, 34664}, {33997, 43535}, {35403, 44456}, {35404, 43621}, {35427, 41748}, {35707, 35921}, {36757, 41121}, {36758, 41122}, {38023, 39870}

X(47353) = midpoint of X(i) and X(j) for these {i,j}: {4, 11180}, {69, 3543}, {381, 18440}, {599, 36990}, {1992, 5921}, {5642, 32250}, {9140, 41737}, {11188, 15305}, {15684, 33878}, {31162, 39885}, {34627, 39898}
X(47353) = reflection of X(i) in X(j) for these {i,j}: {3, 11178}, {6, 381}, {182, 25561}, {376, 141}, {381, 3818}, {549, 18358}, {599, 1352}, {1350, 599}, {1992, 5480}, {5085, 10516}, {5890, 16776}, {6776, 597}, {8724, 25562}, {9140, 32274}, {10488, 12177}, {11178, 18553}, {11179, 5}, {12177, 22566}, {14831, 9969}, {15069, 11180}, {15534, 20423}, {15681, 3098}, {16010, 9140}, {17813, 23049}, {20423, 3845}, {21850, 14893}, {22579, 5479}, {22580, 5478}, {31670, 15687}, {32233, 5642}, {34319, 113}, {43273, 2}, {43621, 35404}, {44882, 20582}, {46264, 549}
X(47353) = X(11180)-of-Euler-triangle
X(47353) = X(11179)-of-Johnson-triangle
X(47353) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 43273, 5085}, {3, 11178, 21358}, {4, 15069, 11477}, {6, 381, 38072}, {182, 25561, 5055}, {381, 14848, 19130}, {381, 39899, 14848}, {1352, 36990, 1350}, {1352, 39884, 36990}, {1992, 3839, 5480}, {3524, 40330, 20582}, {3545, 6776, 597}, {3818, 18440, 6}, {3839, 5921, 1992}, {6054, 10033, 13860}, {6054, 13860, 11184}, {10516, 43273, 2}, {12162, 43130, 37473}, {15534, 20423, 5102}, {18358, 46264, 3763}, {18509, 26346, 6565}, {18511, 26336, 6564}, {19130, 39899, 6}, {20582, 44882, 3524}, {32271, 32272, 16176}, {32274, 41737, 16010}, {35266, 45303, 2}, {41042, 41043, 381}

X(47354) = X(2)X(154) ∩ X(30)X(141)

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

X(47354) = 5 X[2] - 3 X[5085], X[2] - 3 X[10516], 7 X[2] - 3 X[25406], X[5085] - 5 X[10516], 7 X[5085] - 5 X[25406], 9 X[5085] - 5 X[43273], 7 X[10516] - X[25406], 9 X[10516] - X[43273], 9 X[25406] - 7 X[43273], 5 X[5] - 2 X[575], 4 X[5] - X[8550], X[5] + 2 X[18553], 7 X[5] - 4 X[25555], 5 X[5] - 4 X[25565], 13 X[5] - 4 X[33749], 5 X[5] - 3 X[38079], 4 X[575] - 5 X[597], 8 X[575] - 5 X[8550], X[575] + 5 X[18553], 7 X[575] - 10 X[25555], X[575] - 5 X[25561], 13 X[575] - 10 X[33749], 2 X[575] - 3 X[38079], X[597] + 4 X[18553], 7 X[597] - 8 X[25555], X[597] - 4 X[25561], 5 X[597] - 8 X[25565], 13 X[597] - 8 X[33749], 5 X[597] - 6 X[38079], X[8550] + 8 X[18553], and many more

X(47354) lies on these lines: {2, 154}, {3, 20582}, {4, 599}, {5, 542}, {6, 3545}, {30, 141}, {67, 10706}, {69, 3839}, {113, 34113}, {114, 9771}, {182, 547}, {230, 20194}, {343, 15360}, {355, 9041}, {376, 21358}, {381, 524}, {427, 13857}, {511, 3845}, {546, 34507}, {549, 11645}, {576, 3850}, {732, 44422}, {946, 28538}, {1350, 3543}, {1499, 18309}, {1513, 11168}, {1656, 38064}, {1992, 3091}, {1995, 44569}, {2393, 23324}, {2781, 15030}, {2782, 25562}, {2794, 19662}, {2883, 34118}, {3242, 34627}, {3416, 31162}, {3524, 3763}, {3542, 16254}, {3564, 5066}, {3580, 20192}, {3589, 5055}, {3619, 10304}, {3627, 40107}, {3629, 19130}, {3630, 21850}, {3631, 14269}, {3656, 5846}, {3815, 6054}, {3830, 29181}, {3832, 11160}, {3851, 14848}, {3860, 34380}, {4265, 28461}, {5054, 34573}, {5067, 10541}, {5071, 6776}, {5092, 11539}, {5093, 41149}, {5169, 40112}, {5207, 37671}, {5254, 12243}, {5463, 41034}, {5464, 41035}, {5477, 39601}, {5613, 33475}, {5617, 33474}, {5648, 41171}, {5651, 47097}, {5818, 38087}, {5891, 9019}, {5894, 15062}, {5921, 12007}, {5965, 38136}, {5969, 6248}, {6033, 19905}, {6214, 45860}, {6215, 45861}, {6287, 8724}, {6329, 39899}, {6721, 32414}, {7385, 31144}, {7395, 15581}, {7399, 44762}, {7503, 15582}, {7514, 35707}, {7533, 44555}, {7792, 11177}, {7998, 47314}, {8227, 38023}, {8542, 37984}, {8703, 21167}, {9140, 14982}, {9143, 14389}, {9214, 18121}, {9730, 40670}, {9971, 11459}, {9977, 20584}, {10019, 11470}, {10109, 38317}, {10168, 15699}, {10519, 15682}, {11001, 31884}, {11237, 12589}, {11238, 12588}, {11550, 43957}, {11737, 18583}, {11812, 17508}, {12061, 43130}, {12134, 14787}, {12355, 37243}, {12359, 23410}, {13754, 16776}, {13860, 22110}, {13862, 22329}, {14561, 19709}, {14810, 15686}, {14831, 32191}, {14853, 15534}, {14927, 15692}, {15058, 37473}, {15066, 31105}, {15078, 15578}, {15303, 36518}, {15533, 41099}, {15579, 17928}, {15583, 16072}, {15585, 34775}, {15687, 19924}, {15714, 33751}, {16010, 16042}, {16252, 31166}, {16656, 34621}, {17225, 20430}, {18800, 36519}, {19127, 46261}, {19145, 42602}, {19146, 42603}, {19596, 35921}, {19710, 29323}, {20772, 45311}, {20987, 44837}, {21243, 44212}, {23328, 36201}, {25154, 37825}, {25164, 37824}, {26255, 37638}, {29317, 33699}, {30308, 38035}, {31693, 41043}, {31694, 41042}, {32000, 42854}, {32272, 41595}, {32419, 36723}, {32421, 36726}, {33537, 34787}, {33878, 38335}, {34664, 41362}, {37071, 44401}, {38021, 39885}, {38074, 39898}, {40929, 45958}

X(47354) = midpoint of X(i) and X(j) for these {i,j}: {4, 599}, {6, 11180}, {67, 10706}, {376, 36990}, {381, 1352}, {549, 39884}, {1350, 3543}, {1992, 15069}, {3242, 34627}, {3416, 31162}, {3818, 11178}, {6033, 19905}, {6054, 11646}, {9140, 14982}, {9971, 11459}, {11160, 11477}, {11179, 18440}, {15030, 29959}, {18553, 25561}
X(47354) = reflection of X(i) in X(j) for these {i,j}: {3, 20582}, {5, 25561}, {141, 11178}, {182, 547}, {549, 24206}, {575, 25565}, {597, 5}, {5476, 5066}, {5480, 381}, {8550, 597}, {8584, 5476}, {9730, 40670}, {11178, 18358}, {11179, 3589}, {14831, 32191}, {15686, 14810}, {18583, 11737}, {31166, 16252}, {44882, 549}
X(47354) = complement of X(43273)
X(47354) = X(599)-of-Euler-triangle
X(47354) = X(597)-of-Johnson-triangle
X(47354) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 38079, 25565}, {376, 40330, 21358}, {575, 25565, 38079}, {575, 38079, 597}, {1992, 3091, 38072}, {3543, 21356, 1350}, {3545, 11180, 6}, {3818, 18358, 141}, {5055, 11179, 3589}, {5055, 18440, 11179}, {5617, 44219, 33474}, {15069, 38072, 1992}, {21358, 36990, 376}, {21850, 43150, 3630}, {22491, 22492, 40727}, {24206, 39884, 44882}

X(47355) = X(1)X(17267) ∩ X(2)X(6)

X(47355) = 6 X[2] + X[6], 15 X[2] - X[69], 9 X[2] - 2 X[141], 27 X[2] + X[193], 5 X[2] + 2 X[597], 8 X[2] - X[599], 13 X[2] + X[1992], 3 X[2] + 4 X[3589], 9 X[2] + 5 X[3618], 33 X[2] - 5 X[3620], 33 X[2] + 2 X[3629], 51 X[2] - 2 X[3630], 39 X[2] - 4 X[3631], 12 X[2] - 5 X[3763], 25 X[2] + 3 X[5032], 48 X[2] + X[6144], 27 X[2] + 8 X[6329], 19 X[2] + 2 X[8584], 69 X[2] + X[11008], 29 X[2] - X[11160], 22 X[2] - X[15533], 20 X[2] + X[15534], 57 X[2] - X[20080], 11 X[2] - 4 X[20582], 31 X[2] + 4 X[20583], 17 X[2] - 3 X[21356], 10 X[2] - 3 X[21358], 23 X[2] - 2 X[22165], 45 X[2] + 4 X[32455], 15 X[2] - 8 X[34573], 36 X[2] - X[40341], 59 X[2] + 4 X[41149], 71 X[2] - 8 X[41152], 47 X[2] + 16 X[41153], 5 X[6] + 2 X[69], 3 X[6] + 4 X[141], 9 X[6] - 2 X[193], 5 X[6] - 12 X[597], 4 X[6] + 3 X[599], 13 X[6] - 6 X[1992], X[6] - 8 X[3589], 3 X[6] - 10 X[3618], X[6] + 2 X[3619], 11 X[6] + 10 X[3620], 11 X[6] - 4 X[3629], 17 X[6] + 4 X[3630], 13 X[6] + 8 X[3631], 2 X[6] + 5 X[3763], 25 X[6] - 18 X[5032], 8 X[6] - X[6144], 9 X[6] - 16 X[6329], 19 X[6] - 12 X[8584], 23 X[6] - 2 X[11008], 29 X[6] + 6 X[11160], 11 X[6] + 3 X[15533], 10 X[6] - 3 X[15534], 19 X[6] + 2 X[20080], 11 X[6] + 24 X[20582], 31 X[6] - 24 X[20583], 17 X[6] + 18 X[21356], 5 X[6] + 9 X[21358], 23 X[6] + 12 X[22165], 15 X[6] - 8 X[32455], 5 X[6] + 16 X[34573], 6 X[6] + X[40341], 59 X[6] - 24 X[41149], 71 X[6] + 48 X[41152], 47 X[6] - 96 X[41153], 3 X[69] - 10 X[141], 9 X[69] + 5 X[193], X[69] + 6 X[597], 8 X[69] - 15 X[599], 13 X[69] + 15 X[1992], X[69] + 20 X[3589], 3 X[69] + 25 X[3618], X[69] - 5 X[3619], 11 X[69] - 25 X[3620], 11 X[69] + 10 X[3629], 17 X[69] - 10 X[3630], 13 X[69] - 20 X[3631], 4 X[69] - 25 X[3763], 5 X[69] + 9 X[5032], 16 X[69] + 5 X[6144], 9 X[69] + 40 X[6329], 19 X[69] + 30 X[8584], 23 X[69] + 5 X[11008], 29 X[69] - 15 X[11160], 22 X[69] - 15 X[15533], 4 X[69] + 3 X[15534], 19 X[69] - 5 X[20080], 11 X[69] - 60 X[20582], 31 X[69] + 60 X[20583], 17 X[69] - 45 X[21356], 2 X[69] - 9 X[21358], 23 X[69] - 30 X[22165], 3 X[69] + 4 X[32455], X[69] - 8 X[34573], 12 X[69] - 5 X[40341], and many others

X(47355) lies on these lines: {1, 17267}, {2, 6}, {3, 7889}, {4, 33750}, {5, 5085}, {9, 17325}, {10, 4989}, {25, 2916}, {32, 39784}, {37, 29598}, {39, 40332}, {44, 17253}, {45, 4657}, {55, 29663}, {66, 19132}, {67, 6723}, {75, 29630}, {83, 7784}, {110, 25330}, {113, 5621}, {125, 19125}, {140, 1350}, {144, 26104}, {154, 23300}, {159, 11284}, {160, 37338}, {182, 1656}, {190, 17323}, {194, 16896}, {206, 1853}, {239, 17293}, {308, 41259}, {319, 29613}, {344, 16672}, {346, 17395}, {373, 9969}, {381, 5092}, {382, 17508}, {384, 44519}, {405, 5096}, {441, 36751}, {468, 7716}, {474, 4265}, {511, 3526}, {518, 3624}, {542, 15703}, {547, 38064}, {549, 31670}, {551, 38087}, {574, 33237}, {594, 4371}, {620, 6034}, {623, 11311}, {624, 11312}, {625, 1691}, {631, 5480}, {632, 11477}, {694, 40478}, {698, 19694}, {742, 4751}, {894, 17290}, {1001, 29633}, {1003, 44541}, {1030, 21477}, {1086, 5749}, {1100, 17284}, {1125, 3242}, {1176, 7703}, {1191, 19784}, {1351, 25555}, {1352, 3628}, {1385, 38144}, {1386, 1698}, {1400, 31230}, {1449, 17231}, {1503, 3090}, {1506, 40825}, {1743, 17237}, {1757, 25539}, {1843, 37453}, {1974, 5094}, {1975, 16895}, {2030, 31275}, {2076, 7846}, {2097, 6692}, {2176, 16818}, {2330, 29863}, {2345, 4402}, {2548, 8364}, {2930, 5972}, {3008, 17303}, {3053, 8362}, {3066, 7495}, {3070, 7375}, {3071, 7376}, {3091, 44882}, {3094, 6683}, {3098, 5054}, {3124, 25334}, {3247, 41310}, {3313, 5943}, {3416, 3634}, {3521, 34436}, {3523, 29181}, {3525, 14853}, {3530, 38136}, {3533, 10519}, {3622, 9053}, {3636, 38191}, {3672, 17340}, {3729, 17382}, {3731, 41311}, {3734, 12055}, {3751, 34595}, {3758, 7232}, {3759, 4445}, {3793, 7800}, {3796, 37990}, {3818, 5055}, {3826, 38048}, {3828, 38023}, {3830, 25565}, {3844, 16475}, {3851, 29012}, {3867, 6353}, {3875, 17359}, {3912, 16884}, {3934, 13331}, {3946, 17281}, {4000, 7229}, {4045, 11286}, {4048, 7851}, {4254, 21542}, {4255, 17698}, {4357, 16885}, {4360, 17269}, {4361, 17289}, {4363, 16706}, {4364, 26685}, {4384, 17385}, {4393, 17285}, {4422, 16675}, {4423, 12329}, {4670, 17282}, {4687, 29614}, {4698, 29603}, {4851, 29596}, {4852, 17286}, {4859, 31139}, {5013, 7819}, {5017, 6680}, {5020, 20987}, {5023, 16043}, {5024, 7820}, {5026, 14061}, {5031, 33218}, {5033, 7603}, {5038, 7886}, {5043, 16574}, {5050, 5070}, {5056, 25406}, {5064, 44091}, {5067, 6776}, {5068, 14927}, {5079, 20190}, {5093, 40107}, {5102, 16239}, {5103, 7876}, {5116, 7770}, {5120, 21529}, {5124, 11343}, {5157, 18374}, {5158, 20208}, {5159, 15812}, {5207, 14065}, {5210, 8359}, {5228, 28780}, {5254, 16045}, {5339, 11289}, {5340, 11290}, {5432, 10387}, {5461, 14928}, {5475, 14535}, {5476, 15694}, {5585, 33215}, {5596, 23332}, {5646, 34817}, {5695, 24295}, {5750, 17278}, {5800, 17559}, {5846, 9780}, {5901, 38116}, {5921, 46935}, {5925, 15578}, {6179, 31268}, {6292, 30435}, {6375, 34811}, {6409, 11291}, {6410, 11292}, {6593, 15059}, {6666, 38186}, {6684, 38035}, {6687, 25498}, {6688, 9971}, {6694, 43238}, {6695, 43239}, {6697, 19153}, {6704, 7834}, {6722, 11646}, {7388, 23251}, {7389, 23261}, {7405, 37476}, {7494, 45816}, {7499, 17810}, {7514, 40909}, {7745, 32956}, {7773, 7948}, {7776, 7914}, {7786, 24256}, {7787, 16897}, {7789, 22332}, {7803, 47286}, {7804, 11287}, {7810, 21309}, {7813, 7822}, {7815, 12212}, {7853, 15484}, {7854, 43136}, {7874, 31467}, {7878, 7879}, {7887, 7943}, {7894, 10159}, {7919, 44543}, {7932, 12215}, {8360, 31415}, {8367, 43620}, {8550, 40330}, {8703, 43621}, {9002, 31207}, {9055, 27268}, {9466, 41747}, {9822, 9973}, {9924, 23327}, {9956, 38029}, {9970, 34128}, {10007, 33233}, {10124, 38079}, {10172, 39870}, {10191, 40022}, {10192, 36851}, {10198, 12595}, {10200, 12594}, {10219, 29959}, {10303, 21167}, {10436, 17356}, {10576, 19146}, {10577, 19145}, {11108, 36741}, {11175, 24861}, {11178, 39899}, {11179, 15699}, {11288, 15482}, {11295, 42097}, {11296, 42096}, {11297, 42155}, {11298, 42154}, {11299, 42625}, {11300, 42626}, {11303, 42093}, {11304, 42094}, {11305, 42095}, {11306, 42098}, {11307, 42491}, {11308, 42490}, {11313, 42262}, {11314, 42265}, {11318, 18584}, {11328, 41328}, {11331, 36794}, {11338, 18092}, {11480, 37341}, {11481, 37340}, {11539, 20423}, {11695, 19161}, {11742, 33007}, {11898, 39561}, {12045, 21968}, {12177, 34127}, {12220, 16776}, {12900, 14982}, {13394, 41256}, {14001, 15815}, {14043, 18906}, {14643, 16010}, {14786, 37514}, {14788, 20300}, {14789, 18396}, {14810, 15720}, {14848, 15723}, {14940, 39588}, {15024, 32191}, {15028, 41716}, {15040, 32273}, {15118, 32114}, {15462, 20304}, {15526, 15851}, {15701, 19924}, {16042, 35707}, {16298, 19760}, {16299, 19759}, {16408, 36740}, {16419, 37485}, {16491, 19875}, {16666, 17296}, {16667, 17374}, {16669, 17272}, {16670, 17344}, {16674, 41313}, {16677, 25101}, {16777, 17023}, {16792, 29856}, {16826, 17341}, {16832, 16972}, {16834, 17229}, {16863, 37492}, {16922, 39141}, {17014, 17388}, {17063, 18183}, {17120, 17227}, {17121, 17228}, {17240, 29584}, {17243, 26626}, {17248, 25503}, {17255, 17305}, {17260, 17400}, {17261, 17399}, {17262, 17302}, {17263, 17397}, {17264, 17396}, {17266, 17394}, {17268, 17393}, {17275, 29604}, {17280, 17318}, {17301, 17355}, {17304, 17351}, {17308, 17348}, {17317, 29629}, {17319, 17342}, {17320, 17339}, {17322, 17338}, {17324, 17336}, {17326, 17335}, {17362, 29611}, {17377, 29587}, {17390, 29579}, {17597, 29666}, {17599, 26061}, {17710, 40670}, {17723, 30768}, {17783, 29874}, {17800, 33751}, {19121, 30744}, {19126, 30771}, {19127, 31236}, {19136, 31255}, {19149, 40686}, {19154, 31283}, {19876, 28538}, {20182, 33157}, {20301, 32609}, {21241, 25496}, {21242, 25453}, {21514, 36743}, {21526, 36744}, {22260, 45693}, {22493, 43031}, {22494, 43030}, {23042, 32767}, {23049, 35228}, {23515, 32233}, {24471, 31231}, {26083, 32922}, {26982, 27261}, {28634, 41140}, {28653, 29628}, {29646, 33159}, {29660, 42871}, {29686, 41711}, {29867, 31245}, {30745, 32217}, {31088, 46721}, {31173, 38010}, {31183, 31238}, {31244, 36404}, {31252, 43997}, {31276, 32449}, {31401, 33185}, {31404, 33194}, {31639, 39080}, {31658, 38143}, {31860, 44210}, {32113, 37911}, {32271, 38728}, {33242, 37512}, {33364, 41964}, {33365, 41963}, {33414, 33415}, {34360, 44338}, {35018, 39884}, {36757, 42489}, {36758, 42488}, {36836, 37178}, {36843, 37177}, {37326, 37504}, {37751, 40556}, {39668, 46288}, {39979, 39983}, {40334, 42129}, {40335, 42132}, {43150, 46267}

X(47355) = complement of X(3619)
X(47355) = complement of the isotomic conjugate of X(18841)
X(47355) = X(18841)-complementary conjugate of X(2887)
X(47355) = crosspoint of X(2) and X(18841)
X(47355) = crosssum of X(6) and X(9605)
X(47355) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17357, 17267}, {2, 6, 3763}, {2, 69, 34573}, {2, 86, 17265}, {2, 597, 21358}, {2, 3329, 7868}, {2, 3589, 6}, {2, 3618, 141}, {2, 6703, 37682}, {2, 7766, 16988}, {2, 7792, 15271}, {2, 7875, 183}, {2, 11174, 7778}, {2, 17277, 17327}, {2, 17349, 17307}, {2, 17352, 17259}, {2, 17379, 17283}, {2, 17381, 15668}, {2, 17825, 26958}, {2, 37649, 17811}, {2, 37650, 1213}, {5, 5085, 36990}, {6, 69, 15534}, {6, 141, 40341}, {6, 599, 6144}, {6, 3763, 599}, {6, 15533, 3629}, {6, 21358, 69}, {9, 17384, 17325}, {44, 17306, 17253}, {69, 597, 6}, {69, 34573, 21358}, {140, 14561, 1350}, {141, 597, 32455}, {141, 3589, 3618}, {141, 3618, 6}, {141, 6329, 193}, {141, 32455, 69}, {141, 40341, 599}, {182, 1656, 10516}, {190, 17383, 17323}, {193, 3618, 6329}, {193, 6329, 6}, {239, 17371, 17293}, {344, 17045, 16672}, {590, 615, 7736}, {597, 21358, 15534}, {597, 34573, 69}, {631, 5480, 31884}, {894, 17370, 17290}, {1100, 17284, 17311}, {1125, 38047, 3242}, {1691, 7808, 44000}, {2345, 17366, 17119}, {3068, 3069, 14930}, {3068, 13972, 6}, {3069, 13910, 6}, {3329, 7868, 9766}, {3329, 8177, 6}, {3589, 34573, 597}, {3620, 3629, 15533}, {3628, 38110, 1352}, {3629, 20582, 3620}, {3634, 38049, 3416}, {3758, 17291, 7232}, {3759, 17292, 4445}, {3763, 40341, 141}, {3818, 10168, 12017}, {3818, 12017, 43273}, {4000, 17369, 17118}, {4045, 11286, 44526}, {4360, 17358, 17269}, {4393, 17285, 17309}, {4422, 17321, 16675}, {4657, 17353, 45}, {5050, 5070, 24206}, {5050, 24206, 15069}, {5055, 10168, 43273}, {5055, 12017, 3818}, {5157, 19137, 18374}, {5750, 31191, 17278}, {7539, 43650, 1853}, {8252, 8253, 31489}, {15534, 21358, 599}, {16285, 20965, 6}, {16706, 17368, 4363}, {17023, 17279, 16777}, {17280, 17380, 17318}, {17283, 17379, 17313}, {17289, 17367, 4361}, {17302, 17354, 17262}, {17305, 17350, 17255}, {17307, 17349, 17251}, {17324, 17336, 24441}, {21358, 34573, 3763}, {23300, 31267, 154}, {25101, 41312, 16677}, {26061, 29684, 17599}, {32455, 34573, 141}, {39022, 39023, 15480}, {43622, 43623, 3815}

X(47356) = X(1)X(524) ∩ X(6)X(519)

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

X(47356) = X[1] - X[2] + X[6] (Randy Hutson, April 16, 2022)
X(47356) = 5 X[2] - 4 X[3844], 2 X[2] - 3 X[38023], 4 X[1386] - X[3416], 5 X[1386] - 2 X[3844], 4 X[1386] - 3 X[38023], 5 X[3416] - 8 X[3844], X[3416] - 3 X[38023], 8 X[3844] - 15 X[38023], X[69] - 3 X[38314], 2 X[141] - 5 X[16491], 2 X[141] - 3 X[25055], 5 X[16491] - 3 X[25055], X[145] + 2 X[4663], X[145] + 3 X[5032], 2 X[4663] - 3 X[5032], 2 X[381] - 3 X[38035], 2 X[547] - 3 X[38040], 2 X[549] - 3 X[38029], 2 X[551] - 3 X[38315], X[599] - 3 X[38315], 2 X[576] + X[37727], 2 X[597] - 3 X[16475], 4 X[597] - 3 X[38047], X[3679] - 3 X[16475], 2 X[3679] - 3 X[38047], 4 X[1125] - 3 X[21358], 4 X[3589] - 3 X[19875], 5 X[3616] - 3 X[21356], 2 X[3629] + X[16496], 5 X[3763] - 6 X[19883], 2 X[3828] - 3 X[38049], 2 X[4669] - 3 X[38087], 2 X[4745] - 3 X[38089], 3 X[5050] - X[34718], 3 X[5093] + X[34748], 3 X[5603] - X[11180], 2 X[5882] + X[11477], 3 X[5886] - 2 X[11178], 2 X[6173] - 3 X[38046], X[7982] + 2 X[8550], 4 X[20583] + X[34747], 4 X[10168] - 3 X[26446], 7 X[10541] - 4 X[43174], 4 X[13464] - X[15069], 3 X[14853] - X[34627], 3 X[14912] + X[34631], 3 X[25406] - X[34632], 3 X[38021] - X[39885], 3 X[38050] - 2 X[45310]

X(47356) lies on these lines: {1, 524}, {2, 1386}, {6, 519}, {69, 38314}, {141, 16491}, {145, 4663}, {182, 3654}, {193, 17488}, {238, 41313}, {355, 5476}, {381, 38035}, {511, 3655}, {517, 11179}, {518, 1992}, {528, 16834}, {542, 3656}, {547, 38040}, {549, 38029}, {551, 599}, {576, 37727}, {597, 3679}, {742, 4795}, {752, 17301}, {1001, 29574}, {1125, 21358}, {1503, 31162}, {1836, 17150}, {2796, 32921}, {2836, 3873}, {3242, 15534}, {3246, 17316}, {3589, 19875}, {3616, 17387}, {3629, 16496}, {3696, 4344}, {3751, 8584}, {3763, 19883}, {3827, 24473}, {3828, 38049}, {3932, 16469}, {4141, 21747}, {4421, 36741}, {4669, 38087}, {4745, 38089}, {4870, 12588}, {4912, 24695}, {5026, 9881}, {5050, 34718}, {5093, 34748}, {5263, 29617}, {5603, 11180}, {5648, 11720}, {5695, 17133}, {5880, 37756}, {5882, 11477}, {5886, 11178}, {6173, 38046}, {7290, 29573}, {7976, 22486}, {7982, 8550}, {7983, 8593}, {7984, 41720}, {8540, 37740}, {9053, 20583}, {9884, 10754}, {10031, 10755}, {10168, 26446}, {10541, 43174}, {11194, 36740}, {11645, 12699}, {11646, 12258}, {13169, 32238}, {13464, 15069}, {14853, 34627}, {14912, 34631}, {15303, 32278}, {16666, 36479}, {16972, 17330}, {17276, 28558}, {17718, 31179}, {18481, 19924}, {19369, 37738}, {20423, 28204}, {25406, 34632}, {27759, 29658}, {28194, 39870}, {28198, 46264}, {28208, 31670}, {29181, 34628}, {31177, 33143}, {38021, 39885}, {38050, 45310}, {38186, 41140}

X(47356) = midpoint of X(i) and X(j) for these {i,j}: {1992, 3241}, {3242, 15534}, {7976, 22486}, {7983, 8593}, {7984, 41720}, {9884, 10754}, {10031, 10755}
X(47356) = reflection of X(i) in X(j) for these {i,j}: {2, 1386}, {355, 5476}, {599, 551}, {3416, 2}, {3654, 182}, {3679, 597}, {3751, 8584}, {5648, 11720}, {9881, 5026}, {11646, 12258}, {13169, 32238}, {32278, 15303}, {38047, 16475}, {43273, 39870}
X(47356) = X(2)-extraversion of {X(1), X(2), X(6)}
X(47356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1386, 38023}, {597, 3679, 38047}, {599, 38315, 551}, {3416, 38023, 2}, {3679, 16475, 597}

X(47357) = X(1)X(527) ∩ X(2)X(11)

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

X(47357) = 2 X[1] + X[5698], 5 X[2] - 4 X[3826], 2 X[2] - 3 X[38025], 5 X[2] - 3 X[38092], 7 X[2] - 5 X[40333], X[390] + 2 X[1001], 2 X[390] + X[2550], 5 X[390] + 4 X[3826], 2 X[390] + 3 X[38025], 5 X[390] + 3 X[38092], 7 X[390] + 5 X[40333], 4 X[1001] - X[2550], 5 X[1001] - 2 X[3826], 4 X[1001] - 3 X[38025], 10 X[1001] - 3 X[38092], 14 X[1001] - 5 X[40333], 5 X[2550] - 8 X[3826], X[2550] - 3 X[38025], 5 X[2550] - 6 X[38092], 7 X[2550] - 10 X[40333], 8 X[3826] - 15 X[38025], 4 X[3826] - 3 X[38092], 28 X[3826] - 25 X[40333], 5 X[38025] - 2 X[38092], 21 X[38025] - 10 X[40333], 3 X[38060] - 2 X[45310], 21 X[38092] - 25 X[40333], X[7] - 3 X[38314], X[7] - 4 X[42819], 3 X[38314] - 4 X[42819], X[8] - 4 X[15254], X[9] + 2 X[30331], 2 X[142] - 3 X[25055], X[144] + 2 X[42871], X[145] + 2 X[5220], 4 X[551] - 3 X[38053], 5 X[551] - 3 X[38054], 2 X[551] - 3 X[38316], 2 X[6173] - 3 X[38053], 5 X[6173] - 6 X[38054], X[6173] - 3 X[38316], 5 X[38053] - 4 X[38054], 2 X[38054] - 5 X[38316], 2 X[381] - 3 X[38037], X[3241] - 3 X[8236], X[6172] + 3 X[8236], 2 X[547] - 3 X[38043], 2 X[549] - 3 X[38031], 2 X[597] - 3 X[38048], 4 X[1125] - 3 X[38093], 3 X[3524] - X[35514], X[3243] - 4 X[43179], 5 X[3616] - 2 X[5880], 5 X[3616] + X[30332], 2 X[5880] + X[30332], 7 X[3622] - 4 X[25557], 4 X[3636] - X[30424], 2 X[3679] - 3 X[38057], 2 X[3828] - 3 X[38059], 4 X[3828] - 3 X[38200], 3 X[3839] - 4 X[42356], 5 X[3890] + X[10394], X[4312] - 3 X[38024], 2 X[4669] - 3 X[38097], 2 X[4745] - 3 X[38101], 5 X[5071] - 3 X[38149], 3 X[5686] - X[31145], X[5735] - 4 X[13464], 3 X[5817] - X[34627], 4 X[6666] - 3 X[19875], 3 X[10304] - 2 X[11495], X[11372] + 2 X[43175], 5 X[15694] - 3 X[38121], 6 X[19883] - 5 X[20195], 3 X[21168] + X[34631], 3 X[24644] + X[34628]

X(47357) lies on these lines: {1, 527}, {2, 11}, {4, 34486}, {7, 1319}, {8, 4702}, {9, 519}, {21, 11240}, {30, 43161}, {142, 25055}, {144, 42871}, {145, 5220}, {329, 3748}, {354, 2094}, {376, 516}, {381, 38037}, {388, 8543}, {392, 15733}, {443, 4309}, {452, 3303}, {517, 10177}, {518, 1992}, {535, 1056}, {547, 38043}, {549, 38031}, {553, 12560}, {597, 38048}, {631, 10199}, {885, 4762}, {954, 11113}, {966, 32941}, {971, 3655}, {1005, 33925}, {1058, 5248}, {1125, 38093}, {1156, 10031}, {1279, 17301}, {1470, 7677}, {1697, 34711}, {1706, 34639}, {1890, 7714}, {2077, 3524}, {2099, 12848}, {2267, 16503}, {2346, 11239}, {2551, 3295}, {2801, 3898}, {2975, 42886}, {3057, 5766}, {3085, 17556}, {3086, 37298}, {3189, 31435}, {3243, 43179}, {3246, 5222}, {3304, 17576}, {3474, 4666}, {3475, 31164}, {3476, 8545}, {3545, 10197}, {3600, 34620}, {3616, 5880}, {3622, 25557}, {3636, 30424}, {3654, 31658}, {3663, 35227}, {3679, 5853}, {3683, 36845}, {3715, 20015}, {3742, 9778}, {3746, 5084}, {3813, 17558}, {3828, 38059}, {3839, 42356}, {3883, 17294}, {3890, 10394}, {3913, 5129}, {3946, 16487}, {4294, 11112}, {4307, 17392}, {4312, 38024}, {4313, 5784}, {4314, 34701}, {4344, 15569}, {4432, 36479}, {4512, 24477}, {4640, 10580}, {4648, 16484}, {4654, 12573}, {4669, 38097}, {4677, 24393}, {4745, 38101}, {4779, 5695}, {4857, 6856}, {5071, 38149}, {5082, 5259}, {5119, 8257}, {5177, 9670}, {5225, 17577}, {5229, 10587}, {5298, 8732}, {5302, 6764}, {5436, 12575}, {5572, 15933}, {5686, 31145}, {5701, 40779}, {5731, 10179}, {5735, 13464}, {5817, 34627}, {5845, 24441}, {6601, 15175}, {6666, 19875}, {6692, 31508}, {6872, 34605}, {7676, 13587}, {8232, 11237}, {8273, 34630}, {8616, 37642}, {8692, 37681}, {8715, 17559}, {9639, 29815}, {9710, 17554}, {9785, 34640}, {10056, 31160}, {10181, 11206}, {10304, 11495}, {10386, 34707}, {10389, 25568}, {10427, 37606}, {10578, 24703}, {10595, 16113}, {10609, 15346}, {10624, 28629}, {10934, 16370}, {11020, 28610}, {11038, 15677}, {11106, 12513}, {11200, 35110}, {11372, 43175}, {12667, 16202}, {14189, 17079}, {14190, 36887}, {15170, 16418}, {15171, 17528}, {15172, 19843}, {15485, 37650}, {15678, 16133}, {15694, 38121}, {15950, 30275}, {17342, 18230}, {18613, 37400}, {19883, 20195}, {20073, 24841}, {21168, 34631}, {24410, 36220}, {24644, 34628}, {25466, 34706}, {26104, 29660}, {27484, 40891}, {28194, 30503}, {28208, 31672}, {29817, 44447}, {31424, 40270}, {38028, 38173}, {41144, 42850}

X(47357) = midpoint of X(i) and X(j) for these {i,j}: {2, 390}, {1156, 10031}, {3241, 6172}, {3877, 7671}, {15678, 16133}
X(47357) = reflection of X(i) in X(j) for these {i,j}: {2, 1001}, {2550, 2}, {3654, 31658}, {4677, 24393}, {6173, 551}, {38053, 38316}, {38200, 38059}
X(47357) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11111, 34610}, {2, 1001, 38025}, {2, 10385, 34607}, {2, 38092, 3826}, {390, 1001, 2550}, {551, 6173, 38053}, {1058, 5248, 30478}, {2550, 38025, 2}, {3189, 31435, 45085}, {3616, 30332, 5880}, {5284, 20075, 26040}, {6172, 8236, 3241}, {6173, 38316, 551}, {10389, 40998, 25568}, {15170, 16418, 34625}, {40565, 40566, 5218}

X(47358) = X(1)X(524) ∩ X(2)X(210)

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

X(47358) = X[1] + X[2] - X[6] (Randy Hutson, April 16, 2022)
X(47358) = 4 X[2] - 3 X[38047], 2 X[6] - 3 X[38023], 4 X[551] - 3 X[38023], X[8] - 3 X[21356], 2 X[10] - 3 X[21358], 2 X[141] + X[16496], 2 X[182] - 3 X[3653], 2 X[3242] + X[3416], 2 X[597] - 3 X[25055], X[3751] - 3 X[25055], 2 X[1386] - 3 X[38314], X[1992] - 3 X[38314], X[17276] + 2 X[32941], 5 X[3616] - 2 X[4663], 5 X[3620] - X[31145], 7 X[3622] - 3 X[5032], 2 X[3629] - 5 X[16491], 4 X[3631] + X[34747], 5 X[3763] - 4 X[3828], 5 X[3763] - 3 X[38087], 4 X[3828] - 3 X[38087], 2 X[5476] - 3 X[5886], 2 X[5480] - 3 X[38021], 2 X[5882] + X[15069], 2 X[8584] - 3 X[16475], X[11477] - 4 X[13464], X[15534] - 3 X[38315], 2 X[18583] - 3 X[38022], 3 X[19875] - 4 X[20582], 7 X[19876] - 8 X[34573], 2 X[20423] - 3 X[38035], 2 X[34507] + X[37727], 3 X[38074] - 5 X[40330]

X(47358) lies on these lines: {1, 524}, {2, 210}, {6, 551}, {8, 17227}, {10, 21358}, {38, 4933}, {69, 3241}, {141, 3679}, {182, 3653}, {320, 36534}, {355, 11178}, {376, 39898}, {392, 9004}, {511, 3656}, {519, 599}, {528, 17274}, {537, 17281}, {542, 3655}, {597, 3751}, {944, 11180}, {984, 41313}, {1350, 28194}, {1352, 28204}, {1385, 11179}, {1386, 1992}, {2796, 17276}, {2836, 3877}, {3243, 4026}, {3616, 4663}, {3620, 31145}, {3622, 5032}, {3629, 16491}, {3631, 34747}, {3661, 24841}, {3696, 4310}, {3763, 3828}, {3966, 31143}, {4141, 33156}, {4357, 42871}, {4407, 24331}, {4419, 4702}, {4428, 36740}, {4655, 28562}, {4675, 36480}, {4677, 9053}, {4684, 29574}, {4863, 17184}, {4906, 14555}, {4914, 30614}, {4952, 33079}, {4956, 33151}, {4966, 7174}, {5289, 40880}, {5476, 5886}, {5480, 38021}, {5642, 32278}, {5695, 17132}, {5846, 22165}, {5847, 15533}, {5882, 15069}, {5969, 34636}, {8584, 16475}, {9140, 32238}, {9884, 11161}, {11477, 13464}, {11645, 18481}, {11705, 22580}, {11706, 22579}, {11720, 34319}, {12329, 16371}, {12699, 19924}, {15534, 34379}, {16370, 22769}, {16973, 17330}, {17237, 36479}, {17257, 42819}, {17294, 28503}, {17553, 41610}, {17721, 33065}, {17723, 31179}, {18583, 38022}, {19870, 22277}, {19875, 20582}, {19876, 34573}, {20423, 38035}, {24476, 44663}, {27759, 29676}, {29617, 32922}, {30615, 33172}, {31177, 33104}, {34507, 37727}, {36741, 40726}, {38074, 40330}

X(47358) = midpoint of X(i) and X(j) for these {i,j}: {69, 3241}, {376, 39898}, {599, 3242}, {944, 11180}, {3679, 16496}, {9884, 11161}
X(47358) = reflection of X(i) in X(j) for these {i,j}: {6, 551}, {355, 11178}, {1992, 1386}, {3416, 599}, {3679, 141}, {3751, 597}, {9140, 32238}, {11179, 1385}, {22579, 11706}, {22580, 11705}, {32278, 5642}, {34319, 11720}
X(47358) = X(6)-extraversion of {X(1), X(2), X(6)}
X(47358) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 551, 38023}, {1992, 38314, 1386}, {3751, 25055, 597}, {3763, 38087, 3828}

X(47359) = X(1)X(597) ∩ X(2)X(210)

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

X(47359) = - X[1] + X[2] + X[6] (RAndy Hutson, April 16, 2022)
X(47359) = 2 X[1] - 3 X[38023], 4 X[597] - 3 X[38023], 2 X[2] - 3 X[38047], X[8] + 2 X[4663], 2 X[10] - 3 X[38087], X[599] - 3 X[38087], 2 X[141] - 3 X[19875], X[3416] + 2 X[3751], 4 X[575] - X[37727], 2 X[946] - 3 X[38072], 2 X[1001] - 3 X[38088], 2 X[1125] - 3 X[38089], 2 X[1385] - 3 X[38064], 2 X[1387] - 3 X[38090], X[1482] - 3 X[14848], 5 X[1698] - 4 X[20582], 3 X[3545] - X[39898], 4 X[3589] - X[16496], 4 X[3589] - 3 X[25055], X[16496] - 3 X[25055], 5 X[3617] - X[11160], 5 X[3618] - 3 X[38314], X[3632] + 4 X[20583], 3 X[3653] - 4 X[10168], 2 X[3656] - 3 X[38035], 4 X[5476] - 3 X[38035], 4 X[3828] - 3 X[21358], 4 X[3844] - 3 X[21356], 4 X[4085] - X[17276], 2 X[4669] + X[15534], X[4677] + 2 X[8584], 4 X[4745] - X[15533], 2 X[4745] - 3 X[38191], X[15533] - 6 X[38191], 3 X[5032] + X[31145], 3 X[5182] - X[9884], 2 X[5542] - 3 X[38086], X[5881] + 2 X[8550], 2 X[5901] - 3 X[38079], 3 X[6034] - 2 X[12258], 8 X[6329] - 5 X[16491], X[11180] - 3 X[38074], 2 X[11362] + X[11477], 2 X[37737] - 3 X[38091], 6 X[38098] - X[40341]

X(47359) lies on these lines: {1, 597}, {2, 210}, {6, 519}, {8, 1992}, {10, 599}, {42, 4141}, {44, 36479}, {69, 5936}, {81, 30615}, {141, 19875}, {182, 3655}, {355, 542}, {511, 3654}, {515, 43273}, {517, 20423}, {524, 3416}, {537, 17301}, {551, 3242}, {575, 37727}, {946, 38072}, {984, 41312}, {1001, 38088}, {1125, 38089}, {1351, 34718}, {1385, 38064}, {1386, 3241}, {1387, 38090}, {1482, 14848}, {1698, 20582}, {2334, 3710}, {2550, 35578}, {2796, 32935}, {3006, 31179}, {3545, 39898}, {3589, 16496}, {3617, 11160}, {3618, 38314}, {3632, 20583}, {3653, 10168}, {3656, 5476}, {3717, 29574}, {3753, 9004}, {3755, 17132}, {3828, 21358}, {3844, 21356}, {3932, 29573}, {4026, 5223}, {4085, 17276}, {4113, 19822}, {4126, 5287}, {4370, 36404}, {4421, 36740}, {4643, 29659}, {4660, 28558}, {4669, 5847}, {4677, 5846}, {4679, 29835}, {4737, 17790}, {4745, 15533}, {4798, 36531}, {4851, 33165}, {4863, 26223}, {4912, 24248}, {4933, 33161}, {4952, 17716}, {5032, 31145}, {5182, 9884}, {5294, 41711}, {5480, 31162}, {5542, 38086}, {5881, 8550}, {5901, 38079}, {5969, 9881}, {6034, 12258}, {6329, 16491}, {6776, 34627}, {9053, 16475}, {9830, 13178}, {9875, 9903}, {10404, 17679}, {11179, 28204}, {11180, 38074}, {11194, 36741}, {11362, 11477}, {12329, 16370}, {13745, 41229}, {14621, 29617}, {15569, 27549}, {16371, 22769}, {16834, 28503}, {17353, 42871}, {17367, 24841}, {17740, 21870}, {19369, 41687}, {24349, 37756}, {26685, 42819}, {27777, 33140}, {28198, 31670}, {28208, 46264}, {29667, 31143}, {34628, 44882}, {34648, 36990}, {37737, 38091}, {38098, 40341}

X(47359) = midpoint of X(i) and X(j) for these {i,j}: {8, 1992}, {1351, 34718}, {3679, 3751}, {6776, 34627}
X(47359) = reflection of X(i) in X(j) for these {i,j}: {1, 597}, {599, 10}, {1992, 4663}, {3241, 1386}, {3242, 551}, {3416, 3679}, {3655, 182}, {3656, 5476}, {31162, 5480}, {34628, 44882}, {36990, 34648}
X(47359) = X(1)-extraversion of {X(1), X(2), X(6)}
X(47359) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 597, 38023}, {599, 38087, 10}, {3656, 5476, 38035}

X(47360) = X(5)X(49)∩X(24)X(195)

X(47360) lies on these lines: {3,8154}, {4,32215}, {5,49}, {24,195}, {30,32330}, {156,5448}, {184,5876}, {215,10082}, {973,1493}, {1147,1154}, {2477,10066}, {2888,6639}, {2937,15137}, {3575,20424}, {5498,15132}, {5663,32401}, {6145,10224}, {6644,32341}, {6689,10116}, {7502,41590}, {7503,9704}, {7506,41713}, {7542,21230}, {7575,15801}, {7691,22115}, {9306,13565}, {9544,12254}, {9621,9905}, {10115,34986}, {10203,43572}, {10539,22804}, {10628,12038}, {11271,41732}, {11449,32339}, {11464,15091}, {11702,25711}, {11803,37458}, {11805,15463}, {13392,22955}, {14076,43839}, {15345,35467}, {15462,27552}, {15800,34148}, {18281,32337}, {18569,32354}, {22051,31830}, {22584,43605}, {30522,32365}, {32139,32345}

X(47361) = X(2)X(14)∩X(13)X(3414)

X(47361) lies on the circumcircle of the inner Napoleon triangle, the cubics K061a and K293b, and these lines: {2, 14}, {13, 3414}, {30, 1379}, {395, 1380}, {396, 31862}, {524, 47364}, {530, 6190}, {532, 39365}, {533, 6189}, {1340, 6775}, {2040, 36970}, {3413, 5463}, {6040, 41022}, {21359, 47088}, {36759, 46023}, {36967, 47089}

X(47361) = reflection of X(i) in X(j) for these {i,j}: {47362, 2}, {47363, 39022}
X(47361) = psi-transform of X(47363)
X(47361) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 15, 47362}, {617, 623, 47362}, {619, 621, 47362}, {3642, 5978, 47362}, {6109, 10654, 47362}, {6780, 37835, 47362}

X(47362) = X(2)X(14)∩X(13)X(3413)

X(47362) lies on the circumcircle of the inner Napoleon triangle, the cubics K061a and K293a, and these lines: {2, 14}, {13, 3413}, {30, 1380}, {395, 1379}, {396, 31863}, {524, 47363}, {530, 6189}, {532, 39366}, {533, 6190}, {1341, 6775}, {2039, 36970}, {3414, 5463}, {6039, 41022}, {21359, 47089}, {36759, 46024}, {36967, 47088}

X(47361) = reflection of X(i) in X(j) for these {i,j}: {47361, 2}, {47364, 39023}
X(47361) = psi-transform of X(47364)
X(47361) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 15, 47361}, {617, 623, 47361}, {619, 621, 47361}, {3642, 5978, 47361}, {6109, 10654, 47361}, {6780, 37835, 47361}

X(47363) = X(2)X(13)∩X(14)X(3414)

X(47363) lies on the circumcircle of the outer Napoleon triangle, the cubics K061b and K293b, and these lines: {2, 13}, {14, 3414}, {30, 1379}, {395, 31862}, {396, 1380}, {524, 47362}, {531, 6190}, {532, 6189}, {533, 39365}, {1340, 6772}, {2040, 36969}, {3413, 5464}, {6040, 41023}, {21360, 47088}, {36760, 46023}, {36968, 47089}

X(47363) = reflection of X(i) in X(j) for these {i,j}: {47361, 39022}, {47364, 2}
X(47363) = psi-transform of X(47361)
X(47363) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 16, 47364}, {616, 624, 47364}, {618, 622, 47364}, {3643, 5979, 47364}, {6108, 10653, 47364}, {6779, 37832, 47364}

X(47364) = X(2)X(13)∩X(14)X(3413)

X(47364) lies on the circumcircle of the outer Napoleon triangle, the cubics K061b and K293a, and these lines: {2, 13}, {14, 3413}, {30, 1380}, {395, 31863}, {396, 1379}, {524, 47361}, {531, 6189}, {532, 6190}, {533, 39366}, {1341, 6772}, {2039, 36969}, {3414, 5464}, {6039, 41023}, {21360, 47089}, {36760, 46024}, {36968, 47088}

X(47364) = reflection of X(i) in X(j) for these {i,j}: {47362, 39023}, {47363, 2}
X(47364) = psi-transform of X(47362)
X(47364) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 16, 47363}, {616, 624, 47363}, {618, 622, 47363}, {3643, 5979, 47363}, {6108, 10653, 47363}, {6779, 37832, 47363}

X(47365) = X(2)X(98)∩X(3)X(3414)

Barycentrics 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 + 4*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*S^2 : :

X(47365) lies on the cubic K725 and these lines: {2, 98}, {3, 3414}, {4, 14502}, {5, 14631}, {30, 1380}, {69, 14501}, {381, 3413}, {511, 6040}, {1340, 12042}, {1341, 2782}, {1348, 38224}, {1349, 6033}, {1674, 10053}, {1675, 10069}, {2542, 14651}, {2543, 9862}, {2558, 14880}, {2559, 10104}, {3558, 14881}, {3564, 39022}, {5054, 47089}, {5965, 39365}, {6039, 11645}, {6142, 6795}, {11842, 46024}, {23514, 35913}, {35914, 38749}

X(47365) = midpoint of X(6040) and X(6189)
X(47365) = reflection of X(i) in X(j) for these {i,j}: {3, 47088}, {31863, 5}, {47366, 2}
X(47365) = complement of X(47367)
X(47365) = anticomplement of X(47369)
X(47365) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 182, 47366}, {114, 1352, 47366}, {147, 24206, 47366}, {5613, 5617, 47366}, {5921, 6721, 47366}, {6036, 6776, 47366}, {6054, 11178, 47366}, {6055, 11179, 47366}, {6230, 45554, 47366}, {6231, 45555, 47366}, {6770, 6774, 47366}, {6771, 6773, 47366}, {10168, 11177, 47366}

X(47366) = X(2)X(98)∩X(3)X(3413)

Barycentrics 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 - 4*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*S^2 : :

X(47366) lies on the cubic K725 and these lines: {2, 98}, {3, 3413}, {4, 14501}, {5, 14630}, {30, 1379}, {69, 14502}, {381, 3414}, {511, 6039}, {1340, 2782}, {1341, 12042}, {1348, 6033}, {1349, 38224}, {1674, 10069}, {1675, 10053}, {2542, 9862}, {2543, 14651}, {2558, 10104}, {2559, 14880}, {3557, 14881}, {3564, 39023}, {5054, 47088}, {5965, 39366}, {6040, 11645}, {6141, 6795}, {11842, 46023}, {23514, 35914}, {35913, 38749}

X(47366) = midpoint of X(6039) and X(6190)
X(47366) = reflection of X(i) in X(j) for these {i,j}: {3, 47089}, {31862, 5}, {47365, 2}
X(47366) = complement of X(47368)
X(47366) = anticomplement of X(47370)
X(47366) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 182, 47365}, {114, 1352, 47365}, {147, 24206, 47365}, {5613, 5617, 47365}, {5921, 6721, 47365}, {6036, 6776, 47365}, {6054, 11178, 47365}, {6055, 11179, 47365}, {6230, 45554, 47365}, {6231, 45555, 47365}, {6770, 6774, 47365}, {6771, 6773, 47365}, {10168, 11177, 47365}

X(47367) = X(2)X(98)∩X(4)X(3414)

Barycentrics 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 - 2*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*S^2 : :

X(47367) = 3 X[2] - 4 X[47369], 5 X[2] - 4 X[47370], X[47365] - 3 X[47366], 4 X[47365] - 3 X[47368], 5 X[47365] - 6 X[47370], 4 X[47366] - X[47368], 3 X[47366] - 2 X[47369], 5 X[47366] - 2 X[47370], 3 X[47368] - 8 X[47369], 5 X[47368] - 8 X[47370], 5 X[47369] - 3 X[47370], 5 X[631] - 4 X[47088], 3 X[3524] - 4 X[47089], 3 X[3545] - 2 X[31862]

X(47367) lies on these lines: {2, 98}, {4, 3414}, {30, 6190}, {115, 35914}, {376, 3413}, {511, 39365}, {524, 6039}, {631, 47088}, {1503, 6040}, {2543, 12188}, {2794, 35913}, {3524, 47089}, {3545, 31862}, {3564, 6189}, {41022, 47363}, {41023, 47361}

X(47367) = reflection of X(i) in X(j) for these {i,j}: {2, 47366}, {4, 31863}, {6040, 39022}, {47365, 47369}, {47367, 2}
X(47367) = anticomplement of X(47365)
X(47367) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 6776, 47368}, {114, 5921, 47368}, {147, 1352, 47368}, {182, 5984, 47368}, {6054, 11180, 47368}, {6770, 6773, 47368}, {11177, 11179, 47368}, {33430, 45511, 47368}, {33431, 45510, 47368}, {47365, 47366, 47369}, {47365, 47369, 2}

X(47368) = X(2)X(98)∩X(4)X(3413)

Barycentrics 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 + 2*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*S^2 : :

X(47368) = 5 X[2] - 4 X[47369], 3 X[2] - 4 X[47370], 3 X[47365] - X[47366], 4 X[47365] - X[47367], 5 X[47365] - 2 X[47369], 3 X[47365] - 2 X[47370], 4 X[47366] - 3 X[47367], 5 X[47366] - 6 X[47369], 5 X[47367] - 8 X[47369], 3 X[47367] - 8 X[47370], 3 X[47369] - 5 X[47370], 5 X[631] - 4 X[47089], 3 X[3524] - 4 X[47088], 3 X[3545] - 2 X[31863]

X(47368) lies on these lines: {2, 98}, {4, 3413}, {30, 6189}, {115, 35913}, {376, 3414}, {511, 39366}, {524, 6040}, {631, 47089}, {1503, 6039}, {2542, 12188}, {2794, 35914}, {3524, 47088}, {3545, 31863}, {3564, 6190}, {41022, 47364}, {41023, 47362}

X(47368) = reflection of X(i) in X(j) for these {i,j}: {2, 47365}, {4, 31862}, {6039, 39023}, {47366, 47370}, {47367, 2}
X(47368) = anticomplement of X(47366)
X(47368) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 6776, 47367}, {114, 5921, 47367}, {147, 1352, 47367}, {182, 5984, 47367}, {6054, 11180, 47367}, {6770, 6773, 47367}, {11177, 11179, 47367}, {33430, 45511, 47367}, {33431, 45510, 47367}, {47365, 47366, 47370}, {47366, 47370, 2}

X(47369) = X(2)X(98)∩X(5)X(3414)

Barycentrics 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 - 8*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*S^2 : :

X(47369) = 3 X[2] + X[47367], 5 X[2] - X[47368], X[47365] + 3 X[47366], 5 X[47365] - 3 X[47368], 2 X[47365] - 3 X[47370], 3 X[47366] - X[47367], 5 X[47366] + X[47368], 2 X[47366] + X[47370], 5 X[47367] + 3 X[47368], 2 X[47367] + 3 X[47370], 2 X[47368] - 5 X[47370], 3 X[5055] - X[31862]

X(47369) lies on the cubic K798 and these lines: {2, 98}, {3, 31863}, {5, 3414}, {30, 2040}, {115, 1340}, {140, 47088}, {511, 39022}, {549, 3413}, {626, 6178}, {1341, 38737}, {1348, 2794}, {1349, 6722}, {1506, 14630}, {1668, 8980}, {1669, 13967}, {1704, 38220}, {2542, 34473}, {2543, 14061}, {2558, 7749}, {5055, 31862}, {5965, 6189}, {6039, 19924}, {6040, 29012}, {13335, 19659}, {14501, 19130}, {14502, 40107}

X(47369) = midpoint of X(i) and X(j) for these {i,j}: {2, 47366}, {3, 31863}, {47365, 47367}
X(47369) = reflection of X(i) in X(j) for these {i,j}: {47088, 140}, {47370, 2}
X(47369) = complement of X(47365)
X(47369) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47367, 47365}, {114, 24206, 47370}, {182, 6036, 47370}, {1352, 6721, 47370}, {6055, 10168, 47370}, {6771, 6774, 47370}, {47365, 47366, 47367}

X(47370) = X(2)X(98)∩X(5)X(3413)

Barycentrics 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 + 8*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]*S^2 : :

X(47370) = 5 X[2] - X[47367], 3 X[2] + X[47368], 3 X[47365] + X[47366], 5 X[47365] + X[47367], 3 X[47365] - X[47368], 2 X[47365] + X[47369], 5 X[47366] - 3 X[47367], 2 X[47366] - 3 X[47369], 3 X[47367] + 5 X[47368], 2 X[47367] - 5 X[47369], 2 X[47368] + 3 X[47369], 3 X[5055] - X[31863]

X(47370) lies on the cubic K798 and these lines: {2, 98}, {3, 31862}, {5, 3413}, {30, 2039}, {115, 1341}, {140, 47089}, {511, 39023}, {549, 3414}, {626, 6177}, {1340, 38737}, {1348, 6722}, {1349, 2794}, {1506, 14631}, {1668, 13967}, {1669, 8980}, {1705, 38220}, {2542, 14061}, {2543, 34473}, {2559, 7749}, {5055, 31863}, {5965, 6190}, {6039, 29012}, {6040, 19924}, {13335, 19660}, {14501, 40107}, {14502, 19130}

X(47370) = midpoint of X(i) and X(j) for these {i,j}: {2, 47365}, {3, 31862}, {47366, 47367}
X(47370) = reflection of X(i) in X(j) for these {i,j}: {47089, 140}, {47369, 2}
X(47370) = complement of X(47366)
X(47370) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47367, 47366}, {114, 24206, 47369}, {182, 6036, 47369}, {1352, 6721, 47369}, {6055, 10168, 47369}, {6771, 6774, 47369}, {47365, 47366, 47367}

This preamble and centers X(47371)-X(47398) were contributed by César Eliud Lozada, March 27, 2022.

Let AA₁, BB₁, CC₁ be the altitudes in acute triangle ABC, and let X be an arbitrary point. Let M, N, P, Q, R, S be the feet of the perpendiculars from X to the lines AA₁,BC,BB₁,CA,CC₁,AB. Prove that MN, PQ, RS are concurrent. (Source: AOPS 713159, Dec 29, 2006.)

The above ennunciate can be generalized in the following way:

Let ABC be a triangle, X a point and P another point not on the side lines of ABC or on the cevian lines of X. The parallel lines through P to AX and BC cut BC and AX at A' and A", respectively; B', B" and C', C" are built cyclically. Then the lines A'A", B'B", C'C" concur.

The point of intersection Q(X, P) of A'A", B'B", C'C" is named here the X-two parallels point of-P. If X = X : Y : Z and P = x : y : z (both barycentrics) then:

Q(X, P) = x*(-Y*Z*x^2 + (Y + Z)*X*y*z + (Y*z + Z*y)*X*x) : :

Some properties:

Q(X, P) is the midpoint of P and the X-Ceva conjugate of P. (Randy Hutson, March 28, 2022)
For P on the line at infinity, Q(X, P) = P.
For X=X(2), Q(X,P) is W(P), the center of the parallel-conic described above X(10001).
If X=X(4) and P lies on the nine-point-circle of ABC, then Q(X,P) is the complementary conjugate of P.

The appearance of (i, j, k) in the following lists means that X(i)- two parallels point of -X(j) is X(k):

(1, 2, 4664), (1, 3, 47371), (1, 4, 47372), (1, 6, 47373), (1, 7, 47374), (1, 8, 44720), (1, 9, 47375), (1, 10, 4075), (1, 11, 523), (1, 35, 47378), (1, 36, 47379), (1, 55, 47373), (1, 56, 47380), (1, 65, 20617), (1, 73, 20617), (1, 99, 47376), (1, 100, 765), (1, 110, 47377), (1, 192, 4664), (1, 214, 758), (1, 221, 47380), (1, 244, 513), (1, 291, 30663), (1, 1015, 512), (1, 1148, 47372), (1, 3157, 47371), (1, 3158, 47375), (1, 3159, 4075), (1, 6126, 47379), (1, 6163, 765), (1, 8054, 4132), (1, 8299, 518), (1, 17761, 514), (1, 17793, 740), (1, 19582, 44720), (1, 31526, 47374), (1, 34586, 517), (1, 34587, 519), (1, 34588, 521), (1, 34589, 522), (1, 34590, 900), (1, 34591, 3900), (1, 34592, 2574), (1, 34593, 2575), (1, 35197, 47378), (1, 38979, 4145), (1, 38982, 8674), (1, 38986, 4083), (1, 39046, 20718), (1, 40614, 44671)

(2, 1, 1001), (2, 3, 182), (2, 4, 10002), (2, 5, 10003), (2, 6, 182), (2, 7, 10004), (2, 8, 10005), (2, 9, 1001), (2, 10, 3842), (2, 11, 10006), (2, 13, 10217), (2, 14, 10218), (2, 20, 47381), (2, 25, 42820), (2, 32, 42826), (2, 37, 3842), (2, 39, 10007), (2, 55, 42834), (2, 56, 42828), (2, 69, 10008), (2, 75, 10009), (2, 76, 10010), (2, 98, 47382), (2, 99, 4590), (2, 100, 38310), (2, 101, 43979), (2, 114, 10011), (2, 115, 523), (2, 125, 22264), (2, 141, 10007), (2, 142, 10012), (2, 190, 1016), (2, 206, 42826), (2, 216, 10003), (2, 230, 10011), (2, 239, 20142), (2, 298, 11133), (2, 299, 11132), (2, 371, 42866), (2, 372, 42864), (2, 381, 42830), (2, 395, 6672), (2, 396, 6671), (2, 478, 42828), (2, 618, 6671), (2, 619, 6672), (2, 647, 22264), (2, 648, 23582), (2, 650, 10006), (2, 664, 1275), (2, 668, 31625), (2, 670, 44168), (2, 1084, 512), (2, 1086, 514), (2, 1146, 522), (2, 1212, 10012), (2, 1249, 10002), (2, 1494, 31621), (2, 2482, 524), (2, 3068, 42838), (2, 3069, 42840), (2, 3160, 10004), (2, 3161, 10005), (2, 3162, 42820), (2, 3163, 30), (2, 4370, 519), (2, 5375, 38310), (2, 5452, 42834), (2, 6184, 518), (2, 6337, 10008), (2, 6374, 10010), (2, 6376, 10009), (2, 6631, 1016), (2, 6651, 20142), (2, 7026, 14358), (2, 7043, 14359), (2, 9296, 31625), (2, 9410, 31621), (2, 9428, 44168), (2, 10001, 1275), (2, 10960, 42864), (2, 10962, 42866), (2, 11672, 511), (2, 13466, 536), (2, 13636, 8371), (2, 13722, 8371), (2, 15166, 2574), (2, 15167, 2575), (2, 15449, 826), (2, 15525, 3566), (2, 15526, 525), (2, 15527, 7927), (2, 17416, 3906), (2, 17429, 17430), (2, 18334, 526), (2, 20532, 726), (2, 23967, 542), (2, 23972, 516), (2, 23976, 1503), (2, 23980, 517), (2, 23986, 515), (2, 23992, 690), (2, 30471, 11133), (2, 30472, 11132), (2, 31998, 4590), (2, 33364, 42838), (2, 33365, 42840), (2, 35066, 17768), (2, 35067, 3564), (2, 35068, 740), (2, 35069, 758), (2, 35070, 35101), (2, 35072, 521), (2, 35073, 538), (2, 35074, 35102), (2, 35075, 8680), (2, 35076, 4977), (2, 35077, 5969), (2, 35078, 804), (2, 35079, 2787), (2, 35080, 2786), (2, 35081, 2792), (2, 35082, 2784), (2, 35083, 2783), (2, 35084, 2795), (2, 35085, 2796), (2, 35086, 2785), (2, 35087, 543), (2, 35088, 2799), (2, 35089, 35103), (2, 35090, 8674), (2, 35091, 6366), (2, 35092, 900), (2, 35093, 5845), (2, 35094, 918), (2, 35095, 35104), (2, 35110, 527), (2, 35111, 5853), (2, 35113, 528), (2, 35114, 17770), (2, 35116, 2801), (2, 35119, 812), (2, 35121, 545), (2, 35123, 537), (2, 35124, 4715), (2, 35125, 3887), (2, 35126, 9055), (2, 35128, 3738), (2, 35129, 2802), (2, 35133, 1499), (2, 35135, 4160), (2, 35508, 3900), (2, 36668, 3911), (2, 36669, 3911), (2, 36899, 47382), (2, 39008, 9033), (2, 39010, 888), (2, 39011, 891), (2, 39013, 924), (2, 39014, 926), (2, 39015, 6371), (2, 39016, 834), (2, 39017, 928), (2, 39018, 1510), (2, 39019, 6368), (2, 39020, 8057), (2, 39022, 3414), (2, 39023, 3413), (2, 39026, 43979), (2, 39062, 23582), (2, 40578, 10217), (2, 40610, 4083), (2, 40621, 3667), (2, 41887, 11064), (2, 41888, 11064), (2, 41889, 10218), (2, 43961, 23870), (2, 43962, 23871), (2, 45245, 47381)

(3, 1, 10571), (3, 2, 47383), (3, 4, 14249), (3, 5, 6663), (3, 6, 19153), (3, 20, 47384), (3, 98, 47385), (3, 110, 250), (3, 125, 6368), (3, 154, 19153), (3, 1075, 14249), (3, 1511, 1154), (3, 1745, 10571), (3, 2972, 520), (3, 3164, 47383), (3, 15912, 6663), (3, 45255, 47384)

(4, 1, 56), (4, 2, 1992), (4, 3, 1147), (4, 5, 143), (4, 6, 19136), (4, 7, 47386), (4, 8, 42020), (4, 9, 47387), (4, 13, 11080), (4, 14, 11085), (4, 15, 11136), (4, 16, 11135), (4, 20, 27082), (4, 21, 27083), (4, 22, 27084), (4, 23, 27085), (4, 25, 19136), (4, 46, 56), (4, 52, 143), (4, 64, 33583), (4, 69, 36895), (4, 98, 47388), (4, 99, 47389), (4, 107, 32230), (4, 110, 47390), (4, 113, 30), (4, 114, 511), (4, 115, 512), (4, 116, 514), (4, 117, 515), (4, 118, 516), (4, 119, 517), (4, 120, 518), (4, 121, 519), (4, 122, 520), (4, 123, 521), (4, 124, 522), (4, 125, 523), (4, 126, 524), (4, 127, 525), (4, 128, 1154), (4, 129, 32428), (4, 131, 13754), (4, 132, 1503), (4, 133, 6000), (4, 136, 924), (4, 137, 1510), (4, 155, 1147), (4, 193, 1992), (4, 371, 32), (4, 372, 32), (4, 468, 15471), (4, 487, 6337), (4, 488, 6337), (4, 1113, 15461), (4, 1114, 15460), (4, 1263, 27357), (4, 1312, 2575), (4, 1313, 2574), (4, 1560, 2393), (4, 1566, 926), (4, 1785, 1875), (4, 1845, 1875), (4, 2039, 3413), (4, 2040, 3414), (4, 2679, 804), (4, 2898, 47386), (4, 2899, 42020), (4, 2900, 47387), (4, 2902, 11136), (4, 2903, 11135), (4, 3258, 526), (4, 3259, 900), (4, 5095, 15471), (4, 5099, 690), (4, 5139, 3566), (4, 5190, 8676), (4, 5509, 814), (4, 5510, 3667), (4, 5511, 3309), (4, 5512, 1499), (4, 5513, 674), (4, 5514, 3900), (4, 5515, 834), (4, 5516, 6085), (4, 5517, 8678), (4, 5518, 4083), (4, 5519, 6084), (4, 5520, 8674), (4, 5521, 15313), (4, 5952, 8702), (4, 5993, 38469), (4, 6092, 33962), (4, 6110, 1990), (4, 6111, 1990), (4, 9151, 888), (4, 9152, 5969), (4, 9193, 9023), (4, 10017, 8677), (4, 11792, 20188), (4, 12494, 8704), (4, 13234, 3849), (4, 14672, 30209), (4, 15441, 11080), (4, 15442, 11085), (4, 15611, 6371), (4, 15612, 928), (4, 15614, 4777), (4, 16177, 9033), (4, 16188, 542), (4, 18402, 18400), (4, 18809, 2777), (4, 19583, 36895), (4, 20389, 12073), (4, 20551, 726), (4, 20619, 2390), (4, 20621, 3827), (4, 20623, 44670), (4, 20625, 6368), (4, 25640, 6001), (4, 25641, 5663), (4, 31654, 6088), (4, 31655, 2854), (4, 31841, 952), (4, 31842, 3564), (4, 31843, 5965), (4, 31844, 527), (4, 31845, 758), (4, 32605, 27082), (4, 33330, 2782), (4, 33331, 2808), (4, 33333, 25150), (4, 33504, 2881), (4, 35579, 6086), (4, 35580, 6087), (4, 35581, 16171), (4, 35582, 20403), (4, 35583, 6089), (4, 35591, 25149), (4, 35592, 46062), (4, 35968, 8057), (4, 35970, 680), (4, 35971, 688), (4, 35972, 696), (4, 36471, 2799), (4, 38971, 9517), (4, 38973, 6607), (4, 38974, 39469), (4, 38975, 2871), (4, 39535, 2818), (4, 41085, 33583), (4, 42422, 2771), (4, 42423, 912), (4, 42424, 17702), (4, 42425, 6003), (4, 42426, 2781), (4, 44948, 28470), (4, 44949, 32472), (4, 44950, 6002), (4, 44952, 28845), (4, 44953, 29012), (4, 44955, 29181), (4, 44956, 543), (4, 44993, 971), (4, 45158, 2794), (4, 45161, 32478), (4, 45162, 740), (4, 45163, 8705), (4, 45165, 29317), (4, 45166, 32479), (4, 45167, 28146), (4, 45180, 32423), (4, 45183, 30522), (4, 46415, 6366), (4, 46436, 9003), (4, 46439, 45147), (4, 46650, 23870), (4, 46651, 23871), (4, 46652, 23872), (4, 46653, 23873), (4, 46654, 826), (4, 46656, 23878), (4, 46657, 3906), (4, 46659, 2793), (4, 46660, 4977), (4, 46663, 8058), (4, 46665, 7927), (4, 46668, 2786), (4, 46669, 9479), (4, 46670, 2785), (4, 46671, 2787)

(6, 1, 995), (6, 2, 7757), (6, 3, 47391), (6, 4, 47392), (6, 7, 47393), (6, 11, 47394), (6, 43, 995), (6, 98, 47395), (6, 110, 249), (6, 111, 47396), (6, 125, 826), (6, 141, 6665), (6, 194, 7757), (6, 694, 41517), (6, 1084, 688), (6, 3124, 512), (6, 3167, 47391), (6, 3168, 47392), (6, 6593, 9019), (6, 7668, 523), (6, 9218, 249), (6, 31604, 47393), (6, 36213, 511), (6, 38996, 8711), (6, 39080, 732), (6, 41404, 47396), (6, 44312, 514)

X(47371) = X(1)-TWO PARALLELS POINT OF-X(3)

X(47371) lies on these lines: {1, 36059}, {3, 73}, {5, 36949}, {68, 26487}, {72, 1092}, {110, 11107}, {155, 916}, {182, 9940}, {184, 1071}, {515, 14529}, {517, 4347}, {521, 8715}, {569, 10202}, {578, 942}, {651, 7412}, {692, 1158}, {912, 960}, {971, 6759}, {1069, 16202}, {1437, 18446}, {2779, 34935}, {3072, 7175}, {3149, 26884}, {3562, 9637}, {3868, 34148}, {5777, 9306}, {6097, 13754}, {6238, 37621}, {6842, 12428}, {6863, 10071}, {7335, 46974}, {7689, 33862}, {10167, 10984}, {10269, 47391}, {10306, 42460}, {10539, 40263}, {11227, 37515}, {11429, 41344}, {12038, 32612}, {12359, 31659}, {13352, 24474}, {13367, 23154}, {14925, 19904}, {23353, 47372}, {26285, 38607}, {31793, 37480}, {33538, 41608}, {37498, 37547}, {37623, 46330}

X(47371) = midpoint of X(i) and X(j) for these {i, j}: {3, 3157}, {37498, 37547}
X(47371) = reflection of X(42463) in X(1147)
X(47371) = barycentric product X(63)*X(1771)
X(47371) = barycentric quotient X(1771)/X(92)
X(47371) = trilinear product X(3)*X(1771)
X(47371) = trilinear quotient X(1771)/X(4)
X(47371) = X(3157)-of-anti-X3-ABC reflections triangle
X(47371) = X(947)-Ceva conjugate of-X(3)

X(47372) = X(1)-TWO PARALLELS POINT OF-X(4)

X(47372) lies on the cubic K1058 and these lines: {1, 36127}, {4, 65}, {5, 16596}, {12, 3318}, {84, 44697}, {92, 946}, {107, 11107}, {227, 7952}, {243, 3149}, {281, 6523}, {318, 5587}, {342, 6260}, {515, 1895}, {653, 1158}, {1012, 1940}, {1093, 1826}, {1784, 5691}, {1838, 7682}, {1896, 3577}, {1897, 17857}, {5715, 39531}, {5806, 39529}, {6526, 41013}, {7141, 21665}, {15836, 41083}, {22753, 41372}, {23353, 47371}, {37417, 37805}

X(47372) = midpoint of X(4) and X(1148)
X(47372) = polar conjugate of X(41081)
X(47372) = barycentric product X(i)*X(j) for these {i, j}: {33, 40701}, {40, 2052}, {92, 7952}, {158, 329}, {196, 318}, {208, 7017}
X(47372) = barycentric quotient X(i)/X(j) for these (i, j): (4, 41081), (19, 1433), (33, 268), (40, 394), (158, 189), (196, 77)
X(47372) = trilinear product X(i)*X(j) for these {i, j}: {4, 7952}, {33, 342}, {40, 158}, {92, 2331}, {196, 281}, {198, 2052}
X(47372) = trilinear quotient X(i)/X(j) for these (i, j): (4, 1433), (33, 2188), (40, 255), (92, 41081), (158, 84), (196, 222)
X(47372) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1528)}} and {{A, B, C, X(4), X(342)}}
X(47372) = crosspoint of X(92) and X(342)
X(47372) = crosssum of X(48) and X(2188)
X(47372) = pole wrt polar circle of trilinear polar of X(41081) (line X(521)X(4091))
X(47372) = X(i)-Dao conjugate of X(j) for these (i, j): (57, 1804), (281, 63)
X(47372) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 1433}, {48, 41081}, {77, 2188}, {84, 255}
X(47372) = X(1148)-of-Euler triangle
X(47372) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (4, 41081), (19, 1433), (33, 268), (40, 394)

X(47373) = X(1)-TWO PARALLELS POINT OF-X(6)

X(47373) = X(2099)-3*X(38315) = X(3419)-3*X(38047) = X(3428)-3*X(5085) = X(3434)-5*X(3618) = 3*X(5050)+X(10679) = X(5119)+3*X(16475) = 3*X(14561)-X(37820) = 3*X(14853)+X(37000) = 5*X(16491)-X(25415)

X(47373) lies on these lines: {1, 692}, {2, 16792}, {6, 31}, {35, 4259}, {37, 2175}, {41, 4557}, {43, 16793}, {48, 20990}, {63, 9020}, {110, 9347}, {141, 3771}, {171, 5197}, {182, 517}, {184, 3745}, {206, 10537}, {210, 5320}, {284, 15624}, {386, 16791}, {511, 32613}, {518, 993}, {528, 597}, {536, 24264}, {560, 20964}, {572, 3941}, {601, 15622}, {604, 16679}, {611, 8069}, {612, 2194}, {869, 16795}, {995, 16796}, {1083, 41313}, {1193, 16790}, {1201, 16794}, {1400, 1631}, {1428, 2099}, {1469, 4265}, {1503, 7680}, {1824, 1974}, {1908, 9314}, {2174, 34247}, {2183, 4471}, {2223, 2278}, {2245, 37586}, {2260, 4497}, {2264, 21867}, {2810, 34928}, {2886, 3589}, {3085, 12587}, {3295, 45728}, {3303, 12595}, {3419, 38047}, {3428, 5085}, {3434, 3618}, {3573, 4664}, {3751, 33538}, {3758, 4579}, {3763, 29865}, {3769, 19623}, {3870, 16799}, {3939, 4251}, {4362, 9022}, {4517, 17796}, {4640, 34377}, {4663, 43146}, {4682, 9306}, {5010, 33844}, {5050, 10679}, {5091, 17301}, {5119, 16475}, {5256, 16798}, {5269, 20986}, {5480, 5842}, {5711, 14529}, {5820, 39900}, {5845, 8255}, {7113, 21010}, {8186, 45724}, {8187, 45725}, {8647, 23855}, {9004, 42834}, {9026, 12594}, {9028, 13405}, {9037, 47038}, {9310, 35327}, {10830, 42450}, {14561, 37820}, {14853, 37000}, {16491, 25415}, {17599, 26889}, {18082, 26222}, {18407, 19130}, {19121, 20243}, {19136, 44670}, {20617, 47380}, {21009, 35267}, {24253, 32921}, {29867, 31245}, {30142, 42463}, {32760, 37516}, {36404, 40401}, {36741, 40292}, {37492, 45729}

X(47373) = midpoint of X(i) and X(j) for these {i, j}: {6, 55}, {611, 36740}, {3870, 16799}, {5820, 39900}
X(47373) = reflection of X(i) in X(j) for these (i, j): (141, 6690), (2886, 3589), (10537, 206), (18407, 19130)
X(47373) = isogonal conjugate of the isotomic conjugate of X(26227)
X(47373) = barycentric product X(i)*X(j) for these {i, j}: {1, 16788}, {6, 26227}, {101, 29066}
X(47373) = trilinear product X(i)*X(j) for these {i, j}: {6, 16788}, {31, 26227}, {692, 29066}
X(47373) = trilinear quotient X(692)/X(29067)
X(47373) = perspector of the circumconic {{A, B, C, X(101), X(36087)}}
X(47373) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(674)}} and {{A, B, C, X(6), X(2224)}}
X(47373) = crosssum of X(2) and X(29832)
X(47373) = X(693)-isoconjugate-of-X(29067)
X(47373) = center of circle {{X(6), X(55), X(5091)}}
X(47373) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 12329, 22277), (2268, 21059, 8053), (2330, 19133, 6)

X(47374) = X(1)-TWO PARALLELS POINT OF-X(7)

X(47374) lies on these lines: {1, 4626}, {7, 354}, {85, 1121}, {142, 41796}, {279, 17301}, {527, 31627}, {658, 8545}, {3672, 30682}, {5228, 41351}

X(47374) = midpoint of X(7) and X(31526)
X(47374) = reflection of X(41796) in X(142)
X(47374) = barycentric product X(1088)*X(6172)
X(47374) = trilinear product X(i)*X(j) for these {i, j}: {279, 6172}, {658, 46919}, {1088, 35445}
X(47374) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(15726)}} and {{A, B, C, X(7), X(1121)}}
X(47374) = {X(7), X(36888)}-harmonic conjugate of X(47386)

X(47375) = X(1)-TWO PARALLELS POINT OF-X(9)

X(47375) = 2*X(9)+X(3174) = X(9)+2*X(6600) = X(3174)-4*X(6600) = X(3913)+2*X(15254) = 2*X(6594)+X(34894) = X(6601)-4*X(6666) = X(7674)+5*X(18230) = X(7674)+2*X(24389) = X(12629)-4*X(42842) = 5*X(18230)-2*X(24389) = 4*X(42843)-X(43166)

X(47375) lies on these lines: {1, 3939}, {9, 55}, {100, 8545}, {165, 527}, {390, 6735}, {516, 45701}, {518, 3576}, {528, 5587}, {758, 30503}, {908, 36976}, {954, 3753}, {1001, 3880}, {1253, 2324}, {1319, 3243}, {1445, 3873}, {1470, 4321}, {1743, 4878}, {2077, 5732}, {2346, 42470}, {2550, 31434}, {3584, 38052}, {3679, 5853}, {3870, 37787}, {3913, 15254}, {3973, 41457}, {4069, 4936}, {4421, 15726}, {5220, 31424}, {5223, 30282}, {5234, 12437}, {5698, 21075}, {5727, 38211}, {5766, 7080}, {5785, 15296}, {5856, 6173}, {5880, 41865}, {5919, 38316}, {6172, 35258}, {6601, 6666}, {6765, 34486}, {7674, 18230}, {7701, 17857}, {10177, 10389}, {10270, 43177}, {10383, 20588}, {12629, 42842}, {12703, 42843}, {12848, 41570}, {31231, 41555}, {35445, 36973}

X(47375) = midpoint of X(9) and X(3158)
X(47375) = reflection of X(i) in X(j) for these (i, j): (3158, 6600), (3174, 3158), (6601, 24386), (24386, 6666)
X(47375) = barycentric product X(i)*X(j) for these {i, j}: {200, 12848}, {644, 28292}, {765, 43960}
X(47375) = trilinear product X(i)*X(j) for these {i, j}: {220, 12848}, {1252, 43960}
X(47375) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(15733)}} and {{A, B, C, X(9), X(12848)}}
X(47375) = X(23327)-of-excentral triangle
X(47375) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (9, 6600, 3174), (480, 15837, 9), (7674, 18230, 24389)

X(47376) = X(1)-TWO PARALLELS POINT OF-X(99)

X(47376) lies on these lines: {99, 4367}, {1319, 7340}, {4590, 16702}, {11711, 12031}

X(47377) = X(1)-TWO PARALLELS POINT OF-X(110)

X(47377) = barycentric product X(249)*X(47270)
X(47377) = trilinear product X(1101)*X(47270)

X(47378) = X(1)-TWO PARALLELS POINT OF-X(35)

X(47378) lies on these lines: {1, 54}, {3, 7356}, {11, 8254}, {12, 32423}, {35, 500}, {36, 10610}, {55, 195}, {495, 36966}, {498, 2888}, {517, 37472}, {539, 3584}, {1250, 10677}, {1478, 12254}, {1493, 3746}, {2066, 12971}, {2166, 2595}, {2330, 5965}, {2477, 11597}, {3024, 11702}, {3056, 19150}, {3327, 14071}, {3574, 3583}, {3585, 18400}, {4857, 11429}, {5010, 7691}, {5217, 12307}, {5218, 12325}, {5270, 10619}, {5414, 12965}, {5432, 21230}, {6284, 20424}, {6288, 7951}, {7741, 12956}, {9637, 15801}, {10065, 43580}, {10076, 32345}, {10274, 32378}, {10638, 10678}, {11271, 31452}, {11436, 12234}, {12946, 37719}, {13434, 38458}, {15171, 22051}, {20617, 47379}

X(47378) = midpoint of X(35) and X(35197)
X(47378) = barycentric product X(35)*X(24149)
X(47378) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1154)}} and {{A, B, C, X(54), X(6149)}}
X(47378) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (54, 10066, 1), (55, 195, 6286), (10610, 18984, 36)

X(47379) = X(1)-TWO PARALLELS POINT OF-X(36)

X(47379) lies on these lines: {1, 14127}, {36, 1464}, {59, 484}, {110, 2718}, {517, 37477}, {1319, 2771}, {5172, 19470}, {11571, 36059}, {20617, 47378}, {31849, 43610}

X(47379) = center of circle {{X(3024), X(3326), X(5532)}}
X(47379) = reflection of X(36) in the line X(902)X(1459)
X(47379) = X(16173)-of-anti-orthocentroidal triangle
X(47379) = midpoint of X(36) and X(6126)

X(47380) = X(1)-TWO PARALLELS POINT OF-X(56)

X(47380) lies on these lines: {31, 56}, {65, 44104}, {222, 41682}, {517, 4347}, {1456, 1828}, {2122, 22654}, {2818, 32612}, {3827, 42828}, {3915, 7099}, {6001, 24928}, {6691, 20306}, {7114, 23844}, {7125, 23846}, {8069, 10076}, {20617, 47373}

X(47380) = midpoint of X(56) and X(221)
X(47380) = reflection of X(20306) in X(6691)
X(47380) = barycentric product X(56)*X(28997)
X(47380) = trilinear product X(604)*X(28997)

X(47381) = X(2)-TWO PARALLELS POINT OF-X(20)

Barycentrics (3*a^4-2*(b^2+c^2)*a^2-(b^2-c^2)^2)*(13*a^8-16*(b^2+c^2)*a^6+2*(b^4+6*b^2*c^2+c^4)*a^4-8*(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^2*(3*b^2+2*b*c+3*c^2)*(3*b^2-2*b*c+3*c^2)) : :

X(47382) = X(2)-TWO PARALLELS POINT OF-X(98)

X(47382) lies on these lines: {2, 9476}, {98, 230}, {1529, 45031}, {2966, 5999}, {9473, 40428}, {13860, 32545}

X(47382) = midpoint of X(98) and X(36899)
X(47382) = barycentric product X(i)*X(j) for these {i, j}: {287, 45031}, {1350, 34536}
X(47382) = barycentric quotient X(1350)/X(36790)
X(47382) = trilinear product X(293)*X(45031)
X(47382) = trilinear quotient X(1350)/X(23996)
X(47382) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1503)}} and {{A, B, C, X(98), X(9476)}}
X(47382) = {X(98), X(47388)}-harmonic conjugate of X(41932)

X(47383) = X(3)-TWO PARALLELS POINT OF-X(2)

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

X(47383) = 5*X(2)-4*X(14767) = 4*X(216)-X(264) = 2*X(216)+X(3164) = 5*X(216)-2*X(14767) = X(264)+2*X(3164) = 5*X(264)-8*X(14767) = 2*X(599)-3*X(42313) = 5*X(3164)+X(40896) = 3*X(3545)-2*X(39530) = 3*X(3839)-4*X(44924) = 3*X(5055)-4*X(10003) = 6*X(11539)-5*X(40329) = 5*X(19709)-4*X(42862) = 2*X(30258)+X(42329)

X(47383) lies on these lines: {2, 216}, {3, 648}, {6, 35941}, {30, 30258}, {76, 14570}, {95, 9308}, {99, 41614}, {338, 18573}, {376, 511}, {381, 14635}, {401, 5158}, {524, 35937}, {597, 40884}, {599, 1494}, {2966, 19127}, {3003, 40814}, {3545, 39530}, {3839, 44924}, {4558, 7782}, {5055, 10003}, {6179, 7512}, {7667, 41624}, {7760, 10323}, {8541, 11676}, {8719, 17813}, {8754, 37446}, {9307, 20775}, {9813, 35919}, {10602, 13479}, {11163, 31152}, {11257, 20975}, {11539, 40329}, {15080, 34211}, {19153, 35278}, {19188, 41244}, {19709, 42862}, {20477, 36794}, {22329, 44210}, {26895, 35360}, {36212, 44133}, {39575, 41678}, {42459, 45198}

X(47383) = midpoint of X(2) and X(3164)
X(47383) = reflection of X(i) in X(j) for these (i, j): (2, 216), (264, 2)
X(47383) = center of circle {{X(2), X(3164), X(37918)}}
X(47383) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (216, 3164, 264), (9308, 36751, 95), (14767, 40896, 264)

X(47384) = X(3)-TWO PARALLELS POINT OF-X(20)

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

X(47384) lies on these lines: {20, 6525}, {376, 5562}, {3164, 47381}, {3522, 6509}

X(47385) = X(3)-TWO PARALLELS POINT OF-X(98)

X(47385) lies on these lines: {98, 16083}, {511, 2966}, {685, 42671}, {2065, 46142}, {2710, 18858}, {34473, 39201}

X(47386) = X(4)-TWO PARALLELS POINT OF-X(7)

X(47386) lies on these lines: {7, 354}, {142, 41795}, {279, 1086}, {658, 12848}, {948, 41351}, {1996, 8545}, {3668, 30682}, {4569, 6604}, {4572, 42020}, {6173, 17079}, {10509, 11051}, {17093, 30379}

X(47386) = midpoint of X(7) and X(2898)
X(47386) = reflection of X(41795) in X(142)
X(47386) = barycentric product X(i)*X(j) for these {i, j}: {7, 1996}, {658, 30181}, {1088, 8545}
X(47386) = barycentric quotient X(i)/X(j) for these (i, j): (279, 34919), (1996, 8)
X(47386) = trilinear product X(i)*X(j) for these {i, j}: {57, 1996}, {279, 8545}, {934, 30181}, {1088, 37541}
X(47386) = trilinear quotient X(i)/X(j) for these (i, j): (1088, 34919), (1996, 9)
X(47386) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(14077)}} and {{A, B, C, X(7), X(8545)}}
X(47386) = X(1253)-isoconjugate-of-X(34919)
X(47386) = X(279)-reciprocal conjugate of-X(34919)
X(47386) = {X(7), X(36888)}-harmonic conjugate of X(47374)

X(47387) = X(4)-TWO PARALLELS POINT OF-X(9)

X(47387) lies on these lines: {4, 528}, {7, 8730}, {9, 55}, {100, 12848}, {218, 3939}, {329, 36976}, {405, 12437}, {518, 3428}, {527, 7580}, {954, 3419}, {1001, 3488}, {1005, 6172}, {1259, 10394}, {1376, 8255}, {1445, 16465}, {1998, 15348}, {2886, 6601}, {3303, 12625}, {3434, 7674}, {3871, 5766}, {4097, 8804}, {5175, 8543}, {5223, 40292}, {5440, 5728}, {5658, 38454}, {5696, 11507}, {5729, 6594}, {5856, 12831}, {6173, 37240}, {8069, 10398}, {11018, 16411}

X(47387) = midpoint of X(i) and X(j) for these {i, j}: {9, 2900}, {3434, 7674}
X(47387) = reflection of X(i) in X(j) for these (i, j): (55, 6600), (6601, 2886)
X(47387) = barycentric product X(i)*X(j) for these {i, j}: {9, 1998}, {644, 30199}
X(47387) = trilinear product X(55)*X(1998)
X(47387) = trilinear quotient X(1998)/X(7)
X(47387) = X(42014)-of-anti-Mandart-incircle triangle
X(47387) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(15733)}} and {{A, B, C, X(200), X(1998)}}

X(47388) = X(4)-TWO PARALLELS POINT OF-X(98)

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

X(47388) lies on these lines: {6, 32542}, {98, 230}, {182, 14382}, {287, 441}, {419, 685}, {511, 2966}, {523, 2065}, {525, 15407}, {2456, 39941}, {2698, 12176}, {5967, 14912}, {6036, 40428}, {6393, 6394}, {6530, 6531}, {6776, 34156}, {9474, 11676}, {9755, 40820}, {12215, 17932}, {14265, 41760}, {14355, 36820}, {14853, 35906}, {25406, 35912}, {34130, 36897}

X(47388) = isogonal conjugate of X(2967)
X(47388) = isotomic conjugate of the polar conjugate of X(41932)
X(47388) = polar conjugate of X(36426)
X(47388) = barycentric product X(i)*X(j) for these {i, j}: {3, 34536}, {69, 41932}, {98, 287}, {248, 290}, {293, 1821}, {336, 1910}
X(47388) = barycentric quotient X(i)/X(j) for these (i, j): (3, 36790), (4, 36426), (48, 23996), (69, 32458), (98, 297), (125, 35088)
X(47388) = trilinear product X(i)*X(j) for these {i, j}: {48, 34536}, {63, 41932}, {98, 293}, {248, 1821}, {287, 1910}, {336, 1976}
X(47388) = trilinear quotient X(i)/X(j) for these (i, j): (3, 23996), (48, 11672), (63, 36790), (92, 36426), (98, 240), (184, 42075)
X(47388) = trilinear pole of the line {248, 879}
X(47388) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(1513)}} and {{A, B, C, X(3), X(419)}}
X(47388) = Cevapoint of X(i) and X(j) for these (i, j): {98, 32545}, {125, 879}, {184, 248}
X(47388) = X(i)-cross conjugate of-X(j) for these (i, j): (125, 879), (184, 248), (647, 2966)
X(47388) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 36790), (125, 41167), (647, 35088)
X(47388) = X(98)-Hirst inverse of-X(41932)
X(47388) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 23996}, {19, 36790}, {48, 36426}, {92, 11672}
X(47388) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 36790), (4, 36426), (48, 23996), (69, 32458)
X(47388) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (98, 36899, 1513), (41932, 47382, 98)

X(47389) = X(4)-TWO PARALLELS POINT OF-X(99)

X(47389) lies on these lines: {99, 3566}, {249, 524}, {419, 18020}, {525, 4563}, {670, 18878}, {4176, 31614}, {4592, 22093}, {6064, 7340}, {9218, 14607}, {14382, 40050}, {30786, 34953}

X(47389) = reflection of X(99) in X(42398)
X(47389) = isogonal conjugate of X(2971)
X(47389) = isotomic conjugate of X(8754)
X(47389) = barycentric product X(i)*X(j) for these {i, j}: {3, 34537}, {63, 24037}, {69, 4590}, {99, 4563}, {184, 44168}, {249, 305}
X(47389) = barycentric quotient X(i)/X(j) for these (i, j): (3, 3124), (32, 42068), (63, 2643), (69, 115), (72, 21833), (76, 2970)
X(47389) = trilinear product X(i)*X(j) for these {i, j}: {3, 24037}, {48, 34537}, {63, 4590}, {69, 24041}, {77, 6064}, {78, 7340}
X(47389) = trilinear quotient X(i)/X(j) for these (i, j): (31, 42068), (48, 1084), (63, 3124), (69, 2643), (184, 4117), (212, 7063)
X(47389) = trilinear pole of the line {4558, 4563}
X(47389) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(35297)}} and {{A, B, C, X(3), X(419)}}
X(47389) = Cevapoint of X(i) and X(j) for these (i, j): {69, 4563}, {99, 7763}, {110, 193}, {184, 4558}
X(47389) = crosssum of X(1084) and X(42068)
X(47389) = X(i)-cross conjugate of-X(j) for these (i, j): (69, 4563), (184, 4558)
X(47389) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 3124), (69, 6388), (125, 22260), (206, 42068)
X(47389) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 3124}, {25, 2643}, {75, 42068}, {92, 1084}
X(47389) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 3124), (32, 42068), (63, 2643), (69, 115)
X(47389) = {X(6064), X(7340)}-harmonic conjugate of X(24037)

X(47390) = X(4)-TWO PARALLELS POINT OF-X(110)

X(47390) lies on these lines: {50, 3289}, {69, 4590}, {110, 924}, {125, 46087}, {186, 249}, {394, 33927}, {477, 16163}, {520, 4558}, {523, 34968}, {1092, 14385}, {3049, 32661}, {4575, 23226}, {5562, 14366}, {6368, 39193}, {11064, 47348}, {12028, 17702}, {13754, 44174}, {15958, 23181}, {17974, 34950}, {18020, 41203}, {22115, 23200}, {30542, 37638}

X(47390) = isogonal conjugate of X(2970)
X(47390) = isotomic conjugate of the polar conjugate of X(23357)
X(47390) = barycentric product X(i)*X(j) for these {i, j}: {3, 249}, {32, 47389}, {48, 24041}, {60, 44717}, {63, 1101}, {69, 23357}
X(47390) = barycentric quotient X(i)/X(j) for these (i, j): (3, 338), (32, 8754), (48, 1109), (50, 35235), (63, 23994), (69, 23962)
X(47390) = trilinear product X(i)*X(j) for these {i, j}: {3, 1101}, {47, 44174}, {48, 249}, {63, 23357}, {69, 23995}, {110, 4575}
X(47390) = trilinear quotient X(i)/X(j) for these (i, j): (3, 1109), (31, 8754), (47, 136), (48, 115), (63, 338), (69, 23994)
X(47390) = inverse Mimosa transform of X(2617)
X(47390) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(50)}} and {{A, B, C, X(4), X(924)}}
X(47390) = Cevapoint of X(i) and X(j) for these (i, j): {3, 23181}, {110, 34148}, {184, 32661}, {571, 1576}
X(47390) = crosssum of X(115) and X(8754)
X(47390) = X(249)-Ceva conjugate of-X(23357)
X(47390) = X(i)-cross conjugate of-X(j) for these (i, j): (3, 15958), (184, 32661), (577, 4558), (1147, 110)
X(47390) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 338), (125, 23105), (206, 8754), (1147, 125)
X(47390) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 1109}, {19, 338}, {25, 23994}, {75, 8754}, {92, 115}
X(47390) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 338), (32, 8754), (48, 1109), (50, 35235)

X(47391) = X(6)-TWO PARALLELS POINT OF-X(3)

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

X(47391) = 2*X(3)+X(155) = X(3)+2*X(1147) = 5*X(3)-2*X(7689) = X(3)-4*X(12038) = 4*X(3)-X(12163) = 5*X(3)+X(12164) = 7*X(3)+2*X(15083) = 5*X(3)+4*X(41597) = X(155)-4*X(1147) = 5*X(155)+4*X(7689) = X(155)+8*X(12038) = 2*X(155)+X(12163) = 5*X(155)-2*X(12164) = 7*X(155)-4*X(15083) = 5*X(155)-8*X(41597) = 5*X(1147)+X(7689) = X(1147)+2*X(12038) = 8*X(1147)+X(12163) = 10*X(1147)-X(12164) = 7*X(1147)-X(15083) = 5*X(1147)-2*X(41597)

X(47391) lies on these lines: {2, 12022}, {3, 49}, {4, 9820}, {5, 11425}, {6, 1511}, {20, 9707}, {22, 11464}, {24, 3060}, {25, 13352}, {26, 13391}, {30, 154}, {35, 1069}, {36, 3157}, {52, 3515}, {54, 9932}, {64, 11250}, {68, 140}, {69, 44201}, {110, 378}, {113, 44438}, {156, 1498}, {182, 8681}, {186, 1993}, {195, 37490}, {323, 10298}, {372, 8909}, {376, 6800}, {381, 5642}, {382, 5448}, {399, 12901}, {498, 18970}, {499, 12428}, {511, 11202}, {520, 44814}, {525, 8716}, {539, 5054}, {542, 10249}, {549, 599}, {567, 10601}, {568, 45780}, {569, 9937}, {578, 5943}, {631, 6193}, {912, 3576}, {1151, 10666}, {1152, 10665}, {1154, 18324}, {1192, 6102}, {1350, 7502}, {1351, 44102}, {1385, 9928}, {1470, 36059}, {1493, 15748}, {1495, 18534}, {1503, 44441}, {1593, 10539}, {1597, 8780}, {1614, 11413}, {1656, 7666}, {1658, 16266}, {1853, 18281}, {1899, 10257}, {1995, 15033}, {2070, 33586}, {2071, 9544}, {2072, 18396}, {2929, 34114}, {2935, 25487}, {2979, 44837}, {3053, 44221}, {3066, 12310}, {3147, 41587}, {3431, 15066}, {3516, 12162}, {3517, 5446}, {3520, 11441}, {3523, 11411}, {3526, 5449}, {3530, 9936}, {3541, 12134}, {3543, 35265}, {3546, 18925}, {3548, 6146}, {4846, 44241}, {5013, 23128}, {5020, 43586}, {5050, 5892}, {5094, 15115}, {5204, 7352}, {5217, 6238}, {5432, 10055}, {5433, 10071}, {5462, 11426}, {5498, 18356}, {5663, 10606}, {5690, 9933}, {5889, 32534}, {5890, 15035}, {5891, 6090}, {5895, 34350}, {5972, 18390}, {6030, 10323}, {6241, 9705}, {6417, 8912}, {6515, 35486}, {6640, 44076}, {6699, 39899}, {6759, 12085}, {6803, 12318}, {7387, 10282}, {7395, 12301}, {7399, 23307}, {7484, 37513}, {7488, 37486}, {7503, 9938}, {7506, 10982}, {7514, 17811}, {7516, 10610}, {7517, 37495}, {7526, 15060}, {7529, 11424}, {7547, 12278}, {7575, 11477}, {7577, 12383}, {7592, 9545}, {8057, 45681}, {8567, 10226}, {8981, 19062}, {9019, 15577}, {9306, 9818}, {9706, 10574}, {9714, 45186}, {9715, 10625}, {9716, 37952}, {9730, 11402}, {9786, 12161}, {9833, 23335}, {9896, 31423}, {9925, 10541}, {10116, 26944}, {10127, 14561}, {10269, 47371}, {10564, 21312}, {10620, 35495}, {10661, 11481}, {10662, 11480}, {11064, 18531}, {11412, 38444}, {11422, 15020}, {11423, 43597}, {11438, 34986}, {11442, 37118}, {11459, 43572}, {11585, 19467}, {11649, 34787}, {11935, 12893}, {12017, 19588}, {12082, 26881}, {12083, 37477}, {12106, 13451}, {12111, 35477}, {12160, 15750}, {12166, 13336}, {12412, 34778}, {12584, 45025}, {12824, 15463}, {12902, 33547}, {13160, 20302}, {13321, 36749}, {13966, 19061}, {14156, 30771}, {14516, 37119}, {14574, 14703}, {14585, 23115}, {14790, 34782}, {14915, 32063}, {15041, 17853}, {15068, 18570}, {15069, 18580}, {15317, 16867}, {15472, 20771}, {15534, 18579}, {15646, 37487}, {15720, 20191}, {15760, 32123}, {16196, 31804}, {16238, 39571}, {16665, 45788}, {17809, 34966}, {17824, 46939}, {17845, 18569}, {18405, 30522}, {18420, 23292}, {18533, 37645}, {19125, 37511}, {19458, 32046}, {23336, 32140}, {25739, 30744}, {26869, 38793}, {26958, 44452}, {31236, 41171}, {31884, 34513}, {34117, 45171}, {34153, 44263}, {34609, 44407}, {35243, 37480}, {35268, 36987}, {35603, 45172}, {36753, 43809}, {37935, 41588}, {38794, 46085}, {39913, 40349}, {43118, 44198}, {43119, 44197}, {44276, 46817}

X(47391) = midpoint of X(i) and X(j) for these {i, j}: {3, 3167}, {154, 37497}
X(47391) = reflection of X(i) in X(j) for these (i, j): (155, 3167), (1853, 18281), (3167, 1147), (14070, 11202), (14852, 2)
X(47391) = isogonal conjugate of the polar conjugate of X(37645)
X(47391) = barycentric product X(i)*X(j) for these {i, j}: {3, 37645}, {394, 18533}
X(47391) = barycentric quotient X(577)/X(34801)
X(47391) = trilinear product X(i)*X(j) for these {i, j}: {48, 37645}, {255, 18533}
X(47391) = trilinear quotient X(255)/X(34801)
X(47391) = perspector of the circumconic {{A, B, C, X(4558), X(10420)}}
X(47391) = inverse of X(11472) in Stammler hyperbola
X(47391) = inverse of X(35259) in Thomson-Gibert-Moses hyperbola
X(47391) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(14910)}} and {{A, B, C, X(4), X(12163)}}
X(47391) = X(1147)-Dao conjugate of X(34801)
X(47391) = X(158)-isoconjugate-of-X(34801)
X(47391) = X(577)-reciprocal conjugate of-X(34801)
X(47391) = X(155)-of-orthocentroidal triangle
X(47391) = X(3167)-of-anti-X3-ABC reflections triangle
X(47391) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 49, 1181), (3, 155, 12163), (3, 1147, 155), (3, 9703, 18445), (3, 12164, 7689), (3, 18445, 10605), (3, 19347, 40647), (3, 22115, 394), (5, 12118, 12293), (22, 43574, 37483), (24, 34148, 36747), (25, 13352, 44413), (26, 32171, 17821), (54, 17928, 36752), (110, 378, 18451), (156, 12084, 1498), (186, 1993, 37489), (378, 18451, 11472), (631, 6193, 12359), (1092, 13367, 3), (1147, 7689, 41597), (1147, 12038, 3), (1511, 5504, 2931), (7689, 41597, 12164), (9545, 22467, 7592), (9927, 43839, 1656), (10282, 13346, 7387), (11250, 32139, 64), (11449, 34148, 24), (11464, 43574, 22), (12161, 37814, 9786), (12164, 41597, 155), (17821, 37498, 26), (18570, 40111, 15068), (19357, 35602, 3)

X(47392) = X(6)-TWO PARALLELS POINT OF-X(4)

X(47392) lies on these lines: {4, 51}, {6, 6529}, {25, 41372}, {30, 15466}, {107, 378}, {133, 18388}, {264, 339}, {324, 3839}, {393, 5309}, {403, 46259}, {648, 18451}, {1105, 6642}, {1596, 6530}, {1598, 8884}, {1947, 18540}, {3088, 6523}, {3091, 40684}, {3531, 8795}, {3543, 46106}, {5198, 41365}, {6330, 37073}, {6623, 10002}, {7576, 16263}, {10311, 41368}, {13570, 39530}, {15305, 35360}, {41760, 42854}

X(47392) = midpoint of X(4) and X(3168)
X(47392) = polar conjugate of the isogonal conjugate of X(40138)
X(47392) = barycentric product X(i)*X(j) for these {i, j}: {264, 40138}, {376, 2052}, {393, 44133}
X(47392) = barycentric quotient X(i)/X(j) for these (i, j): (376, 394), (393, 3426), (1515, 44436)
X(47392) = trilinear product X(i)*X(j) for these {i, j}: {92, 40138}, {158, 376}, {823, 9209}, {1096, 44133}
X(47392) = trilinear quotient X(i)/X(j) for these (i, j): (158, 3426), (376, 255)
X(47392) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(11381)}} and {{A, B, C, X(4), X(376)}}
X(47392) = X(255)-isoconjugate-of-X(3426)
X(47392) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (376, 394), (393, 3426)
X(47392) = X(3168)-of-Euler triangle
X(47392) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 1075, 11381), (4, 6761, 11550), (4, 14249, 1093)

X(47393) = X(6)-TWO PARALLELS POINT OF-X(7)

X(47394) = X(6)-TWO PARALLELS POINT OF-X(11)

X(47394) lies on these lines: {514, 12736}, {784, 10006}, {2804, 6332}, {21132, 24443}

X(47395) = X(6)-TWO PARALLELS POINT OF-X(98)

X(47395) lies on these lines: {98, 237}, {187, 41932}, {511, 2966}, {842, 18858}, {14355, 41173}, {39291, 47049}

X(47396) = X(6)-TWO PARALLELS POINT OF-X(111)

X(47396) = midpoint of X(111) and X(41404)
X(47396) = inverse of X(15899) in Schoute circle

X(47397) = X(15)-TWO PARALLELS POINT OF-X(16)

X(47397) lies on these lines: {16, 1511}, {110, 39554}, {187, 10658}, {2076, 19140}, {5663, 30559}, {13858, 36760}, {19781, 36209}

X(47398) = X(16)-TWO PARALLELS POINT OF-X(15)

X(47398) lies on these lines: {15, 1511}, {110, 39555}, {187, 10657}, {2076, 19140}, {5663, 30560}, {13859, 36759}, {19780, 36208}

X(47399) = X(11)X(523)-INTERCEPT OF THE EULER LINE

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

X(47399) = 3 X[2] + X[36175], X[1325] + 3 X[37375], 3 X[17533] - X[30447], X[1290] - 5 X[31272], 3 X[23513] - X[42422], 3 X[38693] + X[44982]

X(47399) lies on these lines: {2, 3}, {11, 523}, {125, 6003}, {496, 13869}, {1290, 31272}, {2677, 35057}, {3258, 42425}, {7741, 47270}, {10593, 47272}, {10738, 46635}, {12030, 34172}, {23513, 42422}, {37720, 47274}, {38693, 44982}

X(47399) = midpoint of X(i) and X(j) for these {i,j}: {4, 46618}, {11, 5520}, {10738, 46635}, {12030, 34172}, {36167, 36175}
X(47399) = complement of X(36167)
X(47399) = nine-point-circle inverse of X(867)
X(47399) = polar-circle-inverse of X(4242)
X(47399) = orthoptic-circle-of-Steiner-inellipse-inverse of X(7427)
X(47399) = X(12030)-Ceva conjugate of X(523)
X(47399) = crossdifference of every pair of points on line {647, 1983}
X(47399) = orthogonal projection of X(11) on the Euler line
X(47399) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36175, 36167}, {3, 4, 33662}, {5, 3109, 47400}, {1312, 1313, 867}, {3140, 37986, 14120}

X(47400) = X(12)X(523)-INTERCEPT OF THE EULER LINE

X(47400) = polar-circle-inverse of X(17515)
X(47400) = crossdifference of every pair of points on line {647, 4282}
X(47400) = orthogonal projection of X(12) on the Euler line
X(47400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 3109, 47399}, {442, 30447, 36155}, {30447, 37982, 36195}

X(47401) = X(35)X(523)-INTERCEPT OF THE EULER LINE

X(47401) lies on these lines: {2, 3}, {35, 523}, {55, 13869}, {2800, 11709}, {5010, 47270}, {5217, 47272}, {37621, 46636}

X(47401) = orthogonal projection of X(35) on the Euler line
X(47401) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3109, 47402}, {21, 36167, 36155}

X(47402) = X(36)X(523)-INTERCEPT OF THE EULER LINE

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

X(47402) lies on these lines: {2, 3}, {36, 523}, {56, 13869}, {5204, 47272}, {5520, 15326}, {7280, 47270}, {22765, 46635}

X(47402) = midpoint of X(i) and X(j) for these {i,j}: {1325, 36167}, {5520, 15326}, {6905, 46618}, {22765, 46635}
X(47402) = circumcircle-inverse of X(13744)
X(47402) = orthogonal projection of X(36) on the Euler line
X(47402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3109, 47401}, {1113, 1114, 13744}, {1325, 13587, 36167}

X(47403) = X(42)X(523)-INTERCEPT OF THE EULER LINE

X(47403) lies on these lines: {2, 3}, {42, 523}, {43, 47270}, {1213, 46407}, {3240, 47272}, {13869, 17018}, {42042, 47274}, {42043, 47273}

X(47403) = circumcircle-inverse of X(21522)
X(47403) = crossdifference of every pair of points on line {647, 14964}
X(47403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1113, 1114, 21522}

X(47404) = X(43)X(523)-INTERCEPT OF THE EULER LINE

X(47404) lies on these lines: {2, 3}, {42, 13869}, {43, 523}, {899, 47272}, {16569, 47270}, {36634, 47273}, {42043, 47274}

Let BCC denote the bicevian conic of X(3) and X(6), which is given by the equation

b^4*c^4*(a^2 + b^2 - c^2)*(a^2 - b^2 + c^2)*x^2 - 2*a^2*b^2*c^6*(a^2 + b^2 - c^2)*x*y - a^4*c^4*(a^2 - b^2 - c^2)*(a^2 + b^2 - c^2)*y^2 - 2*a^2*b^6*c^2*(a^2 - b^2 + c^2)*x*z + 2*a^6*b^2*c^2*(a^2 - b^2 - c^2)*y*z - a^4*b^4*(a^2 - b^2 - c^2)*(a^2 - b^2 + c^2)*z^2 = 0.

This conic passes through the points X(i) for these i: 3269, 7117, 9475, 15166, 15167, 20728, 20830, 20975, 22084, 22428. Bernard Gibert has noted that if P is a point on the line at infinity, then the X(3)-Ceva conjugate of the barycentric product X(6)*P is on BCC. (Equivalently, the X(6)-Ceva conjugate of X(3)*P is on BCC.) The line of P and the X(3)-Ceva conjugate of X(6)*P is tangent to the Steiner inellipse, which is bitangent to BCC. Moreover, if X is on the nine-point circle, then the isogonal conjugate of the polar conjugate of X is on BCC.

X(47405) = BARYCENTRIC PRODUCT X(3)*X(113)

X(47405) lies on lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 18877}, {6, 1511}, {110, 8749}, {184, 5158}, {216, 3269}, {520, 9155}, {577, 40082}, {1625, 47228}, {1636, 1637}, {2420, 15469}, {2871, 19153}, {3003, 13754}, {5654, 34288}, {6128, 17702}, {7117, 14597}, {8553, 46375}, {8681, 36213}, {9696, 46432}, {12168, 40354}, {15035, 15291}, {23090, 35069}

X(47405) = isogonal conjugate of the polar conjugate of X(113)
X(47405) = tripolar centroid of X(15329)
X(47405) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 3284}, {110, 21731}, {32661, 1636}, {34834, 34333}, {36789, 40948}
X(47405) = X(i)-isoconjugate of X(j) for these (i,j): {19, 40423}, {75, 40388}, {92, 10419}, {1300, 2349}, {2394, 36114}, {2986, 36119}, {16080, 36053}
X(47405) = crosspoint of X(i) and X(j) for these (i,j): {3, 11064}, {6, 3003}, {1511, 34834}, {3580, 39170}
X(47405) = crosssum of X(i) and X(j) for these (i,j): {2, 2986}, {4, 8749}, {10419, 40388}, {14910, 38936}
X(47405) = crossdifference of every pair of points on line {74, 1300}
X(47405) = barycentric product X(i)*X(j) for these {i,j}: {3, 113}, {30, 13754}, {686, 2407}, {1511, 39170}, {1636, 16237}, {2315, 14206}, {2420, 6334}, {3003, 11064}, {3284, 3580}, {5504, 34104}, {9033, 15329}, {14264, 16163}, {15454, 34333}
X(47405) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 40423}, {32, 40388}, {113, 264}, {184, 10419}, {686, 2394}, {1495, 1300}, {1636, 15421}, {2315, 2349}, {2420, 687}, {3003, 16080}, {3284, 2986}, {9409, 15328}, {11064, 40832}, {13754, 1494}, {15329, 16077}, {21731, 18808}, {34104, 44138}

X(47406) = BARYCENTRIC PRODUCT X(3)*X(114)

X(47406) lies lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 248}, {6, 2987}, {39, 46094}, {99, 6531}, {194, 5976}, {216, 6467}, {232, 15143}, {417, 22401}, {570, 23642}, {577, 20819}, {684, 2491}, {1971, 37183}, {2079, 5013}, {2482, 23976}, {3053, 5889}, {3124, 23181}, {3265, 45672}, {3289, 36212}, {6503, 42295}, {7117, 22345}, {7789, 26166}, {9737, 10311}, {13357, 42548}, {14060, 36751}, {14961, 39000}, {14966, 40083}, {15411, 35068}, {19599, 38382}, {22052, 22078}, {22054, 22084}, {22361, 22447}, {23217, 38356}, {33813, 35906}, {36214, 43718}

X(47406) = isogonal conjugate of the polar conjugate of X(114)
X(47406) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 3289}, {99, 42663}, {4558, 684}
X(47406) = X(i)-isoconjugate of X(j) for these (i,j): {19, 40428}, {92, 2065}, {1821, 3563}, {1910, 35142}, {2395, 36105}, {2987, 36120}, {6531, 8773}, {16081, 36051}
X(47406) = crosspoint of X(i) and X(j) for these (i,j): {3, 36212}, {6, 230}, {249, 4230}
X(47406) = crosssum of X(i) and X(j) for these (i,j): {2, 2987}, {4, 6531}, {115, 879}
X(47406) = crossdifference of every pair of points on line {98, 3563}
X(47406) = barycentric product X(i)*X(j) for these {i,j}: {3, 114}, {63, 17462}, {230, 36212}, {249, 41181}, {511, 3564}, {684, 4226}, {1692, 6393}, {2974, 34157}
X(47406) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 40428}, {114, 264}, {184, 2065}, {230, 16081}, {237, 3563}, {511, 35142}, {1692, 6531}, {3289, 2987}, {3564, 290}, {4226, 22456}, {8772, 36120}, {14966, 32697}, {17462, 92}, {23997, 36105}, {36212, 8781}, {39469, 35364}, {41181, 338}
X(47406) = {X(9155),X(9475)}-harmonic conjugate of X(11672)

X(47407) = BARYCENTRIC PRODUCT X(3)*X(118)

X(47407) lies lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 32657}, {6, 32656}, {41, 2594}, {73, 7117}, {213, 40591}, {216, 22084}, {676, 9502}, {20970, 46095}, {20975, 44093}, {22070, 40944}

X(47407) = isogonal conjugate of the polar conjugate of X(118)
X(47407) = X(i)-isoconjugate of X(j) for these (i,j): {92, 15380}, {917, 36101}, {2400, 36107}, {2989, 36122}
X(47407) = crosspoint of X(i) and X(j) for these (i,j): {3, 26006}, {6, 8608}
X(47407) = crosssum of X(2) and X(2989)
X(47407) = crossdifference of every pair of points on line {103, 917}
X(47407) = barycentric product X(i)*X(j) for these {i,j}: {3, 118}, {516, 916}, {2253, 30807}, {8608, 26006}
X(47407) = barycentric quotient X(i)/X(j) for these {i,j}: {118, 264}, {184, 15380}, {916, 18025}, {2253, 36101}

X(47408) = BARYCENTRIC PRODUCT X(3)*X(119)

X(47408) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 14578}, {6, 906}, {37, 6506}, {42, 37993}, {43, 8557}, {48, 216}, {577, 22055}, {1108, 1145}, {1737, 8609}, {1769, 3310}, {3169, 3554}, {3269, 18591}, {20776, 41215}, {22053, 22069}, {22350, 38353}, {23986, 35069}

X(47408) = isogonal conjugate of the polar conjugate of X(119)
X(47408) = X(i)-isoconjugate of X(j) for these (i,j): {92, 15381}, {104, 37203}, {909, 46133}, {913, 18816}, {915, 34234}, {2401, 36106}, {2990, 36123}, {16082, 36052}
X(47408) = crosspoint of X(6) and X(8609)
X(47408) = crosssum of X(2) and X(2990)
X(47408) = crossdifference of every pair of points on line {104, 915}
X(47408) = barycentric product X(i)*X(j) for these {i,j}: {3, 119}, {100, 42769}, {517, 912}, {908, 2252}, {914, 2183}, {1737, 22350}, {34332, 39173}
X(47408) = barycentric quotient X(i)/X(j) for these {i,j}: {119, 264}, {184, 15381}, {517, 46133}, {912, 18816}, {2183, 37203}, {2252, 34234}, {8609, 16082}, {42769, 693}

X(47409) = BARYCENTRIC PRODUCT X(3)*X(122)

X(47409) lies lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 112}, {115, 1650}, {122, 1562}, {417, 22401}, {574, 20232}, {577, 40082}, {1294, 6529}, {1625, 40948}, {1636, 2972}, {2971, 35236}, {3119, 16573}, {6760, 13509}, {8779, 12096}, {15291, 15905}, {17434, 35579}, {22084, 35072}, {28783, 41489}

X(47409) = isogonal conjugate of the polar conjugate of X(122)
X(47409) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 42658}, {6, 32320}, {1073, 520}, {15466, 8057}, {18890, 17434}, {28783, 647}, {34426, 512}, {34861, 525}, {46353, 44705}
X(47409) = X(i)-isoconjugate of X(j) for these (i,j): {19, 44181}, {92, 15384}, {459, 24000}, {823, 1301}, {1073, 24021}, {2184, 32230}, {19611, 23590}, {19614, 34538}, {23999, 41489}, {24022, 34403}, {36126, 46639}
X(47409) = crosspoint of X(i) and X(j) for these (i,j): {6, 6587}, {520, 1073}, {525, 15318}, {8057, 15466}, {20580, 35602}
X(47409) = crosssum of X(i) and X(j) for these (i,j): {2, 46639}, {4, 6529}, {107, 1249}, {112, 6759}, {648, 46927}, {1301, 14642}
X(47409) = crossdifference of every pair of points on line {107, 1301}
X(47409) = barycentric product X(i)*X(j) for these {i,j}: {3, 122}, {20, 2972}, {125, 35602}, {204, 24020}, {394, 1562}, {520, 8057}, {647, 20580}, {1073, 39020}, {3172, 23974}, {3265, 42658}, {3269, 37669}, {14615, 34980}, {15466, 35071}, {15526, 15905}, {18750, 37754}
X(47409) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 44181}, {122, 264}, {154, 32230}, {184, 15384}, {204, 24021}, {1249, 34538}, {1562, 2052}, {2972, 253}, {3172, 23590}, {3269, 459}, {6587, 15352}, {8057, 6528}, {15905, 23582}, {20580, 6331}, {20975, 6526}, {32320, 46639}, {34980, 64}, {35071, 1073}, {35602, 18020}, {37754, 2184}, {39020, 15466}, {39201, 1301}, {41219, 8798}, {42080, 19614}, {42658, 107}
X(47409) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {122, 39020, 1562}, {3269, 35071, 2972}

X(47410) = BARYCENTRIC PRODUCT X(3)*X(123)

X(47410) lies lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 1415}, {216, 2267}, {441, 45270}, {577, 22055}, {650, 40616}, {1015, 35014}, {1364, 3269}, {2968, 11998}, {7004, 7117}, {9475, 40946}, {20728, 22401}, {21859, 38554}, {22084, 38344}

X(47410) = isogonal conjugate of the polar conjugate of X(123)
X(47410) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 36054}, {23983, 1364}, {34277, 521}
X(47410) = X(i)-isoconjugate of X(j) for these (i,j): {92, 15385}, {653, 40097}, {7128, 43742}, {24033, 34277}, {36127, 46640}
X(47410) = crosspoint of X(i) and X(j) for these (i,j): {6, 6588}, {521, 34277}
X(47410) = crosssum of X(i) and X(j) for these (i,j): {2, 46640}, {108, 478}
X(47410) = crossdifference of every pair of points on line {108, 40097}
X(47410) = barycentric product X(i)*X(j) for these {i,j}: {3, 123}, {478, 23983}, {1364, 3436}, {21147, 24031}, {22132, 26932}
X(47410) = barycentric quotient X(i)/X(j) for these {i,j}: {123, 264}, {184, 15385}, {478, 23984}, {1364, 8048}, {1946, 40097}, {3270, 43742}, {21147, 24032}, {22132, 46102}, {35072, 34277}, {36054, 46640}

X(47411) = BARYCENTRIC PRODUCT X(3)*X(124)

X(47411) lies lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 32660}, {6, 32653}, {11, 1146}, {48, 4271}, {73, 1362}, {102, 32674}, {284, 40081}, {652, 35072}, {1015, 38983}, {1364, 7117}, {2638, 3248}, {3270, 20975}, {11998, 20974}, {17419, 17421}, {20277, 21321}, {20727, 20728}, {20824, 20829}, {22070, 40944}, {22071, 22428}, {22073, 22074}, {22361, 22447}

X(47411) = isogonal conjugate of the isotomic conjugate of X(40626)
X(47411) = isogonal conjugate of the polar conjugate of X(124)
X(47411) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 652}, {2051, 656}
X(47411) = X(i)-isoconjugate of X(j) for these (i,j): {92, 15386}, {108, 44765}, {651, 26704}, {653, 36050}, {2217, 46102}, {2406, 36108}, {2995, 7115}, {5379, 40160}, {7012, 13478}, {7128, 10570}, {18026, 32653}, {24035, 35183}
X(47411) = crosspoint of X(i) and X(j) for these (i,j): {3, 6332}, {6, 6589}, {124, 40626}, {3737, 42467}
X(47411) = crosssum of X(i) and X(j) for these (i,j): {2, 44765}, {4, 32674}, {1766, 4551}
X(47411) = crossdifference of every pair of points on line {109, 23987}
X(47411) = barycentric product X(i)*X(j) for these {i,j}: {1, 34588}, {3, 124}, {6, 40626}, {63, 38345}, {521, 21189}, {573, 26932}, {1364, 17555}, {2968, 10571}, {3185, 17880}, {3869, 7004}, {4417, 7117}, {4858, 22134}, {6332, 6589}, {8611, 16754}, {17080, 34591}, {17219, 22276}
X(47411) = barycentric quotient X(i)/X(j) for these {i,j}: {124, 264}, {184, 15386}, {573, 46102}, {652, 44765}, {663, 26704}, {1946, 36050}, {3185, 7012}, {3270, 10570}, {6589, 653}, {7004, 2995}, {7117, 13478}, {21189, 18026}, {22134, 4564}, {34588, 75}, {38345, 92}, {40626, 76}
X(47411) = {X(1364),X(7117)}-harmonic conjugate of X(38344)

X(47412) = BARYCENTRIC PRODUCT X(3)*X(126)

X(47412) lies lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 895}, {351, 690}, {574, 20859}, {1296, 8753}, {2936, 5191}, {3269, 3917}, {5467, 40078}, {7117, 22060}, {8591, 44420}, {9486, 15268}, {14961, 22087}, {15390, 39689}, {20735, 22414}, {22065, 22084}

X(47412) = isogonal conjugate of the polar conjugate of X(126)
X(47412) = X(6)-Ceva conjugate of X(3292)
X(47412) = X(i)-isoconjugate of X(j) for these (i,j): {19, 44182}, {92, 15387}, {897, 2374}, {36128, 41909}
X(47412) = crosspoint of X(i) and X(j) for these (i,j): {3, 6390}, {6, 3291}
X(47412) = crosssum of X(i) and X(j) for these (i,j): {2, 41909}, {4, 8753}, {5466, 8754}
X(47412) = crossdifference of every pair of points on line {111, 2374}
X(47412) = barycentric product X(i)*X(j) for these {i,j}: {3, 126}, {63, 17466}, {524, 8681}, {3291, 6390}, {3292, 47286}, {4563, 21905}, {11634, 14417}
vbarycentric quotient X(i)/X(j) for these {i,j}: {3, 44182}, {126, 264}, {184, 15387}, {187, 2374}, {3291, 17983}, {3292, 41909}, {8681, 671}, {17466, 92}, {21905, 2501}, {47286, 46111}

X(47413) = BARYCENTRIC PRODUCT X(3)*X(127)

X(47413) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {2, 46151}, {3, 1177}, {6, 46164}, {122, 125}, {216, 9475}, {338, 3150}, {339, 7668}, {441, 3001}, {577, 20819}, {1084, 35071}, {1297, 32713}, {2967, 23583}, {5158, 13409}, {6389, 39080}, {6509, 38998}, {9019, 44894}, {11574, 36213}, {14376, 23327}, {14396, 38356}, {16595, 38989}, {23300, 41168}, {23347, 38624}

X(47413) = midpoint of X(6) and X(46164)
X(47413) = isotomic conjugate of the polar conjugate of X(38356)
X(47413) = isogonal conjugate of the polar conjugate of X(127)
X(47413) = complement of X(46151)
X(47413) = X(i)-complementary conjugate of X(j) for these (i,j): {48, 23285}, {82, 520}, {255, 3005}, {520, 21249}, {822, 6292}, {827, 23998}, {1176, 8062}, {1799, 21259}, {2632, 46654}, {4580, 20305}, {10547, 16612}, {18105, 24005}, {24018, 21248}, {28724, 4369}, {34055, 30476}, {34072, 23583}, {39201, 16587}, {46289, 6587}
X(47413) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 520}, {22, 8673}, {127, 38356}, {18018, 525}, {34129, 3569}, {34427, 512}, {36793, 3269}
X(47413) = X(i)-isoconjugate of X(j) for these (i,j): {19, 44183}, {66, 24000}, {92, 15388}, {162, 1289}, {2156, 23582}, {2353, 23999}, {24019, 44766}, {24024, 46967}, {41937, 46244}
X(47413) = crosspoint of X(i) and X(j) for these (i,j): {3, 3265}, {6, 2485}, {22, 8673}, {523, 34207}, {525, 18018}
X(47413) = crosssum of X(i) and X(j) for these (i,j): {2, 44766}, {4, 32713}, {66, 1289}, {110, 1370}, {112, 206}
X(47413) = crossdifference of every pair of points on line {112, 1289}
X(47413) = X(2)-line conjugate of X(46151)
X(47413) = barycentric product X(i)*X(j) for these {i,j}: {3, 127}, {22, 15526}, {69, 38356}, {72, 18187}, {125, 20806}, {206, 36793}, {315, 3269}, {339, 10316}, {520, 33294}, {525, 8673}, {1760, 2632}, {2172, 17879}, {2485, 3265}, {2972, 17907}, {4456, 17216}, {4611, 5489}, {14396, 34767}, {20975, 34254}
X(47413) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 44183}, {22, 23582}, {125, 43678}, {127, 264}, {184, 15388}, {206, 23964}, {520, 44766}, {647, 1289}, {1760, 23999}, {2172, 24000}, {2485, 107}, {2972, 14376}, {3269, 66}, {8673, 648}, {8743, 32230}, {10316, 250}, {14396, 4240}, {15526, 18018}, {17879, 46244}, {18187, 286}, {20806, 18020}, {20968, 41937}, {20975, 13854}, {33294, 6528}, {36793, 40421}, {38356, 4}
X(47413) = {X(2972),X(20975)}-harmonic conjugate of X(15526)

X(47414) = BARYCENTRIC PRODUCT X(3)*X(3258)

X(47414) lies lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 32662}, {6, 32640}, {50, 186}, {115, 46437}, {187, 9408}, {647, 3269}, {1648, 39021}, {1650, 14401}, {2088, 16186}, {14961, 39000}, {20975, 34982}, {38610, 41392}

X(47414) = circumcircle-of-inner-Napoleon-triangle-inverse of X(34094)
X(47414) = isogonal conjugate of the polar conjugate of X(3258)
X(47414) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 9409}, {3447, 1495}, {34178, 512}
X(47414) = X(i)-isoconjugate of X(j) for these (i,j): {92, 15395}, {162, 39290}, {1304, 32680}, {2410, 36117}, {11079, 23999}, {15459, 36061}, {16077, 32678}, {35139, 36131}, {36034, 46456}, {36119, 39295}, {36129, 44769}, {40355, 46254}
X(47414) = crosspoint of X(i) and X(j) for these (i,j): {3, 8552}, {6, 1637}, {647, 3284}, {1511, 5664}
X(47414) = crosssum of X(i) and X(j) for these (i,j): {2, 44769}, {265, 41392}, {648, 16080}
X(47414) = crossdifference of every pair of points on line {476, 1304}
X(47414) = barycentric product X(i)*X(j) for these {i,j}: {3, 3258}, {30, 16186}, {125, 1511}, {186, 1650}, {399, 19223}, {526, 9033}, {647, 5664}, {1636, 44427}, {1637, 8552}, {2088, 11064}, {2631, 32679}, {2632, 35201}, {3268, 9409}, {3269, 14920}, {6148, 20975}, {6739, 22094}, {13212, 34210}, {14398, 45792}, {15526, 39176}, {41077, 47230}
X(47414) = barycentric quotient X(i)/X(j) for these {i,j}: {184, 15395}, {186, 42308}, {526, 16077}, {647, 39290}, {1511, 18020}, {1637, 46456}, {1650, 328}, {2088, 16080}, {2631, 32680}, {3258, 264}, {3284, 39295}, {5664, 6331}, {9033, 35139}, {9409, 476}, {14270, 1304}, {16186, 1494}, {19223, 40705}, {20975, 5627}, {35201, 23999}, {39176, 23582}, {47230, 15459}

X(47415) = BARYCENTRIC PRODUCT X(3)*X(5099)

X(47415) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {50, 15140}, {187, 23200}, {647, 20975}, {1648, 1649}, {3003, 9475}, {3049, 3269}, {10317, 22151}, {14961, 22087}, {20825, 22428}

X(47415) = isogonal conjugate of the polar conjugate of X(5099)
X(47415) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 42659}, {22258, 512}
X(47415) = X(935)-isoconjugate of X(36085)
X(47415) = crosspoint of X(i) and X(j) for these (i,j): {3, 14417}, {6, 2492}, {187, 647}, {6593, 18311}
X(47415) = crosssum of X(i) and X(j) for these (i,j): {2, 17708}, {648, 671}
X(47415) = crossdifference of every pair of points on line {691, 935}
X(47415) = barycentric product X(i)*X(j) for these {i,j}: {3, 5099}, {125, 6593}, {647, 18311}, {690, 9517}, {1648, 22151}, {2492, 14417}, {7664, 20975}, {21906, 37804}, {32313, 35909}, {35522, 42659}
X(47415) = barycentric quotient X(i)/X(j) for these {i,j}: {351, 935}, {1648, 46105}, {5099, 264}, {6593, 18020}, {9517, 892}, {18311, 6331}, {20975, 10415}, {21906, 8791}, {42659, 691}

X(47416) = BARYCENTRIC PRODUCT X(3)*X(45162)

X(47416) lies on these lines: {71, 20975}, {2269, 23444}, {3269, 20727}, {4010, 4839}, {7117, 20750}, {20730, 22073}, {20733, 20736}, {20821, 20825}

X(47416) = isogonal conjugate of the polar conjugate of X(45162)
X(47416) = barycentric product X(i)*X(j) for these {i,j}: {3, 45162}, {1790, 20658}
X(47416) = barycentric quotient X(45162)/X(264)

X(47417) = BARYCENTRIC PRODUCT X(3)*X(31845)

X(47417) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {71, 3269}, {228, 20975}, {2610, 21828}, {7117, 18591}, {14547, 20966}, {22060, 22084}, {22073, 22074}, {22399, 22433}

X(47417) = isogonal conjugate of the polar conjugate of X(31845)
X(47417) = X(24624)-isoconjugate of X(39439)
X(47417) = crossdifference of every pair of points on line {759, 39439}
X(47417) = barycentric product X(3)*X(31845)
X(47417) = barycentric quotient X(i)/X(j) for these {i,j}: {3724, 39439}, {31845, 264}

X(47418) = BARYCENTRIC PRODUCT X(3)*X(2679)

X(47418) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {6, 2966}, {1691, 40077}, {2021, 9419}, {2086, 11183}, {2524, 3269}, {3049, 20975}, {3124, 38368}, {3289, 36212}, {9427, 14113}, {9475, 32748}, {14602, 18902}, {20825, 20830}

X(47418) = isogonal conjugate of the polar conjugate of X(2679)
X(47418) = X(i)-Ceva conjugate of X(j) for these (i,j): {3224, 3569}, {9217, 237}, {32542, 5027}, {34130, 669}
X(47418) = X(i)-isoconjugate of X(j) for these (i,j): {811, 39291}, {1581, 41174}, {22456, 37134}, {36120, 39292}, {36897, 46254}
X(47418) = crosspoint of X(i) and X(j) for these (i,j): {3, 24284}, {6, 2491}, {3049, 3289}
X(47418) = crosssum of X(i) and X(j) for these (i,j): {2, 43187}, {6331, 16081}
X(47418) = crossdifference of every pair of points on line {805, 877}
X(47418) = barycentric product X(i)*X(j) for these {i,j}: {3, 2679}, {684, 5027}, {804, 39469}, {1691, 41172}, {2086, 36212}, {2491, 24284}, {20975, 36213}, {32542, 38974}
X(47418) = barycentric quotient X(i)/X(j) for these {i,j}: {1691, 41174}, {2086, 16081}, {2679, 264}, {3049, 39291}, {3289, 39292}, {5027, 22456}, {23216, 34238}, {39469, 18829}, {41172, 18896}

X(47419) = X(6)-CEVA CONJUGATE OF X(22384)

X(47419) lies on these lines: {4124, 4448}, {7117, 22090}, {20728, 20729}, {20730, 22428}, {20778, 22350}, {20821, 20828}, {20822, 22414}, {22084, 22095}

X(47420) = BARYCENTRIC PRODUCT X(3)*X(3259)

X(47420) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {6, 32641}, {810, 20975}, {1404, 2251}, {1647, 2087}, {7117, 22383}, {8776, 35505}, {20728, 22082}, {22059, 22414}, {22084, 22090}, {22350, 38353}

X(47420) = isogonal conjugate of the polar conjugate of X(3259)
X(47420) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 23220}, {6, 22086}, {34182, 667}
X(47420) = X(i)-isoconjugate of X(j) for these (i,j): {1309, 3257}, {1320, 39294}, {4582, 36110}, {5376, 36123}, {9268, 16082}
X(47420) = crosspoint of X(6) and X(3310)
X(47420) = crosssum of X(i) and X(j) for these (i,j): {2, 13136}, {6335, 16082}, {39294, 46102}
X(47420) = crossdifference of every pair of points on line {901, 1309}
X(47420) = barycentric product X(i)*X(j) for these {i,j}: {3, 3259}, {900, 8677}, {1145, 3937}, {1319, 35014}, {1364, 1846}, {1459, 23757}, {1647, 22350}, {3285, 42761}, {5440, 42753}, {10015, 22086}, {22356, 42754}, {35012, 36944}
X(47420) = barycentric quotient X(i)/X(j) for these {i,j}: {1404, 39294}, {1960, 1309}, {2087, 16082}, {3259, 264}, {8661, 43933}, {8677, 4555}, {22086, 13136}, {22096, 10428}, {23220, 901}

X(47421) = BARYCENTRIC PRODUCT X(3)*X(136)

X(47421) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 32654}, {6, 1511}, {32, 9475}, {39, 46094}, {110, 39839}, {115, 125}, {182, 39825}, {338, 24978}, {394, 15560}, {512, 2971}, {570, 5892}, {571, 5961}, {574, 20859}, {620, 36790}, {647, 39005}, {661, 39002}, {1015, 38983}, {1084, 35071}, {1501, 9699}, {1625, 2493}, {1976, 39857}, {2548, 9815}, {2549, 3981}, {2967, 31850}, {3094, 31958}, {5013, 15805}, {7117, 20982}, {7746, 22416}, {9427, 14113}, {9696, 20976}, {13754, 45938}, {14270, 17423}, {14397, 39013}, {15141, 32740}, {15544, 16223}, {16592, 39007}, {16613, 39004}, {18334, 39018}, {20728, 23639}, {20970, 46095}, {20998, 39849}, {22084, 39006}, {22109, 32761}, {34481, 39913}, {39643, 44527}, {39833, 40867}, {42445, 44201}

X(47421) = isogonal conjugate of the polar conjugate of X(136)
X(47421) = X(i)-complementary conjugate of X(j) for these (i,j): {275, 42327}, {276, 21263}, {810, 10600}, {933, 21254}, {1973, 18314}, {2190, 512}, {2616, 1368}, {2623, 18589}, {2643, 20625}, {8882, 4369}, {8884, 21259}, {15422, 20305}, {40440, 23301}
X(47421) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 512}, {6, 30451}, {24, 34952}, {1300, 21731}, {1485, 669}, {1993, 924}, {2970, 20975}, {5392, 523}, {8745, 6753}, {22261, 15451}, {32654, 3569}, {45838, 3005}
X(47421) = X(i)-isoconjugate of X(j) for these (i,j): {91, 249}, {92, 44174}, {99, 36145}, {163, 46134}, {662, 925}, {799, 32734}, {1101, 5392}, {1820, 18020}, {2165, 24041}, {2351, 46254}, {4575, 30450}, {20571, 23357}
X(47421) = crosspoint of X(i) and X(j) for these (i,j): {6, 2501}, {523, 5392}, {525, 15316}, {924, 1993}, {2065, 43665}, {2433, 40388}, {6753, 8745}
X(47421) = crosssum of X(i) and X(j) for these (i,j): {2, 4558}, {6, 23181}, {99, 7752}, {110, 571}, {112, 3542}, {114, 14966}, {925, 2165}
X(47421) = crossdifference of every pair of points on line {110, 925}
X(47421) = X(39839)-line conjugate of X(110)
X(47421) = barycentric product X(i)*X(j) for these {i,j}: {3, 136}, {24, 125}, {31, 17881}, {47, 1109}, {52, 8901}, {68, 34338}, {115, 1993}, {135, 15316}, {317, 20975}, {338, 571}, {339, 44077}, {512, 6563}, {523, 924}, {525, 6753}, {526, 43088}, {850, 34952}, {1147, 2970}, {1748, 3708}, {2088, 18883}, {2394, 14397}, {2643, 44179}, {3124, 7763}, {3125, 42700}, {3269, 11547}, {4036, 34948}, {5392, 39013}, {5961, 35235}, {6754, 20563}, {8745, 15526}, {8754, 9723}, {10412, 44808}, {14618, 30451}, {31635, 44114}, {34385, 41213}
X(47421) = barycentric quotient X(i)/X(j) for these {i,j}: {24, 18020}, {47, 24041}, {115, 5392}, {125, 20563}, {136, 264}, {184, 44174}, {512, 925}, {523, 46134}, {571, 249}, {669, 32734}, {798, 36145}, {924, 99}, {1109, 20571}, {1748, 46254}, {1993, 4590}, {2088, 37802}, {2501, 30450}, {2643, 91}, {2971, 14593}, {3124, 2165}, {6563, 670}, {6753, 648}, {6754, 24}, {7763, 34537}, {8745, 23582}, {8754, 847}, {8901, 34385}, {9723, 47389}, {14397, 2407}, {17881, 561}, {20975, 68}, {30451, 4558}, {34338, 317}, {34952, 110}, {34980, 16391}, {39013, 1993}, {41213, 52}, {42700, 4601}, {43088, 35139}, {44077, 250}, {44179, 24037}, {44808, 10411}
X(47421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 2079, 32661}, {115, 2088, 3269}, {3124, 3269, 115}

X(47422) = BARYCENTRIC PRODUCT X(3)*X(1566)

X(47422) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {6, 32642}, {810, 3269}, {1459, 3270}, {1914, 9475}, {1946, 7117}, {2223, 2356}, {14411, 39014}, {20776, 41215}

X(47422) = isogonal conjugate of the polar conjugate of X(1566)
X(47422) = X(34181)-Ceva conjugate of X(649)
X(47422) = X(i)-isoconjugate of X(j) for these (i,j): {9503, 46102}, {34085, 40116}, {36122, 39293}
X(47422) = crosspoint of X(i) and X(j) for these (i,j): {6, 676}, {1946, 2223}
X(47422) = crosssum of X(i) and X(j) for these (i,j): {2, 677}, {2481, 18026}
X(47422) = crossdifference of every pair of points on line {927, 40116}
X(47422) = barycentric product X(i)*X(j) for these {i,j}: {3, 1566}, {926, 39470}, {3270, 39063}, {7004, 9502}
X(47422) = barycentric quotient X(i)/X(j) for these {i,j}: {1566, 264}, {8638, 40116}, {39470, 46135}

X(47423) = BARYCENTRIC PRODUCT X(3)*X(128)

X(47423) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 11077}, {50, 1154}, {231, 10615}, {570, 5892}, {1989, 25150}, {3269, 22052}, {15345, 41335}, {20975, 23195}

X(47423) = isogonal conjugate of the polar conjugate of X(128)
X(47423) = X(92)-isoconjugate of X(15401)
X(47423) = crosspoint of X(6) and X(231)
X(47423) = crosssum of X(137) and X(14582)
X(47423) = crossdifference of every pair of points on line {1141, 2383}
X(47423) = barycentric product X(i)*X(j) for these {i,j}: {3, 128}, {539, 1154}, {6368, 43969}
X(47423) = barycentric quotient X(i)/X(j) for these {i,j}: {128, 264}, {184, 15401}, {539, 46138}, {43969, 18831}

X(47424) = BARYCENTRIC PRODUCT X(3)*X(137)

X(47424) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {6, 11077}, {115, 12077}, {973, 16224}, {2965, 34418}, {3124, 41222}, {5007, 9475}, {11062, 15262}, {14391, 35442}

X(47424) = isogonal conjugate of the polar conjugate of X(137)
X(47424) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 15451}, {3432, 512}, {34433, 647}
X(47424) = X(i)-isoconjugate of X(j) for these (i,j): {18831, 36148}, {36134, 38342}
X(47424) = crosspoint of X(i) and X(j) for these (i,j): {6, 12077}, {143, 20577}
X(47424) = crosssum of X(2) and X(18315)
X(47424) = crossdifference of every pair of points on line {930, 933}
X(47424) = barycentric product X(i)*X(j) for these {i,j}: {3, 137}, {125, 143}, {647, 20577}, {1510, 6368}, {3269, 14129}, {3518, 35442}, {14577, 15526}, {15451, 41298}, {23290, 37084}, {41221, 44180}
X(47424) = barycentric quotient X(i)/X(j) for these {i,j}: {137, 264}, {143, 18020}, {1510, 18831}, {6368, 46139}, {12077, 38342}, {14577, 23582}, {15451, 930}, {20577, 6331}, {20975, 252}, {24862, 25043}, {41221, 93}

X(47425) = BARYCENTRIC PRODUCT X(3)*X(20619)

X(47425) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {6, 32659}, {48, 4271}, {649, 23980}, {900, 1635}, {1017, 3269}, {1404, 2251}, {1473, 4286}, {2347, 7117}, {20966, 20975}

X(47425) = isogonal conjugate of the polar conjugate of X(20619)
X(47425) = X(3)-Ceva conjugate of X(902)
X(47425) = X(88)-isoconjugate of X(2370)
X(47425) = crosspoint of X(6) and X(8756)
X(47425) = crosssum of X(i) and X(j) for these (i,j): {2, 1797}, {4997, 32939}
X(47425) = crossdifference of every pair of points on line {106, 2370}
X(47425) = barycentric product X(i)*X(j) for these {i,j}: {3, 20619}, {519, 2390}, {902, 3007}, {1319, 45269}
X(47425) = barycentric quotient X(i)/X(j) for these {i,j}: {902, 2370}, {2390, 903}, {20619, 264}

X(47426) = BARYCENTRIC PRODUCT X(3)*X(1560)

X(47426) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 1177}, {6, 14908}, {39, 682}, {110, 2936}, {184, 574}, {187, 23200}, {338, 36157}, {351, 690}, {671, 44420}, {2021, 9419}, {2393, 14961}, {2421, 38650}, {3124, 41272}, {5013, 7669}, {5020, 15560}, {5024, 9142}, {5118, 36790}, {5162, 19575}, {5467, 41612}, {7117, 20967}, {8787, 11171}, {9157, 39857}, {9409, 9475}, {11326, 42442}, {11672, 21731}, {15166, 42667}, {15167, 42668}, {20410, 46592}, {20728, 42670}, {21419, 39231}, {22401, 23208}

X(47426) = isogonal conjugate of the isotomic conjugate of X(5181)
X(47426) = isogonal conjugate of the polar conjugate of X(1560)
X(47426) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 187}, {1576, 351}, {6593, 39689}
X(47426) = X(i)-isoconjugate of X(j) for these (i,j): {75, 10422}, {92, 41511}, {111, 37220}, {897, 2373}, {923, 46140}, {1177, 46277}, {14977, 36095}
X(47426) = crosspoint of X(i) and X(j) for these (i,j): {3, 14961}, {6, 468}, {187, 14357}, {1560, 5181}
X(47426) = crosssum of X(i) and X(j) for these (i,j): {2, 895}, {671, 14246}, {8542, 42008}, {10422, 41511}
X(47426) = crossdifference of every pair of points on line {111, 2373}
X(47426) = barycentric product X(i)*X(j) for these {i,j}: {3, 1560}, {6, 5181}, {187, 858}, {468, 14961}, {524, 2393}, {896, 18669}, {922, 20884}, {1236, 14567}, {3292, 5523}, {4235, 42665}, {5467, 47138}, {6390, 14580}, {14417, 46592}, {34158, 34336}
X(47426) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 10422}, {184, 41511}, {187, 2373}, {524, 46140}, {858, 18023}, {896, 37220}, {1560, 264}, {2393, 671}, {5181, 76}, {5523, 46111}, {14567, 1177}, {14580, 17983}, {14961, 30786}, {18669, 46277}, {23200, 18876}, {34158, 15398}, {42665, 14977}

X(47427) = BARYCENTRIC PRODUCT X(3)*X(42426)

X(47427) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 32640}, {187, 3269}, {237, 2393}, {520, 9155}, {647, 9475}, {826, 6793}, {1154, 10317}, {1640, 6041}, {2781, 40079}

X(47427) = isogonal conjugate of the polar conjugate of X(42426)
X(47427) = X(3)-Ceva conjugate of X(5191)
X(47427) = crosspoint of X(6) and X(6103)
X(47427) = crossdifference of every pair of points on line {842, 2697}
X(47427) = barycentric product X(i)*X(j) for these {i,j}: {3, 42426}, {542, 2781}
X(47427) = barycentric quotient X(i)/X(j) for these {i,j}: {2781, 5641}, {5191, 2697}, {42426, 264}

X(47428) = BARYCENTRIC PRODUCT X(3)*X(46668)

X(47428) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {1459, 20975}, {3049, 22084}, {3269, 22090}, {7117, 22093}, {20735, 22414}, {20821, 20825}, {22087, 22428}, {28602, 35080}

X(47428) = isogonal conjugate of the polar conjugate of X(46668)
X(47428) = barycentric product X(3)*X(46668)
X(47428) = barycentric quotient X(46668)/X(264)

X(47429) = BARYCENTRIC PRODUCT X(3)*X(36471)

X(47429) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {520, 20975}, {868, 35088}, {1154, 38608}, {2393, 36790}, {2710, 32696}, {3269, 22089}, {3289, 9475}, {37183, 39072}

X(47429) = isogonal conjugate of the polar conjugate of X(36471)
X(47429) = X(6)-Ceva conjugate of X(684)
X(47429) = X(36104)-isoconjugate of X(44767)
X(47429) = crosspoint of X(3) and X(6333)
X(47429) = crosssum of X(i) and X(j) for these (i,j): {2, 44767}, {4, 32696}
X(47429) = barycentric product X(3)*X(36471)
X(47429) = barycentric quotient X(i)/X(j) for these {i,j}: {684, 44767}, {36471, 264}, {44114, 39645}

X(47430) = BARYCENTRIC PRODUCT X(3)*X(5139)

X(47430) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {6, 2987}, {264, 9224}, {351, 865}, {800, 9475}, {1648, 15526}, {2092, 20728}, {3053, 6091}, {3269, 9427}, {6388, 15525}, {7117, 21755}, {7600, 20976}, {7669, 32740}, {14060, 36696}, {25318, 40708}

X(47430) = isogonal conjugate of the isotomic conjugate of X(6388)
X(47430) = isogonal conjugate of the polar conjugate of X(5139)
X(47430) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 669}, {2971, 3124}, {3053, 8651}, {3563, 42663}, {8770, 512}, {40322, 647}
X(47430) = X(i)-isoconjugate of X(j) for these (i,j): {662, 35136}, {799, 3565}, {2996, 24041}, {4590, 8769}, {6391, 46254}, {8770, 24037}, {34537, 38252}
X(47430) = crosspoint of X(i) and X(j) for these (i,j): {6, 2489}, {512, 8770}, {3053, 8651}, {5139, 6388}, {9178, 15387}
X(47430) = crosssum of X(i) and X(j) for these (i,j): {2, 4563}, {99, 193}, {126, 5468}, {2996, 35136}
X(47430) = crossdifference of every pair of points on line {99, 3565}
X(47430) = barycentric product X(i)*X(j) for these {i,j}: {3, 5139}, {6, 6388}, {31, 17876}, {115, 3053}, {125, 19118}, {193, 3124}, {512, 3566}, {523, 8651}, {1707, 2643}, {2971, 6337}, {3122, 4028}, {3125, 21874}, {3167, 8754}, {3787, 34294}, {3798, 4079}, {6353, 20975}, {8770, 15525}, {33632, 39691}
X(47430) = barycentric quotient X(i)/X(j) for these {i,j}: {193, 34537}, {512, 35136}, {669, 3565}, {1084, 8770}, {1707, 24037}, {2971, 34208}, {3053, 4590}, {3124, 2996}, {3167, 47389}, {3566, 670}, {4117, 38252}, {5139, 264}, {6388, 76}, {8651, 99}, {17876, 561}, {19118, 18020}, {20975, 6340}, {21874, 4601}, {23216, 40319}, {42068, 14248}
X(47430) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1084, 20975, 3124}, {1084, 21906, 20975}

X(47431) = BARYCENTRIC PRODUCT X(3)*X(20621)

X(47431) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {3, 1415}, {6, 3433}, {39, 41}, {73, 1362}, {665, 1642}, {1253, 2197}, {2092, 20455}, {2223, 2356}, {3269, 39686}, {8776, 35505}, {22084, 22402}, {23619, 40957}, {23980, 42769}, {39063, 40590}

X(47431) = isogonal conjugate of the polar conjugate of X(20621)
X(47431) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 2223}, {1415, 665}, {34337, 20455}
X(47431) = X(673)-isoconjugate of X(26703)
X(47431) = crosspoint of X(i) and X(j) for these (i,j): {6, 5089}, {59, 42720}
X(47431) = crosssum of X(i) and X(j) for these (i,j): {2, 1814}, {11, 43929}, {5452, 28071}
X(47431) = crossdifference of every pair of points on line {105, 26703}
X(47431) = barycentric product X(i)*X(j) for these {i,j}: {3, 20621}, {518, 3827}, {34160, 34337}
X(47431) = barycentric quotient X(i)/X(j) for these {i,j}: {2223, 26703}, {3827, 2481}, {20621, 264}

X(47432) = BARYCENTRIC PRODUCT X(3)*X(5514)

X(47432) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {6, 32652}, {55, 3192}, {972, 32714}, {1253, 2197}, {1364, 22084}, {1946, 41215}, {2269, 9475}, {2310, 3119}, {2637, 2638}, {3318, 38362}, {7037, 7151}, {20728, 22071}, {22072, 22399}

X(47432) = isogonal conjugate of the isotomic conjugate of X(7358)
X(47432) = isogonal conjugate of the polar conjugate of X(5514)
X(47432) = X(i)-Ceva conjugate of X(j) for these (i,j): {1433, 652}, {7037, 663}, {7078, 10397}, {7952, 14298}, {19614, 647}, {30457, 657}, {34432, 649}
X(47432) = X(i)-isoconjugate of X(j) for these (i,j): {189, 7128}, {653, 37141}, {658, 40117}, {1275, 7129}, {1422, 46102}, {1433, 24032}, {1440, 7012}, {2358, 4620}, {6355, 24000}, {7020, 7339}, {7045, 40836}, {8059, 18026}, {13138, 36118}, {13149, 36049}, {23984, 41081}, {32714, 44327}
X(47432) = crosspoint of X(i) and X(j) for these (i,j): {6, 6129}, {64, 650}, {281, 521}, {652, 1433}, {5514, 7358}, {7078, 10397}, {7952, 14298}
X(47432) = crosssum of X(i) and X(j) for these (i,j): {2, 13138}, {4, 32714}, {7, 36118}, {20, 651}, {108, 222}, {653, 7952}, {1433, 37141}
X(47432) = crossdifference of every pair of points on line {653, 934}
X(47432) = barycentric product X(i)*X(j) for these {i,j}: {3, 5514}, {6, 7358}, {40, 34591}, {55, 16596}, {198, 2968}, {219, 38357}, {268, 3318}, {329, 3270}, {521, 14298}, {522, 10397}, {652, 8058}, {1146, 7078}, {1565, 7368}, {1819, 21044}, {2324, 7004}, {2331, 24031}, {3119, 7013}, {3195, 23983}, {4081, 7011}, {7074, 26932}, {7080, 7117}, {7952, 35072}, {40616, 41088}
X(47432) = barycentric quotient X(i)/X(j) for these {i,j}: {1364, 34400}, {1819, 4620}, {1946, 37141}, {2187, 7128}, {2331, 24032}, {2638, 41081}, {2968, 44190}, {3022, 7003}, {3119, 7020}, {3195, 23984}, {3269, 6355}, {3270, 189}, {3318, 40701}, {5514, 264}, {6129, 13149}, {7074, 46102}, {7078, 1275}, {7117, 1440}, {7358, 76}, {7368, 15742}, {8058, 46404}, {8641, 40117}, {10397, 664}, {14298, 18026}, {14936, 40836}, {16596, 6063}, {20975, 13853}, {22096, 6612}, {34591, 309}, {38357, 331}, {39687, 1433}

X(47433) = BARYCENTRIC PRODUCT X(3)*X(133)

X(47433) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {6, 74}, {51, 20975}, {154, 32713}, {1636, 1637}, {2260, 7117}, {3168, 40138}, {3284, 11589}, {5158, 13409}

X(47433) = isogonal conjugate of the polar conjugate of X(133)
X(47433) = polar conjugate of the isotomic conjugate of X(40948)
X(47433) = tripolar centroid of X(46587)
X(47433) = X(i)-Ceva conjugate of X(j) for these (i,j): {3, 1495}, {107, 9409}, {15384, 23347}, {23964, 2442}, {43530, 1515}
X(47433) = X(i)-isoconjugate of X(j) for these (i,j): {92, 15404}, {1294, 2349}
X(47433) = crosspoint of X(i) and X(j) for these (i,j): {3, 44436}, {6, 1990}, {2420, 23964}
X(47433) = crosssum of X(i) and X(j) for these (i,j): {2, 14919}, {2394, 15526}, {14401, 34601}
X(47433) = crossdifference of every pair of points on line {74, 1294}
X(47433) = X(i)-line conjugate of X(j) for these (i,j): {6, 74}, {1636, 9033}
X(47433) = barycentric product X(i)*X(j) for these {i,j}: {3, 133}, {4, 40948}, {30, 6000}, {1559, 11589}, {1636, 2404}, {1990, 44436}, {2442, 41077}, {9033, 46587}, {34334, 39174}
X(47433) = barycentric quotient X(i)/X(j) for these {i,j}: {133, 264}, {184, 15404}, {1495, 1294}, {1636, 2416}, {2442, 15459}, {6000, 1494}, {9409, 43701}, {40948, 69}, {46587, 16077}
X(47433) = {X(6),X(47228)}-harmonic conjugate of X(3269)

X(47434) = BARYCENTRIC PRODUCT X(3)*X(25640)

X(47434) lies on the conic {{X(3269), X(7117), X(9475), X(20728), X(20975)} and these lines: {6, 909}, {37, 5514}, {55, 3192}, {198, 32674}, {216, 2267}, {650, 23986}, {1108, 4534}, {1319, 8607}, {1769, 3310}, {2092, 3269}, {2197, 2331}, {20975, 40952}, {23972, 35069}, {40590, 40943}

X(47434) = isogonal conjugate of the polar conjugate of X(25640)
X(47434) = X(7115)-Ceva conjugate of X(2443)
X(47434) = X(i)-isoconjugate of X(j) for these (i,j): {92, 15405}, {1295, 34234}, {2417, 36110}, {37136, 43737}
X(47434) = crosspoint of X(i) and X(j) for these (i,j): {6, 14571}, {2427, 7115}
X(47434) = crosssum of X(2401) and X(26932)
X(47434) = crossdifference of every pair of points on line {104, 1295}
X(47434) = barycentric product X(i)*X(j) for these {i,j}: {3, 25640}, {517, 6001}, {14312, 23981}, {21664, 39175}
X(47434) = barycentric quotient X(i)/X(j) for these {i,j}: {184, 15405}, {6001, 18816}, {25640, 264}

X(47435) = ISOTOMIC CONJUGATE OF X(3344)

X(47435) lies on the cubic K184 and these lines: {2, 34403}, {4, 16096}, {69, 14362}, {85, 34404}, {253, 264}, {3926, 44326}, {6527, 6616}

X(47435) = isogonal conjugate of X(47439)
X(47435) = isotomic conjugate of X(3344)
X(47435) = isotomic conjugate of the complement of X(14362)
X(47435) = isotomic conjugate of the isogonal conjugate of X(3343)
X(47435) = polar conjugate of the isogonal conjugate of X(46351)
X(47435) = X(76)-Ceva conjugate of X(34403)
X(47435) = X(14361)-cross conjugate of X(6527)
X(47435) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3344}, {204, 28783}, {9247, 46353}
X(47435) = cevapoint of X(i) and X(j) for these (i,j): {2, 14362}, {3343, 46351}
X(47435) = barycentric product X(i)*X(j) for these {i,j}: {76, 3343}, {253, 6527}, {264, 46351}, {305, 41085}, {1498, 41530}, {14361, 34403}
X(47435) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3344}, {253, 3346}, {264, 46353}, {1033, 3172}, {1073, 28783}, {1498, 154}, {1712, 204}, {2130, 28782}, {3343, 6}, {3349, 28781}, {6523, 6525}, {6527, 20}, {6616, 3079}, {6617, 15905}, {8807, 30456}, {14361, 1249}, {14362, 3350}, {34403, 1032}, {41085, 25}, {46351, 3}

X(47436) = ISOTOMIC CONJUGATE OF X(3342)

X(47436) lies on the cubic K184 and these lines: {2, 34404}, {69, 34162}, {75, 34403}, {85, 264}, {326, 44327}, {33672, 46350}

X(47436) = isotomic conjugate of X(3342)
X(47436) = isotomic conjugate of the anticomplement of X(20210)
X(47436) = isotomic conjugate of the complement of X(34162)
X(47436) = isotomic conjugate of the isogonal conjugate of X(3341)
X(47436) = X(76)-Ceva conjugate of X(34404)
X(47436) = X(i)-cross conjugate of X(j) for these (i,j): {5932, 33672}, {20210, 2}
X(47436) = X(i)-isoconjugate of X(j) for these (i,j): {31, 3342}, {198, 7152}, {221, 7037}, {2175, 46352}, {2187, 3345}, {7007, 7114}
X(47436) = cevapoint of X(2) and X(34162)
X(47436) = barycentric product X(i)*X(j) for these {i,j}: {76, 3341}, {85, 46350}, {189, 33672}, {1490, 44190}, {1969, 46881}, {5932, 34404}
X(47436) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3342}, {84, 7152}, {85, 46352}, {189, 3345}, {207, 3209}, {282, 7037}, {309, 41514}, {1035, 2199}, {1490, 198}, {3176, 2331}, {3197, 2187}, {3341, 6}, {3352, 34167}, {5932, 223}, {7003, 7007}, {7020, 40838}, {8808, 8811}, {14302, 14298}, {33672, 329}, {34162, 3351}, {34404, 1034}, {40837, 208}, {46350, 9}, {46881, 48}

X(47437) = CROSSSUM OF X(2) AND X(1032)

X(47437) lies on the cubic K346 and these lines: {6, 14092}, {25, 800}, {32, 14642}, {64, 8573}, {577, 14390}, {604, 2155}, {1033, 41085}, {1249, 1301}, {1609, 11589}, {3343, 6617}, {15394, 37344}, {40221, 46831}

X(47437) = isogonal conjugate of the isotomic conjugate of X(3343)
X(47437) = isogonal conjugate of the polar conjugate of X(41085)
X(47437) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 14642}, {14379, 33581}
X(47437) = X(i)-isoconjugate of X(j) for these (i,j): {63, 46353}, {75, 3344}, {1032, 1895}, {3346, 18750}, {8805, 33673}
X(47437) = crosspoint of X(i) and X(j) for these (i,j): {6, 1033}, {3343, 41085}
X(47437) = crosssum of X(2) and X(1032)
X(47437) = barycentric product X(i)*X(j) for these {i,j}: {3, 41085}, {6, 3343}, {25, 46351}, {64, 1498}, {1033, 1073}, {1712, 19614}, {3349, 28785}, {6523, 14379}, {6527, 33581}, {6617, 41489}, {8886, 41088}, {14361, 14642}
X(47437) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 46353}, {32, 3344}, {1033, 15466}, {1498, 14615}, {3343, 76}, {14642, 1032}, {33581, 3346}, {41085, 264}, {46351, 305}

X(47438) = CROSSSUM OF X(2) AND X(1034)

X(47438) lies on the cubic K346 and these lines: {6, 2188}, {25, 604}, {31, 14642}, {32, 7118}, {212, 32652}, {223, 8059}, {3341, 13614}

X(47438) = isogonal conjugate of the isotomic conjugate of X(3341)
X(47438) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 7118}, {2188, 2208}
X(47438) = X(i)-isoconjugate of X(j) for these (i,j): {8, 46352}, {75, 3342}, {322, 3345}, {329, 41514}, {347, 1034}, {8806, 8822}
X(47438) = crosspoint of X(6) and X(1035)
X(47438) = crosssum of X(2) and X(1034)
X(47438) = barycentric product X(i)*X(j) for these {i,j}: {6, 3341}, {19, 46881}, {84, 3197}, {207, 268}, {282, 1035}, {604, 46350}, {1436, 1490}, {2188, 40837}, {3352, 28784}, {5932, 7118}, {8885, 41087}
X(47438) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 3342}, {207, 40701}, {604, 46352}, {1035, 40702}, {2208, 41514}, {3197, 322}, {3341, 76}, {7118, 1034}, {46350, 28659}, {46881, 304}

X(47439) = CROSSSUM OF X(2) AND X(14362)

X(47439) lies on the cubic K346 and these lines: {6, 14092}, {184, 3172}, {2060, 3344}, {3346, 11425}, {14528, 40138}

X(47439) = isogonal conjugate of X(47435)
X(47439) = isogonal conjugate of the isotomic conjugate of X(3344)
X(47439) = X(32)-cross conjugate of X(3172)
X(47439) = X(i)-isoconjugate of X(j) for these (i,j): {75, 3343}, {92, 46351}, {304, 41085}, {1712, 34403}, {2184, 6527}, {5931, 8807}, {14361, 19611}
X(47439) = crosspoint of X(6) and X(28781)
X(47439) = crosssum of X(i) and X(j) for these (i,j): {2, 14362}, {3343, 46351}
X(47439) = barycentric product X(i)*X(j) for these {i,j}: {6, 3344}, {154, 3346}, {184, 46353}, {1032, 3172}, {1249, 28783}, {2131, 28782}, {3350, 28781}
X(47439) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 3343}, {154, 6527}, {184, 46351}, {1974, 41085}, {3172, 14361}, {3344, 76}, {3346, 41530}, {28783, 34403}, {46353, 18022}

X(47440) = CROSSSUM OF X(2) AND X(41080)

X(47440) lies on the cubic K346 and these lines: {6, 34167}, {25, 7118}, {604, 14642}, {3341, 8064}

X(47440) = isogonal conjugate of the isotomic conjugate of X(3351)
X(47440) = X(75)-isoconjugate of X(3352)
X(47440) = crosspoint of X(6) and X(28784)
X(47440) = crosssum of X(2) and X(41080)
X(47440) = barycentric product X(i)*X(j) for these {i,j}: {6, 3351}, {3182, 7037}, {3342, 28784}
X(47440) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 3352}, {3351, 76}

X(47441) = MIDPOINT OF X(4) AND X(3345)

X(47441) lies on these lines: {2, 3182}, {3, 3452}, {4, 282}, {5, 20205}, {10, 2883}, {142, 40657}, {226, 7498}, {908, 27402}, {937, 34546}, {946, 6523}, {1034, 3347}, {1125, 37818}, {2184, 40836}, {5908, 7682}, {7070, 21075}, {9612, 37276}

X(47441) = midpoint of X(4) and X(3345)
X(47441) = reflection of X(37818) in X(1125)
X(47441) = complement of X(3182)
X(47441) = complement of the isogonal conjugate of X(3347)
X(47441) = X(i)-complementary conjugate of X(j) for these (i,j): {2192, 3351}, {3347, 10}, {34167, 7952}, {41080, 20307}
X(47441) = crosspoint of X(1034) and X(7020)
X(47441) = crosssum of X(1035) and X(7114)
X(47441) = X(3345)-of-Euler-triangle

X(47442) = MIDPOINT OF X(23) AND X(647)

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

X(47442) = X[23] + 3 X[47263], X[647] - 3 X[47263], 3 X[44560] - 4 X[47249], 4 X[37897] + X[41300], X[41300] - 4 X[47261], X[684] - 3 X[47221], X[850] - 5 X[37760], X[850] - 3 X[47255], 5 X[37760] - 3 X[47255], X[858] - 3 X[47251], 3 X[7426] - X[47004], 3 X[7426] + X[47258], X[31174] - 3 X[37907], 3 X[31174] - 5 X[47264], 9 X[37907] - 5 X[47264], X[36900] + 3 X[37909], 3 X[37904] + X[47248], 3 X[47001] - X[47248], 3 X[37971] - X[46996]

X(47442) lies on these lines: {23, 647}, {25, 33752}, {30, 44560}, {351, 11616}, {468, 30476}, {511, 42654}, {512, 32237}, {520, 47214}, {523, 8651}, {525, 15448}, {684, 47221}, {850, 37760}, {858, 47251}, {2485, 40350}, {5159, 47253}, {7426, 23878}, {7493, 18312}, {7575, 30209}, {8675, 32217}, {9030, 32218}, {11176, 39509}, {22264, 29012}, {31174, 37907}, {31296, 47254}, {36900, 37909}, {37904, 47001}, {37971, 46996}, {44564, 44820}, {44810, 46425}, {46983, 47312}, {46985, 47340}, {47252, 47256}

X(47442) = midpoint of X(i) and X(j) for these {i,j}: {23, 647}, {31296, 47254}, {37897, 47261}, {37904, 47001}, {46983, 47312}, {46985, 47340}, {47004, 47258}
X(47442) = reflection of X(i) in X(j) for these {i,j}: {5159, 47253}, {30476, 468}, {47252, 47316}
X(47442) = crossdifference of every pair of points on line {5013, 15000}
X(47442) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 47263, 647}, {850, 37760, 47255}, {7426, 47258, 47004}

X(47443) = X(2)X(18020)∩X(25)X(250)

X(47443) lies on these lines: {2, 18020}, {25, 250}, {112, 45773}, {184, 9513}, {249, 394}, {275, 39295}, {2396, 4235}, {2421, 14590}, {4590, 34254}, {6331, 40866}, {11547, 18879}, {14366, 36176}

X(47443) = polar conjugate of X(23105)
X(47443) = X(i)-cross conjugate of X(j) for these (i,j): {110, 18020}, {112, 250}, {2407, 18879}, {4558, 249}, {4611, 4590}, {41679, 23582}, {45215, 27867}
X(47443) = X(i)-isoconjugate of X(j) for these (i,j): {19, 5489}, {37, 21134}, {48, 23105}, {63, 8029}, {72, 21131}, {115, 656}, {125, 661}, {304, 22260}, {338, 810}, {339, 798}, {512, 20902}, {513, 21046}, {523, 3708}, {525, 2643}, {647, 1109}, {822, 2970}, {905, 21043}, {1096, 23616}, {1365, 8611}, {1577, 20975}, {2489, 17879}, {2501, 2632}, {2631, 12079}, {3049, 23994}, {3124, 14208}, {3125, 4064}, {3269, 24006}, {4024, 18210}, {4025, 21833}, {4466, 4705}, {8754, 24018}, {23099, 40364}
X(47443) = cevapoint of X(i) and X(j) for these (i,j): {110, 23357}, {112, 250}, {249, 4558}, {647, 13198}, {39298, 39299}
X(47443) = trilinear pole of line {186, 249}
X(47443) = barycentric product X(i)*X(j) for these {i,j}: {25, 31614}, {99, 250}, {110, 18020}, {112, 4590}, {162, 24041}, {163, 46254}, {249, 648}, {468, 45773}, {811, 1101}, {4558, 23582}, {4563, 23964}, {4575, 23999}, {4592, 24000}, {4611, 44183}, {6331, 23357}, {6528, 47390}, {14590, 39295}, {14966, 41174}, {16237, 18879}, {24037, 32676}, {32713, 47389}, {39298, 39299}
X(47443) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 5489}, {4, 23105}, {25, 8029}, {58, 21134}, {99, 339}, {101, 21046}, {107, 2970}, {110, 125}, {112, 115}, {162, 1109}, {163, 3708}, {249, 525}, {250, 523}, {394, 23616}, {648, 338}, {662, 20902}, {811, 23994}, {933, 8901}, {1101, 656}, {1304, 12079}, {1474, 21131}, {1576, 20975}, {1974, 22260}, {3926, 23107}, {4230, 868}, {4556, 4466}, {4558, 15526}, {4563, 36793}, {4570, 4064}, {4575, 2632}, {4590, 3267}, {4592, 17879}, {4611, 127}, {5379, 4036}, {6331, 23962}, {7480, 6070}, {8750, 21043}, {14587, 23286}, {14591, 2088}, {14966, 41172}, {18020, 850}, {18879, 15421}, {23181, 35442}, {23357, 647}, {23582, 14618}, {23963, 3049}, {23964, 2501}, {23995, 810}, {24000, 24006}, {24041, 14208}, {31614, 305}, {32661, 3269}, {32676, 2643}, {32713, 8754}, {33803, 34953}, {35325, 39691}, {38413, 41998}, {38414, 41997}, {38861, 34978}, {39295, 14592}, {41937, 2489}, {42742, 13212}, {44102, 33919}, {44162, 23099}, {45773, 30786}, {46254, 20948}, {47390, 520}

X(47444) = X(1)X(1358)∩X(2)X(16078)

X(47444) lies on these lines: {1, 1358}, {2, 16078}, {7, 3623}, {9, 25729}, {57, 279}, {65, 21314}, {85, 4554}, {226, 29621}, {269, 34039}, {348, 31231}, {519, 24797}, {1323, 1420}, {1565, 9581}, {2098, 4862}, {3340, 10481}, {3663, 14261}, {3665, 9578}, {3674, 4654}, {3676, 23764}, {3679, 24798}, {4089, 5727}, {4902, 16189}, {7185, 9312}, {10389, 40154}, {16834, 24803}, {20196, 26563}, {21139, 23058}, {24800, 42042}, {24801, 42043}, {24805, 25055}, {30617, 43038}

X(47444) = X(i)-isoconjugate of X(j) for these (i,j): {2175, 34523}, {14827, 18811}
X(47444) = crosspoint of X(279) and X(27818)
X(47444) = barycentric product X(i)*X(j) for these {i,j}: {7, 4862}, {279, 30827}, {1088, 2098}, {6063, 32577}, {17424, 46406}, {20567, 34543}, {23062, 34524}
X(47444) = barycentric quotient X(i)/X(j) for these {i,j}: {85, 34523}, {1088, 18811}, {2098, 200}, {4862, 8}, {17424, 657}, {25737, 30720}, {30827, 346}, {32577, 55}, {34524, 728}, {34543, 41}
X(47444) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1323, 7195, 1420}, {7185, 17089, 9312}

X(47445) = X(6)X(468)∩X(23)X(40341)

Barycentrics a^8 - 7*a^6*b^2 + a^4*b^4 + 7*a^2*b^6 - 2*b^8 - 7*a^6*c^2 + 11*a^4*b^2*c^2 - 7*a^2*b^4*c^2 + a^4*c^4 - 7*a^2*b^2*c^4 + 4*b^4*c^4 + 7*a^2*c^6 - 2*c^8 : :

X(47445) = 5 X[6] - 8 X[468], X[6] - 4 X[32113], X[6] + 2 X[47276], 11 X[6] - 8 X[47277], 7 X[6] + 8 X[47278], X[6] + 8 X[47279], 7 X[6] - 4 X[47280], 17 X[6] - 8 X[47281], 2 X[468] - 5 X[32113], 4 X[468] + 5 X[47276], 11 X[468] - 5 X[47277], 7 X[468] + 5 X[47278], X[468] + 5 X[47279], 14 X[468] - 5 X[47280], 17 X[468] - 5 X[47281], 2 X[32113] + X[47276], 11 X[32113] - 2 X[47277], 7 X[32113] + 2 X[47278], X[32113] + 2 X[47279], 7 X[32113] - X[47280], 17 X[32113] - 2 X[47281], 11 X[47276] + 4 X[47277], 7 X[47276] - 4 X[47278], X[47276] - 4 X[47279], 7 X[47276] + 2 X[47280], 17 X[47276] + 4 X[47281], 7 X[47277] + 11 X[47278], X[47277] + 11 X[47279], 14 X[47277] - 11 X[47280], 17 X[47277] - 11 X[47281], X[47278] - 7 X[47279], 2 X[47278] + X[47280], 17 X[47278] + 7 X[47281], 14 X[47279] + X[47280], 17 X[47279] + X[47281], 17 X[47280] - 14 X[47281], 2 X[23] + X[40341], 5 X[69] + X[20063], X[193] - 4 X[32218], 5 X[599] - 2 X[10989], 4 X[1495] - X[16176], X[2453] + 2 X[47282], X[2930] + 2 X[41721], 2 X[3629] - 5 X[37760], 4 X[3631] - X[5189], X[6144] - 4 X[32217], 5 X[15533] + 4 X[47313], 4 X[15826] - 7 X[47355]

X(47445) lies on these lines: {6, 468}, {23, 40341}, {69, 20063}, {193, 32218}, {511, 38789}, {524, 25331}, {599, 8705}, {1495, 16176}, {1503, 13619}, {2070, 5965}, {2453, 47282}, {2930, 41721}, {3629, 37760}, {3631, 5189}, {6144, 32217}, {14644, 44668}, {15533, 47313}, {15826, 47355}, {18365, 35282}

X(47445) = reflection of X(25331) in X(35265)
X(47445) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32113, 47276, 6}, {32113, 47279, 47276}

X(47446) = X(6)X(468)∩X(23)X(11160)

Barycentrics 2*a^8 - 17*a^6*b^2 + 3*a^4*b^4 + 17*a^2*b^6 - 5*b^8 - 17*a^6*c^2 + 26*a^4*b^2*c^2 - 17*a^2*b^4*c^2 + 3*a^4*c^4 - 17*a^2*b^2*c^4 + 10*b^4*c^4 + 17*a^2*c^6 - 5*c^8 : :

X(47446) = 3 X[6] - 5 X[468], X[6] - 5 X[32113], 3 X[6] + 5 X[47276], 7 X[6] - 5 X[47277], X[6] + 5 X[47279], 9 X[6] - 5 X[47280], 11 X[6] - 5 X[47281], X[468] - 3 X[32113], 7 X[468] - 3 X[47277], 5 X[468] + 3 X[47278], X[468] + 3 X[47279], 3 X[468] - X[47280], 11 X[468] - 3 X[47281], 3 X[32113] + X[47276], 7 X[32113] - X[47277], 5 X[32113] + X[47278], 9 X[32113] - X[47280], 11 X[32113] - X[47281], 7 X[47276] + 3 X[47277], 5 X[47276] - 3 X[47278], X[47276] - 3 X[47279], 3 X[47276] + X[47280], 11 X[47276] + 3 X[47281], 5 X[47277] + 7 X[47278], X[47277] + 7 X[47279], 9 X[47277] - 7 X[47280], 11 X[47277] - 7 X[47281], X[47278] - 5 X[47279], 9 X[47278] + 5 X[47280], 11 X[47278] + 5 X[47281], 9 X[47279] + X[47280], 11 X[47279] + X[47281], 11 X[47280] - 9 X[47281], 5 X[23] + 3 X[11160], 3 X[69] + X[37900], 3 X[599] - X[46517], 5 X[858] - 9 X[21356], 5 X[5159] - 6 X[20582]

X(47446) lies on these lines: {6, 468}, {23, 11160}, {30, 22165}, {69, 37900}, {524, 32267}, {599, 46517}, {858, 21356}, {5159, 20582}, {8550, 11202}, {8705, 14913}, {9813, 15826}, {11649, 11793}, {15069, 47340}, {15533, 47312}, {16334, 47282}, {18914, 37934}, {19140, 34380}, {32621, 37977}, {34986, 41149}

X(47446) = midpoint of X(i) and X(j) for these {i,j}: {6, 47278}, {468, 47276}, {15069, 47340}, {15533, 47312}, {16334, 47282}, {32113, 47279}
X(47446) = reflection of X(15826) in X(37911)
X(47446) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {468, 47279, 47276}, {32113, 47276, 468}

X(47447) = X(6)X(468)∩X(30)X(10519)

Barycentrics 2*a^8 + 13*a^6*b^2 - 7*a^4*b^4 - 13*a^2*b^6 + 5*b^8 + 13*a^6*c^2 - 14*a^4*b^2*c^2 + 13*a^2*b^4*c^2 - 7*a^4*c^4 + 13*a^2*b^2*c^4 - 10*b^4*c^4 - 13*a^2*c^6 + 5*c^8 : :

X(47447) = 2 X[6] - 5 X[468], X[6] + 5 X[32113], 7 X[6] + 5 X[47276], 8 X[6] - 5 X[47277], 2 X[6] + X[47278], 4 X[6] + 5 X[47279], 11 X[6] - 5 X[47280], 14 X[6] - 5 X[47281], X[468] + 2 X[32113], 7 X[468] + 2 X[47276], 4 X[468] - X[47277], 5 X[468] + X[47278], 2 X[468] + X[47279], 11 X[468] - 2 X[47280], 7 X[468] - X[47281], 7 X[32113] - X[47276], 8 X[32113] + X[47277], 10 X[32113] - X[47278], 4 X[32113] - X[47279], 11 X[32113] + X[47280], 14 X[32113] + X[47281], 8 X[47276] + 7 X[47277], 10 X[47276] - 7 X[47278], 4 X[47276] - 7 X[47279], 11 X[47276] + 7 X[47280], 2 X[47276] + X[47281], 5 X[47277] + 4 X[47278], X[47277] + 2 X[47279], 11 X[47277] - 8 X[47280], 7 X[47277] - 4 X[47281], 2 X[47278] - 5 X[47279], 11 X[47278] + 10 X[47280], 7 X[47278] + 5 X[47281], 11 X[47279] + 4 X[47280], 7 X[47279] + 2 X[47281], 14 X[47280] - 11 X[47281], X[69] + 2 X[37897], 4 X[141] - X[46517], 2 X[599] + X[47312], 2 X[1352] + X[47340], 5 X[3620] + X[37900], 2 X[5112] + X[16312], 5 X[5112] + X[47283], 5 X[16312] - 2 X[47283], 8 X[20582] - 5 X[47097], 5 X[7426] + X[11160], 2 X[15993] + X[47154], 4 X[22165] + 5 X[37904], X[32220] - 4 X[47316]

X(47447) lies on these lines: {6, 468}, {30, 10519}, {69, 37897}, {141, 46517}, {511, 38792}, {599, 47312}, {1352, 47340}, {1503, 13399}, {3620, 37900}, {5112, 16312}, {5650, 8705}, {7426, 11160}, {14853, 37942}, {15993, 47154}, {16654, 40107}, {18931, 37934}, {19459, 37977}, {21284, 35219}, {22165, 37904}, {32220, 47316}, {34380, 45016}

X(47447) = reflection of X(14853) in X(37942)
X(47447) = crossdifference of every pair of points on line {12017, 30209}
X(47447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {468, 32113, 47279}, {468, 47278, 6}, {468, 47279, 47277}

X(47448) = X(6)X(468)∩X(23)X(599)

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

X(47448) = 3 X[6] - 8 X[468], X[6] + 4 X[32113], 3 X[6] + 2 X[47276], 13 X[6] - 8 X[47277], 17 X[6] + 8 X[47278], 7 X[6] + 8 X[47279], 9 X[6] - 4 X[47280], 23 X[6] - 8 X[47281], 2 X[468] + 3 X[32113], 4 X[468] + X[47276], 13 X[468] - 3 X[47277], 17 X[468] + 3 X[47278], 7 X[468] + 3 X[47279], 6 X[468] - X[47280], 23 X[468] - 3 X[47281], 6 X[32113] - X[47276], 13 X[32113] + 2 X[47277], 17 X[32113] - 2 X[47278], 7 X[32113] - 2 X[47279], 9 X[32113] + X[47280], 23 X[32113] + 2 X[47281], 13 X[47276] + 12 X[47277], 17 X[47276] - 12 X[47278], 7 X[47276] - 12 X[47279], 3 X[47276] + 2 X[47280], 23 X[47276] + 12 X[47281], 17 X[47277] + 13 X[47278], 7 X[47277] + 13 X[47279], 18 X[47277] - 13 X[47280], 23 X[47277] - 13 X[47281], 7 X[47278] - 17 X[47279], 18 X[47278] + 17 X[47280], 23 X[47278] + 17 X[47281], 18 X[47279] + 7 X[47280], 23 X[47279] + 7 X[47281], 23 X[47280] - 18 X[47281], 2 X[23] + 3 X[599], 2 X[67] + 3 X[19596], X[69] + 4 X[32218], 6 X[141] - X[5189], 4 X[858] - 9 X[21358], 3 X[1350] + 2 X[18325], 3 X[2070] + 2 X[34507], X[2930] + 4 X[8262], 3 X[2930] + 2 X[41724], 6 X[8262] - X[41724], 3 X[3763] - 2 X[30745], 4 X[5112] + X[47284], 3 X[5648] + 2 X[41586], 4 X[7426] + X[15533], 4 X[7575] + X[15069], X[15534] - 6 X[37907], 9 X[10516] - 4 X[18572], 7 X[10541] - 12 X[44214], 3 X[11179] - 8 X[22249], 4 X[15826] - 9 X[47352], 3 X[15993] + 2 X[47245], X[16176] - 6 X[18374], 4 X[16334] + X[47275], 8 X[18571] - 3 X[43273], X[20063] + 9 X[21356], 2 X[22165] + 3 X[37909], X[25336] - 6 X[35265], 4 X[32217] + X[40341], X[37924] + 4 X[40107]

X(47448) lies on these lines: {6, 468}, {23, 599}, {67, 19596}, {69, 32218}, {141, 5189}, {186, 15582}, {524, 37760}, {542, 37958}, {858, 21358}, {1350, 18325}, {1620, 9833}, {1656, 11649}, {2070, 34507}, {2930, 8262}, {3763, 8705}, {5112, 47284}, {5648, 16510}, {7426, 15533}, {7575, 15069}, {9716, 15534}, {10295, 10606}, {10415, 46154}, {10516, 18572}, {10541, 44214}, {11063, 41359}, {11179, 22249}, {14357, 21419}, {15826, 47352}, {15993, 47245}, {16176, 18374}, {16334, 47275}, {16619, 17814}, {18571, 43273}, {20063, 21356}, {22165, 37909}, {25336, 35265}, {32217, 40341}, {37924, 40107}

X(47448) = crossdifference of every pair of points on line {20190, 30209}
X(47448) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {468, 32113, 47276}, {468, 47276, 6}

X(47449) = X(6)X(468)∩X(23)X(3620)

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

X(47449) = X[6] - 3 X[468], X[6] + 3 X[32113], 5 X[6] + 3 X[47276], 5 X[6] - 3 X[47277], 7 X[6] + 3 X[47278], 7 X[6] - 3 X[47280], 3 X[6] - X[47281], 5 X[468] + X[47276], 5 X[468] - X[47277], 7 X[468] + X[47278], 3 X[468] + X[47279], 7 X[468] - X[47280], 9 X[468] - X[47281], 5 X[32113] - X[47276], 5 X[32113] + X[47277], 7 X[32113] - X[47278], 3 X[32113] - X[47279], 7 X[32113] + X[47280], 9 X[32113] + X[47281], 7 X[47276] - 5 X[47278], 3 X[47276] - 5 X[47279], 7 X[47276] + 5 X[47280], 9 X[47276] + 5 X[47281], 7 X[47277] + 5 X[47278], 3 X[47277] + 5 X[47279], 7 X[47277] - 5 X[47280], 9 X[47277] - 5 X[47281], 3 X[47278] - 7 X[47279], 9 X[47278] + 7 X[47281], 7 X[47279] + 3 X[47280], 3 X[47279] + X[47281], 9 X[47280] - 7 X[47281], 3 X[23] + 5 X[3620], X[69] + 3 X[7426], 9 X[186] - X[39874], X[193] - 9 X[37907], 3 X[858] - 7 X[3619], X[3630] + 3 X[32217], X[3630] + 6 X[47316], X[3631] + 3 X[32218], 2 X[3631] + 3 X[37897], 5 X[3763] - 3 X[47097], 3 X[5112] + X[47285], 3 X[16334] - X[47285], 3 X[5159] - 4 X[34573], X[5921] + 7 X[37957], 3 X[10516] - X[47339], 3 X[11799] + X[33878], 5 X[12017] - 9 X[44214], X[16496] + 3 X[47321], X[18440] + 3 X[44265], X[20080] + 3 X[32220], X[20080] + 15 X[37760], X[32220] - 5 X[37760], 3 X[21356] + X[47313], 3 X[21358] - X[47311], X[21850] - 3 X[47334], X[31670] - 3 X[47332], X[32114] + 3 X[32225], X[43621] - 3 X[47309], X[46264] - 3 X[47333]

X(47449) lies on these lines: {6, 468}, {23, 3620}, {30, 141}, {66, 37931}, {69, 7426}, {159, 186}, {193, 37907}, {524, 32223}, {599, 37904}, {858, 3619}, {1495, 47150}, {1503, 20417}, {2393, 47296}, {3153, 15435}, {3564, 8262}, {3628, 12061}, {3630, 32217}, {3631, 13562}, {3763, 47097}, {5112, 16334}, {5159, 8705}, {5181, 32269}, {5921, 37957}, {7716, 10151}, {8675, 47252}, {9030, 47261}, {9822, 11649}, {9969, 37942}, {10169, 37453}, {10516, 47339}, {11064, 41583}, {11216, 38282}, {11799, 33878}, {12017, 44214}, {13383, 44493}, {15066, 16789}, {15585, 37935}, {15993, 16316}, {16312, 47322}, {16496, 47321}, {18440, 44265}, {18571, 35707}, {19510, 29181}, {20080, 32220}, {20987, 37969}, {21356, 47313}, {21358, 47311}, {21850, 47334}, {31670, 47332}, {32114, 32225}, {32237, 32257}, {35370, 44668}, {43621, 47309}, {46264, 47333}

X(47449) = midpoint of X(i) and X(j) for these {i,j}: {6, 47279}, {468, 32113}, {599, 37904}, {5112, 16334}, {5181, 32269}, {11064, 41583}, {15993, 16316}, {16312, 47322}, {32237, 32257}, {47276, 47277}, {47278, 47280}
X(47449) = reflection of X(i) in X(j) for these {i,j}: {32217, 47316}, {37897, 32218}
X(47449) = crossdifference of every pair of points on line {5085, 30209}
X(47449) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 468, 47454}, {6, 32113, 47279}, {468, 47279, 6}

X(47450) = X(6)X(468)∩X(23)X(141)

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

X(47450) = X[6] - 4 X[468], X[6] + 2 X[32113], 2 X[6] + X[47276], 7 X[6] - 4 X[47277], 11 X[6] + 4 X[47278], 5 X[6] + 4 X[47279], 5 X[6] - 2 X[47280], 13 X[6] - 4 X[47281], 2 X[468] + X[32113], 8 X[468] + X[47276], 7 X[468] - X[47277], 11 X[468] + X[47278], 5 X[468] + X[47279], 10 X[468] - X[47280], 13 X[468] - X[47281], 4 X[32113] - X[47276], 7 X[32113] + 2 X[47277], 11 X[32113] - 2 X[47278], 5 X[32113] - 2 X[47279], 5 X[32113] + X[47280], 13 X[32113] + 2 X[47281], 7 X[47276] + 8 X[47277], 11 X[47276] - 8 X[47278], 5 X[47276] - 8 X[47279], 5 X[47276] + 4 X[47280], 13 X[47276] + 8 X[47281], 11 X[47277] + 7 X[47278], 5 X[47277] + 7 X[47279], 10 X[47277] - 7 X[47280], 13 X[47277] - 7 X[47281], 5 X[47278] - 11 X[47279], 10 X[47278] + 11 X[47280], 13 X[47278] + 11 X[47281], 2 X[47279] + X[47280], 13 X[47279] + 5 X[47281], 13 X[47280] - 10 X[47281], X[23] + 2 X[141], X[23] - 4 X[32218], X[141] + 2 X[32218], X[67] + 2 X[1495], X[69] + 2 X[32217], X[69] + 5 X[37760], 2 X[32217] - 5 X[37760], X[110] + 2 X[8262], 2 X[125] + X[12367], X[599] + 2 X[7426], 2 X[858] - 5 X[3763], X[1350] + 2 X[11799], X[1352] + 2 X[7575], X[2453] + 2 X[5112], X[2453] - 4 X[16321], 2 X[2453] + X[47275], X[5112] + 2 X[16321], 4 X[5112] - X[47275], 8 X[16321] + X[47275], X[2930] + 2 X[3580], 2 X[3098] + X[18325], X[3242] + 2 X[47321], 5 X[3618] - 2 X[15826], 7 X[3619] - X[5189], 2 X[5099] + X[5104], X[5181] + 2 X[32223], X[5648] + 2 X[32225], 4 X[5972] - X[10510], 2 X[5972] + X[41583], X[10510] + 2 X[41583], 2 X[6593] + X[41721], X[7574] - 4 X[24206], 2 X[10295] + X[36990], X[10989] - 4 X[20582], X[11646] + 2 X[47326], X[14853] - 3 X[37943], X[14982] + 2 X[32110], X[15993] + 2 X[16320], 4 X[16334] - X[47284], 2 X[16334] + X[47322], X[47284] + 2 X[47322], X[18440] + 5 X[37958], 4 X[18571] - X[46264], 4 X[18579] - X[43273], X[25335] + 2 X[46818], 5 X[30745] - 8 X[34573], X[31670] - 4 X[44961], 2 X[32120] + X[39232], 2 X[32220] + X[40341], 5 X[37952] - 2 X[44882], 2 X[44265] + X[47353]

X(47450) lies on these lines: {2, 6324}, {6, 468}, {23, 141}, {30, 10516}, {50, 35282}, {67, 1495}, {69, 32217}, {110, 8262}, {125, 12367}, {159, 37920}, {186, 1503}, {511, 14643}, {523, 9210}, {524, 25321}, {599, 7426}, {858, 3763}, {1350, 11799}, {1352, 7575}, {2071, 21167}, {2453, 5112}, {2916, 26156}, {2930, 3580}, {3098, 18325}, {3242, 47321}, {3618, 15826}, {3619, 5189}, {3818, 35257}, {5085, 44214}, {5099, 5104}, {5181, 32223}, {5648, 9027}, {5972, 10510}, {6593, 41721}, {7574, 24206}, {7716, 37981}, {7800, 37905}, {8675, 47255}, {9030, 47263}, {10096, 34380}, {10295, 36990}, {10545, 20113}, {10989, 20582}, {11646, 47326}, {11649, 38317}, {12061, 14940}, {14561, 44282}, {14853, 37943}, {14982, 32110}, {15993, 16320}, {16334, 47284}, {18440, 37958}, {18571, 46264}, {18579, 43273}, {20987, 21284}, {21356, 37909}, {25335, 46818}, {29317, 31726}, {30745, 34573}, {31670, 44961}, {32120, 39232}, {32220, 40341}, {35283, 37980}, {37485, 37973}, {37904, 43653}, {37952, 44882}, {38110, 44234}, {44265, 47353}

X(47450) = midpoint of X(21356) and X(37909)
X(47450) = reflection of X(i) in X(j) for these {i,j}: {2071, 21167}, {5085, 44214}, {14561, 44282}, {38110, 44234}
X(47450) = crossdifference of every pair of points on line {5092, 30209}
X(47450) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 468, 47453}, {6, 32113, 47276}, {69, 37760, 32217}, {141, 32218, 23}, {468, 32113, 6}, {2453, 5112, 47275}, {5112, 16321, 2453}, {5972, 41583, 10510}, {16334, 47322, 47284}, {32113, 47280, 47279}

X(47451) = X(6)X(468)∩X(30)X(14810)

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

X(47451) = X[6] - 5 X[468], 3 X[6] + 5 X[32113], 11 X[6] + 5 X[47276], 9 X[6] - 5 X[47277], 3 X[6] + X[47278], 7 X[6] + 5 X[47279], 13 X[6] - 5 X[47280], 17 X[6] - 5 X[47281], 3 X[468] + X[32113], 11 X[468] + X[47276], 9 X[468] - X[47277], 15 X[468] + X[47278], 7 X[468] + X[47279], 13 X[468] - X[47280], 17 X[468] - X[47281], 11 X[32113] - 3 X[47276], 3 X[32113] + X[47277], 5 X[32113] - X[47278], 7 X[32113] - 3 X[47279], 13 X[32113] + 3 X[47280], 17 X[32113] + 3 X[47281], 9 X[47276] + 11 X[47277], 15 X[47276] - 11 X[47278], 7 X[47276] - 11 X[47279], 13 X[47276] + 11 X[47280], 17 X[47276] + 11 X[47281], 5 X[47277] + 3 X[47278], 7 X[47277] + 9 X[47279], 13 X[47277] - 9 X[47280], 17 X[47277] - 9 X[47281], 7 X[47278] - 15 X[47279], 13 X[47278] + 15 X[47280], 17 X[47278] + 15 X[47281], 13 X[47279] + 7 X[47280], 17 X[47279] + 7 X[47281], 17 X[47280] - 13 X[47281], 3 X[20582] + 5 X[32218], 7 X[3619] + X[37900], 5 X[3763] - X[46517], X[5480] - 3 X[37942], 5 X[7426] + 3 X[21356], 3 X[22165] + 5 X[32217], 3 X[10516] + X[47340], 3 X[11160] + 5 X[32220], X[11160] + 15 X[37907], X[32220] - 9 X[37907], 5 X[16334] - X[47283], 3 X[21167] - X[47337], 3 X[21358] + X[47312], X[36990] + 3 X[37931]

X(47451) lies on these lines: {6, 468}, {30, 14810}, {141, 37897}, {159, 37977}, {3619, 37900}, {3763, 46517}, {5480, 37942}, {5646, 47097}, {7426, 21356}, {8705, 9822}, {9306, 22165}, {10169, 38282}, {10516, 47340}, {11160, 32220}, {16334, 47283}, {21167, 47337}, {21358, 47312}, {23328, 37934}, {25556, 34380}, {36990, 37931}

X(47451) = midpoint of X(141) and X(37897)
X(47451) = {X(6),X(32113)}-harmonic conjugate of X(47278)

X(47452) = X(6)X(468)∩X(23)X(3619)

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

X(47452) = X[6] - 6 X[468], 2 X[6] + 3 X[32113], 7 X[6] + 3 X[47276], 11 X[6] - 6 X[47277], 19 X[6] + 6 X[47278], 3 X[6] + 2 X[47279], 8 X[6] - 3 X[47280], 7 X[6] - 2 X[47281], 4 X[468] + X[32113], 14 X[468] + X[47276], 11 X[468] - X[47277], 19 X[468] + X[47278], 9 X[468] + X[47279], 16 X[468] - X[47280], 21 X[468] - X[47281], 7 X[32113] - 2 X[47276], 11 X[32113] + 4 X[47277], 19 X[32113] - 4 X[47278], 9 X[32113] - 4 X[47279], 4 X[32113] + X[47280], 21 X[32113] + 4 X[47281], 11 X[47276] + 14 X[47277], 19 X[47276] - 14 X[47278], 9 X[47276] - 14 X[47279], 8 X[47276] + 7 X[47280], 3 X[47276] + 2 X[47281], 19 X[47277] + 11 X[47278], 9 X[47277] + 11 X[47279], 16 X[47277] - 11 X[47280], 21 X[47277] - 11 X[47281], 9 X[47278] - 19 X[47279], 16 X[47278] + 19 X[47280], 21 X[47278] + 19 X[47281], 16 X[47279] + 9 X[47280], 7 X[47279] + 3 X[47281], 21 X[47280] - 16 X[47281], 3 X[23] + 7 X[3619], X[67] + 4 X[15448], X[69] + 9 X[37907], 2 X[141] + 3 X[7426], X[858] + 4 X[32218], 3 X[858] - 8 X[34573], 3 X[32218] + 2 X[34573], 9 X[2072] - 14 X[42786], 2 X[3098] + 3 X[11799], X[3620] + 3 X[37760], 2 X[3630] + 3 X[32220], 2 X[3631] + 3 X[32217], 2 X[3818] + 3 X[44265], 4 X[5092] - 9 X[44214], 3 X[7575] + 2 X[18358], X[12367] + 4 X[47296], X[15993] + 4 X[47171], 6 X[16321] - X[47285], 4 X[16321] + X[47322], 2 X[47285] + 3 X[47322], 6 X[18579] - X[46264], 4 X[20582] + X[47313], 3 X[21358] + 2 X[37904], X[31670] - 6 X[47334], X[36990] + 4 X[37934], X[43621] - 6 X[47336]

X(47452) lies on these lines: {6, 468}, {23, 3619}, {30, 3763}, {67, 15448}, {69, 37907}, {141, 7426}, {186, 20987}, {511, 38795}, {858, 5888}, {2072, 42786}, {2916, 15646}, {3098, 11799}, {3620, 37760}, {3630, 32220}, {3631, 32217}, {3818, 44265}, {5092, 44214}, {7575, 18358}, {12367, 47296}, {15993, 47171}, {16321, 47285}, {18579, 46264}, {20582, 47313}, {21358, 37904}, {31670, 47334}, {36990, 37934}, {37953, 40330}, {43621, 47336}

X(47452) = midpoint of X(37953) and X(40330)
X(47452) = crossdifference of every pair of points on line {17508, 30209}
X(47452) = {X(6),X(47276)}-harmonic conjugate of X(47281)

X(47453) = X(6)X(468)∩X(23)X(2916)

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

X(47453) = 3 X[2] + 2 X[32217], X[6] + 4 X[468], 3 X[6] + 2 X[32113], 4 X[6] + X[47276], 9 X[6] - 4 X[47277], 21 X[6] + 4 X[47278], 11 X[6] + 4 X[47279], 7 X[6] - 2 X[47280], 19 X[6] - 4 X[47281], 6 X[468] - X[32113], 16 X[468] - X[47276], 9 X[468] + X[47277], 21 X[468] - X[47278], 11 X[468] - X[47279], 14 X[468] + X[47280], 19 X[468] + X[47281], 8 X[32113] - 3 X[47276], 3 X[32113] + 2 X[47277], 7 X[32113] - 2 X[47278], 11 X[32113] - 6 X[47279], 7 X[32113] + 3 X[47280], 19 X[32113] + 6 X[47281], 9 X[47276] + 16 X[47277], 21 X[47276] - 16 X[47278], 11 X[47276] - 16 X[47279], 7 X[47276] + 8 X[47280], 19 X[47276] + 16 X[47281], 7 X[47277] + 3 X[47278], 11 X[47277] + 9 X[47279], 14 X[47277] - 9 X[47280], 19 X[47277] - 9 X[47281], 11 X[47278] - 21 X[47279], 2 X[47278] + 3 X[47280], 19 X[47278] + 21 X[47281], 14 X[47279] + 11 X[47280], 19 X[47279] + 11 X[47281], 19 X[47280] - 14 X[47281], X[23] + 4 X[3589], 2 X[125] + 3 X[18374], 3 X[186] + 2 X[5480], 6 X[403] - X[36990], 3 X[597] + 2 X[32218], 2 X[597] + 3 X[37907], 4 X[32218] - 9 X[37907], 3 X[599] + 2 X[32220], 2 X[858] - 7 X[47355], 4 X[1316] + X[47275], X[1350] - 6 X[44214], X[1352] - 6 X[44282], 3 X[1691] + 2 X[5099], X[2453] + 4 X[16324], 2 X[7426] + 3 X[47352], 3 X[5085] + 2 X[11799], 4 X[5092] + X[18325], 3 X[5621] + 2 X[32111], 3 X[5648] + 2 X[32127], 3 X[6034] + 2 X[47326], X[6776] + 9 X[37943], X[7574] - 6 X[38317], 2 X[7575] + 3 X[14561], 4 X[10272] + X[32599], X[10510] + 4 X[32223], X[12367] + 4 X[15118], 8 X[15448] - 3 X[19596], X[15993] - 6 X[47243], X[16010] + 4 X[46817], 4 X[16303] + X[47284], 4 X[18571] + X[31670], X[21850] + 4 X[22249], 2 X[25328] + 3 X[35265], 3 X[25330] + 2 X[46818], 2 X[25338] + 3 X[38110], 4 X[32300] + X[41583], 3 X[38064] + 2 X[44266], 3 X[38072] + 2 X[44265], 3 X[38315] + 2 X[47321], X[43273] + 4 X[47334], 4 X[44961] + X[46264]

X(47453) lies on these lines: {2, 32217}, {6, 468}, {23, 2916}, {125, 18374}, {186, 5480}, {403, 10249}, {511, 38794}, {597, 32218}, {599, 32220}, {858, 47355}, {1316, 47275}, {1350, 44214}, {1352, 44282}, {1503, 15081}, {1691, 5099}, {2453, 16324}, {3066, 7426}, {3618, 8705}, {5085, 11799}, {5092, 18325}, {5621, 32111}, {5648, 32127}, {6034, 47326}, {6776, 37943}, {7574, 38317}, {7575, 14561}, {9030, 47264}, {10272, 32599}, {10510, 32223}, {12367, 15118}, {15448, 19596}, {15993, 47243}, {16010, 46817}, {16303, 47284}, {18571, 31670}, {19128, 38851}, {21850, 22249}, {25328, 35265}, {25330, 46818}, {25338, 38110}, {29181, 37952}, {32300, 41583}, {38064, 44266}, {38072, 44265}, {38315, 47321}, {43273, 47334}, {44961, 46264}

X(47453) = midpoint of X(3618) and X(37760)
X(47453) = crossdifference of every pair of points on line {14810, 30209}
X(47453) = {X(6),X(468)}-harmonic conjugate of X(47450)
X(47453) = {X(32113),X(47280)}-harmonic conjugate of X(47278)

X(47454) = X(6)X(468)∩X(30)X(3589)

Barycentrics 10*a^8 - a^6*b^2 - 13*a^4*b^4 + a^2*b^6 + 3*b^8 - a^6*c^2 + 18*a^4*b^2*c^2 - a^2*b^4*c^2 - 13*a^4*c^4 - a^2*b^2*c^4 - 6*b^4*c^4 + a^2*c^6 + 3*c^8 : :

X(47454) = X[6] + 3 X[468], 5 X[6] + 3 X[32113], 13 X[6] + 3 X[47276], 7 X[6] - 3 X[47277], 17 X[6] + 3 X[47278], 3 X[6] + X[47279], 11 X[6] - 3 X[47280], 5 X[6] - X[47281], 5 X[468] - X[32113], 13 X[468] - X[47276], 7 X[468] + X[47277], 17 X[468] - X[47278], 9 X[468] - X[47279], 11 X[468] + X[47280], 15 X[468] + X[47281], 13 X[32113] - 5 X[47276], 7 X[32113] + 5 X[47277], 17 X[32113] - 5 X[47278], 9 X[32113] - 5 X[47279], 11 X[32113] + 5 X[47280], 3 X[32113] + X[47281], 7 X[47276] + 13 X[47277], 17 X[47276] - 13 X[47278], 9 X[47276] - 13 X[47279], 11 X[47276] + 13 X[47280], 15 X[47276] + 13 X[47281], 17 X[47277] + 7 X[47278], 9 X[47277] + 7 X[47279], 11 X[47277] - 7 X[47280], 15 X[47277] - 7 X[47281], 9 X[47278] - 17 X[47279], 11 X[47278] + 17 X[47280], 15 X[47278] + 17 X[47281], 11 X[47279] + 9 X[47280], 5 X[47279] + 3 X[47281], 15 X[47280] - 11 X[47281], 5 X[3618] + 3 X[7426], 5 X[3620] + 3 X[32220], 3 X[11799] + 5 X[12017], 3 X[16303] + X[47285], 5 X[16491] + 3 X[47321], X[16619] + 3 X[38110], 3 X[18579] + X[21850], 7 X[42786] - 9 X[44911], X[31670] + 3 X[47333], X[37904] + 3 X[47352], X[33878] - 9 X[44214], 2 X[34573] - 3 X[37911], X[43621] + 3 X[47308], X[46264] + 3 X[47332], 3 X[47097] - 7 X[47355]

X(47454) lies on these lines: {6, 468}, {30, 3589}, {159, 37962}, {206, 37942}, {403, 23300}, {524, 47244}, {2071, 31521}, {3618, 7426}, {3620, 32220}, {5159, 19126}, {5480, 37934}, {6353, 10169}, {8675, 47253}, {8705, 47316}, {9030, 47262}, {11799, 12017}, {15118, 15448}, {16238, 44493}, {16303, 47285}, {16491, 47321}, {16619, 38110}, {18579, 21850}, {19137, 42786}, {19153, 37643}, {23327, 41424}, {31670, 47333}, {31860, 37904}, {33878, 44214}, {34573, 37911}, {43621, 47308}, {46264, 47332}, {47097, 47355}

X(47454) = midpoint of X(i) and X(j) for these {i,j}: {5159, 32217}, {5480, 37934}, {15118, 15448}
X(47454) = crossdifference of every pair of points on line {30209, 31884}
X(47454) = {X(6),X(468)}-harmonic conjugate of X(47449)
X(47454) = {X(6),X(32113)}-harmonic conjugate of X(47281)

X(47455) = X(6)X(468)∩X(23)X(3618)

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

X(47455) = X[6] + 2 X[468], 2 X[6] + X[32113], 5 X[6] + X[47276], 5 X[6] - 2 X[47277], 13 X[6] + 2 X[47278], 7 X[6] + 2 X[47279], 4 X[6] - X[47280], 11 X[6] - 2 X[47281], 4 X[468] - X[32113], 10 X[468] - X[47276], 5 X[468] + X[47277], 13 X[468] - X[47278], 7 X[468] - X[47279], 8 X[468] + X[47280], 11 X[468] + X[47281], 5 X[32113] - 2 X[47276], 5 X[32113] + 4 X[47277], 13 X[32113] - 4 X[47278], 7 X[32113] - 4 X[47279], 2 X[32113] + X[47280], 11 X[32113] + 4 X[47281], X[47276] + 2 X[47277], 13 X[47276] - 10 X[47278], 7 X[47276] - 10 X[47279], 4 X[47276] + 5 X[47280], 11 X[47276] + 10 X[47281], 13 X[47277] + 5 X[47278], 7 X[47277] + 5 X[47279], 8 X[47277] - 5 X[47280], 11 X[47277] - 5 X[47281], 7 X[47278] - 13 X[47279], 8 X[47278] + 13 X[47280], 11 X[47278] + 13 X[47281], 8 X[47279] + 7 X[47280], 11 X[47279] + 7 X[47281], 11 X[47280] - 8 X[47281], X[23] + 5 X[3618], X[67] - 4 X[47296], 2 X[141] + X[32220], 2 X[182] + X[11799], X[14644] + 3 X[19128], 2 X[597] + X[7426], X[858] - 4 X[3589], X[858] + 2 X[32217], 2 X[3589] + X[32217], 2 X[1177] + X[32125], X[1316] + 2 X[16324], 2 X[1316] + X[47322], 4 X[16324] - X[47322], 2 X[1386] + X[47321], X[1495] + 2 X[15118], 2 X[2030] + X[5099], X[2452] + 2 X[16321], X[2453] + 2 X[16303], 2 X[2492] + X[32120], X[3580] + 2 X[6593], 5 X[3763] - 8 X[37911], 4 X[5159] - 7 X[47355], 2 X[5476] + X[44265], 2 X[5480] + X[10295], 4 X[6329] - X[15826], 2 X[6329] + X[32218], X[15826] + 2 X[32218], X[7575] + 2 X[18583], X[10510] + 2 X[32269], X[11179] + 2 X[47334], X[11579] + 2 X[46817], 5 X[12017] + X[18325], X[12367] - 4 X[15448], X[14912] + 3 X[37943], X[15993] - 4 X[47239], 2 X[16333] + X[47285], X[18323] - 4 X[19130], 2 X[18571] + X[21850], 2 X[18579] + X[20423], 2 X[19138] + X[32123], 2 X[25328] + X[46818], 2 X[28662] + X[47325], X[31670] + 2 X[47335], X[32223] + 2 X[32300], X[34319] + 2 X[44569], X[36990] - 4 X[37984], X[40949] - 4 X[44084], X[41146] + 2 X[46998], X[43273] + 2 X[47332], X[46264] + 2 X[47336]

X(47455) lies on these lines: {6, 468}, {23, 3618}, {30, 5085}, {67, 47296}, {141, 32220}, {182, 11799}, {186, 14853}, {403, 1503}, {511, 16222}, {523, 14398}, {524, 47243}, {597, 5640}, {858, 3589}, {1177, 32125}, {1316, 16324}, {1386, 47321}, {1495, 15118}, {1974, 37981}, {2030, 5099}, {2072, 19131}, {2452, 16321}, {2453, 16303}, {2492, 32120}, {3003, 35282}, {3564, 44282}, {3580, 6593}, {3763, 37911}, {5159, 15812}, {5476, 39242}, {5480, 10295}, {5642, 9027}, {6030, 47313}, {6329, 15826}, {7575, 18583}, {8675, 47251}, {9030, 47259}, {9973, 23326}, {10510, 32269}, {10545, 25488}, {11179, 47334}, {11579, 46817}, {12017, 18325}, {12367, 15448}, {14912, 37943}, {15993, 47239}, {16333, 47285}, {18323, 19130}, {18571, 21850}, {18579, 20423}, {19138, 32123}, {19153, 26869}, {20300, 45181}, {20987, 37777}, {25320, 35265}, {25328, 46818}, {25555, 37513}, {28662, 47325}, {29181, 44280}, {29317, 44246}, {31670, 47335}, {32223, 32300}, {34319, 44569}, {34380, 44234}, {34397, 38851}, {35260, 37962}, {36990, 37984}, {37950, 38402}, {40949, 44084}, {41146, 46998}, {41939, 47349}, {43273, 47332}, {46264, 47336}

X(47455) = midpoint of X(i) and X(j) for these {i,j}: {186, 14853}, {25320, 35265}
X(47455) = reflection of X(2072) in X(38317)
X(47455) = crossdifference of every pair of points on line {3098, 30209}
X(47455) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 468, 32113}, {6, 32113, 47280}, {6, 47276, 47277}, {1316, 16324, 47322}, {3589, 32217, 858}, {6329, 32218, 15826}

X(47456) = X(6)X(468)∩X(30)X(3618)

Barycentrics 14*a^8 - 5*a^6*b^2 - 17*a^4*b^4 + 5*a^2*b^6 + 3*b^8 - 5*a^6*c^2 + 30*a^4*b^2*c^2 - 5*a^2*b^4*c^2 - 17*a^4*c^4 - 5*a^2*b^2*c^4 - 6*b^4*c^4 + 5*a^2*c^6 + 3*c^8 : :

X(47456) = 2 X[6] + 3 X[468], 7 X[6] + 3 X[32113], 17 X[6] + 3 X[47276], 8 X[6] - 3 X[47277], 22 X[6] + 3 X[47278], 4 X[6] + X[47279], 13 X[6] - 3 X[47280], 6 X[6] - X[47281], 7 X[468] - 2 X[32113], 17 X[468] - 2 X[47276], 4 X[468] + X[47277], 11 X[468] - X[47278], 6 X[468] - X[47279], 13 X[468] + 2 X[47280], 9 X[468] + X[47281], 17 X[32113] - 7 X[47276], 8 X[32113] + 7 X[47277], 22 X[32113] - 7 X[47278], 12 X[32113] - 7 X[47279], 13 X[32113] + 7 X[47280], 18 X[32113] + 7 X[47281], 8 X[47276] + 17 X[47277], 22 X[47276] - 17 X[47278], 12 X[47276] - 17 X[47279], 13 X[47276] + 17 X[47280], 18 X[47276] + 17 X[47281], 11 X[47277] + 4 X[47278], 3 X[47277] + 2 X[47279], 13 X[47277] - 8 X[47280], 9 X[47277] - 4 X[47281], 6 X[47278] - 11 X[47279], 13 X[47278] + 22 X[47280], 9 X[47278] + 11 X[47281], 13 X[47279] + 12 X[47280], 3 X[47279] + 2 X[47281], 18 X[47280] - 13 X[47281], 9 X[403] + X[39874], 4 X[597] + X[37904], 8 X[3589] - 3 X[47097], 7 X[3619] + 3 X[32220], 7 X[3619] - 12 X[37911], X[32220] + 4 X[37911], 4 X[32217] + X[46517], 6 X[14561] - X[47339], 3 X[14853] + 2 X[37934], 2 X[21850] + 3 X[47333], 2 X[31670] + 3 X[47031], X[32269] + 4 X[32300], 3 X[44102] + 2 X[47296], 9 X[44214] + X[44456], 2 X[46264] + 3 X[47310], X[47311] - 6 X[47352]

X(47456) lies on these lines: {6, 468}, {30, 3618}, {403, 39874}, {597, 34417}, {1974, 10151}, {3589, 47097}, {3619, 32220}, {5157, 32217}, {10297, 19129}, {14561, 47339}, {14805, 18583}, {14853, 37934}, {16314, 37899}, {19125, 37942}, {19459, 37962}, {21850, 47333}, {31670, 47031}, {31726, 41256}, {32269, 32300}, {44102, 47296}, {44214, 44456}, {46264, 47310}, {47311, 47352}

X(47456) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 468, 47279}, {6, 47279, 47277}

X(47457) = X(6)X(468)∩X(30)X(182)

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

X(47457) = 3 X[2] + X[32220], 3 X[6] + X[32113], 7 X[6] + X[47276], 3 X[6] - X[47277], 9 X[6] + X[47278], 5 X[6] + X[47279], 5 X[6] - X[47280], 7 X[6] - X[47281], 3 X[468] - X[32113], 7 X[468] - X[47276], 3 X[468] + X[47277], 9 X[468] - X[47278], 5 X[468] - X[47279], 5 X[468] + X[47280], 7 X[468] + X[47281], 7 X[32113] - 3 X[47276], 3 X[32113] - X[47278], 5 X[32113] - 3 X[47279], 5 X[32113] + 3 X[47280], 7 X[32113] + 3 X[47281], 3 X[47276] + 7 X[47277], 9 X[47276] - 7 X[47278], 5 X[47276] - 7 X[47279], 5 X[47276] + 7 X[47280], 3 X[47277] + X[47278], 5 X[47277] + 3 X[47279], 5 X[47277] - 3 X[47280], 7 X[47277] - 3 X[47281], 5 X[47278] - 9 X[47279], 5 X[47278] + 9 X[47280], 7 X[47278] + 9 X[47281], 7 X[47279] + 5 X[47281], 7 X[47280] - 5 X[47281], 3 X[597] + X[32217], X[125] + 3 X[44102], 3 X[403] + X[6776], X[858] - 5 X[3618], X[1351] + 3 X[44214], X[1353] + 3 X[44282], 3 X[1692] + X[5099], 3 X[5050] + X[11799], 3 X[5622] + X[32111], 3 X[5642] + X[32127], 4 X[6329] + X[37897], 3 X[10151] - X[36990], X[10295] + 3 X[14853], X[10297] - 3 X[14561], 2 X[12007] + 3 X[37942], 3 X[14398] + X[32120], 3 X[14848] + X[44265], X[15122] - 3 X[38110], X[15826] + 2 X[47316], X[15993] - 3 X[47240], 3 X[16227] - X[19161], 3 X[16475] + X[47321], 2 X[24206] - 3 X[44911], 3 X[25320] + X[46818], 3 X[36696] + X[47325], X[47097] - 3 X[47352]

X(47457) lies on these lines: {2, 32220}, {6, 468}, {25, 10169}, {30, 182}, {125, 44102}, {140, 44493}, {141, 37911}, {159, 18919}, {403, 6776}, {511, 9826}, {524, 5972}, {858, 3618}, {1177, 11744}, {1316, 16303}, {1351, 44214}, {1353, 44282}, {1503, 7687}, {1692, 5099}, {2393, 11746}, {2452, 16334}, {2854, 35370}, {3564, 6593}, {3589, 5159}, {5050, 11799}, {5622, 32111}, {5642, 32127}, {6329, 8705}, {6353, 11216}, {8675, 47249}, {10011, 24975}, {10151, 23327}, {10295, 14853}, {10297, 14561}, {11179, 47332}, {11430, 37934}, {12007, 37942}, {13198, 18374}, {14398, 32120}, {14848, 44265}, {15122, 38110}, {15151, 34146}, {15303, 44569}, {15471, 47296}, {15577, 44272}, {15826, 47316}, {15993, 47240}, {16227, 19161}, {16326, 47284}, {16475, 47321}, {17810, 37904}, {18571, 37827}, {19118, 23300}, {19128, 41613}, {20423, 47333}, {21850, 47335}, {24206, 44911}, {25320, 46818}, {31670, 47308}, {32191, 32411}, {32621, 37962}, {32740, 47188}, {35371, 44084}, {36696, 47325}, {43273, 47310}, {46264, 47309}, {47097, 47352}

X(47457) = midpoint of X(i) and X(j) for these {i,j}: {6, 468}, {1316, 16303}, {2452, 16334}, {11179, 47332}, {15303, 44569}, {15471, 47296}, {16326, 47284}, {20423, 47333}, {21850, 47335}, {31670, 47308}, {32113, 47277}, {35371, 44084}, {43273, 47310}, {46264, 47309}, {47276, 47281}, {47279, 47280}
X(47457) = reflection of X(i) in X(j) for these {i,j}: {141, 37911}, {5159, 3589}
X(47457) = crossdifference of every pair of points on line {1350, 30209}
X(47457) = centroid of PU(4)PU(45)
X(47457) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 32113, 47277}, {468, 47277, 32113}

X(47458) = X(6)X(468)∩X(67)X(15471)

Barycentrics 8*a^8 - 5*a^6*b^2 - 9*a^4*b^4 + 5*a^2*b^6 + b^8 - 5*a^6*c^2 + 20*a^4*b^2*c^2 - 5*a^2*b^4*c^2 - 9*a^4*c^4 - 5*a^2*b^2*c^4 - 2*b^4*c^4 + 5*a^2*c^6 + c^8 : :

X(47458) = 3 X[6] + 2 X[468], 4 X[6] + X[32113], 9 X[6] + X[47276], 7 X[6] - 2 X[47277], 23 X[6] + 2 X[47278], 13 X[6] + 2 X[47279], 6 X[6] - X[47280], 17 X[6] - 2 X[47281], 8 X[468] - 3 X[32113], 6 X[468] - X[47276], 7 X[468] + 3 X[47277], 23 X[468] - 3 X[47278], 13 X[468] - 3 X[47279], 4 X[468] + X[47280], 17 X[468] + 3 X[47281], 9 X[32113] - 4 X[47276], 7 X[32113] + 8 X[47277], 23 X[32113] - 8 X[47278], 13 X[32113] - 8 X[47279], 3 X[32113] + 2 X[47280], 17 X[32113] + 8 X[47281], 7 X[47276] + 18 X[47277], 23 X[47276] - 18 X[47278], 13 X[47276] - 18 X[47279], 2 X[47276] + 3 X[47280], 17 X[47276] + 18 X[47281], 23 X[47277] + 7 X[47278], 13 X[47277] + 7 X[47279], 12 X[47277] - 7 X[47280], 17 X[47277] - 7 X[47281], 13 X[47278] - 23 X[47279], 12 X[47278] + 23 X[47280], 17 X[47278] + 23 X[47281], 12 X[47279] + 13 X[47280], 17 X[47279] + 13 X[47281], 17 X[47280] - 12 X[47281], X[67] + 4 X[15471], 3 X[403] + 2 X[8550], 4 X[575] + X[11799], 2 X[576] + 3 X[44214], 6 X[597] - X[858], 3 X[599] - 8 X[37911], 4 X[6329] + X[32217], 24 X[6329] + X[37900], 6 X[32217] - X[37900], 3 X[1316] + 2 X[16333], 3 X[2072] - 8 X[25555], 4 X[3589] + X[32220], 3 X[3618] - X[30745], 9 X[5050] + X[18325], 4 X[5159] - 9 X[47352], 6 X[5476] - X[18323], 3 X[7426] + 2 X[15826], 3 X[11179] + 2 X[47336], 2 X[15118] + 3 X[44102], 3 X[15993] - 8 X[47241], 6 X[16227] - X[37473], X[18572] - 6 X[18583], 3 X[20423] + 2 X[47335], 4 X[35371] + X[40949], 16 X[41153] - X[47314], 3 X[43273] + 2 X[47309]

X(47458) lies on these lines: {6, 468}, {67, 15471}, {403, 8550}, {575, 11799}, {576, 44214}, {597, 858}, {599, 37911}, {1176, 6329}, {1316, 16333}, {2072, 25555}, {3589, 32220}, {3618, 30745}, {5050, 18325}, {5159, 47352}, {5476, 18323}, {7426, 15019}, {10169, 10301}, {10295, 15033}, {11179, 47336}, {11425, 37934}, {15118, 32239}, {15993, 47241}, {16227, 37473}, {18572, 18583}, {20423, 47335}, {35371, 40949}, {40135, 41359}, {41153, 47314}, {43273, 47309}

X(47458) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 468, 47280}, {468, 47280, 32113}

X(47459) = X(6)X(468)∩X(30)X(5050)

Barycentrics 10*a^8 - 7*a^6*b^2 - 11*a^4*b^4 + 7*a^2*b^6 + b^8 - 7*a^6*c^2 + 26*a^4*b^2*c^2 - 7*a^2*b^4*c^2 - 11*a^4*c^4 - 7*a^2*b^2*c^4 - 2*b^4*c^4 + 7*a^2*c^6 + c^8 : :

X(47459) = 2 X[6] + X[468], 5 X[6] + X[32113], 11 X[6] + X[47276], 4 X[6] - X[47277], 14 X[6] + X[47278], 8 X[6] + X[47279], 7 X[6] - X[47280], 10 X[6] - X[47281], 5 X[468] - 2 X[32113], 11 X[468] - 2 X[47276], 2 X[468] + X[47277], 7 X[468] - X[47278], 4 X[468] - X[47279], 7 X[468] + 2 X[47280], 5 X[468] + X[47281], 11 X[32113] - 5 X[47276], 4 X[32113] + 5 X[47277], 14 X[32113] - 5 X[47278], 8 X[32113] - 5 X[47279], 7 X[32113] + 5 X[47280], 2 X[32113] + X[47281], 4 X[47276] + 11 X[47277], 14 X[47276] - 11 X[47278], 8 X[47276] - 11 X[47279], 7 X[47276] + 11 X[47280], 10 X[47276] + 11 X[47281], 7 X[47277] + 2 X[47278], 2 X[47277] + X[47279], 7 X[47277] - 4 X[47280], 5 X[47277] - 2 X[47281], 4 X[47278] - 7 X[47279], X[47278] + 2 X[47280], 5 X[47278] + 7 X[47281], 7 X[47279] + 8 X[47280], 5 X[47279] + 4 X[47281], 10 X[47280] - 7 X[47281], X[69] - 4 X[37911], X[125] + 2 X[15471], 4 X[597] - X[47097], X[1112] + 2 X[35371], 2 X[2452] + X[16312], 2 X[2453] + X[16326], 5 X[3618] - 2 X[5159], 5 X[3618] + X[32220], 2 X[5159] + X[32220], X[5095] + 2 X[47296], 16 X[6329] - X[46517], X[6776] + 2 X[37984], X[10297] - 4 X[18583], X[11064] - 4 X[32300], 2 X[11179] + X[47310], 2 X[20423] + X[47031], 2 X[21850] + X[47308], 4 X[32217] - X[37899]

X(47459) lies on these lines: {6, 468}, {30, 5050}, {51, 8705}, {69, 37911}, {125, 15471}, {403, 14912}, {428, 10169}, {511, 16227}, {524, 47240}, {575, 16657}, {597, 47097}, {1112, 35371}, {1503, 10151}, {1974, 23326}, {2452, 16312}, {2453, 16326}, {3564, 14643}, {3618, 5159}, {5093, 44214}, {5095, 47296}, {6329, 46517}, {6776, 37984}, {6793, 16315}, {10257, 38110}, {10297, 18583}, {10602, 35260}, {11064, 32300}, {11179, 47310}, {11470, 23328}, {19459, 37777}, {20423, 47031}, {21850, 47308}, {22151, 34380}, {32217, 37899}, {35282, 40135}, {37981, 41719}, {43697, 47336}

X(47459) = midpoint of X(i) and X(j) for these {i,j}: {403, 14912}, {5093, 44214}
X(47459) = reflection of X(10257) in X(38110)
X(47459) = crossdifference of every pair of points on line {30209, 33878}
X(47459) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 468, 47277}, {468, 47277, 47279}, {468, 47281, 32113}, {3618, 32220, 5159}

X(47460) = X(6)X(468)∩X(30)X(575)

Barycentrics 14*a^8 - 11*a^6*b^2 - 15*a^4*b^4 + 11*a^2*b^6 + b^8 - 11*a^6*c^2 + 38*a^4*b^2*c^2 - 11*a^2*b^4*c^2 - 15*a^4*c^4 - 11*a^2*b^2*c^4 - 2*b^4*c^4 + 11*a^2*c^6 + c^8 : :

X(47460) = 3 X[6] + X[468], 7 X[6] + X[32113], 15 X[6] + X[47276], 5 X[6] - X[47277], 19 X[6] + X[47278], 11 X[6] + X[47279], 9 X[6] - X[47280], 13 X[6] - X[47281], 7 X[468] - 3 X[32113], 5 X[468] - X[47276], 5 X[468] + 3 X[47277], 19 X[468] - 3 X[47278], 11 X[468] - 3 X[47279], 3 X[468] + X[47280], 13 X[468] + 3 X[47281], 15 X[32113] - 7 X[47276], 5 X[32113] + 7 X[47277], 19 X[32113] - 7 X[47278], 11 X[32113] - 7 X[47279], 9 X[32113] + 7 X[47280], 13 X[32113] + 7 X[47281], X[47276] + 3 X[47277], 19 X[47276] - 15 X[47278], 11 X[47276] - 15 X[47279], 3 X[47276] + 5 X[47280], 13 X[47276] + 15 X[47281], 19 X[47277] + 5 X[47278], 11 X[47277] + 5 X[47279], 9 X[47277] - 5 X[47280], 13 X[47277] - 5 X[47281], 11 X[47278] - 19 X[47279], 9 X[47278] + 19 X[47280], 13 X[47278] + 19 X[47281], 9 X[47279] + 11 X[47280], 13 X[47279] + 11 X[47281], 13 X[47280] - 9 X[47281], 3 X[597] - X[5159], 3 X[11179] + X[47309], 5 X[11482] + 3 X[44214], 9 X[14848] - X[18323], 3 X[20423] + X[47308], 5 X[30745] + 3 X[32220], 3 X[32217] - X[37910], X[34507] - 3 X[44911]

X(47460) lies on these lines: {4, 10169}, {6, 468}, {30, 575}, {524, 32300}, {578, 37934}, {597, 5159}, {4232, 11216}, {5189, 41256}, {8550, 18390}, {11179, 47309}, {11482, 44214}, {14848, 18323}, {15118, 15126}, {15122, 44480}, {15826, 37897}, {20423, 47308}, {30745, 32220}, {32217, 37910}, {32621, 37777}, {34507, 44911}, {35282, 46211}, {37899, 38005}

X(47460) = midpoint of X(i) and X(j) for these {i,j}: {8550, 37984}, {15118, 15471}, {15826, 37897}
X(47460) = {X(6),X(468)}-harmonic conjugate of X(47464)
X(47460) = {X(468),X(47277)}-harmonic conjugate of X(47276)

X(47461) = X(6)X(468)∩X(193)X(21968)

Barycentrics 18*a^8 - 15*a^6*b^2 - 19*a^4*b^4 + 15*a^2*b^6 + b^8 - 15*a^6*c^2 + 50*a^4*b^2*c^2 - 15*a^2*b^4*c^2 - 19*a^4*c^4 - 15*a^2*b^2*c^4 - 2*b^4*c^4 + 15*a^2*c^6 + c^8 : :

X(47461) = 4 X[6] + X[468], 9 X[6] + X[32113], 19 X[6] + X[47276], 6 X[6] - X[47277], 24 X[6] + X[47278], 14 X[6] + X[47279], 11 X[6] - X[47280], 16 X[6] - X[47281], 9 X[468] - 4 X[32113], 19 X[468] - 4 X[47276], 3 X[468] + 2 X[47277], 6 X[468] - X[47278], 7 X[468] - 2 X[47279], 11 X[468] + 4 X[47280], 4 X[468] + X[47281], 19 X[32113] - 9 X[47276], 2 X[32113] + 3 X[47277], 8 X[32113] - 3 X[47278], 14 X[32113] - 9 X[47279], 11 X[32113] + 9 X[47280], 16 X[32113] + 9 X[47281], 6 X[47276] + 19 X[47277], 24 X[47276] - 19 X[47278], 14 X[47276] - 19 X[47279], 11 X[47276] + 19 X[47280], 16 X[47276] + 19 X[47281], 4 X[47277] + X[47278], 7 X[47277] + 3 X[47279], 11 X[47277] - 6 X[47280], 8 X[47277] - 3 X[47281], 7 X[47278] - 12 X[47279], 11 X[47278] + 24 X[47280], 2 X[47278] + 3 X[47281], 11 X[47279] + 14 X[47280], 8 X[47279] + 7 X[47281], 16 X[47280] - 11 X[47281], X[193] + 4 X[37911], 4 X[1316] + X[16326], 8 X[5480] - 3 X[13473], 2 X[6776] + 3 X[10151], X[11898] - 6 X[44911], 3 X[14912] + 2 X[37984], 2 X[15448] + 3 X[21639], 8 X[32217] - 3 X[47312], 2 X[32220] + 3 X[47097]

X(47461) lies on these lines: {6, 468}, {193, 21968}, {1316, 16326}, {5480, 13473}, {6776, 10151}, {7699, 18583}, {9777, 37904}, {11898, 44911}, {14912, 37984}, {15448, 21639}, {32217, 47312}, {32220, 47097}

X(47461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 468, 47463}, {468, 47277, 47278}, {47277, 47278, 47281}

X(47462) = X(6)X(468)∩X(30)X(11482)

Barycentrics 22*a^8 - 25*a^6*b^2 - 21*a^4*b^4 + 25*a^2*b^6 - b^8 - 25*a^6*c^2 + 70*a^4*b^2*c^2 - 25*a^2*b^4*c^2 - 21*a^4*c^4 - 25*a^2*b^2*c^4 + 2*b^4*c^4 + 25*a^2*c^6 - c^8 : :

X(47462) = 6 X[6] - X[468], 11 X[6] - X[32113], 21 X[6] - X[47276], 4 X[6] + X[47277], 26 X[6] - X[47278], 16 X[6] - X[47279], 9 X[6] + X[47280], 14 X[6] + X[47281], 11 X[468] - 6 X[32113], 7 X[468] - 2 X[47276], 2 X[468] + 3 X[47277], 13 X[468] - 3 X[47278], 8 X[468] - 3 X[47279], 3 X[468] + 2 X[47280], 7 X[468] + 3 X[47281], 21 X[32113] - 11 X[47276], 4 X[32113] + 11 X[47277], 26 X[32113] - 11 X[47278], 16 X[32113] - 11 X[47279], 9 X[32113] + 11 X[47280], 14 X[32113] + 11 X[47281], 4 X[47276] + 21 X[47277], 26 X[47276] - 21 X[47278], 16 X[47276] - 21 X[47279], 3 X[47276] + 7 X[47280], 2 X[47276] + 3 X[47281], 13 X[47277] + 2 X[47278], 4 X[47277] + X[47279], 9 X[47277] - 4 X[47280], 7 X[47277] - 2 X[47281], 8 X[47278] - 13 X[47279], 9 X[47278] + 26 X[47280], 7 X[47278] + 13 X[47281], 9 X[47279] + 16 X[47280], 7 X[47279] + 8 X[47281], 14 X[47280] - 9 X[47281], X[858] + 9 X[5032], 3 X[1992] + 2 X[5159], 4 X[8584] + X[47097], 2 X[15471] + 3 X[21639], 4 X[15826] + X[37899], 24 X[20583] + X[46517], 3 X[32220] + 2 X[47315]

X(47462) lies on these lines: {6, 468}, {30, 11482}, {858, 5032}, {1992, 5159}, {8584, 47097}, {10301, 11216}, {11432, 37934}, {13366, 37904}, {15471, 21639}, {15826, 37899}, {20583, 46517}, {32220, 47315}

X(47463) = X(6)X(468)∩X(30)X(5032)

Barycentrics 14*a^8 - 17*a^6*b^2 - 13*a^4*b^4 + 17*a^2*b^6 - b^8 - 17*a^6*c^2 + 46*a^4*b^2*c^2 - 17*a^2*b^4*c^2 - 13*a^4*c^4 - 17*a^2*b^2*c^4 + 2*b^4*c^4 + 17*a^2*c^6 - c^8 : :

X(47463) = 4 X[6] - X[468], 7 X[6] - X[32113], 13 X[6] - X[47276], 2 X[6] + X[47277], 16 X[6] - X[47278], 10 X[6] - X[47279], 5 X[6] + X[47280], 8 X[6] + X[47281], 7 X[468] - 4 X[32113], 13 X[468] - 4 X[47276], X[468] + 2 X[47277], 4 X[468] - X[47278], 5 X[468] - 2 X[47279], 5 X[468] + 4 X[47280], 2 X[468] + X[47281], 13 X[32113] - 7 X[47276], 2 X[32113] + 7 X[47277], 16 X[32113] - 7 X[47278], 10 X[32113] - 7 X[47279], 5 X[32113] + 7 X[47280], 8 X[32113] + 7 X[47281], 2 X[47276] + 13 X[47277], 16 X[47276] - 13 X[47278], 10 X[47276] - 13 X[47279], 5 X[47276] + 13 X[47280], 8 X[47276] + 13 X[47281], 8 X[47277] + X[47278], 5 X[47277] + X[47279], 5 X[47277] - 2 X[47280], 4 X[47277] - X[47281], 5 X[47278] - 8 X[47279], 5 X[47278] + 16 X[47280], X[47278] + 2 X[47281], X[47279] + 2 X[47280], 4 X[47279] + 5 X[47281], 8 X[47280] - 5 X[47281], X[193] + 2 X[5159], 2 X[1353] + X[10297], 2 X[1992] + X[47097], 4 X[2452] - X[16326], 8 X[8584] + X[47311], 16 X[20583] - X[47312], 2 X[32220] + X[46517], 3 X[33748] - X[44280]

X(47463) lies on these lines: {6, 468}, {30, 5032}, {193, 5159}, {428, 11216}, {524, 47237}, {1353, 10297}, {1503, 13473}, {1992, 26869}, {2452, 16326}, {3564, 14644}, {8584, 11245}, {8705, 20583}, {9027, 12099}, {10151, 11405}, {10257, 34380}, {11402, 37904}, {11458, 16658}, {12022, 47339}, {17040, 47316}, {18550, 47309}, {25321, 38789}, {32220, 46517}, {33748, 44280}, {34569, 35282}

X(47463) = reflection of X(10151) in X(14853)
X(47463) = crossdifference of every pair of points on line {30209, 44456}
X(47463) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 468, 47461}, {6, 47277, 468}, {468, 47277, 47281}, {468, 47281, 47278}, {47277, 47279, 47280}

X(47464) = X(6)X(468)∩X(30)X(576)

Barycentrics 10*a^8 - 13*a^6*b^2 - 9*a^4*b^4 + 13*a^2*b^6 - b^8 - 13*a^6*c^2 + 34*a^4*b^2*c^2 - 13*a^2*b^4*c^2 - 9*a^4*c^4 - 13*a^2*b^2*c^4 + 2*b^4*c^4 + 13*a^2*c^6 - c^8 : :

X(47464) = 3 X[6] - X[468], 5 X[6] - X[32113], 9 X[6] - X[47276], 11 X[6] - X[47278], 7 X[6] - X[47279], 3 X[6] + X[47280], 5 X[6] + X[47281], 5 X[468] - 3 X[32113], 3 X[468] - X[47276], X[468] + 3 X[47277], 11 X[468] - 3 X[47278], 7 X[468] - 3 X[47279], 5 X[468] + 3 X[47281], 9 X[32113] - 5 X[47276], X[32113] + 5 X[47277], 11 X[32113] - 5 X[47278], 7 X[32113] - 5 X[47279], 3 X[32113] + 5 X[47280], X[47276] + 9 X[47277], 11 X[47276] - 9 X[47278], 7 X[47276] - 9 X[47279], X[47276] + 3 X[47280], 5 X[47276] + 9 X[47281], 11 X[47277] + X[47278], 7 X[47277] + X[47279], 3 X[47277] - X[47280], 5 X[47277] - X[47281], 7 X[47278] - 11 X[47279], 3 X[47278] + 11 X[47280], 5 X[47278] + 11 X[47281], 3 X[47279] + 7 X[47280], 5 X[47279] + 7 X[47281], 5 X[47280] - 3 X[47281], X[23] - 9 X[5032], 3 X[8584] + X[15826], 3 X[193] + 5 X[30745], 3 X[597] - 2 X[37911], X[858] + 3 X[1992], 3 X[1353] + X[18572], 9 X[5093] - X[18325], X[5095] + 3 X[21639], X[5189] + 3 X[32220], 3 X[11179] - X[47308], 5 X[11482] - X[11799], 3 X[20423] - X[47309], 6 X[20583] - X[37897], 4 X[25555] - 3 X[44911], 6 X[32455] + X[47315]

X(47464) lies on these lines: {4, 11216}, {6, 468}, {23, 5032}, {30, 576}, {193, 30745}, {389, 37934}, {524, 5159}, {597, 37911}, {858, 1992}, {1353, 18572}, {2393, 15471}, {3564, 11801}, {5093, 18325}, {5094, 10169}, {5095, 21639}, {5189, 32220}, {8675, 47247}, {8705, 32366}, {11179, 47308}, {11405, 37981}, {11482, 11799}, {15122, 44469}, {15534, 47097}, {17809, 37904}, {18388, 37984}, {20423, 47309}, {20583, 37897}, {25555, 44911}, {32455, 47315}

X(47464) = midpoint of X(i) and X(j) for these {i,j}: {6, 47277}, {468, 47280}, {15534, 47097}, {32113, 47281}
X(47464) = complement of X(47552)
X(47464) = crossdifference of every pair of points on line {11477, 30209}
X(47464) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 468, 47460}, {6, 47280, 468}, {468, 47277, 47280}

X(47465) = X(6)X(468)∩X(30)X(5102)

Barycentrics 8*a^8 - 11*a^6*b^2 - 7*a^4*b^4 + 11*a^2*b^6 - b^8 - 11*a^6*c^2 + 28*a^4*b^2*c^2 - 11*a^2*b^4*c^2 - 7*a^4*c^4 - 11*a^2*b^2*c^4 + 2*b^4*c^4 + 11*a^2*c^6 - c^8 : :

X(47465) = 5 X[6] - 2 X[468], 4 X[6] - X[32113], 7 X[6] - X[47276], X[6] + 2 X[47277], 17 X[6] - 2 X[47278], 11 X[6] - 2 X[47279], 2 X[6] + X[47280], 7 X[6] + 2 X[47281], 8 X[468] - 5 X[32113], 14 X[468] - 5 X[47276], X[468] + 5 X[47277], 17 X[468] - 5 X[47278], 11 X[468] - 5 X[47279], 4 X[468] + 5 X[47280], 7 X[468] + 5 X[47281], 7 X[32113] - 4 X[47276], X[32113] + 8 X[47277], 17 X[32113] - 8 X[47278], 11 X[32113] - 8 X[47279], X[32113] + 2 X[47280], 7 X[32113] + 8 X[47281], X[47276] + 14 X[47277], 17 X[47276] - 14 X[47278], 11 X[47276] - 14 X[47279], 2 X[47276] + 7 X[47280], X[47276] + 2 X[47281], 17 X[47277] + X[47278], 11 X[47277] + X[47279], 4 X[47277] - X[47280], 7 X[47277] - X[47281], 11 X[47278] - 17 X[47279], 4 X[47278] + 17 X[47280], 7 X[47278] + 17 X[47281], 4 X[47279] + 11 X[47280], 7 X[47279] + 11 X[47281], 7 X[47280] - 4 X[47281], X[858] + 2 X[3629], 5 X[1992] + X[10989], 10 X[8584] - X[47313], 5 X[5032] - X[37909], 4 X[5097] - X[11799], 4 X[5159] - X[40341], X[7426] - 4 X[20583], X[10295] - 4 X[12007], X[11008] + 5 X[30745], X[12367] - 4 X[15471], X[13619] - 5 X[14912], 2 X[15826] + X[32220], X[15826] + 2 X[32455], X[32220] - 4 X[32455], 4 X[41595] - X[46818]

X(47465) lies on these lines: {6, 468}, {30, 5102}, {858, 3629}, {1992, 10989}, {2072, 5965}, {3060, 8584}, {5032, 37909}, {5064, 11216}, {5097, 11799}, {5159, 40341}, {6329, 13622}, {7426, 20583}, {10295, 12007}, {11008, 30745}, {12367, 15471}, {13619, 14912}, {15826, 32220}, {39561, 44214}, {41595, 46818}

X(47465) = reflection of X(44214) in X(39561)
X(47465) = crossdifference of every pair of points on line {30209, 37517}
X(47465) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 47277, 47280}, {6, 47280, 32113}, {15826, 32455, 32220}

X(47466) = X(6)X(468)∩X(23)X(8584)

Barycentrics 7*a^8 - 10*a^6*b^2 - 6*a^4*b^4 + 10*a^2*b^6 - b^8 - 10*a^6*c^2 + 25*a^4*b^2*c^2 - 10*a^2*b^4*c^2 - 6*a^4*c^4 - 10*a^2*b^2*c^4 + 2*b^4*c^4 + 10*a^2*c^6 - c^8 : :

X(47466) = 9 X[6] - 4 X[468], 7 X[6] - 2 X[32113], 6 X[6] - X[47276], X[6] + 4 X[47277], 29 X[6] - 4 X[47278], 19 X[6] - 4 X[47279], 3 X[6] + 2 X[47280], 11 X[6] + 4 X[47281], 14 X[468] - 9 X[32113], 8 X[468] - 3 X[47276], X[468] + 9 X[47277], 29 X[468] - 9 X[47278], 19 X[468] - 9 X[47279], 2 X[468] + 3 X[47280], 11 X[468] + 9 X[47281], 12 X[32113] - 7 X[47276], X[32113] + 14 X[47277], 29 X[32113] - 14 X[47278], 19 X[32113] - 14 X[47279], 3 X[32113] + 7 X[47280], 11 X[32113] + 14 X[47281], X[47276] + 24 X[47277], 29 X[47276] - 24 X[47278], 19 X[47276] - 24 X[47279], X[47276] + 4 X[47280], 11 X[47276] + 24 X[47281], 29 X[47277] + X[47278], 19 X[47277] + X[47279], 6 X[47277] - X[47280], 11 X[47277] - X[47281], 19 X[47278] - 29 X[47279], 6 X[47278] + 29 X[47280], 11 X[47278] + 29 X[47281], 6 X[47279] + 19 X[47280], 11 X[47279] + 19 X[47281], 11 X[47280] - 6 X[47281], X[23] - 6 X[8584], X[67] - 6 X[21639], 6 X[576] - X[18325], 2 X[858] + 3 X[15534], 9 X[1992] + X[5189], 3 X[1992] + 2 X[15826], X[5189] - 6 X[15826], 8 X[5159] - 3 X[15533], X[10989] + 4 X[41149], 8 X[15471] - 3 X[19596], 8 X[16333] - 3 X[47275]

X(47466) lies on these lines: {6, 468}, {23, 8584}, {67, 21639}, {524, 30745}, {576, 18325}, {858, 15534}, {1992, 5189}, {2892, 16176}, {5159, 15533}, {10989, 41149}, {15471, 19596}, {16333, 47275}

X(47467) = X(30)X(599)∩X(53)X(468)

Barycentrics 6*a^8 - 9*a^6*b^2 + 7*a^4*b^4 - 3*a^2*b^6 - b^8 - 9*a^6*c^2 - 2*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + 12*b^6*c^2 + 7*a^4*c^4 + 3*a^2*b^2*c^4 - 22*b^4*c^4 - 3*a^2*c^6 + 12*b^2*c^6 - c^8 : :

X(47467) = 6*X[2] - (Csc[w]^2 - 4)*X[230] + (2*Csc[w]^2 - 11)*X[468] (a triple combo)
X(47467) = 3 X[2453] - X[32113], 3 X[16334] - 2 X[32113], 3 X[16312] - X[47278]

X(47467) lies on these lines: {30, 599}, {53, 468}, {131, 5099}, {523, 47277}, {858, 37690}, {1316, 16303}, {16312, 47278}, {16320, 47097}, {17968, 47242}

X(47467) = reflection of X(i) in X(j) for these {i,j}: {16303, 1316}, {16334, 2453}

X(47468) = X(30)X(599)∩X(468)X(511)

Barycentrics 2*a^12 + 5*a^10*b^2 - 19*a^8*b^4 + 6*a^6*b^6 + 16*a^4*b^8 - 11*a^2*b^10 + b^12 + 5*a^10*c^2 - 22*a^8*b^2*c^2 + 26*a^6*b^4*c^2 - 16*a^4*b^6*c^2 + 9*a^2*b^8*c^2 - 2*b^10*c^2 - 19*a^8*c^4 + 26*a^6*b^2*c^4 - 16*a^4*b^4*c^4 + 2*a^2*b^6*c^4 - b^8*c^4 + 6*a^6*c^6 - 16*a^4*b^2*c^6 + 2*a^2*b^4*c^6 + 4*b^6*c^6 + 16*a^4*c^8 + 9*a^2*b^2*c^8 - b^4*c^8 - 11*a^2*c^10 - 2*b^2*c^10 + c^12 : :

X(47468) = 3 X[186] - X[32220], X[193] - 5 X[37952], 4 X[575] - 3 X[47463], 2 X[576] - 3 X[47459], X[858] - 3 X[10519], X[1351] - 3 X[44214], 3 X[44214] - 2 X[47457], X[1353] - 3 X[15646], 2 X[3098] + X[47279], 5 X[3620] - X[10296], 3 X[5050] - 2 X[47464], 3 X[5085] - X[47280], 4 X[5092] - X[47281], 3 X[5093] - 4 X[47460], 4 X[5097] - 5 X[47461], 3 X[5102] - 5 X[47458], X[6776] - 3 X[44280], X[11477] - 3 X[47455], X[33878] + 2 X[47449], 3 X[14561] - 4 X[37911], 4 X[14810] + X[47278], X[15826] - 3 X[21167], 2 X[18583] - 3 X[44452], 3 X[31884] + X[47276], 4 X[32218] - 3 X[37971], 2 X[37517] - 5 X[47456], 6 X[39561] - 5 X[47462], 4 X[40107] - X[47339], X[44456] - 4 X[47454]

X(47468) lies on these lines: {30, 599}, {69, 10295}, {141, 10297}, {182, 47277}, {186, 32220}, {193, 37952}, {468, 511}, {524, 32110}, {542, 47031}, {575, 47463}, {576, 47459}, {858, 10519}, {1351, 44214}, {1353, 15646}, {1503, 16111}, {3098, 47279}, {3564, 32233}, {3620, 10296}, {5050, 47464}, {5085, 47280}, {5092, 47281}, {5093, 47460}, {5097, 47461}, {5102, 47458}, {6776, 44280}, {7542, 40929}, {8675, 46990}, {9306, 37904}, {9967, 10257}, {11477, 47455}, {11645, 20725}, {11649, 47090}, {11799, 33878}, {13562, 47342}, {14561, 37911}, {14810, 47278}, {14826, 47313}, {14913, 47092}, {15462, 18579}, {15826, 21167}, {18571, 34380}, {18583, 44439}, {19924, 47310}, {21243, 47311}, {29181, 47309}, {31670, 37984}, {31884, 47276}, {32218, 37971}, {32247, 46818}, {37485, 45171}, {37491, 37933}, {37517, 47456}, {39561, 47462}, {40107, 47339}, {44456, 47454}

X(47468) = midpoint of X(i) and X(j) for these {i,j}: {69, 10295}, {1350, 32113}, {11799, 33878}, {32247, 46818}
X(47468) = reflection of X(i) in X(j) for these {i,j}: {1351, 47457}, {10297, 141}, {11799, 47449}, {31670, 37984}, {47277, 182}
X(47468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {599, 1350, 4549}, {1351, 44214, 47457}

X(47469) = X(1)X(30)∩X(468)X(515)

Barycentrics 10*a^10 - 4*a^9*b - 17*a^8*b^2 + 8*a^7*b^3 - 6*a^6*b^4 + 20*a^4*b^6 - 8*a^3*b^7 - 4*a^2*b^8 + 4*a*b^9 - 3*b^10 - 4*a^9*c + 8*a^8*b*c - 8*a^6*b^3*c + 8*a^5*b^4*c - 8*a^4*b^5*c + 8*a^2*b^7*c - 4*a*b^8*c - 17*a^8*c^2 + 44*a^6*b^2*c^2 - 12*a^5*b^3*c^2 - 24*a^4*b^4*c^2 + 20*a^3*b^5*c^2 - 12*a^2*b^6*c^2 - 8*a*b^7*c^2 + 9*b^8*c^2 + 8*a^7*c^3 - 8*a^6*b*c^3 - 12*a^5*b^2*c^3 + 24*a^4*b^3*c^3 - 12*a^3*b^4*c^3 - 8*a^2*b^5*c^3 + 8*a*b^6*c^3 - 6*a^6*c^4 + 8*a^5*b*c^4 - 24*a^4*b^2*c^4 - 12*a^3*b^3*c^4 + 32*a^2*b^4*c^4 - 6*b^6*c^4 - 8*a^4*b*c^5 + 20*a^3*b^2*c^5 - 8*a^2*b^3*c^5 + 20*a^4*c^6 - 12*a^2*b^2*c^6 + 8*a*b^3*c^6 - 6*b^4*c^6 - 8*a^3*c^7 + 8*a^2*b*c^7 - 8*a*b^2*c^7 - 4*a^2*c^8 - 4*a*b*c^8 + 9*b^2*c^8 + 4*a*c^9 - 3*c^10 : :

X(47469) = X[8] - 3 X[44280], X[858] - 3 X[5731], 3 X[3576] - 2 X[5159], 5 X[3617] - 9 X[37941], 3 X[5587] - 4 X[37911], 3 X[10151] - 2 X[31673], 3 X[10246] - X[18323], 3 X[10257] - 4 X[13624], X[12702] - 3 X[44246], 3 X[13473] - 4 X[18483], 3 X[15646] - X[37705], 2 X[18357] - 3 X[44452], X[18525] - 3 X[44214], 5 X[35242] - 6 X[47114]

X(47469) lies on these lines: {1, 30}, {8, 44280}, {186, 9798}, {468, 515}, {517, 47308}, {519, 47031}, {858, 5731}, {944, 10295}, {952, 47335}, {1385, 10297}, {2173, 47161}, {3576, 5159}, {3617, 37941}, {5587, 37911}, {5691, 37984}, {8185, 44272}, {10151, 11363}, {10246, 18323}, {10257, 13624}, {12702, 44246}, {13473, 18483}, {15646, 37705}, {18357, 44452}, {18525, 44214}, {18571, 28224}, {28160, 47309}, {28186, 47336}, {28204, 47333}, {28208, 47332}, {35242, 47114}, {37934, 47321}, {39870, 47277}

X(47469) = midpoint of X(944) and X(10295)
X(47469) = reflection of X(i) in X(j) for these {i,j}: {5691, 37984}, {10297, 1385}, {47277, 39870}, {47321, 37934}
X(47469) = {X(18481),X(34773)}-harmonic conjugate of X(34634)

X(47470) = X(30)X(11372)∩X(468)X(516)

Barycentrics 10*a^9 - 6*a^8*b - 11*a^7*b^2 + 3*a^6*b^3 - 9*a^5*b^4 + 9*a^4*b^5 + 11*a^3*b^6 - 3*a^2*b^7 - a*b^8 - 3*b^9 - 6*a^8*c - 12*a^7*b*c + 7*a^6*b^2*c + 6*a^5*b^3*c + 3*a^4*b^4*c + 12*a^3*b^5*c - 7*a^2*b^6*c - 6*a*b^7*c + 3*b^8*c - 11*a^7*c^2 + 7*a^6*b*c^2 + 30*a^5*b^2*c^2 - 16*a^4*b^3*c^2 - 11*a^3*b^4*c^2 - 5*a^2*b^5*c^2 + 6*b^7*c^2 + 3*a^6*c^3 + 6*a^5*b*c^3 - 16*a^4*b^2*c^3 - 24*a^3*b^3*c^3 + 15*a^2*b^4*c^3 + 6*a*b^5*c^3 - 6*b^6*c^3 - 9*a^5*c^4 + 3*a^4*b*c^4 - 11*a^3*b^2*c^4 + 15*a^2*b^3*c^4 + 2*a*b^4*c^4 + 9*a^4*c^5 + 12*a^3*b*c^5 - 5*a^2*b^2*c^5 + 6*a*b^3*c^5 + 11*a^3*c^6 - 7*a^2*b*c^6 - 6*b^3*c^6 - 3*a^2*c^7 - 6*a*b*c^7 + 6*b^2*c^7 - a*c^8 + 3*b*c^8 - 3*c^9 : :

X(47471) = X(1)X(30)∩X(468)X(517)

Barycentrics 2*a^10 - 4*a^9*b - 5*a^8*b^2 + 8*a^7*b^3 + 2*a^6*b^4 + 4*a^4*b^6 - 8*a^3*b^7 - 4*a^2*b^8 + 4*a*b^9 + b^10 - 4*a^9*c + 8*a^8*b*c - 8*a^6*b^3*c + 8*a^5*b^4*c - 8*a^4*b^5*c + 8*a^2*b^7*c - 4*a*b^8*c - 5*a^8*c^2 + 4*a^6*b^2*c^2 - 12*a^5*b^3*c^2 - 4*a^4*b^4*c^2 + 20*a^3*b^5*c^2 + 8*a^2*b^6*c^2 - 8*a*b^7*c^2 - 3*b^8*c^2 + 8*a^7*c^3 - 8*a^6*b*c^3 - 12*a^5*b^2*c^3 + 24*a^4*b^3*c^3 - 12*a^3*b^4*c^3 - 8*a^2*b^5*c^3 + 8*a*b^6*c^3 + 2*a^6*c^4 + 8*a^5*b*c^4 - 4*a^4*b^2*c^4 - 12*a^3*b^3*c^4 - 8*a^2*b^4*c^4 + 2*b^6*c^4 - 8*a^4*b*c^5 + 20*a^3*b^2*c^5 - 8*a^2*b^3*c^5 + 4*a^4*c^6 + 8*a^2*b^2*c^6 + 8*a*b^3*c^6 + 2*b^4*c^6 - 8*a^3*c^7 + 8*a^2*b*c^7 - 8*a*b^2*c^7 - 4*a^2*c^8 - 4*a*b*c^8 - 3*b^2*c^8 + 4*a*c^9 + c^10 : :

X(47471) = X[8] - 3 X[403], X[858] - 3 X[5603], 4 X[1125] - 3 X[10257], 5 X[1698] - 6 X[44911], 3 X[2071] - 7 X[3622], 3 X[2072] - 5 X[18493], 2 X[5159] - 3 X[5886], X[6361] - 3 X[44280], X[7464] - 5 X[10595], 3 X[10151] - 2 X[18480], 3 X[10247] + X[18325], 3 X[10283] - X[37950], X[12702] - 3 X[44214], X[18526] + 3 X[31726], X[20070] - 5 X[37952], 3 X[26446] - 4 X[37911]

X(47471) lies on these lines: {1, 30}, {8, 403}, {355, 37984}, {468, 517}, {515, 47309}, {516, 47308}, {519, 47332}, {858, 5603}, {946, 10297}, {952, 47336}, {962, 10295}, {1125, 10257}, {1482, 11799}, {1483, 44267}, {1698, 44911}, {2071, 3622}, {2072, 18493}, {3580, 7978}, {5159, 5886}, {5844, 44961}, {5901, 15122}, {6361, 44280}, {7359, 47161}, {7464, 10595}, {7982, 47321}, {7984, 32111}, {10151, 12135}, {10247, 18325}, {10283, 37950}, {11064, 11723}, {12702, 44214}, {18526, 31726}, {18571, 28212}, {20070, 37952}, {26446, 37911}, {28174, 47335}, {28194, 47333}, {28198, 47031}, {28204, 47310}, {32220, 39898}

X(47471) = midpoint of X(i) and X(j) for these {i,j}: {962, 10295}, {1482, 11799}, {1483, 44267}, {3580, 7978}, {7982, 47321}, {7984, 32111}, {32220, 39898}
X(47471) = reflection of X(i) in X(j) for these {i,j}: {355, 37984}, {10297, 946}, {11064, 11723}, {15122, 5901}

X(47472) = X(1)X(30)∩X(468)X(519)

Barycentrics 14*a^7 + 2*a^6*b - 11*a^5*b^2 + a^4*b^3 - 14*a^3*b^4 - 2*a^2*b^5 + 11*a*b^6 - b^7 + 2*a^6*c + a^4*b^2*c - 2*a^2*b^4*c - b^6*c - 11*a^5*c^2 + a^4*b*c^2 + 36*a^3*b^2*c^2 - 11*a*b^4*c^2 + b^5*c^2 + a^4*c^3 + b^4*c^3 - 14*a^3*c^4 - 2*a^2*b*c^4 - 11*a*b^2*c^4 + b^3*c^4 - 2*a^2*c^5 + b^2*c^5 + 11*a*c^6 - b*c^6 - c^7 : :

X(47472) = X[145] + 3 X[37907], 3 X[186] + X[34631], 3 X[403] - X[34627], X[858] - 3 X[38314], 5 X[3623] + 3 X[37909], 2 X[5159] - 3 X[25055], X[7982] + 2 X[37934], 3 X[10151] - 2 X[34648], 4 X[13464] - X[47339], 3 X[19875] - 4 X[37911], X[34632] - 3 X[44280], X[34718] - 3 X[44214]

X(47472) lies on these lines: {1, 30}, {145, 37907}, {186, 34631}, {403, 34627}, {468, 519}, {515, 47310}, {517, 47333}, {551, 47097}, {858, 38314}, {952, 47334}, {1482, 44265}, {1483, 44266}, {3241, 7426}, {3623, 37909}, {5159, 25055}, {7982, 37934}, {8193, 37941}, {10151, 34648}, {12410, 37955}, {13464, 47339}, {15646, 37546}, {19875, 37911}, {28194, 47031}, {28198, 47308}, {28204, 47332}, {28208, 47309}, {34632, 44280}, {34718, 44214}, {47359, 47457}

X(47472) = midpoint of X(i) and X(j) for these {i,j}: {1482, 44265}, {1483, 44266}, {3241, 7426}
X(47472) = reflection of X(i) in X(j) for these {i,j}: {47097, 551}, {47359, 47457}

X(47473) = X(30)X(599)∩X(468)X(524)

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

X(47473) = X[69] + 2 X[47449], 2 X[141] + X[47279], X[193] - 4 X[47454], X[858] - 3 X[21356], X[858] + 2 X[47446], 3 X[21356] + 2 X[47446], 4 X[3589] - X[47281], 5 X[3620] - X[10989], 2 X[3629] - 5 X[47456], 4 X[3631] + X[47312], 3 X[5032] - 4 X[47460], 2 X[5159] - 3 X[21358], 2 X[5159] + X[47276], 3 X[21358] + X[47276], 2 X[8584] - 3 X[47459], X[11160] + 3 X[37907], X[11160] + 4 X[47451], X[32220] - 3 X[37907], X[32220] - 4 X[47451], 3 X[37907] - 4 X[47451], X[15069] + 2 X[37934], X[15533] + 3 X[47450], X[15534] - 3 X[47455], 4 X[20582] + X[47278], 4 X[20583] - 5 X[47461], 2 X[22165] + X[37904], 2 X[22165] + 3 X[47447], X[37904] - 3 X[47447], 2 X[37897] - 5 X[47448], 4 X[37911] - X[47280], 4 X[37911] - 3 X[47352], X[47280] - 3 X[47352], X[40341] + 5 X[47452]

X(47473) lies on these lines: {2, 10169}, {30, 599}, {67, 47335}, {69, 7426}, {141, 16325}, {193, 47454}, {468, 524}, {511, 47332}, {542, 47333}, {597, 47277}, {858, 21356}, {1503, 47031}, {1531, 41583}, {1992, 47457}, {2930, 18571}, {3564, 5648}, {3589, 47281}, {3620, 10989}, {3629, 47456}, {3631, 47312}, {3917, 8705}, {5032, 47460}, {5159, 21358}, {8584, 47459}, {8675, 46989}, {10151, 41585}, {10295, 11180}, {10297, 11178}, {11160, 32220}, {11645, 32257}, {14995, 44216}, {15069, 37934}, {15533, 47450}, {15534, 47455}, {15993, 16303}, {16312, 44395}, {19924, 47309}, {20582, 47278}, {20583, 47461}, {22165, 37904}, {37897, 47448}, {37911, 47280}, {40112, 41721}, {40341, 47452}

X(47473) = midpoint of X(i) and X(j) for these {i,j}: {69, 7426}, {599, 32113}, {10295, 11180}, {11160, 32220}, {40112, 41721}, {47097, 47279}
X(47473) = reflection of X(i) in X(j) for these {i,j}: {1992, 47457}, {7426, 47449}, {10297, 11178}, {47097, 141}, {47277, 597}
X(47473) = {X(11160),X(37907)}-harmonic conjugate of X(32220)

X(47474) = X(30)X(599)∩X(125)X(468)

Barycentrics 6*a^12 - 9*a^10*b^2 - a^8*b^4 + 2*a^6*b^6 + 7*a^2*b^10 - 5*b^12 - 9*a^10*c^2 + 38*a^8*b^2*c^2 - 14*a^6*b^4*c^2 - 8*a^4*b^6*c^2 - 17*a^2*b^8*c^2 + 10*b^10*c^2 - a^8*c^4 - 14*a^6*b^2*c^4 + 16*a^4*b^4*c^4 + 10*a^2*b^6*c^4 + 5*b^8*c^4 + 2*a^6*c^6 - 8*a^4*b^2*c^6 + 10*a^2*b^4*c^6 - 20*b^6*c^6 - 17*a^2*b^2*c^8 + 5*b^4*c^8 + 7*a^2*c^10 + 10*b^2*c^10 - 5*c^12 : :

X(47474) = 3 X[186] - 4 X[47451], 3 X[403] - X[6776], 3 X[403] - 2 X[47457], 3 X[5085] - 4 X[37911], 2 X[5159] - 3 X[10516], 2 X[5480] - 3 X[10151], 3 X[10151] - X[47277], 2 X[8550] - 3 X[47459], 3 X[10257] - 4 X[24206], X[11898] + 3 X[31726], 4 X[12007] - 5 X[47461], 3 X[13473] + X[47278], 3 X[14853] - 2 X[47464], 3 X[14912] - 4 X[47460], X[14927] - 3 X[44280], 2 X[37934] - 3 X[47450], 6 X[37942] - 5 X[47453], X[39874] - 4 X[47454]

X(47474) lies on these lines: {6, 37984}, {30, 599}, {125, 468}, {186, 47451}, {403, 6776}, {511, 47309}, {524, 46988}, {542, 47332}, {974, 35370}, {3564, 9970}, {3580, 41737}, {3818, 10297}, {5085, 37911}, {5159, 10516}, {5480, 8541}, {5651, 47097}, {5921, 32220}, {7575, 20987}, {8550, 47459}, {8675, 46991}, {8705, 15030}, {10257, 24206}, {10295, 47449}, {11579, 18374}, {11645, 47333}, {11646, 16303}, {11799, 18440}, {11898, 31726}, {12007, 47461}, {12294, 13473}, {14853, 47464}, {14912, 47460}, {14927, 44280}, {15122, 18358}, {15577, 44281}, {15811, 47338}, {29012, 47308}, {37934, 47450}, {37942, 47453}, {39874, 47454}

X(47474) = midpoint of X(i) and X(j) for these {i,j}: {1495, 32250}, {3580, 41737}, {5921, 32220}, {11799, 18440}, {32113, 36990}
X(47474) = reflection of X(i) in X(j) for these {i,j}: {6, 37984}, {974, 35370}, {6776, 47457}, {10295, 47449}, {10297, 3818}, {15122, 18358}, {47097, 47354}, {47277, 5480}
X(47474) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {403, 6776, 47457}, {10151, 47277, 5480}

X(47475) = X(30)X(115)∩X(468)X(512)

X(47475) lies on these lines: {30, 115}, {468, 512}, {10295, 34175}, {16760, 44673}

X(47476) = X(1)X(30)∩X(468)X(952)

Barycentrics 6*a^10 - 4*a^9*b - 11*a^8*b^2 + 8*a^7*b^3 - 2*a^6*b^4 + 12*a^4*b^6 - 8*a^3*b^7 - 4*a^2*b^8 + 4*a*b^9 - b^10 - 4*a^9*c + 8*a^8*b*c - 8*a^6*b^3*c + 8*a^5*b^4*c - 8*a^4*b^5*c + 8*a^2*b^7*c - 4*a*b^8*c - 11*a^8*c^2 + 24*a^6*b^2*c^2 - 12*a^5*b^3*c^2 - 14*a^4*b^4*c^2 + 20*a^3*b^5*c^2 - 2*a^2*b^6*c^2 - 8*a*b^7*c^2 + 3*b^8*c^2 + 8*a^7*c^3 - 8*a^6*b*c^3 - 12*a^5*b^2*c^3 + 24*a^4*b^3*c^3 - 12*a^3*b^4*c^3 - 8*a^2*b^5*c^3 + 8*a*b^6*c^3 - 2*a^6*c^4 + 8*a^5*b*c^4 - 14*a^4*b^2*c^4 - 12*a^3*b^3*c^4 + 12*a^2*b^4*c^4 - 2*b^6*c^4 - 8*a^4*b*c^5 + 20*a^3*b^2*c^5 - 8*a^2*b^3*c^5 + 12*a^4*c^6 - 2*a^2*b^2*c^6 + 8*a*b^3*c^6 - 2*b^4*c^6 - 8*a^3*c^7 + 8*a^2*b*c^7 - 8*a*b^2*c^7 - 4*a^2*c^8 - 4*a*b*c^8 + 3*b^2*c^8 + 4*a*c^9 - c^10 : :

X(47476) = X[8] - 3 X[44214], 2 X[10] - 3 X[44452], X[23] + 3 X[7967], X[145] + 3 X[186], 3 X[403] - X[18525], X[858] - 3 X[10246], 3 X[2072] - 5 X[3616], X[3632] - 6 X[16531], 2 X[5159] - 3 X[38028], 3 X[5603] - X[18323], 2 X[5882] + X[16619], X[6361] - 3 X[44246], X[7574] - 5 X[37624], 4 X[9955] - 3 X[23323], 3 X[10283] - X[18572], X[10296] - 5 X[10595], X[12245] - 5 X[37952], X[12702] - 3 X[44280], 4 X[13607] + X[47342], 4 X[15178] - X[47341], X[37705] - 3 X[44282], 4 X[37911] - 3 X[38042]

X(47476) lies on these lines: {1, 30}, {8, 44214}, {10, 44452}, {23, 7967}, {145, 186}, {403, 18525}, {468, 952}, {515, 47336}, {517, 47335}, {519, 18579}, {858, 10246}, {944, 11799}, {1385, 15122}, {1482, 10295}, {1483, 7575}, {2070, 8192}, {2072, 3616}, {3241, 44265}, {3580, 12898}, {3632, 16531}, {5159, 38028}, {5603, 18323}, {5844, 18571}, {5882, 16619}, {5901, 10297}, {6361, 44246}, {7574, 37624}, {9955, 23323}, {10283, 18572}, {10296, 10595}, {12245, 37952}, {12702, 44280}, {13607, 47342}, {15178, 47341}, {16977, 24301}, {28174, 47308}, {28186, 47309}, {28204, 47334}, {28224, 44961}, {37705, 44282}, {37727, 47321}, {37911, 38042}

X(47476) = midpoint of X(i) and X(j) for these {i,j}: {944, 11799}, {1482, 10295}, {1483, 7575}, {3241, 44265}, {3580, 12898}, {37727, 47321}
X(47476) = reflection of X(i) in X(j) for these {i,j}: {10297, 5901}, {15122, 1385}

X(47477) = X(30)X(47358)∩X(468)X(518)

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

X(47477) = 2 X[4663] - 3 X[47459], 3 X[16475] - 2 X[47464], X[16496] + 2 X[47449], 4 X[37911] - 3 X[38047], 3 X[38315] - X[47280]

X(47477) lies on these lines: {30, 47358}, {468, 518}, {1386, 47277}, {3242, 32113}, {3751, 47457}, {4663, 47459}, {10295, 39898}, {16475, 47464}, {16496, 47321}, {37911, 38047}, {38315, 47280}

X(47477) = midpoint of X(i) and X(j) for these {i,j}: {3242, 32113}, {10295, 39898}, {16496, 47321}
X(47477) = reflection of X(i) in X(j) for these {i,j}: {3751, 47457}, {47277, 1386}, {47321, 47449}

X(47478) = 70TH HATZIPOLAKIS-MOSES-EULER POINT

X(47478) = 17 X[2] - 5 X[3], 19 X[2] + 5 X[4], X[2] + 5 X[5], 53 X[2] - 5 X[20], 8 X[2] - 5 X[140], 29 X[2] - 5 X[376], 7 X[2] + 5 X[381], 11 X[2] + X[382], 2 X[2] + X[546], 2 X[2] - 5 X[547], 26 X[2] - 5 X[548], 11 X[2] - 5 X[549], 7 X[2] - X[550], 49 X[2] - 25 X[631], 31 X[2] - 25 X[632], 13 X[2] - 25 X[1656], 89 X[2] - 5 X[1657], 11 X[2] - 35 X[3090], 23 X[2] + 25 X[3091], 91 X[2] + 5 X[3146], 121 X[2] - 25 X[3522], 83 X[2] - 35 X[3523], 13 X[2] - 5 X[3524], 79 X[2] - 55 X[3525], 47 X[2] - 35 X[3526], 31 X[2] - 7 X[3528], 25 X[2] - X[3529], 5 X[2] - 2 X[3530], 109 X[2] - 85 X[3533], 41 X[2] - 5 X[3534], 43 X[2] + 5 X[3543], 7 X[2] + 17 X[3544], and thousands more

X(47478) lies on these lines: {2, 3}, {13, 42628}, {14, 42627}, {395, 43111}, {396, 43110}, {590, 42643}, {615, 42644}, {3055, 39563}, {3592, 43571}, {3594, 43570}, {3629, 11178}, {3636, 18357}, {3817, 38083}, {5587, 38022}, {5603, 38081}, {5817, 38080}, {5844, 7988}, {5907, 12046}, {6329, 18358}, {6431, 43568}, {6432, 43569}, {6564, 43212}, {6565, 43211}, {7173, 15170}, {8227, 34747}, {8960, 41951}, {9691, 34089}, {10170, 13451}, {10171, 28204}, {10172, 28198}, {10175, 38098}, {10283, 38074}, {10516, 38079}, {10653, 43198}, {10654, 43197}, {11230, 38076}, {11542, 16268}, {11543, 16267}, {11694, 12900}, {12816, 42944}, {12817, 42945}, {12820, 33416}, {12821, 33417}, {12902, 22250}, {13925, 35823}, {13993, 35822}, {15060, 16226}, {16962, 42915}, {16963, 42914}, {16966, 43417}, {16967, 43416}, {18581, 42474}, {18582, 42475}, {18583, 20583}, {18874, 21849}, {19875, 38034}, {19883, 38140}, {21358, 38136}, {23234, 38229}, {23302, 42972}, {23303, 42973}, {25055, 28224}, {32134, 38231}, {36969, 43102}, {36970, 43103}, {37832, 42143}, {37835, 42146}, {38021, 38042}, {38075, 38171}, {38082, 38150}, {38093, 38139}, {38138, 38314}, {38628, 41147}, {41121, 42599}, {41122, 42598}, {42107, 43107}, {42110, 43100}, {42121, 42416}, {42124, 42415}, {42147, 42947}, {42148, 42946}, {42488, 43547}, {42489, 43546}, {42506, 42899}, {42507, 42898}, {42580, 42779}, {42581, 42780}, {42590, 42814}, {42591, 42813}, {42641, 43255}, {42642, 43254}, {42781, 43240}, {42782, 43241}, {42892, 43032}, {42893, 43033}, {42902, 42912}, {42903, 42913}, {42918, 43105}, {42919, 43106}, {42938, 43023}, {42939, 43022}

X(47478) = midpoint of X(i) and X(j) for these {i,j}: {2, 38071}, {4, 45759}, {5, 5055}, {381, 11539}, {547, 14892}, {549, 3839}, {3524, 3845}, {3545, 15699}, {3817, 38083}, {3850, 41984}, {3860, 14890}, {5054, 23046}, {5587, 38022}, {5603, 38081}, {5817, 38080}, {8703, 38335}, {10283, 38074}, {10516, 38079}, {11230, 38076}, {12101, 41982}, {14269, 17504}, {15060, 16226}, {15687, 15688}, {19875, 38034}, {19883, 38140}, {21358, 38136}, {23234, 38229}, {35404, 46333}, {38021, 38042}, {38075, 38171}, {38082, 38150}, {38093, 38139}, {38138, 38314}, {41983, 41987}
X(47478) = reflection of X(i) in X(j) for these {i,j}: {3, 14890}, {546, 38071}, {547, 5055}, {548, 3524}, {549, 41984}, {3524, 10124}, {3839, 3850}, {5054, 41985}, {5055, 10109}, {5066, 14892}, {11539, 3628}, {12100, 11539}, {12101, 3839}, {12103, 41982}, {14892, 5}, {15688, 3530}, {15691, 45759}, {15699, 45757}, {38071, 11737}, {41982, 549}, {45759, 11812}, {46333, 44245}
X(47478) = complement of X(17504)
X(47478) = orthocentroidal circle inverse of X(15700)
X(47478) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 15700}, {2, 5, 11737}, {2, 381, 550}, {2, 382, 549}, {2, 546, 34200}, {2, 3544, 381}, {2, 3545, 14269}, {2, 3839, 15710}, {2, 3851, 15687}, {2, 3855, 15681}, {2, 5071, 5079}, {2, 10299, 15694}, {2, 11737, 546}, {2, 14269, 17504}, {2, 14869, 10124}, {2, 15681, 14869}, {2, 15687, 3530}, {2, 15707, 11539}, {2, 34200, 140}, {2, 35018, 547}, {4, 5, 41989}, {4, 11812, 15691}, {5, 547, 5066}, {5, 549, 19709}, {5, 550, 3544}, {5, 632, 5068}, {5, 1656, 12811}, {5, 3090, 3850}, {5, 5056, 3628}, {5, 5071, 10109}, {5, 5079, 35018}, {5, 10109, 547}, {5, 12812, 140}, {5, 15699, 3545}, {5, 35018, 546}, {5, 44904, 12812}, {140, 5066, 14893}, {140, 14893, 15690}, {381, 631, 33699}, {381, 3146, 3845}, {381, 3628, 12100}, {381, 12100, 3853}, {381, 15695, 4}, {381, 15715, 15687}, {381, 46219, 11001}, {382, 3850, 546}, {546, 547, 2}, {546, 550, 3853}, {546, 5079, 12812}, {546, 11737, 5066}, {546, 14269, 41987}, {547, 3545, 41983}, {547, 5066, 140}, {547, 10109, 12812}, {547, 11737, 34200}, {547, 12100, 3628}, {547, 19709, 12103}, {547, 44904, 10109}, {548, 12100, 15714}, {549, 3850, 12101}, {549, 12101, 12103}, {549, 19709, 3850}, {550, 5056, 35018}, {550, 11539, 15707}, {550, 12100, 34200}, {550, 17504, 10304}, {632, 3830, 14891}, {632, 5068, 3856}, {1656, 3845, 10124}, {1656, 3855, 14869}, {1656, 12811, 548}, {1656, 15681, 2}, {3090, 15689, 15699}, {3090, 19709, 549}, {3091, 15703, 8703}, {3091, 15709, 38335}, {3091, 35414, 41099}, {3146, 10124, 12100}, {3523, 44903, 46332}, {3525, 15684, 15711}, {3526, 15686, 44580}, {3526, 41099, 15686}, {3530, 3851, 546}, {3530, 15715, 12100}, {3543, 5070, 15713}, {3543, 15713, 33923}, {3544, 3628, 546}, {3544, 15707, 38071}, {3545, 5054, 23046}, {3545, 5055, 15699}, {3545, 10304, 381}, {3545, 14269, 38071}, {3627, 15694, 15759}, {3628, 3853, 140}, {3628, 12811, 3146}, {3830, 5054, 35418}, {3832, 15693, 35404}, {3839, 15710, 382}, {3839, 41984, 41982}, {3843, 15702, 19710}, {3845, 10124, 548}, {3845, 14869, 15681}, {3845, 15714, 3146}, {3853, 5066, 381}, {3853, 35408, 33699}, {3854, 15698, 35403}, {3855, 15681, 3845}, {3856, 14891, 3830}, {3857, 5070, 33923}, {3857, 15713, 3543}, {3858, 5067, 12108}, {3859, 15690, 14893}, {3861, 11540, 376}, {5054, 15699, 41985}, {5055, 15699, 45757}, {5066, 12812, 547}, {5066, 14893, 3859}, {5066, 34200, 546}, {5066, 41983, 41987}, {5071, 10109, 44904}, {7486, 41106, 15694}, {8703, 15703, 16239}, {10109, 11737, 35018}, {10109, 41986, 15699}, {10124, 12811, 3845}, {10304, 11001, 15689}, {10304, 15707, 17504}, {11001, 46219, 549}, {11737, 35018, 2}, {11812, 15695, 12100}, {12100, 12101, 11001}, {12101, 19709, 5066}, {12102, 41099, 45762}, {12102, 44580, 15686}, {12103, 12812, 3090}, {12811, 14869, 546}, {12812, 41983, 45757}, {14269, 15689, 382}, {14892, 15699, 41987}, {14892, 45757, 41983}, {15682, 15723, 15712}, {15682, 46936, 15723}, {15686, 41099, 12102}, {15688, 15707, 15715}, {15689, 15699, 41984}, {15691, 15700, 34200}, {15691, 41989, 5066}, {15693, 35404, 44245}, {15694, 41106, 3627}, {15699, 17504, 2}, {15699, 23046, 5054}, {15699, 38071, 17504}, {15699, 41986, 14892}, {15699, 41987, 140}, {15699, 45757, 547}, {15703, 15720, 2}, {15703, 38335, 15709}, {15709, 38335, 8703}, {15710, 19709, 38071}, {15710, 41982, 34200}, {17504, 38071, 14269}, {19709, 46219, 381}, {34200, 41983, 17504}, {34559, 34562, 548}, {35404, 41990, 3832}, {36445, 36463, 17578}, {41986, 45757, 3545}

X(47479) = (name pending)

X(47480) = X(60)X(594)∩X(6058)X(35212)

X(47481) = X(15)X(1337)∩X(470)X(8737)

X(47481) lies on these lines: {15, 1337}, {17, 36186}, {470, 8737}, {5995, 11146}, {8837, 39262}, {36296, 44718}, {38403, 40581}, {40707, 41888}

X(47481) = isogonal conjugate of the polar conjugate of X(11119)
X(47481) = isotomic conjugate of the polar conjugate of X(16459)
X(47481) = Cevapoint of X(3) and X(36296)
X(47481) = X(647)-cross conjugate of-X(38414)
X(47481) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 618), (125, 35443)
X(47481) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 618}, {162, 35443}
X(47481) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 618), (647, 35443), (1337, 11094)
X(47481) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(34008)}} and {{A, B, C, X(3), X(15)}}
X(47481) = inverse Mimosa transform of X(2153)
X(47481) = barycentric product X(i)*X(j) for these {i, j}: {3, 11119}, {69, 16459}
X(47481) = barycentric quotient X(i)/X(j) for these (i, j): (3, 618), (647, 35443), (1337, 11094)
X(47481) = trilinear product X(i)*X(j) for these {i, j}: {48, 11119}, {63, 16459}
X(47481) = trilinear quotient X(i)/X(j) for these (i, j): (63, 618), (656, 35443), (2153, 463)

X(47482) = X(16)X(1338)∩X(471)X(8738)

X(47482) lies on these lines: {16, 1338}, {18, 36185}, {471, 8738}, {5994, 11145}, {8839, 39261}, {36297, 44719}, {38404, 40580}, {40706, 41887}

X(47482) = isogonal conjugate of the polar conjugate of X(11120)
X(47482) = isotomic conjugate of the polar conjugate of X(16460)
X(47482) = Cevapoint of X(3) and X(36297)
X(47482) = X(647)-cross conjugate of-X(38413)
X(47482) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 619), (125, 35444)
X(47482) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 619}, {162, 35444}
X(47482) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 619), (647, 35444), (1338, 11093)
X(47482) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(34009)}} and {{A, B, C, X(3), X(16)}}
X(47482) = inverse Mimosa transform of X(2154)
X(47482) = barycentric product X(i)*X(j) for these {i, j}: {3, 11120}, {69, 16460}
X(47482) = barycentric quotient X(i)/X(j) for these (i, j): (3, 619), (647, 35444), (1338, 11093)
X(47482) = trilinear product X(i)*X(j) for these {i, j}: {48, 11120}, {63, 16460}
X(47482) = trilinear quotient X(i)/X(j) for these (i, j): (63, 619), (656, 35444), (2154, 462)

X(47483) = MIDPOINT OF X(2292) AND X(2611)

X(47483) lies on these lines: {517, 21326}, {758, 5048}, {952, 12080}, {2292, 2611}, {2294, 3708}, {2650, 33179}, {3743, 37080}, {3931, 22321}, {4068, 23861}, {4647, 4939}

X(47484) = X(517)X(2292)∩X(2611)X(5045)

X(47484) lies on these lines: {517, 2292}, {523, 13407}, {942, 21325}, {2611, 5045}, {3743, 44913}, {3746, 4068}, {3838, 42005}, {4736, 10107}, {5191, 5266}, {10149, 20129}

X(47485) = EULER LINE INTERCEPT OF X(51)X(11464)

X(47485) lies on these lines: {2, 3}, {51, 11464}, {54, 15004}, {74, 11738}, {107, 13530}, {112, 43656}, {143, 9545}, {154, 15032}, {187, 33885}, {232, 5008}, {389, 26882}, {393, 14579}, {568, 9544}, {569, 12834}, {578, 38848}, {1199, 9707}, {1304, 39239}, {1495, 5890}, {1870, 37587}, {1974, 3043}, {2374, 6236}, {2931, 20125}, {2979, 43586}, {3092, 6429}, {3093, 6430}, {3431, 11202}, {3455, 14651}, {3563, 11636}, {3567, 10282}, {5041, 39575}, {5097, 6403}, {5446, 11449}, {5603, 9590}, {5640, 18475}, {5657, 9625}, {5891, 10546}, {5892, 15080}, {5944, 46084}, {5946, 11003}, {6152, 15532}, {6484, 35765}, {6485, 35764}, {6486, 11473}, {6487, 11474}, {6776, 15580}, {7735, 9699}, {8541, 19128}, {8739, 10632}, {8740, 10633}, {9703, 11004}, {9704, 16881}, {9730, 26881}, {9781, 13367}, {9833, 43808}, {10605, 12112}, {10641, 34755}, {10642, 34754}, {10880, 35771}, {10881, 35770}, {11278, 11363}, {11430, 44106}, {11438, 14157}, {11451, 37513}, {11454, 16194}, {11455, 21663}, {11468, 13474}, {11572, 11704}, {12254, 39571}, {13289, 15081}, {13364, 14805}, {13419, 23294}, {13472, 34567}, {14490, 20421}, {15111, 47327}, {15305, 32110}, {15602, 33843}, {16621, 43607}, {16981, 32609}, {18445, 35265}, {20987, 39874}, {26913, 44407}, {31400, 44525}, {32229, 40119}, {33179, 41722}, {35264, 37489}, {37490, 43605}, {37495, 38942}, {38294,

X(47485) = polar conjugate of the isotomic conjugate of X(11004)
X(47485) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(11004)}} and {{A, B, C, X(3), X(9703)}}
X(47485) = barycentric product X(i)*X(j) for these {i, j}: {4, 11004}, {2052, 9703}
X(47485) = trilinear product X(i)*X(j) for these {i, j}: {19, 11004}, {158, 9703}
X(47485) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 34484, 4), (3, 44878, 186), (23, 6644, 376), (24, 25, 186), (24, 3518, 4), (25, 186, 4), (25, 3515, 1597), (26, 44802, 631), (186, 3518, 25), (186, 13596, 3), (235, 34797, 4), (403, 18559, 4), (1593, 26863, 4), (1598, 14865, 4), (2070, 12106, 2), (3089, 35471, 4), (3515, 35472, 186), (3520, 10594, 4), (3575, 16868, 4), (6240, 44958, 4), (7487, 7505, 4), (7576, 7577, 4), (10298, 14002, 381), (11202, 15033, 3431), (13595, 37940, 3), (17506, 26863, 1593), (35473, 44879, 186), (37077, 44265, 376), (37119, 37122, 4), (37440, 45735, 20), (37962, 45173, 378)

X(47486) = EULER LINE INTERCEPT OF X(54)X(13433)

X(47486) lies on these lines: {2, 3}, {54, 13433}, {389, 44108}, {1199, 10282}, {1495, 13382}, {3092, 6468}, {3093, 6469}, {3431, 10982}, {5944, 34545}, {6102, 35265}, {6241, 44082}, {6403, 15520}, {8718, 32237}, {9590, 13464}, {9625, 43174}, {9705, 16625}, {9781, 11202}, {11363, 31948}, {11430, 41448}, {13367, 38848}, {13421, 22115}, {13423, 32411}, {13431, 25714}, {13598, 15035}, {14449, 32609}, {14491, 14528}, {15032, 26882}, {15516, 19128}, {17821, 46928}

X(47486) = intersection, other than A, B, C, of circumconics {{A, B, C, X(5), X(46864)}} and {{A, B, C, X(6), X(5079)}}
X(47486) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 44880, 186), (4, 3517, 3518), (4, 21844, 3516), (4, 32534, 3520), (24, 3517, 4), (24, 3518, 186), (25, 32534, 4), (25, 44879, 3520), (186, 26863, 3520), (3515, 17506, 186), (3516, 10594, 4), (3518, 3520, 25), (3520, 44879, 186), (3575, 35487, 4), (6240, 44960, 4), (7715, 37118, 4)

X(47487) = X(1)X(1170)∩X(77)X(212)

X(47487) lies on these lines: {1, 1170}, {3, 1803}, {29, 1861}, {55, 3477}, {77, 212}, {102, 7688}, {282, 6605}, {283, 1818}, {284, 672}, {307, 31637}, {656, 23696}, {945, 35239}, {949, 2911}, {1036, 5132}, {1037, 37578}, {1813, 22079}, {2338, 33634}, {3587, 37305}, {9441, 21617}, {22072, 40442}, {24047, 37741}

X(47487) = isogonal conjugate of the polar conjugate of X(32008)
X(47487) = isotomic conjugate of the polar conjugate of X(1174)
X(47487) = Cevapoint of X(3) and X(212)
X(47487) = crosssum of X(1475) and X(40983)
X(47487) = X(i)-cross conjugate of-X(j) for these (i, j): (3, 40443), (905, 1331)
X(47487) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 142), (206, 40983), (1147, 22053)
X(47487) = X(i)-isoconjugate-of-X(j) for these {i, j}: {4, 354}, {7, 1827}, {19, 142}, {25, 20880}
X(47487) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 142), (32, 40983), (41, 1827), (48, 354)
X(47487) = X(652)-Zayin conjugate of-X(21127)
X(47487) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3)}} and {{A, B, C, X(2), X(1796)}}
X(47487) = trilinear pole of the line {652, 22160}
X(47487) = inverse Mimosa transform of X(55)
X(47487) = barycentric product X(i)*X(j) for these {i, j}: {3, 32008}, {8, 1803}, {63, 2346}, {69, 1174}, {77, 6605}, {78, 1170}
X(47487) = barycentric quotient X(i)/X(j) for these (i, j): (3, 142), (32, 40983), (41, 1827), (48, 354), (55, 1855), (63, 20880)
X(47487) = trilinear product X(i)*X(j) for these {i, j}: {3, 2346}, {9, 1803}, {48, 32008}, {63, 1174}, {77, 10482}, {212, 21453}
X(47487) = trilinear quotient X(i)/X(j) for these (i, j): (3, 354), (9, 1855), (31, 40983), (48, 1475), (55, 1827), (63, 142)

This preamble is contributed by Peter Moses, Kiminari Shinagawa, and Clark Kimberling, April 7, 2022.

As in the preamble just before X(47468), suppose that P and U are points, neither on the line at infinity, and that normed (i.e., "normalized") barycentrics are given by P= (p,q,r) and U = (u,v,w) Then the point P-U defined by the combo p-u : q - v : r - w is on the line at infinity. Let T(P,U) denote the point with Euler coordinates (x,y) given by

x = SA*(p-u) + SB*(q - r) + SC*(r - w)
y = SA*(SB - SC)*(p-u) + SB*(SC - SA)*(q - r) + SC*(SA - SB)*(r - w)

The appearance of (i,j;k) in the following lists means that T(X(i),X(j)) = X(k):

P and U on the Nagel line, X(1)X(2):
(1,2; 47472), (1,8; 47489), (1,10; 47491), (1,145; 47490), (1,551; 47495)
(2,1; 47488), (2,8; 47493); (2,10;47495), (2,42; 47529), (2,43; 47530), (2,145; 47531), (2,239; 47532), (2,551; 47496),
(8,1; 47490), (8,2; 47494), (8,10; 47492), (8,145; 47533), (8,551; 47534)
(10,1; 47492), (10,2; 47496), (10,8;47491), (10,551; 47488), (10,145; 47564)
(145,1; 47489), (145,2; 47535), (145,8; 47536), (145,10; 47537), (145,551; 47538)
(239,2; 47539)
(551,2; 47495)

P and U on the IK line, X(1)X(6):
(1,6; 47477), (1,9; 47507), (6,1; 47506), (9,1; 47508)

P and U on the Euler line, X(2)X(3): see the preamble just before X(47332).

P and U on the GK line, X(2)X(6):
(2,6;47473), (2,69; 47541), (2,81; 47542), (2,86; 47543), (2,141;47544)
(6,2;47545), (6,69;47546), (6,81; 47547), (6,86; 47548); (6,141; 47549), (6,230; 47550)
(69,2; 47551), (69,6; 47552), (69,230; 47565)
(81,2; 47566)
(86,2; 47566), (86,6; 47554), (86,69; 47555)
(141,2; 47556), (141,230; 47557)
(230,2; 46998), (230,6; 47559), (230,69; 47560), (230,141; 47561)

P and U on the Brocard axis, X(3)X(6):
(3,6; 47468), (3,32; 47567), (3,39; 47568), (3,182; 47569), (3,187; 47570)
(6,3; 47571), (6,32; 47572), (6,39; 47573), (6,187; 47574)
(15,3; 47575), (15,16; 47497)
(16,3; 47576), (16,15; 47498)
(32,3; 47577), (32,6; 47578)
(39,3; 47579), (39,6;47580)
(182,3; 47581), (182,6; 47569), (182,39; 47583)
(187,3; 47584), (187,6; 47585)

P and U on the anti-orthic axis, X(44)X(513):
(649,650; 47499), (650,649; 47500)

P and U on the Lemoine axis, X(187)X(237):
(182,237;47502), (237,187; 47501), (237,647; 47504), (647,187; 47503); (647,237; 47505)

Note that the transformation T is many-to-one; i.e., for each T(P,U), there are (infinitely) many pairs (P',U') such that T(P',U') = T(P,U). For example, T(X(2),X(551)) = T(X(10),X(2)) = TX(551,X(1)) = X(47562), as listed above.

See also the preambles just before X(47090) and X(47332).

X(47488) = X(30)X(40)∩X(468)X(519)

Barycentrics 2*a^7 - 10*a^6*b - 5*a^5*b^2 + 7*a^4*b^3 - 2*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 - 7*b^7 - 10*a^6*c + 7*a^4*b^2*c + 10*a^2*b^4*c - 7*b^6*c - 5*a^5*c^2 + 7*a^4*b*c^2 + 12*a^3*b^2*c^2 - 24*a^2*b^3*c^2 - 5*a*b^4*c^2 + 7*b^5*c^2 + 7*a^4*c^3 - 24*a^2*b^2*c^3 + 7*b^4*c^3 - 2*a^3*c^4 + 10*a^2*b*c^4 - 5*a*b^2*c^4 + 7*b^3*c^4 + 10*a^2*c^5 + 7*b^2*c^5 + 5*a*c^6 - 7*b*c^6 - 7*c^7 : :

X(47488) = 5 X[3617] - X[10989], 4 X[3626] + X[47312], 2 X[4669] + X[37904], 7 X[4678] + X[37901], 4 X[4745] - X[47311], 2 X[5159] - 3 X[19875], X[5881] + 2 X[37934], 3 X[25055] - 4 X[37911], X[31145] + 3 X[37907], 6 X[38098] - X[46517]

X(47488) = lies on these lines: {8, 7426}, {10, 47097}, {30, 40}, {468, 519}, {515, 47031}, {517, 47332}, {518, 47473}, {528, 47470}, {952, 18579}, {3617, 10989}, {3626, 47312}, {4669, 37904}, {4678, 37901}, {4745, 47311}, {5159, 19875}, {5881, 37934}, {9041, 47477}, {10295, 34627}, {11799, 34718}, {25055, 37911}, {28194, 47310}, {28198, 47309}, {28204, 47333}, {28208, 47308}, {31145, 37907}, {31162, 37984}, {38098, 46517}, {47334, 47471}

X(47488) = midpoint of X(i) and X(j) for these {i,j}: {8, 7426}, {3679, 47321}, {10295, 34627}, {11799, 34718}
X(47488) = reflection of X(i) in X(j) for these {i,j}: {31162, 37984}, {47097, 10}, {47469, 47333}, {47471, 47334}, {47472, 468}

X(47489) = X(30)X(7982)∩X(468)X(519)

Barycentrics 10*a^7 - 2*a^6*b - 9*a^5*b^2 + 3*a^4*b^3 - 10*a^3*b^4 + 2*a^2*b^5 + 9*a*b^6 - 3*b^7 - 2*a^6*c + 3*a^4*b^2*c + 2*a^2*b^4*c - 3*b^6*c - 9*a^5*c^2 + 3*a^4*b*c^2 + 28*a^3*b^2*c^2 - 8*a^2*b^3*c^2 - 9*a*b^4*c^2 + 3*b^5*c^2 + 3*a^4*c^3 - 8*a^2*b^2*c^3 + 3*b^4*c^3 - 10*a^3*c^4 + 2*a^2*b*c^4 - 9*a*b^2*c^4 + 3*b^3*c^4 + 2*a^2*c^5 + 3*b^2*c^5 + 9*a*c^6 - 3*b*c^6 - 3*c^7 : :

X(47489) = 3 X[1] - 2 X[5159], X[23] + 3 X[145], 2 X[468] - 3 X[47472], 2 X[47308] - 3 X[47469], X[858] - 3 X[3241], 2 X[47336] - 3 X[47471], 3 X[1482] - X[18323], 3 X[1483] - X[37950], 6 X[3244] - X[46517], 3 X[3633] + 4 X[47316], 4 X[47316] - 3 X[47321], 3 X[3679] - 4 X[37911], 2 X[18571] - 3 X[47476], 3 X[10257] - 4 X[15178], 6 X[16976] - 7 X[30389], X[18325] + 3 X[34748], 3 X[20049] + 5 X[37760], 3 X[34747] + 2 X[37897], 3 X[47359] - 4 X[47460]

X(47489) lies on these lines: {1, 5159}, {23, 145}, {30, 7982}, {468, 519}, {517, 47308}, {518, 47470}, {858, 3241}, {952, 47336}, {1482, 18323}, {1483, 37950}, {3244, 46517}, {3633, 47316}, {3679, 37911}, {5844, 18571}, {5846, 47477}, {5881, 37984}, {10222, 10297}, {10257, 15178}, {16976, 30389}, {18325, 34748}, {20049, 37760}, {22356, 47161}, {28204, 47309}, {34747, 37897}, {47359, 47460}

X(47489) = midpoint of X(3633) and X(47321)
X(47489) = reflection of X(i) in X(j) for these {i,j}: {5881, 37984}, {10297, 10222}

X(47490) = X(30)X(4677)∩X(468)X(519)

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

X(47490) = 3 X[1] - 4 X[37911], 3 X[8] - X[858], X[23] + 3 X[31145], 4 X[468] - 3 X[47472], 4 X[47335] - 3 X[47469], 3 X[3621] + 5 X[37760], 6 X[3625] + X[37899], 3 X[3632] + 2 X[37897], 2 X[37897] - 3 X[47321], 3 X[3679] - 2 X[5159], 2 X[4301] - 3 X[10151], 12 X[4701] - X[47095], 4 X[44961] - 3 X[47471], 7 X[9588] - 6 X[16976], 15 X[20052] + X[20063], 4 X[22249] - 3 X[47476], 6 X[34641] - X[46517], 3 X[47359] - 2 X[47464]

X(47490) lies on these lines: {1, 37911}, {8, 858}, {23, 31145}, {30, 4677}, {468, 519}, {517, 47309}, {952, 47335}, {3621, 37760}, {3625, 37899}, {3632, 37897}, {3679, 5159}, {4301, 10151}, {4669, 47097}, {4701, 47095}, {5844, 44961}, {5853, 47470}, {7982, 37984}, {9053, 47477}, {9588, 16976}, {20052, 20063}, {22249, 47476}, {28204, 47308}, {34641, 46517}, {47359, 47464}

X(47490) = midpoint of X(3632) and X(47321)
X(47490) = reflection of X(i) in X(j) for these {i,j}: {7982, 37984}, {47097, 4669}

X(47491) = X(30)X(4301)∩X(468)X(519)

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

X(47491) = 3 X[1] - X[858], 3 X[10] - 4 X[37911], X[23] + 3 X[3241], 3 X[145] + 5 X[37760], 5 X[37760] - 3 X[47321], 3 X[403] - X[5881], X[468] - 3 X[47472], X[47309] - 3 X[47471], X[47335] - 3 X[47476], 3 X[551] - 2 X[5159], 3 X[3244] + 2 X[37897], 15 X[3623] + X[20063], 6 X[3635] + X[37899], 3 X[3656] - X[18323], 5 X[5734] - X[10296], X[7991] - 3 X[44280], 5 X[30745] - 9 X[38314], 5 X[31399] - 6 X[44911], 3 X[47359] - 5 X[47458]

X(47491) lies on these lines: {1, 858}, {10, 37911}, {23, 3241}, {30, 4301}, {145, 37760}, {403, 5881}, {468, 519}, {515, 47309}, {516, 47469}, {517, 47335}, {551, 5159}, {952, 44961}, {3244, 37897}, {3623, 20063}, {3635, 37899}, {3656, 18323}, {5734, 10296}, {5844, 22249}, {5847, 47477}, {5850, 47470}, {7982, 10295}, {7991, 44280}, {10297, 13464}, {11799, 37727}, {15122, 15178}, {16496, 32220}, {28194, 47308}, {28204, 47336}, {30745, 38314}, {31399, 44911}, {37546, 37978}, {47359, 47458}

X(47491) = midpoint of X(i) and X(j) for these {i,j}: {145, 47321}, {7982, 10295}, {11799, 37727}, {16496, 32220}
X(47491) = reflection of X(i) in X(j) for these {i,j}: {10297, 13464}, {15122, 15178}

X(47492) = X(30)X(4669)∩X(468)X(519)

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

X(47492) = 3 X[8] + X[23], X[23] - 3 X[47321], 3 X[10] - 2 X[5159], 3 X[355] - X[18323], 3 X[403] - X[7982], 5 X[468] - 3 X[47472], 3 X[551] - 4 X[37911], X[858] - 3 X[3679], 3 X[3625] + 4 X[47316], 6 X[3626] - X[46517], 3 X[5690] - X[37950], 3 X[12645] + 5 X[37958], 2 X[15178] - 3 X[44452], X[18325] + 3 X[34718], 3 X[31145] + 5 X[37760], 3 X[34641] + 2 X[37897], X[37727] - 3 X[44214], X[47280] - 3 X[47359]

X(47492) lies on these lines: {8, 23}, {10, 5159}, {30, 4669}, {355, 18323}, {403, 7982}, {468, 519}, {515, 47308}, {517, 47336}, {551, 37911}, {858, 3679}, {952, 18571}, {3625, 47316}, {3626, 46517}, {4301, 37984}, {4677, 7426}, {4745, 47097}, {5690, 37950}, {5881, 10295}, {12645, 37958}, {15178, 44452}, {18325, 34718}, {28194, 47309}, {28204, 47335}, {28234, 47471}, {28236, 47469}, {31145, 37760}, {34641, 37897}, {37727, 44214}, {47280, 47359}

X(47492) = midpoint of X(i) and X(j) for these {i,j}: {8, 47321}, {4677, 7426}, {5881, 10295}
X(47492) = reflection of X(i) in X(j) for these {i,j}: {4301, 37984}, {47097, 4745}

X(47493) = X(30)X(944)∩X(468)X(519)

Barycentrics 22*a^7 - 2*a^6*b - 19*a^5*b^2 + 5*a^4*b^3 - 22*a^3*b^4 + 2*a^2*b^5 + 19*a*b^6 - 5*b^7 - 2*a^6*c + 5*a^4*b^2*c + 2*a^2*b^4*c - 5*b^6*c - 19*a^5*c^2 + 5*a^4*b*c^2 + 60*a^3*b^2*c^2 - 12*a^2*b^3*c^2 - 19*a*b^4*c^2 + 5*b^5*c^2 + 5*a^4*c^3 - 12*a^2*b^2*c^3 + 5*b^4*c^3 - 22*a^3*c^4 + 2*a^2*b*c^4 - 19*a*b^2*c^4 + 5*b^3*c^4 + 2*a^2*c^5 + 5*b^2*c^5 + 19*a*c^6 - 5*b*c^6 - 5*c^7 : :

X(47493) = 4 X[3244] + X[47312], 5 X[3623] - X[10989], 2 X[5159] - 3 X[38314], 4 X[10222] - X[47339], X[20049] + 3 X[37907], 2 X[47359] - 3 X[47459]

X(47493) lies on these lines: {1, 47097}, {30, 944}, {145, 7426}, {468, 519}, {517, 47031}, {952, 47332}, {3244, 47312}, {3623, 10989}, {5159, 38314}, {5844, 18579}, {5846, 47473}, {10222, 47339}, {10295, 34631}, {11799, 34748}, {20049, 37907}, {28194, 47469}, {28204, 47310}, {28538, 47477}, {34627, 37984}, {34747, 47321}, {47333, 47476}, {47359, 47459}

X(47493) = midpoint of X(i) and X(j) for these {i,j}: {145, 7426}, {10295, 34631}, {11799, 34748}, {34747, 47321}
X(47493) = reflection of X(i) in X(j) for these {i,j}: {468, 47472}, {34627, 37984}, {47097, 1}, {47310, 47471}, {47333, 47476}

X(47494) = X(8)X(30)∩X(468)X(519)

Barycentrics 10*a^7 - 14*a^6*b - 13*a^5*b^2 + 11*a^4*b^3 - 10*a^3*b^4 + 14*a^2*b^5 + 13*a*b^6 - 11*b^7 - 14*a^6*c + 11*a^4*b^2*c + 14*a^2*b^4*c - 11*b^6*c - 13*a^5*c^2 + 11*a^4*b*c^2 + 36*a^3*b^2*c^2 - 36*a^2*b^3*c^2 - 13*a*b^4*c^2 + 11*b^5*c^2 + 11*a^4*c^3 - 36*a^2*b^2*c^3 + 11*b^4*c^3 - 10*a^3*c^4 + 14*a^2*b*c^4 - 13*a*b^2*c^4 + 11*b^3*c^4 + 14*a^2*c^5 + 11*b^2*c^5 + 13*a*c^6 - 11*b*c^6 - 11*c^7 : :

X(47494) = 3 X[403] - X[34631], 3 X[468] - 2 X[47472], X[3621] + 3 X[37907], 4 X[4669] - X[47311], 2 X[4677] + X[37904], 3 X[10151] - 2 X[31162], 3 X[13473] - 4 X[34648], 5 X[20052] + 3 X[37909], 4 X[34641] + X[47312], X[34748] - 3 X[44214], 4 X[37911] - 3 X[38314]

X(47494) lies on these lines: {8, 30}, {403, 34631}, {468, 519}, {517, 47310}, {952, 47333}, {3621, 37907}, {3679, 47097}, {4669, 47311}, {4677, 37904}, {5844, 47334}, {7426, 31145}, {8192, 37941}, {9041, 47473}, {10151, 31162}, {12645, 44265}, {13473, 34648}, {20052, 37909}, {28204, 47031}, {34641, 47312}, {34748, 44214}, {37911, 38314}, {47277, 47359}

X(47494) = midpoint of X(i) and X(j) for these {i,j}: {4677, 47321}, {7426, 31145}, {12645, 44265}
X(47494) = reflection of X(i) in X(j) for these {i,j}: {37904, 47321}, {47097, 3679}, {47277, 47359}

X(47495) = X(30)X(551)∩X(468)X(519)

Barycentrics 10*a^7 + 4*a^6*b - 7*a^5*b^2 - a^4*b^3 - 10*a^3*b^4 - 4*a^2*b^5 + 7*a*b^6 + b^7 + 4*a^6*c - a^4*b^2*c - 4*a^2*b^4*c + b^6*c - 7*a^5*c^2 - a^4*b*c^2 + 24*a^3*b^2*c^2 + 6*a^2*b^3*c^2 - 7*a*b^4*c^2 - b^5*c^2 - a^4*c^3 + 6*a^2*b^2*c^3 - b^4*c^3 - 10*a^3*c^4 - 4*a^2*b*c^4 - 7*a*b^2*c^4 - b^3*c^4 - 4*a^2*c^5 - b^2*c^5 + 7*a*c^6 + b*c^6 + c^7 : :

X(47495) = X[23] + 3 X[38314], X[858] - 3 X[25055], X[3241] + 3 X[37907], 3 X[37907] - X[47321], 5 X[3616] - X[10989], 7 X[3622] + X[37901], 4 X[3636] + X[47312], X[3654] - 3 X[44214], X[4301] + 2 X[37934], 2 X[5159] - 3 X[19883], 5 X[5734] + 7 X[37957], X[12898] + 3 X[15362], 2 X[15178] + X[16619], X[34632] - 5 X[37952], X[47359] - 3 X[47455]

X(47495) lies on these lines: {1, 7426}, {23, 38314}, {30, 551}, {468, 519}, {515, 47332}, {516, 47031}, {517, 18579}, {524, 11720}, {858, 25055}, {1125, 47097}, {3241, 37907}, {3616, 10989}, {3622, 37901}, {3636, 47312}, {3654, 44214}, {3655, 11799}, {3656, 44265}, {4301, 37934}, {5159, 19883}, {5734, 37957}, {5847, 47473}, {10295, 31162}, {11645, 11735}, {12898, 15362}, {15178, 16619}, {28194, 47333}, {28198, 47335}, {28204, 47334}, {28208, 47336}, {34632, 37952}, {34648, 37984}, {47310, 47469}, {47359, 47455}

X(47495) = midpoint of X(i) and X(j) for these {i,j}: {1, 7426}, {468, 47472}, {3241, 47321}, {3655, 11799}, {3656, 44265}, {10295, 31162}, {47310, 47469}, {47333, 47471}, {47334, 47476}
X(47495) = reflection of X(i) in X(j) for these {i,j}: {34648, 37984}, {47097, 1125}
X(47495) = {X(3241),X(37907)}-harmonic conjugate of X(47321)

X(47496) = X(10)X(30)∩X(468)X(519)

Barycentrics 2*a^7 + 8*a^6*b + a^5*b^2 - 5*a^4*b^3 - 2*a^3*b^4 - 8*a^2*b^5 - a*b^6 + 5*b^7 + 8*a^6*c - 5*a^4*b^2*c - 8*a^2*b^4*c + 5*b^6*c + a^5*c^2 - 5*a^4*b*c^2 + 18*a^2*b^3*c^2 + a*b^4*c^2 - 5*b^5*c^2 - 5*a^4*c^3 + 18*a^2*b^2*c^3 - 5*b^4*c^3 - 2*a^3*c^4 - 8*a^2*b*c^4 + a*b^2*c^4 - 5*b^3*c^4 - 8*a^2*c^5 - 5*b^2*c^5 - a*c^6 + 5*b*c^6 + 5*c^7 : :

X(47496) = X[8] + 3 X[37907], 3 X[186] + X[34627], 3 X[403] - X[31162], 3 X[468] - X[47472], X[858] - 3 X[19875], 5 X[3617] + 3 X[37909], X[3655] - 3 X[44214], 2 X[4745] + X[37904], 3 X[19883] - 4 X[37911], X[34628] - 3 X[44280], X[34631] - 9 X[37943], 2 X[37897] + 3 X[38098]

X(47496) lies on these lines: {2, 47321}, {8, 37907}, {10, 30}, {186, 34627}, {355, 44265}, {403, 31162}, {468, 519}, {515, 47333}, {516, 47310}, {517, 47334}, {523, 44566}, {858, 19875}, {3617, 37909}, {3654, 11799}, {3655, 44214}, {3679, 7426}, {3828, 47097}, {4745, 37904}, {5690, 44266}, {9798, 37955}, {16307, 16611}, {18579, 28204}, {19883, 37911}, {28194, 47332}, {28198, 47336}, {28208, 47335}, {32113, 47359}, {34628, 44280}, {34631, 37943}, {37897, 38098}

X(47496) = midpoint of X(i) and X(j) for these {i,j}: {2, 47321}, {355, 44265}, {3654, 11799}, {3679, 7426}, {5690, 44266}, {32113, 47359}
X(47496) = reflection of X(47097) in X(3828)

X(47497) = X(30)X(8594)∩X(468)X(511)

X(47498) = X(30)X(8595)∩X(468)X(511)

X(47499) = X(468)X(513)∩X(523)X(649)

X(47500) = X(468)X(513)∩X(523)X(661)

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

X(47501) = X(30)X(114)∩X(468)X(512)

Barycentrics 2*a^16*b^2 - 5*a^14*b^4 + 7*a^12*b^6 - 7*a^10*b^8 - 2*a^8*b^10 + 11*a^6*b^12 - 7*a^4*b^14 + a^2*b^16 + 2*a^16*c^2 - 10*a^14*b^2*c^2 + 13*a^12*b^4*c^2 + 2*a^10*b^6*c^2 + 6*a^8*b^8*c^2 - 25*a^6*b^10*c^2 + 14*a^4*b^12*c^2 - 3*a^2*b^14*c^2 + b^16*c^2 - 5*a^14*c^4 + 13*a^12*b^2*c^4 - 30*a^10*b^4*c^4 + 6*a^8*b^6*c^4 + 24*a^6*b^8*c^4 - 9*a^4*b^10*c^4 + 9*a^2*b^12*c^4 - 4*b^14*c^4 + 7*a^12*c^6 + 2*a^10*b^2*c^6 + 6*a^8*b^4*c^6 - 24*a^6*b^6*c^6 + 2*a^4*b^8*c^6 - 21*a^2*b^10*c^6 + 6*b^12*c^6 - 7*a^10*c^8 + 6*a^8*b^2*c^8 + 24*a^6*b^4*c^8 + 2*a^4*b^6*c^8 + 28*a^2*b^8*c^8 - 3*b^10*c^8 - 2*a^8*c^10 - 25*a^6*b^2*c^10 - 9*a^4*b^4*c^10 - 21*a^2*b^6*c^10 - 3*b^8*c^10 + 11*a^6*c^12 + 14*a^4*b^2*c^12 + 9*a^2*b^4*c^12 + 6*b^6*c^12 - 7*a^4*c^14 - 3*a^2*b^2*c^14 - 4*b^4*c^14 + a^2*c^16 + b^2*c^16 : :

X(47502) = X(187)X(523)∩X(468)X(512)

Barycentrics (b^2 - c^2)*(4*a^14 - 9*a^12*b^2 + 2*a^10*b^4 + 9*a^8*b^6 - 7*a^6*b^8 + a^2*b^12 - 9*a^12*c^2 + 28*a^10*b^2*c^2 - 23*a^8*b^4*c^2 - 4*a^6*b^6*c^2 + 13*a^4*b^8*c^2 - 6*a^2*b^10*c^2 + b^12*c^2 + 2*a^10*c^4 - 23*a^8*b^2*c^4 + 34*a^6*b^4*c^4 - 14*a^4*b^6*c^4 + 5*a^2*b^8*c^4 - 2*b^10*c^4 + 9*a^8*c^6 - 4*a^6*b^2*c^6 - 14*a^4*b^4*c^6 + b^8*c^6 - 7*a^6*c^8 + 13*a^4*b^2*c^8 + 5*a^2*b^4*c^8 + b^6*c^8 - 6*a^2*b^2*c^10 - 2*b^4*c^10 + a^2*c^12 + b^2*c^12) : :

X(47502) lies on these lines: {3, 18311}, {187, 523}, {316, 47259}, {468, 512}, {511, 46990}, {1316, 8371}, {3849, 46989}, {4108, 47349}, {5099, 47252}, {46984, 47113}

X(47502) = reflection of X(i) in X(j) for these {i,j}: {5099, 47252}, {46984, 47113}

X(47503) = X(115)X(523)∩X(468)X(512)

X(47503) lies on these lines: {115, 523}, {187, 47249}, {316, 47258}, {468, 512}, {511, 47002}, {3849, 47001}, {5996, 47349}, {16760, 46990}

X(47503) = midpoint of X(316) and X(47258)
X(47503) = reflection of X(i) in X(j) for these {i,j}: {187, 47249}, {46990, 16760}

X(47504) = X(237)X(523)∩X(468)X(512)

Barycentrics (b - c)*(b + c)*(4*a^16*b^2 - 11*a^14*b^4 + 5*a^12*b^6 + 10*a^10*b^8 - 10*a^8*b^10 + a^6*b^12 + a^4*b^14 + 4*a^16*c^2 - 14*a^14*b^2*c^2 + 27*a^12*b^4*c^2 - 26*a^10*b^6*c^2 + 2*a^8*b^8*c^2 + 14*a^6*b^10*c^2 - 9*a^4*b^12*c^2 + 2*a^2*b^14*c^2 - 11*a^14*c^4 + 27*a^12*b^2*c^4 - 24*a^10*b^4*c^4 + 20*a^8*b^6*c^4 - 20*a^6*b^8*c^4 + 12*a^4*b^10*c^4 - 5*a^2*b^12*c^4 + b^14*c^4 + 5*a^12*c^6 - 26*a^10*b^2*c^6 + 20*a^8*b^4*c^6 + 6*a^6*b^6*c^6 - 4*a^4*b^8*c^6 + 6*a^2*b^10*c^6 - 3*b^12*c^6 + 10*a^10*c^8 + 2*a^8*b^2*c^8 - 20*a^6*b^4*c^8 - 4*a^4*b^6*c^8 - 6*a^2*b^8*c^8 + 2*b^10*c^8 - 10*a^8*c^10 + 14*a^6*b^2*c^10 + 12*a^4*b^4*c^10 + 6*a^2*b^6*c^10 + 2*b^8*c^10 + a^6*c^12 - 9*a^4*b^2*c^12 - 5*a^2*b^4*c^12 - 3*b^6*c^12 + a^4*c^14 + 2*a^2*b^2*c^14 + b^4*c^14) : :

X(47504) lies on these lines: {30, 31174}, {237, 523}, {468, 512}, {14957, 47259}, {23301, 36189}, {44215, 46983}, {44221, 46984}, {44227, 46985}, {45317, 47249}

X(47504) = reflection of X(i) in X(j) for these {i,j}: {36189, 47252}, {46983, 44215}, {46984, 44221}, {46985, 44227}

X(47505) = X(30)X(647)∩X(468)X(512)

X(47505) lies on these lines: {30, 647}, {237, 47249}, {338, 523}, {468, 512}, {14957, 47258}

X(47505) = midpoint of X(14957) and X(47258)
X(47505) = reflection of X(237) in X(47249)
X(47505) = crossdifference of every pair of points on line {14966, 44889}

X(47506) = X(8)X(32220)∩X(468)X(518)

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

X(47506) = 3 X[403] - X[39898], 2 X[1386] - 3 X[47459], X[3242] - 3 X[47455], 2 X[5159] - 3 X[38047], 3 X[16475] - 4 X[47460], X[16496] - 4 X[47454], 3 X[38315] - 5 X[47458]

X(47506) lies on these lines: {1, 47457}, {8, 32220}, {30, 47359}, {403, 39898}, {468, 518}, {1386, 47459}, {3242, 47455}, {3564, 32278}, {3751, 47321}, {4663, 47277}, {5159, 38047}, {9041, 47472}, {16475, 47460}, {16496, 47454}, {38315, 47458}

X(47506) = midpoint of X(i) and X(j) for these {i,j}: {8, 32220}, {3751, 47321}
X(47506) = reflection of X(i) in X(j) for these {i,j}: {1, 47457}, {47277, 4663}, {47477, 468}

X(47507) = X(468)X(518)∩X(516)X(47469)

Barycentrics 2*a^9 - 10*a^8*b + 5*a^7*b^2 + 11*a^6*b^3 - 9*a^5*b^4 + 9*a^4*b^5 - 5*a^3*b^6 - 11*a^2*b^7 + 7*a*b^8 + b^9 - 10*a^8*c - 12*a^7*b*c + 7*a^6*b^2*c + 6*a^5*b^3*c + 11*a^4*b^4*c + 12*a^3*b^5*c - 7*a^2*b^6*c - 6*a*b^7*c - b^8*c + 5*a^7*c^2 + 7*a^6*b*c^2 - 10*a^5*b^2*c^2 - 28*a^4*b^3*c^2 + 13*a^3*b^4*c^2 + 15*a^2*b^5*c^2 - 2*b^7*c^2 + 11*a^6*c^3 + 6*a^5*b*c^3 - 28*a^4*b^2*c^3 - 24*a^3*b^3*c^3 + 3*a^2*b^4*c^3 + 6*a*b^5*c^3 + 2*b^6*c^3 - 9*a^5*c^4 + 11*a^4*b*c^4 + 13*a^3*b^2*c^4 + 3*a^2*b^3*c^4 - 14*a*b^4*c^4 + 9*a^4*c^5 + 12*a^3*b*c^5 + 15*a^2*b^2*c^5 + 6*a*b^3*c^5 - 5*a^3*c^6 - 7*a^2*b*c^6 + 2*b^3*c^6 - 11*a^2*c^7 - 6*a*b*c^7 - 2*b^2*c^7 + 7*a*c^8 - b*c^8 + c^9 : :

X(47507) = X[47470] - 3 X[47472], X[858] - 3 X[11038], 2 X[5159] - 3 X[38053], 4 X[37911] - 3 X[38057]

X(47507) lies on these lines: {468, 518}, {516, 47469}, {527, 47470}, {858, 11038}, {971, 47471}, {5159, 38053}, {5762, 47476}, {10297, 20330}, {37911, 38057}

X(47508) = X(468)X(518)∩X(858)X(5686)

Barycentrics 2*a^9 + 6*a^8*b - 11*a^7*b^2 - 5*a^6*b^3 + 7*a^5*b^4 - 7*a^4*b^5 + 11*a^3*b^6 + 5*a^2*b^7 - 9*a*b^8 + b^9 + 6*a^8*c - 12*a^7*b*c - 9*a^6*b^2*c + 6*a^5*b^3*c - 5*a^4*b^4*c + 12*a^3*b^5*c + 9*a^2*b^6*c - 6*a*b^7*c - b^8*c - 11*a^7*c^2 - 9*a^6*b*c^2 + 22*a^5*b^2*c^2 + 20*a^4*b^3*c^2 - 19*a^3*b^4*c^2 - a^2*b^5*c^2 - 2*b^7*c^2 - 5*a^6*c^3 + 6*a^5*b*c^3 + 20*a^4*b^2*c^3 - 24*a^3*b^3*c^3 - 13*a^2*b^4*c^3 + 6*a*b^5*c^3 + 2*b^6*c^3 + 7*a^5*c^4 - 5*a^4*b*c^4 - 19*a^3*b^2*c^4 - 13*a^2*b^3*c^4 + 18*a*b^4*c^4 - 7*a^4*c^5 + 12*a^3*b*c^5 - a^2*b^2*c^5 + 6*a*b^3*c^5 + 11*a^3*c^6 + 9*a^2*b*c^6 + 2*b^3*c^6 + 5*a^2*c^7 - 6*a*b*c^7 - 2*b^2*c^7 - 9*a*c^8 - b*c^8 + c^9 : :

X(47508) lies on these lines: {468, 518}, {858, 5686}, {5159, 38057}, {5223, 47321}, {5853, 47470}, {37911, 38053}

X(47509) = 71ST HATZIPOLAKIS-MOSES-EULER POINT

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

X(47509) = 5 X[2] - 3 X[46868], 4 X[3] - X[36179], 4 X[140] - X[36160], 5 X[631] - 2 X[14894], 5 X[632] - 2 X[10223], 5 X[34093] - 6 X[46868], X[2979] + 3 X[9159]

X(47509) lies on these lines: {2, 3}, {343, 12079}, {394, 6795}, {523, 3917}, {2979, 9159}, {14570, 46147}

X(47509) = reflection of X(34093) in X(2)
X(47509) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 36192, 36178}, {1368, 36190, 3154}

X(47510) = EULER LINE INTERCEPT OF X(9)X(12)

X(47510) lies on these lines: {2, 3}, {9, 12}, {10, 13567}, {11, 5436}, {51, 6045}, {72, 495}, {225, 40937}, {226, 960}, {496, 24541}, {950, 2886}, {1182, 1213}, {1260, 3085}, {1698, 1728}, {1708, 26066}, {1713, 5742}, {1837, 3925}, {3419, 19860}, {3487, 5730}, {3488, 24390}, {3701, 26592}, {3822, 12572}, {3826, 8582}, {5175, 33108}, {5705, 10396}, {5715, 31435}, {5728, 6734}, {5729, 9780}, {5745, 15844}, {5794, 10393}, {7679, 8165}, {8583, 11375}, {10039, 46677}, {10477, 26543}, {10826, 25973}, {10954, 18397}, {11523, 15888}, {12625, 37724}, {12848, 18231}, {19753, 19755}, {19861, 37737}, {21077, 45120}, {23292, 43531}, {24703, 31936}, {24953, 26481}, {26131, 37659}, {27383, 33993}

X(47510) = complement of X(37228)
X(47510) = orthocentroidal-circle-inverse of X(37224)
X(47510) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 37224}, {2, 377, 19520}, {2, 17555, 4205}, {2, 24984, 13728}, {2, 25876, 19273}, {2, 37248, 6675}, {5, 405, 14022}, {5, 5428, 37356}, {5, 37424, 20420}, {377, 11344, 20420}, {405, 442, 5}, {405, 7580, 11344}, {405, 37308, 1006}, {429, 37056, 5}, {442, 4187, 6829}, {442, 8226, 2476}, {443, 6908, 37240}, {452, 2476, 8226}, {452, 5177, 3832}, {4197, 5177, 442}, {6675, 31789, 405}, {6829, 16845, 4187}, {6842, 6861, 5}, {6881, 6928, 5}, {6907, 8728, 442}, {6936, 16845, 405}, {11113, 17532, 3845}

X(47511) = EULER LINE INTERCEPT OF X(9)X(31)

X(47511) lies on these lines: {2, 3}, {9, 31}, {42, 41239}, {55, 2345}, {72, 3920}, {81, 10477}, {200, 4251}, {210, 19133}, {226, 32772}, {321, 1621}, {614, 5436}, {943, 26227}, {958, 5716}, {965, 44098}, {1001, 17061}, {1260, 7172}, {1766, 4512}, {2268, 10382}, {2287, 5320}, {2303, 44115}, {2352, 38871}, {2975, 40956}, {3190, 16788}, {3419, 29667}, {5016, 5260}, {5105, 33854}, {5263, 41260}, {5273, 5807}, {5285, 5750}, {5324, 5737}, {5749, 7085}, {9798, 19866}, {11221, 16547}, {14552, 37492}, {16992, 44140}, {19724, 19753}, {19798, 19840}, {21287, 37664}, {31993, 41230}

X(47511) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 21, 4224}, {2, 16865, 25494}, {2, 26032, 4197}, {2, 37090, 37261}, {2, 37254, 16352}, {2, 37325, 4223}, {21, 964, 37399}, {25, 37060, 2}, {405, 19523, 16845}, {405, 37249, 19246}, {1006, 7413, 19649}, {1011, 4206, 37399}, {1011, 37316, 21}, {2049, 37317, 28}, {5020, 16849, 2}, {11358, 13723, 1817}

X(47512) = EULER LINE INTERCEPT OF X(9)X(58)

X(47512) lies on these lines: {2, 3}, {9, 58}, {35, 19857}, {72, 81}, {86, 3487}, {226, 5323}, {284, 936}, {314, 943}, {602, 2328}, {1038, 1396}, {1043, 3488}, {1791, 14534}, {2185, 14868}, {2194, 25917}, {2287, 5044}, {2360, 8583}, {3876, 40571}, {4281, 41239}, {4359, 19848}, {4653, 5436}, {4658, 11523}, {4877, 31424}, {5248, 41230}, {5259, 24210}, {5279, 31445}, {5758, 17183}, {8885, 40937}, {15556, 18417}, {17189, 34937}, {17321, 19844}, {17322, 19841}, {19728, 19753}, {19842, 28653}, {32779, 41507}, {36745, 46889}

X(47512) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 21, 28}, {2, 28, 17581}, {2, 7520, 19285}, {3, 16843, 2}, {3, 37322, 21}, {21, 404, 27174}, {21, 1010, 4221}, {21, 11110, 17560}, {21, 13614, 8021}, {21, 14005, 16049}, {21, 17518, 17512}, {21, 17551, 1325}, {21, 17557, 4228}, {58, 975, 2303}, {405, 19523, 2}, {405, 37244, 19246}, {6675, 21530, 2}, {11110, 16053, 16845}, {14007, 17512, 17518}, {16370, 19285, 7520}, {16844, 37317, 4223}, {17582, 31900, 16054}, {19313, 19527, 17582}, {37060, 37246, 37037}, {37065, 37323, 13726}

X(47513) = EULER LINE INTERCEPT OF X(11)X(42)

X(47513) lies on these lines: {2, 3}, {11, 42}, {12, 3720}, {43, 7741}, {51, 24220}, {325, 18152}, {495, 29814}, {496, 17018}, {899, 7173}, {1329, 31330}, {1506, 21838}, {2886, 5241}, {3240, 10593}, {3614, 30950}, {3741, 3814}, {3822, 25501}, {3825, 39583}, {3937, 40687}, {4651, 24390}, {4685, 24387}, {4858, 21807}, {5943, 17167}, {7951, 26102}, {10453, 11681}, {15666, 25502}, {17135, 17757}, {19714, 19754}, {19787, 19839}, {20256, 31053}, {20486, 29687}, {21239, 30949}, {25079, 27701}, {26561, 27158}, {29846, 30980}, {30959, 33171}, {37720, 42042}

X(47513) = complement of X(4210)
X(47513) = orthocentroidal-circle-inverse of X(4191)
X(47513) = X(43076)-Ceva conjugate of X(523)
X(47513) = crosspoint of X(264) and X(17758)
X(47513) = crosssum of X(184) and X(4251)
X(47513) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 4191}, {2, 5, 3136}, {2, 1985, 37354}, {2, 3091, 6817}, {2, 4184, 140}, {2, 5187, 37193}, {2, 6818, 1011}, {2, 6822, 16373}, {2, 14008, 37365}, {2, 16044, 16956}, {2, 16955, 7807}, {2, 36694, 4196}, {5, 34119, 5133}, {5, 37355, 2}, {1656, 16058, 2}, {3090, 6822, 2}, {14004, 21554, 16064}

X(47514) = EULER LINE INTERCEPT OF X(12)X(43)

X(47514) lies on these lines: {2, 3}, {11, 26102}, {12, 43}, {42, 495}, {141, 674}, {226, 4260}, {310, 3933}, {496, 3720}, {899, 10592}, {1246, 5224}, {1751, 5138}, {3705, 20913}, {3753, 24996}, {3813, 42057}, {3816, 25501}, {3819, 24220}, {3820, 26037}, {3822, 6685}, {3826, 44411}, {3840, 25639}, {3917, 17167}, {3925, 24310}, {4685, 12607}, {5249, 20256}, {5254, 21838}, {7741, 25502}, {7951, 16569}, {10453, 24390}, {10593, 30950}, {11019, 17758}, {11680, 18139}, {11681, 26038}, {12588, 33137}, {15656, 17754}, {15888, 42042}, {17889, 41886}, {19715, 19755}, {20486, 32778}, {20545, 25385}, {23304, 25523}, {24512, 46882}, {25466, 43223}, {26481, 33140}, {31008, 37664}, {31330, 31419}, {37719, 42043}

X(47514) = complement of X(1011)
X(47514) = orthocentroidal-circle-inverse of X(16058)
X(47514) = complement of the isogonal conjugate of X(1246)
X(47514) = X(i)-complementary conjugate of X(j) for these (i,j): {1246, 10}, {2282, 2}, {28624, 650}
X(47514) = X(43359)-Ceva conjugate of X(523)
X(47514) = crosssum of X(6) and X(44120)
X(47514) = crossdifference of every pair of points on line {647, 21791}
X(47514) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 16058}, {2, 5, 37355}, {2, 377, 11358}, {2, 2475, 4203}, {2, 3091, 6822}, {2, 3136, 5}, {2, 4191, 140}, {2, 6817, 3}, {2, 6821, 16059}, {2, 14956, 37319}, {2, 16956, 7807}, {2, 33730, 37148}, {2, 36693, 4213}, {2, 37193, 405}, {5, 1368, 34119}, {377, 37056, 15973}, {442, 13728, 8728}, {1656, 16409, 2}, {36489, 37103, 20841}

X(47515) = EULER LINE INTERCEPT OF X(12)X(58)

X(47515) lies on these lines: {2, 3}, {10, 18180}, {11, 4653}, {12, 58}, {81, 495}, {86, 150}, {333, 17757}, {392, 17182}, {498, 4267}, {517, 17167}, {995, 15950}, {1043, 24390}, {1437, 25466}, {1478, 3286}, {1737, 18165}, {3421, 16713}, {3794, 38058}, {3820, 5235}, {3877, 17174}, {4276, 5432}, {4278, 7354}, {4658, 15888}, {5251, 44411}, {5443, 24161}, {5587, 17194}, {5690, 41723}, {9555, 10950}, {10039, 18178}, {10056, 18185}, {10458, 37715}, {10592, 16948}, {17197, 31397}, {18163, 31434}, {18169, 37716}, {18417, 35628}, {19755, 19765}, {24342, 24346}, {26063, 46882}

X(47515) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 19258}, {5, 21, 37357}, {21, 14005, 37152}, {1010, 25516, 37227}, {3142, 6675, 25648}, {7474, 11103, 36011}, {11103, 36011, 3109}, {11110, 14011, 4187}

X(47516) = EULER LINE INTERCEPT OF X(12)X(63)

X(47516) lies on these lines: {2, 3}, {10, 343}, {12, 63}, {65, 5249}, {80, 41859}, {224, 3925}, {495, 3868}, {498, 1259}, {1329, 15823}, {1698, 17700}, {1836, 31936}, {2646, 2886}, {2894, 3871}, {3188, 27187}, {3295, 43740}, {3822, 4292}, {3826, 5784}, {3841, 17647}, {3878, 12609}, {4259, 26543}, {4304, 25639}, {4313, 11680}, {4999, 26481}, {5273, 11681}, {5443, 8583}, {5799, 17167}, {6734, 16465}, {7951, 31424}, {10198, 11507}, {10942, 38058}, {11520, 15888}, {12616, 17616}, {12671, 18242}, {15950, 19861}, {20880, 26541}, {22766, 26363}, {22768, 31245}, {31419, 37728}, {37649, 43531}

X(47516) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 37228}, {2, 964, 25963}, {2, 4197, 25962}, {2, 11115, 24539}, {2, 24985, 25877}, {2, 26051, 11109}, {2, 37156, 4205}, {5, 21, 37358}, {21, 377, 37468}, {21, 7504, 6884}, {377, 4197, 442}, {377, 6910, 20}, {377, 35976, 11112}, {377, 37112, 1004}, {442, 6831, 2476}, {442, 7483, 5}, {443, 6889, 37229}, {2476, 6910, 6831}, {4208, 37112, 377}, {5141, 17576, 10883}, {6881, 7491, 5}, {7483, 37468, 21}, {8728, 37438, 442}, {11112, 37298, 8703}, {25962, 44256, 2}, {37356, 37438, 5499}

X(47517) = EULER LINE INTERCEPT OF X(17)X(32)

X(47517) lies on these lines: {2, 3}, {15, 24206}, {16, 38317}, {17, 32}, {18, 39}, {61, 34507}, {62, 9115}, {141, 5611}, {182, 41021}, {187, 16966}, {302, 32447}, {373, 40709}, {574, 16967}, {623, 42675}, {624, 2080}, {1384, 42132}, {3095, 33391}, {3105, 11261}, {3398, 6694}, {3519, 21462}, {3643, 20425}, {5008, 16960}, {5024, 42129}, {5460, 8724}, {5615, 14561}, {6114, 15561}, {6287, 33388}, {6771, 10991}, {6772, 36252}, {7685, 35002}, {7697, 22707}, {7820, 40334}, {8836, 9155}, {9605, 42989}, {9821, 22715}, {10645, 42786}, {13859, 20301}, {14075, 43014}, {14538, 19130}, {14981, 20416}, {15004, 40712}, {16645, 43455}, {18553, 41020}, {18581, 40922}, {21309, 42817}, {22861, 23302}, {30435, 42988}, {37835, 46855}

X(47517) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5, 37332}, {3, 1656, 47519}, {5, 140, 37464}, {5, 37340, 3}, {140, 41035, 3}, {11307, 37464, 140}, {14813, 14814, 11289}

X(47518) = EULER LINE INTERCEPT OF X(17)X(69)

X(47518) lies on these lines: {2, 3}, {17, 69}, {18, 3618}, {193, 42988}, {302, 42998}, {303, 32838}, {616, 33413}, {618, 42162}, {622, 31275}, {623, 42152}, {627, 10611}, {628, 12815}, {629, 10653}, {633, 7746}, {636, 42911}, {1506, 11489}, {3619, 16966}, {3620, 42132}, {3642, 6673}, {6669, 40693}, {6671, 42150}, {6694, 18581}, {7755, 37640}, {7781, 33477}, {11008, 16960}, {11121, 44029}, {20080, 42817}, {22113, 43542}, {22489, 42992}, {33387, 36969}, {33414, 37832}, {33560, 42161}, {36770, 42813}, {39143, 40922}, {40900, 42986}, {42156, 44383}

X(47518) = anticomplement of X(11309)
X(47518) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5, 37177}, {2, 1656, 47520}, {2, 3091, 11307}, {2, 5056, 11290}, {2, 11305, 37173}, {4, 32969, 47520}, {5, 37177, 37171}, {3628, 11311, 2}

X(47519) = EULER LINE INTERCEPT OF X(18)X(32)

X(47519) lies on these lines: {2, 3}, {15, 38317}, {16, 24206}, {17, 39}, {18, 32}, {61, 9117}, {62, 34507}, {141, 5615}, {182, 41020}, {187, 16967}, {303, 32447}, {373, 40710}, {574, 16966}, {623, 2080}, {624, 42674}, {1384, 42129}, {3095, 33390}, {3104, 11261}, {3398, 6695}, {3519, 21461}, {3642, 20426}, {5008, 16961}, {5024, 42132}, {5459, 8724}, {5611, 14561}, {6115, 15561}, {6287, 33389}, {6774, 10991}, {6775, 36251}, {7684, 35002}, {7697, 22708}, {7820, 40335}, {8838, 9155}, {9605, 42988}, {9821, 22714}, {10646, 42786}, {13858, 20301}, {14075, 43015}, {14539, 19130}, {14981, 20415}, {15004, 40711}, {16644, 43454}, {18553, 41021}, {18582, 40921}, {21309, 42818}, {22907, 23303}, {30435, 42989}, {37832, 46854}

X(47519) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5, 37333}, {3, 1656, 47517}, {5, 140, 37463}, {5, 37341, 3}, {140, 41034, 3}, {11308, 37463, 140}, {14813, 14814, 11290}

X(47520) = EULER LINE INTERCEPT OF X(18)X(69)

X(47520) lies on these lines: {2, 3}, {17, 3618}, {18, 69}, {193, 42989}, {302, 32838}, {303, 42999}, {617, 33412}, {619, 42159}, {621, 31275}, {624, 42149}, {627, 12815}, {628, 10612}, {630, 10654}, {634, 7746}, {635, 42910}, {1506, 11488}, {3619, 16967}, {3620, 42129}, {3643, 6674}, {6670, 40694}, {6672, 42151}, {6695, 18582}, {7755, 37641}, {7781, 33476}, {11008, 16961}, {11122, 44031}, {20080, 42818}, {22114, 43543}, {22490, 42993}, {33386, 36970}, {33415, 37835}, {33561, 42160}, {39143, 40921}, {40901, 42987}, {42153, 44382}

X(47520) = anticomplement of X(11310)
X(47520) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5, 37178}, {2, 1656, 47518}, {2, 3091, 11308}, {2, 5056, 11289}, {2, 11306, 37172}, {4, 32969, 47518}, {5, 37178, 37170}, {3628, 11312, 2}

X(47521) = EULER LINE INTERCEPT OF X(38)X(65)

X(47521) lies on these lines: {1, 3917}, {2, 3}, {10, 22345}, {31, 28265}, {38, 65}, {78, 21319}, {958, 1473}, {1155, 28377}, {1193, 28356}, {1201, 1279}, {1724, 43650}, {1935, 26890}, {2975, 4645}, {3304, 17392}, {3612, 21214}, {3924, 8240}, {3925, 23361}, {4259, 28369}, {4265, 40980}, {4995, 15625}, {5745, 22344}, {5791, 23206}, {8053, 15338}, {15621, 15888}, {15654, 19854}, {17717, 27657}, {19861, 31394}, {21318, 37613}, {23682, 37575}, {24987, 37619}, {26066, 33115}, {28352, 28364}, {28370, 37606}, {28628, 33123}

X(47521) = crossdifference of every pair of points on line {647, 21390}
X(47521) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3, 28349}, {2, 9840, 13724}, {3, 377, 851}, {3, 442, 27622}, {3, 37225, 30944}, {3, 37228, 13733}, {3, 37468, 37409}, {21, 4201, 37329}, {21, 37261, 37247}, {21, 37328, 16064}, {377, 6910, 26057}, {443, 19262, 13738}, {4197, 4216, 28258}, {9840, 19533, 28378}, {13725, 19283, 4204}, {16452, 17579, 37425}

X(47522) = EULER LINE INTERCEPT OF X(43)X(65)

X(47522) lies on these lines: {2, 3}, {6, 16592}, {43, 65}, {46, 16569}, {55, 29640}, {56, 33140}, {100, 30834}, {226, 20760}, {228, 31266}, {355, 26013}, {899, 36279}, {997, 30986}, {999, 11269}, {1054, 41886}, {1159, 3240}, {1376, 2887}, {1402, 17064}, {1403, 17889}, {1824, 20254}, {2182, 17754}, {2245, 37673}, {2646, 26102}, {2886, 23853}, {3011, 37590}, {3185, 3838}, {3286, 31187}, {3612, 25502}, {3741, 5794}, {3840, 17647}, {4292, 23085}, {4413, 32784}, {5088, 30988}, {5718, 37502}, {5905, 22149}, {6180, 22148}, {6685, 12609}, {7009, 44737}, {10609, 30947}, {11235, 18613}, {16678, 31245}, {17719, 34247}, {17975, 34048}, {18541, 23169}, {19762, 24880}, {21010, 29658}, {24896, 41501}, {28628, 43223}, {30950, 37606}, {35466, 37507}

X(47522) = complement of X(30943)
X(47522) = orthocentroidal-circle-inverse of X(37370)
X(47522) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 37370}, {2, 851, 3}, {2, 4192, 16058}, {2, 4199, 16345}, {2, 6817, 37365}, {2, 16056, 16059}, {2, 35980, 30944}, {2, 37110, 6821}, {2, 37400, 8731}, {4, 28258, 28383}, {377, 27622, 3}, {404, 37397, 3}, {474, 37241, 3}, {851, 30944, 35980}, {4185, 37229, 3}, {4190, 28349, 3}, {4192, 19546, 36670}, {5177, 27621, 9840}, {6856, 37264, 13731}, {6871, 27655, 13724}, {7580, 25514, 20834}, {13733, 35979, 3}, {19517, 37271, 16419}, {30944, 35980, 3}

X(47523) = EULER LINE INTERCEPT OF X(45)X(55)

X(47523) lies on these lines: {2, 3}, {45, 55}, {51, 2328}, {373, 13329}, {572, 1495}, {573, 34417}, {958, 33120}, {991, 5651}, {1001, 20999}, {1621, 15507}, {1623, 5284}, {1626, 4423}, {2177, 3217}, {3060, 22139}, {3192, 5158}, {3303, 3938}, {3746, 3961}, {5007, 40984}, {5251, 29861}, {5259, 23850}, {5563, 29820}, {5640, 37510}, {8053, 20989}, {14475, 44408}, {14547, 22356}, {20988, 23854}, {22080, 44106}, {24329, 32771}, {28387, 41346}, {29659, 37546}, {31860, 37499}, {35259, 37474}

X(47523) = crossdifference of every pair of points on line {647, 3960}
X(47523) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20834, 16064}, {21, 14020, 405}, {21, 33849, 30944}, {25, 1011, 199}, {25, 13615, 1011}, {405, 3145, 37247}, {1005, 4223, 851}, {3129, 3130, 37259}, {4199, 37325, 37061}, {5020, 20835, 4191}, {11345, 19310, 16405}

X(47524) = EULER LINE INTERCEPT OF X(49)X(64)

Barycentrics a^2*(3*a^8 - 6*a^6*b^2 + 6*a^2*b^6 - 3*b^8 - 6*a^6*c^2 + 18*a^4*b^2*c^2 - 8*a^2*b^4*c^2 - 4*b^6*c^2 - 8*a^2*b^2*c^4 + 14*b^4*c^4 + 6*a^2*c^6 - 4*b^2*c^6 - 3*c^8) : :

X(47524) = 3 X[3] - 2 X[38444], 2 X[5] - 3 X[37119], 7 X[3526] - 6 X[6639], 5 X[3843] - 6 X[7547], 3 X[35477] - X[38444]

X(47524) lies on these lines: {2, 3}, {36, 9644}, {49, 64}, {52, 11204}, {74, 12161}, {265, 40686}, {974, 15041}, {1204, 36749}, {1993, 32138}, {3357, 18445}, {3567, 15055}, {4325, 9672}, {4330, 9659}, {6241, 9706}, {6696, 25738}, {7689, 14531}, {8567, 36747}, {9704, 12174}, {9705, 32139}, {9936, 9938}, {10111, 13293}, {10605, 10937}, {10606, 34783}, {10620, 11598}, {10983, 13310}, {11422, 43806}, {11424, 43604}, {11438, 43907}, {11439, 15035}, {11440, 16266}, {11456, 43394}, {11472, 18350}, {12163, 37495}, {12302, 23236}, {12901, 15063}, {13292, 43903}, {13496, 21667}, {14981, 39831}, {15062, 15068}, {18435, 35602}, {18436, 37497}, {18439, 47391}, {18451, 45248}, {21663, 37490}, {32137, 35264}, {33556, 46261}, {39242, 46850}

X(47524) = reflection of X(3) in X(35477)
X(47524) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1593, 7506}, {3, 1597, 45735}, {3, 3517, 37955}, {3, 3830, 3515}, {3, 5073, 14070}, {3, 12085, 12083}, {3, 17800, 9715}, {3, 18378, 15750}, {3, 35452, 11414}, {3, 35501, 7529}, {3, 44457, 7488}, {24, 10226, 3}, {26, 35473, 3}, {378, 11250, 3}, {378, 35477, 37119}, {382, 35498, 3}, {1885, 6640, 381}, {2041, 2042, 15761}, {2070, 35496, 3}, {2071, 7526, 3}, {2071, 35475, 7526}, {3520, 12084, 3}, {3534, 18364, 3}, {5076, 37955, 3517}, {9715, 12085, 17800}, {9715, 17800, 12083}, {11410, 12085, 3}, {11413, 18570, 3}, {12086, 35473, 26}, {12086, 38448, 33703}, {17928, 34152, 3}, {33703, 35473, 38448}, {33703, 38448, 26}, {35495, 45735, 3}

X(47525) = EULER LINE INTERCEPT OF X(49)X(69)

X(47525) lies on these lines: {2, 3}, {49, 69}, {155, 13394}, {184, 9936}, {577, 9698}, {1062, 31452}, {1147, 43653}, {1181, 44201}, {1209, 9833}, {2165, 7749}, {3796, 12359}, {4549, 43831}, {5012, 18951}, {6101, 37645}, {6243, 11427}, {6515, 32046}, {6759, 32348}, {9606, 23115}, {9707, 37636}, {10519, 19139}, {10634, 40694}, {10635, 40693}, {11206, 32337}, {11271, 45794}, {11431, 36753}, {11433, 13353}, {11457, 15080}, {11487, 18350}, {11513, 35813}, {11514, 35812}, {13347, 44673}, {14961, 31450}, {19126, 40107}, {22052, 31455}, {22401, 31457}, {23292, 37486}, {24301, 37727}, {26864, 31831}, {33522, 37484}, {37476, 41587}, {37513, 39571}

X(47525) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 26, 7528}, {2, 7512, 14790}, {2, 31305, 5576}, {2, 37122, 5}, {2, 38435, 4}, {3, 3549, 18531}, {3, 6639, 6643}, {3, 6640, 7386}, {3, 6676, 3549}, {3, 7542, 3548}, {5, 26, 37122}, {5, 37122, 7528}, {25, 140, 14786}, {26, 7502, 38435}, {26, 7568, 2}, {549, 13383, 7395}, {631, 7493, 5}, {3523, 3542, 7514}, {3526, 9714, 5}, {7404, 10565, 7517}, {7488, 7558, 18420}, {7516, 10020, 2}, {11487, 35260, 18350}

X(47526) = EULER LINE INTERCEPT OF X(50)X(67)

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

X(47526) lies on these lines: {2, 3}, {50, 67}, {125, 187}, {340, 6394}, {352, 13509}, {647, 690}, {1384, 26869}, {1495, 35282}, {1503, 5191}, {1990, 9475}, {2080, 3580}, {2393, 41359}, {2482, 13857}, {3001, 38987}, {3003, 15118}, {3258, 47326}, {3284, 5095}, {3292, 14981}, {4576, 6390}, {5650, 7820}, {8550, 34396}, {8724, 40112}, {9155, 11064}, {9486, 24855}, {10510, 41146}, {11171, 14389}, {11594, 24975}, {14357, 16186}, {14961, 23584}, {16176, 18365}, {16280, 23967}, {19504, 22121}, {22463, 47082}, {23635, 34828}, {35278, 43460}, {38227, 41254}

X(47526) = crossdifference of every pair of points on line {647, 1995}
X(47526) = X(i)-line conjugate of X(j) for these (i,j): {2, 1995}, {690, 647}
X(47526) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11676, 5112}, {3, 441, 44888}, {3, 44886, 237}, {237, 441, 44887}, {237, 852, 44895}, {237, 15000, 468}, {441, 468, 15000}, {468, 15000, 44887}, {1513, 40884, 1316}

X(47527) = EULER LINE INTERCEPT OF X(52)X(64)

Barycentrics a^2*(a^8 - 2*a^6*b^2 + 2*a^2*b^6 - b^8 - 2*a^6*c^2 + 16*a^4*b^2*c^2 - 6*a^2*b^4*c^2 - 8*b^6*c^2 - 6*a^2*b^2*c^4 + 18*b^4*c^4 + 2*a^2*c^6 - 8*b^2*c^6 - c^8) : :

X(47527) = 9 X[3] - 8 X[7525], 3 X[3] - 4 X[7526], 3 X[3] - 2 X[11414], 3 X[381] - 4 X[1595], 9 X[1593] - 4 X[7525], 3 X[1593] - 2 X[7526], 3 X[1593] - X[11414], 5 X[1656] - 4 X[6823], 3 X[3830] - 2 X[12173], 5 X[3843] - 6 X[5064], 9 X[5054] - 8 X[16197], 2 X[7525] - 3 X[7526], 4 X[7525] - 3 X[11414], 6 X[34152] - 5 X[37929]

X(47527) lies on these lines: {2, 3}, {6, 10575}, {49, 32063}, {52, 64}, {53, 15075}, {155, 11381}, {185, 37493}, {195, 36983}, {567, 11820}, {1092, 32062}, {1181, 14915}, {1350, 43130}, {1351, 8549}, {1398, 8144}, {1498, 13352}, {1619, 22802}, {1620, 43907}, {1993, 12290}, {2935, 12295}, {3066, 44863}, {3167, 37495}, {3304, 9644}, {3357, 13598}, {3426, 12164}, {3527, 37481}, {4846, 45089}, {5446, 10605}, {5562, 11472}, {5663, 12160}, {5907, 37483}, {6000, 36747}, {7071, 32047}, {7373, 9642}, {7592, 12279}, {7689, 33586}, {8192, 28186}, {8193, 28146}, {8276, 42284}, {8277, 42283}, {8567, 32110}, {9655, 16541}, {9777, 13630}, {10483, 10832}, {10539, 15811}, {10721, 12412}, {10982, 40647}, {10984, 35237}, {11441, 11455}, {11550, 12293}, {12118, 16655}, {12161, 12174}, {12162, 37498}, {12163, 12235}, {12302, 13202}, {12315, 18445}, {12897, 18396}, {13142, 18917}, {13171, 34584}, {13346, 13474}, {13491, 39522}, {14216, 46373}, {14855, 37514}, {15058, 43576}, {15068, 32137}, {16194, 17814}, {19347, 37472}, {20427, 31670}, {22241, 32006}, {22615, 44599}, {22644, 44598}, {26883, 47391}, {29317, 37485}, {33534, 37513}, {33541, 44456}, {34780, 44076}, {35602, 46261}, {36752, 46850}, {37480, 44870}, {39809, 39841}, {39812, 39838}

X(47527) = reflection of X(i) in X(j) for these {i,j}: {3, 1593}, {11414, 7526}, {12174, 12161}, {37201, 5}
X(47527) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4, 7529}, {3, 382, 18534}, {3, 3830, 1598}, {3, 3843, 5020}, {3, 5073, 39568}, {3, 5899, 16195}, {3, 18534, 9714}, {3, 18535, 7506}, {3, 35501, 14130}, {3, 44454, 7387}, {4, 20, 31833}, {4, 7464, 17928}, {4, 11413, 6642}, {4, 11585, 381}, {4, 12085, 3}, {5, 21312, 3}, {20, 9818, 3}, {20, 35502, 9818}, {25, 12084, 3}, {26, 3516, 3}, {185, 44413, 37493}, {376, 7393, 3}, {378, 3146, 7387}, {378, 7387, 3}, {381, 382, 31725}, {382, 31724, 3830}, {548, 7484, 3}, {550, 7395, 3}, {550, 31861, 7395}, {1351, 13093, 34783}, {1593, 11414, 7526}, {1595, 11414, 11484}, {1658, 11410, 3}, {2071, 17578, 10594}, {3146, 7387, 44454}, {3357, 13598, 37489}, {3426, 12164, 18439}, {3515, 11250, 3}, {3520, 14070, 3}, {3529, 7503, 35243}, {3529, 13596, 7503}, {3543, 12086, 24}, {3627, 12084, 25}, {3843, 35452, 3}, {3853, 6644, 5198}, {5059, 7527, 10323}, {5076, 7506, 18535}, {5076, 18859, 7506}, {6642, 11413, 3}, {6642, 12085, 11413}, {7464, 47309, 2070}, {7503, 35243, 3}, {7506, 18859, 3}, {7509, 7553, 7517}, {7514, 15704, 37198}, {7514, 37198, 3}, {7526, 11414, 3}, {7526, 12173, 13621}, {7530, 11250, 3515}, {9715, 18570, 3}, {11403, 21312, 5}, {11819, 34350, 37196}, {12083, 14130, 3}, {13346, 13474, 18451}, {13371, 44276, 37197}, {14865, 33703, 22}, {15811, 37497, 10539}, {34613, 35491, 31304}, {35475, 37925, 38444}

X(47528) = EULER LINE INTERCEPT OF X(69)X(70)

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

X(47528) = 5 X[631] - 4 X[17928], 8 X[1906] - 11 X[3855], 7 X[3090] - 4 X[10594]

X(47528) lies on these lines: {2, 3}, {52, 18911}, {68, 2979}, {69, 70}, {125, 46728}, {388, 4351}, {394, 34224}, {497, 4354}, {511, 18912}, {1058, 9630}, {1092, 44829}, {1173, 20423}, {1216, 11442}, {1352, 7999}, {1614, 46264}, {1899, 11412}, {2888, 33884}, {3574, 37515}, {3580, 37486}, {3618, 44491}, {3917, 18381}, {4549, 11440}, {5447, 18474}, {5562, 11457}, {5651, 13419}, {6101, 25738}, {6243, 18952}, {6403, 15812}, {6515, 43808}, {6759, 41736}, {6776, 18948}, {6800, 9820}, {7752, 46724}, {7858, 47383}, {9707, 11064}, {9781, 31670}, {9934, 13203}, {11179, 11423}, {11204, 35240}, {11271, 18946}, {11459, 14216}, {11550, 11793}, {12022, 37498}, {12134, 15066}, {12317, 15438}, {12318, 12325}, {13416, 44795}, {14651, 39813}, {14912, 41256}, {15800, 40280}, {16659, 17814}, {17834, 26879}, {18382, 31884}, {18400, 43652}, {19467, 43574}, {21659, 37480}, {23039, 32140}, {31383, 43598}, {31815, 37481}, {32142, 34514}, {34118, 36851}, {34781, 34944}

X(47528) = anticomplement of X(7506)
X(47528) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 26}, {2, 14790, 4}, {2, 31305, 3518}, {3, 20, 35503}, {3, 858, 37119}, {3, 1594, 7558}, {3, 12225, 35471}, {3, 13371, 2}, {3, 14791, 37444}, {3, 37119, 631}, {3, 37444, 4}, {3, 47341, 3091}, {4, 3524, 6815}, {4, 3525, 7401}, {4, 5067, 6997}, {4, 6804, 3545}, {4, 7386, 631}, {4, 17538, 37201}, {5, 7391, 4}, {5, 7667, 10323}, {20, 3522, 44246}, {20, 3542, 12088}, {20, 3546, 186}, {20, 18531, 4}, {22, 11585, 7505}, {26, 37452, 2}, {140, 31723, 7544}, {186, 3546, 631}, {550, 10257, 38444}, {550, 18404, 44440}, {631, 46450, 4}, {858, 16063, 7386}, {1370, 6643, 4}, {1370, 6816, 34938}, {1594, 7558, 3090}, {5576, 7516, 2}, {6101, 25738, 45794}, {6243, 18952, 37644}, {6643, 34938, 6816}, {6804, 44442, 4}, {6816, 34938, 4}, {7395, 34609, 15559}, {7401, 46336, 3525}, {7485, 12083, 186}, {7488, 31101, 3548}, {7516, 31181, 5576}, {7525, 37938, 6639}, {7544, 31723, 4}, {7566, 40916, 7405}, {7568, 18569, 7528}, {9715, 30771, 10018}, {10323, 31180, 5}, {11413, 12605, 35481}, {12225, 35471, 3529}, {14784, 14785, 7517}, {14791, 16063, 4}, {16063, 37444, 3}, {16196, 44239, 32534}, {18404, 44440, 4}, {35732, 42282, 7530}

X(47529) = X(30)X(31136)∩X(468)X(519)

X(47529) lies on these lines: {30, 31136}, {468, 519}, {674, 47473}, {3741, 47097}, {7426, 17135}

X(47529) = midpoint of X(7426) and X(17135)
X(47529) = reflection of X(47097) in X(3741)

X(47530) = X(30)X(31137)∩X(468)X(519)

X(47530) lies on these lines: {30, 31137}, {468, 519}, {3840, 47097}, {7426, 10453}, {9025, 47473}

X(47530) = midpoint of X(7426) and X(10453)
X(47530) = reflection of X(47097) in X(3840)

X(47531) = X(30)X(12245)∩X(468)X(519)

Barycentrics 26*a^7 - 22*a^6*b - 29*a^5*b^2 + 19*a^4*b^3 - 26*a^3*b^4 + 22*a^2*b^5 + 29*a*b^6 - 19*b^7 - 22*a^6*c + 19*a^4*b^2*c + 22*a^2*b^4*c - 19*b^6*c - 29*a^5*c^2 + 19*a^4*b*c^2 + 84*a^3*b^2*c^2 - 60*a^2*b^3*c^2 - 29*a*b^4*c^2 + 19*b^5*c^2 + 19*a^4*c^3 - 60*a^2*b^2*c^3 + 19*b^4*c^3 - 26*a^3*c^4 + 22*a^2*b*c^4 - 29*a*b^2*c^4 + 19*b^3*c^4 + 22*a^2*c^5 + 19*b^2*c^5 + 29*a*c^6 - 19*b*c^6 - 19*c^7 : :

X(47531) = 5 X[468] - 4 X[47472], 4 X[3632] + X[47312], 4 X[4677] - X[47311], X[10989] - 5 X[20052], 4 X[47359] - 3 X[47463]

X(47531) lies on these lines: {8, 47097}, {30, 12245}, {468, 519}, {952, 47031}, {3621, 7426}, {3632, 47312}, {4677, 47311}, {5844, 47332}, {9053, 47473}, {10989, 20052}, {34631, 37984}, {47359, 47463}

X(47531) = midpoint of X(3621) and X(7426)
X(47531) = reflection of X(i) in X(j) for these {i,j}: {34631, 37984}, {47097, 8}

X(47532) = X(30)X(17310)∩X(468)X(519)

X(47532) lies on these lines: {30, 17310}, {468, 519}, {742, 47473}, {3912, 47097}, {6542, 7426}, {29331, 47332}

X(47532) = midpoint of X(6542) and X(7426)
X(47532) = reflection of X(47097) in X(3912)

X(47533) = X(23)X(3621)∩X(468)X(519)

Barycentrics 14*a^7 - 10*a^6*b - 15*a^5*b^2 + 9*a^4*b^3 - 14*a^3*b^4 + 10*a^2*b^5 + 15*a*b^6 - 9*b^7 - 10*a^6*c + 9*a^4*b^2*c + 10*a^2*b^4*c - 9*b^6*c - 15*a^5*c^2 + 9*a^4*b*c^2 + 44*a^3*b^2*c^2 - 28*a^2*b^3*c^2 - 15*a*b^4*c^2 + 9*b^5*c^2 + 9*a^4*c^3 - 28*a^2*b^2*c^3 + 9*b^4*c^3 - 14*a^3*c^4 + 10*a^2*b*c^4 - 15*a*b^2*c^4 + 9*b^3*c^4 + 10*a^2*c^5 + 9*b^2*c^5 + 15*a*c^6 - 9*b*c^6 - 9*c^7 : :

X(47533) = 3 X[8] - 2 X[5159], X[23] + 3 X[3621], 7 X[468] - 6 X[47472], X[858] - 3 X[31145], 3 X[3241] - 4 X[37911], 6 X[3632] - X[46517], 2 X[7982] - 3 X[10151], 3 X[12645] - X[18323], 3 X[20053] + 4 X[47316], 6 X[47359] - 5 X[47462]

X(47533) lies on these lines: {8, 5159}, {23, 3621}, {468, 519}, {858, 31145}, {952, 47308}, {3241, 37911}, {3632, 46517}, {4677, 47097}, {5844, 47336}, {7982, 10151}, {12645, 18323}, {20053, 47316}, {47359, 47462}

X(47534) = X(30)X(34641)∩X(468)X(519)

Barycentrics 14*a^7 - 16*a^6*b - 17*a^5*b^2 + 13*a^4*b^3 - 14*a^3*b^4 + 16*a^2*b^5 + 17*a*b^6 - 13*b^7 - 16*a^6*c + 13*a^4*b^2*c + 16*a^2*b^4*c - 13*b^6*c - 17*a^5*c^2 + 13*a^4*b*c^2 + 48*a^3*b^2*c^2 - 42*a^2*b^3*c^2 - 17*a*b^4*c^2 + 13*b^5*c^2 + 13*a^4*c^3 - 42*a^2*b^2*c^3 + 13*b^4*c^3 - 14*a^3*c^4 + 16*a^2*b*c^4 - 17*a*b^2*c^4 + 13*b^3*c^4 + 16*a^2*c^5 + 13*b^2*c^5 + 17*a*c^6 - 13*b*c^6 - 13*c^7 : :

X(47534) = 5 X[8] - X[10989], 7 X[468] - 5 X[47472], 5 X[4677] + X[47313], 2 X[5159] - 3 X[38098], 5 X[31145] + 3 X[37909], 3 X[37909] - 5 X[47321], 5 X[47359] - 3 X[47465]

X(47534) lies on these lines: {8, 10989}, {30, 34641}, {468, 519}, {3626, 47097}, {3632, 7426}, {4677, 47313}, {5159, 38098}, {28234, 47332}, {28236, 47031}, {31145, 37909}, {47359, 47465}

X(47534) = midpoint of X(i) and X(j) for these {i,j}: {3632, 7426}, {31145, 47321}
X(47534) = reflection of X(47097) in X(3626)

X(47535) = X(30)X(145)∩X(468)X(519)

Barycentrics 38*a^7 - 10*a^6*b - 35*a^5*b^2 + 13*a^4*b^3 - 38*a^3*b^4 + 10*a^2*b^5 + 35*a*b^6 - 13*b^7 - 10*a^6*c + 13*a^4*b^2*c + 10*a^2*b^4*c - 13*b^6*c - 35*a^5*c^2 + 13*a^4*b*c^2 + 108*a^3*b^2*c^2 - 36*a^2*b^3*c^2 - 35*a*b^4*c^2 + 13*b^5*c^2 + 13*a^4*c^3 - 36*a^2*b^2*c^3 + 13*b^4*c^3 - 38*a^3*c^4 + 10*a^2*b*c^4 - 35*a*b^2*c^4 + 13*b^3*c^4 + 10*a^2*c^5 + 13*b^2*c^5 + 35*a*c^6 - 13*b*c^6 - 13*c^7 : :

X(47535) = 3 X[468] - 4 X[47472], 3 X[10151] - 2 X[34627], 3 X[13473] - 4 X[31162], X[20014] + 3 X[37907], 4 X[34747] + X[47312], 4 X[47359] - 5 X[47461]

X(47535) lies on these lines: {30, 145}, {468, 519}, {952, 47310}, {3241, 47097}, {5844, 47333}, {7426, 20049}, {10151, 34627}, {12135, 34648}, {13473, 31162}, {20014, 37907}, {34747, 47312}, {47359, 47461}

X(47535) = midpoint of X(7426) and X(20049)
X(47535) = reflection of X(47097) in X(3241)

X(47536) = X(145)X(858)∩X(468)X(519)

Barycentrics 18*a^7 - 6*a^6*b - 17*a^5*b^2 + 7*a^4*b^3 - 18*a^3*b^4 + 6*a^2*b^5 + 17*a*b^6 - 7*b^7 - 6*a^6*c + 7*a^4*b^2*c + 6*a^2*b^4*c - 7*b^6*c - 17*a^5*c^2 + 7*a^4*b*c^2 + 52*a^3*b^2*c^2 - 20*a^2*b^3*c^2 - 17*a*b^4*c^2 + 7*b^5*c^2 + 7*a^4*c^3 - 20*a^2*b^2*c^3 + 7*b^4*c^3 - 18*a^3*c^4 + 6*a^2*b*c^4 - 17*a*b^2*c^4 + 7*b^3*c^4 + 6*a^2*c^5 + 7*b^2*c^5 + 17*a*c^6 - 7*b*c^6 - 7*c^7 : :

X(47536) = 3 X[8] - 4 X[37911], X[23] + 3 X[20049], 3 X[145] - X[858], 5 X[468] - 6 X[47472], 3 X[3241] - 2 X[5159], 6 X[3633] + X[37899], 4 X[4301] - 3 X[13473], 2 X[5881] - 3 X[10151], 3 X[20014] + 5 X[37760], 3 X[20050] + 2 X[37897], 6 X[34747] - X[46517]

X(47536) lies on these lines: {8, 37911}, {23, 20049}, {145, 858}, {468, 519}, {952, 47309}, {3241, 5159}, {3633, 37899}, {4301, 13473}, {5844, 47335}, {5881, 10151}, {20014, 37760}, {20050, 37897}, {28234, 47469}, {34747, 46517}

X(47537) = X(145)X(5189)∩X(468)X(519)

Barycentrics 14*a^7 - 4*a^6*b - 13*a^5*b^2 + 5*a^4*b^3 - 14*a^3*b^4 + 4*a^2*b^5 + 13*a*b^6 - 5*b^7 - 4*a^6*c + 5*a^4*b^2*c + 4*a^2*b^4*c - 5*b^6*c - 13*a^5*c^2 + 5*a^4*b*c^2 + 40*a^3*b^2*c^2 - 14*a^2*b^3*c^2 - 13*a*b^4*c^2 + 5*b^5*c^2 + 5*a^4*c^3 - 14*a^2*b^2*c^3 + 5*b^4*c^3 - 14*a^3*c^4 + 4*a^2*b*c^4 - 13*a*b^2*c^4 + 5*b^3*c^4 + 4*a^2*c^5 + 5*b^2*c^5 + 13*a*c^6 - 5*b*c^6 - 5*c^7 : :

X(47537) = 9 X[145] - X[5189], 7 X[468] - 9 X[47472], 9 X[3241] - 5 X[30745], 3 X[4669] - 4 X[37911], 9 X[34747] + X[37900]

X(47537) lies on these lines: {145, 5189}, {468, 519}, {3241, 30745}, {4669, 37911}, {20050, 47321}, {34747, 37900}

X(47538) = X(145)X(37901)∩X(468)X(519)

Barycentrics 34*a^7 - 8*a^6*b - 31*a^5*b^2 + 11*a^4*b^3 - 34*a^3*b^4 + 8*a^2*b^5 + 31*a*b^6 - 11*b^7 - 8*a^6*c + 11*a^4*b^2*c + 8*a^2*b^4*c - 11*b^6*c - 31*a^5*c^2 + 11*a^4*b*c^2 + 96*a^3*b^2*c^2 - 30*a^2*b^3*c^2 - 31*a*b^4*c^2 + 11*b^5*c^2 + 11*a^4*c^3 - 30*a^2*b^2*c^3 + 11*b^4*c^3 - 34*a^3*c^4 + 8*a^2*b*c^4 - 31*a*b^2*c^4 + 11*b^3*c^4 + 8*a^2*c^5 + 11*b^2*c^5 + 31*a*c^6 - 11*b*c^6 - 11*c^7 : :

X(47538) lies on these lines: {145, 37901}, {468, 519}, {3633, 7426}, {3635, 47097}, {20049, 47321}

X(47538) = midpoint of X(i) and X(j) for these {i,j}: {3633, 7426}, {20049, 47321}
X(47538) = reflection of X(47097) in X(3635)

X(47539) = X(30)X(239)∩X(468)X(519)

Barycentrics 14*a^8 - 2*a^7*b - 9*a^6*b^2 - a^5*b^3 - 13*a^4*b^4 + 2*a^3*b^5 + 9*a^2*b^6 + a*b^7 - b^8 - 2*a^7*c - 14*a^6*b*c - a^5*b^2*c + 11*a^4*b^3*c + 2*a^3*b^4*c + 14*a^2*b^5*c + a*b^6*c - 11*b^7*c - 9*a^6*c^2 - a^5*b*c^2 + 38*a^4*b^2*c^2 - 13*a^2*b^4*c^2 - a*b^5*c^2 - a^5*c^3 + 11*a^4*b*c^3 - 36*a^2*b^3*c^3 - a*b^4*c^3 + 11*b^5*c^3 - 13*a^4*c^4 + 2*a^3*b*c^4 - 13*a^2*b^2*c^4 - a*b^3*c^4 + 2*b^4*c^4 + 2*a^3*c^5 + 14*a^2*b*c^5 - a*b^2*c^5 + 11*b^3*c^5 + 9*a^2*c^6 + a*b*c^6 + a*c^7 - 11*b*c^7 - c^8 : :

X(47539) lies on these lines: {30, 239}, {468, 519}, {7426, 40891}, {20016, 37907}, {29331, 47333}, {41140, 47097}

X(47539) = midpoint of X(7426) and X(40891)
X(47539) = reflection of X(47097) in X(41140)

X(47540) = X(30)X(3244)∩X(468)X(519)

Barycentrics 26*a^7 - 4*a^6*b - 23*a^5*b^2 + 7*a^4*b^3 - 26*a^3*b^4 + 4*a^2*b^5 + 23*a*b^6 - 7*b^7 - 4*a^6*c + 7*a^4*b^2*c + 4*a^2*b^4*c - 7*b^6*c - 23*a^5*c^2 + 7*a^4*b*c^2 + 72*a^3*b^2*c^2 - 18*a^2*b^3*c^2 - 23*a*b^4*c^2 + 7*b^5*c^2 + 7*a^4*c^3 - 18*a^2*b^2*c^3 + 7*b^4*c^3 - 26*a^3*c^4 + 4*a^2*b*c^4 - 23*a*b^2*c^4 + 7*b^3*c^4 + 4*a^2*c^5 + 7*b^2*c^5 + 23*a*c^6 - 7*b*c^6 - 7*c^7 : :

X(47540) = 5 X[145] + 3 X[37909], 3 X[468] - 5 X[47472], 5 X[3241] - X[10989], 3 X[13619] + 5 X[34631], X[20050] + 3 X[37907], 4 X[37911] - 3 X[38098]

X(47540) lies on these lines: {30, 3244}, {145, 37909}, {468, 519}, {3241, 10989}, {7426, 34747}, {13619, 34631}, {20050, 37907}, {28234, 47333}, {28236, 47310}, {37911, 38098}

X(47541) = X(30)X(1351)∩X(468)X(524)

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

X(47541) = 2 X[2] - 3 X[47459], 2 X[32220] + X[47277], 2 X[69] - 5 X[47456], 2 X[15534] + X[37904], 2 X[193] + X[47279], 3 X[468] - 2 X[47473], 4 X[576] - X[47339], 4 X[597] - 5 X[47461], X[858] - 3 X[5032], 2 X[858] - 5 X[47462], 6 X[5032] - 5 X[47462], 4 X[3629] - X[47281], 4 X[3629] + X[47312], X[6144] + 2 X[47449], 4 X[8584] - X[47311], 4 X[8584] - 3 X[47463], X[47311] - 3 X[47463], 3 X[10151] - 2 X[47353], X[15533] - 3 X[47455], 4 X[15826] - X[47095], 3 X[21356] - 4 X[37911], 3 X[21358] - 5 X[47458], 4 X[32217] - X[47278], X[37899] + 2 X[47280], X[40341] - 4 X[47454], X[46517] - 4 X[47464], 3 X[47352] - 4 X[47460]

X(47541) lies on these lines: {2, 47459}, {6, 47097}, {30, 1351}, {69, 47456}, {154, 15534}, {193, 7426}, {468, 524}, {511, 47031}, {542, 1514}, {576, 47339}, {597, 47461}, {599, 47457}, {858, 5032}, {895, 47309}, {3167, 47447}, {3564, 5655}, {3581, 47333}, {3629, 47281}, {6144, 47449}, {8541, 13473}, {8584, 11245}, {8705, 21969}, {10151, 47353}, {11061, 47336}, {11180, 37984}, {15533, 47455}, {15826, 47095}, {18579, 34380}, {21356, 37911}, {21358, 47458}, {32127, 47474}, {32217, 47278}, {37899, 47280}, {40341, 47454}, {41617, 45016}, {46517, 47464}, {47352, 47460}

X(47541) = midpoint of X(i) and X(j) for these {i,j}: {193, 7426}, {1992, 32220}, {47281, 47312}
X(47541) = reflection of X(i) in X(j) for these {i,j}: {599, 47457}, {5642, 15471}, {11180, 37984}, {47097, 6}, {47277, 1992}, {47279, 7426}

X(47542) = X(30)X(31143)∩X(468)X(524)

X(47542) lies on these lines: {30, 31143}, {468, 524}, {1211, 47097}, {2895, 7426}

X(47542) = midpoint of X(2895) and X(7426)
X(47542) = reflection of X(47097) in X(1211)

X(47543) = X(30)X(31144)∩X(468)X(524)

X(47543) lies on these lines: {30, 31144}, {468, 524}, {1213, 47097}, {1544, 47310}, {1654, 7426}

X(47543) = midpoint of X(1654) and X(7426)
X(47543) = reflection of X(47097) in X(1213)

X(47544) = X(30)X(182)∩X(468)X(524)

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

X(47544) = X[2] - 3 X[47455], X[23] + 5 X[47458], X[32217] + 2 X[47457], X[37904] + 3 X[47459], X[141] - 4 X[47454], X[193] + 5 X[47452], 3 X[403] - X[47353], 3 X[468] - X[47473], X[8262] + 2 X[15471], X[15303] - 3 X[44102], X[32225] + 3 X[44102], 2 X[575] + X[16619], X[599] - 5 X[47453], X[32220] + 5 X[47453], X[858] - 3 X[47352], X[1992] + 3 X[37907], X[32113] - 3 X[37907], 2 X[3589] - 5 X[47456], X[47097] - 5 X[47456], 5 X[3618] - X[10989], X[3629] + 2 X[47449], 3 X[5032] + 5 X[37760], 3 X[5032] - X[47280], 5 X[37760] + X[47280], 4 X[6329] + X[47312], X[15534] + 3 X[47450], X[15826] + 2 X[37897], X[15826] - 4 X[47460], X[37897] + 2 X[47460], 2 X[32218] + X[47277], 4 X[25555] - X[47341], 2 X[32455] + X[47279], X[34315] + 3 X[36757], X[34316] + 3 X[36758], 2 X[41149] + 3 X[47447], 2 X[47316] + X[47464]

X(47544) lies on these lines: {2, 47455}, {6, 7426}, {23, 47458}, {30, 182}, {51, 8705}, {141, 47454}, {193, 47452}, {403, 47353}, {468, 524}, {511, 18579}, {523, 9188}, {542, 46817}, {575, 16619}, {599, 32220}, {858, 47352}, {1503, 47332}, {1533, 47310}, {1992, 32113}, {2393, 32267}, {2854, 35266}, {3580, 34319}, {3589, 47097}, {3618, 10989}, {3629, 47449}, {3796, 47313}, {5032, 37760}, {6329, 47312}, {7575, 37827}, {8584, 10192}, {9030, 46989}, {9041, 47472}, {9177, 27088}, {10168, 15122}, {10564, 47333}, {11179, 11799}, {11645, 15118}, {15534, 47450}, {15826, 37897}, {16092, 16306}, {16303, 28662}, {19924, 32300}, {20423, 44265}, {20583, 32218}, {25328, 44961}, {25555, 47341}, {29181, 47031}, {32455, 47279}, {34315, 36757}, {34316, 36758}, {41149, 47447}, {47316, 47464}

X(47544) = midpoint of X(i) and X(j) for these {i,j}: {6, 7426}, {597, 32217}, {599, 32220}, {1992, 32113}, {3580, 34319}, {11179, 11799}, {15303, 32225}, {20423, 44265}, {20583, 32218} X(47544) = reflection of X(i) in X(j) for these {i,j}: {597, 47457}, {15122, 10168}, {47097, 3589}, {47277, 20583}
X(47544) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1992, 37907, 32113}, {12828, 44102, 15471}, {32225, 44102, 15303}, {37897, 47460, 15826}

X(47545) = X(6)X(30)∩X(468)X(524)

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

X(47545) = X[32220] + 2 X[47457], X[23] + 3 X[5032], X[23] + 2 X[47464], 3 X[5032] - 2 X[47464], X[69] - 4 X[47454], 2 X[141] - 5 X[47456], 2 X[8584] + X[37904], 2 X[32217] + X[47277], X[193] + 3 X[37907], X[193] + 2 X[47449], 3 X[37907] - 2 X[47449], 3 X[403] - X[11180], X[5642] - 3 X[44102], 2 X[597] - 3 X[47459], X[47097] - 3 X[47459], X[599] - 3 X[47455], X[858] - 4 X[47460], 2 X[3629] + X[47279], 2 X[5159] - 3 X[47352], 2 X[5159] - 5 X[47458], 3 X[47352] - 5 X[47458], X[6144] + 5 X[47452], 4 X[20583] + X[47312], 4 X[20583] - 3 X[47463], X[47312] + 3 X[47463], X[9143] + 3 X[37784], 4 X[10168] - 3 X[10257], X[11477] + 2 X[37934], X[15533] - 5 X[47453], 2 X[15826] + X[37899], 2 X[15826] - 5 X[47462], X[37899] + 5 X[47462], 3 X[21358] - 4 X[37911], 3 X[25321] + X[44555], 4 X[32218] - X[47278], 4 X[41149] + X[47278], 4 X[32455] - X[47281], 5 X[37760] - 2 X[47446], 2 X[37897] + X[47280], X[47276] - 4 X[47316], X[47311] - 5 X[47461]

X(47545) lies on these lines: {2, 32220}, {6, 30}, {23, 5032}, {69, 47454}, {141, 47456}, {184, 8584}, {193, 37907}, {403, 11180}, {468, 524}, {511, 47333}, {518, 47472}, {542, 47332}, {597, 47097}, {599, 47455}, {858, 47460}, {1351, 44265}, {1353, 44266}, {1503, 47310}, {1992, 7426}, {3564, 34319}, {3580, 41720}, {3629, 47279}, {5159, 47352}, {5467, 27088}, {5476, 10297}, {6144, 47452}, {8675, 47001}, {8705, 20583}, {9143, 37784}, {9188, 47159}, {10168, 10257}, {10169, 31133}, {10510, 47335}, {11477, 37934}, {11645, 47309}, {15462, 18579}, {15533, 47453}, {15534, 32113}, {15826, 37899}, {19136, 20192}, {19924, 47308}, {21358, 37911}, {25321, 44555}, {32218, 41149}, {32455, 47281}, {37485, 37941}, {37491, 37955}, {37760, 47446}, {37897, 47280}, {37984, 47353}, {46980, 47184}, {47276, 47316}, {47311, 47461}

X(47545) = midpoint of X(i) and X(j) for these {i,j}: {2, 32220}, {1351, 44265}, {1353, 44266}, {1992, 7426}, {3580, 41720}, {5095, 32225}, {8584, 32217}, {15534, 32113}, {32218, 41149}, {37904, 47277} X(47545) = reflection of X(i) in X(j) for these {i,j}: {2, 47457}, {10297, 5476}, {15303, 15471}, {37904, 32217}, {47097, 597}, {47159, 9188}, {47277, 8584}, {47353, 37984}, {47468, 18579}, {47473, 468}, {47474, 47332}
X(47545) = crossdifference of every pair of points on line {8675, 10097}
X(47545) = X(47001)-line conjugate of X(8675)
X(47545) = barycentric product X(524)*X(26255)
X(47545) = barycentric quotient X(26255)/X(671)
X(47545) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37899, 47462, 15826}, {47097, 47459, 597}

X(47546) = X(30)X(11477)∩X(468)X(524)

Barycentrics (2*a^2 - b^2 - c^2)*(5*a^6 - 3*a^4*b^2 - 5*a^2*b^4 + 3*b^6 - 3*a^4*c^2 + 14*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(47546) = 3 X[2] - 4 X[47460], 3 X[6] - 2 X[5159], X[23] + 3 X[193], X[23] - 3 X[32220], 3 X[15534] - X[47280], 2 X[141] - 3 X[47459], 4 X[468] - 3 X[47473], X[3292] - 3 X[5095], 4 X[575] - 3 X[10257], 3 X[599] - 4 X[37911], 3 X[599] - 5 X[47458], 4 X[37911] - 5 X[47458], X[858] - 3 X[1992], 3 X[1992] - 2 X[47464], 3 X[1351] - X[18323], 3 X[1353] - X[37950], 3 X[2072] - 5 X[11482], 4 X[47336] - 3 X[47474], 4 X[3589] - 5 X[47461], 3 X[3629] - X[15826], 6 X[3629] - X[46517], 2 X[15826] - 3 X[47277], X[46517] - 3 X[47277], 2 X[3630] - 5 X[47456], 9 X[5032] - 5 X[30745], 3 X[6144] + 4 X[47316], 3 X[32113] - 4 X[47316], 3 X[7426] - 2 X[47446], 6 X[8584] - 5 X[47462], 3 X[47097] - 5 X[47462], 7 X[10541] - 6 X[16976], X[11008] + 2 X[47449], 4 X[18571] - 3 X[47468], X[20080] - 4 X[47454], 4 X[32455] - 3 X[47463], X[40341] - 3 X[47455], 4 X[41149] - X[47311], 2 X[47315] - 5 X[47466]

X(47546) lies on these lines: {2, 47460}, {6, 5159}, {23, 159}, {30, 11477}, {69, 47457}, {141, 47459}, {468, 524}, {511, 44573}, {518, 47470}, {542, 47309}, {575, 10257}, {576, 10297}, {599, 37911}, {858, 1992}, {895, 41738}, {1351, 18323}, {1353, 37950}, {2072, 11482}, {3564, 9970}, {3589, 47461}, {3629, 15826}, {3630, 47456}, {5032, 30745}, {6144, 32113}, {7426, 47446}, {8584, 47097}, {8705, 16327}, {10151, 11470}, {10541, 16976}, {11008, 47449}, {11216, 31099}, {11422, 16387}, {13292, 47341}, {15063, 47310}, {15069, 37984}, {15141, 37784}, {18571, 34380}, {20080, 47454}, {32217, 47279}, {32455, 47463}, {32621, 37929}, {34379, 47477}, {37897, 47276}, {40341, 47455}, {41149, 47311}, {47315, 47466}

X(47546) = midpoint of X(i) and X(j) for these {i,j}: {193, 32220}, {6144, 32113}
X(47546) = reflection of X(i) in X(j) for these {i,j}: {69, 47457}, {858, 47464}, {5181, 15471}, {10297, 576}, {15069, 37984}, {46517, 15826}, {47097, 8584}, {47276, 37897}, {47277, 3629}, {47279, 32217}
X(47546) = crossdifference of every pair of points on line {7652, 10097}
X(47546) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {599, 47458, 37911}, {858, 1992, 47464}, {46517, 47277, 15826}

X(47547) = X(81)X(47457)∩X(468)X(524)

X(47547) lies on these lines: {6, 44898}, {81, 47457}, {468, 524}, {2895, 32220}

X(47547) = midpoint of X(2895) and X(32220)
X(47547) = reflection of X(81) in X(47457)

X(47548) = X(86)X(47457)∩X(468)X(524)

X(47548) lies on these lines: {6, 44908}, {86, 47457}, {468, 524}, {1654, 32220}

X(47548) = midpoint of X(1654) and X(32220)
X(47548) = reflection of X(86) in X(47457)

X(47549) = X(30)X(576)∩X(468)X(524)

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

X(47549) = 3 X[2] - 5 X[47458], 3 X[6] - X[858], X[858] + 3 X[32220], X[23] + 3 X[1992], 3 X[1992] - X[47280], 3 X[8584] - X[15826], 3 X[8584] - 2 X[47464], X[69] - 3 X[47455], 3 X[141] - 4 X[37911], 2 X[37911] - 3 X[47457], 3 X[193] + 5 X[37760], 3 X[32113] - 5 X[37760], 3 X[3629] + 2 X[37897], 3 X[32217] - 2 X[37897], 3 X[403] - X[15069], 5 X[468] - 3 X[47473], X[3292] - 3 X[15303], 3 X[5095] + X[41586], X[5181] - 3 X[44102], 3 X[597] - 2 X[5159], 3 X[597] - 4 X[47460], 2 X[3589] - 3 X[47459], X[3630] - 4 X[47454], 2 X[3631] - 5 X[47456], 9 X[5032] - X[5189], X[6144] + 3 X[47450], 4 X[6329] - 5 X[47461], 6 X[32455] + X[37899], X[37899] + 3 X[47277], 3 X[7426] - X[47276], 3 X[15534] + X[47276], X[7574] - 5 X[11482], X[11008] + 5 X[47452], X[11061] + 3 X[37784], X[18323] - 3 X[20423], X[20063] + 9 X[47465], 6 X[20583] - X[46517], 6 X[20583] - 5 X[47462], X[46517] - 5 X[47462], 4 X[22330] - X[47341], 3 X[25321] + X[41617], X[37900] + 5 X[47466], X[37904] + 2 X[41149], 2 X[40107] - 3 X[44452], X[40341] - 5 X[47453], 3 X[41720] + X[41724], X[47095] - 9 X[47463]

X(47549) lies on these lines: {2, 47458}, {6, 858}, {23, 1992}, {30, 576}, {69, 47455}, {141, 37911}, {193, 32113}, {206, 3629}, {382, 11216}, {403, 15069}, {468, 524}, {511, 14708}, {542, 47336}, {575, 15122}, {597, 5159}, {1503, 12295}, {3564, 19140}, {3589, 47459}, {3630, 47454}, {3631, 47456}, {5032, 5189}, {6144, 47450}, {6329, 47461}, {6467, 8705}, {7426, 15534}, {7574, 11482}, {10295, 11477}, {11008, 47452}, {11061, 37784}, {11649, 32284}, {11799, 18445}, {12241, 47339}, {15119, 19510}, {16511, 16977}, {16534, 47334}, {18323, 20423}, {20063, 47465}, {20583, 46517}, {22249, 34380}, {22330, 43573}, {25321, 41617}, {32218, 47279}, {32621, 37928}, {33749, 40647}, {37900, 47466}, {37904, 41149}, {40107, 44452}, {40341, 47453}, {41720, 41724}, {47095, 47463}, {47316, 47446}

X(47549) = midpoint of X(i) and X(j) for these {i,j}: {6, 32220}, {23, 47280}, {193, 32113}, {3629, 32217}, {7426, 15534}, {10295, 11477}
X(47549) = reflection of X(i) in X(j) for these {i,j}: {141, 47457}, {5159, 47460}, {6593, 15471}, {15122, 575}, {15826, 47464}, {19510, 32300}, {47277, 32455}, {47279, 32218}, {47446, 47316}
X(47549) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 1992, 47280}, {5159, 47460, 597}, {8584, 15826, 47464}

X(47550) = X(6)X(523)∩X(468)X(524)

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

X(47550) = 3 X[5050] - X[46633], 3 X[5182] - X[7472], X[16315] - 3 X[47459], X[15993] - 3 X[47455], 2 X[47239] - 3 X[47455], X[47154] + 3 X[47463], X[47155] - 5 X[47461], 2 X[47238] - 5 X[47458], 3 X[47240] - 5 X[47456], X[47242] - 4 X[47460], 3 X[47243] - 4 X[47454], 4 X[47244] - 5 X[47453], X[47245] + 2 X[47464], 3 X[47246] - 2 X[47449]

X(47550) lies on these lines: {6, 523}, {30, 18800}, {110, 36168}, {182, 46981}, {230, 47457}, {325, 32220}, {468, 524}, {511, 36180}, {542, 14120}, {575, 36157}, {576, 36156}, {597, 46980}, {1351, 46634}, {1503, 2682}, {5050, 46633}, {5099, 5477}, {5107, 47326}, {5112, 41146}, {5182, 7472}, {5480, 46982}, {6793, 16315}, {8593, 36196}, {8779, 16316}, {9418, 32217}, {10753, 36166}, {10754, 47293}, {15993, 47239}, {23992, 35282}, {32113, 47171}, {40112, 47349}, {44398, 47200}, {47154, 47463}, {47155, 47461}, {47238, 47458}, {47240, 47456}, {47242, 47460}, {47243, 47454}, {47244, 47453}, {47245, 47464}, {47246, 47449}

X(47550) = midpoint of X(i) and X(j) for these {i,j}: {325, 32220}, {1351, 46634}, {5099, 5477}, {5107, 47326}, {8593, 36196}, {10753, 36166}, {10754, 47293}, {16316, 47277} X(47550) = reflection of X(i) in X(j) for these {i,j}: {230, 47457}, {15993, 47239}, {32113, 47171}, {46980, 597}, {46981, 182}, {46982, 5480}
X(47550) = crossdifference of every pair of points on line {511, 10097}
X(47550) = X(36180)-line conjugate of X(511)
X(47550) = barycentric product X(524)*X(7417)
X(47550) = barycentric quotient X(7417)/X(671)
X(47550) = {X(15993),X(47455)}-harmonic conjugate of X(47239)

X(47551) = X(30)X(69)∩X(468)X(524)

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

X(47551) = 2 X[69] + X[47279], 4 X[141] - X[47281], 2 X[193] - 5 X[47456], 4 X[597] - 3 X[47463], 2 X[1992] - 3 X[47459], 2 X[5159] - 3 X[21356], X[6144] - 4 X[47454], 2 X[7426] - 3 X[47447], 2 X[11160] + 3 X[47447], 4 X[8584] - 5 X[47461], 2 X[15533] + X[37904], X[20080] + 3 X[37907], 3 X[21358] - X[47280], 4 X[22165] + X[47278], 4 X[22165] - X[47311], 4 X[34507] - X[47339], X[37899] - 4 X[47446], 8 X[37911] - 5 X[47462], X[40341] + 2 X[47449], X[46517] + 2 X[47276], 3 X[47352] - 2 X[47464]

X(47551) lies on these lines: {2, 47277}, {30, 69}, {141, 47281}, {193, 47456}, {468, 524}, {511, 47310}, {542, 47031}, {597, 47463}, {599, 17813}, {1992, 47459}, {3564, 47333}, {5159, 21356}, {5847, 47472}, {6144, 47454}, {7426, 11160}, {8584, 47461}, {11898, 44265}, {13169, 32272}, {15533, 32113}, {15534, 47457}, {15993, 47184}, {19459, 37941}, {19588, 37955}, {20080, 37907}, {21358, 47280}, {22165, 47278}, {28538, 47477}, {34380, 47334}, {34507, 47339}, {37899, 47446}, {37911, 47462}, {40341, 47449}, {41721, 47332}, {44395, 46980}, {46517, 47276}, {47352, 47464}

X(47551) = midpoint of X(i) and X(j) for these {i,j}: {7426, 11160}, {11898, 44265}, {15533, 32113}, {47278, 47311}
X(47551) = reflection of X(i) in X(j) for these {i,j}: {468, 47473}, {15534, 47457}, {37904, 32113}, {46980, 44395}, {47031, 47468}, {47097, 599}, {47277, 2}
X(47551) = barycentric product X(524)*X(30775)
X(47551) = barycentric quotient X(30775)/X(671)

X(47552) = X(30)X(15069)∩X(468)X(524)

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

X(47552) = 3 X[6] - 4 X[37911], X[23] + 3 X[11160], 3 X[11160] + 2 X[47446], 3 X[15533] + X[47276], 3 X[69] - X[858], 2 X[468] - 3 X[47473], 2 X[47309] - 3 X[47474], 6 X[597] - 5 X[47462], 3 X[599] - 2 X[5159], 3 X[599] - X[47280], 3 X[1992] - 4 X[47460], 2 X[47335] - 3 X[47468], 4 X[3589] - 3 X[47463], 2 X[3629] - 3 X[47459], 6 X[3630] + X[37899], 2 X[3630] + X[47279], X[37899] - 3 X[47279], 4 X[3631] - X[47281], 5 X[3763] - 3 X[47465], X[6144] - 3 X[47455], X[47095] + 3 X[47278], 3 X[10257] - 4 X[40107], X[11008] - 4 X[47454], 3 X[15534] - 5 X[47458], X[15826] - 3 X[22165], 2 X[15826] - 3 X[47097], 3 X[20080] + 5 X[37760], X[20080] + 2 X[47449], 3 X[32220] - 5 X[37760], 5 X[37760] - 6 X[47449], 9 X[21358] - 5 X[47466], 3 X[32113] - 2 X[37897], 2 X[37897] + 3 X[40341], 2 X[32217] - 3 X[47447], 4 X[32455] - 5 X[47461], 4 X[47316] - 5 X[47448]

X(47552) lies on these lines: {2, 47464}, {6, 37911}, {23, 11160}, {30, 15069}, {69, 858}, {141, 47277}, {193, 47457}, {468, 524}, {511, 47309}, {542, 47308}, {597, 47462}, {599, 5159}, {1992, 47460}, {3564, 32233}, {3589, 47463}, {3629, 47459}, {3630, 16331}, {3631, 47281}, {3763, 47465}, {5562, 47339}, {5847, 47477}, {6144, 47455}, {8705, 47095}, {10257, 40107}, {10297, 34507}, {11008, 47454}, {11477, 37984}, {15534, 47458}, {15826, 22165}, {18571, 32599}, {20080, 32220}, {21358, 47466}, {32113, 37897}, {32217, 47447}, {32244, 38885}, {32455, 47461}, {34380, 44961}, {47316, 47448}

X(47552) = anticomplement of X(47464)
X(47552) = midpoint of X(i) and X(j) for these {i,j}: {20080, 32220}, {32113, 40341}
X(47552) = reflection of X(i) in X(j) for these {i,j}: {23, 47446}, {193, 47457}, {10297, 34507}, {11477, 37984}, {32220, 47449}, {47097, 22165}, {47277, 141}, {47280, 5159}
X(47552) = barycentric product X(3266)*X(11216)
X(47552) = barycentric quotient X(11216)/X(111)
X(47552) = {X(599),X(47280)}-harmonic conjugate of X(5159)

X(47553) = X(30)X(86)∩X(468)X(524)

Barycentrics (2*a^2 - b^2 - c^2)*(7*a^6 + 9*a^5*b - a^4*b^2 - 7*a^2*b^4 - 9*a*b^5 + b^6 + 9*a^5*c + 9*a^4*b*c - 9*a*b^4*c - 9*b^5*c - a^4*c^2 + 18*a^2*b^2*c^2 + 18*a*b^3*c^2 - b^4*c^2 + 18*a*b^2*c^3 + 18*b^3*c^3 - 7*a^2*c^4 - 9*a*b*c^4 - b^2*c^4 - 9*a*c^5 - 9*b*c^5 + c^6) : :

X(47553) lies on these lines: {30, 86}, {468, 524}, {740, 47472}, {20090, 37907}

X(47554) = X(468)X(524)∩X(599)X(44908)

X(47554) lies on these lines: {468, 524}, {599, 44908}, {740, 47477}, {32113, 47100}

X(47555) = X(468)X(524)∩X(1213)X(47459)

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

X(47555) lies on these lines: {468, 524}, {1213, 47459}, {1992, 33329}, {47098, 47277}

X(47556) = X(30)X(141)∩X(468)X(524)

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

X(47556) = X[23] + 3 X[21356], X[141] + 2 X[47449], X[69] + 3 X[37907], X[69] + 5 X[47452], 3 X[37907] - 5 X[47452], 3 X[186] + X[11180], X[599] + 3 X[47450], X[7426] - 3 X[47450], X[858] - 3 X[21358], X[858] + 5 X[47448], 3 X[21358] + 5 X[47448], X[1992] - 3 X[47455], 2 X[3589] + X[47279], 5 X[3620] + 3 X[37909], X[3629] - 4 X[47454], 3 X[5032] - 5 X[47458], 2 X[20582] + 3 X[47447], X[47097] + 3 X[47447], 4 X[6329] - X[47281], X[22165] + 4 X[47451], X[32217] - 4 X[47451], X[15826] - 4 X[37911], X[15826] + 2 X[47446], 2 X[37911] + X[47446], 2 X[10168] - 3 X[44452], X[11179] - 3 X[44214], X[15534] - 5 X[47453], X[16619] + 2 X[40107], 2 X[20583] - 3 X[47459], 2 X[32455] - 5 X[47456], X[47276] + 3 X[47352]

X(47556) lies on these lines: {2, 32113}, {23, 21356}, {30, 141}, {69, 37907}, {159, 37955}, {186, 11180}, {468, 524}, {511, 47334}, {523, 45336}, {542, 18579}, {599, 7426}, {858, 21358}, {1352, 44265}, {1503, 47333}, {1992, 47455}, {2393, 45311}, {2854, 44569}, {3580, 5648}, {3589, 47279}, {3620, 37909}, {3629, 47454}, {5032, 47458}, {5650, 8705}, {5846, 47472}, {6329, 47281}, {8584, 47457}, {9030, 47001}, {9041, 47477}, {9306, 22165}, {9813, 15826}, {10168, 44452}, {10295, 47353}, {11179, 44214}, {11645, 47335}, {13857, 41583}, {14845, 16776}, {15533, 32220}, {15534, 47453}, {15646, 35707}, {15993, 47169}, {16325, 46980}, {16619, 40107}, {18571, 32305}, {19510, 19924}, {20583, 47459}, {29181, 47310}, {32218, 37904}, {32257, 32267}, {32455, 47456}, {47031, 47474}, {47276, 47352}, {47321, 47358}, {47332, 47468}

X(47556) = midpoint of X(i) and X(j) for these {i,j}: {2, 32113}, {468, 47473}, {599, 7426}, {1352, 44265}, {3580, 5648}, {5181, 32225}, {10295, 47353}, {13857, 41583}, {15533, 32220}, {22165, 32217}, {32257, 32267}, {47031, 47474}, {47321, 47358}, {47332, 47468}
X(47556) = reflection of X(i) in X(j) for these {i,j}: {8584, 47457}, {37904, 32218}, {47097, 20582}
X(47556) = barycentric product X(524)*X(31105)
X(47556) = barycentric quotient X(31105)/X(671)
X(47556) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {599, 47450, 7426}, {37911, 47446, 15826}

X(47557) = X(141)X(523)∩X(468)X(524)

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

X(47557) lies on these lines: {30, 25562}, {141, 523}, {325, 32113}, {468, 524}, {599, 9832}, {858, 45672}, {1352, 46634}, {1503, 46987}, {5969, 14120}, {6786, 8705}, {11646, 47293}, {16092, 21358}, {20582, 46980}, {29181, 46988}, {32217, 47171}

X(47557) = midpoint of X(i) and X(j) for these {i,j}: {325, 32113}, {1352, 46634}, {11646, 47293}
X(47557) = reflection of X(i) in X(j) for these {i,j}: {32217, 47171}, {46980, 20582}
X(47557) = crossdifference of every pair of points on line {1691, 10097}

X(47558) = X(30)X(67)∩X(468)X(524)

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

X(47558) = 3 X[468] - 2 X[6593], X[5095] - 3 X[32225], 2 X[5095] - 3 X[47545], 2 X[5181] - 3 X[47473], X[6593] - 3 X[8262], 2 X[41586] + X[47552], 2 X[41595] - 3 X[47544], X[895] - 3 X[3580], X[895] + 3 X[41721], X[2930] - 3 X[32113], 3 X[3581] + X[32272], 4 X[6698] - 3 X[47097], 3 X[7426] - X[11061], 2 X[15118] - 3 X[44569], 3 X[15360] + X[32244], 3 X[18374] - 4 X[47316], 2 X[32271] - 3 X[47332], X[41724] + 2 X[47446]

X(47558) lies on these lines: {3, 16789}, {5, 599}, {23, 32262}, {30, 67}, {69, 1995}, {110, 47449}, {141, 30747}, {343, 8542}, {468, 524}, {511, 7687}, {546, 9971}, {575, 7542}, {576, 41587}, {895, 3580}, {1205, 8705}, {1352, 40909}, {1503, 41583}, {2854, 47279}, {2930, 2931}, {3575, 41585}, {3581, 32272}, {3631, 16776}, {5159, 10510}, {5201, 40996}, {5562, 29959}, {6639, 11482}, {6698, 47097}, {7426, 11061}, {7464, 32241}, {7499, 32154}, {8263, 12106}, {8546, 11245}, {9019, 46517}, {15069, 37458}, {15118, 44569}, {15360, 32244}, {15533, 44212}, {15993, 16310}, {18374, 47316}, {26926, 35707}, {32233, 37934}, {32271, 47332}, {32274, 47339}, {34827, 44395}, {40949, 47336}, {41724, 47446}

X(47558) = midpoint of X(3580) and X(41721)
X(47558) = reflection of X(i) in X(j) for these {i,j}: {110, 47449}, {468, 8262}, {10510, 5159}, {32233, 37934}, {47339, 32274}, {47545, 32225}

X(47559) = X(6)X(47239)∩X(468)X(524)

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

X(47559) = X[16316] - 3 X[47447], 2 X[47171] - 3 X[47450], 3 X[47237] + X[47278], 2 X[47238] + X[47276], 3 X[47240] - X[47277], 4 X[47241] - X[47280], X[47242] + 2 X[47446], 3 X[47243] - 2 X[47457], 4 X[47244] - 3 X[47455], 3 X[47246] - 4 X[47451]

X(47559) lies on these lines: {6, 47239}, {468, 524}, {511, 14120}, {523, 3569}, {542, 36180}, {599, 1316}, {1503, 47000}, {3580, 47349}, {14999, 41721}, {15360, 36168}, {16315, 47279}, {16316, 47447}, {16320, 47449}, {32220, 44369}, {34507, 36156}, {36157, 40107}, {47171, 47450}, {47237, 47278}, {47238, 47276}, {47240, 47277}, {47241, 47280}, {47242, 47446}, {47243, 47457}, {47244, 47455}, {47246, 47451}

X(47559) = midpoint of X(i) and X(j) for these {i,j}: {14999, 41721}, {15993, 32113}, {16315, 47279}, {32220, 44369}
X(47559) = reflection of X(i) in X(j) for these {i,j}: {6, 47239}, {16320, 47449}
X(47559) = crossdifference of every pair of points on line {182, 10097}

X(47560) = X(69)X(47239)∩X(468)X(524)

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

X(47560) lies on these lines: {69, 47239}, {468, 524}, {511, 47000}, {523, 32220}, {1992, 36163}, {3564, 46999}, {14645, 36180}, {44377, 47459}, {44395, 47240}

X(47560) = reflection of X(69) in X(47239)
X(47560) = crossdifference of every pair of points on line {5028, 10097}

X(47561) = X(6)X(9832)∩X(468)X(524)

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

X(47561) lies on these lines: {6, 9832}, {141, 47239}, {325, 47455}, {468, 524}, {523, 5027}, {597, 11007}, {1503, 46999}, {1691, 7472}, {5969, 36180}, {15993, 32220}, {29181, 47000}, {44380, 47457}

X(47561) = midpoint of X(15993) and X(32220)
X(47561) = reflection of X(i) in X(j) for these {i,j}: {141, 47239}, {44380, 47457}
X(47561) = crossdifference of every pair of points on line {3094, 10097}

X(47562) = X(30)X(165)∩X(468)X(519)

Barycentrics 10*a^7 + 22*a^6*b - a^5*b^2 - 13*a^4*b^3 - 10*a^3*b^4 - 22*a^2*b^5 + a*b^6 + 13*b^7 + 22*a^6*c - 13*a^4*b^2*c - 22*a^2*b^4*c + 13*b^6*c - a^5*c^2 - 13*a^4*b*c^2 + 12*a^3*b^2*c^2 + 48*a^2*b^3*c^2 - a*b^4*c^2 - 13*b^5*c^2 - 13*a^4*c^3 + 48*a^2*b^2*c^3 - 13*b^4*c^3 - 10*a^3*c^4 - 22*a^2*b*c^4 - a*b^2*c^4 - 13*b^3*c^4 - 22*a^2*c^5 - 13*b^2*c^5 + a*c^6 + 13*b*c^6 + 13*c^7 : :

X(47562) = 2 X[10] + X[37904], 4 X[468] - X[47472], 2 X[468] + X[47488], 10 X[468] - X[47489], 8 X[468] + X[47490], 11 X[468] - 2 X[47491], 7 X[468] + 2 X[47492], 7 X[468] - X[47493], 5 X[468] + X[47494], 5 X[468] - 2 X[47495], X[468] + 2 X[47496], 11 X[468] + X[47531], 17 X[468] + X[47533], 13 X[468] + 2 X[47534], 13 X[468] - X[47535], 19 X[468] - X[47536], 29 X[468] - 2 X[47537], 23 X[468] - 2 X[47538], 17 X[468] - 2 X[47540], 25 X[468] + 2 X[47564], and many more

X(47562) lies on these lines: {10, 37904}, {30, 165}, {468, 519}, {3828, 47311}, {9588, 47338}, {9780, 47314}, {18579, 47469}, {25055, 47321}, {28198, 47332}, {28208, 47333}, {28558, 47543}, {47359, 47449}, {47506, 47556}

X(47562) = midpoint of X(25055) and X(47321)
X(47562) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {468, 47488, 47472}, {468, 47494, 47495}, {468, 47496, 47488}, {47472, 47488, 47490}, {47488, 47489, 47494}, {47489, 47495, 47472}, {47494, 47495, 47489}

X(47563) = X(30)X(125)∩X(468)X(519)

X(47563) lies on these lines: {2, 19771}, {30, 125}, {230, 21950}, {468, 519}, {3580, 7478}

X(47563) = midpoint of X(3580) and X(7478)
X(47563) = X(17192)-lineconjugate of X(42332)

X(47564) = X(8)X(30745)∩X(468)X(519)

Barycentrics 10*a^7 - 8*a^6*b - 11*a^5*b^2 + 7*a^4*b^3 - 10*a^3*b^4 + 8*a^2*b^5 + 11*a*b^6 - 7*b^7 - 8*a^6*c + 7*a^4*b^2*c + 8*a^2*b^4*c - 7*b^6*c - 11*a^5*c^2 + 7*a^4*b*c^2 + 32*a^3*b^2*c^2 - 22*a^2*b^3*c^2 - 11*a*b^4*c^2 + 7*b^5*c^2 + 7*a^4*c^3 - 22*a^2*b^2*c^3 + 7*b^4*c^3 - 10*a^3*c^4 + 8*a^2*b*c^4 - 11*a*b^2*c^4 + 7*b^3*c^4 + 8*a^2*c^5 + 7*b^2*c^5 + 11*a*c^6 - 7*b*c^6 - 7*c^7 : :

X(47564) = 9 X[8] - 5 X[30745], 11 X[468] - 9 X[47472], X[858] - 3 X[4677], 9 X[3625] - 2 X[47315], 9 X[3632] + X[37900], 3 X[4669] - 2 X[5159], X[5189] - 9 X[31145]

X(47564) lies on these lines: {8, 30745}, {468, 519}, {858, 4677}, {3621, 47321}, {3625, 47315}, {3632, 37900}, {4669, 5159}, {5189, 31145}

X(47565) = X(69)X(523)∩X(468)X(524)

X(47565) lies on these lines: {69, 523}, {468, 524}, {511, 46988}, {599, 46980}, {1352, 46982}, {3564, 46987}, {11898, 46634}, {14120, 14645}, {16315, 44395}, {32220, 47171}, {44377, 47277}, {47000, 47468}

X(47565) = midpoint of X(11898) and X(46634)
X(47565) = reflection of X(i) in X(j) for these {i,j}: {16315, 44395}, {32220, 47171}, {46980, 599}, {46982, 1352}, {46998, 47473}, {47000, 47468}, {47277, 44377}
X(47565) = crossdifference of every pair of points on line {1692, 10097}

X(47566) = X(30)X(81)∩X(468)X(524)

Barycentrics (2*a^2 - b^2 - c^2)*(7*a^7 + 7*a^6*b - a^5*b^2 - a^4*b^3 - 7*a^3*b^4 - 7*a^2*b^5 + a*b^6 + b^7 + 7*a^6*c + 9*a^5*b*c - a^4*b^2*c - 7*a^2*b^4*c - 9*a*b^5*c + b^6*c - a^5*c^2 - a^4*b*c^2 + 18*a^3*b^2*c^2 + 18*a^2*b^3*c^2 - a*b^4*c^2 - b^5*c^2 - a^4*c^3 + 18*a^2*b^2*c^3 + 18*a*b^3*c^3 - b^4*c^3 - 7*a^3*c^4 - 7*a^2*b*c^4 - a*b^2*c^4 - b^3*c^4 - 7*a^2*c^5 - 9*a*b*c^5 - b^2*c^5 + a*c^6 + b*c^6 + c^7) : :

X(47566) lies on these lines: {30, 81}, {468, 524}, {758, 47472}, {20086, 37907}

X(47567) = X(30)X(7801)∩X(468)X(511)

Barycentrics 2*a^14 - a^12*b^2 - 9*a^8*b^6 + 6*a^6*b^8 + 9*a^4*b^10 - 8*a^2*b^12 + b^14 - a^12*c^2 + 4*a^10*b^2*c^2 - 13*a^8*b^4*c^2 + 12*a^6*b^6*c^2 - 7*a^4*b^8*c^2 + 8*a^2*b^10*c^2 - 3*b^12*c^2 - 13*a^8*b^2*c^4 + 20*a^6*b^4*c^4 - 10*a^4*b^6*c^4 - 8*a^2*b^8*c^4 + 3*b^10*c^4 - 9*a^8*c^6 + 12*a^6*b^2*c^6 - 10*a^4*b^4*c^6 + 16*a^2*b^6*c^6 - b^8*c^6 + 6*a^6*c^8 - 7*a^4*b^2*c^8 - 8*a^2*b^4*c^8 - b^6*c^8 + 9*a^4*c^10 + 8*a^2*b^2*c^10 + 3*b^4*c^10 - 8*a^2*c^12 - 3*b^2*c^12 + c^14 : :

X(47567) = X[20065] - 5 X[37952], 2 X[20576] - 3 X[44452], X[36998] - 3 X[44280]

X(47567) lies on these lines: {30, 7801}, {315, 10295}, {468, 511}, {626, 10297}, {754, 47333}, {2794, 47308}, {3425, 37978}, {20065, 37952}, {20576, 44452}, {35389, 47457}, {36998, 44280}, {46987, 47000}

X(47567) = midpoint of X(315) and X(10295)
X(47567) = reflection of X(i) in X(j) for these {i,j}: {10297, 626}, {35389, 47457}

X(47568) = X(30)X(5188)∩X(468)X(511)

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

X(47568) = X[23] + 3 X[6194], 3 X[186] + X[12251], X[194] - 5 X[37952], X[858] - 3 X[22712], X[3095] - 3 X[44214], 2 X[5159] - 3 X[15819], 3 X[7697] - X[18323], X[10296] - 5 X[31276], X[11257] - 3 X[44280], 2 X[11272] - 3 X[44452], 3 X[15646] - X[32448], X[32520] - 9 X[37955], 5 X[32522] - 9 X[37941]

X(47568) lies on these lines: {23, 6194}, {30, 5188}, {76, 10295}, {186, 12251}, {194, 37952}, {468, 511}, {538, 47333}, {858, 22712}, {2782, 47335}, {3095, 44214}, {3906, 46990}, {3934, 10297}, {5159, 15819}, {7426, 33706}, {7575, 32521}, {7697, 18323}, {9821, 11799}, {9917, 37933}, {10296, 31276}, {11257, 44280}, {11272, 44452}, {15646, 32448}, {18571, 32515}, {32520, 37955}, {32522, 37941}, {35439, 47457}

X(47568) = midpoint of X(i) and X(j) for these {i,j}: {76, 10295}, {7426, 33706}, {7575, 32521}, {9821, 11799}
X(47568) = reflection of X(i) in X(j) for these {i,j}: {10297, 3934}, {35439, 47457}

X(47569) = X(30)X(141)∩X(468)X(511)

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

X(47569) = X[6] - 3 X[44214], X[23] + 3 X[10519], X[3098] + 2 X[47449], X[69] + 3 X[186], 3 X[403] - X[31670], X[1350] + 3 X[47450], X[11799] - 3 X[47450], X[1351] - 3 X[47455], 3 X[2072] - 5 X[3763], 2 X[3589] - 3 X[44452], X[3629] - 6 X[16531], 3 X[5050] - X[47280], 3 X[5085] + X[47276], 2 X[5092] + X[47279], 3 X[5093] - 5 X[47458], 2 X[5097] - 3 X[47459], X[6776] - 5 X[37952], X[10296] - 5 X[40330], 3 X[10516] - X[18323], X[11477] - 5 X[47453], 2 X[14810] + 3 X[47447], 3 X[15035] + X[41721], 4 X[15516] - 3 X[47463], 3 X[15520] - 4 X[47460], 3 X[17508] + 2 X[47446], 4 X[20190] + X[47278], X[21850] - 3 X[44282], 4 X[22330] - 5 X[47461], 3 X[31884] + 5 X[47448], X[32247] + 3 X[35265], X[33878] + 5 X[47452], X[34507] + 2 X[37934], X[37517] - 4 X[47454], 4 X[37911] - 3 X[38317], 3 X[37931] + 2 X[43150], 9 X[37955] - X[39899], 3 X[39561] - 2 X[47464], 3 X[44280] - X[46264]

X(47569) lies on these lines: {3, 32113}, {6, 44214}, {23, 10519}, {30, 141}, {69, 186}, {403, 31670}, {468, 511}, {524, 1511}, {542, 47333}, {575, 47277}, {576, 47457}, {599, 44265}, {858, 21766}, {1350, 11799}, {1351, 47455}, {1352, 10295}, {1503, 12041}, {2070, 37485}, {2072, 3763}, {2393, 6699}, {2781, 46817}, {3564, 12584}, {3589, 44452}, {3629, 16531}, {5050, 47280}, {5085, 47276}, {5092, 47279}, {5093, 47458}, {5097, 47459}, {5181, 32110}, {5846, 47476}, {6776, 37952}, {7426, 15066}, {8262, 33851}, {8705, 15122}, {10020, 40929}, {10257, 11574}, {10296, 40330}, {10297, 24206}, {10516, 18323}, {10564, 41583}, {11477, 47453}, {11645, 37853}, {12061, 23336}, {14356, 44216}, {14810, 47447}, {15035, 41721}, {15067, 16619}, {15516, 47463}, {15520, 47460}, {15646, 35228}, {15993, 46634}, {17508, 47446}, {19924, 47332}, {20190, 47278}, {21850, 44282}, {22249, 34380}, {22330, 47461}, {28408, 37943}, {29012, 47308}, {29181, 47336}, {29317, 47309}, {31884, 47448}, {32247, 35265}, {33878, 47452}, {34351, 44493}, {34507, 37934}, {37488, 37933}, {37517, 47454}, {37911, 38317}, {37931, 43150}, {37955, 39899}, {39561, 47464}, {41584, 44281}, {44280, 46264}

X(47569) = midpoint of X(i) and X(j) for these {i,j}: {3, 32113}, {468, 47468}, {599, 44265}, {1350, 11799}, {1352, 10295}, {5181, 32110}, {8262, 33851}, {10564, 41583}, {15993, 46634}, {47308, 47474}, {47333, 47473}
X(47569) = reflection of X(i) in X(j) for these {i,j}: {576, 47457}, {10297, 24206}, {16619, 32218}, {47277, 575}
X(47569) = {X(1350),X(47450)}-harmonic conjugate of X(11799)

X(47570) = X(30)X(114)∩X(468)X(511)

Barycentrics 2*a^14 - 5*a^12*b^2 + 7*a^10*b^4 - 7*a^8*b^6 - 2*a^6*b^8 + 11*a^4*b^10 - 7*a^2*b^12 + b^14 - 5*a^12*c^2 + 12*a^10*b^2*c^2 - 12*a^8*b^4*c^2 + 10*a^6*b^6*c^2 - 15*a^4*b^8*c^2 + 14*a^2*b^10*c^2 - 4*b^12*c^2 + 7*a^10*c^4 - 12*a^8*b^2*c^4 + 12*a^6*b^4*c^4 - 17*a^2*b^8*c^4 + 6*b^10*c^4 - 7*a^8*c^6 + 10*a^6*b^2*c^6 + 20*a^2*b^6*c^6 - 3*b^8*c^6 - 2*a^6*c^8 - 15*a^4*b^2*c^8 - 17*a^2*b^4*c^8 - 3*b^6*c^8 + 11*a^4*c^10 + 14*a^2*b^2*c^10 + 6*b^4*c^10 - 7*a^2*c^12 - 4*b^2*c^12 + c^14 : :

X(47570) = X[316] + 3 X[38704], X[10295] - 3 X[38704], X[1551] - 3 X[41133], 3 X[2072] - X[38953], X[2080] - 3 X[44214], 5 X[7925] - X[36173], 3 X[10257] - 2 X[40544], 2 X[14693] - 3 X[44452], X[14712] - 5 X[37952]

X(47570) lies on these lines: {2, 11657}, {30, 114}, {122, 5159}, {316, 10295}, {325, 36166}, {468, 511}, {512, 46990}, {625, 10297}, {842, 858}, {1551, 41133}, {2072, 38953}, {2080, 44214}, {2967, 47151}, {3815, 36177}, {3849, 47333}, {6036, 16315}, {7493, 15919}, {7925, 36173}, {10257, 34841}, {11799, 35002}, {14417, 44813}, {14693, 44452}, {14712, 37952}, {15980, 46634}, {30209, 47503}, {36170, 44377}

X(47570) = midpoint of X(i) and X(j) for these {i,j}: {316, 10295}, {325, 36166}, {842, 858}, {5099, 18860}, {11799, 35002}, {15980, 46634}
X(47570) = reflection of X(i) in X(j) for these {i,j}: {468, 16760}, {10297, 625}, {16188, 5159}, {16315, 6036}, {36170, 44377}
X(47570) = {X(316),X(38704)}-harmonic conjugate of X(10295)

X(47571) = X(6)X(30)∩X(468)X(511)

Barycentrics 2*a^12 - 11*a^10*b^2 + 13*a^8*b^4 + 6*a^6*b^6 - 16*a^4*b^8 + 5*a^2*b^10 + b^12 - 11*a^10*c^2 + 10*a^8*b^2*c^2 - 22*a^6*b^4*c^2 + 32*a^4*b^6*c^2 - 7*a^2*b^8*c^2 - 2*b^10*c^2 + 13*a^8*c^4 - 22*a^6*b^2*c^4 - 16*a^4*b^4*c^4 + 2*a^2*b^6*c^4 - b^8*c^4 + 6*a^6*c^6 + 32*a^4*b^2*c^6 + 2*a^2*b^4*c^6 + 4*b^6*c^6 - 16*a^4*c^8 - 7*a^2*b^2*c^8 - b^4*c^8 + 5*a^2*c^10 - 2*b^2*c^10 + c^12 : :

X(47571) = X[69] - 3 X[403], X[146] + 3 X[37784], 2 X[182] - 3 X[47459], 4 X[575] - 5 X[47461], X[858] - 3 X[14853], X[1350] - 3 X[47455], 2 X[3098] - 5 X[47456], 4 X[3589] - 3 X[10257], 5 X[3763] - 6 X[44911], 2 X[3818] - 3 X[10151], 3 X[5050] - 4 X[47460], 3 X[5085] - 5 X[47458], 3 X[5093] + X[18325], 3 X[5093] - 2 X[47464], X[18325] + 2 X[47464], 4 X[5097] - 3 X[47463], 3 X[5102] - X[47280], 2 X[5159] - 3 X[14561], 6 X[15520] - 5 X[47462], X[16163] - 3 X[44102], 3 X[31726] + X[39899], X[33878] - 3 X[44214], X[33878] - 4 X[47454], 3 X[44214] - 4 X[47454], 2 X[37517] + X[47279], X[44456] + 2 X[47449]

X(47571) lies on these lines: {3, 47457}, {4, 32220}, {6, 30}, {69, 403}, {113, 524}, {146, 37784}, {182, 47459}, {468, 511}, {517, 47506}, {518, 47471}, {542, 1514}, {575, 47461}, {576, 47277}, {597, 37470}, {858, 14853}, {895, 32111}, {1350, 47455}, {1351, 11799}, {1352, 37984}, {1353, 44267}, {1503, 12295}, {3098, 47456}, {3564, 9970}, {3580, 10752}, {3589, 10257}, {3763, 44911}, {3818, 10151}, {5050, 47460}, {5085, 47458}, {5093, 18325}, {5097, 47463}, {5102, 47280}, {5159, 14561}, {5476, 37648}, {5480, 10297}, {5504, 18374}, {5654, 11477}, {6053, 8681}, {7426, 37645}, {8675, 47002}, {10564, 47333}, {11649, 47093}, {13352, 32217}, {14389, 16387}, {14984, 46817}, {15063, 32127}, {15122, 18583}, {15520, 47462}, {15585, 37971}, {16163, 44102}, {16227, 47090}, {16657, 47339}, {19924, 47031}, {28419, 37943}, {29181, 47308}, {31726, 39899}, {33878, 44214}, {34380, 44961}, {34664, 44493}, {37497, 37934}, {37517, 47279}, {44456, 47449}, {47334, 47473}

X(47571) = midpoint of X(i) and X(j) for these {i,j}: {4, 32220}, {895, 32111}, {1351, 11799}, {1353, 44267}, {3580, 10752}, {11477, 32113}, {15063, 32127}
X(47571) = reflection of X(i) in X(j) for these {i,j}: {3, 47457}, {1352, 37984}, {10297, 5480}, {15122, 18583}, {47097, 5476}, {47277, 576}, {47468, 468}, {47473, 47334}, {47474, 47336}
X(47571) = X(i)-line conjugate of X(j) for these (i,j): {1102, 18217}, {16491, 17512}, {47002, 8675}
X(47571) = {X(47575),X(47576)}-harmonic conjugate of X(468)
X(47571) = {X(47577),X(47579)}-harmonic conjugate of X(468)

X(47572) = X(30)X(13355)∩X(468)X(511)

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

X(47572) lies on these lines: {30, 13355}, {32, 47457}, {315, 32220}, {468, 511}, {760, 47506}, {5017, 47455}, {14645, 47473}, {41413, 47456}, {44499, 47277}

X(47572) = midpoint of X(315) and X(32220)
X(47572) = reflection of X(i) in X(j) for these {i,j}: {32, 47457}, {47277, 44499}

X(47573) = X(30)X(13354)∩X(468)X(511)

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

X(47573) lies on these lines: {30, 13354}, {39, 47457}, {76, 32220}, {468, 511}, {1316, 31958}, {3094, 47455}, {7426, 22486}, {13330, 32113}, {13331, 47458}, {14839, 47506}, {32217, 36156}, {44453, 47453}, {44500, 47277}

X(47573) = midpoint of X(i) and X(j) for these {i,j}: {76, 32220}, {7426, 22486}, {13330, 32113}
X(47573) = reflection of X(i) in X(j) for these {i,j}: {39, 47457}, {47277, 44500}

X(47574) = X(30)X(18800)∩X(468)X(511)

Barycentrics 2*a^12 - 7*a^10*b^2 + 10*a^8*b^4 + 3*a^6*b^6 - 13*a^4*b^8 + 4*a^2*b^10 + b^12 - 7*a^10*c^2 + 10*a^8*b^2*c^2 - 16*a^6*b^4*c^2 + 23*a^4*b^6*c^2 - 5*a^2*b^8*c^2 - b^10*c^2 + 10*a^8*c^4 - 16*a^6*b^2*c^4 - 12*a^4*b^4*c^4 + a^2*b^6*c^4 - b^8*c^4 + 3*a^6*c^6 + 23*a^4*b^2*c^6 + a^2*b^4*c^6 + 2*b^6*c^6 - 13*a^4*c^8 - 5*a^2*b^2*c^8 - b^4*c^8 + 4*a^2*c^10 - b^2*c^10 + c^12 : :

X(47574) = 3 X[1570] - 2 X[47464], 3 X[1691] - 5 X[47458], 3 X[1692] - 4 X[47460], 2 X[2030] - 3 X[47459], X[5104] - 3 X[47455], 3 X[5111] - X[47280], 3 X[15514] + X[47276]

X(47574) lies on these lines: {30, 18800}, {187, 47457}, {316, 32220}, {468, 511}, {524, 5465}, {1316, 20423}, {1570, 47464}, {1691, 47458}, {1692, 47460}, {2030, 47459}, {5099, 5107}, {5104, 47455}, {5111, 47280}, {8586, 32113}, {8675, 47503}, {11657, 46124}, {15341, 44496}, {15514, 47276}, {31850, 36157}, {36168, 40112}, {37746, 47097}

X(47574) = midpoint of X(i) and X(j) for these {i,j}: {316, 32220}, {5099, 5107}, {8586, 32113}
X(47574) = reflection of X(i) in X(j) for these {i,j}: {187, 47457}, {47277, 44496}, {47468, 16760}

X(47575) = X(13)X(15)∩X(468)X(511)

X(47575) lies on these lines: {13, 15}, {403, 621}, {468, 511}, {531, 47332}, {5611, 11799}, {6671, 10257}, {7684, 10297}, {20428, 37984}, {40334, 44911}, {44659, 47471}, {44666, 47309}

X(47575) = midpoint of X(5611) and X(11799)
X(47575) = reflection of X(i) in X(j) for these {i,j}: {10297, 7684}, {20428, 37984}, {47576, 47584}
X(47575) = {X(468),X(47571)}-harmonic conjugate of X(47576)

X(47576) = X(14)X(16)∩X(468)X(511)

X(47576) lies on these lines: {14, 16}, {403, 622}, {468, 511}, {530, 47332}, {5615, 11799}, {6672, 10257}, {7685, 10297}, {20429, 37984}, {40335, 44911}, {44660, 47471}, {44667, 47309}

X(47576) = midpoint of X(5615) and X(11799)
X(47576) = reflection of X(i) in X(j) for these {i,j}: {10297, 7685}, {20429, 37984}, {47575, 47584}
X(47576) = {X(468),X(47571)}-harmonic conjugate of X(47575)

X(47577) = X(30)X(32)∩X(468)X(511)

Barycentrics 2*a^14 - 9*a^12*b^2 + 8*a^10*b^4 + 7*a^8*b^6 - 10*a^6*b^8 + a^4*b^10 + b^14 - 9*a^12*c^2 + 4*a^10*b^2*c^2 - 5*a^8*b^4*c^2 + 12*a^6*b^6*c^2 - 7*a^4*b^8*c^2 + 8*a^2*b^10*c^2 - 3*b^12*c^2 + 8*a^10*c^4 - 5*a^8*b^2*c^4 - 28*a^6*b^4*c^4 + 14*a^4*b^6*c^4 - 16*a^2*b^8*c^4 + 3*b^10*c^4 + 7*a^8*c^6 + 12*a^6*b^2*c^6 + 14*a^4*b^4*c^6 + 16*a^2*b^6*c^6 - b^8*c^6 - 10*a^6*c^8 - 7*a^4*b^2*c^8 - 16*a^2*b^4*c^8 - b^6*c^8 + a^4*c^10 + 8*a^2*b^2*c^10 + 3*b^4*c^10 - 3*b^2*c^12 + c^14 : :

X(47577) = X[315] - 3 X[403], X[858] - 3 X[9753], 4 X[6680] - 3 X[10257], 5 X[7867] - 6 X[44911]

X(47577) lies on these lines: {23, 3425}, {30, 32}, {315, 403}, {468, 511}, {754, 47332}, {760, 47471}, {858, 9753}, {2794, 47309}, {6680, 10257}, {7867, 44911}, {13355, 47457}, {15122, 20576}, {46988, 46999}

X(47577) = reflection of X(i) in X(j) for these {i,j}: {13355, 47457}, {15122, 20576}
X(47577) = {X(468),X(47571)}-harmonic conjugate of X(47579)

X(47578) = X(30)X(35387)∩X(468)X(511)

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

X(47578) = X(47578) lies on these lines: {30, 35387}, {468, 511}, {754, 47473}, {760, 47477}, {2794, 47474}, {5017, 32113}, {5028, 47457}, {41413, 47279}, {44499, 47459}

X(47578) = midpoint of X(5017) and X(32113)
X(47578) = reflection of X(5028) in X(47457)

X(47579) = X(30)X(39)∩X(468)X(511)

Barycentrics 3*a^10*b^4 - 6*a^8*b^6 + 6*a^4*b^10 - 3*a^2*b^12 + 8*a^10*b^2*c^2 - 3*a^8*b^4*c^2 - 2*a^6*b^6*c^2 - 8*a^4*b^8*c^2 + 6*a^2*b^10*c^2 - b^12*c^2 + 3*a^10*c^4 - 3*a^8*b^2*c^4 + 16*a^6*b^4*c^4 - 2*a^4*b^6*c^4 - 5*a^2*b^8*c^4 + 3*b^10*c^4 - 6*a^8*c^6 - 2*a^6*b^2*c^6 - 2*a^4*b^4*c^6 + 4*a^2*b^6*c^6 - 2*b^8*c^6 - 8*a^4*b^2*c^8 - 5*a^2*b^4*c^8 - 2*b^6*c^8 + 6*a^4*c^10 + 6*a^2*b^2*c^10 + 3*b^4*c^10 - 3*a^2*c^12 - b^2*c^12 : :

X(47579) = X[76] - 3 X[403], 3 X[262] - X[858], 4 X[6683] - 3 X[10257], X[9821] - 3 X[44214], 3 X[15819] - 4 X[37911], X[18325] + 3 X[32447], 5 X[31239] - 6 X[44911], X[32521] - 3 X[44282], 5 X[37760] + 3 X[44434]

X(47579) lies on these lines: {30, 39}, {76, 403}, {262, 858}, {468, 511}, {538, 47332}, {2023, 16306}, {2782, 47336}, {3095, 11799}, {3906, 47002}, {6248, 37984}, {6683, 10257}, {9821, 44214}, {10151, 12143}, {11272, 15122}, {13354, 47457}, {14839, 47471}, {15819, 37911}, {18325, 32447}, {20423, 20977}, {31239, 44911}, {32448, 44267}, {32515, 44961}, {32521, 44282}, {37760, 44434}

X(47579) = midpoint of X(i) and X(j) for these {i,j}: {3095, 11799}, {32448, 44267}
X(47579) = reflection of X(i) in X(j) for these {i,j}: {6248, 37984}, {13354, 47457}, {15122, 11272}
X(47579) = intersection of the orthic axes of the pedal triangles of PU(1)
X(47579) = {X(468),X(47571)}-harmonic conjugate of X(47577)

X(47580) = X(468)X(511)∩X(538)X(47473)

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

X(47580) = X[13330] - 3 X[47455], 3 X[13331] - X[47280], X[44453] + 3 X[47450], 2 X[44500] - 3 X[47459]

X(47580) lies on these lines: {468, 511}, {538, 47473}, {3094, 32113}, {5052, 47457}, {5112, 22677}, {8705, 36157}, {13330, 47455}, {13331, 47280}, {14839, 47477}, {44453, 47450}, {44500, 47459}

X(47580) = midpoint of X(3094) and X(32113)
X(47580) = reflection of X(5052) in X(47457)

X(47581) = X(30)X(182)∩X(468)X(511)

Barycentrics 2*a^12 - 7*a^10*b^2 + 5*a^8*b^4 + 6*a^6*b^6 - 8*a^4*b^8 + a^2*b^10 + b^12 - 7*a^10*c^2 + 2*a^8*b^2*c^2 - 10*a^6*b^4*c^2 + 20*a^4*b^6*c^2 - 3*a^2*b^8*c^2 - 2*b^10*c^2 + 5*a^8*c^4 - 10*a^6*b^2*c^4 - 16*a^4*b^4*c^4 + 2*a^2*b^6*c^4 - b^8*c^4 + 6*a^6*c^6 + 20*a^4*b^2*c^6 + 2*a^2*b^4*c^6 + 4*b^6*c^6 - 8*a^4*c^8 - 3*a^2*b^2*c^8 - b^4*c^8 + a^2*c^10 - 2*b^2*c^10 + c^12 : :

X(47581) = X[3] - 3 X[47455], X[23] + 3 X[14853], 3 X[403] - X[1352], 3 X[403] + X[32220], 3 X[468] - X[47468], 3 X[47332] - X[47474], 2 X[575] - 3 X[47459], X[858] - 3 X[14561], X[1350] - 3 X[44214], X[1350] - 5 X[47453], 3 X[44214] - 5 X[47453], X[1353] + 3 X[11563], X[3098] - 4 X[47454], 5 X[3618] - X[7464], 3 X[5050] + X[18325], 3 X[5050] - 5 X[47458], X[18325] + 5 X[47458], 2 X[5092] - 5 X[47456], 3 X[5093] - X[47280], 3 X[5102] + X[47276], 2 X[5159] - 3 X[38317], X[11477] + 3 X[47450], 5 X[11482] - 3 X[47465], X[12112] + 3 X[25320], 4 X[15516] - 5 X[47461], 3 X[15520] - 2 X[47464], X[18572] - 3 X[38136], 4 X[22330] - 3 X[47463], X[37517] + 2 X[47449], X[37950] - 3 X[38110], 3 X[39561] - 4 X[47460], X[44456] + 5 X[47452]

X(47581) lies on these lines: {3, 47455}, {5, 44493}, {6, 11799}, {23, 14853}, {30, 182}, {403, 1352}, {468, 511}, {524, 47334}, {542, 47332}, {575, 16657}, {858, 14561}, {1350, 44214}, {1351, 32113}, {1353, 11563}, {1503, 10113}, {2854, 46817}, {3098, 47454}, {3564, 19140}, {3580, 9970}, {3589, 15122}, {3618, 7464}, {3818, 37984}, {5050, 18325}, {5092, 47456}, {5093, 47280}, {5097, 47277}, {5102, 47276}, {5159, 38317}, {7426, 20423}, {7575, 21850}, {8705, 15074}, {9027, 16534}, {10295, 31670}, {10297, 19130}, {11477, 47450}, {11482, 47465}, {11579, 32111}, {11645, 47310}, {11649, 37971}, {12112, 25320}, {12900, 19510}, {13446, 47093}, {14915, 15118}, {15516, 47461}, {15520, 47464}, {16836, 25555}, {18572, 38136}, {19924, 47333}, {22330, 47463}, {29012, 47309}, {29181, 47335}, {29317, 47308}, {37517, 47449}, {37950, 38110}, {39561, 47460}, {40929, 44232}, {44456, 47452}, {47471, 47506}

X(47581) = midpoint of X(i) and X(j) for these {i,j}: {6, 11799}, {1351, 32113}, {1352, 32220}, {3580, 9970}, {5480, 32217}, {7426, 20423}, {7575, 21850}, {10295, 31670}, {11579, 32111}, {47471, 47506}
X(47581) = reflection of X(i) in X(j) for these {i,j}: {182, 47457}, {3818, 37984}, {10297, 19130}, {15122, 3589}, {19510, 12900}, {47277, 5097}
X(47581) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {403, 32220, 1352}, {1350, 47453, 44214}

X(47582) = X(30)X(74)∩X(468)X(511)

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

X(47582) = 5 X[23] - X[14683], 3 X[23] + X[37779], 3 X[23] - X[46818], 3 X[14683] + 5 X[37779], 3 X[14683] - 5 X[46818], 5 X[3580] - 3 X[9140], X[3580] - 3 X[15360], 5 X[3581] - X[20127], 3 X[9140] + 5 X[15107], X[9140] - 5 X[15360], X[15107] + 3 X[15360], X[146] - 3 X[47096], X[323] - 3 X[7426], 5 X[468] - 4 X[5972], 3 X[468] - 2 X[11064], 3 X[468] - 4 X[32223], 6 X[5972] - 5 X[11064], and many more

Let L_A, L_B, L_C be the lines through A, B, C, resp. parallel to the orthic axis. Let M_A, M_B, M_C be the reflections of BC, CA, AB in L_A, L_B, L_C, resp. Let A' = M_B∩M_C, and define B' and C' cyclically. Triangle A'B'C' is inversely similar to, and 3 times the size of, ABC. Let A"B"C" be the reflection of A'B'C' in the orthic axis. The triangle A"B"C" is homothetic to ABC, with center of homothety X(11064). X(47582) = X(468)-of-A"B"C". (See Hyacinthos #16741/16782, Sep 2008.) (Randy Hutson, April 16, 2022)

X(47582) lies on these lines: {2, 21850}, {4, 44683}, {5, 37494}, {6, 44210}, {20, 26869}, {22, 11245}, {23, 3564}, {25, 69}, {30, 74}, {51, 3313}, {110, 34380}, {125, 29181}, {140, 5640}, {141, 34417}, {143, 34002}, {146, 47096}, {154, 6144}, {184, 3629}, {193, 26864}, {235, 17834}, {237, 6390}, {297, 43453}, {316, 460}, {323, 7426}, {343, 428}, {378, 44935}, {395, 22827}, {396, 22826}, {427, 31670}, {462, 622}, {463, 621}, {468, 511}, {524, 1495}, {525, 47175}, {542, 47312}, {550, 18911}, {568, 16618}, {576, 13394}, {599, 31860}, {631, 3527}, {1154, 37971}, {1192, 14457}, {1350, 30739}, {1351, 7493}, {1352, 10301}, {1353, 6800}, {1503, 37899}, {1531, 10151}, {1539, 12827}, {1885, 46730}, {1993, 10154}, {2374, 10425}, {2937, 13292}, {2979, 6677}, {3060, 6676}, {3098, 37648}, {3231, 16317}, {3292, 15448}, {3448, 37900}, {3567, 16197}, {3763, 17810}, {3793, 5191}, {3853, 38397}, {3933, 20897}, {4224, 37656}, {4232, 6090}, {4846, 37489}, {5181, 47447}, {5480, 37454}, {5643, 12108}, {5965, 32237}, {6000, 47094}, {6243, 13383}, {6329, 44107}, {6515, 9909}, {6636, 45298}, {6699, 12099}, {6756, 41171}, {7387, 18917}, {7484, 33522}, {7488, 13142}, {7494, 9777}, {7495, 11002}, {7519, 39884}, {7542, 10263}, {7553, 34514}, {7667, 13567}, {7693, 37990}, {8550, 35268}, {9919, 12317}, {10257, 13391}, {10272, 12824}, {10510, 47457}, {10519, 11284}, {10565, 11402}, {10752, 32227}, {11412, 21841}, {11464, 33591}, {11799, 38789}, {12088, 18914}, {12828, 16163}, {13192, 43291}, {13754, 47093}, {14531, 16252}, {14918, 44228}, {15055, 47337}, {15066, 44212}, {16238, 37484}, {17702, 47340}, {18378, 31831}, {19924, 44569}, {21167, 22112}, {21849, 37649}, {21969, 23292}, {23039, 44233}, {23061, 47316}, {26881, 41628}, {29317, 47095}, {31152, 37643}, {32225, 47097}, {32423, 47342}, {32455, 44109}, {34148, 44277}, {34664, 35254}, {35283, 40107}, {37488, 39871}, {37496, 44214}, {37645, 44456}, {37910, 41724}, {37913, 45968}, {37935, 43574}, {40341, 41424}, {41203, 44704}, {44555, 47313}

X(47582) = midpoint of X(i) and X(j) for these {i,j}: {3448, 37900}, {3580, 15107}, {37779, 46818}, {44555, 47313}
X(47582) = reflection of X(i) in X(j) for these {i,j}: {110, 37897}, {468, 32269}, {3292, 15448}, {10510, 47457}, {11064, 32223}, {43574, 37935}, {46517, 125}, {47097, 32225}, {47279, 41583}, {47311, 44569}
X(47582) = crosspoint of X(1494) and X(18840)
X(47582) = crosssum of X(1495) and X(30435)
X(47582) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {22, 41588, 11245}, {23, 37779, 46818}, {3098, 37648, 43957}, {7495, 11002, 18583}, {11064, 32223, 468}, {11064, 32269, 32223}, {15107, 15360, 3580}, {17810, 43653, 37439}, {21970, 33878, 2}, {31670, 37638, 427}, {33586, 37638, 31670}

X(47583) = X(30)X(24256)∩X(468)X(511)

Barycentrics 4*a^14*b^2 - 7*a^12*b^4 - a^10*b^6 + 6*a^8*b^8 - 2*a^6*b^10 + a^4*b^12 - a^2*b^14 + 4*a^14*c^2 - 8*a^12*b^2*c^2 - 4*a^10*b^4*c^2 - 5*a^8*b^6*c^2 + 22*a^6*b^8*c^2 - 8*a^4*b^10*c^2 - 2*a^2*b^12*c^2 + b^14*c^2 - 7*a^12*c^4 - 4*a^10*b^2*c^4 - 10*a^8*b^4*c^4 + 15*a^4*b^8*c^4 - 4*a^2*b^10*c^4 - 2*b^12*c^4 - a^10*c^6 - 5*a^8*b^2*c^6 - 24*a^4*b^6*c^6 + 7*a^2*b^8*c^6 - b^10*c^6 + 6*a^8*c^8 + 22*a^6*b^2*c^8 + 15*a^4*b^4*c^8 + 7*a^2*b^6*c^8 + 4*b^8*c^8 - 2*a^6*c^10 - 8*a^4*b^2*c^10 - 4*a^2*b^4*c^10 - b^6*c^10 + a^4*c^12 - 2*a^2*b^2*c^12 - 2*b^4*c^12 - a^2*c^14 + b^2*c^14 : :

X(47583) = 3 X[186] + X[18906], 3 X[2072] - 5 X[40332], X[3094] - 3 X[44214], X[3095] - 3 X[47455], 2 X[10007] - 3 X[44452]

X(47583) lies on these lines: {30, 24256}, {186, 18906}, {468, 511}, {2072, 40332}, {3094, 44214}, {3095, 47455}, {5969, 18579}, {9832, 31958}, {10007, 44452}

X(47584) = X(30)X(115)∩X(468)X(511)

Barycentrics 2*a^14 - 9*a^12*b^2 + 11*a^10*b^4 + a^8*b^6 - 10*a^6*b^8 + 7*a^4*b^10 - 3*a^2*b^12 + b^14 - 9*a^12*c^2 + 12*a^10*b^2*c^2 - 8*a^8*b^4*c^2 + 10*a^6*b^6*c^2 - 15*a^4*b^8*c^2 + 14*a^2*b^10*c^2 - 4*b^12*c^2 + 11*a^10*c^4 - 8*a^8*b^2*c^4 - 12*a^6*b^4*c^4 + 12*a^4*b^6*c^4 - 21*a^2*b^8*c^4 + 6*b^10*c^4 + a^8*c^6 + 10*a^6*b^2*c^6 + 12*a^4*b^4*c^6 + 20*a^2*b^6*c^6 - 3*b^8*c^6 - 10*a^6*c^8 - 15*a^4*b^2*c^8 - 21*a^2*b^4*c^8 - 3*b^6*c^8 + 7*a^4*c^10 + 14*a^2*b^2*c^10 + 6*b^4*c^10 - 3*a^2*c^12 - 4*b^2*c^12 + c^14 : :

X(47584) = 3 X[186] + X[43453], X[316] - 3 X[403], 3 X[468] - 2 X[16760], X[842] - 3 X[7426], X[858] - 3 X[38227], 2 X[6036] - 3 X[47240], 5 X[31275] - 6 X[44911], X[35002] - 3 X[44214], X[37950] - 3 X[38230]

X(47584) lies on these lines: {2, 15919}, {23, 13558}, {30, 115}, {186, 43453}, {316, 403}, {468, 511}, {512, 47002}, {842, 1302}, {858, 38227}, {2080, 11799}, {3849, 47332}, {6036, 47240}, {6785, 14389}, {6795, 7735}, {7493, 14687}, {7806, 15915}, {9752, 36163}, {9753, 9832}, {13449, 37984}, {14693, 15122}, {20423, 41939}, {30209, 47502}, {31275, 44911}, {32762, 37929}, {35002, 44214}, {36183, 37688}, {37950, 38230}, {46817, 47501}

X(47584) = midpoint of X(2080) and X(11799)
X(47584) = midpoint of X(47575) and X(47576)
X(47584) = reflection of X(i) in X(j) for these {i,j}: {13449, 37984}, {15122, 14693}

X(47585) = X(468)X(511)∩X(524)X(36180)

Barycentrics 2*a^12 + 5*a^10*b^2 - 14*a^8*b^4 + 3*a^6*b^6 + 11*a^4*b^8 - 8*a^2*b^10 + b^12 + 5*a^10*c^2 - 14*a^8*b^2*c^2 + 20*a^6*b^4*c^2 - 13*a^4*b^6*c^2 + 7*a^2*b^8*c^2 - b^10*c^2 - 14*a^8*c^4 + 20*a^6*b^2*c^4 - 12*a^4*b^4*c^4 + a^2*b^6*c^4 - b^8*c^4 + 3*a^6*c^6 - 13*a^4*b^2*c^6 + a^2*b^4*c^6 + 2*b^6*c^6 + 11*a^4*c^8 + 7*a^2*b^2*c^8 - b^4*c^8 - 8*a^2*c^10 - b^2*c^10 + c^12 : :

X(47585) = 3 X[1570] - 4 X[47460], 3 X[1691] - X[47280], 3 X[1692] - 2 X[47464], 3 X[2076] + X[47276], 3 X[5111] - 5 X[47458], X[8586] - 3 X[47455], 9 X[35006] - 5 X[47466], 4 X[38010] - X[47281], 2 X[44496] - 3 X[47459]

X(47585) lies on these lines: {468, 511}, {524, 36180}, {1570, 47460}, {1691, 47280}, {1692, 47464}, {2030, 47277}, {2076, 47276}, {3849, 47473}, {5099, 47449}, {5104, 32113}, {5107, 47457}, {5111, 47458}, {8586, 47455}, {8675, 47502}, {15360, 47349}, {35006, 47466}, {38010, 47281}, {44496, 47459}

X(47585) = midpoint of X(5104) and X(32113)
X(47585) = reflection of X(i) in X(j) for these {i,j}: {5099, 47449}, {5107, 47457}, {47277, 2030}

X(47586) = X(20)X(5485)∩X(76)X(3522)

X(47586) lies on Kiepert circumhyperbola and these lines: {2, 10541}, {4, 21309}, {20, 5485}, {76, 3522}, {83, 5068}, {262, 14930}, {383, 33605}, {459, 4232}, {468, 38253}, {598, 3832}, {671, 3146}, {1080, 33604}, {1446, 7268}, {1503, 43537}, {2996, 5059}, {3091, 18842}, {3523, 18840}, {3543, 32532}, {3854, 5395}, {5056, 18841}, {5189, 6504}, {5304, 43951}, {5503, 11177}, {5984, 8781}, {6776, 7608}, {6811, 43536}, {7000, 14226}, {7374, 14241}, {7408, 39284}, {10302, 15717}, {10513, 40824}, {17578, 41895}, {37460, 46105}, {37463, 43554}, {37464, 43555}

X(47586) = reflection of X(3543) in X(32532)
X(47586) = isotomic conjugate of the anticomplement of X(37689)
X(47586) = X(3)-vertex conjugate of-X(43537)
X(47586) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(7268)}} and Kiepert hyperbola
X(47586) = trilinear pole of the line {523, 47460}

X(47587) = ORTHIC AXIS INTERCEPT OF X(373)X(512)

X(47587) lies on these lines: {2, 8599}, {230, 231}, {373, 512}, {690, 31174}, {1316, 17964}, {1499, 37350}, {2793, 8644}, {3906, 9208}, {4108, 5466}, {5642, 35087}, {9185, 23878}, {9191, 30476}, {9485, 15724}

X(47587) = midpoint of X(i) and X(j) for these {i, j}: {2, 8599}, {4108, 5466}
X(47587) = reflection of X(i) in X(j) for these (i, j): (647, 9189), (9191, 30476)
X(47587) = orthic axis intercept of X(373)X(512)
X(47587) = crossdifference of every pair of points on line {X(3), X(352)}
X(47587) = X(2)-Ceva conjugate of-X(13994)
X(47587) = X(31)-complementary conjugate of-X(13994)
X(47587) = perspector of the circumconic {{A, B, C, X(4), X(6094)}}
X(47587) = intersection of orthic axes of ABC and anti-McCay triangle
X(47587) = barycentric product X(523)*X(11159)
X(47587) = trilinear product X(661)*X(11159)

X(47588) = ISOGONAL CONJUGATE OF X(34795)

X(47588) = isogonal conjugate of X(34795)
X(47588) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(6094)}} and {{A, B, C, X(64), X(9831)}}

X(47589) = X(4)X(575)∩X(546)X(46673)

Barycentrics 4*a^10+3*(b^2+c^2)*a^8-(55*b^4-32*b^2*c^2+55*c^4)*a^6+(b^2+c^2)*(43*b^4-106*b^2*c^2+43*c^4)*a^4+3*(b^2-c^2)^2*(5*b^4-4*b^2*c^2+5*c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(-10*b^4+28*b^2*c^2-10*c^4) : :

X(47589) lies on these lines: {4, 575}, {5, 47590}, {546, 46673}, {1499, 31749}, {3091, 13378}, {14866, 14867}, {19924, 45980}, {30516, 34792}, {31727, 31824}, {31744, 31827}, {38791, 40927}

X(47589) = midpoint of X(i) and X(j) for these {i, j}: {4, 31748}, {14866, 14867}, {31727, 31824}, {31744, 31827}
X(47589) = reflection of X(i) in X(j) for these (i, j): (46673, 546), (46732, 4)
X(47589) = {X(5),X(47590)}-harmonic conjugate of X(47592)
X(47589) = {X(5),X(47591)}-harmonic conjugate of X(47590)

X(47590) = X(20)X(31748)∩X(382)X(576)

Barycentrics 12*a^10-7*(b^2+c^2)*a^8-(125*b^4-112*b^2*c^2+125*c^4)*a^6+129*(b^4-c^4)*(b^2-c^2)*a^4+(5*b^8+5*c^8-2*(41*b^4-93*b^2*c^2+41*c^4)*b^2*c^2)*a^2-2*(b^4-c^4)*(b^2-c^2)*(7*b^4-22*b^2*c^2+7*c^4) : :

X(47590) = X(20)-3*X(31748), 4*X(3853)-3*X(46732), 11*X(3855)-9*X(13378), 4*X(3861)-3*X(46673)

X(47590) lies on these lines: {5, 47589}, {20, 31748}, {382, 576}, {3853, 46732}, {3855, 13378}, {3861, 46673}

X(47590) = reflection of X(47592) in X(5)
X(47590) = X(47592)-of-Johnson-triangle
X(47590) = {X(5),X(47591)}-harmonic conjugate of X(47589)
X(47590) = {X(47589),X(47592)}-harmonic conjugate of X(5)

X(47591) = X(382)X(31748)∩X(3843)X(46673)

Barycentrics 12*a^10+(b^2+c^2)*a^8-(145*b^4-104*b^2*c^2+145*c^4)*a^6+3*(b^2+c^2)*(43*b^4-96*b^2*c^2+43*c^4)*a^4+(25*b^8+25*c^8-2*b^2*c^2*(52*b^4-87*b^2*c^2+52*c^4))*a^2-2*(b^4-c^4)*(b^2-c^2)*(11*b^4-32*b^2*c^2+11*c^4) : :

X(47591) lies on these lines: {5, 47589}, {382, 31748}, {3843, 46673}, {3853, 9731}

X(47592) = X(20)X(11180)∩X(382)X(46732)

Barycentrics 12*a^10-23*(b^2+c^2)*a^8-(85*b^4-128*b^2*c^2+85*c^4)*a^6+3*(b^2+c^2)*(43*b^4-66*b^2*c^2+43*c^4)*a^4-(35*b^8+35*c^8+2*b^2*c^2*(19*b^4-105*b^2*c^2+19*c^4))*a^2+2*(b^4-c^4)^2*(b^2+c^2) : :

X(47592) = 2*X(382)-3*X(46732), 5*X(631)-3*X(31748), 7*X(3832)-9*X(13378), 2*X(3853)-3*X(46673)

X(47592) lies on these lines: {5, 47589}, {20, 11180}, {382, 46732}, {631, 31748}, {3832, 13378}, {3853, 46673}

X(47592) = reflection of X(47590) in X(5)
X(47592) = X(47590)-of-Johnson-triangle
X(47592) = {X(5),X(47590)}-harmonic conjugate of X(47589)

X(47593) = X(1)X(30)∩X(468)X(551)

Barycentrics 10*a^7 - 2*a^6*b - 13*a^5*b^2 - a^4*b^3 - 10*a^3*b^4 + 2*a^2*b^5 + 13*a*b^6 + b^7 - 2*a^6*c - a^4*b^2*c + 2*a^2*b^4*c + b^6*c - 13*a^5*c^2 - a^4*b*c^2 + 36*a^3*b^2*c^2 - 13*a*b^4*c^2 - b^5*c^2 - a^4*c^3 - b^4*c^3 - 10*a^3*c^4 + 2*a^2*b*c^4 - 13*a*b^2*c^4 - b^3*c^4 + 2*a^2*c^5 - b^2*c^5 + 13*a*c^6 + b*c^6 + c^7 : :

X(47593) = 2 X[858] + X[47489], 7 X[3622] - 3 X[37907], 4 X[5159] - X[47490], 2 X[5882] + X[47339], X[7426] - 3 X[38314], 3 X[10246] - X[44265], 3 X[10283] - X[44266], 3 X[25055] - X[47321], 5 X[30745] - X[31145], 2 X[37984] - 3 X[38021], 3 X[38023] - 2 X[47457], X[46517] + 2 X[47491]

X(47593) is the solution P of the equation T(P,X(1)) = X(2), where T is the transformation defined in the preamble just before X(47488)

X(47593) lies on these lines: {1, 30}, {2, 47488}, {10, 47494}, {468, 551}, {519, 47097}, {597, 47506}, {858, 3241}, {946, 47310}, {1125, 47496}, {1385, 47333}, {3622, 37907}, {3679, 5159}, {3828, 47492}, {5882, 47339}, {5901, 47334}, {7426, 38314}, {7984, 40112}, {8193, 37948}, {10246, 44265}, {10283, 44266}, {10297, 28204}, {11735, 44569}, {25055, 47321}, {30745, 31145}, {34152, 37546}, {37904, 47495}, {37984, 38021}, {38023, 47457}, {46517, 47491}, {47311, 47493}, {47357, 47470}

X(47593) = midpoint of X(i) and X(j) for these {i,j}: {858, 3241}, {7984, 40112}, {47311, 47493}
X(47593) = reflection of X(i) in X(j) for these {i,j}: {468, 551}, {3679, 5159}, {37904, 47495}, {44569, 11735}, {47310, 946}, {47333, 1385}, {47334, 5901}, {47469, 3655}, {47470, 47357}, {47472, 1}, {47488, 2}, {47489, 3241}, {47490, 3679}, {47492, 3828}, {47494, 10}, {47496, 1125}, {47506, 597}

X(47594) = X(230)X(231)∩X(7)X(8)

X(47595) = X(6)X(142)∩X(7)X(8)

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

X(47595) = 4 X[2] - 3 X[38088], 4 X[5] - 3 X[38145], 2 X[6] - 3 X[38186], 4 X[142] - 3 X[38186], 4 X[10] - 3 X[38190], 4 X[140] - 3 X[38117], X[144] - 5 X[3620], 2 X[182] - 3 X[38122], 2 X[597] - 3 X[38093], 4 X[1125] - 3 X[38048], X[1351] - 3 X[38107], X[1353] - 3 X[38111], 2 X[1386] - 3 X[38053], 4 X[3589] - 5 X[20195], 7 X[3619] - 5 X[18230], 4 X[3628] - 3 X[38166], 4 X[3634] - 3 X[38194], X[3751] - 3 X[38052], 5 X[3763] - 4 X[6666], 4 X[3826] - 3 X[38047], 4 X[3844] - 3 X[38057], 2 X[5480] - 3 X[38150], X[5759] - 3 X[10519], 3 X[5817] - 5 X[40330], X[6172] - 3 X[21356], 4 X[6667] - 3 X[38195], 4 X[6668] - 3 X[38196], X[6776] - 3 X[21151], X[11477] - 3 X[38143], X[15069] + 2 X[43177], X[15534] - 3 X[38086], 2 X[18583] - 3 X[38171], 4 X[24206] - 3 X[38108], 4 X[25557] - 3 X[38046]

X(47595) lies on these lines: {2, 2348}, {5, 38145}, {6, 142}, {7, 8}, {9, 141}, {10, 38190}, {78, 3665}, {140, 38117}, {144, 3620}, {182, 38122}, {193, 24599}, {390, 24723}, {511, 5805}, {516, 1350}, {524, 6173}, {527, 599}, {528, 17274}, {597, 38093}, {673, 3662}, {742, 4851}, {960, 17170}, {971, 1352}, {997, 1565}, {1001, 4357}, {1086, 16973}, {1111, 3419}, {1125, 38048}, {1351, 38107}, {1353, 38111}, {1376, 9436}, {1386, 3945}, {1503, 5732}, {1814, 37659}, {1836, 20347}, {1837, 21285}, {2886, 40719}, {3056, 40505}, {3242, 3663}, {3243, 5846}, {3254, 9024}, {3564, 31657}, {3589, 20195}, {3598, 24477}, {3618, 31189}, {3619, 17256}, {3628, 38166}, {3634, 38194}, {3674, 12635}, {3729, 4437}, {3742, 14548}, {3751, 4888}, {3763, 6666}, {3818, 31672}, {3826, 10436}, {3844, 5232}, {3879, 42871}, {4267, 16887}, {4657, 16503}, {4862, 16496}, {4872, 24703}, {4896, 38185}, {5223, 33165}, {5480, 38150}, {5542, 5847}, {5759, 10519}, {5817, 40330}, {5848, 10427}, {6172, 17342}, {6646, 20533}, {6667, 38195}, {6668, 38196}, {6706, 26036}, {6776, 21151}, {7181, 35262}, {7232, 24699}, {9053, 17151}, {10442, 29181}, {10452, 35892}, {10521, 24391}, {11038, 39567}, {11477, 38143}, {12586, 17668}, {12589, 14100}, {15069, 43177}, {15534, 38086}, {16972, 17392}, {17046, 46835}, {17181, 25681}, {17245, 36404}, {17276, 33869}, {17300, 27475}, {17321, 42819}, {17343, 27484}, {17728, 26229}, {18165, 30941}, {18482, 31670}, {18583, 38171}, {20335, 24694}, {20468, 24309}, {21044, 31135}, {24206, 38108}, {24213, 24389}, {24247, 44664}, {25050, 25279}, {25557, 38046}, {25590, 38200}, {26543, 39273}, {30615, 31130}, {30825, 40869}, {31671, 33878}, {33298, 37828}, {35514, 39898}

X(47595) = midpoint of X(i) and X(j) for these {i,j}: {7, 69}, {31671, 33878}, {35514, 39898}
X(47595) = reflection of X(i) in X(j) for these {i,j}: {6, 142}, {9, 141}, {31670, 18482}, {31672, 3818}
X(47595) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 142, 38186}, {4872, 30946, 24703}, {21285, 26563, 1837}

X(47596) = EULER LINE INTERCEPT OF X(110)X(599)

X(47596) = 2*X(2)+X(22), 5*X(2)-2*X(427), X(2)-4*X(6676), 7*X(2)-X(7391), 11*X(2)+X(20062), 4*X(2)-X(31133), 8*X(2)-5*X(31236), X(2)+2*X(44210), X(3)+2*X(44262), X(4)+2*X(44261), 5*X(22)+4*X(427), X(22)+8*X(6676), 7*X(22)+2*X(7391), 11*X(22)-2*X(20062), 3*X(22)+2*X(31105), 2*X(22)+X(31133), 4*X(22)+5*X(31236), X(22)-4*X(44210), 8*X(140)+X(12082), X(376)+2*X(15760)

X(47596) lies on these lines: {2, 3}, {6, 15360}, {110, 599}, {111, 37637}, {141, 35266}, {182, 32225}, {183, 7664}, {187, 9745}, {476, 11628}, {524, 13394}, {542, 6800}, {597, 32269}, {1302, 14388}, {1383, 15484}, {1495, 11178}, {1853, 6030}, {1992, 16789}, {1993, 44493}, {2453, 9158}, {2781, 7998}, {3098, 13857}, {3580, 11179}, {3589, 20192}, {3734, 10163}, {3763, 10546}, {3849, 11187}, {4108, 34291}, {5467, 11163}, {5640, 9019}, {5642, 15066}, {5913, 21843}, {5972, 21766}, {7610, 44420}, {7622, 9177}, {7665, 17004}, {7712, 18440}, {7735, 14836}, {7788, 26233}, {7811, 37804}, {7865, 15822}, {8588, 39602}, {9084, 33638}, {9140, 15080}, {9143, 26864}, {9172, 14662}, {9465, 18573}, {10130, 11058}, {10168, 32223}, {10418, 20481}, {10545, 47355}, {11002, 14848}, {11003, 44555}, {11180, 46818}, {11422, 15534}, {11645, 35268}, {14389, 20423}, {15018, 21970}, {15448, 20582}, {16644, 37776}, {16645, 37775}, {18911, 44569}, {20126, 32227}, {21356, 35260}, {21358, 35259}, {22240, 47228}, {22712, 33927}, {24206, 32267}, {25561, 32237}, {31166, 34177}, {39576, 44535}

X(47597) = EULER LINE INTERCEPT OF X(6)X(5642)

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

X(47597) = 2*X(2)+X(25), 5*X(2)-2*X(1368), 7*X(2)-X(1370), X(2)-4*X(6677), 11*X(2)+X(7500), 4*X(2)-X(31152), 8*X(2)-5*X(31255), X(2)+2*X(44212), X(3)+2*X(44275), X(4)+2*X(44273), 8*X(5)+X(37196), 5*X(25)+4*X(1368), 7*X(25)+2*X(1370), X(25)+8*X(6677), 11*X(25)-2*X(7500), 2*X(25)+X(31152), 4*X(25)+5*X(31255), X(25)-4*X(44212), X(376)+2*X(1596), X(381)+2*X(6644), 4*X(381)-X(44438)

X(47597) lies on these lines: {2, 3}, {6, 5642}, {125, 47353}, {182, 40114}, {230, 21448}, {373, 2393}, {524, 6090}, {542, 26869}, {597, 10602}, {599, 5651}, {1351, 40112}, {1352, 44569}, {1384, 5913}, {1495, 43273}, {1992, 8263}, {3066, 5476}, {3292, 15534}, {3818, 45311}, {5306, 40126}, {5640, 14848}, {5967, 9169}, {6055, 15928}, {7610, 9176}, {7665, 31859}, {7693, 21968}, {7703, 40920}, {7735, 16317}, {7737, 24855}, {8585, 37637}, {9140, 10546}, {9143, 39899}, {9155, 11165}, {9172, 14995}, {9306, 44490}, {9745, 15484}, {10603, 36889}, {11064, 20192}, {11178, 37638}, {11179, 26864}, {11180, 37643}, {11181, 14356}, {11188, 12099}, {11648, 40350}, {11693, 47391}, {11898, 44555}, {13394, 38064}, {13857, 34417}, {14685, 47220}, {15066, 15360}, {15355, 44467}, {15533, 41586}, {22329, 36207}, {25055, 44662}, {32111, 44750}, {33752, 44560}, {37775, 42975}, {37776, 42974}, {40879, 46998}, {44823, 45317}, {45141, 47187}, {47296, 47354}

X(47598) = EULER LINE INTERCEPT OF X(6)X(43513)

X(47598) = 11*X(2)+X(3), 7*X(2)-X(5), 2*X(2)+X(140), 13*X(2)-X(381), 16*X(2)-X(546), 4*X(2)-X(547), 20*X(2)+X(548), 5*X(2)+X(549), 19*X(2)+5*X(631), X(2)+5*X(632), 17*X(2)-5*X(1656), 7*X(2)+X(3524), 13*X(2)+11*X(3525), 5*X(2)+7*X(3526), 13*X(2)+2*X(3530), 7*X(2)+17*X(3533), 9*X(2)-X(3545), 5*X(2)-2*X(3628), 17*X(2)-X(3839), 19*X(2)-X(3845), 3*X(2)+X(5054), 5*X(2)-X(5055), 10*X(2)-X(5066), 17*X(2)+X(8703), 11*X(2)-2*X(10109), X(2)+2*X(10124), 15*X(2)+X(10304), 5*X(2)+4*X(11540), 17*X(2)-2*X(11737), 7*X(2)+2*X(11812), 8*X(2)+X(12100), 17*X(2)+4*X(12108), 5*X(2)+2*X(14890), 19*X(2)+2*X(14891), 8*X(2)-X(14892), 19*X(2)+X(15688), 7*X(2)+5*X(15694), 17*X(2)+7*X(15702), 19*X(2)-7*X(15703), 17*X(2)+3*X(15707), 13*X(2)+3*X(15708), 5*X(2)+3*X(15709), 13*X(2)+5*X(15713), X(2)+11*X(15723), X(2)-4*X(16239), 9*X(2)+X(17504), 15*X(2)-X(23046), 14*X(2)+X(34200), 19*X(2)-4*X(35018), 11*X(2)-X(38071), 16*X(2)+X(41982), 6*X(2)+X(41983), 18*X(2)-X(41987), 9*X(2)-2*X(45757), 3*X(2)+4*X(45758), 13*X(2)+X(45759), 11*X(2)+10*X(45760), X(2)-13*X(46219), 6*X(2)-X(47478)

X(47598) lies on these lines: {2, 3}, {6, 43513}, {230, 11614}, {395, 42595}, {396, 42594}, {397, 33607}, {398, 33606}, {590, 6436}, {615, 6435}, {1151, 43341}, {1152, 43340}, {1154, 15082}, {3582, 5326}, {3584, 7294}, {3589, 46114}, {3653, 38042}, {3656, 34595}, {3815, 14075}, {3828, 13607}, {5550, 34718}, {5642, 40685}, {5844, 25055}, {6417, 43506}, {6418, 43505}, {6453, 41951}, {6454, 41952}, {6498, 19053}, {6499, 19054}, {6688, 13451}, {7850, 37647}, {8252, 43254}, {8253, 43255}, {8981, 43431}, {9140, 13392}, {9167, 34127}, {9300, 34571}, {10165, 38083}, {10168, 34573}, {10171, 28202}, {10172, 28208}, {10187, 42419}, {10188, 42420}, {10219, 13364}, {10246, 38081}, {10283, 38066}, {11230, 38068}, {11231, 19883}, {11693, 32423}, {11694, 45311}, {12007, 20582}, {13363, 44324}, {13966, 43430}, {15059, 22250}, {15067, 16226}, {16267, 33416}, {16268, 33417}, {16772, 42591}, {16773, 42590}, {16960, 42636}, {16961, 42635}, {16962, 23303}, {16963, 23302}, {16966, 42501}, {16967, 42500}, {17502, 38076}, {18357, 31253}, {19872, 34773}, {19875, 38028}, {21358, 38110}, {21849, 32205}, {26446, 38022}, {32515, 41139}, {32787, 35814}, {32788, 35815}, {34380, 47352}, {34748, 46933}, {38067, 38171}, {38082, 38122}, {38084, 38760}, {38093, 38113}, {38112, 38314}, {41112, 42491}, {41113, 42490}, {41121, 42944}, {41122, 42945}, {41943, 42949}, {41944, 42948}, {42090, 42475}, {42091, 42474}, {42119, 43644}, {42120, 43649}, {42121, 42496}, {42122, 42795}, {42123, 42796}, {42124, 42497}, {42143, 42972}, {42146, 42973}, {42163, 43108}, {42166, 43109}, {42215, 43343}, {42216, 43342}, {42566, 42643}, {42567, 42644}, {42582, 43380}, {42583, 43381}, {42598, 42935}, {42599, 42934}, {42791, 43634}, {42792, 43635}, {42898, 42977}, {42899, 42976}, {42936, 43228}, {42937, 43229}, {42956, 43014}, {42957, 43015}, {43558, 43568}, {43559, 43569}

X(47599) = EULER LINE INTERCEPT OF X(13)X(43100)

X(47599) = 13*X(2)-X(3), 5*X(2)+X(5), 4*X(2)-X(140), 11*X(2)+X(381), 14*X(2)+X(546), 2*X(2)+X(547), 7*X(2)-X(549), 11*X(2)-5*X(632), 7*X(2)+5*X(1656), 17*X(2)+7*X(3090), 9*X(2)-X(3524), 19*X(2)-7*X(3526), 17*X(2)-2*X(3530), 7*X(2)+X(3545), X(2)+2*X(3628), 15*X(2)+X(3839), 17*X(2)+X(3845), 19*X(2)+2*X(3850), 5*X(2)-X(5054), 3*X(2)+X(5055), 8*X(2)+X(5066), 11*X(2)+13*X(5067), X(2)+11*X(5070), 19*X(2)+5*X(5071), 19*X(2)-X(8703), 7*X(2)+2*X(10109), 5*X(2)-2*X(10124), 17*X(2)-X(10304), 13*X(2)-4*X(11540), 13*X(2)+2*X(11737), 11*X(2)-2*X(11812), 10*X(2)-X(12100), 16*X(2)+5*X(12812), 19*X(2)+X(14269), 9*X(2)-2*X(14890), 6*X(2)+X(14892), 20*X(2)+X(14893), 17*X(2)-5*X(15694), 5*X(2)+7*X(15703), 19*X(2)-3*X(15708), 11*X(2)-3*X(15709), 7*X(2)-4*X(16239), 11*X(2)-X(17504), 13*X(2)+X(23046), 16*X(2)-X(34200), 11*X(2)+4*X(35018), 9*X(2)+X(38071), 18*X(2)-X(41982), 8*X(2)-X(41983), 19*X(2)+4*X(41986), 16*X(2)+X(41987), 5*X(2)+2*X(45757), 11*X(2)-4*X(45758), 15*X(2)-X(45759), 4*X(2)+X(47478)

X(47599) lies on these lines: {2, 3}, {13, 43100}, {14, 43103}, {17, 42591}, {18, 42590}, {371, 42573}, {372, 42572}, {395, 42627}, {396, 42628}, {590, 42557}, {615, 42558}, {952, 19883}, {3311, 42640}, {3312, 42639}, {3411, 42898}, {3412, 42899}, {3653, 28224}, {3655, 34595}, {3819, 13451}, {3828, 5901}, {5339, 43247}, {5340, 43246}, {5368, 9300}, {5690, 19876}, {5843, 38082}, {5844, 19875}, {5943, 44324}, {6200, 43790}, {6396, 43789}, {6431, 43558}, {6432, 43559}, {6437, 43343}, {6438, 43342}, {6439, 43792}, {6440, 43791}, {6441, 8253}, {6442, 8252}, {6476, 35255}, {6477, 35256}, {7988, 28216}, {8254, 15605}, {8981, 42603}, {10147, 43433}, {10148, 43432}, {10168, 18358}, {10171, 28198}, {10172, 28204}, {10187, 42506}, {10188, 42507}, {10219, 13363}, {10272, 45311}, {11230, 38127}, {11542, 16963}, {11543, 16962}, {11694, 20304}, {11695, 31834}, {12045, 13754}, {12046, 15644}, {12815, 39593}, {13391, 15082}, {13925, 32788}, {13966, 42602}, {13993, 32787}, {16241, 42143}, {16242, 42146}, {16267, 23303}, {16268, 23302}, {16644, 42497}, {16645, 42496}, {16966, 42913}, {16967, 42912}, {18357, 19878}, {18583, 20582}, {19872, 22791}, {19877, 34718}, {21358, 34380}, {21849, 32142}, {25055, 38042}, {26614, 36519}, {28174, 38068}, {28186, 38076}, {28212, 38021}, {32789, 43211}, {32790, 43212}, {33416, 42973}, {33417, 42972}, {34631, 46931}, {34748, 46934}, {37712, 38028}, {37832, 42895}, {37835, 42894}, {38081, 38314}, {38229, 41134}, {41119, 43239}, {41120, 43238}, {41121, 42924}, {41122, 42925}, {41943, 42599}, {41944, 42598}, {42087, 42594}, {42088, 42595}, {42101, 42498}, {42102, 42499}, {42121, 42911}, {42122, 42500}, {42123, 42501}, {42124, 42910}, {42129, 42492}, {42132, 42493}, {42164, 42596}, {42165, 42597}, {42215, 43254}, {42216, 43255}, {42488, 43229}, {42489, 43228}, {42625, 42889}, {42626, 42888}, {42635, 43199}, {42636, 43200}, {42686, 43240}, {42687, 43241}, {42692, 42914}, {42693, 42915}, {42786, 47354}, {42817, 42985}, {42818, 42984}, {42892, 43011}, {42893, 43010}, {42930, 43638}, {42931, 43643}, {42938, 42952}, {42939, 42953}, {42942, 44016}, {42943, 44015}, {42944, 43109}, {42945, 43108}, {42946, 43442}, {42947, 43443}, {42954, 43418}, {42955, 43419}, {42998, 43207}, {42999, 43208}, {43014, 43874}, {43015, 43873}, {43028, 43198}, {43029, 43197}

X(47600) = X(133)X(14249)∩X(1562)X(38976)

X(47600) lies on the nine-point circle and these lines: {133, 14249}, {1562, 38976}

X(47600) = reflection of X(47606) in X(5)
X(47600) = X(47606)-of-Johnson-triangle
X(47600) = point of tangency of nine-point circle and pedal circle of X(1075)
X(47600) = reflection of X(47606) in X(5)
X(47600) = X(47606)-of-Johnson-triangle
X(47600) = point of tangency of nine-point circle and pedal circle of X(1075)
X(47600) = center of the circumconic {{A, B, C, X(4), X(1075)}}

X(47601) = X(11)X(38985)∩X(12)X(3318)

X(47601) lies on the nine-point circle and these lines: {11, 38985}, {12, 3318}, {26956, 38969}

X(47601) = reflection of X(47607) in X(5)
X(47601) = X(47607)-of-Johnson-triangle
X(47601) = X(42)-complementary conjugate of-X(822)
X(47601) = center of the circumconic {{A, B, C, X(4), X(1148)}}

X(47602) = X(4)X(51)∩X(13855)X(14059)

X(47603) = X(4)X(13855)∩X(1075)X(14057)

X(47604) = X(4)X(3362)∩X(1745)X(14056)

X(47605) = X(1)X(4)∩X(3362)X(14058)

X(47606) = ANTIPODE OF X(47600) IN NINE-POINT CIRCLE

X(47606) lies on the nine-point circle and these lines: {5, 47600}, {122, 14059}

X(47606) = reflection of X(47600) in X(5)
X(47606) = X(47600)-of-Johnson-triangle
X(47606) = antipode of X(47600) in nine-point circle

X(47607) = ANTIPODE OF X(47601) IN NINE-POINT CIRCLE

X(47607) lies on the nine-point circle and these lines: {5, 47601}, {123, 26470}, {124, 14058}

X(47607) = reflection of X(47601) in X(5)
X(47607) = X(47601)-of-Johnson-triangle
X(47607) = antipode of X(47601) in nine-point circle

X(47608) = X(5)X(11538)∩X(110)X(10203)

Barycentrics 2*a^22-17*(b^2+c^2)*a^20+2*(31*b^4+47*b^2*c^2+31*c^4)*a^18-(b^2+c^2)*(123*b^4+71*b^2*c^2+123*c^4)*a^16+(132*b^8+132*c^8+(147*b^4+152*b^2*c^2+147*c^4)*b^2*c^2)*a^14-(b^2+c^2)*(42*b^8+42*c^8-(95*b^4-29*b^2*c^2+95*c^4)*b^2*c^2)*a^12-(84*b^12+84*c^12+(109*b^8+109*c^8+2*(29*b^4+22*b^2*c^2+29*c^4)*b^2*c^2)*b^2*c^2)*a^10+(b^2+c^2)*(138*b^12+138*c^12-(227*b^8+227*c^8-(166*b^4-217*b^2*c^2+166*c^4)*b^2*c^2)*b^2*c^2)*a^8-(b^2-c^2)^2*(102*b^12+102*c^12-(45*b^8+45*c^8+(86*b^4+103*b^2*c^2+86*c^4)*b^2*c^2)*b^2*c^2)*a^6+(b^4-c^4)*(b^2-c^2)^3*(43*b^8+43*c^8-7*(9*b^4-b^2*c^2+9*c^4)*b^2*c^2)*a^4-(b^2-c^2)^6*(10*b^8+10*c^8-7*(b^2+c^2)^2*b^2*c^2)*a^2+(b^2+c^2)*(b^2-c^2)^10 : :

X(47608) lies on these lines: {5, 11538}, {110, 10203}, {140, 6150}, {546, 31607}, {550, 34794}, {8703, 34793}, {10096, 32551}

X(47608) = midpoint of X(550) and X(34794)
X(47608) = reflection of X(546) in X(31607)
X(47608) = {X(14097), X(34577)}-harmonic conjugate of X(10227)

X(47609) = X(6)X(23)∩X(141)X(2482)

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

X(47609) = X(6)-3*X(353), 2*X(3589)-3*X(10166), 3*X(31884)-X(34795), 3*X(34512)-4*X(34573)

X(47609) lies on these lines: {5, 32150}, {6, 23}, {141, 2482}, {511, 31727}, {518, 31740}, {524, 47075}, {1350, 31962}, {1503, 31731}, {3589, 10166}, {5092, 14650}, {5480, 31608}, {6323, 12074}, {14867, 29181}, {29317, 31827}, {31884, 34795}, {34512, 34573}

X(47609) = midpoint of X(i) and X(j) for these {i, j}: {1350, 31962}, {31731, 31959}
X(47609) = reflection of X(i) in X(j) for these (i, j): (5, 32150), (5480, 31608)
X(47609) = X(141)-of-circumsymmedial-triangle

X(47610) = X(3)X(299)∩X(13)X(15)

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

X(47610) = 3*X(3)-X(616), 3*X(5)-4*X(6669), 3*X(5)-2*X(22796), 5*X(13)-3*X(25154), 2*X(140)-3*X(21156), 6*X(140)-5*X(36770), 2*X(140)+X(41020), 3*X(549)-2*X(618), X(616)+3*X(6770), X(3627)-4*X(20415), 4*X(3628)-3*X(36765), 2*X(5066)-3*X(22489), X(5617)-3*X(21156), 3*X(5617)-5*X(36770), 2*X(6669)-3*X(6771), 3*X(6771)-X(22796), 2*X(12100)+X(36383), 9*X(21156)-5*X(36770), 3*X(21156)+X(41020), 5*X(36770)+3*X(41020)

X(47610) lies on these lines: {3, 299}, {4, 20252}, {5, 6669}, {13, 15}, {14, 22847}, {20, 13103}, {98, 5978}, {115, 42117}, {140, 5617}, {141, 542}, {182, 33390}, {385, 46708}, {398, 22511}, {524, 6582}, {530, 8703}, {531, 33460}, {532, 36755}, {546, 36961}, {547, 41042}, {548, 5473}, {550, 33465}, {617, 12188}, {1503, 33388}, {2782, 25183}, {3627, 5478}, {3628, 36765}, {3642, 14880}, {3767, 10654}, {3845, 5459}, {5066, 22489}, {5306, 6108}, {5321, 46054}, {5463, 12100}, {5472, 42118}, {5479, 38229}, {5980, 11129}, {6033, 37351}, {6055, 6114}, {6115, 22892}, {6298, 13083}, {6644, 9916}, {6777, 23303}, {6778, 10645}, {6782, 42121}, {7792, 44219}, {9749, 33378}, {9862, 11299}, {9901, 18481}, {10062, 18990}, {10078, 15171}, {11078, 15768}, {11301, 18440}, {11302, 12017}, {11645, 45879}, {11705, 22791}, {11812, 36363}, {12054, 37341}, {12142, 37458}, {12952, 15325}, {13102, 14651}, {13350, 25559}, {14170, 32461}, {14830, 14904}, {15686, 32907}, {15687, 35019}, {15690, 35752}, {15693, 36318}, {15695, 35749}, {15701, 36344}, {15704, 16001}, {15711, 36769}, {15759, 35751}, {15764, 33440}, {15765, 33361}, {15769, 40855}, {16530, 16773}, {16964, 22846}, {18585, 33358}, {19711, 36768}, {20253, 38224}, {21157, 22507}, {21850, 42633}, {23006, 42123}, {32521, 33466}, {33380, 44382}, {33392, 34551}, {33394, 34552}, {35725, 35729}, {35753, 42259}, {35754, 42258}, {36767, 44580}, {36771, 42627}, {36782, 42945}, {41631, 42634}, {42147, 46855}

X(47610) = midpoint of X(i) and X(j) for these {i, j}: {3, 6770}, {20, 13103}, {617, 12188}, {5463, 36383}, {5617, 41020}, {9901, 18481}
X(47610) = reflection of X(i) in X(j) for these (i, j): (4, 20252), (5, 6771), (3627, 5478), (3845, 5459), (5463, 12100), (5473, 548), (5478, 20415), (5617, 140), (22791, 11705), (22796, 6669), (36961, 546), (41042, 547), (47611, 12042)
X(47610) = X(6770)-of-anti-X3-ABC reflections triangle
X(47610) = X(20252)-of-anti-Euler triangle
X(47610) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (619, 5092, 549), (5617, 21156, 140), (6669, 22796, 5), (6771, 22796, 6669), (11078, 41472, 15768), (21156, 41020, 5617)

X(47611) = X(3)X(298)∩X(14)X(16)

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

X(47611) = 3*X(3)-X(617), 3*X(5)-4*X(6670), 3*X(5)-2*X(22797), 5*X(14)-3*X(25164), 2*X(140)-3*X(21157), 2*X(140)+X(41021), 3*X(549)-2*X(619), X(617)+3*X(6773), X(3627)-4*X(20416), 2*X(5066)-3*X(22490), 2*X(5478)-3*X(38229), X(5613)-3*X(21157), X(6299)-3*X(13084), 2*X(6670)-3*X(6774), 3*X(6774)-X(22797), 4*X(11812)-X(36362), 2*X(12100)+X(36382), X(13103)-3*X(14651), X(15686)+2*X(32909), 3*X(21157)+X(41021)

X(47611) lies on these lines: {3, 298}, {4, 20253}, {5, 6670}, {13, 22893}, {14, 16}, {20, 13102}, {98, 5979}, {115, 42118}, {140, 5613}, {141, 542}, {182, 33391}, {385, 46709}, {397, 22510}, {524, 6295}, {530, 33461}, {531, 8703}, {533, 36756}, {546, 36962}, {547, 41043}, {548, 5474}, {550, 33464}, {616, 12188}, {1503, 33389}, {2782, 25187}, {3627, 5479}, {3643, 14880}, {3767, 10653}, {3845, 5460}, {5066, 22490}, {5306, 6109}, {5318, 46053}, {5464, 12100}, {5471, 42117}, {5478, 38229}, {5981, 11128}, {6033, 37352}, {6055, 6115}, {6114, 22848}, {6299, 13084}, {6644, 9915}, {6777, 10646}, {6778, 23302}, {6783, 42124}, {9750, 33379}, {9862, 11300}, {10061, 18990}, {10077, 15171}, {11092, 15769}, {11301, 12017}, {11302, 18440}, {11645, 45880}, {11706, 22791}, {11812, 36362}, {12054, 37340}, {12141, 37458}, {12951, 15325}, {13103, 14651}, {13349, 25560}, {14169, 32460}, {14830, 14905}, {15686, 32909}, {15687, 35020}, {15690, 36330}, {15693, 36320}, {15695, 36327}, {15701, 36319}, {15704, 16002}, {15759, 36329}, {15764, 33443}, {15765, 33360}, {15768, 40854}, {16529, 16772}, {16965, 22891}, {18585, 33359}, {20252, 38224}, {21156, 22509}, {21850, 42634}, {23013, 42122}, {32521, 33467}, {33381, 44383}, {33393, 34551}, {33395, 34552}, {33450, 35748}, {35726, 35729}, {35850, 42259}, {35851, 42258}, {41641, 42633}, {42148, 46854}, {43460, 44219}

X(47611) = midpoint of X(i) and X(j) for these {i, j}: {3, 6773}, {20, 13102}, {616, 12188}, {5464, 36382}, {5613, 41021}
X(47611) = reflection of X(i) in X(j) for these (i, j): (4, 20253), (5, 6774), (3627, 5479), (3845, 5460), (5464, 12100), (5474, 548), (5479, 20416), (5613, 140), (22791, 11706), (22797, 6670), (36962, 546), (41043, 547), (47610, 12042)
X(47611) = X(6773)-of-anti-X3-ABC reflections triangle
X(47611) = X(20253)-of-anti-Euler triangle
X(47611) = (22848)-of-outer-Fermat triangle
X(47611) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (618, 5092, 549), (5613, 21157, 140), (6670, 22797, 5), (6774, 22797, 6670), (11092, 41473, 15769), (21157, 41021, 5613)

X(47612) = COMPLEMENT OF X(5000)

X(47612) lies on these lines: {2, 3}, {230, 41196}, {325, 42811}, {3564, 32618}, {3815, 41197}, {37688, 42812}

X(47612) = complement of X(5000)
X(47612) = complementary conjugate of the complement of X(32618)
X(47612) = crosspoint of X(2) and X(42811)
X(47612) = crosssum of X(6) and X(44778)

X(47613) = COMPLEMENT OF X(5001)

X(47613) lies on these lines: {2, 3}, {230, 41197}, {325, 42812}, {3564, 32619}, {3815, 41196}, {37688, 42811}

X(47613) = complement of X(5001)
X(47613) = complementary conjugate of the complement of X(32619)
X(47613) = crosspoint of X(2) and X(42812)
X(47613) = crosssum of X(6) and X(44779)

X(47614) = POINT WITH EULER COORDINATES ((E - 8F) S / (E+F), 0) = (4*J^2*R^2*S/SW, 0)

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

X(47614) = 2 X[6560] - 3 X[47459], 4 X[42215] - 3 X[47463], 4 X[42216] - 5 X[47461], 4 X[42225] - X[47281], 2 X[42275] + X[47279], 2 X[42276] - 5 X[47456]

X(47614) lies on these lines: {2, 3}, {6560, 47459}, {6561, 47277}, {42215, 47463}, {42216, 47461}, {42225, 47281}, {42264, 47457}, {42275, 47279}, {42276, 47456}

X(47614) = reflection of X(i) in X(j) for these {i,j}: {42264, 47457}, {47277, 6561}, {47615, 468}

X(47615) = POINT WITH EULER COORDINATES (- (E - 8F) S / (E+F), 0) = (-4*J^2*R^2*S/SW, 0)

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

X(47615) = 2 X[6561] - 3 X[47459], 4 X[42215] - 5 X[47461], 4 X[42216] - 3 X[47463], 4 X[42226] - X[47281], 2 X[42275] - 5 X[47456], 2 X[42276] + X[47279]

X(47615) lies on these lines: {2, 3}, {6560, 47277}, {6561, 47459}, {42215, 47461}, {42216, 47463}, {42226, 47281}, {42263, 47457}, {42275, 47456}, {42276, 47279}

X(47615) = reflection of X(i) in X(j) for these {i,j}: {42263, 47457}, {47277, 6560}, {47614, 468}

X(47616) = X(4)X(524)∩X(5)X(525)

Barycentrics a^8*b^2 - 5*a^6*b^4 + 6*a^4*b^6 - a^2*b^8 - b^10 + a^8*c^2 + 6*a^6*b^2*c^2 - 5*a^4*b^4*c^2 - 8*a^2*b^6*c^2 + 6*b^8*c^2 - 5*a^6*c^4 - 5*a^4*b^2*c^4 + 18*a^2*b^4*c^4 - 5*b^6*c^4 + 6*a^4*c^6 - 8*a^2*b^2*c^6 - 5*b^4*c^6 - a^2*c^8 + 6*b^2*c^8 - c^10 : :

X(47616) lies on these lines: {4, 524}, {5, 525}, {140, 33509}, {698, 18304}, {1640, 32525}, {1975, 11064}, {2394, 18122}, {3589, 6794}, {5181, 5969}, {7422, 13468}, {13881, 47296}, {14999, 32819}, {22265, 32233}

X(47617) = X(2)X(7748)∩X(3)X(1153)

X(47617) = 2 X[3] - 3 X[1153], X[3] - 3 X[7617], X[4] + 3 X[7615], 2 X[4] + X[7780], 6 X[7615] - X[7780], 5 X[5] - 3 X[9771], 7 X[5] - 3 X[12040], X[5] - 3 X[20112], 7 X[9771] - 5 X[12040], X[9771] - 5 X[20112], X[12040] - 7 X[20112], X[20] - 3 X[5569], 4 X[34506] - 3 X[46893], 3 X[381] - X[7775], 5 X[381] - X[9766], 3 X[381] + X[34505], 5 X[7775] - 3 X[9766], X[7775] + 3 X[18546], X[9766] + 5 X[18546], 3 X[9766] + 5 X[34505], 3 X[18546] - X[34505], X[382] + 3 X[7610], 4 X[546] - X[7843], X[550] - 3 X[15597], 5 X[1656] - 3 X[7622], 7 X[3090] - 3 X[7618], 5 X[3091] + 3 X[7620], 5 X[3091] - 3 X[8176], 35 X[3091] - 3 X[11148], 5 X[3091] - X[34511], 7 X[7620] + X[11148], 3 X[7620] + X[34511], 7 X[8176] - X[11148], 3 X[8176] - X[34511], 3 X[11148] - 7 X[34511], X[3146] + 3 X[8182], X[3627] + 3 X[16509], 4 X[3628] - 3 X[7619], 7 X[3832] - X[7759], 5 X[3843] + X[7751], 5 X[3843] + 3 X[40727], X[7751] - 3 X[40727], 4 X[3850] - X[7764], 7 X[3851] - X[7781], 7 X[3851] - 3 X[11184], X[7781] - 3 X[11184], 11 X[3855] - 3 X[9770], 11 X[5072] - 3 X[11165], 3 X[5485] + X[7758], 3 X[7606] - 2 X[20190], X[8667] + 3 X[14269], X[8716] - 5 X[19709], X[14023] + 3 X[23334], 2 X[22330] - 3 X[42536]

X(47617) lies on these lines: {2, 7748}, {3, 1153}, {4, 3849}, {5, 543}, {20, 5569}, {30, 34506}, {32, 11317}, {39, 671}, {76, 31173}, {99, 39601}, {115, 5939}, {148, 7603}, {381, 538}, {382, 7610}, {384, 9166}, {524, 546}, {550, 15597}, {575, 9830}, {598, 5007}, {599, 7825}, {625, 7801}, {626, 37350}, {736, 22681}, {754, 3845}, {1003, 18362}, {1078, 8597}, {1656, 7622}, {2482, 32819}, {3090, 7618}, {3091, 7620}, {3146, 8182}, {3363, 5254}, {3543, 47101}, {3552, 5215}, {3627, 16509}, {3628, 7619}, {3734, 11318}, {3788, 32984}, {3832, 7759}, {3843, 7751}, {3850, 7764}, {3851, 7781}, {3855, 9770}, {3934, 7841}, {4045, 8367}, {5047, 7621}, {5072, 11165}, {5077, 7815}, {5206, 8860}, {5309, 33016}, {5461, 7886}, {5475, 32457}, {5485, 7758}, {5969, 25561}, {6655, 15810}, {6658, 26613}, {6683, 44518}, {7606, 20190}, {7746, 33007}, {7747, 22329}, {7749, 8598}, {7752, 39785}, {7769, 8591}, {7785, 11054}, {7789, 8355}, {7805, 7812}, {7807, 14971}, {7809, 14711}, {7810, 7842}, {7821, 32993}, {7827, 16044}, {7830, 11168}, {7844, 33237}, {7849, 14063}, {7854, 32996}, {7863, 41133}, {7870, 32966}, {7873, 14062}, {7880, 33228}, {7883, 9466}, {7902, 47352}, {7915, 8360}, {8667, 14269}, {8716, 19709}, {8859, 14042}, {9167, 33249}, {9855, 15513}, {9880, 37345}, {10150, 32961}, {11159, 13881}, {11163, 32450}, {11164, 33233}, {11645, 40279}, {11648, 44543}, {13468, 15687}, {14023, 23334}, {14160, 32515}, {14537, 14568}, {14645, 47354}, {14762, 16924}, {16042, 42008}, {19570, 41750}, {22330, 42536}, {22491, 37825}, {22492, 37824}, {22575, 37333}, {22576, 37332}, {23234, 38228}, {31406, 41147}, {31457, 33009}, {31652, 32480}, {32832, 33192}, {32967, 41134}, {32985, 43620}, {32990, 41895}, {33017, 40344}, {33476, 37341}, {33477, 37340}, {43457, 47286}

X(47617) = midpoint of X(i) and X(j) for these {i,j}: {381, 18546}, {3543, 47101}, {7620, 8176}, {7775, 34505}, {13468, 15687}
X(47617) = reflection of X(1153) in X(7617)
X(47617) = complement of X(34504)
X(47617) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {115, 8370, 7817}, {381, 34505, 7775}, {671, 15031, 33013}, {671, 33013, 39}, {3091, 7620, 34511}, {3091, 34511, 8176}, {5461, 8369, 7886}, {7775, 18546, 34505}, {7801, 18424, 33006}, {7801, 33006, 625}, {7810, 8352, 7842}, {7817, 8370, 7804}, {11185, 18424, 625}, {11185, 33006, 7801}, {11648, 44543, 44562}, {16044, 41135, 7827}

X(47618) = X(3)X(6)∩X(4)X(7897)

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

X(47618) = 5 X[3] - 4 X[187], 3 X[3] - 2 X[2080], 3 X[3] - 4 X[18860], 7 X[3] - 6 X[38225], 9 X[3] - 8 X[47113], 10 X[182] - 9 X[35006], 6 X[187] - 5 X[2080], 8 X[187] - 5 X[9301], 3 X[187] - 5 X[18860], 2 X[187] - 5 X[35002], 14 X[187] - 15 X[38225], 9 X[187] - 10 X[47113], 2 X[1350] - 3 X[35456], 5 X[1351] - 6 X[5111], X[1351] - 3 X[35458], 3 X[2076] - 4 X[14810], 4 X[2080] - 3 X[9301], X[2080] - 3 X[35002], 7 X[2080] - 9 X[38225], 3 X[2080] - 4 X[47113], 9 X[5085] - 8 X[8590], 2 X[5111] - 5 X[35458], 3 X[9301] - 8 X[18860], X[9301] - 4 X[35002], 7 X[9301] - 12 X[38225], 9 X[9301] - 16 X[47113], 2 X[18860] - 3 X[35002], 14 X[18860] - 9 X[38225], 3 X[18860] - 2 X[47113], 7 X[35002] - 3 X[38225], 9 X[35002] - 4 X[47113], 27 X[38225] - 28 X[47113], 4 X[325] - 3 X[38743], 8 X[625] - 7 X[3851], 2 X[691] - 3 X[18859], 3 X[2070] - 4 X[38613], 7 X[3523] - 6 X[38230], 7 X[3526] - 6 X[38227], 3 X[3830] - 4 X[13449], 3 X[5207] - 2 X[39884], 9 X[5054] - 8 X[14693], 2 X[6781] - 3 X[38731], 3 X[7809] - 2 X[22505], 3 X[10242] - 2 X[39809], 3 X[14269] - 4 X[31173], 7 X[15700] - 6 X[26613], 4 X[15980] - 3 X[38732], 8 X[32456] - 9 X[38635], 5 X[37958] - 6 X[38704]

X(47618) lies on these lines: {3, 6}, {4, 7897}, {5, 7931}, {30, 147}, {110, 6660}, {316, 382}, {323, 37916}, {325, 38743}, {376, 34682}, {384, 13111}, {546, 17128}, {550, 7762}, {625, 3851}, {691, 18859}, {754, 38741}, {755, 2709}, {842, 12074}, {1003, 10334}, {2070, 38613}, {2705, 28485}, {3314, 40250}, {3523, 38230}, {3526, 38227}, {3830, 13449}, {3849, 8716}, {3933, 5207}, {5054, 14693}, {5103, 7795}, {5148, 7373}, {5152, 39093}, {5191, 23061}, {5194, 6767}, {5999, 12188}, {6234, 35399}, {6287, 7794}, {6781, 38731}, {7464, 38582}, {7470, 32448}, {7809, 22505}, {7813, 29012}, {8724, 19924}, {9019, 9145}, {9155, 15107}, {10242, 39809}, {10353, 13586}, {11003, 46546}, {11328, 33873}, {11673, 21766}, {11674, 32444}, {14269, 31173}, {14981, 29317}, {15700, 26613}, {15980, 38732}, {20854, 36212}, {22503, 22728}, {32456, 38635}, {32520, 39646}, {32521, 37334}, {35925, 44434}, {37461, 41137}, {37958, 38704}

X(47618) = reflection of X(i) in X(j) for these {i,j}: {3, 35002}, {382, 316}, {2080, 18860}, {5611, 14539}, {5615, 14538}, {9301, 3}, {12188, 5999}, {14712, 550}, {22728, 22503}, {37924, 842}, {38582, 7464}, {43453, 5}
X(47618) = circumcircle-inverse of X(14810)
X(47618) = Stammler-circle-inverse of X(1350)
X(47618) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 11842}, {187, 5111, 30435}, {187, 7772, 35006}, {1379, 1380, 14810}, {2080, 18860, 3}, {2080, 35002, 18860}, {3095, 11171, 44423}, {3095, 30270, 3}, {3098, 11171, 3}, {9155, 15107, 37914}, {9737, 9821, 3}, {35248, 37479, 3}, {38596, 38597, 1350}

X(47619) = X(3)X(6)∩X(4)X(4048)

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

X(47619) = 3 X[3] - 2 X[35375], X[6] + 2 X[35002], 4 X[182] - 3 X[35006], X[1350] - 4 X[18860], 4 X[1570] - 3 X[5102], 2 X[1691] - 3 X[5085], 3 X[2076] - 4 X[35375], X[2076] + 2 X[35458], 3 X[5050] - 2 X[35377], 4 X[5092] - X[9301], X[15514] + 2 X[35456], 3 X[31884] - 2 X[35383], 2 X[35375] + 3 X[35458], 4 X[3589] - X[43453], 4 X[5031] - 3 X[10516]

X(47619) lies on these lines: {3, 6}, {4, 4048}, {5, 24273}, {22, 33873}, {98, 732}, {141, 37334}, {147, 325}, {262, 42534}, {384, 5480}, {394, 2001}, {698, 38654}, {827, 2710}, {1297, 46970}, {2700, 28486}, {3589, 43453}, {5026, 38383}, {5031, 7778}, {6033, 29012}, {6660, 36213}, {7467, 10329}, {7470, 12252}, {7485, 11673}, {7774, 25406}, {7792, 37455}, {7796, 15069}, {8177, 12251}, {8290, 40236}, {8295, 39093}, {8550, 13571}, {9467, 36214}, {9766, 43273}, {10353, 10997}, {10998, 46307}, {11286, 38072}, {11413, 32529}, {11676, 29181}, {14853, 35925}, {16010, 38653}, {18583, 44224}, {29317, 38738}, {46284, 46286}

X(47619) = midpoint of X(i) and X(j) for these {i,j}: {3, 35458}, {2456, 35002}, {5999, 12215}
X(47619) = reflection of X(i) in X(j) for these {i,j}: {4, 5103}, {6, 2456}, {2076, 3}, {11477, 5111}
X(47619) = circumcircle-inverse of X(5188)
X(47619) = 2nd-Lemoine-circle-inverse of X(44499)
X(47619) = isogonal conjugate of the anticomplement of X(39096)
X(47619) = X(46310)-Ceva conjugate of X(6)
X(47619) = barycentric product X(39096)*X(46310)
X(47619) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 35424}, {3, 43155, 1151}, {3, 43156, 1152}, {182, 3095, 6}, {1351, 44507, 6}, {1379, 1380, 5188}, {1666, 1667, 44499}, {9737, 13355, 3094}, {13335, 35439, 12212}, {38720, 38721, 18860}

X(47620) = X(2)X(3)∩X(74)X(805)

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

X(47620) = 3 X[3] - 2 X[44221], 3 X[237] - 4 X[44221], 3 X[2071] - X[7468], 5 X[3522] - X[46518], 3 X[3524] - 2 X[44215]

X(47620) lies on these lines: {2, 3}, {74, 805}, {511, 20975}, {512, 684}, {1294, 6394}, {1503, 1634}, {2080, 9218}, {2387, 30270}, {2781, 3001}, {2790, 3260}, {3095, 5890}, {3098, 22062}, {3331, 11672}, {3398, 15033}, {5188, 36987}, {5191, 10564}, {5938, 12168}, {6000, 36212}, {6403, 30262}, {9155, 14915}, {9407, 15462}, {9475, 14961}, {9737, 15429}, {12042, 32518}, {12058, 13409}, {13352, 34396}, {20775, 46264}, {20794, 39874}, {23635, 37511}, {31670, 40981}, {33801, 35228}, {34146, 44716}

X(47620) = anticomplement of X(44227)
X(47620) = midpoint of X(20) and X(14957)
X(47620) = reflection of X(i) in X(j) for these {i,j}: {4, 21531}, {237, 3}
X(47620) = crossdifference of every pair of points on line {647, 7735}
X(47620) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1597, 37344}, {3, 6660, 186}, {3, 31952, 4}, {3, 32444, 2}, {3, 35934, 14096}, {237, 45900, 46522}, {2071, 37183, 3}, {42789, 42790, 419}

X(47621) = X(1)X(7)∩X(103)X(517)

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

X(47621) lies on these lines: {1, 7}, {3, 5011}, {4, 5074}, {30, 35110}, {103, 517}, {104, 39640}, {109, 41339}, {165, 28125}, {220, 5779}, {514, 44827}, {910, 38690}, {936, 5199}, {971, 6603}, {1212, 31658}, {1530, 10727}, {1536, 17044}, {1936, 43047}, {2340, 5531}, {2688, 36516}, {2700, 6011}, {2717, 28291}, {2723, 29067}, {2736, 28848}, {3576, 5144}, {4658, 9943}, {5179, 5720}, {5184, 9441}, {5723, 37374}, {5759, 42050}, {6510, 15726}, {6909, 34056}, {13329, 43065}, {25930, 31042}, {35293, 44425}

X(47621) = midpoint of X(i) and X(j) for these {i,j}: {1, 5527}, {20, 5195}
X(47621) = reflection of X(i) in X(j) for these {i,j}: {4, 5074}, {1536, 17044}, {5011, 3}, {10727, 1530}, {18328, 5179}, {38666, 6603}
X(47621) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11200, 18473, 1}, {31563, 31564, 43178}

X(47622) = X(1)X(2)∩X(106)X(517)

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

X(47622) = 5 X[1] + X[5524], 3 X[1] + X[5529], 2 X[1] + X[45763], 3 X[3582] - 2 X[16338], 3 X[5524] - 5 X[5529], 2 X[5524] - 5 X[45763], 2 X[5529] - 3 X[45763]

X(47622) lies on these lines: {1, 2}, {40, 31979}, {58, 20323}, {104, 35186}, {106, 517}, {109, 1319}, {222, 1388}, {595, 24928}, {758, 11717}, {1191, 23071}, {1279, 25405}, {1320, 1739}, {1459, 3667}, {1482, 3445}, {2098, 24046}, {3579, 15854}, {3756, 5844}, {3880, 10700}, {3898, 37617}, {3953, 5330}, {4256, 5919}, {4653, 10179}, {4695, 41702}, {5011, 9259}, {5697, 32577}, {6126, 11720}, {7262, 8666}, {10246, 16486}, {10306, 15663}, {12740, 45272}, {15178, 35233}, {16784, 17439}, {31792, 33771}

X(47622) = reflection of X(2718) in X(1319)
X(47622) = isogonal conjugate of X(6095)
X(47622) = X(1)-isoconjugate of X(6095)
X(47622) = X(3)-Dao conjugate of X(6095)
X(47622) = barycentric quotient X(6)/X(6095)
X(47622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1149, 30117}, {1, 1201, 15955}, {1, 21214, 22837}, {24928, 45219, 595}

X(47623) = X(1)X(2)∩X(106)X(758)

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

X(47623) lies on the cubic K913 and these lines: {1, 2}, {36, 23205}, {56, 4650}, {105, 2705}, {106, 758}, {110, 2718}, {214, 40091}, {238, 1319}, {392, 846}, {517, 1054}, {518, 1052}, {663, 3667}, {902, 4881}, {982, 5289}, {999, 22149}, {1046, 5563}, {1318, 4674}, {1320, 4695}, {1385, 3073}, {1397, 1420}, {1457, 5018}, {1482, 24174}, {1575, 4919}, {1707, 13462}, {1721, 46957}, {2098, 24440}, {2099, 17063}, {2726, 18786}, {2743, 38452}, {2748, 9109}, {3445, 12635}, {3509, 9259}, {3550, 35262}, {3576, 5197}, {3750, 10179}, {3756, 5855}, {3869, 32577}, {3877, 17596}, {3880, 13541}, {3898, 4256}, {3976, 5730}, {4694, 4867}, {5048, 16610}, {5247, 24928}, {5255, 17614}, {5315, 5429}, {5330, 24443}, {5434, 33096}, {5603, 17889}, {5844, 26727}, {5901, 24161}, {7262, 11194}, {7312, 28558}, {7963, 7991}, {7982, 11512}, {7987, 8647}, {8056, 11224}, {11531, 45047}, {11533, 37592}, {11707, 36940}, {11708, 36941}, {11814, 36926}, {13464, 24178}, {15829, 15839}, {15950, 33130}, {16486, 17715}, {17439, 33854}, {18201, 44663}, {24398, 46180}, {33103, 34647}, {34195, 46190}, {37588, 45219}

X(47623) = midpoint of X(1) and X(5529)
X(47623) = reflection of X(i) in X(j) for these {i,j}: {5524, 5529}, {5529, 45763}, {9282, 238}, {36926, 11814}
X(47623) = incircle-inverse of X(6738)
X(47623) = orthoptic-circle-of-Steiner-inellipse-inverse of X(24239)
X(47623) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(29840)
X(47623) = psi-transform of X(17596)
X(47623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 995, 29821}, {1, 997, 3961}, {1, 16569, 3872}, {1, 45763, 5524}, {1, 46943, 5272}, {392, 37617, 846}, {1149, 4511, 1}, {5272, 46943, 21214}

X(47624) = X(1)X(2)∩X(59)X(4076)

X(47624) lies on these lines: {1, 2}, {59, 4076}, {110, 2757}, {193, 41780}, {341, 37738}, {515, 17777}, {944, 19582}, {952, 36926}, {1311, 2705}, {3476, 32937}, {3667, 31291}, {3699, 38455}, {3784, 3869}, {3992, 7972}, {4388, 5289}, {4449, 20293}, {5048, 32850}, {6079, 38452}, {18743, 37740}, {37727, 46937}

X(47624) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(3705)
X(47624) = incircle-of-anticomplementary-triangle-inverse of X(6736)

X(47625) = X(1)X(2)∩X(23)X(5168)

X(47625) lies on the Parry circle and these lines: {1, 2}, {23, 5168}, {110, 902}, {111, 2705}, {500, 9959}, {518, 17476}, {741, 2651}, {2605, 9508}, {3667, 9147}, {7113, 17735}

X(47626) = X(1)X(2)∩X(106)X(740)

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

X(47626) lies on these lines: {1, 2}, {36, 4742}, {99, 2718}, {105, 2759}, {106, 740}, {321, 37602}, {999, 5695}, {1387, 4966}, {1757, 34587}, {2726, 8691}, {3245, 24593}, {3898, 14829}, {3936, 16173}, {4645, 21630}, {4702, 5126}, {16490, 46897}, {26240, 33936}, {32929, 37587}, {36974, 37722}

X(47626) = reflection of X(i) in X(j) for these {i,j}: {5211, 23869}, {5524, 6789}

X(47627) = MIDPOINT OF X(23) AND X(6563)

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

X(47627) = 3 X[468] - 2 X[41357], 3 X[2501] - 4 X[41357], X[2501] - 4 X[47217], 2 X[6587] - 3 X[47251], 3 X[9209] - 4 X[47249], X[12077] - 3 X[47255], X[16230] - 3 X[47221], X[41357] - 3 X[47217], X[47004] - 3 X[47219], X[47122] + 2 X[47216], 3 X[403] - 2 X[39533], X[33294] - 3 X[47263]

X(47627) lies on these lines: {4, 9168}, {23, 6563}, {24, 8151}, {25, 11123}, {110, 525}, {136, 5099}, {186, 5926}, {230, 231}, {297, 47324}, {403, 39533}, {427, 10190}, {669, 21284}, {1499, 10295}, {1649, 5094}, {2770, 3563}, {2799, 47442}, {4232, 44010}, {8029, 37453}, {8723, 44080}, {9123, 44427}, {9131, 47325}, {10018, 10279}, {10280, 14940}, {11005, 17986}, {16220, 35486}, {18020, 30716}, {19504, 30219}, {33294, 47263}, {42671, 47326}

X(47627) = midpoint of X(23) and X(6563)
X(47627) = reflection of X(i) in X(j) for these {i,j}: {468, 47217}, {2501, 468}
X(47627) = reflection of X(2501) in the Euler line
X(47627) = barycentric product X(i)*X(j) for these {i,j}: {648, 15357}, {2501, 38940}
X(47627) = barycentric quotient X(i)/X(j) for these {i,j}: {15357, 525}, {38940, 4563}

X(47628) = X(20)X(250)∩X(1503)X(10151)

X(47628) = complement of the isogonal conjugate of X(15647)
X(47628) = X(15647)-complementary conjugate of X(10)
X(47628) = X(494)-lineconjugate of X(844)

This preamble is contributed by Peter Moses, Kiminari Shinagawa, and Clark Kimberling, April 21, 2022.

See the preambles just before X(47090), X(47332), and X(47488).

The appearance of (k,n) in the following list means that the point having Euler coordinates (k*S_ω, 0) is X(n):

(-3,37900), (-2,37899), (-1,23), (-3/4,47630), (-2/3,37904), (-1/2,37897), (-1/3,7426), (-1/4,47316), (1/4,37911), (1/3,2), (1/2,5159), (2/3,47097), (3/4,47629), (1,858), (2,46517), (3,5189)

X(47629) = SHINAGAWA-EULER POINT (3*S_ω/4, 0)

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

X(47629) = 21 X[2] - 5 X[23], 9 X[2] - 5 X[468], 3 X[2] + 5 X[858], 3 X[2] - 5 X[5159], 27 X[2] + 5 X[5189], 13 X[2] - 5 X[7426], 11 X[2] + 5 X[10989], 69 X[2] - 5 X[20063], 9 X[2] - 25 X[30745], 57 X[2] - 25 X[37760], 33 X[2] - 5 X[37899], 9 X[2] - X[37900], 37 X[2] - 5 X[37901], 17 X[2] - 5 X[37904], 31 X[2] - 15 X[37907], 47 X[2] - 15 X[37909], 27 X[2] - 5 X[37910], 6 X[2] - 5 X[37911], 3 X[2] + X[46517], 39 X[2] + 5 X[47095], X[2] - 5 X[47097], 7 X[2] + 5 X[47311], 5 X[2] - X[47312], 29 X[2] - 5 X[47313], 19 X[2] + 5 X[47314], 9 X[2] + 5 X[47315], 12 X[2] - 5 X[47316], X[4] + 3 X[47090], 3 X[23] - 7 X[468], X[23] + 7 X[858], X[23] - 7 X[5159], 9 X[23] + 7 X[5189], 13 X[23] - 21 X[7426], 11 X[23] + 21 X[10989], 23 X[23] - 7 X[20063], 3 X[23] - 35 X[30745], 19 X[23] - 35 X[37760], 5 X[23] - 7 X[37897], 11 X[23] - 7 X[37899], 15 X[23] - 7 X[37900], 37 X[23] - 21 X[37901], 17 X[23] - 21 X[37904], 31 X[23] - 63 X[37907], 47 X[23] - 63 X[37909], 9 X[23] - 7 X[37910], 2 X[23] - 7 X[37911], 5 X[23] + 7 X[46517], 13 X[23] + 7 X[47095], X[23] - 21 X[47097], X[23] + 3 X[47311], 25 X[23] - 21 X[47312], 29 X[23] - 21 X[47313], 19 X[23] + 21 X[47314], 3 X[23] + 7 X[47315], 4 X[23] - 7 X[47316], 5 X[140] - 3 X[16531], X[382] - 5 X[10297], and many more

X(47629) lies on these lines: {2, 3}, {125, 34380}, {141, 47446}, {3244, 47537}, {3619, 47447}, {3620, 47278}, {3629, 47464}, {3631, 6697}, {6329, 47460}, {6340, 32825}, {6723, 29181}, {7925, 47154}, {11008, 47277}, {11064, 24981}, {15059, 47582}, {15302, 47180}, {15613, 16188}, {23332, 34507}, {34573, 47451}, {34641, 47564}, {34747, 47593}, {38098, 47492}, {39602, 47298}, {40341, 47280}, {41300, 47247}, {47248, 47257}

X(47629) = midpoint of X(i) and X(j) for these {i,j}: {4, 47337}, {468, 47315}, {858, 5159}, {3153, 47114}, {5189, 37910}, {7574, 37934}, {37897, 46517}, {47092, 47338}
X(47629) = reflection of X(i) in X(j) for these {i,j}: {37911, 5159}, {47316, 37911}, {47451, 34573}
X(47629) = complement of X(37897)
X(47629) = orthoptic-circle-of-Steiner-inellipse-inverse of X(3522)
X(47629) = crossdifference of every pair of points on line {647, 22331}
X(47629) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 858, 46517}, {2, 10300, 3530}, {2, 37900, 468}, {2, 46517, 37897}, {4, 47090, 47337}, {23, 858, 47311}, {403, 47092, 47338}, {468, 858, 47315}, {468, 5189, 37910}, {468, 30745, 5159}, {468, 37900, 37897}, {468, 46517, 37900}, {468, 47097, 30745}, {858, 30745, 468}, {858, 47097, 5159}, {1368, 5094, 140}, {3548, 37458, 140}, {5159, 37897, 2}, {5159, 47315, 468}, {6676, 16063, 33923}, {7574, 10257, 37934}, {31099, 44212, 3853}, {37910, 47315, 5189}, {47090, 47097, 30771}

X(47630) = SHINAGAWA-EULER POINT (-3*S_ω/4, 0)

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

X(47630) = 3 X[2] + 13 X[23], 9 X[2] - 13 X[468], 21 X[2] - 13 X[858], 15 X[2] - 13 X[5159], 45 X[2] - 13 X[5189], 5 X[2] - 13 X[7426], 29 X[2] - 13 X[10989], 51 X[2] + 13 X[20063], 81 X[2] - 65 X[30745], 33 X[2] - 65 X[37760], 3 X[2] - 13 X[37897], 15 X[2] + 13 X[37899], 27 X[2] + 13 X[37900], 19 X[2] + 13 X[37901], X[2] - 13 X[37904], 23 X[2] - 39 X[37907], 7 X[2] - 39 X[37909], 9 X[2] + 13 X[37910], 12 X[2] - 13 X[37911], 33 X[2] - 13 X[46517], 57 X[2] - 13 X[47095], 17 X[2] - 13 X[47097], 25 X[2] - 13 X[47311], 7 X[2] + 13 X[47312], 11 X[2] + 13 X[47313], 37 X[2] - 13 X[47314], 27 X[2] - 13 X[47315], 6 X[2] - 13 X[47316], 3 X[23] + X[468], 7 X[23] + X[858], 5 X[23] + X[5159], 15 X[23] + X[5189], 5 X[23] + 3 X[7426], 29 X[23] + 3 X[10989], 17 X[23] - X[20063], 27 X[23] + 5 X[30745], 11 X[23] + 5 X[37760], 5 X[23] - X[37899], 9 X[23] - X[37900], 19 X[23] - 3 X[37901], X[23] + 3 X[37904], 23 X[23] + 9 X[37907], 7 X[23] + 9 X[37909], 3 X[23] - X[37910], 4 X[23] + X[37911], 11 X[23] + X[46517], 19 X[23] + X[47095], 17 X[23] + 3 X[47097], 25 X[23] + 3 X[47311], 7 X[23] - 3 X[47312], 11 X[23] - 3 X[47313], 37 X[23] + 3 X[47314], 9 X[23] + X[47315], 2 X[23] + X[47316], 3 X[186] - X[47337], and many more

X(47630) lies on these lines: {2, 3}, {1495, 34380}, {3564, 32237}, {4816, 47321}, {8705, 47460}, {31860, 38110}, {32217, 47464}, {47247, 47442}, {47250, 47261}, {47466, 47545}

X(47630) = midpoint of X(i) and X(j) for these {i,j}: {23, 37897}, {468, 37910}, {5159, 37899}, {5899, 37935}, {10295, 47338}, {16976, 37925}, {37900, 47315}, {47094, 47114}
X(47630) = reflection of X(i) in X(j) for these {i,j}: {37911, 47316}, {47316, 37897}
X(47630) = orthoptic-circle-of-Steiner-inellipse-inverse of X(5068)
X(47630) = crossdifference of every pair of points on line {647, 22332}
X(47630) = X(7806)-lineconjugate of X(10791)
X(47630) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 468, 37910}, {23, 858, 47312}, {23, 7426, 37899}, {23, 37760, 47313}, {23, 37777, 5899}, {23, 37904, 37897}, {23, 37909, 858}, {23, 37972, 37947}, {468, 5189, 5159}, {468, 37899, 5189}, {468, 37900, 47315}, {550, 4232, 6677}, {4232, 9909, 550}, {5159, 37897, 7426}, {5189, 7426, 468}, {6676, 10301, 3850}, {7426, 37899, 5159}, {10295, 47093, 47338}, {37760, 47313, 46517}, {37897, 37910, 468}, {37904, 47312, 37909}, {37910, 47315, 37900}, {37940, 47094, 47114}

X(47631) = SHINAGAWA-EULER POINT (S, 0)

X(47631 lies on these lines: {2, 3}, {523, 17432}, {3292, 32419}, {6414, 44633}, {13884, 42459}, {16333, 32787}, {32421, 41586}, {34417, 45544}, {35299, 45554}

X(47631) = circumcircle-inverse of X(3156)
X(47631) = polar-circle-inverse of X(1586)
X(47631) = orthoptic-circle-of-Steiner-inellipse-inverse of X(6813)
X(47631) = psi-transform of X(45510)
X(47631) = crossdifference of every pair of points on line {372, 647}
X(47631) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1113, 1114, 3156}

X(47632) = SHINAGAWA-EULER POINT (-S, 0)

X(47632) lies on these lines: {2, 3}, {523, 17431}, {3292, 32421}, {6413, 44634}, {13937, 42459}, {16333, 32788}, {32419, 41586}, {34417, 45545}, {35300, 45555}

X(47632) = circumcircle-inverse of X(3155)
X(47632) = polar-circle-inverse of X(1585)
X(47632) = orthoptic-circle-of-Steiner-inellipse-inverse of X(6811)
X(47632) = psi-transform of X(45511)
X(47632) = crossdifference of every pair of points on line {371, 647}
X(47632) = X(29860)-lineconjugate of X(17237)
X(47632) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1113, 1114, 3155}

X(47633) = CEVAPOINT OF X(2) AND X(1032)

X(47633) lies on the cubic K184 and these lines: {69, 1032}, {76, 47435}, {312, 47436}, {6616, 37669}

X(47633) = isogonal conjugate of X(47437)
X(47633) = isotomic conjugate of X(3343)
X(47633) = polar conjugate of X(41085)
X(47633) = isotomic conjugate of the complement of X(1032)
X(47633) = isotomic conjugate of the isogonal conjugate of X(3344)
X(47633) = isotomic conjugate of the polar conjugate of X(46353)
X(47633) = X(i)-cross conjugate of X(j) for these (i,j): {2, 15466}, {3344, 46353}, {14249, 14615}, {20265, 20}
X(47633) = X(i)-isoconjugate of X(j) for these (i,j): {1, 47437}, {31, 3343}, {48, 41085}, {560, 47435}, {1033, 19614}, {1498, 2155}, {1712, 14642}, {1973, 46351}
X(47633) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 3343), (3, 47437), (4, 1033), (1249, 41085), (3344, 28785), (3350, 6), (6337, 46351), (6374, 47435), (45245, 1498)
X(47633) = cevapoint of X(2) and X(1032)
X(47633) = barycentric product X(i)*X(j) for these {i,j}: {69, 46353}, {76, 3344}, {1032, 15466}, {1502, 47439}, {3346, 14615}
X(47633) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3343}, {4, 41085}, {6, 47437}, {20, 1498}, {69, 46351}, {76, 47435}, {1032, 1073}, {1249, 1033}, {1895, 1712}, {2060, 31944}, {3344, 6}, {3346, 64}, {3350, 28785}, {5930, 8803}, {8805, 30457}, {14249, 6523}, {14365, 3349}, {14615, 6527}, {15466, 14361}, {28783, 14642}, {37669, 6617}, {41084, 8886}, {46353, 4}, {47439, 32}

X(47634) = CEVAPOINT OF X(2) AND X(1034)

X(47634) lies on the cubic K184 and these lines: {69, 1034}, {75, 47435}, {76, 47436}, {312, 15466}

X(47634) = isogonal conjugate of X(47438)
X(47634) = isotomic conjugate of X(3341)
X(47634) = isotomic conjugate of the anticomplement of X(20209)
X(47634) = isotomic conjugate of the complement of X(1034)
X(47634) = isotomic conjugate of the isogonal conjugate of X(3342)
X(47634) = X(i)-cross conjugate of X(j) for these (i,j): {2, 40702}, {342, 322}, {20209, 2}, {20264, 329}
X(47634) = X(i)-isoconjugate of X(j) for these (i,j): {1, 47438}, {25, 46881}, {31, 3341}, {207, 2188}, {560, 47436}, {1035, 2192}, {1397, 46350}, {1436, 3197}, {1490, 2208}
X(47634) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 3341), (3, 47438), (57, 1035), (3342, 28784), (3351, 6), (6374, 47436), (6505, 46881)
X(47634) = cevapoint of X(2) and X(1034)
X(47634) = barycentric product X(i)*X(j) for these {i,j}: {76, 3342}, {312, 46352}, {322, 41514}, {1034, 40702}
X(47634) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3341}, {6, 47438}, {40, 3197}, {63, 46881}, {76, 47436}, {196, 207}, {223, 1035}, {312, 46350}, {329, 1490}, {342, 40837}, {1034, 282}, {3342, 6}, {3345, 1436}, {3351, 28784}, {7007, 7154}, {7037, 7118}, {7149, 7129}, {7152, 2208}, {8806, 1903}, {27398, 13614}, {40702, 5932}, {40838, 7008}, {41080, 3352}, {41083, 8885}, {41514, 84}, {46352, 57}

X(47635) = X(23)X(94)∩X(186)X(685)

X(47635) lies on these lines: {3, 5967}, {23, 94}, {186, 685}, {237, 1503}, {248, 1177}, {287, 35296}, {511, 1976}, {523, 3447}, {879, 46608}, {2395, 21525}, {3001, 14601}, {3148, 46124}, {3260, 31635}, {5191, 38987}, {5201, 25322}, {6636, 40820}, {11063, 34369}, {13137, 15107}, {13198, 23357}, {32305, 35298}

X(47635) = X(240)-isoconjugate of X(46087)
X(47635) = X(39085)-Dao conjugate of X(46087)
X(47635) = crosssum of X(i) and X(j) for these (i,j): {511, 868}, {3150, 3564}
X(47635) = barycentric product X(i)*X(j) for these {i,j}: {98, 34990}, {287, 1112}, {16081, 23217}
X(47635) = barycentric quotient X(i)/X(j) for these {i,j}: {248, 46087}, {1112, 297}, {23217, 36212}, {34990, 325}

X(47636) = X(1)X(16079)∩X(2)X(2415)

X(47636) lies on the cuybic K365 and these lines: {1, 16079}, {2, 2415}, {7, 44301}, {75, 27813}, {192, 27830}, {1743, 27834}, {3062, 4947}, {3242, 3680}, {3445, 38316}, {3672, 27818}, {4346, 27832}, {4441, 27824}, {4452, 27828}, {4862, 12053}, {4902, 31162}, {4941, 10980}, {16673, 27827}, {17151, 27835}, {17321, 27820}, {23511, 24151}

X(47636) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 19604}, {27828, 24151}
X(47636) = X(2136)-cross conjugate of X(23511)
X(47636) = cevapoint of X(2136) and X(24151)
X(47636) = crosspoint of X(7) and X(4452)
X(47636) = X(i)-isoconjugate of X(j) for these (i,j): {6, 24150}, {55, 44301}, {2137, 3158}, {3052, 6553}
X(47636) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 24150), (223, 44301), (8056, 8), (17071, 4546), (24151, 6553)
X(47636) = barycentric product X(i)*X(j) for these {i,j}: {1, 27828}, {7, 24151}, {1616, 40014}, {2136, 27818}, {3445, 33780}, {4373, 23511}, {4452, 8056}, {8055, 19604}
X(47636) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 24150}, {57, 44301}, {1616, 1743}, {2136, 3161}, {4452, 18743}, {8055, 44720}, {8056, 6553}, {19604, 8051}, {21896, 3950}, {23089, 4855}, {23511, 145}, {24151, 8}, {27828, 75}, {40151, 2137}
X(47636) = {X(3731),X(8056)}-harmonic conjugate of X(27819)

X(47637) = X(1)X(19611)∩X(2)X(1032)

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

X(47637) lies on the cubic K317 and these lines: {1, 19611}, {2, 1032}, {7, 29}, {81, 41081}, {253, 5738}, {2287, 46639}

X(47637) = cevapoint of X(1) and X(3343)
X(47637) = X(86)-Ceva conjugate of X(41082)
X(47637) = X(i)-isoconjugate of X(j) for these (i,j): {154, 8806}, {3198, 3345}, {3342, 41086}, {5930, 7037}, {7070, 8811}, {7152, 8804}
X(47637) = X(13612)-Dao conjugate of X(14308)
X(47637) = barycentric product X(8885)*X(34403)
X(47637) = barycentric quotient X(i)/X(j) for these {i,j}: {1035, 30456}, {1490, 8804}, {2184, 8806}, {3197, 3198}, {8885, 1249}, {13614, 27382}

X(47638) = X(2)X(51)∩X(22)X(35375)

Barycentrics a^2*(a^4*b^4 - a^2*b^6 + 4*a^4*b^2*c^2 - 2*a^2*b^4*c^2 + b^6*c^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(47638) = X[6785] - 3 X[38227], 3 X[11673] + X[33873], 2 X[187] + X[5167], 3 X[8859] - X[46303], X[9879] + 3 X[13586], X[11675] + 2 X[14693]

X(47638) lies on the cubics K048 and K756 and these lines: {2, 51}, {22, 35375}, {25, 2076}, {50, 44127}, {140, 27374}, {154, 36650}, {184, 1613}, {187, 237}, {211, 7749}, {230, 6784}, {385, 33755}, {420, 14165}, {524, 6786}, {612, 19586}, {694, 3291}, {1570, 20965}, {1627, 16385}, {1692, 3051}, {1993, 35377}, {2021, 3117}, {2030, 9463}, {2080, 5651}, {2456, 43650}, {3111, 10166}, {3148, 5162}, {3292, 36213}, {3491, 7793}, {3552, 6310}, {3767, 35704}, {5031, 21248}, {5103, 37439}, {5104, 8585}, {5107, 44107}, {5111, 15004}, {5562, 37466}, {5642, 44215}, {6072, 41586}, {6108, 31707}, {6109, 31708}, {7484, 47619}, {8590, 11003}, {8617, 34098}, {8705, 46980}, {8859, 46303}, {9777, 15514}, {9879, 13586}, {10565, 32529}, {11159, 12525}, {11402, 35006}, {11675, 14693}, {13170, 35279}, {13240, 37637}, {13394, 38230}, {14096, 18860}, {14135, 33014}, {15247, 38720}, {15248, 38721}, {16419, 35458}, {18371, 44102}, {20403, 47327}, {22329, 34383}, {31848, 37465}, {35268, 38225}, {35287, 35687}, {37184, 47113}

X(47638) = midpoint of X(i) and X(j) for these {i,j}: {2, 11673}, {5167, 32442}
X(47638) = reflection of X(i) in X(j) for these {i,j}: {6784, 230}, {32442, 187}
X(47638) = reflection of X(32442) in the Brocard axis
X(47638) = isogonal conjugate of X(43664)
X(47638) = isogonal conjugate of the isotomic conjugate of X(32515)
X(47638) = isotomic conjugate of the polar conjugate of X(33874)
X(47638) = complement of X(33873)
X(47638) = orthoptic-circle-of-Steiner-inellipes-inverse of X(262)
X(47638) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(44434)
X(47638) = circumcircle-of-inner-Napoleon-triangle-inverse of X(44460)
X(47638) = circumcircle-of-outer-Napoleon-triangle-inverse of X(44464)
X(47638) = psi-transform of X(7709)
X(47638) = X(1)-isoconjugate of X(43664)
X(47638) = X(3)-Dao conjugate of X(43664)
X(47638) = crosssum of X(2) and X(32515)
X(47638) = crossdifference of every pair of points on line {2, 3288}
X(47638) = X(i)-line conjugate of X(j) for these (i,j): {51, 2}, {187, 3288}
X(47638) = barycentric product X(i)*X(j) for these {i,j}: {6, 32515}, {69, 33874}
X(47638) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 43664}, {32515, 76}, {33874, 4}
X(47638) = {X(1613),X(20885)}-harmonic conjugate of X(184)

X(47639) = X(1)X(1357)∩X(3)X(8616)

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

X(47639) lies on the cubic K736 and these lines: {1, 1357}, {3, 8616}, {40, 376}, {165, 6048}, {601, 727}, {1293, 8715}, {3576, 47302}, {5450, 21306}, {5881, 16528}, {6210, 15601}, {9778, 10476}, {15803, 33551}, {20368, 31730}

X(47640) = X(3)X(194)∩X(183)X(14937)

X(47640) lies on the cubic K736 and these lines: {3, 194}, {183, 14937}, {2080, 5651}, {3398, 43652}, {5171, 6310}, {10104, 31952}

X(47640) = reflection of X(32524) in X(3)
X(47640) = {X(6194),X(32518)}-harmonic conjugate of X(3)

X(47641) = X(3)X(170)∩X(376)X(516)

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

X(47641) = 2 X[3] + X[170], X[4] - 4 X[43158], 5 X[631] - 2 X[34848], 4 X[2140] - X[41869], 2 X[3730] - 5 X[35242], 2 X[12512] + X[43168], 7 X[16192] - X[41680], X[17753] + 2 X[31730]

X(47641) lies on the cubic K736 and these lines: {1, 39790}, {3, 170}, {4, 43158}, {40, 15506}, {165, 2808}, {376, 516}, {631, 34848}, {1742, 22520}, {2140, 41869}, {2187, 7411}, {2272, 3730}, {3220, 7688}, {11495, 18162}, {12512, 43168}, {15803, 39789}, {16192, 41680}, {17753, 31730}

X(47642) = X(2)X(694)∩X(3)X(3224)

X(47642) lies on the cubics K756, K783, and K787, and on these lines: {2, 694}, {3, 3224}, {6, 17970}, {39, 695}, {232, 16068}, {292, 1967}, {670, 19590}, {699, 805}, {733, 25424}, {864, 17938}, {1569, 30229}, {5989, 39087}, {6656, 18896}, {9292, 9475}

X(47643) = X(2)X(3504)∩X(3)X(194)

X(47643) lies on the cubics K756 and K1016 and these lines: {2, 3504}, {3, 194}, {6, 17970}, {32, 11325}, {182, 40811}, {183, 10010}, {184, 1613}, {228, 21877}, {3407, 11328}, {4027, 20794}, {5976, 8858}, {7081, 14199}, {7484, 37894}, {10547, 38834}, {18105, 34811}, {18899, 40825}, {19587, 20964}, {32540, 41932}, {34870, 40319}, {40947, 41533}

X(47643) = isogonal conjugate of X(18906)
X(47643) = isogonal conjugate of the anticomplement of X(3094)
X(47643) = isogonal conjugate of the isotomic conjugate of X(19222)
X(47643) = X(i)-cross conjugate of X(j) for these (i,j): {3117, 6}, {7735, 25}
X(47643) = cevapoint of X(32) and X(41277)
X(47643) = crosssum of X(194) and X(6194)
X(47643) = trilinear pole of line {3049, 3221}
X(47643) = X(i)-isoconjugate of X(j) for these (i,j): {1, 18906}, {2, 19591}, {75, 11328}, {799, 45907}, {1966, 6234}, {3113, 19602}, {3114, 19603}, {3407, 19600}
X(47643) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 18906), (206, 11328), (9467, 6234), (32664, 19591), (38996, 45907)
X(47643) = barycentric product X(6)*X(19222)
X(47643) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 18906}, {31, 19591}, {32, 11328}, {669, 45907}, {3116, 19600}, {3117, 19602}, {9468, 6234}, {19222, 76}

X(47644) = X(6)X(74)∩X(110)X(1599)

X(47644) lies on these lines: {6,74}, {110,1599}, {125,1586}, {542,35949}, {6699,32807}, {10706,13663}, {11653,35826}, {12041,45578}, {13198,15206}

X(47645) = ISOGONAL CONJUGATE OF X(6326)

X(47645) lies on the cubics K269 and K340 and these lines: {36, 1455}, {153, 515}, {517, 2182}, {953, 1421}, {1325, 5535}, {2778, 29374}, {32899, 38458}, {34535, 40437}

X(47645) = isogonal conjugate of X(6326)
X(47645) = isogonal conjugate of the anticomplement of X(10265)
X(47645) = isogonal conjugate of the complement of X(9803)
X(47645) = X(i)-cross conjugate of X(j) for these (i,j): {102, 84}, {909, 57}, {1411, 1}, {34442, 267}
X(47645) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6326}, {55, 36918}
X(47645) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 6326), (223, 36918)
X(47645) = trilinear pole of line {654, 1769}
X(47645) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 6326}, {57, 36918}

X(47646) = X(98)X(39291)∩X(99)X(187)

X(47646) lies on the cubics K248 and K705 and these lines: {98, 39291}, {99, 187}, {671, 729}, {880, 5026}, {2782, 33757}, {3225, 10754}, {3972, 43765}, {4027, 17941}

X(47646) = X(i)-isoconjugate of X(j) for these (i,j): {1581, 5106}, {1967, 5969}
X(47646) = X(i)-Dao conjugate of X(j) for these (i, j): (8290, 5969), (19576, 5106), (35078, 11182)
X(47646) = barycentric product X(i)*X(j) for these {i,j}: {385, 35146}, {880, 14606}, {3978, 5970}
X(47646) = barycentric quotient X(i)/X(j) for these {i,j}: {385, 5969}, {804, 11182}, {1691, 5106}, {5026, 45330}, {5970, 694}, {14606, 882}, {17941, 14607}, {35146, 1916}
X(47646) = {X(11152),X(33756)}-harmonic conjugate of X(99)

X(47647) = ISOGONAL CONJUGATE OF X(19586)

X(47647) lies on the cubics K1018 and K1031 and these lines: {6, 40757}, {183, 1001}, {985, 1471}, {2280, 2344}, {3329, 14621}

X(47647) = isogonal conjugate of X(19586)
X(47647) = X(i)-cross conjugate of X(j) for these (i,j): {1, 14621}, {24172, 871}
X(47647) = X(i)-isoconjugate of X(j) for these (i,j): {1, 19586}, {2, 19587}, {6, 19584}, {37, 25429}, {869, 24349}, {984, 21010}, {2276, 17754}, {4334, 4517}, {20917, 40728}
X(47647) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 19586), (9, 19584), (32664, 19587), (40589, 25429)
X(47647) = trilinear pole of line {4785, 23597}
X(47647) = barycentric product X(i)*X(j) for these {i,j}: {86, 25425}, {14621, 41527}
X(47647) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 19584}, {6, 19586}, {31, 19587}, {58, 25429}, {870, 20917}, {985, 17754}, {4817, 24720}, {14621, 24349}, {25425, 10}, {40718, 21101}, {40746, 21010}, {41527, 3661}

X(47648) = ISOGONAL CONJUGATE OF X(32544)

X(47648) lies on the cubics K512, K1012, K1068 and these lines: {3, 3224}, {6, 9467}, {32, 805}, {39, 512}, {76, 115}, {194, 18829}, {694, 44453}, {1581, 3061}, {3094, 40810}, {3095, 33330}, {3117, 39092}, {3493, 46292}, {5013, 45146}, {5028, 34238}, {7748, 38947}, {17970, 43183}, {19222, 36897}, {30496, 36214}, {39935, 41259}

X(47648) = isogonal conjugate of X(32544)
X(47648) = complement of the isogonal conjugate of X(32540)
X(47648) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 40810}, {32540, 10}, {32748, 16591}, {36036, 9429}
X(47648) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 40810}, {805, 9429}, {1916, 698}
X(47648) = crosspoint of X(1916) and X(41517)
X(47648) = crosssum of X(i) and X(j) for these (i,j): {385, 39080}, {1691, 4027}
X(47648) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32544}, {385, 43761}, {699, 1966}, {1580, 3225}
X(47648) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 32544), (9467, 699), (39080, 385), (39092, 3225), (40810, 2)
X(47648) = barycentric product X(i)*X(j) for these {i,j}: {694, 698}, {1581, 2227}, {1916, 3229}, {9468, 35524}, {18896, 32748}, {39080, 41517}
X(47648) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 32544}, {694, 3225}, {698, 3978}, {1967, 43761}, {2227, 1966}, {3229, 385}, {9429, 5027}, {9468, 699}, {32540, 40820}, {32748, 1691}, {35524, 14603}, {36214, 8858}, {41337, 17941}
X(47648) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 14251, 18872}, {3094, 41517, 40810}

X(47649) = X(6)X(1597)∩X(193)X(2986)

X(47649) lies on the cubics K429 and K1171 and these lines: {6, 1597}, {193, 2986}, {1974, 40352}

X(47649) = X(63)-isoconjugate of X(39263)
X(47649) = X(3162)-Dao conjugate of X(39263)
X(47649) = barycentric product X(i)*X(j) for these {i,j}: {378, 3426}, {8675, 9064}, {36889, 44080}
X(47649) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 39263}, {378, 44133}, {40354, 40385}, {42660, 9007}, {44080, 376}

If L1 and L2 are lines that meet in a point P not at infinity, then the [L1,L2]-coordinate system is here defined as a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 = L(31) = X(514)X(661) = trilinear polar of (75);
L1 is given by the equation a α + b β + c γ = 0.

L2 = L(32) = X(325)X(523) = deLongchamps axis = trilinear polar of X(76);
L2 is given by the equation a^2 α + b^2 β + c^2 γ = 0.

The origin is given by (0,0) = X(693) = b c (b + c) : c a (c + a) : a b (a + b) = isotomic conjugate of X(100)

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b-c)(bc + x - (b+c) y) : (c-a)(ca + x - (c+a)y) : (b-c)(ab + x - (a+b)y),

where, as functions of a,b,c, the coordinate x is symmetric and homogeneous of degree 2, and y is symmetric and homogeneous of degree 1. Note that these results depend on the repesentations of L1 and L2 as shown, and that the systems [L2,L1] and [L1,L2] differ.

The appearance of (x,y), k in the following table means that (x,y) = X(k):

(-a^2 - b^2 - c^2, -a - b - c), 26824
(0, 0), 693
(0, a + b + c), 45746
(a^2 + b^2 + c^2, a + b + c), 17494
(-2 (b c + c a + a b), -a - b - c), 25259
(-b c - c a - a b, -2 (a + b + c)), 4838
(-b c - c a - a b, -a - b - c), 4024
(-b c - c a - a b, 0), 661
(-b c - c a - a b, a + b + c), 4988
(b c + c a + a b, a + b + c), 16892
(-2 a b c)/(a + b + c), 0), 4391
(-a b c)/(a + b + c), 0), 1577
(a b c/(a + b + c), 0), 4978
(2 a b c/(a + b + c), 0), 4801
(-a^2 - b^2 - c^2, - (a^2 + b^2 + c^2)/(a + b + c)), 46403
(-b c - c a - a b, -(a^2 + b^2 + c^2)/(a + b + c)), 4088
((a^3 + b^3 + c^3)/(a + b + c), (a^2 + b^2 + c^2)/(a + b + c)), 1
(-2 (a^2 + b^2 + c^2), -a - b - c), 47650
(-2 (a^2 + b^2 + c^2), 0), 47651
(-a^2 - b^2 - c^2, 0), 47652
(-a^2 - b^2 - c^2, a + b + c), 47653
(-a^2 - b^2 - c^2, 2(a + b + c)), 47654
(0, -2 (a + b + c)), 47655
(0, -(a + b + c)), 47656
(0, 2 (a + b + c)), 47657
(a^2 + b^2 + c^2, -2 (a + b + c), 47658
(a^2 + b^2 + c^2, - a - b - c), 47659
(a^2 + b^2 + c^2, 0), 47660
(a^2 + b^2 + c^2, 2 (a + b + c)), 47661
(2 (a^2 + b^2 + c^2), 0), 47662
(2 (a^2 + b^2 + c^2), a + b + c), 47663
(2 (a^2 + b^2 + c^2), 2 (a + b + c)), 47664
(-2 (b c + c a + a b ), -2 (a + b + c)), 47665
(-2 (b c + c a + a b ), 0), 47666
(-2 (b c + c a + a b ), a + b + c), 47667
(-2 (b c + c a + a b ), 2*(a + b + c)), 47668
(-(b c + c a + a b ), 2 (a + b + c) ), 47669
(b c + c a + a b, -2 (a + b + c) ), 47670
(b c + c a + a b, -a - b - c), 47671
(b c + c a + a b, 0), 47672
(b c + c a + a b, 2 (a + b + c) ), 47673
(2*(b c + c a + a b ), -a - b - c), 47674
({2*(b c + c a + a b ), 0), 47675
(2 (b c + c a + a b ), a + b + c), 47676
(2 (b c + c a + a b ), 2 (a + b + c)), 47677
(-a b c/(a + b + c)), -a - b - c), 47678
(-a b c/(a + b + c)), a + b + c), 47679
(-a b c/(a + b + c)), 0), 47680
((a^3 + b^3 + c^3)/(a + b + c), -a - b - c), 47681
((a^3 + b^3 + c^3)/(a + b + c), 0 ), 47682
((a^3 + b^3 + c^3)/(a + b + c), a + b + c), 47683
(2 (a^3 + b^3 + c^3)/(a + b + c), 0), 47684
(-2 (a^2 + b^2 + c^2), -2 (a^2 + b^2 + c^2)/(a + b + c)), 47685
(-2 (a^2 + b^2 + c^2), -(a^2 + b^2 + c^2)/(a + b + c)), 47686
(-a^2 - b^2 - c^2, -2 (a^2 + b^2 + c^2)/(a + b + c) ), 47687
(-a^2 - b^2 - c^2, (a^2 + b^2 + c^2)/(a + b + c)), 47688
(0, -2 (a^2 + b^2 + c^2)/(a + b + c), 47689
(0, -(a^2 + b^2 + c^2)/(a + b + c)), 47690
(0, (a^2 + b^2 + c^2)/(a + b + c) ), 47691
(0, (2 (a^2 + b^2 + c^2))/(a + b + c)), 47692
(a^2 + b^2 + c^2, -(a^2 + b^2 + c^2)/(a + b + c)), 47693
(a^2 + b^2 + c^2, (a^2 + b^2 + c^2)/(a + b + c)), 47694
(a^2 + b^2 + c^2, 2 (a^2 + b^2 + c^2)/(a + b + c) ), 47695
(2 (a^2 + b^2 + c^2), (a^2 + b^2 + c^2)/(a + b + c)), 47696
(2 (a^2 + b^2 + c^2), 2 (a^2 + b^2 + c^2)/(a + b + c)), 47697
(-2 (b c + c a + a b ), -(a^2 + b^2 + c^2)/(a + b + c)), 47698
(-2 (b c + c a + a b ), (a^2 + b^2 + c^2)/(a + b + c) ), 47699
(-b c - c a - a b, -2 (a^2 + b^2 + c^2)/(a + b + c)), 47700
(-b c - c a - a b, -2 (a^2 + b^2 + c^2)/(a + b + c)), 47701
(-b c - c a - a b, 2 (a^2 + b^2 + c^2)/(a + b + c)), 47702
(b c + c a + a b, -(a^2 + b^2 + c^2)/(a + b + c)), 47703
(b c + c a + a b, (a^2 + b^2 + c^2)/(a + b + c)), 47704
(b c + c a + a b, 2 (a^2 + b^2 + c^2)/(a + b + c)), 47705
(-2 a b c/(a + b + c), -2 (a^2 + b^2 + c^2))/(a + b + c)), 47706
(-2 a b c/(a + b + c), -(a^2 + b^2 + c^2))/(a + b + c)), 47707
(-2 a b c/(a + b + c), (a^2 + b^2 + c^2))/(a + b + c)), 47708
(-2 a b c/(a + b + c), 2 (a^2 + b^2 + c^2)/(a + b + c)), 47709
(-a b c/(a + b + c), -2 (a^2 + b^2 + c^2)/(a + b + c)), 47710
(-a b c/(a + b + c), -(a^2 + b^2 + c^2)/(a + b + c)), 47711
(-a b c/(a + b + c), (a^2 + b^2 + c^2)/(a + b + c)), 47712
(-a b c/(a + b + c), 2 (a^2 + b^2 + c^2)/(a + b + c)), 47713
(a b c/(a + b + c), -2 (a^2 + b^2 + c^2)/(a + b + c)), 47714
(a b c/(a + b + c), -(a^2 + b^2 + c^2)/(a + b + c)), 47715
(a b c/(a + b + c), (a^2 + b^2 + c^2)/(a + b + c)), 47716
(a b c/(a + b + c), 2 (a^2 + b^2 + c^2)/(a + b + c)), 47717
(2 a b c/(a + b + c), -2 (a^2 + b^2 + c^2)/(a + b + c)), 47718
(2 a b c/(a + b + c), -(a^2 + b^2 + c^2)/(a + b + c)), 47719
(2 a b c/(a + b + c), (a^2 + b^2 + c^2)/(a + b + c)), 47720
(-2 (a^3 + b^3 + c^3)/(a + b + c), -2 (a^2 + b^2 + c^2))/(a + b + c)), 47721
(-2 (a^3 + b^3 + c^3)/(a + b + c), -(a^2 + b^2 + c^2))/(a + b + c)), 47722
(-(a^3 + b^3 + c^3)/(a + b + c), -2 (a^2 + b^2 + c^2))/(a + b + c)), 47723
(-(a^3 + b^3 + c^3)/(a + b + c), -(a^2 + b^2 + c^2))/(a + b + c)), 47724
(-(a^3 + b^3 + c^3)/(a + b + c), (a^2 + b^2 + c^2))/(a + b + c)), 47725
((a^3 + b^3 + c^3)/(a + b + c), -(a^2 + b^2 + c^2))/(a + b + c)), 47726
((a^3 + b^3 + c^3)/(a + b + c), 2 (a^2 + b^2 + c^2))/(a + b + c)), 4777
(2 (a^3 + b^3 + c^3)/(a + b + c), (a^2 + b^2 + c^2))/(a + b + c)), 47728
(2 (a^3 + b^3 + c^3)/(a + b + c), 2 (a^2 + b^2 + c^2))/(a + b + c)), 4779

X(47650) = X(514)X(4024)∩X(693)X(6084)

X(47650) = X[3776] - 3 X[27486], 2 X[4468] - 3 X[21297], 6 X[4927] - 5 X[31209], 2 X[4932] - 3 X[21116], 9 X[6548] - 8 X[7658], 4 X[11068] - 5 X[26985], 2 X[17494] - 3 X[44435], 6 X[21183] - 5 X[27013], 4 X[23813] - 3 X[30565]

X(47650) lies on these lines: {514, 4024}, {693, 6084}, {3776, 27486}, {4380, 6009}, {4468, 21297}, {4762, 45746}, {4927, 31209}, {4932, 21116}, {6548, 7658}, {11068, 26985}, {17494, 44435}, {21183, 27013}, {23813, 30565}
X(47650) = reflection of X(i) in X(j) for these {i,j}: {4380, 21104}, {25259, 4382}

X(47651) = X(514)X(661)∩X(2976)X(4977)

X(47651) = 7 X[693] - 6 X[4789], 5 X[693] - 4 X[6590], 15 X[4789] - 14 X[6590], 16 X[14350] - 15 X[30565], 4 X[3004] - 3 X[31150], 5 X[4380] - 6 X[4984], 3 X[4984] - 5 X[16892], 2 X[4932] - 3 X[21115], 4 X[4949] - 5 X[20295], 24 X[14425] - 25 X[31209], 4 X[14425] - 5 X[44435], 5 X[31209] - 6 X[44435]

X(47651) lies on these lines: {514, 661}, {2976, 4977}, {3004, 31150}, {4378, 18108}, {4380, 4984}, {4382, 28863}, {4802, 46403}, {4813, 28890}, {4932, 21115}, {4949, 20295}, {6084, 45746}, {14425, 31209}, {23729, 25259}, {23731, 28851}, {23770, 28213}, {26824, 28894}, {28220, 47131}, {28229, 47123}

X(47651) = reflection of X(i) in X(j) for these {i,j}: {4380, 16892}, {25259, 23729}
X(47651) = X(43527)-Ceva conjugate of X(1086)
X(47651) = barycentric product X(i)*X(j) for these {i,j}: {514, 17370}, {693, 17024}
X(47651) = barycentric quotient X(i)/X(j) for these {i,j}: {17024, 100}, {17370, 190}

X(47652) = X(2)X(2490)∩X(81)X(6654)

X(47652) = 9 X[2] - 8 X[2490], 4 X[693] - 3 X[4789], 3 X[693] - 2 X[6590], 4 X[3835] - 3 X[30565], 2 X[4468] - 3 X[4776], 9 X[4789] - 8 X[6590], 2 X[649] - 3 X[4453], 4 X[3776] - 3 X[4453], 2 X[650] - 3 X[44435], 4 X[23729] - X[44449], 3 X[1635] - 4 X[21212], 6 X[1638] - 5 X[27013], 6 X[1639] - 7 X[27138], 2 X[3700] - 3 X[21297], 2 X[4369] - 3 X[6545], 6 X[4927] - 5 X[26985], 3 X[23770] - 2 X[47132], X[4979] - 3 X[21115], 3 X[6546] - 4 X[25666], 4 X[11068] - 5 X[31209], 4 X[14321] - 5 X[26798], 6 X[21204] - 5 X[24924]

X(47652) lies on these lines: {2, 2490}, {81, 6654}, {513, 41794}, {514, 661}, {523, 2528}, {649, 3776}, {650, 44435}, {764, 29029}, {812, 4467}, {824, 4382}, {850, 18071}, {918, 20295}, {1635, 21212}, {1638, 27013}, {1639, 27138}, {2530, 29098}, {3004, 6084}, {3261, 30041}, {3669, 16757}, {3700, 21297}, {3732, 5375}, {3777, 29025}, {4024, 28863}, {4025, 4380}, {4106, 25259}, {4367, 18108}, {4369, 6545}, {4762, 45746}, {4778, 47123}, {4813, 28851}, {4897, 26853}, {4905, 23687}, {4927, 26985}, {4976, 6009}, {4977, 23770}, {4979, 21115}, {6546, 25666}, {7662, 28195}, {11068, 31209}, {14321, 26798}, {17496, 29162}, {17778, 31290}, {20090, 28209}, {20952, 29739}, {21120, 37680}, {21204, 24924}, {21222, 29126}, {21301, 29288}, {23731, 28840}, {23765, 29120}, {27647, 29984}, {27710, 41809}

X(47652) = reflection of X(i) in X(j) for these {i,j}: {649, 3776}, {4380, 4025}, {4467, 16892}, {7192, 21104}, {17494, 3004}, {20295, 23729}, {25259, 4106}, {26853, 4897}, {44449, 20295}
X(47652) = X(i)-Ceva conjugate of X(j) for these (i,j): {83, 1086}, {33951, 16706}, {40038, 244}
X(47652) = X(4557)-isoconjugate of X(40398)
X(47652) = X(21249)-Dao conjugate of X(1018)
X(47652) = crosspoint of X(16706) and X(33951)
X(47652) = crossdifference of every pair of points on line {31, 5007}
X(47652) = barycentric product X(i)*X(j) for these {i,j}: {81, 27712}, {513, 33940}, {514, 16706}, {523, 33955}, {693, 7191}, {1086, 33951}, {3261, 5299}, {3676, 4514}, {4972, 7192}, {7199, 16600}, {7293, 46107}, {10566, 17192}, {21425, 39179}, {24002, 33950}
X(47652) = barycentric quotient X(i)/X(j) for these {i,j}: {1019, 40398}, {4514, 3699}, {4972, 3952}, {5299, 101}, {7191, 100}, {7293, 1331}, {16600, 1018}, {16706, 190}, {17192, 4568}, {17456, 35309}, {18183, 4553}, {21125, 15523}, {27712, 321}, {33940, 668}, {33950, 644}, {33951, 1016}, {33955, 99}
X(47652) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 3776, 4453}, {18071, 20950, 850}

X(47653) = X(2)X(3004)∩X(239)X(514)

X(47653) = 3 X[2] - 4 X[3004], 3 X[17494] - 4 X[45745], 2 X[17494] - 3 X[46915], 2 X[45745] - 3 X[45746], 8 X[45745] - 9 X[46915], 4 X[45746] - 3 X[46915], 4 X[3700] - 5 X[26798], 2 X[4024] - 3 X[21297], 4 X[6590] - 5 X[26985], 2 X[6590] - 3 X[44435], 5 X[26985] - 6 X[44435]

X(47653) lies on these lines: {2, 3004}, {239, 514}, {523, 2528}, {661, 28863}, {693, 20950}, {812, 17161}, {824, 20295}, {918, 31290}, {2786, 23731}, {3700, 26798}, {4024, 21297}, {4444, 4608}, {4467, 26853}, {4802, 21146}, {4813, 30519}, {6590, 26985}, {14779, 41821}

X(47653) = reflection of X(i) in X(j) for these {i,j}: {7192, 16892}, {17494, 45746}, {26853, 4467}
X(47653) = X(831)-anticomplementary conjugate of X(69)
X(47653) = crosssum of X(213) and X(8635)
X(47653) = crossdifference of every pair of points on line {42, 5007}
X(47653) = barycentric product X(514)*X(17307)
X(47653) = barycentric quotient X(17307)/X(190)
X(47653) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6590, 44435, 26985}, {17494, 45746, 46915}

X(47654) = X(514)X(4380)∩X(523)X(2528)

X(47654) = 3 X[4467] - 2 X[4979], 2 X[650] - 3 X[45746], 4 X[4813] - 3 X[44449], 4 X[3004] - 3 X[4789], 6 X[3004] - 5 X[26985], 7 X[3004] - 6 X[45677], 9 X[4789] - 10 X[26985], 7 X[4789] - 8 X[45677], 35 X[26985] - 36 X[45677], 5 X[6590] - 6 X[44432]

X(47654) lies on these lines: {514, 4380}, {523, 2528}, {650, 16757}, {824, 4813}, {2254, 28147}, {3004, 4789}, {3960, 30600}, {4608, 21104}, {4784, 28175}, {4988, 28863}, {6590, 44432}

X(47654) = reflection of X(4608) in X(21104)
X(47654) = crossdifference of every pair of points on line {5007, 37586}

X(47655) = X(325)X(523)∩X(513)X(4608)

X(47655) = 5 X[693] - 4 X[3004], 13 X[693] - 12 X[4927], 7 X[693] - 6 X[44435], 3 X[693] - 2 X[45746], 13 X[3004] - 15 X[4927], 14 X[3004] - 15 X[44435], 6 X[3004] - 5 X[45746], 14 X[4927] - 13 X[44435], 18 X[4927] - 13 X[45746], 9 X[44435] - 7 X[45746], 4 X[4500] - 3 X[4776], 3 X[4776] - 2 X[4988], 6 X[4789] - 5 X[31209], 3 X[4789] - 2 X[45745], 5 X[31209] - 4 X[45745], 4 X[4885] - 3 X[46915], 4 X[6590] - 3 X[31150]

X(47655) lies on these lines: {325, 523}, {513, 4608}, {514, 4838}, {4025, 28169}, {4106, 28151}, {4467, 28161}, {4500, 4776}, {4777, 7192}, {4789, 25594}, {4801, 23685}, {4802, 20295}, {4820, 31290}, {4885, 46915}, {4897, 28187}, {4978, 20909}, {6590, 31150}, {17161, 28165}, {26824, 28894}

X(47655) = reflection of X(i) in X(j) for these {i,j}: {4988, 4500}, {17161, 43067}, {31290, 4820}
X(47655) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4500, 4988, 4776}, {4789, 45745, 31209}

X(47656) = X(2)X(45745)∩X(325)X(523)

X(47656) = 3 X[693] - 2 X[3004], 7 X[693] - 6 X[4927], 4 X[693] - 3 X[44435], 7 X[3004] - 9 X[4927], 8 X[3004] - 9 X[44435], 4 X[3004] - 3 X[45746], 8 X[4927] - 7 X[44435], 12 X[4927] - 7 X[45746], 3 X[44435] - 2 X[45746], 2 X[650] - 3 X[4789], 4 X[4369] - 3 X[27486], 3 X[4379] - 2 X[21196], 4 X[4765] - 5 X[27013], 3 X[4776] - 2 X[4841], 3 X[6590] - 2 X[11068], 4 X[11068] - 3 X[17494], X[14779] - 5 X[26798], 5 X[26985] - 3 X[46915]

X(47656) lies on these lines: {2, 45745}, {325, 523}, {514, 4024}, {522, 7192}, {650, 4789}, {661, 4500}, {824, 4838}, {3676, 28169}, {3835, 4988}, {4025, 17161}, {4088, 21297}, {4106, 4122}, {4369, 27486}, {4379, 20522}, {4453, 28165}, {4467, 4777}, {4765, 27013}, {4776, 4841}, {4801, 21438}, {4820, 44449}, {4897, 28183}, {4960, 29216}, {6589, 24900}, {6590, 11068}, {7662, 26248}, {14779, 26798}, {21832, 27673}, {23813, 28151}, {26985, 46915}

X(47656) = midpoint of X(4608) and X(20295)
X(47656) = reflection of X(i) in X(j) for these {i,j}: {661, 4500}, {4467, 43067}, {4988, 3835}, {17161, 4025}, {17494, 6590}, {25259, 4024}, {44449, 4820}, {45746, 693}
X(47656) = anticomplement of X(45745)
X(47656) = isotomic conjugate of X(46961)
X(47656) = isotomic conjugate of the anticomplement of X(38960)
X(47656) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {967, 149}, {969, 150}
X(47656) = X(38960)-cross conjugate of X(2)
X(47656) = X(31)-isoconjugate of X(46961)
X(47656) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 46961), (28651, 100), (40622, 35576)
X(47656) = crossdifference of every pair of points on line {32, 2308}
X(47656) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 46961}, {7178, 35576}, {38960, 45745}
X(47656) = {X(693),X(45746)}-harmonic conjugate of X(44435)

X(47657) = X(325)X(523)∩X(513)X(17161)

X(47657) = 3 X[693] - 4 X[3004], 11 X[693] - 12 X[4927], 5 X[693] - 6 X[44435], 11 X[3004] - 9 X[4927], 10 X[3004] - 9 X[44435], 2 X[3004] - 3 X[45746], 10 X[4927] - 11 X[44435], 6 X[4927] - 11 X[45746], 3 X[44435] - 5 X[45746], 2 X[650] - 3 X[46915], 2 X[4024] - 3 X[4776], 4 X[6590] - 5 X[31209], 8 X[11068] - 9 X[31150], 2 X[11068] - 3 X[45745], 3 X[31150] - 4 X[45745]

X(47657) lies on these lines: {325, 523}, {513, 17161}, {514, 4380}, {650, 46915}, {824, 4988}, {1734, 40471}, {3835, 4838}, {4024, 4776}, {4025, 28147}, {4106, 28165}, {4453, 28155}, {4608, 28151}, {4705, 21350}, {4777, 20295}, {4802, 7192}, {4841, 25259}, {4897, 28175}, {6590, 31209}, {11068, 31150}, {17458, 27647}, {17494, 28894}, {21348, 24948}, {28898, 31290}

X(47657) = reflection of X(i) in X(j) for these {i,j}: {693, 45746}, {4608, 43067}, {4838, 3835}, {25259, 4841}
X(47657) = barycentric product X(3261)*X(5312)
X(47657) = barycentric quotient X(5312)/X(101)

X(47658) = X(23)X(385)∩X(514)X(4838)

X(47658) = 3 X[4467] - 4 X[4932], 9 X[4789] - 8 X[4885], 3 X[4789] - 2 X[45746], 4 X[4885] - 3 X[45746], 2 X[4988] - 3 X[30565], 6 X[6590] - 5 X[31209]

X(47658) lies on these lines: {23, 385}, {514, 4838}, {918, 4608}, {4380, 28161}, {4467, 4932}, {4468, 28155}, {4789, 4885}, {4802, 25259}, {4804, 28147}, {4810, 28175}, {4988, 30565}, {6590, 31209}, {26853, 28183}

X(47659) = X(23)X(385)∩X(514)X(4024)

X(47659) = 3 X[2] - 4 X[6590], 7 X[2] - 8 X[45685], 7 X[6590] - 6 X[45685], 12 X[45685] - 7 X[45746], 3 X[4024] - X[23731], 3 X[20295] - 2 X[23731], 4 X[650] - 3 X[46915], 2 X[3004] - 3 X[4789], 4 X[3004] - 5 X[26985], 5 X[3004] - 6 X[45677], 6 X[4789] - 5 X[26985], 5 X[4789] - 4 X[45677], 25 X[26985] - 24 X[45677], 4 X[4468] - X[14779], 4 X[4500] - 3 X[21297], 2 X[4841] - 3 X[30565], 4 X[21196] - 5 X[27013], 5 X[26777] - 4 X[45745]

X(47658) lies on these lines: {2, 6590}, {23, 385}, {514, 4024}, {522, 26853}, {649, 17161}, {650, 46915}, {693, 20950}, {812, 4838}, {824, 7192}, {3004, 4789}, {4010, 4802}, {4380, 4777}, {4468, 14779}, {4500, 21297}, {4841, 30565}, {4977, 44449}, {21196, 27013}, {21348, 27648}, {26777, 45745}

X(47659) = reflection of X(i) in X(j) for these {i,j}: {17161, 649}, {20295, 4024}, {31290, 25259}, {45746, 6590}
X(47659) = anticomplement of X(45746)
X(47659) = anticomplement of the isotomic conjugate of X(835)
X(47659) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {835, 6327}, {2214, 150}, {37218, 315}, {43531, 21293}
X(47659) = X(835)-Ceva conjugate of X(2)
X(47659) = crosssum of X(i) and X(j) for these (i,j): {3051, 8637}, {20970, 42664}
X(47659) = crossdifference of every pair of points on line {39, 2308}
X(47659) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 4789, 26985}, {6590, 45746, 2}

X(47660) = X(2)X(3004)∩X(23)X(385)

X(47660) = 2 X[661] - 3 X[30565], 2 X[693] - 3 X[4789], 4 X[3239] - 3 X[4776], 3 X[4789] - 4 X[6590], 3 X[1635] - 2 X[21196], 8 X[2490] - 7 X[27115], 2 X[3776] - 3 X[4379], 3 X[4120] - X[23731], 4 X[4369] - 3 X[4453], 3 X[4453] - 2 X[16892], 4 X[4394] - 3 X[27486], 4 X[4885] - 3 X[44435], 2 X[4940] - 3 X[4944], X[4988] - 3 X[6546], 4 X[11068] - 3 X[31150], 3 X[31150] - 2 X[45745], X[14779] - 9 X[44009], 4 X[17069] - 5 X[27013], 4 X[21212] - 5 X[24924], 3 X[21297] - 2 X[23729], 5 X[26777] - 3 X[46915]

X(47600) lies on these lines: {2, 3004}, {23, 385}, {257, 18015}, {513, 4122}, {514, 661}, {522, 4380}, {649, 824}, {650, 16757}, {665, 16751}, {786, 14296}, {812, 4024}, {850, 20952}, {900, 26853}, {918, 7192}, {1255, 4608}, {1635, 21196}, {2254, 23954}, {2483, 23885}, {2490, 27115}, {2786, 4979}, {3005, 21349}, {3261, 29971}, {3700, 20295}, {3776, 4379}, {4063, 23879}, {4120, 23731}, {4369, 4453}, {4374, 21408}, {4382, 4500}, {4394, 27486}, {4790, 28898}, {4802, 7662}, {4813, 28859}, {4820, 6008}, {4885, 44435}, {4932, 30519}, {4940, 4944}, {4976, 17161}, {4977, 18004}, {4988, 6546}, {6084, 26824}, {6586, 27648}, {7199, 21584}, {10015, 26146}, {11068, 31150}, {14779, 28179}, {17069, 27013}, {17166, 29288}, {18154, 20950}, {20906, 30061}, {21118, 29116}, {21123, 27469}, {21179, 28147}, {21212, 24924}, {21297, 23729}, {21348, 28374}, {23770, 28175}, {25356, 27730}, {26777, 46915}, {26854, 27258}, {26985, 30815}, {28151, 47131}, {29278, 31291}, {30520, 43067}

X(47660) = reflection of X(i) in X(j) for these {i,j}: {693, 6590}, {4382, 4500}, {4467, 649}, {16892, 4369}, {17161, 4976}, {20295, 3700}, {20906, 47129}, {44449, 25259}, {45745, 11068}, {45746, 650}
X(47660) = anticomplement of X(3004)
X(47660) = anticomplement of the isogonal conjugate of X(32736)
X(47660) = anticomplement of the isotomic conjugate of X(8707)
X(47660) = isotomic conjugate of the isogonal conjugate of X(2483)
X(47660) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {692, 5484}, {1220, 21293}, {2298, 150}, {6648, 21285}, {8687, 7}, {8707, 6327}, {14624, 21294}, {32736, 8}, {35334, 1369}, {36098, 3434}, {36147, 69}
X(47660) = X(i)-Ceva conjugate of X(j) for these (i,j): {8707, 2}, {10159, 1086}, {40033, 244}, {40044, 1111}
X(47660) = X(i)-isoconjugate of X(j) for these (i,j): {6, 831}, {17108, 32736}
X(47660) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 831), (830, 2483)
X(47660) = crosspoint of X(85) and X(6648)
X(47660) = crossdifference of every pair of points on line {31, 39}
X(47660) = barycentric product X(i)*X(j) for these {i,j}: {75, 830}, {76, 2483}, {83, 23885}, {513, 33941}, {514, 17289}, {522, 7247}, {561, 8635}, {693, 3920}, {786, 14622}, {1255, 27610}, {3261, 5280}, {5314, 46107}, {7199, 28594}
X(47660) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 831}, {830, 1}, {2483, 6}, {3920, 100}, {4538, 4069}, {5280, 101}, {5314, 1331}, {7247, 664}, {7859, 33951}, {8635, 31}, {17289, 190}, {23885, 141}, {27610, 4359}, {28594, 1018}, {33941, 668}
X(47660) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 6590, 4789}, {4369, 16892, 4453}, {11068, 45745, 31150}

X(47661) = X(23)X(385)∩X(514)X(4380)

X(47661) = 4 X[650] - 3 X[4789], 3 X[4988] - X[23731], 2 X[3004] - 3 X[46915], X[26824] - 3 X[46915], 2 X[4024] - 3 X[30565], 3 X[4453] - 4 X[21196], 2 X[4500] - 3 X[4893], 2 X[6590] - 3 X[31150], 3 X[27486] - 2 X[43067]

X(47661) lies on these lines: {23, 385}, {514, 4380}, {522, 44449}, {650, 4789}, {693, 24622}, {812, 4988}, {850, 29771}, {900, 31290}, {918, 17161}, {3004, 26824}, {3310, 24900}, {4024, 30565}, {4453, 21196}, {4468, 28161}, {4500, 4893}, {4762, 45746}, {4777, 25259}, {4841, 20295}, {4976, 7192}, {4977, 26853}, {6590, 31150}, {14779, 28175}, {21727, 24462}, {25020, 26545}, {27486, 43067}

X(47661) = reflection of X(i) in X(j) for these {i,j}: {693, 45745}, {7192, 4976}, {20295, 4841}, {26824, 3004}
X(47661) = {X(26824),X(46915)}-harmonic conjugate of X(3004)

X(47662) = X(514)X(661)∩X(523)X(8664)

X(47662) = 5 X[693] - 6 X[4789], 3 X[693] - 4 X[6590], 9 X[4789] - 10 X[6590], 4 X[2490] - 3 X[3004], 16 X[2490] - 15 X[31209], 4 X[3004] - 5 X[31209], 6 X[4944] - 5 X[26798], 3 X[31150] - 2 X[45746]

X(47662) lies on these lines: {514, 661}, {523, 8664}, {649, 28863}, {824, 4380}, {2490, 3004}, {2496, 4802}, {4024, 28882}, {4944, 26798}, {4979, 30519}, {7192, 30520}, {7662, 28199}, {17494, 28894}, {24623, 28890}, {26853, 28898}, {28175, 47132}, {28191, 47123}, {28195, 46403}, {31150, 45746}

X(47662) = crossdifference of every pair of points on line {31, 7772}
X(47662) = barycentric product X(i)*X(j) for these {i,j}: {514, 17371}, {693, 29815}
X(47662) = barycentric quotient X(i)/X(j) for these {i,j}: {17371, 190}, {29815, 100}

X(47663) = X(2)X(11068)∩X(239)X(514)

X(47663) = 3 X[2] - 4 X[11068], 2 X[16892] - 3 X[27486], 3 X[17494] - 2 X[45745], 5 X[17494] - 3 X[46915], 4 X[45745] - 3 X[45746], 10 X[45745] - 9 X[46915], 5 X[45746] - 6 X[46915], 4 X[650] - 3 X[44435], 3 X[1635] - 2 X[3776], 4 X[2490] - 3 X[4927], 4 X[2529] - 3 X[43067], 4 X[2977] - 3 X[44429], 2 X[3004] - 3 X[31150], 4 X[3239] - 3 X[21297], 4 X[3676] - 5 X[27013], 2 X[3835] - 3 X[6546], 2 X[4106] - 3 X[30565], 4 X[4394] - 3 X[4453], 8 X[4521] - 7 X[27138], 8 X[4521] - 9 X[31992], 7 X[27138] - 9 X[31992], 3 X[4776] - 2 X[23729], 3 X[6545] - 4 X[31286], 3 X[9778] - 2 X[28589], 6 X[10196] - 5 X[30835], 3 X[21183] - 4 X[43061], 6 X[21204] - 7 X[31207], 5 X[26798] - 9 X[44009], 3 X[44433] - 2 X[47131]

X(47661) lies on these lines: {2, 11068}, {239, 514}, {329, 4468}, {523, 8664}, {650, 44435}, {659, 8654}, {661, 28882}, {693, 6084}, {812, 25259}, {918, 4380}, {1252, 3732}, {1635, 3776}, {2490, 4927}, {2529, 43067}, {2977, 44429}, {3004, 31150}, {3239, 21297}, {3676, 5435}, {3700, 6009}, {3808, 20983}, {3835, 6546}, {4106, 30565}, {4394, 4453}, {4462, 20298}, {4467, 30520}, {4521, 5328}, {4776, 23729}, {4979, 28851}, {6008, 44449}, {6545, 31286}, {6590, 26824}, {9778, 28589}, {10196, 30835}, {20078, 26853}, {21183, 43061}, {21204, 31207}, {26267, 26277}, {26798, 44009}, {44433, 47131}

X(47663) = reflection of X(i) in X(j) for these {i,j}: {20295, 4468}, {26824, 6590}, {45746, 17494}
X(47663) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {7084, 4440}, {7123, 149}, {8269, 6604}, {30701, 21293}, {42384, 11442}
X(47663) = crossdifference of every pair of points on line {42, 7772}
X(47663) = barycentric product X(514)*X(17352)
X(47663) = barycentric quotient X(17352)/X(190)
X(47663) = {X(27138),X(31992)}-harmonic conjugate of X(4521)

X(47664) = X(2)X(650)∩X(514)X(4380)

X(47664) = 9 X[2] - 10 X[650], 6 X[2] - 5 X[693], 21 X[2] - 20 X[4885], 3 X[2] - 5 X[17494], 21 X[2] - 25 X[26777], 9 X[2] - 5 X[26824], 27 X[2] - 25 X[26985], 33 X[2] - 35 X[27115], 4 X[2] - 5 X[31150], 24 X[2] - 25 X[31209], 51 X[2] - 50 X[31250], 39 X[2] - 40 X[31287], 19 X[2] - 20 X[44567], 11 X[2] - 10 X[45320], 4 X[650] - 3 X[693], 7 X[650] - 6 X[4885], 2 X[650] - 3 X[17494], 14 X[650] - 15 X[26777], 6 X[650] - 5 X[26985], 22 X[650] - 21 X[27115], 8 X[650] - 9 X[31150], 16 X[650] - 15 X[31209], 17 X[650] - 15 X[31250], 13 X[650] - 12 X[31287], 19 X[650] - 18 X[44567], 11 X[650] - 9 X[45320], 7 X[693] - 8 X[4885], 7 X[693] - 10 X[26777], 3 X[693] - 2 X[26824], 9 X[693] - 10 X[26985], 11 X[693] - 14 X[27115], 2 X[693] - 3 X[31150], 4 X[693] - 5 X[31209], 17 X[693] - 20 X[31250], 13 X[693] - 16 X[31287], 19 X[693] - 24 X[44567], 11 X[693] - 12 X[45320], 4 X[4885] - 7 X[17494], 4 X[4885] - 5 X[26777], 12 X[4885] - 7 X[26824], 36 X[4885] - 35 X[26985], 44 X[4885] - 49 X[27115], 16 X[4885] - 21 X[31150], 32 X[4885] - 35 X[31209], 34 X[4885] - 35 X[31250], 13 X[4885] - 14 X[31287], 19 X[4885] - 21 X[44567], 22 X[4885] - 21 X[45320], 7 X[17494] - 5 X[26777], 3 X[17494] - X[26824], 9 X[17494] - 5 X[26985], 11 X[17494] - 7 X[27115], 4 X[17494] - 3 X[31150], 8 X[17494] - 5 X[31209], 17 X[17494] - 10 X[31250], 13 X[17494] - 8 X[31287], 19 X[17494] - 12 X[44567], 11 X[17494] - 6 X[45320], 15 X[26777] - 7 X[26824], 9 X[26777] - 7 X[26985], 55 X[26777] - 49 X[27115], 20 X[26777] - 21 X[31150], 8 X[26777] - 7 X[31209], 17 X[26777] - 14 X[31250], 65 X[26777] - 56 X[31287], 95 X[26777] - 84 X[44567], 55 X[26777] - 42 X[45320], 3 X[26824] - 5 X[26985], 11 X[26824] - 21 X[27115], 4 X[26824] - 9 X[31150], 8 X[26824] - 15 X[31209], 17 X[26824] - 30 X[31250], 13 X[26824] - 24 X[31287], 19 X[26824] - 36 X[44567], 11 X[26824] - 18 X[45320], 55 X[26985] - 63 X[27115], 20 X[26985] - 27 X[31150], 8 X[26985] - 9 X[31209], 17 X[26985] - 18 X[31250], 65 X[26985] - 72 X[31287], 95 X[26985] - 108 X[44567], 55 X[26985] - 54 X[45320], 28 X[27115] - 33 X[31150], 56 X[27115] - 55 X[31209], 91 X[27115] - 88 X[31287], 7 X[27115] - 6 X[45320], 6 X[31150] - 5 X[31209], 51 X[31150] - 40 X[31250], 39 X[31150] - 32 X[31287], 19 X[31150] - 16 X[44567], 11 X[31150] - 8 X[45320], 17 X[31209] - 16 X[31250], 65 X[31209] - 64 X[31287], 95 X[31209] - 96 X[44567], 55 X[31209] - 48 X[45320], 65 X[31250] - 68 X[31287], 95 X[31250] - 102 X[44567], 55 X[31250] - 51 X[45320], 38 X[31287] - 39 X[44567], 44 X[31287] - 39 X[45320], 22 X[44567] - 19 X[45320], 3 X[4380] - 2 X[4979], 4 X[3960] - 3 X[4801], 2 X[4382] - 3 X[4776], 3 X[4453] - 4 X[4765], 2 X[4500] - 3 X[6546], 3 X[4789] - 4 X[11068], 2 X[21104] - 3 X[27486], 6 X[37897] - 5 X[47174]

X(47664) lies on these lines: {2, 650}, {514, 4380}, {523, 8664}, {812, 4813}, {3529, 8760}, {3632, 29066}, {3644, 4777}, {3960, 4801}, {4382, 4776}, {4453, 4765}, {4462, 23882}, {4500, 6546}, {4789, 11068}, {4814, 29051}, {4841, 6009}, {4988, 28882}, {6008, 31290}, {6084, 45746}, {9001, 11008}, {9015, 40341}, {14077, 20050}, {17161, 30520}, {21104, 27486}, {37897, 47174}

X(47664) = reflection of X(i) in X(j) for these {i,j}: {693, 17494}, {26824, 650}
X(47664) = crossdifference of every pair of points on line {2223, 7772}
X(47664) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 26824, 693}, {693, 17494, 31150}, {693, 31150, 31209}, {17494, 26824, 650}

X(47665) = X(37)X(27648)∩X(192)X(4777)

X(47665) = 7 X[17494] - 9 X[44009], 5 X[693] - 4 X[3776], 3 X[693] - 4 X[4500], 7 X[693] - 6 X[6545], 3 X[693] - 2 X[16892], 2 X[3776] - 5 X[4024], 3 X[3776] - 5 X[4500], 14 X[3776] - 15 X[6545], 6 X[3776] - 5 X[16892], 3 X[4024] - 2 X[4500], 7 X[4024] - 3 X[6545], 3 X[4024] - X[16892], 14 X[4500] - 9 X[6545], 9 X[6545] - 7 X[16892], 4 X[3700] - 3 X[4776], 3 X[4776] - 2 X[45746], 4 X[3798] - 3 X[4467], 2 X[3798] - 3 X[6590], 2 X[3835] - 3 X[4931], 2 X[4025] - 3 X[4789], 4 X[21196] - 5 X[31209], 7 X[21196] - 9 X[45684], 35 X[31209] - 36 X[45684], 2 X[21212] - 3 X[45343], 3 X[30565] - 2 X[45745]

X(47665) lies on these lines: {37, 27648}, {192, 4777}, {321, 693}, {514, 4838}, {522, 4380}, {523, 8663}, {650, 17161}, {1577, 20909}, {3700, 4776}, {3798, 4467}, {3835, 4931}, {3869, 14077}, {4025, 4789}, {4359, 30024}, {4382, 28863}, {4391, 23879}, {4468, 28161}, {4762, 42044}, {4802, 31290}, {4820, 20295}, {4926, 26853}, {7192, 28898}, {16751, 21348}, {17458, 27469}, {21196, 31209}, {21212, 45343}, {24547, 25009}, {24900, 25098}, {26824, 30520}, {30565, 45745}

X(47665) = reflection of X(i) in X(j) for these {i,j}: {693, 4024}, {4467, 6590}, {16892, 4500}, {17161, 650}, {20295, 4820}, {45746, 3700}
X(47665) = barycentric product X(313)*X(5216)
X(47665) = barycentric quotient X(5216)/X(58)
X(47665) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3700, 45746, 4776}, {4024, 16892, 4500}, {4500, 16892, 693}

X(47666) = X(2)X(43067)∩X(513)X(4380)

X(47666) = 3 X[4380] - 2 X[26853], X[4380] + 2 X[31290], 3 X[17494] - X[26853], X[26853] + 3 X[31290], 3 X[661] - 2 X[3835], 5 X[661] - 3 X[4728], 4 X[661] - 3 X[4776], 3 X[693] - 4 X[3835], 5 X[693] - 6 X[4728], 2 X[693] - 3 X[4776], 4 X[3239] - 3 X[4789], 10 X[3835] - 9 X[4728], 8 X[3835] - 9 X[4776], 4 X[4728] - 5 X[4776], 2 X[6590] - 3 X[30565], 2 X[649] - 3 X[31150], 6 X[650] - 5 X[27013], 3 X[7192] - 5 X[27013], 3 X[1635] - 2 X[4932], 3 X[4120] - 2 X[4500], 2 X[4369] - 3 X[4893], 6 X[4369] - 7 X[31207], 4 X[4369] - 5 X[31209], 5 X[4369] - 6 X[45675], 9 X[4893] - 7 X[31207], 6 X[4893] - 5 X[31209], 5 X[4893] - 4 X[45675], 14 X[31207] - 15 X[31209], 35 X[31207] - 36 X[45675], 25 X[31209] - 24 X[45675], 3 X[4379] - 4 X[25666], 4 X[4394] - 5 X[26777], 2 X[4897] - 3 X[27486], 4 X[4940] - 3 X[21297], 2 X[21104] - 3 X[44435], 2 X[21146] - 3 X[44429], 4 X[23813] - 5 X[26798], 7 X[27138] - 6 X[45320], 5 X[30835] - 6 X[45315], 3 X[31148] - 4 X[31286]

X(47666) lies on these lines: {2, 43067}, {513, 4380}, {514, 661}, {522, 44449}, {523, 8663}, {649, 28840}, {650, 7192}, {659, 4963}, {812, 4813}, {824, 4988}, {905, 24948}, {918, 4841}, {1491, 2977}, {1635, 4932}, {1734, 21727}, {2254, 4778}, {3005, 23768}, {3669, 27674}, {3837, 28213}, {4010, 4802}, {4025, 28878}, {4106, 26824}, {4120, 4500}, {4369, 4893}, {4379, 25666}, {4394, 26777}, {4444, 6546}, {4467, 28846}, {4724, 23655}, {4762, 20295}, {4804, 28147}, {4806, 28175}, {4897, 27486}, {4940, 21297}, {14404, 29198}, {14779, 28151}, {16892, 28851}, {17161, 28898}, {18080, 28199}, {20974, 40619}, {21104, 44435}, {21146, 28195}, {21196, 28855}, {21385, 29807}, {23731, 28882}, {23813, 26798}, {24720, 25627}, {25511, 27045}, {25902, 26545}, {27138, 45320}, {27417, 46393}, {27469, 30061}, {27647, 30024}, {30835, 45315}, {31148, 31286}, {36848, 44009}

X(47666) = midpoint of X(i) and X(j) for these {i,j}: {659, 4963}, {17494, 31290}
X(47666) = reflection of X(i) in X(j) for these {i,j}: {693, 661}, {4380, 17494}, {4467, 45745}, {4801, 14349}, {7192, 650}, {26824, 4106}, {45746, 4841}
X(47666) = anticomplement of X(43067)
X(47666) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {931, 17135}, {941, 150}, {2258, 149}, {31359, 21293}, {32038, 21285}, {32693, 7}
X(47666) = X(i)-isoconjugate of X(j) for these (i,j): {6, 6013}, {101, 10013}, {163, 46772}
X(47666) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 6013), (115, 46772), (1015, 10013)
X(47666) = crosspoint of X(i) and X(j) for these (i,j): {85, 32038}, {668, 1218}
X(47666) = crosssum of X(i) and X(j) for these (i,j): {667, 1185}, {8639, 21753}
X(47666) = crossdifference of every pair of points on line {31, 2241}
X(47666) = barycentric product X(i)*X(j) for these {i,j}: {75, 6005}, {514, 4687}, {561, 8655}, {693, 17018}, {850, 39673}, {16878, 35519}
X(47666) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 6013}, {513, 10013}, {523, 46772}, {4687, 190}, {6005, 1}, {8655, 31}, {16878, 109}, {17018, 100}, {39673, 110}
X(47666) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 693, 4776}, {4369, 4893, 31209}

X(47667) = X(239)X(514)∩X(522)X(31290)

X(47667) = 4 X[3798] - 3 X[7192], 8 X[3798] - 9 X[27486], 2 X[3798] - 3 X[45745], 2 X[4025] - 3 X[46915], 3 X[4988] - X[16892], 2 X[7192] - 3 X[27486], 2 X[16892] - 3 X[45746], 3 X[27486] - 4 X[45745], 3 X[661] - 2 X[4500], 2 X[4468] + X[14779]

X(47667) lies on these lines: {239, 514}, {522, 31290}, {523, 8663}, {661, 4500}, {693, 4841}, {3005, 4490}, {4380, 4977}, {4468, 14779}, {4608, 6590}, {4777, 44449}, {4778, 26853}, {4802, 7662}, {4963, 29078}, {17161, 28846}, {30765, 44435}

X(47667) = reflection of X(i) in X(j) for these {i,j}: {693, 4841}, {4608, 6590}, {7192, 45745}, {45746, 4988}
X(47667) = X(692)-anticomplementary conjugate of X(41921)
X(47667) = crossdifference of every pair of points on line {42, 31451}
X(47667) = {X(7192),X(45745)}-harmonic conjugate of X(27486)

X(47668) = X(514)X(4380)∩X(523)X(8663)

X(47668) = 3 X[4776] - 4 X[4841], 2 X[21104] - 3 X[45746], 2 X[43067] - 3 X[46915]

X(47668) lies on these lines: {514, 4380}, {523, 8663}, {650, 4608}, {693, 4988}, {4468, 28155}, {4776, 4841}, {4777, 31290}, {4782, 4802}, {21104, 45746}, {21179, 28147}, {26853, 28195}, {28161, 44449}, {43067, 46915}

X(47668) = midpoint of X(14779) and X(17494)
X(47668) = reflection of X(i) in X(j) for these {i,j}: {693, 4988}, {4608, 650}

X(47669) = X(514)X(4380)∩X(523)X(661)

X(47669) = 5 X[661] - 4 X[3700], 3 X[661] - 2 X[4024], 7 X[661] - 6 X[4120], 3 X[661] - 4 X[4841], 4 X[661] - 3 X[4931], 9 X[661] - 8 X[14321], 6 X[3700] - 5 X[4024], 14 X[3700] - 15 X[4120], 8 X[3700] - 5 X[4838], 3 X[3700] - 5 X[4841], 16 X[3700] - 15 X[4931], 2 X[3700] - 5 X[4988], 9 X[3700] - 10 X[14321], 7 X[4024] - 9 X[4120], 4 X[4024] - 3 X[4838], 8 X[4024] - 9 X[4931], X[4024] - 3 X[4988], 3 X[4024] - 4 X[14321], 12 X[4120] - 7 X[4838], 9 X[4120] - 14 X[4841], 8 X[4120] - 7 X[4931], 3 X[4120] - 7 X[4988], 27 X[4120] - 28 X[14321], 3 X[4838] - 8 X[4841], 2 X[4838] - 3 X[4931], X[4838] - 4 X[4988], 9 X[4838] - 16 X[14321], 16 X[4841] - 9 X[4931], 2 X[4841] - 3 X[4988], 3 X[4841] - 2 X[14321], 3 X[4931] - 8 X[4988], 27 X[4931] - 32 X[14321], 9 X[4988] - 4 X[14321], 3 X[1635] - 4 X[45745], 2 X[3776] - 3 X[45746], 2 X[4369] - 3 X[46915], X[4608] - 3 X[46915], 4 X[21196] - 3 X[31148]

X(47669) lies on these lines: {514, 4380}, {523, 661}, {649, 4802}, {650, 23758}, {1635, 4458}, {3776, 45746}, {4041, 40471}, {4369, 4608}, {4490, 21350}, {4777, 4813}, {4790, 28199}, {4822, 6367}, {4958, 28165}, {4976, 28175}, {6590, 28155}, {7192, 14779}, {17161, 28840}, {21196, 31148}

X(47669) = midpoint of X(7192) and X(14779)
X(47669) = reflection of X(i) in X(j) for these {i,j}: {661, 4988}, {4024, 4841}, {4608, 4369}, {4838, 661}
X(47669) = X(i)-isoconjugate of X(j) for these (i,j): {81, 28196}, {110, 27789}, {163, 28650}
X(47669) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 28650), (244, 27789), (40586, 28196)
X(47669) = crossdifference of every pair of points on line {58, 5010}
X(47669) = barycentric product X(i)*X(j) for these {i,j}: {10, 28195}, {513, 42031}, {523, 3624}, {1577, 16884}, {4024, 42025}, {4034, 7178}, {4064, 31901}, {7265, 43261}
X(47669) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 28196}, {523, 28650}, {661, 27789}, {3624, 99}, {4034, 645}, {16884, 662}, {28195, 86}, {42025, 4610}, {42031, 668}
X(47669) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4838, 4931}, {4024, 4841, 661}, {4024, 4988, 4841}, {4608, 46915, 4369}

X(47670) = X(244)X(24137)∩X(514)X(4838)

X(47670) = 5 X[16892] - 6 X[21104], 8 X[16892] - 9 X[21115], 7 X[16892] - 9 X[21116], 16 X[21104] - 15 X[21115], 14 X[21104] - 15 X[21116], 7 X[21115] - 8 X[21116], 3 X[661] - 4 X[4500], 8 X[3798] - 9 X[31148], 3 X[4728] - 2 X[4988], 3 X[4958] - 2 X[31290], X[14779] - 3 X[21297], 5 X[24924] - 4 X[45745], 25 X[24924] - 24 X[46919], 5 X[45745] - 6 X[46919]

X(47670) lies on these lines: {244, 24137}, {514, 4838}, {523, 2254}, {661, 4500}, {812, 4608}, {3798, 31148}, {4382, 4802}, {4728, 4988}, {4801, 20909}, {4958, 31290}, {14779, 21297}, {23729, 28179}, {23731, 28175}, {24924, 45745}

X(47670) = barycentric product X(514)*X(28633)
X(47670) = barycentric quotient X(28633)/X(190)

X(47671) = X(514)X(4024)∩X(523)X(2254)

X(47671) = 3 X[4024] - 2 X[25259], 3 X[16892] - 4 X[21104], 5 X[16892] - 6 X[21115], 2 X[16892] - 3 X[21116], 10 X[21104] - 9 X[21115], 8 X[21104] - 9 X[21116], 4 X[21115] - 5 X[21116], 3 X[4120] - 4 X[4500], 9 X[4379] - 8 X[7658], 3 X[4379] - 2 X[45745], 4 X[7658] - 3 X[45745], 3 X[4728] - 2 X[4841], 3 X[4750] - 4 X[43067], 4 X[4932] - 3 X[4984], 2 X[4976] - 3 X[31148], 3 X[6545] - 2 X[45746], 3 X[6546] - 4 X[6590], 4 X[21212] - 3 X[46915]

X(47671) lies on these lines: {514, 4024}, {523, 2254}, {693, 4988}, {850, 4978}, {918, 4838}, {4088, 4802}, {4120, 4500}, {4122, 23729}, {4379, 7658}, {4728, 4841}, {4750, 43067}, {4932, 4984}, {4976, 31148}, {6545, 25381}, {6546, 6590}, {21212, 46915}

X(47671) = midpoint of X(4608) and X(26824)
X(47671) = reflection of X(i) in X(j) for these {i,j}: {4988, 693}, {23731, 4382}
X(47671) = crossdifference of every pair of points on line {2308, 4251}

X(47672) = X(244)X(24135)∩X(513)X(4382)

X(47672) = 3 X[661] - 4 X[3835], 2 X[661] - 3 X[4728], 5 X[661] - 6 X[4776], 3 X[693] - 2 X[3835], 4 X[693] - 3 X[4728], 5 X[693] - 3 X[4776], 8 X[3835] - 9 X[4728], 10 X[3835] - 9 X[4776], 5 X[4728] - 4 X[4776], 2 X[16892] - 3 X[21115], X[16892] - 3 X[21116], 4 X[21104] - 3 X[21115], 2 X[21104] - 3 X[21116], 2 X[649] - 3 X[31148], 3 X[31148] - 4 X[43067], 2 X[650] - 3 X[4379], 4 X[650] - 5 X[24924], 6 X[650] - 7 X[31207], 6 X[4379] - 5 X[24924], 9 X[4379] - 7 X[31207], 15 X[24924] - 14 X[31207], X[4979] + 2 X[26824], 3 X[4979] - 2 X[26853], 3 X[7192] - X[26853], 3 X[26824] + X[26853], 3 X[1635] - 4 X[4369], 3 X[1635] - 2 X[17494], 9 X[1635] - 10 X[27013], 6 X[4369] - 5 X[27013], 3 X[17494] - 5 X[27013], 2 X[3004] - 3 X[6545], X[4988] - 3 X[6545], 3 X[4453] - 2 X[21196], 2 X[4490] - 3 X[21052], 4 X[4500] - 3 X[4931], 3 X[4931] - 2 X[25259], 3 X[4750] - 2 X[4976], 6 X[4763] - 5 X[26777], 4 X[4885] - 3 X[4893], 3 X[4958] - 2 X[44449], 3 X[14392] - 4 X[15584], 3 X[21297] - X[31290], 4 X[23813] - 3 X[31147], 4 X[25666] - 5 X[26985], 7 X[27138] - 6 X[45315], 5 X[30835] - 6 X[45320], 3 X[31150] - 4 X[31286]

X(47672) lies on these lines: {244, 24135}, {513, 4382}, {514, 661}, {523, 2254}, {649, 4762}, {650, 4379}, {812, 4979}, {824, 4838}, {918, 4024}, {1491, 4802}, {1635, 4369}, {2533, 20507}, {3004, 4988}, {3676, 45745}, {3776, 45746}, {3837, 4824}, {3910, 23755}, {3960, 16751}, {4010, 4977}, {4106, 4813}, {4380, 4932}, {4444, 4608}, {4453, 21196}, {4490, 21052}, {4500, 4931}, {4724, 7662}, {4750, 4976}, {4763, 26777}, {4806, 28213}, {4885, 4893}, {4895, 29188}, {4958, 28855}, {7199, 18071}, {7200, 24137}, {14392, 15584}, {17166, 29051}, {17420, 23743}, {18199, 21758}, {20295, 28840}, {20511, 24107}, {21107, 21118}, {21125, 23753}, {21133, 23749}, {21297, 31290}, {23813, 31147}, {24720, 28147}, {25381, 27790}, {25666, 26985}, {25900, 26546}, {26854, 27527}, {27138, 45315}, {28179, 36848}, {28191, 44429}, {30765, 44435}, {30835, 45320}, {31150, 31286}

X(47672) = midpoint of X(7192) and X(26824)
X(47672) = reflection of X(i) in X(j) for these {i,j}: {649, 43067}, {661, 693}, {2254, 21146}, {4380, 4932}, {4724, 7662}, {4813, 4106}, {4824, 3837}, {4979, 7192}, {4988, 3004}, {16892, 21104}, {17494, 4369}, {21115, 21116}, {23731, 23729}, {25259, 4500}, {45745, 3676}, {45746, 3776}
X(47672) = X(i)-Ceva conjugate of X(j) for these (i,j): {10, 1086}, {310, 244}, {40004, 1111}
X(47672) = X(i)-isoconjugate of X(j) for these (i,j): {6, 8708}, {101, 40433}, {692, 32009}, {4557, 40408}
X(47672) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 8708), (1015, 40433), (1086, 32009), (2486, 3294), (3121, 42), (3739, 1018), (16589, 190), (17205, 86), (40620, 40439)
X(47672) = crosspoint of X(514) and X(7199)
X(47672) = crossdifference of every pair of points on line {31, 4251}
X(47672) = barycentric product X(i)*X(j) for these {i,j}: {75, 6372}, {513, 20888}, {514, 3739}, {522, 4059}, {523, 17175}, {661, 16748}, {693, 3720}, {1111, 4436}, {1577, 18166}, {3261, 20963}, {3676, 3706}, {3691, 24002}, {7192, 21020}, {7199, 16589}, {15413, 40975}, {16892, 18089}, {18155, 39793}, {22060, 46107}
X(47672) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8708}, {513, 40433}, {514, 32009}, {1019, 40408}, {2667, 4557}, {3691, 644}, {3706, 3699}, {3720, 100}, {3739, 190}, {4059, 664}, {4111, 4069}, {4436, 765}, {4754, 18047}, {4891, 43290}, {6372, 1}, {7192, 40439}, {16589, 1018}, {16748, 799}, {17175, 99}, {18166, 662}, {20888, 668}, {20963, 101}, {21020, 3952}, {21699, 40521}, {22060, 1331}, {39793, 4551}, {40975, 1783}
X(47672) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 43067, 31148}, {650, 4379, 24924}, {661, 693, 4728}, {4369, 17494, 1635}, {4500, 25259, 4931}, {4988, 6545, 3004}, {16892, 21104, 21115}, {16892, 21116, 21104}, {21104, 23741, 23748}

X(47673) = X(244)X(24134)∩X(514)X(4380)

X(47673) = 3 X[16892] - 2 X[21104], 4 X[16892] - 3 X[21115], 5 X[16892] - 3 X[21116], 8 X[21104] - 9 X[21115], 10 X[21104] - 9 X[21116], 5 X[21115] - 4 X[21116], 3 X[661] - 2 X[25259], X[25259] - 3 X[45746], 3 X[1635] - 4 X[21196], 4 X[3004] - 3 X[4728], 2 X[4024] - 3 X[4728], 4 X[3835] - 3 X[4931], 4 X[4025] - 3 X[31148], 2 X[4500] - 3 X[44435], 3 X[4789] - 4 X[21212], 2 X[4820] - 3 X[31147], 3 X[6590] - 4 X[7658], 4 X[6590] - 5 X[24924], 16 X[7658] - 15 X[24924], 2 X[10015] - 3 X[21124]

X(47673) lies on these lines: {244, 24134}, {514, 4380}, {523, 2254}, {649, 28894}, {661, 824}, {693, 4838}, {812, 17161}, {900, 23731}, {905, 30600}, {918, 4988}, {1491, 21350}, {1635, 21196}, {3004, 4024}, {3835, 4931}, {4025, 31148}, {4382, 4777}, {4500, 44435}, {4784, 4802}, {4789, 21212}, {4813, 28898}, {4820, 31147}, {6590, 7658}, {10015, 21124}, {17494, 28863}, {23729, 28183}, {24721, 26824}

X(47673) = reflection of X(i) in X(j) for these {i,j}: {661, 45746}, {4024, 3004}, {4838, 693}, {4979, 4467}
X(47673) = X(17239)-Dao conjugate of X(35342)
X(47673) = barycentric product X(i)*X(j) for these {i,j}: {514, 17239}, {523, 17210}, {693, 3989}
X(47673) = barycentric quotient X(i)/X(j) for these {i,j}: {3989, 100}, {17210, 99}, {17239, 190}
X(47673) = {X(3004),X(4024)}-harmonic conjugate of X(4728)

X(47674) = X(514)X(4024)∩X(693)X(4841)

X(47674) = 4 X[4024] - 3 X[25259], 3 X[693] - 2 X[4841], 4 X[3676] - 3 X[46915], 4 X[3776] - 3 X[45746], 2 X[4988] - 3 X[44435], 15 X[26777] - 16 X[31182], 3 X[27486] - 4 X[43067]

X(47674) lies on these lines: {514, 4024}, {693, 4841}, {850, 4801}, {3676, 46915}, {3776, 45746}, {4088, 28191}, {4122, 28199}, {4838, 28851}, {4988, 44435}, {26777, 31182}, {27486, 43067}

X(47675) = X(513)X(26824)∩X(514)X(661)

X(47675) = 2 X[661] - 3 X[693], 5 X[661] - 6 X[3835], 7 X[661] - 9 X[4728], 8 X[661] - 9 X[4776], 5 X[693] - 4 X[3835], 7 X[693] - 6 X[4728], 4 X[693] - 3 X[4776], 14 X[3835] - 15 X[4728], 16 X[3835] - 15 X[4776], 2 X[4468] - 3 X[4789], 8 X[4728] - 7 X[4776], 2 X[3776] - 3 X[21116], X[4988] - 3 X[21116], 4 X[4369] - 3 X[31150], 6 X[4379] - 5 X[31209], 3 X[4380] - 4 X[4790], 2 X[4790] - 3 X[7192], 5 X[4394] - 6 X[7653], 4 X[4394] - 3 X[17494], 2 X[4394] - 3 X[43067], 8 X[7653] - 5 X[17494], 4 X[7653] - 5 X[43067], 3 X[4453] - 2 X[45745], 2 X[4824] - 3 X[44429], 2 X[4841] - 3 X[44435]

X(47675) lies on these lines: {513, 26824}, {514, 661}, {1491, 28175}, {2254, 28147}, {3669, 16751}, {3776, 4988}, {4010, 28195}, {4024, 28851}, {4106, 31290}, {4369, 31150}, {4379, 31209}, {4380, 4762}, {4382, 28840}, {4394, 7653}, {4453, 45745}, {4608, 28894}, {4778, 4804}, {4802, 21146}, {4820, 28910}, {4824, 28199}, {4838, 30519}, {4841, 44435}, {4960, 29302}, {21104, 45746}, {24720, 28191}, {28878, 44449}

X(47675) = reflection of X(i) in X(j) for these {i,j}: {4380, 7192}, {4988, 3776}, {17494, 43067}, {31290, 4106}, {45746, 21104}
X(47675) = barycentric product X(i)*X(j) for these {i,j}: {514, 4751}, {693, 29814}
X(47675) = barycentric quotient X(i)/X(j) for these {i,j}: {4751, 190}, {29814, 100}
X(47675) = {X(4988),X(21116)}-harmonic conjugate of X(3776)

X(47676) = X(2)X(3676)∩X(145)X(28292)

X(47676) = 3 X[2] - 4 X[3676], 9 X[2] - 8 X[4521], 5 X[2] - 4 X[45670], 3 X[3676] - 2 X[4521], 5 X[3676] - 3 X[45670], 3 X[4468] - 4 X[4521], 5 X[4468] - 6 X[45670], 10 X[4521] - 9 X[45670], 3 X[4025] - 2 X[4765], 4 X[4025] - 3 X[27486], 4 X[4765] - 3 X[17494], 8 X[4765] - 9 X[27486], 9 X[4786] - 8 X[14351], X[4988] - 3 X[16892], 2 X[4988] - 3 X[45746], 2 X[17494] - 3 X[27486], 2 X[650] - 3 X[4453], X[661] - 3 X[21115], 2 X[661] - 3 X[44435], 2 X[3776] - 3 X[21115], 4 X[3776] - 3 X[44435], 3 X[693] - 2 X[3700], X[3700] - 3 X[21104], 4 X[3700] - 3 X[25259], 4 X[21104] - X[25259], 6 X[1638] - 5 X[31209], 2 X[2488] - 3 X[30704], 2 X[3239] - 3 X[21183], 4 X[3239] - 5 X[26985], 6 X[21183] - 5 X[26985], 2 X[3835] - 3 X[6545], X[4024] - 3 X[21116], 3 X[4106] - 2 X[4949], 4 X[4949] - 3 X[44449], 6 X[4147] - 7 X[21952], 4 X[4885] - 3 X[30565], 3 X[4893] - 4 X[21212], 3 X[4927] - 2 X[14321], 3 X[6546] - 4 X[31286], 9 X[6548] - 7 X[27138], 8 X[7658] - 7 X[27115], 6 X[10196] - 7 X[31207], 4 X[11068] - 5 X[27013], 4 X[17069] - 3 X[31150], 6 X[21204] - 5 X[30835]

X(47676) lies on these lines: {2, 3676}, {145, 28292}, {192, 23760}, {239, 514}, {513, 41794}, {518, 44319}, {522, 26824}, {525, 4801}, {650, 4453}, {661, 3776}, {664, 1252}, {693, 918}, {824, 4838}, {919, 43190}, {1638, 31209}, {2488, 30704}, {2786, 4382}, {3005, 3777}, {3239, 21183}, {3669, 24562}, {3801, 29198}, {3810, 23738}, {3835, 6545}, {3873, 23761}, {4024, 21116}, {4088, 24720}, {4106, 4949}, {4147, 21952}, {4367, 8654}, {4369, 28890}, {4378, 29102}, {4380, 4897}, {4458, 4724}, {4462, 7178}, {4467, 4762}, {4813, 28855}, {4885, 30565}, {4893, 21212}, {4927, 14321}, {4978, 23875}, {4979, 28882}, {5098, 20507}, {5905, 20295}, {6006, 20059}, {6078, 37206}, {6360, 23726}, {6546, 31286}, {6548, 27138}, {7658, 27115}, {8661, 21128}, {9965, 26853}, {10196, 31207}, {11068, 27013}, {17069, 31150}, {20075, 28589}, {20089, 21132}, {20504, 25301}, {21129, 24184}, {21204, 30835}, {23655, 24111}, {23743, 23794}, {23764, 28565}, {23788, 26775}, {23989, 35505}, {24002, 26546}, {24126, 24749}, {25924, 27065}, {26580, 26596}, {26641, 31603}, {28878, 31290}, {30520, 43067}

X(47676) = reflection of X(i) in X(j) for these {i,j}: {661, 3776}, {693, 21104}, {4088, 24720}, {4380, 4897}, {4462, 7178}, {4468, 3676}, {4724, 4458}, {17494, 4025}, {23794, 23743}, {25259, 693}, {44435, 21115}, {44449, 4106}, {45746, 16892}
X(47676) = anticomplement of X(4468)
X(47676) = anticomplement of the isotomic conjugate of X(37206)
X(47676) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {6, 34547}, {277, 21293}, {1292, 69}, {1415, 7674}, {2191, 150}, {2428, 20344}, {32644, 518}, {36041, 20347}, {37206, 6327}
X(47676) = X(37206)-Ceva conjugate of X(2)
X(47676) = X(17059)-Dao conjugate of X(220)
X(47676) = crosspoint of X(190) and X(32019)
X(47676) = crosssum of X(i) and X(j) for these (i,j): {213, 8642}, {663, 14827}
X(47676) = crossdifference of every pair of points on line {42, 8647}
X(47676) = barycentric product X(i)*X(j) for these {i,j}: {75, 4905}, {513, 33933}, {514, 17234}, {664, 17059}, {693, 3873}, {3261, 4253}, {3941, 40495}, {3970, 7199}, {4391, 17092}, {4462, 27827}, {4573, 21946}, {4998, 23761}, {24002, 25082}
X(47676) = barycentric quotient X(i)/X(j) for these {i,j}: {3873, 100}, {3941, 692}, {3970, 1018}, {4253, 101}, {4905, 1}, {17059, 522}, {17092, 651}, {17234, 190}, {21946, 3700}, {22277, 4557}, {23761, 11}, {25082, 644}, {27827, 27834}, {33933, 668}
X(47676) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 3776, 44435}, {661, 21115, 3776}, {3239, 21183, 26985}, {3676, 4468, 2}, {4025, 17494, 27486}

X(47677) = X(321)X(693)∩X(514)X(4380)

X(47677) = 3 X[693] - 4 X[3776], 3 X[693] - 2 X[4024], 5 X[693] - 4 X[4500], 5 X[693] - 6 X[6545], 5 X[3776] - 3 X[4500], 10 X[3776] - 9 X[6545], 2 X[3776] - 3 X[16892], 5 X[4024] - 6 X[4500], 5 X[4024] - 9 X[6545], X[4024] - 3 X[16892], 2 X[4500] - 3 X[6545], 2 X[4500] - 5 X[16892], 3 X[6545] - 5 X[16892], 10 X[650] - 9 X[31992], 2 X[4841] - 3 X[45746], 4 X[3004] - 3 X[4776], 3 X[3004] - 2 X[14321], 9 X[4776] - 8 X[14321], 3 X[4776] - 2 X[25259], 4 X[14321] - 3 X[25259], 4 X[3676] - 3 X[4789], 2 X[3700] - 3 X[44435], 2 X[4122] - 3 X[44429], 3 X[4453] - 2 X[6590], 2 X[4820] - 3 X[21297], X[4838] - 3 X[21115], 6 X[4944] - 7 X[27138], 3 X[14349] - 2 X[22037], 4 X[21196] - 3 X[31150]

X(47677) lies on these lines: {321, 693}, {514, 4380}, {649, 28863}, {650, 4850}, {661, 30519}, {768, 20906}, {918, 4841}, {1278, 4777}, {2530, 21350}, {3004, 4776}, {3210, 17494}, {3676, 4789}, {3700, 44435}, {4088, 4818}, {4122, 44429}, {4359, 30061}, {4453, 6590}, {4462, 21124}, {4762, 17161}, {4801, 23879}, {4820, 21297}, {4838, 21115}, {4905, 40471}, {4944, 27138}, {4988, 28851}, {7192, 28894}, {14077, 14923}, {14349, 22037}, {15413, 23885}, {20295, 28898}, {21196, 31150}, {23731, 28867}, {26538, 26546}, {28374, 28606}

X(47677) = reflection of X(i) in X(j) for these {i,j}: {693, 16892}, {4024, 3776}, {4088, 4818}, {4380, 4467}, {4462, 21124}, {25259, 3004}
X(47677) = barycentric product X(i)*X(j) for these {i,j}: {514, 17228}, {693, 7226}
X(47677) = barycentric quotient X(i)/X(j) for these {i,j}: {7226, 100}, {17228, 190}
X(47677) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 25259, 4776}, {3776, 4024, 693}, {4024, 16892, 3776}, {4500, 6545, 693}

X(47678) = X(321)X(4801)∩X(514)X(4024)

X(47678) = 5 X[4024] - 2 X[22037], 5 X[7265] - 4 X[22037], X[7265] - 4 X[31010], X[22037] - 5 X[31010], X[4707] + 2 X[4838], 3 X[4789] - 2 X[14838]

X(47678) lies on these lines: {321, 4801}, {514, 4024}, {523, 1577}, {784, 876}, {2533, 6367}, {2786, 4960}, {2901, 29186}, {4040, 21831}, {4064, 28147}, {4129, 4988}, {4500, 14349}, {4707, 4838}, {4789, 14838}, {4802, 23282}, {4823, 45746}, {14837, 28169}, {14977, 23894}, {17161, 21192}, {20509, 23945}

X(47678) = reflection of X(i) in X(j) for these {i,j}: {4024, 31010}, {4988, 4129}, {7265, 4024}, {14349, 4500}, {17161, 21192}, {45746, 4823}
X(47678) = X(58)-isoconjugate of X(15322)
X(47678) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 15322), (4841, 4778)
X(47678) = crosspoint of X(1441) and X(4624)
X(47678) = crossdifference of every pair of points on line {1333, 2308}
X(47678) = barycentric product X(i)*X(j) for these {i,j}: {321, 15309}, {523, 28653}, {1577, 17019}, {31010, 41818}
X(47678) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 15322}, {15309, 81}, {17019, 662}, {28653, 99}

X(47679) = X(239)X(514)∩X(523)X(1577)

X(47679) = X[4560] - 3 X[46915], X[4707] + 2 X[4988], 3 X[4707] - 2 X[23755], 3 X[4988] + X[23755], 3 X[21124] - X[23755]

X(47679) lies on these lines: {239, 514}, {523, 1577}, {525, 4841}, {661, 7265}, {826, 4824}, {3004, 4978}, {3125, 45213}, {4010, 6367}, {4024, 4129}, {4467, 15309}, {4802, 21121}, {4813, 29216}, {4818, 4905}, {4977, 30595}, {8045, 25665}, {14837, 23752}, {14838, 21828}, {23883, 44449}, {27709, 27730}

X(47679) = midpoint of X(4988) and X(21124)
X(47679) = reflection of X(i) in X(j) for these {i,j}: {1019, 21196}, {4024, 4129}, {4707, 21124}, {4905, 4818}, {4978, 3004}, {7192, 21192}, {7265, 661}
X(47679) = X(i)-Ceva conjugate of X(j) for these (i,j): {1268, 3120}, {4359, 1086}
X(47679) = X(163)-isoconjugate of X(1224)
X(47679) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 1224), (3743, 4115), (41820, 190)
X(47679) = crosspoint of X(514) and X(31010)
X(47679) = crossdifference of every pair of points on line {42, 1333}
X(47679) = barycentric product X(i)*X(j) for these {i,j}: {514, 41809}, {523, 17322}, {693, 3743}, {850, 1203}, {1577, 17011}, {3261, 4272}, {4886, 7178}, {31010, 41820}
X(47679) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 1224}, {1203, 110}, {3743, 100}, {4272, 101}, {4886, 645}, {17011, 662}, {17322, 99}, {41809, 190}

X(47680) = X(1)X(23770)∩X(514)X(661)

X(47680) = 3 X[1022] - 2 X[30725], 5 X[1698] - 4 X[2977], 2 X[3960] - 3 X[6545], 4 X[21212] - 3 X[45671]

X(47680) lies on these lines: {1, 23770}, {514, 661}, {667, 29244}, {690, 4810}, {812, 4707}, {1019, 29162}, {1022, 2006}, {1111, 3942}, {1438, 2224}, {1698, 2977}, {2533, 29098}, {2832, 21109}, {3801, 29070}, {3960, 6545}, {4010, 29102}, {4063, 7178}, {4122, 29224}, {4367, 29336}, {4378, 29156}, {4382, 23876}, {5540, 6084}, {21104, 29126}, {21146, 29029}, {21212, 45671}, {21303, 23879}, {23887, 46403}

X(47680) = reflection of X(i) in X(j) for these {i,j}: {1, 23770}, {4063, 7178}, {21385, 10015}
X(47680) = X(24624)-Ceva conjugate of X(1086)
X(47680) = X(4574)-isoconjugate of X(39439)
X(47680) = X(31845)-Dao conjugate of X(1018)
X(47680) = barycentric product X(i)*X(j) for these {i,j}: {514, 33129}, {693, 30117}, {1111, 13589}, {1731, 24002}, {4025, 5146}, {4453, 38938}
X(47680) = barycentric quotient X(i)/X(j) for these {i,j}: {1731, 644}, {5146, 1897}, {13589, 765}, {30117, 100}, {33129, 190}

X(47681) = X(1)X(523)∩X(514)X(4024)

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

X(47681) lies on these lines: {1, 523}, {514, 4024}, {525, 4960}, {1019, 4467}, {1022, 39722}, {4049, 29591}, {4789, 17308}, {7199, 33935}, {8045, 25665}, {17397, 46915}, {17762, 28863}, {21124, 24899}

X(47681) = reflection of X(31290) in X(22037)
X(47681) = crossdifference of every pair of points on line {2245, 2308}

X(47682) = X(1)X(523)∩X(304)X(7199)

X(47682) lies on these lines: {1, 523}, {304, 7199}, {514, 661}, {525, 1019}, {649, 23876}, {659, 29312}, {663, 29021}, {667, 29017}, {690, 4784}, {826, 4367}, {1930, 4374}, {1960, 29166}, {2533, 29094}, {2785, 4761}, {2787, 4122}, {3287, 5280}, {3700, 29126}, {3801, 29154}, {3910, 4063}, {3960, 16892}, {3970, 22044}, {4010, 29029}, {4040, 29142}, {4049, 29596}, {4088, 4160}, {4170, 29118}, {4369, 4707}, {4449, 29047}, {4560, 17161}, {4770, 29659}, {4774, 32847}, {4775, 29144}, {4834, 29284}, {4874, 29172}, {4879, 7927}, {4922, 29110}, {6002, 7265}, {14838, 21124}, {21126, 28863}, {21146, 29102}, {21196, 45671}, {22037, 44449}, {25259, 29148}, {26626, 46915}, {28602, 36478}

X(47682) = reflection of X(i) in X(j) for these {i,j}: {1577, 8045}, {4707, 4369}, {14349, 6332}, {16892, 3960}, {21124, 14838}, {44449, 22037}
X(47682) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {996, 21294}, {9059, 21287}, {40401, 3448}
X(47682) = X(6)-isoconjugate of X(9070)
X(47682) = X(9)-Dao conjugate of X(9070)
X(47682) = crossdifference of every pair of points on line {31, 2245}
X(47682) = barycentric product X(i)*X(j) for these {i,j}: {75, 9013}, {514, 32779}, {693, 30115}, {14015, 14208}
X(47682) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 9070}, {9013, 1}, {14015, 162}, {30115, 100}, {32779, 190}

X(47683) = X(1)X(523)∩X(239)X(514)

X(47683) = 3 X[1019] - 2 X[7192], 4 X[4560] - X[4960], 3 X[4560] - X[7192], 3 X[4960] - 4 X[7192], 3 X[1577] - 4 X[25666], 3 X[3679] - 4 X[4770], 3 X[3679] - 2 X[4774], 2 X[4770] - 3 X[4948], X[4774] - 3 X[4948], 2 X[4106] - 3 X[14349], 2 X[4369] - 3 X[45671], 2 X[4791] - 3 X[4893], 6 X[14838] - 5 X[24924], 3 X[21130] - 2 X[43052]

X(47683) lies on these lines: {1, 523}, {99, 28875}, {239, 514}, {274, 1022}, {784, 4040}, {1577, 25666}, {2401, 39950}, {2787, 4824}, {3064, 17925}, {3679, 4770}, {3733, 4378}, {3762, 18155}, {3960, 16751}, {4049, 16815}, {4083, 5216}, {4106, 14349}, {4369, 45671}, {4374, 32092}, {4481, 4762}, {4693, 4775}, {4761, 4913}, {4789, 16831}, {4791, 4893}, {4813, 29178}, {4814, 4844}, {4840, 28195}, {4841, 29126}, {4978, 18071}, {5235, 23598}, {7203, 30725}, {7253, 28161}, {14570, 21362}, {14838, 16754}, {16552, 21388}, {16759, 18184}, {17175, 17218}, {18827, 35168}, {21130, 43052}, {28863, 33296}, {35145, 46136}

X(47683) = reflection of X(i) in X(j) for these {i,j}: {1019, 4560}, {3679, 4948}, {4707, 21196}, {4761, 4913}, {4774, 4770}, {4960, 1019}, {5214, 3737}, {21385, 17494}, {23755, 21192}
X(47683) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {39974, 3448}, {42285, 21294}
X(47683) = X(799)-Ceva conjugate of X(17196)
X(47683) = X(i)-cross conjugate of X(j) for these (i,j): {4893, 4833}, {4957, 5219}, {23884, 23598}
X(47683) = X(i)-isoconjugate of X(j) for these (i,j): {10, 34073}, {37, 4588}, {42, 4604}, {65, 5549}, {89, 4557}, {100, 28658}, {213, 4597}, {512, 5385}, {692, 30588}, {1018, 2163}, {2320, 4559}, {2364, 4551}, {3952, 28607}, {3997, 8695}
X(47683) = X(i)-Dao conjugate of X(j) for these (i, j): (1086, 30588), (4777, 4931), (6626, 4597), (8054, 28658), (36911, 3952), (36912, 4169), (39054, 5385), (40587, 1018), (40589, 4588), (40592, 4604), (40602, 5549), (40620, 39704), (40625, 30608)
X(47683) = cevapoint of X(4777) and X(4893)
X(47683) = crossdifference of every pair of points on line {42, 2245}
X(47683) = barycentric product X(i)*X(j) for these {i,j}: {45, 7199}, {75, 4833}, {81, 4791}, {86, 4777}, {274, 4893}, {310, 4775}, {333, 43052}, {514, 5235}, {662, 4957}, {693, 4653}, {873, 4770}, {1019, 4671}, {1434, 4944}, {1509, 4931}, {2099, 18155}, {3261, 4273}, {3676, 4720}, {3679, 7192}, {4560, 5219}, {4752, 16727}, {4767, 17205}, {4774, 32010}, {4800, 18827}, {4873, 17096}, {4960, 30590}, {16704, 23598}, {23352, 30939}, {23788, 36921}, {23884, 24624}
X(47683) = barycentric quotient X(i)/X(j) for these {i,j}: {45, 1018}, {58, 4588}, {81, 4604}, {86, 4597}, {284, 5549}, {514, 30588}, {649, 28658}, {662, 5385}, {1019, 89}, {1333, 34073}, {1405, 4559}, {2099, 4551}, {2177, 4557}, {3679, 3952}, {3711, 4069}, {3733, 2163}, {3737, 2320}, {4273, 101}, {4560, 30608}, {4653, 100}, {4671, 4033}, {4720, 3699}, {4770, 756}, {4774, 1215}, {4775, 42}, {4777, 10}, {4791, 321}, {4800, 740}, {4803, 4767}, {4814, 210}, {4833, 1}, {4844, 46897}, {4873, 30730}, {4893, 37}, {4908, 4169}, {4931, 594}, {4944, 2321}, {4948, 3842}, {4951, 3773}, {4957, 1577}, {4960, 30589}, {5219, 4552}, {5235, 190}, {7192, 39704}, {7199, 20569}, {7252, 2364}, {21130, 26580}, {23352, 4674}, {23598, 4080}, {23758, 3822}, {23884, 3936}, {28603, 3994}, {30604, 21674}, {30605, 4062}, {43052, 226}
X(47683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1019, 21385, 18197}, {4770, 4774, 3679}, {4774, 4948, 4770}

X(47684) = X(1)X(29160)∩X(514)X(661)

X(47684) lies on these lines: {1, 29160}, {514, 661}, {659, 29172}, {663, 29116}, {667, 29154}, {1019, 29220}, {4010, 29122}, {4040, 29130}, {4122, 29156}, {4170, 29140}, {4367, 29332}, {4378, 29224}, {4380, 23876}, {4775, 29128}, {4879, 29174}, {4922, 29204}, {7265, 29114}, {16892, 44550}, {21222, 30520}, {25259, 29126}

X(47685) = X(320)X(350)∩X(659)X(31209)

X(47685) = 5 X[693] - 4 X[7662], 2 X[7662] - 5 X[46403], 4 X[659] - 5 X[31209], 2 X[659] - 3 X[44429], 5 X[31209] - 6 X[44429], 3 X[667] - 4 X[19947], 4 X[1491] - 3 X[31150], 2 X[4724] - 3 X[4776], 2 X[4782] - 3 X[36848]

X(47685) lies on these lines: {320, 350}, {659, 31209}, {667, 5253}, {764, 34605}, {830, 4801}, {962, 3309}, {1027, 24601}, {1491, 31150}, {2254, 4380}, {2526, 17494}, {3436, 4462}, {3600, 3669}, {3667, 21115}, {4083, 14923}, {4292, 4905}, {4397, 44444}, {4724, 4776}, {4782, 36848}, {6006, 47123}, {6590, 28225}, {7659, 26853}, {8165, 20317}, {8712, 21302}, {21222, 28475}, {23770, 28217}

X(47685) = reflection of X(i) in X(j) for these {i,j}: {693, 46403}, {4380, 2254}, {4397, 44444}, {4462, 21301}, {17494, 2526}, {26853, 7659}, {31291, 3669}
X(47685) = anticomplement of the isogonal conjugate of X(37223)
X(47685) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {37223, 8}, {39749, 150}, {39959, 149}
X(47685) = {X(659),X(44429)}-harmonic conjugate of X(31209)

X(47686) = X(513)X(41794)∩X(514)X(4088)

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

X(47686) lies on these lines: {513, 41794}, {514, 4088}, {659, 44435}, {693, 4806}, {2254, 28882}, {4778, 21116}, {6590, 28229}, {7662, 28220}, {23770, 28209}, {24719, 25259}, {28225, 47123}, {29362, 45746}

X(47687) = X(513)X(4122)∩X(522)X(693)

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

X(47687) = 3 X[693] - 2 X[47123], 3 X[4453] - 4 X[24720], 4 X[676] - 5 X[26985], 2 X[1491] - 3 X[31131], 3 X[1577] - 2 X[21201], 4 X[4522] - 3 X[30565], 2 X[4724] - 3 X[30565], 4 X[4874] - 3 X[44433], 4 X[13246] - 5 X[24924]

X(47687) lies on these lines: {513, 4122}, {522, 693}, {523, 2528}, {676, 26985}, {764, 29110}, {824, 24721}, {900, 4784}, {1010, 4560}, {1491, 31131}, {1577, 5051}, {1734, 29190}, {2475, 6362}, {2517, 24990}, {2526, 45746}, {2530, 29086}, {3667, 4931}, {3777, 29074}, {3904, 29066}, {3907, 21105}, {3910, 21302}, {4151, 4647}, {4522, 4724}, {4874, 44433}, {4905, 29062}, {4925, 4976}, {4926, 7662}, {7265, 42325}, {13246, 24924}, {17496, 29278}, {21301, 29142}, {23770, 28183}, {24719, 29144}, {28205, 47131}

X(47687) = reflection of X(i) in X(j) for these {i,j}: {4467, 2254}, {4724, 4522}, {4976, 4925}, {45746, 2526}
X(47687) = X(1390)-anticomplementary conjugate of X(33650)
X(47687) = crossdifference of every pair of points on line {41, 5007}
X(47687) = {X(4522),X(4724)}-harmonic conjugate of X(30565)

X(47688) = X(1)X(514)∩X(523)X(2528)

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

X(47688) lies on these lines: {1, 514}, {523, 2528}, {693, 4036}, {764, 29128}, {1491, 31079}, {3777, 29174}, {4122, 21297}, {4560, 29098}, {4804, 28863}, {6590, 28191}, {7662, 28199}, {17496, 29025}, {18004, 26798}, {21222, 29029}, {21301, 29047}, {21302, 29208}, {23765, 29134}, {23770, 28175}, {24623, 46915}, {24719, 29204}, {28195, 47131}

X(47689) = X(325)X(523)∩X(522)X(4380)

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

X(47689) = 5 X[693] - 4 X[23770], 4 X[4522] - 3 X[4776], 3 X[4789] - 2 X[47123], 2 X[4806] - 3 X[4951]

X(47689) lies on these lines: {325, 523}, {522, 4380}, {1019, 29196}, {1577, 29164}, {1635, 4765}, {2533, 29146}, {4122, 29144}, {4367, 29250}, {4391, 29021}, {4462, 29142}, {4522, 4776}, {4761, 29318}, {4774, 29172}, {4777, 4782}, {4784, 29370}, {4789, 21180}, {4801, 29047}, {4802, 46403}, {4806, 4951}, {4834, 29194}, {4978, 29260}, {7662, 28165}, {21146, 29204}

X(47690) = X(1)X(29192)∩X(325)X(523)

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

X(47690) = 3 X[693] - 2 X[23770], 2 X[3004] - 3 X[44429], 4 X[3837] - 3 X[44435], 2 X[2526] - 3 X[31131], 4 X[2977] - 3 X[31150], 3 X[4379] - 2 X[4458], 3 X[4789] - 2 X[7662], 4 X[9508] - 3 X[27486], 3 X[4951] - 2 X[18004]

X(47690) lies on these lines: {1, 29192}, {325, 523}, {513, 4122}, {514, 4088}, {522, 649}, {659, 26249}, {661, 4522}, {663, 8045}, {667, 29086}, {824, 2254}, {1019, 29062}, {1577, 29021}, {1734, 23879}, {2526, 28894}, {2533, 29017}, {2977, 31150}, {3801, 29146}, {4010, 29144}, {4063, 29190}, {4367, 29074}, {4374, 23684}, {4378, 29110}, {4379, 4458}, {4391, 29142}, {4500, 4804}, {4707, 29318}, {4761, 23876}, {4777, 4789}, {4784, 29078}, {4801, 29288}, {4823, 29164}, {4834, 29106}, {4951, 18004}, {4978, 29047}, {6005, 7265}, {7658, 21186}, {7659, 28898}, {14475, 28169}, {16892, 24720}, {17072, 21124}, {26080, 45745}, {28165, 47131}, {28187, 47132}

X(47690) = reflection of X(i) in X(j) for these {i,j}: {661, 4522}, {663, 8045}, {4804, 4500}, {16892, 24720}, {21124, 17072}, {25259, 4122}, {45746, 1491}
X(47690) = crossdifference of every pair of points on line {32, 1193}
X(47690) = barycentric product X(3261)*X(41265)
X(47690) = barycentric quotient X(41265)/X(101)

X(47691) = X(1)X(514)∩X(325)X(523)

X(47691) = 3 X[663] - 2 X[5592], 2 X[1491] - 3 X[44435], 4 X[2977] - 5 X[31209], 2 X[4522] - 3 X[4728], 2 X[4782] - 3 X[4809], 3 X[6545] - 2 X[24720]

X(47691) lies on these lines: {1, 514}, {325, 523}, {513, 41794}, {522, 4382}, {649, 4458}, {659, 8654}, {667, 29098}, {824, 4804}, {1019, 29158}, {1577, 29047}, {2254, 3776}, {2533, 29208}, {2976, 4977}, {2977, 31209}, {3801, 4083}, {3835, 4088}, {4010, 25259}, {4063, 20517}, {4122, 29204}, {4142, 4498}, {4170, 23875}, {4367, 29025}, {4378, 29029}, {4379, 29631}, {4391, 29288}, {4521, 4893}, {4522, 4728}, {4707, 29350}, {4775, 29102}, {4782, 4809}, {4789, 28151}, {4801, 29142}, {4802, 7662}, {4808, 21260}, {4810, 29078}, {4823, 29260}, {4874, 26230}, {4879, 29082}, {4922, 29156}, {4978, 29021}, {6545, 24720}, {6546, 29638}, {7265, 29358}, {10196, 29860}, {17072, 36568}, {21146, 29144}, {21204, 29861}, {21302, 36500}, {23687, 23800}, {24623, 27486}, {28155, 29862}, {28175, 47132}

X(47691) = reflection of X(i) in X(j) for these {i,j}: {649, 4458}, {693, 23770}, {2254, 3776}, {4063, 20517}, {4088, 3835}, {4498, 4142}, {4808, 21260}, {25259, 4010}
X(47691) = isotomic conjugate of the isogonal conjugate of X(9313)
X(47691) = crossdifference of every pair of points on line {32, 672}
X(47691) = barycentric product X(i)*X(j) for these {i,j}: {76, 9313}, {514, 4429}, {693, 26242}, {35519, 41264}
X(47691) = barycentric quotient X(i)/X(j) for these {i,j}: {4429, 190}, {9313, 6}, {26242, 100}, {41264, 109}

X(47692) = X(1)X(29160)∩X(325)X(523)

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

X(47692) lies on these lines: {1, 29160}, {325, 523}, {1577, 29260}, {2496, 4802}, {3801, 29208}, {4010, 29204}, {4088, 4776}, {4170, 29358}, {4367, 29174}, {4378, 29128}, {4391, 29047}, {4449, 29116}, {4462, 29288}, {4775, 29224}, {4777, 46403}, {4801, 29021}, {4810, 29370}, {4879, 29332}, {4922, 29122}, {4978, 29164}, {6590, 28155}, {7662, 28151}, {21179, 28147}, {21343, 29172}, {23687, 40471}

X(47693) = X(23)X(385)∩X(514)X(4088)

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

X(47693) lies on these lines: {23, 385}, {514, 4088}, {693, 4036}, {2254, 28863}, {2517, 27610}, {3837, 31096}, {4122, 20295}, {4521, 4893}, {4789, 23770}, {7662, 28151}, {17166, 29047}, {26853, 29078}, {28155, 47123}, {29074, 31291}

X(47693) = reflection of X(20295) in X(4122)
X(47693) = crossdifference of every pair of points on line {39, 21764}

X(47694) = X(1)X(514)∩X(23)X(385)

X(47694) = 3 X[2] - 4 X[4874], 5 X[2] - 4 X[45323], 5 X[1491] - 6 X[45323], 5 X[4874] - 3 X[45323], 4 X[7662] - X[46403], 3 X[21297] - 2 X[24719], 3 X[1635] - 2 X[4913], 2 X[2526] - 3 X[44429], 4 X[4885] - 3 X[44429], 3 X[2530] - 4 X[19947], 4 X[3837] - 5 X[26985], 3 X[4379] - 2 X[24720], 3 X[4448] - X[4824], 4 X[4791] - 3 X[30709], 3 X[4800] - 2 X[4806], 4 X[9508] - 5 X[27013], 5 X[24924] - 4 X[25380]

X(47694) lies on these lines: {1, 514}, {2, 1491}, {23, 385}, {69, 9014}, {320, 350}, {522, 649}, {661, 3716}, {667, 784}, {676, 3004}, {812, 4804}, {814, 31291}, {824, 4817}, {830, 1577}, {900, 4784}, {1019, 8714}, {1635, 4913}, {2254, 4369}, {2496, 4802}, {2517, 25299}, {2526, 4885}, {2530, 19894}, {2533, 17751}, {3667, 4932}, {3762, 4160}, {3803, 23882}, {3837, 26985}, {3887, 4761}, {4063, 4151}, {4142, 21124}, {4367, 17496}, {4378, 21222}, {4379, 24720}, {4391, 8678}, {4397, 30061}, {4448, 4824}, {4458, 16892}, {4705, 26115}, {4777, 4782}, {4778, 21116}, {4791, 30709}, {4800, 4806}, {4948, 45314}, {4977, 23770}, {5214, 18197}, {6129, 28374}, {6161, 29188}, {6371, 39547}, {8062, 27647}, {8689, 28147}, {9508, 27013}, {13246, 21196}, {13266, 15571}, {16757, 27648}, {20293, 25301}, {21173, 23805}, {21189, 26146}, {23646, 27010}, {24924, 25380}, {25537, 27675}, {26242, 29956}, {26277, 45746}, {26824, 29362}, {26853, 29328}, {27952, 38348}

X(47694) = reflection of X(i) in X(j) for these {i,j}: {661, 3716}, {693, 7662}, {1491, 4874}, {2254, 4369}, {2526, 4885}, {3004, 676}, {4560, 667}, {4948, 45314}, {16892, 4458}, {17494, 659}, {17496, 4367}, {20295, 4010}, {21124, 4142}, {21196, 13246}, {21222, 4378}, {21301, 1577}, {21302, 2533}, {23770, 47132}, {46403, 693}
X(47694) = anticomplement of X(1491)
X(47694) = anticomplement of the isogonal conjugate of X(1492)
X(47694) = anticomplement of the isotomic conjugate of X(789)
X(47694) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {6, 39345}, {560, 39347}, {789, 6327}, {825, 2}, {870, 21293}, {985, 149}, {1492, 8}, {2344, 37781}, {4586, 69}, {4613, 1330}, {5384, 513}, {5388, 21304}, {14621, 150}, {30664, 4645}, {30670, 4388}, {34069, 192}, {37133, 315}, {37207, 20553}, {40718, 3448}, {40746, 4440}, {40747, 21221}, {46132, 21275}
X(47694) = X(i)-Ceva conjugate of X(j) for these (i,j): {789, 2}, {14612, 5276}
X(47694) = X(i)-isoconjugate of X(j) for these (i,j): {101, 39957}, {190, 45785}, {692, 39712}
X(47694) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39957), (1086, 39712)
X(47694) = crosspoint of X(i) and X(j) for these (i,j): {86, 4586}, {190, 39717}, {308, 46132}
X(47694) = crosssum of X(i) and X(j) for these (i,j): {42, 3250}, {649, 20985}, {667, 21764}, {3051, 8630}
X(47694) = crossdifference of every pair of points on line {39, 213}
X(47694) = barycentric product X(i)*X(j) for these {i,j}: {11, 14612}, {514, 5263}, {522, 41245}, {693, 5276}
X(47694) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 39957}, {514, 39712}, {667, 45785}, {5263, 190}, {5276, 100}, {14612, 4998}, {41245, 664}
X(47694) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 4874, 2}, {2526, 4885, 44429}

X(47695) = X(1)X(3904)∩X(2)X(676)

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

X(47695) = 3 X[2] - 4 X[676], 7 X[2] - 8 X[45318], 7 X[676] - 6 X[45318], 2 X[659] - 3 X[44433], 2 X[2254] - 3 X[4453], 3 X[4453] - 4 X[4458], 3 X[1635] - 4 X[13246], 3 X[1638] - 2 X[4925], 4 X[1769] - 3 X[25020], 2 X[2526] - 3 X[44435], 2 X[2977] - 3 X[26275], 7 X[3523] - 8 X[44819], 5 X[3617] - 4 X[4528], 4 X[3716] - 3 X[30565], 2 X[4088] - 3 X[30565], 4 X[3837] - 3 X[31131], 2 X[4768] - 3 X[23678], 4 X[21180] - 3 X[23678], 3 X[4789] - 4 X[7662], 3 X[4809] - 2 X[9508], 3 X[4800] - 2 X[18004], 3 X[38314] - 2 X[45341]

X(47695) lies on these lines: {1, 3904}, {2, 676}, {8, 10015}, {20, 9521}, {23, 385}, {100, 108}, {105, 26703}, {145, 6366}, {149, 900}, {244, 17888}, {321, 23684}, {513, 41794}, {519, 44553}, {522, 693}, {663, 23877}, {918, 1280}, {928, 3868}, {1281, 2799}, {1635, 4765}, {1638, 4925}, {1734, 20517}, {1769, 23541}, {2526, 44435}, {2785, 4895}, {2826, 13252}, {2977, 26275}, {3523, 44819}, {3617, 4528}, {3667, 21115}, {3716, 4088}, {3722, 12080}, {3762, 21201}, {3766, 39714}, {3810, 4449}, {3837, 31126}, {3887, 4707}, {3907, 21118}, {4041, 4142}, {4086, 21179}, {4391, 13259}, {4397, 7649}, {4560, 45695}, {4712, 24014}, {4768, 21180}, {4777, 4789}, {4800, 18004}, {4811, 23874}, {5057, 42763}, {6084, 20097}, {6129, 16757}, {6161, 29102}, {6362, 17496}, {7178, 21302}, {9511, 42337}, {14310, 27628}, {14837, 44448}, {17166, 29142}, {18359, 41683}, {21189, 23687}, {24462, 27951}, {25600, 33115}, {28183, 47132}, {29162, 31291}, {30577, 45290}, {38314, 45341}

X(47695) = reflection of X(i) in X(j) for these {i,j}: {8, 10015}, {693, 47123}, {1734, 20517}, {2254, 4458}, {3762, 21201}, {3904, 1}, {4041, 4142}, {4086, 21179}, {4088, 3716}, {4391, 21185}, {4397, 7649}, {4768, 21180}, {5057, 42763}, {20294, 6129}, {21302, 7178}, {44448, 14837}, {46403, 23770}
X(47695) = anticomplement of the isogonal conjugate of X(32735)
X(47695) = anticomplement of the isotomic conjugate of X(927)
X(47695) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {31, 14732}, {105, 33650}, {109, 20344}, {604, 39353}, {651, 20552}, {666, 21286}, {919, 329}, {927, 6327}, {1415, 20533}, {1416, 149}, {1438, 37781}, {1462, 150}, {32666, 144}, {32735, 8}, {34085, 315}, {36057, 34188}, {36086, 3436}, {36146, 69}, {39293, 21301}, {46135, 21275}
X(47695) = X(927)-Ceva conjugate of X(2)
X(47695) = cevapoint of X(522) and X(20516)
X(47695) = crosspoint of X(i) and X(j) for these (i,j): {75, 666}, {308, 46135}, {664, 36807}, {2481, 6335}
X(47695) = crosssum of X(i) and X(j) for these (i,j): {31, 665}, {2223, 22383}, {3051, 8638}
X(47695) = crossdifference of every pair of points on line {39, 41}
X(47695) = barycentric product X(i)*X(j) for these {i,j}: {514, 32850}, {3261, 40910}, {4318, 4391}, {36803, 38363}
X(47695) = barycentric quotient X(i)/X(j) for these {i,j}: {4318, 651}, {32850, 190}, {38363, 665}, {40910, 101}
X(47695) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2254, 4458, 4453}, {3716, 4088, 30565}, {4768, 21180, 23678}

X(47696) = X(1)X(514)∩X(513)X(4122)

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

X(47696) = 5 X[1491] - 6 X[28602], 3 X[1635] - 2 X[4818], 4 X[4782] - 3 X[27486], 4 X[4874] - 3 X[44435]

X(47696) lies on these lines: {1, 514}, {513, 4122}, {523, 8664}, {659, 45746}, {693, 4806}, {1491, 26251}, {1635, 4818}, {4120, 4778}, {4782, 27486}, {4789, 28220}, {4804, 28882}, {4874, 44435}, {7662, 28195}, {23770, 28213}, {28199, 47131}

X(47696) = reflection of X(i) in X(j) for these {i,j}: {45746, 659}, {46403, 6590}
X(47696) = crossdifference of every pair of points on line {672, 7772}

X(47697) = X(2)X(2526)∩X(320)X(350)

X(47697) = 3 X[693] - 4 X[7662], 3 X[693] - 2 X[46403], 5 X[659] - 3 X[4948], 4 X[659] - 3 X[31150], 4 X[4948] - 5 X[31150], 4 X[676] - 3 X[44435], 4 X[1491] - 5 X[31209], 4 X[3716] - 3 X[4776], 6 X[4874] - 5 X[30795], 4 X[4874] - 3 X[44429], 10 X[30795] - 9 X[44429]

X(47697) lies on these lines: {2, 2526}, {320, 350}, {522, 4380}, {523, 8664}, {659, 4948}, {676, 44435}, {830, 4391}, {1491, 31209}, {2976, 4977}, {3667, 4931}, {3716, 4776}, {3803, 4560}, {4462, 8678}, {4724, 23655}, {4778, 47123}, {4789, 6006}, {4874, 30795}, {23770, 28209}, {23880, 31291}, {28195, 47131}

X(47697) = reflection of X(i) in X(j) for these {i,j}: {4560, 3803}, {46403, 7662}
X(47697) = anticomplement of X(2526)
X(47697) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {39716, 150}, {39958, 149}
X(47697) = crossdifference of every pair of points on line {213, 7772}
X(47697) = {X(7662),X(46403)}-harmonic conjugate of X(693)

X(47698) = X(514)X(4088)∩X(523)X(8663)

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

X(47698) = 2 X[4458] - 3 X[4893], 3 X[4776] - 2 X[23770], 2 X[7662] - 3 X[30565], 2 X[21104] - 3 X[44429]

X(47698) lies on these lines: {514, 4088}, {523, 8663}, {2254, 28851}, {4024, 28147}, {4106, 4122}, {4147, 23755}, {4458, 4893}, {4776, 23770}, {4824, 45746}, {7659, 28910}, {7662, 30565}, {21104, 44429}

X(47698) = reflection of X(i) in X(j) for these {i,j}: {23755, 4147}, {45746, 4824}

X(47699) = X(1)X(514)∩X(513)X(4467)

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

X(47699) = 3 X[661] - 2 X[4522], 2 X[4784] - 3 X[27486], 2 X[21146] - 3 X[44435]

X(47699) lies on these lines: {1, 514}, {513, 4467}, {522, 4813}, {523, 8663}, {661, 4522}, {1491, 8034}, {4778, 16892}, {4784, 27486}, {4824, 29144}, {4960, 20517}, {21146, 44435}, {28195, 44433}

X(47700) = X(523)X(661)∩X(525)X(4729)

X(47700) = 4 X[4122] - 3 X[4931], 2 X[4804] - 3 X[4931], 2 X[3801] - 3 X[21052], 4 X[4458] - 5 X[24924], 4 X[4522] - 3 X[4728], 3 X[21115] - 4 X[24720]

X(47700) lies on these lines: {523, 661}, {525, 4729}, {826, 4041}, {1491, 29204}, {1577, 3701}, {1734, 29358}, {3801, 21052}, {3906, 4730}, {4397, 20909}, {4404, 14208}, {4458, 24924}, {4468, 28161}, {4490, 29146}, {4522, 4728}, {4705, 7950}, {4724, 4777}, {4822, 7927}, {14349, 29260}, {21115, 24720}

X(47700) = reflection of X(i) in X(j) for these {i,j}: {661, 4088}, {4041, 4808}, {4804, 4122}
X(47700) = X(81)-isoconjugate of X(30555)
X(47700) = X(40586)-Dao conjugate of X(30555)
X(47700) = barycentric product X(i)*X(j) for these {i,j}: {10, 30520}, {523, 17284}, {661, 31130}, {1577, 3242}, {4064, 31925}, {4901, 7178}
X(47700) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 30555}, {3242, 662}, {4901, 645}, {17284, 99}, {30520, 86}, {31130, 799}
X(47700) = {X(4122),X(4804)}-harmonic conjugate of X(4931)

X(47701) = X(1)X(514)∩X(512)X(21124)

X(47701) = 3 X[4120] - 2 X[4122], 3 X[4120] - 4 X[4806], 2 X[4522] - 3 X[4776], 3 X[4750] - 2 X[4784], 2 X[4761] - 3 X[30574], 3 X[6545] - 2 X[21146], 2 X[24720] - 3 X[44435]

X(47701) lies on these lines: {1, 514}, {512, 21124}, {513, 16892}, {522, 17161}, {523, 661}, {525, 4822}, {659, 8635}, {826, 4983}, {1491, 29144}, {2254, 3004}, {2530, 29168}, {2533, 27714}, {3800, 4041}, {3801, 23755}, {4017, 17094}, {4170, 23879}, {4458, 7192}, {4468, 14779}, {4490, 29208}, {4522, 4776}, {4560, 29118}, {4705, 7927}, {4730, 12073}, {4750, 4784}, {4761, 30574}, {4815, 14208}, {4977, 21125}, {6545, 21146}, {14349, 29021}, {24720, 44435}

X(47701) = reflection of X(i) in X(j) for these {i,j}: {2254, 3004}, {4024, 4010}, {4088, 661}, {4122, 4806}, {7192, 4458}, {23755, 3801}
X(47701) = X(40718)-Ceva conjugate of X(3120)
X(47701) = X(110)-isoconjugate of X(1390)
X(47701) = X(244)-Dao conjugate of X(1390)
X(47701) = crossdifference of every pair of points on line {58, 672}
X(47701) = barycentric product X(i)*X(j) for these {i,j}: {514, 4026}, {522, 5244}, {523, 17023}, {525, 1890}, {661, 26234}, {693, 21840}, {850, 21764}, {1386, 1577}, {3883, 7178}, {4064, 31906}, {14618, 22390}
X(47701) = barycentric quotient X(i)/X(j) for these {i,j}: {661, 1390}, {1386, 662}, {1890, 648}, {3883, 645}, {4026, 190}, {5244, 664}, {17023, 99}, {21764, 110}, {21840, 100}, {22390, 4558}, {26234, 799}
X(47701) = {X(4122),X(4806)}-harmonic conjugate of X(4120)

X(47702) = X(523)X(661)∩X(826)X(4822)

X(47702) = 3 X[661] - 2 X[4088], 4 X[4010] - 3 X[4931], 3 X[3004] - 2 X[4925], 4 X[4458] - 3 X[31148]

X(47702) lies on these lines: {523, 661}, {826, 4822}, {2254, 29144}, {3004, 4925}, {3800, 4729}, {4017, 40471}, {4041, 7927}, {4458, 31148}, {4468, 28155}, {4724, 4802}, {4777, 4810}, {4983, 7950}, {14349, 29164}

X(47702) = reflection of X(i) in X(j) for these {i,j}: {4729, 21124}, {4838, 4804}
X(47702) = barycentric product X(i)*X(j) for these {i,j}: {523, 29598}, {1577, 38315}, {4064, 31918}
X(47702) = barycentric quotient X(i)/X(j) for these {i,j}: {29598, 99}, {38315, 662}

X(47703) = X(513)X(4024)∩X(514)X(4088)

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

X(47703) lies on these lines: {513, 4024}, {514, 4088}, {522, 7192}, {523, 2254}, {1491, 4988}, {2526, 4802}, {3064, 17418}, {3716, 4789}, {4122, 4977}, {4724, 6590}, {4777, 7659}, {4778, 25259}, {21108, 21118}, {23731, 24719}, {23755, 29017}, {24720, 45746}

X(47703) = reflection of X(i) in X(j) for these {i,j}: {4724, 6590}, {4988, 1491}, {16892, 21146}, {23731, 24719}, {45746, 24720}
X(47703) = crossdifference of every pair of points on line {1203, 4251}

X(47704) = X(1)X(514)∩X(522)X(26824)

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

X(47704) = 3 X[21118] - 2 X[21132], 3 X[21116] - 2 X[21146], 3 X[693] - 2 X[4522], 3 X[4088] - 4 X[4522], 2 X[1491] - 3 X[6545], 4 X[2977] - 5 X[24924], 3 X[4453] - 2 X[4913], 4 X[4874] - 3 X[6546]

X(47704) lies on these lines: {1, 514}, {522, 26824}, {523, 2254}, {650, 4802}, {661, 23770}, {676, 21102}, {693, 4088}, {918, 4804}, {1491, 6545}, {1638, 28179}, {2826, 23746}, {2977, 24924}, {3676, 4608}, {4083, 23755}, {4453, 4913}, {4458, 17494}, {4801, 23877}, {4874, 6546}, {6362, 23738}

X(47704) = reflection of X(i) in X(j) for these {i,j}: {661, 23770}, {2254, 21104}, {4088, 693}, {4724, 47123}, {17494, 4458}, {21119, 23752}
X(47704) = X(30571)-Ceva conjugate of X(3120)
X(47704) = crossdifference of every pair of points on line {35, 672}
X(47704) = barycentric product X(514)*X(3826)
X(47704) = barycentric quotient X(3826)/X(190)

X(47705) = X(244)X(23772)∩X(523)X(2254)

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

X(47705) = 2 X[2254] - 3 X[21115], 4 X[676] - 3 X[6546], 3 X[1635] - 4 X[4458], 2 X[4088] - 3 X[4728], 3 X[4728] - 4 X[23770]

X(47705) lies on these lines: {244, 23772}, {523, 2254}, {659, 4802}, {676, 6546}, {1635, 4458}, {4088, 4728}, {4453, 28155}, {4724, 47131}, {4809, 28179}, {4895, 29102}, {9508, 28151}, {13259, 29047}, {28191, 44433}

X(47705) = reflection of X(i) in X(j) for these {i,j}: {4088, 23770}, {4724, 47131}
X(47705) = barycentric product X(514)*X(3823)
X(47705) = barycentric quotient X(3823)/X(190)
X(47705) = {X(4088),X(23770)}-harmonic conjugate of X(4728)

X(47706) = X(523)X(4391)∩X(659)X(29250)

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

X(47706) lies on these lines: {523, 4391}, {659, 29250}, {693, 29047}, {1577, 29260}, {2533, 29204}, {3762, 29164}, {3800, 25259}, {3806, 25902}, {4063, 29196}, {4122, 29208}, {4380, 29062}, {4462, 29021}, {4474, 29116}, {4761, 29358}, {4774, 29332}, {4801, 29288}, {4802, 21301}, {4834, 29292}, {4951, 4992}

X(47707) = X(512)X(25259)∩X(514)X(4088)

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

X(47707) lies on these lines: {512, 25259}, {514, 4088}, {522, 4498}, {523, 4391}, {649, 29037}, {659, 29074}, {667, 29110}, {693, 29288}, {784, 4808}, {824, 4041}, {885, 7160}, {1019, 29212}, {1577, 29047}, {3762, 29021}, {3801, 29204}, {4010, 29208}, {4040, 29192}, {4063, 29062}, {4083, 4122}, {4147, 21124}, {4380, 29232}, {4449, 8045}, {4462, 29142}, {4581, 23874}, {4705, 45746}, {4707, 29358}, {4761, 23875}, {4774, 29082}, {4791, 29260}, {4834, 29090}, {6590, 17166}, {7265, 29350}, {14077, 18344}, {16892, 17072}, {21260, 44435}, {21385, 29190}, {28147, 30709}

X(47707) = reflection of X(i) in X(j) for these {i,j}: {4449, 8045}, {16892, 17072}, {17166, 6590}, {21124, 4147}, {45746, 4705}
X(47707) = crossdifference of every pair of points on line {5019, 21764}

X(47708) = X(1)X(514)∩X(513)X(3801)

X(47708) lies on these lines: {1, 514}, {513, 3801}, {522, 21124}, {523, 4391}, {649, 4142}, {659, 8636}, {661, 23877}, {667, 29029}, {693, 29142}, {784, 3766}, {826, 25259}, {1019, 20517}, {1577, 29021}, {1960, 29138}, {2530, 44435}, {2533, 29144}, {3004, 6362}, {3716, 29116}, {3762, 29047}, {3800, 10015}, {3803, 44433}, {4010, 29017}, {4063, 29158}, {4122, 29146}, {4170, 23876}, {4367, 29120}, {4379, 29845}, {4401, 29140}, {4462, 29288}, {4581, 7649}, {4707, 6005}, {4775, 29094}, {4791, 29164}, {4801, 23770}, {4874, 29134}, {4893, 29846}, {6546, 29848}, {7265, 29318}, {14349, 23887}, {24601, 27486}, {28161, 30709}

X(47708) = reflection of X(i) in X(j) for these {i,j}: {649, 4142}, {1019, 20517}, {4581, 7649}, {4801, 23770}, {17166, 47123}
X(47708) = crossdifference of every pair of points on line {672, 2273}
X(47708) = barycentric product X(514)*X(32773)
X(47708) = barycentric quotient X(32773)/X(190)

X(47709) = X(1)X(29130)∩X(523)X(4391)

X(47709) lies on these lines: {1, 29130}, {523, 4391}, {659, 29174}, {663, 29116}, {667, 29128}, {693, 29021}, {1577, 29164}, {3762, 29260}, {3801, 29144}, {4010, 29146}, {4040, 29160}, {4170, 29318}, {4367, 29134}, {4380, 29158}, {4462, 29047}, {4775, 29154}, {4777, 21301}, {4801, 29142}, {4810, 29248}, {4879, 29172}, {17166, 47131}, {30804, 45746}

X(47710) = X(523)X(1577)∩X(649)X(29196)

X(47710) lies on these lines: {523, 1577}, {649, 29196}, {667, 29250}, {693, 29260}, {826, 4761}, {2533, 7950}, {3762, 29021}, {3800, 7265}, {4122, 4170}, {4391, 29164}, {4474, 29130}, {4774, 29154}, {4784, 29292}, {4834, 29370}, {4978, 29047}, {21185, 28169}

X(47710) = reflection of X(4170) in X(4122)
X(47710) = barycentric product X(i)*X(j) for these {i,j}: {523, 17371}, {1577, 29815}
X(47710) = barycentric quotient X(i)/X(j) for these {i,j}: {17371, 99}, {29815, 662}

X(47711) = X(1)X(8045)∩X(10)X(21124)

X(47711) lies on these lines: {1, 8045}, {10, 21124}, {512, 4122}, {514, 4088}, {522, 4063}, {523, 1577}, {525, 4761}, {649, 29062}, {659, 29086}, {663, 29192}, {667, 29074}, {693, 29047}, {824, 1734}, {826, 2533}, {1019, 29037}, {3064, 14330}, {3700, 3800}, {3762, 29142}, {3801, 7950}, {3806, 27731}, {4010, 7927}, {4024, 4039}, {4041, 23879}, {4132, 23282}, {4367, 29110}, {4391, 29021}, {4498, 29190}, {4522, 14349}, {4774, 29094}, {4784, 29090}, {4791, 29164}, {4823, 29260}, {4834, 29078}, {4874, 29250}, {4978, 29288}, {4983, 18004}, {6005, 25259}, {21146, 29354}, {21185, 28161}, {31096, 44435}

X(47711) = reflection of X(i) in X(j) for these {i,j}: {1, 8045}, {4170, 3700}, {4707, 2533}, {4983, 18004}, {7265, 4122}, {14349, 4522}, {21124, 10}
X(47711) = X(58)-isoconjugate of X(831)
X(47711) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 831), (3125, 17108)
X(47711) = crossdifference of every pair of points on line {1333, 17187}
X(47711) = barycentric product X(i)*X(j) for these {i,j}: {313, 2483}, {321, 830}, {523, 17289}, {661, 33941}, {693, 28594}, {850, 5280}, {1577, 3920}, {3700, 7247}, {4538, 24002}, {5314, 14618}, {8635, 27801}, {18082, 23885}
X(47711) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 831}, {830, 81}, {2483, 58}, {3920, 662}, {4538, 644}, {5280, 110}, {5314, 4558}, {7247, 4573}, {8635, 1333}, {17289, 99}, {23885, 16887}, {27610, 16709}, {28594, 100}, {33941, 799}

X(47712) = X(1)X(514)∩X(512)X(3801)

X(47712) lies on these lines: {1, 514}, {512, 3801}, {522, 44444}, {523, 1577}, {525, 4170}, {649, 20517}, {659, 29098}, {667, 29025}, {693, 29021}, {826, 4010}, {1019, 4458}, {1491, 30171}, {1960, 29184}, {2533, 7927}, {3705, 44435}, {3762, 29288}, {3771, 4893}, {3776, 4905}, {3800, 4761}, {4024, 21064}, {4063, 4142}, {4088, 4129}, {4122, 7950}, {4132, 21121}, {4151, 21124}, {4367, 29029}, {4378, 29120}, {4379, 29635}, {4382, 29190}, {4391, 29047}, {4775, 29082}, {4791, 29260}, {4804, 23879}, {4807, 30574}, {4810, 29106}, {4823, 29164}, {4874, 29174}, {4879, 29094}, {4978, 23770}, {6545, 23789}, {6546, 29656}, {8678, 47131}, {8714, 16892}, {12073, 21145}, {14349, 23877}, {21146, 29168}, {23729, 28481}, {25259, 29358}

X(47712) = reflection of X(i) in X(j) for these {i,j}: {649, 20517}, {1019, 4458}, {4063, 4142}, {4088, 4129}, {4707, 3801}, {4761, 7178}, {4808, 21051}, {4905, 3776}, {4978, 23770}, {7265, 4010}
X(47712) = X(18082)-Ceva conjugate of X(3120)
X(47712) = X(101)-isoconjugate of X(40398)
X(47712) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 40398), (16600, 4568), (21249, 100)
X(47712) = crosspoint of X(693) and X(10566)
X(47712) = crosssum of X(692) and X(46148)
X(47712) = crossdifference of every pair of points on line {672, 1333}
X(47712) = barycentric product X(i)*X(j) for these {i,j}: {1, 27712}, {83, 21125}, {514, 4972}, {523, 16706}, {661, 33940}, {693, 16600}, {850, 5299}, {1577, 7191}, {3120, 33951}, {4024, 33955}, {4077, 33950}, {4514, 7178}, {7293, 14618}, {10566, 21249}, {18070, 18183}, {18108, 21425}
X(47712) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 40398}, {4514, 645}, {4972, 190}, {5299, 110}, {7191, 662}, {7293, 4558}, {16600, 100}, {16706, 99}, {17192, 4576}, {17456, 4553}, {20969, 46148}, {21125, 141}, {21249, 4568}, {23203, 906}, {27712, 75}, {33940, 799}, {33950, 643}, {33951, 4600}, {33955, 4610}

X(47713) = X(1)X(29116)∩X(523)X(1577)

X(47713) lies on these lines: {1, 29116}, {523, 1577}, {663, 29160}, {667, 29174}, {693, 29164}, {826, 4170}, {3762, 29047}, {3800, 4707}, {3801, 4761}, {4010, 7950}, {4367, 29128}, {4378, 29134}, {4391, 29260}, {4449, 29130}, {4775, 29332}, {4810, 29194}, {4879, 29154}, {4922, 29138}, {4978, 29021}, {21185, 28147}

X(47713) = reflection of X(4761) in X(3801)
X(47713) = barycentric product X(i)*X(j) for these {i,j}: {523, 17370}, {1577, 17024}
X(47713) = barycentric quotient X(i)/X(j) for these {i,j}: {17024, 662}, {17370, 99}

X(47714) = X(523)X(2530)∩X(693)X(29164)

X(47714) lies on these lines: {523, 2530}, {693, 29164}, {1577, 29021}, {2533, 29166}, {3762, 29142}, {4122, 29168}, {4170, 29144}, {4378, 29250}, {4761, 29017}, {4784, 29194}, {4801, 29260}, {4834, 29248}, {7950, 21146}

X(47715) = X(513)X(7265)∩X(514)X(4088)

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

X(47715) lies on these lines: {513, 7265}, {514, 4088}, {522, 1019}, {523, 2530}, {649, 29190}, {693, 29021}, {784, 876}, {824, 4905}, {826, 21146}, {1577, 29142}, {2254, 23879}, {2533, 29312}, {3801, 29166}, {3910, 4761}, {4010, 29168}, {4024, 8714}, {4040, 8045}, {4077, 23599}, {4122, 6372}, {4367, 29086}, {4378, 29074}, {4379, 20517}, {4382, 29158}, {4449, 29192}, {4500, 24287}, {4707, 29017}, {4784, 29106}, {4801, 29047}, {16892, 23789}, {28161, 30572}

X(47715) = reflection of X(i) in X(j) for these {i,j}: {4040, 8045}, {16892, 23789}
X(47715) = crossdifference of every pair of points on line {2220, 21764}

X(47716) = X(1)X(514)∩X(522)X(28591)

X(47716) lies on these lines: {1, 514}, {522, 28591}, {523, 2530}, {693, 29047}, {891, 3801}, {918, 4170}, {1577, 23770}, {1734, 3776}, {3800, 21104}, {3837, 4808}, {4010, 29354}, {4063, 4458}, {4083, 4707}, {4142, 21385}, {4151, 16892}, {4367, 29098}, {4378, 29025}, {4379, 25453}, {4382, 29062}, {4498, 20517}, {4801, 29021}, {4810, 29090}, {4879, 29102}, {4893, 29642}, {4922, 29336}, {6545, 29673}, {6546, 29672}, {7628, 28155}, {7927, 21146}, {21343, 29094}, {29641, 44435}

X(47716) = reflection of X(i) in X(j) for these {i,j}: {1577, 23770}, {1734, 3776}, {4063, 4458}, {4498, 20517}, {4808, 3837}, {21385, 4142}
X(47716) = crossdifference of every pair of points on line {672, 2220}

X(47717) = X(523)X(2530)∩X(693)X(29260)

X(47717) lies on these lines: {523, 2530}, {693, 29260}, {1577, 29047}, {3762, 29288}, {4378, 29174}, {4382, 29196}, {4449, 29160}, {4761, 29208}, {4801, 29164}, {4810, 29292}, {4879, 29224}, {4922, 29184}, {7649, 28147}, {21343, 29154}

X(47718) = X(523)X(3777)∩X(693)X(29021)

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

X(47718) lies on these lines: {523, 3777}, {693, 29021}, {4380, 29190}, {4391, 29142}, {4777, 17166}, {4784, 29248}, {4789, 21185}, {4802, 44444}, {4905, 40471}, {4978, 29164}, {21146, 29146}

X(47719) = X(514)X(4088)∩X(522)X(17166)

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

X(47719) lies on these lines: {514, 4088}, {522, 17166}, {523, 3777}, {693, 29142}, {1019, 29190}, {2530, 45746}, {4122, 29198}, {4142, 4379}, {4378, 29086}, {4382, 29118}, {4724, 8045}, {4905, 23879}, {4978, 29021}, {6372, 25259}, {21124, 24720}, {21146, 29017}, {23815, 44435}

X(47719) = reflection of X(i) in X(j) for these {i,j}: {4724, 8045}, {21124, 24720}, {45746, 2530}
X(47719) = crossdifference of every pair of points on line {16946, 21764}

X(47720) = X(1)X(514)∩X(523)X(3777)

X(47720) lies on these lines: {1, 514}, {523, 3777}, {693, 29288}, {3776, 4041}, {3801, 29226}, {4378, 29098}, {4379, 29850}, {4382, 29037}, {4391, 23770}, {4458, 4498}, {4705, 44435}, {4729, 21115}, {4808, 23815}, {4822, 28851}, {4893, 29851}, {4922, 29244}, {4978, 29047}, {6545, 17072}, {6546, 29853}, {20517, 21385}, {21146, 29208}, {21343, 29082}, {25259, 29354}

X(47720) = reflection of X(i) in X(j) for these {i,j}: {4041, 3776}, {4391, 23770}, {4498, 4458}, {4808, 23815}, {21385, 20517}
X(47720) = crossdifference of every pair of points on line {672, 16946}

X(47721) = X(1)X(693)∩X(8)X(4762)

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

X(47721) = 2 X[1] - 3 X[693], 4 X[10] - 3 X[31150], 6 X[650] - 7 X[9780], 3 X[1577] - 2 X[4794], 3 X[2533] - 2 X[4782], 5 X[3616] - 6 X[45320], 5 X[3617] - 3 X[17494], X[3621] + 3 X[26824], 16 X[3634] - 15 X[31209], 3 X[4391] - 2 X[4724], 12 X[4885] - 11 X[5550], 13 X[19877] - 12 X[44567], 4 X[24720] - 3 X[44550], 15 X[26985] - 13 X[46934], 21 X[27115] - 23 X[46931]

X(47721) lies on these lines: {1, 693}, {8, 4762}, {10, 31150}, {650, 9780}, {814, 4784}, {1577, 4794}, {2533, 4782}, {3616, 45320}, {3617, 17494}, {3621, 14077}, {3634, 31209}, {3907, 4801}, {4380, 4761}, {4391, 4724}, {4462, 29186}, {4774, 29362}, {4885, 5550}, {7192, 28475}, {19877, 44567}, {21146, 29236}, {21302, 23882}, {24720, 44550}, {26985, 46934}, {27115, 46931}

X(47722) = X(514)X(4088)∩X(522)X(12625)

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

X(47722) lies on these lines: {514, 4088}, {522, 12625}, {693, 29240}, {2533, 29244}, {2785, 4382}, {3801, 29274}, {4468, 30709}, {4707, 29033}, {21146, 29156}, {23738, 28490}, {25259, 29102}

X(47723) = X(522)X(4761)∩X(693)X(29192)

X(47723) lies on these lines: {522, 4761}, {693, 29192}, {1019, 29278}, {2533, 29086}, {3887, 4024}, {4122, 29188}, {4774, 29312}, {4784, 29058}, {4810, 12073}, {4834, 29276}, {21146, 29110}, {21302, 23879}

X(47724) = X(1)X(693)∩X(8)X(26824)

X(47724) = 4 X[650] - 5 X[1698], 4 X[1125] - 5 X[26985], 3 X[1577] - 2 X[3716], 4 X[3716] - 3 X[4040], 7 X[3624] - 8 X[4885], 8 X[3634] - 7 X[27115], 3 X[4828] - 2 X[24325], 7 X[9780] - 5 X[26777], 17 X[19872] - 16 X[31287], 3 X[19875] - 2 X[31150], 3 X[25055] - 4 X[45320], 4 X[25380] - 3 X[45671]

X(47724) lies on these lines: {1, 693}, {8, 26824}, {10, 17494}, {512, 4810}, {514, 4088}, {522, 4707}, {649, 29033}, {650, 1698}, {663, 4823}, {667, 29274}, {812, 4761}, {814, 1019}, {832, 5214}, {891, 4774}, {1089, 21611}, {1125, 26985}, {1577, 3716}, {1734, 23882}, {2533, 4063}, {2787, 21146}, {3216, 25667}, {3293, 29771}, {3624, 4885}, {3632, 14077}, {3634, 27115}, {3679, 4762}, {3751, 9015}, {3801, 29086}, {3887, 4804}, {3907, 4978}, {4010, 29188}, {4122, 29102}, {4151, 21302}, {4367, 29182}, {4378, 29236}, {4382, 29350}, {4391, 29186}, {4724, 4791}, {4784, 29340}, {4828, 24325}, {4834, 29238}, {4905, 23880}, {5691, 8760}, {9780, 26777}, {16828, 26049}, {17496, 23789}, {19863, 27346}, {19864, 27139}, {19872, 31287}, {19875, 31150}, {21196, 44314}, {21385, 29362}, {25055, 45320}, {25380, 45671}, {25512, 27193}, {28475, 43067}

X(47724) = midpoint of X(8) and X(26824)
X(47724) = reflection of X(i) in X(j) for these {i,j}: {1, 693}, {663, 4823}, {4040, 1577}, {4063, 2533}, {4724, 4791}, {17494, 10}, {17496, 23789}, {21196, 44314}
X(47724) = crossdifference of every pair of points on line {2225, 21764}

X(47725) = X(1)X(514)∩X(693)X(29160)

X(47725) lies on these lines: {1, 514}, {693, 29160}, {1019, 29025}, {3801, 4063}, {3906, 4810}, {4010, 29224}, {4367, 29184}, {4378, 29122}, {4379, 29856}, {4382, 29318}, {4801, 29130}, {4879, 29272}, {4893, 29858}, {4978, 29116}, {6545, 29861}, {6546, 29860}, {21146, 29128}, {21181, 27013}, {29857, 44435}

X(47726) = X(1)X(523)∩X(514)X(4088)

X(47726) lies on these lines: {1, 523}, {514, 4088}, {649, 29318}, {659, 29166}, {663, 29164}, {667, 29146}, {693, 29160}, {826, 1019}, {1577, 29116}, {1930, 7199}, {2533, 29154}, {3906, 4784}, {4010, 29128}, {4040, 29021}, {4063, 29017}, {4122, 29029}, {4367, 7950}, {4378, 29204}, {4391, 29130}, {4449, 29260}, {4789, 17284}, {4834, 29202}, {7265, 29118}, {17023, 46915}, {21146, 29224}, {21385, 29312}, {25259, 29132}

X(47727) = X(1)X(523)∩X(663)X(29047)

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

X(47727) lies on these lines: {1, 523}, {663, 29047}, {667, 29208}, {693, 29192}, {826, 4879}, {1019, 3800}, {3287, 5299}, {3801, 29298}, {3887, 16892}, {4010, 29110}, {4040, 29288}, {4170, 29037}, {4367, 7927}, {4378, 29144}, {4449, 29021}, {4458, 4761}, {4729, 21192}, {4770, 29674}, {4784, 12073}, {4789, 17023}, {4810, 29058}, {4922, 29029}, {6742, 32678}, {7199, 39731}, {17316, 46915}, {21343, 29312}, {39578, 42660}

X(47727) = reflection of X(i) in X(j) for these {i,j}: {4729, 21192}, {4761, 4458}

X(47728) = X(1)X(514)∩X(513)X(3904)

X(47728) = 4 X[3239] - 3 X[30709], 2 X[3776] - 3 X[14413], 3 X[3777] - 4 X[24099], 2 X[3835] - 3 X[14432], 2 X[4142] - 3 X[8643], 5 X[8656] - 4 X[13246], 3 X[30574] - 4 X[31286]

X(47728) lies on these lines: {1, 514}, {513, 3904}, {649, 2785}, {664, 32735}, {667, 29094}, {693, 29240}, {832, 20294}, {1019, 29304}, {2787, 25259}, {2789, 4474}, {3239, 30709}, {3776, 14413}, {3777, 24099}, {3835, 14432}, {4010, 29156}, {4122, 29236}, {4142, 8643}, {4147, 36568}, {4170, 29114}, {4367, 8636}, {4378, 29102}, {4379, 29632}, {4406, 35550}, {4775, 29029}, {4879, 29025}, {4893, 29631}, {6332, 21301}, {6545, 29638}, {6546, 33120}, {7265, 29344}, {8633, 45746}, {8656, 13246}, {10196, 29861}, {21204, 29860}, {26230, 30580}, {30574, 31286}

X(47728) = reflection of X(i) in X(j) for these {i,j}: {4724, 5592}, {21301, 6332}, {44435, 30580}
X(47728) = barycentric product X(1)*X(30910)
X(47728) = barycentric quotient X(30910)/X(75)

X(47729) = X(1)X(693)∩X(8)X(650)

X(47729) = 4 X[10] - 5 X[31209], 3 X[663] - 2 X[3716], 3 X[663] - X[4474], 4 X[3716] - 3 X[4391], 3 X[4391] - 2 X[4474], X[4810] - 3 X[4879], 2 X[2254] - 3 X[44550], 5 X[3616] - 4 X[4885], 5 X[3617] - 7 X[27115], X[3621] - 5 X[26777], 7 X[3622] - 5 X[26985], 5 X[3623] - X[26824], 2 X[4522] - 3 X[14432], X[4774] - 3 X[25569], 2 X[4874] - 3 X[25569], X[4804] - 3 X[23057], 11 X[5550] - 10 X[31250], 4 X[8142] - 3 X[9778], 7 X[9780] - 8 X[31287], 3 X[14413] - 2 X[24720], 5 X[27013] - 6 X[30234], 3 X[38314] - 2 X[45320]

X(47729) lies on these lines: {1, 693}, {8, 650}, {10, 31209}, {21, 8641}, {78, 27417}, {145, 14077}, {513, 4922}, {519, 31150}, {522, 3904}, {663, 3716}, {667, 16158}, {814, 4810}, {905, 21302}, {938, 30235}, {944, 8760}, {1938, 3868}, {2254, 44550}, {2517, 2605}, {2787, 4775}, {2978, 30203}, {3241, 4762}, {3242, 9015}, {3309, 17496}, {3486, 11934}, {3616, 4885}, {3617, 27115}, {3621, 26777}, {3622, 26985}, {3623, 26824}, {3737, 4397}, {3762, 4794}, {3885, 9366}, {3900, 4560}, {4010, 29236}, {4025, 28292}, {4040, 4462}, {4041, 13256}, {4162, 23880}, {4170, 29344}, {4193, 15283}, {4367, 29366}, {4378, 29188}, {4380, 29350}, {4449, 4801}, {4522, 14432}, {4761, 4844}, {4774, 4874}, {4804, 23057}, {4814, 4913}, {4968, 21438}, {5550, 31250}, {6161, 7976}, {8142, 9778}, {8710, 44448}, {9373, 36977}, {9534, 24948}, {9780, 31287}, {10449, 24900}, {10459, 30061}, {10527, 28834}, {14413, 24720}, {16086, 30913}, {19767, 25667}, {19860, 25009}, {19861, 26695}, {20295, 28475}, {21343, 29362}, {27013, 30234}, {28294, 44435}, {38314, 45320}

X(47729) = midpoint of X(145) and X(17494)
X(47729) = reflection of X(i) in X(j) for these {i,j}: {8, 650}, {693, 1}, {2517, 2605}, {3762, 4794}, {4391, 663}, {4397, 3737}, {4462, 4040}, {4474, 3716}, {4774, 4874}, {4801, 4449}, {4814, 4913}, {21302, 905}
X(47729) = crossdifference of every pair of points on line {1405, 2225}
X(47729) = X(i)-isoconjugate of X(j) for these (i,j): {109, 4492}, {2099, 8695}
X(47729) = X(i)-Dao conjugate of X(j) for these (i, j): (11, 4492), (40624, 30635)
X(47729) = barycentric product X(i)*X(j) for these {i,j}: {9, 4406}, {333, 4761}, {522, 3758}, {609, 35519}, {3699, 7208}, {3716, 43262}, {3997, 18155}, {4391, 17126}, {4560, 46897}, {4844, 30608}
X(47729) = barycentric quotient X(i)/X(j) for these {i,j}: {609, 109}, {650, 4492}, {2364, 8695}, {3758, 664}, {3997, 4551}, {4391, 30635}, {4406, 85}, {4761, 226}, {4844, 5219}, {7208, 3676}, {7276, 4605}, {17126, 651}, {46897, 4552}
X(47729) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 4474, 3716}, {3716, 4474, 4391}, {4774, 25569, 4874}

X(47730) = X(1)X(16079)∩X(2)X(2415)

X(47730) lies on the cubics K517 and K618 and these lines: {4, 193}, {427, 19568}, {468, 8770}, {550, 3565}, {1656, 40809}, {5094, 6340}, {7768, 35136}, {27376, 41584}

X(47730) = X(141)-cross conjugate of X(427)
X(47730) = X(i)-isoconjugate of X(j) for these (i,j): {63, 33632}, {82, 3167}, {1176, 1707}, {3053, 34055}, {6337, 46289}, {10547, 18156}
X(47730) = X(i)-Dao conjugate of X(j) for these (i, j): (39, 6337), (141, 3167), (3162, 33632), (15261, 10547), (40938, 193)
X(47730) = barycentric product X(i)*X(j) for these {i,j}: {141, 34208}, {427, 2996}, {1235, 8770}, {5203, 31125}, {6340, 27376}, {8024, 14248}, {8769, 20883}
X(47730) = barycentric quotient X (i)/X(j) for these {i,j}: {25, 33632}, {39, 3167}, {141, 6337}, {427, 193}, {1843, 3053}, {2996, 1799}, {3917, 10607}, {6391, 28724}, {8769, 34055}, {8770, 1176}, {14248, 251}, {17442, 1707}, {20883, 18156}, {21016, 4028}, {21108, 3798}, {27371, 41588}, {27376, 6353}, {34208, 83}, {41584, 439}, {46154, 6091}
X(47730) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2996, 14248, 5203}, {2996, 34208, 14248}

X(47731) = X(5)X(6)∩X(25)X(39111)

X(47731) lies on the cubics K350 anjhd K429 and these lines: {5, 6}, {25, 39111}, {51, 14593}, {52, 8906}, {53, 41524}, {131, 571}, {317, 30450}, {454, 1609}, {1974, 32734}, {5392, 11433}, {5962, 12004}, {6515, 39116}, {8940, 24246}, {8944, 24245}, {11442, 33494}, {32132, 36747}, {37643, 37802}

X(47731) = isogonal conjugate of the isotomic conjugate of X(39116)
X(47731) = polar conjugate of the isotomic conjugate of X(34853)
X(47731) = orthic isogonal conjugate of X(14593)
X(47731) = crosspoint of X(4) and X(6515)
X(47731) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 14593}, {1993, 34757}, {39116, 34853}
X(47731) = X(i)-isoconjugate of X(j) for these (i,j): {47, 6504}, {63, 34756}, {563, 46746}, {921, 1993}, {1748, 15316}, {2167, 40678}, {2169, 39114}
X(47731) = X(i)-Dao conjugate of X(j) for these (i, j): (2165, 69), (3162, 34756), (14363, 39114), (34853, 6504), (40588, 40678)
X(47731) = barycentric product X(i)*X(j) for these {i,j}: {4, 34853}, {6, 39116}, {68, 3542}, {91, 920}, {96, 41587}, {155, 847}, {1609, 5392}, {2165, 6515}, {7505, 15242}, {14593, 40697}, {39111, 39115}
X(47731) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 34756}, {51, 40678}, {53, 39114}, {155, 9723}, {847, 46746}, {920, 44179}, {1609, 1993}, {2165, 6504}, {2351, 15316}, {3542, 317}, {6515, 7763}, {14593, 254}, {32734, 13398}, {34853, 69}, {39116, 76}, {41587, 39113}

X(47732) = X(25)X(571)∩X(52)X(53)

X(47732) lies on the cubic K350 and these lines: {6, 39110}, {25, 571}, {52, 53}, {135, 9722}, {139, 5891}, {254, 6403}, {467, 39114}, {3133, 14576}, {8745, 34756}, {39416, 45135}

X(47732) = isogonal conjugate of the isotomic conjugate of X(39114)
X(47732) = polar conjugate of the isotomic conjugate of X(40678)
X(47732) = X(i)-Ceva conjugate of X(j) for these (i,j): {39114, 40678}, {39416, 6753}
X(47732) = X(51)-cross conjugate of X(52)
X(47732) = X(i)-isoconjugate of X(j) for these (i,j): {2167, 34853}, {2168, 40697}, {2169, 39116}
X(47732) = X(i)-Dao conjugate of X(j) for these (i, j): (14363, 39116), (40588, 34853)
X(47732) = barycentric product X(i)*X(j) for these {i,j}: {4, 40678}, {5, 34756}, {6, 39114}, {24, 8800}, {52, 254}, {1993, 41536}, {6504, 14576}, {39109, 39113}, {39110, 39117}
X(47732) = barycentric quotient X(i)/X(j) for these {i,j}: {51, 34853}, {52, 40697}, {53, 39116}, {254, 34385}, {8800, 20563}, {14576, 6515}, {34756, 95}, {39109, 96}, {39114, 76}, {40678, 69}, {41536, 5392}, {44077, 8883}

X(47733) = X(2)X(9292)∩X(6)X(194)

X(47733) lies on the cubic K677 and these lines: {2, 9292}, {6, 194}, {458, 14248}, {1593, 15369}, {3504, 37344}, {5395, 40162}, {14001, 19602}, {19118, 37199}

X(47733) = X(i)-isoconjugate of X(j) for these (i,j): {194, 38252}, {1613, 8769}, {1740, 8770}, {23503, 35136}
X(47733) = X(15525)-Dao conjugate of X(23301)
X(47733) = barycentric product X(i)*X(j) for these {i,j}: {193, 2998}, {1707, 18832}, {3053, 40162}, {3222, 3566}, {3223, 18156}, {6353, 43714}
X(47733) = barycentric quotient X(i)/X(j) for these {i,j}: {193, 194}, {1707, 1740}, {2998, 2996}, {3053, 1613}, {3167, 20794}, {3222, 35136}, {3223, 8769}, {3224, 8770}, {3504, 6391}, {3566, 23301}, {3798, 21191}, {4028, 21080}, {6353, 3186}, {8651, 3221}, {15389, 40319}, {17081, 17082}, {18156, 17149}, {19118, 11325}, {21874, 21877}, {33632, 38834}, {34248, 38252}, {43714, 6340}
X(47733) = {X(3224),X(43714)}-harmonic conjugate of X(2998)

X(47734) = X(2)X(694)∩X(6)X(36897)

X(47734) lieson the cubic K677 and these lines: {2, 694}, {6, 36897}, {25, 17938}, {51, 16068}, {262, 41517}, {427, 2501}, {458, 39291}, {733, 930}, {805, 3060}, {1316, 15391}, {2548, 3493}, {3095, 39092}, {3815, 40810}, {8770, 39292}, {9300, 18872}, {9766, 18829}, {14593, 17980}, {34238, 42535}, {38947, 39906}

X(47734) = X(114)-cross conjugate of X(230)
X(47734) = X(i)-isoconjugate of X(j) for these (i,j): {385, 36051}, {1580, 2987}, {1691, 8773}, {1933, 8781}, {1966, 32654}
X(47734) = X(i)-Dao conjugate of X(j) for these (i, j): (114, 385), (230, 5976), (9467, 32654), (35067, 12215), (39069, 1580), (39072, 1691), (39092, 2987)
X(47734) = cevapoint of X(230) and X(12830)
X(47734) = crosspoint of X(1916) and X(36897)
X(47734) = crosssum of X(1691) and X(36213)
X(47734) = barycentric product X(i)*X(j) for these {i,j}: {114, 36897}, {230, 1916}, {460, 40708}, {1581, 1733}, {1692, 18896}, {1934, 8772}, {9477, 12830}, {14265, 40810}, {36214, 44145}
X(47734) = barycentric quotient X(i)/X(j) for these {i,j}: {114, 5976}, {230, 385}, {460, 419}, {694, 2987}, {805, 10425}, {882, 35364}, {1581, 8773}, {1692, 1691}, {1733, 1966}, {1916, 8781}, {1967, 36051}, {3564, 12215}, {4226, 17941}, {5477, 5026}, {8772, 1580}, {9468, 32654}, {12829, 4027}, {12830, 8290}, {14251, 34157}, {14265, 14382}, {17970, 42065}, {17980, 3563}, {34238, 2065}, {36214, 43705}, {36897, 40428}, {42663, 5027}, {44099, 44089}, {44145, 17984}, {46039, 16069}

X(47735) = X(2)X(35067)∩X(4)X(230)

X(47735) lies on the cubic K677 and these lines: {2, 35067}, {4, 230}, {6, 34208}, {193, 264}, {254, 5286}, {393, 460}, {458, 1007}, {1249, 36611}, {1300, 43448}, {3068, 24243}, {3069, 24244}, {6344, 41370}, {8743, 36612}, {10314, 32979}, {17983, 40138}, {21874, 41013}, {30558, 32971}, {32085, 33632}, {41515, 44596}, {41516, 44595}

X(47735) = isotomic conjugate of X(10008)
X(47735) = polar conjugate of X(1007)
X(47735) = isogonal conjugate of the isotomic conjugate of X(42298)
X(47735) = polar conjugate of the isotomic conjugate of X(7612)
X(47735) = X(42298)-Ceva conjugate of X(7612)
X(47735) = X(i)-cross conjugate of X(j) for these (i,j): {5052, 25}, {7735, 393}
X(47735) = cevapoint of X(7612) and X(40819)
X(47735) = trilinear pole of line {2501, 6562}
X(47735) = X(i)-isoconjugate of X(j) for these (i,j): {31, 10008}, {48, 1007}, {63, 1351}, {255, 37174}
X(47735) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 10008), (1249, 1007), (3162, 1351), (6523, 37174)
X(47735) = barycentric product X(i)*X(j) for these {i,j}: {4, 7612}, {6, 42298}, {34208, 40819}
X(47735) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 10008}, {4, 1007}, {25, 1351}, {393, 37174}, {460, 10011}, {6620, 9752}, {7612, 69}, {14248, 40809}, {40819, 6337}, {42298, 76}

X(47736) = X(4)X(99)∩X(76)X(10425)

X(47736) lies on the cubic K677 and these lines: {4, 99}, {76, 10425}, {264, 2065}, {401, 40812}, {419, 17941}, {458, 39291}, {880, 17984}, {1840, 18047}, {9756, 40428}, {12829, 39931}

X(47736) = X(5976)-cross conjugate of X(17984)
X(47736) = cevapoint of X(419) and X(39931)
X(47736) = X(i)-isoconjugate of X(j) for these (i,j): {1733, 17970}, {1967, 3564}, {8772, 36214}, {15391, 17462}
X(47736) = X(i)-Dao conjugate of X(j) for these (i, j): (8290, 3564), (8623, 47406)
X(47736) = barycentric product X(i)*X(j) for these {i,j}: {385, 35142}, {419, 8781}, {2987, 17984}, {3563, 3978}, {14295, 32697}, {39931, 40428}
X(47736) = barycentric quotient X(i)/X(j) for these {i,j}: {385, 3564}, {419, 230}, {2065, 15391}, {2987, 36214}, {3563, 694}, {8781, 40708}, {32654, 17970}, {32697, 805}, {35142, 1916}, {36105, 37134}, {36213, 47406}, {39931, 114}, {44089, 1692}

X(47737) = X(2)X(9473)∩X(4)X(32)

X(47736) lies on the cubics K677 and K1013 and these lines: {2, 9473}, {4, 32}, {6, 36897}, {183, 2966}, {262, 40823}, {287, 7774}, {685, 45141}, {1007, 42287}, {1910, 7132}, {3815, 34369}, {5967, 37665}, {7766, 46806}, {8870, 13356}, {9756, 47382}, {13860, 47388}

X(47737) = X(3407)-Ceva conjugate of X(40820)
X(47737) = X(1959)-isoconjugate of X(43702)
X(47737) = barycentric product X(98)*X(5999)
X(47737) = barycentric quotient X(i)/X(j) for these {i,j}: {1976, 43702}, {5999, 325}
X(47737) = {X(6),X(41932)}-harmonic conjugate of X(40820)

X(47738) = X(2)X(9475)∩X(4)X(39)

X(47738) lies on the cubics K423 and K677 and these lines: {2, 9475}, {4, 39}, {6, 419}, {83, 8863}, {264, 1249}, {297, 7777}, {458, 3329}, {1075, 8743}, {1715, 45985}, {1843, 40065}, {3183, 9729}, {3289, 12251}, {3462, 41361}, {3815, 5117}, {5667, 41370}, {6620, 37665}, {7875, 16318}, {7925, 11331}, {22240, 37190}, {35925, 40799}, {43711, 43717}

X(47738) = polar conjugate of the isotomic conjugate of X(6194)
X(47738) = X(i)-Ceva conjugate of X(j) for these (i,j): {458, 4}, {45141, 1249}
X(47738) = X(262)-Dao conjugate of X(42313)
X(47738) = barycentric product X(4)*X(6194)
X(47738) = barycentric quotient X(6194)/X(69)

X(47739) = X(2)X(216)∩X(4)X(1987)

X(47739) lies on the cubic K677 and these lines: {2, 216}, {4, 1987}, {6, 436}, {39, 1093}, {51, 3087}, {53, 23332}, {107, 10311}, {217, 1075}, {262, 10002}, {378, 41368}, {458, 43711}, {1968, 45255}, {2207, 37124}, {3088, 36434}, {3815, 6530}, {6524, 7736}, {6526, 45207}, {7735, 47202}, {9756, 33971}, {11672, 18027}, {13450, 39575}, {33843, 47392}

X(47739) = polar conjugate of X(43711)
X(47739) = X(99)-Ceva conjugate of X(10002)
X(47739) = X(i)-isoconjugate of X(j) for these (i,j): {48, 43711}, {255, 40815}
X(47739) = X(i)-Dao conjugate of X(j) for these (i, j): (1249, 43711), (6523, 40815)
X(47739) = barycentric product X(2052)*X(40805)
X(47739) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 43711}, {393, 40815}, {40805, 394}
X(47739) = {X(232),X(2052)}-harmonic conjugate of X(393)

X(47740) = X(2)X(51)∩X(4)X(40867)

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

X(47740) = 4 X[6] - X[164], X[193] + 2 X[264], 5 X[3620] - 8 X[14767], X[5921] - 4 X[39530]

X(47740) lies on the cubic K677 and these lines: {2, 51}, {4, 40867}, {6, 401}, {52, 37337}, {69, 17035}, {143, 28407}, {193, 264}, {287, 576}, {297, 21850}, {458, 1351}, {1972, 42287}, {1992, 39358}, {1994, 34137}, {2456, 35926}, {3620, 14767}, {5050, 35941}, {5052, 40814}, {5921, 39530}, {6515, 8878}, {7665, 37645}, {7766, 46806}, {10002, 37174}, {11179, 44651}, {11427, 20859}, {14912, 32428}, {15013, 39522}, {15014, 44413}, {15033, 35952}, {15741, 33023}, {17037, 40896}, {17350, 25245}, {30258, 37188}, {31670, 40853}, {33878, 37067}

X(47740) = anticomplement of X(42313)
X(47740) = anticomplement of the isogonal conjugate of X(10311)
X(47740) = anticomplement of the isotomic conjugate of X(458)
X(47740) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19, 1352}, {182, 4329}, {458, 6327}, {1973, 7774}, {2148, 42329}, {10311, 8}, {32676, 23878}, {33971, 21270}, {34396, 6360}, {44144, 21275}, {46289, 22240}
X(47740) = X(i)-Ceva conjugate of X(j) for these (i,j): {458, 2}, {1351, 193}
X(47740) = {X(2),X(44434)}-harmonic conjugate of X(46807)

X(47741) = X(2)X(98)∩X(4)X(46237)

X(47741) lies on the cubic K677 and these lines: {2, 98}, {4, 46237}, {6, 32542}, {262, 40823}, {264, 2065}, {685, 33971}, {1351, 2966}, {2456, 14382}, {5480, 34369}, {6531, 41371}, {9753, 36899}, {9755, 47382}, {13860, 41932}, {14912, 34156}, {18906, 43711}

X(47741) = barycentric product X(14265)*X(40812)
X(47741) = {X(6),X(47388)}-harmonic conjugate of X(32545)

X(47742) = COMPLEMENT OF X(496)

X(47742) = 3*X(2)+X(5687), X(56)-3*X(17564), 3*X(165)+X(12679), 5*X(632)-X(32214), X(1479)-5*X(31246), 5*X(1698)-X(1837), X(3436)+3*X(16371), 3*X(3679)+X(37738), X(4299)+3*X(31141), X(17857)+7*X(31423), 9*X(19875)-X(37711), 3*X(26446)+X(45770)

X(47742) lies on these lines: {2, 496}, {3, 1603}, {5, 1376}, {8, 13747}, {9, 3652}, {10, 140}, {21, 2932}, {30, 1329}, {35, 6174}, {36, 21031}, {55, 17527}, {56, 17564}, {78, 41574}, {100, 4187}, {119, 31775}, {141, 43146}, {165, 12679}, {230, 1574}, {355, 5438}, {376, 8165}, {377, 10592}, {388, 16417}, {404, 17757}, {442, 26060}, {443, 31479}, {474, 495}, {498, 4413}, {517, 6700}, {518, 34753}, {519, 6691}, {528, 3825}, {546, 3814}, {547, 25639}, {549, 958}, {631, 9708}, {632, 26363}, {936, 26446}, {942, 6745}, {956, 6921}, {993, 3530}, {997, 5690}, {999, 7080}, {1056, 27525}, {1125, 3880}, {1377, 8981}, {1378, 13966}, {1387, 10914}, {1478, 17563}, {1479, 31246}, {1532, 31777}, {1575, 5305}, {1621, 17575}, {1656, 2550}, {1698, 1837}, {1706, 5886}, {1788, 3940}, {1861, 21841}, {2886, 3628}, {3055, 31488}, {3085, 16408}, {3293, 37634}, {3434, 10593}, {3436, 16371}, {3452, 3579}, {3526, 19843}, {3616, 40587}, {3617, 17566}, {3624, 37556}, {3626, 6681}, {3634, 6690}, {3650, 26792}, {3654, 15829}, {3679, 5433}, {3695, 5205}, {3702, 37762}, {3753, 27385}, {3812, 5719}, {3816, 8715}, {3841, 6668}, {3884, 32157}, {3911, 34790}, {3913, 10200}, {3953, 43055}, {4002, 24541}, {4293, 17573}, {4299, 31141}, {4421, 10386}, {4423, 31452}, {4857, 6154}, {4861, 34123}, {4995, 5259}, {5044, 6001}, {5045, 6692}, {5054, 30478}, {5055, 31418}, {5086, 34122}, {5087, 40273}, {5119, 24954}, {5122, 12527}, {5123, 17647}, {5218, 11108}, {5260, 37298}, {5264, 37663}, {5267, 12100}, {5281, 17559}, {5288, 5298}, {5326, 10959}, {5328, 6361}, {5440, 24982}, {5445, 21677}, {5482, 23841}, {5554, 37728}, {5708, 25568}, {5720, 33899}, {5791, 8580}, {5794, 38042}, {5795, 13624}, {5836, 5901}, {5844, 8256}, {6244, 6848}, {6259, 10270}, {6376, 6390}, {6667, 24387}, {6705, 9947}, {6735, 17614}, {6736, 24928}, {6759, 20307}, {6765, 31190}, {6842, 38752}, {6904, 9654}, {6905, 31799}, {6919, 9668}, {6922, 11499}, {6944, 7956}, {6970, 22770}, {7173, 31263}, {7280, 34606}, {7373, 34619}, {7483, 9780}, {7499, 29679}, {7525, 9713}, {7741, 34612}, {7789, 27076}, {7819, 27091}, {8164, 17580}, {8359, 26558}, {8361, 26582}, {8369, 26687}, {8582, 24929}, {8976, 31413}, {9342, 17529}, {9540, 31485}, {9669, 17784}, {9679, 42215}, {9701, 40111}, {9710, 16239}, {9712, 12106}, {9945, 10572}, {10164, 31445}, {10585, 44217}, {10588, 17528}, {11112, 11681}, {11277, 18253}, {11500, 37364}, {11544, 31053}, {11545, 25005}, {12019, 17619}, {12572, 31663}, {12678, 16209}, {12699, 30827}, {13226, 14872}, {15338, 44847}, {16197, 34822}, {17694, 26752}, {17792, 18583}, {18236, 40263}, {19875, 24953}, {20306, 23329}, {21075, 37582}, {21077, 24470}, {21616, 28174}, {22791, 25681}, {24047, 38930}, {24443, 39544}, {24885, 25669}, {24902, 24938}, {24914, 34489}, {25524, 45701}, {26062, 36279}, {29958, 35059}, {31405, 31467}, {31416, 31489}, {31453, 35255}, {33814, 37290}, {35249, 45631}, {37561, 37725}

X(47742) = midpoint of X(i) and X(j) for these {i, j}: {496, 5687}, {1329, 25440}, {6736, 24928}, {6922, 11499}, {8256, 30144}, {21075, 37582}
X(47742) = complement of X(496)
X(47742) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5687, 496), (8, 13747, 15325), (10, 3035, 140), (100, 4187, 15171), (404, 17757, 18990), (474, 5552, 495), (498, 4413, 8728), (997, 37828, 5690), (1376, 26364, 5), (1698, 5432, 6675), (3753, 27385, 37737), (3816, 8715, 15172), (5123, 17647, 18357), (5440, 24982, 37730), (6684, 20103, 5044), (6944, 10306, 7956), (7080, 17567, 999), (8580, 31423, 5791), (11231, 31659, 140)

X(47743) = X(2)X(496)∩X(4)X(11)

X(47743) lies on these lines: {1, 3090}, {2, 496}, {3, 5274}, {4, 11}, {5, 1056}, {7, 9955}, {8, 10584}, {10, 1000}, {12, 5071}, {20, 9669}, {30, 5265}, {35, 497}, {36, 3529}, {55, 3525}, {72, 26129}, {140, 390}, {145, 1387}, {149, 6921}, {226, 3296}, {350, 32818}, {376, 1479}, {381, 3600}, {388, 3545}, {443, 11680}, {459, 7049}, {495, 5056}, {517, 5704}, {614, 6198}, {936, 24386}, {938, 5886}, {943, 4423}, {944, 6969}, {946, 3339}, {952, 6981}, {956, 6919}, {962, 7743}, {999, 3091}, {1062, 7292}, {1124, 13886}, {1125, 3488}, {1210, 3340}, {1250, 43464}, {1329, 34625}, {1335, 13939}, {1398, 6623}, {1428, 9638}, {1476, 18519}, {1478, 3855}, {1482, 6978}, {1484, 6959}, {1538, 6223}, {1591, 38016}, {1698, 30337}, {1737, 12245}, {1776, 17437}, {1788, 30384}, {1837, 7967}, {1870, 6622}, {2067, 23273}, {2078, 6927}, {2476, 10586}, {2550, 10200}, {2551, 3825}, {2886, 17582}, {3058, 15702}, {3085, 5067}, {3304, 3544}, {3333, 3817}, {3361, 18483}, {3421, 4193}, {3434, 17567}, {3475, 37692}, {3476, 10826}, {3485, 23708}, {3487, 8227}, {3518, 10832}, {3522, 9668}, {3523, 15171}, {3524, 4294}, {3526, 5281}, {3528, 6284}, {3533, 5218}, {3555, 5748}, {3583, 33703}, {3585, 41099}, {3616, 5086}, {3621, 11545}, {3622, 6933}, {3628, 6767}, {3634, 31393}, {3671, 38021}, {3816, 17559}, {3829, 25524}, {3832, 18990}, {3839, 9655}, {3847, 12513}, {3911, 6361}, {3913, 6667}, {4295, 17728}, {4299, 15682}, {4302, 21735}, {4308, 18480}, {4313, 18527}, {4315, 18492}, {4355, 30308}, {4366, 32970}, {4392, 35194}, {4847, 25522}, {4857, 10299}, {4939, 20320}, {5045, 5226}, {5054, 10386}, {5068, 9654}, {5084, 5260}, {5175, 17614}, {5204, 17538}, {5229, 5563}, {5298, 11001}, {5328, 34790}, {5353, 42987}, {5357, 42986}, {5434, 41106}, {5435, 12699}, {5533, 10320}, {5550, 24929}, {5552, 31272}, {5657, 12053}, {5703, 11230}, {5708, 38034}, {5777, 17626}, {5901, 6859}, {6049, 28204}, {6459, 35803}, {6460, 35802}, {6502, 23267}, {6645, 32983}, {6691, 11235}, {6700, 24392}, {6738, 9624}, {6824, 8543}, {6833, 37541}, {6858, 12433}, {6864, 26470}, {6865, 35239}, {6879, 10595}, {6891, 35448}, {6918, 38149}, {6926, 35514}, {6935, 10531}, {6944, 10943}, {6948, 11928}, {6949, 10806}, {6952, 10596}, {6965, 10629}, {6970, 45043}, {6982, 16203}, {6985, 7677}, {7005, 11488}, {7006, 11489}, {7191, 37696}, {7285, 43733}, {7296, 9599}, {7486, 31479}, {7504, 10587}, {7512, 10046}, {7550, 10831}, {7581, 44623}, {7582, 44624}, {7704, 11023}, {7705, 12648}, {7956, 37434}, {7988, 21620}, {8972, 31474}, {9341, 9665}, {9645, 44442}, {9671, 15326}, {9672, 44879}, {9780, 9957}, {9785, 26446}, {9812, 37582}, {9947, 17624}, {10171, 21625}, {10321, 10948}, {10385, 15709}, {10394, 13373}, {10573, 16173}, {10580, 11374}, {10585, 37739}, {10592, 15022}, {10624, 31231}, {10638, 43463}, {10805, 26476}, {11041, 13464}, {11047, 12608}, {11240, 11681}, {12575, 31423}, {12589, 14912}, {12647, 15079}, {12675, 17604}, {13462, 31673}, {13747, 17784}, {14039, 26686}, {15338, 19708}, {16215, 18908}, {16845, 26105}, {16863, 40333}, {17566, 20075}, {18419, 40266}, {19878, 30331}, {20076, 37375}, {20401, 44858}, {21616, 24477}, {22836, 33709}, {24914, 30305}, {26561, 33285}, {26590, 32960}, {26629, 32959}, {26877, 30223}, {26959, 32956}, {30332, 31663}, {31412, 35769}, {32785, 35808}, {32786, 35809}, {34619, 45310}, {34631, 41687}, {35768, 42561}, {37545, 40273}, {37709, 38074}

X(47743) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3090, 8164), (1, 10589, 3090), (2, 496, 1058), (5, 7373, 5261), (5, 14986, 1056), (11, 56, 10591), (11, 3086, 4), (36, 5225, 3529), (56, 10591, 4), (104, 10598, 4), (388, 7741, 3545), (497, 499, 631), (499, 37720, 497), (999, 10593, 3091), (1479, 3582, 7288), (1479, 7288, 376), (3086, 10591, 56), (3304, 7173, 10590), (3333, 3817, 5714), (3825, 45700, 2551), (4193, 10529, 3421), (4293, 10896, 4), (4294, 5433, 3524), (5261, 7373, 1056), (5261, 14986, 7373), (7173, 10590, 3544), (7741, 10072, 388), (8227, 11019, 3487), (9581, 44675, 944), (9669, 15325, 20), (10200, 24387, 2550), (26105, 26363, 16845)

X(47744) = X(4)X(11)∩X(8)X(4767)

X(47744) lies on these lines: {1, 10711}, {4, 11}, {8, 4767}, {80, 12053}, {100, 4187}, {149, 6919}, {474, 17100}, {496, 38669}, {497, 38665}, {498, 6975}, {499, 37430}, {1056, 38757}, {1058, 37725}, {1387, 9654}, {1479, 6963}, {1537, 5804}, {1706, 6702}, {1737, 3245}, {3254, 10916}, {3680, 15863}, {5046, 13279}, {5274, 37726}, {5281, 38763}, {5714, 38055}, {5840, 6926}, {6246, 12650}, {6744, 21635}, {6922, 10738}, {6940, 10058}, {6946, 7741}, {6955, 10589}, {6964, 23513}, {6965, 15845}, {6967, 34474}, {7319, 18543}, {7743, 37375}, {9614, 12758}, {10090, 37403}, {10106, 16173}, {10593, 11112}, {10724, 37022}, {10742, 15179}, {12619, 12700}, {12738, 18527}

X(47745) = X(8)X(20)∩X(10)X(140)

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

X(47745) = 5*X(1)-7*X(3090), 3*X(1)-5*X(5818), 2*X(1)-3*X(10175), 2*X(3)-3*X(38127), 3*X(4)-X(11531), X(4)-3*X(37712), 3*X(5)-2*X(33179), 2*X(5)-3*X(38155), 5*X(8)-X(20), 3*X(8)-X(40), 11*X(8)-3*X(9778), 4*X(8)-X(31730), 14*X(3090)-15*X(10175), 3*X(3244)-4*X(33179), X(3244)-3*X(38155), 4*X(3626)-3*X(38127), 3*X(3632)+X(11531), X(3632)+3*X(37712), 10*X(5818)-9*X(10175), X(11531)-9*X(37712), 4*X(33179)-9*X(38155)

X(47745) lies on these lines: {1, 3090}, {2, 13607}, {3, 3626}, {4, 3632}, {5, 3244}, {8, 20}, {10, 140}, {30, 34641}, {35, 38665}, {80, 12053}, {119, 24387}, {145, 5068}, {150, 25719}, {182, 38191}, {226, 37710}, {355, 381}, {382, 28228}, {516, 4701}, {517, 3625}, {546, 11278}, {549, 38098}, {551, 1483}, {944, 3524}, {950, 6976}, {956, 6796}, {962, 31145}, {1056, 17706}, {1125, 5070}, {1210, 10944}, {1317, 17606}, {1389, 41696}, {1490, 4915}, {1656, 3636}, {1698, 7967}, {1737, 37707}, {1766, 4060}, {2800, 10914}, {2801, 37562}, {2802, 5887}, {3057, 18908}, {3091, 16200}, {3146, 28232}, {3241, 8227}, {3336, 4848}, {3338, 10106}, {3419, 6260}, {3525, 30392}, {3545, 34747}, {3555, 31870}, {3560, 25439}, {3576, 3617}, {3579, 28224}, {3616, 10172}, {3621, 7982}, {3623, 9624}, {3628, 15808}, {3633, 5603}, {3634, 10246}, {3635, 5886}, {3654, 12512}, {3655, 4745}, {3680, 38307}, {3753, 12005}, {3813, 33956}, {3814, 10943}, {3817, 10222}, {3825, 37726}, {3832, 20054}, {3861, 4301}, {3872, 17857}, {3880, 5777}, {3883, 7609}, {3893, 12672}, {3918, 10202}, {3919, 24475}, {4292, 41687}, {4297, 4669}, {4311, 40663}, {4662, 31786}, {4668, 5657}, {4677, 5691}, {4678, 5731}, {4691, 18526}, {4746, 18481}, {4816, 7991}, {4853, 6261}, {4861, 6326}, {4863, 36972}, {4882, 12650}, {5056, 20057}, {5082, 6256}, {5086, 12531}, {5176, 21075}, {5245, 6192}, {5246, 6191}, {5252, 14563}, {5258, 11491}, {5260, 34486}, {5267, 32141}, {5288, 6905}, {5290, 11041}, {5450, 5687}, {5493, 28160}, {5531, 21740}, {5693, 14923}, {5727, 37556}, {5734, 20014}, {5815, 36922}, {5836, 5884}, {5854, 6246}, {5901, 10109}, {5930, 15319}, {6253, 34689}, {6361, 28172}, {6736, 12616}, {7173, 33176}, {7354, 36920}, {7971, 11525}, {7989, 10595}, {8168, 10306}, {8666, 11499}, {8715, 22758}, {8983, 35788}, {9897, 10572}, {9947, 12448}, {9955, 38138}, {10039, 37571}, {10164, 34773}, {10445, 17362}, {10915, 12437}, {10942, 25639}, {10950, 31397}, {11545, 24928}, {12101, 22793}, {12702, 28164}, {12749, 41558}, {13405, 37739}, {13411, 37740}, {13624, 38112}, {13971, 35789}, {14869, 31662}, {15178, 19862}, {15685, 34718}, {15716, 38066}, {15721, 31423}, {16174, 25416}, {17636, 45288}, {18391, 37709}, {18492, 20053}, {20052, 41869}, {20107, 33812}, {22837, 24386}, {24042, 37821}, {24390, 37725}, {24391, 37532}, {25485, 33895}, {28208, 44903}, {28212, 33697}, {29605, 36662}, {30538, 41541}, {31657, 38201}, {31658, 38210}, {31806, 34790}, {32537, 44669}, {32900, 38028}, {32905, 40260}, {37561, 38669}, {37738, 44675}, {38108, 43179}, {38121, 43176}, {38130, 43175}, {38146, 42785}

X(47745) = midpoint of X(i) and X(j) for these {i, j}: {4, 3632}, {8, 5881}, {355, 12645}, {3621, 7982}, {3893, 12672}, {4677, 34627}, {5691, 12245}, {5693, 14923}, {10914, 14872}, {12531, 12751}
X(47745) = reflection of X(i) in X(j) for these (i, j): (3, 3626), (145, 13464), (944, 6684), (946, 355), (1482, 19925), (1483, 9956), (3057, 20117), (3244, 5), (3555, 31870), (3655, 4745), (4297, 5690), (4301, 18480), (5882, 10), (5884, 5836), (7982, 18483), (10222, 18357), (10265, 15863), (11278, 546), (11362, 8), (11715, 3036), (12437, 10915), (18481, 43174), (25416, 16174), (31730, 11362), (31786, 4662), (31806, 34790), (32905, 40260), (37727, 1125), (43174, 4746), (45776, 9947)
X(47745) = anticomplement of X(13607)
X(47745) = X(8)-beth conjugate of-X(5882)
X(47745) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 3626, 38127), (10, 5882, 10165), (140, 38176, 10), (145, 5587, 13464), (355, 1482, 19925), (944, 3679, 6684), (1125, 5790, 31399), (1482, 19925, 946), (1483, 9956, 551), (3057, 18908, 20117), (3091, 20050, 16200), (3244, 38155, 5), (3625, 37705, 31673), (3632, 37712, 4), (3633, 37714, 5603), (3655, 4745, 38068), (3656, 12571, 946), (3872, 17857, 40257), (4297, 4669, 5690), (4677, 5691, 12245), (5790, 37727, 1125), (10222, 18357, 3817), (10573, 37708, 10106), (10595, 38074, 7989), (12245, 34627, 5691), (12647, 37711, 950), (15178, 38042, 19862), (25416, 38156, 16174), (41684, 45287, 4848)

X(47746) = X(145)X(942)∩X(355)X(381)

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

X(47746) = 5*X(355)-6*X(11235), 7*X(355)-6*X(34717), 3*X(3654)-4*X(11260), 3*X(3656)-2*X(32049), 3*X(5886)-4*X(33895), 3*X(10246)-2*X(12640), 5*X(10912)-3*X(11235), 7*X(10912)-3*X(34717), 7*X(11235)-5*X(34717), 4*X(22837)-3*X(26446), 4*X(31663)-3*X(34711), 4*X(33179)-3*X(34619)

X(47746) lies on these lines: {8, 10584}, {11, 3632}, {78, 25416}, {145, 942}, {355, 381}, {499, 44784}, {517, 17648}, {952, 3680}, {1159, 17647}, {1376, 3244}, {1483, 2136}, {1837, 41702}, {2802, 18481}, {3241, 17614}, {3340, 3633}, {3434, 20050}, {3654, 11260}, {3811, 32426}, {3869, 17652}, {3872, 5791}, {3880, 12675}, {3913, 16203}, {5734, 17618}, {5844, 12629}, {5854, 12737}, {5886, 33895}, {8666, 13205}, {9957, 17658}, {10246, 12640}, {11278, 18516}, {11374, 12648}, {12114, 28234}, {12513, 35448}, {12653, 12701}, {12699, 38455}, {13996, 37618}, {17622, 34790}, {22837, 26446}, {24928, 26062}, {26492, 34625}, {30384, 36972}, {31663, 34711}, {33179, 34619}, {34612, 34747}

X(47746) = reflection of X(i) in X(j) for these (i, j): (355, 10912), (2136, 1483), (12645, 21627)
X(47746) = {X(10893), X(47745)}-harmonic conjugate of X(355)

X(47747) = X(99)X(2705)∩X(900)X(9145)

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

X(47747) lies on these lines: {99, 2705}, {110, 13250}, {900, 9145}, {9216, 13251}, {28481, 45722}, {38664, 45710}

X(47748) = EULER LINE INTERCEPT OF X(49)X(37496)

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

X(47748) = 3*X(3)-4*X(7512), 5*X(3)-4*X(14118), 3*X(3)-2*X(14130), 7*X(3)-4*X(14865), 2*X(3)-3*X(34006)

X(47748) lies on these lines: {2, 3}, {49, 37496}, {143, 43600}, {161, 13093}, {195, 13391}, {399, 6101}, {511, 12316}, {1154, 8718}, {2777, 2917}, {2916, 29317}, {3581, 43807}, {5446, 15037}, {5663, 5898}, {6000, 9920}, {6030, 10610}, {6288, 29012}, {6407, 44598}, {6408, 44599}, {6449, 35776}, {6450, 35777}, {6759, 9919}, {6781, 44525}, {7689, 12310}, {9704, 37498}, {9911, 10247}, {10110, 13339}, {10263, 43845}, {10540, 15644}, {10627, 14157}, {11017, 14926}, {11438, 43829}, {11439, 33533}, {11750, 12902}, {12112, 31834}, {12289, 13171}, {12308, 18436}, {12606, 41464}, {13353, 13598}, {13491, 32608}, {13630, 15107}, {14627, 44111}, {15109, 39590}, {15655, 44527}, {18439, 46728}, {18551, 46849}, {22550, 32110}, {33543, 35259}, {33887, 45813}, {43394, 43576}

X(47748) = reflection of X(i) in X(j) for these (i, j): (3, 13564), (382, 34007), (14130, 7512)
X(47748) = inverse of X(46450) in Stammler circle
X(47748) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 37949, 4), (20, 2937, 3), (22, 1657, 3), (24, 15696, 3), (26, 3534, 3), (376, 45735, 3), (381, 10323, 3), (548, 43809, 3), (550, 2070, 3), (6636, 34864, 3), (7488, 18859, 3), (7512, 14130, 3), (7517, 35243, 3), (7555, 35001, 3), (11414, 12083, 3), (15688, 17928, 3), (35495, 38438, 3)

X(47749) = EULER LINE INTERCEPT OF X(40)X(2940)

X(47749) lies on these lines: {2, 3}, {40, 2940}, {500, 5902}, {3579, 35468}, {5495, 5885}, {5535, 13391}, {6003, 46611}, {16143, 33535}

X(47749) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1325, 3651, 3), (36001, 37294, 3)

X(47750) = EULER LINE INTERCEPT OF X(2777)X(34438)

X(47750) lies on these lines: {2, 3}, {2777, 34438}, {7723, 16266}, {7728, 32321}, {9914, 38790}, {9937, 12902}, {12164, 22584}, {13754, 15317}, {22120, 44528}

X(47750) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 2071, 26), (4, 14118, 6644), (378, 18404, 3), (2072, 12084, 3), (6640, 11413, 3), (7526, 18563, 3), (9818, 12085, 3515)

X(47751) = EULER LINE INTERCEPT OF X(5663)X(33542)

Barycentrics a^2*(a^8-2*(b^2+c^2)*a^6-27*b^2*c^2*a^4+(b^2+c^2)*(2*b^4+19*b^2*c^2+2*c^4)*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2) : :

X(47751) lies on these lines: {2, 3}, {5663, 33542}, {10627, 12308}, {12902, 17712}

X(47751) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (20, 45971, 1657), (548, 5899, 3), (3522, 13621, 3), (7387, 15695, 3), (15681, 37198, 3), (15688, 18378, 3)

X(47752) = (name pending)

X(47753) = (name pending)

If L1 and L2 are lines that meet in a point P not at infinity, then the {L1,L2}-coordiinate system is here defined as a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 = X(2)X(513), given by the equation (2a-b-c)α + (2b-c-a)β + (2c-a-b)γ = 0.

L2 = X(2)X(513), given by the equation (2bc-ca-ab)α + (2ca-ab-bc)β + (2ab-bc-ca)γ = 0.

The origin is given by (0,0) = X(2) = 1 : 1 : 1

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b-c)((a-b)(a-c) + x + ay) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogeneous of degree 2, and y is symmetric and homogeneous of degree 1.

The appearance of (x,y), k in the following table means that (x,y) = X(k):

(-a^2 - b^2 - c^2, 0), 44435
(-a^2 - b^2 - c^2, a + b + c), 4453
((-a^2 - b^2 - c^2)/2, (a + b + c)/2), 1638
(0, -a - b - c), 4776
(0, 0), 2
((a^2 + b^2 + c^2)/2, (-a - b - c)/2), 1639
(a^2 + b^2 + c^2, -a - b - c), 30565
(-2 (b c + c a + a b ), a + b + c), 31150
(- b c - c a - a b, -a - b - c), 661
(- b c - c a - a b, 0), 4893
(- b c - c a - a b, (a + b + c)/2), 650
(- b c - c a - a b, a + b + c), 1635
(- b c - c a - a b, 2 (a + b + c)), 649
((- b c - c a - a b )/2, (-a - b - c)/2), 45315
((- b c - c a - a b )/2, (a + b + c)/2), 4763
((- b c - c a - a b )/2, a + b + c), 45313
((b c + c a + a b )/2, -a - b - c), 3835
((b c + c a + a b )/2, (-a - b - c)/2), 4928
((b c + c a + a b )/2, (a + b + c)/2), 4369
((b c + c a + a b )/2, 2 (a + b + c)), 4932
(b c + c a + a b , -2 (a + b + c)), 31147
(b c + c a + a b , -a - b - c), 4728
(b c + c a + a b , (-a - b - c)/2), 45320
(b c + c a + a b , 0), 4379
(b c + c a + a b , a + b + c), 31148
(2 (b c + c a + a b ), -2 (a + b + c)), 21297
(2 (b c + c a + a b ), -a - b - c), 693
(2 (b c + c a + a b ), (a + b + c)/2), 43067
(2 (b c + c a + a b ), 2 (a + b + c)), 7192
(-2 (a + b + c)^2, 2 (a + b + c)), 46915
(-(a + b + c)^2, 2 (a + b + c)), 27486
((-1/2) (a + b + c)^2, 2 (a + b + c)), 4786
((a + b + c)^2, -a - b - c), 4789
(0, - (a^2 + b^2 + c^2)/(a + b + c))), 44429
(- b c - c a - a b, (2 (a^3 + b^3 + c^3))/(a + b + c)^2), 46385
(-a^2 - b^2 - c^2, (a + b + c)/2), 47754
(-a^2 - b^2 - c^2, 2(a + b + c)), 47755
((-a^2 - b^2 - c^2)/2, (-a - b - c)/2), 47756
((-a^2 - b^2 - c^2)/2, 0), 47757
((-a^2 - b^2 - c^2)/2, a + b + c), 47758
(0, -2 (a + b + c)), 47759
(0, (-a - b - c)/2), 47760
(0, (a + b + c)/2), 47761
(0, a + b + c), 47762
(0, 2 (a + b + c)), 47763
((a^2 + b^2 + c^2)/2, -2 (a + b + c)), 47764
((a^2 + b^2 + c^2)/2, -a - b - c), 47765
((a^2 + b^2 + c^2)/2, 0), 47766
((a^2 + b^2 + c^2)/2, (a + b + c)/2), 47767
((a^2 + b^2 + c^2)/2, a + b + c), 47768
(a^2 + b^2 + c^2, -2 (a + b + c)), 47769
(a^2 + b^2 + c^2, (-a - b - c)/2), 47770
(a^2 + b^2 + c^2, 0), 47771
(2 (a^2 + b^2 + c^2), -2 (a + b + c)), 47772
(2 (a^2 + b^2 + c^2), 0), 47773
(-2 (b c + c a + a b ), -2 (a + b + c)), 47774
(-2 (b c + c a + a b ), 0), 47775
(-2 (b c + c a + a b ), 2 (a + b + c)), 47776
(- b c - c a - a b, (-a - b - c)/2), 47777
((- b c - c a - a b)/2, 0), 47778
((b c + c a + a b )/2, 0), 47779
(2 (b c + c a + a b ), 0), 47780
(-(a + b + c)^2, 0), 47781
(-(a + b + c)^2, a + b + c), 47782
((-1/2) (a + b + c)^2), 47783
((-1/2) (a + b + c)^2, (a + b + c)/2), 47784
((-1/2) (a + b + c)^2, a + b + c), 47785
((a + b + c)^2/2, -2 (a + b + c)), 47786
((a + b + c)^2/2, -a - b - c), 47787
((a + b + c)^2/2, (-a - b - c)/2), 47788
((a + b + c)^2/2, 0), 47789
((a + b + c)^2, -2 (a + b + c)), 47790
((a + b + c)^2, 0), 47791
(2 (a + b + c)^2, -2 (a + b + c)), 47792
((-2 a b c)/(a + b + c)), 47793
(-a b c /(a + b + c)), 0), 47794
a b c /(a + b + c), 0), 47795
((2 a b c)/(a + b + c), 0), 47796
(-a^2 - b^2 - c^2, (a^2 + b^2 + c^2)/(a + b + c)), 47797
(-a^2 - b^2 - c^2, 2 (a^2 + b^2 + c^2)/(a + b + c)), 47798
((-a^2 - b^2 - c^2)/2, (a^2 + b^2 + c^2)/(2 (a + b + c))), 47799
((-a^2 - b^2 - c^2)/2, (a^2 + b^2 + c^2)/(a + b + c)), 47800
((-a^2 - b^2 - c^2)/2, 2 (a^2 + b^2 + c^2)/(a + b + c)), 47801
(0, (-1/2) (a^2 + b^2 + c^2)/(a + b + c)), 47802
(0, (a^2 + b^2 + c^2)/(2 (a + b + c))), 47803
(0, (a^2 + b^2 + c^2)/(a + b + c)), 47804
(0, (2 (a^2 + b^2 + c^2))/(a + b + c)), 47805
((a^2 + b^2 + c^2)/2, (-1/2) (a^2 + b^2 + c^2)/(a + b + c)), 47807
(a^2 + b^2 + c^2, (-2 (a^2 + b^2 + c^2))/(a + b + c)), 47808
(a^2 + b^2 + c^2, -(a^2 + b^2 + c^2)/(a + b + c))), 47809
(- b c - c a - a b, -(a^2 + b^2 + c^2)/(a + b + c))), 47810
(- b c - c a - a b, (a^2 + b^2 + c^2)/(a + b + c)), 47811
(b c + c a + a b , -(a^2 + b^2 + c^2)/(a + b + c))), 47812
(b c + c a + a b , (a^2 + b^2 + c^2)/(a + b + c)), 47813
(-2 a b c)/(a + b + c), -(a^2 + b^2 + c^2)/(a + b + c))), 47814
(-2 a b c)/(a + b + c), (a^2 + b^2 + c^2)/(a + b + c)), 47815
(-a b c /(a + b + c)), -(a^2 + b^2 + c^2)/(a + b + c))), 47816
(-a b c /(a + b + c)), (a^2 + b^2 + c^2)/(a + b + c)), 47817
a b c /(a + b + c), (a^2 + b^2 + c^2)/(a + b + c)), 47818
(2 a b c)/(a + b + c), -(a^2 + b^2 + c^2)/(a + b + c))), 47819
(2 a b c)/(a + b + c), (a^2 + b^2 + c^2)/(a + b + c)), 47820
(0, (-2 (b c + c a + a b ))/(a + b + c)), 47821
(0, -(b c + c a + a b )/(a + b + c))), 47822
(0, (b c + c a + a b )/(a + b + c)), 47823
(0, (2 (b c + c a + a b ))/(a + b + c)), 47824
(-2 (b c + c a + a b ), 2 (b c + c a + a b )/(a + b + c)), 47825
(- b c - c a - a b, -2 (b c + c a + a b )/(a + b + c), 47826
(- b c - c a - a b, (b c + c a + a b )/(a + b + c)), 47827
(- b c - c a - a b, 2 (b c + c a + a b )/(a + b + c)), 47828
((- b c - c a - a b )/2, (b c + c a + a b )/(2 (a + b + c))), 47829
((- b c - c a - a b )/2, (b c + c a + a b )/(a + b + c)), 47830
((b c + c a + a b )/2, -(b c + c a + a b )/(a + b + c)), 47831
(b c + c a + a b , -2 (b c + c a + a b )/(a + b + c)), 47832
(b c + c a + a b , -(b c + c a + a b )/(a + b + c))), 47833
(2 (b c + c a + a b ), -2 (b c + c a + a b )/(a + b + c)), 47834
(-2 a b c)/(a + b + c), (b c + c a + a b )/(a + b + c)), 47835
(-2 a b c)/(a + b + c), 2 (b c + c a + a b )/(a + b + c)), 47836
(-a b c /(a + b + c)), (b c + c a + a b )/(a + b + c)), 47837
a b c /(a + b + c), -2 (b c + c a + a b )/(a + b + c)), 47838
a b c /(a + b + c), -(b c + c a + a b )/(a + b + c))), 47839
((2 a b c)/(a + b + c), -2 (b c + c a + a b )/(a + b + c)), 47840
((2 a b c)/(a + b + c), -(b c + c a + a b )/(a + b + c))), 47841
(- b c - c a - a b, -(a^3 + b^3 + c^3)/(a + b + c)^2)), 47842
((b c + c a + a b )/2, -(a^3 + b^3 + c^3)/(a + b + c)^2)), 47843
(2 (b c + c a + a b ), 2 (a^3 + b^3 + c^3)/(a + b + c)^2), 47844
(2 a b c/(a + b + c), 2 (a^3 + b^3 + c^3)/(a + b + c)^2), 47845

X(47754) = X(75)X(693)∩X(241)X(514)

X(47754) = X[693] - 3 X[6548], 5 X[693] + X[17161], 15 X[6548] + X[17161], X[650] + 2 X[3776], X[650] - 4 X[21212], X[3004] + 2 X[3676], 2 X[3004] + X[43067], 4 X[3676] - X[43067], X[3776] + 2 X[21212], 2 X[4025] + X[4106], X[2526] + 2 X[4458], 2 X[4885] - 3 X[14475], 2 X[4885] + X[16892], 3 X[14475] + X[16892]

X(47754) lies on these lines: {75, 693}, {241, 514}, {513, 4453}, {522, 4927}, {900, 4025}, {2526, 4458}, {4750, 6008}, {4762, 6545}, {4885, 14475}, {4897, 6006}, {4928, 4944}, {6009, 17069}

X(47754) = midpoint of X(4453) and X(44435)
X(47754) = reflection of X(4944) in X(4928)
X(47754) = crossdifference of every pair of points on line {55, 2251}
X(47754) = barycentric product X(i)*X(j) for these {i,j}: {514, 17274}, {693, 17595}, {5289, 24002}
X(47754) = barycentric quotient X(i)/X(j) for these {i,j}: {5289, 644}, {17274, 190}, {17595, 100}, {27739, 4767}
X(47754) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 3676, 43067}, {3776, 21212, 650}

X(47755) = X(7)X(3676)∩X(239)X(514)

X(47755) = 4 X[3676] - 3 X[6548], 4 X[3676] - X[20295], 3 X[6548] - X[20295], 4 X[3798] - X[17494], 2 X[4025] + X[7192], 4 X[4025] - X[45746], 2 X[4932] + X[16892], 2 X[7192] + X[45746], X[693] + 2 X[4897], 2 X[3776] + X[4979], 2 X[3835] - 3 X[14475], X[4380] + 2 X[21104], X[4467] + 2 X[43067], 2 X[4468] - 5 X[27013], 2 X[4468] - 3 X[31992], 5 X[27013] - 3 X[31992]

X(47755) lies on these lines: {7, 3676}, {239, 514}, {513, 4453}, {664, 901}, {675, 840}, {693, 900}, {1638, 4776}, {2786, 4379}, {3776, 4979}, {3835, 14475}, {4380, 6009}, {4467, 4777}, {4468, 5744}, {4785, 6545}, {4828, 18155}

X(47755) = reflection of X(i) in X(j) for these {i,j}: {4776, 1638}, {27486, 4750}, {44435, 4453}
X(47755) = X(46962)-anticomplementary conjugate of X(69)
X(47755) = barycentric product X(i)*X(j) for these {i,j}: {514, 17378}, {3261, 4257}
X(47755) = barycentric quotient X(i)/X(j) for these {i,j}: {4257, 101}, {17378, 190}, {27754, 4767}
X(47755) = {X(4025),X(7192)}-harmonic conjugate of X(45746)

X(47756) = X(513)X(1638)∩X(514)X(1639)

X(47756) = 2 X[661] + X[21104], 2 X[693] + X[4841], 2 X[3004] + X[3700], X[3004] + 2 X[3835], X[3700] - 4 X[3835], 4 X[2487] - X[4979], X[4025] + 2 X[4940], 2 X[4106] + X[4976], 3 X[14475] - X[31148], X[4790] - 4 X[7658], X[7178] + 2 X[14349], 2 X[14321] + X[16892]

X(47756) lies on these lines: {513, 1638}, {514, 1639}, {523, 4728}, {661, 6545}, {693, 4841}, {824, 3004}, {918, 4776}, {2487, 4979}, {4025, 4940}, {4106, 4976}, {4379, 4977}, {4448, 14475}, {4773, 6008}, {4790, 7658}, {4893, 6084}, {5333, 7192}, {7178, 14349}, {14321, 16892}

X(47756) = midpoint of X(i) and X(j) for these {i,j}: {661, 6545}, {4776, 44435}
X(47756) = reflection of X(i) in X(j) for these {i,j}: {4379, 45677}, {21104, 6545}
X(47756) = {X(3004),X(3835)}-harmonic conjugate of X(3700)

X(47757) = X(2)X(514)∩X(354)X(9029)

X(47757) = X[4379] - 3 X[14475], 2 X[44432] + X[44435], X[31131] - 3 X[44429], X[649] - 4 X[7658], X[661] + 2 X[3676], 2 X[676] + X[2526], 2 X[2473] + X[2520], 4 X[2487] - X[4790], 2 X[3835] + X[4025], X[3835] + 2 X[21212], X[4025] - 4 X[21212], X[3004] + 2 X[4885], 2 X[3004] + X[6590], 4 X[4885] - X[6590], 2 X[3239] + X[16892], 2 X[3239] - 5 X[30835], X[16892] + 5 X[30835], X[31147] + 2 X[44551], 2 X[3776] + X[4468], X[3776] + 2 X[25666], X[4468] - 4 X[25666], X[4106] + 2 X[17069], X[4382] + 2 X[4765], X[4897] + 2 X[4940]

X(47757) lies on these lines: {2, 514}, {354, 9029}, {513, 1638}, {522, 4728}, {523, 7625}, {612, 4449}, {614, 663}, {649, 7658}, {650, 6084}, {661, 3676}, {676, 2526}, {824, 4928}, {1086, 3259}, {2473, 2520}, {2487, 4790}, {2786, 3835}, {3004, 4885}, {3239, 16892}, {3667, 4750}, {3776, 4468}, {4040, 5272}, {4106, 17069}, {4151, 5996}, {4382, 4765}, {4453, 4776}, {4762, 4927}, {4785, 4786}, {4794, 7292}, {4897, 4940}

X(47757) = midpoint of X(i) and X(j) for these {i,j}: {2, 44435}, {4453, 4776}, {4750, 31147}, {4893, 6545}
X(47757) = reflection of X(i) in X(j) for these {i,j}: {2, 44432}, {4750, 44551}, {4786, 45674}, {21183, 21204}, {45320, 45677}
X(47757) = X(4363)-Dao conjugate of X(4482)
X(47757) = crossdifference of every pair of points on line {902, 1384}
X(47757) = barycentric product X(514)*X(4419)
X(47757) = barycentric quotient X(4419)/X(190)
X(47757) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 4885, 6590}, {3776, 25666, 4468}, {3835, 21212, 4025}, {16892, 30835, 3239}

X(47758) = X(57)X(649)∩X(513)X(1638)

X(47758) = X[649] + 2 X[3676], X[31148] + 2 X[44551], X[650] - 4 X[2487], X[661] - 4 X[7658], 2 X[676] + X[7659], X[693] + 2 X[3798], X[4025] + 2 X[4369], 2 X[4025] + X[6590], 4 X[4369] - X[6590], X[4468] - 4 X[31286], 2 X[4885] + X[4897], 3 X[14475] - X[31147]

X(47758) lies on these lines: {57, 649}, {513, 1638}, {514, 1635}, {522, 4379}, {650, 2487}, {661, 7658}, {676, 7659}, {693, 3798}, {812, 4786}, {824, 4025}, {1086, 6075}, {1790, 18200}, {3310, 3669}, {3667, 4728}, {3835, 5249}, {4367, 9511}, {4468, 10196}, {4885, 4897}, {4927, 6008}, {6006, 6173}, {8643, 8713}, {15599, 15931}

X(47758) = midpoint of X(i) and X(j) for these {i,j}: {649, 6545}, {4379, 4750}, {4786, 21183}
X(47758) = reflection of X(i) in X(j) for these {i,j}: {4468, 10196}, {6545, 3676}, {10196, 31286}
X(47758) = crossdifference of every pair of points on line {2177, 2340}
X(47758) = barycentric product X(i)*X(j) for these {i,j}: {514, 4644}, {3676, 5218}
X(47758) = barycentric quotient X(i)/X(j) for these {i,j}: {4644, 190}, {5218, 3699}
X(47758) = {X(4025),X(4369)}-harmonic conjugate of X(6590)

X(47759) = X(2)X(513)∩X(514)X(4120)

X(47759) = 4 X[661] - X[17494], 2 X[661] + X[20295], X[17494] + 2 X[20295], X[693] - 4 X[4940], 2 X[693] - 5 X[26798], 2 X[693] + X[31290], 8 X[4940] - 5 X[26798], 8 X[4940] + X[31290], 5 X[26798] + X[31290], 2 X[3835] + X[4813], 4 X[3835] - X[7192], 8 X[3835] - 5 X[26985], 4 X[4379] - 5 X[26985], 2 X[4813] + X[7192], 4 X[4813] + 5 X[26985], 2 X[7192] - 5 X[26985], 4 X[4500] - X[4608], 4 X[14349] - X[17496]

X(47759) lies on these lines: {2, 513}, {514, 4120}, {661, 812}, {693, 4940}, {3835, 4379}, {3995, 4079}, {4393, 4775}, {4500, 4608}, {4502, 17147}, {4785, 4893}, {4789, 4977}, {4800, 4806}, {9400, 14404}, {14349, 17496}

X(47759) = midpoint of X(4379) and X(4813)
X(47759) = reflection of X(i) in X(j) for these {i,j}: {2, 4776}, {4379, 3835}, {4800, 4806}, {7192, 4379}, {21297, 31147}
X(47759) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {4492, 150}, {8695, 42697}
X(47759) = crossdifference of every pair of points on line {3230, 20985}
X(47759) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 20295, 17494}, {693, 4940, 26798}, {3835, 4813, 7192}, {3835, 7192, 26985}, {26798, 31290, 693}

X(47760) = X(2)X(513)∩X(514)X(1639)

X(47760) = 2 X[45315] + X[45320], X[45315] + 2 X[45339], X[45320] - 4 X[45339], X[649] + 2 X[4940], X[649] - 4 X[31287], X[4940] + 2 X[31287], X[650] + 2 X[3835], 2 X[650] + X[4106], X[650] - 4 X[25666], 4 X[3835] - X[4106], X[3835] + 2 X[25666], X[4106] + 8 X[25666], X[661] + 2 X[4885], X[661] + 5 X[30835], 2 X[661] + X[43067], X[4379] - 5 X[30835], 2 X[4885] - 5 X[30835], 4 X[4885] - X[43067], 10 X[30835] - X[43067], X[905] + 2 X[4129], X[31147] + 2 X[44567], 4 X[2516] - X[4380], 4 X[2516] + 5 X[26798], 4 X[2516] - 7 X[27115], X[4380] + 5 X[26798], X[4380] - 7 X[27115], 5 X[26798] + 7 X[27115], X[2526] + 2 X[3716], X[3004] + 2 X[3239], X[4025] + 2 X[14321], X[4897] - 4 X[7658]

X(47760) lies on these lines: {2, 513}, {469, 16228}, {514, 1639}, {649, 4940}, {650, 812}, {661, 4379}, {788, 14426}, {824, 4944}, {905, 4129}, {1491, 4800}, {1635, 6008}, {2516, 4380}, {2526, 3716}, {3004, 3239}, {3063, 4383}, {3250, 14433}, {4025, 14321}, {4378, 16831}, {4384, 4775}, {4728, 4762}, {4763, 4785}, {4789, 4802}, {4897, 7658}, {9260, 17310}

X(47760) = midpoint of X(i) and X(j) for these {i,j}: {2, 4776}, {661, 4379}, {1491, 4800}, {1635, 31147}, {3250, 14433}, {4728, 4893}, {4928, 45315}
X(47760) = reflection of X(i) in X(j) for these {i,j}: {1635, 44567}, {4379, 4885}, {4928, 45339}, {4944, 45661}, {43067, 4379}, {45320, 4928}
X(47760) = X(i)-complementary conjugate of X(j) for these (i,j): {4492, 116}, {8695, 34824}
X(47760) = crossdifference of every pair of points on line {3230, 21010}
X(47760) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 3835, 4106}, {661, 4885, 43067}, {661, 30835, 4885}, {3835, 25666, 650}, {4380, 27115, 2516}, {4940, 31287, 649}, {26798, 27115, 4380}, {45315, 45339, 45320}

X(47761) = X(2)X(513)∩X(241)X(514)

X(47761) = X[650] + 2 X[4369], X[650] - 4 X[31286], 2 X[650] + X[43067], X[3004] - 4 X[7658], X[3676] + 2 X[43061], X[4369] + 2 X[31286], 4 X[4369] - X[43067], 4 X[4763] + X[43067], 2 X[11068] + X[21104], 8 X[31286] + X[43067], 2 X[649] + X[4106], X[649] + 2 X[4885], X[649] + 5 X[24924], X[4106] - 4 X[4885], X[4106] - 10 X[24924], X[4728] - 5 X[24924], 2 X[4885] - 5 X[24924], X[693] + 2 X[4394], X[693] + 5 X[27013], 2 X[4394] - 5 X[27013], 4 X[2487] - X[4025], 4 X[2490] - X[4468], 4 X[2516] - X[17494], 2 X[3239] + X[4897], X[3700] + 2 X[3798], 2 X[3716] + X[7659], 2 X[3835] + X[4790], 2 X[3835] - 5 X[31250], X[4790] + 5 X[31250], X[4790] + 4 X[45678], 5 X[31250] - 4 X[45678], X[7662] + 2 X[9508], 2 X[4940] + X[4979], 2 X[4940] - 5 X[30835], X[4979] + 5 X[30835], X[6590] + 2 X[17069], X[7192] - 4 X[7653], X[7192] + 5 X[31209], 4 X[7653] + 5 X[31209]

X(47761) lies on these lines: {2, 513}, {27, 16228}, {239, 9260}, {241, 514}, {333, 17212}, {649, 4106}, {693, 4394}, {900, 4786}, {940, 3063}, {1635, 4379}, {2487, 4025}, {2490, 4468}, {2516, 17494}, {2786, 4944}, {3239, 4897}, {3700, 3798}, {3716, 6006}, {3835, 4790}, {4378, 4384}, {4775, 16831}, {4777, 4789}, {4785, 4928}, {4940, 4979}, {6590, 17069}, {7192, 7653}

X(47761) = midpoint of X(i) and X(j) for these {i,j}: {649, 4728}, {1635, 4379}, {4369, 4763}, {4378, 30583}, {4789, 27486}
X(47761) = reflection of X(i) in X(j) for these {i,j}: {650, 4763}, {3835, 45678}, {4106, 4728}, {4728, 4885}, {4763, 31286}
X(47761) = complement of X(4776)
X(47761) = complement of the isotomic conjugate of X(37209)
X(47761) = X(i)-complementary conjugate of X(j) for these (i,j): {29351, 141}, {36871, 21252}, {37209, 2887}
X(47761) = crosspoint of X(2) and X(37209)
X(47761) = crosssum of X(650) and X(16975)
X(47761) = crossdifference of every pair of points on line {55, 3230}
X(47761) = barycentric product X(693)*X(37540)
X(47761) = barycentric quotient X(37540)/X(100)
X(47761) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4885, 4106}, {649, 24924, 4885}, {650, 4369, 43067}, {693, 27013, 4394}, {4369, 31286, 650}, {4790, 31250, 3835}, {4979, 30835, 4940}

X(47762) = X(2)X(513)∩X(514)X(1635)

X(47762) = 2 X[31148] + X[31150], X[31148] + 2 X[45313], X[31150] - 4 X[45313], 2 X[4786] + X[4789], 2 X[649] + X[693], X[649] + 2 X[4369], 4 X[649] - X[4380], 5 X[649] + X[4382], X[693] - 4 X[4369], 2 X[693] + X[4380], 5 X[693] - 2 X[4382], 8 X[4369] + X[4380], 10 X[4369] - X[4382], 4 X[4379] + X[4380], 5 X[4379] - X[4382], 5 X[4380] + 4 X[4382], 2 X[650] + X[7192], 2 X[650] - 5 X[27013], X[7192] + 5 X[27013], X[661] + 2 X[4932], 2 X[661] - 5 X[31209], X[661] - 4 X[31286], 4 X[4932] + 5 X[31209], X[4932] + 2 X[31286], 5 X[31209] - 8 X[31286], 2 X[1019] + X[4391], 2 X[2483] + X[15413], 4 X[2487] - X[3004], 4 X[3798] - X[4467], 2 X[3798] + X[6590], X[4467] + 2 X[6590], 2 X[3835] + X[4979], 2 X[3835] - 5 X[24924], X[4979] + 5 X[24924], 2 X[4063] + X[4801], X[4394] + 2 X[7653], 4 X[4394] - X[17494], 2 X[4394] + X[43067], 8 X[7653] + X[17494], 4 X[7653] - X[43067], X[17494] + 2 X[43067], X[4784] + 2 X[4874], X[4790] + 2 X[4885], 2 X[4790] + X[20295], 4 X[4885] - X[20295]

X(47762) lies on these lines: {2, 513}, {81, 3063}, {239, 4378}, {514, 1635}, {522, 4786}, {649, 693}, {650, 7192}, {661, 4932}, {668, 4607}, {764, 17367}, {824, 4750}, {1019, 4391}, {2483, 15413}, {2487, 3004}, {3798, 4467}, {3835, 4979}, {4063, 4801}, {4394, 7653}, {4728, 4785}, {4761, 4844}, {4763, 4893}, {4775, 16826}, {4784, 4800}, {4790, 4885}, {6161, 17244}, {6994, 16228}, {10566, 18087}

X(47762) = midpoint of X(i) and X(j) for these {i,j}: {649, 4379}, {1635, 31148}, {4784, 4800}
X(47762) = reflection of X(i) in X(j) for these {i,j}: {693, 4379}, {1635, 45313}, {4379, 4369}, {4776, 2}, {4800, 4874}, {4893, 4763}, {31150, 1635}
X(47762) = X(3758)-Ceva conjugate of X(7208)
X(47762) = X(i)-cross conjugate of X(j) for these (i,j): {4761, 4406}, {7208, 3758}
X(47762) = X(i)-isoconjugate of X(j) for these (i,j): {45, 8695}, {101, 4492}, {30635, 32739}
X(47762) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 4492), (40619, 30635)
X(47762) = crossdifference of every pair of points on line {869, 2177}
X(47762) = barycentric product X(i)*X(j) for these {i,j}: {1, 4406}, {86, 4761}, {190, 7208}, {514, 3758}, {609, 3261}, {693, 17126}, {812, 43262}, {3997, 7199}, {4844, 39704}, {7192, 46897}
X(47762) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 4492}, {609, 101}, {693, 30635}, {2163, 8695}, {3758, 190}, {3809, 3799}, {3997, 1018}, {4406, 75}, {4761, 10}, {4844, 3679}, {7208, 514}, {17126, 100}, {43262, 4562}, {46897, 3952}
X(47762) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 693, 4380}, {649, 4369, 693}, {661, 31286, 31209}, {3798, 6590, 4467}, {4394, 7653, 43067}, {4394, 43067, 17494}, {4790, 4885, 20295}, {4932, 31286, 661}, {4979, 24924, 3835}, {7192, 27013, 650}, {31148, 45313, 31150}

X(47763) = X(2)X(513)∩X(239)X(514)

X(47763) = X[649] + 2 X[4932], 2 X[649] + X[7192], 4 X[649] - X[17494], 4 X[1019] - X[17496], 4 X[3798] - X[45746], 4 X[4786] - X[46915], 4 X[4932] - X[7192], 8 X[4932] + X[17494], 2 X[7192] + X[17494], 2 X[661] - 5 X[27013], 4 X[661] - 7 X[27115], 4 X[4763] - 5 X[27013], 8 X[4763] - 7 X[27115], 10 X[27013] - 7 X[27115], X[693] + 2 X[4790], 2 X[693] + X[26853], 4 X[4790] - X[26853], X[4106] - 4 X[7653], 2 X[4369] + X[4979], 4 X[4369] - X[20295], 8 X[4369] - 5 X[26985], 4 X[4728] - 5 X[26985], 2 X[4979] + X[20295], 4 X[4979] + 5 X[26985], 2 X[20295] - 5 X[26985], 2 X[4834] + X[17166]

X(47763) lies on these lines: {2, 513}, {239, 514}, {661, 4763}, {693, 4790}, {890, 4367}, {900, 4784}, {4106, 7653}, {4369, 4728}, {4375, 14475}, {4378, 4393}, {4379, 4785}, {4781, 6633}, {4817, 6548}, {4834, 17166}, {8025, 17212}, {10566, 18089}, {17147, 17159}

X(47763) = midpoint of X(4728) and X(4979)
X(47763) = reflection of X(i) in X(j) for these {i,j}: {661, 4763}, {4728, 4369}, {20295, 4728}, {21297, 4379}, {27486, 4786}, {46915, 27486}
X(47763) = anticomplement of X(4776)
X(47763) = anticomplement of the isotomic conjugate of X(37209)
X(47763) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {29351, 69}, {36871, 21293}, {37209, 6327}
X(47763) = X(37209)-Ceva conjugate of X(2)
X(47763) = crosssum of X(649) and X(16971)
X(47763) = crossdifference of every pair of points on line {42, 3230}
X(47763) = barycentric product X(i)*X(j) for these {i,j}: {514, 46922}, {7192, 29822}
X(47763) = barycentric quotient X(i)/X(j) for these {i,j}: {29822, 3952}, {46922, 190}
X(47763) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4932, 7192}, {649, 7192, 17494}, {661, 27013, 27115}, {693, 4790, 26853}, {4369, 4979, 20295}, {4369, 20295, 26985}

X(47764) = X(513)X(1639)∩X(514)X(4120)

X(47764) = 3 X[661] + X[4958], 4 X[661] - X[45745], 4 X[4958] + 3 X[45745], 2 X[3239] + X[4813], 3 X[4893] - X[4984], X[4453] - 3 X[4776], 4 X[4521] - X[4979], X[6590] - 4 X[14321], 2 X[4949] + X[4976]

X(47764) lies on these lines: {513, 1639}, {514, 4120}, {522, 661}, {1635, 6006}, {3239, 4813}, {3667, 4893}, {3700, 4802}, {4453, 4776}, {4521, 4979}, {4944, 4977}, {4949, 4976}

X(47764) = reflection of X(i) in X(j) for these {i,j}: {4944, 14321}, {6590, 4944}
X(47764) = crossdifference of every pair of points on line {1468, 7373}

X(47765) = X(513)X(1639)∩X(514)X(661)

X(47765) = X[649] - 4 X[4521], X[649] - 3 X[6544], 4 X[4521] - 3 X[6544], X[661] + 2 X[3239], 2 X[661] + X[6590], X[661] + 8 X[14350], 4 X[3239] - X[6590], X[3239] - 4 X[14350], 2 X[3835] + X[4468], X[6590] - 16 X[14350], X[650] + 2 X[14321], 4 X[2490] - X[4790], 2 X[2516] + X[4949], 2 X[3676] - 3 X[14475], 2 X[3676] - 5 X[30835], 3 X[14475] - 5 X[30835], 2 X[3700] + X[45745]

X(478) lies on these lines: {9, 649}, {513, 1639}, {514, 661}, {522, 4120}, {523, 4944}, {650, 900}, {1146, 3259}, {1635, 3667}, {1826, 3064}, {2490, 4790}, {2516, 4949}, {3676, 5219}, {3700, 4777}, {4106, 6009}, {4763, 4786}, {4785, 10196}, {4958, 4962}

X(47765) = midpoint of X(i) and X(j) for these {i,j}: {4120, 4893}, {4776, 30565}
X(47765) = reflection of X(4786) in X(4763)
X(47765) = X(6)-isoconjugate of X(46962)
X(47765) = X(9)-Dao conjugate of X(46962)
X(47765) = crossdifference of every pair of points on line {31, 999}
X(47765) = barycentric quotient X(1)/X(46962)
X(47765) = {X(661),X(3239)}-harmonic conjugate of X(6590)

X(47766) = X(2)X(514)∩X(230)X(231)

3 X[4379] - X[21116], X[4893] - 3 X[6544], 3 X[6546] + X[21116], X[650] - 4 X[2490], 2 X[650] + X[6590], 4 X[650] - X[45745], 8 X[2490] + X[6590], 16 X[2490] - X[45745], 2 X[2977] + X[7662], 4 X[4874] - X[47123], 4 X[6133] - X[47136], 2 X[6586] + X[47129], X[6590] + 4 X[14425], 2 X[6590] + X[45745], 8 X[14425] - X[45745], 2 X[21348] + X[47130], 3 X[1635] + X[4931], X[649] + 2 X[3239], X[649] - 4 X[43061], X[3239] + 2 X[43061], X[4120] + 4 X[43061], X[661] - 4 X[4521], X[693] + 2 X[11068], 4 X[2516] - X[4976], 4 X[2527] - X[4790], 2 X[2527] + X[14321], X[4790] + 2 X[14321], X[3700] + 2 X[4394], X[4024] + 2 X[4765], X[4024] + 8 X[31182], X[4765] - 4 X[31182], 2 X[4369] + X[4468], 4 X[7658] - X[16892], 4 X[7658] - 7 X[31207], X[16892] - 7 X[31207]

X(47766) lies on these lines: {2, 514}, {111, 2758}, {210, 9029}, {230, 231}, {513, 1639}, {522, 1635}, {612, 663}, {614, 4449}, {649, 3239}, {661, 4521}, {693, 11068}, {824, 4763}, {900, 4944}, {1146, 6075}, {2516, 4976}, {2527, 4790}, {2786, 4786}, {3700, 4394}, {4024, 4765}, {4040, 5268}, {4108, 4151}, {4369, 4468}, {4477, 8642}, {4546, 7172}, {4794, 5297}, {4885, 4927}, {4962, 4984}, {7658, 16892}

X(47766) = midpoint of X(i) and X(j) for these {i,j}: {649, 4120}, {3700, 4773}, {4379, 6546}
X(47766) = reflection of X(i) in X(j) for these {i,j}: {650, 14425}, {4120, 3239}, {4773, 4394}, {4786, 45313}, {4927, 4885}, {14425, 2490}, {44435, 44432}
X(47766) = complement of X(44435)
X(47766) = anticomplement of X(44432)
X(47766) = complement of the isotomic conjugate of X(9059)
X(47766) = polar conjugate of the isotomic conjugate of X(9031)
X(47766) = X(i)-complementary conjugate of X(j) for these (i,j): {996, 21252}, {9059, 2887}, {32686, 3834}, {36091, 21241}, {40401, 116}
X(47766) = X(i)-isoconjugate of X(j) for these (i,j): {63, 9088}, {651, 3478}
X(47766) = X(i)-Dao conjugate of X(j) for these (i, j): (3162, 9088), (38991, 3478)
X(47766) = crosspoint of X(i) and X(j) for these (i,j): {2, 9059}, {190, 1000}
X(47766) = crosssum of X(i) and X(j) for these (i,j): {6, 9002}, {649, 999}
X(47766) = crossdifference of every pair of points on line {3, 902}
X(47766) = barycentric product X(i)*X(j) for these {i,j}: {4, 9031}, {513, 4737}, {522, 3476}, {523, 4234}
X(47766) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 9088}, {663, 3478}, {3476, 664}, {4234, 99}, {4737, 668}, {9031, 69}
X(47766) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 44435, 44432}, {650, 6590, 45745}, {650, 21348, 3310}, {2527, 14321, 4790}, {3239, 43061, 649}, {3310, 47130, 45745}, {16892, 31207, 7658}

X(47767) = X(241)X(514)∩X(513)X(1639)

X(47767) = 4 X[650] - X[4841], 5 X[650] - 8 X[31182], X[650] - 4 X[43061], X[3004] - 4 X[31286], 4 X[4369] - X[21104], 5 X[4841] - 32 X[31182], X[4841] - 16 X[43061], 2 X[11068] + X[43067], 2 X[31182] - 5 X[43061], X[649] - 4 X[2527], 2 X[649] + X[3700], 8 X[2527] + X[3700], X[661] - 4 X[2490], X[661] - 3 X[6544], 4 X[2490] - 3 X[6544], 4 X[2487] - X[16892], 2 X[3239] + X[4790], X[4024] + 3 X[14435], 4 X[4394] - X[4976], 2 X[4394] + X[6590], X[4976] + 2 X[6590], X[4979] + 2 X[14321], X[7192] + 3 X[31992]

X(47767) lies on these lines: {241, 514}, {513, 1639}, {522, 4773}, {523, 1635}, {649, 900}, {661, 1213}, {693, 6009}, {2303, 7252}, {2487, 16892}, {3239, 4790}, {3667, 4944}, {3807, 9362}, {4024, 14435}, {4379, 6084}, {4394, 4777}, {4893, 4977}, {4931, 4984}, {4979, 14321}, {5235, 7192}

X(47767) = midpoint of X(4931) and X(4984)
X(47767) = reflection of X(4893) in X(14425)
X(47767) = crossdifference of every pair of points on line {55, 995}
X(47767) = barycentric product X(522)*X(4315)
X(47767) = barycentric quotient X(4315)/X(664)
X(47767) = {X(4394),X(6590)}-harmonic conjugate of X(4976)

X(47768) = X(513)X(1639)∩X(514)X(1635)

X(47768) = 5 X[649] + X[4024], 3 X[649] - X[4984], 2 X[649] + X[6590], 3 X[4024] + 5 X[4984], 2 X[4024] - 5 X[6590], 2 X[4984] + 3 X[6590], X[650] - 4 X[2527], 4 X[2516] - X[4841], 2 X[2529] + X[4394], 8 X[2529] + X[45745], 4 X[4394] - X[45745], 2 X[3239] + X[4979], X[4468] + 2 X[4932], 4 X[4521] - X[4813], X[4838] + 8 X[14351], X[7192] + 2 X[11068]

X(47768) lies on these lines: {513, 1639}, {514, 1635}, {522, 649}, {650, 2523}, {824, 4786}, {2516, 4841}, {2529, 4394}, {3239, 4979}, {3667, 4958}, {4120, 6006}, {4468, 4932}, {4521, 4813}, {4773, 4777}, {4778, 4893}, {4790, 4944}, {4838, 14351}, {4931, 4962}, {7192, 11068}

X(47768) = midpoint of X(4790) and X(4944)
X(47768) = crossdifference of every pair of points on line {1193, 2177}

X(47769) = X(190)X(14513)∩X(514)X(4120)

X(47769) = 2 X[4468] + X[20295], 2 X[661] + X[25259], 4 X[661] - X[45746], 2 X[25259] + X[45746], X[693] - 4 X[14321], 4 X[3239] - X[7192], 4 X[3676] - 7 X[27138], 8 X[4521] - 5 X[27013], 3 X[31992] - 4 X[45670]

X(47769) lies on these lines: {190, 14513}, {329, 4468}, {514, 4120}, {649, 3219}, {661, 824}, {666, 15343}, {693, 14321}, {900, 14410}, {918, 4776}, {2786, 4893}, {3239, 7192}, {3676, 5226}, {3835, 6545}, {4521, 5273}, {4785, 6546}, {4789, 4944}, {4951, 18004}, {6006, 6172}

X(47769) = reflection of X(i) in X(j) for these {i,j}: {649, 10196}, {4789, 4944}, {4951, 18004}, {6545, 3835}, {27486, 4893}, {44435, 4776}
X(47769) = {X(661),X(25259)}-harmonic conjugate of X(45746)

X(47770) = X(514)X(1639)∩X(650)X(824)

X(47770) = 5 X[650] - 2 X[21196], 5 X[10196] - X[21196], 4 X[2490] - X[4025], 4 X[2516] - X[4467], X[3004] - 4 X[4521], 4 X[3239] - X[4106], X[3700] + 2 X[11068], X[31150] - 3 X[31992]

X(47770) lies on these lines: {514, 1639}, {650, 824}, {659, 4951}, {693, 18743}, {812, 4944}, {2490, 4025}, {2516, 4467}, {3004, 4521}, {3239, 4106}, {3700, 11068}, {4120, 6008}, {4448, 4664}, {4762, 6546}, {4885, 6545}, {5919, 14077}

X(47770) = midpoint of X(659) and X(4951)
X(47770) = reflection of X(i) in X(j) for these {i,j}: {650, 10196}, {6545, 4885}

X(47771) = X(2)X(514)∩X(190)X(901)

X(47771) = 5 X[2] - 4 X[44432], 8 X[44432] - 5 X[44435], 2 X[649] + X[25259], 4 X[650] - X[45746], 4 X[2490] - X[3004], 8 X[2490] - 5 X[31209], 2 X[3004] - 5 X[31209], 4 X[2527] - X[4897], 2 X[3700] + X[4380], X[4122] + 2 X[4782], 4 X[4394] - X[4467], 2 X[4468] + X[7192], X[4498] + 2 X[8045], 4 X[4765] - X[17161], X[6590] + 2 X[11068], 2 X[6590] + X[17494], 4 X[11068] - X[17494]

X(47771) lies on these lines: {2, 514}, {190, 901}, {351, 523}, {612, 4040}, {649, 2786}, {650, 16757}, {663, 3920}, {693, 6084}, {824, 1635}, {900, 4951}, {1639, 4776}, {2490, 3004}, {2527, 4897}, {3263, 4406}, {3681, 9029}, {3700, 4380}, {4120, 4785}, {4122, 4782}, {4394, 4467}, {4449, 7191}, {4468, 7192}, {4498, 8045}, {4724, 5297}, {4762, 4789}, {4765, 17161}, {4944, 6008}, {6590, 11068}

X(47771) = reflection of X(i) in X(j) for these {i,j}: {4776, 1639}, {4893, 10196}, {27486, 1635}, {44435, 2}
X(47771) = crosssum of X(649) and X(2242)
X(47771) = crossdifference of every pair of points on line {574, 902}
X(47771) = barycentric product X(514)*X(17354)
X(47771) = barycentric quotient X(17354)/X(190)
X(47771) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2490, 3004, 31209}, {6590, 11068, 17494}

X(47772) = X(2)X(918)∩X(514)X(4120)

X(47772) = 5 X[2] - 4 X[1638], 3 X[2] - 4 X[1639], 9 X[2] - 8 X[44902], 7 X[2] - 8 X[45326], 3 X[1638] - 5 X[1639], 6 X[1638] - 5 X[4453], 2 X[1638] - 5 X[30565], 9 X[1638] - 10 X[44902], 7 X[1638] - 10 X[45326], 2 X[1639] - 3 X[30565], 3 X[1639] - 2 X[44902], 7 X[1639] - 6 X[45326], X[4453] - 3 X[30565], 3 X[4453] - 4 X[44902], 7 X[4453] - 12 X[45326], 9 X[30565] - 4 X[44902], 7 X[30565] - 4 X[45326], 7 X[44902] - 9 X[45326], 4 X[4468] - X[17494], 2 X[4468] + X[25259], X[17494] + 2 X[25259], X[4984] - 3 X[6546], 4 X[4928] - 3 X[6548], 3 X[6548] - 2 X[21115], 4 X[18004] - X[46403]

X(47772) lies on these lines: {2, 918}, {149, 6366}, {514, 4120}, {522, 3935}, {693, 4944}, {812, 4958}, {900, 17487}, {926, 4661}, {1026, 3952}, {2786, 4984}, {3732, 15343}, {3762, 4080}, {4010, 4802}, {4750, 10196}, {4928, 6548}, {4977, 18004}

X(47772) = reflection of X(i) in X(j) for these {i,j}: {2, 30565}, {693, 4944}, {4453, 1639}, {4750, 10196}, {21115, 4928}, {21297, 4120}
X(47772) = anticomplement of X(4453)
X(47772) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {80, 21293}, {655, 21285}, {692, 6224}, {1415, 41803}, {2161, 150}, {2222, 3434}, {6187, 149}, {14560, 3874}, {32671, 4360}, {32675, 7}, {34857, 3448}, {35174, 21280}, {36069, 17140}, {36804, 315}, {37140, 17143}, {47318, 17137}
X(47772) = crosspoint of X(i) and X(j) for these (i,j): {190, 20568}, {31618, 35174}
X(47772) = crosssum of X(i) and X(j) for these (i,j): {649, 2251}, {8648, 20229}
X(47772) = crossdifference of every pair of points on line {1475, 21747}
X(47772) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1639, 4453, 2}, {4453, 30565, 1639}, {4468, 25259, 17494}, {4928, 21115, 6548}

X(47773) = X(2)X(514)∩X(23)X(385)

X(47773) = 9 X[2] - 8 X[44432], 2 X[4893] - 3 X[31992], 4 X[44432] - 3 X[44435], 4 X[3004] - 7 X[27115], 8 X[14425] - 7 X[27115], 4 X[4468] - X[31290]

X(47773) lies on these lines: {2, 514}, {23, 385}, {812, 4931}, {3004, 14425}, {3920, 4040}, {4380, 4926}, {4449, 17024}, {4467, 4773}, {4468, 4778}, {4661, 9029}, {4789, 6084}

X(47773) = reflection of X(i) in X(j) for these {i,j}: {3004, 14425}, {4467, 4773}
X(47773) = anticomplement of X(44435)
X(47773) = anticomplement of the isotomic conjugate of X(9059)
X(47773) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {996, 21293}, {9059, 6327}, {32686, 320}, {36091, 21282}, {40401, 150}
X(47773) = X(9059)-Ceva conjugate of X(2)
X(47773) = crossdifference of every pair of points on line {39, 902}

X(47774) = X(2)X(661)∩X(513)X(14404)

X(47774) = 5 X[2] - 4 X[4369], 11 X[2] - 10 X[24924], 7 X[2] - 8 X[25666], 3 X[2] - 4 X[45315], 9 X[2] - 8 X[45663], 5 X[661] - 2 X[4369], 4 X[661] - X[7192], 11 X[661] - 5 X[24924], 7 X[661] - 4 X[25666], 3 X[661] - X[31148], 2 X[661] + X[31290], 3 X[661] - 2 X[45315], 9 X[661] - 4 X[45663], 8 X[4369] - 5 X[7192], 22 X[4369] - 25 X[24924], 7 X[4369] - 10 X[25666], 6 X[4369] - 5 X[31148], 4 X[4369] + 5 X[31290], 3 X[4369] - 5 X[45315], 9 X[4369] - 10 X[45663], 11 X[7192] - 20 X[24924], 7 X[7192] - 16 X[25666], 3 X[7192] - 4 X[31148], X[7192] + 2 X[31290], 3 X[7192] - 8 X[45315], 9 X[7192] - 16 X[45663], 35 X[24924] - 44 X[25666], 15 X[24924] - 11 X[31148], 10 X[24924] + 11 X[31290], 15 X[24924] - 22 X[45315], 45 X[24924] - 44 X[45663], 12 X[25666] - 7 X[31148], 8 X[25666] + 7 X[31290], 6 X[25666] - 7 X[45315], 9 X[25666] - 7 X[45663], 2 X[31148] + 3 X[31290], 3 X[31148] - 4 X[45663], 3 X[31290] + 4 X[45315], 9 X[31290] + 8 X[45663], 3 X[45315] - 2 X[45663], 3 X[4120] - 2 X[45343], 3 X[21297] - 4 X[31147], 4 X[3700] - X[4608], 2 X[4813] + X[17494], 2 X[4806] + X[4963], 2 X[4838] + X[14779], 4 X[4841] - X[17161], 2 X[4841] + X[44449], X[17161] + 2 X[44449]

X(47774) lies on these lines: {2, 661}, {513, 14404}, {514, 4120}, {1992, 9013}, {3241, 4160}, {3700, 4608}, {3952, 4562}, {4785, 4813}, {4806, 4963}, {4838, 14779}, {4841, 17161}

X(47774) = midpoint of X(2) and X(31290)
X(47774) = reflection of X(i) in X(j) for these {i,j}: {2, 661}, {7192, 2}, {31148, 45315}
X(47774) = anticomplement of X(31148)
X(47774) = crossdifference of every pair of points on line {3747, 16971}
X(47774) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 31148, 45315}, {661, 31290, 7192}, {4841, 44449, 17161}, {31148, 45315, 2}

X(47775) = X(2)X(514)∩X(8)X(4844)

X(47775) = X[4379] - 3 X[4893], 4 X[650] - X[7192], 8 X[650] - 5 X[27013], 2 X[7192] - 5 X[27013], 2 X[661] + X[17494], 4 X[661] - X[20295], 2 X[17494] + X[20295], X[4608] - 4 X[6590], 4 X[4705] - X[21302]

X(47775) lies on these lines: {2, 514}, {8, 4844}, {42, 4040}, {513, 14404}, {523, 4800}, {650, 7192}, {661, 812}, {663, 17018}, {666, 14513}, {900, 4948}, {1639, 4789}, {3240, 4724}, {4448, 4824}, {4490, 17135}, {4608, 6590}, {4651, 4705}, {4762, 4776}, {9147, 9279}

X(47775) = midpoint of X(4448) and X(4824)
X(47775) = reflection of X(i) in X(j) for these {i,j}: {2, 4893}, {4789, 1639}, {21116, 21204}, {21297, 4776}
X(47775) = anticomplement of X(4379)
X(47775) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {751, 150}, {30650, 149}
X(47775) = crossdifference of every pair of points on line {902, 16971}
X(47775) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 7192, 27013}, {661, 17494, 20295}

X(47776) = X(100)X(190)∩X(239)X(514)

X(47776) = 3 X[2] - 4 X[4763], 5 X[2] - 4 X[4928], 7 X[2] - 8 X[45675], 9 X[2] - 8 X[45678], 3 X[1635] - X[4728], 3 X[1635] - 2 X[4763], 5 X[1635] - 2 X[4928], 4 X[1635] - X[21297], 7 X[1635] - 4 X[45675], 9 X[1635] - 4 X[45678], 5 X[4728] - 6 X[4928], 4 X[4728] - 3 X[21297], 7 X[4728] - 12 X[45675], 3 X[4728] - 4 X[45678], 5 X[4763] - 3 X[4928], 8 X[4763] - 3 X[21297], 7 X[4763] - 6 X[45675], 3 X[4763] - 2 X[45678], 8 X[4928] - 5 X[21297], 7 X[4928] - 10 X[45675], 9 X[4928] - 10 X[45678], 7 X[21297] - 16 X[45675], 9 X[21297] - 16 X[45678], 9 X[45675] - 7 X[45678], 4 X[1638] - 3 X[6548], 2 X[30565] - 3 X[31992], 5 X[649] - 2 X[4932], 4 X[649] - X[7192], 2 X[649] + X[17494], 2 X[4063] + X[4560], 2 X[4498] + X[17496], X[4750] - 3 X[14435], 4 X[4765] - X[45746], 8 X[4932] - 5 X[7192], 4 X[4932] + 5 X[17494], X[7192] + 2 X[17494], 3 X[14435] - 2 X[45679], X[21222] + 2 X[21385], 2 X[650] + X[4380], 5 X[650] - 2 X[4940], 4 X[650] - X[20295], 5 X[4380] + 4 X[4940], 2 X[4380] + X[20295], 5 X[4776] - 4 X[4940], 8 X[4940] - 5 X[20295], X[693] - 4 X[4394], 2 X[693] - 5 X[27013], 8 X[4394] - 5 X[27013], X[2254] + 2 X[4830], 4 X[2516] - X[4106], 16 X[2516] - 7 X[27138], 8 X[2516] - 5 X[31209], 4 X[4106] - 7 X[27138], 2 X[4106] - 5 X[31209], 7 X[27138] - 10 X[31209], 3 X[6544] - 2 X[45661], 4 X[4976] - X[17161], 4 X[8661] - X[17145]

X(47776) lies on these lines: {2, 812}, {88, 673}, {100, 190}, {239, 514}, {513, 14404}, {650, 4380}, {666, 901}, {675, 2291}, {693, 4394}, {804, 17163}, {885, 6139}, {891, 3227}, {918, 4773}, {2254, 4830}, {2516, 4106}, {2786, 4984}, {2820, 9778}, {3121, 16726}, {4120, 10196}, {4155, 9147}, {4375, 6544}, {4453, 6084}, {4508, 16816}, {4724, 6006}, {4777, 4782}, {4785, 4893}, {4922, 9260}, {4976, 17161}, {6089, 9979}, {8661, 17145}, {14286, 17256}

X(47776) = midpoint of X(i) and X(j) for these {i,j}: {4380, 4776}, {4984, 6546}
X(47776) = reflection of X(i) in X(j) for these {i,j}: {2, 1635}, {4120, 10196}, {4728, 4763}, {4750, 45679}, {4776, 650}, {20295, 4776}, {21297, 2}, {27804, 9147}
X(47776) = anticomplement of X(4728)
X(47776) = anticomplement of the isogonal conjugate of X(34075)
X(47776) = anticomplement of the isotomic conjugate of X(4607)
X(47776) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {692, 39360}, {739, 149}, {889, 315}, {898, 69}, {1252, 44008}, {3227, 21293}, {4607, 6327}, {5381, 21301}, {32718, 2}, {34075, 8}, {37129, 150}, {41683, 21294}
X(47776) = X(4607)-Ceva conjugate of X(2)
X(47776) = crosspoint of X(i) and X(j) for these (i,j): {190, 3227}, {274, 889}
X(47776) = crosssum of X(i) and X(j) for these (i,j): {213, 890}, {649, 3230}, {4436, 23343}
X(47776) = crossdifference of every pair of points on line {42, 1015}
X(47776) = barycentric product X(i)*X(j) for these {i,j}: {668, 16507}, {7192, 19998}, {31002, 38349}
X(47776) = barycentric quotient X(i)/X(j) for these {i,j}: {4954, 4767}, {16507, 513}, {19998, 3952}, {38349, 899}
X(47776) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 17494, 7192}, {650, 4380, 20295}, {693, 4394, 27013}, {1635, 4728, 4763}, {2516, 4106, 31209}, {4106, 31209, 27138}, {4728, 4763, 2}, {4750, 14435, 45679}

X(47777) = X(44)X(513)∩X(514)X(1639)

X(47777) = 2 X[649] - 5 X[650], X[649] + 5 X[661], 3 X[649] - 5 X[1635], 11 X[649] - 20 X[2516], 7 X[649] - 10 X[4394], 8 X[649] - 5 X[4790], 7 X[649] + 5 X[4813], X[649] - 5 X[4893], 11 X[649] - 5 X[4979], X[650] + 2 X[661], 3 X[650] - 2 X[1635], 11 X[650] - 8 X[2516], 7 X[650] - 4 X[4394], 4 X[650] - X[4790], 7 X[650] + 2 X[4813], 11 X[650] - 2 X[4979], 3 X[661] + X[1635], 11 X[661] + 4 X[2516], 7 X[661] + 2 X[4394], 8 X[661] + X[4790], 7 X[661] - X[4813], 11 X[661] + X[4979], 11 X[1635] - 12 X[2516], 7 X[1635] - 6 X[4394], 8 X[1635] - 3 X[4790], 7 X[1635] + 3 X[4813], X[1635] - 3 X[4893], 11 X[1635] - 3 X[4979], 14 X[2516] - 11 X[4394], 32 X[2516] - 11 X[4790], 28 X[2516] + 11 X[4813], 4 X[2516] - 11 X[4893], 4 X[2516] - X[4979], 16 X[4394] - 7 X[4790], 2 X[4394] + X[4813], 2 X[4394] - 7 X[4893], 22 X[4394] - 7 X[4979], 7 X[4790] + 8 X[4813], X[4790] - 8 X[4893], 11 X[4790] - 8 X[4979], X[4813] + 7 X[4893], 11 X[4813] + 7 X[4979], 11 X[4893] - X[4979], X[4928] - 3 X[45315], 4 X[4928] - 3 X[45320], 5 X[4928] - 6 X[45339], 4 X[45315] - X[45320], 5 X[45315] - 2 X[45339], 5 X[45320] - 8 X[45339], 2 X[3239] + X[4841], 3 X[4705] - X[4825], 3 X[4776] - X[21297], X[4820] - 4 X[14321], X[4820] + 2 X[45745], 2 X[14321] + X[45745], 2 X[4940] + X[17494]

X(47777) lies on these lines: {44, 513}, {514, 1639}, {523, 4944}, {3239, 4841}, {4120, 4777}, {4705, 4825}, {4762, 4776}, {4773, 6006}, {4820, 14321}, {4867, 14077}, {4940, 17494}, {4962, 4976}

X(47777) = midpoint of X(661) and X(4893)
X(47777) = reflection of X(650) in X(4893)
X(47777) = X(2)-isoconjugate of X(28170)
X(47777) = X(32664)-Dao conjugate of X(28170)
X(47777) = crosssum of X(650) and X(13384)
X(47777) = crossdifference of every pair of points on line {1, 9332}
X(47777) = barycentric product X(i)*X(j) for these {i,j}: {1, 28169}, {514, 16676}, {522, 18421}
X(47777) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28170}, {16676, 190}, {18421, 664}, {28169, 75}
X(47777) = {X(14321),X(45745)}-harmonic conjugate of X(4820)

X(47778) = X(2)X(514)∩X(513)X(4763)

X(47778) = X[4379] + 3 X[4893], 4 X[44567] - X[45313], 2 X[44567] + X[45315], X[45313] + 2 X[45315], 2 X[45323] + X[45673], 2 X[650] + X[3835], 5 X[650] + X[4106], X[650] + 2 X[25666], 5 X[3835] - 2 X[4106], X[3835] - 4 X[25666], X[4106] - 10 X[25666], 2 X[661] + X[4932], X[661] + 5 X[31209], X[661] + 2 X[31286], X[4932] - 10 X[31209], X[4932] - 4 X[31286], 5 X[31209] - 2 X[31286], 2 X[2516] + X[4940]

X(47778) lies on these lines: {2, 514}, {10, 4844}, {43, 663}, {513, 4763}, {519, 14410}, {522, 4800}, {650, 812}, {661, 4932}, {824, 1639}, {899, 4794}, {1491, 4448}, {1635, 4776}, {2516, 4940}, {3741, 4147}, {4040, 16569}, {4762, 4928}, {9279, 11176}

X(47778) = midpoint of X(i) and X(j) for these {i,j}: {2, 4893}, {1491, 4448}, {1635, 4776}, {4763, 45315}, {6546, 44435}
X(47778) = reflection of X(i) in X(j) for these {i,j}: {4763, 44567}, {21204, 44432}, {45313, 4763}
X(47778) = complement of X(4379)
X(47778) = X(i)-complementary conjugate of X(j) for these (i,j): {751, 116}, {30650, 11}
X(47778) = crossdifference of every pair of points on line {902, 21010}
X(47778) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 25666, 3835}, {661, 31209, 31286}, {661, 31286, 4932}, {44567, 45315, 45313}

X(47779) = X(2)X(514)∩X(513)X(3716)

X(47779) = 3 X[4379] + X[4893], 3 X[6544] + X[21116], 3 X[14475] - X[44435], X[3835] + 2 X[4369], X[3835] - 4 X[4885], 2 X[3835] + X[4932], 7 X[3835] - 4 X[4940], 7 X[3835] + 8 X[7653], X[4369] + 2 X[4885], 4 X[4369] - X[4932], 7 X[4369] + 2 X[4940], 7 X[4369] - 4 X[7653], 2 X[4874] + X[24720], 8 X[4885] + X[4932], 7 X[4885] - X[4940], 7 X[4885] + 2 X[7653], 4 X[4928] + X[4932], 7 X[4928] - 2 X[4940], 7 X[4928] + 4 X[7653], 7 X[4932] + 8 X[4940], 7 X[4932] - 16 X[7653], X[4940] + 2 X[7653], X[693] + 5 X[24924], X[693] + 2 X[31286], X[1635] - 5 X[24924], 5 X[24924] - 2 X[31286], X[4500] + 2 X[17069]

X(47779) lies on these lines: {2, 514}, {43, 4449}, {116, 6075}, {513, 3716}, {522, 4809}, {551, 4844}, {693, 1635}, {824, 1638}, {3741, 17072}, {3798, 4962}, {4406, 14437}, {4500, 17069}, {4728, 4785}, {4762, 4763}, {4800, 6006}

X(47779) = midpoint of X(i) and X(j) for these {i,j}: {2, 4379}, {693, 1635}, {4369, 4928}, {4406, 14437}
X(47779) = reflection of X(i) in X(j) for these {i,j}: {1635, 31286}, {3835, 4928}, {4928, 4885}
X(47779) = complement of X(4893)
X(47779) = complement of the isogonal conjugate of X(4604)
X(47779) = X(i)-complementary conjugate of X(j) for these (i,j): {2, 15614}, {89, 11}, {101, 16590}, {190, 21251}, {651, 17057}, {901, 27751}, {2163, 1086}, {2320, 26932}, {2364, 1146}, {4588, 2}, {4597, 141}, {4604, 10}, {5385, 513}, {5549, 9}, {8652, 30563}, {8695, 17237}, {20569, 21252}, {28607, 1015}, {28658, 115}, {30588, 125}, {30608, 124}, {34073, 37}, {39704, 116}
X(47779) = crossdifference of every pair of points on line {902, 2176}
X(47779) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 24924, 31286}, {3835, 4369, 4932}, {4369, 4885, 3835}

X(47780) = X(2)X(514)∩X(320)X(350)

X(47780) = 3 X[4379] - X[4893], 3 X[6548] - 4 X[21183], 3 X[6548] - 2 X[44435], 5 X[693] - 2 X[4106], 2 X[693] + X[7192], 4 X[693] - X[20295], 7 X[693] - 4 X[23813], X[693] + 2 X[43067], 4 X[4106] + 5 X[7192], 8 X[4106] - 5 X[20295], 4 X[4106] - 5 X[21297], 7 X[4106] - 10 X[23813], X[4106] + 5 X[43067], 2 X[7192] + X[20295], 7 X[7192] + 8 X[23813], X[7192] - 4 X[43067], 7 X[20295] - 16 X[23813], X[20295] + 8 X[43067], 7 X[21297] - 8 X[23813], X[21297] + 4 X[43067], 2 X[23813] + 7 X[43067], 2 X[649] + X[26824], 2 X[661] - 5 X[26985], 4 X[661] - 7 X[27138], 4 X[4928] - 5 X[26985], 8 X[4928] - 7 X[27138], 10 X[26985] - 7 X[27138], 4 X[1635] - 5 X[27013], 4 X[4369] - X[17494], 8 X[4369] - 5 X[27013], 2 X[17494] - 5 X[27013], 8 X[3676] + X[4608], 4 X[3676] - X[45746], X[4608] + 2 X[45746], 4 X[4025] - X[17161], X[4382] + 2 X[4932], 2 X[4382] + X[26853], 4 X[4932] - X[26853], 2 X[17166] + X[21302]

X(47780) lies on these lines: {2, 514}, {320, 350}, {523, 4453}, {649, 17029}, {661, 4928}, {918, 4789}, {1635, 4369}, {2533, 4651}, {2977, 3004}, {3241, 4844}, {3676, 4608}, {3720, 4040}, {4025, 17161}, {4382, 4932}, {4406, 4441}, {4449, 17018}, {4927, 4977}, {16737, 16748}, {17135, 17166}

X(47780) = midpoint of X(7192) and X(21297)
X(47780) = reflection of X(i) in X(j) for these {i,j}: {2, 4379}, {661, 4928}, {1635, 4369}, {17494, 1635}, {20295, 21297}, {21297, 693}, {44435, 21183}
X(47780) = anticomplement of X(4893)
X(47780) = anticomplement of the isogonal conjugate of X(4604)
X(47780) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {6, 39364}, {89, 149}, {101, 17488}, {110, 30564}, {190, 21291}, {2163, 4440}, {2320, 37781}, {2364, 39351}, {4588, 2}, {4597, 69}, {4604, 8}, {5385, 513}, {5549, 144}, {8695, 4741}, {20569, 21293}, {28607, 9263}, {28658, 148}, {30588, 3448}, {30608, 33650}, {34073, 192}, {39704, 150}
X(47780) = X(i)-isoconjugate of X(j) for these (i,j): {41, 46480}, {101, 39974}, {692, 42285}
X(47780) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39974), (1086, 42285), (3160, 46480)
X(47780) = crosspoint of X(i) and X(j) for these (i,j): {86, 4597}, {190, 32013}
X(47780) = crosssum of X(i) and X(j) for these (i,j): {42, 4775}, {667, 21747}
X(47780) = crossdifference of every pair of points on line {213, 902}
X(47780) = barycentric product X(i)*X(j) for these {i,j}: {1, 4828}, {693, 37633}, {5035, 40495}, {7192, 31025}
X(47780) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 46480}, {513, 39974}, {514, 42285}, {4828, 75}, {5035, 692}, {31025, 3952}, {37633, 100}
X(47780) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 26985, 27138}, {693, 7192, 20295}, {693, 43067, 7192}, {4369, 17494, 27013}, {4382, 4932, 26853}, {21183, 44435, 6548}

X(47781) = X(2)X(514)∩X(523)X(4776)

X(47781) = 3 X[4893] - 2 X[10196], 5 X[6545] - 3 X[21116], 2 X[6545] - 3 X[44435], 2 X[21116] - 5 X[44435], 4 X[661] - X[25259], 2 X[661] + X[45746], X[25259] + 2 X[45746], X[693] + 2 X[4841], 2 X[3835] + X[4988]

X(47781) lies on these lines: {2, 514}, {523, 4776}, {661, 824}, {663, 17011}, {693, 4841}, {1491, 8034}, {3835, 4988}, {4040, 5256}, {4359, 4406}, {4449, 17019}, {4509, 14207}, {4724, 17012}, {4789, 4802}, {4794, 17013}

X(47782) = X(2)X(523)∩X(514)X(1635)

X(47782) = X[4789] + 2 X[46915], 2 X[650] + X[45746], 2 X[661] + X[4467], X[661] + 2 X[21196], 4 X[661] - X[44449], X[4467] - 4 X[21196]

X(47782) lies on these lines: {2, 523}, {379, 18118}, {514, 1635}, {522, 4776}, {650, 16757}, {661, 2786}, {824, 4893}, {2605, 17011}, {3004, 6084}, {3661, 4770}, {3700, 17161}, {3737, 5256}, {3805, 14404}, {4359, 4374}, {4369, 4988}, {4380, 4765}, {4724, 4818}, {4778, 4786}, {4841, 7192}, {7180, 16751}, {7199, 19804}

X(47782) = midpoint of X(2) and X(46915)
X(47782) = reflection of X(i) in X(j) for these {i,j}: {4789, 2}, {30565, 4893}, {31148, 45674}, {44553, 21130}
X(47782) = reflection of X(4789) in the Euler line
X(47782) = X(44572)-complementary conjugate of X(21252)
X(47782) = crossdifference of every pair of points on line {187, 2177}
X(47782) = barycentric product X(514)*X(17256)
X(47782) = barycentric quotient X(17256)/X(190)
X(47782) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4467, 44449}, {661, 21196, 4467}, {4841, 17069, 7192}

X(47783) = X(2)X(514)∩X(513)X(4786)

X(47783) = 3 X[4893] - X[6546], 3 X[21183] - 4 X[21204], 2 X[661] + X[4025], 2 X[3004] + X[4468], 2 X[3798] + X[4813]

X(47783) lies on these lines: {2, 514}, {306, 4705}, {513, 4786}, {522, 4776}, {661, 4025}, {663, 5256}, {2999, 4040}, {3004, 4468}, {3798, 4813}, {4406, 19804}, {4449, 5287}, {4794, 17012}, {4841, 4885}, {4940, 4976}, {5592, 17367}, {7192, 7658}, {14207, 15413}

X(47783) = reflection of X(4379) in X(44432)
X(47783) = X(9348)-complementary conjugate of X(116)

X(47784) = X(2)X(523)∩X(513)X(4786)

X(47784) = 3 X[2] + X[46915], 2 X[650] + X[3004], 5 X[650] - 2 X[11068], 5 X[3004] + 4 X[11068], 2 X[4369] + X[4841], 4 X[7658] - X[43067], X[21104] - 4 X[21212], 2 X[661] + X[4897], X[661] + 2 X[17069], X[4897] - 4 X[17069], 4 X[2487] - X[7192], 2 X[3835] + X[4976], X[4106] + 2 X[4765], X[4467] + 2 X[14321]

X(47784) lies on these lines: {2, 523}, {241, 514}, {513, 4786}, {661, 4750}, {824, 1639}, {900, 1491}, {918, 4893}, {2487, 7192}, {2526, 6006}, {2605, 5256}, {2999, 3737}, {3287, 4383}, {3666, 3709}, {3835, 4976}, {3912, 4770}, {4106, 4765}, {4374, 19804}, {4467, 14321}, {4762, 4927}, {4773, 4785}, {9040, 14404}

X(47784) = midpoint of X(i) and X(j) for these {i,j}: {661, 4750}, {4776, 27486}, {4789, 46915}
X(47784) = reflection of X(i) in X(j) for these {i,j}: {4750, 17069}, {4897, 4750}
X(47784) = complement of X(4789)
X(47784) = complement of the isotomic conjugate of X(37210)
X(47784) = X(i)-complementary conjugate of X(j) for these (i,j): {32, 35135}, {8691, 141}, {32672, 524}, {34914, 21252}, {34916, 116}, {35181, 626}, {36070, 4892}, {37210, 2887}
X(47784) = crosspoint of X(2) and X(37210)
X(47784) = crossdifference of every pair of points on line {55, 187}
X(47784) = barycentric product X(693)*X(4689)
X(47784) = barycentric quotient X(4689)/X(100)
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 46915, 4789}, {661, 17069, 4897}

X(47785) = X(2)X(522)∩X(513)X(4786)

X(47785) = X[27486] + 2 X[46919], X[31150] + 2 X[44551], 2 X[650] + X[4025], 4 X[650] - X[4468], X[650] + 2 X[17069], 2 X[4025] + X[4468], X[4025] - 4 X[17069], X[4468] + 8 X[17069], X[661] + 2 X[3798], X[693] + 2 X[4765], X[693] - 4 X[7658], X[4765] + 2 X[7658], X[3004] + 2 X[4394], 2 X[3239] + X[4467], 2 X[3239] - 5 X[31209], X[4467] + 5 X[31209], 2 X[3676] + X[17494], X[4560] + 2 X[14837], 2 X[4885] + X[4976], X[6332] - 4 X[14838], 2 X[11068] + X[16892]

X(47785) lies on these lines: {2, 522}, {63, 657}, {333, 16755}, {513, 4786}, {514, 1635}, {650, 918}, {661, 3798}, {693, 4765}, {824, 4763}, {905, 3310}, {1459, 5256}, {1638, 4762}, {3004, 4394}, {3239, 4467}, {3261, 19804}, {3666, 6586}, {3667, 4776}, {3676, 17494}, {4560, 14837}, {4750, 4893}, {4773, 6008}, {4814, 17316}, {4885, 4976}, {5744, 14330}, {6332, 14838}, {11068, 16892}

X(47785) = midpoint of X(i) and X(j) for these {i,j}: {2, 27486}, {4453, 31150}, {4750, 4893}
X(47785) = reflection of X(i) in X(j) for these {i,j}: {2, 46919}, {4453, 44551}, {21183, 1638}
X(47785) = X(44559)-anticomplementary conjugate of X(21293)
X(47785) = crossdifference of every pair of points on line {1055, 2177}
X(47785) = barycentric product X(693)*X(35258)
X(47785) = barycentric quotient X(35258)/X(100)
X(47785) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 4025, 4468}, {650, 17069, 4025}, {4467, 31209, 3239}, {4765, 7658, 693}

X(47786) = X(2)X(3667)∩X(514)X(4120)

X(47786) = 4 X[3835] - X[4025], 5 X[3835] - 2 X[21212], 5 X[4025] - 8 X[21212], X[3700] + 2 X[4940], 2 X[4106] + X[4468], X[4106] + 2 X[14321], X[4468] - 4 X[14321], X[4380] - 4 X[4521], X[4897] + 2 X[4949]

X(47786) lies on these lines: {2, 3667}, {469, 7649}, {514, 4120}, {522, 4776}, {1639, 6008}, {2786, 3835}, {3700, 4940}, {4106, 4468}, {4380, 4521}, {4778, 4789}, {4897, 4949}

X(47786) = midpoint of X(4120) and X(31147)
X(47786) = reflection of X(4786) in X(2)
X(47786) = reflection of X(4786) in the Nagel line
X(47786) = {X(4106),X(14321)}-harmonic conjugate of X(4468)

X(47787) = X(2)X(522)∩X(514)X(661)

X(47787) = X[693] + 2 X[3239], 2 X[693] + X[4468], 2 X[1577] + X[6332], 4 X[3239] - X[4468], 2 X[3835] + X[6590], 2 X[4944] + X[21183], 2 X[3700] + X[4025], X[3700] + 2 X[4885], X[4025] - 4 X[4885], X[4382] + 2 X[11068], X[4467] - 4 X[7658], 4 X[4521] - X[17494], X[4820] + 2 X[17069], X[4820] + 5 X[31250], 2 X[17069] - 5 X[31250], X[4949] + 2 X[7653]

X(47787) lies on these lines: {2, 522}, {306, 4036}, {312, 3261}, {514, 661}, {657, 3305}, {824, 4928}, {900, 4786}, {918, 4944}, {1459, 5287}, {1638, 3700}, {1639, 4762}, {4120, 4379}, {4382, 11068}, {4467, 7658}, {4474, 17316}, {4521, 17494}, {4767, 6633}, {4820, 17069}, {4949, 7653}, {18134, 18158}

X(47787) = midpoint of X(i) and X(j) for these {i,j}: {693, 30565}, {1638, 3700}, {4120, 4379}, {4474, 30573}, {4776, 4789}, {4944, 45320}
X(47787) = reflection of X(i) in X(j) for these {i,j}: {1638, 4885}, {4025, 1638}, {4468, 30565}, {21183, 45320}, {27486, 46919}, {30565, 3239}
X(47787) = complement of X(27486)
X(47787) = anticomplement of X(46919)
X(47787) = X(14077)-cross conjugate of X(30181)
X(47787) = X(i)-isoconjugate of X(j) for these (i,j): {6, 14074}, {1415, 34919}
X(47787) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 14074), (1146, 34919)
X(47787) = crossdifference of every pair of points on line {31, 1055}
X(47787) = barycentric product X(i)*X(j) for these {i,j}: {8, 30181}, {75, 14077}, {1996, 3239}, {4163, 47386}, {4391, 8545}, {35519, 37541}
X(47787) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14074}, {522, 34919}, {1996, 658}, {8545, 651}, {14077, 1}, {30181, 7}, {37541, 109}, {46644, 37139}, {47386, 4626}
X(47787) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 27486, 46919}, {693, 3239, 4468}, {3700, 4885, 4025}, {4820, 31250, 17069}

X(47788) = X(2)X(523)∩X(514)X(1639)

X(47788) = 5 X[2] - X[46915], 5 X[4789] + X[46915], X[4927] + 4 X[45685], X[45320] + 2 X[45685], 4 X[2487] - X[4467], 4 X[2490] - X[17494], 4 X[2527] - X[4380], X[3700] + 2 X[4369], 2 X[3700] + X[4897], 4 X[4369] - X[4897], X[3004] - 4 X[4885], X[3004] + 2 X[6590], 2 X[4885] + X[6590], 2 X[3798] + X[4820], X[4024] + 2 X[17069], X[4024] + 5 X[24924], 2 X[17069] - 5 X[24924], 2 X[4500] + X[4976], X[4500] + 2 X[31286], X[4976] - 4 X[31286], X[7178] + 2 X[8045], X[7192] + 2 X[14321]

X(47788) lies on these lines: {2, 523}, {312, 4374}, {514, 1639}, {693, 6084}, {824, 1638}, {918, 4379}, {940, 3287}, {2487, 4467}, {2490, 17494}, {2527, 4380}, {2605, 5287}, {2786, 3700}, {3004, 4885}, {3737, 17022}, {3798, 4820}, {4024, 17069}, {4500, 4976}, {4750, 4931}, {4774, 17316}, {4776, 4977}, {4786, 4926}, {5214, 18229}, {7178, 8045}, {7192, 14321}, {7199, 18743}

X(47788) = midpoint of X(i) and X(j) for these {i,j}: {2, 4789}, {4750, 4931}
X(47788) = reflection of X(4927) in X(45320)
X(47788) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3700, 4369, 4897}, {4024, 24924, 17069}, {4500, 31286, 4976}, {4885, 6590, 3004}

X(47789) = X(2)X(514)∩X(306)X(2533)

X(47789) = 3 X[4379] - X[6545], 2 X[6545] - 3 X[21183], X[4786] + 2 X[4789], X[4025] - 4 X[4369], X[4025] + 2 X[6590], 2 X[4369] + X[6590], 2 X[3239] + X[7192], 2 X[3798] + X[4024], X[4897] - 4 X[7653]

X(47789) lies on these lines: {2, 514}, {306, 2533}, {312, 4406}, {522, 4786}, {663, 5287}, {824, 4025}, {3239, 7192}, {3798, 4024}, {4040, 17022}, {4449, 5256}, {4776, 4778}, {4794, 17021}, {4897, 7653}, {5271, 17166}, {5592, 17244}

X(47789) = reflection of X(21183) in X(4379)
X(47789) = {X(4369),X(6590)}-harmonic conjugate of X(4025)

X(47790) = X(2)X(522)∩X(514)X(4120)

X(47790) = 5 X[2] - 4 X[46919], 5 X[27486] - 8 X[46919], X[31147] + 2 X[45343], X[661] + 2 X[4500], X[693] + 2 X[3700], 5 X[693] - 2 X[21104], 2 X[693] + X[25259], 5 X[3700] + X[21104], 4 X[3700] - X[25259], 4 X[21104] + 5 X[25259], 2 X[4931] + X[44435], 4 X[3239] - X[17494], 2 X[3835] + X[4024], 4 X[3835] - X[45746], 2 X[4024] + X[45746], X[4467] + 2 X[4820], X[4467] - 4 X[4885], X[4820] + 2 X[4885], 2 X[4522] + X[4804], 2 X[4823] + X[7265]

X(47790) lies on these lines: {2, 522}, {321, 3261}, {513, 4789}, {514, 4120}, {523, 4776}, {661, 4500}, {693, 918}, {824, 4728}, {1459, 17019}, {1577, 2610}, {2786, 4379}, {3239, 17494}, {3661, 4791}, {3835, 4024}, {4467, 4820}, {4474, 6542}, {4522, 4804}, {4762, 4944}, {4786, 4962}, {4823, 7265}, {5333, 16755}

X(47790) = midpoint of X(4728) and X(4931)
X(47790) = reflection of X(i) in X(j) for these {i,j}: {27486, 2}, {30565, 4944}, {44435, 4728}
X(47790) = crossdifference of every pair of points on line {1055, 21747}
X(47790) = barycentric product X(4397)*X(23839)
X(47790) = barycentric quotient X(23839)/X(934)
X(47790) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 3700, 25259}, {3835, 4024, 45746}, {4820, 4885, 4467}

X(47791) = X(2)X(514)∩X(513)X(4789)

X(47791) = 3 X[4379] - 2 X[21204], 4 X[21204] - 3 X[44435], 4 X[3798] - X[17161], X[4024] + 2 X[4932], 2 X[4500] + X[4979], 2 X[6590] + X[7192], 4 X[6590] - X[25259], 2 X[7192] + X[25259]

X(47791) lies on these lines: {2, 514}, {321, 4406}, {513, 4789}, {663, 17019}, {3187, 17166}, {3798, 17161}, {4024, 4932}, {4040, 5287}, {4449, 17011}, {4500, 4979}, {4724, 17021}, {4776, 4977}, {4844, 17389}, {6590, 7192}

X(47791) = reflection of X(44435) in X(4379)
X(47791) = X(101)-isoconjugate of X(9348)
X(47791) = X(1015)-Dao conjugate of X(9348)
X(47791) = crosssum of X(649) and X(9346)
X(47791) = barycentric product X(693)*X(9347)
X(47791) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 9348}, {9347, 100}
X(47791) = {X(6590),X(7192)}-harmonic conjugate of X(25259)

X(47792) = X(2)X(523)∩X(514)X(4120)

X(47792) = 4 X[4789] - X[46915], 2 X[661] + X[4608], 2 X[4024] + X[7192], 2 X[4369] + X[4838], 4 X[4369] - X[17161], 2 X[4838] + X[17161], 4 X[4841] - X[14779], 5 X[6590] - 2 X[11068], 4 X[6590] - X[17494], 8 X[11068] - 5 X[17494]

X(47792) lies on these lines: {2, 523}, {321, 7199}, {514, 4120}, {661, 4608}, {1999, 5214}, {2786, 4024}, {3737, 17019}, {4369, 4838}, {4776, 4802}, {4841, 14779}, {6590, 11068}

X(47792) = reflection of X(i) in X(j) for these {i,j}: {2, 4789}, {4120, 45343}, {46915, 2}
X(47792) = reflection of X(46915) in the Euler line
X(47792) = X(692)-isoconjugate of X(44572)
X(47792) = X(1086)-Dao conjugate of X(44572)
X(47792) = crossdifference of every pair of points on line {187, 21747}
X(47792) = barycentric product X(4608)*X(46896)
X(47792) = barycentric quotient X(i)/X(j) for these {i,j}: {514, 44572}, {46896, 4427}
X(47792) = {X(4369),X(4838)}-harmonic conjugate of X(17161)

X(47793) = X(2)X(514)∩X(8)X(663)

X(47793) = X[8] + 2 X[663], X[8] - 4 X[4147], X[663] + 2 X[4147], 2 X[10] + X[4040], 4 X[10] - X[21302], 2 X[4040] + X[21302], 2 X[650] + X[4391], 4 X[650] - X[4560], X[650] + 2 X[20317], 2 X[4391] + X[4560], X[4391] - 4 X[20317], X[4560] + 8 X[20317], 2 X[905] + X[4462], 4 X[905] - X[21222], 2 X[905] - 5 X[31209], 2 X[4462] + X[21222], X[4462] + 5 X[31209], X[21222] - 10 X[31209], 2 X[1577] + X[17494], 5 X[3616] - 2 X[4449], 5 X[3617] + 4 X[4794], 2 X[3716] + X[4041], X[3762] + 2 X[14838], 2 X[3762] + X[17496], 2 X[3762] + 7 X[27115], 4 X[14838] - X[17496], 4 X[14838] - 7 X[27115], X[17496] - 7 X[27115], 2 X[3835] + X[4498], X[4063] + 2 X[4129], 2 X[4063] + X[20295], 4 X[4129] - X[20295], X[4088] + 2 X[4142], X[4468] + 2 X[14837], X[4490] + 2 X[4874], 2 X[4490] + X[17166], 4 X[4874] - X[17166], 4 X[4521] - X[6332], X[4581] - 4 X[6133], 2 X[4724] + 7 X[9780], X[4724] + 2 X[17072], 7 X[9780] - 4 X[17072], X[4801] - 4 X[4885]

X(47773) lies on these lines: {2, 514}, {8, 663}, {10, 4040}, {650, 3975}, {905, 4462}, {1016, 5548}, {1577, 17494}, {1635, 6002}, {1639, 3910}, {2533, 19874}, {3616, 4449}, {3617, 4794}, {3716, 4041}, {3762, 14838}, {3835, 4498}, {3907, 14430}, {4063, 4129}, {4088, 4142}, {4468, 14837}, {4490, 4874}, {4521, 6332}, {4581, 6133}, {4724, 9780}, {4801, 4885}

X(47793) = X(46187)-complementary conjugate of X(116)
X(47793) = X(20949)-Ceva conjugate of X(20295)
X(47793) = X(i)-isoconjugate of X(j) for these (i,j): {57, 40519}, {101, 20615}, {109, 39798}, {596, 1415}, {604, 8050}, {651, 40148}, {1400, 34594}, {1402, 37205}, {2149, 40086}, {4559, 39949}
X(47793) = X(i)-Dao conjugate of X(j) for these (i, j): (11, 39798), (649, 43924), (650, 40086), (1015, 20615), (1146, 596), (3161, 8050), (4129, 3669), (5452, 40519), (6741, 40085), (21208, 3665), (38991, 40148), (40582, 34594), (40605, 37205), (40624, 40013), (40625, 39747)
X(47793) = crosspoint of X(i) and X(j) for these (i,j): {190, 2985}, {333, 646}
X(47793) = crosssum of X(i) and X(j) for these (i,j): {649, 17053}, {1401, 43924}
X(47793) = crossdifference of every pair of points on line {902, 1402}
X(47793) = barycentric product X(i)*X(j) for these {i,j}: {8, 20295}, {9, 20949}, {312, 4063}, {314, 4132}, {333, 4129}, {345, 17922}, {522, 4360}, {595, 35519}, {650, 18140}, {663, 40087}, {693, 3871}, {3293, 18155}, {3596, 4057}, {3699, 21208}, {3716, 40093}, {3995, 4560}, {4222, 35518}, {4391, 32911}, {7017, 22154}
X(47793) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 8050}, {11, 40086}, {21, 34594}, {55, 40519}, {333, 37205}, {513, 20615}, {522, 596}, {595, 109}, {650, 39798}, {663, 40148}, {2220, 1415}, {3293, 4551}, {3700, 40085}, {3737, 39949}, {3871, 100}, {3995, 4552}, {4057, 56}, {4063, 57}, {4129, 226}, {4132, 65}, {4222, 108}, {4360, 664}, {4391, 40013}, {4560, 39747}, {8054, 43924}, {17922, 278}, {18140, 4554}, {20295, 7}, {20949, 85}, {21208, 3676}, {22154, 222}, {32911, 651}, {40087, 4572}
X(47793) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 4040, 21302}, {650, 4391, 4560}, {650, 20317, 4391}, {663, 4147, 8}, {905, 4462, 21222}, {3762, 14838, 17496}, {4063, 4129, 20295}, {4462, 31209, 905}, {4490, 4874, 17166}, {17494, 27045, 27293}, {17496, 27115, 14838}

X(47794) = X(1)X(4147)∩X(2)X(514)

X(47794) = X[1] + 2 X[4147], 2 X[10] + X[663], X[649] + 2 X[4129], 2 X[650] + X[1577], 2 X[905] + X[3762], X[905] + 2 X[20317], X[905] - 4 X[31287], X[3762] - 4 X[20317], X[3762] + 8 X[31287], X[20317] + 2 X[31287], 4 X[1125] - X[4449], 5 X[1698] + X[4040], 5 X[1698] - 2 X[17072], X[4040] + 2 X[17072], X[1734] + 2 X[3716], 4 X[3239] - X[7265], 8 X[3634] + X[4724], 2 X[3835] + X[4063], 2 X[3960] + X[4462], X[4391] + 2 X[14838], X[4391] + 5 X[31209], 2 X[14838] - 5 X[31209], X[4404] + 2 X[6129], 8 X[4521] + X[4707], 2 X[4521] + X[14837], X[4707] - 4 X[14837], X[4560] + 2 X[4791], X[4560] - 7 X[27115], 2 X[4791] + 7 X[27115], X[4705] + 2 X[4874], 2 X[4794] + 7 X[9780], 2 X[4794] + X[21302], 7 X[9780] - X[21302], 2 X[4806] + X[4834], 2 X[4823] + X[17494], 4 X[4885] - X[4978]

X(47794) lies on these lines: {1, 4147}, {2, 514}, {10, 663}, {522, 14429}, {525, 1639}, {649, 4129}, {650, 1577}, {814, 14431}, {905, 3762}, {1125, 4449}, {1698, 4040}, {1734, 3716}, {2533, 16828}, {3239, 7265}, {3634, 4724}, {3835, 4063}, {3960, 4462}, {4391, 14838}, {4404, 6129}, {4448, 6004}, {4521, 4707}, {4546, 7080}, {4560, 4791}, {4705, 4874}, {4763, 6002}, {4794, 9780}, {4806, 4834}, {4823, 17494}, {4885, 4978}

X(47794) = X(i)-complementary conjugate of X(j) for these (i,j): {41, 39006}, {40518, 34822}
X(47794) = crossdifference of every pair of points on line {902, 2352}
X(47794) = barycentric product X(i)*X(j) for these {i,j}: {693, 8715}, {3204, 3261}, {4521, 27814}, {20566, 39478}
X(47794) = barycentric quotient X(i)/X(j) for these {i,j}: {3204, 101}, {8715, 100}, {39478, 36}
X(47794) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {905, 20317, 3762}, {1698, 4040, 17072}, {4391, 31209, 14838}, {20317, 31287, 905}

X(47795) = X(1)X(17072)∩X(2)X(514)

X(47795) = X[1] + 2 X[17072], 2 X[10] + X[4449], 2 X[650] + X[4978], X[663] - 4 X[1125], X[667] + 2 X[3837], X[693] + 2 X[14838], 2 X[905] + X[1577], X[905] + 2 X[4885], X[1577] - 4 X[4885], X[1019] + 2 X[3835], 5 X[1698] - 2 X[4147], X[2530] + 2 X[4874], 7 X[3624] - X[4040], 7 X[3624] + 2 X[24720], X[4040] + 2 X[24720], 2 X[3669] + X[3762], X[3669] + 5 X[31250], X[3762] - 10 X[31250], 2 X[3716] + X[4905], X[3777] - 4 X[19947], 2 X[3960] + X[4391], 2 X[4025] + X[7265], 2 X[4369] + X[14349], X[4560] + 2 X[4823], X[4560] + 5 X[26985], 2 X[4823] - 5 X[26985], X[4707] + 2 X[6332], X[4707] - 4 X[21188], X[6332] + 2 X[21188], X[4724] - 10 X[19862], X[4724] + 2 X[23789], 5 X[19862] + X[23789], 2 X[4791] + X[17496], 2 X[4794] - 11 X[5550], X[4834] + 2 X[4992]

X(47795) lies on these lines: {1, 17072}, {2, 514}, {10, 4449}, {522, 3582}, {525, 1638}, {650, 4978}, {663, 1125}, {667, 3837}, {693, 14838}, {814, 14419}, {905, 1577}, {1019, 3835}, {1491, 19863}, {1698, 4147}, {2530, 4874}, {3624, 4040}, {3669, 3762}, {3716, 4905}, {3777, 19847}, {3960, 4391}, {4025, 7265}, {4369, 14349}, {4406, 17322}, {4560, 4823}, {4705, 16828}, {4707, 6332}, {4724, 19862}, {4776, 15309}, {4791, 17496}, {4794, 5550}, {4834, 4992}, {4928, 6002}, {17166, 19858}, {19948, 19949}

X(47795) = X(i)-complementary conjugate of X(j) for these (i,j): {604, 8054}, {1415, 4075}, {8050, 21244}, {20615, 116}, {34594, 21246}, {39798, 124}, {40148, 26932}, {40519, 3452}
X(47795) = crossdifference of every pair of points on line {902, 3185}
X(47795) = barycentric product X(i)*X(j) for these {i,j}: {514, 32933}, {693, 25440}
X(47795) = barycentric quotient X(i)/X(j) for these {i,j}: {25440, 100}, {32933, 190}
X(47795) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {905, 4885, 1577}, {4560, 26985, 4823}, {6332, 21188, 4707}

X(47796) = X(2)X(514)∩X(8)X(4449)

X(47796) = X[8] + 2 X[4449], X[8] - 4 X[17072], X[4449] + 2 X[17072], 2 X[650] + X[4801], 2 X[663] - 5 X[3616], X[663] + 2 X[24720], 5 X[3616] + 4 X[24720], X[693] + 2 X[905], 2 X[693] + X[4560], 4 X[905] - X[4560], 2 X[1019] + X[20295], 4 X[1125] - X[4040], 2 X[1125] + X[23789], X[4040] + 2 X[23789], 2 X[1491] + X[17166], X[1577] + 2 X[3960], 2 X[1577] + X[17496], 2 X[1577] - 5 X[26985], 4 X[3960] - X[17496], 4 X[3960] + 5 X[26985], X[17496] + 5 X[26985], X[2530] - 4 X[19947], 2 X[3669] + X[4391], X[3669] + 2 X[4885], 4 X[3669] - X[21222], X[4391] - 4 X[4885], 2 X[4391] + X[21222], 8 X[4885] + X[21222], 2 X[3676] + X[6332], X[3777] + 2 X[4874], 2 X[3837] + X[4367], 4 X[3837] - X[21301], 2 X[4367] + X[21301], X[3904] + 2 X[7178], 4 X[4147] - 7 X[9780], 2 X[4724] - 11 X[5550], X[4784] + 2 X[4992], X[4978] + 2 X[14838], 2 X[4978] + X[17494], 4 X[14838] - X[17494], X[7192] + 2 X[14349], 2 X[8045] + X[16892]

X(47796) lies on these lines: {2, 514}, {8, 4449}, {525, 4453}, {650, 4801}, {663, 3616}, {693, 905}, {1019, 17174}, {1125, 4040}, {1491, 17166}, {1577, 3960}, {1638, 3910}, {2530, 19894}, {3669, 4391}, {3676, 6332}, {3777, 4874}, {3837, 4367}, {3904, 7178}, {3907, 14413}, {4147, 9780}, {4406, 17321}, {4705, 19874}, {4724, 5550}, {4728, 6002}, {4784, 4992}, {4978, 14838}, {7192, 14349}, {8045, 16892}, {15413, 17096}, {16705, 16737}

X(47796) = X(46404)-Ceva conjugate of X(7)
X(47796) = X(i)-isoconjugate of X(j) for these (i,j): {33, 40518}, {1415, 44040}
X(47796) = X(i)-Dao conjugate of X(j) for these (i, j): (1146, 44040), (1459, 652)
X(47796) = crosspoint of X(86) and X(4554)
X(47796) = crosssum of X(42) and X(3063)
X(47796) = crossdifference of every pair of points on line {228, 902}
X(47796) = barycentric product X(i)*X(j) for these {i,j}: {7, 20293}, {404, 693}, {513, 44139}, {514, 32939}, {664, 44311}, {1509, 21721}, {17925, 42705}, {39006, 46404}, {40495, 44085}
X(47796) = barycentric quotient X(i)/X(j) for these {i,j}: {222, 40518}, {404, 100}, {522, 44040}, {20293, 8}, {21721, 594}, {32939, 190}, {39006, 652}, {44085, 692}, {44139, 668}, {44311, 522}
X(47796) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 905, 4560}, {1125, 23789, 4040}, {1577, 3960, 17496}, {3669, 4391, 21222}, {3669, 4885, 4391}, {3837, 4367, 21301}, {4449, 17072, 8}, {4978, 14838, 17494}, {17496, 26985, 1577}

X(47797) = X(2)X(523)∩X(513)X(4453)

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

X(47797) = X[44433] + 2 X[44435], X[661] + 2 X[4458], 2 X[676] + X[3004], 2 X[3716] + X[16892], 2 X[3776] + X[4724], 2 X[4010] + X[4467]

X(47797) lies on these lines: {2, 523}, {513, 4453}, {514, 14413}, {522, 4728}, {614, 3737}, {661, 4458}, {676, 3004}, {2605, 7191}, {3716, 16892}, {3776, 4724}, {4010, 4467}

X(47797) = reflection of X(31131) in X(44429)
X(47797) = crossdifference of every pair of points on line {187, 41423}
X(47797) = barycentric product X(514)*X(24723)
X(47797) = barycentric quotient X(24723)/X(190)

X(47798) = X(2)X(522)∩X(351)X(523)

X(47798) = 2 X[44433] + X[44435], X[649] - 4 X[13246], X[663] + 2 X[4142], 4 X[676] - X[693], 2 X[4458] + X[4724], X[4707] + 2 X[4794]

X(47798) lies on these lines: {2, 522}, {351, 523}, {513, 4453}, {514, 8643}, {649, 13246}, {659, 8654}, {663, 2785}, {664, 9086}, {676, 693}, {1459, 7191}, {3667, 4750}, {3873, 9000}, {4458, 4724}, {4707, 4794}

X(47799) = X(2)X(523)∩X(513)X(1638)

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

X(47799) = 2 X[676] + X[1491], 4 X[2487] - X[4784], X[3004] + 2 X[4874], X[4010] + 2 X[17069], 2 X[4806] + X[4897]

X(47799) lies on these lines: {2, 523}, {513, 1638}, {522, 4928}, {614, 2605}, {676, 1491}, {2487, 4784}, {3004, 4874}, {3290, 3709}, {3737, 5272}, {4010, 17069}, {4806, 4897}

X(47800) = X(2)X(522)∩X(230)X(231)

Barycentrics (b - 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(47800) = X[650] + 2 X[676], 2 X[650] + X[47123], 4 X[676] - X[47123], 2 X[2977] + X[47131], 4 X[4874] - X[6590], 2 X[6129] + X[47136], 2 X[7662] + X[45745], X[663] + 2 X[14837], 2 X[3676] + X[4724], X[2254] - 4 X[7658], X[3835] + 2 X[13246], 2 X[44432] + X[44433], 4 X[2487] - X[7659], 2 X[3716] + X[4025], X[4088] - 4 X[4521], 2 X[4142] + X[6332], 2 X[4458] + X[4468], 2 X[4765] + X[4804], 2 X[7661] + X[17418]

X(47800) lies on these lines: {2, 522}, {105, 2717}, {230, 231}, {354, 9000}, {513, 1638}, {514, 14413}, {614, 1459}, {663, 14837}, {905, 2826}, {1443, 1447}, {2254, 3667}, {2487, 7659}, {3716, 4025}, {4088, 4521}, {4142, 6332}, {4458, 4468}, {4765, 4804}, {7661, 17418}, {8058, 14392}

X(47800) = midpoint of X(i) and X(j) for these {i,j}: {663, 30574}, {44429, 44433}
X(47800) = reflection of X(i) in X(j) for these {i,j}: {30574, 14837}, {44429, 44432}
X(47800) = complement of the isotomic conjugate of X(9086)
X(47800) = X(9086)-complementary conjugate of X(2887)
X(47800) = crosspoint of X(2) and X(9086)
X(47800) = crosssum of X(6) and X(9029)
X(47800) = crossdifference of every pair of points on line {3, 1055}
X(47800) = barycentric product X(i)*X(j) for these {i,j}: {514, 5698}, {523, 35935}
X(47800) = barycentric quotient X(i)/X(j) for these {i,j}: {5698, 190}, {35935, 99}
X(47800) = {X(650),X(676)}-harmonic conjugate of X(47123)

X(47801) = X(2)X(3667)∩X(513)X(1638)

Barycentrics (b - c)*(-5*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(47801) = 2 X[4057] + X[7649], 2 X[659] + X[47123], 2 X[2487] + X[2976], 2 X[2496] + X[4394], X[4025] - 4 X[13246], X[4458] + 2 X[8689]

X(47801) lies on these lines: {2, 3667}, {25, 4057}, {513, 1638}, {514, 8643}, {522, 1635}, {523, 8644}, {659, 8642}, {2487, 2976}, {2496, 4394}, {4025, 13246}, {4458, 8689}, {6995, 16231}

X(47802) = X(2)X(513)∩X(427)X(16228)

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

X(47802) = X[45320] + 2 X[45323], X[45320] - 4 X[45340], X[45323] + 2 X[45340], X[650] + 2 X[3837], X[905] + 2 X[21260], X[1491] + 2 X[4885], 2 X[1491] + X[7662], X[1491] + 5 X[30795], 4 X[4885] - X[7662], 2 X[4885] - 5 X[30795], X[7662] - 10 X[30795], X[2526] + 2 X[4874], X[2526] + 5 X[31250], 2 X[4874] - 5 X[31250], X[4106] + 2 X[9508], X[4784] + 2 X[4940], 2 X[4806] + X[7659]

X(47802) lies on these lines: {2, 513}, {427, 16228}, {522, 4928}, {523, 7625}, {650, 3837}, {905, 2787}, {1491, 4885}, {2526, 4874}, {4106, 9508}, {4132, 5996}, {4784, 4940}, {4806, 7659}

X(47802) = midpoint of X(2) and X(44429)
X(47802) = crossdifference of every pair of points on line {1384, 3230}
X(47802) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 4885, 7662}, {1491, 30795, 4885}, {2526, 31250, 4874}, {30764, 30765, 4885}, {45323, 45340, 45320}

X(47803) = X(2)X(513)∩X(230)X(231)

X(47803) = X[650] + 2 X[4874], 2 X[650] + X[7662], X[676] + 2 X[2490], 4 X[676] - X[47131], 8 X[2490] + X[47131], 2 X[2977] + X[47123], 4 X[4874] - X[7662], X[6129] + 2 X[6133], X[659] + 2 X[4885], X[1577] + 2 X[6050], X[3716] + 2 X[31286], X[4010] + 2 X[4394], X[4106] + 2 X[4782], X[4522] + 2 X[13246], X[4790] + 2 X[4806]

X(47803) lies on these lines: {2, 513}, {25, 16228}, {230, 231}, {522, 4763}, {659, 4885}, {667, 14431}, {1577, 6050}, {2496, 4926}, {2505, 7659}, {3063, 5275}, {3667, 3716}, {4010, 4394}, {4106, 4782}, {4108, 4132}, {4369, 4778}, {4522, 13246}, {4790, 4806}

X(47803) = midpoint of X(667) and X(14431)
X(47803) = complement of the isotomic conjugate of X(9067)
X(47803) = complement of X(44429)
X(47803) = X(9067)-complementary conjugate of X(2887)
X(47803) = crosspoint of X(2) and X(9067)
X(47803) = crosssum of X(6) and X(9010)
X(47803) = crossdifference of every pair of points on line {3, 3230}
X(47803) = barycentric product X(523)*X(16046)
X(47803) = barycentric quotient X(16046)/X(99)
X(47803) = {X(650),X(4874)}-harmonic conjugate of X(7662)

X(47804) = X(2)X(513)∩X(351)X(523)

X(47804) = X[4776] - 4 X[45666], X[31150] - 4 X[45314], X[649] + 2 X[3716], 2 X[659] + X[693], X[659] + 2 X[4874], X[693] - 4 X[4874], 2 X[667] + X[4391], X[1577] + 2 X[4401], X[2517] + 2 X[4057], 2 X[4010] + X[4380], X[4010] + 2 X[4782], X[4380] - 4 X[4782], 2 X[4367] + X[4462], 2 X[4369] + X[4724], X[4382] + 2 X[4830], X[4397] - 4 X[6133], X[4474] + 5 X[8656], X[4560] - 4 X[6050], X[4761] + 2 X[4794], 2 X[7662] + X[17494]

X(47804) lies on these lines: {2, 513}, {98, 2752}, {105, 2726}, {351, 523}, {514, 14413}, {522, 1635}, {649, 3716}, {659, 693}, {667, 2787}, {668, 898}, {1577, 4401}, {2517, 4057}, {3063, 5276}, {3907, 8643}, {4010, 4380}, {4367, 4462}, {4369, 4724}, {4378, 16823}, {4382, 4830}, {4397, 6133}, {4474, 8656}, {4560, 6050}, {4761, 4794}, {4775, 16830}, {6995, 16228}, {7662, 17494}, {8642, 16158}

X(47804) = reflection of X(44429) in X(2)
X(47804) = crossdifference of every pair of points on line {574, 3230}
X(47804) = barycentric product X(514)*X(4676)
X(47804) = barycentric quotient X(4676)/X(190)
X(47804) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 4874, 693}, {4010, 4782, 4380}, {26248, 26277, 693}

X(47805) = X(2)X(513)∩X(23)X(385)

X(47805) = 4 X[659] - X[17494], 4 X[667] - X[17496], 2 X[4724] + X[7192], X[4724] - 4 X[8689], X[7192] + 8 X[8689], 2 X[2527] + X[2976], 2 X[3803] + X[4391], 4 X[3803] - X[31291], 2 X[4391] + X[31291], 4 X[4401] - X[4560], X[4804] + 2 X[4830], 4 X[13246] - X[16892]

X(47805) lies on these lines: {2, 513}, {23, 385}, {514, 8643}, {649, 3239}, {667, 17496}, {1443, 1447}, {2527, 2976}, {3803, 4391}, {4108, 8672}, {4401, 4560}, {4782, 4926}, {4804, 4830}, {7408, 16228}, {13246, 16892}

X(47805) = anticomplement of X(44429)
X(47805) = anticomplement of the isotomic conjugate of X(9067)
X(47805) = X(9067)-anticomplementary conjugate of X(6327)
X(47805) = X(9067)-Ceva conjugate of X(2)
X(47805) = crossdifference of every pair of points on line {39, 1201}
X(47805) = {X(3803),X(4391)}-harmonic conjugate of X(31291)

X(47806) = X(2)X(522)∩X(513)X(1639)

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

X(47806) = 2 X[1491] + X[6590], X[2254] + 2 X[3239], X[6332] + 2 X[17072], 2 X[3676] + X[4088], X[4025] + 2 X[4522], X[4025] - 4 X[25380], X[4522] + 2 X[25380], 2 X[4163] + X[4449], 4 X[4521] - X[4724], X[7659] + 2 X[14321]

X(47806) lies on these lines: {2, 522}, {210, 9000}, {513, 1639}, {514, 14430}, {523, 7625}, {612, 1459}, {1491, 6590}, {2254, 3239}, {2785, 6332}, {3676, 4088}, {4025, 4522}, {4163, 4449}, {4521, 4724}, {7659, 14321}

X(47806) = crossdifference of every pair of points on line {1055, 1384}
X(47806) = {X(4522),X(25380)}-harmonic conjugate of X(4025)

X(47807) = X(2)X(523)∩X(513)X(1639)

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

X(47807) = X[659] - 4 X[2490], X[693] + 2 X[2977], X[3700] + 2 X[9508], X[4122] + 2 X[17069], X[4784] + 2 X[14321], X[4897] + 2 X[18004]

X(47807) lies on these lines: {2, 523}, {513, 1639}, {522, 4763}, {612, 2605}, {659, 2490}, {693, 2977}, {3287, 5275}, {3700, 9508}, {3737, 5268}, {4122, 17069}, {4784, 14321}, {4897, 18004}

X(47808) = X(2)X(522)∩X(325)X(523)

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

X(47808) = 4 X[1491] - X[45746], 2 X[2517] + X[20294], X[2254] + 2 X[4522], 2 X[2254] + X[25259], 4 X[4522] - X[25259], X[3700] + 2 X[4925]

X(47808) lies on these lines: {2, 522}, {325, 523}, {649, 3239}, {1459, 3920}, {2254, 4522}, {2496, 4926}, {2826, 4391}, {3681, 9000}, {3700, 4925}, {4468, 4778}, {4767, 6163}

X(47808) = reflection of X(44435) in X(44429)
X(47808) = isotomic conjugate of X(9086)
X(47808) = isotomic conjugate of the isogonal conjugate of X(9029)
X(47808) = X(31)-isoconjugate of X(9086)
X(47808) = X(2)-Dao conjugate of X(9086)
X(47808) = crossdifference of every pair of points on line {32, 1055}
X(47808) = barycentric product X(i)*X(j) for these {i,j}: {76, 9029}, {3261, 41276}
X(47808) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 9086}, {9029, 6}, {41276, 101}
X(47808) = {X(2254),X(4522)}-harmonic conjugate of X(25259)

X(47809) = X(2)X(523)∩X(514)X(14430)

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

X(47809) = X[649] + 2 X[4522], 4 X[2977] - X[17494], X[4024] + 2 X[4913], X[4041] + 2 X[8045], X[4088] + 2 X[4369], 2 X[4122] + X[4467], X[4122] + 2 X[9508], X[4467] - 4 X[9508], X[4784] + 2 X[18004], 2 X[4784] + X[44449], 4 X[18004] - X[44449]

X(47809) lies on these lines: {2, 523}, {514, 14430}, {522, 1635}, {612, 3737}, {649, 4522}, {2605, 3920}, {2977, 17494}, {3263, 4374}, {3287, 5276}, {4024, 4913}, {4041, 8045}, {4088, 4369}, {4122, 4467}, {4477, 16158}, {4784, 18004}

X(47809) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4122, 9508, 4467}, {4784, 18004, 44449}

X(47810) = X(44)X(513)∩X(514)X(14430)

X(47810) = X[661] + 2 X[1491], 2 X[661] + X[2254], 4 X[1491] - X[2254], 2 X[2526] + X[4724], X[4979] - 4 X[9508], 2 X[1734] + X[4822], 2 X[3004] + X[4088], 4 X[3835] - X[4804], 2 X[3837] + X[4824], X[4041] + 2 X[14349]

X(47810) lies on these lines: {44, 513}, {514, 14430}, {522, 4776}, {523, 4728}, {693, 4086}, {891, 4705}, {1734, 4822}, {3004, 4088}, {3835, 4804}, {3837, 4824}, {4041, 14349}, {4160, 14413}, {4977, 6546}, {6371, 14404}

X(47811) = X(44)X(513)∩X(514)X(14413)

X(47811) = 4 X[650] - X[2254], 2 X[650] + X[4724], 2 X[659] + X[661], X[2254] + 2 X[4724], 4 X[2516] - X[7659], 4 X[4782] - X[4979], X[17420] + 2 X[46385], X[31150] + 2 X[45673], X[31148] - 4 X[45314], 4 X[3716] - X[4804], 2 X[3716] + X[17494], X[4804] + 2 X[17494], 2 X[4040] + X[4041], 2 X[4063] + X[4822], 2 X[4770] + X[6161], 4 X[4794] - X[4895]

X(478) lies on these lines: {44, 513}, {81, 3737}, {514, 14413}, {522, 14392}, {523, 1962}, {663, 14077}, {846, 6615}, {1638, 4977}, {3716, 4804}, {3887, 4040}, {4063, 4822}, {4770, 6161}, {4794, 4895}

X(47811) = reflection of X(23057) in X(663)
X(47811) = crossdifference of every pair of points on line {1, 5030}
X(47811) = barycentric product X(514)*X(15254)
X(47811) = barycentric quotient X(15254)/X(190)
X(47811) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 4724, 2254}, {3716, 17494, 4804}

X(47812) = X(513)X(4379)∩X(514)X(14413)

Barycentrics (b - c)*(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(47812) = 2 X[14430] - 3 X[21052], 2 X[693] + X[2254], 4 X[693] - X[4804], X[693] + 2 X[24720], 2 X[2254] + X[4804], X[2254] - 4 X[24720], X[4804] + 8 X[24720], X[661] - 4 X[3837], X[661] + 2 X[21146], 2 X[3837] + X[21146], X[4041] + 2 X[4978], X[4724] - 4 X[4885], X[4801] + 2 X[17072], 2 X[4823] + X[4905]

X(47812) lies on these lines: {513, 4379}, {514, 14430}, {522, 693}, {523, 6545}, {661, 1639}, {1491, 4802}, {3737, 5333}, {4041, 4978}, {4425, 6615}, {4724, 4885}, {4776, 4778}, {4801, 17072}, {4823, 4905}

X(47812) = crossdifference of every pair of points on line {41, 595}
X(47812) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 2254, 4804}, {693, 24720, 2254}, {3837, 21146, 661}

X(47813) = X(513)X(4379)∩X(514)X(14413)

Barycentrics (b - c)*(2*a^3 + 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(47813) = 2 X[649] + X[4804], X[649] + 2 X[7662], X[4804] - 4 X[7662], X[661] - 4 X[4874], X[2254] - 4 X[4369], 2 X[3716] + X[7192], 2 X[4010] + X[4979], 2 X[4761] + X[4895], 4 X[7653] - X[7659]

X(47813) lies on these lines: {513, 4379}, {514, 14413}, {522, 4786}, {523, 1635}, {649, 4804}, {661, 4874}, {2254, 4369}, {3716, 7192}, {4010, 4979}, {4160, 14430}, {4448, 4977}, {4761, 4895}, {7653, 7659}

X(47813) = crossdifference of every pair of points on line {4256, 41423}
X(47813) = {X(649),X(7662)}-harmonic conjugate of X(4804)

X(47814) = X(2)X(8678)∩X(514)X(14430)

X(47814) = 2 X[10] + X[14349], X[661] + 2 X[17072], X[693] + 2 X[4705], X[693] - 4 X[21260], X[4705] + 2 X[21260], 2 X[1491] + X[4391], X[1491] + 2 X[21051], X[4391] - 4 X[21051], X[1734] + 2 X[4129], 2 X[2530] + X[4462], 2 X[3835] + X[4041], 2 X[3837] + X[4490], 4 X[3837] - X[4801], 2 X[4490] + X[4801], 4 X[4885] - X[17166]

X(47814) lies on these lines: {2, 8678}, {10, 14349}, {512, 4776}, {514, 14430}, {661, 17072}, {693, 4705}, {784, 14431}, {1491, 4391}, {1734, 4129}, {2530, 4462}, {3835, 4041}, {3837, 4490}, {4885, 17166}

X(47814) = crosspoint of X(i) and X(j) for these (i,j): {6386, 34258}, {7033, 37218}
X(47814) = crosssum of X(1980) and X(5019)
X(47814) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 21051, 4391}, {3837, 4490, 4801}, {4705, 21260, 693}

X(47815) = X(514)X(14413)∩X(659)X(814)

X(47815) = 2 X[659] + X[4391], 2 X[667] + X[4462], 2 X[3716] + X[4498], X[3762] + 2 X[4401], X[4147] + 2 X[8689], 2 X[4504] - 5 X[8656], X[4801] - 4 X[4874], 4 X[6050] - X[17496]

X(47815) lies on these lines: {514, 14413}, {659, 814}, {667, 2975}, {3309, 5657}, {3669, 7288}, {3716, 4498}, {3762, 4401}, {3877, 4083}, {4063, 12514}, {4147, 8689}, {4504, 8656}, {4801, 4874}, {6050, 17496}

X(47816) = X(2)X(830)∩X(514)X(14430)

X(47816) = 2 X[1491] + X[1577], X[1491] + 2 X[21260], X[1577] - 4 X[21260], X[1734] + 2 X[3835], 2 X[1734] + X[4170], 4 X[3835] - X[4170], X[2254] + 2 X[4129], 2 X[2530] + X[3762], X[2530] + 2 X[21051], X[3762] - 4 X[21051], 2 X[3837] + X[4705], 4 X[3837] - X[4978], 2 X[4705] + X[4978], X[4730] + 2 X[4992], X[4761] + 2 X[14349], X[4761] - 4 X[17072], X[14349] + 2 X[17072]

X(47816) lies on these lines: {2, 830}, {514, 14430}, {784, 1491}, {1734, 3835}, {2254, 4129}, {2530, 3762}, {3837, 4705}, {4151, 4728}, {4730, 4992}, {4761, 14349}, {4776, 6005}

X(47816) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 21260, 1577}, {1734, 3835, 4170}, {2530, 21051, 3762}, {3837, 4705, 4978}, {14349, 17072, 4761}

X(47817) = X(512)X(4448)∩X(514)X(14413)

X(47817) = 2 X[659] + X[1577], 2 X[667] + X[3762], 2 X[3716] + X[4063], 4 X[3716] - X[4170], 2 X[4063] + X[4170], 2 X[4040] + X[4761], 2 X[4057] + X[4086], X[4391] + 2 X[4401], 4 X[4874] - X[4978], 2 X[8689] + X[17072]

X(47817) lies on these lines: {512, 4448}, {514, 14413}, {659, 1577}, {667, 3762}, {1635, 8714}, {3716, 4063}, {4040, 4761}, {4057, 4086}, {4108, 6546}, {4391, 4401}, {4874, 4978}, {8689, 17072}

X(47818) = X(2)X(830)∩X(514)X(14413)

X(47818) = 2 X[649] + X[4170], 2 X[659] + X[4978], 2 X[663] + X[4761], 2 X[667] + X[1577], X[667] + 2 X[4874], X[1577] - 4 X[4874], X[693] + 2 X[4401], X[1019] + 2 X[3716], 2 X[1960] + X[2533], 2 X[3733] + X[4985], X[3762] + 2 X[4367], X[3803] + 2 X[4885], X[4040] + 2 X[4369], X[4404] - 4 X[6133], 2 X[4807] + X[4895], 2 X[6050] + X[7662], X[8045] + 2 X[13246]

X(47818) lies on these lines: {2, 830}, {514, 14413}, {649, 4170}, {659, 4978}, {663, 4761}, {667, 814}, {693, 4401}, {826, 4809}, {1019, 3716}, {1635, 4151}, {1960, 2533}, {3733, 4985}, {3762, 4367}, {3803, 4885}, {4040, 4369}, {4404, 6133}, {4448, 6372}, {4807, 4895}, {6050, 7662}, {8045, 13246}

X(47819) = X(388)X(3669)∩X(514)X(14430)

X(47819) =2 X[3669] + X[21301], X[667] - 4 X[19947], X[693] + 2 X[2530], X[693] - 4 X[23815], X[2530] + 2 X[23815], 2 X[764] + X[4462], X[764] + 2 X[21260], X[4462] - 4 X[21260], 2 X[1491] + X[4801], 2 X[2526] + X[17166], X[3777] + 2 X[3837], 2 X[3777] + X[4391], 4 X[3837] - X[4391], X[4905] - 4 X[23814]

X(47819) lies on these lines: {388, 3669}, {514, 14430}, {667, 5253}, {693, 784}, {764, 4462}, {1491, 4801}, {2526, 17166}, {3309, 5603}, {3777, 3837}, {4776, 6372}, {4905, 12047}, {4927, 6362}

X(47819) ={X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {764, 21260, 4462}, {2530, 23815, 693}, {3777, 3837, 4391}

X(47820) = X(2)X(8678)∩X(514)X(14413)

X(47820) = 2 X[650] + X[17166], 2 X[659] + X[4801], X[663] + 2 X[4369], 2 X[667] + X[693], 4 X[1125] - X[14349], 2 X[3733] + X[7650], 2 X[4367] + X[4391], X[4367] + 2 X[4874], X[4391] - 4 X[4874], 2 X[4378] + X[4462], 2 X[4401] + X[4978], X[4474] + 2 X[4504], X[4560] + 2 X[7662], X[4581] + 2 X[6129], X[4822] + 2 X[4932], X[4897] + 2 X[4990], 4 X[6050] - X[17494]

X(47888) lies on these lines: {2, 8678}, {514, 14413}, {650, 17166}, {659, 4801}, {663, 4369}, {667, 693}, {784, 14419}, {1125, 14349}, {3733, 7650}, {4367, 4391}, {4378, 4462}, {4379, 8643}, {4401, 4978}, {4474, 4504}, {4560, 7662}, {4581, 6129}, {4822, 4932}, {4897, 4990}, {6050, 17494}

X(47820) = midpoint of X(4379) and X(8643)
X(47820) = crosspoint of X(4623) and X(37870)
X(47820) = crossdifference of every pair of points on line {21814, 41423}
X(47820) = barycentric product X(513)*X(34283)
X(47820) = barycentric quotient X(34283)/X(668)
X(47820) = {X(4367),X(4874)}-harmonic conjugate of X(4391)

X(47821) = X(2)X(513)∩X(514)X(14432)

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

X(47821) = X[8] + 2 X[4775], X[659] + 2 X[4806], 2 X[659] + X[20295], 4 X[4806] - X[20295], X[661] + 2 X[3716], 5 X[3616] - 2 X[4378], 2 X[3835] + X[4724], 4 X[3835] - X[46403], 2 X[4724] + X[46403], 2 X[4010] + X[17494], X[4040] + 2 X[4129], 2 X[4040] + X[21301], 4 X[4129] - X[21301], 4 X[4874] - X[7192]

X(47821) lies on these lines: {2, 513}, {8, 4775}, {514, 14432}, {522, 4120}, {523, 4800}, {659, 4806}, {661, 3716}, {3616, 4378}, {3835, 4724}, {4010, 17494}, {4040, 4129}, {4379, 4778}, {4874, 7192}, {4927, 4977}

X(47821) = crosssum of X(649) and X(46908)
X(47821) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 4806, 20295}, {3835, 4724, 46403}, {4040, 4129, 21301}

X(47822) = X(2)X(513)∩X(10)X(4775)

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

X(47822) = X[4776] + 2 X[45666], 2 X[10] + X[4775], X[649] + 2 X[4806], 2 X[650] + X[4010], X[659] + 2 X[3835], 2 X[659] + X[24719], 4 X[3835] - X[24719], X[661] + 2 X[4874], X[667] + 2 X[4129], 4 X[1125] - X[4378], X[1491] + 2 X[3716], X[1491] - 4 X[25666], X[3716] + 2 X[25666], 4 X[3239] - X[4122], 2 X[3837] + X[4724], 2 X[3837] - 5 X[30835], X[4724] + 5 X[30835], 2 X[4147] + X[4879], X[4498] + 2 X[4992], X[4824] + 2 X[7662], 4 X[10006] - X[13277]

X(47822) lies on these lines: {2, 513}, {10, 4775}, {522, 4800}, {523, 1639}, {649, 4806}, {650, 4010}, {659, 3835}, {661, 4874}, {667, 4129}, {1125, 4378}, {1491, 3716}, {2238, 3063}, {3239, 4122}, {3837, 4724}, {4147, 4879}, {4207, 16228}, {4379, 4977}, {4498, 4992}, {4777, 17264}, {4824, 7662}, {10006, 13277}

X(47822) = crossdifference of every pair of points on line {3230, 4257}
X(47822) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 3835, 24719}, {3716, 25666, 1491}, {4724, 30835, 3837}

X(47823) = X(2)X(513)∩X(10)X(4378)

X(47823) = 2 X[10] + X[4378], X[649] + 2 X[3837], 2 X[649] + X[24719], 4 X[3837] - X[24719], X[693] + 2 X[9508], 2 X[905] + X[2533], 4 X[1125] - X[4775], X[1491] + 2 X[4369], X[1491] - 4 X[25380], X[4369] + 2 X[25380], X[2254] + 2 X[4874], X[2254] + 5 X[24924], 2 X[4874] - 5 X[24924], 2 X[3835] + X[4784], 2 X[3835] - 5 X[30795], X[4784] + 5 X[30795], X[4010] - 4 X[4885], 2 X[4025] + X[4122], X[4367] + 2 X[17072]

X(47823) lies on these lines: {2, 513}, {10, 4378}, {522, 4809}, {523, 1638}, {649, 3837}, {693, 9508}, {905, 2533}, {1125, 4775}, {1491, 4369}, {2254, 4874}, {3667, 4800}, {3835, 4784}, {4010, 4885}, {4025, 4122}, {4196, 16228}, {4367, 17072}, {4893, 4977}

X(47823) = crossdifference of every pair of points on line {3230, 4262}
X(47823) = barycentric product X(514)*X(32935)
X(47823) = barycentric quotient X(32935)/X(190)
X(47823) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 3837, 24719}, {2254, 24924, 4874}, {4369, 25380, 1491}, {4784, 30795, 3835}

X(47824) = X(2)X(513)∩X(8)X(4378)

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

X(47824) = X[8] + 2 X[4378], 2 X[1491] + X[7192], 2 X[1734] + X[17166], X[2254] + 2 X[4369], 2 X[2533] + X[17496], 5 X[3616] - 2 X[4775], 2 X[3837] + X[4784], 4 X[3837] - X[20295], 2 X[4784] + X[20295], 2 X[3960] + X[4761], 2 X[4885] + X[7659], 4 X[9508] - X[17494], 2 X[9508] + X[21146], X[17494] + 2 X[21146]

X(47824) lies on these lines: {2, 513}, {8, 4378}, {522, 4379}, {523, 4453}, {1491, 7192}, {1734, 17166}, {2254, 4369}, {2533, 17496}, {3616, 4775}, {3837, 4784}, {3960, 4761}, {4778, 4893}, {4885, 7659}, {9508, 17494}

X(47824) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3837, 4784, 20295}, {9508, 21146, 17494}

X(47825) = X(2)X(523)∩X(8)X(4770)

X(47825) = X[2] + 2 X[4948], X[8] - 4 X[4770], X[661] + 2 X[4913], 2 X[1491] + X[17494], 4 X[1491] - X[46403], 2 X[17494] + X[46403], X[4560] + 2 X[4705], 5 X[3617] - 2 X[4774], 2 X[4122] + X[17161], 2 X[4490] + X[17496], 2 X[4824] + X[7192], X[4824] + 2 X[9508], X[7192] - 4 X[9508], 4 X[14838] - X[17166]

X(47825) lies on these lines: {2, 523}, {8, 4770}, {42, 3737}, {99, 5380}, {513, 14404}, {522, 4120}, {661, 4913}, {1491, 17494}, {2605, 17018}, {2787, 4560}, {3617, 4774}, {4122, 17161}, {4490, 17496}, {4777, 17264}, {4824, 7192}, {14838, 17166}

X(47825) = crossdifference of every pair of points on line {187, 16971}
X(47825) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 17494, 46403}, {4824, 9508, 7192}

X(47826) = X(2)X(4778)∩X(44)X(513)

X(47826) = 2 X[659] + X[4813], 2 X[661] + X[4724], X[4382] - 4 X[4806], X[4498] + 2 X[4983]

X(47826) lies on these lines: {2, 4778}, {44, 513}, {351, 8672}, {514, 14432}, {663, 4160}, {2832, 14349}, {4139, 8663}, {4379, 4977}, {4382, 4806}, {4468, 14779}, {4498, 4983}, {4800, 4802}, {4833, 8540}, {4926, 4948}, {4985, 14207}

X(47827) = X(2)X(523)∩X(44)X(513)

X(47827) = X[1] + 2 X[4770], 2 X[2] + X[4948], 4 X[10] - X[4774], 4 X[650] - X[659], 2 X[650] + X[1491], 5 X[650] + X[2526], X[659] + 2 X[1491], 5 X[659] + 4 X[2526], 2 X[661] + X[4784], X[661] + 2 X[9508], 5 X[1491] - 2 X[2526], X[4784] - 4 X[9508], 2 X[905] + X[4490], 2 X[2977] + X[3004], 4 X[3835] - X[4810], 2 X[3837] + X[17494], X[4010] + 2 X[4913], X[4010] - 4 X[25666], X[4913] + 2 X[25666], 2 X[4041] + X[4879], X[4367] + 2 X[4705], X[4367] - 4 X[14838], X[4705] + 2 X[14838], 2 X[4369] + X[4824], X[4467] + 2 X[18004], X[4963] + 2 X[7192]

X(47827) lies on these lines: {1, 4770}, {2, 523}, {10, 4774}, {42, 2605}, {43, 3737}, {44, 513}, {522, 4800}, {905, 4490}, {2276, 3709}, {2530, 2832}, {2977, 3004}, {3835, 4810}, {3837, 17494}, {4010, 4913}, {4041, 4879}, {4160, 4367}, {4369, 4824}, {4379, 4802}, {4467, 18004}, {4963, 7192}, {9253, 14395}, {9397, 14414}

X(47827) = midpoint of X(4705) and X(14419)
X(47827) = reflection of X(i) in X(j) for these {i,j}: {4367, 14419}, {14419, 14838}
X(47827) = X(7608)-Ceva conjugate of X(11)
X(47827) = X(6)-isoconjugate of X(35180)
X(47827) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 35180), (35134, 75)
X(47827) = crossdifference of every pair of points on line {1, 187}
X(47827) = X(4770)-line conjugate of X(1)
X(47827) = barycentric product X(i)*X(j) for these {i,j}: {513, 29615}, {1019, 4535}, {4391, 19369}
X(47827) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 35180}, {4535, 4033}, {19369, 651}, {29615, 668}
X(47827) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 1491, 659}, {661, 9508, 4784}, {4705, 14838, 4367}, {4913, 25666, 4010}

X(47828) = X(2)X(522)∩X(44)X(513)

X(47828) = 2 X[1] + X[4814], 4 X[10] - X[4474], X[649] + 2 X[1491], X[649] - 4 X[9508], 2 X[650] + X[2254], 4 X[650] - X[4724], 2 X[656] + X[17418], X[1491] + 2 X[9508], 2 X[2254] + X[4724], X[2526] + 2 X[4394], 2 X[4784] + X[4813], 4 X[8043] - X[46385], X[663] + 2 X[1734], X[663] - 4 X[14838], X[1734] + 2 X[14838], X[693] + 2 X[4913], X[693] - 4 X[25380], X[4913] + 2 X[25380], 2 X[905] + X[4041], 4 X[905] - X[4449], 2 X[4041] + X[4449], 2 X[3126] + X[45755], 5 X[1698] - 2 X[4791], 2 X[2530] + X[4498], 4 X[3837] - X[4382], 2 X[4025] + X[4088], 2 X[4147] + X[17496], X[4378] + 2 X[4770], X[4467] + 2 X[4522], X[4560] + 2 X[17072], X[4804] - 4 X[4885], X[4825] + 2 X[14422]

X(47828) lies on these lines: {1, 4814}, {2, 522}, {10, 4474}, {42, 1459}, {44, 513}, {521, 14392}, {523, 1638}, {663, 1734}, {693, 4913}, {905, 4041}, {1643, 3126}, {1698, 4791}, {2276, 6586}, {2530, 4498}, {3005, 4139}, {3676, 4608}, {3837, 4382}, {3900, 14414}, {3989, 4951}, {4025, 4088}, {4147, 17496}, {4378, 4770}, {4467, 4522}, {4560, 17072}, {4800, 4926}, {4802, 4948}, {4804, 4885}, {4825, 14422}

X(47828) = midpoint of X(4041) and X(14413)
X(47828) = reflection of X(i) in X(j) for these {i,j}: {4449, 14413}, {14413, 905}
X(47828) = X(i)-isoconjugate of X(j) for these (i,j): {2, 28899}, {4588, 32631}
X(47828) = X(32664)-Dao conjugate of X(28899)
X(47828) = crossdifference of every pair of points on line {1, 1055}
X(47828) = X(4814)-line conjugate of X(1)
X(47828) = barycentric product X(i)*X(j) for these {i,j}: {1, 28898}, {513, 17294}, {514, 5220}, {693, 41423}, {4791, 19654}
X(47828) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28899}, {4893, 32631}, {5220, 190}, {17294, 668}, {19654, 4604}, {28898, 75}, {41423, 100}
X(47828) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 2254, 4724}, {905, 4041, 4449}, {1491, 9508, 649}, {1734, 14838, 663}, {4913, 25380, 693}

X(47829) = X(2)X(523)∩X(513)X(4763)

X(47829) = 5 X[2] + X[4948], 4 X[44567] - X[45314], 2 X[44567] + X[45323], X[45314] + 2 X[45323], X[45315] + 2 X[45691], 2 X[650] + X[3837], 2 X[1125] + X[4770], 2 X[14838] + X[21051], X[4774] - 7 X[9780], X[4806] + 2 X[9508], X[4806] - 4 X[25666], X[9508] + 2 X[25666], 2 X[17069] + X[18004]

X(47829) lies on these lines: {2, 523}, {43, 2605}, {513, 4763}, {650, 3837}, {1125, 4770}, {1575, 3709}, {2787, 14838}, {3737, 16569}, {4774, 9780}, {4806, 9508}, {4893, 4977}, {17069, 18004}

X(47829) = crossdifference of every pair of points on line {187, 37590}
X(47829) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9508, 25666, 4806}, {44567, 45323, 45314}

X(47830) = X(2)X(522)∩X(513)X(4763)

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

X(47830) = 2 X[44567] + X[45328], 4 X[44567] - X[45673], X[45313] + 2 X[45323], X[45313] - 4 X[45691], X[45323] + 2 X[45691], 2 X[45328] + X[45673], 2 X[905] + X[4147], 4 X[2516] - X[4830], 2 X[2977] + X[3776], 5 X[3616] + X[4814], 4 X[3634] - X[4791], X[3835] + 2 X[9508], X[4458] - 4 X[7658], X[4474] - 7 X[9780], X[4522] + 2 X[17069], 2 X[4885] + X[4913], 2 X[14838] + X[17072]

X(47830) lies on these lines: {2, 522}, {43, 1459}, {513, 4763}, {657, 17754}, {905, 4147}, {1575, 6586}, {2516, 4830}, {2977, 3776}, {3616, 4814}, {3634, 4791}, {3835, 9508}, {4458, 7658}, {4474, 9780}, {4522, 17069}, {4778, 4893}, {4800, 4962}, {4885, 4913}, {14838, 17072}

X(47830) = crossdifference of every pair of points on line {1055, 10987}
X(47830) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {44567, 45328, 45673}, {45323, 45691, 45313}

X(47831) = X(2)X(522)∩X(513)X(3716)

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

X(47831) = X[3716] + 2 X[4885], 2 X[3716] + X[24720], X[3835] + 2 X[4874], 2 X[4806] + X[4932], 4 X[4885] - X[24720], 2 X[676] + X[4522], 2 X[1125] + X[4791], 2 X[3239] + X[4458], 5 X[3616] + X[4474], X[4814] - 7 X[9780]

X(47831) lies on these lines: {2, 522}, {513, 3716}, {676, 4522}, {1125, 4791}, {3239, 4458}, {3616, 4474}, {3667, 4800}, {3887, 17072}, {4147, 14077}, {4379, 4778}, {4391, 14413}, {4521, 4893}, {4814, 9780}, {4962, 13246}

X(47831) = midpoint of X(4391) and X(14413)
X(47831) = X(i)-complementary conjugate of X(j) for these (i,j): {28899, 2}, {32631, 15614}
X(47831) = crossdifference of every pair of points on line {1055, 2176}
X(47831) = {X(3716),X(4885)}-harmonic conjugate of X(24720)

X(47832) = X(2)X(522)∩X(513)X(4379)

X(47832) = 2 X[1] + X[4474], X[1] + 2 X[4791], X[4474] - 4 X[4791], 4 X[10] - X[4814], X[4379] + 2 X[4800], X[31147] - 4 X[45342], X[649] + 2 X[4010], X[649] - 4 X[4874], X[4010] + 2 X[4874], 2 X[650] + X[4804], 2 X[659] + X[4382], X[661] + 2 X[7662], X[663] + 2 X[1577], 2 X[676] + X[3700], X[693] + 2 X[3716], 2 X[693] + X[4724], 4 X[3716] - X[4724], X[2254] - 4 X[4885], 4 X[3239] - X[4088], 2 X[3239] + X[47123], X[4088] + 2 X[47123], X[4040] + 2 X[4823], 2 X[4391] + X[4449], 2 X[4782] + X[4810], 4 X[4806] - X[4813], 2 X[4990] + X[7178], X[7650] + 2 X[8062], 2 X[7650] + X[17418], 4 X[8062] - X[17418]

X(47832) lies on these lines: {1, 4474}, {2, 522}, {10, 4814}, {42, 4036}, {350, 3261}, {513, 4379}, {514, 14432}, {523, 1639}, {649, 4010}, {650, 4804}, {659, 4382}, {661, 7662}, {663, 1577}, {676, 3700}, {693, 3716}, {814, 8643}, {1459, 3720}, {2254, 4885}, {3239, 4088}, {4040, 4823}, {4391, 4449}, {4782, 4810}, {4806, 4813}, {4990, 7178}, {7650, 8062}, {14077, 14430}

X(47832) = reflection of X(14430) in X(45664)
X(47832) = crossdifference of every pair of points on line {1055, 4257}
X(47832) = barycentric product X(514)*X(5695)
X(47832) = barycentric quotient X(5695)/X(190)
X(47832) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4791, 4474}, {693, 3716, 4724}, {3239, 47123, 4088}, {4010, 4874, 649}, {7650, 8062, 17418}

X(47833) = X(2)X(523)∩X(513)X(4379)

X(47833) = 2 X[1] + X[4774], 4 X[2] - X[4948], 2 X[4379] + X[4800], X[31148] + 2 X[45342], 2 X[649] + X[4810], X[659] + 2 X[693], X[659] - 4 X[4874], X[693] + 2 X[4874], 4 X[661] - X[4963], X[667] + 2 X[4823], X[1491] - 4 X[4885], X[1491] + 2 X[7662], 2 X[1491] - 5 X[30795], 2 X[4885] + X[7662], 8 X[4885] - 5 X[30795], 4 X[7662] + 5 X[30795], 2 X[1577] + X[4367], 5 X[1698] - 2 X[4770], 2 X[2533] + X[4879], X[3801] + 2 X[8045], X[4010] + 2 X[4369], 2 X[4010] + X[4784], 4 X[4369] - X[4784], X[4122] + 2 X[4458], X[4378] + 2 X[4791], X[4382] + 2 X[4782], X[4804] + 2 X[9508], X[4804] + 5 X[24924], 2 X[9508] - 5 X[24924], 2 X[4806] + X[7192]

X(47833) lies on these lines: {1, 4774}, {2, 523}, {350, 4374}, {513, 4379}, {522, 4809}, {649, 4810}, {659, 693}, {661, 4963}, {667, 4823}, {1491, 4885}, {1577, 2787}, {1698, 4770}, {2533, 4879}, {2605, 3720}, {3801, 8045}, {4010, 4369}, {4122, 4458}, {4160, 14431}, {4378, 4791}, {4382, 4782}, {4802, 4893}, {4804, 9508}, {4806, 7192}, {4927, 4977}

X(47833) = reflection of X(14431) in X(45324)
X(47833) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 4874, 659}, {1491, 4885, 30795}, {4010, 4369, 4784}, {4804, 24924, 9508}, {4885, 7662, 1491}

X(47834) = X(2)X(523)∩X(320)X(350)

X(47834) = 5 X[2] - 2 X[4948], X[145] + 2 X[4774], X[693] + 2 X[7662], 4 X[693] - X[46403], 2 X[4010] + X[7192], 8 X[7662] + X[46403], 2 X[1577] + X[17166], X[4024] + 2 X[4458], 2 X[4369] + X[4804], X[4581] + 2 X[4815], 4 X[4770] - 7 X[9780], 4 X[4874] - X[17494]

X(47834) lies on these lines: {2, 523}, {145, 4774}, {320, 350}, {514, 14432}, {522, 4379}, {1577, 4160}, {2832, 4978}, {3720, 3737}, {3741, 5214}, {4024, 4458}, {4369, 4804}, {4374, 4441}, {4521, 4893}, {4560, 14419}, {4581, 4815}, {4770, 9780}, {4800, 4977}, {4874, 17494}

X(47834) = midpoint of X(17166) and X(30709)
X(47834) = reflection of X(i) in X(j) for these {i,j}: {4560, 14419}, {30709, 1577}
X(47834) = X(35180)-anticomplementary conjugate of X(69)
X(47834) = crosspoint of X(86) and X(35180)
X(47834) = crossdifference of every pair of points on line {187, 213}
X(47834) = barycentric product X(693)*X(37675)
X(47834) = barycentric quotient X(37675)/X(100)

X(47835) = X(2)X(4083)∩X(10)X(667)

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

X(47835) = 2 X[10] + X[667], 2 X[650] + X[2533], X[656] + 2 X[6133], X[659] + 2 X[17072], 5 X[1698] + X[4063], 5 X[1698] - 2 X[21260], 10 X[1698] - X[24719], X[4063] + 2 X[21260], 2 X[4063] + X[24719], 4 X[21260] - X[24719], 2 X[2977] + X[7178], X[3801] - 4 X[14837], 2 X[3837] + X[4498], X[4041] + 2 X[4874], 2 X[4129] + X[4834], 2 X[4147] + X[4367], X[4147] + 2 X[31286], X[4367] - 4 X[31286], 2 X[4369] + X[4490], X[4391] + 2 X[9508], X[4775] + 2 X[4807], 2 X[4782] + 7 X[9780], 2 X[4782] + X[21301], 7 X[9780] - X[21301]

X(47835) lies on these lines: {2, 4083}, {10, 667}, {650, 2533}, {656, 6133}, {659, 17072}, {814, 1635}, {1639, 3566}, {1698, 4063}, {2977, 7178}, {3309, 4448}, {3801, 14837}, {3837, 4498}, {3907, 4763}, {4041, 4874}, {4129, 4834}, {4147, 4367}, {4369, 4490}, {4391, 9508}, {4775, 4807}, {4782, 9780}, {4905, 5445}

X(47835) = midpoint of X(1635) and X(21052)
X(47835) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1698, 4063, 21260}, {4063, 21260, 24719}, {4147, 31286, 4367}

X(47836) = X(1)X(4087)∩X(2)X(512)

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

X(47836) = X[1] + 2 X[4807], X[8] + 2 X[4367], 2 X[10] + X[1019], X[649] + 2 X[17072], 2 X[649] + X[21301], 4 X[17072] - X[21301], 2 X[656] + X[4581], 5 X[1698] - 2 X[4129], 2 X[2533] + X[4560], X[2533] + 2 X[9508], X[4560] - 4 X[9508], 5 X[3616] - 2 X[4879], X[4041] + 2 X[4369], 2 X[4041] + X[17166], 4 X[4369] - X[17166], 2 X[4705] + X[7192], X[4761] + 2 X[14838], 2 X[4784] + 7 X[9780], X[4784] + 2 X[21051], 7 X[9780] - 4 X[21051], 4 X[4806] - 13 X[19877]

X(47836) lies on these lines: {1, 4807}, {2, 512}, {8, 4367}, {10, 1019}, {649, 17072}, {656, 4581}, {1574, 14991}, {1698, 4129}, {1788, 7178}, {2533, 4560}, {3616, 4879}, {4041, 4369}, {4705, 7192}, {4761, 14838}, {4784, 9780}, {4806, 19877}, {14018, 14618}

X(47836) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 17072, 21301}, {2533, 9508, 4560}, {4041, 4369, 17166}

X(47837) = X(2)X(512)∩X(10)X(4367)

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

X(47837) = 2 X[10] + X[4367], X[667] + 2 X[17072], X[667] - 4 X[31286], X[17072] + 2 X[31286], X[1019] + 5 X[1698], X[1019] + 2 X[21051], 5 X[1698] - 2 X[21051], 2 X[1125] + X[4807], 4 X[1125] - X[4879], 2 X[4807] + X[4879], X[1577] + 2 X[9508], X[1734] + 2 X[4874], X[2533] + 2 X[14838], 4 X[3634] - X[4129], 8 X[3634] + X[4784], 2 X[4129] + X[4784], 2 X[3835] + X[4834], 2 X[3835] - 5 X[31251], X[4834] + 5 X[31251], 2 X[3837] + X[4063], 2 X[4147] + X[4378], 2 X[4369] + X[4705], X[4374] + 2 X[17990], 2 X[4458] + X[4808], 2 X[4770] + X[17166]

X(47837) lies on these lines: {2, 512}, {10, 4367}, {667, 17072}, {1019, 1698}, {1125, 4807}, {1577, 9508}, {1734, 4874}, {2533, 14838}, {3634, 4129}, {3835, 4834}, {3837, 4063}, {3907, 14419}, {4147, 4378}, {4369, 4705}, {4374, 17990}, {4458, 4808}, {4770, 17166}, {4789, 6367}, {6002, 14431}, {14018, 16229}, {17899, 18003}

X(47837) = crosspoint of X(1268) and X(4598)
X(47837) = crosssum of X(i) and X(j) for these (i,j): {2308, 20979}, {3056, 9404}
X(47837) = crossdifference of every pair of points on line {3231, 10987}
X(47837) = barycentric product X(514)*X(32938)
X(47837) = barycentric quotient X(32938)/X(190)
X(47837) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1019, 1698, 21051}, {1125, 4807, 4879}, {4834, 31251, 3835}, {17072, 31286, 667}

X(47838) = X(2)X(6005)∩X(514)X(14432)

Barycentrics (b - c)*(a^3 - 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(47838) = 2 X[650] + X[4170], X[663] + 2 X[4129], X[667] + 2 X[4806], 2 X[3716] + X[14349], X[3803] + 2 X[4940], 2 X[3835] + X[4040], 2 X[4874] + X[4983]

X(47838) lies on these lines: {2, 6005}, {514, 14432}, {650, 4170}, {663, 4129}, {667, 4806}, {784, 4800}, {830, 4776}, {1639, 3800}, {3716, 14349}, {3803, 4940}, {3835, 4040}, {4151, 4893}, {4874, 4983}

X(47839) = X(2)X(512)∩X(10)X(4879)

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

X(47839) = 2 X[10] + X[4879], X[663] + 2 X[21260], X[663] + 5 X[30835], 2 X[21260] - 5 X[30835], X[667] + 2 X[3835], X[1019] - 7 X[3624], X[1019] + 2 X[4806], 7 X[3624] + 2 X[4806], 2 X[1125] + X[4129], 4 X[1125] - X[4367], 2 X[4129] + X[4367], X[2530] + 2 X[3716], 4 X[3634] - X[4807], 2 X[3837] + X[4040], X[4010] + 2 X[14838], X[4063] + 2 X[4992], X[4106] + 2 X[6050], X[4170] + 2 X[9508], 2 X[4369] + X[4983], X[4775] + 2 X[17072], X[4775] + 5 X[31251], 2 X[17072] - 5 X[31251], X[4784] - 10 X[19862], 2 X[4874] + X[14349]

X(47839) lies on these lines: {2, 512}, {10, 4879}, {663, 15283}, {667, 3835}, {1019, 3624}, {1125, 4129}, {2530, 3716}, {3634, 4807}, {3837, 4040}, {3907, 14431}, {4010, 14838}, {4063, 4992}, {4106, 6050}, {4170, 9508}, {4369, 4983}, {4775, 17072}, {4784, 19862}, {4800, 8714}, {4874, 14349}, {6002, 14419}, {7178, 11375}, {10278, 14844}

X(47839) = barycentric product X(514)*X(32936)
X(47839) = barycentric quotient X(32936)/X(190)
X(47839) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 30835, 21260}, {1125, 4129, 4367}, {4775, 31251, 17072}

X(47840) = X(2)X(512)∩X(514)X(14432)

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

X(47840) = X[1] + 2 X[4129], X[8] + 2 X[4879], X[8] - 4 X[21051], X[4879] + 2 X[21051], X[659] + 2 X[4992], 2 X[661] + X[17166], X[663] + 2 X[3835], 2 X[663] + X[21301], 4 X[3835] - X[21301], X[1019] - 4 X[1125], 5 X[1698] - 2 X[4807], X[3004] + 2 X[4990], 5 X[3616] - 2 X[4367], 5 X[3616] + 4 X[4806], X[4367] + 2 X[4806], 2 X[4010] + X[4560], X[4170] + 2 X[14838], 2 X[4369] + X[4822], X[4380] - 4 X[6050], 2 X[4455] + X[17217], X[4581] - 4 X[8062], 2 X[4784] - 11 X[5550], 2 X[4983] + X[7192]

X(47840) lies on these lines: {1, 4129}, {2, 512}, {8, 4879}, {514, 14432}, {650, 4839}, {659, 4992}, {661, 17166}, {663, 3835}, {1019, 1125}, {1698, 4807}, {3004, 4990}, {3485, 7178}, {3616, 4367}, {4010, 4560}, {4170, 14838}, {4369, 4822}, {4380, 6050}, {4455, 17217}, {4581, 8062}, {4776, 8678}, {4784, 5550}, {4983, 7192}, {5216, 19863}

X(47840) = crosspoint of X(86) and X(27805)
X(47840) = crosssum of X(42) and X(20981)
X(47840) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 3835, 21301}, {4879, 21051, 8}

X(47841) = X(2)X(4083)∩X(649)X(4992)

X(47841) = X[649] + 2 X[4992], X[663] + 2 X[3837], X[667] - 4 X[1125], 2 X[667] + X[24719], 8 X[1125] + X[24719], 2 X[905] + X[4010], X[2533] - 4 X[4885], 7 X[3624] - X[4063], 7 X[3624] - 4 X[31288], X[4063] - 4 X[31288], 2 X[3716] + X[3777], X[3801] + 2 X[6332], 2 X[3835] + X[4367], 2 X[4129] + X[4378], 2 X[4782] - 11 X[5550], X[4879] + 2 X[17072], X[4879] + 5 X[30795], 2 X[17072] - 5 X[30795], X[4905] - 4 X[19947]

X(47841) lies on these lines: {2, 4083}, {649, 4992}, {663, 3837}, {667, 1125}, {693, 18077}, {814, 4728}, {905, 4010}, {1638, 3566}, {2533, 4885}, {3309, 5886}, {3624, 4063}, {3669, 11375}, {3716, 3777}, {3801, 6332}, {3835, 4367}, {3907, 4928}, {4129, 4378}, {4162, 11376}, {4782, 5550}, {4879, 17072}, {4905, 5443}

X(47841) = crosssum of X(42) and X(23472)
X(47841) = barycentric product X(514)*X(32934)
X(47841) = barycentric quotient X(32934)/X(190)
X(47841) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3624, 4063, 31288}, {4879, 30795, 17072}

X(47842) = X(44)X(513)∩X(522)X(4129)

X(47842) lies on these lines: {44, 513}, {522, 4129}, {523, 1577}, {810, 2605}, {830, 4057}, {834, 14349}, {2485, 3709}, {2530, 4977}, {3004, 14208}, {3733, 14838}, {3737, 9013}, {4041, 4132}, {4139, 4770}, {4490, 4802}, {4833, 6003}, {4840, 15309}, {4858, 7668}, {4879, 8702}, {8287, 17463}, {8672, 17990}

X(47842) = midpoint of X(656) and X(661)
X(47842) = reflection of X(i) in X(j) for these {i,j}: {1577, 31946}, {3733, 14838}, {4036, 21051}
X(47842) = X(i)-complementary conjugate of X(j) for these (i,j): {42, 5517}, {1036, 34589}, {1245, 11}, {1310, 3741}, {1472, 244}, {2221, 17761}, {2281, 1086}, {32691, 942}, {36099, 34830}, {37215, 21240}
X(47842) = X(i)-Ceva conjugate of X(j) for these (i,j): {2282, 3708}, {14349, 42664}, {17038, 2643}, {37218, 4016}, {45746, 23879}
X(47842) = X(i)-isoconjugate of X(j) for these (i,j): {58, 835}, {110, 43531}, {662, 2214}, {1333, 37218}, {4570, 43927}
X(47842) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 835), (37, 37218), (244, 43531), (1084, 2214), (39016, 81), (41849, 799)
X(47842) = crosspoint of X(i) and X(j) for these (i,j): {14349, 45746}, {27808, 34258}
X(47842) = crossdifference of every pair of points on line {1, 1333}
X(47842) = barycentric product X(i)*X(j) for these {i,j}: {1, 23879}, {10, 14349}, {37, 45746}, {75, 42664}, {81, 23282}, {321, 834}, {386, 1577}, {469, 656}, {512, 33935}, {523, 28606}, {649, 42714}, {661, 5224}, {3125, 33948}, {3876, 7178}, {4041, 33949}, {8637, 27801}, {14208, 44103}
X(47842) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 37218}, {37, 835}, {386, 662}, {469, 811}, {512, 2214}, {661, 43531}, {834, 81}, {3125, 43927}, {3876, 645}, {5224, 799}, {8637, 1333}, {14349, 86}, {23282, 321}, {23879, 75}, {28606, 99}, {33935, 670}, {33948, 4601}, {33949, 4625}, {42664, 1}, {42714, 1978}, {44103, 162}, {45746, 274}
X(47842) = {X(8287),X(20975)}-harmonic conjugate of X(17463)

X(47843) = X(513)X(3716)∩X(522)X(4823)

X(47843) lies on these lines: {513, 3716}, {522, 4823}, {523, 17072}, {656, 693}, {1734, 4815}, {2254, 7650}, {2517, 4017}, {3667, 14288}, {4147, 4802}, {4905, 4985}, {6590, 8061}

X(47843) = midpoint of X(i) and X(j) for these {i,j}: {656, 693}, {1734, 4815}, {2254, 7650}, {2517, 4017}, {4905, 4985}
X(47843) = reflection of X(i) in X(j) for these {i,j}: {8062, 4885}, {21187, 21188}
X(47843) = X(i)-complementary conjugate of X(j) for these (i,j): {2215, 1086}, {2335, 26932}, {36077, 942}, {36080, 2}
X(47843) = crossdifference of every pair of points on line {2174, 2176}

X(47844) = X(522)X(1019)∩X(523)X(1325)

X(47844) lies on these lines: {242, 514}, {320, 350}, {522, 1019}, {523, 1325}, {656, 4369}, {661, 8062}, {900, 4840}, {1632, 4565}, {1634, 4552}, {2484, 6590}, {2517, 8678}, {3267, 4374}, {4064, 8045}, {4086, 4160}, {4490, 6133}, {4778, 4960}, {4833, 4977}, {15419, 17212}

X(47844) = midpoint of X(i) and X(j) for these {i,j}: {1019, 5214}, {4581, 17166}, {7192, 7253}
X(47844) = reflection of X(i) in X(j) for these {i,j}: {656, 4369}, {661, 8062}, {4064, 8045}, {4490, 6133}, {4560, 3733}, {7650, 7662}
X(47844) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {835, 1330}, {2214, 21221}, {37218, 21287}, {43531, 3448}
X(47844) = X(i)-isoconjugate of X(j) for these (i,j): {42, 1310}, {71, 36099}, {72, 32691}, {100, 1245}, {190, 2281}, {213, 37215}, {1018, 2221}, {1036, 4551}, {1039, 23067}, {1472, 3952}, {2339, 4559}
X(47844) = X(i)-Dao conjugate of X(j) for these (i, j): (5515, 10), (6590, 23879), (6626, 37215), (8054, 1245), (17421, 72), (26933, 41340), (40181, 1018), (40592, 1310), (40625, 30479)
X(47844) = cevapoint of X(6590) and X(8678)
X(47844) = crosspoint of X(99) and X(37870)
X(47844) = crosssum of X(i) and X(j) for these (i,j): {42, 42664}, {2300, 8637}, {21670, 23282}
X(47844) = trilinear pole of line {5515, 5517}
X(47844) = crossdifference of every pair of points on line {71, 213}
X(47844) = barycentric product X(i)*X(j) for these {i,j}: {27, 23874}, {81, 2517}, {86, 6590}, {274, 8678}, {286, 2522}, {310, 2484}, {388, 4560}, {514, 1010}, {612, 7199}, {648, 26933}, {649, 44154}, {693, 2303}, {1019, 4385}, {2285, 18155}, {2345, 7192}, {3261, 44119}, {3974, 17096}, {4206, 15413}, {4391, 5323}, {6385, 8646}, {7102, 15419}, {7103, 15411}, {7253, 7365}, {14594, 17197}
X(47844) = barycentric quotient X(i)/X(j) for these {i,j}: {28, 36099}, {81, 1310}, {86, 37215}, {388, 4552}, {612, 1018}, {649, 1245}, {667, 2281}, {1010, 190}, {1460, 4559}, {1474, 32691}, {2285, 4551}, {2286, 23067}, {2303, 100}, {2345, 3952}, {2484, 42}, {2517, 321}, {2522, 72}, {3733, 2221}, {3737, 2339}, {3974, 30730}, {4206, 1783}, {4320, 1020}, {4385, 4033}, {4560, 30479}, {5323, 651}, {5515, 23879}, {6590, 10}, {7085, 4574}, {7252, 1036}, {7365, 4566}, {8646, 213}, {8678, 37}, {23874, 306}, {26933, 525}, {44119, 101}, {44154, 1978}

X(47845) = X(242)X(514)∩X(523)X(7478)

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

X(47845) lies on these lines: {2, 9013}, {86, 4833}, {242, 514}, {523, 7478}, {900, 3733}, {1019, 6006}, {1474, 17926}, {2303, 7252}, {2605, 4581}, {4369, 4648}, {4560, 4777}

X(47845) = crossdifference of every pair of points on line {71, 21796}
X(47845) = X(i)-isoconjugate of X(j) for these (i,j): {72, 9088}, {3478, 4551}
X(47845) = barycentric product X(i)*X(j) for these {i,j}: {27, 9031}, {514, 4234}, {1019, 4737}, {3476, 4560}
X(47845) = barycentric quotient X(i)/X(j) for these {i,j}: {1474, 9088}, {3476, 4552}, {4234, 190}, {4737, 4033}, {7252, 3478}, {9031, 306}

X(47846) = ISOGONAL CONJUGATE OF X(15371)

X(47846) lies on the cubic K517 and these lines: {2, 8890}, {76, 141}, {83, 3224}, {99, 11325}, {194, 35524}, {305, 626}, {315, 1899}, {427, 7752}, {670, 7754}, {1506, 11059}, {2207, 6331}, {3266, 7912}, {5025, 35540}, {5989, 10828}, {6292, 40022}, {6382, 33941}, {6383, 33940}, {7763, 37337}, {7782, 35924}, {7803, 9230}, {7879, 33769}, {7938, 8024}, {8920, 12203}, {33786, 39080}

X(47846) = isogonal conjugate of X(15371)
X(47846) = orthic-isogonal conjugate of X(76)
X(47846) = X(4)-Ceva conjugate of X(76)
X(47846) = X(1)-isoconjugate of X(15371)
X(47846) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 15371), (305, 69)
X(47846) = barycentric product X(18022)*X(19597)
X(47846) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 15371}, {19597, 184}
X(47846) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1502, 6656, 76}, {5254, 30736, 40050}, {5254, 40050, 76}

X(47847) = POLAR CONJUGATE OF X(7754)

X(47847) lies on the cubic K517 and these lines: {4, 19568}, {22, 36898}, {25, 6179}, {193, 1843}, {305, 2971}, {427, 7752}, {2374, 8770}, {3291, 6353}, {8940, 8956}

X(47847) = polar conjugate of X(7754)
X(47847) = X(i)-cross conjugate of X(j) for these (i,j): {141, 4}, {3981, 2052}
X(47847) = X(i)-isoconjugate of X(j) for these (i,j): {48, 7754}, {184, 18056}
X(47847) = X(i)-Dao conjugate of X(j) for these (i, j): (1249, 7754), (40938, 19568)
X(47847) = cevapoint of X(523) and X(2971)
X(47847) = crosssum of X(3167) and X(19597)
X(47847) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 7754}, {92, 18056}, {427, 19568}

X(47848) = X(347)-CEVA CONJUGATE OF X(1)

X(47848) lies on the cubic K343 and these lines: {1, 84}, {3, 41403}, {9, 223}, {19, 57}, {34, 10396}, {40, 3182}, {46, 9572}, {63, 347}, {77, 34035}, {109, 7070}, {207, 8885}, {219, 34488}, {226, 41010}, {281, 8808}, {610, 7011}, {664, 3719}, {971, 38288}, {1020, 1763}, {1035, 1490}, {1108, 1407}, {1396, 40979}, {1419, 18675}, {1427, 8557}, {1456, 30223}, {1461, 34499}, {1465, 1723}, {1617, 3220}, {1630, 7125}, {1708, 16572}, {1711, 5018}, {1712, 42451}, {1744, 6357}, {1762, 43045}, {1785, 15239}, {2003, 34492}, {2124, 3929}, {2182, 6611}, {3101, 7013}, {3176, 3341}, {4641, 43064}, {5437, 37695}, {6762, 34039}, {10365, 39130}, {10382, 15285}, {10571, 31435}, {11372, 40960}, {18652, 31600}, {28606, 34028}, {34042, 40937}, {37818, 40660}

X(47848) = reflection of X(196) in X(36908)
X(47848) = isotomic conjugate of the polar conjugate of X(207)
X(47848) = X(i)-Ceva conjugate of X(j) for these (i,j): {63, 57}, {347, 1}, {5932, 1490}, {18623, 223}
X(47848) = X(3197)-cross conjugate of X(1490)
X(47848) = X(i)-isoconjugate of X(j) for these (i,j): {2, 7037}, {3, 40838}, {6, 1034}, {8, 7152}, {9, 3345}, {55, 41514}, {63, 7007}, {219, 7149}, {282, 3342}, {284, 8806}, {2287, 8811}, {3347, 3351}, {7118, 47634}, {7367, 46352}, {8058, 8064}
X(47848) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 1034), (223, 41514), (278, 92), (282, 280), (478, 3345), (3162, 7007), (13612, 3239), (32664, 7037), (36103, 40838), (40590, 8806)
X(47848) = cevapoint of X(i) and X(j) for these (i,j): {1035, 3197}, {8803, 30456}
X(47848) = X(25201)-lineconjugate of X(43656)
X(47848) = barycentric product X(i)*X(j) for these {i,j}: {1, 5932}, {7, 1490}, {56, 33672}, {63, 40837}, {69, 207}, {75, 1035}, {77, 3176}, {85, 3197}, {221, 47436}, {307, 8885}, {342, 46881}, {347, 3341}, {934, 14302}, {3668, 13614}, {5930, 47637}, {8063, 37141}
X(47848) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1034}, {19, 40838}, {25, 7007}, {31, 7037}, {34, 7149}, {56, 3345}, {57, 41514}, {65, 8806}, {207, 4}, {221, 3342}, {347, 47634}, {604, 7152}, {1035, 1}, {1042, 8811}, {1490, 8}, {3176, 318}, {3197, 9}, {3341, 280}, {5932, 75}, {8885, 29}, {13614, 1043}, {14302, 4397}, {33672, 3596}, {40837, 92}, {46881, 271}, {47438, 2192}, {47637, 5931}
X(47848) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2956, 1498}, {222, 43044, 1422}, {1020, 1763, 40212}, {1435, 26934, 57}, {34032, 43058, 223}

X(47849) = ISOGONAL CONJUGATE OF X(1712)

X(47849) lies on the cubic K343 and these lines: {9, 3341}, {40, 3182}, {57, 3342}, {63, 1712}, {84, 3347}, {255, 610}, {1819, 6507}

X(47849) = isogonal conjugate of X(1712)
X(47849) = X(i)-cross conjugate of X(j) for these (i,j): {19, 63}, {19614, 1}
X(47849) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1712}, {2, 1033}, {3, 6523}, {4, 1498}, {6, 14361}, {20, 41085}, {25, 6527}, {29, 8803}, {64, 6616}, {393, 6617}, {1172, 8807}, {1249, 3343}, {3172, 47435}, {3183, 3349}, {6525, 46351}, {7952, 8886}, {15466, 47437}, {31944, 42465}
X(47849) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 1712), (9, 14361), (3350, 1895), (6505, 6527), (32664, 1033), (36033, 1498), (36103, 6523)
X(47849) = barycentric product X(i)*X(j) for these {i,j}: {1, 1032}, {63, 3346}, {75, 28783}, {77, 8805}, {78, 8810}, {3344, 19611}, {19614, 47633}
X(47849) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 14361}, {6, 1712}, {19, 6523}, {31, 1033}, {48, 1498}, {63, 6527}, {73, 8807}, {255, 6617}, {610, 6616}, {1032, 75}, {1409, 8803}, {2155, 41085}, {3344, 1895}, {3346, 92}, {8805, 318}, {8810, 273}, {19611, 47435}, {19614, 3343}, {28783, 1}, {47439, 204}

X(47850) = X(19)-CROSS CONJUGATE OF X(9)

X(47850) lies on the cubic K343 and these lines: {1, 268}, {9, 1249}, {40, 219}, {57, 1073}, {63, 347}, {84, 3346}, {282, 44692}, {1034, 3692}, {1260, 2324}, {1295, 8064}, {2270, 15629}, {2328, 7007}, {3347, 8805}

X(47850) = isotomic conjugate of the polar conjugate of X(7007)
X(47850) = X(41514)-Ceva conjugate of X(3345)
X(47850) = X(i)-cross conjugate of X(j) for these (i,j): {19, 9}, {2192, 1}, {7037, 3345}, {17832, 4}, {30457, 282}
X(47850) = X(i)-isoconjugate of X(j) for these (i,j): {2, 1035}, {3, 40837}, {6, 5932}, {7, 3197}, {57, 1490}, {63, 207}, {196, 46881}, {222, 3176}, {223, 3341}, {604, 33672}, {1214, 8885}, {1427, 13614}, {1461, 14302}, {2199, 47436}, {3182, 3352}, {6611, 46350}, {8059, 8063}, {30456, 47637}, {40702, 47438}
X(47850) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 5932), (3161, 33672), (3162, 207), (3351, 347), (5452, 1490), (32664, 1035), (35508, 14302), (36103, 40837)
X(47850) = crosspoint of X(1034) and X(41514)
X(47850) = crosssum of X(i) and X(j) for these (i,j): {1035, 3197}, {8803, 30456}
X(47850) = X(31407)-lineconjugate of X(42216)
X(47850) = barycentric product X(i)*X(j) for these {i,j}: {1, 1034}, {8, 3345}, {9, 41514}, {21, 8806}, {63, 40838}, {69, 7007}, {75, 7037}, {78, 7149}, {280, 3342}, {312, 7152}, {1043, 8811}, {2192, 47634}
X(47850) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 5932}, {8, 33672}, {19, 40837}, {25, 207}, {31, 1035}, {33, 3176}, {41, 3197}, {55, 1490}, {280, 47436}, {1034, 75}, {2188, 46881}, {2192, 3341}, {2299, 8885}, {2328, 13614}, {3342, 347}, {3345, 7}, {3900, 14302}, {7007, 4}, {7037, 1}, {7149, 273}, {7152, 57}, {8064, 37141}, {8806, 1441}, {8811, 3668}, {14298, 8063}, {40838, 92}, {41514, 85}

X(47851) = X(63)-CEVA CONJUGATE OF X(84)

X(47851) lies on the cubic K343 and these lines: {1, 268}, {9, 3341}, {19, 84}, {40, 3348}, {57, 282}, {610, 46881}, {3182, 8894}

X(47851) = X(63)-Ceva conjugate of X(84)
X(47851) = X(8802)-cross conjugate of X(3182)
X(47851) = X(i)-isoconjugate of X(j) for these (i,j): {2, 34167}, {6, 41080}, {223, 3347}, {3342, 3352}, {3354, 46978}
X(47851) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 41080), (32664, 34167), (40836, 92)
X(47851) = barycentric product X(i)*X(j) for these {i,j}: {1, 34162}, {75, 28784}, {271, 42451}, {280, 3182}, {8894, 41081}
X(47851) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 41080}, {31, 34167}, {2192, 3347}, {3182, 347}, {8802, 7952}, {28784, 1}, {34162, 75}, {42451, 342}

X(47852) = X(3)X(34209)∩X(20)X(21316)

Barycentrics 4*a^16 - 13*a^14*b^2 + 8*a^12*b^4 + 14*a^10*b^6 - 15*a^8*b^8 - 9*a^6*b^10 + 18*a^4*b^12 - 8*a^2*b^14 + b^16 - 13*a^14*c^2 + 48*a^12*b^2*c^2 - 52*a^10*b^4*c^2 - 11*a^8*b^6*c^2 + 63*a^6*b^8*c^2 - 50*a^4*b^10*c^2 + 18*a^2*b^12*c^2 - 3*b^14*c^2 + 8*a^12*c^4 - 52*a^10*b^2*c^4 + 96*a^8*b^4*c^4 - 59*a^6*b^6*c^4 + 15*a^4*b^8*c^4 - 6*a^2*b^10*c^4 - 2*b^12*c^4 + 14*a^10*c^6 - 11*a^8*b^2*c^6 - 59*a^6*b^4*c^6 + 34*a^4*b^6*c^6 - 4*a^2*b^8*c^6 + 19*b^10*c^6 - 15*a^8*c^8 + 63*a^6*b^2*c^8 + 15*a^4*b^4*c^8 - 4*a^2*b^6*c^8 - 30*b^8*c^8 - 9*a^6*c^10 - 50*a^4*b^2*c^10 - 6*a^2*b^4*c^10 + 19*b^6*c^10 + 18*a^4*c^12 + 18*a^2*b^2*c^12 - 2*b^4*c^12 - 8*a^2*c^14 - 3*b^2*c^14 + c^16 : :

X(47852) = 2 X[3] + X[34209], X[20] + 2 X[21316], 2 X[140] + X[46632], X[476] + 5 X[38728], X[14851] - 5 X[38728], 4 X[548] - X[21317], 2 X[548] + X[34150], X[21317] + 2 X[34150], 2 X[550] + X[21269], 4 X[3530] - X[14934], 4 X[3628] - X[46045], 4 X[6699] - X[16340], 2 X[6699] + X[38609], X[16340] + 2 X[38609], 2 X[11657] + X[37950], X[12041] + 2 X[22104], 2 X[12079] + X[34153], X[14677] + 2 X[36169], 5 X[15712] - 2 X[47084], 2 X[33505] - 5 X[38794], X[36184] - 4 X[40685]

X(47852) lies on these lines: {3, 34209}, {20, 21316}, {30, 14644}, {140, 46632}, {476, 14851}, {523, 549}, {548, 21317}, {550, 21269}, {3530, 14934}, {3628, 46045}, {5627, 38723}, {6699, 16340}, {11657, 37950}, {12041, 22104}, {12079, 34153}, {14677, 36169}, {14993, 38701}, {15712, 47084}, {16168, 38727}, {33505, 38794}, {36184, 40685}

X(47852) = midpoint of X(i) and X(j) for these {i,j}: {476, 14851}, {5627, 38723}, {14993, 38701}, {15061, 38700}
X(47852) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {548, 34150, 21317}, {6699, 38609, 16340}

X(47853) = X(4)X(13) ∩ X(530)X(41016)

Barycentrics -2*sqrt(3)*(2*a^6+5*(b^2+c^2)*a^4-4*(b^2-c^2)^2*a^2-3*(b^4-c^4)*(b^2-c^2))*S+2*a^8-11*(b^2+c^2)*a^6-(3*b^2+c^2)*(b^2+3*c^2)*a^4+15*(b^4-c^4)*(b^2-c^2)*a^2-(3*b^4-14*b^2*c^2+3*c^4)*(b^2-c^2)^2 : :

X(47853) lies on these lines: {4, 13}, {530, 41016}, {616, 41019}, {618, 33411}, {1503, 47861}, {3424, 42134}, {6115, 41036}, {6669, 41034}, {11488, 36761}, {35751, 41032}, {35752, 41030}, {36769, 41026}, {39838, 42102}, {41018, 47868}, {41024, 47859}, {41028, 47865}, {41038, 47863}

X(47854) = X(4)X(14) ∩ X(531)X(41017)

Barycentrics 2*sqrt(3)*(2*a^6+5*(b^2+c^2)*a^4-4*(b^2-c^2)^2*a^2-3*(b^4-c^4)*(b^2-c^2))*S+2*a^8-11*(b^2+c^2)*a^6-(3*b^2+c^2)*(b^2+3*c^2)*a^4+15*(b^4-c^4)*(b^2-c^2)*a^2-(3*b^4-14*b^2*c^2+3*c^4)*(b^2-c^2)^2 : :

X(47854) lies on these lines: {4, 14}, {531, 41017}, {619, 33410}, {1503, 47862}, {3424, 42133}, {6114, 41037}, {6670, 41035}, {11489, 41458}, {36329, 41033}, {36330, 41031}, {39838, 42101}, {41025, 47860}, {41027, 47867}, {41029, 47866}, {41039, 47864}

X(47855) = X(4)X(13) ∩ X(5)X(10611)

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

X(47855) = X(13)+2*X(47857) = X(15)+2*X(47861) = 2*X(5472)+X(6115) = X(5472)+2*X(11542) = X(6115)-4*X(11542) = 5*X(16960)+X(47859) = X(41020)+2*X(47853)

X(47855) lies on these lines: {4, 13}, {5, 10611}, {15, 47861}, {17, 618}, {62, 6669}, {230, 5472}, {396, 13350}, {397, 6771}, {530, 16267}, {616, 36763}, {3389, 13917}, {3390, 13982}, {5459, 22511}, {5473, 42152}, {5615, 6108}, {5617, 42156}, {5921, 43403}, {5982, 46709}, {6782, 9112}, {10612, 15092}, {10653, 21156}, {11488, 23006}, {13103, 42988}, {16530, 37832}, {16808, 47863}, {16960, 47859}, {19781, 33517}, {22513, 42815}, {22691, 44422}, {22796, 42166}, {22846, 33464}, {22893, 25560}, {23514, 47856}, {25235, 43004}, {31683, 42119}, {32552, 46854}, {33529, 36304}, {35730, 47868}, {41042, 41119}, {42506, 47865}

X(47855) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (13, 61, 5478), (13, 14136, 36251), (13, 36961, 42162), (13, 37640, 31710), (13, 40693, 14136), (5472, 11542, 6115)

X(47856) = X(4)X(14) ∩ X(5)X(10612)

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

X(47856) = X(14)+2*X(47858) = X(16)+2*X(47862) = 2*X(5471)+X(6114) = X(5471)+2*X(11543) = X(6114)-4*X(11543) = 5*X(16961)+X(47860) = X(41021)+2*X(47854)

X(47856) lies on these lines: {4, 14}, {5, 10612}, {16, 47862}, {18, 619}, {61, 6670}, {230, 5471}, {395, 13349}, {398, 6774}, {531, 16268}, {3364, 13916}, {3365, 13981}, {5460, 22510}, {5474, 42149}, {5611, 6109}, {5613, 42153}, {5921, 43404}, {5983, 46708}, {6783, 9113}, {10611, 15092}, {10654, 21157}, {11489, 23013}, {13102, 42989}, {16529, 37835}, {16809, 47864}, {16961, 47860}, {19780, 33518}, {22512, 42816}, {22692, 44422}, {22797, 42163}, {22847, 25559}, {22891, 33465}, {23514, 47855}, {25236, 43005}, {31684, 42120}, {32553, 46855}, {33530, 36305}, {41043, 41120}, {42507, 47866}

X(47856) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (14, 62, 5479), (14, 14137, 36252), (14, 36962, 42159), (14, 37641, 31709), (14, 40694, 14137), (395, 44250, 14139), (5471, 11543, 6114), (9113, 18581, 6783)

X(47857) = X(4)X(13) ∩ X(6)X(5459)

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

X(47857) lies on these lines: {2, 9112}, {4, 13}, {6, 5459}, {17, 22998}, {30, 47861}, {115, 41621}, {187, 396}, {381, 47863}, {395, 1506}, {542, 11542}, {616, 36764}, {618, 16644}, {1560, 46652}, {3412, 25156}, {5007, 20394}, {5460, 5477}, {5461, 41672}, {5463, 11488}, {5470, 43014}, {6055, 47864}, {6115, 16267}, {6302, 13917}, {6306, 13982}, {6772, 47865}, {6775, 32552}, {6777, 36319}, {6778, 42506}, {6779, 41943}, {6782, 37832}, {8584, 33477}, {8787, 33476}, {9113, 9166}, {9115, 23302}, {11054, 37786}, {11147, 12155}, {11180, 18582}, {11485, 25154}, {13705, 36468}, {13825, 36449}, {15682, 31683}, {16241, 35230}, {16962, 47859}, {20415, 22330}, {21401, 42912}, {22489, 37641}, {22892, 33465}, {35731, 47868}, {36771, 43542}, {37785, 42062}, {41042, 43403}, {41633, 44382}, {44497, 46079}

X(47857) = midpoint of X(i) and X(j) for these {i, j}: {396, 5472}, {37786, 40671}
X(47857) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 9112, 41620), (13, 61, 31710), (13, 10654, 5478), (5461, 41672, 47858), (16644, 41745, 618)

X(47858) = X(4)X(14) ∩ X(6)X(5460)

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

X(47858) lies on these lines: {2, 9113}, {4, 14}, {6, 5460}, {18, 22997}, {30, 47862}, {115, 41620}, {187, 395}, {381, 47864}, {396, 1506}, {542, 11543}, {619, 16645}, {1560, 46653}, {3411, 25166}, {5007, 20395}, {5459, 5477}, {5461, 41672}, {5464, 11489}, {5469, 43015}, {6055, 47863}, {6114, 16268}, {6303, 13916}, {6307, 13981}, {6772, 32553}, {6775, 47866}, {6777, 42507}, {6778, 36344}, {6780, 41944}, {6783, 37835}, {8584, 33476}, {8787, 33477}, {9112, 9166}, {9117, 23303}, {11054, 37785}, {11147, 12154}, {11180, 18581}, {11486, 25164}, {13703, 36450}, {13823, 36467}, {15682, 31684}, {16242, 35229}, {16963, 47860}, {20416, 22330}, {21402, 42913}, {22490, 37640}, {22848, 33464}, {37786, 42063}, {41043, 43404}, {41643, 44383}, {44498, 46080}

X(47858) = midpoint of X(i) and X(j) for these {i, j}: {395, 5471}, {37785, 40672}
X(47858) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 9113, 41621), (14, 62, 31709), (14, 10653, 5479), (5461, 41672, 47857), (16645, 41746, 619)

X(47859) = X(2)X(13) ∩ X(4)X(6777)

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

X(47859) = 3*X(13)-2*X(6115) = 3*X(13)-4*X(47861) = 5*X(16960)-6*X(47855) = 3*X(16962)-4*X(47857) = 3*X(41024)-4*X(47853)

X(47859) lies on these lines: {2, 13}, {4, 6777}, {6, 13103}, {14, 25154}, {15, 5472}, {61, 7737}, {62, 115}, {99, 34509}, {381, 22998}, {542, 23004}, {543, 22495}, {576, 6321}, {2782, 3105}, {3180, 25236}, {5237, 20415}, {5318, 31703}, {5469, 37641}, {5473, 10645}, {5478, 6782}, {5617, 16808}, {6770, 42086}, {6771, 10646}, {6772, 25156}, {8018, 37848}, {9115, 37835}, {9830, 22580}, {11486, 22511}, {11488, 36782}, {11646, 46854}, {12816, 36363}, {14537, 44497}, {16530, 18581}, {16960, 47855}, {16962, 47857}, {16964, 47863}, {19106, 41022}, {20094, 22113}, {20252, 23303}, {20423, 36970}, {22496, 22576}, {22510, 41406}, {22684, 43538}, {22846, 34755}, {31683, 42162}, {31710, 41620}, {32465, 44464}, {33388, 36995}, {34754, 36772}, {35696, 36366}, {35733, 47868}, {36251, 42990}, {36765, 42919}, {36776, 43451}, {38730, 47068}, {41020, 42431}, {41024, 47853}, {42088, 47610}

X(47859) = reflection of X(i) in X(j) for these (i, j): (15, 5472), (5463, 40671), (6115, 47861)
X(47859) = Psi-transform of X(46053)
X(47859) = inverse of X(37832) in inner-Napoleon circle
X(47859) = reflection of X(13) in the line X(20579)X(27551)
X(47859) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 13103, 23005), (6, 23005, 46855), (13, 16, 46054), (13, 5463, 37832), (13, 6779, 2), (13, 16242, 5459), (13, 23006, 16), (13, 36766, 18582), (13, 41100, 6108), (616, 18582, 36766), (5478, 6782, 16809), (6108, 47865, 13), (6115, 47861, 13), (6778, 16965, 22513), (16808, 25235, 5617), (25154, 41745, 14)

X(47860) = X(2)X(14) ∩ X(4)X(6778)

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

X(47860) = 3*X(14)-2*X(6114) = 3*X(14)-4*X(47862) = 5*X(16961)-6*X(47856) = 3*X(16963)-4*X(47858) = 3*X(41025)-4*X(47854)

X(47860) lies on these lines: {2, 14}, {4, 6778}, {6, 13102}, {13, 25164}, {16, 5471}, {61, 115}, {62, 7737}, {99, 34508}, {381, 22997}, {542, 23005}, {543, 22496}, {576, 6321}, {2782, 3104}, {3181, 25235}, {5238, 20416}, {5321, 31704}, {5470, 37640}, {5474, 10646}, {5479, 6783}, {5613, 16809}, {6773, 42085}, {6774, 10645}, {6775, 25166}, {8019, 37850}, {9117, 37832}, {9830, 22579}, {11485, 22510}, {11646, 46855}, {12817, 36362}, {14537, 44498}, {16529, 18582}, {16961, 47856}, {16963, 47858}, {16965, 47864}, {19107, 41023}, {20094, 22114}, {20253, 23302}, {20423, 36969}, {22495, 22575}, {22511, 41407}, {22686, 43539}, {22891, 34754}, {31684, 42159}, {31709, 41621}, {32466, 44460}, {33389, 36993}, {35692, 36368}, {36252, 42991}, {38730, 47066}, {41021, 42432}, {41025, 47854}, {42087, 47611}

X(47860) = reflection of X(i) in X(j) for these (i, j): (16, 5471), (5464, 40672), (6114, 47862)
X(47860) = Psi-transform of X(46054)
X(47860) = inverse of X(37835) in outer-Napoleon circle
X(47860) = reflection of X(14) in the line X(20578)X(27550)
X(47860) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 13102, 23004), (6, 23004, 46854), (14, 15, 46053), (14, 5464, 37835), (14, 6780, 2), (14, 16241, 5460), (14, 23013, 15), (14, 41101, 6109), (5479, 6783, 16808), (6109, 47866, 14), (6114, 47862, 14), (6777, 16964, 22512), (16809, 25236, 5613), (25164, 41746, 13)

X(47861) = X(2)X(13) ∩ X(4)X(9112)

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

X(47861) = 3*X(13)-X(6115) = 3*X(13)+X(47859) = X(15)-3*X(47855) = X(5980)-3*X(40671)

X(47861) lies on these lines: {2, 13}, {4, 9112}, {6, 5478}, {15, 47855}, {30, 47857}, {115, 397}, {381, 41620}, {542, 43416}, {1503, 47853}, {5318, 5472}, {5340, 22513}, {5344, 41020}, {5473, 11488}, {5477, 5479}, {5617, 42128}, {6771, 42118}, {6777, 42813}, {6778, 38664}, {6782, 16808}, {9113, 14639}, {9880, 41621}, {10611, 23302}, {13103, 42815}, {13646, 36436}, {13765, 36454}, {14136, 22906}, {16530, 42919}, {21156, 42120}, {22609, 22638}, {22796, 42138}, {25154, 42974}, {31687, 34321}, {33419, 42156}, {33602, 36344}, {35740, 47868}, {36764, 43542}, {36765, 42142}, {36961, 42134}, {41672, 47862}

X(47861) = midpoint of X(i) and X(j) for these {i, j}: {5318, 5472}, {6115, 47859}
X(47861) = inverse of X(43403) in inner-Napoleon circle
X(47861) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 9112, 47863), (13, 5463, 43403), (13, 6779, 41121), (13, 10653, 5459), (13, 23006, 18582), (13, 41107, 6108), (13, 47859, 6115), (18582, 23006, 618)

X(47862) = X(2)X(14) ∩ X(4)X(9113)

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

X(47862) = 3*X(14)-X(6114) = 3*X(14)+X(47860) = X(16)-3*X(47856) = X(5981)-3*X(40672)

X(47862) lies on these lines: {2, 14}, {4, 9113}, {6, 5479}, {16, 47856}, {30, 47858}, {115, 398}, {381, 41621}, {542, 43417}, {1503, 47854}, {5321, 5471}, {5339, 22512}, {5343, 41021}, {5474, 11489}, {5477, 5478}, {5613, 42125}, {6774, 42117}, {6777, 38664}, {6778, 42814}, {6783, 16809}, {9112, 14639}, {9880, 41620}, {10612, 23303}, {13102, 42816}, {13645, 36454}, {13764, 36436}, {14137, 22862}, {16529, 42918}, {21157, 42119}, {22610, 22639}, {22797, 42135}, {25164, 42975}, {31688, 34322}, {33418, 42153}, {33603, 36319}, {35742, 42242}, {36962, 42133}, {41672, 47861}

X(47862) = midpoint of X(i) and X(j) for these {i, j}: {5321, 5471}, {6114, 47860}
X(47862) = inverse of X(43404) in outer-Napoleon circle
X(47862) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 9113, 47864), (14, 5464, 43404), (14, 6780, 41122), (14, 10654, 5460), (14, 23013, 18581), (14, 41108, 6109), (14, 47860, 6114), (18581, 23013, 619)

X(47863) = X(13)X(3839) ∩ X(14)X(5459)

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

X(47863) lies on these lines: {4, 9112}, {6, 22513}, {13, 3839}, {14, 5459}, {15, 298}, {30, 41620}, {61, 147}, {98, 9113}, {115, 398}, {381, 47857}, {530, 1992}, {531, 18800}, {542, 41621}, {616, 36772}, {1151, 47868}, {2794, 8550}, {5111, 44667}, {5321, 5472}, {5335, 36961}, {5473, 42119}, {5477, 41023}, {5617, 11485}, {6055, 47858}, {6114, 7792}, {6669, 18581}, {6771, 11543}, {6778, 36251}, {7735, 9749}, {9115, 42942}, {10611, 42110}, {10645, 16530}, {11488, 36765}, {11489, 21156}, {11542, 22796}, {13646, 36445}, {13765, 36463}, {16808, 47855}, {16964, 47859}, {22489, 43404}, {22998, 36769}, {23006, 42085}, {31710, 41108}, {33517, 46855}, {34754, 36766}, {35931, 43275}, {36768, 42511}, {37640, 41042}, {41020, 42999}, {41038, 47853}, {41745, 42154}

X(47863) = midpoint of X(i) and X(j) for these {i, j}: {23006, 42085}, {41745, 42154}
X(47863) = reflection of X(47864) in X(41672)
X(47863) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 9112, 47861), (15, 6782, 618), (61, 6777, 6115), (5321, 5472, 5478), (8550, 15048, 47864)

X(47864) = X(13)X(5460) ∩ X(14)X(3839)

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

X(47864) lies on these lines: {4, 9113}, {6, 22512}, {13, 5460}, {14, 3839}, {16, 299}, {30, 41621}, {62, 147}, {98, 9112}, {115, 397}, {372, 35742}, {381, 47858}, {530, 18800}, {531, 1992}, {542, 41620}, {2794, 8550}, {5111, 44666}, {5318, 5471}, {5334, 36962}, {5474, 42120}, {5477, 41022}, {5613, 11486}, {6055, 47857}, {6115, 7792}, {6670, 18582}, {6774, 11542}, {6777, 36252}, {7735, 9750}, {9117, 42943}, {10612, 42107}, {10646, 16529}, {11488, 21157}, {11543, 22797}, {13645, 36463}, {13764, 36445}, {16809, 47856}, {16965, 47860}, {22490, 43403}, {22997, 41100}, {23013, 42086}, {31709, 41107}, {33518, 46854}, {35932, 43274}, {37641, 41043}, {41021, 42998}, {41039, 47854}, {41746, 42155}

X(47864) = midpoint of X(i) and X(j) for these {i, j}: {23013, 42086}, {41746, 42155}
X(47864) = reflection of X(47863) in X(41672)
X(47864) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 9113, 47862), (16, 6783, 619), (62, 6778, 6114), (5318, 5471, 5479), (8550, 15048, 47863)

X(47865) = X(2)X(13) ∩ X(4)X(36318)

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

X(47865) = X(2)-3*X(13) = 7*X(2)-3*X(616) = 4*X(2)-3*X(618) = 2*X(2)-3*X(5459) = 5*X(2)-3*X(5463) = 5*X(2)-6*X(6669) = 7*X(2)-9*X(22489) = 7*X(2)-12*X(35019) = 3*X(2)+X(35749) = 5*X(2)-X(35750) = 7*X(2)-5*X(36767) = 17*X(2)-15*X(36770) = 7*X(13)-X(616) = 4*X(13)-X(618) = 5*X(13)-X(5463) = 5*X(13)-2*X(6669) = 7*X(13)-3*X(22489) = 7*X(13)-4*X(35019) = 9*X(13)+X(35749) = 15*X(13)-X(35750) = 9*X(13)-X(35751) = 3*X(13)+X(35752) = 9*X(13)-2*X(36768) = 6*X(13)-X(36769) = 17*X(13)-5*X(36770)

X(47865) lies on these lines: {2, 13}, {4, 36318}, {30, 16001}, {115, 41620}, {148, 36331}, {381, 36363}, {395, 39601}, {396, 6781}, {397, 31694}, {524, 43416}, {531, 5318}, {532, 31693}, {533, 11054}, {542, 1353}, {543, 32552}, {549, 20415}, {617, 22577}, {619, 36521}, {671, 6778}, {1994, 10657}, {3534, 13103}, {3543, 41020}, {3830, 25154}, {3860, 22796}, {5340, 11296}, {5460, 46080}, {5461, 32553}, {5472, 14537}, {5473, 19708}, {5617, 19709}, {5859, 35697}, {5862, 33602}, {5863, 31683}, {6674, 42935}, {6770, 15682}, {6771, 12100}, {6772, 47857}, {6777, 41135}, {6782, 41122}, {8029, 27551}, {9761, 42128}, {9763, 35696}, {10109, 20252}, {11303, 22494}, {11542, 45879}, {11603, 45103}, {11632, 36382}, {12243, 36319}, {13083, 42155}, {13595, 13859}, {15534, 16943}, {15698, 21156}, {16267, 35931}, {16808, 37785}, {16965, 35932}, {19710, 47610}, {20583, 43417}, {22496, 42813}, {22511, 42533}, {22846, 42977}, {23005, 41101}, {25185, 36400}, {25186, 36401}, {31710, 41108}, {33475, 42118}, {33607, 42062}, {33623, 46335}, {34508, 42162}, {35691, 36775}, {35735, 47868}, {36329, 36366}, {36340, 36342}, {36344, 41042}, {36348, 36349}, {36969, 37786}, {41028, 47853}, {42506, 47855}

X(47865) = midpoint of X(i) and X(j) for these {i, j}: {2, 35752}, {617, 22577}, {671, 6778}, {3543, 41020}, {3830, 36383}, {5859, 35697}, {16001, 32907}, {35749, 35751}, {36969, 37786}
X(47865) = reflection of X(i) in X(j) for these (i, j): (549, 20415), (618, 5459), (5459, 13), (5463, 6669), (32553, 5461), (35751, 36768), (36769, 2), (45879, 11542), (47866, 36523)
X(47865) = complement of X(35751)
X(47865) = anticomplement of X(36768)
X(47865) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (2, 10278, 27551), (16, 27551, 32193)
X(47865) = X(36363)-of-Ehrmann-mid triangle
X(47865) = X(47865)-of-outer-Fermat triangle
X(47865) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 616, 36767), (2, 35749, 35751), (2, 35750, 5463), (2, 35751, 36768), (2, 36769, 618), (13, 616, 35019), (13, 35752, 2), (13, 47859, 6108), (3845, 8584, 47866), (5459, 36769, 2), (22489, 35019, 5459), (22489, 36767, 2), (25154, 36383, 3830), (35751, 35752, 35749), (35751, 36768, 36769), (36344, 41099, 41042)

X(47866) = X(2)X(14) ∩ X(4)X(36320)

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

X(47866) = X(2)-3*X(14) = 7*X(2)-3*X(617) = 4*X(2)-3*X(619) = 2*X(2)-3*X(5460) = 5*X(2)-3*X(5464) = 5*X(2)-6*X(6670) = 7*X(2)-9*X(22490) = 7*X(2)-12*X(35020) = 3*X(2)+X(36327) = 5*X(2)-X(36331) = 7*X(14)-X(617) = 4*X(14)-X(619) = 5*X(14)-X(5464) = 5*X(14)-2*X(6670) = 7*X(14)-3*X(22490) = 7*X(14)-4*X(35020) = 9*X(14)+X(36327) = 9*X(14)-X(36329) = 3*X(14)+X(36330) = 15*X(14)-X(36331) = 6*X(14)-X(47867)

X(47866) lies on these lines: {2, 14}, {4, 36320}, {30, 16002}, {99, 36767}, {115, 41621}, {148, 35750}, {381, 36362}, {395, 6781}, {396, 39601}, {398, 31693}, {524, 43417}, {530, 5321}, {532, 11054}, {533, 31694}, {542, 1353}, {543, 32553}, {549, 20416}, {616, 22578}, {618, 36521}, {671, 6777}, {1994, 10658}, {3534, 13102}, {3543, 41021}, {3830, 25164}, {3860, 22797}, {5339, 11295}, {5459, 46079}, {5461, 32552}, {5471, 14537}, {5474, 19708}, {5613, 19709}, {5858, 35693}, {5862, 31684}, {5863, 33603}, {6673, 42934}, {6773, 15682}, {6774, 12100}, {6775, 47858}, {6778, 41135}, {6783, 41121}, {8029, 27550}, {9761, 35692}, {9763, 42125}, {10109, 20253}, {11304, 22493}, {11543, 45880}, {11602, 45103}, {11632, 36383}, {12243, 36344}, {13084, 42154}, {13595, 13858}, {15300, 36768}, {15534, 16942}, {15698, 21157}, {16268, 35932}, {16809, 37786}, {16964, 35931}, {19710, 47611}, {20583, 43416}, {22495, 42814}, {22510, 42532}, {22891, 42976}, {23004, 41100}, {25189, 36396}, {25190, 36397}, {31709, 41107}, {33474, 42117}, {33606, 42063}, {33625, 46334}, {34509, 42159}, {35741, 42242}, {35751, 36368}, {36319, 41043}, {36341, 36343}, {36356, 36357}, {36970, 37785}, {41029, 47854}, {42507, 47856}

X(47866) = midpoint of X(i) and X(j) for these {i, j}: {2, 36330}, {616, 22578}, {671, 6777}, {3543, 41021}, {3830, 36382}, {5858, 35693}, {16002, 32909}, {36327, 36329}, {36970, 37785}
X(47866) = reflection of X(i) in X(j) for these (i, j): (549, 20416), (619, 5460), (5460, 14), (5464, 6670), (15300, 36768), (32552, 5461), (45880, 11543), (47865, 36523), (47867, 2)
X(47866) = complement of X(36329)
X(47866) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (2, 10278, 27550), (15, 27550, 32193)
X(47866) = X(36362)-of-Ehrmann-mid triangle
X(47866) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 36327, 36329), (2, 36331, 5464), (2, 47867, 619), (14, 617, 35020), (14, 36330, 2), (14, 47860, 6109), (3845, 8584, 47865), (5460, 47867, 2), (22490, 35020, 5460), (25164, 36382, 3830), (36319, 41099, 41043), (36329, 36330, 36327)

X(47867) = X(2)X(14) ∩ X(3)X(36382)

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

X(47867) = 5*X(2)-3*X(14) = X(2)+3*X(617) = 2*X(2)-3*X(619) = 4*X(2)-3*X(5460) = X(2)-3*X(5464) = 7*X(2)-6*X(6670) = 11*X(2)-9*X(22490) = 17*X(2)-12*X(35020) = 5*X(2)-X(36327) = 3*X(2)+X(36331) = X(14)+5*X(617) = 2*X(14)-5*X(619) = 4*X(14)-5*X(5460) = X(14)-5*X(5464) = 7*X(14)-10*X(6670) = 11*X(14)-15*X(22490) = 17*X(14)-20*X(35020) = 3*X(14)-X(36327) = 3*X(14)+5*X(36329) = 9*X(14)-5*X(36330) = 9*X(14)+5*X(36331) = 6*X(14)-5*X(47866)

X(47867) lies on these lines: {2, 14}, {3, 36382}, {99, 35751}, {140, 32909}, {376, 36319}, {530, 15300}, {532, 35932}, {533, 35303}, {542, 8703}, {543, 32552}, {547, 16002}, {624, 42136}, {636, 11295}, {2482, 32553}, {3081, 12792}, {3534, 36362}, {3830, 5613}, {4677, 12780}, {5008, 41621}, {5066, 5479}, {5459, 36523}, {5474, 11001}, {5858, 9886}, {5859, 35692}, {6636, 13858}, {6669, 31696}, {6773, 15698}, {6774, 11812}, {6777, 41134}, {6778, 8591}, {6783, 41107}, {8724, 36363}, {9113, 46453}, {9114, 35752}, {9116, 35750}, {9117, 43228}, {9763, 35693}, {10304, 41021}, {10611, 42502}, {11123, 27550}, {11539, 20416}, {12101, 22797}, {14144, 36386}, {15640, 36962}, {15682, 41043}, {15711, 47611}, {15719, 21157}, {16962, 36252}, {19708, 36320}, {19709, 25164}, {21358, 43421}, {22495, 41974}, {22997, 41100}, {31693, 42598}, {31709, 41121}, {33459, 46893}, {33602, 35694}, {33605, 33617}, {33612, 33623}, {34508, 43239}, {34509, 42161}, {36332, 36333}, {36360, 36361}, {41027, 47854}, {42506, 46854}

X(47867) = midpoint of X(i) and X(j) for these {i, j}: {2, 36329}, {617, 5464}, {3534, 36362}, {5859, 35692}, {6778, 8591}, {36330, 36331}
X(47867) = reflection of X(i) in X(j) for these (i, j): (619, 5464), (5460, 619), (16002, 547), (31696, 6669), (32553, 2482), (32909, 140), (36769, 36521), (47866, 2)
X(47867) = complement of X(36330)
X(47867) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (2, 10190, 27550), (15, 14610, 27550)
X(47867) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 617, 36329), (2, 36327, 14), (2, 36331, 36330), (2, 47866, 5460), (619, 47866, 2), (5464, 36329, 2), (8703, 22165, 36769), (36329, 36330, 36331)

X(47868) = X(3)X(618) ∩ X(530)X(34551)

X(47868) lies on these lines: {3, 618}, {530, 34551}, {616, 36762}, {1151, 47863}, {2042, 6302}, {5478, 35732}, {6115, 35739}, {6410, 22513}, {6669, 35738}, {35730, 47855}, {35731, 47857}, {35733, 47859}, {35734, 36769}, {35735, 47865}, {35736, 35752}, {35737, 35751}, {35740, 47861}, {41018, 47853}

If L1 and L2 are lines that meet in a point P not at infinity, then an {L1,L2}-coordiinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1: (2a-b-c)α + (2b-c-a)β + (2c-a-b)γ = 0.

L2: (2a^2 - b^2 - c^2)α + (2b^2 - c^2-a^2)β + (2c^2 - a^2 - b^2)γ = 0.

The origin is given by (0,0) = X(2) = 1 : 1 : 1

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b-c)((a-b)(a-c) + x + (b+c)y) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogenous of degree 2, and y is symmetric and homogeneous of degree 1.

The appearance of {x,y}, k in the following table means that (x,y) = X(k):

{-2 (a b+a c+b c),-((2 (a b+a c+b c))/(a+b+c))}, 47821
{-2 (a b+a c+b c),-a-b-c}, 30565
{-2 (a b+a c+b c),0}, 47775
{-((2 a b c)/(a+b+c)),0}, 47793
{-a^2-b^2-c^2,-((2 (a^2+b^2+c^2))/(a+b+c))}, 47808
{-a b-a c-b c,-((2 (a b+a c+b c))/(a+b+c))}, 47832
{-a^2-b^2-c^2,-a-b-c}, 693
{-a^2-b^2-c^2,-((a^2+b^2+c^2)/(a+b+c))}, 44429
{-a b-a c-b c,-((a b+a c+b c)/(a+b+c))}, 47822
{-a^2-b^2-c^2,1/2 (-a-b-c)}, 4927
{-a b-a c-b c,1/2 (-a-b-c)}, 1639
{-a^2-b^2-c^2,0}, 44435
{-a b-a c-b c,0}, 4893
{-((a b c)/(a+b+c)),0}, 47794
{-a^2-b^2-c^2,1/2 (a+b+c)}, 3004
{-a^2-b^2-c^2,2 (a+b+c)}, 45746
{1/2 (-a^2-b^2-c^2),-((a^2+b^2+c^2)/(a+b+c))}, 47806
{1/2 (-a b-a c-b c),-((a b+a c+b c)/(a+b+c))}, 47831
{1/2 (-a^2-b^2-c^2),1/2 (-a-b-c)}, 45320
{1/2 (-a^2-b^2-c^2),-((a^2+b^2+c^2)/(2 (a+b+c)))}, 47802
{1/2 (-a^2-b^2-c^2),0}, 47757
{1/2 (-a b-a c-b c),0}, 47778
{0,-2 (a+b+c)}, 47792
{0,-((2 (a b+a c+b c))/(a+b+c))}, 47834
{0,-a-b-c}, 4789
{0,-((a^2+b^2+c^2)/(a+b+c))}, 47809
{0,-((a b+a c+b c)/(a+b+c))}, 47833
{0,1/2 (-a-b-c)}, 47788
{0,-((a^2+b^2+c^2)/(2 (a+b+c)))}, 47807
{0,0}, 2
{0,1/2 (a+b+c)}, 47784
{0,(a^2+b^2+c^2)/(2 (a+b+c))}, 47799
{0,(a b+a c+b c)/(2 (a+b+c))}, 47829
{0,a+b+c}, 47782
{0,(a^2+b^2+c^2)/(a+b+c)}, 47797
{0,(a b+a c+b c)/(a+b+c)}, 47827
{0,2 (a+b+c)}, 46915
{0,(2 (a b+a c+b c))/(a+b+c)}, 47825
{1/2 (a^2+b^2+c^2),-a-b-c}, 6590
{1/2 (a^2+b^2+c^2),0}, 47766
{1/2 (a b+a c+b c),0}, 47779
{1/2 (a^2+b^2+c^2),1/2 (a+b+c)}, 650
{1/2 (a^2+b^2+c^2),(a^2+b^2+c^2)/(2 (a+b+c))}, 47803
{1/2 (a^2+b^2+c^2),(a^2+b^2+c^2)/(a+b+c)}, 47800
{1/2 (a b+a c+b c),(a b+a c+b c)/(a+b+c)}, 47830
{1/2 (a^2+b^2+c^2),2 (a+b+c)}, 45745
{a^2+b^2+c^2,0}, 47771
{a b+a c+b c,0}, 4379
{(a b c)/(a+b+c),0}, 47795
{a b+a c+b c,1/2 (a+b+c)}, 1638
{a^2+b^2+c^2,a+b+c}, 31150
{a^2+b^2+c^2,(a^2+b^2+c^2)/(a+b+c)}, 47804
{a b+a c+b c,(a b+a c+b c)/(a+b+c)}, 47823
{a^2+b^2+c^2,(2 (a^2+b^2+c^2))/(a+b+c)}, 47798
{a b+a c+b c,(2 (a b+a c+b c))/(a+b+c)}, 47828
{2 (a^2+b^2+c^2),-a-b-c}, 47660
{2 (a^2+b^2+c^2),0}, 47773
{2 (a b+a c+b c),0}, 47780
{(2 a b c)/(a+b+c),0}, 47796
{2 (a b+a c+b c),a+b+c}, 4453
{2 (a^2+b^2+c^2),2 (a+b+c)}, 17494
{2 (a^2+b^2+c^2),(2 (a^2+b^2+c^2))/(a+b+c)}, 47805
{2 (a b+a c+b c),(2 (a b+a c+b c))/(a+b+c)}, 47824
{-2*(a^2 + b^2 + c^2), -2*(a + b + c)}, 47869
{-2*(a*b + a*c + b*c), -2*(a + b + c)}, 47870
{-2*(a^2 + b^2 + c^2), -a - b - c}, 47871
{(-2*a*b*c)/(a + b + c), -((a*b + a*c + b*c)/(a + b + c))}, 47872
{-(a*b) - a*c - b*c, -2*(a + b + c)}, 47873
{-(a*b) - a*c - b*c, -a - b - c}, 47874
{-((a*b*c)/(a + b + c)), -((a*b + a*c + b*c)/(a + b + c))}, 47875
{-(a*b) - a*c - b*c, (a + b + c)/2}, 47876
{-a^2 - b^2 - c^2, (a*b + a*c + b*c)/(a + b + c)}, 47877
{-(a*b) - a*c - b*c, a + b + c}, 47878
{(-(a*b) - a*c - b*c)/2, (-a - b - c)/2}, 47879
{(-a^2 - b^2 - c^2)/2, (a + b + c)/2}, 47880
{(a^2 + b^2 + c^2)/2, (-a - b - c)/2}, 47881
{(a*b + a*c + b*c)/2, (a + b + c)/2}, 47882
{(a^2 + b^2 + c^2)/2, a + b + c}, 47883
{a^2 + b^2 + c^2, (a + b + c)/2}, 47884
{a^2 + b^2 + c^2, (a*b + a*c + b*c)/(a + b + c)}, 47885
{a*b + a*c + b*c, a + b + c}, 47886
{a*b + a*c + b*c, (a^2 + b^2 + c^2)/(a + b + c)}, 47887
{(a*b*c)/(a + b + c), (a*b + a*c + b*c)/(a + b + c)}, 47888
{(2*a*b*c)/(a + b + c), -((a*b + a*c + b*c)/(a + b + c))}, 47889
{2*(a^2 + b^2 + c^2), (a + b + c)/2}, 47890
{2*(a*b + a*c + b*c), (a + b + c)/2}, 47891
{2*(a^2 + b^2 + c^2), a + b + c}, 47892
{(2*a*b*c)/(a + b + c), (a*b + a*c + b*c)/(a + b + c)}, 47893
{2*(a*b + a*c + b*c), 2*(a + b + c)}, 47894

X(47869) = X(2)X(650)∩X(514)X(4120)

X(47869) = 5 X[2] - 4 X[650], 7 X[2] - 8 X[4885], 7 X[2] - 5 X[26777], 4 X[2] - 5 X[26985], 8 X[2] - 7 X[27115], 11 X[2] - 10 X[31209], 19 X[2] - 20 X[31250], 17 X[2] - 16 X[31287], 9 X[2] - 8 X[44567], 3 X[2] - 4 X[45320], 7 X[2] - 2 X[47664], 2 X[650] - 5 X[693], 7 X[650] - 10 X[4885], 8 X[650] - 5 X[17494], 28 X[650] - 25 X[26777], 4 X[650] + 5 X[26824], 16 X[650] - 25 X[26985], 32 X[650] - 35 X[27115], 6 X[650] - 5 X[31150], 22 X[650] - 25 X[31209], 19 X[650] - 25 X[31250], 17 X[650] - 20 X[31287], 9 X[650] - 10 X[44567], 3 X[650] - 5 X[45320], 14 X[650] - 5 X[47664], 7 X[693] - 4 X[4885], 4 X[693] - X[17494], 14 X[693] - 5 X[26777], 2 X[693] + X[26824], 8 X[693] - 5 X[26985], 16 X[693] - 7 X[27115], 3 X[693] - X[31150], 11 X[693] - 5 X[31209], 19 X[693] - 10 X[31250], 17 X[693] - 8 X[31287], 9 X[693] - 4 X[44567], 3 X[693] - 2 X[45320], 7 X[693] - X[47664], 16 X[4885] - 7 X[17494], 8 X[4885] - 5 X[26777], 8 X[4885] + 7 X[26824], 32 X[4885] - 35 X[26985], 64 X[4885] - 49 X[27115], 12 X[4885] - 7 X[31150], 44 X[4885] - 35 X[31209], 38 X[4885] - 35 X[31250], 17 X[4885] - 14 X[31287], 9 X[4885] - 7 X[44567], 6 X[4885] - 7 X[45320], 4 X[4885] - X[47664], 7 X[17494] - 10 X[26777], X[17494] + 2 X[26824], 2 X[17494] - 5 X[26985], 4 X[17494] - 7 X[27115], 3 X[17494] - 4 X[31150], 11 X[17494] - 20 X[31209], 19 X[17494] - 40 X[31250], 17 X[17494] - 32 X[31287], 9 X[17494] - 16 X[44567], 3 X[17494] - 8 X[45320], 7 X[17494] - 4 X[47664], 5 X[26777] + 7 X[26824], 4 X[26777] - 7 X[26985], 40 X[26777] - 49 X[27115], 15 X[26777] - 14 X[31150], 11 X[26777] - 14 X[31209], 19 X[26777] - 28 X[31250], 85 X[26777] - 112 X[31287], 45 X[26777] - 56 X[44567], 15 X[26777] - 28 X[45320], 5 X[26777] - 2 X[47664], 4 X[26824] + 5 X[26985], 8 X[26824] + 7 X[27115], 3 X[26824] + 2 X[31150], 11 X[26824] + 10 X[31209], 19 X[26824] + 20 X[31250], 17 X[26824] + 16 X[31287], 9 X[26824] + 8 X[44567], 3 X[26824] + 4 X[45320], 7 X[26824] + 2 X[47664], 10 X[26985] - 7 X[27115], 15 X[26985] - 8 X[31150], 11 X[26985] - 8 X[31209], 19 X[26985] - 16 X[31250], 85 X[26985] - 64 X[31287], 45 X[26985] - 32 X[44567], 15 X[26985] - 16 X[45320], 35 X[26985] - 8 X[47664], 21 X[27115] - 16 X[31150], 77 X[27115] - 80 X[31209], 63 X[27115] - 64 X[44567], 21 X[27115] - 32 X[45320], 49 X[27115] - 16 X[47664], 11 X[31150] - 15 X[31209], 19 X[31150] - 30 X[31250], 17 X[31150] - 24 X[31287], 3 X[31150] - 4 X[44567], 7 X[31150] - 3 X[47664], 19 X[31209] - 22 X[31250], 85 X[31209] - 88 X[31287], 45 X[31209] - 44 X[44567], 15 X[31209] - 22 X[45320], 35 X[31209] - 11 X[47664], 85 X[31250] - 76 X[31287], 45 X[31250] - 38 X[44567], 15 X[31250] - 19 X[45320], 70 X[31250] - 19 X[47664], 18 X[31287] - 17 X[44567], 12 X[31287] - 17 X[45320], 56 X[31287] - 17 X[47664], 2 X[44567] - 3 X[45320], 28 X[44567] - 9 X[47664], 14 X[45320] - 3 X[47664], 3 X[21297] - 2 X[31147], 3 X[21297] - X[47774], 4 X[31147] - 3 X[47759], 3 X[47759] - 2 X[47774], 2 X[4382] + X[7192], 2 X[4688] - 3 X[4828]

X(47869) lies on these lines: {2, 650}, {514, 4120}, {523, 7840}, {1992, 9015}, {3543, 8760}, {3837, 4948}, {4382, 4785}, {4661, 9443}, {4688, 4828}, {4740, 4777}, {4789, 6084}, {9001, 11160}

X(47869) = midpoint of X(2) and X(26824)
X(47869) = reflection of X(i) in X(j) for these {i,j}: {2, 693}, {4948, 3837}, {17494, 2}, {31150, 45320}, {47759, 21297}, {47772, 47790}, {47773, 4789}, {47774, 31147}
X(47869) = anticomplement of X(31150)
X(47869) = crossdifference of every pair of points on line {2223, 5008}
X(47869) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 17494, 26985}, {693, 26824, 17494}, {693, 31150, 45320}, {693, 47664, 4885}, {4885, 47664, 26777}, {17494, 26985, 27115}, {21297, 47774, 31147}, {26777, 47664, 17494}, {31147, 47774, 47759}, {31150, 45320, 2}

X(47870) = X(2)X(824)∩X(514)X(4120)

X(47870) =2 X[4931] + X[47773], 2 X[4024] + X[17494], X[4380] + 2 X[4820], 2 X[31150] - 3 X[31992], 3 X[31992] - 4 X[47770], 4 X[6590] - X[7192], 2 X[6590] + X[25259], X[7192] + 2 X[25259]

X(47870) lies on these lines: {2, 824}, {312, 693}, {514, 4120}, {523, 4800}, {812, 4931}, {918, 4789}, {3877, 14077}, {3995, 4024}, {4380, 4820}, {4448, 4664}, {4776, 4944}, {6590, 7192}

X(47870) = midpoint of X(i) and X(j) for these {i,j}: {4024, 6546}, {25259, 47791}, {47772, 47792}
X(47870) = reflection of X(i) in X(j) for these {i,j}: {4776, 4944}, {7192, 47791}, {17494, 6546}, {21297, 47790}, {31150, 47770}, {47759, 4120}, {47774, 47769}, {47775, 30565}, {47780, 4789}, {47791, 6590}
X(47870) =crossdifference of every pair of points on line {8626, 21747}
X(47870) ={X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6590, 25259, 7192}, {31150, 47770, 31992}

X(47871) = X(2)X(4927)∩X(514)X(661)

X(47871) = 5 X[2] - 4 X[14425], 3 X[2] - 4 X[45677], 5 X[4927] - 2 X[14425], 3 X[4927] - 2 X[45677], 3 X[14425] - 5 X[45677], 2 X[1638] - 3 X[6548], 3 X[6548] - X[47776], 2 X[23770] + X[46403], 4 X[23770] - X[47695], 2 X[46403] + X[47695], 5 X[693] - 2 X[6590], 5 X[693] + X[47651], 2 X[693] + X[47652], 4 X[693] - X[47660], 7 X[693] - X[47662], X[3904] + 2 X[47680], 5 X[4468] - 8 X[14350], 3 X[4728] - 2 X[45661], 5 X[4789] - 4 X[6590], 5 X[4789] + 2 X[47651], 7 X[4789] - 2 X[47662], 2 X[6590] + X[47651], 4 X[6590] + 5 X[47652], 8 X[6590] - 5 X[47660], 14 X[6590] - 5 X[47662], 3 X[30565] - 4 X[45661], 2 X[47651] - 5 X[47652], 4 X[47651] + 5 X[47660], 7 X[47651] + 5 X[47662], 2 X[47652] + X[47660], 7 X[47652] + 2 X[47662], 7 X[47660] - 4 X[47662], 3 X[4453] - 2 X[4750], 5 X[4453] - 2 X[4984], 5 X[4750] - 3 X[4984], X[4750] - 3 X[6545], X[4984] - 5 X[6545], 4 X[3676] - X[4380], 2 X[3776] + X[4382], 4 X[3776] - X[4467], 2 X[4382] + X[4467], 5 X[4106] - 2 X[4949], 4 X[4106] - X[44449], 2 X[4106] + X[47676], 8 X[4949] - 5 X[44449], 4 X[4949] + 5 X[47676], X[44449] + 2 X[47676], 2 X[4763] - 3 X[14475]

X(47871) lies on these lines: {2, 4927}, {88, 673}, {149, 900}, {514, 661}, {523, 7840}, {812, 4453}, {2403, 4945}, {2826, 10707}, {3676, 4380}, {3776, 4382}, {4106, 4949}, {4763, 14475}, {4800, 4977}, {4928, 6546}

X(47871) = midpoint of X(4789) and X(47652)
X(47871) = reflection of X(i) in X(j) for these {i,j}: {2, 4927}, {4380, 4786}, {4453, 6545}, {4786, 3676}, {4789, 693}, {6546, 4928}, {30565, 4728}, {47660, 4789}, {47776, 1638}
X(47871) = X(671)-Ceva conjugate of X(1086)
X(47871) = X(i)-isoconjugate of X(j) for these (i,j): {6, 2748}, {101, 34893}, {667, 5387}, {692, 34892}
X(47871) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 2748), (1015, 34893), (1086, 34892), (6631, 5387), (16597, 1018)
X(47871) = crossdifference of every pair of points on line {31, 5008}
X(47871) = barycentric product X(i)*X(j) for these {i,j}: {75, 2832}, {514, 37756}, {561, 8650}, {693, 7292}, {3261, 16784}, {4442, 7192}, {7199, 16611}
X(47871) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 2748}, {190, 5387}, {513, 34893}, {514, 34892}, {2832, 1}, {4442, 3952}, {4956, 4767}, {7292, 100}, {8650, 31}, {16611, 1018}, {16784, 101}, {24394, 4069}, {37756, 190}, {39688, 4557}
X(47871) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 47651, 6590}, {693, 47652, 47660}, {3776, 4382, 4467}, {4106, 47676, 44449}, {6548, 47776, 1638}, {23770, 46403, 47695}

X(47872) = X(512)X(4800)∩X(659)X(1577)

X(47872) = X[659] + 2 X[1577], 2 X[663] + X[4774], X[667] + 2 X[4791], X[2533] + 2 X[3716], X[3777] - 4 X[4885], 2 X[4063] + X[4810], X[4122] + 2 X[4142], X[4367] + 2 X[4391], X[4367] - 4 X[4874], X[4391] + 2 X[4874], X[4490] + 2 X[7662], X[4490] - 4 X[20317], X[7662] + 2 X[20317], 2 X[6133] + X[7650]

X(47872) lies on these lines: {512, 4800}, {659, 1577}, {663, 4774}, {667, 4791}, {830, 14431}, {2533, 3716}, {3777, 4885}, {4063, 4810}, {4122, 4142}, {4367, 4391}, {4490, 7662}, {6133, 7650}

X(47872) = midpoint of X(i) and X(j) for these {i,j}: {1577, 47817}, {4391, 47820}
X(47872) = reflection of X(i) in X(j) for these {i,j}: {659, 47817}, {4367, 47820}, {47820, 4874}
X(47872) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4391, 4874, 4367}, {7662, 20317, 4490}

X(47873) = X(513)X(4931)∩X(514)X(4120)

X(47873) = 3 X[4931] - X[4958], 3 X[4120] - 2 X[47764], X[31147] - 4 X[45343], X[47772] + 3 X[47792], X[649] + 2 X[4024], 3 X[649] - 2 X[4984], X[649] - 4 X[6590], 3 X[649] - 4 X[47768], 3 X[4024] + X[4984], X[4024] + 2 X[6590], 3 X[4024] + 2 X[47768], X[4984] - 6 X[6590], 3 X[6590] - X[47768], 4 X[1639] - 3 X[4893], 2 X[650] + X[4838], 3 X[4379] - 2 X[4453], X[4453] - 3 X[4789], 4 X[3239] - X[4988], 4 X[3700] - X[4813], X[4382] - 4 X[4500], X[4382] + 2 X[47660], 2 X[4500] + X[47660], 2 X[4820] + X[4979]

X(47873) lies on these lines: {513, 4931}, {514, 4120}, {522, 649}, {523, 1639}, {650, 4838}, {657, 14400}, {661, 4802}, {824, 4379}, {1635, 4777}, {1637, 6367}, {3239, 4988}, {3700, 4813}, {4382, 4500}, {4820, 4979}

X(47873) = reflection of X(i) in X(j) for these {i,j}: {661, 4944}, {4379, 4789}, {4984, 47768}, {31147, 47790}, {47790, 45343}
X(47873) = crossdifference of every pair of points on line {1193, 4257}
X(47873) = barycentric product X(522)*X(11237)
X(47873) = barycentric quotient X(11237)/X(664)
X(47873) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4024, 6590, 649}, {4500, 47660, 4382}, {4984, 47768, 649}

X(47874) = X(2)X(824)∩X(514)X(661)

X(47874) = 2 X[650] + X[4024], 2 X[650] - 3 X[6544], X[4024] + 3 X[6544], X[661] - 4 X[3239], X[661] + 2 X[6590], 7 X[661] - 16 X[14350], 2 X[3239] + X[6590], 7 X[3239] - 4 X[14350], 2 X[3835] + X[47660], X[4391] + 2 X[8045], 2 X[4468] + X[47672], 2 X[4791] + X[47682], 7 X[6590] + 8 X[14350], 8 X[14350] - 7 X[47765], X[4931] + 2 X[47766], 5 X[649] - 8 X[2527], X[649] + 2 X[3700], 4 X[2527] + 5 X[3700], 4 X[2527] - 5 X[47767], 4 X[2490] - X[4976], 2 X[2529] + X[4949], X[4958] + 2 X[47768], 2 X[3776] - 3 X[6548], 2 X[3776] - 5 X[26985], 3 X[6548] - 5 X[26985], X[4088] + 2 X[7662], X[4122] + 2 X[4874], 2 X[4394] + X[4820], 4 X[4394] - 3 X[14435], 2 X[4820] + 3 X[14435], 8 X[4521] + X[4838], 4 X[4521] - X[45745], X[4838] + 2 X[45745], X[4813] - 4 X[14321], 4 X[4885] - 3 X[14475], 4 X[4885] - X[16892], 3 X[14475] - X[16892], 3 X[14475] - 2 X[47754]

X(47874) lies on these lines: {2, 824}, {37, 650}, {392, 14077}, {513, 4120}, {514, 661}, {522, 1635}, {523, 1639}, {649, 900}, {918, 4379}, {2490, 4976}, {2529, 4949}, {3667, 4958}, {3776, 6548}, {3807, 7035}, {4088, 7662}, {4122, 4809}, {4382, 6009}, {4394, 4820}, {4521, 4838}, {4762, 6546}, {4813, 14321}, {4885, 14475}, {4926, 4984}, {4979, 6006}, {6588, 11125}

X(47874) = midpoint of X(i) and X(j) for these {i,j}: {1635, 4931}, {3700, 47767}, {4122, 4809}, {4789, 30565}, {6590, 47765}
X(47874) = reflection of X(i) in X(j) for these {i,j}: {649, 47767}, {661, 47765}, {1635, 47766}, {4120, 4944}, {4379, 47788}, {4728, 47787}, {4776, 45661}, {4809, 4874}, {4893, 1639}, {6546, 47770}, {16892, 47754}, {47754, 4885}, {47765, 3239}
X(47874) = X(6)-isoconjugate of X(13396)
X(47874) = X(9)-Dao conjugate of X(13396)
X(47874) = crossdifference of every pair of points on line {31, 36}
X(47874) = barycentric product X(i)*X(j) for these {i,j}: {514, 17281}, {522, 5252}
X(47874) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 13396}, {5252, 664}, {17281, 190}
X(47874) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3239, 6590, 661}, {4885, 47754, 14475}, {14475, 16892, 47754}

X(47875) = X(2)X(784)∩X(659)X(4823)

X(47875) = X[659] + 2 X[4823], X[667] + 2 X[1577], X[667] - 4 X[4874], X[1577] + 2 X[4874], X[2530] - 4 X[4885], 2 X[2533] + X[4775], 2 X[4010] + X[4834], X[4367] + 2 X[4791], X[4378] + 2 X[4391], X[4705] + 2 X[7662], X[4815] + 2 X[6133]

X(47875) lies on these lines: {2, 784}, {659, 4823}, {667, 814}, {2530, 4885}, {2533, 4775}, {4010, 4834}, {4367, 4791}, {4378, 4391}, {4379, 6372}, {4705, 7662}, {4800, 6005}, {4815, 6133}, {8678, 14431}

X(47875) = midpoint of X(1577) and X(47818)
X(47875) = reflection of X(i) in X(j) for these {i,j}: {667, 47818}, {47818, 4874}
X(47875) = {X(1577),X(4874)}-harmonic conjugate of X(667)

X(47876) = X(241)X(514)∩X(513)X(4773)

X(47876) = 2 X[650] + X[4841], 11 X[650] - 8 X[31182], 7 X[650] - 4 X[43061], 11 X[4841] + 16 X[31182], 7 X[4841] + 8 X[43061], 14 X[31182] - 11 X[43061], 16 X[31182] - 11 X[47767], 8 X[43061] - 7 X[47767], 2 X[661] + X[4976], X[3700] + 2 X[45745], X[4979] - 3 X[14435], X[4988] + 3 X[6544]

X(47876) lies on these lines: {241, 514}, {513, 4773}, {523, 1639}, {661, 900}, {1635, 4977}, {3700, 4777}, {4765, 6006}, {4809, 4824}, {4979, 14435}, {4988, 6544}

X(47876) = midpoint of X(i) and X(j) for these {i,j}: {4809, 4824}, {4841, 47767}, {45745, 47765}
X(47876) = reflection of X(i) in X(j) for these {i,j}: {1638, 47784}, {1639, 4893}, {3700, 47765}, {21104, 47754}, {47767, 650}
X(47876) = crossdifference of every pair of points on line {55, 4257}

X(47877) = X(325)X(523)∩X(513)X(4750)

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

X(47877) = X[1491] + 2 X[3004], 2 X[3837] + X[45746], 2 X[3776] + X[4824], X[4010] + 2 X[4818]

X(47877) lies on these lines: {325, 523}, {513, 4750}, {650, 2457}, {659, 4778}, {690, 14349}, {1734, 12073}, {2526, 4926}, {3776, 4824}, {4010, 4818}, {4802, 6545}

X(47878) = X(513)X(4984)∩X(514)X(1635)

X(47878) = 3 X[1635] - 2 X[47768], X[4453] - 3 X[47782], 3 X[661] - X[4958], X[661] + 2 X[45745], 3 X[661] - 2 X[47764], X[4958] + 6 X[45745], 3 X[45745] + X[47764], 2 X[1639] - 3 X[4893], X[649] + 2 X[4841], 2 X[650] + X[4988], 4 X[3239] - X[4838], 4 X[4765] - X[4979], X[4813] + 2 X[4976]

X(47878) lies on these lines: {513, 4984}, {514, 1635}, {522, 661}, {523, 1639}, {649, 4841}, {650, 4802}, {3239, 4838}, {4024, 4944}, {4120, 4777}, {4765, 4979}, {4813, 4976}

X(47878) = reflection of X(i) in X(j) for these {i,j}: {4024, 4944}, {4120, 47777}, {4958, 47764}, {31148, 47785}
X(47878) = crossdifference of every pair of points on line {35, 1468}
X(47878) = {X(661),X(4958)}-harmonic conjugate of X(47764)

X(47879) = X(2)X(824)∩X(514)X(1639)

X(47879) = X(47879) = X[45315] - 4 X[45334], X[45315] + 2 X[45685], 2 X[45334] + X[45685], 2 X[650] + X[4500], 2 X[3239] + X[4369], X[3776] - 4 X[4885], X[4522] + 2 X[4874], 2 X[44567] + X[45343], 2 X[44567] - 3 X[45684], X[45343] + 3 X[45684], X[4932] + 2 X[14321]

X(47879) lies on these lines: {2, 824}, {514, 1639}, {522, 4763}, {650, 4500}, {693, 6546}, {2786, 4944}, {3239, 4369}, {3776, 4885}, {4522, 4874}, {4755, 4777}, {4762, 10196}, {4789, 4893}, {4809, 4951}, {4932, 14321}

X(47879) = midpoint of X(i) and X(j) for these {i,j}: {693, 6546}, {1639, 47788}, {4789, 4893}, {4809, 4951}, {4944, 47761}, {45320, 47770}
X(47879) = reflection of X(i) in X(j) for these {i,j}: {3776, 21204}, {21204, 4885}, {47756, 45339}
X(47879) = {X(45334),X(45685)}-harmonic conjugate of X(45315)

X(47880) = X(241)X(514)∩X(513)X(4750)

X(47880) = X[650] + 2 X[3004], 7 X[650] - 4 X[11068], 7 X[3004] + 2 X[11068], 2 X[3676] + X[4841], 2 X[11068] - 7 X[47784], 4 X[21212] - X[43067], 3 X[45320] - 4 X[45677], 2 X[45677] - 3 X[47757], 3 X[4944] - 4 X[45661], 2 X[45661] - 3 X[47760], 4 X[3835] - X[4820], X[4467] + 2 X[4940], X[4790] - 4 X[17069], 5 X[4789] - X[47658], 2 X[4885] + X[45746], 10 X[4885] - X[47658], 5 X[45746] + X[47658]

X(47880) lies on these lines: {241, 514}, {513, 4750}, {523, 7625}, {824, 4944}, {900, 2526}, {1491, 4728}, {3835, 4820}, {4379, 4802}, {4467, 4940}, {4786, 4790}, {4789, 4885}

X(47880) = midpoint of X(i) and X(j) for these {i,j}: {3004, 47784}, {4789, 45746}
X(47880) = reflection of X(i) in X(j) for these {i,j}: {650, 47784}, {4786, 17069}, {4789, 4885}, {4790, 4786}, {4944, 47760}, {45320, 47757}, {47767, 46919}
X(47880) = crosssum of X(6) and X(2515)
X(47880) = crossdifference of every pair of points on line {55, 609}

X(47881) = X(230)X(231)∩X(513)X(4120)

X(47881) = 5 X[650] - 8 X[2490], X[650] + 2 X[6590], 3 X[650] - 4 X[14425], 5 X[650] - 2 X[45745], 4 X[2490] + 5 X[6590], 6 X[2490] - 5 X[14425], 4 X[2490] - X[45745], 4 X[2490] - 5 X[47766], 3 X[6590] + 2 X[14425], 5 X[6590] + X[45745], 10 X[14425] - 3 X[45745], 2 X[14425] - 3 X[47766], X[45745] - 5 X[47766], 2 X[4120] - 3 X[4944], 2 X[4927] - 3 X[45320], X[4927] - 6 X[45685], X[4927] - 3 X[47788], X[45320] - 4 X[45685], X[4773] - 3 X[47767], 2 X[649] + X[4820], 4 X[2529] - X[4979], 2 X[3700] + X[4790], X[4024] + 2 X[4394], 4 X[4521] - X[4841]

X(47881) lies on these lines: {230, 231}, {513, 4120}, {514, 1639}, {522, 4773}, {649, 4820}, {1635, 4777}, {2529, 4979}, {3239, 4778}, {3667, 3700}, {4024, 4394}, {4521, 4841}, {4762, 4789}, {4802, 4893}

X(47881) = midpoint of X(i) and X(j) for these {i,j}: {649, 4931}, {4789, 47771}, {6590, 47766}
X(47881) = reflection of X(i) in X(j) for these {i,j}: {650, 47766}, {4820, 4931}, {45320, 47788}, {47777, 1639}, {47788, 45685}
X(47881) = crossdifference of every pair of points on line {3, 5315}
X(47881) = {X(2490),X(45745)}-harmonic conjugate of X(650)

X(47882) = X(2)X(824)∩X(241)X(514)

X(47882) = 2 X[650] + X[3776], X[650] + 2 X[21212], X[3004] + 2 X[31286], X[3776] - 4 X[21212], X[4369] - 4 X[7658], X[693] - 3 X[14475], X[3835] + 2 X[17069], 4 X[2487] - X[4932], X[2526] + 2 X[13246], X[4500] - 4 X[4885], X[4500] + 2 X[21196], 2 X[4885] + X[21196], X[4380] - 3 X[14435], X[4818] + 2 X[4874]

X(47882) lies on these lines: {2, 824}, {241, 514}, {522, 4928}, {693, 14475}, {900, 3835}, {1491, 4809}, {2487, 4932}, {2526, 13246}, {3739, 4500}, {3798, 6006}, {4380, 14435}, {4453, 4893}, {4750, 4776}, {4818, 4874}

X(47882) = midpoint of X(i) and X(j) for these {i,j}: {650, 47754}, {1491, 4809}, {1638, 47784}, {3004, 47767}, {4453, 4893}, {4750, 4776}
X(47882) = reflection of X(i) in X(j) for these {i,j}: {3776, 47754}, {4763, 46919}, {4928, 44432}, {47754, 21212}, {47767, 31286}
X(47882) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 38963}, {13396, 141}
X(47882) = crossdifference of every pair of points on line {55, 8626}
X(47882) = barycentric product X(i)*X(j) for these {i,j}: {514, 17333}, {693, 17601}
X(47882) = barycentric quotient X(i)/X(j) for these {i,j}: {17333, 190}, {17601, 100}
X(47882) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 21212, 3776}, {4885, 21196, 4500}

X(47883) = X(230)X(231)∩X(513)X(4773)

X(47883) = 7 X[650] - 4 X[2490], 4 X[650] - X[6590], 3 X[650] - 2 X[14425], 2 X[650] + X[45745], 16 X[2490] - 7 X[6590], 6 X[2490] - 7 X[14425], 8 X[2490] + 7 X[45745], 8 X[2490] - 7 X[47766], 3 X[6590] - 8 X[14425], X[6590] + 2 X[45745], 4 X[14425] + 3 X[45745], 4 X[14425] - 3 X[47766], 4 X[45674] - 3 X[47758], 2 X[45674] - 3 X[47785], X[4120] - 3 X[4893], 2 X[4120] - 3 X[47765], X[661] + 2 X[4765], X[4024] - 4 X[4521], 2 X[4394] + X[4841], 2 X[4927] - 3 X[47757], X[4927] - 3 X[47784]

X(47883) lies on these lines: {230, 231}, {513, 4773}, {514, 1635}, {522, 4120}, {649, 4778}, {661, 3667}, {1639, 4777}, {3239, 4931}, {4024, 4521}, {4394, 4841}, {4762, 4927}, {4926, 4976}, {4984, 6006}

X(47883) = midpoint of X(i) and X(j) for these {i,j}: {31150, 47782}, {45745, 47766}
X(47883) = reflection of X(i) in X(j) for these {i,j}: {4931, 3239}, {6590, 47766}, {47757, 47784}, {47758, 47785}, {47765, 4893}, {47766, 650}, {47768, 1635}
X(47883) = crossdifference of every pair of points on line {3, 2177}
X(47883) = {X(650),X(45745)}-harmonic conjugate of X(6590)

X(47884) = X(100)X(190)∩X(241)X(514)

X(47884) = X[4927] - 4 X[14425], 3 X[4927] - 4 X[45677], 3 X[14425] - X[45677], X[659] + 2 X[2977], X[30565] - 3 X[31992], 3 X[31992] + X[47776], 4 X[650] - X[3004], X[650] + 2 X[11068], X[3004] + 8 X[11068], X[3676] - 4 X[31182], 4 X[11068] + X[47784], X[21104] - 4 X[31286], 4 X[43061] - X[43067], X[693] - 4 X[2490], 3 X[1639] - 2 X[45661], 3 X[10196] - X[45661], 3 X[1635] - X[4750], X[4750] + 3 X[6546], 4 X[2516] - X[4025], 4 X[2527] - X[7192], X[4106] - 4 X[4521], X[4380] + 2 X[14321], 2 X[4394] + X[4468], 4 X[4394] - X[4897], 2 X[4468] + X[4897], X[4728] - 3 X[6544], 3 X[6544] - 2 X[45326]

X(47884) lies on these lines: {2, 4927}, {100, 190}, {241, 514}, {351, 523}, {524, 9810}, {693, 2490}, {812, 1639}, {918, 1635}, {2496, 4777}, {2516, 4025}, {2527, 7192}, {2786, 4773}, {2826, 6174}, {4106, 4521}, {4380, 14321}, {4394, 4468}, {4728, 6009}

X(47884) = midpoint of X(i) and X(j) for these {i,j}: {1635, 6546}, {4468, 4786}, {30565, 47776}, {31150, 47771}
X(47884) = reflection of X(i) in X(j) for these {i,j}: {2, 14425}, {1638, 4763}, {1639, 10196}, {3004, 47784}, {4728, 45326}, {4786, 4394}, {4897, 4786}, {4927, 2}, {26275, 45314}, {47754, 46919}, {47784, 650}
X(47884) = anticomplement of X(45677)
X(47884) = X(17222)-anticomplementary conjugate of X(149)
X(47884) = X(i)-complementary conjugate of X(j) for these (i,j): {2748, 141}, {5387, 21260}, {34892, 21252}, {34893, 116}
X(47884) = crosspoint of X(100) and X(9061)
X(47884) = crosssum of X(513) and X(9004)
X(47884) = crossdifference of every pair of points on line {55, 574}
X(47884) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4394, 4468, 4897}, {4728, 6544, 45326}, {31992, 47776, 30565}

X(47885) = X(210)X(513)∩X(351)X(523)

Barycentrics (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(47885) = X[659] - 4 X[11068], X[1491] - 4 X[2977], 4 X[3239] - X[4810], X[4088] + 2 X[4782], 2 X[4401] + X[4808], 2 X[4468] + X[4784]

X(47885) lies on these lines: {210, 513}, {351, 523}, {522, 659}, {650, 4802}, {1491, 2977}, {3239, 4810}, {4083, 14432}, {4088, 4782}, {4401, 4808}, {4468, 4784}

X(47885) = reflection of X(47798) in X(45314)
X(47885) = crossdifference of every pair of points on line {35, 574}

X(47886) = X(2)X(824)∩X(513)X(4750)

X(47886) = X[31148] - 4 X[44551], X[649] + 2 X[3004], X[649] - 4 X[17069], X[3004] + 2 X[17069], 2 X[650] + X[16892], X[661] + 2 X[4025], X[693] + 2 X[21196], X[693] - 4 X[21212], X[21196] + 2 X[21212], 4 X[3798] - X[4979], 2 X[3835] + X[4467], X[4024] - 4 X[4885], X[4382] + 2 X[4976], 3 X[14475] - 2 X[45320], X[4813] + 2 X[4897], X[6590] - 4 X[7658], 2 X[6590] - 5 X[24924], 2 X[6590] + X[47673], 8 X[7658] - 5 X[24924], 8 X[7658] + X[47673], 5 X[24924] + X[47673]

X(47886) lies on these lines: {2, 824}, {513, 4750}, {514, 1635}, {522, 4728}, {523, 1638}, {649, 3004}, {650, 3752}, {661, 4025}, {693, 4359}, {918, 4893}, {2786, 4776}, {3753, 14077}, {3798, 4979}, {3835, 4467}, {4024, 4885}, {4382, 4976}, {4688, 4777}, {4762, 6545}, {4813, 4897}, {4984, 6008}, {6590, 7658}

X(47886) = midpoint of X(i) and X(j) for these {i,j}: {4025, 47783}, {4453, 47782}, {6546, 16892}, {21196, 21204}
X(47886) = reflection of X(i) in X(j) for these {i,j}: {661, 47783}, {693, 21204}, {1635, 47785}, {4379, 1638}, {4728, 47757}, {4893, 47784}, {6545, 47754}, {6546, 650}, {21204, 21212}, {31148, 47758}, {47758, 44551}, {47762, 45674}
X(47886) = crossdifference of every pair of points on line {2177, 4262}
X(47886) = barycentric product X(i)*X(j) for these {i,j}: {513, 33936}, {514, 4643}, {693, 4414}
X(47886) = barycentric quotient X(i)/X(j) for these {i,j}: {4414, 100}, {4643, 190}, {33936, 668}
X(47886) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 17069, 649}, {6590, 7658, 24924}, {21196, 21212, 693}, {24924, 47673, 6590}

X(47887) = X(354)X(513)∩X(514)X(14413)

X(47887) = X[693] + 2 X[4458], X[2254] - 4 X[3676], X[2254] + 2 X[47123], 2 X[3676] + X[47123], 2 X[4025] + X[4804], 2 X[24720] + X[47695], 2 X[650] + X[47704], 4 X[676] - X[4724], 2 X[676] + X[21104], X[4724] + 2 X[21104], X[4088] - 4 X[4885], 2 X[4142] + X[4801], X[4449] + 2 X[7178]

X(47887) lies on these lines: {354, 513}, {514, 14413}, {522, 693}, {523, 1638}, {650, 4802}, {676, 1459}, {985, 4817}, {4088, 4885}, {4142, 4801}, {4449, 6366}

X(47887) = reflection of X(i) in X(j) for these {i,j}: {47811, 47800}, {47812, 21183}, {47828, 1638}
X(47887) = X(28868)-anticomplementary conjugate of X(329)
X(47887) = crossdifference of every pair of points on line {35, 41}
X(47887) = barycentric product X(i)*X(j) for these {i,j}: {514, 5880}, {24002, 28125}
X(47887) = barycentric quotient X(i)/X(j) for these {i,j}: {5880, 190}, {28125, 644}
X(47887) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {676, 21104, 4724}, {3676, 47123, 2254}

X(47888) = X(2)X(784)∩X(513)X(5131)

X(47888) = 2 X[650] + X[2530], X[667] + 2 X[1491], X[667] - 4 X[14838], X[1491] + 2 X[14838], 4 X[905] - X[4378], 2 X[905] + X[4705], X[4378] + 2 X[4705], 2 X[1734] + X[4775], X[2526] + 2 X[6050], 2 X[3960] + X[4490], X[4449] + 2 X[4770], X[4834] - 4 X[9508], X[4834] + 2 X[14349], 2 X[9508] + X[14349]

X(47888) lies on these lines: {2, 784}, {513, 5131}, {650, 2530}, {667, 830}, {905, 4378}, {1734, 4775}, {2526, 6050}, {3960, 4490}, {4449, 4770}, {4834, 9508}, {4893, 6372}, {8678, 14419}

X(47888) = crossdifference of every pair of points on line {3723, 3744}
X(47888) = barycentric product X(i)*X(j) for these {i,j}: {513, 4445}, {693, 31451}
X(47888) = barycentric quotient X(i)/X(j) for these {i,j}: {4445, 668}, {31451, 100}
X(47888) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {905, 4705, 4378}, {1491, 14838, 667}, {9508, 14349, 4834}

X(47889) = X(659)X(4978)∩X(693)X(814)

X(47889) = X[659] + 2 X[4978], 2 X[693] + X[4367], 2 X[1019] + X[4810], X[3777] + 2 X[7662], X[4378] + 2 X[4823], 2 X[4449] + X[4774], X[4490] - 4 X[4885], X[4801] + 2 X[4874], 2 X[4992] + X[7192]

X(47889) lies on these lines: {659, 4978}, {693, 814}, {1019, 4810}, {3777, 7662}, {4083, 4379}, {4378, 4823}, {4449, 4774}, {4490, 4885}, {4800, 6372}, {4801, 4874}, {4992, 7192}

X(47889) = midpoint of X(i) and X(j) for these {i,j}: {4801, 47815}, {4978, 47818}
X(47889) = reflection of X(i) in X(j) for these {i,j}: {659, 47818}, {47815, 4874}

X(47890) = X(2)X(2490)∩X(241)X(514)

X(47890) = 3 X[2] - 4 X[2490], 4 X[2490] - X[47652], 5 X[17494] + X[47658], 3 X[17494] + X[47659], 3 X[17494] - X[47661], X[17494] + 3 X[47773], 3 X[47658] - 5 X[47659], X[47658] - 5 X[47660], 3 X[47658] + 5 X[47661], X[47658] - 15 X[47773], X[47659] - 3 X[47660], X[47659] - 9 X[47773], 3 X[47660] + X[47661], X[47660] - 3 X[47773], X[47661] + 9 X[47773], X[47695] - 3 X[47805], 4 X[650] - 3 X[47784], 3 X[1638] - 2 X[3776], 3 X[1638] - 4 X[31286], X[3004] - 4 X[11068], 2 X[3004] - 3 X[47784], 2 X[3676] - 3 X[47761], 2 X[4369] - 3 X[47767], 3 X[4763] - 2 X[21212], 4 X[7658] - 3 X[47754], 8 X[11068] - 3 X[47784], X[21104] - 3 X[47767], 4 X[31182] - 3 X[46919], 4 X[43061] - 3 X[47761], X[661] - 3 X[6546], 3 X[661] - X[23731], 9 X[6546] - X[23731], 3 X[693] - X[47650], X[693] - 3 X[47771], 2 X[693] - 3 X[47788], X[47650] + 3 X[47663], X[47650] - 9 X[47771], 2 X[47650] - 9 X[47788], X[47663] + 3 X[47771], 2 X[47663] + 3 X[47788], 3 X[1639] - 2 X[3835], 3 X[1639] - X[23729], 4 X[2487] - 3 X[4453], 4 X[2487] - 5 X[27013], 3 X[4453] - 5 X[27013], 2 X[3239] - 3 X[47770], X[4106] - 3 X[47770], 4 X[4885] - 3 X[4927], 2 X[4885] - 3 X[47766]

X(47890) lies on these lines: {2, 2490}, {23, 385}, {241, 514}, {333, 7192}, {513, 4468}, {522, 4830}, {525, 4063}, {649, 918}, {661, 1211}, {693, 6084}, {812, 3700}, {824, 4976}, {884, 2402}, {900, 4380}, {1491, 2977}, {1639, 3835}, {2487, 4453}, {2526, 4778}, {3239, 4106}, {3800, 4040}, {3910, 4498}, {4025, 4394}, {4382, 6009}, {4477, 6362}, {4762, 6590}, {4885, 4927}, {6332, 8712}

X(47890) = midpoint of X(i) and X(j) for these {i,j}: {693, 47663}, {4380, 25259}, {17494, 47660}, {47659, 47661}
X(47890) = reflection of X(i) in X(j) for these {i,j}: {650, 11068}, {1491, 2977}, {3004, 650}, {3676, 43061}, {3776, 31286}, {4025, 4394}, {4106, 3239}, {4897, 649}, {4927, 47766}, {21104, 4369}, {23729, 3835}, {47788, 47771}
X(47890) = complement of X(47652)
X(47890) = anticomplement of the isotomic conjugate of X(8706)
X(47890) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1222, 21293}, {1261, 33650}, {8706, 6327}, {23617, 150}
X(47890) = X(i)-Ceva conjugate of X(j) for these (i,j): {7185, 24840}, {8706, 2}
X(47890) = X(17353)-Dao conjugate of X(33946)
X(47890) = crosspoint of X(6613) and X(30705)
X(47890) = crossdifference of every pair of points on line {39, 55}
X(47890) = barycentric product X(i)*X(j) for these {i,j}: {514, 17353}, {693, 3744}, {24002, 30618}
X(47890) = barycentric quotient X(i)/X(j) for these {i,j}: {3744, 100}, {17353, 190}, {30618, 644}
X(47890) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 3004, 47784}, {1639, 23729, 3835}, {3676, 43061, 47761}, {3776, 31286, 1638}, {4106, 47770, 3239}, {4453, 27013, 2487}, {17494, 47659, 47661}, {17494, 47773, 47660}, {21104, 47767, 4369}, {47660, 47661, 47659}, {47663, 47771, 693}

X(47891) = X(241)X(514)∩X(513)X(4927)

X(47891) = 3 X[6548] + X[7192], X[3004] - 4 X[3676], X[3004] + 2 X[43067], 2 X[3676] + X[43067], 2 X[4369] + X[21104], X[4841] - 4 X[21212], X[661] - 3 X[14475], 2 X[693] + X[4897]

X(47891) lies on these lines: {86, 4833}, {241, 514}, {513, 4927}, {523, 4453}, {649, 6009}, {661, 14475}, {693, 900}, {918, 4379}, {4025, 4777}, {4106, 6006}

X(47891) = midpoint of X(i) and X(j) for these {i,j}: {693, 47755}, {4453, 47780}, {21104, 47767}, {43067, 47754}
X(47891) = reflection of X(i) in X(j) for these {i,j}: {3004, 47754}, {4897, 47755}, {4927, 21183}, {47754, 3676}, {47767, 4369}, {47784, 1638}, {47788, 4379}
X(47891) = barycentric product X(693)*X(37520)
X(47891) = barycentric quotient X(i)/X(j) for these {i,j}: {27747, 4767}, {37520, 100}
X(47891) = {X(3676),X(43067)}-harmonic conjugate of X(3004)

X(47892) = X(2)X(4927)∩X(514)X(1635)

X(47892) = 3 X[2] - 4 X[14425], 5 X[2] - 4 X[45677], 5 X[4927] - 6 X[45677], 5 X[14425] - 3 X[45677], 4 X[659] - X[47695], 8 X[17494] + X[47658], 5 X[17494] + X[47659], 2 X[17494] + X[47660], 4 X[17494] - X[47661], 5 X[47658] - 8 X[47659], X[47658] - 4 X[47660], X[47658] + 2 X[47661], X[47658] - 8 X[47773], 2 X[47659] - 5 X[47660], 4 X[47659] + 5 X[47661], X[47659] - 5 X[47773], 2 X[47660] + X[47661], X[47661] + 4 X[47773], 3 X[1635] - X[21115], 3 X[1635] - 2 X[45674], 3 X[4453] - 2 X[21115], 3 X[4453] - 4 X[45674], X[693] - 4 X[11068], X[4120] - 3 X[6546], 2 X[4120] - 3 X[30565], 2 X[4773] - 3 X[47776], 2 X[1639] - 3 X[31992], X[21297] - 3 X[31992], X[4380] + 2 X[4468], 2 X[4380] + X[44449], 4 X[4468] - X[44449], X[4088] + 2 X[4830], 2 X[4928] - 3 X[6544]

X(47892) lies on these lines: {2, 4927}, {23, 385}, {88, 2403}, {100, 1292}, {105, 2402}, {514, 1635}, {693, 11068}, {812, 4120}, {918, 4773}, {1281, 2793}, {1639, 6009}, {2254, 4778}, {3667, 4380}, {3808, 14404}, {4088, 4830}, {4728, 10196}, {4762, 4789}, {4763, 6545}, {4802, 4809}, {4928, 6544}

X(47892) = midpoint of X(17494) and X(47773)
X(47892) = reflection of X(i) in X(j) for these {i,j}: {693, 47766}, {2403, 30725}, {4453, 1635}, {4728, 10196}, {4789, 47771}, {4927, 14425}, {6545, 4763}, {21115, 45674}, {21297, 1639}, {30565, 6546}, {44433, 659}, {47660, 47773}, {47695, 44433}, {47766, 11068}, {47782, 31150}
X(47892) = anticomplement of X(4927)
X(47892) = anticomplement of the isotomic conjugate of X(6079)
X(47892) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1120, 21293}, {6079, 6327}, {40400, 150}
X(47892) = X(6079)-Ceva conjugate of X(2)
X(47892) = crosssum of X(3051) and X(8660)
X(47892) = crossdifference of every pair of points on line {39, 2177}
X(47892) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1635, 21115, 45674}, {4380, 4468, 44449}, {4927, 14425, 2}, {17494, 47660, 47661}, {21115, 45674, 4453}, {21297, 31992, 1639}, {47660, 47661, 47658}

X(47893) = X(650)X(3777)∩X(659)X(2530)

X(47893) = 2 X[650] + X[3777], X[659] + 2 X[2530], X[659] - 4 X[14838], X[2530] + 2 X[14838], 2 X[905] + X[1491], 4 X[905] - X[4367], 2 X[1491] + X[4367], 2 X[1734] + X[4879], 2 X[3669] + X[4490], 2 X[3837] + X[4560], 2 X[3960] + X[4705], X[4784] + 2 X[14349]

X(47893) lies on these lines: {650, 3777}, {659, 2530}, {830, 14419}, {905, 1491}, {1734, 4879}, {3669, 4490}, {3837, 4560}, {3960, 4705}, {4784, 14349}, {4800, 8714}

X(47893) = reflection of X(4800) in X(47839)
X(47893) = crossdifference of every pair of points on line {3247, 3749}
X(47893) = barycentric product X(513)*X(17287)
X(47893) = barycentric quotient X(17287)/X(668)
X(47893) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {905, 1491, 4367}, {2530, 14838, 659}

X(47894) = X(2)X(824)∩X(239)X(514)

X(47894) = 2 X[693] - 3 X[6548], 2 X[693] + X[17161], 3 X[6548] + X[17161], 3 X[6548] - 4 X[47754], X[17161] + 4 X[47754], 2 X[649] + X[47653], 4 X[4025] - X[7192], 2 X[4025] + X[45746], 4 X[4765] - X[47663], X[7192] + 2 X[45746], 2 X[16892] + X[17494], X[16892] + 2 X[21196], X[17494] - 4 X[21196], X[17496] + 2 X[21124], 2 X[45745] + X[47676], 4 X[650] - 3 X[31992], 2 X[650] + X[47677], 3 X[31992] + 2 X[47677], 2 X[3004] + X[4467], 4 X[3004] - X[20295], 2 X[4467] + X[20295], X[4024] - 3 X[14475], X[4024] - 4 X[21212], 2 X[4024] - 5 X[26985], 3 X[14475] - 4 X[21212], 6 X[14475] - 5 X[26985], 8 X[21212] - 5 X[26985], 2 X[4976] + X[47652]

X(47894) lies on these lines: {2, 824}, {75, 693}, {239, 514}, {523, 4453}, {650, 4850}, {900, 3004}, {1638, 4789}, {4024, 14475}, {4928, 4931}, {4976, 6009}

X(47894) = midpoint of X(45746) and X(47755)
X(47894) = reflection of X(i) in X(j) for these {i,j}: {693, 47754}, {4789, 1638}, {4931, 4928}, {7192, 47755}, {47755, 4025}, {47763, 4750}, {47776, 27486}, {47780, 4453}
X(47894) = X(13396)-anticomplementary conjugate of X(69)
X(47894) = crossdifference of every pair of points on line {42, 2251}
X(47894) = barycentric product X(i)*X(j) for these {i,j}: {514, 17271}, {3261, 4256}
X(47894) = barycentric quotient X(i)/X(j) for these {i,j}: {4256, 101}, {17271, 190}
X(47894) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 47754, 6548}, {3004, 4467, 20295}, {4024, 21212, 26985}, {4025, 45746, 7192}, {16892, 21196, 17494}

X(47895) = (name pending)

X(47896) = ISOGONAL CONJUGATE OF X(15929)

X(47896) lies on these lines: {61, 17402}, {533, 34219}, {10409, 11127}, {11581, 23895}, {15609, 19778}

X(47896) = reflection of X(i) in X(j) for these (i, j): (10409, 11127), (19778, 15609)
X(47896) = isogonal conjugate of X(15929)
X(47896) = antigonal conjugate of X(19778)

X(47897) = ISOGONAL CONJUGATE OF X(15930)

X(47897) lies on these lines: {62, 17403}, {532, 34220}, {10410, 11126}, {11582, 23896}, {15610, 19779}

X(47897) = reflection of X(i) in X(j) for these (i, j): (10410, 11126), (19779, 15610)
X(47897) = isogonal conjugate of X(15930)
X(47897) = antigonal conjugate of X(19779)

X(47898) = X(4)X(5995)∩X(8754)X(46667)

X(47898) lies on the nine-point circle and these lines: {4, 5995}, {8754, 46667}, {16229, 34981}

X(47898) = center of the circumconic {{A, B, C, X(4), X(470)}}
X(47898) = inverse of X(5995) in polar circle
X(47898) = orthoassociate of X(5995)
X(47898) = orthopole of the tripolar of X(38414)
X(47898) = Poncelet point of X(i) for these i: {470, 1832}

X(47899) = X(4)X(5994)∩X(8754)X(46666)

X(47899) lies on the nine-point circle and these lines: {4, 5994}, {8754, 46666}, {16229, 34981}

X(47899) = center of the circumconic {{A, B, C, X(4), X(471)}}
X(47899) = inverse of X(5994) in polar circle
X(47899) = orthoassociate of X(5994)
X(47899) = Poncelet point of X(i) for these i: {471, 1833}

If L1 and L2 are lines that meet in a point P not at infinity, then the {L1,L2}-coordiinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1: a α + b β + 2 γ = 0.

L2 = anti-orthic axis: b c α + c a β + a b γ = 0.

The origin is given by (0,0) = X(661) = a (b^2 - c^2) : b (c^2 - a^2) : c (a^2 - b^2.

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b - c) (a b + a c - x - a y) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogenous of degree 2, and y is symmetric and homogeneous of degree 1.

The appearance of {x,y}, k in the following table means that (x,y) = X(k):

{-((2 a b c)/(a+b+c)), a+b+c}, 4498}
{-((2 a b c)/(a+b+c)), (a b+a c+b c)/(a+b+c)}, 4490}
{-2 (a^2+b^2+c^2), (2 (a^2+b^2+c^2))/(a+b+c)}, 47702}
{-((2 a b c)/(a+b+c)), (2 (a b+a c+b c))/(a+b+c)}, 4041}
{-a^2-b^2-c^2,-a-b-c}, 23731}
{-a b-a c-b c,-a-b-c}, 31290}
{-a b-a c-b c,0}, 47666}
{-a^2-b^2-c^2,a+b+c}, 16892}
{-a^2-b^2-c^2,(a^2+b^2+c^2)/(a+b+c)}, 47701}
{-a b-a c-b c,a+b+c}, 17494}
{-a b-a c-b c,(a b+a c+b c)/(a+b+c)}, 4824}
{-((a b c)/(a+b+c)), a+b+c}, 4063}
{-((a b c)/(a+b+c)), (a b+a c+b c)/(a+b+c)}, 4705}
{-a b-a c-b c,2 (a+b+c)}, 4380}
{-((a b c)/(a+b+c)), (2 (a b+a c+b c))/(a+b+c)}, 1734}
{1/2 (-a^2-b^2-c^2), 1/2 (a+b+c)}, 3004}
{1/2 (-a^2-b^2-c^2), a+b+c}, 4025}
{0,-a-b-c}, 4813}
{0,0}, 661}
{0,1/2 (a+b+c)}, 650}
{0,a+b+c}, 649}
{0,(a^2+b^2+c^2)/(a+b+c)}, 4724}
{0,(a b+a c+b c)/(a+b+c)}, 1491}
{0,2 (a+b+c)}, 4979}
{0,(2 (a b+a c+b c))/(a+b+c)}, 2254}
{1/2 (a b+a c+b c), -((a b+a c+b c)/(2 (a+b+c)))}, 4806}
{1/2 (a^2+b^2+c^2), 0}, 4468}
{1/2 (a b+a c+b c), 0}, 3835}
{1/2 (a^2+b^2+c^2), 1/2 (a+b+c)}, 47890}
{1/2 (a b+a c+b c), 1/2 (a+b+c)}, 4369}
{1/2 (a b+a c+b c), (a^2+b^2+c^2)/(2 (a+b+c))}, 3716}
{1/2 (a b+a c+b c), (a b+a c+b c)/(2 (a+b+c))}, 3837}
{(a b c)/(2 (a+b+c)), 1/2 (a+b+c)}, 14838}
{1/2 (a b+a c+b c), a+b+c}, 4932}
{1/2 (a b+a c+b c), (a b+a c+b c)/(a+b+c)}, 24720}
{a b+a c+b c,-((2 (a^2+b^2+c^2))/(a+b+c))}, 47685}
{a b+a c+b c,-((2 a b c)/(a^2+b^2+c^2))}, 15413}
{a^2+b^2+c^2,-((a^2+b^2+c^2)/(a+b+c))}, 4088}
{a b+a c+b c,-a-b-c}, 20295}
{a b+a c+b c,-((a^2+b^2+c^2)/(a+b+c))}, 46403}
{a b+a c+b c,-((a b+a c+b c)/(a+b+c))}, 4010}
{(a b c)/(a+b+c), -((a b+a c+b c)/(a+b+c))}, 4983}
{a b+a c+b c,1/2 (-a-b-c)}, 4106}
{a b+a c+b c,0}, 693}
{(a b c)/(a+b+c), 0}, 14349}
{a b+a c+b c,1/2 (a+b+c)}, 43067}
{a b+a c+b c,(a^2+b^2+c^2)/(2 (a+b+c))}, 7662}
{(a b c)/(a+b+c), 1/2 (a+b+c)}, 905}
{a b+a c+b c,a+b+c}, 7192}
{a b+a c+b c,(a^2+b^2+c^2)/(a+b+c)}, 47694}
{a b+a c+b c,(a b+a c+b c)/(a+b+c)}, 21146}
{(a b c)/(a+b+c), a+b+c}, 1019}
{(a b c)/(a+b+c), (a^2+b^2+c^2)/(a+b+c)}, 4040}
{(a b c)/(a+b+c), (a b+a c+b c)/(a+b+c)}, 2530}
{a b+a c+b c,(2 (a^2+b^2+c^2))/(a+b+c)}, 47697}
{(a b c)/(a+b+c), (2 (a b+a c+b c))/(a+b+c)}, 4905}
{2 (a^2+b^2+c^2), -((2 (a^2+b^2+c^2))/(a+b+c))}, 47700}
{2 (a b+a c+b c), -((2 (a b+a c+b c))/(a+b+c))}, 4804}
{(2 a b c)/(a+b+c), -((2 (a b+a c+b c))/(a+b+c))}, 4822}
{2 (a b+a c+b c), -a-b-c}, 4382}
{2 (a b+a c+b c), 0}, 47672}
{(2 a b c)/(a+b+c), 1/2 (a+b+c)}, 3669}
{(2 a b c)/(a+b+c), (a^2+b^2+c^2)/(a+b+c)}, 663}
{(2 a b c)/(a+b+c), (a b+a c+b c)/(a+b+c)}, 3777}
{-2*(a^2 + b^2 + c^2), -2*(a + b + c)}, 47900
{-2*(a^2 + b^2 + c^2), (-2*(a^2 + b^2 + c^2))/(a + b + c)}, 47901
{-2*(a^2 + b^2 + c^2), (-2*(a*b + a*c + b*c))/(a + b + c)};, 47902
{-2*(a*b + a*c + b*c), -2*(a + b + c)}, 47903
{-2*(a*b + a*c + b*c), (-2*(a*b + a*c + b*c))/(a + b + c)}, 47904
{(-2*a*b*c)/(a + b + c), (-2*(a^2 + b^2 + c^2))/(a + b + c)}, 47905
{(-2*a*b*c)/(a + b + c), (-2*(a*b + a*c + b*c))/(a + b + c)}, 47906
{-2*(a^2 + b^2 + c^2), -a - b - c}, 47907
{-2*(a*b + a*c + b*c), -a - b - c}, 47908
{-2*(a*b + a*c + b*c), -((a^2 + b^2 + c^2)/(a + b + c))}, 47909
{-2*(a*b + a*c + b*c), -((a*b + a*c + b*c)/(a + b + c))}, 47910
{(-2*a*b*c)/(a + b + c), -a - b - c}, 47911
{(-2*a*b*c)/(a + b + c), -((a^2 + b^2 + c^2)/(a + b + c))}, 47912
{(-2*a*b*c)/(a + b + c), -((a*b + a*c + b*c)/(a + b + c))}, 47913
{-2*(a*b + a*c + b*c), (-a - b - c)/2}, 47914
{(-2*a*b*c)/(a + b + c), (-a - b - c)/2}, 47915
{-2*(a^2 + b^2 + c^2), 0}, 47916
{-2*(a*b + a*c + b*c), 0}, 47917
{(-2*a*b*c)/(a + b + c), 0}, 47918
{-2*(a^2 + b^2 + c^2), (a + b + c)/2}, 47919
{-2*(a*b + a*c + b*c), (a + b + c)/2}, 47920
{(-2*a*b*c)/(a + b + c), (a + b + c)/2}, 47921
{(-2*a*b*c)/(a + b + c), (a*b + a*c + b*c)/(2*(a + b + c))}, 47922
{-2*(a^2 + b^2 + c^2), a + b + c}, 47923
{-2*(a^2 + b^2 + c^2), (a^2 + b^2 + c^2)/(a + b + c)}, 47924
{-2*(a^2 + b^2 + c^2), (a*b + a*c + b*c)/(a + b + c)}, 47925
{-2*(a*b + a*c + b*c), a + b + c}, 47926
{-2*(a*b + a*c + b*c), (a^2 + b^2 + c^2)/(a + b + c)}, 47927
{-2*(a*b + a*c + b*c), (a*b + a*c + b*c)/(a + b + c)}, 47928
{(-2*a*b*c)/(a + b + c), (a^2 + b^2 + c^2)/(a + b + c)}, 47929
{-2*(a^2 + b^2 + c^2), 2*(a + b + c)}, 47930 {-2*(a^2 + b^2 + c^2), (2*(a*b + a*c + b*c))/(a + b + c)}, 47931 {-2*(a*b + a*c + b*c), 2*(a + b + c)}, 47932
{-2*(a*b + a*c + b*c), (2*(a^2 + b^2 + c^2))/(a + b + c)}, 47933
{-2*(a*b + a*c + b*c), (2*(a*b + a*c + b*c))/(a + b + c)}, 47934
{(-2*a*b*c)/(a + b + c), 2*(a + b + c)}, 47935
{(-2*a*b*c)/(a + b + c), (2*(a^2 + b^2 + c^2))/(a + b + c)}, 47936
{-a^2 - b^2 - c^2, -2*(a + b + c)}, 47937
{-a^2 - b^2 - c^2, (-2*(a*b + a*c + b*c))/(a + b + c)}, 47938
{-(a*b) - a*c - b*c, -2*(a + b + c)}, 47939
{-(a*b) - a*c - b*c, (-2*(a^2 + b^2 + c^2))/(a + b + c)}, 47940
{-(a*b) - a*c - b*c, (-2*(a*b + a*c + b*c))/(a + b + c)}, 47941
{-((a*b*c)/(a + b + c)), (-2*(a*b + a*c + b*c))/(a + b + c)}, 47942
{-a^2 - b^2 - c^2, -((a^2 + b^2 + c^2)/(a + b + c))}, 47943
{-a^2 - b^2 - c^2, -((a*b + a*c + b*c)/(a + b + c))}, 47944
{-(a*b) - a*c - b*c, -((a^2 + b^2 + c^2)/(a + b + c))}, 47945
{-(a*b) - a*c - b*c, -((a*b + a*c + b*c)/(a + b + c))}, 47946
{-((a*b*c)/(a + b + c)), -a - b - c}, 47947
{-((a*b*c)/(a + b + c)), -((a^2 + b^2 + c^2)/(a + b + c))}, 47948
{-((a*b*c)/(a + b + c)), -((a*b + a*c + b*c)/(a + b + c))}, 47949
{-a^2 - b^2 - c^2, (-a - b - c)/2}, 47950
{-a^2 - b^2 - c^2, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 47951
{-(a*b) - a*c - b*c, (-a - b - c)/2}, 47952
{-(a*b) - a*c - b*c, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 47953
{-(a*b) - a*c - b*c, -1/2*(a*b + a*c + b*c)/(a + b + c)}, 47954
{-((a*b*c)/(a + b + c)), (-a - b - c)/2}, 47955
{-((a*b*c)/(a + b + c)), -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 47956
{-((a*b*c)/(a + b + c)), -1/2*(a*b + a*c + b*c)/(a + b + c)}, 47957
{-a^2 - b^2 - c^2, 0}, 47958
{-((a*b*c)/(a + b + c)), 0}, 47959
{-a^2 - b^2 - c^2, (a + b + c)/2}, 47960
{-a^2 - b^2 - c^2, (a^2 + b^2 + c^2)/(2*(a + b + c))}, 47961
{-(a*b) - a*c - b*c, (a + b + c)/2}, 47962
{-(a*b) - a*c - b*c, (a^2 + b^2 + c^2)/(2*(a + b + c))}, 47963
{-(a*b) - a*c - b*c, (a*b + a*c + b*c)/(2*(a + b + c))}, 47964
{-((a*b*c)/(a + b + c)), (a + b + c)/2}, 47965
{-((a*b*c)/(a + b + c)), (a^2 + b^2 + c^2)/(2*(a + b + c))}, 47966
{-((a*b*c)/(a + b + c)), (a*b + a*c + b*c)/(2*(a + b + c))}, 47967
{-a^2 - b^2 - c^2, (a*b + a*c + b*c)/(a + b + c)}, 47968
{-(a*b) - a*c - b*c, (a^2 + b^2 + c^2)/(a + b + c)}, 47969
{-((a*b*c)/(a + b + c)), (a^2 + b^2 + c^2)/(a + b + c)}, 47970
{-a^2 - b^2 - c^2, 2*(a + b + c)}, 47971
{-a^2 - b^2 - c^2, (2*(a^2 + b^2 + c^2))/(a + b + c)}, 47972
{-a^2 - b^2 - c^2, (2*(a*b + a*c + b*c))/(a + b + c)}, 47973
{-(a*b) - a*c - b*c, (2*(a^2 + b^2 + c^2))/(a + b + c)}, 47974
{-(a*b) - a*c - b*c, (2*(a*b + a*c + b*c))/(a + b + c)}, 47975
{-((a*b*c)/(a + b + c)), 2*(a + b + c)}, 47976
{-((a*b*c)/(a + b + c)), (2*(a^2 + b^2 + c^2))/(a + b + c)}, 47977
{(-a^2 - b^2 - c^2)/2, -2*(a + b + c)}, 47978
{(-a^2 - b^2 - c^2)/2, (-2*(a*b + a*c + b*c))/(a + b + c)}, 47979
{(-(a*b) - a*c - b*c)/2, (-2*(a*b + a*c + b*c))/(a + b + c)}, 47980
{(-a^2 - b^2 - c^2)/2, -a - b - c}, 47981
{(-a^2 - b^2 - c^2)/2, -((a^2 + b^2 + c^2)/(a + b + c))}, 47982
{(-a^2 - b^2 - c^2)/2, -((a*b + a*c + b*c)/(a + b + c))}, 47983
{(-(a*b) - a*c - b*c)/2, -a - b - c}, 47984
{(-(a*b) - a*c - b*c)/2, -((a^2 + b^2 + c^2)/(a + b + c))}, 47985v {(-(a*b) - a*c - b*c)/2, -((a*b + a*c + b*c)/(a + b + c))}, 47986
{-1/2*(a*b*c)/(a + b + c), -((a*b + a*c + b*c)/(a + b + c))}, 47987
{(-a^2 - b^2 - c^2)/2, (-a - b - c)/2}, 47988
{(-a^2 - b^2 - c^2)/2, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 47989
{(-a^2 - b^2 - c^2)/2, -1/2*(a*b + a*c + b*c)/(a + b + c)}, 47990
{(-(a*b) - a*c - b*c)/2, (-a - b - c)/2}, 47991
{(-(a*b) - a*c - b*c)/2, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 47992
{(-(a*b) - a*c - b*c)/2, -1/2*(a*b + a*c + b*c)/(a + b + c)}, 47993
{-1/2*(a*b*c)/(a + b + c), -1/2*(a*b + a*c + b*c)/(a + b + c)}, 47994
{(-a^2 - b^2 - c^2)/2, 0}, 47995
{(-(a*b) - a*c - b*c)/2, 0}, 47996
{-1/2*(a*b*c)/(a + b + c), 0}, 47997
{(-a^2 - b^2 - c^2)/2, (a^2 + b^2 + c^2)/(2*(a + b + c))}, 47998
{(-a^2 - b^2 - c^2)/2, (a*b + a*c + b*c)/(2*(a + b + c))}, 47999
{(-(a*b) - a*c - b*c)/2, (a + b + c)/2}, 48000
{(-(a*b) - a*c - b*c)/2, (a^2 + b^2 + c^2)/(2*(a + b + c))}, 48001
{(-(a*b) - a*c - b*c)/2, (a*b + a*c + b*c)/(2*(a + b + c))}, 48002
{-1/2*(a*b*c)/(a + b + c), (a + b + c)/2}, 48003
{-1/2*(a*b*c)/(a + b + c), (a^2 + b^2 + c^2)/(2*(a + b + c))}, 48004;
{-1/2*(a*b*c)/(a + b + c), (a*b + a*c + b*c)/(2*(a + b + c))}, 48005
{(-a^2 - b^2 - c^2)/2, (a^2 + b^2 + c^2)/(a + b + c)}, 48006
{(-a^2 - b^2 - c^2)/2, (a*b + a*c + b*c)/(a + b + c)}, 48007
{(-(a*b) - a*c - b*c)/2, a + b + c}, 48008
{(-(a*b) - a*c - b*c)/2, (a^2 + b^2 + c^2)/(a + b + c)}, 48009
{(-(a*b) - a*c - b*c)/2, (a*b + a*c + b*c)/(a + b + c)}, 48010
{-1/2*(a*b*c)/(a + b + c), a + b + c}, 48011
{-1/2*(a*b*c)/(a + b + c), (a*b + a*c + b*c)/(a + b + c)}, 48012
{(-a^2 - b^2 - c^2)/2, 2*(a + b + c)}, 48013
{(-a^2 - b^2 - c^2)/2, (2*(a^2 + b^2 + c^2))/(a + b + c)}, 48014
{(-a^2 - b^2 - c^2)/2, (2*(a*b + a*c + b*c))/(a + b + c)}, 48015
{(-(a*b) - a*c - b*c)/2, 2*(a + b + c)}, 48016
{(-(a*b) - a*c - b*c)/2, (2*(a*b + a*c + b*c))/(a + b + c)}, 48017
{-1/2*(a*b*c)/(a + b + c), (2*(a*b + a*c + b*c))/(a + b + c)}, 48018
{0, -2*(a + b + c)}, 48019
{0, (-2*(a^2 + b^2 + c^2))/(a + b + c)}, 48020
{0, (-2*(a*b + a*c + b*c))/(a + b + c)}, 48021
{0, (-2*a*b*c)/(a^2 + b^2 + c^2)}, 48022
{0, -((a^2 + b^2 + c^2)/(a + b + c))}, 48023
{0, -((a*b + a*c + b*c)/(a + b + c))}, 48024
{0, -((a*b*c)/(a^2 + b^2 + c^2))}, 48025
{0, (-a - b - c)/2}, 48026
{0, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 48027
{0, -1/2*(a*b + a*c + b*c)/(a + b + c)}, 48028
{0, (a^2 + b^2 + c^2)/(2*(a + b + c))}, 48029
{0, (a*b + a*c + b*c)/(2*(a + b + c))}, 48030
{0, (a*b*c)/(a^2 + b^2 + c^2)}, 48031
{0, (2*(a^2 + b^2 + c^2))/(a + b + c)}, 48032
{0, (2*a*b*c)/(a^2 + b^2 + c^2)}, 48033;
{(a^2 + b^2 + c^2)/2, -2*(a + b + c)}, 48034
{(a^2 + b^2 + c^2)/2, (-2*(a^2 + b^2 + c^2))/(a + b + c)}, 48035
{(a^2 + b^2 + c^2)/2, (-2*(a*b + a*c + b*c))/(a + b + c)}, 48036
{(a*b + a*c + b*c)/2, (-2*(a*b + a*c + b*c))/(a + b + c)}, 48037
{(a^2 + b^2 + c^2)/2, -a - b - c}, 48038
{(a^2 + b^2 + c^2)/2, -((a^2 + b^2 + c^2)/(a + b + c))}, 48039
{(a^2 + b^2 + c^2)/2, -((a*b + a*c + b*c)/(a + b + c))}, 48040
{(a*b + a*c + b*c)/2, -a - b - c}, 48041
{(a*b + a*c + b*c)/2, -((a^2 + b^2 + c^2)/(a + b + c))}, 48042
{(a*b + a*c + b*c)/2, -((a*b + a*c + b*c)/(a + b + c))}, 48043
{(a*b + a*c + b*c)/2, -((a*b*c)/(a^2 + b^2 + c^2))}, 48044
{(a*b*c)/(2*(a + b + c)), -((a*b + a*c + b*c)/(a + b + c))} 48045
{(a^2 + b^2 + c^2)/2, (-a - b - c)/2}, 48046
{(a^2 + b^2 + c^2)/2, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 48047
{(a^2 + b^2 + c^2)/2, -1/2*(a*b + a*c + b*c)/(a + b + c)}, 48048
{(a*b + a*c + b*c)/2, (-a - b - c)/2}, 48049
{(a*b + a*c + b*c)/2, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 48050
{(a*b*c)/(2*(a + b + c)), (-a - b - c)/2}, 48051
{(a*b*c)/(2*(a + b + c)), -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 48052
{(a*b*c)/(2*(a + b + c)), -1/2*(a*b + a*c + b*c)/(a + b + c)}, 48053
{(a*b*c)/(2*(a + b + c)), 0}, 48054
{(a^2 + b^2 + c^2)/2, (a^2 + b^2 + c^2)/(2*(a + b + c))}, 48055
{(a^2 + b^2 + c^2)/2, (a*b + a*c + b*c)/(2*(a + b + c))}, 48056
{(a*b + a*c + b*c)/2, (a*b*c)/(2*(a^2 + b^2 + c^2))}, 48057
{(a*b*c)/(2*(a + b + c)), (a^2 + b^2 + c^2)/(2*(a + b + c))}, 48058
{(a*b*c)/(2*(a + b + c)), (a*b + a*c + b*c)/(2*(a + b + c))}, 48059
{(a^2 + b^2 + c^2)/2, a + b + c}, 48060
{(a^2 + b^2 + c^2)/2, (a^2 + b^2 + c^2)/(a + b + c)}, 48061
{(a^2 + b^2 + c^2)/2, (a*b + a*c + b*c)/(a + b + c)}, 48062
{(a*b + a*c + b*c)/2, (a^2 + b^2 + c^2)/(a + b + c)}, 48063
{(a*b*c)/(2*(a + b + c)), a + b + c}, 48064
{(a*b*c)/(2*(a + b + c)), (a^2 + b^2 + c^2)/(a + b + c)}, 48065
{(a*b*c)/(2*(a + b + c)), (a*b + a*c + b*c)/(a + b + c)}, 48066
{(a^2 + b^2 + c^2)/2, 2*(a + b + c)}, 48067
{(a^2 + b^2 + c^2)/2, (2*(a^2 + b^2 + c^2))/(a + b + c)}, 48068
{(a^2 + b^2 + c^2)/2, (2*(a*b + a*c + b*c))/(a + b + c)}, 48069
{(a^2 + b^2 + c^2)/2, (2*a*b*c)/(a^2 + b^2 + c^2)}, 48070
{(a*b + a*c + b*c)/2, 2*(a + b + c)}, 48071
{(a*b + a*c + b*c)/2, (2*(a^2 + b^2 + c^2))/(a + b + c)}, 48072
{(a*b + a*c + b*c)/2, (2*(a*b + a*c + b*c))/(a + b + c)}, 48073
{(a*b*c)/(2*(a + b + c)), 2*(a + b + c)}, 48074
{(a*b*c)/(2*(a + b + c)), (2*(a*b + a*c + b*c))/(a + b + c)}, 48075
{a^2 + b^2 + c^2, -2*(a + b + c)}, 48076
{a^2 + b^2 + c^2, (-2*(a^2 + b^2 + c^2))/(a + b + c)}, 48077
{a^2 + b^2 + c^2, (-2*(a*b + a*c + b*c))/(a + b + c)}, 48078
{a*b + a*c + b*c, -2*(a + b + c)}, 48079
{a*b + a*c + b*c, (-2*(a*b + a*c + b*c))/(a + b + c)}, 48080
{(a*b*c)/(a + b + c), (-2*(a*b + a*c + b*c))/(a + b + c)}, 48081
{a^2 + b^2 + c^2, -a - b - c}, 48082
{a^2 + b^2 + c^2, -((a*b + a*c + b*c)/(a + b + c))}, 48083
{a*b + a*c + b*c, -((a*b*c)/(a^2 + b^2 + c^2))}, 48084
{(a*b*c)/(a + b + c), -a - b - c}, 48085
{(a*b*c)/(a + b + c), -((a^2 + b^2 + c^2)/(a + b + c))}, 48086
{a^2 + b^2 + c^2, (-a - b - c)/2}, 48087
{a^2 + b^2 + c^2, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 48088
{a*b + a*c + b*c, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 48089
{a*b + a*c + b*c, -1/2*(a*b + a*c + b*c)/(a + b + c)}, 48090
{(a*b*c)/(a + b + c), (-a - b - c)/2}, 48091
{(a*b*c)/(a + b + c), -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 48092
{(a*b*c)/(a + b + c), -1/2*(a*b + a*c + b*c)/(a + b + c)}, 48093
{a^2 + b^2 + c^2, 0}, 48094
{a^2 + b^2 + c^2, (a + b + c)/2}, 48095
{a^2 + b^2 + c^2, (a^2 + b^2 + c^2)/(2*(a + b + c))}, 48096
{a^2 + b^2 + c^2, (a*b + a*c + b*c)/(2*(a + b + c))}, 48097
{a*b + a*c + b*c, (a*b + a*c + b*c)/(2*(a + b + c))}, 48098
{(a*b*c)/(a + b + c), (a^2 + b^2 + c^2)/(2*(a + b + c))}, 48099
{(a*b*c)/(a + b + c), (a*b + a*c + b*c)/(2*(a + b + c))}, 48100
{a^2 + b^2 + c^2, a + b + c}, 48101
{a^2 + b^2 + c^2, (a^2 + b^2 + c^2)/(a + b + c)}, 48102
{a^2 + b^2 + c^2, (a*b + a*c + b*c)/(a + b + c)}, 48103
{a^2 + b^2 + c^2, 2*(a + b + c)}48104
{a^2 + b^2 + c^2, (2*(a^2 + b^2 + c^2))/(a + b + c)}, 48105
{a^2 + b^2 + c^2, (2*(a*b + a*c + b*c))/(a + b + c)}, 48106
{a*b + a*c + b*c, 2*(a + b + c)}, 48107
{a*b + a*c + b*c, (2*(a*b + a*c + b*c))/(a + b + c)}, 48108
{a*b + a*c + b*c, (2*a*b*c)/(a^2 + b^2 + c^2)}, 48109
{(a*b*c)/(a + b + c), 2*(a + b + c)}, 48110
{(a*b*c)/(a + b + c), (2*(a^2 + b^2 + c^2))/(a + b + c)}, 48111
{2*(a^2 + b^2 + c^2), -2*(a + b + c)}, 48112
{2*(a^2 + b^2 + c^2), (-2*(a*b + a*c + b*c))/(a + b + c)}, 48113
{2*(a*b + a*c + b*c), -2*(a + b + c)}, 48114
{2*(a*b + a*c + b*c), (-2*(a^2 + b^2 + c^2))/(a + b + c)}, 48115
{(2*a*b*c)/(a + b + c), (-2*(a^2 + b^2 + c^2))/(a + b + c)}, 48116
{2*(a^2 + b^2 + c^2), -a - b - c}, 48117
{2*(a^2 + b^2 + c^2), -((a^2 + b^2 + c^2)/(a + b + c))}, 48118
{2*(a*b + a*c + b*c), -((a^2 + b^2 + c^2)/(a + b + c))}, 48119
{2*(a*b + a*c + b*c), -((a*b + a*c + b*c)/(a + b + c))}, 48120
{(2*a*b*c)/(a + b + c), -a - b - c}, 48121
{(2*a*b*c)/(a + b + c), -((a^2 + b^2 + c^2)/(a + b + c))}, 48122
{(2*a*b*c)/(a + b + c), -((a*b + a*c + b*c)/(a + b + c))}, 48123
{2*(a^2 + b^2 + c^2), (-a - b - c)/2}, 48124
{2*(a*b + a*c + b*c), (-a - b - c)/2}, 48125
{2*(a*b + a*c + b*c), -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 48126
{2*(a*b + a*c + b*c), -1/2*(a*b + a*c + b*c)/(a + b + c)}, 48127
{(2*a*b*c)/(a + b + c), (-a - b - c)/2}, 48128
{(2*a*b*c)/(a + b + c), -1/2*(a*b + a*c + b*c)/(a + b + c)}, 48129
{2*(a^2 + b^2 + c^2), 0}, 48130
{(2*a*b*c)/(a + b + c), 0}, 48131
{2*(a^2 + b^2 + c^2), (a + b + c)/2}, 48132
{2*(a*b + a*c + b*c), (a + b + c)/2}, 48133
{2*(a*b + a*c + b*c), (a^2 + b^2 + c^2)/(2*(a + b + c))}, 48134
{2*(a*b + a*c + b*c), (a*b + a*c + b*c)/(2*(a + b + c))}, 48135
{(2*a*b*c)/(a + b + c), (a^2 + b^2 + c^2)/(2*(a + b + c))}, 48136
{(2*a*b*c)/(a + b + c), (a*b + a*c + b*c)/(2*(a + b + c))}, 48137
{2*(a^2 + b^2 + c^2), a + b + c}, 48138
{2*(a^2 + b^2 + c^2), (a^2 + b^2 + c^2)/(a + b + c)}, 48139
{2*(a^2 + b^2 + c^2), (a*b + a*c + b*c)/(a + b + c)}, 48140
{2*(a*b + a*c + b*c), a + b + c}, 48141
{2*(a*b + a*c + b*c), (a^2 + b^2 + c^2)/(a + b + c)}, 48142
{2*(a*b + a*c + b*c), (a*b + a*c + b*c)/(a + b + c)}, 48143
{(2*a*b*c)/(a + b + c), a + b + c}, 48144
{2*(a^2 + b^2 + c^2), 2*(a + b + c)}, 48145
{2*(a^2 + b^2 + c^2), (2*(a*b + a*c + b*c))/(a + b + c)}, 48146
{2*(a*b + a*c + b*c), 2*(a + b + c)}, 48147
{2*(a*b + a*c + b*c), (2*(a*b + a*c + b*c))/(a + b + c)}, 48148
{(2*a*b*c)/(a + b + c), 2*(a + b + c)}, 48149
{(2*a*b*c)/(a + b + c), (2*(a^2 + b^2 + c^2))/(a + b + c)}, 48150
{(2*a*b*c)/(a + b + c), (2*(a*b + a*c + b*c))/(a + b + c)}, 48151
{a*b + a*c + b*c, (a*b*c)/(a^2 + b^2 + c^2)}, 48152
{2*(a*b + a*c + b*c), (2*(a^2 + b^2 + c^2))/(a + b + c)}, 48153

X(47900) = X(513)X(47702)∩X(514)X(4838)

X(47900) = 5 X[4838] - 4 X[47658], 5 X[649] - 6 X[47880], 7 X[661] - 6 X[6546], 5 X[661] - 4 X[47890], 3 X[6546] - 7 X[23731], 15 X[6546] - 14 X[47890], 5 X[23731] - 2 X[47890], 4 X[4025] - 3 X[4979], 3 X[4931] - 4 X[20295]

X(47900) lies on these lines: {513, 47702}, {514, 4838}, {649, 47880}, {661, 1211}, {812, 47669}, {4025, 4979}, {4785, 47673}, {4804, 4977}, {4810, 28195}, {4931, 20295}, {7192, 26860}, {28225, 47695}, {28859, 47672}

X(47901) = X(513)X(47702)∩X(514)X(47685)

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

X(47901) lies on these lines: {513, 47702}, {514, 47685}, {661, 1639}, {4088, 28213}, {4458, 4778}, {4724, 28220}, {4728, 47696}, {4931, 24719}, {4963, 28195}, {28209, 47701}, {29362, 47669}, {47651, 47705}, {47672, 47686}

X(47901) = reflection of X(i) in X(j) for these {i,j}: {47672, 47686}, {47705, 47651}

X(47902) = X(513)X(47702)∩X(514)X(4170)

X(4902) lies on these lines: {513, 47702}, {514, 4170}, {522, 47654}, {523, 23731}, {4658, 4960}, {4727, 4802}, {4778, 47651}, {4977, 47704}, {23729, 47703}, {28191, 47658}, {28840, 47688}, {28859, 47691}, {28882, 47699}, {29328, 47673}

X(47902) = reflection of X(i) in X(j) for these {i,j}: {4838, 4810}, {47703, 23729}
X(47902) = X(1390)-isoconjugate of X(8652)
X(47902) = barycentric product X(i)*X(j) for these {i,j}: {1386, 4823}, {4026, 4960}, {4802, 17023}, {4813, 26234}, {5333, 47701}
X(47902) = barycentric quotient X(i)/X(j) for these {i,j}: {1386, 37211}, {4813, 1390}, {17023, 32042}, {21764, 8652}

X(47903) = X(2)X(661)∩X(513)X(4963)

X(47903) = 6 X[2] - 7 X[661], 15 X[2] - 14 X[4369], 9 X[2] - 7 X[7192], 36 X[2] - 35 X[24924], 27 X[2] - 28 X[25666], 8 X[2] - 7 X[31148], 3 X[2] - 7 X[31290], 13 X[2] - 14 X[45315], 29 X[2] - 28 X[45663], 5 X[2] - 7 X[47774], 5 X[661] - 4 X[4369], 3 X[661] - 2 X[7192], 6 X[661] - 5 X[24924], 9 X[661] - 8 X[25666], 4 X[661] - 3 X[31148], 13 X[661] - 12 X[45315], 29 X[661] - 24 X[45663], 5 X[661] - 6 X[47774], 6 X[4369] - 5 X[7192], 24 X[4369] - 25 X[24924], 9 X[4369] - 10 X[25666], 16 X[4369] - 15 X[31148], 2 X[4369] - 5 X[31290], 13 X[4369] - 15 X[45315], 29 X[4369] - 30 X[45663], 2 X[4369] - 3 X[47774], 4 X[7192] - 5 X[24924], 3 X[7192] - 4 X[25666], 8 X[7192] - 9 X[31148], X[7192] - 3 X[31290], 13 X[7192] - 18 X[45315], 29 X[7192] - 36 X[45663], 5 X[7192] - 9 X[47774], 15 X[24924] - 16 X[25666], 10 X[24924] - 9 X[31148], 5 X[24924] - 12 X[31290], 65 X[24924] - 72 X[45315], 25 X[24924] - 36 X[47774], 32 X[25666] - 27 X[31148], 4 X[25666] - 9 X[31290], 26 X[25666] - 27 X[45315], 29 X[25666] - 27 X[45663], 20 X[25666] - 27 X[47774], 3 X[31148] - 8 X[31290], 13 X[31148] - 16 X[45315], 29 X[31148] - 32 X[45663], 5 X[31148] - 8 X[47774], 13 X[31290] - 6 X[45315], 29 X[31290] - 12 X[45663], 5 X[31290] - 3 X[47774], 29 X[45315] - 26 X[45663], 10 X[45315] - 13 X[47774], 20 X[45663] - 29 X[47774], 2 X[4106] - 3 X[4813], 4 X[4106] - 3 X[47672], 8 X[4691] - 7 X[4761], 3 X[4958] - 2 X[47656]

X(47903) lies on these lines: {2, 661}, {513, 4963}, {514, 4838}, {2786, 47669}, {3633, 4160}, {4106, 4813}, {4122, 4977}, {4691, 4761}, {4958, 47656}, {4979, 47666}, {6144, 9013}, {15309, 47683}, {16892, 28902}, {28846, 47673}, {28867, 47667}, {28871, 47653}, {28886, 45746}, {28906, 47657}

X(47903) = reflection of X(i) in X(j) for these {i,j}: {661, 31290}, {4838, 44449}, {4979, 47666}, {47672, 4813}
(47903) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 7192, 24924}, {4369, 47774, 661}, {7192, 24924, 31148}

X(47904) = X(513)X(4963)∩X(514)X(4170)

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

X(47904) = 5 X[661] - 4 X[3837], 3 X[661] - 2 X[21146], 4 X[661] - 3 X[47812], 6 X[3837] - 5 X[21146], 16 X[3837] - 15 X[47812], 8 X[21146] - 9 X[47812], 2 X[7192] - 3 X[47811], 2 X[43067] - 3 X[47826]

X(47904) lies on these lines: {513, 4963}, {514, 4170}, {661, 1639}, {693, 28229}, {1491, 28220}, {2254, 4778}, {4010, 28213}, {4824, 28209}, {7192, 47811}, {28195, 47672}, {28851, 47699}, {43067, 47826}

X(47905) = X(513)X(4041)∩X(514)X(47685)

X(47905) = 3 X[661] - 2 X[4040], 2 X[667] - 3 X[47810], 2 X[3803] - 3 X[4893], 4 X[21260] - 3 X[47813], 5 X[24924] - 6 X[47816]

X(47905) lies on these lines: {513, 4041}, {514, 47685}, {661, 830}, {667, 47810}, {1734, 4979}, {3309, 4813}, {3800, 23731}, {3803, 4893}, {4449, 8678}, {21260, 47813}, {24924, 47816}, {29062, 47673}

X(47905) = reflection of X(4979) in X(1734)
X(47905) = crossdifference of every pair of points on line {38, 1449}

X(47906) = X(513)X(4041)∩X(514)X(4170)

X(47906) = 3 X[4041] - 4 X[4490], 3 X[661] - 2 X[2530], 2 X[905] - 3 X[47826], 2 X[1019] - 3 X[47811], 2 X[3803] - 3 X[4724], 4 X[4129] - 3 X[47812], 2 X[4905] - 3 X[47810], 2 X[4932] - 3 X[47815]

X(47906) lies on these lines: {513, 4041}, {514, 4170}, {661, 665}, {905, 47826}, {1019, 47811}, {2533, 21714}, {3803, 4724}, {4129, 47812}, {4391, 4778}, {4905, 47810}, {4932, 47815}, {6615, 8672}, {14349, 23738}, {14430, 28225}, {23765, 29198}, {28851, 47708}, {29168, 47700}, {29354, 47702}

X(47906) = reflection of X(23738) in X(14349)
X(47906) = X(39983)-Ceva conjugate of X(244)
X(47906) = crossdifference of every pair of points on line {1449, 1621}

X(47907) = X(513)X(47702)∩X(514)X(4024)

X(47907) = 3 X[4382] - 2 X[47656], 3 X[649] - 4 X[3004], 7 X[649] - 8 X[17069], 5 X[649] - 6 X[47886], 7 X[3004] - 6 X[17069], 10 X[3004] - 9 X[47886], 20 X[17069] - 21 X[47886], 4 X[4106] - 3 X[47873], 9 X[4893] - 8 X[11068], 3 X[31147] - 2 X[47660]

X(47907) lies on these lines: {513, 47702}, {514, 4024}, {649, 3004}, {812, 47657}, {4106, 47873}, {4778, 47691}, {4785, 47653}, {4893, 11068}, {6008, 47673}, {28840, 47651}, {28859, 47652}, {31147, 47660}

X(47907) = reflection of X(4813) in X(23731)
X(47907) = crossdifference of every pair of points on line {2308, 41265}

X(47908) = X(513)X(4963)∩X(514)X(4024)

X(47908) = 3 X[4382] - 4 X[20295], 5 X[4382] - 4 X[26824], X[4382] - 4 X[31290], 3 X[4813] - 2 X[20295], 5 X[4813] - 2 X[26824], 5 X[20295] - 3 X[26824], X[20295] - 3 X[31290], X[26824] - 5 X[31290], 5 X[649] - 6 X[31150], 3 X[31150] - 5 X[47666], 4 X[661] - 3 X[4379], 5 X[661] - 4 X[4885], 6 X[661] - 5 X[30835], 3 X[661] - 2 X[43067], 7 X[661] - 6 X[47760], 15 X[4379] - 16 X[4885], 9 X[4379] - 10 X[30835], 9 X[4379] - 8 X[43067], 7 X[4379] - 8 X[47760], 24 X[4885] - 25 X[30835], 6 X[4885] - 5 X[43067], 14 X[4885] - 15 X[47760], 5 X[30835] - 4 X[43067], 35 X[30835] - 36 X[47760], 7 X[43067] - 9 X[47760], 2 X[3835] - 3 X[47774], 3 X[4893] - 2 X[7192], 15 X[4893] - 14 X[27115], 9 X[4893] - 8 X[31286], 5 X[7192] - 7 X[27115], 3 X[7192] - 4 X[31286], 21 X[27115] - 20 X[31286], 2 X[4897] - 3 X[47878], 2 X[4932] - 3 X[47775], 8 X[23813] - 9 X[31147], 4 X[23813] - 3 X[47672], 3 X[31147] - 2 X[47672], 5 X[24924] - 6 X[47777], 6 X[31148] - 7 X[31207]

X(47908) lies on these lines: {513, 4963}, {514, 4024}, {649, 28840}, {661, 4379}, {2786, 47667}, {3835, 47774}, {4467, 28886}, {4810, 28199}, {4820, 47670}, {4841, 28902}, {4893, 7192}, {4897, 47878}, {4932, 47775}, {4988, 28846}, {6372, 20983}, {16892, 28878}, {17161, 28906}, {23813, 31147}, {24719, 28213}, {24924, 47777}, {26822, 47794}, {28229, 46403}, {28855, 45746}, {28867, 47661}, {28871, 47677}, {28898, 47669}, {31148, 31207}

X(47908) = reflection of X(i) in X(j) for these {i,j}: {649, 47666}, {4382, 4813}, {4813, 31290}, {47670, 4820}
X(47908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 43067, 30835}, {30835, 43067, 4379}

X(47909) = X(513)X(4963)∩X(514)X(4088)

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

X(47909) = 3 X[661] - 2 X[7662], 4 X[661] - 3 X[47832], 8 X[7662] - 9 X[47832], 9 X[4379] - 10 X[30795], 2 X[4458] - 3 X[47781], 3 X[4724] - 2 X[47697], 3 X[47666] - X[47697], 2 X[4932] - 3 X[47825], 2 X[7192] - 3 X[47828], 4 X[18004] - 3 X[47873], 2 X[43067] - 3 X[47810], 2 X[47694] - 3 X[47826]

X(47909) lies on these lines: {513, 4963}, {514, 4088}, {522, 31290}, {523, 4813}, {649, 4824}, {661, 7662}, {4378, 27675}, {4379, 30795}, {4382, 4802}, {4458, 47781}, {4724, 23655}, {4778, 47663}, {4810, 28151}, {4932, 47825}, {7192, 47828}, {8672, 20983}, {18004, 47873}, {20295, 28147}, {24719, 28175}, {25637, 43067}, {26824, 28191}, {47694, 47826}

X(47909) = reflection of X(i) in X(j) for these {i,j}: {649, 4824}, {4724, 47666}

X(47910) = X(513)X(4963)∩X(514)X(4010)

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

X(47910) = 3 X[4490] - 2 X[4761], 3 X[4948] - 2 X[7659], 3 X[4951] - 2 X[47703], 5 X[30795] - 6 X[47777]

X(47910) lies on these lines: {513, 4963}, {514, 4010}, {661, 28195}, {693, 28213}, {1491, 2977}, {2254, 28220}, {4490, 4761}, {4778, 4824}, {4804, 28199}, {4806, 47675}, {4830, 28840}, {4948, 7659}, {4951, 47703}, {21146, 28229}, {29362, 31290}, {30795, 47777}

X(47910) = reflection of X(i) in X(j) for these {i,j}: {1491, 47666}, {47675, 4806}
X(47910) = X(44217)-line conjugate of X(24254)

X(47911) = X(513)X(4041)∩X(514)X(4024)

X(47911) = 3 X[661] - 2 X[905], 2 X[667] - 3 X[47826], 2 X[1019] - 3 X[4893], 4 X[4129] - 3 X[4379], 2 X[4932] - 3 X[47793], 2 X[4978] - 3 X[31147], 2 X[8045] - 3 X[47769], X[17496] - 3 X[47774]

X(47911) lies on these lines: {513, 4041}, {514, 4024}, {649, 15309}, {661, 905}, {667, 47826}, {1019, 4893}, {4129, 4379}, {4391, 28840}, {4449, 4983}, {4778, 21301}, {4791, 4960}, {4824, 29170}, {4932, 47793}, {4978, 31147}, {6002, 47666}, {7178, 28902}, {7192, 30023}, {8045, 47769}, {8672, 42661}, {17496, 47774}, {21124, 28846}, {26775, 47794}, {29037, 47699}, {29118, 47698}

X(47911) = reflection of X(i) in X(j) for these {i,j}: {4449, 4983}, {4960, 4791}
X(47911) = crosssum of X(649) and X(4270)
X(47911) = crossdifference of every pair of points on line {968, 1449}

X(47912) = X(513)X(4041)∩X(514)X(4088)

X(47912) = 2 X[4813] + X[4814], 2 X[667] - 3 X[4893], 2 X[905] - 3 X[47810], 2 X[1019] - 3 X[47828], 2 X[3803] - 3 X[47811], 2 X[4040] - 3 X[47826], 4 X[4129] - 3 X[47832], 2 X[4369] - 3 X[47814], 3 X[4379] - 4 X[21260], 2 X[4932] - 3 X[47836], X[4959] - 4 X[4983], 4 X[25666] - 3 X[47820], X[31291] - 3 X[47775]

X(47912) lies on these lines: {512, 4813}, {513, 4041}, {514, 4088}, {649, 4705}, {661, 663}, {667, 4893}, {814, 4824}, {830, 4724}, {905, 47810}, {1019, 47828}, {1734, 15309}, {3803, 47811}, {3835, 17166}, {3900, 4822}, {4040, 47826}, {4129, 47832}, {4160, 4449}, {4163, 4778}, {4369, 25637}, {4379, 21260}, {4770, 4834}, {4841, 29278}, {4932, 47836}, {4959, 4983}, {7192, 17072}, {9279, 42661}, {21302, 31290}, {25666, 47820}, {29037, 45746}, {29051, 47666}, {29062, 47679}, {29344, 47683}, {31291, 47775}

X(47912) = midpoint of X(21302) and X(31290)
X(47912) = reflection of X(i) in X(j) for these {i,j}: {649, 4705}, {663, 661}, {4449, 14349}, {4498, 4490}, {4834, 4770}, {7192, 17072}, {17166, 3835}
X(47912) = crossdifference of every pair of points on line {63, 1449}
X(47912) = barycentric product X(i)*X(j) for these {i,j}: {650, 5290}, {661, 14005}
X(47912) = barycentric quotient X(i)/X(j) for these {i,j}: {5290, 4554}, {14005, 799}

X(47913) = X(513)X(4041)∩X(514)X(4010)

X(47913) = 2 X[4041] - 3 X[4490], 3 X[661] - X[23738], 3 X[3777] - 2 X[23738], 3 X[1491] - 2 X[4905], 3 X[4951] - 2 X[47715], 2 X[43067] - 3 X[47872]

X(47913) lies on these lines: {513, 4041}, {514, 4010}, {661, 3777}, {1491, 4905}, {2533, 4778}, {3801, 28851}, {4147, 28225}, {4391, 4977}, {4801, 4806}, {4822, 29226}, {4951, 47715}, {14349, 23765}, {17494, 29170}, {18004, 47719}, {43067, 47872}

X(47913) = reflection of X(i) in X(j) for these {i,j}: {3777, 661}, {4801, 4806}, {23765, 14349}, {47719, 18004}
X(47913) = crossdifference of every pair of points on line {1449, 8616}

X(47914) = X(513)X(4963)∩X(514)X(3700)

X(47914) = 3 X[650] - 2 X[7192], 11 X[650] - 10 X[27013], 7 X[650] - 6 X[47762], 5 X[650] - 6 X[47775], 11 X[7192] - 15 X[27013], X[7192] - 3 X[47666], 7 X[7192] - 9 X[47762], 5 X[7192] - 9 X[47775], 5 X[27013] - 11 X[47666], 35 X[27013] - 33 X[47762], 25 X[27013] - 33 X[47775], 7 X[47666] - 3 X[47762], 5 X[47666] - 3 X[47775], 5 X[47762] - 7 X[47775], 4 X[661] - 3 X[45320], 2 X[4940] - 3 X[47774], X[47675] - 3 X[47774], 16 X[25666] - 15 X[31250], 4 X[25666] - 3 X[43067], 8 X[25666] - 9 X[47777], 10 X[25666] - 9 X[47779], 5 X[31250] - 4 X[43067], 5 X[31250] - 6 X[47777], 25 X[31250] - 24 X[47779], 2 X[43067] - 3 X[47777], 5 X[43067] - 6 X[47779], 5 X[47777] - 4 X[47779]

X(47914) lies on these lines: {513, 4963}, {514, 3700}, {650, 7192}, {661, 45320}, {2505, 2526}, {4762, 31290}, {4790, 28840}, {4824, 7659}, {4841, 28878}, {4940, 47675}, {25666, 31250}, {28898, 47667}, {28902, 45745}, {28910, 45746}

X(47914) = reflection of X(i) in X(j) for these {i,j}: {650, 47666}, {7659, 4824}, {47675, 4940}
X(47914) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {43067, 47777, 31250}, {47675, 47774, 4940}

X(47915) = X(513)X(4041)∩X(514)X(3700)

X(47915) = 3 X[650] - 2 X[1019], 2 X[905] - 3 X[47777], 3 X[1022] - 5 X[14349], 4 X[4129] - 3 X[45320]

X(47915) lies on these lines: {513, 4041}, {514, 3700}, {650, 1019}, {661, 3669}, {876, 29198}, {905, 47777}, {1022, 14349}, {1027, 2334}, {1308, 8694}, {2501, 43052}, {2526, 6372}, {3257, 4606}, {4129, 45320}, {4160, 4162}, {4391, 7199}, {4462, 31290}, {4705, 7659}, {4790, 15309}, {4801, 4940}, {4813, 8712}, {4833, 18344}, {4866, 35355}, {5545, 9090}, {7178, 28878}, {7192, 20317}, {23880, 47666}, {34074, 36146}

X(47915) = midpoint of X(4462) and X(31290)
X(47915) = reflection of X(i) in X(j) for these {i,j}: {3669, 661}, {4801, 4940}, {7192, 20317}, {7659, 4705}
X(47915) = X(4606)-Ceva conjugate of X(25430)
X(47915) = X(i)-cross conjugate of X(j) for these (i,j): {4813, 513}, {8712, 3669}
X(47915) = X(i)-isoconjugate of X(j) for these (i,j): {56, 30728}, {59, 4765}, {100, 1449}, {101, 3616}, {109, 391}, {110, 5257}, {112, 4101}, {162, 4047}, {461, 1813}, {644, 3361}, {651, 4512}, {662, 37593}, {664, 4258}, {692, 19804}, {765, 4790}, {901, 4700}, {906, 5342}, {919, 4684}, {1110, 4801}, {1252, 4778}, {1332, 5338}, {1415, 4673}, {1783, 4652}, {2149, 4811}, {3671, 5546}, {3939, 21454}, {4061, 4565}, {4557, 42028}, {4567, 4822}, {4570, 4841}, {4574, 31903}, {4591, 4819}, {4600, 4832}, {4620, 8653}, {4706, 34075}, {4719, 36147}, {4734, 34071}, {4742, 32665}, {4773, 9268}, {4827, 7045}, {6065, 30723}
X(47915) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 30728), (11, 391), (125, 4047), (244, 5257), (513, 4790), (514, 4801), (650, 4811), (661, 4778), (1015, 3616), (1084, 37593), (1086, 19804), (1146, 4673), (4988, 4815), (5190, 5342), (6615, 4765), (6741, 42712), (8054, 1449), (17115, 4827), (34591, 4101), (35092, 4742), (38979, 4700), (38980, 4684), (38991, 4512), (39006, 4652), (39011, 4706), (39015, 4719), (39025, 4258), (40610, 4734), (40617, 21454), (40627, 4822)
X(47915) = cevapoint of X(i) and X(j) for these (i,j): {661, 8672}, {20317, 23880}
X(47915) = crosspoint of X(4606) and X(25430)
X(47915) = crosssum of X(i) and X(j) for these (i,j): {1449, 4790}, {4512, 4827}, {4765, 5257}
X(47915) = trilinear pole of line {244, 4516}
X(47915) = crossdifference of every pair of points on line {1449, 4047}
X(47915) = barycentric product X(i)*X(j) for these {i,j}: {513, 5936}, {514, 25430}, {649, 40023}, {693, 2334}, {1086, 4606}, {1111, 8694}, {2170, 4624}, {3120, 4614}, {3125, 4633}, {3676, 4866}, {4627, 16732}, {23989, 34074}, {24002, 34820}
X(47915) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 30728}, {11, 4811}, {244, 4778}, {512, 37593}, {513, 3616}, {514, 19804}, {522, 4673}, {647, 4047}, {649, 1449}, {650, 391}, {656, 4101}, {661, 5257}, {663, 4512}, {891, 4706}, {900, 4742}, {1015, 4790}, {1019, 42028}, {1086, 4801}, {1459, 4652}, {1635, 4700}, {2087, 4773}, {2170, 4765}, {2254, 4684}, {2334, 100}, {3063, 4258}, {3120, 4815}, {3121, 4832}, {3122, 4822}, {3125, 4841}, {3669, 21454}, {3700, 42712}, {4017, 3671}, {4041, 4061}, {4083, 4734}, {4155, 4829}, {4475, 4818}, {4516, 4843}, {4606, 1016}, {4614, 4600}, {4627, 4567}, {4633, 4601}, {4730, 4819}, {4833, 17553}, {4866, 3699}, {5936, 668}, {6371, 4719}, {7649, 5342}, {8694, 765}, {14419, 4831}, {14626, 1026}, {14936, 4827}, {18344, 461}, {21832, 4771}, {25430, 190}, {27846, 4830}, {34074, 1252}, {34820, 644}, {39786, 4839}, {40023, 1978}, {43924, 3361}

X(47916) = X(513)X(47702)∩X(514)X(661)

X(47916) = 5 X[661] - 4 X[4468], 3 X[4728] - 2 X[47660], X[17161] - 3 X[47653], 2 X[17161] - 3 X[47673], 3 X[1635] - 4 X[3004], 4 X[3776] - 3 X[31148], 4 X[4106] - 3 X[4931], 4 X[4897] - 3 X[4979], 2 X[4897] - 3 X[16892], 3 X[4958] - 4 X[20295], 2 X[7192] - 3 X[21115], 4 X[23813] - 3 X[47873], 5 X[24924] - 6 X[44435], 4 X[25666] - 3 X[47773]

X(47916) lies on these lines: {513, 47702}, {514, 661}, {812, 17161}, {918, 23731}, {1635, 3004}, {2605, 4724}, {3776, 31148}, {4024, 23729}, {4088, 28175}, {4106, 4931}, {4382, 4838}, {4762, 47669}, {4785, 47677}, {4802, 47700}, {4813, 30520}, {4897, 4979}, {4958, 20295}, {4977, 21125}, {4988, 6084}, {7192, 21115}, {23813, 47873}, {24924, 44435}, {25666, 47773}, {26824, 47670}, {28859, 47676}, {28882, 45746}, {28890, 31290}, {47688, 47705}

X(47916) = reflection of X(i) in X(j) for these {i,j}: {4024, 23729}, {4838, 4382}, {4979, 16892}, {47662, 3835}, {47670, 26824}, {47672, 47652}, {47673, 47653}, {47705, 47688}
X(47916) = barycentric product X(i)*X(j) for these {i,j}: {514, 17384}, {693, 29819}, {3676, 4914}
X(47916) = barycentric quotient X(i)/X(j) for these {i,j}: {4914, 3699}, {17384, 190}, {29819, 100}

X(47917) = X(513)X(4963)∩X(514)X(661)

X(47917) = 3 X[661] - 2 X[693], 5 X[661] - 4 X[3835], 4 X[661] - 3 X[4728], 7 X[661] - 6 X[4776], 5 X[661] - 2 X[47675], 5 X[693] - 6 X[3835], 8 X[693] - 9 X[4728], 7 X[693] - 9 X[4776], X[693] - 3 X[47666], 4 X[693] - 3 X[47672], 5 X[693] - 3 X[47675], 16 X[3835] - 15 X[4728], 14 X[3835] - 15 X[4776], 2 X[3835] - 5 X[47666], 8 X[3835] - 5 X[47672], 7 X[4728] - 8 X[4776], 3 X[4728] - 8 X[47666], 3 X[4728] - 2 X[47672], 15 X[4728] - 8 X[47675], 3 X[4776] - 7 X[47666], 12 X[4776] - 7 X[47672], 15 X[4776] - 7 X[47675], 4 X[47666] - X[47672], 5 X[47666] - X[47675], 5 X[47672] - 4 X[47675], 5 X[650] - 4 X[7653], 4 X[650] - 3 X[31148], 16 X[7653] - 15 X[31148], 3 X[1635] - 2 X[7192], 9 X[1635] - 10 X[26777], 3 X[7192] - 5 X[26777], 4 X[3004] - 3 X[21115], 2 X[3776] - 3 X[47781], 2 X[4025] - 3 X[47878], 6 X[4369] - 7 X[27115], 2 X[4369] - 3 X[47775], 7 X[27115] - 9 X[47775], 9 X[4379] - 10 X[31250], 2 X[4500] - 3 X[47769], X[47674] - 3 X[47769], X[4608] - 3 X[47772], 6 X[4893] - 5 X[24924], 9 X[4893] - 8 X[31287], 3 X[4893] - 2 X[43067], 15 X[24924] - 16 X[31287], 5 X[24924] - 4 X[43067], 4 X[31287] - 3 X[43067], 3 X[4931] - 2 X[47656], 2 X[4932] - 3 X[31150], 2 X[7662] - 3 X[47826], 2 X[21146] - 3 X[47810], 4 X[25666] - 3 X[47780], X[26824] - 3 X[47774], 5 X[26985] - 6 X[45315], 5 X[30835] - 6 X[47777]

X(47917) lies on these lines: {513, 4963}, {514, 661}, {650, 7653}, {812, 31290}, {824, 47667}, {918, 4988}, {1491, 28195}, {1635, 7192}, {2254, 4824}, {2786, 47661}, {3004, 21115}, {3700, 47671}, {3776, 47781}, {3960, 24948}, {4010, 28175}, {4024, 47670}, {4025, 47878}, {4369, 27115}, {4379, 31250}, {4467, 28855}, {4500, 47674}, {4608, 47772}, {4762, 4813}, {4785, 47664}, {4802, 4804}, {4838, 25259}, {4841, 16892}, {4893, 24924}, {4931, 47656}, {4932, 31150}, {4960, 16751}, {4976, 28902}, {4979, 17494}, {6084, 23731}, {7662, 47826}, {21146, 28213}, {25666, 47780}, {26824, 47774}, {26985, 45315}, {28851, 45746}, {28859, 47663}, {28878, 45745}, {28890, 47653}, {30519, 47657}, {30765, 47771}, {30835, 47777}, {47698, 47700}, {47699, 47702}, {47701, 47705}

X(47917) = reflection of X(i) in X(j) for these {i,j}: {661, 47666}, {2254, 4824}, {4838, 25259}, {4979, 17494}, {16892, 4841}, {47669, 47667}, {47670, 4024}, {47671, 3700}, {47672, 661}, {47673, 4988}, {47674, 4500}, {47675, 3835}, {47700, 47698}, {47702, 47699}, {47705, 47701}
X(47917) = X(20888)-Ceva conjugate of X(3122)
X(47917) = barycentric product X(i)*X(j) for these {i,j}: {514, 4698}, {522, 4955}, {3676, 4113}
X(47917) = barycentric quotient X(i)/X(j) for these {i,j}: {4113, 3699}, {4698, 190}, {4955, 664}
X(47917) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47672, 4728}, {4893, 43067, 24924}, {47674, 47769, 4500}

X(47918) = X(513)X(4041)∩X(514)X(661)

X(47918) = 3 X[661] - 2 X[14349], 4 X[4129] - 3 X[4728], 3 X[4728] - 2 X[4978], 2 X[8045] - 3 X[30565], 2 X[667] - 3 X[47811], 2 X[905] - 3 X[4893], 2 X[1019] - 3 X[1635], 2 X[2530] - 3 X[47810], X[23738] - 3 X[47810], 2 X[2533] - 3 X[14430], 2 X[4369] - 3 X[47793], X[4449] - 3 X[47826], X[17496] - 3 X[47775], 4 X[21260] - 3 X[47812], 2 X[23789] - 3 X[47816], 2 X[24720] - 3 X[47814], 5 X[24924] - 6 X[47794], 4 X[25666] - 3 X[47796]

X(47918) lies on these lines: {513, 4041}, {514, 661}, {667, 47811}, {830, 13259}, {891, 4983}, {905, 4893}, {918, 21124}, {1019, 1635}, {1491, 29198}, {2254, 4705}, {2530, 23738}, {2533, 4977}, {3716, 17166}, {4040, 4160}, {4063, 4979}, {4083, 4822}, {4088, 29142}, {4147, 4778}, {4369, 47793}, {4449, 47826}, {4522, 47719}, {4724, 8678}, {4729, 6005}, {4808, 29168}, {6002, 17494}, {8672, 17420}, {10015, 23755}, {17496, 47775}, {20317, 43067}, {21051, 21146}, {21127, 28878}, {21260, 47812}, {23789, 47816}, {23877, 47698}, {24720, 47814}, {24924, 47794}, {25666, 47796}, {28473, 38329}, {29021, 47700}, {29047, 47702}, {29288, 47701}, {47670, 47678}, {47673, 47679}, {47705, 47712}

X(47918) = midpoint of X(4462) and X(47666)
X(47918) = reflection of X(i) in X(j) for these {i,j}: {2254, 4705}, {4041, 4490}, {4801, 3835}, {4978, 4129}, {4979, 4063}, {17166, 3716}, {21146, 21051}, {23738, 2530}, {23755, 10015}, {43067, 20317}, {47670, 47678}, {47672, 1577}, {47673, 47679}, {47705, 47712}, {47719, 4522}
X(47918) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {43069, 3434}, {43073, 150}
X(47918) = X(1268)-Ceva conjugate of X(244)
X(47918) = crosssum of X(101) and X(35342)
X(47918) = crossdifference of every pair of points on line {31, 1449}
X(47918) = barycentric product X(i)*X(j) for these {i,j}: {513, 4967}, {514, 44307}, {1900, 4025}, {3676, 4662}
X(47918) = barycentric quotient X(i)/X(j) for these {i,j}: {1900, 1897}, {4662, 3699}, {4967, 668}, {44307, 190}
X(47918) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4129, 4978, 4728}, {23738, 47810, 2530}

X(47919) = X(241)X(514)∩X(513)X(47702)

X(47919) = 3 X[650] - 4 X[3004], 9 X[650] - 8 X[11068], 11 X[650] - 12 X[47784], 5 X[650] - 6 X[47880], 13 X[650] - 12 X[47884], 5 X[650] - 4 X[47890], 3 X[3004] - 2 X[11068], 11 X[3004] - 9 X[47784], 10 X[3004] - 9 X[47880], 13 X[3004] - 9 X[47884], 5 X[3004] - 3 X[47890], 22 X[11068] - 27 X[47784], 20 X[11068] - 27 X[47880], 26 X[11068] - 27 X[47884], 10 X[11068] - 9 X[47890], 10 X[47784] - 11 X[47880], 13 X[47784] - 11 X[47884], 15 X[47784] - 11 X[47890], 13 X[47880] - 10 X[47884], 3 X[47880] - 2 X[47890], 15 X[47884] - 13 X[47890], 3 X[47651] + X[47657], 3 X[47653] - X[47657], 3 X[47652] - X[47656], 5 X[47652] - X[47658], 5 X[47656] - 3 X[47658], 5 X[31250] - 6 X[44435], 4 X[31287] - 3 X[47773], 3 X[45320] - 2 X[47660]

X(47919) lies on these lines: {241, 514}, {513, 47702}, {523, 47095}, {1491, 28199}, {2526, 4802}, {4106, 28863}, {4762, 47651}, {4790, 16892}, {4820, 23729}, {4885, 47662}, {6008, 47677}, {28894, 47652}, {31250, 44435}, {31287, 47773}, {45320, 47660}, {47650, 47654}

X(47919) = midpoint of X(i) and X(j) for these {i,j}: {47650, 47654}, {47651, 47653}
X(47919) = reflection of X(i) in X(j) for these {i,j}: {4790, 16892}, {4820, 23729}, {47662, 4885}
X(47919) = crossdifference of every pair of points on line {55, 43136}
X(47919) = {X(47880),X(47890)}-harmonic conjugate of X(650)

X(47920) = X(241)X(514)∩X(513)X(4963)

X(47920) = 5 X[650] - 4 X[4369], 13 X[650] - 12 X[4763], 9 X[650] - 8 X[31286], 3 X[650] - 2 X[43067], 7 X[650] - 6 X[47761], 2 X[3676] - 3 X[47876], 13 X[4369] - 15 X[4763], 9 X[4369] - 10 X[31286], 6 X[4369] - 5 X[43067], 14 X[4369] - 15 X[47761], 27 X[4763] - 26 X[31286], 18 X[4763] - 13 X[43067], 14 X[4763] - 13 X[47761], 2 X[21104] - 3 X[47880], 4 X[31286] - 3 X[43067], 28 X[31286] - 27 X[47761], 7 X[43067] - 9 X[47761], 3 X[661] - 2 X[23813], 2 X[693] - 3 X[47777], 4 X[2516] - 3 X[31148], X[20295] - 3 X[47666], 5 X[20295] - 9 X[47774], 5 X[47666] - 3 X[47774], 2 X[4885] - 3 X[47775], X[47675] - 3 X[47775], 6 X[4893] - 5 X[31250], 3 X[30565] - X[47674], 10 X[30835] - 9 X[45320], 5 X[30835] - 3 X[47672], 3 X[45320] - 2 X[47672], 4 X[31287] - 3 X[47780], X[47655] - 3 X[47772]

X(47920) lies on these lines: {241, 514}, {513, 4963}, {661, 23813}, {693, 47777}, {2516, 31148}, {2526, 4824}, {3716, 28191}, {4462, 29771}, {4467, 28910}, {4762, 20295}, {4790, 17494}, {4802, 47701}, {4885, 47675}, {4893, 31250}, {4913, 28229}, {4940, 26824}, {4976, 28878}, {4977, 7659}, {4988, 30520}, {6008, 31290}, {7662, 28175}, {28894, 47667}, {28898, 47661}, {30565, 47674}, {30835, 45320}, {31287, 47780}, {47655, 47772}

X(47920) = midpoint of X(31290) and X(47664)
X(47920) = reflection of X(i) in X(j) for these {i,j}: {2526, 4824}, {4790, 17494}, {26824, 4940}, {47675, 4885}
X(47920) = {X(47675),X(47775)}-harmonic conjugate of X(4885)

X(47921) = X(241)X(514)∩X(513)X(4041)

X(47921) = 3 X[650] - 2 X[905], 7 X[650] - 4 X[3960], 5 X[650] - 4 X[14838], 4 X[905] - 3 X[3669], 7 X[905] - 6 X[3960], 5 X[905] - 6 X[14838], 7 X[3669] - 8 X[3960], 5 X[3669] - 8 X[14838], 5 X[3960] - 7 X[14838], 4 X[7658] - 3 X[30724], 2 X[30723] - 3 X[46919], X[4449] - 3 X[47811], X[4801] - 3 X[47793], 2 X[4885] - 3 X[47793], 2 X[4823] - 3 X[45664], 2 X[4978] - 3 X[45320], 2 X[8045] - 3 X[47770], 2 X[14349] - 3 X[47777], X[17166] - 3 X[47815], X[17496] - 3 X[31150], X[23738] - 3 X[47828], X[23765] - 3 X[47827], 5 X[31250] - 6 X[47794], 4 X[31287] - 3 X[47796]

X(47921) lies on these lines: {241, 514}, {513, 4041}, {661, 8712}, {693, 20317}, {2526, 4705}, {3732, 21859}, {3762, 23882}, {3803, 4160}, {3900, 4724}, {3910, 4468}, {4040, 4162}, {4063, 4790}, {4130, 4391}, {4378, 6050}, {4449, 47811}, {4462, 17494}, {4801, 4885}, {4802, 6129}, {4823, 45664}, {4978, 45320}, {6372, 7659}, {8045, 47770}, {14349, 47777}, {17166, 47815}, {17410, 28878}, {17496, 31150}, {21124, 30520}, {21385, 24290}, {23738, 47828}, {23749, 47679}, {23765, 47827}, {27674, 47675}, {28195, 30574}, {31250, 47794}, {31287, 47796}

X(47921) = midpoint of X(4462) and X(17494)
X(47921) = reflection of X(i) in X(j) for these {i,j}: {693, 20317}, {2526, 4705}, {3669, 650}, {4162, 4040}, {4378, 6050}, {4790, 4063}, {4801, 4885}, {21104, 14837}, {43052, 21120}
X(47921) = X(28226)-complementary conjugate of X(141)
X(47921) = X(101)-isoconjugate of X(5558)
X(47921) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 5558), (12631, 644)
X(47921) = crosspoint of X(651) and X(39948)
X(47921) = crosssum of X(650) and X(3247)
X(47921) = crossdifference of every pair of points on line {55, 1449}
X(47921) = barycentric product X(i)*X(j) for these {i,j}: {513, 32087}, {514, 7308}, {522, 4328}, {693, 3303}, {3676, 4882}, {3983, 7192}
X(47921) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 5558}, {3303, 100}, {3983, 3952}, {4328, 664}, {4882, 3699}, {7308, 190}, {32087, 668}
X(47921) = {X(4801),X(47793)}-harmonic conjugate of X(4885)

X(47922) = X(513)X(4041)∩X(514)X(3837)

X(47922) = X[4041] - 3 X[4490], 3 X[1491] - X[23738], 3 X[4705] - X[4905], X[4879] - 3 X[47826], X[23765] - 3 X[47810]

X(47922) lies on these lines: {513, 4041}, {514, 3837}, {661, 14470}, {1491, 23738}, {2533, 28195}, {4083, 4983}, {4147, 4977}, {4391, 4802}, {4462, 4824}, {4705, 4905}, {4879, 47826}, {17494, 29152}, {23765, 47810}

X(47922) = midpoint of X(4462) and X(4824)
X(47922) = crossdifference of every pair of points on line {1449, 21793}

X(47923) = X(239)X(514)∩X(513)X(47702)

X(47923) = 7 X[649] - 8 X[3798], 3 X[649] - 4 X[4025], 5 X[649] - 6 X[4750], 11 X[649] - 12 X[4786], 6 X[3798] - 7 X[4025], 20 X[3798] - 21 X[4750], 22 X[3798] - 21 X[4786], 4 X[3798] - 7 X[16892], 10 X[4025] - 9 X[4750], 11 X[4025] - 9 X[4786], 2 X[4025] - 3 X[16892], 11 X[4750] - 10 X[4786], 3 X[4750] - 5 X[16892], 6 X[4786] - 11 X[16892], 4 X[693] - 3 X[47873], 4 X[3004] - 3 X[4893], 4 X[3776] - 3 X[4379], 3 X[4379] - 2 X[47660], 2 X[4500] - 3 X[47871], 3 X[4931] - 4 X[23813], 3 X[6545] - 2 X[6590], 3 X[21115] - 2 X[43067], 8 X[21212] - 7 X[31207], 4 X[21212] - 3 X[47771], 7 X[31207] - 6 X[47771], 5 X[24924] - 6 X[47754], 2 X[25259] - 3 X[31147], 5 X[30835] - 6 X[44435], 4 X[31286] - 3 X[47773], 3 X[47886] - 2 X[47890]

X(47923) lies on these lines: {239, 514}, {513, 47702}, {522, 47686}, {661, 30520}, {693, 28863}, {812, 47651}, {824, 4382}, {918, 4813}, {1459, 21126}, {2254, 4802}, {2526, 47700}, {3004, 4893}, {3669, 46380}, {3776, 4379}, {4369, 47662}, {4378, 8635}, {4458, 47696}, {4467, 28882}, {4500, 47871}, {4762, 47673}, {4931, 23813}, {6545, 6590}, {7950, 8665}, {18071, 20909}, {20295, 30519}, {21115, 43067}, {21212, 31207}, {23731, 28846}, {23776, 38346}, {24720, 47693}, {24924, 47754}, {25259, 31147}, {28890, 47666}, {28894, 47672}, {30835, 44435}, {31286, 47773}, {47886, 47890}

X(47923) = midpoint of X(47651) and X(47677)
X(47923) = reflection of X(i) in X(j) for these {i,j}: {649, 16892}, {4382, 47652}, {47660, 3776}, {47662, 4369}, {47663, 21196}, {47693, 24720}, {47696, 4458}, {47700, 2526}
X(47923) = X(39730)-anticomplementary conjugate of X(21293)
X(47923) = X(i)-isoconjugate of X(j) for these (i,j): {37, 7954}, {100, 39955}, {692, 43527}
X(47923) = X(i)-Dao conjugate of X(j) for these (i, j): (1086, 43527), (8054, 39955), (40589, 7954)
X(47923) = crossdifference of every pair of points on line {42, 39955}
X(47923) = barycentric product X(i)*X(j) for these {i,j}: {86, 7950}, {310, 8665}, {514, 3763}, {3261, 7772}, {4025, 5064}, {16892, 39668}
X(47923) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 7954}, {514, 43527}, {649, 39955}, {3763, 190}, {5064, 1897}, {7772, 101}, {7950, 10}, {8665, 42}
X(47923) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3776, 47660, 4379}, {21212, 47771, 31207}

X(47924) = X(1)X(514)∩X(513)X(47702)

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

X(47924) = 4 X[3004] - 3 X[47828], 2 X[4122] - 3 X[31147], 2 X[47660] - 3 X[47832]

X(47924) lies on these lines: {1, 514}, {513, 47702}, {522, 47653}, {523, 4382}, {661, 4802}, {3004, 47828}, {3716, 47662}, {3835, 47693}, {4088, 21297}, {4122, 31147}, {4468, 28191}, {4804, 28894}, {28151, 47700}, {28175, 47826}, {47660, 47832}

X(47924) = reflection of X(i) in X(j) for these {i,j}: {4724, 47701}, {47662, 3716}, {47693, 3835}

X(47925) = X(10)X(514)∩X(513)X(47702)

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

X(47925) lies on these lines: {10, 514}, {513, 47702}, {523, 47650}, {659, 21115}, {2526, 28199}, {3004, 28213}, {3837, 47662}, {4977, 47676}, {24719, 28863}, {29362, 47653}, {47877, 47890}

X(47925) = reflection of X(47662) in X(3837)
X(47925) = barycentric product X(514)*X(25539)
X(47925) = barycentric quotient X(25539)/X(190)

X(47926) = X(239)X(514)∩X(513)X(4963)

X(47926) = 5 X[649] - 4 X[4932], 3 X[649] - 2 X[7192], 7 X[649] - 6 X[47763], 5 X[649] - 6 X[47776], 3 X[4750] - 4 X[4765], 6 X[4932] - 5 X[7192], 2 X[4932] - 5 X[17494], 14 X[4932] - 15 X[47763], 2 X[4932] - 3 X[47776], X[7192] - 3 X[17494], 7 X[7192] - 9 X[47763], 5 X[7192] - 9 X[47776], 7 X[17494] - 3 X[47763], 5 X[17494] - 3 X[47776], 5 X[47763] - 7 X[47776], 4 X[650] - 3 X[4379], 6 X[650] - 5 X[24924], 8 X[650] - 7 X[31207], 9 X[4379] - 10 X[24924], 6 X[4379] - 7 X[31207], 3 X[4379] - 2 X[47672], 20 X[24924] - 21 X[31207], 5 X[24924] - 3 X[47672], 7 X[31207] - 4 X[47672], 3 X[661] - 2 X[4106], 5 X[661] - 4 X[4940], 4 X[661] - 3 X[31147], 4 X[4106] - 3 X[4382], 5 X[4106] - 6 X[4940], 8 X[4106] - 9 X[31147], 5 X[4382] - 8 X[4940], 2 X[4382] - 3 X[31147], 16 X[4940] - 15 X[31147], 2 X[693] - 3 X[4893], 5 X[693] - 6 X[4928], 3 X[693] - 4 X[25666], 4 X[693] - 5 X[30835], 5 X[4893] - 4 X[4928], 9 X[4893] - 8 X[25666], 6 X[4893] - 5 X[30835], 9 X[4928] - 10 X[25666], 24 X[4928] - 25 X[30835], 16 X[25666] - 15 X[30835], X[4813] + 2 X[47664], 3 X[1635] - 2 X[43067], 2 X[3004] - 3 X[47878], 4 X[3676] - 3 X[21116], 2 X[3676] - 3 X[47883], 2 X[3776] - 3 X[47782], 2 X[3835] - 3 X[47775], X[26824] - 3 X[47775], 2 X[4010] - 3 X[47826], 2 X[4369] - 3 X[31150], 3 X[31150] - X[47675], 4 X[4394] - 3 X[31148], 2 X[4500] - 3 X[30565], X[4608] - 3 X[47773], 3 X[6546] - 2 X[6590], 3 X[6546] - X[47671], 2 X[7662] - 3 X[47811], 3 X[8643] - 2 X[17166], 4 X[8689] - 3 X[47694], 2 X[21104] - 3 X[47886], 2 X[21146] - 3 X[47828], 2 X[23813] - 3 X[47777], 2 X[24720] - 3 X[47825], 5 X[26777] - 4 X[31286], 5 X[26777] - 3 X[47780], 4 X[31286] - 3 X[47780], 5 X[26985] - 6 X[47778], 7 X[27115] - 6 X[47779], X[47650] - 3 X[47781], 2 X[47656] - 3 X[47873], X[47674] - 3 X[47771]

X(47926) lies on these lines: {239, 514}, {513, 4963}, {522, 47698}, {523, 4724}, {650, 4379}, {659, 4802}, {661, 4106}, {693, 4893}, {812, 4813}, {824, 47661}, {891, 2978}, {1635, 43067}, {3004, 47878}, {3676, 21116}, {3776, 47782}, {3835, 26824}, {4010, 47826}, {4024, 4468}, {4369, 31150}, {4375, 47659}, {4380, 28840}, {4394, 31148}, {4467, 28851}, {4500, 30565}, {4608, 26277}, {4782, 28199}, {4784, 28195}, {4785, 31290}, {4801, 30061}, {4814, 29188}, {4824, 29362}, {4841, 6084}, {6546, 6590}, {7662, 47811}, {8643, 17166}, {8689, 28147}, {17161, 30519}, {21104, 47886}, {21146, 47828}, {23506, 28151}, {23813, 47777}, {24623, 47651}, {24720, 47825}, {26777, 31286}, {26854, 47793}, {26985, 47778}, {27115, 47779}, {28863, 47657}, {28890, 47677}, {28894, 47669}, {30520, 47673}, {47650, 47781}, {47656, 47873}, {47662, 47668}, {47674, 47771}

X(47926) = midpoint of X(i) and X(j) for these {i,j}: {47662, 47668}, {47663, 47667}, {47664, 47666}
X(47926) = reflection of X(i) in X(j) for these {i,j}: {649, 17494}, {4024, 4468}, {4382, 661}, {4813, 47666}, {16892, 45745}, {21116, 47883}, {26824, 3835}, {47671, 6590}, {47672, 650}, {47675, 4369}, {47676, 21196}
X(47926) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {29199, 69}, {32739, 41912}, {39738, 21293}, {39972, 150}
X(47926) = X(i)-isoconjugate of X(j) for these (i,j): {100, 39965}, {101, 39739}
X(47926) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39739), (8054, 39965)
X(47926) = crossdifference of every pair of points on line {42, 4253}
X(47926) = barycentric product X(i)*X(j) for these {i,j}: {513, 32104}, {514, 17259}
X(47926) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 39739}, {649, 39965}, {17259, 190}, {32104, 668}
X(47926) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 4379, 31207}, {650, 47672, 4379}, {661, 4382, 31147}, {693, 4893, 30835}, {4932, 47776, 649}, {6546, 47671, 6590}, {26777, 47780, 31286}, {26824, 47775, 3835}, {31150, 47675, 4369}

X(47927) = X(1)X(514)∩X(513)X(4963)

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

X(47927) = 3 X[4724] - 2 X[47694], 2 X[693] - 3 X[47826], 5 X[1491] - 6 X[45676], 3 X[4893] - 2 X[21146], 2 X[24720] - 3 X[47775], 2 X[43067] - 3 X[47811], 3 X[47666] - X[47685], 2 X[47672] - 3 X[47832]

X(47927) lies on these lines: {1, 514}, {513, 4963}, {649, 4841}, {659, 21115}, {693, 47826}, {1491, 45676}, {3716, 47675}, {4468, 47703}, {4778, 17494}, {4784, 28220}, {4813, 29362}, {4893, 21146}, {7192, 28229}, {24720, 47775}, {43067, 47811}, {47666, 47685}, {47672, 47832}

X(47927) = reflection of X(i) in X(j) for these {i,j}: {47675, 3716}, {47703, 4468}

X(47928) = X(10)X(514)∩X(513)X(4963)

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

X(47928) = 3 X[1491] - 2 X[21146], 5 X[1491] - 4 X[24720], 7 X[1491] - 6 X[36848], 3 X[4824] - X[21146], 5 X[4824] - 2 X[24720], 7 X[4824] - 3 X[36848], 5 X[21146] - 6 X[24720], 7 X[21146] - 9 X[36848], 14 X[24720] - 15 X[36848], 2 X[4874] - 3 X[47775], 2 X[21104] - 3 X[47877], 2 X[43067] - 3 X[47827]

X(47928) lies on these lines: {10, 514}, {513, 4963}, {523, 8663}, {661, 4802}, {693, 28175}, {2254, 28195}, {3835, 28191}, {3837, 47675}, {4010, 28147}, {4804, 28151}, {4806, 28179}, {4874, 47775}, {4977, 47663}, {18004, 47656}, {21104, 47877}, {28199, 47672}, {29078, 47661}, {29328, 31290}, {43067, 47827}

X(47928) = midpoint of X(47667) and X(47698)
X(47928) = reflection of X(i) in X(j) for these {i,j}: {1491, 4824}, {47656, 18004}, {47675, 3837}

X(47929) = X(1)X(514)∩X(513)X(4041)

X(47929) = 4 X[1] - 5 X[663], 3 X[1] - 5 X[4040], 6 X[1] - 5 X[4449], 2 X[1] - 5 X[4724], 7 X[1] - 10 X[4794], 3 X[663] - 4 X[4040], 3 X[663] - 2 X[4449], 7 X[663] - 8 X[4794], 2 X[4040] - 3 X[4724], 7 X[4040] - 6 X[4794], X[4449] - 3 X[4724], 7 X[4449] - 12 X[4794], 7 X[4724] - 4 X[4794], 2 X[905] - 3 X[47811], X[23738] - 3 X[47811], 2 X[2530] - 3 X[4893], 2 X[14349] - 3 X[47826], 4 X[4367] - 5 X[8656], 2 X[4369] - 3 X[47815], 2 X[4378] - 3 X[8643], 7 X[4678] - 5 X[21302], 2 X[4905] - 3 X[47828], 2 X[4978] - 3 X[47832], 10 X[17072] - 11 X[46933], 13 X[19877] - 10 X[24720], 13 X[19877] - 15 X[47793], 2 X[24720] - 3 X[47793], 16 X[19878] - 15 X[47795], 2 X[23789] - 3 X[47794], 4 X[23815] - 5 X[30835], 4 X[25666] - 3 X[47819]

X(47929) lies on these lines: {1, 514}, {513, 4041}, {649, 6372}, {659, 29198}, {905, 23738}, {1459, 28195}, {2530, 4893}, {2832, 14349}, {3309, 4814}, {3716, 4801}, {3737, 28229}, {3762, 29186}, {3777, 28257}, {4105, 6362}, {4142, 47676}, {4367, 8656}, {4369, 47815}, {4378, 8643}, {4462, 4474}, {4678, 21302}, {4778, 17418}, {4813, 24290}, {4822, 8712}, {4905, 47828}, {4959, 14077}, {4977, 7178}, {4978, 47832}, {6005, 21385}, {17020, 47781}, {17072, 46933}, {19877, 24720}, {19878, 47795}, {21139, 38365}, {23789, 47794}, {23815, 30835}, {25666, 47819}, {28147, 42312}, {29118, 47663}, {29138, 42662}

X(47929) = reflection of X(i) in X(j) for these {i,j}: {663, 4724}, {4449, 4040}, {4474, 4462}, {4801, 3716}, {23738, 905}, {43924, 46385}, {47676, 4142}, {47704, 21185}
X(47929) = crossdifference of every pair of points on line {672, 1449}
X(47929) = barycentric product X(514)*X(4423)
X(47929) = barycentric quotient X(4423)/X(190)
X(47929) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4040, 4449, 663}, {4449, 4724, 4040}, {23738, 47811, 905}

X(47930) = X(513)X(47702)∩X(514)X(4380)

X(47930) = 5 X[47657] - 3 X[47668], 4 X[47657] - 3 X[47669], 2 X[47657] - 3 X[47673], X[47657] - 3 X[47677], 4 X[47668] - 5 X[47669], 2 X[47668] - 5 X[47673], X[47668] - 5 X[47677], X[47669] - 4 X[47677], 3 X[661] - 4 X[3004], 2 X[3004] - 3 X[16892], 4 X[693] - 3 X[4931], 2 X[693] - 3 X[21115], 3 X[4838] - 4 X[47656], X[4838] - 4 X[47676], 2 X[47656] - 3 X[47672], X[47656] - 3 X[47676], 3 X[1635] - 4 X[4025], 9 X[1635] - 8 X[11068], 3 X[4025] - 2 X[11068], 4 X[3676] - 3 X[47874], 2 X[3700] - 3 X[6545], 4 X[3776] - 3 X[4728], 3 X[4728] - 2 X[25259], 4 X[4106] - 3 X[4958], 2 X[4122] - 3 X[47812], 6 X[4453] - 5 X[24924], 2 X[4468] - 3 X[47886], 3 X[4750] - 2 X[47890], 3 X[6546] - 4 X[17069], 4 X[21212] - 3 X[30565], 4 X[25666] - 3 X[47772], 5 X[30835] - 6 X[47754], 3 X[31148] - 2 X[47660], 7 X[31207] - 6 X[47770]

X(47930) lies on these lines: {513, 47702}, {514, 4380}, {522, 47705}, {649, 30520}, {661, 918}, {693, 4931}, {764, 3906}, {824, 4838}, {826, 40471}, {1635, 4025}, {2254, 47700}, {2786, 47652}, {3667, 47692}, {3676, 47874}, {3700, 6545}, {3776, 4728}, {3777, 21350}, {4024, 21104}, {4041, 29354}, {4106, 4958}, {4122, 47812}, {4382, 28898}, {4453, 24924}, {4468, 47886}, {4729, 29288}, {4750, 47890}, {4785, 47651}, {4818, 47698}, {4822, 29252}, {4905, 29358}, {4932, 47662}, {6546, 17069}, {7192, 28863}, {17494, 28890}, {21212, 30565}, {23738, 29017}, {23765, 29202}, {25666, 47772}, {28840, 47653}, {28851, 45746}, {28871, 31290}, {30835, 47754}, {31148, 47660}, {31207, 47770}, {47670, 47675}

X(47930) = reflection of X(i) in X(j) for these {i,j}: {661, 16892}, {4024, 21104}, {4838, 47672}, {4931, 21115}, {25259, 3776}, {47662, 4932}, {47669, 47673}, {47670, 47675}, {47672, 47676}, {47673, 47677}, {47698, 4818}, {47700, 2254}
X(47930) = barycentric product X(i)*X(j) for these {i,j}: {514, 17231}, {522, 24798}
X(47930) = barycentric quotient X(i)/X(j) for these {i,j}: {17231, 190}, {24798, 664}
X(47930) = {X(3776),X(25259)}-harmonic conjugate of X(4728)

X(47931) = X(513)X(47702)∩X(514)X(1734)

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

X(47931) = 4 X[3004] - 3 X[47811], 4 X[3776] - 3 X[47813], 2 X[47696] - 3 X[47813], 2 X[4830] - 3 X[47894], 4 X[25380] - 3 X[47773], 2 X[47660] - 3 X[47812]

X(47931) lies on these lines: {513, 47702}, {514, 1734}, {522, 47651}, {649, 28195}, {824, 47686}, {3004, 47811}, {3776, 47696}, {4025, 28229}, {4804, 47652}, {4818, 47663}, {4830, 47894}, {4977, 16892}, {24720, 47662}, {25380, 47773}, {28863, 46403}, {29362, 47673}, {47660, 47812}

X(47931) = reflection of X(i) in X(j) for these {i,j}: {4804, 47652}, {47662, 24720}, {47663, 4818}, {47696, 3776}
X(47931) = {X(3776),X(47696)}-harmonic conjugate of X(47813)

X(47932) = X(513)X(4963)∩X(514)X(4380)

X(47932) = X[4979] + 2 X[47664], 4 X[649] - 3 X[31148], 3 X[649] - 2 X[43067], 9 X[31148] - 8 X[43067], 3 X[31148] - 2 X[47672], 4 X[43067] - 3 X[47672], 4 X[650] - 3 X[4728], 3 X[650] - 2 X[23813], 6 X[650] - 5 X[30835], 2 X[4382] - 3 X[4728], 3 X[4382] - 4 X[23813], 3 X[4382] - 5 X[30835], 9 X[4728] - 8 X[23813], 9 X[4728] - 10 X[30835], 4 X[23813] - 5 X[30835], 3 X[661] - 2 X[20295], 7 X[661] - 6 X[47759], 5 X[661] - 6 X[47775], 3 X[17494] - X[20295], 7 X[17494] - 3 X[47759], 5 X[17494] - 3 X[47775], 7 X[20295] - 9 X[47759], 5 X[20295] - 9 X[47775], 5 X[47759] - 7 X[47775], 2 X[693] - 3 X[1635], 4 X[693] - 5 X[24924], 3 X[693] - 4 X[31286], 5 X[693] - 6 X[47779], 6 X[1635] - 5 X[24924], 9 X[1635] - 8 X[31286], 5 X[1635] - 4 X[47779], 15 X[24924] - 16 X[31286], 25 X[24924] - 24 X[47779], 10 X[31286] - 9 X[47779], 8 X[2516] - 7 X[31207], 4 X[2516] - 3 X[45320], 7 X[31207] - 6 X[45320], 2 X[3700] - 3 X[6546], 2 X[3776] - 3 X[27486], 3 X[27486] - X[47650], 2 X[3835] - 3 X[31150], 2 X[4010] - 3 X[47811], 4 X[4025] - 3 X[21115], 2 X[4106] - 3 X[4893], 2 X[4369] - 3 X[47776], X[26824] - 3 X[47776], 3 X[4379] - 4 X[4394], 2 X[4500] - 3 X[47771], 3 X[4750] - 2 X[21104], 6 X[4763] - 5 X[26985], 4 X[4765] - 3 X[47886], 4 X[4782] - 3 X[47813], 2 X[4897] - 3 X[4984], 6 X[4928] - 7 X[27115], 3 X[6545] - 4 X[17069], 4 X[9508] - 3 X[47812], 4 X[11068] - 3 X[47874], 3 X[14435] - 2 X[47891], 4 X[21212] - 3 X[47871], 3 X[21297] - 4 X[25666], 3 X[21297] - 5 X[26777], 4 X[25666] - 5 X[26777], 2 X[24719] - 3 X[47810], 5 X[26798] - 6 X[45315], 5 X[27013] - 3 X[47869]

X(47932) lies on these lines: {513, 4963}, {514, 4380}, {522, 47700}, {649, 4762}, {650, 4382}, {659, 4804}, {661, 812}, {693, 1635}, {824, 47663}, {2254, 29362}, {2516, 31207}, {3004, 6009}, {3700, 6546}, {3776, 27486}, {3835, 31150}, {4010, 47811}, {4024, 47890}, {4025, 21115}, {4041, 29070}, {4106, 4893}, {4369, 26824}, {4379, 4394}, {4490, 29238}, {4498, 23882}, {4500, 47771}, {4729, 29051}, {4750, 21104}, {4763, 26985}, {4765, 47886}, {4773, 21116}, {4782, 47813}, {4785, 47666}, {4813, 6008}, {4818, 47686}, {4830, 47694}, {4838, 47660}, {4841, 23731}, {4897, 4984}, {4913, 46403}, {4928, 27115}, {4931, 47892}, {4932, 47675}, {4976, 6084}, {6545, 17069}, {6608, 38325}, {9508, 47812}, {11068, 47874}, {14435, 47891}, {17161, 28863}, {21196, 47652}, {21212, 47871}, {21297, 25666}, {21385, 29545}, {24719, 47810}, {26798, 45315}, {26853, 28840}, {27013, 47869}, {28161, 47697}, {28859, 47667}, {28882, 45746}

X(47932) = midpoint of X(4380) and X(47664)
X(47932) = reflection of X(i) in X(j) for these {i,j}: {661, 17494}, {4024, 47890}, {4382, 650}, {4804, 659}, {4838, 47660}, {4931, 47892}, {4979, 4380}, {16892, 4976}, {21116, 4773}, {23731, 4841}, {26824, 4369}, {46403, 4913}, {47650, 3776}, {47652, 21196}, {47669, 47661}, {47672, 649}, {47675, 4932}, {47686, 4818}, {47694, 4830}
X(47932) = barycentric product X(514)*X(17348)
X(47932) = barycentric quotient X(17348)/X(190)
X(47932) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 47672, 31148}, {650, 4382, 4728}, {650, 23813, 30835}, {693, 1635, 24924}, {2516, 45320, 31207}, {4382, 30835, 23813}, {21297, 26777, 25666}, {23813, 30835, 4728}, {26824, 47776, 4369}, {27486, 47650, 3776}

X(47933) = X(513)X(4963)∩X(514)X(47692)

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

X(47933) = 4 X[659] - 3 X[31148], 3 X[661] - 2 X[46403], 4 X[676] - 3 X[21116], 3 X[4724] - 2 X[7662], 4 X[7662] - 3 X[47672], 4 X[21146] - 5 X[24924], 2 X[21146] - 3 X[47811], 5 X[24924] - 6 X[47811], 10 X[30795] - 9 X[47812]

X(47933) lies on these lines: {513, 4963}, {514, 47692}, {659, 31148}, {661, 46403}, {676, 21116}, {3667, 47664}, {4380, 28225}, {4724, 7662}, {4778, 4979}, {4977, 16892}, {21146, 24924}, {30795, 47812}

X(47933) = reflection of X(47672) in X(4724)
X(47933) = {X(21146),X(47811)}-harmonic conjugate of X(24924)

X(47934) = X(513)X(4963)∩X(514)X(1734)

X(47934) = 3 X[4041] - 2 X[4761], 5 X[4041] - 4 X[4807], 5 X[4761] - 6 X[4807], 3 X[661] - 2 X[4010], 5 X[661] - 4 X[4806], 4 X[4010] - 3 X[4804], 5 X[4010] - 6 X[4806], X[4010] - 3 X[4824], 5 X[4804] - 8 X[4806], X[4804] - 4 X[4824], 2 X[4806] - 5 X[4824], 3 X[4931] - 4 X[18004], 4 X[650] - 3 X[47813], 2 X[676] - 3 X[47876], 2 X[693] - 3 X[47810], 4 X[1491] - 3 X[47812], 2 X[47672] - 3 X[47812], 2 X[3716] - 3 X[47775], 2 X[4369] - 3 X[47825], 2 X[4458] - 3 X[47782], 4 X[4705] - 3 X[21052], 2 X[4830] - 3 X[17494], 3 X[4893] - 2 X[7662], 3 X[4948] - 2 X[9508], 4 X[9508] - 3 X[31148], 5 X[24924] - 6 X[47827], 4 X[25380] - 3 X[47780], 4 X[25666] - 3 X[47834], 2 X[43067] - 3 X[47828], X[47674] - 3 X[47808], 2 X[47694] - 3 X[47811]

X(47934) lies on these lines: {513, 4963}, {514, 1734}, {522, 44449}, {523, 661}, {650, 47813}, {656, 21727}, {676, 47876}, {693, 4086}, {824, 47698}, {1491, 4802}, {3004, 47704}, {3716, 47775}, {3835, 28155}, {3837, 28179}, {4151, 4822}, {4160, 47683}, {4369, 47825}, {4458, 47782}, {4522, 47656}, {4705, 21052}, {4724, 24769}, {4728, 28151}, {4818, 47676}, {4830, 17494}, {4893, 7662}, {4913, 7192}, {4948, 9508}, {21146, 28175}, {24720, 28191}, {24924, 47827}, {25380, 47780}, {25666, 47834}, {30765, 47809}, {43067, 47828}, {47668, 47689}, {47674, 47808}, {47694, 47811}

X(47934) = midpoint of X(i) and X(j) for these {i,j}: {47668, 47689}, {47669, 47700}
X(47934) = reflection of X(i) in X(j) for these {i,j}: {661, 4824}, {4804, 661}, {4838, 4122}, {7192, 4913}, {31148, 4948}, {47656, 4522}, {47672, 1491}, {47675, 24720}, {47676, 4818}, {47701, 4841}, {47704, 3004}
X(47934) = crossdifference of every pair of points on line {58, 2280}
X(47934) = barycentric product X(i)*X(j) for these {i,j}: {523, 16831}, {4064, 31919}
X(47934) = barycentric quotient X(16831)/X(99)
X(47934) = {X(1491),X(47672)}-harmonic conjugate of X(47812)

X(47935) = X(513)X(4041)∩X(514)X(4380)

X(47935) = 5 X[1019] - 3 X[1022], 3 X[649] - 2 X[905], 3 X[1635] - 2 X[14349], 2 X[4978] - 3 X[31148], 2 X[4983] - 3 X[47811]

X(47935) lies on these lines: {81, 1019}, {512, 2292}, {513, 4041}, {514, 4380}, {649, 905}, {659, 4822}, {661, 4063}, {830, 4729}, {1635, 14349}, {2254, 4834}, {4129, 23825}, {4391, 4785}, {4435, 4790}, {4801, 4932}, {4978, 31148}, {4983, 47811}, {6002, 26853}, {11684, 42325}, {15309, 21385}, {25259, 28493}, {29302, 47672}

X(47935) = reflection of X(i) in X(j) for these {i,j}: {661, 4063}, {2254, 4834}, {4801, 4932}, {4822, 659}
X(47935) = crossdifference of every pair of points on line {612, 1449}

X(47936) = X(513)X(4041)∩X(514)X(47692)

X(47936) = 3 X[1635] - 2 X[4905], 2 X[2530] - 3 X[47811], 4 X[8689] - 3 X[47820], 3 X[14413] - 2 X[23765], 4 X[20517] - 3 X[21115], 4 X[23789] - 5 X[24924], 2 X[23789] - 3 X[47817], 5 X[24924] - 6 X[47817], 2 X[24720] - 3 X[47815]

X(47936) lies on these lines: {513, 4041}, {514, 47692}, {661, 16546}, {667, 23738}, {1635, 4905}, {2530, 47811}, {2832, 4040}, {3801, 4977}, {4729, 21385}, {4895, 29226}, {8689, 47820}, {14413, 23765}, {20517, 21115}, {23789, 24924}, {24720, 47815}

X(47936) = reflection of X(i) in X(j) for these {i,j}: {4729, 21385}, {23738, 667}
X(47936) = crossdifference of every pair of points on line {1449, 17469}
X(47936) = {X(23789),X(47817)}-harmonic conjugate of X(24924)

X(47937) = X(513)X(16892)∩X(514)X(4838)

X(47937) = X[16892] - 3 X[23731], 5 X[649] - 6 X[47784], 5 X[661] - 4 X[11068], 4 X[3798] - 3 X[4979], 8 X[3798] - 9 X[47886], 2 X[4979] - 3 X[47886], 2 X[4380] - 3 X[47878], 2 X[4500] - 3 X[20295], 10 X[4500] - 9 X[47792], 5 X[20295] - 3 X[47792], 8 X[7653] - 9 X[14475]

X(47937) lies on these lines: {513, 16892}, {514, 4838}, {649, 47784}, {661, 11068}, {812, 47667}, {3667, 47673}, {3798, 4979}, {4380, 47878}, {4382, 4977}, {4500, 20295}, {4778, 47672}, {4988, 6008}, {7653, 14475}, {23727, 23736}, {23729, 28209}, {28195, 47671}, {28225, 47697}, {28855, 47651}, {28867, 47653}, {28882, 31290}

X(47938) = X(513)X(16892)∩X(514)X(4170)

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

X(47938) = 2 X[4522] - 3 X[47759], 2 X[4784] - 3 X[47886], 4 X[4806] - 3 X[47874], 2 X[4913] - 3 X[47781], 2 X[4932] - 3 X[47797], 2 X[7192] - 3 X[47887], 3 X[47826] - 2 X[47890]

X(47938) lies on these lines: {513, 16892}, {514, 4170}, {522, 47657}, {523, 4813}, {812, 47699}, {4106, 47703}, {4522, 47759}, {4778, 47123}, {4784, 47886}, {4806, 47874}, {4913, 47781}, {4932, 47797}, {7192, 47887}, {28147, 47665}, {28840, 47691}, {28851, 47688}, {28859, 47694}, {47826, 47890}

X(47939) = X(513)X(4380)∩X(514)X(4838)

X(47939) = 9 X[2] - 8 X[7653], 3 X[4380] - 4 X[17494], 5 X[4380] - 4 X[26853], X[4380] - 4 X[31290], 5 X[17494] - 3 X[26853], X[17494] - 3 X[31290], 2 X[17494] - 3 X[47666], X[26853] - 5 X[31290], 2 X[26853] - 5 X[47666], 3 X[44449] - X[47658], 2 X[47658] - 3 X[47665], 2 X[650] - 3 X[47774], 3 X[661] - 2 X[4932], 6 X[661] - 5 X[31209], 5 X[661] - 4 X[31286], 4 X[661] - 3 X[47762], 7 X[661] - 6 X[47778], 4 X[4932] - 5 X[31209], 5 X[4932] - 6 X[31286], 8 X[4932] - 9 X[47762], 7 X[4932] - 9 X[47778], 25 X[31209] - 24 X[31286], 10 X[31209] - 9 X[47762], 35 X[31209] - 36 X[47778], 16 X[31286] - 15 X[47762], 14 X[31286] - 15 X[47778], 7 X[47762] - 8 X[47778], 5 X[693] - 6 X[31147], 5 X[4813] - 3 X[31147], 9 X[4776] - 8 X[4885], 3 X[4776] - 2 X[7192], 15 X[4776] - 14 X[27138], 4 X[4885] - 3 X[7192], 20 X[4885] - 21 X[27138], 5 X[7192] - 7 X[27138], 2 X[4790] - 3 X[47775], 2 X[4897] - 3 X[47781], 4 X[4940] - 3 X[47780], 2 X[4979] - 3 X[31150], 4 X[14321] - 3 X[47791], 5 X[27013] - 6 X[47777], 2 X[43067] - 3 X[47759]

X(47939) lies on these lines: {2, 7653}, {513, 4380}, {514, 4838}, {522, 47668}, {650, 47774}, {661, 4932}, {693, 4813}, {900, 47667}, {2786, 47657}, {3667, 47661}, {4468, 28225}, {4608, 4820}, {4776, 4885}, {4778, 47660}, {4785, 47664}, {4790, 47775}, {4897, 47781}, {4940, 47780}, {4963, 29328}, {4977, 25259}, {4979, 31150}, {4988, 28867}, {14321, 47791}, {14779, 28165}, {16892, 28886}, {20295, 47675}, {23731, 28851}, {27013, 47777}, {28195, 47659}, {28846, 47677}, {28859, 47662}, {28878, 47652}, {28902, 47676}, {28906, 47673}, {43067, 47759}

X(47939) = reflection of X(i) in X(j) for these {i,j}: {693, 4813}, {4380, 47666}, {4608, 4820}, {47651, 23731}, {47665, 44449}, {47666, 31290}, {47675, 20295}
X(47939) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4932, 31209}, {4932, 31209, 47762}

X(47940) = X(513)X(4380)∩X(514)X(47685)

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

X(47940) = 4 X[1491] - 3 X[47762], 3 X[4776] - 2 X[47694], 5 X[31209] - 6 X[47810]

X(47940) lies on these lines: {513, 4380}, {514, 47685}, {522, 47657}, {661, 47697}, {900, 47699}, {1491, 47762}, {2526, 7192}, {4088, 47662}, {4776, 47694}, {4977, 47698}, {31095, 44429}, {31209, 47810}, {46403, 47675}

X(47940) = reflection of X(i) in X(j) for these {i,j}: {7192, 2526}, {47662, 4088}, {47675, 46403}, {47697, 661}

X(47941) = X(513)X(4380)∩X(514)X(4170)

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

X(47941) = 2 X[4824] - 3 X[47666], 3 X[661] - 2 X[24720], 4 X[661] - 3 X[44429], 8 X[24720] - 9 X[44429], 3 X[693] - 4 X[4806], 2 X[4369] - 3 X[47826], 3 X[4776] - 2 X[21146], 2 X[4784] - 3 X[31150], 2 X[4932] - 3 X[47811], 2 X[7192] - 3 X[47804], 2 X[7659] - 3 X[47825], 2 X[43067] - 3 X[47821]

X(47941) lies on these lines: {513, 4380}, {514, 4170}, {661, 4521}, {693, 4806}, {918, 47699}, {1491, 28209}, {2254, 28225}, {4010, 28195}, {4369, 47826}, {4724, 4817}, {4776, 21146}, {4784, 31150}, {4801, 4983}, {4932, 47811}, {7192, 47804}, {7659, 47825}, {28229, 47672}, {28851, 47701}, {29328, 47664}, {43067, 47821}

X(47941) = reflection of X(i) in X(j) for these {i,j}: {4801, 4983}, {47675, 4010}
X(47941) = crossdifference of every pair of points on line {3915, 20963}

X(47942) = X(484)X(513)∩X(514)X(4170)

X(47942) = 3 X[1734] - 4 X[4705], 3 X[1019] - 4 X[6050], 2 X[3777] - 3 X[14349], 3 X[4776] - 2 X[23789], 2 X[4932] - 3 X[47817], 2 X[14838] - 3 X[47826]

X(47942) lies on these lines: {484, 513}, {514, 4170}, {661, 4905}, {1019, 6050}, {1577, 4778}, {3777, 6372}, {4724, 15309}, {4729, 6005}, {4776, 23789}, {4932, 47817}, {4983, 29198}, {8714, 47666}, {14838, 47826}, {21185, 28878}, {28851, 47712}, {29190, 44449}

X(47942) = reflection of X(4905) in X(661)
X(47942) = barycentric product X(1)*X(47674)
X(47942) = barycentric quotient X(47674)/X(75)

X(47943) = X(513)X(16892)∩X(514)X(4088)

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

X(47943) = 2 X[4782] - 3 X[47877], 2 X[4830] - 3 X[47782], 3 X[47810] - 2 X[47890]

X(47943) lies on these lines: {513, 16892}, {514, 4088}, {522, 47653}, {661, 1639}, {830, 47727}, {900, 47702}, {1443, 1447}, {3835, 47696}, {4024, 24719}, {4380, 4818}, {4444, 28859}, {4468, 28229}, {4522, 47662}, {4782, 47877}, {4804, 23729}, {4809, 28209}, {4830, 47782}, {4988, 29362}, {14475, 28220}, {28147, 47650}, {28175, 47700}, {47652, 47704}, {47779, 47826}, {47810, 47890}

X(47943) = reflection of X(i) in X(j) for these {i,j}: {4024, 24719}, {4380, 4818}, {4804, 23729}, {47662, 4522}, {47696, 3835}, {47703, 46403}, {47704, 47652}
X(47943) = crossdifference of every pair of points on line {595, 1334}

X(47944) = X(513)X(16892)∩X(514)X(4010)

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

X(47944) = 2 X[18004] - 3 X[47759], X[47693] - 3 X[47759], 5 X[30795] - 6 X[47756]

X(47944) lies on these lines: {513, 16892}, {514, 4010}, {523, 4810}, {3004, 4784}, {4024, 4802}, {4375, 28859}, {4806, 47660}, {4977, 23770}, {18004, 47693}, {28175, 47659}, {29328, 45746}, {29362, 47699}, {30795, 47756}, {31094, 47809}, {31290, 47688}

X(47944) = midpoint of X(i) and X(j) for these {i,j}: {23731, 47701}, {31290, 47688}
X(47944) = reflection of X(i) in X(j) for these {i,j}: {4784, 3004}, {47660, 4806}, {47693, 18004}
X(47944) = {X(47693),X(47759)}-harmonic conjugate of X(18004)

X(47945) = X(513)X(4380)∩X(514)X(4088)

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

X(47945) = 3 X[21301] - 2 X[47724], 2 X[4810] - 3 X[20295], 2 X[649] - 3 X[47825], 2 X[659] - 3 X[47775], 3 X[661] - 2 X[3716], 4 X[661] - 3 X[47821], 4 X[3716] - 3 X[47694], 8 X[3716] - 9 X[47821], 2 X[47694] - 3 X[47821], 4 X[1491] - 3 X[47824], 2 X[7192] - 3 X[47824], 4 X[3835] - 3 X[47834], 4 X[3837] - 3 X[47780], 2 X[4010] - 3 X[47759], 2 X[4369] - 3 X[47810], 3 X[4776] - 2 X[7662], 4 X[4782] - 5 X[26777], 2 X[4932] - 3 X[47828], 4 X[9508] - 3 X[47763], 4 X[18004] - 3 X[47870], 4 X[25380] - 3 X[31148], 4 X[25666] - 3 X[47813], 5 X[27013] - 6 X[47827], 7 X[27138] - 6 X[47833], 2 X[43067] - 3 X[44429]

X(47945) lies on these lines: {513, 4380}, {514, 4088}, {522, 4813}, {523, 4810}, {649, 47825}, {659, 47775}, {661, 3716}, {1491, 7192}, {2254, 28840}, {3835, 47834}, {3837, 47780}, {4010, 47759}, {4122, 47659}, {4367, 27675}, {4369, 47810}, {4382, 28147}, {4468, 47696}, {4776, 7662}, {4782, 26777}, {4802, 24719}, {4913, 4979}, {4932, 47828}, {4963, 4977}, {7650, 27575}, {8678, 47729}, {9508, 47763}, {14349, 17166}, {17161, 29078}, {18004, 47870}, {25380, 31148}, {25666, 47813}, {27013, 47827}, {27138, 47833}, {43067, 44429}

X(47945) = reflection of X(i) in X(j) for these {i,j}: {4979, 4913}, {7192, 1491}, {17166, 14349}, {17494, 4824}, {26824, 24719}, {47659, 4122}, {47693, 4088}, {47694, 661}, {47696, 4468}
X(47945) = crossdifference of every pair of points on line {20963, 21764}
X(47945) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47694, 47821}, {1491, 7192, 47824}

X(47946) = X(513)X(4380)∩X(514)X(4010)

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

X(47946) = 3 X[661] - 2 X[3837], 5 X[661] - 3 X[47812], 4 X[3837] - 3 X[21146], 10 X[3837] - 9 X[47812], 5 X[21146] - 6 X[47812], 2 X[4874] - 3 X[47826], 2 X[9508] - 3 X[47775], 5 X[30795] - 6 X[45315], 2 X[43067] - 3 X[47822], X[46403] - 3 X[47774]

X(47946) lies on these lines: {513, 4380}, {514, 4010}, {659, 28840}, {661, 1639}, {693, 18158}, {1491, 4778}, {2254, 28209}, {3835, 28229}, {4804, 28175}, {4806, 28213}, {4813, 29362}, {4874, 47826}, {9508, 47775}, {18004, 47703}, {28220, 31992}, {29144, 47698}, {29252, 47679}, {30795, 45315}, {43067, 47822}, {46403, 47774}

X(47946) = reflection of X(i) in X(j) for these {i,j}: {4824, 47666}, {21146, 661}, {47672, 4806}, {47703, 18004}
X(47946) = crossdifference of every pair of points on line {595, 20963}

X(47947) = X(484)X(513)∩X(514)X(4024)

X(47947) = 3 X[661] - 2 X[14838], 3 X[1019] - 4 X[14838], 2 X[3669] - 3 X[14349], 2 X[4401] - 3 X[47826], X[4560] - 3 X[47774], 2 X[4932] - 3 X[47794]

X(47947) lies on these lines: {1, 4983}, {148, 6630}, {484, 513}, {514, 4024}, {661, 1019}, {830, 1027}, {876, 6372}, {1022, 1255}, {1308, 8701}, {1577, 4960}, {2786, 47679}, {3257, 3882}, {3669, 14349}, {4129, 7192}, {4160, 4822}, {4401, 47826}, {4444, 32014}, {4560, 47774}, {4562, 6540}, {4567, 4596}, {4824, 29150}, {4932, 47794}, {4977, 32846}, {4988, 24969}, {6002, 47683}, {23879, 44449}, {23894, 40438}, {29013, 47666}, {29062, 47699}, {29158, 47698}, {32635, 35355}, {32678, 37140}

X(47947) = reflection of X(i) in X(j) for these {i,j}: {1, 4983}, {1019, 661}, {4608, 31010}, {4960, 1577}, {7192, 4129}, {47681, 7265}
X(47947) = isogonal conjugate of X(35342)
X(47947) = isotomic conjugate of the anticomplement of X(16726)
X(47947) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {213, 39348}, {1018, 2891}, {4557, 41821}, {4596, 17143}, {4629, 17140}, {6538, 21294}, {6539, 21293}, {6540, 17137}, {8701, 75}, {28615, 17154}, {37212, 17135}
X(47947) = X(i)-Ceva conjugate of X(j) for these (i,j): {4596, 1}, {37212, 1255}
X(47947) = X(i)-cross conjugate of X(j) for these (i,j): {3125, 1}, {7202, 57}, {16726, 2}, {18184, 39797}, {21385, 1022}, {21824, 267}, {21833, 13610}
X(47947) = cevapoint of X(i) and X(j) for these (i,j): {513, 661}, {514, 4129}, {649, 2605}
X(47947) = crosspoint of X(i) and X(j) for these (i,j): {1255, 37212}, {6540, 32014}
X(47947) = crosssum of X(i) and X(j) for these (i,j): {649, 4272}, {661, 3723}, {1100, 4979}, {1213, 4976}
X(47947) = trilinear pole of line {244, 2611}
X(47947) = crossdifference of every pair of points on line {1100, 1962}
X(47947) = X(i)-isoconjugate of X(j) for these (i,j): {1, 35342}, {2, 35327}, {6, 4427}, {8, 36075}, {56, 30729}, {58, 4115}, {59, 4976}, {99, 20970}, {100, 1100}, {101, 1125}, {109, 3686}, {110, 1213}, {112, 41014}, {162, 3958}, {163, 4647}, {190, 2308}, {249, 6367}, {430, 4558}, {553, 3939}, {644, 32636}, {648, 22080}, {651, 3683}, {662, 1962}, {692, 4359}, {765, 4979}, {813, 4974}, {825, 3775}, {901, 4969}, {919, 4966}, {1110, 4978}, {1230, 1576}, {1252, 4977}, {1262, 4990}, {1269, 32739}, {1293, 4856}, {1331, 1839}, {1332, 2355}, {1415, 3702}, {1449, 35339}, {1783, 3916}, {1897, 22054}, {2149, 4985}, {2981, 35343}, {3649, 5546}, {4001, 8750}, {4046, 4565}, {4556, 8013}, {4557, 8025}, {4567, 4983}, {4570, 4988}, {4574, 31900}, {4590, 8663}, {4629, 8040}, {4717, 34073}, {4870, 5549}, {4970, 34071}, {4975, 32665}, {4982, 6014}, {4984, 9268}, {4991, 43077}, {5298, 5548}, {5625, 28841}, {6065, 30724}, {6151, 35344}, {6335, 23201}, {6742, 17454}, {28469, 41656}, {28486, 41662}, {30581, 40521}, {32661, 44143}, {40519, 45222}
X(47947) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 30729), (3, 35342), (9, 4427), (10, 4115), (11, 3686), (115, 4647), (116, 17746), (125, 3958), (244, 1213), (513, 4979), (514, 4978), (650, 4985), (661, 4977), (1015, 1125), (1084, 1962), (1086, 4359), (1146, 3702), (4858, 1230), (4988, 30591), (5521, 1839), (6615, 4976), (8054, 1100), (8287, 3578), (26932, 4001), (32664, 35327), (34467, 22054), (34591, 41014), (35076, 6533), (35092, 4975), (38979, 4969), (38980, 4966), (38986, 20970), (38991, 3683), (39006, 3916), (40610, 4970), (40617, 553), (40619, 1269), (40620, 16709), (40623, 4974), (40627, 4983)
X(47947) = barycentric product X(i)*X(j) for these {i,j}: {1, 4608}, {81, 31010}, {244, 6540}, {513, 1268}, {514, 1255}, {523, 40438}, {649, 32018}, {661, 32014}, {693, 1126}, {1019, 6539}, {1022, 31011}, {1086, 37212}, {1109, 6578}, {1111, 8701}, {1171, 1577}, {1796, 17924}, {3120, 4596}, {3125, 4632}, {3261, 28615}, {3669, 4102}, {3676, 32635}, {4629, 16732}, {24002, 33635}
X(47947) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4427}, {6, 35342}, {9, 30729}, {11, 4985}, {31, 35327}, {37, 4115}, {244, 4977}, {512, 1962}, {513, 1125}, {514, 4359}, {522, 3702}, {523, 4647}, {604, 36075}, {647, 3958}, {649, 1100}, {650, 3686}, {656, 41014}, {659, 4974}, {661, 1213}, {663, 3683}, {667, 2308}, {693, 1269}, {798, 20970}, {810, 22080}, {900, 4975}, {905, 4001}, {1015, 4979}, {1019, 8025}, {1086, 4978}, {1126, 100}, {1171, 662}, {1255, 190}, {1268, 668}, {1459, 3916}, {1491, 3775}, {1577, 1230}, {1635, 4969}, {1796, 1332}, {2087, 4984}, {2170, 4976}, {2254, 4966}, {2310, 4990}, {2334, 35339}, {2605, 3647}, {2643, 6367}, {3120, 30591}, {3122, 4983}, {3123, 4992}, {3125, 4988}, {3669, 553}, {4017, 3649}, {4041, 4046}, {4063, 45222}, {4079, 21816}, {4083, 4970}, {4102, 646}, {4132, 4065}, {4367, 4697}, {4379, 4410}, {4394, 4856}, {4596, 4600}, {4608, 75}, {4629, 4567}, {4632, 4601}, {4705, 8013}, {4777, 4717}, {4782, 4991}, {4784, 5625}, {4977, 6533}, {4983, 8040}, {6539, 4033}, {65X(47947) = 40, 7035}, {6578, 24041}, {6586, 17746}, {6591, 1839}, {7192, 16709}, {8701, 765}, {14838, 3578}, {15309, 41818}, {19945, 30592}, {22383, 22054}, {24006, 44143}, {28615, 101}, {31010, 321}, {31011, 24004}, {31013, 42721}, {32014, 799}, {32018, 1978}, {32635, 3699}, {33635, 644}, {37212, 1016}, {40438, 99}, {43924, 32636}

X(47948) = X(484)X(513)∩X(514)X(4088)

X(47948) = 5 X[1698] - 6 X[47814], 7 X[3624] - 6 X[47820], 5 X[4367] - 6 X[14422], 2 X[4369] - 3 X[47816], 2 X[4401] - 3 X[4893], 2 X[14838] - 3 X[47810], 4 X[25666] - 3 X[47818], 2 X[34958] - 3 X[47756]

X(47948) lies on these lines: {1, 8678}, {484, 513}, {514, 4088}, {522, 47679}, {661, 830}, {788, 5216}, {814, 47683}, {1019, 1491}, {1698, 47814}, {2254, 15309}, {2526, 4905}, {3624, 47820}, {3887, 4822}, {4129, 47694}, {4151, 20295}, {4367, 14422}, {4369, 47816}, {4401, 4893}, {4489, 4813}, {4490, 21385}, {4824, 29070}, {4866, 35355}, {8672, 24462}, {14838, 47810}, {25666, 47818}, {29062, 45746}, {29186, 47666}, {34958, 47756}

X(47948) = reflection of X(i) in X(j) for these {i,j}: {1, 14349}, {1019, 1491}, {4040, 661}, {4063, 4705}, {4905, 2526}, {21385, 4490}, {47694, 4129}, {47724, 21301}
X(47948) = crosspoint of X(3112) and X(37218)
X(47948) = crosssum of X(1962) and X(47842)
X(47948) = crossdifference of every pair of points on line {38, 1100}
X(47948) = barycentric product X(1)*X(47659)
X(47948) = barycentric quotient X(47659)/X(75)

X(47949) = X(484)X(513)∩X(514)X(4010)

X(47949) = 2 X[1734] - 3 X[4705], 3 X[4776] - 2 X[23815], 2 X[4801] - 3 X[30592], 2 X[43067] - 3 X[47875], X[47719] - 3 X[47769]

X(47949) lies on these lines: {484, 513}, {514, 4010}, {659, 15309}, {661, 665}, {764, 14349}, {784, 47666}, {891, 4822}, {1027, 2334}, {1577, 4977}, {1769, 8672}, {4088, 29168}, {4129, 21146}, {4142, 28855}, {4490, 4730}, {4776, 23815}, {4778, 14431}, {4801, 30592}, {4806, 4978}, {4813, 24290}, {4824, 8714}, {14419, 47826}, {17072, 28225}, {17494, 29150}, {18004, 47715}, {21051, 28209}, {21124, 29252}, {29106, 44449}, {29354, 47701}, {43067, 47875}, {47719, 47769}

X(47949) = reflection of X(i) in X(j) for these {i,j}: {764, 14349}, {2530, 661}, {4730, 4490}, {4978, 4806}, {14419, 47826}, {21146, 4129}, {47715, 18004}
X(47949) = crossdifference of every pair of points on line {1100, 1621}
X(47949) = barycentric product X(1)*X(47671)
X(47949) = barycentric quotient X(47671)/X(75)

X(47950) = X(513)X(16892)∩X(514)X(3700)

X(47950) = X[16892] + 3 X[23731], 3 X[4106] - 2 X[4500], 2 X[649] - 3 X[47880], 5 X[650] - 6 X[47783], 4 X[2529] - 5 X[24924], 3 X[3004] - 2 X[3798], 4 X[3798] - 3 X[4790], 4 X[3835] - 3 X[47881], 3 X[4382] - X[47670], 3 X[4820] - 2 X[47665], 3 X[20295] - X[47665], 2 X[4932] - 3 X[47754], 4 X[4940] - 3 X[4944], 3 X[4944] - 2 X[47660], 5 X[31250] - 6 X[47756], X[47662] - 3 X[47759], 3 X[47777] - 2 X[47890]

X(47950) lies on these lines: {513, 16892}, {514, 3700}, {649, 47880}, {650, 47783}, {2529, 24924}, {3004, 3798}, {3835, 47881}, {4382, 4802}, {4762, 47667}, {4778, 21104}, {4813, 30520}, {4820, 20295}, {4926, 47673}, {4932, 47754}, {4940, 4944}, {4977, 7662}, {6008, 45746}, {28195, 47672}, {28199, 47671}, {28859, 43067}, {28898, 47653}, {31250, 47756}, {31290, 47651}, {47662, 47759}, {47777, 47890}

X(47950) = midpoint of X(31290) and X(47651)
X(47950) = reflection of X(i) in X(j) for these {i,j}: {4790, 3004}, {4820, 20295}, {47660, 4940}
X(47950) = {X(4940),X(47660)}-harmonic conjugate of X(4944)

X(47951) = X(513)X(16892)∩X(514)X(4522)

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

X(47951) lies on these lines: {513, 16892}, {514, 4522}, {661, 28195}, {3776, 4778}, {4088, 28199}, {4394, 47877}, {4468, 28213}, {4724, 28220}, {4782, 47880}, {4802, 47700}, {4874, 4977}, {4926, 47702}, {4928, 28229}, {24719, 28894}

X(47952) = X(513)X(4380)∩X(514)X(3700)

X(47952) = 3 X[4380] - 5 X[17494], 7 X[4380] - 5 X[26853], X[4380] + 5 X[31290], X[4380] - 5 X[47666], 7 X[17494] - 3 X[26853], X[17494] + 3 X[31290], X[17494] - 3 X[47666], X[26853] + 7 X[31290], X[26853] - 7 X[47666], 3 X[650] - 2 X[4932], 7 X[650] - 6 X[45313], 7 X[4932] - 9 X[45313], 5 X[661] - 3 X[4379], 3 X[661] - 2 X[4885], 7 X[661] - 5 X[30835], 4 X[661] - 3 X[47760], 9 X[4379] - 10 X[4885], 21 X[4379] - 25 X[30835], 6 X[4379] - 5 X[43067], 4 X[4379] - 5 X[47760], 14 X[4885] - 15 X[30835], 4 X[4885] - 3 X[43067], 8 X[4885] - 9 X[47760], 10 X[30835] - 7 X[43067], 20 X[30835] - 21 X[47760], 2 X[43067] - 3 X[47760], X[693] - 3 X[47774], 4 X[2516] - 3 X[47763], 2 X[3798] - 3 X[47876], 2 X[4369] - 3 X[47777], 2 X[4394] - 3 X[47775], 3 X[25259] - X[47658], 3 X[7192] - 4 X[7653], 3 X[7192] - 5 X[31209], 2 X[7192] - 3 X[47761], 4 X[7653] - 5 X[31209], 8 X[7653] - 9 X[47761], 10 X[31209] - 9 X[47761], 2 X[23813] - 3 X[47759], X[47675] - 3 X[47759], 3 X[31148] - 4 X[31287], 5 X[31250] - 6 X[45315]

X(47952) lies on these lines: {513, 4380}, {514, 3700}, {650, 4932}, {661, 4379}, {693, 47774}, {2516, 47763}, {2526, 4778}, {3004, 28878}, {3798, 47876}, {4025, 28902}, {4369, 47777}, {4394, 47775}, {4468, 4977}, {4762, 4813}, {4777, 44449}, {4802, 25259}, {4841, 28846}, {4926, 47661}, {4940, 47672}, {4988, 28898}, {7192, 7653}, {16892, 28910}, {21196, 28886}, {23813, 47675}, {28151, 47665}, {28165, 47668}, {28195, 47660}, {28199, 47659}, {31148, 31287}, {31250, 45315}

X(47952) = midpoint of X(i) and X(j) for these {i,j}: {31290, 47666}, {44449, 47667}
X(47952) = reflection of X(i) in X(j) for these {i,j}: {43067, 661}, {47672, 4940}, {47675, 23813}
X(47952) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 43067, 47760}, {7192, 31209, 7653}, {7653, 31209, 47761}, {47675, 47759, 23813}

X(47953) = X(513)X(4380)∩X(514)X(4522)

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

X(47953) = 5 X[661] - 3 X[47832], 5 X[7662] - 6 X[47832], 2 X[4874] - 3 X[47777], 2 X[43067] - 3 X[47802]

X(47953) lies on these lines: {513, 4380}, {514, 4522}, {523, 4820}, {661, 7662}, {1491, 4963}, {2505, 2526}, {4106, 4122}, {4777, 47699}, {4818, 28855}, {4874, 47777}, {28195, 47808}, {43067, 47802}

X(47953) = midpoint of X(1491) and X(4963)
X(47953) = reflection of X(7662) in X(661)

X(47954) = X(513)X(4380)∩X(514)X(4806)

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

X(47954) lies on these lines: {513, 4380}, {514, 4806}, {661, 28195}, {1491, 28220}, {3835, 28213}, {3837, 28229}, {4010, 28199}, {4724, 4963}, {4782, 28840}, {4802, 4804}, {4977, 20316}, {24719, 47774}, {29204, 47699}

X(47955) = X(484)X(513)∩X(514)X(3700)

X(47955) lies on these lines: {484, 513}, {514, 3700}, {650, 15309}, {661, 905}, {4129, 43067}, {4391, 31290}, {4801, 47759}, {4822, 14077}, {4940, 4978}, {14838, 47777}, {21191, 28840}, {23882, 47666}, {28898, 47679}

X(47955) = midpoint of X(4391) and X(31290)
X(47955) = reflection of X(i) in X(j) for these {i,j}: {905, 661}, {4978, 4940}, {43067, 4129}
X(47955) = crossdifference of every pair of points on line {968, 1100}

X(47956) = X(484)X(513)∩X(514)X(4522)

X(47956) = 3 X[4705] - X[4834], 3 X[661] - X[663], 3 X[4776] - X[17166], 3 X[4893] - 2 X[6050], X[7192] - 3 X[47814], X[21302] + 3 X[47774]

X(47956) lies on these lines: {484, 513}, {514, 4522}, {661, 663}, {2526, 6372}, {3900, 4983}, {4041, 4813}, {4129, 7662}, {4776, 17166}, {4820, 6367}, {4824, 23882}, {4893, 6050}, {7192, 47814}, {17072, 28840}, {21260, 43067}, {21301, 47666}, {21302, 47774}, {29232, 45745}

X(47956) = midpoint of X(i) and X(j) for these {i,j}: {4041, 4813}, {21301, 47666}
X(47956) = reflection of X(i) in X(j) for these {i,j}: {7662, 4129}, {43067, 21260}
X(47956) = crossdifference of every pair of points on line {63, 1100}
X(47956) = barycentric product X(661)*X(14007)
X(47956) = barycentric quotient X(14007)/X(799)

X(47957) = X(484)X(513)∩X(514)X(4806)

X(47957) = 3 X[1734] - 5 X[4705], 3 X[661] - X[3777], 5 X[661] - X[23738], 5 X[3777] - 3 X[23738], X[4367] - 3 X[47826], 3 X[4490] - X[4729]

X(47957) lies on these lines: {484, 513}, {514, 4806}, {661, 3777}, {1577, 28195}, {4083, 4822}, {4367, 47826}, {4490, 4729}, {4778, 21051}, {4782, 15309}, {4983, 29226}, {17072, 28209}

X(47958) = X(513)X(16892)∩X(514)X(661)

X(47958) = 3 X[661] - 2 X[4468], 4 X[3835] - 3 X[47874], 3 X[4728] - 2 X[6590], 3 X[4776] - X[47662], 2 X[47660] - 3 X[47874], 3 X[649] - 4 X[17069], 2 X[649] - 3 X[47886], 3 X[3004] - 2 X[17069], 4 X[3004] - 3 X[47886], 8 X[17069] - 9 X[47886], 4 X[3676] - 3 X[31148], 2 X[3700] - 3 X[31147], 3 X[4120] - 4 X[4940], 2 X[4369] - 3 X[44435], 2 X[4394] - 3 X[47880], 3 X[4453] - 2 X[4932], 2 X[4500] - 3 X[21297], 3 X[21297] - X[47659], X[4608] - 3 X[47869], 3 X[4750] - 2 X[4790], 3 X[4893] - 2 X[47890], 3 X[6545] - 2 X[43067], 4 X[7658] - 3 X[47768], 2 X[9508] - 3 X[47877], 2 X[11068] - 3 X[47783], X[14779] + 3 X[26824], 2 X[17494] - 3 X[47878], 4 X[21212] - 3 X[47762], 5 X[24924] - 6 X[47757], 4 X[25666] - 3 X[47771], 5 X[26798] - 3 X[47870], X[26853] - 3 X[47894], 5 X[27013] - 6 X[47882], 7 X[27138] - 6 X[47879], 5 X[30835] - 6 X[47756], 7 X[31207] - 6 X[47767], X[47663] - 3 X[47781]

X(47958) lies on these lines: {513, 16892}, {514, 661}, {522, 47673}, {523, 4382}, {649, 3004}, {676, 1459}, {812, 45746}, {824, 20295}, {918, 4813}, {2786, 47677}, {3676, 31148}, {3700, 31147}, {3716, 47696}, {3776, 4817}, {4024, 4106}, {4025, 4979}, {4088, 4802}, {4120, 4940}, {4369, 44435}, {4380, 21196}, {4394, 47880}, {4453, 4932}, {4458, 4778}, {4467, 4785}, {4500, 21297}, {4522, 47693}, {4608, 47869}, {4750, 4790}, {4762, 4988}, {4841, 6084}, {4893, 47890}, {6545, 41850}, {7658, 47768}, {9508, 47877}, {11068, 47783}, {14779, 26824}, {17494, 28882}, {18071, 20949}, {21116, 28195}, {21212, 47762}, {21828, 28374}, {23780, 29120}, {24924, 47757}, {25259, 28863}, {25666, 47771}, {26798, 47870}, {26853, 47894}, {27013, 47882}, {27138, 47879}, {28147, 47670}, {28213, 47826}, {28840, 47676}, {28851, 31290}, {29302, 47679}, {30519, 44449}, {30835, 47756}, {31207, 47767}, {47650, 47667}, {47663, 47781}, {47686, 47699}

X(47958) = midpoint of X(i) and X(j) for these {i,j}: {16892, 23731}, {20295, 47653}, {47650, 47667}, {47651, 47666}, {47686, 47699}
X(47958) = reflection of X(i) in X(j) for these {i,j}: {649, 3004}, {4024, 4106}, {4380, 21196}, {4382, 23729}, {4979, 4025}, {7192, 3776}, {47659, 4500}, {47660, 3835}, {47693, 4522}, {47696, 3716}
X(47958) = X(i)-Ceva conjugate of X(j) for these (i,j): {33952, 4657}, {43531, 1086}
X(47958) = crosspoint of X(4657) and X(33952)
X(47958) = crossdifference of every pair of points on line {31, 3730}
X(47958) = barycentric product X(i)*X(j) for these {i,j}: {513, 33945}, {514, 4657}, {693, 17017}, {1086, 33952}, {3676, 3966}
X(47958) = barycentric quotient X(i)/X(j) for these {i,j}: {3966, 3699}, {4657, 190}, {17017, 100}, {33945, 668}, {33952, 1016}
X(47958) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 3004, 47886}, {3835, 47660, 47874}, {21297, 47659, 4500}

X(47959) = X(484)X(513)∩X(514)X(661)

X(47959) = 3 X[4776] - X[4801], X[663] - 3 X[47826], X[3669] - 3 X[47777], 2 X[4369] - 3 X[47794], 2 X[4401] - 3 X[47811], X[4960] - 4 X[20317], X[4560] - 3 X[47775], 3 X[4893] - 2 X[14838], X[7192] - 3 X[47793], X[17166] - 3 X[47821], 2 X[23789] - 3 X[44429], 2 X[24720] - 3 X[47816], 4 X[25666] - 3 X[47795]

X(47959) lies on these lines: {484, 513}, {512, 4490}, {514, 661}, {649, 15309}, {650, 1019}, {663, 4160}, {784, 4824}, {824, 47679}, {830, 4724}, {1491, 4905}, {2530, 29198}, {3669, 47777}, {4040, 8678}, {4041, 6005}, {4079, 47678}, {4083, 4983}, {4088, 29021}, {4147, 4761}, {4369, 47794}, {4401, 47811}, {4481, 4960}, {4498, 4813}, {4522, 47715}, {4560, 29148}, {4778, 17072}, {4808, 29144}, {4822, 29350}, {4893, 14838}, {4977, 21051}, {7192, 47793}, {8672, 21189}, {14431, 28195}, {14837, 28878}, {17166, 47821}, {17494, 29013}, {18184, 21044}, {20295, 29302}, {20949, 40495}, {21124, 23875}, {21146, 21260}, {21301, 29186}, {21385, 24290}, {23789, 44429}, {23800, 47842}, {23879, 25259}, {23880, 47683}, {24720, 47816}, {25666, 47795}, {29047, 47701}, {29164, 47700}, {29216, 44449}, {29260, 47702}, {31010, 47655}, {42664, 47667}, {47698, 47708}, {47699, 47707}

X(47959) = midpoint of X(i) and X(j) for these {i,j}: {4391, 47666}, {4498, 4813}, {47698, 47708}, {47699, 47707}
X(47959) = reflection of X(i) in X(j) for these {i,j}: {693, 4129}, {1019, 650}, {1734, 4705}, {4761, 4147}, {4905, 1491}, {4978, 3835}, {14349, 661}, {21146, 21260}, {23800, 47842}, {47655, 31010}, {47672, 4823}, {47715, 4522}
X(47959) = X(28650)-Ceva conjugate of X(244)
X(47959) = X(i)-isoconjugate of X(j) for these (i,j): {6, 46961}, {5546, 35576}
X(47959) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 46961), (28651, 190), (45745, 7650)
X(47959) = crosspoint of X(100) and X(39737)
X(47959) = crossdifference of every pair of points on line {31, 1100}
X(47959) = barycentric product X(1)*X(47656)
X(47959) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 46961}, {4017, 35576}, {38960, 7650}, {47656, 75}

X(47960) = X(241)X(514)∩X(513)X(16892)

X(47960) = 5 X[650] - 4 X[11068], 5 X[650] - 6 X[47784], 2 X[650] - 3 X[47880], 7 X[650] - 6 X[47884], 3 X[650] - 2 X[47890], 5 X[3004] - 2 X[11068], 5 X[3004] - 3 X[47784], 4 X[3004] - 3 X[47880], 7 X[3004] - 3 X[47884], 3 X[3004] - X[47890], 2 X[4369] - 3 X[47754], 4 X[7658] - 3 X[47767], 2 X[11068] - 3 X[47784], 8 X[11068] - 15 X[47880], 14 X[11068] - 15 X[47884], 6 X[11068] - 5 X[47890], 4 X[21212] - 3 X[47761], 4 X[47784] - 5 X[47880], 7 X[47784] - 5 X[47884], 9 X[47784] - 5 X[47890], 7 X[47880] - 4 X[47884], 9 X[47880] - 4 X[47890], 9 X[47884] - 7 X[47890], 3 X[16892] + X[23731], 3 X[693] - X[47659], 5 X[693] - 3 X[47792], 3 X[47653] + X[47659], 5 X[47653] + 3 X[47792], 5 X[47659] - 9 X[47792], 4 X[2487] - 3 X[47768], 2 X[3239] - 3 X[47756], 4 X[3835] - 3 X[4944], X[4380] - 3 X[47894], 2 X[4394] - 3 X[47886], 2 X[4468] - 3 X[47777], 3 X[45746] + X[47650], 3 X[45746] - X[47661], X[47650] - 3 X[47652], 3 X[47652] + X[47661], 2 X[4885] - 3 X[44435], 4 X[4885] - 3 X[47881], 3 X[44435] - X[47660], 2 X[47660] - 3 X[47881], 2 X[6590] - 3 X[45320], 3 X[21297] - X[47665], 4 X[25666] - 3 X[47770], 5 X[31209] - 3 X[47773], 5 X[31250] - 6 X[47757], 4 X[31287] - 3 X[47771], 3 X[44429] - X[47693], 3 X[46915] - X[47664], X[47654] + 3 X[47871], X[47656] - 3 X[47871], X[47655] - 3 X[47869], X[47663] - 3 X[47782], X[47696] - 3 X[47797]

X(47960) lies on these lines: {2, 47662}, {241, 514}, {513, 16892}, {522, 23729}, {523, 2525}, {659, 21115}, {661, 30520}, {693, 20950}, {824, 4106}, {1491, 4802}, {2487, 47768}, {3239, 47756}, {3835, 4944}, {4024, 23813}, {4025, 4790}, {4378, 21005}, {4380, 47894}, {4382, 4777}, {4394, 47886}, {4467, 6008}, {4468, 47777}, {4762, 45746}, {4801, 35518}, {4885, 44435}, {4940, 25259}, {6084, 45745}, {6590, 45320}, {8712, 21124}, {17494, 47651}, {18071, 20906}, {20295, 28898}, {21116, 28199}, {21196, 28882}, {21297, 47665}, {25666, 47770}, {26824, 47657}, {28151, 47671}, {28651, 47675}, {28910, 31290}, {31209, 47773}, {31250, 47757}, {31287, 47771}, {44429, 47693}, {46915, 47664}, {47654, 47656}, {47655, 47869}, {47663, 47782}, {47696, 47797}

X(47960) = complement of X(47662)
X(47960) = midpoint of X(i) and X(j) for these {i,j}: {693, 47653}, {4382, 47673}, {17494, 47651}, {20295, 47677}, {26824, 47657}, {45746, 47652}, {47650, 47661}, {47654, 47656}
X(47960) = reflection of X(i) in X(j) for these {i,j}: {650, 3004}, {4024, 23813}, {4790, 4025}, {4820, 4106}, {25259, 4940}, {43067, 3776}, {47660, 4885}, {47881, 44435}
X(47960) = crossdifference of every pair of points on line {55, 5280}
X(47960) = barycentric product X(i)*X(j) for these {i,j}: {514, 17306}, {693, 17599}
X(47960) = barycentric quotient X(i)/X(j) for these {i,j}: {17306, 190}, {17599, 100}
X(47960) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 3004, 47880}, {4885, 47660, 47881}, {11068, 47784, 650}, {44435, 47660, 4885}, {45746, 47650, 47661}, {47652, 47661, 47650}, {47654, 47871, 47656}

X(47961) = X(513)X(16892)∩X(514)X(3716)

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

X(47961) = 2 X[2977] - 3 X[47783], 3 X[4776] - X[47693], 2 X[9508] - 3 X[47880], 3 X[14349] - X[47726], X[47662] - 3 X[47821]

X(47961) lies on these lines: {513, 16892}, {514, 3716}, {523, 4106}, {661, 4802}, {2526, 29144}, {2605, 4724}, {2977, 47783}, {4010, 28894}, {4088, 28151}, {4122, 4940}, {4458, 28859}, {4468, 28175}, {4500, 28147}, {4776, 47693}, {4777, 4810}, {8678, 47727}, {9508, 47880}, {14349, 47726}, {47652, 47699}, {47662, 47821}, {47666, 47688}

X(47961) = midpoint of X(i) and X(j) for these {i,j}: {47652, 47699}, {47666, 47688}
X(47961) = reflection of X(4122) in X(4940)

X(47962) = X(241)X(514)∩X(513)X(4380)

X(47962) = 3 X[650] - 2 X[4369], 7 X[650] - 6 X[4763], 5 X[650] - 4 X[31286], 4 X[650] - 3 X[47761], 2 X[3676] - 3 X[47784], 2 X[3776] - 3 X[47880], 7 X[4369] - 9 X[4763], 5 X[4369] - 6 X[31286], 4 X[4369] - 3 X[43067], 8 X[4369] - 9 X[47761], 15 X[4763] - 14 X[31286], 12 X[4763] - 7 X[43067], 8 X[4763] - 7 X[47761], 4 X[7658] - 3 X[47891], 2 X[21104] - 3 X[47754], X[21104] - 3 X[47876], 8 X[31286] - 5 X[43067], 16 X[31286] - 15 X[47761], 2 X[43067] - 3 X[47761], X[4380] - 3 X[17494], 5 X[4380] - 3 X[26853], X[4380] + 3 X[47666], 5 X[17494] - X[26853], 3 X[17494] + X[31290], 3 X[26853] + 5 X[31290], X[26853] + 5 X[47666], X[31290] - 3 X[47666], 3 X[661] - X[4382], 3 X[661] - 2 X[4940], 5 X[661] - 3 X[31147], 3 X[4106] - 2 X[4382], 3 X[4106] - 4 X[4940], 5 X[4106] - 6 X[31147], 5 X[4382] - 9 X[31147], 10 X[4940] - 9 X[31147], 5 X[693] - 7 X[27138], 2 X[693] - 3 X[47760], X[693] - 3 X[47775], 14 X[27138] - 15 X[47760], 7 X[27138] - 15 X[47775], 4 X[2490] - 3 X[47789], 4 X[2516] - 5 X[26777], 4 X[2516] - 3 X[47762], 5 X[26777] - 3 X[47762], 2 X[3835] - 3 X[47777], 3 X[4379] - 4 X[31287], 2 X[4394] - 3 X[31150], X[7192] - 3 X[31150], 3 X[4490] - X[4774], 2 X[4500] - 3 X[4944], 4 X[4521] - 3 X[47788], 3 X[4776] - 2 X[23813], 3 X[4776] - X[26824], 3 X[4789] - X[47674], X[4804] - 3 X[47826], 2 X[4885] - 3 X[4893], 3 X[4893] - X[47672], 2 X[6590] - 3 X[47770], 4 X[7653] - 5 X[27013], X[16892] - 3 X[47878], 2 X[17069] - 3 X[47883], 5 X[24924] - 6 X[44567], 4 X[25666] - 3 X[45320], X[47665] - 3 X[47772], 3 X[30565] - X[47656], 5 X[31209] - 3 X[47780], 5 X[31250] - 6 X[47778], 3 X[46915] - X[47677], X[47652] - 3 X[47781], X[47655] - 3 X[47870], X[47670] - 3 X[47873], X[47671] - 3 X[47874], X[47676] - 3 X[47782]

X(47962) lies on these lines: {2, 47675}, {241, 514}, {513, 4380}, {523, 4468}, {661, 4106}, {693, 27138}, {918, 45745}, {2490, 47789}, {2516, 26777}, {3716, 28147}, {3835, 47777}, {4379, 31287}, {4391, 29771}, {4394, 7192}, {4462, 18155}, {4490, 4774}, {4500, 4944}, {4507, 6372}, {4521, 47788}, {4724, 24769}, {4765, 4897}, {4776, 23813}, {4777, 25259}, {4778, 4913}, {4789, 47674}, {4790, 28840}, {4801, 18154}, {4802, 7662}, {4804, 47826}, {4813, 6008}, {4874, 28175}, {4885, 4893}, {4926, 44449}, {4976, 28846}, {4988, 28894}, {6590, 47770}, {7199, 30061}, {7653, 27013}, {9508, 28195}, {16892, 47878}, {17069, 47883}, {20295, 47664}, {21196, 28851}, {24924, 44567}, {25511, 47793}, {25666, 45320}, {28151, 47659}, {28165, 47665}, {28199, 47773}, {30520, 45746}, {30565, 47656}, {31209, 47780}, {31250, 47778}, {44009, 45666}, {46915, 47677}, {47652, 47781}, {47655, 47870}, {47670, 47873}, {47671, 47874}, {47676, 47782}

X(47962) = complement of X(47675)
X(47962) = midpoint of X(i) and X(j) for these {i,j}: {4380, 31290}, {17494, 47666}, {20295, 47664}, {25259, 47661}, {47659, 47668}, {47660, 47667}
X(47962) = reflection of X(i) in X(j) for these {i,j}: {4106, 661}, {4382, 4940}, {4897, 4765}, {7192, 4394}, {7659, 4913}, {26824, 23813}, {43067, 650}, {47672, 4885}, {47754, 47876}, {47760, 47775}
X(47962) = crossdifference of every pair of points on line {55, 5021}
X(47962) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 43067, 47761}, {661, 4382, 4940}, {4380, 47666, 31290}, {4382, 4940, 4106}, {4776, 26824, 23813}, {4893, 47672, 4885}, {7192, 31150, 4394}, {17494, 31290, 4380}, {26777, 47762, 2516}

X(47963) = X(513)X(4380)∩X(514)X(3716)

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

X(47963) = 4 X[3716] - 3 X[7662], 2 X[3837] - 3 X[47777], 2 X[21146] - 3 X[47802], 2 X[43067] - 3 X[47803], X[47672] - 3 X[47826], X[47675] - 3 X[47821]

X(47963) lies on these lines: {513, 4380}, {514, 3716}, {650, 2523}, {3837, 47777}, {4369, 28229}, {4762, 4810}, {4777, 47698}, {4802, 47699}, {4874, 28213}, {4913, 28225}, {7659, 28209}, {9508, 28220}, {21146, 47802}, {26248, 28195}, {47672, 47826}, {47675, 47821}

X(47964) = X(513)X(4380)∩X(514)X(3837)

X(47964) lies on these lines: {513, 4380}, {514, 3837}, {649, 4963}, {661, 4802}, {693, 28199}, {1491, 28195}, {2254, 28220}, {3835, 28175}, {4010, 28151}, {4122, 47667}, {4806, 28147}, {24720, 28213}, {29204, 47698}, {29280, 47679}

X(47964) = midpoint of X(i) and X(j) for these {i,j}: {649, 4963}, {4122, 47667}, {4824, 47666}
X(47964) = crossdifference of every pair of points on line {20963, 21793}

X(47965) = X(241)X(514)∩X(484)X(513)

X(47965) = 3 X[650] - X[3669], 5 X[650] - 2 X[3960], 3 X[650] - 2 X[14838], 3 X[905] - 2 X[3669], 5 X[905] - 4 X[3960], 3 X[905] - 4 X[14838], 5 X[3669] - 6 X[3960], 2 X[3676] - 3 X[41800], 3 X[3960] - 5 X[14838], X[3803] + 2 X[4490], 5 X[663] - 3 X[23057], X[663] - 3 X[47811], X[23057] - 5 X[47811], X[693] - 3 X[47793], X[764] - 3 X[47888], 2 X[1577] - 3 X[45664], 4 X[20317] - 3 X[45664], X[3777] - 3 X[47827], 2 X[4367] - 3 X[30234], 4 X[6050] - 3 X[30234], X[4462] + 3 X[31150], X[4560] - 3 X[31150], X[4822] - 3 X[47826], 2 X[4885] - 3 X[47794], X[4978] - 3 X[47794], X[17166] - 3 X[47804], X[17496] - 5 X[26777], X[21146] - 3 X[47835], X[23765] - 3 X[47893], 2 X[23815] - 3 X[47802], 5 X[31209] - 3 X[47796], 4 X[31287] - 3 X[47795], 2 X[34958] - 3 X[47800], X[46403] - 3 X[47814], X[47694] - 3 X[47815], X[47719] - 3 X[47809], X[47720] - 3 X[47797]

X(47965) lies on these lines: {2, 4801}, {10, 29186}, {37, 47678}, {241, 514}, {449, 525}, {484, 513}, {521, 46385}, {523, 21185}, {659, 3803}, {661, 4498}, {663, 14077}, {693, 47793}, {764, 47888}, {1019, 4394}, {1577, 4762}, {2401, 44794}, {2826, 33969}, {3309, 4041}, {3762, 23880}, {3777, 47827}, {3900, 4040}, {4106, 4129}, {4147, 29051}, {4160, 4401}, {4162, 4794}, {4367, 6050}, {4391, 17494}, {4462, 4560}, {4770, 6004}, {4777, 4808}, {4790, 15309}, {4802, 21112}, {4822, 47826}, {4885, 4978}, {6129, 28147}, {6591, 47660}, {8043, 28195}, {8712, 14349}, {9000, 44410}, {9508, 29198}, {16757, 47662}, {17166, 47804}, {17496, 26777}, {20516, 29047}, {21051, 29362}, {21132, 35100}, {21146, 47835}, {21611, 23685}, {23765, 47893}, {23815, 47802}, {24948, 47675}, {25098, 45745}, {27674, 47672}, {28199, 31947}, {28894, 47679}, {31209, 47796}, {31287, 47795}, {34958, 47800}, {40134, 47771}, {46403, 47814}, {47694, 47815}, {47719, 47809}, {47720, 47797}

X(47965) = midpoint of X(i) and X(j) for these {i,j}: {659, 4490}, {661, 4498}, {4041, 4724}, {4391, 17494}, {4462, 4560}, {14349, 21385}
X(47965) = reflection of X(i) in X(j) for these {i,j}: {905, 650}, {1019, 4394}, {1577, 20317}, {3669, 14838}, {3803, 659}, {4106, 4129}, {4162, 4794}, {4367, 6050}, {4978, 4885}, {21104, 21188}
X(47965) = complement of X(4801)
X(47965) = complement of the isogonal conjugate of X(34074)
X(47965) = complement of the isotomic conjugate of X(4606)
X(47965) = X(i)-complementary conjugate of X(j) for these (i,j): {2334, 116}, {4606, 2887}, {4614, 21240}, {4624, 17047}, {4627, 3741}, {5545, 17050}, {8694, 141}, {25430, 21252}, {34074, 10}, {34820, 124}
X(47965) = X(i)-isoconjugate of X(j) for these (i,j): {101, 3296}, {8750, 30679}
X(47965) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 3296), (4765, 4811), (16777, 4756), (26932, 30679)
X(47965) = crosspoint of X(i) and X(j) for these (i,j): {2, 4606}, {651, 25417}
X(47965) = crosssum of X(i) and X(j) for these (i,j): {6, 4790}, {650, 16777}
X(47965) = crossdifference of every pair of points on line {55, 1100}
X(47965) = barycentric product X(i)*X(j) for these {i,j}: {513, 42696}, {514, 3305}, {522, 7190}, {693, 3295}, {3669, 42032}, {3697, 7192}
X(47965) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 3296}, {905, 30679}, {3295, 100}, {3305, 190}, {3697, 3952}, {4917, 43290}, {7190, 664}, {42032, 646}, {42696, 668}
X(47965) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 3669, 14838}, {1577, 20317, 45664}, {3669, 14838, 905}, {4367, 6050, 30234}, {4462, 31150, 4560}, {4978, 47794, 4885}

X(47966) = X(484)X(513)∩X(514)X(3716)

X(47966) = X[4801] - 3 X[47821], 2 X[6050] - 3 X[47811], X[7192] - 3 X[47815], 2 X[23789] - 3 X[47802], 2 X[23815] - 3 X[47760], 3 X[30565] - X[47719]

X(47966) lies on these lines: {484, 513}, {514, 3716}, {650, 6372}, {905, 29198}, {3309, 4490}, {4142, 28851}, {4468, 29142}, {4724, 8678}, {4801, 47821}, {4983, 8712}, {6050, 47811}, {7192, 47815}, {23789, 47802}, {23815, 47760}, {30565, 47719}

X(47967) = X(484)X(513)∩X(514)X(3837)

X(47967) = X[1734] - 3 X[4705], X[3777] - 3 X[47810], X[4367] - 3 X[4893], X[7192] - 3 X[47835], X[17166] - 3 X[47822], X[21146] - 3 X[47814], 5 X[30835] - 3 X[47889]

X(47967) lies on these lines: {484, 513}, {514, 3837}, {661, 4083}, {1491, 29198}, {1577, 4802}, {2533, 47666}, {3777, 47810}, {3801, 47698}, {4088, 29146}, {4367, 4893}, {4391, 4824}, {4770, 6005}, {4913, 29170}, {4977, 17072}, {7192, 47835}, {14349, 29226}, {14431, 28199}, {17166, 47822}, {17494, 29238}, {21124, 29280}, {21146, 47814}, {29236, 47775}, {30835, 47889}

X(47967) = midpoint of X(i) and X(j) for these {i,j}: {661, 4490}, {2533, 47666}, {3801, 47698}, {4391, 4824}
X(47967) = crossdifference of every pair of points on line {1100, 4640}

X(47968) = X(10)X(514)∩X(513)X(16892)

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

X(47968) = 3 X[2533] - 4 X[44314], 2 X[650] - 3 X[47877], 2 X[4782] - 3 X[47886], 2 X[4874] - 3 X[44435], 3 X[44435] - X[47696], 3 X[47827] - 2 X[47890], 3 X[44429] - X[47662]

X(47968) lies on these lines: {10, 514}, {513, 16892}, {523, 2528}, {650, 2457}, {659, 3004}, {824, 24719}, {2526, 4802}, {3837, 47660}, {4122, 28863}, {4782, 47886}, {4810, 23729}, {4818, 28882}, {4874, 44435}, {28213, 47827}, {29078, 47677}, {29362, 45746}, {29823, 47694}, {44429, 47662}

X(47968) = midpoint of X(i) and X(j) for these {i,j}: {45746, 47686}, {46403, 47653}
X(47968) = reflection of X(i) in X(j) for these {i,j}: {659, 3004}, {4810, 23729}, {47660, 3837}, {47696, 4874}
X(47968) = crossdifference of every pair of points on line {1500, 1914}
X(47968) = {X(44435),X(47696)}-harmonic conjugate of X(4874)

X(47969) = X(1)X(514)∩X(513)X(4380)

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

X(47969) = 4 X[650] - 3 X[47824], 2 X[693] - 3 X[47821], 2 X[1491] - 3 X[47775], 2 X[2254] - 3 X[47825], 4 X[3716] - 3 X[47834], 2 X[47672] - 3 X[47834], 2 X[3835] - 3 X[47826], 2 X[4122] - 3 X[47772], 2 X[4369] - 3 X[47811], 4 X[4782] - 3 X[47763], 2 X[4784] - 3 X[47776], 4 X[4806] - 3 X[21297], 2 X[4818] - 3 X[47878], 4 X[4874] - 3 X[47780], 3 X[4893] - 2 X[24720], 2 X[4978] - 3 X[47840], 4 X[9508] - 5 X[26777], 2 X[21104] - 3 X[47797], 2 X[24719] - 3 X[47759], 4 X[25666] - 3 X[47812], 5 X[26985] - 6 X[47822], 7 X[27115] - 6 X[47823], 3 X[30709] - 2 X[47724], 2 X[43067] - 3 X[47804]

X(47969) lies on these lines: {1, 514}, {2, 21146}, {8, 29188}, {513, 4380}, {522, 47698}, {649, 4778}, {650, 47824}, {659, 3004}, {661, 46403}, {693, 47821}, {1491, 47775}, {2254, 47825}, {3716, 47672}, {3835, 47826}, {4010, 26824}, {4122, 47772}, {4369, 47811}, {4468, 47690}, {4490, 21302}, {4560, 6372}, {4782, 28220}, {4784, 28209}, {4806, 21297}, {4818, 47878}, {4830, 4979}, {4874, 47780}, {4893, 24720}, {4978, 47840}, {7662, 47675}, {9508, 26777}, {17496, 29198}, {20295, 29362}, {21104, 47797}, {21301, 29186}, {24719, 47759}, {25666, 47812}, {26985, 47822}, {27115, 47823}, {28195, 47805}, {30709, 47724}, {39706, 43928}, {43067, 47804}

X(47969) = reflection of X(i) in X(j) for these {i,j}: {4979, 4830}, {7192, 659}, {17166, 4040}, {21302, 4490}, {26824, 4010}, {46403, 661}, {47672, 3716}, {47675, 7662}, {47688, 47701}, {47690, 4468}, {47694, 4724}
X(47969) = anticomplement of X(21146)
X(47969) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {39717, 21293}, {39971, 150}
X(47969) = crossdifference of every pair of points on line {672, 1500}
X(47969) = {X(3716),X(47672)}-harmonic conjugate of X(47834)

X(47970) = X(1)X(514)∩X(484)X(513)

X(47970) = 3 X[1] - 4 X[663], 5 X[1] - 4 X[4449], X[1] - 4 X[4724], 5 X[1] - 8 X[4794], 2 X[663] - 3 X[4040], 5 X[663] - 3 X[4449], X[663] - 3 X[4724], 5 X[663] - 6 X[4794], 5 X[4040] - 2 X[4449], 5 X[4040] - 4 X[4794], X[4449] - 5 X[4724], 5 X[4724] - 2 X[4794], 3 X[4063] - 2 X[4834], 5 X[1698] - 6 X[47793], 7 X[3624] - 6 X[47796], 3 X[3679] - 2 X[21302], 2 X[4369] - 3 X[47817], 2 X[14838] - 3 X[47811], 8 X[17072] - 9 X[19875], 2 X[23795] - 5 X[26777], 4 X[23796] - 7 X[27115], 2 X[23815] - 3 X[47822], 2 X[24720] - 3 X[47794], 13 X[34595] - 12 X[47795]

X(47970) lies on these lines: {1, 514}, {2, 23789}, {43, 47775}, {484, 513}, {512, 21385}, {612, 47773}, {650, 4905}, {659, 1019}, {661, 16546}, {667, 23394}, {830, 13259}, {1459, 28229}, {1698, 47793}, {2457, 4778}, {2605, 28213}, {2999, 47781}, {3624, 47796}, {3679, 21302}, {3716, 4978}, {3737, 4960}, {3762, 29051}, {3960, 23738}, {4041, 42325}, {4129, 46403}, {4369, 47817}, {4379, 25502}, {4391, 29186}, {4406, 25590}, {4462, 29066}, {4490, 6004}, {4498, 6005}, {4775, 29226}, {4882, 44448}, {4893, 16569}, {5216, 6371}, {5268, 47771}, {5272, 44435}, {7192, 20520}, {7274, 30181}, {7280, 44408}, {8714, 17494}, {14838, 47811}, {17022, 47791}, {17072, 19875}, {17418, 28225}, {20517, 47676}, {23511, 47783}, {23795, 26777}, {23796, 27115}, {23815, 47822}, {24720, 47794}, {25259, 29190}, {26102, 47780}, {28155, 42312}, {29142, 47726}, {29158, 47663}, {34595, 47795}

X(47970) = reflection of X(i) in X(j) for these {i,j}: {1, 4040}, {1019, 659}, {4040, 4724}, {4449, 4794}, {4905, 650}, {4978, 3716}, {21173, 46385}, {23738, 3960}, {46403, 4129}, {47676, 20517}, {47724, 4391}, {47725, 47708}
X(47970) = anticomplement of X(23789)
X(47970) = X(27807)-anticomplementary conjugate of X(21293)
X(47970) = X(17494)-Dao conjugate of X(20954)
X(47970) = crosspoint of X(190) and X(873)
X(47970) = crosssum of X(i) and X(j) for these (i,j): {649, 872}, {4557, 35326}
X(47970) = crossdifference of every pair of points on line {672, 1100}
X(47970) = barycentric product X(i)*X(j) for these {i,j}: {1, 26824}, {514, 5284}, {1019, 17163}, {4068, 7199}, {7192, 46196}
X(47970) = barycentric quotient X(i)/X(j) for these {i,j}: {4068, 1018}, {5284, 190}, {17163, 4033}, {26824, 75}, {46196, 3952}

X(47971) = X(513)X(16892)∩X(514)X(4380)

X(47971) = 3 X[16892] - X[23731], 3 X[4467] - X[47661], 3 X[649] - 2 X[47890], 3 X[4897] - X[47890], 2 X[650] - 3 X[4750], 5 X[661] - 6 X[47783], 2 X[661] - 3 X[47886], 5 X[4025] - 3 X[47783], 4 X[4025] - 3 X[47886], 4 X[47783] - 5 X[47886], X[47650] - 3 X[47676], 3 X[7192] - X[47659], 3 X[1635] - 4 X[3798], 3 X[1635] - 2 X[4468], 3 X[1638] - 2 X[14321], 6 X[1638] - 5 X[30835], 4 X[14321] - 5 X[30835], 3 X[1639] - 4 X[2487], 6 X[1639] - 7 X[31207], 8 X[2487] - 7 X[31207], 4 X[3239] - 5 X[24924], 2 X[3239] - 3 X[47758], 5 X[24924] - 6 X[47758], 4 X[3676] - 3 X[4728], 2 X[3700] - 3 X[4379], 2 X[3835] - 3 X[4453], 3 X[4453] - X[44449], 2 X[4010] - 3 X[47887], 2 X[4106] - 3 X[6545], 3 X[4120] - 4 X[4885], 2 X[4369] - 3 X[47755], 4 X[4369] - 3 X[47874], X[25259] - 3 X[47755], 2 X[25259] - 3 X[47874], 4 X[4394] - 3 X[6546], 2 X[4500] - 3 X[47780], 2 X[4522] - 3 X[47824], 3 X[4776] - 4 X[21212], 3 X[4786] - 2 X[11068], 3 X[4893] - 4 X[17069], 2 X[4940] - 3 X[47754], 2 X[6590] - 3 X[31148], 4 X[7653] - 3 X[47881], 4 X[7658] - 3

X(47971) lies on these lines: {513, 16892}, {514, 4380}, {522, 47672}, {649, 918}, {650, 4750}, {661, 4025}, {667, 29252}, {690, 4378}, {693, 2786}, {812, 47650}, {824, 7192}, {876, 21350}, {900, 4382}, {1019, 21392}, {1635, 3798}, {1638, 14321}, {1639, 2487}, {1980, 24286}, {3004, 4813}, {3239, 24924}, {3250, 23829}, {3566, 4449}, {3667, 21115}, {3676, 4728}, {3700, 4379}, {3776, 20295}, {3801, 29170}, {3835, 4453}, {4010, 47887}, {4024, 28898}, {4106, 6545}, {4120, 4885}, {4367, 29200}, {4369, 25259}, {4394, 6546}, {4500, 47780}, {4502, 23785}, {4522, 47824}, {4707, 29148}, {4761, 29212}, {4776, 21212}, {4777, 47671}, {4785, 47652}, {4786, 11068}, {4790, 30520}, {4834, 29354}, {4841, 28902}, {4893, 17069}, {4913, 47698}, {4926, 21116}, {4932, 30519}, {4940, 47754}, {4958, 21183}, {4978, 29216}, {6590, 31148}, {7653, 47881}, {7658, 47765}, {15313, 23726}, {17155, 20505}, {17494, 28851}, {18004, 47823}, {21117, 23781}, {21146, 29078}, {21196, 28855}, {21222, 28468}, {21828, 25098}, {23727, 23737}, {23729, 28217}, {23755, 23880}, {25666, 47769}, {26853, 28882}, {27013, 47772}, {27486, 28871}, {28161, 47670}, {28840, 45746}, {28859, 47653}, {28878, 45745}, {28886, 31290}, {28890, 47663}, {29178, 47680}, {29294, 47715}, {30565, 31286}, {31209, 45674}

X(47971) = reflection of X(i) in X(j) for these {i,j}: {649, 4897}, {661, 4025}, {3250, 23829}, {4024, 43067}, {4382, 21104}, {4468, 3798}, {4502, 23785}, {4813, 3004}, {4958, 21183}, {20295, 3776}, {25259, 4369}, {44449, 3835}, {47660, 4932}, {47666, 21196}, {47698, 4913}, {47874, 47755}
X(47971) = barycentric product X(i)*X(j) for these {i,j}: {513, 33942}, {514, 4851}, {693, 32912}
X(47971) = barycentric quotient X(i)/X(j) for these {i,j}: {4851, 190}, {32912, 100}, {33942, 668}
X(47971) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4025, 47886}, {1638, 14321, 30835}, {1639, 2487, 31207}, {3239, 47758, 24924}, {3798, 4468, 1635}, {4369, 25259, 47874}, {4453, 44449, 3835}, {21196, 47666, 47878}, {25259, 47755, 4369}

X(47972) = X(513)X(16892)∩X(514)X(47692)

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

X(47972) = 4 X[676] - 3 X[4379], 2 X[2254] - 3 X[47886], 4 X[3716] - 3 X[47874], 2 X[47690] - 3 X[47874], 3 X[4040] - X[47726], 2 X[4369] - 3 X[47798], 2 X[4522] - 3 X[47821], 3 X[4750] - 2 X[7659], 2 X[4925] - 3 X[47784], 4 X[13246] - 3 X[47762], 2 X[21146] - 3 X[47887], 2 X[24720] - 3 X[47797], 5 X[24924] - 6 X[47800], 4 X[25666] - 3 X[47808], 3 X[47708] - X[47722]

X(47962) lies on these lines: {513, 16892}, {514, 47692}, {522, 661}, {523, 4724}, {659, 29144}, {663, 29142}, {667, 29168}, {676, 4379}, {2254, 47886}, {3309, 21124}, {3667, 4467}, {3716, 47690}, {3762, 29192}, {3800, 4498}, {3801, 29246}, {3835, 47687}, {4040, 29021}, {4088, 4777}, {4170, 29190}, {4369, 47798}, {4468, 28161}, {4522, 47821}, {4750, 7659}, {4775, 29312}, {4791, 47723}, {4794, 47682}, {4925, 47784}, {5592, 47684}, {7662, 47703}, {8045, 47718}, {13246, 47762}, {21146, 47887}, {24720, 47797}, {24924, 47800}, {25666, 47808}, {28183, 47826}, {29051, 47708}, {29186, 47712}, {47123, 47672}, {47131, 47704}

X(47972) = reflection of X(i) in X(j) for these {i,j}: {47672, 47123}, {47682, 4794}, {47684, 5592}, {47687, 3835}, {47690, 3716}, {47700, 4468}, {47703, 7662}, {47704, 47131}, {47718, 8045}, {47723, 4791}
X(47972) = crossdifference of every pair of points on line {1468, 4253}
X(47972) = {X(3716),X(47690)}-harmonic conjugate of X(47874)

X(47973) = X(513)X(16892)∩X(514)X(1734)

X(47973) = 2 X[659] - 3 X[47886], 4 X[3676] - 3 X[47813], 2 X[3716] - 3 X[44435], 4 X[3776] - 3 X[47887], 2 X[47694] - 3 X[47887], 4 X[3837] - 3 X[47874], 2 X[4468] - 3 X[47810], 2 X[4830] - 3 X[27486], 3 X[6545] - 2 X[7662], 2 X[6590] - 3 X[47812], 2 X[8045] - 3 X[47819], 4 X[21212] - 3 X[47804], 4 X[25380] - 3 X[47771], 3 X[47828] - 2 X[47890]

X(47973) lies on these lines: {513, 16892}, {514, 1734}, {522, 47652}, {649, 4841}, {659, 47886}, {812, 47686}, {824, 46403}, {2526, 4088}, {3004, 4724}, {3676, 47813}, {3716, 44435}, {3776, 47694}, {3837, 47874}, {4025, 4778}, {4369, 47696}, {4458, 47697}, {4468, 47810}, {4750, 28220}, {4818, 17494}, {4830, 27486}, {4913, 47663}, {6545, 7662}, {6590, 47812}, {8045, 47819}, {17094, 43924}, {21212, 47804}, {24720, 47660}, {25380, 47771}, {28863, 47690}, {28890, 47698}, {28894, 47703}, {47828, 47890}

X(47973) = midpoint of X(47677) and X(47685)
X(47973) = reflection of X(i) in X(j) for these {i,j}: {4088, 2526}, {4724, 3004}, {17494, 4818}, {47660, 24720}, {47663, 4913}, {47694, 3776}, {47696, 4369}, {47697, 4458}
X(47973) = crossdifference of every pair of points on line {2280, 5280}
X(47973) = {X(3776),X(47694)}-harmonic conjugate of X(47887)

X(47974) = X(513)X(4380)∩X(514)X(47692)

X(47974) = 4 X[659] - 3 X[47762], 3 X[693] - 4 X[3716], 5 X[693] - 6 X[47832], 2 X[3716] - 3 X[4724], 10 X[3716] - 9 X[47832], 5 X[4724] - 3 X[47832], 2 X[2254] - 3 X[31150], 2 X[2526] - 3 X[47775], 3 X[4391] - 2 X[47724], 3 X[4462] - 2 X[4474], 3 X[4776] - 2 X[46403], 2 X[7659] - 3 X[47776], 4 X[8689] - 3 X[47813], 2 X[21104] - 3 X[47798], 2 X[21146] - 3 X[47804], 4 X[24720] - 5 X[31209], 2 X[24720] - 3 X[47811], 5 X[31209] - 6 X[47811], 2 X[43067] - 3 X[47805]

X(47974) lies on these lines: {513, 4380}, {514, 47692}, {522, 47664}, {659, 47762}, {661, 47685}, {693, 3716}, {900, 47698}, {2254, 31150}, {2526, 47775}, {3762, 47721}, {4025, 4778}, {4040, 4801}, {4391, 29186}, {4462, 4474}, {4468, 47687}, {4765, 4979}, {4776, 46403}, {4810, 29362}, {4977, 47676}, {7659, 47776}, {8689, 47813}, {21104, 47798}, {21146, 47804}, {24720, 31209}, {25009, 46385}, {27486, 28209}, {43067, 47805}, {47651, 47701}, {47675, 47694}

X(47974) = reflection of X(i) in X(j) for these {i,j}: {693, 4724}, {4801, 4040}, {47651, 47701}, {47675, 47694}, {47685, 661}, {47687, 4468}, {47721, 3762}
X(47974) = {X(24720),X(47811)}-harmonic conjugate of X(31209)

X(47975) = X(513)X(4380)∩X(514)X(1734)

X(47975) = 3 X[693] - 4 X[3837], 2 X[693] - 3 X[44429], 3 X[1491] - 2 X[3837], 4 X[1491] - 3 X[44429], 8 X[3837] - 9 X[44429], 2 X[23770] - 3 X[44435], X[47656] - 3 X[47808], 4 X[650] - 3 X[47804], 2 X[650] - 3 X[47825], 2 X[47694] - 3 X[47804], X[47694] - 3 X[47825], X[659] - 3 X[4948], 2 X[659] - 3 X[31150], 6 X[4948] - X[47697], 3 X[31150] - X[47697], 2 X[676] - 3 X[47784], 2 X[1577] - 3 X[47814], 4 X[2977] - 3 X[47771], 2 X[3716] - 3 X[4893], 2 X[4010] - 3 X[4776], 2 X[3835] - 3 X[47810], X[4804] - 3 X[47810], 2 X[4369] - 3 X[47828], 2 X[4378] - 3 X[44550], 3 X[4379] - 4 X[25380], 2 X[4458] - 3 X[47886], 2 X[4823] - 3 X[47816], 4 X[4874] - 5 X[31209], 2 X[4874] - 3 X[47827], 5 X[31209] - 6 X[47827], 4 X[4885] - 3 X[47834], 2 X[4978] - 3 X[47819], 2 X[6590] - 3 X[47809], 4 X[9508] - 3 X[47762], 4 X[14838] - 3 X[47820], 4 X[21212] - 3 X[47887], 5 X[24924] - 6 X[47830], 4 X[25666] - 3 X[47832], 5 X[26777] - 3 X[47805], 5 X[26985] - 6 X[47802], 7 X[27115] - 6 X[47803], 5 X[30795] - 6 X[45323], 4 X[31286] - 3 X[47813], 2 X[43067] - 3 X[47824], 2 X[47123] - 3 X[47797], 2 X[47132] - 3 X[47799], X[47695] - 3 X[47782]

X(47975) lies on these lines: {2, 7662}, {325, 523}, {513, 4380}, {514, 1734}, {522, 661}, {649, 4913}, {650, 47694}, {659, 4948}, {676, 47784}, {784, 4391}, {824, 4088}, {905, 17166}, {918, 47698}, {1577, 47814}, {2526, 4762}, {2530, 4801}, {2977, 47771}, {3716, 4893}, {3776, 47704}, {3797, 4010}, {3835, 4804}, {4024, 4522}, {4122, 47665}, {4151, 14349}, {4369, 47828}, {4378, 44550}, {4379, 25380}, {4444, 47703}, {4458, 47886}, {4462, 4490}, {4560, 8678}, {4728, 28169}, {4802, 21146}, {4806, 28183}, {4808, 47706}, {4818, 16892}, {4823, 47816}, {4841, 47699}, {4874, 31209}, {4885, 47834}, {4977, 47663}, {4978, 47819}, {6084, 47686}, {6129, 27674}, {6590, 47809}, {7650, 47842}, {9508, 47762}, {14838, 47820}, {16751, 47844}, {17418, 23655}, {21124, 23877}, {21212, 47887}, {21301, 23882}, {24720, 28147}, {24924, 47830}, {25666, 47832}, {26777, 47805}, {26985, 47802}, {27115, 47803}, {28151, 36848}, {28155, 47812}, {28894, 47693}, {29021, 47679}, {29066, 47683}, {29362, 47664}, {30765, 47806}, {30795, 45323}, {31286, 47813}, {43067, 47824}, {44433, 47883}, {47123, 47797}, {47132, 47799}, {47661, 47687}, {47673, 47700}, {47695, 47782}, {47696, 47890}

X(47975) = midpoint of X(i) and X(j) for these {i,j}: {47657, 47689}, {47661, 47687}, {47664, 47685}, {47673, 47700}
X(47975) = reflection of X(i) in X(j) for these {i,j}: {649, 4913}, {693, 1491}, {4024, 4522}, {4391, 4705}, {4462, 4490}, {4801, 2530}, {4804, 3835}, {7650, 47842}, {16892, 4818}, {17166, 905}, {31150, 4948}, {44433, 47883}, {46403, 2526}, {47665, 4122}, {47666, 4824}, {47672, 24720}, {47675, 21146}, {47691, 3004}, {47694, 650}, {47696, 47890}, {47697, 659}, {47699, 4841}, {47704, 3776}, {47706, 4808}, {47804, 47825}
X(47975) = anticomplement of X(7662)
X(47975) = crossdifference of every pair of points on line {32, 1468}
X(47975) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 47694, 47804}, {693, 1491, 44429}, {4804, 47810, 3835}, {4874, 47827, 31209}, {31150, 47697, 659}, {47694, 47825, 650}

X(47976) = X(484)X(513)∩X(514)X(4380)

X(47976) = 3 X[649] - 2 X[14838], 3 X[14349] - 4 X[14838], 3 X[1019] - 2 X[3669], X[3669] - 3 X[4790]

X(47976) lies on these lines: {484, 513}, {514, 4380}, {649, 14349}, {1019, 1429}, {1577, 4785}, {4401, 4822}, {4498, 15309}, {4762, 4960}, {4782, 4983}, {4784, 4905}, {4804, 4961}, {4932, 4978}, {7192, 29302}, {7265, 28493}, {26853, 29013}, {28478, 47682}, {28859, 47679}, {29216, 47660}, {29294, 47693}

X(47976) = reflection of X(i) in X(j) for these {i,j}: {1019, 4790}, {1734, 4834}, {4822, 4401}, {4905, 4784}, {4978, 4932}, {4983, 4782}, {14349, 649}
X(47976) = crossdifference of every pair of points on line {210, 1100}

X(47977) = X(484)X(513)∩X(514)X(47692)

X(47977) = 3 X[4448] - 2 X[23815], 4 X[8689] - 3 X[47818], 2 X[23789] - 3 X[47804], 2 X[24720] - 3 X[47817]

X(47977) lies on these lines: {484, 513}, {514, 47692}, {659, 4905}, {663, 2832}, {905, 45047}, {1960, 23765}, {3309, 21385}, {4129, 47685}, {4142, 4778}, {4448, 23815}, {4498, 42325}, {4724, 14349}, {6161, 29226}, {8689, 47818}, {23789, 47804}, {24720, 47817}

X(47977) = reflection of X(i) in X(j) for these {i,j}: {4905, 659}, {14349, 4724}, {23765, 1960}, {47685, 4129}
X(47977) = crosssum of X(649) and X(4878)
X(47977) = barycentric product X(1)*X(47650)
X(47977) = barycentric quotient X(47650)/X(75)

X(47978) = X(513)X(3004)∩X(514)X(4838)

X(47978) = 6 X[3004] - 5 X[4025], 7 X[3004] - 5 X[4897], 7 X[4025] - 6 X[4897], 2 X[4790] - 3 X[47783], 4 X[4940] - 3 X[47789], 2 X[4979] - 3 X[47785]

X(47978) lies on these lines: {513, 3004}, {514, 4838}, {693, 28225}, {4106, 28209}, {4468, 4813}, {4778, 20295}, {4790, 47783}, {4940, 47789}, {4962, 47657}, {4979, 47785}, {6006, 45746}, {23731, 28846}, {28229, 47656}

X(47979) = X(513)X(3004)∩X(514)X(4170)

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

X(47979) = 2 X[4522] - 3 X[47764], 2 X[4784] - 3 X[47785], 4 X[4806] - 3 X[47787], 2 X[4932] - 3 X[47800], 2 X[11068] - 3 X[47826]

X(47979) lies on these lines: {513, 3004}, {514, 4170}, {522, 4813}, {4522, 47764}, {4778, 21116}, {4784, 47785}, {4806, 47787}, {4932, 47800}, {4983, 6332}, {11068, 47826}, {28225, 47887}, {28840, 47123}, {28846, 47701}, {28878, 47691}

X(47980) = X(513)X(4507)∩X(514)X(4170)

Barycentrics (b - c)*(7*a^2*b + 3*a*b^2 + 7*a^2*c + 11*a*b*c + b^2*c + 3*a*c^2 + b*c^2) : :

X(47980) lies on these lines: {513, 4507}, {514, 4170}, {661, 28225}, {3667, 47666}, {3835, 4778}, {4010, 28229}, {4806, 28220}, {4824, 6006}, {24720, 28209}, {30519, 47699}, {31286, 47826}

X(47981) = X(513)X(3004)∩X(514)X(4024)

X(47981) = 4 X[3004] - 3 X[4025], 5 X[3004] - 3 X[4897], 5 X[4025] - 4 X[4897], X[4608] - 5 X[20295], 3 X[4608] - 5 X[47656], 3 X[20295] - X[47656], 2 X[649] - 3 X[47783], 3 X[661] - 2 X[11068], 2 X[3239] - 3 X[47759], 4 X[3835] - 3 X[47789], 2 X[4765] - 3 X[47781], X[26853] - 3 X[47781], 3 X[4786] - 2 X[4979], 2 X[4790] - 3 X[47785], 2 X[4932] - 3 X[47757], 4 X[4940] - 3 X[47787], 2 X[6590] - 3 X[47786], 2 X[7192] - 3 X[21183], 4 X[7658] - 3 X[47763], 4 X[25666] - 3 X[47768], 5 X[26798] - 3 X[47791], X[47663] - 3 X[47774]

X(47981) lies on these lines: {513, 3004}, {514, 4024}, {522, 47657}, {649, 47783}, {661, 11068}, {693, 4778}, {3239, 47759}, {3667, 45746}, {3835, 47789}, {4106, 4977}, {4467, 6006}, {4765, 26853}, {4785, 45745}, {4786, 4979}, {4790, 47785}, {4841, 6008}, {4932, 26277}, {4940, 47787}, {4962, 17161}, {6590, 28859}, {7192, 17218}, {7658, 47763}, {8713, 17896}, {17894, 20949}, {21186, 23733}, {23813, 28220}, {25666, 47768}, {26798, 47791}, {28191, 47655}, {28209, 43067}, {28878, 47652}, {47663, 47774}

X(47981) = midpoint of X(4813) and X(23731)
X(47981) = reflection of X(26853) in X(4765)
X(47981) = {X(26853),X(47781)}-harmonic conjugate of X(4765)

X(47982) = X(513)X(3004)∩X(514)X(4088)

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

X(47982) = 2 X[659] - 3 X[47783], 3 X[2526] - 2 X[4925], 4 X[3837] - 3 X[47789], 2 X[4830] - 3 X[47883], 2 X[11068] - 3 X[47810], 4 X[25380] - 3 X[47768]

X(47982) lies on these lines: {513, 3004}, {514, 4088}, {522, 47673}, {659, 47783}, {661, 4521}, {2526, 4925}, {3239, 47696}, {3667, 47701}, {3837, 47789}, {4468, 4977}, {4724, 4932}, {4830, 47883}, {11068, 47810}, {25380, 47768}, {28191, 47700}, {28209, 47761}, {44305, 45684}

X(47982) = reflection of X(47696) in X(3239)
X(47982) = crossdifference of every pair of points on line {3915, 21764}

X(47983) = X(513)X(3004)∩X(514)X(4010)

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

X(47983) = 2 X[2977] - 3 X[47777], 2 X[9508] - 3 X[47783], 2 X[18004] - 3 X[47764], 3 X[31147] - X[47703], X[47690] - 3 X[47759], X[47693] - 3 X[47769], X[47698] - 3 X[47774]

X(47983) lies on these lines: {513, 3004}, {514, 4010}, {523, 4820}, {676, 28209}, {2977, 47777}, {3716, 28859}, {4724, 23731}, {4806, 6590}, {4813, 47701}, {4977, 7662}, {9508, 47783}, {18004, 47764}, {20295, 47699}, {29328, 45745}, {31147, 47703}, {31290, 47691}, {47690, 47759}, {47693, 47769}, {47698, 47774}

X(47983) = midpoint of X(i) and X(j) for these {i,j}: {4724, 23731}, {4813, 47701}, {20295, 47699}, {31290, 47691}
X(47983) = reflection of X(6590) in X(4806)

X(47984) = X(513)X(4507)∩X(514)X(4024)

X(47984) = X[4382] - 5 X[4813], 3 X[4382] - 5 X[20295], 7 X[4382] - 5 X[26824], X[4382] + 5 X[31290], 3 X[4813] - X[20295], 7 X[4813] - X[26824], 7 X[20295] - 3 X[26824], X[20295] + 3 X[31290], X[26824] + 7 X[31290], X[649] - 3 X[47774], 7 X[661] - 5 X[31209], 3 X[661] - 2 X[31286], 5 X[661] - 3 X[47762], 4 X[661] - 3 X[47778], 7 X[4932] - 10 X[31209], 3 X[4932] - 4 X[31286], 5 X[4932] - 6 X[47762], 2 X[4932] - 3 X[47778], 15 X[31209] - 14 X[31286], 25 X[31209] - 21 X[47762], 20 X[31209] - 21 X[47778], 10 X[31286] - 9 X[47762], 8 X[31286] - 9 X[47778], 4 X[47762] - 5 X[47778], 3 X[3835] - 2 X[43067], 7 X[3835] - 6 X[45320], 7 X[43067] - 9 X[45320], 3 X[4958] - X[47655], 3 X[7192] - 5 X[30835], 2 X[7192] - 3 X[47779], 10 X[30835] - 9 X[47779]

X(47984) lies on these lines: {513, 4507}, {514, 4024}, {649, 47774}, {661, 4932}, {3004, 28886}, {3776, 28902}, {3835, 28840}, {4785, 47666}, {4810, 28191}, {4841, 28867}, {4958, 47655}, {4963, 28147}, {6005, 20983}, {7192, 30835}, {24719, 28229}, {28906, 45746}

X(47984) = midpoint of X(4813) and X(31290)
X(47984) = reflection of X(4932) in X(661)
X(47984) = {X(661),X(4932)}-harmonic conjugate of X(47778)

X(47985) = X(513)X(4507)∩X(514)X(4088)

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

X(47985) = 3 X[661] - X[47697], 3 X[3835] - 2 X[7662], 2 X[13246] - 3 X[47783], 10 X[30795] - 9 X[47779], 2 X[31286] - 3 X[47810]

X(47985) lies on these lines: {513, 4507}, {514, 4088}, {661, 47697}, {1491, 4932}, {2526, 28840}, {3667, 4813}, {3835, 7662}, {4378, 28399}, {4382, 28155}, {4810, 28169}, {4925, 28209}, {4963, 28229}, {13246, 47783}, {20295, 28161}, {24719, 28147}, {28225, 31290}, {30795, 47779}, {31286, 47810}

X(47986) = X(513)X(4507)∩X(514)X(4010)

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

X(47986) = 5 X[661] - 3 X[44429], 5 X[24720] - 6 X[44429], 3 X[4147] - 2 X[4761], X[7192] - 3 X[47826], 2 X[25380] - 3 X[47777], 2 X[43067] - 3 X[47831], X[47703] - 3 X[47769]

X(47986) lies on these lines: {513, 4507}, {514, 4010}, {522, 44449}, {661, 4521}, {693, 28229}, {1491, 28225}, {3667, 4824}, {3835, 4977}, {3837, 28220}, {4147, 4761}, {4458, 28878}, {4724, 31290}, {4804, 28191}, {4806, 28195}, {7192, 47826}, {25380, 47777}, {28840, 45673}, {43067, 47831}, {47703, 47769}

X(47986) = midpoint of X(4724) and X(31290)
X(47986) = reflection of X(24720) in X(661)

X(47987) = X(514)X(4010)∩X(661)X(4905)

X(47987) = 3 X[661] - X[4905], X[1019] - 3 X[47826], 3 X[14349] - X[23738], X[47715] - 3 X[47769]

X(47987) lies on these lines: {514, 4010}, {661, 4905}, {1019, 47826}, {4041, 6005}, {4129, 4778}, {4160, 4162}, {4401, 15309}, {4823, 4977}, {14349, 23738}, {20517, 28855}, {21260, 28209}, {47715, 47769}

X(47988) = X(513)X(3004)∩X(514)X(3700)

X(47988) = 9 X[6548] - 5 X[7192], 6 X[6548] - 5 X[47891], 2 X[7192] - 3 X[47891], 3 X[3004] - 2 X[4025], 4 X[4025] - 3 X[4897], 2 X[649] - 3 X[47784], 5 X[661] - 3 X[6546], 3 X[6546] + 5 X[23731], 6 X[6546] - 5 X[47890], 2 X[23731] + X[47890], 3 X[1638] - 2 X[4932], 4 X[2487] - 3 X[47763], 4 X[2527] - 5 X[31209], 3 X[4927] - 2 X[43067], 2 X[3798] - 3 X[47880], 4 X[3835] - 3 X[47788], 2 X[4369] - 3 X[47756], X[4380] - 3 X[47781], 2 X[4394] - 3 X[47783], 3 X[4789] - 5 X[26798], 2 X[11068] - 3 X[47777], 2 X[14321] - 3 X[47759], X[47660] - 3 X[47759], 10 X[25666] - 9 X[45684], 4 X[25666] - 3 X[47767], 6 X[45684] - 5 X[47767], X[26853] - 3 X[47782], 4 X[31287] - 3 X[47768], X[47662] - 3 X[47769]

X(47988) lies on these lines: {86, 4833}, {513, 3004}, {514, 3700}, {523, 4810}, {649, 47784}, {661, 1211}, {693, 4806}, {812, 4841}, {900, 45746}, {918, 4813}, {1213, 27574}, {1638, 4932}, {2487, 47763}, {2527, 31209}, {3649, 4077}, {3676, 28225}, {3716, 4778}, {3798, 47880}, {3835, 28859}, {4369, 47756}, {4380, 47781}, {4394, 47783}, {4467, 28217}, {4785, 4976}, {4789, 26798}, {4940, 6590}, {4979, 17069}, {6008, 45745}, {6084, 47666}, {11068, 47777}, {14321, 47660}, {17161, 28221}, {17778, 31290}, {21104, 28840}, {21143, 28372}, {21297, 28213}, {23813, 28195}, {25666, 45684}, {26277, 47799}, {26853, 47782}, {28175, 47656}, {28179, 47655}, {28183, 47657}, {28902, 47676}, {31287, 47768}, {44449, 47653}, {47662, 47769}

X(47988) = midpoint of X(i) and X(j) for these {i,j}: {661, 23731}, {31290, 47652}, {44449, 47653}
X(47988) = reflection of X(i) in X(j) for these {i,j}: {4897, 3004}, {4979, 17069}, {6590, 4940}, {47660, 14321}, {47890, 661}
X(47988) = {X(47660),X(47759)}-harmonic conjugate of X(14321)

X(47989) = X(513)X(3004)∩X(514)X(4522)

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

X(47989) = 2 X[2977] - 3 X[47810], 3 X[4776] - X[47696], 2 X[4782] - 3 X[47784], 2 X[4874] - 3 X[47756], 2 X[17069] - 3 X[47877]

X(47989) lies on these lines: {513, 3004}, {514, 4522}, {523, 4382}, {661, 1639}, {900, 47701}, {1638, 4724}, {2254, 23731}, {2977, 47810}, {4088, 28175}, {4369, 4778}, {4468, 28195}, {4776, 47696}, {4782, 47784}, {4785, 4818}, {4824, 6084}, {4841, 29362}, {4874, 47756}, {17069, 47877}, {21212, 28225}, {24720, 28859}, {28179, 47700}, {28183, 47702}, {47651, 47698}, {47666, 47686}, {47685, 47699}

X(47989) = midpoint of X(i) and X(j) for these {i,j}: {2254, 23731}, {47651, 47698}, {47666, 47686}, {47685, 47699}

X(47990) = X(513)X(3004)∩X(514)X(4806)

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

X(47990) lies on these lines: {513, 3004}, {514, 4806}, {659, 23731}, {3700, 4802}, {3716, 4977}, {4122, 47759}, {4810, 4988}, {4874, 28859}, {4963, 47704}, {24719, 47699}, {47688, 47774}

X(47990) = midpoint of X(i) and X(j) for these {i,j}: {659, 23731}, {4810, 4988}, {4963, 47704}, {24719, 47699}

X(47991) = X(513)X(4507)∩X(514)X(3700)

X(47991) = 3 X[2] - 5 X[661], 6 X[2] - 5 X[4369], 9 X[2] - 5 X[7192], 27 X[2] - 25 X[24924], 9 X[2] - 10 X[25666], 7 X[2] - 5 X[31148], 3 X[2] + 5 X[31290], 4 X[2] - 5 X[45315], 11 X[2] - 10 X[45663], X[2] - 5 X[47774], 3 X[661] - X[7192], 9 X[661] - 5 X[24924], 3 X[661] - 2 X[25666], 7 X[661] - 3 X[31148], 4 X[661] - 3 X[45315], 11 X[661] - 6 X[45663], X[661] - 3 X[47774], 3 X[4369] - 2 X[7192], 9 X[4369] - 10 X[24924], 3 X[4369] - 4 X[25666], 7 X[4369] - 6 X[31148], X[4369] + 2 X[31290], 2 X[4369] - 3 X[45315], 11 X[4369] - 12 X[45663], X[4369] - 6 X[47774], 3 X[7192] - 5 X[24924], 7 X[7192] - 9 X[31148], X[7192] + 3 X[31290], 4 X[7192] - 9 X[45315], 11 X[7192] - 18 X[45663], X[7192] - 9 X[47774], 5 X[24924] - 6 X[25666], 35 X[24924] - 27 X[31148], 5 X[24924] + 9 X[31290], 20 X[24924] - 27 X[45315], 55 X[24924] - 54 X[45663], 5 X[24924] - 27 X[47774], 14 X[25666] - 9 X[31148], 2 X[25666] + 3 X[31290], 8 X[25666] - 9 X[45315], 11 X[25666] - 9 X[45663], 2 X[25666] - 9 X[47774], 3 X[31148] + 7 X[31290], 4 X[31148] - 7 X[45315], 11 X[31148] - 14 X[45663], X[31148] - 7 X[47774], 4 X[31290] + 3 X[45315], 11 X[31290] + 6 X[45663], X[31290] + 3 X[47774], 11 X[45315] - 8 X[45663], X[45315] - 4 X[47774], 2 X[45663] - 11 X[47774], 5 X[4813] + X[47664], X[47664] - 5 X[47666], X[4608] - 3 X[4931], 3 X[4763] - 2 X[4932], 3 X[4928] - 2 X[43067], X[4979] - 3 X[47775], 4 X[14350] - 3 X[45685], 3 X[31147] - X[47675], 2 X[31286] - 3 X[47777], X[47672] - 3 X[47759]

X(47991) lies on these lines: {2, 661}, {513, 4507}, {514, 3700}, {812, 4813}, {2526, 11068}, {2786, 4841}, {3004, 28855}, {3244, 4160}, {3629, 9013}, {3776, 28878}, {4010, 4963}, {4025, 28886}, {4468, 28859}, {4608, 4931}, {4763, 4932}, {4928, 43067}, {4979, 47775}, {4988, 44449}, {6002, 47683}, {8672, 41300}, {14350, 45685}, {16892, 28871}, {28867, 45745}, {31147, 47675}, {31286, 47777}, {47672, 47759}

X(47991) = midpoint of X(i) and X(j) for these {i,j}: {661, 31290}, {4010, 4963}, {4813, 47666}, {4988, 44449}
X(47991) = reflection of X(i) in X(j) for these {i,j}: {4369, 661}, {7192, 25666}
X(47991) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4369, 45315}, {661, 7192, 25666}, {7192, 25666, 4369}, {31290, 47774, 661}

X(47992) = X(513)X(4507)∩X(514)X(4522)

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

X(47992) = 3 X[661] - X[47694], 5 X[661] - 3 X[47821], 3 X[3716] - 2 X[47694], 5 X[3716] - 6 X[47821], 5 X[47694] - 9 X[47821], 4 X[1491] - 3 X[45328], X[4804] - 3 X[47759], 2 X[4874] - 3 X[45315], X[4960] - 3 X[47816], X[4979] - 3 X[47825], X[7192] - 3 X[47810], 2 X[25380] - 3 X[47810], 3 X[47666] + X[47685], X[47697] - 3 X[47826]

X(47992) lies on these lines: {513, 4507}, {514, 4522}, {522, 4841}, {661, 3716}, {812, 4824}, {1491, 28840}, {2254, 31290}, {2526, 4778}, {4106, 28147}, {4804, 47759}, {4818, 28846}, {4874, 45315}, {4960, 47816}, {4963, 21146}, {4979, 47825}, {7192, 25380}, {47666, 47685}, {47697, 47826}

X(47992) = midpoint of X(i) and X(j) for these {i,j}: {2254, 31290}, {4963, 21146}
X(47992) = reflection of X(i) in X(j) for these {i,j}: {3716, 661}, {7192, 25380}
X(47992) = {X(7192),X(47810)}-harmonic conjugate of X(25380)

X(47993) = X(513)X(4507)∩X(514)X(4806)

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

X(47993) = 3 X[661] - X[21146], 7 X[661] - 3 X[47812], 3 X[3837] - 2 X[21146], 7 X[3837] - 6 X[47812], 7 X[21146] - 9 X[47812], X[4784] - 3 X[47775]

X(47993) lies on these lines: {513, 4507}, {514, 4806}, {523, 8663}, {659, 31290}, {661, 1639}, {693, 28213}, {900, 4824}, {1491, 28209}, {3835, 28195}, {4010, 28175}, {4784, 47775}, {4804, 28179}, {4963, 47694}, {24720, 28220}, {28840, 45314}

X(47993) = midpoint of X(i) and X(j) for these {i,j}: {659, 31290}, {4963, 47694}
X(47993) = reflection of X(3837) in X(661)

X(47994) = X(512)X(4490)∩X(514)X(4806)

X(47994) = 3 X[661] - X[2530], X[667] - 3 X[47826], 2 X[2533] - 3 X[28603], X[4960] - 3 X[47872], 3 X[14349] - X[23765]

X(47994) lies on these lines: {512, 4490}, {514, 4806}, {661, 665}, {667, 47826}, {891, 4983}, {2533, 28603}, {4129, 4977}, {4770, 6005}, {4778, 21260}, {4823, 28195}, {4960, 47872}, {8672, 42653}, {14349, 23765}

X(47994) = crossdifference of every pair of points on line {1621, 16884}
X(47994) = barycentric product X(i)*X(j) for these {i,j}: {1, 47670}, {513, 28633}
X(47994) = barycentric quotient X(i)/X(j) for these {i,j}: {28633, 668}, {47670, 75}

X(47995) = X(513)X(3004)∩X(514)X(661)

X(47995) = 3 X[3004] - X[4897], 3 X[4025] - 2 X[4897], 2 X[3239] - 3 X[4776], 4 X[3835] - 3 X[47787], 3 X[4776] - X[47660], 3 X[6332] - 2 X[47682], 2 X[6590] - 3 X[47787], 3 X[14349] - X[47682], 3 X[30565] - X[47662], X[47675] - 3 X[47871], X[17161] + 3 X[20295], X[17161] - 3 X[45746], 2 X[649] - 3 X[47785], 2 X[23731] + 3 X[47785], 2 X[650] - 3 X[47783], 2 X[3676] - 3 X[44435], X[7192] - 3 X[44435], 2 X[3700] - 3 X[47786], 4 X[4940] - 3 X[47786], 2 X[3798] - 3 X[47886], X[4979] - 3 X[47886], X[4024] - 3 X[31147], 3 X[21297] - X[47656], 2 X[4369] - 3 X[47757], X[4380] - 3 X[47782], 2 X[4765] - 3 X[47782], 2 X[4394] - 3 X[47784], 4 X[4521] - 3 X[47771], X[4784] - 3 X[47877], 3 X[4786] - 2 X[4790], 3 X[4786] - 4 X[17069], X[4790] - 3 X[47880], 2 X[17069] - 3 X[47880], 3 X[21183] - 2 X[43067], 2 X[4885] - 3 X[47756], 4 X[4885] - 3 X[47789], 3 X[4893] - 2 X[11068], 2 X[4932] - 3 X[47758], 4 X[21212] - 3 X[47758], 4 X[7658] - 3 X[47762], X[17494] - 3 X[47781], 5 X[24924] - 6 X[44432], X[25259] - 3 X[47759], X[47653] + 3 X[47759], 4 X[25666] - 3 X[47766], 5 X[26798] - X[47659], 5 X[26798] - 3 X[47790], X[47659] - 3 X[47790], X[26853] - 3 X[27486], 5 X[26985] - 3 X[47791], 5 X[27013] - 6 X[46919], 5 X[31209] - 4 X[43061], 4 X[31286] - 3 X[47768], 4 X[31287] - 3 X[47767], X[47663] - 3 X[47775], X[47674] - 3 X[47869], X[47696] - 3 X[47821]

X(47995) lies on these lines: {513, 3004}, {514, 661}, {522, 17161}, {523, 4106}, {649, 23731}, {650, 47783}, {665, 27674}, {812, 45745}, {1443, 1447}, {3667, 4467}, {3700, 4940}, {3776, 28840}, {3798, 4979}, {3800, 44448}, {4024, 31147}, {4040, 21174}, {4088, 21297}, {4369, 28859}, {4380, 4765}, {4382, 4988}, {4394, 47784}, {4453, 13246}, {4521, 47771}, {4608, 28191}, {4762, 4841}, {4784, 47877}, {4785, 21196}, {4786, 4790}, {4802, 23813}, {4813, 16892}, {4874, 4977}, {4885, 47756}, {4893, 11068}, {4927, 28195}, {4932, 21212}, {4976, 6008}, {6006, 47894}, {6545, 41930}, {6548, 28626}, {7180, 28374}, {7658, 47762}, {17094, 31605}, {17494, 47781}, {17894, 20906}, {20949, 35519}, {21124, 28478}, {24924, 44432}, {25259, 47653}, {25666, 47766}, {26798, 47659}, {26824, 47667}, {26853, 27486}, {26985, 47791}, {27013, 46919}, {28155, 47655}, {28161, 47657}, {28209, 47754}, {28220, 47891}, {28229, 47780}, {28863, 47764}, {28878, 31290}, {31209, 43061}, {31286, 47768}, {31287, 47767}, {44449, 47677}, {46403, 47699}, {47654, 47665}, {47663, 47775}, {47674, 47869}, {47688, 47698}, {47696, 47821}

X(47995) = midpoint of X(i) and X(j) for these {i,j}: {649, 23731}, {4382, 4988}, {4813, 16892}, {4841, 23729}, {20295, 45746}, {25259, 47653}, {26824, 47667}, {31290, 47676}, {44449, 47677}, {46403, 47699}, {47652, 47666}, {47654, 47665}, {47688, 47698}
X(47995) = reflection of X(i) in X(j) for these {i,j}: {3700, 4940}, {4025, 3004}, {4380, 4765}, {4468, 661}, {4786, 47880}, {4790, 17069}, {4932, 21212}, {4979, 3798}, {6332, 14349}, {6590, 3835}, {7192, 3676}, {47660, 3239}, {47789, 47756}
X(47995) = crossdifference of every pair of points on line {31, 1334}
X(47995) = barycentric product X(i)*X(j) for these {i,j}: {514, 17321}, {693, 5256}, {3261, 16466}, {3676, 14555}, {3931, 7199}, {5250, 24002}, {7713, 15413}, {15419, 39579}
X(47995) = barycentric quotient X(i)/X(j) for these {i,j}: {3931, 1018}, {4254, 3939}, {5250, 644}, {5256, 100}, {7713, 1783}, {14555, 3699}, {16466, 101}, {17321, 190}
X(47995) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3700, 4940, 47786}, {3835, 6590, 47787}, {4380, 47782, 4765}, {4776, 47660, 3239}, {4790, 17069, 4786}, {4790, 47880, 17069}, {4932, 21212, 47758}, {4979, 47886, 3798}, {7192, 44435, 3676}, {26798, 47659, 47790}, {47653, 47759, 25259}

X(47996) = X(513)X(4507)∩X(514)X(661)

X(47996) = 3 X[661] - X[693], 7 X[661] - 3 X[4728], 5 X[661] - 3 X[4776], 5 X[661] - X[47672], 7 X[661] - X[47675], 2 X[693] - 3 X[3835], 7 X[693] - 9 X[4728], 5 X[693] - 9 X[4776], X[693] + 3 X[47666], 5 X[693] - 3 X[47672], 7 X[693] - 3 X[47675], 7 X[3835] - 6 X[4728], 5 X[3835] - 6 X[4776], X[3835] + 2 X[47666], 5 X[3835] - 2 X[47672], 7 X[3835] - 2 X[47675], 5 X[4728] - 7 X[4776], 3 X[4728] + 7 X[47666], 15 X[4728] - 7 X[47672], 3 X[4728] - X[47675], 3 X[4776] + 5 X[47666], 3 X[4776] - X[47672], 21 X[4776] - 5 X[47675], 5 X[47666] + X[47672], 7 X[47666] + X[47675], 7 X[47672] - 5 X[47675], 3 X[649] - 5 X[26777], X[649] - 3 X[47775], 5 X[26777] + 3 X[31290], 5 X[26777] - 9 X[47775], X[31290] + 3 X[47775], 4 X[650] - 3 X[45313], 2 X[4932] - 3 X[45313], X[4024] - 3 X[47769], X[47667] + 3 X[47769], 3 X[4120] - X[47656], 3 X[4369] - 4 X[31287], 2 X[4369] - 3 X[47778], 8 X[31287] - 9 X[47778], X[4382] - 3 X[47759], X[4467] - 3 X[47878], X[4608] - 3 X[47873], X[4813] - 3 X[47774], X[17494] + 3 X[47774], 2 X[4885] - 3 X[45315], 3 X[4893] - X[7192], 9 X[4893] - 7 X[27115], 3 X[4893] - 2 X[31286], 3 X[7192] - 7 X[27115], 7 X[27115] - 6 X[31286], X[4897] - 3 X[47876], 3 X[4931] - X[47655], X[4960] - 3 X[47794], X[4979] - 3 X[31150], 2 X[7653] - 3 X[44567], X[16892] - 3 X[47781], 2 X[21212] - 3 X[47783], 6 X[25666] - 5 X[31250], 2 X[25666] - 3 X[47777], 4 X[25666] - 3 X[47779], 5 X[31250] - 3 X[43067], 5 X[31250] - 9 X[47777], 10 X[31250] - 9 X[47779], X[43067] - 3 X[47777], 2 X[43067] - 3 X[47779], X[26824] - 3 X[31147], 5 X[26985] - 6 X[45339], 5 X[30835] - 3 X[47780], 3 X[31148] - 5 X[31209], X[47671] - 3 X[47790], X[47694] - 3 X[47826]

X(47996) lies on these lines: {513, 4507}, {514, 661}, {522, 4824}, {649, 26777}, {650, 4932}, {824, 4841}, {1491, 4778}, {2254, 28225}, {2786, 45745}, {3004, 28851}, {3837, 28195}, {3960, 27674}, {4010, 28147}, {4024, 47667}, {4025, 28855}, {4040, 23655}, {4088, 47699}, {4120, 47656}, {4369, 31287}, {4378, 25537}, {4382, 47759}, {4444, 10196}, {4467, 28906}, {4498, 29807}, {4500, 14321}, {4608, 47873}, {4785, 4813}, {4802, 4806}, {4804, 28155}, {4838, 47668}, {4885, 45315}, {4893, 7192}, {4897, 28886}, {4931, 47655}, {4960, 47794}, {4976, 28867}, {4977, 20316}, {4979, 31150}, {4988, 25259}, {6546, 25381}, {7653, 44567}, {14404, 23795}, {16892, 47781}, {17069, 28902}, {21051, 23818}, {21146, 28229}, {21196, 28846}, {21212, 47783}, {23731, 47663}, {23827, 46390}, {25142, 29198}, {25666, 31250}, {26824, 31147}, {26985, 45339}, {28859, 47890}, {30519, 45746}, {30835, 47780}, {31148, 31209}, {47665, 47669}, {47671, 47790}, {47694, 47826}, {47698, 47701}

X(47996) = midpoint of X(i) and X(j) for these {i,j}: {649, 31290}, {661, 47666}, {4024, 47667}, {4088, 47699}, {4813, 17494}, {4838, 47668}, {4988, 25259}, {23731, 47663}, {47665, 47669}, {47698, 47701}
X(47996) = reflection of X(i) in X(j) for these {i,j}: {3835, 661}, {4500, 14321}, {4932, 650}, {7192, 31286}, {43067, 25666}, {47779, 47777}
X(47996) = X(i)-complementary conjugate of X(j) for these (i,j): {39737, 116}, {39961, 11}
X(47996) = X(692)-isoconjugate of X(39736)
X(47996) = X(1086)-Dao conjugate of X(39736)
X(47996) = barycentric product X(i)*X(j) for these {i,j}: {514, 27268}, {693, 42042}
X(47996) = barycentric quotient X(i)/X(j) for these {i,j}: {514, 39736}, {27268, 190}, {42042, 100}
X(47996) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 4932, 45313}, {661, 47672, 4776}, {4893, 7192, 31286}, {17494, 47774, 4813}, {25666, 43067, 47779}, {31290, 47775, 649}, {43067, 47777, 25666}, {47667, 47769, 4024}

X(47997) = X(514)X(661)∩X(650)X(15309)

X(47997) = 3 X[661] - X[14349], 3 X[4776] - X[4978], X[905] - 3 X[47777], X[1019] - 3 X[4893], X[4040] - 3 X[47826], X[4905] - 3 X[47810], X[4963] + 3 X[47872], X[7192] - 3 X[47794], X[7265] - 3 X[47769], X[17166] - 3 X[47838], X[31290] + 3 X[47793]

X(47997) lies on these lines: {514, 661}, {650, 15309}, {905, 47777}, {1019, 4893}, {4040, 47826}, {4063, 4813}, {4079, 31010}, {4088, 29164}, {4490, 4983}, {4705, 6005}, {4778, 20316}, {4794, 8678}, {4905, 47810}, {4963, 47872}, {4977, 21260}, {7192, 47794}, {7265, 47769}, {17166, 47838}, {17494, 29270}, {21188, 28878}, {21192, 28846}, {25259, 47679}, {29178, 47775}, {29260, 47701}, {31290, 47793}, {47667, 47678}, {47698, 47712}, {47699, 47711}

X(47997) = midpoint of X(i) and X(j) for these {i,j}: {1577, 47666}, {4063, 4813}, {4490, 4983}, {25259, 47679}, {47667, 47678}, {47698, 47712}, {47699, 47711}
X(47997) = reflection of X(4823) in X(4129)
X(47997) = crossdifference of every pair of points on line {31, 16884}
X(47997) = barycentric product X(1)*X(47655)
X(47997) = barycentric quotient X(47655)/X(75)

X(47998) = X(513)X(3004)∩X(514)X(3716)

X(47998) = 3 X[661] - X[4088], 5 X[661] - X[47700], 3 X[661] + X[47702], 5 X[4088] - 3 X[47700], X[4088] + 3 X[47701], X[47700] + 5 X[47701], 3 X[47700] + 5 X[47702], 3 X[47701] - X[47702], 3 X[1491] - 2 X[4925], 2 X[2977] - 3 X[4893], 2 X[3837] - 3 X[47756], 2 X[4369] - 3 X[47799], 3 X[4728] - X[47703], 3 X[4776] - X[47690], X[7192] - 3 X[47797], X[7659] - 3 X[47880], 2 X[9508] - 3 X[47784], 4 X[25666] - 3 X[47807], 3 X[30565] - X[47693], X[47660] - 3 X[47821]

X(47998) lies on these lines: {513, 3004}, {514, 3716}, {523, 661}, {525, 4983}, {676, 1459}, {693, 47699}, {1491, 4925}, {2512, 47842}, {2977, 4893}, {3566, 4822}, {3667, 4818}, {3776, 4778}, {3800, 4705}, {3837, 47756}, {4170, 47679}, {4369, 47799}, {4458, 28840}, {4468, 4802}, {4728, 47703}, {4770, 12073}, {4776, 47690}, {4784, 17069}, {4809, 28209}, {4976, 29328}, {7192, 47797}, {7659, 47880}, {9508, 47784}, {14208, 30591}, {14349, 29142}, {23729, 29362}, {25666, 47807}, {26275, 28859}, {28175, 47826}, {30565, 47693}, {47660, 47821}, {47666, 47691}, {47692, 47698}

X(47998) = midpoint of X(i) and X(j) for these {i,j}: {661, 47701}, {693, 47699}, {4088, 47702}, {4170, 47679}, {4804, 4988}, {4822, 21124}, {47666, 47691}, {47692, 47698}
X(47998) = reflection of X(i) in X(j) for these {i,j}: {3700, 4806}, {4122, 14321}, {4784, 17069}
X(47998) = crossdifference of every pair of points on line {58, 3730}
X(47998) = barycentric product X(i)*X(j) for these {i,j}: {523, 26626}, {1577, 16475}, {4064, 31910}
X(47998) = barycentric quotient X(i)/X(j) for these {i,j}: {16475, 662}, {26626, 99}
X(47998) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47702, 4088}, {4088, 47701, 47702}

X(47999) = X(513)X(3004)∩X(514)X(3837)

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

X(47999) lies on these lines: {513, 3004}, {514, 3837}, {649, 47877}, {1638, 28220}, {2526, 29144}, {4122, 47653}, {4369, 4977}, {4778, 21212}, {4784, 23731}, {4818, 29328}, {4824, 47652}, {18004, 28863}, {24623, 47686}, {24719, 45746}, {28195, 47766}, {47696, 47822}

X(47999) = midpoint of X(i) and X(j) for these {i,j}: {4122, 47653}, {4784, 23731}, {4824, 47652}, {24719, 45746}

X(48000) = X(241)X(514)∩X(513)X(4507)

X(48000) = 4 X[650] - 3 X[4763], 3 X[650] - 2 X[31286], 3 X[650] - X[43067], 5 X[650] - 3 X[47761], X[3004] - 3 X[47876], 2 X[3676] - 3 X[47882], 2 X[4369] - 3 X[4763], 3 X[4369] - 4 X[31286], 3 X[4369] - 2 X[43067], 5 X[4369] - 6 X[47761], 9 X[4763] - 8 X[31286], 9 X[4763] - 4 X[43067], 5 X[4763] - 4 X[47761], X[21104] - 3 X[47784], 2 X[21212] - 3 X[47784], 10 X[31286] - 9 X[47761], 5 X[43067] - 9 X[47761], X[649] - 3 X[31150], 3 X[31150] + X[47666], 3 X[661] - X[20295], 5 X[661] - 3 X[47759], X[661] - 3 X[47775], 3 X[17494] + X[20295], 5 X[17494] + 3 X[47759], X[17494] + 3 X[47775], 5 X[20295] - 9 X[47759], X[20295] - 9 X[47775], X[47759] - 5 X[47775], X[693] - 3 X[4893], 2 X[693] - 3 X[4928], 3 X[693] - 5 X[30835], 3 X[4893] - 2 X[25666], 9 X[4893] - 5 X[30835], 3 X[4928] - 4 X[25666], 9 X[4928] - 10 X[30835], 6 X[25666] - 5 X[30835], 3 X[1635] - X[7192], 3 X[1635] - 5 X[26777], X[7192] - 5 X[26777], X[2254] - 3 X[47825], 4 X[2516] - 3 X[45313], 3 X[3835] - 2 X[23813], 2 X[3835] - 3 X[45315], 4 X[23813] - 9 X[45315], X[4024] - 3 X[30565], 3 X[30565] + X[47661], X[4025] - 3 X[47883], X[4106] - 3 X[47777], 3 X[4379] - 5 X[31209], 3 X[4379] - X[47675], 5 X[31209] - X[47675], X[4382] - 3 X[4776], 3 X[4776] + X[47664], 4 X[4521] - 3 X[47879], X[4608] - 9 X[31992], 3 X[4728] - X[26824], 3 X[4789] - X[47671], X[4804] - 3 X[47821], X[4838] - 3 X[47870], 2 X[4885] - 3 X[47778], X[4979] - 3 X[47776], X[31290] + 3 X[47776], X[4988] + 3 X[6546], 3 X[6546] - X[47660], X[16892] - 3 X[47782], X[17161] + 3 X[47772], X[21146] - 3 X[47827], 2 X[25380] - 3 X[47827], 5 X[24924] - 7 X[27115], 5 X[24924] - 6 X[45675], 5 X[24924] - 3 X[47780], 7 X[27115] - 6 X[45675], 7 X[27115] - 3 X[47780], X[26853] + 3 X[47774], 5 X[26985] - 6 X[45678], 5 X[27013] - 3 X[31148], 7 X[27138] - 3 X[47869], X[45746] - 3 X[47878], 7 X[31207] - 6 X[45663], 4 X[31287] - 3 X[47779], X[46403] - 3 X[47810], 3 X[46915] - X[47673], X[47655] - 3 X[47873], X[47656] - 3 X[47874], X[47663] + 3 X[47781], X[47667] + 3 X[47771], X[47670] - 3 X[47792], X[47676] - 3 X[47886], X[47694] - 3 X[47811], X[47703] - 3 X[47809], X[47704] - 3 X[47797]

X(48000) lies on these lines: {2, 47672}, {241, 514}, {513, 4507}, {523, 3716}, {649, 28840}, {659, 4824}, {661, 812}, {693, 4893}, {824, 4468}, {918, 21196}, {1577, 29771}, {1635, 7192}, {2254, 47825}, {2516, 45313}, {2786, 4976}, {3239, 4500}, {3762, 18155}, {3768, 29545}, {3798, 28878}, {3835, 4762}, {3907, 4490}, {4024, 30565}, {4025, 28851}, {4106, 47777}, {4379, 31209}, {4380, 4813}, {4382, 4776}, {4394, 4932}, {4521, 47879}, {4608, 31992}, {4705, 29051}, {4728, 26824}, {4765, 28846}, {4770, 29188}, {4789, 47671}, {4801, 30024}, {4802, 4874}, {4804, 47821}, {4838, 47870}, {4885, 47778}, {4897, 28855}, {4977, 9508}, {4978, 18154}, {4979, 31290}, {4988, 6546}, {7199, 29404}, {7659, 28225}, {7662, 28147}, {16892, 28890}, {17161, 47772}, {21146, 25380}, {21385, 29487}, {23740, 24462}, {24924, 27115}, {24948, 29457}, {25511, 47794}, {26017, 26641}, {26114, 47793}, {26248, 47773}, {26853, 47774}, {26985, 45678}, {27013, 31148}, {27138, 47869}, {27486, 28871}, {28179, 45666}, {28191, 47803}, {28863, 45746}, {28902, 45679}, {31207, 45663}, {31287, 47779}, {46403, 47810}, {46915, 47673}, {47655, 47873}, {47656, 47874}, {47659, 47669}, {47663, 47781}, {47667, 47771}, {47670, 47792}, {47676, 47886}, {47694, 47811}, {47703, 47809}, {47704, 47797}

X(48000) = midpoint of X(i) and X(j) for these {i,j}: {649, 47666}, {659, 4824}, {661, 17494}, {3762, 47683}, {4024, 47661}, {4380, 4813}, {4382, 47664}, {4468, 45745}, {4841, 47890}, {4979, 31290}, {4988, 47660}, {47659, 47669}
X(48000) = reflection of X(i) in X(j) for these {i,j}: {693, 25666}, {4369, 650}, {4500, 3239}, {4928, 4893}, {4932, 4394}, {21104, 21212}, {21146, 25380}, {43067, 31286}, {47780, 45675}
X(48000) = complement of X(47672)
X(48000) = X(i)-complementary conjugate of X(j) for these (i,j): {8708, 141}, {32009, 21252}, {40433, 116}
X(48000) = crossdifference of every pair of points on line {55, 20985}
X(48000) = barycentric product X(i)*X(j) for these {i,j}: {514, 17260}, {693, 3750}
X(48000) = barycentric quotient X(i)/X(j) for these {i,j}: {3750, 100}, {17260, 190}
X(48000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 4369, 4763}, {650, 43067, 31286}, {693, 4893, 25666}, {693, 25666, 4928}, {4776, 47664, 4382}, {4988, 6546, 47660}, {7192, 26777, 1635}, {17494, 47775, 661}, {21104, 47784, 21212}, {21146, 47827, 25380}, {24924, 27115, 45675}, {27115, 47780, 24924}, {30565, 47661, 4024}, {31150, 47666, 649}, {31209, 47675, 4379}, {31286, 43067, 4369}, {31290, 47776, 4979}

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)

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)

This is PART 24: Centers X(46001) - X(48000)

X(46001) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(2) AND X(6)

X(46002) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(5) AND X(54)

X(46003) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(7) AND X(55)

X(46004) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(8) AND X(56)

X(46005) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(20) AND X(64)

X(46006) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(9) AND X(57)

X(46007) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(11) AND X(59)

X(46008) = CENTER OF THE PANCHAPAKESAN CIRCLE OF X(186) AND X(265)

X(46009) = X(1)X(37413)∩X(2)X(1804)

X(46010) = X(2)X(1444)∩X(3)X(37)

X(46011) = X(3)X(281)∩X(4)X(6)

X(46012) = X(3)X(9)∩X(19)X(18237)

X(46013) = X(4)X(961)∩X(6)X(42467)

X(46014) = X(4)X(960)∩X(57)X(573)

X(46015) = X(6)X(104)∩X(57)X(2051)

X(46016) = X(1)X(25490)∩X(4)X(386)

X(46017) = X(1)X(9786)∩X(4)X(65)

X(46018) = X(2)X(2245)∩X(6)X(859)

X(46019) = X(4)X(6)∩X(19)X(946)

X(46020) = X(4)X(959)∩X(6)X(2050)

X(46021) = X(4)X(57)∩X(271)X(5739)

X(46022) = X(3)X(9)∩X(189)X(5739)

X(46023) = ISOGONAL CONJUGATE OF X(1340)

X(46024) = ISOGONAL CONJUGATE OF X(1341)

X(46025) = X(3)X(54)∩X(5)X(53)

X(46026) = X(4)X(83)∩X(141)X(427)

X(46027) = X(6)X(382)∩X(143)X(185)

X(46028) = EULER LINE INTERCEPT OF X(11)X(16137)

X(46029) = EULER LINE INTERCEPT OF X(113)X(15060)

X(46030) = EULER LINE INTERCEPT OF X(51)X(113)

X(46031) = EULER LINE INTERCEPT OF X(113)X(16227)

X(46032) = X(8)X(291)∩X(10)X(75)

X(46033) = X(4)X(14941)∩X(5)X(264)

X(46034) = X(4)X(6)∩X(20)X(1078)

X(46035) = X(3)X(2133)∩X(4)X(1138)

X(46036) = X(3)X(2132)∩X(4)X(2133)

X(46037) = ISOGONAL CONJUGATE OF X(38934)

X(46038) = X(2)X(914)∩(3)X(2164)

X(46039) = X(4)X(804)∩X(99)X(511)

X(46040) = X(4)X(804)∩X(98)X(512)

X(46041) = X(1)X(1769)∩X(4)X(900)

X(46042) = X(4)X(926)∩X(103)X(514)

X(46043) = X(4)X(2457)∩X(519)X(1293)

X(46044) = X(4)X(14266)∩X(100)X(517)

X(46045) = X(4)X(523)∩X(30)X(110)

X(46046) = X(4)X(512)∩X(99)X(511)

X(46047) = X(4)X(525)∩X(112)X(1503)

X(46048) = X(2)X(98)∩X(3081)X(8029)

X(46049) = X(2)X(690)∩X(524)X(10190)

X(46050) = X(2)X(900)∩X(519)X(10196)

X(46051) = X(2)X(812)∩X(4375)X(27855)

X(46052) = X(2)X(1637)∩X(2395)X(43673)

X(46053) = X(2)X(14)∩X(16)X(115)

X(46054) = X(2)X(13)∩X(15)X(115)

X(46055) = X(14)X(36248)∩X(15)X(302)

X(46056) = X(13)X(36249)∩X(16)X(303)

X(46057) = X(4)X(51)∩X(520)X(6587)

X(46058) = X(13)X(2992)∩X(14)X(14372)

X(46059) = X(13)X(14373)∩X(14)X(2993)

X(46060) = X(14)X(19776)∩X(16)X(3440)

X(46061) = X(13)X(19777)∩X(15)X(3441)

X(46062) = X(30)X(511)∩X(9409)X(11587)

X(46063) = X(30)X(511)∩X(1301)X(32713)

X(46064) = X(30)X(3484)∩X(54)X(3575)

X(46065) = X(2)X(1032)∩X(393)X(459)

X(46066) = EULER LINE INTERCEPT OF X(1511)X(18800)

X(46067) = EULER LINE INTERCEPT OF X(113)X(18800)

X(46068) = EULER LINE INTERCEPT OF X(10272)X(18800)

X(46069) = EULER LINE INTERCEPT OF X(16163)X(18800)

X(46070) = EULER LINE INTERCEPT OF X(16165)X(18800)

X(46071) = X(13)-CEVA CONJUGATE OF X(39153)

X(46072) = ISOGONAL CONJUGATE OF X(5616)

X(46073) = ISOGONAL CONJUGATE OF X(39152)

X(46074) = X(13)-CEVA CONJUGATE OF X(14)

X(46075) = X(13)X(79)∩X(14)X(37772)

X(46076) = ISOGONAL CONJUGATE OF X(5612)

X(46077) = X(13)-ISOCONJUGATE OF X(36)

X(46078) = X(14)-CEVA CONJUGATE OF X(13)

X(46079) = X(16)X(3815)∩X(381)X(396)