X(73009) = X(4)X(1854)∩X(46)X(80)
Barycentrics (2*a^4-a^3*b-a^2*b^2+a*b^3-b^4-a^3*c+2*a^2*b*c-a*b^2*c-a^2*c^2-a*b*c^2+2*b^2*c^2+a*c^3-c^4)*(2*a^6-a^5*b-a^4*b^2+2*a^3*b^3-4*a^2*b^4-a*b^5+3*b^6-a^5*c+2*a^4*b*c-2*a^3*b^2*c+3*a*b^4*c-2*b^5*c-a^4*c^2-2*a^3*b*c^2+8*a^2*b^2*c^2-2*a*b^3*c^2-3*b^4*c^2+2*a^3*c^3-2*a*b^2*c^3+4*b^3*c^3-4*a^2*c^4+3*a*b*c^4-3*b^2*c^4-a*c^5-2*b*c^5+3*c^6) : :X(73909) = 2*X[4]-X[38357], X[102]-2*X[60758], 2*X[117]-X[38554], 4*X[117]-3*X[51408], 2*X[1535]-X[51424], 2*X[1542]-X[51361], X[10017]-2*X[72517], 2*X[38554]-3*X[51408], X[2968]-2*X[67226], X[10726]+X[18339], 2*X[15252]-X[67464]
Let A'B'C' be the orthic triangle, P a point and Pa, Pb, Pc the P-points of AB'C', A'BC', A'B'C, resp. The perpendiculars from Pa, Pb, Pc to BC, CA, AB, resp. are concurrent. The locus of the point of concurrence, which always is the crosssum of X(3) and P, is a conic passing through X(i) for i = 125, 1146, 1562, 13202, 38357, 38388, 38389, 57424, 57430, 57445, 72568, 73909, 73910, 73911, here named Hatzipolakis - García Capitán conic.
Antreas Hatzipolakis and Francisco Javier García Capitán conic, euclid 10286.
X(73009) lies on the Hatzipolakis - García Capitán conic and these lines: {4, 1854}, {19, 1146}, {46, 80}, {102, 60758}, {117, 515}, {125, 407}, {208, 1837}, {900, 42755}, {952, 10696}, {1503, 41499}, {1562, 1901}, {1718, 63988}, {1783, 5776}, {1827, 38388}, {1828, 12688}, {1844, 7686}, {1845, 6001}, {1846, 57445}, {2968, 64507}, {10726, 18339}, {15252, 67464}, {18391, 67169}, {18480, 19904}
X(73009) = midpoint of X(10726) and X(18339)
X(73009) = reflection of X(i) in X(j) for these {i,j}: {102, 60758}, {2968, 67226}, {10017, 72517}, {38357, 4}, {38554, 117}, {51361, 1542}, {51424, 1535}, {67464, 15252}
X(73009) = crosspoint and X(4) and X(515)
X(73009) = crosssum of X(3) and X(102)
X(73009) = orthopole of trilinear polar of X(52780)
X(73009) = Zosma transform of X(36121)
X(73009) = intersection, other than A, B, C, of the circumconics: {{A,B,C,X(4),X(38554)}, {A,B,C,X(80),X(51375)}, {A,B,C,X(84),X(11700)}, {A,B,C,X(36121),X(46974)}, {A,B,C,X(36127),X(66957)}}
X(73009) = center of circle {X(i),X(j),X(k)} for these {i,j,k}: {10726, 10771, 18339}
X(73009) = foot of the perpendicular from X(i) to the line X(j)X(k) for these {i,j,k}: {42755, 10696, 10740}, {10696, 42755, 52836}
X(73009) = pole of line {39471, 53152} with respect to the polar circle
X(73009) = pole of tripolar of X(515) with respect to the orthic inconic
X(73009) = pole of line {125, 2968} with respect to the orthoptic circle of Jerabek hyperbola
X(73009) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {117, 38554, 51408}
X(73010) = X(4)X(1146)∩X(33)X(1836)
Barycentrics (2*a^3-a^2*b-b^3-a^2*c+b^2*c+b*c^2-c^3)*(2*a^5-a^4*b-2*a^2*b^3-2*a*b^4+3*b^5-a^4*c+2*a^2*b^2*c-b^4*c+2*a^2*b*c^2+4*a*b^2*c^2-2*b^3*c^2-2*a^2*c^3-2*b^2*c^3-2*a*c^4-b*c^4+3*c^5) : :X(73910) = 2*X[4]-X[1146], X[20]-2*X[17044], 2*X[103]-3*X[61673], X[103]-2*X[68552], 3*X[61673]-4*X[68552], 4*X[118]-3*X[51406], 2*X[118]-X[65745], 2*X[118]-3*X[72418], X[910]-2*X[1541], 2*X[1530]-X[17747], 3*X[51406]-2*X[65745], X[51406]-2*X[72418], X[65745]-3*X[72418], X[664]+X[3146], X[1121]-3*X[50687], X[1565]-2*X[31851], 3*X[1699]-2*X[62674], 5*X[3091]-4*X[40483], 7*X[3832]-5*X[31640], 3*X[9812]-X[14942], X[10727]+X[67568], 5*X[17578]-X[39351], X[33521]-2*X[58898], X[39357]+3*X[62032], 2*X[65808]-X[67721]
Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 10286.
X(73010) lies the circunconic {{A,B,C,X(4),X(65745)}}, the Hatzipolakis - García Capitán conic and these lines: {4, 1146}, {20, 17044}, {30, 35110}, {33, 1836}, {65, 38388}, {103, 61673}, {118, 516}, {125, 430}, {152, 5845}, {223, 9580}, {528, 1750}, {664, 3146}, {952, 10725}, {1086, 60017}, {1121, 50687}, {1360, 69805}, {1503, 52468}, {1562, 1834}, {1565, 31851}, {1699, 62674}, {1824, 38389}, {1830, 1864}, {2785, 39838}, {2901, 22035}, {2910, 41869}, {3058, 20277}, {3091, 40483}, {3543, 64462}, {3832, 31640}, {4872, 70607}, {6001, 71374}, {6366, 52836}, {9579, 62793}, {9812, 14942}, {10727, 67568}, {17578, 39351}, {18328, 53804}, {33521, 58898}, {36990, 64130}, {39357, 62032}, {65808, 67721}
X(73010) = midpoint of X(i) and X(j) for these {i,j}: {664, 3146}, {10727, 67568}
X(73010) = reflection of X(i) in X(j) for these {i,j}: {20, 17044}, {103, 68552}, {910, 1541}, {1146, 4}, {1565, 31851}, {17747, 1530}, {33521, 58898}, {51406, 72418}, {65745, 118}, {67721, 65808}
X(73010) = reflection of X(i) in X(j)X(k) for these {i,j,k}}: {1566, 4, 514}
X(73010) = crosspoint of X(4) and X(516)
X(73010) = crossum of X(3) and X(103)
X(73010) = Zosma transform of X(36122)
X(73010) = orthopole of trilinear polar of X(52781)
X(73010) = pole of line {39470, 53150} with respect to the polar circle
X(73010) = pole of line {1886, 69787} with respect to the Kiepert hyperbola
X(73010) = pole of tripolar of X(516) with respect to the orthic inconic
X(73010) = pole of line {125, 1565} with respect to the orthoptic circle of Jerabek hyperbola
X(73010) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {103, 68552, 61673}, {118, 65745, 51406}, {65745, 72418, 118}
X(73011) = X(4)X(151)∩X(40)X(13724)
Barycentrics a*(a^2*b-b^3+a^2*c-2*a*b*c+b^2*c+b*c^2-c^3)*(a^5*b-2*a^3*b^3+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^3*b*c^2+2*a*b^3*c^2-2*a^3*c^3+2*a*b^2*c^3-4*b^3*c^3-3*a*b*c^4+a*c^5+2*b*c^5) : :X(73011) = 2*X[4]-X[38389], 2*X[104]-3*X[61674], X[104]-3*X[61731], X[61674]-2*X[61731], 4*X[119]-3*X[61672], 2*X[119]-X[65743], 2*X[119]-3*X[72417], 2*X[1512]-X[51377], X[3259]-2*X[72518], 3*X[61672]-2*X[65743], X[61672]-2*X[72417], X[65743]-3*X[72417], X[3937]-2*X[31849], 2*X[3035]-X[67420], 2*X[6713]-3*X[67216], 2*X[12019]-X[34462], X[31847]-2*X[67864], 3*X[34583]-2*X[38759], 2*X[38390]-3*X[59390], 3*X[38693]-4*X[64489], X[38761]-2*X[67414], 5*X[64008]-3*X[67634], X[67494]-2*X[68548]
Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 10286.
X(73011) lies the circunconic {{A,B,C,X(4),X(65743)}}, the Hatzipolakis - García Capitán conic and these lines: {4, 151}, {40, 13724}, {65, 1830}, {80, 2807}, {102, 52242}, {104, 61674}, {117, 867}, {119, 517}, {125, 429}, {153, 2810}, {185, 1837}, {355, 15030}, {513, 52836}, {957, 8166}, {962, 2899}, {1146, 1826}, {1361, 35015}, {1562, 53417}, {1863, 5185}, {2197, 17452}, {2779, 6246}, {2800, 22321}, {2808, 9803}, {2815, 3762}, {2823, 12736}, {2829, 3937}, {2841, 34789}, {3035, 67420}, {3040, 24410}, {3753, 25019}, {5086, 5907}, {5151, 6001}, {6256, 23154}, {6713, 67216}, {10724, 29349}, {12019, 34462}, {14127, 38607}, {17516, 63435}, {21044, 34457}, {21664, 42759}, {22306, 41507}, {22799, 61638}, {31847, 67864}, {34583, 38759}, {37437, 67968}, {38390, 59390}, {38693, 64489}, {38761, 67414}, {45022, 53548}, {53530, 72581}, {64008, 67634}, {67494, 68548}
X(73011) = reflection of X(i) in X(j) for these {i,j}: {3259, 72518}, {3937, 31849}, {31847, 67864}, {34462, 12019}, {38389, 4}, {38761, 67414}, {51377, 1512}, {61672, 72417}, {61674, 61731}, {65743, 119}, {67420, 3035}, {67494, 68548}
X(73011) = crosspoint of X(4) and X(517)
X(73011) = crosssum of X(3) and X(104)
X(73011) = perspector of the circumconic through X(2397)and X(26011)
X(73011) = orthopole of tripolar of X(16082)
X(73011) = Zosma transform of X(36123)
X(73011) = foot of the perpendicular from X(i) to the line X(j)X(k) for these {i,j,k}: {52836, 119, 908}
X(73011) = pole of line {8677, 43933} with respect to the polar circle
X(73011) = pole of line {1877, 12138} with respect to the Feuerbach hyperbola
X(73011) = pole of tripolar of X(517) with respect to the orthic inconic
X(73011) = pole of tripolar of X(15420) with respect to the orthoptic circle of Jerabek hyperbola
X(73011) = barycentric product X(517)*X(26011)
X(73011) = barycentric quotient X(26011)/X(18816)
X(73011) = trilinear product X(2183)*X(26011)
X(73011) = trilinear quotient X(26011)/X(34234)
X(73011) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {119, 65743, 61672}, {65743, 72417, 119}
X(73012) = X(2)X(9705)∩X(3)X(41586)
Barycentrics 2*a^10-6*a^8*b^2+7*a^6*b^4-5*a^4*b^6+3*a^2*b^8-b^10-6*a^8*c^2+11*a^4*b^4*c^2-8*a^2*b^6*c^2+3*b^8*c^2+7*a^6*c^4+11*a^4*b^2*c^4+10*a^2*b^4*c^4-2*b^6*c^4-5*a^4*c^6-8*a^2*b^2*c^6-2*b^4*c^6+3*a^2*c^8+3*b^2*c^8-c^10 : :X(73012) = 3*X[2]+X[10116], X[3]+3*X[43573], X[3]+X[58806], 3*X[43573]-X[58806], X[5]+X[18128], 2*X[40240]-3*X[58807], 3*X[6689]+X[32377], 3*X[140]+X[11264], X[143]-3*X[32068], 9*X[373]-X[64036], 3*X[547]+X[45732], 3*X[549]+X[10112], 5*X[631]+3*X[61713], X[44862]+2*X[50476], X[1216]+3*X[11245], X[1885]+3*X[40647], 3*X[3819]+X[32358], X[5446]+X[17712], X[5447]+X[13292], 3*X[5462]-X[6756], X[5462]-3*X[45298], X[6756]-9*X[45298], 3*X[5892]+X[6146], 3*X[5946]+X[44829], X[32142]+X[32165], X[6101]+3*X[11225], X[6240]-9*X[9730], X[6243]-9*X[61712], X[10114]+3*X[34128], 5*X[10574]-X[43577], X[10627]+3*X[45969], X[11232]+3*X[64730], X[11565]+3*X[12006], X[11750]+7*X[15043], X[11793]+X[43588], X[12370]+3*X[16836], X[12897]+3*X[64100], 3*X[13364]-X[67322], X[13382]+X[52073], X[13419]-5*X[15026], X[13421]+3*X[60749], X[14449]-3*X[61677], X[14641]+3*X[16657], 9*X[14845]-X[16659], X[16656]-2*X[44871], 9*X[40280]-X[72735]
Antreas Hatzipolakis and Ercole Suppa, euclid 10288.
X(73012) lies on these lines: {2, 9705}, {3, 41586}, {4, 12834}, {5, 18128}, {30, 12002}, {54, 14156}, {125, 6689}, {140, 539}, {143, 32068}, {182, 5449}, {373, 64036}, {542, 3628}, {547, 45732}, {549, 10112}, {569, 18911}, {575, 13371}, {631, 61713}, {1154, 44862}, {1173, 5189}, {1199, 51392}, {1209, 43808}, {1216, 11245}, {1503, 23411}, {1568, 43845}, {1885, 40647}, {1899, 14786}, {3153, 43600}, {3542, 64049}, {3574, 15037}, {3819, 32358}, {4550, 18909}, {5012, 14940}, {5055, 56516}, {5092, 63734}, {5446, 17712}, {5447, 13292}, {5462, 6756}, {5892, 6146}, {5946, 44829}, {5965, 32142}, {6101, 11225}, {6240, 9730}, {6243, 61712}, {6723, 58407}, {7507, 36752}, {7514, 52104}, {8550, 41597}, {9140, 46865}, {9704, 72733}, {9729, 17702}, {9927, 37514}, {10095, 29012}, {10114, 34128}, {10574, 43577}, {10610, 44673}, {10619, 43809}, {10627, 45969}, {11232, 64730}, {11565, 12006}, {11750, 15043}, {11793, 43588}, {12038, 22966}, {12242, 36153}, {12254, 43584}, {12370, 16836}, {12897, 64100}, {13154, 34507}, {13160, 36253}, {13336, 18912}, {13364, 67322}, {13366, 37452}, {13382, 52073}, {13419, 15026}, {13421, 60749}, {13434, 35482}, {13619, 43603}, {13630, 63683}, {13754, 64038}, {14449, 61677}, {14627, 51360}, {14641, 16657}, {14845, 16659}, {16003, 35500}, {16534, 50143}, {16656, 44871}, {16982, 19924}, {18356, 24206}, {18475, 68720}, {23060, 25338}, {25555, 50138}, {25738, 43650}, {26879, 37513}, {30551, 32267}, {31804, 43586}, {32046, 43839}, {32136, 33749}, {32767, 50664}, {35488, 66609}, {36201, 63697}, {40280, 72735}
X(73012) = midpoint of X(i) and X(j) for these {i,j}: {3, 58806}, {5, 18128}, {5446, 17712}, {5447, 13292}, {11793, 43588}, {13382, 52073}, {32142, 32165}
X(73012) = reflection of X(16656) in X(44871)
X(73012) = QAP1: Quadrangle Centroid of X(10116)
X(73012) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 43573, 58806}, {125, 13353, 6689}, {182, 18952, 5449}, {5012, 43817, 44516}, {32142, 32165, 5965}, {36153, 37938, 12242}
X(73013) = X(3)X(54)∩X(20)X(45185)
Barycentrics a^2*(a^8-5*a^6*b^2+9*a^4*b^4-7*a^2*b^6+2*b^8-5*a^6*c^2+19*a^4*b^2*c^2-11*a^2*b^4*c^2-3*b^6*c^2+9*a^4*c^4-11*a^2*b^2*c^4+2*b^4*c^4-7*a^2*c^6-3*b^2*c^6+2*c^8) : :X(73013) = 2*X[26863]-3*X[43614]
Antreas Hatzipolakis and Ercole Suppa, euclid 10288.
X(73013) lies on these lines: {3, 54}, {20, 45185}, {110, 15644}, {140, 1173}, {323, 13348}, {376, 15083}, {394, 33524}, {576, 61820}, {578, 41462}, {631, 53863}, {930, 43994}, {1092, 38435}, {1147, 6030}, {1216, 14865}, {1350, 11449}, {2071, 15606}, {2889, 44450}, {3146, 14826}, {3292, 16661}, {3518, 10625}, {3523, 67302}, {3525, 5643}, {3627, 54040}, {3628, 59776}, {5198, 15066}, {5447, 13434}, {5562, 13445}, {5876, 16835}, {5888, 13154}, {6243, 43584}, {7998, 37498}, {9706, 67321}, {9970, 55597}, {10303, 15019}, {10594, 64050}, {10982, 44299}, {11004, 13347}, {11403, 15056}, {11440, 37480}, {11444, 35502}, {11591, 43576}, {11592, 14627}, {12100, 43600}, {12103, 14094}, {12111, 41468}, {13336, 13472}, {13340, 17714}, {13346, 33884}, {13391, 18369}, {13564, 43572}, {14130, 72921}, {14157, 63414}, {15004, 61834}, {15062, 23039}, {15582, 41464}, {26863, 43614}, {32142, 37496}, {33923, 43602}, {35479, 37486}, {41597, 52525}, {43652, 62188}, {44245, 63720}, {44879, 68659}, {52093, 58891}, {54173, 66731}, {58922, 71230}
X(73013) = intersection, other than A, B, C, of the circumconics: {{A,B,C,X(54),X(26862)}, {A,B,C,X(11423),X(15318)}}
X(73013) = pole of the line {5, 14862} with respect to Stammler hyperbola
X(73013) = pole of the line {550, 11565} with respect to Stammler reflection hyperbola
X(73013) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1493, 61134}, {3, 16266, 11423}, {20, 45185, 54036}, {11423, 54041, 3}
X(73014) = X(4)X(16880)∩X(30)X(67739)
Barycentrics (2*a^4 + a^2*b^2 + 2*b^4 - 4*a^2*c^2 - 4*b^2*c^2 + 2*c^4)*(2*a^4 - 4*a^2*b^2 + 2*b^4 + a^2*c^2 - 4*b^2*c^2 + 2*c^4)*(2*a^8 - 4*a^6*b^2 + 4*a^2*b^6 - 2*b^8 - 4*a^6*c^2 + 8*a^4*b^2*c^2 - 5*a^2*b^4*c^2 + b^6*c^2 - 5*a^2*b^2*c^4 + 2*b^4*c^4 + 4*a^2*c^6 + b^2*c^6 - 2*c^8) : :Antreas Hatzipolakis and Peter Moses, euclid 10293.
X(73014) lies on the cubic K025 and these lines: {4, 16880}, {30, 67739}
X(73014) = polar circle inverse of X(16880)
X(73014) = antigonal image of X(15646)
X(73015) = X(4)X(3167)∩X(141)X(631)
Barycentrics 15*a^10 - 43*a^8*b^2 + 42*a^6*b^4 - 18*a^4*b^6 + 7*a^2*b^8 - 3*b^10 - 43*a^8*c^2 + 52*a^6*b^2*c^2 - 14*a^4*b^4*c^2 - 4*a^2*b^6*c^2 + 9*b^8*c^2 + 42*a^6*c^4 - 14*a^4*b^2*c^4 - 6*a^2*b^4*c^4 - 6*b^6*c^4 - 18*a^4*c^6 - 4*a^2*b^2*c^6 - 6*b^4*c^6 + 7*a^2*c^8 + 9*b^2*c^8 - 3*c^10 : :X(73015) = 7 X[3090] - 4 X[15077], 5 X[631] - 8 X[45248], 5 X[631] - 4 X[58378], 3 X[376] - 4 X[27082], 5 X[3529] - 8 X[44788], 8 X[3532] - 11 X[21735], 9 X[3545] - 8 X[68009], 16 X[43592] - 19 X[61886]
Antreas Hatzipolakis and Peter Moses, euclid 10300.
X(73015) lies on these lines: {4, 3167}, {24, 19588}, {54, 3090}, {68, 52290}, {110, 6622}, {141, 631}, {376, 5562}, {1092, 39874}, {1147, 8889}, {1498, 3529}, {3528, 40912}, {3532, 21735}, {3545, 12241}, {3855, 7699}, {5446, 7714}, {5663, 45771}, {5889, 63174}, {6101, 59346}, {6193, 6353}, {10721, 12383}, {11793, 18925}, {12134, 62975}, {12162, 66735}, {12309, 37777}, {12324, 24981}, {13754, 25712}, {14516, 64177}, {14912, 14913}, {16195, 20080}, {17538, 35253}, {34774, 63428}, {37669, 61751}, {38282, 64756}, {43592, 61886}
X(73015) = reflection of X(i) in X(j) for these {i,j}: {4, 32605}, {58378, 45248}
X(73016) = X(4)X(5609)∩X(3830)X(13530)
Barycentrics 8*a^16-32*a^14*b^2+56*a^12*b^4-64*a^10*b^6+40*a^8*b^8+32*a^6*b^10-88*a^4*b^12+64*a^2*b^14-16*b^16-32*a^14*c^2+82*a^12*b^2*c^2-75*a^10*b^4*c^2+25*a^8*b^6*c^2-65*a^6*b^8*c^2+237*a^4*b^10*c^2-272*a^2*b^12*c^2+100*b^14*c^2+56*a^12*c^4-75*a^10*b^2*c^4+60*a^8*b^4*c^4+8*a^6*b^6*c^4-201*a^4*b^8*c^4+432*a^2*b^10*c^4-280*b^12*c^4-64*a^10*c^6+25*a^8*b^2*c^6+8*a^6*b^4*c^6+104*a^4*b^6*c^6-224*a^2*b^8*c^6+476*b^10*c^6+40*a^8*c^8-65*a^6*b^2*c^8-201*a^4*b^4*c^8-224*a^2*b^6*c^8-560*b^8*c^8+32*a^6*c^10+237*a^4*b^2*c^10+432*a^2*b^4*c^10+476*b^6*c^10-88*a^4*c^12-272*a^2*b^2*c^12-280*b^4*c^12+64*a^2*c^14+100*b^2*c^14-16*c^16 : :X(73016) = X[4]+X[52173], X[3830]+X[13530], 3*X[5055]-X[53693]
Marian Cucoanes and Ercole Suppa, euclid 10307.
X(73016) lies on these lines: {4, 5609}, {3830, 13530}, {5055, 53693}, {44266, 67872}
X(73016) = midpoint of X(i) and X(j) for these {i,j}: {4, 52173}, {3830, 13530}
X(73016) = center of the orthopolar conic of X(52173)
X(73017) = X(4)X(195)∩X(5)X(930)
Barycentrics 2*a^16-9*a^14*b^2+17*a^12*b^4-17*a^10*b^6+5*a^8*b^8+13*a^6*b^10-21*a^4*b^12+13*a^2*b^14-3*b^16-9*a^14*c^2+26*a^12*b^2*c^2-29*a^10*b^4*c^2+18*a^8*b^6*c^2-25*a^6*b^8*c^2+56*a^4*b^10*c^2-57*a^2*b^12*c^2+20*b^14*c^2+17*a^12*c^4-29*a^10*b^2*c^4+20*a^8*b^4*c^4+3*a^6*b^6*c^4-44*a^4*b^8*c^4+93*a^2*b^10*c^4-60*b^12*c^4-17*a^10*c^6+18*a^8*b^2*c^6+3*a^6*b^4*c^6+18*a^4*b^6*c^6-49*a^2*b^8*c^6+108*b^10*c^6+5*a^8*c^8-25*a^6*b^2*c^8-44*a^4*b^4*c^8-49*a^2*b^6*c^8-130*b^8*c^8+13*a^6*c^10+56*a^4*b^2*c^10+93*a^2*b^4*c^10+108*b^6*c^10-21*a^4*c^12-57*a^2*b^2*c^12-60*b^4*c^12+13*a^2*c^14+20*b^2*c^14-3*c^16 : :X(73017) = 3*X[2]-4*X[25339], X[3]-3*X[25147], X[4]+X[1263], 3*X[4]+X[38587], 3*X[1263]-X[38587], 3*X[5]-X[930], 2*X[5]-X[6592], 5*X[5]-3*X[57316], 2*X[930]-3*X[6592], 5*X[930]-9*X[57316], 5*X[6592]-6*X[57316], 2*X[137]-X[12026], 3*X[137]-X[38618], 5*X[137]-X[63409], 3*X[12026]-2*X[38618], 5*X[12026]-2*X[63409], 5*X[38618]-3*X[63409], X[128]-2*X[3850], 3*X[140]-4*X[58432], X[140]-2*X[61594], 2*X[58432]-3*X[61594], 3*X[381]+X[11671], 3*X[381]-X[14072], X[11671]+X[14072], X[382]+3*X[47065], 3*X[547]-2*X[13372], X[548]-2*X[34837], X[550]+X[44976], X[550]-3*X[57324], X[44976]+3*X[57324], 5*X[632]-3*X[38706], X[1141]+X[3627], 5*X[3091]-X[13512], 5*X[3091]-3*X[23237], X[13512]-3*X[23237], 2*X[3530]-X[63412], 2*X[3628]-3*X[23516], 2*X[3628]-X[38615], 3*X[23516]-X[38615], 7*X[3832]-X[23238], 5*X[3843]-X[67091], 3*X[3845]-X[31656], 7*X[3857]-X[38681], 5*X[3858]-X[14073], 3*X[5066]-2*X[61587], X[6343]-3*X[61715], 5*X[12812]-4*X[58429], 3*X[13451]-2*X[68069], 3*X[15687]-X[44981], X[15704]-3*X[38710]
Marian Cucoanes and Ercole Suppa, euclid 10307.
X(73017) lies on the circumconic {{A,B,C,X(25148),X(68638)}} and these lines: {2, 25339}, {3, 25147}, {4, 195}, {5, 930}, {30, 137}, {128, 3850}, {140, 58432}, {381, 11671}, {382, 47065}, {546, 25150}, {547, 13372}, {548, 34837}, {550, 44976}, {632, 38706}, {1141, 3627}, {1154, 24306}, {3091, 13512}, {3530, 63412}, {3574, 20030}, {3583, 14101}, {3628, 23516}, {3832, 23238}, {3843, 67091}, {3845, 31656}, {3857, 38681}, {3858, 14073}, {5066, 61587}, {5899, 14652}, {6343, 61715}, {8254, 10285}, {11801, 45147}, {12812, 58429}, {13451, 68069}, {14143, 68467}, {15367, 61750}, {15687, 44981}, {15704, 38710}, {18378, 34418}, {20414, 22051}, {24144, 27423}, {38640, 55857}, {38683, 61988}, {45258, 61548}, {61504, 72664}
X(73017) = midpoint of X(i) and X(j) for these {i,j}: {4, 1263}, {550, 44976}, {1141, 3627}, {11671, 14072}
X(73017) = reflection of X(i) in X(j) for these {i,j}: {128, 3850}, {140, 61594}, {548, 34837}, {6592, 5}, {12026, 137}, {27423, 30531}, {31675, 22051}, {38615, 3628}, {61504, 72664}, {61548, 45258}, {63412, 3530}
X(73017) = center of circle {X(3448), X(11671), X(14072)}
X(73017) = center of the orthopolar conic of X(1263)
X(73017) = foot of the perpendicular from X(i) to the line X(j)X(k) for these {i,j,k}: {11801, 4, 195}, {4, 11801, 68330}
X(73017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 1263, 32423}, {381, 11671, 14072}, {3091, 13512, 23237}, {23516, 38615, 3628}, {44976, 57324, 550}
X(73918) = X(4)X(1511)∩X(30)X(20480)
Barycentrics (3*a^4-a^2*b^2-2*b^4-a^2*c^2+4*b^2*c^2-2*c^4)*(2*a^6-2*a^4*b^2-2*a^2*b^4+2*b^6-3*a^4*c^2+5*a^2*b^2*c^2-3*b^4*c^2+c^6)*(2*a^6-3*a^4*b^2+b^6-2*a^4*c^2+5*a^2*b^2*c^2-2*a^2*c^4-3*b^2*c^4+2*c^6) : :X(73018) = 2*X[550]-X[67739]
Marian Cucoanes and Ercole Suppa, euclid 10307.
X(73018) lies on the circumconic with center X(550), the cubics K025, K446 and these lines: {4, 1511}, {30, 20480}, {550, 67739}, {11589, 14993}, {13481, 38730}, {34150, 37968}
X(73018) = reflection of X(67739) in X(550)
X(73018) = antigonal conjugate of X(382)
X(73018) = symgonal image of X(550)
X(73018) = X(56063)-reciprocal conjugate of X(57823)
X(73018) = intersection, other than A, B, C, of the circumconics: {{A,B,C,X(3),X(38942)}, {A,B,C,X(4),X(382)}, {A,B,C,X(1511),X(11589)}, {A,B,C,X(11270),X(44748)}}
X(73018) = barycentric product X(382)*X(56063)
X(73018) = barycentric quotient X(56063)/X(57823)
X(73019) = X(3)X(20480)∩X(4)X(1511)
Barycentrics -8*a^16+24*a^14*b^2-8*a^12*b^4-40*a^10*b^6+40*a^8*b^8+8*a^6*b^10-24*a^4*b^12+8*a^2*b^14+24*a^14*c^2-98*a^12*b^2*c^2+107*a^10*b^4*c^2+27*a^8*b^6*c^2-107*a^6*b^8*c^2+55*a^4*b^10*c^2-12*a^2*b^12*c^2+4*b^14*c^2-8*a^12*c^4+107*a^10*b^2*c^4-212*a^8*b^4*c^4+108*a^6*b^6*c^4+41*a^4*b^8*c^4-12*a^2*b^10*c^4-24*b^12*c^4-40*a^10*c^6+27*a^8*b^2*c^6+108*a^6*b^4*c^6-144*a^4*b^6*c^6+16*a^2*b^8*c^6+60*b^10*c^6+40*a^8*c^8-107*a^6*b^2*c^8+41*a^4*b^4*c^8+16*a^2*b^6*c^8-80*b^8*c^8+8*a^6*c^10+55*a^4*b^2*c^10-12*a^2*b^4*c^10+60*b^6*c^10-24*a^4*c^12-12*a^2*b^2*c^12-24*b^4*c^12+8*a^2*c^14+4*b^2*c^14 : :X(73019) = X[3]+X[20480], 3*X[3]-X[67739], 3*X[20480]+X[67739]
Marian Cucoanes and Ercole Suppa, euclid 10307.
X(73019) lies on these lines: {3, 20480}, {4, 1511}, {37968, 38609}
X(73019) = midpoint of X(3) and X(20480)
X(73920) = X(49)X(18349)∩X(93)X(18350)
Barycentrics a^2*(a^2*b^2 - b^4 + a^2*c^2 + 2*b^2*c^2 - c^4)*(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8 - 2*a^6*c^2 + 2*a^4*b^2*c^2 + 2*a^2*b^4*c^2 - 2*b^6*c^2 + a^4*c^4 - a^2*b^2*c^4 + b^4*c^4)*(a^8 - 2*a^6*b^2 + a^4*b^4 - 4*a^6*c^2 + 2*a^4*b^2*c^2 - a^2*b^4*c^2 + 6*a^4*c^4 + 2*a^2*b^2*c^4 + b^4*c^4 - 4*a^2*c^6 - 2*b^2*c^6 + c^8) : :Antreas Hatzipolakis and Peter Moses, euclid 10308.
X(73020) lies on these lines: {49, 18349}, {93, 18350}, {110, 18351}, {186, 6243}, {63734, 66883}
X(73020) = X(i)-isoconjugate of X(j) for these (i,j): {54, 18352}, {2167, 18353}
X(73020) = X(i)-Dao conjugate of X(j) for these (i,j): {6663, 565}, {40588, 18353} .
X(73020) = barycentric quotient X(i)/X(j) for these {i,j}: {51, 18353}, {1953, 18352}, {36412, 565}
X(73021) = X(4)X(69)∩X(30)X(51426)
Barycentrics a^2*(a^6*b^2 + a^4*b^4 - a^2*b^6 - b^8 + a^6*c^2 - 12*a^4*b^2*c^2 + a^2*b^4*c^2 + 14*b^6*c^2 + a^4*c^4 + a^2*b^2*c^4 - 18*b^4*c^4 - a^2*c^6 + 14*b^2*c^6 - c^8) : :Antreas Hatzipolakis and Peter Moses, euclid 10310.
X(73021) lies on these lines: {4, 69}, {30, 51426}, {187, 5020}, {512, 58882}, {625, 1368}, {3849, 66529}, {5107, 6391}, {7398, 14712}, {8681, 53419}, {9822, 53418}, {10219, 60855}, {18860, 67885}, {21849, 23334}, {31173, 34609}, {47092, 47570}, {47113, 66607}, {52520, 53017}
X(73021) = midpoint of X(316) and X(5140)
X(73022) = X(3)X(74)∩X(113)X(550)
Barycentrics a^2*(4*a^8-9*a^6*b^2+3*a^4*b^4+5*a^2*b^6-3*b^8-9*a^6*c^2+18*a^4*b^2*c^2-10*a^2*b^4*c^2+b^6*c^2+3*a^4*c^4-10*a^2*b^2*c^4+4*b^4*c^4+5*a^2*c^6+b^2*c^6-3*c^8) : :X(73022) = 3*X[2]-X[10113], 3*X[2]+X[12121], 3*X[2]-2*X[15088], X[10113]+X[12121], X[10113]-2*X[15088], X[12121]+2*X[15088], 5*X[3]-X[74], 3*X[3]+X[110], 7*X[3]+X[399], X[3]+X[1511], 5*X[3]+X[5609], 9*X[3]-X[10620], 3*X[3]-X[12041], 5*X[3]+7*X[15020], 7*X[3]-19*X[15023], 7*X[3]+5*X[15034], X[3]+3*X[15035], 3*X[3]-7*X[15036], 3*X[3]+5*X[15040], 5*X[3]-13*X[15042], X[3]-5*X[15051], 7*X[3]-3*X[15055], 5*X[3]+3*X[32609], 10*X[3]-X[38626], 8*X[3]+X[38632], 7*X[3]+9*X[38638], 7*X[3]-X[51522], 3*X[74]+5*X[110], 7*X[74]+5*X[399], X[74]+5*X[1511], X[74]+X[5609], 9*X[74]-5*X[10620], 3*X[74]-5*X[12041], 3*X[74]+X[12308], X[74]+7*X[15020], 7*X[74]-95*X[15023], 3*X[74]-35*X[15036], X[74]-13*X[15042], X[74]-25*X[15051], 7*X[74]-15*X[15055], X[74]+3*X[32609], 2*X[74]-X[38626], 8*X[74]+5*X[38632], 5*X[74]-9*X[38633], 7*X[74]-5*X[51522], 7*X[110]-3*X[399], X[110]-3*X[1511], 5*X[110]-3*X[5609], 3*X[110]+X[10620], X[110]+X[12041]
Marian Cucoanes and Ercole Suppa, euclid 10312.
X(73022) lies on these lines: {2, 10113}, {3, 74}, {4, 38723}, {5, 12295}, {20, 1539}, {30, 5972}, {113, 550}, {125, 549}, {140, 6723}, {143, 9826}, {146, 3528}, {182, 12893}, {186, 1112}, {265, 631}, {376, 7728}, {382, 64101}, {511, 18571}, {517, 58601}, {523, 68307}, {526, 39477}, {541, 11694}, {542, 12100}, {546, 12900}, {548, 2777}, {567, 12006}, {632, 23515}, {895, 12017}, {974, 13367}, {1147, 39084}, {1151, 10820}, {1152, 10819}, {1154, 14708}, {1350, 15462}, {1495, 37950}, {1656, 10733}, {1658, 25487}, {1986, 6101}, {2070, 43576}, {2781, 14810}, {2854, 5092}, {2930, 55676}, {2948, 67706}, {3024, 5010}, {3028, 7280}, {3043, 13148}, {3066, 6644}, {3098, 6593}, {3431, 40280}, {3448, 3524}, {3515, 15472}, {3520, 12133}, {3522, 20127}, {3523, 12383}, {3526, 14644}, {3530, 6699}, {3534, 10721}, {3576, 12778}, {3579, 11720}, {3581, 37952}, {3620, 32272}, {3627, 36518}, {3628, 7687}, {3850, 68280}, {3917, 11562}, {5054, 12902}, {5073, 15046}, {5122, 59817}, {5181, 48906}, {5204, 10088}, {5217, 10091}, {5351, 36208}, {5352, 36209}, {5418, 13915}, {5420, 13979}, {5432, 18968}, {5433, 12896}, {5447, 10628}, {5504, 14528}, {5621, 55671}, {5642, 8703}, {5646, 7514}, {5650, 62516}, {5651, 16165}, {5655, 10304}, {5657, 12898}, {5890, 11935}, {5892, 11800}, {6053, 58190}, {6070, 47852}, {6200, 49269}, {6221, 19110}, {6396, 49268}, {6398, 19111}, {6449, 19060}, {6450, 19059}, {6640, 18379}, {6759, 11598}, {7471, 38610}, {7516, 19457}, {7525, 13289}
X(73022) = midpoint of X(i) and X(j) for these {i,j}: {3, 1511}, {5, 16163}, {20, 1539}, {74, 5609}, {110, 12041}, {113, 550}, {125, 34153}, {182, 33851}, {399, 51522}, {548, 10272}, {1495, 37950}, {1658, 25487}, {1986, 6101}, {3098, 6593}, {3579, 11720}, {5181, 48906}, {5642, 8703}, {5972, 38726}, {6759, 11598}, {7471, 38610}, {10113, 12121}, {11694, 34200}, {12825, 13491}, {14708, 41673}, {15646, 51394}, {16165, 18570}, {37814, 59495}
X(73022) = reflection of X(i) in X(j) for these {i,j}: {140, 48378}, {143, 9826}, {265, 20396}, {546, 12900}, {6699, 3530}, {7687, 3628}, {10113, 15088}, {11801, 6723}, {12133, 45958}, {12236, 12006}, {12358, 32142}, {20304, 140}, {20379, 6699}, {38626, 74}, {61574, 5972}, {68555, 61574}
X(73022) = complement of X(10113)
X(73022) = anticomplement of X(15088)
X(73022) = inverse of X(12308) in circumcircle
X(73022) = X(15088)-Dao conjugate of X(15088)
X(73022) = X(526)-vertex conjugate of X(12308)
X(73022) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3, 1511, 47084}, {113, 550, 36169}, {1495, 37950, 47351}, {3233, 7471, 38610}, {5972, 34844, 38726}
X(73022) = reflection of X(i) in the line X(j)X(k) for these {i,j,k}: {68307, 2, 3}, {72487, 3, 523}, {72511, 140, 523}
X(73022) = foot of the perpendicular from X(i) to the line X(j)X(k) for these {i,j,k}: {39477, 3, 74}, {68307, 5972, 14156}
X(73022) = QAP1: Quadrangle Centroid of X(12121)
X(73022) = intersection, other than A, B, C, of the circumconics: {{A,B,C,X(30),X(15055)}, {A,B,C,X(74),X(72395)}, {A,B,C,X(250),X(12041)}, {A,B,C,X(3431),X(39239)}, {A,B,C,X(12308),X(15395)}, {A,B,C,X(13472),X(52130)}, {A,B,C,X(14094),X(15469)}, {A,B,C,X(14264),X(14528)}, {A,B,C,X(61574),X(66268)}}
X(73022) = pole of the line {526, 12308} with respect to circumcircle
X(73022) = pole of the line {9412, 46253} with respect to Moses-Parry circle
X(73022) = pole of the line {30, 14644} with respect to Stammler hyperbola
X(73022) = pole of the line {30, 15059} with respect to Stammler reflection hyperbola
X(73022) = pole of the line {25, 7722} with respect to Walsmith rectangular hyperbola
X(73022) = pole of the line {1495, 12041} with respect to Thomson-Gibert-Moses hyperbola
X(73022) = pole of the line {125, 38393} with respect to orthoptic circle of Jerabek hyperbola
X(73022) = pole of tripolar of X(249) with respect to orthoptic circle of Stammler hyperbola
X(73022) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10113, 15088}, {2, 12121, 10113}, {3, 110, 12041}, {3, 399, 15055}, {3, 1511, 5663}, {3, 11449, 13491}, {3, 15020, 5609}, {3, 15034, 51522}, {3, 15035, 1511}, {3, 15039, 15021}, {3, 15040, 110}, {3, 32609, 74}, {3, 38638, 399}, {3, 61753, 32210}, {20, 14643, 1539}, {74, 110, 12308}, {74, 5609, 5663}, {74, 15020, 32609}, {74, 15035, 15020}, {74, 15051, 15042}, {74, 32609, 5609}, {110, 12041, 5663}, {110, 12308, 5609}, {110, 15035, 15040}, {110, 15036, 3}, {110, 15040, 1511}, {110, 15051, 15036}, {113, 550, 34584}, {140, 11801, 6723}, {146, 3528, 38788}, {182, 33851, 14984}, {265, 631, 34128}, {265, 34128, 20396}, {399, 15055, 51522}, {399, 38638, 15034}, {399, 51522, 5663}, {548, 10272, 2777}, {549, 34153, 125}, {1511, 5609, 32609}, {1511, 12041, 110}, {3448, 3524, 38728}, {3523, 12383, 15061}, {5054, 12902, 15059}, {5972, 38726, 30}, {6699, 48375, 3530}, {6723, 11801, 20304}, {11694, 34200, 541}, {12308, 32609, 110}, {12825, 13491, 5663}, {14708, 41673, 1154}, {15020, 32609, 1511}, {15023, 15034, 3}, {15023, 15035, 399}, {15034, 15055, 399}, {15034, 38638, 1511}, {15035, 15036, 110}, {15035, 15042, 5609}, {15035, 15051, 3}, {15035, 15055, 38638}, {15036, 15040, 12041}, {15042, 32609, 3}, {15051, 15055, 15023}, {15646, 51394, 1154}, {16163, 38793, 5}, {22467, 43394, 12006}, {38723, 38794, 4}, {38726, 68316, 5972}, {38728, 64182, 3448}
X(73023) = X(3)X(10113)∩X(381)X(20480)
Barycentrics (a^6-3*a^2*b^4+2*b^6+5*a^2*b^2*c^2-2*b^4*c^2-3*a^2*c^4-2*b^2*c^4+2*c^6)*(8*a^10-16*a^8*b^2+4*a^6*b^4+4*a^4*b^6+4*a^2*b^8-4*b^10-16*a^8*c^2+34*a^6*b^2*c^2-13*a^4*b^4*c^2-17*a^2*b^6*c^2+12*b^8*c^2+4*a^6*c^4-13*a^4*b^2*c^4+26*a^2*b^4*c^4-8*b^6*c^4+4*a^4*c^6-17*a^2*b^2*c^6-8*b^4*c^6+4*a^2*c^8+12*b^2*c^8-4*c^10) : :X(73023) = 3*X[381]-X[20480], X[382]+X[67739]
Marian Cucoanes and Ercole Suppa, euclid 10312.
X(73023) lies on the cubic K038 and these lines: {3, 10113}, {381, 20480}, {382, 67739}
X(73023) = midpoint of X(i) and X(j) for these {i,j}: {3, 1511}, {5, 16163}, {20, 1539}, {74, 5609}, {110, 12041}, {113, 550}, {125, 34153}, {182, 33851}, {399, 51522}, {548, 10272}, {1495, 37950}, {1658, 25487}, {1986, 6101}, {3098, 6593}, {3579, 11720}, {5181, 48906}, {5642, 8703}, {5972, 38726}, {6759, 11598}, {7471, 38610}, {10113, 12121}, {11694, 34200}, {12825, 13491}, {14708, 41673}, {15646, 51394}, {16165, 18570}, {37814, 59495}
X(73023) = midpoint of X(382) and X(67739)
X(73023) = center of the circumconic through X(382)and X(67739)
X(73023) = center of circles {X(110), X(382), X(67739)}
X(73023) = QAP3: Gergonne-Steiner Point of X(382)
X(73024) = X(3)X(10113)∩X(381)X(67739)
Barycentrics 12*a^14*b^2-48*a^12*b^4+68*a^10*b^6-40*a^8*b^8+20*a^6*b^10-32*a^4*b^12+28*a^2*b^14-8*b^16+12*a^14*c^2-24*a^12*b^2*c^2+43*a^10*b^4*c^2-91*a^8*b^6*c^2+43*a^6*b^8*c^2+95*a^4*b^10*c^2-110*a^2*b^12*c^2+32*b^14*c^2-48*a^12*c^4+43*a^10*b^2*c^4+82*a^8*b^4*c^4-36*a^6*b^6*c^4-171*a^4*b^8*c^4+162*a^2*b^10*c^4-32*b^12*c^4+68*a^10*c^6-91*a^8*b^2*c^6-36*a^6*b^4*c^6+216*a^4*b^6*c^6-80*a^2*b^8*c^6-32*b^10*c^6-40*a^8*c^8+43*a^6*b^2*c^8-171*a^4*b^4*c^8-80*a^2*b^6*c^8+80*b^8*c^8+20*a^6*c^10+95*a^4*b^2*c^10+162*a^2*b^4*c^10-32*b^6*c^10-32*a^4*c^12-110*a^2*b^2*c^12-32*b^4*c^12+28*a^2*c^14+32*b^2*c^14-8*c^16 : :X(73024) = 3*X[381]+X[67739], 5*X[1656]-X[20480]
Marian Cucoanes and Ercole Suppa, euclid 10312.
X(73024) lies on these lines: {3, 10113}, {381, 67739}, {1656, 20480}
X(73025) = X(2)X(52173)∩X(3)X(9140)
Barycentrics a^6-4*a^4*b^2+5*a^2*b^4-2*b^6-4*a^4*c^2-3*a^2*b^2*c^2+2*b^4*c^2+5*a^2*c^4+2*b^2*c^4-2*c^6)*(8*a^10-24*a^8*b^2+28*a^6*b^4-20*a^4*b^6+12*a^2*b^8-4*b^10-24*a^8*c^2+34*a^6*b^2*c^2-5*a^4*b^4*c^2-17*a^2*b^6*c^2+12*b^8*c^2+28*a^6*c^4-5*a^4*b^2*c^4+10*a^2*b^4*c^4-8*b^6*c^4-20*a^4*c^6-17*a^2*b^2*c^6-8*b^4*c^6+12*a^2*c^8+12*b^2*c^8-4*c^10 : :X(73025) = 3*X[2]-X[52173], X[381]+X[53693], 3*X[5054]-X[13530]
Marian Cucoanes and Ercole Suppa, euclid 10312.
X(73025) lies on the cubic K038 and these lines: {2, 52173}, {3, 9140}, {30, 46438}, {381, 53693}, {5054, 13530}, {47079, 52105}
X(73025) = midpoint of X(381) and X(53693)
X(73025) = complement of X(52173)
X(73025) = X(69770)-complementary conjugate of X(10)
X(73025) = inverse of X(44751) in Warren reflection circle
X(73025) = center of the circumconic through X(381)and X(53693)
X(73025) = center of circles {X(110), X(381), X(53693)}
X(73025) = QAP3: Gergonne-Steiner Point of X(381)
X(73025) = pole of the line {7575, 67795} with respect to Stammler hyperbola
X(73026) = X(3)X(9140)∩X(631)X(52173)
Barycentrics 32*a^16-164*a^14*b^2+368*a^12*b^4-508*a^10*b^6+520*a^8*b^8-412*a^6*b^10+224*a^4*b^12-68*a^2*b^14+8*b^16-164*a^14*c^2+544*a^12*b^2*c^2-669*a^10*b^4*c^2+289*a^8*b^6*c^2+199*a^6*b^8*c^2-357*a^4*b^10*c^2+190*a^2*b^12*c^2-32*b^14*c^2+368*a^12*c^4-669*a^10*b^2*c^4+402*a^8*b^4*c^4-112*a^6*b^6*c^4+141*a^4*b^8*c^4-162*a^2*b^10*c^4+32*b^12*c^4-508*a^10*c^6+289*a^8*b^2*c^6-112*a^6*b^4*c^6-16*a^4*b^6*c^6+40*a^2*b^8*c^6+32*b^10*c^6+520*a^8*c^8+199*a^6*b^2*c^8+141*a^4*b^4*c^8+40*a^2*b^6*c^8-80*b^8*c^8-412*a^6*c^10-357*a^4*b^2*c^10-162*a^2*b^4*c^10+32*b^6*c^10+224*a^4*c^12+190*a^2*b^2*c^12+32*b^4*c^12-68*a^2*c^14-32*b^2*c^14+8*c^16 : :X(73026) = 5*X[631]-X[52173], 3*X[5054]+X[53693], X[13530]-5*X[15693]
Marian Cucoanes and Ercole Suppa, euclid 10312.
X(73026) lies on these lines: {3, 9140}, {631, 52173}, {5054, 53693}, {13530, 15693}
X(73027) = (name pending)
Barycentrics 3*a^6-4*a^4*b^2-a^2*b^4+2*b^6-4*a^4*c^2+7*a^2*b^2*c^2-2*b^4*c^2-a^2*c^4-2*b^2*c^4+2*c^6)*(8*a^10-8*a^8*b^2-20*a^6*b^4+28*a^4*b^6-4*a^2*b^8-4*b^10-8*a^8*c^2+50*a^6*b^2*c^2-29*a^4*b^4*c^2-25*a^2*b^6*c^2+12*b^8*c^2-20*a^6*c^4-29*a^4*b^2*c^4+58*a^2*b^4*c^4-8*b^6*c^4+28*a^4*c^6-25*a^2*b^2*c^6-8*b^4*c^6-4*a^2*c^8+12*b^2*c^8-4*c^10 : :X(73027) = 5*X[631]-X[52173], 3*X[5054]+X[53693], X[13530]-5*X[15693]
Marian Cucoanes and Ercole Suppa, euclid 10312.
X(73027) lies on the cubic K038 and this line: {3, 1539}
X(73027) = QAP3: Gergonne-Steiner Point of X(1657)
X(73028) = (name pending)
Barycentrics 32*a^16-76*a^14*b^2-48*a^12*b^4+268*a^10*b^6-200*a^8*b^8-52*a^6*b^10+96*a^4*b^12-12*a^2*b^14-8*b^16-76*a^14*c^2+368*a^12*b^2*c^2-383*a^10*b^4*c^2-317*a^8*b^6*c^2+677*a^6*b^8*c^2-223*a^4*b^10*c^2-78*a^2*b^12*c^2+32*b^14*c^2-48*a^12*c^4-383*a^10*b^2*c^4+1126*a^8*b^4*c^4-632*a^6*b^6*c^4-337*a^4*b^8*c^4+306*a^2*b^10*c^4-32*b^12*c^4+268*a^10*c^6-317*a^8*b^2*c^6-632*a^6*b^4*c^6+928*a^4*b^6*c^6-216*a^2*b^8*c^6-32*b^10*c^6-200*a^8*c^8+677*a^6*b^2*c^8-337*a^4*b^4*c^8-216*a^2*b^6*c^8+80*b^8*c^8-52*a^6*c^10-223*a^4*b^2*c^10+306*a^2*b^4*c^10-32*b^6*c^10+96*a^4*c^12-78*a^2*b^2*c^12-32*b^4*c^12-12*a^2*c^14+32*b^2*c^14-8*c^16 : :Marian Cucoanes and Ercole Suppa, euclid 10312.
X(73028) lies on this line: {3, 1539}
X(73029) = (name pending)
Barycentrics (a^8-a^6*b^2-3*a^4*b^4+a^2*b^6+2*b^8+7*a^6*c^2+3*a^4*b^2*c^2+24*a^2*b^4*c^2+b^6*c^2+12*a^4*c^4+3*a^2*b^2*c^4-3*b^4*c^4+7*a^2*c^6-b^2*c^6+c^8)*(a^8+7*a^6*b^2+12*a^4*b^4+7*a^2*b^6+b^8-a^6*c^2+3*a^4*b^2*c^2+3*a^2*b^4*c^2-b^6*c^2-3*a^4*c^4+24*a^2*b^2*c^4-3*b^4*c^4+a^2*c^6+b^2*c^6+2*c^8) : :Francisco Javier García Capitán, euclid 10314.
X(73029) lies on these lines: { }
X(73029) = intersection, other than A, B, C, of the circumconics: {{A,B,C,X(6),X(8546)}, {A,B,C,X(76),X(6094)}, {A,B,C,X(7608),X(53774)}, {A,B,C,X(7827),X(43528)}}
X(73030) = (name pending)
Barycentrics (a^2-b^2-c^2)*(a^16-2*a^14*b^2-a^12*b^4+6*a^10*b^6-8*a^8*b^8+6*a^6*b^10-a^4*b^12-2*a^2*b^14+b^16-5*a^14*c^2+8*a^12*b^2*c^2+2*a^10*b^4*c^2-5*a^8*b^6*c^2-5*a^6*b^8*c^2+2*a^4*b^10*c^2+8*a^2*b^12*c^2-5*b^14*c^2+10*a^12*c^4-12*a^10*b^2*c^4+4*a^6*b^6*c^4-12*a^2*b^10*c^4+10*b^12*c^4-11*a^10*c^6+3*a^8*b^2*c^6-12*a^6*b^4*c^6-12*a^4*b^6*c^6+3*a^2*b^8*c^6-11*b^10*c^6+10*a^8*c^8+18*a^6*b^2*c^8+31*a^4*b^4*c^8+18*a^2*b^6*c^8+10*b^8*c^8-11*a^6*c^10-30*a^4*b^2*c^10-30*a^2*b^4*c^10-11*b^6*c^10+10*a^4*c^12+20*a^2*b^2*c^12+10*b^4*c^12-5*a^2*c^14-5*b^2*c^14+c^16)*(a^16-5*a^14*b^2+10*a^12*b^4-11*a^10*b^6+10*a^8*b^8-11*a^6*b^10+10*a^4*b^12-5*a^2*b^14+b^16-2*a^14*c^2+8*a^12*b^2*c^2-12*a^10*b^4*c^2+3*a^8*b^6*c^2+18*a^6*b^8*c^2-30*a^4*b^10*c^2+20*a^2*b^12*c^2-5*b^14*c^2-a^12*c^4+2*a^10*b^2*c^4-12*a^6*b^6*c^4+31*a^4*b^8*c^4-30*a^2*b^10*c^4+10*b^12*c^4+6*a^10*c^6-5*a^8*b^2*c^6+4*a^6*b^4*c^6-12*a^4*b^6*c^6+18*a^2*b^8*c^6-11*b^10*c^6-8*a^8*c^8-5*a^6*b^2*c^8+3*a^2*b^6*c^8+10*b^8*c^8+6*a^6*c^10+2*a^4*b^2*c^10-12*a^2*b^4*c^10-11*b^6*c^10-a^4*c^12+8*a^2*b^2*c^12+10*b^4*c^12-2*a^2*c^14-5*b^2*c^14+c^16) : :Francisco Javier García Capitán, euclid 10314.
X(73030) lies on this line: {6102, 57473}
X(73030) = intersection, other than A, B, C, of the circumconics: {{A,B,C,X(54),X(57473)}, {A,B,C,X(250),X(3521)}, {A,B,C,X(265),X(6102)}}}
X(73031) = X(1)X(6)∩X(30)X(511)
Barycentrics a*(b + c)*(a^5 - a^3*b^2 + a^2*b^3 - b^5 - a^2*b^2*c + b^4*c - a^3*c^2 - a^2*b*c^2 + a*b^2*c^2 + a^2*c^3 + b*c^4 - c^5) : :
X(73031) lies on these lines: {1, 60}, {2, 50921}, {3, 11709}, {4, 12368}, {5, 12261}, {6, 32278}, {8, 3448}, {10, 125}, {30, 511}, {36, 54078}, {40, 74}, {46, 10081}, {49, 43822}, {55, 13208}, {65, 1365}, {67, 3416}, {72, 7068}, {80, 1109}, {100, 4736}, {101, 3708}, {106, 17476}, {113, 946}, {115, 21890}, {141, 32238}, {145, 14683}, {146, 962}, {149, 16110}, {150, 17886}, {165, 15055}, {214, 16598}, {265, 355}, {399, 1482}, {551, 5642}, {895, 3751}, {942, 35063}, {944, 12383}, {950, 46687}, {974, 65423}, {1112, 1829}, {1125, 5972}, {1283, 2292}, {1385, 1511}, {1386, 6593}, {1484, 13753}, {1495, 51693}, {1539, 22793}, {1698, 15059}, {1702, 19060}, {1703, 19059}, {1836, 12373}, {1837, 12904}, {1902, 12133}, {1986, 31732}, {2650, 6126}, {2652, 53114}, {2930, 3242}, {3017, 5902}, {3024, 3057}, {3109, 14985}, {3241, 9143}, {3244, 24981}, {3576, 15035}, {3579, 12041}, {3580, 47321}, {3626, 72475}, {3634, 6723}, {3640, 7733}, {3641, 7732}, {3654, 20126}, {3655, 64182}, {3656, 5655}, {3678, 61166}, {3679, 9140}, {3743, 37080}, {3817, 36518}, {3828, 45311}, {3844, 6698}, {3868, 19642}, {3869, 56951}, {4246, 36063}, {4297, 16163}, {4301, 15063}, {4347, 19505}, {4551, 43692}, {4647, 5178}, {4669, 50919}, {4677, 50920}, {4745, 50922}, {5044, 58671}, {5045, 58601}, {5086, 42005}, {5095, 51196}, {5119, 10065}, {5164, 21862}, {5181, 49511}, {5252, 12903}, {5465, 12258}, {5493, 10990}, {5494, 10902}, {5496, 42440}, {5504, 9928}, {5546, 16562}, {5587, 14644}, {5609, 10222}, {5648, 47358}, {5690, 10264}, {5691, 10733}, {5692, 33156}, {5697, 7727}, {5709, 49151}, {5790, 38724}, {5812, 12372}, {5818, 15081}, {5881, 12407}, {5882, 30714}, {5886, 14643}, {5887, 14680}, {5901, 10272}, {5903, 19470}, {6224, 6758}, {6361, 12244}, {6684, 6699}, {6740, 47270}, {6742, 47274}, {7117, 23993}, {7471, 66789}, {7687, 19925}, {7724, 37625}, {7725, 12697}, {7726, 12698}, {7728, 12699}, {7968, 49269}, {7969, 49268}, {7974, 37753}, {7975, 37752}, {7978, 7982}, {7983, 15342}, {7987, 15051}, {7991, 9904}, {8148, 12308}, {8193, 13171}, {8227, 64101}, {8983, 8998}, {8994, 13912}, {9129, 11721}, {9144, 50886}, {9588, 15057}, {9798, 12310}, {9864, 11005}, {9881, 11006}, {9911, 9919}, {9940, 58582}, {9941, 13210}, {9955, 61574}, {9956, 20304}, {9984, 12497}, {10106, 46683}, {10113, 18480}, {10117, 49553}, {10164, 38727}, {10165, 38793}, {10171, 68280}, {10175, 23515}, {10246, 32609}, {10306, 12327}, {10572, 12896}, {10595, 20125}, {10620, 12702}, {10706, 31162}, {10721, 41869}, {10752, 64084}, {10767, 14217}, {11010, 38566}, {11011, 63769}, {11014, 38555}, {11061, 51192}, {11231, 34128}, {11362, 16003}, {11396, 19504}, {11570, 67440}, {11597, 12266}, {11598, 12262}, {11599, 16278}, {11700, 53758}, {11710, 53725}, {11711, 53735}, {11712, 53747}, {11713, 53749}, {11714, 53751}, {11715, 53753}, {11716, 53756}, {11718, 53757}, {11722, 53760}, {11723, 13464}, {11744, 12779}, {11746, 44547}, {11801, 18357}, {12121, 18481}, {12192, 12197}, {12194, 13193}, {12236, 31760}, {12245, 12317}, {12259, 46085}, {12295, 31673}, {12358, 31752}, {12365, 12458}, {12366, 12459}, {12369, 12696}, {12371, 12700}, {12374, 12701}, {12375, 35641}, {12376, 35642}, {12377, 22841}, {12378, 22842}, {12381, 12703}, {12382, 12704}, {12438, 13212}, {12440, 13215}, {12441, 13216}, {12512, 37853}, {12785, 33565}, {12826, 39772}, {12890, 37700}, {12898, 23236}, {12902, 18525}, {13169, 50950}, {13198, 64040}, {13202, 51118}, {13392, 51700}, {13416, 37613}, {13417, 67967}, {13434, 43830}, {13604, 17638}, {13752, 13868}, {13883, 46688}, {13936, 46689}, {13969, 13975}, {13971, 13990}, {14480, 66800}, {14513, 72976}, {14690, 53717}, {14934, 66770}, {14982, 64085}, {15020, 30389}, {15021, 63469}, {15034, 64953}, {15036, 67706}, {15049, 61722}, {15061, 26446}, {15303, 51005}, {15462, 38029}, {15647, 40660}, {15904, 45946}, {16111, 31730}, {16164, 35016}, {16165, 51692}, {16173, 34311}, {16223, 64662}, {16475, 52699}, {17100, 68154}, {17511, 66796}, {17647, 67846}, {17718, 60116}, {17847, 67963}, {18180, 47319}, {18421, 51771}, {18483, 46686}, {18968, 45287}, {18991, 19111}, {18992, 19110}, {19469, 59285}, {20070, 64102}, {20417, 43174}, {20771, 51694}, {20772, 51695}, {20773, 51696}, {22265, 64749}, {22583, 22770}, {23059, 52362}, {23994, 68337}, {25320, 59406}, {25328, 49524}, {25330, 59407}, {31523, 64137}, {31728, 67912}, {31737, 64039}, {31746, 32311}, {31793, 52820}, {31803, 67535}, {32114, 49505}, {32126, 68489}, {32298, 49681}, {34153, 34773}, {34319, 47356}, {35266, 47495}, {35610, 35826}, {35611, 35827}, {37621, 64753}, {38315, 52697}, {38632, 58240}, {38638, 58230}, {38790, 48661}, {38982, 45764}, {41671, 58469}, {41673, 65399}, {43598, 43824}, {43808, 43827}, {44569, 47496}, {45711, 48535}, {45712, 48536}, {45713, 49369}, {45714, 49370}, {45715, 48786}, {45716, 48787}, {45717, 49441}, {45718, 49442}, {45719, 49098}, {45720, 49099}, {45920, 49598}, {46623, 69227}, {46682, 49542}, {46684, 53715}, {47484, 63354}, {48472, 48487}, {48473, 48488}, {48730, 48740}, {48731, 48741}, {49044, 49054}, {49045, 49055}, {49152, 49163}, {49216, 49226}, {49217, 49227}, {49222, 49601}, {49223, 49602}, {49313, 49323}, {49314, 49324}, {49383, 49395}, {49384, 49396}, {49684, 56565}, {50295, 66679}, {50802, 68317}, {50808, 69874}, {50828, 68316}, {50877, 68686}, {50923, 51093}, {51393, 51701}, {51425, 51713}, {51703, 64601}, {51710, 64602}, {51711, 64603}, {53616, 66289}, {56839, 59320}, {58487, 58498}, {58643, 58654}, {61524, 61548}, {62316, 63210}, {63348, 63356}, {64104, 67964}, {69226, 71682}
X(73031) = isogonal conjugate of X(12030)
X(73031) = Thomson-isogonal conjugate of X(53936)
X(73031) = crossdifference of every pair of points on line {6, 2610}
X(73031) = X(32278)-line conjugate of X(6)
X(73031) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 110, 11720}, {1, 2948, 110}, {1, 21381, 759}, {1, 56289, 37816}, {1, 57263, 11101}, {8, 3448, 13211}, {10, 13605, 125}, {40, 33535, 74}, {65, 3028, 59817}, {110, 7984, 1}, {110, 13217, 10088}, {110, 13218, 10091}, {1829, 71375, 1112}, {2948, 7984, 11720}, {5972, 11735, 1125}, {13204, 22586, 3}, {13208, 13209, 55}, {13213, 13214, 265}, {31525, 53743, 214}, {49203, 49204, 110}, {61722, 61726, 15049}
X(73032) = X(1)X(512)∩X(187)X(292)
Barycentrics a^2*(-b^2 + a*c)*(a*b - c^2)*(a^4 - b^4 - 2*a^2*b*c + b^3*c + b^2*c^2 + b*c^3 - c^4) : :X(73032) = X[7077] - 3 X[30648]
X(73032) lies on the cubic K1452 and these lines: {1, 512}, {187, 292}, {291, 484}, {316, 334}, {511, 1757}, {691, 741}, {758, 56154}, {759, 805}, {813, 53180}, {893, 51494}, {1438, 2702}, {3065, 4876}, {3849, 7245}, {3862, 5104}, {3865, 16068}, {4589, 14210}, {14712, 30669}, {20403, 61432}, {29660, 68376}, {43262, 51224}, {67546, 71685}
X(73032) = X(740)-isoconjugate of X(59827)
X(73032) = barycentric product X(i)*X(j) for these {i,j}: {335, 24436}, {2503, 18827}
X(73032) = barycentric quotient X(i)/X(j) for these {i,j}: {2503, 740}, {18268, 59827}, {24436, 239}
X(73032) = {X(14196),X(68243)}-harmonic conjugate of X(68235)
X(73033) = X(1)X(513)∩X(36)X(20918)
Barycentrics a*(a + b - 2*c)*(a - 2*b + c)*(2*a^4 - a^3*b - a^2*b^2 + a*b^3 - b^4 - a^3*c - a^2*c^2 + 2*b^2*c^2 + a*c^3 - c^4) : :X(73033) = 4 X[14190] - X[17960], 3 X[15015] - 4 X[63755]
X(73033) lies on the cubic K1452 and thise lines: {1, 513}, {36, 20918}, {106, 1290}, {484, 759}, {758, 1320}, {896, 4792}, {1318, 56844}, {1739, 67520}, {1757, 39154}, {3125, 17969}, {3336, 38541}, {3337, 16944}, {3924, 39264}, {4013, 5080}, {4316, 60578}, {5540, 67150}, {7984, 70225}, {15015, 63755}, {24291, 52755}, {30117, 43922}, {37563, 61768}, {37616, 62703}, {52031, 71733}, {56950, 66285}, {61479, 65856}, {67495, 70853}
X(73033) = reflection of X(484) in X(52680)
X(73033) = X(519)-isoconjugate of X(65875)
X(73033) = X(65932)-Dao conjugate of X(4358)
X(73033) = barycentric product X(i)*X(j) for these {i,j}: {88, 70797}, {106, 70799}, {903, 70798}, {1320, 70796}, {56049, 70800}
X(73033) = barycentric quotient X(i)/X(j) for these {i,j}: {9456, 65875}, {70795, 69753}, {70796, 69734}, {70797, 4358}, {70798, 519}, {70799, 3264}, {70800, 4723}
X(73033) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {901, 1168, 4674}, {901, 4674, 484}, {14190, 52478, 61476}, {52478, 61476, 1}
X(73034) = X(1)X(690)∩X(99)X(14210)
Barycentrics (a^2 - b*c)*(a^4 - a^3*b - a^2*b^2 - a*b^3 + b^4 + 2*a*b*c^2 - c^4)*(a^4 - b^4 - a^3*c + 2*a*b^2*c - a^2*c^2 - a*c^3 + c^4) : :
X(73034) lies on the cubic K1452 and thise lines: {1, 690}, {99, 14210}, {484, 1018}, {758, 3903}, {759, 20404}, {804, 36815}, {1281, 69899}, {3065, 7313}, {19557, 69901}
X(73034) = X(i)-isoconjugate of X(j) for these (i,j): {291, 24436}, {2503, 37128}
X(73034) = X(39029)-Dao conjugate of X(24436)
X(73034) = barycentric product X(3948)*X(59827)
X(73034) = barycentric quotient X(i)/X(j) for these {i,j}: {1914, 24436}, {3747, 2503}, {59827, 37128}
X(73035) = X(1)X(523)∩X(30)X(80)
Barycentrics (a^2 - a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^6 - 2*a^4*b^2 + a^2*b^4 + 2*a^4*b*c - a^2*b^3*c - b^5*c - 2*a^4*c^2 + a^2*b^2*c^2 - a^2*b*c^3 + 2*b^3*c^3 + a^2*c^4 - b*c^5) : :X(73035) = X[80] - 3 X[63868]
X(73035) lies on the cubic K1452 and thise lines: {1, 523}, {11, 53809}, {30, 80}, {35, 46635}, {36, 46636}, {79, 34209}, {186, 10260}, {476, 759}, {499, 38514}, {758, 6740}, {952, 31524}, {1290, 10090}, {1387, 31522}, {1479, 67716}, {1758, 56419}, {2006, 11809}, {2222, 43655}, {2687, 10058}, {3582, 62500}, {3583, 62496}, {4316, 62493}, {5520, 8068}, {5525, 36910}, {6797, 67441}, {7280, 67722}, {10573, 36171}, {15325, 39751}, {18393, 68385}, {18395, 36154}, {33964, 61502}, {34172, 56790}, {34300, 64791}, {37735, 52200}, {39692, 42422}, {40437, 56691}, {47149, 56417}, {52351, 67608}
X(73035) = reflection of X(i) in X(j) for these {i,j}: {11809, 47140}, {31522, 1387}, {39751, 15325}
X(73035) = excentral-polar-circle-inverse of X(53406)
X(73035) = X(758)-isoconjugate of X(59826)
X(73035) = barycentric product X(3013)*X(14616)
X(73035) = barycentric quotient X(i)/X(j) for these {i,j}: {3013, 758}, {34079, 59826}
X(73035) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {476, 62713, 759}, {14194, 68242, 61479}
X(73036) = X(1)X(8674)∩X(100)X(484)
Barycentrics a*(2*a - b - c)*(a^4 - 2*a^2*b^2 + b^4 - a^3*c - b^3*c + a^2*c^2 + b^2*c^2 + a*c^3 + b*c^3 - 2*c^4)*(a^4 - a^3*b + a^2*b^2 + a*b^3 - 2*b^4 + b^3*c - 2*a^2*c^2 + b^2*c^2 - b*c^3 + c^4) : :
X(73036) lies on the cubic K1452 and these lines: {1, 8674}, {100, 484}, {214, 69838}, {759, 3065}, {900, 56950}, {1023, 40988}, {1227, 55243}, {4674, 56422}, {23703, 41541}, {41558, 69463}, {51310, 52934}
X(73036) = reflection of X(69838) in X(214)
X(73036) = X(i)-isoconjugate of X(j) for these (i,j): {88, 70798}, {106, 70797}, {2316, 70796}, {5548, 70795}, {9456, 70799}
X(73036) = X(i)-Dao conjugate of X(j) for these (i,j): {214, 70797}, {4370, 70799}
X(73036) = barycentric product X(4358)*X(65875)
X(73036) = barycentric quotient X(i)/X(j) for these {i,j}: {44, 70797}, {519, 70799}, {902, 70798}, {1319, 70796}, {3689, 70800}, {53528, 70795}, {65875, 88}
X(73037) = X(1)X(8674)∩X(100)X(484)
Barycentrics a^2*(a^2 - b^2 + b*c - c^2)*(-(a^4*b^2) + 2*a^2*b^4 - b^6 + a^5*c + a^3*b^2*c - 2*a*b^4*c - a^2*b^2*c^2 + 2*b^4*c^2 - 2*a^3*c^3 + a*b^2*c^3 - b^2*c^4 + a*c^5)*(a^5*b - 2*a^3*b^3 + a*b^5 - a^4*c^2 + a^3*b*c^2 - a^2*b^2*c^2 + a*b^3*c^2 - b^4*c^2 + 2*a^2*c^4 - 2*a*b*c^4 + 2*b^2*c^4 - c^6) : :
X(73037) lies on the cubic K1452 and these lines: {1, 526}, {110, 6149}, {484, 4551}, {758, 6742}, {759, 16170}, {3028, 68430}, {3065, 7727}
X(73037) = X(3013)-isoconjugate of X(24624)
X(73037) = barycentric product X(3936)*X(59826)
X(73037) = barycentric quotient X(i)/X(j) for these {i,j}: {3724, 3013}, {59826, 24624}
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